Properties

Label 1.62.a.a.1.4
Level 1
Weight 62
Character 1.1
Self dual yes
Analytic conductor 23.566
Analytic rank 1
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 62 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.5656183265\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 180363795469121 x^{2} + 166129321978984507920 x + 2785609847439483545242446300\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{28}\cdot 3^{8}\cdot 5^{2}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.33086e7\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.84183e9 q^{2} -3.79563e14 q^{3} +5.77017e18 q^{4} -6.89620e20 q^{5} -1.07865e24 q^{6} -9.80127e25 q^{7} +9.84504e27 q^{8} +1.68945e28 q^{9} +O(q^{10})\) \(q+2.84183e9 q^{2} -3.79563e14 q^{3} +5.77017e18 q^{4} -6.89620e20 q^{5} -1.07865e24 q^{6} -9.80127e25 q^{7} +9.84504e27 q^{8} +1.68945e28 q^{9} -1.95979e30 q^{10} -2.74880e31 q^{11} -2.19014e33 q^{12} +2.74592e32 q^{13} -2.78536e35 q^{14} +2.61754e35 q^{15} +1.46728e37 q^{16} -2.27394e37 q^{17} +4.80113e37 q^{18} -1.42689e39 q^{19} -3.97923e39 q^{20} +3.72020e40 q^{21} -7.81164e40 q^{22} +1.13228e41 q^{23} -3.73681e42 q^{24} -3.86123e42 q^{25} +7.80343e41 q^{26} +4.18578e43 q^{27} -5.65550e44 q^{28} +2.20574e44 q^{29} +7.43862e44 q^{30} -7.87465e44 q^{31} +1.89967e46 q^{32} +1.04334e46 q^{33} -6.46217e46 q^{34} +6.75915e46 q^{35} +9.74841e46 q^{36} +5.41627e47 q^{37} -4.05499e48 q^{38} -1.04225e47 q^{39} -6.78934e48 q^{40} +3.44353e48 q^{41} +1.05722e50 q^{42} -2.45361e49 q^{43} -1.58611e50 q^{44} -1.16508e49 q^{45} +3.21774e50 q^{46} +7.88915e50 q^{47} -5.56927e51 q^{48} +6.05033e51 q^{49} -1.09730e52 q^{50} +8.63104e51 q^{51} +1.58444e51 q^{52} +4.85762e52 q^{53} +1.18953e53 q^{54} +1.89563e52 q^{55} -9.64938e53 q^{56} +5.41596e53 q^{57} +6.26833e53 q^{58} -1.37665e54 q^{59} +1.51037e54 q^{60} +4.54704e53 q^{61} -2.23784e54 q^{62} -1.65587e54 q^{63} +2.01520e55 q^{64} -1.89364e53 q^{65} +2.96501e55 q^{66} -8.79176e55 q^{67} -1.31210e56 q^{68} -4.29770e55 q^{69} +1.92084e56 q^{70} +3.27010e56 q^{71} +1.66327e56 q^{72} -6.07880e56 q^{73} +1.53921e57 q^{74} +1.46558e57 q^{75} -8.23342e57 q^{76} +2.69418e57 q^{77} -2.96189e56 q^{78} +1.23160e58 q^{79} -1.01187e58 q^{80} -1.80362e58 q^{81} +9.78594e57 q^{82} -6.61561e58 q^{83} +2.14662e59 q^{84} +1.56816e58 q^{85} -6.97276e58 q^{86} -8.37216e58 q^{87} -2.70621e59 q^{88} -1.38088e59 q^{89} -3.31096e58 q^{90} -2.69135e58 q^{91} +6.53342e59 q^{92} +2.98892e59 q^{93} +2.24196e60 q^{94} +9.84014e59 q^{95} -7.21043e60 q^{96} -3.96687e60 q^{97} +1.71940e61 q^{98} -4.64396e59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} + O(q^{10}) \) \( 4q + 1146312000q^{2} - 573723599022000q^{3} + 4402997675828604928q^{4} - \)\(52\!\cdots\!00\)\(q^{5} - \)\(81\!\cdots\!52\)\(q^{6} - \)\(63\!\cdots\!00\)\(q^{7} + \)\(97\!\cdots\!00\)\(q^{8} + \)\(11\!\cdots\!52\)\(q^{9} - \)\(14\!\cdots\!00\)\(q^{10} - \)\(41\!\cdots\!52\)\(q^{11} - \)\(99\!\cdots\!00\)\(q^{12} + \)\(10\!\cdots\!00\)\(q^{13} - \)\(21\!\cdots\!04\)\(q^{14} + \)\(11\!\cdots\!00\)\(q^{15} + \)\(10\!\cdots\!24\)\(q^{16} - \)\(40\!\cdots\!00\)\(q^{17} + \)\(15\!\cdots\!00\)\(q^{18} - \)\(35\!\cdots\!20\)\(q^{19} - \)\(50\!\cdots\!00\)\(q^{20} - \)\(55\!\cdots\!72\)\(q^{21} - \)\(17\!\cdots\!00\)\(q^{22} - \)\(41\!\cdots\!00\)\(q^{23} - \)\(61\!\cdots\!60\)\(q^{24} - \)\(16\!\cdots\!00\)\(q^{25} - \)\(49\!\cdots\!32\)\(q^{26} - \)\(12\!\cdots\!00\)\(q^{27} - \)\(79\!\cdots\!00\)\(q^{28} + \)\(66\!\cdots\!20\)\(q^{29} + \)\(95\!\cdots\!00\)\(q^{30} + \)\(32\!\cdots\!28\)\(q^{31} + \)\(29\!\cdots\!00\)\(q^{32} + \)\(80\!\cdots\!00\)\(q^{33} + \)\(39\!\cdots\!16\)\(q^{34} + \)\(94\!\cdots\!00\)\(q^{35} - \)\(49\!\cdots\!36\)\(q^{36} - \)\(71\!\cdots\!00\)\(q^{37} - \)\(65\!\cdots\!00\)\(q^{38} - \)\(53\!\cdots\!76\)\(q^{39} - \)\(69\!\cdots\!00\)\(q^{40} + \)\(16\!\cdots\!68\)\(q^{41} + \)\(15\!\cdots\!00\)\(q^{42} + \)\(75\!\cdots\!00\)\(q^{43} + \)\(15\!\cdots\!36\)\(q^{44} + \)\(60\!\cdots\!00\)\(q^{45} - \)\(15\!\cdots\!12\)\(q^{46} - \)\(21\!\cdots\!00\)\(q^{47} - \)\(84\!\cdots\!00\)\(q^{48} + \)\(15\!\cdots\!28\)\(q^{49} - \)\(37\!\cdots\!00\)\(q^{50} + \)\(20\!\cdots\!88\)\(q^{51} + \)\(34\!\cdots\!00\)\(q^{52} + \)\(84\!\cdots\!00\)\(q^{53} + \)\(20\!\cdots\!80\)\(q^{54} - \)\(18\!\cdots\!00\)\(q^{55} - \)\(89\!\cdots\!20\)\(q^{56} - \)\(48\!\cdots\!00\)\(q^{57} - \)\(42\!\cdots\!00\)\(q^{58} - \)\(21\!\cdots\!60\)\(q^{59} + \)\(16\!\cdots\!00\)\(q^{60} + \)\(42\!\cdots\!48\)\(q^{61} + \)\(51\!\cdots\!00\)\(q^{62} + \)\(17\!\cdots\!00\)\(q^{63} + \)\(19\!\cdots\!08\)\(q^{64} - \)\(40\!\cdots\!00\)\(q^{65} - \)\(32\!\cdots\!24\)\(q^{66} - \)\(15\!\cdots\!00\)\(q^{67} - \)\(19\!\cdots\!00\)\(q^{68} - \)\(65\!\cdots\!16\)\(q^{69} + \)\(16\!\cdots\!00\)\(q^{70} + \)\(26\!\cdots\!88\)\(q^{71} + \)\(10\!\cdots\!00\)\(q^{72} + \)\(43\!\cdots\!00\)\(q^{73} + \)\(27\!\cdots\!56\)\(q^{74} + \)\(22\!\cdots\!00\)\(q^{75} - \)\(91\!\cdots\!40\)\(q^{76} - \)\(62\!\cdots\!00\)\(q^{77} - \)\(62\!\cdots\!00\)\(q^{78} - \)\(21\!\cdots\!80\)\(q^{79} - \)\(81\!\cdots\!00\)\(q^{80} + \)\(16\!\cdots\!84\)\(q^{81} + \)\(41\!\cdots\!00\)\(q^{82} - \)\(19\!\cdots\!00\)\(q^{83} + \)\(26\!\cdots\!96\)\(q^{84} + \)\(23\!\cdots\!00\)\(q^{85} - \)\(71\!\cdots\!72\)\(q^{86} - \)\(25\!\cdots\!00\)\(q^{87} - \)\(45\!\cdots\!00\)\(q^{88} - \)\(60\!\cdots\!40\)\(q^{89} - \)\(12\!\cdots\!00\)\(q^{90} - \)\(45\!\cdots\!52\)\(q^{91} + \)\(16\!\cdots\!00\)\(q^{92} - \)\(43\!\cdots\!00\)\(q^{93} + \)\(64\!\cdots\!76\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} + \)\(15\!\cdots\!08\)\(q^{96} - \)\(80\!\cdots\!00\)\(q^{97} + \)\(17\!\cdots\!00\)\(q^{98} - \)\(31\!\cdots\!76\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.84183e9 1.87147 0.935737 0.352699i \(-0.114736\pi\)
0.935737 + 0.352699i \(0.114736\pi\)
\(3\) −3.79563e14 −1.06435 −0.532176 0.846634i \(-0.678626\pi\)
−0.532176 + 0.846634i \(0.678626\pi\)
\(4\) 5.77017e18 2.50241
\(5\) −6.89620e20 −0.331150 −0.165575 0.986197i \(-0.552948\pi\)
−0.165575 + 0.986197i \(0.552948\pi\)
\(6\) −1.07865e24 −1.99191
\(7\) −9.80127e25 −1.64358 −0.821792 0.569787i \(-0.807026\pi\)
−0.821792 + 0.569787i \(0.807026\pi\)
\(8\) 9.84504e27 2.81172
\(9\) 1.68945e28 0.132846
\(10\) −1.95979e30 −0.619738
\(11\) −2.74880e31 −0.474971 −0.237485 0.971391i \(-0.576323\pi\)
−0.237485 + 0.971391i \(0.576323\pi\)
\(12\) −2.19014e33 −2.66345
\(13\) 2.74592e32 0.0290680 0.0145340 0.999894i \(-0.495374\pi\)
0.0145340 + 0.999894i \(0.495374\pi\)
\(14\) −2.78536e35 −3.07592
\(15\) 2.61754e35 0.352460
\(16\) 1.46728e37 2.75966
\(17\) −2.27394e37 −0.673112 −0.336556 0.941663i \(-0.609262\pi\)
−0.336556 + 0.941663i \(0.609262\pi\)
\(18\) 4.80113e37 0.248618
\(19\) −1.42689e39 −1.42039 −0.710193 0.704007i \(-0.751393\pi\)
−0.710193 + 0.704007i \(0.751393\pi\)
\(20\) −3.97923e39 −0.828674
\(21\) 3.72020e40 1.74935
\(22\) −7.81164e40 −0.888895
\(23\) 1.13228e41 0.332088 0.166044 0.986118i \(-0.446901\pi\)
0.166044 + 0.986118i \(0.446901\pi\)
\(24\) −3.73681e42 −2.99267
\(25\) −3.86123e42 −0.890340
\(26\) 7.80343e41 0.0544000
\(27\) 4.18578e43 0.922957
\(28\) −5.65550e44 −4.11293
\(29\) 2.20574e44 0.550066 0.275033 0.961435i \(-0.411311\pi\)
0.275033 + 0.961435i \(0.411311\pi\)
\(30\) 7.43862e44 0.659620
\(31\) −7.87465e44 −0.256862 −0.128431 0.991718i \(-0.540994\pi\)
−0.128431 + 0.991718i \(0.540994\pi\)
\(32\) 1.89967e46 2.35290
\(33\) 1.04334e46 0.505536
\(34\) −6.46217e46 −1.25971
\(35\) 6.75915e46 0.544273
\(36\) 9.74841e46 0.332436
\(37\) 5.41627e47 0.800843 0.400422 0.916331i \(-0.368864\pi\)
0.400422 + 0.916331i \(0.368864\pi\)
\(38\) −4.05499e48 −2.65822
\(39\) −1.04225e47 −0.0309386
\(40\) −6.78934e48 −0.931103
\(41\) 3.44353e48 0.222380 0.111190 0.993799i \(-0.464534\pi\)
0.111190 + 0.993799i \(0.464534\pi\)
\(42\) 1.05722e50 3.27387
\(43\) −2.45361e49 −0.370696 −0.185348 0.982673i \(-0.559341\pi\)
−0.185348 + 0.982673i \(0.559341\pi\)
\(44\) −1.58611e50 −1.18857
\(45\) −1.16508e49 −0.0439920
\(46\) 3.21774e50 0.621494
\(47\) 7.88915e50 0.790761 0.395381 0.918517i \(-0.370613\pi\)
0.395381 + 0.918517i \(0.370613\pi\)
\(48\) −5.56927e51 −2.93725
\(49\) 6.05033e51 1.70137
\(50\) −1.09730e52 −1.66625
\(51\) 8.63104e51 0.716429
\(52\) 1.58444e51 0.0727401
\(53\) 4.85762e52 1.24741 0.623706 0.781659i \(-0.285626\pi\)
0.623706 + 0.781659i \(0.285626\pi\)
\(54\) 1.18953e53 1.72729
\(55\) 1.89563e52 0.157287
\(56\) −9.64938e53 −4.62131
\(57\) 5.41596e53 1.51179
\(58\) 6.26833e53 1.02943
\(59\) −1.37665e54 −1.34226 −0.671130 0.741340i \(-0.734191\pi\)
−0.671130 + 0.741340i \(0.734191\pi\)
\(60\) 1.51037e54 0.882001
\(61\) 4.54704e53 0.160387 0.0801934 0.996779i \(-0.474446\pi\)
0.0801934 + 0.996779i \(0.474446\pi\)
\(62\) −2.23784e54 −0.480710
\(63\) −1.65587e54 −0.218344
\(64\) 2.01520e55 1.64373
\(65\) −1.89364e53 −0.00962587
\(66\) 2.96501e55 0.946097
\(67\) −8.79176e55 −1.77335 −0.886675 0.462393i \(-0.846991\pi\)
−0.886675 + 0.462393i \(0.846991\pi\)
\(68\) −1.31210e56 −1.68440
\(69\) −4.29770e55 −0.353459
\(70\) 1.92084e56 1.01859
\(71\) 3.27010e56 1.12508 0.562538 0.826772i \(-0.309825\pi\)
0.562538 + 0.826772i \(0.309825\pi\)
\(72\) 1.66327e56 0.373527
\(73\) −6.07880e56 −0.896336 −0.448168 0.893949i \(-0.647923\pi\)
−0.448168 + 0.893949i \(0.647923\pi\)
\(74\) 1.53921e57 1.49876
\(75\) 1.46558e57 0.947635
\(76\) −8.23342e57 −3.55439
\(77\) 2.69418e57 0.780654
\(78\) −2.96189e56 −0.0579007
\(79\) 1.23160e58 1.63246 0.816229 0.577729i \(-0.196061\pi\)
0.816229 + 0.577729i \(0.196061\pi\)
\(80\) −1.01187e58 −0.913860
\(81\) −1.80362e58 −1.11520
\(82\) 9.78594e57 0.416179
\(83\) −6.61561e58 −1.94396 −0.971981 0.235058i \(-0.924472\pi\)
−0.971981 + 0.235058i \(0.924472\pi\)
\(84\) 2.14662e59 4.37760
\(85\) 1.56816e58 0.222901
\(86\) −6.97276e58 −0.693749
\(87\) −8.37216e58 −0.585464
\(88\) −2.70621e59 −1.33549
\(89\) −1.38088e59 −0.482793 −0.241396 0.970427i \(-0.577605\pi\)
−0.241396 + 0.970427i \(0.577605\pi\)
\(90\) −3.31096e58 −0.0823298
\(91\) −2.69135e58 −0.0477757
\(92\) 6.53342e59 0.831021
\(93\) 2.98892e59 0.273391
\(94\) 2.24196e60 1.47989
\(95\) 9.84014e59 0.470361
\(96\) −7.21043e60 −2.50431
\(97\) −3.96687e60 −1.00441 −0.502204 0.864749i \(-0.667477\pi\)
−0.502204 + 0.864749i \(0.667477\pi\)
\(98\) 1.71940e61 3.18407
\(99\) −4.64396e59 −0.0630980
\(100\) −2.22800e61 −2.22800
\(101\) −4.90481e60 −0.362093 −0.181047 0.983474i \(-0.557949\pi\)
−0.181047 + 0.983474i \(0.557949\pi\)
\(102\) 2.45280e61 1.34078
\(103\) −2.48884e61 −1.01033 −0.505163 0.863024i \(-0.668568\pi\)
−0.505163 + 0.863024i \(0.668568\pi\)
\(104\) 2.70337e60 0.0817312
\(105\) −2.56552e61 −0.579298
\(106\) 1.38046e62 2.33450
\(107\) −1.15288e62 −1.46413 −0.732063 0.681237i \(-0.761442\pi\)
−0.732063 + 0.681237i \(0.761442\pi\)
\(108\) 2.41527e62 2.30962
\(109\) −6.30613e61 −0.455255 −0.227627 0.973748i \(-0.573097\pi\)
−0.227627 + 0.973748i \(0.573097\pi\)
\(110\) 5.38706e61 0.294358
\(111\) −2.05581e62 −0.852379
\(112\) −1.43812e63 −4.53573
\(113\) 3.81996e62 0.918685 0.459343 0.888259i \(-0.348085\pi\)
0.459343 + 0.888259i \(0.348085\pi\)
\(114\) 1.53912e63 2.82928
\(115\) −7.80840e61 −0.109971
\(116\) 1.27275e63 1.37649
\(117\) 4.63909e60 0.00386157
\(118\) −3.91220e63 −2.51200
\(119\) 2.22875e63 1.10632
\(120\) 2.57698e63 0.991021
\(121\) −2.59371e63 −0.774403
\(122\) 1.29219e63 0.300160
\(123\) −1.30704e63 −0.236691
\(124\) −4.54381e63 −0.642774
\(125\) 5.65353e63 0.625986
\(126\) −4.70572e63 −0.408624
\(127\) −2.01045e64 −1.37176 −0.685881 0.727714i \(-0.740583\pi\)
−0.685881 + 0.727714i \(0.740583\pi\)
\(128\) 1.34654e64 0.723296
\(129\) 9.31301e63 0.394552
\(130\) −5.38141e62 −0.0180146
\(131\) 1.95810e64 0.518872 0.259436 0.965760i \(-0.416463\pi\)
0.259436 + 0.965760i \(0.416463\pi\)
\(132\) 6.02027e64 1.26506
\(133\) 1.39854e65 2.33453
\(134\) −2.49847e65 −3.31878
\(135\) −2.88660e64 −0.305637
\(136\) −2.23871e65 −1.89261
\(137\) 2.25308e65 1.52335 0.761673 0.647962i \(-0.224378\pi\)
0.761673 + 0.647962i \(0.224378\pi\)
\(138\) −1.22133e65 −0.661488
\(139\) −1.19702e65 −0.520174 −0.260087 0.965585i \(-0.583751\pi\)
−0.260087 + 0.965585i \(0.583751\pi\)
\(140\) 3.90014e65 1.36200
\(141\) −2.99443e65 −0.841649
\(142\) 9.29308e65 2.10555
\(143\) −7.54798e63 −0.0138064
\(144\) 2.47890e65 0.366609
\(145\) −1.52112e65 −0.182154
\(146\) −1.72749e66 −1.67747
\(147\) −2.29648e66 −1.81086
\(148\) 3.12528e66 2.00404
\(149\) 8.52805e65 0.445316 0.222658 0.974897i \(-0.428527\pi\)
0.222658 + 0.974897i \(0.428527\pi\)
\(150\) 4.16493e66 1.77347
\(151\) −5.28415e65 −0.183729 −0.0918646 0.995772i \(-0.529283\pi\)
−0.0918646 + 0.995772i \(0.529283\pi\)
\(152\) −1.40478e67 −3.99374
\(153\) −3.84171e65 −0.0894203
\(154\) 7.65640e66 1.46097
\(155\) 5.43052e65 0.0850598
\(156\) −6.01395e65 −0.0774211
\(157\) 7.85892e66 0.832575 0.416287 0.909233i \(-0.363331\pi\)
0.416287 + 0.909233i \(0.363331\pi\)
\(158\) 3.49999e67 3.05510
\(159\) −1.84377e67 −1.32769
\(160\) −1.31005e67 −0.779162
\(161\) −1.10977e67 −0.545815
\(162\) −5.12559e67 −2.08706
\(163\) 4.04897e67 1.36654 0.683270 0.730166i \(-0.260557\pi\)
0.683270 + 0.730166i \(0.260557\pi\)
\(164\) 1.98698e67 0.556487
\(165\) −7.19511e66 −0.167408
\(166\) −1.88004e68 −3.63807
\(167\) 3.79481e67 0.611417 0.305708 0.952125i \(-0.401107\pi\)
0.305708 + 0.952125i \(0.401107\pi\)
\(168\) 3.66255e68 4.91870
\(169\) −8.91615e67 −0.999155
\(170\) 4.45644e67 0.417154
\(171\) −2.41066e67 −0.188693
\(172\) −1.41578e68 −0.927635
\(173\) −2.38020e67 −0.130679 −0.0653397 0.997863i \(-0.520813\pi\)
−0.0653397 + 0.997863i \(0.520813\pi\)
\(174\) −2.37923e68 −1.09568
\(175\) 3.78450e68 1.46335
\(176\) −4.03328e68 −1.31076
\(177\) 5.22524e68 1.42864
\(178\) −3.92423e68 −0.903534
\(179\) 1.05792e68 0.205323 0.102661 0.994716i \(-0.467264\pi\)
0.102661 + 0.994716i \(0.467264\pi\)
\(180\) −6.72270e67 −0.110086
\(181\) −4.17583e68 −0.577493 −0.288746 0.957406i \(-0.593238\pi\)
−0.288746 + 0.957406i \(0.593238\pi\)
\(182\) −7.64835e67 −0.0894109
\(183\) −1.72589e68 −0.170708
\(184\) 1.11473e69 0.933740
\(185\) −3.73517e68 −0.265199
\(186\) 8.49402e68 0.511645
\(187\) 6.25062e68 0.319709
\(188\) 4.55217e69 1.97881
\(189\) −4.10260e69 −1.51696
\(190\) 2.79640e69 0.880268
\(191\) −3.75239e69 −1.00644 −0.503222 0.864157i \(-0.667852\pi\)
−0.503222 + 0.864157i \(0.667852\pi\)
\(192\) −7.64897e69 −1.74951
\(193\) −4.33214e69 −0.845678 −0.422839 0.906205i \(-0.638966\pi\)
−0.422839 + 0.906205i \(0.638966\pi\)
\(194\) −1.12732e70 −1.87972
\(195\) 7.18755e67 0.0102453
\(196\) 3.49114e70 4.25753
\(197\) 1.20339e70 1.25657 0.628285 0.777983i \(-0.283757\pi\)
0.628285 + 0.777983i \(0.283757\pi\)
\(198\) −1.31974e69 −0.118086
\(199\) −3.29217e69 −0.252618 −0.126309 0.991991i \(-0.540313\pi\)
−0.126309 + 0.991991i \(0.540313\pi\)
\(200\) −3.80140e70 −2.50339
\(201\) 3.33703e70 1.88747
\(202\) −1.39387e70 −0.677648
\(203\) −2.16190e70 −0.904079
\(204\) 4.98026e70 1.79280
\(205\) −2.37473e69 −0.0736412
\(206\) −7.07287e70 −1.89080
\(207\) 1.91292e69 0.0441166
\(208\) 4.02904e69 0.0802176
\(209\) 3.92225e70 0.674642
\(210\) −7.29079e70 −1.08414
\(211\) 1.05468e68 0.00135677 0.000678387 1.00000i \(-0.499784\pi\)
0.000678387 1.00000i \(0.499784\pi\)
\(212\) 2.80293e71 3.12154
\(213\) −1.24121e71 −1.19748
\(214\) −3.27629e71 −2.74007
\(215\) 1.69206e70 0.122756
\(216\) 4.12092e71 2.59510
\(217\) 7.71815e70 0.422174
\(218\) −1.79210e71 −0.851997
\(219\) 2.30729e71 0.954017
\(220\) 1.09381e71 0.393596
\(221\) −6.24406e69 −0.0195660
\(222\) −5.84228e71 −1.59521
\(223\) 2.72351e71 0.648381 0.324191 0.945992i \(-0.394908\pi\)
0.324191 + 0.945992i \(0.394908\pi\)
\(224\) −1.86191e72 −3.86718
\(225\) −6.52336e70 −0.118278
\(226\) 1.08557e72 1.71929
\(227\) −2.72607e71 −0.377354 −0.188677 0.982039i \(-0.560420\pi\)
−0.188677 + 0.982039i \(0.560420\pi\)
\(228\) 3.12510e72 3.78313
\(229\) −1.01160e72 −1.07158 −0.535791 0.844351i \(-0.679986\pi\)
−0.535791 + 0.844351i \(0.679986\pi\)
\(230\) −2.21902e71 −0.205808
\(231\) −1.02261e72 −0.830891
\(232\) 2.17156e72 1.54663
\(233\) 1.13228e72 0.707291 0.353646 0.935379i \(-0.384942\pi\)
0.353646 + 0.935379i \(0.384942\pi\)
\(234\) 1.31835e70 0.00722682
\(235\) −5.44052e71 −0.261861
\(236\) −7.94349e72 −3.35889
\(237\) −4.67468e72 −1.73751
\(238\) 6.33374e72 2.07044
\(239\) 2.78705e72 0.801695 0.400847 0.916145i \(-0.368716\pi\)
0.400847 + 0.916145i \(0.368716\pi\)
\(240\) 3.84068e72 0.972669
\(241\) 2.43249e72 0.542664 0.271332 0.962486i \(-0.412536\pi\)
0.271332 + 0.962486i \(0.412536\pi\)
\(242\) −7.37088e72 −1.44927
\(243\) 1.52267e72 0.264006
\(244\) 2.62372e72 0.401354
\(245\) −4.17243e72 −0.563408
\(246\) −3.71438e72 −0.442961
\(247\) −3.91813e71 −0.0412878
\(248\) −7.75262e72 −0.722225
\(249\) 2.51104e73 2.06906
\(250\) 1.60664e73 1.17152
\(251\) 8.38055e72 0.541033 0.270517 0.962715i \(-0.412806\pi\)
0.270517 + 0.962715i \(0.412806\pi\)
\(252\) −9.55468e72 −0.546386
\(253\) −3.11240e72 −0.157732
\(254\) −5.71335e73 −2.56722
\(255\) −5.95214e72 −0.237245
\(256\) −8.20094e72 −0.290098
\(257\) 2.92677e73 0.919239 0.459620 0.888116i \(-0.347986\pi\)
0.459620 + 0.888116i \(0.347986\pi\)
\(258\) 2.64660e73 0.738393
\(259\) −5.30863e73 −1.31625
\(260\) −1.09266e72 −0.0240879
\(261\) 3.72648e72 0.0730741
\(262\) 5.56459e73 0.971055
\(263\) −5.79108e73 −0.899724 −0.449862 0.893098i \(-0.648527\pi\)
−0.449862 + 0.893098i \(0.648527\pi\)
\(264\) 1.02718e74 1.42143
\(265\) −3.34991e73 −0.413080
\(266\) 3.97441e74 4.36900
\(267\) 5.24131e73 0.513862
\(268\) −5.07300e74 −4.43765
\(269\) −1.60983e74 −1.25700 −0.628499 0.777810i \(-0.716330\pi\)
−0.628499 + 0.777810i \(0.716330\pi\)
\(270\) −8.20323e73 −0.571992
\(271\) 1.09220e74 0.680360 0.340180 0.940360i \(-0.389512\pi\)
0.340180 + 0.940360i \(0.389512\pi\)
\(272\) −3.33652e74 −1.85756
\(273\) 1.02153e73 0.0508502
\(274\) 6.40286e74 2.85090
\(275\) 1.06138e74 0.422885
\(276\) −2.47984e74 −0.884499
\(277\) 2.91497e74 0.931112 0.465556 0.885018i \(-0.345854\pi\)
0.465556 + 0.885018i \(0.345854\pi\)
\(278\) −3.40172e74 −0.973492
\(279\) −1.33038e73 −0.0341231
\(280\) 6.65441e74 1.53035
\(281\) −4.21232e74 −0.868917 −0.434458 0.900692i \(-0.643060\pi\)
−0.434458 + 0.900692i \(0.643060\pi\)
\(282\) −8.50966e74 −1.57512
\(283\) −1.72539e74 −0.286682 −0.143341 0.989673i \(-0.545785\pi\)
−0.143341 + 0.989673i \(0.545785\pi\)
\(284\) 1.88690e75 2.81540
\(285\) −3.73495e74 −0.500630
\(286\) −2.14501e73 −0.0258384
\(287\) −3.37510e74 −0.365501
\(288\) 3.20939e74 0.312573
\(289\) −6.24177e74 −0.546920
\(290\) −4.32277e74 −0.340897
\(291\) 1.50568e75 1.06904
\(292\) −3.50757e75 −2.24300
\(293\) 2.63304e75 1.51703 0.758517 0.651654i \(-0.225924\pi\)
0.758517 + 0.651654i \(0.225924\pi\)
\(294\) −6.52621e75 −3.38897
\(295\) 9.49364e74 0.444489
\(296\) 5.33234e75 2.25175
\(297\) −1.15059e75 −0.438378
\(298\) 2.42353e75 0.833397
\(299\) 3.10913e73 0.00965313
\(300\) 8.45665e75 2.37137
\(301\) 2.40485e75 0.609271
\(302\) −1.50167e75 −0.343844
\(303\) 1.86169e75 0.385395
\(304\) −2.09366e76 −3.91978
\(305\) −3.13573e74 −0.0531121
\(306\) −1.09175e75 −0.167348
\(307\) −1.01914e76 −1.41421 −0.707103 0.707110i \(-0.749998\pi\)
−0.707103 + 0.707110i \(0.749998\pi\)
\(308\) 1.55458e76 1.95352
\(309\) 9.44671e75 1.07534
\(310\) 1.54326e75 0.159187
\(311\) −1.92950e76 −1.80406 −0.902032 0.431669i \(-0.857925\pi\)
−0.902032 + 0.431669i \(0.857925\pi\)
\(312\) −1.02610e75 −0.0869908
\(313\) −1.21312e76 −0.932825 −0.466413 0.884567i \(-0.654454\pi\)
−0.466413 + 0.884567i \(0.654454\pi\)
\(314\) 2.23337e76 1.55814
\(315\) 1.14192e75 0.0723045
\(316\) 7.10652e76 4.08508
\(317\) −1.56107e76 −0.814918 −0.407459 0.913224i \(-0.633585\pi\)
−0.407459 + 0.913224i \(0.633585\pi\)
\(318\) −5.23970e76 −2.48473
\(319\) −6.06313e75 −0.261265
\(320\) −1.38973e76 −0.544321
\(321\) 4.37590e76 1.55835
\(322\) −3.15379e76 −1.02148
\(323\) 3.24467e76 0.956080
\(324\) −1.04072e77 −2.79069
\(325\) −1.06026e75 −0.0258804
\(326\) 1.15065e77 2.55744
\(327\) 2.39357e76 0.484551
\(328\) 3.39017e76 0.625272
\(329\) −7.73236e76 −1.29968
\(330\) −2.04473e76 −0.313300
\(331\) 6.24069e76 0.871924 0.435962 0.899965i \(-0.356408\pi\)
0.435962 + 0.899965i \(0.356408\pi\)
\(332\) −3.81732e77 −4.86460
\(333\) 9.15051e75 0.106389
\(334\) 1.07842e77 1.14425
\(335\) 6.06298e76 0.587245
\(336\) 5.45859e77 4.82761
\(337\) 1.13017e77 0.912922 0.456461 0.889743i \(-0.349117\pi\)
0.456461 + 0.889743i \(0.349117\pi\)
\(338\) −2.53382e77 −1.86989
\(339\) −1.44992e77 −0.977805
\(340\) 9.04853e76 0.557791
\(341\) 2.16459e76 0.122002
\(342\) −6.85070e76 −0.353134
\(343\) −2.44461e77 −1.15276
\(344\) −2.41559e77 −1.04230
\(345\) 2.96378e76 0.117048
\(346\) −6.76413e76 −0.244563
\(347\) 8.92703e76 0.295568 0.147784 0.989020i \(-0.452786\pi\)
0.147784 + 0.989020i \(0.452786\pi\)
\(348\) −4.83088e77 −1.46507
\(349\) −2.05483e77 −0.570953 −0.285476 0.958386i \(-0.592152\pi\)
−0.285476 + 0.958386i \(0.592152\pi\)
\(350\) 1.07549e78 2.73862
\(351\) 1.14938e76 0.0268285
\(352\) −5.22181e77 −1.11756
\(353\) 7.47126e77 1.46644 0.733222 0.679990i \(-0.238016\pi\)
0.733222 + 0.679990i \(0.238016\pi\)
\(354\) 1.48493e78 2.67366
\(355\) −2.25513e77 −0.372569
\(356\) −7.96791e77 −1.20815
\(357\) −8.45952e77 −1.17751
\(358\) 3.00645e77 0.384256
\(359\) −9.45141e77 −1.10947 −0.554736 0.832027i \(-0.687181\pi\)
−0.554736 + 0.832027i \(0.687181\pi\)
\(360\) −1.14702e77 −0.123693
\(361\) 1.02684e78 1.01750
\(362\) −1.18670e78 −1.08076
\(363\) 9.84475e77 0.824238
\(364\) −1.55295e77 −0.119554
\(365\) 4.19206e77 0.296822
\(366\) −4.90468e77 −0.319476
\(367\) −1.08283e78 −0.649002 −0.324501 0.945885i \(-0.605196\pi\)
−0.324501 + 0.945885i \(0.605196\pi\)
\(368\) 1.66137e78 0.916448
\(369\) 5.81767e76 0.0295423
\(370\) −1.06147e78 −0.496313
\(371\) −4.76109e78 −2.05023
\(372\) 1.72466e78 0.684138
\(373\) 3.84170e78 1.40412 0.702059 0.712119i \(-0.252264\pi\)
0.702059 + 0.712119i \(0.252264\pi\)
\(374\) 1.77632e78 0.598326
\(375\) −2.14587e78 −0.666270
\(376\) 7.76690e78 2.22340
\(377\) 6.05677e76 0.0159893
\(378\) −1.16589e79 −2.83895
\(379\) 1.78001e78 0.399876 0.199938 0.979809i \(-0.435926\pi\)
0.199938 + 0.979809i \(0.435926\pi\)
\(380\) 5.67793e78 1.17704
\(381\) 7.63090e78 1.46004
\(382\) −1.06637e79 −1.88353
\(383\) 1.00847e79 1.64475 0.822374 0.568947i \(-0.192649\pi\)
0.822374 + 0.568947i \(0.192649\pi\)
\(384\) −5.11098e78 −0.769842
\(385\) −1.85796e78 −0.258514
\(386\) −1.23112e79 −1.58266
\(387\) −4.14526e77 −0.0492456
\(388\) −2.28895e79 −2.51344
\(389\) −1.43823e78 −0.146004 −0.0730021 0.997332i \(-0.523258\pi\)
−0.0730021 + 0.997332i \(0.523258\pi\)
\(390\) 2.04258e77 0.0191738
\(391\) −2.57473e78 −0.223533
\(392\) 5.95657e79 4.78378
\(393\) −7.43222e78 −0.552263
\(394\) 3.41983e79 2.35164
\(395\) −8.49333e78 −0.540588
\(396\) −2.67965e78 −0.157897
\(397\) 1.30448e79 0.711751 0.355875 0.934533i \(-0.384183\pi\)
0.355875 + 0.934533i \(0.384183\pi\)
\(398\) −9.35580e78 −0.472767
\(399\) −5.30832e79 −2.48476
\(400\) −5.66553e79 −2.45703
\(401\) −1.11670e79 −0.448778 −0.224389 0.974500i \(-0.572039\pi\)
−0.224389 + 0.974500i \(0.572039\pi\)
\(402\) 9.48327e79 3.53235
\(403\) −2.16231e77 −0.00746646
\(404\) −2.83016e79 −0.906107
\(405\) 1.24381e79 0.369298
\(406\) −6.14376e79 −1.69196
\(407\) −1.48883e79 −0.380377
\(408\) 8.49730e79 2.01440
\(409\) 6.64811e79 1.46264 0.731320 0.682035i \(-0.238905\pi\)
0.731320 + 0.682035i \(0.238905\pi\)
\(410\) −6.74858e78 −0.137818
\(411\) −8.55184e79 −1.62138
\(412\) −1.43610e80 −2.52825
\(413\) 1.34929e80 2.20612
\(414\) 5.43621e78 0.0825630
\(415\) 4.56226e79 0.643743
\(416\) 5.21632e78 0.0683940
\(417\) 4.54343e79 0.553649
\(418\) 1.11464e80 1.26257
\(419\) −1.13113e80 −1.19120 −0.595602 0.803279i \(-0.703087\pi\)
−0.595602 + 0.803279i \(0.703087\pi\)
\(420\) −1.48035e80 −1.44964
\(421\) −2.50575e78 −0.0228210 −0.0114105 0.999935i \(-0.503632\pi\)
−0.0114105 + 0.999935i \(0.503632\pi\)
\(422\) 2.99723e77 0.00253916
\(423\) 1.33283e79 0.105050
\(424\) 4.78235e80 3.50738
\(425\) 8.78022e79 0.599299
\(426\) −3.52731e80 −2.24105
\(427\) −4.45667e79 −0.263609
\(428\) −6.65231e80 −3.66385
\(429\) 2.86493e78 0.0146949
\(430\) 4.80856e79 0.229735
\(431\) −4.22944e80 −1.88246 −0.941231 0.337763i \(-0.890330\pi\)
−0.941231 + 0.337763i \(0.890330\pi\)
\(432\) 6.14173e80 2.54704
\(433\) 4.38659e80 1.69530 0.847650 0.530556i \(-0.178017\pi\)
0.847650 + 0.530556i \(0.178017\pi\)
\(434\) 2.19337e80 0.790087
\(435\) 5.77361e79 0.193876
\(436\) −3.63874e80 −1.13924
\(437\) −1.61564e80 −0.471693
\(438\) 6.55692e80 1.78542
\(439\) 1.27552e80 0.323981 0.161991 0.986792i \(-0.448209\pi\)
0.161991 + 0.986792i \(0.448209\pi\)
\(440\) 1.86625e80 0.442246
\(441\) 1.02217e80 0.226020
\(442\) −1.77446e79 −0.0366173
\(443\) −3.94931e80 −0.760691 −0.380345 0.924845i \(-0.624195\pi\)
−0.380345 + 0.924845i \(0.624195\pi\)
\(444\) −1.18624e81 −2.13300
\(445\) 9.52283e79 0.159877
\(446\) 7.73975e80 1.21343
\(447\) −3.23693e80 −0.473973
\(448\) −1.97516e81 −2.70161
\(449\) 3.41850e80 0.436840 0.218420 0.975855i \(-0.429910\pi\)
0.218420 + 0.975855i \(0.429910\pi\)
\(450\) −1.85383e80 −0.221354
\(451\) −9.46559e79 −0.105624
\(452\) 2.20418e81 2.29893
\(453\) 2.00567e80 0.195553
\(454\) −7.74704e80 −0.706207
\(455\) 1.85601e79 0.0158209
\(456\) 5.33203e81 4.25074
\(457\) −1.01306e81 −0.755423 −0.377711 0.925923i \(-0.623289\pi\)
−0.377711 + 0.925923i \(0.623289\pi\)
\(458\) −2.87479e81 −2.00544
\(459\) −9.51823e80 −0.621254
\(460\) −4.50558e80 −0.275193
\(461\) −3.55139e80 −0.203011 −0.101506 0.994835i \(-0.532366\pi\)
−0.101506 + 0.994835i \(0.532366\pi\)
\(462\) −2.90608e81 −1.55499
\(463\) 6.17959e80 0.309556 0.154778 0.987949i \(-0.450534\pi\)
0.154778 + 0.987949i \(0.450534\pi\)
\(464\) 3.23644e81 1.51799
\(465\) −2.06122e80 −0.0905336
\(466\) 3.21775e81 1.32368
\(467\) −2.32266e81 −0.894997 −0.447499 0.894285i \(-0.647685\pi\)
−0.447499 + 0.894285i \(0.647685\pi\)
\(468\) 2.67683e79 0.00966324
\(469\) 8.61704e81 2.91465
\(470\) −1.54610e81 −0.490065
\(471\) −2.98295e81 −0.886153
\(472\) −1.35531e82 −3.77406
\(473\) 6.74450e80 0.176070
\(474\) −1.32847e82 −3.25170
\(475\) 5.50957e81 1.26463
\(476\) 1.28603e82 2.76846
\(477\) 8.20671e80 0.165714
\(478\) 7.92034e81 1.50035
\(479\) −6.48492e81 −1.15258 −0.576290 0.817245i \(-0.695500\pi\)
−0.576290 + 0.817245i \(0.695500\pi\)
\(480\) 4.97245e81 0.829303
\(481\) 1.48726e80 0.0232789
\(482\) 6.91272e81 1.01558
\(483\) 4.21229e81 0.580939
\(484\) −1.49661e82 −1.93788
\(485\) 2.73563e81 0.332610
\(486\) 4.32717e81 0.494081
\(487\) 1.13904e82 1.22153 0.610765 0.791812i \(-0.290862\pi\)
0.610765 + 0.791812i \(0.290862\pi\)
\(488\) 4.47658e81 0.450964
\(489\) −1.53684e82 −1.45448
\(490\) −1.18573e82 −1.05440
\(491\) −8.43794e81 −0.705101 −0.352550 0.935793i \(-0.614685\pi\)
−0.352550 + 0.935793i \(0.614685\pi\)
\(492\) −7.54182e81 −0.592298
\(493\) −5.01572e81 −0.370256
\(494\) −1.11347e81 −0.0772690
\(495\) 3.20257e80 0.0208949
\(496\) −1.15543e82 −0.708850
\(497\) −3.20511e82 −1.84916
\(498\) 7.13595e82 3.87219
\(499\) 4.77379e81 0.243667 0.121833 0.992551i \(-0.461123\pi\)
0.121833 + 0.992551i \(0.461123\pi\)
\(500\) 3.26219e82 1.56648
\(501\) −1.44037e82 −0.650763
\(502\) 2.38161e82 1.01253
\(503\) −7.98855e81 −0.319628 −0.159814 0.987147i \(-0.551089\pi\)
−0.159814 + 0.987147i \(0.551089\pi\)
\(504\) −1.63021e82 −0.613922
\(505\) 3.38246e81 0.119907
\(506\) −8.84493e81 −0.295191
\(507\) 3.38424e82 1.06345
\(508\) −1.16006e83 −3.43271
\(509\) 5.44275e82 1.51679 0.758396 0.651794i \(-0.225983\pi\)
0.758396 + 0.651794i \(0.225983\pi\)
\(510\) −1.69150e82 −0.443998
\(511\) 5.95800e82 1.47320
\(512\) −5.43549e82 −1.26621
\(513\) −5.97266e82 −1.31096
\(514\) 8.31740e82 1.72033
\(515\) 1.71635e82 0.334570
\(516\) 5.37376e82 0.987331
\(517\) −2.16857e82 −0.375588
\(518\) −1.50862e83 −2.46333
\(519\) 9.03435e81 0.139089
\(520\) −1.86429e81 −0.0270653
\(521\) 3.83339e82 0.524847 0.262424 0.964953i \(-0.415478\pi\)
0.262424 + 0.964953i \(0.415478\pi\)
\(522\) 1.05900e82 0.136756
\(523\) 8.06645e82 0.982609 0.491305 0.870988i \(-0.336520\pi\)
0.491305 + 0.870988i \(0.336520\pi\)
\(524\) 1.12986e83 1.29843
\(525\) −1.43645e83 −1.55752
\(526\) −1.64573e83 −1.68381
\(527\) 1.79065e82 0.172897
\(528\) 1.53088e83 1.39511
\(529\) −1.03431e83 −0.889718
\(530\) −9.51990e82 −0.773069
\(531\) −2.32578e82 −0.178314
\(532\) 8.06979e83 5.84195
\(533\) 9.45564e80 0.00646415
\(534\) 1.48949e83 0.961678
\(535\) 7.95048e82 0.484845
\(536\) −8.65553e83 −4.98617
\(537\) −4.01549e82 −0.218536
\(538\) −4.57486e83 −2.35244
\(539\) −1.66312e83 −0.808100
\(540\) −1.66562e83 −0.764831
\(541\) 3.06629e83 1.33075 0.665375 0.746509i \(-0.268272\pi\)
0.665375 + 0.746509i \(0.268272\pi\)
\(542\) 3.10385e83 1.27328
\(543\) 1.58499e83 0.614656
\(544\) −4.31973e83 −1.58376
\(545\) 4.34883e82 0.150758
\(546\) 2.90303e82 0.0951648
\(547\) 1.45425e83 0.450842 0.225421 0.974261i \(-0.427624\pi\)
0.225421 + 0.974261i \(0.427624\pi\)
\(548\) 1.30006e84 3.81204
\(549\) 7.68199e81 0.0213068
\(550\) 3.01626e83 0.791418
\(551\) −3.14735e83 −0.781306
\(552\) −4.23110e83 −0.993828
\(553\) −1.20712e84 −2.68308
\(554\) 8.28387e83 1.74255
\(555\) 1.41773e83 0.282265
\(556\) −6.90699e83 −1.30169
\(557\) 3.06138e83 0.546177 0.273089 0.961989i \(-0.411955\pi\)
0.273089 + 0.961989i \(0.411955\pi\)
\(558\) −3.78072e82 −0.0638604
\(559\) −6.73742e81 −0.0107754
\(560\) 9.91760e83 1.50201
\(561\) −2.37250e83 −0.340283
\(562\) −1.19707e84 −1.62615
\(563\) 2.96460e83 0.381470 0.190735 0.981642i \(-0.438913\pi\)
0.190735 + 0.981642i \(0.438913\pi\)
\(564\) −1.72784e84 −2.10615
\(565\) −2.63432e83 −0.304223
\(566\) −4.90327e83 −0.536518
\(567\) 1.76778e84 1.83292
\(568\) 3.21943e84 3.16340
\(569\) −7.76465e83 −0.723099 −0.361549 0.932353i \(-0.617752\pi\)
−0.361549 + 0.932353i \(0.617752\pi\)
\(570\) −1.06141e84 −0.936916
\(571\) −3.44139e83 −0.287960 −0.143980 0.989581i \(-0.545990\pi\)
−0.143980 + 0.989581i \(0.545990\pi\)
\(572\) −4.35531e82 −0.0345494
\(573\) 1.42427e84 1.07121
\(574\) −9.59146e83 −0.684025
\(575\) −4.37198e83 −0.295671
\(576\) 3.40459e83 0.218363
\(577\) −1.84102e84 −1.11995 −0.559973 0.828511i \(-0.689189\pi\)
−0.559973 + 0.828511i \(0.689189\pi\)
\(578\) −1.77381e84 −1.02355
\(579\) 1.64432e84 0.900099
\(580\) −8.77712e83 −0.455825
\(581\) 6.48413e84 3.19507
\(582\) 4.27888e84 2.00069
\(583\) −1.33526e84 −0.592484
\(584\) −5.98460e84 −2.52025
\(585\) −3.19921e81 −0.00127876
\(586\) 7.48266e84 2.83909
\(587\) −5.03892e84 −1.81500 −0.907498 0.420057i \(-0.862010\pi\)
−0.907498 + 0.420057i \(0.862010\pi\)
\(588\) −1.32511e85 −4.53151
\(589\) 1.12363e84 0.364843
\(590\) 2.69793e84 0.831850
\(591\) −4.56762e84 −1.33743
\(592\) 7.94720e84 2.21005
\(593\) −9.78641e82 −0.0258497 −0.0129248 0.999916i \(-0.504114\pi\)
−0.0129248 + 0.999916i \(0.504114\pi\)
\(594\) −3.26978e84 −0.820412
\(595\) −1.53699e84 −0.366357
\(596\) 4.92083e84 1.11436
\(597\) 1.24959e84 0.268874
\(598\) 8.83564e82 0.0180656
\(599\) 8.94959e83 0.173894 0.0869471 0.996213i \(-0.472289\pi\)
0.0869471 + 0.996213i \(0.472289\pi\)
\(600\) 1.44287e85 2.66449
\(601\) −4.15804e84 −0.729822 −0.364911 0.931042i \(-0.618901\pi\)
−0.364911 + 0.931042i \(0.618901\pi\)
\(602\) 6.83419e84 1.14023
\(603\) −1.48532e84 −0.235583
\(604\) −3.04904e84 −0.459766
\(605\) 1.78867e84 0.256444
\(606\) 5.29060e84 0.721257
\(607\) −1.10453e85 −1.43193 −0.715966 0.698135i \(-0.754014\pi\)
−0.715966 + 0.698135i \(0.754014\pi\)
\(608\) −2.71062e85 −3.34202
\(609\) 8.20577e84 0.962259
\(610\) −8.91122e83 −0.0993979
\(611\) 2.16629e83 0.0229858
\(612\) −2.21673e84 −0.223766
\(613\) 4.37303e83 0.0419989 0.0209994 0.999779i \(-0.493315\pi\)
0.0209994 + 0.999779i \(0.493315\pi\)
\(614\) −2.89622e85 −2.64665
\(615\) 9.01358e83 0.0783802
\(616\) 2.65243e85 2.19498
\(617\) 1.63068e85 1.28432 0.642158 0.766572i \(-0.278039\pi\)
0.642158 + 0.766572i \(0.278039\pi\)
\(618\) 2.68460e85 2.01248
\(619\) 2.95589e84 0.210923 0.105462 0.994423i \(-0.466368\pi\)
0.105462 + 0.994423i \(0.466368\pi\)
\(620\) 3.13350e84 0.212855
\(621\) 4.73946e84 0.306503
\(622\) −5.48330e85 −3.37626
\(623\) 1.35344e85 0.793511
\(624\) −1.52927e84 −0.0853798
\(625\) 1.28466e85 0.683044
\(626\) −3.44747e85 −1.74576
\(627\) −1.48874e85 −0.718057
\(628\) 4.53473e85 2.08345
\(629\) −1.23163e85 −0.539057
\(630\) 3.24516e84 0.135316
\(631\) −2.00789e85 −0.797710 −0.398855 0.917014i \(-0.630592\pi\)
−0.398855 + 0.917014i \(0.630592\pi\)
\(632\) 1.21251e86 4.59002
\(633\) −4.00319e82 −0.00144408
\(634\) −4.43629e85 −1.52510
\(635\) 1.38644e85 0.454259
\(636\) −1.06389e86 −3.32242
\(637\) 1.66137e84 0.0494554
\(638\) −1.72304e85 −0.488951
\(639\) 5.52467e84 0.149462
\(640\) −9.28603e84 −0.239520
\(641\) −5.74852e85 −1.41379 −0.706897 0.707316i \(-0.749906\pi\)
−0.706897 + 0.707316i \(0.749906\pi\)
\(642\) 1.24356e86 2.91640
\(643\) 1.81186e85 0.405219 0.202610 0.979260i \(-0.435058\pi\)
0.202610 + 0.979260i \(0.435058\pi\)
\(644\) −6.40358e85 −1.36585
\(645\) −6.42244e84 −0.130656
\(646\) 9.22082e85 1.78928
\(647\) −6.46742e84 −0.119716 −0.0598578 0.998207i \(-0.519065\pi\)
−0.0598578 + 0.998207i \(0.519065\pi\)
\(648\) −1.77567e86 −3.13563
\(649\) 3.78413e85 0.637534
\(650\) −3.01309e84 −0.0484345
\(651\) −2.92952e85 −0.449342
\(652\) 2.33632e86 3.41965
\(653\) 5.18677e85 0.724511 0.362256 0.932079i \(-0.382007\pi\)
0.362256 + 0.932079i \(0.382007\pi\)
\(654\) 6.80213e85 0.906825
\(655\) −1.35035e85 −0.171825
\(656\) 5.05264e85 0.613693
\(657\) −1.02698e85 −0.119075
\(658\) −2.19741e86 −2.43232
\(659\) −1.56604e85 −0.165500 −0.0827501 0.996570i \(-0.526370\pi\)
−0.0827501 + 0.996570i \(0.526370\pi\)
\(660\) −4.15170e85 −0.418925
\(661\) 5.66912e85 0.546224 0.273112 0.961982i \(-0.411947\pi\)
0.273112 + 0.961982i \(0.411947\pi\)
\(662\) 1.77350e86 1.63178
\(663\) 2.37001e84 0.0208251
\(664\) −6.51309e86 −5.46589
\(665\) −9.64459e85 −0.773078
\(666\) 2.60042e85 0.199104
\(667\) 2.49750e85 0.182670
\(668\) 2.18967e86 1.53002
\(669\) −1.03374e86 −0.690106
\(670\) 1.72300e86 1.09901
\(671\) −1.24989e85 −0.0761790
\(672\) 7.06713e86 4.11605
\(673\) 5.64478e85 0.314186 0.157093 0.987584i \(-0.449788\pi\)
0.157093 + 0.987584i \(0.449788\pi\)
\(674\) 3.21177e86 1.70851
\(675\) −1.61623e86 −0.821746
\(676\) −5.14477e86 −2.50030
\(677\) −3.08615e86 −1.43371 −0.716857 0.697220i \(-0.754420\pi\)
−0.716857 + 0.697220i \(0.754420\pi\)
\(678\) −4.12042e86 −1.82994
\(679\) 3.88803e86 1.65083
\(680\) 1.54386e86 0.626737
\(681\) 1.03472e86 0.401637
\(682\) 6.15139e85 0.228323
\(683\) 2.92712e86 1.03898 0.519491 0.854476i \(-0.326121\pi\)
0.519491 + 0.854476i \(0.326121\pi\)
\(684\) −1.39099e86 −0.472187
\(685\) −1.55377e86 −0.504456
\(686\) −6.94717e86 −2.15736
\(687\) 3.83964e86 1.14054
\(688\) −3.60015e86 −1.02299
\(689\) 1.33386e85 0.0362598
\(690\) 8.42256e85 0.219052
\(691\) 6.58507e86 1.63863 0.819313 0.573347i \(-0.194355\pi\)
0.819313 + 0.573347i \(0.194355\pi\)
\(692\) −1.37342e86 −0.327014
\(693\) 4.55167e85 0.103707
\(694\) 2.53691e86 0.553148
\(695\) 8.25487e85 0.172256
\(696\) −8.24242e86 −1.64616
\(697\) −7.83039e85 −0.149687
\(698\) −5.83948e86 −1.06852
\(699\) −4.29771e86 −0.752807
\(700\) 2.18372e87 3.66190
\(701\) −1.19477e87 −1.91817 −0.959083 0.283124i \(-0.908629\pi\)
−0.959083 + 0.283124i \(0.908629\pi\)
\(702\) 3.26635e85 0.0502089
\(703\) −7.72843e86 −1.13751
\(704\) −5.53940e86 −0.780723
\(705\) 2.06502e86 0.278712
\(706\) 2.12321e87 2.74441
\(707\) 4.80734e86 0.595131
\(708\) 3.01505e87 3.57504
\(709\) −8.38841e86 −0.952729 −0.476365 0.879248i \(-0.658046\pi\)
−0.476365 + 0.879248i \(0.658046\pi\)
\(710\) −6.40870e86 −0.697253
\(711\) 2.08072e86 0.216866
\(712\) −1.35948e87 −1.35748
\(713\) −8.91627e85 −0.0853007
\(714\) −2.40405e87 −2.20368
\(715\) 5.20524e84 0.00457200
\(716\) 6.10441e86 0.513803
\(717\) −1.05786e87 −0.853286
\(718\) −2.68593e87 −2.07635
\(719\) −1.44491e86 −0.107055 −0.0535277 0.998566i \(-0.517047\pi\)
−0.0535277 + 0.998566i \(0.517047\pi\)
\(720\) −1.70950e86 −0.121403
\(721\) 2.43938e87 1.66056
\(722\) 2.91811e87 1.90422
\(723\) −9.23282e86 −0.577585
\(724\) −2.40953e87 −1.44512
\(725\) −8.51686e86 −0.489745
\(726\) 2.79771e87 1.54254
\(727\) 1.05896e87 0.559861 0.279931 0.960020i \(-0.409689\pi\)
0.279931 + 0.960020i \(0.409689\pi\)
\(728\) −2.64964e86 −0.134332
\(729\) 1.71578e87 0.834202
\(730\) 1.19131e87 0.555494
\(731\) 5.57938e86 0.249520
\(732\) −9.95866e86 −0.427182
\(733\) 6.14850e86 0.252987 0.126493 0.991967i \(-0.459628\pi\)
0.126493 + 0.991967i \(0.459628\pi\)
\(734\) −3.07723e87 −1.21459
\(735\) 1.58370e87 0.599665
\(736\) 2.15095e87 0.781369
\(737\) 2.41668e87 0.842289
\(738\) 1.65328e86 0.0552877
\(739\) −1.06088e87 −0.340417 −0.170209 0.985408i \(-0.554444\pi\)
−0.170209 + 0.985408i \(0.554444\pi\)
\(740\) −2.15525e87 −0.663638
\(741\) 1.48718e86 0.0439448
\(742\) −1.35302e88 −3.83694
\(743\) −7.11678e87 −1.93698 −0.968490 0.249054i \(-0.919880\pi\)
−0.968490 + 0.249054i \(0.919880\pi\)
\(744\) 2.94261e87 0.768701
\(745\) −5.88111e86 −0.147466
\(746\) 1.09175e88 2.62777
\(747\) −1.11767e87 −0.258248
\(748\) 3.60672e87 0.800043
\(749\) 1.12997e88 2.40641
\(750\) −6.09821e87 −1.24691
\(751\) −2.75527e87 −0.540936 −0.270468 0.962729i \(-0.587178\pi\)
−0.270468 + 0.962729i \(0.587178\pi\)
\(752\) 1.15756e88 2.18223
\(753\) −3.18094e87 −0.575850
\(754\) 1.72123e86 0.0299236
\(755\) 3.64406e86 0.0608419
\(756\) −2.36727e88 −3.79606
\(757\) −5.08599e87 −0.783342 −0.391671 0.920105i \(-0.628103\pi\)
−0.391671 + 0.920105i \(0.628103\pi\)
\(758\) 5.05848e87 0.748358
\(759\) 1.18135e87 0.167882
\(760\) 9.68766e87 1.32253
\(761\) −6.17119e87 −0.809351 −0.404675 0.914460i \(-0.632615\pi\)
−0.404675 + 0.914460i \(0.632615\pi\)
\(762\) 2.16858e88 2.73242
\(763\) 6.18080e87 0.748250
\(764\) −2.16519e88 −2.51854
\(765\) 2.64932e86 0.0296115
\(766\) 2.86590e88 3.07810
\(767\) −3.78016e86 −0.0390168
\(768\) 3.11277e87 0.308767
\(769\) −9.88338e87 −0.942219 −0.471110 0.882075i \(-0.656146\pi\)
−0.471110 + 0.882075i \(0.656146\pi\)
\(770\) −5.28000e87 −0.483801
\(771\) −1.11089e88 −0.978395
\(772\) −2.49972e88 −2.11623
\(773\) 1.65349e88 1.34563 0.672816 0.739810i \(-0.265085\pi\)
0.672816 + 0.739810i \(0.265085\pi\)
\(774\) −1.17801e87 −0.0921618
\(775\) 3.04058e87 0.228694
\(776\) −3.90540e88 −2.82412
\(777\) 2.01496e88 1.40096
\(778\) −4.08721e87 −0.273243
\(779\) −4.91355e87 −0.315866
\(780\) 4.14734e86 0.0256380
\(781\) −8.98887e87 −0.534378
\(782\) −7.31695e87 −0.418335
\(783\) 9.23273e87 0.507687
\(784\) 8.87755e88 4.69519
\(785\) −5.41967e87 −0.275707
\(786\) −2.11211e88 −1.03355
\(787\) −3.40866e88 −1.60455 −0.802277 0.596952i \(-0.796378\pi\)
−0.802277 + 0.596952i \(0.796378\pi\)
\(788\) 6.94377e88 3.14446
\(789\) 2.19808e88 0.957624
\(790\) −2.41366e88 −1.01170
\(791\) −3.74405e88 −1.50994
\(792\) −4.57200e87 −0.177414
\(793\) 1.24858e86 0.00466212
\(794\) 3.70712e88 1.33202
\(795\) 1.27150e88 0.439663
\(796\) −1.89964e88 −0.632153
\(797\) 5.14649e88 1.64828 0.824142 0.566384i \(-0.191658\pi\)
0.824142 + 0.566384i \(0.191658\pi\)
\(798\) −1.50854e89 −4.65016
\(799\) −1.79395e88 −0.532271
\(800\) −7.33505e88 −2.09488
\(801\) −2.33293e87 −0.0641371
\(802\) −3.17346e88 −0.839876
\(803\) 1.67094e88 0.425733
\(804\) 1.92552e89 4.72323
\(805\) 7.65322e87 0.180747
\(806\) −6.14493e86 −0.0139733
\(807\) 6.11031e88 1.33789
\(808\) −4.82881e88 −1.01811
\(809\) −3.94596e88 −0.801167 −0.400583 0.916260i \(-0.631192\pi\)
−0.400583 + 0.916260i \(0.631192\pi\)
\(810\) 3.53471e88 0.691131
\(811\) 5.01413e88 0.944189 0.472095 0.881548i \(-0.343498\pi\)
0.472095 + 0.881548i \(0.343498\pi\)
\(812\) −1.24745e89 −2.26238
\(813\) −4.14559e88 −0.724143
\(814\) −4.23099e88 −0.711865
\(815\) −2.79225e88 −0.452530
\(816\) 1.26642e89 1.97710
\(817\) 3.50105e88 0.526532
\(818\) 1.88928e89 2.73729
\(819\) −4.54689e86 −0.00634681
\(820\) −1.37026e88 −0.184281
\(821\) −2.71849e88 −0.352258 −0.176129 0.984367i \(-0.556358\pi\)
−0.176129 + 0.984367i \(0.556358\pi\)
\(822\) −2.43029e89 −3.03436
\(823\) 1.12457e89 1.35299 0.676493 0.736449i \(-0.263499\pi\)
0.676493 + 0.736449i \(0.263499\pi\)
\(824\) −2.45027e89 −2.84076
\(825\) −4.02859e88 −0.450099
\(826\) 3.83445e89 4.12869
\(827\) −7.06235e88 −0.732877 −0.366439 0.930442i \(-0.619423\pi\)
−0.366439 + 0.930442i \(0.619423\pi\)
\(828\) 1.10379e88 0.110398
\(829\) −1.28843e89 −1.24207 −0.621035 0.783783i \(-0.713288\pi\)
−0.621035 + 0.783783i \(0.713288\pi\)
\(830\) 1.29652e89 1.20475
\(831\) −1.10642e89 −0.991031
\(832\) 5.53358e87 0.0477799
\(833\) −1.37581e89 −1.14521
\(834\) 1.29117e89 1.03614
\(835\) −2.61697e88 −0.202471
\(836\) 2.26320e89 1.68823
\(837\) −3.29615e88 −0.237072
\(838\) −3.21449e89 −2.22931
\(839\) 1.19830e89 0.801355 0.400678 0.916219i \(-0.368775\pi\)
0.400678 + 0.916219i \(0.368775\pi\)
\(840\) −2.52577e89 −1.62883
\(841\) −1.12144e89 −0.697428
\(842\) −7.12093e87 −0.0427089
\(843\) 1.59884e89 0.924834
\(844\) 6.08570e86 0.00339521
\(845\) 6.14876e88 0.330870
\(846\) 3.78768e88 0.196597
\(847\) 2.54216e89 1.27280
\(848\) 7.12751e89 3.44243
\(849\) 6.54894e88 0.305131
\(850\) 2.49519e89 1.12157
\(851\) 6.13271e88 0.265950
\(852\) −7.16199e89 −2.99658
\(853\) 2.72024e89 1.09815 0.549075 0.835773i \(-0.314980\pi\)
0.549075 + 0.835773i \(0.314980\pi\)
\(854\) −1.26651e89 −0.493338
\(855\) 1.66244e88 0.0624856
\(856\) −1.13501e90 −4.11672
\(857\) −4.40217e89 −1.54082 −0.770409 0.637549i \(-0.779948\pi\)
−0.770409 + 0.637549i \(0.779948\pi\)
\(858\) 8.14166e87 0.0275012
\(859\) 4.73420e89 1.54332 0.771659 0.636036i \(-0.219427\pi\)
0.771659 + 0.636036i \(0.219427\pi\)
\(860\) 9.76348e88 0.307186
\(861\) 1.28106e89 0.389022
\(862\) −1.20194e90 −3.52298
\(863\) −2.92227e89 −0.826781 −0.413390 0.910554i \(-0.635656\pi\)
−0.413390 + 0.910554i \(0.635656\pi\)
\(864\) 7.95158e89 2.17162
\(865\) 1.64143e88 0.0432745
\(866\) 1.24660e90 3.17271
\(867\) 2.36914e89 0.582115
\(868\) 4.45351e89 1.05645
\(869\) −3.38541e89 −0.775369
\(870\) 1.64076e89 0.362834
\(871\) −2.41415e88 −0.0515477
\(872\) −6.20841e89 −1.28005
\(873\) −6.70182e88 −0.133432
\(874\) −4.59137e89 −0.882762
\(875\) −5.54118e89 −1.02886
\(876\) 1.33134e90 2.38734
\(877\) 8.38175e89 1.45160 0.725800 0.687905i \(-0.241470\pi\)
0.725800 + 0.687905i \(0.241470\pi\)
\(878\) 3.62482e89 0.606322
\(879\) −9.99404e89 −1.61466
\(880\) 2.78143e89 0.434057
\(881\) −4.60933e89 −0.694820 −0.347410 0.937713i \(-0.612939\pi\)
−0.347410 + 0.937713i \(0.612939\pi\)
\(882\) 2.90484e89 0.422991
\(883\) −1.05185e90 −1.47963 −0.739815 0.672810i \(-0.765087\pi\)
−0.739815 + 0.672810i \(0.765087\pi\)
\(884\) −3.60293e88 −0.0489623
\(885\) −3.60343e89 −0.473093
\(886\) −1.12233e90 −1.42361
\(887\) 1.61456e90 1.97871 0.989357 0.145510i \(-0.0464824\pi\)
0.989357 + 0.145510i \(0.0464824\pi\)
\(888\) −2.02396e90 −2.39666
\(889\) 1.97049e90 2.25461
\(890\) 2.70623e89 0.299205
\(891\) 4.95780e89 0.529686
\(892\) 1.57151e90 1.62252
\(893\) −1.12570e90 −1.12319
\(894\) −9.19881e89 −0.887028
\(895\) −7.29566e88 −0.0679927
\(896\) −1.31978e90 −1.18880
\(897\) −1.18011e88 −0.0102743
\(898\) 9.71480e89 0.817534
\(899\) −1.73694e89 −0.141291
\(900\) −3.76409e89 −0.295981
\(901\) −1.10460e90 −0.839648
\(902\) −2.68996e89 −0.197673
\(903\) −9.12793e89 −0.648479
\(904\) 3.76077e90 2.58309
\(905\) 2.87974e89 0.191237
\(906\) 5.69977e89 0.365971
\(907\) 1.02664e90 0.637376 0.318688 0.947860i \(-0.396758\pi\)
0.318688 + 0.947860i \(0.396758\pi\)
\(908\) −1.57299e90 −0.944295
\(909\) −8.28644e88 −0.0481027
\(910\) 5.27446e88 0.0296084
\(911\) −1.66692e90 −0.904910 −0.452455 0.891787i \(-0.649452\pi\)
−0.452455 + 0.891787i \(0.649452\pi\)
\(912\) 7.94675e90 4.17203
\(913\) 1.81850e90 0.923325
\(914\) −2.87894e90 −1.41375
\(915\) 1.19021e89 0.0565300
\(916\) −5.83708e90 −2.68154
\(917\) −1.91919e90 −0.852810
\(918\) −2.70492e90 −1.16266
\(919\) 1.08032e90 0.449188 0.224594 0.974452i \(-0.427894\pi\)
0.224594 + 0.974452i \(0.427894\pi\)
\(920\) −7.68740e89 −0.309208
\(921\) 3.86827e90 1.50521
\(922\) −1.00925e90 −0.379930
\(923\) 8.97943e88 0.0327037
\(924\) −5.90063e90 −2.07923
\(925\) −2.09135e90 −0.713022
\(926\) 1.75614e90 0.579326
\(927\) −4.20477e89 −0.134218
\(928\) 4.19016e90 1.29425
\(929\) 4.46225e90 1.33375 0.666875 0.745170i \(-0.267632\pi\)
0.666875 + 0.745170i \(0.267632\pi\)
\(930\) −5.85765e89 −0.169431
\(931\) −8.63317e90 −2.41660
\(932\) 6.53345e90 1.76993
\(933\) 7.32365e90 1.92016
\(934\) −6.60062e90 −1.67496
\(935\) −4.31055e89 −0.105871
\(936\) 4.56720e88 0.0108577
\(937\) −2.19447e89 −0.0504978 −0.0252489 0.999681i \(-0.508038\pi\)
−0.0252489 + 0.999681i \(0.508038\pi\)
\(938\) 2.44882e91 5.45469
\(939\) 4.60454e90 0.992855
\(940\) −3.13927e90 −0.655283
\(941\) −4.73247e90 −0.956321 −0.478161 0.878272i \(-0.658696\pi\)
−0.478161 + 0.878272i \(0.658696\pi\)
\(942\) −8.47705e90 −1.65841
\(943\) 3.89902e89 0.0738498
\(944\) −2.01993e91 −3.70417
\(945\) 2.82923e90 0.502341
\(946\) 1.91667e90 0.329510
\(947\) −6.68420e90 −1.11269 −0.556346 0.830951i \(-0.687797\pi\)
−0.556346 + 0.830951i \(0.687797\pi\)
\(948\) −2.69737e91 −4.34797
\(949\) −1.66919e89 −0.0260547
\(950\) 1.56573e91 2.36672
\(951\) 5.92523e90 0.867359
\(952\) 2.19422e91 3.11066
\(953\) −8.38193e89 −0.115083 −0.0575414 0.998343i \(-0.518326\pi\)
−0.0575414 + 0.998343i \(0.518326\pi\)
\(954\) 2.33221e90 0.310129
\(955\) 2.58772e90 0.333284
\(956\) 1.60818e91 2.00617
\(957\) 2.30134e90 0.278078
\(958\) −1.84291e91 −2.15702
\(959\) −2.20830e91 −2.50375
\(960\) 5.27488e90 0.579349
\(961\) −8.77850e90 −0.934022
\(962\) 4.22655e89 0.0435658
\(963\) −1.94773e90 −0.194503
\(964\) 1.40359e91 1.35797
\(965\) 2.98753e90 0.280046
\(966\) 1.19706e91 1.08721
\(967\) 5.11590e90 0.450209 0.225105 0.974335i \(-0.427728\pi\)
0.225105 + 0.974335i \(0.427728\pi\)
\(968\) −2.55351e91 −2.17741
\(969\) −1.23156e91 −1.01761
\(970\) 7.77421e90 0.622470
\(971\) 5.40878e90 0.419675 0.209837 0.977736i \(-0.432707\pi\)
0.209837 + 0.977736i \(0.432707\pi\)
\(972\) 8.78606e90 0.660653
\(973\) 1.17323e91 0.854950
\(974\) 3.23695e91 2.28606
\(975\) 4.02436e89 0.0275459
\(976\) 6.67180e90 0.442612
\(977\) −1.46776e90 −0.0943778 −0.0471889 0.998886i \(-0.515026\pi\)
−0.0471889 + 0.998886i \(0.515026\pi\)
\(978\) −4.36743e91 −2.72202
\(979\) 3.79577e90 0.229312
\(980\) −2.40756e91 −1.40988
\(981\) −1.06539e90 −0.0604788
\(982\) −2.39792e91 −1.31958
\(983\) 3.29286e91 1.75667 0.878337 0.478041i \(-0.158653\pi\)
0.878337 + 0.478041i \(0.158653\pi\)
\(984\) −1.28678e91 −0.665510
\(985\) −8.29882e90 −0.416113
\(986\) −1.42538e91 −0.692924
\(987\) 2.93492e91 1.38332
\(988\) −2.26083e90 −0.103319
\(989\) −2.77817e90 −0.123104
\(990\) 9.10117e89 0.0391042
\(991\) 1.54521e91 0.643785 0.321893 0.946776i \(-0.395681\pi\)
0.321893 + 0.946776i \(0.395681\pi\)
\(992\) −1.49592e91 −0.604369
\(993\) −2.36873e91 −0.928034
\(994\) −9.10840e91 −3.46065
\(995\) 2.27035e90 0.0836543
\(996\) 1.44891e92 5.17764
\(997\) −7.52005e90 −0.260626 −0.130313 0.991473i \(-0.541598\pi\)
−0.130313 + 0.991473i \(0.541598\pi\)
\(998\) 1.35663e91 0.456016
\(999\) 2.26713e91 0.739144
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.62.a.a.1.4 4
3.2 odd 2 9.62.a.a.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.62.a.a.1.4 4 1.1 even 1 trivial
9.62.a.a.1.1 4 3.2 odd 2