Properties

Label 177.11.c.a.58.12
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.12
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.89

$q$-expansion

\(f(q)\) \(=\) \(q-51.4146i q^{2} -140.296 q^{3} -1619.46 q^{4} -2372.07 q^{5} +7213.27i q^{6} +15485.2 q^{7} +30615.5i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-51.4146i q^{2} -140.296 q^{3} -1619.46 q^{4} -2372.07 q^{5} +7213.27i q^{6} +15485.2 q^{7} +30615.5i q^{8} +19683.0 q^{9} +121959. i q^{10} -207798. i q^{11} +227204. q^{12} +9463.66i q^{13} -796164. i q^{14} +332792. q^{15} -84244.9 q^{16} +393426. q^{17} -1.01199e6i q^{18} -3.27325e6 q^{19} +3.84147e6 q^{20} -2.17251e6 q^{21} -1.06839e7 q^{22} -3.87647e6i q^{23} -4.29524e6i q^{24} -4.13893e6 q^{25} +486571. q^{26} -2.76145e6 q^{27} -2.50777e7 q^{28} +1.36358e7 q^{29} -1.71104e7i q^{30} +2.27647e7i q^{31} +3.56817e7i q^{32} +2.91533e7i q^{33} -2.02279e7i q^{34} -3.67318e7 q^{35} -3.18759e7 q^{36} +8.26010e7i q^{37} +1.68293e8i q^{38} -1.32772e6i q^{39} -7.26220e7i q^{40} -1.06754e8 q^{41} +1.11699e8i q^{42} -7.40752e7i q^{43} +3.36521e8i q^{44} -4.66894e7 q^{45} -1.99307e8 q^{46} +2.11955e7i q^{47} +1.18192e7 q^{48} -4.26846e7 q^{49} +2.12802e8i q^{50} -5.51962e7 q^{51} -1.53261e7i q^{52} +2.58725e7 q^{53} +1.41979e8i q^{54} +4.92911e8i q^{55} +4.74087e8i q^{56} +4.59224e8 q^{57} -7.01080e8i q^{58} +(-5.38229e8 - 4.70560e8i) q^{59} -5.38944e8 q^{60} +1.35826e9i q^{61} +1.17044e9 q^{62} +3.04795e8 q^{63} +1.74830e9 q^{64} -2.24484e7i q^{65} +1.49890e9 q^{66} -1.48600e9i q^{67} -6.37140e8 q^{68} +5.43854e8i q^{69} +1.88855e9i q^{70} -8.76816e8 q^{71} +6.02605e8i q^{72} -8.52461e8i q^{73} +4.24690e9 q^{74} +5.80676e8 q^{75} +5.30091e9 q^{76} -3.21779e9i q^{77} -6.82640e7 q^{78} -9.09746e7 q^{79} +1.99834e8 q^{80} +3.87420e8 q^{81} +5.48872e9i q^{82} +1.22363e8i q^{83} +3.51830e9 q^{84} -9.33233e8 q^{85} -3.80855e9 q^{86} -1.91305e9 q^{87} +6.36185e9 q^{88} -5.23788e8i q^{89} +2.40052e9i q^{90} +1.46546e8i q^{91} +6.27780e9i q^{92} -3.19380e9i q^{93} +1.08976e9 q^{94} +7.76436e9 q^{95} -5.00601e9i q^{96} +6.29776e9i q^{97} +2.19462e9i q^{98} -4.09009e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 51.4146i 1.60671i −0.595502 0.803353i \(-0.703047\pi\)
0.595502 0.803353i \(-0.296953\pi\)
\(3\) −140.296 −0.577350
\(4\) −1619.46 −1.58151
\(5\) −2372.07 −0.759061 −0.379530 0.925179i \(-0.623914\pi\)
−0.379530 + 0.925179i \(0.623914\pi\)
\(6\) 7213.27i 0.927633i
\(7\) 15485.2 0.921353 0.460676 0.887568i \(-0.347607\pi\)
0.460676 + 0.887568i \(0.347607\pi\)
\(8\) 30615.5i 0.934312i
\(9\) 19683.0 0.333333
\(10\) 121959.i 1.21959i
\(11\) 207798.i 1.29026i −0.764072 0.645131i \(-0.776803\pi\)
0.764072 0.645131i \(-0.223197\pi\)
\(12\) 227204. 0.913084
\(13\) 9463.66i 0.0254884i 0.999919 + 0.0127442i \(0.00405671\pi\)
−0.999919 + 0.0127442i \(0.995943\pi\)
\(14\) 796164.i 1.48034i
\(15\) 332792. 0.438244
\(16\) −84244.9 −0.0803422
\(17\) 393426. 0.277089 0.138544 0.990356i \(-0.455758\pi\)
0.138544 + 0.990356i \(0.455758\pi\)
\(18\) 1.01199e6i 0.535569i
\(19\) −3.27325e6 −1.32194 −0.660969 0.750413i \(-0.729855\pi\)
−0.660969 + 0.750413i \(0.729855\pi\)
\(20\) 3.84147e6 1.20046
\(21\) −2.17251e6 −0.531943
\(22\) −1.06839e7 −2.07307
\(23\) 3.87647e6i 0.602278i −0.953580 0.301139i \(-0.902633\pi\)
0.953580 0.301139i \(-0.0973669\pi\)
\(24\) 4.29524e6i 0.539425i
\(25\) −4.13893e6 −0.423827
\(26\) 486571. 0.0409524
\(27\) −2.76145e6 −0.192450
\(28\) −2.50777e7 −1.45713
\(29\) 1.36358e7 0.664800 0.332400 0.943139i \(-0.392142\pi\)
0.332400 + 0.943139i \(0.392142\pi\)
\(30\) 1.71104e7i 0.704130i
\(31\) 2.27647e7i 0.795158i 0.917568 + 0.397579i \(0.130150\pi\)
−0.917568 + 0.397579i \(0.869850\pi\)
\(32\) 3.56817e7i 1.06340i
\(33\) 2.91533e7i 0.744934i
\(34\) 2.02279e7i 0.445200i
\(35\) −3.67318e7 −0.699363
\(36\) −3.18759e7 −0.527169
\(37\) 8.26010e7i 1.19118i 0.803289 + 0.595589i \(0.203081\pi\)
−0.803289 + 0.595589i \(0.796919\pi\)
\(38\) 1.68293e8i 2.12397i
\(39\) 1.32772e6i 0.0147157i
\(40\) 7.26220e7i 0.709199i
\(41\) −1.06754e8 −0.921437 −0.460718 0.887546i \(-0.652408\pi\)
−0.460718 + 0.887546i \(0.652408\pi\)
\(42\) 1.11699e8i 0.854677i
\(43\) 7.40752e7i 0.503884i −0.967742 0.251942i \(-0.918931\pi\)
0.967742 0.251942i \(-0.0810692\pi\)
\(44\) 3.36521e8i 2.04056i
\(45\) −4.66894e7 −0.253020
\(46\) −1.99307e8 −0.967685
\(47\) 2.11955e7i 0.0924176i 0.998932 + 0.0462088i \(0.0147140\pi\)
−0.998932 + 0.0462088i \(0.985286\pi\)
\(48\) 1.18192e7 0.0463856
\(49\) −4.26846e7 −0.151109
\(50\) 2.12802e8i 0.680965i
\(51\) −5.51962e7 −0.159977
\(52\) 1.53261e7i 0.0403101i
\(53\) 2.58725e7 0.0618671 0.0309335 0.999521i \(-0.490152\pi\)
0.0309335 + 0.999521i \(0.490152\pi\)
\(54\) 1.41979e8i 0.309211i
\(55\) 4.92911e8i 0.979388i
\(56\) 4.74087e8i 0.860830i
\(57\) 4.59224e8 0.763221
\(58\) 7.01080e8i 1.06814i
\(59\) −5.38229e8 4.70560e8i −0.752847 0.658195i
\(60\) −5.38944e8 −0.693086
\(61\) 1.35826e9i 1.60818i 0.594509 + 0.804089i \(0.297347\pi\)
−0.594509 + 0.804089i \(0.702653\pi\)
\(62\) 1.17044e9 1.27759
\(63\) 3.04795e8 0.307118
\(64\) 1.74830e9 1.62823
\(65\) 2.24484e7i 0.0193472i
\(66\) 1.49890e9 1.19689
\(67\) 1.48600e9i 1.10064i −0.834953 0.550321i \(-0.814505\pi\)
0.834953 0.550321i \(-0.185495\pi\)
\(68\) −6.37140e8 −0.438218
\(69\) 5.43854e8i 0.347726i
\(70\) 1.88855e9i 1.12367i
\(71\) −8.76816e8 −0.485978 −0.242989 0.970029i \(-0.578128\pi\)
−0.242989 + 0.970029i \(0.578128\pi\)
\(72\) 6.02605e8i 0.311437i
\(73\) 8.52461e8i 0.411207i −0.978635 0.205603i \(-0.934084\pi\)
0.978635 0.205603i \(-0.0659157\pi\)
\(74\) 4.24690e9 1.91387
\(75\) 5.80676e8 0.244696
\(76\) 5.30091e9 2.09065
\(77\) 3.21779e9i 1.18879i
\(78\) −6.82640e7 −0.0236439
\(79\) −9.09746e7 −0.0295655 −0.0147827 0.999891i \(-0.504706\pi\)
−0.0147827 + 0.999891i \(0.504706\pi\)
\(80\) 1.99834e8 0.0609846
\(81\) 3.87420e8 0.111111
\(82\) 5.48872e9i 1.48048i
\(83\) 1.22363e8i 0.0310642i 0.999879 + 0.0155321i \(0.00494423\pi\)
−0.999879 + 0.0155321i \(0.995056\pi\)
\(84\) 3.51830e9 0.841272
\(85\) −9.33233e8 −0.210327
\(86\) −3.80855e9 −0.809594
\(87\) −1.91305e9 −0.383822
\(88\) 6.36185e9 1.20551
\(89\) 5.23788e8i 0.0938005i −0.998900 0.0469002i \(-0.985066\pi\)
0.998900 0.0469002i \(-0.0149343\pi\)
\(90\) 2.40052e9i 0.406529i
\(91\) 1.46546e8i 0.0234838i
\(92\) 6.27780e9i 0.952508i
\(93\) 3.19380e9i 0.459085i
\(94\) 1.08976e9 0.148488
\(95\) 7.76436e9 1.00343
\(96\) 5.00601e9i 0.613953i
\(97\) 6.29776e9i 0.733377i 0.930344 + 0.366689i \(0.119509\pi\)
−0.930344 + 0.366689i \(0.880491\pi\)
\(98\) 2.19462e9i 0.242788i
\(99\) 4.09009e9i 0.430088i
\(100\) 6.70285e9 0.670285
\(101\) 9.07488e9i 0.863444i 0.902007 + 0.431722i \(0.142094\pi\)
−0.902007 + 0.431722i \(0.857906\pi\)
\(102\) 2.83789e9i 0.257037i
\(103\) 5.43941e9i 0.469209i 0.972091 + 0.234604i \(0.0753794\pi\)
−0.972091 + 0.234604i \(0.924621\pi\)
\(104\) −2.89735e8 −0.0238141
\(105\) 5.15333e9 0.403777
\(106\) 1.33023e9i 0.0994023i
\(107\) 6.07134e8 0.0432878 0.0216439 0.999766i \(-0.493110\pi\)
0.0216439 + 0.999766i \(0.493110\pi\)
\(108\) 4.47206e9 0.304361
\(109\) 8.52551e9i 0.554100i −0.960856 0.277050i \(-0.910643\pi\)
0.960856 0.277050i \(-0.0893568\pi\)
\(110\) 2.53428e10 1.57359
\(111\) 1.15886e10i 0.687727i
\(112\) −1.30455e9 −0.0740235
\(113\) 2.98035e10i 1.61762i 0.588072 + 0.808808i \(0.299887\pi\)
−0.588072 + 0.808808i \(0.700113\pi\)
\(114\) 2.36108e10i 1.22627i
\(115\) 9.19524e9i 0.457166i
\(116\) −2.20827e10 −1.05139
\(117\) 1.86273e8i 0.00849613i
\(118\) −2.41937e10 + 2.76728e10i −1.05753 + 1.20960i
\(119\) 6.09228e9 0.255296
\(120\) 1.01886e10i 0.409456i
\(121\) −1.72426e10 −0.664779
\(122\) 6.98345e10 2.58387
\(123\) 1.49772e10 0.531992
\(124\) 3.68666e10i 1.25755i
\(125\) 3.29825e10 1.08077
\(126\) 1.56709e10i 0.493448i
\(127\) −8.16922e9 −0.247265 −0.123632 0.992328i \(-0.539454\pi\)
−0.123632 + 0.992328i \(0.539454\pi\)
\(128\) 5.33499e10i 1.55269i
\(129\) 1.03925e10i 0.290918i
\(130\) −1.15418e9 −0.0310854
\(131\) 2.12207e10i 0.550051i −0.961437 0.275025i \(-0.911314\pi\)
0.961437 0.275025i \(-0.0886863\pi\)
\(132\) 4.72127e10i 1.17812i
\(133\) −5.06868e10 −1.21797
\(134\) −7.64024e10 −1.76841
\(135\) 6.55034e9 0.146081
\(136\) 1.20450e10i 0.258887i
\(137\) 6.03369e10 1.25020 0.625101 0.780544i \(-0.285058\pi\)
0.625101 + 0.780544i \(0.285058\pi\)
\(138\) 2.79620e10 0.558693
\(139\) −2.81739e10 −0.542966 −0.271483 0.962443i \(-0.587514\pi\)
−0.271483 + 0.962443i \(0.587514\pi\)
\(140\) 5.94859e10 1.10605
\(141\) 2.97365e9i 0.0533573i
\(142\) 4.50812e10i 0.780825i
\(143\) 1.96653e9 0.0328867
\(144\) −1.65819e9 −0.0267807
\(145\) −3.23450e10 −0.504623
\(146\) −4.38290e10 −0.660689
\(147\) 5.98849e9 0.0872430
\(148\) 1.33769e11i 1.88386i
\(149\) 3.53969e10i 0.481985i −0.970527 0.240993i \(-0.922527\pi\)
0.970527 0.240993i \(-0.0774730\pi\)
\(150\) 2.98552e10i 0.393155i
\(151\) 7.55219e10i 0.962029i −0.876713 0.481015i \(-0.840268\pi\)
0.876713 0.481015i \(-0.159732\pi\)
\(152\) 1.00212e11i 1.23510i
\(153\) 7.74381e9 0.0923629
\(154\) −1.65441e11 −1.91003
\(155\) 5.39994e10i 0.603574i
\(156\) 2.15019e9i 0.0232730i
\(157\) 7.86464e10i 0.824481i −0.911075 0.412240i \(-0.864746\pi\)
0.911075 0.412240i \(-0.135254\pi\)
\(158\) 4.67742e9i 0.0475030i
\(159\) −3.62982e9 −0.0357190
\(160\) 8.46394e10i 0.807184i
\(161\) 6.00278e10i 0.554911i
\(162\) 1.99191e10i 0.178523i
\(163\) 1.75024e11 1.52110 0.760552 0.649277i \(-0.224928\pi\)
0.760552 + 0.649277i \(0.224928\pi\)
\(164\) 1.72884e11 1.45726
\(165\) 6.91535e10i 0.565450i
\(166\) 6.29126e9 0.0499111
\(167\) −9.22995e9 −0.0710586 −0.0355293 0.999369i \(-0.511312\pi\)
−0.0355293 + 0.999369i \(0.511312\pi\)
\(168\) 6.65125e10i 0.497001i
\(169\) 1.37769e11 0.999350
\(170\) 4.79818e10i 0.337934i
\(171\) −6.44274e10 −0.440646
\(172\) 1.19962e11i 0.796896i
\(173\) 5.92302e10i 0.382219i −0.981569 0.191110i \(-0.938791\pi\)
0.981569 0.191110i \(-0.0612086\pi\)
\(174\) 9.83588e10i 0.616690i
\(175\) −6.40921e10 −0.390494
\(176\) 1.75059e10i 0.103663i
\(177\) 7.55114e10 + 6.60177e10i 0.434657 + 0.380009i
\(178\) −2.69303e10 −0.150710
\(179\) 2.00252e11i 1.08971i 0.838530 + 0.544855i \(0.183415\pi\)
−0.838530 + 0.544855i \(0.816585\pi\)
\(180\) 7.56117e10 0.400153
\(181\) −1.09128e11 −0.561750 −0.280875 0.959744i \(-0.590625\pi\)
−0.280875 + 0.959744i \(0.590625\pi\)
\(182\) 7.53463e9 0.0377316
\(183\) 1.90559e11i 0.928482i
\(184\) 1.18680e11 0.562716
\(185\) 1.95935e11i 0.904177i
\(186\) −1.64208e11 −0.737615
\(187\) 8.17533e10i 0.357517i
\(188\) 3.43254e10i 0.146159i
\(189\) −4.27615e10 −0.177314
\(190\) 3.99202e11i 1.61222i
\(191\) 2.66205e11i 1.04725i −0.851950 0.523623i \(-0.824580\pi\)
0.851950 0.523623i \(-0.175420\pi\)
\(192\) −2.45279e11 −0.940057
\(193\) 1.58248e11 0.590952 0.295476 0.955350i \(-0.404522\pi\)
0.295476 + 0.955350i \(0.404522\pi\)
\(194\) 3.23797e11 1.17832
\(195\) 3.14943e9i 0.0111701i
\(196\) 6.91262e10 0.238981
\(197\) 3.48221e11 1.17361 0.586806 0.809728i \(-0.300385\pi\)
0.586806 + 0.809728i \(0.300385\pi\)
\(198\) −2.10290e11 −0.691025
\(199\) −3.62970e11 −1.16307 −0.581534 0.813522i \(-0.697547\pi\)
−0.581534 + 0.813522i \(0.697547\pi\)
\(200\) 1.26716e11i 0.395986i
\(201\) 2.08481e11i 0.635456i
\(202\) 4.66581e11 1.38730
\(203\) 2.11153e11 0.612515
\(204\) 8.93882e10 0.253005
\(205\) 2.53228e11 0.699426
\(206\) 2.79665e11 0.753881
\(207\) 7.63006e10i 0.200759i
\(208\) 7.97266e8i 0.00204779i
\(209\) 6.80175e11i 1.70565i
\(210\) 2.64957e11i 0.648752i
\(211\) 3.43143e11i 0.820471i −0.911980 0.410236i \(-0.865446\pi\)
0.911980 0.410236i \(-0.134554\pi\)
\(212\) −4.18996e10 −0.0978433
\(213\) 1.23014e11 0.280580
\(214\) 3.12156e10i 0.0695509i
\(215\) 1.75711e11i 0.382479i
\(216\) 8.45432e10i 0.179808i
\(217\) 3.52516e11i 0.732621i
\(218\) −4.38336e11 −0.890276
\(219\) 1.19597e11i 0.237410i
\(220\) 7.98251e11i 1.54891i
\(221\) 3.72325e9i 0.00706255i
\(222\) −5.95824e11 −1.10498
\(223\) −1.45253e11 −0.263391 −0.131695 0.991290i \(-0.542042\pi\)
−0.131695 + 0.991290i \(0.542042\pi\)
\(224\) 5.52538e11i 0.979765i
\(225\) −8.14666e10 −0.141276
\(226\) 1.53234e12 2.59904
\(227\) 8.25512e11i 1.36960i 0.728731 + 0.684801i \(0.240111\pi\)
−0.728731 + 0.684801i \(0.759889\pi\)
\(228\) −7.43697e11 −1.20704
\(229\) 2.38084e11i 0.378052i 0.981972 + 0.189026i \(0.0605331\pi\)
−0.981972 + 0.189026i \(0.939467\pi\)
\(230\) 4.72770e11 0.734532
\(231\) 4.51443e11i 0.686347i
\(232\) 4.17467e11i 0.621130i
\(233\) 1.15231e12i 1.67799i 0.544140 + 0.838994i \(0.316856\pi\)
−0.544140 + 0.838994i \(0.683144\pi\)
\(234\) 9.57717e9 0.0136508
\(235\) 5.02772e10i 0.0701506i
\(236\) 8.71642e11 + 7.62054e11i 1.19063 + 1.04094i
\(237\) 1.27634e10 0.0170696
\(238\) 3.13232e11i 0.410187i
\(239\) 5.78195e11 0.741455 0.370728 0.928742i \(-0.379108\pi\)
0.370728 + 0.928742i \(0.379108\pi\)
\(240\) −2.80360e10 −0.0352095
\(241\) 4.61412e11 0.567550 0.283775 0.958891i \(-0.408413\pi\)
0.283775 + 0.958891i \(0.408413\pi\)
\(242\) 8.86524e11i 1.06810i
\(243\) −5.43536e10 −0.0641500
\(244\) 2.19965e12i 2.54335i
\(245\) 1.01251e11 0.114701
\(246\) 7.70047e11i 0.854755i
\(247\) 3.09769e10i 0.0336941i
\(248\) −6.96954e11 −0.742926
\(249\) 1.71671e10i 0.0179349i
\(250\) 1.69578e12i 1.73648i
\(251\) −7.89068e10 −0.0792038 −0.0396019 0.999216i \(-0.512609\pi\)
−0.0396019 + 0.999216i \(0.512609\pi\)
\(252\) −4.93604e11 −0.485709
\(253\) −8.05523e11 −0.777098
\(254\) 4.20017e11i 0.397282i
\(255\) 1.30929e11 0.121432
\(256\) −9.52708e11 −0.866483
\(257\) 1.38822e12 1.23821 0.619104 0.785309i \(-0.287496\pi\)
0.619104 + 0.785309i \(0.287496\pi\)
\(258\) 5.34325e11 0.467419
\(259\) 1.27909e12i 1.09750i
\(260\) 3.63544e10i 0.0305978i
\(261\) 2.68394e11 0.221600
\(262\) −1.09105e12 −0.883771
\(263\) 2.06493e12 1.64107 0.820535 0.571596i \(-0.193676\pi\)
0.820535 + 0.571596i \(0.193676\pi\)
\(264\) −8.92543e11 −0.696000
\(265\) −6.13714e10 −0.0469609
\(266\) 2.60604e12i 1.95692i
\(267\) 7.34854e10i 0.0541557i
\(268\) 2.40653e12i 1.74067i
\(269\) 7.98504e10i 0.0566912i 0.999598 + 0.0283456i \(0.00902390\pi\)
−0.999598 + 0.0283456i \(0.990976\pi\)
\(270\) 3.36783e11i 0.234710i
\(271\) 8.27816e11 0.566353 0.283177 0.959068i \(-0.408612\pi\)
0.283177 + 0.959068i \(0.408612\pi\)
\(272\) −3.31442e10 −0.0222619
\(273\) 2.05599e10i 0.0135584i
\(274\) 3.10220e12i 2.00871i
\(275\) 8.60062e11i 0.546848i
\(276\) 8.80751e11i 0.549931i
\(277\) 2.75212e12 1.68760 0.843799 0.536659i \(-0.180314\pi\)
0.843799 + 0.536659i \(0.180314\pi\)
\(278\) 1.44855e12i 0.872387i
\(279\) 4.48078e11i 0.265053i
\(280\) 1.12456e12i 0.653423i
\(281\) −9.85832e10 −0.0562693 −0.0281346 0.999604i \(-0.508957\pi\)
−0.0281346 + 0.999604i \(0.508957\pi\)
\(282\) −1.52889e11 −0.0857296
\(283\) 8.55168e11i 0.471107i 0.971861 + 0.235553i \(0.0756902\pi\)
−0.971861 + 0.235553i \(0.924310\pi\)
\(284\) 1.41997e12 0.768578
\(285\) −1.08931e12 −0.579331
\(286\) 1.01108e11i 0.0528393i
\(287\) −1.65311e12 −0.848968
\(288\) 7.02323e11i 0.354466i
\(289\) −1.86121e12 −0.923222
\(290\) 1.66301e12i 0.810782i
\(291\) 8.83551e11i 0.423416i
\(292\) 1.38053e12i 0.650326i
\(293\) 3.40558e12 1.57708 0.788538 0.614986i \(-0.210838\pi\)
0.788538 + 0.614986i \(0.210838\pi\)
\(294\) 3.07896e11i 0.140174i
\(295\) 1.27671e12 + 1.11620e12i 0.571457 + 0.499610i
\(296\) −2.52887e12 −1.11293
\(297\) 5.73824e11i 0.248311i
\(298\) −1.81992e12 −0.774409
\(299\) 3.66856e10 0.0153511
\(300\) −9.40384e11 −0.386989
\(301\) 1.14707e12i 0.464255i
\(302\) −3.88293e12 −1.54570
\(303\) 1.27317e12i 0.498509i
\(304\) 2.75755e11 0.106207
\(305\) 3.22188e12i 1.22071i
\(306\) 3.98145e11i 0.148400i
\(307\) −3.76502e12 −1.38062 −0.690312 0.723512i \(-0.742527\pi\)
−0.690312 + 0.723512i \(0.742527\pi\)
\(308\) 5.21109e12i 1.88008i
\(309\) 7.63128e11i 0.270898i
\(310\) −2.77636e12 −0.969766
\(311\) −5.66700e12 −1.94783 −0.973915 0.226912i \(-0.927137\pi\)
−0.973915 + 0.226912i \(0.927137\pi\)
\(312\) 4.06487e10 0.0137491
\(313\) 1.16286e12i 0.387084i 0.981092 + 0.193542i \(0.0619976\pi\)
−0.981092 + 0.193542i \(0.938002\pi\)
\(314\) −4.04358e12 −1.32470
\(315\) −7.22993e11 −0.233121
\(316\) 1.47330e11 0.0467580
\(317\) −1.75108e12 −0.547028 −0.273514 0.961868i \(-0.588186\pi\)
−0.273514 + 0.961868i \(0.588186\pi\)
\(318\) 1.86626e11i 0.0573899i
\(319\) 2.83350e12i 0.857766i
\(320\) −4.14707e12 −1.23592
\(321\) −8.51786e10 −0.0249922
\(322\) −3.08631e12 −0.891579
\(323\) −1.28778e12 −0.366294
\(324\) −6.27413e11 −0.175723
\(325\) 3.91695e10i 0.0108027i
\(326\) 8.99878e12i 2.44397i
\(327\) 1.19610e12i 0.319910i
\(328\) 3.26833e12i 0.860909i
\(329\) 3.28216e11i 0.0851492i
\(330\) −3.55550e12 −0.908512
\(331\) −6.66533e12 −1.67758 −0.838788 0.544459i \(-0.816735\pi\)
−0.838788 + 0.544459i \(0.816735\pi\)
\(332\) 1.98163e11i 0.0491283i
\(333\) 1.62584e12i 0.397059i
\(334\) 4.74554e11i 0.114170i
\(335\) 3.52490e12i 0.835454i
\(336\) 1.83023e11 0.0427375
\(337\) 3.31280e12i 0.762160i 0.924542 + 0.381080i \(0.124448\pi\)
−0.924542 + 0.381080i \(0.875552\pi\)
\(338\) 7.08334e12i 1.60566i
\(339\) 4.18132e12i 0.933931i
\(340\) 1.51134e12 0.332634
\(341\) 4.73046e12 1.02596
\(342\) 3.31251e12i 0.707989i
\(343\) −5.03516e12 −1.06058
\(344\) 2.26785e12 0.470785
\(345\) 1.29006e12i 0.263945i
\(346\) −3.04530e12 −0.614114
\(347\) 4.81033e12i 0.956153i 0.878318 + 0.478076i \(0.158666\pi\)
−0.878318 + 0.478076i \(0.841334\pi\)
\(348\) 3.09812e12 0.607018
\(349\) 1.57464e12i 0.304126i 0.988371 + 0.152063i \(0.0485917\pi\)
−0.988371 + 0.152063i \(0.951408\pi\)
\(350\) 3.29527e12i 0.627409i
\(351\) 2.61334e10i 0.00490524i
\(352\) 7.41459e12 1.37206
\(353\) 2.26537e12i 0.413300i 0.978415 + 0.206650i \(0.0662562\pi\)
−0.978415 + 0.206650i \(0.933744\pi\)
\(354\) 3.39428e12 3.88239e12i 0.610563 0.698366i
\(355\) 2.07987e12 0.368887
\(356\) 8.48255e11i 0.148346i
\(357\) −8.54723e11 −0.147395
\(358\) 1.02959e13 1.75084
\(359\) 6.50960e12 1.09165 0.545824 0.837900i \(-0.316217\pi\)
0.545824 + 0.837900i \(0.316217\pi\)
\(360\) 1.42942e12i 0.236400i
\(361\) 4.58309e12 0.747520
\(362\) 5.61077e12i 0.902567i
\(363\) 2.41908e12 0.383810
\(364\) 2.37327e11i 0.0371398i
\(365\) 2.02209e12i 0.312131i
\(366\) −9.79751e12 −1.49180
\(367\) 6.69893e12i 1.00618i 0.864234 + 0.503090i \(0.167803\pi\)
−0.864234 + 0.503090i \(0.832197\pi\)
\(368\) 3.26573e11i 0.0483884i
\(369\) −2.10124e12 −0.307146
\(370\) −1.00739e13 −1.45275
\(371\) 4.00641e11 0.0570014
\(372\) 5.17224e12i 0.726046i
\(373\) 2.32947e12 0.322635 0.161318 0.986903i \(-0.448426\pi\)
0.161318 + 0.986903i \(0.448426\pi\)
\(374\) −4.20331e12 −0.574426
\(375\) −4.62732e12 −0.623983
\(376\) −6.48912e11 −0.0863469
\(377\) 1.29045e11i 0.0169447i
\(378\) 2.19857e12i 0.284892i
\(379\) 1.03290e13 1.32087 0.660436 0.750882i \(-0.270371\pi\)
0.660436 + 0.750882i \(0.270371\pi\)
\(380\) −1.25741e13 −1.58693
\(381\) 1.14611e12 0.142758
\(382\) −1.36868e13 −1.68262
\(383\) 1.21823e13 1.47820 0.739102 0.673594i \(-0.235250\pi\)
0.739102 + 0.673594i \(0.235250\pi\)
\(384\) 7.48478e12i 0.896443i
\(385\) 7.63281e12i 0.902362i
\(386\) 8.13627e12i 0.949486i
\(387\) 1.45802e12i 0.167961i
\(388\) 1.01990e13i 1.15984i
\(389\) 1.17149e13 1.31520 0.657599 0.753368i \(-0.271572\pi\)
0.657599 + 0.753368i \(0.271572\pi\)
\(390\) 1.61927e11 0.0179471
\(391\) 1.52511e12i 0.166885i
\(392\) 1.30681e12i 0.141183i
\(393\) 2.97718e12i 0.317572i
\(394\) 1.79037e13i 1.88565i
\(395\) 2.15798e11 0.0224420
\(396\) 6.62375e12i 0.680187i
\(397\) 8.14478e12i 0.825899i −0.910754 0.412950i \(-0.864499\pi\)
0.910754 0.412950i \(-0.135501\pi\)
\(398\) 1.86620e13i 1.86871i
\(399\) 7.11117e12 0.703196
\(400\) 3.48684e11 0.0340512
\(401\) 9.47598e12i 0.913907i −0.889491 0.456954i \(-0.848941\pi\)
0.889491 0.456954i \(-0.151059\pi\)
\(402\) 1.07190e13 1.02099
\(403\) −2.15438e11 −0.0202673
\(404\) 1.46964e13i 1.36554i
\(405\) −9.18987e11 −0.0843401
\(406\) 1.08563e13i 0.984132i
\(407\) 1.71643e13 1.53693
\(408\) 1.68986e12i 0.149469i
\(409\) 1.12656e12i 0.0984326i 0.998788 + 0.0492163i \(0.0156724\pi\)
−0.998788 + 0.0492163i \(0.984328\pi\)
\(410\) 1.30196e13i 1.12377i
\(411\) −8.46503e12 −0.721804
\(412\) 8.80893e12i 0.742057i
\(413\) −8.33457e12 7.28670e12i −0.693638 0.606430i
\(414\) −3.92297e12 −0.322562
\(415\) 2.90254e11i 0.0235796i
\(416\) −3.37680e11 −0.0271043
\(417\) 3.95268e12 0.313481
\(418\) 3.49709e13 2.74048
\(419\) 2.01771e13i 1.56239i 0.624289 + 0.781193i \(0.285389\pi\)
−0.624289 + 0.781193i \(0.714611\pi\)
\(420\) −8.34564e12 −0.638577
\(421\) 1.04111e13i 0.787199i 0.919282 + 0.393600i \(0.128770\pi\)
−0.919282 + 0.393600i \(0.871230\pi\)
\(422\) −1.76426e13 −1.31826
\(423\) 4.17191e11i 0.0308059i
\(424\) 7.92101e11i 0.0578031i
\(425\) −1.62836e12 −0.117438
\(426\) 6.32471e12i 0.450809i
\(427\) 2.10329e13i 1.48170i
\(428\) −9.83232e11 −0.0684600
\(429\) −2.75897e11 −0.0189872
\(430\) 9.03413e12 0.614531
\(431\) 1.69638e13i 1.14061i 0.821433 + 0.570305i \(0.193175\pi\)
−0.821433 + 0.570305i \(0.806825\pi\)
\(432\) 2.32638e11 0.0154619
\(433\) 1.53769e13 1.01025 0.505127 0.863045i \(-0.331446\pi\)
0.505127 + 0.863045i \(0.331446\pi\)
\(434\) 1.81245e13 1.17711
\(435\) 4.53788e12 0.291344
\(436\) 1.38068e13i 0.876313i
\(437\) 1.26887e13i 0.796175i
\(438\) 6.14903e12 0.381449
\(439\) −1.65688e13 −1.01618 −0.508088 0.861305i \(-0.669648\pi\)
−0.508088 + 0.861305i \(0.669648\pi\)
\(440\) −1.50907e13 −0.915054
\(441\) −8.40162e11 −0.0503698
\(442\) 1.91430e11 0.0113474
\(443\) 8.43036e12i 0.494114i −0.969001 0.247057i \(-0.920536\pi\)
0.969001 0.247057i \(-0.0794636\pi\)
\(444\) 1.87673e13i 1.08765i
\(445\) 1.24246e12i 0.0712003i
\(446\) 7.46813e12i 0.423192i
\(447\) 4.96605e12i 0.278274i
\(448\) 2.70727e13 1.50017
\(449\) −2.91559e13 −1.59770 −0.798849 0.601531i \(-0.794558\pi\)
−0.798849 + 0.601531i \(0.794558\pi\)
\(450\) 4.18857e12i 0.226988i
\(451\) 2.21833e13i 1.18890i
\(452\) 4.82657e13i 2.55827i
\(453\) 1.05954e13i 0.555428i
\(454\) 4.24434e13 2.20055
\(455\) 3.47618e11i 0.0178256i
\(456\) 1.40594e13i 0.713086i
\(457\) 1.45565e13i 0.730259i 0.930957 + 0.365129i \(0.118975\pi\)
−0.930957 + 0.365129i \(0.881025\pi\)
\(458\) 1.22410e13 0.607420
\(459\) −1.08643e12 −0.0533257
\(460\) 1.48914e13i 0.723011i
\(461\) 7.73613e12 0.371552 0.185776 0.982592i \(-0.440520\pi\)
0.185776 + 0.982592i \(0.440520\pi\)
\(462\) 2.32108e13 1.10276
\(463\) 1.09254e13i 0.513490i 0.966479 + 0.256745i \(0.0826501\pi\)
−0.966479 + 0.256745i \(0.917350\pi\)
\(464\) −1.14875e12 −0.0534115
\(465\) 7.57590e12i 0.348473i
\(466\) 5.92455e13 2.69604
\(467\) 1.60922e13i 0.724488i −0.932083 0.362244i \(-0.882011\pi\)
0.932083 0.362244i \(-0.117989\pi\)
\(468\) 3.01663e11i 0.0134367i
\(469\) 2.30110e13i 1.01408i
\(470\) −2.58498e12 −0.112711
\(471\) 1.10338e13i 0.476014i
\(472\) 1.44064e13 1.64782e13i 0.614959 0.703394i
\(473\) −1.53927e13 −0.650143
\(474\) 6.56224e11i 0.0274259i
\(475\) 1.35478e13 0.560272
\(476\) −9.86622e12 −0.403753
\(477\) 5.09249e11 0.0206224
\(478\) 2.97277e13i 1.19130i
\(479\) −3.75735e13 −1.49006 −0.745031 0.667030i \(-0.767565\pi\)
−0.745031 + 0.667030i \(0.767565\pi\)
\(480\) 1.18746e13i 0.466028i
\(481\) −7.81708e11 −0.0303612
\(482\) 2.37233e13i 0.911886i
\(483\) 8.42167e12i 0.320378i
\(484\) 2.79238e13 1.05135
\(485\) 1.49387e13i 0.556678i
\(486\) 2.79457e12i 0.103070i
\(487\) −3.48485e13 −1.27215 −0.636076 0.771626i \(-0.719444\pi\)
−0.636076 + 0.771626i \(0.719444\pi\)
\(488\) −4.15839e13 −1.50254
\(489\) −2.45552e13 −0.878210
\(490\) 5.20577e12i 0.184291i
\(491\) −2.22606e13 −0.780061 −0.390031 0.920802i \(-0.627536\pi\)
−0.390031 + 0.920802i \(0.627536\pi\)
\(492\) −2.42550e13 −0.841349
\(493\) 5.36469e12 0.184208
\(494\) −1.59267e12 −0.0541365
\(495\) 9.70196e12i 0.326463i
\(496\) 1.91781e12i 0.0638848i
\(497\) −1.35777e13 −0.447757
\(498\) −8.82640e11 −0.0288162
\(499\) 4.69879e13 1.51874 0.759370 0.650659i \(-0.225507\pi\)
0.759370 + 0.650659i \(0.225507\pi\)
\(500\) −5.34140e13 −1.70925
\(501\) 1.29493e12 0.0410257
\(502\) 4.05697e12i 0.127257i
\(503\) 1.27426e13i 0.395748i 0.980227 + 0.197874i \(0.0634037\pi\)
−0.980227 + 0.197874i \(0.936596\pi\)
\(504\) 9.33145e12i 0.286943i
\(505\) 2.15262e13i 0.655406i
\(506\) 4.14157e13i 1.24857i
\(507\) −1.93284e13 −0.576975
\(508\) 1.32298e13 0.391051
\(509\) 5.19116e13i 1.51941i −0.650267 0.759706i \(-0.725343\pi\)
0.650267 0.759706i \(-0.274657\pi\)
\(510\) 6.73166e12i 0.195106i
\(511\) 1.32005e13i 0.378866i
\(512\) 5.64711e12i 0.160500i
\(513\) 9.03891e12 0.254407
\(514\) 7.13750e13i 1.98944i
\(515\) 1.29026e13i 0.356158i
\(516\) 1.68302e13i 0.460088i
\(517\) 4.40439e12 0.119243
\(518\) 6.57640e13 1.76335
\(519\) 8.30976e12i 0.220674i
\(520\) 6.87270e11 0.0180764
\(521\) −1.40221e13 −0.365278 −0.182639 0.983180i \(-0.558464\pi\)
−0.182639 + 0.983180i \(0.558464\pi\)
\(522\) 1.37994e13i 0.356046i
\(523\) −5.23571e13 −1.33803 −0.669017 0.743247i \(-0.733285\pi\)
−0.669017 + 0.743247i \(0.733285\pi\)
\(524\) 3.43661e13i 0.869909i
\(525\) 8.99187e12 0.225452
\(526\) 1.06168e14i 2.63672i
\(527\) 8.95624e12i 0.220329i
\(528\) 2.45602e12i 0.0598496i
\(529\) 2.63995e13 0.637261
\(530\) 3.15538e12i 0.0754524i
\(531\) −1.05940e13 9.26203e12i −0.250949 0.219398i
\(532\) 8.20855e13 1.92623
\(533\) 1.01029e12i 0.0234859i
\(534\) 3.77822e12 0.0870124
\(535\) −1.44016e12 −0.0328581
\(536\) 4.54948e13 1.02834
\(537\) 2.80945e13i 0.629144i
\(538\) 4.10548e12 0.0910862
\(539\) 8.86979e12i 0.194971i
\(540\) −1.06080e13 −0.231029
\(541\) 7.10673e13i 1.53350i −0.641947 0.766749i \(-0.721873\pi\)
0.641947 0.766749i \(-0.278127\pi\)
\(542\) 4.25618e13i 0.909963i
\(543\) 1.53102e13 0.324326
\(544\) 1.40381e13i 0.294656i
\(545\) 2.02231e13i 0.420596i
\(546\) −1.05708e12 −0.0217843
\(547\) −1.72935e13 −0.353140 −0.176570 0.984288i \(-0.556500\pi\)
−0.176570 + 0.984288i \(0.556500\pi\)
\(548\) −9.77134e13 −1.97720
\(549\) 2.67347e13i 0.536059i
\(550\) 4.42198e13 0.878624
\(551\) −4.46334e13 −0.878824
\(552\) −1.66504e13 −0.324884
\(553\) −1.40876e12 −0.0272402
\(554\) 1.41499e14i 2.71148i
\(555\) 2.74889e13i 0.522027i
\(556\) 4.56266e13 0.858704
\(557\) −3.54388e13 −0.661003 −0.330502 0.943805i \(-0.607218\pi\)
−0.330502 + 0.943805i \(0.607218\pi\)
\(558\) 2.30378e13 0.425862
\(559\) 7.01023e11 0.0128432
\(560\) 3.09447e12 0.0561884
\(561\) 1.14697e13i 0.206413i
\(562\) 5.06862e12i 0.0904082i
\(563\) 3.72684e13i 0.658869i −0.944178 0.329435i \(-0.893142\pi\)
0.944178 0.329435i \(-0.106858\pi\)
\(564\) 4.81572e12i 0.0843850i
\(565\) 7.06959e13i 1.22787i
\(566\) 4.39681e13 0.756930
\(567\) 5.99927e12 0.102373
\(568\) 2.68442e13i 0.454055i
\(569\) 3.76671e13i 0.631541i 0.948836 + 0.315770i \(0.102263\pi\)
−0.948836 + 0.315770i \(0.897737\pi\)
\(570\) 5.60064e13i 0.930816i
\(571\) 3.06504e13i 0.504959i −0.967602 0.252479i \(-0.918754\pi\)
0.967602 0.252479i \(-0.0812460\pi\)
\(572\) −3.18473e12 −0.0520106
\(573\) 3.73475e13i 0.604628i
\(574\) 8.49938e13i 1.36404i
\(575\) 1.60444e13i 0.255262i
\(576\) 3.44117e13 0.542742
\(577\) 2.72045e11 0.00425364 0.00212682 0.999998i \(-0.499323\pi\)
0.00212682 + 0.999998i \(0.499323\pi\)
\(578\) 9.56934e13i 1.48335i
\(579\) −2.22016e13 −0.341186
\(580\) 5.23816e13 0.798066
\(581\) 1.89482e12i 0.0286211i
\(582\) −4.54275e13 −0.680305
\(583\) 5.37627e12i 0.0798248i
\(584\) 2.60985e13 0.384195
\(585\) 4.41852e11i 0.00644908i
\(586\) 1.75097e14i 2.53390i
\(587\) 6.02247e13i 0.864139i 0.901840 + 0.432070i \(0.142217\pi\)
−0.901840 + 0.432070i \(0.857783\pi\)
\(588\) −9.69814e12 −0.137975
\(589\) 7.45146e13i 1.05115i
\(590\) 5.73889e13 6.56418e13i 0.802727 0.918164i
\(591\) −4.88541e13 −0.677585
\(592\) 6.95872e12i 0.0957019i
\(593\) −4.32391e13 −0.589662 −0.294831 0.955549i \(-0.595263\pi\)
−0.294831 + 0.955549i \(0.595263\pi\)
\(594\) 2.95029e13 0.398963
\(595\) −1.44513e13 −0.193786
\(596\) 5.73240e13i 0.762263i
\(597\) 5.09233e13 0.671498
\(598\) 1.88618e12i 0.0246647i
\(599\) −5.02386e13 −0.651483 −0.325742 0.945459i \(-0.605614\pi\)
−0.325742 + 0.945459i \(0.605614\pi\)
\(600\) 1.77777e13i 0.228623i
\(601\) 4.09214e13i 0.521889i 0.965354 + 0.260945i \(0.0840340\pi\)
−0.965354 + 0.260945i \(0.915966\pi\)
\(602\) −5.89760e13 −0.745922
\(603\) 2.92490e13i 0.366881i
\(604\) 1.22305e14i 1.52146i
\(605\) 4.09007e13 0.504607
\(606\) −6.54596e13 −0.800958
\(607\) −6.92676e13 −0.840595 −0.420298 0.907386i \(-0.638074\pi\)
−0.420298 + 0.907386i \(0.638074\pi\)
\(608\) 1.16795e14i 1.40575i
\(609\) −2.96239e13 −0.353636
\(610\) −1.65652e14 −1.96132
\(611\) −2.00587e11 −0.00235558
\(612\) −1.25408e13 −0.146073
\(613\) 8.23233e13i 0.951087i 0.879692 + 0.475543i \(0.157749\pi\)
−0.879692 + 0.475543i \(0.842251\pi\)
\(614\) 1.93577e14i 2.21826i
\(615\) −3.55269e13 −0.403814
\(616\) 9.85143e13 1.11070
\(617\) −7.21436e12 −0.0806811 −0.0403406 0.999186i \(-0.512844\pi\)
−0.0403406 + 0.999186i \(0.512844\pi\)
\(618\) −3.92360e13 −0.435253
\(619\) −4.97946e13 −0.547935 −0.273968 0.961739i \(-0.588336\pi\)
−0.273968 + 0.961739i \(0.588336\pi\)
\(620\) 8.74500e13i 0.954556i
\(621\) 1.07047e13i 0.115909i
\(622\) 2.91367e14i 3.12959i
\(623\) 8.11094e12i 0.0864233i
\(624\) 1.11853e11i 0.00118229i
\(625\) −3.78174e13 −0.396544
\(626\) 5.97880e13 0.621931
\(627\) 9.54259e13i 0.984756i
\(628\) 1.27365e14i 1.30392i
\(629\) 3.24974e13i 0.330062i
\(630\) 3.71724e13i 0.374557i
\(631\) −8.82637e13 −0.882339 −0.441169 0.897424i \(-0.645436\pi\)
−0.441169 + 0.897424i \(0.645436\pi\)
\(632\) 2.78523e12i 0.0276233i
\(633\) 4.81417e13i 0.473699i
\(634\) 9.00311e13i 0.878914i
\(635\) 1.93779e13 0.187689
\(636\) 5.87836e12 0.0564898
\(637\) 4.03953e11i 0.00385153i
\(638\) −1.45683e14 −1.37818
\(639\) −1.72584e13 −0.161993
\(640\) 1.26549e14i 1.17858i
\(641\) −6.88079e13 −0.635840 −0.317920 0.948117i \(-0.602984\pi\)
−0.317920 + 0.948117i \(0.602984\pi\)
\(642\) 4.37943e12i 0.0401552i
\(643\) 1.12758e14 1.02587 0.512937 0.858426i \(-0.328557\pi\)
0.512937 + 0.858426i \(0.328557\pi\)
\(644\) 9.72129e13i 0.877595i
\(645\) 2.46516e13i 0.220824i
\(646\) 6.62108e13i 0.588527i
\(647\) −8.96543e13 −0.790769 −0.395385 0.918516i \(-0.629389\pi\)
−0.395385 + 0.918516i \(0.629389\pi\)
\(648\) 1.18611e13i 0.103812i
\(649\) −9.77815e13 + 1.11843e14i −0.849245 + 0.971371i
\(650\) −2.01388e12 −0.0173567
\(651\) 4.94566e13i 0.422979i
\(652\) −2.83445e14 −2.40564
\(653\) 8.89596e13 0.749251 0.374625 0.927176i \(-0.377771\pi\)
0.374625 + 0.927176i \(0.377771\pi\)
\(654\) 6.14969e13 0.514001
\(655\) 5.03368e13i 0.417522i
\(656\) 8.99349e12 0.0740303
\(657\) 1.67790e13i 0.137069i
\(658\) 1.68751e13 0.136810
\(659\) 3.64044e13i 0.292905i −0.989218 0.146453i \(-0.953214\pi\)
0.989218 0.146453i \(-0.0467856\pi\)
\(660\) 1.11991e14i 0.894263i
\(661\) −4.09725e13 −0.324702 −0.162351 0.986733i \(-0.551908\pi\)
−0.162351 + 0.986733i \(0.551908\pi\)
\(662\) 3.42696e14i 2.69537i
\(663\) 5.22358e11i 0.00407756i
\(664\) −3.74622e12 −0.0290237
\(665\) 1.20232e14 0.924514
\(666\) 8.35917e13 0.637958
\(667\) 5.28588e13i 0.400395i
\(668\) 1.49476e13 0.112380
\(669\) 2.03784e13 0.152069
\(670\) 1.81231e14 1.34233
\(671\) 2.82244e14 2.07497
\(672\) 7.75189e13i 0.565667i
\(673\) 4.87480e12i 0.0353087i −0.999844 0.0176544i \(-0.994380\pi\)
0.999844 0.0176544i \(-0.00561985\pi\)
\(674\) 1.70326e14 1.22457
\(675\) 1.14294e13 0.0815655
\(676\) −2.23112e14 −1.58048
\(677\) 9.64158e13 0.677961 0.338981 0.940793i \(-0.389918\pi\)
0.338981 + 0.940793i \(0.389918\pi\)
\(678\) −2.14981e14 −1.50055
\(679\) 9.75219e13i 0.675699i
\(680\) 2.85714e13i 0.196511i
\(681\) 1.15816e14i 0.790740i
\(682\) 2.43215e14i 1.64842i
\(683\) 7.87699e13i 0.529977i 0.964252 + 0.264988i \(0.0853682\pi\)
−0.964252 + 0.264988i \(0.914632\pi\)
\(684\) 1.04338e14 0.696885
\(685\) −1.43123e14 −0.948979
\(686\) 2.58881e14i 1.70404i
\(687\) 3.34022e13i 0.218269i
\(688\) 6.24046e12i 0.0404832i
\(689\) 2.44849e11i 0.00157689i
\(690\) −6.63278e13 −0.424082
\(691\) 6.25229e13i 0.396871i −0.980114 0.198435i \(-0.936414\pi\)
0.980114 0.198435i \(-0.0635860\pi\)
\(692\) 9.59211e13i 0.604482i
\(693\) 6.33358e13i 0.396262i
\(694\) 2.47321e14 1.53626
\(695\) 6.68303e13 0.412144
\(696\) 5.85690e13i 0.358610i
\(697\) −4.19999e13 −0.255320
\(698\) 8.09595e13 0.488642
\(699\) 1.61664e14i 0.968787i
\(700\) 1.03795e14 0.617569
\(701\) 2.41001e14i 1.42373i 0.702316 + 0.711865i \(0.252149\pi\)
−0.702316 + 0.711865i \(0.747851\pi\)
\(702\) −1.34364e12 −0.00788129
\(703\) 2.70374e14i 1.57466i
\(704\) 3.63292e14i 2.10084i
\(705\) 7.05369e12i 0.0405015i
\(706\) 1.16473e14 0.664052
\(707\) 1.40526e14i 0.795536i
\(708\) −1.22288e14 1.06913e14i −0.687412 0.600987i
\(709\) −2.57817e14 −1.43906 −0.719532 0.694459i \(-0.755644\pi\)
−0.719532 + 0.694459i \(0.755644\pi\)
\(710\) 1.06935e14i 0.592693i
\(711\) −1.79065e12 −0.00985515
\(712\) 1.60360e13 0.0876389
\(713\) 8.82467e13 0.478907
\(714\) 4.39452e13i 0.236821i
\(715\) −4.66474e12 −0.0249630
\(716\) 3.24300e14i 1.72338i
\(717\) −8.11185e13 −0.428079
\(718\) 3.34689e14i 1.75396i
\(719\) 1.74694e14i 0.909148i 0.890709 + 0.454574i \(0.150209\pi\)
−0.890709 + 0.454574i \(0.849791\pi\)
\(720\) 3.93334e12 0.0203282
\(721\) 8.42302e13i 0.432306i
\(722\) 2.35638e14i 1.20105i
\(723\) −6.47344e13 −0.327675
\(724\) 1.76729e14 0.888411
\(725\) −5.64377e13 −0.281760
\(726\) 1.24376e14i 0.616670i
\(727\) −1.26239e13 −0.0621617 −0.0310809 0.999517i \(-0.509895\pi\)
−0.0310809 + 0.999517i \(0.509895\pi\)
\(728\) −4.48660e12 −0.0219412
\(729\) 7.62560e12 0.0370370
\(730\) 1.03965e14 0.501503
\(731\) 2.91431e13i 0.139621i
\(732\) 3.08603e14i 1.46840i
\(733\) −2.14382e13 −0.101314 −0.0506569 0.998716i \(-0.516131\pi\)
−0.0506569 + 0.998716i \(0.516131\pi\)
\(734\) 3.44423e14 1.61664
\(735\) −1.42051e13 −0.0662228
\(736\) 1.38319e14 0.640462
\(737\) −3.08789e14 −1.42012
\(738\) 1.08035e14i 0.493493i
\(739\) 1.33153e14i 0.604127i −0.953288 0.302063i \(-0.902325\pi\)
0.953288 0.302063i \(-0.0976754\pi\)
\(740\) 3.17310e14i 1.42996i
\(741\) 4.34594e12i 0.0194533i
\(742\) 2.05988e13i 0.0915846i
\(743\) 1.42151e14 0.627777 0.313889 0.949460i \(-0.398368\pi\)
0.313889 + 0.949460i \(0.398368\pi\)
\(744\) 9.77799e13 0.428928
\(745\) 8.39638e13i 0.365856i
\(746\) 1.19769e14i 0.518381i
\(747\) 2.40848e12i 0.0103547i
\(748\) 1.32396e14i 0.565416i
\(749\) 9.40158e12 0.0398834
\(750\) 2.37912e14i 1.00256i
\(751\) 2.91415e14i 1.21986i −0.792453 0.609932i \(-0.791197\pi\)
0.792453 0.609932i \(-0.208803\pi\)
\(752\) 1.78562e12i 0.00742504i
\(753\) 1.10703e13 0.0457283
\(754\) 6.63478e12 0.0272251
\(755\) 1.79143e14i 0.730239i
\(756\) 6.92507e13 0.280424
\(757\) −1.57836e14 −0.634933 −0.317466 0.948269i \(-0.602832\pi\)
−0.317466 + 0.948269i \(0.602832\pi\)
\(758\) 5.31060e14i 2.12226i
\(759\) 1.13012e14 0.448657
\(760\) 2.37710e14i 0.937518i
\(761\) −2.73383e14 −1.07115 −0.535573 0.844489i \(-0.679904\pi\)
−0.535573 + 0.844489i \(0.679904\pi\)
\(762\) 5.89268e13i 0.229371i
\(763\) 1.32019e14i 0.510521i
\(764\) 4.31109e14i 1.65623i
\(765\) −1.83688e13 −0.0701091
\(766\) 6.26346e14i 2.37504i
\(767\) 4.45322e12 5.09362e12i 0.0167763 0.0191889i
\(768\) 1.33661e14 0.500264
\(769\) 4.46828e14i 1.66153i 0.556622 + 0.830766i \(0.312097\pi\)
−0.556622 + 0.830766i \(0.687903\pi\)
\(770\) 3.92438e14 1.44983
\(771\) −1.94762e14 −0.714880
\(772\) −2.56277e14 −0.934594
\(773\) 2.97425e12i 0.0107766i −0.999985 0.00538828i \(-0.998285\pi\)
0.999985 0.00538828i \(-0.00171515\pi\)
\(774\) −7.49637e13 −0.269865
\(775\) 9.42216e13i 0.337009i
\(776\) −1.92809e14 −0.685203
\(777\) 1.79451e14i 0.633639i
\(778\) 6.02318e14i 2.11314i
\(779\) 3.49433e14 1.21808