Properties

Label 21.30.c.a.20.20
Level $21$
Weight $30$
Character 21.20
Analytic conductor $111.884$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(111.883889004\)
Analytic rank: \(0\)
Dimension: \(76\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.20
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.19

$q$-expansion

\(f(q)\) \(=\) \(q+1646.15i q^{2} +(2.25912e6 + 7.97037e6i) q^{3} +5.34161e8 q^{4} +1.37077e10 q^{5} +(-1.31204e10 + 3.71885e9i) q^{6} +(-1.61859e12 - 7.74652e11i) q^{7} +1.76308e12i q^{8} +(-5.84231e13 + 3.60121e13i) q^{9} +O(q^{10})\) \(q+1646.15i q^{2} +(2.25912e6 + 7.97037e6i) q^{3} +5.34161e8 q^{4} +1.37077e10 q^{5} +(-1.31204e10 + 3.71885e9i) q^{6} +(-1.61859e12 - 7.74652e11i) q^{7} +1.76308e12i q^{8} +(-5.84231e13 + 3.60121e13i) q^{9} +2.25649e13i q^{10} -1.65225e15i q^{11} +(1.20674e15 + 4.25746e15i) q^{12} +7.11308e15i q^{13} +(1.27519e15 - 2.66443e15i) q^{14} +(3.09673e16 + 1.09255e17i) q^{15} +2.83873e17 q^{16} -1.14786e18 q^{17} +(-5.92812e16 - 9.61731e16i) q^{18} +4.19951e18i q^{19} +7.32210e18 q^{20} +(2.51768e18 - 1.46508e19i) q^{21} +2.71985e18 q^{22} -6.01642e19i q^{23} +(-1.40524e19 + 3.98301e18i) q^{24} +1.63560e18 q^{25} -1.17092e19 q^{26} +(-4.19014e20 - 3.84298e20i) q^{27} +(-8.64586e20 - 4.13789e20i) q^{28} -2.75913e21i q^{29} +(-1.79850e20 + 5.09768e19i) q^{30} -2.77443e21i q^{31} +1.41384e21i q^{32} +(1.31691e22 - 3.73264e21i) q^{33} -1.88956e21i q^{34} +(-2.21870e22 - 1.06187e22i) q^{35} +(-3.12074e22 + 1.92362e22i) q^{36} -2.45582e22 q^{37} -6.91302e21 q^{38} +(-5.66939e22 + 1.60693e22i) q^{39} +2.41677e22i q^{40} +2.01845e23 q^{41} +(2.41173e22 + 4.14448e21i) q^{42} -7.28553e23 q^{43} -8.82569e23i q^{44} +(-8.00845e23 + 4.93641e23i) q^{45} +9.90392e22 q^{46} -2.16367e24 q^{47} +(6.41304e23 + 2.26257e24i) q^{48} +(2.01973e24 + 2.50768e24i) q^{49} +2.69244e21i q^{50} +(-2.59317e24 - 9.14890e24i) q^{51} +3.79953e24i q^{52} +1.10372e25i q^{53} +(6.32612e23 - 6.89760e23i) q^{54} -2.26485e25i q^{55} +(1.36577e24 - 2.85369e24i) q^{56} +(-3.34716e25 + 9.48721e24i) q^{57} +4.54195e24 q^{58} +2.77774e25 q^{59} +(1.65415e25 + 5.83598e25i) q^{60} -9.03685e25i q^{61} +4.56713e24 q^{62} +(1.22460e26 - 1.30310e25i) q^{63} +1.50076e26 q^{64} +9.75038e25i q^{65} +(6.14448e24 + 2.16782e25i) q^{66} -2.34833e25 q^{67} -6.13144e26 q^{68} +(4.79530e26 - 1.35918e26i) q^{69} +(1.74799e25 - 3.65232e25i) q^{70} -4.44198e26i q^{71} +(-6.34921e25 - 1.03004e26i) q^{72} +7.29866e25i q^{73} -4.04265e25i q^{74} +(3.69503e24 + 1.30364e25i) q^{75} +2.24322e27i q^{76} +(-1.27992e27 + 2.67431e27i) q^{77} +(-2.64525e25 - 9.33266e25i) q^{78} -4.11080e27 q^{79} +3.89124e27 q^{80} +(2.11639e27 - 4.20787e27i) q^{81} +3.32267e26i q^{82} -7.11680e27 q^{83} +(1.34485e27 - 7.82586e27i) q^{84} -1.57345e28 q^{85} -1.19931e27i q^{86} +(2.19913e28 - 6.23322e27i) q^{87} +2.91305e27 q^{88} -1.23620e28 q^{89} +(-8.12607e26 - 1.31831e27i) q^{90} +(5.51017e27 - 1.15131e28i) q^{91} -3.21374e28i q^{92} +(2.21132e28 - 6.26778e27i) q^{93} -3.56173e27i q^{94} +5.75655e28i q^{95} +(-1.12688e28 + 3.19404e27i) q^{96} +2.43776e28i q^{97} +(-4.12802e27 + 3.32478e27i) q^{98} +(5.95010e28 + 9.65297e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} + O(q^{10}) \) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} - 116668222909200048q^{15} + 4964525139713333892q^{16} + 1542346202347854996q^{18} + 33840646982361357348q^{21} - 9870996616978150672q^{22} + \)\(32\!\cdots\!12\)\(q^{25} - \)\(31\!\cdots\!64\)\(q^{28} + \)\(51\!\cdots\!44\)\(q^{30} - \)\(85\!\cdots\!52\)\(q^{36} - \)\(17\!\cdots\!76\)\(q^{37} + \)\(38\!\cdots\!96\)\(q^{39} + \)\(80\!\cdots\!56\)\(q^{42} + \)\(23\!\cdots\!20\)\(q^{43} - \)\(10\!\cdots\!00\)\(q^{46} - \)\(51\!\cdots\!40\)\(q^{49} - \)\(96\!\cdots\!00\)\(q^{51} + \)\(20\!\cdots\!48\)\(q^{57} - \)\(40\!\cdots\!72\)\(q^{58} - \)\(16\!\cdots\!96\)\(q^{60} - \)\(36\!\cdots\!84\)\(q^{63} - \)\(16\!\cdots\!28\)\(q^{64} + \)\(48\!\cdots\!64\)\(q^{67} - \)\(65\!\cdots\!20\)\(q^{70} + \)\(19\!\cdots\!24\)\(q^{72} - \)\(80\!\cdots\!36\)\(q^{78} - \)\(11\!\cdots\!52\)\(q^{79} + \)\(18\!\cdots\!32\)\(q^{81} - \)\(72\!\cdots\!52\)\(q^{84} + \)\(14\!\cdots\!48\)\(q^{85} - \)\(16\!\cdots\!84\)\(q^{88} + \)\(44\!\cdots\!40\)\(q^{91} + \)\(22\!\cdots\!32\)\(q^{93} - \)\(23\!\cdots\!24\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1646.15i 0.0710451i 0.999369 + 0.0355225i \(0.0113096\pi\)
−0.999369 + 0.0355225i \(0.988690\pi\)
\(3\) 2.25912e6 + 7.97037e6i 0.272698 + 0.962100i
\(4\) 5.34161e8 0.994953
\(5\) 1.37077e10 1.00438 0.502190 0.864757i \(-0.332528\pi\)
0.502190 + 0.864757i \(0.332528\pi\)
\(6\) −1.31204e10 + 3.71885e9i −0.0683525 + 0.0193738i
\(7\) −1.61859e12 7.74652e11i −0.902016 0.431703i
\(8\) 1.76308e12i 0.141732i
\(9\) −5.84231e13 + 3.60121e13i −0.851272 + 0.524725i
\(10\) 2.25649e13i 0.0713563i
\(11\) 1.65225e15i 1.31184i −0.754829 0.655922i \(-0.772280\pi\)
0.754829 0.655922i \(-0.227720\pi\)
\(12\) 1.20674e15 + 4.25746e15i 0.271321 + 0.957244i
\(13\) 7.11308e15i 0.501048i 0.968110 + 0.250524i \(0.0806029\pi\)
−0.968110 + 0.250524i \(0.919397\pi\)
\(14\) 1.27519e15 2.66443e15i 0.0306704 0.0640838i
\(15\) 3.09673e16 + 1.09255e17i 0.273892 + 0.966315i
\(16\) 2.83873e17 0.984883
\(17\) −1.14786e18 −1.65341 −0.826706 0.562634i \(-0.809788\pi\)
−0.826706 + 0.562634i \(0.809788\pi\)
\(18\) −5.92812e16 9.61731e16i −0.0372791 0.0604787i
\(19\) 4.19951e18i 1.20579i 0.797821 + 0.602895i \(0.205986\pi\)
−0.797821 + 0.602895i \(0.794014\pi\)
\(20\) 7.32210e18 0.999311
\(21\) 2.51768e18 1.46508e19i 0.169364 0.985554i
\(22\) 2.71985e18 0.0932001
\(23\) 6.01642e19i 1.08214i −0.840977 0.541071i \(-0.818019\pi\)
0.840977 0.541071i \(-0.181981\pi\)
\(24\) −1.40524e19 + 3.98301e18i −0.136360 + 0.0386499i
\(25\) 1.63560e18 0.00878107
\(26\) −1.17092e19 −0.0355970
\(27\) −4.19014e20 3.84298e20i −0.736977 0.675917i
\(28\) −8.64586e20 4.13789e20i −0.897463 0.429524i
\(29\) 2.75913e21i 1.72188i −0.508710 0.860938i \(-0.669877\pi\)
0.508710 0.860938i \(-0.330123\pi\)
\(30\) −1.79850e20 + 5.09768e19i −0.0686519 + 0.0194587i
\(31\) 2.77443e21i 0.658309i −0.944276 0.329154i \(-0.893236\pi\)
0.944276 0.329154i \(-0.106764\pi\)
\(32\) 1.41384e21i 0.211703i
\(33\) 1.31691e22 3.73264e21i 1.26212 0.357737i
\(34\) 1.88956e21i 0.117467i
\(35\) −2.21870e22 1.06187e22i −0.905967 0.433594i
\(36\) −3.12074e22 + 1.92362e22i −0.846975 + 0.522076i
\(37\) −2.45582e22 −0.447994 −0.223997 0.974590i \(-0.571911\pi\)
−0.223997 + 0.974590i \(0.571911\pi\)
\(38\) −6.91302e21 −0.0856654
\(39\) −5.66939e22 + 1.60693e22i −0.482058 + 0.136635i
\(40\) 2.41677e22i 0.142353i
\(41\) 2.01845e23 0.831099 0.415549 0.909571i \(-0.363589\pi\)
0.415549 + 0.909571i \(0.363589\pi\)
\(42\) 2.41173e22 + 4.14448e21i 0.0700187 + 0.0120325i
\(43\) −7.28553e23 −1.50373 −0.751863 0.659320i \(-0.770844\pi\)
−0.751863 + 0.659320i \(0.770844\pi\)
\(44\) 8.82569e23i 1.30522i
\(45\) −8.00845e23 + 4.93641e23i −0.855001 + 0.527024i
\(46\) 9.90392e22 0.0768809
\(47\) −2.16367e24 −1.22962 −0.614812 0.788674i \(-0.710768\pi\)
−0.614812 + 0.788674i \(0.710768\pi\)
\(48\) 6.41304e23 + 2.26257e24i 0.268575 + 0.947556i
\(49\) 2.01973e24 + 2.50768e24i 0.627265 + 0.778806i
\(50\) 2.69244e21i 0.000623852i
\(51\) −2.59317e24 9.14890e24i −0.450882 1.59075i
\(52\) 3.79953e24i 0.498519i
\(53\) 1.10372e25i 1.09865i 0.835609 + 0.549325i \(0.185115\pi\)
−0.835609 + 0.549325i \(0.814885\pi\)
\(54\) 6.32612e23 6.89760e23i 0.0480206 0.0523586i
\(55\) 2.26485e25i 1.31759i
\(56\) 1.36577e24 2.85369e24i 0.0611860 0.127844i
\(57\) −3.34716e25 + 9.48721e24i −1.16009 + 0.328816i
\(58\) 4.54195e24 0.122331
\(59\) 2.77774e25 0.583898 0.291949 0.956434i \(-0.405696\pi\)
0.291949 + 0.956434i \(0.405696\pi\)
\(60\) 1.65415e25 + 5.83598e25i 0.272510 + 0.961437i
\(61\) 9.03685e25i 1.17148i −0.810500 0.585739i \(-0.800804\pi\)
0.810500 0.585739i \(-0.199196\pi\)
\(62\) 4.56713e24 0.0467696
\(63\) 1.22460e26 1.30310e25i 0.994386 0.105813i
\(64\) 1.50076e26 0.969843
\(65\) 9.75038e25i 0.503243i
\(66\) 6.14448e24 + 2.16782e25i 0.0254154 + 0.0896678i
\(67\) −2.34833e25 −0.0781043 −0.0390521 0.999237i \(-0.512434\pi\)
−0.0390521 + 0.999237i \(0.512434\pi\)
\(68\) −6.13144e26 −1.64507
\(69\) 4.79530e26 1.35918e26i 1.04113 0.295098i
\(70\) 1.74799e25 3.65232e25i 0.0308048 0.0643645i
\(71\) 4.44198e26i 0.637280i −0.947876 0.318640i \(-0.896774\pi\)
0.947876 0.318640i \(-0.103226\pi\)
\(72\) −6.34921e25 1.03004e26i −0.0743701 0.120652i
\(73\) 7.29866e25i 0.0699942i 0.999387 + 0.0349971i \(0.0111422\pi\)
−0.999387 + 0.0349971i \(0.988858\pi\)
\(74\) 4.04265e25i 0.0318278i
\(75\) 3.69503e24 + 1.30364e25i 0.00239458 + 0.00844827i
\(76\) 2.24322e27i 1.19970i
\(77\) −1.27992e27 + 2.67431e27i −0.566327 + 1.18330i
\(78\) −2.64525e25 9.33266e25i −0.00970722 0.0342479i
\(79\) −4.11080e27 −1.25410 −0.627052 0.778978i \(-0.715739\pi\)
−0.627052 + 0.778978i \(0.715739\pi\)
\(80\) 3.89124e27 0.989198
\(81\) 2.11639e27 4.20787e27i 0.449328 0.893367i
\(82\) 3.32267e26i 0.0590455i
\(83\) −7.11680e27 −1.06085 −0.530423 0.847733i \(-0.677967\pi\)
−0.530423 + 0.847733i \(0.677967\pi\)
\(84\) 1.34485e27 7.82586e27i 0.168509 0.980579i
\(85\) −1.57345e28 −1.66066
\(86\) 1.19931e27i 0.106832i
\(87\) 2.19913e28 6.23322e27i 1.65662 0.469552i
\(88\) 2.91305e27 0.185930
\(89\) −1.23620e28 −0.669784 −0.334892 0.942256i \(-0.608700\pi\)
−0.334892 + 0.942256i \(0.608700\pi\)
\(90\) −8.12607e26 1.31831e27i −0.0374424 0.0607436i
\(91\) 5.51017e27 1.15131e28i 0.216304 0.451953i
\(92\) 3.21374e28i 1.07668i
\(93\) 2.21132e28 6.26778e27i 0.633359 0.179519i
\(94\) 3.56173e27i 0.0873588i
\(95\) 5.75655e28i 1.21107i
\(96\) −1.12688e28 + 3.19404e27i −0.203679 + 0.0577308i
\(97\) 2.43776e28i 0.379142i 0.981867 + 0.189571i \(0.0607097\pi\)
−0.981867 + 0.189571i \(0.939290\pi\)
\(98\) −4.12802e27 + 3.32478e27i −0.0553304 + 0.0445641i
\(99\) 5.95010e28 + 9.65297e28i 0.688357 + 1.11674i
\(100\) 8.73675e26 0.00873675
\(101\) 1.37010e29 1.18602 0.593010 0.805195i \(-0.297940\pi\)
0.593010 + 0.805195i \(0.297940\pi\)
\(102\) 1.50604e28 4.26874e27i 0.113015 0.0320329i
\(103\) 1.06328e29i 0.692643i −0.938116 0.346321i \(-0.887431\pi\)
0.938116 0.346321i \(-0.112569\pi\)
\(104\) −1.25409e28 −0.0710143
\(105\) 3.45115e28 2.00828e29i 0.170106 0.989871i
\(106\) −1.81689e28 −0.0780537
\(107\) 3.85749e28i 0.144624i 0.997382 + 0.0723119i \(0.0230377\pi\)
−0.997382 + 0.0723119i \(0.976962\pi\)
\(108\) −2.23821e29 2.05277e29i −0.733258 0.672506i
\(109\) −5.36212e29 −1.53692 −0.768461 0.639896i \(-0.778977\pi\)
−0.768461 + 0.639896i \(0.778977\pi\)
\(110\) 3.72828e28 0.0936084
\(111\) −5.54800e28 1.95738e29i −0.122167 0.431015i
\(112\) −4.59473e29 2.19903e29i −0.888380 0.425177i
\(113\) 2.88250e29i 0.489927i −0.969532 0.244964i \(-0.921224\pi\)
0.969532 0.244964i \(-0.0787761\pi\)
\(114\) −1.56174e28 5.50993e28i −0.0233608 0.0824187i
\(115\) 8.24710e29i 1.08688i
\(116\) 1.47382e30i 1.71319i
\(117\) −2.56157e29 4.15568e29i −0.262912 0.426528i
\(118\) 4.57257e28i 0.0414831i
\(119\) 1.85792e30 + 8.89196e29i 1.49140 + 0.713783i
\(120\) −1.92625e29 + 5.45977e28i −0.136957 + 0.0388192i
\(121\) −1.14363e30 −0.720935
\(122\) 1.48760e29 0.0832278
\(123\) 4.55993e29 + 1.60878e30i 0.226639 + 0.799600i
\(124\) 1.48199e30i 0.654986i
\(125\) −2.53083e30 −0.995561
\(126\) 2.14510e28 + 2.01587e29i 0.00751751 + 0.0706462i
\(127\) −1.21450e30 −0.379528 −0.189764 0.981830i \(-0.560772\pi\)
−0.189764 + 0.981830i \(0.560772\pi\)
\(128\) 1.00610e30i 0.280605i
\(129\) −1.64589e30 5.80684e30i −0.410063 1.44673i
\(130\) −1.60506e29 −0.0357529
\(131\) 6.54668e30 1.30493 0.652465 0.757819i \(-0.273735\pi\)
0.652465 + 0.757819i \(0.273735\pi\)
\(132\) 7.03439e30 1.99383e30i 1.25575 0.355931i
\(133\) 3.25316e30 6.79727e30i 0.520543 1.08764i
\(134\) 3.86570e28i 0.00554892i
\(135\) −5.74371e30 5.26783e30i −0.740206 0.678878i
\(136\) 2.02377e30i 0.234341i
\(137\) 5.00608e30i 0.521254i 0.965440 + 0.260627i \(0.0839293\pi\)
−0.965440 + 0.260627i \(0.916071\pi\)
\(138\) 2.23742e29 + 7.89378e29i 0.0209652 + 0.0739671i
\(139\) 2.24857e31i 1.89755i −0.315958 0.948773i \(-0.602326\pi\)
0.315958 0.948773i \(-0.397674\pi\)
\(140\) −1.18514e31 5.67208e30i −0.901395 0.431406i
\(141\) −4.88800e30 1.72453e31i −0.335316 1.18302i
\(142\) 7.31216e29 0.0452756
\(143\) 1.17526e31 0.657297
\(144\) −1.65848e31 + 1.02229e31i −0.838403 + 0.516793i
\(145\) 3.78213e31i 1.72942i
\(146\) −1.20147e29 −0.00497274
\(147\) −1.54243e31 + 2.17632e31i −0.578235 + 0.815870i
\(148\) −1.31180e31 −0.445732
\(149\) 8.53378e30i 0.262991i −0.991317 0.131495i \(-0.958022\pi\)
0.991317 0.131495i \(-0.0419779\pi\)
\(150\) −2.14598e28 + 6.08256e27i −0.000600208 + 0.000170123i
\(151\) −1.60350e31 −0.407289 −0.203644 0.979045i \(-0.565279\pi\)
−0.203644 + 0.979045i \(0.565279\pi\)
\(152\) −7.40407e30 −0.170898
\(153\) 6.70618e31 4.13370e31i 1.40750 0.867586i
\(154\) −4.40231e30 2.10694e30i −0.0840679 0.0402348i
\(155\) 3.80310e31i 0.661193i
\(156\) −3.02837e31 + 8.58361e30i −0.479625 + 0.135945i
\(157\) 1.56917e31i 0.226530i 0.993565 + 0.113265i \(0.0361309\pi\)
−0.993565 + 0.113265i \(0.963869\pi\)
\(158\) 6.76698e30i 0.0890979i
\(159\) −8.79707e31 + 2.49344e31i −1.05701 + 0.299600i
\(160\) 1.93805e31i 0.212630i
\(161\) −4.66063e31 + 9.73809e31i −0.467164 + 0.976109i
\(162\) 6.92678e30 + 3.48390e30i 0.0634693 + 0.0319225i
\(163\) 7.51416e31 0.629739 0.314869 0.949135i \(-0.398039\pi\)
0.314869 + 0.949135i \(0.398039\pi\)
\(164\) 1.07818e32 0.826904
\(165\) 1.80517e32 5.11658e31i 1.26765 0.359304i
\(166\) 1.17153e31i 0.0753679i
\(167\) −1.08713e32 −0.641051 −0.320526 0.947240i \(-0.603860\pi\)
−0.320526 + 0.947240i \(0.603860\pi\)
\(168\) 2.58304e31 + 4.43887e30i 0.139684 + 0.0240042i
\(169\) 1.50942e32 0.748951
\(170\) 2.59014e31i 0.117981i
\(171\) −1.51233e32 2.45349e32i −0.632708 1.02645i
\(172\) −3.89165e32 −1.49614
\(173\) 4.41231e32 1.55954 0.779771 0.626065i \(-0.215335\pi\)
0.779771 + 0.626065i \(0.215335\pi\)
\(174\) 1.02608e31 + 3.62010e31i 0.0333593 + 0.117694i
\(175\) −2.64736e30 1.26702e30i −0.00792067 0.00379082i
\(176\) 4.69030e32i 1.29201i
\(177\) 6.27524e31 + 2.21396e32i 0.159228 + 0.561768i
\(178\) 2.03498e31i 0.0475849i
\(179\) 9.16633e32i 1.97618i 0.153878 + 0.988090i \(0.450824\pi\)
−0.153878 + 0.988090i \(0.549176\pi\)
\(180\) −4.27780e32 + 2.63684e32i −0.850686 + 0.524363i
\(181\) 6.74836e32i 1.23839i 0.785235 + 0.619197i \(0.212542\pi\)
−0.785235 + 0.619197i \(0.787458\pi\)
\(182\) 1.89523e31 + 9.07055e30i 0.0321091 + 0.0153673i
\(183\) 7.20270e32 2.04153e32i 1.12708 0.319459i
\(184\) 1.06074e32 0.153374
\(185\) −3.36636e32 −0.449956
\(186\) 1.03177e31 + 3.64017e31i 0.0127540 + 0.0449970i
\(187\) 1.89656e33i 2.16902i
\(188\) −1.15575e33 −1.22342
\(189\) 3.80513e32 + 9.46610e32i 0.372970 + 0.927844i
\(190\) −9.47614e31 −0.0860407
\(191\) 1.63445e33i 1.37527i −0.726059 0.687633i \(-0.758650\pi\)
0.726059 0.687633i \(-0.241350\pi\)
\(192\) 3.39040e32 + 1.19616e33i 0.264474 + 0.933086i
\(193\) 2.33949e32 0.169255 0.0846273 0.996413i \(-0.473030\pi\)
0.0846273 + 0.996413i \(0.473030\pi\)
\(194\) −4.01292e31 −0.0269362
\(195\) −7.77141e32 + 2.20273e32i −0.484170 + 0.137233i
\(196\) 1.07886e33 + 1.33951e33i 0.624099 + 0.774875i
\(197\) 2.64605e32i 0.142180i −0.997470 0.0710899i \(-0.977352\pi\)
0.997470 0.0710899i \(-0.0226477\pi\)
\(198\) −1.58902e32 + 9.79475e31i −0.0793386 + 0.0489044i
\(199\) 2.12781e33i 0.987558i −0.869587 0.493779i \(-0.835615\pi\)
0.869587 0.493779i \(-0.164385\pi\)
\(200\) 2.88369e30i 0.00124456i
\(201\) −5.30517e31 1.87171e32i −0.0212989 0.0751441i
\(202\) 2.25539e32i 0.0842609i
\(203\) −2.13737e33 + 4.46590e33i −0.743339 + 1.55316i
\(204\) −1.38517e33 4.88699e33i −0.448606 1.58272i
\(205\) 2.76683e33 0.834740
\(206\) 1.75032e32 0.0492089
\(207\) 2.16664e33 + 3.51498e33i 0.567827 + 0.921197i
\(208\) 2.01921e33i 0.493474i
\(209\) 6.93865e33 1.58181
\(210\) 3.30592e32 + 5.68111e31i 0.0703255 + 0.0120852i
\(211\) 1.53466e33 0.304731 0.152366 0.988324i \(-0.451311\pi\)
0.152366 + 0.988324i \(0.451311\pi\)
\(212\) 5.89565e33i 1.09311i
\(213\) 3.54042e33 1.00350e33i 0.613127 0.173785i
\(214\) −6.35000e31 −0.0102748
\(215\) −9.98676e33 −1.51031
\(216\) 6.77547e32 7.38755e32i 0.0957988 0.104453i
\(217\) −2.14922e33 + 4.49066e33i −0.284194 + 0.593805i
\(218\) 8.82684e32i 0.109191i
\(219\) −5.81730e32 + 1.64886e32i −0.0673414 + 0.0190873i
\(220\) 1.20980e34i 1.31094i
\(221\) 8.16485e33i 0.828439i
\(222\) 3.22214e32 9.13283e31i 0.0306215 0.00867936i
\(223\) 4.39028e33i 0.390905i −0.980713 0.195453i \(-0.937382\pi\)
0.980713 0.195453i \(-0.0626176\pi\)
\(224\) 1.09524e33 2.28843e33i 0.0913927 0.190959i
\(225\) −9.55570e31 + 5.89014e31i −0.00747508 + 0.00460765i
\(226\) 4.74502e32 0.0348069
\(227\) 7.33316e33 0.504564 0.252282 0.967654i \(-0.418819\pi\)
0.252282 + 0.967654i \(0.418819\pi\)
\(228\) −1.78793e34 + 5.06770e33i −1.15423 + 0.327156i
\(229\) 8.31384e33i 0.503717i 0.967764 + 0.251859i \(0.0810418\pi\)
−0.967764 + 0.251859i \(0.918958\pi\)
\(230\) 1.35760e33 0.0772177
\(231\) −2.42067e34 4.15984e33i −1.29289 0.222179i
\(232\) 4.86457e33 0.244044
\(233\) 3.48244e34i 1.64143i −0.571337 0.820716i \(-0.693575\pi\)
0.571337 0.820716i \(-0.306425\pi\)
\(234\) 6.84087e32 4.21672e32i 0.0303027 0.0186786i
\(235\) −2.96589e34 −1.23501
\(236\) 1.48376e34 0.580951
\(237\) −9.28679e33 3.27646e34i −0.341991 1.20657i
\(238\) −1.46375e33 + 3.05841e33i −0.0507108 + 0.105957i
\(239\) 2.34983e34i 0.766067i 0.923734 + 0.383033i \(0.125121\pi\)
−0.923734 + 0.383033i \(0.874879\pi\)
\(240\) 8.79079e33 + 3.10146e34i 0.269752 + 0.951707i
\(241\) 6.85561e34i 1.98061i −0.138912 0.990305i \(-0.544361\pi\)
0.138912 0.990305i \(-0.455639\pi\)
\(242\) 1.88258e33i 0.0512189i
\(243\) 3.83195e34 + 7.36232e33i 0.982039 + 0.188679i
\(244\) 4.82713e34i 1.16557i
\(245\) 2.76858e34 + 3.43745e34i 0.630013 + 0.782218i
\(246\) −2.64829e33 + 7.50632e32i −0.0568077 + 0.0161016i
\(247\) −2.98715e34 −0.604158
\(248\) 4.89154e33 0.0933031
\(249\) −1.60777e34 5.67235e34i −0.289290 1.02064i
\(250\) 4.16612e33i 0.0707298i
\(251\) 4.08692e34 0.654828 0.327414 0.944881i \(-0.393823\pi\)
0.327414 + 0.944881i \(0.393823\pi\)
\(252\) 6.54132e34 6.96066e33i 0.989367 0.105279i
\(253\) −9.94063e34 −1.41960
\(254\) 1.99925e33i 0.0269636i
\(255\) −3.55462e34 1.25410e35i −0.452857 1.59772i
\(256\) 7.89152e34 0.949907
\(257\) −8.50905e34 −0.967945 −0.483972 0.875083i \(-0.660806\pi\)
−0.483972 + 0.875083i \(0.660806\pi\)
\(258\) 9.55891e33 2.70938e33i 0.102783 0.0291329i
\(259\) 3.97496e34 + 1.90241e34i 0.404097 + 0.193400i
\(260\) 5.20827e34i 0.500703i
\(261\) 9.93621e34 + 1.61197e35i 0.903511 + 1.46578i
\(262\) 1.07768e34i 0.0927089i
\(263\) 1.53828e35i 1.25221i −0.779740 0.626103i \(-0.784649\pi\)
0.779740 0.626103i \(-0.215351\pi\)
\(264\) 6.58093e33 + 2.32181e34i 0.0507026 + 0.178883i
\(265\) 1.51295e35i 1.10346i
\(266\) 1.11893e34 + 5.35519e33i 0.0772716 + 0.0369820i
\(267\) −2.79274e34 9.85300e34i −0.182649 0.644399i
\(268\) −1.25439e34 −0.0777100
\(269\) 6.38364e34 0.374680 0.187340 0.982295i \(-0.440013\pi\)
0.187340 + 0.982295i \(0.440013\pi\)
\(270\) 8.67163e33 9.45500e33i 0.0482310 0.0525880i
\(271\) 1.91619e35i 1.01015i 0.863076 + 0.505074i \(0.168535\pi\)
−0.863076 + 0.505074i \(0.831465\pi\)
\(272\) −3.25848e35 −1.62842
\(273\) 1.04212e35 + 1.79085e34i 0.493810 + 0.0848594i
\(274\) −8.24075e33 −0.0370325
\(275\) 2.70243e33i 0.0115194i
\(276\) 2.56147e35 7.26022e34i 1.03587 0.293608i
\(277\) −4.75727e35 −1.82558 −0.912791 0.408427i \(-0.866077\pi\)
−0.912791 + 0.408427i \(0.866077\pi\)
\(278\) 3.70149e34 0.134811
\(279\) 9.99130e34 + 1.62091e35i 0.345431 + 0.560400i
\(280\) 1.87216e34 3.91175e34i 0.0614540 0.128404i
\(281\) 5.51041e35i 1.71768i 0.512245 + 0.858839i \(0.328814\pi\)
−0.512245 + 0.858839i \(0.671186\pi\)
\(282\) 2.83883e34 8.04637e33i 0.0840479 0.0238225i
\(283\) 1.66431e35i 0.468092i 0.972226 + 0.234046i \(0.0751966\pi\)
−0.972226 + 0.234046i \(0.924803\pi\)
\(284\) 2.37273e35i 0.634064i
\(285\) −4.58818e35 + 1.30047e35i −1.16517 + 0.330257i
\(286\) 1.93465e34i 0.0466977i
\(287\) −3.26704e35 1.56360e35i −0.749664 0.358788i
\(288\) −5.09154e34 8.26011e34i −0.111086 0.180217i
\(289\) 8.35624e35 1.73377
\(290\) 6.22595e34 0.122867
\(291\) −1.94299e35 + 5.50721e34i −0.364772 + 0.103391i
\(292\) 3.89866e34i 0.0696409i
\(293\) 4.84366e35 0.823366 0.411683 0.911327i \(-0.364941\pi\)
0.411683 + 0.911327i \(0.364941\pi\)
\(294\) −3.58254e34 2.53907e34i −0.0579636 0.0410808i
\(295\) 3.80763e35 0.586456
\(296\) 4.32981e34i 0.0634949i
\(297\) −6.34957e35 + 6.92317e35i −0.886698 + 0.966800i
\(298\) 1.40479e34 0.0186842
\(299\) 4.27953e35 0.542205
\(300\) 1.97374e33 + 6.96351e33i 0.00238249 + 0.00840563i
\(301\) 1.17923e36 + 5.64375e35i 1.35638 + 0.649163i
\(302\) 2.63959e34i 0.0289359i
\(303\) 3.09522e35 + 1.09202e36i 0.323425 + 1.14107i
\(304\) 1.19213e36i 1.18756i
\(305\) 1.23874e36i 1.17661i
\(306\) 6.80468e34 + 1.10394e35i 0.0616378 + 0.0999962i
\(307\) 4.14891e35i 0.358449i −0.983808 0.179224i \(-0.942641\pi\)
0.983808 0.179224i \(-0.0573588\pi\)
\(308\) −6.83684e35 + 1.42851e36i −0.563469 + 1.17733i
\(309\) 8.47476e35 2.40209e35i 0.666391 0.188882i
\(310\) 6.26047e34 0.0469745
\(311\) −7.22914e35 −0.517680 −0.258840 0.965920i \(-0.583340\pi\)
−0.258840 + 0.965920i \(0.583340\pi\)
\(312\) −2.83315e34 9.99557e34i −0.0193654 0.0683229i
\(313\) 6.81116e35i 0.444455i −0.974995 0.222228i \(-0.928667\pi\)
0.974995 0.222228i \(-0.0713328\pi\)
\(314\) −2.58309e34 −0.0160938
\(315\) 1.67864e36 1.78625e35i 0.998742 0.106277i
\(316\) −2.19583e36 −1.24777
\(317\) 1.68810e36i 0.916300i 0.888875 + 0.458150i \(0.151488\pi\)
−0.888875 + 0.458150i \(0.848512\pi\)
\(318\) −4.10458e34 1.44813e35i −0.0212851 0.0750955i
\(319\) −4.55878e36 −2.25883
\(320\) 2.05719e36 0.974092
\(321\) −3.07456e35 + 8.71454e34i −0.139143 + 0.0394386i
\(322\) −1.60303e35 7.67209e34i −0.0693478 0.0331897i
\(323\) 4.82047e36i 1.99367i
\(324\) 1.13049e36 2.24768e36i 0.447060 0.888858i
\(325\) 1.16342e34i 0.00439974i
\(326\) 1.23694e35i 0.0447398i
\(327\) −1.21137e36 4.27380e36i −0.419115 1.47867i
\(328\) 3.55869e35i 0.117793i
\(329\) 3.50209e36 + 1.67609e36i 1.10914 + 0.530833i
\(330\) 8.42264e34 + 2.97158e35i 0.0255268 + 0.0900606i
\(331\) 4.91857e34 0.0142670 0.00713350 0.999975i \(-0.497729\pi\)
0.00713350 + 0.999975i \(0.497729\pi\)
\(332\) −3.80152e36 −1.05549
\(333\) 1.43477e36 8.84392e35i 0.381364 0.235073i
\(334\) 1.78958e35i 0.0455435i
\(335\) −3.21901e35 −0.0784464
\(336\) 7.14702e35 4.15896e36i 0.166804 0.970655i
\(337\) −3.67526e36 −0.821589 −0.410794 0.911728i \(-0.634749\pi\)
−0.410794 + 0.911728i \(0.634749\pi\)
\(338\) 2.48473e35i 0.0532093i
\(339\) 2.29746e36 6.51192e35i 0.471359 0.133602i
\(340\) −8.40478e36 −1.65227
\(341\) −4.58406e36 −0.863598
\(342\) 4.03880e35 2.48952e35i 0.0729246 0.0449508i
\(343\) −1.32653e36 5.62349e36i −0.229590 0.973288i
\(344\) 1.28450e36i 0.213125i
\(345\) 6.57324e36 1.86312e36i 1.04569 0.296390i
\(346\) 7.26331e35i 0.110798i
\(347\) 6.02613e36i 0.881579i 0.897610 + 0.440790i \(0.145302\pi\)
−0.897610 + 0.440790i \(0.854698\pi\)
\(348\) 1.17469e37 3.32954e36i 1.64826 0.467182i
\(349\) 2.04744e36i 0.275576i 0.990462 + 0.137788i \(0.0439993\pi\)
−0.990462 + 0.137788i \(0.956001\pi\)
\(350\) 2.08571e33 4.35795e33i 0.000269319 0.000562725i
\(351\) 2.73354e36 2.98048e36i 0.338667 0.369261i
\(352\) 2.33602e36 0.277721
\(353\) 1.26440e37 1.44262 0.721308 0.692614i \(-0.243541\pi\)
0.721308 + 0.692614i \(0.243541\pi\)
\(354\) −3.64450e35 + 1.03300e35i −0.0399109 + 0.0113123i
\(355\) 6.08892e36i 0.640072i
\(356\) −6.60332e36 −0.666404
\(357\) −2.88996e36 + 1.68171e37i −0.280028 + 1.62953i
\(358\) −1.50891e36 −0.140398
\(359\) 4.98569e36i 0.445508i 0.974875 + 0.222754i \(0.0715047\pi\)
−0.974875 + 0.222754i \(0.928495\pi\)
\(360\) −8.70328e35 1.41195e36i −0.0746959 0.121181i
\(361\) −5.50607e36 −0.453929
\(362\) −1.11088e36 −0.0879819
\(363\) −2.58359e36 9.11512e36i −0.196597 0.693611i
\(364\) 2.94332e36 6.14987e36i 0.215212 0.449672i
\(365\) 1.00048e36i 0.0703008i
\(366\) 3.36067e35 + 1.18567e36i 0.0226960 + 0.0800734i
\(367\) 1.86060e37i 1.20780i 0.797059 + 0.603901i \(0.206388\pi\)
−0.797059 + 0.603901i \(0.793612\pi\)
\(368\) 1.70790e37i 1.06578i
\(369\) −1.17924e37 + 7.26886e36i −0.707491 + 0.436098i
\(370\) 5.54153e35i 0.0319672i
\(371\) 8.55001e36 1.78647e37i 0.474291 0.991000i
\(372\) 1.18120e37 3.34800e36i 0.630162 0.178613i
\(373\) −2.32369e37 −1.19234 −0.596169 0.802859i \(-0.703311\pi\)
−0.596169 + 0.802859i \(0.703311\pi\)
\(374\) −3.12202e36 −0.154098
\(375\) −5.71746e36 2.01717e37i −0.271487 0.957829i
\(376\) 3.81472e36i 0.174277i
\(377\) 1.96260e37 0.862743
\(378\) −1.55826e36 + 6.26381e35i −0.0659187 + 0.0264977i
\(379\) −8.33717e36 −0.339430 −0.169715 0.985493i \(-0.554285\pi\)
−0.169715 + 0.985493i \(0.554285\pi\)
\(380\) 3.07493e37i 1.20496i
\(381\) −2.74370e36 9.68001e36i −0.103496 0.365144i
\(382\) 2.69054e36 0.0977059
\(383\) −1.59429e37 −0.557424 −0.278712 0.960375i \(-0.589907\pi\)
−0.278712 + 0.960375i \(0.589907\pi\)
\(384\) −8.01897e36 + 2.27290e36i −0.269970 + 0.0765204i
\(385\) −1.75447e37 + 3.66586e37i −0.568808 + 1.18849i
\(386\) 3.85115e35i 0.0120247i
\(387\) 4.25643e37 2.62367e37i 1.28008 0.789042i
\(388\) 1.30216e37i 0.377228i
\(389\) 4.83465e36i 0.134926i 0.997722 + 0.0674630i \(0.0214905\pi\)
−0.997722 + 0.0674630i \(0.978510\pi\)
\(390\) −3.62602e35 1.27929e36i −0.00974975 0.0343979i
\(391\) 6.90603e37i 1.78923i
\(392\) −4.42124e36 + 3.56095e36i −0.110381 + 0.0889032i
\(393\) 1.47897e37 + 5.21794e37i 0.355852 + 1.25547i
\(394\) 4.35579e35 0.0101012
\(395\) −5.63494e37 −1.25960
\(396\) 3.17831e37 + 5.15624e37i 0.684883 + 1.11110i
\(397\) 8.92922e37i 1.85503i 0.373786 + 0.927515i \(0.378060\pi\)
−0.373786 + 0.927515i \(0.621940\pi\)
\(398\) 3.50269e36 0.0701612
\(399\) 6.15260e37 + 1.05730e37i 1.18837 + 0.204217i
\(400\) 4.64304e35 0.00864833
\(401\) 2.41874e37i 0.434505i −0.976115 0.217253i \(-0.930290\pi\)
0.976115 0.217253i \(-0.0697095\pi\)
\(402\) 3.08111e35 8.73309e34i 0.00533862 0.00151318i
\(403\) 1.97348e37 0.329844
\(404\) 7.31853e37 1.18003
\(405\) 2.90108e37 5.76801e37i 0.451296 0.897281i
\(406\) −7.35153e36 3.51843e36i −0.110344 0.0528106i
\(407\) 4.05764e37i 0.587698i
\(408\) 1.61302e37 4.57195e36i 0.225459 0.0639042i
\(409\) 6.27784e37i 0.846881i −0.905924 0.423441i \(-0.860822\pi\)
0.905924 0.423441i \(-0.139178\pi\)
\(410\) 4.55461e36i 0.0593042i
\(411\) −3.99003e37 + 1.13093e37i −0.501498 + 0.142145i
\(412\) 5.67965e37i 0.689147i
\(413\) −4.49600e37 2.15178e37i −0.526685 0.252070i
\(414\) −5.78618e36 + 3.56660e36i −0.0654465 + 0.0403413i
\(415\) −9.75547e37 −1.06549
\(416\) −1.00568e37 −0.106073
\(417\) 1.79220e38 5.07980e37i 1.82563 0.517457i
\(418\) 1.14220e37i 0.112380i
\(419\) −1.17454e38 −1.11626 −0.558130 0.829754i \(-0.688481\pi\)
−0.558130 + 0.829754i \(0.688481\pi\)
\(420\) 1.84347e37 1.07274e38i 0.169247 0.984875i
\(421\) −1.73657e38 −1.54029 −0.770145 0.637869i \(-0.779816\pi\)
−0.770145 + 0.637869i \(0.779816\pi\)
\(422\) 2.52628e36i 0.0216496i
\(423\) 1.26408e38 7.79183e37i 1.04674 0.645214i
\(424\) −1.94595e37 −0.155714
\(425\) −1.87745e36 −0.0145187
\(426\) 1.65191e36 + 5.82806e36i 0.0123466 + 0.0435597i
\(427\) −7.00041e37 + 1.46269e38i −0.505731 + 1.05669i
\(428\) 2.06052e37i 0.143894i
\(429\) 2.65506e37 + 9.36726e37i 0.179243 + 0.632385i
\(430\) 1.64397e37i 0.107300i
\(431\) 3.99375e37i 0.252034i 0.992028 + 0.126017i \(0.0402195\pi\)
−0.992028 + 0.126017i \(0.959781\pi\)
\(432\) −1.18947e38 1.09092e38i −0.725837 0.665700i
\(433\) 2.69975e37i 0.159312i −0.996822 0.0796562i \(-0.974618\pi\)
0.996822 0.0796562i \(-0.0253822\pi\)
\(434\) −7.39229e36 3.53794e36i −0.0421869 0.0201906i
\(435\) 3.01450e38 8.54429e37i 1.66387 0.471609i
\(436\) −2.86423e38 −1.52917
\(437\) 2.52660e38 1.30484
\(438\) −2.71426e35 9.57615e35i −0.00135606 0.00478427i
\(439\) 2.22268e38i 1.07434i 0.843475 + 0.537169i \(0.180506\pi\)
−0.843475 + 0.537169i \(0.819494\pi\)
\(440\) 3.99311e37 0.186744
\(441\) −2.08306e38 7.37718e37i −0.942632 0.333834i
\(442\) 1.34406e37 0.0588565
\(443\) 1.84884e38i 0.783509i −0.920070 0.391755i \(-0.871868\pi\)
0.920070 0.391755i \(-0.128132\pi\)
\(444\) −2.96353e37 1.04556e38i −0.121550 0.428839i
\(445\) −1.69455e38 −0.672719
\(446\) 7.22705e36 0.0277719
\(447\) 6.80174e37 1.92788e37i 0.253023 0.0717170i
\(448\) −2.42911e38 1.16257e38i −0.874813 0.418684i
\(449\) 2.08938e38i 0.728525i 0.931296 + 0.364263i \(0.118679\pi\)
−0.931296 + 0.364263i \(0.881321\pi\)
\(450\) −9.69605e34 1.57301e35i −0.000327351 0.000531068i
\(451\) 3.33499e38i 1.09027i
\(452\) 1.53972e38i 0.487455i
\(453\) −3.62249e37 1.27805e38i −0.111067 0.391852i
\(454\) 1.20715e37i 0.0358468i
\(455\) 7.55315e37 1.57818e38i 0.217252 0.453933i
\(456\) −1.67267e37 5.90131e37i −0.0466036 0.164421i
\(457\) −1.08516e38 −0.292892 −0.146446 0.989219i \(-0.546783\pi\)
−0.146446 + 0.989219i \(0.546783\pi\)
\(458\) −1.36858e37 −0.0357867
\(459\) 4.80971e38 + 4.41122e38i 1.21853 + 1.11757i
\(460\) 4.40528e38i 1.08140i
\(461\) −2.64900e36 −0.00630114 −0.00315057 0.999995i \(-0.501003\pi\)
−0.00315057 + 0.999995i \(0.501003\pi\)
\(462\) 6.84772e36 3.98479e37i 0.0157847 0.0918537i
\(463\) 2.91043e38 0.650179 0.325089 0.945683i \(-0.394606\pi\)
0.325089 + 0.945683i \(0.394606\pi\)
\(464\) 7.83245e38i 1.69585i
\(465\) 3.03121e38 8.59166e37i 0.636133 0.180306i
\(466\) 5.73261e37 0.116616
\(467\) 1.17358e38 0.231430 0.115715 0.993282i \(-0.463084\pi\)
0.115715 + 0.993282i \(0.463084\pi\)
\(468\) −1.36829e38 2.21981e38i −0.261585 0.424375i
\(469\) 3.80098e37 + 1.81914e37i 0.0704513 + 0.0337179i
\(470\) 4.88229e37i 0.0877415i
\(471\) −1.25069e38 + 3.54495e37i −0.217944 + 0.0617742i
\(472\) 4.89736e37i 0.0827568i
\(473\) 1.20375e39i 1.97265i
\(474\) 5.39353e37 1.52874e37i 0.0857211 0.0242968i
\(475\) 6.86873e36i 0.0105881i
\(476\) 9.92427e38 + 4.74974e38i 1.48388 + 0.710181i
\(477\) −3.97473e38 6.44829e38i −0.576489 0.935251i
\(478\) −3.86817e37 −0.0544253
\(479\) −1.15260e39 −1.57331 −0.786654 0.617394i \(-0.788188\pi\)
−0.786654 + 0.617394i \(0.788188\pi\)
\(480\) −1.54470e38 + 4.37829e37i −0.204571 + 0.0579838i
\(481\) 1.74685e38i 0.224466i
\(482\) 1.12853e38 0.140713
\(483\) −8.81451e38 1.51474e38i −1.06651 0.183276i
\(484\) −6.10880e38 −0.717296
\(485\) 3.34161e38i 0.380803i
\(486\) −1.21195e37 + 6.30796e37i −0.0134047 + 0.0697690i
\(487\) 1.01199e39 1.08644 0.543219 0.839591i \(-0.317205\pi\)
0.543219 + 0.839591i \(0.317205\pi\)
\(488\) 1.59327e38 0.166035
\(489\) 1.69754e38 + 5.98906e38i 0.171728 + 0.605871i
\(490\) −5.65855e37 + 4.55750e37i −0.0555728 + 0.0447593i
\(491\) 1.37756e39i 1.31350i −0.754109 0.656749i \(-0.771931\pi\)
0.754109 0.656749i \(-0.228069\pi\)
\(492\) 2.43574e38 + 8.59348e38i 0.225495 + 0.795564i
\(493\) 3.16711e39i 2.84697i
\(494\) 4.91729e37i 0.0429225i
\(495\) 8.15620e38 + 1.32320e39i 0.691373 + 1.12163i
\(496\) 7.87587e38i 0.648357i
\(497\) −3.44099e38 + 7.18972e38i −0.275116 + 0.574837i
\(498\) 9.33753e37 2.64663e37i 0.0725115 0.0205527i
\(499\) −3.04074e38 −0.229362 −0.114681 0.993402i \(-0.536585\pi\)
−0.114681 + 0.993402i \(0.536585\pi\)
\(500\) −1.35187e39 −0.990536
\(501\) −2.45596e38 8.66483e38i −0.174813 0.616755i
\(502\) 6.72768e37i 0.0465223i
\(503\) −1.49463e39 −1.00415 −0.502073 0.864825i \(-0.667429\pi\)
−0.502073 + 0.864825i \(0.667429\pi\)
\(504\) 2.29747e37 + 2.15906e38i 0.0149971 + 0.140936i
\(505\) 1.87809e39 1.19122
\(506\) 1.63638e38i 0.100856i
\(507\) 3.40997e38 + 1.20306e39i 0.204237 + 0.720566i
\(508\) −6.48739e38 −0.377612
\(509\) −4.02828e37 −0.0227883 −0.0113941 0.999935i \(-0.503627\pi\)
−0.0113941 + 0.999935i \(0.503627\pi\)
\(510\) 2.06444e38 5.85144e37i 0.113510 0.0321733i
\(511\) 5.65393e37 1.18135e38i 0.0302167 0.0631359i
\(512\) 6.70051e38i 0.348092i
\(513\) 1.61386e39 1.75966e39i 0.815014 0.888640i
\(514\) 1.40072e38i 0.0687677i
\(515\) 1.45751e39i 0.695677i
\(516\) −8.79171e38 3.10179e39i −0.407993 1.43943i
\(517\) 3.57493e39i 1.61308i
\(518\) −3.13165e37 + 6.54337e37i −0.0137401 + 0.0287091i
\(519\) 9.96794e38 + 3.51677e39i 0.425284 + 1.50043i
\(520\) −1.71907e38 −0.0713254
\(521\) 3.08072e38 0.124310 0.0621550 0.998067i \(-0.480203\pi\)
0.0621550 + 0.998067i \(0.480203\pi\)
\(522\) −2.65355e38 + 1.63565e38i −0.104137 + 0.0641900i
\(523\) 4.34830e38i 0.165976i −0.996551 0.0829880i \(-0.973554\pi\)
0.996551 0.0829880i \(-0.0264463\pi\)
\(524\) 3.49698e39 1.29834
\(525\) 4.11792e36 2.39628e37i 0.00148720 0.00865422i
\(526\) 2.53223e38 0.0889632
\(527\) 3.18467e39i 1.08846i
\(528\) 3.73834e39 1.05960e39i 1.24305 0.352329i
\(529\) −5.28669e38 −0.171032
\(530\) −2.49053e38 −0.0783957
\(531\) −1.62284e39 + 1.00032e39i −0.497056 + 0.306386i
\(532\) 1.73771e39 3.63084e39i 0.517916 1.08215i
\(533\) 1.43574e39i 0.416420i
\(534\) 1.62195e38 4.59726e37i 0.0457814 0.0129763i
\(535\) 5.28772e38i 0.145257i
\(536\) 4.14029e37i 0.0110698i
\(537\) −7.30590e39 + 2.07079e39i −1.90128 + 0.538900i
\(538\) 1.05084e38i 0.0266192i
\(539\) 4.14332e39 3.33711e39i 1.02167 0.822874i
\(540\) −3.06807e39 2.81387e39i −0.736470 0.675452i
\(541\) 2.94250e39 0.687632 0.343816 0.939037i \(-0.388280\pi\)
0.343816 + 0.939037i \(0.388280\pi\)
\(542\) −3.15434e38 −0.0717660
\(543\) −5.37869e39 + 1.52454e39i −1.19146 + 0.337707i
\(544\) 1.62290e39i 0.350032i
\(545\) −7.35021e39 −1.54366
\(546\) −2.94800e37 + 1.71549e38i −0.00602885 + 0.0350828i
\(547\) 4.86226e38 0.0968326 0.0484163 0.998827i \(-0.484583\pi\)
0.0484163 + 0.998827i \(0.484583\pi\)
\(548\) 2.67405e39i 0.518623i
\(549\) 3.25435e39 + 5.27961e39i 0.614704 + 0.997247i
\(550\) 4.44860e36 0.000818397
\(551\) 1.15870e40 2.07622
\(552\) 2.39634e38 + 8.45450e38i 0.0418247 + 0.147561i
\(553\) 6.65368e39 + 3.18444e39i 1.13122 + 0.541400i
\(554\) 7.83118e38i 0.129699i
\(555\) −7.60502e38 2.68311e39i −0.122702 0.432903i
\(556\) 1.20110e40i 1.88797i
\(557\) 9.72938e39i 1.49000i −0.667067 0.744998i \(-0.732450\pi\)
0.667067 0.744998i \(-0.267550\pi\)
\(558\) −2.66826e38 + 1.64472e38i −0.0398136 + 0.0245412i
\(559\) 5.18226e39i 0.753439i
\(560\) −6.29831e39 3.01436e39i −0.892272 0.427040i
\(561\) −1.51163e40 + 4.28456e39i −2.08681 + 0.591487i
\(562\) −9.07095e38 −0.122033
\(563\) −8.04726e39 −1.05506 −0.527529 0.849537i \(-0.676881\pi\)
−0.527529 + 0.849537i \(0.676881\pi\)
\(564\) −2.61098e39 9.21175e39i −0.333623 1.17705i
\(565\) 3.95123e39i 0.492074i
\(566\) −2.73970e38 −0.0332556
\(567\) −6.68520e39 + 5.17134e39i −0.790970 + 0.611855i
\(568\) 7.83155e38 0.0903227
\(569\) 4.92946e39i 0.554206i 0.960840 + 0.277103i \(0.0893744\pi\)
−0.960840 + 0.277103i \(0.910626\pi\)
\(570\) −2.14077e38 7.55283e38i −0.0234631 0.0827798i
\(571\) −3.01134e39 −0.321763 −0.160881 0.986974i \(-0.551434\pi\)
−0.160881 + 0.986974i \(0.551434\pi\)
\(572\) 6.27778e39 0.653979
\(573\) 1.30271e40 3.69241e39i 1.32314 0.375032i
\(574\) 2.57392e38 5.37803e38i 0.0254901 0.0532600i
\(575\) 9.84047e37i 0.00950237i
\(576\) −8.76790e39 + 5.40454e39i −0.825600 + 0.508901i
\(577\) 1.29813e40i 1.19198i −0.802990 0.595992i \(-0.796759\pi\)
0.802990 0.595992i \(-0.203241\pi\)
\(578\) 1.37556e39i 0.123176i
\(579\) 5.28520e38 + 1.86466e39i 0.0461554 + 0.162840i
\(580\) 2.02027e40i 1.72069i
\(581\) 1.15192e40 + 5.51305e39i 0.956900 + 0.457971i
\(582\) −9.06568e37 3.19845e38i −0.00734543 0.0259153i
\(583\) 1.82363e40 1.44126
\(584\) −1.28681e38 −0.00992039
\(585\) −3.51131e39 5.69647e39i −0.264064 0.428397i
\(586\) 7.97338e38i 0.0584961i
\(587\) 3.87385e38 0.0277262 0.0138631 0.999904i \(-0.495587\pi\)
0.0138631 + 0.999904i \(0.495587\pi\)
\(588\) −8.23907e39 + 1.16250e40i −0.575317 + 0.811752i
\(589\) 1.16513e40 0.793782
\(590\) 6.26792e38i 0.0416648i
\(591\) 2.10900e39 5.97775e38i 0.136791 0.0387721i
\(592\) −6.97142e39 −0.441221
\(593\) −1.25692e40 −0.776274 −0.388137 0.921602i \(-0.626881\pi\)
−0.388137 + 0.921602i \(0.626881\pi\)
\(594\) −1.13966e39 1.04523e39i −0.0686864 0.0629956i
\(595\) 2.54677e40 + 1.21888e40i 1.49794 + 0.716910i
\(596\) 4.55841e39i 0.261663i
\(597\) 1.69594e40 4.80698e39i 0.950130 0.269305i
\(598\) 7.04474e38i 0.0385210i
\(599\) 2.11358e40i 1.12805i 0.825756 + 0.564027i \(0.190749\pi\)
−0.825756 + 0.564027i \(0.809251\pi\)
\(600\) −2.29841e37 + 6.51462e36i −0.00119739 + 0.000339387i
\(601\) 2.64978e40i 1.34750i 0.738957 + 0.673752i \(0.235318\pi\)
−0.738957 + 0.673752i \(0.764682\pi\)
\(602\) −9.29046e38 + 1.94118e39i −0.0461199 + 0.0963644i
\(603\) 1.37197e39 8.45683e38i 0.0664880 0.0409832i
\(604\) −8.56525e39 −0.405233
\(605\) −1.56764e40 −0.724093
\(606\) −1.79763e39 + 5.09519e38i −0.0810674 + 0.0229777i
\(607\) 5.48665e39i 0.241586i 0.992678 + 0.120793i \(0.0385437\pi\)
−0.992678 + 0.120793i \(0.961456\pi\)
\(608\) −5.93745e39 −0.255269
\(609\) −4.04234e40 6.94662e39i −1.69700 0.291624i
\(610\) 2.03915e39 0.0835924
\(611\) 1.53904e40i 0.616101i
\(612\) 3.58218e40 2.20806e40i 1.40040 0.863207i
\(613\) −7.35368e38 −0.0280755 −0.0140378 0.999901i \(-0.504469\pi\)
−0.0140378 + 0.999901i \(0.504469\pi\)
\(614\) 6.82972e38 0.0254660
\(615\) 6.25060e39 + 2.20526e40i 0.227632 + 0.803103i
\(616\) −4.71502e39 2.25660e39i −0.167712 0.0802665i
\(617\) 1.29963e40i 0.451530i −0.974182 0.225765i \(-0.927512\pi\)
0.974182 0.225765i \(-0.0724881\pi\)
\(618\) 3.95419e38 + 1.39507e39i 0.0134191 + 0.0473438i
\(619\) 1.74106e40i 0.577164i 0.957455 + 0.288582i \(0.0931838\pi\)
−0.957455 + 0.288582i \(0.906816\pi\)
\(620\) 2.03147e40i 0.657855i
\(621\) −2.31210e40 + 2.52096e40i −0.731439 + 0.797514i
\(622\) 1.19002e39i 0.0367786i
\(623\) 2.00090e40 + 9.57628e39i 0.604156 + 0.289148i
\(624\) −1.60939e40 + 4.56165e39i −0.474771 + 0.134569i
\(625\) −3.49964e40 −1.00870
\(626\) 1.12122e39 0.0315764
\(627\) 1.56753e40 + 5.53036e40i 0.431355 + 1.52186i
\(628\) 8.38191e39i 0.225387i
\(629\) 2.81895e40 0.740718
\(630\) 2.94043e38 + 2.76328e39i 0.00755045 + 0.0709557i
\(631\) 5.93501e40 1.48935 0.744673 0.667429i \(-0.232605\pi\)
0.744673 + 0.667429i \(0.232605\pi\)
\(632\) 7.24766e39i 0.177746i
\(633\) 3.46699e39 + 1.22318e40i 0.0830995 + 0.293182i
\(634\) −2.77886e39 −0.0650987
\(635\) −1.66480e40 −0.381190
\(636\) −4.69905e40 + 1.33190e40i −1.05168 + 0.298087i
\(637\) −1.78374e40 + 1.43665e40i −0.390219 + 0.314290i
\(638\) 7.50444e39i 0.160479i
\(639\) 1.59965e40 + 2.59514e40i 0.334397 + 0.542499i
\(640\) 1.37913e40i 0.281835i
\(641\) 1.93964e39i 0.0387507i 0.999812 + 0.0193753i \(0.00616774\pi\)
−0.999812 + 0.0193753i \(0.993832\pi\)
\(642\) −1.43454e38 5.06118e38i −0.00280192 0.00988540i
\(643\) 3.24762e40i 0.620164i 0.950710 + 0.310082i \(0.100357\pi\)
−0.950710 + 0.310082i \(0.899643\pi\)
\(644\) −2.48953e40 + 5.20171e40i −0.464806 + 0.971182i
\(645\) −2.25613e40 7.95982e40i −0.411859 1.45307i
\(646\) 7.93521e39 0.141640
\(647\) −1.25775e40 −0.219525 −0.109762 0.993958i \(-0.535009\pi\)
−0.109762 + 0.993958i \(0.535009\pi\)
\(648\) 7.41881e39 + 3.73136e39i 0.126618 + 0.0636839i
\(649\) 4.58952e40i 0.765983i
\(650\) −1.91516e37 −0.000312580
\(651\) −4.06475e40 6.98513e39i −0.648798 0.111494i
\(652\) 4.01377e40 0.626560
\(653\) 2.19281e40i 0.334780i −0.985891 0.167390i \(-0.946466\pi\)
0.985891 0.167390i \(-0.0535339\pi\)
\(654\) 7.03532e39 1.99409e39i 0.105052 0.0297761i
\(655\) 8.97397e40 1.31065
\(656\) 5.72985e40 0.818535
\(657\) −2.62840e39 4.26411e39i −0.0367277 0.0595841i
\(658\) −2.75910e39 + 5.76496e39i −0.0377131 + 0.0787990i
\(659\) 9.04042e40i 1.20879i 0.796686 + 0.604394i \(0.206585\pi\)
−0.796686 + 0.604394i \(0.793415\pi\)
\(660\) 9.64251e40 2.73308e40i 1.26126 0.357491i
\(661\) 9.58277e39i 0.122622i 0.998119 + 0.0613112i \(0.0195282\pi\)
−0.998119 + 0.0613112i \(0.980472\pi\)
\(662\) 8.09670e37i 0.00101360i
\(663\) 6.50769e40 1.84454e40i 0.797041 0.225913i
\(664\) 1.25475e40i 0.150355i
\(665\) 4.45932e40 9.31747e40i 0.522824 1.09241i
\(666\) 1.45584e39 + 2.36184e39i 0.0167008 + 0.0270941i
\(667\) −1.66001e41 −1.86331
\(668\) −5.80703e40 −0.637816
\(669\) 3.49921e40 9.91817e39i 0.376090 0.106599i
\(670\) 5.29898e38i 0.00557323i
\(671\) −1.49311e41 −1.53680
\(672\) 2.07139e40 + 3.55960e39i 0.208644 + 0.0358548i
\(673\) −7.68644e40 −0.757717 −0.378858 0.925455i \(-0.623683\pi\)
−0.378858 + 0.925455i \(0.623683\pi\)
\(674\) 6.05003e39i 0.0583699i
\(675\) −6.85341e38 6.28559e38i −0.00647145 0.00593528i
\(676\) 8.06274e40 0.745171
\(677\) 9.98234e40 0.903018 0.451509 0.892266i \(-0.350886\pi\)
0.451509 + 0.892266i \(0.350886\pi\)
\(678\) 1.07196e39 + 3.78196e39i 0.00949177 + 0.0334878i
\(679\) 1.88842e40 3.94573e40i 0.163677 0.341992i
\(680\) 2.77412e40i 0.235367i
\(681\) 1.65665e40 + 5.84480e40i 0.137594 + 0.485441i
\(682\) 7.54604e39i 0.0613544i
\(683\) 2.16857e41i 1.72613i 0.505092 + 0.863065i \(0.331459\pi\)
−0.505092 + 0.863065i \(0.668541\pi\)
\(684\) −8.07828e40 1.31056e41i −0.629514 1.02127i
\(685\) 6.86216e40i 0.523538i
\(686\) 9.25710e39 2.18367e39i 0.0691473 0.0163112i
\(687\) −6.62643e40 + 1.87820e40i −0.484626 + 0.137363i
\(688\) −2.06817e41 −1.48099
\(689\) −7.85087e40 −0.550477
\(690\) 3.06697e39 + 1.08205e40i 0.0210571 + 0.0742911i
\(691\) 2.37839e41i 1.59901i −0.600657 0.799507i \(-0.705094\pi\)
0.600657 0.799507i \(-0.294906\pi\)
\(692\) 2.35688e41 1.55167
\(693\) −2.15305e40 2.02334e41i −0.138810 1.30448i
\(694\) −9.91991e39 −0.0626319
\(695\) 3.08227e41i 1.90586i
\(696\) 1.09897e40 + 3.87724e40i 0.0665503 + 0.234795i
\(697\) −2.31691e41 −1.37415
\(698\) −3.37038e39 −0.0195783
\(699\) 2.77563e41 7.86726e40i 1.57922 0.447615i
\(700\) −1.41412e39 6.76795e38i −0.00788069 0.00377168i
\(701\) 1.20046e41i 0.655293i 0.944800 + 0.327647i \(0.106256\pi\)
−0.944800 + 0.327647i \(0.893744\pi\)
\(702\) 4.90632e39 + 4.49982e39i 0.0262342 + 0.0240606i
\(703\) 1.03133e41i 0.540186i
\(704\) 2.47963e41i 1.27228i
\(705\) −6.70031e40 2.36392e41i −0.336785 1.18820i
\(706\) 2.08139e40i 0.102491i
\(707\) −2.21762e41 1.06135e41i −1.06981 0.512008i
\(708\) 3.35199e40 + 1.18261e41i 0.158424 + 0.558932i
\(709\) −2.47898e41 −1.14790 −0.573948 0.818892i \(-0.694589\pi\)
−0.573948 + 0.818892i \(0.694589\pi\)
\(710\) 1.00233e40 0.0454740
\(711\) 2.40166e41 1.48038e41i 1.06758 0.658059i
\(712\) 2.17952e40i 0.0949296i
\(713\) −1.66921e41 −0.712384
\(714\) −2.76834e40 4.75730e39i −0.115770 0.0198946i
\(715\) 1.61101e41 0.660176
\(716\) 4.89630e41i 1.96621i
\(717\) −1.87290e41 + 5.30855e40i −0.737033 + 0.208905i
\(718\) −8.20719e39 −0.0316512
\(719\) 1.70882e41 0.645843 0.322921 0.946426i \(-0.395335\pi\)
0.322921 + 0.946426i \(0.395335\pi\)
\(720\) −2.27338e41 + 1.40132e41i −0.842076 + 0.519057i
\(721\) −8.23675e40 + 1.72102e41i −0.299016 + 0.624775i
\(722\) 9.06382e39i 0.0322494i
\(723\) 5.46417e41 1.54877e41i 1.90554 0.540108i
\(724\) 3.60471e41i 1.23214i
\(725\) 4.51285e39i 0.0151199i
\(726\) 1.50048e40 4.25297e39i 0.0492777 0.0139673i
\(727\) 1.00781e41i 0.324437i −0.986755 0.162219i \(-0.948135\pi\)
0.986755 0.162219i \(-0.0518650\pi\)
\(728\) 2.02986e40 + 9.71485e39i 0.0640560 + 0.0306571i
\(729\) 2.78880e40 + 3.22053e41i 0.0862716 + 0.996272i
\(730\) −1.64693e39 −0.00499453
\(731\) 8.36280e41 2.48628
\(732\) 3.84740e41 1.09051e41i 1.12139 0.317847i
\(733\) 2.15111e39i 0.00614689i 0.999995 + 0.00307345i \(0.000978310\pi\)
−0.999995 + 0.00307345i \(0.999022\pi\)
\(734\) −3.06283e40 −0.0858084
\(735\) −2.11431e41 + 2.98322e41i −0.580769 + 0.819444i
\(736\) 8.50627e40 0.229092
\(737\) 3.88003e40i 0.102461i
\(738\) −1.19656e40 1.94121e40i −0.0309826 0.0502638i
\(739\) −3.98177e41 −1.01095 −0.505477 0.862840i \(-0.668684\pi\)
−0.505477 + 0.862840i \(0.668684\pi\)
\(740\) −1.79818e41 −0.447685
\(741\) −6.74833e40 2.38087e41i −0.164753 0.581261i
\(742\) 2.94079e40 + 1.40746e40i 0.0704057 + 0.0336960i
\(743\) 2.27165e40i 0.0533338i −0.999644 0.0266669i \(-0.991511\pi\)
0.999644 0.0266669i \(-0.00848935\pi\)
\(744\) 1.10506e40 + 3.89874e40i 0.0254435 + 0.0897669i
\(745\) 1.16978e41i 0.264143i
\(746\) 3.82513e40i 0.0847098i
\(747\) 4.15786e41 2.56291e41i 0.903069 0.556652i
\(748\) 1.01307e42i 2.15807i
\(749\) 2.98821e40 6.24368e40i 0.0624346 0.130453i
\(750\) 3.32055e40 9.41178e39i 0.0680491 0.0192878i
\(751\) −4.42565e41 −0.889606 −0.444803 0.895628i \(-0.646726\pi\)
−0.444803 + 0.895628i \(0.646726\pi\)
\(752\) −6.14209e41 −1.21104
\(753\) 9.23286e40 + 3.25743e41i 0.178570 + 0.630010i