Properties

Label 1.106.a.a.1.4
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 1.4
Root \(-9.82818e12\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56214e15 q^{2} +7.24197e24 q^{3} -3.40003e31 q^{4} -1.17115e36 q^{5} -1.85549e40 q^{6} -1.82598e44 q^{7} +1.91046e47 q^{8} -7.27906e49 q^{9} +O(q^{10})\) \(q-2.56214e15 q^{2} +7.24197e24 q^{3} -3.40003e31 q^{4} -1.17115e36 q^{5} -1.85549e40 q^{6} -1.82598e44 q^{7} +1.91046e47 q^{8} -7.27906e49 q^{9} +3.00065e51 q^{10} +6.21211e54 q^{11} -2.46229e56 q^{12} +9.87817e57 q^{13} +4.67841e59 q^{14} -8.48143e60 q^{15} +8.89729e62 q^{16} +1.10681e64 q^{17} +1.86500e65 q^{18} +1.61722e67 q^{19} +3.98194e67 q^{20} -1.32237e69 q^{21} -1.59163e70 q^{22} -2.39949e71 q^{23} +1.38355e72 q^{24} -2.32803e73 q^{25} -2.53092e73 q^{26} -1.43411e75 q^{27} +6.20838e75 q^{28} +4.95038e76 q^{29} +2.17306e76 q^{30} +8.41659e76 q^{31} -1.00294e79 q^{32} +4.49879e79 q^{33} -2.83579e79 q^{34} +2.13850e80 q^{35} +2.47490e81 q^{36} +2.33838e82 q^{37} -4.14355e82 q^{38} +7.15374e82 q^{39} -2.23744e83 q^{40} +3.56271e84 q^{41} +3.38809e84 q^{42} -2.88851e85 q^{43} -2.11214e86 q^{44} +8.52488e85 q^{45} +6.14782e86 q^{46} +8.77673e86 q^{47} +6.44339e87 q^{48} -2.10199e88 q^{49} +5.96474e88 q^{50} +8.01546e88 q^{51} -3.35860e89 q^{52} -1.32848e90 q^{53} +3.67438e90 q^{54} -7.27532e90 q^{55} -3.48846e91 q^{56} +1.17119e92 q^{57} -1.26835e92 q^{58} +9.30110e92 q^{59} +2.88371e92 q^{60} -9.36850e93 q^{61} -2.15645e92 q^{62} +1.32914e94 q^{63} -1.03951e94 q^{64} -1.15688e94 q^{65} -1.15265e95 q^{66} -4.39312e95 q^{67} -3.76317e95 q^{68} -1.73770e96 q^{69} -5.47912e95 q^{70} -2.93219e97 q^{71} -1.39064e97 q^{72} -6.72839e97 q^{73} -5.99126e97 q^{74} -1.68595e98 q^{75} -5.49860e98 q^{76} -1.13432e99 q^{77} -1.83289e98 q^{78} -7.95646e99 q^{79} -1.04201e99 q^{80} -1.26970e99 q^{81} -9.12816e99 q^{82} +6.25680e100 q^{83} +4.49609e100 q^{84} -1.29624e100 q^{85} +7.40076e100 q^{86} +3.58505e101 q^{87} +1.18680e102 q^{88} +3.11302e102 q^{89} -2.18419e101 q^{90} -1.80373e102 q^{91} +8.15832e102 q^{92} +6.09527e101 q^{93} -2.24872e102 q^{94} -1.89401e103 q^{95} -7.26323e103 q^{96} -3.96647e104 q^{97} +5.38558e103 q^{98} -4.52184e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56214e15 −0.402279 −0.201140 0.979563i \(-0.564464\pi\)
−0.201140 + 0.979563i \(0.564464\pi\)
\(3\) 7.24197e24 0.647129 0.323564 0.946206i \(-0.395119\pi\)
0.323564 + 0.946206i \(0.395119\pi\)
\(4\) −3.40003e31 −0.838171
\(5\) −1.17115e36 −0.235878 −0.117939 0.993021i \(-0.537629\pi\)
−0.117939 + 0.993021i \(0.537629\pi\)
\(6\) −1.85549e40 −0.260326
\(7\) −1.82598e44 −0.783156 −0.391578 0.920145i \(-0.628071\pi\)
−0.391578 + 0.920145i \(0.628071\pi\)
\(8\) 1.91046e47 0.739458
\(9\) −7.27906e49 −0.581224
\(10\) 3.00065e51 0.0948888
\(11\) 6.21211e54 1.31863 0.659316 0.751866i \(-0.270846\pi\)
0.659316 + 0.751866i \(0.270846\pi\)
\(12\) −2.46229e56 −0.542405
\(13\) 9.87817e57 0.325575 0.162787 0.986661i \(-0.447952\pi\)
0.162787 + 0.986661i \(0.447952\pi\)
\(14\) 4.67841e59 0.315048
\(15\) −8.48143e60 −0.152643
\(16\) 8.89729e62 0.540703
\(17\) 1.10681e64 0.278935 0.139468 0.990227i \(-0.455461\pi\)
0.139468 + 0.990227i \(0.455461\pi\)
\(18\) 1.86500e65 0.233814
\(19\) 1.61722e67 1.18633 0.593165 0.805081i \(-0.297878\pi\)
0.593165 + 0.805081i \(0.297878\pi\)
\(20\) 3.98194e67 0.197706
\(21\) −1.32237e69 −0.506803
\(22\) −1.59163e70 −0.530458
\(23\) −2.39949e71 −0.775188 −0.387594 0.921830i \(-0.626694\pi\)
−0.387594 + 0.921830i \(0.626694\pi\)
\(24\) 1.38355e72 0.478525
\(25\) −2.32803e73 −0.944362
\(26\) −2.53092e73 −0.130972
\(27\) −1.43411e75 −1.02326
\(28\) 6.20838e75 0.656419
\(29\) 4.95038e76 0.829360 0.414680 0.909967i \(-0.363893\pi\)
0.414680 + 0.909967i \(0.363893\pi\)
\(30\) 2.17306e76 0.0614053
\(31\) 8.41659e76 0.0425253 0.0212627 0.999774i \(-0.493231\pi\)
0.0212627 + 0.999774i \(0.493231\pi\)
\(32\) −1.00294e79 −0.956972
\(33\) 4.49879e79 0.853324
\(34\) −2.83579e79 −0.112210
\(35\) 2.13850e80 0.184729
\(36\) 2.47490e81 0.487166
\(37\) 2.33838e82 1.09226 0.546129 0.837701i \(-0.316101\pi\)
0.546129 + 0.837701i \(0.316101\pi\)
\(38\) −4.14355e82 −0.477236
\(39\) 7.15374e82 0.210689
\(40\) −2.23744e83 −0.174422
\(41\) 3.56271e84 0.759676 0.379838 0.925053i \(-0.375980\pi\)
0.379838 + 0.925053i \(0.375980\pi\)
\(42\) 3.38809e84 0.203876
\(43\) −2.88851e85 −0.505336 −0.252668 0.967553i \(-0.581308\pi\)
−0.252668 + 0.967553i \(0.581308\pi\)
\(44\) −2.11214e86 −1.10524
\(45\) 8.52488e85 0.137098
\(46\) 6.14782e86 0.311842
\(47\) 8.77673e86 0.143944 0.0719722 0.997407i \(-0.477071\pi\)
0.0719722 + 0.997407i \(0.477071\pi\)
\(48\) 6.44339e87 0.349904
\(49\) −2.10199e88 −0.386666
\(50\) 5.96474e88 0.379897
\(51\) 8.01546e88 0.180507
\(52\) −3.35860e89 −0.272887
\(53\) −1.32848e90 −0.397074 −0.198537 0.980093i \(-0.563619\pi\)
−0.198537 + 0.980093i \(0.563619\pi\)
\(54\) 3.67438e90 0.411635
\(55\) −7.27532e90 −0.311036
\(56\) −3.48846e91 −0.579111
\(57\) 1.17119e92 0.767709
\(58\) −1.26835e92 −0.333634
\(59\) 9.30110e92 0.997250 0.498625 0.866818i \(-0.333839\pi\)
0.498625 + 0.866818i \(0.333839\pi\)
\(60\) 2.88371e92 0.127941
\(61\) −9.36850e93 −1.74523 −0.872617 0.488406i \(-0.837579\pi\)
−0.872617 + 0.488406i \(0.837579\pi\)
\(62\) −2.15645e92 −0.0171070
\(63\) 1.32914e94 0.455190
\(64\) −1.03951e94 −0.155733
\(65\) −1.15688e94 −0.0767959
\(66\) −1.15265e95 −0.343275
\(67\) −4.39312e95 −0.594081 −0.297040 0.954865i \(-0.596000\pi\)
−0.297040 + 0.954865i \(0.596000\pi\)
\(68\) −3.76317e95 −0.233796
\(69\) −1.73770e96 −0.501647
\(70\) −5.47912e95 −0.0743128
\(71\) −2.93219e97 −1.88855 −0.944276 0.329154i \(-0.893236\pi\)
−0.944276 + 0.329154i \(0.893236\pi\)
\(72\) −1.39064e97 −0.429791
\(73\) −6.72839e97 −1.00800 −0.504000 0.863703i \(-0.668139\pi\)
−0.504000 + 0.863703i \(0.668139\pi\)
\(74\) −5.99126e97 −0.439393
\(75\) −1.68595e98 −0.611124
\(76\) −5.49860e98 −0.994349
\(77\) −1.13432e99 −1.03269
\(78\) −1.83289e98 −0.0847557
\(79\) −7.95646e99 −1.88494 −0.942470 0.334290i \(-0.891503\pi\)
−0.942470 + 0.334290i \(0.891503\pi\)
\(80\) −1.04201e99 −0.127540
\(81\) −1.26970e99 −0.0809539
\(82\) −9.12816e99 −0.305602
\(83\) 6.25680e100 1.10854 0.554272 0.832336i \(-0.312997\pi\)
0.554272 + 0.832336i \(0.312997\pi\)
\(84\) 4.49609e100 0.424788
\(85\) −1.29624e100 −0.0657947
\(86\) 7.40076e100 0.203286
\(87\) 3.58505e101 0.536703
\(88\) 1.18680e102 0.975073
\(89\) 3.11302e102 1.41321 0.706606 0.707607i \(-0.250225\pi\)
0.706606 + 0.707607i \(0.250225\pi\)
\(90\) −2.18419e101 −0.0551517
\(91\) −1.80373e102 −0.254976
\(92\) 8.15832e102 0.649740
\(93\) 6.09527e101 0.0275193
\(94\) −2.24872e102 −0.0579059
\(95\) −1.89401e103 −0.279829
\(96\) −7.26323e103 −0.619284
\(97\) −3.96647e104 −1.96285 −0.981427 0.191838i \(-0.938555\pi\)
−0.981427 + 0.191838i \(0.938555\pi\)
\(98\) 5.38558e103 0.155548
\(99\) −4.52184e104 −0.766421
\(100\) 7.91537e104 0.791537
\(101\) −1.19764e105 −0.710319 −0.355160 0.934806i \(-0.615573\pi\)
−0.355160 + 0.934806i \(0.615573\pi\)
\(102\) −2.05367e104 −0.0726142
\(103\) 1.60564e105 0.340169 0.170085 0.985429i \(-0.445596\pi\)
0.170085 + 0.985429i \(0.445596\pi\)
\(104\) 1.88718e105 0.240749
\(105\) 1.54869e105 0.119544
\(106\) 3.40374e105 0.159734
\(107\) 4.52744e106 1.29779 0.648895 0.760878i \(-0.275231\pi\)
0.648895 + 0.760878i \(0.275231\pi\)
\(108\) 4.87601e106 0.857664
\(109\) −1.52154e106 −0.164965 −0.0824826 0.996593i \(-0.526285\pi\)
−0.0824826 + 0.996593i \(0.526285\pi\)
\(110\) 1.86404e106 0.125123
\(111\) 1.69345e107 0.706832
\(112\) −1.62463e107 −0.423455
\(113\) −9.69099e107 −1.58398 −0.791990 0.610534i \(-0.790955\pi\)
−0.791990 + 0.610534i \(0.790955\pi\)
\(114\) −3.00074e107 −0.308833
\(115\) 2.81016e107 0.182850
\(116\) −1.68314e108 −0.695146
\(117\) −7.19038e107 −0.189232
\(118\) −2.38307e108 −0.401173
\(119\) −2.02101e108 −0.218450
\(120\) −1.62034e108 −0.112873
\(121\) 1.63965e109 0.738789
\(122\) 2.40034e109 0.702071
\(123\) 2.58011e109 0.491608
\(124\) −2.86166e108 −0.0356435
\(125\) 5.61358e109 0.458632
\(126\) −3.40544e109 −0.183113
\(127\) 9.27636e109 0.329369 0.164684 0.986346i \(-0.447339\pi\)
0.164684 + 0.986346i \(0.447339\pi\)
\(128\) 4.33473e110 1.01962
\(129\) −2.09185e110 −0.327017
\(130\) 2.96409e109 0.0308934
\(131\) −2.18559e111 −1.52344 −0.761721 0.647905i \(-0.775645\pi\)
−0.761721 + 0.647905i \(0.775645\pi\)
\(132\) −1.52960e111 −0.715232
\(133\) −2.95301e111 −0.929083
\(134\) 1.12558e111 0.238986
\(135\) 1.67956e111 0.241364
\(136\) 2.11451e111 0.206261
\(137\) −3.76107e111 −0.249736 −0.124868 0.992173i \(-0.539851\pi\)
−0.124868 + 0.992173i \(0.539851\pi\)
\(138\) 4.45223e111 0.201802
\(139\) 3.64309e112 1.13030 0.565149 0.824989i \(-0.308819\pi\)
0.565149 + 0.824989i \(0.308819\pi\)
\(140\) −7.27094e111 −0.154835
\(141\) 6.35608e111 0.0931506
\(142\) 7.51268e112 0.759725
\(143\) 6.13643e112 0.429313
\(144\) −6.47639e112 −0.314270
\(145\) −5.79763e112 −0.195628
\(146\) 1.72391e113 0.405498
\(147\) −1.52225e113 −0.250223
\(148\) −7.95057e113 −0.915500
\(149\) −6.94410e113 −0.561483 −0.280742 0.959783i \(-0.590580\pi\)
−0.280742 + 0.959783i \(0.590580\pi\)
\(150\) 4.31964e113 0.245842
\(151\) −4.13611e114 −1.66074 −0.830372 0.557210i \(-0.811872\pi\)
−0.830372 + 0.557210i \(0.811872\pi\)
\(152\) 3.08964e114 0.877242
\(153\) −8.05652e113 −0.162124
\(154\) 2.90628e114 0.415432
\(155\) −9.85710e112 −0.0100308
\(156\) −2.43229e114 −0.176593
\(157\) 2.62565e115 1.36303 0.681515 0.731804i \(-0.261321\pi\)
0.681515 + 0.731804i \(0.261321\pi\)
\(158\) 2.03855e115 0.758272
\(159\) −9.62079e114 −0.256958
\(160\) 1.17459e115 0.225729
\(161\) 4.38141e115 0.607094
\(162\) 3.25315e114 0.0325661
\(163\) −2.06745e116 −1.49825 −0.749126 0.662428i \(-0.769526\pi\)
−0.749126 + 0.662428i \(0.769526\pi\)
\(164\) −1.21133e116 −0.636739
\(165\) −5.26876e115 −0.201280
\(166\) −1.60308e116 −0.445944
\(167\) 6.33450e116 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(168\) −2.52633e116 −0.374760
\(169\) −8.22982e116 −0.894001
\(170\) 3.32114e115 0.0264678
\(171\) −1.17719e117 −0.689524
\(172\) 9.82101e116 0.423558
\(173\) 4.01565e117 1.27742 0.638712 0.769446i \(-0.279468\pi\)
0.638712 + 0.769446i \(0.279468\pi\)
\(174\) −9.18538e116 −0.215904
\(175\) 4.25093e117 0.739583
\(176\) 5.52710e117 0.712988
\(177\) 6.73583e117 0.645349
\(178\) −7.97600e117 −0.568506
\(179\) −1.42554e118 −0.757175 −0.378587 0.925566i \(-0.623590\pi\)
−0.378587 + 0.925566i \(0.623590\pi\)
\(180\) −2.89848e117 −0.114912
\(181\) 1.74104e117 0.0516041 0.0258021 0.999667i \(-0.491786\pi\)
0.0258021 + 0.999667i \(0.491786\pi\)
\(182\) 4.62141e117 0.102571
\(183\) −6.78463e118 −1.12939
\(184\) −4.58412e118 −0.573219
\(185\) −2.73860e118 −0.257640
\(186\) −1.56169e117 −0.0110705
\(187\) 6.87561e118 0.367813
\(188\) −2.98411e118 −0.120650
\(189\) 2.61865e119 0.801369
\(190\) 4.85272e118 0.112570
\(191\) 3.92171e119 0.690595 0.345297 0.938493i \(-0.387778\pi\)
0.345297 + 0.938493i \(0.387778\pi\)
\(192\) −7.52810e118 −0.100779
\(193\) 5.37554e118 0.0547852 0.0273926 0.999625i \(-0.491280\pi\)
0.0273926 + 0.999625i \(0.491280\pi\)
\(194\) 1.01626e120 0.789615
\(195\) −8.37810e118 −0.0496968
\(196\) 7.14681e119 0.324092
\(197\) −4.45142e120 −1.54533 −0.772667 0.634812i \(-0.781078\pi\)
−0.772667 + 0.634812i \(0.781078\pi\)
\(198\) 1.15856e120 0.308315
\(199\) 1.12654e120 0.230122 0.115061 0.993358i \(-0.463294\pi\)
0.115061 + 0.993358i \(0.463294\pi\)
\(200\) −4.44761e120 −0.698316
\(201\) −3.18148e120 −0.384447
\(202\) 3.06851e120 0.285747
\(203\) −9.03928e120 −0.649519
\(204\) −2.72528e120 −0.151296
\(205\) −4.17247e120 −0.179191
\(206\) −4.11388e120 −0.136843
\(207\) 1.74660e121 0.450558
\(208\) 8.78889e120 0.176039
\(209\) 1.00464e122 1.56433
\(210\) −3.96796e120 −0.0480899
\(211\) 1.16814e122 1.10323 0.551615 0.834099i \(-0.314012\pi\)
0.551615 + 0.834099i \(0.314012\pi\)
\(212\) 4.51686e121 0.332816
\(213\) −2.12348e122 −1.22214
\(214\) −1.15999e122 −0.522074
\(215\) 3.38288e121 0.119198
\(216\) −2.73981e122 −0.756655
\(217\) −1.53685e121 −0.0333040
\(218\) 3.89839e121 0.0663620
\(219\) −4.87268e122 −0.652306
\(220\) 2.47363e122 0.260702
\(221\) 1.09332e122 0.0908142
\(222\) −4.33885e122 −0.284344
\(223\) −2.12569e123 −1.10026 −0.550130 0.835079i \(-0.685422\pi\)
−0.550130 + 0.835079i \(0.685422\pi\)
\(224\) 1.83134e123 0.749459
\(225\) 1.69459e123 0.548886
\(226\) 2.48296e123 0.637202
\(227\) 5.43051e123 1.10531 0.552654 0.833411i \(-0.313615\pi\)
0.552654 + 0.833411i \(0.313615\pi\)
\(228\) −3.98207e123 −0.643472
\(229\) 3.86165e123 0.495919 0.247959 0.968770i \(-0.420240\pi\)
0.247959 + 0.968770i \(0.420240\pi\)
\(230\) −7.20002e122 −0.0735567
\(231\) −8.21470e123 −0.668286
\(232\) 9.45749e123 0.613277
\(233\) −2.50053e123 −0.129374 −0.0646868 0.997906i \(-0.520605\pi\)
−0.0646868 + 0.997906i \(0.520605\pi\)
\(234\) 1.84227e123 0.0761241
\(235\) −1.02789e123 −0.0339533
\(236\) −3.16240e124 −0.835866
\(237\) −5.76204e124 −1.21980
\(238\) 5.17809e123 0.0878779
\(239\) 2.77950e124 0.378509 0.189255 0.981928i \(-0.439393\pi\)
0.189255 + 0.981928i \(0.439393\pi\)
\(240\) −7.54617e123 −0.0825347
\(241\) −7.57110e124 −0.665678 −0.332839 0.942984i \(-0.608007\pi\)
−0.332839 + 0.942984i \(0.608007\pi\)
\(242\) −4.20102e124 −0.297199
\(243\) 1.70408e125 0.970868
\(244\) 3.18531e125 1.46280
\(245\) 2.46174e124 0.0912060
\(246\) −6.61059e124 −0.197764
\(247\) 1.59752e125 0.386239
\(248\) 1.60796e124 0.0314457
\(249\) 4.53116e125 0.717370
\(250\) −1.43828e125 −0.184498
\(251\) −6.06940e125 −0.631357 −0.315679 0.948866i \(-0.602232\pi\)
−0.315679 + 0.948866i \(0.602232\pi\)
\(252\) −4.51912e125 −0.381527
\(253\) −1.49059e126 −1.02219
\(254\) −2.37673e125 −0.132498
\(255\) −9.38731e124 −0.0425776
\(256\) −6.88941e125 −0.254439
\(257\) 2.79612e126 0.841525 0.420762 0.907171i \(-0.361763\pi\)
0.420762 + 0.907171i \(0.361763\pi\)
\(258\) 5.35961e125 0.131552
\(259\) −4.26984e126 −0.855409
\(260\) 3.93343e125 0.0643681
\(261\) −3.60341e126 −0.482044
\(262\) 5.59979e126 0.612849
\(263\) 2.58860e126 0.231946 0.115973 0.993252i \(-0.463001\pi\)
0.115973 + 0.993252i \(0.463001\pi\)
\(264\) 8.59476e126 0.630998
\(265\) 1.55585e126 0.0936609
\(266\) 7.56603e126 0.373751
\(267\) 2.25444e127 0.914530
\(268\) 1.49367e127 0.497941
\(269\) −3.07299e127 −0.842493 −0.421247 0.906946i \(-0.638407\pi\)
−0.421247 + 0.906946i \(0.638407\pi\)
\(270\) −4.30325e126 −0.0970955
\(271\) −6.80647e127 −1.26484 −0.632418 0.774627i \(-0.717937\pi\)
−0.632418 + 0.774627i \(0.717937\pi\)
\(272\) 9.84758e126 0.150821
\(273\) −1.30626e127 −0.165002
\(274\) 9.63637e126 0.100464
\(275\) −1.44620e128 −1.24526
\(276\) 5.90823e127 0.420466
\(277\) 4.37682e127 0.257615 0.128807 0.991670i \(-0.458885\pi\)
0.128807 + 0.991670i \(0.458885\pi\)
\(278\) −9.33409e127 −0.454695
\(279\) −6.12649e126 −0.0247167
\(280\) 4.08551e127 0.136600
\(281\) 3.24288e127 0.0899184 0.0449592 0.998989i \(-0.485684\pi\)
0.0449592 + 0.998989i \(0.485684\pi\)
\(282\) −1.62851e127 −0.0374726
\(283\) 5.75459e128 1.09958 0.549789 0.835303i \(-0.314708\pi\)
0.549789 + 0.835303i \(0.314708\pi\)
\(284\) 9.96953e128 1.58293
\(285\) −1.37164e128 −0.181086
\(286\) −1.57224e128 −0.172704
\(287\) −6.50544e128 −0.594945
\(288\) 7.30043e128 0.556215
\(289\) −1.45198e129 −0.922195
\(290\) 1.48543e128 0.0786970
\(291\) −2.87250e129 −1.27022
\(292\) 2.28767e129 0.844878
\(293\) −2.15304e129 −0.664512 −0.332256 0.943189i \(-0.607810\pi\)
−0.332256 + 0.943189i \(0.607810\pi\)
\(294\) 3.90022e128 0.100659
\(295\) −1.08930e129 −0.235229
\(296\) 4.46739e129 0.807679
\(297\) −8.90884e129 −1.34930
\(298\) 1.77917e129 0.225873
\(299\) −2.37025e129 −0.252382
\(300\) 5.73228e129 0.512226
\(301\) 5.27436e129 0.395757
\(302\) 1.05973e130 0.668083
\(303\) −8.67326e129 −0.459668
\(304\) 1.43889e130 0.641452
\(305\) 1.09719e130 0.411662
\(306\) 2.06419e129 0.0652191
\(307\) −1.55007e130 −0.412654 −0.206327 0.978483i \(-0.566151\pi\)
−0.206327 + 0.978483i \(0.566151\pi\)
\(308\) 3.85671e130 0.865575
\(309\) 1.16280e130 0.220133
\(310\) 2.52552e128 0.00403518
\(311\) −1.05354e131 −1.42145 −0.710724 0.703471i \(-0.751633\pi\)
−0.710724 + 0.703471i \(0.751633\pi\)
\(312\) 1.36669e130 0.155795
\(313\) −1.51544e131 −1.46036 −0.730181 0.683253i \(-0.760564\pi\)
−0.730181 + 0.683253i \(0.760564\pi\)
\(314\) −6.72729e130 −0.548319
\(315\) −1.55662e130 −0.107369
\(316\) 2.70522e131 1.57990
\(317\) −3.01876e131 −1.49354 −0.746770 0.665083i \(-0.768396\pi\)
−0.746770 + 0.665083i \(0.768396\pi\)
\(318\) 2.46498e130 0.103369
\(319\) 3.07523e131 1.09362
\(320\) 1.21742e130 0.0367340
\(321\) 3.27876e131 0.839837
\(322\) −1.12258e131 −0.244221
\(323\) 1.78995e131 0.330910
\(324\) 4.31702e130 0.0678532
\(325\) −2.29967e131 −0.307460
\(326\) 5.29708e131 0.602716
\(327\) −1.10189e131 −0.106754
\(328\) 6.80642e131 0.561749
\(329\) −1.60261e131 −0.112731
\(330\) 1.34993e131 0.0809709
\(331\) −1.11942e132 −0.572828 −0.286414 0.958106i \(-0.592463\pi\)
−0.286414 + 0.958106i \(0.592463\pi\)
\(332\) −2.12733e132 −0.929150
\(333\) −1.70212e132 −0.634847
\(334\) −1.62299e132 −0.517160
\(335\) 5.14500e131 0.140131
\(336\) −1.17655e132 −0.274030
\(337\) 6.42673e132 1.28062 0.640310 0.768117i \(-0.278806\pi\)
0.640310 + 0.768117i \(0.278806\pi\)
\(338\) 2.10859e132 0.359638
\(339\) −7.01818e132 −1.02504
\(340\) 4.40724e131 0.0551472
\(341\) 5.22848e131 0.0560752
\(342\) 3.01611e132 0.277381
\(343\) 1.37645e133 1.08598
\(344\) −5.51838e132 −0.373675
\(345\) 2.03511e132 0.118327
\(346\) −1.02886e133 −0.513881
\(347\) 2.99641e133 1.28619 0.643093 0.765788i \(-0.277651\pi\)
0.643093 + 0.765788i \(0.277651\pi\)
\(348\) −1.21893e133 −0.449849
\(349\) 4.87919e133 1.54886 0.774431 0.632659i \(-0.218036\pi\)
0.774431 + 0.632659i \(0.218036\pi\)
\(350\) −1.08915e133 −0.297519
\(351\) −1.41664e133 −0.333146
\(352\) −6.23035e133 −1.26189
\(353\) −5.34299e133 −0.932421 −0.466210 0.884674i \(-0.654381\pi\)
−0.466210 + 0.884674i \(0.654381\pi\)
\(354\) −1.72581e133 −0.259611
\(355\) 3.43404e133 0.445468
\(356\) −1.05844e134 −1.18451
\(357\) −1.46361e133 −0.141365
\(358\) 3.65244e133 0.304596
\(359\) 7.64396e133 0.550630 0.275315 0.961354i \(-0.411218\pi\)
0.275315 + 0.961354i \(0.411218\pi\)
\(360\) 1.62864e133 0.101378
\(361\) 7.57057e133 0.407381
\(362\) −4.46079e132 −0.0207593
\(363\) 1.18743e134 0.478091
\(364\) 6.13274e133 0.213713
\(365\) 7.87995e133 0.237765
\(366\) 1.73832e134 0.454330
\(367\) 2.15324e134 0.487669 0.243834 0.969817i \(-0.421595\pi\)
0.243834 + 0.969817i \(0.421595\pi\)
\(368\) −2.13489e134 −0.419146
\(369\) −2.59332e134 −0.441542
\(370\) 7.01667e133 0.103643
\(371\) 2.42577e134 0.310971
\(372\) −2.07241e133 −0.0230659
\(373\) −1.48002e135 −1.43072 −0.715358 0.698758i \(-0.753737\pi\)
−0.715358 + 0.698758i \(0.753737\pi\)
\(374\) −1.76163e134 −0.147963
\(375\) 4.06534e134 0.296794
\(376\) 1.67676e134 0.106441
\(377\) 4.89006e134 0.270019
\(378\) −6.70934e134 −0.322374
\(379\) −3.14867e135 −1.31695 −0.658474 0.752604i \(-0.728798\pi\)
−0.658474 + 0.752604i \(0.728798\pi\)
\(380\) 6.43969e134 0.234545
\(381\) 6.71791e134 0.213144
\(382\) −1.00479e135 −0.277812
\(383\) 2.26604e135 0.546176 0.273088 0.961989i \(-0.411955\pi\)
0.273088 + 0.961989i \(0.411955\pi\)
\(384\) 3.13919e135 0.659825
\(385\) 1.32846e135 0.243590
\(386\) −1.37729e134 −0.0220389
\(387\) 2.10256e135 0.293713
\(388\) 1.34861e136 1.64521
\(389\) −7.51665e135 −0.801070 −0.400535 0.916281i \(-0.631176\pi\)
−0.400535 + 0.916281i \(0.631176\pi\)
\(390\) 2.14659e134 0.0199920
\(391\) −2.65577e135 −0.216227
\(392\) −4.01576e135 −0.285923
\(393\) −1.58280e136 −0.985863
\(394\) 1.14052e136 0.621656
\(395\) 9.31821e135 0.444616
\(396\) 1.53744e136 0.642392
\(397\) −4.62294e136 −1.69206 −0.846031 0.533133i \(-0.821014\pi\)
−0.846031 + 0.533133i \(0.821014\pi\)
\(398\) −2.88634e135 −0.0925733
\(399\) −2.13856e136 −0.601236
\(400\) −2.07132e136 −0.510619
\(401\) −1.12123e136 −0.242446 −0.121223 0.992625i \(-0.538682\pi\)
−0.121223 + 0.992625i \(0.538682\pi\)
\(402\) 8.15139e135 0.154655
\(403\) 8.31405e134 0.0138452
\(404\) 4.07200e136 0.595369
\(405\) 1.48701e135 0.0190952
\(406\) 2.31599e136 0.261288
\(407\) 1.45263e137 1.44029
\(408\) 1.53132e136 0.133477
\(409\) 8.99941e136 0.689827 0.344914 0.938634i \(-0.387908\pi\)
0.344914 + 0.938634i \(0.387908\pi\)
\(410\) 1.06905e136 0.0720848
\(411\) −2.72375e136 −0.161611
\(412\) −5.45923e136 −0.285120
\(413\) −1.69836e137 −0.781003
\(414\) −4.47503e136 −0.181250
\(415\) −7.32766e136 −0.261481
\(416\) −9.90717e136 −0.311566
\(417\) 2.63831e137 0.731448
\(418\) −2.57402e137 −0.629299
\(419\) 2.61797e137 0.564584 0.282292 0.959329i \(-0.408905\pi\)
0.282292 + 0.959329i \(0.408905\pi\)
\(420\) −5.26559e136 −0.100198
\(421\) −4.32460e137 −0.726333 −0.363166 0.931724i \(-0.618304\pi\)
−0.363166 + 0.931724i \(0.618304\pi\)
\(422\) −2.99294e137 −0.443807
\(423\) −6.38864e136 −0.0836640
\(424\) −2.53800e137 −0.293619
\(425\) −2.57668e137 −0.263416
\(426\) 5.44066e137 0.491640
\(427\) 1.71067e138 1.36679
\(428\) −1.53934e138 −1.08777
\(429\) 4.44398e137 0.277821
\(430\) −8.66740e136 −0.0479507
\(431\) 2.80133e138 1.37185 0.685926 0.727672i \(-0.259397\pi\)
0.685926 + 0.727672i \(0.259397\pi\)
\(432\) −1.27597e138 −0.553277
\(433\) 3.15333e138 1.21103 0.605516 0.795833i \(-0.292967\pi\)
0.605516 + 0.795833i \(0.292967\pi\)
\(434\) 3.93763e136 0.0133975
\(435\) −4.19863e137 −0.126596
\(436\) 5.17328e137 0.138269
\(437\) −3.88051e138 −0.919630
\(438\) 1.24845e138 0.262409
\(439\) −2.85338e138 −0.532075 −0.266037 0.963963i \(-0.585714\pi\)
−0.266037 + 0.963963i \(0.585714\pi\)
\(440\) −1.38992e138 −0.229998
\(441\) 1.53005e138 0.224740
\(442\) −2.80124e137 −0.0365327
\(443\) −8.53493e138 −0.988564 −0.494282 0.869302i \(-0.664569\pi\)
−0.494282 + 0.869302i \(0.664569\pi\)
\(444\) −5.75778e138 −0.592446
\(445\) −3.64582e138 −0.333346
\(446\) 5.44632e138 0.442612
\(447\) −5.02889e138 −0.363352
\(448\) 1.89812e138 0.121963
\(449\) 1.33416e139 0.762563 0.381282 0.924459i \(-0.375483\pi\)
0.381282 + 0.924459i \(0.375483\pi\)
\(450\) −4.34177e138 −0.220805
\(451\) 2.21320e139 1.00173
\(452\) 3.29496e139 1.32765
\(453\) −2.99536e139 −1.07471
\(454\) −1.39137e139 −0.444643
\(455\) 2.11244e138 0.0601432
\(456\) 2.23751e139 0.567689
\(457\) 5.91284e139 1.33720 0.668599 0.743623i \(-0.266894\pi\)
0.668599 + 0.743623i \(0.266894\pi\)
\(458\) −9.89409e138 −0.199498
\(459\) −1.58728e139 −0.285422
\(460\) −9.55462e138 −0.153259
\(461\) −3.82087e139 −0.546844 −0.273422 0.961894i \(-0.588155\pi\)
−0.273422 + 0.961894i \(0.588155\pi\)
\(462\) 2.10472e139 0.268838
\(463\) −1.58389e140 −1.80602 −0.903012 0.429616i \(-0.858649\pi\)
−0.903012 + 0.429616i \(0.858649\pi\)
\(464\) 4.40449e139 0.448437
\(465\) −7.13848e137 −0.00649121
\(466\) 6.40669e138 0.0520443
\(467\) −1.90647e140 −1.38386 −0.691932 0.721962i \(-0.743240\pi\)
−0.691932 + 0.721962i \(0.743240\pi\)
\(468\) 2.44475e139 0.158609
\(469\) 8.02173e139 0.465258
\(470\) 2.63359e138 0.0136587
\(471\) 1.90149e140 0.882056
\(472\) 1.77694e140 0.737425
\(473\) −1.79438e140 −0.666351
\(474\) 1.47631e140 0.490700
\(475\) −3.76495e140 −1.12033
\(476\) 6.87147e139 0.183099
\(477\) 9.67007e139 0.230789
\(478\) −7.12146e139 −0.152266
\(479\) 6.06845e140 1.16269 0.581344 0.813658i \(-0.302527\pi\)
0.581344 + 0.813658i \(0.302527\pi\)
\(480\) 8.50633e139 0.146075
\(481\) 2.30990e140 0.355611
\(482\) 1.93982e140 0.267788
\(483\) 3.17300e140 0.392868
\(484\) −5.57487e140 −0.619232
\(485\) 4.64533e140 0.462994
\(486\) −4.36608e140 −0.390560
\(487\) −6.06707e140 −0.487201 −0.243601 0.969876i \(-0.578329\pi\)
−0.243601 + 0.969876i \(0.578329\pi\)
\(488\) −1.78981e141 −1.29053
\(489\) −1.49724e141 −0.969562
\(490\) −6.30732e139 −0.0366903
\(491\) 8.94476e140 0.467509 0.233755 0.972296i \(-0.424899\pi\)
0.233755 + 0.972296i \(0.424899\pi\)
\(492\) −8.77243e140 −0.412052
\(493\) 5.47911e140 0.231338
\(494\) −4.09307e140 −0.155376
\(495\) 5.29575e140 0.180782
\(496\) 7.48849e139 0.0229935
\(497\) 5.35412e141 1.47903
\(498\) −1.16094e141 −0.288583
\(499\) 6.99369e140 0.156469 0.0782344 0.996935i \(-0.475072\pi\)
0.0782344 + 0.996935i \(0.475072\pi\)
\(500\) −1.90863e141 −0.384412
\(501\) 4.58742e141 0.831933
\(502\) 1.55506e141 0.253982
\(503\) −9.78558e140 −0.143968 −0.0719842 0.997406i \(-0.522933\pi\)
−0.0719842 + 0.997406i \(0.522933\pi\)
\(504\) 2.53927e141 0.336594
\(505\) 1.40261e141 0.167549
\(506\) 3.81909e141 0.411205
\(507\) −5.96001e141 −0.578534
\(508\) −3.15399e141 −0.276067
\(509\) −6.84286e141 −0.540199 −0.270100 0.962832i \(-0.587057\pi\)
−0.270100 + 0.962832i \(0.587057\pi\)
\(510\) 2.40516e140 0.0171281
\(511\) 1.22859e142 0.789422
\(512\) −1.58186e142 −0.917264
\(513\) −2.31927e142 −1.21392
\(514\) −7.16404e141 −0.338528
\(515\) −1.88045e141 −0.0802384
\(516\) 7.11235e141 0.274096
\(517\) 5.45220e141 0.189810
\(518\) 1.09399e142 0.344113
\(519\) 2.90812e142 0.826658
\(520\) −2.21018e141 −0.0567873
\(521\) −6.61502e142 −1.53656 −0.768282 0.640111i \(-0.778888\pi\)
−0.768282 + 0.640111i \(0.778888\pi\)
\(522\) 9.23243e141 0.193916
\(523\) 2.02789e142 0.385218 0.192609 0.981276i \(-0.438305\pi\)
0.192609 + 0.981276i \(0.438305\pi\)
\(524\) 7.43107e142 1.27691
\(525\) 3.07851e142 0.478605
\(526\) −6.63234e141 −0.0933072
\(527\) 9.31554e140 0.0118618
\(528\) 4.00271e142 0.461395
\(529\) −3.82372e142 −0.399083
\(530\) −3.98629e141 −0.0376778
\(531\) −6.77033e142 −0.579626
\(532\) 1.00403e143 0.778731
\(533\) 3.51931e142 0.247331
\(534\) −5.77619e142 −0.367896
\(535\) −5.30231e142 −0.306120
\(536\) −8.39287e142 −0.439298
\(537\) −1.03237e143 −0.489990
\(538\) 7.87342e142 0.338918
\(539\) −1.30578e143 −0.509870
\(540\) −5.71054e142 −0.202304
\(541\) −2.71630e143 −0.873214 −0.436607 0.899652i \(-0.643820\pi\)
−0.436607 + 0.899652i \(0.643820\pi\)
\(542\) 1.74391e143 0.508817
\(543\) 1.26086e142 0.0333945
\(544\) −1.11006e143 −0.266933
\(545\) 1.78195e142 0.0389116
\(546\) 3.34681e142 0.0663770
\(547\) −1.10405e142 −0.0198909 −0.00994546 0.999951i \(-0.503166\pi\)
−0.00994546 + 0.999951i \(0.503166\pi\)
\(548\) 1.27877e143 0.209322
\(549\) 6.81939e143 1.01437
\(550\) 3.70536e143 0.500944
\(551\) 8.00586e143 0.983896
\(552\) −3.31981e143 −0.370947
\(553\) 1.45283e144 1.47620
\(554\) −1.12140e143 −0.103633
\(555\) −1.98328e143 −0.166726
\(556\) −1.23866e144 −0.947383
\(557\) −2.49231e144 −1.73462 −0.867308 0.497771i \(-0.834152\pi\)
−0.867308 + 0.497771i \(0.834152\pi\)
\(558\) 1.56969e142 0.00994303
\(559\) −2.85332e143 −0.164524
\(560\) 1.90268e143 0.0998837
\(561\) 4.97929e143 0.238022
\(562\) −8.30869e142 −0.0361723
\(563\) −5.67998e143 −0.225245 −0.112623 0.993638i \(-0.535925\pi\)
−0.112623 + 0.993638i \(0.535925\pi\)
\(564\) −2.16108e143 −0.0780762
\(565\) 1.13496e144 0.373626
\(566\) −1.47440e144 −0.442338
\(567\) 2.31845e143 0.0633996
\(568\) −5.60184e144 −1.39651
\(569\) 5.71338e144 1.29867 0.649336 0.760502i \(-0.275047\pi\)
0.649336 + 0.760502i \(0.275047\pi\)
\(570\) 3.51432e143 0.0728470
\(571\) −1.15237e144 −0.217869 −0.108934 0.994049i \(-0.534744\pi\)
−0.108934 + 0.994049i \(0.534744\pi\)
\(572\) −2.08640e144 −0.359838
\(573\) 2.84009e144 0.446904
\(574\) 1.66678e144 0.239334
\(575\) 5.58608e144 0.732058
\(576\) 7.56666e143 0.0905157
\(577\) 6.44279e144 0.703629 0.351815 0.936070i \(-0.385565\pi\)
0.351815 + 0.936070i \(0.385565\pi\)
\(578\) 3.72016e144 0.370980
\(579\) 3.89295e143 0.0354531
\(580\) 1.97121e144 0.163970
\(581\) −1.14248e145 −0.868163
\(582\) 7.35975e144 0.510983
\(583\) −8.25265e144 −0.523594
\(584\) −1.28543e145 −0.745375
\(585\) 8.42102e143 0.0446356
\(586\) 5.51639e144 0.267319
\(587\) −1.50682e145 −0.667670 −0.333835 0.942632i \(-0.608343\pi\)
−0.333835 + 0.942632i \(0.608343\pi\)
\(588\) 5.17570e144 0.209729
\(589\) 1.36115e144 0.0504491
\(590\) 2.79093e144 0.0946278
\(591\) −3.22371e145 −1.00003
\(592\) 2.08053e145 0.590587
\(593\) −6.35659e145 −1.65140 −0.825702 0.564107i \(-0.809220\pi\)
−0.825702 + 0.564107i \(0.809220\pi\)
\(594\) 2.28257e145 0.542794
\(595\) 2.36690e144 0.0515275
\(596\) 2.36101e145 0.470619
\(597\) 8.15833e144 0.148919
\(598\) 6.07292e144 0.101528
\(599\) 4.32195e145 0.661868 0.330934 0.943654i \(-0.392636\pi\)
0.330934 + 0.943654i \(0.392636\pi\)
\(600\) −3.22094e145 −0.451900
\(601\) 6.55679e145 0.842910 0.421455 0.906849i \(-0.361519\pi\)
0.421455 + 0.906849i \(0.361519\pi\)
\(602\) −1.35136e145 −0.159205
\(603\) 3.19778e145 0.345294
\(604\) 1.40629e146 1.39199
\(605\) −1.92028e145 −0.174264
\(606\) 2.22221e145 0.184915
\(607\) 2.18967e145 0.167098 0.0835492 0.996504i \(-0.473374\pi\)
0.0835492 + 0.996504i \(0.473374\pi\)
\(608\) −1.62197e146 −1.13529
\(609\) −6.54622e145 −0.420322
\(610\) −2.81116e145 −0.165603
\(611\) 8.66980e144 0.0468647
\(612\) 2.73924e145 0.135888
\(613\) −2.25524e146 −1.02688 −0.513438 0.858127i \(-0.671628\pi\)
−0.513438 + 0.858127i \(0.671628\pi\)
\(614\) 3.97148e145 0.166002
\(615\) −3.02169e145 −0.115960
\(616\) −2.16707e146 −0.763635
\(617\) −2.13544e146 −0.691060 −0.345530 0.938408i \(-0.612301\pi\)
−0.345530 + 0.938408i \(0.612301\pi\)
\(618\) −2.97926e145 −0.0885550
\(619\) 2.66610e146 0.727977 0.363989 0.931403i \(-0.381415\pi\)
0.363989 + 0.931403i \(0.381415\pi\)
\(620\) 3.35144e144 0.00840752
\(621\) 3.44112e146 0.793216
\(622\) 2.69932e146 0.571819
\(623\) −5.68432e146 −1.10677
\(624\) 6.36489e145 0.113920
\(625\) 5.08160e146 0.836180
\(626\) 3.88276e146 0.587474
\(627\) 7.27555e146 1.01232
\(628\) −8.92729e146 −1.14245
\(629\) 2.58814e146 0.304669
\(630\) 3.98829e145 0.0431924
\(631\) 1.72070e146 0.171460 0.0857302 0.996318i \(-0.472678\pi\)
0.0857302 + 0.996318i \(0.472678\pi\)
\(632\) −1.52005e147 −1.39383
\(633\) 8.45964e146 0.713932
\(634\) 7.73447e146 0.600820
\(635\) −1.08640e146 −0.0776908
\(636\) 3.27110e146 0.215375
\(637\) −2.07638e146 −0.125889
\(638\) −7.87916e146 −0.439941
\(639\) 2.13436e147 1.09767
\(640\) −5.07662e146 −0.240506
\(641\) −4.25546e147 −1.85738 −0.928689 0.370859i \(-0.879063\pi\)
−0.928689 + 0.370859i \(0.879063\pi\)
\(642\) −8.40063e146 −0.337849
\(643\) 3.00504e146 0.111372 0.0556858 0.998448i \(-0.482265\pi\)
0.0556858 + 0.998448i \(0.482265\pi\)
\(644\) −1.48969e147 −0.508848
\(645\) 2.44987e146 0.0771362
\(646\) −4.58611e146 −0.133118
\(647\) −2.99856e147 −0.802486 −0.401243 0.915972i \(-0.631422\pi\)
−0.401243 + 0.915972i \(0.631422\pi\)
\(648\) −2.42571e146 −0.0598620
\(649\) 5.77795e147 1.31500
\(650\) 5.89207e146 0.123685
\(651\) −1.11298e146 −0.0215520
\(652\) 7.02937e147 1.25579
\(653\) −6.59787e146 −0.108758 −0.0543791 0.998520i \(-0.517318\pi\)
−0.0543791 + 0.998520i \(0.517318\pi\)
\(654\) 2.82320e146 0.0429448
\(655\) 2.55966e147 0.359346
\(656\) 3.16985e147 0.410759
\(657\) 4.89764e147 0.585875
\(658\) 4.10611e146 0.0453494
\(659\) −1.06461e148 −1.08569 −0.542844 0.839834i \(-0.682652\pi\)
−0.542844 + 0.839834i \(0.682652\pi\)
\(660\) 1.79139e147 0.168707
\(661\) −1.04052e148 −0.905051 −0.452526 0.891751i \(-0.649477\pi\)
−0.452526 + 0.891751i \(0.649477\pi\)
\(662\) 2.86811e147 0.230437
\(663\) 7.91781e146 0.0587685
\(664\) 1.19534e148 0.819722
\(665\) 3.45842e147 0.219150
\(666\) 4.36108e147 0.255386
\(667\) −1.18784e148 −0.642910
\(668\) −2.15375e148 −1.07753
\(669\) −1.53942e148 −0.712010
\(670\) −1.31822e147 −0.0563716
\(671\) −5.81982e148 −2.30132
\(672\) 1.32625e148 0.484996
\(673\) 4.95268e148 1.67513 0.837567 0.546335i \(-0.183977\pi\)
0.837567 + 0.546335i \(0.183977\pi\)
\(674\) −1.64662e148 −0.515167
\(675\) 3.33865e148 0.966323
\(676\) 2.79816e148 0.749326
\(677\) −6.34338e148 −1.57187 −0.785934 0.618311i \(-0.787817\pi\)
−0.785934 + 0.618311i \(0.787817\pi\)
\(678\) 1.79815e148 0.412352
\(679\) 7.24268e148 1.53722
\(680\) −2.47641e147 −0.0486524
\(681\) 3.93276e148 0.715277
\(682\) −1.33961e147 −0.0225579
\(683\) −4.16276e148 −0.649074 −0.324537 0.945873i \(-0.605209\pi\)
−0.324537 + 0.945873i \(0.605209\pi\)
\(684\) 4.00247e148 0.577940
\(685\) 4.40478e147 0.0589073
\(686\) −3.52666e148 −0.436866
\(687\) 2.79660e148 0.320923
\(688\) −2.56999e148 −0.273236
\(689\) −1.31229e148 −0.129277
\(690\) −5.21423e147 −0.0476006
\(691\) 3.41789e148 0.289175 0.144587 0.989492i \(-0.453815\pi\)
0.144587 + 0.989492i \(0.453815\pi\)
\(692\) −1.36533e149 −1.07070
\(693\) 8.25678e148 0.600227
\(694\) −7.67721e148 −0.517406
\(695\) −4.26660e148 −0.266612
\(696\) 6.84909e148 0.396869
\(697\) 3.94324e148 0.211901
\(698\) −1.25011e149 −0.623075
\(699\) −1.81087e148 −0.0837214
\(700\) −1.44533e149 −0.619897
\(701\) −2.33245e149 −0.928146 −0.464073 0.885797i \(-0.653612\pi\)
−0.464073 + 0.885797i \(0.653612\pi\)
\(702\) 3.62962e148 0.134018
\(703\) 3.78169e149 1.29578
\(704\) −6.45756e148 −0.205354
\(705\) −7.44392e147 −0.0219722
\(706\) 1.36895e149 0.375094
\(707\) 2.18686e149 0.556291
\(708\) −2.29020e149 −0.540913
\(709\) −3.10165e148 −0.0680244 −0.0340122 0.999421i \(-0.510829\pi\)
−0.0340122 + 0.999421i \(0.510829\pi\)
\(710\) −8.79847e148 −0.179203
\(711\) 5.79156e149 1.09557
\(712\) 5.94731e149 1.04501
\(713\) −2.01955e148 −0.0329651
\(714\) 3.74996e148 0.0568683
\(715\) −7.18668e148 −0.101265
\(716\) 4.84688e149 0.634642
\(717\) 2.01290e149 0.244944
\(718\) −1.95849e149 −0.221507
\(719\) −1.69695e150 −1.78403 −0.892015 0.452005i \(-0.850709\pi\)
−0.892015 + 0.452005i \(0.850709\pi\)
\(720\) 7.58483e148 0.0741293
\(721\) −2.93187e149 −0.266406
\(722\) −1.93969e149 −0.163881
\(723\) −5.48297e149 −0.430779
\(724\) −5.91959e148 −0.0432531
\(725\) −1.15246e150 −0.783216
\(726\) −3.04236e149 −0.192326
\(727\) −8.19359e148 −0.0481856 −0.0240928 0.999710i \(-0.507670\pi\)
−0.0240928 + 0.999710i \(0.507670\pi\)
\(728\) −3.44596e149 −0.188544
\(729\) 1.39310e150 0.709231
\(730\) −2.01895e149 −0.0956480
\(731\) −3.19702e149 −0.140956
\(732\) 2.30679e150 0.946623
\(733\) 1.32500e150 0.506126 0.253063 0.967450i \(-0.418562\pi\)
0.253063 + 0.967450i \(0.418562\pi\)
\(734\) −5.51691e149 −0.196179
\(735\) 1.78279e149 0.0590220
\(736\) 2.40653e150 0.741833
\(737\) −2.72905e150 −0.783373
\(738\) 6.64445e149 0.177623
\(739\) 5.43053e149 0.135210 0.0676051 0.997712i \(-0.478464\pi\)
0.0676051 + 0.997712i \(0.478464\pi\)
\(740\) 9.31131e149 0.215946
\(741\) 1.15692e150 0.249946
\(742\) −6.21516e149 −0.125097
\(743\) 3.72400e150 0.698388 0.349194 0.937051i \(-0.386455\pi\)
0.349194 + 0.937051i \(0.386455\pi\)
\(744\) 1.16448e149 0.0203494
\(745\) 8.13258e149 0.132441
\(746\) 3.79201e150 0.575548
\(747\) −4.55437e150 −0.644313
\(748\) −2.33773e150 −0.308290
\(749\) −8.26701e150 −1.01637
\(750\) −1.04160e150 −0.119394
\(751\) −7.26582e150 −0.776583 −0.388292 0.921537i \(-0.626935\pi\)
−0.388292 + 0.921537i \(0.626935\pi\)
\(752\) 7.80891e149 0.0778312
\(753\) −4.39544e150 −0.408569
\(754\) −1.25290e150 −0.108623
\(755\) 4.84401e150 0.391733
\(756\) −8.90348e150 −0.671685
\(757\) 6.80097e150 0.478671 0.239336 0.970937i \(-0.423070\pi\)
0.239336 + 0.970937i \(0.423070\pi\)
\(758\) 8.06732e150 0.529781
\(759\) −1.07948e151 −0.661487
\(760\) −3.61843e150 −0.206922
\(761\) 3.21674e151 1.71681 0.858405 0.512973i \(-0.171456\pi\)
0.858405 + 0.512973i \(0.171456\pi\)
\(762\) −1.72122e150 −0.0857434
\(763\) 2.77830e150 0.129194
\(764\) −1.33339e151 −0.578837
\(765\) 9.43539e149 0.0382415
\(766\) −5.80591e150 −0.219715
\(767\) 9.18779e150 0.324679
\(768\) −4.98929e150 −0.164655
\(769\) 1.66173e151 0.512185 0.256093 0.966652i \(-0.417565\pi\)
0.256093 + 0.966652i \(0.417565\pi\)
\(770\) −3.40369e150 −0.0979912
\(771\) 2.02494e151 0.544575
\(772\) −1.82770e150 −0.0459194
\(773\) 7.47787e151 1.75531 0.877656 0.479291i \(-0.159106\pi\)
0.877656 + 0.479291i \(0.159106\pi\)
\(774\) −5.38706e150 −0.118155
\(775\) −1.95941e150 −0.0401593
\(776\) −7.57778e151 −1.45145
\(777\) −3.09220e151 −0.553560
\(778\) 1.92587e151 0.322254
\(779\) 5.76170e151 0.901227
\(780\) 2.84858e150 0.0416545
\(781\) −1.82151e152 −2.49030
\(782\) 6.80445e150 0.0869838
\(783\) −7.09937e151 −0.848648
\(784\) −1.87020e151 −0.209071
\(785\) −3.07503e151 −0.321509
\(786\) 4.05535e151 0.396592
\(787\) −2.94929e151 −0.269801 −0.134900 0.990859i \(-0.543071\pi\)
−0.134900 + 0.990859i \(0.543071\pi\)
\(788\) 1.51350e152 1.29525
\(789\) 1.87465e151 0.150099
\(790\) −2.38745e151 −0.178860
\(791\) 1.76955e152 1.24050
\(792\) −8.63879e151 −0.566736
\(793\) −9.25436e151 −0.568204
\(794\) 1.18446e152 0.680682
\(795\) 1.12674e151 0.0606107
\(796\) −3.83025e151 −0.192882
\(797\) 3.01507e152 1.42146 0.710731 0.703464i \(-0.248364\pi\)
0.710731 + 0.703464i \(0.248364\pi\)
\(798\) 5.47929e151 0.241865
\(799\) 9.71414e150 0.0401512
\(800\) 2.33486e152 0.903727
\(801\) −2.26599e152 −0.821393
\(802\) 2.87275e151 0.0975310
\(803\) −4.17975e152 −1.32918
\(804\) 1.08171e152 0.322232
\(805\) −5.13129e151 −0.143200
\(806\) −2.13017e150 −0.00556962
\(807\) −2.22545e152 −0.545202
\(808\) −2.28804e152 −0.525251
\(809\) 4.42609e151 0.0952188 0.0476094 0.998866i \(-0.484840\pi\)
0.0476094 + 0.998866i \(0.484840\pi\)
\(810\) −3.80992e150 −0.00768162
\(811\) 1.17673e152 0.222373 0.111186 0.993800i \(-0.464535\pi\)
0.111186 + 0.993800i \(0.464535\pi\)
\(812\) 3.07338e152 0.544408
\(813\) −4.92922e152 −0.818512
\(814\) −3.72184e152 −0.579397
\(815\) 2.42129e152 0.353405
\(816\) 7.13159e151 0.0976007
\(817\) −4.67136e152 −0.599495
\(818\) −2.30577e152 −0.277503
\(819\) 1.31295e152 0.148198
\(820\) 1.41865e152 0.150193
\(821\) 9.52380e152 0.945789 0.472895 0.881119i \(-0.343209\pi\)
0.472895 + 0.881119i \(0.343209\pi\)
\(822\) 6.97863e151 0.0650129
\(823\) 2.93577e152 0.256585 0.128292 0.991736i \(-0.459050\pi\)
0.128292 + 0.991736i \(0.459050\pi\)
\(824\) 3.06752e152 0.251541
\(825\) −1.04733e153 −0.805847
\(826\) 4.35144e152 0.314181
\(827\) 4.85556e152 0.329003 0.164502 0.986377i \(-0.447398\pi\)
0.164502 + 0.986377i \(0.447398\pi\)
\(828\) −5.93850e152 −0.377645
\(829\) 3.22510e153 1.92500 0.962500 0.271282i \(-0.0874477\pi\)
0.962500 + 0.271282i \(0.0874477\pi\)
\(830\) 1.87745e152 0.105188
\(831\) 3.16968e152 0.166710
\(832\) −1.02685e152 −0.0507027
\(833\) −2.32649e152 −0.107855
\(834\) −6.75972e152 −0.294246
\(835\) −7.41865e152 −0.303239
\(836\) −3.41579e153 −1.31118
\(837\) −1.20703e152 −0.0435143
\(838\) −6.70760e152 −0.227120
\(839\) 4.24065e152 0.134874 0.0674372 0.997724i \(-0.478518\pi\)
0.0674372 + 0.997724i \(0.478518\pi\)
\(840\) 2.95871e152 0.0883976
\(841\) −1.11216e153 −0.312162
\(842\) 1.10802e153 0.292189
\(843\) 2.34848e152 0.0581888
\(844\) −3.97171e153 −0.924696
\(845\) 9.63835e152 0.210875
\(846\) 1.63686e152 0.0336563
\(847\) −2.99397e153 −0.578587
\(848\) −1.18198e153 −0.214699
\(849\) 4.16745e153 0.711569
\(850\) 6.60181e152 0.105967
\(851\) −5.61092e153 −0.846705
\(852\) 7.21990e153 1.02436
\(853\) −2.26454e152 −0.0302103 −0.0151052 0.999886i \(-0.504808\pi\)
−0.0151052 + 0.999886i \(0.504808\pi\)
\(854\) −4.38296e153 −0.549832
\(855\) 1.37866e153 0.162644
\(856\) 8.64949e153 0.959661
\(857\) 1.27702e154 1.33262 0.666309 0.745675i \(-0.267873\pi\)
0.666309 + 0.745675i \(0.267873\pi\)
\(858\) −1.13861e153 −0.111762
\(859\) 1.34385e154 1.24083 0.620414 0.784275i \(-0.286965\pi\)
0.620414 + 0.784275i \(0.286965\pi\)
\(860\) −1.15019e153 −0.0999080
\(861\) −4.71122e153 −0.385006
\(862\) −7.17738e153 −0.551867
\(863\) −3.76062e153 −0.272078 −0.136039 0.990703i \(-0.543437\pi\)
−0.136039 + 0.990703i \(0.543437\pi\)
\(864\) 1.43832e154 0.979227
\(865\) −4.70293e153 −0.301316
\(866\) −8.07928e153 −0.487173
\(867\) −1.05152e154 −0.596779
\(868\) 5.22534e152 0.0279144
\(869\) −4.94264e154 −2.48554
\(870\) 1.07575e153 0.0509271
\(871\) −4.33959e153 −0.193418
\(872\) −2.90684e153 −0.121985
\(873\) 2.88722e154 1.14086
\(874\) 9.94239e153 0.369948
\(875\) −1.02503e154 −0.359181
\(876\) 1.65672e154 0.546745
\(877\) 4.57524e153 0.142212 0.0711058 0.997469i \(-0.477347\pi\)
0.0711058 + 0.997469i \(0.477347\pi\)
\(878\) 7.31076e153 0.214043
\(879\) −1.55923e154 −0.430025
\(880\) −6.47306e153 −0.168178
\(881\) −3.46430e154 −0.847969 −0.423985 0.905669i \(-0.639369\pi\)
−0.423985 + 0.905669i \(0.639369\pi\)
\(882\) −3.92020e153 −0.0904081
\(883\) 7.08435e154 1.53944 0.769720 0.638381i \(-0.220396\pi\)
0.769720 + 0.638381i \(0.220396\pi\)
\(884\) −3.71733e153 −0.0761179
\(885\) −7.88867e153 −0.152224
\(886\) 2.18677e154 0.397679
\(887\) −3.38114e153 −0.0579525 −0.0289763 0.999580i \(-0.509225\pi\)
−0.0289763 + 0.999580i \(0.509225\pi\)
\(888\) 3.23527e154 0.522672
\(889\) −1.69384e154 −0.257947
\(890\) 9.34109e153 0.134098
\(891\) −7.88752e153 −0.106748
\(892\) 7.22741e154 0.922206
\(893\) 1.41939e154 0.170766
\(894\) 1.28847e154 0.146169
\(895\) 1.66952e154 0.178601
\(896\) −7.91512e154 −0.798522
\(897\) −1.71653e154 −0.163323
\(898\) −3.41831e154 −0.306763
\(899\) 4.16653e153 0.0352688
\(900\) −5.76165e154 −0.460061
\(901\) −1.47037e154 −0.110758
\(902\) −5.67052e154 −0.402976
\(903\) 3.81967e154 0.256106
\(904\) −1.85142e155 −1.17129
\(905\) −2.03902e153 −0.0121723
\(906\) 7.67452e154 0.432335
\(907\) 7.45945e154 0.396574 0.198287 0.980144i \(-0.436462\pi\)
0.198287 + 0.980144i \(0.436462\pi\)
\(908\) −1.84639e155 −0.926438
\(909\) 8.71768e154 0.412855
\(910\) −5.41237e153 −0.0241944
\(911\) −2.85703e155 −1.20559 −0.602796 0.797895i \(-0.705947\pi\)
−0.602796 + 0.797895i \(0.705947\pi\)
\(912\) 1.04204e155 0.415102
\(913\) 3.88680e155 1.46176
\(914\) −1.51495e155 −0.537927
\(915\) 7.94583e154 0.266398
\(916\) −1.31297e155 −0.415665
\(917\) 3.99084e155 1.19309
\(918\) 4.06683e154 0.114819
\(919\) 5.08138e155 1.35493 0.677465 0.735555i \(-0.263078\pi\)
0.677465 + 0.735555i \(0.263078\pi\)
\(920\) 5.36870e154 0.135210
\(921\) −1.12255e155 −0.267040
\(922\) 9.78958e154 0.219984
\(923\) −2.89647e155 −0.614865
\(924\) 2.79302e155 0.560139
\(925\) −5.44383e155 −1.03149
\(926\) 4.05815e155 0.726526
\(927\) −1.16876e155 −0.197715
\(928\) −4.96491e155 −0.793674
\(929\) 1.26997e155 0.191853 0.0959267 0.995388i \(-0.469419\pi\)
0.0959267 + 0.995388i \(0.469419\pi\)
\(930\) 1.82898e153 0.00261128
\(931\) −3.39938e155 −0.458714
\(932\) 8.50186e154 0.108437
\(933\) −7.62971e155 −0.919860
\(934\) 4.88464e155 0.556700
\(935\) −8.05237e154 −0.0867590
\(936\) −1.37369e155 −0.139929
\(937\) −6.80517e155 −0.655406 −0.327703 0.944781i \(-0.606275\pi\)
−0.327703 + 0.944781i \(0.606275\pi\)
\(938\) −2.05528e155 −0.187164
\(939\) −1.09748e156 −0.945043
\(940\) 3.49484e154 0.0284587
\(941\) 1.63427e156 1.25855 0.629274 0.777184i \(-0.283352\pi\)
0.629274 + 0.777184i \(0.283352\pi\)
\(942\) −4.87188e155 −0.354833
\(943\) −8.54869e155 −0.588892
\(944\) 8.27546e155 0.539216
\(945\) −3.06683e155 −0.189025
\(946\) 4.59744e155 0.268059
\(947\) 3.35162e156 1.84876 0.924380 0.381472i \(-0.124583\pi\)
0.924380 + 0.381472i \(0.124583\pi\)
\(948\) 1.95911e156 1.02240
\(949\) −6.64642e155 −0.328179
\(950\) 9.64631e155 0.450684
\(951\) −2.18617e156 −0.966513
\(952\) −3.86105e155 −0.161535
\(953\) 1.15047e156 0.455508 0.227754 0.973719i \(-0.426862\pi\)
0.227754 + 0.973719i \(0.426862\pi\)
\(954\) −2.47761e155 −0.0928416
\(955\) −4.59291e155 −0.162896
\(956\) −9.45037e155 −0.317256
\(957\) 2.22707e156 0.707713
\(958\) −1.55482e156 −0.467725
\(959\) 6.86763e155 0.195583
\(960\) 8.81654e154 0.0237716
\(961\) −3.91014e156 −0.998192
\(962\) −5.91827e155 −0.143055
\(963\) −3.29555e156 −0.754307
\(964\) 2.57419e156 0.557952
\(965\) −6.29556e154 −0.0129226
\(966\) −8.12967e155 −0.158043
\(967\) 2.29280e156 0.422159 0.211079 0.977469i \(-0.432302\pi\)
0.211079 + 0.977469i \(0.432302\pi\)
\(968\) 3.13249e156 0.546303
\(969\) 1.29628e156 0.214141
\(970\) −1.19020e156 −0.186253
\(971\) −4.42509e156 −0.656013 −0.328006 0.944676i \(-0.606377\pi\)
−0.328006 + 0.944676i \(0.606377\pi\)
\(972\) −5.79391e156 −0.813754
\(973\) −6.65220e156 −0.885199
\(974\) 1.55447e156 0.195991
\(975\) −1.66541e156 −0.198966
\(976\) −8.33542e156 −0.943652
\(977\) 5.67880e156 0.609244 0.304622 0.952473i \(-0.401470\pi\)
0.304622 + 0.952473i \(0.401470\pi\)
\(978\) 3.83613e156 0.390035
\(979\) 1.93385e157 1.86351
\(980\) −8.36999e155 −0.0764462
\(981\) 1.10754e156 0.0958817
\(982\) −2.29177e156 −0.188069
\(983\) 1.60539e157 1.24888 0.624441 0.781072i \(-0.285327\pi\)
0.624441 + 0.781072i \(0.285327\pi\)
\(984\) 4.92919e156 0.363524
\(985\) 5.21329e156 0.364510
\(986\) −1.40382e156 −0.0930624
\(987\) −1.16061e156 −0.0729515
\(988\) −5.43161e156 −0.323735
\(989\) 6.93094e156 0.391730
\(990\) −1.35684e156 −0.0727247
\(991\) −1.04972e157 −0.533591 −0.266795 0.963753i \(-0.585965\pi\)
−0.266795 + 0.963753i \(0.585965\pi\)
\(992\) −8.44130e155 −0.0406955
\(993\) −8.10682e156 −0.370693
\(994\) −1.37180e157 −0.594984
\(995\) −1.31934e156 −0.0542807
\(996\) −1.54061e157 −0.601279
\(997\) 1.20849e157 0.447451 0.223726 0.974652i \(-0.428178\pi\)
0.223726 + 0.974652i \(0.428178\pi\)
\(998\) −1.79188e156 −0.0629441
\(999\) −3.35349e157 −1.11766
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.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.4 8 1.1 even 1 trivial