Properties

Label 1.64.a.a.1.1
Level $1$
Weight $64$
Character 1.1
Self dual yes
Analytic conductor $25.136$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 64 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.1360966918\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 5096287552528786 x^{3} + 574038763744383494840 x^{2} + 3502610791787684740809332695881 x - 35880030333954415007358004861309901934\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{37}\cdot 3^{17}\cdot 5^{3}\cdot 7^{2}\cdot 13 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(6.64596e7\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.68363e9 q^{2} -3.45751e14 q^{3} +1.27130e19 q^{4} -3.68153e21 q^{5} +1.61937e24 q^{6} +6.76929e26 q^{7} -1.63440e28 q^{8} -1.02502e30 q^{9} +O(q^{10})\) \(q-4.68363e9 q^{2} -3.45751e14 q^{3} +1.27130e19 q^{4} -3.68153e21 q^{5} +1.61937e24 q^{6} +6.76929e26 q^{7} -1.63440e28 q^{8} -1.02502e30 q^{9} +1.72429e31 q^{10} -4.60404e32 q^{11} -4.39553e33 q^{12} -1.39483e35 q^{13} -3.17048e36 q^{14} +1.27289e36 q^{15} -4.07073e37 q^{16} +6.98067e38 q^{17} +4.80080e39 q^{18} -2.26762e40 q^{19} -4.68032e40 q^{20} -2.34049e41 q^{21} +2.15636e42 q^{22} +9.79250e42 q^{23} +5.65096e42 q^{24} -9.48666e43 q^{25} +6.53284e44 q^{26} +7.50134e44 q^{27} +8.60579e45 q^{28} +1.02400e46 q^{29} -5.96175e45 q^{30} -7.88084e46 q^{31} +3.41405e47 q^{32} +1.59185e47 q^{33} -3.26949e48 q^{34} -2.49213e48 q^{35} -1.30310e49 q^{36} -4.47306e48 q^{37} +1.06207e50 q^{38} +4.82263e49 q^{39} +6.01710e49 q^{40} -2.61515e50 q^{41} +1.09620e51 q^{42} +1.36209e51 q^{43} -5.85311e51 q^{44} +3.77363e51 q^{45} -4.58644e52 q^{46} -1.83368e52 q^{47} +1.40746e52 q^{48} +2.83982e53 q^{49} +4.44320e53 q^{50} -2.41358e53 q^{51} -1.77324e54 q^{52} +3.07821e54 q^{53} -3.51335e54 q^{54} +1.69499e54 q^{55} -1.10637e55 q^{56} +7.84031e54 q^{57} -4.79604e55 q^{58} +6.07846e55 q^{59} +1.61823e55 q^{60} +2.59347e56 q^{61} +3.69109e56 q^{62} -6.93864e56 q^{63} -1.22355e57 q^{64} +5.13509e56 q^{65} -7.45565e56 q^{66} -2.81696e57 q^{67} +8.87452e57 q^{68} -3.38577e57 q^{69} +1.16722e58 q^{70} -2.35862e58 q^{71} +1.67529e58 q^{72} +3.66441e58 q^{73} +2.09502e58 q^{74} +3.28002e58 q^{75} -2.88282e59 q^{76} -3.11661e59 q^{77} -2.25874e59 q^{78} +9.89281e59 q^{79} +1.49865e59 q^{80} +9.13835e59 q^{81} +1.22484e60 q^{82} +3.72735e59 q^{83} -2.97546e60 q^{84} -2.56996e60 q^{85} -6.37951e60 q^{86} -3.54049e60 q^{87} +7.52486e60 q^{88} +2.65947e61 q^{89} -1.76743e61 q^{90} -9.44199e61 q^{91} +1.24492e62 q^{92} +2.72481e61 q^{93} +8.58826e61 q^{94} +8.34829e61 q^{95} -1.18041e62 q^{96} +2.06784e62 q^{97} -1.33006e63 q^{98} +4.71923e62 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 507315096q^{2} + 953245351116252q^{3} + 6772922881670488640q^{4} - \)\(50\!\cdots\!30\)\(q^{5} + \)\(10\!\cdots\!60\)\(q^{6} + \)\(37\!\cdots\!56\)\(q^{7} + \)\(73\!\cdots\!00\)\(q^{8} + \)\(63\!\cdots\!85\)\(q^{9} + O(q^{10}) \) \( 5q + 507315096q^{2} + 953245351116252q^{3} + 6772922881670488640q^{4} - \)\(50\!\cdots\!30\)\(q^{5} + \)\(10\!\cdots\!60\)\(q^{6} + \)\(37\!\cdots\!56\)\(q^{7} + \)\(73\!\cdots\!00\)\(q^{8} + \)\(63\!\cdots\!85\)\(q^{9} + \)\(34\!\cdots\!20\)\(q^{10} - \)\(54\!\cdots\!40\)\(q^{11} - \)\(26\!\cdots\!84\)\(q^{12} + \)\(10\!\cdots\!62\)\(q^{13} - \)\(54\!\cdots\!20\)\(q^{14} - \)\(34\!\cdots\!60\)\(q^{15} - \)\(15\!\cdots\!20\)\(q^{16} + \)\(23\!\cdots\!26\)\(q^{17} - \)\(87\!\cdots\!08\)\(q^{18} - \)\(78\!\cdots\!00\)\(q^{19} + \)\(11\!\cdots\!60\)\(q^{20} + \)\(12\!\cdots\!60\)\(q^{21} + \)\(52\!\cdots\!72\)\(q^{22} + \)\(15\!\cdots\!72\)\(q^{23} + \)\(81\!\cdots\!00\)\(q^{24} + \)\(29\!\cdots\!75\)\(q^{25} + \)\(18\!\cdots\!60\)\(q^{26} + \)\(59\!\cdots\!00\)\(q^{27} + \)\(20\!\cdots\!48\)\(q^{28} + \)\(50\!\cdots\!50\)\(q^{29} + \)\(11\!\cdots\!40\)\(q^{30} + \)\(15\!\cdots\!60\)\(q^{31} - \)\(28\!\cdots\!44\)\(q^{32} - \)\(19\!\cdots\!36\)\(q^{33} - \)\(77\!\cdots\!20\)\(q^{34} - \)\(10\!\cdots\!80\)\(q^{35} - \)\(37\!\cdots\!20\)\(q^{36} - \)\(17\!\cdots\!34\)\(q^{37} + \)\(96\!\cdots\!00\)\(q^{38} + \)\(49\!\cdots\!20\)\(q^{39} + \)\(89\!\cdots\!00\)\(q^{40} + \)\(15\!\cdots\!10\)\(q^{41} + \)\(20\!\cdots\!52\)\(q^{42} - \)\(29\!\cdots\!08\)\(q^{43} - \)\(18\!\cdots\!20\)\(q^{44} - \)\(42\!\cdots\!10\)\(q^{45} - \)\(51\!\cdots\!40\)\(q^{46} - \)\(48\!\cdots\!64\)\(q^{47} + \)\(10\!\cdots\!72\)\(q^{48} + \)\(33\!\cdots\!65\)\(q^{49} + \)\(11\!\cdots\!00\)\(q^{50} + \)\(15\!\cdots\!60\)\(q^{51} + \)\(11\!\cdots\!96\)\(q^{52} - \)\(69\!\cdots\!98\)\(q^{53} - \)\(12\!\cdots\!00\)\(q^{54} - \)\(20\!\cdots\!60\)\(q^{55} - \)\(23\!\cdots\!00\)\(q^{56} - \)\(17\!\cdots\!00\)\(q^{57} + \)\(24\!\cdots\!00\)\(q^{58} + \)\(10\!\cdots\!00\)\(q^{59} + \)\(34\!\cdots\!20\)\(q^{60} + \)\(39\!\cdots\!10\)\(q^{61} + \)\(51\!\cdots\!32\)\(q^{62} - \)\(68\!\cdots\!88\)\(q^{63} - \)\(21\!\cdots\!60\)\(q^{64} - \)\(17\!\cdots\!60\)\(q^{65} - \)\(55\!\cdots\!80\)\(q^{66} - \)\(47\!\cdots\!24\)\(q^{67} - \)\(12\!\cdots\!92\)\(q^{68} + \)\(17\!\cdots\!20\)\(q^{69} + \)\(40\!\cdots\!20\)\(q^{70} + \)\(50\!\cdots\!60\)\(q^{71} + \)\(61\!\cdots\!00\)\(q^{72} - \)\(29\!\cdots\!78\)\(q^{73} - \)\(14\!\cdots\!20\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(45\!\cdots\!00\)\(q^{76} - \)\(58\!\cdots\!08\)\(q^{77} - \)\(22\!\cdots\!96\)\(q^{78} + \)\(58\!\cdots\!00\)\(q^{79} + \)\(10\!\cdots\!20\)\(q^{80} + \)\(45\!\cdots\!05\)\(q^{81} + \)\(39\!\cdots\!12\)\(q^{82} + \)\(27\!\cdots\!32\)\(q^{83} - \)\(12\!\cdots\!20\)\(q^{84} - \)\(12\!\cdots\!80\)\(q^{85} - \)\(25\!\cdots\!40\)\(q^{86} - \)\(16\!\cdots\!00\)\(q^{87} - \)\(37\!\cdots\!00\)\(q^{88} + \)\(32\!\cdots\!50\)\(q^{89} + \)\(39\!\cdots\!40\)\(q^{90} + \)\(10\!\cdots\!60\)\(q^{91} + \)\(16\!\cdots\!76\)\(q^{92} + \)\(37\!\cdots\!84\)\(q^{93} - \)\(20\!\cdots\!20\)\(q^{94} + \)\(13\!\cdots\!00\)\(q^{95} - \)\(90\!\cdots\!40\)\(q^{96} - \)\(17\!\cdots\!14\)\(q^{97} - \)\(19\!\cdots\!72\)\(q^{98} - \)\(12\!\cdots\!80\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.68363e9 −1.54219 −0.771094 0.636721i \(-0.780290\pi\)
−0.771094 + 0.636721i \(0.780290\pi\)
\(3\) −3.45751e14 −0.323180 −0.161590 0.986858i \(-0.551662\pi\)
−0.161590 + 0.986858i \(0.551662\pi\)
\(4\) 1.27130e19 1.37834
\(5\) −3.68153e21 −0.353568 −0.176784 0.984250i \(-0.556569\pi\)
−0.176784 + 0.984250i \(0.556569\pi\)
\(6\) 1.61937e24 0.498404
\(7\) 6.76929e26 1.62164 0.810821 0.585294i \(-0.199021\pi\)
0.810821 + 0.585294i \(0.199021\pi\)
\(8\) −1.63440e28 −0.583478
\(9\) −1.02502e30 −0.895555
\(10\) 1.72429e31 0.545268
\(11\) −4.60404e32 −0.723219 −0.361610 0.932330i \(-0.617773\pi\)
−0.361610 + 0.932330i \(0.617773\pi\)
\(12\) −4.39553e33 −0.445453
\(13\) −1.39483e35 −1.13581 −0.567903 0.823095i \(-0.692245\pi\)
−0.567903 + 0.823095i \(0.692245\pi\)
\(14\) −3.17048e36 −2.50088
\(15\) 1.27289e36 0.114266
\(16\) −4.07073e37 −0.478512
\(17\) 6.98067e38 1.21550 0.607752 0.794127i \(-0.292072\pi\)
0.607752 + 0.794127i \(0.292072\pi\)
\(18\) 4.80080e39 1.38111
\(19\) −2.26762e40 −1.18804 −0.594020 0.804450i \(-0.702460\pi\)
−0.594020 + 0.804450i \(0.702460\pi\)
\(20\) −4.68032e40 −0.487338
\(21\) −2.34049e41 −0.524082
\(22\) 2.15636e42 1.11534
\(23\) 9.79250e42 1.24872 0.624362 0.781135i \(-0.285359\pi\)
0.624362 + 0.781135i \(0.285359\pi\)
\(24\) 5.65096e42 0.188568
\(25\) −9.48666e43 −0.874990
\(26\) 6.53284e44 1.75163
\(27\) 7.50134e44 0.612605
\(28\) 8.60579e45 2.23518
\(29\) 1.02400e46 0.880569 0.440284 0.897858i \(-0.354878\pi\)
0.440284 + 0.897858i \(0.354878\pi\)
\(30\) −5.96175e45 −0.176220
\(31\) −7.88084e46 −0.829238 −0.414619 0.909995i \(-0.636085\pi\)
−0.414619 + 0.909995i \(0.636085\pi\)
\(32\) 3.41405e47 1.32143
\(33\) 1.59185e47 0.233730
\(34\) −3.26949e48 −1.87454
\(35\) −2.49213e48 −0.573361
\(36\) −1.30310e49 −1.23438
\(37\) −4.47306e48 −0.178752 −0.0893760 0.995998i \(-0.528487\pi\)
−0.0893760 + 0.995998i \(0.528487\pi\)
\(38\) 1.06207e50 1.83218
\(39\) 4.82263e49 0.367070
\(40\) 6.01710e49 0.206299
\(41\) −2.61515e50 −0.411912 −0.205956 0.978561i \(-0.566030\pi\)
−0.205956 + 0.978561i \(0.566030\pi\)
\(42\) 1.09620e51 0.808233
\(43\) 1.36209e51 0.478574 0.239287 0.970949i \(-0.423086\pi\)
0.239287 + 0.970949i \(0.423086\pi\)
\(44\) −5.85311e51 −0.996845
\(45\) 3.77363e51 0.316640
\(46\) −4.58644e52 −1.92577
\(47\) −1.83368e52 −0.391057 −0.195529 0.980698i \(-0.562642\pi\)
−0.195529 + 0.980698i \(0.562642\pi\)
\(48\) 1.40746e52 0.154645
\(49\) 2.83982e53 1.62972
\(50\) 4.44320e53 1.34940
\(51\) −2.41358e53 −0.392826
\(52\) −1.77324e54 −1.56553
\(53\) 3.07821e54 1.49145 0.745725 0.666254i \(-0.232103\pi\)
0.745725 + 0.666254i \(0.232103\pi\)
\(54\) −3.51335e54 −0.944752
\(55\) 1.69499e54 0.255707
\(56\) −1.10637e55 −0.946192
\(57\) 7.84031e54 0.383950
\(58\) −4.79604e55 −1.35800
\(59\) 6.07846e55 1.00451 0.502256 0.864719i \(-0.332503\pi\)
0.502256 + 0.864719i \(0.332503\pi\)
\(60\) 1.61823e55 0.157498
\(61\) 2.59347e56 1.49965 0.749827 0.661634i \(-0.230137\pi\)
0.749827 + 0.661634i \(0.230137\pi\)
\(62\) 3.69109e56 1.27884
\(63\) −6.93864e56 −1.45227
\(64\) −1.22355e57 −1.55939
\(65\) 5.13509e56 0.401585
\(66\) −7.45565e56 −0.360455
\(67\) −2.81696e57 −0.848056 −0.424028 0.905649i \(-0.639384\pi\)
−0.424028 + 0.905649i \(0.639384\pi\)
\(68\) 8.87452e57 1.67538
\(69\) −3.38577e57 −0.403562
\(70\) 1.16722e58 0.884230
\(71\) −2.35862e58 −1.14293 −0.571465 0.820627i \(-0.693625\pi\)
−0.571465 + 0.820627i \(0.693625\pi\)
\(72\) 1.67529e58 0.522536
\(73\) 3.66441e58 0.740175 0.370087 0.928997i \(-0.379328\pi\)
0.370087 + 0.928997i \(0.379328\pi\)
\(74\) 2.09502e58 0.275669
\(75\) 3.28002e58 0.282779
\(76\) −2.88282e59 −1.63753
\(77\) −3.11661e59 −1.17280
\(78\) −2.25874e59 −0.566091
\(79\) 9.89281e59 1.65984 0.829920 0.557882i \(-0.188386\pi\)
0.829920 + 0.557882i \(0.188386\pi\)
\(80\) 1.49865e59 0.169186
\(81\) 9.13835e59 0.697573
\(82\) 1.22484e60 0.635246
\(83\) 3.72735e59 0.131959 0.0659797 0.997821i \(-0.478983\pi\)
0.0659797 + 0.997821i \(0.478983\pi\)
\(84\) −2.97546e60 −0.722365
\(85\) −2.56996e60 −0.429763
\(86\) −6.37951e60 −0.738051
\(87\) −3.54049e60 −0.284582
\(88\) 7.52486e60 0.421982
\(89\) 2.65947e61 1.04475 0.522373 0.852717i \(-0.325047\pi\)
0.522373 + 0.852717i \(0.325047\pi\)
\(90\) −1.76743e61 −0.488318
\(91\) −9.44199e61 −1.84187
\(92\) 1.24492e62 1.72117
\(93\) 2.72481e61 0.267993
\(94\) 8.58826e61 0.603084
\(95\) 8.34829e61 0.420053
\(96\) −1.18041e62 −0.427060
\(97\) 2.06784e62 0.539769 0.269884 0.962893i \(-0.413015\pi\)
0.269884 + 0.962893i \(0.413015\pi\)
\(98\) −1.33006e63 −2.51334
\(99\) 4.71923e62 0.647682
\(100\) −1.20604e63 −1.20604
\(101\) 3.75368e62 0.274368 0.137184 0.990546i \(-0.456195\pi\)
0.137184 + 0.990546i \(0.456195\pi\)
\(102\) 1.13043e63 0.605812
\(103\) 4.47631e63 1.76420 0.882099 0.471065i \(-0.156130\pi\)
0.882099 + 0.471065i \(0.156130\pi\)
\(104\) 2.27971e63 0.662718
\(105\) 8.61659e62 0.185299
\(106\) −1.44172e64 −2.30010
\(107\) 1.06364e63 0.126243 0.0631214 0.998006i \(-0.479894\pi\)
0.0631214 + 0.998006i \(0.479894\pi\)
\(108\) 9.53644e63 0.844380
\(109\) −4.54972e63 −0.301336 −0.150668 0.988584i \(-0.548142\pi\)
−0.150668 + 0.988584i \(0.548142\pi\)
\(110\) −7.93871e63 −0.394349
\(111\) 1.54657e63 0.0577690
\(112\) −2.75560e64 −0.775975
\(113\) 4.59886e64 0.978767 0.489384 0.872069i \(-0.337222\pi\)
0.489384 + 0.872069i \(0.337222\pi\)
\(114\) −3.67211e64 −0.592124
\(115\) −3.60514e64 −0.441509
\(116\) 1.30181e65 1.21373
\(117\) 1.42972e65 1.01718
\(118\) −2.84692e65 −1.54915
\(119\) 4.72542e65 1.97111
\(120\) −2.08042e64 −0.0666717
\(121\) −1.93293e65 −0.476954
\(122\) −1.21468e66 −2.31275
\(123\) 9.04190e64 0.133122
\(124\) −1.00189e66 −1.14297
\(125\) 7.48406e65 0.662936
\(126\) 3.24980e66 2.23967
\(127\) −1.05063e66 −0.564459 −0.282230 0.959347i \(-0.591074\pi\)
−0.282230 + 0.959347i \(0.591074\pi\)
\(128\) 2.58176e66 1.08343
\(129\) −4.70944e65 −0.154665
\(130\) −2.40509e66 −0.619320
\(131\) 1.98761e65 0.0402056 0.0201028 0.999798i \(-0.493601\pi\)
0.0201028 + 0.999798i \(0.493601\pi\)
\(132\) 2.02372e66 0.322160
\(133\) −1.53502e67 −1.92658
\(134\) 1.31936e67 1.30786
\(135\) −2.76164e66 −0.216598
\(136\) −1.14092e67 −0.709219
\(137\) 1.22845e67 0.606263 0.303132 0.952949i \(-0.401968\pi\)
0.303132 + 0.952949i \(0.401968\pi\)
\(138\) 1.58577e67 0.622369
\(139\) −3.22368e67 −1.00783 −0.503914 0.863754i \(-0.668107\pi\)
−0.503914 + 0.863754i \(0.668107\pi\)
\(140\) −3.16825e67 −0.790289
\(141\) 6.33996e66 0.126382
\(142\) 1.10469e68 1.76261
\(143\) 6.42184e67 0.821437
\(144\) 4.17257e67 0.428534
\(145\) −3.76989e67 −0.311341
\(146\) −1.71627e68 −1.14149
\(147\) −9.81871e67 −0.526694
\(148\) −5.68660e67 −0.246382
\(149\) −2.87976e68 −1.00923 −0.504614 0.863345i \(-0.668365\pi\)
−0.504614 + 0.863345i \(0.668365\pi\)
\(150\) −1.53624e68 −0.436098
\(151\) 5.32727e68 1.22668 0.613339 0.789820i \(-0.289826\pi\)
0.613339 + 0.789820i \(0.289826\pi\)
\(152\) 3.70619e68 0.693195
\(153\) −7.15531e68 −1.08855
\(154\) 1.45970e69 1.80868
\(155\) 2.90135e68 0.293192
\(156\) 6.13100e68 0.505948
\(157\) 8.62466e68 0.581973 0.290987 0.956727i \(-0.406016\pi\)
0.290987 + 0.956727i \(0.406016\pi\)
\(158\) −4.63342e69 −2.55979
\(159\) −1.06430e69 −0.482006
\(160\) −1.25689e69 −0.467216
\(161\) 6.62883e69 2.02498
\(162\) −4.28006e69 −1.07579
\(163\) 3.38297e69 0.700467 0.350234 0.936662i \(-0.386102\pi\)
0.350234 + 0.936662i \(0.386102\pi\)
\(164\) −3.32463e69 −0.567757
\(165\) −5.86046e68 −0.0826394
\(166\) −1.74575e69 −0.203506
\(167\) −2.69262e69 −0.259780 −0.129890 0.991528i \(-0.541462\pi\)
−0.129890 + 0.991528i \(0.541462\pi\)
\(168\) 3.82530e69 0.305790
\(169\) 4.37436e69 0.290057
\(170\) 1.20367e70 0.662776
\(171\) 2.32435e70 1.06395
\(172\) 1.73162e70 0.659639
\(173\) −5.58968e70 −1.77392 −0.886961 0.461844i \(-0.847188\pi\)
−0.886961 + 0.461844i \(0.847188\pi\)
\(174\) 1.65823e70 0.438879
\(175\) −6.42180e70 −1.41892
\(176\) 1.87418e70 0.346069
\(177\) −2.10163e70 −0.324638
\(178\) −1.24560e71 −1.61119
\(179\) 4.93030e70 0.534568 0.267284 0.963618i \(-0.413874\pi\)
0.267284 + 0.963618i \(0.413874\pi\)
\(180\) 4.79741e70 0.436438
\(181\) 6.89051e70 0.526473 0.263237 0.964731i \(-0.415210\pi\)
0.263237 + 0.964731i \(0.415210\pi\)
\(182\) 4.42227e71 2.84051
\(183\) −8.96694e70 −0.484658
\(184\) −1.60049e71 −0.728603
\(185\) 1.64677e70 0.0632010
\(186\) −1.27620e71 −0.413295
\(187\) −3.21393e71 −0.879076
\(188\) −2.33115e71 −0.539012
\(189\) 5.07788e71 0.993426
\(190\) −3.91003e71 −0.647801
\(191\) 3.94494e69 0.00553974 0.00276987 0.999996i \(-0.499118\pi\)
0.00276987 + 0.999996i \(0.499118\pi\)
\(192\) 4.23045e71 0.503962
\(193\) −2.30825e71 −0.233468 −0.116734 0.993163i \(-0.537242\pi\)
−0.116734 + 0.993163i \(0.537242\pi\)
\(194\) −9.68500e71 −0.832425
\(195\) −1.77546e71 −0.129784
\(196\) 3.61026e72 2.24632
\(197\) −1.29231e72 −0.684986 −0.342493 0.939520i \(-0.611271\pi\)
−0.342493 + 0.939520i \(0.611271\pi\)
\(198\) −2.21031e72 −0.998848
\(199\) 1.50454e72 0.580139 0.290070 0.957006i \(-0.406322\pi\)
0.290070 + 0.957006i \(0.406322\pi\)
\(200\) 1.55050e72 0.510537
\(201\) 9.73968e71 0.274075
\(202\) −1.75808e72 −0.423128
\(203\) 6.93176e72 1.42797
\(204\) −3.06837e72 −0.541450
\(205\) 9.62774e71 0.145639
\(206\) −2.09653e73 −2.72072
\(207\) −1.00375e73 −1.11830
\(208\) 5.67796e72 0.543497
\(209\) 1.04402e73 0.859213
\(210\) −4.03569e72 −0.285765
\(211\) 1.01840e73 0.620900 0.310450 0.950590i \(-0.399520\pi\)
0.310450 + 0.950590i \(0.399520\pi\)
\(212\) 3.91332e73 2.05573
\(213\) 8.15494e72 0.369372
\(214\) −4.98171e72 −0.194690
\(215\) −5.01457e72 −0.169208
\(216\) −1.22602e73 −0.357441
\(217\) −5.33477e73 −1.34473
\(218\) 2.13092e73 0.464716
\(219\) −1.26698e73 −0.239210
\(220\) 2.15484e73 0.352452
\(221\) −9.73683e73 −1.38058
\(222\) −7.24354e72 −0.0890907
\(223\) −4.32470e73 −0.461693 −0.230846 0.972990i \(-0.574149\pi\)
−0.230846 + 0.972990i \(0.574149\pi\)
\(224\) 2.31107e74 2.14289
\(225\) 9.72399e73 0.783601
\(226\) −2.15393e74 −1.50944
\(227\) −2.44832e72 −0.0149298 −0.00746489 0.999972i \(-0.502376\pi\)
−0.00746489 + 0.999972i \(0.502376\pi\)
\(228\) 9.96737e73 0.529216
\(229\) −1.64003e74 −0.758637 −0.379318 0.925266i \(-0.623842\pi\)
−0.379318 + 0.925266i \(0.623842\pi\)
\(230\) 1.68851e74 0.680890
\(231\) 1.07757e74 0.379026
\(232\) −1.67363e74 −0.513792
\(233\) 6.73503e74 1.80563 0.902813 0.430034i \(-0.141498\pi\)
0.902813 + 0.430034i \(0.141498\pi\)
\(234\) −6.69628e74 −1.56868
\(235\) 6.75074e73 0.138265
\(236\) 7.72753e74 1.38456
\(237\) −3.42045e74 −0.536427
\(238\) −2.21321e75 −3.03983
\(239\) −1.33708e74 −0.160925 −0.0804627 0.996758i \(-0.525640\pi\)
−0.0804627 + 0.996758i \(0.525640\pi\)
\(240\) −5.18160e73 −0.0546777
\(241\) 1.10284e75 1.02088 0.510439 0.859914i \(-0.329483\pi\)
0.510439 + 0.859914i \(0.329483\pi\)
\(242\) 9.05311e74 0.735553
\(243\) −1.17453e75 −0.838047
\(244\) 3.29707e75 2.06704
\(245\) −1.04549e75 −0.576218
\(246\) −4.23489e74 −0.205299
\(247\) 3.16293e75 1.34938
\(248\) 1.28805e75 0.483842
\(249\) −1.28874e74 −0.0426466
\(250\) −3.50525e75 −1.02237
\(251\) −9.21465e74 −0.237004 −0.118502 0.992954i \(-0.537809\pi\)
−0.118502 + 0.992954i \(0.537809\pi\)
\(252\) −8.82108e75 −2.00173
\(253\) −4.50851e75 −0.903101
\(254\) 4.92076e75 0.870502
\(255\) 8.88565e74 0.138891
\(256\) −8.06728e74 −0.111473
\(257\) 1.38953e76 1.69814 0.849072 0.528277i \(-0.177162\pi\)
0.849072 + 0.528277i \(0.177162\pi\)
\(258\) 2.20572e75 0.238523
\(259\) −3.02795e75 −0.289872
\(260\) 6.52823e75 0.553522
\(261\) −1.04962e76 −0.788598
\(262\) −9.30924e74 −0.0620045
\(263\) −5.06450e75 −0.299179 −0.149589 0.988748i \(-0.547795\pi\)
−0.149589 + 0.988748i \(0.547795\pi\)
\(264\) −2.60173e75 −0.136376
\(265\) −1.13325e76 −0.527329
\(266\) 7.18944e76 2.97114
\(267\) −9.19516e75 −0.337641
\(268\) −3.58120e76 −1.16891
\(269\) −1.81764e76 −0.527609 −0.263804 0.964576i \(-0.584977\pi\)
−0.263804 + 0.964576i \(0.584977\pi\)
\(270\) 1.29345e76 0.334034
\(271\) −2.99891e76 −0.689335 −0.344667 0.938725i \(-0.612008\pi\)
−0.344667 + 0.938725i \(0.612008\pi\)
\(272\) −2.84164e76 −0.581633
\(273\) 3.26458e76 0.595256
\(274\) −5.75362e76 −0.934972
\(275\) 4.36770e76 0.632809
\(276\) −4.30432e76 −0.556248
\(277\) −5.79140e76 −0.667837 −0.333919 0.942602i \(-0.608371\pi\)
−0.333919 + 0.942602i \(0.608371\pi\)
\(278\) 1.50985e77 1.55426
\(279\) 8.07800e76 0.742628
\(280\) 4.07315e76 0.334543
\(281\) 1.07550e77 0.789516 0.394758 0.918785i \(-0.370828\pi\)
0.394758 + 0.918785i \(0.370828\pi\)
\(282\) −2.96940e76 −0.194905
\(283\) 2.31865e77 1.36133 0.680663 0.732596i \(-0.261692\pi\)
0.680663 + 0.732596i \(0.261692\pi\)
\(284\) −2.99850e77 −1.57535
\(285\) −2.88643e76 −0.135753
\(286\) −3.00775e77 −1.26681
\(287\) −1.77027e77 −0.667974
\(288\) −3.49946e77 −1.18342
\(289\) 1.57474e77 0.477450
\(290\) 1.76567e77 0.480146
\(291\) −7.14959e76 −0.174442
\(292\) 4.65856e77 1.02022
\(293\) 1.01167e77 0.198935 0.0994674 0.995041i \(-0.468286\pi\)
0.0994674 + 0.995041i \(0.468286\pi\)
\(294\) 4.59872e77 0.812261
\(295\) −2.23780e77 −0.355163
\(296\) 7.31078e76 0.104298
\(297\) −3.45365e77 −0.443048
\(298\) 1.34877e78 1.55642
\(299\) −1.36588e78 −1.41831
\(300\) 4.16989e77 0.389767
\(301\) 9.22038e77 0.776076
\(302\) −2.49509e78 −1.89177
\(303\) −1.29784e77 −0.0886704
\(304\) 9.23085e77 0.568491
\(305\) −9.54792e77 −0.530230
\(306\) 3.35128e78 1.67875
\(307\) 1.53803e77 0.0695194 0.0347597 0.999396i \(-0.488933\pi\)
0.0347597 + 0.999396i \(0.488933\pi\)
\(308\) −3.96214e78 −1.61653
\(309\) −1.54769e78 −0.570153
\(310\) −1.35889e78 −0.452157
\(311\) 5.75345e78 1.72972 0.864860 0.502013i \(-0.167407\pi\)
0.864860 + 0.502013i \(0.167407\pi\)
\(312\) −7.88211e77 −0.214177
\(313\) −5.33509e78 −1.31067 −0.655337 0.755336i \(-0.727474\pi\)
−0.655337 + 0.755336i \(0.727474\pi\)
\(314\) −4.03947e78 −0.897512
\(315\) 2.55448e78 0.513476
\(316\) 1.25767e79 2.28783
\(317\) 7.37010e78 1.21369 0.606843 0.794822i \(-0.292436\pi\)
0.606843 + 0.794822i \(0.292436\pi\)
\(318\) 4.98476e78 0.743344
\(319\) −4.71454e78 −0.636844
\(320\) 4.50455e78 0.551349
\(321\) −3.67756e77 −0.0407992
\(322\) −3.10470e79 −3.12291
\(323\) −1.58295e79 −1.44407
\(324\) 1.16176e79 0.961496
\(325\) 1.32322e79 0.993819
\(326\) −1.58445e79 −1.08025
\(327\) 1.57307e78 0.0973856
\(328\) 4.27420e78 0.240342
\(329\) −1.24127e79 −0.634155
\(330\) 2.74482e78 0.127445
\(331\) 4.20263e79 1.77394 0.886971 0.461824i \(-0.152805\pi\)
0.886971 + 0.461824i \(0.152805\pi\)
\(332\) 4.73857e78 0.181885
\(333\) 4.58497e78 0.160082
\(334\) 1.26112e79 0.400630
\(335\) 1.03707e79 0.299846
\(336\) 9.52750e78 0.250779
\(337\) −3.09538e79 −0.741947 −0.370973 0.928644i \(-0.620976\pi\)
−0.370973 + 0.928644i \(0.620976\pi\)
\(338\) −2.04879e79 −0.447323
\(339\) −1.59006e79 −0.316318
\(340\) −3.26718e79 −0.592362
\(341\) 3.62837e79 0.599721
\(342\) −1.08864e80 −1.64082
\(343\) 7.42797e79 1.02119
\(344\) −2.22620e79 −0.279237
\(345\) 1.24648e79 0.142687
\(346\) 2.61800e80 2.73572
\(347\) −2.06715e80 −1.97240 −0.986199 0.165567i \(-0.947055\pi\)
−0.986199 + 0.165567i \(0.947055\pi\)
\(348\) −4.50102e79 −0.392252
\(349\) −2.40903e80 −1.91796 −0.958982 0.283467i \(-0.908516\pi\)
−0.958982 + 0.283467i \(0.908516\pi\)
\(350\) 3.00773e80 2.18824
\(351\) −1.04631e80 −0.695801
\(352\) −1.57184e80 −0.955686
\(353\) 2.33198e80 1.29665 0.648324 0.761365i \(-0.275470\pi\)
0.648324 + 0.761365i \(0.275470\pi\)
\(354\) 9.84327e79 0.500653
\(355\) 8.68331e79 0.404103
\(356\) 3.38098e80 1.44002
\(357\) −1.63382e80 −0.637024
\(358\) −2.30917e80 −0.824405
\(359\) 1.65059e80 0.539716 0.269858 0.962900i \(-0.413023\pi\)
0.269858 + 0.962900i \(0.413023\pi\)
\(360\) −6.16763e79 −0.184752
\(361\) 1.49893e80 0.411439
\(362\) −3.22726e80 −0.811921
\(363\) 6.68312e79 0.154142
\(364\) −1.20036e81 −2.53873
\(365\) −1.34906e80 −0.261702
\(366\) 4.19978e80 0.747433
\(367\) 6.87592e79 0.112292 0.0561462 0.998423i \(-0.482119\pi\)
0.0561462 + 0.998423i \(0.482119\pi\)
\(368\) −3.98626e80 −0.597529
\(369\) 2.68057e80 0.368890
\(370\) −7.71286e79 −0.0974678
\(371\) 2.08373e81 2.41860
\(372\) 3.46404e80 0.369386
\(373\) −2.35569e80 −0.230829 −0.115414 0.993317i \(-0.536820\pi\)
−0.115414 + 0.993317i \(0.536820\pi\)
\(374\) 1.50529e81 1.35570
\(375\) −2.58762e80 −0.214248
\(376\) 2.99697e80 0.228173
\(377\) −1.42830e81 −1.00016
\(378\) −2.37829e81 −1.53205
\(379\) −2.03819e81 −1.20812 −0.604059 0.796939i \(-0.706451\pi\)
−0.604059 + 0.796939i \(0.706451\pi\)
\(380\) 1.06132e81 0.578977
\(381\) 3.63257e80 0.182422
\(382\) −1.84766e79 −0.00854333
\(383\) 8.15876e80 0.347426 0.173713 0.984796i \(-0.444423\pi\)
0.173713 + 0.984796i \(0.444423\pi\)
\(384\) −8.92648e80 −0.350144
\(385\) 1.14739e81 0.414666
\(386\) 1.08110e81 0.360051
\(387\) −1.39616e81 −0.428589
\(388\) 2.62884e81 0.743987
\(389\) −6.11039e81 −1.59462 −0.797308 0.603572i \(-0.793743\pi\)
−0.797308 + 0.603572i \(0.793743\pi\)
\(390\) 8.31561e80 0.200152
\(391\) 6.83582e81 1.51783
\(392\) −4.64140e81 −0.950907
\(393\) −6.87220e79 −0.0129936
\(394\) 6.05271e81 1.05638
\(395\) −3.64207e81 −0.586867
\(396\) 5.99954e81 0.892729
\(397\) 1.31327e81 0.180490 0.0902452 0.995920i \(-0.471235\pi\)
0.0902452 + 0.995920i \(0.471235\pi\)
\(398\) −7.04671e81 −0.894684
\(399\) 5.30733e81 0.622630
\(400\) 3.86176e81 0.418693
\(401\) −1.16872e82 −1.17129 −0.585643 0.810569i \(-0.699158\pi\)
−0.585643 + 0.810569i \(0.699158\pi\)
\(402\) −4.56170e81 −0.422675
\(403\) 1.09924e82 0.941854
\(404\) 4.77205e81 0.378174
\(405\) −3.36431e81 −0.246640
\(406\) −3.24658e82 −2.20219
\(407\) 2.05942e81 0.129277
\(408\) 3.94475e81 0.229205
\(409\) −2.59503e82 −1.39591 −0.697957 0.716140i \(-0.745907\pi\)
−0.697957 + 0.716140i \(0.745907\pi\)
\(410\) −4.50927e81 −0.224603
\(411\) −4.24740e81 −0.195932
\(412\) 5.69072e82 2.43167
\(413\) 4.11469e82 1.62896
\(414\) 4.70118e82 1.72463
\(415\) −1.37223e81 −0.0466566
\(416\) −4.76200e82 −1.50089
\(417\) 1.11459e82 0.325709
\(418\) −4.88980e82 −1.32507
\(419\) 3.00047e82 0.754133 0.377066 0.926186i \(-0.376933\pi\)
0.377066 + 0.926186i \(0.376933\pi\)
\(420\) 1.09542e82 0.255405
\(421\) −4.33724e82 −0.938269 −0.469134 0.883127i \(-0.655434\pi\)
−0.469134 + 0.883127i \(0.655434\pi\)
\(422\) −4.76981e82 −0.957544
\(423\) 1.87955e82 0.350213
\(424\) −5.03103e82 −0.870227
\(425\) −6.62233e82 −1.06355
\(426\) −3.81947e82 −0.569640
\(427\) 1.75559e83 2.43190
\(428\) 1.35221e82 0.174006
\(429\) −2.22036e82 −0.265472
\(430\) 2.34864e82 0.260951
\(431\) 1.18372e82 0.122241 0.0611205 0.998130i \(-0.480533\pi\)
0.0611205 + 0.998130i \(0.480533\pi\)
\(432\) −3.05359e82 −0.293139
\(433\) −3.90701e82 −0.348719 −0.174359 0.984682i \(-0.555785\pi\)
−0.174359 + 0.984682i \(0.555785\pi\)
\(434\) 2.49861e83 2.07382
\(435\) 1.30344e82 0.100619
\(436\) −5.78406e82 −0.415344
\(437\) −2.22056e83 −1.48353
\(438\) 5.93404e82 0.368906
\(439\) 3.38234e82 0.195697 0.0978487 0.995201i \(-0.468804\pi\)
0.0978487 + 0.995201i \(0.468804\pi\)
\(440\) −2.77030e82 −0.149199
\(441\) −2.91086e83 −1.45951
\(442\) 4.56037e83 2.12911
\(443\) 3.83253e82 0.166636 0.0833178 0.996523i \(-0.473448\pi\)
0.0833178 + 0.996523i \(0.473448\pi\)
\(444\) 1.96615e82 0.0796256
\(445\) −9.79093e82 −0.369389
\(446\) 2.02553e83 0.712017
\(447\) 9.95681e82 0.326162
\(448\) −8.28259e83 −2.52877
\(449\) −1.29874e83 −0.369626 −0.184813 0.982774i \(-0.559168\pi\)
−0.184813 + 0.982774i \(0.559168\pi\)
\(450\) −4.55435e83 −1.20846
\(451\) 1.20403e83 0.297903
\(452\) 5.84652e83 1.34908
\(453\) −1.84191e83 −0.396438
\(454\) 1.14670e82 0.0230245
\(455\) 3.47609e83 0.651227
\(456\) −1.28142e83 −0.224026
\(457\) 7.28125e83 1.18808 0.594040 0.804436i \(-0.297532\pi\)
0.594040 + 0.804436i \(0.297532\pi\)
\(458\) 7.68128e83 1.16996
\(459\) 5.23644e83 0.744624
\(460\) −4.58320e83 −0.608551
\(461\) −4.72569e83 −0.585985 −0.292992 0.956115i \(-0.594651\pi\)
−0.292992 + 0.956115i \(0.594651\pi\)
\(462\) −5.04695e83 −0.584530
\(463\) 1.19085e84 1.28841 0.644205 0.764853i \(-0.277188\pi\)
0.644205 + 0.764853i \(0.277188\pi\)
\(464\) −4.16843e83 −0.421362
\(465\) −1.00315e83 −0.0947537
\(466\) −3.15443e84 −2.78461
\(467\) 3.45548e83 0.285119 0.142560 0.989786i \(-0.454467\pi\)
0.142560 + 0.989786i \(0.454467\pi\)
\(468\) 1.81760e84 1.40202
\(469\) −1.90688e84 −1.37524
\(470\) −3.16179e83 −0.213231
\(471\) −2.98199e83 −0.188082
\(472\) −9.93464e83 −0.586110
\(473\) −6.27112e83 −0.346114
\(474\) 1.60201e84 0.827271
\(475\) 2.15121e84 1.03952
\(476\) 6.00742e84 2.71687
\(477\) −3.15522e84 −1.33567
\(478\) 6.26240e83 0.248177
\(479\) 1.65644e84 0.614621 0.307311 0.951609i \(-0.400571\pi\)
0.307311 + 0.951609i \(0.400571\pi\)
\(480\) 4.34572e83 0.150995
\(481\) 6.23915e83 0.203028
\(482\) −5.16527e84 −1.57439
\(483\) −2.29193e84 −0.654434
\(484\) −2.45733e84 −0.657407
\(485\) −7.61282e83 −0.190845
\(486\) 5.50108e84 1.29243
\(487\) 1.93325e84 0.425722 0.212861 0.977083i \(-0.431722\pi\)
0.212861 + 0.977083i \(0.431722\pi\)
\(488\) −4.23877e84 −0.875014
\(489\) −1.16966e84 −0.226377
\(490\) 4.89667e84 0.888637
\(491\) −1.63772e84 −0.278723 −0.139361 0.990242i \(-0.544505\pi\)
−0.139361 + 0.990242i \(0.544505\pi\)
\(492\) 1.14950e84 0.183487
\(493\) 7.14821e84 1.07033
\(494\) −1.48140e85 −2.08100
\(495\) −1.73740e84 −0.229000
\(496\) 3.20808e84 0.396800
\(497\) −1.59662e85 −1.85342
\(498\) 6.03596e83 0.0657691
\(499\) 1.54865e85 1.58412 0.792058 0.610446i \(-0.209010\pi\)
0.792058 + 0.610446i \(0.209010\pi\)
\(500\) 9.51447e84 0.913754
\(501\) 9.30976e83 0.0839557
\(502\) 4.31580e84 0.365506
\(503\) −1.28749e85 −1.02412 −0.512060 0.858950i \(-0.671118\pi\)
−0.512060 + 0.858950i \(0.671118\pi\)
\(504\) 1.13405e85 0.847367
\(505\) −1.38193e84 −0.0970079
\(506\) 2.11162e85 1.39275
\(507\) −1.51244e84 −0.0937406
\(508\) −1.33566e85 −0.778019
\(509\) 8.05010e84 0.440749 0.220374 0.975415i \(-0.429272\pi\)
0.220374 + 0.975415i \(0.429272\pi\)
\(510\) −4.16171e84 −0.214196
\(511\) 2.48055e85 1.20030
\(512\) −2.00342e85 −0.911522
\(513\) −1.70102e85 −0.727799
\(514\) −6.50804e85 −2.61886
\(515\) −1.64796e85 −0.623764
\(516\) −5.98710e84 −0.213182
\(517\) 8.44233e84 0.282820
\(518\) 1.41818e85 0.447037
\(519\) 1.93264e85 0.573296
\(520\) −8.39280e84 −0.234316
\(521\) 6.39549e85 1.68068 0.840341 0.542058i \(-0.182355\pi\)
0.840341 + 0.542058i \(0.182355\pi\)
\(522\) 4.91602e85 1.21617
\(523\) −1.50070e85 −0.349535 −0.174767 0.984610i \(-0.555917\pi\)
−0.174767 + 0.984610i \(0.555917\pi\)
\(524\) 2.52685e84 0.0554171
\(525\) 2.22034e85 0.458566
\(526\) 2.37202e85 0.461390
\(527\) −5.50136e85 −1.00794
\(528\) −6.48000e84 −0.111842
\(529\) 3.43960e85 0.559312
\(530\) 5.30773e85 0.813240
\(531\) −6.23053e85 −0.899596
\(532\) −1.95146e86 −2.65548
\(533\) 3.64768e85 0.467853
\(534\) 4.30667e85 0.520705
\(535\) −3.91583e84 −0.0446355
\(536\) 4.60405e85 0.494822
\(537\) −1.70466e85 −0.172762
\(538\) 8.51316e85 0.813672
\(539\) −1.30747e86 −1.17865
\(540\) −3.51087e85 −0.298546
\(541\) −1.29548e86 −1.03924 −0.519620 0.854398i \(-0.673926\pi\)
−0.519620 + 0.854398i \(0.673926\pi\)
\(542\) 1.40458e86 1.06308
\(543\) −2.38240e85 −0.170146
\(544\) 2.38323e86 1.60621
\(545\) 1.67499e85 0.106543
\(546\) −1.52901e86 −0.917997
\(547\) 1.47098e86 0.833691 0.416846 0.908977i \(-0.363136\pi\)
0.416846 + 0.908977i \(0.363136\pi\)
\(548\) 1.56173e86 0.835639
\(549\) −2.65835e86 −1.34302
\(550\) −2.04567e86 −0.975911
\(551\) −2.32204e86 −1.04615
\(552\) 5.53370e85 0.235470
\(553\) 6.69673e86 2.69167
\(554\) 2.71247e86 1.02993
\(555\) −5.69373e84 −0.0204253
\(556\) −4.09826e86 −1.38913
\(557\) 5.12761e86 1.64239 0.821195 0.570647i \(-0.193308\pi\)
0.821195 + 0.570647i \(0.193308\pi\)
\(558\) −3.78343e86 −1.14527
\(559\) −1.89988e86 −0.543567
\(560\) 1.01448e86 0.274360
\(561\) 1.11122e86 0.284099
\(562\) −5.03723e86 −1.21758
\(563\) −6.46481e86 −1.47755 −0.738774 0.673954i \(-0.764595\pi\)
−0.738774 + 0.673954i \(0.764595\pi\)
\(564\) 8.05998e85 0.174198
\(565\) −1.69308e86 −0.346061
\(566\) −1.08597e87 −2.09942
\(567\) 6.18602e86 1.13121
\(568\) 3.85493e86 0.666874
\(569\) 8.48170e86 1.38818 0.694091 0.719887i \(-0.255806\pi\)
0.694091 + 0.719887i \(0.255806\pi\)
\(570\) 1.35190e86 0.209356
\(571\) 4.25578e86 0.623651 0.311825 0.950139i \(-0.399060\pi\)
0.311825 + 0.950139i \(0.399060\pi\)
\(572\) 8.16407e86 1.13222
\(573\) −1.36397e84 −0.00179033
\(574\) 8.29128e86 1.03014
\(575\) −9.28980e86 −1.09262
\(576\) 1.25416e87 1.39652
\(577\) −1.19085e87 −1.25551 −0.627754 0.778412i \(-0.716025\pi\)
−0.627754 + 0.778412i \(0.716025\pi\)
\(578\) −7.37551e86 −0.736317
\(579\) 7.98079e85 0.0754520
\(580\) −4.79265e86 −0.429135
\(581\) 2.52315e86 0.213991
\(582\) 3.34860e86 0.269023
\(583\) −1.41722e87 −1.07864
\(584\) −5.98912e86 −0.431875
\(585\) −5.26356e86 −0.359641
\(586\) −4.73830e86 −0.306795
\(587\) −2.19873e86 −0.134918 −0.0674592 0.997722i \(-0.521489\pi\)
−0.0674592 + 0.997722i \(0.521489\pi\)
\(588\) −1.24825e87 −0.725965
\(589\) 1.78707e87 0.985168
\(590\) 1.04810e87 0.547729
\(591\) 4.46819e86 0.221374
\(592\) 1.82086e86 0.0855349
\(593\) 3.06509e87 1.36527 0.682637 0.730758i \(-0.260833\pi\)
0.682637 + 0.730758i \(0.260833\pi\)
\(594\) 1.61756e87 0.683263
\(595\) −1.73968e87 −0.696922
\(596\) −3.66103e87 −1.39106
\(597\) −5.20197e86 −0.187489
\(598\) 6.39728e87 2.18730
\(599\) −3.03085e87 −0.983148 −0.491574 0.870836i \(-0.663578\pi\)
−0.491574 + 0.870836i \(0.663578\pi\)
\(600\) −5.36087e86 −0.164995
\(601\) −2.35430e87 −0.687568 −0.343784 0.939049i \(-0.611709\pi\)
−0.343784 + 0.939049i \(0.611709\pi\)
\(602\) −4.31848e87 −1.19685
\(603\) 2.88743e87 0.759481
\(604\) 6.77255e87 1.69078
\(605\) 7.11613e86 0.168636
\(606\) 6.07860e86 0.136746
\(607\) 3.81141e87 0.814032 0.407016 0.913421i \(-0.366569\pi\)
0.407016 + 0.913421i \(0.366569\pi\)
\(608\) −7.74174e87 −1.56991
\(609\) −2.39666e87 −0.461490
\(610\) 4.47189e87 0.817714
\(611\) 2.55766e87 0.444166
\(612\) −9.09653e87 −1.50040
\(613\) −1.02633e88 −1.60798 −0.803990 0.594643i \(-0.797293\pi\)
−0.803990 + 0.594643i \(0.797293\pi\)
\(614\) −7.20355e86 −0.107212
\(615\) −3.32880e86 −0.0470676
\(616\) 5.09380e87 0.684304
\(617\) −4.00841e87 −0.511670 −0.255835 0.966721i \(-0.582350\pi\)
−0.255835 + 0.966721i \(0.582350\pi\)
\(618\) 7.24879e87 0.879283
\(619\) 3.79065e87 0.436977 0.218489 0.975840i \(-0.429887\pi\)
0.218489 + 0.975840i \(0.429887\pi\)
\(620\) 3.68848e87 0.404119
\(621\) 7.34569e87 0.764975
\(622\) −2.69470e88 −2.66755
\(623\) 1.80028e88 1.69420
\(624\) −1.96316e87 −0.175647
\(625\) 7.53018e87 0.640596
\(626\) 2.49876e88 2.02131
\(627\) −3.60971e87 −0.277680
\(628\) 1.09645e88 0.802159
\(629\) −3.12250e87 −0.217274
\(630\) −1.19642e88 −0.791877
\(631\) 4.40470e87 0.277327 0.138663 0.990340i \(-0.455719\pi\)
0.138663 + 0.990340i \(0.455719\pi\)
\(632\) −1.61688e88 −0.968480
\(633\) −3.52113e87 −0.200662
\(634\) −3.45188e88 −1.87173
\(635\) 3.86792e87 0.199575
\(636\) −1.35304e88 −0.664371
\(637\) −3.96105e88 −1.85105
\(638\) 2.20812e88 0.982133
\(639\) 2.41762e88 1.02356
\(640\) −9.50484e87 −0.383068
\(641\) 1.45362e88 0.557729 0.278865 0.960330i \(-0.410042\pi\)
0.278865 + 0.960330i \(0.410042\pi\)
\(642\) 1.72243e87 0.0629200
\(643\) −3.36875e88 −1.17172 −0.585858 0.810413i \(-0.699243\pi\)
−0.585858 + 0.810413i \(0.699243\pi\)
\(644\) 8.42722e88 2.79112
\(645\) 1.73379e87 0.0546847
\(646\) 7.41394e88 2.22702
\(647\) −2.12507e88 −0.607980 −0.303990 0.952675i \(-0.598319\pi\)
−0.303990 + 0.952675i \(0.598319\pi\)
\(648\) −1.49357e88 −0.407018
\(649\) −2.79855e88 −0.726482
\(650\) −6.19748e88 −1.53266
\(651\) 1.84450e88 0.434589
\(652\) 4.30076e88 0.965485
\(653\) −4.78683e88 −1.02396 −0.511980 0.858997i \(-0.671088\pi\)
−0.511980 + 0.858997i \(0.671088\pi\)
\(654\) −7.36768e87 −0.150187
\(655\) −7.31745e86 −0.0142154
\(656\) 1.06456e88 0.197105
\(657\) −3.75609e88 −0.662867
\(658\) 5.81365e88 0.977987
\(659\) 1.13944e89 1.82726 0.913630 0.406546i \(-0.133267\pi\)
0.913630 + 0.406546i \(0.133267\pi\)
\(660\) −7.45039e87 −0.113906
\(661\) −6.00258e88 −0.874967 −0.437484 0.899226i \(-0.644130\pi\)
−0.437484 + 0.899226i \(0.644130\pi\)
\(662\) −1.96836e89 −2.73575
\(663\) 3.36652e88 0.446175
\(664\) −6.09199e87 −0.0769954
\(665\) 5.65120e88 0.681176
\(666\) −2.14743e88 −0.246877
\(667\) 1.00275e89 1.09959
\(668\) −3.42312e88 −0.358066
\(669\) 1.49527e88 0.149210
\(670\) −4.85726e88 −0.462418
\(671\) −1.19404e89 −1.08458
\(672\) −7.99055e88 −0.692539
\(673\) 1.31832e89 1.09030 0.545150 0.838338i \(-0.316473\pi\)
0.545150 + 0.838338i \(0.316473\pi\)
\(674\) 1.44976e89 1.14422
\(675\) −7.11627e88 −0.536023
\(676\) 5.56112e88 0.399799
\(677\) 6.31151e88 0.433102 0.216551 0.976271i \(-0.430519\pi\)
0.216551 + 0.976271i \(0.430519\pi\)
\(678\) 7.44726e88 0.487821
\(679\) 1.39978e89 0.875312
\(680\) 4.20034e88 0.250757
\(681\) 8.46510e86 0.00482501
\(682\) −1.69939e89 −0.924882
\(683\) −4.07620e88 −0.211838 −0.105919 0.994375i \(-0.533778\pi\)
−0.105919 + 0.994375i \(0.533778\pi\)
\(684\) 2.95494e89 1.46650
\(685\) −4.52259e88 −0.214355
\(686\) −3.47898e89 −1.57486
\(687\) 5.67042e88 0.245176
\(688\) −5.54469e88 −0.229003
\(689\) −4.29357e89 −1.69400
\(690\) −5.83805e88 −0.220050
\(691\) −3.22787e89 −1.16241 −0.581203 0.813758i \(-0.697418\pi\)
−0.581203 + 0.813758i \(0.697418\pi\)
\(692\) −7.10615e89 −2.44508
\(693\) 3.19458e89 1.05031
\(694\) 9.68178e89 3.04181
\(695\) 1.18681e89 0.356335
\(696\) 5.78659e88 0.166047
\(697\) −1.82555e89 −0.500681
\(698\) 1.12830e90 2.95786
\(699\) −2.32864e89 −0.583542
\(700\) −8.16402e89 −1.95576
\(701\) 1.80265e89 0.412851 0.206426 0.978462i \(-0.433817\pi\)
0.206426 + 0.978462i \(0.433817\pi\)
\(702\) 4.90051e89 1.07306
\(703\) 1.01432e89 0.212364
\(704\) 5.63329e89 1.12778
\(705\) −2.33408e88 −0.0446846
\(706\) −1.09221e90 −1.99967
\(707\) 2.54098e89 0.444928
\(708\) −2.67180e89 −0.447463
\(709\) 9.67376e89 1.54967 0.774835 0.632164i \(-0.217833\pi\)
0.774835 + 0.632164i \(0.217833\pi\)
\(710\) −4.06694e89 −0.623203
\(711\) −1.01403e90 −1.48648
\(712\) −4.34665e89 −0.609586
\(713\) −7.71731e89 −1.03549
\(714\) 7.65221e89 0.982410
\(715\) −2.36422e89 −0.290434
\(716\) 6.26789e89 0.736819
\(717\) 4.62298e88 0.0520078
\(718\) −7.73077e89 −0.832343
\(719\) −8.44444e88 −0.0870183 −0.0435091 0.999053i \(-0.513854\pi\)
−0.0435091 + 0.999053i \(0.513854\pi\)
\(720\) −1.53614e89 −0.151516
\(721\) 3.03014e90 2.86090
\(722\) −7.02044e89 −0.634516
\(723\) −3.81307e89 −0.329927
\(724\) 8.75989e89 0.725661
\(725\) −9.71434e89 −0.770488
\(726\) −3.13012e89 −0.237716
\(727\) −2.62811e90 −1.91122 −0.955609 0.294637i \(-0.904801\pi\)
−0.955609 + 0.294637i \(0.904801\pi\)
\(728\) 1.54320e90 1.07469
\(729\) −6.39844e89 −0.426734
\(730\) 6.31851e89 0.403594
\(731\) 9.50830e89 0.581708
\(732\) −1.13997e90 −0.668025
\(733\) 2.53172e90 1.42115 0.710577 0.703620i \(-0.248434\pi\)
0.710577 + 0.703620i \(0.248434\pi\)
\(734\) −3.22043e89 −0.173176
\(735\) 3.61479e89 0.186222
\(736\) 3.34320e90 1.65011
\(737\) 1.29694e90 0.613330
\(738\) −1.25548e90 −0.568898
\(739\) −3.90382e89 −0.169508 −0.0847540 0.996402i \(-0.527010\pi\)
−0.0847540 + 0.996402i \(0.527010\pi\)
\(740\) 2.09354e89 0.0871127
\(741\) −1.09359e90 −0.436094
\(742\) −9.75942e90 −3.72993
\(743\) 1.26958e90 0.465065 0.232532 0.972589i \(-0.425299\pi\)
0.232532 + 0.972589i \(0.425299\pi\)
\(744\) −4.45343e89 −0.156368
\(745\) 1.06019e90 0.356830
\(746\) 1.10332e90 0.355981
\(747\) −3.82060e89 −0.118177
\(748\) −4.08587e90 −1.21167
\(749\) 7.20011e89 0.204721
\(750\) 1.21195e90 0.330410
\(751\) 9.06659e89 0.237021 0.118510 0.992953i \(-0.462188\pi\)
0.118510 + 0.992953i \(0.462188\pi\)
\(752\) 7.46440e89 0.187126
\(753\) 3.18598e89 0.0765951
\(754\) 6.68964e90 1.54243
\(755\) −1.96125e90 −0.433714
\(756\) 6.45550e90 1.36928
\(757\) −5.56139e90 −1.13152 −0.565761 0.824569i \(-0.691417\pi\)
−0.565761 + 0.824569i \(0.691417\pi\)
\(758\) 9.54612e90 1.86315
\(759\) 1.55882e90 0.291864
\(760\) −1.36445e90 −0.245091
\(761\) −1.22236e90 −0.210660 −0.105330 0.994437i \(-0.533590\pi\)
−0.105330 + 0.994437i \(0.533590\pi\)
\(762\) −1.70136e90 −0.281329
\(763\) −3.07984e90 −0.488659
\(764\) 5.01520e88 0.00763567
\(765\) 2.63425e90 0.384877
\(766\) −3.82126e90 −0.535797
\(767\) −8.47839e90 −1.14093
\(768\) 2.78927e89 0.0360257
\(769\) −2.79253e90 −0.346193 −0.173097 0.984905i \(-0.555377\pi\)
−0.173097 + 0.984905i \(0.555377\pi\)
\(770\) −5.37395e90 −0.639492
\(771\) −4.80432e90 −0.548806
\(772\) −2.93447e90 −0.321799
\(773\) −4.97182e90 −0.523433 −0.261717 0.965145i \(-0.584289\pi\)
−0.261717 + 0.965145i \(0.584289\pi\)
\(774\) 6.53911e90 0.660965
\(775\) 7.47628e90 0.725574
\(776\) −3.37968e90 −0.314943
\(777\) 1.04692e90 0.0936807
\(778\) 2.86188e91 2.45920
\(779\) 5.93015e90 0.489368
\(780\) −2.25714e90 −0.178887
\(781\) 1.08592e91 0.826588
\(782\) −3.20164e91 −2.34078
\(783\) 7.68138e90 0.539441
\(784\) −1.15601e91 −0.779842
\(785\) −3.17519e90 −0.205767
\(786\) 3.21868e89 0.0200386
\(787\) 1.72439e91 1.03141 0.515705 0.856766i \(-0.327530\pi\)
0.515705 + 0.856766i \(0.327530\pi\)
\(788\) −1.64292e91 −0.944147
\(789\) 1.75106e90 0.0966885
\(790\) 1.70581e91 0.905059
\(791\) 3.11310e91 1.58721
\(792\) −7.71311e90 −0.377908
\(793\) −3.61744e91 −1.70332
\(794\) −6.15088e90 −0.278350
\(795\) 3.91823e90 0.170422
\(796\) 1.91272e91 0.799632
\(797\) 3.06190e91 1.23042 0.615210 0.788363i \(-0.289071\pi\)
0.615210 + 0.788363i \(0.289071\pi\)
\(798\) −2.48576e91 −0.960213
\(799\) −1.28003e91 −0.475332
\(800\) −3.23879e91 −1.15624
\(801\) −2.72601e91 −0.935627
\(802\) 5.47385e91 1.80634
\(803\) −1.68711e91 −0.535309
\(804\) 1.23820e91 0.377769
\(805\) −2.44042e91 −0.715970
\(806\) −5.14843e91 −1.45252
\(807\) 6.28452e90 0.170512
\(808\) −6.13502e90 −0.160088
\(809\) 1.38283e91 0.347049 0.173524 0.984830i \(-0.444484\pi\)
0.173524 + 0.984830i \(0.444484\pi\)
\(810\) 1.57572e91 0.380365
\(811\) −9.95913e90 −0.231241 −0.115620 0.993293i \(-0.536886\pi\)
−0.115620 + 0.993293i \(0.536886\pi\)
\(812\) 8.81233e91 1.96823
\(813\) 1.03688e91 0.222779
\(814\) −9.64554e90 −0.199369
\(815\) −1.24545e91 −0.247663
\(816\) 9.82501e90 0.187972
\(817\) −3.08869e91 −0.568565
\(818\) 1.21542e92 2.15276
\(819\) 9.67820e91 1.64950
\(820\) 1.22397e91 0.200741
\(821\) −9.97222e91 −1.57392 −0.786960 0.617004i \(-0.788346\pi\)
−0.786960 + 0.617004i \(0.788346\pi\)
\(822\) 1.98932e91 0.302164
\(823\) −1.09412e91 −0.159945 −0.0799723 0.996797i \(-0.525483\pi\)
−0.0799723 + 0.996797i \(0.525483\pi\)
\(824\) −7.31608e91 −1.02937
\(825\) −1.51014e91 −0.204511
\(826\) −1.92717e92 −2.51216
\(827\) 3.84584e91 0.482578 0.241289 0.970453i \(-0.422430\pi\)
0.241289 + 0.970453i \(0.422430\pi\)
\(828\) −1.27606e92 −1.54140
\(829\) −1.14682e92 −1.33361 −0.666806 0.745232i \(-0.732339\pi\)
−0.666806 + 0.745232i \(0.732339\pi\)
\(830\) 6.42703e90 0.0719533
\(831\) 2.00238e91 0.215831
\(832\) 1.70664e92 1.77116
\(833\) 1.98238e92 1.98094
\(834\) −5.22033e91 −0.502305
\(835\) 9.91295e90 0.0918500
\(836\) 1.32726e92 1.18429
\(837\) −5.91169e91 −0.507995
\(838\) −1.40531e92 −1.16301
\(839\) 8.93222e91 0.711963 0.355982 0.934493i \(-0.384147\pi\)
0.355982 + 0.934493i \(0.384147\pi\)
\(840\) −1.40830e91 −0.108118
\(841\) −3.03726e91 −0.224599
\(842\) 2.03140e92 1.44699
\(843\) −3.71855e91 −0.255156
\(844\) 1.29469e92 0.855813
\(845\) −1.61043e91 −0.102555
\(846\) −8.80312e91 −0.540095
\(847\) −1.30846e92 −0.773449
\(848\) −1.25306e92 −0.713676
\(849\) −8.01676e91 −0.439953
\(850\) 3.10165e92 1.64020
\(851\) −4.38025e91 −0.223212
\(852\) 1.03674e92 0.509121
\(853\) 3.43257e92 1.62452 0.812259 0.583297i \(-0.198238\pi\)
0.812259 + 0.583297i \(0.198238\pi\)
\(854\) −8.22254e92 −3.75045
\(855\) −8.55714e91 −0.376180
\(856\) −1.73842e91 −0.0736599
\(857\) 3.05295e92 1.24688 0.623439 0.781872i \(-0.285735\pi\)
0.623439 + 0.781872i \(0.285735\pi\)
\(858\) 1.03993e92 0.409408
\(859\) −1.41823e92 −0.538222 −0.269111 0.963109i \(-0.586730\pi\)
−0.269111 + 0.963109i \(0.586730\pi\)
\(860\) −6.37501e91 −0.233227
\(861\) 6.12073e91 0.215876
\(862\) −5.54412e91 −0.188518
\(863\) −1.45435e92 −0.476791 −0.238396 0.971168i \(-0.576621\pi\)
−0.238396 + 0.971168i \(0.576621\pi\)
\(864\) 2.56099e92 0.809516
\(865\) 2.05786e92 0.627202
\(866\) 1.82990e92 0.537790
\(867\) −5.44469e91 −0.154302
\(868\) −6.78208e92 −1.85350
\(869\) −4.55469e92 −1.20043
\(870\) −6.10484e91 −0.155174
\(871\) 3.92917e92 0.963228
\(872\) 7.43608e91 0.175823
\(873\) −2.11957e92 −0.483393
\(874\) 1.04003e93 2.28789
\(875\) 5.06618e92 1.07505
\(876\) −1.61070e92 −0.329713
\(877\) 1.58350e92 0.312702 0.156351 0.987702i \(-0.450027\pi\)
0.156351 + 0.987702i \(0.450027\pi\)
\(878\) −1.58416e92 −0.301802
\(879\) −3.49788e91 −0.0642917
\(880\) −6.89985e91 −0.122359
\(881\) 5.92978e92 1.01461 0.507303 0.861768i \(-0.330642\pi\)
0.507303 + 0.861768i \(0.330642\pi\)
\(882\) 1.36334e93 2.25083
\(883\) −1.21127e93 −1.92965 −0.964826 0.262888i \(-0.915325\pi\)
−0.964826 + 0.262888i \(0.915325\pi\)
\(884\) −1.23784e93 −1.90291
\(885\) 7.73723e91 0.114782
\(886\) −1.79501e92 −0.256983
\(887\) −1.03885e93 −1.43535 −0.717676 0.696377i \(-0.754794\pi\)
−0.717676 + 0.696377i \(0.754794\pi\)
\(888\) −2.52771e91 −0.0337069
\(889\) −7.11202e92 −0.915351
\(890\) 4.58570e92 0.569667
\(891\) −4.20734e92 −0.504498
\(892\) −5.49798e92 −0.636371
\(893\) 4.15808e92 0.464592
\(894\) −4.66340e92 −0.503003
\(895\) −1.81511e92 −0.189006
\(896\) 1.74767e93 1.75694
\(897\) 4.72256e92 0.458369
\(898\) 6.08281e92 0.570032
\(899\) −8.06998e92 −0.730201
\(900\) 1.23621e93 1.08007
\(901\) 2.14880e93 1.81286
\(902\) −5.63920e92 −0.459422
\(903\) −3.18796e92 −0.250812
\(904\) −7.51639e92 −0.571089
\(905\) −2.53676e92 −0.186144
\(906\) 8.62682e92 0.611381
\(907\) 1.06453e93 0.728664 0.364332 0.931269i \(-0.381297\pi\)
0.364332 + 0.931269i \(0.381297\pi\)
\(908\) −3.11254e91 −0.0205784
\(909\) −3.84759e92 −0.245712
\(910\) −1.62807e93 −1.00432
\(911\) 4.84991e92 0.289005 0.144502 0.989504i \(-0.453842\pi\)
0.144502 + 0.989504i \(0.453842\pi\)
\(912\) −3.19158e92 −0.183725
\(913\) −1.71609e92 −0.0954356
\(914\) −3.41026e93 −1.83224
\(915\) 3.30121e92 0.171359
\(916\) −2.08497e93 −1.04566
\(917\) 1.34547e92 0.0651990
\(918\) −2.45255e93 −1.14835
\(919\) 3.96894e93 1.79571 0.897855 0.440292i \(-0.145125\pi\)
0.897855 + 0.440292i \(0.145125\pi\)
\(920\) 5.89224e92 0.257611
\(921\) −5.31775e91 −0.0224673
\(922\) 2.21334e93 0.903699
\(923\) 3.28986e93 1.29815
\(924\) 1.36992e93 0.522428
\(925\) 4.24344e92 0.156406
\(926\) −5.57747e93 −1.98697
\(927\) −4.58829e93 −1.57994
\(928\) 3.49598e93 1.16361
\(929\) 4.78473e92 0.153944 0.0769719 0.997033i \(-0.475475\pi\)
0.0769719 + 0.997033i \(0.475475\pi\)
\(930\) 4.69836e92 0.146128
\(931\) −6.43962e93 −1.93618
\(932\) 8.56222e93 2.48877
\(933\) −1.98926e93 −0.559011
\(934\) −1.61842e93 −0.439707
\(935\) 1.18322e93 0.310813
\(936\) −2.33674e93 −0.593500
\(937\) 4.55020e92 0.111746 0.0558731 0.998438i \(-0.482206\pi\)
0.0558731 + 0.998438i \(0.482206\pi\)
\(938\) 8.93113e93 2.12088
\(939\) 1.84461e93 0.423584
\(940\) 8.58220e92 0.190577
\(941\) −1.42886e93 −0.306843 −0.153421 0.988161i \(-0.549029\pi\)
−0.153421 + 0.988161i \(0.549029\pi\)
\(942\) 1.39665e93 0.290058
\(943\) −2.56088e93 −0.514365
\(944\) −2.47438e93 −0.480671
\(945\) −1.86944e93 −0.351244
\(946\) 2.93716e93 0.533773
\(947\) 4.96995e93 0.873631 0.436815 0.899551i \(-0.356106\pi\)
0.436815 + 0.899551i \(0.356106\pi\)
\(948\) −4.34841e93 −0.739381
\(949\) −5.11122e93 −0.840696
\(950\) −1.00755e94 −1.60314
\(951\) −2.54822e93 −0.392239
\(952\) −7.72324e93 −1.15010
\(953\) −3.58376e92 −0.0516313 −0.0258156 0.999667i \(-0.508218\pi\)
−0.0258156 + 0.999667i \(0.508218\pi\)
\(954\) 1.47779e94 2.05986
\(955\) −1.45234e91 −0.00195868
\(956\) −1.69983e93 −0.221810
\(957\) 1.63006e93 0.205815
\(958\) −7.75816e93 −0.947862
\(959\) 8.31577e93 0.983142
\(960\) −1.55745e93 −0.178185
\(961\) −2.82130e93 −0.312365
\(962\) −2.92218e93 −0.313107
\(963\) −1.09025e93 −0.113057
\(964\) 1.40203e94 1.40712
\(965\) 8.49787e92 0.0825467
\(966\) 1.07345e94 1.00926
\(967\) 1.31062e94 1.19273 0.596364 0.802714i \(-0.296611\pi\)
0.596364 + 0.802714i \(0.296611\pi\)
\(968\) 3.15918e93 0.278292
\(969\) 5.47306e93 0.466693
\(970\) 3.56556e93 0.294319
\(971\) 1.68011e94 1.34256 0.671278 0.741206i \(-0.265746\pi\)
0.671278 + 0.741206i \(0.265746\pi\)
\(972\) −1.49318e94 −1.15512
\(973\) −2.18221e94 −1.63434
\(974\) −9.05462e93 −0.656543
\(975\) −4.57506e93 −0.321182
\(976\) −1.05573e94 −0.717602
\(977\) −2.36832e94 −1.55870 −0.779349 0.626591i \(-0.784450\pi\)
−0.779349 + 0.626591i \(0.784450\pi\)
\(978\) 5.47827e93 0.349116
\(979\) −1.22443e94 −0.755580
\(980\) −1.32913e94 −0.794227
\(981\) 4.66355e93 0.269863
\(982\) 7.67046e93 0.429843
\(983\) 3.09223e94 1.67817 0.839086 0.543999i \(-0.183090\pi\)
0.839086 + 0.543999i \(0.183090\pi\)
\(984\) −1.47781e93 −0.0776735
\(985\) 4.75769e93 0.242189
\(986\) −3.34796e94 −1.65066
\(987\) 4.29171e93 0.204946
\(988\) 4.02103e94 1.85992
\(989\) 1.33382e94 0.597607
\(990\) 8.13731e93 0.353161
\(991\) −1.34419e94 −0.565119 −0.282560 0.959250i \(-0.591184\pi\)
−0.282560 + 0.959250i \(0.591184\pi\)
\(992\) −2.69055e94 −1.09578
\(993\) −1.45307e94 −0.573303
\(994\) 7.47795e94 2.85833
\(995\) −5.53901e93 −0.205119
\(996\) −1.63837e93 −0.0587817
\(997\) 6.27291e93 0.218058 0.109029 0.994039i \(-0.465226\pi\)
0.109029 + 0.994039i \(0.465226\pi\)
\(998\) −7.25331e94 −2.44300
\(999\) −3.35540e93 −0.109504
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 1.64.a.a.1.1 5
3.2 odd 2 9.64.a.c.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.64.a.a.1.1 5 1.1 even 1 trivial
9.64.a.c.1.5 5 3.2 odd 2