Properties

Label 1.74.a.a.1.3
Level 1
Weight 74
Character 1.1
Self dual yes
Analytic conductor 33.748
Analytic rank 1
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 74 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.7483973737\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - x^{4} - 10073499617947743056 x^{3} + 1429272143092482488433869600 x^{2} + 7661214288514935343595600445215756800 x + 1722510836040319301450745177697157900206688000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.60629e8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.90767e9 q^{2} +3.95253e17 q^{3} -9.40983e21 q^{4} +1.69056e25 q^{5} -2.33502e27 q^{6} -2.69951e30 q^{7} +1.11387e32 q^{8} +8.86395e34 q^{9} +O(q^{10})\) \(q-5.90767e9 q^{2} +3.95253e17 q^{3} -9.40983e21 q^{4} +1.69056e25 q^{5} -2.33502e27 q^{6} -2.69951e30 q^{7} +1.11387e32 q^{8} +8.86395e34 q^{9} -9.98727e34 q^{10} -1.46803e38 q^{11} -3.71926e39 q^{12} -3.34896e40 q^{13} +1.59478e40 q^{14} +6.68198e42 q^{15} +8.82153e43 q^{16} -1.35791e45 q^{17} -5.23653e44 q^{18} +7.35113e46 q^{19} -1.59079e47 q^{20} -1.06699e48 q^{21} +8.67264e47 q^{22} +2.07741e49 q^{23} +4.40258e49 q^{24} -7.72992e50 q^{25} +1.97845e50 q^{26} +8.32175e51 q^{27} +2.54020e52 q^{28} -3.30017e53 q^{29} -3.94750e52 q^{30} +1.78429e54 q^{31} -1.57316e54 q^{32} -5.80243e55 q^{33} +8.02211e54 q^{34} -4.56369e55 q^{35} -8.34082e56 q^{36} -3.22112e57 q^{37} -4.34280e56 q^{38} -1.32368e58 q^{39} +1.88306e57 q^{40} -6.12341e58 q^{41} +6.30343e57 q^{42} +2.07892e59 q^{43} +1.38139e60 q^{44} +1.49850e60 q^{45} -1.22727e59 q^{46} +5.09761e58 q^{47} +3.48673e61 q^{48} -4.19344e61 q^{49} +4.56658e60 q^{50} -5.36719e62 q^{51} +3.15131e62 q^{52} -1.65493e62 q^{53} -4.91622e61 q^{54} -2.48179e63 q^{55} -3.00690e62 q^{56} +2.90555e64 q^{57} +1.94963e63 q^{58} +1.57646e64 q^{59} -6.28764e64 q^{60} +3.70457e64 q^{61} -1.05410e64 q^{62} -2.39283e65 q^{63} -8.23876e65 q^{64} -5.66162e65 q^{65} +3.42788e65 q^{66} -2.21412e66 q^{67} +1.27777e67 q^{68} +8.21103e66 q^{69} +2.69608e65 q^{70} -1.08186e67 q^{71} +9.87324e66 q^{72} +2.15731e67 q^{73} +1.90293e67 q^{74} -3.05527e68 q^{75} -6.91729e68 q^{76} +3.96297e68 q^{77} +7.81989e67 q^{78} +1.93510e69 q^{79} +1.49133e69 q^{80} -2.70152e69 q^{81} +3.61751e68 q^{82} +1.17002e70 q^{83} +1.00402e70 q^{84} -2.29564e70 q^{85} -1.22816e69 q^{86} -1.30440e71 q^{87} -1.63519e70 q^{88} +1.65587e71 q^{89} -8.85267e69 q^{90} +9.04056e70 q^{91} -1.95481e71 q^{92} +7.05247e71 q^{93} -3.01150e68 q^{94} +1.24275e72 q^{95} -6.21797e71 q^{96} -9.74539e71 q^{97} +2.47734e71 q^{98} -1.30125e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} + O(q^{10}) \) \( 5q - 92089333488q^{2} - 129195798226305804q^{3} + \)\(89\!\cdots\!60\)\(q^{4} + \)\(23\!\cdots\!50\)\(q^{5} - \)\(33\!\cdots\!40\)\(q^{6} - \)\(43\!\cdots\!08\)\(q^{7} - \)\(38\!\cdots\!80\)\(q^{8} + \)\(32\!\cdots\!65\)\(q^{9} - \)\(10\!\cdots\!00\)\(q^{10} + \)\(50\!\cdots\!60\)\(q^{11} + \)\(13\!\cdots\!92\)\(q^{12} + \)\(47\!\cdots\!86\)\(q^{13} + \)\(26\!\cdots\!20\)\(q^{14} - \)\(50\!\cdots\!00\)\(q^{15} + \)\(57\!\cdots\!80\)\(q^{16} + \)\(66\!\cdots\!02\)\(q^{17} + \)\(69\!\cdots\!16\)\(q^{18} + \)\(31\!\cdots\!00\)\(q^{19} + \)\(68\!\cdots\!00\)\(q^{20} + \)\(87\!\cdots\!60\)\(q^{21} - \)\(94\!\cdots\!16\)\(q^{22} - \)\(41\!\cdots\!24\)\(q^{23} + \)\(16\!\cdots\!00\)\(q^{24} + \)\(32\!\cdots\!75\)\(q^{25} + \)\(44\!\cdots\!60\)\(q^{26} - \)\(12\!\cdots\!80\)\(q^{27} - \)\(37\!\cdots\!16\)\(q^{28} - \)\(21\!\cdots\!50\)\(q^{29} - \)\(80\!\cdots\!00\)\(q^{30} - \)\(39\!\cdots\!40\)\(q^{31} - \)\(94\!\cdots\!68\)\(q^{32} - \)\(73\!\cdots\!28\)\(q^{33} - \)\(32\!\cdots\!80\)\(q^{34} - \)\(10\!\cdots\!00\)\(q^{35} - \)\(34\!\cdots\!20\)\(q^{36} - \)\(67\!\cdots\!78\)\(q^{37} - \)\(20\!\cdots\!20\)\(q^{38} - \)\(53\!\cdots\!20\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(89\!\cdots\!90\)\(q^{41} + \)\(15\!\cdots\!84\)\(q^{42} + \)\(11\!\cdots\!56\)\(q^{43} + \)\(36\!\cdots\!20\)\(q^{44} + \)\(86\!\cdots\!50\)\(q^{45} + \)\(13\!\cdots\!60\)\(q^{46} + \)\(26\!\cdots\!32\)\(q^{47} - \)\(30\!\cdots\!24\)\(q^{48} - \)\(47\!\cdots\!15\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(66\!\cdots\!40\)\(q^{51} - \)\(18\!\cdots\!28\)\(q^{52} - \)\(22\!\cdots\!54\)\(q^{53} - \)\(98\!\cdots\!00\)\(q^{54} + \)\(52\!\cdots\!00\)\(q^{55} + \)\(17\!\cdots\!00\)\(q^{56} + \)\(39\!\cdots\!40\)\(q^{57} + \)\(63\!\cdots\!20\)\(q^{58} + \)\(49\!\cdots\!00\)\(q^{59} + \)\(91\!\cdots\!00\)\(q^{60} - \)\(20\!\cdots\!90\)\(q^{61} - \)\(45\!\cdots\!96\)\(q^{62} - \)\(14\!\cdots\!44\)\(q^{63} - \)\(26\!\cdots\!40\)\(q^{64} - \)\(22\!\cdots\!00\)\(q^{65} - \)\(79\!\cdots\!80\)\(q^{66} + \)\(17\!\cdots\!52\)\(q^{67} + \)\(25\!\cdots\!04\)\(q^{68} + \)\(43\!\cdots\!80\)\(q^{69} + \)\(60\!\cdots\!00\)\(q^{70} + \)\(29\!\cdots\!60\)\(q^{71} + \)\(59\!\cdots\!60\)\(q^{72} - \)\(23\!\cdots\!74\)\(q^{73} - \)\(38\!\cdots\!80\)\(q^{74} - \)\(78\!\cdots\!00\)\(q^{75} - \)\(40\!\cdots\!00\)\(q^{76} - \)\(11\!\cdots\!56\)\(q^{77} + \)\(33\!\cdots\!72\)\(q^{78} + \)\(12\!\cdots\!00\)\(q^{79} + \)\(76\!\cdots\!00\)\(q^{80} + \)\(12\!\cdots\!05\)\(q^{81} + \)\(19\!\cdots\!64\)\(q^{82} + \)\(10\!\cdots\!16\)\(q^{83} - \)\(17\!\cdots\!80\)\(q^{84} - \)\(28\!\cdots\!00\)\(q^{85} - \)\(13\!\cdots\!40\)\(q^{86} - \)\(15\!\cdots\!40\)\(q^{87} - \)\(22\!\cdots\!60\)\(q^{88} - \)\(44\!\cdots\!50\)\(q^{89} + \)\(20\!\cdots\!00\)\(q^{90} + \)\(50\!\cdots\!60\)\(q^{91} + \)\(10\!\cdots\!52\)\(q^{92} + \)\(20\!\cdots\!32\)\(q^{93} + \)\(12\!\cdots\!20\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} - \)\(12\!\cdots\!40\)\(q^{96} - \)\(47\!\cdots\!18\)\(q^{97} - \)\(76\!\cdots\!16\)\(q^{98} - \)\(15\!\cdots\!20\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.90767e9 −0.0607885 −0.0303943 0.999538i \(-0.509676\pi\)
−0.0303943 + 0.999538i \(0.509676\pi\)
\(3\) 3.95253e17 1.52037 0.760184 0.649707i \(-0.225109\pi\)
0.760184 + 0.649707i \(0.225109\pi\)
\(4\) −9.40983e21 −0.996305
\(5\) 1.69056e25 0.519548 0.259774 0.965669i \(-0.416352\pi\)
0.259774 + 0.965669i \(0.416352\pi\)
\(6\) −2.33502e27 −0.0924209
\(7\) −2.69951e30 −0.384775 −0.192388 0.981319i \(-0.561623\pi\)
−0.192388 + 0.981319i \(0.561623\pi\)
\(8\) 1.11387e32 0.121352
\(9\) 8.86395e34 1.31152
\(10\) −9.98727e34 −0.0315825
\(11\) −1.46803e38 −1.43187 −0.715933 0.698169i \(-0.753998\pi\)
−0.715933 + 0.698169i \(0.753998\pi\)
\(12\) −3.71926e39 −1.51475
\(13\) −3.34896e40 −0.734476 −0.367238 0.930127i \(-0.619696\pi\)
−0.367238 + 0.930127i \(0.619696\pi\)
\(14\) 1.59478e40 0.0233899
\(15\) 6.68198e42 0.789904
\(16\) 8.82153e43 0.988928
\(17\) −1.35791e45 −1.66528 −0.832639 0.553817i \(-0.813171\pi\)
−0.832639 + 0.553817i \(0.813171\pi\)
\(18\) −5.23653e44 −0.0797254
\(19\) 7.35113e46 1.55542 0.777710 0.628624i \(-0.216381\pi\)
0.777710 + 0.628624i \(0.216381\pi\)
\(20\) −1.59079e47 −0.517628
\(21\) −1.06699e48 −0.585000
\(22\) 8.67264e47 0.0870409
\(23\) 2.07741e49 0.411583 0.205791 0.978596i \(-0.434023\pi\)
0.205791 + 0.978596i \(0.434023\pi\)
\(24\) 4.40258e49 0.184500
\(25\) −7.72992e50 −0.730070
\(26\) 1.97845e50 0.0446477
\(27\) 8.32175e51 0.473628
\(28\) 2.54020e52 0.383353
\(29\) −3.30017e53 −1.38360 −0.691799 0.722091i \(-0.743181\pi\)
−0.691799 + 0.722091i \(0.743181\pi\)
\(30\) −3.94750e52 −0.0480171
\(31\) 1.78429e54 0.655790 0.327895 0.944714i \(-0.393661\pi\)
0.327895 + 0.944714i \(0.393661\pi\)
\(32\) −1.57316e54 −0.181468
\(33\) −5.80243e55 −2.17696
\(34\) 8.02211e54 0.101230
\(35\) −4.56369e55 −0.199909
\(36\) −8.34082e56 −1.30668
\(37\) −3.22112e57 −1.85628 −0.928140 0.372230i \(-0.878593\pi\)
−0.928140 + 0.372230i \(0.878593\pi\)
\(38\) −4.34280e56 −0.0945516
\(39\) −1.32368e58 −1.11667
\(40\) 1.88306e57 0.0630484
\(41\) −6.12341e58 −0.832497 −0.416249 0.909251i \(-0.636655\pi\)
−0.416249 + 0.909251i \(0.636655\pi\)
\(42\) 6.30343e57 0.0355613
\(43\) 2.07892e59 0.496867 0.248434 0.968649i \(-0.420084\pi\)
0.248434 + 0.968649i \(0.420084\pi\)
\(44\) 1.38139e60 1.42657
\(45\) 1.49850e60 0.681398
\(46\) −1.22727e59 −0.0250195
\(47\) 5.09761e58 0.00474018 0.00237009 0.999997i \(-0.499246\pi\)
0.00237009 + 0.999997i \(0.499246\pi\)
\(48\) 3.48673e61 1.50354
\(49\) −4.19344e61 −0.851948
\(50\) 4.56658e60 0.0443799
\(51\) −5.36719e62 −2.53184
\(52\) 3.15131e62 0.731762
\(53\) −1.65493e62 −0.191739 −0.0958697 0.995394i \(-0.530563\pi\)
−0.0958697 + 0.995394i \(0.530563\pi\)
\(54\) −4.91622e61 −0.0287911
\(55\) −2.48179e63 −0.743923
\(56\) −3.00690e62 −0.0466934
\(57\) 2.90555e64 2.36481
\(58\) 1.94963e63 0.0841068
\(59\) 1.57646e64 0.364404 0.182202 0.983261i \(-0.441677\pi\)
0.182202 + 0.983261i \(0.441677\pi\)
\(60\) −6.28764e64 −0.786985
\(61\) 3.70457e64 0.253629 0.126814 0.991926i \(-0.459525\pi\)
0.126814 + 0.991926i \(0.459525\pi\)
\(62\) −1.05410e64 −0.0398645
\(63\) −2.39283e65 −0.504641
\(64\) −8.23876e65 −0.977897
\(65\) −5.66162e65 −0.381595
\(66\) 3.42788e65 0.132334
\(67\) −2.21412e66 −0.493709 −0.246855 0.969053i \(-0.579397\pi\)
−0.246855 + 0.969053i \(0.579397\pi\)
\(68\) 1.27777e67 1.65912
\(69\) 8.21103e66 0.625757
\(70\) 2.69608e65 0.0121522
\(71\) −1.08186e67 −0.290564 −0.145282 0.989390i \(-0.546409\pi\)
−0.145282 + 0.989390i \(0.546409\pi\)
\(72\) 9.87324e66 0.159156
\(73\) 2.15731e67 0.210197 0.105099 0.994462i \(-0.466484\pi\)
0.105099 + 0.994462i \(0.466484\pi\)
\(74\) 1.90293e67 0.112841
\(75\) −3.05527e68 −1.10998
\(76\) −6.91729e68 −1.54967
\(77\) 3.96297e68 0.550946
\(78\) 7.81989e67 0.0678809
\(79\) 1.93510e69 1.05515 0.527575 0.849508i \(-0.323101\pi\)
0.527575 + 0.849508i \(0.323101\pi\)
\(80\) 1.49133e69 0.513795
\(81\) −2.70152e69 −0.591433
\(82\) 3.61751e68 0.0506063
\(83\) 1.17002e70 1.05158 0.525791 0.850614i \(-0.323769\pi\)
0.525791 + 0.850614i \(0.323769\pi\)
\(84\) 1.00402e70 0.582839
\(85\) −2.29564e70 −0.865191
\(86\) −1.22816e69 −0.0302038
\(87\) −1.30440e71 −2.10358
\(88\) −1.63519e70 −0.173760
\(89\) 1.65587e71 1.16490 0.582452 0.812865i \(-0.302093\pi\)
0.582452 + 0.812865i \(0.302093\pi\)
\(90\) −8.85267e69 −0.0414212
\(91\) 9.04056e70 0.282608
\(92\) −1.95481e71 −0.410062
\(93\) 7.05247e71 0.997043
\(94\) −3.01150e68 −0.000288149 0
\(95\) 1.24275e72 0.808115
\(96\) −6.21797e71 −0.275898
\(97\) −9.74539e71 −0.296231 −0.148116 0.988970i \(-0.547321\pi\)
−0.148116 + 0.988970i \(0.547321\pi\)
\(98\) 2.47734e71 0.0517886
\(99\) −1.30125e73 −1.87792
\(100\) 7.27372e72 0.727372
\(101\) −1.40279e73 −0.975582 −0.487791 0.872961i \(-0.662197\pi\)
−0.487791 + 0.872961i \(0.662197\pi\)
\(102\) 3.17076e72 0.153907
\(103\) 4.70385e73 1.59917 0.799586 0.600552i \(-0.205052\pi\)
0.799586 + 0.600552i \(0.205052\pi\)
\(104\) −3.73029e72 −0.0891304
\(105\) −1.80381e73 −0.303936
\(106\) 9.77680e71 0.0116555
\(107\) 1.24306e74 1.05192 0.525962 0.850508i \(-0.323705\pi\)
0.525962 + 0.850508i \(0.323705\pi\)
\(108\) −7.83063e73 −0.471878
\(109\) 2.39112e74 1.02928 0.514641 0.857406i \(-0.327925\pi\)
0.514641 + 0.857406i \(0.327925\pi\)
\(110\) 1.46616e73 0.0452219
\(111\) −1.27316e75 −2.82223
\(112\) −2.38139e74 −0.380515
\(113\) 7.57224e74 0.874704 0.437352 0.899290i \(-0.355916\pi\)
0.437352 + 0.899290i \(0.355916\pi\)
\(114\) −1.71650e74 −0.143753
\(115\) 3.51199e74 0.213837
\(116\) 3.10541e75 1.37848
\(117\) −2.96850e75 −0.963281
\(118\) −9.31319e73 −0.0221516
\(119\) 3.66571e75 0.640758
\(120\) 7.44283e74 0.0958568
\(121\) 1.10396e76 1.05024
\(122\) −2.18854e74 −0.0154177
\(123\) −2.42030e76 −1.26570
\(124\) −1.67899e76 −0.653367
\(125\) −3.09674e76 −0.898854
\(126\) 1.41361e75 0.0306764
\(127\) 3.10832e76 0.505463 0.252732 0.967536i \(-0.418671\pi\)
0.252732 + 0.967536i \(0.418671\pi\)
\(128\) 1.97253e76 0.240913
\(129\) 8.21701e76 0.755421
\(130\) 3.34470e75 0.0231966
\(131\) −2.13454e77 −1.11919 −0.559593 0.828768i \(-0.689042\pi\)
−0.559593 + 0.828768i \(0.689042\pi\)
\(132\) 5.45999e77 2.16892
\(133\) −1.98445e77 −0.598487
\(134\) 1.30803e76 0.0300118
\(135\) 1.40684e77 0.246072
\(136\) −1.51253e77 −0.202085
\(137\) −1.04031e78 −1.06381 −0.531905 0.846804i \(-0.678524\pi\)
−0.531905 + 0.846804i \(0.678524\pi\)
\(138\) −4.85081e76 −0.0380388
\(139\) −1.48817e78 −0.896626 −0.448313 0.893877i \(-0.647975\pi\)
−0.448313 + 0.893877i \(0.647975\pi\)
\(140\) 4.29436e77 0.199170
\(141\) 2.01484e76 0.00720682
\(142\) 6.39128e76 0.0176630
\(143\) 4.91637e78 1.05167
\(144\) 7.81936e78 1.29700
\(145\) −5.57914e78 −0.718845
\(146\) −1.27447e77 −0.0127776
\(147\) −1.65747e79 −1.29528
\(148\) 3.03102e79 1.84942
\(149\) −8.64312e78 −0.412450 −0.206225 0.978505i \(-0.566118\pi\)
−0.206225 + 0.978505i \(0.566118\pi\)
\(150\) 1.80495e78 0.0674738
\(151\) −2.28898e79 −0.671403 −0.335701 0.941968i \(-0.608973\pi\)
−0.335701 + 0.941968i \(0.608973\pi\)
\(152\) 8.18817e78 0.188754
\(153\) −1.20365e80 −2.18405
\(154\) −2.34119e78 −0.0334912
\(155\) 3.01646e79 0.340714
\(156\) 1.24557e80 1.11255
\(157\) 1.93279e80 1.36725 0.683623 0.729835i \(-0.260403\pi\)
0.683623 + 0.729835i \(0.260403\pi\)
\(158\) −1.14319e79 −0.0641410
\(159\) −6.54117e79 −0.291515
\(160\) −2.65953e79 −0.0942812
\(161\) −5.60801e79 −0.158367
\(162\) 1.59597e79 0.0359523
\(163\) −9.29339e78 −0.0167235 −0.00836174 0.999965i \(-0.502662\pi\)
−0.00836174 + 0.999965i \(0.502662\pi\)
\(164\) 5.76203e80 0.829421
\(165\) −9.80936e80 −1.13104
\(166\) −6.91210e79 −0.0639241
\(167\) −1.36355e81 −1.01279 −0.506397 0.862300i \(-0.669023\pi\)
−0.506397 + 0.862300i \(0.669023\pi\)
\(168\) −1.18848e80 −0.0709912
\(169\) −9.57497e80 −0.460546
\(170\) 1.35619e80 0.0525937
\(171\) 6.51600e81 2.03997
\(172\) −1.95623e81 −0.495031
\(173\) 4.09283e81 0.838188 0.419094 0.907943i \(-0.362348\pi\)
0.419094 + 0.907943i \(0.362348\pi\)
\(174\) 7.70597e80 0.127873
\(175\) 2.08670e81 0.280913
\(176\) −1.29503e82 −1.41601
\(177\) 6.23099e81 0.554029
\(178\) −9.78231e80 −0.0708127
\(179\) 6.62628e81 0.390962 0.195481 0.980708i \(-0.437373\pi\)
0.195481 + 0.980708i \(0.437373\pi\)
\(180\) −1.41007e82 −0.678880
\(181\) −2.47756e82 −0.974442 −0.487221 0.873279i \(-0.661989\pi\)
−0.487221 + 0.873279i \(0.661989\pi\)
\(182\) −5.34087e80 −0.0171793
\(183\) 1.46424e82 0.385609
\(184\) 2.31396e81 0.0499465
\(185\) −5.44549e82 −0.964427
\(186\) −4.16637e81 −0.0606087
\(187\) 1.99346e83 2.38445
\(188\) −4.79677e80 −0.00472267
\(189\) −2.24647e82 −0.182240
\(190\) −7.34177e81 −0.0491241
\(191\) 3.23309e83 1.78608 0.893038 0.449981i \(-0.148569\pi\)
0.893038 + 0.449981i \(0.148569\pi\)
\(192\) −3.25639e83 −1.48676
\(193\) −3.80588e83 −1.43752 −0.718759 0.695259i \(-0.755290\pi\)
−0.718759 + 0.695259i \(0.755290\pi\)
\(194\) 5.75725e81 0.0180075
\(195\) −2.23777e83 −0.580166
\(196\) 3.94595e83 0.848800
\(197\) −5.12328e80 −0.000915232 0 −0.000457616 1.00000i \(-0.500146\pi\)
−0.000457616 1.00000i \(0.500146\pi\)
\(198\) 7.68738e82 0.114156
\(199\) −2.77399e83 −0.342742 −0.171371 0.985207i \(-0.554820\pi\)
−0.171371 + 0.985207i \(0.554820\pi\)
\(200\) −8.61009e82 −0.0885957
\(201\) −8.75138e83 −0.750620
\(202\) 8.28724e82 0.0593042
\(203\) 8.90886e83 0.532374
\(204\) 5.05044e84 2.52248
\(205\) −1.03520e84 −0.432522
\(206\) −2.77888e83 −0.0972113
\(207\) 1.84141e84 0.539799
\(208\) −2.95429e84 −0.726343
\(209\) −1.07917e85 −2.22715
\(210\) 1.06563e83 0.0184758
\(211\) 4.96555e84 0.723865 0.361932 0.932204i \(-0.382117\pi\)
0.361932 + 0.932204i \(0.382117\pi\)
\(212\) 1.55726e84 0.191031
\(213\) −4.27609e84 −0.441765
\(214\) −7.34359e83 −0.0639449
\(215\) 3.51455e84 0.258146
\(216\) 9.26931e83 0.0574759
\(217\) −4.81673e84 −0.252332
\(218\) −1.41259e84 −0.0625685
\(219\) 8.52681e84 0.319578
\(220\) 2.33533e85 0.741174
\(221\) 4.54760e85 1.22311
\(222\) 7.52138e84 0.171559
\(223\) −4.40493e85 −0.852730 −0.426365 0.904551i \(-0.640206\pi\)
−0.426365 + 0.904551i \(0.640206\pi\)
\(224\) 4.24678e84 0.0698243
\(225\) −6.85176e85 −0.957503
\(226\) −4.47343e84 −0.0531720
\(227\) 2.14705e85 0.217220 0.108610 0.994084i \(-0.465360\pi\)
0.108610 + 0.994084i \(0.465360\pi\)
\(228\) −2.73408e86 −2.35607
\(229\) 1.57271e86 1.15519 0.577595 0.816323i \(-0.303991\pi\)
0.577595 + 0.816323i \(0.303991\pi\)
\(230\) −2.07477e84 −0.0129988
\(231\) 1.56637e86 0.837642
\(232\) −3.67595e85 −0.167903
\(233\) 7.07062e85 0.276036 0.138018 0.990430i \(-0.455927\pi\)
0.138018 + 0.990430i \(0.455927\pi\)
\(234\) 1.75369e85 0.0585564
\(235\) 8.61782e83 0.00246275
\(236\) −1.48342e86 −0.363058
\(237\) 7.64853e86 1.60422
\(238\) −2.16558e85 −0.0389507
\(239\) −7.62711e86 −1.17716 −0.588582 0.808438i \(-0.700313\pi\)
−0.588582 + 0.808438i \(0.700313\pi\)
\(240\) 5.89453e86 0.781159
\(241\) 3.73671e86 0.425468 0.212734 0.977110i \(-0.431763\pi\)
0.212734 + 0.977110i \(0.431763\pi\)
\(242\) −6.52184e85 −0.0638424
\(243\) −1.63021e87 −1.37282
\(244\) −3.48594e86 −0.252692
\(245\) −7.08926e86 −0.442628
\(246\) 1.42983e86 0.0769402
\(247\) −2.46186e87 −1.14242
\(248\) 1.98746e86 0.0795817
\(249\) 4.62454e87 1.59879
\(250\) 1.82945e86 0.0546400
\(251\) 4.47993e87 1.15659 0.578296 0.815827i \(-0.303718\pi\)
0.578296 + 0.815827i \(0.303718\pi\)
\(252\) 2.25162e87 0.502776
\(253\) −3.04971e87 −0.589331
\(254\) −1.83629e86 −0.0307264
\(255\) −9.07356e87 −1.31541
\(256\) 7.66476e87 0.963252
\(257\) −6.05754e86 −0.0660294 −0.0330147 0.999455i \(-0.510511\pi\)
−0.0330147 + 0.999455i \(0.510511\pi\)
\(258\) −4.85434e86 −0.0459209
\(259\) 8.69545e87 0.714251
\(260\) 5.32749e87 0.380185
\(261\) −2.92525e88 −1.81462
\(262\) 1.26102e87 0.0680336
\(263\) −2.40877e88 −1.13086 −0.565432 0.824795i \(-0.691290\pi\)
−0.565432 + 0.824795i \(0.691290\pi\)
\(264\) −6.46313e87 −0.264180
\(265\) −2.79776e87 −0.0996178
\(266\) 1.17235e87 0.0363811
\(267\) 6.54485e88 1.77108
\(268\) 2.08345e88 0.491885
\(269\) 4.13585e88 0.852328 0.426164 0.904646i \(-0.359865\pi\)
0.426164 + 0.904646i \(0.359865\pi\)
\(270\) −8.31116e86 −0.0149584
\(271\) 3.37612e87 0.0530932 0.0265466 0.999648i \(-0.491549\pi\)
0.0265466 + 0.999648i \(0.491549\pi\)
\(272\) −1.19789e89 −1.64684
\(273\) 3.57331e88 0.429669
\(274\) 6.14583e87 0.0646674
\(275\) 1.13478e89 1.04536
\(276\) −7.72644e88 −0.623445
\(277\) −1.55810e89 −1.10175 −0.550875 0.834588i \(-0.685706\pi\)
−0.550875 + 0.834588i \(0.685706\pi\)
\(278\) 8.79160e87 0.0545046
\(279\) 1.58159e89 0.860083
\(280\) −5.08334e87 −0.0242595
\(281\) −4.48983e89 −1.88126 −0.940630 0.339432i \(-0.889765\pi\)
−0.940630 + 0.339432i \(0.889765\pi\)
\(282\) −1.19030e86 −0.000438092 0
\(283\) −3.25365e88 −0.105236 −0.0526182 0.998615i \(-0.516757\pi\)
−0.0526182 + 0.998615i \(0.516757\pi\)
\(284\) 1.01801e89 0.289490
\(285\) 4.91201e89 1.22863
\(286\) −2.90443e88 −0.0639295
\(287\) 1.65302e89 0.320324
\(288\) −1.39444e89 −0.237999
\(289\) 1.17901e90 1.77315
\(290\) 3.29597e88 0.0436975
\(291\) −3.85189e89 −0.450381
\(292\) −2.02999e89 −0.209421
\(293\) −1.51494e90 −1.37952 −0.689760 0.724038i \(-0.742284\pi\)
−0.689760 + 0.724038i \(0.742284\pi\)
\(294\) 9.79177e88 0.0787378
\(295\) 2.66509e89 0.189325
\(296\) −3.58789e89 −0.225264
\(297\) −1.22166e90 −0.678171
\(298\) 5.10607e88 0.0250722
\(299\) −6.95717e89 −0.302297
\(300\) 2.87496e90 1.10587
\(301\) −5.61209e89 −0.191182
\(302\) 1.35225e89 0.0408136
\(303\) −5.54458e90 −1.48324
\(304\) 6.48482e90 1.53820
\(305\) 6.26280e89 0.131772
\(306\) 7.11075e89 0.132765
\(307\) 1.83701e90 0.304482 0.152241 0.988343i \(-0.451351\pi\)
0.152241 + 0.988343i \(0.451351\pi\)
\(308\) −3.72909e90 −0.548910
\(309\) 1.85921e91 2.43133
\(310\) −1.78202e89 −0.0207115
\(311\) −1.36709e91 −1.41268 −0.706339 0.707874i \(-0.749655\pi\)
−0.706339 + 0.707874i \(0.749655\pi\)
\(312\) −1.47441e90 −0.135511
\(313\) −1.01164e91 −0.827292 −0.413646 0.910438i \(-0.635745\pi\)
−0.413646 + 0.910438i \(0.635745\pi\)
\(314\) −1.14183e90 −0.0831128
\(315\) −4.04523e90 −0.262185
\(316\) −1.82090e91 −1.05125
\(317\) −8.49508e90 −0.437023 −0.218512 0.975834i \(-0.570120\pi\)
−0.218512 + 0.975834i \(0.570120\pi\)
\(318\) 3.86431e89 0.0177207
\(319\) 4.84475e91 1.98112
\(320\) −1.39281e91 −0.508064
\(321\) 4.91323e91 1.59931
\(322\) 3.31303e89 0.00962688
\(323\) −9.98220e91 −2.59020
\(324\) 2.54209e91 0.589247
\(325\) 2.58872e91 0.536219
\(326\) 5.49023e88 0.00101659
\(327\) 9.45096e91 1.56489
\(328\) −6.82066e90 −0.101026
\(329\) −1.37611e89 −0.00182390
\(330\) 5.79505e90 0.0687540
\(331\) 1.05949e92 1.12558 0.562790 0.826600i \(-0.309728\pi\)
0.562790 + 0.826600i \(0.309728\pi\)
\(332\) −1.10097e92 −1.04770
\(333\) −2.85518e92 −2.43455
\(334\) 8.05543e90 0.0615662
\(335\) −3.74311e91 −0.256506
\(336\) −9.41249e91 −0.578523
\(337\) 7.23797e91 0.399140 0.199570 0.979884i \(-0.436045\pi\)
0.199570 + 0.979884i \(0.436045\pi\)
\(338\) 5.65658e90 0.0279959
\(339\) 2.99295e92 1.32987
\(340\) 2.16015e92 0.861994
\(341\) −2.61940e92 −0.939003
\(342\) −3.84944e91 −0.124006
\(343\) 2.46077e92 0.712584
\(344\) 2.31564e91 0.0602960
\(345\) 1.38812e92 0.325111
\(346\) −2.41791e91 −0.0509522
\(347\) −6.97644e92 −1.32315 −0.661574 0.749880i \(-0.730111\pi\)
−0.661574 + 0.749880i \(0.730111\pi\)
\(348\) 1.22742e93 2.09580
\(349\) −3.78993e92 −0.582778 −0.291389 0.956605i \(-0.594117\pi\)
−0.291389 + 0.956605i \(0.594117\pi\)
\(350\) −1.23275e91 −0.0170763
\(351\) −2.78692e92 −0.347868
\(352\) 2.30945e92 0.259837
\(353\) −1.10203e93 −1.11794 −0.558970 0.829188i \(-0.688803\pi\)
−0.558970 + 0.829188i \(0.688803\pi\)
\(354\) −3.68106e91 −0.0336786
\(355\) −1.82895e92 −0.150962
\(356\) −1.55814e93 −1.16060
\(357\) 1.44888e93 0.974188
\(358\) −3.91459e91 −0.0237660
\(359\) −1.96885e93 −1.07961 −0.539804 0.841791i \(-0.681502\pi\)
−0.539804 + 0.841791i \(0.681502\pi\)
\(360\) 1.66913e92 0.0826893
\(361\) 3.17027e93 1.41933
\(362\) 1.46366e92 0.0592349
\(363\) 4.36344e93 1.59675
\(364\) −8.50702e92 −0.281564
\(365\) 3.64706e92 0.109208
\(366\) −8.65025e91 −0.0234406
\(367\) −1.57037e93 −0.385205 −0.192603 0.981277i \(-0.561693\pi\)
−0.192603 + 0.981277i \(0.561693\pi\)
\(368\) 1.83260e93 0.407025
\(369\) −5.42776e93 −1.09184
\(370\) 3.21702e92 0.0586261
\(371\) 4.46752e92 0.0737766
\(372\) −6.63626e93 −0.993358
\(373\) 9.09346e93 1.23412 0.617059 0.786917i \(-0.288324\pi\)
0.617059 + 0.786917i \(0.288324\pi\)
\(374\) −1.17767e93 −0.144947
\(375\) −1.22399e94 −1.36659
\(376\) 5.67805e90 0.000575232 0
\(377\) 1.10521e94 1.01622
\(378\) 1.32714e92 0.0110781
\(379\) −1.61012e94 −1.22047 −0.610235 0.792220i \(-0.708925\pi\)
−0.610235 + 0.792220i \(0.708925\pi\)
\(380\) −1.16941e94 −0.805129
\(381\) 1.22857e94 0.768491
\(382\) −1.91000e93 −0.108573
\(383\) 3.65366e94 1.88787 0.943937 0.330125i \(-0.107091\pi\)
0.943937 + 0.330125i \(0.107091\pi\)
\(384\) 7.79648e93 0.366276
\(385\) 6.69964e93 0.286243
\(386\) 2.24839e93 0.0873846
\(387\) 1.84275e94 0.651652
\(388\) 9.17025e93 0.295137
\(389\) −5.06109e94 −1.48280 −0.741402 0.671061i \(-0.765839\pi\)
−0.741402 + 0.671061i \(0.765839\pi\)
\(390\) 1.32200e93 0.0352674
\(391\) −2.82095e94 −0.685399
\(392\) −4.67092e93 −0.103386
\(393\) −8.43683e94 −1.70157
\(394\) 3.02667e90 5.56356e−5 0
\(395\) 3.27140e94 0.548201
\(396\) 1.22446e95 1.87098
\(397\) −2.77522e94 −0.386762 −0.193381 0.981124i \(-0.561945\pi\)
−0.193381 + 0.981124i \(0.561945\pi\)
\(398\) 1.63878e93 0.0208348
\(399\) −7.84358e94 −0.909921
\(400\) −6.81897e94 −0.721987
\(401\) 6.35711e94 0.614455 0.307228 0.951636i \(-0.400599\pi\)
0.307228 + 0.951636i \(0.400599\pi\)
\(402\) 5.17002e93 0.0456291
\(403\) −5.97553e94 −0.481662
\(404\) 1.32001e95 0.971977
\(405\) −4.56709e94 −0.307278
\(406\) −5.26306e93 −0.0323622
\(407\) 4.72870e95 2.65794
\(408\) −5.97833e94 −0.307244
\(409\) 1.42308e95 0.668851 0.334426 0.942422i \(-0.391458\pi\)
0.334426 + 0.942422i \(0.391458\pi\)
\(410\) 6.11562e93 0.0262924
\(411\) −4.11187e95 −1.61738
\(412\) −4.42625e95 −1.59326
\(413\) −4.25567e94 −0.140214
\(414\) −1.08784e94 −0.0328136
\(415\) 1.97799e95 0.546347
\(416\) 5.26846e94 0.133284
\(417\) −5.88202e95 −1.36320
\(418\) 6.37537e94 0.135385
\(419\) 3.45923e95 0.673237 0.336618 0.941641i \(-0.390717\pi\)
0.336618 + 0.941641i \(0.390717\pi\)
\(420\) 1.69736e95 0.302813
\(421\) −3.52446e94 −0.0576495 −0.0288248 0.999584i \(-0.509176\pi\)
−0.0288248 + 0.999584i \(0.509176\pi\)
\(422\) −2.93348e94 −0.0440026
\(423\) 4.51850e93 0.00621685
\(424\) −1.84337e94 −0.0232680
\(425\) 1.04966e96 1.21577
\(426\) 2.52617e94 0.0268542
\(427\) −1.00005e95 −0.0975901
\(428\) −1.16970e96 −1.04804
\(429\) 1.94321e96 1.59893
\(430\) −2.07628e94 −0.0156923
\(431\) −7.25552e95 −0.503788 −0.251894 0.967755i \(-0.581053\pi\)
−0.251894 + 0.967755i \(0.581053\pi\)
\(432\) 7.34106e95 0.468384
\(433\) 1.48595e95 0.0871354 0.0435677 0.999050i \(-0.486128\pi\)
0.0435677 + 0.999050i \(0.486128\pi\)
\(434\) 2.84556e94 0.0153389
\(435\) −2.20517e96 −1.09291
\(436\) −2.25000e96 −1.02548
\(437\) 1.52713e96 0.640183
\(438\) −5.03736e94 −0.0194266
\(439\) −1.75652e96 −0.623302 −0.311651 0.950197i \(-0.600882\pi\)
−0.311651 + 0.950197i \(0.600882\pi\)
\(440\) −2.76439e95 −0.0902768
\(441\) −3.71704e96 −1.11735
\(442\) −2.68657e95 −0.0743508
\(443\) −7.67761e95 −0.195654 −0.0978272 0.995203i \(-0.531189\pi\)
−0.0978272 + 0.995203i \(0.531189\pi\)
\(444\) 1.19802e97 2.81180
\(445\) 2.79934e96 0.605223
\(446\) 2.60229e95 0.0518362
\(447\) −3.41621e96 −0.627077
\(448\) 2.22407e96 0.376270
\(449\) −2.38413e96 −0.371826 −0.185913 0.982566i \(-0.559524\pi\)
−0.185913 + 0.982566i \(0.559524\pi\)
\(450\) 4.04779e95 0.0582052
\(451\) 8.98936e96 1.19202
\(452\) −7.12535e96 −0.871472
\(453\) −9.04725e96 −1.02078
\(454\) −1.26841e95 −0.0132045
\(455\) 1.52836e96 0.146828
\(456\) 3.23640e96 0.286975
\(457\) 1.08572e97 0.888744 0.444372 0.895842i \(-0.353427\pi\)
0.444372 + 0.895842i \(0.353427\pi\)
\(458\) −9.29105e95 −0.0702223
\(459\) −1.13002e97 −0.788722
\(460\) −3.30473e96 −0.213047
\(461\) −2.25885e97 −1.34525 −0.672625 0.739984i \(-0.734833\pi\)
−0.672625 + 0.739984i \(0.734833\pi\)
\(462\) −9.25362e95 −0.0509190
\(463\) 1.05828e97 0.538137 0.269068 0.963121i \(-0.413284\pi\)
0.269068 + 0.963121i \(0.413284\pi\)
\(464\) −2.91126e97 −1.36828
\(465\) 1.19226e97 0.518011
\(466\) −4.17709e95 −0.0167798
\(467\) 2.18220e97 0.810642 0.405321 0.914174i \(-0.367160\pi\)
0.405321 + 0.914174i \(0.367160\pi\)
\(468\) 2.79331e97 0.959721
\(469\) 5.97705e96 0.189967
\(470\) −5.09112e93 −0.000149707 0
\(471\) 7.63939e97 2.07872
\(472\) 1.75596e96 0.0442213
\(473\) −3.05193e97 −0.711447
\(474\) −4.51850e96 −0.0975180
\(475\) −5.68236e97 −1.13557
\(476\) −3.44937e97 −0.638390
\(477\) −1.46692e97 −0.251470
\(478\) 4.50585e96 0.0715580
\(479\) −1.96022e97 −0.288442 −0.144221 0.989546i \(-0.546068\pi\)
−0.144221 + 0.989546i \(0.546068\pi\)
\(480\) −1.05119e97 −0.143342
\(481\) 1.07874e98 1.36339
\(482\) −2.20753e96 −0.0258636
\(483\) −2.21658e97 −0.240776
\(484\) −1.03881e98 −1.04636
\(485\) −1.64752e97 −0.153906
\(486\) 9.63075e96 0.0834519
\(487\) −4.70183e97 −0.377972 −0.188986 0.981980i \(-0.560520\pi\)
−0.188986 + 0.981980i \(0.560520\pi\)
\(488\) 4.12639e96 0.0307785
\(489\) −3.67324e96 −0.0254258
\(490\) 4.18810e96 0.0269067
\(491\) −8.71377e97 −0.519675 −0.259838 0.965652i \(-0.583669\pi\)
−0.259838 + 0.965652i \(0.583669\pi\)
\(492\) 2.27746e98 1.26103
\(493\) 4.48135e98 2.30407
\(494\) 1.45439e97 0.0694459
\(495\) −2.19985e98 −0.975670
\(496\) 1.57402e98 0.648529
\(497\) 2.92050e97 0.111802
\(498\) −2.73203e97 −0.0971882
\(499\) −4.82312e98 −1.59462 −0.797312 0.603567i \(-0.793745\pi\)
−0.797312 + 0.603567i \(0.793745\pi\)
\(500\) 2.91398e98 0.895533
\(501\) −5.38948e98 −1.53982
\(502\) −2.64659e97 −0.0703075
\(503\) 2.59870e98 0.641985 0.320992 0.947082i \(-0.395984\pi\)
0.320992 + 0.947082i \(0.395984\pi\)
\(504\) −2.66530e97 −0.0612394
\(505\) −2.37151e98 −0.506861
\(506\) 1.80167e97 0.0358245
\(507\) −3.78453e98 −0.700199
\(508\) −2.92488e98 −0.503596
\(509\) 7.47042e98 1.19714 0.598572 0.801069i \(-0.295735\pi\)
0.598572 + 0.801069i \(0.295735\pi\)
\(510\) 5.36036e97 0.0799618
\(511\) −5.82368e97 −0.0808788
\(512\) −2.31581e98 −0.299467
\(513\) 6.11742e98 0.736690
\(514\) 3.57859e96 0.00401383
\(515\) 7.95215e98 0.830846
\(516\) −7.73206e98 −0.752630
\(517\) −7.48345e96 −0.00678730
\(518\) −5.13699e97 −0.0434182
\(519\) 1.61770e99 1.27435
\(520\) −6.30628e97 −0.0463075
\(521\) 2.02966e98 0.138946 0.0694729 0.997584i \(-0.477868\pi\)
0.0694729 + 0.997584i \(0.477868\pi\)
\(522\) 1.72814e98 0.110308
\(523\) −2.22396e99 −1.32378 −0.661890 0.749601i \(-0.730245\pi\)
−0.661890 + 0.749601i \(0.730245\pi\)
\(524\) 2.00857e99 1.11505
\(525\) 8.24775e98 0.427091
\(526\) 1.42302e98 0.0687435
\(527\) −2.42292e99 −1.09207
\(528\) −5.11863e99 −2.15286
\(529\) −2.11604e99 −0.830600
\(530\) 1.65283e97 0.00605561
\(531\) 1.39736e99 0.477924
\(532\) 1.86733e99 0.596275
\(533\) 2.05071e99 0.611449
\(534\) −3.86648e98 −0.107661
\(535\) 2.10147e99 0.546525
\(536\) −2.46623e98 −0.0599128
\(537\) 2.61906e99 0.594406
\(538\) −2.44333e98 −0.0518117
\(539\) 6.15609e99 1.21987
\(540\) −1.32381e99 −0.245163
\(541\) −1.61237e99 −0.279102 −0.139551 0.990215i \(-0.544566\pi\)
−0.139551 + 0.990215i \(0.544566\pi\)
\(542\) −1.99450e97 −0.00322746
\(543\) −9.79262e99 −1.48151
\(544\) 2.13622e99 0.302194
\(545\) 4.04233e99 0.534761
\(546\) −2.11099e98 −0.0261189
\(547\) 1.79750e99 0.208033 0.104016 0.994576i \(-0.466831\pi\)
0.104016 + 0.994576i \(0.466831\pi\)
\(548\) 9.78918e99 1.05988
\(549\) 3.28371e99 0.332640
\(550\) −6.70388e98 −0.0635460
\(551\) −2.42600e100 −2.15207
\(552\) 9.14599e98 0.0759371
\(553\) −5.22383e99 −0.405996
\(554\) 9.20473e98 0.0669738
\(555\) −2.15235e100 −1.46628
\(556\) 1.40034e100 0.893313
\(557\) −8.70004e99 −0.519764 −0.259882 0.965640i \(-0.583684\pi\)
−0.259882 + 0.965640i \(0.583684\pi\)
\(558\) −9.34351e98 −0.0522831
\(559\) −6.96223e99 −0.364937
\(560\) −4.02588e99 −0.197696
\(561\) 7.87920e100 3.62525
\(562\) 2.65244e99 0.114359
\(563\) −1.34453e100 −0.543267 −0.271634 0.962401i \(-0.587564\pi\)
−0.271634 + 0.962401i \(0.587564\pi\)
\(564\) −1.89593e98 −0.00718019
\(565\) 1.28013e100 0.454451
\(566\) 1.92215e98 0.00639717
\(567\) 7.29280e99 0.227569
\(568\) −1.20505e99 −0.0352606
\(569\) −4.71804e100 −1.29468 −0.647342 0.762200i \(-0.724119\pi\)
−0.647342 + 0.762200i \(0.724119\pi\)
\(570\) −2.90185e99 −0.0746867
\(571\) −2.57174e100 −0.620882 −0.310441 0.950593i \(-0.600477\pi\)
−0.310441 + 0.950593i \(0.600477\pi\)
\(572\) −4.62623e100 −1.04778
\(573\) 1.27789e101 2.71549
\(574\) −9.76552e98 −0.0194720
\(575\) −1.60582e100 −0.300484
\(576\) −7.30280e100 −1.28253
\(577\) 5.80535e100 0.956998 0.478499 0.878088i \(-0.341181\pi\)
0.478499 + 0.878088i \(0.341181\pi\)
\(578\) −6.96519e99 −0.107787
\(579\) −1.50428e101 −2.18556
\(580\) 5.24988e100 0.716189
\(581\) −3.15849e100 −0.404623
\(582\) 2.27557e99 0.0273780
\(583\) 2.42949e100 0.274545
\(584\) 2.40295e99 0.0255080
\(585\) −5.01843e100 −0.500470
\(586\) 8.94978e99 0.0838589
\(587\) 1.38113e101 1.21603 0.608013 0.793927i \(-0.291967\pi\)
0.608013 + 0.793927i \(0.291967\pi\)
\(588\) 1.55965e101 1.29049
\(589\) 1.31166e101 1.02003
\(590\) −1.57445e99 −0.0115088
\(591\) −2.02499e98 −0.00139149
\(592\) −2.84152e101 −1.83573
\(593\) 9.03719e100 0.548956 0.274478 0.961593i \(-0.411495\pi\)
0.274478 + 0.961593i \(0.411495\pi\)
\(594\) 7.21716e99 0.0412250
\(595\) 6.19710e100 0.332904
\(596\) 8.13303e100 0.410926
\(597\) −1.09643e101 −0.521095
\(598\) 4.11007e99 0.0183762
\(599\) −4.41983e101 −1.85920 −0.929601 0.368568i \(-0.879848\pi\)
−0.929601 + 0.368568i \(0.879848\pi\)
\(600\) −3.40316e100 −0.134698
\(601\) 5.61076e100 0.208980 0.104490 0.994526i \(-0.466679\pi\)
0.104490 + 0.994526i \(0.466679\pi\)
\(602\) 3.31544e99 0.0116217
\(603\) −1.96259e101 −0.647510
\(604\) 2.15389e101 0.668922
\(605\) 1.86631e101 0.545649
\(606\) 3.27555e100 0.0901642
\(607\) −3.42040e101 −0.886524 −0.443262 0.896392i \(-0.646179\pi\)
−0.443262 + 0.896392i \(0.646179\pi\)
\(608\) −1.15645e101 −0.282259
\(609\) 3.52125e101 0.809405
\(610\) −3.69985e99 −0.00801024
\(611\) −1.70717e99 −0.00348155
\(612\) 1.13261e102 2.17598
\(613\) −1.01689e102 −1.84062 −0.920312 0.391185i \(-0.872065\pi\)
−0.920312 + 0.391185i \(0.872065\pi\)
\(614\) −1.08525e100 −0.0185090
\(615\) −4.09165e101 −0.657593
\(616\) 4.41422e100 0.0668586
\(617\) 1.26801e102 1.81015 0.905077 0.425247i \(-0.139813\pi\)
0.905077 + 0.425247i \(0.139813\pi\)
\(618\) −1.09836e101 −0.147797
\(619\) 8.97168e101 1.13806 0.569030 0.822317i \(-0.307319\pi\)
0.569030 + 0.822317i \(0.307319\pi\)
\(620\) −2.83844e101 −0.339455
\(621\) 1.72877e101 0.194937
\(622\) 8.07632e100 0.0858746
\(623\) −4.47003e101 −0.448226
\(624\) −1.16769e102 −1.10431
\(625\) 2.94914e101 0.263072
\(626\) 5.97645e100 0.0502898
\(627\) −4.26544e102 −3.38609
\(628\) −1.81872e102 −1.36219
\(629\) 4.37400e102 3.09122
\(630\) 2.38979e100 0.0159378
\(631\) −1.05597e102 −0.664629 −0.332314 0.943169i \(-0.607829\pi\)
−0.332314 + 0.943169i \(0.607829\pi\)
\(632\) 2.15544e101 0.128045
\(633\) 1.96265e102 1.10054
\(634\) 5.01862e100 0.0265660
\(635\) 5.25480e101 0.262612
\(636\) 6.15513e101 0.290437
\(637\) 1.40436e102 0.625735
\(638\) −2.86212e101 −0.120430
\(639\) −9.58956e101 −0.381081
\(640\) 3.33468e101 0.125166
\(641\) −1.64809e102 −0.584336 −0.292168 0.956367i \(-0.594377\pi\)
−0.292168 + 0.956367i \(0.594377\pi\)
\(642\) −2.90258e101 −0.0972198
\(643\) 1.19000e102 0.376570 0.188285 0.982114i \(-0.439707\pi\)
0.188285 + 0.982114i \(0.439707\pi\)
\(644\) 5.27704e101 0.157782
\(645\) 1.38913e102 0.392477
\(646\) 5.89715e101 0.157455
\(647\) 3.27438e102 0.826273 0.413136 0.910669i \(-0.364433\pi\)
0.413136 + 0.910669i \(0.364433\pi\)
\(648\) −3.00913e101 −0.0717717
\(649\) −2.31429e102 −0.521778
\(650\) −1.52933e101 −0.0325959
\(651\) −1.90382e102 −0.383637
\(652\) 8.74492e100 0.0166617
\(653\) −7.85065e102 −1.41441 −0.707204 0.707010i \(-0.750044\pi\)
−0.707204 + 0.707010i \(0.750044\pi\)
\(654\) −5.58332e101 −0.0951272
\(655\) −3.60857e102 −0.581470
\(656\) −5.40179e102 −0.823280
\(657\) 1.91222e102 0.275679
\(658\) 8.12959e98 0.000110872 0
\(659\) −2.63756e102 −0.340318 −0.170159 0.985417i \(-0.554428\pi\)
−0.170159 + 0.985417i \(0.554428\pi\)
\(660\) 9.23044e102 1.12686
\(661\) 4.82101e102 0.556910 0.278455 0.960449i \(-0.410178\pi\)
0.278455 + 0.960449i \(0.410178\pi\)
\(662\) −6.25914e101 −0.0684224
\(663\) 1.79745e103 1.85957
\(664\) 1.30325e102 0.127612
\(665\) −3.35483e102 −0.310943
\(666\) 1.68675e102 0.147993
\(667\) −6.85582e102 −0.569464
\(668\) 1.28308e103 1.00905
\(669\) −1.74106e103 −1.29646
\(670\) 2.21130e101 0.0155926
\(671\) −5.43842e102 −0.363162
\(672\) 1.67855e102 0.106159
\(673\) 1.51214e103 0.905822 0.452911 0.891556i \(-0.350386\pi\)
0.452911 + 0.891556i \(0.350386\pi\)
\(674\) −4.27595e101 −0.0242631
\(675\) −6.43264e102 −0.345782
\(676\) 9.00988e102 0.458844
\(677\) −2.33256e103 −1.12550 −0.562751 0.826626i \(-0.690257\pi\)
−0.562751 + 0.826626i \(0.690257\pi\)
\(678\) −1.76814e102 −0.0808410
\(679\) 2.63078e102 0.113982
\(680\) −2.55703e102 −0.104993
\(681\) 8.48628e102 0.330254
\(682\) 1.54745e102 0.0570806
\(683\) −1.30508e103 −0.456334 −0.228167 0.973622i \(-0.573273\pi\)
−0.228167 + 0.973622i \(0.573273\pi\)
\(684\) −6.13145e103 −2.03243
\(685\) −1.75871e103 −0.552700
\(686\) −1.45374e102 −0.0433169
\(687\) 6.21618e103 1.75632
\(688\) 1.83393e103 0.491366
\(689\) 5.54230e102 0.140828
\(690\) −8.20058e101 −0.0197630
\(691\) 6.78656e103 1.55132 0.775660 0.631151i \(-0.217417\pi\)
0.775660 + 0.631151i \(0.217417\pi\)
\(692\) −3.85129e103 −0.835090
\(693\) 3.51275e103 0.722578
\(694\) 4.12145e102 0.0804321
\(695\) −2.51584e103 −0.465840
\(696\) −1.45293e103 −0.255274
\(697\) 8.31507e103 1.38634
\(698\) 2.23897e102 0.0354262
\(699\) 2.79468e103 0.419677
\(700\) −1.96355e103 −0.279875
\(701\) −7.61065e103 −1.02971 −0.514854 0.857278i \(-0.672154\pi\)
−0.514854 + 0.857278i \(0.672154\pi\)
\(702\) 1.64642e102 0.0211464
\(703\) −2.36788e104 −2.88730
\(704\) 1.20948e104 1.40022
\(705\) 3.40622e101 0.00374429
\(706\) 6.51045e102 0.0679579
\(707\) 3.78686e103 0.375380
\(708\) −5.86325e103 −0.551982
\(709\) −1.25155e104 −1.11908 −0.559538 0.828805i \(-0.689021\pi\)
−0.559538 + 0.828805i \(0.689021\pi\)
\(710\) 1.08048e102 0.00917675
\(711\) 1.71526e104 1.38385
\(712\) 1.84441e103 0.141364
\(713\) 3.70672e103 0.269912
\(714\) −8.55951e102 −0.0592194
\(715\) 8.31143e103 0.546393
\(716\) −6.23522e103 −0.389517
\(717\) −3.01464e104 −1.78972
\(718\) 1.16313e103 0.0656277
\(719\) 2.65219e104 1.42233 0.711164 0.703026i \(-0.248168\pi\)
0.711164 + 0.703026i \(0.248168\pi\)
\(720\) 1.32191e104 0.673854
\(721\) −1.26981e104 −0.615322
\(722\) −1.87289e103 −0.0862789
\(723\) 1.47694e104 0.646869
\(724\) 2.33134e104 0.970842
\(725\) 2.55101e104 1.01012
\(726\) −2.57777e103 −0.0970640
\(727\) 2.80516e103 0.100451 0.0502253 0.998738i \(-0.484006\pi\)
0.0502253 + 0.998738i \(0.484006\pi\)
\(728\) 1.00700e103 0.0342952
\(729\) −4.61762e104 −1.49577
\(730\) −2.15456e102 −0.00663857
\(731\) −2.82300e104 −0.827421
\(732\) −1.37783e104 −0.384184
\(733\) −4.71011e104 −1.24950 −0.624750 0.780825i \(-0.714799\pi\)
−0.624750 + 0.780825i \(0.714799\pi\)
\(734\) 9.27726e102 0.0234160
\(735\) −2.80205e104 −0.672957
\(736\) −3.26811e103 −0.0746890
\(737\) 3.25040e104 0.706925
\(738\) 3.20654e103 0.0663712
\(739\) 7.23905e104 1.42613 0.713065 0.701098i \(-0.247306\pi\)
0.713065 + 0.701098i \(0.247306\pi\)
\(740\) 5.12412e104 0.960863
\(741\) −9.73057e104 −1.73690
\(742\) −2.63926e102 −0.00448477
\(743\) 7.11987e104 1.15181 0.575905 0.817517i \(-0.304650\pi\)
0.575905 + 0.817517i \(0.304650\pi\)
\(744\) 7.85551e103 0.120993
\(745\) −1.46117e104 −0.214288
\(746\) −5.37212e103 −0.0750202
\(747\) 1.03710e105 1.37917
\(748\) −1.87581e105 −2.37564
\(749\) −3.35566e104 −0.404754
\(750\) 7.23096e103 0.0830730
\(751\) 1.54302e105 1.68855 0.844277 0.535907i \(-0.180030\pi\)
0.844277 + 0.535907i \(0.180030\pi\)
\(752\) 4.49687e102 0.00468770
\(753\) 1.77070e105 1.75845
\(754\) −6.52924e103 −0.0617744
\(755\) −3.86966e104 −0.348826
\(756\) 2.11389e104 0.181567
\(757\) −1.58740e105 −1.29923 −0.649617 0.760262i \(-0.725071\pi\)
−0.649617 + 0.760262i \(0.725071\pi\)
\(758\) 9.51207e103 0.0741906
\(759\) −1.20540e105 −0.896000
\(760\) 1.38426e104 0.0980666
\(761\) 7.55382e104 0.510066 0.255033 0.966932i \(-0.417914\pi\)
0.255033 + 0.966932i \(0.417914\pi\)
\(762\) −7.25799e103 −0.0467154
\(763\) −6.45486e104 −0.396042
\(764\) −3.04228e105 −1.77948
\(765\) −2.03484e105 −1.13472
\(766\) −2.15846e104 −0.114761
\(767\) −5.27949e104 −0.267646
\(768\) 3.02952e105 1.46450
\(769\) 3.16605e105 1.45951 0.729754 0.683710i \(-0.239635\pi\)
0.729754 + 0.683710i \(0.239635\pi\)
\(770\) −3.95793e103 −0.0174003
\(771\) −2.39426e104 −0.100389
\(772\) 3.58127e105 1.43221
\(773\) −6.80947e104 −0.259754 −0.129877 0.991530i \(-0.541458\pi\)
−0.129877 + 0.991530i \(0.541458\pi\)
\(774\) −1.08863e104 −0.0396129
\(775\) −1.37925e105 −0.478773
\(776\) −1.08551e104 −0.0359484
\(777\) 3.43690e105 1.08593
\(778\) 2.98993e104 0.0901374
\(779\) −4.50140e105 −1.29488
\(780\) 2.10570e105 0.578022
\(781\) 1.58821e105 0.416049
\(782\) 1.66652e104 0.0416644
\(783\) −2.74632e105 −0.655310
\(784\) −3.69925e105 −0.842515
\(785\) 3.26749e105 0.710350
\(786\) 4.98420e104 0.103436
\(787\) 5.43922e105 1.07760 0.538801 0.842433i \(-0.318877\pi\)
0.538801 + 0.842433i \(0.318877\pi\)
\(788\) 4.82092e102 0.000911850 0
\(789\) −9.52072e105 −1.71933
\(790\) −1.93264e104 −0.0333243
\(791\) −2.04414e105 −0.336565
\(792\) −1.44942e105 −0.227890
\(793\) −1.24064e105 −0.186284
\(794\) 1.63951e104 0.0235107
\(795\) −1.10582e105 −0.151456
\(796\) 2.61028e105 0.341476
\(797\) −7.11246e105 −0.888773 −0.444387 0.895835i \(-0.646578\pi\)
−0.444387 + 0.895835i \(0.646578\pi\)
\(798\) 4.63373e104 0.0553127
\(799\) −6.92212e103 −0.00789372
\(800\) 1.21604e105 0.132484
\(801\) 1.46775e106 1.52780
\(802\) −3.75557e104 −0.0373518
\(803\) −3.16699e105 −0.300974
\(804\) 8.23490e105 0.747846
\(805\) −9.48068e104 −0.0822791
\(806\) 3.53015e104 0.0292795
\(807\) 1.63471e106 1.29585
\(808\) −1.56252e105 −0.118389
\(809\) 7.46404e105 0.540571 0.270286 0.962780i \(-0.412882\pi\)
0.270286 + 0.962780i \(0.412882\pi\)
\(810\) 2.69808e104 0.0186789
\(811\) −1.03340e106 −0.683920 −0.341960 0.939715i \(-0.611091\pi\)
−0.341960 + 0.939715i \(0.611091\pi\)
\(812\) −8.38309e105 −0.530407
\(813\) 1.33442e105 0.0807213
\(814\) −2.79356e105 −0.161572
\(815\) −1.57110e104 −0.00868864
\(816\) −4.73468e106 −2.50380
\(817\) 1.52824e106 0.772837
\(818\) −8.40711e104 −0.0406585
\(819\) 8.01350e105 0.370647
\(820\) 9.74106e105 0.430924
\(821\) −1.85960e106 −0.786855 −0.393428 0.919356i \(-0.628711\pi\)
−0.393428 + 0.919356i \(0.628711\pi\)
\(822\) 2.42916e105 0.0983183
\(823\) −1.97114e106 −0.763172 −0.381586 0.924333i \(-0.624622\pi\)
−0.381586 + 0.924333i \(0.624622\pi\)
\(824\) 5.23946e105 0.194063
\(825\) 4.48523e106 1.58934
\(826\) 2.51411e104 0.00852339
\(827\) 1.57846e106 0.512014 0.256007 0.966675i \(-0.417593\pi\)
0.256007 + 0.966675i \(0.417593\pi\)
\(828\) −1.73273e106 −0.537805
\(829\) −3.37721e106 −1.00304 −0.501519 0.865146i \(-0.667225\pi\)
−0.501519 + 0.865146i \(0.667225\pi\)
\(830\) −1.16853e105 −0.0332116
\(831\) −6.15843e106 −1.67507
\(832\) 2.75913e106 0.718241
\(833\) 5.69432e106 1.41873
\(834\) 3.47490e105 0.0828670
\(835\) −2.30517e106 −0.526195
\(836\) 1.01548e107 2.21892
\(837\) 1.48485e106 0.310600
\(838\) −2.04360e105 −0.0409251
\(839\) 4.15571e106 0.796771 0.398385 0.917218i \(-0.369571\pi\)
0.398385 + 0.917218i \(0.369571\pi\)
\(840\) −2.00920e105 −0.0368833
\(841\) 5.20190e106 0.914341
\(842\) 2.08213e104 0.00350443
\(843\) −1.77462e107 −2.86021
\(844\) −4.67250e106 −0.721190
\(845\) −1.61871e106 −0.239275
\(846\) −2.66938e103 −0.000377913 0
\(847\) −2.98016e106 −0.404106
\(848\) −1.45990e106 −0.189616
\(849\) −1.28601e106 −0.159998
\(850\) −6.20102e105 −0.0739048
\(851\) −6.69159e106 −0.764013
\(852\) 4.02373e106 0.440132
\(853\) 3.24533e106 0.340110 0.170055 0.985435i \(-0.445605\pi\)
0.170055 + 0.985435i \(0.445605\pi\)
\(854\) 5.90799e104 0.00593236
\(855\) 1.10157e107 1.05986
\(856\) 1.38460e106 0.127654
\(857\) 1.48340e107 1.31056 0.655282 0.755385i \(-0.272550\pi\)
0.655282 + 0.755385i \(0.272550\pi\)
\(858\) −1.14798e106 −0.0971964
\(859\) −1.87004e107 −1.51740 −0.758699 0.651441i \(-0.774165\pi\)
−0.758699 + 0.651441i \(0.774165\pi\)
\(860\) −3.30713e106 −0.257192
\(861\) 6.53362e106 0.487011
\(862\) 4.28632e105 0.0306245
\(863\) −1.06435e107 −0.728939 −0.364469 0.931215i \(-0.618750\pi\)
−0.364469 + 0.931215i \(0.618750\pi\)
\(864\) −1.30915e106 −0.0859482
\(865\) 6.91918e106 0.435479
\(866\) −8.77848e104 −0.00529683
\(867\) 4.66006e107 2.69584
\(868\) 4.53246e106 0.251399
\(869\) −2.84078e107 −1.51083
\(870\) 1.30274e106 0.0664363
\(871\) 7.41500e106 0.362617
\(872\) 2.66339e106 0.124906
\(873\) −8.63826e106 −0.388514
\(874\) −9.02180e105 −0.0389158
\(875\) 8.35969e106 0.345857
\(876\) −8.02359e106 −0.318397
\(877\) −7.50757e106 −0.285768 −0.142884 0.989739i \(-0.545638\pi\)
−0.142884 + 0.989739i \(0.545638\pi\)
\(878\) 1.03769e106 0.0378896
\(879\) −5.98785e107 −2.09738
\(880\) −2.18932e107 −0.735686
\(881\) −1.46469e107 −0.472199 −0.236099 0.971729i \(-0.575869\pi\)
−0.236099 + 0.971729i \(0.575869\pi\)
\(882\) 2.19590e106 0.0679219
\(883\) 6.01925e107 1.78639 0.893196 0.449667i \(-0.148457\pi\)
0.893196 + 0.449667i \(0.148457\pi\)
\(884\) −4.27921e107 −1.21859
\(885\) 1.05339e107 0.287845
\(886\) 4.53568e105 0.0118935
\(887\) 5.72253e107 1.44004 0.720022 0.693951i \(-0.244132\pi\)
0.720022 + 0.693951i \(0.244132\pi\)
\(888\) −1.41812e107 −0.342485
\(889\) −8.39095e106 −0.194490
\(890\) −1.65376e106 −0.0367906
\(891\) 3.96592e107 0.846852
\(892\) 4.14497e107 0.849579
\(893\) 3.74732e105 0.00737297
\(894\) 2.01819e106 0.0381190
\(895\) 1.12021e107 0.203123
\(896\) −5.32487e106 −0.0926972
\(897\) −2.74984e107 −0.459603
\(898\) 1.40847e106 0.0226027
\(899\) −5.88848e107 −0.907349
\(900\) 6.44739e107 0.953964
\(901\) 2.24726e107 0.319299
\(902\) −5.31062e106 −0.0724613
\(903\) −2.21819e107 −0.290667
\(904\) 8.43446e106 0.106147
\(905\) −4.18846e107 −0.506269
\(906\) 5.34482e106 0.0620517
\(907\) 4.68331e107 0.522261 0.261130 0.965304i \(-0.415905\pi\)
0.261130 + 0.965304i \(0.415905\pi\)
\(908\) −2.02034e107 −0.216417
\(909\) −1.24343e108 −1.27950
\(910\) −9.02906e105 −0.00892548
\(911\) −1.35405e108 −1.28592 −0.642959 0.765901i \(-0.722293\pi\)
−0.642959 + 0.765901i \(0.722293\pi\)
\(912\) 2.56314e108 2.33863
\(913\) −1.71763e108 −1.50572
\(914\) −6.41408e106 −0.0540254
\(915\) 2.47539e107 0.200343
\(916\) −1.47989e108 −1.15092
\(917\) 5.76222e107 0.430635
\(918\) 6.67580e106 0.0479452
\(919\) 1.02309e108 0.706148 0.353074 0.935595i \(-0.385136\pi\)
0.353074 + 0.935595i \(0.385136\pi\)
\(920\) 3.91189e106 0.0259496
\(921\) 7.26084e107 0.462925
\(922\) 1.33445e107 0.0817757
\(923\) 3.62311e107 0.213412
\(924\) −1.47393e108 −0.834546
\(925\) 2.48990e108 1.35522
\(926\) −6.25194e106 −0.0327125
\(927\) 4.16947e108 2.09735
\(928\) 5.19171e107 0.251078
\(929\) 4.67277e107 0.217271 0.108635 0.994082i \(-0.465352\pi\)
0.108635 + 0.994082i \(0.465352\pi\)
\(930\) −7.04350e106 −0.0314891
\(931\) −3.08265e108 −1.32514
\(932\) −6.65333e107 −0.275016
\(933\) −5.40346e108 −2.14779
\(934\) −1.28917e107 −0.0492777
\(935\) 3.37006e108 1.23884
\(936\) −3.30651e107 −0.116896
\(937\) −1.30332e108 −0.443156 −0.221578 0.975143i \(-0.571121\pi\)
−0.221578 + 0.975143i \(0.571121\pi\)
\(938\) −3.53105e106 −0.0115478
\(939\) −3.99854e108 −1.25779
\(940\) −8.10923e105 −0.00245365
\(941\) 3.96389e108 1.15372 0.576860 0.816843i \(-0.304278\pi\)
0.576860 + 0.816843i \(0.304278\pi\)
\(942\) −4.51310e107 −0.126362
\(943\) −1.27209e108 −0.342641
\(944\) 1.39068e108 0.360370
\(945\) −3.79779e107 −0.0946825
\(946\) 1.80298e107 0.0432478
\(947\) 7.26911e108 1.67767 0.838835 0.544385i \(-0.183237\pi\)
0.838835 + 0.544385i \(0.183237\pi\)
\(948\) −7.19714e108 −1.59829
\(949\) −7.22473e107 −0.154385
\(950\) 3.35695e107 0.0690293
\(951\) −3.35770e108 −0.664437
\(952\) 4.08311e107 0.0777575
\(953\) −9.62132e108 −1.76337 −0.881685 0.471838i \(-0.843591\pi\)
−0.881685 + 0.471838i \(0.843591\pi\)
\(954\) 8.66610e106 0.0152865
\(955\) 5.46573e108 0.927952
\(956\) 7.17698e108 1.17281
\(957\) 1.91490e109 3.01204
\(958\) 1.15803e107 0.0175340
\(959\) 2.80834e108 0.409328
\(960\) −5.50513e108 −0.772445
\(961\) −4.21922e108 −0.569940
\(962\) −6.37283e107 −0.0828786
\(963\) 1.10184e109 1.37962
\(964\) −3.51618e108 −0.423896
\(965\) −6.43407e108 −0.746859
\(966\) 1.30948e107 0.0146364
\(967\) −1.54885e108 −0.166703 −0.0833513 0.996520i \(-0.526562\pi\)
−0.0833513 + 0.996520i \(0.526562\pi\)
\(968\) 1.22966e108 0.127449
\(969\) −3.94549e109 −3.93807
\(970\) 9.73299e106 0.00935573
\(971\) −5.52113e108 −0.511124 −0.255562 0.966793i \(-0.582260\pi\)
−0.255562 + 0.966793i \(0.582260\pi\)
\(972\) 1.53400e109 1.36775
\(973\) 4.01733e108 0.345000
\(974\) 2.77769e107 0.0229764
\(975\) 1.02320e109 0.815250
\(976\) 3.26800e108 0.250821
\(977\) 2.30000e108 0.170050 0.0850250 0.996379i \(-0.472903\pi\)
0.0850250 + 0.996379i \(0.472903\pi\)
\(978\) 2.17003e106 0.00154560
\(979\) −2.43086e109 −1.66799
\(980\) 6.67087e108 0.440992
\(981\) 2.11948e109 1.34992
\(982\) 5.14781e107 0.0315903
\(983\) −8.64281e108 −0.511036 −0.255518 0.966804i \(-0.582246\pi\)
−0.255518 + 0.966804i \(0.582246\pi\)
\(984\) −2.69588e108 −0.153596
\(985\) −8.66122e105 −0.000475507 0
\(986\) −2.64743e108 −0.140061
\(987\) −5.43910e106 −0.00277301
\(988\) 2.31657e109 1.13820
\(989\) 4.31879e108 0.204502
\(990\) 1.29960e108 0.0593095
\(991\) −1.02125e109 −0.449202 −0.224601 0.974451i \(-0.572108\pi\)
−0.224601 + 0.974451i \(0.572108\pi\)
\(992\) −2.80699e108 −0.119005
\(993\) 4.18768e109 1.71130
\(994\) −1.72534e107 −0.00679627
\(995\) −4.68960e108 −0.178071
\(996\) −4.35161e109 −1.59289
\(997\) 4.58848e109 1.61918 0.809592 0.586994i \(-0.199689\pi\)
0.809592 + 0.586994i \(0.199689\pi\)
\(998\) 2.84934e108 0.0969348
\(999\) −2.68053e109 −0.879186
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 1.74.a.a.1.3 5
3.2 odd 2 9.74.a.a.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.74.a.a.1.3 5 1.1 even 1 trivial
9.74.a.a.1.3 5 3.2 odd 2