Properties

Label 1.106.a.a.1.8
Level 1
Weight 106
Character 1.1
Self dual yes
Analytic conductor 69.819
Analytic rank 1
Dimension 8
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 106 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(69.8187388595\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(10\!\cdots\!04\)\( x^{6} - \)\(62\!\cdots\!96\)\( x^{5} + \)\(32\!\cdots\!36\)\( x^{4} - \)\(88\!\cdots\!20\)\( x^{3} - \)\(32\!\cdots\!00\)\( x^{2} + \)\(21\!\cdots\!00\)\( x + \)\(48\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(7.96777e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.03267e16 q^{2} -2.77402e24 q^{3} +6.60762e31 q^{4} -1.38808e36 q^{5} -2.86465e40 q^{6} -3.04428e43 q^{7} +2.63449e47 q^{8} -1.17542e50 q^{9} +O(q^{10})\) \(q+1.03267e16 q^{2} -2.77402e24 q^{3} +6.60762e31 q^{4} -1.38808e36 q^{5} -2.86465e40 q^{6} -3.04428e43 q^{7} +2.63449e47 q^{8} -1.17542e50 q^{9} -1.43343e52 q^{10} +4.98478e54 q^{11} -1.83297e56 q^{12} +2.40158e58 q^{13} -3.14374e59 q^{14} +3.85057e60 q^{15} +4.01897e61 q^{16} -3.48835e64 q^{17} -1.21382e66 q^{18} -1.66529e67 q^{19} -9.17192e67 q^{20} +8.44489e67 q^{21} +5.14764e70 q^{22} -2.46240e70 q^{23} -7.30812e71 q^{24} -2.27251e73 q^{25} +2.48005e74 q^{26} +6.73472e74 q^{27} -2.01154e75 q^{28} -7.76434e76 q^{29} +3.97637e76 q^{30} +1.96420e78 q^{31} -1.02717e79 q^{32} -1.38279e79 q^{33} -3.60231e80 q^{34} +4.22571e79 q^{35} -7.76670e81 q^{36} -3.69942e82 q^{37} -1.71969e83 q^{38} -6.66204e82 q^{39} -3.65688e83 q^{40} -4.85828e84 q^{41} +8.72080e83 q^{42} +9.79144e85 q^{43} +3.29376e86 q^{44} +1.63157e86 q^{45} -2.54285e86 q^{46} -3.79881e87 q^{47} -1.11487e86 q^{48} -5.34351e88 q^{49} -2.34676e89 q^{50} +9.67674e88 q^{51} +1.58687e90 q^{52} +1.90979e90 q^{53} +6.95475e90 q^{54} -6.91929e90 q^{55} -8.02011e90 q^{56} +4.61954e91 q^{57} -8.01801e92 q^{58} -2.84039e92 q^{59} +2.54431e92 q^{60} +3.64939e93 q^{61} +2.02837e94 q^{62} +3.57829e93 q^{63} -1.07703e95 q^{64} -3.33360e94 q^{65} -1.42797e95 q^{66} -4.96150e95 q^{67} -2.30497e96 q^{68} +6.83075e94 q^{69} +4.36377e95 q^{70} +1.33111e97 q^{71} -3.09662e97 q^{72} -8.83827e97 q^{73} -3.82028e98 q^{74} +6.30400e97 q^{75} -1.10036e99 q^{76} -1.51751e98 q^{77} -6.87970e98 q^{78} -1.15100e99 q^{79} -5.57867e97 q^{80} +1.28523e100 q^{81} -5.01700e100 q^{82} -5.00947e100 q^{83} +5.58006e99 q^{84} +4.84211e100 q^{85} +1.01113e102 q^{86} +2.15384e101 q^{87} +1.31323e102 q^{88} +6.61147e101 q^{89} +1.68488e102 q^{90} -7.31109e101 q^{91} -1.62706e102 q^{92} -5.44873e102 q^{93} -3.92292e103 q^{94} +2.31155e103 q^{95} +2.84940e103 q^{96} +1.82524e104 q^{97} -5.51809e104 q^{98} -5.85919e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.03267e16 1.62139 0.810695 0.585469i \(-0.199090\pi\)
0.810695 + 0.585469i \(0.199090\pi\)
\(3\) −2.77402e24 −0.247881 −0.123941 0.992290i \(-0.539553\pi\)
−0.123941 + 0.992290i \(0.539553\pi\)
\(4\) 6.60762e31 1.62890
\(5\) −1.38808e36 −0.279570 −0.139785 0.990182i \(-0.544641\pi\)
−0.139785 + 0.990182i \(0.544641\pi\)
\(6\) −2.86465e40 −0.401912
\(7\) −3.04428e43 −0.130568 −0.0652841 0.997867i \(-0.520795\pi\)
−0.0652841 + 0.997867i \(0.520795\pi\)
\(8\) 2.63449e47 1.01970
\(9\) −1.17542e50 −0.938555
\(10\) −1.43343e52 −0.453291
\(11\) 4.98478e54 1.05811 0.529055 0.848588i \(-0.322547\pi\)
0.529055 + 0.848588i \(0.322547\pi\)
\(12\) −1.83297e56 −0.403775
\(13\) 2.40158e58 0.791538 0.395769 0.918350i \(-0.370478\pi\)
0.395769 + 0.918350i \(0.370478\pi\)
\(14\) −3.14374e59 −0.211702
\(15\) 3.85057e60 0.0693001
\(16\) 4.01897e61 0.0244240
\(17\) −3.48835e64 −0.879126 −0.439563 0.898212i \(-0.644867\pi\)
−0.439563 + 0.898212i \(0.644867\pi\)
\(18\) −1.21382e66 −1.52176
\(19\) −1.66529e67 −1.22159 −0.610794 0.791789i \(-0.709150\pi\)
−0.610794 + 0.791789i \(0.709150\pi\)
\(20\) −9.17192e67 −0.455392
\(21\) 8.44489e67 0.0323654
\(22\) 5.14764e70 1.71561
\(23\) −2.46240e70 −0.0795513 −0.0397757 0.999209i \(-0.512664\pi\)
−0.0397757 + 0.999209i \(0.512664\pi\)
\(24\) −7.30812e71 −0.252764
\(25\) −2.27251e73 −0.921841
\(26\) 2.48005e74 1.28339
\(27\) 6.73472e74 0.480532
\(28\) −2.01154e75 −0.212683
\(29\) −7.76434e76 −1.30080 −0.650399 0.759593i \(-0.725398\pi\)
−0.650399 + 0.759593i \(0.725398\pi\)
\(30\) 3.97637e76 0.112362
\(31\) 1.96420e78 0.992422 0.496211 0.868202i \(-0.334724\pi\)
0.496211 + 0.868202i \(0.334724\pi\)
\(32\) −1.02717e79 −0.980097
\(33\) −1.38279e79 −0.262286
\(34\) −3.60231e80 −1.42541
\(35\) 4.22571e79 0.0365029
\(36\) −7.76670e81 −1.52882
\(37\) −3.69942e82 −1.72800 −0.863998 0.503494i \(-0.832047\pi\)
−0.863998 + 0.503494i \(0.832047\pi\)
\(38\) −1.71969e83 −1.98067
\(39\) −6.66204e82 −0.196207
\(40\) −3.65688e83 −0.285077
\(41\) −4.85828e84 −1.03593 −0.517964 0.855402i \(-0.673310\pi\)
−0.517964 + 0.855402i \(0.673310\pi\)
\(42\) 8.72080e83 0.0524769
\(43\) 9.79144e85 1.71298 0.856491 0.516162i \(-0.172640\pi\)
0.856491 + 0.516162i \(0.172640\pi\)
\(44\) 3.29376e86 1.72356
\(45\) 1.63157e86 0.262391
\(46\) −2.54285e86 −0.128984
\(47\) −3.79881e87 −0.623031 −0.311516 0.950241i \(-0.600837\pi\)
−0.311516 + 0.950241i \(0.600837\pi\)
\(48\) −1.11487e86 −0.00605424
\(49\) −5.34351e88 −0.982952
\(50\) −2.34676e89 −1.49466
\(51\) 9.67674e88 0.217919
\(52\) 1.58687e90 1.28934
\(53\) 1.90979e90 0.570823 0.285412 0.958405i \(-0.407870\pi\)
0.285412 + 0.958405i \(0.407870\pi\)
\(54\) 6.95475e90 0.779129
\(55\) −6.91929e90 −0.295815
\(56\) −8.02011e90 −0.133140
\(57\) 4.61954e91 0.302809
\(58\) −8.01801e92 −2.10910
\(59\) −2.84039e92 −0.304542 −0.152271 0.988339i \(-0.548659\pi\)
−0.152271 + 0.988339i \(0.548659\pi\)
\(60\) 2.54431e92 0.112883
\(61\) 3.64939e93 0.679835 0.339917 0.940455i \(-0.389601\pi\)
0.339917 + 0.940455i \(0.389601\pi\)
\(62\) 2.02837e94 1.60910
\(63\) 3.57829e93 0.122545
\(64\) −1.07703e95 −1.61354
\(65\) −3.33360e94 −0.221290
\(66\) −1.42797e95 −0.425267
\(67\) −4.96150e95 −0.670944 −0.335472 0.942050i \(-0.608896\pi\)
−0.335472 + 0.942050i \(0.608896\pi\)
\(68\) −2.30497e96 −1.43201
\(69\) 6.83075e94 0.0197193
\(70\) 4.36377e95 0.0591854
\(71\) 1.33111e97 0.857336 0.428668 0.903462i \(-0.358983\pi\)
0.428668 + 0.903462i \(0.358983\pi\)
\(72\) −3.09662e97 −0.957043
\(73\) −8.83827e97 −1.32409 −0.662044 0.749465i \(-0.730311\pi\)
−0.662044 + 0.749465i \(0.730311\pi\)
\(74\) −3.82028e98 −2.80176
\(75\) 6.30400e97 0.228507
\(76\) −1.10036e99 −1.98985
\(77\) −1.51751e98 −0.138155
\(78\) −6.87970e98 −0.318129
\(79\) −1.15100e99 −0.272679 −0.136340 0.990662i \(-0.543534\pi\)
−0.136340 + 0.990662i \(0.543534\pi\)
\(80\) −5.57867e97 −0.00682820
\(81\) 1.28523e100 0.819440
\(82\) −5.01700e100 −1.67964
\(83\) −5.00947e100 −0.887548 −0.443774 0.896139i \(-0.646361\pi\)
−0.443774 + 0.896139i \(0.646361\pi\)
\(84\) 5.58006e99 0.0527201
\(85\) 4.84211e100 0.245777
\(86\) 1.01113e102 2.77741
\(87\) 2.15384e101 0.322443
\(88\) 1.31323e102 1.07895
\(89\) 6.61147e101 0.300139 0.150070 0.988675i \(-0.452050\pi\)
0.150070 + 0.988675i \(0.452050\pi\)
\(90\) 1.68488e102 0.425439
\(91\) −7.31109e101 −0.103350
\(92\) −1.62706e102 −0.129581
\(93\) −5.44873e102 −0.246003
\(94\) −3.92292e103 −1.01018
\(95\) 2.31155e103 0.341519
\(96\) 2.84940e103 0.242948
\(97\) 1.82524e104 0.903239 0.451620 0.892211i \(-0.350846\pi\)
0.451620 + 0.892211i \(0.350846\pi\)
\(98\) −5.51809e104 −1.59375
\(99\) −5.85919e104 −0.993093
\(100\) −1.50159e105 −1.50159
\(101\) −1.19154e105 −0.706705 −0.353353 0.935490i \(-0.614958\pi\)
−0.353353 + 0.935490i \(0.614958\pi\)
\(102\) 9.99290e104 0.353332
\(103\) 5.84658e105 1.23865 0.619324 0.785136i \(-0.287407\pi\)
0.619324 + 0.785136i \(0.287407\pi\)
\(104\) 6.32694e105 0.807130
\(105\) −1.17222e104 −0.00904839
\(106\) 1.97218e106 0.925527
\(107\) 3.82326e106 1.09594 0.547969 0.836499i \(-0.315401\pi\)
0.547969 + 0.836499i \(0.315401\pi\)
\(108\) 4.45005e106 0.782740
\(109\) −1.46820e107 −1.59183 −0.795913 0.605411i \(-0.793009\pi\)
−0.795913 + 0.605411i \(0.793009\pi\)
\(110\) −7.14536e106 −0.479632
\(111\) 1.02623e107 0.428338
\(112\) −1.22349e105 −0.00318899
\(113\) 1.89904e107 0.310396 0.155198 0.987883i \(-0.450399\pi\)
0.155198 + 0.987883i \(0.450399\pi\)
\(114\) 4.77047e107 0.490971
\(115\) 3.41802e106 0.0222401
\(116\) −5.13038e108 −2.11887
\(117\) −2.82286e108 −0.742902
\(118\) −2.93319e108 −0.493782
\(119\) 1.06195e108 0.114786
\(120\) 1.01443e108 0.0706652
\(121\) 2.65426e108 0.119595
\(122\) 3.76862e109 1.10228
\(123\) 1.34770e109 0.256787
\(124\) 1.29787e110 1.61656
\(125\) 6.57632e109 0.537288
\(126\) 3.69520e109 0.198694
\(127\) −1.05260e110 −0.373739 −0.186869 0.982385i \(-0.559834\pi\)
−0.186869 + 0.982385i \(0.559834\pi\)
\(128\) −6.95552e110 −1.63609
\(129\) −2.71617e110 −0.424616
\(130\) −3.44251e110 −0.358797
\(131\) 2.13428e111 1.48768 0.743838 0.668360i \(-0.233003\pi\)
0.743838 + 0.668360i \(0.233003\pi\)
\(132\) −9.13695e110 −0.427238
\(133\) 5.06959e110 0.159500
\(134\) −5.12360e111 −1.08786
\(135\) −9.34835e110 −0.134342
\(136\) −9.19000e111 −0.896443
\(137\) −4.09322e111 −0.271791 −0.135895 0.990723i \(-0.543391\pi\)
−0.135895 + 0.990723i \(0.543391\pi\)
\(138\) 7.05392e110 0.0319727
\(139\) 4.93193e112 1.53017 0.765085 0.643930i \(-0.222697\pi\)
0.765085 + 0.643930i \(0.222697\pi\)
\(140\) 2.79219e111 0.0594597
\(141\) 1.05380e112 0.154438
\(142\) 1.37460e113 1.39007
\(143\) 1.19714e113 0.837533
\(144\) −4.72396e111 −0.0229232
\(145\) 1.07775e113 0.363663
\(146\) −9.12703e113 −2.14686
\(147\) 1.48230e113 0.243655
\(148\) −2.44443e114 −2.81474
\(149\) 1.21380e114 0.981446 0.490723 0.871316i \(-0.336733\pi\)
0.490723 + 0.871316i \(0.336733\pi\)
\(150\) 6.50996e113 0.370499
\(151\) 2.65500e114 1.06604 0.533021 0.846102i \(-0.321057\pi\)
0.533021 + 0.846102i \(0.321057\pi\)
\(152\) −4.38717e114 −1.24565
\(153\) 4.10026e114 0.825108
\(154\) −1.56709e114 −0.224004
\(155\) −2.72647e114 −0.277451
\(156\) −4.40202e114 −0.319603
\(157\) 3.38855e115 1.75907 0.879533 0.475839i \(-0.157855\pi\)
0.879533 + 0.475839i \(0.157855\pi\)
\(158\) −1.18860e115 −0.442119
\(159\) −5.29779e114 −0.141497
\(160\) 1.42580e115 0.274006
\(161\) 7.49623e113 0.0103869
\(162\) 1.32722e116 1.32863
\(163\) 1.30750e116 0.947531 0.473766 0.880651i \(-0.342894\pi\)
0.473766 + 0.880651i \(0.342894\pi\)
\(164\) −3.21017e116 −1.68743
\(165\) 1.91943e115 0.0733271
\(166\) −5.17313e116 −1.43906
\(167\) −8.47344e116 −1.71967 −0.859835 0.510572i \(-0.829434\pi\)
−0.859835 + 0.510572i \(0.829434\pi\)
\(168\) 2.22480e115 0.0330029
\(169\) −3.43799e116 −0.373468
\(170\) 5.00031e116 0.398500
\(171\) 1.95740e117 1.14653
\(172\) 6.46981e117 2.79028
\(173\) −5.65562e117 −1.79912 −0.899560 0.436798i \(-0.856112\pi\)
−0.899560 + 0.436798i \(0.856112\pi\)
\(174\) 2.22421e117 0.522806
\(175\) 6.91816e116 0.120363
\(176\) 2.00337e116 0.0258432
\(177\) 7.87931e116 0.0754904
\(178\) 6.82747e117 0.486642
\(179\) −2.82664e118 −1.50137 −0.750683 0.660662i \(-0.770276\pi\)
−0.750683 + 0.660662i \(0.770276\pi\)
\(180\) 1.07808e118 0.427411
\(181\) −1.03605e117 −0.0307083 −0.0153542 0.999882i \(-0.504888\pi\)
−0.0153542 + 0.999882i \(0.504888\pi\)
\(182\) −7.54995e117 −0.167570
\(183\) −1.01235e118 −0.168518
\(184\) −6.48716e117 −0.0811183
\(185\) 5.13510e118 0.483096
\(186\) −5.62674e118 −0.398867
\(187\) −1.73887e119 −0.930211
\(188\) −2.51011e119 −1.01486
\(189\) −2.05024e118 −0.0627421
\(190\) 2.38708e119 0.553735
\(191\) 1.02181e120 1.79937 0.899685 0.436540i \(-0.143796\pi\)
0.899685 + 0.436540i \(0.143796\pi\)
\(192\) 2.98771e119 0.399967
\(193\) 3.21850e119 0.328016 0.164008 0.986459i \(-0.447558\pi\)
0.164008 + 0.986459i \(0.447558\pi\)
\(194\) 1.88487e120 1.46450
\(195\) 9.24747e118 0.0548537
\(196\) −3.53079e120 −1.60113
\(197\) 1.33975e120 0.465100 0.232550 0.972584i \(-0.425293\pi\)
0.232550 + 0.972584i \(0.425293\pi\)
\(198\) −6.05062e120 −1.61019
\(199\) 1.61212e120 0.329315 0.164657 0.986351i \(-0.447348\pi\)
0.164657 + 0.986351i \(0.447348\pi\)
\(200\) −5.98690e120 −0.939999
\(201\) 1.37633e120 0.166314
\(202\) −1.23047e121 −1.14584
\(203\) 2.36368e120 0.169843
\(204\) 6.39402e120 0.354969
\(205\) 6.74369e120 0.289614
\(206\) 6.03760e121 2.00833
\(207\) 2.89434e120 0.0746633
\(208\) 9.65190e119 0.0193325
\(209\) −8.30109e121 −1.29257
\(210\) −1.21052e120 −0.0146710
\(211\) −5.16909e121 −0.488186 −0.244093 0.969752i \(-0.578490\pi\)
−0.244093 + 0.969752i \(0.578490\pi\)
\(212\) 1.26191e122 0.929817
\(213\) −3.69253e121 −0.212518
\(214\) 3.94817e122 1.77694
\(215\) −1.35913e122 −0.478898
\(216\) 1.77425e122 0.489997
\(217\) −5.97957e121 −0.129579
\(218\) −1.51617e123 −2.58097
\(219\) 2.45176e122 0.328217
\(220\) −4.57201e122 −0.481855
\(221\) −8.37755e122 −0.695862
\(222\) 1.05975e123 0.694503
\(223\) −1.13362e123 −0.586765 −0.293382 0.955995i \(-0.594781\pi\)
−0.293382 + 0.955995i \(0.594781\pi\)
\(224\) 3.12700e122 0.127969
\(225\) 2.67115e123 0.865198
\(226\) 1.96108e123 0.503272
\(227\) 3.47011e123 0.706295 0.353147 0.935568i \(-0.385111\pi\)
0.353147 + 0.935568i \(0.385111\pi\)
\(228\) 3.05242e123 0.493247
\(229\) 8.38603e123 1.07695 0.538473 0.842643i \(-0.319002\pi\)
0.538473 + 0.842643i \(0.319002\pi\)
\(230\) 3.52969e122 0.0360599
\(231\) 4.20960e122 0.0342461
\(232\) −2.04550e124 −1.32642
\(233\) −1.19820e124 −0.619930 −0.309965 0.950748i \(-0.600317\pi\)
−0.309965 + 0.950748i \(0.600317\pi\)
\(234\) −2.91508e124 −1.20453
\(235\) 5.27306e123 0.174181
\(236\) −1.87682e124 −0.496070
\(237\) 3.19289e123 0.0675921
\(238\) 1.09664e124 0.186113
\(239\) 1.34965e125 1.83795 0.918973 0.394320i \(-0.129020\pi\)
0.918973 + 0.394320i \(0.129020\pi\)
\(240\) 1.54753e122 0.00169258
\(241\) −1.84320e125 −1.62061 −0.810305 0.586008i \(-0.800699\pi\)
−0.810305 + 0.586008i \(0.800699\pi\)
\(242\) 2.74098e124 0.193910
\(243\) −1.19996e125 −0.683656
\(244\) 2.41138e125 1.10739
\(245\) 7.41723e124 0.274804
\(246\) 1.39173e125 0.416352
\(247\) −3.99932e125 −0.966933
\(248\) 5.17465e125 1.01197
\(249\) 1.38964e125 0.220007
\(250\) 6.79118e125 0.871154
\(251\) −5.04861e125 −0.525172 −0.262586 0.964909i \(-0.584575\pi\)
−0.262586 + 0.964909i \(0.584575\pi\)
\(252\) 2.36440e125 0.199615
\(253\) −1.22745e125 −0.0841740
\(254\) −1.08699e126 −0.605976
\(255\) −1.34321e125 −0.0609235
\(256\) −2.81379e126 −1.03919
\(257\) −4.52195e126 −1.36093 −0.680467 0.732779i \(-0.738223\pi\)
−0.680467 + 0.732779i \(0.738223\pi\)
\(258\) −2.80491e126 −0.688468
\(259\) 1.12621e126 0.225621
\(260\) −2.20271e126 −0.360460
\(261\) 9.12632e126 1.22087
\(262\) 2.20401e127 2.41210
\(263\) 8.08828e126 0.724735 0.362367 0.932035i \(-0.381969\pi\)
0.362367 + 0.932035i \(0.381969\pi\)
\(264\) −3.64294e126 −0.267452
\(265\) −2.65094e126 −0.159585
\(266\) 5.23522e126 0.258612
\(267\) −1.83403e126 −0.0743989
\(268\) −3.27837e127 −1.09290
\(269\) −1.02359e127 −0.280628 −0.140314 0.990107i \(-0.544811\pi\)
−0.140314 + 0.990107i \(0.544811\pi\)
\(270\) −9.65377e126 −0.217821
\(271\) 1.97338e127 0.366710 0.183355 0.983047i \(-0.441304\pi\)
0.183355 + 0.983047i \(0.441304\pi\)
\(272\) −1.40196e126 −0.0214717
\(273\) 2.02811e126 0.0256184
\(274\) −4.22695e127 −0.440679
\(275\) −1.13280e128 −0.975408
\(276\) 4.51350e126 0.0321208
\(277\) −6.48997e127 −0.381992 −0.190996 0.981591i \(-0.561172\pi\)
−0.190996 + 0.981591i \(0.561172\pi\)
\(278\) 5.09306e128 2.48100
\(279\) −2.30875e128 −0.931442
\(280\) 1.11326e127 0.0372219
\(281\) −1.98290e128 −0.549818 −0.274909 0.961470i \(-0.588648\pi\)
−0.274909 + 0.961470i \(0.588648\pi\)
\(282\) 1.08823e128 0.250404
\(283\) −7.67388e128 −1.46632 −0.733158 0.680059i \(-0.761954\pi\)
−0.733158 + 0.680059i \(0.761954\pi\)
\(284\) 8.79547e128 1.39652
\(285\) −6.41230e127 −0.0846562
\(286\) 1.23625e129 1.35797
\(287\) 1.47899e128 0.135259
\(288\) 1.20735e129 0.919875
\(289\) −3.57623e128 −0.227137
\(290\) 1.11297e129 0.589640
\(291\) −5.06324e128 −0.223896
\(292\) −5.83999e129 −2.15681
\(293\) −4.81415e129 −1.48583 −0.742916 0.669385i \(-0.766558\pi\)
−0.742916 + 0.669385i \(0.766558\pi\)
\(294\) 1.53073e129 0.395060
\(295\) 3.94270e128 0.0851408
\(296\) −9.74607e129 −1.76204
\(297\) 3.35711e129 0.508455
\(298\) 1.25345e130 1.59131
\(299\) −5.91366e128 −0.0629679
\(300\) 4.16544e129 0.372216
\(301\) −2.98079e129 −0.223661
\(302\) 2.74174e130 1.72847
\(303\) 3.30537e129 0.175179
\(304\) −6.69274e128 −0.0298360
\(305\) −5.06565e129 −0.190061
\(306\) 4.23422e130 1.33782
\(307\) −6.76464e130 −1.80086 −0.900430 0.435001i \(-0.856748\pi\)
−0.900430 + 0.435001i \(0.856748\pi\)
\(308\) −1.00271e130 −0.225042
\(309\) −1.62185e130 −0.307038
\(310\) −2.81555e130 −0.449856
\(311\) −1.62681e130 −0.219491 −0.109746 0.993960i \(-0.535004\pi\)
−0.109746 + 0.993960i \(0.535004\pi\)
\(312\) −1.75511e130 −0.200072
\(313\) −1.22308e131 −1.17863 −0.589315 0.807903i \(-0.700602\pi\)
−0.589315 + 0.807903i \(0.700602\pi\)
\(314\) 3.49926e131 2.85213
\(315\) −4.96696e129 −0.0342600
\(316\) −7.60535e130 −0.444168
\(317\) −8.81854e130 −0.436300 −0.218150 0.975915i \(-0.570002\pi\)
−0.218150 + 0.975915i \(0.570002\pi\)
\(318\) −5.47088e130 −0.229421
\(319\) −3.87036e131 −1.37639
\(320\) 1.49501e131 0.451098
\(321\) −1.06058e131 −0.271663
\(322\) 7.74115e129 0.0168412
\(323\) 5.80909e131 1.07393
\(324\) 8.49231e131 1.33479
\(325\) −5.45763e131 −0.729672
\(326\) 1.35022e132 1.53632
\(327\) 4.07283e131 0.394584
\(328\) −1.27991e132 −1.05633
\(329\) 1.15646e131 0.0813480
\(330\) 1.98214e131 0.118892
\(331\) −4.77509e131 −0.244350 −0.122175 0.992509i \(-0.538987\pi\)
−0.122175 + 0.992509i \(0.538987\pi\)
\(332\) −3.31007e132 −1.44573
\(333\) 4.34835e132 1.62182
\(334\) −8.75028e132 −2.78825
\(335\) 6.88697e131 0.187575
\(336\) 3.39398e129 0.000790491 0
\(337\) −7.27203e131 −0.144906 −0.0724529 0.997372i \(-0.523083\pi\)
−0.0724529 + 0.997372i \(0.523083\pi\)
\(338\) −3.55032e132 −0.605537
\(339\) −5.26797e131 −0.0769413
\(340\) 3.19948e132 0.400347
\(341\) 9.79110e132 1.05009
\(342\) 2.02135e133 1.85897
\(343\) 3.28164e132 0.258910
\(344\) 2.57954e133 1.74672
\(345\) −9.48165e130 −0.00551292
\(346\) −5.84040e133 −2.91707
\(347\) −3.89677e132 −0.167266 −0.0836328 0.996497i \(-0.526652\pi\)
−0.0836328 + 0.996497i \(0.526652\pi\)
\(348\) 1.42318e133 0.525229
\(349\) −3.25515e133 −1.03332 −0.516662 0.856190i \(-0.672825\pi\)
−0.516662 + 0.856190i \(0.672825\pi\)
\(350\) 7.14419e132 0.195155
\(351\) 1.61740e133 0.380359
\(352\) −5.12023e133 −1.03705
\(353\) 6.25734e133 1.09199 0.545994 0.837789i \(-0.316152\pi\)
0.545994 + 0.837789i \(0.316152\pi\)
\(354\) 8.13674e132 0.122399
\(355\) −1.84769e133 −0.239685
\(356\) 4.36861e133 0.488898
\(357\) −2.94587e132 −0.0284533
\(358\) −2.91899e134 −2.43430
\(359\) 1.08453e134 0.781236 0.390618 0.920553i \(-0.372261\pi\)
0.390618 + 0.920553i \(0.372261\pi\)
\(360\) 4.29836e133 0.267560
\(361\) 9.14826e133 0.492278
\(362\) −1.06990e133 −0.0497902
\(363\) −7.36298e132 −0.0296453
\(364\) −4.83089e133 −0.168347
\(365\) 1.22682e134 0.370175
\(366\) −1.04542e134 −0.273234
\(367\) 4.80224e134 1.08762 0.543808 0.839210i \(-0.316982\pi\)
0.543808 + 0.839210i \(0.316982\pi\)
\(368\) −9.89633e131 −0.00194296
\(369\) 5.71050e134 0.972276
\(370\) 5.30287e134 0.783286
\(371\) −5.81392e133 −0.0745314
\(372\) −3.60031e134 −0.400715
\(373\) −3.40674e134 −0.329325 −0.164663 0.986350i \(-0.552654\pi\)
−0.164663 + 0.986350i \(0.552654\pi\)
\(374\) −1.79568e135 −1.50823
\(375\) −1.82429e134 −0.133184
\(376\) −1.00079e135 −0.635304
\(377\) −1.86467e135 −1.02963
\(378\) −2.11722e134 −0.101729
\(379\) −2.63938e135 −1.10394 −0.551968 0.833865i \(-0.686123\pi\)
−0.551968 + 0.833865i \(0.686123\pi\)
\(380\) 1.52739e135 0.556302
\(381\) 2.91994e134 0.0926429
\(382\) 1.05520e136 2.91748
\(383\) −3.06697e133 −0.00739220 −0.00369610 0.999993i \(-0.501177\pi\)
−0.00369610 + 0.999993i \(0.501177\pi\)
\(384\) 1.92947e135 0.405555
\(385\) 2.10643e134 0.0386240
\(386\) 3.32365e135 0.531841
\(387\) −1.15090e136 −1.60773
\(388\) 1.20605e136 1.47129
\(389\) −3.94802e135 −0.420751 −0.210376 0.977621i \(-0.567469\pi\)
−0.210376 + 0.977621i \(0.567469\pi\)
\(390\) 9.54959e134 0.0889392
\(391\) 8.58971e134 0.0699356
\(392\) −1.40774e136 −1.00231
\(393\) −5.92054e135 −0.368767
\(394\) 1.38352e136 0.754109
\(395\) 1.59768e135 0.0762328
\(396\) −3.87153e136 −1.61765
\(397\) −2.49919e135 −0.0914740 −0.0457370 0.998954i \(-0.514564\pi\)
−0.0457370 + 0.998954i \(0.514564\pi\)
\(398\) 1.66479e136 0.533947
\(399\) −1.40632e135 −0.0395372
\(400\) −9.13317e134 −0.0225150
\(401\) 2.08911e136 0.451734 0.225867 0.974158i \(-0.427479\pi\)
0.225867 + 0.974158i \(0.427479\pi\)
\(402\) 1.42130e136 0.269660
\(403\) 4.71719e136 0.785540
\(404\) −7.87327e136 −1.15115
\(405\) −1.78400e136 −0.229091
\(406\) 2.44091e136 0.275381
\(407\) −1.84408e137 −1.82841
\(408\) 2.54933e136 0.222212
\(409\) 1.89309e137 1.45110 0.725551 0.688168i \(-0.241585\pi\)
0.725551 + 0.688168i \(0.241585\pi\)
\(410\) 6.96402e136 0.469578
\(411\) 1.13547e136 0.0673719
\(412\) 3.86320e137 2.01764
\(413\) 8.64695e135 0.0397635
\(414\) 2.98891e136 0.121058
\(415\) 6.95356e136 0.248131
\(416\) −2.46684e137 −0.775784
\(417\) −1.36813e137 −0.379300
\(418\) −8.57230e137 −2.09577
\(419\) −3.76420e136 −0.0811777 −0.0405889 0.999176i \(-0.512923\pi\)
−0.0405889 + 0.999176i \(0.512923\pi\)
\(420\) −7.74559e135 −0.0147390
\(421\) −6.26646e137 −1.05248 −0.526238 0.850337i \(-0.676398\pi\)
−0.526238 + 0.850337i \(0.676398\pi\)
\(422\) −5.33797e137 −0.791539
\(423\) 4.46518e137 0.584749
\(424\) 5.03131e137 0.582068
\(425\) 7.92731e137 0.810414
\(426\) −3.81317e137 −0.344574
\(427\) −1.11097e137 −0.0887648
\(428\) 2.52627e138 1.78518
\(429\) −3.32089e137 −0.207609
\(430\) −1.40354e138 −0.776480
\(431\) 2.82998e138 1.38588 0.692941 0.720994i \(-0.256314\pi\)
0.692941 + 0.720994i \(0.256314\pi\)
\(432\) 2.70667e136 0.0117365
\(433\) 3.83279e138 1.47198 0.735988 0.676994i \(-0.236718\pi\)
0.735988 + 0.676994i \(0.236718\pi\)
\(434\) −6.17493e137 −0.210098
\(435\) −2.98971e137 −0.0901454
\(436\) −9.70134e138 −2.59293
\(437\) 4.10060e137 0.0971790
\(438\) 2.53186e138 0.532168
\(439\) −7.85880e138 −1.46544 −0.732722 0.680529i \(-0.761750\pi\)
−0.732722 + 0.680529i \(0.761750\pi\)
\(440\) −1.82288e138 −0.301642
\(441\) 6.28084e138 0.922554
\(442\) −8.65126e138 −1.12826
\(443\) 1.56157e139 1.80870 0.904349 0.426794i \(-0.140357\pi\)
0.904349 + 0.426794i \(0.140357\pi\)
\(444\) 6.78091e138 0.697722
\(445\) −9.17726e137 −0.0839098
\(446\) −1.17066e139 −0.951374
\(447\) −3.36709e138 −0.243282
\(448\) 3.27879e138 0.210677
\(449\) −2.40110e139 −1.37239 −0.686196 0.727417i \(-0.740721\pi\)
−0.686196 + 0.727417i \(0.740721\pi\)
\(450\) 2.75842e139 1.40282
\(451\) −2.42175e139 −1.09613
\(452\) 1.25481e139 0.505604
\(453\) −7.36501e138 −0.264252
\(454\) 3.58348e139 1.14518
\(455\) 1.01484e138 0.0288934
\(456\) 1.21701e139 0.308774
\(457\) 5.92334e138 0.133957 0.0669786 0.997754i \(-0.478664\pi\)
0.0669786 + 0.997754i \(0.478664\pi\)
\(458\) 8.66001e139 1.74615
\(459\) −2.34930e139 −0.422448
\(460\) 2.25849e138 0.0362270
\(461\) −1.13272e140 −1.62115 −0.810577 0.585632i \(-0.800846\pi\)
−0.810577 + 0.585632i \(0.800846\pi\)
\(462\) 4.34713e138 0.0555263
\(463\) 4.89305e139 0.557928 0.278964 0.960302i \(-0.410009\pi\)
0.278964 + 0.960302i \(0.410009\pi\)
\(464\) −3.12047e138 −0.0317706
\(465\) 7.56328e138 0.0687750
\(466\) −1.23734e140 −1.00515
\(467\) −1.36004e140 −0.987221 −0.493610 0.869683i \(-0.664323\pi\)
−0.493610 + 0.869683i \(0.664323\pi\)
\(468\) −1.86524e140 −1.21012
\(469\) 1.51042e139 0.0876038
\(470\) 5.44534e139 0.282415
\(471\) −9.39991e139 −0.436040
\(472\) −7.48298e139 −0.310541
\(473\) 4.88082e140 1.81252
\(474\) 3.29721e139 0.109593
\(475\) 3.78438e140 1.12611
\(476\) 7.01696e139 0.186975
\(477\) −2.24479e140 −0.535749
\(478\) 1.39375e141 2.98003
\(479\) 2.16327e140 0.414473 0.207237 0.978291i \(-0.433553\pi\)
0.207237 + 0.978291i \(0.433553\pi\)
\(480\) −3.95520e139 −0.0679209
\(481\) −8.88446e140 −1.36777
\(482\) −1.90342e141 −2.62764
\(483\) −2.07947e138 −0.00257471
\(484\) 1.75384e140 0.194808
\(485\) −2.53358e140 −0.252518
\(486\) −1.23916e141 −1.10847
\(487\) 1.52760e141 1.22670 0.613349 0.789812i \(-0.289822\pi\)
0.613349 + 0.789812i \(0.289822\pi\)
\(488\) 9.61426e140 0.693226
\(489\) −3.62704e140 −0.234875
\(490\) 7.65956e140 0.445564
\(491\) −2.51656e141 −1.31531 −0.657656 0.753318i \(-0.728452\pi\)
−0.657656 + 0.753318i \(0.728452\pi\)
\(492\) 8.90507e140 0.418282
\(493\) 2.70847e141 1.14356
\(494\) −4.12999e141 −1.56778
\(495\) 8.13304e140 0.277639
\(496\) 7.89406e139 0.0242389
\(497\) −4.05227e140 −0.111941
\(498\) 1.43504e141 0.356716
\(499\) −1.66340e141 −0.372150 −0.186075 0.982536i \(-0.559577\pi\)
−0.186075 + 0.982536i \(0.559577\pi\)
\(500\) 4.34538e141 0.875191
\(501\) 2.35055e141 0.426274
\(502\) −5.21356e141 −0.851509
\(503\) 5.11786e141 0.752956 0.376478 0.926426i \(-0.377135\pi\)
0.376478 + 0.926426i \(0.377135\pi\)
\(504\) 9.42696e140 0.124959
\(505\) 1.65396e141 0.197573
\(506\) −1.26756e141 −0.136479
\(507\) 9.53707e140 0.0925757
\(508\) −6.95518e141 −0.608785
\(509\) 2.08898e142 1.64912 0.824558 0.565778i \(-0.191424\pi\)
0.824558 + 0.565778i \(0.191424\pi\)
\(510\) −1.38710e141 −0.0987808
\(511\) 2.69062e141 0.172884
\(512\) −8.42315e140 −0.0488429
\(513\) −1.12152e142 −0.587012
\(514\) −4.66969e142 −2.20660
\(515\) −8.11554e141 −0.346288
\(516\) −1.79474e142 −0.691659
\(517\) −1.89362e142 −0.659235
\(518\) 1.16300e142 0.365820
\(519\) 1.56888e142 0.445968
\(520\) −8.78231e141 −0.225649
\(521\) −7.88634e140 −0.0183187 −0.00915936 0.999958i \(-0.502916\pi\)
−0.00915936 + 0.999958i \(0.502916\pi\)
\(522\) 9.42449e142 1.97950
\(523\) −3.47386e142 −0.659893 −0.329947 0.944000i \(-0.607031\pi\)
−0.329947 + 0.944000i \(0.607031\pi\)
\(524\) 1.41025e143 2.42328
\(525\) −1.91911e141 −0.0298358
\(526\) 8.35253e142 1.17508
\(527\) −6.85180e142 −0.872464
\(528\) −5.55740e140 −0.00640605
\(529\) −9.52063e142 −0.993672
\(530\) −2.73755e142 −0.258749
\(531\) 3.33864e142 0.285830
\(532\) 3.34979e142 0.259811
\(533\) −1.16676e143 −0.819977
\(534\) −1.89396e142 −0.120630
\(535\) −5.30701e142 −0.306391
\(536\) −1.30710e143 −0.684160
\(537\) 7.84117e142 0.372161
\(538\) −1.05703e143 −0.455007
\(539\) −2.66362e143 −1.04007
\(540\) −6.17703e142 −0.218830
\(541\) 2.80623e143 0.902126 0.451063 0.892492i \(-0.351045\pi\)
0.451063 + 0.892492i \(0.351045\pi\)
\(542\) 2.03785e143 0.594580
\(543\) 2.87403e141 0.00761202
\(544\) 3.58313e143 0.861629
\(545\) 2.03799e143 0.445026
\(546\) 2.09437e142 0.0415375
\(547\) 1.36569e143 0.246047 0.123024 0.992404i \(-0.460741\pi\)
0.123024 + 0.992404i \(0.460741\pi\)
\(548\) −2.70464e143 −0.442721
\(549\) −4.28955e143 −0.638062
\(550\) −1.16981e144 −1.58152
\(551\) 1.29298e144 1.58904
\(552\) 1.79955e142 0.0201077
\(553\) 3.50395e142 0.0356032
\(554\) −6.70200e143 −0.619358
\(555\) −1.42449e143 −0.119750
\(556\) 3.25883e144 2.49250
\(557\) 5.17009e143 0.359833 0.179916 0.983682i \(-0.442417\pi\)
0.179916 + 0.983682i \(0.442417\pi\)
\(558\) −2.38418e144 −1.51023
\(559\) 2.35150e144 1.35589
\(560\) 1.69830e141 0.000891545 0
\(561\) 4.82365e143 0.230582
\(562\) −2.04768e144 −0.891469
\(563\) −4.74938e144 −1.88342 −0.941709 0.336429i \(-0.890781\pi\)
−0.941709 + 0.336429i \(0.890781\pi\)
\(564\) 6.96309e143 0.251564
\(565\) −2.63602e143 −0.0867772
\(566\) −7.92460e144 −2.37747
\(567\) −3.91260e143 −0.106993
\(568\) 3.50679e144 0.874224
\(569\) 1.10238e144 0.250574 0.125287 0.992121i \(-0.460015\pi\)
0.125287 + 0.992121i \(0.460015\pi\)
\(570\) −6.62180e143 −0.137261
\(571\) 4.01955e144 0.759944 0.379972 0.924998i \(-0.375934\pi\)
0.379972 + 0.924998i \(0.375934\pi\)
\(572\) 7.91023e144 1.36426
\(573\) −2.83454e144 −0.446030
\(574\) 1.52732e144 0.219308
\(575\) 5.59584e143 0.0733337
\(576\) 1.26596e145 1.51440
\(577\) 1.09495e144 0.119582 0.0597909 0.998211i \(-0.480957\pi\)
0.0597909 + 0.998211i \(0.480957\pi\)
\(578\) −3.69307e144 −0.368278
\(579\) −8.92818e143 −0.0813090
\(580\) 7.12139e144 0.592373
\(581\) 1.52502e144 0.115885
\(582\) −5.22866e144 −0.363023
\(583\) 9.51988e144 0.603993
\(584\) −2.32843e145 −1.35017
\(585\) 3.91836e144 0.207693
\(586\) −4.97144e145 −2.40911
\(587\) 2.23123e144 0.0988652 0.0494326 0.998777i \(-0.484259\pi\)
0.0494326 + 0.998777i \(0.484259\pi\)
\(588\) 9.79448e144 0.396891
\(589\) −3.27095e145 −1.21233
\(590\) 4.07151e144 0.138046
\(591\) −3.71649e144 −0.115290
\(592\) −1.48679e144 −0.0422045
\(593\) 4.65023e145 1.20810 0.604050 0.796946i \(-0.293553\pi\)
0.604050 + 0.796946i \(0.293553\pi\)
\(594\) 3.46679e145 0.824403
\(595\) −1.47407e144 −0.0320906
\(596\) 8.02030e145 1.59868
\(597\) −4.47206e144 −0.0816310
\(598\) −6.10687e144 −0.102095
\(599\) −6.28831e145 −0.962999 −0.481499 0.876446i \(-0.659908\pi\)
−0.481499 + 0.876446i \(0.659908\pi\)
\(600\) 1.66078e145 0.233008
\(601\) −1.30706e146 −1.68029 −0.840147 0.542359i \(-0.817531\pi\)
−0.840147 + 0.542359i \(0.817531\pi\)
\(602\) −3.07817e145 −0.362641
\(603\) 5.83183e145 0.629717
\(604\) 1.75432e146 1.73648
\(605\) −3.68433e144 −0.0334350
\(606\) 3.41336e145 0.284033
\(607\) −1.74931e146 −1.33494 −0.667469 0.744638i \(-0.732622\pi\)
−0.667469 + 0.744638i \(0.732622\pi\)
\(608\) 1.71054e146 1.19728
\(609\) −6.55690e144 −0.0421008
\(610\) −5.23115e145 −0.308163
\(611\) −9.12315e145 −0.493153
\(612\) 2.70929e146 1.34402
\(613\) 2.63791e146 1.20112 0.600558 0.799581i \(-0.294945\pi\)
0.600558 + 0.799581i \(0.294945\pi\)
\(614\) −6.98565e146 −2.91989
\(615\) −1.87071e145 −0.0717900
\(616\) −3.99785e145 −0.140877
\(617\) −1.82675e146 −0.591164 −0.295582 0.955317i \(-0.595513\pi\)
−0.295582 + 0.955317i \(0.595513\pi\)
\(618\) −1.67484e146 −0.497828
\(619\) 3.49692e146 0.954832 0.477416 0.878677i \(-0.341574\pi\)
0.477416 + 0.878677i \(0.341574\pi\)
\(620\) −1.80155e146 −0.451941
\(621\) −1.65836e145 −0.0382269
\(622\) −1.67997e146 −0.355881
\(623\) −2.01271e145 −0.0391886
\(624\) −2.67746e144 −0.00479216
\(625\) 4.68933e146 0.771631
\(626\) −1.26304e147 −1.91102
\(627\) 2.30274e146 0.320405
\(628\) 2.23902e147 2.86535
\(629\) 1.29049e147 1.51913
\(630\) −5.12924e145 −0.0555487
\(631\) 8.83472e146 0.880342 0.440171 0.897914i \(-0.354918\pi\)
0.440171 + 0.897914i \(0.354918\pi\)
\(632\) −3.03229e146 −0.278050
\(633\) 1.43392e146 0.121012
\(634\) −9.10666e146 −0.707413
\(635\) 1.46110e146 0.104486
\(636\) −3.50058e146 −0.230484
\(637\) −1.28329e147 −0.778044
\(638\) −3.99681e147 −2.23166
\(639\) −1.56461e147 −0.804656
\(640\) 9.65483e146 0.457400
\(641\) −1.21859e147 −0.531875 −0.265937 0.963990i \(-0.585681\pi\)
−0.265937 + 0.963990i \(0.585681\pi\)
\(642\) −1.09523e147 −0.440471
\(643\) 1.50782e147 0.558822 0.279411 0.960172i \(-0.409861\pi\)
0.279411 + 0.960172i \(0.409861\pi\)
\(644\) 4.95323e145 0.0169192
\(645\) 3.77026e146 0.118710
\(646\) 5.99888e147 1.74126
\(647\) −1.59600e146 −0.0427128 −0.0213564 0.999772i \(-0.506798\pi\)
−0.0213564 + 0.999772i \(0.506798\pi\)
\(648\) 3.38592e147 0.835581
\(649\) −1.41587e147 −0.322239
\(650\) −5.63594e147 −1.18308
\(651\) 1.65874e146 0.0321201
\(652\) 8.63948e147 1.54344
\(653\) −6.07906e147 −1.00206 −0.501030 0.865430i \(-0.667046\pi\)
−0.501030 + 0.865430i \(0.667046\pi\)
\(654\) 4.20590e147 0.639774
\(655\) −2.96256e147 −0.415909
\(656\) −1.95253e146 −0.0253015
\(657\) 1.03886e148 1.24273
\(658\) 1.19425e147 0.131897
\(659\) −7.04451e147 −0.718401 −0.359200 0.933260i \(-0.616951\pi\)
−0.359200 + 0.933260i \(0.616951\pi\)
\(660\) 1.26828e147 0.119443
\(661\) −5.89028e147 −0.512341 −0.256171 0.966632i \(-0.582461\pi\)
−0.256171 + 0.966632i \(0.582461\pi\)
\(662\) −4.93110e147 −0.396186
\(663\) 2.32395e147 0.172491
\(664\) −1.31974e148 −0.905031
\(665\) −7.03702e146 −0.0445915
\(666\) 4.49042e148 2.62960
\(667\) 1.91189e147 0.103480
\(668\) −5.59893e148 −2.80118
\(669\) 3.14470e147 0.145448
\(670\) 7.11198e147 0.304133
\(671\) 1.81914e148 0.719340
\(672\) −8.67435e146 −0.0317213
\(673\) −1.13637e148 −0.384350 −0.192175 0.981361i \(-0.561554\pi\)
−0.192175 + 0.981361i \(0.561554\pi\)
\(674\) −7.50961e147 −0.234949
\(675\) −1.53047e148 −0.442974
\(676\) −2.27170e148 −0.608343
\(677\) −1.55016e148 −0.384123 −0.192062 0.981383i \(-0.561517\pi\)
−0.192062 + 0.981383i \(0.561517\pi\)
\(678\) −5.44008e147 −0.124752
\(679\) −5.55652e147 −0.117934
\(680\) 1.27565e148 0.250618
\(681\) −9.62616e147 −0.175077
\(682\) 1.01110e149 1.70261
\(683\) 3.44980e148 0.537907 0.268954 0.963153i \(-0.413322\pi\)
0.268954 + 0.963153i \(0.413322\pi\)
\(684\) 1.29338e149 1.86758
\(685\) 5.68172e147 0.0759845
\(686\) 3.38885e148 0.419795
\(687\) −2.32630e148 −0.266955
\(688\) 3.93515e147 0.0418378
\(689\) 4.58651e148 0.451828
\(690\) −9.79143e146 −0.00893858
\(691\) −1.05892e149 −0.895915 −0.447957 0.894055i \(-0.647848\pi\)
−0.447957 + 0.894055i \(0.647848\pi\)
\(692\) −3.73702e149 −2.93059
\(693\) 1.78370e148 0.129666
\(694\) −4.02408e148 −0.271203
\(695\) −6.84592e148 −0.427789
\(696\) 5.67427e148 0.328795
\(697\) 1.69474e149 0.910712
\(698\) −3.36150e149 −1.67542
\(699\) 3.32382e148 0.153669
\(700\) 4.57126e148 0.196060
\(701\) −1.63990e149 −0.652561 −0.326280 0.945273i \(-0.605795\pi\)
−0.326280 + 0.945273i \(0.605795\pi\)
\(702\) 1.67024e149 0.616710
\(703\) 6.16059e149 2.11090
\(704\) −5.36878e149 −1.70730
\(705\) −1.46276e148 −0.0431761
\(706\) 6.46177e149 1.77054
\(707\) 3.62739e148 0.0922732
\(708\) 5.20635e148 0.122967
\(709\) 4.35222e149 0.954516 0.477258 0.878763i \(-0.341631\pi\)
0.477258 + 0.878763i \(0.341631\pi\)
\(710\) −1.90806e149 −0.388623
\(711\) 1.35290e149 0.255924
\(712\) 1.74178e149 0.306051
\(713\) −4.83664e148 −0.0789485
\(714\) −3.04212e148 −0.0461338
\(715\) −1.66173e149 −0.234149
\(716\) −1.86774e150 −2.44558
\(717\) −3.74397e149 −0.455593
\(718\) 1.11996e150 1.26669
\(719\) −4.96405e149 −0.521878 −0.260939 0.965355i \(-0.584032\pi\)
−0.260939 + 0.965355i \(0.584032\pi\)
\(720\) 6.55725e147 0.00640864
\(721\) −1.77986e149 −0.161728
\(722\) 9.44714e149 0.798174
\(723\) 5.11309e149 0.401719
\(724\) −6.84583e148 −0.0500209
\(725\) 1.76446e150 1.19913
\(726\) −7.60354e148 −0.0480666
\(727\) −2.41824e150 −1.42214 −0.711072 0.703119i \(-0.751790\pi\)
−0.711072 + 0.703119i \(0.751790\pi\)
\(728\) −1.92610e149 −0.105385
\(729\) −1.27671e150 −0.649974
\(730\) 1.26691e150 0.600198
\(731\) −3.41559e150 −1.50593
\(732\) −6.68921e149 −0.274500
\(733\) −2.05795e150 −0.786096 −0.393048 0.919518i \(-0.628579\pi\)
−0.393048 + 0.919518i \(0.628579\pi\)
\(734\) 4.95914e150 1.76345
\(735\) −2.05756e149 −0.0681187
\(736\) 2.52931e149 0.0779680
\(737\) −2.47320e150 −0.709931
\(738\) 5.89706e150 1.57644
\(739\) 2.20246e150 0.548372 0.274186 0.961677i \(-0.411592\pi\)
0.274186 + 0.961677i \(0.411592\pi\)
\(740\) 3.39308e150 0.786916
\(741\) 1.10942e150 0.239685
\(742\) −6.00387e149 −0.120844
\(743\) 4.42483e150 0.829819 0.414910 0.909863i \(-0.363813\pi\)
0.414910 + 0.909863i \(0.363813\pi\)
\(744\) −1.43546e150 −0.250849
\(745\) −1.68485e150 −0.274383
\(746\) −3.51804e150 −0.533964
\(747\) 5.88821e150 0.833012
\(748\) −1.14898e151 −1.51522
\(749\) −1.16391e150 −0.143095
\(750\) −1.88389e150 −0.215943
\(751\) 2.63233e150 0.281348 0.140674 0.990056i \(-0.455073\pi\)
0.140674 + 0.990056i \(0.455073\pi\)
\(752\) −1.52673e149 −0.0152169
\(753\) 1.40050e150 0.130180
\(754\) −1.92559e151 −1.66943
\(755\) −3.68535e150 −0.298033
\(756\) −1.35472e150 −0.102201
\(757\) −2.55196e150 −0.179614 −0.0898072 0.995959i \(-0.528625\pi\)
−0.0898072 + 0.995959i \(0.528625\pi\)
\(758\) −2.72562e151 −1.78991
\(759\) 3.40498e149 0.0208652
\(760\) 6.08976e150 0.348246
\(761\) 3.67649e151 1.96218 0.981091 0.193549i \(-0.0619997\pi\)
0.981091 + 0.193549i \(0.0619997\pi\)
\(762\) 3.01533e150 0.150210
\(763\) 4.46962e150 0.207842
\(764\) 6.75176e151 2.93100
\(765\) −5.69149e150 −0.230675
\(766\) −3.16717e149 −0.0119856
\(767\) −6.82144e150 −0.241057
\(768\) 7.80552e150 0.257595
\(769\) −8.16388e150 −0.251631 −0.125815 0.992054i \(-0.540155\pi\)
−0.125815 + 0.992054i \(0.540155\pi\)
\(770\) 2.17524e150 0.0626246
\(771\) 1.25440e151 0.337350
\(772\) 2.12666e151 0.534306
\(773\) −3.70048e151 −0.868630 −0.434315 0.900761i \(-0.643009\pi\)
−0.434315 + 0.900761i \(0.643009\pi\)
\(774\) −1.18850e152 −2.60675
\(775\) −4.46367e151 −0.914855
\(776\) 4.80856e151 0.921032
\(777\) −3.12412e150 −0.0559273
\(778\) −4.07701e151 −0.682202
\(779\) 8.09042e151 1.26548
\(780\) 6.11037e150 0.0893514
\(781\) 6.63530e151 0.907155
\(782\) 8.87034e150 0.113393
\(783\) −5.22907e151 −0.625074
\(784\) −2.14754e150 −0.0240076
\(785\) −4.70359e151 −0.491781
\(786\) −6.11397e151 −0.597915
\(787\) 1.07166e151 0.0980352 0.0490176 0.998798i \(-0.484391\pi\)
0.0490176 + 0.998798i \(0.484391\pi\)
\(788\) 8.85255e151 0.757603
\(789\) −2.24370e151 −0.179648
\(790\) 1.64988e151 0.123603
\(791\) −5.78120e150 −0.0405278
\(792\) −1.54360e152 −1.01266
\(793\) 8.76431e151 0.538115
\(794\) −2.58084e151 −0.148315
\(795\) 7.35377e150 0.0395581
\(796\) 1.06523e152 0.536422
\(797\) 5.71590e151 0.269478 0.134739 0.990881i \(-0.456980\pi\)
0.134739 + 0.990881i \(0.456980\pi\)
\(798\) −1.45226e151 −0.0641052
\(799\) 1.32516e152 0.547723
\(800\) 2.33426e152 0.903494
\(801\) −7.77122e151 −0.281697
\(802\) 2.15737e152 0.732436
\(803\) −4.40569e152 −1.40103
\(804\) 9.09427e151 0.270910
\(805\) −1.04054e150 −0.00290385
\(806\) 4.87130e152 1.27367
\(807\) 2.83945e151 0.0695623
\(808\) −3.13911e152 −0.720626
\(809\) 9.92211e151 0.213455 0.106728 0.994288i \(-0.465963\pi\)
0.106728 + 0.994288i \(0.465963\pi\)
\(810\) −1.84229e152 −0.371445
\(811\) −4.56922e152 −0.863471 −0.431735 0.902000i \(-0.642099\pi\)
−0.431735 + 0.902000i \(0.642099\pi\)
\(812\) 1.56183e152 0.276657
\(813\) −5.47420e151 −0.0909006
\(814\) −1.90433e153 −2.96456
\(815\) −1.81492e152 −0.264901
\(816\) 3.88906e150 0.00532244
\(817\) −1.63056e153 −2.09256
\(818\) 1.95494e153 2.35280
\(819\) 8.59357e151 0.0969993
\(820\) 4.45597e152 0.471754
\(821\) 1.02228e153 1.01520 0.507602 0.861592i \(-0.330532\pi\)
0.507602 + 0.861592i \(0.330532\pi\)
\(822\) 1.17256e152 0.109236
\(823\) 1.57311e153 1.37489 0.687443 0.726238i \(-0.258733\pi\)
0.687443 + 0.726238i \(0.258733\pi\)
\(824\) 1.54027e153 1.26305
\(825\) 3.14241e152 0.241785
\(826\) 8.92945e151 0.0644722
\(827\) −3.06424e152 −0.207627 −0.103813 0.994597i \(-0.533104\pi\)
−0.103813 + 0.994597i \(0.533104\pi\)
\(828\) 1.91247e152 0.121619
\(829\) −1.45148e153 −0.866360 −0.433180 0.901307i \(-0.642609\pi\)
−0.433180 + 0.901307i \(0.642609\pi\)
\(830\) 7.18074e152 0.402318
\(831\) 1.80033e152 0.0946888
\(832\) −2.58659e153 −1.27718
\(833\) 1.86400e153 0.864139
\(834\) −1.41283e153 −0.614994
\(835\) 1.17618e153 0.480767
\(836\) −5.48505e153 −2.10548
\(837\) 1.32283e153 0.476890
\(838\) −3.88719e152 −0.131621
\(839\) 1.03463e153 0.329064 0.164532 0.986372i \(-0.447389\pi\)
0.164532 + 0.986372i \(0.447389\pi\)
\(840\) −3.08820e151 −0.00922662
\(841\) 2.46571e153 0.692073
\(842\) −6.47119e153 −1.70647
\(843\) 5.50061e152 0.136290
\(844\) −3.41554e153 −0.795207
\(845\) 4.77222e152 0.104410
\(846\) 4.61106e153 0.948106
\(847\) −8.08031e151 −0.0156153
\(848\) 7.67538e151 0.0139418
\(849\) 2.12875e153 0.363472
\(850\) 8.18631e153 1.31400
\(851\) 9.10945e152 0.137464
\(852\) −2.43988e153 −0.346171
\(853\) 8.89160e152 0.118619 0.0593097 0.998240i \(-0.481110\pi\)
0.0593097 + 0.998240i \(0.481110\pi\)
\(854\) −1.14727e153 −0.143922
\(855\) −2.71704e153 −0.320534
\(856\) 1.00723e154 1.11753
\(857\) −1.49289e154 −1.55788 −0.778942 0.627096i \(-0.784243\pi\)
−0.778942 + 0.627096i \(0.784243\pi\)
\(858\) −3.42938e153 −0.336615
\(859\) 3.27076e153 0.302000 0.151000 0.988534i \(-0.451751\pi\)
0.151000 + 0.988534i \(0.451751\pi\)
\(860\) −8.98063e153 −0.780078
\(861\) −4.10276e152 −0.0335283
\(862\) 2.92244e154 2.24706
\(863\) −1.47873e154 −1.06985 −0.534925 0.844899i \(-0.679660\pi\)
−0.534925 + 0.844899i \(0.679660\pi\)
\(864\) −6.91772e153 −0.470968
\(865\) 7.85047e153 0.502979
\(866\) 3.95802e154 2.38665
\(867\) 9.92054e152 0.0563031
\(868\) −3.95107e153 −0.211071
\(869\) −5.73747e153 −0.288524
\(870\) −3.08739e153 −0.146161
\(871\) −1.19155e154 −0.531077
\(872\) −3.86797e154 −1.62318
\(873\) −2.14541e154 −0.847740
\(874\) 4.23457e153 0.157565
\(875\) −2.00202e153 −0.0701527
\(876\) 1.62003e154 0.534634
\(877\) −4.01870e154 −1.24913 −0.624565 0.780973i \(-0.714724\pi\)
−0.624565 + 0.780973i \(0.714724\pi\)
\(878\) −8.11556e154 −2.37605
\(879\) 1.33546e154 0.368310
\(880\) −2.78085e152 −0.00722498
\(881\) 7.65040e154 1.87262 0.936308 0.351180i \(-0.114219\pi\)
0.936308 + 0.351180i \(0.114219\pi\)
\(882\) 6.48605e154 1.49582
\(883\) 3.55919e154 0.773418 0.386709 0.922202i \(-0.373612\pi\)
0.386709 + 0.922202i \(0.373612\pi\)
\(884\) −5.53557e154 −1.13349
\(885\) −1.09371e153 −0.0211048
\(886\) 1.61259e155 2.93260
\(887\) −7.16354e154 −1.22783 −0.613914 0.789373i \(-0.710406\pi\)
−0.613914 + 0.789373i \(0.710406\pi\)
\(888\) 2.70358e154 0.436776
\(889\) 3.20441e153 0.0487984
\(890\) −9.47710e153 −0.136050
\(891\) 6.40659e154 0.867057
\(892\) −7.49056e154 −0.955783
\(893\) 6.32610e154 0.761088
\(894\) −3.47710e154 −0.394455
\(895\) 3.92361e154 0.419737
\(896\) 2.11745e154 0.213621
\(897\) 1.64046e153 0.0156086
\(898\) −2.47955e155 −2.22518
\(899\) −1.52507e155 −1.29094
\(900\) 1.76499e155 1.40932
\(901\) −6.66200e154 −0.501826
\(902\) −2.50087e155 −1.77725
\(903\) 8.26877e153 0.0554414
\(904\) 5.00299e154 0.316510
\(905\) 1.43812e153 0.00858512
\(906\) −7.60564e154 −0.428455
\(907\) −5.78217e154 −0.307403 −0.153701 0.988117i \(-0.549119\pi\)
−0.153701 + 0.988117i \(0.549119\pi\)
\(908\) 2.29292e155 1.15049
\(909\) 1.40056e155 0.663281
\(910\) 1.04800e154 0.0468475
\(911\) 3.54703e155 1.49675 0.748377 0.663274i \(-0.230834\pi\)
0.748377 + 0.663274i \(0.230834\pi\)
\(912\) 1.85658e153 0.00739579
\(913\) −2.49711e155 −0.939122
\(914\) 6.11686e154 0.217197
\(915\) 1.40522e154 0.0471126
\(916\) 5.54117e155 1.75424
\(917\) −6.49734e154 −0.194243
\(918\) −2.42606e155 −0.684953
\(919\) −2.75804e155 −0.735421 −0.367710 0.929940i \(-0.619858\pi\)
−0.367710 + 0.929940i \(0.619858\pi\)
\(920\) 9.00472e153 0.0226782
\(921\) 1.87652e155 0.446400
\(922\) −1.16973e156 −2.62852
\(923\) 3.19677e155 0.678614
\(924\) 2.78154e154 0.0557837
\(925\) 8.40698e155 1.59294
\(926\) 5.05292e155 0.904618
\(927\) −6.87216e155 −1.16254
\(928\) 7.97531e155 1.27491
\(929\) −4.30019e155 −0.649625 −0.324812 0.945778i \(-0.605301\pi\)
−0.324812 + 0.945778i \(0.605301\pi\)
\(930\) 7.81039e154 0.111511
\(931\) 8.89847e155 1.20076
\(932\) −7.91723e155 −1.00981
\(933\) 4.51282e154 0.0544079
\(934\) −1.40447e156 −1.60067
\(935\) 2.41369e155 0.260059
\(936\) −7.43678e155 −0.757535
\(937\) −1.31573e155 −0.126718 −0.0633589 0.997991i \(-0.520181\pi\)
−0.0633589 + 0.997991i \(0.520181\pi\)
\(938\) 1.55977e155 0.142040
\(939\) 3.39285e155 0.292161
\(940\) 3.48424e155 0.283724
\(941\) −1.44411e156 −1.11210 −0.556051 0.831148i \(-0.687684\pi\)
−0.556051 + 0.831148i \(0.687684\pi\)
\(942\) −9.70701e155 −0.706990
\(943\) 1.19630e155 0.0824095
\(944\) −1.14155e154 −0.00743813
\(945\) 2.84590e154 0.0175408
\(946\) 5.04029e156 2.93880
\(947\) −2.81570e156 −1.55314 −0.776572 0.630028i \(-0.783043\pi\)
−0.776572 + 0.630028i \(0.783043\pi\)
\(948\) 2.10974e155 0.110101
\(949\) −2.12258e156 −1.04807
\(950\) 3.90803e156 1.82586
\(951\) 2.44628e155 0.108151
\(952\) 2.79769e155 0.117047
\(953\) 1.37104e156 0.542842 0.271421 0.962461i \(-0.412506\pi\)
0.271421 + 0.962461i \(0.412506\pi\)
\(954\) −2.31813e156 −0.868658
\(955\) −1.41836e156 −0.503049
\(956\) 8.91800e156 2.99384
\(957\) 1.07364e156 0.341180
\(958\) 2.23395e156 0.672022
\(959\) 1.24609e155 0.0354872
\(960\) −4.14719e155 −0.111819
\(961\) −5.91443e154 −0.0150985
\(962\) −9.17473e156 −2.21770
\(963\) −4.49392e156 −1.02860
\(964\) −1.21792e157 −2.63982
\(965\) −4.46754e155 −0.0917032
\(966\) −2.14741e154 −0.00417461
\(967\) −3.40133e155 −0.0626266 −0.0313133 0.999510i \(-0.509969\pi\)
−0.0313133 + 0.999510i \(0.509969\pi\)
\(968\) 6.99262e155 0.121950
\(969\) −1.61145e156 −0.266207
\(970\) −2.61635e156 −0.409431
\(971\) 1.34108e157 1.98812 0.994062 0.108811i \(-0.0347044\pi\)
0.994062 + 0.108811i \(0.0347044\pi\)
\(972\) −7.92888e156 −1.11361
\(973\) −1.50142e156 −0.199791
\(974\) 1.57750e157 1.98896
\(975\) 1.51396e156 0.180872
\(976\) 1.46668e155 0.0166043
\(977\) 1.30307e157 1.39798 0.698991 0.715130i \(-0.253633\pi\)
0.698991 + 0.715130i \(0.253633\pi\)
\(978\) −3.74554e156 −0.380824
\(979\) 3.29567e156 0.317580
\(980\) 4.90102e156 0.447629
\(981\) 1.72575e157 1.49402
\(982\) −2.59878e157 −2.13263
\(983\) −1.96199e157 −1.52629 −0.763145 0.646227i \(-0.776346\pi\)
−0.763145 + 0.646227i \(0.776346\pi\)
\(984\) 3.55049e156 0.261846
\(985\) −1.85968e156 −0.130028
\(986\) 2.79696e157 1.85416
\(987\) −3.20805e155 −0.0201647
\(988\) −2.64260e157 −1.57504
\(989\) −2.41105e156 −0.136270
\(990\) 8.39876e156 0.450161
\(991\) 2.45550e157 1.24817 0.624085 0.781356i \(-0.285472\pi\)
0.624085 + 0.781356i \(0.285472\pi\)
\(992\) −2.01757e157 −0.972670
\(993\) 1.32462e156 0.0605698
\(994\) −4.18466e156 −0.181499
\(995\) −2.23776e156 −0.0920664
\(996\) 9.18219e156 0.358370
\(997\) −8.88450e156 −0.328955 −0.164478 0.986381i \(-0.552594\pi\)
−0.164478 + 0.986381i \(0.552594\pi\)
\(998\) −1.71775e157 −0.603400
\(999\) −2.49146e157 −0.830357
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 1.106.a.a.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.8 8 1.1 even 1 trivial