Properties

Label 1.32.a.a.1.1
Level $1$
Weight $32$
Character 1.1
Self dual yes
Analytic conductor $6.088$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 32 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.08771328190\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\mathbb{Q}[x]/(x^{2} - \cdots)\)
Defining polynomial: \(x^{2} - x - 4573872\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{3}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2139.16\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-31347.9 q^{2} -1.34921e7 q^{3} -1.16479e9 q^{4} +6.31161e10 q^{5} +4.22947e11 q^{6} +1.88207e13 q^{7} +1.03833e14 q^{8} -4.35638e14 q^{9} +O(q^{10})\) \(q-31347.9 q^{2} -1.34921e7 q^{3} -1.16479e9 q^{4} +6.31161e10 q^{5} +4.22947e11 q^{6} +1.88207e13 q^{7} +1.03833e14 q^{8} -4.35638e14 q^{9} -1.97855e15 q^{10} -5.37973e15 q^{11} +1.57155e16 q^{12} +2.76595e17 q^{13} -5.89989e17 q^{14} -8.51566e17 q^{15} -7.53562e17 q^{16} +6.29817e18 q^{17} +1.36563e19 q^{18} +1.91455e18 q^{19} -7.35172e19 q^{20} -2.53930e20 q^{21} +1.68643e20 q^{22} +1.90120e21 q^{23} -1.40092e21 q^{24} -6.72976e20 q^{25} -8.67065e21 q^{26} +1.42113e22 q^{27} -2.19223e22 q^{28} +5.22675e22 q^{29} +2.66948e22 q^{30} -6.09679e22 q^{31} -1.99357e23 q^{32} +7.25837e22 q^{33} -1.97434e23 q^{34} +1.18789e24 q^{35} +5.07428e23 q^{36} -2.07091e24 q^{37} -6.00172e22 q^{38} -3.73183e24 q^{39} +6.55352e24 q^{40} -5.09498e24 q^{41} +7.96017e24 q^{42} +8.39002e24 q^{43} +6.26628e24 q^{44} -2.74957e25 q^{45} -5.95984e25 q^{46} +2.13587e25 q^{47} +1.01671e25 q^{48} +1.96444e26 q^{49} +2.10964e25 q^{50} -8.49753e25 q^{51} -3.22176e26 q^{52} +1.59213e26 q^{53} -4.45495e26 q^{54} -3.39547e26 q^{55} +1.95421e27 q^{56} -2.58313e25 q^{57} -1.63847e27 q^{58} +2.16250e27 q^{59} +9.91899e26 q^{60} -6.60780e27 q^{61} +1.91122e27 q^{62} -8.19901e27 q^{63} +7.86767e27 q^{64} +1.74576e28 q^{65} -2.27534e27 q^{66} -2.77322e26 q^{67} -7.33607e27 q^{68} -2.56510e28 q^{69} -3.72378e28 q^{70} +7.68524e28 q^{71} -4.52335e28 q^{72} +2.29610e28 q^{73} +6.49186e28 q^{74} +9.07984e27 q^{75} -2.23006e27 q^{76} -1.01250e29 q^{77} +1.16985e29 q^{78} -2.99014e29 q^{79} -4.75619e28 q^{80} +7.73416e28 q^{81} +1.59717e29 q^{82} +1.89466e29 q^{83} +2.95777e29 q^{84} +3.97516e29 q^{85} -2.63009e29 q^{86} -7.05196e29 q^{87} -5.58593e29 q^{88} -2.41523e30 q^{89} +8.61933e29 q^{90} +5.20571e30 q^{91} -2.21450e30 q^{92} +8.22583e29 q^{93} -6.69551e29 q^{94} +1.20839e29 q^{95} +2.68973e30 q^{96} -3.68010e30 q^{97} -6.15810e30 q^{98} +2.34361e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 39960q^{2} + 17363160q^{3} + 1772534336q^{4} - 19391218020q^{5} + 2623167496224q^{6} + 30257527577200q^{7} + 160155058705920q^{8} - 101266456303926q^{9} + O(q^{10}) \) \( 2q + 39960q^{2} + 17363160q^{3} + 1772534336q^{4} - 19391218020q^{5} + 2623167496224q^{6} + 30257527577200q^{7} + 160155058705920q^{8} - 101266456303926q^{9} - 7861972212281520q^{10} - 7782353745118776q^{11} + 106347410955313920q^{12} + 74708953050260620q^{13} + 225544963845241152q^{14} - 3397345822674581040q^{15} - 3045212913684901888q^{16} + 17224607828987089380q^{17} + 37499616229575978360q^{18} - 12370563328022164040q^{19} - \)\(31\!\cdots\!60\)\(q^{20} + 98954957416071161664q^{21} - 2682713032996690080q^{22} + \)\(18\!\cdots\!80\)\(q^{23} + \)\(33\!\cdots\!80\)\(q^{24} + \)\(14\!\cdots\!50\)\(q^{25} - \)\(23\!\cdots\!16\)\(q^{26} + \)\(54\!\cdots\!80\)\(q^{27} + \)\(11\!\cdots\!20\)\(q^{28} + \)\(12\!\cdots\!40\)\(q^{29} - \)\(15\!\cdots\!40\)\(q^{30} + \)\(12\!\cdots\!64\)\(q^{31} - \)\(48\!\cdots\!40\)\(q^{32} - \)\(15\!\cdots\!80\)\(q^{33} + \)\(58\!\cdots\!92\)\(q^{34} + \)\(24\!\cdots\!80\)\(q^{35} + \)\(14\!\cdots\!32\)\(q^{36} - \)\(83\!\cdots\!60\)\(q^{37} - \)\(10\!\cdots\!20\)\(q^{38} - \)\(99\!\cdots\!12\)\(q^{39} + \)\(19\!\cdots\!00\)\(q^{40} + \)\(87\!\cdots\!84\)\(q^{41} + \)\(33\!\cdots\!80\)\(q^{42} - \)\(18\!\cdots\!00\)\(q^{43} - \)\(79\!\cdots\!68\)\(q^{44} - \)\(55\!\cdots\!40\)\(q^{45} - \)\(59\!\cdots\!56\)\(q^{46} + \)\(95\!\cdots\!20\)\(q^{47} - \)\(60\!\cdots\!20\)\(q^{48} + \)\(16\!\cdots\!86\)\(q^{49} + \)\(17\!\cdots\!00\)\(q^{50} + \)\(25\!\cdots\!44\)\(q^{51} - \)\(91\!\cdots\!00\)\(q^{52} + \)\(19\!\cdots\!60\)\(q^{53} - \)\(10\!\cdots\!40\)\(q^{54} - \)\(14\!\cdots\!40\)\(q^{55} + \)\(25\!\cdots\!40\)\(q^{56} - \)\(46\!\cdots\!40\)\(q^{57} + \)\(38\!\cdots\!20\)\(q^{58} - \)\(19\!\cdots\!20\)\(q^{59} - \)\(64\!\cdots\!20\)\(q^{60} - \)\(12\!\cdots\!76\)\(q^{61} + \)\(15\!\cdots\!20\)\(q^{62} - \)\(43\!\cdots\!60\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} + \)\(34\!\cdots\!60\)\(q^{65} - \)\(75\!\cdots\!12\)\(q^{66} - \)\(96\!\cdots\!20\)\(q^{67} + \)\(24\!\cdots\!60\)\(q^{68} - \)\(25\!\cdots\!92\)\(q^{69} - \)\(10\!\cdots\!20\)\(q^{70} + \)\(55\!\cdots\!44\)\(q^{71} - \)\(26\!\cdots\!60\)\(q^{72} + \)\(62\!\cdots\!80\)\(q^{73} + \)\(15\!\cdots\!72\)\(q^{74} + \)\(75\!\cdots\!00\)\(q^{75} - \)\(44\!\cdots\!20\)\(q^{76} - \)\(12\!\cdots\!00\)\(q^{77} - \)\(32\!\cdots\!00\)\(q^{78} - \)\(11\!\cdots\!60\)\(q^{79} + \)\(14\!\cdots\!80\)\(q^{80} - \)\(39\!\cdots\!58\)\(q^{81} + \)\(11\!\cdots\!20\)\(q^{82} - \)\(26\!\cdots\!60\)\(q^{83} + \)\(13\!\cdots\!52\)\(q^{84} - \)\(50\!\cdots\!20\)\(q^{85} - \)\(21\!\cdots\!36\)\(q^{86} + \)\(16\!\cdots\!40\)\(q^{87} - \)\(69\!\cdots\!60\)\(q^{88} - \)\(21\!\cdots\!80\)\(q^{89} - \)\(11\!\cdots\!40\)\(q^{90} + \)\(28\!\cdots\!24\)\(q^{91} - \)\(22\!\cdots\!20\)\(q^{92} + \)\(65\!\cdots\!20\)\(q^{93} + \)\(46\!\cdots\!12\)\(q^{94} + \)\(12\!\cdots\!00\)\(q^{95} - \)\(60\!\cdots\!96\)\(q^{96} - \)\(90\!\cdots\!80\)\(q^{97} - \)\(80\!\cdots\!20\)\(q^{98} + \)\(15\!\cdots\!88\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31347.9 −0.676462 −0.338231 0.941063i \(-0.609828\pi\)
−0.338231 + 0.941063i \(0.609828\pi\)
\(3\) −1.34921e7 −0.542874 −0.271437 0.962456i \(-0.587499\pi\)
−0.271437 + 0.962456i \(0.587499\pi\)
\(4\) −1.16479e9 −0.542400
\(5\) 6.31161e10 0.924921 0.462461 0.886640i \(-0.346967\pi\)
0.462461 + 0.886640i \(0.346967\pi\)
\(6\) 4.22947e11 0.367233
\(7\) 1.88207e13 1.49836 0.749181 0.662366i \(-0.230447\pi\)
0.749181 + 0.662366i \(0.230447\pi\)
\(8\) 1.03833e14 1.04337
\(9\) −4.35638e14 −0.705288
\(10\) −1.97855e15 −0.625674
\(11\) −5.37973e15 −0.388306 −0.194153 0.980971i \(-0.562196\pi\)
−0.194153 + 0.980971i \(0.562196\pi\)
\(12\) 1.57155e16 0.294455
\(13\) 2.76595e17 1.49872 0.749362 0.662161i \(-0.230360\pi\)
0.749362 + 0.662161i \(0.230360\pi\)
\(14\) −5.89989e17 −1.01358
\(15\) −8.51566e17 −0.502115
\(16\) −7.53562e17 −0.163403
\(17\) 6.29817e18 0.533649 0.266825 0.963745i \(-0.414026\pi\)
0.266825 + 0.963745i \(0.414026\pi\)
\(18\) 1.36563e19 0.477100
\(19\) 1.91455e18 0.0289326 0.0144663 0.999895i \(-0.495395\pi\)
0.0144663 + 0.999895i \(0.495395\pi\)
\(20\) −7.35172e19 −0.501677
\(21\) −2.53930e20 −0.813421
\(22\) 1.68643e20 0.262674
\(23\) 1.90120e21 1.48678 0.743388 0.668861i \(-0.233218\pi\)
0.743388 + 0.668861i \(0.233218\pi\)
\(24\) −1.40092e21 −0.566420
\(25\) −6.72976e20 −0.144521
\(26\) −8.67065e21 −1.01383
\(27\) 1.42113e22 0.925756
\(28\) −2.19223e22 −0.812711
\(29\) 5.22675e22 1.12477 0.562384 0.826877i \(-0.309884\pi\)
0.562384 + 0.826877i \(0.309884\pi\)
\(30\) 2.66948e22 0.339662
\(31\) −6.09679e22 −0.466654 −0.233327 0.972398i \(-0.574961\pi\)
−0.233327 + 0.972398i \(0.574961\pi\)
\(32\) −1.99357e23 −0.932838
\(33\) 7.25837e22 0.210801
\(34\) −1.97434e23 −0.360993
\(35\) 1.18789e24 1.38587
\(36\) 5.07428e23 0.382548
\(37\) −2.07091e24 −1.02102 −0.510510 0.859872i \(-0.670543\pi\)
−0.510510 + 0.859872i \(0.670543\pi\)
\(38\) −6.00172e22 −0.0195718
\(39\) −3.73183e24 −0.813618
\(40\) 6.55352e24 0.965039
\(41\) −5.09498e24 −0.511673 −0.255837 0.966720i \(-0.582351\pi\)
−0.255837 + 0.966720i \(0.582351\pi\)
\(42\) 7.96017e24 0.550248
\(43\) 8.39002e24 0.402719 0.201359 0.979517i \(-0.435464\pi\)
0.201359 + 0.979517i \(0.435464\pi\)
\(44\) 6.26628e24 0.210617
\(45\) −2.74957e25 −0.652336
\(46\) −5.95984e25 −1.00575
\(47\) 2.13587e25 0.258261 0.129130 0.991628i \(-0.458781\pi\)
0.129130 + 0.991628i \(0.458781\pi\)
\(48\) 1.01671e25 0.0887071
\(49\) 1.96444e26 1.24509
\(50\) 2.10964e25 0.0977626
\(51\) −8.49753e25 −0.289704
\(52\) −3.22176e26 −0.812907
\(53\) 1.59213e26 0.299022 0.149511 0.988760i \(-0.452230\pi\)
0.149511 + 0.988760i \(0.452230\pi\)
\(54\) −4.45495e26 −0.626238
\(55\) −3.39547e26 −0.359152
\(56\) 1.95421e27 1.56335
\(57\) −2.58313e25 −0.0157067
\(58\) −1.63847e27 −0.760862
\(59\) 2.16250e27 0.770459 0.385229 0.922821i \(-0.374122\pi\)
0.385229 + 0.922821i \(0.374122\pi\)
\(60\) 9.91899e26 0.272347
\(61\) −6.60780e27 −1.40425 −0.702125 0.712053i \(-0.747765\pi\)
−0.702125 + 0.712053i \(0.747765\pi\)
\(62\) 1.91122e27 0.315674
\(63\) −8.19901e27 −1.05678
\(64\) 7.86767e27 0.794432
\(65\) 1.74576e28 1.38620
\(66\) −2.27534e27 −0.142599
\(67\) −2.77322e26 −0.0137665 −0.00688326 0.999976i \(-0.502191\pi\)
−0.00688326 + 0.999976i \(0.502191\pi\)
\(68\) −7.33607e27 −0.289451
\(69\) −2.56510e28 −0.807131
\(70\) −3.72378e28 −0.937485
\(71\) 7.68524e28 1.55293 0.776467 0.630158i \(-0.217010\pi\)
0.776467 + 0.630158i \(0.217010\pi\)
\(72\) −4.52335e28 −0.735879
\(73\) 2.29610e28 0.301639 0.150819 0.988561i \(-0.451809\pi\)
0.150819 + 0.988561i \(0.451809\pi\)
\(74\) 6.49186e28 0.690681
\(75\) 9.07984e27 0.0784564
\(76\) −2.23006e27 −0.0156930
\(77\) −1.01250e29 −0.581823
\(78\) 1.16985e29 0.550381
\(79\) −2.99014e29 −1.15471 −0.577353 0.816494i \(-0.695914\pi\)
−0.577353 + 0.816494i \(0.695914\pi\)
\(80\) −4.75619e28 −0.151135
\(81\) 7.73416e28 0.202719
\(82\) 1.59717e29 0.346127
\(83\) 1.89466e29 0.340267 0.170134 0.985421i \(-0.445580\pi\)
0.170134 + 0.985421i \(0.445580\pi\)
\(84\) 2.95777e29 0.441199
\(85\) 3.97516e29 0.493584
\(86\) −2.63009e29 −0.272424
\(87\) −7.05196e29 −0.610606
\(88\) −5.58593e29 −0.405148
\(89\) −2.41523e30 −1.47032 −0.735162 0.677892i \(-0.762894\pi\)
−0.735162 + 0.677892i \(0.762894\pi\)
\(90\) 8.61933e29 0.441280
\(91\) 5.20571e30 2.24563
\(92\) −2.21450e30 −0.806426
\(93\) 8.22583e29 0.253334
\(94\) −6.69551e29 −0.174704
\(95\) 1.20839e29 0.0267603
\(96\) 2.68973e30 0.506414
\(97\) −3.68010e30 −0.590062 −0.295031 0.955488i \(-0.595330\pi\)
−0.295031 + 0.955488i \(0.595330\pi\)
\(98\) −6.15810e30 −0.842254
\(99\) 2.34361e30 0.273868
\(100\) 7.83879e29 0.0783879
\(101\) −4.69650e30 −0.402526 −0.201263 0.979537i \(-0.564505\pi\)
−0.201263 + 0.979537i \(0.564505\pi\)
\(102\) 2.66379e30 0.195974
\(103\) 5.49646e30 0.347621 0.173811 0.984779i \(-0.444392\pi\)
0.173811 + 0.984779i \(0.444392\pi\)
\(104\) 2.87196e31 1.56373
\(105\) −1.60271e31 −0.752351
\(106\) −4.99100e30 −0.202277
\(107\) 5.31108e30 0.186095 0.0930475 0.995662i \(-0.470339\pi\)
0.0930475 + 0.995662i \(0.470339\pi\)
\(108\) −1.65533e31 −0.502130
\(109\) −5.09224e31 −1.33906 −0.669528 0.742787i \(-0.733503\pi\)
−0.669528 + 0.742787i \(0.733503\pi\)
\(110\) 1.06441e31 0.242953
\(111\) 2.79408e31 0.554285
\(112\) −1.41826e31 −0.244836
\(113\) 5.75758e31 0.866012 0.433006 0.901391i \(-0.357453\pi\)
0.433006 + 0.901391i \(0.357453\pi\)
\(114\) 8.09756e29 0.0106250
\(115\) 1.19996e32 1.37515
\(116\) −6.08809e31 −0.610073
\(117\) −1.20495e32 −1.05703
\(118\) −6.77897e31 −0.521186
\(119\) 1.18536e32 0.799600
\(120\) −8.84205e31 −0.523894
\(121\) −1.63002e32 −0.849219
\(122\) 2.07141e32 0.949922
\(123\) 6.87418e31 0.277774
\(124\) 7.10151e31 0.253113
\(125\) −3.36383e32 −1.05859
\(126\) 2.57022e32 0.714869
\(127\) 3.71246e32 0.913490 0.456745 0.889598i \(-0.349015\pi\)
0.456745 + 0.889598i \(0.349015\pi\)
\(128\) 1.81481e32 0.395436
\(129\) −1.13199e32 −0.218626
\(130\) −5.47257e32 −0.937712
\(131\) −6.43836e32 −0.979648 −0.489824 0.871821i \(-0.662939\pi\)
−0.489824 + 0.871821i \(0.662939\pi\)
\(132\) −8.45451e31 −0.114338
\(133\) 3.60333e31 0.0433514
\(134\) 8.69344e30 0.00931252
\(135\) 8.96964e32 0.856252
\(136\) 6.53957e32 0.556796
\(137\) −5.70054e32 −0.433259 −0.216629 0.976254i \(-0.569506\pi\)
−0.216629 + 0.976254i \(0.569506\pi\)
\(138\) 8.04106e32 0.545993
\(139\) 1.35322e33 0.821557 0.410779 0.911735i \(-0.365257\pi\)
0.410779 + 0.911735i \(0.365257\pi\)
\(140\) −1.38365e33 −0.751694
\(141\) −2.88173e32 −0.140203
\(142\) −2.40916e33 −1.05050
\(143\) −1.48800e33 −0.581963
\(144\) 3.28280e32 0.115246
\(145\) 3.29892e33 1.04032
\(146\) −7.19780e32 −0.204047
\(147\) −2.65044e33 −0.675925
\(148\) 2.41218e33 0.553801
\(149\) 5.42559e33 1.12217 0.561086 0.827757i \(-0.310384\pi\)
0.561086 + 0.827757i \(0.310384\pi\)
\(150\) −2.84634e32 −0.0530727
\(151\) −2.39015e33 −0.402051 −0.201026 0.979586i \(-0.564427\pi\)
−0.201026 + 0.979586i \(0.564427\pi\)
\(152\) 1.98794e32 0.0301875
\(153\) −2.74372e33 −0.376377
\(154\) 3.17399e33 0.393581
\(155\) −3.84806e33 −0.431619
\(156\) 4.34682e33 0.441306
\(157\) −1.98794e34 −1.82792 −0.913961 0.405802i \(-0.866992\pi\)
−0.913961 + 0.405802i \(0.866992\pi\)
\(158\) 9.37345e33 0.781115
\(159\) −2.14812e33 −0.162331
\(160\) −1.25826e34 −0.862802
\(161\) 3.57819e34 2.22773
\(162\) −2.42449e33 −0.137132
\(163\) 7.84574e33 0.403391 0.201696 0.979448i \(-0.435355\pi\)
0.201696 + 0.979448i \(0.435355\pi\)
\(164\) 5.93460e33 0.277531
\(165\) 4.58119e33 0.194974
\(166\) −5.93935e33 −0.230178
\(167\) −5.15166e34 −1.81904 −0.909519 0.415662i \(-0.863550\pi\)
−0.909519 + 0.415662i \(0.863550\pi\)
\(168\) −2.63663e34 −0.848703
\(169\) 4.24446e34 1.24617
\(170\) −1.24613e34 −0.333890
\(171\) −8.34052e32 −0.0204058
\(172\) −9.77265e33 −0.218435
\(173\) 5.04795e34 1.03134 0.515668 0.856788i \(-0.327544\pi\)
0.515668 + 0.856788i \(0.327544\pi\)
\(174\) 2.21064e34 0.413052
\(175\) −1.26659e34 −0.216544
\(176\) 4.05396e33 0.0634503
\(177\) −2.91765e34 −0.418262
\(178\) 7.57122e34 0.994617
\(179\) −2.60297e34 −0.313507 −0.156754 0.987638i \(-0.550103\pi\)
−0.156754 + 0.987638i \(0.550103\pi\)
\(180\) 3.20269e34 0.353827
\(181\) −1.20765e35 −1.22440 −0.612198 0.790705i \(-0.709714\pi\)
−0.612198 + 0.790705i \(0.709714\pi\)
\(182\) −1.63188e35 −1.51908
\(183\) 8.91529e34 0.762331
\(184\) 1.97407e35 1.55126
\(185\) −1.30708e35 −0.944363
\(186\) −2.57862e34 −0.171371
\(187\) −3.38825e34 −0.207219
\(188\) −2.48785e34 −0.140081
\(189\) 2.67468e35 1.38712
\(190\) −3.78805e33 −0.0181023
\(191\) 2.27571e35 1.00253 0.501267 0.865293i \(-0.332868\pi\)
0.501267 + 0.865293i \(0.332868\pi\)
\(192\) −1.06151e35 −0.431276
\(193\) −1.78027e35 −0.667339 −0.333670 0.942690i \(-0.608287\pi\)
−0.333670 + 0.942690i \(0.608287\pi\)
\(194\) 1.15363e35 0.399154
\(195\) −2.35538e35 −0.752532
\(196\) −2.28817e35 −0.675335
\(197\) −2.53071e35 −0.690264 −0.345132 0.938554i \(-0.612166\pi\)
−0.345132 + 0.938554i \(0.612166\pi\)
\(198\) −7.34673e34 −0.185261
\(199\) 4.51723e35 1.05354 0.526768 0.850009i \(-0.323404\pi\)
0.526768 + 0.850009i \(0.323404\pi\)
\(200\) −6.98771e34 −0.150789
\(201\) 3.74164e33 0.00747348
\(202\) 1.47225e35 0.272293
\(203\) 9.83712e35 1.68531
\(204\) 9.89787e34 0.157136
\(205\) −3.21575e35 −0.473257
\(206\) −1.72302e35 −0.235152
\(207\) −8.28232e35 −1.04860
\(208\) −2.08431e35 −0.244896
\(209\) −1.02998e34 −0.0112347
\(210\) 5.02415e35 0.508936
\(211\) 6.25554e34 0.0588690 0.0294345 0.999567i \(-0.490629\pi\)
0.0294345 + 0.999567i \(0.490629\pi\)
\(212\) −1.85451e35 −0.162190
\(213\) −1.03690e36 −0.843047
\(214\) −1.66491e35 −0.125886
\(215\) 5.29545e35 0.372483
\(216\) 1.47560e36 0.965910
\(217\) −1.14746e36 −0.699217
\(218\) 1.59631e36 0.905819
\(219\) −3.09792e35 −0.163752
\(220\) 3.95503e35 0.194804
\(221\) 1.74204e36 0.799793
\(222\) −8.75886e35 −0.374953
\(223\) 1.14032e35 0.0455303 0.0227652 0.999741i \(-0.492753\pi\)
0.0227652 + 0.999741i \(0.492753\pi\)
\(224\) −3.75204e36 −1.39773
\(225\) 2.93174e35 0.101929
\(226\) −1.80488e36 −0.585824
\(227\) 1.82276e35 0.0552496 0.0276248 0.999618i \(-0.491206\pi\)
0.0276248 + 0.999618i \(0.491206\pi\)
\(228\) 3.00881e34 0.00851932
\(229\) 2.02123e36 0.534768 0.267384 0.963590i \(-0.413841\pi\)
0.267384 + 0.963590i \(0.413841\pi\)
\(230\) −3.76162e36 −0.930236
\(231\) 1.36608e36 0.315856
\(232\) 5.42708e36 1.17355
\(233\) 3.92949e35 0.0794912 0.0397456 0.999210i \(-0.487345\pi\)
0.0397456 + 0.999210i \(0.487345\pi\)
\(234\) 3.77726e36 0.715042
\(235\) 1.34808e36 0.238871
\(236\) −2.51886e36 −0.417897
\(237\) 4.03432e36 0.626860
\(238\) −3.71585e36 −0.540898
\(239\) −1.39161e37 −1.89823 −0.949115 0.314931i \(-0.898019\pi\)
−0.949115 + 0.314931i \(0.898019\pi\)
\(240\) 6.41708e35 0.0820471
\(241\) −1.56350e36 −0.187428 −0.0937140 0.995599i \(-0.529874\pi\)
−0.0937140 + 0.995599i \(0.529874\pi\)
\(242\) 5.10976e36 0.574464
\(243\) −9.82146e36 −1.03581
\(244\) 7.69673e36 0.761665
\(245\) 1.23988e37 1.15161
\(246\) −2.15491e36 −0.187903
\(247\) 5.29555e35 0.0433619
\(248\) −6.33048e36 −0.486895
\(249\) −2.55628e36 −0.184722
\(250\) 1.05449e37 0.716096
\(251\) 7.69469e36 0.491189 0.245594 0.969373i \(-0.421017\pi\)
0.245594 + 0.969373i \(0.421017\pi\)
\(252\) 9.55017e36 0.573195
\(253\) −1.02279e37 −0.577324
\(254\) −1.16378e37 −0.617941
\(255\) −5.36330e36 −0.267954
\(256\) −2.25847e37 −1.06193
\(257\) 4.19824e37 1.85825 0.929125 0.369765i \(-0.120562\pi\)
0.929125 + 0.369765i \(0.120562\pi\)
\(258\) 3.54854e36 0.147892
\(259\) −3.89760e37 −1.52986
\(260\) −2.03345e37 −0.751875
\(261\) −2.27697e37 −0.793285
\(262\) 2.01829e37 0.662694
\(263\) 5.61748e37 1.73871 0.869356 0.494186i \(-0.164534\pi\)
0.869356 + 0.494186i \(0.164534\pi\)
\(264\) 7.53657e36 0.219944
\(265\) 1.00489e37 0.276572
\(266\) −1.12957e36 −0.0293256
\(267\) 3.25864e37 0.798200
\(268\) 3.23023e35 0.00746696
\(269\) −3.06746e37 −0.669296 −0.334648 0.942343i \(-0.608617\pi\)
−0.334648 + 0.942343i \(0.608617\pi\)
\(270\) −2.81179e37 −0.579221
\(271\) −6.26560e35 −0.0121882 −0.00609409 0.999981i \(-0.501940\pi\)
−0.00609409 + 0.999981i \(0.501940\pi\)
\(272\) −4.74606e36 −0.0871998
\(273\) −7.02357e37 −1.21909
\(274\) 1.78700e37 0.293083
\(275\) 3.62043e36 0.0561182
\(276\) 2.98782e37 0.437788
\(277\) −4.05908e37 −0.562330 −0.281165 0.959660i \(-0.590721\pi\)
−0.281165 + 0.959660i \(0.590721\pi\)
\(278\) −4.24205e37 −0.555752
\(279\) 2.65599e37 0.329126
\(280\) 1.23342e38 1.44598
\(281\) 7.11328e37 0.789082 0.394541 0.918878i \(-0.370904\pi\)
0.394541 + 0.918878i \(0.370904\pi\)
\(282\) 9.03362e36 0.0948420
\(283\) −5.52066e36 −0.0548657 −0.0274329 0.999624i \(-0.508733\pi\)
−0.0274329 + 0.999624i \(0.508733\pi\)
\(284\) −8.95173e37 −0.842311
\(285\) −1.63037e36 −0.0145275
\(286\) 4.66458e37 0.393676
\(287\) −9.58912e37 −0.766671
\(288\) 8.68473e37 0.657920
\(289\) −9.96220e37 −0.715218
\(290\) −1.03414e38 −0.703737
\(291\) 4.96521e37 0.320329
\(292\) −2.67449e37 −0.163609
\(293\) −5.84412e36 −0.0339056 −0.0169528 0.999856i \(-0.505396\pi\)
−0.0169528 + 0.999856i \(0.505396\pi\)
\(294\) 8.30855e37 0.457237
\(295\) 1.36488e38 0.712614
\(296\) −2.15028e38 −1.06531
\(297\) −7.64532e37 −0.359477
\(298\) −1.70081e38 −0.759107
\(299\) 5.25860e38 2.22827
\(300\) −1.05761e37 −0.0425547
\(301\) 1.57906e38 0.603419
\(302\) 7.49260e37 0.271972
\(303\) 6.33655e37 0.218521
\(304\) −1.44274e36 −0.00472766
\(305\) −4.17058e38 −1.29882
\(306\) 8.60098e37 0.254604
\(307\) −5.70867e38 −1.60653 −0.803267 0.595619i \(-0.796907\pi\)
−0.803267 + 0.595619i \(0.796907\pi\)
\(308\) 1.17936e38 0.315580
\(309\) −7.41586e37 −0.188714
\(310\) 1.20628e38 0.291973
\(311\) −2.73000e38 −0.628604 −0.314302 0.949323i \(-0.601770\pi\)
−0.314302 + 0.949323i \(0.601770\pi\)
\(312\) −3.87487e38 −0.848908
\(313\) 7.96309e38 1.66014 0.830070 0.557659i \(-0.188301\pi\)
0.830070 + 0.557659i \(0.188301\pi\)
\(314\) 6.23176e38 1.23652
\(315\) −5.17489e38 −0.977435
\(316\) 3.48290e38 0.626313
\(317\) 3.34956e38 0.573548 0.286774 0.957998i \(-0.407417\pi\)
0.286774 + 0.957998i \(0.407417\pi\)
\(318\) 6.73389e37 0.109811
\(319\) −2.81185e38 −0.436754
\(320\) 4.96577e38 0.734787
\(321\) −7.16575e37 −0.101026
\(322\) −1.12169e39 −1.50697
\(323\) 1.20582e37 0.0154398
\(324\) −9.00871e37 −0.109955
\(325\) −1.86142e38 −0.216596
\(326\) −2.45947e38 −0.272879
\(327\) 6.87049e38 0.726938
\(328\) −5.29026e38 −0.533866
\(329\) 4.01987e38 0.386968
\(330\) −1.43611e38 −0.131893
\(331\) −8.30533e38 −0.727818 −0.363909 0.931435i \(-0.618558\pi\)
−0.363909 + 0.931435i \(0.618558\pi\)
\(332\) −2.20689e38 −0.184561
\(333\) 9.02166e38 0.720113
\(334\) 1.61494e39 1.23051
\(335\) −1.75034e37 −0.0127330
\(336\) 1.91352e38 0.132915
\(337\) 1.14148e39 0.757187 0.378594 0.925563i \(-0.376408\pi\)
0.378594 + 0.925563i \(0.376408\pi\)
\(338\) −1.33055e39 −0.842988
\(339\) −7.76816e38 −0.470135
\(340\) −4.63024e38 −0.267720
\(341\) 3.27991e38 0.181205
\(342\) 2.61457e37 0.0138037
\(343\) 7.27773e38 0.367229
\(344\) 8.71160e38 0.420187
\(345\) −1.61899e39 −0.746533
\(346\) −1.58242e39 −0.697660
\(347\) −3.74946e39 −1.58075 −0.790373 0.612626i \(-0.790113\pi\)
−0.790373 + 0.612626i \(0.790113\pi\)
\(348\) 8.21408e38 0.331193
\(349\) 7.67977e38 0.296179 0.148089 0.988974i \(-0.452688\pi\)
0.148089 + 0.988974i \(0.452688\pi\)
\(350\) 3.97049e38 0.146484
\(351\) 3.93078e39 1.38745
\(352\) 1.07249e39 0.362227
\(353\) −2.48278e39 −0.802472 −0.401236 0.915975i \(-0.631419\pi\)
−0.401236 + 0.915975i \(0.631419\pi\)
\(354\) 9.14622e38 0.282938
\(355\) 4.85062e39 1.43634
\(356\) 2.81324e39 0.797503
\(357\) −1.59930e39 −0.434082
\(358\) 8.15976e38 0.212076
\(359\) −6.14909e39 −1.53055 −0.765274 0.643704i \(-0.777397\pi\)
−0.765274 + 0.643704i \(0.777397\pi\)
\(360\) −2.85496e39 −0.680631
\(361\) −4.37520e39 −0.999163
\(362\) 3.78571e39 0.828256
\(363\) 2.19923e39 0.461018
\(364\) −6.06358e39 −1.21803
\(365\) 1.44921e39 0.278992
\(366\) −2.79475e39 −0.515687
\(367\) 5.66753e39 1.00247 0.501233 0.865312i \(-0.332880\pi\)
0.501233 + 0.865312i \(0.332880\pi\)
\(368\) −1.43267e39 −0.242943
\(369\) 2.21956e39 0.360877
\(370\) 4.09741e39 0.638826
\(371\) 2.99651e39 0.448043
\(372\) −9.58140e38 −0.137409
\(373\) −8.05893e39 −1.10864 −0.554320 0.832303i \(-0.687022\pi\)
−0.554320 + 0.832303i \(0.687022\pi\)
\(374\) 1.06214e39 0.140176
\(375\) 4.53850e39 0.574682
\(376\) 2.21774e39 0.269463
\(377\) 1.44569e40 1.68572
\(378\) −8.38454e39 −0.938332
\(379\) −9.24240e39 −0.992835 −0.496417 0.868084i \(-0.665351\pi\)
−0.496417 + 0.868084i \(0.665351\pi\)
\(380\) −1.40753e38 −0.0145148
\(381\) −5.00887e39 −0.495910
\(382\) −7.13385e39 −0.678175
\(383\) 9.14893e39 0.835198 0.417599 0.908631i \(-0.362872\pi\)
0.417599 + 0.908631i \(0.362872\pi\)
\(384\) −2.44855e39 −0.214672
\(385\) −6.39053e39 −0.538140
\(386\) 5.58076e39 0.451429
\(387\) −3.65501e39 −0.284033
\(388\) 4.28656e39 0.320049
\(389\) −2.19075e40 −1.57172 −0.785858 0.618407i \(-0.787778\pi\)
−0.785858 + 0.618407i \(0.787778\pi\)
\(390\) 7.38363e39 0.509059
\(391\) 1.19741e40 0.793417
\(392\) 2.03974e40 1.29909
\(393\) 8.68667e39 0.531825
\(394\) 7.93323e39 0.466937
\(395\) −1.88726e40 −1.06801
\(396\) −2.72983e39 −0.148546
\(397\) 2.07807e40 1.08744 0.543722 0.839265i \(-0.317015\pi\)
0.543722 + 0.839265i \(0.317015\pi\)
\(398\) −1.41605e40 −0.712676
\(399\) −4.86163e38 −0.0235343
\(400\) 5.07130e38 0.0236151
\(401\) −2.58688e40 −1.15888 −0.579441 0.815014i \(-0.696729\pi\)
−0.579441 + 0.815014i \(0.696729\pi\)
\(402\) −1.17292e38 −0.00505552
\(403\) −1.68634e40 −0.699386
\(404\) 5.47046e39 0.218330
\(405\) 4.88150e39 0.187500
\(406\) −3.08373e40 −1.14005
\(407\) 1.11409e40 0.396468
\(408\) −8.82323e39 −0.302270
\(409\) 4.06410e40 1.34046 0.670229 0.742155i \(-0.266196\pi\)
0.670229 + 0.742155i \(0.266196\pi\)
\(410\) 1.00807e40 0.320140
\(411\) 7.69121e39 0.235205
\(412\) −6.40225e39 −0.188550
\(413\) 4.06997e40 1.15443
\(414\) 2.59633e40 0.709341
\(415\) 1.19583e40 0.314721
\(416\) −5.51410e40 −1.39807
\(417\) −1.82577e40 −0.446002
\(418\) 3.22876e38 0.00759983
\(419\) −6.77858e40 −1.53752 −0.768761 0.639536i \(-0.779126\pi\)
−0.768761 + 0.639536i \(0.779126\pi\)
\(420\) 1.86683e40 0.408075
\(421\) 3.82000e40 0.804805 0.402403 0.915463i \(-0.368175\pi\)
0.402403 + 0.915463i \(0.368175\pi\)
\(422\) −1.96098e39 −0.0398226
\(423\) −9.30467e39 −0.182148
\(424\) 1.65316e40 0.311992
\(425\) −4.23852e39 −0.0771233
\(426\) 3.25045e40 0.570289
\(427\) −1.24364e41 −2.10407
\(428\) −6.18632e39 −0.100938
\(429\) 2.00762e40 0.315933
\(430\) −1.66001e40 −0.251971
\(431\) 1.21642e41 1.78109 0.890547 0.454890i \(-0.150322\pi\)
0.890547 + 0.454890i \(0.150322\pi\)
\(432\) −1.07091e40 −0.151271
\(433\) 3.18876e39 0.0434570 0.0217285 0.999764i \(-0.493083\pi\)
0.0217285 + 0.999764i \(0.493083\pi\)
\(434\) 3.59704e40 0.472993
\(435\) −4.45092e40 −0.564763
\(436\) 5.93142e40 0.726303
\(437\) 3.63994e39 0.0430162
\(438\) 9.71131e39 0.110772
\(439\) 7.39242e40 0.813929 0.406965 0.913444i \(-0.366587\pi\)
0.406965 + 0.913444i \(0.366587\pi\)
\(440\) −3.52562e40 −0.374730
\(441\) −8.55785e40 −0.878145
\(442\) −5.46092e40 −0.541029
\(443\) 2.28069e40 0.218177 0.109088 0.994032i \(-0.465207\pi\)
0.109088 + 0.994032i \(0.465207\pi\)
\(444\) −3.25453e40 −0.300644
\(445\) −1.52440e41 −1.35993
\(446\) −3.57466e39 −0.0307995
\(447\) −7.32024e40 −0.609198
\(448\) 1.48075e41 1.19035
\(449\) 6.27451e40 0.487261 0.243630 0.969868i \(-0.421662\pi\)
0.243630 + 0.969868i \(0.421662\pi\)
\(450\) −9.19038e39 −0.0689508
\(451\) 2.74096e40 0.198686
\(452\) −6.70639e40 −0.469725
\(453\) 3.22480e40 0.218263
\(454\) −5.71397e39 −0.0373742
\(455\) 3.28564e41 2.07703
\(456\) −2.68214e39 −0.0163880
\(457\) −2.37596e39 −0.0140326 −0.00701629 0.999975i \(-0.502233\pi\)
−0.00701629 + 0.999975i \(0.502233\pi\)
\(458\) −6.33612e40 −0.361750
\(459\) 8.95054e40 0.494029
\(460\) −1.39771e41 −0.745881
\(461\) −6.79165e40 −0.350438 −0.175219 0.984529i \(-0.556063\pi\)
−0.175219 + 0.984529i \(0.556063\pi\)
\(462\) −4.28236e40 −0.213665
\(463\) −1.40330e41 −0.677090 −0.338545 0.940950i \(-0.609935\pi\)
−0.338545 + 0.940950i \(0.609935\pi\)
\(464\) −3.93868e40 −0.183790
\(465\) 5.19182e40 0.234314
\(466\) −1.23181e40 −0.0537727
\(467\) −2.95535e41 −1.24795 −0.623976 0.781444i \(-0.714484\pi\)
−0.623976 + 0.781444i \(0.714484\pi\)
\(468\) 1.40352e41 0.573334
\(469\) −5.21939e39 −0.0206272
\(470\) −4.22594e40 −0.161587
\(471\) 2.68214e41 0.992331
\(472\) 2.24538e41 0.803877
\(473\) −4.51361e40 −0.156378
\(474\) −1.26467e41 −0.424047
\(475\) −1.28845e39 −0.00418135
\(476\) −1.38070e41 −0.433703
\(477\) −6.93593e40 −0.210897
\(478\) 4.36239e41 1.28408
\(479\) 3.59879e41 1.02555 0.512774 0.858524i \(-0.328618\pi\)
0.512774 + 0.858524i \(0.328618\pi\)
\(480\) 1.69765e41 0.468393
\(481\) −5.72802e41 −1.53023
\(482\) 4.90125e40 0.126788
\(483\) −4.82771e41 −1.20937
\(484\) 1.89864e41 0.460616
\(485\) −2.32273e41 −0.545761
\(486\) 3.07882e41 0.700684
\(487\) 8.64633e41 1.90604 0.953022 0.302901i \(-0.0979550\pi\)
0.953022 + 0.302901i \(0.0979550\pi\)
\(488\) −6.86107e41 −1.46516
\(489\) −1.05855e41 −0.218990
\(490\) −3.88675e41 −0.779018
\(491\) −8.25010e41 −1.60212 −0.801062 0.598582i \(-0.795731\pi\)
−0.801062 + 0.598582i \(0.795731\pi\)
\(492\) −8.00700e40 −0.150664
\(493\) 3.29189e41 0.600231
\(494\) −1.66004e40 −0.0293327
\(495\) 1.47920e41 0.253306
\(496\) 4.59431e40 0.0762526
\(497\) 1.44642e42 2.32686
\(498\) 8.01340e40 0.124957
\(499\) −4.70553e41 −0.711295 −0.355647 0.934620i \(-0.615740\pi\)
−0.355647 + 0.934620i \(0.615740\pi\)
\(500\) 3.91817e41 0.574180
\(501\) 6.95065e41 0.987508
\(502\) −2.41212e41 −0.332270
\(503\) 1.02731e41 0.137214 0.0686068 0.997644i \(-0.478145\pi\)
0.0686068 + 0.997644i \(0.478145\pi\)
\(504\) −8.51327e41 −1.10261
\(505\) −2.96425e41 −0.372304
\(506\) 3.20624e41 0.390537
\(507\) −5.72665e41 −0.676515
\(508\) −4.32425e41 −0.495477
\(509\) −6.79468e41 −0.755168 −0.377584 0.925975i \(-0.623245\pi\)
−0.377584 + 0.925975i \(0.623245\pi\)
\(510\) 1.68128e41 0.181260
\(511\) 4.32143e41 0.451964
\(512\) 3.18257e41 0.322919
\(513\) 2.72084e40 0.0267845
\(514\) −1.31606e42 −1.25704
\(515\) 3.46915e41 0.321522
\(516\) 1.31853e41 0.118582
\(517\) −1.14904e41 −0.100284
\(518\) 1.22181e42 1.03489
\(519\) −6.81073e41 −0.559886
\(520\) 1.81267e42 1.44633
\(521\) 4.70689e41 0.364543 0.182272 0.983248i \(-0.441655\pi\)
0.182272 + 0.983248i \(0.441655\pi\)
\(522\) 7.13781e41 0.536627
\(523\) −1.48934e42 −1.08697 −0.543485 0.839419i \(-0.682895\pi\)
−0.543485 + 0.839419i \(0.682895\pi\)
\(524\) 7.49937e41 0.531361
\(525\) 1.70889e41 0.117556
\(526\) −1.76096e42 −1.17617
\(527\) −3.83986e41 −0.249030
\(528\) −5.46963e40 −0.0344455
\(529\) 1.97937e42 1.21050
\(530\) −3.15012e41 −0.187090
\(531\) −9.42065e41 −0.543395
\(532\) −4.19714e40 −0.0235138
\(533\) −1.40924e42 −0.766857
\(534\) −1.02151e42 −0.539951
\(535\) 3.35215e41 0.172123
\(536\) −2.87951e40 −0.0143636
\(537\) 3.51194e41 0.170195
\(538\) 9.61583e41 0.452753
\(539\) −1.05682e42 −0.483475
\(540\) −1.04478e42 −0.464431
\(541\) 2.37435e42 1.02562 0.512811 0.858502i \(-0.328604\pi\)
0.512811 + 0.858502i \(0.328604\pi\)
\(542\) 1.96413e40 0.00824484
\(543\) 1.62936e42 0.664692
\(544\) −1.25558e42 −0.497809
\(545\) −3.21402e42 −1.23852
\(546\) 2.20174e42 0.824670
\(547\) 3.75591e42 1.36745 0.683725 0.729740i \(-0.260359\pi\)
0.683725 + 0.729740i \(0.260359\pi\)
\(548\) 6.63996e41 0.235000
\(549\) 2.87861e42 0.990401
\(550\) −1.13493e41 −0.0379618
\(551\) 1.00069e41 0.0325424
\(552\) −2.66342e42 −0.842140
\(553\) −5.62766e42 −1.73017
\(554\) 1.27243e42 0.380394
\(555\) 1.76352e42 0.512670
\(556\) −1.57622e42 −0.445613
\(557\) −5.38624e42 −1.48092 −0.740458 0.672103i \(-0.765391\pi\)
−0.740458 + 0.672103i \(0.765391\pi\)
\(558\) −8.32597e41 −0.222641
\(559\) 2.32063e42 0.603565
\(560\) −8.95149e41 −0.226454
\(561\) 4.57144e41 0.112494
\(562\) −2.22986e42 −0.533784
\(563\) 2.93646e42 0.683823 0.341912 0.939732i \(-0.388926\pi\)
0.341912 + 0.939732i \(0.388926\pi\)
\(564\) 3.35663e41 0.0760461
\(565\) 3.63395e42 0.800993
\(566\) 1.73061e41 0.0371145
\(567\) 1.45562e42 0.303747
\(568\) 7.97981e42 1.62029
\(569\) 1.22480e42 0.242005 0.121002 0.992652i \(-0.461389\pi\)
0.121002 + 0.992652i \(0.461389\pi\)
\(570\) 5.11086e40 0.00982728
\(571\) −8.00625e42 −1.49820 −0.749099 0.662458i \(-0.769513\pi\)
−0.749099 + 0.662458i \(0.769513\pi\)
\(572\) 1.73322e42 0.315657
\(573\) −3.07040e42 −0.544249
\(574\) 3.00598e42 0.518624
\(575\) −1.27946e42 −0.214870
\(576\) −3.42746e42 −0.560304
\(577\) −5.67748e42 −0.903505 −0.451753 0.892143i \(-0.649201\pi\)
−0.451753 + 0.892143i \(0.649201\pi\)
\(578\) 3.12294e42 0.483818
\(579\) 2.40195e42 0.362281
\(580\) −3.84256e42 −0.564270
\(581\) 3.56588e42 0.509843
\(582\) −1.55649e42 −0.216690
\(583\) −8.56525e41 −0.116112
\(584\) 2.38411e42 0.314722
\(585\) −7.60517e42 −0.977672
\(586\) 1.83201e41 0.0229358
\(587\) 3.58214e41 0.0436770 0.0218385 0.999762i \(-0.493048\pi\)
0.0218385 + 0.999762i \(0.493048\pi\)
\(588\) 3.08721e42 0.366622
\(589\) −1.16726e41 −0.0135015
\(590\) −4.27862e42 −0.482056
\(591\) 3.41445e42 0.374726
\(592\) 1.56056e42 0.166838
\(593\) 1.84785e43 1.92450 0.962251 0.272164i \(-0.0877395\pi\)
0.962251 + 0.272164i \(0.0877395\pi\)
\(594\) 2.39664e42 0.243172
\(595\) 7.48153e42 0.739567
\(596\) −6.31970e42 −0.608666
\(597\) −6.09467e42 −0.571937
\(598\) −1.64846e43 −1.50734
\(599\) −3.08643e42 −0.275005 −0.137503 0.990501i \(-0.543908\pi\)
−0.137503 + 0.990501i \(0.543908\pi\)
\(600\) 9.42786e41 0.0818594
\(601\) 2.05195e43 1.73625 0.868125 0.496346i \(-0.165325\pi\)
0.868125 + 0.496346i \(0.165325\pi\)
\(602\) −4.95003e42 −0.408189
\(603\) 1.20812e41 0.00970937
\(604\) 2.78403e42 0.218073
\(605\) −1.02880e43 −0.785460
\(606\) −1.98637e42 −0.147821
\(607\) −2.07151e43 −1.50267 −0.751333 0.659923i \(-0.770589\pi\)
−0.751333 + 0.659923i \(0.770589\pi\)
\(608\) −3.81679e41 −0.0269894
\(609\) −1.32723e43 −0.914909
\(610\) 1.30739e43 0.878603
\(611\) 5.90771e42 0.387062
\(612\) 3.19587e42 0.204147
\(613\) −6.35024e42 −0.395506 −0.197753 0.980252i \(-0.563364\pi\)
−0.197753 + 0.980252i \(0.563364\pi\)
\(614\) 1.78955e43 1.08676
\(615\) 4.33871e42 0.256919
\(616\) −1.05131e43 −0.607059
\(617\) 1.92676e43 1.08495 0.542473 0.840073i \(-0.317488\pi\)
0.542473 + 0.840073i \(0.317488\pi\)
\(618\) 2.32471e42 0.127658
\(619\) 7.41921e42 0.397331 0.198666 0.980067i \(-0.436339\pi\)
0.198666 + 0.980067i \(0.436339\pi\)
\(620\) 4.48220e42 0.234110
\(621\) 2.70185e43 1.37639
\(622\) 8.55798e42 0.425226
\(623\) −4.54563e43 −2.20308
\(624\) 2.81217e42 0.132947
\(625\) −1.80974e43 −0.834593
\(626\) −2.49626e43 −1.12302
\(627\) 1.38965e41 0.00609901
\(628\) 2.31554e43 0.991465
\(629\) −1.30429e43 −0.544867
\(630\) 1.62222e43 0.661197
\(631\) −1.64967e43 −0.656058 −0.328029 0.944668i \(-0.606384\pi\)
−0.328029 + 0.944668i \(0.606384\pi\)
\(632\) −3.10475e43 −1.20479
\(633\) −8.44001e41 −0.0319584
\(634\) −1.05002e43 −0.387983
\(635\) 2.34316e43 0.844906
\(636\) 2.50211e42 0.0880485
\(637\) 5.43354e43 1.86604
\(638\) 8.81455e42 0.295447
\(639\) −3.34798e43 −1.09527
\(640\) 1.14543e43 0.365747
\(641\) 1.02463e43 0.319349 0.159675 0.987170i \(-0.448955\pi\)
0.159675 + 0.987170i \(0.448955\pi\)
\(642\) 2.24631e42 0.0683403
\(643\) 1.32606e43 0.393817 0.196908 0.980422i \(-0.436910\pi\)
0.196908 + 0.980422i \(0.436910\pi\)
\(644\) −4.16785e43 −1.20832
\(645\) −7.14466e42 −0.202211
\(646\) −3.77998e41 −0.0104445
\(647\) 4.58618e43 1.23718 0.618592 0.785712i \(-0.287703\pi\)
0.618592 + 0.785712i \(0.287703\pi\)
\(648\) 8.03060e42 0.211512
\(649\) −1.16337e43 −0.299174
\(650\) 5.83514e42 0.146519
\(651\) 1.54816e43 0.379586
\(652\) −9.13868e42 −0.218799
\(653\) −1.96584e43 −0.459614 −0.229807 0.973236i \(-0.573810\pi\)
−0.229807 + 0.973236i \(0.573810\pi\)
\(654\) −2.15375e43 −0.491746
\(655\) −4.06364e43 −0.906097
\(656\) 3.83938e42 0.0836088
\(657\) −1.00027e43 −0.212742
\(658\) −1.26014e43 −0.261769
\(659\) 4.60611e43 0.934568 0.467284 0.884107i \(-0.345233\pi\)
0.467284 + 0.884107i \(0.345233\pi\)
\(660\) −5.33615e42 −0.105754
\(661\) −6.03515e43 −1.16833 −0.584165 0.811635i \(-0.698578\pi\)
−0.584165 + 0.811635i \(0.698578\pi\)
\(662\) 2.60354e43 0.492341
\(663\) −2.35037e43 −0.434187
\(664\) 1.96728e43 0.355026
\(665\) 2.27428e42 0.0400967
\(666\) −2.82810e43 −0.487129
\(667\) 9.93707e43 1.67228
\(668\) 6.00063e43 0.986646
\(669\) −1.53853e42 −0.0247172
\(670\) 5.48696e41 0.00861335
\(671\) 3.55482e43 0.545279
\(672\) 5.06227e43 0.758790
\(673\) −5.70208e43 −0.835218 −0.417609 0.908627i \(-0.637132\pi\)
−0.417609 + 0.908627i \(0.637132\pi\)
\(674\) −3.57829e43 −0.512208
\(675\) −9.56389e42 −0.133791
\(676\) −4.94392e43 −0.675924
\(677\) −1.60365e43 −0.214282 −0.107141 0.994244i \(-0.534170\pi\)
−0.107141 + 0.994244i \(0.534170\pi\)
\(678\) 2.43515e43 0.318028
\(679\) −6.92621e43 −0.884126
\(680\) 4.12752e43 0.514992
\(681\) −2.45928e42 −0.0299935
\(682\) −1.02818e43 −0.122578
\(683\) −6.08600e43 −0.709269 −0.354634 0.935005i \(-0.615395\pi\)
−0.354634 + 0.935005i \(0.615395\pi\)
\(684\) 9.71499e41 0.0110681
\(685\) −3.59796e43 −0.400730
\(686\) −2.28141e43 −0.248416
\(687\) −2.72705e43 −0.290311
\(688\) −6.32240e42 −0.0658054
\(689\) 4.40375e43 0.448152
\(690\) 5.07520e43 0.505001
\(691\) 1.43014e44 1.39146 0.695729 0.718304i \(-0.255082\pi\)
0.695729 + 0.718304i \(0.255082\pi\)
\(692\) −5.87983e43 −0.559397
\(693\) 4.41085e43 0.410353
\(694\) 1.17538e44 1.06931
\(695\) 8.54097e43 0.759876
\(696\) −7.32225e43 −0.637091
\(697\) −3.20890e43 −0.273054
\(698\) −2.40744e43 −0.200354
\(699\) −5.30169e42 −0.0431537
\(700\) 1.47532e43 0.117453
\(701\) −5.20421e43 −0.405252 −0.202626 0.979256i \(-0.564948\pi\)
−0.202626 + 0.979256i \(0.564948\pi\)
\(702\) −1.23222e44 −0.938559
\(703\) −3.96487e42 −0.0295407
\(704\) −4.23260e43 −0.308483
\(705\) −1.81884e43 −0.129677
\(706\) 7.78298e43 0.542842
\(707\) −8.83916e43 −0.603129
\(708\) 3.39847e43 0.226865
\(709\) 2.25028e44 1.46967 0.734836 0.678245i \(-0.237259\pi\)
0.734836 + 0.678245i \(0.237259\pi\)
\(710\) −1.52057e44 −0.971630
\(711\) 1.30262e44 0.814401
\(712\) −2.50780e44 −1.53410
\(713\) −1.15912e44 −0.693810
\(714\) 5.01345e43 0.293640
\(715\) −9.39170e43 −0.538270
\(716\) 3.03193e43 0.170046
\(717\) 1.87756e44 1.03050
\(718\) 1.92761e44 1.03536
\(719\) −2.22431e44 −1.16922 −0.584611 0.811314i \(-0.698753\pi\)
−0.584611 + 0.811314i \(0.698753\pi\)
\(720\) 2.07197e43 0.106594
\(721\) 1.03447e44 0.520862
\(722\) 1.37153e44 0.675895
\(723\) 2.10949e43 0.101750
\(724\) 1.40666e44 0.664112
\(725\) −3.51748e43 −0.162552
\(726\) −6.89412e43 −0.311861
\(727\) −4.26635e44 −1.88918 −0.944591 0.328251i \(-0.893541\pi\)
−0.944591 + 0.328251i \(0.893541\pi\)
\(728\) 5.40524e44 2.34303
\(729\) 8.47399e43 0.359593
\(730\) −4.54297e43 −0.188727
\(731\) 5.28418e43 0.214911
\(732\) −1.03845e44 −0.413488
\(733\) −2.38496e44 −0.929758 −0.464879 0.885374i \(-0.653902\pi\)
−0.464879 + 0.885374i \(0.653902\pi\)
\(734\) −1.77665e44 −0.678130
\(735\) −1.67285e44 −0.625178
\(736\) −3.79016e44 −1.38692
\(737\) 1.49192e42 0.00534562
\(738\) −6.95786e43 −0.244119
\(739\) 3.50761e44 1.20510 0.602549 0.798082i \(-0.294152\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(740\) 1.52248e44 0.512223
\(741\) −7.14479e42 −0.0235400
\(742\) −9.39342e43 −0.303084
\(743\) −7.53875e43 −0.238217 −0.119108 0.992881i \(-0.538004\pi\)
−0.119108 + 0.992881i \(0.538004\pi\)
\(744\) 8.54112e43 0.264323
\(745\) 3.42442e44 1.03792
\(746\) 2.52630e44 0.749953
\(747\) −8.25384e43 −0.239986
\(748\) 3.94661e43 0.112396
\(749\) 9.99584e43 0.278838
\(750\) −1.42272e44 −0.388750
\(751\) 6.25728e44 1.67481 0.837407 0.546580i \(-0.184071\pi\)
0.837407 + 0.546580i \(0.184071\pi\)
\(752\) −1.60951e43 −0.0422006
\(753\) −1.03817e44 −0.266654
\(754\) −4.53193e44 −1.14032
\(755\) −1.50857e44 −0.371866
\(756\) −3.11545e44 −0.752372
\(757\) −2.09917e43 −0.0496663 −0.0248332 0.999692i \(-0.507905\pi\)
−0.0248332 + 0.999692i \(0.507905\pi\)
\(758\) 2.89730e44 0.671615
\(759\) 1.37996e44 0.313414
\(760\) 1.25471e43 0.0279210
\(761\) −3.45290e43 −0.0752873 −0.0376436 0.999291i \(-0.511985\pi\)
−0.0376436 + 0.999291i \(0.511985\pi\)
\(762\) 1.57017e44 0.335464
\(763\) −9.58397e44 −2.00639
\(764\) −2.65073e44 −0.543774
\(765\) −1.73173e44 −0.348119
\(766\) −2.86800e44 −0.564979
\(767\) 5.98135e44 1.15470
\(768\) 3.04715e44 0.576493
\(769\) 7.01102e44 1.29994 0.649970 0.759960i \(-0.274782\pi\)
0.649970 + 0.759960i \(0.274782\pi\)
\(770\) 2.00329e44 0.364031
\(771\) −5.66430e44 −1.00880
\(772\) 2.07364e44 0.361965
\(773\) −2.53762e44 −0.434154 −0.217077 0.976154i \(-0.569652\pi\)
−0.217077 + 0.976154i \(0.569652\pi\)
\(774\) 1.14577e44 0.192137
\(775\) 4.10300e43 0.0674411
\(776\) −3.82115e44 −0.615655
\(777\) 5.25867e44 0.830519
\(778\) 6.86753e44 1.06321
\(779\) −9.75461e42 −0.0148040
\(780\) 2.74354e44 0.408173
\(781\) −4.13445e44 −0.603014
\(782\) −3.75361e44 −0.536716
\(783\) 7.42791e44 1.04126
\(784\) −1.48033e44 −0.203451
\(785\) −1.25471e45 −1.69068
\(786\) −2.72309e44 −0.359759
\(787\) 5.16912e44 0.669589 0.334795 0.942291i \(-0.391333\pi\)
0.334795 + 0.942291i \(0.391333\pi\)
\(788\) 2.94775e44 0.374399
\(789\) −7.57914e44 −0.943901
\(790\) 5.91615e44 0.722470
\(791\) 1.08362e45 1.29760
\(792\) 2.43344e44 0.285746
\(793\) −1.82768e45 −2.10458
\(794\) −6.51430e44 −0.735614
\(795\) −1.35581e44 −0.150144
\(796\) −5.26164e44 −0.571437
\(797\) −2.24914e44 −0.239559 −0.119780 0.992800i \(-0.538219\pi\)
−0.119780 + 0.992800i \(0.538219\pi\)
\(798\) 1.52402e43 0.0159201
\(799\) 1.34521e44 0.137821
\(800\) 1.34162e44 0.134814
\(801\) 1.05216e45 1.03700
\(802\) 8.10933e44 0.783939
\(803\) −1.23524e44 −0.117128
\(804\) −4.35824e42 −0.00405362
\(805\) 2.25841e45 2.06047
\(806\) 5.28632e44 0.473108
\(807\) 4.13863e44 0.363343
\(808\) −4.87652e44 −0.419985
\(809\) −1.09436e45 −0.924612 −0.462306 0.886720i \(-0.652978\pi\)
−0.462306 + 0.886720i \(0.652978\pi\)
\(810\) −1.53025e44 −0.126836
\(811\) −1.65483e44 −0.134564 −0.0672821 0.997734i \(-0.521433\pi\)
−0.0672821 + 0.997734i \(0.521433\pi\)
\(812\) −1.14582e45 −0.914110
\(813\) 8.45359e42 0.00661664
\(814\) −3.49245e44 −0.268196
\(815\) 4.95192e44 0.373105
\(816\) 6.40342e43 0.0473385
\(817\) 1.60632e43 0.0116517
\(818\) −1.27401e45 −0.906768
\(819\) −2.26780e45 −1.58382
\(820\) 3.74569e44 0.256695
\(821\) 1.30182e45 0.875454 0.437727 0.899108i \(-0.355784\pi\)
0.437727 + 0.899108i \(0.355784\pi\)
\(822\) −2.41103e44 −0.159107
\(823\) −8.40972e43 −0.0544608 −0.0272304 0.999629i \(-0.508669\pi\)
−0.0272304 + 0.999629i \(0.508669\pi\)
\(824\) 5.70713e44 0.362699
\(825\) −4.88471e43 −0.0304651
\(826\) −1.27585e45 −0.780924
\(827\) 2.14145e45 1.28639 0.643196 0.765702i \(-0.277608\pi\)
0.643196 + 0.765702i \(0.277608\pi\)
\(828\) 9.64721e44 0.568763
\(829\) −8.75462e44 −0.506573 −0.253286 0.967391i \(-0.581512\pi\)
−0.253286 + 0.967391i \(0.581512\pi\)
\(830\) −3.74868e44 −0.212896
\(831\) 5.47653e44 0.305274
\(832\) 2.17616e45 1.19063
\(833\) 1.23724e45 0.664440
\(834\) 5.72339e44 0.301703
\(835\) −3.25152e45 −1.68247
\(836\) 1.19971e43 0.00609369
\(837\) −8.66436e44 −0.432008
\(838\) 2.12494e45 1.04007
\(839\) 8.96946e44 0.430979 0.215489 0.976506i \(-0.430865\pi\)
0.215489 + 0.976506i \(0.430865\pi\)
\(840\) −1.66414e45 −0.784983
\(841\) 5.72465e44 0.265101
\(842\) −1.19749e45 −0.544420
\(843\) −9.59728e44 −0.428372
\(844\) −7.28641e43 −0.0319305
\(845\) 2.67894e45 1.15261
\(846\) 2.91682e44 0.123216
\(847\) −3.06781e45 −1.27244
\(848\) −1.19977e44 −0.0488611
\(849\) 7.44850e43 0.0297851
\(850\) 1.32869e44 0.0521710
\(851\) −3.93720e45 −1.51803
\(852\) 1.20777e45 0.457269
\(853\) −3.47906e45 −1.29346 −0.646728 0.762721i \(-0.723863\pi\)
−0.646728 + 0.762721i \(0.723863\pi\)
\(854\) 3.89853e45 1.42333
\(855\) −5.26421e43 −0.0188737
\(856\) 5.51465e44 0.194167
\(857\) 7.25970e44 0.251024 0.125512 0.992092i \(-0.459943\pi\)
0.125512 + 0.992092i \(0.459943\pi\)
\(858\) −6.29348e44 −0.213716
\(859\) 4.44826e45 1.48353 0.741765 0.670660i \(-0.233989\pi\)
0.741765 + 0.670660i \(0.233989\pi\)
\(860\) −6.16811e44 −0.202035
\(861\) 1.29377e45 0.416206
\(862\) −3.81323e45 −1.20484
\(863\) 2.69165e45 0.835318 0.417659 0.908604i \(-0.362851\pi\)
0.417659 + 0.908604i \(0.362851\pi\)
\(864\) −2.83313e45 −0.863581
\(865\) 3.18607e45 0.953905
\(866\) −9.99609e43 −0.0293970
\(867\) 1.34411e45 0.388273
\(868\) 1.33656e45 0.379255
\(869\) 1.60862e45 0.448379
\(870\) 1.39527e45 0.382040
\(871\) −7.67056e43 −0.0206322
\(872\) −5.28742e45 −1.39714
\(873\) 1.60319e45 0.416164
\(874\) −1.14104e44 −0.0290988
\(875\) −6.33096e45 −1.58615
\(876\) 3.60844e44 0.0888189
\(877\) −5.87091e44 −0.141975 −0.0709875 0.997477i \(-0.522615\pi\)
−0.0709875 + 0.997477i \(0.522615\pi\)
\(878\) −2.31737e45 −0.550592
\(879\) 7.88492e43 0.0184064
\(880\) 2.55870e44 0.0586865
\(881\) −5.61916e45 −1.26632 −0.633162 0.774020i \(-0.718243\pi\)
−0.633162 + 0.774020i \(0.718243\pi\)
\(882\) 2.68270e45 0.594031
\(883\) 3.14941e45 0.685232 0.342616 0.939476i \(-0.388687\pi\)
0.342616 + 0.939476i \(0.388687\pi\)
\(884\) −2.02912e45 −0.433808
\(885\) −1.84151e45 −0.386859
\(886\) −7.14947e44 −0.147588
\(887\) 3.05461e45 0.619641 0.309821 0.950795i \(-0.399731\pi\)
0.309821 + 0.950795i \(0.399731\pi\)
\(888\) 2.90118e45 0.578327
\(889\) 6.98711e45 1.36874
\(890\) 4.77866e45 0.919942
\(891\) −4.16077e44 −0.0787171
\(892\) −1.32824e44 −0.0246956
\(893\) 4.08924e43 0.00747215
\(894\) 2.29474e45 0.412099
\(895\) −1.64289e45 −0.289969
\(896\) 3.41560e45 0.592506
\(897\) −7.09494e45 −1.20967
\(898\) −1.96692e45 −0.329613
\(899\) −3.18664e45 −0.524877
\(900\) −3.41487e44 −0.0552861
\(901\) 1.00275e45 0.159573
\(902\) −8.59233e44 −0.134403
\(903\) −2.13048e45 −0.327580
\(904\) 5.97826e45 0.903574
\(905\) −7.62218e45 −1.13247
\(906\) −1.01091e45 −0.147647
\(907\) 1.69836e44 0.0243847 0.0121924 0.999926i \(-0.496119\pi\)
0.0121924 + 0.999926i \(0.496119\pi\)
\(908\) −2.12314e44 −0.0299673
\(909\) 2.04597e45 0.283896
\(910\) −1.02998e46 −1.40503
\(911\) 1.24574e46 1.67067 0.835336 0.549739i \(-0.185273\pi\)
0.835336 + 0.549739i \(0.185273\pi\)
\(912\) 1.94655e43 0.00256652
\(913\) −1.01927e45 −0.132128
\(914\) 7.44812e43 0.00949250
\(915\) 5.62698e45 0.705096
\(916\) −2.35432e45 −0.290058
\(917\) −1.21175e46 −1.46787
\(918\) −2.80580e45 −0.334192
\(919\) −1.08191e46 −1.26707 −0.633535 0.773714i \(-0.718397\pi\)
−0.633535 + 0.773714i \(0.718397\pi\)
\(920\) 1.24595e46 1.43480
\(921\) 7.70217e45 0.872145
\(922\) 2.12904e45 0.237058
\(923\) 2.12570e46 2.32742
\(924\) −1.59120e45 −0.171320
\(925\) 1.39367e45 0.147558
\(926\) 4.39906e45 0.458025
\(927\) −2.39447e45 −0.245173
\(928\) −1.04199e46 −1.04923
\(929\) −9.79872e45 −0.970344 −0.485172 0.874419i \(-0.661243\pi\)
−0.485172 + 0.874419i \(0.661243\pi\)
\(930\) −1.62753e45 −0.158505
\(931\) 3.76103e44 0.0360235
\(932\) −4.57704e44 −0.0431160
\(933\) 3.68334e45 0.341253
\(934\) 9.26440e45 0.844191
\(935\) −2.13853e45 −0.191661
\(936\) −1.25113e46 −1.10288
\(937\) 1.01455e46 0.879650 0.439825 0.898083i \(-0.355040\pi\)
0.439825 + 0.898083i \(0.355040\pi\)
\(938\) 1.63617e44 0.0139535
\(939\) −1.07439e46 −0.901246
\(940\) −1.57024e45 −0.129564
\(941\) −1.48680e46 −1.20674 −0.603370 0.797461i \(-0.706176\pi\)
−0.603370 + 0.797461i \(0.706176\pi\)
\(942\) −8.40792e45 −0.671274
\(943\) −9.68655e45 −0.760743
\(944\) −1.62958e45 −0.125895
\(945\) 1.68815e46 1.28297
\(946\) 1.41492e45 0.105784
\(947\) 2.27265e46 1.67151 0.835754 0.549104i \(-0.185031\pi\)
0.835754 + 0.549104i \(0.185031\pi\)
\(948\) −4.69915e45 −0.340009
\(949\) 6.35090e45 0.452073
\(950\) 4.03901e43 0.00282852
\(951\) −4.51925e45 −0.311364
\(952\) 1.23079e46 0.834282
\(953\) −7.58661e45 −0.505950 −0.252975 0.967473i \(-0.581409\pi\)
−0.252975 + 0.967473i \(0.581409\pi\)
\(954\) 2.17427e45 0.142664
\(955\) 1.43634e46 0.927265
\(956\) 1.62093e46 1.02960
\(957\) 3.79377e45 0.237102
\(958\) −1.12814e46 −0.693744
\(959\) −1.07288e46 −0.649178
\(960\) −6.69984e45 −0.398897
\(961\) −1.33521e46 −0.782234
\(962\) 1.79561e46 1.03514
\(963\) −2.31371e45 −0.131251
\(964\) 1.82116e45 0.101661
\(965\) −1.12363e46 −0.617236
\(966\) 1.51338e46 0.818095
\(967\) −3.35350e46 −1.78397 −0.891986 0.452064i \(-0.850688\pi\)
−0.891986 + 0.452064i \(0.850688\pi\)
\(968\) −1.69250e46 −0.886053
\(969\) −1.62690e44 −0.00838188
\(970\) 7.28127e45 0.369186
\(971\) −2.14498e46 −1.07035 −0.535175 0.844741i \(-0.679754\pi\)
−0.535175 + 0.844741i \(0.679754\pi\)
\(972\) 1.14400e46 0.561822
\(973\) 2.54685e46 1.23099
\(974\) −2.71044e46 −1.28937
\(975\) 2.51143e45 0.117584
\(976\) 4.97939e45 0.229458
\(977\) 1.98478e46 0.900215 0.450107 0.892974i \(-0.351386\pi\)
0.450107 + 0.892974i \(0.351386\pi\)
\(978\) 3.31834e45 0.148139
\(979\) 1.29933e46 0.570935
\(980\) −1.44420e46 −0.624632
\(981\) 2.21837e46 0.944420
\(982\) 2.58623e46 1.08377
\(983\) −1.53482e46 −0.633107 −0.316554 0.948575i \(-0.602526\pi\)
−0.316554 + 0.948575i \(0.602526\pi\)
\(984\) 7.13765e45 0.289822
\(985\) −1.59728e46 −0.638440
\(986\) −1.03194e46 −0.406033
\(987\) −5.42363e45 −0.210075
\(988\) −6.16823e44 −0.0235195
\(989\) 1.59511e46 0.598753
\(990\) −4.63697e45 −0.171352
\(991\) −8.58630e45 −0.312367 −0.156183 0.987728i \(-0.549919\pi\)
−0.156183 + 0.987728i \(0.549919\pi\)
\(992\) 1.21544e46 0.435313
\(993\) 1.12056e46 0.395113
\(994\) −4.53421e46 −1.57403
\(995\) 2.85109e46 0.974437
\(996\) 2.97754e45 0.100193
\(997\) 3.45614e46 1.14503 0.572514 0.819895i \(-0.305968\pi\)
0.572514 + 0.819895i \(0.305968\pi\)
\(998\) 1.47508e46 0.481164
\(999\) −2.94304e46 −0.945216
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 1.32.a.a.1.1 2
3.2 odd 2 9.32.a.a.1.2 2
4.3 odd 2 16.32.a.b.1.2 2
5.2 odd 4 25.32.b.a.24.2 4
5.3 odd 4 25.32.b.a.24.3 4
5.4 even 2 25.32.a.a.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.32.a.a.1.1 2 1.1 even 1 trivial
9.32.a.a.1.2 2 3.2 odd 2
16.32.a.b.1.2 2 4.3 odd 2
25.32.a.a.1.2 2 5.4 even 2
25.32.b.a.24.2 4 5.2 odd 4
25.32.b.a.24.3 4 5.3 odd 4