Properties

Label 1.56.a.a.1.1
Level 1
Weight 56
Character 1.1
Self dual Yes
Analytic conductor 19.158
Analytic rank 0
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 56 \)
Character orbit: \([\chi]\) = 1.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(19.1581467685\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{20}\cdot 3^{9}\cdot 5^{2}\cdot 7\cdot 11 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.27360e7\)
Character \(\chi\) = 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53509e8 q^{2} -1.66915e12 q^{3} +2.82382e16 q^{4} +1.07257e19 q^{5} +4.23145e20 q^{6} -1.10352e23 q^{7} +1.97498e24 q^{8} -1.71663e26 q^{9} +O(q^{10})\) \(q-2.53509e8 q^{2} -1.66915e12 q^{3} +2.82382e16 q^{4} +1.07257e19 q^{5} +4.23145e20 q^{6} -1.10352e23 q^{7} +1.97498e24 q^{8} -1.71663e26 q^{9} -2.71906e27 q^{10} -7.94038e28 q^{11} -4.71339e28 q^{12} +3.15893e30 q^{13} +2.79753e31 q^{14} -1.79028e31 q^{15} -1.51807e33 q^{16} +3.96364e33 q^{17} +4.35182e34 q^{18} +1.06873e35 q^{19} +3.02875e35 q^{20} +1.84194e35 q^{21} +2.01296e37 q^{22} +2.36516e37 q^{23} -3.29654e36 q^{24} -1.62515e38 q^{25} -8.00820e38 q^{26} +5.77713e38 q^{27} -3.11615e39 q^{28} -2.07372e40 q^{29} +4.53852e39 q^{30} +1.26132e41 q^{31} +3.13688e41 q^{32} +1.32537e41 q^{33} -1.00482e42 q^{34} -1.18360e42 q^{35} -4.84747e42 q^{36} +1.05611e43 q^{37} -2.70933e43 q^{38} -5.27273e42 q^{39} +2.11830e43 q^{40} +3.96211e44 q^{41} -4.66949e43 q^{42} +4.12421e44 q^{43} -2.24222e45 q^{44} -1.84121e45 q^{45} -5.99590e45 q^{46} +1.78010e46 q^{47} +2.53388e45 q^{48} -1.80492e46 q^{49} +4.11992e46 q^{50} -6.61590e45 q^{51} +8.92027e46 q^{52} -1.03445e47 q^{53} -1.46456e47 q^{54} -8.51661e47 q^{55} -2.17943e47 q^{56} -1.78387e47 q^{57} +5.25709e48 q^{58} +3.49395e48 q^{59} -5.05543e47 q^{60} -1.91493e48 q^{61} -3.19757e49 q^{62} +1.89434e49 q^{63} -2.48288e49 q^{64} +3.38818e49 q^{65} -3.35993e49 q^{66} +1.84247e49 q^{67} +1.11926e50 q^{68} -3.94780e49 q^{69} +3.00054e50 q^{70} +7.05155e50 q^{71} -3.39031e50 q^{72} -2.58805e51 q^{73} -2.67734e51 q^{74} +2.71262e50 q^{75} +3.01790e51 q^{76} +8.76237e51 q^{77} +1.33669e51 q^{78} +9.12558e51 q^{79} -1.62823e52 q^{80} +2.89822e52 q^{81} -1.00443e53 q^{82} +4.34346e52 q^{83} +5.20132e51 q^{84} +4.25128e52 q^{85} -1.04553e53 q^{86} +3.46136e52 q^{87} -1.56821e53 q^{88} +4.67666e53 q^{89} +4.66763e53 q^{90} -3.48595e53 q^{91} +6.67879e53 q^{92} -2.10534e53 q^{93} -4.51272e54 q^{94} +1.14629e54 q^{95} -5.23592e53 q^{96} -8.39518e53 q^{97} +4.57565e54 q^{98} +1.36307e55 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 208622520q^{2} - 6821470691280q^{3} + 38727758778743872q^{4} + 14396937963387167160q^{5} + \)\(20\!\cdots\!08\)\(q^{6} - \)\(20\!\cdots\!00\)\(q^{7} + \)\(45\!\cdots\!40\)\(q^{8} + \)\(47\!\cdots\!28\)\(q^{9} + O(q^{10}) \) \( 4q + 208622520q^{2} - 6821470691280q^{3} + 38727758778743872q^{4} + 14396937963387167160q^{5} + \)\(20\!\cdots\!08\)\(q^{6} - \)\(20\!\cdots\!00\)\(q^{7} + \)\(45\!\cdots\!40\)\(q^{8} + \)\(47\!\cdots\!28\)\(q^{9} + \)\(46\!\cdots\!60\)\(q^{10} + \)\(19\!\cdots\!08\)\(q^{11} + \)\(51\!\cdots\!40\)\(q^{12} - \)\(44\!\cdots\!60\)\(q^{13} - \)\(28\!\cdots\!56\)\(q^{14} + \)\(24\!\cdots\!20\)\(q^{15} + \)\(97\!\cdots\!04\)\(q^{16} + \)\(85\!\cdots\!60\)\(q^{17} + \)\(38\!\cdots\!20\)\(q^{18} + \)\(33\!\cdots\!00\)\(q^{19} + \)\(29\!\cdots\!80\)\(q^{20} + \)\(92\!\cdots\!08\)\(q^{21} + \)\(38\!\cdots\!40\)\(q^{22} + \)\(49\!\cdots\!60\)\(q^{23} + \)\(19\!\cdots\!00\)\(q^{24} + \)\(35\!\cdots\!00\)\(q^{25} - \)\(29\!\cdots\!92\)\(q^{26} - \)\(85\!\cdots\!40\)\(q^{27} - \)\(14\!\cdots\!60\)\(q^{28} - \)\(18\!\cdots\!00\)\(q^{29} + \)\(81\!\cdots\!20\)\(q^{30} + \)\(22\!\cdots\!08\)\(q^{31} + \)\(63\!\cdots\!20\)\(q^{32} + \)\(84\!\cdots\!40\)\(q^{33} + \)\(89\!\cdots\!44\)\(q^{34} - \)\(48\!\cdots\!40\)\(q^{35} - \)\(23\!\cdots\!96\)\(q^{36} - \)\(32\!\cdots\!20\)\(q^{37} - \)\(49\!\cdots\!40\)\(q^{38} + \)\(66\!\cdots\!56\)\(q^{39} + \)\(42\!\cdots\!00\)\(q^{40} + \)\(24\!\cdots\!08\)\(q^{41} + \)\(50\!\cdots\!60\)\(q^{42} - \)\(86\!\cdots\!00\)\(q^{43} - \)\(48\!\cdots\!56\)\(q^{44} - \)\(95\!\cdots\!80\)\(q^{45} - \)\(12\!\cdots\!92\)\(q^{46} + \)\(42\!\cdots\!40\)\(q^{47} + \)\(19\!\cdots\!60\)\(q^{48} + \)\(51\!\cdots\!72\)\(q^{49} + \)\(17\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!08\)\(q^{51} - \)\(26\!\cdots\!00\)\(q^{52} - \)\(48\!\cdots\!80\)\(q^{53} - \)\(13\!\cdots\!00\)\(q^{54} - \)\(12\!\cdots\!80\)\(q^{55} - \)\(29\!\cdots\!00\)\(q^{56} + \)\(16\!\cdots\!20\)\(q^{57} + \)\(60\!\cdots\!40\)\(q^{58} + \)\(81\!\cdots\!00\)\(q^{59} + \)\(10\!\cdots\!60\)\(q^{60} + \)\(70\!\cdots\!08\)\(q^{61} - \)\(30\!\cdots\!60\)\(q^{62} - \)\(71\!\cdots\!20\)\(q^{63} - \)\(98\!\cdots\!28\)\(q^{64} - \)\(96\!\cdots\!80\)\(q^{65} + \)\(64\!\cdots\!16\)\(q^{66} + \)\(41\!\cdots\!60\)\(q^{67} + \)\(62\!\cdots\!20\)\(q^{68} + \)\(51\!\cdots\!56\)\(q^{69} - \)\(47\!\cdots\!40\)\(q^{70} + \)\(99\!\cdots\!08\)\(q^{71} - \)\(43\!\cdots\!20\)\(q^{72} - \)\(89\!\cdots\!40\)\(q^{73} - \)\(79\!\cdots\!56\)\(q^{74} + \)\(52\!\cdots\!00\)\(q^{75} - \)\(60\!\cdots\!00\)\(q^{76} + \)\(14\!\cdots\!00\)\(q^{77} + \)\(39\!\cdots\!00\)\(q^{78} + \)\(48\!\cdots\!00\)\(q^{79} - \)\(35\!\cdots\!40\)\(q^{80} + \)\(62\!\cdots\!04\)\(q^{81} - \)\(16\!\cdots\!60\)\(q^{82} - \)\(71\!\cdots\!20\)\(q^{83} - \)\(31\!\cdots\!56\)\(q^{84} + \)\(24\!\cdots\!60\)\(q^{85} - \)\(39\!\cdots\!92\)\(q^{86} + \)\(79\!\cdots\!80\)\(q^{87} + \)\(26\!\cdots\!80\)\(q^{88} + \)\(15\!\cdots\!00\)\(q^{89} - \)\(12\!\cdots\!80\)\(q^{90} + \)\(16\!\cdots\!08\)\(q^{91} - \)\(27\!\cdots\!40\)\(q^{92} - \)\(11\!\cdots\!60\)\(q^{93} - \)\(40\!\cdots\!56\)\(q^{94} + \)\(90\!\cdots\!00\)\(q^{95} - \)\(54\!\cdots\!92\)\(q^{96} + \)\(51\!\cdots\!40\)\(q^{97} + \)\(43\!\cdots\!60\)\(q^{98} + \)\(79\!\cdots\!56\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53509e8 −1.33558 −0.667789 0.744351i \(-0.732759\pi\)
−0.667789 + 0.744351i \(0.732759\pi\)
\(3\) −1.66915e12 −0.126375 −0.0631874 0.998002i \(-0.520127\pi\)
−0.0631874 + 0.998002i \(0.520127\pi\)
\(4\) 2.82382e16 0.783769
\(5\) 1.07257e19 0.643799 0.321899 0.946774i \(-0.395679\pi\)
0.321899 + 0.946774i \(0.395679\pi\)
\(6\) 4.23145e20 0.168784
\(7\) −1.10352e23 −0.634723 −0.317362 0.948305i \(-0.602797\pi\)
−0.317362 + 0.948305i \(0.602797\pi\)
\(8\) 1.97498e24 0.288794
\(9\) −1.71663e26 −0.984029
\(10\) −2.71906e27 −0.859844
\(11\) −7.94038e28 −1.82618 −0.913088 0.407763i \(-0.866309\pi\)
−0.913088 + 0.407763i \(0.866309\pi\)
\(12\) −4.71339e28 −0.0990487
\(13\) 3.15893e30 0.734680 0.367340 0.930087i \(-0.380269\pi\)
0.367340 + 0.930087i \(0.380269\pi\)
\(14\) 2.79753e31 0.847722
\(15\) −1.79028e31 −0.0813600
\(16\) −1.51807e33 −1.16948
\(17\) 3.96364e33 0.576433 0.288216 0.957565i \(-0.406938\pi\)
0.288216 + 0.957565i \(0.406938\pi\)
\(18\) 4.35182e34 1.31425
\(19\) 1.06873e35 0.729699 0.364849 0.931067i \(-0.381120\pi\)
0.364849 + 0.931067i \(0.381120\pi\)
\(20\) 3.02875e35 0.504589
\(21\) 1.84194e35 0.0802131
\(22\) 2.01296e37 2.43900
\(23\) 2.36516e37 0.844004 0.422002 0.906595i \(-0.361327\pi\)
0.422002 + 0.906595i \(0.361327\pi\)
\(24\) −3.29654e36 −0.0364963
\(25\) −1.62515e38 −0.585523
\(26\) −8.00820e38 −0.981223
\(27\) 5.77713e38 0.250731
\(28\) −3.11615e39 −0.497476
\(29\) −2.07372e40 −1.26126 −0.630632 0.776082i \(-0.717204\pi\)
−0.630632 + 0.776082i \(0.717204\pi\)
\(30\) 4.53852e39 0.108663
\(31\) 1.26132e41 1.22569 0.612843 0.790204i \(-0.290026\pi\)
0.612843 + 0.790204i \(0.290026\pi\)
\(32\) 3.13688e41 1.27313
\(33\) 1.32537e41 0.230783
\(34\) −1.00482e42 −0.769871
\(35\) −1.18360e42 −0.408634
\(36\) −4.84747e42 −0.771251
\(37\) 1.05611e43 0.790974 0.395487 0.918472i \(-0.370576\pi\)
0.395487 + 0.918472i \(0.370576\pi\)
\(38\) −2.70933e43 −0.974570
\(39\) −5.27273e42 −0.0928451
\(40\) 2.11830e43 0.185925
\(41\) 3.96211e44 1.76348 0.881739 0.471737i \(-0.156373\pi\)
0.881739 + 0.471737i \(0.156373\pi\)
\(42\) −4.66949e43 −0.107131
\(43\) 4.12421e44 0.495402 0.247701 0.968836i \(-0.420325\pi\)
0.247701 + 0.968836i \(0.420325\pi\)
\(44\) −2.24222e45 −1.43130
\(45\) −1.84121e45 −0.633517
\(46\) −5.99590e45 −1.12723
\(47\) 1.78010e46 1.85248 0.926239 0.376936i \(-0.123022\pi\)
0.926239 + 0.376936i \(0.123022\pi\)
\(48\) 2.53388e45 0.147792
\(49\) −1.80492e46 −0.597127
\(50\) 4.11992e46 0.782012
\(51\) −6.61590e45 −0.0728466
\(52\) 8.92027e46 0.575819
\(53\) −1.03445e47 −0.395480 −0.197740 0.980254i \(-0.563360\pi\)
−0.197740 + 0.980254i \(0.563360\pi\)
\(54\) −1.46456e47 −0.334871
\(55\) −8.51661e47 −1.17569
\(56\) −2.17943e47 −0.183304
\(57\) −1.78387e47 −0.0922156
\(58\) 5.25709e48 1.68452
\(59\) 3.49395e48 0.699659 0.349829 0.936813i \(-0.386240\pi\)
0.349829 + 0.936813i \(0.386240\pi\)
\(60\) −5.05543e47 −0.0637674
\(61\) −1.91493e48 −0.153314 −0.0766571 0.997058i \(-0.524425\pi\)
−0.0766571 + 0.997058i \(0.524425\pi\)
\(62\) −3.19757e49 −1.63700
\(63\) 1.89434e49 0.624586
\(64\) −2.48288e49 −0.530892
\(65\) 3.38818e49 0.472986
\(66\) −3.35993e49 −0.308228
\(67\) 1.84247e49 0.111775 0.0558873 0.998437i \(-0.482201\pi\)
0.0558873 + 0.998437i \(0.482201\pi\)
\(68\) 1.11926e50 0.451790
\(69\) −3.94780e49 −0.106661
\(70\) 3.00054e50 0.545763
\(71\) 7.05155e50 0.868320 0.434160 0.900836i \(-0.357045\pi\)
0.434160 + 0.900836i \(0.357045\pi\)
\(72\) −3.39031e50 −0.284182
\(73\) −2.58805e51 −1.48455 −0.742273 0.670098i \(-0.766252\pi\)
−0.742273 + 0.670098i \(0.766252\pi\)
\(74\) −2.67734e51 −1.05641
\(75\) 2.71262e50 0.0739954
\(76\) 3.01790e51 0.571915
\(77\) 8.76237e51 1.15912
\(78\) 1.33669e51 0.124002
\(79\) 9.12558e51 0.596369 0.298185 0.954508i \(-0.403619\pi\)
0.298185 + 0.954508i \(0.403619\pi\)
\(80\) −1.62823e52 −0.752907
\(81\) 2.89822e52 0.952343
\(82\) −1.00443e53 −2.35526
\(83\) 4.34346e52 0.729774 0.364887 0.931052i \(-0.381108\pi\)
0.364887 + 0.931052i \(0.381108\pi\)
\(84\) 5.20132e51 0.0628685
\(85\) 4.25128e52 0.371107
\(86\) −1.04553e53 −0.661648
\(87\) 3.46136e52 0.159392
\(88\) −1.56821e53 −0.527388
\(89\) 4.67666e53 1.15268 0.576342 0.817209i \(-0.304480\pi\)
0.576342 + 0.817209i \(0.304480\pi\)
\(90\) 4.66763e53 0.846111
\(91\) −3.48595e53 −0.466319
\(92\) 6.67879e53 0.661504
\(93\) −2.10534e53 −0.154896
\(94\) −4.51272e54 −2.47413
\(95\) 1.14629e54 0.469779
\(96\) −5.23592e53 −0.160892
\(97\) −8.39518e53 −0.194002 −0.0970012 0.995284i \(-0.530925\pi\)
−0.0970012 + 0.995284i \(0.530925\pi\)
\(98\) 4.57565e54 0.797509
\(99\) 1.36307e55 1.79701
\(100\) −4.58915e54 −0.458915
\(101\) −1.39147e54 −0.105837 −0.0529183 0.998599i \(-0.516852\pi\)
−0.0529183 + 0.998599i \(0.516852\pi\)
\(102\) 1.67719e54 0.0972923
\(103\) −3.24089e55 −1.43761 −0.718805 0.695211i \(-0.755311\pi\)
−0.718805 + 0.695211i \(0.755311\pi\)
\(104\) 6.23883e54 0.212171
\(105\) 1.97561e54 0.0516411
\(106\) 2.62244e55 0.528195
\(107\) −3.99263e55 −0.621163 −0.310582 0.950547i \(-0.600524\pi\)
−0.310582 + 0.950547i \(0.600524\pi\)
\(108\) 1.63136e55 0.196515
\(109\) −1.39528e56 −1.30447 −0.652233 0.758019i \(-0.726167\pi\)
−0.652233 + 0.758019i \(0.726167\pi\)
\(110\) 2.15904e56 1.57023
\(111\) −1.76281e55 −0.0999592
\(112\) 1.67522e56 0.742293
\(113\) −1.93685e55 −0.0672107 −0.0336053 0.999435i \(-0.510699\pi\)
−0.0336053 + 0.999435i \(0.510699\pi\)
\(114\) 4.52228e55 0.123161
\(115\) 2.53679e56 0.543369
\(116\) −5.85583e56 −0.988539
\(117\) −5.42273e56 −0.722947
\(118\) −8.85749e56 −0.934449
\(119\) −4.37396e56 −0.365875
\(120\) −3.53576e55 −0.0234963
\(121\) 4.41437e57 2.33492
\(122\) 4.85453e56 0.204763
\(123\) −6.61335e56 −0.222859
\(124\) 3.56175e57 0.960655
\(125\) −4.72007e57 −1.02076
\(126\) −4.80233e57 −0.834184
\(127\) 4.09181e57 0.571891 0.285945 0.958246i \(-0.407692\pi\)
0.285945 + 0.958246i \(0.407692\pi\)
\(128\) −5.00747e57 −0.564085
\(129\) −6.88392e56 −0.0626064
\(130\) −8.58934e57 −0.631710
\(131\) 1.51902e58 0.904906 0.452453 0.891788i \(-0.350549\pi\)
0.452453 + 0.891788i \(0.350549\pi\)
\(132\) 3.74261e57 0.180880
\(133\) −1.17936e58 −0.463157
\(134\) −4.67083e57 −0.149284
\(135\) 6.19637e57 0.161421
\(136\) 7.82810e57 0.166470
\(137\) 7.02070e58 1.22058 0.610288 0.792180i \(-0.291054\pi\)
0.610288 + 0.792180i \(0.291054\pi\)
\(138\) 1.00081e58 0.142454
\(139\) −1.53029e58 −0.178594 −0.0892968 0.996005i \(-0.528462\pi\)
−0.0892968 + 0.996005i \(0.528462\pi\)
\(140\) −3.34228e58 −0.320275
\(141\) −2.97125e58 −0.234107
\(142\) −1.78763e59 −1.15971
\(143\) −2.50831e59 −1.34166
\(144\) 2.60596e59 1.15080
\(145\) −2.22421e59 −0.812000
\(146\) 6.56095e59 1.98273
\(147\) 3.01269e58 0.0754618
\(148\) 2.98227e59 0.619941
\(149\) 1.10917e59 0.191592 0.0957960 0.995401i \(-0.469460\pi\)
0.0957960 + 0.995401i \(0.469460\pi\)
\(150\) −6.87676e58 −0.0988266
\(151\) −5.47256e59 −0.655125 −0.327563 0.944829i \(-0.606227\pi\)
−0.327563 + 0.944829i \(0.606227\pi\)
\(152\) 2.11072e59 0.210732
\(153\) −6.80411e59 −0.567227
\(154\) −2.22134e60 −1.54809
\(155\) 1.35286e60 0.789096
\(156\) −1.48893e59 −0.0727691
\(157\) 3.00285e60 1.23110 0.615550 0.788097i \(-0.288934\pi\)
0.615550 + 0.788097i \(0.288934\pi\)
\(158\) −2.31342e60 −0.796498
\(159\) 1.72666e59 0.0499788
\(160\) 3.36452e60 0.819641
\(161\) −2.61000e60 −0.535709
\(162\) −7.34726e60 −1.27193
\(163\) 9.84807e60 1.43944 0.719718 0.694267i \(-0.244271\pi\)
0.719718 + 0.694267i \(0.244271\pi\)
\(164\) 1.11883e61 1.38216
\(165\) 1.42155e60 0.148578
\(166\) −1.10111e61 −0.974670
\(167\) −1.02128e61 −0.766374 −0.383187 0.923671i \(-0.625174\pi\)
−0.383187 + 0.923671i \(0.625174\pi\)
\(168\) 3.63779e59 0.0231650
\(169\) −8.50890e60 −0.460245
\(170\) −1.07774e61 −0.495642
\(171\) −1.83461e61 −0.718045
\(172\) 1.16460e61 0.388281
\(173\) 4.21525e61 1.19827 0.599137 0.800647i \(-0.295511\pi\)
0.599137 + 0.800647i \(0.295511\pi\)
\(174\) −8.77486e60 −0.212881
\(175\) 1.79339e61 0.371645
\(176\) 1.20540e62 2.13567
\(177\) −5.83192e60 −0.0884193
\(178\) −1.18558e62 −1.53950
\(179\) 9.72914e60 0.108297 0.0541485 0.998533i \(-0.482756\pi\)
0.0541485 + 0.998533i \(0.482756\pi\)
\(180\) −5.19924e61 −0.496531
\(181\) −1.95829e62 −1.60589 −0.802946 0.596051i \(-0.796736\pi\)
−0.802946 + 0.596051i \(0.796736\pi\)
\(182\) 8.83721e61 0.622805
\(183\) 3.19631e60 0.0193751
\(184\) 4.67114e61 0.243743
\(185\) 1.13275e62 0.509228
\(186\) 5.33722e61 0.206876
\(187\) −3.14728e62 −1.05267
\(188\) 5.02669e62 1.45191
\(189\) −6.37519e61 −0.159145
\(190\) −2.90594e62 −0.627427
\(191\) 3.89576e62 0.728073 0.364037 0.931385i \(-0.381398\pi\)
0.364037 + 0.931385i \(0.381398\pi\)
\(192\) 4.14429e61 0.0670914
\(193\) −1.32355e62 −0.185743 −0.0928716 0.995678i \(-0.529605\pi\)
−0.0928716 + 0.995678i \(0.529605\pi\)
\(194\) 2.12826e62 0.259105
\(195\) −5.65537e61 −0.0597736
\(196\) −5.09678e62 −0.468009
\(197\) 1.20320e63 0.960542 0.480271 0.877120i \(-0.340538\pi\)
0.480271 + 0.877120i \(0.340538\pi\)
\(198\) −3.45551e63 −2.40005
\(199\) 5.87498e62 0.355260 0.177630 0.984097i \(-0.443157\pi\)
0.177630 + 0.984097i \(0.443157\pi\)
\(200\) −3.20964e62 −0.169095
\(201\) −3.07536e61 −0.0141255
\(202\) 3.52751e62 0.141353
\(203\) 2.28840e63 0.800553
\(204\) −1.86822e62 −0.0570949
\(205\) 4.24963e63 1.13533
\(206\) 8.21597e63 1.92004
\(207\) −4.06010e63 −0.830525
\(208\) −4.79547e63 −0.859190
\(209\) −8.48612e63 −1.33256
\(210\) −5.00836e62 −0.0689707
\(211\) −5.03247e63 −0.608154 −0.304077 0.952647i \(-0.598348\pi\)
−0.304077 + 0.952647i \(0.598348\pi\)
\(212\) −2.92112e63 −0.309965
\(213\) −1.17701e63 −0.109734
\(214\) 1.01217e64 0.829612
\(215\) 4.42350e63 0.318939
\(216\) 1.14097e63 0.0724097
\(217\) −1.39189e64 −0.777972
\(218\) 3.53716e64 1.74221
\(219\) 4.31984e63 0.187609
\(220\) −2.40494e64 −0.921469
\(221\) 1.25209e64 0.423494
\(222\) 4.46888e63 0.133503
\(223\) −1.07577e64 −0.284011 −0.142005 0.989866i \(-0.545355\pi\)
−0.142005 + 0.989866i \(0.545355\pi\)
\(224\) −3.46161e64 −0.808086
\(225\) 2.78979e64 0.576172
\(226\) 4.91009e63 0.0897651
\(227\) 1.74540e64 0.282608 0.141304 0.989966i \(-0.454870\pi\)
0.141304 + 0.989966i \(0.454870\pi\)
\(228\) −5.03733e63 −0.0722757
\(229\) −5.35119e64 −0.680729 −0.340365 0.940293i \(-0.610551\pi\)
−0.340365 + 0.940293i \(0.610551\pi\)
\(230\) −6.43101e64 −0.725711
\(231\) −1.46257e64 −0.146483
\(232\) −4.09556e64 −0.364245
\(233\) −1.94781e63 −0.0153907 −0.00769534 0.999970i \(-0.502450\pi\)
−0.00769534 + 0.999970i \(0.502450\pi\)
\(234\) 1.37471e65 0.965552
\(235\) 1.90928e65 1.19262
\(236\) 9.86630e64 0.548371
\(237\) −1.52320e64 −0.0753661
\(238\) 1.10884e65 0.488655
\(239\) −2.84709e65 −1.11804 −0.559021 0.829153i \(-0.688823\pi\)
−0.559021 + 0.829153i \(0.688823\pi\)
\(240\) 2.71776e64 0.0951485
\(241\) 5.56433e65 1.73758 0.868789 0.495183i \(-0.164899\pi\)
0.868789 + 0.495183i \(0.164899\pi\)
\(242\) −1.11909e66 −3.11846
\(243\) −1.49157e65 −0.371084
\(244\) −5.40743e64 −0.120163
\(245\) −1.93590e65 −0.384429
\(246\) 1.67655e65 0.297646
\(247\) 3.37604e65 0.536095
\(248\) 2.49108e65 0.353971
\(249\) −7.24988e64 −0.0922251
\(250\) 1.19658e66 1.36330
\(251\) 6.88623e65 0.702998 0.351499 0.936188i \(-0.385672\pi\)
0.351499 + 0.936188i \(0.385672\pi\)
\(252\) 5.34928e65 0.489531
\(253\) −1.87803e66 −1.54130
\(254\) −1.03731e66 −0.763805
\(255\) −7.09601e64 −0.0468986
\(256\) 2.16399e66 1.28427
\(257\) −2.10402e66 −1.12173 −0.560865 0.827907i \(-0.689531\pi\)
−0.560865 + 0.827907i \(0.689531\pi\)
\(258\) 1.74514e65 0.0836157
\(259\) −1.16544e66 −0.502049
\(260\) 9.56761e65 0.370712
\(261\) 3.55982e66 1.24112
\(262\) −3.85087e66 −1.20857
\(263\) −2.52532e66 −0.713729 −0.356864 0.934156i \(-0.616154\pi\)
−0.356864 + 0.934156i \(0.616154\pi\)
\(264\) 2.61757e65 0.0666486
\(265\) −1.10952e66 −0.254610
\(266\) 2.98980e66 0.618582
\(267\) −7.80604e65 −0.145670
\(268\) 5.20281e65 0.0876054
\(269\) 7.93206e66 1.20559 0.602793 0.797898i \(-0.294054\pi\)
0.602793 + 0.797898i \(0.294054\pi\)
\(270\) −1.57084e66 −0.215590
\(271\) 1.24975e67 1.54942 0.774708 0.632320i \(-0.217897\pi\)
0.774708 + 0.632320i \(0.217897\pi\)
\(272\) −6.01706e66 −0.674124
\(273\) 5.81857e65 0.0589310
\(274\) −1.77981e67 −1.63017
\(275\) 1.29043e67 1.06927
\(276\) −1.11479e66 −0.0835975
\(277\) −2.46968e67 −1.67666 −0.838332 0.545159i \(-0.816469\pi\)
−0.838332 + 0.545159i \(0.816469\pi\)
\(278\) 3.87942e66 0.238526
\(279\) −2.16523e67 −1.20611
\(280\) −2.33759e66 −0.118011
\(281\) 8.92136e66 0.408326 0.204163 0.978937i \(-0.434553\pi\)
0.204163 + 0.978937i \(0.434553\pi\)
\(282\) 7.53240e66 0.312668
\(283\) 3.98122e67 1.49930 0.749652 0.661832i \(-0.230221\pi\)
0.749652 + 0.661832i \(0.230221\pi\)
\(284\) 1.99123e67 0.680562
\(285\) −1.91332e66 −0.0593683
\(286\) 6.35881e67 1.79189
\(287\) −4.37227e67 −1.11932
\(288\) −5.38487e67 −1.25280
\(289\) −3.15710e67 −0.667725
\(290\) 5.63859e67 1.08449
\(291\) 1.40128e66 0.0245170
\(292\) −7.30819e67 −1.16354
\(293\) −1.37145e67 −0.198756 −0.0993781 0.995050i \(-0.531685\pi\)
−0.0993781 + 0.995050i \(0.531685\pi\)
\(294\) −7.63744e66 −0.100785
\(295\) 3.74750e67 0.450439
\(296\) 2.08580e67 0.228428
\(297\) −4.58726e67 −0.457880
\(298\) −2.81186e67 −0.255886
\(299\) 7.47138e67 0.620073
\(300\) 7.65997e66 0.0579953
\(301\) −4.55115e67 −0.314443
\(302\) 1.38735e68 0.874971
\(303\) 2.32257e66 0.0133751
\(304\) −1.62240e68 −0.853365
\(305\) −2.05390e67 −0.0987036
\(306\) 1.72491e68 0.757576
\(307\) 1.08516e68 0.435700 0.217850 0.975982i \(-0.430096\pi\)
0.217850 + 0.975982i \(0.430096\pi\)
\(308\) 2.47434e68 0.908479
\(309\) 5.40954e67 0.181678
\(310\) −3.42962e68 −1.05390
\(311\) 1.44511e67 0.0406435 0.0203218 0.999793i \(-0.493531\pi\)
0.0203218 + 0.999793i \(0.493531\pi\)
\(312\) −1.04135e67 −0.0268131
\(313\) −5.45217e68 −1.28558 −0.642792 0.766041i \(-0.722224\pi\)
−0.642792 + 0.766041i \(0.722224\pi\)
\(314\) −7.61252e68 −1.64423
\(315\) 2.03181e68 0.402108
\(316\) 2.57690e68 0.467416
\(317\) −1.76696e68 −0.293831 −0.146915 0.989149i \(-0.546935\pi\)
−0.146915 + 0.989149i \(0.546935\pi\)
\(318\) −4.37725e67 −0.0667506
\(319\) 1.64662e69 2.30329
\(320\) −2.66306e68 −0.341787
\(321\) 6.66430e67 0.0784994
\(322\) 6.61660e68 0.715481
\(323\) 4.23606e68 0.420622
\(324\) 8.18407e68 0.746417
\(325\) −5.13375e68 −0.430172
\(326\) −2.49658e69 −1.92248
\(327\) 2.32893e68 0.164852
\(328\) 7.82508e68 0.509282
\(329\) −1.96438e69 −1.17581
\(330\) −3.60376e68 −0.198437
\(331\) −8.48541e68 −0.429935 −0.214968 0.976621i \(-0.568965\pi\)
−0.214968 + 0.976621i \(0.568965\pi\)
\(332\) 1.22652e69 0.571974
\(333\) −1.81295e69 −0.778341
\(334\) 2.58904e69 1.02355
\(335\) 1.97617e68 0.0719603
\(336\) −2.79619e68 −0.0938072
\(337\) 1.81937e69 0.562469 0.281235 0.959639i \(-0.409256\pi\)
0.281235 + 0.959639i \(0.409256\pi\)
\(338\) 2.15709e69 0.614693
\(339\) 3.23289e67 0.00849374
\(340\) 1.20049e69 0.290862
\(341\) −1.00154e70 −2.23832
\(342\) 4.65092e69 0.959005
\(343\) 5.32736e69 1.01373
\(344\) 8.14522e68 0.143069
\(345\) −4.23429e68 −0.0686682
\(346\) −1.06861e70 −1.60039
\(347\) 1.13939e70 1.57620 0.788102 0.615545i \(-0.211064\pi\)
0.788102 + 0.615545i \(0.211064\pi\)
\(348\) 9.77426e68 0.124927
\(349\) 6.76066e68 0.0798527 0.0399264 0.999203i \(-0.487288\pi\)
0.0399264 + 0.999203i \(0.487288\pi\)
\(350\) −4.54641e69 −0.496361
\(351\) 1.82496e69 0.184207
\(352\) −2.49080e70 −2.32496
\(353\) −5.30555e69 −0.458063 −0.229032 0.973419i \(-0.573556\pi\)
−0.229032 + 0.973419i \(0.573556\pi\)
\(354\) 1.47845e69 0.118091
\(355\) 7.56327e69 0.559024
\(356\) 1.32061e70 0.903438
\(357\) 7.30079e68 0.0462374
\(358\) −2.46643e69 −0.144639
\(359\) 2.52249e70 1.37004 0.685019 0.728525i \(-0.259794\pi\)
0.685019 + 0.728525i \(0.259794\pi\)
\(360\) −3.63634e69 −0.182956
\(361\) −1.00292e70 −0.467540
\(362\) 4.96445e70 2.14480
\(363\) −7.36825e69 −0.295075
\(364\) −9.84371e69 −0.365486
\(365\) −2.77586e70 −0.955749
\(366\) −8.10294e68 −0.0258769
\(367\) 1.59497e70 0.472536 0.236268 0.971688i \(-0.424076\pi\)
0.236268 + 0.971688i \(0.424076\pi\)
\(368\) −3.59046e70 −0.987042
\(369\) −6.80148e70 −1.73532
\(370\) −2.87163e70 −0.680114
\(371\) 1.14154e70 0.251021
\(372\) −5.94510e69 −0.121403
\(373\) 5.86255e70 1.11197 0.555986 0.831192i \(-0.312341\pi\)
0.555986 + 0.831192i \(0.312341\pi\)
\(374\) 7.97865e70 1.40592
\(375\) 7.87850e69 0.128998
\(376\) 3.51566e70 0.534984
\(377\) −6.55076e70 −0.926626
\(378\) 1.61617e70 0.212551
\(379\) 2.57732e70 0.315203 0.157601 0.987503i \(-0.449624\pi\)
0.157601 + 0.987503i \(0.449624\pi\)
\(380\) 3.23691e70 0.368198
\(381\) −6.82984e69 −0.0722726
\(382\) −9.87613e70 −0.972399
\(383\) −9.29502e69 −0.0851695 −0.0425848 0.999093i \(-0.513559\pi\)
−0.0425848 + 0.999093i \(0.513559\pi\)
\(384\) 8.35822e69 0.0712861
\(385\) 9.39825e70 0.746237
\(386\) 3.35531e70 0.248075
\(387\) −7.07974e70 −0.487490
\(388\) −2.37065e70 −0.152053
\(389\) −1.45270e71 −0.868083 −0.434042 0.900893i \(-0.642913\pi\)
−0.434042 + 0.900893i \(0.642913\pi\)
\(390\) 1.43369e70 0.0798323
\(391\) 9.37463e70 0.486512
\(392\) −3.56468e70 −0.172446
\(393\) −2.53548e70 −0.114357
\(394\) −3.05022e71 −1.28288
\(395\) 9.78781e70 0.383942
\(396\) 3.84907e71 1.40844
\(397\) −2.04970e71 −0.699762 −0.349881 0.936794i \(-0.613778\pi\)
−0.349881 + 0.936794i \(0.613778\pi\)
\(398\) −1.48936e71 −0.474478
\(399\) 1.96854e70 0.0585314
\(400\) 2.46709e71 0.684755
\(401\) 4.58836e71 1.18901 0.594507 0.804090i \(-0.297347\pi\)
0.594507 + 0.804090i \(0.297347\pi\)
\(402\) 7.79632e69 0.0188657
\(403\) 3.98443e71 0.900488
\(404\) −3.92927e70 −0.0829514
\(405\) 3.10854e71 0.613117
\(406\) −5.80130e71 −1.06920
\(407\) −8.38592e71 −1.44446
\(408\) −1.30663e70 −0.0210376
\(409\) 4.48457e71 0.675040 0.337520 0.941318i \(-0.390412\pi\)
0.337520 + 0.941318i \(0.390412\pi\)
\(410\) −1.07732e72 −1.51632
\(411\) −1.17186e71 −0.154250
\(412\) −9.15172e71 −1.12675
\(413\) −3.85564e71 −0.444090
\(414\) 1.02927e72 1.10923
\(415\) 4.65866e71 0.469827
\(416\) 9.90919e71 0.935345
\(417\) 2.55428e70 0.0225697
\(418\) 2.15131e72 1.77974
\(419\) −1.42128e72 −1.10102 −0.550510 0.834829i \(-0.685567\pi\)
−0.550510 + 0.834829i \(0.685567\pi\)
\(420\) 5.57877e70 0.0404747
\(421\) 1.37600e72 0.935105 0.467553 0.883965i \(-0.345136\pi\)
0.467553 + 0.883965i \(0.345136\pi\)
\(422\) 1.27578e72 0.812237
\(423\) −3.05577e72 −1.82289
\(424\) −2.04303e71 −0.114212
\(425\) −6.44152e71 −0.337515
\(426\) 2.98383e71 0.146558
\(427\) 2.11317e71 0.0973121
\(428\) −1.12745e72 −0.486848
\(429\) 4.18675e71 0.169552
\(430\) −1.12140e72 −0.425968
\(431\) −7.40627e71 −0.263921 −0.131961 0.991255i \(-0.542127\pi\)
−0.131961 + 0.991255i \(0.542127\pi\)
\(432\) −8.77007e71 −0.293224
\(433\) 6.68781e71 0.209830 0.104915 0.994481i \(-0.466543\pi\)
0.104915 + 0.994481i \(0.466543\pi\)
\(434\) 3.52859e72 1.03904
\(435\) 3.71254e71 0.102616
\(436\) −3.94002e72 −1.02240
\(437\) 2.52771e72 0.615869
\(438\) −1.09512e72 −0.250567
\(439\) −8.16335e70 −0.0175426 −0.00877130 0.999962i \(-0.502792\pi\)
−0.00877130 + 0.999962i \(0.502792\pi\)
\(440\) −1.68201e72 −0.339532
\(441\) 3.09839e72 0.587590
\(442\) −3.17416e72 −0.565609
\(443\) 5.10956e72 0.855620 0.427810 0.903869i \(-0.359285\pi\)
0.427810 + 0.903869i \(0.359285\pi\)
\(444\) −4.97786e71 −0.0783449
\(445\) 5.01604e72 0.742097
\(446\) 2.72717e72 0.379319
\(447\) −1.85138e71 −0.0242124
\(448\) 2.73991e72 0.336969
\(449\) 1.18229e73 1.36757 0.683783 0.729686i \(-0.260334\pi\)
0.683783 + 0.729686i \(0.260334\pi\)
\(450\) −7.07238e72 −0.769523
\(451\) −3.14607e73 −3.22042
\(452\) −5.46932e71 −0.0526776
\(453\) 9.13452e71 0.0827914
\(454\) −4.42476e72 −0.377445
\(455\) −3.73892e72 −0.300215
\(456\) −3.52310e71 −0.0266313
\(457\) 2.45595e72 0.174793 0.0873965 0.996174i \(-0.472145\pi\)
0.0873965 + 0.996174i \(0.472145\pi\)
\(458\) 1.35658e73 0.909167
\(459\) 2.28985e72 0.144530
\(460\) 7.16346e72 0.425875
\(461\) −1.10101e73 −0.616617 −0.308308 0.951286i \(-0.599763\pi\)
−0.308308 + 0.951286i \(0.599763\pi\)
\(462\) 3.70776e72 0.195640
\(463\) 1.97086e73 0.979893 0.489946 0.871753i \(-0.337016\pi\)
0.489946 + 0.871753i \(0.337016\pi\)
\(464\) 3.14805e73 1.47502
\(465\) −2.25812e72 −0.0997219
\(466\) 4.93787e71 0.0205555
\(467\) 1.75061e72 0.0687029 0.0343514 0.999410i \(-0.489063\pi\)
0.0343514 + 0.999410i \(0.489063\pi\)
\(468\) −1.53128e73 −0.566623
\(469\) −2.03320e72 −0.0709459
\(470\) −4.84020e73 −1.59284
\(471\) −5.01221e72 −0.155580
\(472\) 6.90047e72 0.202057
\(473\) −3.27478e73 −0.904692
\(474\) 3.86144e72 0.100657
\(475\) −1.73685e73 −0.427256
\(476\) −1.23513e73 −0.286762
\(477\) 1.77578e73 0.389164
\(478\) 7.21763e73 1.49323
\(479\) 2.63640e73 0.514973 0.257486 0.966282i \(-0.417106\pi\)
0.257486 + 0.966282i \(0.417106\pi\)
\(480\) −5.61589e72 −0.103582
\(481\) 3.33618e73 0.581113
\(482\) −1.41061e74 −2.32067
\(483\) 4.35648e72 0.0677002
\(484\) 1.24654e74 1.83004
\(485\) −9.00441e72 −0.124899
\(486\) 3.78128e73 0.495611
\(487\) −1.06044e74 −1.31353 −0.656764 0.754097i \(-0.728075\pi\)
−0.656764 + 0.754097i \(0.728075\pi\)
\(488\) −3.78195e72 −0.0442762
\(489\) −1.64379e73 −0.181908
\(490\) 4.90770e73 0.513435
\(491\) 1.83618e74 1.81624 0.908120 0.418709i \(-0.137517\pi\)
0.908120 + 0.418709i \(0.137517\pi\)
\(492\) −1.86749e73 −0.174670
\(493\) −8.21949e73 −0.727034
\(494\) −8.55859e73 −0.715997
\(495\) 1.46199e74 1.15691
\(496\) −1.91477e74 −1.43341
\(497\) −7.78153e73 −0.551143
\(498\) 1.83791e73 0.123174
\(499\) 5.91416e73 0.375084 0.187542 0.982257i \(-0.439948\pi\)
0.187542 + 0.982257i \(0.439948\pi\)
\(500\) −1.33286e74 −0.800038
\(501\) 1.70467e73 0.0968505
\(502\) −1.74572e74 −0.938909
\(503\) −4.36885e73 −0.222458 −0.111229 0.993795i \(-0.535479\pi\)
−0.111229 + 0.993795i \(0.535479\pi\)
\(504\) 3.74128e73 0.180377
\(505\) −1.49245e73 −0.0681375
\(506\) 4.76097e74 2.05853
\(507\) 1.42026e73 0.0581634
\(508\) 1.15545e74 0.448230
\(509\) 1.21337e74 0.445918 0.222959 0.974828i \(-0.428428\pi\)
0.222959 + 0.974828i \(0.428428\pi\)
\(510\) 1.79891e73 0.0626367
\(511\) 2.85596e74 0.942276
\(512\) −3.68179e74 −1.15116
\(513\) 6.17419e73 0.182958
\(514\) 5.33388e74 1.49816
\(515\) −3.47608e74 −0.925532
\(516\) −1.94390e73 −0.0490689
\(517\) −1.41347e75 −3.38295
\(518\) 2.95450e74 0.670526
\(519\) −7.03589e73 −0.151432
\(520\) 6.69157e73 0.136595
\(521\) −1.79330e74 −0.347228 −0.173614 0.984814i \(-0.555544\pi\)
−0.173614 + 0.984814i \(0.555544\pi\)
\(522\) −9.02448e74 −1.65761
\(523\) 9.32612e74 1.62519 0.812595 0.582828i \(-0.198054\pi\)
0.812595 + 0.582828i \(0.198054\pi\)
\(524\) 4.28945e74 0.709237
\(525\) −2.99344e73 −0.0469666
\(526\) 6.40192e74 0.953240
\(527\) 4.99942e74 0.706526
\(528\) −2.01200e74 −0.269895
\(529\) −2.25895e74 −0.287657
\(530\) 2.81275e74 0.340051
\(531\) −5.99782e74 −0.688485
\(532\) −3.33032e74 −0.363008
\(533\) 1.25160e75 1.29559
\(534\) 1.97890e74 0.194554
\(535\) −4.28238e74 −0.399904
\(536\) 3.63884e73 0.0322798
\(537\) −1.62394e73 −0.0136860
\(538\) −2.01085e75 −1.61015
\(539\) 1.43318e75 1.09046
\(540\) 1.74975e74 0.126516
\(541\) 1.34700e75 0.925643 0.462821 0.886452i \(-0.346837\pi\)
0.462821 + 0.886452i \(0.346837\pi\)
\(542\) −3.16824e75 −2.06936
\(543\) 3.26868e74 0.202945
\(544\) 1.24335e75 0.733875
\(545\) −1.49653e75 −0.839813
\(546\) −1.47506e74 −0.0787069
\(547\) 4.61467e74 0.234147 0.117074 0.993123i \(-0.462649\pi\)
0.117074 + 0.993123i \(0.462649\pi\)
\(548\) 1.98252e75 0.956649
\(549\) 3.28723e74 0.150866
\(550\) −3.27137e75 −1.42809
\(551\) −2.21625e75 −0.920343
\(552\) −7.79682e73 −0.0308030
\(553\) −1.00703e75 −0.378530
\(554\) 6.26086e75 2.23932
\(555\) −1.89073e74 −0.0643536
\(556\) −4.32126e74 −0.139976
\(557\) 6.63429e74 0.204539 0.102270 0.994757i \(-0.467390\pi\)
0.102270 + 0.994757i \(0.467390\pi\)
\(558\) 5.48905e75 1.61086
\(559\) 1.30281e75 0.363962
\(560\) 1.79679e75 0.477887
\(561\) 5.25328e74 0.133031
\(562\) −2.26165e75 −0.545351
\(563\) −5.61240e75 −1.28875 −0.644374 0.764711i \(-0.722882\pi\)
−0.644374 + 0.764711i \(0.722882\pi\)
\(564\) −8.39029e74 −0.183486
\(565\) −2.07740e74 −0.0432701
\(566\) −1.00928e76 −2.00244
\(567\) −3.19825e75 −0.604474
\(568\) 1.39267e75 0.250765
\(569\) 4.79302e75 0.822284 0.411142 0.911571i \(-0.365130\pi\)
0.411142 + 0.911571i \(0.365130\pi\)
\(570\) 4.85045e74 0.0792910
\(571\) −5.95554e74 −0.0927744 −0.0463872 0.998924i \(-0.514771\pi\)
−0.0463872 + 0.998924i \(0.514771\pi\)
\(572\) −7.08304e75 −1.05155
\(573\) −6.50261e74 −0.0920102
\(574\) 1.10841e76 1.49494
\(575\) −3.84374e75 −0.494184
\(576\) 4.26218e75 0.522413
\(577\) 1.32597e76 1.54952 0.774760 0.632255i \(-0.217870\pi\)
0.774760 + 0.632255i \(0.217870\pi\)
\(578\) 8.00355e75 0.891799
\(579\) 2.20920e74 0.0234733
\(580\) −6.28078e75 −0.636420
\(581\) −4.79310e75 −0.463204
\(582\) −3.55238e74 −0.0327444
\(583\) 8.21397e75 0.722217
\(584\) −5.11134e75 −0.428728
\(585\) −5.81625e75 −0.465432
\(586\) 3.47676e75 0.265454
\(587\) −2.33966e76 −1.70453 −0.852264 0.523112i \(-0.824771\pi\)
−0.852264 + 0.523112i \(0.824771\pi\)
\(588\) 8.50730e74 0.0591446
\(589\) 1.34801e76 0.894382
\(590\) −9.50027e75 −0.601597
\(591\) −2.00832e75 −0.121388
\(592\) −1.60325e76 −0.925024
\(593\) 2.05903e76 1.13412 0.567060 0.823677i \(-0.308081\pi\)
0.567060 + 0.823677i \(0.308081\pi\)
\(594\) 1.16291e76 0.611534
\(595\) −4.69137e75 −0.235550
\(596\) 3.13211e75 0.150164
\(597\) −9.80621e74 −0.0448960
\(598\) −1.89406e76 −0.828156
\(599\) 6.44964e75 0.269338 0.134669 0.990891i \(-0.457003\pi\)
0.134669 + 0.990891i \(0.457003\pi\)
\(600\) 5.35737e74 0.0213694
\(601\) −8.53957e75 −0.325378 −0.162689 0.986677i \(-0.552017\pi\)
−0.162689 + 0.986677i \(0.552017\pi\)
\(602\) 1.15376e76 0.419964
\(603\) −3.16284e75 −0.109989
\(604\) −1.54535e76 −0.513467
\(605\) 4.73472e76 1.50322
\(606\) −5.88794e74 −0.0178635
\(607\) −1.28402e76 −0.372292 −0.186146 0.982522i \(-0.559600\pi\)
−0.186146 + 0.982522i \(0.559600\pi\)
\(608\) 3.35247e76 0.929003
\(609\) −3.81968e75 −0.101170
\(610\) 5.20682e75 0.131826
\(611\) 5.62322e76 1.36098
\(612\) −1.92136e76 −0.444575
\(613\) −4.44481e76 −0.983310 −0.491655 0.870790i \(-0.663608\pi\)
−0.491655 + 0.870790i \(0.663608\pi\)
\(614\) −2.75098e76 −0.581911
\(615\) −7.09328e75 −0.143477
\(616\) 1.73055e76 0.334745
\(617\) −7.75771e76 −1.43513 −0.717565 0.696491i \(-0.754743\pi\)
−0.717565 + 0.696491i \(0.754743\pi\)
\(618\) −1.37137e76 −0.242645
\(619\) −5.51294e76 −0.933018 −0.466509 0.884516i \(-0.654489\pi\)
−0.466509 + 0.884516i \(0.654489\pi\)
\(620\) 3.82023e76 0.618468
\(621\) 1.36638e76 0.211618
\(622\) −3.66350e75 −0.0542826
\(623\) −5.16079e76 −0.731635
\(624\) 8.00436e75 0.108580
\(625\) −5.51891e75 −0.0716396
\(626\) 1.38218e77 1.71700
\(627\) 1.41646e76 0.168402
\(628\) 8.47953e76 0.964898
\(629\) 4.18604e76 0.455943
\(630\) −5.15083e76 −0.537046
\(631\) 4.85602e76 0.484700 0.242350 0.970189i \(-0.422082\pi\)
0.242350 + 0.970189i \(0.422082\pi\)
\(632\) 1.80228e76 0.172228
\(633\) 8.39995e75 0.0768554
\(634\) 4.47941e76 0.392434
\(635\) 4.38875e76 0.368182
\(636\) 4.87578e75 0.0391718
\(637\) −5.70163e76 −0.438697
\(638\) −4.17433e77 −3.07622
\(639\) −1.21049e77 −0.854453
\(640\) −5.37086e76 −0.363157
\(641\) 6.99794e76 0.453288 0.226644 0.973978i \(-0.427225\pi\)
0.226644 + 0.973978i \(0.427225\pi\)
\(642\) −1.68946e76 −0.104842
\(643\) 3.34658e77 1.98976 0.994878 0.101085i \(-0.0322315\pi\)
0.994878 + 0.101085i \(0.0322315\pi\)
\(644\) −7.37018e76 −0.419872
\(645\) −7.38348e75 −0.0403059
\(646\) −1.07388e77 −0.561774
\(647\) 2.48806e77 1.24736 0.623682 0.781678i \(-0.285636\pi\)
0.623682 + 0.781678i \(0.285636\pi\)
\(648\) 5.72393e76 0.275031
\(649\) −2.77433e77 −1.27770
\(650\) 1.30145e77 0.574529
\(651\) 2.32328e76 0.0983161
\(652\) 2.78092e77 1.12818
\(653\) −2.62237e77 −1.01995 −0.509977 0.860188i \(-0.670346\pi\)
−0.509977 + 0.860188i \(0.670346\pi\)
\(654\) −5.90406e76 −0.220172
\(655\) 1.62926e77 0.582578
\(656\) −6.01474e77 −2.06235
\(657\) 4.44272e77 1.46084
\(658\) 4.97988e77 1.57039
\(659\) 1.03940e77 0.314364 0.157182 0.987570i \(-0.449759\pi\)
0.157182 + 0.987570i \(0.449759\pi\)
\(660\) 4.01421e76 0.116451
\(661\) −6.71301e77 −1.86800 −0.934001 0.357271i \(-0.883707\pi\)
−0.934001 + 0.357271i \(0.883707\pi\)
\(662\) 2.15113e77 0.574212
\(663\) −2.08992e76 −0.0535190
\(664\) 8.57824e76 0.210754
\(665\) −1.26495e77 −0.298180
\(666\) 4.59601e77 1.03954
\(667\) −4.90468e77 −1.06451
\(668\) −2.88391e77 −0.600660
\(669\) 1.79562e76 0.0358918
\(670\) −5.00979e76 −0.0961086
\(671\) 1.52053e77 0.279979
\(672\) 5.77795e76 0.102122
\(673\) −6.81160e77 −1.15567 −0.577836 0.816153i \(-0.696103\pi\)
−0.577836 + 0.816153i \(0.696103\pi\)
\(674\) −4.61228e77 −0.751222
\(675\) −9.38873e76 −0.146809
\(676\) −2.40276e77 −0.360726
\(677\) 9.16173e77 1.32065 0.660327 0.750978i \(-0.270418\pi\)
0.660327 + 0.750978i \(0.270418\pi\)
\(678\) −8.19568e75 −0.0113441
\(679\) 9.26425e76 0.123138
\(680\) 8.39618e76 0.107173
\(681\) −2.91334e76 −0.0357146
\(682\) 2.53899e78 2.98945
\(683\) 4.97477e77 0.562605 0.281302 0.959619i \(-0.409234\pi\)
0.281302 + 0.959619i \(0.409234\pi\)
\(684\) −5.18063e77 −0.562781
\(685\) 7.53018e77 0.785805
\(686\) −1.35054e78 −1.35392
\(687\) 8.93193e76 0.0860271
\(688\) −6.26082e77 −0.579361
\(689\) −3.26777e77 −0.290552
\(690\) 1.07343e77 0.0917117
\(691\) −8.52274e77 −0.699734 −0.349867 0.936799i \(-0.613773\pi\)
−0.349867 + 0.936799i \(0.613773\pi\)
\(692\) 1.19031e78 0.939169
\(693\) −1.50418e78 −1.14060
\(694\) −2.88846e78 −2.10514
\(695\) −1.64134e77 −0.114978
\(696\) 6.83610e76 0.0460314
\(697\) 1.57044e78 1.01653
\(698\) −1.71389e77 −0.106650
\(699\) 3.25118e75 0.00194500
\(700\) 5.06422e77 0.291284
\(701\) 7.03498e77 0.389061 0.194530 0.980897i \(-0.437682\pi\)
0.194530 + 0.980897i \(0.437682\pi\)
\(702\) −4.62644e77 −0.246023
\(703\) 1.12870e78 0.577173
\(704\) 1.97150e78 0.969501
\(705\) −3.18687e77 −0.150718
\(706\) 1.34501e78 0.611779
\(707\) 1.53552e77 0.0671769
\(708\) −1.64683e77 −0.0693003
\(709\) 2.01205e77 0.0814455 0.0407227 0.999170i \(-0.487034\pi\)
0.0407227 + 0.999170i \(0.487034\pi\)
\(710\) −1.91736e78 −0.746620
\(711\) −1.56653e78 −0.586845
\(712\) 9.23630e77 0.332888
\(713\) 2.98323e78 1.03448
\(714\) −1.85082e77 −0.0617537
\(715\) −2.69034e78 −0.863756
\(716\) 2.74734e77 0.0848797
\(717\) 4.75221e77 0.141292
\(718\) −6.39476e78 −1.82979
\(719\) −2.93009e76 −0.00806930 −0.00403465 0.999992i \(-0.501284\pi\)
−0.00403465 + 0.999992i \(0.501284\pi\)
\(720\) 2.79507e78 0.740882
\(721\) 3.57639e78 0.912485
\(722\) 2.54250e78 0.624436
\(723\) −9.28770e77 −0.219586
\(724\) −5.52987e78 −1.25865
\(725\) 3.37012e78 0.738499
\(726\) 1.86792e78 0.394096
\(727\) −8.75892e78 −1.77932 −0.889660 0.456623i \(-0.849059\pi\)
−0.889660 + 0.456623i \(0.849059\pi\)
\(728\) −6.88467e77 −0.134670
\(729\) −4.80696e78 −0.905448
\(730\) 7.03707e78 1.27648
\(731\) 1.63469e78 0.285566
\(732\) 9.02581e76 0.0151856
\(733\) −2.53375e77 −0.0410587 −0.0205293 0.999789i \(-0.506535\pi\)
−0.0205293 + 0.999789i \(0.506535\pi\)
\(734\) −4.04340e78 −0.631109
\(735\) 3.23131e77 0.0485822
\(736\) 7.41921e78 1.07453
\(737\) −1.46299e78 −0.204120
\(738\) 1.72424e79 2.31765
\(739\) 1.48231e78 0.191963 0.0959814 0.995383i \(-0.469401\pi\)
0.0959814 + 0.995383i \(0.469401\pi\)
\(740\) 3.19869e78 0.399117
\(741\) −5.63512e77 −0.0677490
\(742\) −2.89392e78 −0.335258
\(743\) −5.63544e78 −0.629123 −0.314562 0.949237i \(-0.601857\pi\)
−0.314562 + 0.949237i \(0.601857\pi\)
\(744\) −4.15799e77 −0.0447330
\(745\) 1.18967e78 0.123347
\(746\) −1.48621e79 −1.48512
\(747\) −7.45612e78 −0.718119
\(748\) −8.88736e78 −0.825048
\(749\) 4.40595e78 0.394267
\(750\) −1.99727e78 −0.172287
\(751\) 1.33575e79 1.11078 0.555390 0.831590i \(-0.312569\pi\)
0.555390 + 0.831590i \(0.312569\pi\)
\(752\) −2.70231e79 −2.16643
\(753\) −1.14941e78 −0.0888413
\(754\) 1.66068e79 1.23758
\(755\) −5.86970e78 −0.421769
\(756\) −1.80024e78 −0.124733
\(757\) 1.85609e79 1.24011 0.620057 0.784557i \(-0.287109\pi\)
0.620057 + 0.784557i \(0.287109\pi\)
\(758\) −6.53374e78 −0.420978
\(759\) 3.13471e78 0.194782
\(760\) 2.26389e78 0.135669
\(761\) 1.97639e79 1.14234 0.571170 0.820832i \(-0.306490\pi\)
0.571170 + 0.820832i \(0.306490\pi\)
\(762\) 1.73143e78 0.0965257
\(763\) 1.53972e79 0.827974
\(764\) 1.10010e79 0.570641
\(765\) −7.29787e78 −0.365180
\(766\) 2.35638e78 0.113751
\(767\) 1.10372e79 0.514025
\(768\) −3.61203e78 −0.162300
\(769\) −3.59924e79 −1.56040 −0.780200 0.625530i \(-0.784883\pi\)
−0.780200 + 0.625530i \(0.784883\pi\)
\(770\) −2.38255e79 −0.996658
\(771\) 3.51192e78 0.141758
\(772\) −3.73746e78 −0.145580
\(773\) −2.27297e79 −0.854392 −0.427196 0.904159i \(-0.640499\pi\)
−0.427196 + 0.904159i \(0.640499\pi\)
\(774\) 1.79478e79 0.651081
\(775\) −2.04984e79 −0.717668
\(776\) −1.65803e78 −0.0560267
\(777\) 1.94529e78 0.0634464
\(778\) 3.68273e79 1.15939
\(779\) 4.23442e79 1.28681
\(780\) −1.59698e78 −0.0468487
\(781\) −5.59920e79 −1.58571
\(782\) −2.37656e79 −0.649774
\(783\) −1.19802e79 −0.316239
\(784\) 2.73999e79 0.698325
\(785\) 3.22077e79 0.792581
\(786\) 6.42767e78 0.152733
\(787\) −5.18302e79 −1.18926 −0.594632 0.803998i \(-0.702702\pi\)
−0.594632 + 0.803998i \(0.702702\pi\)
\(788\) 3.39762e79 0.752843
\(789\) 4.21514e78 0.0901974
\(790\) −2.48130e79 −0.512784
\(791\) 2.13735e78 0.0426602
\(792\) 2.69204e79 0.518965
\(793\) −6.04914e78 −0.112637
\(794\) 5.19617e79 0.934587
\(795\) 1.85196e78 0.0321763
\(796\) 1.65899e79 0.278442
\(797\) 9.77267e78 0.158456 0.0792281 0.996857i \(-0.474754\pi\)
0.0792281 + 0.996857i \(0.474754\pi\)
\(798\) −4.99042e78 −0.0781732
\(799\) 7.05567e79 1.06783
\(800\) −5.09791e79 −0.745448
\(801\) −8.02810e79 −1.13428
\(802\) −1.16319e80 −1.58802
\(803\) 2.05501e80 2.71104
\(804\) −8.68426e77 −0.0110711
\(805\) −2.79941e79 −0.344889
\(806\) −1.01009e80 −1.20267
\(807\) −1.32398e79 −0.152356
\(808\) −2.74812e78 −0.0305649
\(809\) −9.21478e79 −0.990605 −0.495302 0.868721i \(-0.664943\pi\)
−0.495302 + 0.868721i \(0.664943\pi\)
\(810\) −7.88045e79 −0.818866
\(811\) −1.39482e80 −1.40102 −0.700512 0.713640i \(-0.747045\pi\)
−0.700512 + 0.713640i \(0.747045\pi\)
\(812\) 6.46203e79 0.627449
\(813\) −2.08602e79 −0.195807
\(814\) 2.12591e80 1.92919
\(815\) 1.05627e80 0.926707
\(816\) 1.00434e79 0.0851923
\(817\) 4.40766e79 0.361494
\(818\) −1.13688e80 −0.901569
\(819\) 5.98409e79 0.458871
\(820\) 1.20002e80 0.889833
\(821\) 2.16763e80 1.55435 0.777173 0.629287i \(-0.216653\pi\)
0.777173 + 0.629287i \(0.216653\pi\)
\(822\) 2.97077e79 0.206013
\(823\) 1.36117e79 0.0912885 0.0456443 0.998958i \(-0.485466\pi\)
0.0456443 + 0.998958i \(0.485466\pi\)
\(824\) −6.40070e79 −0.415173
\(825\) −2.15393e79 −0.135129
\(826\) 9.77442e79 0.593116
\(827\) −2.71679e80 −1.59461 −0.797304 0.603578i \(-0.793741\pi\)
−0.797304 + 0.603578i \(0.793741\pi\)
\(828\) −1.14650e80 −0.650939
\(829\) −4.14313e79 −0.227551 −0.113775 0.993506i \(-0.536294\pi\)
−0.113775 + 0.993506i \(0.536294\pi\)
\(830\) −1.18101e80 −0.627491
\(831\) 4.12226e79 0.211888
\(832\) −7.84324e79 −0.390036
\(833\) −7.15406e79 −0.344203
\(834\) −6.47534e78 −0.0301437
\(835\) −1.09539e80 −0.493391
\(836\) −2.39633e80 −1.04442
\(837\) 7.28683e79 0.307318
\(838\) 3.60309e80 1.47050
\(839\) 2.91878e80 1.15278 0.576392 0.817173i \(-0.304460\pi\)
0.576392 + 0.817173i \(0.304460\pi\)
\(840\) 3.90179e78 0.0149136
\(841\) 1.59706e80 0.590787
\(842\) −3.48829e80 −1.24891
\(843\) −1.48911e79 −0.0516022
\(844\) −1.42108e80 −0.476652
\(845\) −9.12638e79 −0.296305
\(846\) 7.74668e80 2.43462
\(847\) −4.87135e80 −1.48203
\(848\) 1.57037e80 0.462505
\(849\) −6.64526e79 −0.189474
\(850\) 1.63299e80 0.450777
\(851\) 2.49787e80 0.667585
\(852\) −3.32367e79 −0.0860060
\(853\) −1.94977e80 −0.488523 −0.244262 0.969709i \(-0.578546\pi\)
−0.244262 + 0.969709i \(0.578546\pi\)
\(854\) −5.35707e79 −0.129968
\(855\) −1.96775e80 −0.462277
\(856\) −7.88537e79 −0.179388
\(857\) 5.30574e80 1.16889 0.584444 0.811434i \(-0.301313\pi\)
0.584444 + 0.811434i \(0.301313\pi\)
\(858\) −1.06138e80 −0.226449
\(859\) −3.08064e80 −0.636545 −0.318272 0.947999i \(-0.603103\pi\)
−0.318272 + 0.947999i \(0.603103\pi\)
\(860\) 1.24912e80 0.249975
\(861\) 7.29797e79 0.141454
\(862\) 1.87756e80 0.352488
\(863\) −7.74696e80 −1.40875 −0.704376 0.709827i \(-0.748773\pi\)
−0.704376 + 0.709827i \(0.748773\pi\)
\(864\) 1.81222e80 0.319214
\(865\) 4.52115e80 0.771447
\(866\) −1.69542e80 −0.280244
\(867\) 5.26967e79 0.0843837
\(868\) −3.93047e80 −0.609750
\(869\) −7.24606e80 −1.08908
\(870\) −9.41165e79 −0.137052
\(871\) 5.82024e79 0.0821186
\(872\) −2.75565e80 −0.376721
\(873\) 1.44114e80 0.190904
\(874\) −6.40799e80 −0.822541
\(875\) 5.20869e80 0.647899
\(876\) 1.21985e80 0.147042
\(877\) 1.11936e81 1.30762 0.653809 0.756659i \(-0.273170\pi\)
0.653809 + 0.756659i \(0.273170\pi\)
\(878\) 2.06949e79 0.0234295
\(879\) 2.28916e79 0.0251178
\(880\) 1.29288e81 1.37494
\(881\) 9.53097e80 0.982425 0.491213 0.871040i \(-0.336554\pi\)
0.491213 + 0.871040i \(0.336554\pi\)
\(882\) −7.85470e80 −0.784772
\(883\) 1.42786e81 1.38282 0.691409 0.722463i \(-0.256990\pi\)
0.691409 + 0.722463i \(0.256990\pi\)
\(884\) 3.53567e80 0.331921
\(885\) −6.25514e79 −0.0569242
\(886\) −1.29532e81 −1.14275
\(887\) −6.03898e80 −0.516492 −0.258246 0.966079i \(-0.583145\pi\)
−0.258246 + 0.966079i \(0.583145\pi\)
\(888\) −3.48151e79 −0.0288676
\(889\) −4.51539e80 −0.362992
\(890\) −1.27161e81 −0.991128
\(891\) −2.30130e81 −1.73915
\(892\) −3.03778e80 −0.222599
\(893\) 1.90244e81 1.35175
\(894\) 4.69342e79 0.0323376
\(895\) 1.04352e80 0.0697214
\(896\) 5.52585e80 0.358038
\(897\) −1.24708e80 −0.0783617
\(898\) −2.99721e81 −1.82649
\(899\) −2.61563e81 −1.54591
\(900\) 7.87787e80 0.451586
\(901\) −4.10020e80 −0.227968
\(902\) 7.97557e81 4.30112
\(903\) 7.59655e79 0.0397377
\(904\) −3.82523e79 −0.0194100
\(905\) −2.10040e81 −1.03387
\(906\) −2.31569e80 −0.110574
\(907\) 2.59302e81 1.20117 0.600587 0.799559i \(-0.294934\pi\)
0.600587 + 0.799559i \(0.294934\pi\)
\(908\) 4.92871e80 0.221499
\(909\) 2.38864e80 0.104146
\(910\) 9.47852e80 0.400961
\(911\) 6.45047e80 0.264750 0.132375 0.991200i \(-0.457740\pi\)
0.132375 + 0.991200i \(0.457740\pi\)
\(912\) 2.70803e80 0.107844
\(913\) −3.44887e81 −1.33269
\(914\) −6.22606e80 −0.233450
\(915\) 3.42826e79 0.0124737
\(916\) −1.51108e81 −0.533534
\(917\) −1.67627e81 −0.574365
\(918\) −5.80498e80 −0.193031
\(919\) 6.10099e80 0.196890 0.0984450 0.995142i \(-0.468613\pi\)
0.0984450 + 0.995142i \(0.468613\pi\)
\(920\) 5.01012e80 0.156922
\(921\) −1.81129e80 −0.0550615
\(922\) 2.79116e81 0.823540
\(923\) 2.22754e81 0.637938
\(924\) −4.13004e80 −0.114809
\(925\) −1.71634e81 −0.463133
\(926\) −4.99632e81 −1.30872
\(927\) 5.56342e81 1.41465
\(928\) −6.50502e81 −1.60576
\(929\) 2.88980e81 0.692524 0.346262 0.938138i \(-0.387451\pi\)
0.346262 + 0.938138i \(0.387451\pi\)
\(930\) 5.72454e80 0.133186
\(931\) −1.92897e81 −0.435723
\(932\) −5.50026e79 −0.0120627
\(933\) −2.41211e79 −0.00513632
\(934\) −4.43796e80 −0.0917580
\(935\) −3.37567e81 −0.677706
\(936\) −1.07098e81 −0.208783
\(937\) 4.29454e81 0.812976 0.406488 0.913656i \(-0.366753\pi\)
0.406488 + 0.913656i \(0.366753\pi\)
\(938\) 5.15436e80 0.0947538
\(939\) 9.10049e80 0.162465
\(940\) 5.39147e81 0.934741
\(941\) −4.72249e80 −0.0795164 −0.0397582 0.999209i \(-0.512659\pi\)
−0.0397582 + 0.999209i \(0.512659\pi\)
\(942\) 1.27064e81 0.207790
\(943\) 9.37101e81 1.48838
\(944\) −5.30404e81 −0.818233
\(945\) −6.83783e80 −0.102457
\(946\) 8.30187e81 1.20829
\(947\) −1.72711e81 −0.244171 −0.122086 0.992520i \(-0.538958\pi\)
−0.122086 + 0.992520i \(0.538958\pi\)
\(948\) −4.30124e80 −0.0590696
\(949\) −8.17547e81 −1.09067
\(950\) 4.40308e81 0.570633
\(951\) 2.94932e80 0.0371328
\(952\) −8.63847e80 −0.105662
\(953\) −8.99783e81 −1.06926 −0.534629 0.845087i \(-0.679549\pi\)
−0.534629 + 0.845087i \(0.679549\pi\)
\(954\) −4.50176e81 −0.519759
\(955\) 4.17848e81 0.468733
\(956\) −8.03967e81 −0.876287
\(957\) −2.74845e81 −0.291078
\(958\) −6.68352e81 −0.687786
\(959\) −7.74748e81 −0.774727
\(960\) 4.44504e80 0.0431933
\(961\) 5.31940e81 0.502308
\(962\) −8.45754e81 −0.776122
\(963\) 6.85388e81 0.611243
\(964\) 1.57127e82 1.36186
\(965\) −1.41959e81 −0.119581
\(966\) −1.10441e81 −0.0904188
\(967\) 7.38949e81 0.588012 0.294006 0.955804i \(-0.405011\pi\)
0.294006 + 0.955804i \(0.405011\pi\)
\(968\) 8.71830e81 0.674310
\(969\) −7.07061e80 −0.0531561
\(970\) 2.28270e81 0.166812
\(971\) 1.41189e82 1.00293 0.501467 0.865177i \(-0.332794\pi\)
0.501467 + 0.865177i \(0.332794\pi\)
\(972\) −4.21194e81 −0.290844
\(973\) 1.68870e81 0.113358
\(974\) 2.68831e82 1.75432
\(975\) 8.56900e80 0.0543630
\(976\) 2.90699e81 0.179297
\(977\) −2.95152e82 −1.76989 −0.884944 0.465698i \(-0.845803\pi\)
−0.884944 + 0.465698i \(0.845803\pi\)
\(978\) 4.16716e81 0.242953
\(979\) −3.71344e82 −2.10500
\(980\) −5.46665e81 −0.301304
\(981\) 2.39518e82 1.28363
\(982\) −4.65488e82 −2.42573
\(983\) −5.45113e80 −0.0276226 −0.0138113 0.999905i \(-0.504396\pi\)
−0.0138113 + 0.999905i \(0.504396\pi\)
\(984\) −1.30612e81 −0.0643604
\(985\) 1.29051e82 0.618396
\(986\) 2.08372e82 0.971010
\(987\) 3.27884e81 0.148593
\(988\) 9.53336e81 0.420175
\(989\) 9.75440e81 0.418122
\(990\) −3.70628e82 −1.54515
\(991\) −3.10771e82 −1.26013 −0.630065 0.776542i \(-0.716972\pi\)
−0.630065 + 0.776542i \(0.716972\pi\)
\(992\) 3.95661e82 1.56046
\(993\) 1.41634e81 0.0543330
\(994\) 1.97269e82 0.736094
\(995\) 6.30132e81 0.228716
\(996\) −2.04724e81 −0.0722831
\(997\) −2.32086e82 −0.797134 −0.398567 0.917139i \(-0.630492\pi\)
−0.398567 + 0.917139i \(0.630492\pi\)
\(998\) −1.49930e82 −0.500954
\(999\) 6.10129e81 0.198322
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 \(a_p\))