Properties

Label 1.90.a.a.1.7
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 1.7
Root \(-1.01484e12\) 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

\(f(q)\) \(=\) \(q+4.42254e13 q^{2} -3.38901e20 q^{3} +1.33691e27 q^{4} +3.67006e30 q^{5} -1.49880e34 q^{6} -4.35255e37 q^{7} +3.17513e40 q^{8} -2.79447e42 q^{9} +O(q^{10})\) \(q+4.42254e13 q^{2} -3.38901e20 q^{3} +1.33691e27 q^{4} +3.67006e30 q^{5} -1.49880e34 q^{6} -4.35255e37 q^{7} +3.17513e40 q^{8} -2.79447e42 q^{9} +1.62310e44 q^{10} -2.45458e46 q^{11} -4.53081e47 q^{12} -6.70001e49 q^{13} -1.92493e51 q^{14} -1.24379e51 q^{15} +5.76705e53 q^{16} +4.97159e54 q^{17} -1.23586e56 q^{18} +4.54728e56 q^{19} +4.90655e57 q^{20} +1.47508e58 q^{21} -1.08555e60 q^{22} +2.88267e60 q^{23} -1.07605e61 q^{24} -1.48089e62 q^{25} -2.96311e63 q^{26} +1.93302e63 q^{27} -5.81898e64 q^{28} -1.57790e65 q^{29} -5.50069e64 q^{30} +4.07570e66 q^{31} +5.85187e66 q^{32} +8.31859e66 q^{33} +2.19871e68 q^{34} -1.59741e68 q^{35} -3.73596e69 q^{36} -7.75996e69 q^{37} +2.01105e70 q^{38} +2.27064e70 q^{39} +1.16529e71 q^{40} +2.95976e71 q^{41} +6.52360e71 q^{42} -1.81368e72 q^{43} -3.28156e73 q^{44} -1.02559e73 q^{45} +1.27487e74 q^{46} +1.54316e73 q^{47} -1.95446e74 q^{48} +2.58682e74 q^{49} -6.54931e75 q^{50} -1.68488e75 q^{51} -8.95734e76 q^{52} +3.79389e76 q^{53} +8.54884e76 q^{54} -9.00846e76 q^{55} -1.38199e78 q^{56} -1.54108e77 q^{57} -6.97831e78 q^{58} +4.03039e78 q^{59} -1.66283e78 q^{60} -2.95660e79 q^{61} +1.80249e80 q^{62} +1.21630e80 q^{63} -9.81620e79 q^{64} -2.45894e80 q^{65} +3.67893e80 q^{66} +5.44278e80 q^{67} +6.64659e81 q^{68} -9.76940e80 q^{69} -7.06461e81 q^{70} +6.75644e81 q^{71} -8.87281e82 q^{72} -1.55795e82 q^{73} -3.43187e83 q^{74} +5.01876e82 q^{75} +6.07933e83 q^{76} +1.06837e84 q^{77} +1.00420e84 q^{78} -4.89294e84 q^{79} +2.11654e84 q^{80} +7.47490e84 q^{81} +1.30897e85 q^{82} -5.34367e84 q^{83} +1.97206e85 q^{84} +1.82460e85 q^{85} -8.02105e85 q^{86} +5.34750e85 q^{87} -7.79362e86 q^{88} -7.65546e86 q^{89} -4.53569e86 q^{90} +2.91621e87 q^{91} +3.85389e87 q^{92} -1.38126e87 q^{93} +6.82466e86 q^{94} +1.66888e87 q^{95} -1.98320e87 q^{96} -1.46156e87 q^{97} +1.14403e88 q^{98} +6.85925e88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} + O(q^{10}) \) \( 7q - 31407330351408q^{2} - \)\(13\!\cdots\!64\)\(q^{3} + \)\(22\!\cdots\!04\)\(q^{4} + \)\(10\!\cdots\!50\)\(q^{5} - \)\(47\!\cdots\!76\)\(q^{6} + \)\(38\!\cdots\!92\)\(q^{7} - \)\(17\!\cdots\!20\)\(q^{8} + \)\(56\!\cdots\!71\)\(q^{9} - \)\(33\!\cdots\!00\)\(q^{10} - \)\(33\!\cdots\!56\)\(q^{11} - \)\(10\!\cdots\!28\)\(q^{12} - \)\(10\!\cdots\!34\)\(q^{13} - \)\(33\!\cdots\!32\)\(q^{14} - \)\(39\!\cdots\!00\)\(q^{15} + \)\(11\!\cdots\!32\)\(q^{16} + \)\(83\!\cdots\!42\)\(q^{17} - \)\(14\!\cdots\!04\)\(q^{18} + \)\(56\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} - \)\(90\!\cdots\!36\)\(q^{21} - \)\(57\!\cdots\!36\)\(q^{22} - \)\(11\!\cdots\!04\)\(q^{23} + \)\(10\!\cdots\!40\)\(q^{24} - \)\(21\!\cdots\!75\)\(q^{25} + \)\(25\!\cdots\!24\)\(q^{26} + \)\(11\!\cdots\!80\)\(q^{27} + \)\(42\!\cdots\!84\)\(q^{28} - \)\(14\!\cdots\!30\)\(q^{29} + \)\(68\!\cdots\!00\)\(q^{30} + \)\(68\!\cdots\!04\)\(q^{31} - \)\(18\!\cdots\!48\)\(q^{32} - \)\(86\!\cdots\!88\)\(q^{33} + \)\(31\!\cdots\!28\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} - \)\(16\!\cdots\!88\)\(q^{36} - \)\(54\!\cdots\!58\)\(q^{37} + \)\(45\!\cdots\!20\)\(q^{38} - \)\(52\!\cdots\!48\)\(q^{39} - \)\(36\!\cdots\!00\)\(q^{40} - \)\(65\!\cdots\!66\)\(q^{41} + \)\(11\!\cdots\!04\)\(q^{42} + \)\(32\!\cdots\!56\)\(q^{43} - \)\(15\!\cdots\!32\)\(q^{44} - \)\(47\!\cdots\!50\)\(q^{45} - \)\(56\!\cdots\!76\)\(q^{46} - \)\(58\!\cdots\!08\)\(q^{47} - \)\(38\!\cdots\!04\)\(q^{48} - \)\(30\!\cdots\!01\)\(q^{49} - \)\(11\!\cdots\!00\)\(q^{50} - \)\(44\!\cdots\!56\)\(q^{51} - \)\(19\!\cdots\!68\)\(q^{52} - \)\(18\!\cdots\!14\)\(q^{53} - \)\(10\!\cdots\!20\)\(q^{54} - \)\(12\!\cdots\!00\)\(q^{55} - \)\(58\!\cdots\!20\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} - \)\(30\!\cdots\!20\)\(q^{58} - \)\(90\!\cdots\!60\)\(q^{59} - \)\(28\!\cdots\!00\)\(q^{60} + \)\(87\!\cdots\!94\)\(q^{61} + \)\(16\!\cdots\!24\)\(q^{62} + \)\(60\!\cdots\!96\)\(q^{63} + \)\(14\!\cdots\!44\)\(q^{64} + \)\(13\!\cdots\!00\)\(q^{65} + \)\(57\!\cdots\!08\)\(q^{66} + \)\(58\!\cdots\!92\)\(q^{67} + \)\(33\!\cdots\!84\)\(q^{68} - \)\(59\!\cdots\!48\)\(q^{69} - \)\(48\!\cdots\!00\)\(q^{70} - \)\(54\!\cdots\!76\)\(q^{71} - \)\(19\!\cdots\!60\)\(q^{72} - \)\(19\!\cdots\!54\)\(q^{73} - \)\(96\!\cdots\!52\)\(q^{74} - \)\(44\!\cdots\!00\)\(q^{75} - \)\(62\!\cdots\!40\)\(q^{76} + \)\(13\!\cdots\!64\)\(q^{77} + \)\(51\!\cdots\!92\)\(q^{78} + \)\(26\!\cdots\!20\)\(q^{79} + \)\(27\!\cdots\!00\)\(q^{80} + \)\(48\!\cdots\!47\)\(q^{81} + \)\(63\!\cdots\!04\)\(q^{82} - \)\(35\!\cdots\!24\)\(q^{83} - \)\(91\!\cdots\!92\)\(q^{84} - \)\(14\!\cdots\!00\)\(q^{85} - \)\(24\!\cdots\!76\)\(q^{86} - \)\(41\!\cdots\!60\)\(q^{87} - \)\(18\!\cdots\!40\)\(q^{88} - \)\(16\!\cdots\!90\)\(q^{89} - \)\(15\!\cdots\!00\)\(q^{90} - \)\(30\!\cdots\!36\)\(q^{91} + \)\(72\!\cdots\!92\)\(q^{92} + \)\(87\!\cdots\!92\)\(q^{93} + \)\(22\!\cdots\!08\)\(q^{94} + \)\(22\!\cdots\!00\)\(q^{95} + \)\(84\!\cdots\!44\)\(q^{96} + \)\(71\!\cdots\!42\)\(q^{97} - \)\(17\!\cdots\!56\)\(q^{98} - \)\(19\!\cdots\!68\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.42254e13 1.77761 0.888805 0.458285i \(-0.151536\pi\)
0.888805 + 0.458285i \(0.151536\pi\)
\(3\) −3.38901e20 −0.198690 −0.0993451 0.995053i \(-0.531675\pi\)
−0.0993451 + 0.995053i \(0.531675\pi\)
\(4\) 1.33691e27 2.15990
\(5\) 3.67006e30 0.288741 0.144370 0.989524i \(-0.453884\pi\)
0.144370 + 0.989524i \(0.453884\pi\)
\(6\) −1.49880e34 −0.353194
\(7\) −4.35255e37 −1.07617 −0.538085 0.842891i \(-0.680852\pi\)
−0.538085 + 0.842891i \(0.680852\pi\)
\(8\) 3.17513e40 2.06185
\(9\) −2.79447e42 −0.960522
\(10\) 1.62310e44 0.513269
\(11\) −2.45458e46 −1.11687 −0.558435 0.829548i \(-0.688598\pi\)
−0.558435 + 0.829548i \(0.688598\pi\)
\(12\) −4.53081e47 −0.429151
\(13\) −6.70001e49 −1.80134 −0.900672 0.434501i \(-0.856925\pi\)
−0.900672 + 0.434501i \(0.856925\pi\)
\(14\) −1.92493e51 −1.91301
\(15\) −1.24379e51 −0.0573700
\(16\) 5.76705e53 1.50527
\(17\) 4.97159e54 0.874014 0.437007 0.899458i \(-0.356038\pi\)
0.437007 + 0.899458i \(0.356038\pi\)
\(18\) −1.23586e56 −1.70743
\(19\) 4.54728e56 0.566522 0.283261 0.959043i \(-0.408584\pi\)
0.283261 + 0.959043i \(0.408584\pi\)
\(20\) 4.90655e57 0.623651
\(21\) 1.47508e58 0.213824
\(22\) −1.08555e60 −1.98536
\(23\) 2.88267e60 0.729301 0.364650 0.931144i \(-0.381188\pi\)
0.364650 + 0.931144i \(0.381188\pi\)
\(24\) −1.07605e61 −0.409670
\(25\) −1.48089e62 −0.916629
\(26\) −2.96311e63 −3.20209
\(27\) 1.93302e63 0.389537
\(28\) −5.81898e64 −2.32442
\(29\) −1.57790e65 −1.32242 −0.661208 0.750203i \(-0.729956\pi\)
−0.661208 + 0.750203i \(0.729956\pi\)
\(30\) −5.50069e64 −0.101981
\(31\) 4.07570e66 1.75633 0.878166 0.478356i \(-0.158767\pi\)
0.878166 + 0.478356i \(0.158767\pi\)
\(32\) 5.85187e66 0.613932
\(33\) 8.31859e66 0.221911
\(34\) 2.19871e68 1.55366
\(35\) −1.59741e68 −0.310734
\(36\) −3.73596e69 −2.07463
\(37\) −7.75996e69 −1.27316 −0.636580 0.771211i \(-0.719651\pi\)
−0.636580 + 0.771211i \(0.719651\pi\)
\(38\) 2.01105e70 1.00706
\(39\) 2.27064e70 0.357909
\(40\) 1.16529e71 0.595340
\(41\) 2.95976e71 0.503936 0.251968 0.967736i \(-0.418922\pi\)
0.251968 + 0.967736i \(0.418922\pi\)
\(42\) 6.52360e71 0.380096
\(43\) −1.81368e72 −0.370863 −0.185431 0.982657i \(-0.559368\pi\)
−0.185431 + 0.982657i \(0.559368\pi\)
\(44\) −3.28156e73 −2.41233
\(45\) −1.02559e73 −0.277342
\(46\) 1.27487e74 1.29641
\(47\) 1.54316e73 0.0602636 0.0301318 0.999546i \(-0.490407\pi\)
0.0301318 + 0.999546i \(0.490407\pi\)
\(48\) −1.95446e74 −0.299082
\(49\) 2.58682e74 0.158140
\(50\) −6.54931e75 −1.62941
\(51\) −1.68488e75 −0.173658
\(52\) −8.95734e76 −3.89072
\(53\) 3.79389e76 0.706005 0.353003 0.935622i \(-0.385161\pi\)
0.353003 + 0.935622i \(0.385161\pi\)
\(54\) 8.54884e76 0.692445
\(55\) −9.00846e76 −0.322486
\(56\) −1.38199e78 −2.21890
\(57\) −1.54108e77 −0.112562
\(58\) −6.97831e78 −2.35074
\(59\) 4.03039e78 0.634502 0.317251 0.948342i \(-0.397240\pi\)
0.317251 + 0.948342i \(0.397240\pi\)
\(60\) −1.66283e78 −0.123913
\(61\) −2.95660e79 −1.05588 −0.527940 0.849282i \(-0.677035\pi\)
−0.527940 + 0.849282i \(0.677035\pi\)
\(62\) 1.80249e80 3.12207
\(63\) 1.21630e80 1.03368
\(64\) −9.81620e79 −0.413937
\(65\) −2.45894e80 −0.520121
\(66\) 3.67893e80 0.394472
\(67\) 5.44278e80 0.298877 0.149438 0.988771i \(-0.452253\pi\)
0.149438 + 0.988771i \(0.452253\pi\)
\(68\) 6.64659e81 1.88778
\(69\) −9.76940e80 −0.144905
\(70\) −7.06461e81 −0.552364
\(71\) 6.75644e81 0.281010 0.140505 0.990080i \(-0.455127\pi\)
0.140505 + 0.990080i \(0.455127\pi\)
\(72\) −8.87281e82 −1.98045
\(73\) −1.55795e82 −0.188229 −0.0941146 0.995561i \(-0.530002\pi\)
−0.0941146 + 0.995561i \(0.530002\pi\)
\(74\) −3.43187e83 −2.26318
\(75\) 5.01876e82 0.182125
\(76\) 6.07933e83 1.22363
\(77\) 1.06837e84 1.20194
\(78\) 1.00420e84 0.636223
\(79\) −4.89294e84 −1.75859 −0.879294 0.476280i \(-0.841985\pi\)
−0.879294 + 0.476280i \(0.841985\pi\)
\(80\) 2.11654e84 0.434633
\(81\) 7.47490e84 0.883125
\(82\) 1.30897e85 0.895802
\(83\) −5.34367e84 −0.213238 −0.106619 0.994300i \(-0.534003\pi\)
−0.106619 + 0.994300i \(0.534003\pi\)
\(84\) 1.97206e85 0.461839
\(85\) 1.82460e85 0.252363
\(86\) −8.02105e85 −0.659250
\(87\) 5.34750e85 0.262751
\(88\) −7.79362e86 −2.30282
\(89\) −7.65546e86 −1.36809 −0.684047 0.729438i \(-0.739782\pi\)
−0.684047 + 0.729438i \(0.739782\pi\)
\(90\) −4.53569e86 −0.493006
\(91\) 2.91621e87 1.93855
\(92\) 3.85389e87 1.57522
\(93\) −1.38126e87 −0.348966
\(94\) 6.82466e86 0.107125
\(95\) 1.66888e87 0.163578
\(96\) −1.98320e87 −0.121982
\(97\) −1.46156e87 −0.0566859 −0.0283430 0.999598i \(-0.509023\pi\)
−0.0283430 + 0.999598i \(0.509023\pi\)
\(98\) 1.14403e88 0.281111
\(99\) 6.85925e88 1.07278
\(100\) −1.97983e89 −1.97983
\(101\) 1.76473e89 1.13338 0.566691 0.823931i \(-0.308223\pi\)
0.566691 + 0.823931i \(0.308223\pi\)
\(102\) −7.45143e88 −0.308697
\(103\) 1.57477e89 0.422632 0.211316 0.977418i \(-0.432225\pi\)
0.211316 + 0.977418i \(0.432225\pi\)
\(104\) −2.12734e90 −3.71410
\(105\) 5.41363e88 0.0617398
\(106\) 1.67786e90 1.25500
\(107\) 1.57684e90 0.776621 0.388311 0.921529i \(-0.373059\pi\)
0.388311 + 0.921529i \(0.373059\pi\)
\(108\) 2.58428e90 0.841360
\(109\) 8.09287e90 1.74833 0.874164 0.485630i \(-0.161410\pi\)
0.874164 + 0.485630i \(0.161410\pi\)
\(110\) −3.98402e90 −0.573255
\(111\) 2.62986e90 0.252964
\(112\) −2.51013e91 −1.61992
\(113\) 1.43205e91 0.622255 0.311128 0.950368i \(-0.399293\pi\)
0.311128 + 0.950368i \(0.399293\pi\)
\(114\) −6.81547e90 −0.200092
\(115\) 1.05796e91 0.210579
\(116\) −2.10951e92 −2.85629
\(117\) 1.87230e92 1.73023
\(118\) 1.78246e92 1.12790
\(119\) −2.16391e92 −0.940587
\(120\) −3.94918e91 −0.118288
\(121\) 1.19495e92 0.247400
\(122\) −1.30757e93 −1.87694
\(123\) −1.00307e92 −0.100127
\(124\) 5.44886e93 3.79350
\(125\) −1.13643e93 −0.553409
\(126\) 5.37915e93 1.83749
\(127\) −4.89751e93 −1.17682 −0.588409 0.808563i \(-0.700246\pi\)
−0.588409 + 0.808563i \(0.700246\pi\)
\(128\) −7.96338e93 −1.34975
\(129\) 6.14656e92 0.0736868
\(130\) −1.08748e94 −0.924573
\(131\) −1.69999e94 −1.02772 −0.513858 0.857875i \(-0.671784\pi\)
−0.513858 + 0.857875i \(0.671784\pi\)
\(132\) 1.11212e94 0.479306
\(133\) −1.97923e94 −0.609674
\(134\) 2.40709e94 0.531287
\(135\) 7.09429e93 0.112475
\(136\) 1.57855e95 1.80209
\(137\) 6.04210e94 0.497878 0.248939 0.968519i \(-0.419918\pi\)
0.248939 + 0.968519i \(0.419918\pi\)
\(138\) −4.32055e94 −0.257585
\(139\) −1.73639e95 −0.750739 −0.375370 0.926875i \(-0.622484\pi\)
−0.375370 + 0.926875i \(0.622484\pi\)
\(140\) −2.13560e95 −0.671154
\(141\) −5.22976e93 −0.0119738
\(142\) 2.98806e95 0.499526
\(143\) 1.64457e96 2.01187
\(144\) −1.61158e96 −1.44585
\(145\) −5.79098e95 −0.381835
\(146\) −6.89010e95 −0.334598
\(147\) −8.76676e94 −0.0314208
\(148\) −1.03744e97 −2.74990
\(149\) 8.32082e96 1.63447 0.817236 0.576304i \(-0.195506\pi\)
0.817236 + 0.576304i \(0.195506\pi\)
\(150\) 2.21956e96 0.323748
\(151\) −1.01165e96 −0.109788 −0.0548942 0.998492i \(-0.517482\pi\)
−0.0548942 + 0.998492i \(0.517482\pi\)
\(152\) 1.44382e97 1.16808
\(153\) −1.38930e97 −0.839510
\(154\) 4.72490e97 2.13658
\(155\) 1.49581e97 0.507124
\(156\) 3.03565e97 0.773048
\(157\) −3.72359e97 −0.713554 −0.356777 0.934190i \(-0.616124\pi\)
−0.356777 + 0.934190i \(0.616124\pi\)
\(158\) −2.16392e98 −3.12608
\(159\) −1.28575e97 −0.140276
\(160\) 2.14767e97 0.177267
\(161\) −1.25470e98 −0.784851
\(162\) 3.30580e98 1.56985
\(163\) −1.03319e98 −0.373107 −0.186554 0.982445i \(-0.559732\pi\)
−0.186554 + 0.982445i \(0.559732\pi\)
\(164\) 3.95695e98 1.08845
\(165\) 3.05297e97 0.0640748
\(166\) −2.36326e98 −0.379054
\(167\) −1.50110e99 −1.84301 −0.921503 0.388372i \(-0.873038\pi\)
−0.921503 + 0.388372i \(0.873038\pi\)
\(168\) 4.68358e98 0.440874
\(169\) 3.10558e99 2.24484
\(170\) 8.06938e98 0.448604
\(171\) −1.27072e99 −0.544157
\(172\) −2.42473e99 −0.801027
\(173\) 1.10447e99 0.281906 0.140953 0.990016i \(-0.454983\pi\)
0.140953 + 0.990016i \(0.454983\pi\)
\(174\) 2.36495e99 0.467069
\(175\) 6.44566e99 0.986448
\(176\) −1.41557e100 −1.68119
\(177\) −1.36590e99 −0.126069
\(178\) −3.38566e100 −2.43194
\(179\) 1.69588e100 0.949372 0.474686 0.880155i \(-0.342562\pi\)
0.474686 + 0.880155i \(0.342562\pi\)
\(180\) −1.37112e100 −0.599031
\(181\) −2.52788e100 −0.863099 −0.431549 0.902089i \(-0.642033\pi\)
−0.431549 + 0.902089i \(0.642033\pi\)
\(182\) 1.28971e101 3.44599
\(183\) 1.00199e100 0.209793
\(184\) 9.15287e100 1.50371
\(185\) −2.84795e100 −0.367613
\(186\) −6.10866e100 −0.620326
\(187\) −1.22032e101 −0.976161
\(188\) 2.06307e100 0.130163
\(189\) −8.41355e100 −0.419207
\(190\) 7.38069e100 0.290778
\(191\) −3.78547e101 −1.18069 −0.590344 0.807152i \(-0.701008\pi\)
−0.590344 + 0.807152i \(0.701008\pi\)
\(192\) 3.32672e100 0.0822453
\(193\) 1.50651e101 0.295578 0.147789 0.989019i \(-0.452784\pi\)
0.147789 + 0.989019i \(0.452784\pi\)
\(194\) −6.46382e100 −0.100766
\(195\) 8.33338e100 0.103343
\(196\) 3.45836e101 0.341566
\(197\) −6.14218e101 −0.483700 −0.241850 0.970314i \(-0.577754\pi\)
−0.241850 + 0.970314i \(0.577754\pi\)
\(198\) 3.03353e102 1.90698
\(199\) −1.92526e102 −0.967223 −0.483611 0.875283i \(-0.660675\pi\)
−0.483611 + 0.875283i \(0.660675\pi\)
\(200\) −4.70203e102 −1.88995
\(201\) −1.84456e101 −0.0593839
\(202\) 7.80456e102 2.01471
\(203\) 6.86787e102 1.42314
\(204\) −2.25253e102 −0.375084
\(205\) 1.08625e102 0.145507
\(206\) 6.96450e102 0.751275
\(207\) −8.05554e102 −0.700510
\(208\) −3.86393e103 −2.71151
\(209\) −1.11617e103 −0.632732
\(210\) 2.39420e102 0.109749
\(211\) −2.45026e103 −0.909166 −0.454583 0.890704i \(-0.650212\pi\)
−0.454583 + 0.890704i \(0.650212\pi\)
\(212\) 5.07210e103 1.52490
\(213\) −2.28976e102 −0.0558339
\(214\) 6.97363e103 1.38053
\(215\) −6.65630e102 −0.107083
\(216\) 6.13759e103 0.803167
\(217\) −1.77397e104 −1.89011
\(218\) 3.57910e104 3.10785
\(219\) 5.27991e102 0.0373993
\(220\) −1.20435e104 −0.696538
\(221\) −3.33097e104 −1.57440
\(222\) 1.16306e104 0.449672
\(223\) −4.73510e104 −1.49887 −0.749434 0.662079i \(-0.769674\pi\)
−0.749434 + 0.662079i \(0.769674\pi\)
\(224\) −2.54705e104 −0.660695
\(225\) 4.13831e104 0.880442
\(226\) 6.33331e104 1.10613
\(227\) −1.36699e104 −0.196161 −0.0980807 0.995178i \(-0.531270\pi\)
−0.0980807 + 0.995178i \(0.531270\pi\)
\(228\) −2.06029e104 −0.243124
\(229\) 2.84461e104 0.276276 0.138138 0.990413i \(-0.455888\pi\)
0.138138 + 0.990413i \(0.455888\pi\)
\(230\) 4.67886e104 0.374327
\(231\) −3.62070e104 −0.238814
\(232\) −5.01003e105 −2.72662
\(233\) −1.32351e104 −0.0594823 −0.0297411 0.999558i \(-0.509468\pi\)
−0.0297411 + 0.999558i \(0.509468\pi\)
\(234\) 8.28030e105 3.07568
\(235\) 5.66347e103 0.0174005
\(236\) 5.38829e105 1.37046
\(237\) 1.65822e105 0.349414
\(238\) −9.56997e105 −1.67200
\(239\) 1.73403e105 0.251391 0.125696 0.992069i \(-0.459884\pi\)
0.125696 + 0.992069i \(0.459884\pi\)
\(240\) −7.17297e104 −0.0863573
\(241\) −3.77326e105 −0.377536 −0.188768 0.982022i \(-0.560449\pi\)
−0.188768 + 0.982022i \(0.560449\pi\)
\(242\) 5.28470e105 0.439781
\(243\) −8.15702e105 −0.565005
\(244\) −3.95271e106 −2.28059
\(245\) 9.49380e104 0.0456614
\(246\) −4.43610e105 −0.177987
\(247\) −3.04669e106 −1.02050
\(248\) 1.29409e107 3.62130
\(249\) 1.81097e105 0.0423683
\(250\) −5.02589e106 −0.983745
\(251\) 1.00216e107 1.64231 0.821155 0.570705i \(-0.193330\pi\)
0.821155 + 0.570705i \(0.193330\pi\)
\(252\) 1.62609e107 2.23266
\(253\) −7.07576e106 −0.814535
\(254\) −2.16594e107 −2.09192
\(255\) −6.18360e105 −0.0501422
\(256\) −2.91424e107 −1.98540
\(257\) 1.47865e107 0.846920 0.423460 0.905915i \(-0.360815\pi\)
0.423460 + 0.905915i \(0.360815\pi\)
\(258\) 2.71834e106 0.130986
\(259\) 3.37756e107 1.37014
\(260\) −3.28740e107 −1.12341
\(261\) 4.40938e107 1.27021
\(262\) −7.51826e107 −1.82688
\(263\) 5.33852e106 0.109494 0.0547469 0.998500i \(-0.482565\pi\)
0.0547469 + 0.998500i \(0.482565\pi\)
\(264\) 2.64126e107 0.457548
\(265\) 1.39238e107 0.203852
\(266\) −8.75320e107 −1.08376
\(267\) 2.59444e107 0.271827
\(268\) 7.27653e107 0.645544
\(269\) 1.15813e108 0.870524 0.435262 0.900304i \(-0.356656\pi\)
0.435262 + 0.900304i \(0.356656\pi\)
\(270\) 3.13748e107 0.199937
\(271\) −2.64602e108 −1.43041 −0.715203 0.698917i \(-0.753666\pi\)
−0.715203 + 0.698917i \(0.753666\pi\)
\(272\) 2.86714e108 1.31563
\(273\) −9.88306e107 −0.385171
\(274\) 2.67214e108 0.885033
\(275\) 3.63497e108 1.02376
\(276\) −1.30608e108 −0.312980
\(277\) −1.07845e108 −0.220015 −0.110007 0.993931i \(-0.535087\pi\)
−0.110007 + 0.993931i \(0.535087\pi\)
\(278\) −7.67926e108 −1.33452
\(279\) −1.13894e109 −1.68700
\(280\) −5.07199e108 −0.640687
\(281\) −4.97309e108 −0.536037 −0.268019 0.963414i \(-0.586369\pi\)
−0.268019 + 0.963414i \(0.586369\pi\)
\(282\) −2.31288e107 −0.0212847
\(283\) 1.20179e109 0.944785 0.472392 0.881388i \(-0.343391\pi\)
0.472392 + 0.881388i \(0.343391\pi\)
\(284\) 9.03278e108 0.606953
\(285\) −5.65585e107 −0.0325013
\(286\) 7.27318e109 3.57632
\(287\) −1.28825e109 −0.542320
\(288\) −1.63529e109 −0.589696
\(289\) −7.63920e108 −0.236099
\(290\) −2.56108e109 −0.678754
\(291\) 4.95325e107 0.0112629
\(292\) −2.08285e109 −0.406556
\(293\) 3.43775e109 0.576322 0.288161 0.957582i \(-0.406956\pi\)
0.288161 + 0.957582i \(0.406956\pi\)
\(294\) −3.87713e108 −0.0558540
\(295\) 1.47918e109 0.183206
\(296\) −2.46389e110 −2.62507
\(297\) −4.74475e109 −0.435062
\(298\) 3.67991e110 2.90545
\(299\) −1.93140e110 −1.31372
\(300\) 6.70965e109 0.393372
\(301\) 7.89410e109 0.399111
\(302\) −4.47407e109 −0.195161
\(303\) −5.98067e109 −0.225192
\(304\) 2.62244e110 0.852769
\(305\) −1.08509e110 −0.304875
\(306\) −6.14421e110 −1.49232
\(307\) −5.58639e110 −1.17347 −0.586737 0.809778i \(-0.699588\pi\)
−0.586737 + 0.809778i \(0.699588\pi\)
\(308\) 1.42832e111 2.59607
\(309\) −5.33692e109 −0.0839728
\(310\) 6.61525e110 0.901470
\(311\) 9.96934e110 1.17714 0.588572 0.808445i \(-0.299691\pi\)
0.588572 + 0.808445i \(0.299691\pi\)
\(312\) 7.20958e110 0.737956
\(313\) −7.36331e110 −0.653657 −0.326828 0.945084i \(-0.605980\pi\)
−0.326828 + 0.945084i \(0.605980\pi\)
\(314\) −1.64677e111 −1.26842
\(315\) 4.46391e110 0.298467
\(316\) −6.54143e111 −3.79837
\(317\) 1.40479e111 0.708721 0.354361 0.935109i \(-0.384698\pi\)
0.354361 + 0.935109i \(0.384698\pi\)
\(318\) −5.68628e110 −0.249357
\(319\) 3.87308e111 1.47697
\(320\) −3.60260e110 −0.119520
\(321\) −5.34392e110 −0.154307
\(322\) −5.54894e111 −1.39516
\(323\) 2.26072e111 0.495148
\(324\) 9.99330e111 1.90746
\(325\) 9.92201e111 1.65116
\(326\) −4.56934e111 −0.663239
\(327\) −2.74268e111 −0.347376
\(328\) 9.39764e111 1.03904
\(329\) −6.71665e110 −0.0648538
\(330\) 1.35019e111 0.113900
\(331\) −1.93674e112 −1.42799 −0.713997 0.700149i \(-0.753117\pi\)
−0.713997 + 0.700149i \(0.753117\pi\)
\(332\) −7.14403e111 −0.460573
\(333\) 2.16850e112 1.22290
\(334\) −6.63867e112 −3.27615
\(335\) 1.99753e111 0.0862979
\(336\) 8.50686e111 0.321863
\(337\) −3.04243e112 −1.00853 −0.504266 0.863548i \(-0.668237\pi\)
−0.504266 + 0.863548i \(0.668237\pi\)
\(338\) 1.37346e113 3.99045
\(339\) −4.85324e111 −0.123636
\(340\) 2.43934e112 0.545080
\(341\) −1.00041e113 −1.96160
\(342\) −5.61982e112 −0.967300
\(343\) 5.99389e112 0.905984
\(344\) −5.75866e112 −0.764664
\(345\) −3.58543e111 −0.0418400
\(346\) 4.88458e112 0.501119
\(347\) 5.62569e112 0.507591 0.253796 0.967258i \(-0.418321\pi\)
0.253796 + 0.967258i \(0.418321\pi\)
\(348\) 7.14915e112 0.567516
\(349\) −4.27631e111 −0.0298771 −0.0149385 0.999888i \(-0.504755\pi\)
−0.0149385 + 0.999888i \(0.504755\pi\)
\(350\) 2.85062e113 1.75352
\(351\) −1.29512e113 −0.701689
\(352\) −1.43639e113 −0.685683
\(353\) 1.17997e113 0.496473 0.248236 0.968699i \(-0.420149\pi\)
0.248236 + 0.968699i \(0.420149\pi\)
\(354\) −6.04076e112 −0.224102
\(355\) 2.47965e112 0.0811390
\(356\) −1.02347e114 −2.95495
\(357\) 7.33350e112 0.186886
\(358\) 7.50011e113 1.68761
\(359\) −3.09309e113 −0.614738 −0.307369 0.951590i \(-0.599449\pi\)
−0.307369 + 0.951590i \(0.599449\pi\)
\(360\) −3.25637e113 −0.571838
\(361\) −4.37496e113 −0.679053
\(362\) −1.11797e114 −1.53425
\(363\) −4.04969e112 −0.0491560
\(364\) 3.89872e114 4.18707
\(365\) −5.71778e112 −0.0543494
\(366\) 4.43135e113 0.372930
\(367\) 8.47042e113 0.631342 0.315671 0.948869i \(-0.397770\pi\)
0.315671 + 0.948869i \(0.397770\pi\)
\(368\) 1.66245e114 1.09779
\(369\) −8.27096e113 −0.484042
\(370\) −1.25952e114 −0.653473
\(371\) −1.65131e114 −0.759781
\(372\) −1.84662e114 −0.753732
\(373\) −1.26483e114 −0.458131 −0.229066 0.973411i \(-0.573567\pi\)
−0.229066 + 0.973411i \(0.573567\pi\)
\(374\) −5.39690e114 −1.73523
\(375\) 3.85136e113 0.109957
\(376\) 4.89972e113 0.124255
\(377\) 1.05719e115 2.38212
\(378\) −3.72092e114 −0.745187
\(379\) −1.05579e114 −0.187989 −0.0939943 0.995573i \(-0.529964\pi\)
−0.0939943 + 0.995573i \(0.529964\pi\)
\(380\) 2.23115e114 0.353312
\(381\) 1.65977e114 0.233822
\(382\) −1.67414e115 −2.09880
\(383\) 1.02001e115 1.13831 0.569155 0.822230i \(-0.307270\pi\)
0.569155 + 0.822230i \(0.307270\pi\)
\(384\) 2.69879e114 0.268182
\(385\) 3.92097e114 0.347049
\(386\) 6.66260e114 0.525422
\(387\) 5.06826e114 0.356222
\(388\) −1.95398e114 −0.122436
\(389\) −2.00350e115 −1.11952 −0.559760 0.828655i \(-0.689107\pi\)
−0.559760 + 0.828655i \(0.689107\pi\)
\(390\) 3.68547e114 0.183704
\(391\) 1.43315e115 0.637420
\(392\) 8.21351e114 0.326061
\(393\) 5.76127e114 0.204197
\(394\) −2.71640e115 −0.859830
\(395\) −1.79574e115 −0.507776
\(396\) 9.17022e115 2.31710
\(397\) 1.43963e115 0.325142 0.162571 0.986697i \(-0.448021\pi\)
0.162571 + 0.986697i \(0.448021\pi\)
\(398\) −8.51452e115 −1.71935
\(399\) 6.70761e114 0.121136
\(400\) −8.54039e115 −1.37977
\(401\) −6.32353e115 −0.914187 −0.457093 0.889419i \(-0.651110\pi\)
−0.457093 + 0.889419i \(0.651110\pi\)
\(402\) −8.15765e114 −0.105561
\(403\) −2.73072e116 −3.16376
\(404\) 2.35929e116 2.44799
\(405\) 2.74333e115 0.254994
\(406\) 3.03734e116 2.52979
\(407\) 1.90475e116 1.42195
\(408\) −5.34971e115 −0.358057
\(409\) 5.70354e114 0.0342339 0.0171170 0.999853i \(-0.494551\pi\)
0.0171170 + 0.999853i \(0.494551\pi\)
\(410\) 4.80399e115 0.258654
\(411\) −2.04767e115 −0.0989235
\(412\) 2.10534e116 0.912842
\(413\) −1.75425e116 −0.682831
\(414\) −3.56259e116 −1.24523
\(415\) −1.96116e115 −0.0615705
\(416\) −3.92076e116 −1.10590
\(417\) 5.88464e115 0.149165
\(418\) −4.93629e116 −1.12475
\(419\) 2.82318e116 0.578382 0.289191 0.957271i \(-0.406614\pi\)
0.289191 + 0.957271i \(0.406614\pi\)
\(420\) 7.23756e115 0.133352
\(421\) 6.04056e116 1.00121 0.500604 0.865676i \(-0.333111\pi\)
0.500604 + 0.865676i \(0.333111\pi\)
\(422\) −1.08364e117 −1.61614
\(423\) −4.31230e115 −0.0578845
\(424\) 1.20461e117 1.45568
\(425\) −7.36240e116 −0.801147
\(426\) −1.01266e116 −0.0992510
\(427\) 1.28687e117 1.13630
\(428\) 2.10810e117 1.67742
\(429\) −5.57347e116 −0.399738
\(430\) −2.94377e116 −0.190352
\(431\) −2.26583e117 −1.32126 −0.660632 0.750710i \(-0.729712\pi\)
−0.660632 + 0.750710i \(0.729712\pi\)
\(432\) 1.11478e117 0.586358
\(433\) 7.27088e116 0.345045 0.172522 0.985006i \(-0.444808\pi\)
0.172522 + 0.985006i \(0.444808\pi\)
\(434\) −7.84543e117 −3.35988
\(435\) 1.96257e116 0.0758669
\(436\) 1.08195e118 3.77622
\(437\) 1.31083e117 0.413165
\(438\) 2.33506e116 0.0664814
\(439\) 4.51676e116 0.116187 0.0580933 0.998311i \(-0.481498\pi\)
0.0580933 + 0.998311i \(0.481498\pi\)
\(440\) −2.86031e117 −0.664918
\(441\) −7.22879e116 −0.151897
\(442\) −1.47314e118 −2.79867
\(443\) 8.00727e117 1.37568 0.687842 0.725860i \(-0.258558\pi\)
0.687842 + 0.725860i \(0.258558\pi\)
\(444\) 3.51589e117 0.546378
\(445\) −2.80960e117 −0.395024
\(446\) −2.09412e118 −2.66440
\(447\) −2.81993e117 −0.324753
\(448\) 4.27254e117 0.445466
\(449\) 1.58652e118 1.49790 0.748949 0.662627i \(-0.230559\pi\)
0.748949 + 0.662627i \(0.230559\pi\)
\(450\) 1.83018e118 1.56508
\(451\) −7.26498e117 −0.562831
\(452\) 1.91453e118 1.34401
\(453\) 3.42849e116 0.0218139
\(454\) −6.04555e117 −0.348699
\(455\) 1.07027e118 0.559738
\(456\) −4.89313e117 −0.232087
\(457\) −1.01717e117 −0.0437644 −0.0218822 0.999761i \(-0.506966\pi\)
−0.0218822 + 0.999761i \(0.506966\pi\)
\(458\) 1.25804e118 0.491111
\(459\) 9.61018e117 0.340461
\(460\) 1.41440e118 0.454829
\(461\) −5.67592e118 −1.65709 −0.828543 0.559926i \(-0.810830\pi\)
−0.828543 + 0.559926i \(0.810830\pi\)
\(462\) −1.60127e118 −0.424519
\(463\) −3.42212e118 −0.824028 −0.412014 0.911178i \(-0.635174\pi\)
−0.412014 + 0.911178i \(0.635174\pi\)
\(464\) −9.09981e118 −1.99059
\(465\) −5.06929e117 −0.100761
\(466\) −5.85326e117 −0.105736
\(467\) −5.74060e118 −0.942662 −0.471331 0.881956i \(-0.656226\pi\)
−0.471331 + 0.881956i \(0.656226\pi\)
\(468\) 2.50310e119 3.73712
\(469\) −2.36900e118 −0.321642
\(470\) 2.50469e117 0.0309314
\(471\) 1.26193e118 0.141776
\(472\) 1.27970e119 1.30825
\(473\) 4.45181e118 0.414206
\(474\) 7.33354e118 0.621122
\(475\) −6.73405e118 −0.519291
\(476\) −2.89296e119 −2.03157
\(477\) −1.06019e119 −0.678134
\(478\) 7.66882e118 0.446876
\(479\) −7.35495e118 −0.390526 −0.195263 0.980751i \(-0.562556\pi\)
−0.195263 + 0.980751i \(0.562556\pi\)
\(480\) −7.27847e117 −0.0352213
\(481\) 5.19918e119 2.29340
\(482\) −1.66874e119 −0.671112
\(483\) 4.25218e118 0.155942
\(484\) 1.59754e119 0.534360
\(485\) −5.36402e117 −0.0163675
\(486\) −3.60747e119 −1.00436
\(487\) 1.73116e119 0.439843 0.219922 0.975518i \(-0.429420\pi\)
0.219922 + 0.975518i \(0.429420\pi\)
\(488\) −9.38758e119 −2.17707
\(489\) 3.50150e118 0.0741327
\(490\) 4.19867e118 0.0811682
\(491\) 9.48426e119 1.67447 0.837234 0.546845i \(-0.184171\pi\)
0.837234 + 0.546845i \(0.184171\pi\)
\(492\) −1.34101e119 −0.216265
\(493\) −7.84466e119 −1.15581
\(494\) −1.34741e120 −1.81405
\(495\) 2.51738e119 0.309755
\(496\) 2.35047e120 2.64375
\(497\) −2.94077e119 −0.302414
\(498\) 8.00910e118 0.0753144
\(499\) 2.96564e119 0.255061 0.127530 0.991835i \(-0.459295\pi\)
0.127530 + 0.991835i \(0.459295\pi\)
\(500\) −1.51930e120 −1.19531
\(501\) 5.08724e119 0.366187
\(502\) 4.43208e120 2.91939
\(503\) −1.72800e120 −1.04176 −0.520881 0.853630i \(-0.674396\pi\)
−0.520881 + 0.853630i \(0.674396\pi\)
\(504\) 3.86193e120 2.13130
\(505\) 6.47665e119 0.327253
\(506\) −3.12928e120 −1.44793
\(507\) −1.05248e120 −0.446027
\(508\) −6.54754e120 −2.54181
\(509\) −1.24174e120 −0.441661 −0.220830 0.975312i \(-0.570877\pi\)
−0.220830 + 0.975312i \(0.570877\pi\)
\(510\) −2.73472e119 −0.0891333
\(511\) 6.78106e119 0.202566
\(512\) −7.95925e120 −2.17951
\(513\) 8.78998e119 0.220681
\(514\) 6.53940e120 1.50549
\(515\) 5.77952e119 0.122031
\(516\) 8.21742e119 0.159156
\(517\) −3.78780e119 −0.0673066
\(518\) 1.49374e121 2.43557
\(519\) −3.74307e119 −0.0560120
\(520\) −7.80748e120 −1.07241
\(521\) 6.02844e120 0.760197 0.380099 0.924946i \(-0.375890\pi\)
0.380099 + 0.924946i \(0.375890\pi\)
\(522\) 1.95007e121 2.25794
\(523\) −1.30371e121 −1.38630 −0.693148 0.720796i \(-0.743777\pi\)
−0.693148 + 0.720796i \(0.743777\pi\)
\(524\) −2.27274e121 −2.21976
\(525\) −2.18444e120 −0.195998
\(526\) 2.36098e120 0.194638
\(527\) 2.02627e121 1.53506
\(528\) 4.79737e120 0.334036
\(529\) −7.31366e120 −0.468120
\(530\) 6.15785e120 0.362370
\(531\) −1.12628e121 −0.609453
\(532\) −2.64605e121 −1.31683
\(533\) −1.98305e121 −0.907762
\(534\) 1.14740e121 0.483203
\(535\) 5.78709e120 0.224242
\(536\) 1.72816e121 0.616240
\(537\) −5.74736e120 −0.188631
\(538\) 5.12187e121 1.54745
\(539\) −6.34957e120 −0.176622
\(540\) 9.48445e120 0.242935
\(541\) −3.02509e121 −0.713609 −0.356804 0.934179i \(-0.616134\pi\)
−0.356804 + 0.934179i \(0.616134\pi\)
\(542\) −1.17021e122 −2.54270
\(543\) 8.56702e120 0.171489
\(544\) 2.90931e121 0.536586
\(545\) 2.97013e121 0.504814
\(546\) −4.37082e121 −0.684684
\(547\) 6.07810e120 0.0877671 0.0438836 0.999037i \(-0.486027\pi\)
0.0438836 + 0.999037i \(0.486027\pi\)
\(548\) 8.07777e121 1.07537
\(549\) 8.26211e121 1.01420
\(550\) 1.60758e122 1.81984
\(551\) −7.17515e121 −0.749178
\(552\) −3.10191e121 −0.298773
\(553\) 2.12967e122 1.89254
\(554\) −4.76950e121 −0.391101
\(555\) 9.65173e120 0.0730411
\(556\) −2.32141e122 −1.62152
\(557\) −9.48715e121 −0.611758 −0.305879 0.952070i \(-0.598950\pi\)
−0.305879 + 0.952070i \(0.598950\pi\)
\(558\) −5.03701e122 −2.99882
\(559\) 1.21516e122 0.668051
\(560\) −9.21234e121 −0.467738
\(561\) 4.13566e121 0.193954
\(562\) −2.19937e122 −0.952866
\(563\) 3.99353e122 1.59858 0.799288 0.600949i \(-0.205210\pi\)
0.799288 + 0.600949i \(0.205210\pi\)
\(564\) −6.99174e120 −0.0258622
\(565\) 5.25572e121 0.179670
\(566\) 5.31497e122 1.67946
\(567\) −3.25349e122 −0.950392
\(568\) 2.14526e122 0.579401
\(569\) −4.99506e122 −1.24751 −0.623756 0.781619i \(-0.714394\pi\)
−0.623756 + 0.781619i \(0.714394\pi\)
\(570\) −2.50132e121 −0.0577748
\(571\) −7.98755e121 −0.170650 −0.0853251 0.996353i \(-0.527193\pi\)
−0.0853251 + 0.996353i \(0.527193\pi\)
\(572\) 2.19865e123 4.34543
\(573\) 1.28290e122 0.234591
\(574\) −5.69734e122 −0.964035
\(575\) −4.26893e122 −0.668498
\(576\) 2.74310e122 0.397596
\(577\) −1.20737e123 −1.62000 −0.810001 0.586429i \(-0.800533\pi\)
−0.810001 + 0.586429i \(0.800533\pi\)
\(578\) −3.37847e122 −0.419692
\(579\) −5.10557e121 −0.0587284
\(580\) −7.74204e122 −0.824726
\(581\) 2.32586e122 0.229480
\(582\) 2.19059e121 0.0200211
\(583\) −9.31240e122 −0.788517
\(584\) −4.94671e122 −0.388101
\(585\) 6.87144e122 0.499588
\(586\) 1.52036e123 1.02448
\(587\) 6.63777e122 0.414597 0.207299 0.978278i \(-0.433533\pi\)
0.207299 + 0.978278i \(0.433533\pi\)
\(588\) −1.17204e122 −0.0678659
\(589\) 1.85334e123 0.995001
\(590\) 6.54172e122 0.325670
\(591\) 2.08159e122 0.0961064
\(592\) −4.47521e123 −1.91645
\(593\) −3.67636e123 −1.46044 −0.730221 0.683211i \(-0.760583\pi\)
−0.730221 + 0.683211i \(0.760583\pi\)
\(594\) −2.09838e123 −0.773371
\(595\) −7.94167e122 −0.271586
\(596\) 1.11242e124 3.53029
\(597\) 6.52470e122 0.192178
\(598\) −8.54167e123 −2.33529
\(599\) 7.52276e123 1.90934 0.954671 0.297663i \(-0.0962073\pi\)
0.954671 + 0.297663i \(0.0962073\pi\)
\(600\) 1.59352e123 0.375515
\(601\) 2.62225e123 0.573798 0.286899 0.957961i \(-0.407376\pi\)
0.286899 + 0.957961i \(0.407376\pi\)
\(602\) 3.49120e123 0.709464
\(603\) −1.52097e123 −0.287078
\(604\) −1.35249e123 −0.237132
\(605\) 4.38553e122 0.0714345
\(606\) −2.64497e123 −0.400303
\(607\) −5.96123e123 −0.838377 −0.419188 0.907899i \(-0.637685\pi\)
−0.419188 + 0.907899i \(0.637685\pi\)
\(608\) 2.66101e123 0.347806
\(609\) −2.32753e123 −0.282764
\(610\) −4.79884e123 −0.541950
\(611\) −1.03392e123 −0.108555
\(612\) −1.85737e124 −1.81326
\(613\) 1.49430e124 1.35659 0.678293 0.734792i \(-0.262720\pi\)
0.678293 + 0.734792i \(0.262720\pi\)
\(614\) −2.47060e124 −2.08598
\(615\) −3.68131e122 −0.0289108
\(616\) 3.39221e124 2.47823
\(617\) −1.42286e124 −0.967101 −0.483551 0.875316i \(-0.660653\pi\)
−0.483551 + 0.875316i \(0.660653\pi\)
\(618\) −2.36027e123 −0.149271
\(619\) −1.75124e124 −1.03065 −0.515327 0.856994i \(-0.672329\pi\)
−0.515327 + 0.856994i \(0.672329\pi\)
\(620\) 1.99976e124 1.09534
\(621\) 5.57226e123 0.284089
\(622\) 4.40898e124 2.09250
\(623\) 3.33207e124 1.47230
\(624\) 1.30949e124 0.538750
\(625\) 1.97544e124 0.756837
\(626\) −3.25645e124 −1.16195
\(627\) 3.78270e123 0.125718
\(628\) −4.97811e124 −1.54121
\(629\) −3.85794e124 −1.11276
\(630\) 1.97418e124 0.530558
\(631\) 2.10999e124 0.528413 0.264207 0.964466i \(-0.414890\pi\)
0.264207 + 0.964466i \(0.414890\pi\)
\(632\) −1.55357e125 −3.62595
\(633\) 8.30396e123 0.180642
\(634\) 6.21276e124 1.25983
\(635\) −1.79741e124 −0.339795
\(636\) −1.71894e124 −0.302983
\(637\) −1.73317e124 −0.284864
\(638\) 1.71288e125 2.62547
\(639\) −1.88807e124 −0.269916
\(640\) −2.92261e124 −0.389728
\(641\) 9.40134e124 1.16952 0.584759 0.811207i \(-0.301189\pi\)
0.584759 + 0.811207i \(0.301189\pi\)
\(642\) −2.36337e124 −0.274298
\(643\) −5.35874e124 −0.580330 −0.290165 0.956977i \(-0.593710\pi\)
−0.290165 + 0.956977i \(0.593710\pi\)
\(644\) −1.67742e125 −1.69520
\(645\) 2.25582e123 0.0212764
\(646\) 9.99814e124 0.880181
\(647\) −1.76192e125 −1.44792 −0.723962 0.689840i \(-0.757681\pi\)
−0.723962 + 0.689840i \(0.757681\pi\)
\(648\) 2.37338e125 1.82087
\(649\) −9.89293e124 −0.708657
\(650\) 4.38804e125 2.93513
\(651\) 6.01198e124 0.375546
\(652\) −1.38129e125 −0.805874
\(653\) −2.70255e125 −1.47278 −0.736388 0.676560i \(-0.763470\pi\)
−0.736388 + 0.676560i \(0.763470\pi\)
\(654\) −1.21296e125 −0.617499
\(655\) −6.23906e124 −0.296743
\(656\) 1.70691e125 0.758560
\(657\) 4.35365e124 0.180798
\(658\) −2.97047e124 −0.115285
\(659\) 4.92460e125 1.78636 0.893182 0.449696i \(-0.148468\pi\)
0.893182 + 0.449696i \(0.148468\pi\)
\(660\) 4.08156e124 0.138395
\(661\) 1.53102e123 0.00485306 0.00242653 0.999997i \(-0.499228\pi\)
0.00242653 + 0.999997i \(0.499228\pi\)
\(662\) −8.56532e125 −2.53842
\(663\) 1.12887e125 0.312818
\(664\) −1.69669e125 −0.439665
\(665\) −7.26388e124 −0.176038
\(666\) 9.59026e125 2.17384
\(667\) −4.54856e125 −0.964439
\(668\) −2.00684e126 −3.98071
\(669\) 1.60473e125 0.297810
\(670\) 8.83417e124 0.153404
\(671\) 7.25720e125 1.17928
\(672\) 8.63197e124 0.131274
\(673\) 1.14314e126 1.62716 0.813579 0.581455i \(-0.197516\pi\)
0.813579 + 0.581455i \(0.197516\pi\)
\(674\) −1.34553e126 −1.79278
\(675\) −2.86259e125 −0.357061
\(676\) 4.15190e126 4.84862
\(677\) 8.57614e125 0.937770 0.468885 0.883259i \(-0.344656\pi\)
0.468885 + 0.883259i \(0.344656\pi\)
\(678\) −2.14636e125 −0.219777
\(679\) 6.36152e124 0.0610036
\(680\) 5.79336e125 0.520336
\(681\) 4.63273e124 0.0389754
\(682\) −4.42436e126 −3.48695
\(683\) −8.28357e125 −0.611641 −0.305820 0.952089i \(-0.598931\pi\)
−0.305820 + 0.952089i \(0.598931\pi\)
\(684\) −1.69885e126 −1.17533
\(685\) 2.21749e125 0.143758
\(686\) 2.65082e126 1.61049
\(687\) −9.64039e124 −0.0548934
\(688\) −1.04596e126 −0.558249
\(689\) −2.54191e126 −1.27176
\(690\) −1.58567e125 −0.0743752
\(691\) 4.99715e125 0.219760 0.109880 0.993945i \(-0.464953\pi\)
0.109880 + 0.993945i \(0.464953\pi\)
\(692\) 1.47659e126 0.608889
\(693\) −2.98552e126 −1.15449
\(694\) 2.48798e126 0.902299
\(695\) −6.37266e125 −0.216769
\(696\) 1.69790e126 0.541754
\(697\) 1.47147e126 0.440447
\(698\) −1.89121e125 −0.0531098
\(699\) 4.48537e124 0.0118185
\(700\) 8.61729e126 2.13063
\(701\) 1.20764e126 0.280212 0.140106 0.990137i \(-0.455256\pi\)
0.140106 + 0.990137i \(0.455256\pi\)
\(702\) −5.72774e126 −1.24733
\(703\) −3.52868e126 −0.721273
\(704\) 2.40947e126 0.462314
\(705\) −1.91935e124 −0.00345732
\(706\) 5.21845e126 0.882535
\(707\) −7.68105e126 −1.21971
\(708\) −1.82609e126 −0.272297
\(709\) −4.71841e126 −0.660751 −0.330376 0.943850i \(-0.607175\pi\)
−0.330376 + 0.943850i \(0.607175\pi\)
\(710\) 1.09664e126 0.144234
\(711\) 1.36731e127 1.68916
\(712\) −2.43071e127 −2.82081
\(713\) 1.17489e127 1.28089
\(714\) 3.24327e126 0.332210
\(715\) 6.03568e126 0.580908
\(716\) 2.26725e127 2.05055
\(717\) −5.87664e125 −0.0499490
\(718\) −1.36793e127 −1.09276
\(719\) −1.53894e127 −1.15554 −0.577770 0.816200i \(-0.696077\pi\)
−0.577770 + 0.816200i \(0.696077\pi\)
\(720\) −5.91461e126 −0.417474
\(721\) −6.85428e126 −0.454823
\(722\) −1.93484e127 −1.20709
\(723\) 1.27876e126 0.0750127
\(724\) −3.37956e127 −1.86421
\(725\) 2.33670e127 1.21216
\(726\) −1.79099e126 −0.0873802
\(727\) −9.29984e126 −0.426770 −0.213385 0.976968i \(-0.568449\pi\)
−0.213385 + 0.976968i \(0.568449\pi\)
\(728\) 9.25936e127 3.99700
\(729\) −1.89825e127 −0.770864
\(730\) −2.52871e126 −0.0966121
\(731\) −9.01685e126 −0.324139
\(732\) 1.33958e127 0.453132
\(733\) 2.90574e127 0.924974 0.462487 0.886626i \(-0.346957\pi\)
0.462487 + 0.886626i \(0.346957\pi\)
\(734\) 3.74607e127 1.12228
\(735\) −3.21745e125 −0.00907247
\(736\) 1.68690e127 0.447741
\(737\) −1.33598e127 −0.333807
\(738\) −3.65786e127 −0.860438
\(739\) −3.49478e127 −0.774002 −0.387001 0.922079i \(-0.626489\pi\)
−0.387001 + 0.922079i \(0.626489\pi\)
\(740\) −3.80747e127 −0.794008
\(741\) 1.03252e127 0.202764
\(742\) −7.30296e127 −1.35060
\(743\) 8.90897e127 1.55176 0.775882 0.630879i \(-0.217305\pi\)
0.775882 + 0.630879i \(0.217305\pi\)
\(744\) −4.38567e127 −0.719516
\(745\) 3.05379e127 0.471938
\(746\) −5.59377e127 −0.814379
\(747\) 1.49327e127 0.204820
\(748\) −1.63146e128 −2.10841
\(749\) −6.86326e127 −0.835776
\(750\) 1.70328e127 0.195461
\(751\) 5.71982e127 0.618594 0.309297 0.950966i \(-0.399906\pi\)
0.309297 + 0.950966i \(0.399906\pi\)
\(752\) 8.89945e126 0.0907130
\(753\) −3.39632e127 −0.326311
\(754\) 4.67548e128 4.23449
\(755\) −3.71282e126 −0.0317004
\(756\) −1.12482e128 −0.905446
\(757\) 2.03779e128 1.54665 0.773325 0.634010i \(-0.218592\pi\)
0.773325 + 0.634010i \(0.218592\pi\)
\(758\) −4.66926e127 −0.334171
\(759\) 2.39798e127 0.161840
\(760\) 5.29892e127 0.337274
\(761\) −1.17204e126 −0.00703599 −0.00351799 0.999994i \(-0.501120\pi\)
−0.00351799 + 0.999994i \(0.501120\pi\)
\(762\) 7.34039e127 0.415645
\(763\) −3.52246e128 −1.88150
\(764\) −5.06085e128 −2.55017
\(765\) −5.09880e127 −0.242401
\(766\) 4.51105e128 2.02347
\(767\) −2.70037e128 −1.14296
\(768\) 9.87638e127 0.394479
\(769\) 3.19825e127 0.120556 0.0602782 0.998182i \(-0.480801\pi\)
0.0602782 + 0.998182i \(0.480801\pi\)
\(770\) 1.73406e128 0.616919
\(771\) −5.01117e127 −0.168275
\(772\) 2.01407e128 0.638419
\(773\) 3.28146e128 0.981929 0.490965 0.871179i \(-0.336644\pi\)
0.490965 + 0.871179i \(0.336644\pi\)
\(774\) 2.24146e128 0.633224
\(775\) −6.03567e128 −1.60990
\(776\) −4.64066e127 −0.116878
\(777\) −1.14466e128 −0.272232
\(778\) −8.86055e128 −1.99007
\(779\) 1.34589e128 0.285491
\(780\) 1.11410e128 0.223211
\(781\) −1.65842e128 −0.313852
\(782\) 6.33815e128 1.13308
\(783\) −3.05010e128 −0.515129
\(784\) 1.49183e128 0.238043
\(785\) −1.36658e128 −0.206032
\(786\) 2.54794e128 0.362983
\(787\) 1.37748e129 1.85443 0.927214 0.374532i \(-0.122197\pi\)
0.927214 + 0.374532i \(0.122197\pi\)
\(788\) −8.21157e128 −1.04474
\(789\) −1.80923e127 −0.0217554
\(790\) −7.94171e128 −0.902628
\(791\) −6.23308e128 −0.669652
\(792\) 2.17790e129 2.21191
\(793\) 1.98092e129 1.90200
\(794\) 6.36681e128 0.577976
\(795\) −4.71878e127 −0.0405035
\(796\) −2.57390e129 −2.08910
\(797\) −4.39500e128 −0.337337 −0.168668 0.985673i \(-0.553947\pi\)
−0.168668 + 0.985673i \(0.553947\pi\)
\(798\) 2.96647e128 0.215333
\(799\) 7.67194e127 0.0526712
\(800\) −8.66599e128 −0.562748
\(801\) 2.13929e129 1.31408
\(802\) −2.79660e129 −1.62507
\(803\) 3.82412e128 0.210228
\(804\) −2.46602e128 −0.128263
\(805\) −4.60481e128 −0.226618
\(806\) −1.20767e130 −5.62393
\(807\) −3.92491e128 −0.172965
\(808\) 5.60324e129 2.33686
\(809\) 3.31962e129 1.31032 0.655162 0.755488i \(-0.272600\pi\)
0.655162 + 0.755488i \(0.272600\pi\)
\(810\) 1.21325e129 0.453280
\(811\) −3.97411e129 −1.40544 −0.702720 0.711467i \(-0.748031\pi\)
−0.702720 + 0.711467i \(0.748031\pi\)
\(812\) 9.18175e129 3.07385
\(813\) 8.96737e128 0.284208
\(814\) 8.42381e129 2.52768
\(815\) −3.79188e128 −0.107731
\(816\) −9.71676e128 −0.261402
\(817\) −8.24730e128 −0.210102
\(818\) 2.52241e128 0.0608546
\(819\) −8.14926e129 −1.86202
\(820\) 1.45222e129 0.314280
\(821\) −1.35805e129 −0.278386 −0.139193 0.990265i \(-0.544451\pi\)
−0.139193 + 0.990265i \(0.544451\pi\)
\(822\) −9.05591e128 −0.175847
\(823\) 1.64457e129 0.302524 0.151262 0.988494i \(-0.451666\pi\)
0.151262 + 0.988494i \(0.451666\pi\)
\(824\) 5.00012e129 0.871404
\(825\) −1.23189e129 −0.203410
\(826\) −7.75822e129 −1.21381
\(827\) 6.57180e127 0.00974292 0.00487146 0.999988i \(-0.498449\pi\)
0.00487146 + 0.999988i \(0.498449\pi\)
\(828\) −1.07696e130 −1.51303
\(829\) 4.74673e129 0.632001 0.316000 0.948759i \(-0.397660\pi\)
0.316000 + 0.948759i \(0.397660\pi\)
\(830\) −8.67330e128 −0.109448
\(831\) 3.65489e128 0.0437148
\(832\) 6.57686e129 0.745643
\(833\) 1.28606e129 0.138216
\(834\) 2.60250e129 0.265157
\(835\) −5.50913e129 −0.532151
\(836\) −1.49222e130 −1.36664
\(837\) 7.87839e129 0.684156
\(838\) 1.24856e130 1.02814
\(839\) −1.79965e130 −1.40533 −0.702667 0.711518i \(-0.748008\pi\)
−0.702667 + 0.711518i \(0.748008\pi\)
\(840\) 1.71890e129 0.127298
\(841\) 1.06605e130 0.748782
\(842\) 2.67146e130 1.77976
\(843\) 1.68538e129 0.106505
\(844\) −3.27579e130 −1.96371
\(845\) 1.13977e130 0.648176
\(846\) −1.90713e129 −0.102896
\(847\) −5.20106e129 −0.266244
\(848\) 2.18795e130 1.06273
\(849\) −4.07288e129 −0.187719
\(850\) −3.25605e130 −1.42413
\(851\) −2.23694e130 −0.928517
\(852\) −3.06121e129 −0.120596
\(853\) 3.67965e130 1.37586 0.687930 0.725777i \(-0.258519\pi\)
0.687930 + 0.725777i \(0.258519\pi\)
\(854\) 5.69124e130 2.01991
\(855\) −4.66363e129 −0.157120
\(856\) 5.00667e130 1.60128
\(857\) 7.78814e129 0.236476 0.118238 0.992985i \(-0.462275\pi\)
0.118238 + 0.992985i \(0.462275\pi\)
\(858\) −2.46489e130 −0.710579
\(859\) −9.94984e129 −0.272346 −0.136173 0.990685i \(-0.543480\pi\)
−0.136173 + 0.990685i \(0.543480\pi\)
\(860\) −8.89889e129 −0.231289
\(861\) 4.36589e129 0.107754
\(862\) −1.00207e131 −2.34869
\(863\) −8.18207e130 −1.82131 −0.910653 0.413172i \(-0.864421\pi\)
−0.910653 + 0.413172i \(0.864421\pi\)
\(864\) 1.13118e130 0.239149
\(865\) 4.05349e129 0.0813977
\(866\) 3.21557e130 0.613356
\(867\) 2.58893e129 0.0469105
\(868\) −2.37164e131 −4.08245
\(869\) 1.20101e131 1.96411
\(870\) 8.67952e129 0.134862
\(871\) −3.64667e130 −0.538380
\(872\) 2.56959e131 3.60480
\(873\) 4.08429e129 0.0544481
\(874\) 5.79721e130 0.734447
\(875\) 4.94635e130 0.595561
\(876\) 7.05878e129 0.0807788
\(877\) 2.51544e130 0.273610 0.136805 0.990598i \(-0.456317\pi\)
0.136805 + 0.990598i \(0.456317\pi\)
\(878\) 1.99756e130 0.206535
\(879\) −1.16506e130 −0.114510
\(880\) −5.19522e130 −0.485428
\(881\) 9.16844e130 0.814456 0.407228 0.913327i \(-0.366495\pi\)
0.407228 + 0.913327i \(0.366495\pi\)
\(882\) −3.19696e130 −0.270013
\(883\) 8.89867e130 0.714618 0.357309 0.933986i \(-0.383694\pi\)
0.357309 + 0.933986i \(0.383694\pi\)
\(884\) −4.45322e131 −3.40055
\(885\) −5.01294e129 −0.0364013
\(886\) 3.54125e131 2.44543
\(887\) −2.22905e131 −1.46393 −0.731963 0.681344i \(-0.761396\pi\)
−0.731963 + 0.681344i \(0.761396\pi\)
\(888\) 8.35014e130 0.521575
\(889\) 2.13166e131 1.26646
\(890\) −1.24256e131 −0.702200
\(891\) −1.83478e131 −0.986336
\(892\) −6.33043e131 −3.23740
\(893\) 7.01717e129 0.0341407
\(894\) −1.24713e131 −0.577285
\(895\) 6.22400e130 0.274122
\(896\) 3.46610e131 1.45256
\(897\) 6.54551e130 0.261024
\(898\) 7.01643e131 2.66268
\(899\) −6.43103e131 −2.32260
\(900\) 5.53256e131 1.90167
\(901\) 1.88617e131 0.617059
\(902\) −3.21296e131 −1.00050
\(903\) −2.67532e130 −0.0792995
\(904\) 4.54696e131 1.28300
\(905\) −9.27749e130 −0.249212
\(906\) 1.51626e130 0.0387766
\(907\) −3.83857e131 −0.934642 −0.467321 0.884088i \(-0.654781\pi\)
−0.467321 + 0.884088i \(0.654781\pi\)
\(908\) −1.82754e131 −0.423689
\(909\) −4.93147e131 −1.08864
\(910\) 4.73329e131 0.994997
\(911\) −1.57548e131 −0.315387 −0.157694 0.987488i \(-0.550406\pi\)
−0.157694 + 0.987488i \(0.550406\pi\)
\(912\) −8.88747e130 −0.169437
\(913\) 1.31165e131 0.238159
\(914\) −4.49845e130 −0.0777960
\(915\) 3.67737e130 0.0605758
\(916\) 3.80299e131 0.596729
\(917\) 7.39928e131 1.10600
\(918\) 4.25014e131 0.605207
\(919\) 3.76660e131 0.510987 0.255493 0.966811i \(-0.417762\pi\)
0.255493 + 0.966811i \(0.417762\pi\)
\(920\) 3.35916e131 0.434182
\(921\) 1.89323e131 0.233158
\(922\) −2.51020e132 −2.94565
\(923\) −4.52682e131 −0.506195
\(924\) −4.84057e131 −0.515815
\(925\) 1.14917e132 1.16701
\(926\) −1.51345e132 −1.46480
\(927\) −4.40066e131 −0.405947
\(928\) −9.23365e131 −0.811873
\(929\) 1.74031e132 1.45857 0.729286 0.684209i \(-0.239853\pi\)
0.729286 + 0.684209i \(0.239853\pi\)
\(930\) −2.24191e131 −0.179113
\(931\) 1.17630e131 0.0895897
\(932\) −1.76941e131 −0.128476
\(933\) −3.37862e131 −0.233887
\(934\) −2.53880e132 −1.67569
\(935\) −4.47864e131 −0.281857
\(936\) 5.94479e132 3.56748
\(937\) 1.51226e132 0.865397 0.432698 0.901539i \(-0.357562\pi\)
0.432698 + 0.901539i \(0.357562\pi\)
\(938\) −1.04770e132 −0.571754
\(939\) 2.49543e131 0.129875
\(940\) 7.57157e130 0.0375835
\(941\) −6.31705e131 −0.299072 −0.149536 0.988756i \(-0.547778\pi\)
−0.149536 + 0.988756i \(0.547778\pi\)
\(942\) 5.58091e131 0.252023
\(943\) 8.53203e131 0.367521
\(944\) 2.32435e132 0.955097
\(945\) −3.08782e131 −0.121042
\(946\) 1.96883e132 0.736297
\(947\) −1.15806e132 −0.413196 −0.206598 0.978426i \(-0.566239\pi\)
−0.206598 + 0.978426i \(0.566239\pi\)
\(948\) 2.21690e132 0.754700
\(949\) 1.04383e132 0.339065
\(950\) −2.97816e132 −0.923097
\(951\) −4.76086e131 −0.140816
\(952\) −6.87070e132 −1.93935
\(953\) −6.23693e132 −1.68011 −0.840053 0.542504i \(-0.817476\pi\)
−0.840053 + 0.542504i \(0.817476\pi\)
\(954\) −4.68873e132 −1.20546
\(955\) −1.38929e132 −0.340913
\(956\) 2.31825e132 0.542980
\(957\) −1.31259e132 −0.293459
\(958\) −3.25276e132 −0.694203
\(959\) −2.62985e132 −0.535801
\(960\) 1.22092e131 0.0237476
\(961\) 1.12262e133 2.08470
\(962\) 2.29936e133 4.07677
\(963\) −4.40643e132 −0.745962
\(964\) −5.04452e132 −0.815440
\(965\) 5.52898e131 0.0853454
\(966\) 1.88054e132 0.277205
\(967\) −2.82355e132 −0.397482 −0.198741 0.980052i \(-0.563685\pi\)
−0.198741 + 0.980052i \(0.563685\pi\)
\(968\) 3.79412e132 0.510102
\(969\) −7.66161e131 −0.0983812
\(970\) −2.37226e131 −0.0290951
\(971\) 1.37580e132 0.161176 0.0805879 0.996748i \(-0.474320\pi\)
0.0805879 + 0.996748i \(0.474320\pi\)
\(972\) −1.09052e133 −1.22035
\(973\) 7.55772e132 0.807922
\(974\) 7.65611e132 0.781870
\(975\) −3.36257e132 −0.328070
\(976\) −1.70508e133 −1.58938
\(977\) −1.36516e133 −1.21584 −0.607920 0.793998i \(-0.707996\pi\)
−0.607920 + 0.793998i \(0.707996\pi\)
\(978\) 1.54855e132 0.131779
\(979\) 1.87909e133 1.52798
\(980\) 1.26924e132 0.0986241
\(981\) −2.26152e133 −1.67931
\(982\) 4.19445e133 2.97655
\(983\) 1.70343e133 1.15530 0.577649 0.816285i \(-0.303970\pi\)
0.577649 + 0.816285i \(0.303970\pi\)
\(984\) −3.18487e132 −0.206447
\(985\) −2.25422e132 −0.139664
\(986\) −3.46933e133 −2.05458
\(987\) 2.27628e131 0.0128858
\(988\) −4.07316e133 −2.20418
\(989\) −5.22823e132 −0.270471
\(990\) 1.11332e133 0.550624
\(991\) 1.06033e133 0.501375 0.250687 0.968068i \(-0.419343\pi\)
0.250687 + 0.968068i \(0.419343\pi\)
\(992\) 2.38504e133 1.07827
\(993\) 6.56364e132 0.283728
\(994\) −1.30057e133 −0.537575
\(995\) −7.06580e132 −0.279277
\(996\) 2.42112e132 0.0915114
\(997\) 1.46285e133 0.528768 0.264384 0.964417i \(-0.414831\pi\)
0.264384 + 0.964417i \(0.414831\pi\)
\(998\) 1.31156e133 0.453399
\(999\) −1.50001e133 −0.495942
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.1.7 7
3.2 odd 2 9.90.a.b.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.90.a.a.1.7 7 1.1 even 1 trivial
9.90.a.b.1.1 7 3.2 odd 2