Properties

Label 5.34.a.a.1.5
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 1.5
Root \(-33002.4\)
Character \(\chi\) = 5.1

$q$-expansion

\(f(q)\) \(=\) \(q+138106. q^{2} -1.45282e7 q^{3} +1.04832e10 q^{4} -1.52588e11 q^{5} -2.00642e12 q^{6} +3.75584e13 q^{7} +2.61472e14 q^{8} -5.34799e15 q^{9} +O(q^{10})\) \(q+138106. q^{2} -1.45282e7 q^{3} +1.04832e10 q^{4} -1.52588e11 q^{5} -2.00642e12 q^{6} +3.75584e13 q^{7} +2.61472e14 q^{8} -5.34799e15 q^{9} -2.10732e16 q^{10} -7.18987e16 q^{11} -1.52302e17 q^{12} +1.13201e18 q^{13} +5.18702e18 q^{14} +2.21682e18 q^{15} -5.39393e19 q^{16} -1.70846e20 q^{17} -7.38588e20 q^{18} -8.48651e20 q^{19} -1.59961e21 q^{20} -5.45655e20 q^{21} -9.92962e21 q^{22} -3.95696e22 q^{23} -3.79872e21 q^{24} +2.32831e22 q^{25} +1.56337e23 q^{26} +1.58460e23 q^{27} +3.93732e23 q^{28} +9.30999e23 q^{29} +3.06156e23 q^{30} -8.60649e23 q^{31} -9.69535e24 q^{32} +1.04456e24 q^{33} -2.35948e25 q^{34} -5.73095e24 q^{35} -5.60641e25 q^{36} -5.07725e25 q^{37} -1.17203e26 q^{38} -1.64461e25 q^{39} -3.98975e25 q^{40} -1.78283e26 q^{41} -7.53580e25 q^{42} +8.10579e26 q^{43} -7.53730e26 q^{44} +8.16039e26 q^{45} -5.46479e27 q^{46} -5.64217e27 q^{47} +7.83641e26 q^{48} -6.32036e27 q^{49} +3.21552e27 q^{50} +2.48208e27 q^{51} +1.18671e28 q^{52} +5.15002e28 q^{53} +2.18842e28 q^{54} +1.09709e28 q^{55} +9.82047e27 q^{56} +1.23294e28 q^{57} +1.28576e29 q^{58} +1.40126e29 q^{59} +2.32394e28 q^{60} -8.28448e28 q^{61} -1.18860e29 q^{62} -2.00862e29 q^{63} -8.75647e29 q^{64} -1.72731e29 q^{65} +1.44259e29 q^{66} +2.02520e29 q^{67} -1.79102e30 q^{68} +5.74875e29 q^{69} -7.91476e29 q^{70} +6.89895e30 q^{71} -1.39835e30 q^{72} -3.84757e30 q^{73} -7.01196e30 q^{74} -3.38261e29 q^{75} -8.89659e30 q^{76} -2.70040e30 q^{77} -2.27129e30 q^{78} +9.36491e30 q^{79} +8.23049e30 q^{80} +2.74277e31 q^{81} -2.46218e31 q^{82} +7.23102e31 q^{83} -5.72021e30 q^{84} +2.60691e31 q^{85} +1.11945e32 q^{86} -1.35257e31 q^{87} -1.87995e31 q^{88} +4.37547e31 q^{89} +1.12700e32 q^{90} +4.25165e31 q^{91} -4.14817e32 q^{92} +1.25037e31 q^{93} -7.79216e32 q^{94} +1.29494e32 q^{95} +1.40856e32 q^{96} -1.02091e33 q^{97} -8.72877e32 q^{98} +3.84514e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} + O(q^{10}) \) \( 5q + 30472q^{2} - 14988714q^{3} + 1141311360q^{4} - 762939453125q^{5} + 12925063115760q^{6} - 65452561787158q^{7} + 155610638035200q^{8} + 14541250990408965q^{9} - 4649658203125000q^{10} - 287801801877976640q^{11} - 405379955363513088q^{12} + 2397201150889907466q^{13} + 11676449916272482320q^{14} + 2287096252441406250q^{15} - 89180089543245957120q^{16} - \)\(30\!\cdots\!18\)\(q^{17} + \)\(53\!\cdots\!56\)\(q^{18} + \)\(91\!\cdots\!00\)\(q^{19} - \)\(17\!\cdots\!00\)\(q^{20} - \)\(10\!\cdots\!40\)\(q^{21} - \)\(13\!\cdots\!96\)\(q^{22} + \)\(55\!\cdots\!46\)\(q^{23} - \)\(71\!\cdots\!00\)\(q^{24} + \)\(11\!\cdots\!25\)\(q^{25} - \)\(42\!\cdots\!40\)\(q^{26} + \)\(67\!\cdots\!00\)\(q^{27} - \)\(13\!\cdots\!36\)\(q^{28} - \)\(92\!\cdots\!50\)\(q^{29} - \)\(19\!\cdots\!00\)\(q^{30} - \)\(13\!\cdots\!40\)\(q^{31} - \)\(81\!\cdots\!08\)\(q^{32} - \)\(33\!\cdots\!48\)\(q^{33} - \)\(68\!\cdots\!80\)\(q^{34} + \)\(99\!\cdots\!50\)\(q^{35} - \)\(18\!\cdots\!20\)\(q^{36} - \)\(14\!\cdots\!38\)\(q^{37} - \)\(33\!\cdots\!00\)\(q^{38} - \)\(78\!\cdots\!20\)\(q^{39} - \)\(23\!\cdots\!00\)\(q^{40} - \)\(13\!\cdots\!90\)\(q^{41} - \)\(26\!\cdots\!36\)\(q^{42} - \)\(23\!\cdots\!94\)\(q^{43} - \)\(18\!\cdots\!80\)\(q^{44} - \)\(22\!\cdots\!25\)\(q^{45} - \)\(28\!\cdots\!40\)\(q^{46} - \)\(77\!\cdots\!98\)\(q^{47} - \)\(73\!\cdots\!04\)\(q^{48} + \)\(41\!\cdots\!85\)\(q^{49} + \)\(70\!\cdots\!00\)\(q^{50} + \)\(73\!\cdots\!60\)\(q^{51} + \)\(48\!\cdots\!72\)\(q^{52} + \)\(10\!\cdots\!86\)\(q^{53} + \)\(64\!\cdots\!00\)\(q^{54} + \)\(43\!\cdots\!00\)\(q^{55} + \)\(14\!\cdots\!00\)\(q^{56} + \)\(20\!\cdots\!00\)\(q^{57} + \)\(21\!\cdots\!00\)\(q^{58} + \)\(25\!\cdots\!00\)\(q^{59} + \)\(61\!\cdots\!00\)\(q^{60} + \)\(74\!\cdots\!10\)\(q^{61} + \)\(53\!\cdots\!24\)\(q^{62} - \)\(10\!\cdots\!34\)\(q^{63} - \)\(10\!\cdots\!40\)\(q^{64} - \)\(36\!\cdots\!50\)\(q^{65} - \)\(33\!\cdots\!80\)\(q^{66} - \)\(37\!\cdots\!18\)\(q^{67} + \)\(11\!\cdots\!44\)\(q^{68} - \)\(27\!\cdots\!20\)\(q^{69} - \)\(17\!\cdots\!00\)\(q^{70} - \)\(55\!\cdots\!40\)\(q^{71} - \)\(15\!\cdots\!00\)\(q^{72} - \)\(13\!\cdots\!54\)\(q^{73} - \)\(36\!\cdots\!80\)\(q^{74} - \)\(34\!\cdots\!50\)\(q^{75} + \)\(71\!\cdots\!00\)\(q^{76} + \)\(47\!\cdots\!44\)\(q^{77} + \)\(12\!\cdots\!72\)\(q^{78} - \)\(10\!\cdots\!00\)\(q^{79} + \)\(13\!\cdots\!00\)\(q^{80} + \)\(78\!\cdots\!05\)\(q^{81} + \)\(27\!\cdots\!84\)\(q^{82} + \)\(92\!\cdots\!26\)\(q^{83} + \)\(17\!\cdots\!20\)\(q^{84} + \)\(47\!\cdots\!50\)\(q^{85} + \)\(65\!\cdots\!60\)\(q^{86} + \)\(13\!\cdots\!00\)\(q^{87} + \)\(19\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!50\)\(q^{89} - \)\(82\!\cdots\!00\)\(q^{90} - \)\(26\!\cdots\!40\)\(q^{91} - \)\(69\!\cdots\!68\)\(q^{92} - \)\(69\!\cdots\!88\)\(q^{93} - \)\(36\!\cdots\!80\)\(q^{94} - \)\(14\!\cdots\!00\)\(q^{95} - \)\(34\!\cdots\!40\)\(q^{96} - \)\(86\!\cdots\!98\)\(q^{97} - \)\(19\!\cdots\!96\)\(q^{98} - \)\(17\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 138106. 1.49010 0.745051 0.667007i \(-0.232425\pi\)
0.745051 + 0.667007i \(0.232425\pi\)
\(3\) −1.45282e7 −0.194855 −0.0974273 0.995243i \(-0.531061\pi\)
−0.0974273 + 0.995243i \(0.531061\pi\)
\(4\) 1.04832e10 1.22041
\(5\) −1.52588e11 −0.447214
\(6\) −2.00642e12 −0.290353
\(7\) 3.75584e13 0.427158 0.213579 0.976926i \(-0.431488\pi\)
0.213579 + 0.976926i \(0.431488\pi\)
\(8\) 2.61472e14 0.328428
\(9\) −5.34799e15 −0.962032
\(10\) −2.10732e16 −0.666394
\(11\) −7.18987e16 −0.471783 −0.235891 0.971779i \(-0.575801\pi\)
−0.235891 + 0.971779i \(0.575801\pi\)
\(12\) −1.52302e17 −0.237802
\(13\) 1.13201e18 0.471830 0.235915 0.971774i \(-0.424191\pi\)
0.235915 + 0.971774i \(0.424191\pi\)
\(14\) 5.18702e18 0.636510
\(15\) 2.21682e18 0.0871416
\(16\) −5.39393e19 −0.731014
\(17\) −1.70846e20 −0.851526 −0.425763 0.904835i \(-0.639994\pi\)
−0.425763 + 0.904835i \(0.639994\pi\)
\(18\) −7.38588e20 −1.43353
\(19\) −8.48651e20 −0.674986 −0.337493 0.941328i \(-0.609579\pi\)
−0.337493 + 0.941328i \(0.609579\pi\)
\(20\) −1.59961e21 −0.545782
\(21\) −5.45655e20 −0.0832338
\(22\) −9.92962e21 −0.703005
\(23\) −3.95696e22 −1.34540 −0.672702 0.739914i \(-0.734866\pi\)
−0.672702 + 0.739914i \(0.734866\pi\)
\(24\) −3.79872e21 −0.0639958
\(25\) 2.32831e22 0.200000
\(26\) 1.56337e23 0.703075
\(27\) 1.58460e23 0.382311
\(28\) 3.93732e23 0.521307
\(29\) 9.30999e23 0.690848 0.345424 0.938447i \(-0.387735\pi\)
0.345424 + 0.938447i \(0.387735\pi\)
\(30\) 3.06156e23 0.129850
\(31\) −8.60649e23 −0.212500 −0.106250 0.994339i \(-0.533884\pi\)
−0.106250 + 0.994339i \(0.533884\pi\)
\(32\) −9.69535e24 −1.41772
\(33\) 1.04456e24 0.0919290
\(34\) −2.35948e25 −1.26886
\(35\) −5.73095e24 −0.191031
\(36\) −5.60641e25 −1.17407
\(37\) −5.07725e25 −0.676550 −0.338275 0.941047i \(-0.609843\pi\)
−0.338275 + 0.941047i \(0.609843\pi\)
\(38\) −1.17203e26 −1.00580
\(39\) −1.64461e25 −0.0919383
\(40\) −3.98975e25 −0.146878
\(41\) −1.78283e26 −0.436692 −0.218346 0.975871i \(-0.570066\pi\)
−0.218346 + 0.975871i \(0.570066\pi\)
\(42\) −7.53580e25 −0.124027
\(43\) 8.10579e26 0.904827 0.452414 0.891808i \(-0.350563\pi\)
0.452414 + 0.891808i \(0.350563\pi\)
\(44\) −7.53730e26 −0.575767
\(45\) 8.16039e26 0.430234
\(46\) −5.46479e27 −2.00479
\(47\) −5.64217e27 −1.45155 −0.725775 0.687933i \(-0.758518\pi\)
−0.725775 + 0.687933i \(0.758518\pi\)
\(48\) 7.83641e26 0.142441
\(49\) −6.32036e27 −0.817536
\(50\) 3.21552e27 0.298021
\(51\) 2.48208e27 0.165924
\(52\) 1.18671e28 0.575825
\(53\) 5.15002e28 1.82497 0.912487 0.409105i \(-0.134159\pi\)
0.912487 + 0.409105i \(0.134159\pi\)
\(54\) 2.18842e28 0.569682
\(55\) 1.09709e28 0.210988
\(56\) 9.82047e27 0.140291
\(57\) 1.23294e28 0.131524
\(58\) 1.28576e29 1.02943
\(59\) 1.40126e29 0.846175 0.423088 0.906089i \(-0.360946\pi\)
0.423088 + 0.906089i \(0.360946\pi\)
\(60\) 2.32394e28 0.106348
\(61\) −8.28448e28 −0.288618 −0.144309 0.989533i \(-0.546096\pi\)
−0.144309 + 0.989533i \(0.546096\pi\)
\(62\) −1.18860e29 −0.316646
\(63\) −2.00862e29 −0.410940
\(64\) −8.75647e29 −1.38153
\(65\) −1.72731e29 −0.211009
\(66\) 1.44259e29 0.136984
\(67\) 2.02520e29 0.150049 0.0750246 0.997182i \(-0.476096\pi\)
0.0750246 + 0.997182i \(0.476096\pi\)
\(68\) −1.79102e30 −1.03921
\(69\) 5.74875e29 0.262158
\(70\) −7.91476e29 −0.284656
\(71\) 6.89895e30 1.96345 0.981726 0.190302i \(-0.0609466\pi\)
0.981726 + 0.190302i \(0.0609466\pi\)
\(72\) −1.39835e30 −0.315959
\(73\) −3.84757e30 −0.692404 −0.346202 0.938160i \(-0.612529\pi\)
−0.346202 + 0.938160i \(0.612529\pi\)
\(74\) −7.01196e30 −1.00813
\(75\) −3.38261e29 −0.0389709
\(76\) −8.89659e30 −0.823757
\(77\) −2.70040e30 −0.201526
\(78\) −2.27129e30 −0.136997
\(79\) 9.36491e30 0.457780 0.228890 0.973452i \(-0.426490\pi\)
0.228890 + 0.973452i \(0.426490\pi\)
\(80\) 8.23049e30 0.326920
\(81\) 2.74277e31 0.887537
\(82\) −2.46218e31 −0.650716
\(83\) 7.23102e31 1.56463 0.782314 0.622884i \(-0.214039\pi\)
0.782314 + 0.622884i \(0.214039\pi\)
\(84\) −5.72021e30 −0.101579
\(85\) 2.60691e31 0.380814
\(86\) 1.11945e32 1.34829
\(87\) −1.35257e31 −0.134615
\(88\) −1.87995e31 −0.154947
\(89\) 4.37547e31 0.299288 0.149644 0.988740i \(-0.452187\pi\)
0.149644 + 0.988740i \(0.452187\pi\)
\(90\) 1.12700e32 0.641092
\(91\) 4.25165e31 0.201546
\(92\) −4.14817e32 −1.64194
\(93\) 1.25037e31 0.0414065
\(94\) −7.79216e32 −2.16296
\(95\) 1.29494e32 0.301863
\(96\) 1.40856e32 0.276248
\(97\) −1.02091e33 −1.68754 −0.843771 0.536703i \(-0.819669\pi\)
−0.843771 + 0.536703i \(0.819669\pi\)
\(98\) −8.72877e32 −1.21821
\(99\) 3.84514e32 0.453870
\(100\) 2.44081e32 0.244081
\(101\) 2.20022e33 1.86709 0.933543 0.358466i \(-0.116700\pi\)
0.933543 + 0.358466i \(0.116700\pi\)
\(102\) 3.42790e32 0.247244
\(103\) −1.21369e33 −0.745234 −0.372617 0.927985i \(-0.621539\pi\)
−0.372617 + 0.927985i \(0.621539\pi\)
\(104\) 2.95990e32 0.154962
\(105\) 8.32603e31 0.0372233
\(106\) 7.11246e33 2.71940
\(107\) −3.78167e33 −1.23837 −0.619187 0.785244i \(-0.712538\pi\)
−0.619187 + 0.785244i \(0.712538\pi\)
\(108\) 1.66117e33 0.466575
\(109\) −4.93974e33 −1.19170 −0.595849 0.803096i \(-0.703184\pi\)
−0.595849 + 0.803096i \(0.703184\pi\)
\(110\) 1.51514e33 0.314393
\(111\) 7.37632e32 0.131829
\(112\) −2.02587e33 −0.312259
\(113\) −3.63884e33 −0.484360 −0.242180 0.970231i \(-0.577862\pi\)
−0.242180 + 0.970231i \(0.577862\pi\)
\(114\) 1.70275e33 0.195984
\(115\) 6.03785e33 0.601683
\(116\) 9.75986e33 0.843115
\(117\) −6.05399e33 −0.453916
\(118\) 1.93522e34 1.26089
\(119\) −6.41670e33 −0.363737
\(120\) 5.79638e32 0.0286198
\(121\) −1.80557e34 −0.777421
\(122\) −1.14413e34 −0.430070
\(123\) 2.59012e33 0.0850915
\(124\) −9.02236e33 −0.259336
\(125\) −3.55271e33 −0.0894427
\(126\) −2.77401e34 −0.612343
\(127\) 3.03012e34 0.587082 0.293541 0.955947i \(-0.405166\pi\)
0.293541 + 0.955947i \(0.405166\pi\)
\(128\) −3.76492e34 −0.640902
\(129\) −1.17762e34 −0.176310
\(130\) −2.38552e34 −0.314425
\(131\) −7.83378e34 −0.909903 −0.454951 0.890516i \(-0.650343\pi\)
−0.454951 + 0.890516i \(0.650343\pi\)
\(132\) 1.09503e34 0.112191
\(133\) −3.18739e34 −0.288326
\(134\) 2.79691e34 0.223589
\(135\) −2.41790e34 −0.170975
\(136\) −4.46715e34 −0.279665
\(137\) 1.43675e35 0.797060 0.398530 0.917155i \(-0.369520\pi\)
0.398530 + 0.917155i \(0.369520\pi\)
\(138\) 7.93934e34 0.390642
\(139\) 3.03428e35 1.32529 0.662647 0.748932i \(-0.269433\pi\)
0.662647 + 0.748932i \(0.269433\pi\)
\(140\) −6.00788e34 −0.233136
\(141\) 8.19705e34 0.282841
\(142\) 9.52783e35 2.92574
\(143\) −8.13902e34 −0.222601
\(144\) 2.88467e35 0.703259
\(145\) −1.42059e35 −0.308957
\(146\) −5.31371e35 −1.03175
\(147\) 9.18234e34 0.159301
\(148\) −5.32259e35 −0.825666
\(149\) −8.47533e35 −1.17648 −0.588238 0.808688i \(-0.700178\pi\)
−0.588238 + 0.808688i \(0.700178\pi\)
\(150\) −4.67157e34 −0.0580707
\(151\) −1.42730e36 −1.59000 −0.794999 0.606610i \(-0.792529\pi\)
−0.794999 + 0.606610i \(0.792529\pi\)
\(152\) −2.21899e35 −0.221685
\(153\) 9.13684e35 0.819195
\(154\) −3.72940e35 −0.300294
\(155\) 1.31325e35 0.0950327
\(156\) −1.72408e35 −0.112202
\(157\) −1.47748e36 −0.865320 −0.432660 0.901557i \(-0.642425\pi\)
−0.432660 + 0.901557i \(0.642425\pi\)
\(158\) 1.29335e36 0.682139
\(159\) −7.48204e35 −0.355605
\(160\) 1.47939e36 0.634021
\(161\) −1.48617e36 −0.574701
\(162\) 3.78792e36 1.32252
\(163\) −1.91804e36 −0.605011 −0.302505 0.953148i \(-0.597823\pi\)
−0.302505 + 0.953148i \(0.597823\pi\)
\(164\) −1.86897e36 −0.532942
\(165\) −1.59387e35 −0.0411119
\(166\) 9.98644e36 2.33146
\(167\) −3.91696e36 −0.828185 −0.414093 0.910235i \(-0.635901\pi\)
−0.414093 + 0.910235i \(0.635901\pi\)
\(168\) −1.42674e35 −0.0273363
\(169\) −4.47468e36 −0.777376
\(170\) 3.60028e36 0.567452
\(171\) 4.53858e36 0.649358
\(172\) 8.49747e36 1.10426
\(173\) −1.42658e37 −1.68475 −0.842375 0.538892i \(-0.818843\pi\)
−0.842375 + 0.538892i \(0.818843\pi\)
\(174\) −1.86798e36 −0.200590
\(175\) 8.74474e35 0.0854317
\(176\) 3.87817e36 0.344880
\(177\) −2.03577e36 −0.164881
\(178\) 6.04277e36 0.445970
\(179\) −1.89294e37 −1.27368 −0.636842 0.770994i \(-0.719760\pi\)
−0.636842 + 0.770994i \(0.719760\pi\)
\(180\) 8.55471e36 0.525060
\(181\) 2.60338e37 1.45828 0.729140 0.684365i \(-0.239920\pi\)
0.729140 + 0.684365i \(0.239920\pi\)
\(182\) 5.87177e36 0.300325
\(183\) 1.20358e36 0.0562385
\(184\) −1.03464e37 −0.441869
\(185\) 7.74727e36 0.302562
\(186\) 1.72683e36 0.0616999
\(187\) 1.22836e37 0.401735
\(188\) −5.91481e37 −1.77148
\(189\) 5.95148e36 0.163307
\(190\) 1.78838e37 0.449807
\(191\) −7.37079e37 −1.70006 −0.850029 0.526736i \(-0.823415\pi\)
−0.850029 + 0.526736i \(0.823415\pi\)
\(192\) 1.27216e37 0.269197
\(193\) 9.51744e36 0.184852 0.0924261 0.995720i \(-0.470538\pi\)
0.0924261 + 0.995720i \(0.470538\pi\)
\(194\) −1.40994e38 −2.51461
\(195\) 2.50947e36 0.0411160
\(196\) −6.62577e37 −0.997726
\(197\) 5.57117e37 0.771353 0.385677 0.922634i \(-0.373968\pi\)
0.385677 + 0.922634i \(0.373968\pi\)
\(198\) 5.31035e37 0.676313
\(199\) 1.97421e37 0.231375 0.115688 0.993286i \(-0.463093\pi\)
0.115688 + 0.993286i \(0.463093\pi\)
\(200\) 6.08787e36 0.0656857
\(201\) −2.94225e36 −0.0292378
\(202\) 3.03863e38 2.78215
\(203\) 3.49668e37 0.295101
\(204\) 2.60202e37 0.202494
\(205\) 2.72038e37 0.195295
\(206\) −1.67617e38 −1.11048
\(207\) 2.11618e38 1.29432
\(208\) −6.10600e37 −0.344915
\(209\) 6.10169e37 0.318447
\(210\) 1.14987e37 0.0554665
\(211\) 1.86677e37 0.0832589 0.0416294 0.999133i \(-0.486745\pi\)
0.0416294 + 0.999133i \(0.486745\pi\)
\(212\) 5.39887e38 2.22721
\(213\) −1.00229e38 −0.382587
\(214\) −5.22270e38 −1.84530
\(215\) −1.23684e38 −0.404651
\(216\) 4.14328e37 0.125562
\(217\) −3.23246e37 −0.0907710
\(218\) −6.82205e38 −1.77575
\(219\) 5.58983e37 0.134918
\(220\) 1.15010e38 0.257491
\(221\) −1.93400e38 −0.401776
\(222\) 1.01871e38 0.196439
\(223\) −2.13813e38 −0.382828 −0.191414 0.981509i \(-0.561307\pi\)
−0.191414 + 0.981509i \(0.561307\pi\)
\(224\) −3.64142e38 −0.605589
\(225\) −1.24518e38 −0.192406
\(226\) −5.02544e38 −0.721746
\(227\) 2.97111e38 0.396727 0.198364 0.980128i \(-0.436437\pi\)
0.198364 + 0.980128i \(0.436437\pi\)
\(228\) 1.29251e38 0.160513
\(229\) −6.71382e38 −0.775683 −0.387841 0.921726i \(-0.626779\pi\)
−0.387841 + 0.921726i \(0.626779\pi\)
\(230\) 8.33860e38 0.896569
\(231\) 3.92319e37 0.0392683
\(232\) 2.43430e38 0.226894
\(233\) 1.66756e39 1.44780 0.723899 0.689906i \(-0.242348\pi\)
0.723899 + 0.689906i \(0.242348\pi\)
\(234\) −8.36090e38 −0.676381
\(235\) 8.60927e38 0.649153
\(236\) 1.46897e39 1.03268
\(237\) −1.36055e38 −0.0892005
\(238\) −8.86182e38 −0.542005
\(239\) 6.59391e38 0.376338 0.188169 0.982137i \(-0.439745\pi\)
0.188169 + 0.982137i \(0.439745\pi\)
\(240\) −1.19574e38 −0.0637018
\(241\) 1.79835e39 0.894524 0.447262 0.894403i \(-0.352399\pi\)
0.447262 + 0.894403i \(0.352399\pi\)
\(242\) −2.49360e39 −1.15844
\(243\) −1.27936e39 −0.555251
\(244\) −8.68479e38 −0.352231
\(245\) 9.64411e38 0.365613
\(246\) 3.57710e38 0.126795
\(247\) −9.60683e38 −0.318479
\(248\) −2.25036e38 −0.0697909
\(249\) −1.05054e39 −0.304875
\(250\) −4.90650e38 −0.133279
\(251\) 4.62035e39 1.17506 0.587528 0.809204i \(-0.300101\pi\)
0.587528 + 0.809204i \(0.300101\pi\)
\(252\) −2.10568e39 −0.501514
\(253\) 2.84501e39 0.634738
\(254\) 4.18477e39 0.874812
\(255\) −3.78736e38 −0.0742034
\(256\) 2.32218e39 0.426517
\(257\) 4.29716e39 0.740090 0.370045 0.929014i \(-0.379342\pi\)
0.370045 + 0.929014i \(0.379342\pi\)
\(258\) −1.62636e39 −0.262720
\(259\) −1.90693e39 −0.288994
\(260\) −1.81078e39 −0.257517
\(261\) −4.97898e39 −0.664618
\(262\) −1.08189e40 −1.35585
\(263\) −5.41479e39 −0.637253 −0.318627 0.947880i \(-0.603222\pi\)
−0.318627 + 0.947880i \(0.603222\pi\)
\(264\) 2.73123e38 0.0301921
\(265\) −7.85830e39 −0.816154
\(266\) −4.40197e39 −0.429635
\(267\) −6.35677e38 −0.0583177
\(268\) 2.12306e39 0.183121
\(269\) 9.46661e39 0.767860 0.383930 0.923362i \(-0.374570\pi\)
0.383930 + 0.923362i \(0.374570\pi\)
\(270\) −3.33926e39 −0.254770
\(271\) −2.02716e40 −1.45511 −0.727555 0.686050i \(-0.759343\pi\)
−0.727555 + 0.686050i \(0.759343\pi\)
\(272\) 9.21533e39 0.622478
\(273\) −6.17688e38 −0.0392722
\(274\) 1.98423e40 1.18770
\(275\) −1.67402e39 −0.0943565
\(276\) 6.02653e39 0.319939
\(277\) −2.14513e40 −1.07285 −0.536423 0.843949i \(-0.680225\pi\)
−0.536423 + 0.843949i \(0.680225\pi\)
\(278\) 4.19052e40 1.97482
\(279\) 4.60274e39 0.204431
\(280\) −1.49848e39 −0.0627400
\(281\) −2.22768e40 −0.879425 −0.439712 0.898139i \(-0.644920\pi\)
−0.439712 + 0.898139i \(0.644920\pi\)
\(282\) 1.13206e40 0.421462
\(283\) 1.45996e40 0.512702 0.256351 0.966584i \(-0.417480\pi\)
0.256351 + 0.966584i \(0.417480\pi\)
\(284\) 7.23231e40 2.39621
\(285\) −1.88131e39 −0.0588193
\(286\) −1.12404e40 −0.331699
\(287\) −6.69600e39 −0.186537
\(288\) 5.18507e40 1.36389
\(289\) −1.10661e40 −0.274903
\(290\) −1.96192e40 −0.460377
\(291\) 1.48320e40 0.328825
\(292\) −4.03349e40 −0.845015
\(293\) −3.33509e40 −0.660377 −0.330188 0.943915i \(-0.607112\pi\)
−0.330188 + 0.943915i \(0.607112\pi\)
\(294\) 1.26813e40 0.237374
\(295\) −2.13815e40 −0.378421
\(296\) −1.32756e40 −0.222198
\(297\) −1.13931e40 −0.180368
\(298\) −1.17049e41 −1.75307
\(299\) −4.47933e40 −0.634802
\(300\) −3.54606e39 −0.0475604
\(301\) 3.04440e40 0.386504
\(302\) −1.97119e41 −2.36926
\(303\) −3.19653e40 −0.363810
\(304\) 4.57757e40 0.493424
\(305\) 1.26411e40 0.129074
\(306\) 1.26185e41 1.22069
\(307\) 8.68250e40 0.795906 0.397953 0.917406i \(-0.369721\pi\)
0.397953 + 0.917406i \(0.369721\pi\)
\(308\) −2.83089e40 −0.245944
\(309\) 1.76327e40 0.145212
\(310\) 1.81367e40 0.141608
\(311\) 1.66474e41 1.23254 0.616270 0.787535i \(-0.288643\pi\)
0.616270 + 0.787535i \(0.288643\pi\)
\(312\) −4.30019e39 −0.0301951
\(313\) 2.38300e41 1.58724 0.793618 0.608416i \(-0.208195\pi\)
0.793618 + 0.608416i \(0.208195\pi\)
\(314\) −2.04048e41 −1.28942
\(315\) 3.06491e40 0.183778
\(316\) 9.81743e40 0.558677
\(317\) −1.03851e41 −0.560964 −0.280482 0.959859i \(-0.590494\pi\)
−0.280482 + 0.959859i \(0.590494\pi\)
\(318\) −1.03331e41 −0.529888
\(319\) −6.69377e40 −0.325930
\(320\) 1.33613e41 0.617838
\(321\) 5.49408e40 0.241303
\(322\) −2.05248e41 −0.856363
\(323\) 1.44989e41 0.574768
\(324\) 2.87530e41 1.08316
\(325\) 2.63567e40 0.0943660
\(326\) −2.64893e41 −0.901528
\(327\) 7.17654e40 0.232208
\(328\) −4.66160e40 −0.143422
\(329\) −2.11911e41 −0.620041
\(330\) −2.20122e40 −0.0612610
\(331\) −1.38040e41 −0.365463 −0.182732 0.983163i \(-0.558494\pi\)
−0.182732 + 0.983163i \(0.558494\pi\)
\(332\) 7.58043e41 1.90948
\(333\) 2.71531e41 0.650863
\(334\) −5.40954e41 −1.23408
\(335\) −3.09021e40 −0.0671040
\(336\) 2.94323e40 0.0608451
\(337\) 1.52333e40 0.0299847 0.0149923 0.999888i \(-0.495228\pi\)
0.0149923 + 0.999888i \(0.495228\pi\)
\(338\) −6.17978e41 −1.15837
\(339\) 5.28657e40 0.0943798
\(340\) 2.73287e41 0.464748
\(341\) 6.18796e40 0.100254
\(342\) 6.26803e41 0.967610
\(343\) −5.27746e41 −0.776376
\(344\) 2.11944e41 0.297171
\(345\) −8.77189e40 −0.117241
\(346\) −1.97019e42 −2.51045
\(347\) 1.11878e42 1.35928 0.679639 0.733547i \(-0.262136\pi\)
0.679639 + 0.733547i \(0.262136\pi\)
\(348\) −1.41793e41 −0.164285
\(349\) −6.63572e41 −0.733278 −0.366639 0.930363i \(-0.619492\pi\)
−0.366639 + 0.930363i \(0.619492\pi\)
\(350\) 1.20770e41 0.127302
\(351\) 1.79378e41 0.180386
\(352\) 6.97084e41 0.668853
\(353\) 4.28180e41 0.392052 0.196026 0.980599i \(-0.437196\pi\)
0.196026 + 0.980599i \(0.437196\pi\)
\(354\) −2.81152e41 −0.245690
\(355\) −1.05270e42 −0.878082
\(356\) 4.58690e41 0.365253
\(357\) 9.32230e40 0.0708757
\(358\) −2.61426e42 −1.89792
\(359\) −9.04901e41 −0.627397 −0.313698 0.949523i \(-0.601568\pi\)
−0.313698 + 0.949523i \(0.601568\pi\)
\(360\) 2.13371e41 0.141301
\(361\) −8.60562e41 −0.544394
\(362\) 3.59541e42 2.17299
\(363\) 2.62317e41 0.151484
\(364\) 4.45710e41 0.245968
\(365\) 5.87093e41 0.309653
\(366\) 1.66222e41 0.0838011
\(367\) −2.16128e41 −0.104165 −0.0520823 0.998643i \(-0.516586\pi\)
−0.0520823 + 0.998643i \(0.516586\pi\)
\(368\) 2.13436e42 0.983510
\(369\) 9.53454e41 0.420112
\(370\) 1.06994e42 0.450849
\(371\) 1.93426e42 0.779553
\(372\) 1.31079e41 0.0505328
\(373\) 3.17253e42 1.17007 0.585033 0.811009i \(-0.301081\pi\)
0.585033 + 0.811009i \(0.301081\pi\)
\(374\) 1.69644e42 0.598627
\(375\) 5.16145e40 0.0174283
\(376\) −1.47527e42 −0.476730
\(377\) 1.05390e42 0.325963
\(378\) 8.21933e41 0.243345
\(379\) −5.62885e42 −1.59541 −0.797705 0.603048i \(-0.793953\pi\)
−0.797705 + 0.603048i \(0.793953\pi\)
\(380\) 1.35751e42 0.368395
\(381\) −4.40221e41 −0.114396
\(382\) −1.01795e43 −2.53326
\(383\) 1.01197e42 0.241205 0.120603 0.992701i \(-0.461517\pi\)
0.120603 + 0.992701i \(0.461517\pi\)
\(384\) 5.46975e41 0.124883
\(385\) 4.12048e41 0.0901251
\(386\) 1.31441e42 0.275449
\(387\) −4.33497e42 −0.870472
\(388\) −1.07024e43 −2.05949
\(389\) −9.74782e42 −1.79779 −0.898896 0.438163i \(-0.855629\pi\)
−0.898896 + 0.438163i \(0.855629\pi\)
\(390\) 3.46572e41 0.0612671
\(391\) 6.76032e42 1.14565
\(392\) −1.65260e42 −0.268502
\(393\) 1.13811e42 0.177299
\(394\) 7.69409e42 1.14940
\(395\) −1.42897e42 −0.204725
\(396\) 4.03094e42 0.553906
\(397\) −5.84553e42 −0.770514 −0.385257 0.922809i \(-0.625887\pi\)
−0.385257 + 0.922809i \(0.625887\pi\)
\(398\) 2.72649e42 0.344773
\(399\) 4.63070e41 0.0561816
\(400\) −1.25587e42 −0.146203
\(401\) 6.82021e42 0.761931 0.380966 0.924589i \(-0.375592\pi\)
0.380966 + 0.924589i \(0.375592\pi\)
\(402\) −4.06341e41 −0.0435673
\(403\) −9.74265e41 −0.100264
\(404\) 2.30654e43 2.27860
\(405\) −4.18513e42 −0.396918
\(406\) 4.82911e42 0.439732
\(407\) 3.65048e42 0.319185
\(408\) 6.48996e41 0.0544941
\(409\) −7.09650e42 −0.572281 −0.286141 0.958188i \(-0.592372\pi\)
−0.286141 + 0.958188i \(0.592372\pi\)
\(410\) 3.75699e42 0.291009
\(411\) −2.08733e42 −0.155311
\(412\) −1.27233e43 −0.909488
\(413\) 5.26290e42 0.361451
\(414\) 2.92256e43 1.92867
\(415\) −1.10337e43 −0.699723
\(416\) −1.09753e43 −0.668921
\(417\) −4.40826e42 −0.258239
\(418\) 8.42678e42 0.474518
\(419\) −1.41115e43 −0.763912 −0.381956 0.924181i \(-0.624749\pi\)
−0.381956 + 0.924181i \(0.624749\pi\)
\(420\) 8.72835e41 0.0454275
\(421\) −9.28037e42 −0.464420 −0.232210 0.972666i \(-0.574596\pi\)
−0.232210 + 0.972666i \(0.574596\pi\)
\(422\) 2.57811e42 0.124064
\(423\) 3.01743e43 1.39644
\(424\) 1.34659e43 0.599374
\(425\) −3.97782e42 −0.170305
\(426\) −1.38422e43 −0.570095
\(427\) −3.11151e42 −0.123285
\(428\) −3.96441e43 −1.51132
\(429\) 1.18245e42 0.0433749
\(430\) −1.70815e43 −0.602972
\(431\) −2.40707e43 −0.817738 −0.408869 0.912593i \(-0.634077\pi\)
−0.408869 + 0.912593i \(0.634077\pi\)
\(432\) −8.54721e42 −0.279475
\(433\) 4.96426e43 1.56244 0.781222 0.624253i \(-0.214597\pi\)
0.781222 + 0.624253i \(0.214597\pi\)
\(434\) −4.46420e42 −0.135258
\(435\) 2.06386e42 0.0602016
\(436\) −5.17843e43 −1.45436
\(437\) 3.35808e43 0.908128
\(438\) 7.71986e42 0.201042
\(439\) 4.80839e43 1.20597 0.602984 0.797754i \(-0.293978\pi\)
0.602984 + 0.797754i \(0.293978\pi\)
\(440\) 2.86858e42 0.0692943
\(441\) 3.38013e43 0.786495
\(442\) −2.67096e43 −0.598687
\(443\) −8.49113e42 −0.183360 −0.0916799 0.995789i \(-0.529224\pi\)
−0.0916799 + 0.995789i \(0.529224\pi\)
\(444\) 7.73275e42 0.160885
\(445\) −6.67644e42 −0.133846
\(446\) −2.95287e43 −0.570453
\(447\) 1.23131e43 0.229242
\(448\) −3.28879e43 −0.590131
\(449\) −8.15651e43 −1.41072 −0.705359 0.708851i \(-0.749214\pi\)
−0.705359 + 0.708851i \(0.749214\pi\)
\(450\) −1.71966e43 −0.286705
\(451\) 1.28183e43 0.206024
\(452\) −3.81467e43 −0.591116
\(453\) 2.07361e43 0.309819
\(454\) 4.10327e43 0.591165
\(455\) −6.48751e42 −0.0901342
\(456\) 3.22378e42 0.0431962
\(457\) 3.82156e43 0.493882 0.246941 0.969030i \(-0.420575\pi\)
0.246941 + 0.969030i \(0.420575\pi\)
\(458\) −9.27216e43 −1.15585
\(459\) −2.70722e43 −0.325548
\(460\) 6.32960e43 0.734298
\(461\) 1.42045e44 1.58987 0.794933 0.606698i \(-0.207506\pi\)
0.794933 + 0.606698i \(0.207506\pi\)
\(462\) 5.41814e42 0.0585137
\(463\) 1.76412e43 0.183841 0.0919203 0.995766i \(-0.470700\pi\)
0.0919203 + 0.995766i \(0.470700\pi\)
\(464\) −5.02175e43 −0.505020
\(465\) −1.90791e42 −0.0185176
\(466\) 2.30299e44 2.15737
\(467\) 1.44747e44 1.30882 0.654410 0.756140i \(-0.272917\pi\)
0.654410 + 0.756140i \(0.272917\pi\)
\(468\) −6.34653e43 −0.553962
\(469\) 7.60631e42 0.0640947
\(470\) 1.18899e44 0.967304
\(471\) 2.14651e43 0.168612
\(472\) 3.66390e43 0.277908
\(473\) −5.82796e43 −0.426882
\(474\) −1.87900e43 −0.132918
\(475\) −1.97592e43 −0.134997
\(476\) −6.72677e43 −0.443907
\(477\) −2.75423e44 −1.75568
\(478\) 9.10656e43 0.560782
\(479\) −2.82253e44 −1.67920 −0.839602 0.543203i \(-0.817212\pi\)
−0.839602 + 0.543203i \(0.817212\pi\)
\(480\) −2.14929e43 −0.123542
\(481\) −5.74751e43 −0.319217
\(482\) 2.48362e44 1.33293
\(483\) 2.15914e43 0.111983
\(484\) −1.89282e44 −0.948770
\(485\) 1.55779e44 0.754692
\(486\) −1.76687e44 −0.827382
\(487\) −2.41873e44 −1.09486 −0.547432 0.836850i \(-0.684395\pi\)
−0.547432 + 0.836850i \(0.684395\pi\)
\(488\) −2.16616e43 −0.0947902
\(489\) 2.78657e43 0.117889
\(490\) 1.33191e44 0.544801
\(491\) −3.36324e44 −1.33019 −0.665095 0.746759i \(-0.731609\pi\)
−0.665095 + 0.746759i \(0.731609\pi\)
\(492\) 2.71528e43 0.103846
\(493\) −1.59058e44 −0.588275
\(494\) −1.32676e44 −0.474566
\(495\) −5.86722e43 −0.202977
\(496\) 4.64228e43 0.155340
\(497\) 2.59113e44 0.838705
\(498\) −1.45085e44 −0.454295
\(499\) −8.01313e43 −0.242741 −0.121371 0.992607i \(-0.538729\pi\)
−0.121371 + 0.992607i \(0.538729\pi\)
\(500\) −3.72439e43 −0.109156
\(501\) 5.69063e43 0.161376
\(502\) 6.38096e44 1.75095
\(503\) 2.08304e44 0.553129 0.276565 0.960995i \(-0.410804\pi\)
0.276565 + 0.960995i \(0.410804\pi\)
\(504\) −5.25198e43 −0.134964
\(505\) −3.35728e44 −0.834986
\(506\) 3.92911e44 0.945825
\(507\) 6.50090e43 0.151475
\(508\) 3.17654e44 0.716478
\(509\) 3.65736e44 0.798591 0.399296 0.916822i \(-0.369255\pi\)
0.399296 + 0.916822i \(0.369255\pi\)
\(510\) −5.23056e43 −0.110571
\(511\) −1.44509e44 −0.295766
\(512\) 6.44110e44 1.27646
\(513\) −1.34477e44 −0.258054
\(514\) 5.93461e44 1.10281
\(515\) 1.85194e44 0.333279
\(516\) −1.23453e44 −0.215169
\(517\) 4.05665e44 0.684816
\(518\) −2.63358e44 −0.430631
\(519\) 2.07256e44 0.328281
\(520\) −4.51644e43 −0.0693013
\(521\) −3.73678e44 −0.555488 −0.277744 0.960655i \(-0.589587\pi\)
−0.277744 + 0.960655i \(0.589587\pi\)
\(522\) −6.87625e44 −0.990349
\(523\) −2.43582e44 −0.339913 −0.169957 0.985452i \(-0.554363\pi\)
−0.169957 + 0.985452i \(0.554363\pi\)
\(524\) −8.21232e44 −1.11045
\(525\) −1.27045e43 −0.0166468
\(526\) −7.47813e44 −0.949573
\(527\) 1.47039e44 0.180949
\(528\) −5.63428e43 −0.0672014
\(529\) 7.00750e44 0.810111
\(530\) −1.08528e45 −1.21615
\(531\) −7.49392e44 −0.814047
\(532\) −3.34141e44 −0.351875
\(533\) −2.01818e44 −0.206045
\(534\) −8.77905e43 −0.0868994
\(535\) 5.77037e44 0.553817
\(536\) 5.29533e43 0.0492804
\(537\) 2.75010e44 0.248183
\(538\) 1.30739e45 1.14419
\(539\) 4.54426e44 0.385699
\(540\) −2.53474e44 −0.208659
\(541\) 1.83384e45 1.46422 0.732112 0.681184i \(-0.238535\pi\)
0.732112 + 0.681184i \(0.238535\pi\)
\(542\) −2.79963e45 −2.16826
\(543\) −3.78224e44 −0.284153
\(544\) 1.65641e45 1.20722
\(545\) 7.53744e44 0.532944
\(546\) −8.53061e43 −0.0585196
\(547\) −2.32228e45 −1.54570 −0.772848 0.634592i \(-0.781168\pi\)
−0.772848 + 0.634592i \(0.781168\pi\)
\(548\) 1.50617e45 0.972738
\(549\) 4.43053e44 0.277659
\(550\) −2.31192e44 −0.140601
\(551\) −7.90093e44 −0.466312
\(552\) 1.50314e44 0.0861002
\(553\) 3.51731e44 0.195544
\(554\) −2.96255e45 −1.59865
\(555\) −1.12554e44 −0.0589557
\(556\) 3.18090e45 1.61740
\(557\) −2.15312e45 −1.06281 −0.531406 0.847117i \(-0.678336\pi\)
−0.531406 + 0.847117i \(0.678336\pi\)
\(558\) 6.35664e44 0.304624
\(559\) 9.17585e44 0.426925
\(560\) 3.09124e44 0.139646
\(561\) −1.78459e44 −0.0782800
\(562\) −3.07655e45 −1.31043
\(563\) −2.18829e45 −0.905142 −0.452571 0.891728i \(-0.649493\pi\)
−0.452571 + 0.891728i \(0.649493\pi\)
\(564\) 8.59314e44 0.345181
\(565\) 5.55242e44 0.216612
\(566\) 2.01629e45 0.763979
\(567\) 1.03014e45 0.379119
\(568\) 1.80388e45 0.644853
\(569\) 3.69991e45 1.28481 0.642404 0.766366i \(-0.277937\pi\)
0.642404 + 0.766366i \(0.277937\pi\)
\(570\) −2.59819e44 −0.0876469
\(571\) 4.09741e44 0.134281 0.0671403 0.997744i \(-0.478612\pi\)
0.0671403 + 0.997744i \(0.478612\pi\)
\(572\) −8.53231e44 −0.271664
\(573\) 1.07084e45 0.331264
\(574\) −9.24755e44 −0.277959
\(575\) −9.21302e44 −0.269081
\(576\) 4.68295e45 1.32907
\(577\) 2.41392e45 0.665767 0.332884 0.942968i \(-0.391978\pi\)
0.332884 + 0.942968i \(0.391978\pi\)
\(578\) −1.52829e45 −0.409634
\(579\) −1.38271e44 −0.0360193
\(580\) −1.48924e45 −0.377053
\(581\) 2.71585e45 0.668344
\(582\) 2.04838e45 0.489983
\(583\) −3.70280e45 −0.860992
\(584\) −1.00603e45 −0.227405
\(585\) 9.23766e44 0.202997
\(586\) −4.60594e45 −0.984029
\(587\) −3.30502e45 −0.686507 −0.343253 0.939243i \(-0.611529\pi\)
−0.343253 + 0.939243i \(0.611529\pi\)
\(588\) 9.62604e44 0.194411
\(589\) 7.30390e44 0.143434
\(590\) −2.95291e45 −0.563886
\(591\) −8.09389e44 −0.150302
\(592\) 2.73863e45 0.494568
\(593\) 3.04911e45 0.535514 0.267757 0.963486i \(-0.413718\pi\)
0.267757 + 0.963486i \(0.413718\pi\)
\(594\) −1.57344e45 −0.268766
\(595\) 9.79111e44 0.162668
\(596\) −8.88487e45 −1.43578
\(597\) −2.86816e44 −0.0450845
\(598\) −6.18620e45 −0.945920
\(599\) 4.77681e45 0.710551 0.355276 0.934762i \(-0.384387\pi\)
0.355276 + 0.934762i \(0.384387\pi\)
\(600\) −8.84457e43 −0.0127992
\(601\) −1.11023e46 −1.56310 −0.781549 0.623844i \(-0.785570\pi\)
−0.781549 + 0.623844i \(0.785570\pi\)
\(602\) 4.20449e45 0.575931
\(603\) −1.08307e45 −0.144352
\(604\) −1.49627e46 −1.94045
\(605\) 2.75508e45 0.347673
\(606\) −4.41458e45 −0.542115
\(607\) 9.37646e44 0.112054 0.0560268 0.998429i \(-0.482157\pi\)
0.0560268 + 0.998429i \(0.482157\pi\)
\(608\) 8.22797e45 0.956937
\(609\) −5.08004e44 −0.0575019
\(610\) 1.74581e45 0.192333
\(611\) −6.38701e45 −0.684885
\(612\) 9.57834e45 0.999751
\(613\) 3.40725e45 0.346183 0.173092 0.984906i \(-0.444624\pi\)
0.173092 + 0.984906i \(0.444624\pi\)
\(614\) 1.19910e46 1.18598
\(615\) −3.95221e44 −0.0380541
\(616\) −7.06079e44 −0.0661869
\(617\) 1.51984e46 1.38705 0.693525 0.720432i \(-0.256057\pi\)
0.693525 + 0.720432i \(0.256057\pi\)
\(618\) 2.43517e45 0.216381
\(619\) −3.99242e45 −0.345415 −0.172707 0.984973i \(-0.555251\pi\)
−0.172707 + 0.984973i \(0.555251\pi\)
\(620\) 1.37670e45 0.115979
\(621\) −6.27019e45 −0.514362
\(622\) 2.29910e46 1.83661
\(623\) 1.64336e45 0.127844
\(624\) 8.87091e44 0.0672082
\(625\) 5.42101e44 0.0400000
\(626\) 3.29105e46 2.36515
\(627\) −8.86465e44 −0.0620508
\(628\) −1.54887e46 −1.05604
\(629\) 8.67429e45 0.576100
\(630\) 4.23281e45 0.273848
\(631\) −8.68878e45 −0.547614 −0.273807 0.961785i \(-0.588283\pi\)
−0.273807 + 0.961785i \(0.588283\pi\)
\(632\) 2.44866e45 0.150348
\(633\) −2.71208e44 −0.0162234
\(634\) −1.43425e46 −0.835894
\(635\) −4.62360e45 −0.262551
\(636\) −7.84358e45 −0.433982
\(637\) −7.15473e45 −0.385738
\(638\) −9.24447e45 −0.485669
\(639\) −3.68955e46 −1.88890
\(640\) 5.74482e45 0.286620
\(641\) 1.75762e46 0.854609 0.427305 0.904108i \(-0.359463\pi\)
0.427305 + 0.904108i \(0.359463\pi\)
\(642\) 7.58763e45 0.359566
\(643\) −3.90754e46 −1.80477 −0.902386 0.430928i \(-0.858186\pi\)
−0.902386 + 0.430928i \(0.858186\pi\)
\(644\) −1.55798e46 −0.701368
\(645\) 1.79691e45 0.0788481
\(646\) 2.00238e46 0.856464
\(647\) −3.44345e46 −1.43573 −0.717865 0.696182i \(-0.754881\pi\)
−0.717865 + 0.696182i \(0.754881\pi\)
\(648\) 7.17158e45 0.291492
\(649\) −1.00749e46 −0.399211
\(650\) 3.64001e45 0.140615
\(651\) 4.69617e44 0.0176871
\(652\) −2.01073e46 −0.738359
\(653\) 4.09793e46 1.46723 0.733613 0.679567i \(-0.237832\pi\)
0.733613 + 0.679567i \(0.237832\pi\)
\(654\) 9.91120e45 0.346014
\(655\) 1.19534e46 0.406921
\(656\) 9.61645e45 0.319228
\(657\) 2.05768e46 0.666115
\(658\) −2.92661e46 −0.923926
\(659\) 7.05687e44 0.0217271 0.0108636 0.999941i \(-0.496542\pi\)
0.0108636 + 0.999941i \(0.496542\pi\)
\(660\) −1.67089e45 −0.0501732
\(661\) 5.13888e45 0.150503 0.0752514 0.997165i \(-0.476024\pi\)
0.0752514 + 0.997165i \(0.476024\pi\)
\(662\) −1.90641e46 −0.544578
\(663\) 2.80975e45 0.0782878
\(664\) 1.89071e46 0.513868
\(665\) 4.86358e45 0.128943
\(666\) 3.74999e46 0.969852
\(667\) −3.68393e46 −0.929469
\(668\) −4.10623e46 −1.01072
\(669\) 3.10631e45 0.0745958
\(670\) −4.26775e45 −0.0999919
\(671\) 5.95644e45 0.136165
\(672\) 5.29031e45 0.118002
\(673\) 8.48563e46 1.84687 0.923434 0.383758i \(-0.125370\pi\)
0.923434 + 0.383758i \(0.125370\pi\)
\(674\) 2.10380e45 0.0446803
\(675\) 3.68943e45 0.0764622
\(676\) −4.69090e46 −0.948715
\(677\) 1.97690e46 0.390185 0.195093 0.980785i \(-0.437499\pi\)
0.195093 + 0.980785i \(0.437499\pi\)
\(678\) 7.30105e45 0.140636
\(679\) −3.83438e46 −0.720848
\(680\) 6.81633e45 0.125070
\(681\) −4.31648e45 −0.0773042
\(682\) 8.54591e45 0.149388
\(683\) 1.05640e47 1.80254 0.901272 0.433254i \(-0.142635\pi\)
0.901272 + 0.433254i \(0.142635\pi\)
\(684\) 4.75789e46 0.792480
\(685\) −2.19230e46 −0.356456
\(686\) −7.28847e46 −1.15688
\(687\) 9.75396e45 0.151145
\(688\) −4.37221e46 −0.661442
\(689\) 5.82988e46 0.861078
\(690\) −1.21145e46 −0.174701
\(691\) −2.86100e46 −0.402838 −0.201419 0.979505i \(-0.564555\pi\)
−0.201419 + 0.979505i \(0.564555\pi\)
\(692\) −1.49551e47 −2.05608
\(693\) 1.44417e46 0.193874
\(694\) 1.54510e47 2.02546
\(695\) −4.62995e46 −0.592689
\(696\) −3.53660e45 −0.0442113
\(697\) 3.04589e46 0.371855
\(698\) −9.16430e46 −1.09266
\(699\) −2.42266e46 −0.282110
\(700\) 9.16729e45 0.104261
\(701\) 5.94385e46 0.660269 0.330134 0.943934i \(-0.392906\pi\)
0.330134 + 0.943934i \(0.392906\pi\)
\(702\) 2.47731e46 0.268793
\(703\) 4.30881e46 0.456662
\(704\) 6.29579e46 0.651781
\(705\) −1.25077e46 −0.126490
\(706\) 5.91340e46 0.584197
\(707\) 8.26368e46 0.797541
\(708\) −2.13415e46 −0.201222
\(709\) 6.13936e46 0.565536 0.282768 0.959188i \(-0.408747\pi\)
0.282768 + 0.959188i \(0.408747\pi\)
\(710\) −1.45383e47 −1.30843
\(711\) −5.00835e46 −0.440399
\(712\) 1.14406e46 0.0982948
\(713\) 3.40555e46 0.285898
\(714\) 1.28746e46 0.105612
\(715\) 1.24192e46 0.0995503
\(716\) −1.98441e47 −1.55441
\(717\) −9.57976e45 −0.0733311
\(718\) −1.24972e47 −0.934886
\(719\) −2.54160e47 −1.85815 −0.929075 0.369891i \(-0.879395\pi\)
−0.929075 + 0.369891i \(0.879395\pi\)
\(720\) −4.40166e46 −0.314507
\(721\) −4.55841e46 −0.318333
\(722\) −1.18848e47 −0.811203
\(723\) −2.61267e46 −0.174302
\(724\) 2.72918e47 1.77969
\(725\) 2.16765e46 0.138170
\(726\) 3.62274e46 0.225727
\(727\) −1.41220e47 −0.860157 −0.430079 0.902791i \(-0.641514\pi\)
−0.430079 + 0.902791i \(0.641514\pi\)
\(728\) 1.11169e46 0.0661935
\(729\) −1.33885e47 −0.779343
\(730\) 8.10808e46 0.461414
\(731\) −1.38484e47 −0.770484
\(732\) 1.26174e46 0.0686338
\(733\) 1.82342e47 0.969778 0.484889 0.874576i \(-0.338860\pi\)
0.484889 + 0.874576i \(0.338860\pi\)
\(734\) −2.98484e46 −0.155216
\(735\) −1.40111e46 −0.0712414
\(736\) 3.83641e47 1.90740
\(737\) −1.45609e46 −0.0707906
\(738\) 1.31677e47 0.626010
\(739\) 5.23297e46 0.243285 0.121642 0.992574i \(-0.461184\pi\)
0.121642 + 0.992574i \(0.461184\pi\)
\(740\) 8.12162e46 0.369249
\(741\) 1.39570e46 0.0620570
\(742\) 2.67132e47 1.16161
\(743\) 2.92156e47 1.24251 0.621255 0.783609i \(-0.286623\pi\)
0.621255 + 0.783609i \(0.286623\pi\)
\(744\) 3.26936e45 0.0135991
\(745\) 1.29323e47 0.526136
\(746\) 4.38145e47 1.74352
\(747\) −3.86715e47 −1.50522
\(748\) 1.28772e47 0.490281
\(749\) −1.42033e47 −0.528982
\(750\) 7.12825e45 0.0259700
\(751\) −3.59878e47 −1.28261 −0.641307 0.767284i \(-0.721608\pi\)
−0.641307 + 0.767284i \(0.721608\pi\)
\(752\) 3.04335e47 1.06110
\(753\) −6.71252e46 −0.228965
\(754\) 1.45550e47 0.485718
\(755\) 2.17789e47 0.711069
\(756\) 6.23907e46 0.199301
\(757\) −3.31803e47 −1.03705 −0.518524 0.855063i \(-0.673518\pi\)
−0.518524 + 0.855063i \(0.673518\pi\)
\(758\) −7.77375e47 −2.37733
\(759\) −4.13328e46 −0.123682
\(760\) 3.38590e46 0.0991403
\(761\) 4.31914e47 1.23752 0.618758 0.785582i \(-0.287636\pi\)
0.618758 + 0.785582i \(0.287636\pi\)
\(762\) −6.07970e46 −0.170461
\(763\) −1.85528e47 −0.509044
\(764\) −7.72696e47 −2.07476
\(765\) −1.39417e47 −0.366355
\(766\) 1.39758e47 0.359420
\(767\) 1.58624e47 0.399251
\(768\) −3.37370e46 −0.0831087
\(769\) −7.36766e46 −0.177642 −0.0888209 0.996048i \(-0.528310\pi\)
−0.0888209 + 0.996048i \(0.528310\pi\)
\(770\) 5.69062e46 0.134296
\(771\) −6.24299e46 −0.144210
\(772\) 9.97733e46 0.225595
\(773\) 3.43337e47 0.759904 0.379952 0.925006i \(-0.375941\pi\)
0.379952 + 0.925006i \(0.375941\pi\)
\(774\) −5.98683e47 −1.29709
\(775\) −2.00385e46 −0.0424999
\(776\) −2.66940e47 −0.554237
\(777\) 2.77042e46 0.0563118
\(778\) −1.34623e48 −2.67889
\(779\) 1.51300e47 0.294761
\(780\) 2.63073e46 0.0501783
\(781\) −4.96026e47 −0.926322
\(782\) 9.33638e47 1.70713
\(783\) 1.47526e47 0.264119
\(784\) 3.40916e47 0.597630
\(785\) 2.25445e47 0.386983
\(786\) 1.57179e47 0.264193
\(787\) 2.31817e47 0.381560 0.190780 0.981633i \(-0.438898\pi\)
0.190780 + 0.981633i \(0.438898\pi\)
\(788\) 5.84037e47 0.941365
\(789\) 7.86671e46 0.124172
\(790\) −1.97349e47 −0.305062
\(791\) −1.36669e47 −0.206898
\(792\) 1.00540e47 0.149064
\(793\) −9.37813e46 −0.136179
\(794\) −8.07300e47 −1.14815
\(795\) 1.14167e47 0.159031
\(796\) 2.06960e47 0.282372
\(797\) 9.59340e47 1.28206 0.641032 0.767514i \(-0.278506\pi\)
0.641032 + 0.767514i \(0.278506\pi\)
\(798\) 6.39526e46 0.0837164
\(799\) 9.63944e47 1.23603
\(800\) −2.25738e47 −0.283543
\(801\) −2.34000e47 −0.287925
\(802\) 9.41909e47 1.13536
\(803\) 2.76636e47 0.326664
\(804\) −3.08442e46 −0.0356819
\(805\) 2.26772e47 0.257014
\(806\) −1.34551e47 −0.149403
\(807\) −1.37533e47 −0.149621
\(808\) 5.75297e47 0.613204
\(809\) −2.85029e47 −0.297672 −0.148836 0.988862i \(-0.547553\pi\)
−0.148836 + 0.988862i \(0.547553\pi\)
\(810\) −5.77990e47 −0.591449
\(811\) −1.46166e48 −1.46555 −0.732777 0.680469i \(-0.761776\pi\)
−0.732777 + 0.680469i \(0.761776\pi\)
\(812\) 3.66565e47 0.360144
\(813\) 2.94510e47 0.283535
\(814\) 5.04151e47 0.475618
\(815\) 2.92670e47 0.270569
\(816\) −1.33882e47 −0.121293
\(817\) −6.87898e47 −0.610745
\(818\) −9.80066e47 −0.852758
\(819\) −2.27378e47 −0.193894
\(820\) 2.85183e47 0.238339
\(821\) −1.92594e48 −1.57754 −0.788771 0.614687i \(-0.789282\pi\)
−0.788771 + 0.614687i \(0.789282\pi\)
\(822\) −2.88272e47 −0.231429
\(823\) 4.92693e47 0.387685 0.193842 0.981033i \(-0.437905\pi\)
0.193842 + 0.981033i \(0.437905\pi\)
\(824\) −3.17345e47 −0.244756
\(825\) 2.43205e46 0.0183858
\(826\) 7.26836e47 0.538599
\(827\) −4.17990e46 −0.0303616 −0.0151808 0.999885i \(-0.504832\pi\)
−0.0151808 + 0.999885i \(0.504832\pi\)
\(828\) 2.21844e48 1.57960
\(829\) 1.71716e48 1.19857 0.599283 0.800538i \(-0.295453\pi\)
0.599283 + 0.800538i \(0.295453\pi\)
\(830\) −1.52381e48 −1.04266
\(831\) 3.11649e47 0.209049
\(832\) −9.91243e47 −0.651846
\(833\) 1.07981e48 0.696153
\(834\) −6.08806e47 −0.384803
\(835\) 5.97681e47 0.370376
\(836\) 6.39653e47 0.388634
\(837\) −1.36378e47 −0.0812409
\(838\) −1.94888e48 −1.13831
\(839\) 4.33094e46 0.0248033 0.0124016 0.999923i \(-0.496052\pi\)
0.0124016 + 0.999923i \(0.496052\pi\)
\(840\) 2.17703e46 0.0122252
\(841\) −9.49316e47 −0.522729
\(842\) −1.28167e48 −0.692033
\(843\) 3.23641e47 0.171360
\(844\) 1.95698e47 0.101610
\(845\) 6.82782e47 0.347653
\(846\) 4.16724e48 2.08083
\(847\) −6.78143e47 −0.332082
\(848\) −2.77789e48 −1.33408
\(849\) −2.12106e47 −0.0999024
\(850\) −5.49359e47 −0.253772
\(851\) 2.00905e48 0.910233
\(852\) −1.05072e48 −0.466912
\(853\) −3.98289e48 −1.73596 −0.867979 0.496601i \(-0.834581\pi\)
−0.867979 + 0.496601i \(0.834581\pi\)
\(854\) −4.29717e47 −0.183708
\(855\) −6.92532e47 −0.290402
\(856\) −9.88802e47 −0.406717
\(857\) −3.66149e48 −1.47732 −0.738660 0.674078i \(-0.764541\pi\)
−0.738660 + 0.674078i \(0.764541\pi\)
\(858\) 1.63303e47 0.0646330
\(859\) 4.14441e48 1.60907 0.804536 0.593904i \(-0.202414\pi\)
0.804536 + 0.593904i \(0.202414\pi\)
\(860\) −1.29661e48 −0.493839
\(861\) 9.72808e46 0.0363475
\(862\) −3.32430e48 −1.21851
\(863\) 2.44535e48 0.879353 0.439676 0.898156i \(-0.355093\pi\)
0.439676 + 0.898156i \(0.355093\pi\)
\(864\) −1.53632e48 −0.542008
\(865\) 2.17679e48 0.753443
\(866\) 6.85593e48 2.32820
\(867\) 1.60770e47 0.0535661
\(868\) −3.38865e47 −0.110777
\(869\) −6.73325e47 −0.215973
\(870\) 2.85031e47 0.0897066
\(871\) 2.29255e47 0.0707977
\(872\) −1.29160e48 −0.391388
\(873\) 5.45983e48 1.62347
\(874\) 4.63769e48 1.35320
\(875\) −1.33434e47 −0.0382062
\(876\) 5.85993e47 0.164655
\(877\) −5.05120e48 −1.39284 −0.696420 0.717635i \(-0.745225\pi\)
−0.696420 + 0.717635i \(0.745225\pi\)
\(878\) 6.64066e48 1.79702
\(879\) 4.84528e47 0.128677
\(880\) −5.91762e47 −0.154235
\(881\) −3.16644e48 −0.809971 −0.404985 0.914323i \(-0.632723\pi\)
−0.404985 + 0.914323i \(0.632723\pi\)
\(882\) 4.66814e48 1.17196
\(883\) −1.69432e48 −0.417489 −0.208744 0.977970i \(-0.566938\pi\)
−0.208744 + 0.977970i \(0.566938\pi\)
\(884\) −2.02745e48 −0.490330
\(885\) 3.10635e47 0.0737371
\(886\) −1.17267e48 −0.273225
\(887\) 3.16518e48 0.723868 0.361934 0.932204i \(-0.382117\pi\)
0.361934 + 0.932204i \(0.382117\pi\)
\(888\) 1.92870e47 0.0432964
\(889\) 1.13806e48 0.250777
\(890\) −9.22054e47 −0.199444
\(891\) −1.97202e48 −0.418724
\(892\) −2.24145e48 −0.467206
\(893\) 4.78823e48 0.979775
\(894\) 1.70051e48 0.341594
\(895\) 2.88840e48 0.569609
\(896\) −1.41404e48 −0.273767
\(897\) 6.50765e47 0.123694
\(898\) −1.12646e49 −2.10211
\(899\) −8.01263e47 −0.146805
\(900\) −1.30535e48 −0.234814
\(901\) −8.79861e48 −1.55401
\(902\) 1.77028e48 0.306997
\(903\) −4.42296e47 −0.0753122
\(904\) −9.51455e47 −0.159078
\(905\) −3.97244e48 −0.652163
\(906\) 2.86378e48 0.461661
\(907\) 1.08873e48 0.172346 0.0861731 0.996280i \(-0.472536\pi\)
0.0861731 + 0.996280i \(0.472536\pi\)
\(908\) 3.11468e48 0.484169
\(909\) −1.17668e49 −1.79620
\(910\) −8.95961e47 −0.134309
\(911\) −4.59000e48 −0.675708 −0.337854 0.941199i \(-0.609701\pi\)
−0.337854 + 0.941199i \(0.609701\pi\)
\(912\) −6.65037e47 −0.0961460
\(913\) −5.19901e48 −0.738165
\(914\) 5.27779e48 0.735935
\(915\) −1.83652e47 −0.0251506
\(916\) −7.03824e48 −0.946648
\(917\) −2.94224e48 −0.388673
\(918\) −3.73883e48 −0.485100
\(919\) −2.32948e48 −0.296861 −0.148431 0.988923i \(-0.547422\pi\)
−0.148431 + 0.988923i \(0.547422\pi\)
\(920\) 1.57873e48 0.197610
\(921\) −1.26141e48 −0.155086
\(922\) 1.96172e49 2.36906
\(923\) 7.80969e48 0.926416
\(924\) 4.11276e47 0.0479232
\(925\) −1.18214e48 −0.135310
\(926\) 2.43634e48 0.273941
\(927\) 6.49079e48 0.716939
\(928\) −9.02637e48 −0.979425
\(929\) −3.31257e48 −0.353107 −0.176553 0.984291i \(-0.556495\pi\)
−0.176553 + 0.984291i \(0.556495\pi\)
\(930\) −2.63493e47 −0.0275931
\(931\) 5.36378e48 0.551825
\(932\) 1.74814e49 1.76690
\(933\) −2.41857e48 −0.240166
\(934\) 1.99903e49 1.95028
\(935\) −1.87433e48 −0.179662
\(936\) −1.58295e48 −0.149079
\(937\) 8.43738e48 0.780737 0.390368 0.920659i \(-0.372348\pi\)
0.390368 + 0.920659i \(0.372348\pi\)
\(938\) 1.05047e48 0.0955078
\(939\) −3.46206e48 −0.309280
\(940\) 9.02528e48 0.792230
\(941\) 1.19866e49 1.03387 0.516937 0.856023i \(-0.327072\pi\)
0.516937 + 0.856023i \(0.327072\pi\)
\(942\) 2.96445e48 0.251249
\(943\) 7.05458e48 0.587527
\(944\) −7.55830e48 −0.618566
\(945\) −9.08125e47 −0.0730332
\(946\) −8.04873e48 −0.636098
\(947\) −1.53140e49 −1.18936 −0.594681 0.803961i \(-0.702722\pi\)
−0.594681 + 0.803961i \(0.702722\pi\)
\(948\) −1.42629e48 −0.108861
\(949\) −4.35550e48 −0.326697
\(950\) −2.72885e48 −0.201160
\(951\) 1.50877e48 0.109306
\(952\) −1.67779e48 −0.119461
\(953\) 4.05106e48 0.283488 0.141744 0.989903i \(-0.454729\pi\)
0.141744 + 0.989903i \(0.454729\pi\)
\(954\) −3.80374e49 −2.61615
\(955\) 1.12469e49 0.760289
\(956\) 6.91254e48 0.459285
\(957\) 9.72483e47 0.0635090
\(958\) −3.89808e49 −2.50219
\(959\) 5.39619e48 0.340471
\(960\) −1.94116e48 −0.120388
\(961\) −1.56628e49 −0.954844
\(962\) −7.93763e48 −0.475666
\(963\) 2.02244e49 1.19135
\(964\) 1.88525e49 1.09168
\(965\) −1.45225e48 −0.0826684
\(966\) 2.98189e48 0.166866
\(967\) 1.43741e49 0.790757 0.395378 0.918518i \(-0.370613\pi\)
0.395378 + 0.918518i \(0.370613\pi\)
\(968\) −4.72107e48 −0.255327
\(969\) −2.10642e48 −0.111996
\(970\) 2.15139e49 1.12457
\(971\) 1.56174e49 0.802585 0.401293 0.915950i \(-0.368561\pi\)
0.401293 + 0.915950i \(0.368561\pi\)
\(972\) −1.34118e49 −0.677632
\(973\) 1.13963e49 0.566110
\(974\) −3.34041e49 −1.63146
\(975\) −3.82915e47 −0.0183877
\(976\) 4.46859e48 0.210984
\(977\) −1.09477e49 −0.508235 −0.254117 0.967173i \(-0.581785\pi\)
−0.254117 + 0.967173i \(0.581785\pi\)
\(978\) 3.84841e48 0.175667
\(979\) −3.14591e48 −0.141199
\(980\) 1.01101e49 0.446197
\(981\) 2.64177e49 1.14645
\(982\) −4.64482e49 −1.98212
\(983\) 1.92109e49 0.806150 0.403075 0.915167i \(-0.367941\pi\)
0.403075 + 0.915167i \(0.367941\pi\)
\(984\) 6.77245e47 0.0279465
\(985\) −8.50092e48 −0.344960
\(986\) −2.19668e49 −0.876591
\(987\) 3.07868e48 0.120818
\(988\) −1.00710e49 −0.388673
\(989\) −3.20743e49 −1.21736
\(990\) −8.10295e48 −0.302456
\(991\) 2.18652e49 0.802672 0.401336 0.915931i \(-0.368546\pi\)
0.401336 + 0.915931i \(0.368546\pi\)
\(992\) 8.34429e48 0.301264
\(993\) 2.00547e48 0.0712122
\(994\) 3.57850e49 1.24976
\(995\) −3.01240e48 −0.103474
\(996\) −1.10130e49 −0.372071
\(997\) 1.75251e49 0.582357 0.291179 0.956669i \(-0.405953\pi\)
0.291179 + 0.956669i \(0.405953\pi\)
\(998\) −1.10666e49 −0.361709
\(999\) −8.04539e48 −0.258652
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 \(a_p\))