Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,26,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(7.91993559904\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 97956.0 | 0.106418 | 0.0532090 | − | 0.998583i | \(-0.483055\pi\) | ||||
0.0532090 | + | 0.998583i | \(0.483055\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 3.41005e8 | 0.624649 | 0.312325 | − | 0.949975i | \(-0.398892\pi\) | ||||
0.312325 | + | 0.949975i | \(0.398892\pi\) | |||||||
\(6\) | −4.01228e8 | −0.0752489 | ||||||||
\(7\) | −4.08826e10 | −1.11638 | −0.558192 | − | 0.829712i | \(-0.688505\pi\) | ||||
−0.558192 | + | 0.829712i | \(0.688505\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | −8.37693e11 | −0.988675 | ||||||||
\(10\) | −1.39676e12 | −0.441694 | ||||||||
\(11\) | −1.45062e13 | −1.39362 | −0.696812 | − | 0.717254i | \(-0.745399\pi\) | ||||
−0.696812 | + | 0.717254i | \(0.745399\pi\) | |||||||
\(12\) | 1.64343e12 | 0.0532090 | ||||||||
\(13\) | 8.78440e13 | 1.04573 | 0.522866 | − | 0.852415i | \(-0.324863\pi\) | ||||
0.522866 | + | 0.852415i | \(0.324863\pi\) | |||||||
\(14\) | 1.67455e14 | 0.789402 | ||||||||
\(15\) | 3.34035e13 | 0.0664740 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −2.65543e15 | −1.10541 | −0.552704 | − | 0.833378i | \(-0.686404\pi\) | ||||
−0.552704 | + | 0.833378i | \(0.686404\pi\) | |||||||
\(18\) | 3.43119e15 | 0.699099 | ||||||||
\(19\) | −1.39994e16 | −1.45108 | −0.725538 | − | 0.688182i | \(-0.758409\pi\) | ||||
−0.725538 | + | 0.688182i | \(0.758409\pi\) | |||||||
\(20\) | 5.72112e15 | 0.312325 | ||||||||
\(21\) | −4.00470e15 | −0.118803 | ||||||||
\(22\) | 5.94175e16 | 0.985441 | ||||||||
\(23\) | 8.58528e16 | 0.816877 | 0.408438 | − | 0.912786i | \(-0.366074\pi\) | ||||
0.408438 | + | 0.912786i | \(0.366074\pi\) | |||||||
\(24\) | −6.73149e15 | −0.0376245 | ||||||||
\(25\) | −1.81739e17 | −0.609813 | ||||||||
\(26\) | −3.59809e17 | −0.739444 | ||||||||
\(27\) | −1.65054e17 | −0.211631 | ||||||||
\(28\) | −6.85897e17 | −0.558192 | ||||||||
\(29\) | 2.08023e18 | 1.09178 | 0.545892 | − | 0.837856i | \(-0.316191\pi\) | ||||
0.545892 | + | 0.837856i | \(0.316191\pi\) | |||||||
\(30\) | −1.36821e17 | −0.0470042 | ||||||||
\(31\) | 2.66353e18 | 0.607347 | 0.303673 | − | 0.952776i | \(-0.401787\pi\) | ||||
0.303673 | + | 0.952776i | \(0.401787\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | −1.42097e18 | −0.148307 | ||||||||
\(34\) | 1.08766e19 | 0.781642 | ||||||||
\(35\) | −1.39412e19 | −0.697348 | ||||||||
\(36\) | −1.40542e19 | −0.494338 | ||||||||
\(37\) | −5.13796e19 | −1.28313 | −0.641563 | − | 0.767070i | \(-0.721714\pi\) | ||||
−0.641563 | + | 0.767070i | \(0.721714\pi\) | |||||||
\(38\) | 5.73416e19 | 1.02607 | ||||||||
\(39\) | 8.60485e18 | 0.111285 | ||||||||
\(40\) | −2.34337e19 | −0.220847 | ||||||||
\(41\) | 2.33560e20 | 1.61659 | 0.808295 | − | 0.588778i | \(-0.200391\pi\) | ||||
0.808295 | + | 0.588778i | \(0.200391\pi\) | |||||||
\(42\) | 1.64032e19 | 0.0840067 | ||||||||
\(43\) | −4.01336e19 | −0.153162 | −0.0765812 | − | 0.997063i | \(-0.524400\pi\) | ||||
−0.0765812 | + | 0.997063i | \(0.524400\pi\) | |||||||
\(44\) | −2.43374e20 | −0.696812 | ||||||||
\(45\) | −2.85658e20 | −0.617575 | ||||||||
\(46\) | −3.51653e20 | −0.577619 | ||||||||
\(47\) | 2.79826e20 | 0.351290 | 0.175645 | − | 0.984454i | \(-0.443799\pi\) | ||||
0.175645 | + | 0.984454i | \(0.443799\pi\) | |||||||
\(48\) | 2.75722e19 | 0.0266045 | ||||||||
\(49\) | 3.30321e20 | 0.246312 | ||||||||
\(50\) | 7.44401e20 | 0.431203 | ||||||||
\(51\) | −2.60115e20 | −0.117635 | ||||||||
\(52\) | 1.47378e21 | 0.522866 | ||||||||
\(53\) | 4.25070e20 | 0.118854 | 0.0594268 | − | 0.998233i | \(-0.481073\pi\) | ||||
0.0594268 | + | 0.998233i | \(0.481073\pi\) | |||||||
\(54\) | 6.76062e20 | 0.149646 | ||||||||
\(55\) | −4.94670e21 | −0.870526 | ||||||||
\(56\) | 2.80943e21 | 0.394701 | ||||||||
\(57\) | −1.37133e21 | −0.154421 | ||||||||
\(58\) | −8.52062e21 | −0.772007 | ||||||||
\(59\) | −8.33891e21 | −0.610181 | −0.305091 | − | 0.952323i | \(-0.598687\pi\) | ||||
−0.305091 | + | 0.952323i | \(0.598687\pi\) | |||||||
\(60\) | 5.60418e20 | 0.0332370 | ||||||||
\(61\) | 2.42979e22 | 1.17205 | 0.586026 | − | 0.810292i | \(-0.300692\pi\) | ||||
0.586026 | + | 0.810292i | \(0.300692\pi\) | |||||||
\(62\) | −1.09098e22 | −0.429459 | ||||||||
\(63\) | 3.42471e22 | 1.10374 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 2.99553e22 | 0.653215 | ||||||||
\(66\) | 5.82030e21 | 0.104869 | ||||||||
\(67\) | −1.24700e23 | −1.86179 | −0.930897 | − | 0.365282i | \(-0.880973\pi\) | ||||
−0.930897 | + | 0.365282i | \(0.880973\pi\) | |||||||
\(68\) | −4.45507e22 | −0.552704 | ||||||||
\(69\) | 8.40979e21 | 0.0869304 | ||||||||
\(70\) | 5.71031e22 | 0.493099 | ||||||||
\(71\) | −9.30490e22 | −0.672949 | −0.336475 | − | 0.941693i | \(-0.609235\pi\) | ||||
−0.336475 | + | 0.941693i | \(0.609235\pi\) | |||||||
\(72\) | 5.75658e22 | 0.349549 | ||||||||
\(73\) | 4.04218e22 | 0.206576 | 0.103288 | − | 0.994651i | \(-0.467064\pi\) | ||||
0.103288 | + | 0.994651i | \(0.467064\pi\) | |||||||
\(74\) | 2.10451e23 | 0.907307 | ||||||||
\(75\) | −1.78024e22 | −0.0648952 | ||||||||
\(76\) | −2.34871e23 | −0.725538 | ||||||||
\(77\) | 5.93053e23 | 1.55582 | ||||||||
\(78\) | −3.52454e22 | −0.0786902 | ||||||||
\(79\) | −8.05270e23 | −1.53321 | −0.766607 | − | 0.642116i | \(-0.778057\pi\) | ||||
−0.766607 | + | 0.642116i | \(0.778057\pi\) | |||||||
\(80\) | 9.59845e22 | 0.156162 | ||||||||
\(81\) | 6.93600e23 | 0.966154 | ||||||||
\(82\) | −9.56661e23 | −1.14310 | ||||||||
\(83\) | 8.98335e21 | 0.00922491 | 0.00461245 | − | 0.999989i | \(-0.498532\pi\) | ||||
0.00461245 | + | 0.999989i | \(0.498532\pi\) | |||||||
\(84\) | −6.71877e22 | −0.0594017 | ||||||||
\(85\) | −9.05514e23 | −0.690492 | ||||||||
\(86\) | 1.64387e23 | 0.108302 | ||||||||
\(87\) | 2.03771e23 | 0.116185 | ||||||||
\(88\) | 9.96860e23 | 0.492721 | ||||||||
\(89\) | 3.55600e24 | 1.52611 | 0.763057 | − | 0.646331i | \(-0.223697\pi\) | ||||
0.763057 | + | 0.646331i | \(0.223697\pi\) | |||||||
\(90\) | 1.17005e24 | 0.436692 | ||||||||
\(91\) | −3.59129e24 | −1.16744 | ||||||||
\(92\) | 1.44037e24 | 0.408438 | ||||||||
\(93\) | 2.60909e23 | 0.0646327 | ||||||||
\(94\) | −1.14617e24 | −0.248399 | ||||||||
\(95\) | −4.77388e24 | −0.906413 | ||||||||
\(96\) | −1.12936e23 | −0.0188122 | ||||||||
\(97\) | −8.66049e24 | −1.26735 | −0.633674 | − | 0.773600i | \(-0.718454\pi\) | ||||
−0.633674 | + | 0.773600i | \(0.718454\pi\) | |||||||
\(98\) | −1.35300e24 | −0.174169 | ||||||||
\(99\) | 1.21518e25 | 1.37784 | ||||||||
\(100\) | −3.04907e24 | −0.304907 | ||||||||
\(101\) | 7.28380e24 | 0.643193 | 0.321596 | − | 0.946877i | \(-0.395781\pi\) | ||||
0.321596 | + | 0.946877i | \(0.395781\pi\) | |||||||
\(102\) | 1.06543e24 | 0.0831808 | ||||||||
\(103\) | 1.52392e25 | 1.05317 | 0.526583 | − | 0.850123i | \(-0.323473\pi\) | ||||
0.526583 | + | 0.850123i | \(0.323473\pi\) | |||||||
\(104\) | −6.03659e24 | −0.369722 | ||||||||
\(105\) | −1.36562e24 | −0.0742104 | ||||||||
\(106\) | −1.74109e24 | −0.0840422 | ||||||||
\(107\) | −6.27006e24 | −0.269138 | −0.134569 | − | 0.990904i | \(-0.542965\pi\) | ||||
−0.134569 | + | 0.990904i | \(0.542965\pi\) | |||||||
\(108\) | −2.76915e24 | −0.105815 | ||||||||
\(109\) | −1.66220e25 | −0.566047 | −0.283024 | − | 0.959113i | \(-0.591337\pi\) | ||||
−0.283024 | + | 0.959113i | \(0.591337\pi\) | |||||||
\(110\) | 2.02617e25 | 0.615555 | ||||||||
\(111\) | −5.03294e24 | −0.136548 | ||||||||
\(112\) | −1.15074e25 | −0.279096 | ||||||||
\(113\) | −4.59044e25 | −0.996263 | −0.498131 | − | 0.867102i | \(-0.665980\pi\) | ||||
−0.498131 | + | 0.867102i | \(0.665980\pi\) | |||||||
\(114\) | 5.61696e24 | 0.109192 | ||||||||
\(115\) | 2.92763e25 | 0.510261 | ||||||||
\(116\) | 3.49005e25 | 0.545892 | ||||||||
\(117\) | −7.35863e25 | −1.03389 | ||||||||
\(118\) | 3.41562e25 | 0.431463 | ||||||||
\(119\) | 1.08561e26 | 1.23406 | ||||||||
\(120\) | −2.29547e24 | −0.0235021 | ||||||||
\(121\) | 1.02083e26 | 0.942189 | ||||||||
\(122\) | −9.95244e25 | −0.828766 | ||||||||
\(123\) | 2.28786e25 | 0.172034 | ||||||||
\(124\) | 4.46867e25 | 0.303673 | ||||||||
\(125\) | −1.63601e26 | −1.00557 | ||||||||
\(126\) | −1.40276e26 | −0.780463 | ||||||||
\(127\) | −3.66137e24 | −0.0184543 | −0.00922713 | − | 0.999957i | \(-0.502937\pi\) | ||||
−0.00922713 | + | 0.999957i | \(0.502937\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | −3.93133e24 | −0.0162993 | ||||||||
\(130\) | −1.22697e26 | −0.461893 | ||||||||
\(131\) | −1.37888e26 | −0.471667 | −0.235833 | − | 0.971793i | \(-0.575782\pi\) | ||||
−0.235833 | + | 0.971793i | \(0.575782\pi\) | |||||||
\(132\) | −2.38399e25 | −0.0741534 | ||||||||
\(133\) | 5.72333e26 | 1.61996 | ||||||||
\(134\) | 5.10772e26 | 1.31649 | ||||||||
\(135\) | −5.62843e25 | −0.132195 | ||||||||
\(136\) | 1.82479e26 | 0.390821 | ||||||||
\(137\) | −4.32281e26 | −0.844810 | −0.422405 | − | 0.906407i | \(-0.638814\pi\) | ||||
−0.422405 | + | 0.906407i | \(0.638814\pi\) | |||||||
\(138\) | −3.44465e25 | −0.0614691 | ||||||||
\(139\) | −4.00646e25 | −0.0653245 | −0.0326622 | − | 0.999466i | \(-0.510399\pi\) | ||||
−0.0326622 | + | 0.999466i | \(0.510399\pi\) | |||||||
\(140\) | −2.33894e26 | −0.348674 | ||||||||
\(141\) | 2.74107e25 | 0.0373836 | ||||||||
\(142\) | 3.81129e26 | 0.475847 | ||||||||
\(143\) | −1.27428e27 | −1.45736 | ||||||||
\(144\) | −2.35790e26 | −0.247169 | ||||||||
\(145\) | 7.09370e26 | 0.681982 | ||||||||
\(146\) | −1.65568e26 | −0.146071 | ||||||||
\(147\) | 3.23570e25 | 0.0262121 | ||||||||
\(148\) | −8.62007e26 | −0.641563 | ||||||||
\(149\) | 1.12193e27 | 0.767601 | 0.383801 | − | 0.923416i | \(-0.374615\pi\) | ||||
0.383801 | + | 0.923416i | \(0.374615\pi\) | |||||||
\(150\) | 7.29186e25 | 0.0458878 | ||||||||
\(151\) | −2.65183e26 | −0.153580 | −0.0767900 | − | 0.997047i | \(-0.524467\pi\) | ||||
−0.0767900 | + | 0.997047i | \(0.524467\pi\) | |||||||
\(152\) | 9.62033e26 | 0.513033 | ||||||||
\(153\) | 2.22443e27 | 1.09289 | ||||||||
\(154\) | −2.42914e27 | −1.10013 | ||||||||
\(155\) | 9.08279e26 | 0.379379 | ||||||||
\(156\) | 1.44365e26 | 0.0556424 | ||||||||
\(157\) | −8.32328e26 | −0.296175 | −0.148088 | − | 0.988974i | \(-0.547312\pi\) | ||||
−0.148088 | + | 0.988974i | \(0.547312\pi\) | |||||||
\(158\) | 3.29839e27 | 1.08415 | ||||||||
\(159\) | 4.16382e25 | 0.0126482 | ||||||||
\(160\) | −3.93152e26 | −0.110423 | ||||||||
\(161\) | −3.50989e27 | −0.911947 | ||||||||
\(162\) | −2.84099e27 | −0.683174 | ||||||||
\(163\) | −7.22281e27 | −1.60828 | −0.804139 | − | 0.594442i | \(-0.797373\pi\) | ||||
−0.804139 | + | 0.594442i | \(0.797373\pi\) | |||||||
\(164\) | 3.91848e27 | 0.808295 | ||||||||
\(165\) | −4.84559e26 | −0.0926397 | ||||||||
\(166\) | −3.67958e25 | −0.00652300 | ||||||||
\(167\) | 3.82503e27 | 0.629041 | 0.314520 | − | 0.949251i | \(-0.398156\pi\) | ||||
0.314520 | + | 0.949251i | \(0.398156\pi\) | |||||||
\(168\) | 2.75201e26 | 0.0420033 | ||||||||
\(169\) | 6.60156e26 | 0.0935542 | ||||||||
\(170\) | 3.70899e27 | 0.488252 | ||||||||
\(171\) | 1.17272e28 | 1.43464 | ||||||||
\(172\) | −6.73330e26 | −0.0765812 | ||||||||
\(173\) | −4.74370e27 | −0.501812 | −0.250906 | − | 0.968012i | \(-0.580728\pi\) | ||||
−0.250906 | + | 0.968012i | \(0.580728\pi\) | |||||||
\(174\) | −8.34646e26 | −0.0821555 | ||||||||
\(175\) | 7.42995e27 | 0.680786 | ||||||||
\(176\) | −4.08314e27 | −0.348406 | ||||||||
\(177\) | −8.16846e26 | −0.0649343 | ||||||||
\(178\) | −1.45654e28 | −1.07913 | ||||||||
\(179\) | −6.99171e27 | −0.482970 | −0.241485 | − | 0.970405i | \(-0.577635\pi\) | ||||
−0.241485 | + | 0.970405i | \(0.577635\pi\) | |||||||
\(180\) | −4.79254e27 | −0.308788 | ||||||||
\(181\) | −6.34714e27 | −0.381589 | −0.190794 | − | 0.981630i | \(-0.561106\pi\) | ||||
−0.190794 | + | 0.981630i | \(0.561106\pi\) | |||||||
\(182\) | 1.47099e28 | 0.825503 | ||||||||
\(183\) | 2.38013e27 | 0.124727 | ||||||||
\(184\) | −5.89976e27 | −0.288809 | ||||||||
\(185\) | −1.75207e28 | −0.801503 | ||||||||
\(186\) | −1.06868e27 | −0.0457022 | ||||||||
\(187\) | 3.85202e28 | 1.54052 | ||||||||
\(188\) | 4.69471e27 | 0.175645 | ||||||||
\(189\) | 6.74785e27 | 0.236261 | ||||||||
\(190\) | 1.95538e28 | 0.640931 | ||||||||
\(191\) | −3.59244e28 | −1.10274 | −0.551369 | − | 0.834261i | \(-0.685894\pi\) | ||||
−0.551369 | + | 0.834261i | \(0.685894\pi\) | |||||||
\(192\) | 4.62584e26 | 0.0133023 | ||||||||
\(193\) | −3.76264e27 | −0.101397 | −0.0506987 | − | 0.998714i | \(-0.516145\pi\) | ||||
−0.0506987 | + | 0.998714i | \(0.516145\pi\) | |||||||
\(194\) | 3.54734e28 | 0.896150 | ||||||||
\(195\) | 2.93430e27 | 0.0695139 | ||||||||
\(196\) | 5.54187e27 | 0.123156 | ||||||||
\(197\) | −1.84478e28 | −0.384696 | −0.192348 | − | 0.981327i | \(-0.561610\pi\) | ||||
−0.192348 | + | 0.981327i | \(0.561610\pi\) | |||||||
\(198\) | −4.97736e28 | −0.974281 | ||||||||
\(199\) | 3.23533e28 | 0.594641 | 0.297321 | − | 0.954778i | \(-0.403907\pi\) | ||||
0.297321 | + | 0.954778i | \(0.403907\pi\) | |||||||
\(200\) | 1.24890e28 | 0.215602 | ||||||||
\(201\) | −1.22151e28 | −0.198129 | ||||||||
\(202\) | −2.98345e28 | −0.454806 | ||||||||
\(203\) | −8.50453e28 | −1.21885 | ||||||||
\(204\) | −4.36400e27 | −0.0588177 | ||||||||
\(205\) | 7.96451e28 | 1.00980 | ||||||||
\(206\) | −6.24198e28 | −0.744701 | ||||||||
\(207\) | −7.19183e28 | −0.807626 | ||||||||
\(208\) | 2.47259e28 | 0.261433 | ||||||||
\(209\) | 2.03079e29 | 2.02226 | ||||||||
\(210\) | 5.59360e27 | 0.0524747 | ||||||||
\(211\) | 7.34820e28 | 0.649607 | 0.324803 | − | 0.945782i | \(-0.394702\pi\) | ||||
0.324803 | + | 0.945782i | \(0.394702\pi\) | |||||||
\(212\) | 7.13150e27 | 0.0594268 | ||||||||
\(213\) | −9.11471e27 | −0.0716140 | ||||||||
\(214\) | 2.56822e28 | 0.190309 | ||||||||
\(215\) | −1.36858e28 | −0.0956728 | ||||||||
\(216\) | 1.13424e28 | 0.0748228 | ||||||||
\(217\) | −1.08892e29 | −0.678032 | ||||||||
\(218\) | 6.80838e28 | 0.400256 | ||||||||
\(219\) | 3.95956e27 | 0.0219834 | ||||||||
\(220\) | −8.29918e28 | −0.435263 | ||||||||
\(221\) | −2.33263e29 | −1.15596 | ||||||||
\(222\) | 2.06149e28 | 0.0965539 | ||||||||
\(223\) | −3.83771e29 | −1.69927 | −0.849634 | − | 0.527373i | \(-0.823177\pi\) | ||||
−0.849634 | + | 0.527373i | \(0.823177\pi\) | |||||||
\(224\) | 4.71345e28 | 0.197351 | ||||||||
\(225\) | 1.52241e29 | 0.602907 | ||||||||
\(226\) | 1.88024e29 | 0.704464 | ||||||||
\(227\) | 2.86396e28 | 0.101541 | 0.0507707 | − | 0.998710i | \(-0.483832\pi\) | ||||
0.0507707 | + | 0.998710i | \(0.483832\pi\) | |||||||
\(228\) | −2.30071e28 | −0.0772104 | ||||||||
\(229\) | 5.18014e29 | 1.64588 | 0.822939 | − | 0.568129i | \(-0.192333\pi\) | ||||
0.822939 | + | 0.568129i | \(0.192333\pi\) | |||||||
\(230\) | −1.19916e29 | −0.360809 | ||||||||
\(231\) | 5.80931e28 | 0.165567 | ||||||||
\(232\) | −1.42952e29 | −0.386004 | ||||||||
\(233\) | −1.11488e29 | −0.285285 | −0.142643 | − | 0.989774i | \(-0.545560\pi\) | ||||
−0.142643 | + | 0.989774i | \(0.545560\pi\) | |||||||
\(234\) | 3.01410e29 | 0.731070 | ||||||||
\(235\) | 9.54223e28 | 0.219433 | ||||||||
\(236\) | −1.39904e29 | −0.305091 | ||||||||
\(237\) | −7.88810e28 | −0.163162 | ||||||||
\(238\) | −4.44665e29 | −0.872612 | ||||||||
\(239\) | 9.81417e29 | 1.82759 | 0.913797 | − | 0.406170i | \(-0.133136\pi\) | ||||
0.913797 | + | 0.406170i | \(0.133136\pi\) | |||||||
\(240\) | 9.40226e27 | 0.0166185 | ||||||||
\(241\) | −1.00294e30 | −1.68292 | −0.841459 | − | 0.540320i | \(-0.818303\pi\) | ||||
−0.841459 | + | 0.540320i | \(0.818303\pi\) | |||||||
\(242\) | −4.18134e29 | −0.666228 | ||||||||
\(243\) | 2.07791e29 | 0.314447 | ||||||||
\(244\) | 4.07652e29 | 0.586026 | ||||||||
\(245\) | 1.12641e29 | 0.153859 | ||||||||
\(246\) | −9.37107e28 | −0.121647 | ||||||||
\(247\) | −1.22977e30 | −1.51744 | ||||||||
\(248\) | −1.83037e29 | −0.214730 | ||||||||
\(249\) | 8.79973e26 | 0.000981697 0 | ||||||||
\(250\) | 6.70111e29 | 0.711044 | ||||||||
\(251\) | 1.14894e30 | 1.15978 | 0.579892 | − | 0.814694i | \(-0.303095\pi\) | ||||
0.579892 | + | 0.814694i | \(0.303095\pi\) | |||||||
\(252\) | 5.74571e29 | 0.551870 | ||||||||
\(253\) | −1.24540e30 | −1.13842 | ||||||||
\(254\) | 1.49970e28 | 0.0130491 | ||||||||
\(255\) | −8.87006e28 | −0.0734808 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 1.28454e30 | 0.965123 | 0.482562 | − | 0.875862i | \(-0.339706\pi\) | ||||
0.482562 | + | 0.875862i | \(0.339706\pi\) | |||||||
\(258\) | 1.61027e28 | 0.0115253 | ||||||||
\(259\) | 2.10053e30 | 1.43246 | ||||||||
\(260\) | 5.02566e29 | 0.326608 | ||||||||
\(261\) | −1.74259e30 | −1.07942 | ||||||||
\(262\) | 5.64789e29 | 0.333519 | ||||||||
\(263\) | −2.47079e30 | −1.39120 | −0.695598 | − | 0.718431i | \(-0.744860\pi\) | ||||
−0.695598 | + | 0.718431i | \(0.744860\pi\) | |||||||
\(264\) | 9.76484e28 | 0.0524344 | ||||||||
\(265\) | 1.44951e29 | 0.0742418 | ||||||||
\(266\) | −2.34428e30 | −1.14548 | ||||||||
\(267\) | 3.48332e29 | 0.162406 | ||||||||
\(268\) | −2.09212e30 | −0.930897 | ||||||||
\(269\) | 8.32933e29 | 0.353758 | 0.176879 | − | 0.984233i | \(-0.443400\pi\) | ||||
0.176879 | + | 0.984233i | \(0.443400\pi\) | |||||||
\(270\) | 2.30541e29 | 0.0934761 | ||||||||
\(271\) | −3.89840e29 | −0.150928 | −0.0754641 | − | 0.997149i | \(-0.524044\pi\) | ||||
−0.0754641 | + | 0.997149i | \(0.524044\pi\) | |||||||
\(272\) | −7.47436e29 | −0.276352 | ||||||||
\(273\) | −3.51789e29 | −0.124236 | ||||||||
\(274\) | 1.77062e30 | 0.597371 | ||||||||
\(275\) | 2.63634e30 | 0.849851 | ||||||||
\(276\) | 1.41093e29 | 0.0434652 | ||||||||
\(277\) | 5.75822e30 | 1.69548 | 0.847738 | − | 0.530416i | \(-0.177964\pi\) | ||||
0.847738 | + | 0.530416i | \(0.177964\pi\) | |||||||
\(278\) | 1.64105e29 | 0.0461914 | ||||||||
\(279\) | −2.23122e30 | −0.600469 | ||||||||
\(280\) | 9.58032e29 | 0.246550 | ||||||||
\(281\) | −7.34745e29 | −0.180846 | −0.0904228 | − | 0.995903i | \(-0.528822\pi\) | ||||
−0.0904228 | + | 0.995903i | \(0.528822\pi\) | |||||||
\(282\) | −1.12274e29 | −0.0264342 | ||||||||
\(283\) | −1.15692e30 | −0.260600 | −0.130300 | − | 0.991475i | \(-0.541594\pi\) | ||||
−0.130300 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(284\) | −1.56110e30 | −0.336475 | ||||||||
\(285\) | −4.67630e29 | −0.0964588 | ||||||||
\(286\) | 5.21947e30 | 1.03051 | ||||||||
\(287\) | −9.54854e30 | −1.80473 | ||||||||
\(288\) | 9.65795e29 | 0.174775 | ||||||||
\(289\) | 1.28066e30 | 0.221927 | ||||||||
\(290\) | −2.90558e30 | −0.482234 | ||||||||
\(291\) | −8.48347e29 | −0.134869 | ||||||||
\(292\) | 6.78165e29 | 0.103288 | ||||||||
\(293\) | −9.96443e29 | −0.145414 | −0.0727072 | − | 0.997353i | \(-0.523164\pi\) | ||||
−0.0727072 | + | 0.997353i | \(0.523164\pi\) | |||||||
\(294\) | −1.32534e29 | −0.0185347 | ||||||||
\(295\) | −2.84361e30 | −0.381149 | ||||||||
\(296\) | 3.53078e30 | 0.453653 | ||||||||
\(297\) | 2.39431e30 | 0.294934 | ||||||||
\(298\) | −4.59541e30 | −0.542776 | ||||||||
\(299\) | 7.54165e30 | 0.854233 | ||||||||
\(300\) | −2.98674e29 | −0.0324476 | ||||||||
\(301\) | 1.64077e30 | 0.170988 | ||||||||
\(302\) | 1.08619e30 | 0.108597 | ||||||||
\(303\) | 7.13492e29 | 0.0684473 | ||||||||
\(304\) | −3.94049e30 | −0.362769 | ||||||||
\(305\) | 8.28573e30 | 0.732121 | ||||||||
\(306\) | −9.11127e30 | −0.772790 | ||||||||
\(307\) | 1.11603e31 | 0.908755 | 0.454378 | − | 0.890809i | \(-0.349862\pi\) | ||||
0.454378 | + | 0.890809i | \(0.349862\pi\) | |||||||
\(308\) | 9.94977e30 | 0.777910 | ||||||||
\(309\) | 1.49277e30 | 0.112076 | ||||||||
\(310\) | −3.72031e30 | −0.268261 | ||||||||
\(311\) | −8.47315e30 | −0.586867 | −0.293434 | − | 0.955979i | \(-0.594798\pi\) | ||||
−0.293434 | + | 0.955979i | \(0.594798\pi\) | |||||||
\(312\) | −5.91321e29 | −0.0393451 | ||||||||
\(313\) | −1.15783e31 | −0.740184 | −0.370092 | − | 0.928995i | \(-0.620674\pi\) | ||||
−0.370092 | + | 0.928995i | \(0.620674\pi\) | |||||||
\(314\) | 3.40921e30 | 0.209427 | ||||||||
\(315\) | 1.16784e31 | 0.689451 | ||||||||
\(316\) | −1.35102e31 | −0.766607 | ||||||||
\(317\) | −1.97191e31 | −1.07559 | −0.537796 | − | 0.843075i | \(-0.680743\pi\) | ||||
−0.537796 | + | 0.843075i | \(0.680743\pi\) | |||||||
\(318\) | −1.70550e29 | −0.00894361 | ||||||||
\(319\) | −3.01763e31 | −1.52154 | ||||||||
\(320\) | 1.61035e30 | 0.0780811 | ||||||||
\(321\) | −6.14190e29 | −0.0286411 | ||||||||
\(322\) | 1.43765e31 | 0.644844 | ||||||||
\(323\) | 3.71744e31 | 1.60403 | ||||||||
\(324\) | 1.16367e31 | 0.483077 | ||||||||
\(325\) | −1.59646e31 | −0.637701 | ||||||||
\(326\) | 2.95846e31 | 1.13722 | ||||||||
\(327\) | −1.62823e30 | −0.0602376 | ||||||||
\(328\) | −1.60501e31 | −0.571551 | ||||||||
\(329\) | −1.14400e31 | −0.392174 | ||||||||
\(330\) | 1.98475e30 | 0.0655062 | ||||||||
\(331\) | 4.77112e31 | 1.51625 | 0.758124 | − | 0.652110i | \(-0.226116\pi\) | ||||
0.758124 | + | 0.652110i | \(0.226116\pi\) | |||||||
\(332\) | 1.50716e29 | 0.00461245 | ||||||||
\(333\) | 4.30403e31 | 1.26859 | ||||||||
\(334\) | −1.56673e31 | −0.444799 | ||||||||
\(335\) | −4.25234e31 | −1.16297 | ||||||||
\(336\) | −1.12722e30 | −0.0297008 | ||||||||
\(337\) | −3.28717e31 | −0.834542 | −0.417271 | − | 0.908782i | \(-0.637013\pi\) | ||||
−0.417271 | + | 0.908782i | \(0.637013\pi\) | |||||||
\(338\) | −2.70400e30 | −0.0661528 | ||||||||
\(339\) | −4.49661e30 | −0.106020 | ||||||||
\(340\) | −1.51920e31 | −0.345246 | ||||||||
\(341\) | −3.86378e31 | −0.846413 | ||||||||
\(342\) | −4.80347e31 | −1.01445 | ||||||||
\(343\) | 4.13220e31 | 0.841405 | ||||||||
\(344\) | 2.75796e30 | 0.0541511 | ||||||||
\(345\) | 2.86779e30 | 0.0543010 | ||||||||
\(346\) | 1.94302e31 | 0.354834 | ||||||||
\(347\) | 3.13233e31 | 0.551759 | 0.275879 | − | 0.961192i | \(-0.411031\pi\) | ||||
0.275879 | + | 0.961192i | \(0.411031\pi\) | |||||||
\(348\) | 3.41871e30 | 0.0580927 | ||||||||
\(349\) | 3.37807e31 | 0.553796 | 0.276898 | − | 0.960899i | \(-0.410694\pi\) | ||||
0.276898 | + | 0.960899i | \(0.410694\pi\) | |||||||
\(350\) | −3.04331e31 | −0.481388 | ||||||||
\(351\) | −1.44990e31 | −0.221309 | ||||||||
\(352\) | 1.67245e31 | 0.246360 | ||||||||
\(353\) | 4.38482e31 | 0.623401 | 0.311701 | − | 0.950180i | \(-0.399101\pi\) | ||||
0.311701 | + | 0.950180i | \(0.399101\pi\) | |||||||
\(354\) | 3.34580e30 | 0.0459155 | ||||||||
\(355\) | −3.17302e31 | −0.420357 | ||||||||
\(356\) | 5.96599e31 | 0.763057 | ||||||||
\(357\) | 1.06342e31 | 0.131326 | ||||||||
\(358\) | 2.86380e31 | 0.341512 | ||||||||
\(359\) | −1.50427e32 | −1.73239 | −0.866193 | − | 0.499710i | \(-0.833440\pi\) | ||||
−0.866193 | + | 0.499710i | \(0.833440\pi\) | |||||||
\(360\) | 1.96303e31 | 0.218346 | ||||||||
\(361\) | 1.02907e32 | 1.10562 | ||||||||
\(362\) | 2.59979e31 | 0.269824 | ||||||||
\(363\) | 9.99968e30 | 0.100266 | ||||||||
\(364\) | −6.02519e31 | −0.583719 | ||||||||
\(365\) | 1.37840e31 | 0.129038 | ||||||||
\(366\) | −9.74901e30 | −0.0881956 | ||||||||
\(367\) | −6.93296e31 | −0.606168 | −0.303084 | − | 0.952964i | \(-0.598016\pi\) | ||||
−0.303084 | + | 0.952964i | \(0.598016\pi\) | |||||||
\(368\) | 2.41654e31 | 0.204219 | ||||||||
\(369\) | −1.95651e32 | −1.59828 | ||||||||
\(370\) | 7.17649e31 | 0.566748 | ||||||||
\(371\) | −1.73780e31 | −0.132686 | ||||||||
\(372\) | 4.37733e30 | 0.0323163 | ||||||||
\(373\) | 6.14410e31 | 0.438630 | 0.219315 | − | 0.975654i | \(-0.429618\pi\) | ||||
0.219315 | + | 0.975654i | \(0.429618\pi\) | |||||||
\(374\) | −1.57779e32 | −1.08931 | ||||||||
\(375\) | −1.60257e31 | −0.107011 | ||||||||
\(376\) | −1.92295e31 | −0.124200 | ||||||||
\(377\) | 1.82736e32 | 1.14171 | ||||||||
\(378\) | −2.76392e31 | −0.167062 | ||||||||
\(379\) | 6.25980e31 | 0.366075 | 0.183038 | − | 0.983106i | \(-0.441407\pi\) | ||||
0.183038 | + | 0.983106i | \(0.441407\pi\) | |||||||
\(380\) | −8.00924e31 | −0.453207 | ||||||||
\(381\) | −3.58653e29 | −0.00196387 | ||||||||
\(382\) | 1.47146e32 | 0.779754 | ||||||||
\(383\) | 1.95859e32 | 1.00452 | 0.502260 | − | 0.864716i | \(-0.332502\pi\) | ||||
0.502260 | + | 0.864716i | \(0.332502\pi\) | |||||||
\(384\) | −1.89474e30 | −0.00940612 | ||||||||
\(385\) | 2.02234e32 | 0.971841 | ||||||||
\(386\) | 1.54118e31 | 0.0716988 | ||||||||
\(387\) | 3.36196e31 | 0.151428 | ||||||||
\(388\) | −1.45299e32 | −0.633674 | ||||||||
\(389\) | −5.55896e31 | −0.234760 | −0.117380 | − | 0.993087i | \(-0.537450\pi\) | ||||
−0.117380 | + | 0.993087i | \(0.537450\pi\) | |||||||
\(390\) | −1.20189e31 | −0.0491537 | ||||||||
\(391\) | −2.27976e32 | −0.902982 | ||||||||
\(392\) | −2.26995e31 | −0.0870845 | ||||||||
\(393\) | −1.35070e31 | −0.0501939 | ||||||||
\(394\) | 7.55624e31 | 0.272021 | ||||||||
\(395\) | −2.74601e32 | −0.957721 | ||||||||
\(396\) | 2.03873e32 | 0.688921 | ||||||||
\(397\) | −4.00706e32 | −1.31203 | −0.656017 | − | 0.754746i | \(-0.727760\pi\) | ||||
−0.656017 | + | 0.754746i | \(0.727760\pi\) | |||||||
\(398\) | −1.32519e32 | −0.420475 | ||||||||
\(399\) | 5.60635e31 | 0.172393 | ||||||||
\(400\) | −5.11549e31 | −0.152453 | ||||||||
\(401\) | −2.79804e32 | −0.808258 | −0.404129 | − | 0.914702i | \(-0.632425\pi\) | ||||
−0.404129 | + | 0.914702i | \(0.632425\pi\) | |||||||
\(402\) | 5.00331e31 | 0.140098 | ||||||||
\(403\) | 2.33975e32 | 0.635122 | ||||||||
\(404\) | 1.22202e32 | 0.321596 | ||||||||
\(405\) | 2.36521e32 | 0.603507 | ||||||||
\(406\) | 3.48346e32 | 0.861856 | ||||||||
\(407\) | 7.45324e32 | 1.78820 | ||||||||
\(408\) | 1.78750e31 | 0.0415904 | ||||||||
\(409\) | −7.22159e32 | −1.62964 | −0.814820 | − | 0.579715i | \(-0.803164\pi\) | ||||
−0.814820 | + | 0.579715i | \(0.803164\pi\) | |||||||
\(410\) | −3.26227e32 | −0.714038 | ||||||||
\(411\) | −4.23445e31 | −0.0899030 | ||||||||
\(412\) | 2.55672e32 | 0.526583 | ||||||||
\(413\) | 3.40916e32 | 0.681196 | ||||||||
\(414\) | 2.94577e32 | 0.571078 | ||||||||
\(415\) | 3.06337e30 | 0.00576233 | ||||||||
\(416\) | −1.01277e32 | −0.184861 | ||||||||
\(417\) | −3.92457e30 | −0.00695170 | ||||||||
\(418\) | −8.31811e32 | −1.42995 | ||||||||
\(419\) | 5.13071e32 | 0.856057 | 0.428028 | − | 0.903765i | \(-0.359208\pi\) | ||||
0.428028 | + | 0.903765i | \(0.359208\pi\) | |||||||
\(420\) | −2.29114e31 | −0.0371052 | ||||||||
\(421\) | −1.30991e32 | −0.205927 | −0.102964 | − | 0.994685i | \(-0.532833\pi\) | ||||
−0.102964 | + | 0.994685i | \(0.532833\pi\) | |||||||
\(422\) | −3.00982e32 | −0.459341 | ||||||||
\(423\) | −2.34409e32 | −0.347311 | ||||||||
\(424\) | −2.92106e31 | −0.0420211 | ||||||||
\(425\) | 4.82593e32 | 0.674093 | ||||||||
\(426\) | 3.73338e31 | 0.0506387 | ||||||||
\(427\) | −9.93364e32 | −1.30846 | ||||||||
\(428\) | −1.05194e32 | −0.134569 | ||||||||
\(429\) | −1.24824e32 | −0.155089 | ||||||||
\(430\) | 5.60569e31 | 0.0676509 | ||||||||
\(431\) | 4.25042e32 | 0.498271 | 0.249135 | − | 0.968469i | \(-0.419854\pi\) | ||||
0.249135 | + | 0.968469i | \(0.419854\pi\) | |||||||
\(432\) | −4.64586e31 | −0.0529077 | ||||||||
\(433\) | 2.18224e32 | 0.241437 | 0.120719 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120719 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(434\) | 4.46023e32 | 0.479441 | ||||||||
\(435\) | 6.94870e31 | 0.0725752 | ||||||||
\(436\) | −2.78871e32 | −0.283024 | ||||||||
\(437\) | −1.20189e33 | −1.18535 | ||||||||
\(438\) | −1.62183e31 | −0.0155446 | ||||||||
\(439\) | 1.96041e33 | 1.82617 | 0.913084 | − | 0.407771i | \(-0.133694\pi\) | ||||
0.913084 | + | 0.407771i | \(0.133694\pi\) | |||||||
\(440\) | 3.39935e32 | 0.307778 | ||||||||
\(441\) | −2.76708e32 | −0.243523 | ||||||||
\(442\) | 9.55446e32 | 0.817387 | ||||||||
\(443\) | −1.81076e33 | −1.50596 | −0.752980 | − | 0.658043i | \(-0.771385\pi\) | ||||
−0.752980 | + | 0.658043i | \(0.771385\pi\) | |||||||
\(444\) | −8.44387e31 | −0.0682739 | ||||||||
\(445\) | 1.21262e33 | 0.953286 | ||||||||
\(446\) | 1.57193e33 | 1.20156 | ||||||||
\(447\) | 1.09899e32 | 0.0816866 | ||||||||
\(448\) | −1.93063e32 | −0.139548 | ||||||||
\(449\) | 1.96738e33 | 1.38296 | 0.691480 | − | 0.722396i | \(-0.256959\pi\) | ||||
0.691480 | + | 0.722396i | \(0.256959\pi\) | |||||||
\(450\) | −6.23580e32 | −0.426320 | ||||||||
\(451\) | −3.38807e33 | −2.25292 | ||||||||
\(452\) | −7.70148e32 | −0.498131 | ||||||||
\(453\) | −2.59763e31 | −0.0163437 | ||||||||
\(454\) | −1.17308e32 | −0.0718006 | ||||||||
\(455\) | −1.22465e33 | −0.729239 | ||||||||
\(456\) | 9.42369e31 | 0.0545960 | ||||||||
\(457\) | −6.51681e32 | −0.367352 | −0.183676 | − | 0.982987i | \(-0.558800\pi\) | ||||
−0.183676 | + | 0.982987i | \(0.558800\pi\) | |||||||
\(458\) | −2.12178e33 | −1.16381 | ||||||||
\(459\) | 4.38289e32 | 0.233939 | ||||||||
\(460\) | 4.91174e32 | 0.255131 | ||||||||
\(461\) | −3.73344e32 | −0.188733 | −0.0943666 | − | 0.995538i | \(-0.530083\pi\) | ||||
−0.0943666 | + | 0.995538i | \(0.530083\pi\) | |||||||
\(462\) | −2.37949e32 | −0.117074 | ||||||||
\(463\) | 3.92901e33 | 1.88157 | 0.940787 | − | 0.338999i | \(-0.110088\pi\) | ||||
0.940787 | + | 0.338999i | \(0.110088\pi\) | |||||||
\(464\) | 5.85533e32 | 0.272946 | ||||||||
\(465\) | 8.89714e31 | 0.0403727 | ||||||||
\(466\) | 4.56655e32 | 0.201727 | ||||||||
\(467\) | −2.19321e33 | −0.943235 | −0.471618 | − | 0.881803i | \(-0.656330\pi\) | ||||
−0.471618 | + | 0.881803i | \(0.656330\pi\) | |||||||
\(468\) | −1.23457e33 | −0.516944 | ||||||||
\(469\) | 5.09807e33 | 2.07848 | ||||||||
\(470\) | −3.90850e32 | −0.155162 | ||||||||
\(471\) | −8.15315e31 | −0.0315184 | ||||||||
\(472\) | 5.73045e32 | 0.215732 | ||||||||
\(473\) | 5.82187e32 | 0.213451 | ||||||||
\(474\) | 3.23097e32 | 0.115373 | ||||||||
\(475\) | 2.54424e33 | 0.884886 | ||||||||
\(476\) | 1.82135e33 | 0.617030 | ||||||||
\(477\) | −3.56079e32 | −0.117508 | ||||||||
\(478\) | −4.01989e33 | −1.29230 | ||||||||
\(479\) | −4.26617e33 | −1.33612 | −0.668058 | − | 0.744110i | \(-0.732874\pi\) | ||||
−0.668058 | + | 0.744110i | \(0.732874\pi\) | |||||||
\(480\) | −3.85116e31 | −0.0117510 | ||||||||
\(481\) | −4.51339e33 | −1.34180 | ||||||||
\(482\) | 4.10805e33 | 1.19000 | ||||||||
\(483\) | −3.43815e32 | −0.0970477 | ||||||||
\(484\) | 1.71268e33 | 0.471095 | ||||||||
\(485\) | −2.95327e33 | −0.791648 | ||||||||
\(486\) | −8.51111e32 | −0.222348 | ||||||||
\(487\) | 2.19049e33 | 0.557737 | 0.278869 | − | 0.960329i | \(-0.410041\pi\) | ||||
0.278869 | + | 0.960329i | \(0.410041\pi\) | |||||||
\(488\) | −1.66974e33 | −0.414383 | ||||||||
\(489\) | −7.07517e32 | −0.171150 | ||||||||
\(490\) | −4.61379e32 | −0.108794 | ||||||||
\(491\) | −1.06443e32 | −0.0244681 | −0.0122340 | − | 0.999925i | \(-0.503894\pi\) | ||||
−0.0122340 | + | 0.999925i | \(0.503894\pi\) | |||||||
\(492\) | 3.83839e32 | 0.0860172 | ||||||||
\(493\) | −5.52390e33 | −1.20687 | ||||||||
\(494\) | 5.03712e33 | 1.07299 | ||||||||
\(495\) | 4.14382e33 | 0.860668 | ||||||||
\(496\) | 7.49718e32 | 0.151837 | ||||||||
\(497\) | 3.80409e33 | 0.751269 | ||||||||
\(498\) | −3.60437e30 | −0.000694165 0 | ||||||||
\(499\) | −3.46371e33 | −0.650555 | −0.325278 | − | 0.945619i | \(-0.605458\pi\) | ||||
−0.325278 | + | 0.945619i | \(0.605458\pi\) | |||||||
\(500\) | −2.74478e33 | −0.502784 | ||||||||
\(501\) | 3.74684e32 | 0.0669413 | ||||||||
\(502\) | −4.70607e33 | −0.820090 | ||||||||
\(503\) | 1.02261e34 | 1.73824 | 0.869121 | − | 0.494599i | \(-0.164685\pi\) | ||||
0.869121 | + | 0.494599i | \(0.164685\pi\) | |||||||
\(504\) | −2.35344e33 | −0.390231 | ||||||||
\(505\) | 2.48382e33 | 0.401770 | ||||||||
\(506\) | 5.10116e33 | 0.804984 | ||||||||
\(507\) | 6.46663e31 | 0.00995585 | ||||||||
\(508\) | −6.14275e31 | −0.00922713 | ||||||||
\(509\) | −2.69685e33 | −0.395261 | −0.197630 | − | 0.980277i | \(-0.563325\pi\) | ||||
−0.197630 | + | 0.980277i | \(0.563325\pi\) | |||||||
\(510\) | 3.63318e32 | 0.0519588 | ||||||||
\(511\) | −1.65255e33 | −0.230618 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 2.31066e33 | 0.307093 | ||||||||
\(514\) | −5.26147e33 | −0.682445 | ||||||||
\(515\) | 5.19665e33 | 0.657860 | ||||||||
\(516\) | −6.59567e31 | −0.00814963 | ||||||||
\(517\) | −4.05922e33 | −0.489566 | ||||||||
\(518\) | −8.60379e33 | −1.01290 | ||||||||
\(519\) | −4.64674e32 | −0.0534018 | ||||||||
\(520\) | −2.05851e33 | −0.230946 | ||||||||
\(521\) | −9.39972e33 | −1.02954 | −0.514770 | − | 0.857328i | \(-0.672123\pi\) | ||||
−0.514770 | + | 0.857328i | \(0.672123\pi\) | |||||||
\(522\) | 7.13767e33 | 0.763265 | ||||||||
\(523\) | −4.23584e33 | −0.442250 | −0.221125 | − | 0.975245i | \(-0.570973\pi\) | ||||
−0.221125 | + | 0.975245i | \(0.570973\pi\) | |||||||
\(524\) | −2.31338e33 | −0.235833 | ||||||||
\(525\) | 7.27808e32 | 0.0724479 | ||||||||
\(526\) | 1.01203e34 | 0.983724 | ||||||||
\(527\) | −7.07281e33 | −0.671366 | ||||||||
\(528\) | −3.99968e32 | −0.0370767 | ||||||||
\(529\) | −3.67507e33 | −0.332713 | ||||||||
\(530\) | −5.93721e32 | −0.0524969 | ||||||||
\(531\) | 6.98544e33 | 0.603271 | ||||||||
\(532\) | 9.60216e33 | 0.809979 | ||||||||
\(533\) | 2.05168e34 | 1.69052 | ||||||||
\(534\) | −1.42677e33 | −0.114839 | ||||||||
\(535\) | −2.13813e33 | −0.168117 | ||||||||
\(536\) | 8.56932e33 | 0.658244 | ||||||||
\(537\) | −6.84880e32 | −0.0513968 | ||||||||
\(538\) | −3.41170e33 | −0.250145 | ||||||||
\(539\) | −4.79172e33 | −0.343267 | ||||||||
\(540\) | −9.44294e32 | −0.0660975 | ||||||||
\(541\) | 3.36042e33 | 0.229841 | 0.114921 | − | 0.993375i | \(-0.463339\pi\) | ||||
0.114921 | + | 0.993375i | \(0.463339\pi\) | |||||||
\(542\) | 1.59678e33 | 0.106722 | ||||||||
\(543\) | −6.21740e32 | −0.0406080 | ||||||||
\(544\) | 3.06150e33 | 0.195410 | ||||||||
\(545\) | −5.66820e33 | −0.353581 | ||||||||
\(546\) | 1.44093e33 | 0.0878484 | ||||||||
\(547\) | −1.80091e33 | −0.107313 | −0.0536563 | − | 0.998559i | \(-0.517088\pi\) | ||||
−0.0536563 | + | 0.998559i | \(0.517088\pi\) | |||||||
\(548\) | −7.25247e33 | −0.422405 | ||||||||
\(549\) | −2.03542e34 | −1.15878 | ||||||||
\(550\) | −1.07984e34 | −0.600935 | ||||||||
\(551\) | −2.91220e34 | −1.58426 | ||||||||
\(552\) | −5.77917e32 | −0.0307345 | ||||||||
\(553\) | 3.29216e34 | 1.71166 | ||||||||
\(554\) | −2.35857e34 | −1.19888 | ||||||||
\(555\) | −1.71626e33 | −0.0852944 | ||||||||
\(556\) | −6.72172e32 | −0.0326622 | ||||||||
\(557\) | 3.61276e34 | 1.71652 | 0.858261 | − | 0.513214i | \(-0.171545\pi\) | ||||
0.858261 | + | 0.513214i | \(0.171545\pi\) | |||||||
\(558\) | 9.13909e33 | 0.424596 | ||||||||
\(559\) | −3.52550e33 | −0.160167 | ||||||||
\(560\) | −3.92410e33 | −0.174337 | ||||||||
\(561\) | 3.77328e33 | 0.163940 | ||||||||
\(562\) | 3.00952e33 | 0.127877 | ||||||||
\(563\) | 2.65943e34 | 1.10518 | 0.552591 | − | 0.833452i | \(-0.313639\pi\) | ||||
0.552591 | + | 0.833452i | \(0.313639\pi\) | |||||||
\(564\) | 4.59875e32 | 0.0186918 | ||||||||
\(565\) | −1.56537e34 | −0.622315 | ||||||||
\(566\) | 4.73876e33 | 0.184272 | ||||||||
\(567\) | −2.83562e34 | −1.07860 | ||||||||
\(568\) | 6.39428e33 | 0.237923 | ||||||||
\(569\) | 7.96966e33 | 0.290093 | 0.145046 | − | 0.989425i | \(-0.453667\pi\) | ||||
0.145046 | + | 0.989425i | \(0.453667\pi\) | |||||||
\(570\) | 1.91541e33 | 0.0682066 | ||||||||
\(571\) | 4.13744e34 | 1.44139 | 0.720693 | − | 0.693254i | \(-0.243824\pi\) | ||||
0.720693 | + | 0.693254i | \(0.243824\pi\) | |||||||
\(572\) | −2.13789e34 | −0.728678 | ||||||||
\(573\) | −3.51901e33 | −0.117351 | ||||||||
\(574\) | 3.91108e34 | 1.27614 | ||||||||
\(575\) | −1.56028e34 | −0.498142 | ||||||||
\(576\) | −3.95589e33 | −0.123584 | ||||||||
\(577\) | −3.07665e34 | −0.940548 | −0.470274 | − | 0.882520i | \(-0.655845\pi\) | ||||
−0.470274 | + | 0.882520i | \(0.655845\pi\) | |||||||
\(578\) | −5.24558e33 | −0.156926 | ||||||||
\(579\) | −3.68573e32 | −0.0107905 | ||||||||
\(580\) | 1.19012e34 | 0.340991 | ||||||||
\(581\) | −3.67263e32 | −0.0102985 | ||||||||
\(582\) | 3.47483e33 | 0.0953666 | ||||||||
\(583\) | −6.16617e33 | −0.165637 | ||||||||
\(584\) | −2.77776e33 | −0.0730356 | ||||||||
\(585\) | −2.50933e34 | −0.645818 | ||||||||
\(586\) | 4.08143e33 | 0.102824 | ||||||||
\(587\) | −2.58213e34 | −0.636798 | −0.318399 | − | 0.947957i | \(-0.603145\pi\) | ||||
−0.318399 | + | 0.947957i | \(0.603145\pi\) | |||||||
\(588\) | 5.42860e32 | 0.0131060 | ||||||||
\(589\) | −3.72879e34 | −0.881307 | ||||||||
\(590\) | 1.16474e34 | 0.269513 | ||||||||
\(591\) | −1.80708e33 | −0.0409386 | ||||||||
\(592\) | −1.44621e34 | −0.320781 | ||||||||
\(593\) | 4.00098e34 | 0.868925 | 0.434463 | − | 0.900690i | \(-0.356938\pi\) | ||||
0.434463 | + | 0.900690i | \(0.356938\pi\) | |||||||
\(594\) | −9.80710e33 | −0.208550 | ||||||||
\(595\) | 3.70198e34 | 0.770854 | ||||||||
\(596\) | 1.88228e34 | 0.383801 | ||||||||
\(597\) | 3.16920e33 | 0.0632806 | ||||||||
\(598\) | −3.08906e34 | −0.604034 | ||||||||
\(599\) | −2.84196e34 | −0.544230 | −0.272115 | − | 0.962265i | \(-0.587723\pi\) | ||||
−0.272115 | + | 0.962265i | \(0.587723\pi\) | |||||||
\(600\) | 1.22337e33 | 0.0229439 | ||||||||
\(601\) | −1.02008e34 | −0.187371 | −0.0936856 | − | 0.995602i | \(-0.529865\pi\) | ||||
−0.0936856 | + | 0.995602i | \(0.529865\pi\) | |||||||
\(602\) | −6.72058e33 | −0.120907 | ||||||||
\(603\) | 1.04460e35 | 1.84071 | ||||||||
\(604\) | −4.44904e33 | −0.0767900 | ||||||||
\(605\) | 3.48110e34 | 0.588538 | ||||||||
\(606\) | −2.92246e33 | −0.0483996 | ||||||||
\(607\) | 7.37377e34 | 1.19628 | 0.598138 | − | 0.801393i | \(-0.295908\pi\) | ||||
0.598138 | + | 0.801393i | \(0.295908\pi\) | |||||||
\(608\) | 1.61402e34 | 0.256516 | ||||||||
\(609\) | −8.33070e33 | −0.129708 | ||||||||
\(610\) | −3.39384e34 | −0.517688 | ||||||||
\(611\) | 2.45811e34 | 0.367355 | ||||||||
\(612\) | 3.73198e34 | 0.546445 | ||||||||
\(613\) | −9.86145e34 | −1.41477 | −0.707384 | − | 0.706830i | \(-0.750125\pi\) | ||||
−0.707384 | + | 0.706830i | \(0.750125\pi\) | |||||||
\(614\) | −4.57127e34 | −0.642587 | ||||||||
\(615\) | 7.80172e33 | 0.107461 | ||||||||
\(616\) | −4.07543e34 | −0.550065 | ||||||||
\(617\) | −6.22897e34 | −0.823857 | −0.411928 | − | 0.911216i | \(-0.635145\pi\) | ||||
−0.411928 | + | 0.911216i | \(0.635145\pi\) | |||||||
\(618\) | −6.11440e33 | −0.0792497 | ||||||||
\(619\) | −1.66187e34 | −0.211089 | −0.105544 | − | 0.994415i | \(-0.533659\pi\) | ||||
−0.105544 | + | 0.994415i | \(0.533659\pi\) | |||||||
\(620\) | 1.52384e34 | 0.189689 | ||||||||
\(621\) | −1.41704e34 | −0.172876 | ||||||||
\(622\) | 3.47060e34 | 0.414978 | ||||||||
\(623\) | −1.45379e35 | −1.70373 | ||||||||
\(624\) | 2.42205e33 | 0.0278212 | ||||||||
\(625\) | −1.62662e33 | −0.0183141 | ||||||||
\(626\) | 4.74246e34 | 0.523389 | ||||||||
\(627\) | 1.98928e34 | 0.215204 | ||||||||
\(628\) | −1.39641e34 | −0.148088 | ||||||||
\(629\) | 1.36435e35 | 1.41838 | ||||||||
\(630\) | −4.78349e34 | −0.487515 | ||||||||
\(631\) | −5.71133e34 | −0.570650 | −0.285325 | − | 0.958431i | \(-0.592102\pi\) | ||||
−0.285325 | + | 0.958431i | \(0.592102\pi\) | |||||||
\(632\) | 5.53377e34 | 0.542073 | ||||||||
\(633\) | 7.19801e33 | 0.0691299 | ||||||||
\(634\) | 8.07696e34 | 0.760558 | ||||||||
\(635\) | −1.24855e33 | −0.0115274 | ||||||||
\(636\) | 6.98573e32 | 0.00632409 | ||||||||
\(637\) | 2.90168e34 | 0.257576 | ||||||||
\(638\) | 1.23602e35 | 1.07589 | ||||||||
\(639\) | 7.79465e34 | 0.665328 | ||||||||
\(640\) | −6.59600e33 | −0.0552117 | ||||||||
\(641\) | 1.28313e34 | 0.105329 | 0.0526643 | − | 0.998612i | \(-0.483229\pi\) | ||||
0.0526643 | + | 0.998612i | \(0.483229\pi\) | |||||||
\(642\) | 2.51572e33 | 0.0202523 | ||||||||
\(643\) | −1.37614e35 | −1.08649 | −0.543246 | − | 0.839574i | \(-0.682805\pi\) | ||||
−0.543246 | + | 0.839574i | \(0.682805\pi\) | |||||||
\(644\) | −5.88862e34 | −0.455974 | ||||||||
\(645\) | −1.34060e33 | −0.0101813 | ||||||||
\(646\) | −1.52266e35 | −1.13422 | ||||||||
\(647\) | 9.39917e34 | 0.686730 | 0.343365 | − | 0.939202i | \(-0.388433\pi\) | ||||
0.343365 | + | 0.939202i | \(0.388433\pi\) | |||||||
\(648\) | −4.76638e34 | −0.341587 | ||||||||
\(649\) | 1.20966e35 | 0.850364 | ||||||||
\(650\) | 6.53912e34 | 0.450923 | ||||||||
\(651\) | −1.06666e34 | −0.0721549 | ||||||||
\(652\) | −1.21179e35 | −0.804139 | ||||||||
\(653\) | −1.48718e35 | −0.968164 | −0.484082 | − | 0.875023i | \(-0.660846\pi\) | ||||
−0.484082 | + | 0.875023i | \(0.660846\pi\) | |||||||
\(654\) | 6.66921e33 | 0.0425944 | ||||||||
\(655\) | −4.70206e34 | −0.294626 | ||||||||
\(656\) | 6.57412e34 | 0.404148 | ||||||||
\(657\) | −3.38611e34 | −0.204237 | ||||||||
\(658\) | 4.68584e34 | 0.277309 | ||||||||
\(659\) | −1.21873e35 | −0.707683 | −0.353842 | − | 0.935305i | \(-0.615125\pi\) | ||||
−0.353842 | + | 0.935305i | \(0.615125\pi\) | |||||||
\(660\) | −8.12955e33 | −0.0463199 | ||||||||
\(661\) | 2.07522e35 | 1.16023 | 0.580117 | − | 0.814533i | \(-0.303007\pi\) | ||||
0.580117 | + | 0.814533i | \(0.303007\pi\) | |||||||
\(662\) | −1.95425e35 | −1.07215 | ||||||||
\(663\) | −2.28495e34 | −0.123015 | ||||||||
\(664\) | −6.17331e32 | −0.00326150 | ||||||||
\(665\) | 1.95169e35 | 1.01190 | ||||||||
\(666\) | −1.76293e35 | −0.897032 | ||||||||
\(667\) | 1.78594e35 | 0.891852 | ||||||||
\(668\) | 6.41733e34 | 0.314520 | ||||||||
\(669\) | −3.75927e34 | −0.180833 | ||||||||
\(670\) | 1.74176e35 | 0.822343 | ||||||||
\(671\) | −3.52471e35 | −1.63340 | ||||||||
\(672\) | 4.61710e33 | 0.0210017 | ||||||||
\(673\) | −2.63064e34 | −0.117455 | −0.0587277 | − | 0.998274i | \(-0.518704\pi\) | ||||
−0.0587277 | + | 0.998274i | \(0.518704\pi\) | |||||||
\(674\) | 1.34642e35 | 0.590110 | ||||||||
\(675\) | 2.99967e34 | 0.129055 | ||||||||
\(676\) | 1.10756e34 | 0.0467771 | ||||||||
\(677\) | 1.31255e35 | 0.544198 | 0.272099 | − | 0.962269i | \(-0.412282\pi\) | ||||
0.272099 | + | 0.962269i | \(0.412282\pi\) | |||||||
\(678\) | 1.84181e34 | 0.0749677 | ||||||||
\(679\) | 3.54064e35 | 1.41485 | ||||||||
\(680\) | 6.22265e34 | 0.244126 | ||||||||
\(681\) | 2.80542e33 | 0.0108058 | ||||||||
\(682\) | 1.58260e35 | 0.598505 | ||||||||
\(683\) | −4.53998e35 | −1.68576 | −0.842879 | − | 0.538104i | \(-0.819141\pi\) | ||||
−0.842879 | + | 0.538104i | \(0.819141\pi\) | |||||||
\(684\) | 1.96750e35 | 0.717321 | ||||||||
\(685\) | −1.47410e35 | −0.527710 | ||||||||
\(686\) | −1.69255e35 | −0.594963 | ||||||||
\(687\) | 5.07426e34 | 0.175151 | ||||||||
\(688\) | −1.12966e34 | −0.0382906 | ||||||||
\(689\) | 3.73399e34 | 0.124289 | ||||||||
\(690\) | −1.17464e34 | −0.0383966 | ||||||||
\(691\) | 1.42914e35 | 0.458773 | 0.229387 | − | 0.973335i | \(-0.426328\pi\) | ||||
0.229387 | + | 0.973335i | \(0.426328\pi\) | |||||||
\(692\) | −7.95860e34 | −0.250906 | ||||||||
\(693\) | −4.96796e35 | −1.53820 | ||||||||
\(694\) | −1.28300e35 | −0.390152 | ||||||||
\(695\) | −1.36622e34 | −0.0408049 | ||||||||
\(696\) | −1.40030e34 | −0.0410778 | ||||||||
\(697\) | −6.20201e35 | −1.78699 | ||||||||
\(698\) | −1.38366e35 | −0.391593 | ||||||||
\(699\) | −1.09209e34 | −0.0303595 | ||||||||
\(700\) | 1.24654e35 | 0.340393 | ||||||||
\(701\) | 4.38686e35 | 1.17673 | 0.588367 | − | 0.808594i | \(-0.299771\pi\) | ||||
0.588367 | + | 0.808594i | \(0.299771\pi\) | |||||||
\(702\) | 5.93879e34 | 0.156489 | ||||||||
\(703\) | 7.19285e35 | 1.86191 | ||||||||
\(704\) | −6.85037e34 | −0.174203 | ||||||||
\(705\) | 9.34719e33 | 0.0233516 | ||||||||
\(706\) | −1.79602e35 | −0.440811 | ||||||||
\(707\) | −2.97781e35 | −0.718050 | ||||||||
\(708\) | −1.37044e34 | −0.0324672 | ||||||||
\(709\) | 3.53471e35 | 0.822766 | 0.411383 | − | 0.911463i | \(-0.365046\pi\) | ||||
0.411383 | + | 0.911463i | \(0.365046\pi\) | |||||||
\(710\) | 1.29967e35 | 0.297237 | ||||||||
\(711\) | 6.74569e35 | 1.51585 | ||||||||
\(712\) | −2.44367e35 | −0.539563 | ||||||||
\(713\) | 2.28672e35 | 0.496127 | ||||||||
\(714\) | −4.35576e34 | −0.0928617 | ||||||||
\(715\) | −4.34538e35 | −0.910337 | ||||||||
\(716\) | −1.17301e35 | −0.241485 | ||||||||
\(717\) | 9.61357e34 | 0.194489 | ||||||||
\(718\) | 6.16148e35 | 1.22498 | ||||||||
\(719\) | 8.06410e35 | 1.57560 | 0.787798 | − | 0.615934i | \(-0.211221\pi\) | ||||
0.787798 | + | 0.615934i | \(0.211221\pi\) | |||||||
\(720\) | −8.04055e34 | −0.154394 | ||||||||
\(721\) | −6.23019e35 | −1.17574 | ||||||||
\(722\) | −4.21509e35 | −0.781793 | ||||||||
\(723\) | −9.82443e34 | −0.179093 | ||||||||
\(724\) | −1.06487e35 | −0.190794 | ||||||||
\(725\) | −3.78058e35 | −0.665784 | ||||||||
\(726\) | −4.09587e34 | −0.0708987 | ||||||||
\(727\) | −4.49933e35 | −0.765539 | −0.382770 | − | 0.923844i | \(-0.625030\pi\) | ||||
−0.382770 | + | 0.923844i | \(0.625030\pi\) | |||||||
\(728\) | 2.46792e35 | 0.412751 | ||||||||
\(729\) | −5.67325e35 | −0.932691 | ||||||||
\(730\) | −5.64595e34 | −0.0912433 | ||||||||
\(731\) | 1.06572e35 | 0.169307 | ||||||||
\(732\) | 3.99320e34 | 0.0623637 | ||||||||
\(733\) | −1.09791e36 | −1.68565 | −0.842827 | − | 0.538185i | \(-0.819110\pi\) | ||||
−0.842827 | + | 0.538185i | \(0.819110\pi\) | |||||||
\(734\) | 2.83974e35 | 0.428626 | ||||||||
\(735\) | 1.10339e34 | 0.0163733 | ||||||||
\(736\) | −9.89815e34 | −0.144405 | ||||||||
\(737\) | 1.80893e36 | 2.59464 | ||||||||
\(738\) | 8.01388e35 | 1.13016 | ||||||||
\(739\) | −6.34879e35 | −0.880309 | −0.440155 | − | 0.897922i | \(-0.645076\pi\) | ||||
−0.440155 | + | 0.897922i | \(0.645076\pi\) | |||||||
\(740\) | −2.93949e35 | −0.400752 | ||||||||
\(741\) | −1.20463e35 | −0.161483 | ||||||||
\(742\) | 7.11803e34 | 0.0938234 | ||||||||
\(743\) | −6.17895e35 | −0.800856 | −0.400428 | − | 0.916328i | \(-0.631139\pi\) | ||||
−0.400428 | + | 0.916328i | \(0.631139\pi\) | |||||||
\(744\) | −1.79295e34 | −0.0228511 | ||||||||
\(745\) | 3.82583e35 | 0.479481 | ||||||||
\(746\) | −2.51662e35 | −0.310158 | ||||||||
\(747\) | −7.52529e33 | −0.00912044 | ||||||||
\(748\) | 6.46262e35 | 0.770262 | ||||||||
\(749\) | 2.56337e35 | 0.300461 | ||||||||
\(750\) | 6.56414e34 | 0.0756680 | ||||||||
\(751\) | 6.31220e35 | 0.715619 | 0.357809 | − | 0.933795i | \(-0.383524\pi\) | ||||
0.357809 | + | 0.933795i | \(0.383524\pi\) | |||||||
\(752\) | 7.87641e34 | 0.0878224 | ||||||||
\(753\) | 1.12546e35 | 0.123422 | ||||||||
\(754\) | −7.48486e35 | −0.807312 | ||||||||
\(755\) | −9.04290e34 | −0.0959336 | ||||||||
\(756\) | 1.13210e35 | 0.118131 | ||||||||
\(757\) | 2.78268e35 | 0.285605 | 0.142802 | − | 0.989751i | \(-0.454389\pi\) | ||||
0.142802 | + | 0.989751i | \(0.454389\pi\) | |||||||
\(758\) | −2.56401e35 | −0.258854 | ||||||||
\(759\) | −1.21994e35 | −0.121148 | ||||||||
\(760\) | 3.28058e35 | 0.320466 | ||||||||
\(761\) | 2.91390e35 | 0.280005 | 0.140003 | − | 0.990151i | \(-0.455289\pi\) | ||||
0.140003 | + | 0.990151i | \(0.455289\pi\) | |||||||
\(762\) | 1.46904e33 | 0.00138866 | ||||||||
\(763\) | 6.79552e35 | 0.631926 | ||||||||
\(764\) | −6.02712e35 | −0.551369 | ||||||||
\(765\) | 7.58543e35 | 0.682673 | ||||||||
\(766\) | −8.02238e35 | −0.710303 | ||||||||
\(767\) | −7.32523e35 | −0.638086 | ||||||||
\(768\) | 7.76087e33 | 0.00665113 | ||||||||
\(769\) | −1.59678e36 | −1.34637 | −0.673187 | − | 0.739473i | \(-0.735075\pi\) | ||||
−0.673187 | + | 0.739473i | \(0.735075\pi\) | |||||||
\(770\) | −8.28351e35 | −0.687196 | ||||||||
\(771\) | 1.25828e35 | 0.102707 | ||||||||
\(772\) | −6.31267e34 | −0.0506987 | ||||||||
\(773\) | 1.26764e36 | 1.00173 | 0.500866 | − | 0.865525i | \(-0.333015\pi\) | ||||
0.500866 | + | 0.865525i | \(0.333015\pi\) | |||||||
\(774\) | −1.37706e35 | −0.107076 | ||||||||
\(775\) | −4.84067e35 | −0.370368 | ||||||||
\(776\) | 5.95144e35 | 0.448075 | ||||||||
\(777\) | 2.05760e35 | 0.152440 | ||||||||
\(778\) | 2.27695e35 | 0.166000 | ||||||||
\(779\) | −3.26970e36 | −2.34580 | ||||||||
\(780\) | 4.92294e34 | 0.0347569 | ||||||||
\(781\) | 1.34979e36 | 0.937838 | ||||||||
\(782\) | 9.33788e35 | 0.638505 | ||||||||
\(783\) | −3.43351e35 | −0.231055 | ||||||||
\(784\) | 9.29772e34 | 0.0615780 | ||||||||
\(785\) | −2.83828e35 | −0.185006 | ||||||||
\(786\) | 5.53245e34 | 0.0354924 | ||||||||
\(787\) | 1.69750e36 | 1.07183 | 0.535915 | − | 0.844272i | \(-0.319967\pi\) | ||||
0.535915 | + | 0.844272i | \(0.319967\pi\) | |||||||
\(788\) | −3.09503e35 | −0.192348 | ||||||||
\(789\) | −2.42028e35 | −0.148048 | ||||||||
\(790\) | 1.12477e36 | 0.677211 | ||||||||
\(791\) | 1.87669e36 | 1.11221 | ||||||||
\(792\) | −8.35063e35 | −0.487141 | ||||||||
\(793\) | 2.13443e36 | 1.22565 | ||||||||
\(794\) | 1.64129e36 | 0.927748 | ||||||||
\(795\) | 1.41988e34 | 0.00790067 | ||||||||
\(796\) | 5.42798e35 | 0.297321 | ||||||||
\(797\) | −1.94040e36 | −1.04631 | −0.523157 | − | 0.852236i | \(-0.675246\pi\) | ||||
−0.523157 | + | 0.852236i | \(0.675246\pi\) | |||||||
\(798\) | −2.29636e35 | −0.121900 | ||||||||
\(799\) | −7.43058e35 | −0.388319 | ||||||||
\(800\) | 2.09530e35 | 0.107801 | ||||||||
\(801\) | −2.97884e36 | −1.50883 | ||||||||
\(802\) | 1.14608e36 | 0.571525 | ||||||||
\(803\) | −5.86368e35 | −0.287889 | ||||||||
\(804\) | −2.04936e35 | −0.0990643 | ||||||||
\(805\) | −1.19689e36 | −0.569647 | ||||||||
\(806\) | −9.58363e35 | −0.449099 | ||||||||
\(807\) | 8.15908e34 | 0.0376463 | ||||||||
\(808\) | −5.00539e35 | −0.227403 | ||||||||
\(809\) | 8.07086e35 | 0.361047 | 0.180523 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180523 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(810\) | −9.68791e35 | −0.426744 | ||||||||
\(811\) | 1.23381e36 | 0.535165 | 0.267583 | − | 0.963535i | \(-0.413775\pi\) | ||||
0.267583 | + | 0.963535i | \(0.413775\pi\) | |||||||
\(812\) | −1.42682e36 | −0.609424 | ||||||||
\(813\) | −3.81872e34 | −0.0160615 | ||||||||
\(814\) | −3.05285e36 | −1.26445 | ||||||||
\(815\) | −2.46302e36 | −1.00461 | ||||||||
\(816\) | −7.32158e34 | −0.0294088 | ||||||||
\(817\) | 5.61847e35 | 0.222250 | ||||||||
\(818\) | 2.95796e36 | 1.15233 | ||||||||
\(819\) | 3.00840e36 | 1.15422 | ||||||||
\(820\) | 1.33622e36 | 0.504901 | ||||||||
\(821\) | −6.01008e34 | −0.0223661 | −0.0111831 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111831 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(822\) | 1.73443e35 | 0.0635710 | ||||||||
\(823\) | 1.64344e36 | 0.593274 | 0.296637 | − | 0.954990i | \(-0.404135\pi\) | ||||
0.296637 | + | 0.954990i | \(0.404135\pi\) | |||||||
\(824\) | −1.04723e36 | −0.372351 | ||||||||
\(825\) | 2.58245e35 | 0.0904395 | ||||||||
\(826\) | −1.39639e36 | −0.481679 | ||||||||
\(827\) | 4.86438e36 | 1.65276 | 0.826378 | − | 0.563116i | \(-0.190398\pi\) | ||||
0.826378 | + | 0.563116i | \(0.190398\pi\) | |||||||
\(828\) | −1.20659e36 | −0.403813 | ||||||||
\(829\) | −1.30083e36 | −0.428834 | −0.214417 | − | 0.976742i | \(-0.568785\pi\) | ||||
−0.214417 | + | 0.976742i | \(0.568785\pi\) | |||||||
\(830\) | −1.25476e34 | −0.00407458 | ||||||||
\(831\) | 5.64053e35 | 0.180429 | ||||||||
\(832\) | 4.14832e35 | 0.130716 | ||||||||
\(833\) | −8.77144e35 | −0.272275 | ||||||||
\(834\) | 1.60750e34 | 0.00491560 | ||||||||
\(835\) | 1.30435e36 | 0.392930 | ||||||||
\(836\) | 3.40710e36 | 1.01113 | ||||||||
\(837\) | −4.39627e35 | −0.128533 | ||||||||
\(838\) | −2.10154e36 | −0.605323 | ||||||||
\(839\) | −3.56272e36 | −1.01101 | −0.505506 | − | 0.862823i | \(-0.668694\pi\) | ||||
−0.505506 | + | 0.862823i | \(0.668694\pi\) | |||||||
\(840\) | 9.38450e34 | 0.0262373 | ||||||||
\(841\) | 6.96997e35 | 0.191991 | ||||||||
\(842\) | 5.36538e35 | 0.145613 | ||||||||
\(843\) | −7.19727e34 | −0.0192452 | ||||||||
\(844\) | 1.23282e36 | 0.324803 | ||||||||
\(845\) | 2.25117e35 | 0.0584385 | ||||||||
\(846\) | 9.60138e35 | 0.245586 | ||||||||
\(847\) | −4.17344e36 | −1.05184 | ||||||||
\(848\) | 1.19647e35 | 0.0297134 | ||||||||
\(849\) | −1.13328e35 | −0.0277325 | ||||||||
\(850\) | −1.97670e36 | −0.476656 | ||||||||
\(851\) | −4.41108e36 | −1.04816 | ||||||||
\(852\) | −1.52919e35 | −0.0358070 | ||||||||
\(853\) | −2.91289e36 | −0.672142 | −0.336071 | − | 0.941837i | \(-0.609098\pi\) | ||||
−0.336071 | + | 0.941837i | \(0.609098\pi\) | |||||||
\(854\) | 4.06882e36 | 0.925220 | ||||||||
\(855\) | 3.99905e36 | 0.896148 | ||||||||
\(856\) | 4.30876e35 | 0.0951546 | ||||||||
\(857\) | −6.85495e36 | −1.49192 | −0.745958 | − | 0.665993i | \(-0.768008\pi\) | ||||
−0.745958 | + | 0.665993i | \(0.768008\pi\) | |||||||
\(858\) | 5.11278e35 | 0.109665 | ||||||||
\(859\) | 6.94361e36 | 1.46781 | 0.733907 | − | 0.679250i | \(-0.237695\pi\) | ||||
0.733907 | + | 0.679250i | \(0.237695\pi\) | |||||||
\(860\) | −2.29609e35 | −0.0478364 | ||||||||
\(861\) | −9.35337e35 | −0.192056 | ||||||||
\(862\) | −1.74097e36 | −0.352331 | ||||||||
\(863\) | −5.37478e35 | −0.107208 | −0.0536038 | − | 0.998562i | \(-0.517071\pi\) | ||||
−0.0536038 | + | 0.998562i | \(0.517071\pi\) | |||||||
\(864\) | 1.90294e35 | 0.0374114 | ||||||||
\(865\) | −1.61763e36 | −0.313456 | ||||||||
\(866\) | −8.93846e35 | −0.170722 | ||||||||
\(867\) | 1.25448e35 | 0.0236171 | ||||||||
\(868\) | −1.82691e36 | −0.339016 | ||||||||
\(869\) | 1.16814e37 | 2.13673 | ||||||||
\(870\) | −2.84619e35 | −0.0513184 | ||||||||
\(871\) | −1.09542e37 | −1.94694 | ||||||||
\(872\) | 1.14226e36 | 0.200128 | ||||||||
\(873\) | 7.25483e36 | 1.25300 | ||||||||
\(874\) | 4.92294e36 | 0.838169 | ||||||||
\(875\) | 6.68845e36 | 1.12260 | ||||||||
\(876\) | 6.64304e34 | 0.0109917 | ||||||||
\(877\) | 1.45532e36 | 0.237391 | 0.118695 | − | 0.992931i | \(-0.462129\pi\) | ||||
0.118695 | + | 0.992931i | \(0.462129\pi\) | |||||||
\(878\) | −8.02985e36 | −1.29130 | ||||||||
\(879\) | −9.76076e34 | −0.0154747 | ||||||||
\(880\) | −1.39237e36 | −0.217632 | ||||||||
\(881\) | 7.73993e36 | 1.19272 | 0.596360 | − | 0.802717i | \(-0.296613\pi\) | ||||
0.596360 | + | 0.802717i | \(0.296613\pi\) | |||||||
\(882\) | 1.13340e36 | 0.172197 | ||||||||
\(883\) | −1.08821e35 | −0.0163006 | −0.00815031 | − | 0.999967i | \(-0.502594\pi\) | ||||
−0.00815031 | + | 0.999967i | \(0.502594\pi\) | |||||||
\(884\) | −3.91351e36 | −0.577980 | ||||||||
\(885\) | −2.78549e35 | −0.0405612 | ||||||||
\(886\) | 7.41686e36 | 1.06488 | ||||||||
\(887\) | −7.82913e36 | −1.10833 | −0.554164 | − | 0.832407i | \(-0.686962\pi\) | ||||
−0.554164 | + | 0.832407i | \(0.686962\pi\) | |||||||
\(888\) | 3.45861e35 | 0.0482769 | ||||||||
\(889\) | 1.49686e35 | 0.0206020 | ||||||||
\(890\) | −4.96688e36 | −0.674075 | ||||||||
\(891\) | −1.00615e37 | −1.34646 | ||||||||
\(892\) | −6.43861e36 | −0.849634 | ||||||||
\(893\) | −3.91741e36 | −0.509748 | ||||||||
\(894\) | −4.50148e35 | −0.0577612 | ||||||||
\(895\) | −2.38421e36 | −0.301687 | ||||||||
\(896\) | 7.90785e35 | 0.0986753 | ||||||||
\(897\) | 7.38750e35 | 0.0909059 | ||||||||
\(898\) | −8.05840e36 | −0.977900 | ||||||||
\(899\) | 5.54076e36 | 0.663091 | ||||||||
\(900\) | 2.55418e36 | 0.301454 | ||||||||
\(901\) | −1.12874e36 | −0.131382 | ||||||||
\(902\) | 1.38775e37 | 1.59305 | ||||||||
\(903\) | 1.60723e35 | 0.0181962 | ||||||||
\(904\) | 3.15453e36 | 0.352232 | ||||||||
\(905\) | −2.16441e36 | −0.238359 | ||||||||
\(906\) | 1.06399e35 | 0.0115567 | ||||||||
\(907\) | 1.06412e36 | 0.113999 | 0.0569993 | − | 0.998374i | \(-0.481847\pi\) | ||||
0.0569993 | + | 0.998374i | \(0.481847\pi\) | |||||||
\(908\) | 4.80492e35 | 0.0507707 | ||||||||
\(909\) | −6.10159e36 | −0.635909 | ||||||||
\(910\) | 5.01617e36 | 0.515650 | ||||||||
\(911\) | 7.34268e36 | 0.744517 | 0.372259 | − | 0.928129i | \(-0.378583\pi\) | ||||
0.372259 | + | 0.928129i | \(0.378583\pi\) | |||||||
\(912\) | −3.85994e35 | −0.0386052 | ||||||||
\(913\) | −1.30314e35 | −0.0128561 | ||||||||
\(914\) | 2.66928e36 | 0.259757 | ||||||||
\(915\) | 8.11637e35 | 0.0779109 | ||||||||
\(916\) | 8.69083e36 | 0.822939 | ||||||||
\(917\) | 5.63723e36 | 0.526561 | ||||||||
\(918\) | −1.79523e36 | −0.165420 | ||||||||
\(919\) | 5.22115e36 | 0.474594 | 0.237297 | − | 0.971437i | \(-0.423738\pi\) | ||||
0.237297 | + | 0.971437i | \(0.423738\pi\) | |||||||
\(920\) | −2.01185e36 | −0.180405 | ||||||||
\(921\) | 1.09322e36 | 0.0967080 | ||||||||
\(922\) | 1.52922e36 | 0.133454 | ||||||||
\(923\) | −8.17379e36 | −0.703724 | ||||||||
\(924\) | 9.74640e35 | 0.0827836 | ||||||||
\(925\) | 9.33766e36 | 0.782467 | ||||||||
\(926\) | −1.60932e37 | −1.33047 | ||||||||
\(927\) | −1.27658e37 | −1.04124 | ||||||||
\(928\) | −2.39834e36 | −0.193002 | ||||||||
\(929\) | −1.16329e37 | −0.923618 | −0.461809 | − | 0.886979i | \(-0.652799\pi\) | ||||
−0.461809 | + | 0.886979i | \(0.652799\pi\) | |||||||
\(930\) | −3.64427e35 | −0.0285478 | ||||||||
\(931\) | −4.62431e36 | −0.357418 | ||||||||
\(932\) | −1.87046e36 | −0.142643 | ||||||||
\(933\) | −8.29996e35 | −0.0624533 | ||||||||
\(934\) | 8.98341e36 | 0.666968 | ||||||||
\(935\) | 1.31356e37 | 0.962287 | ||||||||
\(936\) | 5.05681e36 | 0.365535 | ||||||||
\(937\) | 5.72513e36 | 0.408358 | 0.204179 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204179 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(938\) | −2.08817e37 | −1.46970 | ||||||||
\(939\) | −1.13416e36 | −0.0787690 | ||||||||
\(940\) | 1.60092e36 | 0.109716 | ||||||||
\(941\) | −2.32727e37 | −1.57390 | −0.786950 | − | 0.617016i | \(-0.788341\pi\) | ||||
−0.786950 | + | 0.617016i | \(0.788341\pi\) | |||||||
\(942\) | 3.33953e35 | 0.0222869 | ||||||||
\(943\) | 2.00518e37 | 1.32055 | ||||||||
\(944\) | −2.34719e36 | −0.152545 | ||||||||
\(945\) | 2.30105e36 | 0.147580 | ||||||||
\(946\) | −2.38464e36 | −0.150933 | ||||||||
\(947\) | 2.10624e37 | 1.31563 | 0.657814 | − | 0.753180i | \(-0.271481\pi\) | ||||
0.657814 | + | 0.753180i | \(0.271481\pi\) | |||||||
\(948\) | −1.32340e36 | −0.0815809 | ||||||||
\(949\) | 3.55081e36 | 0.216023 | ||||||||
\(950\) | −1.04212e37 | −0.625709 | ||||||||
\(951\) | −1.93161e36 | −0.114462 | ||||||||
\(952\) | −7.46024e36 | −0.436306 | ||||||||
\(953\) | −1.00956e36 | −0.0582736 | −0.0291368 | − | 0.999575i | \(-0.509276\pi\) | ||||
−0.0291368 | + | 0.999575i | \(0.509276\pi\) | |||||||
\(954\) | 1.45850e36 | 0.0830905 | ||||||||
\(955\) | −1.22504e37 | −0.688825 | ||||||||
\(956\) | 1.64654e37 | 0.913797 | ||||||||
\(957\) | −2.95595e36 | −0.161919 | ||||||||
\(958\) | 1.74742e37 | 0.944776 | ||||||||
\(959\) | 1.76728e37 | 0.943131 | ||||||||
\(960\) | 1.57744e35 | 0.00830924 | ||||||||
\(961\) | −1.21384e37 | −0.631130 | ||||||||
\(962\) | 1.84868e37 | 0.948799 | ||||||||
\(963\) | 5.25239e36 | 0.266090 | ||||||||
\(964\) | −1.68266e37 | −0.841459 | ||||||||
\(965\) | −1.28308e36 | −0.0633378 | ||||||||
\(966\) | 1.40826e36 | 0.0686231 | ||||||||
\(967\) | 5.41536e36 | 0.260493 | 0.130247 | − | 0.991482i | \(-0.458423\pi\) | ||||
0.130247 | + | 0.991482i | \(0.458423\pi\) | |||||||
\(968\) | −7.01512e36 | −0.333114 | ||||||||
\(969\) | 3.64146e36 | 0.170698 | ||||||||
\(970\) | 1.20966e37 | 0.559779 | ||||||||
\(971\) | −5.44528e36 | −0.248759 | −0.124380 | − | 0.992235i | \(-0.539694\pi\) | ||||
−0.124380 | + | 0.992235i | \(0.539694\pi\) | |||||||
\(972\) | 3.48615e36 | 0.157224 | ||||||||
\(973\) | 1.63795e36 | 0.0729271 | ||||||||
\(974\) | −8.97226e36 | −0.394380 | ||||||||
\(975\) | −1.56383e36 | −0.0678629 | ||||||||
\(976\) | 6.83926e36 | 0.293013 | ||||||||
\(977\) | −3.00155e37 | −1.26959 | −0.634794 | − | 0.772681i | \(-0.718915\pi\) | ||||
−0.634794 | + | 0.772681i | \(0.718915\pi\) | |||||||
\(978\) | 2.89799e36 | 0.121021 | ||||||||
\(979\) | −5.15842e37 | −2.12683 | ||||||||
\(980\) | 1.88981e36 | 0.0769293 | ||||||||
\(981\) | 1.39242e37 | 0.559637 | ||||||||
\(982\) | 4.35992e35 | 0.0173015 | ||||||||
\(983\) | 2.29888e36 | 0.0900737 | 0.0450368 | − | 0.998985i | \(-0.485659\pi\) | ||||
0.0450368 | + | 0.998985i | \(0.485659\pi\) | |||||||
\(984\) | −1.57220e36 | −0.0608233 | ||||||||
\(985\) | −6.29081e36 | −0.240300 | ||||||||
\(986\) | 2.26259e37 | 0.853383 | ||||||||
\(987\) | −1.12062e36 | −0.0417344 | ||||||||
\(988\) | −2.06320e37 | −0.758718 | ||||||||
\(989\) | −3.44558e36 | −0.125115 | ||||||||
\(990\) | −1.69731e37 | −0.608584 | ||||||||
\(991\) | 9.88586e36 | 0.350021 | 0.175010 | − | 0.984567i | \(-0.444004\pi\) | ||||
0.175010 | + | 0.984567i | \(0.444004\pi\) | |||||||
\(992\) | −3.07084e36 | −0.107365 | ||||||||
\(993\) | 4.67360e36 | 0.161356 | ||||||||
\(994\) | −1.55815e37 | −0.531228 | ||||||||
\(995\) | 1.10326e37 | 0.371442 | ||||||||
\(996\) | 1.47635e34 | 0.000490848 0 | ||||||||
\(997\) | 2.20132e37 | 0.722759 | 0.361380 | − | 0.932419i | \(-0.382306\pi\) | ||||
0.361380 | + | 0.932419i | \(0.382306\pi\) | |||||||
\(998\) | 1.41873e37 | 0.460012 | ||||||||
\(999\) | 8.48041e36 | 0.271549 |
(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 | 2.26.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.26.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 16.26.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 50.26.b.a.49.1 | 2 | |||
5.3 | odd | 4 | 50.26.b.a.49.2 | 2 | |||
5.4 | even | 2 | 50.26.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.26.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
18.26.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
50.26.a.b.1.1 | 1 | 5.4 | even | 2 | |||
50.26.b.a.49.1 | 2 | 5.2 | odd | 4 | |||
50.26.b.a.49.2 | 2 | 5.3 | odd | 4 |