Properties

Label 5.34.a.a.1.3
Level 5
Weight 34
Character 5.1
Self dual Yes
Analytic conductor 34.491
Analytic rank 1
Dimension 5
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(34.4914144405\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(117.007\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+5627.97 q^{2} -1.24605e8 q^{3} -8.55826e9 q^{4} -1.52588e11 q^{5} -7.01272e11 q^{6} +7.01560e13 q^{7} -9.65096e13 q^{8} +9.96727e15 q^{9} +O(q^{10})\) \(q+5627.97 q^{2} -1.24605e8 q^{3} -8.55826e9 q^{4} -1.52588e11 q^{5} -7.01272e11 q^{6} +7.01560e13 q^{7} -9.65096e13 q^{8} +9.96727e15 q^{9} -8.58760e14 q^{10} +9.39806e16 q^{11} +1.06640e18 q^{12} +9.95093e17 q^{13} +3.94836e17 q^{14} +1.90132e19 q^{15} +7.29717e19 q^{16} -2.59085e20 q^{17} +5.60955e19 q^{18} -1.31117e21 q^{19} +1.30589e21 q^{20} -8.74176e21 q^{21} +5.28920e20 q^{22} +5.44854e22 q^{23} +1.20255e22 q^{24} +2.32831e22 q^{25} +5.60036e21 q^{26} -5.49284e23 q^{27} -6.00413e23 q^{28} -9.77301e23 q^{29} +1.07006e23 q^{30} +6.82815e24 q^{31} +1.23969e24 q^{32} -1.17104e25 q^{33} -1.45812e24 q^{34} -1.07050e25 q^{35} -8.53025e25 q^{36} -7.50351e25 q^{37} -7.37925e24 q^{38} -1.23993e26 q^{39} +1.47262e25 q^{40} -2.94248e25 q^{41} -4.91984e25 q^{42} -1.00868e27 q^{43} -8.04311e26 q^{44} -1.52088e27 q^{45} +3.06642e26 q^{46} +1.91365e27 q^{47} -9.09262e27 q^{48} -2.80913e27 q^{49} +1.31036e26 q^{50} +3.22832e28 q^{51} -8.51627e27 q^{52} +4.33344e28 q^{53} -3.09135e27 q^{54} -1.43403e28 q^{55} -6.77072e27 q^{56} +1.63379e29 q^{57} -5.50022e27 q^{58} -1.21137e29 q^{59} -1.62720e29 q^{60} +4.03792e29 q^{61} +3.84287e28 q^{62} +6.99264e29 q^{63} -6.19846e29 q^{64} -1.51839e29 q^{65} -6.59060e28 q^{66} -1.33311e30 q^{67} +2.21732e30 q^{68} -6.78914e30 q^{69} -6.02472e28 q^{70} -4.10877e30 q^{71} -9.61937e29 q^{72} +8.64070e30 q^{73} -4.22295e29 q^{74} -2.90118e30 q^{75} +1.12214e31 q^{76} +6.59330e30 q^{77} -6.97831e29 q^{78} -1.76553e31 q^{79} -1.11346e31 q^{80} +1.30347e31 q^{81} -1.65602e29 q^{82} -6.43615e30 q^{83} +7.48143e31 q^{84} +3.95332e31 q^{85} -5.67680e30 q^{86} +1.21776e32 q^{87} -9.07003e30 q^{88} +1.32441e32 q^{89} -8.55950e30 q^{90} +6.98117e31 q^{91} -4.66300e32 q^{92} -8.50820e32 q^{93} +1.07700e31 q^{94} +2.00069e32 q^{95} -1.54472e32 q^{96} +2.90988e32 q^{97} -1.58097e31 q^{98} +9.36730e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} + O(q^{10}) \) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} - 4649658203125000q^{10} - 287801801877976640q^{11} - 405379955363513088q^{12} + 2397201150889907466q^{13} + 11676449916272482320q^{14} + 2287096252441406250q^{15} - 89180089543245957120q^{16} - \)\(30\!\cdots\!18\)\(q^{17} + \)\(53\!\cdots\!56\)\(q^{18} + \)\(91\!\cdots\!00\)\(q^{19} - \)\(17\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!40\)\(q^{21} - \)\(13\!\cdots\!96\)\(q^{22} + \)\(55\!\cdots\!46\)\(q^{23} - \)\(71\!\cdots\!00\)\(q^{24} + \)\(11\!\cdots\!25\)\(q^{25} - \)\(42\!\cdots\!40\)\(q^{26} + \)\(67\!\cdots\!00\)\(q^{27} - \)\(13\!\cdots\!36\)\(q^{28} - \)\(92\!\cdots\!50\)\(q^{29} - \)\(19\!\cdots\!00\)\(q^{30} - \)\(13\!\cdots\!40\)\(q^{31} - \)\(81\!\cdots\!08\)\(q^{32} - \)\(33\!\cdots\!48\)\(q^{33} - \)\(68\!\cdots\!80\)\(q^{34} + \)\(99\!\cdots\!50\)\(q^{35} - \)\(18\!\cdots\!20\)\(q^{36} - \)\(14\!\cdots\!38\)\(q^{37} - \)\(33\!\cdots\!00\)\(q^{38} - \)\(78\!\cdots\!20\)\(q^{39} - \)\(23\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!90\)\(q^{41} - \)\(26\!\cdots\!36\)\(q^{42} - \)\(23\!\cdots\!94\)\(q^{43} - \)\(18\!\cdots\!80\)\(q^{44} - \)\(22\!\cdots\!25\)\(q^{45} - \)\(28\!\cdots\!40\)\(q^{46} - \)\(77\!\cdots\!98\)\(q^{47} - \)\(73\!\cdots\!04\)\(q^{48} + \)\(41\!\cdots\!85\)\(q^{49} + \)\(70\!\cdots\!00\)\(q^{50} + \)\(73\!\cdots\!60\)\(q^{51} + \)\(48\!\cdots\!72\)\(q^{52} + \)\(10\!\cdots\!86\)\(q^{53} + \)\(64\!\cdots\!00\)\(q^{54} + \)\(43\!\cdots\!00\)\(q^{55} + \)\(14\!\cdots\!00\)\(q^{56} + \)\(20\!\cdots\!00\)\(q^{57} + \)\(21\!\cdots\!00\)\(q^{58} + \)\(25\!\cdots\!00\)\(q^{59} + \)\(61\!\cdots\!00\)\(q^{60} + \)\(74\!\cdots\!10\)\(q^{61} + \)\(53\!\cdots\!24\)\(q^{62} - \)\(10\!\cdots\!34\)\(q^{63} - \)\(10\!\cdots\!40\)\(q^{64} - \)\(36\!\cdots\!50\)\(q^{65} - \)\(33\!\cdots\!80\)\(q^{66} - \)\(37\!\cdots\!18\)\(q^{67} + \)\(11\!\cdots\!44\)\(q^{68} - \)\(27\!\cdots\!20\)\(q^{69} - \)\(17\!\cdots\!00\)\(q^{70} - \)\(55\!\cdots\!40\)\(q^{71} - \)\(15\!\cdots\!00\)\(q^{72} - \)\(13\!\cdots\!54\)\(q^{73} - \)\(36\!\cdots\!80\)\(q^{74} - \)\(34\!\cdots\!50\)\(q^{75} + \)\(71\!\cdots\!00\)\(q^{76} + \)\(47\!\cdots\!44\)\(q^{77} + \)\(12\!\cdots\!72\)\(q^{78} - \)\(10\!\cdots\!00\)\(q^{79} + \)\(13\!\cdots\!00\)\(q^{80} + \)\(78\!\cdots\!05\)\(q^{81} + \)\(27\!\cdots\!84\)\(q^{82} + \)\(92\!\cdots\!26\)\(q^{83} + \)\(17\!\cdots\!20\)\(q^{84} + \)\(47\!\cdots\!50\)\(q^{85} + \)\(65\!\cdots\!60\)\(q^{86} + \)\(13\!\cdots\!00\)\(q^{87} + \)\(19\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!50\)\(q^{89} - \)\(82\!\cdots\!00\)\(q^{90} - \)\(26\!\cdots\!40\)\(q^{91} - \)\(69\!\cdots\!68\)\(q^{92} - \)\(69\!\cdots\!88\)\(q^{93} - \)\(36\!\cdots\!80\)\(q^{94} - \)\(14\!\cdots\!00\)\(q^{95} - \)\(34\!\cdots\!40\)\(q^{96} - \)\(86\!\cdots\!98\)\(q^{97} - \)\(19\!\cdots\!96\)\(q^{98} - \)\(17\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5627.97 0.0607235 0.0303618 0.999539i \(-0.490334\pi\)
0.0303618 + 0.999539i \(0.490334\pi\)
\(3\) −1.24605e8 −1.67122 −0.835610 0.549323i \(-0.814886\pi\)
−0.835610 + 0.549323i \(0.814886\pi\)
\(4\) −8.55826e9 −0.996313
\(5\) −1.52588e11 −0.447214
\(6\) −7.01272e11 −0.101482
\(7\) 7.01560e13 0.797897 0.398949 0.916973i \(-0.369375\pi\)
0.398949 + 0.916973i \(0.369375\pi\)
\(8\) −9.65096e13 −0.121223
\(9\) 9.96727e15 1.79298
\(10\) −8.58760e14 −0.0271564
\(11\) 9.39806e16 0.616679 0.308339 0.951276i \(-0.400227\pi\)
0.308339 + 0.951276i \(0.400227\pi\)
\(12\) 1.06640e18 1.66506
\(13\) 9.95093e17 0.414761 0.207381 0.978260i \(-0.433506\pi\)
0.207381 + 0.978260i \(0.433506\pi\)
\(14\) 3.94836e17 0.0484511
\(15\) 1.90132e19 0.747392
\(16\) 7.29717e19 0.988952
\(17\) −2.59085e20 −1.29132 −0.645662 0.763624i \(-0.723418\pi\)
−0.645662 + 0.763624i \(0.723418\pi\)
\(18\) 5.60955e19 0.108876
\(19\) −1.31117e21 −1.04286 −0.521430 0.853294i \(-0.674601\pi\)
−0.521430 + 0.853294i \(0.674601\pi\)
\(20\) 1.30589e21 0.445565
\(21\) −8.74176e21 −1.33346
\(22\) 5.28920e20 0.0374469
\(23\) 5.44854e22 1.85255 0.926277 0.376843i \(-0.122990\pi\)
0.926277 + 0.376843i \(0.122990\pi\)
\(24\) 1.20255e22 0.202591
\(25\) 2.32831e22 0.200000
\(26\) 5.60036e21 0.0251858
\(27\) −5.49284e23 −1.32524
\(28\) −6.00413e23 −0.794955
\(29\) −9.77301e23 −0.725206 −0.362603 0.931944i \(-0.618112\pi\)
−0.362603 + 0.931944i \(0.618112\pi\)
\(30\) 1.07006e23 0.0453843
\(31\) 6.82815e24 1.68591 0.842957 0.537981i \(-0.180813\pi\)
0.842957 + 0.537981i \(0.180813\pi\)
\(32\) 1.23969e24 0.181276
\(33\) −1.17104e25 −1.03061
\(34\) −1.45812e24 −0.0784137
\(35\) −1.07050e25 −0.356831
\(36\) −8.53025e25 −1.78637
\(37\) −7.50351e25 −0.999852 −0.499926 0.866068i \(-0.666640\pi\)
−0.499926 + 0.866068i \(0.666640\pi\)
\(38\) −7.37925e24 −0.0633262
\(39\) −1.23993e26 −0.693158
\(40\) 1.47262e25 0.0542126
\(41\) −2.94248e25 −0.0720741 −0.0360371 0.999350i \(-0.511473\pi\)
−0.0360371 + 0.999350i \(0.511473\pi\)
\(42\) −4.91984e25 −0.0809725
\(43\) −1.00868e27 −1.12596 −0.562979 0.826471i \(-0.690345\pi\)
−0.562979 + 0.826471i \(0.690345\pi\)
\(44\) −8.04311e26 −0.614405
\(45\) −1.52088e27 −0.801844
\(46\) 3.06642e26 0.112494
\(47\) 1.91365e27 0.492321 0.246160 0.969229i \(-0.420831\pi\)
0.246160 + 0.969229i \(0.420831\pi\)
\(48\) −9.09262e27 −1.65276
\(49\) −2.80913e27 −0.363360
\(50\) 1.31036e26 0.0121447
\(51\) 3.22832e28 2.15809
\(52\) −8.51627e27 −0.413232
\(53\) 4.33344e28 1.53561 0.767804 0.640684i \(-0.221349\pi\)
0.767804 + 0.640684i \(0.221349\pi\)
\(54\) −3.09135e27 −0.0804733
\(55\) −1.43403e28 −0.275787
\(56\) −6.77072e27 −0.0967236
\(57\) 1.63379e29 1.74285
\(58\) −5.50022e27 −0.0440371
\(59\) −1.21137e29 −0.731507 −0.365754 0.930712i \(-0.619189\pi\)
−0.365754 + 0.930712i \(0.619189\pi\)
\(60\) −1.62720e29 −0.744637
\(61\) 4.03792e29 1.40674 0.703372 0.710822i \(-0.251677\pi\)
0.703372 + 0.710822i \(0.251677\pi\)
\(62\) 3.84287e28 0.102375
\(63\) 6.99264e29 1.43061
\(64\) −6.19846e29 −0.977944
\(65\) −1.51839e29 −0.185487
\(66\) −6.59060e28 −0.0625821
\(67\) −1.33311e30 −0.987713 −0.493856 0.869543i \(-0.664413\pi\)
−0.493856 + 0.869543i \(0.664413\pi\)
\(68\) 2.21732e30 1.28656
\(69\) −6.78914e30 −3.09603
\(70\) −6.02472e28 −0.0216680
\(71\) −4.10877e30 −1.16936 −0.584681 0.811263i \(-0.698780\pi\)
−0.584681 + 0.811263i \(0.698780\pi\)
\(72\) −9.61937e29 −0.217350
\(73\) 8.64070e30 1.55497 0.777484 0.628902i \(-0.216495\pi\)
0.777484 + 0.628902i \(0.216495\pi\)
\(74\) −4.22295e29 −0.0607146
\(75\) −2.90118e30 −0.334244
\(76\) 1.12214e31 1.03901
\(77\) 6.59330e30 0.492046
\(78\) −6.97831e29 −0.0420910
\(79\) −1.76553e31 −0.863033 −0.431516 0.902105i \(-0.642021\pi\)
−0.431516 + 0.902105i \(0.642021\pi\)
\(80\) −1.11346e31 −0.442273
\(81\) 1.30347e31 0.421790
\(82\) −1.65602e29 −0.00437659
\(83\) −6.43615e30 −0.139264 −0.0696318 0.997573i \(-0.522182\pi\)
−0.0696318 + 0.997573i \(0.522182\pi\)
\(84\) 7.48143e31 1.32855
\(85\) 3.95332e31 0.577497
\(86\) −5.67680e30 −0.0683722
\(87\) 1.21776e32 1.21198
\(88\) −9.07003e30 −0.0747558
\(89\) 1.32441e32 0.905911 0.452956 0.891533i \(-0.350370\pi\)
0.452956 + 0.891533i \(0.350370\pi\)
\(90\) −8.55950e30 −0.0486908
\(91\) 6.98117e31 0.330937
\(92\) −4.66300e32 −1.84572
\(93\) −8.50820e32 −2.81753
\(94\) 1.07700e31 0.0298955
\(95\) 2.00069e32 0.466381
\(96\) −1.54472e32 −0.302952
\(97\) 2.90988e32 0.480996 0.240498 0.970650i \(-0.422689\pi\)
0.240498 + 0.970650i \(0.422689\pi\)
\(98\) −1.58097e31 −0.0220645
\(99\) 9.36730e32 1.10569
\(100\) −1.99263e32 −0.199263
\(101\) −2.11490e33 −1.79468 −0.897341 0.441338i \(-0.854504\pi\)
−0.897341 + 0.441338i \(0.854504\pi\)
\(102\) 1.81689e32 0.131047
\(103\) 9.19643e32 0.564684 0.282342 0.959314i \(-0.408889\pi\)
0.282342 + 0.959314i \(0.408889\pi\)
\(104\) −9.60360e31 −0.0502787
\(105\) 1.33389e33 0.596342
\(106\) 2.43885e32 0.0932476
\(107\) −3.10653e33 −1.01729 −0.508644 0.860977i \(-0.669853\pi\)
−0.508644 + 0.860977i \(0.669853\pi\)
\(108\) 4.70091e33 1.32035
\(109\) −4.33103e33 −1.04485 −0.522425 0.852685i \(-0.674972\pi\)
−0.522425 + 0.852685i \(0.674972\pi\)
\(110\) −8.07069e31 −0.0167468
\(111\) 9.34972e33 1.67097
\(112\) 5.11940e33 0.789082
\(113\) 1.60843e33 0.214096 0.107048 0.994254i \(-0.465860\pi\)
0.107048 + 0.994254i \(0.465860\pi\)
\(114\) 9.19490e32 0.105832
\(115\) −8.31381e33 −0.828487
\(116\) 8.36400e33 0.722532
\(117\) 9.91836e33 0.743658
\(118\) −6.81756e32 −0.0444197
\(119\) −1.81764e34 −1.03034
\(120\) −1.83495e33 −0.0906013
\(121\) −1.43928e34 −0.619707
\(122\) 2.27253e33 0.0854225
\(123\) 3.66646e33 0.120452
\(124\) −5.84371e34 −1.67970
\(125\) −3.55271e33 −0.0894427
\(126\) 3.93544e33 0.0868718
\(127\) −6.65683e34 −1.28975 −0.644876 0.764287i \(-0.723091\pi\)
−0.644876 + 0.764287i \(0.723091\pi\)
\(128\) −1.41374e34 −0.240660
\(129\) 1.25686e35 1.88173
\(130\) −8.54547e32 −0.0112634
\(131\) −3.69750e34 −0.429469 −0.214734 0.976672i \(-0.568889\pi\)
−0.214734 + 0.976672i \(0.568889\pi\)
\(132\) 1.00221e35 1.02681
\(133\) −9.19867e34 −0.832095
\(134\) −7.50269e33 −0.0599774
\(135\) 8.38140e34 0.592665
\(136\) 2.50042e34 0.156538
\(137\) −1.76237e34 −0.0977705 −0.0488853 0.998804i \(-0.515567\pi\)
−0.0488853 + 0.998804i \(0.515567\pi\)
\(138\) −3.82091e34 −0.188002
\(139\) 1.00540e35 0.439130 0.219565 0.975598i \(-0.429536\pi\)
0.219565 + 0.975598i \(0.429536\pi\)
\(140\) 9.16158e34 0.355515
\(141\) −2.38450e35 −0.822776
\(142\) −2.31240e34 −0.0710078
\(143\) 9.35195e34 0.255775
\(144\) 7.27329e35 1.77317
\(145\) 1.49124e35 0.324322
\(146\) 4.86296e34 0.0944232
\(147\) 3.50031e35 0.607254
\(148\) 6.42170e35 0.996165
\(149\) −1.14557e36 −1.59019 −0.795093 0.606487i \(-0.792578\pi\)
−0.795093 + 0.606487i \(0.792578\pi\)
\(150\) −1.63278e34 −0.0202965
\(151\) −6.40257e35 −0.713239 −0.356619 0.934250i \(-0.616071\pi\)
−0.356619 + 0.934250i \(0.616071\pi\)
\(152\) 1.26541e35 0.126419
\(153\) −2.58237e36 −2.31531
\(154\) 3.71069e34 0.0298788
\(155\) −1.04189e36 −0.753964
\(156\) 1.06117e36 0.690602
\(157\) 1.01110e36 0.592172 0.296086 0.955161i \(-0.404319\pi\)
0.296086 + 0.955161i \(0.404319\pi\)
\(158\) −9.93633e34 −0.0524064
\(159\) −5.39967e36 −2.56634
\(160\) −1.89162e35 −0.0810690
\(161\) 3.82248e36 1.47815
\(162\) 7.33587e34 0.0256126
\(163\) 4.84374e36 1.52786 0.763932 0.645296i \(-0.223266\pi\)
0.763932 + 0.645296i \(0.223266\pi\)
\(164\) 2.51825e35 0.0718083
\(165\) 1.78687e36 0.460901
\(166\) −3.62225e34 −0.00845658
\(167\) 1.75726e36 0.371548 0.185774 0.982593i \(-0.440521\pi\)
0.185774 + 0.982593i \(0.440521\pi\)
\(168\) 8.43664e35 0.161647
\(169\) −4.76592e36 −0.827973
\(170\) 2.22492e35 0.0350677
\(171\) −1.30688e37 −1.86982
\(172\) 8.63252e36 1.12181
\(173\) 1.04480e36 0.123388 0.0616942 0.998095i \(-0.480350\pi\)
0.0616942 + 0.998095i \(0.480350\pi\)
\(174\) 6.85354e35 0.0735957
\(175\) 1.63345e36 0.159579
\(176\) 6.85793e36 0.609866
\(177\) 1.50942e37 1.22251
\(178\) 7.45372e35 0.0550101
\(179\) 6.89417e36 0.463881 0.231941 0.972730i \(-0.425492\pi\)
0.231941 + 0.972730i \(0.425492\pi\)
\(180\) 1.30161e37 0.798887
\(181\) 2.73403e36 0.153146 0.0765732 0.997064i \(-0.475602\pi\)
0.0765732 + 0.997064i \(0.475602\pi\)
\(182\) 3.92898e35 0.0200957
\(183\) −5.03143e37 −2.35098
\(184\) −5.25836e36 −0.224572
\(185\) 1.14494e37 0.447148
\(186\) −4.78839e36 −0.171091
\(187\) −2.43490e37 −0.796332
\(188\) −1.63775e37 −0.490505
\(189\) −3.85355e37 −1.05741
\(190\) 1.12598e36 0.0283203
\(191\) −7.33764e37 −1.69241 −0.846206 0.532856i \(-0.821119\pi\)
−0.846206 + 0.532856i \(0.821119\pi\)
\(192\) 7.72357e37 1.63436
\(193\) −3.39286e37 −0.658978 −0.329489 0.944159i \(-0.606876\pi\)
−0.329489 + 0.944159i \(0.606876\pi\)
\(194\) 1.63767e36 0.0292078
\(195\) 1.89199e37 0.309990
\(196\) 2.40413e37 0.362020
\(197\) 1.22669e38 1.69841 0.849205 0.528063i \(-0.177081\pi\)
0.849205 + 0.528063i \(0.177081\pi\)
\(198\) 5.27189e36 0.0671415
\(199\) −4.90395e37 −0.574738 −0.287369 0.957820i \(-0.592781\pi\)
−0.287369 + 0.957820i \(0.592781\pi\)
\(200\) −2.24704e36 −0.0242446
\(201\) 1.66111e38 1.65069
\(202\) −1.19026e37 −0.108979
\(203\) −6.85635e37 −0.578640
\(204\) −2.76288e38 −2.15013
\(205\) 4.48986e36 0.0322325
\(206\) 5.17573e36 0.0342896
\(207\) 5.43071e38 3.32159
\(208\) 7.26137e37 0.410179
\(209\) −1.23225e38 −0.643110
\(210\) 7.50708e36 0.0362120
\(211\) −2.26597e38 −1.01063 −0.505316 0.862934i \(-0.668624\pi\)
−0.505316 + 0.862934i \(0.668624\pi\)
\(212\) −3.70867e38 −1.52995
\(213\) 5.11972e38 1.95426
\(214\) −1.74835e37 −0.0617733
\(215\) 1.53912e38 0.503544
\(216\) 5.30111e37 0.160650
\(217\) 4.79036e38 1.34519
\(218\) −2.43749e37 −0.0634469
\(219\) −1.07667e39 −2.59870
\(220\) 1.22728e38 0.274770
\(221\) −2.57814e38 −0.535591
\(222\) 5.26200e37 0.101467
\(223\) −7.70736e38 −1.37999 −0.689994 0.723815i \(-0.742387\pi\)
−0.689994 + 0.723815i \(0.742387\pi\)
\(224\) 8.69719e37 0.144639
\(225\) 2.32069e38 0.358595
\(226\) 9.05221e36 0.0130007
\(227\) 3.75970e38 0.502026 0.251013 0.967984i \(-0.419236\pi\)
0.251013 + 0.967984i \(0.419236\pi\)
\(228\) −1.39824e39 −1.73642
\(229\) 8.87055e38 1.02486 0.512431 0.858729i \(-0.328745\pi\)
0.512431 + 0.858729i \(0.328745\pi\)
\(230\) −4.67899e37 −0.0503087
\(231\) −8.21557e38 −0.822318
\(232\) 9.43189e37 0.0879118
\(233\) −9.06227e38 −0.786800 −0.393400 0.919367i \(-0.628701\pi\)
−0.393400 + 0.919367i \(0.628701\pi\)
\(234\) 5.58203e37 0.0451575
\(235\) −2.92000e38 −0.220173
\(236\) 1.03672e39 0.728810
\(237\) 2.19993e39 1.44232
\(238\) −1.02296e38 −0.0625661
\(239\) 2.67931e39 1.52918 0.764589 0.644518i \(-0.222942\pi\)
0.764589 + 0.644518i \(0.222942\pi\)
\(240\) 1.38742e39 0.739135
\(241\) 4.69772e38 0.233672 0.116836 0.993151i \(-0.462725\pi\)
0.116836 + 0.993151i \(0.462725\pi\)
\(242\) −8.10022e37 −0.0376308
\(243\) 1.42932e39 0.620335
\(244\) −3.45575e39 −1.40156
\(245\) 4.28640e38 0.162499
\(246\) 2.06348e37 0.00731425
\(247\) −1.30474e39 −0.432538
\(248\) −6.58982e38 −0.204372
\(249\) 8.01974e38 0.232740
\(250\) −1.99946e37 −0.00543128
\(251\) −1.31521e38 −0.0334486 −0.0167243 0.999860i \(-0.505324\pi\)
−0.0167243 + 0.999860i \(0.505324\pi\)
\(252\) −5.98448e39 −1.42534
\(253\) 5.12057e39 1.14243
\(254\) −3.74645e38 −0.0783183
\(255\) −4.92603e39 −0.965125
\(256\) 5.24487e39 0.963330
\(257\) 4.96495e39 0.855104 0.427552 0.903991i \(-0.359376\pi\)
0.427552 + 0.903991i \(0.359376\pi\)
\(258\) 7.07356e38 0.114265
\(259\) −5.26416e39 −0.797779
\(260\) 1.29948e39 0.184803
\(261\) −9.74103e39 −1.30028
\(262\) −2.08094e38 −0.0260789
\(263\) 6.41705e39 0.755206 0.377603 0.925968i \(-0.376748\pi\)
0.377603 + 0.925968i \(0.376748\pi\)
\(264\) 1.13017e39 0.124933
\(265\) −6.61230e39 −0.686745
\(266\) −5.17699e38 −0.0505278
\(267\) −1.65027e40 −1.51398
\(268\) 1.14091e40 0.984071
\(269\) −1.97544e39 −0.160233 −0.0801164 0.996786i \(-0.525529\pi\)
−0.0801164 + 0.996786i \(0.525529\pi\)
\(270\) 4.71703e38 0.0359887
\(271\) −1.48531e40 −1.06616 −0.533082 0.846063i \(-0.678966\pi\)
−0.533082 + 0.846063i \(0.678966\pi\)
\(272\) −1.89059e40 −1.27706
\(273\) −8.69887e39 −0.553069
\(274\) −9.91858e37 −0.00593697
\(275\) 2.18816e39 0.123336
\(276\) 5.81032e40 3.08461
\(277\) 6.46494e39 0.323332 0.161666 0.986846i \(-0.448313\pi\)
0.161666 + 0.986846i \(0.448313\pi\)
\(278\) 5.65835e38 0.0266655
\(279\) 6.80581e40 3.02281
\(280\) 1.03313e39 0.0432561
\(281\) −1.46554e40 −0.578554 −0.289277 0.957245i \(-0.593415\pi\)
−0.289277 + 0.957245i \(0.593415\pi\)
\(282\) −1.34199e39 −0.0499619
\(283\) −2.68962e40 −0.944529 −0.472265 0.881457i \(-0.656563\pi\)
−0.472265 + 0.881457i \(0.656563\pi\)
\(284\) 3.51639e40 1.16505
\(285\) −2.49296e40 −0.779426
\(286\) 5.26325e38 0.0155315
\(287\) −2.06432e39 −0.0575077
\(288\) 1.23564e40 0.325023
\(289\) 2.68705e40 0.667516
\(290\) 8.39268e38 0.0196940
\(291\) −3.62584e40 −0.803850
\(292\) −7.39493e40 −1.54923
\(293\) −4.27715e40 −0.846912 −0.423456 0.905917i \(-0.639183\pi\)
−0.423456 + 0.905917i \(0.639183\pi\)
\(294\) 1.96997e39 0.0368746
\(295\) 1.84840e40 0.327140
\(296\) 7.24160e39 0.121205
\(297\) −5.16220e40 −0.817248
\(298\) −6.44723e39 −0.0965617
\(299\) 5.42181e40 0.768368
\(300\) 2.48290e40 0.333012
\(301\) −7.07647e40 −0.898399
\(302\) −3.60335e39 −0.0433104
\(303\) 2.63527e41 2.99931
\(304\) −9.56787e40 −1.03134
\(305\) −6.16137e40 −0.629115
\(306\) −1.45335e40 −0.140594
\(307\) −5.26223e40 −0.482377 −0.241189 0.970478i \(-0.577537\pi\)
−0.241189 + 0.970478i \(0.577537\pi\)
\(308\) −5.64272e40 −0.490232
\(309\) −1.14592e41 −0.943711
\(310\) −5.86375e39 −0.0457833
\(311\) 3.83170e40 0.283691 0.141845 0.989889i \(-0.454696\pi\)
0.141845 + 0.989889i \(0.454696\pi\)
\(312\) 1.19665e40 0.0840268
\(313\) −8.13055e40 −0.541550 −0.270775 0.962643i \(-0.587280\pi\)
−0.270775 + 0.962643i \(0.587280\pi\)
\(314\) 5.69042e39 0.0359588
\(315\) −1.06699e41 −0.639789
\(316\) 1.51098e41 0.859850
\(317\) 7.49503e40 0.404852 0.202426 0.979298i \(-0.435118\pi\)
0.202426 + 0.979298i \(0.435118\pi\)
\(318\) −3.03892e40 −0.155837
\(319\) −9.18474e40 −0.447219
\(320\) 9.45809e40 0.437350
\(321\) 3.87089e41 1.70011
\(322\) 2.15128e40 0.0897584
\(323\) 3.39706e41 1.34667
\(324\) −1.11554e41 −0.420235
\(325\) 2.31688e40 0.0829523
\(326\) 2.72604e40 0.0927774
\(327\) 5.39666e41 1.74617
\(328\) 2.83977e39 0.00873705
\(329\) 1.34254e41 0.392821
\(330\) 1.00565e40 0.0279875
\(331\) −5.91449e41 −1.56587 −0.782935 0.622103i \(-0.786278\pi\)
−0.782935 + 0.622103i \(0.786278\pi\)
\(332\) 5.50822e40 0.138750
\(333\) −7.47895e41 −1.79271
\(334\) 9.88982e39 0.0225617
\(335\) 2.03416e41 0.441719
\(336\) −6.37902e41 −1.31873
\(337\) 1.33169e41 0.262126 0.131063 0.991374i \(-0.458161\pi\)
0.131063 + 0.991374i \(0.458161\pi\)
\(338\) −2.68225e40 −0.0502774
\(339\) −2.00418e41 −0.357801
\(340\) −3.38336e41 −0.575368
\(341\) 6.41714e41 1.03967
\(342\) −7.35510e40 −0.113542
\(343\) −7.39453e41 −1.08782
\(344\) 9.73469e40 0.136492
\(345\) 1.03594e42 1.38458
\(346\) 5.88013e39 0.00749257
\(347\) 1.89271e41 0.229957 0.114979 0.993368i \(-0.463320\pi\)
0.114979 + 0.993368i \(0.463320\pi\)
\(348\) −1.04219e42 −1.20751
\(349\) −5.82757e41 −0.643974 −0.321987 0.946744i \(-0.604351\pi\)
−0.321987 + 0.946744i \(0.604351\pi\)
\(350\) 9.19299e39 0.00969023
\(351\) −5.46588e41 −0.549658
\(352\) 1.16507e41 0.111789
\(353\) 5.33261e41 0.488267 0.244134 0.969742i \(-0.421496\pi\)
0.244134 + 0.969742i \(0.421496\pi\)
\(354\) 8.49500e40 0.0742351
\(355\) 6.26948e41 0.522954
\(356\) −1.13346e42 −0.902571
\(357\) 2.26486e42 1.72193
\(358\) 3.88002e40 0.0281685
\(359\) −1.28621e42 −0.891772 −0.445886 0.895090i \(-0.647111\pi\)
−0.445886 + 0.895090i \(0.647111\pi\)
\(360\) 1.46780e41 0.0972020
\(361\) 1.38408e41 0.0875575
\(362\) 1.53871e40 0.00929959
\(363\) 1.79341e42 1.03567
\(364\) −5.97467e41 −0.329717
\(365\) −1.31847e42 −0.695403
\(366\) −2.83168e41 −0.142760
\(367\) −1.99600e42 −0.961988 −0.480994 0.876724i \(-0.659724\pi\)
−0.480994 + 0.876724i \(0.659724\pi\)
\(368\) 3.97589e42 1.83209
\(369\) −2.93284e41 −0.129227
\(370\) 6.44371e40 0.0271524
\(371\) 3.04017e42 1.22526
\(372\) 7.28154e42 2.80714
\(373\) −4.88676e42 −1.80229 −0.901146 0.433516i \(-0.857273\pi\)
−0.901146 + 0.433516i \(0.857273\pi\)
\(374\) −1.37035e41 −0.0483561
\(375\) 4.42685e41 0.149478
\(376\) −1.84686e41 −0.0596807
\(377\) −9.72506e41 −0.300788
\(378\) −2.16877e41 −0.0642094
\(379\) −6.55646e42 −1.85833 −0.929164 0.369667i \(-0.879472\pi\)
−0.929164 + 0.369667i \(0.879472\pi\)
\(380\) −1.71225e42 −0.464662
\(381\) 8.29473e42 2.15546
\(382\) −4.12961e41 −0.102769
\(383\) −8.72699e41 −0.208010 −0.104005 0.994577i \(-0.533166\pi\)
−0.104005 + 0.994577i \(0.533166\pi\)
\(384\) 1.76158e42 0.402196
\(385\) −1.00606e42 −0.220050
\(386\) −1.90949e41 −0.0400155
\(387\) −1.00538e43 −2.01882
\(388\) −2.49035e42 −0.479222
\(389\) 1.58040e42 0.291474 0.145737 0.989323i \(-0.453445\pi\)
0.145737 + 0.989323i \(0.453445\pi\)
\(390\) 1.06481e41 0.0188237
\(391\) −1.41164e43 −2.39225
\(392\) 2.71108e41 0.0440476
\(393\) 4.60726e42 0.717737
\(394\) 6.90379e41 0.103133
\(395\) 2.69398e42 0.385960
\(396\) −8.01678e42 −1.10161
\(397\) −5.01270e42 −0.660736 −0.330368 0.943852i \(-0.607173\pi\)
−0.330368 + 0.943852i \(0.607173\pi\)
\(398\) −2.75993e41 −0.0349001
\(399\) 1.14620e43 1.39061
\(400\) 1.69901e42 0.197790
\(401\) 8.66109e42 0.967588 0.483794 0.875182i \(-0.339258\pi\)
0.483794 + 0.875182i \(0.339258\pi\)
\(402\) 9.34870e41 0.100235
\(403\) 6.79465e42 0.699252
\(404\) 1.80999e43 1.78806
\(405\) −1.98893e42 −0.188630
\(406\) −3.85874e41 −0.0351371
\(407\) −7.05184e42 −0.616588
\(408\) −3.11564e42 −0.261610
\(409\) 6.15808e42 0.496605 0.248302 0.968683i \(-0.420127\pi\)
0.248302 + 0.968683i \(0.420127\pi\)
\(410\) 2.52688e40 0.00195727
\(411\) 2.19600e42 0.163396
\(412\) −7.87055e42 −0.562601
\(413\) −8.49849e42 −0.583668
\(414\) 3.05639e42 0.201699
\(415\) 9.82078e41 0.0622806
\(416\) 1.23361e42 0.0751862
\(417\) −1.25277e43 −0.733883
\(418\) −6.93507e41 −0.0390519
\(419\) 1.55362e43 0.841031 0.420516 0.907285i \(-0.361849\pi\)
0.420516 + 0.907285i \(0.361849\pi\)
\(420\) −1.14158e43 −0.594144
\(421\) 1.08104e43 0.540987 0.270494 0.962722i \(-0.412813\pi\)
0.270494 + 0.962722i \(0.412813\pi\)
\(422\) −1.27528e42 −0.0613691
\(423\) 1.90739e43 0.882720
\(424\) −4.18218e42 −0.186151
\(425\) −6.03229e42 −0.258265
\(426\) 2.88136e42 0.118670
\(427\) 2.83284e43 1.12244
\(428\) 2.65865e43 1.01354
\(429\) −1.16530e43 −0.427456
\(430\) 8.66212e41 0.0305770
\(431\) −4.98547e42 −0.169368 −0.0846840 0.996408i \(-0.526988\pi\)
−0.0846840 + 0.996408i \(0.526988\pi\)
\(432\) −4.00822e43 −1.31060
\(433\) −1.01098e43 −0.318194 −0.159097 0.987263i \(-0.550858\pi\)
−0.159097 + 0.987263i \(0.550858\pi\)
\(434\) 2.69600e42 0.0816845
\(435\) −1.85816e43 −0.542014
\(436\) 3.70661e43 1.04100
\(437\) −7.14399e43 −1.93195
\(438\) −6.05948e42 −0.157802
\(439\) −4.36398e43 −1.09451 −0.547253 0.836967i \(-0.684326\pi\)
−0.547253 + 0.836967i \(0.684326\pi\)
\(440\) 1.38398e42 0.0334318
\(441\) −2.79994e43 −0.651496
\(442\) −1.45097e42 −0.0325230
\(443\) 1.22624e43 0.264798 0.132399 0.991196i \(-0.457732\pi\)
0.132399 + 0.991196i \(0.457732\pi\)
\(444\) −8.00174e43 −1.66481
\(445\) −2.02088e43 −0.405136
\(446\) −4.33768e42 −0.0837978
\(447\) 1.42743e44 2.65755
\(448\) −4.34859e43 −0.780299
\(449\) 8.39293e43 1.45161 0.725803 0.687903i \(-0.241468\pi\)
0.725803 + 0.687903i \(0.241468\pi\)
\(450\) 1.30608e42 0.0217752
\(451\) −2.76536e42 −0.0444466
\(452\) −1.37654e43 −0.213306
\(453\) 7.97791e43 1.19198
\(454\) 2.11595e42 0.0304848
\(455\) −1.06524e43 −0.148000
\(456\) −1.57676e43 −0.211274
\(457\) 9.02636e42 0.116653 0.0583264 0.998298i \(-0.481424\pi\)
0.0583264 + 0.998298i \(0.481424\pi\)
\(458\) 4.99232e42 0.0622332
\(459\) 1.42311e44 1.71131
\(460\) 7.11518e43 0.825432
\(461\) −3.52096e42 −0.0394091 −0.0197045 0.999806i \(-0.506273\pi\)
−0.0197045 + 0.999806i \(0.506273\pi\)
\(462\) −4.62370e42 −0.0499341
\(463\) 2.80824e42 0.0292650 0.0146325 0.999893i \(-0.495342\pi\)
0.0146325 + 0.999893i \(0.495342\pi\)
\(464\) −7.13154e43 −0.717194
\(465\) 1.29825e44 1.26004
\(466\) −5.10022e42 −0.0477773
\(467\) −1.17834e44 −1.06547 −0.532736 0.846282i \(-0.678836\pi\)
−0.532736 + 0.846282i \(0.678836\pi\)
\(468\) −8.48839e43 −0.740916
\(469\) −9.35254e43 −0.788094
\(470\) −1.64337e42 −0.0133697
\(471\) −1.25987e44 −0.989650
\(472\) 1.16909e43 0.0886756
\(473\) −9.47961e43 −0.694355
\(474\) 1.23811e43 0.0875826
\(475\) −3.05282e43 −0.208572
\(476\) 1.55558e44 1.02654
\(477\) 4.31925e44 2.75331
\(478\) 1.50791e43 0.0928571
\(479\) 2.89874e43 0.172454 0.0862271 0.996276i \(-0.472519\pi\)
0.0862271 + 0.996276i \(0.472519\pi\)
\(480\) 2.35705e43 0.135484
\(481\) −7.46669e43 −0.414700
\(482\) 2.64386e42 0.0141894
\(483\) −4.76299e44 −2.47031
\(484\) 1.23177e44 0.617422
\(485\) −4.44012e43 −0.215108
\(486\) 8.04418e42 0.0376689
\(487\) 2.41311e44 1.09232 0.546158 0.837682i \(-0.316090\pi\)
0.546158 + 0.837682i \(0.316090\pi\)
\(488\) −3.89698e43 −0.170530
\(489\) −6.03552e44 −2.55340
\(490\) 2.41237e42 0.00986754
\(491\) −2.36480e44 −0.935297 −0.467648 0.883915i \(-0.654899\pi\)
−0.467648 + 0.883915i \(0.654899\pi\)
\(492\) −3.13785e43 −0.120008
\(493\) 2.53204e44 0.936476
\(494\) −7.34305e42 −0.0262653
\(495\) −1.42934e44 −0.494480
\(496\) 4.98262e44 1.66729
\(497\) −2.88255e44 −0.933031
\(498\) 4.51349e42 0.0141328
\(499\) −4.17695e44 −1.26532 −0.632659 0.774430i \(-0.718037\pi\)
−0.632659 + 0.774430i \(0.718037\pi\)
\(500\) 3.04050e43 0.0891129
\(501\) −2.18963e44 −0.620938
\(502\) −7.40196e41 −0.00203112
\(503\) 1.63646e44 0.434543 0.217271 0.976111i \(-0.430284\pi\)
0.217271 + 0.976111i \(0.430284\pi\)
\(504\) −6.74856e43 −0.173423
\(505\) 3.22708e44 0.802606
\(506\) 2.88184e43 0.0693724
\(507\) 5.93856e44 1.38373
\(508\) 5.69709e44 1.28500
\(509\) −9.46414e43 −0.206651 −0.103326 0.994648i \(-0.532948\pi\)
−0.103326 + 0.994648i \(0.532948\pi\)
\(510\) −2.77235e43 −0.0586058
\(511\) 6.06197e44 1.24071
\(512\) 1.50957e44 0.299157
\(513\) 7.20207e44 1.38204
\(514\) 2.79426e43 0.0519249
\(515\) −1.40326e44 −0.252534
\(516\) −1.07565e45 −1.87479
\(517\) 1.79846e44 0.303604
\(518\) −2.96265e43 −0.0484440
\(519\) −1.30187e44 −0.206209
\(520\) 1.46539e43 0.0224853
\(521\) 7.82192e44 1.16276 0.581381 0.813631i \(-0.302512\pi\)
0.581381 + 0.813631i \(0.302512\pi\)
\(522\) −5.48222e43 −0.0789575
\(523\) −8.02848e44 −1.12035 −0.560177 0.828373i \(-0.689267\pi\)
−0.560177 + 0.828373i \(0.689267\pi\)
\(524\) 3.16442e44 0.427885
\(525\) −2.03535e44 −0.266692
\(526\) 3.61150e43 0.0458588
\(527\) −1.76907e45 −2.17706
\(528\) −8.54530e44 −1.01922
\(529\) 2.10365e45 2.43196
\(530\) −3.72138e43 −0.0417016
\(531\) −1.20741e45 −1.31158
\(532\) 7.87246e44 0.829027
\(533\) −2.92804e43 −0.0298936
\(534\) −9.28768e43 −0.0919341
\(535\) 4.74019e44 0.454945
\(536\) 1.28658e44 0.119734
\(537\) −8.59046e44 −0.775248
\(538\) −1.11177e43 −0.00972990
\(539\) −2.64004e44 −0.224076
\(540\) −7.17302e44 −0.590480
\(541\) −2.90457e44 −0.231914 −0.115957 0.993254i \(-0.536994\pi\)
−0.115957 + 0.993254i \(0.536994\pi\)
\(542\) −8.35929e43 −0.0647413
\(543\) −3.40673e44 −0.255941
\(544\) −3.21186e44 −0.234086
\(545\) 6.60862e44 0.467271
\(546\) −4.89570e43 −0.0335843
\(547\) −2.63690e45 −1.75511 −0.877553 0.479480i \(-0.840825\pi\)
−0.877553 + 0.479480i \(0.840825\pi\)
\(548\) 1.50828e44 0.0974100
\(549\) 4.02470e45 2.52226
\(550\) 1.23149e43 0.00748938
\(551\) 1.28141e45 0.756289
\(552\) 6.55217e44 0.375310
\(553\) −1.23862e45 −0.688611
\(554\) 3.63845e43 0.0196338
\(555\) −1.42665e45 −0.747282
\(556\) −8.60445e44 −0.437511
\(557\) −1.37430e45 −0.678378 −0.339189 0.940718i \(-0.610153\pi\)
−0.339189 + 0.940718i \(0.610153\pi\)
\(558\) 3.83029e44 0.183555
\(559\) −1.00373e45 −0.467004
\(560\) −7.81159e44 −0.352888
\(561\) 3.03400e45 1.33085
\(562\) −8.24803e43 −0.0351319
\(563\) 1.83620e45 0.759505 0.379753 0.925088i \(-0.376009\pi\)
0.379753 + 0.925088i \(0.376009\pi\)
\(564\) 2.04072e45 0.819743
\(565\) −2.45427e44 −0.0957466
\(566\) −1.51371e44 −0.0573552
\(567\) 9.14459e44 0.336546
\(568\) 3.96535e44 0.141754
\(569\) −5.13991e45 −1.78485 −0.892427 0.451192i \(-0.850999\pi\)
−0.892427 + 0.451192i \(0.850999\pi\)
\(570\) −1.40303e44 −0.0473295
\(571\) 5.28676e45 1.73258 0.866291 0.499540i \(-0.166498\pi\)
0.866291 + 0.499540i \(0.166498\pi\)
\(572\) −8.00364e44 −0.254832
\(573\) 9.14305e45 2.82839
\(574\) −1.16180e43 −0.00349207
\(575\) 1.26859e45 0.370511
\(576\) −6.17817e45 −1.75343
\(577\) −1.37030e45 −0.377934 −0.188967 0.981983i \(-0.560514\pi\)
−0.188967 + 0.981983i \(0.560514\pi\)
\(578\) 1.51227e44 0.0405340
\(579\) 4.22767e45 1.10130
\(580\) −1.27624e45 −0.323126
\(581\) −4.51534e44 −0.111118
\(582\) −2.04062e44 −0.0488126
\(583\) 4.07259e45 0.946978
\(584\) −8.33910e44 −0.188498
\(585\) −1.51342e45 −0.332574
\(586\) −2.40717e44 −0.0514275
\(587\) 1.82654e45 0.379402 0.189701 0.981842i \(-0.439248\pi\)
0.189701 + 0.981842i \(0.439248\pi\)
\(588\) −2.99566e45 −0.605015
\(589\) −8.95290e45 −1.75817
\(590\) 1.04028e44 0.0198651
\(591\) −1.52852e46 −2.83842
\(592\) −5.47544e45 −0.988805
\(593\) −9.10503e45 −1.59911 −0.799556 0.600592i \(-0.794932\pi\)
−0.799556 + 0.600592i \(0.794932\pi\)
\(594\) −2.90527e44 −0.0496262
\(595\) 2.77349e45 0.460784
\(596\) 9.80408e45 1.58432
\(597\) 6.11055e45 0.960514
\(598\) 3.05138e44 0.0466580
\(599\) 1.51052e45 0.224690 0.112345 0.993669i \(-0.464164\pi\)
0.112345 + 0.993669i \(0.464164\pi\)
\(600\) 2.79992e44 0.0405181
\(601\) 1.17313e46 1.65165 0.825825 0.563927i \(-0.190710\pi\)
0.825825 + 0.563927i \(0.190710\pi\)
\(602\) −3.98262e44 −0.0545540
\(603\) −1.32874e46 −1.77095
\(604\) 5.47949e45 0.710609
\(605\) 2.19617e45 0.277141
\(606\) 1.48312e45 0.182129
\(607\) −9.39432e45 −1.12267 −0.561335 0.827589i \(-0.689712\pi\)
−0.561335 + 0.827589i \(0.689712\pi\)
\(608\) −1.62546e45 −0.189045
\(609\) 8.54334e45 0.967035
\(610\) −3.46760e44 −0.0382021
\(611\) 1.90426e45 0.204196
\(612\) 2.21006e46 2.30678
\(613\) −9.71928e45 −0.987498 −0.493749 0.869604i \(-0.664374\pi\)
−0.493749 + 0.869604i \(0.664374\pi\)
\(614\) −2.96157e44 −0.0292916
\(615\) −5.59458e44 −0.0538676
\(616\) −6.36317e44 −0.0596474
\(617\) 1.24293e46 1.13433 0.567166 0.823603i \(-0.308040\pi\)
0.567166 + 0.823603i \(0.308040\pi\)
\(618\) −6.44920e44 −0.0573054
\(619\) −1.07266e46 −0.928043 −0.464021 0.885824i \(-0.653594\pi\)
−0.464021 + 0.885824i \(0.653594\pi\)
\(620\) 8.91680e45 0.751183
\(621\) −2.99279e46 −2.45508
\(622\) 2.15647e44 0.0172267
\(623\) 9.29149e45 0.722824
\(624\) −9.04801e45 −0.685499
\(625\) 5.42101e44 0.0400000
\(626\) −4.57585e44 −0.0328848
\(627\) 1.53544e46 1.07478
\(628\) −8.65322e45 −0.589988
\(629\) 1.94405e46 1.29113
\(630\) −6.00500e44 −0.0388503
\(631\) −1.79249e46 −1.12972 −0.564862 0.825186i \(-0.691071\pi\)
−0.564862 + 0.825186i \(0.691071\pi\)
\(632\) 1.70390e45 0.104620
\(633\) 2.82350e46 1.68899
\(634\) 4.21818e44 0.0245840
\(635\) 1.01575e46 0.576795
\(636\) 4.62117e46 2.55688
\(637\) −2.79535e45 −0.150708
\(638\) −5.16915e44 −0.0271567
\(639\) −4.09532e46 −2.09664
\(640\) 2.15719e45 0.107626
\(641\) 2.31165e46 1.12400 0.561998 0.827138i \(-0.310033\pi\)
0.561998 + 0.827138i \(0.310033\pi\)
\(642\) 2.17852e45 0.103237
\(643\) −3.13717e45 −0.144896 −0.0724480 0.997372i \(-0.523081\pi\)
−0.0724480 + 0.997372i \(0.523081\pi\)
\(644\) −3.27138e46 −1.47270
\(645\) −1.91781e46 −0.841533
\(646\) 1.91185e45 0.0817746
\(647\) −1.23833e46 −0.516318 −0.258159 0.966102i \(-0.583116\pi\)
−0.258159 + 0.966102i \(0.583116\pi\)
\(648\) −1.25797e45 −0.0511308
\(649\) −1.13845e46 −0.451105
\(650\) 1.30393e44 0.00503716
\(651\) −5.96901e46 −2.24810
\(652\) −4.14540e46 −1.52223
\(653\) −9.15492e45 −0.327784 −0.163892 0.986478i \(-0.552405\pi\)
−0.163892 + 0.986478i \(0.552405\pi\)
\(654\) 3.03723e45 0.106034
\(655\) 5.64194e45 0.192064
\(656\) −2.14718e45 −0.0712778
\(657\) 8.61242e46 2.78802
\(658\) 7.55578e44 0.0238535
\(659\) −4.32900e46 −1.33284 −0.666420 0.745577i \(-0.732174\pi\)
−0.666420 + 0.745577i \(0.732174\pi\)
\(660\) −1.52925e46 −0.459202
\(661\) 1.40663e46 0.411961 0.205980 0.978556i \(-0.433962\pi\)
0.205980 + 0.978556i \(0.433962\pi\)
\(662\) −3.32866e45 −0.0950852
\(663\) 3.21248e46 0.895091
\(664\) 6.21150e44 0.0168820
\(665\) 1.40361e46 0.372124
\(666\) −4.20913e45 −0.108860
\(667\) −5.32487e46 −1.34348
\(668\) −1.50391e46 −0.370178
\(669\) 9.60373e46 2.30626
\(670\) 1.14482e45 0.0268227
\(671\) 3.79486e46 0.867509
\(672\) −1.08371e46 −0.241724
\(673\) 2.27399e46 0.494926 0.247463 0.968897i \(-0.420403\pi\)
0.247463 + 0.968897i \(0.420403\pi\)
\(674\) 7.49473e44 0.0159172
\(675\) −1.27890e46 −0.265048
\(676\) 4.07880e46 0.824920
\(677\) 4.02008e46 0.793453 0.396727 0.917937i \(-0.370146\pi\)
0.396727 + 0.917937i \(0.370146\pi\)
\(678\) −1.12795e45 −0.0217270
\(679\) 2.04145e46 0.383785
\(680\) −3.81534e45 −0.0700061
\(681\) −4.68476e46 −0.838996
\(682\) 3.61155e45 0.0631323
\(683\) −8.62730e46 −1.47209 −0.736043 0.676935i \(-0.763308\pi\)
−0.736043 + 0.676935i \(0.763308\pi\)
\(684\) 1.11846e47 1.86293
\(685\) 2.68917e45 0.0437243
\(686\) −4.16162e45 −0.0660563
\(687\) −1.10531e47 −1.71277
\(688\) −7.36049e46 −1.11352
\(689\) 4.31217e46 0.636911
\(690\) 5.83024e45 0.0840769
\(691\) 2.76452e46 0.389252 0.194626 0.980877i \(-0.437651\pi\)
0.194626 + 0.980877i \(0.437651\pi\)
\(692\) −8.94170e45 −0.122933
\(693\) 6.57172e46 0.882228
\(694\) 1.06521e45 0.0139638
\(695\) −1.53411e46 −0.196385
\(696\) −1.17526e46 −0.146920
\(697\) 7.62351e45 0.0930710
\(698\) −3.27974e45 −0.0391043
\(699\) 1.12920e47 1.31492
\(700\) −1.39795e46 −0.158991
\(701\) 5.83426e45 0.0648094 0.0324047 0.999475i \(-0.489683\pi\)
0.0324047 + 0.999475i \(0.489683\pi\)
\(702\) −3.07618e45 −0.0333772
\(703\) 9.83841e46 1.04271
\(704\) −5.82535e46 −0.603077
\(705\) 3.63846e46 0.367957
\(706\) 3.00118e45 0.0296493
\(707\) −1.48373e47 −1.43197
\(708\) −1.29180e47 −1.21800
\(709\) −3.21473e46 −0.296130 −0.148065 0.988978i \(-0.547304\pi\)
−0.148065 + 0.988978i \(0.547304\pi\)
\(710\) 3.52845e45 0.0317556
\(711\) −1.75975e47 −1.54740
\(712\) −1.27818e46 −0.109817
\(713\) 3.72035e47 3.12325
\(714\) 1.27466e46 0.104562
\(715\) −1.42699e46 −0.114386
\(716\) −5.90021e46 −0.462171
\(717\) −3.33855e47 −2.55559
\(718\) −7.23876e45 −0.0541515
\(719\) −5.61687e46 −0.410646 −0.205323 0.978694i \(-0.565824\pi\)
−0.205323 + 0.978694i \(0.565824\pi\)
\(720\) −1.10982e47 −0.792985
\(721\) 6.45185e46 0.450560
\(722\) 7.78958e44 0.00531680
\(723\) −5.85358e46 −0.390517
\(724\) −2.33986e46 −0.152582
\(725\) −2.27546e46 −0.145041
\(726\) 1.00933e46 0.0628894
\(727\) 2.29582e47 1.39836 0.699181 0.714944i \(-0.253548\pi\)
0.699181 + 0.714944i \(0.253548\pi\)
\(728\) −6.73750e45 −0.0401172
\(729\) −2.50561e47 −1.45851
\(730\) −7.42029e45 −0.0422273
\(731\) 2.61333e47 1.45398
\(732\) 4.30603e47 2.34231
\(733\) 1.21401e46 0.0645662 0.0322831 0.999479i \(-0.489722\pi\)
0.0322831 + 0.999479i \(0.489722\pi\)
\(734\) −1.12334e46 −0.0584153
\(735\) −5.34105e46 −0.271572
\(736\) 6.75452e46 0.335823
\(737\) −1.25286e47 −0.609102
\(738\) −1.65060e45 −0.00784713
\(739\) 3.32044e47 1.54370 0.771848 0.635807i \(-0.219333\pi\)
0.771848 + 0.635807i \(0.219333\pi\)
\(740\) −9.79873e46 −0.445499
\(741\) 1.62577e47 0.722867
\(742\) 1.71100e46 0.0744020
\(743\) −1.84054e47 −0.782762 −0.391381 0.920229i \(-0.628003\pi\)
−0.391381 + 0.920229i \(0.628003\pi\)
\(744\) 8.21123e46 0.341550
\(745\) 1.74800e47 0.711153
\(746\) −2.75025e46 −0.109442
\(747\) −6.41508e46 −0.249696
\(748\) 2.08385e47 0.793396
\(749\) −2.17942e47 −0.811691
\(750\) 2.49142e45 0.00907686
\(751\) −7.67452e45 −0.0273522 −0.0136761 0.999906i \(-0.504353\pi\)
−0.0136761 + 0.999906i \(0.504353\pi\)
\(752\) 1.39642e47 0.486881
\(753\) 1.63881e46 0.0559000
\(754\) −5.47324e45 −0.0182649
\(755\) 9.76955e46 0.318970
\(756\) 3.29797e47 1.05351
\(757\) −1.14623e47 −0.358254 −0.179127 0.983826i \(-0.557327\pi\)
−0.179127 + 0.983826i \(0.557327\pi\)
\(758\) −3.68996e46 −0.112844
\(759\) −6.38047e47 −1.90925
\(760\) −1.93086e46 −0.0565362
\(761\) −6.74831e47 −1.93352 −0.966759 0.255690i \(-0.917697\pi\)
−0.966759 + 0.255690i \(0.917697\pi\)
\(762\) 4.66825e46 0.130887
\(763\) −3.03847e47 −0.833682
\(764\) 6.27975e47 1.68617
\(765\) 3.94038e47 1.03544
\(766\) −4.91152e45 −0.0126311
\(767\) −1.20543e47 −0.303401
\(768\) −6.53535e47 −1.60994
\(769\) 1.58437e47 0.382007 0.191004 0.981589i \(-0.438826\pi\)
0.191004 + 0.981589i \(0.438826\pi\)
\(770\) −5.66207e45 −0.0133622
\(771\) −6.18657e47 −1.42907
\(772\) 2.90370e47 0.656548
\(773\) −1.15351e47 −0.255305 −0.127652 0.991819i \(-0.540744\pi\)
−0.127652 + 0.991819i \(0.540744\pi\)
\(774\) −5.65822e46 −0.122590
\(775\) 1.58980e47 0.337183
\(776\) −2.80831e46 −0.0583078
\(777\) 6.55939e47 1.33327
\(778\) 8.89447e45 0.0176993
\(779\) 3.85810e46 0.0751632
\(780\) −1.61921e47 −0.308847
\(781\) −3.86145e47 −0.721121
\(782\) −7.94464e46 −0.145266
\(783\) 5.36816e47 0.961072
\(784\) −2.04987e47 −0.359345
\(785\) −1.54281e47 −0.264827
\(786\) 2.59295e46 0.0435835
\(787\) 7.25057e47 1.19341 0.596704 0.802461i \(-0.296477\pi\)
0.596704 + 0.802461i \(0.296477\pi\)
\(788\) −1.04983e48 −1.69215
\(789\) −7.99595e47 −1.26212
\(790\) 1.51616e46 0.0234369
\(791\) 1.12841e47 0.170827
\(792\) −9.04034e46 −0.134035
\(793\) 4.01810e47 0.583463
\(794\) −2.82113e46 −0.0401222
\(795\) 8.23924e47 1.14770
\(796\) 4.19693e47 0.572619
\(797\) −5.72072e47 −0.764519 −0.382260 0.924055i \(-0.624854\pi\)
−0.382260 + 0.924055i \(0.624854\pi\)
\(798\) 6.45077e46 0.0844430
\(799\) −4.95798e47 −0.635745
\(800\) 2.88639e46 0.0362552
\(801\) 1.32007e48 1.62428
\(802\) 4.87444e46 0.0587553
\(803\) 8.12058e47 0.958916
\(804\) −1.42162e48 −1.64460
\(805\) −5.83264e47 −0.661048
\(806\) 3.82401e46 0.0424611
\(807\) 2.46149e47 0.267784
\(808\) 2.04108e47 0.217557
\(809\) 1.25233e48 1.30788 0.653939 0.756547i \(-0.273115\pi\)
0.653939 + 0.756547i \(0.273115\pi\)
\(810\) −1.11936e46 −0.0114543
\(811\) −1.43044e48 −1.43425 −0.717126 0.696944i \(-0.754543\pi\)
−0.717126 + 0.696944i \(0.754543\pi\)
\(812\) 5.86785e47 0.576506
\(813\) 1.85077e48 1.78180
\(814\) −3.96876e46 −0.0374414
\(815\) −7.39095e47 −0.683282
\(816\) 2.35576e48 2.13424
\(817\) 1.32255e48 1.17422
\(818\) 3.46575e46 0.0301556
\(819\) 6.95832e47 0.593363
\(820\) −3.84254e46 −0.0321137
\(821\) −7.52133e47 −0.616074 −0.308037 0.951374i \(-0.599672\pi\)
−0.308037 + 0.951374i \(0.599672\pi\)
\(822\) 1.23590e46 0.00992199
\(823\) −2.11125e47 −0.166128 −0.0830638 0.996544i \(-0.526471\pi\)
−0.0830638 + 0.996544i \(0.526471\pi\)
\(824\) −8.87544e46 −0.0684527
\(825\) −2.72655e47 −0.206121
\(826\) −4.78292e46 −0.0354424
\(827\) −1.64488e47 −0.119480 −0.0597399 0.998214i \(-0.519027\pi\)
−0.0597399 + 0.998214i \(0.519027\pi\)
\(828\) −4.64774e48 −3.30934
\(829\) −2.28060e48 −1.59184 −0.795919 0.605404i \(-0.793012\pi\)
−0.795919 + 0.605404i \(0.793012\pi\)
\(830\) 5.52711e45 0.00378190
\(831\) −8.05561e47 −0.540358
\(832\) −6.16804e47 −0.405613
\(833\) 7.27804e47 0.469215
\(834\) −7.05056e46 −0.0445640
\(835\) −2.68137e47 −0.166161
\(836\) 1.05459e48 0.640739
\(837\) −3.75059e48 −2.23424
\(838\) 8.74370e46 0.0510704
\(839\) 1.56509e48 0.896327 0.448163 0.893952i \(-0.352078\pi\)
0.448163 + 0.893952i \(0.352078\pi\)
\(840\) −1.28733e47 −0.0722905
\(841\) −8.60958e47 −0.474076
\(842\) 6.08406e46 0.0328506
\(843\) 1.82613e48 0.966892
\(844\) 1.93927e48 1.00691
\(845\) 7.27222e47 0.370281
\(846\) 1.07347e47 0.0536019
\(847\) −1.00974e48 −0.494463
\(848\) 3.16218e48 1.51864
\(849\) 3.35140e48 1.57852
\(850\) −3.39496e46 −0.0156827
\(851\) −4.08832e48 −1.85228
\(852\) −4.38159e48 −1.94706
\(853\) −1.60296e48 −0.698657 −0.349329 0.937000i \(-0.613590\pi\)
−0.349329 + 0.937000i \(0.613590\pi\)
\(854\) 1.59431e47 0.0681584
\(855\) 1.99415e48 0.836211
\(856\) 2.99810e47 0.123319
\(857\) 3.00131e48 1.21095 0.605476 0.795864i \(-0.292983\pi\)
0.605476 + 0.795864i \(0.292983\pi\)
\(858\) −6.55826e46 −0.0259566
\(859\) 4.48822e48 1.74256 0.871279 0.490788i \(-0.163291\pi\)
0.871279 + 0.490788i \(0.163291\pi\)
\(860\) −1.31722e48 −0.501687
\(861\) 2.57224e47 0.0961081
\(862\) −2.80581e46 −0.0102846
\(863\) 5.23525e47 0.188260 0.0941302 0.995560i \(-0.469993\pi\)
0.0941302 + 0.995560i \(0.469993\pi\)
\(864\) −6.80943e47 −0.240234
\(865\) −1.59424e47 −0.0551809
\(866\) −5.68977e46 −0.0193219
\(867\) −3.34819e48 −1.11557
\(868\) −4.09971e48 −1.34023
\(869\) −1.65925e48 −0.532214
\(870\) −1.04577e47 −0.0329130
\(871\) −1.32657e48 −0.409665
\(872\) 4.17985e47 0.126660
\(873\) 2.90035e48 0.862414
\(874\) −4.02062e47 −0.117315
\(875\) −2.49244e47 −0.0713661
\(876\) 9.21444e48 2.58911
\(877\) −1.66421e48 −0.458898 −0.229449 0.973321i \(-0.573692\pi\)
−0.229449 + 0.973321i \(0.573692\pi\)
\(878\) −2.45603e47 −0.0664622
\(879\) 5.32952e48 1.41538
\(880\) −1.04644e48 −0.272740
\(881\) 1.63041e48 0.417055 0.208528 0.978016i \(-0.433133\pi\)
0.208528 + 0.978016i \(0.433133\pi\)
\(882\) −1.57580e47 −0.0395611
\(883\) 3.57816e48 0.881674 0.440837 0.897587i \(-0.354682\pi\)
0.440837 + 0.897587i \(0.354682\pi\)
\(884\) 2.20644e48 0.533616
\(885\) −2.30320e48 −0.546723
\(886\) 6.90126e46 0.0160795
\(887\) 3.83241e48 0.876461 0.438230 0.898863i \(-0.355605\pi\)
0.438230 + 0.898863i \(0.355605\pi\)
\(888\) −9.02338e47 −0.202561
\(889\) −4.67017e48 −1.02909
\(890\) −1.13735e47 −0.0246013
\(891\) 1.22501e48 0.260109
\(892\) 6.59616e48 1.37490
\(893\) −2.50913e48 −0.513422
\(894\) 8.03356e47 0.161376
\(895\) −1.05197e48 −0.207454
\(896\) −9.91821e47 −0.192022
\(897\) −6.75582e48 −1.28411
\(898\) 4.72352e47 0.0881467
\(899\) −6.67316e48 −1.22264
\(900\) −1.98610e48 −0.357273
\(901\) −1.12273e49 −1.98297
\(902\) −1.55634e46 −0.00269895
\(903\) 8.81761e48 1.50142
\(904\) −1.55229e47 −0.0259534
\(905\) −4.17180e47 −0.0684892
\(906\) 4.48994e47 0.0723812
\(907\) −9.46008e48 −1.49753 −0.748763 0.662838i \(-0.769352\pi\)
−0.748763 + 0.662838i \(0.769352\pi\)
\(908\) −3.21765e48 −0.500175
\(909\) −2.10798e49 −3.21782
\(910\) −5.99516e46 −0.00898706
\(911\) 7.92211e48 1.16624 0.583120 0.812386i \(-0.301832\pi\)
0.583120 + 0.812386i \(0.301832\pi\)
\(912\) 1.19220e49 1.72359
\(913\) −6.04873e47 −0.0858809
\(914\) 5.08001e46 0.00708357
\(915\) 7.67736e48 1.05139
\(916\) −7.59165e48 −1.02108
\(917\) −2.59402e48 −0.342672
\(918\) 8.00923e47 0.103917
\(919\) 4.92680e48 0.627854 0.313927 0.949447i \(-0.398355\pi\)
0.313927 + 0.949447i \(0.398355\pi\)
\(920\) 8.02362e47 0.100432
\(921\) 6.55699e48 0.806158
\(922\) −1.98159e46 −0.00239306
\(923\) −4.08861e48 −0.485006
\(924\) 7.03110e48 0.819286
\(925\) −1.74705e48 −0.199970
\(926\) 1.58047e46 0.00177707
\(927\) 9.16633e48 1.01246
\(928\) −1.21155e48 −0.131462
\(929\) 2.38059e48 0.253761 0.126881 0.991918i \(-0.459503\pi\)
0.126881 + 0.991918i \(0.459503\pi\)
\(930\) 7.30651e47 0.0765140
\(931\) 3.68326e48 0.378934
\(932\) 7.75573e48 0.783899
\(933\) −4.77448e48 −0.474110
\(934\) −6.63166e47 −0.0646992
\(935\) 3.71536e48 0.356130
\(936\) −9.57217e47 −0.0901486
\(937\) −4.20946e47 −0.0389514 −0.0194757 0.999810i \(-0.506200\pi\)
−0.0194757 + 0.999810i \(0.506200\pi\)
\(938\) −5.26358e47 −0.0478558
\(939\) 1.01310e49 0.905049
\(940\) 2.49901e48 0.219361
\(941\) −1.57932e49 −1.36221 −0.681103 0.732188i \(-0.738499\pi\)
−0.681103 + 0.732188i \(0.738499\pi\)
\(942\) −7.09053e47 −0.0600950
\(943\) −1.60322e48 −0.133521
\(944\) −8.83958e48 −0.723425
\(945\) 5.88005e48 0.472886
\(946\) −5.33510e47 −0.0421637
\(947\) 1.67820e49 1.30337 0.651685 0.758490i \(-0.274062\pi\)
0.651685 + 0.758490i \(0.274062\pi\)
\(948\) −1.88276e49 −1.43700
\(949\) 8.59830e48 0.644941
\(950\) −1.71812e47 −0.0126652
\(951\) −9.33916e48 −0.676596
\(952\) 1.75419e48 0.124902
\(953\) 2.07777e49 1.45400 0.726999 0.686639i \(-0.240915\pi\)
0.726999 + 0.686639i \(0.240915\pi\)
\(954\) 2.43086e48 0.167191
\(955\) 1.11964e49 0.756870
\(956\) −2.29303e49 −1.52354
\(957\) 1.14446e49 0.747402
\(958\) 1.63141e47 0.0104720
\(959\) −1.23641e48 −0.0780109
\(960\) −1.17852e49 −0.730908
\(961\) 3.02202e49 1.84231
\(962\) −4.20223e47 −0.0251821
\(963\) −3.09637e49 −1.82397
\(964\) −4.02043e48 −0.232810
\(965\) 5.17710e48 0.294704
\(966\) −2.68060e48 −0.150006
\(967\) 1.42054e48 0.0781480 0.0390740 0.999236i \(-0.487559\pi\)
0.0390740 + 0.999236i \(0.487559\pi\)
\(968\) 1.38904e48 0.0751229
\(969\) −4.23289e49 −2.25058
\(970\) −2.49889e47 −0.0130621
\(971\) 3.67703e49 1.88964 0.944821 0.327588i \(-0.106236\pi\)
0.944821 + 0.327588i \(0.106236\pi\)
\(972\) −1.22325e49 −0.618048
\(973\) 7.05346e48 0.350381
\(974\) 1.35809e48 0.0663293
\(975\) −2.88694e48 −0.138632
\(976\) 2.94654e49 1.39120
\(977\) −5.91833e48 −0.274751 −0.137375 0.990519i \(-0.543867\pi\)
−0.137375 + 0.990519i \(0.543867\pi\)
\(978\) −3.39678e48 −0.155051
\(979\) 1.24468e49 0.558657
\(980\) −3.66841e48 −0.161900
\(981\) −4.31685e49 −1.87339
\(982\) −1.33090e48 −0.0567945
\(983\) −4.20754e49 −1.76561 −0.882805 0.469740i \(-0.844348\pi\)
−0.882805 + 0.469740i \(0.844348\pi\)
\(984\) −3.53849e47 −0.0146015
\(985\) −1.87178e49 −0.759552
\(986\) 1.42503e48 0.0568661
\(987\) −1.67287e49 −0.656491
\(988\) 1.11663e49 0.430943
\(989\) −5.49582e49 −2.08590
\(990\) −8.04427e47 −0.0300266
\(991\) −8.36780e48 −0.307182 −0.153591 0.988134i \(-0.549084\pi\)
−0.153591 + 0.988134i \(0.549084\pi\)
\(992\) 8.46482e48 0.305615
\(993\) 7.36974e49 2.61691
\(994\) −1.62229e48 −0.0566569
\(995\) 7.48283e48 0.257031
\(996\) −6.86351e48 −0.231882
\(997\) 4.11174e49 1.36633 0.683166 0.730264i \(-0.260603\pi\)
0.683166 + 0.730264i \(0.260603\pi\)
\(998\) −2.35077e48 −0.0768346
\(999\) 4.12155e49 1.32504
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 \(a_p\))