Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(46.8682610909\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + 31594524240 x^{7} + 3232668379296 x^{6} + \cdots - 24\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(41.8127\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −39.8127 | −1.75949 | −0.879744 | − | 0.475448i | \(-0.842286\pi\) | ||||
−0.879744 | + | 0.475448i | \(0.842286\pi\) | |||||||
\(3\) | 138.193 | 0.985006 | 0.492503 | − | 0.870311i | \(-0.336082\pi\) | ||||
0.492503 | + | 0.870311i | \(0.336082\pi\) | |||||||
\(4\) | 1073.05 | 2.09580 | ||||||||
\(5\) | 553.584 | 0.396113 | 0.198056 | − | 0.980191i | \(-0.436537\pi\) | ||||
0.198056 | + | 0.980191i | \(0.436537\pi\) | |||||||
\(6\) | −5501.81 | −1.73311 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | −22336.8 | −1.92804 | ||||||||
\(9\) | −585.818 | −0.0297626 | ||||||||
\(10\) | −22039.7 | −0.696956 | ||||||||
\(11\) | −12620.6 | −0.259905 | −0.129952 | − | 0.991520i | \(-0.541482\pi\) | ||||
−0.129952 | + | 0.991520i | \(0.541482\pi\) | |||||||
\(12\) | 148287. | 2.06437 | ||||||||
\(13\) | −28561.0 | −0.277350 | ||||||||
\(14\) | −95590.2 | −0.665024 | ||||||||
\(15\) | 76501.2 | 0.390174 | ||||||||
\(16\) | 339888. | 1.29657 | ||||||||
\(17\) | 411254. | 1.19424 | 0.597118 | − | 0.802153i | \(-0.296312\pi\) | ||||
0.597118 | + | 0.802153i | \(0.296312\pi\) | |||||||
\(18\) | 23323.0 | 0.0523670 | ||||||||
\(19\) | 660516. | 1.16277 | 0.581383 | − | 0.813630i | \(-0.302512\pi\) | ||||
0.581383 | + | 0.813630i | \(0.302512\pi\) | |||||||
\(20\) | 594023. | 0.830172 | ||||||||
\(21\) | 331800. | 0.372297 | ||||||||
\(22\) | 502461. | 0.457299 | ||||||||
\(23\) | 2.32926e6 | 1.73557 | 0.867785 | − | 0.496940i | \(-0.165543\pi\) | ||||
0.867785 | + | 0.496940i | \(0.165543\pi\) | |||||||
\(24\) | −3.08678e6 | −1.89913 | ||||||||
\(25\) | −1.64667e6 | −0.843095 | ||||||||
\(26\) | 1.13709e6 | 0.487994 | ||||||||
\(27\) | −2.80100e6 | −1.01432 | ||||||||
\(28\) | 2.57639e6 | 0.792137 | ||||||||
\(29\) | −5.99627e6 | −1.57431 | −0.787154 | − | 0.616756i | \(-0.788447\pi\) | ||||
−0.787154 | + | 0.616756i | \(0.788447\pi\) | |||||||
\(30\) | −3.04572e6 | −0.686506 | ||||||||
\(31\) | 1.54887e6 | 0.301223 | 0.150611 | − | 0.988593i | \(-0.451876\pi\) | ||||
0.150611 | + | 0.988593i | \(0.451876\pi\) | |||||||
\(32\) | −2.09539e6 | −0.353257 | ||||||||
\(33\) | −1.74408e6 | −0.256008 | ||||||||
\(34\) | −1.63731e7 | −2.10125 | ||||||||
\(35\) | 1.32916e6 | 0.149717 | ||||||||
\(36\) | −628611. | −0.0623764 | ||||||||
\(37\) | 4.46126e6 | 0.391336 | 0.195668 | − | 0.980670i | \(-0.437313\pi\) | ||||
0.195668 | + | 0.980670i | \(0.437313\pi\) | |||||||
\(38\) | −2.62969e7 | −2.04587 | ||||||||
\(39\) | −3.94692e6 | −0.273192 | ||||||||
\(40\) | −1.23653e7 | −0.763722 | ||||||||
\(41\) | −3.21595e6 | −0.177739 | −0.0888693 | − | 0.996043i | \(-0.528325\pi\) | ||||
−0.0888693 | + | 0.996043i | \(0.528325\pi\) | |||||||
\(42\) | −1.32099e7 | −0.655053 | ||||||||
\(43\) | 2.23767e7 | 0.998134 | 0.499067 | − | 0.866563i | \(-0.333676\pi\) | ||||
0.499067 | + | 0.866563i | \(0.333676\pi\) | |||||||
\(44\) | −1.35426e7 | −0.544708 | ||||||||
\(45\) | −324299. | −0.0117894 | ||||||||
\(46\) | −9.27339e7 | −3.05371 | ||||||||
\(47\) | 1.94726e7 | 0.582083 | 0.291041 | − | 0.956710i | \(-0.405998\pi\) | ||||
0.291041 | + | 0.956710i | \(0.405998\pi\) | |||||||
\(48\) | 4.69700e7 | 1.27713 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 6.55583e7 | 1.48341 | ||||||||
\(51\) | 5.68323e7 | 1.17633 | ||||||||
\(52\) | −3.06473e7 | −0.581270 | ||||||||
\(53\) | 2.46033e7 | 0.428304 | 0.214152 | − | 0.976800i | \(-0.431301\pi\) | ||||
0.214152 | + | 0.976800i | \(0.431301\pi\) | |||||||
\(54\) | 1.11515e8 | 1.78469 | ||||||||
\(55\) | −6.98659e6 | −0.102952 | ||||||||
\(56\) | −5.36307e7 | −0.728732 | ||||||||
\(57\) | 9.12784e7 | 1.14533 | ||||||||
\(58\) | 2.38727e8 | 2.76998 | ||||||||
\(59\) | 1.19261e8 | 1.28135 | 0.640673 | − | 0.767814i | \(-0.278656\pi\) | ||||
0.640673 | + | 0.767814i | \(0.278656\pi\) | |||||||
\(60\) | 8.20895e7 | 0.817725 | ||||||||
\(61\) | −1.74738e8 | −1.61586 | −0.807930 | − | 0.589278i | \(-0.799412\pi\) | ||||
−0.807930 | + | 0.589278i | \(0.799412\pi\) | |||||||
\(62\) | −6.16647e7 | −0.529998 | ||||||||
\(63\) | −1.40655e6 | −0.0112492 | ||||||||
\(64\) | −9.05995e7 | −0.675019 | ||||||||
\(65\) | −1.58109e7 | −0.109862 | ||||||||
\(66\) | 6.94364e7 | 0.450442 | ||||||||
\(67\) | −1.94831e8 | −1.18120 | −0.590598 | − | 0.806966i | \(-0.701108\pi\) | ||||
−0.590598 | + | 0.806966i | \(0.701108\pi\) | |||||||
\(68\) | 4.41296e8 | 2.50288 | ||||||||
\(69\) | 3.21886e8 | 1.70955 | ||||||||
\(70\) | −5.29172e7 | −0.263424 | ||||||||
\(71\) | 2.88148e8 | 1.34571 | 0.672857 | − | 0.739773i | \(-0.265067\pi\) | ||||
0.672857 | + | 0.739773i | \(0.265067\pi\) | |||||||
\(72\) | 1.30853e7 | 0.0573836 | ||||||||
\(73\) | 7.11716e7 | 0.293328 | 0.146664 | − | 0.989186i | \(-0.453146\pi\) | ||||
0.146664 | + | 0.989186i | \(0.453146\pi\) | |||||||
\(74\) | −1.77615e8 | −0.688551 | ||||||||
\(75\) | −2.27557e8 | −0.830454 | ||||||||
\(76\) | 7.08766e8 | 2.43692 | ||||||||
\(77\) | −3.03021e7 | −0.0982347 | ||||||||
\(78\) | 1.57137e8 | 0.480677 | ||||||||
\(79\) | 2.60602e8 | 0.752759 | 0.376380 | − | 0.926466i | \(-0.377169\pi\) | ||||
0.376380 | + | 0.926466i | \(0.377169\pi\) | |||||||
\(80\) | 1.88157e8 | 0.513588 | ||||||||
\(81\) | −3.75547e8 | −0.969352 | ||||||||
\(82\) | 1.28036e8 | 0.312729 | ||||||||
\(83\) | 4.08082e8 | 0.943834 | 0.471917 | − | 0.881643i | \(-0.343562\pi\) | ||||
0.471917 | + | 0.881643i | \(0.343562\pi\) | |||||||
\(84\) | 3.56038e8 | 0.780260 | ||||||||
\(85\) | 2.27664e8 | 0.473052 | ||||||||
\(86\) | −8.90878e8 | −1.75621 | ||||||||
\(87\) | −8.28639e8 | −1.55070 | ||||||||
\(88\) | 2.81905e8 | 0.501107 | ||||||||
\(89\) | 7.99234e7 | 0.135027 | 0.0675133 | − | 0.997718i | \(-0.478494\pi\) | ||||
0.0675133 | + | 0.997718i | \(0.478494\pi\) | |||||||
\(90\) | 1.29112e7 | 0.0207432 | ||||||||
\(91\) | −6.85750e7 | −0.104828 | ||||||||
\(92\) | 2.49941e9 | 3.63740 | ||||||||
\(93\) | 2.14043e8 | 0.296707 | ||||||||
\(94\) | −7.75258e8 | −1.02417 | ||||||||
\(95\) | 3.65651e8 | 0.460586 | ||||||||
\(96\) | −2.89568e8 | −0.347960 | ||||||||
\(97\) | 7.73718e8 | 0.887380 | 0.443690 | − | 0.896180i | \(-0.353669\pi\) | ||||
0.443690 | + | 0.896180i | \(0.353669\pi\) | |||||||
\(98\) | −2.29512e8 | −0.251355 | ||||||||
\(99\) | 7.39339e6 | 0.00773544 | ||||||||
\(100\) | −1.76696e9 | −1.76696 | ||||||||
\(101\) | 1.62529e9 | 1.55412 | 0.777062 | − | 0.629425i | \(-0.216709\pi\) | ||||
0.777062 | + | 0.629425i | \(0.216709\pi\) | |||||||
\(102\) | −2.26265e9 | −2.06974 | ||||||||
\(103\) | −1.32659e8 | −0.116137 | −0.0580685 | − | 0.998313i | \(-0.518494\pi\) | ||||
−0.0580685 | + | 0.998313i | \(0.518494\pi\) | |||||||
\(104\) | 6.37962e8 | 0.534743 | ||||||||
\(105\) | 1.83679e8 | 0.147472 | ||||||||
\(106\) | −9.79523e8 | −0.753595 | ||||||||
\(107\) | −7.59386e8 | −0.560062 | −0.280031 | − | 0.959991i | \(-0.590345\pi\) | ||||
−0.280031 | + | 0.959991i | \(0.590345\pi\) | |||||||
\(108\) | −3.00561e9 | −2.12582 | ||||||||
\(109\) | −6.18958e8 | −0.419993 | −0.209996 | − | 0.977702i | \(-0.567345\pi\) | ||||
−0.209996 | + | 0.977702i | \(0.567345\pi\) | |||||||
\(110\) | 2.78155e8 | 0.181142 | ||||||||
\(111\) | 6.16513e8 | 0.385468 | ||||||||
\(112\) | 8.16071e8 | 0.490057 | ||||||||
\(113\) | −4.93344e8 | −0.284641 | −0.142320 | − | 0.989821i | \(-0.545456\pi\) | ||||
−0.142320 | + | 0.989821i | \(0.545456\pi\) | |||||||
\(114\) | −3.63404e9 | −2.01520 | ||||||||
\(115\) | 1.28944e9 | 0.687481 | ||||||||
\(116\) | −6.43428e9 | −3.29943 | ||||||||
\(117\) | 1.67315e7 | 0.00825466 | ||||||||
\(118\) | −4.74812e9 | −2.25451 | ||||||||
\(119\) | 9.87422e8 | 0.451379 | ||||||||
\(120\) | −1.70880e9 | −0.752271 | ||||||||
\(121\) | −2.19867e9 | −0.932450 | ||||||||
\(122\) | 6.95680e9 | 2.84309 | ||||||||
\(123\) | −4.44420e8 | −0.175074 | ||||||||
\(124\) | 1.66202e9 | 0.631302 | ||||||||
\(125\) | −1.99279e9 | −0.730073 | ||||||||
\(126\) | 5.59984e7 | 0.0197929 | ||||||||
\(127\) | 3.76640e9 | 1.28473 | 0.642363 | − | 0.766401i | \(-0.277954\pi\) | ||||
0.642363 | + | 0.766401i | \(0.277954\pi\) | |||||||
\(128\) | 4.67985e9 | 1.54094 | ||||||||
\(129\) | 3.09230e9 | 0.983168 | ||||||||
\(130\) | 6.29475e8 | 0.193301 | ||||||||
\(131\) | 1.18325e9 | 0.351039 | 0.175519 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175519 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(132\) | −1.87148e9 | −0.536540 | ||||||||
\(133\) | 1.58590e9 | 0.439484 | ||||||||
\(134\) | 7.75675e9 | 2.07830 | ||||||||
\(135\) | −1.55059e9 | −0.401786 | ||||||||
\(136\) | −9.18612e9 | −2.30254 | ||||||||
\(137\) | 4.33363e9 | 1.05102 | 0.525508 | − | 0.850788i | \(-0.323875\pi\) | ||||
0.525508 | + | 0.850788i | \(0.323875\pi\) | |||||||
\(138\) | −1.28151e10 | −3.00793 | ||||||||
\(139\) | 6.24361e9 | 1.41863 | 0.709315 | − | 0.704892i | \(-0.249005\pi\) | ||||
0.709315 | + | 0.704892i | \(0.249005\pi\) | |||||||
\(140\) | 1.42625e9 | 0.313776 | ||||||||
\(141\) | 2.69097e9 | 0.573355 | ||||||||
\(142\) | −1.14719e10 | −2.36777 | ||||||||
\(143\) | 3.60458e8 | 0.0720846 | ||||||||
\(144\) | −1.99112e8 | −0.0385893 | ||||||||
\(145\) | −3.31944e9 | −0.623604 | ||||||||
\(146\) | −2.83353e9 | −0.516107 | ||||||||
\(147\) | 7.96653e8 | 0.140715 | ||||||||
\(148\) | 4.78715e9 | 0.820161 | ||||||||
\(149\) | 4.71550e9 | 0.783771 | 0.391885 | − | 0.920014i | \(-0.371823\pi\) | ||||
0.391885 | + | 0.920014i | \(0.371823\pi\) | |||||||
\(150\) | 9.05967e9 | 1.46117 | ||||||||
\(151\) | 1.78637e9 | 0.279625 | 0.139813 | − | 0.990178i | \(-0.455350\pi\) | ||||
0.139813 | + | 0.990178i | \(0.455350\pi\) | |||||||
\(152\) | −1.47538e10 | −2.24186 | ||||||||
\(153\) | −2.40920e8 | −0.0355436 | ||||||||
\(154\) | 1.20641e9 | 0.172843 | ||||||||
\(155\) | 8.57432e8 | 0.119318 | ||||||||
\(156\) | −4.23523e9 | −0.572554 | ||||||||
\(157\) | 5.27823e9 | 0.693330 | 0.346665 | − | 0.937989i | \(-0.387314\pi\) | ||||
0.346665 | + | 0.937989i | \(0.387314\pi\) | |||||||
\(158\) | −1.03753e10 | −1.32447 | ||||||||
\(159\) | 3.39999e9 | 0.421882 | ||||||||
\(160\) | −1.15998e9 | −0.139930 | ||||||||
\(161\) | 5.59255e9 | 0.655984 | ||||||||
\(162\) | 1.49515e10 | 1.70556 | ||||||||
\(163\) | 1.65396e10 | 1.83518 | 0.917592 | − | 0.397523i | \(-0.130130\pi\) | ||||
0.917592 | + | 0.397523i | \(0.130130\pi\) | |||||||
\(164\) | −3.45087e9 | −0.372504 | ||||||||
\(165\) | −9.65494e8 | −0.101408 | ||||||||
\(166\) | −1.62468e10 | −1.66066 | ||||||||
\(167\) | 4.17251e9 | 0.415119 | 0.207560 | − | 0.978222i | \(-0.433448\pi\) | ||||
0.207560 | + | 0.978222i | \(0.433448\pi\) | |||||||
\(168\) | −7.41137e9 | −0.717805 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | −9.06391e9 | −0.832330 | ||||||||
\(171\) | −3.86942e8 | −0.0346069 | ||||||||
\(172\) | 2.40113e10 | 2.09189 | ||||||||
\(173\) | −5.90018e9 | −0.500792 | −0.250396 | − | 0.968143i | \(-0.580561\pi\) | ||||
−0.250396 | + | 0.968143i | \(0.580561\pi\) | |||||||
\(174\) | 3.29903e10 | 2.72844 | ||||||||
\(175\) | −3.95365e9 | −0.318660 | ||||||||
\(176\) | −4.28960e9 | −0.336985 | ||||||||
\(177\) | 1.64810e10 | 1.26213 | ||||||||
\(178\) | −3.18197e9 | −0.237578 | ||||||||
\(179\) | 1.17087e10 | 0.852453 | 0.426226 | − | 0.904617i | \(-0.359843\pi\) | ||||
0.426226 | + | 0.904617i | \(0.359843\pi\) | |||||||
\(180\) | −3.47989e8 | −0.0247081 | ||||||||
\(181\) | −1.70008e10 | −1.17738 | −0.588689 | − | 0.808359i | \(-0.700356\pi\) | ||||
−0.588689 | + | 0.808359i | \(0.700356\pi\) | |||||||
\(182\) | 2.73015e9 | 0.184444 | ||||||||
\(183\) | −2.41475e10 | −1.59163 | ||||||||
\(184\) | −5.20282e10 | −3.34625 | ||||||||
\(185\) | 2.46968e9 | 0.155013 | ||||||||
\(186\) | −8.52161e9 | −0.522052 | ||||||||
\(187\) | −5.19029e9 | −0.310388 | ||||||||
\(188\) | 2.08951e10 | 1.21993 | ||||||||
\(189\) | −6.72520e9 | −0.383378 | ||||||||
\(190\) | −1.45576e10 | −0.810396 | ||||||||
\(191\) | −3.30137e9 | −0.179492 | −0.0897459 | − | 0.995965i | \(-0.528605\pi\) | ||||
−0.0897459 | + | 0.995965i | \(0.528605\pi\) | |||||||
\(192\) | −1.25202e10 | −0.664898 | ||||||||
\(193\) | −9.15988e9 | −0.475206 | −0.237603 | − | 0.971362i | \(-0.576362\pi\) | ||||
−0.237603 | + | 0.971362i | \(0.576362\pi\) | |||||||
\(194\) | −3.08038e10 | −1.56133 | ||||||||
\(195\) | −2.18495e9 | −0.108215 | ||||||||
\(196\) | 6.18591e9 | 0.299400 | ||||||||
\(197\) | 2.22367e10 | 1.05190 | 0.525949 | − | 0.850516i | \(-0.323710\pi\) | ||||
0.525949 | + | 0.850516i | \(0.323710\pi\) | |||||||
\(198\) | −2.94350e8 | −0.0136104 | ||||||||
\(199\) | −3.44398e10 | −1.55676 | −0.778380 | − | 0.627793i | \(-0.783958\pi\) | ||||
−0.778380 | + | 0.627793i | \(0.783958\pi\) | |||||||
\(200\) | 3.67814e10 | 1.62552 | ||||||||
\(201\) | −2.69242e10 | −1.16349 | ||||||||
\(202\) | −6.47072e10 | −2.73446 | ||||||||
\(203\) | −1.43970e10 | −0.595033 | ||||||||
\(204\) | 6.09838e10 | 2.46535 | ||||||||
\(205\) | −1.78030e9 | −0.0704045 | ||||||||
\(206\) | 5.28153e9 | 0.204342 | ||||||||
\(207\) | −1.36452e9 | −0.0516551 | ||||||||
\(208\) | −9.70754e9 | −0.359604 | ||||||||
\(209\) | −8.33613e9 | −0.302208 | ||||||||
\(210\) | −7.31277e9 | −0.259475 | ||||||||
\(211\) | 4.62942e10 | 1.60789 | 0.803944 | − | 0.594705i | \(-0.202731\pi\) | ||||
0.803944 | + | 0.594705i | \(0.202731\pi\) | |||||||
\(212\) | 2.64005e10 | 0.897638 | ||||||||
\(213\) | 3.98199e10 | 1.32554 | ||||||||
\(214\) | 3.02332e10 | 0.985422 | ||||||||
\(215\) | 1.23874e10 | 0.395374 | ||||||||
\(216\) | 6.25655e10 | 1.95566 | ||||||||
\(217\) | 3.71884e9 | 0.113852 | ||||||||
\(218\) | 2.46424e10 | 0.738972 | ||||||||
\(219\) | 9.83538e9 | 0.288930 | ||||||||
\(220\) | −7.49694e9 | −0.215766 | ||||||||
\(221\) | −1.17458e10 | −0.331222 | ||||||||
\(222\) | −2.45450e10 | −0.678227 | ||||||||
\(223\) | −4.99563e10 | −1.35275 | −0.676376 | − | 0.736556i | \(-0.736451\pi\) | ||||
−0.676376 | + | 0.736556i | \(0.736451\pi\) | |||||||
\(224\) | −5.03104e9 | −0.133519 | ||||||||
\(225\) | 9.64648e8 | 0.0250927 | ||||||||
\(226\) | 1.96413e10 | 0.500822 | ||||||||
\(227\) | 4.33225e10 | 1.08292 | 0.541462 | − | 0.840726i | \(-0.317871\pi\) | ||||
0.541462 | + | 0.840726i | \(0.317871\pi\) | |||||||
\(228\) | 9.79462e10 | 2.40038 | ||||||||
\(229\) | 2.15084e10 | 0.516832 | 0.258416 | − | 0.966034i | \(-0.416800\pi\) | ||||
0.258416 | + | 0.966034i | \(0.416800\pi\) | |||||||
\(230\) | −5.13361e10 | −1.20962 | ||||||||
\(231\) | −4.18753e9 | −0.0967618 | ||||||||
\(232\) | 1.33938e11 | 3.03533 | ||||||||
\(233\) | −5.05216e10 | −1.12299 | −0.561494 | − | 0.827481i | \(-0.689773\pi\) | ||||
−0.561494 | + | 0.827481i | \(0.689773\pi\) | |||||||
\(234\) | −6.66127e8 | −0.0145240 | ||||||||
\(235\) | 1.07798e10 | 0.230570 | ||||||||
\(236\) | 1.27973e11 | 2.68544 | ||||||||
\(237\) | 3.60133e10 | 0.741473 | ||||||||
\(238\) | −3.93119e10 | −0.794196 | ||||||||
\(239\) | 8.44479e10 | 1.67417 | 0.837083 | − | 0.547076i | \(-0.184259\pi\) | ||||
0.837083 | + | 0.547076i | \(0.184259\pi\) | |||||||
\(240\) | 2.60019e10 | 0.505887 | ||||||||
\(241\) | −6.36142e10 | −1.21472 | −0.607362 | − | 0.794426i | \(-0.707772\pi\) | ||||
−0.607362 | + | 0.794426i | \(0.707772\pi\) | |||||||
\(242\) | 8.75348e10 | 1.64063 | ||||||||
\(243\) | 3.23432e9 | 0.0595053 | ||||||||
\(244\) | −1.87503e11 | −3.38652 | ||||||||
\(245\) | 3.19130e9 | 0.0565875 | ||||||||
\(246\) | 1.76936e10 | 0.308040 | ||||||||
\(247\) | −1.88650e10 | −0.322493 | ||||||||
\(248\) | −3.45969e10 | −0.580771 | ||||||||
\(249\) | 5.63938e10 | 0.929682 | ||||||||
\(250\) | 7.93383e10 | 1.28456 | ||||||||
\(251\) | −8.46103e10 | −1.34552 | −0.672762 | − | 0.739859i | \(-0.734892\pi\) | ||||
−0.672762 | + | 0.739859i | \(0.734892\pi\) | |||||||
\(252\) | −1.50929e9 | −0.0235761 | ||||||||
\(253\) | −2.93967e10 | −0.451083 | ||||||||
\(254\) | −1.49951e11 | −2.26046 | ||||||||
\(255\) | 3.14615e10 | 0.465960 | ||||||||
\(256\) | −1.39930e11 | −2.03625 | ||||||||
\(257\) | 5.29639e10 | 0.757322 | 0.378661 | − | 0.925535i | \(-0.376385\pi\) | ||||
0.378661 | + | 0.925535i | \(0.376385\pi\) | |||||||
\(258\) | −1.23113e11 | −1.72987 | ||||||||
\(259\) | 1.07115e10 | 0.147911 | ||||||||
\(260\) | −1.69659e10 | −0.230248 | ||||||||
\(261\) | 3.51272e9 | 0.0468555 | ||||||||
\(262\) | −4.71083e10 | −0.617649 | ||||||||
\(263\) | 5.51620e10 | 0.710950 | 0.355475 | − | 0.934686i | \(-0.384319\pi\) | ||||
0.355475 | + | 0.934686i | \(0.384319\pi\) | |||||||
\(264\) | 3.89572e10 | 0.493594 | ||||||||
\(265\) | 1.36200e10 | 0.169657 | ||||||||
\(266\) | −6.31389e10 | −0.773267 | ||||||||
\(267\) | 1.10448e10 | 0.133002 | ||||||||
\(268\) | −2.09063e11 | −2.47555 | ||||||||
\(269\) | 7.68173e10 | 0.894486 | 0.447243 | − | 0.894412i | \(-0.352406\pi\) | ||||
0.447243 | + | 0.894412i | \(0.352406\pi\) | |||||||
\(270\) | 6.17331e10 | 0.706938 | ||||||||
\(271\) | 6.23826e10 | 0.702590 | 0.351295 | − | 0.936265i | \(-0.385741\pi\) | ||||
0.351295 | + | 0.936265i | \(0.385741\pi\) | |||||||
\(272\) | 1.39780e11 | 1.54841 | ||||||||
\(273\) | −9.47655e9 | −0.103257 | ||||||||
\(274\) | −1.72533e11 | −1.84925 | ||||||||
\(275\) | 2.07820e10 | 0.219124 | ||||||||
\(276\) | 3.45399e11 | 3.58287 | ||||||||
\(277\) | −8.55324e10 | −0.872915 | −0.436457 | − | 0.899725i | \(-0.643767\pi\) | ||||
−0.436457 | + | 0.899725i | \(0.643767\pi\) | |||||||
\(278\) | −2.48575e11 | −2.49606 | ||||||||
\(279\) | −9.07357e8 | −0.00896518 | ||||||||
\(280\) | −2.96891e10 | −0.288660 | ||||||||
\(281\) | −1.43962e10 | −0.137743 | −0.0688713 | − | 0.997626i | \(-0.521940\pi\) | ||||
−0.0688713 | + | 0.997626i | \(0.521940\pi\) | |||||||
\(282\) | −1.07135e11 | −1.00881 | ||||||||
\(283\) | −1.67936e11 | −1.55635 | −0.778173 | − | 0.628050i | \(-0.783853\pi\) | ||||
−0.778173 | + | 0.628050i | \(0.783853\pi\) | |||||||
\(284\) | 3.09196e11 | 2.82034 | ||||||||
\(285\) | 5.05303e10 | 0.453680 | ||||||||
\(286\) | −1.43508e10 | −0.126832 | ||||||||
\(287\) | −7.72149e9 | −0.0671789 | ||||||||
\(288\) | 1.22752e9 | 0.0105138 | ||||||||
\(289\) | 5.05424e10 | 0.426202 | ||||||||
\(290\) | 1.32156e11 | 1.09722 | ||||||||
\(291\) | 1.06922e11 | 0.874075 | ||||||||
\(292\) | 7.63705e10 | 0.614756 | ||||||||
\(293\) | −2.04851e10 | −0.162381 | −0.0811904 | − | 0.996699i | \(-0.525872\pi\) | ||||
−0.0811904 | + | 0.996699i | \(0.525872\pi\) | |||||||
\(294\) | −3.17169e10 | −0.247587 | ||||||||
\(295\) | 6.60213e10 | 0.507557 | ||||||||
\(296\) | −9.96504e10 | −0.754512 | ||||||||
\(297\) | 3.53504e10 | 0.263627 | ||||||||
\(298\) | −1.87736e11 | −1.37904 | ||||||||
\(299\) | −6.65259e10 | −0.481361 | ||||||||
\(300\) | −2.44180e11 | −1.74046 | ||||||||
\(301\) | 5.37266e10 | 0.377259 | ||||||||
\(302\) | −7.11203e10 | −0.491997 | ||||||||
\(303\) | 2.24603e11 | 1.53082 | ||||||||
\(304\) | 2.24502e11 | 1.50761 | ||||||||
\(305\) | −9.67324e10 | −0.640063 | ||||||||
\(306\) | 9.59167e9 | 0.0625386 | ||||||||
\(307\) | −1.23744e11 | −0.795064 | −0.397532 | − | 0.917588i | \(-0.630133\pi\) | ||||
−0.397532 | + | 0.917588i | \(0.630133\pi\) | |||||||
\(308\) | −3.25157e10 | −0.205880 | ||||||||
\(309\) | −1.83325e10 | −0.114396 | ||||||||
\(310\) | −3.41366e10 | −0.209939 | ||||||||
\(311\) | −3.78281e10 | −0.229294 | −0.114647 | − | 0.993406i | \(-0.536574\pi\) | ||||
−0.114647 | + | 0.993406i | \(0.536574\pi\) | |||||||
\(312\) | 8.81616e10 | 0.526725 | ||||||||
\(313\) | −3.07459e11 | −1.81066 | −0.905332 | − | 0.424704i | \(-0.860378\pi\) | ||||
−0.905332 | + | 0.424704i | \(0.860378\pi\) | |||||||
\(314\) | −2.10140e11 | −1.21990 | ||||||||
\(315\) | −7.78643e8 | −0.00445596 | ||||||||
\(316\) | 2.79639e11 | 1.57763 | ||||||||
\(317\) | −2.01235e11 | −1.11927 | −0.559637 | − | 0.828738i | \(-0.689059\pi\) | ||||
−0.559637 | + | 0.828738i | \(0.689059\pi\) | |||||||
\(318\) | −1.35363e11 | −0.742296 | ||||||||
\(319\) | 7.56767e10 | 0.409170 | ||||||||
\(320\) | −5.01545e10 | −0.267384 | ||||||||
\(321\) | −1.04942e11 | −0.551664 | ||||||||
\(322\) | −2.22654e11 | −1.15420 | ||||||||
\(323\) | 2.71640e11 | 1.38862 | ||||||||
\(324\) | −4.02980e11 | −2.03156 | ||||||||
\(325\) | 4.70305e10 | 0.233832 | ||||||||
\(326\) | −6.58484e11 | −3.22899 | ||||||||
\(327\) | −8.55354e10 | −0.413696 | ||||||||
\(328\) | 7.18341e10 | 0.342688 | ||||||||
\(329\) | 4.67538e10 | 0.220007 | ||||||||
\(330\) | 3.84389e10 | 0.178426 | ||||||||
\(331\) | 1.53397e11 | 0.702408 | 0.351204 | − | 0.936299i | \(-0.385772\pi\) | ||||
0.351204 | + | 0.936299i | \(0.385772\pi\) | |||||||
\(332\) | 4.37891e11 | 1.97809 | ||||||||
\(333\) | −2.61348e9 | −0.0116472 | ||||||||
\(334\) | −1.66119e11 | −0.730397 | ||||||||
\(335\) | −1.07856e11 | −0.467887 | ||||||||
\(336\) | 1.12775e11 | 0.482710 | ||||||||
\(337\) | 1.76243e11 | 0.744350 | 0.372175 | − | 0.928163i | \(-0.378612\pi\) | ||||
0.372175 | + | 0.928163i | \(0.378612\pi\) | |||||||
\(338\) | −3.24764e10 | −0.135345 | ||||||||
\(339\) | −6.81765e10 | −0.280373 | ||||||||
\(340\) | 2.44295e11 | 0.991422 | ||||||||
\(341\) | −1.95478e10 | −0.0782893 | ||||||||
\(342\) | 1.54052e10 | 0.0608905 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | −4.99826e11 | −1.92445 | ||||||||
\(345\) | 1.78191e11 | 0.677173 | ||||||||
\(346\) | 2.34902e11 | 0.881138 | ||||||||
\(347\) | −1.75261e11 | −0.648936 | −0.324468 | − | 0.945897i | \(-0.605185\pi\) | ||||
−0.324468 | + | 0.945897i | \(0.605185\pi\) | |||||||
\(348\) | −8.89170e11 | −3.24996 | ||||||||
\(349\) | −1.50786e11 | −0.544059 | −0.272030 | − | 0.962289i | \(-0.587695\pi\) | ||||
−0.272030 | + | 0.962289i | \(0.587695\pi\) | |||||||
\(350\) | 1.57405e11 | 0.560678 | ||||||||
\(351\) | 7.99994e10 | 0.281322 | ||||||||
\(352\) | 2.64452e10 | 0.0918131 | ||||||||
\(353\) | 1.26764e11 | 0.434519 | 0.217259 | − | 0.976114i | \(-0.430288\pi\) | ||||
0.217259 | + | 0.976114i | \(0.430288\pi\) | |||||||
\(354\) | −6.56154e11 | −2.22071 | ||||||||
\(355\) | 1.59514e11 | 0.533054 | ||||||||
\(356\) | 8.57617e10 | 0.282988 | ||||||||
\(357\) | 1.36454e11 | 0.444611 | ||||||||
\(358\) | −4.66155e11 | −1.49988 | ||||||||
\(359\) | −2.28942e10 | −0.0727446 | −0.0363723 | − | 0.999338i | \(-0.511580\pi\) | ||||
−0.0363723 | + | 0.999338i | \(0.511580\pi\) | |||||||
\(360\) | 7.24382e9 | 0.0227304 | ||||||||
\(361\) | 1.13594e11 | 0.352024 | ||||||||
\(362\) | 6.76848e11 | 2.07158 | ||||||||
\(363\) | −3.03839e11 | −0.918469 | ||||||||
\(364\) | −7.35843e10 | −0.219699 | ||||||||
\(365\) | 3.93995e10 | 0.116191 | ||||||||
\(366\) | 9.61378e11 | 2.80046 | ||||||||
\(367\) | −3.45619e11 | −0.994489 | −0.497244 | − | 0.867611i | \(-0.665655\pi\) | ||||
−0.497244 | + | 0.867611i | \(0.665655\pi\) | |||||||
\(368\) | 7.91687e11 | 2.25029 | ||||||||
\(369\) | 1.88396e9 | 0.00528997 | ||||||||
\(370\) | −9.83247e10 | −0.272744 | ||||||||
\(371\) | 5.90725e10 | 0.161884 | ||||||||
\(372\) | 2.29678e11 | 0.621837 | ||||||||
\(373\) | 1.47684e11 | 0.395043 | 0.197521 | − | 0.980299i | \(-0.436711\pi\) | ||||
0.197521 | + | 0.980299i | \(0.436711\pi\) | |||||||
\(374\) | 2.06639e11 | 0.546123 | ||||||||
\(375\) | −2.75389e11 | −0.719127 | ||||||||
\(376\) | −4.34957e11 | −1.12228 | ||||||||
\(377\) | 1.71259e11 | 0.436635 | ||||||||
\(378\) | 2.67748e11 | 0.674549 | ||||||||
\(379\) | 5.23972e11 | 1.30446 | 0.652232 | − | 0.758020i | \(-0.273833\pi\) | ||||
0.652232 | + | 0.758020i | \(0.273833\pi\) | |||||||
\(380\) | 3.92362e11 | 0.965296 | ||||||||
\(381\) | 5.20489e11 | 1.26546 | ||||||||
\(382\) | 1.31436e11 | 0.315813 | ||||||||
\(383\) | −1.24106e11 | −0.294712 | −0.147356 | − | 0.989084i | \(-0.547076\pi\) | ||||
−0.147356 | + | 0.989084i | \(0.547076\pi\) | |||||||
\(384\) | 6.46720e11 | 1.51784 | ||||||||
\(385\) | −1.67748e10 | −0.0389120 | ||||||||
\(386\) | 3.64679e11 | 0.836120 | ||||||||
\(387\) | −1.31087e10 | −0.0297071 | ||||||||
\(388\) | 8.30237e11 | 1.85977 | ||||||||
\(389\) | −5.73191e11 | −1.26919 | −0.634594 | − | 0.772845i | \(-0.718833\pi\) | ||||
−0.634594 | + | 0.772845i | \(0.718833\pi\) | |||||||
\(390\) | 8.69888e10 | 0.190402 | ||||||||
\(391\) | 9.57917e11 | 2.07268 | ||||||||
\(392\) | −1.28767e11 | −0.275435 | ||||||||
\(393\) | 1.63516e11 | 0.345776 | ||||||||
\(394\) | −8.85304e11 | −1.85080 | ||||||||
\(395\) | 1.44265e11 | 0.298178 | ||||||||
\(396\) | 7.93346e9 | 0.0162119 | ||||||||
\(397\) | 3.61128e11 | 0.729632 | 0.364816 | − | 0.931080i | \(-0.381132\pi\) | ||||
0.364816 | + | 0.931080i | \(0.381132\pi\) | |||||||
\(398\) | 1.37114e12 | 2.73910 | ||||||||
\(399\) | 2.19159e11 | 0.432895 | ||||||||
\(400\) | −5.59683e11 | −1.09313 | ||||||||
\(401\) | −2.67566e11 | −0.516751 | −0.258376 | − | 0.966045i | \(-0.583187\pi\) | ||||
−0.258376 | + | 0.966045i | \(0.583187\pi\) | |||||||
\(402\) | 1.07193e12 | 2.04714 | ||||||||
\(403\) | −4.42374e10 | −0.0835442 | ||||||||
\(404\) | 1.74402e12 | 3.25713 | ||||||||
\(405\) | −2.07897e11 | −0.383972 | ||||||||
\(406\) | 5.73184e11 | 1.04695 | ||||||||
\(407\) | −5.63039e10 | −0.101710 | ||||||||
\(408\) | −1.26945e12 | −2.26802 | ||||||||
\(409\) | −8.10480e11 | −1.43215 | −0.716073 | − | 0.698025i | \(-0.754062\pi\) | ||||
−0.716073 | + | 0.698025i | \(0.754062\pi\) | |||||||
\(410\) | 7.08785e10 | 0.123876 | ||||||||
\(411\) | 5.98876e11 | 1.03526 | ||||||||
\(412\) | −1.42350e11 | −0.243400 | ||||||||
\(413\) | 2.86347e11 | 0.484303 | ||||||||
\(414\) | 5.43252e10 | 0.0908865 | ||||||||
\(415\) | 2.25908e11 | 0.373865 | ||||||||
\(416\) | 5.98465e10 | 0.0979758 | ||||||||
\(417\) | 8.62820e11 | 1.39736 | ||||||||
\(418\) | 3.31884e11 | 0.531732 | ||||||||
\(419\) | 5.82263e11 | 0.922904 | 0.461452 | − | 0.887165i | \(-0.347329\pi\) | ||||
0.461452 | + | 0.887165i | \(0.347329\pi\) | |||||||
\(420\) | 1.97097e11 | 0.309071 | ||||||||
\(421\) | −1.06151e12 | −1.64685 | −0.823427 | − | 0.567422i | \(-0.807941\pi\) | ||||
−0.823427 | + | 0.567422i | \(0.807941\pi\) | |||||||
\(422\) | −1.84310e12 | −2.82906 | ||||||||
\(423\) | −1.14074e10 | −0.0173243 | ||||||||
\(424\) | −5.49560e11 | −0.825788 | ||||||||
\(425\) | −6.77200e11 | −1.00685 | ||||||||
\(426\) | −1.58534e12 | −2.33227 | ||||||||
\(427\) | −4.19547e11 | −0.610738 | ||||||||
\(428\) | −8.14858e11 | −1.17378 | ||||||||
\(429\) | 4.98126e10 | 0.0710038 | ||||||||
\(430\) | −4.93176e11 | −0.695655 | ||||||||
\(431\) | 5.70015e11 | 0.795681 | 0.397840 | − | 0.917455i | \(-0.369760\pi\) | ||||
0.397840 | + | 0.917455i | \(0.369760\pi\) | |||||||
\(432\) | −9.52026e11 | −1.31514 | ||||||||
\(433\) | −8.14009e11 | −1.11284 | −0.556421 | − | 0.830900i | \(-0.687826\pi\) | ||||
−0.556421 | + | 0.830900i | \(0.687826\pi\) | |||||||
\(434\) | −1.48057e11 | −0.200320 | ||||||||
\(435\) | −4.58722e11 | −0.614254 | ||||||||
\(436\) | −6.64172e11 | −0.880220 | ||||||||
\(437\) | 1.53851e12 | 2.01806 | ||||||||
\(438\) | −3.91573e11 | −0.508369 | ||||||||
\(439\) | −4.20664e11 | −0.540562 | −0.270281 | − | 0.962781i | \(-0.587117\pi\) | ||||
−0.270281 | + | 0.962781i | \(0.587117\pi\) | |||||||
\(440\) | 1.56058e11 | 0.198495 | ||||||||
\(441\) | −3.37712e9 | −0.00425180 | ||||||||
\(442\) | 4.67633e11 | 0.582781 | ||||||||
\(443\) | 3.07063e11 | 0.378800 | 0.189400 | − | 0.981900i | \(-0.439346\pi\) | ||||
0.189400 | + | 0.981900i | \(0.439346\pi\) | |||||||
\(444\) | 6.61548e11 | 0.807864 | ||||||||
\(445\) | 4.42444e10 | 0.0534857 | ||||||||
\(446\) | 1.98889e12 | 2.38015 | ||||||||
\(447\) | 6.51646e11 | 0.772019 | ||||||||
\(448\) | −2.17529e11 | −0.255133 | ||||||||
\(449\) | −1.57334e12 | −1.82690 | −0.913448 | − | 0.406956i | \(-0.866590\pi\) | ||||
−0.913448 | + | 0.406956i | \(0.866590\pi\) | |||||||
\(450\) | −3.84052e10 | −0.0441503 | ||||||||
\(451\) | 4.05873e10 | 0.0461951 | ||||||||
\(452\) | −5.29382e11 | −0.596549 | ||||||||
\(453\) | 2.46864e11 | 0.275432 | ||||||||
\(454\) | −1.72479e12 | −1.90539 | ||||||||
\(455\) | −3.79620e10 | −0.0415239 | ||||||||
\(456\) | −2.03887e12 | −2.20825 | ||||||||
\(457\) | −7.24916e11 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(458\) | −8.56308e11 | −0.909359 | ||||||||
\(459\) | −1.15192e12 | −1.21134 | ||||||||
\(460\) | 1.38363e12 | 1.44082 | ||||||||
\(461\) | 1.66071e11 | 0.171254 | 0.0856268 | − | 0.996327i | \(-0.472711\pi\) | ||||
0.0856268 | + | 0.996327i | \(0.472711\pi\) | |||||||
\(462\) | 1.66717e11 | 0.170251 | ||||||||
\(463\) | 9.76413e11 | 0.987459 | 0.493729 | − | 0.869616i | \(-0.335633\pi\) | ||||
0.493729 | + | 0.869616i | \(0.335633\pi\) | |||||||
\(464\) | −2.03806e12 | −2.04120 | ||||||||
\(465\) | 1.18491e11 | 0.117529 | ||||||||
\(466\) | 2.01140e12 | 1.97588 | ||||||||
\(467\) | 1.33384e12 | 1.29771 | 0.648854 | − | 0.760913i | \(-0.275248\pi\) | ||||
0.648854 | + | 0.760913i | \(0.275248\pi\) | |||||||
\(468\) | 1.79537e10 | 0.0173001 | ||||||||
\(469\) | −4.67790e11 | −0.446450 | ||||||||
\(470\) | −4.29171e11 | −0.405686 | ||||||||
\(471\) | 7.29412e11 | 0.682934 | ||||||||
\(472\) | −2.66392e12 | −2.47049 | ||||||||
\(473\) | −2.82409e11 | −0.259420 | ||||||||
\(474\) | −1.43378e12 | −1.30461 | ||||||||
\(475\) | −1.08765e12 | −0.980322 | ||||||||
\(476\) | 1.05955e12 | 0.945999 | ||||||||
\(477\) | −1.44130e10 | −0.0127474 | ||||||||
\(478\) | −3.36210e12 | −2.94567 | ||||||||
\(479\) | 6.18218e11 | 0.536576 | 0.268288 | − | 0.963339i | \(-0.413542\pi\) | ||||
0.268288 | + | 0.963339i | \(0.413542\pi\) | |||||||
\(480\) | −1.60300e11 | −0.137831 | ||||||||
\(481\) | −1.27418e11 | −0.108537 | ||||||||
\(482\) | 2.53265e12 | 2.13729 | ||||||||
\(483\) | 7.72848e11 | 0.646148 | ||||||||
\(484\) | −2.35928e12 | −1.95423 | ||||||||
\(485\) | 4.28318e11 | 0.351503 | ||||||||
\(486\) | −1.28767e11 | −0.104699 | ||||||||
\(487\) | −2.24518e12 | −1.80872 | −0.904359 | − | 0.426773i | \(-0.859650\pi\) | ||||
−0.904359 | + | 0.426773i | \(0.859650\pi\) | |||||||
\(488\) | 3.90310e12 | 3.11545 | ||||||||
\(489\) | 2.28564e12 | 1.80767 | ||||||||
\(490\) | −1.27054e11 | −0.0995651 | ||||||||
\(491\) | 1.89681e12 | 1.47285 | 0.736423 | − | 0.676521i | \(-0.236513\pi\) | ||||
0.736423 | + | 0.676521i | \(0.236513\pi\) | |||||||
\(492\) | −4.76884e11 | −0.366919 | ||||||||
\(493\) | −2.46599e12 | −1.88010 | ||||||||
\(494\) | 7.51066e11 | 0.567423 | ||||||||
\(495\) | 4.09286e9 | 0.00306411 | ||||||||
\(496\) | 5.26443e11 | 0.390557 | ||||||||
\(497\) | 6.91843e11 | 0.508632 | ||||||||
\(498\) | −2.24519e12 | −1.63577 | ||||||||
\(499\) | 1.20702e12 | 0.871491 | 0.435746 | − | 0.900070i | \(-0.356485\pi\) | ||||
0.435746 | + | 0.900070i | \(0.356485\pi\) | |||||||
\(500\) | −2.13836e12 | −1.53009 | ||||||||
\(501\) | 5.76609e11 | 0.408895 | ||||||||
\(502\) | 3.36856e12 | 2.36743 | ||||||||
\(503\) | −1.00787e12 | −0.702021 | −0.351010 | − | 0.936372i | \(-0.614162\pi\) | ||||
−0.351010 | + | 0.936372i | \(0.614162\pi\) | |||||||
\(504\) | 3.14178e10 | 0.0216890 | ||||||||
\(505\) | 8.99737e11 | 0.615608 | ||||||||
\(506\) | 1.17036e12 | 0.793675 | ||||||||
\(507\) | 1.12728e11 | 0.0757697 | ||||||||
\(508\) | 4.04153e12 | 2.69252 | ||||||||
\(509\) | −2.32967e12 | −1.53838 | −0.769191 | − | 0.639019i | \(-0.779340\pi\) | ||||
−0.769191 | + | 0.639019i | \(0.779340\pi\) | |||||||
\(510\) | −1.25257e12 | −0.819850 | ||||||||
\(511\) | 1.70883e11 | 0.110868 | ||||||||
\(512\) | 3.17492e12 | 2.04182 | ||||||||
\(513\) | −1.85011e12 | −1.17942 | ||||||||
\(514\) | −2.10863e12 | −1.33250 | ||||||||
\(515\) | −7.34382e10 | −0.0460034 | ||||||||
\(516\) | 3.31819e12 | 2.06052 | ||||||||
\(517\) | −2.45757e11 | −0.151286 | ||||||||
\(518\) | −4.26453e11 | −0.260248 | ||||||||
\(519\) | −8.15361e11 | −0.493284 | ||||||||
\(520\) | 3.53166e11 | 0.211818 | ||||||||
\(521\) | −1.71354e12 | −1.01888 | −0.509440 | − | 0.860506i | \(-0.670148\pi\) | ||||
−0.509440 | + | 0.860506i | \(0.670148\pi\) | |||||||
\(522\) | −1.39851e11 | −0.0824418 | ||||||||
\(523\) | 2.58042e12 | 1.50811 | 0.754055 | − | 0.656812i | \(-0.228095\pi\) | ||||
0.754055 | + | 0.656812i | \(0.228095\pi\) | |||||||
\(524\) | 1.26968e12 | 0.735707 | ||||||||
\(525\) | −5.46365e11 | −0.313882 | ||||||||
\(526\) | −2.19615e12 | −1.25091 | ||||||||
\(527\) | 6.36981e11 | 0.359732 | ||||||||
\(528\) | −5.92791e11 | −0.331932 | ||||||||
\(529\) | 3.62429e12 | 2.01220 | ||||||||
\(530\) | −5.42249e11 | −0.298509 | ||||||||
\(531\) | −6.98655e10 | −0.0381362 | ||||||||
\(532\) | 1.70175e12 | 0.921070 | ||||||||
\(533\) | 9.18507e10 | 0.0492958 | ||||||||
\(534\) | −4.39724e11 | −0.234015 | ||||||||
\(535\) | −4.20384e11 | −0.221848 | ||||||||
\(536\) | 4.35191e12 | 2.27740 | ||||||||
\(537\) | 1.61806e12 | 0.839671 | ||||||||
\(538\) | −3.05830e12 | −1.57384 | ||||||||
\(539\) | −7.27554e10 | −0.0371292 | ||||||||
\(540\) | −1.66386e12 | −0.842062 | ||||||||
\(541\) | 1.61260e12 | 0.809356 | 0.404678 | − | 0.914459i | \(-0.367384\pi\) | ||||
0.404678 | + | 0.914459i | \(0.367384\pi\) | |||||||
\(542\) | −2.48362e12 | −1.23620 | ||||||||
\(543\) | −2.34939e12 | −1.15973 | ||||||||
\(544\) | −8.61740e11 | −0.421872 | ||||||||
\(545\) | −3.42645e11 | −0.166365 | ||||||||
\(546\) | 3.77287e11 | 0.181679 | ||||||||
\(547\) | −2.96173e12 | −1.41450 | −0.707249 | − | 0.706965i | \(-0.750064\pi\) | ||||
−0.707249 | + | 0.706965i | \(0.750064\pi\) | |||||||
\(548\) | 4.65020e12 | 2.20272 | ||||||||
\(549\) | 1.02365e11 | 0.0480922 | ||||||||
\(550\) | −8.27387e11 | −0.385546 | ||||||||
\(551\) | −3.96063e12 | −1.83055 | ||||||||
\(552\) | −7.18991e12 | −3.29608 | ||||||||
\(553\) | 6.25706e11 | 0.284516 | ||||||||
\(554\) | 3.40527e12 | 1.53588 | ||||||||
\(555\) | 3.41292e11 | 0.152689 | ||||||||
\(556\) | 6.69969e12 | 2.97316 | ||||||||
\(557\) | −2.46069e12 | −1.08320 | −0.541600 | − | 0.840636i | \(-0.682181\pi\) | ||||
−0.541600 | + | 0.840636i | \(0.682181\pi\) | |||||||
\(558\) | 3.61243e10 | 0.0157741 | ||||||||
\(559\) | −6.39102e11 | −0.276833 | ||||||||
\(560\) | 4.51764e11 | 0.194118 | ||||||||
\(561\) | −7.17260e11 | −0.305734 | ||||||||
\(562\) | 5.73150e11 | 0.242356 | ||||||||
\(563\) | −2.01247e12 | −0.844194 | −0.422097 | − | 0.906551i | \(-0.638706\pi\) | ||||
−0.422097 | + | 0.906551i | \(0.638706\pi\) | |||||||
\(564\) | 2.88755e12 | 1.20164 | ||||||||
\(565\) | −2.73108e11 | −0.112750 | ||||||||
\(566\) | 6.68600e12 | 2.73837 | ||||||||
\(567\) | −9.01688e11 | −0.366380 | ||||||||
\(568\) | −6.43631e12 | −2.59459 | ||||||||
\(569\) | −1.33203e11 | −0.0532730 | −0.0266365 | − | 0.999645i | \(-0.508480\pi\) | ||||
−0.0266365 | + | 0.999645i | \(0.508480\pi\) | |||||||
\(570\) | −2.01175e12 | −0.798245 | ||||||||
\(571\) | 4.81051e12 | 1.89378 | 0.946888 | − | 0.321563i | \(-0.104208\pi\) | ||||
0.946888 | + | 0.321563i | \(0.104208\pi\) | |||||||
\(572\) | 3.86789e11 | 0.151075 | ||||||||
\(573\) | −4.56225e11 | −0.176800 | ||||||||
\(574\) | 3.07413e11 | 0.118200 | ||||||||
\(575\) | −3.83552e12 | −1.46325 | ||||||||
\(576\) | 5.30748e10 | 0.0200903 | ||||||||
\(577\) | 8.13533e11 | 0.305551 | 0.152776 | − | 0.988261i | \(-0.451179\pi\) | ||||
0.152776 | + | 0.988261i | \(0.451179\pi\) | |||||||
\(578\) | −2.01223e12 | −0.749897 | ||||||||
\(579\) | −1.26583e12 | −0.468081 | ||||||||
\(580\) | −3.56192e12 | −1.30695 | ||||||||
\(581\) | 9.79804e11 | 0.356736 | ||||||||
\(582\) | −4.25685e12 | −1.53792 | ||||||||
\(583\) | −3.10509e11 | −0.111318 | ||||||||
\(584\) | −1.58975e12 | −0.565549 | ||||||||
\(585\) | 9.26232e9 | 0.00326978 | ||||||||
\(586\) | 8.15568e11 | 0.285707 | ||||||||
\(587\) | −2.69805e12 | −0.937947 | −0.468973 | − | 0.883212i | \(-0.655376\pi\) | ||||
−0.468973 | + | 0.883212i | \(0.655376\pi\) | |||||||
\(588\) | 8.54847e11 | 0.294911 | ||||||||
\(589\) | 1.02306e12 | 0.350252 | ||||||||
\(590\) | −2.62848e12 | −0.893041 | ||||||||
\(591\) | 3.07295e12 | 1.03613 | ||||||||
\(592\) | 1.51633e12 | 0.507395 | ||||||||
\(593\) | −3.52113e12 | −1.16933 | −0.584664 | − | 0.811276i | \(-0.698774\pi\) | ||||
−0.584664 | + | 0.811276i | \(0.698774\pi\) | |||||||
\(594\) | −1.40739e12 | −0.463849 | ||||||||
\(595\) | 5.46621e11 | 0.178797 | ||||||||
\(596\) | 5.05996e12 | 1.64263 | ||||||||
\(597\) | −4.75932e12 | −1.53342 | ||||||||
\(598\) | 2.64857e12 | 0.846948 | ||||||||
\(599\) | 1.64754e12 | 0.522895 | 0.261448 | − | 0.965218i | \(-0.415800\pi\) | ||||
0.261448 | + | 0.965218i | \(0.415800\pi\) | |||||||
\(600\) | 5.08291e12 | 1.60115 | ||||||||
\(601\) | 6.24386e12 | 1.95217 | 0.976085 | − | 0.217387i | \(-0.0697535\pi\) | ||||
0.976085 | + | 0.217387i | \(0.0697535\pi\) | |||||||
\(602\) | −2.13900e12 | −0.663783 | ||||||||
\(603\) | 1.14136e11 | 0.0351555 | ||||||||
\(604\) | 1.91687e12 | 0.586037 | ||||||||
\(605\) | −1.21715e12 | −0.369355 | ||||||||
\(606\) | −8.94206e12 | −2.69346 | ||||||||
\(607\) | −4.61694e12 | −1.38040 | −0.690200 | − | 0.723618i | \(-0.742478\pi\) | ||||
−0.690200 | + | 0.723618i | \(0.742478\pi\) | |||||||
\(608\) | −1.38404e12 | −0.410755 | ||||||||
\(609\) | −1.98956e12 | −0.586111 | ||||||||
\(610\) | 3.85117e12 | 1.12618 | ||||||||
\(611\) | −5.56158e11 | −0.161441 | ||||||||
\(612\) | −2.58519e11 | −0.0744922 | ||||||||
\(613\) | 3.90806e12 | 1.11786 | 0.558932 | − | 0.829214i | \(-0.311211\pi\) | ||||
0.558932 | + | 0.829214i | \(0.311211\pi\) | |||||||
\(614\) | 4.92659e12 | 1.39891 | ||||||||
\(615\) | −2.46024e11 | −0.0693489 | ||||||||
\(616\) | 6.76854e11 | 0.189401 | ||||||||
\(617\) | −2.71463e12 | −0.754098 | −0.377049 | − | 0.926193i | \(-0.623061\pi\) | ||||
−0.377049 | + | 0.926193i | \(0.623061\pi\) | |||||||
\(618\) | 7.29868e11 | 0.201278 | ||||||||
\(619\) | −1.75668e12 | −0.480932 | −0.240466 | − | 0.970658i | \(-0.577300\pi\) | ||||
−0.240466 | + | 0.970658i | \(0.577300\pi\) | |||||||
\(620\) | 9.20066e11 | 0.250067 | ||||||||
\(621\) | −6.52425e12 | −1.76043 | ||||||||
\(622\) | 1.50604e12 | 0.403440 | ||||||||
\(623\) | 1.91896e11 | 0.0510352 | ||||||||
\(624\) | −1.34151e12 | −0.354212 | ||||||||
\(625\) | 2.11297e12 | 0.553903 | ||||||||
\(626\) | 1.22408e13 | 3.18584 | ||||||||
\(627\) | −1.15199e12 | −0.297677 | ||||||||
\(628\) | 5.66379e12 | 1.45308 | ||||||||
\(629\) | 1.83471e12 | 0.467348 | ||||||||
\(630\) | 3.09999e10 | 0.00784020 | ||||||||
\(631\) | −4.89370e12 | −1.22887 | −0.614434 | − | 0.788968i | \(-0.710616\pi\) | ||||
−0.614434 | + | 0.788968i | \(0.710616\pi\) | |||||||
\(632\) | −5.82103e12 | −1.45135 | ||||||||
\(633\) | 6.39752e12 | 1.58378 | ||||||||
\(634\) | 8.01170e12 | 1.96935 | ||||||||
\(635\) | 2.08502e12 | 0.508896 | ||||||||
\(636\) | 3.64836e12 | 0.884179 | ||||||||
\(637\) | −1.64648e11 | −0.0396214 | ||||||||
\(638\) | −3.01289e12 | −0.719930 | ||||||||
\(639\) | −1.68802e11 | −0.0400520 | ||||||||
\(640\) | 2.59069e12 | 0.610388 | ||||||||
\(641\) | −3.16251e12 | −0.739896 | −0.369948 | − | 0.929052i | \(-0.620625\pi\) | ||||
−0.369948 | + | 0.929052i | \(0.620625\pi\) | |||||||
\(642\) | 4.17800e12 | 0.970646 | ||||||||
\(643\) | 1.55515e12 | 0.358776 | 0.179388 | − | 0.983778i | \(-0.442588\pi\) | ||||
0.179388 | + | 0.983778i | \(0.442588\pi\) | |||||||
\(644\) | 6.00107e12 | 1.37481 | ||||||||
\(645\) | 1.71185e12 | 0.389446 | ||||||||
\(646\) | −1.08147e13 | −2.44326 | ||||||||
\(647\) | −1.55484e12 | −0.348832 | −0.174416 | − | 0.984672i | \(-0.555804\pi\) | ||||
−0.174416 | + | 0.984672i | \(0.555804\pi\) | |||||||
\(648\) | 8.38852e12 | 1.86895 | ||||||||
\(649\) | −1.50516e12 | −0.333028 | ||||||||
\(650\) | −1.87241e12 | −0.411425 | ||||||||
\(651\) | 5.13916e11 | 0.112145 | ||||||||
\(652\) | 1.77478e13 | 3.84618 | ||||||||
\(653\) | −6.64297e11 | −0.142973 | −0.0714863 | − | 0.997442i | \(-0.522774\pi\) | ||||
−0.0714863 | + | 0.997442i | \(0.522774\pi\) | |||||||
\(654\) | 3.40539e12 | 0.727893 | ||||||||
\(655\) | 6.55028e11 | 0.139051 | ||||||||
\(656\) | −1.09306e12 | −0.230451 | ||||||||
\(657\) | −4.16936e10 | −0.00873021 | ||||||||
\(658\) | −1.86139e12 | −0.387099 | ||||||||
\(659\) | −5.68774e12 | −1.17478 | −0.587388 | − | 0.809305i | \(-0.699844\pi\) | ||||
−0.587388 | + | 0.809305i | \(0.699844\pi\) | |||||||
\(660\) | −1.03602e12 | −0.212530 | ||||||||
\(661\) | 6.80122e11 | 0.138574 | 0.0692868 | − | 0.997597i | \(-0.477928\pi\) | ||||
0.0692868 | + | 0.997597i | \(0.477928\pi\) | |||||||
\(662\) | −6.10713e12 | −1.23588 | ||||||||
\(663\) | −1.62319e12 | −0.326255 | ||||||||
\(664\) | −9.11525e12 | −1.81975 | ||||||||
\(665\) | 8.77929e11 | 0.174085 | ||||||||
\(666\) | 1.04050e11 | 0.0204931 | ||||||||
\(667\) | −1.39668e13 | −2.73232 | ||||||||
\(668\) | 4.47730e12 | 0.870006 | ||||||||
\(669\) | −6.90359e12 | −1.33247 | ||||||||
\(670\) | 4.29402e12 | 0.823241 | ||||||||
\(671\) | 2.20531e12 | 0.419970 | ||||||||
\(672\) | −6.95252e11 | −0.131517 | ||||||||
\(673\) | 1.80171e12 | 0.338545 | 0.169272 | − | 0.985569i | \(-0.445858\pi\) | ||||
0.169272 | + | 0.985569i | \(0.445858\pi\) | |||||||
\(674\) | −7.01670e12 | −1.30967 | ||||||||
\(675\) | 4.61232e12 | 0.855170 | ||||||||
\(676\) | 8.75319e11 | 0.161215 | ||||||||
\(677\) | −9.29465e12 | −1.70053 | −0.850264 | − | 0.526356i | \(-0.823558\pi\) | ||||
−0.850264 | + | 0.526356i | \(0.823558\pi\) | |||||||
\(678\) | 2.71429e12 | 0.493313 | ||||||||
\(679\) | 1.85770e12 | 0.335398 | ||||||||
\(680\) | −5.08529e12 | −0.912065 | ||||||||
\(681\) | 5.98685e12 | 1.06669 | ||||||||
\(682\) | 7.78248e11 | 0.137749 | ||||||||
\(683\) | −9.01059e12 | −1.58438 | −0.792191 | − | 0.610273i | \(-0.791060\pi\) | ||||
−0.792191 | + | 0.610273i | \(0.791060\pi\) | |||||||
\(684\) | −4.15207e11 | −0.0725292 | ||||||||
\(685\) | 2.39903e12 | 0.416321 | ||||||||
\(686\) | −5.51059e11 | −0.0950034 | ||||||||
\(687\) | 2.97231e12 | 0.509082 | ||||||||
\(688\) | 7.60559e12 | 1.29415 | ||||||||
\(689\) | −7.02695e11 | −0.118790 | ||||||||
\(690\) | −7.09426e12 | −1.19148 | ||||||||
\(691\) | −9.77754e12 | −1.63147 | −0.815734 | − | 0.578428i | \(-0.803666\pi\) | ||||
−0.815734 | + | 0.578428i | \(0.803666\pi\) | |||||||
\(692\) | −6.33118e12 | −1.04956 | ||||||||
\(693\) | 1.77515e10 | 0.00292372 | ||||||||
\(694\) | 6.97759e12 | 1.14179 | ||||||||
\(695\) | 3.45636e12 | 0.561937 | ||||||||
\(696\) | 1.85092e13 | 2.98982 | ||||||||
\(697\) | −1.32257e12 | −0.212262 | ||||||||
\(698\) | 6.00319e12 | 0.957266 | ||||||||
\(699\) | −6.98170e12 | −1.10615 | ||||||||
\(700\) | −4.24246e12 | −0.667847 | ||||||||
\(701\) | 8.29383e12 | 1.29725 | 0.648626 | − | 0.761108i | \(-0.275344\pi\) | ||||
0.648626 | + | 0.761108i | \(0.275344\pi\) | |||||||
\(702\) | −3.18499e12 | −0.494984 | ||||||||
\(703\) | 2.94673e12 | 0.455032 | ||||||||
\(704\) | 1.14342e12 | 0.175441 | ||||||||
\(705\) | 1.48968e12 | 0.227113 | ||||||||
\(706\) | −5.04680e12 | −0.764530 | ||||||||
\(707\) | 3.90233e12 | 0.587403 | ||||||||
\(708\) | 1.76850e13 | 2.64518 | ||||||||
\(709\) | 7.06044e12 | 1.04936 | 0.524679 | − | 0.851300i | \(-0.324185\pi\) | ||||
0.524679 | + | 0.851300i | \(0.324185\pi\) | |||||||
\(710\) | −6.35068e12 | −0.937903 | ||||||||
\(711\) | −1.52665e11 | −0.0224041 | ||||||||
\(712\) | −1.78524e12 | −0.260337 | ||||||||
\(713\) | 3.60772e12 | 0.522794 | ||||||||
\(714\) | −5.43261e12 | −0.782288 | ||||||||
\(715\) | 1.99544e11 | 0.0285536 | ||||||||
\(716\) | 1.25640e13 | 1.78657 | ||||||||
\(717\) | 1.16701e13 | 1.64906 | ||||||||
\(718\) | 9.11480e11 | 0.127993 | ||||||||
\(719\) | 6.47046e12 | 0.902932 | 0.451466 | − | 0.892288i | \(-0.350901\pi\) | ||||
0.451466 | + | 0.892288i | \(0.350901\pi\) | |||||||
\(720\) | −1.10226e11 | −0.0152857 | ||||||||
\(721\) | −3.18515e11 | −0.0438957 | ||||||||
\(722\) | −4.52247e12 | −0.619382 | ||||||||
\(723\) | −8.79101e12 | −1.19651 | ||||||||
\(724\) | −1.82427e13 | −2.46755 | ||||||||
\(725\) | 9.87387e12 | 1.32729 | ||||||||
\(726\) | 1.20967e13 | 1.61603 | ||||||||
\(727\) | 4.63198e12 | 0.614981 | 0.307490 | − | 0.951551i | \(-0.400511\pi\) | ||||
0.307490 | + | 0.951551i | \(0.400511\pi\) | |||||||
\(728\) | 1.53175e12 | 0.202114 | ||||||||
\(729\) | 7.83884e12 | 1.02796 | ||||||||
\(730\) | −1.56860e12 | −0.204437 | ||||||||
\(731\) | 9.20254e12 | 1.19201 | ||||||||
\(732\) | −2.59115e13 | −3.33574 | ||||||||
\(733\) | 2.64815e12 | 0.338824 | 0.169412 | − | 0.985545i | \(-0.445813\pi\) | ||||
0.169412 | + | 0.985545i | \(0.445813\pi\) | |||||||
\(734\) | 1.37600e13 | 1.74979 | ||||||||
\(735\) | 4.41014e11 | 0.0557391 | ||||||||
\(736\) | −4.88071e12 | −0.613102 | ||||||||
\(737\) | 2.45889e12 | 0.306998 | ||||||||
\(738\) | −7.50055e10 | −0.00930763 | ||||||||
\(739\) | −3.40925e12 | −0.420493 | −0.210247 | − | 0.977648i | \(-0.567427\pi\) | ||||
−0.210247 | + | 0.977648i | \(0.567427\pi\) | |||||||
\(740\) | 2.65009e12 | 0.324876 | ||||||||
\(741\) | −2.60700e12 | −0.317658 | ||||||||
\(742\) | −2.35183e12 | −0.284832 | ||||||||
\(743\) | −1.42937e13 | −1.72066 | −0.860328 | − | 0.509741i | \(-0.829741\pi\) | ||||
−0.860328 | + | 0.509741i | \(0.829741\pi\) | |||||||
\(744\) | −4.78104e12 | −0.572063 | ||||||||
\(745\) | 2.61042e12 | 0.310462 | ||||||||
\(746\) | −5.87970e12 | −0.695073 | ||||||||
\(747\) | −2.39061e11 | −0.0280910 | ||||||||
\(748\) | −5.56943e12 | −0.650510 | ||||||||
\(749\) | −1.82329e12 | −0.211683 | ||||||||
\(750\) | 1.09640e13 | 1.26529 | ||||||||
\(751\) | −2.17272e12 | −0.249243 | −0.124622 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124622 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(752\) | 6.61852e12 | 0.754711 | ||||||||
\(753\) | −1.16925e13 | −1.32535 | ||||||||
\(754\) | −6.81829e12 | −0.768253 | ||||||||
\(755\) | 9.88908e11 | 0.110763 | ||||||||
\(756\) | −7.21647e12 | −0.803483 | ||||||||
\(757\) | −1.09645e12 | −0.121355 | −0.0606776 | − | 0.998157i | \(-0.519326\pi\) | ||||
−0.0606776 | + | 0.998157i | \(0.519326\pi\) | |||||||
\(758\) | −2.08607e13 | −2.29519 | ||||||||
\(759\) | −4.06240e12 | −0.444319 | ||||||||
\(760\) | −8.16749e12 | −0.888030 | ||||||||
\(761\) | −1.37438e12 | −0.148551 | −0.0742754 | − | 0.997238i | \(-0.523664\pi\) | ||||
−0.0742754 | + | 0.997238i | \(0.523664\pi\) | |||||||
\(762\) | −2.07221e13 | −2.22657 | ||||||||
\(763\) | −1.48612e12 | −0.158742 | ||||||||
\(764\) | −3.54253e12 | −0.376178 | ||||||||
\(765\) | −1.33370e11 | −0.0140793 | ||||||||
\(766\) | 4.94099e12 | 0.518542 | ||||||||
\(767\) | −3.40623e12 | −0.355381 | ||||||||
\(768\) | −1.93373e13 | −2.00572 | ||||||||
\(769\) | 3.02105e12 | 0.311523 | 0.155761 | − | 0.987795i | \(-0.450217\pi\) | ||||
0.155761 | + | 0.987795i | \(0.450217\pi\) | |||||||
\(770\) | 6.67849e11 | 0.0684652 | ||||||||
\(771\) | 7.31922e12 | 0.745967 | ||||||||
\(772\) | −9.82900e12 | −0.995936 | ||||||||
\(773\) | −1.04927e13 | −1.05701 | −0.528504 | − | 0.848931i | \(-0.677247\pi\) | ||||
−0.528504 | + | 0.848931i | \(0.677247\pi\) | |||||||
\(774\) | 5.21892e11 | 0.0522693 | ||||||||
\(775\) | −2.55048e12 | −0.253959 | ||||||||
\(776\) | −1.72824e13 | −1.71091 | ||||||||
\(777\) | 1.48025e12 | 0.145693 | ||||||||
\(778\) | 2.28203e13 | 2.23312 | ||||||||
\(779\) | −2.12419e12 | −0.206668 | ||||||||
\(780\) | −2.34456e12 | −0.226796 | ||||||||
\(781\) | −3.63661e12 | −0.349757 | ||||||||
\(782\) | −3.81372e13 | −3.64686 | ||||||||
\(783\) | 1.67955e13 | 1.59686 | ||||||||
\(784\) | 1.95939e12 | 0.185224 | ||||||||
\(785\) | 2.92194e12 | 0.274637 | ||||||||
\(786\) | −6.51002e12 | −0.608388 | ||||||||
\(787\) | 7.81781e12 | 0.726439 | 0.363219 | − | 0.931704i | \(-0.381678\pi\) | ||||
0.363219 | + | 0.931704i | \(0.381678\pi\) | |||||||
\(788\) | 2.38611e13 | 2.20456 | ||||||||
\(789\) | 7.62298e12 | 0.700291 | ||||||||
\(790\) | −5.74359e12 | −0.524640 | ||||||||
\(791\) | −1.18452e12 | −0.107584 | ||||||||
\(792\) | −1.65145e11 | −0.0149143 | ||||||||
\(793\) | 4.99070e12 | 0.448159 | ||||||||
\(794\) | −1.43775e13 | −1.28378 | ||||||||
\(795\) | 1.88218e12 | 0.167113 | ||||||||
\(796\) | −3.69556e13 | −3.26265 | ||||||||
\(797\) | 8.53286e12 | 0.749087 | 0.374543 | − | 0.927209i | \(-0.377799\pi\) | ||||
0.374543 | + | 0.927209i | \(0.377799\pi\) | |||||||
\(798\) | −8.72532e12 | −0.761673 | ||||||||
\(799\) | 8.00821e12 | 0.695145 | ||||||||
\(800\) | 3.45042e12 | 0.297829 | ||||||||
\(801\) | −4.68205e10 | −0.00401874 | ||||||||
\(802\) | 1.06525e13 | 0.909217 | ||||||||
\(803\) | −8.98230e11 | −0.0762373 | ||||||||
\(804\) | −2.88910e13 | −2.43843 | ||||||||
\(805\) | 3.09595e12 | 0.259844 | ||||||||
\(806\) | 1.76121e12 | 0.146995 | ||||||||
\(807\) | 1.06156e13 | 0.881075 | ||||||||
\(808\) | −3.63039e13 | −2.99642 | ||||||||
\(809\) | 1.10666e13 | 0.908338 | 0.454169 | − | 0.890916i | \(-0.349936\pi\) | ||||
0.454169 | + | 0.890916i | \(0.349936\pi\) | |||||||
\(810\) | 8.27692e12 | 0.675595 | ||||||||
\(811\) | 5.03979e12 | 0.409090 | 0.204545 | − | 0.978857i | \(-0.434429\pi\) | ||||
0.204545 | + | 0.978857i | \(0.434429\pi\) | |||||||
\(812\) | −1.54487e13 | −1.24707 | ||||||||
\(813\) | 8.62082e12 | 0.692056 | ||||||||
\(814\) | 2.24161e12 | 0.178958 | ||||||||
\(815\) | 9.15604e12 | 0.726940 | ||||||||
\(816\) | 1.93166e13 | 1.52520 | ||||||||
\(817\) | 1.47802e13 | 1.16060 | ||||||||
\(818\) | 3.22674e13 | 2.51984 | ||||||||
\(819\) | 4.01724e10 | 0.00311997 | ||||||||
\(820\) | −1.91035e12 | −0.147554 | ||||||||
\(821\) | 8.10308e12 | 0.622452 | 0.311226 | − | 0.950336i | \(-0.399260\pi\) | ||||
0.311226 | + | 0.950336i | \(0.399260\pi\) | |||||||
\(822\) | −2.38428e13 | −1.82152 | ||||||||
\(823\) | −1.29467e13 | −0.983692 | −0.491846 | − | 0.870682i | \(-0.663678\pi\) | ||||
−0.491846 | + | 0.870682i | \(0.663678\pi\) | |||||||
\(824\) | 2.96319e12 | 0.223917 | ||||||||
\(825\) | 2.87192e12 | 0.215839 | ||||||||
\(826\) | −1.14002e13 | −0.852125 | ||||||||
\(827\) | 3.68205e12 | 0.273725 | 0.136862 | − | 0.990590i | \(-0.456298\pi\) | ||||
0.136862 | + | 0.990590i | \(0.456298\pi\) | |||||||
\(828\) | −1.46420e12 | −0.108259 | ||||||||
\(829\) | 1.62662e13 | 1.19617 | 0.598084 | − | 0.801434i | \(-0.295929\pi\) | ||||
0.598084 | + | 0.801434i | \(0.295929\pi\) | |||||||
\(830\) | −8.99398e12 | −0.657810 | ||||||||
\(831\) | −1.18199e13 | −0.859826 | ||||||||
\(832\) | 2.58761e12 | 0.187217 | ||||||||
\(833\) | 2.37080e12 | 0.170605 | ||||||||
\(834\) | −3.43512e13 | −2.45864 | ||||||||
\(835\) | 2.30983e12 | 0.164434 | ||||||||
\(836\) | −8.94507e12 | −0.633367 | ||||||||
\(837\) | −4.33839e12 | −0.305537 | ||||||||
\(838\) | −2.31815e13 | −1.62384 | ||||||||
\(839\) | −1.27324e13 | −0.887115 | −0.443558 | − | 0.896246i | \(-0.646284\pi\) | ||||
−0.443558 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(840\) | −4.10282e12 | −0.284332 | ||||||||
\(841\) | 2.14481e13 | 1.47845 | ||||||||
\(842\) | 4.22616e13 | 2.89762 | ||||||||
\(843\) | −1.98944e12 | −0.135677 | ||||||||
\(844\) | 4.96760e13 | 3.36981 | ||||||||
\(845\) | 4.51576e11 | 0.0304702 | ||||||||
\(846\) | 4.54160e11 | 0.0304819 | ||||||||
\(847\) | −5.27900e12 | −0.352433 | ||||||||
\(848\) | 8.36237e12 | 0.555326 | ||||||||
\(849\) | −2.32076e13 | −1.53301 | ||||||||
\(850\) | 2.69611e13 | 1.77155 | ||||||||
\(851\) | 1.03914e13 | 0.679191 | ||||||||
\(852\) | 4.27287e13 | 2.77806 | ||||||||
\(853\) | 2.12089e13 | 1.37166 | 0.685831 | − | 0.727761i | \(-0.259439\pi\) | ||||
0.685831 | + | 0.727761i | \(0.259439\pi\) | |||||||
\(854\) | 1.67033e13 | 1.07459 | ||||||||
\(855\) | −2.14205e11 | −0.0137083 | ||||||||
\(856\) | 1.69623e13 | 1.07982 | ||||||||
\(857\) | 2.44933e13 | 1.55108 | 0.775540 | − | 0.631299i | \(-0.217478\pi\) | ||||
0.775540 | + | 0.631299i | \(0.217478\pi\) | |||||||
\(858\) | −1.98317e12 | −0.124930 | ||||||||
\(859\) | −2.91849e13 | −1.82889 | −0.914447 | − | 0.404705i | \(-0.867374\pi\) | ||||
−0.914447 | + | 0.404705i | \(0.867374\pi\) | |||||||
\(860\) | 1.32923e13 | 0.828623 | ||||||||
\(861\) | −1.06705e12 | −0.0661716 | ||||||||
\(862\) | −2.26938e13 | −1.39999 | ||||||||
\(863\) | 9.87328e12 | 0.605917 | 0.302958 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302958 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(864\) | 5.86919e12 | 0.358316 | ||||||||
\(865\) | −3.26625e12 | −0.198370 | ||||||||
\(866\) | 3.24079e13 | 1.95803 | ||||||||
\(867\) | 6.98458e12 | 0.419811 | ||||||||
\(868\) | 3.99050e12 | 0.238610 | ||||||||
\(869\) | −3.28896e12 | −0.195646 | ||||||||
\(870\) | 1.82629e13 | 1.08077 | ||||||||
\(871\) | 5.56458e12 | 0.327605 | ||||||||
\(872\) | 1.38256e13 | 0.809764 | ||||||||
\(873\) | −4.53257e11 | −0.0264108 | ||||||||
\(874\) | −6.12523e13 | −3.55075 | ||||||||
\(875\) | −4.78469e12 | −0.275942 | ||||||||
\(876\) | 1.05538e13 | 0.605539 | ||||||||
\(877\) | 2.00460e13 | 1.14427 | 0.572137 | − | 0.820158i | \(-0.306115\pi\) | ||||
0.572137 | + | 0.820158i | \(0.306115\pi\) | |||||||
\(878\) | 1.67478e13 | 0.951112 | ||||||||
\(879\) | −2.83089e12 | −0.159946 | ||||||||
\(880\) | −2.37466e12 | −0.133484 | ||||||||
\(881\) | −1.74200e13 | −0.974218 | −0.487109 | − | 0.873341i | \(-0.661949\pi\) | ||||
−0.487109 | + | 0.873341i | \(0.661949\pi\) | |||||||
\(882\) | 1.34452e11 | 0.00748099 | ||||||||
\(883\) | −1.98206e13 | −1.09722 | −0.548609 | − | 0.836079i | \(-0.684842\pi\) | ||||
−0.548609 | + | 0.836079i | \(0.684842\pi\) | |||||||
\(884\) | −1.26039e13 | −0.694174 | ||||||||
\(885\) | 9.12365e12 | 0.499947 | ||||||||
\(886\) | −1.22250e13 | −0.666495 | ||||||||
\(887\) | −2.43482e11 | −0.0132072 | −0.00660361 | − | 0.999978i | \(-0.502102\pi\) | ||||
−0.00660361 | + | 0.999978i | \(0.502102\pi\) | |||||||
\(888\) | −1.37709e13 | −0.743199 | ||||||||
\(889\) | 9.04314e12 | 0.485580 | ||||||||
\(890\) | −1.76149e12 | −0.0941075 | ||||||||
\(891\) | 4.73964e12 | 0.251939 | ||||||||
\(892\) | −5.36055e13 | −2.83510 | ||||||||
\(893\) | 1.28620e13 | 0.676826 | ||||||||
\(894\) | −2.59438e13 | −1.35836 | ||||||||
\(895\) | 6.48176e12 | 0.337667 | ||||||||
\(896\) | 1.12363e13 | 0.582422 | ||||||||
\(897\) | −9.19339e12 | −0.474143 | ||||||||
\(898\) | 6.26388e13 | 3.21440 | ||||||||
\(899\) | −9.28745e12 | −0.474218 | ||||||||
\(900\) | 1.03511e12 | 0.0525892 | ||||||||
\(901\) | 1.01182e13 | 0.511496 | ||||||||
\(902\) | −1.61589e12 | −0.0812797 | ||||||||
\(903\) | 7.42461e12 | 0.371603 | ||||||||
\(904\) | 1.10197e13 | 0.548799 | ||||||||
\(905\) | −9.41138e12 | −0.466375 | ||||||||
\(906\) | −9.82830e12 | −0.484620 | ||||||||
\(907\) | 3.25572e13 | 1.59740 | 0.798702 | − | 0.601727i | \(-0.205520\pi\) | ||||
0.798702 | + | 0.601727i | \(0.205520\pi\) | |||||||
\(908\) | 4.64872e13 | 2.26959 | ||||||||
\(909\) | −9.52125e11 | −0.0462548 | ||||||||
\(910\) | 1.51137e12 | 0.0730608 | ||||||||
\(911\) | 3.73752e13 | 1.79784 | 0.898921 | − | 0.438112i | \(-0.144353\pi\) | ||||
0.898921 | + | 0.438112i | \(0.144353\pi\) | |||||||
\(912\) | 3.10244e13 | 1.48500 | ||||||||
\(913\) | −5.15025e12 | −0.245307 | ||||||||
\(914\) | 2.88608e13 | 1.36789 | ||||||||
\(915\) | −1.33677e13 | −0.630466 | ||||||||
\(916\) | 2.30796e13 | 1.08317 | ||||||||
\(917\) | 2.84098e12 | 0.132680 | ||||||||
\(918\) | 4.58612e13 | 2.13134 | ||||||||
\(919\) | −1.71224e13 | −0.791854 | −0.395927 | − | 0.918282i | \(-0.629577\pi\) | ||||
−0.395927 | + | 0.918282i | \(0.629577\pi\) | |||||||
\(920\) | −2.88020e13 | −1.32549 | ||||||||
\(921\) | −1.71005e13 | −0.783143 | ||||||||
\(922\) | −6.61173e12 | −0.301319 | ||||||||
\(923\) | −8.22979e12 | −0.373234 | ||||||||
\(924\) | −4.49342e12 | −0.202793 | ||||||||
\(925\) | −7.34622e12 | −0.329933 | ||||||||
\(926\) | −3.88736e13 | −1.73742 | ||||||||
\(927\) | 7.77142e10 | 0.00345654 | ||||||||
\(928\) | 1.25645e13 | 0.556135 | ||||||||
\(929\) | 3.61729e13 | 1.59336 | 0.796678 | − | 0.604404i | \(-0.206589\pi\) | ||||
0.796678 | + | 0.604404i | \(0.206589\pi\) | |||||||
\(930\) | −4.71743e12 | −0.206791 | ||||||||
\(931\) | 3.80774e12 | 0.166109 | ||||||||
\(932\) | −5.42121e13 | −2.35356 | ||||||||
\(933\) | −5.22756e12 | −0.225856 | ||||||||
\(934\) | −5.31037e13 | −2.28330 | ||||||||
\(935\) | −2.87326e12 | −0.122949 | ||||||||
\(936\) | −3.73729e11 | −0.0159153 | ||||||||
\(937\) | −2.74411e13 | −1.16298 | −0.581492 | − | 0.813552i | \(-0.697531\pi\) | ||||
−0.581492 | + | 0.813552i | \(0.697531\pi\) | |||||||
\(938\) | 1.86240e13 | 0.785524 | ||||||||
\(939\) | −4.24886e13 | −1.78352 | ||||||||
\(940\) | 1.15672e13 | 0.483229 | ||||||||
\(941\) | −3.63435e13 | −1.51103 | −0.755515 | − | 0.655131i | \(-0.772613\pi\) | ||||
−0.755515 | + | 0.655131i | \(0.772613\pi\) | |||||||
\(942\) | −2.90398e13 | −1.20161 | ||||||||
\(943\) | −7.49077e12 | −0.308478 | ||||||||
\(944\) | 4.05356e13 | 1.66135 | ||||||||
\(945\) | −3.72297e12 | −0.151861 | ||||||||
\(946\) | 1.12434e13 | 0.456446 | ||||||||
\(947\) | −3.42860e13 | −1.38530 | −0.692648 | − | 0.721276i | \(-0.743556\pi\) | ||||
−0.692648 | + | 0.721276i | \(0.743556\pi\) | |||||||
\(948\) | 3.86440e13 | 1.55398 | ||||||||
\(949\) | −2.03273e12 | −0.0813546 | ||||||||
\(950\) | 4.33023e13 | 1.72486 | ||||||||
\(951\) | −2.78092e13 | −1.10249 | ||||||||
\(952\) | −2.20559e13 | −0.870278 | ||||||||
\(953\) | 3.00422e13 | 1.17981 | 0.589907 | − | 0.807471i | \(-0.299165\pi\) | ||||
0.589907 | + | 0.807471i | \(0.299165\pi\) | |||||||
\(954\) | 5.73822e11 | 0.0224290 | ||||||||
\(955\) | −1.82759e12 | −0.0710989 | ||||||||
\(956\) | 9.06167e13 | 3.50871 | ||||||||
\(957\) | 1.04580e13 | 0.403035 | ||||||||
\(958\) | −2.46129e13 | −0.944100 | ||||||||
\(959\) | 1.04051e13 | 0.397247 | ||||||||
\(960\) | −6.93098e12 | −0.263375 | ||||||||
\(961\) | −2.40406e13 | −0.909265 | ||||||||
\(962\) | 5.07285e12 | 0.190970 | ||||||||
\(963\) | 4.44862e11 | 0.0166689 | ||||||||
\(964\) | −6.82611e13 | −2.54581 | ||||||||
\(965\) | −5.07077e12 | −0.188235 | ||||||||
\(966\) | −3.07691e13 | −1.13689 | ||||||||
\(967\) | −2.34806e12 | −0.0863555 | −0.0431778 | − | 0.999067i | \(-0.513748\pi\) | ||||
−0.0431778 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(968\) | 4.91113e13 | 1.79780 | ||||||||
\(969\) | 3.75387e13 | 1.36780 | ||||||||
\(970\) | −1.70525e13 | −0.618465 | ||||||||
\(971\) | 1.90529e11 | 0.00687818 | 0.00343909 | − | 0.999994i | \(-0.498905\pi\) | ||||
0.00343909 | + | 0.999994i | \(0.498905\pi\) | |||||||
\(972\) | 3.47059e12 | 0.124711 | ||||||||
\(973\) | 1.49909e13 | 0.536192 | ||||||||
\(974\) | 8.93866e13 | 3.18242 | ||||||||
\(975\) | 6.49927e12 | 0.230326 | ||||||||
\(976\) | −5.93915e13 | −2.09508 | ||||||||
\(977\) | −4.08114e13 | −1.43303 | −0.716516 | − | 0.697571i | \(-0.754264\pi\) | ||||
−0.716516 | + | 0.697571i | \(0.754264\pi\) | |||||||
\(978\) | −9.09976e13 | −3.18057 | ||||||||
\(979\) | −1.00868e12 | −0.0350940 | ||||||||
\(980\) | 3.42442e12 | 0.118596 | ||||||||
\(981\) | 3.62596e11 | 0.0125001 | ||||||||
\(982\) | −7.55171e13 | −2.59146 | ||||||||
\(983\) | −4.98504e13 | −1.70285 | −0.851427 | − | 0.524473i | \(-0.824262\pi\) | ||||
−0.851427 | + | 0.524473i | \(0.824262\pi\) | |||||||
\(984\) | 9.92694e12 | 0.337550 | ||||||||
\(985\) | 1.23099e13 | 0.416670 | ||||||||
\(986\) | 9.81777e13 | 3.30801 | ||||||||
\(987\) | 6.46103e12 | 0.216708 | ||||||||
\(988\) | −2.02431e13 | −0.675880 | ||||||||
\(989\) | 5.21212e13 | 1.73233 | ||||||||
\(990\) | −1.62948e11 | −0.00539126 | ||||||||
\(991\) | −2.22205e13 | −0.731852 | −0.365926 | − | 0.930644i | \(-0.619248\pi\) | ||||
−0.365926 | + | 0.930644i | \(0.619248\pi\) | |||||||
\(992\) | −3.24550e12 | −0.106409 | ||||||||
\(993\) | 2.11983e13 | 0.691877 | ||||||||
\(994\) | −2.75441e13 | −0.894932 | ||||||||
\(995\) | −1.90653e13 | −0.616653 | ||||||||
\(996\) | 6.05133e13 | 1.94843 | ||||||||
\(997\) | −6.99200e12 | −0.224116 | −0.112058 | − | 0.993702i | \(-0.535744\pi\) | ||||
−0.112058 | + | 0.993702i | \(0.535744\pi\) | |||||||
\(998\) | −4.80548e13 | −1.53338 | ||||||||
\(999\) | −1.24960e13 | −0.396941 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 91.10.a.c.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.c.1.1 | ✓ | 14 | 1.1 | even | 1 | trivial |