Properties

Label 1.90.a.a.1.3
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: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
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 1.3
Root \(3.74539e11\) of \(x^{7} - 3 x^{6} - 1400531600527934473811256 x^{5} + 92429106535860966322690362643440028 x^{4} + 486502004825754823566786579226467181483733375376 x^{3} - 41390338158988484679355574715314473323669246141474080139600 x^{2} - 47785461930919140795588898989186212855196409324706742802409577734342400 x + 5612439960923763868733925256800794059272997589318959539312206365735127554315560000\)
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.24646e13 q^{2} -6.44834e20 q^{3} -1.14310e26 q^{4} -1.81181e31 q^{5} +1.44860e34 q^{6} -2.76134e37 q^{7} +1.64729e40 q^{8} -2.49351e42 q^{9} +O(q^{10})\) \(q-2.24646e13 q^{2} -6.44834e20 q^{3} -1.14310e26 q^{4} -1.81181e31 q^{5} +1.44860e34 q^{6} -2.76134e37 q^{7} +1.64729e40 q^{8} -2.49351e42 q^{9} +4.07017e44 q^{10} +2.89211e46 q^{11} +7.37110e46 q^{12} -2.93091e49 q^{13} +6.20325e50 q^{14} +1.16832e52 q^{15} -2.99303e53 q^{16} +3.53494e54 q^{17} +5.60158e55 q^{18} -2.73074e56 q^{19} +2.07108e57 q^{20} +1.78060e58 q^{21} -6.49703e59 q^{22} +5.99973e60 q^{23} -1.06223e61 q^{24} +1.66707e62 q^{25} +6.58419e62 q^{26} +3.48393e63 q^{27} +3.15649e63 q^{28} +2.05712e65 q^{29} -2.62458e65 q^{30} -1.59142e66 q^{31} -3.47249e66 q^{32} -1.86493e67 q^{33} -7.94112e67 q^{34} +5.00303e68 q^{35} +2.85033e68 q^{36} +1.13777e69 q^{37} +6.13450e69 q^{38} +1.88995e70 q^{39} -2.98457e71 q^{40} +8.14082e70 q^{41} -4.00006e71 q^{42} +3.18229e72 q^{43} -3.30598e72 q^{44} +4.51777e73 q^{45} -1.34782e74 q^{46} -3.19743e74 q^{47} +1.93000e74 q^{48} -8.73283e74 q^{49} -3.74502e75 q^{50} -2.27945e75 q^{51} +3.35033e75 q^{52} -1.04143e77 q^{53} -7.82652e76 q^{54} -5.23996e77 q^{55} -4.54872e77 q^{56} +1.76087e77 q^{57} -4.62126e78 q^{58} +8.65856e78 q^{59} -1.33550e78 q^{60} -3.87413e79 q^{61} +3.57506e79 q^{62} +6.88543e79 q^{63} +2.63268e80 q^{64} +5.31026e80 q^{65} +4.18950e80 q^{66} +1.41209e81 q^{67} -4.04080e80 q^{68} -3.86883e81 q^{69} -1.12391e82 q^{70} +1.52471e82 q^{71} -4.10753e82 q^{72} -5.28056e82 q^{73} -2.55595e82 q^{74} -1.07498e83 q^{75} +3.12151e82 q^{76} -7.98611e83 q^{77} -4.24571e83 q^{78} +4.95085e84 q^{79} +5.42280e84 q^{80} +5.00787e84 q^{81} -1.82881e84 q^{82} +5.30230e84 q^{83} -2.03541e84 q^{84} -6.40465e85 q^{85} -7.14891e85 q^{86} -1.32650e86 q^{87} +4.76414e86 q^{88} -6.27807e86 q^{89} -1.01490e87 q^{90} +8.09324e86 q^{91} -6.85829e86 q^{92} +1.02620e87 q^{93} +7.18291e87 q^{94} +4.94758e87 q^{95} +2.23918e87 q^{96} +2.15232e88 q^{97} +1.96180e88 q^{98} -7.21151e88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24646e13 −0.902952 −0.451476 0.892283i \(-0.649102\pi\)
−0.451476 + 0.892283i \(0.649102\pi\)
\(3\) −6.44834e20 −0.378052 −0.189026 0.981972i \(-0.560533\pi\)
−0.189026 + 0.981972i \(0.560533\pi\)
\(4\) −1.14310e26 −0.184678
\(5\) −1.81181e31 −1.42544 −0.712718 0.701451i \(-0.752536\pi\)
−0.712718 + 0.701451i \(0.752536\pi\)
\(6\) 1.44860e34 0.341363
\(7\) −2.76134e37 −0.682743 −0.341371 0.939929i \(-0.610891\pi\)
−0.341371 + 0.939929i \(0.610891\pi\)
\(8\) 1.64729e40 1.06971
\(9\) −2.49351e42 −0.857076
\(10\) 4.07017e44 1.28710
\(11\) 2.89211e46 1.31595 0.657977 0.753038i \(-0.271412\pi\)
0.657977 + 0.753038i \(0.271412\pi\)
\(12\) 7.37110e46 0.0698179
\(13\) −2.93091e49 −0.787995 −0.393998 0.919111i \(-0.628908\pi\)
−0.393998 + 0.919111i \(0.628908\pi\)
\(14\) 6.20325e50 0.616484
\(15\) 1.16832e52 0.538889
\(16\) −2.99303e53 −0.781216
\(17\) 3.53494e54 0.621449 0.310725 0.950500i \(-0.399428\pi\)
0.310725 + 0.950500i \(0.399428\pi\)
\(18\) 5.60158e55 0.773899
\(19\) −2.73074e56 −0.340208 −0.170104 0.985426i \(-0.554410\pi\)
−0.170104 + 0.985426i \(0.554410\pi\)
\(20\) 2.07108e57 0.263246
\(21\) 1.78060e58 0.258112
\(22\) −6.49703e59 −1.18824
\(23\) 5.99973e60 1.51790 0.758949 0.651150i \(-0.225713\pi\)
0.758949 + 0.651150i \(0.225713\pi\)
\(24\) −1.06223e61 −0.404405
\(25\) 1.66707e62 1.03187
\(26\) 6.58419e62 0.711522
\(27\) 3.48393e63 0.702072
\(28\) 3.15649e63 0.126087
\(29\) 2.05712e65 1.72405 0.862025 0.506867i \(-0.169196\pi\)
0.862025 + 0.506867i \(0.169196\pi\)
\(30\) −2.62458e65 −0.486591
\(31\) −1.59142e66 −0.685786 −0.342893 0.939375i \(-0.611407\pi\)
−0.342893 + 0.939375i \(0.611407\pi\)
\(32\) −3.47249e66 −0.364306
\(33\) −1.86493e67 −0.497499
\(34\) −7.94112e67 −0.561139
\(35\) 5.00303e68 0.973206
\(36\) 2.85033e68 0.158283
\(37\) 1.13777e69 0.186671 0.0933353 0.995635i \(-0.470247\pi\)
0.0933353 + 0.995635i \(0.470247\pi\)
\(38\) 6.13450e69 0.307191
\(39\) 1.88995e70 0.297903
\(40\) −2.98457e71 −1.52480
\(41\) 8.14082e70 0.138607 0.0693037 0.997596i \(-0.477922\pi\)
0.0693037 + 0.997596i \(0.477922\pi\)
\(42\) −4.00006e71 −0.233063
\(43\) 3.18229e72 0.650720 0.325360 0.945590i \(-0.394515\pi\)
0.325360 + 0.945590i \(0.394515\pi\)
\(44\) −3.30598e72 −0.243028
\(45\) 4.51777e73 1.22171
\(46\) −1.34782e74 −1.37059
\(47\) −3.19743e74 −1.24867 −0.624333 0.781159i \(-0.714629\pi\)
−0.624333 + 0.781159i \(0.714629\pi\)
\(48\) 1.93000e74 0.295341
\(49\) −8.73283e74 −0.533862
\(50\) −3.74502e75 −0.931727
\(51\) −2.27945e75 −0.234940
\(52\) 3.35033e75 0.145525
\(53\) −1.04143e77 −1.93800 −0.968999 0.247063i \(-0.920534\pi\)
−0.968999 + 0.247063i \(0.920534\pi\)
\(54\) −7.82652e76 −0.633937
\(55\) −5.23996e77 −1.87581
\(56\) −4.54872e77 −0.730335
\(57\) 1.76087e77 0.128616
\(58\) −4.62126e78 −1.55673
\(59\) 8.65856e78 1.36311 0.681556 0.731766i \(-0.261304\pi\)
0.681556 + 0.731766i \(0.261304\pi\)
\(60\) −1.33550e78 −0.0995209
\(61\) −3.87413e79 −1.38356 −0.691778 0.722110i \(-0.743172\pi\)
−0.691778 + 0.722110i \(0.743172\pi\)
\(62\) 3.57506e79 0.619231
\(63\) 6.88543e79 0.585163
\(64\) 2.63268e80 1.11017
\(65\) 5.31026e80 1.12324
\(66\) 4.18950e80 0.449218
\(67\) 1.41209e81 0.775416 0.387708 0.921782i \(-0.373267\pi\)
0.387708 + 0.921782i \(0.373267\pi\)
\(68\) −4.04080e80 −0.114768
\(69\) −3.86883e81 −0.573845
\(70\) −1.12391e82 −0.878758
\(71\) 1.52471e82 0.634148 0.317074 0.948401i \(-0.397300\pi\)
0.317074 + 0.948401i \(0.397300\pi\)
\(72\) −4.10753e82 −0.916821
\(73\) −5.28056e82 −0.637989 −0.318994 0.947757i \(-0.603345\pi\)
−0.318994 + 0.947757i \(0.603345\pi\)
\(74\) −2.55595e82 −0.168555
\(75\) −1.07498e83 −0.390100
\(76\) 3.12151e82 0.0628289
\(77\) −7.98611e83 −0.898458
\(78\) −4.24571e83 −0.268992
\(79\) 4.95085e84 1.77940 0.889702 0.456542i \(-0.150912\pi\)
0.889702 + 0.456542i \(0.150912\pi\)
\(80\) 5.42280e84 1.11357
\(81\) 5.00787e84 0.591657
\(82\) −1.82881e84 −0.125156
\(83\) 5.30230e84 0.211587 0.105794 0.994388i \(-0.466262\pi\)
0.105794 + 0.994388i \(0.466262\pi\)
\(84\) −2.03541e84 −0.0476676
\(85\) −6.40465e85 −0.885836
\(86\) −7.14891e85 −0.587568
\(87\) −1.32650e86 −0.651781
\(88\) 4.76414e86 1.40769
\(89\) −6.27807e86 −1.12194 −0.560972 0.827835i \(-0.689572\pi\)
−0.560972 + 0.827835i \(0.689572\pi\)
\(90\) −1.01490e87 −1.10314
\(91\) 8.09324e86 0.537998
\(92\) −6.85829e86 −0.280322
\(93\) 1.02620e87 0.259263
\(94\) 7.18291e87 1.12748
\(95\) 4.94758e87 0.484945
\(96\) 2.23918e87 0.137727
\(97\) 2.15232e88 0.834766 0.417383 0.908731i \(-0.362947\pi\)
0.417383 + 0.908731i \(0.362947\pi\)
\(98\) 1.96180e88 0.482052
\(99\) −7.21151e88 −1.12787
\(100\) −1.90563e88 −0.190563
\(101\) −2.76146e89 −1.77353 −0.886763 0.462225i \(-0.847051\pi\)
−0.886763 + 0.462225i \(0.847051\pi\)
\(102\) 5.12070e88 0.212140
\(103\) 1.89577e89 0.508780 0.254390 0.967102i \(-0.418125\pi\)
0.254390 + 0.967102i \(0.418125\pi\)
\(104\) −4.82805e89 −0.842924
\(105\) −3.22612e89 −0.367923
\(106\) 2.33953e90 1.74992
\(107\) −3.99265e89 −0.196645 −0.0983226 0.995155i \(-0.531348\pi\)
−0.0983226 + 0.995155i \(0.531348\pi\)
\(108\) −3.98248e89 −0.129657
\(109\) −3.60049e90 −0.777826 −0.388913 0.921274i \(-0.627149\pi\)
−0.388913 + 0.921274i \(0.627149\pi\)
\(110\) 1.17714e91 1.69376
\(111\) −7.33669e89 −0.0705713
\(112\) 8.26476e90 0.533370
\(113\) 1.16933e91 0.508095 0.254047 0.967192i \(-0.418238\pi\)
0.254047 + 0.967192i \(0.418238\pi\)
\(114\) −3.95573e90 −0.116134
\(115\) −1.08704e92 −2.16367
\(116\) −2.35150e91 −0.318394
\(117\) 7.30826e91 0.675372
\(118\) −1.94511e92 −1.23082
\(119\) −9.76118e91 −0.424290
\(120\) 1.92455e92 0.576454
\(121\) 3.53430e92 0.731735
\(122\) 8.70310e92 1.24928
\(123\) −5.24948e91 −0.0524009
\(124\) 1.81915e92 0.126649
\(125\) −9.32811e91 −0.0454253
\(126\) −1.54679e93 −0.528374
\(127\) 4.35388e93 1.04619 0.523096 0.852274i \(-0.324777\pi\)
0.523096 + 0.852274i \(0.324777\pi\)
\(128\) −3.76484e93 −0.638121
\(129\) −2.05205e93 −0.246006
\(130\) −1.19293e94 −1.01423
\(131\) 2.78935e93 0.168628 0.0843141 0.996439i \(-0.473130\pi\)
0.0843141 + 0.996439i \(0.473130\pi\)
\(132\) 2.13180e93 0.0918771
\(133\) 7.54049e93 0.232274
\(134\) −3.17222e94 −0.700164
\(135\) −6.31222e94 −1.00076
\(136\) 5.82307e94 0.664769
\(137\) 1.13533e95 0.935530 0.467765 0.883853i \(-0.345059\pi\)
0.467765 + 0.883853i \(0.345059\pi\)
\(138\) 8.69118e94 0.518155
\(139\) 2.67554e95 1.15679 0.578394 0.815758i \(-0.303680\pi\)
0.578394 + 0.815758i \(0.303680\pi\)
\(140\) −5.71896e94 −0.179730
\(141\) 2.06181e95 0.472061
\(142\) −3.42520e95 −0.572605
\(143\) −8.47653e95 −1.03697
\(144\) 7.46314e95 0.669562
\(145\) −3.72712e96 −2.45752
\(146\) 1.18626e96 0.576073
\(147\) 5.63122e95 0.201828
\(148\) −1.30058e95 −0.0344739
\(149\) 1.67237e96 0.328505 0.164253 0.986418i \(-0.447479\pi\)
0.164253 + 0.986418i \(0.447479\pi\)
\(150\) 2.41491e96 0.352241
\(151\) 5.57662e96 0.605197 0.302599 0.953118i \(-0.402146\pi\)
0.302599 + 0.953118i \(0.402146\pi\)
\(152\) −4.49831e96 −0.363923
\(153\) −8.81442e96 −0.532629
\(154\) 1.79405e97 0.811264
\(155\) 2.88335e97 0.977543
\(156\) −2.16040e96 −0.0550162
\(157\) 1.11335e96 0.0213351 0.0106676 0.999943i \(-0.496604\pi\)
0.0106676 + 0.999943i \(0.496604\pi\)
\(158\) −1.11219e98 −1.60672
\(159\) 6.71549e97 0.732665
\(160\) 6.29149e97 0.519295
\(161\) −1.65673e98 −1.03633
\(162\) −1.12500e98 −0.534237
\(163\) −2.70141e98 −0.975534 −0.487767 0.872974i \(-0.662188\pi\)
−0.487767 + 0.872974i \(0.662188\pi\)
\(164\) −9.30578e96 −0.0255977
\(165\) 3.37890e98 0.709154
\(166\) −1.19114e98 −0.191053
\(167\) 1.44407e99 1.77299 0.886493 0.462743i \(-0.153135\pi\)
0.886493 + 0.462743i \(0.153135\pi\)
\(168\) 2.93317e98 0.276105
\(169\) −5.24409e98 −0.379063
\(170\) 1.43878e99 0.799867
\(171\) 6.80912e98 0.291584
\(172\) −3.63768e98 −0.120173
\(173\) −6.16711e99 −1.57409 −0.787046 0.616895i \(-0.788390\pi\)
−0.787046 + 0.616895i \(0.788390\pi\)
\(174\) 2.97994e99 0.588527
\(175\) −4.60335e99 −0.704500
\(176\) −8.65617e99 −1.02804
\(177\) −5.58333e99 −0.515327
\(178\) 1.41035e100 1.01306
\(179\) 2.48664e100 1.39204 0.696022 0.718020i \(-0.254951\pi\)
0.696022 + 0.718020i \(0.254951\pi\)
\(180\) −5.16427e99 −0.225622
\(181\) −3.55444e100 −1.21360 −0.606799 0.794856i \(-0.707547\pi\)
−0.606799 + 0.794856i \(0.707547\pi\)
\(182\) −1.81812e100 −0.485786
\(183\) 2.49817e100 0.523057
\(184\) 9.88328e100 1.62371
\(185\) −2.06142e100 −0.266087
\(186\) −2.30532e100 −0.234102
\(187\) 1.02235e101 0.817799
\(188\) 3.65498e100 0.230601
\(189\) −9.62031e100 −0.479335
\(190\) −1.11146e101 −0.437882
\(191\) −4.56087e100 −0.142253 −0.0711267 0.997467i \(-0.522659\pi\)
−0.0711267 + 0.997467i \(0.522659\pi\)
\(192\) −1.69764e101 −0.419701
\(193\) −3.40846e101 −0.668740 −0.334370 0.942442i \(-0.608524\pi\)
−0.334370 + 0.942442i \(0.608524\pi\)
\(194\) −4.83511e101 −0.753753
\(195\) −3.42423e101 −0.424642
\(196\) 9.98250e100 0.0985926
\(197\) 1.93426e102 1.52324 0.761619 0.648025i \(-0.224405\pi\)
0.761619 + 0.648025i \(0.224405\pi\)
\(198\) 1.62004e102 1.01842
\(199\) −2.15474e102 −1.08251 −0.541257 0.840857i \(-0.682051\pi\)
−0.541257 + 0.840857i \(0.682051\pi\)
\(200\) 2.74615e102 1.10380
\(201\) −9.10566e101 −0.293148
\(202\) 6.20352e102 1.60141
\(203\) −5.68042e102 −1.17708
\(204\) 2.60564e101 0.0433883
\(205\) −1.47496e102 −0.197576
\(206\) −4.25878e102 −0.459404
\(207\) −1.49604e103 −1.30096
\(208\) 8.77230e102 0.615595
\(209\) −7.89760e102 −0.447698
\(210\) 7.24736e102 0.332217
\(211\) 8.21019e101 0.0304638 0.0152319 0.999884i \(-0.495151\pi\)
0.0152319 + 0.999884i \(0.495151\pi\)
\(212\) 1.19046e103 0.357905
\(213\) −9.83184e102 −0.239741
\(214\) 8.96935e102 0.177561
\(215\) −5.76571e103 −0.927559
\(216\) 5.73903e103 0.751011
\(217\) 4.39444e103 0.468215
\(218\) 8.08837e103 0.702340
\(219\) 3.40509e103 0.241193
\(220\) 5.98980e103 0.346420
\(221\) −1.03606e104 −0.489699
\(222\) 1.64816e103 0.0637224
\(223\) −1.00410e104 −0.317842 −0.158921 0.987291i \(-0.550801\pi\)
−0.158921 + 0.987291i \(0.550801\pi\)
\(224\) 9.58872e103 0.248728
\(225\) −4.15686e104 −0.884389
\(226\) −2.62685e104 −0.458785
\(227\) −1.08320e105 −1.55439 −0.777194 0.629261i \(-0.783358\pi\)
−0.777194 + 0.629261i \(0.783358\pi\)
\(228\) −2.01285e103 −0.0237526
\(229\) −3.66875e104 −0.356319 −0.178160 0.984002i \(-0.557014\pi\)
−0.178160 + 0.984002i \(0.557014\pi\)
\(230\) 2.44199e105 1.95369
\(231\) 5.14971e104 0.339664
\(232\) 3.38867e105 1.84423
\(233\) −3.17011e105 −1.42474 −0.712371 0.701803i \(-0.752379\pi\)
−0.712371 + 0.701803i \(0.752379\pi\)
\(234\) −1.64177e105 −0.609829
\(235\) 5.79313e105 1.77989
\(236\) −9.89761e104 −0.251736
\(237\) −3.19248e105 −0.672708
\(238\) 2.19281e105 0.383113
\(239\) −3.35013e105 −0.485686 −0.242843 0.970066i \(-0.578080\pi\)
−0.242843 + 0.970066i \(0.578080\pi\)
\(240\) −3.49680e105 −0.420989
\(241\) 2.48905e105 0.249044 0.124522 0.992217i \(-0.460260\pi\)
0.124522 + 0.992217i \(0.460260\pi\)
\(242\) −7.93967e105 −0.660722
\(243\) −1.33651e106 −0.925749
\(244\) 4.42852e105 0.255512
\(245\) 1.58222e106 0.760987
\(246\) 1.17928e105 0.0473155
\(247\) 8.00355e105 0.268082
\(248\) −2.62152e106 −0.733590
\(249\) −3.41910e105 −0.0799910
\(250\) 2.09553e105 0.0410169
\(251\) 4.34459e106 0.711981 0.355991 0.934490i \(-0.384143\pi\)
0.355991 + 0.934490i \(0.384143\pi\)
\(252\) −7.87074e105 −0.108067
\(253\) 1.73519e107 1.99749
\(254\) −9.78084e106 −0.944660
\(255\) 4.12993e106 0.334892
\(256\) −7.83789e106 −0.533974
\(257\) −1.84254e106 −0.105534 −0.0527671 0.998607i \(-0.516804\pi\)
−0.0527671 + 0.998607i \(0.516804\pi\)
\(258\) 4.60986e106 0.222132
\(259\) −3.14176e106 −0.127448
\(260\) −6.07016e106 −0.207437
\(261\) −5.12946e107 −1.47764
\(262\) −6.26617e106 −0.152263
\(263\) −5.95118e107 −1.22060 −0.610299 0.792171i \(-0.708951\pi\)
−0.610299 + 0.792171i \(0.708951\pi\)
\(264\) −3.07208e107 −0.532179
\(265\) 1.88687e108 2.76249
\(266\) −1.69394e107 −0.209733
\(267\) 4.04831e107 0.424153
\(268\) −1.61417e107 −0.143202
\(269\) 1.60452e108 1.20606 0.603028 0.797720i \(-0.293961\pi\)
0.603028 + 0.797720i \(0.293961\pi\)
\(270\) 1.41802e108 0.903637
\(271\) −1.64745e108 −0.890591 −0.445296 0.895384i \(-0.646901\pi\)
−0.445296 + 0.895384i \(0.646901\pi\)
\(272\) −1.05802e108 −0.485486
\(273\) −5.21880e107 −0.203391
\(274\) −2.55048e108 −0.844739
\(275\) 4.82136e108 1.35789
\(276\) 4.42246e107 0.105976
\(277\) −7.83782e108 −1.59899 −0.799495 0.600673i \(-0.794899\pi\)
−0.799495 + 0.600673i \(0.794899\pi\)
\(278\) −6.01051e108 −1.04452
\(279\) 3.96821e108 0.587771
\(280\) 8.24142e108 1.04105
\(281\) −5.27154e107 −0.0568206 −0.0284103 0.999596i \(-0.509045\pi\)
−0.0284103 + 0.999596i \(0.509045\pi\)
\(282\) −4.63178e108 −0.426248
\(283\) −3.88406e108 −0.305344 −0.152672 0.988277i \(-0.548788\pi\)
−0.152672 + 0.988277i \(0.548788\pi\)
\(284\) −1.74290e108 −0.117113
\(285\) −3.19036e108 −0.183334
\(286\) 1.90422e109 0.936330
\(287\) −2.24796e108 −0.0946332
\(288\) 8.65869e108 0.312238
\(289\) −1.98601e109 −0.613801
\(290\) 8.37284e109 2.21902
\(291\) −1.38789e109 −0.315585
\(292\) 6.03621e108 0.117822
\(293\) −1.22983e109 −0.206174 −0.103087 0.994672i \(-0.532872\pi\)
−0.103087 + 0.994672i \(0.532872\pi\)
\(294\) −1.26503e109 −0.182241
\(295\) −1.56877e110 −1.94303
\(296\) 1.87423e109 0.199683
\(297\) 1.00759e110 0.923895
\(298\) −3.75691e109 −0.296624
\(299\) −1.75847e110 −1.19610
\(300\) 1.22881e109 0.0720428
\(301\) −8.78739e109 −0.444274
\(302\) −1.25277e110 −0.546464
\(303\) 1.78068e110 0.670485
\(304\) 8.17316e109 0.265776
\(305\) 7.01920e110 1.97217
\(306\) 1.98013e110 0.480939
\(307\) 9.59258e109 0.201501 0.100751 0.994912i \(-0.467876\pi\)
0.100751 + 0.994912i \(0.467876\pi\)
\(308\) 9.12892e109 0.165925
\(309\) −1.22246e110 −0.192345
\(310\) −6.47733e110 −0.882675
\(311\) −4.76737e110 −0.562914 −0.281457 0.959574i \(-0.590818\pi\)
−0.281457 + 0.959574i \(0.590818\pi\)
\(312\) 3.11329e110 0.318669
\(313\) 5.26526e109 0.0467409 0.0233704 0.999727i \(-0.492560\pi\)
0.0233704 + 0.999727i \(0.492560\pi\)
\(314\) −2.50109e109 −0.0192646
\(315\) −1.24751e111 −0.834112
\(316\) −5.65932e110 −0.328616
\(317\) −2.68580e110 −0.135499 −0.0677494 0.997702i \(-0.521582\pi\)
−0.0677494 + 0.997702i \(0.521582\pi\)
\(318\) −1.50861e111 −0.661561
\(319\) 5.94944e111 2.26877
\(320\) −4.76991e111 −1.58247
\(321\) 2.57460e110 0.0743422
\(322\) 3.72178e111 0.935760
\(323\) −9.65300e110 −0.211422
\(324\) −5.72450e110 −0.109266
\(325\) −4.88604e111 −0.813107
\(326\) 6.06862e111 0.880860
\(327\) 2.32172e111 0.294059
\(328\) 1.34103e111 0.148269
\(329\) 8.82918e111 0.852517
\(330\) −7.59059e111 −0.640332
\(331\) 1.92028e112 1.41586 0.707928 0.706284i \(-0.249630\pi\)
0.707928 + 0.706284i \(0.249630\pi\)
\(332\) −6.06106e110 −0.0390754
\(333\) −2.83703e111 −0.159991
\(334\) −3.24405e112 −1.60092
\(335\) −2.55845e112 −1.10531
\(336\) −5.32940e111 −0.201642
\(337\) 3.45050e111 0.114381 0.0571903 0.998363i \(-0.481786\pi\)
0.0571903 + 0.998363i \(0.481786\pi\)
\(338\) 1.17807e112 0.342276
\(339\) −7.54021e111 −0.192086
\(340\) 7.32116e111 0.163594
\(341\) −4.60256e112 −0.902462
\(342\) −1.52964e112 −0.263287
\(343\) 6.92838e112 1.04723
\(344\) 5.24215e112 0.696079
\(345\) 7.00958e112 0.817980
\(346\) 1.38542e113 1.42133
\(347\) −8.88897e112 −0.802028 −0.401014 0.916072i \(-0.631342\pi\)
−0.401014 + 0.916072i \(0.631342\pi\)
\(348\) 1.51633e112 0.120369
\(349\) −1.03428e113 −0.722615 −0.361308 0.932447i \(-0.617670\pi\)
−0.361308 + 0.932447i \(0.617670\pi\)
\(350\) 1.03413e113 0.636130
\(351\) −1.02111e113 −0.553229
\(352\) −1.00428e113 −0.479411
\(353\) −1.22789e113 −0.516637 −0.258318 0.966060i \(-0.583168\pi\)
−0.258318 + 0.966060i \(0.583168\pi\)
\(354\) 1.25428e113 0.465316
\(355\) −2.76248e113 −0.903937
\(356\) 7.17647e112 0.207198
\(357\) 6.29434e112 0.160404
\(358\) −5.58615e113 −1.25695
\(359\) 6.91261e112 0.137385 0.0686924 0.997638i \(-0.478117\pi\)
0.0686924 + 0.997638i \(0.478117\pi\)
\(360\) 7.44206e113 1.30687
\(361\) −5.69705e113 −0.884259
\(362\) 7.98492e113 1.09582
\(363\) −2.27903e113 −0.276634
\(364\) −9.25139e112 −0.0993563
\(365\) 9.56738e113 0.909412
\(366\) −5.61205e113 −0.472295
\(367\) 1.07815e114 0.803600 0.401800 0.915727i \(-0.368385\pi\)
0.401800 + 0.915727i \(0.368385\pi\)
\(368\) −1.79573e114 −1.18581
\(369\) −2.02992e113 −0.118797
\(370\) 4.63090e113 0.240264
\(371\) 2.87574e114 1.32315
\(372\) −1.17305e113 −0.0478801
\(373\) 2.32613e114 0.842542 0.421271 0.906935i \(-0.361584\pi\)
0.421271 + 0.906935i \(0.361584\pi\)
\(374\) −2.29666e114 −0.738433
\(375\) 6.01508e112 0.0171731
\(376\) −5.26708e114 −1.33571
\(377\) −6.02925e114 −1.35854
\(378\) 2.16117e114 0.432816
\(379\) −1.50115e114 −0.267288 −0.133644 0.991029i \(-0.542668\pi\)
−0.133644 + 0.991029i \(0.542668\pi\)
\(380\) −5.65558e113 −0.0895585
\(381\) −2.80753e114 −0.395515
\(382\) 1.02458e114 0.128448
\(383\) 4.26852e114 0.476357 0.238178 0.971221i \(-0.423450\pi\)
0.238178 + 0.971221i \(0.423450\pi\)
\(384\) 2.42770e114 0.241243
\(385\) 1.44693e115 1.28069
\(386\) 7.65697e114 0.603840
\(387\) −7.93508e114 −0.557716
\(388\) −2.46032e114 −0.154163
\(389\) 1.36736e115 0.764054 0.382027 0.924151i \(-0.375226\pi\)
0.382027 + 0.924151i \(0.375226\pi\)
\(390\) 7.69242e114 0.383432
\(391\) 2.12087e115 0.943297
\(392\) −1.43855e115 −0.571076
\(393\) −1.79867e114 −0.0637502
\(394\) −4.34524e115 −1.37541
\(395\) −8.97001e115 −2.53643
\(396\) 8.24349e114 0.208293
\(397\) 5.64489e115 1.27491 0.637453 0.770489i \(-0.279988\pi\)
0.637453 + 0.770489i \(0.279988\pi\)
\(398\) 4.84055e115 0.977458
\(399\) −4.86236e114 −0.0878119
\(400\) −4.98959e115 −0.806112
\(401\) −5.09288e115 −0.736274 −0.368137 0.929772i \(-0.620004\pi\)
−0.368137 + 0.929772i \(0.620004\pi\)
\(402\) 2.04555e115 0.264698
\(403\) 4.66430e115 0.540396
\(404\) 3.15662e115 0.327531
\(405\) −9.07331e115 −0.843368
\(406\) 1.27609e116 1.06285
\(407\) 3.29055e115 0.245650
\(408\) −3.75491e115 −0.251317
\(409\) 1.50131e116 0.901120 0.450560 0.892746i \(-0.351224\pi\)
0.450560 + 0.892746i \(0.351224\pi\)
\(410\) 3.31345e115 0.178402
\(411\) −7.32100e115 −0.353679
\(412\) −2.16706e115 −0.0939603
\(413\) −2.39092e116 −0.930654
\(414\) 3.36080e116 1.17470
\(415\) −9.60676e115 −0.301604
\(416\) 1.01776e116 0.287072
\(417\) −1.72528e116 −0.437326
\(418\) 1.77417e116 0.404250
\(419\) −2.86274e116 −0.586487 −0.293244 0.956038i \(-0.594735\pi\)
−0.293244 + 0.956038i \(0.594735\pi\)
\(420\) 3.68778e115 0.0679472
\(421\) −9.74749e116 −1.61562 −0.807811 0.589442i \(-0.799348\pi\)
−0.807811 + 0.589442i \(0.799348\pi\)
\(422\) −1.84439e115 −0.0275073
\(423\) 7.97282e116 1.07020
\(424\) −1.71553e117 −2.07309
\(425\) 5.89301e116 0.641253
\(426\) 2.20869e116 0.216475
\(427\) 1.06978e117 0.944613
\(428\) 4.56400e115 0.0363160
\(429\) 5.46595e116 0.392027
\(430\) 1.29525e117 0.837541
\(431\) 8.68467e116 0.506425 0.253212 0.967411i \(-0.418513\pi\)
0.253212 + 0.967411i \(0.418513\pi\)
\(432\) −1.04275e117 −0.548470
\(433\) 1.47184e117 0.698471 0.349235 0.937035i \(-0.386441\pi\)
0.349235 + 0.937035i \(0.386441\pi\)
\(434\) −9.87195e116 −0.422776
\(435\) 2.40337e117 0.929072
\(436\) 4.11572e116 0.143647
\(437\) −1.63837e117 −0.516401
\(438\) −7.64940e116 −0.217786
\(439\) −6.00723e117 −1.54527 −0.772633 0.634853i \(-0.781061\pi\)
−0.772633 + 0.634853i \(0.781061\pi\)
\(440\) −8.63172e117 −2.00657
\(441\) 2.17754e117 0.457561
\(442\) 2.32747e117 0.442175
\(443\) −1.62705e117 −0.279535 −0.139767 0.990184i \(-0.544635\pi\)
−0.139767 + 0.990184i \(0.544635\pi\)
\(444\) 8.38658e115 0.0130329
\(445\) 1.13747e118 1.59926
\(446\) 2.25567e117 0.286996
\(447\) −1.07840e117 −0.124192
\(448\) −7.26971e117 −0.757959
\(449\) −1.55698e117 −0.147001 −0.0735006 0.997295i \(-0.523417\pi\)
−0.0735006 + 0.997295i \(0.523417\pi\)
\(450\) 9.33824e117 0.798561
\(451\) 2.35442e117 0.182401
\(452\) −1.33666e117 −0.0938339
\(453\) −3.59599e117 −0.228796
\(454\) 2.43338e118 1.40354
\(455\) −1.46634e118 −0.766882
\(456\) 2.90066e117 0.137582
\(457\) −8.39164e117 −0.361057 −0.180529 0.983570i \(-0.557781\pi\)
−0.180529 + 0.983570i \(0.557781\pi\)
\(458\) 8.24172e117 0.321739
\(459\) 1.23155e118 0.436302
\(460\) 1.24259e118 0.399581
\(461\) −5.23843e118 −1.52936 −0.764680 0.644410i \(-0.777103\pi\)
−0.764680 + 0.644410i \(0.777103\pi\)
\(462\) −1.15686e118 −0.306700
\(463\) 4.31741e118 1.03961 0.519804 0.854286i \(-0.326005\pi\)
0.519804 + 0.854286i \(0.326005\pi\)
\(464\) −6.15703e118 −1.34686
\(465\) −1.85928e118 −0.369563
\(466\) 7.12154e118 1.28647
\(467\) −2.94860e118 −0.484189 −0.242094 0.970253i \(-0.577834\pi\)
−0.242094 + 0.970253i \(0.577834\pi\)
\(468\) −8.35408e117 −0.124726
\(469\) −3.89927e118 −0.529410
\(470\) −1.30141e119 −1.60716
\(471\) −7.17923e116 −0.00806580
\(472\) 1.42631e119 1.45813
\(473\) 9.20355e118 0.856317
\(474\) 7.17178e118 0.607423
\(475\) −4.55233e118 −0.351050
\(476\) 1.11580e118 0.0783569
\(477\) 2.59681e119 1.66101
\(478\) 7.52596e118 0.438551
\(479\) −1.88316e119 −0.999899 −0.499950 0.866054i \(-0.666648\pi\)
−0.499950 + 0.866054i \(0.666648\pi\)
\(480\) −4.05697e118 −0.196321
\(481\) −3.33469e118 −0.147096
\(482\) −5.59156e118 −0.224874
\(483\) 1.06831e119 0.391789
\(484\) −4.04006e118 −0.135135
\(485\) −3.89960e119 −1.18991
\(486\) 3.00242e119 0.835907
\(487\) −3.85031e119 −0.978266 −0.489133 0.872209i \(-0.662687\pi\)
−0.489133 + 0.872209i \(0.662687\pi\)
\(488\) −6.38181e119 −1.48000
\(489\) 1.74196e119 0.368803
\(490\) −3.55441e119 −0.687134
\(491\) 2.29064e119 0.404417 0.202209 0.979342i \(-0.435188\pi\)
0.202209 + 0.979342i \(0.435188\pi\)
\(492\) 6.00068e117 0.00967728
\(493\) 7.27182e119 1.07141
\(494\) −1.79797e119 −0.242065
\(495\) 1.30659e120 1.60771
\(496\) 4.76315e119 0.535747
\(497\) −4.21024e119 −0.432960
\(498\) 7.68089e118 0.0722280
\(499\) 3.59737e119 0.309393 0.154697 0.987962i \(-0.450560\pi\)
0.154697 + 0.987962i \(0.450560\pi\)
\(500\) 1.06630e118 0.00838905
\(501\) −9.31185e119 −0.670281
\(502\) −9.75997e119 −0.642885
\(503\) −8.86242e119 −0.534290 −0.267145 0.963656i \(-0.586080\pi\)
−0.267145 + 0.963656i \(0.586080\pi\)
\(504\) 1.13423e120 0.625953
\(505\) 5.00324e120 2.52805
\(506\) −3.89804e120 −1.80363
\(507\) 3.38157e119 0.143306
\(508\) −4.97692e119 −0.193208
\(509\) −4.22196e120 −1.50166 −0.750832 0.660493i \(-0.770347\pi\)
−0.750832 + 0.660493i \(0.770347\pi\)
\(510\) −9.27775e119 −0.302392
\(511\) 1.45814e120 0.435582
\(512\) 4.09108e120 1.12027
\(513\) −9.51369e119 −0.238850
\(514\) 4.13920e119 0.0952923
\(515\) −3.43478e120 −0.725233
\(516\) 2.34570e119 0.0454319
\(517\) −9.24732e120 −1.64319
\(518\) 7.05784e119 0.115079
\(519\) 3.97676e120 0.595089
\(520\) 8.74752e120 1.20153
\(521\) −6.53932e120 −0.824620 −0.412310 0.911044i \(-0.635278\pi\)
−0.412310 + 0.911044i \(0.635278\pi\)
\(522\) 1.15231e121 1.33424
\(523\) 2.91241e120 0.309690 0.154845 0.987939i \(-0.450512\pi\)
0.154845 + 0.987939i \(0.450512\pi\)
\(524\) −3.18850e119 −0.0311419
\(525\) 2.96840e120 0.266338
\(526\) 1.33691e121 1.10214
\(527\) −5.62557e120 −0.426181
\(528\) 5.58179e120 0.388655
\(529\) 2.03733e121 1.30402
\(530\) −4.23879e121 −2.49440
\(531\) −2.15902e121 −1.16829
\(532\) −8.61954e119 −0.0428960
\(533\) −2.38600e120 −0.109222
\(534\) −9.09439e120 −0.382990
\(535\) 7.23393e120 0.280305
\(536\) 2.32612e121 0.829468
\(537\) −1.60347e121 −0.526266
\(538\) −3.60449e121 −1.08901
\(539\) −2.52563e121 −0.702538
\(540\) 7.21550e120 0.184818
\(541\) 1.96807e121 0.464260 0.232130 0.972685i \(-0.425430\pi\)
0.232130 + 0.972685i \(0.425430\pi\)
\(542\) 3.70093e121 0.804161
\(543\) 2.29202e121 0.458803
\(544\) −1.22751e121 −0.226398
\(545\) 6.52341e121 1.10874
\(546\) 1.17238e121 0.183653
\(547\) 5.06309e121 0.731105 0.365552 0.930791i \(-0.380880\pi\)
0.365552 + 0.930791i \(0.380880\pi\)
\(548\) −1.29780e121 −0.172772
\(549\) 9.66019e121 1.18581
\(550\) −1.08310e122 −1.22611
\(551\) −5.61746e121 −0.586535
\(552\) −6.37307e121 −0.613846
\(553\) −1.36710e122 −1.21487
\(554\) 1.76074e122 1.44381
\(555\) 1.32927e121 0.100595
\(556\) −3.05842e121 −0.213633
\(557\) 7.70908e121 0.497103 0.248551 0.968619i \(-0.420045\pi\)
0.248551 + 0.968619i \(0.420045\pi\)
\(558\) −8.91445e121 −0.530729
\(559\) −9.32702e121 −0.512764
\(560\) −1.49742e122 −0.760284
\(561\) −6.59243e121 −0.309171
\(562\) 1.18423e121 0.0513063
\(563\) 3.40007e122 1.36102 0.680509 0.732740i \(-0.261759\pi\)
0.680509 + 0.732740i \(0.261759\pi\)
\(564\) −2.35685e121 −0.0871792
\(565\) −2.11860e122 −0.724257
\(566\) 8.72541e121 0.275711
\(567\) −1.38284e122 −0.403949
\(568\) 2.51163e122 0.678352
\(569\) −1.07140e122 −0.267580 −0.133790 0.991010i \(-0.542715\pi\)
−0.133790 + 0.991010i \(0.542715\pi\)
\(570\) 7.16704e121 0.165542
\(571\) 4.63901e121 0.0991103 0.0495551 0.998771i \(-0.484220\pi\)
0.0495551 + 0.998771i \(0.484220\pi\)
\(572\) 9.68952e121 0.191505
\(573\) 2.94100e121 0.0537792
\(574\) 5.04995e121 0.0854493
\(575\) 1.00020e123 1.56627
\(576\) −6.56460e122 −0.951498
\(577\) 4.29228e121 0.0575922 0.0287961 0.999585i \(-0.490833\pi\)
0.0287961 + 0.999585i \(0.490833\pi\)
\(578\) 4.46150e122 0.554233
\(579\) 2.19789e122 0.252819
\(580\) 4.26047e122 0.453850
\(581\) −1.46414e122 −0.144460
\(582\) 3.11784e122 0.284958
\(583\) −3.01193e123 −2.55032
\(584\) −8.69860e122 −0.682461
\(585\) −1.32412e123 −0.962700
\(586\) 2.76276e122 0.186166
\(587\) −5.10199e122 −0.318672 −0.159336 0.987224i \(-0.550935\pi\)
−0.159336 + 0.987224i \(0.550935\pi\)
\(588\) −6.43705e121 −0.0372731
\(589\) 4.34574e122 0.233310
\(590\) 3.52418e123 1.75446
\(591\) −1.24728e123 −0.575863
\(592\) −3.40536e122 −0.145830
\(593\) 3.16373e123 1.25680 0.628400 0.777891i \(-0.283710\pi\)
0.628400 + 0.777891i \(0.283710\pi\)
\(594\) −2.26352e123 −0.834232
\(595\) 1.76854e123 0.604798
\(596\) −1.91168e122 −0.0606676
\(597\) 1.38945e123 0.409247
\(598\) 3.95033e123 1.08002
\(599\) 2.38447e123 0.605199 0.302599 0.953118i \(-0.402146\pi\)
0.302599 + 0.953118i \(0.402146\pi\)
\(600\) −1.77081e123 −0.417293
\(601\) −2.41864e123 −0.529245 −0.264623 0.964352i \(-0.585247\pi\)
−0.264623 + 0.964352i \(0.585247\pi\)
\(602\) 1.97406e123 0.401158
\(603\) −3.52107e123 −0.664591
\(604\) −6.37464e122 −0.111766
\(605\) −6.40348e123 −1.04304
\(606\) −4.00024e123 −0.605416
\(607\) 2.86566e123 0.403021 0.201511 0.979486i \(-0.435415\pi\)
0.201511 + 0.979486i \(0.435415\pi\)
\(608\) 9.48245e122 0.123940
\(609\) 3.66293e123 0.444999
\(610\) −1.57684e124 −1.78078
\(611\) 9.37138e123 0.983942
\(612\) 1.00758e123 0.0983648
\(613\) 5.03326e123 0.456939 0.228469 0.973551i \(-0.426628\pi\)
0.228469 + 0.973551i \(0.426628\pi\)
\(614\) −2.15494e123 −0.181946
\(615\) 9.51106e122 0.0746941
\(616\) −1.31554e124 −0.961087
\(617\) 2.23873e122 0.0152164 0.00760819 0.999971i \(-0.497578\pi\)
0.00760819 + 0.999971i \(0.497578\pi\)
\(618\) 2.74621e123 0.173679
\(619\) 5.07827e123 0.298870 0.149435 0.988772i \(-0.452255\pi\)
0.149435 + 0.988772i \(0.452255\pi\)
\(620\) −3.29595e123 −0.180531
\(621\) 2.09026e124 1.06567
\(622\) 1.07097e124 0.508284
\(623\) 1.73359e124 0.765999
\(624\) −5.65667e123 −0.232727
\(625\) −2.52429e124 −0.967117
\(626\) −1.18282e123 −0.0422048
\(627\) 5.09264e123 0.169253
\(628\) −1.27267e122 −0.00394013
\(629\) 4.02194e123 0.116006
\(630\) 2.80249e124 0.753163
\(631\) −6.55453e124 −1.64148 −0.820739 0.571304i \(-0.806438\pi\)
−0.820739 + 0.571304i \(0.806438\pi\)
\(632\) 8.15548e124 1.90344
\(633\) −5.29421e122 −0.0115169
\(634\) 6.03354e123 0.122349
\(635\) −7.88841e124 −1.49128
\(636\) −7.67647e123 −0.135307
\(637\) 2.55952e124 0.420681
\(638\) −1.33652e125 −2.04859
\(639\) −3.80188e124 −0.543513
\(640\) 6.82119e124 0.909601
\(641\) −1.12609e125 −1.40085 −0.700426 0.713725i \(-0.747006\pi\)
−0.700426 + 0.713725i \(0.747006\pi\)
\(642\) −5.78374e123 −0.0671274
\(643\) 1.67853e125 1.81777 0.908886 0.417044i \(-0.136934\pi\)
0.908886 + 0.417044i \(0.136934\pi\)
\(644\) 1.89381e124 0.191388
\(645\) 3.71793e124 0.350666
\(646\) 2.16851e124 0.190904
\(647\) −1.03514e125 −0.850666 −0.425333 0.905037i \(-0.639843\pi\)
−0.425333 + 0.905037i \(0.639843\pi\)
\(648\) 8.24940e124 0.632899
\(649\) 2.50415e125 1.79379
\(650\) 1.09763e125 0.734196
\(651\) −2.83368e124 −0.177010
\(652\) 3.08798e124 0.180159
\(653\) −1.56383e125 −0.852222 −0.426111 0.904671i \(-0.640117\pi\)
−0.426111 + 0.904671i \(0.640117\pi\)
\(654\) −5.21566e124 −0.265521
\(655\) −5.05377e124 −0.240369
\(656\) −2.43657e124 −0.108282
\(657\) 1.31671e125 0.546805
\(658\) −1.98344e125 −0.769782
\(659\) 1.26588e125 0.459191 0.229595 0.973286i \(-0.426260\pi\)
0.229595 + 0.973286i \(0.426260\pi\)
\(660\) −3.86243e124 −0.130965
\(661\) −5.50470e125 −1.74489 −0.872447 0.488709i \(-0.837468\pi\)
−0.872447 + 0.488709i \(0.837468\pi\)
\(662\) −4.31384e125 −1.27845
\(663\) 6.68087e124 0.185132
\(664\) 8.73441e124 0.226336
\(665\) −1.36619e125 −0.331092
\(666\) 6.37328e124 0.144464
\(667\) 1.23422e126 2.61693
\(668\) −1.65072e125 −0.327431
\(669\) 6.47478e124 0.120161
\(670\) 5.74746e125 0.998038
\(671\) −1.12044e126 −1.82070
\(672\) −6.18313e124 −0.0940320
\(673\) −1.57404e125 −0.224050 −0.112025 0.993705i \(-0.535734\pi\)
−0.112025 + 0.993705i \(0.535734\pi\)
\(674\) −7.75143e124 −0.103280
\(675\) 5.80796e125 0.724445
\(676\) 5.99452e124 0.0700046
\(677\) 1.04038e126 1.13762 0.568809 0.822470i \(-0.307405\pi\)
0.568809 + 0.822470i \(0.307405\pi\)
\(678\) 1.69388e125 0.173445
\(679\) −5.94329e125 −0.569930
\(680\) −1.05503e126 −0.947585
\(681\) 6.98486e125 0.587640
\(682\) 1.03395e126 0.814880
\(683\) 1.23854e126 0.914513 0.457256 0.889335i \(-0.348832\pi\)
0.457256 + 0.889335i \(0.348832\pi\)
\(684\) −7.78351e124 −0.0538491
\(685\) −2.05701e126 −1.33354
\(686\) −1.55644e126 −0.945601
\(687\) 2.36573e125 0.134707
\(688\) −9.52469e125 −0.508353
\(689\) 3.05234e126 1.52713
\(690\) −1.57468e126 −0.738596
\(691\) −3.68627e126 −1.62111 −0.810557 0.585659i \(-0.800836\pi\)
−0.810557 + 0.585659i \(0.800836\pi\)
\(692\) 7.04962e125 0.290700
\(693\) 1.99134e126 0.770047
\(694\) 1.99687e126 0.724193
\(695\) −4.84758e126 −1.64893
\(696\) −2.18513e126 −0.697214
\(697\) 2.87773e125 0.0861375
\(698\) 2.32347e126 0.652487
\(699\) 2.04420e126 0.538627
\(700\) 5.26209e125 0.130106
\(701\) 4.13787e125 0.0960119 0.0480059 0.998847i \(-0.484713\pi\)
0.0480059 + 0.998847i \(0.484713\pi\)
\(702\) 2.29388e126 0.499540
\(703\) −3.10694e125 −0.0635068
\(704\) 7.61399e126 1.46093
\(705\) −3.73561e126 −0.672892
\(706\) 2.75841e126 0.466498
\(707\) 7.62532e126 1.21086
\(708\) 6.38231e125 0.0951695
\(709\) −3.99945e126 −0.560070 −0.280035 0.959990i \(-0.590346\pi\)
−0.280035 + 0.959990i \(0.590346\pi\)
\(710\) 6.20582e126 0.816212
\(711\) −1.23450e127 −1.52509
\(712\) −1.03418e127 −1.20015
\(713\) −9.54806e126 −1.04095
\(714\) −1.41400e126 −0.144837
\(715\) 1.53579e127 1.47813
\(716\) −2.84248e126 −0.257080
\(717\) 2.16028e126 0.183615
\(718\) −1.55289e126 −0.124052
\(719\) −2.03979e127 −1.53162 −0.765808 0.643070i \(-0.777661\pi\)
−0.765808 + 0.643070i \(0.777661\pi\)
\(720\) −1.35218e127 −0.954418
\(721\) −5.23487e126 −0.347366
\(722\) 1.27982e127 0.798443
\(723\) −1.60502e126 −0.0941515
\(724\) 4.06308e126 0.224124
\(725\) 3.42937e127 1.77899
\(726\) 5.11977e126 0.249787
\(727\) 1.86391e127 0.855350 0.427675 0.903933i \(-0.359333\pi\)
0.427675 + 0.903933i \(0.359333\pi\)
\(728\) 1.33319e127 0.575500
\(729\) −5.95123e126 −0.241675
\(730\) −2.14928e127 −0.821155
\(731\) 1.12492e127 0.404389
\(732\) −2.85566e126 −0.0965970
\(733\) 2.07676e126 0.0661089 0.0330544 0.999454i \(-0.489477\pi\)
0.0330544 + 0.999454i \(0.489477\pi\)
\(734\) −2.42203e127 −0.725612
\(735\) −1.02027e127 −0.287693
\(736\) −2.08340e127 −0.552980
\(737\) 4.08394e127 1.02041
\(738\) 4.56015e126 0.107268
\(739\) 2.17012e127 0.480624 0.240312 0.970696i \(-0.422750\pi\)
0.240312 + 0.970696i \(0.422750\pi\)
\(740\) 2.35641e126 0.0491404
\(741\) −5.16096e126 −0.101349
\(742\) −6.46024e127 −1.19474
\(743\) 3.44373e127 0.599828 0.299914 0.953966i \(-0.403042\pi\)
0.299914 + 0.953966i \(0.403042\pi\)
\(744\) 1.69044e127 0.277335
\(745\) −3.03001e127 −0.468263
\(746\) −5.22557e127 −0.760775
\(747\) −1.32213e127 −0.181346
\(748\) −1.16864e127 −0.151029
\(749\) 1.10251e127 0.134258
\(750\) −1.35127e126 −0.0155065
\(751\) −9.41430e127 −1.01815 −0.509074 0.860723i \(-0.670012\pi\)
−0.509074 + 0.860723i \(0.670012\pi\)
\(752\) 9.56998e127 0.975478
\(753\) −2.80154e127 −0.269166
\(754\) 1.35445e128 1.22670
\(755\) −1.01038e128 −0.862670
\(756\) 1.09970e127 0.0885225
\(757\) −8.67950e124 −0.000658761 0 −0.000329381 1.00000i \(-0.500105\pi\)
−0.000329381 1.00000i \(0.500105\pi\)
\(758\) 3.37228e127 0.241348
\(759\) −1.11891e128 −0.755154
\(760\) 8.15008e127 0.518749
\(761\) 2.99513e128 1.79804 0.899018 0.437911i \(-0.144282\pi\)
0.899018 + 0.437911i \(0.144282\pi\)
\(762\) 6.30701e127 0.357131
\(763\) 9.94218e127 0.531055
\(764\) 5.21353e126 0.0262711
\(765\) 1.59701e128 0.759229
\(766\) −9.58909e127 −0.430127
\(767\) −2.53775e128 −1.07413
\(768\) 5.05413e127 0.201870
\(769\) −1.81575e128 −0.684439 −0.342220 0.939620i \(-0.611179\pi\)
−0.342220 + 0.939620i \(0.611179\pi\)
\(770\) −3.25048e128 −1.15641
\(771\) 1.18813e127 0.0398974
\(772\) 3.89621e127 0.123502
\(773\) −4.64806e128 −1.39086 −0.695432 0.718592i \(-0.744787\pi\)
−0.695432 + 0.718592i \(0.744787\pi\)
\(774\) 1.78259e128 0.503591
\(775\) −2.65301e128 −0.707640
\(776\) 3.54549e128 0.892955
\(777\) 2.02591e127 0.0481820
\(778\) −3.07171e128 −0.689904
\(779\) −2.22304e127 −0.0471554
\(780\) 3.91424e127 0.0784220
\(781\) 4.40963e128 0.834509
\(782\) −4.76446e128 −0.851752
\(783\) 7.16687e128 1.21041
\(784\) 2.61376e128 0.417062
\(785\) −2.01717e127 −0.0304119
\(786\) 4.04064e127 0.0575634
\(787\) 1.58248e128 0.213040 0.106520 0.994311i \(-0.466029\pi\)
0.106520 + 0.994311i \(0.466029\pi\)
\(788\) −2.21105e128 −0.281308
\(789\) 3.83752e128 0.461450
\(790\) 2.01508e129 2.29027
\(791\) −3.22891e128 −0.346898
\(792\) −1.18794e129 −1.20649
\(793\) 1.13547e129 1.09024
\(794\) −1.26810e129 −1.15118
\(795\) −1.21672e129 −1.04437
\(796\) 2.46309e128 0.199916
\(797\) −9.45352e128 −0.725602 −0.362801 0.931867i \(-0.618179\pi\)
−0.362801 + 0.931867i \(0.618179\pi\)
\(798\) 1.09231e128 0.0792899
\(799\) −1.13027e129 −0.775982
\(800\) −5.78889e128 −0.375916
\(801\) 1.56544e129 0.961592
\(802\) 1.14410e129 0.664820
\(803\) −1.52720e129 −0.839564
\(804\) 1.04087e128 0.0541379
\(805\) 3.00168e129 1.47723
\(806\) −1.04782e129 −0.487951
\(807\) −1.03465e129 −0.455952
\(808\) −4.54891e129 −1.89715
\(809\) 1.50426e129 0.593762 0.296881 0.954914i \(-0.404054\pi\)
0.296881 + 0.954914i \(0.404054\pi\)
\(810\) 2.03829e129 0.761521
\(811\) −1.51351e129 −0.535249 −0.267625 0.963523i \(-0.586239\pi\)
−0.267625 + 0.963523i \(0.586239\pi\)
\(812\) 6.49329e128 0.217381
\(813\) 1.06233e129 0.336690
\(814\) −7.39209e128 −0.221810
\(815\) 4.89445e129 1.39056
\(816\) 6.82246e128 0.183539
\(817\) −8.69000e128 −0.221380
\(818\) −3.37264e129 −0.813668
\(819\) −2.01806e129 −0.461105
\(820\) 1.68603e128 0.0364879
\(821\) 6.94292e129 1.42322 0.711609 0.702575i \(-0.247967\pi\)
0.711609 + 0.702575i \(0.247967\pi\)
\(822\) 1.64464e129 0.319355
\(823\) 3.78802e129 0.696818 0.348409 0.937343i \(-0.386722\pi\)
0.348409 + 0.937343i \(0.386722\pi\)
\(824\) 3.12288e129 0.544245
\(825\) −3.10898e129 −0.513354
\(826\) 5.37112e129 0.840336
\(827\) −1.29618e130 −1.92163 −0.960816 0.277185i \(-0.910598\pi\)
−0.960816 + 0.277185i \(0.910598\pi\)
\(828\) 1.71012e129 0.240258
\(829\) −7.78087e129 −1.03598 −0.517990 0.855386i \(-0.673320\pi\)
−0.517990 + 0.855386i \(0.673320\pi\)
\(830\) 2.15812e129 0.272334
\(831\) 5.05409e129 0.604502
\(832\) −7.71614e129 −0.874807
\(833\) −3.08701e129 −0.331768
\(834\) 3.87578e129 0.394885
\(835\) −2.61638e130 −2.52728
\(836\) 9.02775e128 0.0826799
\(837\) −5.54438e129 −0.481471
\(838\) 6.43105e129 0.529570
\(839\) 2.28971e129 0.178802 0.0894011 0.995996i \(-0.471505\pi\)
0.0894011 + 0.995996i \(0.471505\pi\)
\(840\) −5.31435e129 −0.393570
\(841\) 2.80805e130 1.97235
\(842\) 2.18974e130 1.45883
\(843\) 3.39927e128 0.0214812
\(844\) −9.38507e127 −0.00562599
\(845\) 9.50130e129 0.540331
\(846\) −1.79107e130 −0.966341
\(847\) −9.75939e129 −0.499587
\(848\) 3.11702e130 1.51400
\(849\) 2.50458e129 0.115436
\(850\) −1.32384e130 −0.579021
\(851\) 6.82628e129 0.283347
\(852\) 1.12388e129 0.0442748
\(853\) 1.69945e130 0.635443 0.317722 0.948184i \(-0.397082\pi\)
0.317722 + 0.948184i \(0.397082\pi\)
\(854\) −2.40322e130 −0.852940
\(855\) −1.23368e130 −0.415635
\(856\) −6.57705e129 −0.210353
\(857\) 3.15524e130 0.958044 0.479022 0.877803i \(-0.340991\pi\)
0.479022 + 0.877803i \(0.340991\pi\)
\(858\) −1.22791e130 −0.353982
\(859\) −7.05135e130 −1.93008 −0.965042 0.262095i \(-0.915587\pi\)
−0.965042 + 0.262095i \(0.915587\pi\)
\(860\) 6.59079e129 0.171300
\(861\) 1.44956e129 0.0357763
\(862\) −1.95098e130 −0.457277
\(863\) −5.08141e130 −1.13111 −0.565554 0.824711i \(-0.691338\pi\)
−0.565554 + 0.824711i \(0.691338\pi\)
\(864\) −1.20979e130 −0.255769
\(865\) 1.11736e131 2.24377
\(866\) −3.30643e130 −0.630686
\(867\) 1.28065e130 0.232049
\(868\) −5.02329e129 −0.0864690
\(869\) 1.43184e131 2.34161
\(870\) −5.39909e130 −0.838907
\(871\) −4.13872e130 −0.611024
\(872\) −5.93104e130 −0.832046
\(873\) −5.36683e130 −0.715458
\(874\) 3.68053e130 0.466286
\(875\) 2.57581e129 0.0310138
\(876\) −3.89235e129 −0.0445430
\(877\) 6.84567e130 0.744618 0.372309 0.928109i \(-0.378566\pi\)
0.372309 + 0.928109i \(0.378566\pi\)
\(878\) 1.34950e131 1.39530
\(879\) 7.93033e129 0.0779447
\(880\) 1.56833e131 1.46541
\(881\) −1.42433e131 −1.26526 −0.632632 0.774453i \(-0.718025\pi\)
−0.632632 + 0.774453i \(0.718025\pi\)
\(882\) −4.89176e130 −0.413155
\(883\) −1.48435e131 −1.19202 −0.596012 0.802975i \(-0.703249\pi\)
−0.596012 + 0.802975i \(0.703249\pi\)
\(884\) 1.18432e130 0.0904366
\(885\) 1.01159e131 0.734566
\(886\) 3.65511e130 0.252406
\(887\) 8.44535e130 0.554647 0.277323 0.960777i \(-0.410553\pi\)
0.277323 + 0.960777i \(0.410553\pi\)
\(888\) −1.20856e130 −0.0754906
\(889\) −1.20225e131 −0.714279
\(890\) −2.55528e131 −1.44405
\(891\) 1.44833e131 0.778593
\(892\) 1.14779e130 0.0586983
\(893\) 8.73133e130 0.424806
\(894\) 2.42258e130 0.112140
\(895\) −4.50532e131 −1.98427
\(896\) 1.03960e131 0.435673
\(897\) 1.13392e131 0.452187
\(898\) 3.49770e130 0.132735
\(899\) −3.27374e131 −1.18233
\(900\) 4.75171e130 0.163327
\(901\) −3.68139e131 −1.20437
\(902\) −5.28911e130 −0.164699
\(903\) 5.66641e130 0.167959
\(904\) 1.92622e131 0.543513
\(905\) 6.43997e131 1.72990
\(906\) 8.07826e130 0.206592
\(907\) 3.96830e131 0.966229 0.483114 0.875557i \(-0.339506\pi\)
0.483114 + 0.875557i \(0.339506\pi\)
\(908\) 1.23821e131 0.287061
\(909\) 6.88573e131 1.52005
\(910\) 3.29409e131 0.692457
\(911\) −9.54692e131 −1.91115 −0.955577 0.294742i \(-0.904766\pi\)
−0.955577 + 0.294742i \(0.904766\pi\)
\(912\) −5.27033e130 −0.100477
\(913\) 1.53348e131 0.278439
\(914\) 1.88515e131 0.326017
\(915\) −4.52621e131 −0.745584
\(916\) 4.19375e130 0.0658043
\(917\) −7.70234e130 −0.115130
\(918\) −2.76663e131 −0.393960
\(919\) 3.40413e130 0.0461812 0.0230906 0.999733i \(-0.492649\pi\)
0.0230906 + 0.999733i \(0.492649\pi\)
\(920\) −1.79066e132 −2.31449
\(921\) −6.18562e130 −0.0761780
\(922\) 1.17679e132 1.38094
\(923\) −4.46879e131 −0.499705
\(924\) −5.88664e130 −0.0627284
\(925\) 1.89674e131 0.192619
\(926\) −9.69891e131 −0.938716
\(927\) −4.72713e131 −0.436063
\(928\) −7.14334e131 −0.628082
\(929\) 1.84470e132 1.54606 0.773032 0.634368i \(-0.218739\pi\)
0.773032 + 0.634368i \(0.218739\pi\)
\(930\) 4.17680e131 0.333697
\(931\) 2.38470e131 0.181624
\(932\) 3.62376e131 0.263118
\(933\) 3.07416e131 0.212811
\(934\) 6.62393e131 0.437199
\(935\) −1.85230e132 −1.16572
\(936\) 1.20388e132 0.722450
\(937\) 1.38071e132 0.790114 0.395057 0.918657i \(-0.370725\pi\)
0.395057 + 0.918657i \(0.370725\pi\)
\(938\) 8.75957e131 0.478032
\(939\) −3.39522e130 −0.0176705
\(940\) −6.62213e131 −0.328707
\(941\) −8.90199e131 −0.421453 −0.210726 0.977545i \(-0.567583\pi\)
−0.210726 + 0.977545i \(0.567583\pi\)
\(942\) 1.61279e130 0.00728303
\(943\) 4.88427e131 0.210392
\(944\) −2.59153e132 −1.06488
\(945\) 1.74302e132 0.683261
\(946\) −2.06754e132 −0.773213
\(947\) 3.43186e132 1.22449 0.612245 0.790668i \(-0.290266\pi\)
0.612245 + 0.790668i \(0.290266\pi\)
\(948\) 3.64932e131 0.124234
\(949\) 1.54769e132 0.502732
\(950\) 1.02267e132 0.316981
\(951\) 1.73189e131 0.0512257
\(952\) −1.60795e132 −0.453866
\(953\) −2.81753e132 −0.758987 −0.379493 0.925194i \(-0.623902\pi\)
−0.379493 + 0.925194i \(0.623902\pi\)
\(954\) −5.83365e132 −1.49981
\(955\) 8.26343e131 0.202773
\(956\) 3.82954e131 0.0896955
\(957\) −3.83640e132 −0.857714
\(958\) 4.23044e132 0.902861
\(959\) −3.13504e132 −0.638726
\(960\) 3.07580e132 0.598257
\(961\) −2.85246e132 −0.529698
\(962\) 7.49126e131 0.132820
\(963\) 9.95573e131 0.168540
\(964\) −2.84524e131 −0.0459929
\(965\) 6.17548e132 0.953247
\(966\) −2.39993e132 −0.353766
\(967\) −1.21293e133 −1.70748 −0.853742 0.520697i \(-0.825672\pi\)
−0.853742 + 0.520697i \(0.825672\pi\)
\(968\) 5.82200e132 0.782743
\(969\) 6.22458e131 0.0799285
\(970\) 8.76030e132 1.07443
\(971\) 7.55835e132 0.885465 0.442733 0.896654i \(-0.354009\pi\)
0.442733 + 0.896654i \(0.354009\pi\)
\(972\) 1.52777e132 0.170965
\(973\) −7.38809e132 −0.789788
\(974\) 8.64958e132 0.883327
\(975\) 3.15068e132 0.307397
\(976\) 1.15954e133 1.08086
\(977\) 3.97667e132 0.354170 0.177085 0.984196i \(-0.443333\pi\)
0.177085 + 0.984196i \(0.443333\pi\)
\(978\) −3.91325e132 −0.333011
\(979\) −1.81569e133 −1.47643
\(980\) −1.80864e132 −0.140537
\(981\) 8.97786e132 0.666657
\(982\) −5.14583e132 −0.365169
\(983\) 6.63961e132 0.450310 0.225155 0.974323i \(-0.427711\pi\)
0.225155 + 0.974323i \(0.427711\pi\)
\(984\) −8.64739e131 −0.0560536
\(985\) −3.50451e133 −2.17128
\(986\) −1.63359e133 −0.967431
\(987\) −5.69335e132 −0.322296
\(988\) −9.14886e131 −0.0495089
\(989\) 1.90929e133 0.987727
\(990\) −2.93521e133 −1.45169
\(991\) 1.70757e133 0.807423 0.403712 0.914886i \(-0.367720\pi\)
0.403712 + 0.914886i \(0.367720\pi\)
\(992\) 5.52617e132 0.249836
\(993\) −1.23826e133 −0.535268
\(994\) 9.45815e132 0.390942
\(995\) 3.90399e133 1.54305
\(996\) 3.90838e131 0.0147726
\(997\) −1.42027e133 −0.513378 −0.256689 0.966494i \(-0.582632\pi\)
−0.256689 + 0.966494i \(0.582632\pi\)
\(998\) −8.08136e132 −0.279367
\(999\) 3.96389e132 0.131056
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.1.3 7
3.2 odd 2 9.90.a.b.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.3 7 1.1 even 1 trivial
9.90.a.b.1.5 7 3.2 odd 2