Properties

Label 1.90.a.a.1.4
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 1.4
Root \(1.22894e11\) 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

\(f(q)\) \(=\) \(q-1.03857e13 q^{2} -5.04839e20 q^{3} -5.11108e26 q^{4} +2.06848e31 q^{5} +5.24310e33 q^{6} -1.95248e37 q^{7} +1.17366e40 q^{8} -2.65446e42 q^{9} +O(q^{10})\) \(q-1.03857e13 q^{2} -5.04839e20 q^{3} -5.11108e26 q^{4} +2.06848e31 q^{5} +5.24310e33 q^{6} -1.95248e37 q^{7} +1.17366e40 q^{8} -2.65446e42 q^{9} -2.14826e44 q^{10} -3.33800e46 q^{11} +2.58027e47 q^{12} +6.87926e49 q^{13} +2.02778e50 q^{14} -1.04425e52 q^{15} +1.94468e53 q^{16} -2.38635e54 q^{17} +2.75683e55 q^{18} +1.04038e57 q^{19} -1.05722e58 q^{20} +9.85687e57 q^{21} +3.46674e59 q^{22} -1.76924e60 q^{23} -5.92511e60 q^{24} +2.66302e62 q^{25} -7.14457e62 q^{26} +2.80881e63 q^{27} +9.97926e63 q^{28} +3.58840e64 q^{29} +1.08452e65 q^{30} -5.07783e65 q^{31} -9.28429e66 q^{32} +1.68515e67 q^{33} +2.47839e67 q^{34} -4.03866e68 q^{35} +1.35671e69 q^{36} +3.65900e69 q^{37} -1.08050e70 q^{38} -3.47292e70 q^{39} +2.42770e71 q^{40} -8.30251e71 q^{41} -1.02370e71 q^{42} +1.00136e72 q^{43} +1.70608e73 q^{44} -5.49069e73 q^{45} +1.83748e73 q^{46} -1.68772e74 q^{47} -9.81749e73 q^{48} -1.25457e75 q^{49} -2.76573e75 q^{50} +1.20472e75 q^{51} -3.51604e76 q^{52} -3.74926e76 q^{53} -2.91714e76 q^{54} -6.90459e77 q^{55} -2.29155e77 q^{56} -5.25223e77 q^{57} -3.72680e77 q^{58} -6.54064e78 q^{59} +5.33724e78 q^{60} +6.58668e78 q^{61} +5.27367e78 q^{62} +5.18277e79 q^{63} -2.39460e79 q^{64} +1.42296e81 q^{65} -1.75015e80 q^{66} -6.71698e80 q^{67} +1.21968e81 q^{68} +8.93182e80 q^{69} +4.19442e81 q^{70} -3.76636e82 q^{71} -3.11544e82 q^{72} +8.64712e81 q^{73} -3.80012e82 q^{74} -1.34440e83 q^{75} -5.31745e83 q^{76} +6.51737e83 q^{77} +3.60686e83 q^{78} +1.41908e84 q^{79} +4.02252e84 q^{80} +6.30467e84 q^{81} +8.62271e84 q^{82} -6.96531e84 q^{83} -5.03792e84 q^{84} -4.93612e85 q^{85} -1.03998e85 q^{86} -1.81157e85 q^{87} -3.91768e86 q^{88} -1.63496e86 q^{89} +5.70246e86 q^{90} -1.34316e87 q^{91} +9.04273e86 q^{92} +2.56349e86 q^{93} +1.75281e87 q^{94} +2.15200e88 q^{95} +4.68708e87 q^{96} -3.58411e88 q^{97} +1.30295e88 q^{98} +8.86058e88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03857e13 −0.417446 −0.208723 0.977975i \(-0.566931\pi\)
−0.208723 + 0.977975i \(0.566931\pi\)
\(3\) −5.04839e20 −0.295977 −0.147988 0.988989i \(-0.547280\pi\)
−0.147988 + 0.988989i \(0.547280\pi\)
\(4\) −5.11108e26 −0.825739
\(5\) 2.06848e31 1.62737 0.813685 0.581307i \(-0.197458\pi\)
0.813685 + 0.581307i \(0.197458\pi\)
\(6\) 5.24310e33 0.123554
\(7\) −1.95248e37 −0.482751 −0.241376 0.970432i \(-0.577599\pi\)
−0.241376 + 0.970432i \(0.577599\pi\)
\(8\) 1.17366e40 0.762147
\(9\) −2.65446e42 −0.912398
\(10\) −2.14826e44 −0.679338
\(11\) −3.33800e46 −1.51884 −0.759420 0.650601i \(-0.774517\pi\)
−0.759420 + 0.650601i \(0.774517\pi\)
\(12\) 2.58027e47 0.244399
\(13\) 6.87926e49 1.84953 0.924767 0.380534i \(-0.124260\pi\)
0.924767 + 0.380534i \(0.124260\pi\)
\(14\) 2.02778e50 0.201522
\(15\) −1.04425e52 −0.481663
\(16\) 1.94468e53 0.507584
\(17\) −2.38635e54 −0.419525 −0.209762 0.977752i \(-0.567269\pi\)
−0.209762 + 0.977752i \(0.567269\pi\)
\(18\) 2.75683e55 0.380877
\(19\) 1.04038e57 1.29615 0.648075 0.761576i \(-0.275574\pi\)
0.648075 + 0.761576i \(0.275574\pi\)
\(20\) −1.05722e58 −1.34378
\(21\) 9.85687e57 0.142883
\(22\) 3.46674e59 0.634033
\(23\) −1.76924e60 −0.447609 −0.223804 0.974634i \(-0.571848\pi\)
−0.223804 + 0.974634i \(0.571848\pi\)
\(24\) −5.92511e60 −0.225578
\(25\) 2.66302e62 1.64833
\(26\) −7.14457e62 −0.772080
\(27\) 2.80881e63 0.566025
\(28\) 9.97926e63 0.398626
\(29\) 3.58840e64 0.300739 0.150370 0.988630i \(-0.451954\pi\)
0.150370 + 0.988630i \(0.451954\pi\)
\(30\) 1.08452e65 0.201068
\(31\) −5.07783e65 −0.218818 −0.109409 0.993997i \(-0.534896\pi\)
−0.109409 + 0.993997i \(0.534896\pi\)
\(32\) −9.28429e66 −0.974036
\(33\) 1.68515e67 0.449541
\(34\) 2.47839e67 0.175129
\(35\) −4.03866e68 −0.785614
\(36\) 1.35671e69 0.753403
\(37\) 3.65900e69 0.600324 0.300162 0.953888i \(-0.402959\pi\)
0.300162 + 0.953888i \(0.402959\pi\)
\(38\) −1.08050e70 −0.541072
\(39\) −3.47292e70 −0.547419
\(40\) 2.42770e71 1.24029
\(41\) −8.30251e71 −1.41360 −0.706802 0.707412i \(-0.749863\pi\)
−0.706802 + 0.707412i \(0.749863\pi\)
\(42\) −1.02370e71 −0.0596459
\(43\) 1.00136e72 0.204760 0.102380 0.994745i \(-0.467354\pi\)
0.102380 + 0.994745i \(0.467354\pi\)
\(44\) 1.70608e73 1.25417
\(45\) −5.49069e73 −1.48481
\(46\) 1.83748e73 0.186852
\(47\) −1.68772e74 −0.659091 −0.329545 0.944140i \(-0.606895\pi\)
−0.329545 + 0.944140i \(0.606895\pi\)
\(48\) −9.81749e73 −0.150233
\(49\) −1.25457e75 −0.766951
\(50\) −2.76573e75 −0.688089
\(51\) 1.20472e75 0.124170
\(52\) −3.51604e76 −1.52723
\(53\) −3.74926e76 −0.697701 −0.348851 0.937178i \(-0.613428\pi\)
−0.348851 + 0.937178i \(0.613428\pi\)
\(54\) −2.91714e76 −0.236285
\(55\) −6.90459e77 −2.47171
\(56\) −2.29155e77 −0.367927
\(57\) −5.25223e77 −0.383630
\(58\) −3.72680e77 −0.125542
\(59\) −6.54064e78 −1.02969 −0.514844 0.857284i \(-0.672150\pi\)
−0.514844 + 0.857284i \(0.672150\pi\)
\(60\) 5.33724e78 0.397728
\(61\) 6.58668e78 0.235228 0.117614 0.993059i \(-0.462475\pi\)
0.117614 + 0.993059i \(0.462475\pi\)
\(62\) 5.27367e78 0.0913446
\(63\) 5.18277e79 0.440461
\(64\) −2.39460e79 −0.100977
\(65\) 1.42296e81 3.00987
\(66\) −1.75015e80 −0.187659
\(67\) −6.71698e80 −0.368846 −0.184423 0.982847i \(-0.559042\pi\)
−0.184423 + 0.982847i \(0.559042\pi\)
\(68\) 1.21968e81 0.346418
\(69\) 8.93182e80 0.132482
\(70\) 4.19442e81 0.327951
\(71\) −3.76636e82 −1.56648 −0.783240 0.621719i \(-0.786434\pi\)
−0.783240 + 0.621719i \(0.786434\pi\)
\(72\) −3.11544e82 −0.695381
\(73\) 8.64712e81 0.104473 0.0522365 0.998635i \(-0.483365\pi\)
0.0522365 + 0.998635i \(0.483365\pi\)
\(74\) −3.80012e82 −0.250603
\(75\) −1.34440e83 −0.487867
\(76\) −5.31745e83 −1.07028
\(77\) 6.51737e83 0.733221
\(78\) 3.60686e83 0.228518
\(79\) 1.41908e84 0.510037 0.255019 0.966936i \(-0.417918\pi\)
0.255019 + 0.966936i \(0.417918\pi\)
\(80\) 4.02252e84 0.826027
\(81\) 6.30467e84 0.744868
\(82\) 8.62271e84 0.590103
\(83\) −6.96531e84 −0.277949 −0.138975 0.990296i \(-0.544381\pi\)
−0.138975 + 0.990296i \(0.544381\pi\)
\(84\) −5.03792e84 −0.117984
\(85\) −4.93612e85 −0.682722
\(86\) −1.03998e85 −0.0854761
\(87\) −1.81157e85 −0.0890117
\(88\) −3.91768e86 −1.15758
\(89\) −1.63496e86 −0.292182 −0.146091 0.989271i \(-0.546669\pi\)
−0.146091 + 0.989271i \(0.546669\pi\)
\(90\) 5.70246e86 0.619827
\(91\) −1.34316e87 −0.892864
\(92\) 9.04273e86 0.369608
\(93\) 2.56349e86 0.0647650
\(94\) 1.75281e87 0.275135
\(95\) 2.15200e88 2.10932
\(96\) 4.68708e87 0.288292
\(97\) −3.58411e88 −1.39008 −0.695038 0.718973i \(-0.744612\pi\)
−0.695038 + 0.718973i \(0.744612\pi\)
\(98\) 1.30295e88 0.320161
\(99\) 8.86058e88 1.38579
\(100\) −1.36109e89 −1.36109
\(101\) −1.52336e89 −0.978368 −0.489184 0.872181i \(-0.662705\pi\)
−0.489184 + 0.872181i \(0.662705\pi\)
\(102\) −1.25119e88 −0.0518340
\(103\) −6.65603e89 −1.78632 −0.893159 0.449740i \(-0.851517\pi\)
−0.893159 + 0.449740i \(0.851517\pi\)
\(104\) 8.07392e89 1.40962
\(105\) 2.03887e89 0.232523
\(106\) 3.89386e89 0.291252
\(107\) −8.04305e89 −0.396135 −0.198067 0.980188i \(-0.563466\pi\)
−0.198067 + 0.980188i \(0.563466\pi\)
\(108\) −1.43561e90 −0.467389
\(109\) 6.24667e90 1.34949 0.674745 0.738051i \(-0.264254\pi\)
0.674745 + 0.738051i \(0.264254\pi\)
\(110\) 7.17088e90 1.03181
\(111\) −1.84721e90 −0.177682
\(112\) −3.79694e90 −0.245037
\(113\) 1.14980e89 0.00499610 0.00249805 0.999997i \(-0.499205\pi\)
0.00249805 + 0.999997i \(0.499205\pi\)
\(114\) 5.45480e90 0.160145
\(115\) −3.65964e91 −0.728424
\(116\) −1.83406e91 −0.248332
\(117\) −1.82607e92 −1.68751
\(118\) 6.79290e91 0.429839
\(119\) 4.65930e91 0.202526
\(120\) −1.22560e92 −0.367098
\(121\) 6.31222e92 1.30687
\(122\) −6.84072e91 −0.0981949
\(123\) 4.19143e92 0.418393
\(124\) 2.59532e92 0.180687
\(125\) 2.16660e93 1.05507
\(126\) −5.38266e92 −0.183869
\(127\) −6.09607e93 −1.46482 −0.732411 0.680863i \(-0.761605\pi\)
−0.732411 + 0.680863i \(0.761605\pi\)
\(128\) 5.99540e93 1.01619
\(129\) −5.05527e92 −0.0606041
\(130\) −1.47784e94 −1.25646
\(131\) 1.93866e93 0.117201 0.0586003 0.998282i \(-0.481336\pi\)
0.0586003 + 0.998282i \(0.481336\pi\)
\(132\) −8.61295e93 −0.371203
\(133\) −2.03131e94 −0.625718
\(134\) 6.97603e93 0.153973
\(135\) 5.80998e94 0.921131
\(136\) −2.80077e94 −0.319740
\(137\) 3.30510e94 0.272345 0.136172 0.990685i \(-0.456520\pi\)
0.136172 + 0.990685i \(0.456520\pi\)
\(138\) −9.27630e93 −0.0553039
\(139\) 2.72553e95 1.17840 0.589200 0.807987i \(-0.299443\pi\)
0.589200 + 0.807987i \(0.299443\pi\)
\(140\) 2.06419e95 0.648712
\(141\) 8.52026e94 0.195075
\(142\) 3.91162e95 0.653920
\(143\) −2.29630e96 −2.80915
\(144\) −5.16206e95 −0.463119
\(145\) 7.42253e95 0.489414
\(146\) −8.98062e94 −0.0436118
\(147\) 6.33354e95 0.227000
\(148\) −1.87014e96 −0.495711
\(149\) −2.76855e96 −0.543830 −0.271915 0.962321i \(-0.587657\pi\)
−0.271915 + 0.962321i \(0.587657\pi\)
\(150\) 1.39625e96 0.203658
\(151\) 6.33879e96 0.687910 0.343955 0.938986i \(-0.388233\pi\)
0.343955 + 0.938986i \(0.388233\pi\)
\(152\) 1.22105e97 0.987857
\(153\) 6.33448e96 0.382774
\(154\) −6.76873e96 −0.306080
\(155\) −1.05034e97 −0.356098
\(156\) 1.77504e97 0.452025
\(157\) 1.38061e97 0.264567 0.132283 0.991212i \(-0.457769\pi\)
0.132283 + 0.991212i \(0.457769\pi\)
\(158\) −1.47381e97 −0.212913
\(159\) 1.89277e97 0.206503
\(160\) −1.92044e98 −1.58512
\(161\) 3.45440e97 0.216084
\(162\) −6.54783e97 −0.310942
\(163\) −3.99376e98 −1.44223 −0.721113 0.692817i \(-0.756369\pi\)
−0.721113 + 0.692817i \(0.756369\pi\)
\(164\) 4.24348e98 1.16727
\(165\) 3.48571e98 0.731569
\(166\) 7.23395e97 0.116029
\(167\) −5.58501e98 −0.685711 −0.342855 0.939388i \(-0.611394\pi\)
−0.342855 + 0.939388i \(0.611394\pi\)
\(168\) 1.15686e98 0.108898
\(169\) 3.34898e99 2.42078
\(170\) 5.12650e98 0.284999
\(171\) −2.76164e99 −1.18261
\(172\) −5.11804e98 −0.169078
\(173\) −5.30954e98 −0.135521 −0.0677603 0.997702i \(-0.521585\pi\)
−0.0677603 + 0.997702i \(0.521585\pi\)
\(174\) 1.88143e98 0.0371576
\(175\) −5.19949e99 −0.795733
\(176\) −6.49133e99 −0.770939
\(177\) 3.30197e99 0.304764
\(178\) 1.69802e99 0.121970
\(179\) −1.66743e100 −0.933442 −0.466721 0.884405i \(-0.654565\pi\)
−0.466721 + 0.884405i \(0.654565\pi\)
\(180\) 2.80634e100 1.22606
\(181\) −2.59959e99 −0.0887581 −0.0443790 0.999015i \(-0.514131\pi\)
−0.0443790 + 0.999015i \(0.514131\pi\)
\(182\) 1.39496e100 0.372722
\(183\) −3.32522e99 −0.0696220
\(184\) −2.07649e100 −0.341143
\(185\) 7.56857e100 0.976949
\(186\) −2.66236e99 −0.0270359
\(187\) 7.96565e100 0.637191
\(188\) 8.62606e100 0.544237
\(189\) −5.48415e100 −0.273249
\(190\) −2.23500e101 −0.880525
\(191\) −5.02287e101 −1.56663 −0.783315 0.621624i \(-0.786473\pi\)
−0.783315 + 0.621624i \(0.786473\pi\)
\(192\) 1.20889e100 0.0298869
\(193\) 5.15777e100 0.101196 0.0505979 0.998719i \(-0.483887\pi\)
0.0505979 + 0.998719i \(0.483887\pi\)
\(194\) 3.72234e101 0.580281
\(195\) −7.18366e101 −0.890852
\(196\) 6.41218e101 0.633302
\(197\) −3.96960e101 −0.312608 −0.156304 0.987709i \(-0.549958\pi\)
−0.156304 + 0.987709i \(0.549958\pi\)
\(198\) −9.20231e101 −0.578490
\(199\) 2.43079e102 1.22119 0.610597 0.791941i \(-0.290929\pi\)
0.610597 + 0.791941i \(0.290929\pi\)
\(200\) 3.12549e102 1.25627
\(201\) 3.39099e101 0.109170
\(202\) 1.58211e102 0.408415
\(203\) −7.00627e101 −0.145182
\(204\) −6.15744e101 −0.102532
\(205\) −1.71736e103 −2.30046
\(206\) 6.91274e102 0.745691
\(207\) 4.69638e102 0.408397
\(208\) 1.33779e103 0.938794
\(209\) −3.47278e103 −1.96864
\(210\) −2.11751e102 −0.0970659
\(211\) −1.60967e103 −0.597265 −0.298633 0.954368i \(-0.596531\pi\)
−0.298633 + 0.954368i \(0.596531\pi\)
\(212\) 1.91628e103 0.576119
\(213\) 1.90140e103 0.463641
\(214\) 8.35325e102 0.165365
\(215\) 2.07130e103 0.333220
\(216\) 3.29660e103 0.431394
\(217\) 9.91435e102 0.105635
\(218\) −6.48759e103 −0.563339
\(219\) −4.36541e102 −0.0309216
\(220\) 3.52899e104 2.04099
\(221\) −1.64163e104 −0.775926
\(222\) 1.91845e103 0.0741725
\(223\) −3.21841e104 −1.01877 −0.509384 0.860539i \(-0.670127\pi\)
−0.509384 + 0.860539i \(0.670127\pi\)
\(224\) 1.81274e104 0.470217
\(225\) −7.06888e104 −1.50393
\(226\) −1.19414e102 −0.00208560
\(227\) −6.65358e104 −0.954783 −0.477392 0.878691i \(-0.658418\pi\)
−0.477392 + 0.878691i \(0.658418\pi\)
\(228\) 2.68446e104 0.316778
\(229\) 6.59926e104 0.640938 0.320469 0.947259i \(-0.396159\pi\)
0.320469 + 0.947259i \(0.396159\pi\)
\(230\) 3.80078e104 0.304078
\(231\) −3.29022e104 −0.217016
\(232\) 4.21157e104 0.229207
\(233\) 2.60299e105 1.16986 0.584931 0.811083i \(-0.301122\pi\)
0.584931 + 0.811083i \(0.301122\pi\)
\(234\) 1.89650e105 0.704444
\(235\) −3.49101e105 −1.07258
\(236\) 3.34297e105 0.850254
\(237\) −7.16408e104 −0.150959
\(238\) −4.83900e104 −0.0845436
\(239\) −6.66813e105 −0.966713 −0.483357 0.875424i \(-0.660583\pi\)
−0.483357 + 0.875424i \(0.660583\pi\)
\(240\) −2.03073e105 −0.244485
\(241\) 1.08349e106 1.08409 0.542045 0.840350i \(-0.317650\pi\)
0.542045 + 0.840350i \(0.317650\pi\)
\(242\) −6.55567e105 −0.545549
\(243\) −1.13546e106 −0.786488
\(244\) −3.36651e105 −0.194237
\(245\) −2.59504e106 −1.24811
\(246\) −4.35308e105 −0.174657
\(247\) 7.15702e106 2.39727
\(248\) −5.95966e105 −0.166771
\(249\) 3.51636e105 0.0822665
\(250\) −2.25016e106 −0.440436
\(251\) 2.49391e106 0.408696 0.204348 0.978898i \(-0.434493\pi\)
0.204348 + 0.978898i \(0.434493\pi\)
\(252\) −2.64895e106 −0.363706
\(253\) 5.90573e106 0.679846
\(254\) 6.33118e106 0.611483
\(255\) 2.49195e106 0.202070
\(256\) −4.74444e106 −0.323226
\(257\) 3.95594e106 0.226582 0.113291 0.993562i \(-0.463861\pi\)
0.113291 + 0.993562i \(0.463861\pi\)
\(258\) 5.25024e105 0.0252989
\(259\) −7.14411e106 −0.289807
\(260\) −7.27286e107 −2.48537
\(261\) −9.52526e106 −0.274394
\(262\) −2.01343e106 −0.0489249
\(263\) 7.74466e107 1.58844 0.794221 0.607629i \(-0.207879\pi\)
0.794221 + 0.607629i \(0.207879\pi\)
\(264\) 1.97780e107 0.342616
\(265\) −7.75527e107 −1.13542
\(266\) 2.10965e107 0.261203
\(267\) 8.25394e106 0.0864789
\(268\) 3.43310e107 0.304571
\(269\) 1.98879e108 1.49490 0.747449 0.664319i \(-0.231278\pi\)
0.747449 + 0.664319i \(0.231278\pi\)
\(270\) −6.03405e107 −0.384522
\(271\) 1.60523e108 0.867768 0.433884 0.900969i \(-0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(272\) −4.64069e107 −0.212944
\(273\) 6.78079e107 0.264267
\(274\) −3.43257e107 −0.113689
\(275\) −8.88917e108 −2.50355
\(276\) −4.56513e107 −0.109395
\(277\) 7.19461e108 1.46777 0.733885 0.679274i \(-0.237705\pi\)
0.733885 + 0.679274i \(0.237705\pi\)
\(278\) −2.83065e108 −0.491918
\(279\) 1.34789e108 0.199649
\(280\) −4.74002e108 −0.598753
\(281\) 1.68676e108 0.181812 0.0909061 0.995859i \(-0.471024\pi\)
0.0909061 + 0.995859i \(0.471024\pi\)
\(282\) −8.84887e107 −0.0814334
\(283\) −1.91816e109 −1.50796 −0.753979 0.656899i \(-0.771868\pi\)
−0.753979 + 0.656899i \(0.771868\pi\)
\(284\) 1.92501e109 1.29350
\(285\) −1.08641e109 −0.624308
\(286\) 2.38486e109 1.17267
\(287\) 1.62105e109 0.682419
\(288\) 2.46448e109 0.888708
\(289\) −2.66613e109 −0.823999
\(290\) −7.70880e108 −0.204304
\(291\) 1.80940e109 0.411430
\(292\) −4.41961e108 −0.0862675
\(293\) 4.27672e109 0.716972 0.358486 0.933535i \(-0.383293\pi\)
0.358486 + 0.933535i \(0.383293\pi\)
\(294\) −6.57781e108 −0.0947600
\(295\) −1.35292e110 −1.67568
\(296\) 4.29443e109 0.457535
\(297\) −9.37582e109 −0.859701
\(298\) 2.87532e109 0.227019
\(299\) −1.21711e110 −0.827867
\(300\) 6.87132e109 0.402851
\(301\) −1.95514e109 −0.0988480
\(302\) −6.58326e109 −0.287165
\(303\) 7.69053e109 0.289574
\(304\) 2.02320e110 0.657906
\(305\) 1.36244e110 0.382803
\(306\) −6.57878e109 −0.159787
\(307\) 7.49397e110 1.57418 0.787090 0.616838i \(-0.211587\pi\)
0.787090 + 0.616838i \(0.211587\pi\)
\(308\) −3.33108e110 −0.605450
\(309\) 3.36023e110 0.528708
\(310\) 1.09085e110 0.148651
\(311\) −2.85176e109 −0.0336725 −0.0168362 0.999858i \(-0.505359\pi\)
−0.0168362 + 0.999858i \(0.505359\pi\)
\(312\) −4.07603e110 −0.417213
\(313\) −2.07857e111 −1.84520 −0.922598 0.385764i \(-0.873938\pi\)
−0.922598 + 0.385764i \(0.873938\pi\)
\(314\) −1.43385e110 −0.110442
\(315\) 1.07205e111 0.716793
\(316\) −7.25304e110 −0.421158
\(317\) 9.87009e110 0.497948 0.248974 0.968510i \(-0.419907\pi\)
0.248974 + 0.968510i \(0.419907\pi\)
\(318\) −1.96577e110 −0.0862038
\(319\) −1.19781e111 −0.456775
\(320\) −4.95318e110 −0.164327
\(321\) 4.06045e110 0.117247
\(322\) −3.58763e110 −0.0902031
\(323\) −2.48271e111 −0.543767
\(324\) −3.22237e111 −0.615067
\(325\) 1.83196e112 3.04864
\(326\) 4.14779e111 0.602051
\(327\) −3.15357e111 −0.399417
\(328\) −9.74434e111 −1.07737
\(329\) 3.29523e111 0.318177
\(330\) −3.62014e111 −0.305390
\(331\) 9.02317e111 0.665293 0.332647 0.943052i \(-0.392058\pi\)
0.332647 + 0.943052i \(0.392058\pi\)
\(332\) 3.56003e111 0.229514
\(333\) −9.71266e111 −0.547734
\(334\) 5.80041e111 0.286247
\(335\) −1.38939e112 −0.600249
\(336\) 1.91684e111 0.0725251
\(337\) −4.14663e112 −1.37456 −0.687281 0.726392i \(-0.741196\pi\)
−0.687281 + 0.726392i \(0.741196\pi\)
\(338\) −3.47815e112 −1.01054
\(339\) −5.80464e109 −0.00147873
\(340\) 2.52289e112 0.563750
\(341\) 1.69498e112 0.332349
\(342\) 2.86815e112 0.493673
\(343\) 5.64334e112 0.852998
\(344\) 1.17526e112 0.156057
\(345\) 1.84753e112 0.215597
\(346\) 5.51432e111 0.0565725
\(347\) 4.79621e112 0.432749 0.216375 0.976310i \(-0.430577\pi\)
0.216375 + 0.976310i \(0.430577\pi\)
\(348\) 9.25905e111 0.0735005
\(349\) −1.99610e113 −1.39461 −0.697303 0.716776i \(-0.745617\pi\)
−0.697303 + 0.716776i \(0.745617\pi\)
\(350\) 5.40002e112 0.332175
\(351\) 1.93226e113 1.04688
\(352\) 3.09910e113 1.47940
\(353\) −3.89397e113 −1.63840 −0.819198 0.573512i \(-0.805581\pi\)
−0.819198 + 0.573512i \(0.805581\pi\)
\(354\) −3.42932e112 −0.127222
\(355\) −7.79063e113 −2.54924
\(356\) 8.35643e112 0.241266
\(357\) −2.35220e112 −0.0599430
\(358\) 1.73174e113 0.389661
\(359\) 6.09419e113 1.21119 0.605596 0.795772i \(-0.292935\pi\)
0.605596 + 0.795772i \(0.292935\pi\)
\(360\) −6.44422e113 −1.13164
\(361\) 4.38110e113 0.680006
\(362\) 2.69985e112 0.0370517
\(363\) −3.18666e113 −0.386804
\(364\) 6.86499e113 0.737273
\(365\) 1.78864e113 0.170016
\(366\) 3.45346e112 0.0290634
\(367\) 3.55965e112 0.0265318 0.0132659 0.999912i \(-0.495777\pi\)
0.0132659 + 0.999912i \(0.495777\pi\)
\(368\) −3.44060e113 −0.227199
\(369\) 2.20387e114 1.28977
\(370\) −7.86047e113 −0.407823
\(371\) 7.32035e113 0.336816
\(372\) −1.31022e113 −0.0534790
\(373\) −1.39504e114 −0.505294 −0.252647 0.967559i \(-0.581301\pi\)
−0.252647 + 0.967559i \(0.581301\pi\)
\(374\) −8.27286e113 −0.265993
\(375\) −1.09378e114 −0.312277
\(376\) −1.98081e114 −0.502324
\(377\) 2.46855e114 0.556227
\(378\) 5.69566e113 0.114067
\(379\) −6.43130e114 −1.14513 −0.572564 0.819860i \(-0.694051\pi\)
−0.572564 + 0.819860i \(0.694051\pi\)
\(380\) −1.09990e115 −1.74174
\(381\) 3.07754e114 0.433553
\(382\) 5.21658e114 0.653983
\(383\) 1.10630e115 1.23460 0.617301 0.786727i \(-0.288226\pi\)
0.617301 + 0.786727i \(0.288226\pi\)
\(384\) −3.02671e114 −0.300768
\(385\) 1.34810e115 1.19322
\(386\) −5.35670e113 −0.0422437
\(387\) −2.65807e114 −0.186822
\(388\) 1.83186e115 1.14784
\(389\) −1.57957e115 −0.882638 −0.441319 0.897350i \(-0.645489\pi\)
−0.441319 + 0.897350i \(0.645489\pi\)
\(390\) 7.46072e114 0.371882
\(391\) 4.22204e114 0.187783
\(392\) −1.47244e115 −0.584530
\(393\) −9.78713e113 −0.0346886
\(394\) 4.12270e114 0.130497
\(395\) 2.93534e115 0.830019
\(396\) −4.52871e115 −1.14430
\(397\) −6.52560e115 −1.47381 −0.736907 0.675994i \(-0.763715\pi\)
−0.736907 + 0.675994i \(0.763715\pi\)
\(398\) −2.52454e115 −0.509782
\(399\) 1.02549e115 0.185198
\(400\) 5.17872e115 0.836667
\(401\) −2.09460e115 −0.302815 −0.151407 0.988471i \(-0.548381\pi\)
−0.151407 + 0.988471i \(0.548381\pi\)
\(402\) −3.52177e114 −0.0455724
\(403\) −3.49317e115 −0.404711
\(404\) 7.78602e115 0.807876
\(405\) 1.30411e116 1.21218
\(406\) 7.27649e114 0.0606057
\(407\) −1.22137e116 −0.911796
\(408\) 1.41394e115 0.0946354
\(409\) −1.11593e116 −0.669808 −0.334904 0.942252i \(-0.608704\pi\)
−0.334904 + 0.942252i \(0.608704\pi\)
\(410\) 1.78359e116 0.960315
\(411\) −1.66854e115 −0.0806077
\(412\) 3.40195e116 1.47503
\(413\) 1.27705e116 0.497083
\(414\) −4.87751e115 −0.170484
\(415\) −1.44076e116 −0.452326
\(416\) −6.38690e116 −1.80151
\(417\) −1.37596e116 −0.348779
\(418\) 3.60671e116 0.821802
\(419\) −5.10063e116 −1.04496 −0.522480 0.852652i \(-0.674993\pi\)
−0.522480 + 0.852652i \(0.674993\pi\)
\(420\) −1.04208e116 −0.192004
\(421\) 1.89402e116 0.313929 0.156965 0.987604i \(-0.449829\pi\)
0.156965 + 0.987604i \(0.449829\pi\)
\(422\) 1.67175e116 0.249326
\(423\) 4.47998e116 0.601353
\(424\) −4.40036e116 −0.531751
\(425\) −6.35491e116 −0.691516
\(426\) −1.97474e116 −0.193545
\(427\) −1.28604e116 −0.113557
\(428\) 4.11087e116 0.327104
\(429\) 1.15926e117 0.831441
\(430\) −2.15118e116 −0.139101
\(431\) 3.16057e117 1.84301 0.921503 0.388371i \(-0.126962\pi\)
0.921503 + 0.388371i \(0.126962\pi\)
\(432\) 5.46223e116 0.287305
\(433\) 6.43348e116 0.305306 0.152653 0.988280i \(-0.451218\pi\)
0.152653 + 0.988280i \(0.451218\pi\)
\(434\) −1.02967e116 −0.0440967
\(435\) −3.74719e116 −0.144855
\(436\) −3.19272e117 −1.11433
\(437\) −1.84068e117 −0.580168
\(438\) 4.53377e115 0.0129081
\(439\) 9.35169e116 0.240558 0.120279 0.992740i \(-0.461621\pi\)
0.120279 + 0.992740i \(0.461621\pi\)
\(440\) −8.10365e117 −1.88381
\(441\) 3.33019e117 0.699765
\(442\) 1.70495e117 0.323907
\(443\) −1.84634e117 −0.317210 −0.158605 0.987342i \(-0.550700\pi\)
−0.158605 + 0.987342i \(0.550700\pi\)
\(444\) 9.44122e116 0.146719
\(445\) −3.38189e117 −0.475488
\(446\) 3.34254e117 0.425280
\(447\) 1.39767e117 0.160961
\(448\) 4.67540e116 0.0487469
\(449\) −1.21900e118 −1.15091 −0.575457 0.817832i \(-0.695176\pi\)
−0.575457 + 0.817832i \(0.695176\pi\)
\(450\) 7.34151e117 0.627811
\(451\) 2.77138e118 2.14704
\(452\) −5.87672e115 −0.00412548
\(453\) −3.20007e117 −0.203605
\(454\) 6.91019e117 0.398570
\(455\) −2.77830e118 −1.45302
\(456\) −6.16434e117 −0.292382
\(457\) 3.95962e118 1.70366 0.851829 0.523820i \(-0.175493\pi\)
0.851829 + 0.523820i \(0.175493\pi\)
\(458\) −6.85378e117 −0.267557
\(459\) −6.70282e117 −0.237462
\(460\) 1.87047e118 0.601489
\(461\) −2.43828e118 −0.711857 −0.355928 0.934513i \(-0.615835\pi\)
−0.355928 + 0.934513i \(0.615835\pi\)
\(462\) 3.41712e117 0.0905925
\(463\) −6.30692e118 −1.51867 −0.759335 0.650700i \(-0.774476\pi\)
−0.759335 + 0.650700i \(0.774476\pi\)
\(464\) 6.97828e117 0.152650
\(465\) 5.30252e117 0.105397
\(466\) −2.70339e118 −0.488354
\(467\) −7.19968e118 −1.18226 −0.591129 0.806577i \(-0.701318\pi\)
−0.591129 + 0.806577i \(0.701318\pi\)
\(468\) 9.33319e118 1.39344
\(469\) 1.31147e118 0.178061
\(470\) 3.62565e118 0.447746
\(471\) −6.96984e117 −0.0783055
\(472\) −7.67651e118 −0.784774
\(473\) −3.34255e118 −0.310997
\(474\) 7.44038e117 0.0630172
\(475\) 2.77055e119 2.13648
\(476\) −2.38140e118 −0.167234
\(477\) 9.95226e118 0.636581
\(478\) 6.92531e118 0.403550
\(479\) −2.34376e119 −1.24446 −0.622232 0.782833i \(-0.713774\pi\)
−0.622232 + 0.782833i \(0.713774\pi\)
\(480\) 9.69512e118 0.469157
\(481\) 2.51712e119 1.11032
\(482\) −1.12527e119 −0.452549
\(483\) −1.74392e118 −0.0639556
\(484\) −3.22623e119 −1.07914
\(485\) −7.41365e119 −2.26217
\(486\) 1.17925e119 0.328316
\(487\) 2.11455e119 0.537253 0.268627 0.963244i \(-0.413430\pi\)
0.268627 + 0.963244i \(0.413430\pi\)
\(488\) 7.73054e118 0.179278
\(489\) 2.01621e119 0.426865
\(490\) 2.69513e119 0.521019
\(491\) −6.64397e119 −1.17301 −0.586504 0.809946i \(-0.699496\pi\)
−0.586504 + 0.809946i \(0.699496\pi\)
\(492\) −2.14227e119 −0.345484
\(493\) −8.56319e118 −0.126168
\(494\) −7.43305e119 −1.00073
\(495\) 1.83279e120 2.25519
\(496\) −9.87474e118 −0.111069
\(497\) 7.35372e119 0.756220
\(498\) −3.65198e118 −0.0343418
\(499\) 1.68726e120 1.45114 0.725568 0.688150i \(-0.241577\pi\)
0.725568 + 0.688150i \(0.241577\pi\)
\(500\) −1.10737e120 −0.871216
\(501\) 2.81953e119 0.202954
\(502\) −2.59009e119 −0.170608
\(503\) 9.10170e118 0.0548715 0.0274358 0.999624i \(-0.491266\pi\)
0.0274358 + 0.999624i \(0.491266\pi\)
\(504\) 6.08282e119 0.335696
\(505\) −3.15104e120 −1.59217
\(506\) −6.13350e119 −0.283799
\(507\) −1.69070e120 −0.716493
\(508\) 3.11575e120 1.20956
\(509\) 1.64557e120 0.585295 0.292647 0.956220i \(-0.405464\pi\)
0.292647 + 0.956220i \(0.405464\pi\)
\(510\) −2.58806e119 −0.0843531
\(511\) −1.68833e119 −0.0504345
\(512\) −3.21823e120 −0.881259
\(513\) 2.92223e120 0.733653
\(514\) −4.10851e119 −0.0945857
\(515\) −1.37679e121 −2.90700
\(516\) 2.58379e119 0.0500432
\(517\) 5.63360e120 1.00105
\(518\) 7.41965e119 0.120979
\(519\) 2.68047e119 0.0401109
\(520\) 1.67007e121 2.29397
\(521\) −3.57068e120 −0.450269 −0.225135 0.974328i \(-0.572282\pi\)
−0.225135 + 0.974328i \(0.572282\pi\)
\(522\) 9.89263e119 0.114545
\(523\) 6.21466e120 0.660834 0.330417 0.943835i \(-0.392811\pi\)
0.330417 + 0.943835i \(0.392811\pi\)
\(524\) −9.90866e119 −0.0967771
\(525\) 2.62491e120 0.235518
\(526\) −8.04335e120 −0.663088
\(527\) 1.21175e120 0.0917996
\(528\) 3.27708e120 0.228180
\(529\) −1.24933e121 −0.799647
\(530\) 8.05437e120 0.473975
\(531\) 1.73619e121 0.939486
\(532\) 1.03822e121 0.516680
\(533\) −5.71151e121 −2.61451
\(534\) −8.57228e119 −0.0361003
\(535\) −1.66369e121 −0.644657
\(536\) −7.88346e120 −0.281115
\(537\) 8.41784e120 0.276277
\(538\) −2.06549e121 −0.624039
\(539\) 4.18774e121 1.16488
\(540\) −2.96952e121 −0.760614
\(541\) 2.95502e121 0.697079 0.348539 0.937294i \(-0.386678\pi\)
0.348539 + 0.937294i \(0.386678\pi\)
\(542\) −1.66714e121 −0.362246
\(543\) 1.31237e120 0.0262703
\(544\) 2.21556e121 0.408632
\(545\) 1.29211e122 2.19612
\(546\) −7.04231e120 −0.110317
\(547\) −6.53228e121 −0.943255 −0.471627 0.881798i \(-0.656333\pi\)
−0.471627 + 0.881798i \(0.656333\pi\)
\(548\) −1.68926e121 −0.224886
\(549\) −1.74841e121 −0.214622
\(550\) 9.23200e121 1.04510
\(551\) 3.73329e121 0.389803
\(552\) 1.04829e121 0.100970
\(553\) −2.77072e121 −0.246221
\(554\) −7.47209e121 −0.612714
\(555\) −3.82091e121 −0.289154
\(556\) −1.39304e122 −0.973051
\(557\) 4.41176e120 0.0284483 0.0142241 0.999899i \(-0.495472\pi\)
0.0142241 + 0.999899i \(0.495472\pi\)
\(558\) −1.39987e121 −0.0833426
\(559\) 6.88863e121 0.378710
\(560\) −7.85389e121 −0.398765
\(561\) −4.02137e121 −0.188594
\(562\) −1.75182e121 −0.0758967
\(563\) 6.13774e121 0.245688 0.122844 0.992426i \(-0.460798\pi\)
0.122844 + 0.992426i \(0.460798\pi\)
\(564\) −4.35477e121 −0.161081
\(565\) 2.37834e120 0.00813051
\(566\) 1.99214e122 0.629490
\(567\) −1.23097e122 −0.359586
\(568\) −4.42043e122 −1.19389
\(569\) 3.46558e122 0.865526 0.432763 0.901508i \(-0.357539\pi\)
0.432763 + 0.901508i \(0.357539\pi\)
\(570\) 1.12831e122 0.260615
\(571\) −1.51810e122 −0.324335 −0.162167 0.986763i \(-0.551848\pi\)
−0.162167 + 0.986763i \(0.551848\pi\)
\(572\) 1.17365e123 2.31962
\(573\) 2.53574e122 0.463686
\(574\) −1.68357e122 −0.284873
\(575\) −4.71153e122 −0.737807
\(576\) 6.35636e121 0.0921315
\(577\) −3.65421e122 −0.490309 −0.245155 0.969484i \(-0.578839\pi\)
−0.245155 + 0.969484i \(0.578839\pi\)
\(578\) 2.76895e122 0.343975
\(579\) −2.60385e121 −0.0299516
\(580\) −3.79372e122 −0.404128
\(581\) 1.35996e122 0.134180
\(582\) −1.87918e122 −0.171750
\(583\) 1.25150e123 1.05970
\(584\) 1.01488e122 0.0796238
\(585\) −3.77719e123 −2.74620
\(586\) −4.44166e122 −0.299297
\(587\) −4.37714e122 −0.273398 −0.136699 0.990613i \(-0.543649\pi\)
−0.136699 + 0.990613i \(0.543649\pi\)
\(588\) −3.23712e122 −0.187442
\(589\) −5.28286e122 −0.283621
\(590\) 1.40510e123 0.699507
\(591\) 2.00401e122 0.0925246
\(592\) 7.11557e122 0.304715
\(593\) 3.28296e123 1.30416 0.652082 0.758148i \(-0.273896\pi\)
0.652082 + 0.758148i \(0.273896\pi\)
\(594\) 9.73742e122 0.358878
\(595\) 9.63767e122 0.329585
\(596\) 1.41503e123 0.449062
\(597\) −1.22716e123 −0.361445
\(598\) 1.26405e123 0.345590
\(599\) 1.53295e123 0.389077 0.194538 0.980895i \(-0.437679\pi\)
0.194538 + 0.980895i \(0.437679\pi\)
\(600\) −1.57787e123 −0.371826
\(601\) −6.22438e123 −1.36202 −0.681008 0.732276i \(-0.738458\pi\)
−0.681008 + 0.732276i \(0.738458\pi\)
\(602\) 2.03054e122 0.0412637
\(603\) 1.78299e123 0.336534
\(604\) −3.23980e123 −0.568035
\(605\) 1.30567e124 2.12677
\(606\) −7.98713e122 −0.120881
\(607\) −4.03681e123 −0.567730 −0.283865 0.958864i \(-0.591617\pi\)
−0.283865 + 0.958864i \(0.591617\pi\)
\(608\) −9.65917e123 −1.26250
\(609\) 3.53704e122 0.0429705
\(610\) −1.41499e123 −0.159799
\(611\) −1.16102e124 −1.21901
\(612\) −3.23760e123 −0.316071
\(613\) 3.27247e123 0.297087 0.148544 0.988906i \(-0.452541\pi\)
0.148544 + 0.988906i \(0.452541\pi\)
\(614\) −7.78300e123 −0.657135
\(615\) 8.66989e123 0.680881
\(616\) 7.64919e123 0.558822
\(617\) 1.99774e124 1.35784 0.678921 0.734211i \(-0.262448\pi\)
0.678921 + 0.734211i \(0.262448\pi\)
\(618\) −3.48982e123 −0.220707
\(619\) −3.28784e123 −0.193498 −0.0967491 0.995309i \(-0.530844\pi\)
−0.0967491 + 0.995309i \(0.530844\pi\)
\(620\) 5.36837e123 0.294044
\(621\) −4.96947e123 −0.253358
\(622\) 2.96174e122 0.0140564
\(623\) 3.19223e123 0.141051
\(624\) −6.75370e123 −0.277861
\(625\) 1.79220e123 0.0686635
\(626\) 2.15874e124 0.770269
\(627\) 1.75319e124 0.582673
\(628\) −7.05638e123 −0.218463
\(629\) −8.73167e123 −0.251851
\(630\) −1.11339e124 −0.299222
\(631\) 1.80467e124 0.451952 0.225976 0.974133i \(-0.427443\pi\)
0.225976 + 0.974133i \(0.427443\pi\)
\(632\) 1.66552e124 0.388723
\(633\) 8.12624e123 0.176776
\(634\) −1.02508e124 −0.207866
\(635\) −1.26096e125 −2.38381
\(636\) −9.67411e123 −0.170518
\(637\) −8.63048e124 −1.41850
\(638\) 1.24400e124 0.190679
\(639\) 9.99764e124 1.42925
\(640\) 1.24014e125 1.65371
\(641\) −8.89073e124 −1.10600 −0.553000 0.833181i \(-0.686517\pi\)
−0.553000 + 0.833181i \(0.686517\pi\)
\(642\) −4.21705e123 −0.0489441
\(643\) −9.77592e124 −1.05869 −0.529345 0.848406i \(-0.677562\pi\)
−0.529345 + 0.848406i \(0.677562\pi\)
\(644\) −1.76557e124 −0.178429
\(645\) −1.04567e124 −0.0986253
\(646\) 2.57846e124 0.226993
\(647\) 1.88260e125 1.54710 0.773550 0.633735i \(-0.218479\pi\)
0.773550 + 0.633735i \(0.218479\pi\)
\(648\) 7.39956e124 0.567699
\(649\) 2.18327e125 1.56393
\(650\) −1.90262e125 −1.27264
\(651\) −5.00515e123 −0.0312654
\(652\) 2.04124e125 1.19090
\(653\) −1.38084e125 −0.752503 −0.376252 0.926518i \(-0.622787\pi\)
−0.376252 + 0.926518i \(0.622787\pi\)
\(654\) 3.27519e124 0.166735
\(655\) 4.01009e124 0.190729
\(656\) −1.61457e125 −0.717523
\(657\) −2.29534e124 −0.0953210
\(658\) −3.42232e124 −0.132821
\(659\) −3.19975e125 −1.16069 −0.580344 0.814372i \(-0.697082\pi\)
−0.580344 + 0.814372i \(0.697082\pi\)
\(660\) −1.78157e125 −0.604085
\(661\) 2.58615e125 0.819764 0.409882 0.912139i \(-0.365570\pi\)
0.409882 + 0.912139i \(0.365570\pi\)
\(662\) −9.37117e124 −0.277724
\(663\) 8.28761e124 0.229656
\(664\) −8.17492e124 −0.211838
\(665\) −4.20173e125 −1.01827
\(666\) 1.00873e125 0.228649
\(667\) −6.34875e124 −0.134613
\(668\) 2.85454e125 0.566218
\(669\) 1.62478e125 0.301532
\(670\) 1.44298e125 0.250571
\(671\) −2.19864e125 −0.357274
\(672\) −9.15141e124 −0.139173
\(673\) 6.54859e125 0.932132 0.466066 0.884750i \(-0.345671\pi\)
0.466066 + 0.884750i \(0.345671\pi\)
\(674\) 4.30655e125 0.573805
\(675\) 7.47993e125 0.932996
\(676\) −1.71169e126 −1.99893
\(677\) 7.59313e125 0.830281 0.415140 0.909757i \(-0.363732\pi\)
0.415140 + 0.909757i \(0.363732\pi\)
\(678\) 6.02851e122 0.000617289 0
\(679\) 6.99788e125 0.671061
\(680\) −5.79334e125 −0.520334
\(681\) 3.35899e125 0.282593
\(682\) −1.76035e125 −0.138738
\(683\) −9.21145e125 −0.680153 −0.340077 0.940398i \(-0.610453\pi\)
−0.340077 + 0.940398i \(0.610453\pi\)
\(684\) 1.41149e126 0.976523
\(685\) 6.83653e125 0.443206
\(686\) −5.86099e125 −0.356080
\(687\) −3.33157e125 −0.189703
\(688\) 1.94733e125 0.103933
\(689\) −2.57921e126 −1.29042
\(690\) −1.91878e125 −0.0899998
\(691\) −3.51288e126 −1.54487 −0.772433 0.635096i \(-0.780960\pi\)
−0.772433 + 0.635096i \(0.780960\pi\)
\(692\) 2.71375e125 0.111905
\(693\) −1.73001e126 −0.668990
\(694\) −4.98118e125 −0.180649
\(695\) 5.63771e126 1.91769
\(696\) −2.12617e125 −0.0678400
\(697\) 1.98127e126 0.593042
\(698\) 2.07309e126 0.582173
\(699\) −1.31409e126 −0.346252
\(700\) 2.65750e126 0.657068
\(701\) −5.19129e126 −1.20455 −0.602273 0.798290i \(-0.705738\pi\)
−0.602273 + 0.798290i \(0.705738\pi\)
\(702\) −2.00678e126 −0.437016
\(703\) 3.80674e126 0.778110
\(704\) 7.99317e125 0.153368
\(705\) 1.76240e126 0.317460
\(706\) 4.04415e126 0.683941
\(707\) 2.97433e126 0.472308
\(708\) −1.68766e126 −0.251655
\(709\) 7.37489e125 0.103276 0.0516378 0.998666i \(-0.483556\pi\)
0.0516378 + 0.998666i \(0.483556\pi\)
\(710\) 8.09110e126 1.06417
\(711\) −3.76689e126 −0.465357
\(712\) −1.91890e126 −0.222685
\(713\) 8.98391e125 0.0979448
\(714\) 2.44292e125 0.0250229
\(715\) −4.74984e127 −4.57152
\(716\) 8.52236e126 0.770780
\(717\) 3.36634e126 0.286124
\(718\) −6.32923e126 −0.505607
\(719\) 2.06006e127 1.54684 0.773419 0.633895i \(-0.218545\pi\)
0.773419 + 0.633895i \(0.218545\pi\)
\(720\) −1.06776e127 −0.753665
\(721\) 1.29958e127 0.862347
\(722\) −4.55007e126 −0.283866
\(723\) −5.46987e126 −0.320865
\(724\) 1.32867e126 0.0732910
\(725\) 9.55599e126 0.495718
\(726\) 3.30956e126 0.161470
\(727\) 3.42949e127 1.57380 0.786898 0.617083i \(-0.211686\pi\)
0.786898 + 0.617083i \(0.211686\pi\)
\(728\) −1.57642e127 −0.680494
\(729\) −1.26101e127 −0.512086
\(730\) −1.85762e126 −0.0709725
\(731\) −2.38960e126 −0.0859019
\(732\) 1.69954e126 0.0574896
\(733\) 3.37168e127 1.07330 0.536649 0.843806i \(-0.319690\pi\)
0.536649 + 0.843806i \(0.319690\pi\)
\(734\) −3.69694e125 −0.0110756
\(735\) 1.31008e127 0.369412
\(736\) 1.64262e127 0.435987
\(737\) 2.24213e127 0.560218
\(738\) −2.28886e127 −0.538408
\(739\) −5.17935e127 −1.14709 −0.573546 0.819174i \(-0.694432\pi\)
−0.573546 + 0.819174i \(0.694432\pi\)
\(740\) −3.86835e127 −0.806705
\(741\) −3.61314e127 −0.709537
\(742\) −7.60267e126 −0.140602
\(743\) 7.49695e127 1.30582 0.652909 0.757437i \(-0.273549\pi\)
0.652909 + 0.757437i \(0.273549\pi\)
\(744\) 3.00867e126 0.0493604
\(745\) −5.72669e127 −0.885012
\(746\) 1.44884e127 0.210933
\(747\) 1.84891e127 0.253600
\(748\) −4.07130e127 −0.526154
\(749\) 1.57039e127 0.191234
\(750\) 1.13597e127 0.130359
\(751\) −8.01748e127 −0.867083 −0.433542 0.901134i \(-0.642736\pi\)
−0.433542 + 0.901134i \(0.642736\pi\)
\(752\) −3.28207e127 −0.334544
\(753\) −1.25902e127 −0.120964
\(754\) −2.56376e127 −0.232195
\(755\) 1.31116e128 1.11948
\(756\) 2.80299e127 0.225632
\(757\) 2.70790e127 0.205525 0.102763 0.994706i \(-0.467232\pi\)
0.102763 + 0.994706i \(0.467232\pi\)
\(758\) 6.67934e127 0.478029
\(759\) −2.98144e127 −0.201218
\(760\) 2.52572e128 1.60761
\(761\) −2.72586e127 −0.163639 −0.0818195 0.996647i \(-0.526073\pi\)
−0.0818195 + 0.996647i \(0.526073\pi\)
\(762\) −3.19623e127 −0.180985
\(763\) −1.21965e128 −0.651468
\(764\) 2.56723e128 1.29363
\(765\) 1.31027e128 0.622914
\(766\) −1.14897e128 −0.515379
\(767\) −4.49948e128 −1.90444
\(768\) 2.39518e127 0.0956673
\(769\) 1.43554e128 0.541118 0.270559 0.962703i \(-0.412791\pi\)
0.270559 + 0.962703i \(0.412791\pi\)
\(770\) −1.40010e128 −0.498105
\(771\) −1.99711e127 −0.0670630
\(772\) −2.63618e127 −0.0835613
\(773\) −1.30472e128 −0.390419 −0.195210 0.980762i \(-0.562539\pi\)
−0.195210 + 0.980762i \(0.562539\pi\)
\(774\) 2.76059e127 0.0779882
\(775\) −1.35224e128 −0.360684
\(776\) −4.20653e128 −1.05944
\(777\) 3.60663e127 0.0857761
\(778\) 1.64049e128 0.368454
\(779\) −8.63774e128 −1.83224
\(780\) 3.67163e128 0.735612
\(781\) 1.25721e129 2.37923
\(782\) −4.38487e127 −0.0783892
\(783\) 1.00792e128 0.170226
\(784\) −2.43972e128 −0.389292
\(785\) 2.85575e128 0.430547
\(786\) 1.01646e127 0.0144806
\(787\) 3.37148e128 0.453884 0.226942 0.973908i \(-0.427127\pi\)
0.226942 + 0.973908i \(0.427127\pi\)
\(788\) 2.02889e128 0.258133
\(789\) −3.90981e128 −0.470141
\(790\) −3.04855e128 −0.346488
\(791\) −2.24496e126 −0.00241187
\(792\) 1.03993e129 1.05617
\(793\) 4.53115e128 0.435062
\(794\) 6.77727e128 0.615237
\(795\) 3.91516e128 0.336057
\(796\) −1.24239e129 −1.00839
\(797\) −1.75623e129 −1.34799 −0.673993 0.738738i \(-0.735422\pi\)
−0.673993 + 0.738738i \(0.735422\pi\)
\(798\) −1.06504e128 −0.0773100
\(799\) 4.02749e128 0.276505
\(800\) −2.47243e129 −1.60553
\(801\) 4.33995e128 0.266586
\(802\) 2.17539e128 0.126409
\(803\) −2.88641e128 −0.158678
\(804\) −1.73316e128 −0.0901457
\(805\) 7.14536e128 0.351648
\(806\) 3.62789e128 0.168945
\(807\) −1.00402e129 −0.442455
\(808\) −1.78791e129 −0.745660
\(809\) 4.20411e129 1.65945 0.829726 0.558171i \(-0.188497\pi\)
0.829726 + 0.558171i \(0.188497\pi\)
\(810\) −1.35441e129 −0.506017
\(811\) 2.68092e129 0.948104 0.474052 0.880497i \(-0.342791\pi\)
0.474052 + 0.880497i \(0.342791\pi\)
\(812\) 3.58096e128 0.119883
\(813\) −8.10383e128 −0.256839
\(814\) 1.26848e129 0.380625
\(815\) −8.26101e129 −2.34704
\(816\) 2.34280e128 0.0630265
\(817\) 1.04179e129 0.265400
\(818\) 1.15897e129 0.279609
\(819\) 3.56536e129 0.814648
\(820\) 8.77755e129 1.89958
\(821\) 7.91079e129 1.62162 0.810810 0.585309i \(-0.199027\pi\)
0.810810 + 0.585309i \(0.199027\pi\)
\(822\) 1.73289e128 0.0336493
\(823\) −5.95240e129 −1.09496 −0.547481 0.836818i \(-0.684413\pi\)
−0.547481 + 0.836818i \(0.684413\pi\)
\(824\) −7.81193e129 −1.36144
\(825\) 4.48760e129 0.740992
\(826\) −1.32630e129 −0.207505
\(827\) −6.51955e128 −0.0966546 −0.0483273 0.998832i \(-0.515389\pi\)
−0.0483273 + 0.998832i \(0.515389\pi\)
\(828\) −2.40036e129 −0.337229
\(829\) −1.23651e130 −1.64634 −0.823170 0.567795i \(-0.807797\pi\)
−0.823170 + 0.567795i \(0.807797\pi\)
\(830\) 1.49633e129 0.188822
\(831\) −3.63212e129 −0.434425
\(832\) −1.64731e129 −0.186761
\(833\) 2.99384e129 0.321755
\(834\) 1.42902e129 0.145596
\(835\) −1.15525e130 −1.11591
\(836\) 1.77496e130 1.62559
\(837\) −1.42627e129 −0.123856
\(838\) 5.29735e129 0.436214
\(839\) −1.77540e130 −1.38641 −0.693203 0.720743i \(-0.743801\pi\)
−0.693203 + 0.720743i \(0.743801\pi\)
\(840\) 2.39295e129 0.177217
\(841\) −1.29494e130 −0.909556
\(842\) −1.96707e129 −0.131048
\(843\) −8.51544e128 −0.0538121
\(844\) 8.22714e129 0.493185
\(845\) 6.92731e130 3.93950
\(846\) −4.65276e129 −0.251032
\(847\) −1.23245e130 −0.630894
\(848\) −7.29110e129 −0.354142
\(849\) 9.68364e129 0.446320
\(850\) 6.60000e129 0.288670
\(851\) −6.47365e129 −0.268710
\(852\) −9.71822e129 −0.382847
\(853\) 2.44364e130 0.913704 0.456852 0.889543i \(-0.348977\pi\)
0.456852 + 0.889543i \(0.348977\pi\)
\(854\) 1.33563e129 0.0474037
\(855\) −5.71239e130 −1.92454
\(856\) −9.43982e129 −0.301913
\(857\) −3.08645e129 −0.0937159 −0.0468579 0.998902i \(-0.514921\pi\)
−0.0468579 + 0.998902i \(0.514921\pi\)
\(858\) −1.20397e130 −0.347081
\(859\) 3.12518e130 0.855421 0.427710 0.903916i \(-0.359320\pi\)
0.427710 + 0.903916i \(0.359320\pi\)
\(860\) −1.05866e130 −0.275153
\(861\) −8.18367e129 −0.201980
\(862\) −3.28246e130 −0.769355
\(863\) 4.69595e130 1.04530 0.522652 0.852546i \(-0.324943\pi\)
0.522652 + 0.852546i \(0.324943\pi\)
\(864\) −2.60779e130 −0.551328
\(865\) −1.09827e130 −0.220542
\(866\) −6.68161e129 −0.127448
\(867\) 1.34596e130 0.243884
\(868\) −5.06730e129 −0.0872266
\(869\) −4.73689e130 −0.774665
\(870\) 3.89171e129 0.0604691
\(871\) −4.62078e130 −0.682193
\(872\) 7.33149e130 1.02851
\(873\) 9.51386e130 1.26830
\(874\) 1.91167e130 0.242189
\(875\) −4.23023e130 −0.509338
\(876\) 2.23119e129 0.0255331
\(877\) 1.47350e131 1.60276 0.801382 0.598153i \(-0.204099\pi\)
0.801382 + 0.598153i \(0.204099\pi\)
\(878\) −9.71237e129 −0.100420
\(879\) −2.15906e130 −0.212207
\(880\) −1.34272e131 −1.25460
\(881\) 1.74519e131 1.55030 0.775149 0.631778i \(-0.217675\pi\)
0.775149 + 0.631778i \(0.217675\pi\)
\(882\) −3.45863e130 −0.292114
\(883\) −1.48587e131 −1.19324 −0.596621 0.802523i \(-0.703490\pi\)
−0.596621 + 0.802523i \(0.703490\pi\)
\(884\) 8.39052e130 0.640712
\(885\) 6.83007e130 0.495963
\(886\) 1.91755e130 0.132418
\(887\) −1.59345e131 −1.04649 −0.523246 0.852182i \(-0.675279\pi\)
−0.523246 + 0.852182i \(0.675279\pi\)
\(888\) −2.16800e130 −0.135420
\(889\) 1.19024e131 0.707144
\(890\) 3.51232e130 0.198490
\(891\) −2.10450e131 −1.13133
\(892\) 1.64496e131 0.841237
\(893\) −1.75586e131 −0.854281
\(894\) −1.45158e130 −0.0671924
\(895\) −3.44904e131 −1.51906
\(896\) −1.17059e131 −0.490566
\(897\) 6.14443e130 0.245029
\(898\) 1.26602e131 0.480444
\(899\) −1.82213e130 −0.0658071
\(900\) 3.61296e131 1.24186
\(901\) 8.94706e130 0.292703
\(902\) −2.87826e131 −0.896271
\(903\) 9.87030e129 0.0292567
\(904\) 1.34948e129 0.00380776
\(905\) −5.37719e130 −0.144442
\(906\) 3.32349e130 0.0849942
\(907\) 1.57911e131 0.384492 0.192246 0.981347i \(-0.438423\pi\)
0.192246 + 0.981347i \(0.438423\pi\)
\(908\) 3.40070e131 0.788402
\(909\) 4.04370e131 0.892660
\(910\) 2.88545e131 0.606557
\(911\) 2.16123e131 0.432647 0.216324 0.976322i \(-0.430593\pi\)
0.216324 + 0.976322i \(0.430593\pi\)
\(912\) −1.02139e131 −0.194725
\(913\) 2.32502e131 0.422160
\(914\) −4.11233e131 −0.711185
\(915\) −6.87814e130 −0.113301
\(916\) −3.37293e131 −0.529248
\(917\) −3.78520e130 −0.0565787
\(918\) 6.96133e130 0.0991273
\(919\) −3.78728e131 −0.513792 −0.256896 0.966439i \(-0.582700\pi\)
−0.256896 + 0.966439i \(0.582700\pi\)
\(920\) −4.29518e131 −0.555166
\(921\) −3.78325e131 −0.465920
\(922\) 2.53232e131 0.297162
\(923\) −2.59097e132 −2.89726
\(924\) 1.68166e131 0.179199
\(925\) 9.74400e131 0.989533
\(926\) 6.55016e131 0.633962
\(927\) 1.76682e132 1.62983
\(928\) −3.33158e131 −0.292931
\(929\) 4.01039e131 0.336115 0.168057 0.985777i \(-0.446251\pi\)
0.168057 + 0.985777i \(0.446251\pi\)
\(930\) −5.50703e130 −0.0439973
\(931\) −1.30522e132 −0.994085
\(932\) −1.33041e132 −0.966001
\(933\) 1.43968e130 0.00996627
\(934\) 7.47736e131 0.493528
\(935\) 1.64768e132 1.03695
\(936\) −2.14319e132 −1.28613
\(937\) 1.77275e132 1.01446 0.507230 0.861811i \(-0.330669\pi\)
0.507230 + 0.861811i \(0.330669\pi\)
\(938\) −1.36205e131 −0.0743307
\(939\) 1.04935e132 0.546134
\(940\) 1.78428e132 0.885675
\(941\) 1.19449e132 0.565517 0.282759 0.959191i \(-0.408750\pi\)
0.282759 + 0.959191i \(0.408750\pi\)
\(942\) 7.23864e130 0.0326883
\(943\) 1.46891e132 0.632741
\(944\) −1.27194e132 −0.522654
\(945\) −1.13438e132 −0.444677
\(946\) 3.47146e131 0.129824
\(947\) −3.58699e132 −1.27984 −0.639921 0.768441i \(-0.721033\pi\)
−0.639921 + 0.768441i \(0.721033\pi\)
\(948\) 3.66162e131 0.124653
\(949\) 5.94858e131 0.193226
\(950\) −2.87740e132 −0.891866
\(951\) −4.98281e131 −0.147381
\(952\) 5.46844e131 0.154355
\(953\) 6.31274e132 1.70053 0.850264 0.526357i \(-0.176442\pi\)
0.850264 + 0.526357i \(0.176442\pi\)
\(954\) −1.03361e132 −0.265738
\(955\) −1.03897e133 −2.54949
\(956\) 3.40813e132 0.798253
\(957\) 6.04701e131 0.135195
\(958\) 2.43415e132 0.519496
\(959\) −6.45313e131 −0.131475
\(960\) 2.50056e131 0.0486370
\(961\) −5.12722e132 −0.952119
\(962\) −2.61420e132 −0.463498
\(963\) 2.13499e132 0.361432
\(964\) −5.53778e132 −0.895175
\(965\) 1.06688e132 0.164683
\(966\) 1.81118e131 0.0266980
\(967\) 2.25037e132 0.316793 0.158396 0.987376i \(-0.449368\pi\)
0.158396 + 0.987376i \(0.449368\pi\)
\(968\) 7.40842e132 0.996029
\(969\) 1.25337e132 0.160942
\(970\) 7.69958e132 0.944332
\(971\) 1.34386e133 1.57434 0.787168 0.616739i \(-0.211547\pi\)
0.787168 + 0.616739i \(0.211547\pi\)
\(972\) 5.80342e132 0.649434
\(973\) −5.32154e132 −0.568874
\(974\) −2.19610e132 −0.224274
\(975\) −9.24846e132 −0.902327
\(976\) 1.28090e132 0.119398
\(977\) −1.09375e133 −0.974118 −0.487059 0.873369i \(-0.661930\pi\)
−0.487059 + 0.873369i \(0.661930\pi\)
\(978\) −2.09397e132 −0.178193
\(979\) 5.45751e132 0.443777
\(980\) 1.32635e133 1.03062
\(981\) −1.65815e133 −1.23127
\(982\) 6.90021e132 0.489667
\(983\) 1.10364e132 0.0748505 0.0374253 0.999299i \(-0.488084\pi\)
0.0374253 + 0.999299i \(0.488084\pi\)
\(984\) 4.91932e132 0.318877
\(985\) −8.21104e132 −0.508728
\(986\) 8.89345e131 0.0526681
\(987\) −1.66356e132 −0.0941728
\(988\) −3.65801e133 −1.97952
\(989\) −1.77165e132 −0.0916523
\(990\) −1.90348e133 −0.941417
\(991\) 7.24307e132 0.342488 0.171244 0.985229i \(-0.445221\pi\)
0.171244 + 0.985229i \(0.445221\pi\)
\(992\) 4.71441e132 0.213136
\(993\) −4.55525e132 −0.196911
\(994\) −7.63734e132 −0.315681
\(995\) 5.02803e133 1.98733
\(996\) −1.79724e132 −0.0679306
\(997\) −2.56102e132 −0.0925716 −0.0462858 0.998928i \(-0.514738\pi\)
−0.0462858 + 0.998928i \(0.514738\pi\)
\(998\) −1.75234e133 −0.605771
\(999\) 1.02775e133 0.339798
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.1.4 7
3.2 odd 2 9.90.a.b.1.4 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.4 7 1.1 even 1 trivial
9.90.a.b.1.4 7 3.2 odd 2