Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} - 15486550 x^{8} - 930225020 x^{7} + 80619202368510 x^{6} + \cdots + 47\!\cdots\!18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{14}\cdot 5^{24}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-294.921\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 359.921 | 0.248538 | 0.124269 | − | 0.992249i | \(-0.460341\pi\) | ||||
0.124269 | + | 0.992249i | \(0.460341\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | −1.96761e6 | −0.938229 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.12530e7 | −0.143493 | ||||||||
\(7\) | −2.25801e8 | −0.302131 | −0.151066 | − | 0.988524i | \(-0.548271\pi\) | ||||
−0.151066 | + | 0.988524i | \(0.548271\pi\) | |||||||
\(8\) | −1.46299e9 | −0.481723 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.39385e10 | −0.394520 | −0.197260 | − | 0.980351i | \(-0.563204\pi\) | ||||
−0.197260 | + | 0.980351i | \(0.563204\pi\) | |||||||
\(12\) | 1.16185e11 | 0.541687 | ||||||||
\(13\) | 7.87206e11 | 1.58374 | 0.791869 | − | 0.610691i | \(-0.209108\pi\) | ||||
0.791869 | + | 0.610691i | \(0.209108\pi\) | |||||||
\(14\) | −8.12704e10 | −0.0750911 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.59981e12 | 0.818503 | ||||||||
\(17\) | −1.90567e12 | −0.229263 | −0.114632 | − | 0.993408i | \(-0.536569\pi\) | ||||
−0.114632 | + | 0.993408i | \(0.536569\pi\) | |||||||
\(18\) | 1.25497e12 | 0.0828459 | ||||||||
\(19\) | 3.53051e13 | 1.32107 | 0.660533 | − | 0.750797i | \(-0.270330\pi\) | ||||
0.660533 | + | 0.750797i | \(0.270330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.33333e13 | 0.174436 | ||||||||
\(22\) | −1.22152e13 | −0.0980532 | ||||||||
\(23\) | −1.05097e14 | −0.528989 | −0.264495 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264495 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(24\) | 8.63883e13 | 0.278123 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.83332e14 | 0.393619 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 4.44287e14 | 0.283468 | ||||||||
\(29\) | −1.97643e15 | −0.872373 | −0.436187 | − | 0.899856i | \(-0.643671\pi\) | ||||
−0.436187 | + | 0.899856i | \(0.643671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.94447e15 | −1.52174 | −0.760872 | − | 0.648902i | \(-0.775228\pi\) | ||||
−0.760872 | + | 0.648902i | \(0.775228\pi\) | |||||||
\(32\) | 4.36377e15 | 0.685152 | ||||||||
\(33\) | 2.00403e15 | 0.227776 | ||||||||
\(34\) | −6.85892e14 | −0.0569806 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.86063e15 | −0.312743 | ||||||||
\(37\) | −3.71887e16 | −1.27143 | −0.635715 | − | 0.771924i | \(-0.719295\pi\) | ||||
−0.635715 | + | 0.771924i | \(0.719295\pi\) | |||||||
\(38\) | 1.27070e16 | 0.328335 | ||||||||
\(39\) | −4.64837e16 | −0.914371 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.35296e17 | 1.57418 | 0.787089 | − | 0.616839i | \(-0.211587\pi\) | ||||
0.787089 | + | 0.616839i | \(0.211587\pi\) | |||||||
\(42\) | 4.79894e15 | 0.0433538 | ||||||||
\(43\) | 4.58115e16 | 0.323263 | 0.161631 | − | 0.986851i | \(-0.448324\pi\) | ||||
0.161631 | + | 0.986851i | \(0.448324\pi\) | |||||||
\(44\) | 6.67777e16 | 0.370150 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.78265e16 | −0.131474 | ||||||||
\(47\) | −4.29974e17 | −1.19238 | −0.596190 | − | 0.802843i | \(-0.703320\pi\) | ||||
−0.596190 | + | 0.802843i | \(0.703320\pi\) | |||||||
\(48\) | −2.12565e17 | −0.472563 | ||||||||
\(49\) | −5.07560e17 | −0.908717 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.12528e17 | 0.132365 | ||||||||
\(52\) | −1.54891e18 | −1.48591 | ||||||||
\(53\) | 2.26519e18 | 1.77913 | 0.889565 | − | 0.456808i | \(-0.151007\pi\) | ||||
0.889565 | + | 0.456808i | \(0.151007\pi\) | |||||||
\(54\) | −7.41046e16 | −0.0478311 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.30345e17 | 0.145544 | ||||||||
\(57\) | −2.08473e18 | −0.762718 | ||||||||
\(58\) | −7.11359e17 | −0.216818 | ||||||||
\(59\) | 2.27777e17 | 0.0580180 | 0.0290090 | − | 0.999579i | \(-0.490765\pi\) | ||||
0.0290090 | + | 0.999579i | \(0.490765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.52948e18 | 0.633502 | 0.316751 | − | 0.948509i | \(-0.397408\pi\) | ||||
0.316751 | + | 0.948509i | \(0.397408\pi\) | |||||||
\(62\) | −2.49946e18 | −0.378211 | ||||||||
\(63\) | −7.87318e17 | −0.100710 | ||||||||
\(64\) | −5.97874e18 | −0.648217 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.21294e17 | 0.0566110 | ||||||||
\(67\) | −1.45192e19 | −0.973100 | −0.486550 | − | 0.873653i | \(-0.661745\pi\) | ||||
−0.486550 | + | 0.873653i | \(0.661745\pi\) | |||||||
\(68\) | 3.74962e18 | 0.215101 | ||||||||
\(69\) | 6.20586e18 | 0.305412 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.96266e19 | −1.08011 | −0.540057 | − | 0.841629i | \(-0.681597\pi\) | ||||
−0.540057 | + | 0.841629i | \(0.681597\pi\) | |||||||
\(72\) | −5.10114e18 | −0.160574 | ||||||||
\(73\) | −3.47560e19 | −0.946540 | −0.473270 | − | 0.880917i | \(-0.656927\pi\) | ||||
−0.473270 | + | 0.880917i | \(0.656927\pi\) | |||||||
\(74\) | −1.33850e19 | −0.315998 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.94666e19 | −1.23946 | ||||||||
\(77\) | 7.66333e18 | 0.119197 | ||||||||
\(78\) | −1.67305e19 | −0.227256 | ||||||||
\(79\) | 3.47111e19 | 0.412462 | 0.206231 | − | 0.978503i | \(-0.433880\pi\) | ||||
0.206231 | + | 0.978503i | \(0.433880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 4.86958e19 | 0.391243 | ||||||||
\(83\) | −1.56621e20 | −1.10798 | −0.553988 | − | 0.832525i | \(-0.686895\pi\) | ||||
−0.553988 | + | 0.832525i | \(0.686895\pi\) | |||||||
\(84\) | −2.62347e19 | −0.163661 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.64885e19 | 0.0803430 | ||||||||
\(87\) | 1.16706e20 | 0.503665 | ||||||||
\(88\) | 4.96518e19 | 0.190049 | ||||||||
\(89\) | 1.89658e20 | 0.644727 | 0.322364 | − | 0.946616i | \(-0.395523\pi\) | ||||
0.322364 | + | 0.946616i | \(0.395523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.77752e20 | −0.478497 | ||||||||
\(92\) | 2.06789e20 | 0.496313 | ||||||||
\(93\) | 4.10064e20 | 0.878579 | ||||||||
\(94\) | −1.54757e20 | −0.296352 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.57676e20 | −0.395573 | ||||||||
\(97\) | 1.11510e20 | 0.153536 | 0.0767682 | − | 0.997049i | \(-0.475540\pi\) | ||||
0.0767682 | + | 0.997049i | \(0.475540\pi\) | |||||||
\(98\) | −1.82682e20 | −0.225850 | ||||||||
\(99\) | −1.18336e20 | −0.131507 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.95776e20 | −0.716830 | −0.358415 | − | 0.933562i | \(-0.616683\pi\) | ||||
−0.358415 | + | 0.933562i | \(0.616683\pi\) | |||||||
\(102\) | 4.05012e19 | 0.0328978 | ||||||||
\(103\) | 5.47853e20 | 0.401673 | 0.200837 | − | 0.979625i | \(-0.435634\pi\) | ||||
0.200837 | + | 0.979625i | \(0.435634\pi\) | |||||||
\(104\) | −1.15168e21 | −0.762923 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.15289e20 | 0.442181 | ||||||||
\(107\) | −1.16424e21 | −0.572154 | −0.286077 | − | 0.958207i | \(-0.592351\pi\) | ||||
−0.286077 | + | 0.958207i | \(0.592351\pi\) | |||||||
\(108\) | 4.05113e20 | 0.180562 | ||||||||
\(109\) | 8.74266e20 | 0.353725 | 0.176862 | − | 0.984236i | \(-0.443405\pi\) | ||||
0.176862 | + | 0.984236i | \(0.443405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.19595e21 | 0.734060 | ||||||||
\(112\) | −8.12840e20 | −0.247295 | ||||||||
\(113\) | 5.05935e21 | 1.40208 | 0.701038 | − | 0.713124i | \(-0.252721\pi\) | ||||
0.701038 | + | 0.713124i | \(0.252721\pi\) | |||||||
\(114\) | −7.50338e20 | −0.189564 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.88884e21 | 0.818486 | ||||||||
\(117\) | 2.74482e21 | 0.527913 | ||||||||
\(118\) | 8.19816e19 | 0.0144197 | ||||||||
\(119\) | 4.30302e20 | 0.0692676 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.24843e21 | −0.844354 | ||||||||
\(122\) | 1.27033e21 | 0.157449 | ||||||||
\(123\) | −7.98908e21 | −0.908852 | ||||||||
\(124\) | 1.36640e22 | 1.42774 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.83372e20 | −0.0250304 | ||||||||
\(127\) | −5.06817e21 | −0.412014 | −0.206007 | − | 0.978551i | \(-0.566047\pi\) | ||||
−0.206007 | + | 0.978551i | \(0.566047\pi\) | |||||||
\(128\) | −1.13034e22 | −0.846258 | ||||||||
\(129\) | −2.70512e21 | −0.186636 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.92504e21 | 0.465214 | 0.232607 | − | 0.972571i | \(-0.425274\pi\) | ||||
0.232607 | + | 0.972571i | \(0.425274\pi\) | |||||||
\(132\) | −3.94315e21 | −0.213706 | ||||||||
\(133\) | −7.97191e21 | −0.399135 | ||||||||
\(134\) | −5.22577e21 | −0.241852 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.78799e21 | 0.110441 | ||||||||
\(137\) | 7.84646e21 | 0.287811 | 0.143906 | − | 0.989591i | \(-0.454034\pi\) | ||||
0.143906 | + | 0.989591i | \(0.454034\pi\) | |||||||
\(138\) | 2.23362e21 | 0.0759064 | ||||||||
\(139\) | 3.12526e22 | 0.984534 | 0.492267 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492267 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.53895e22 | 0.688421 | ||||||||
\(142\) | −1.06632e22 | −0.268449 | ||||||||
\(143\) | −2.67166e22 | −0.624817 | ||||||||
\(144\) | 1.25518e22 | 0.272834 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.25094e22 | −0.235251 | ||||||||
\(147\) | 2.99709e22 | 0.524648 | ||||||||
\(148\) | 7.31727e22 | 1.19289 | ||||||||
\(149\) | 3.26426e22 | 0.495826 | 0.247913 | − | 0.968782i | \(-0.420255\pi\) | ||||
0.247913 | + | 0.968782i | \(0.420255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.84186e22 | −0.507322 | −0.253661 | − | 0.967293i | \(-0.581635\pi\) | ||||
−0.253661 | + | 0.967293i | \(0.581635\pi\) | |||||||
\(152\) | −5.16511e22 | −0.636388 | ||||||||
\(153\) | −6.64467e21 | −0.0764211 | ||||||||
\(154\) | 2.75820e21 | 0.0296249 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.14618e22 | 0.857890 | ||||||||
\(157\) | −3.94963e22 | −0.346426 | −0.173213 | − | 0.984884i | \(-0.555415\pi\) | ||||
−0.173213 | + | 0.984884i | \(0.555415\pi\) | |||||||
\(158\) | 1.24933e22 | 0.102512 | ||||||||
\(159\) | −1.33757e23 | −1.02718 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.37309e22 | 0.159824 | ||||||||
\(162\) | 4.37580e21 | 0.0276153 | ||||||||
\(163\) | 3.02701e23 | 1.79079 | 0.895395 | − | 0.445273i | \(-0.146893\pi\) | ||||
0.895395 | + | 0.445273i | \(0.146893\pi\) | |||||||
\(164\) | −2.66209e23 | −1.47694 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.63712e22 | −0.275374 | ||||||||
\(167\) | 3.58711e23 | 1.64521 | 0.822607 | − | 0.568611i | \(-0.192519\pi\) | ||||
0.822607 | + | 0.568611i | \(0.192519\pi\) | |||||||
\(168\) | −1.95065e22 | −0.0840297 | ||||||||
\(169\) | 3.72629e23 | 1.50823 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.23101e23 | 0.440355 | ||||||||
\(172\) | −9.01391e22 | −0.303295 | ||||||||
\(173\) | −2.25208e22 | −0.0713017 | −0.0356508 | − | 0.999364i | \(-0.511350\pi\) | ||||
−0.0356508 | + | 0.999364i | \(0.511350\pi\) | |||||||
\(174\) | 4.20050e22 | 0.125180 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.22172e23 | −0.322916 | ||||||||
\(177\) | −1.34500e22 | −0.0334967 | ||||||||
\(178\) | 6.82619e22 | 0.160239 | ||||||||
\(179\) | −2.97381e23 | −0.658197 | −0.329099 | − | 0.944296i | \(-0.606745\pi\) | ||||
−0.329099 | + | 0.944296i | \(0.606745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.34042e23 | −1.24880 | −0.624400 | − | 0.781105i | \(-0.714656\pi\) | ||||
−0.624400 | + | 0.781105i | \(0.714656\pi\) | |||||||
\(182\) | −6.39766e22 | −0.118925 | ||||||||
\(183\) | −2.08412e23 | −0.365752 | ||||||||
\(184\) | 1.53756e23 | 0.254826 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.47591e23 | 0.218360 | ||||||||
\(187\) | 6.46756e22 | 0.0904490 | ||||||||
\(188\) | 8.46021e23 | 1.11873 | ||||||||
\(189\) | 4.64904e22 | 0.0581452 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.59653e24 | −1.78783 | −0.893914 | − | 0.448238i | \(-0.852052\pi\) | ||||
−0.893914 | + | 0.448238i | \(0.852052\pi\) | |||||||
\(192\) | 3.53039e23 | 0.374248 | ||||||||
\(193\) | −1.28260e24 | −1.28748 | −0.643739 | − | 0.765245i | \(-0.722618\pi\) | ||||
−0.643739 | + | 0.765245i | \(0.722618\pi\) | |||||||
\(194\) | 4.01349e22 | 0.0381596 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.98679e23 | 0.852584 | ||||||||
\(197\) | 1.15374e24 | 0.933709 | 0.466854 | − | 0.884334i | \(-0.345387\pi\) | ||||
0.466854 | + | 0.884334i | \(0.345387\pi\) | |||||||
\(198\) | −4.25917e22 | −0.0326844 | ||||||||
\(199\) | −8.81552e22 | −0.0641639 | −0.0320819 | − | 0.999485i | \(-0.510214\pi\) | ||||
−0.0320819 | + | 0.999485i | \(0.510214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.57344e23 | 0.561819 | ||||||||
\(202\) | −2.86416e23 | −0.178159 | ||||||||
\(203\) | 4.46279e23 | 0.263571 | ||||||||
\(204\) | −2.21411e23 | −0.124189 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.97184e23 | 0.0998310 | ||||||||
\(207\) | −3.66450e23 | −0.176330 | ||||||||
\(208\) | 2.83379e24 | 1.29629 | ||||||||
\(209\) | −1.19820e24 | −0.521187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.77022e24 | 0.696724 | 0.348362 | − | 0.937360i | \(-0.386738\pi\) | ||||
0.348362 | + | 0.937360i | \(0.386738\pi\) | |||||||
\(212\) | −4.45701e24 | −1.66923 | ||||||||
\(213\) | 1.74942e24 | 0.623604 | ||||||||
\(214\) | −4.19034e23 | −0.142202 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.01217e23 | 0.0927076 | ||||||||
\(217\) | 1.56807e24 | 0.459767 | ||||||||
\(218\) | 3.14667e23 | 0.0879139 | ||||||||
\(219\) | 2.05230e24 | 0.546485 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.50016e24 | −0.363093 | ||||||||
\(222\) | 7.90370e23 | 0.182442 | ||||||||
\(223\) | 6.37800e24 | 1.40438 | 0.702188 | − | 0.711991i | \(-0.252206\pi\) | ||||
0.702188 | + | 0.711991i | \(0.252206\pi\) | |||||||
\(224\) | −9.85342e23 | −0.207006 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.82097e24 | 0.348469 | ||||||||
\(227\) | 5.77167e24 | 1.05446 | 0.527230 | − | 0.849723i | \(-0.323231\pi\) | ||||
0.527230 | + | 0.849723i | \(0.323231\pi\) | |||||||
\(228\) | 4.10193e24 | 0.715604 | ||||||||
\(229\) | −4.49646e24 | −0.749201 | −0.374600 | − | 0.927186i | \(-0.622220\pi\) | ||||
−0.374600 | + | 0.927186i | \(0.622220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.52512e23 | −0.0688184 | ||||||||
\(232\) | 2.89150e24 | 0.420242 | ||||||||
\(233\) | 1.04080e25 | 1.44587 | 0.722937 | − | 0.690914i | \(-0.242792\pi\) | ||||
0.722937 | + | 0.690914i | \(0.242792\pi\) | |||||||
\(234\) | 9.87918e23 | 0.131206 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.48175e23 | −0.0544342 | ||||||||
\(237\) | −2.04966e24 | −0.238135 | ||||||||
\(238\) | 1.54875e23 | 0.0172156 | ||||||||
\(239\) | 9.90599e24 | 1.05371 | 0.526854 | − | 0.849956i | \(-0.323372\pi\) | ||||
0.526854 | + | 0.849956i | \(0.323372\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.33934e25 | 1.30531 | 0.652654 | − | 0.757656i | \(-0.273656\pi\) | ||||
0.652654 | + | 0.757656i | \(0.273656\pi\) | |||||||
\(242\) | −2.24894e24 | −0.209854 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | −6.94464e24 | −0.594369 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.87544e24 | −0.225884 | ||||||||
\(247\) | 2.77924e25 | 2.09222 | ||||||||
\(248\) | 1.01597e25 | 0.733059 | ||||||||
\(249\) | 9.24832e24 | 0.639690 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.23731e25 | −1.42283 | −0.711413 | − | 0.702774i | \(-0.751944\pi\) | ||||
−0.711413 | + | 0.702774i | \(0.751944\pi\) | |||||||
\(252\) | 1.54913e24 | 0.0944895 | ||||||||
\(253\) | 3.56682e24 | 0.208697 | ||||||||
\(254\) | −1.82414e24 | −0.102401 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.47001e24 | 0.437889 | ||||||||
\(257\) | 2.43723e25 | 1.20948 | 0.604740 | − | 0.796423i | \(-0.293277\pi\) | ||||
0.604740 | + | 0.796423i | \(0.293277\pi\) | |||||||
\(258\) | −9.73631e23 | −0.0463861 | ||||||||
\(259\) | 8.39723e24 | 0.384139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.89138e24 | −0.290791 | ||||||||
\(262\) | 2.85239e24 | 0.115623 | ||||||||
\(263\) | 2.84968e25 | 1.10984 | 0.554921 | − | 0.831903i | \(-0.312748\pi\) | ||||
0.554921 | + | 0.831903i | \(0.312748\pi\) | |||||||
\(264\) | −2.93189e24 | −0.109725 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.86926e24 | −0.0992002 | ||||||||
\(267\) | −1.11991e25 | −0.372233 | ||||||||
\(268\) | 2.85681e25 | 0.912990 | ||||||||
\(269\) | −3.91028e24 | −0.120174 | −0.0600868 | − | 0.998193i | \(-0.519138\pi\) | ||||
−0.0600868 | + | 0.998193i | \(0.519138\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.15108e25 | −1.18028 | −0.590138 | − | 0.807302i | \(-0.700927\pi\) | ||||
−0.590138 | + | 0.807302i | \(0.700927\pi\) | |||||||
\(272\) | −6.86006e24 | −0.187653 | ||||||||
\(273\) | 1.04961e25 | 0.276260 | ||||||||
\(274\) | 2.82411e24 | 0.0715319 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.22107e25 | −0.286546 | ||||||||
\(277\) | −4.68304e25 | −1.05801 | −0.529006 | − | 0.848618i | \(-0.677435\pi\) | ||||
−0.529006 | + | 0.848618i | \(0.677435\pi\) | |||||||
\(278\) | 1.12485e25 | 0.244694 | ||||||||
\(279\) | −2.42139e25 | −0.507248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.18476e25 | 1.59070 | 0.795352 | − | 0.606148i | \(-0.207286\pi\) | ||||
0.795352 | + | 0.606148i | \(0.207286\pi\) | |||||||
\(282\) | 9.13824e24 | 0.171099 | ||||||||
\(283\) | 6.88309e25 | 1.24173 | 0.620863 | − | 0.783919i | \(-0.286782\pi\) | ||||
0.620863 | + | 0.783919i | \(0.286782\pi\) | |||||||
\(284\) | 5.82936e25 | 1.01339 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.61586e24 | −0.155290 | ||||||||
\(287\) | −3.05499e25 | −0.475609 | ||||||||
\(288\) | 1.52155e25 | 0.228384 | ||||||||
\(289\) | −6.54603e25 | −0.947438 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.58457e24 | −0.0886443 | ||||||||
\(292\) | 6.83861e25 | 0.888072 | ||||||||
\(293\) | 1.04180e26 | 1.30519 | 0.652594 | − | 0.757708i | \(-0.273681\pi\) | ||||
0.652594 | + | 0.757708i | \(0.273681\pi\) | |||||||
\(294\) | 1.07872e25 | 0.130395 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.44068e25 | 0.612477 | ||||||||
\(297\) | 6.98763e24 | 0.0759254 | ||||||||
\(298\) | 1.17488e25 | 0.123231 | ||||||||
\(299\) | −8.27328e25 | −0.837780 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.03443e25 | −0.0976679 | ||||||||
\(302\) | −1.38277e25 | −0.126089 | ||||||||
\(303\) | 4.69898e25 | 0.413862 | ||||||||
\(304\) | 1.27092e26 | 1.08130 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.39156e24 | −0.0189935 | ||||||||
\(307\) | 1.21443e25 | 0.0932005 | 0.0466003 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466003 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(308\) | −1.50784e25 | −0.111834 | ||||||||
\(309\) | −3.23501e25 | −0.231906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.12643e25 | 0.343424 | 0.171712 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171712 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(312\) | 6.80054e25 | 0.440474 | ||||||||
\(313\) | 2.40814e26 | 1.50822 | 0.754111 | − | 0.656747i | \(-0.228068\pi\) | ||||
0.754111 | + | 0.656747i | \(0.228068\pi\) | |||||||
\(314\) | −1.42156e25 | −0.0860999 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.82979e25 | −0.386984 | ||||||||
\(317\) | 2.81853e26 | 1.54490 | 0.772451 | − | 0.635074i | \(-0.219031\pi\) | ||||
0.772451 | + | 0.635074i | \(0.219031\pi\) | |||||||
\(318\) | −4.81420e25 | −0.255293 | ||||||||
\(319\) | 6.70770e25 | 0.344169 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.87472e25 | 0.330333 | ||||||||
\(322\) | 8.54126e24 | 0.0397224 | ||||||||
\(323\) | −6.72799e25 | −0.302872 | ||||||||
\(324\) | −2.39215e25 | −0.104248 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.08949e26 | 0.445079 | ||||||||
\(327\) | −5.16245e25 | −0.204223 | ||||||||
\(328\) | −1.97937e26 | −0.758318 | ||||||||
\(329\) | 9.70885e25 | 0.360256 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.97534e26 | −1.38414 | −0.692070 | − | 0.721830i | \(-0.743301\pi\) | ||||
−0.692070 | + | 0.721830i | \(0.743301\pi\) | |||||||
\(332\) | 3.08169e26 | 1.03954 | ||||||||
\(333\) | −1.29669e26 | −0.423810 | ||||||||
\(334\) | 1.29108e26 | 0.408898 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.79974e25 | 0.142776 | ||||||||
\(337\) | 9.29580e25 | 0.268023 | 0.134012 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134012 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(338\) | 1.34117e26 | 0.374851 | ||||||||
\(339\) | −2.98750e26 | −0.809488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.35685e26 | 0.600359 | ||||||||
\(342\) | 4.43067e25 | 0.109445 | ||||||||
\(343\) | 2.40727e26 | 0.576683 | ||||||||
\(344\) | −6.70219e25 | −0.155723 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.10571e24 | −0.0177212 | ||||||||
\(347\) | −8.71900e26 | −1.84930 | −0.924650 | − | 0.380818i | \(-0.875642\pi\) | ||||
−0.924650 | + | 0.380818i | \(0.875642\pi\) | |||||||
\(348\) | −2.29632e26 | −0.472553 | ||||||||
\(349\) | −2.14177e26 | −0.427667 | −0.213834 | − | 0.976870i | \(-0.568595\pi\) | ||||
−0.213834 | + | 0.976870i | \(0.568595\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.62079e26 | −0.304790 | ||||||||
\(352\) | −1.48100e26 | −0.270306 | ||||||||
\(353\) | −2.63256e26 | −0.466384 | −0.233192 | − | 0.972431i | \(-0.574917\pi\) | ||||
−0.233192 | + | 0.972431i | \(0.574917\pi\) | |||||||
\(354\) | −4.84093e24 | −0.00832520 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.73173e26 | −0.604902 | ||||||||
\(357\) | −2.54089e25 | −0.0399917 | ||||||||
\(358\) | −1.07034e26 | −0.163587 | ||||||||
\(359\) | −2.16196e26 | −0.320890 | −0.160445 | − | 0.987045i | \(-0.551293\pi\) | ||||
−0.160445 | + | 0.987045i | \(0.551293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.32239e26 | 0.745214 | ||||||||
\(362\) | −2.28205e26 | −0.310374 | ||||||||
\(363\) | 3.68964e26 | 0.487488 | ||||||||
\(364\) | 3.49746e26 | 0.448940 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.50120e25 | −0.0909032 | ||||||||
\(367\) | −7.58083e25 | −0.0892736 | −0.0446368 | − | 0.999003i | \(-0.514213\pi\) | ||||
−0.0446368 | + | 0.999003i | \(0.514213\pi\) | |||||||
\(368\) | −3.78328e26 | −0.432979 | ||||||||
\(369\) | 4.71747e26 | 0.524726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.11481e26 | −0.537531 | ||||||||
\(372\) | −8.06846e26 | −0.824309 | ||||||||
\(373\) | −4.98462e26 | −0.495095 | −0.247548 | − | 0.968876i | \(-0.579625\pi\) | ||||
−0.247548 | + | 0.968876i | \(0.579625\pi\) | |||||||
\(374\) | 2.32781e25 | 0.0224800 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.29049e26 | 0.574397 | ||||||||
\(377\) | −1.55586e27 | −1.38161 | ||||||||
\(378\) | 1.67329e25 | 0.0144513 | ||||||||
\(379\) | −1.76506e27 | −1.48268 | −0.741340 | − | 0.671130i | \(-0.765809\pi\) | ||||
−0.741340 | + | 0.671130i | \(0.765809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.99270e26 | 0.237876 | ||||||||
\(382\) | −5.74624e26 | −0.444343 | ||||||||
\(383\) | −2.00746e27 | −1.51029 | −0.755143 | − | 0.655560i | \(-0.772432\pi\) | ||||
−0.755143 | + | 0.655560i | \(0.772432\pi\) | |||||||
\(384\) | 6.67452e26 | 0.488587 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.61635e26 | −0.319987 | ||||||||
\(387\) | 1.59735e26 | 0.107754 | ||||||||
\(388\) | −2.19409e26 | −0.144052 | ||||||||
\(389\) | −5.35448e26 | −0.342174 | −0.171087 | − | 0.985256i | \(-0.554728\pi\) | ||||
−0.171087 | + | 0.985256i | \(0.554728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00280e26 | 0.121278 | ||||||||
\(392\) | 7.42557e26 | 0.437750 | ||||||||
\(393\) | −4.67966e26 | −0.268591 | ||||||||
\(394\) | 4.15254e26 | 0.232062 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.32839e26 | 0.123383 | ||||||||
\(397\) | 3.53227e27 | 1.82286 | 0.911431 | − | 0.411452i | \(-0.134978\pi\) | ||||
0.911431 | + | 0.411452i | \(0.134978\pi\) | |||||||
\(398\) | −3.17289e25 | −0.0159471 | ||||||||
\(399\) | 4.70733e26 | 0.230441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.12842e27 | −1.91765 | −0.958823 | − | 0.284006i | \(-0.908336\pi\) | ||||
−0.958823 | + | 0.284006i | \(0.908336\pi\) | |||||||
\(402\) | 3.08576e26 | 0.139633 | ||||||||
\(403\) | −5.46673e27 | −2.41004 | ||||||||
\(404\) | 1.56578e27 | 0.672551 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.60625e26 | 0.0655074 | ||||||||
\(407\) | 1.26213e27 | 0.501605 | ||||||||
\(408\) | −1.64628e26 | −0.0637634 | ||||||||
\(409\) | 1.84613e27 | 0.696894 | 0.348447 | − | 0.937328i | \(-0.386709\pi\) | ||||
0.348447 | + | 0.937328i | \(0.386709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.63325e26 | −0.166168 | ||||||||
\(412\) | −1.07796e27 | −0.376861 | ||||||||
\(413\) | −5.14321e25 | −0.0175291 | ||||||||
\(414\) | −1.31893e26 | −0.0438246 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.43518e27 | 1.08510 | ||||||||
\(417\) | −1.84543e27 | −0.568421 | ||||||||
\(418\) | −4.31258e26 | −0.129535 | ||||||||
\(419\) | 3.00419e27 | 0.879996 | 0.439998 | − | 0.897999i | \(-0.354979\pi\) | ||||
0.439998 | + | 0.897999i | \(0.354979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.22566e27 | 1.73470 | 0.867348 | − | 0.497702i | \(-0.165823\pi\) | ||||
0.867348 | + | 0.497702i | \(0.165823\pi\) | |||||||
\(422\) | 6.37139e26 | 0.173162 | ||||||||
\(423\) | −1.49923e27 | −0.397460 | ||||||||
\(424\) | −3.31396e27 | −0.857048 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.29654e26 | 0.154989 | ||||||||
\(427\) | −7.96959e26 | −0.191401 | ||||||||
\(428\) | 2.29077e27 | 0.536811 | ||||||||
\(429\) | 1.57759e27 | 0.360738 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.84115e25 | 0.0127200 | 0.00636000 | − | 0.999980i | \(-0.497976\pi\) | ||||
0.00636000 | + | 0.999980i | \(0.497976\pi\) | |||||||
\(432\) | −7.41169e26 | −0.157521 | ||||||||
\(433\) | −2.80239e27 | −0.581307 | −0.290653 | − | 0.956828i | \(-0.593873\pi\) | ||||
−0.290653 | + | 0.956828i | \(0.593873\pi\) | |||||||
\(434\) | 5.64380e26 | 0.114269 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.72021e27 | −0.331875 | ||||||||
\(437\) | −3.71045e27 | −0.698830 | ||||||||
\(438\) | 7.38668e26 | 0.135822 | ||||||||
\(439\) | −6.01312e26 | −0.107950 | −0.0539749 | − | 0.998542i | \(-0.517189\pi\) | ||||
−0.0539749 | + | 0.998542i | \(0.517189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.76975e27 | −0.302906 | ||||||||
\(442\) | −5.39938e26 | −0.0902423 | ||||||||
\(443\) | −8.83755e27 | −1.44242 | −0.721212 | − | 0.692715i | \(-0.756414\pi\) | ||||
−0.721212 | + | 0.692715i | \(0.756414\pi\) | |||||||
\(444\) | −4.32078e27 | −0.688717 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.29558e27 | 0.349041 | ||||||||
\(447\) | −1.92751e27 | −0.286265 | ||||||||
\(448\) | 1.35000e27 | 0.195847 | ||||||||
\(449\) | −5.63925e27 | −0.799162 | −0.399581 | − | 0.916698i | \(-0.630844\pi\) | ||||
−0.399581 | + | 0.916698i | \(0.630844\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.59173e27 | −0.621045 | ||||||||
\(452\) | −9.95483e27 | −1.31547 | ||||||||
\(453\) | 2.26858e27 | 0.292902 | ||||||||
\(454\) | 2.07735e27 | 0.262073 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.04995e27 | 0.367419 | ||||||||
\(457\) | −7.44037e27 | −0.875940 | −0.437970 | − | 0.898990i | \(-0.644302\pi\) | ||||
−0.437970 | + | 0.898990i | \(0.644302\pi\) | |||||||
\(458\) | −1.61837e27 | −0.186205 | ||||||||
\(459\) | 3.92361e26 | 0.0441217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.45643e27 | −0.371337 | −0.185668 | − | 0.982612i | \(-0.559445\pi\) | ||||
−0.185668 | + | 0.982612i | \(0.559445\pi\) | |||||||
\(462\) | −1.62869e26 | −0.0171040 | ||||||||
\(463\) | 1.22618e28 | 1.25879 | 0.629397 | − | 0.777084i | \(-0.283302\pi\) | ||||
0.629397 | + | 0.777084i | \(0.283302\pi\) | |||||||
\(464\) | −7.11478e27 | −0.714040 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.74606e27 | 0.359354 | ||||||||
\(467\) | 4.64105e27 | 0.435300 | 0.217650 | − | 0.976027i | \(-0.430161\pi\) | ||||
0.217650 | + | 0.976027i | \(0.430161\pi\) | |||||||
\(468\) | −5.40073e27 | −0.495303 | ||||||||
\(469\) | 3.27845e27 | 0.294004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.33222e27 | 0.200009 | ||||||||
\(472\) | −3.33236e26 | −0.0279486 | ||||||||
\(473\) | −1.55477e27 | −0.127534 | ||||||||
\(474\) | −7.37715e26 | −0.0591856 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.46666e26 | −0.0649889 | ||||||||
\(477\) | 7.89823e27 | 0.593044 | ||||||||
\(478\) | 3.56538e27 | 0.261886 | ||||||||
\(479\) | 4.75956e27 | 0.342014 | 0.171007 | − | 0.985270i | \(-0.445298\pi\) | ||||
0.171007 | + | 0.985270i | \(0.445298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.92751e28 | −2.01361 | ||||||||
\(482\) | 4.82058e27 | 0.324418 | ||||||||
\(483\) | −1.40129e27 | −0.0922746 | ||||||||
\(484\) | 1.22945e28 | 0.792197 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.58387e26 | −0.0159437 | ||||||||
\(487\) | 2.21192e28 | 1.33572 | 0.667860 | − | 0.744287i | \(-0.267210\pi\) | ||||
0.667860 | + | 0.744287i | \(0.267210\pi\) | |||||||
\(488\) | −5.16361e27 | −0.305172 | ||||||||
\(489\) | −1.78742e28 | −1.03391 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.24006e28 | 1.79555 | 0.897774 | − | 0.440456i | \(-0.145183\pi\) | ||||
0.897774 | + | 0.440456i | \(0.145183\pi\) | |||||||
\(492\) | 1.57194e28 | 0.852711 | ||||||||
\(493\) | 3.76643e27 | 0.200003 | ||||||||
\(494\) | 1.00031e28 | 0.519996 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.49988e28 | −1.24555 | ||||||||
\(497\) | 6.68971e27 | 0.326336 | ||||||||
\(498\) | 3.32867e27 | 0.158987 | ||||||||
\(499\) | −2.01743e28 | −0.943502 | −0.471751 | − | 0.881732i | \(-0.656378\pi\) | ||||
−0.471751 | + | 0.881732i | \(0.656378\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.11816e28 | −0.949865 | ||||||||
\(502\) | −8.05255e27 | −0.353626 | ||||||||
\(503\) | 2.90806e28 | 1.25066 | 0.625330 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625330 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(504\) | 1.15184e27 | 0.0485146 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.28377e27 | 0.0518691 | ||||||||
\(507\) | −2.20034e28 | −0.870774 | ||||||||
\(508\) | 9.97217e27 | 0.386563 | ||||||||
\(509\) | 2.66984e28 | 1.01379 | 0.506895 | − | 0.862008i | \(-0.330793\pi\) | ||||
0.506895 | + | 0.862008i | \(0.330793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.84792e27 | 0.285980 | ||||||||
\(512\) | 2.67534e28 | 0.955090 | ||||||||
\(513\) | −7.26900e27 | −0.254239 | ||||||||
\(514\) | 8.77210e27 | 0.300601 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.32263e27 | 0.175107 | ||||||||
\(517\) | 1.45927e28 | 0.470418 | ||||||||
\(518\) | 3.02234e27 | 0.0954730 | ||||||||
\(519\) | 1.32983e27 | 0.0411660 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.59165e28 | 0.473208 | 0.236604 | − | 0.971606i | \(-0.423966\pi\) | ||||
0.236604 | + | 0.971606i | \(0.423966\pi\) | |||||||
\(522\) | −2.48035e27 | −0.0722726 | ||||||||
\(523\) | 3.68283e28 | 1.05175 | 0.525877 | − | 0.850561i | \(-0.323737\pi\) | ||||
0.525877 | + | 0.850561i | \(0.323737\pi\) | |||||||
\(524\) | −1.55934e28 | −0.436477 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.02566e28 | 0.275838 | ||||||||
\(527\) | 1.32339e28 | 0.348880 | ||||||||
\(528\) | 7.21414e27 | 0.186436 | ||||||||
\(529\) | −2.84263e28 | −0.720170 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.94208e26 | 0.0193393 | ||||||||
\(532\) | 1.56856e28 | 0.374480 | ||||||||
\(533\) | 1.06506e29 | 2.49309 | ||||||||
\(534\) | −4.03080e27 | −0.0925140 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.12415e28 | 0.468765 | ||||||||
\(537\) | 1.75600e28 | 0.380010 | ||||||||
\(538\) | −1.40739e27 | −0.0298677 | ||||||||
\(539\) | 1.72258e28 | 0.358507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.57342e28 | 1.71626 | 0.858130 | − | 0.513433i | \(-0.171627\pi\) | ||||
0.858130 | + | 0.513433i | \(0.171627\pi\) | |||||||
\(542\) | −1.49406e28 | −0.293343 | ||||||||
\(543\) | 3.74395e28 | 0.720995 | ||||||||
\(544\) | −8.31591e27 | −0.157080 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.77775e27 | 0.0686611 | ||||||||
\(547\) | −9.45029e28 | −1.68492 | −0.842458 | − | 0.538762i | \(-0.818892\pi\) | ||||
−0.842458 | + | 0.538762i | \(0.818892\pi\) | |||||||
\(548\) | −1.54388e28 | −0.270033 | ||||||||
\(549\) | 1.23065e28 | 0.211167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.97780e28 | −1.15246 | ||||||||
\(552\) | −9.07913e27 | −0.147124 | ||||||||
\(553\) | −7.83780e27 | −0.124618 | ||||||||
\(554\) | −1.68553e28 | −0.262956 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.14929e28 | −0.923718 | ||||||||
\(557\) | −5.79016e28 | −0.853514 | −0.426757 | − | 0.904366i | \(-0.640344\pi\) | ||||
−0.426757 | + | 0.904366i | \(0.640344\pi\) | |||||||
\(558\) | −8.71509e27 | −0.126070 | ||||||||
\(559\) | 3.60631e28 | 0.511964 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.81903e27 | −0.0522207 | ||||||||
\(562\) | 2.94587e28 | 0.395350 | ||||||||
\(563\) | −3.38680e28 | −0.446119 | −0.223060 | − | 0.974805i | \(-0.571604\pi\) | ||||
−0.223060 | + | 0.974805i | \(0.571604\pi\) | |||||||
\(564\) | −4.99567e28 | −0.645897 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.47737e28 | 0.308616 | ||||||||
\(567\) | −2.74521e27 | −0.0335702 | ||||||||
\(568\) | 4.33435e28 | 0.520316 | ||||||||
\(569\) | 1.61113e29 | 1.89869 | 0.949343 | − | 0.314242i | \(-0.101750\pi\) | ||||
0.949343 | + | 0.314242i | \(0.101750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.94989e28 | 0.902988 | 0.451494 | − | 0.892274i | \(-0.350891\pi\) | ||||
0.451494 | + | 0.892274i | \(0.350891\pi\) | |||||||
\(572\) | 5.25678e28 | 0.586221 | ||||||||
\(573\) | 9.42733e28 | 1.03220 | ||||||||
\(574\) | −1.09956e28 | −0.118207 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.08466e28 | −0.216072 | ||||||||
\(577\) | 1.61242e29 | 1.64109 | 0.820544 | − | 0.571583i | \(-0.193670\pi\) | ||||
0.820544 | + | 0.571583i | \(0.193670\pi\) | |||||||
\(578\) | −2.35606e28 | −0.235474 | ||||||||
\(579\) | 7.57363e28 | 0.743326 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.53652e28 | 0.334754 | ||||||||
\(582\) | −2.36993e27 | −0.0220315 | ||||||||
\(583\) | −7.68771e28 | −0.701903 | ||||||||
\(584\) | 5.08477e28 | 0.455970 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.74965e28 | 0.324389 | ||||||||
\(587\) | 7.40062e28 | 0.628880 | 0.314440 | − | 0.949277i | \(-0.398183\pi\) | ||||
0.314440 | + | 0.949277i | \(0.398183\pi\) | |||||||
\(588\) | −5.89710e28 | −0.492240 | ||||||||
\(589\) | −2.45175e29 | −2.01032 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.81270e28 | −0.539077 | ||||||||
\(592\) | −1.33872e29 | −1.04067 | ||||||||
\(593\) | −2.27346e28 | −0.173625 | −0.0868126 | − | 0.996225i | \(-0.527668\pi\) | ||||
−0.0868126 | + | 0.996225i | \(0.527668\pi\) | |||||||
\(594\) | 2.51500e27 | 0.0188703 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.42279e28 | −0.465198 | ||||||||
\(597\) | 5.20548e27 | 0.0370450 | ||||||||
\(598\) | −2.97773e28 | −0.208220 | ||||||||
\(599\) | −1.57021e28 | −0.107889 | −0.0539444 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539444 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.01910e28 | −0.399346 | −0.199673 | − | 0.979863i | \(-0.563988\pi\) | ||||
−0.199673 | + | 0.979863i | \(0.563988\pi\) | |||||||
\(602\) | −3.72312e27 | −0.0242742 | ||||||||
\(603\) | −5.06253e28 | −0.324367 | ||||||||
\(604\) | 7.55928e28 | 0.475984 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.69126e28 | 0.102860 | ||||||||
\(607\) | 1.63356e29 | 0.976458 | 0.488229 | − | 0.872715i | \(-0.337643\pi\) | ||||
0.488229 | + | 0.872715i | \(0.337643\pi\) | |||||||
\(608\) | 1.54063e29 | 0.905130 | ||||||||
\(609\) | −2.63523e28 | −0.152173 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.38478e29 | −1.88842 | ||||||||
\(612\) | 1.30741e28 | 0.0717005 | ||||||||
\(613\) | −6.75283e28 | −0.364042 | −0.182021 | − | 0.983295i | \(-0.558264\pi\) | ||||
−0.182021 | + | 0.983295i | \(0.558264\pi\) | |||||||
\(614\) | 4.37098e27 | 0.0231638 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.12114e28 | −0.0574199 | ||||||||
\(617\) | −1.20545e29 | −0.606955 | −0.303477 | − | 0.952839i | \(-0.598148\pi\) | ||||
−0.303477 | + | 0.952839i | \(0.598148\pi\) | |||||||
\(618\) | −1.16435e28 | −0.0576374 | ||||||||
\(619\) | −1.41237e29 | −0.687381 | −0.343691 | − | 0.939083i | \(-0.611677\pi\) | ||||
−0.343691 | + | 0.939083i | \(0.611677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.16385e28 | 0.101804 | ||||||||
\(622\) | 1.84511e28 | 0.0853539 | ||||||||
\(623\) | −4.28249e28 | −0.194792 | ||||||||
\(624\) | −1.67333e29 | −0.748415 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.66739e28 | 0.374850 | ||||||||
\(627\) | 7.07526e28 | 0.300907 | ||||||||
\(628\) | 7.77133e28 | 0.325027 | ||||||||
\(629\) | 7.08694e28 | 0.291492 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.36528e28 | −0.332792 | −0.166396 | − | 0.986059i | \(-0.553213\pi\) | ||||
−0.166396 | + | 0.986059i | \(0.553213\pi\) | |||||||
\(632\) | −5.07821e28 | −0.198693 | ||||||||
\(633\) | −1.04530e29 | −0.402254 | ||||||||
\(634\) | 1.01445e29 | 0.383966 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.63182e29 | 0.963731 | ||||||||
\(637\) | −3.99554e29 | −1.43917 | ||||||||
\(638\) | 2.41424e28 | 0.0855390 | ||||||||
\(639\) | −1.03302e29 | −0.360038 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.35898e29 | 1.13292 | 0.566458 | − | 0.824091i | \(-0.308313\pi\) | ||||
0.566458 | + | 0.824091i | \(0.308313\pi\) | |||||||
\(642\) | 2.47436e28 | 0.0821002 | ||||||||
\(643\) | −1.61665e29 | −0.527716 | −0.263858 | − | 0.964561i | \(-0.584995\pi\) | ||||
−0.263858 | + | 0.964561i | \(0.584995\pi\) | |||||||
\(644\) | −4.66932e28 | −0.149952 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.42155e28 | −0.0752751 | ||||||||
\(647\) | 1.20758e29 | 0.369336 | 0.184668 | − | 0.982801i | \(-0.440879\pi\) | ||||
0.184668 | + | 0.982801i | \(0.440879\pi\) | |||||||
\(648\) | −1.77866e28 | −0.0535248 | ||||||||
\(649\) | −7.73039e27 | −0.0228893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.25928e28 | −0.265446 | ||||||||
\(652\) | −5.95598e29 | −1.68017 | ||||||||
\(653\) | −4.54361e29 | −1.26128 | −0.630641 | − | 0.776074i | \(-0.717208\pi\) | ||||
−0.630641 | + | 0.776074i | \(0.717208\pi\) | |||||||
\(654\) | −1.85808e28 | −0.0507571 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.87040e29 | 1.28847 | ||||||||
\(657\) | −1.21187e29 | −0.315513 | ||||||||
\(658\) | 3.49442e28 | 0.0895371 | ||||||||
\(659\) | 1.57194e29 | 0.396406 | 0.198203 | − | 0.980161i | \(-0.436489\pi\) | ||||
0.198203 | + | 0.980161i | \(0.436489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.03408e27 | −0.0122972 | −0.00614858 | − | 0.999981i | \(-0.501957\pi\) | ||||
−0.00614858 | + | 0.999981i | \(0.501957\pi\) | |||||||
\(662\) | −1.43081e29 | −0.344011 | ||||||||
\(663\) | 8.85828e28 | 0.209632 | ||||||||
\(664\) | 2.29136e29 | 0.533738 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.66706e28 | −0.105333 | ||||||||
\(667\) | 2.07716e29 | 0.461476 | ||||||||
\(668\) | −7.05804e29 | −1.54359 | ||||||||
\(669\) | −3.76615e29 | −0.810817 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.19785e29 | −0.249929 | ||||||||
\(672\) | 5.81834e28 | 0.119515 | ||||||||
\(673\) | −4.72877e29 | −0.956290 | −0.478145 | − | 0.878281i | \(-0.658691\pi\) | ||||
−0.478145 | + | 0.878281i | \(0.658691\pi\) | |||||||
\(674\) | 3.34575e28 | 0.0666139 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.33188e29 | −1.41506 | ||||||||
\(677\) | −1.26340e29 | −0.240082 | −0.120041 | − | 0.992769i | \(-0.538303\pi\) | ||||
−0.120041 | + | 0.992769i | \(0.538303\pi\) | |||||||
\(678\) | −1.07526e29 | −0.201188 | ||||||||
\(679\) | −2.51791e28 | −0.0463882 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.40811e29 | −0.608792 | ||||||||
\(682\) | 8.48280e28 | 0.149212 | ||||||||
\(683\) | −4.69895e29 | −0.813923 | −0.406961 | − | 0.913445i | \(-0.633412\pi\) | ||||
−0.406961 | + | 0.913445i | \(0.633412\pi\) | |||||||
\(684\) | −2.42215e29 | −0.413154 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.66429e28 | 0.143328 | ||||||||
\(687\) | 2.65511e29 | 0.432551 | ||||||||
\(688\) | 1.64913e29 | 0.264592 | ||||||||
\(689\) | 1.78317e30 | 2.81768 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.34128e28 | −0.0205589 | −0.0102795 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102795 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(692\) | 4.43121e28 | 0.0668973 | ||||||||
\(693\) | 2.67204e28 | 0.0397323 | ||||||||
\(694\) | −3.13815e29 | −0.459621 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.70740e29 | −0.242627 | ||||||||
\(697\) | −2.57829e29 | −0.360901 | ||||||||
\(698\) | −7.70868e28 | −0.106291 | ||||||||
\(699\) | −6.14582e29 | −0.834776 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.13909e30 | 1.50148 | 0.750742 | − | 0.660596i | \(-0.229696\pi\) | ||||
0.750742 | + | 0.660596i | \(0.229696\pi\) | |||||||
\(702\) | −5.83356e28 | −0.0757519 | ||||||||
\(703\) | −1.31295e30 | −1.67964 | ||||||||
\(704\) | 2.02909e29 | 0.255734 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.47513e28 | −0.115914 | ||||||||
\(707\) | 1.79687e29 | 0.216577 | ||||||||
\(708\) | 2.64643e28 | 0.0314276 | ||||||||
\(709\) | −1.14479e30 | −1.33949 | −0.669747 | − | 0.742589i | \(-0.733598\pi\) | ||||
−0.669747 | + | 0.742589i | \(0.733598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.21030e29 | 0.137487 | ||||||||
\(712\) | −2.77468e29 | −0.310580 | ||||||||
\(713\) | 7.29841e29 | 0.804986 | ||||||||
\(714\) | −9.14520e27 | −0.00993944 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.85129e29 | 0.617540 | ||||||||
\(717\) | −5.84939e29 | −0.608358 | ||||||||
\(718\) | −7.78135e28 | −0.0797532 | ||||||||
\(719\) | 9.42126e29 | 0.951603 | 0.475801 | − | 0.879553i | \(-0.342158\pi\) | ||||
0.475801 | + | 0.879553i | \(0.342158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.23706e29 | −0.121358 | ||||||||
\(722\) | 1.91564e29 | 0.185214 | ||||||||
\(723\) | −7.90868e29 | −0.753620 | ||||||||
\(724\) | 1.24755e30 | 1.17166 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.32798e29 | 0.121159 | ||||||||
\(727\) | 9.77996e29 | 0.879479 | 0.439740 | − | 0.898125i | \(-0.355071\pi\) | ||||
0.439740 | + | 0.898125i | \(0.355071\pi\) | |||||||
\(728\) | 2.60050e29 | 0.230503 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.73017e28 | −0.0741123 | ||||||||
\(732\) | 4.10074e29 | 0.343159 | ||||||||
\(733\) | 2.16239e30 | 1.78378 | 0.891892 | − | 0.452249i | \(-0.149378\pi\) | ||||
0.891892 | + | 0.452249i | \(0.149378\pi\) | |||||||
\(734\) | −2.72850e28 | −0.0221878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.58618e29 | −0.362438 | ||||||||
\(737\) | 4.92760e29 | 0.383907 | ||||||||
\(738\) | 1.69792e29 | 0.130414 | ||||||||
\(739\) | −2.19604e30 | −1.66293 | −0.831463 | − | 0.555580i | \(-0.812496\pi\) | ||||
−0.831463 | + | 0.555580i | \(0.812496\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.64111e30 | −1.20794 | ||||||||
\(742\) | −1.84093e29 | −0.133597 | ||||||||
\(743\) | 2.05357e30 | 1.46936 | 0.734679 | − | 0.678414i | \(-0.237333\pi\) | ||||
0.734679 | + | 0.678414i | \(0.237333\pi\) | |||||||
\(744\) | −5.99921e29 | −0.423232 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.79407e29 | −0.123050 | ||||||||
\(747\) | −5.46104e29 | −0.369325 | ||||||||
\(748\) | −1.27256e29 | −0.0848619 | ||||||||
\(749\) | 2.62886e29 | 0.172866 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.76058e29 | 0.624103 | 0.312052 | − | 0.950065i | \(-0.398984\pi\) | ||||
0.312052 | + | 0.950065i | \(0.398984\pi\) | |||||||
\(752\) | −1.54783e30 | −0.975967 | ||||||||
\(753\) | 1.32111e30 | 0.821469 | ||||||||
\(754\) | −5.59986e29 | −0.343382 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.14748e28 | −0.0545535 | ||||||||
\(757\) | 1.52530e29 | 0.0897113 | 0.0448557 | − | 0.998993i | \(-0.485717\pi\) | ||||
0.0448557 | + | 0.998993i | \(0.485717\pi\) | |||||||
\(758\) | −6.35282e29 | −0.368502 | ||||||||
\(759\) | −2.10617e29 | −0.120491 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.43376e30 | 0.797878 | 0.398939 | − | 0.916977i | \(-0.369378\pi\) | ||||
0.398939 | + | 0.916977i | \(0.369378\pi\) | |||||||
\(762\) | 1.07714e29 | 0.0591212 | ||||||||
\(763\) | −1.97410e29 | −0.106871 | ||||||||
\(764\) | 3.14134e30 | 1.67739 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.22526e29 | −0.375363 | ||||||||
\(767\) | 1.79307e29 | 0.0918853 | ||||||||
\(768\) | −5.00146e29 | −0.252816 | ||||||||
\(769\) | −3.06925e30 | −1.53040 | −0.765202 | − | 0.643790i | \(-0.777361\pi\) | ||||
−0.765202 | + | 0.643790i | \(0.777361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.43916e30 | −0.698293 | ||||||||
\(772\) | 2.52366e30 | 1.20795 | ||||||||
\(773\) | 1.11134e30 | 0.524760 | 0.262380 | − | 0.964965i | \(-0.415493\pi\) | ||||
0.262380 | + | 0.964965i | \(0.415493\pi\) | |||||||
\(774\) | 5.74920e28 | 0.0267810 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.63139e29 | −0.0739621 | ||||||||
\(777\) | −4.95848e29 | −0.221783 | ||||||||
\(778\) | −1.92719e29 | −0.0850431 | ||||||||
\(779\) | 4.77663e30 | 2.07959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.00548e30 | 0.426126 | ||||||||
\(782\) | 7.20850e28 | 0.0301421 | ||||||||
\(783\) | 4.06929e29 | 0.167888 | ||||||||
\(784\) | −1.82712e30 | −0.743787 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.68431e29 | −0.0667551 | ||||||||
\(787\) | 2.74489e30 | 1.07347 | 0.536735 | − | 0.843751i | \(-0.319657\pi\) | ||||
0.536735 | + | 0.843751i | \(0.319657\pi\) | |||||||
\(788\) | −2.27010e30 | −0.876032 | ||||||||
\(789\) | −1.68271e30 | −0.640768 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.14241e30 | −0.423611 | ||||||||
\(792\) | 1.73125e29 | 0.0633498 | ||||||||
\(793\) | 2.77843e30 | 1.00330 | ||||||||
\(794\) | 1.27134e30 | 0.453050 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.73455e29 | 0.0602004 | ||||||||
\(797\) | −1.59912e30 | −0.547731 | −0.273866 | − | 0.961768i | \(-0.588302\pi\) | ||||
−0.273866 | + | 0.961768i | \(0.588302\pi\) | |||||||
\(798\) | 1.69427e29 | 0.0572733 | ||||||||
\(799\) | 8.19390e29 | 0.273369 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.61296e29 | 0.214909 | ||||||||
\(802\) | −1.48591e30 | −0.476607 | ||||||||
\(803\) | 1.17956e30 | 0.373429 | ||||||||
\(804\) | −1.68692e30 | −0.527115 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.96759e30 | −0.598987 | ||||||||
\(807\) | 2.30898e29 | 0.0693823 | ||||||||
\(808\) | 1.16421e30 | 0.345314 | ||||||||
\(809\) | −1.45623e30 | −0.426354 | −0.213177 | − | 0.977014i | \(-0.568381\pi\) | ||||
−0.213177 | + | 0.977014i | \(0.568381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.66640e29 | 0.133126 | 0.0665631 | − | 0.997782i | \(-0.478797\pi\) | ||||
0.0665631 | + | 0.997782i | \(0.478797\pi\) | |||||||
\(812\) | −8.78103e29 | −0.247290 | ||||||||
\(813\) | 2.45117e30 | 0.681433 | ||||||||
\(814\) | 4.54266e29 | 0.124668 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.05080e29 | 0.108341 | ||||||||
\(817\) | 1.61738e30 | 0.427051 | ||||||||
\(818\) | 6.64460e29 | 0.173205 | ||||||||
\(819\) | −6.19782e29 | −0.159499 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.92587e30 | 0.483084 | 0.241542 | − | 0.970390i | \(-0.422347\pi\) | ||||
0.241542 | + | 0.970390i | \(0.422347\pi\) | |||||||
\(822\) | −1.66761e29 | −0.0412990 | ||||||||
\(823\) | −3.60800e29 | −0.0882202 | −0.0441101 | − | 0.999027i | \(-0.514045\pi\) | ||||
−0.0441101 | + | 0.999027i | \(0.514045\pi\) | |||||||
\(824\) | −8.01505e29 | −0.193495 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.85115e28 | −0.00435663 | ||||||||
\(827\) | 6.95742e30 | 1.61674 | 0.808371 | − | 0.588674i | \(-0.200350\pi\) | ||||
0.808371 | + | 0.588674i | \(0.200350\pi\) | |||||||
\(828\) | 7.21029e29 | 0.165438 | ||||||||
\(829\) | 1.71309e30 | 0.388112 | 0.194056 | − | 0.980990i | \(-0.437836\pi\) | ||||
0.194056 | + | 0.980990i | \(0.437836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.76529e30 | 0.610844 | ||||||||
\(832\) | −4.70650e30 | −1.02661 | ||||||||
\(833\) | 9.67243e29 | 0.208335 | ||||||||
\(834\) | −6.64211e29 | −0.141274 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.35759e30 | 0.488993 | ||||||||
\(837\) | 1.42981e30 | 0.292860 | ||||||||
\(838\) | 1.08127e30 | 0.218712 | ||||||||
\(839\) | 8.66052e30 | 1.72999 | 0.864995 | − | 0.501781i | \(-0.167322\pi\) | ||||
0.864995 | + | 0.501781i | \(0.167322\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22657e30 | −0.238965 | ||||||||
\(842\) | 2.24075e30 | 0.431138 | ||||||||
\(843\) | −4.83302e30 | −0.918393 | ||||||||
\(844\) | −3.48310e30 | −0.653687 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.39604e29 | −0.0987839 | ||||||||
\(847\) | 1.41090e30 | 0.255106 | ||||||||
\(848\) | 8.15426e30 | 1.45622 | ||||||||
\(849\) | −4.06440e30 | −0.716911 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.90841e30 | 0.672573 | ||||||||
\(852\) | −3.44218e30 | −0.585083 | ||||||||
\(853\) | 1.10259e31 | 1.85118 | 0.925588 | − | 0.378532i | \(-0.123571\pi\) | ||||
0.925588 | + | 0.378532i | \(0.123571\pi\) | |||||||
\(854\) | −2.86843e29 | −0.0475703 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.70327e30 | 0.275620 | ||||||||
\(857\) | −4.05713e30 | −0.648516 | −0.324258 | − | 0.945969i | \(-0.605115\pi\) | ||||
−0.324258 | + | 0.945969i | \(0.605115\pi\) | |||||||
\(858\) | 5.67807e29 | 0.0896570 | ||||||||
\(859\) | −1.70873e30 | −0.266530 | −0.133265 | − | 0.991080i | \(-0.542546\pi\) | ||||
−0.133265 | + | 0.991080i | \(0.542546\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.80394e30 | 0.274593 | ||||||||
\(862\) | 2.10235e28 | 0.00316140 | ||||||||
\(863\) | 6.61629e30 | 0.982882 | 0.491441 | − | 0.870911i | \(-0.336470\pi\) | ||||
0.491441 | + | 0.870911i | \(0.336470\pi\) | |||||||
\(864\) | −8.98461e29 | −0.131858 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.00864e30 | −0.144477 | ||||||||
\(867\) | 3.86537e30 | 0.547004 | ||||||||
\(868\) | −3.08534e30 | −0.431366 | ||||||||
\(869\) | −1.17804e30 | −0.162725 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.14296e31 | −1.54113 | ||||||||
\(872\) | −1.27904e30 | −0.170397 | ||||||||
\(873\) | 3.88812e29 | 0.0511788 | ||||||||
\(874\) | −1.33547e30 | −0.173686 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.03813e30 | −0.512728 | ||||||||
\(877\) | 5.96651e30 | 0.748556 | 0.374278 | − | 0.927317i | \(-0.377891\pi\) | ||||
0.374278 | + | 0.927317i | \(0.377891\pi\) | |||||||
\(878\) | −2.16425e29 | −0.0268296 | ||||||||
\(879\) | −6.15171e30 | −0.753551 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.83453e29 | 0.0578239 | 0.0289119 | − | 0.999582i | \(-0.490796\pi\) | ||||
0.0289119 | + | 0.999582i | \(0.490796\pi\) | |||||||
\(882\) | −6.36971e29 | −0.0752835 | ||||||||
\(883\) | −9.20409e30 | −1.07496 | −0.537482 | − | 0.843276i | \(-0.680624\pi\) | ||||
−0.537482 | + | 0.843276i | \(0.680624\pi\) | |||||||
\(884\) | 2.95172e30 | 0.340664 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.18082e30 | −0.358497 | ||||||||
\(887\) | 6.74053e30 | 0.750752 | 0.375376 | − | 0.926873i | \(-0.377514\pi\) | ||||
0.375376 | + | 0.926873i | \(0.377514\pi\) | |||||||
\(888\) | −3.21267e30 | −0.353614 | ||||||||
\(889\) | 1.14440e30 | 0.124482 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.12613e29 | −0.0438356 | ||||||||
\(892\) | −1.25494e31 | −1.31763 | ||||||||
\(893\) | −1.51803e31 | −1.57521 | ||||||||
\(894\) | −6.93753e29 | −0.0711477 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.55231e30 | 0.255681 | ||||||||
\(897\) | 4.88529e30 | 0.483693 | ||||||||
\(898\) | −2.02969e30 | −0.198622 | ||||||||
\(899\) | 1.37253e31 | 1.32753 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.31671e30 | −0.407889 | ||||||||
\(902\) | −1.65266e30 | −0.154353 | ||||||||
\(903\) | 6.10819e29 | 0.0563886 | ||||||||
\(904\) | −7.40180e30 | −0.675412 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.16510e29 | 0.0727973 | ||||||||
\(907\) | 3.81758e30 | 0.336443 | 0.168221 | − | 0.985749i | \(-0.446198\pi\) | ||||
0.168221 | + | 0.985749i | \(0.446198\pi\) | |||||||
\(908\) | −1.13564e31 | −0.989324 | ||||||||
\(909\) | −2.77470e30 | −0.238943 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.19309e30 | 0.268701 | 0.134350 | − | 0.990934i | \(-0.457105\pi\) | ||||
0.134350 | + | 0.990934i | \(0.457105\pi\) | |||||||
\(912\) | −7.50464e30 | −0.624286 | ||||||||
\(913\) | 5.31548e30 | 0.437119 | ||||||||
\(914\) | −2.67795e30 | −0.217704 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.84727e30 | 0.702922 | ||||||||
\(917\) | −1.78948e30 | −0.140556 | ||||||||
\(918\) | 1.41219e29 | 0.0109659 | ||||||||
\(919\) | 1.69470e31 | 1.30101 | 0.650503 | − | 0.759504i | \(-0.274558\pi\) | ||||
0.650503 | + | 0.759504i | \(0.274558\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.17107e29 | −0.0538093 | ||||||||
\(922\) | −1.24404e30 | −0.0922912 | ||||||||
\(923\) | −2.33223e31 | −1.71062 | ||||||||
\(924\) | 8.90367e29 | 0.0645674 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.41329e30 | 0.312858 | ||||||||
\(927\) | 1.91024e30 | 0.133891 | ||||||||
\(928\) | −8.62468e30 | −0.597708 | ||||||||
\(929\) | 2.76272e31 | 1.89309 | 0.946546 | − | 0.322569i | \(-0.104546\pi\) | ||||
0.946546 | + | 0.322569i | \(0.104546\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.79194e31 | −1.20047 | ||||||||
\(932\) | −2.04789e31 | −1.35656 | ||||||||
\(933\) | −3.02711e30 | −0.198276 | ||||||||
\(934\) | 1.67041e30 | 0.108189 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.01565e30 | −0.254308 | ||||||||
\(937\) | −8.51699e30 | −0.533360 | −0.266680 | − | 0.963785i | \(-0.585927\pi\) | ||||
−0.266680 | + | 0.963785i | \(0.585927\pi\) | |||||||
\(938\) | 1.17998e30 | 0.0730711 | ||||||||
\(939\) | −1.42198e31 | −0.870772 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.60192e31 | 0.959288 | 0.479644 | − | 0.877463i | \(-0.340766\pi\) | ||||
0.479644 | + | 0.877463i | \(0.340766\pi\) | |||||||
\(942\) | 8.39415e29 | 0.0497098 | ||||||||
\(943\) | −1.42191e31 | −0.832723 | ||||||||
\(944\) | 8.19953e29 | 0.0474879 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.59596e29 | −0.0316969 | ||||||||
\(947\) | 9.01245e30 | 0.504856 | 0.252428 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252428 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(948\) | 4.03292e30 | 0.223425 | ||||||||
\(949\) | −2.73601e31 | −1.49907 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.66432e31 | −0.891950 | ||||||||
\(952\) | −6.29529e29 | −0.0333678 | ||||||||
\(953\) | −1.14770e30 | −0.0601664 | −0.0300832 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300832 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(954\) | 2.84274e30 | 0.147394 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.94911e31 | −0.988619 | ||||||||
\(957\) | −3.96083e30 | −0.198706 | ||||||||
\(958\) | 1.71307e30 | 0.0850034 | ||||||||
\(959\) | −1.77174e30 | −0.0869568 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.74002e31 | 1.31570 | ||||||||
\(962\) | −1.05367e31 | −0.500459 | ||||||||
\(963\) | −4.05945e30 | −0.190718 | ||||||||
\(964\) | −2.63530e31 | −1.22468 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.04353e29 | −0.0229337 | ||||||||
\(967\) | −3.66156e30 | −0.164698 | −0.0823489 | − | 0.996604i | \(-0.526242\pi\) | ||||
−0.0823489 | + | 0.996604i | \(0.526242\pi\) | |||||||
\(968\) | 9.14141e30 | 0.406745 | ||||||||
\(969\) | 3.97281e30 | 0.174863 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.28650e31 | 1.41557 | 0.707785 | − | 0.706428i | \(-0.249694\pi\) | ||||
0.707785 | + | 0.706428i | \(0.249694\pi\) | |||||||
\(972\) | 1.41254e30 | 0.0601874 | ||||||||
\(973\) | −7.05686e30 | −0.297459 | ||||||||
\(974\) | 7.96117e30 | 0.331977 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.27055e31 | 0.518523 | ||||||||
\(977\) | −3.53328e30 | −0.142655 | −0.0713273 | − | 0.997453i | \(-0.522723\pi\) | ||||
−0.0713273 | + | 0.997453i | \(0.522723\pi\) | |||||||
\(978\) | −6.43331e30 | −0.256966 | ||||||||
\(979\) | −6.43670e30 | −0.254358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.04838e30 | 0.117908 | ||||||||
\(982\) | 1.16617e31 | 0.446262 | ||||||||
\(983\) | 3.20399e31 | 1.21305 | 0.606526 | − | 0.795064i | \(-0.292563\pi\) | ||||
0.606526 | + | 0.795064i | \(0.292563\pi\) | |||||||
\(984\) | 1.16880e31 | 0.437815 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.35562e30 | 0.0497083 | ||||||||
\(987\) | −5.73298e30 | −0.207994 | ||||||||
\(988\) | −5.46845e31 | −1.96298 | ||||||||
\(989\) | −4.81464e30 | −0.171003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.12209e30 | 0.282419 | 0.141210 | − | 0.989980i | \(-0.454901\pi\) | ||||
0.141210 | + | 0.989980i | \(0.454901\pi\) | |||||||
\(992\) | −3.03041e31 | −1.04263 | ||||||||
\(993\) | 2.34740e31 | 0.799134 | ||||||||
\(994\) | 2.40777e30 | 0.0811069 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.81971e31 | −0.600176 | ||||||||
\(997\) | −1.48762e31 | −0.485504 | −0.242752 | − | 0.970088i | \(-0.578050\pi\) | ||||
−0.242752 | + | 0.970088i | \(0.578050\pi\) | |||||||
\(998\) | −7.26116e30 | −0.234496 | ||||||||
\(999\) | 7.65682e30 | 0.244687 |
(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 | 75.22.a.n.1.6 | 10 | ||
5.2 | odd | 4 | 15.22.b.a.4.12 | yes | 20 | ||
5.3 | odd | 4 | 15.22.b.a.4.9 | ✓ | 20 | ||
5.4 | even | 2 | 75.22.a.m.1.5 | 10 | |||
15.2 | even | 4 | 45.22.b.d.19.9 | 20 | |||
15.8 | even | 4 | 45.22.b.d.19.12 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.22.b.a.4.9 | ✓ | 20 | 5.3 | odd | 4 | ||
15.22.b.a.4.12 | yes | 20 | 5.2 | odd | 4 | ||
45.22.b.d.19.9 | 20 | 15.2 | even | 4 | |||
45.22.b.d.19.12 | 20 | 15.8 | even | 4 | |||
75.22.a.m.1.5 | 10 | 5.4 | even | 2 | |||
75.22.a.n.1.6 | 10 | 1.1 | even | 1 | trivial |