Properties

Label 1.102.a.a.1.2
Level $1$
Weight $102$
Character 1.1
Self dual yes
Analytic conductor $64.601$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 102 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.6006978936\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(15\!\cdots\!64\)\( x^{6} - \)\(13\!\cdots\!76\)\( x^{5} + \)\(79\!\cdots\!56\)\( x^{4} + \)\(16\!\cdots\!20\)\( x^{3} - \)\(12\!\cdots\!00\)\( x^{2} - \)\(46\!\cdots\!00\)\( x + \)\(14\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{119}\cdot 3^{37}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.42719e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38447e15 q^{2} +1.43714e24 q^{3} +3.15040e30 q^{4} +7.99157e34 q^{5} -3.42682e39 q^{6} +3.14769e42 q^{7} -1.46670e45 q^{8} +5.19237e47 q^{9} +O(q^{10})\) \(q-2.38447e15 q^{2} +1.43714e24 q^{3} +3.15040e30 q^{4} +7.99157e34 q^{5} -3.42682e39 q^{6} +3.14769e42 q^{7} -1.46670e45 q^{8} +5.19237e47 q^{9} -1.90557e50 q^{10} +6.08310e52 q^{11} +4.52757e54 q^{12} -2.09809e56 q^{13} -7.50557e57 q^{14} +1.14850e59 q^{15} -4.48993e60 q^{16} -1.97536e62 q^{17} -1.23811e63 q^{18} -2.54133e64 q^{19} +2.51767e65 q^{20} +4.52366e66 q^{21} -1.45050e68 q^{22} -6.11246e68 q^{23} -2.10785e69 q^{24} -3.30565e70 q^{25} +5.00284e71 q^{26} -1.47579e72 q^{27} +9.91648e72 q^{28} +7.52088e73 q^{29} -2.73857e74 q^{30} -1.26748e75 q^{31} +1.44246e76 q^{32} +8.74226e76 q^{33} +4.71018e77 q^{34} +2.51550e77 q^{35} +1.63581e78 q^{36} +1.84306e79 q^{37} +6.05972e79 q^{38} -3.01525e80 q^{39} -1.17212e80 q^{40} -3.79846e81 q^{41} -1.07865e82 q^{42} -1.82567e82 q^{43} +1.91642e83 q^{44} +4.14952e82 q^{45} +1.45750e84 q^{46} -1.21503e84 q^{47} -6.45265e84 q^{48} -1.27334e85 q^{49} +7.88223e85 q^{50} -2.83886e86 q^{51} -6.60984e86 q^{52} +1.92092e87 q^{53} +3.51898e87 q^{54} +4.86136e87 q^{55} -4.61670e87 q^{56} -3.65224e88 q^{57} -1.79333e89 q^{58} -9.03706e88 q^{59} +3.61824e89 q^{60} -9.82351e89 q^{61} +3.02228e90 q^{62} +1.63439e90 q^{63} -2.30118e91 q^{64} -1.67671e91 q^{65} -2.08457e92 q^{66} +1.68394e92 q^{67} -6.22317e92 q^{68} -8.78445e92 q^{69} -5.99813e92 q^{70} +2.66050e92 q^{71} -7.61563e92 q^{72} -1.19661e94 q^{73} -4.39473e94 q^{74} -4.75068e94 q^{75} -8.00620e94 q^{76} +1.91477e95 q^{77} +7.18978e95 q^{78} +8.68984e95 q^{79} -3.58816e95 q^{80} -2.92373e96 q^{81} +9.05733e96 q^{82} -2.05551e96 q^{83} +1.42514e97 q^{84} -1.57862e97 q^{85} +4.35327e97 q^{86} +1.08086e98 q^{87} -8.92207e97 q^{88} -4.58460e98 q^{89} -9.89441e97 q^{90} -6.60413e98 q^{91} -1.92567e99 q^{92} -1.82155e99 q^{93} +2.89721e99 q^{94} -2.03092e99 q^{95} +2.07302e100 q^{96} -9.41618e99 q^{97} +3.03625e100 q^{98} +3.15857e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38447e15 −1.49754 −0.748768 0.662832i \(-0.769354\pi\)
−0.748768 + 0.662832i \(0.769354\pi\)
\(3\) 1.43714e24 1.15578 0.577890 0.816114i \(-0.303876\pi\)
0.577890 + 0.816114i \(0.303876\pi\)
\(4\) 3.15040e30 1.24262
\(5\) 7.99157e34 0.402390 0.201195 0.979551i \(-0.435518\pi\)
0.201195 + 0.979551i \(0.435518\pi\)
\(6\) −3.42682e39 −1.73082
\(7\) 3.14769e42 0.661516 0.330758 0.943716i \(-0.392696\pi\)
0.330758 + 0.943716i \(0.392696\pi\)
\(8\) −1.46670e45 −0.363326
\(9\) 5.19237e47 0.335829
\(10\) −1.90557e50 −0.602594
\(11\) 6.08310e52 1.56241 0.781204 0.624276i \(-0.214606\pi\)
0.781204 + 0.624276i \(0.214606\pi\)
\(12\) 4.52757e54 1.43619
\(13\) −2.09809e56 −1.16865 −0.584326 0.811519i \(-0.698641\pi\)
−0.584326 + 0.811519i \(0.698641\pi\)
\(14\) −7.50557e57 −0.990644
\(15\) 1.14850e59 0.465075
\(16\) −4.48993e60 −0.698522
\(17\) −1.97536e62 −1.43872 −0.719358 0.694640i \(-0.755564\pi\)
−0.719358 + 0.694640i \(0.755564\pi\)
\(18\) −1.23811e63 −0.502917
\(19\) −2.54133e64 −0.672982 −0.336491 0.941687i \(-0.609240\pi\)
−0.336491 + 0.941687i \(0.609240\pi\)
\(20\) 2.51767e65 0.500016
\(21\) 4.52366e66 0.764567
\(22\) −1.45050e68 −2.33976
\(23\) −6.11246e68 −1.04462 −0.522312 0.852754i \(-0.674930\pi\)
−0.522312 + 0.852754i \(0.674930\pi\)
\(24\) −2.10785e69 −0.419925
\(25\) −3.30565e70 −0.838082
\(26\) 5.00284e71 1.75010
\(27\) −1.47579e72 −0.767636
\(28\) 9.91648e72 0.822010
\(29\) 7.52088e73 1.05967 0.529834 0.848101i \(-0.322254\pi\)
0.529834 + 0.848101i \(0.322254\pi\)
\(30\) −2.73857e74 −0.696466
\(31\) −1.26748e75 −0.615428 −0.307714 0.951479i \(-0.599564\pi\)
−0.307714 + 0.951479i \(0.599564\pi\)
\(32\) 1.44246e76 1.40939
\(33\) 8.74226e76 1.80580
\(34\) 4.71018e77 2.15453
\(35\) 2.51550e77 0.266187
\(36\) 1.63581e78 0.417307
\(37\) 1.84306e79 1.17856 0.589281 0.807928i \(-0.299411\pi\)
0.589281 + 0.807928i \(0.299411\pi\)
\(38\) 6.05972e79 1.00781
\(39\) −3.01525e80 −1.35071
\(40\) −1.17212e80 −0.146199
\(41\) −3.79846e81 −1.36152 −0.680758 0.732508i \(-0.738350\pi\)
−0.680758 + 0.732508i \(0.738350\pi\)
\(42\) −1.07865e82 −1.14497
\(43\) −1.82567e82 −0.590563 −0.295282 0.955410i \(-0.595413\pi\)
−0.295282 + 0.955410i \(0.595413\pi\)
\(44\) 1.91642e83 1.94147
\(45\) 4.14952e82 0.135134
\(46\) 1.45750e84 1.56436
\(47\) −1.21503e84 −0.440196 −0.220098 0.975478i \(-0.570638\pi\)
−0.220098 + 0.975478i \(0.570638\pi\)
\(48\) −6.45265e84 −0.807339
\(49\) −1.27334e85 −0.562397
\(50\) 7.88223e85 1.25506
\(51\) −2.83886e86 −1.66284
\(52\) −6.60984e86 −1.45219
\(53\) 1.92092e87 1.61279 0.806393 0.591380i \(-0.201416\pi\)
0.806393 + 0.591380i \(0.201416\pi\)
\(54\) 3.51898e87 1.14956
\(55\) 4.86136e87 0.628697
\(56\) −4.61670e87 −0.240346
\(57\) −3.65224e88 −0.777820
\(58\) −1.79333e89 −1.58689
\(59\) −9.03706e88 −0.337288 −0.168644 0.985677i \(-0.553939\pi\)
−0.168644 + 0.985677i \(0.553939\pi\)
\(60\) 3.61824e89 0.577909
\(61\) −9.82351e89 −0.680942 −0.340471 0.940255i \(-0.610586\pi\)
−0.340471 + 0.940255i \(0.610586\pi\)
\(62\) 3.02228e90 0.921625
\(63\) 1.63439e90 0.222157
\(64\) −2.30118e91 −1.41209
\(65\) −1.67671e91 −0.470254
\(66\) −2.08457e92 −2.70425
\(67\) 1.68394e92 1.02223 0.511116 0.859512i \(-0.329232\pi\)
0.511116 + 0.859512i \(0.329232\pi\)
\(68\) −6.22317e92 −1.78777
\(69\) −8.78445e92 −1.20736
\(70\) −5.99813e92 −0.398625
\(71\) 2.66050e92 0.0863806 0.0431903 0.999067i \(-0.486248\pi\)
0.0431903 + 0.999067i \(0.486248\pi\)
\(72\) −7.61563e92 −0.122015
\(73\) −1.19661e94 −0.955316 −0.477658 0.878546i \(-0.658514\pi\)
−0.477658 + 0.878546i \(0.658514\pi\)
\(74\) −4.39473e94 −1.76494
\(75\) −4.75068e94 −0.968640
\(76\) −8.00620e94 −0.836258
\(77\) 1.91477e95 1.03356
\(78\) 7.18978e95 2.02273
\(79\) 8.68984e95 1.28482 0.642412 0.766360i \(-0.277934\pi\)
0.642412 + 0.766360i \(0.277934\pi\)
\(80\) −3.58816e95 −0.281078
\(81\) −2.92373e96 −1.22305
\(82\) 9.05733e96 2.03892
\(83\) −2.05551e96 −0.250885 −0.125443 0.992101i \(-0.540035\pi\)
−0.125443 + 0.992101i \(0.540035\pi\)
\(84\) 1.42514e97 0.950063
\(85\) −1.57862e97 −0.578925
\(86\) 4.35327e97 0.884390
\(87\) 1.08086e98 1.22474
\(88\) −8.92207e97 −0.567663
\(89\) −4.58460e98 −1.64857 −0.824283 0.566178i \(-0.808421\pi\)
−0.824283 + 0.566178i \(0.808421\pi\)
\(90\) −9.89441e97 −0.202369
\(91\) −6.60413e98 −0.773082
\(92\) −1.92567e99 −1.29807
\(93\) −1.82155e99 −0.711300
\(94\) 2.89721e99 0.659210
\(95\) −2.03092e99 −0.270801
\(96\) 2.07302e100 1.62894
\(97\) −9.41618e99 −0.438432 −0.219216 0.975676i \(-0.570350\pi\)
−0.219216 + 0.975676i \(0.570350\pi\)
\(98\) 3.03625e100 0.842210
\(99\) 3.15857e100 0.524703
\(100\) −1.04141e101 −1.04141
\(101\) −1.91765e101 −1.16022 −0.580110 0.814538i \(-0.696991\pi\)
−0.580110 + 0.814538i \(0.696991\pi\)
\(102\) 6.76919e101 2.49016
\(103\) 5.30544e101 1.19245 0.596227 0.802816i \(-0.296666\pi\)
0.596227 + 0.802816i \(0.296666\pi\)
\(104\) 3.07727e101 0.424601
\(105\) 3.61512e101 0.307654
\(106\) −4.58037e102 −2.41521
\(107\) −2.09657e102 −0.688064 −0.344032 0.938958i \(-0.611793\pi\)
−0.344032 + 0.938958i \(0.611793\pi\)
\(108\) −4.64934e102 −0.953876
\(109\) 1.37901e101 0.0177636 0.00888179 0.999961i \(-0.497173\pi\)
0.00888179 + 0.999961i \(0.497173\pi\)
\(110\) −1.15918e103 −0.941497
\(111\) 2.64874e103 1.36216
\(112\) −1.41329e103 −0.462083
\(113\) 4.37593e102 0.0913290 0.0456645 0.998957i \(-0.485459\pi\)
0.0456645 + 0.998957i \(0.485459\pi\)
\(114\) 8.70866e103 1.16481
\(115\) −4.88482e103 −0.420346
\(116\) 2.36938e104 1.31676
\(117\) −1.08941e104 −0.392468
\(118\) 2.15486e104 0.505101
\(119\) −6.21780e104 −0.951733
\(120\) −1.68450e104 −0.168974
\(121\) 2.18454e105 1.44112
\(122\) 2.34239e105 1.01973
\(123\) −5.45892e105 −1.57362
\(124\) −3.99309e105 −0.764740
\(125\) −5.79386e105 −0.739626
\(126\) −3.89717e105 −0.332687
\(127\) −2.11318e106 −1.21018 −0.605088 0.796159i \(-0.706862\pi\)
−0.605088 + 0.796159i \(0.706862\pi\)
\(128\) 1.83002e106 0.705265
\(129\) −2.62375e106 −0.682562
\(130\) 3.99806e106 0.704222
\(131\) 1.48036e107 1.77079 0.885393 0.464842i \(-0.153889\pi\)
0.885393 + 0.464842i \(0.153889\pi\)
\(132\) 2.75417e107 2.24392
\(133\) −7.99929e106 −0.445188
\(134\) −4.01531e107 −1.53083
\(135\) −1.17939e107 −0.308889
\(136\) 2.89725e107 0.522722
\(137\) −1.25472e108 −1.56372 −0.781859 0.623455i \(-0.785728\pi\)
−0.781859 + 0.623455i \(0.785728\pi\)
\(138\) 2.09463e108 1.80806
\(139\) −1.05964e108 −0.635199 −0.317599 0.948225i \(-0.602877\pi\)
−0.317599 + 0.948225i \(0.602877\pi\)
\(140\) 7.92483e107 0.330769
\(141\) −1.74617e108 −0.508770
\(142\) −6.34388e107 −0.129358
\(143\) −1.27629e109 −1.82591
\(144\) −2.33134e108 −0.234584
\(145\) 6.01037e108 0.426400
\(146\) 2.85327e109 1.43062
\(147\) −1.82997e109 −0.650007
\(148\) 5.80639e109 1.46450
\(149\) −8.73079e109 −1.56728 −0.783641 0.621214i \(-0.786640\pi\)
−0.783641 + 0.621214i \(0.786640\pi\)
\(150\) 1.13279e110 1.45057
\(151\) 1.82348e110 1.66942 0.834708 0.550693i \(-0.185637\pi\)
0.834708 + 0.550693i \(0.185637\pi\)
\(152\) 3.72735e109 0.244512
\(153\) −1.02568e110 −0.483163
\(154\) −4.56571e110 −1.54779
\(155\) −1.01292e110 −0.247642
\(156\) −9.49926e110 −1.67841
\(157\) 6.49484e110 0.831067 0.415533 0.909578i \(-0.363595\pi\)
0.415533 + 0.909578i \(0.363595\pi\)
\(158\) −2.07207e111 −1.92407
\(159\) 2.76062e111 1.86403
\(160\) 1.15275e111 0.567124
\(161\) −1.92401e111 −0.691036
\(162\) 6.97155e111 1.83156
\(163\) −2.38327e111 −0.458880 −0.229440 0.973323i \(-0.573689\pi\)
−0.229440 + 0.973323i \(0.573689\pi\)
\(164\) −1.19667e112 −1.69184
\(165\) 6.98645e111 0.726636
\(166\) 4.90130e111 0.375710
\(167\) 1.51500e112 0.857491 0.428746 0.903425i \(-0.358956\pi\)
0.428746 + 0.903425i \(0.358956\pi\)
\(168\) −6.63484e111 −0.277787
\(169\) 1.17885e112 0.365747
\(170\) 3.76418e112 0.866961
\(171\) −1.31955e112 −0.226007
\(172\) −5.75162e112 −0.733843
\(173\) 8.48260e110 0.00807609 0.00403804 0.999992i \(-0.498715\pi\)
0.00403804 + 0.999992i \(0.498715\pi\)
\(174\) −2.57727e113 −1.83410
\(175\) −1.04052e113 −0.554405
\(176\) −2.73127e113 −1.09138
\(177\) −1.29875e113 −0.389831
\(178\) 1.09319e114 2.46879
\(179\) 7.70832e113 1.31184 0.655921 0.754829i \(-0.272280\pi\)
0.655921 + 0.754829i \(0.272280\pi\)
\(180\) 1.30727e113 0.167920
\(181\) −9.10499e113 −0.884121 −0.442060 0.896985i \(-0.645752\pi\)
−0.442060 + 0.896985i \(0.645752\pi\)
\(182\) 1.57474e114 1.15772
\(183\) −1.41177e114 −0.787019
\(184\) 8.96512e113 0.379539
\(185\) 1.47290e114 0.474242
\(186\) 4.34344e114 1.06520
\(187\) −1.20163e115 −2.24786
\(188\) −3.82785e114 −0.546995
\(189\) −4.64533e114 −0.507803
\(190\) 4.84267e114 0.405535
\(191\) 1.29493e115 0.831879 0.415939 0.909392i \(-0.363453\pi\)
0.415939 + 0.909392i \(0.363453\pi\)
\(192\) −3.30711e115 −1.63206
\(193\) 2.90903e115 1.10434 0.552171 0.833731i \(-0.313799\pi\)
0.552171 + 0.833731i \(0.313799\pi\)
\(194\) 2.24526e115 0.656568
\(195\) −2.40966e115 −0.543510
\(196\) −4.01154e115 −0.698843
\(197\) 1.44395e115 0.194539 0.0972697 0.995258i \(-0.468989\pi\)
0.0972697 + 0.995258i \(0.468989\pi\)
\(198\) −7.53152e115 −0.785761
\(199\) 1.20582e116 0.975440 0.487720 0.873000i \(-0.337829\pi\)
0.487720 + 0.873000i \(0.337829\pi\)
\(200\) 4.84839e115 0.304497
\(201\) 2.42006e116 1.18148
\(202\) 4.57259e116 1.73747
\(203\) 2.36734e116 0.700987
\(204\) −8.94357e116 −2.06627
\(205\) −3.03557e116 −0.547861
\(206\) −1.26507e117 −1.78574
\(207\) −3.17381e116 −0.350816
\(208\) 9.42028e116 0.816329
\(209\) −1.54591e117 −1.05147
\(210\) −8.62015e116 −0.460723
\(211\) −3.28579e116 −0.138158 −0.0690789 0.997611i \(-0.522006\pi\)
−0.0690789 + 0.997611i \(0.522006\pi\)
\(212\) 6.05166e117 2.00407
\(213\) 3.82351e116 0.0998371
\(214\) 4.99922e117 1.03040
\(215\) −1.45900e117 −0.237637
\(216\) 2.16454e117 0.278902
\(217\) −3.98964e117 −0.407115
\(218\) −3.28822e116 −0.0266016
\(219\) −1.71969e118 −1.10414
\(220\) 1.53152e118 0.781229
\(221\) 4.14448e118 1.68136
\(222\) −6.31583e118 −2.03988
\(223\) −7.08484e117 −0.182362 −0.0911810 0.995834i \(-0.529064\pi\)
−0.0911810 + 0.995834i \(0.529064\pi\)
\(224\) 4.54042e118 0.932333
\(225\) −1.71642e118 −0.281453
\(226\) −1.04343e118 −0.136769
\(227\) −7.11138e118 −0.745844 −0.372922 0.927863i \(-0.621644\pi\)
−0.372922 + 0.927863i \(0.621644\pi\)
\(228\) −1.15060e119 −0.966531
\(229\) −7.22725e118 −0.486722 −0.243361 0.969936i \(-0.578250\pi\)
−0.243361 + 0.969936i \(0.578250\pi\)
\(230\) 1.16477e119 0.629484
\(231\) 2.75179e119 1.19457
\(232\) −1.10309e119 −0.385005
\(233\) 1.44195e119 0.405020 0.202510 0.979280i \(-0.435090\pi\)
0.202510 + 0.979280i \(0.435090\pi\)
\(234\) 2.59766e119 0.587735
\(235\) −9.71003e118 −0.177131
\(236\) −2.84704e119 −0.419119
\(237\) 1.24885e120 1.48497
\(238\) 1.48262e120 1.42526
\(239\) −7.34680e119 −0.571484 −0.285742 0.958307i \(-0.592240\pi\)
−0.285742 + 0.958307i \(0.592240\pi\)
\(240\) −5.15668e119 −0.324865
\(241\) −1.91398e120 −0.977411 −0.488706 0.872449i \(-0.662531\pi\)
−0.488706 + 0.872449i \(0.662531\pi\)
\(242\) −5.20899e120 −2.15813
\(243\) −1.92003e120 −0.645940
\(244\) −3.09480e120 −0.846149
\(245\) −1.01760e120 −0.226303
\(246\) 1.30166e121 2.35655
\(247\) 5.33193e120 0.786482
\(248\) 1.85902e120 0.223601
\(249\) −2.95405e120 −0.289969
\(250\) 1.38153e121 1.10762
\(251\) −1.31699e121 −0.863098 −0.431549 0.902089i \(-0.642033\pi\)
−0.431549 + 0.902089i \(0.642033\pi\)
\(252\) 5.14900e120 0.276055
\(253\) −3.71827e121 −1.63213
\(254\) 5.03881e121 1.81228
\(255\) −2.26870e121 −0.669110
\(256\) 1.47055e121 0.355928
\(257\) −3.41822e121 −0.679480 −0.339740 0.940519i \(-0.610339\pi\)
−0.339740 + 0.940519i \(0.610339\pi\)
\(258\) 6.25626e121 1.02216
\(259\) 5.80137e121 0.779638
\(260\) −5.28230e121 −0.584345
\(261\) 3.90512e121 0.355868
\(262\) −3.52987e122 −2.65182
\(263\) 4.70322e121 0.291494 0.145747 0.989322i \(-0.453441\pi\)
0.145747 + 0.989322i \(0.453441\pi\)
\(264\) −1.28223e122 −0.656094
\(265\) 1.53511e122 0.648969
\(266\) 1.90741e122 0.666686
\(267\) −6.58871e122 −1.90538
\(268\) 5.30509e122 1.27024
\(269\) 3.47750e121 0.0689886 0.0344943 0.999405i \(-0.489018\pi\)
0.0344943 + 0.999405i \(0.489018\pi\)
\(270\) 2.81222e122 0.462572
\(271\) 8.93405e122 1.21927 0.609634 0.792683i \(-0.291317\pi\)
0.609634 + 0.792683i \(0.291317\pi\)
\(272\) 8.86921e122 1.00497
\(273\) −9.49106e122 −0.893513
\(274\) 2.99185e123 2.34173
\(275\) −2.01086e123 −1.30943
\(276\) −2.76746e123 −1.50028
\(277\) −2.61374e123 −1.18042 −0.590208 0.807252i \(-0.700954\pi\)
−0.590208 + 0.807252i \(0.700954\pi\)
\(278\) 2.52667e123 0.951233
\(279\) −6.58125e122 −0.206679
\(280\) −3.68947e122 −0.0967127
\(281\) −7.67814e123 −1.68108 −0.840538 0.541753i \(-0.817761\pi\)
−0.840538 + 0.541753i \(0.817761\pi\)
\(282\) 4.16370e123 0.761902
\(283\) −3.67598e123 −0.562546 −0.281273 0.959628i \(-0.590757\pi\)
−0.281273 + 0.959628i \(0.590757\pi\)
\(284\) 8.38165e122 0.107338
\(285\) −2.91871e123 −0.312987
\(286\) 3.04328e124 2.73437
\(287\) −1.19564e124 −0.900665
\(288\) 7.48980e123 0.473314
\(289\) 2.01690e124 1.06990
\(290\) −1.43316e124 −0.638549
\(291\) −1.35324e124 −0.506731
\(292\) −3.76980e124 −1.18709
\(293\) 1.82743e124 0.484201 0.242100 0.970251i \(-0.422164\pi\)
0.242100 + 0.970251i \(0.422164\pi\)
\(294\) 4.36351e124 0.973410
\(295\) −7.22204e123 −0.135721
\(296\) −2.70321e124 −0.428202
\(297\) −8.97739e124 −1.19936
\(298\) 2.08183e125 2.34706
\(299\) 1.28245e125 1.22080
\(300\) −1.49666e125 −1.20365
\(301\) −5.74665e124 −0.390667
\(302\) −4.34803e125 −2.50001
\(303\) −2.75593e125 −1.34096
\(304\) 1.14104e125 0.470093
\(305\) −7.85053e124 −0.274004
\(306\) 2.44570e125 0.723554
\(307\) 4.99534e125 1.25336 0.626681 0.779276i \(-0.284413\pi\)
0.626681 + 0.779276i \(0.284413\pi\)
\(308\) 6.03230e125 1.28431
\(309\) 7.62466e125 1.37822
\(310\) 2.41528e125 0.370853
\(311\) −1.21415e126 −1.58443 −0.792215 0.610243i \(-0.791072\pi\)
−0.792215 + 0.610243i \(0.791072\pi\)
\(312\) 4.42246e125 0.490746
\(313\) 4.93941e125 0.466322 0.233161 0.972438i \(-0.425093\pi\)
0.233161 + 0.972438i \(0.425093\pi\)
\(314\) −1.54868e126 −1.24455
\(315\) 1.30614e125 0.0893935
\(316\) 2.73765e126 1.59654
\(317\) −3.07972e126 −1.53115 −0.765576 0.643346i \(-0.777546\pi\)
−0.765576 + 0.643346i \(0.777546\pi\)
\(318\) −6.58263e126 −2.79145
\(319\) 4.57503e126 1.65563
\(320\) −1.83900e126 −0.568210
\(321\) −3.01307e126 −0.795252
\(322\) 4.58775e126 1.03485
\(323\) 5.02002e126 0.968230
\(324\) −9.21093e126 −1.51978
\(325\) 6.93556e126 0.979427
\(326\) 5.68283e126 0.687189
\(327\) 1.98184e125 0.0205308
\(328\) 5.57119e126 0.494674
\(329\) −3.82454e126 −0.291197
\(330\) −1.66590e127 −1.08816
\(331\) 2.91257e127 1.63291 0.816456 0.577407i \(-0.195936\pi\)
0.816456 + 0.577407i \(0.195936\pi\)
\(332\) −6.47568e126 −0.311754
\(333\) 9.56985e126 0.395796
\(334\) −3.61247e127 −1.28412
\(335\) 1.34573e127 0.411336
\(336\) −2.03109e127 −0.534067
\(337\) 7.69384e127 1.74114 0.870568 0.492047i \(-0.163751\pi\)
0.870568 + 0.492047i \(0.163751\pi\)
\(338\) −2.81094e127 −0.547720
\(339\) 6.28882e126 0.105556
\(340\) −4.97329e127 −0.719381
\(341\) −7.71024e127 −0.961549
\(342\) 3.14643e127 0.338454
\(343\) −1.11349e128 −1.03355
\(344\) 2.67771e127 0.214567
\(345\) −7.02016e127 −0.485828
\(346\) −2.02265e126 −0.0120942
\(347\) 5.05616e127 0.261326 0.130663 0.991427i \(-0.458289\pi\)
0.130663 + 0.991427i \(0.458289\pi\)
\(348\) 3.40513e128 1.52189
\(349\) −3.51214e128 −1.35796 −0.678981 0.734156i \(-0.737578\pi\)
−0.678981 + 0.734156i \(0.737578\pi\)
\(350\) 2.48108e128 0.830241
\(351\) 3.09635e128 0.897099
\(352\) 8.77464e128 2.20204
\(353\) −5.20749e127 −0.113242 −0.0566208 0.998396i \(-0.518033\pi\)
−0.0566208 + 0.998396i \(0.518033\pi\)
\(354\) 3.09684e128 0.583786
\(355\) 2.12616e127 0.0347587
\(356\) −1.44433e129 −2.04853
\(357\) −8.93584e128 −1.09999
\(358\) −1.83803e129 −1.96453
\(359\) 1.83400e128 0.170267 0.0851336 0.996370i \(-0.472868\pi\)
0.0851336 + 0.996370i \(0.472868\pi\)
\(360\) −6.08609e127 −0.0490978
\(361\) −7.80148e128 −0.547095
\(362\) 2.17106e129 1.32400
\(363\) 3.13950e129 1.66562
\(364\) −2.08057e129 −0.960643
\(365\) −9.56277e128 −0.384409
\(366\) 3.36634e129 1.17859
\(367\) −2.13701e129 −0.651884 −0.325942 0.945390i \(-0.605681\pi\)
−0.325942 + 0.945390i \(0.605681\pi\)
\(368\) 2.74445e129 0.729693
\(369\) −1.97230e129 −0.457237
\(370\) −3.51208e129 −0.710194
\(371\) 6.04644e129 1.06688
\(372\) −5.73862e129 −0.883872
\(373\) −6.00257e129 −0.807311 −0.403656 0.914911i \(-0.632261\pi\)
−0.403656 + 0.914911i \(0.632261\pi\)
\(374\) 2.86525e130 3.36625
\(375\) −8.32658e129 −0.854845
\(376\) 1.78209e129 0.159935
\(377\) −1.57795e130 −1.23838
\(378\) 1.10767e130 0.760454
\(379\) 1.67101e129 0.100392 0.0501959 0.998739i \(-0.484015\pi\)
0.0501959 + 0.998739i \(0.484015\pi\)
\(380\) −6.39822e129 −0.336502
\(381\) −3.03693e130 −1.39870
\(382\) −3.08772e130 −1.24577
\(383\) 4.14692e130 1.46618 0.733091 0.680131i \(-0.238077\pi\)
0.733091 + 0.680131i \(0.238077\pi\)
\(384\) 2.62999e130 0.815132
\(385\) 1.53020e130 0.415893
\(386\) −6.93649e130 −1.65379
\(387\) −9.47958e129 −0.198329
\(388\) −2.96648e130 −0.544802
\(389\) −6.92348e130 −1.11653 −0.558264 0.829663i \(-0.688532\pi\)
−0.558264 + 0.829663i \(0.688532\pi\)
\(390\) 5.74577e130 0.813927
\(391\) 1.20743e131 1.50292
\(392\) 1.86761e130 0.204333
\(393\) 2.12748e131 2.04664
\(394\) −3.44306e130 −0.291330
\(395\) 6.94455e130 0.517000
\(396\) 9.95078e130 0.652004
\(397\) −8.86213e130 −0.511231 −0.255616 0.966778i \(-0.582278\pi\)
−0.255616 + 0.966778i \(0.582278\pi\)
\(398\) −2.87523e131 −1.46076
\(399\) −1.14961e131 −0.514540
\(400\) 1.48421e131 0.585419
\(401\) −6.21084e129 −0.0215953 −0.0107977 0.999942i \(-0.503437\pi\)
−0.0107977 + 0.999942i \(0.503437\pi\)
\(402\) −5.77056e131 −1.76930
\(403\) 2.65930e131 0.719221
\(404\) −6.04138e131 −1.44171
\(405\) −2.33652e131 −0.492142
\(406\) −5.64485e131 −1.04975
\(407\) 1.12115e132 1.84140
\(408\) 4.16375e131 0.604152
\(409\) 1.03956e132 1.33297 0.666487 0.745517i \(-0.267797\pi\)
0.666487 + 0.745517i \(0.267797\pi\)
\(410\) 7.23823e131 0.820441
\(411\) −1.80321e132 −1.80732
\(412\) 1.67143e132 1.48176
\(413\) −2.84458e131 −0.223121
\(414\) 7.56787e131 0.525359
\(415\) −1.64267e131 −0.100954
\(416\) −3.02642e132 −1.64708
\(417\) −1.52285e132 −0.734151
\(418\) 3.68619e132 1.57462
\(419\) −1.38531e132 −0.524491 −0.262246 0.965001i \(-0.584463\pi\)
−0.262246 + 0.965001i \(0.584463\pi\)
\(420\) 1.13891e132 0.382296
\(421\) 1.31976e132 0.392869 0.196435 0.980517i \(-0.437064\pi\)
0.196435 + 0.980517i \(0.437064\pi\)
\(422\) 7.83486e131 0.206896
\(423\) −6.30890e131 −0.147831
\(424\) −2.81740e132 −0.585967
\(425\) 6.52984e132 1.20576
\(426\) −9.11704e131 −0.149510
\(427\) −3.09213e132 −0.450454
\(428\) −6.60505e132 −0.855000
\(429\) −1.83421e133 −2.11035
\(430\) 3.47895e132 0.355870
\(431\) −1.47645e133 −1.34313 −0.671564 0.740946i \(-0.734377\pi\)
−0.671564 + 0.740946i \(0.734377\pi\)
\(432\) 6.62620e132 0.536210
\(433\) 2.39695e133 1.72592 0.862958 0.505276i \(-0.168609\pi\)
0.862958 + 0.505276i \(0.168609\pi\)
\(434\) 9.51319e132 0.609670
\(435\) 8.63774e132 0.492825
\(436\) 4.34445e131 0.0220733
\(437\) 1.55337e133 0.703013
\(438\) 4.10055e133 1.65348
\(439\) −1.80750e133 −0.649563 −0.324781 0.945789i \(-0.605291\pi\)
−0.324781 + 0.945789i \(0.605291\pi\)
\(440\) −7.13014e132 −0.228422
\(441\) −6.61166e132 −0.188869
\(442\) −9.88239e133 −2.51789
\(443\) 5.76910e133 1.31135 0.655677 0.755041i \(-0.272383\pi\)
0.655677 + 0.755041i \(0.272383\pi\)
\(444\) 8.34459e133 1.69264
\(445\) −3.66382e133 −0.663366
\(446\) 1.68936e133 0.273094
\(447\) −1.25474e134 −1.81143
\(448\) −7.24339e133 −0.934119
\(449\) −1.99115e133 −0.229437 −0.114718 0.993398i \(-0.536597\pi\)
−0.114718 + 0.993398i \(0.536597\pi\)
\(450\) 4.09275e133 0.421486
\(451\) −2.31064e134 −2.12724
\(452\) 1.37859e133 0.113487
\(453\) 2.62059e134 1.92948
\(454\) 1.69569e134 1.11693
\(455\) −5.27774e133 −0.311080
\(456\) 5.35673e133 0.282602
\(457\) 3.63995e133 0.171921 0.0859603 0.996299i \(-0.472604\pi\)
0.0859603 + 0.996299i \(0.472604\pi\)
\(458\) 1.72332e134 0.728884
\(459\) 2.91522e134 1.10441
\(460\) −1.53891e134 −0.522329
\(461\) 7.99190e133 0.243082 0.121541 0.992586i \(-0.461216\pi\)
0.121541 + 0.992586i \(0.461216\pi\)
\(462\) −6.56156e134 −1.78891
\(463\) 3.09340e134 0.756129 0.378064 0.925779i \(-0.376590\pi\)
0.378064 + 0.925779i \(0.376590\pi\)
\(464\) −3.37682e134 −0.740202
\(465\) −1.45571e134 −0.286220
\(466\) −3.43829e134 −0.606532
\(467\) 6.56173e134 1.03876 0.519381 0.854543i \(-0.326163\pi\)
0.519381 + 0.854543i \(0.326163\pi\)
\(468\) −3.43207e134 −0.487687
\(469\) 5.30051e134 0.676222
\(470\) 2.31533e134 0.265259
\(471\) 9.33399e134 0.960531
\(472\) 1.32546e134 0.122545
\(473\) −1.11058e135 −0.922701
\(474\) −2.97785e135 −2.22380
\(475\) 8.40074e134 0.564014
\(476\) −1.95886e135 −1.18264
\(477\) 9.97410e134 0.541621
\(478\) 1.75182e135 0.855819
\(479\) −7.37311e134 −0.324121 −0.162061 0.986781i \(-0.551814\pi\)
−0.162061 + 0.986781i \(0.551814\pi\)
\(480\) 1.65667e135 0.655471
\(481\) −3.86691e135 −1.37733
\(482\) 4.56384e135 1.46371
\(483\) −2.76507e135 −0.798686
\(484\) 6.88220e135 1.79076
\(485\) −7.52501e134 −0.176421
\(486\) 4.57827e135 0.967319
\(487\) 6.08383e135 1.15868 0.579341 0.815085i \(-0.303310\pi\)
0.579341 + 0.815085i \(0.303310\pi\)
\(488\) 1.44081e135 0.247404
\(489\) −3.42509e135 −0.530364
\(490\) 2.42644e135 0.338897
\(491\) −4.22617e135 −0.532514 −0.266257 0.963902i \(-0.585787\pi\)
−0.266257 + 0.963902i \(0.585787\pi\)
\(492\) −1.71978e136 −1.95540
\(493\) −1.48564e136 −1.52456
\(494\) −1.27138e136 −1.17778
\(495\) 2.52420e135 0.211135
\(496\) 5.69091e135 0.429890
\(497\) 8.37441e134 0.0571422
\(498\) 7.04385e135 0.434239
\(499\) 1.79965e136 1.00256 0.501279 0.865286i \(-0.332863\pi\)
0.501279 + 0.865286i \(0.332863\pi\)
\(500\) −1.82530e136 −0.919071
\(501\) 2.17726e136 0.991072
\(502\) 3.14033e136 1.29252
\(503\) −3.61622e136 −1.34608 −0.673041 0.739605i \(-0.735012\pi\)
−0.673041 + 0.739605i \(0.735012\pi\)
\(504\) −2.39716e135 −0.0807152
\(505\) −1.53251e136 −0.466861
\(506\) 8.86611e136 2.44417
\(507\) 1.69418e136 0.422724
\(508\) −6.65737e136 −1.50378
\(509\) −3.70155e135 −0.0757069 −0.0378535 0.999283i \(-0.512052\pi\)
−0.0378535 + 0.999283i \(0.512052\pi\)
\(510\) 5.40965e136 1.00202
\(511\) −3.76654e136 −0.631957
\(512\) −8.14614e136 −1.23828
\(513\) 3.75047e136 0.516605
\(514\) 8.15064e136 1.01755
\(515\) 4.23989e136 0.479832
\(516\) −8.26587e136 −0.848162
\(517\) −7.39117e136 −0.687766
\(518\) −1.38332e137 −1.16754
\(519\) 1.21907e135 0.00933419
\(520\) 2.45922e136 0.170855
\(521\) 1.29061e137 0.813746 0.406873 0.913485i \(-0.366619\pi\)
0.406873 + 0.913485i \(0.366619\pi\)
\(522\) −9.31165e136 −0.532925
\(523\) −1.43042e137 −0.743240 −0.371620 0.928385i \(-0.621198\pi\)
−0.371620 + 0.928385i \(0.621198\pi\)
\(524\) 4.66373e137 2.20041
\(525\) −1.49537e137 −0.640770
\(526\) −1.12147e137 −0.436523
\(527\) 2.50373e137 0.885425
\(528\) −3.92521e137 −1.26139
\(529\) 3.12389e136 0.0912399
\(530\) −3.66044e137 −0.971855
\(531\) −4.69238e136 −0.113271
\(532\) −2.52010e137 −0.553198
\(533\) 7.96952e137 1.59114
\(534\) 1.57106e138 2.85338
\(535\) −1.67549e137 −0.276870
\(536\) −2.46983e137 −0.371403
\(537\) 1.10779e138 1.51620
\(538\) −8.29201e136 −0.103313
\(539\) −7.74587e137 −0.878693
\(540\) −3.71556e137 −0.383830
\(541\) 4.27854e136 0.0402563 0.0201282 0.999797i \(-0.493593\pi\)
0.0201282 + 0.999797i \(0.493593\pi\)
\(542\) −2.13030e138 −1.82590
\(543\) −1.30851e138 −1.02185
\(544\) −2.84938e138 −2.02771
\(545\) 1.10205e136 0.00714789
\(546\) 2.26312e138 1.33807
\(547\) 2.81194e138 1.51582 0.757908 0.652361i \(-0.226221\pi\)
0.757908 + 0.652361i \(0.226221\pi\)
\(548\) −3.95288e138 −1.94310
\(549\) −5.10073e137 −0.228680
\(550\) 4.79484e138 1.96091
\(551\) −1.91130e138 −0.713137
\(552\) 1.28841e138 0.438664
\(553\) 2.73529e138 0.849931
\(554\) 6.23240e138 1.76771
\(555\) 2.11676e138 0.548119
\(556\) −3.33828e138 −0.789308
\(557\) −4.55257e138 −0.983036 −0.491518 0.870867i \(-0.663558\pi\)
−0.491518 + 0.870867i \(0.663558\pi\)
\(558\) 1.56928e138 0.309509
\(559\) 3.83043e138 0.690163
\(560\) −1.12944e138 −0.185938
\(561\) −1.72691e139 −2.59803
\(562\) 1.83083e139 2.51747
\(563\) −1.09186e139 −1.37243 −0.686217 0.727397i \(-0.740730\pi\)
−0.686217 + 0.727397i \(0.740730\pi\)
\(564\) −5.50115e138 −0.632206
\(565\) 3.49705e137 0.0367499
\(566\) 8.76527e138 0.842433
\(567\) −9.20297e138 −0.809066
\(568\) −3.90215e137 −0.0313843
\(569\) 1.38183e139 1.01692 0.508460 0.861086i \(-0.330215\pi\)
0.508460 + 0.861086i \(0.330215\pi\)
\(570\) 6.95959e138 0.468709
\(571\) −1.25037e139 −0.770750 −0.385375 0.922760i \(-0.625928\pi\)
−0.385375 + 0.922760i \(0.625928\pi\)
\(572\) −4.02083e139 −2.26891
\(573\) 1.86099e139 0.961470
\(574\) 2.85096e139 1.34878
\(575\) 2.02057e139 0.875481
\(576\) −1.19486e139 −0.474221
\(577\) −4.89173e139 −1.77862 −0.889312 0.457301i \(-0.848816\pi\)
−0.889312 + 0.457301i \(0.848816\pi\)
\(578\) −4.80925e139 −1.60222
\(579\) 4.18068e139 1.27638
\(580\) 1.89351e139 0.529851
\(581\) −6.47009e138 −0.165965
\(582\) 3.22675e139 0.758849
\(583\) 1.16851e140 2.51983
\(584\) 1.75506e139 0.347091
\(585\) −8.70607e138 −0.157925
\(586\) −4.35745e139 −0.725109
\(587\) −3.73373e139 −0.570057 −0.285029 0.958519i \(-0.592003\pi\)
−0.285029 + 0.958519i \(0.592003\pi\)
\(588\) −5.76514e139 −0.807709
\(589\) 3.22109e139 0.414172
\(590\) 1.72207e139 0.203248
\(591\) 2.07516e139 0.224845
\(592\) −8.27521e139 −0.823252
\(593\) −8.44292e139 −0.771313 −0.385656 0.922642i \(-0.626025\pi\)
−0.385656 + 0.922642i \(0.626025\pi\)
\(594\) 2.14063e140 1.79609
\(595\) −4.96900e139 −0.382968
\(596\) −2.75055e140 −1.94753
\(597\) 1.73293e140 1.12740
\(598\) −3.05797e140 −1.82820
\(599\) −1.37418e140 −0.755074 −0.377537 0.925995i \(-0.623229\pi\)
−0.377537 + 0.925995i \(0.623229\pi\)
\(600\) 6.96781e139 0.351932
\(601\) −2.04647e140 −0.950264 −0.475132 0.879914i \(-0.657600\pi\)
−0.475132 + 0.879914i \(0.657600\pi\)
\(602\) 1.37027e140 0.585038
\(603\) 8.74364e139 0.343295
\(604\) 5.74469e140 2.07444
\(605\) 1.74580e140 0.579892
\(606\) 6.57145e140 2.00814
\(607\) −1.81132e140 −0.509292 −0.254646 0.967034i \(-0.581959\pi\)
−0.254646 + 0.967034i \(0.581959\pi\)
\(608\) −3.66577e140 −0.948493
\(609\) 3.40219e140 0.810188
\(610\) 1.87194e140 0.410331
\(611\) 2.54925e140 0.514436
\(612\) −3.23130e140 −0.600386
\(613\) −5.22003e139 −0.0893139 −0.0446570 0.999002i \(-0.514219\pi\)
−0.0446570 + 0.999002i \(0.514219\pi\)
\(614\) −1.19112e141 −1.87696
\(615\) −4.36254e140 −0.633207
\(616\) −2.80839e140 −0.375518
\(617\) 4.53230e140 0.558365 0.279182 0.960238i \(-0.409937\pi\)
0.279182 + 0.960238i \(0.409937\pi\)
\(618\) −1.81808e141 −2.06393
\(619\) 4.58319e140 0.479502 0.239751 0.970834i \(-0.422934\pi\)
0.239751 + 0.970834i \(0.422934\pi\)
\(620\) −3.19111e140 −0.307724
\(621\) 9.02072e140 0.801891
\(622\) 2.89511e141 2.37274
\(623\) −1.44309e141 −1.09055
\(624\) 1.35383e141 0.943498
\(625\) 8.40829e140 0.540464
\(626\) −1.17779e141 −0.698334
\(627\) −2.22169e141 −1.21527
\(628\) 2.04614e141 1.03270
\(629\) −3.64070e141 −1.69562
\(630\) −3.11445e140 −0.133870
\(631\) 1.90514e140 0.0755866 0.0377933 0.999286i \(-0.487967\pi\)
0.0377933 + 0.999286i \(0.487967\pi\)
\(632\) −1.27454e141 −0.466809
\(633\) −4.72213e140 −0.159680
\(634\) 7.34350e141 2.29296
\(635\) −1.68876e141 −0.486962
\(636\) 8.69708e141 2.31627
\(637\) 2.67159e141 0.657246
\(638\) −1.09090e142 −2.47937
\(639\) 1.38143e140 0.0290092
\(640\) 1.46247e141 0.283792
\(641\) −2.72348e141 −0.488421 −0.244210 0.969722i \(-0.578529\pi\)
−0.244210 + 0.969722i \(0.578529\pi\)
\(642\) 7.18457e141 1.19092
\(643\) 5.31375e141 0.814230 0.407115 0.913377i \(-0.366535\pi\)
0.407115 + 0.913377i \(0.366535\pi\)
\(644\) −6.06141e141 −0.858691
\(645\) −2.09679e141 −0.274656
\(646\) −1.19701e142 −1.44996
\(647\) 6.34797e140 0.0711162 0.0355581 0.999368i \(-0.488679\pi\)
0.0355581 + 0.999368i \(0.488679\pi\)
\(648\) 4.28822e141 0.444365
\(649\) −5.49734e141 −0.526981
\(650\) −1.65377e142 −1.46673
\(651\) −5.73367e141 −0.470536
\(652\) −7.50826e141 −0.570211
\(653\) 1.11233e142 0.781837 0.390919 0.920425i \(-0.372157\pi\)
0.390919 + 0.920425i \(0.372157\pi\)
\(654\) −4.72563e140 −0.0307456
\(655\) 1.18304e142 0.712547
\(656\) 1.70548e142 0.951050
\(657\) −6.21322e141 −0.320823
\(658\) 9.11951e141 0.436078
\(659\) 2.40144e142 1.06355 0.531776 0.846885i \(-0.321525\pi\)
0.531776 + 0.846885i \(0.321525\pi\)
\(660\) 2.20101e142 0.902930
\(661\) 2.18550e142 0.830571 0.415285 0.909691i \(-0.363682\pi\)
0.415285 + 0.909691i \(0.363682\pi\)
\(662\) −6.94494e142 −2.44535
\(663\) 5.95619e142 1.94328
\(664\) 3.01481e141 0.0911531
\(665\) −6.39269e141 −0.179139
\(666\) −2.28190e142 −0.592719
\(667\) −4.59711e142 −1.10695
\(668\) 4.77285e142 1.06553
\(669\) −1.01819e142 −0.210771
\(670\) −3.20886e142 −0.615990
\(671\) −5.97574e142 −1.06391
\(672\) 6.52521e142 1.07757
\(673\) −3.76621e142 −0.576958 −0.288479 0.957486i \(-0.593150\pi\)
−0.288479 + 0.957486i \(0.593150\pi\)
\(674\) −1.83457e143 −2.60742
\(675\) 4.87846e142 0.643342
\(676\) 3.71387e142 0.454483
\(677\) 9.42279e142 1.07017 0.535084 0.844799i \(-0.320280\pi\)
0.535084 + 0.844799i \(0.320280\pi\)
\(678\) −1.49955e142 −0.158074
\(679\) −2.96392e142 −0.290030
\(680\) 2.31536e142 0.210338
\(681\) −1.02200e143 −0.862032
\(682\) 1.83848e143 1.43995
\(683\) 1.77484e143 1.29096 0.645481 0.763777i \(-0.276657\pi\)
0.645481 + 0.763777i \(0.276657\pi\)
\(684\) −4.15712e142 −0.280840
\(685\) −1.00272e143 −0.629225
\(686\) 2.65508e143 1.54778
\(687\) −1.03866e143 −0.562544
\(688\) 8.19715e142 0.412522
\(689\) −4.03026e143 −1.88479
\(690\) 1.67394e143 0.727546
\(691\) −2.13672e143 −0.863190 −0.431595 0.902068i \(-0.642049\pi\)
−0.431595 + 0.902068i \(0.642049\pi\)
\(692\) 2.67236e141 0.0100355
\(693\) 9.94218e142 0.347099
\(694\) −1.20563e143 −0.391345
\(695\) −8.46817e142 −0.255598
\(696\) −1.58529e143 −0.444981
\(697\) 7.50332e143 1.95884
\(698\) 8.37459e143 2.03360
\(699\) 2.07228e143 0.468114
\(700\) −3.27804e143 −0.688912
\(701\) −1.00021e143 −0.195582 −0.0977912 0.995207i \(-0.531178\pi\)
−0.0977912 + 0.995207i \(0.531178\pi\)
\(702\) −7.38315e143 −1.34344
\(703\) −4.68382e143 −0.793151
\(704\) −1.39983e144 −2.20626
\(705\) −1.39547e143 −0.204724
\(706\) 1.24171e143 0.169583
\(707\) −6.03617e143 −0.767504
\(708\) −4.09159e143 −0.484410
\(709\) 1.19635e144 1.31893 0.659466 0.751735i \(-0.270783\pi\)
0.659466 + 0.751735i \(0.270783\pi\)
\(710\) −5.06976e142 −0.0520524
\(711\) 4.51208e143 0.431482
\(712\) 6.72422e143 0.598966
\(713\) 7.74744e143 0.642891
\(714\) 2.13073e144 1.64728
\(715\) −1.01996e144 −0.734728
\(716\) 2.42843e144 1.63012
\(717\) −1.05584e144 −0.660511
\(718\) −4.37313e143 −0.254981
\(719\) 6.63155e143 0.360418 0.180209 0.983628i \(-0.442323\pi\)
0.180209 + 0.983628i \(0.442323\pi\)
\(720\) −1.86310e143 −0.0943944
\(721\) 1.66999e144 0.788828
\(722\) 1.86024e144 0.819295
\(723\) −2.75066e144 −1.12967
\(724\) −2.86844e144 −1.09862
\(725\) −2.48614e144 −0.888089
\(726\) −7.48604e144 −2.49432
\(727\) 2.70060e144 0.839407 0.419704 0.907661i \(-0.362134\pi\)
0.419704 + 0.907661i \(0.362134\pi\)
\(728\) 9.68626e143 0.280880
\(729\) 1.76111e144 0.476483
\(730\) 2.28022e144 0.575667
\(731\) 3.60636e144 0.849653
\(732\) −4.44766e144 −0.977962
\(733\) −7.92252e144 −1.62597 −0.812985 0.582284i \(-0.802159\pi\)
−0.812985 + 0.582284i \(0.802159\pi\)
\(734\) 5.09564e144 0.976220
\(735\) −1.46243e144 −0.261556
\(736\) −8.81699e144 −1.47228
\(737\) 1.02436e145 1.59714
\(738\) 4.70290e144 0.684730
\(739\) 4.09564e144 0.556900 0.278450 0.960451i \(-0.410179\pi\)
0.278450 + 0.960451i \(0.410179\pi\)
\(740\) 4.64022e144 0.589300
\(741\) 7.66273e144 0.909000
\(742\) −1.44176e145 −1.59770
\(743\) 1.16041e145 1.20136 0.600682 0.799488i \(-0.294896\pi\)
0.600682 + 0.799488i \(0.294896\pi\)
\(744\) 2.67166e144 0.258433
\(745\) −6.97728e144 −0.630658
\(746\) 1.43130e145 1.20898
\(747\) −1.06730e144 −0.0842547
\(748\) −3.78562e145 −2.79323
\(749\) −6.59935e144 −0.455166
\(750\) 1.98545e145 1.28016
\(751\) 1.16350e144 0.0701371 0.0350686 0.999385i \(-0.488835\pi\)
0.0350686 + 0.999385i \(0.488835\pi\)
\(752\) 5.45541e144 0.307487
\(753\) −1.89270e145 −0.997552
\(754\) 3.76258e145 1.85452
\(755\) 1.45725e145 0.671756
\(756\) −1.46347e145 −0.631004
\(757\) −5.51960e144 −0.222621 −0.111310 0.993786i \(-0.535505\pi\)
−0.111310 + 0.993786i \(0.535505\pi\)
\(758\) −3.98447e144 −0.150340
\(759\) −5.34367e145 −1.88638
\(760\) 2.97874e144 0.0983890
\(761\) −5.40410e145 −1.67031 −0.835157 0.550011i \(-0.814623\pi\)
−0.835157 + 0.550011i \(0.814623\pi\)
\(762\) 7.24148e145 2.09460
\(763\) 4.34070e143 0.0117509
\(764\) 4.07954e145 1.03371
\(765\) −8.19678e144 −0.194420
\(766\) −9.88822e145 −2.19566
\(767\) 1.89606e145 0.394172
\(768\) 2.11339e145 0.411374
\(769\) 2.96750e145 0.540891 0.270446 0.962735i \(-0.412829\pi\)
0.270446 + 0.962735i \(0.412829\pi\)
\(770\) −3.64872e145 −0.622815
\(771\) −4.91245e145 −0.785330
\(772\) 9.16461e145 1.37227
\(773\) 9.98016e144 0.139982 0.0699911 0.997548i \(-0.477703\pi\)
0.0699911 + 0.997548i \(0.477703\pi\)
\(774\) 2.26038e145 0.297004
\(775\) 4.18986e145 0.515779
\(776\) 1.38107e145 0.159294
\(777\) 8.33738e145 0.901090
\(778\) 1.65089e146 1.67204
\(779\) 9.65313e145 0.916276
\(780\) −7.59140e145 −0.675374
\(781\) 1.61841e145 0.134962
\(782\) −2.87908e146 −2.25067
\(783\) −1.10993e146 −0.813439
\(784\) 5.71721e145 0.392847
\(785\) 5.19040e145 0.334413
\(786\) −5.07292e146 −3.06492
\(787\) −1.20626e146 −0.683465 −0.341732 0.939797i \(-0.611014\pi\)
−0.341732 + 0.939797i \(0.611014\pi\)
\(788\) 4.54902e145 0.241738
\(789\) 6.75918e145 0.336903
\(790\) −1.65591e146 −0.774227
\(791\) 1.37740e145 0.0604156
\(792\) −4.63267e145 −0.190638
\(793\) 2.06106e146 0.795784
\(794\) 2.11315e146 0.765587
\(795\) 2.20617e146 0.750066
\(796\) 3.79881e146 1.21210
\(797\) 2.00327e146 0.599921 0.299961 0.953952i \(-0.403026\pi\)
0.299961 + 0.953952i \(0.403026\pi\)
\(798\) 2.74121e146 0.770542
\(799\) 2.40012e146 0.633317
\(800\) −4.76828e146 −1.18118
\(801\) −2.38049e146 −0.553637
\(802\) 1.48096e145 0.0323398
\(803\) −7.27908e146 −1.49259
\(804\) 7.62416e146 1.46812
\(805\) −1.53759e146 −0.278066
\(806\) −6.34102e146 −1.07706
\(807\) 4.99765e145 0.0797357
\(808\) 2.81262e146 0.421538
\(809\) 2.46422e145 0.0346960 0.0173480 0.999850i \(-0.494478\pi\)
0.0173480 + 0.999850i \(0.494478\pi\)
\(810\) 5.57136e146 0.737001
\(811\) −4.96232e146 −0.616781 −0.308391 0.951260i \(-0.599790\pi\)
−0.308391 + 0.951260i \(0.599790\pi\)
\(812\) 7.45807e146 0.871058
\(813\) 1.28395e147 1.40921
\(814\) −2.67336e147 −2.75756
\(815\) −1.90461e146 −0.184649
\(816\) 1.27463e147 1.16153
\(817\) 4.63963e146 0.397438
\(818\) −2.47880e147 −1.99618
\(819\) −3.42911e146 −0.259624
\(820\) −9.56327e146 −0.680780
\(821\) −2.07513e147 −1.38904 −0.694522 0.719472i \(-0.744384\pi\)
−0.694522 + 0.719472i \(0.744384\pi\)
\(822\) 4.29970e147 2.70652
\(823\) 2.08912e147 1.23672 0.618361 0.785894i \(-0.287797\pi\)
0.618361 + 0.785894i \(0.287797\pi\)
\(824\) −7.78148e146 −0.433249
\(825\) −2.88989e147 −1.51341
\(826\) 6.78283e146 0.334132
\(827\) 3.48507e147 1.61504 0.807521 0.589839i \(-0.200809\pi\)
0.807521 + 0.589839i \(0.200809\pi\)
\(828\) −9.99880e146 −0.435929
\(829\) −3.30518e147 −1.35579 −0.677894 0.735160i \(-0.737107\pi\)
−0.677894 + 0.735160i \(0.737107\pi\)
\(830\) 3.91691e146 0.151182
\(831\) −3.75631e147 −1.36430
\(832\) 4.82809e147 1.65024
\(833\) 2.51530e147 0.809129
\(834\) 3.63118e147 1.09942
\(835\) 1.21072e147 0.345046
\(836\) −4.87025e147 −1.30658
\(837\) 1.87054e147 0.472424
\(838\) 3.30323e147 0.785445
\(839\) 4.20113e147 0.940561 0.470281 0.882517i \(-0.344153\pi\)
0.470281 + 0.882517i \(0.344153\pi\)
\(840\) −5.30228e146 −0.111779
\(841\) 6.19065e146 0.122896
\(842\) −3.14692e147 −0.588336
\(843\) −1.10346e148 −1.94295
\(844\) −1.03516e147 −0.171677
\(845\) 9.42090e146 0.147173
\(846\) 1.50434e147 0.221382
\(847\) 6.87626e147 0.953323
\(848\) −8.62477e147 −1.12657
\(849\) −5.28289e147 −0.650180
\(850\) −1.55702e148 −1.80567
\(851\) −1.12656e148 −1.23115
\(852\) 1.20456e147 0.124059
\(853\) 1.14274e148 1.10923 0.554614 0.832108i \(-0.312866\pi\)
0.554614 + 0.832108i \(0.312866\pi\)
\(854\) 7.37310e147 0.674571
\(855\) −1.05453e147 −0.0909430
\(856\) 3.07504e147 0.249991
\(857\) −1.25430e148 −0.961328 −0.480664 0.876905i \(-0.659604\pi\)
−0.480664 + 0.876905i \(0.659604\pi\)
\(858\) 4.37362e148 3.16033
\(859\) 2.03083e148 1.38362 0.691812 0.722078i \(-0.256813\pi\)
0.691812 + 0.722078i \(0.256813\pi\)
\(860\) −4.59645e147 −0.295291
\(861\) −1.71830e148 −1.04097
\(862\) 3.52056e148 2.01138
\(863\) 8.95017e147 0.482266 0.241133 0.970492i \(-0.422481\pi\)
0.241133 + 0.970492i \(0.422481\pi\)
\(864\) −2.12877e148 −1.08190
\(865\) 6.77894e145 0.00324974
\(866\) −5.71545e148 −2.58462
\(867\) 2.89857e148 1.23657
\(868\) −1.25690e148 −0.505888
\(869\) 5.28612e148 2.00742
\(870\) −2.05964e148 −0.738023
\(871\) −3.53306e148 −1.19463
\(872\) −2.02260e146 −0.00645397
\(873\) −4.88923e147 −0.147238
\(874\) −3.70398e148 −1.05279
\(875\) −1.82372e148 −0.489274
\(876\) −5.41772e148 −1.37202
\(877\) 2.88741e148 0.690285 0.345142 0.938550i \(-0.387831\pi\)
0.345142 + 0.938550i \(0.387831\pi\)
\(878\) 4.30994e148 0.972744
\(879\) 2.62627e148 0.559630
\(880\) −2.18271e148 −0.439159
\(881\) 6.06187e148 1.15166 0.575828 0.817571i \(-0.304680\pi\)
0.575828 + 0.817571i \(0.304680\pi\)
\(882\) 1.57653e148 0.282839
\(883\) −1.10147e148 −0.186619 −0.0933097 0.995637i \(-0.529745\pi\)
−0.0933097 + 0.995637i \(0.529745\pi\)
\(884\) 1.30568e149 2.08928
\(885\) −1.03791e148 −0.156864
\(886\) −1.37563e149 −1.96380
\(887\) −4.72512e148 −0.637192 −0.318596 0.947891i \(-0.603211\pi\)
−0.318596 + 0.947891i \(0.603211\pi\)
\(888\) −3.88489e148 −0.494908
\(889\) −6.65162e148 −0.800550
\(890\) 8.73627e148 0.993415
\(891\) −1.77853e149 −1.91090
\(892\) −2.23201e148 −0.226606
\(893\) 3.08779e148 0.296244
\(894\) 2.99188e149 2.71269
\(895\) 6.16016e148 0.527872
\(896\) 5.76033e148 0.466544
\(897\) 1.84306e149 1.41098
\(898\) 4.74784e148 0.343590
\(899\) −9.53260e148 −0.652149
\(900\) −5.40741e148 −0.349738
\(901\) −3.79449e149 −2.32034
\(902\) 5.50966e149 3.18563
\(903\) −8.25874e148 −0.451525
\(904\) −6.41816e147 −0.0331822
\(905\) −7.27632e148 −0.355761
\(906\) −6.24872e149 −2.88946
\(907\) 1.12427e149 0.491703 0.245852 0.969307i \(-0.420932\pi\)
0.245852 + 0.969307i \(0.420932\pi\)
\(908\) −2.24037e149 −0.926797
\(909\) −9.95716e148 −0.389636
\(910\) 1.25846e149 0.465854
\(911\) 4.17428e148 0.146185 0.0730926 0.997325i \(-0.476713\pi\)
0.0730926 + 0.997325i \(0.476713\pi\)
\(912\) 1.63983e149 0.543324
\(913\) −1.25039e149 −0.391985
\(914\) −8.67937e148 −0.257457
\(915\) −1.12823e149 −0.316689
\(916\) −2.27688e149 −0.604809
\(917\) 4.65970e149 1.17140
\(918\) −6.95125e149 −1.65389
\(919\) 8.30867e149 1.87111 0.935553 0.353186i \(-0.114902\pi\)
0.935553 + 0.353186i \(0.114902\pi\)
\(920\) 7.16454e148 0.152723
\(921\) 7.17899e149 1.44861
\(922\) −1.90564e149 −0.364024
\(923\) −5.58197e148 −0.100949
\(924\) 8.66925e149 1.48439
\(925\) −6.09252e149 −0.987732
\(926\) −7.37612e149 −1.13233
\(927\) 2.75478e149 0.400461
\(928\) 1.08486e150 1.49348
\(929\) 7.17354e149 0.935277 0.467638 0.883920i \(-0.345105\pi\)
0.467638 + 0.883920i \(0.345105\pi\)
\(930\) 3.47109e149 0.428625
\(931\) 3.23597e149 0.378483
\(932\) 4.54272e149 0.503284
\(933\) −1.74490e150 −1.83125
\(934\) −1.56463e150 −1.55558
\(935\) −9.60291e149 −0.904517
\(936\) 1.59783e149 0.142594
\(937\) −1.12560e150 −0.951774 −0.475887 0.879507i \(-0.657873\pi\)
−0.475887 + 0.879507i \(0.657873\pi\)
\(938\) −1.26389e150 −1.01267
\(939\) 7.09861e149 0.538966
\(940\) −3.05905e149 −0.220105
\(941\) 8.61109e149 0.587195 0.293597 0.955929i \(-0.405147\pi\)
0.293597 + 0.955929i \(0.405147\pi\)
\(942\) −2.22566e150 −1.43843
\(943\) 2.32179e150 1.42227
\(944\) 4.05758e149 0.235603
\(945\) −3.71235e149 −0.204335
\(946\) 2.64814e150 1.38178
\(947\) −1.36513e150 −0.675307 −0.337654 0.941270i \(-0.609633\pi\)
−0.337654 + 0.941270i \(0.609633\pi\)
\(948\) 3.93438e150 1.84525
\(949\) 2.51059e150 1.11643
\(950\) −2.00313e150 −0.844632
\(951\) −4.42598e150 −1.76968
\(952\) 9.11963e149 0.345789
\(953\) 4.18075e149 0.150336 0.0751680 0.997171i \(-0.476051\pi\)
0.0751680 + 0.997171i \(0.476051\pi\)
\(954\) −2.37830e150 −0.811098
\(955\) 1.03485e150 0.334740
\(956\) −2.31454e150 −0.710135
\(957\) 6.57495e150 1.91355
\(958\) 1.75810e150 0.485383
\(959\) −3.94947e150 −1.03442
\(960\) −2.64291e150 −0.656726
\(961\) −2.63510e150 −0.621249
\(962\) 9.22054e150 2.06260
\(963\) −1.08862e150 −0.231072
\(964\) −6.02982e150 −1.21455
\(965\) 2.32477e150 0.444376
\(966\) 6.59323e150 1.19606
\(967\) −1.04342e150 −0.179648 −0.0898238 0.995958i \(-0.528630\pi\)
−0.0898238 + 0.995958i \(0.528630\pi\)
\(968\) −3.20407e150 −0.523595
\(969\) 7.21447e150 1.11906
\(970\) 1.79432e150 0.264196
\(971\) −3.53326e150 −0.493861 −0.246930 0.969033i \(-0.579422\pi\)
−0.246930 + 0.969033i \(0.579422\pi\)
\(972\) −6.04888e150 −0.802655
\(973\) −3.33540e150 −0.420194
\(974\) −1.45067e151 −1.73517
\(975\) 9.96737e150 1.13200
\(976\) 4.41068e150 0.475653
\(977\) −1.53694e151 −1.57392 −0.786960 0.617004i \(-0.788346\pi\)
−0.786960 + 0.617004i \(0.788346\pi\)
\(978\) 8.16702e150 0.794240
\(979\) −2.78886e151 −2.57573
\(980\) −3.20585e150 −0.281207
\(981\) 7.16035e148 0.00596554
\(982\) 1.00772e151 0.797460
\(983\) 9.55031e150 0.717901 0.358951 0.933357i \(-0.383135\pi\)
0.358951 + 0.933357i \(0.383135\pi\)
\(984\) 8.00658e150 0.571735
\(985\) 1.15394e150 0.0782807
\(986\) 3.54247e151 2.28309
\(987\) −5.49640e150 −0.336560
\(988\) 1.67977e151 0.977294
\(989\) 1.11594e151 0.616917
\(990\) −6.01887e150 −0.316182
\(991\) −5.87889e150 −0.293478 −0.146739 0.989175i \(-0.546878\pi\)
−0.146739 + 0.989175i \(0.546878\pi\)
\(992\) −1.82830e151 −0.867376
\(993\) 4.18577e151 1.88729
\(994\) −1.99685e150 −0.0855725
\(995\) 9.63637e150 0.392507
\(996\) −9.30646e150 −0.360320
\(997\) −3.59519e150 −0.132317 −0.0661586 0.997809i \(-0.521074\pi\)
−0.0661586 + 0.997809i \(0.521074\pi\)
\(998\) −4.29120e151 −1.50137
\(999\) −2.71997e151 −0.904706
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 1.102.a.a.1.2 8
3.2 odd 2 9.102.a.b.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.2 8 1.1 even 1 trivial
9.102.a.b.1.7 8 3.2 odd 2