(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 236438, 4539]*) (*NotebookOutlinePosition[ 237103, 4562]*) (* CellTagsIndexPosition[ 237059, 4558]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Prob. 3.12", "Subsection"], Cell[BoxData[ \(Clear["\<`*\>"]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Integrate[\[Rho]\ BesselJ[0, k\ \[Rho]], {\[Rho], 0, a}]\)], "Input"], Cell[BoxData[ \(\(a\ BesselJ[1, a\ k]\)\/k\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[\[Rho]_, z_]\ = \ V\ a\ Integrate[ BesselJ[1, k\ a]\ BesselJ[0, \ k\ \[Rho]]\ Exp[\(-k\)\ z], {k, 0, Infinity}, Assumptions \[Rule] \ {a > 0, \ z > 0, \[Rho] \[GreaterEqual] 0}]\)], "Input"], Cell[BoxData[ \(a\ V\ Integrate[\[ExponentialE]\^\(\(-k\)\ z\)\ BesselJ[0, k\ \[Rho]]\ BesselJ[1, a\ k], {k, 0, \[Infinity]}, Assumptions \[Rule] {a > 0, z > 0, \[Rho] \[GreaterEqual] 0}]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[f[0, z], Assumptions \[Rule] \ {a > 0, z > 0}]\)], "Input"], Cell[BoxData[ \(V - \(V\ z\)\/\@\(a\^2 + z\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[ Simplify[f[a, z], Assumptions \[Rule] \ {a > 0, z > 0}]]\)], "Input"], Cell[BoxData[ \(V\/2 - \(V\ EllipticK[\(-\(\(4\ a\^2\)\/z\^2\)\)]\)\/\[Pi]\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Prob 3.13", "Subsection"], Cell[BoxData[ \(Clear["\<`*\>"]\)], "Input"], Cell[TextData[{ "Evaluate the first radial integral c1[k] = ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\((1 - x\^\(\(2\)\(/\)\)/ d\^2)\)\ [\((\(r\_ < \))\)\^k/\((\(r\_ > \))\)\^\(k + 1\)] \ \[DifferentialD]x\)]] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(F1\ = \ \((1 - x^2/d^2)\)\ x^k/r^\((k + 1)\)\)], "Input"], Cell[BoxData[ \(r\^\(\(-1\) - k\)\ x\^k\ \((1 - x\^2\/d\^2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Int1\ = \ Integrate[F1, {x, 0, r}, Assumptions\ \[Rule] \ k \[GreaterEqual] 0]\)], "Input"], Cell[BoxData[ \(1\/\(1 + k\) - r\^2\/\(d\^2\ \((3 + k)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(F2 = \ \((1 - x^2/d^2)\)\ r^k/x^\((k + 1)\)\)], "Input"], Cell[BoxData[ \(r\^k\ x\^\(\(-1\) - k\)\ \((1 - x\^2\/d\^2)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Int2\ = \ Integrate[F2, {x, r, d}, Assumptions \[Rule] {\ \ d > r, \ d > 0, \ r > \ 0, \ k \[Element] \ Integers}]\)], "Input"], Cell[BoxData[ \(\(\(-r\^2\) + d\^\(2 - k\)\ r\^k\)\/\(d\^2\ \((\(-2\) + k)\)\) - \(\(-1\ \) + \((r\/d)\)\^k\)\/k\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(q\ \ = Expand[Int1\ + \ Int2]\)], "Input"], Cell[BoxData[ \(1\/k + 1\/\(1 + k\) - r\^2\/\(d\^2\ \((\(-2\) + k)\)\) - r\^2\/\(d\^2\ \((3 + k)\)\) + \(d\^\(-k\)\ r\^k\)\/\(\(-2\) + k\) - \ \((r\/d)\)\^k\/k\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p1\ = \ Together[q[\([1]\)] + q[\([2]\)]]\)], "Input"], Cell[BoxData[ \(\(1 + 2\ k\)\/\(k\ \((1 + k)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p2 = \ Together[q[\([3]\)] + q[\([4]\)]]\)], "Input"], Cell[BoxData[ \(\(\(-r\^2\) - 2\ k\ r\^2\)\/\(d\^2\ \((\(-2\) + k)\)\ \((3 + k)\)\)\)], \ "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p3\ = \ Together[q[\([5]\)] + q[\([6]\)]] /. \ r^k \[Rule] \ \((r/d)\)^k\ d^k\)], "Input"], Cell[BoxData[ \(\(2\ \((r\/d)\)\^k\)\/\(\((\(-2\) + k)\)\ k\)\)], "Output"] }, Open ]], Cell[TextData[{ "q = ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\^r\)]], " dx ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\((d\^2\), "TraditionalForm"], "-", \(x\^2\)}], TraditionalForm]]], ") ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(x\^k\), "TraditionalForm"], "/", \(r\^\(k + 1\)\)}], TraditionalForm]]], " " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(q[k_]\ = \ p1 + p2 + p3\)], "Input"], Cell[BoxData[ \(\(1 + 2\ k\)\/\(k\ \((1 + k)\)\) + \(2\ \((r\/d)\)\^k\)\/\(\((\(-2\) + \ k)\)\ k\) + \(\(-r\^2\) - 2\ k\ r\^2\)\/\(d\^2\ \((\(-2\) + k)\)\ \((3 + k)\)\ \)\)], "Output"] }, Open ]], Cell["Take care of the special case k=0", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Int10\ = \ Int1 /. \ k \[Rule] 0\)], "Input"], Cell[BoxData[ \(1 - r\^2\/\(3\ d\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f2\ = \ F2 /. \ k \[Rule] 0\)], "Input"], Cell[BoxData[ \(\(1 - x\^2\/d\^2\)\/x\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Int20\ = \ Integrate[f2, {x, r, d}, \ Assumptions \[Rule] \ {d > r, \ r \[GreaterEqual] 0}]\)], "Input"], Cell[BoxData[ \(1\/2\ \((\(-1\) + r\^2\/d\^2)\) + Log[d\/r]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(q0\ = \ Expand[Int10 + Int20]\)], "Input"], Cell[BoxData[ \(1\/2 + r\^2\/\(6\ d\^2\) + Log[d\/r]\)], "Output"] }, Open ]], Cell["Take care of the special case k = 2", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Int12\ = \ Int1 /. \ k \[Rule] 2\)], "Input"], Cell[BoxData[ \(1\/3 - r\^2\/\(5\ d\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f2\ = \ F2 /. \ k \[Rule] \ 2\)], "Input"], Cell[BoxData[ \(\(r\^2\ \((1 - x\^2\/d\^2)\)\)\/x\^3\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Int22\ = \ \ Integrate[f2, {x, r, d}, \ Assumptions \[Rule] \ {d > r, \ r \[GreaterEqual] 0}]\)], "Input"], Cell[BoxData[ \(\(d\^2 - r\^2 - 2\ r\^2\ Log[d\/r]\)\/\(2\ d\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(q2\ = \ Expand[Int12 + Int22]\)], "Input"], Cell[BoxData[ \(5\/6 - \(7\ r\^2\)\/\(10\ d\^2\) - \(r\^2\ Log[d\/r]\)\/d\^2\)], \ "Output"] }, Open ]], Cell["Evaluate the second radial integral in the Green function", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Int3\ = \ \((r^k/b^\((2 k + 1)\))\) Integrate[\((1 - x^2/d^2)\) x^k, {x, 0, d}, Assumptions \[Rule] \ k > 0]\)], "Input"], Cell[BoxData[ \(\(2\ b\^\(\(-1\) - 2\ k\)\ d\^\(1 + k\)\ r\^k\)\/\(3 + 4\ k + \ k\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t0 = \ Int3 /. \ k \[Rule] \ 0\)], "Input"], Cell[BoxData[ \(\(2\ d\)\/\(3\ b\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(c0\ = \ q0 - t0\)], "Input"], Cell[BoxData[ \(1\/2 - \(2\ d\)\/\(3\ b\) + r\^2\/\(6\ d\^2\) + Log[d\/r]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t2\ = \ Int3 /. \ k \[Rule] \ 2\)], "Input"], Cell[BoxData[ \(\(2\ d\^3\ r\^2\)\/\(15\ b\^5\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(c2\ = \ q2 - t2\)], "Input"], Cell[BoxData[ \(5\/6 - \(7\ r\^2\)\/\(10\ d\^2\) - \(2\ d\^3\ r\^2\)\/\(15\ b\^5\) - \ \(r\^2\ Log[d\/r]\)\/d\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(c[k_]\ = q - Int3\)], "Input"], Cell[BoxData[ \(\(1 + 2\ k\)\/\(k\ \((1 + k)\)\) - \(2\ b\^\(\(-1\) - 2\ k\)\ d\^\(1 + \ k\)\ r\^k\)\/\(3 + 4\ k + k\^2\) + \(2\ \((r\/d)\)\^k\)\/\(\((\(-2\) + k)\)\ \ k\) + \(\(-r\^2\) - 2\ k\ r\^2\)\/\(d\^2\ \((\(-2\) + k)\)\ \((3 + k)\)\)\)], \ "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Nt\ = \ 20\)], "Input"], Cell[BoxData[ \(20\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Phi]1[r_, \[Mu]_]\ = \ c0\ + \ c2\ LegendreP[2, \[Mu]]\ + \ Sum[c[k]\ LegendreP[k, \[Mu]], {k, 4, Nt, 2}]\)], "Input"], Cell[BoxData[ \(1\/2 - \(2\ d\)\/\(3\ b\) + r\^2\/\(6\ d\^2\) + 1\/8\ \((9\/20 - \(9\ r\^2\)\/\(14\ d\^2\) + r\^4\/\(4\ d\^4\) - \(2\ d\^5\ r\^4\)\/\(35\ b\^9\))\)\ \((3 - 30\ \[Mu]\^2 + 35\ \[Mu]\^4)\) + 1\/16\ \((13\/42 - \(13\ r\^2\)\/\(36\ d\^2\) + r\^6\/\(12\ d\^6\) - \(2\ d\^7\ r\^6\)\/\(63\ b\^13\))\)\ \((\(-5\ \) + 105\ \[Mu]\^2 - 315\ \[Mu]\^4 + 231\ \[Mu]\^6)\) + 1\/128\ \((17\/72 - \(17\ r\^2\)\/\(66\ d\^2\) + r\^8\/\(24\ d\^8\) - \(2\ d\^9\ r\^8\)\/\(99\ b\^17\))\)\ \((35 - 1260\ \[Mu]\^2 + 6930\ \[Mu]\^4 - 12012\ \[Mu]\^6 + 6435\ \[Mu]\^8)\) + 1\/256\ \((21\/110 - \(21\ r\^2\)\/\(104\ d\^2\) + r\^10\/\(40\ d\^10\) - \(2\ d\^11\ r\^10\)\/\(143\ b\^21\))\)\ \ \((\(-63\) + 3465\ \[Mu]\^2 - 30030\ \[Mu]\^4 + 90090\ \[Mu]\^6 - 109395\ \[Mu]\^8 + 46189\ \[Mu]\^10)\) + \(\(1\/1024\)\((\((25\/156 - r\^2\/\(6\ d\^2\) + r\^12\/\(60\ d\^12\) - \(2\ d\^13\ r\^12\)\/\(195\ b\^25\))\)\ \ \((231 - 18018\ \[Mu]\^2 + 225225\ \[Mu]\^4 - 1021020\ \[Mu]\^6 + 2078505\ \[Mu]\^8 - 1939938\ \[Mu]\^10 + 676039\ \[Mu]\^12)\))\)\) + \(\(1\/2048\)\((\((29\/210 - \(29\ \ r\^2\)\/\(204\ d\^2\) + r\^14\/\(84\ d\^14\) - \(2\ d\^15\ r\^14\)\/\(255\ b\^29\))\)\ \ \((\(-429\) + 45045\ \[Mu]\^2 - 765765\ \[Mu]\^4 + 4849845\ \[Mu]\^6 - 14549535\ \[Mu]\^8 + 22309287\ \[Mu]\^10 - 16900975\ \[Mu]\^12 + 5014575\ \[Mu]\^14)\))\)\) + \(\(1\/32768\)\((\((33\/272 - \(33\ \ r\^2\)\/\(266\ d\^2\) + r\^16\/\(112\ d\^16\) - \(2\ d\^17\ r\^16\)\/\(323\ b\^33\))\)\ \ \((6435 - 875160\ \[Mu]\^2 + 19399380\ \[Mu]\^4 - 162954792\ \[Mu]\^6 + 669278610\ \[Mu]\^8 - 1487285800\ \[Mu]\^10 + 1825305300\ \[Mu]\^12 - 1163381400\ \[Mu]\^14 + 300540195\ \[Mu]\^16)\))\)\) + \(\(1\/65536\)\((\((37\/342 - \ \(37\ r\^2\)\/\(336\ d\^2\) + r\^18\/\(144\ d\^18\) - \(2\ d\^19\ r\^18\)\/\(399\ b\^37\))\)\ \ \((\(-12155\) + 2078505\ \[Mu]\^2 - 58198140\ \[Mu]\^4 + 624660036\ \[Mu]\^6 - 3346393050\ \[Mu]\^8 + 10039179150\ \[Mu]\^10 - 17644617900\ \[Mu]\^12 + 18032411700\ \[Mu]\^14 - 9917826435\ \[Mu]\^16 + 2268783825\ \[Mu]\^18)\))\)\) + \(\(1\/262144\)\((\((41\/420 - \ \(41\ r\^2\)\/\(414\ d\^2\) + r\^20\/\(180\ d\^20\) - \(2\ d\^21\ r\^20\)\/\(483\ b\^41\))\)\ \ \((46189 - 9699690\ \[Mu]\^2 + 334639305\ \[Mu]\^4 - 4461857400\ \[Mu]\^6 + 30117537450\ \[Mu]\^8 - 116454478140\ \[Mu]\^10 + 273491577450\ \[Mu]\^12 - 396713057400\ \[Mu]\^14 + 347123925225\ \[Mu]\^16 - 167890003050\ \[Mu]\^18 + 34461632205\ \[Mu]\^20)\))\)\) + Log[d\/r] + 1\/2\ \((\(-1\) + 3\ \[Mu]\^2)\)\ \((5\/6 - \(7\ r\^2\)\/\(10\ d\^2\) - \(2\ d\^3\ \ r\^2\)\/\(15\ b\^5\) - \(r\^2\ Log[d\/r]\)\/d\^2)\)\)], "Output"] }, Open ]], Cell["Now consider the case r > d", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Int4\ = \ Integrate[F1, {x, 0, d}, Assumptions \[Rule] \ \ k\ > \ 0]\)], "Input"], Cell[BoxData[ \(\(2\ d\^\(1 + k\)\ r\^\(\(-1\) - k\)\)\/\(3 + 4\ k + k\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(s[k_]\ = Int4 - Int3\)], "Input"], Cell[BoxData[ \(\(2\ d\^\(1 + k\)\ r\^\(\(-1\) - k\)\)\/\(3 + 4\ k + k\^2\) - \(2\ \ b\^\(\(-1\) - 2\ k\)\ d\^\(1 + k\)\ r\^k\)\/\(3 + 4\ k + k\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Phi]2[r_, \[Mu]_]\ = \ Sum[s[k]\ LegendreP[k, \[Mu]], {k, 0, Nt, 2}]\)], "Input"], Cell[BoxData[ \(\(-\(\(2\ d\)\/\(3\ b\)\)\) + \(2\ d\)\/\(3\ r\) + 1\/2\ \((\(2\ d\^3\)\/\(15\ r\^3\) - \(2\ d\^3\ r\^2\)\/\(15\ b\^5\))\)\ \ \((\(-1\) + 3\ \[Mu]\^2)\) + 1\/8\ \((\(2\ d\^5\)\/\(35\ r\^5\) - \(2\ d\^5\ r\^4\)\/\(35\ b\^9\))\)\ \ \((3 - 30\ \[Mu]\^2 + 35\ \[Mu]\^4)\) + 1\/16\ \((\(2\ d\^7\)\/\(63\ r\^7\) - \(2\ d\^7\ r\^6\)\/\(63\ b\^13\))\ \)\ \((\(-5\) + 105\ \[Mu]\^2 - 315\ \[Mu]\^4 + 231\ \[Mu]\^6)\) + 1\/128\ \((\(2\ d\^9\)\/\(99\ r\^9\) - \(2\ d\^9\ r\^8\)\/\(99\ \ b\^17\))\)\ \((35 - 1260\ \[Mu]\^2 + 6930\ \[Mu]\^4 - 12012\ \[Mu]\^6 + 6435\ \[Mu]\^8)\) + 1\/256\ \((\(2\ d\^11\)\/\(143\ r\^11\) - \(2\ d\^11\ r\^10\)\/\(143\ b\ \^21\))\)\ \((\(-63\) + 3465\ \[Mu]\^2 - 30030\ \[Mu]\^4 + 90090\ \[Mu]\^6 - 109395\ \[Mu]\^8 + 46189\ \[Mu]\^10)\) + \(\((\(2\ d\^13\)\/\(195\ r\^13\) - \(2\ \ d\^13\ r\^12\)\/\(195\ b\^25\))\)\ \((231 - 18018\ \[Mu]\^2 + 225225\ \ \[Mu]\^4 - 1021020\ \[Mu]\^6 + 2078505\ \[Mu]\^8 - 1939938\ \[Mu]\^10 + \ 676039\ \[Mu]\^12)\)\)\/1024 + \(\(1\/2048\)\((\((\(2\ d\^15\)\/\(255\ \ r\^15\) - \(2\ d\^15\ r\^14\)\/\(255\ b\^29\))\)\ \((\(-429\) + 45045\ \[Mu]\^2 - 765765\ \[Mu]\^4 + 4849845\ \[Mu]\^6 - 14549535\ \[Mu]\^8 + 22309287\ \[Mu]\^10 - 16900975\ \[Mu]\^12 + 5014575\ \[Mu]\^14)\))\)\) + \(\(1\/32768\)\((\((\(2\ d\^17\)\/\ \(323\ r\^17\) - \(2\ d\^17\ r\^16\)\/\(323\ b\^33\))\)\ \((6435 - 875160\ \[Mu]\^2 + 19399380\ \[Mu]\^4 - 162954792\ \[Mu]\^6 + 669278610\ \[Mu]\^8 - 1487285800\ \[Mu]\^10 + 1825305300\ \[Mu]\^12 - 1163381400\ \[Mu]\^14 + 300540195\ \[Mu]\^16)\))\)\) + \(\(1\/65536\)\((\((\(2\ d\^19\)\ \/\(399\ r\^19\) - \(2\ d\^19\ r\^18\)\/\(399\ b\^37\))\)\ \((\(-12155\) + 2078505\ \[Mu]\^2 - 58198140\ \[Mu]\^4 + 624660036\ \[Mu]\^6 - 3346393050\ \[Mu]\^8 + 10039179150\ \[Mu]\^10 - 17644617900\ \[Mu]\^12 + 18032411700\ \[Mu]\^14 - 9917826435\ \[Mu]\^16 + 2268783825\ \[Mu]\^18)\))\)\) + \(\(1\/262144\)\((\((\(2\ d\^21\ \)\/\(483\ r\^21\) - \(2\ d\^21\ r\^20\)\/\(483\ b\^41\))\)\ \((46189 - 9699690\ \[Mu]\^2 + 334639305\ \[Mu]\^4 - 4461857400\ \[Mu]\^6 + 30117537450\ \[Mu]\^8 - 116454478140\ \[Mu]\^10 + 273491577450\ \[Mu]\^12 - 396713057400\ \[Mu]\^14 + 347123925225\ \[Mu]\^16 - 167890003050\ \[Mu]\^18 + 34461632205\ \[Mu]\^20)\))\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Phi]1[d, \[Mu]] - \[Phi]2[d, \[Mu]]\)], "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[CapitalPhi][r_, \[Mu]_]\ = \ Piecewise[{{\[Phi]1[r, \[Mu]], r < d}, {\[Phi]2[r, \[Mu]], r > d}}]\)], "Input"], Cell[BoxData[ RowBox[{"\[Piecewise]", GridBox[{ {\(1\/2 - \(2\ d\)\/\(3\ b\) + r\^2\/\(6\ d\^2\) + 1\/8\ \((9\/20 - \(9\ r\^2\)\/\(14\ d\^2\) + r\^4\/\(4\ d\^4\) - \(2\ d\^5\ r\^4\)\/\(35\ b\^9\))\)\ \ \((3 - 30\ \[Mu]\^2 + 35\ \[Mu]\^4)\) + 1\/16\ \((13\/42 - \(13\ r\^2\)\/\(36\ d\^2\) + r\^6\/\(12\ d\^6\) - \(2\ d\^7\ r\^6\)\/\(63\ b\^13\))\)\ \ \((\(-5\) + 105\ \[Mu]\^2 - 315\ \[Mu]\^4 + 231\ \[Mu]\^6)\) + 1\/128\ \((17\/72 - \(17\ r\^2\)\/\(66\ d\^2\) + r\^8\/\(24\ d\^8\) - \(2\ d\^9\ r\^8\)\/\(99\ b\^17\))\)\ \ \((35 - 1260\ \[Mu]\^2 + 6930\ \[Mu]\^4 - 12012\ \[Mu]\^6 + 6435\ \[Mu]\^8)\) + 1\/256\ \((21\/110 - \(21\ r\^2\)\/\(104\ d\^2\) + r\^10\/\(40\ d\^10\) - \(2\ d\^11\ r\^10\)\/\(143\ \ b\^21\))\)\ \((\(-63\) + 3465\ \[Mu]\^2 - 30030\ \[Mu]\^4 + 90090\ \[Mu]\^6 - 109395\ \[Mu]\^8 + 46189\ \[Mu]\^10)\) + \(\((25\/156 - r\^2\/\(6\ d\^2\) + \ r\^12\/\(60\ d\^12\) - \(2\ d\^13\ r\^12\)\/\(195\ b\^25\))\)\ \((231 - 18018\ \ \[Mu]\^2 + 225225\ \[Mu]\^4 - 1021020\ \[Mu]\^6 + 2078505\ \[Mu]\^8 - \ 1939938\ \[Mu]\^10 + 676039\ \[Mu]\^12)\)\)\/1024 + \(\((29\/210 - \(29\ r\^2\ \)\/\(204\ d\^2\) + r\^14\/\(84\ d\^14\) - \(2\ d\^15\ r\^14\)\/\(255\ \ b\^29\))\)\ \((\(-429\) + 45045\ \[Mu]\^2 - 765765\ \[Mu]\^4 + 4849845\ \[Mu]\ \^6 - 14549535\ \[Mu]\^8 + 22309287\ \[Mu]\^10 - 16900975\ \[Mu]\^12 + \ 5014575\ \[Mu]\^14)\)\)\/2048 + \(\((33\/272 - \(33\ r\^2\)\/\(266\ d\^2\) + \ r\^16\/\(112\ d\^16\) - \(2\ d\^17\ r\^16\)\/\(323\ b\^33\))\)\ \((6435 - \ 875160\ \[Mu]\^2 + 19399380\ \[Mu]\^4 - 162954792\ \[Mu]\^6 + 669278610\ \ \[Mu]\^8 - 1487285800\ \[Mu]\^10 + 1825305300\ \[Mu]\^12 - 1163381400\ \ \[Mu]\^14 + 300540195\ \[Mu]\^16)\)\)\/32768 + \(\((37\/342 - \(37\ \ r\^2\)\/\(336\ d\^2\) + r\^18\/\(144\ d\^18\) - \(2\ d\^19\ r\^18\)\/\(399\ b\ \^37\))\)\ \((\(-12155\) + 2078505\ \[Mu]\^2 - 58198140\ \[Mu]\^4 + 624660036\ \ \[Mu]\^6 - 3346393050\ \[Mu]\^8 + 10039179150\ \[Mu]\^10 - 17644617900\ \ \[Mu]\^12 + 18032411700\ \[Mu]\^14 - 9917826435\ \[Mu]\^16 + 2268783825\ \ \[Mu]\^18)\)\)\/65536 + \(\((41\/420 - \(41\ r\^2\)\/\(414\ d\^2\) + \ r\^20\/\(180\ d\^20\) - \(2\ d\^21\ r\^20\)\/\(483\ b\^41\))\)\ \((46189 - \ 9699690\ \[Mu]\^2 + 334639305\ \[Mu]\^4 - 4461857400\ \[Mu]\^6 + 30117537450\ \ \[Mu]\^8 - 116454478140\ \[Mu]\^10 + 273491577450\ \[Mu]\^12 - 396713057400\ \ \[Mu]\^14 + 347123925225\ \[Mu]\^16 - 167890003050\ \[Mu]\^18 + 34461632205\ \ \[Mu]\^20)\)\)\/262144 + Log[d\/r] + 1\/2\ \((\(-1\) + 3\ \[Mu]\^2)\)\ \((5\/6 - \(7\ r\^2\)\/\(10\ d\^2\) - \(2\ \ d\^3\ r\^2\)\/\(15\ b\^5\) - \(r\^2\ Log[d\/r]\)\/d\^2)\)\), \(r < d\)}, {\(\(-\(\(2\ d\)\/\(3\ b\)\)\) + \(2\ d\)\/\(3\ r\) + 1\/2\ \((\(2\ d\^3\)\/\(15\ r\^3\) - \(2\ d\^3\ r\^2\)\/\(15\ b\ \^5\))\)\ \((\(-1\) + 3\ \[Mu]\^2)\) + 1\/8\ \((\(2\ d\^5\)\/\(35\ r\^5\) - \(2\ d\^5\ r\^4\)\/\(35\ b\ \^9\))\)\ \((3 - 30\ \[Mu]\^2 + 35\ \[Mu]\^4)\) + 1\/16\ \((\(2\ d\^7\)\/\(63\ r\^7\) - \(2\ d\^7\ r\^6\)\/\(63\ \ b\^13\))\)\ \((\(-5\) + 105\ \[Mu]\^2 - 315\ \[Mu]\^4 + 231\ \[Mu]\^6)\) + 1\/128\ \((\(2\ d\^9\)\/\(99\ r\^9\) - \(2\ d\^9\ r\^8\)\/\(99\ \ b\^17\))\)\ \((35 - 1260\ \[Mu]\^2 + 6930\ \[Mu]\^4 - 12012\ \[Mu]\^6 + 6435\ \[Mu]\^8)\) + 1\/256\ \((\(2\ d\^11\)\/\(143\ r\^11\) - \(2\ d\^11\ r\^10\)\/\ \(143\ b\^21\))\)\ \((\(-63\) + 3465\ \[Mu]\^2 - 30030\ \[Mu]\^4 + 90090\ \[Mu]\^6 - 109395\ \[Mu]\^8 + 46189\ \[Mu]\^10)\) + \(\((\(2\ d\^13\)\/\(195\ r\^13\) - \ \(2\ d\^13\ r\^12\)\/\(195\ b\^25\))\)\ \((231 - 18018\ \[Mu]\^2 + 225225\ \ \[Mu]\^4 - 1021020\ \[Mu]\^6 + 2078505\ \[Mu]\^8 - 1939938\ \[Mu]\^10 + \ 676039\ \[Mu]\^12)\)\)\/1024 + \(\((\(2\ d\^15\)\/\(255\ r\^15\) - \(2\ d\^15\ \ r\^14\)\/\(255\ b\^29\))\)\ \((\(-429\) + 45045\ \[Mu]\^2 - 765765\ \ \[Mu]\^4 + 4849845\ \[Mu]\^6 - 14549535\ \[Mu]\^8 + 22309287\ \[Mu]\^10 - \ 16900975\ \[Mu]\^12 + 5014575\ \[Mu]\^14)\)\)\/2048 + \(\((\(2\ \ d\^17\)\/\(323\ r\^17\) - \(2\ d\^17\ r\^16\)\/\(323\ b\^33\))\)\ \((6435 - \ 875160\ \[Mu]\^2 + 19399380\ \[Mu]\^4 - 162954792\ \[Mu]\^6 + 669278610\ \ \[Mu]\^8 - 1487285800\ \[Mu]\^10 + 1825305300\ \[Mu]\^12 - 1163381400\ \ \[Mu]\^14 + 300540195\ \[Mu]\^16)\)\)\/32768 + \(\((\(2\ d\^19\)\/\(399\ \ r\^19\) - \(2\ d\^19\ r\^18\)\/\(399\ b\^37\))\)\ \((\(-12155\) + 2078505\ \ \[Mu]\^2 - 58198140\ \[Mu]\^4 + 624660036\ \[Mu]\^6 - 3346393050\ \[Mu]\^8 + \ 10039179150\ \[Mu]\^10 - 17644617900\ \[Mu]\^12 + 18032411700\ \[Mu]\^14 - \ 9917826435\ \[Mu]\^16 + 2268783825\ \[Mu]\^18)\)\)\/65536 + \(\((\(2\ d\^21\)\ \/\(483\ r\^21\) - \(2\ d\^21\ r\^20\)\/\(483\ b\^41\))\)\ \((46189 - 9699690\ \ \[Mu]\^2 + 334639305\ \[Mu]\^4 - 4461857400\ \[Mu]\^6 + 30117537450\ \ \[Mu]\^8 - 116454478140\ \[Mu]\^10 + 273491577450\ \[Mu]\^12 - 396713057400\ \ \[Mu]\^14 + 347123925225\ \[Mu]\^16 - 167890003050\ \[Mu]\^18 + 34461632205\ \ \[Mu]\^20)\)\)\/262144\), \(r > d\)} }, ColumnSpacings->1.2, ColumnAlignments->{Left}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(F[x_, z_]\ = \ \[CapitalPhi][Sqrt[x^2 + z^2], z/Sqrt[x^2 + z^2]]\)], "Input"], Cell[BoxData[ RowBox[{"\[Piecewise]", GridBox[{ {\(1\/2 - \(2\ d\)\/\(3\ b\) + \(x\^2 + z\^2\)\/\(6\ d\^2\) + 1\/8\ \((3 + \(35\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(30\ \ z\^2\)\/\(x\^2 + z\^2\))\)\ \((9\/20 - \(9\ \((x\^2 + z\^2)\)\)\/\(14\ d\^2\) \ + \((x\^2 + z\^2)\)\^2\/\(4\ d\^4\) - \(2\ d\^5\ \((x\^2 + z\^2)\)\^2\)\/\(35\ \ b\^9\))\) + 1\/16\ \((\(-5\) + \(231\ z\^6\)\/\((x\^2 + z\^2)\)\^3 - \(315\ \ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(105\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((13\/42 - \ \(13\ \((x\^2 + z\^2)\)\)\/\(36\ d\^2\) + \((x\^2 + z\^2)\)\^3\/\(12\ d\^6\) \ - \(2\ d\^7\ \((x\^2 + z\^2)\)\^3\)\/\(63\ b\^13\))\) + 1\/128\ \((35 + \(6435\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \(12012\ \ z\^6\)\/\((x\^2 + z\^2)\)\^3 + \(6930\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(1260\ \ z\^2\)\/\(x\^2 + z\^2\))\)\ \((17\/72 - \(17\ \((x\^2 + z\^2)\)\)\/\(66\ d\^2\ \) + \((x\^2 + z\^2)\)\^4\/\(24\ d\^8\) - \(2\ d\^9\ \((x\^2 + z\^2)\)\^4\)\/\ \(99\ b\^17\))\) + 1\/256\ \((\(-63\) + \(46189\ z\^10\)\/\((x\^2 + z\^2)\)\^5 - \ \(109395\ z\^8\)\/\((x\^2 + z\^2)\)\^4 + \(90090\ z\^6\)\/\((x\^2 + \ z\^2)\)\^3 - \(30030\ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(3465\ z\^2\)\/\(x\^2 + \ z\^2\))\)\ \((21\/110 - \(21\ \((x\^2 + z\^2)\)\)\/\(104\ d\^2\) + \((x\^2 + \ z\^2)\)\^5\/\(40\ d\^10\) - \(2\ d\^11\ \((x\^2 + z\^2)\)\^5\)\/\(143\ \ b\^21\))\) + \(\((231 + \(676039\ z\^12\)\/\((x\^2 + z\^2)\)\^6 - \(1939938\ \ z\^10\)\/\((x\^2 + z\^2)\)\^5 + \(2078505\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \ \(1021020\ z\^6\)\/\((x\^2 + z\^2)\)\^3 + \(225225\ z\^4\)\/\((x\^2 + z\^2)\)\ \^2 - \(18018\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((25\/156 - \(x\^2 + z\^2\)\/\(6\ \ d\^2\) + \((x\^2 + z\^2)\)\^6\/\(60\ d\^12\) - \(2\ d\^13\ \((x\^2 + \ z\^2)\)\^6\)\/\(195\ b\^25\))\)\)\/1024 + \(\((\(-429\) + \(5014575\ \ z\^14\)\/\((x\^2 + z\^2)\)\^7 - \(16900975\ z\^12\)\/\((x\^2 + z\^2)\)\^6 + \ \(22309287\ z\^10\)\/\((x\^2 + z\^2)\)\^5 - \(14549535\ z\^8\)\/\((x\^2 + \ z\^2)\)\^4 + \(4849845\ z\^6\)\/\((x\^2 + z\^2)\)\^3 - \(765765\ z\^4\)\/\((x\ \^2 + z\^2)\)\^2 + \(45045\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((29\/210 - \(29\ \ \((x\^2 + z\^2)\)\)\/\(204\ d\^2\) + \((x\^2 + z\^2)\)\^7\/\(84\ d\^14\) - \ \(2\ d\^15\ \((x\^2 + z\^2)\)\^7\)\/\(255\ b\^29\))\)\)\/2048 + \(\((6435 + \ \(300540195\ z\^16\)\/\((x\^2 + z\^2)\)\^8 - \(1163381400\ z\^14\)\/\((x\^2 + \ z\^2)\)\^7 + \(1825305300\ z\^12\)\/\((x\^2 + z\^2)\)\^6 - \(1487285800\ \ z\^10\)\/\((x\^2 + z\^2)\)\^5 + \(669278610\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \ \(162954792\ z\^6\)\/\((x\^2 + z\^2)\)\^3 + \(19399380\ z\^4\)\/\((x\^2 + \ z\^2)\)\^2 - \(875160\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((33\/272 - \(33\ \((x\^2 \ + z\^2)\)\)\/\(266\ d\^2\) + \((x\^2 + z\^2)\)\^8\/\(112\ d\^16\) - \(2\ \ d\^17\ \((x\^2 + z\^2)\)\^8\)\/\(323\ b\^33\))\)\)\/32768 + \(\((\(-12155\) + \ \(2268783825\ z\^18\)\/\((x\^2 + z\^2)\)\^9 - \(9917826435\ z\^16\)\/\((x\^2 \ + z\^2)\)\^8 + \(18032411700\ z\^14\)\/\((x\^2 + z\^2)\)\^7 - \(17644617900\ \ z\^12\)\/\((x\^2 + z\^2)\)\^6 + \(10039179150\ z\^10\)\/\((x\^2 + z\^2)\)\^5 \ - \(3346393050\ z\^8\)\/\((x\^2 + z\^2)\)\^4 + \(624660036\ z\^6\)\/\((x\^2 + \ z\^2)\)\^3 - \(58198140\ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(2078505\ \ z\^2\)\/\(x\^2 + z\^2\))\)\ \((37\/342 - \(37\ \((x\^2 + z\^2)\)\)\/\(336\ \ d\^2\) + \((x\^2 + z\^2)\)\^9\/\(144\ d\^18\) - \(2\ d\^19\ \((x\^2 + z\^2)\)\ \^9\)\/\(399\ b\^37\))\)\)\/65536 + \(\((46189 + \(34461632205\ z\^20\)\/\((x\ \^2 + z\^2)\)\^10 - \(167890003050\ z\^18\)\/\((x\^2 + z\^2)\)\^9 + \ \(347123925225\ z\^16\)\/\((x\^2 + z\^2)\)\^8 - \(396713057400\ z\^14\)\/\((x\ \^2 + z\^2)\)\^7 + \(273491577450\ z\^12\)\/\((x\^2 + z\^2)\)\^6 - \ \(116454478140\ z\^10\)\/\((x\^2 + z\^2)\)\^5 + \(30117537450\ \ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \(4461857400\ z\^6\)\/\((x\^2 + z\^2)\)\^3 + \ \(334639305\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(9699690\ z\^2\)\/\(x\^2 + \ z\^2\))\)\ \((41\/420 - \(41\ \((x\^2 + z\^2)\)\)\/\(414\ d\^2\) + \((x\^2 + \ z\^2)\)\^10\/\(180\ d\^20\) - \(2\ d\^21\ \((x\^2 + z\^2)\)\^10\)\/\(483\ \ b\^41\))\)\)\/262144 + Log[d\/\@\(x\^2 + z\^2\)] + 1\/2\ \((\(-1\) + \(3\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((5\/6 - \ \(7\ \((x\^2 + z\^2)\)\)\/\(10\ d\^2\) - \(2\ d\^3\ \((x\^2 + z\^2)\)\)\/\(15\ \ b\^5\) - \(\((x\^2 + z\^2)\)\ Log[d\/\@\(x\^2 + z\^2\)]\)\/d\^2)\)\), \ \(\@\(x\^2 + z\^2\) < d\)}, {\(\(-\(\(2\ d\)\/\(3\ b\)\)\) + \(2\ d\)\/\(3\ \@\(x\^2 + z\^2\)\) \ + 1\/2\ \((\(-1\) + \(3\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ d\^3\)\/\(15\ \ \((x\^2 + z\^2)\)\^\(3/2\)\) - \(2\ d\^3\ \((x\^2 + z\^2)\)\)\/\(15\ \ b\^5\))\) + 1\/8\ \((3 + \(35\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(30\ \ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ d\^5\)\/\(35\ \((x\^2 + \ z\^2)\)\^\(5/2\)\) - \(2\ d\^5\ \((x\^2 + z\^2)\)\^2\)\/\(35\ b\^9\))\) + 1\/16\ \((\(-5\) + \(231\ z\^6\)\/\((x\^2 + z\^2)\)\^3 - \(315\ \ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(105\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ \ d\^7\)\/\(63\ \((x\^2 + z\^2)\)\^\(7/2\)\) - \(2\ d\^7\ \((x\^2 + \ z\^2)\)\^3\)\/\(63\ b\^13\))\) + 1\/128\ \((35 + \(6435\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \(12012\ \ z\^6\)\/\((x\^2 + z\^2)\)\^3 + \(6930\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(1260\ \ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ d\^9\)\/\(99\ \((x\^2 + \ z\^2)\)\^\(9/2\)\) - \(2\ d\^9\ \((x\^2 + z\^2)\)\^4\)\/\(99\ b\^17\))\) + 1\/256\ \((\(-63\) + \(46189\ z\^10\)\/\((x\^2 + z\^2)\)\^5 - \ \(109395\ z\^8\)\/\((x\^2 + z\^2)\)\^4 + \(90090\ z\^6\)\/\((x\^2 + \ z\^2)\)\^3 - \(30030\ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(3465\ z\^2\)\/\(x\^2 + \ z\^2\))\)\ \((\(2\ d\^11\)\/\(143\ \((x\^2 + z\^2)\)\^\(11/2\)\) - \(2\ d\^11\ \ \((x\^2 + z\^2)\)\^5\)\/\(143\ b\^21\))\) + \(\((231 + \(676039\ \ z\^12\)\/\((x\^2 + z\^2)\)\^6 - \(1939938\ z\^10\)\/\((x\^2 + z\^2)\)\^5 + \ \(2078505\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \(1021020\ z\^6\)\/\((x\^2 + \ z\^2)\)\^3 + \(225225\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(18018\ z\^2\)\/\(x\^2 \ + z\^2\))\)\ \((\(2\ d\^13\)\/\(195\ \((x\^2 + z\^2)\)\^\(13/2\)\) - \(2\ \ d\^13\ \((x\^2 + z\^2)\)\^6\)\/\(195\ b\^25\))\)\)\/1024 + \(\((\(-429\) + \ \(5014575\ z\^14\)\/\((x\^2 + z\^2)\)\^7 - \(16900975\ z\^12\)\/\((x\^2 + \ z\^2)\)\^6 + \(22309287\ z\^10\)\/\((x\^2 + z\^2)\)\^5 - \(14549535\ z\^8\)\/\ \((x\^2 + z\^2)\)\^4 + \(4849845\ z\^6\)\/\((x\^2 + z\^2)\)\^3 - \(765765\ \ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(45045\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ d\ \^15\)\/\(255\ \((x\^2 + z\^2)\)\^\(15/2\)\) - \(2\ d\^15\ \((x\^2 + \ z\^2)\)\^7\)\/\(255\ b\^29\))\)\)\/2048 + \(\((6435 + \(300540195\ \ z\^16\)\/\((x\^2 + z\^2)\)\^8 - \(1163381400\ z\^14\)\/\((x\^2 + z\^2)\)\^7 + \ \(1825305300\ z\^12\)\/\((x\^2 + z\^2)\)\^6 - \(1487285800\ z\^10\)\/\((x\^2 \ + z\^2)\)\^5 + \(669278610\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \(162954792\ \ z\^6\)\/\((x\^2 + z\^2)\)\^3 + \(19399380\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \ \(875160\ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ d\^17\)\/\(323\ \((x\^2 + z\^2)\ \)\^\(17/2\)\) - \(2\ d\^17\ \((x\^2 + z\^2)\)\^8\)\/\(323\ \ b\^33\))\)\)\/32768 + \(\((\(-12155\) + \(2268783825\ z\^18\)\/\((x\^2 + \ z\^2)\)\^9 - \(9917826435\ z\^16\)\/\((x\^2 + z\^2)\)\^8 + \(18032411700\ \ z\^14\)\/\((x\^2 + z\^2)\)\^7 - \(17644617900\ z\^12\)\/\((x\^2 + z\^2)\)\^6 \ + \(10039179150\ z\^10\)\/\((x\^2 + z\^2)\)\^5 - \(3346393050\ \ z\^8\)\/\((x\^2 + z\^2)\)\^4 + \(624660036\ z\^6\)\/\((x\^2 + z\^2)\)\^3 - \ \(58198140\ z\^4\)\/\((x\^2 + z\^2)\)\^2 + \(2078505\ z\^2\)\/\(x\^2 + \ z\^2\))\)\ \((\(2\ d\^19\)\/\(399\ \((x\^2 + z\^2)\)\^\(19/2\)\) - \(2\ d\^19\ \ \((x\^2 + z\^2)\)\^9\)\/\(399\ b\^37\))\)\)\/65536 + \(\((46189 + \ \(34461632205\ z\^20\)\/\((x\^2 + z\^2)\)\^10 - \(167890003050\ z\^18\)\/\((x\ \^2 + z\^2)\)\^9 + \(347123925225\ z\^16\)\/\((x\^2 + z\^2)\)\^8 - \ \(396713057400\ z\^14\)\/\((x\^2 + z\^2)\)\^7 + \(273491577450\ z\^12\)\/\((x\ \^2 + z\^2)\)\^6 - \(116454478140\ z\^10\)\/\((x\^2 + z\^2)\)\^5 + \ \(30117537450\ z\^8\)\/\((x\^2 + z\^2)\)\^4 - \(4461857400\ z\^6\)\/\((x\^2 + \ z\^2)\)\^3 + \(334639305\ z\^4\)\/\((x\^2 + z\^2)\)\^2 - \(9699690\ \ z\^2\)\/\(x\^2 + z\^2\))\)\ \((\(2\ d\^21\)\/\(483\ \((x\^2 + z\^2)\)\^\(21/2\ \)\) - \(2\ d\^21\ \((x\^2 + z\^2)\)\^10\)\/\(483\ b\^41\))\)\)\/262144\), \(\ \@\(x\^2 + z\^2\) > d\)} }, ColumnSpacings->1.2, ColumnAlignments->{Left}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Plot3D[ F[x, z] /. {b \[Rule] 2, d \[Rule] 1}, {x, \(-2\), 2}, {z, \(-2\), 2}]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .81114 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% SurfaceGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -1.55041e-017 1.04977 -0.0679587 1.04977 [ [.02757 .24618 -12 -8.70276 ] [.02757 .24618 0 .29724 ] [.17646 .18758 -11.7989 -9 ] [.17646 .18758 .20112 0 ] [.3345 .12542 -5.5867 -9 ] [.3345 .12542 .4133 0 ] [.50253 .05935 -5.27396 -9 ] [.50253 .05935 .72604 0 ] [.68156 -0.01098 -4.96123 -9 ] [.68156 -0.01098 1.03877 0 ] [.70096 -0.00478 0 -6.26206 ] [.70096 -0.00478 12 2.73794 ] [.78313 .12104 0 -6.13858 ] [.78313 .12104 12 2.86142 ] [.8565 .23339 0 -6.03127 ] [.8565 .23339 6 2.96873 ] [.9224 .33431 0 -5.93715 ] [.9224 .33431 6 3.06285 ] [.98191 .42546 0 -5.85393 ] [.98191 .42546 6 3.14607 ] [.02087 .28543 -6 -2.75948 ] [.02087 .28543 0 6.24052 ] [.01271 .33659 -24 -2.80279 ] [.01271 .33659 0 6.19721 ] [.00427 .38946 -18 -2.8477 ] [.00427 .38946 0 6.1523 ] [-0.00445 .44414 -24 -2.8943 ] [-0.00445 .44414 0 6.1057 ] [ 0 0 0 0 ] [ 1 .81114 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .03716 .25514 m .68874 0 L s .03716 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.7708 .12553 m .76464 .12778 L s [(-1)] .78313 .12104 -1 .36413 Mshowa .84407 .23761 m .83786 .23973 L s [(0)] .8565 .23339 -1 .34028 Mshowa .9099 .3383 m .90365 .34029 L s [(1)] .9224 .33431 -1 .31937 Mshowa .96935 .42924 m .96306 .43113 L s [(2)] .98191 .42546 -1 .30087 Mshowa .125 Mabswid .70593 .0263 m .70226 .02771 L s .72272 .05198 m .71904 .05338 L s .73912 .07706 m .73543 .07845 L s .75514 .10158 m .75145 .10294 L s .78611 .14895 m .78241 .15028 L s .80108 .17185 m .79737 .17317 L s .81573 .19425 m .81201 .19555 L s .83006 .21617 m .82633 .21745 L s .8578 .2586 m .85407 .25986 L s .87123 .27915 m .8675 .28039 L s .88439 .29928 m .88065 .3005 L s .89727 .31899 m .89353 .3202 L s .92227 .35722 m .91851 .3584 L s .93439 .37576 m .93063 .37693 L s .94627 .39394 m .94251 .3951 L s .95792 .41176 m .95416 .41291 L s .25 Mabswid .03716 .25514 m 0 .48963 L s .03311 .2807 m .03923 .27833 L s [(0)] .02087 .28543 1 -0.38678 Mshowa .02499 .33196 m .03113 .32964 L s [(0.25)] .01271 .33659 1 -0.37716 Mshowa .01659 .38494 m .02275 .38267 L s [(0.5)] .00427 .38946 1 -0.36718 Mshowa .00791 .43973 m .01409 .43752 L s [(0.75)] -0.00445 .44414 1 -0.35682 Mshowa .125 Mabswid .03151 .29081 m .03518 .2894 L s .02989 .301 m .03357 .29959 L s .02827 .31125 m .03195 .30985 L s .02663 .32157 m .03031 .32017 L s .02333 .34241 m .02702 .34103 L s .02166 .35294 m .02535 .35156 L s .01998 .36353 m .02367 .36216 L s .01829 .3742 m .02199 .37283 L s .01488 .39575 m .01858 .3944 L s .01315 .40663 m .01685 .40529 L s .01142 .41759 m .01512 .41625 L s .00967 .42862 m .01337 .42729 L s .0347 .27064 m .03837 .26922 L s .03629 .26066 m .03995 .25922 L s .00614 .45091 m .00985 .44959 L s .00435 .46217 m .00806 .46086 L s .00255 .47351 m .00627 .47221 L s .00075 .48493 m .00446 .48363 L s .25 Mabswid .03716 .25514 m 0 .48963 L s 0 .48963 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s .40529 .59895 m .03716 .25514 L s .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .40529 .59895 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s 0 0 m 1 0 L 1 .81114 L 0 .81114 L closepath clip newpath .5 Mabswid .618 .768 .952 r .39227 .59401 .40512 .60371 .42646 .5989 .41372 .58941 Metetra .612 .772 .957 r .41372 .58941 .42646 .5989 .44799 .59416 .43536 .58491 Metetra .606 .777 .962 r .43536 .58491 .44799 .59416 .46971 .58948 .45719 .58053 Metetra .599 .782 .968 r .45719 .58053 .46971 .58948 .49163 .58484 .47923 .57624 Metetra .591 .789 .974 r .47923 .57624 .49163 .58484 .51375 .58022 .50148 .57203 Metetra .584 .796 .98 r .50148 .57203 .51375 .58022 .53608 .57556 .52395 .56784 Metetra .577 .805 .986 r .52395 .56784 .53608 .57556 .55861 .57082 .54663 .56361 Metetra .571 .815 .991 r .54663 .56361 .55861 .57082 .58136 .5659 .56954 .55922 Metetra .568 .827 .994 r .56954 .55922 .58136 .5659 .60431 .5607 .59266 .55453 Metetra .571 .84 .996 r .59266 .55453 .60431 .5607 .62746 .55511 .616 .54936 Metetra .582 .854 .995 r .616 .54936 .62746 .55511 .65081 .54901 .63954 .54352 Metetra .599 .867 .993 r .63954 .54352 .65081 .54901 .67434 .54232 .66326 .53687 Metetra .621 .876 .989 r .66326 .53687 .67434 .54232 .69804 .535 .68715 .52933 Metetra .645 .881 .984 r .68715 .52933 .69804 .535 .7219 .52708 .71119 .52095 Metetra .665 .879 .978 r .71119 .52095 .7219 .52708 .74593 .51864 .73538 .51189 Metetra .68 .873 .971 r .73538 .51189 .74593 .51864 .77011 .50978 .75973 .50233 Metetra .69 .863 .964 r .75973 .50233 .77011 .50978 .79446 .50062 .78423 .49243 Metetra .695 .852 .958 r .78423 .49243 .79446 .50062 .81898 .49126 .80889 .48235 Metetra .698 .841 .951 r .80889 .48235 .81898 .49126 .84367 .48179 .83373 .47219 Metetra .698 .83 .946 r .83373 .47219 .84367 .48179 .86855 .47225 .85875 .46202 Metetra .698 .82 .941 r .85875 .46202 .86855 .47225 .89362 .46271 .88396 .4519 Metetra .696 .811 .936 r .88396 .4519 .89362 .46271 .91888 .45318 .90937 .44186 Metetra .694 .803 .933 r .90937 .44186 .91888 .45318 .94435 .44369 .93499 .43189 Metetra .692 .796 .93 r .93499 .43189 .94435 .44369 .97003 .43424 .96082 .42201 Metetra .61 .766 .954 r .37922 .58415 .39227 .59401 .41372 .58941 .40076 .57978 Metetra .603 .77 .96 r .40076 .57978 .41372 .58941 .43536 .58491 .42251 .57557 Metetra .594 .774 .966 r .42251 .57557 .43536 .58491 .45719 .58053 .44446 .57154 Metetra .584 .78 .973 r .44446 .57154 .45719 .58053 .47923 .57624 .46661 .56768 Metetra .572 .786 .98 r .46661 .56768 .47923 .57624 .50148 .57203 .48899 .56399 Metetra .559 .794 .987 r .48899 .56399 .50148 .57203 .52395 .56784 .51159 .56041 Metetra .544 .803 .993 r .51159 .56041 .52395 .56784 .54663 .56361 .53443 .55688 Metetra .53 .813 .998 r .53443 .55688 .54663 .56361 .56954 .55922 .5575 .55326 Metetra .52 .826 1 r .5575 .55326 .56954 .55922 .59266 .55453 .58081 .54936 Metetra .516 .842 .998 r .58081 .54936 .59266 .55453 .616 .54936 .60435 .5449 Metetra .527 .86 .995 r .60435 .5449 .616 .54936 .63954 .54352 .62809 .53955 Metetra .553 .881 .99 r .62809 .53955 .63954 .54352 .66326 .53687 .65202 .53302 Metetra .592 .898 .987 r .65202 .53302 .66326 .53687 .68715 .52933 .67611 .52517 Metetra .632 .908 .983 r .67611 .52517 .68715 .52933 .71119 .52095 .70034 .51612 Metetra .666 .907 .978 r .70034 .51612 .71119 .52095 .73538 .51189 .7247 .50615 Metetra .688 .897 .972 r .7247 .50615 .73538 .51189 .75973 .50233 .7492 .49559 Metetra .701 .883 .965 r .7492 .49559 .75973 .50233 .78423 .49243 .77384 .48471 Metetra .707 .868 .958 r .77384 .48471 .78423 .49243 .80889 .48235 .79864 .4737 Metetra .709 .853 .951 r .79864 .4737 .80889 .48235 .83373 .47219 .82362 .46271 Metetra .708 .839 .945 r .82362 .46271 .83373 .47219 .85875 .46202 .84878 .4518 Metetra .706 .826 .939 r .84878 .4518 .85875 .46202 .88396 .4519 .87414 .44102 Metetra .703 .816 .935 r .87414 .44102 .88396 .4519 .90937 .44186 .8997 .43039 Metetra .7 .806 .931 r .8997 .43039 .90937 .44186 .93499 .43189 .92547 .4199 Metetra .697 .798 .928 r .92547 .4199 .93499 .43189 .96082 .42201 .95145 .40956 Metetra .602 .763 .956 r .36595 .57411 .37922 .58415 .40076 .57978 .3876 .56999 Metetra .592 .767 .963 r .3876 .56999 .40076 .57978 .42251 .57557 .40944 .56611 Metetra .58 .771 .97 r .40944 .56611 .42251 .57557 .44446 .57154 .4315 .56249 Metetra .565 .776 .977 r .4315 .56249 .44446 .57154 .46661 .56768 .45377 .55915 Metetra .547 .781 .985 r .45377 .55915 .46661 .56768 .48899 .56399 .47627 .5561 Metetra .524 .788 .993 r .47627 .5561 .48899 .56399 .51159 .56041 .49901 .55332 Metetra .497 .794 .998 r .49901 .55332 .51159 .56041 .53443 .55688 .522 .55074 Metetra .465 .801 .999 r .522 .55074 .53443 .55688 .5575 .55326 .54524 .54825 Metetra .432 .808 .992 r .54524 .54825 .5575 .55326 .58081 .54936 .56874 .54559 Metetra .406 .818 .976 r .56874 .54559 .58081 .54936 .60435 .5449 .59249 .54235 Metetra .405 .835 .955 r .59249 .54235 .60435 .5449 .62809 .53955 .61647 .53794 Metetra .444 .866 .942 r .61647 .53794 .62809 .53955 .65202 .53302 .64064 .53171 Metetra .519 .905 .944 r .64064 .53171 .65202 .53302 .67611 .52517 .66494 .52338 Metetra .601 .933 .956 r .66494 .52338 .67611 .52517 .70034 .51612 .68935 .5132 Metetra .663 .94 .965 r .68935 .5132 .70034 .51612 .7247 .50615 .71388 .50181 Metetra .7 .928 .966 r .71388 .50181 .7247 .50615 .7492 .49559 .73852 .4898 Metetra .717 .908 .962 r .73852 .4898 .7492 .49559 .77384 .48471 .7633 .47757 Metetra .723 .886 .955 r .7633 .47757 .77384 .48471 .79864 .4737 .78824 .46537 Metetra .723 .865 .949 r .78824 .46537 .79864 .4737 .82362 .46271 .81335 .45335 Metetra .72 .848 .942 r .81335 .45335 .82362 .46271 .84878 .4518 .83865 .44157 Metetra .716 .833 .937 r .83865 .44157 .84878 .4518 .87414 .44102 .86414 .43003 Metetra .711 .82 .933 r .86414 .43003 .87414 .44102 .8997 .43039 .88985 .41875 Metetra .706 .809 .929 r .88985 .41875 .8997 .43039 .92547 .4199 .91577 .4077 Metetra .702 .8 .926 r .91577 .4077 .92547 .4199 .95145 .40956 .94191 .39686 Metetra .593 .76 .958 r .35247 .56385 .36595 .57411 .3876 .56999 .37421 .56001 Metetra .58 .763 .965 r .37421 .56001 .3876 .56999 .40944 .56611 .39616 .55649 Metetra .564 .766 .973 r .39616 .55649 .40944 .56611 .4315 .56249 .41832 .55333 Metetra .543 .769 .981 r .41832 .55333 .4315 .56249 .45377 .55915 .4407 .5506 Metetra .516 .773 .99 r .4407 .5506 .45377 .55915 .47627 .5561 .46332 .54833 Metetra .478 .775 .996 r .46332 .54833 .47627 .5561 .49901 .55332 .48618 .54656 Metetra .428 .774 .997 r .48618 .54656 .49901 .55332 .522 .55074 .50931 .54527 Metetra .359 .765 .983 r .50931 .54527 .522 .55074 .54524 .54825 .53272 .5444 Metetra .271 .742 .941 r .53272 .5444 .54524 .54825 .56874 .54559 .55642 .54371 Metetra .178 .704 .863 r .55642 .54371 .56874 .54559 .59249 .54235 .58041 .54267 Metetra .126 .676 .767 r .58041 .54267 .59249 .54235 .61647 .53794 .60467 .54022 Metetra .173 .705 .714 r .60467 .54022 .61647 .53794 .64064 .53171 .62912 .53481 Metetra .328 .806 .746 r .62912 .53481 .64064 .53171 .66494 .52338 .65366 .52549 Metetra .516 .915 .836 r .65366 .52549 .66494 .52338 .68935 .5132 .67826 .51317 Metetra .65 .965 .91 r .67826 .51317 .68935 .5132 .71388 .50181 .70292 .49937 Metetra .716 .961 .944 r .70292 .49937 .71388 .50181 .73852 .4898 .72769 .48516 Metetra .739 .934 .952 r .72769 .48516 .73852 .4898 .7633 .47757 .7526 .47108 Metetra .743 .905 .949 r .7526 .47108 .7633 .47757 .78824 .46537 .77766 .45736 Metetra .74 .878 .944 r .77766 .45736 .78824 .46537 .81335 .45335 .8029 .44409 Metetra .733 .856 .939 r .8029 .44409 .81335 .45335 .83865 .44157 .82833 .43128 Metetra .726 .838 .934 r .82833 .43128 .83865 .44157 .86414 .43003 .85397 .41889 Metetra .72 .823 .929 r .85397 .41889 .86414 .43003 .88985 .41875 .87982 .40689 Metetra .713 .812 .926 r .87982 .40689 .88985 .41875 .91577 .4077 .90589 .39524 Metetra .708 .802 .923 r .90589 .39524 .91577 .4077 .94191 .39686 .93219 .38388 Metetra .584 .756 .96 r .33877 .55333 .35247 .56385 .37421 .56001 .3606 .54978 Metetra .568 .757 .967 r .3606 .54978 .37421 .56001 .39616 .55649 .38265 .54664 Metetra .547 .759 .976 r .38265 .54664 .39616 .55649 .41832 .55333 .4049 .54401 Metetra .518 .76 .984 r .4049 .54401 .41832 .55333 .4407 .5506 .42739 .54196 Metetra .478 .759 .992 r .42739 .54196 .4407 .5506 .46332 .54833 .45011 .54061 Metetra .419 .752 .995 r .45011 .54061 .46332 .54833 .48618 .54656 .4731 .54007 Metetra .33 .732 .981 r .4731 .54007 .48618 .54656 .50931 .54527 .49636 .54045 Metetra .194 .681 .926 r .49636 .54045 .50931 .54527 .53272 .5444 .51994 .54185 Metetra .004 .571 .787 r .51994 .54185 .53272 .5444 .55642 .54371 .54384 .54424 Metetra .198 0 0 r .54384 .54424 .55642 .54371 .58041 .54267 .5681 .54726 Metetra .32 0 0 r .5681 .54726 .58041 .54267 .60467 .54022 .59271 .54957 Metetra .269 0 0 r .59271 .54957 .60467 .54022 .62912 .53481 .61754 .5468 Metetra .013 0 0 r .61754 .5468 .62912 .53481 .65366 .52549 .64233 .5347 Metetra .64233 .5347 .65366 .52549 .67826 .51317 .66706 .51744 Metetra .614 .947 .77 r .66706 .51744 .67826 .51317 .70292 .49937 .69184 .49936 Metetra .737 .987 .894 r .69184 .49936 .70292 .49937 .72769 .48516 .71671 .48183 Metetra .769 .96 .931 r .71671 .48183 .72769 .48516 .7526 .47108 .74172 .46524 Metetra .768 .922 .938 r .74172 .46524 .7526 .47108 .77766 .45736 .7669 .4496 Metetra .759 .889 .936 r .7669 .4496 .77766 .45736 .8029 .44409 .79226 .43484 Metetra .748 .863 .933 r .79226 .43484 .8029 .44409 .82833 .43128 .81782 .42085 Metetra .738 .842 .929 r .81782 .42085 .82833 .43128 .85397 .41889 .8436 .40752 Metetra .728 .826 .925 r .8436 .40752 .85397 .41889 .87982 .40689 .86959 .39476 Metetra .72 .813 .922 r .86959 .39476 .87982 .40689 .90589 .39524 .89582 .38246 Metetra .713 .802 .92 r .89582 .38246 .90589 .39524 .93219 .38388 .92227 .37057 Metetra .575 .75 .96 r .32485 .54251 .33877 .55333 .3606 .54978 .34677 .53924 Metetra .555 .751 .968 r .34677 .53924 .3606 .54978 .38265 .54664 .36891 .5365 Metetra .529 .75 .977 r .36891 .5365 .38265 .54664 .4049 .54401 .39125 .53441 Metetra .491 .748 .986 r .39125 .53441 .4049 .54401 .42739 .54196 .41383 .53311 Metetra .435 .74 .991 r .41383 .53311 .42739 .54196 .45011 .54061 .43666 .53279 Metetra .347 .718 .986 r .43666 .53279 .45011 .54061 .4731 .54007 .45975 .53369 Metetra .204 .664 .944 r .45975 .53369 .4731 .54007 .49636 .54045 .48314 .53613 Metetra 0 .534 .808 r .48314 .53613 .49636 .54045 .51994 .54185 .50685 .54052 Metetra .31 0 0 r .50685 .54052 .51994 .54185 .54384 .54424 .53095 .54744 Metetra .534 0 0 r .53095 .54744 .54384 .54424 .5681 .54726 .5555 .55763 Metetra .65 .182 .128 r .5555 .55763 .5681 .54726 .59271 .54957 .58061 .57299 Metetra .993 .843 .484 r .58061 .57299 .59271 .54957 .61754 .5468 .60324 .46097 Metetra 0 0 .496 r .60324 .46097 .61754 .5468 .64233 .5347 .63109 .55804 Metetra .63109 .55804 .64233 .5347 .66706 .51744 .65578 .52752 Metetra .576 .871 .562 r .65578 .52752 .66706 .51744 .69184 .49936 .68059 .50205 Metetra .768 .996 .817 r .68059 .50205 .69184 .49936 .71671 .48183 .70554 .47973 Metetra .806 .977 .9 r .70554 .47973 .71671 .48183 .74172 .46524 .73064 .45987 Metetra .797 .934 .921 r .73064 .45987 .74172 .46524 .7669 .4496 .75593 .44192 Metetra .781 .896 .925 r .75593 .44192 .7669 .4496 .79226 .43484 .78141 .42545 Metetra .764 .867 .924 r .78141 .42545 .79226 .43484 .81782 .42085 .8071 .41017 Metetra .75 .844 .922 r .8071 .41017 .81782 .42085 .8436 .40752 .83302 .39583 Metetra .737 .826 .92 r .83302 .39583 .8436 .40752 .86959 .39476 .85916 .38227 Metetra .727 .813 .918 r .85916 .38227 .86959 .39476 .89582 .38246 .88554 .36931 Metetra .719 .802 .916 r .88554 .36931 .89582 .38246 .92227 .37057 .91216 .35687 Metetra .566 .744 .96 r .31071 .53132 .32485 .54251 .34677 .53924 .33272 .52833 Metetra .543 .743 .968 r .33272 .52833 .34677 .53924 .36891 .5365 .35494 .52598 Metetra .511 .74 .977 r .35494 .52598 .36891 .5365 .39125 .53441 .37737 .52443 Metetra .464 .732 .985 r .37737 .52443 .39125 .53441 .41383 .53311 .40004 .5239 Metetra .391 .715 .987 r .40004 .5239 .41383 .53311 .43666 .53279 .42295 .52467 Metetra .27 .674 .969 r .42295 .52467 .43666 .53279 .45975 .53369 .44613 .52715 Metetra .065 .572 .885 r .44613 .52715 .45975 .53369 .48314 .53613 .46962 .53193 Metetra .243 0 0 r .46962 .53193 .48314 .53613 .50685 .54052 .49345 .53996 Metetra .535 0 0 r .49345 .53996 .50685 .54052 .53095 .54744 .51771 .55247 Metetra .723 .238 .093 r .51771 .55247 .53095 .54744 .5555 .55763 .54254 .57486 Metetra .777 .387 .316 r .54254 .57486 .5555 .55763 .58061 .57299 .56823 .61352 Metetra .696 .358 .4 r .56823 .61352 .58061 .57299 .60324 .46097 .59474 .64673 Metetra .459 .234 .485 r .59474 .64673 .60324 .46097 .63109 .55804 .61986 .59858 Metetra 0 0 .036 r .61986 .59858 .63109 .55804 .65578 .52752 .64438 .54454 Metetra .61 .813 .402 r .64438 .54454 .65578 .52752 .68059 .50205 .66912 .50657 Metetra .823 .995 .758 r .66912 .50657 .68059 .50205 .70554 .47973 .69413 .47839 Metetra .847 .982 .865 r .69413 .47839 .70554 .47973 .73064 .45987 .71932 .45461 Metetra .827 .937 .9 r .71932 .45461 .73064 .45987 .75593 .44192 .74472 .43403 Metetra .802 .898 .911 r .74472 .43403 .75593 .44192 .78141 .42545 .77033 .41571 Metetra .779 .867 .914 r .77033 .41571 .78141 .42545 .8071 .41017 .79616 .39907 Metetra .76 .843 .914 r .79616 .39907 .8071 .41017 .83302 .39583 .82222 .3837 Metetra .746 .825 .913 r .82222 .3837 .83302 .39583 .85916 .38227 .84851 .36932 Metetra .733 .811 .913 r .84851 .36932 .85916 .38227 .88554 .36931 .87505 .35571 Metetra .723 .8 .912 r .87505 .35571 .88554 .36931 .91216 .35687 .90183 .34272 Metetra .559 .738 .96 r .29635 .51972 .31071 .53132 .33272 .52833 .31845 .51697 Metetra .533 .735 .967 r .31845 .51697 .33272 .52833 .35494 .52598 .34075 .51497 Metetra .496 .728 .976 r .34075 .51497 .35494 .52598 .37737 .52443 .36326 .51393 Metetra .44 .716 .983 r .36326 .51393 .37737 .52443 .40004 .5239 .386 .51413 Metetra .35 .688 .981 r .386 .51413 .40004 .5239 .42295 .52467 .40899 .51598 Metetra .198 .624 .948 r .40899 .51598 .42295 .52467 .44613 .52715 .43225 .52005 Metetra 0 .474 .821 r .43225 .52005 .44613 .52715 .46962 .53193 .45581 .52726 Metetra .403 0 0 r .45581 .52726 .46962 .53193 .49345 .53996 .47973 .53908 Metetra .682 .141 0 r .47973 .53908 .49345 .53996 .51771 .55247 .5041 .55904 Metetra .794 .355 .206 r .5041 .55904 .51771 .55247 .54254 .57486 .52911 .5932 Metetra .799 .418 .335 r .52911 .5932 .54254 .57486 .56823 .61352 .5551 .64047 Metetra .381 0 .176 r .5551 .64047 .56823 .61352 .59474 .64673 .58126 .63301 Metetra .645 .763 .934 r .58126 .63301 .59474 .64673 .61986 .59858 .60767 .62548 Metetra .746 .812 .339 r .60767 .62548 .61986 .59858 .64438 .54454 .63258 .56266 Metetra .787 .88 .455 r .63258 .56266 .64438 .54454 .66912 .50657 .65737 .51264 Metetra .884 .983 .704 r .65737 .51264 .66912 .50657 .69413 .47839 .68242 .47671 Metetra .886 .97 .836 r .68242 .47671 .69413 .47839 .71932 .45461 .70772 .44885 Metetra .852 .929 .878 r .70772 .44885 .71932 .45461 .74472 .43403 .73324 .42555 Metetra .819 .891 .894 r .73324 .42555 .74472 .43403 .77033 .41571 .75898 .40535 Metetra .792 .861 .901 r .75898 .40535 .77033 .41571 .79616 .39907 .78496 .38735 Metetra .77 .838 .904 r .78496 .38735 .79616 .39907 .82222 .3837 .81117 .37097 Metetra .752 .821 .906 r .81117 .37097 .82222 .3837 .84851 .36932 .83763 .35581 Metetra .739 .808 .907 r .83763 .35581 .84851 .36932 .87505 .35571 .86433 .34158 Metetra .728 .797 .907 r .86433 .34158 .87505 .35571 .90183 .34272 .89129 .32807 Metetra .554 .731 .958 r .28177 .50764 .29635 .51972 .31845 .51697 .30395 .50508 Metetra .525 .726 .965 r .30395 .50508 .31845 .51697 .34075 .51497 .32633 .50338 Metetra .484 .716 .973 r .32633 .50338 .34075 .51497 .36326 .51393 .34892 .50277 Metetra .422 .699 .978 r .34892 .50277 .36326 .51393 .386 .51413 .37173 .50361 Metetra .32 .662 .973 r .37173 .50361 .386 .51413 .40899 .51598 .39479 .50641 Metetra .146 .579 .93 r .39479 .50641 .40899 .51598 .43225 .52005 .41811 .51194 Metetra 0 .389 .77 r .41811 .51194 .43225 .52005 .45581 .52726 .44172 .52154 Metetra .512 0 0 r .44172 .52154 .45581 .52726 .47973 .53908 .46569 .53722 Metetra .741 .224 0 r .46569 .53722 .47973 .53908 .5041 .55904 .49012 .56246 Metetra .839 .411 .218 r .49012 .56246 .5041 .55904 .52911 .5932 .51521 .60672 Metetra .68 .234 .186 r .51521 .60672 .52911 .5932 .5551 .64047 .54121 .62664 Metetra .645 .763 .934 r .54121 .62664 .5551 .64047 .58126 .63301 .56754 .61905 Metetra .645 .763 .934 r .56754 .61905 .58126 .63301 .60767 .62548 .59412 .61138 Metetra .872 .798 .774 r .59412 .61138 .60767 .62548 .63258 .56266 .62017 .57592 Metetra .946 .925 .565 r .62017 .57592 .63258 .56266 .65737 .51264 .64515 .51551 Metetra .945 .959 .723 r .64515 .51551 .65737 .51264 .68242 .47671 .67037 .474 Metetra .913 .946 .809 r .67037 .474 .68242 .47671 .70772 .44885 .6958 .44198 Metetra .87 .91 .855 r .6958 .44198 .70772 .44885 .73324 .42555 .72146 .41599 Metetra .831 .877 .877 r .72146 .41599 .73324 .42555 .75898 .40535 .74736 .39405 Metetra .8 .851 .888 r .74736 .39405 .75898 .40535 .78496 .38735 .77349 .37481 Metetra .776 .83 .894 r .77349 .37481 .78496 .38735 .81117 .37097 .79987 .35751 Metetra .757 .815 .898 r .79987 .35751 .81117 .37097 .83763 .35581 .8265 .34163 Metetra .742 .803 .9 r .8265 .34163 .83763 .35581 .86433 .34158 .85338 .32683 Metetra .731 .793 .902 r .85338 .32683 .86433 .34158 .89129 .32807 .88052 .31286 Metetra .55 .724 .955 r .26698 .49502 .28177 .50764 .30395 .50508 .28924 .4926 Metetra .521 .717 .962 r .28924 .4926 .30395 .50508 .32633 .50338 .3117 .49109 Metetra .478 .705 .969 r .3117 .49109 .32633 .50338 .34892 .50277 .33436 .4908 Metetra .412 .683 .973 r .33436 .4908 .34892 .50277 .37173 .50361 .35725 .49213 Metetra .305 .64 .966 r .35725 .49213 .37173 .50361 .39479 .50641 .38036 .49568 Metetra .12 .545 .918 r .38036 .49568 .39479 .50641 .41811 .51194 .40373 .5024 Metetra 0 .35 .76 r .40373 .5024 .41811 .51194 .44172 .52154 .42738 .51361 Metetra .523 0 0 r .42738 .51361 .44172 .52154 .46569 .53722 .45138 .53164 Metetra .797 .302 0 r .45138 .53164 .46569 .53722 .49012 .56246 .47577 .56481 Metetra .864 .451 .243 r .47577 .56481 .49012 .56246 .51521 .60672 .50086 .61821 Metetra .182 0 0 r .50086 .61821 .51521 .60672 .54121 .62664 .52708 .61256 Metetra .645 .763 .934 r .52708 .61256 .54121 .62664 .56754 .61905 .55357 .60484 Metetra .645 .763 .934 r .55357 .60484 .56754 .61905 .59412 .61138 .58032 .59703 Metetra .677 .773 .923 r .58032 .59703 .59412 .61138 .62017 .57592 .60728 .58713 Metetra .981 .905 .58 r .60728 .58713 .62017 .57592 .64515 .51551 .63254 .51727 Metetra .968 .924 .694 r .63254 .51727 .64515 .51551 .67037 .474 .65787 .46748 Metetra .915 .895 .795 r .65787 .46748 .67037 .474 .6958 .44198 .68351 .43281 Metetra .873 .877 .836 r .68351 .43281 .6958 .44198 .72146 .41599 .70936 .40493 Metetra .836 .857 .86 r .70936 .40493 .72146 .41599 .74736 .39405 .73543 .38151 Metetra .804 .836 .875 r .73543 .38151 .74736 .39405 .77349 .37481 .76174 .36123 Metetra .78 .819 .884 r .76174 .36123 .77349 .37481 .79987 .35751 .7883 .34315 Metetra .76 .806 .89 r .7883 .34315 .79987 .35751 .8265 .34163 .81511 .32668 Metetra .745 .796 .894 r .81511 .32668 .8265 .34163 .85338 .32683 .84218 .31139 Metetra .732 .787 .897 r .84218 .31139 .85338 .32683 .88052 .31286 .86951 .29701 Metetra .549 .718 .951 r .25197 .48184 .26698 .49502 .28924 .4926 .27431 .47945 Metetra .52 .709 .957 r .27431 .47945 .28924 .4926 .3117 .49109 .29685 .47804 Metetra .477 .695 .964 r .29685 .47804 .3117 .49109 .33436 .4908 .3196 .47791 Metetra .412 .671 .967 r .3196 .47791 .33436 .4908 .35725 .49213 .34255 .47952 Metetra .307 .624 .96 r .34255 .47952 .35725 .49213 .38036 .49568 .36573 .48353 Metetra .131 .53 .918 r .36573 .48353 .38036 .49568 .40373 .5024 .38914 .49091 Metetra 0 .34 .778 r .38914 .49091 .40373 .5024 .42738 .51361 .41283 .50329 Metetra .554 .009 0 r .41283 .50329 .42738 .51361 .45138 .53164 .4368 .52458 Metetra .804 .312 0 r .4368 .52458 .45138 .53164 .47577 .56481 .46117 .55961 Metetra .857 .407 .113 r .46117 .55961 .47577 .56481 .50086 .61821 .4863 .60603 Metetra .64 .792 .955 r .4863 .60603 .50086 .61821 .52708 .61256 .5127 .59824 Metetra .645 .763 .934 r .5127 .59824 .52708 .61256 .55357 .60484 .53936 .59037 Metetra .645 .763 .934 r .53936 .59037 .55357 .60484 .58032 .59703 .56628 .58243 Metetra .645 .763 .934 r .56628 .58243 .58032 .59703 .60728 .58713 .59346 .5744 Metetra .936 .794 .678 r .59346 .5744 .60728 .58713 .63254 .51727 .61936 .51136 Metetra .954 .861 .709 r .61936 .51136 .63254 .51727 .65787 .46748 .64502 .45943 Metetra .92 .872 .774 r .64502 .45943 .65787 .46748 .68351 .43281 .67085 .42119 Metetra .869 .846 .819 r .67085 .42119 .68351 .43281 .70936 .40493 .69691 .39184 Metetra .833 .831 .845 r .69691 .39184 .70936 .40493 .73543 .38151 .72319 .36746 Metetra .804 .818 .862 r .72319 .36746 .73543 .38151 .76174 .36123 .7497 .34644 Metetra .78 .806 .874 r .7497 .34644 .76174 .36123 .7883 .34315 .77645 .32779 Metetra .761 .796 .882 r .77645 .32779 .7883 .34315 .81511 .32668 .80346 .31086 Metetra .745 .788 .887 r .80346 .31086 .81511 .32668 .84218 .31139 .83073 .2952 Metetra .733 .781 .891 r .83073 .2952 .84218 .31139 .86951 .29701 .85825 .28049 Metetra .551 .712 .947 r .23675 .46805 .25197 .48184 .27431 .47945 .25918 .4656 Metetra .523 .702 .952 r .25918 .4656 .27431 .47945 .29685 .47804 .2818 .46416 Metetra .482 .687 .957 r .2818 .46416 .29685 .47804 .3196 .47791 .30463 .46403 Metetra .421 .661 .96 r .30463 .46403 .3196 .47791 .34255 .47952 .32766 .46567 Metetra .325 .616 .954 r .32766 .46567 .34255 .47952 .36573 .48353 .3509 .46978 Metetra .891 .763 .714 r .3509 .46978 .36573 .48353 .38914 .49091 .37694 .42098 Metetra 0 0 .458 r .37694 .42098 .38914 .49091 .41283 .50329 .39806 .49082 Metetra .504 0 0 r .39806 .49082 .41283 .50329 .4368 .52458 .42204 .51252 Metetra .775 .284 0 r .42204 .51252 .4368 .52458 .46117 .55961 .44636 .54857 Metetra .827 .356 0 r .44636 .54857 .46117 .55961 .4863 .60603 .47149 .59159 Metetra .645 .763 .934 r .47149 .59159 .4863 .60603 .5127 .59824 .49806 .58365 Metetra .645 .763 .934 r .49806 .58365 .5127 .59824 .53936 .59037 .52489 .57564 Metetra .645 .763 .934 r .52489 .57564 .53936 .59037 .56628 .58243 .55198 .56755 Metetra .645 .763 .934 r .55198 .56755 .56628 .58243 .59346 .5744 .57934 .55938 Metetra .924 .784 .687 r .57934 .55938 .59346 .5744 .61936 .51136 .60572 .49951 Metetra .932 .814 .707 r .60572 .49951 .61936 .51136 .64502 .45943 .63173 .44627 Metetra .897 .82 .763 r .63173 .44627 .64502 .45943 .67085 .42119 .65784 .40732 Metetra .96 .775 .608 r .65784 .40732 .67085 .42119 .69691 .39184 .68124 .31882 Metetra .355 .294 .65 r .68124 .31882 .69691 .39184 .72319 .36746 .71062 .35172 Metetra .799 .799 .851 r .71062 .35172 .72319 .36746 .7497 .34644 .73735 .3303 Metetra .777 .791 .865 r .73735 .3303 .7497 .34644 .77645 .32779 .76432 .31133 Metetra .759 .785 .874 r .76432 .31133 .77645 .32779 .80346 .31086 .79154 .29412 Metetra .744 .779 .881 r .79154 .29412 .80346 .31086 .83073 .2952 .81901 .2782 Metetra .732 .774 .887 r .81901 .2782 .83073 .2952 .85825 .28049 .84675 .26326 Metetra .555 .708 .942 r .22131 .45363 .23675 .46805 .25918 .4656 .24384 .45103 Metetra .529 .697 .946 r .24384 .45103 .25918 .4656 .2818 .46416 .26655 .44942 Metetra .492 .681 .95 r .26655 .44942 .2818 .46416 .30463 .46403 .28947 .4491 Metetra .438 .656 .952 r .28947 .4491 .30463 .46403 .32766 .46567 .31258 .45052 Metetra .355 .613 .948 r .31258 .45052 .32766 .46567 .3509 .46978 .3359 .45435 Metetra .224 .538 .925 r .3359 .45435 .3509 .46978 .37694 .42098 .35944 .46159 Metetra .591 .242 .346 r .35944 .46159 .37694 .42098 .39806 .49082 .38321 .47387 Metetra 0 .124 .643 r .38321 .47387 .39806 .49082 .42204 .51252 .40719 .49512 Metetra .68 .207 0 r .40719 .49512 .42204 .51252 .44636 .54857 .43146 .53024 Metetra .791 .341 0 r .43146 .53024 .44636 .54857 .47149 .59159 .45642 .57688 Metetra .645 .763 .934 r .45642 .57688 .47149 .59159 .49806 .58365 .48315 .5688 Metetra .645 .763 .934 r .48315 .5688 .49806 .58365 .52489 .57564 .51015 .56065 Metetra .645 .763 .934 r .51015 .56065 .52489 .57564 .55198 .56755 .53742 .55241 Metetra .645 .763 .934 r .53742 .55241 .55198 .56755 .57934 .55938 .56496 .54409 Metetra .928 .781 .678 r .56496 .54409 .57934 .55938 .60572 .49951 .59166 .48024 Metetra .898 .763 .704 r .59166 .48024 .60572 .49951 .63173 .44627 .61802 .42765 Metetra .869 .772 .752 r .61802 .42765 .63173 .44627 .65784 .40732 .64443 .38885 Metetra .836 .773 .791 r .64443 .38885 .65784 .40732 .68124 .31882 .671 .35903 Metetra .225 0 .199 r .671 .35903 .68124 .31882 .71062 .35172 .69775 .33421 Metetra .791 .779 .842 r .69775 .33421 .71062 .35172 .73735 .3303 .72472 .31278 Metetra .771 .776 .857 r .72472 .31278 .73735 .3303 .76432 .31133 .75191 .29373 Metetra .755 .773 .868 r .75191 .29373 .76432 .31133 .79154 .29412 .77935 .27642 Metetra .741 .77 .876 r .77935 .27642 .79154 .29412 .81901 .2782 .80704 .26037 Metetra .73 .767 .882 r .80704 .26037 .81901 .2782 .84675 .26326 .83499 .24529 Metetra .561 .704 .937 r .20567 .43859 .22131 .45363 .24384 .45103 .22829 .43574 Metetra .537 .693 .94 r .22829 .43574 .24384 .45103 .26655 .44942 .25111 .43382 Metetra .505 .677 .942 r .25111 .43382 .26655 .44942 .28947 .4491 .27412 .43314 Metetra .459 .653 .944 r .27412 .43314 .28947 .4491 .31258 .45052 .29733 .43409 Metetra .392 .616 .94 r .29733 .43409 .31258 .45052 .3359 .45435 .32074 .43729 Metetra .288 .552 .925 r .32074 .43729 .3359 .45435 .35944 .46159 .34436 .4437 Metetra .126 .445 .88 r .34436 .4437 .35944 .46159 .38321 .47387 .36821 .45467 Metetra 0 .259 .766 r .36821 .45467 .38321 .47387 .40719 .49512 .39229 .47259 Metetra 0 0 .464 r .39229 .47259 .40719 .49512 .43146 .53024 .41651 .50591 Metetra .784 .37 0 r .41651 .50591 .43146 .53024 .45642 .57688 .44112 .55986 Metetra .614 .724 .924 r .44112 .55986 .45642 .57688 .48315 .5688 .46797 .55368 Metetra .645 .763 .934 r .46797 .55368 .48315 .5688 .51015 .56065 .49514 .54537 Metetra .645 .763 .934 r .49514 .54537 .51015 .56065 .53742 .55241 .52259 .53698 Metetra .677 .773 .923 r .52259 .53698 .53742 .55241 .56496 .54409 .55029 .52644 Metetra .928 .765 .659 r .55029 .52644 .56496 .54409 .59166 .48024 .57727 .45487 Metetra .87 .726 .7 r .57727 .45487 .59166 .48024 .61802 .42765 .60397 .40377 Metetra .833 .729 .749 r .60397 .40377 .61802 .42765 .64443 .38885 .63072 .36806 Metetra .819 .751 .788 r .63072 .36806 .64443 .38885 .671 .35903 .65757 .33924 Metetra .799 .758 .815 r .65757 .33924 .671 .35903 .69775 .33421 .68458 .31497 Metetra .78 .761 .836 r .68458 .31497 .69775 .33421 .72472 .31278 .71179 .29387 Metetra .763 .762 .851 r .71179 .29387 .72472 .31278 .75191 .29373 .73922 .27501 Metetra .749 .762 .863 r .73922 .27501 .75191 .29373 .77935 .27642 .76689 .25776 Metetra .737 .761 .872 r .76689 .25776 .77935 .27642 .80704 .26037 .7948 .24172 Metetra .727 .759 .878 r .7948 .24172 .80704 .26037 .83499 .24529 .82298 .22659 Metetra .568 .701 .931 r .18981 .42293 .20567 .43859 .22829 .43574 .21253 .41974 Metetra .547 .69 .933 r .21253 .41974 .22829 .43574 .25111 .43382 .23546 .41741 Metetra .52 .675 .935 r .23546 .41741 .25111 .43382 .27412 .43314 .25858 .4162 Metetra .483 .653 .935 r .25858 .4162 .27412 .43314 .29733 .43409 .2819 .41646 Metetra .431 .621 .931 r .2819 .41646 .29733 .43409 .32074 .43729 .30543 .41871 Metetra .355 .57 .92 r .30543 .41871 .32074 .43729 .34436 .4437 .32916 .42376 Metetra .236 .486 .891 r .32916 .42376 .34436 .4437 .36821 .45467 .3531 .43296 Metetra .049 .346 .823 r .3531 .43296 .36821 .45467 .39229 .47259 .37726 .44839 Metetra 0 .122 .671 r .37726 .44839 .39229 .47259 .41651 .50591 .40166 .47364 Metetra 0 0 .429 r .40166 .47364 .41651 .50591 .44112 .55986 .42626 .51845 Metetra .274 .334 .743 r .42626 .51845 .44112 .55986 .46797 .55368 .45251 .53828 Metetra .645 .763 .934 r .45251 .53828 .46797 .55368 .49514 .54537 .47985 .52982 Metetra .645 .763 .934 r .47985 .52982 .49514 .54537 .52259 .53698 .50748 .52127 Metetra .872 .798 .774 r .50748 .52127 .52259 .53698 .55029 .52644 .5353 .48414 Metetra .834 .654 .659 r .5353 .48414 .55029 .52644 .57727 .45487 .56262 .42143 Metetra .818 .675 .705 r .56262 .42143 .57727 .45487 .60397 .40377 .58969 .37817 Metetra .818 .716 .752 r .58969 .37817 .60397 .40377 .63072 .36806 .61673 .34465 Metetra .8 .727 .784 r .61673 .34465 .63072 .36806 .65757 .33924 .64385 .31732 Metetra .782 .736 .811 r .64385 .31732 .65757 .33924 .68458 .31497 .67112 .29412 Metetra .768 .744 .831 r .67112 .29412 .68458 .31497 .71179 .29387 .69858 .27368 Metetra .754 .748 .847 r .69858 .27368 .71179 .29387 .73922 .27501 .72625 .25521 Metetra .742 .751 .859 r .72625 .25521 .73922 .27501 .76689 .25776 .75416 .23819 Metetra .732 .752 .868 r .75416 .23819 .76689 .25776 .7948 .24172 .78231 .22226 Metetra .723 .752 .875 r .78231 .22226 .7948 .24172 .82298 .22659 .81072 .20716 Metetra .576 .699 .926 r .17373 .40669 .18981 .42293 .21253 .41974 .19657 .40309 Metetra .559 .689 .927 r .19657 .40309 .21253 .41974 .23546 .41741 .21961 .40024 Metetra .536 .675 .927 r .21961 .40024 .23546 .41741 .25858 .4162 .24285 .39837 Metetra .508 .655 .926 r .24285 .39837 .25858 .4162 .2819 .41646 .2663 .39777 Metetra .469 .628 .922 r .2663 .39777 .2819 .41646 .30543 .41871 .28995 .39885 Metetra .416 .588 .913 r .28995 .39885 .30543 .41871 .32916 .42376 .31382 .40223 Metetra .341 .529 .894 r .31382 .40223 .32916 .42376 .3531 .43296 .33792 .40883 Metetra .236 .438 .856 r .33792 .40883 .3531 .43296 .37726 .44839 .36224 .42019 Metetra .056 .282 .773 r .36224 .42019 .37726 .44839 .40166 .47364 .38675 .43996 Metetra 0 .037 .606 r .38675 .43996 .40166 .47364 .42626 .51845 .41146 .47444 Metetra 0 0 .522 r .41146 .47444 .42626 .51845 .45251 .53828 .43676 .52259 Metetra .645 .763 .934 r .43676 .52259 .45251 .53828 .47985 .52982 .46428 .51397 Metetra .645 .763 .934 r .46428 .51397 .47985 .52982 .50748 .52127 .49209 .50526 Metetra .927 .778 .676 r .49209 .50526 .50748 .52127 .5353 .48414 .52026 .43923 Metetra .805 .634 .67 r .52026 .43923 .5353 .48414 .56262 .42143 .54784 .38655 Metetra .797 .662 .714 r .54784 .38655 .56262 .42143 .58969 .37817 .57517 .34847 Metetra .784 .681 .751 r .57517 .34847 .58969 .37817 .61673 .34465 .60249 .31875 Metetra .776 .704 .784 r .60249 .31875 .61673 .34465 .64385 .31732 .62988 .29374 Metetra .766 .72 .81 r .62988 .29374 .64385 .31732 .67112 .29412 .65741 .27191 Metetra .755 .73 .829 r .65741 .27191 .67112 .29412 .69858 .27368 .68511 .25234 Metetra .744 .737 .845 r .68511 .25234 .69858 .27368 .72625 .25521 .71303 .23443 Metetra .735 .741 .857 r .71303 .23443 .72625 .25521 .75416 .23819 .74117 .21776 Metetra .726 .744 .866 r .74117 .21776 .75416 .23819 .78231 .22226 .76956 .20203 Metetra .719 .746 .873 r .76956 .20203 .78231 .22226 .81072 .20716 .7982 .18703 Metetra .584 .698 .921 r .15742 .3899 .17373 .40669 .19657 .40309 .18039 .38582 Metetra .57 .688 .92 r .18039 .38582 .19657 .40309 .21961 .40024 .20355 .38239 Metetra .553 .675 .92 r .20355 .38239 .21961 .40024 .24285 .39837 .22692 .37978 Metetra .531 .658 .917 r .22692 .37978 .24285 .39837 .2663 .39777 .25051 .37821 Metetra .503 .636 .913 r .25051 .37821 .2663 .39777 .28995 .39885 .27431 .37798 Metetra .467 .604 .904 r .27431 .37798 .28995 .39885 .31382 .40223 .29834 .37952 Metetra .421 .561 .889 r .29834 .37952 .31382 .40223 .33792 .40883 .3226 .38343 Metetra .36 .5 .863 r .3226 .38343 .33792 .40883 .36224 .42019 .34711 .39071 Metetra .289 .421 .822 r .34711 .39071 .36224 .42019 .38675 .43996 .37189 .40265 Metetra .148 .273 .737 r .37189 .40265 .38675 .43996 .41146 .47444 .39685 .4249 Metetra 0 .098 .62 r .39685 .4249 .41146 .47444 .43676 .52259 .42203 .46417 Metetra .185 .211 .655 r .42203 .46417 .43676 .52259 .46428 .51397 .44841 .49782 Metetra .904 .786 .719 r .44841 .49782 .46428 .51397 .49209 .50526 .47702 .4463 Metetra .781 .595 .648 r .47702 .4463 .49209 .50526 .52026 .43923 .50524 .38873 Metetra .757 .596 .677 r .50524 .38873 .52026 .43923 .54784 .38655 .53294 .34798 Metetra .755 .629 .721 r .53294 .34798 .54784 .38655 .57517 .34847 .56049 .31746 Metetra .76 .666 .759 r .56049 .31746 .57517 .34847 .60249 .31875 .58804 .29152 Metetra .756 .689 .788 r .58804 .29152 .60249 .31875 .62988 .29374 .61567 .2689 Metetra .749 .706 .811 r .61567 .2689 .62988 .29374 .65741 .27191 .64345 .24861 Metetra .742 .719 .83 r .64345 .24861 .65741 .27191 .68511 .25234 .6714 .23005 Metetra .734 .727 .844 r .6714 .23005 .68511 .25234 .71303 .23443 .69955 .21279 Metetra .727 .733 .856 r .69955 .21279 .71303 .23443 .74117 .21776 .72793 .19654 Metetra .72 .737 .865 r .72793 .19654 .74117 .21776 .76956 .20203 .75655 .18108 Metetra .714 .74 .872 r .75655 .18108 .76956 .20203 .7982 .18703 .78543 .16624 Metetra .593 .698 .916 r .14089 .37259 .15742 .3899 .18039 .38582 .16398 .36801 Metetra .581 .689 .915 r .16398 .36801 .18039 .38582 .20355 .38239 .18728 .36395 Metetra .568 .677 .913 r .18728 .36395 .20355 .38239 .22692 .37978 .21079 .36055 Metetra .552 .663 .91 r .21079 .36055 .22692 .37978 .25051 .37821 .23452 .35797 Metetra .532 .644 .905 r .23452 .35797 .25051 .37821 .27431 .37798 .25848 .35639 Metetra .509 .619 .896 r .25848 .35639 .27431 .37798 .29834 .37952 .28268 .35607 Metetra .482 .587 .883 r .28268 .35607 .29834 .37952 .3226 .38343 .30713 .35734 Metetra .452 .546 .862 r .30713 .35734 .3226 .38343 .34711 .39071 .33186 .36064 Metetra .42 .495 .83 r .33186 .36064 .34711 .39071 .37189 .40265 .35689 .36659 Metetra .391 .437 .788 r .35689 .36659 .37189 .40265 .39685 .4249 .38225 .37595 Metetra .372 .363 .72 r .38225 .37595 .39685 .4249 .42203 .46417 .40798 .39074 Metetra .84 .614 .597 r .40798 .39074 .42203 .46417 .44841 .49782 .43811 .27202 Metetra .27 .14 .513 r .43811 .27202 .44841 .49782 .47702 .4463 .46237 .37228 Metetra .685 .514 .648 r .46237 .37228 .47702 .4463 .50524 .38873 .49024 .33882 Metetra .712 .572 .695 r .49024 .33882 .50524 .38873 .53294 .34798 .51796 .31067 Metetra .732 .624 .738 r .51796 .31067 .53294 .34798 .56049 .31746 .54566 .28583 Metetra .736 .655 .769 r .54566 .28583 .56049 .31746 .58804 .29152 .57341 .26356 Metetra .737 .679 .795 r .57341 .26356 .58804 .29152 .61567 .2689 .60126 .24327 Metetra .734 .697 .815 r .60126 .24327 .61567 .2689 .64345 .24861 .62926 .22452 Metetra .73 .71 .832 r .62926 .22452 .64345 .24861 .6714 .23005 .65744 .20699 Metetra .725 .72 .845 r .65744 .20699 .6714 .23005 .69955 .21279 .68583 .19043 Metetra .719 .726 .856 r .68583 .19043 .69955 .21279 .72793 .19654 .71444 .17464 Metetra .714 .731 .864 r .71444 .17464 .72793 .19654 .75655 .18108 .7433 .15948 Metetra .709 .735 .871 r .7433 .15948 .75655 .18108 .78543 .16624 .77241 .14482 Metetra .601 .698 .911 r .12412 .35483 .14089 .37259 .16398 .36801 .14734 .34971 Metetra .592 .69 .91 r .14734 .34971 .16398 .36801 .18728 .36395 .17077 .345 Metetra .582 .68 .908 r .17077 .345 .18728 .36395 .21079 .36055 .19443 .34081 Metetra .57 .667 .904 r .19443 .34081 .21079 .36055 .23452 .35797 .21831 .33721 Metetra .557 .652 .898 r .21831 .33721 .23452 .35797 .25848 .35639 .24244 .33433 Metetra .542 .632 .89 r .24244 .33433 .25848 .35639 .28268 .35607 .26682 .33228 Metetra .528 .609 .877 r .26682 .33228 .28268 .35607 .30713 .35734 .29147 .33118 Metetra .514 .58 .859 r .29147 .33118 .30713 .35734 .33186 .36064 .31641 .33113 Metetra .504 .548 .834 r .31641 .33113 .33186 .36064 .35689 .36659 .34169 .3321 Metetra .504 .514 .8 r .34169 .3321 .35689 .36659 .38225 .37595 .36735 .33373 Metetra .522 .485 .756 r .36735 .33373 .38225 .37595 .40798 .39074 .39348 .33458 Metetra .568 .468 .7 r .39348 .33458 .40798 .39074 .43811 .27202 .42022 .33003 Metetra .364 .036 .269 r .42022 .33003 .43811 .27202 .46237 .37228 .44755 .31561 Metetra .659 .524 .689 r .44755 .31561 .46237 .37228 .49024 .33882 .47517 .2957 Metetra .693 .582 .727 r .47517 .2957 .49024 .33882 .51796 .31067 .50289 .27493 Metetra .71 .622 .757 r .50289 .27493 .51796 .31067 .54566 .28583 .53069 .25473 Metetra .718 .652 .783 r .53069 .25473 .54566 .28583 .57341 .26356 .5586 .23549 Metetra .721 .675 .804 r .5586 .23549 .57341 .26356 .60126 .24327 .58664 .21724 Metetra .721 .692 .821 r .58664 .21724 .60126 .24327 .62926 .22452 .61485 .19989 Metetra .719 .705 .836 r .61485 .19989 .62926 .22452 .65744 .20699 .64325 .18334 Metetra .715 .714 .848 r .64325 .18334 .65744 .20699 .68583 .19043 .67187 .16746 Metetra .712 .721 .857 r .67187 .16746 .68583 .19043 .71444 .17464 .70071 .15214 Metetra .707 .726 .865 r .70071 .15214 .71444 .17464 .7433 .15948 .7298 .13729 Metetra .703 .73 .871 r .7298 .13729 .7433 .15948 .77241 .14482 .75915 .12283 Metetra .608 .699 .908 r .1071 .33664 .12412 .35483 .14734 .34971 .13045 .33098 Metetra .602 .691 .906 r .13045 .33098 .14734 .34971 .17077 .345 .15403 .32563 Metetra .594 .683 .903 r .15403 .32563 .17077 .345 .19443 .34081 .17783 .32066 Metetra .586 .672 .899 r .17783 .32066 .19443 .34081 .21831 .33721 .20188 .3161 Metetra .577 .659 .893 r .20188 .3161 .21831 .33721 .24244 .33433 .22617 .31201 Metetra .568 .644 .885 r .22617 .31201 .24244 .33433 .26682 .33228 .25073 .30842 Metetra .561 .626 .874 r .25073 .30842 .26682 .33228 .29147 .33118 .27557 .30533 Metetra .555 .606 .859 r .27557 .30533 .29147 .33118 .31641 .33113 .30072 .30264 Metetra .554 .584 .839 r .30072 .30264 .31641 .33113 .34169 .3321 .32621 .30012 Metetra .56 .563 .813 r .32621 .30012 .34169 .3321 .36735 .33373 .35209 .29721 Metetra .577 .545 .783 r .35209 .29721 .36735 .33373 .39348 .33458 .3784 .29277 Metetra .603 .535 .752 r .3784 .29277 .39348 .33458 .42022 .33003 .40519 .28515 Metetra .631 .54 .734 r .40519 .28515 .42022 .33003 .44755 .31561 .43241 .27335 Metetra .658 .566 .74 r .43241 .27335 .44755 .31561 .47517 .2957 .45993 .25833 Metetra .681 .6 .759 r .45993 .25833 .47517 .2957 .50289 .27493 .48766 .24172 Metetra .696 .63 .779 r .48766 .24172 .50289 .27493 .53069 .25473 .51555 .22465 Metetra .704 .655 .798 r .51555 .22465 .53069 .25473 .5586 .23549 .5436 .2077 Metetra .709 .674 .814 r .5436 .2077 .5586 .23549 .58664 .21724 .57182 .1911 Metetra .71 .689 .829 r .57182 .1911 .58664 .21724 .61485 .19989 .60023 .17496 Metetra .709 .701 .841 r .60023 .17496 .61485 .19989 .64325 .18334 .62884 .15927 Metetra .707 .71 .851 r .62884 .15927 .64325 .18334 .67187 .16746 .65767 .144 Metetra .705 .717 .859 r .65767 .144 .67187 .16746 .70071 .15214 .68673 .12912 Metetra .702 .723 .866 r .68673 .12912 .70071 .15214 .7298 .13729 .71605 .11457 Metetra .699 .727 .872 r .71605 .11457 .7298 .13729 .75915 .12283 .74563 .10029 Metetra .616 .7 .904 r .08982 .31807 .1071 .33664 .13045 .33098 .11331 .31188 Metetra .61 .693 .902 r .11331 .31188 .13045 .33098 .15403 .32563 .13703 .30591 Metetra .605 .686 .899 r .13703 .30591 .15403 .32563 .17783 .32066 .16099 .30019 Metetra .599 .677 .895 r .16099 .30019 .17783 .32066 .20188 .3161 .18519 .29475 Metetra .593 .667 .89 r .18519 .29475 .20188 .3161 .22617 .31201 .20965 .28958 Metetra .588 .655 .883 r .20965 .28958 .22617 .31201 .25073 .30842 .23438 .28467 Metetra .584 .641 .873 r .23438 .28467 .25073 .30842 .27557 .30533 .2594 .27996 Metetra .583 .627 .861 r .2594 .27996 .27557 .30533 .30072 .30264 .28474 .2753 Metetra .585 .612 .845 r .28474 .2753 .30072 .30264 .32621 .30012 .31041 .27043 Metetra .592 .598 .827 r .31041 .27043 .32621 .30012 .35209 .29721 .33646 .26491 Metetra .605 .587 .807 r .33646 .26491 .35209 .29721 .3784 .29277 .36291 .2581 Metetra .622 .582 .789 r .36291 .2581 .3784 .29277 .40519 .28515 .38975 .24933 Metetra .64 .587 .779 r .38975 .24933 .40519 .28515 .43241 .27335 .41697 .23826 Metetra .659 .601 .779 r .41697 .23826 .43241 .27335 .45993 .25833 .44449 .2252 Metetra .674 .621 .788 r .44449 .2252 .45993 .25833 .48766 .24172 .47226 .2108 Metetra .686 .642 .8 r .47226 .2108 .48766 .24172 .51555 .22465 .50024 .19571 Metetra .694 .661 .813 r .50024 .19571 .51555 .22465 .5436 .2077 .52842 .18037 Metetra .698 .676 .825 r .52842 .18037 .5436 .2077 .57182 .1911 .5568 .16503 Metetra .7 .689 .836 r .5568 .16503 .57182 .1911 .60023 .17496 .58539 .14984 Metetra .701 .7 .846 r .58539 .14984 .60023 .17496 .62884 .15927 .61419 .13487 Metetra .7 .708 .854 r .61419 .13487 .62884 .15927 .65767 .144 .64323 .12014 Metetra .698 .715 .862 r .64323 .12014 .65767 .144 .68673 .12912 .67252 .10564 Metetra .696 .72 .868 r .67252 .10564 .68673 .12912 .71605 .11457 .70206 .09136 Metetra .694 .724 .873 r .70206 .09136 .71605 .11457 .74563 .10029 .73187 .07726 Metetra .622 .701 .902 r .07227 .29915 .08982 .31807 .11331 .31188 .09591 .29243 Metetra .618 .696 .9 r .09591 .29243 .11331 .31188 .13703 .30591 .11977 .28587 Metetra .614 .689 .897 r .11977 .28587 .13703 .30591 .16099 .30019 .14388 .27946 Metetra .61 .682 .893 r .14388 .27946 .16099 .30019 .18519 .29475 .16824 .27321 Metetra .607 .673 .888 r .16824 .27321 .18519 .29475 .20965 .28958 .19286 .26711 Metetra .604 .664 .881 r .19286 .26711 .20965 .28958 .23438 .28467 .21776 .26109 Metetra .602 .654 .873 r .21776 .26109 .23438 .28467 .2594 .27996 .24295 .25509 Metetra .602 .643 .863 r .24295 .25509 .2594 .27996 .28474 .2753 .26846 .24897 Metetra .605 .633 .852 r .26846 .24897 .28474 .2753 .31041 .27043 .2943 .2425 Metetra .612 .624 .839 r .2943 .2425 .31041 .27043 .33646 .26491 .32049 .2354 Metetra .621 .617 .825 r .32049 .2354 .33646 .26491 .36291 .2581 .34705 .2273 Metetra .633 .615 .814 r .34705 .2273 .36291 .2581 .38975 .24933 .37397 .21789 Metetra .646 .618 .808 r .37397 .21789 .38975 .24933 .41697 .23826 .40123 .20704 Metetra .659 .627 .807 r .40123 .20704 .41697 .23826 .44449 .2252 .4288 .19485 Metetra .67 .64 .811 r .4288 .19485 .44449 .2252 .47226 .2108 .45664 .18165 Metetra .679 .654 .818 r .45664 .18165 .47226 .2108 .50024 .19571 .48472 .16777 Metetra .686 .668 .826 r .48472 .16777 .50024 .19571 .52842 .18037 .51303 .15351 Metetra .69 .68 .835 r .51303 .15351 .52842 .18037 .5568 .16503 .54156 .13908 Metetra .692 .69 .844 r .54156 .13908 .5568 .16503 .58539 .14984 .57032 .12463 Metetra .693 .699 .851 r .57032 .12463 .58539 .14984 .61419 .13487 .59931 .11023 Metetra .693 .707 .858 r .59931 .11023 .61419 .13487 .64323 .12014 .62856 .09594 Metetra .692 .713 .864 r .62856 .09594 .64323 .12014 .67252 .10564 .65805 .08176 Metetra .691 .718 .87 r .65805 .08176 .67252 .10564 .70206 .09136 .68781 .0677 Metetra .69 .722 .874 r .68781 .0677 .70206 .09136 .73187 .07726 .71785 .05375 Metetra .628 .703 .899 r .05445 .2799 .07227 .29915 .09591 .29243 .07822 .27268 Metetra .625 .698 .897 r .07822 .27268 .09591 .29243 .11977 .28587 .10223 .26556 Metetra .622 .692 .894 r .10223 .26556 .11977 .28587 .14388 .27946 .12649 .25851 Metetra .619 .686 .891 r .12649 .25851 .14388 .27946 .16824 .27321 .151 .25154 Metetra .617 .679 .886 r .151 .25154 .16824 .27321 .19286 .26711 .17578 .24461 Metetra .616 .672 .881 r .17578 .24461 .19286 .26711 .21776 .26109 .20084 .23768 Metetra .615 .664 .874 r .20084 .23768 .21776 .26109 .24295 .25509 .2262 .23065 Metetra .616 .656 .866 r .2262 .23065 .24295 .25509 .26846 .24897 .25186 .22343 Metetra .619 .649 .858 r 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