Properties

Label 1.90.a.a.1.6
Level 1
Weight 90
Character 1.1
Self dual yes
Analytic conductor 50.162
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 90 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(50.1624291928\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 1400531600527934473811256 x^{5} + 92429106535860966322690362643440028 x^{4} + 486502004825754823566786579226467181483733375376 x^{3} - 41390338158988484679355574715314473323669246141474080139600 x^{2} - 47785461930919140795588898989186212855196409324706742802409577734342400 x + 5612439960923763868733925256800794059272997589318959539312206365735127554315560000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{83}\cdot 3^{29}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-4.94369e11\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.92430e13 q^{2} +1.59613e21 q^{3} -2.48679e26 q^{4} -3.02831e30 q^{5} +3.07142e34 q^{6} +1.70526e37 q^{7} -1.66961e40 q^{8} -3.61697e41 q^{9} +O(q^{10})\) \(q+1.92430e13 q^{2} +1.59613e21 q^{3} -2.48679e26 q^{4} -3.02831e30 q^{5} +3.07142e34 q^{6} +1.70526e37 q^{7} -1.66961e40 q^{8} -3.61697e41 q^{9} -5.82737e43 q^{10} +1.93063e46 q^{11} -3.96923e47 q^{12} +1.74324e49 q^{13} +3.28142e50 q^{14} -4.83358e51 q^{15} -1.67358e53 q^{16} -6.51031e54 q^{17} -6.96012e54 q^{18} -9.59966e56 q^{19} +7.53078e56 q^{20} +2.72181e58 q^{21} +3.71509e59 q^{22} -9.89412e59 q^{23} -2.66492e61 q^{24} -1.52388e62 q^{25} +3.35451e62 q^{26} -5.22096e63 q^{27} -4.24062e63 q^{28} -1.35771e65 q^{29} -9.30123e64 q^{30} +1.59360e66 q^{31} +7.11394e66 q^{32} +3.08153e67 q^{33} -1.25278e68 q^{34} -5.16406e67 q^{35} +8.99464e67 q^{36} -2.47785e68 q^{37} -1.84726e70 q^{38} +2.78243e70 q^{39} +5.05611e70 q^{40} +4.58319e71 q^{41} +5.23757e71 q^{42} -7.07930e72 q^{43} -4.80106e72 q^{44} +1.09533e72 q^{45} -1.90392e73 q^{46} +1.32347e74 q^{47} -2.67125e74 q^{48} -1.34499e75 q^{49} -2.93240e75 q^{50} -1.03913e76 q^{51} -4.33507e75 q^{52} -9.22610e76 q^{53} -1.00467e77 q^{54} -5.84654e76 q^{55} -2.84712e77 q^{56} -1.53223e78 q^{57} -2.61263e78 q^{58} -8.06039e78 q^{59} +1.20201e78 q^{60} +4.49999e79 q^{61} +3.06655e79 q^{62} -6.16787e78 q^{63} +2.40483e80 q^{64} -5.27908e79 q^{65} +5.92976e80 q^{66} +1.54319e81 q^{67} +1.61898e81 q^{68} -1.57923e81 q^{69} -9.93718e80 q^{70} -2.24358e82 q^{71} +6.03894e81 q^{72} -1.49797e83 q^{73} -4.76812e81 q^{74} -2.43231e83 q^{75} +2.38723e83 q^{76} +3.29222e83 q^{77} +5.35422e83 q^{78} +3.12365e84 q^{79} +5.06813e83 q^{80} -7.28103e84 q^{81} +8.81941e84 q^{82} +3.77338e85 q^{83} -6.76857e84 q^{84} +1.97153e85 q^{85} -1.36227e86 q^{86} -2.16707e86 q^{87} -3.22340e86 q^{88} +2.53389e85 q^{89} +2.10774e85 q^{90} +2.97268e86 q^{91} +2.46046e86 q^{92} +2.54358e87 q^{93} +2.54675e87 q^{94} +2.90708e87 q^{95} +1.13548e88 q^{96} +3.77341e87 q^{97} -2.58816e88 q^{98} -6.98301e87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92430e13 0.773458 0.386729 0.922193i \(-0.373605\pi\)
0.386729 + 0.922193i \(0.373605\pi\)
\(3\) 1.59613e21 0.935776 0.467888 0.883788i \(-0.345015\pi\)
0.467888 + 0.883788i \(0.345015\pi\)
\(4\) −2.48679e26 −0.401762
\(5\) −3.02831e30 −0.238252 −0.119126 0.992879i \(-0.538009\pi\)
−0.119126 + 0.992879i \(0.538009\pi\)
\(6\) 3.07142e34 0.723784
\(7\) 1.70526e37 0.421626 0.210813 0.977526i \(-0.432389\pi\)
0.210813 + 0.977526i \(0.432389\pi\)
\(8\) −1.66961e40 −1.08420
\(9\) −3.61697e41 −0.124323
\(10\) −5.82737e43 −0.184278
\(11\) 1.93063e46 0.878463 0.439232 0.898374i \(-0.355251\pi\)
0.439232 + 0.898374i \(0.355251\pi\)
\(12\) −3.96923e47 −0.375959
\(13\) 1.74324e49 0.468682 0.234341 0.972155i \(-0.424707\pi\)
0.234341 + 0.972155i \(0.424707\pi\)
\(14\) 3.28142e50 0.326110
\(15\) −4.83358e51 −0.222950
\(16\) −1.67358e53 −0.436825
\(17\) −6.51031e54 −1.14452 −0.572262 0.820071i \(-0.693934\pi\)
−0.572262 + 0.820071i \(0.693934\pi\)
\(18\) −6.96012e54 −0.0961590
\(19\) −9.59966e56 −1.19597 −0.597985 0.801507i \(-0.704032\pi\)
−0.597985 + 0.801507i \(0.704032\pi\)
\(20\) 7.53078e56 0.0957205
\(21\) 2.72181e58 0.394548
\(22\) 3.71509e59 0.679455
\(23\) −9.89412e59 −0.250316 −0.125158 0.992137i \(-0.539944\pi\)
−0.125158 + 0.992137i \(0.539944\pi\)
\(24\) −2.66492e61 −1.01457
\(25\) −1.52388e62 −0.943236
\(26\) 3.35451e62 0.362506
\(27\) −5.22096e63 −1.05211
\(28\) −4.24062e63 −0.169394
\(29\) −1.35771e65 −1.13788 −0.568938 0.822381i \(-0.692645\pi\)
−0.568938 + 0.822381i \(0.692645\pi\)
\(30\) −9.30123e64 −0.172443
\(31\) 1.59360e66 0.686725 0.343363 0.939203i \(-0.388434\pi\)
0.343363 + 0.939203i \(0.388434\pi\)
\(32\) 7.11394e66 0.746339
\(33\) 3.08153e67 0.822045
\(34\) −1.25278e68 −0.885242
\(35\) −5.16406e67 −0.100453
\(36\) 8.99464e67 0.0499485
\(37\) −2.47785e68 −0.0406535 −0.0203268 0.999793i \(-0.506471\pi\)
−0.0203268 + 0.999793i \(0.506471\pi\)
\(38\) −1.84726e70 −0.925033
\(39\) 2.78243e70 0.438581
\(40\) 5.05611e70 0.258313
\(41\) 4.58319e71 0.780344 0.390172 0.920742i \(-0.372416\pi\)
0.390172 + 0.920742i \(0.372416\pi\)
\(42\) 5.23757e71 0.305166
\(43\) −7.07930e72 −1.44758 −0.723792 0.690018i \(-0.757603\pi\)
−0.723792 + 0.690018i \(0.757603\pi\)
\(44\) −4.80106e72 −0.352933
\(45\) 1.09533e72 0.0296203
\(46\) −1.90392e73 −0.193609
\(47\) 1.32347e74 0.516844 0.258422 0.966032i \(-0.416797\pi\)
0.258422 + 0.966032i \(0.416797\pi\)
\(48\) −2.67125e74 −0.408770
\(49\) −1.34499e75 −0.822231
\(50\) −2.93240e75 −0.729554
\(51\) −1.03913e76 −1.07102
\(52\) −4.33507e75 −0.188299
\(53\) −9.22610e76 −1.71689 −0.858444 0.512907i \(-0.828568\pi\)
−0.858444 + 0.512907i \(0.828568\pi\)
\(54\) −1.00467e77 −0.813767
\(55\) −5.84654e76 −0.209295
\(56\) −2.84712e77 −0.457129
\(57\) −1.53223e78 −1.11916
\(58\) −2.61263e78 −0.880099
\(59\) −8.06039e78 −1.26894 −0.634471 0.772947i \(-0.718782\pi\)
−0.634471 + 0.772947i \(0.718782\pi\)
\(60\) 1.20201e78 0.0895729
\(61\) 4.49999e79 1.60707 0.803534 0.595259i \(-0.202951\pi\)
0.803534 + 0.595259i \(0.202951\pi\)
\(62\) 3.06655e79 0.531153
\(63\) −6.16787e78 −0.0524181
\(64\) 2.40483e80 1.01409
\(65\) −5.27908e79 −0.111664
\(66\) 5.92976e80 0.635817
\(67\) 1.54319e81 0.847404 0.423702 0.905802i \(-0.360730\pi\)
0.423702 + 0.905802i \(0.360730\pi\)
\(68\) 1.61898e81 0.459827
\(69\) −1.57923e81 −0.234240
\(70\) −9.93718e80 −0.0776963
\(71\) −2.24358e82 −0.933136 −0.466568 0.884485i \(-0.654510\pi\)
−0.466568 + 0.884485i \(0.654510\pi\)
\(72\) 6.03894e81 0.134792
\(73\) −1.49797e83 −1.80982 −0.904908 0.425607i \(-0.860061\pi\)
−0.904908 + 0.425607i \(0.860061\pi\)
\(74\) −4.76812e81 −0.0314438
\(75\) −2.43231e83 −0.882658
\(76\) 2.38723e83 0.480496
\(77\) 3.29222e83 0.370383
\(78\) 5.35422e83 0.339224
\(79\) 3.12365e84 1.12268 0.561342 0.827584i \(-0.310285\pi\)
0.561342 + 0.827584i \(0.310285\pi\)
\(80\) 5.06813e83 0.104074
\(81\) −7.28103e84 −0.860220
\(82\) 8.81941e84 0.603564
\(83\) 3.77338e85 1.50576 0.752880 0.658158i \(-0.228664\pi\)
0.752880 + 0.658158i \(0.228664\pi\)
\(84\) −6.76857e84 −0.158514
\(85\) 1.97153e85 0.272685
\(86\) −1.36227e86 −1.11965
\(87\) −2.16707e86 −1.06480
\(88\) −3.22340e86 −0.952434
\(89\) 2.53389e85 0.0452828 0.0226414 0.999744i \(-0.492792\pi\)
0.0226414 + 0.999744i \(0.492792\pi\)
\(90\) 2.10774e85 0.0229100
\(91\) 2.97268e86 0.197609
\(92\) 2.46046e86 0.100567
\(93\) 2.54358e87 0.642621
\(94\) 2.54675e87 0.399758
\(95\) 2.90708e87 0.284942
\(96\) 1.13548e88 0.698406
\(97\) 3.77341e87 0.146350 0.0731749 0.997319i \(-0.476687\pi\)
0.0731749 + 0.997319i \(0.476687\pi\)
\(98\) −2.58816e88 −0.635962
\(99\) −6.98301e87 −0.109214
\(100\) 3.78957e88 0.378957
\(101\) −6.63329e88 −0.426018 −0.213009 0.977050i \(-0.568326\pi\)
−0.213009 + 0.977050i \(0.568326\pi\)
\(102\) −1.99959e89 −0.828388
\(103\) −6.09276e88 −0.163515 −0.0817575 0.996652i \(-0.526053\pi\)
−0.0817575 + 0.996652i \(0.526053\pi\)
\(104\) −2.91053e89 −0.508147
\(105\) −8.24251e88 −0.0940017
\(106\) −1.77537e90 −1.32794
\(107\) 3.96513e90 1.95290 0.976448 0.215751i \(-0.0692198\pi\)
0.976448 + 0.215751i \(0.0692198\pi\)
\(108\) 1.29834e90 0.422700
\(109\) 7.03908e90 1.52068 0.760338 0.649528i \(-0.225034\pi\)
0.760338 + 0.649528i \(0.225034\pi\)
\(110\) −1.12505e90 −0.161881
\(111\) −3.95497e89 −0.0380426
\(112\) −2.85389e90 −0.184177
\(113\) −1.14772e91 −0.498706 −0.249353 0.968413i \(-0.580218\pi\)
−0.249353 + 0.968413i \(0.580218\pi\)
\(114\) −2.94846e91 −0.865624
\(115\) 2.99625e90 0.0596381
\(116\) 3.37633e91 0.457156
\(117\) −6.30524e90 −0.0582681
\(118\) −1.55106e92 −0.981473
\(119\) −1.11018e92 −0.482562
\(120\) 8.07020e91 0.241724
\(121\) −1.10271e92 −0.228302
\(122\) 8.65932e92 1.24300
\(123\) 7.31536e92 0.730227
\(124\) −3.96294e92 −0.275900
\(125\) 9.50730e92 0.462979
\(126\) −1.18688e92 −0.0405432
\(127\) 2.56627e93 0.616648 0.308324 0.951281i \(-0.400232\pi\)
0.308324 + 0.951281i \(0.400232\pi\)
\(128\) 2.24284e92 0.0380149
\(129\) −1.12995e94 −1.35461
\(130\) −1.01585e93 −0.0863675
\(131\) −1.52696e94 −0.923114 −0.461557 0.887110i \(-0.652709\pi\)
−0.461557 + 0.887110i \(0.652709\pi\)
\(132\) −7.66310e93 −0.330267
\(133\) −1.63699e94 −0.504253
\(134\) 2.96955e94 0.655432
\(135\) 1.58107e94 0.250668
\(136\) 1.08697e95 1.24090
\(137\) 4.13375e94 0.340627 0.170313 0.985390i \(-0.445522\pi\)
0.170313 + 0.985390i \(0.445522\pi\)
\(138\) −3.03890e94 −0.181174
\(139\) −4.37002e94 −0.188940 −0.0944701 0.995528i \(-0.530116\pi\)
−0.0944701 + 0.995528i \(0.530116\pi\)
\(140\) 1.28419e94 0.0403583
\(141\) 2.11243e95 0.483650
\(142\) −4.31731e95 −0.721742
\(143\) 3.36554e95 0.411719
\(144\) 6.05329e94 0.0543076
\(145\) 4.11156e95 0.271101
\(146\) −2.88253e96 −1.39982
\(147\) −2.14678e96 −0.769424
\(148\) 6.16189e94 0.0163331
\(149\) 2.82695e94 0.00555303 0.00277651 0.999996i \(-0.499116\pi\)
0.00277651 + 0.999996i \(0.499116\pi\)
\(150\) −4.68048e96 −0.682699
\(151\) 1.26902e97 1.37720 0.688598 0.725143i \(-0.258226\pi\)
0.688598 + 0.725143i \(0.258226\pi\)
\(152\) 1.60277e97 1.29668
\(153\) 2.35476e96 0.142291
\(154\) 6.33520e96 0.286476
\(155\) −4.82591e96 −0.163613
\(156\) −6.91932e96 −0.176205
\(157\) −2.10812e97 −0.403981 −0.201990 0.979387i \(-0.564741\pi\)
−0.201990 + 0.979387i \(0.564741\pi\)
\(158\) 6.01083e97 0.868349
\(159\) −1.47260e98 −1.60662
\(160\) −2.15432e97 −0.177816
\(161\) −1.68720e97 −0.105540
\(162\) −1.40109e98 −0.665344
\(163\) 1.44678e98 0.522462 0.261231 0.965276i \(-0.415872\pi\)
0.261231 + 0.965276i \(0.415872\pi\)
\(164\) −1.13974e98 −0.313513
\(165\) −9.33183e97 −0.195853
\(166\) 7.26110e98 1.16464
\(167\) 9.38473e98 1.15223 0.576115 0.817369i \(-0.304568\pi\)
0.576115 + 0.817369i \(0.304568\pi\)
\(168\) −4.54437e98 −0.427771
\(169\) −1.07955e99 −0.780338
\(170\) 3.79380e98 0.210910
\(171\) 3.47217e98 0.148687
\(172\) 1.76047e99 0.581585
\(173\) 3.32605e99 0.848941 0.424471 0.905442i \(-0.360460\pi\)
0.424471 + 0.905442i \(0.360460\pi\)
\(174\) −4.17009e99 −0.823576
\(175\) −2.59861e99 −0.397693
\(176\) −3.23106e99 −0.383734
\(177\) −1.28654e100 −1.18744
\(178\) 4.87596e98 0.0350243
\(179\) −1.11777e100 −0.625736 −0.312868 0.949797i \(-0.601290\pi\)
−0.312868 + 0.949797i \(0.601290\pi\)
\(180\) −2.72386e98 −0.0119003
\(181\) 2.69295e100 0.919457 0.459728 0.888060i \(-0.347947\pi\)
0.459728 + 0.888060i \(0.347947\pi\)
\(182\) 5.72031e99 0.152842
\(183\) 7.18256e100 1.50386
\(184\) 1.65193e100 0.271394
\(185\) 7.50371e98 0.00968577
\(186\) 4.89461e100 0.497041
\(187\) −1.25690e101 −1.00542
\(188\) −3.29119e100 −0.207649
\(189\) −8.90310e100 −0.443599
\(190\) 5.59408e100 0.220391
\(191\) −2.28014e101 −0.711177 −0.355588 0.934643i \(-0.615719\pi\)
−0.355588 + 0.934643i \(0.615719\pi\)
\(192\) 3.83841e101 0.948958
\(193\) −6.90447e101 −1.35466 −0.677330 0.735679i \(-0.736863\pi\)
−0.677330 + 0.735679i \(0.736863\pi\)
\(194\) 7.26116e100 0.113195
\(195\) −8.42608e100 −0.104493
\(196\) 3.34471e101 0.330341
\(197\) −3.78554e100 −0.0298113 −0.0149056 0.999889i \(-0.504745\pi\)
−0.0149056 + 0.999889i \(0.504745\pi\)
\(198\) −1.34374e101 −0.0844722
\(199\) 2.74343e101 0.137826 0.0689132 0.997623i \(-0.478047\pi\)
0.0689132 + 0.997623i \(0.478047\pi\)
\(200\) 2.54429e102 1.02266
\(201\) 2.46313e102 0.792981
\(202\) −1.27644e102 −0.329507
\(203\) −2.31524e102 −0.479758
\(204\) 2.58409e102 0.430295
\(205\) −1.38793e102 −0.185918
\(206\) −1.17243e102 −0.126472
\(207\) 3.57867e101 0.0311201
\(208\) −2.91745e102 −0.204732
\(209\) −1.85333e103 −1.05062
\(210\) −1.58610e102 −0.0727064
\(211\) −3.13690e103 −1.16394 −0.581971 0.813209i \(-0.697718\pi\)
−0.581971 + 0.813209i \(0.697718\pi\)
\(212\) 2.29434e103 0.689781
\(213\) −3.58104e103 −0.873206
\(214\) 7.63008e103 1.51048
\(215\) 2.14383e103 0.344889
\(216\) 8.71699e103 1.14071
\(217\) 2.71750e103 0.289542
\(218\) 1.35453e104 1.17618
\(219\) −2.39094e104 −1.69358
\(220\) 1.45391e103 0.0840869
\(221\) −1.13490e104 −0.536417
\(222\) −7.61052e102 −0.0294244
\(223\) −2.51321e104 −0.795539 −0.397770 0.917485i \(-0.630216\pi\)
−0.397770 + 0.917485i \(0.630216\pi\)
\(224\) 1.21311e104 0.314676
\(225\) 5.51183e103 0.117266
\(226\) −2.20855e104 −0.385729
\(227\) 3.43863e104 0.493440 0.246720 0.969087i \(-0.420647\pi\)
0.246720 + 0.969087i \(0.420647\pi\)
\(228\) 3.81033e104 0.449637
\(229\) −1.97608e105 −1.91922 −0.959610 0.281334i \(-0.909223\pi\)
−0.959610 + 0.281334i \(0.909223\pi\)
\(230\) 5.76567e103 0.0461276
\(231\) 5.25480e104 0.346596
\(232\) 2.26684e105 1.23369
\(233\) 4.43243e104 0.199206 0.0996032 0.995027i \(-0.468243\pi\)
0.0996032 + 0.995027i \(0.468243\pi\)
\(234\) −1.21332e104 −0.0450680
\(235\) −4.00789e104 −0.123139
\(236\) 2.00445e105 0.509813
\(237\) 4.98575e105 1.05058
\(238\) −2.13631e105 −0.373241
\(239\) −1.01112e105 −0.146587 −0.0732933 0.997310i \(-0.523351\pi\)
−0.0732933 + 0.997310i \(0.523351\pi\)
\(240\) 8.08938e104 0.0973901
\(241\) −1.92058e106 −1.92165 −0.960823 0.277163i \(-0.910606\pi\)
−0.960823 + 0.277163i \(0.910606\pi\)
\(242\) −2.12193e105 −0.176582
\(243\) 3.56800e105 0.247142
\(244\) −1.11905e106 −0.645659
\(245\) 4.07306e105 0.195898
\(246\) 1.40769e106 0.564800
\(247\) −1.67345e106 −0.560529
\(248\) −2.66069e106 −0.744551
\(249\) 6.02280e106 1.40905
\(250\) 1.82948e106 0.358095
\(251\) 6.63724e106 1.08769 0.543847 0.839184i \(-0.316967\pi\)
0.543847 + 0.839184i \(0.316967\pi\)
\(252\) 1.53382e105 0.0210596
\(253\) −1.91018e106 −0.219893
\(254\) 4.93827e106 0.476951
\(255\) 3.14681e106 0.255172
\(256\) −1.44536e107 −0.984684
\(257\) −5.06905e106 −0.290337 −0.145168 0.989407i \(-0.546372\pi\)
−0.145168 + 0.989407i \(0.546372\pi\)
\(258\) −2.17435e107 −1.04774
\(259\) −4.22538e105 −0.0171406
\(260\) 1.31279e106 0.0448624
\(261\) 4.91078e106 0.141465
\(262\) −2.93832e107 −0.713990
\(263\) 7.92155e107 1.62472 0.812362 0.583154i \(-0.198181\pi\)
0.812362 + 0.583154i \(0.198181\pi\)
\(264\) −5.14495e107 −0.891265
\(265\) 2.79395e107 0.409051
\(266\) −3.15005e107 −0.390019
\(267\) 4.04442e106 0.0423745
\(268\) −3.83759e107 −0.340455
\(269\) 1.49563e107 0.112421 0.0562104 0.998419i \(-0.482098\pi\)
0.0562104 + 0.998419i \(0.482098\pi\)
\(270\) 3.04245e107 0.193881
\(271\) 2.64960e108 1.43234 0.716171 0.697925i \(-0.245893\pi\)
0.716171 + 0.697925i \(0.245893\pi\)
\(272\) 1.08955e108 0.499956
\(273\) 4.74477e107 0.184917
\(274\) 7.95455e107 0.263461
\(275\) −2.94204e108 −0.828598
\(276\) 3.92720e107 0.0941086
\(277\) −8.85589e108 −1.80668 −0.903342 0.428921i \(-0.858894\pi\)
−0.903342 + 0.428921i \(0.858894\pi\)
\(278\) −8.40920e107 −0.146137
\(279\) −5.76399e107 −0.0853761
\(280\) 8.62199e107 0.108912
\(281\) −1.15862e109 −1.24885 −0.624426 0.781084i \(-0.714667\pi\)
−0.624426 + 0.781084i \(0.714667\pi\)
\(282\) 4.06494e108 0.374083
\(283\) 1.13837e109 0.894930 0.447465 0.894302i \(-0.352327\pi\)
0.447465 + 0.894302i \(0.352327\pi\)
\(284\) 5.57931e108 0.374899
\(285\) 4.64007e108 0.266642
\(286\) 6.47630e108 0.318448
\(287\) 7.81553e108 0.329014
\(288\) −2.57309e108 −0.0927875
\(289\) 1.00282e109 0.309935
\(290\) 7.91186e108 0.209685
\(291\) 6.02285e108 0.136951
\(292\) 3.72512e109 0.727116
\(293\) −8.89977e109 −1.49200 −0.746002 0.665944i \(-0.768029\pi\)
−0.746002 + 0.665944i \(0.768029\pi\)
\(294\) −4.13104e109 −0.595117
\(295\) 2.44094e109 0.302327
\(296\) 4.13705e108 0.0440768
\(297\) −1.00797e110 −0.924244
\(298\) 5.43989e107 0.00429504
\(299\) −1.72478e109 −0.117318
\(300\) 6.04863e109 0.354619
\(301\) −1.20720e110 −0.610340
\(302\) 2.44198e110 1.06520
\(303\) −1.05876e110 −0.398657
\(304\) 1.60658e110 0.522430
\(305\) −1.36274e110 −0.382887
\(306\) 4.53125e109 0.110056
\(307\) 5.02296e110 1.05512 0.527560 0.849518i \(-0.323107\pi\)
0.527560 + 0.849518i \(0.323107\pi\)
\(308\) −8.18705e109 −0.148806
\(309\) −9.72483e109 −0.153013
\(310\) −9.28648e109 −0.126548
\(311\) 5.98946e110 0.707213 0.353606 0.935394i \(-0.384955\pi\)
0.353606 + 0.935394i \(0.384955\pi\)
\(312\) −4.64558e110 −0.475511
\(313\) 7.96129e110 0.706741 0.353371 0.935483i \(-0.385035\pi\)
0.353371 + 0.935483i \(0.385035\pi\)
\(314\) −4.05665e110 −0.312462
\(315\) 1.86783e109 0.0124887
\(316\) −7.76786e110 −0.451052
\(317\) −1.75038e111 −0.883068 −0.441534 0.897244i \(-0.645566\pi\)
−0.441534 + 0.897244i \(0.645566\pi\)
\(318\) −2.83372e111 −1.24266
\(319\) −2.62122e111 −0.999582
\(320\) −7.28258e110 −0.241608
\(321\) 6.32885e111 1.82747
\(322\) −3.24668e110 −0.0816306
\(323\) 6.24968e111 1.36882
\(324\) 1.81064e111 0.345604
\(325\) −2.65649e111 −0.442077
\(326\) 2.78403e111 0.404102
\(327\) 1.12353e112 1.42301
\(328\) −7.65215e111 −0.846053
\(329\) 2.25686e111 0.217915
\(330\) −1.79572e111 −0.151484
\(331\) −1.64032e112 −1.20943 −0.604717 0.796441i \(-0.706714\pi\)
−0.604717 + 0.796441i \(0.706714\pi\)
\(332\) −9.38361e111 −0.604958
\(333\) 8.96231e109 0.00505419
\(334\) 1.80590e112 0.891201
\(335\) −4.67327e111 −0.201895
\(336\) −4.55517e111 −0.172348
\(337\) −8.55619e110 −0.0283628 −0.0141814 0.999899i \(-0.504514\pi\)
−0.0141814 + 0.999899i \(0.504514\pi\)
\(338\) −2.07736e112 −0.603559
\(339\) −1.83191e112 −0.466677
\(340\) −4.90277e111 −0.109554
\(341\) 3.07664e112 0.603263
\(342\) 6.68148e111 0.115003
\(343\) −5.08299e112 −0.768301
\(344\) 1.18197e113 1.56948
\(345\) 4.78240e111 0.0558079
\(346\) 6.40031e112 0.656621
\(347\) −8.64589e112 −0.780096 −0.390048 0.920795i \(-0.627542\pi\)
−0.390048 + 0.920795i \(0.627542\pi\)
\(348\) 5.38905e112 0.427795
\(349\) 8.46384e112 0.591338 0.295669 0.955290i \(-0.404457\pi\)
0.295669 + 0.955290i \(0.404457\pi\)
\(350\) −5.00050e112 −0.307599
\(351\) −9.10139e112 −0.493107
\(352\) 1.37344e113 0.655631
\(353\) −3.61884e112 −0.152263 −0.0761316 0.997098i \(-0.524257\pi\)
−0.0761316 + 0.997098i \(0.524257\pi\)
\(354\) −2.47569e113 −0.918439
\(355\) 6.79427e112 0.222321
\(356\) −6.30125e111 −0.0181929
\(357\) −1.77199e113 −0.451569
\(358\) −2.15091e113 −0.483980
\(359\) −5.09085e113 −1.01178 −0.505891 0.862597i \(-0.668836\pi\)
−0.505891 + 0.862597i \(0.668836\pi\)
\(360\) −1.82878e112 −0.0321144
\(361\) 2.77261e113 0.430346
\(362\) 5.18203e113 0.711161
\(363\) −1.76006e113 −0.213640
\(364\) −7.39242e112 −0.0793916
\(365\) 4.53631e113 0.431192
\(366\) 1.38214e114 1.16317
\(367\) 1.40897e114 1.05017 0.525087 0.851048i \(-0.324033\pi\)
0.525087 + 0.851048i \(0.324033\pi\)
\(368\) 1.65586e113 0.109344
\(369\) −1.65773e113 −0.0970151
\(370\) 1.44394e112 0.00749154
\(371\) −1.57329e114 −0.723885
\(372\) −6.32536e113 −0.258181
\(373\) −1.68014e114 −0.608557 −0.304279 0.952583i \(-0.598415\pi\)
−0.304279 + 0.952583i \(0.598415\pi\)
\(374\) −2.41864e114 −0.777652
\(375\) 1.51749e114 0.433245
\(376\) −2.20968e114 −0.560365
\(377\) −2.36681e114 −0.533301
\(378\) −1.71322e114 −0.343106
\(379\) 6.69736e114 1.19250 0.596251 0.802798i \(-0.296656\pi\)
0.596251 + 0.802798i \(0.296656\pi\)
\(380\) −7.22929e113 −0.114479
\(381\) 4.09610e114 0.577044
\(382\) −4.38767e114 −0.550065
\(383\) 6.76908e114 0.755413 0.377706 0.925925i \(-0.376713\pi\)
0.377706 + 0.925925i \(0.376713\pi\)
\(384\) 3.57985e113 0.0355734
\(385\) −9.96987e113 −0.0882444
\(386\) −1.32862e115 −1.04777
\(387\) 2.56056e114 0.179969
\(388\) −9.38368e113 −0.0587978
\(389\) 2.97836e115 1.66425 0.832127 0.554585i \(-0.187123\pi\)
0.832127 + 0.554585i \(0.187123\pi\)
\(390\) −1.62143e114 −0.0808207
\(391\) 6.44138e114 0.286492
\(392\) 2.24561e115 0.891467
\(393\) −2.43723e115 −0.863828
\(394\) −7.28449e113 −0.0230578
\(395\) −9.45941e114 −0.267481
\(396\) 1.73653e114 0.0438779
\(397\) −7.96520e115 −1.79895 −0.899475 0.436973i \(-0.856051\pi\)
−0.899475 + 0.436973i \(0.856051\pi\)
\(398\) 5.27918e114 0.106603
\(399\) −2.61285e115 −0.471868
\(400\) 2.55034e115 0.412029
\(401\) −5.80386e115 −0.839059 −0.419530 0.907742i \(-0.637805\pi\)
−0.419530 + 0.907742i \(0.637805\pi\)
\(402\) 4.73979e115 0.613337
\(403\) 2.77802e115 0.321856
\(404\) 1.64956e115 0.171158
\(405\) 2.20493e115 0.204949
\(406\) −4.45521e115 −0.371073
\(407\) −4.78380e114 −0.0357126
\(408\) 1.73494e116 1.16120
\(409\) 1.48135e116 0.889139 0.444570 0.895744i \(-0.353357\pi\)
0.444570 + 0.895744i \(0.353357\pi\)
\(410\) −2.67079e115 −0.143800
\(411\) 6.59799e115 0.318750
\(412\) 1.51514e115 0.0656942
\(413\) −1.37451e116 −0.535019
\(414\) 6.88642e114 0.0240701
\(415\) −1.14270e116 −0.358750
\(416\) 1.24013e116 0.349795
\(417\) −6.97510e115 −0.176806
\(418\) −3.56636e116 −0.812608
\(419\) −6.48329e116 −1.32822 −0.664112 0.747633i \(-0.731190\pi\)
−0.664112 + 0.747633i \(0.731190\pi\)
\(420\) 2.04974e115 0.0377663
\(421\) 6.60560e114 0.0109486 0.00547430 0.999985i \(-0.498257\pi\)
0.00547430 + 0.999985i \(0.498257\pi\)
\(422\) −6.03632e116 −0.900261
\(423\) −4.78695e115 −0.0642559
\(424\) 1.54040e117 1.86146
\(425\) 9.92094e116 1.07956
\(426\) −6.89098e116 −0.675389
\(427\) 7.67366e116 0.677582
\(428\) −9.86044e116 −0.784600
\(429\) 5.37184e116 0.385277
\(430\) 4.12537e116 0.266757
\(431\) −1.17992e117 −0.688042 −0.344021 0.938962i \(-0.611789\pi\)
−0.344021 + 0.938962i \(0.611789\pi\)
\(432\) 8.73770e116 0.459590
\(433\) 4.77799e116 0.226743 0.113372 0.993553i \(-0.463835\pi\)
0.113372 + 0.993553i \(0.463835\pi\)
\(434\) 5.22927e116 0.223948
\(435\) 6.56258e116 0.253689
\(436\) −1.75047e117 −0.610950
\(437\) 9.49801e116 0.299370
\(438\) −4.60088e117 −1.30992
\(439\) 5.26626e117 1.35466 0.677332 0.735678i \(-0.263136\pi\)
0.677332 + 0.735678i \(0.263136\pi\)
\(440\) 9.76146e116 0.226919
\(441\) 4.86479e116 0.102223
\(442\) −2.18389e117 −0.414896
\(443\) −1.09118e118 −1.87469 −0.937344 0.348406i \(-0.886723\pi\)
−0.937344 + 0.348406i \(0.886723\pi\)
\(444\) 9.83516e115 0.0152841
\(445\) −7.67343e115 −0.0107887
\(446\) −4.83615e117 −0.615317
\(447\) 4.51218e115 0.00519639
\(448\) 4.10086e117 0.427566
\(449\) 4.36528e117 0.412145 0.206073 0.978537i \(-0.433932\pi\)
0.206073 + 0.978537i \(0.433932\pi\)
\(450\) 1.06064e117 0.0907007
\(451\) 8.84842e117 0.685504
\(452\) 2.85413e117 0.200361
\(453\) 2.02553e118 1.28875
\(454\) 6.61694e117 0.381655
\(455\) −9.00220e116 −0.0470805
\(456\) 2.55823e118 1.21340
\(457\) −3.59688e118 −1.54759 −0.773793 0.633438i \(-0.781643\pi\)
−0.773793 + 0.633438i \(0.781643\pi\)
\(458\) −3.80255e118 −1.48444
\(459\) 3.39901e118 1.20417
\(460\) −7.45104e116 −0.0239604
\(461\) −5.08794e118 −1.48542 −0.742712 0.669611i \(-0.766461\pi\)
−0.742712 + 0.669611i \(0.766461\pi\)
\(462\) 1.01118e118 0.268077
\(463\) −3.69277e118 −0.889196 −0.444598 0.895730i \(-0.646654\pi\)
−0.444598 + 0.895730i \(0.646654\pi\)
\(464\) 2.27223e118 0.497052
\(465\) −7.70278e117 −0.153106
\(466\) 8.52930e117 0.154078
\(467\) −2.67556e118 −0.439352 −0.219676 0.975573i \(-0.570500\pi\)
−0.219676 + 0.975573i \(0.570500\pi\)
\(468\) 1.56798e117 0.0234099
\(469\) 2.63154e118 0.357288
\(470\) −7.71236e117 −0.0952429
\(471\) −3.36483e118 −0.378036
\(472\) 1.34577e119 1.37579
\(473\) −1.36675e119 −1.27165
\(474\) 9.59406e118 0.812580
\(475\) 1.46287e119 1.12808
\(476\) 2.76078e118 0.193875
\(477\) 3.33705e118 0.213450
\(478\) −1.94569e118 −0.113379
\(479\) 2.72713e118 0.144802 0.0724011 0.997376i \(-0.476934\pi\)
0.0724011 + 0.997376i \(0.476934\pi\)
\(480\) −3.43858e118 −0.166396
\(481\) −4.31949e117 −0.0190536
\(482\) −3.69576e119 −1.48631
\(483\) −2.69299e118 −0.0987616
\(484\) 2.74219e118 0.0917233
\(485\) −1.14271e118 −0.0348681
\(486\) 6.86589e118 0.191154
\(487\) 5.36131e119 1.36217 0.681087 0.732203i \(-0.261508\pi\)
0.681087 + 0.732203i \(0.261508\pi\)
\(488\) −7.51325e119 −1.74239
\(489\) 2.30925e119 0.488907
\(490\) 7.83776e118 0.151519
\(491\) −8.26069e119 −1.45844 −0.729222 0.684277i \(-0.760118\pi\)
−0.729222 + 0.684277i \(0.760118\pi\)
\(492\) −1.81917e119 −0.293378
\(493\) 8.83909e119 1.30233
\(494\) −3.22021e119 −0.433546
\(495\) 2.11468e118 0.0260203
\(496\) −2.66701e119 −0.299979
\(497\) −3.82589e119 −0.393435
\(498\) 1.15897e120 1.08984
\(499\) 9.69692e119 0.833987 0.416994 0.908909i \(-0.363084\pi\)
0.416994 + 0.908909i \(0.363084\pi\)
\(500\) −2.36426e119 −0.186008
\(501\) 1.49792e120 1.07823
\(502\) 1.27720e120 0.841286
\(503\) −8.76853e119 −0.528629 −0.264315 0.964436i \(-0.585146\pi\)
−0.264315 + 0.964436i \(0.585146\pi\)
\(504\) 1.02980e119 0.0568319
\(505\) 2.00877e119 0.101499
\(506\) −3.67576e119 −0.170078
\(507\) −1.72309e120 −0.730221
\(508\) −6.38178e119 −0.247746
\(509\) −4.82992e120 −1.71790 −0.858951 0.512057i \(-0.828883\pi\)
−0.858951 + 0.512057i \(0.828883\pi\)
\(510\) 6.05539e119 0.197365
\(511\) −2.55442e120 −0.763066
\(512\) −2.92012e120 −0.799627
\(513\) 5.01195e120 1.25830
\(514\) −9.75434e119 −0.224564
\(515\) 1.84508e119 0.0389577
\(516\) 2.80994e120 0.544233
\(517\) 2.55513e120 0.454029
\(518\) −8.13088e118 −0.0132575
\(519\) 5.30881e120 0.794419
\(520\) 8.81401e119 0.121067
\(521\) −2.52036e120 −0.317822 −0.158911 0.987293i \(-0.550798\pi\)
−0.158911 + 0.987293i \(0.550798\pi\)
\(522\) 9.44979e119 0.109417
\(523\) 1.51452e120 0.161046 0.0805229 0.996753i \(-0.474341\pi\)
0.0805229 + 0.996753i \(0.474341\pi\)
\(524\) 3.79723e120 0.370872
\(525\) −4.14772e120 −0.372152
\(526\) 1.52434e121 1.25666
\(527\) −1.03748e121 −0.785974
\(528\) −5.15718e120 −0.359089
\(529\) −1.46445e121 −0.937342
\(530\) 5.37639e120 0.316384
\(531\) 2.91542e120 0.157759
\(532\) 4.07085e120 0.202590
\(533\) 7.98960e120 0.365733
\(534\) 7.78265e119 0.0327749
\(535\) −1.20077e121 −0.465281
\(536\) −2.57653e121 −0.918760
\(537\) −1.78410e121 −0.585548
\(538\) 2.87803e120 0.0869528
\(539\) −2.59667e121 −0.722300
\(540\) −3.93179e120 −0.100709
\(541\) 2.85949e121 0.674544 0.337272 0.941407i \(-0.390496\pi\)
0.337272 + 0.941407i \(0.390496\pi\)
\(542\) 5.09861e121 1.10786
\(543\) 4.29829e121 0.860405
\(544\) −4.63140e121 −0.854203
\(545\) −2.13165e121 −0.362303
\(546\) 9.13034e120 0.143026
\(547\) 8.63056e121 1.24624 0.623122 0.782125i \(-0.285864\pi\)
0.623122 + 0.782125i \(0.285864\pi\)
\(548\) −1.02798e121 −0.136851
\(549\) −1.62763e121 −0.199796
\(550\) −5.66136e121 −0.640886
\(551\) 1.30335e122 1.36087
\(552\) 2.63670e121 0.253964
\(553\) 5.32664e121 0.473353
\(554\) −1.70413e122 −1.39740
\(555\) 1.19769e120 0.00906371
\(556\) 1.08673e121 0.0759091
\(557\) 5.63943e120 0.0363646 0.0181823 0.999835i \(-0.494212\pi\)
0.0181823 + 0.999835i \(0.494212\pi\)
\(558\) −1.10916e121 −0.0660349
\(559\) −1.23409e122 −0.678456
\(560\) 8.64247e120 0.0438804
\(561\) −2.00617e122 −0.940850
\(562\) −2.22953e122 −0.965934
\(563\) −4.00702e121 −0.160397 −0.0801987 0.996779i \(-0.525555\pi\)
−0.0801987 + 0.996779i \(0.525555\pi\)
\(564\) −5.25316e121 −0.194313
\(565\) 3.47565e121 0.118818
\(566\) 2.19057e122 0.692191
\(567\) −1.24161e122 −0.362692
\(568\) 3.74591e122 1.01171
\(569\) 7.53120e122 1.88091 0.940455 0.339918i \(-0.110399\pi\)
0.940455 + 0.339918i \(0.110399\pi\)
\(570\) 8.92886e121 0.206236
\(571\) 2.54331e122 0.543366 0.271683 0.962387i \(-0.412420\pi\)
0.271683 + 0.962387i \(0.412420\pi\)
\(572\) −8.36939e121 −0.165413
\(573\) −3.63940e122 −0.665502
\(574\) 1.50394e122 0.254478
\(575\) 1.50774e122 0.236107
\(576\) −8.69819e121 −0.126075
\(577\) −6.75470e122 −0.906321 −0.453161 0.891429i \(-0.649704\pi\)
−0.453161 + 0.891429i \(0.649704\pi\)
\(578\) 1.92973e122 0.239722
\(579\) −1.10204e123 −1.26766
\(580\) −1.02246e122 −0.108918
\(581\) 6.43460e122 0.634868
\(582\) 1.15897e122 0.105926
\(583\) −1.78121e123 −1.50822
\(584\) 2.50102e123 1.96221
\(585\) 1.90943e121 0.0138825
\(586\) −1.71258e123 −1.15400
\(587\) 3.95250e121 0.0246875 0.0123437 0.999924i \(-0.496071\pi\)
0.0123437 + 0.999924i \(0.496071\pi\)
\(588\) 5.33858e122 0.309126
\(589\) −1.52980e123 −0.821304
\(590\) 4.69709e122 0.233838
\(591\) −6.04220e121 −0.0278967
\(592\) 4.14688e121 0.0177585
\(593\) 2.53221e123 1.00593 0.502963 0.864308i \(-0.332243\pi\)
0.502963 + 0.864308i \(0.332243\pi\)
\(594\) −1.93964e123 −0.714864
\(595\) 3.36197e122 0.114971
\(596\) −7.03004e120 −0.00223100
\(597\) 4.37887e122 0.128975
\(598\) −3.31899e122 −0.0907409
\(599\) 4.15936e123 1.05568 0.527840 0.849344i \(-0.323002\pi\)
0.527840 + 0.849344i \(0.323002\pi\)
\(600\) 4.06101e123 0.956982
\(601\) 2.63415e123 0.576404 0.288202 0.957570i \(-0.406943\pi\)
0.288202 + 0.957570i \(0.406943\pi\)
\(602\) −2.32302e123 −0.472072
\(603\) −5.58167e122 −0.105352
\(604\) −3.15580e123 −0.553306
\(605\) 3.33934e122 0.0543934
\(606\) −2.03736e123 −0.308345
\(607\) −6.29951e122 −0.0885952 −0.0442976 0.999018i \(-0.514105\pi\)
−0.0442976 + 0.999018i \(0.514105\pi\)
\(608\) −6.82914e123 −0.892599
\(609\) −3.69542e123 −0.448946
\(610\) −2.62231e123 −0.296147
\(611\) 2.30713e123 0.242235
\(612\) −5.85579e122 −0.0571672
\(613\) −9.19228e123 −0.834511 −0.417256 0.908789i \(-0.637008\pi\)
−0.417256 + 0.908789i \(0.637008\pi\)
\(614\) 9.66565e123 0.816091
\(615\) −2.21532e123 −0.173978
\(616\) −5.49673e123 −0.401571
\(617\) −4.08750e123 −0.277823 −0.138911 0.990305i \(-0.544360\pi\)
−0.138911 + 0.990305i \(0.544360\pi\)
\(618\) −1.87134e123 −0.118350
\(619\) 2.80595e124 1.65138 0.825688 0.564127i \(-0.190787\pi\)
0.825688 + 0.564127i \(0.190787\pi\)
\(620\) 1.20010e123 0.0657337
\(621\) 5.16568e123 0.263361
\(622\) 1.15255e124 0.547000
\(623\) 4.32095e122 0.0190924
\(624\) −4.65662e123 −0.191583
\(625\) 2.17405e124 0.832931
\(626\) 1.53199e124 0.546635
\(627\) −2.95816e124 −0.983141
\(628\) 5.24245e123 0.162304
\(629\) 1.61316e123 0.0465289
\(630\) 3.59425e122 0.00965948
\(631\) 2.74236e124 0.686781 0.343391 0.939193i \(-0.388425\pi\)
0.343391 + 0.939193i \(0.388425\pi\)
\(632\) −5.21529e124 −1.21722
\(633\) −5.00690e124 −1.08919
\(634\) −3.36824e124 −0.683017
\(635\) −7.77148e123 −0.146917
\(636\) 3.66205e124 0.645480
\(637\) −2.34464e124 −0.385365
\(638\) −5.04400e124 −0.773135
\(639\) 8.11496e123 0.116011
\(640\) −6.79202e122 −0.00905712
\(641\) 1.82007e124 0.226415 0.113207 0.993571i \(-0.463888\pi\)
0.113207 + 0.993571i \(0.463888\pi\)
\(642\) 1.21786e125 1.41347
\(643\) 1.88790e124 0.204452 0.102226 0.994761i \(-0.467404\pi\)
0.102226 + 0.994761i \(0.467404\pi\)
\(644\) 4.19572e123 0.0424019
\(645\) 3.42183e124 0.322739
\(646\) 1.20262e125 1.05872
\(647\) −2.17534e125 −1.78766 −0.893832 0.448402i \(-0.851993\pi\)
−0.893832 + 0.448402i \(0.851993\pi\)
\(648\) 1.21565e125 0.932655
\(649\) −1.55616e125 −1.11472
\(650\) −5.11187e124 −0.341928
\(651\) 4.33747e124 0.270946
\(652\) −3.59784e124 −0.209905
\(653\) 1.56942e125 0.855268 0.427634 0.903952i \(-0.359347\pi\)
0.427634 + 0.903952i \(0.359347\pi\)
\(654\) 2.16200e125 1.10064
\(655\) 4.62412e124 0.219933
\(656\) −7.67033e124 −0.340874
\(657\) 5.41810e124 0.225003
\(658\) 4.34287e124 0.168548
\(659\) −3.65512e125 −1.32587 −0.662935 0.748677i \(-0.730690\pi\)
−0.662935 + 0.748677i \(0.730690\pi\)
\(660\) 2.32063e124 0.0786865
\(661\) 3.53397e125 1.12021 0.560104 0.828423i \(-0.310761\pi\)
0.560104 + 0.828423i \(0.310761\pi\)
\(662\) −3.15645e125 −0.935447
\(663\) −1.81145e125 −0.501966
\(664\) −6.30009e125 −1.63255
\(665\) 4.95733e124 0.120139
\(666\) 1.72461e123 0.00390920
\(667\) 1.34333e125 0.284828
\(668\) −2.33378e125 −0.462922
\(669\) −4.01140e125 −0.744447
\(670\) −8.99274e124 −0.156158
\(671\) 8.68780e125 1.41175
\(672\) 1.93628e125 0.294466
\(673\) 9.88007e125 1.40634 0.703169 0.711023i \(-0.251768\pi\)
0.703169 + 0.711023i \(0.251768\pi\)
\(674\) −1.64646e124 −0.0219375
\(675\) 7.95612e125 0.992393
\(676\) 2.68460e125 0.313510
\(677\) −5.70038e125 −0.623316 −0.311658 0.950194i \(-0.600884\pi\)
−0.311658 + 0.950194i \(0.600884\pi\)
\(678\) −3.52513e125 −0.360955
\(679\) 6.43465e124 0.0617050
\(680\) −3.29169e125 −0.295646
\(681\) 5.48849e125 0.461750
\(682\) 5.92036e125 0.466599
\(683\) −3.27309e125 −0.241678 −0.120839 0.992672i \(-0.538558\pi\)
−0.120839 + 0.992672i \(0.538558\pi\)
\(684\) −8.63454e124 −0.0597369
\(685\) −1.25183e125 −0.0811548
\(686\) −9.78118e125 −0.594249
\(687\) −3.15407e126 −1.79596
\(688\) 1.18478e126 0.632341
\(689\) −1.60833e126 −0.804674
\(690\) 9.20275e124 0.0431651
\(691\) 2.05988e126 0.905877 0.452938 0.891542i \(-0.350376\pi\)
0.452938 + 0.891542i \(0.350376\pi\)
\(692\) −8.27119e125 −0.341073
\(693\) −1.19079e125 −0.0460473
\(694\) −1.66372e126 −0.603372
\(695\) 1.32338e125 0.0450153
\(696\) 3.61817e126 1.15446
\(697\) −2.98380e126 −0.893123
\(698\) 1.62869e126 0.457376
\(699\) 7.07472e125 0.186412
\(700\) 6.46220e125 0.159778
\(701\) 4.71347e126 1.09368 0.546839 0.837238i \(-0.315831\pi\)
0.546839 + 0.837238i \(0.315831\pi\)
\(702\) −1.75138e126 −0.381398
\(703\) 2.37865e125 0.0486204
\(704\) 4.64282e126 0.890838
\(705\) −6.39710e125 −0.115230
\(706\) −6.96371e125 −0.117769
\(707\) −1.13115e126 −0.179620
\(708\) 3.19936e126 0.477070
\(709\) −7.09898e126 −0.994120 −0.497060 0.867716i \(-0.665587\pi\)
−0.497060 + 0.867716i \(0.665587\pi\)
\(710\) 1.30742e126 0.171956
\(711\) −1.12982e126 −0.139576
\(712\) −4.23062e125 −0.0490958
\(713\) −1.57672e126 −0.171898
\(714\) −3.40982e126 −0.349270
\(715\) −1.01919e126 −0.0980928
\(716\) 2.77965e126 0.251397
\(717\) −1.61387e126 −0.137172
\(718\) −9.79630e126 −0.782572
\(719\) 1.17855e127 0.884939 0.442470 0.896783i \(-0.354102\pi\)
0.442470 + 0.896783i \(0.354102\pi\)
\(720\) −1.83313e125 −0.0129389
\(721\) −1.03897e126 −0.0689423
\(722\) 5.33531e126 0.332855
\(723\) −3.06549e127 −1.79823
\(724\) −6.69679e126 −0.369403
\(725\) 2.06898e127 1.07329
\(726\) −3.38687e126 −0.165242
\(727\) −1.19951e127 −0.550458 −0.275229 0.961379i \(-0.588754\pi\)
−0.275229 + 0.961379i \(0.588754\pi\)
\(728\) −4.96322e126 −0.214248
\(729\) 2.68778e127 1.09149
\(730\) 8.72920e126 0.333509
\(731\) 4.60884e127 1.65679
\(732\) −1.78615e127 −0.604192
\(733\) 8.96644e125 0.0285426 0.0142713 0.999898i \(-0.495457\pi\)
0.0142713 + 0.999898i \(0.495457\pi\)
\(734\) 2.71127e127 0.812266
\(735\) 6.50112e126 0.183317
\(736\) −7.03861e126 −0.186820
\(737\) 2.97932e127 0.744414
\(738\) −3.18995e126 −0.0750371
\(739\) −1.58170e127 −0.350306 −0.175153 0.984541i \(-0.556042\pi\)
−0.175153 + 0.984541i \(0.556042\pi\)
\(740\) −1.86601e125 −0.00389138
\(741\) −2.67104e127 −0.524530
\(742\) −3.02747e127 −0.559895
\(743\) −1.06713e128 −1.85872 −0.929360 0.369176i \(-0.879640\pi\)
−0.929360 + 0.369176i \(0.879640\pi\)
\(744\) −4.24680e127 −0.696733
\(745\) −8.56091e124 −0.00132302
\(746\) −3.23308e127 −0.470693
\(747\) −1.36482e127 −0.187201
\(748\) 3.12564e127 0.403941
\(749\) 6.76158e127 0.823393
\(750\) 2.92009e127 0.335097
\(751\) 5.91843e127 0.640072 0.320036 0.947405i \(-0.396305\pi\)
0.320036 + 0.947405i \(0.396305\pi\)
\(752\) −2.21493e127 −0.225770
\(753\) 1.05939e128 1.01784
\(754\) −4.55443e127 −0.412486
\(755\) −3.84301e127 −0.328119
\(756\) 2.21401e127 0.178222
\(757\) 1.35916e127 0.103158 0.0515792 0.998669i \(-0.483575\pi\)
0.0515792 + 0.998669i \(0.483575\pi\)
\(758\) 1.28877e128 0.922350
\(759\) −3.04890e127 −0.205771
\(760\) −4.85370e127 −0.308935
\(761\) −1.07211e128 −0.643607 −0.321804 0.946806i \(-0.604289\pi\)
−0.321804 + 0.946806i \(0.604289\pi\)
\(762\) 7.88211e127 0.446320
\(763\) 1.20035e128 0.641157
\(764\) 5.67023e127 0.285724
\(765\) −7.13096e126 −0.0339011
\(766\) 1.30257e128 0.584280
\(767\) −1.40512e128 −0.594729
\(768\) −2.30698e128 −0.921443
\(769\) −6.47273e124 −0.000243986 0 −0.000121993 1.00000i \(-0.500039\pi\)
−0.000121993 1.00000i \(0.500039\pi\)
\(770\) −1.91850e127 −0.0682534
\(771\) −8.09085e127 −0.271690
\(772\) 1.71700e128 0.544251
\(773\) −3.33193e128 −0.997030 −0.498515 0.866881i \(-0.666121\pi\)
−0.498515 + 0.866881i \(0.666121\pi\)
\(774\) 4.92727e127 0.139198
\(775\) −2.42845e128 −0.647744
\(776\) −6.30014e127 −0.158673
\(777\) −6.74424e126 −0.0160398
\(778\) 5.73124e128 1.28723
\(779\) −4.39971e128 −0.933269
\(780\) 2.09539e127 0.0419812
\(781\) −4.33151e128 −0.819726
\(782\) 1.23951e128 0.221590
\(783\) 7.08853e128 1.19718
\(784\) 2.25095e128 0.359171
\(785\) 6.38405e127 0.0962491
\(786\) −4.68994e128 −0.668135
\(787\) 8.30772e127 0.111842 0.0559212 0.998435i \(-0.482190\pi\)
0.0559212 + 0.998435i \(0.482190\pi\)
\(788\) 9.41383e126 0.0119770
\(789\) 1.26438e129 1.52038
\(790\) −1.82027e128 −0.206885
\(791\) −1.95716e128 −0.210268
\(792\) 1.16589e128 0.118410
\(793\) 7.84457e128 0.753203
\(794\) −1.53274e129 −1.39141
\(795\) 4.45951e128 0.382780
\(796\) −6.82234e127 −0.0553735
\(797\) 2.28637e129 1.75490 0.877448 0.479671i \(-0.159244\pi\)
0.877448 + 0.479671i \(0.159244\pi\)
\(798\) −5.02789e128 −0.364970
\(799\) −8.61621e128 −0.591541
\(800\) −1.08408e129 −0.703974
\(801\) −9.16501e126 −0.00562971
\(802\) −1.11683e129 −0.648977
\(803\) −2.89201e129 −1.58986
\(804\) −6.12528e128 −0.318590
\(805\) 5.10938e127 0.0251450
\(806\) 5.34573e128 0.248942
\(807\) 2.38721e128 0.105201
\(808\) 1.10750e129 0.461891
\(809\) −1.46938e129 −0.579997 −0.289999 0.957027i \(-0.593655\pi\)
−0.289999 + 0.957027i \(0.593655\pi\)
\(810\) 4.24293e128 0.158519
\(811\) −8.00048e128 −0.282936 −0.141468 0.989943i \(-0.545182\pi\)
−0.141468 + 0.989943i \(0.545182\pi\)
\(812\) 5.75751e128 0.192749
\(813\) 4.22910e129 1.34035
\(814\) −9.20545e127 −0.0276222
\(815\) −4.38131e128 −0.124477
\(816\) 1.73907e129 0.467847
\(817\) 6.79588e129 1.73127
\(818\) 2.85055e129 0.687712
\(819\) −1.07521e128 −0.0245674
\(820\) 3.45150e128 0.0746949
\(821\) −4.07345e129 −0.835010 −0.417505 0.908675i \(-0.637095\pi\)
−0.417505 + 0.908675i \(0.637095\pi\)
\(822\) 1.26965e129 0.246540
\(823\) −7.86998e129 −1.44771 −0.723854 0.689953i \(-0.757631\pi\)
−0.723854 + 0.689953i \(0.757631\pi\)
\(824\) 1.01726e129 0.177284
\(825\) −4.69588e129 −0.775382
\(826\) −2.64496e129 −0.413815
\(827\) −4.50103e129 −0.667293 −0.333646 0.942698i \(-0.608279\pi\)
−0.333646 + 0.942698i \(0.608279\pi\)
\(828\) −8.89940e127 −0.0125029
\(829\) 1.34040e130 1.78467 0.892336 0.451371i \(-0.149065\pi\)
0.892336 + 0.451371i \(0.149065\pi\)
\(830\) −2.19889e129 −0.277478
\(831\) −1.41351e130 −1.69065
\(832\) 4.19219e129 0.475284
\(833\) 8.75631e129 0.941063
\(834\) −1.34222e129 −0.136752
\(835\) −2.84199e129 −0.274520
\(836\) 4.60885e129 0.422098
\(837\) −8.32011e129 −0.722514
\(838\) −1.24758e130 −1.02733
\(839\) 1.46067e130 1.14063 0.570315 0.821426i \(-0.306821\pi\)
0.570315 + 0.821426i \(0.306821\pi\)
\(840\) 1.37618e129 0.101917
\(841\) 4.19654e129 0.294761
\(842\) 1.27111e128 0.00846829
\(843\) −1.84931e130 −1.16864
\(844\) 7.80081e129 0.467628
\(845\) 3.26920e129 0.185917
\(846\) −9.21151e128 −0.0496992
\(847\) −1.88040e129 −0.0962583
\(848\) 1.54406e130 0.749979
\(849\) 1.81699e130 0.837454
\(850\) 1.90908e130 0.834992
\(851\) 2.45161e128 0.0101762
\(852\) 8.90529e129 0.350821
\(853\) −1.41360e130 −0.528562 −0.264281 0.964446i \(-0.585135\pi\)
−0.264281 + 0.964446i \(0.585135\pi\)
\(854\) 1.47664e130 0.524082
\(855\) −1.05148e129 −0.0354250
\(856\) −6.62023e130 −2.11734
\(857\) 3.80993e130 1.15683 0.578417 0.815742i \(-0.303671\pi\)
0.578417 + 0.815742i \(0.303671\pi\)
\(858\) 1.03370e130 0.297996
\(859\) −5.21106e130 −1.42636 −0.713182 0.700979i \(-0.752746\pi\)
−0.713182 + 0.700979i \(0.752746\pi\)
\(860\) −5.33126e129 −0.138563
\(861\) 1.24746e130 0.307883
\(862\) −2.27052e130 −0.532172
\(863\) −1.19612e130 −0.266253 −0.133127 0.991099i \(-0.542502\pi\)
−0.133127 + 0.991099i \(0.542502\pi\)
\(864\) −3.71416e130 −0.785234
\(865\) −1.00723e130 −0.202262
\(866\) 9.19427e129 0.175376
\(867\) 1.60064e130 0.290030
\(868\) −6.75784e129 −0.116327
\(869\) 6.03061e130 0.986236
\(870\) 1.26283e130 0.196218
\(871\) 2.69015e130 0.397163
\(872\) −1.17525e131 −1.64872
\(873\) −1.36483e129 −0.0181947
\(874\) 1.82770e130 0.231551
\(875\) 1.62124e130 0.195204
\(876\) 5.94577e130 0.680418
\(877\) 1.16850e131 1.27101 0.635503 0.772099i \(-0.280793\pi\)
0.635503 + 0.772099i \(0.280793\pi\)
\(878\) 1.01338e131 1.04778
\(879\) −1.42052e131 −1.39618
\(880\) 9.78466e129 0.0914254
\(881\) 1.91284e131 1.69923 0.849614 0.527406i \(-0.176835\pi\)
0.849614 + 0.527406i \(0.176835\pi\)
\(882\) 9.36130e129 0.0790650
\(883\) −3.55710e130 −0.285657 −0.142828 0.989747i \(-0.545620\pi\)
−0.142828 + 0.989747i \(0.545620\pi\)
\(884\) 2.82226e130 0.215512
\(885\) 3.89605e130 0.282911
\(886\) −2.09974e131 −1.44999
\(887\) −2.68906e131 −1.76603 −0.883017 0.469341i \(-0.844492\pi\)
−0.883017 + 0.469341i \(0.844492\pi\)
\(888\) 6.60326e129 0.0412460
\(889\) 4.37616e130 0.259995
\(890\) −1.47659e129 −0.00834460
\(891\) −1.40569e131 −0.755672
\(892\) 6.24981e130 0.319618
\(893\) −1.27049e131 −0.618131
\(894\) 8.68277e128 0.00401919
\(895\) 3.38495e130 0.149083
\(896\) 3.82462e129 0.0160281
\(897\) −2.75297e130 −0.109784
\(898\) 8.40009e130 0.318777
\(899\) −2.16364e131 −0.781408
\(900\) −1.37067e130 −0.0471132
\(901\) 6.00648e131 1.96502
\(902\) 1.70270e131 0.530208
\(903\) −1.92685e131 −0.571141
\(904\) 1.91625e131 0.540700
\(905\) −8.15509e130 −0.219062
\(906\) 3.89771e131 0.996792
\(907\) −4.49131e131 −1.09357 −0.546787 0.837272i \(-0.684149\pi\)
−0.546787 + 0.837272i \(0.684149\pi\)
\(908\) −8.55114e130 −0.198246
\(909\) 2.39924e130 0.0529641
\(910\) −1.73229e130 −0.0364148
\(911\) −2.09946e131 −0.420282 −0.210141 0.977671i \(-0.567392\pi\)
−0.210141 + 0.977671i \(0.567392\pi\)
\(912\) 2.56431e131 0.488877
\(913\) 7.28499e131 1.32276
\(914\) −6.92146e131 −1.19699
\(915\) −2.17511e131 −0.358296
\(916\) 4.91408e131 0.771070
\(917\) −2.60387e131 −0.389209
\(918\) 6.54070e131 0.931376
\(919\) −3.59597e131 −0.487839 −0.243919 0.969796i \(-0.578433\pi\)
−0.243919 + 0.969796i \(0.578433\pi\)
\(920\) −5.00258e130 −0.0646600
\(921\) 8.01728e131 0.987355
\(922\) −9.79069e131 −1.14891
\(923\) −3.91110e131 −0.437344
\(924\) −1.30676e131 −0.139249
\(925\) 3.77595e130 0.0383459
\(926\) −7.10597e131 −0.687756
\(927\) 2.20373e130 0.0203288
\(928\) −9.65864e131 −0.849241
\(929\) −1.24505e132 −1.04349 −0.521745 0.853102i \(-0.674719\pi\)
−0.521745 + 0.853102i \(0.674719\pi\)
\(930\) −1.48224e131 −0.118421
\(931\) 1.29115e132 0.983364
\(932\) −1.10225e131 −0.0800336
\(933\) 9.55994e131 0.661793
\(934\) −5.14856e131 −0.339821
\(935\) 3.80628e131 0.239543
\(936\) 1.05273e131 0.0631746
\(937\) 1.91446e132 1.09555 0.547777 0.836624i \(-0.315474\pi\)
0.547777 + 0.836624i \(0.315474\pi\)
\(938\) 5.06386e131 0.276347
\(939\) 1.27072e132 0.661351
\(940\) 9.96676e130 0.0494726
\(941\) 2.75820e132 1.30583 0.652916 0.757431i \(-0.273546\pi\)
0.652916 + 0.757431i \(0.273546\pi\)
\(942\) −6.47493e131 −0.292395
\(943\) −4.53466e131 −0.195332
\(944\) 1.34897e132 0.554305
\(945\) 2.69614e131 0.105688
\(946\) −2.63003e132 −0.983568
\(947\) −1.89826e132 −0.677300 −0.338650 0.940912i \(-0.609970\pi\)
−0.338650 + 0.940912i \(0.609970\pi\)
\(948\) −1.23985e132 −0.422083
\(949\) −2.61131e132 −0.848227
\(950\) 2.81500e132 0.872525
\(951\) −2.79382e132 −0.826354
\(952\) 1.85357e132 0.523195
\(953\) −2.66119e132 −0.716871 −0.358436 0.933554i \(-0.616690\pi\)
−0.358436 + 0.933554i \(0.616690\pi\)
\(954\) 6.42147e131 0.165094
\(955\) 6.90499e131 0.169439
\(956\) 2.51443e131 0.0588930
\(957\) −4.18381e132 −0.935385
\(958\) 5.24780e131 0.111999
\(959\) 7.04911e131 0.143617
\(960\) −1.16239e132 −0.226091
\(961\) −2.84551e132 −0.528408
\(962\) −8.31197e130 −0.0147371
\(963\) −1.43418e132 −0.242791
\(964\) 4.77607e132 0.772045
\(965\) 2.09089e132 0.322750
\(966\) −5.18211e131 −0.0763880
\(967\) 5.83176e132 0.820959 0.410480 0.911870i \(-0.365361\pi\)
0.410480 + 0.911870i \(0.365361\pi\)
\(968\) 1.84109e132 0.247527
\(969\) 9.97529e132 1.28091
\(970\) −2.19891e131 −0.0269690
\(971\) −5.38578e132 −0.630947 −0.315473 0.948934i \(-0.602163\pi\)
−0.315473 + 0.948934i \(0.602163\pi\)
\(972\) −8.87286e131 −0.0992921
\(973\) −7.45201e131 −0.0796622
\(974\) 1.03167e133 1.05358
\(975\) −4.24009e132 −0.413685
\(976\) −7.53110e132 −0.702007
\(977\) 4.38063e132 0.390147 0.195073 0.980789i \(-0.437505\pi\)
0.195073 + 0.980789i \(0.437505\pi\)
\(978\) 4.44367e132 0.378149
\(979\) 4.89200e131 0.0397792
\(980\) −1.01288e132 −0.0787044
\(981\) −2.54601e132 −0.189056
\(982\) −1.58960e133 −1.12805
\(983\) −1.19142e133 −0.808042 −0.404021 0.914750i \(-0.632388\pi\)
−0.404021 + 0.914750i \(0.632388\pi\)
\(984\) −1.22138e133 −0.791716
\(985\) 1.14638e131 0.00710258
\(986\) 1.70090e133 1.00729
\(987\) 3.60224e132 0.203920
\(988\) 4.16152e132 0.225200
\(989\) 7.00434e132 0.362353
\(990\) 4.06926e131 0.0201256
\(991\) −2.01317e132 −0.0951923 −0.0475962 0.998867i \(-0.515156\pi\)
−0.0475962 + 0.998867i \(0.515156\pi\)
\(992\) 1.13368e133 0.512530
\(993\) −2.61816e133 −1.13176
\(994\) −7.36214e132 −0.304305
\(995\) −8.30798e131 −0.0328374
\(996\) −1.49774e133 −0.566105
\(997\) −9.22203e132 −0.333344 −0.166672 0.986012i \(-0.553302\pi\)
−0.166672 + 0.986012i \(0.553302\pi\)
\(998\) 1.86597e133 0.645054
\(999\) 1.29368e132 0.0427722
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.90.a.a.1.6 7
3.2 odd 2 9.90.a.b.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.6 7 1.1 even 1 trivial
9.90.a.b.1.2 7 3.2 odd 2