Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,10,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(11.8458242318\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 640x^{5} - 1455x^{4} + 114552x^{3} + 321544x^{2} - 5741296x - 13379024 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(8.70295\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 17.4059 | 0.769239 | 0.384620 | − | 0.923075i | \(-0.374333\pi\) | ||||
0.384620 | + | 0.923075i | \(0.374333\pi\) | |||||||
\(3\) | 86.8015 | 0.618702 | 0.309351 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309351 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(4\) | −209.035 | −0.408271 | ||||||||
\(5\) | −1221.93 | −0.874343 | −0.437171 | − | 0.899378i | \(-0.644020\pi\) | ||||
−0.437171 | + | 0.899378i | \(0.644020\pi\) | |||||||
\(6\) | 1510.86 | 0.475930 | ||||||||
\(7\) | −4757.43 | −0.748913 | −0.374456 | − | 0.927244i | \(-0.622171\pi\) | ||||
−0.374456 | + | 0.927244i | \(0.622171\pi\) | |||||||
\(8\) | −12550.3 | −1.08330 | ||||||||
\(9\) | −12148.5 | −0.617207 | ||||||||
\(10\) | −21268.8 | −0.672579 | ||||||||
\(11\) | 27321.2 | 0.562643 | 0.281321 | − | 0.959614i | \(-0.409227\pi\) | ||||
0.281321 | + | 0.959614i | \(0.409227\pi\) | |||||||
\(12\) | −18144.5 | −0.252598 | ||||||||
\(13\) | 38402.5 | 0.372919 | 0.186459 | − | 0.982463i | \(-0.440299\pi\) | ||||
0.186459 | + | 0.982463i | \(0.440299\pi\) | |||||||
\(14\) | −82807.4 | −0.576093 | ||||||||
\(15\) | −106066. | −0.540958 | ||||||||
\(16\) | −111423. | −0.425044 | ||||||||
\(17\) | −179820. | −0.522178 | −0.261089 | − | 0.965315i | \(-0.584082\pi\) | ||||
−0.261089 | + | 0.965315i | \(0.584082\pi\) | |||||||
\(18\) | −211455. | −0.474780 | ||||||||
\(19\) | −248560. | −0.437563 | −0.218781 | − | 0.975774i | \(-0.570208\pi\) | ||||
−0.218781 | + | 0.975774i | \(0.570208\pi\) | |||||||
\(20\) | 255426. | 0.356969 | ||||||||
\(21\) | −412952. | −0.463354 | ||||||||
\(22\) | 475550. | 0.432807 | ||||||||
\(23\) | −279841. | −0.208514 | ||||||||
\(24\) | −1.08938e6 | −0.670239 | ||||||||
\(25\) | −460009. | −0.235524 | ||||||||
\(26\) | 668429. | 0.286864 | ||||||||
\(27\) | −2.76302e6 | −1.00057 | ||||||||
\(28\) | 994469. | 0.305760 | ||||||||
\(29\) | 1.71960e6 | 0.451477 | 0.225739 | − | 0.974188i | \(-0.427520\pi\) | ||||
0.225739 | + | 0.974188i | \(0.427520\pi\) | |||||||
\(30\) | −1.84617e6 | −0.416126 | ||||||||
\(31\) | 2.85950e6 | 0.556112 | 0.278056 | − | 0.960565i | \(-0.410310\pi\) | ||||
0.278056 | + | 0.960565i | \(0.410310\pi\) | |||||||
\(32\) | 4.48632e6 | 0.756337 | ||||||||
\(33\) | 2.37152e6 | 0.348108 | ||||||||
\(34\) | −3.12993e6 | −0.401680 | ||||||||
\(35\) | 5.81325e6 | 0.654807 | ||||||||
\(36\) | 2.53946e6 | 0.251988 | ||||||||
\(37\) | 3.16336e6 | 0.277486 | 0.138743 | − | 0.990328i | \(-0.455694\pi\) | ||||
0.138743 | + | 0.990328i | \(0.455694\pi\) | |||||||
\(38\) | −4.32641e6 | −0.336590 | ||||||||
\(39\) | 3.33339e6 | 0.230726 | ||||||||
\(40\) | 1.53356e7 | 0.947173 | ||||||||
\(41\) | 2.07242e7 | 1.14538 | 0.572691 | − | 0.819771i | \(-0.305900\pi\) | ||||
0.572691 | + | 0.819771i | \(0.305900\pi\) | |||||||
\(42\) | −7.18781e6 | −0.356430 | ||||||||
\(43\) | 1.29160e7 | 0.576130 | 0.288065 | − | 0.957611i | \(-0.406988\pi\) | ||||
0.288065 | + | 0.957611i | \(0.406988\pi\) | |||||||
\(44\) | −5.71108e6 | −0.229711 | ||||||||
\(45\) | 1.48446e7 | 0.539651 | ||||||||
\(46\) | −4.87088e6 | −0.160397 | ||||||||
\(47\) | −5.01135e7 | −1.49801 | −0.749005 | − | 0.662565i | \(-0.769468\pi\) | ||||
−0.749005 | + | 0.662565i | \(0.769468\pi\) | |||||||
\(48\) | −9.67166e6 | −0.262976 | ||||||||
\(49\) | −1.77205e7 | −0.439129 | ||||||||
\(50\) | −8.00686e6 | −0.181175 | ||||||||
\(51\) | −1.56087e7 | −0.323073 | ||||||||
\(52\) | −8.02745e6 | −0.152252 | ||||||||
\(53\) | −9.57964e7 | −1.66766 | −0.833830 | − | 0.552021i | \(-0.813857\pi\) | ||||
−0.833830 | + | 0.552021i | \(0.813857\pi\) | |||||||
\(54\) | −4.80929e7 | −0.769678 | ||||||||
\(55\) | −3.33846e7 | −0.491942 | ||||||||
\(56\) | 5.97070e7 | 0.811295 | ||||||||
\(57\) | −2.15754e7 | −0.270721 | ||||||||
\(58\) | 2.99311e7 | 0.347294 | ||||||||
\(59\) | 2.30378e6 | 0.0247519 | 0.0123759 | − | 0.999923i | \(-0.496061\pi\) | ||||
0.0123759 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(60\) | 2.21714e7 | 0.220858 | ||||||||
\(61\) | 3.45895e7 | 0.319860 | 0.159930 | − | 0.987128i | \(-0.448873\pi\) | ||||
0.159930 | + | 0.987128i | \(0.448873\pi\) | |||||||
\(62\) | 4.97721e7 | 0.427783 | ||||||||
\(63\) | 5.77956e7 | 0.462235 | ||||||||
\(64\) | 1.35137e8 | 1.00685 | ||||||||
\(65\) | −4.69252e7 | −0.326059 | ||||||||
\(66\) | 4.12785e7 | 0.267779 | ||||||||
\(67\) | −2.87322e8 | −1.74193 | −0.870967 | − | 0.491342i | \(-0.836507\pi\) | ||||
−0.870967 | + | 0.491342i | \(0.836507\pi\) | |||||||
\(68\) | 3.75887e7 | 0.213190 | ||||||||
\(69\) | −2.42906e7 | −0.129008 | ||||||||
\(70\) | 1.01185e8 | 0.503703 | ||||||||
\(71\) | −6.74618e7 | −0.315061 | −0.157531 | − | 0.987514i | \(-0.550353\pi\) | ||||
−0.157531 | + | 0.987514i | \(0.550353\pi\) | |||||||
\(72\) | 1.52467e8 | 0.668619 | ||||||||
\(73\) | 2.71643e8 | 1.11955 | 0.559777 | − | 0.828643i | \(-0.310887\pi\) | ||||
0.559777 | + | 0.828643i | \(0.310887\pi\) | |||||||
\(74\) | 5.50610e7 | 0.213453 | ||||||||
\(75\) | −3.99295e7 | −0.145720 | ||||||||
\(76\) | 5.19577e7 | 0.178644 | ||||||||
\(77\) | −1.29979e8 | −0.421370 | ||||||||
\(78\) | 5.80207e7 | 0.177483 | ||||||||
\(79\) | −8.11254e7 | −0.234334 | −0.117167 | − | 0.993112i | \(-0.537381\pi\) | ||||
−0.117167 | + | 0.993112i | \(0.537381\pi\) | |||||||
\(80\) | 1.36151e8 | 0.371634 | ||||||||
\(81\) | −715836. | −0.00184770 | ||||||||
\(82\) | 3.60723e8 | 0.881073 | ||||||||
\(83\) | −7.39059e8 | −1.70934 | −0.854669 | − | 0.519173i | \(-0.826240\pi\) | ||||
−0.854669 | + | 0.519173i | \(0.826240\pi\) | |||||||
\(84\) | 8.63214e7 | 0.189174 | ||||||||
\(85\) | 2.19728e8 | 0.456563 | ||||||||
\(86\) | 2.24815e8 | 0.443182 | ||||||||
\(87\) | 1.49264e8 | 0.279330 | ||||||||
\(88\) | −3.42888e8 | −0.609509 | ||||||||
\(89\) | 9.38670e6 | 0.0158583 | 0.00792917 | − | 0.999969i | \(-0.497476\pi\) | ||||
0.00792917 | + | 0.999969i | \(0.497476\pi\) | |||||||
\(90\) | 2.58384e8 | 0.415121 | ||||||||
\(91\) | −1.82697e8 | −0.279284 | ||||||||
\(92\) | 5.84965e7 | 0.0851304 | ||||||||
\(93\) | 2.48209e8 | 0.344068 | ||||||||
\(94\) | −8.72271e8 | −1.15233 | ||||||||
\(95\) | 3.03723e8 | 0.382580 | ||||||||
\(96\) | 3.89420e8 | 0.467948 | ||||||||
\(97\) | −8.96236e7 | −0.102790 | −0.0513948 | − | 0.998678i | \(-0.516367\pi\) | ||||
−0.0513948 | + | 0.998678i | \(0.516367\pi\) | |||||||
\(98\) | −3.08440e8 | −0.337795 | ||||||||
\(99\) | −3.31911e8 | −0.347267 | ||||||||
\(100\) | 9.61578e7 | 0.0961578 | ||||||||
\(101\) | −9.77148e7 | −0.0934360 | −0.0467180 | − | 0.998908i | \(-0.514876\pi\) | ||||
−0.0467180 | + | 0.998908i | \(0.514876\pi\) | |||||||
\(102\) | −2.71683e8 | −0.248520 | ||||||||
\(103\) | −4.56398e8 | −0.399555 | −0.199777 | − | 0.979841i | \(-0.564022\pi\) | ||||
−0.199777 | + | 0.979841i | \(0.564022\pi\) | |||||||
\(104\) | −4.81961e8 | −0.403982 | ||||||||
\(105\) | 5.04599e8 | 0.405131 | ||||||||
\(106\) | −1.66742e9 | −1.28283 | ||||||||
\(107\) | 3.48422e8 | 0.256967 | 0.128484 | − | 0.991712i | \(-0.458989\pi\) | ||||
0.128484 | + | 0.991712i | \(0.458989\pi\) | |||||||
\(108\) | 5.77568e8 | 0.408504 | ||||||||
\(109\) | −2.27997e9 | −1.54707 | −0.773536 | − | 0.633752i | \(-0.781514\pi\) | ||||
−0.773536 | + | 0.633752i | \(0.781514\pi\) | |||||||
\(110\) | −5.81089e8 | −0.378421 | ||||||||
\(111\) | 2.74584e8 | 0.171681 | ||||||||
\(112\) | 5.30086e8 | 0.318321 | ||||||||
\(113\) | 1.23565e9 | 0.712925 | 0.356463 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356463 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(114\) | −3.75539e8 | −0.208249 | ||||||||
\(115\) | 3.41946e8 | 0.182313 | ||||||||
\(116\) | −3.59456e8 | −0.184325 | ||||||||
\(117\) | −4.66532e8 | −0.230168 | ||||||||
\(118\) | 4.00994e7 | 0.0190401 | ||||||||
\(119\) | 8.55483e8 | 0.391066 | ||||||||
\(120\) | 1.33115e9 | 0.586018 | ||||||||
\(121\) | −1.61150e9 | −0.683433 | ||||||||
\(122\) | 6.02061e8 | 0.246049 | ||||||||
\(123\) | 1.79889e9 | 0.708651 | ||||||||
\(124\) | −5.97735e8 | −0.227044 | ||||||||
\(125\) | 2.94868e9 | 1.08027 | ||||||||
\(126\) | 1.00598e9 | 0.355569 | ||||||||
\(127\) | 4.71970e9 | 1.60990 | 0.804948 | − | 0.593345i | \(-0.202193\pi\) | ||||
0.804948 | + | 0.593345i | \(0.202193\pi\) | |||||||
\(128\) | 5.51813e7 | 0.0181697 | ||||||||
\(129\) | 1.12113e9 | 0.356453 | ||||||||
\(130\) | −8.16775e8 | −0.250817 | ||||||||
\(131\) | 4.41996e8 | 0.131129 | 0.0655643 | − | 0.997848i | \(-0.479115\pi\) | ||||
0.0655643 | + | 0.997848i | \(0.479115\pi\) | |||||||
\(132\) | −4.95731e8 | −0.142123 | ||||||||
\(133\) | 1.18251e9 | 0.327696 | ||||||||
\(134\) | −5.00109e9 | −1.33996 | ||||||||
\(135\) | 3.37622e9 | 0.874841 | ||||||||
\(136\) | 2.25679e9 | 0.565674 | ||||||||
\(137\) | −1.47146e9 | −0.356867 | −0.178433 | − | 0.983952i | \(-0.557103\pi\) | ||||
−0.178433 | + | 0.983952i | \(0.557103\pi\) | |||||||
\(138\) | −4.22800e8 | −0.0992383 | ||||||||
\(139\) | −8.12026e8 | −0.184503 | −0.0922515 | − | 0.995736i | \(-0.529406\pi\) | ||||
−0.0922515 | + | 0.995736i | \(0.529406\pi\) | |||||||
\(140\) | −1.21517e9 | −0.267339 | ||||||||
\(141\) | −4.34993e9 | −0.926822 | ||||||||
\(142\) | −1.17423e9 | −0.242358 | ||||||||
\(143\) | 1.04920e9 | 0.209820 | ||||||||
\(144\) | 1.35362e9 | 0.262340 | ||||||||
\(145\) | −2.10123e9 | −0.394746 | ||||||||
\(146\) | 4.72819e9 | 0.861205 | ||||||||
\(147\) | −1.53816e9 | −0.271690 | ||||||||
\(148\) | −6.61251e8 | −0.113289 | ||||||||
\(149\) | 7.31833e9 | 1.21639 | 0.608196 | − | 0.793787i | \(-0.291893\pi\) | ||||
0.608196 | + | 0.793787i | \(0.291893\pi\) | |||||||
\(150\) | −6.95008e8 | −0.112093 | ||||||||
\(151\) | −7.84048e9 | −1.22729 | −0.613644 | − | 0.789583i | \(-0.710297\pi\) | ||||
−0.613644 | + | 0.789583i | \(0.710297\pi\) | |||||||
\(152\) | 3.11949e9 | 0.474010 | ||||||||
\(153\) | 2.18455e9 | 0.322292 | ||||||||
\(154\) | −2.26240e9 | −0.324135 | ||||||||
\(155\) | −3.49411e9 | −0.486232 | ||||||||
\(156\) | −6.96795e8 | −0.0941986 | ||||||||
\(157\) | −1.00803e10 | −1.32412 | −0.662059 | − | 0.749452i | \(-0.730317\pi\) | ||||
−0.662059 | + | 0.749452i | \(0.730317\pi\) | |||||||
\(158\) | −1.41206e9 | −0.180259 | ||||||||
\(159\) | −8.31527e9 | −1.03179 | ||||||||
\(160\) | −5.48198e9 | −0.661298 | ||||||||
\(161\) | 1.33132e9 | 0.156159 | ||||||||
\(162\) | −1.24598e7 | −0.00142132 | ||||||||
\(163\) | −3.70861e9 | −0.411497 | −0.205748 | − | 0.978605i | \(-0.565963\pi\) | ||||
−0.205748 | + | 0.978605i | \(0.565963\pi\) | |||||||
\(164\) | −4.33208e9 | −0.467626 | ||||||||
\(165\) | −2.89784e9 | −0.304366 | ||||||||
\(166\) | −1.28640e10 | −1.31489 | ||||||||
\(167\) | 1.85468e10 | 1.84521 | 0.922604 | − | 0.385748i | \(-0.126057\pi\) | ||||
0.922604 | + | 0.385748i | \(0.126057\pi\) | |||||||
\(168\) | 5.18266e9 | 0.501950 | ||||||||
\(169\) | −9.12975e9 | −0.860932 | ||||||||
\(170\) | 3.82457e9 | 0.351206 | ||||||||
\(171\) | 3.01963e9 | 0.270067 | ||||||||
\(172\) | −2.69990e9 | −0.235217 | ||||||||
\(173\) | 2.30537e10 | 1.95674 | 0.978370 | − | 0.206862i | \(-0.0663250\pi\) | ||||
0.978370 | + | 0.206862i | \(0.0663250\pi\) | |||||||
\(174\) | 2.59807e9 | 0.214872 | ||||||||
\(175\) | 2.18846e9 | 0.176387 | ||||||||
\(176\) | −3.04420e9 | −0.239148 | ||||||||
\(177\) | 1.99972e8 | 0.0153140 | ||||||||
\(178\) | 1.63384e8 | 0.0121989 | ||||||||
\(179\) | 1.30784e10 | 0.952175 | 0.476087 | − | 0.879398i | \(-0.342055\pi\) | ||||
0.476087 | + | 0.879398i | \(0.342055\pi\) | |||||||
\(180\) | −3.10304e9 | −0.220324 | ||||||||
\(181\) | 1.02950e9 | 0.0712972 | 0.0356486 | − | 0.999364i | \(-0.488650\pi\) | ||||
0.0356486 | + | 0.999364i | \(0.488650\pi\) | |||||||
\(182\) | −3.18001e9 | −0.214836 | ||||||||
\(183\) | 3.00242e9 | 0.197898 | ||||||||
\(184\) | 3.51208e9 | 0.225883 | ||||||||
\(185\) | −3.86540e9 | −0.242617 | ||||||||
\(186\) | 4.32030e9 | 0.264670 | ||||||||
\(187\) | −4.91291e9 | −0.293800 | ||||||||
\(188\) | 1.04755e10 | 0.611594 | ||||||||
\(189\) | 1.31449e10 | 0.749340 | ||||||||
\(190\) | 5.28658e9 | 0.294295 | ||||||||
\(191\) | 1.74223e10 | 0.947229 | 0.473614 | − | 0.880732i | \(-0.342949\pi\) | ||||
0.473614 | + | 0.880732i | \(0.342949\pi\) | |||||||
\(192\) | 1.17301e10 | 0.622939 | ||||||||
\(193\) | −9.23682e9 | −0.479198 | −0.239599 | − | 0.970872i | \(-0.577016\pi\) | ||||
−0.239599 | + | 0.970872i | \(0.577016\pi\) | |||||||
\(194\) | −1.55998e9 | −0.0790699 | ||||||||
\(195\) | −4.07318e9 | −0.201733 | ||||||||
\(196\) | 3.70419e9 | 0.179284 | ||||||||
\(197\) | −7.76986e9 | −0.367549 | −0.183774 | − | 0.982968i | \(-0.558832\pi\) | ||||
−0.183774 | + | 0.982968i | \(0.558832\pi\) | |||||||
\(198\) | −5.77721e9 | −0.267131 | ||||||||
\(199\) | −2.26974e9 | −0.102598 | −0.0512989 | − | 0.998683i | \(-0.516336\pi\) | ||||
−0.0512989 | + | 0.998683i | \(0.516336\pi\) | |||||||
\(200\) | 5.77323e9 | 0.255143 | ||||||||
\(201\) | −2.49400e10 | −1.07774 | ||||||||
\(202\) | −1.70081e9 | −0.0718746 | ||||||||
\(203\) | −8.18087e9 | −0.338117 | ||||||||
\(204\) | 3.26276e9 | 0.131901 | ||||||||
\(205\) | −2.53235e10 | −1.00146 | ||||||||
\(206\) | −7.94402e9 | −0.307353 | ||||||||
\(207\) | 3.39965e9 | 0.128697 | ||||||||
\(208\) | −4.27890e9 | −0.158507 | ||||||||
\(209\) | −6.79096e9 | −0.246191 | ||||||||
\(210\) | 8.78301e9 | 0.311642 | ||||||||
\(211\) | 1.46051e10 | 0.507264 | 0.253632 | − | 0.967301i | \(-0.418375\pi\) | ||||
0.253632 | + | 0.967301i | \(0.418375\pi\) | |||||||
\(212\) | 2.00248e10 | 0.680858 | ||||||||
\(213\) | −5.85579e9 | −0.194929 | ||||||||
\(214\) | 6.06459e9 | 0.197669 | ||||||||
\(215\) | −1.57825e10 | −0.503736 | ||||||||
\(216\) | 3.46766e10 | 1.08391 | ||||||||
\(217\) | −1.36039e10 | −0.416479 | ||||||||
\(218\) | −3.96850e10 | −1.19007 | ||||||||
\(219\) | 2.35790e10 | 0.692671 | ||||||||
\(220\) | 6.97855e9 | 0.200846 | ||||||||
\(221\) | −6.90555e9 | −0.194730 | ||||||||
\(222\) | 4.77938e9 | 0.132064 | ||||||||
\(223\) | 3.29844e10 | 0.893176 | 0.446588 | − | 0.894740i | \(-0.352639\pi\) | ||||
0.446588 | + | 0.894740i | \(0.352639\pi\) | |||||||
\(224\) | −2.13434e10 | −0.566431 | ||||||||
\(225\) | 5.58841e9 | 0.145367 | ||||||||
\(226\) | 2.15077e10 | 0.548410 | ||||||||
\(227\) | −5.49978e10 | −1.37477 | −0.687383 | − | 0.726295i | \(-0.741241\pi\) | ||||
−0.687383 | + | 0.726295i | \(0.741241\pi\) | |||||||
\(228\) | 4.51001e9 | 0.110528 | ||||||||
\(229\) | −5.66697e10 | −1.36173 | −0.680865 | − | 0.732408i | \(-0.738396\pi\) | ||||
−0.680865 | + | 0.732408i | \(0.738396\pi\) | |||||||
\(230\) | 5.95189e9 | 0.140242 | ||||||||
\(231\) | −1.12824e10 | −0.260703 | ||||||||
\(232\) | −2.15814e10 | −0.489084 | ||||||||
\(233\) | −2.20205e10 | −0.489469 | −0.244735 | − | 0.969590i | \(-0.578701\pi\) | ||||
−0.244735 | + | 0.969590i | \(0.578701\pi\) | |||||||
\(234\) | −8.12041e9 | −0.177054 | ||||||||
\(235\) | 6.12353e10 | 1.30977 | ||||||||
\(236\) | −4.81571e8 | −0.0101055 | ||||||||
\(237\) | −7.04181e9 | −0.144983 | ||||||||
\(238\) | 1.48905e10 | 0.300823 | ||||||||
\(239\) | 2.61002e10 | 0.517432 | 0.258716 | − | 0.965953i | \(-0.416701\pi\) | ||||
0.258716 | + | 0.965953i | \(0.416701\pi\) | |||||||
\(240\) | 1.18181e10 | 0.229931 | ||||||||
\(241\) | −7.14912e10 | −1.36514 | −0.682568 | − | 0.730822i | \(-0.739137\pi\) | ||||
−0.682568 | + | 0.730822i | \(0.739137\pi\) | |||||||
\(242\) | −2.80496e10 | −0.525724 | ||||||||
\(243\) | 5.43224e10 | 0.999427 | ||||||||
\(244\) | −7.23041e9 | −0.130590 | ||||||||
\(245\) | 2.16532e10 | 0.383950 | ||||||||
\(246\) | 3.13113e10 | 0.545122 | ||||||||
\(247\) | −9.54532e9 | −0.163175 | ||||||||
\(248\) | −3.58874e10 | −0.602434 | ||||||||
\(249\) | −6.41515e10 | −1.05757 | ||||||||
\(250\) | 5.13245e10 | 0.830988 | ||||||||
\(251\) | −4.35139e10 | −0.691984 | −0.345992 | − | 0.938238i | \(-0.612458\pi\) | ||||
−0.345992 | + | 0.938238i | \(0.612458\pi\) | |||||||
\(252\) | −1.20813e10 | −0.188717 | ||||||||
\(253\) | −7.64559e9 | −0.117319 | ||||||||
\(254\) | 8.21506e10 | 1.23840 | ||||||||
\(255\) | 1.90727e10 | 0.282477 | ||||||||
\(256\) | −6.82296e10 | −0.992871 | ||||||||
\(257\) | −7.66199e10 | −1.09558 | −0.547788 | − | 0.836617i | \(-0.684530\pi\) | ||||
−0.547788 | + | 0.836617i | \(0.684530\pi\) | |||||||
\(258\) | 1.95143e10 | 0.274198 | ||||||||
\(259\) | −1.50494e10 | −0.207813 | ||||||||
\(260\) | 9.80900e9 | 0.133120 | ||||||||
\(261\) | −2.08905e10 | −0.278655 | ||||||||
\(262\) | 7.69334e9 | 0.100869 | ||||||||
\(263\) | 1.11739e11 | 1.44013 | 0.720067 | − | 0.693904i | \(-0.244111\pi\) | ||||
0.720067 | + | 0.693904i | \(0.244111\pi\) | |||||||
\(264\) | −2.97632e10 | −0.377105 | ||||||||
\(265\) | 1.17057e11 | 1.45811 | ||||||||
\(266\) | 2.05826e10 | 0.252077 | ||||||||
\(267\) | 8.14780e8 | 0.00981160 | ||||||||
\(268\) | 6.00602e10 | 0.711181 | ||||||||
\(269\) | 8.03903e10 | 0.936092 | 0.468046 | − | 0.883704i | \(-0.344958\pi\) | ||||
0.468046 | + | 0.883704i | \(0.344958\pi\) | |||||||
\(270\) | 5.87662e10 | 0.672962 | ||||||||
\(271\) | 1.13706e11 | 1.28063 | 0.640314 | − | 0.768113i | \(-0.278804\pi\) | ||||
0.640314 | + | 0.768113i | \(0.278804\pi\) | |||||||
\(272\) | 2.00361e10 | 0.221949 | ||||||||
\(273\) | −1.58584e10 | −0.172793 | ||||||||
\(274\) | −2.56121e10 | −0.274516 | ||||||||
\(275\) | −1.25680e10 | −0.132516 | ||||||||
\(276\) | 5.07759e9 | 0.0526704 | ||||||||
\(277\) | 1.21360e11 | 1.23856 | 0.619278 | − | 0.785172i | \(-0.287425\pi\) | ||||
0.619278 | + | 0.785172i | \(0.287425\pi\) | |||||||
\(278\) | −1.41340e10 | −0.141927 | ||||||||
\(279\) | −3.47386e10 | −0.343236 | ||||||||
\(280\) | −7.29578e10 | −0.709350 | ||||||||
\(281\) | −5.81904e10 | −0.556766 | −0.278383 | − | 0.960470i | \(-0.589798\pi\) | ||||
−0.278383 | + | 0.960470i | \(0.589798\pi\) | |||||||
\(282\) | −7.57144e10 | −0.712948 | ||||||||
\(283\) | 1.03826e11 | 0.962203 | 0.481102 | − | 0.876665i | \(-0.340237\pi\) | ||||
0.481102 | + | 0.876665i | \(0.340237\pi\) | |||||||
\(284\) | 1.41019e10 | 0.128630 | ||||||||
\(285\) | 2.63637e10 | 0.236703 | ||||||||
\(286\) | 1.82623e10 | 0.161402 | ||||||||
\(287\) | −9.85939e10 | −0.857791 | ||||||||
\(288\) | −5.45020e10 | −0.466817 | ||||||||
\(289\) | −8.62525e10 | −0.727330 | ||||||||
\(290\) | −3.65738e10 | −0.303654 | ||||||||
\(291\) | −7.77947e9 | −0.0635962 | ||||||||
\(292\) | −5.67828e10 | −0.457082 | ||||||||
\(293\) | −8.50392e9 | −0.0674086 | −0.0337043 | − | 0.999432i | \(-0.510730\pi\) | ||||
−0.0337043 | + | 0.999432i | \(0.510730\pi\) | |||||||
\(294\) | −2.67731e10 | −0.208995 | ||||||||
\(295\) | −2.81507e9 | −0.0216416 | ||||||||
\(296\) | −3.97009e10 | −0.300599 | ||||||||
\(297\) | −7.54891e10 | −0.562963 | ||||||||
\(298\) | 1.27382e11 | 0.935697 | ||||||||
\(299\) | −1.07466e10 | −0.0777589 | ||||||||
\(300\) | 8.34665e9 | 0.0594931 | ||||||||
\(301\) | −6.14471e10 | −0.431472 | ||||||||
\(302\) | −1.36471e11 | −0.944077 | ||||||||
\(303\) | −8.48180e9 | −0.0578091 | ||||||||
\(304\) | 2.76952e10 | 0.185983 | ||||||||
\(305\) | −4.22660e10 | −0.279667 | ||||||||
\(306\) | 3.80240e10 | 0.247920 | ||||||||
\(307\) | −1.78304e11 | −1.14561 | −0.572806 | − | 0.819691i | \(-0.694145\pi\) | ||||
−0.572806 | + | 0.819691i | \(0.694145\pi\) | |||||||
\(308\) | 2.71701e10 | 0.172033 | ||||||||
\(309\) | −3.96161e10 | −0.247205 | ||||||||
\(310\) | −6.08181e10 | −0.374029 | ||||||||
\(311\) | 1.47575e11 | 0.894522 | 0.447261 | − | 0.894403i | \(-0.352400\pi\) | ||||
0.447261 | + | 0.894403i | \(0.352400\pi\) | |||||||
\(312\) | −4.18349e10 | −0.249944 | ||||||||
\(313\) | 2.46802e11 | 1.45344 | 0.726722 | − | 0.686931i | \(-0.241043\pi\) | ||||
0.726722 | + | 0.686931i | \(0.241043\pi\) | |||||||
\(314\) | −1.75457e11 | −1.01856 | ||||||||
\(315\) | −7.06223e10 | −0.404152 | ||||||||
\(316\) | 1.69580e10 | 0.0956718 | ||||||||
\(317\) | 4.21754e10 | 0.234581 | 0.117290 | − | 0.993098i | \(-0.462579\pi\) | ||||
0.117290 | + | 0.993098i | \(0.462579\pi\) | |||||||
\(318\) | −1.44735e11 | −0.793690 | ||||||||
\(319\) | 4.69815e10 | 0.254020 | ||||||||
\(320\) | −1.65128e11 | −0.880330 | ||||||||
\(321\) | 3.02435e10 | 0.158986 | ||||||||
\(322\) | 2.31729e10 | 0.120124 | ||||||||
\(323\) | 4.46962e10 | 0.228486 | ||||||||
\(324\) | 1.49635e8 | 0.000754362 0 | ||||||||
\(325\) | −1.76655e10 | −0.0878315 | ||||||||
\(326\) | −6.45516e10 | −0.316539 | ||||||||
\(327\) | −1.97905e11 | −0.957177 | ||||||||
\(328\) | −2.60094e11 | −1.24079 | ||||||||
\(329\) | 2.38412e11 | 1.12188 | ||||||||
\(330\) | −5.04394e10 | −0.234130 | ||||||||
\(331\) | 3.27950e11 | 1.50170 | 0.750848 | − | 0.660475i | \(-0.229645\pi\) | ||||
0.750848 | + | 0.660475i | \(0.229645\pi\) | |||||||
\(332\) | 1.54489e11 | 0.697873 | ||||||||
\(333\) | −3.84300e10 | −0.171266 | ||||||||
\(334\) | 3.22824e11 | 1.41941 | ||||||||
\(335\) | 3.51087e11 | 1.52305 | ||||||||
\(336\) | 4.60122e10 | 0.196946 | ||||||||
\(337\) | −3.96900e11 | −1.67628 | −0.838140 | − | 0.545455i | \(-0.816357\pi\) | ||||
−0.838140 | + | 0.545455i | \(0.816357\pi\) | |||||||
\(338\) | −1.58911e11 | −0.662262 | ||||||||
\(339\) | 1.07257e11 | 0.441089 | ||||||||
\(340\) | −4.59308e10 | −0.186401 | ||||||||
\(341\) | 7.81249e10 | 0.312892 | ||||||||
\(342\) | 5.25594e10 | 0.207746 | ||||||||
\(343\) | 2.76283e11 | 1.07778 | ||||||||
\(344\) | −1.62099e11 | −0.624121 | ||||||||
\(345\) | 2.96815e10 | 0.112798 | ||||||||
\(346\) | 4.01270e11 | 1.50520 | ||||||||
\(347\) | 1.37404e11 | 0.508765 | 0.254383 | − | 0.967104i | \(-0.418128\pi\) | ||||
0.254383 | + | 0.967104i | \(0.418128\pi\) | |||||||
\(348\) | −3.12013e10 | −0.114042 | ||||||||
\(349\) | 1.29416e11 | 0.466954 | 0.233477 | − | 0.972362i | \(-0.424990\pi\) | ||||
0.233477 | + | 0.972362i | \(0.424990\pi\) | |||||||
\(350\) | 3.80921e10 | 0.135684 | ||||||||
\(351\) | −1.06107e11 | −0.373131 | ||||||||
\(352\) | 1.22572e11 | 0.425547 | ||||||||
\(353\) | −1.00183e11 | −0.343405 | −0.171703 | − | 0.985149i | \(-0.554927\pi\) | ||||
−0.171703 | + | 0.985149i | \(0.554927\pi\) | |||||||
\(354\) | 3.48069e9 | 0.0117802 | ||||||||
\(355\) | 8.24336e10 | 0.275472 | ||||||||
\(356\) | −1.96215e9 | −0.00647450 | ||||||||
\(357\) | 7.42573e10 | 0.241954 | ||||||||
\(358\) | 2.27642e11 | 0.732450 | ||||||||
\(359\) | 5.68478e10 | 0.180630 | 0.0903148 | − | 0.995913i | \(-0.471213\pi\) | ||||
0.0903148 | + | 0.995913i | \(0.471213\pi\) | |||||||
\(360\) | −1.86304e11 | −0.584602 | ||||||||
\(361\) | −2.60906e11 | −0.808539 | ||||||||
\(362\) | 1.79194e10 | 0.0548446 | ||||||||
\(363\) | −1.39881e11 | −0.422842 | ||||||||
\(364\) | 3.81901e10 | 0.114023 | ||||||||
\(365\) | −3.31929e11 | −0.978875 | ||||||||
\(366\) | 5.22599e10 | 0.152231 | ||||||||
\(367\) | −1.76569e11 | −0.508063 | −0.254031 | − | 0.967196i | \(-0.581757\pi\) | ||||
−0.254031 | + | 0.967196i | \(0.581757\pi\) | |||||||
\(368\) | 3.11806e10 | 0.0886277 | ||||||||
\(369\) | −2.51768e11 | −0.706938 | ||||||||
\(370\) | −6.72808e10 | −0.186631 | ||||||||
\(371\) | 4.55745e11 | 1.24893 | ||||||||
\(372\) | −5.18843e10 | −0.140473 | ||||||||
\(373\) | −6.26809e11 | −1.67666 | −0.838331 | − | 0.545161i | \(-0.816468\pi\) | ||||
−0.838331 | + | 0.545161i | \(0.816468\pi\) | |||||||
\(374\) | −8.55135e10 | −0.226002 | ||||||||
\(375\) | 2.55950e11 | 0.668367 | ||||||||
\(376\) | 6.28937e11 | 1.62279 | ||||||||
\(377\) | 6.60368e10 | 0.168364 | ||||||||
\(378\) | 2.28799e11 | 0.576422 | ||||||||
\(379\) | −3.36046e11 | −0.836608 | −0.418304 | − | 0.908307i | \(-0.637375\pi\) | ||||
−0.418304 | + | 0.908307i | \(0.637375\pi\) | |||||||
\(380\) | −6.34888e10 | −0.156196 | ||||||||
\(381\) | 4.09677e11 | 0.996046 | ||||||||
\(382\) | 3.03250e11 | 0.728645 | ||||||||
\(383\) | −7.94383e11 | −1.88641 | −0.943203 | − | 0.332216i | \(-0.892204\pi\) | ||||
−0.943203 | + | 0.332216i | \(0.892204\pi\) | |||||||
\(384\) | 4.78982e9 | 0.0112416 | ||||||||
\(385\) | 1.58825e11 | 0.368422 | ||||||||
\(386\) | −1.60775e11 | −0.368618 | ||||||||
\(387\) | −1.56910e11 | −0.355592 | ||||||||
\(388\) | 1.87344e10 | 0.0419661 | ||||||||
\(389\) | −6.84594e11 | −1.51586 | −0.757932 | − | 0.652334i | \(-0.773790\pi\) | ||||
−0.757932 | + | 0.652334i | \(0.773790\pi\) | |||||||
\(390\) | −7.08973e10 | −0.155181 | ||||||||
\(391\) | 5.03211e10 | 0.108882 | ||||||||
\(392\) | 2.22396e11 | 0.475708 | ||||||||
\(393\) | 3.83659e10 | 0.0811296 | ||||||||
\(394\) | −1.35241e11 | −0.282733 | ||||||||
\(395\) | 9.91297e10 | 0.204888 | ||||||||
\(396\) | 6.93810e10 | 0.141779 | ||||||||
\(397\) | −9.42340e11 | −1.90393 | −0.951964 | − | 0.306211i | \(-0.900939\pi\) | ||||
−0.951964 | + | 0.306211i | \(0.900939\pi\) | |||||||
\(398\) | −3.95069e10 | −0.0789222 | ||||||||
\(399\) | 1.02643e11 | 0.202747 | ||||||||
\(400\) | 5.12554e10 | 0.100108 | ||||||||
\(401\) | 7.70083e11 | 1.48726 | 0.743632 | − | 0.668589i | \(-0.233101\pi\) | ||||
0.743632 | + | 0.668589i | \(0.233101\pi\) | |||||||
\(402\) | −4.34102e11 | −0.829039 | ||||||||
\(403\) | 1.09812e11 | 0.207384 | ||||||||
\(404\) | 2.04258e10 | 0.0381472 | ||||||||
\(405\) | 8.74702e8 | 0.00161552 | ||||||||
\(406\) | −1.42395e11 | −0.260093 | ||||||||
\(407\) | 8.64267e10 | 0.156125 | ||||||||
\(408\) | 1.95893e11 | 0.349984 | ||||||||
\(409\) | −8.77773e11 | −1.55106 | −0.775528 | − | 0.631313i | \(-0.782516\pi\) | ||||
−0.775528 | + | 0.631313i | \(0.782516\pi\) | |||||||
\(410\) | −4.40779e11 | −0.770360 | ||||||||
\(411\) | −1.27725e11 | −0.220794 | ||||||||
\(412\) | 9.54031e10 | 0.163127 | ||||||||
\(413\) | −1.09601e10 | −0.0185370 | ||||||||
\(414\) | 5.91739e10 | 0.0989985 | ||||||||
\(415\) | 9.03080e11 | 1.49455 | ||||||||
\(416\) | 1.72286e11 | 0.282052 | ||||||||
\(417\) | −7.04851e10 | −0.114152 | ||||||||
\(418\) | −1.18203e11 | −0.189380 | ||||||||
\(419\) | −8.32714e11 | −1.31988 | −0.659938 | − | 0.751320i | \(-0.729417\pi\) | ||||
−0.659938 | + | 0.751320i | \(0.729417\pi\) | |||||||
\(420\) | −1.05479e11 | −0.165403 | ||||||||
\(421\) | −2.38934e11 | −0.370689 | −0.185344 | − | 0.982674i | \(-0.559340\pi\) | ||||
−0.185344 | + | 0.982674i | \(0.559340\pi\) | |||||||
\(422\) | 2.54215e11 | 0.390207 | ||||||||
\(423\) | 6.08804e11 | 0.924582 | ||||||||
\(424\) | 1.20227e12 | 1.80657 | ||||||||
\(425\) | 8.27189e10 | 0.122986 | ||||||||
\(426\) | −1.01925e11 | −0.149947 | ||||||||
\(427\) | −1.64557e11 | −0.239547 | ||||||||
\(428\) | −7.28322e10 | −0.104912 | ||||||||
\(429\) | 9.10723e10 | 0.129816 | ||||||||
\(430\) | −2.74709e11 | −0.387493 | ||||||||
\(431\) | 1.24978e12 | 1.74456 | 0.872282 | − | 0.489003i | \(-0.162639\pi\) | ||||
0.872282 | + | 0.489003i | \(0.162639\pi\) | |||||||
\(432\) | 3.07863e11 | 0.425286 | ||||||||
\(433\) | −1.65520e11 | −0.226284 | −0.113142 | − | 0.993579i | \(-0.536092\pi\) | ||||
−0.113142 | + | 0.993579i | \(0.536092\pi\) | |||||||
\(434\) | −2.36787e11 | −0.320372 | ||||||||
\(435\) | −1.82390e11 | −0.244230 | ||||||||
\(436\) | 4.76594e11 | 0.631625 | ||||||||
\(437\) | 6.95573e10 | 0.0912381 | ||||||||
\(438\) | 4.10414e11 | 0.532830 | ||||||||
\(439\) | −1.47477e12 | −1.89510 | −0.947552 | − | 0.319601i | \(-0.896451\pi\) | ||||
−0.947552 | + | 0.319601i | \(0.896451\pi\) | |||||||
\(440\) | 4.18986e11 | 0.532920 | ||||||||
\(441\) | 2.15277e11 | 0.271034 | ||||||||
\(442\) | −1.20197e11 | −0.149794 | ||||||||
\(443\) | −1.24460e12 | −1.53537 | −0.767687 | − | 0.640825i | \(-0.778592\pi\) | ||||
−0.767687 | + | 0.640825i | \(0.778592\pi\) | |||||||
\(444\) | −5.73976e10 | −0.0700924 | ||||||||
\(445\) | −1.14699e10 | −0.0138656 | ||||||||
\(446\) | 5.74124e11 | 0.687066 | ||||||||
\(447\) | 6.35242e11 | 0.752585 | ||||||||
\(448\) | −6.42904e11 | −0.754041 | ||||||||
\(449\) | 1.26508e12 | 1.46896 | 0.734479 | − | 0.678631i | \(-0.237426\pi\) | ||||
0.734479 | + | 0.678631i | \(0.237426\pi\) | |||||||
\(450\) | 9.72713e10 | 0.111822 | ||||||||
\(451\) | 5.66210e11 | 0.644441 | ||||||||
\(452\) | −2.58295e11 | −0.291067 | ||||||||
\(453\) | −6.80565e11 | −0.759325 | ||||||||
\(454\) | −9.57286e11 | −1.05752 | ||||||||
\(455\) | 2.23243e11 | 0.244190 | ||||||||
\(456\) | 2.70777e11 | 0.293271 | ||||||||
\(457\) | 2.54937e10 | 0.0273407 | 0.0136703 | − | 0.999907i | \(-0.495648\pi\) | ||||
0.0136703 | + | 0.999907i | \(0.495648\pi\) | |||||||
\(458\) | −9.86387e11 | −1.04750 | ||||||||
\(459\) | 4.96848e11 | 0.522476 | ||||||||
\(460\) | −7.14787e10 | −0.0744332 | ||||||||
\(461\) | 1.25077e12 | 1.28981 | 0.644903 | − | 0.764264i | \(-0.276898\pi\) | ||||
0.644903 | + | 0.764264i | \(0.276898\pi\) | |||||||
\(462\) | −1.96379e11 | −0.200543 | ||||||||
\(463\) | 7.17086e11 | 0.725199 | 0.362599 | − | 0.931945i | \(-0.381889\pi\) | ||||
0.362599 | + | 0.931945i | \(0.381889\pi\) | |||||||
\(464\) | −1.91602e11 | −0.191898 | ||||||||
\(465\) | −3.03294e11 | −0.300833 | ||||||||
\(466\) | −3.83286e11 | −0.376519 | ||||||||
\(467\) | −4.76349e11 | −0.463446 | −0.231723 | − | 0.972782i | \(-0.574436\pi\) | ||||
−0.231723 | + | 0.972782i | \(0.574436\pi\) | |||||||
\(468\) | 9.75215e10 | 0.0939710 | ||||||||
\(469\) | 1.36691e12 | 1.30456 | ||||||||
\(470\) | 1.06585e12 | 1.00753 | ||||||||
\(471\) | −8.74989e11 | −0.819235 | ||||||||
\(472\) | −2.89131e10 | −0.0268136 | ||||||||
\(473\) | 3.52881e11 | 0.324156 | ||||||||
\(474\) | −1.22569e11 | −0.111527 | ||||||||
\(475\) | 1.14340e11 | 0.103057 | ||||||||
\(476\) | −1.78826e11 | −0.159661 | ||||||||
\(477\) | 1.16378e12 | 1.02929 | ||||||||
\(478\) | 4.54298e11 | 0.398029 | ||||||||
\(479\) | 2.64981e11 | 0.229988 | 0.114994 | − | 0.993366i | \(-0.463315\pi\) | ||||
0.114994 | + | 0.993366i | \(0.463315\pi\) | |||||||
\(480\) | −4.75844e11 | −0.409147 | ||||||||
\(481\) | 1.21481e11 | 0.103480 | ||||||||
\(482\) | −1.24437e12 | −1.05012 | ||||||||
\(483\) | 1.15561e11 | 0.0966160 | ||||||||
\(484\) | 3.36860e11 | 0.279026 | ||||||||
\(485\) | 1.09514e11 | 0.0898734 | ||||||||
\(486\) | 9.45531e11 | 0.768798 | ||||||||
\(487\) | −1.44171e12 | −1.16144 | −0.580720 | − | 0.814103i | \(-0.697229\pi\) | ||||
−0.580720 | + | 0.814103i | \(0.697229\pi\) | |||||||
\(488\) | −4.34107e11 | −0.346504 | ||||||||
\(489\) | −3.21913e11 | −0.254594 | ||||||||
\(490\) | 3.76893e11 | 0.295349 | ||||||||
\(491\) | 4.61624e10 | 0.0358444 | 0.0179222 | − | 0.999839i | \(-0.494295\pi\) | ||||
0.0179222 | + | 0.999839i | \(0.494295\pi\) | |||||||
\(492\) | −3.76031e11 | −0.289322 | ||||||||
\(493\) | −3.09219e11 | −0.235752 | ||||||||
\(494\) | −1.66145e11 | −0.125521 | ||||||||
\(495\) | 4.05573e11 | 0.303631 | ||||||||
\(496\) | −3.18613e11 | −0.236372 | ||||||||
\(497\) | 3.20945e11 | 0.235954 | ||||||||
\(498\) | −1.11661e12 | −0.813525 | ||||||||
\(499\) | 3.30266e11 | 0.238458 | 0.119229 | − | 0.992867i | \(-0.461958\pi\) | ||||
0.119229 | + | 0.992867i | \(0.461958\pi\) | |||||||
\(500\) | −6.16378e11 | −0.441044 | ||||||||
\(501\) | 1.60989e12 | 1.14163 | ||||||||
\(502\) | −7.57398e11 | −0.532301 | ||||||||
\(503\) | −8.35422e11 | −0.581902 | −0.290951 | − | 0.956738i | \(-0.593972\pi\) | ||||
−0.290951 | + | 0.956738i | \(0.593972\pi\) | |||||||
\(504\) | −7.25350e11 | −0.500738 | ||||||||
\(505\) | 1.19401e11 | 0.0816951 | ||||||||
\(506\) | −1.33078e11 | −0.0902464 | ||||||||
\(507\) | −7.92476e11 | −0.532660 | ||||||||
\(508\) | −9.86582e11 | −0.657274 | ||||||||
\(509\) | −2.24802e12 | −1.48446 | −0.742232 | − | 0.670144i | \(-0.766233\pi\) | ||||
−0.742232 | + | 0.670144i | \(0.766233\pi\) | |||||||
\(510\) | 3.31978e11 | 0.217292 | ||||||||
\(511\) | −1.29232e12 | −0.838449 | ||||||||
\(512\) | −1.21585e12 | −0.781925 | ||||||||
\(513\) | 6.86777e11 | 0.437812 | ||||||||
\(514\) | −1.33364e12 | −0.842760 | ||||||||
\(515\) | 5.57687e11 | 0.349348 | ||||||||
\(516\) | −2.34355e11 | −0.145530 | ||||||||
\(517\) | −1.36916e12 | −0.842844 | ||||||||
\(518\) | −2.61949e11 | −0.159858 | ||||||||
\(519\) | 2.00110e12 | 1.21064 | ||||||||
\(520\) | 5.88923e11 | 0.353219 | ||||||||
\(521\) | −1.16406e12 | −0.692158 | −0.346079 | − | 0.938205i | \(-0.612487\pi\) | ||||
−0.346079 | + | 0.938205i | \(0.612487\pi\) | |||||||
\(522\) | −3.63618e11 | −0.214352 | ||||||||
\(523\) | −1.70100e12 | −0.994136 | −0.497068 | − | 0.867712i | \(-0.665590\pi\) | ||||
−0.497068 | + | 0.867712i | \(0.665590\pi\) | |||||||
\(524\) | −9.23925e10 | −0.0535360 | ||||||||
\(525\) | 1.89962e11 | 0.109131 | ||||||||
\(526\) | 1.94491e12 | 1.10781 | ||||||||
\(527\) | −5.14196e11 | −0.290389 | ||||||||
\(528\) | −2.64241e11 | −0.147961 | ||||||||
\(529\) | 7.83110e10 | 0.0434783 | ||||||||
\(530\) | 2.03748e12 | 1.12163 | ||||||||
\(531\) | −2.79875e10 | −0.0152770 | ||||||||
\(532\) | −2.47185e11 | −0.133789 | ||||||||
\(533\) | 7.95860e11 | 0.427134 | ||||||||
\(534\) | 1.41820e10 | 0.00754746 | ||||||||
\(535\) | −4.25747e11 | −0.224678 | ||||||||
\(536\) | 3.60596e12 | 1.88703 | ||||||||
\(537\) | 1.13523e12 | 0.589113 | ||||||||
\(538\) | 1.39927e12 | 0.720079 | ||||||||
\(539\) | −4.84144e11 | −0.247073 | ||||||||
\(540\) | −7.05748e11 | −0.357172 | ||||||||
\(541\) | 2.74399e12 | 1.37719 | 0.688596 | − | 0.725145i | \(-0.258227\pi\) | ||||
0.688596 | + | 0.725145i | \(0.258227\pi\) | |||||||
\(542\) | 1.97916e12 | 0.985109 | ||||||||
\(543\) | 8.93621e10 | 0.0441117 | ||||||||
\(544\) | −8.06732e11 | −0.394943 | ||||||||
\(545\) | 2.78597e12 | 1.35267 | ||||||||
\(546\) | −2.76030e11 | −0.132919 | ||||||||
\(547\) | −2.82754e12 | −1.35041 | −0.675205 | − | 0.737630i | \(-0.735945\pi\) | ||||
−0.675205 | + | 0.737630i | \(0.735945\pi\) | |||||||
\(548\) | 3.07587e11 | 0.145698 | ||||||||
\(549\) | −4.20210e11 | −0.197420 | ||||||||
\(550\) | −2.18757e11 | −0.101937 | ||||||||
\(551\) | −4.27424e11 | −0.197550 | ||||||||
\(552\) | 3.04854e11 | 0.139754 | ||||||||
\(553\) | 3.85949e11 | 0.175496 | ||||||||
\(554\) | 2.11237e12 | 0.952746 | ||||||||
\(555\) | −3.35523e11 | −0.150108 | ||||||||
\(556\) | 1.69742e11 | 0.0753272 | ||||||||
\(557\) | 2.18194e12 | 0.960495 | 0.480248 | − | 0.877133i | \(-0.340547\pi\) | ||||
0.480248 | + | 0.877133i | \(0.340547\pi\) | |||||||
\(558\) | −6.04656e11 | −0.264031 | ||||||||
\(559\) | 4.96007e11 | 0.214850 | ||||||||
\(560\) | −6.47728e11 | −0.278321 | ||||||||
\(561\) | −4.26448e11 | −0.181775 | ||||||||
\(562\) | −1.01286e12 | −0.428286 | ||||||||
\(563\) | −4.18295e11 | −0.175467 | −0.0877334 | − | 0.996144i | \(-0.527962\pi\) | ||||
−0.0877334 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(564\) | 9.09287e11 | 0.378395 | ||||||||
\(565\) | −1.50988e12 | −0.623341 | ||||||||
\(566\) | 1.80718e12 | 0.740164 | ||||||||
\(567\) | 3.40554e9 | 0.00138376 | ||||||||
\(568\) | 8.46662e11 | 0.341305 | ||||||||
\(569\) | 3.01046e12 | 1.20400 | 0.602001 | − | 0.798495i | \(-0.294370\pi\) | ||||
0.602001 | + | 0.798495i | \(0.294370\pi\) | |||||||
\(570\) | 4.58883e11 | 0.182081 | ||||||||
\(571\) | −1.96565e11 | −0.0773825 | −0.0386913 | − | 0.999251i | \(-0.512319\pi\) | ||||
−0.0386913 | + | 0.999251i | \(0.512319\pi\) | |||||||
\(572\) | −2.19320e11 | −0.0856634 | ||||||||
\(573\) | 1.51228e12 | 0.586053 | ||||||||
\(574\) | −1.71612e12 | −0.659847 | ||||||||
\(575\) | 1.28729e11 | 0.0491102 | ||||||||
\(576\) | −1.64171e12 | −0.621434 | ||||||||
\(577\) | 1.24381e12 | 0.467157 | 0.233578 | − | 0.972338i | \(-0.424956\pi\) | ||||
0.233578 | + | 0.972338i | \(0.424956\pi\) | |||||||
\(578\) | −1.50130e12 | −0.559491 | ||||||||
\(579\) | −8.01770e11 | −0.296481 | ||||||||
\(580\) | 4.39230e11 | 0.161163 | ||||||||
\(581\) | 3.51602e12 | 1.28015 | ||||||||
\(582\) | −1.35409e11 | −0.0489207 | ||||||||
\(583\) | −2.61727e12 | −0.938297 | ||||||||
\(584\) | −3.40919e12 | −1.21281 | ||||||||
\(585\) | 5.70070e11 | 0.201246 | ||||||||
\(586\) | −1.48018e11 | −0.0518533 | ||||||||
\(587\) | 2.36780e11 | 0.0823139 | 0.0411570 | − | 0.999153i | \(-0.486896\pi\) | ||||
0.0411570 | + | 0.999153i | \(0.486896\pi\) | |||||||
\(588\) | 3.21529e11 | 0.110923 | ||||||||
\(589\) | −7.10757e11 | −0.243334 | ||||||||
\(590\) | −4.89987e10 | −0.0166476 | ||||||||
\(591\) | −6.74436e11 | −0.227403 | ||||||||
\(592\) | −3.52469e11 | −0.117943 | ||||||||
\(593\) | −1.88281e12 | −0.625259 | −0.312630 | − | 0.949875i | \(-0.601210\pi\) | ||||
−0.312630 | + | 0.949875i | \(0.601210\pi\) | |||||||
\(594\) | −1.31395e12 | −0.433053 | ||||||||
\(595\) | −1.04534e12 | −0.341926 | ||||||||
\(596\) | −1.52979e12 | −0.496618 | ||||||||
\(597\) | −1.97017e11 | −0.0634775 | ||||||||
\(598\) | −1.87054e11 | −0.0598152 | ||||||||
\(599\) | −9.75007e11 | −0.309447 | −0.154724 | − | 0.987958i | \(-0.549449\pi\) | ||||
−0.154724 | + | 0.987958i | \(0.549449\pi\) | |||||||
\(600\) | 5.01125e11 | 0.157858 | ||||||||
\(601\) | −5.03518e12 | −1.57427 | −0.787135 | − | 0.616780i | \(-0.788437\pi\) | ||||
−0.787135 | + | 0.616780i | \(0.788437\pi\) | |||||||
\(602\) | −1.06954e12 | −0.331905 | ||||||||
\(603\) | 3.49052e12 | 1.07513 | ||||||||
\(604\) | 1.63893e12 | 0.501066 | ||||||||
\(605\) | 1.96914e12 | 0.597555 | ||||||||
\(606\) | −1.47633e11 | −0.0444690 | ||||||||
\(607\) | 9.31056e11 | 0.278373 | 0.139186 | − | 0.990266i | \(-0.455551\pi\) | ||||
0.139186 | + | 0.990266i | \(0.455551\pi\) | |||||||
\(608\) | −1.11512e12 | −0.330945 | ||||||||
\(609\) | −7.10112e11 | −0.209194 | ||||||||
\(610\) | −7.35678e11 | −0.215131 | ||||||||
\(611\) | −1.92448e12 | −0.558636 | ||||||||
\(612\) | −4.56646e11 | −0.131583 | ||||||||
\(613\) | 1.84008e12 | 0.526337 | 0.263168 | − | 0.964750i | \(-0.415233\pi\) | ||||
0.263168 | + | 0.964750i | \(0.415233\pi\) | |||||||
\(614\) | −3.10353e12 | −0.881249 | ||||||||
\(615\) | −2.19812e12 | −0.619604 | ||||||||
\(616\) | 1.63127e12 | 0.456469 | ||||||||
\(617\) | −4.14604e12 | −1.15173 | −0.575865 | − | 0.817545i | \(-0.695335\pi\) | ||||
−0.575865 | + | 0.817545i | \(0.695335\pi\) | |||||||
\(618\) | −6.89553e11 | −0.190160 | ||||||||
\(619\) | 5.89090e11 | 0.161277 | 0.0806387 | − | 0.996743i | \(-0.474304\pi\) | ||||
0.0806387 | + | 0.996743i | \(0.474304\pi\) | |||||||
\(620\) | 7.30391e11 | 0.198515 | ||||||||
\(621\) | 7.73207e11 | 0.208633 | ||||||||
\(622\) | 2.56867e12 | 0.688101 | ||||||||
\(623\) | −4.46566e10 | −0.0118765 | ||||||||
\(624\) | −3.71416e11 | −0.0980685 | ||||||||
\(625\) | −2.70463e12 | −0.709004 | ||||||||
\(626\) | 4.29580e12 | 1.11805 | ||||||||
\(627\) | −5.89466e11 | −0.152319 | ||||||||
\(628\) | 2.10714e12 | 0.540599 | ||||||||
\(629\) | −5.68836e11 | −0.144897 | ||||||||
\(630\) | −1.22924e12 | −0.310889 | ||||||||
\(631\) | 4.58081e12 | 1.15030 | 0.575149 | − | 0.818049i | \(-0.304944\pi\) | ||||
0.575149 | + | 0.818049i | \(0.304944\pi\) | |||||||
\(632\) | 1.01815e12 | 0.253853 | ||||||||
\(633\) | 1.26775e12 | 0.313845 | ||||||||
\(634\) | 7.34101e11 | 0.180449 | ||||||||
\(635\) | −5.76715e12 | −1.40760 | ||||||||
\(636\) | 1.73818e12 | 0.421248 | ||||||||
\(637\) | −6.80509e11 | −0.163760 | ||||||||
\(638\) | 8.17755e11 | 0.195402 | ||||||||
\(639\) | 8.19559e11 | 0.194458 | ||||||||
\(640\) | −6.74277e10 | −0.0158865 | ||||||||
\(641\) | −1.39671e12 | −0.326772 | −0.163386 | − | 0.986562i | \(-0.552242\pi\) | ||||
−0.163386 | + | 0.986562i | \(0.552242\pi\) | |||||||
\(642\) | 5.26416e11 | 0.122299 | ||||||||
\(643\) | 3.37971e12 | 0.779704 | 0.389852 | − | 0.920877i | \(-0.372526\pi\) | ||||
0.389852 | + | 0.920877i | \(0.372526\pi\) | |||||||
\(644\) | −2.78293e11 | −0.0637553 | ||||||||
\(645\) | −1.36995e12 | −0.311662 | ||||||||
\(646\) | 7.77977e11 | 0.175760 | ||||||||
\(647\) | −5.91132e12 | −1.32622 | −0.663110 | − | 0.748522i | \(-0.730764\pi\) | ||||
−0.663110 | + | 0.748522i | \(0.730764\pi\) | |||||||
\(648\) | 8.98393e9 | 0.00200161 | ||||||||
\(649\) | 6.29421e10 | 0.0139264 | ||||||||
\(650\) | −3.07483e11 | −0.0675634 | ||||||||
\(651\) | −1.18084e12 | −0.257677 | ||||||||
\(652\) | 7.75228e11 | 0.168002 | ||||||||
\(653\) | 3.76996e12 | 0.811385 | 0.405692 | − | 0.914010i | \(-0.367030\pi\) | ||||
0.405692 | + | 0.914010i | \(0.367030\pi\) | |||||||
\(654\) | −3.44472e12 | −0.736298 | ||||||||
\(655\) | −5.40089e11 | −0.114651 | ||||||||
\(656\) | −2.30914e12 | −0.486837 | ||||||||
\(657\) | −3.30005e12 | −0.690997 | ||||||||
\(658\) | 4.14977e12 | 0.862993 | ||||||||
\(659\) | 3.45188e12 | 0.712969 | 0.356485 | − | 0.934301i | \(-0.383975\pi\) | ||||
0.356485 | + | 0.934301i | \(0.383975\pi\) | |||||||
\(660\) | 6.05749e11 | 0.124264 | ||||||||
\(661\) | −5.09909e12 | −1.03893 | −0.519465 | − | 0.854492i | \(-0.673869\pi\) | ||||
−0.519465 | + | 0.854492i | \(0.673869\pi\) | |||||||
\(662\) | 5.70827e12 | 1.15516 | ||||||||
\(663\) | −5.99412e11 | −0.120480 | ||||||||
\(664\) | 9.27538e12 | 1.85172 | ||||||||
\(665\) | −1.44494e12 | −0.286519 | ||||||||
\(666\) | −6.68909e11 | −0.131745 | ||||||||
\(667\) | −4.81214e11 | −0.0941395 | ||||||||
\(668\) | −3.87693e12 | −0.753345 | ||||||||
\(669\) | 2.86310e12 | 0.552610 | ||||||||
\(670\) | 6.11099e12 | 1.17159 | ||||||||
\(671\) | 9.45027e11 | 0.179967 | ||||||||
\(672\) | −1.85264e12 | −0.350452 | ||||||||
\(673\) | 9.60092e12 | 1.80403 | 0.902017 | − | 0.431700i | \(-0.142086\pi\) | ||||
0.902017 | + | 0.431700i | \(0.142086\pi\) | |||||||
\(674\) | −6.90840e12 | −1.28946 | ||||||||
\(675\) | 1.27101e12 | 0.235659 | ||||||||
\(676\) | 1.90844e12 | 0.351494 | ||||||||
\(677\) | −1.75260e12 | −0.320652 | −0.160326 | − | 0.987064i | \(-0.551254\pi\) | ||||
−0.160326 | + | 0.987064i | \(0.551254\pi\) | |||||||
\(678\) | 1.86690e12 | 0.339303 | ||||||||
\(679\) | 4.26378e11 | 0.0769805 | ||||||||
\(680\) | −2.75764e12 | −0.494593 | ||||||||
\(681\) | −4.77389e12 | −0.850571 | ||||||||
\(682\) | 1.35983e12 | 0.240689 | ||||||||
\(683\) | 8.15393e12 | 1.43375 | 0.716876 | − | 0.697201i | \(-0.245571\pi\) | ||||
0.716876 | + | 0.697201i | \(0.245571\pi\) | |||||||
\(684\) | −6.31208e11 | −0.110260 | ||||||||
\(685\) | 1.79802e12 | 0.312024 | ||||||||
\(686\) | 4.80896e12 | 0.829073 | ||||||||
\(687\) | −4.91902e12 | −0.842506 | ||||||||
\(688\) | −1.43914e12 | −0.244881 | ||||||||
\(689\) | −3.67882e12 | −0.621902 | ||||||||
\(690\) | 5.16633e11 | 0.0867683 | ||||||||
\(691\) | −1.49514e12 | −0.249477 | −0.124738 | − | 0.992190i | \(-0.539809\pi\) | ||||
−0.124738 | + | 0.992190i | \(0.539809\pi\) | |||||||
\(692\) | −4.81903e12 | −0.798881 | ||||||||
\(693\) | 1.57905e12 | 0.260073 | ||||||||
\(694\) | 2.39164e12 | 0.391362 | ||||||||
\(695\) | 9.92240e11 | 0.161319 | ||||||||
\(696\) | −1.87330e12 | −0.302598 | ||||||||
\(697\) | −3.72663e12 | −0.598094 | ||||||||
\(698\) | 2.25260e12 | 0.359199 | ||||||||
\(699\) | −1.91141e12 | −0.302836 | ||||||||
\(700\) | −4.57464e11 | −0.0720139 | ||||||||
\(701\) | 3.86276e12 | 0.604181 | 0.302090 | − | 0.953279i | \(-0.402316\pi\) | ||||
0.302090 | + | 0.953279i | \(0.402316\pi\) | |||||||
\(702\) | −1.84689e12 | −0.287027 | ||||||||
\(703\) | −7.86284e11 | −0.121417 | ||||||||
\(704\) | 3.69210e12 | 0.566495 | ||||||||
\(705\) | 5.31532e12 | 0.810360 | ||||||||
\(706\) | −1.74377e12 | −0.264161 | ||||||||
\(707\) | 4.64872e11 | 0.0699754 | ||||||||
\(708\) | −4.18011e10 | −0.00625228 | ||||||||
\(709\) | 3.87552e12 | 0.575999 | 0.287999 | − | 0.957631i | \(-0.407010\pi\) | ||||
0.287999 | + | 0.957631i | \(0.407010\pi\) | |||||||
\(710\) | 1.43483e12 | 0.211904 | ||||||||
\(711\) | 9.85552e11 | 0.144633 | ||||||||
\(712\) | −1.17805e11 | −0.0171793 | ||||||||
\(713\) | −8.00205e11 | −0.115957 | ||||||||
\(714\) | 1.29251e12 | 0.186120 | ||||||||
\(715\) | −1.28205e12 | −0.183455 | ||||||||
\(716\) | −2.73385e12 | −0.388746 | ||||||||
\(717\) | 2.26554e12 | 0.320137 | ||||||||
\(718\) | 9.89487e11 | 0.138947 | ||||||||
\(719\) | −1.06531e12 | −0.148661 | −0.0743303 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743303 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(720\) | −1.65403e12 | −0.229375 | ||||||||
\(721\) | 2.17128e12 | 0.299232 | ||||||||
\(722\) | −4.54130e12 | −0.621960 | ||||||||
\(723\) | −6.20554e12 | −0.844613 | ||||||||
\(724\) | −2.15201e11 | −0.0291086 | ||||||||
\(725\) | −7.91030e11 | −0.106334 | ||||||||
\(726\) | −2.43475e12 | −0.325267 | ||||||||
\(727\) | −1.00157e13 | −1.32977 | −0.664885 | − | 0.746946i | \(-0.731520\pi\) | ||||
−0.664885 | + | 0.746946i | \(0.731520\pi\) | |||||||
\(728\) | 2.29290e12 | 0.302547 | ||||||||
\(729\) | 4.72936e12 | 0.620195 | ||||||||
\(730\) | −5.77752e12 | −0.752989 | ||||||||
\(731\) | −2.32256e12 | −0.300843 | ||||||||
\(732\) | −6.27611e11 | −0.0807961 | ||||||||
\(733\) | 9.32137e11 | 0.119265 | 0.0596323 | − | 0.998220i | \(-0.481007\pi\) | ||||
0.0596323 | + | 0.998220i | \(0.481007\pi\) | |||||||
\(734\) | −3.07334e12 | −0.390822 | ||||||||
\(735\) | 1.87953e12 | 0.237551 | ||||||||
\(736\) | −1.25546e12 | −0.157707 | ||||||||
\(737\) | −7.84997e12 | −0.980086 | ||||||||
\(738\) | −4.38224e12 | −0.543805 | ||||||||
\(739\) | 1.25556e13 | 1.54860 | 0.774298 | − | 0.632821i | \(-0.218103\pi\) | ||||
0.774298 | + | 0.632821i | \(0.218103\pi\) | |||||||
\(740\) | 8.08004e11 | 0.0990537 | ||||||||
\(741\) | −8.28549e11 | −0.100957 | ||||||||
\(742\) | 7.93265e12 | 0.960728 | ||||||||
\(743\) | −1.07581e12 | −0.129504 | −0.0647522 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647522 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(744\) | −3.11508e12 | −0.372728 | ||||||||
\(745\) | −8.94250e12 | −1.06354 | ||||||||
\(746\) | −1.09102e13 | −1.28975 | ||||||||
\(747\) | 8.97846e12 | 1.05502 | ||||||||
\(748\) | 1.02697e12 | 0.119950 | ||||||||
\(749\) | −1.65759e12 | −0.192446 | ||||||||
\(750\) | 4.45504e12 | 0.514134 | ||||||||
\(751\) | −7.04814e11 | −0.0808527 | −0.0404264 | − | 0.999183i | \(-0.512872\pi\) | ||||
−0.0404264 | + | 0.999183i | \(0.512872\pi\) | |||||||
\(752\) | 5.58378e12 | 0.636719 | ||||||||
\(753\) | −3.77707e12 | −0.428132 | ||||||||
\(754\) | 1.14943e12 | 0.129512 | ||||||||
\(755\) | 9.58052e12 | 1.07307 | ||||||||
\(756\) | −2.74774e12 | −0.305934 | ||||||||
\(757\) | 1.39364e13 | 1.54248 | 0.771239 | − | 0.636545i | \(-0.219637\pi\) | ||||
0.771239 | + | 0.636545i | \(0.219637\pi\) | |||||||
\(758\) | −5.84918e12 | −0.643552 | ||||||||
\(759\) | −6.63649e11 | −0.0725856 | ||||||||
\(760\) | −3.81181e12 | −0.414448 | ||||||||
\(761\) | −1.23010e13 | −1.32957 | −0.664784 | − | 0.747036i | \(-0.731476\pi\) | ||||
−0.664784 | + | 0.747036i | \(0.731476\pi\) | |||||||
\(762\) | 7.13080e12 | 0.766198 | ||||||||
\(763\) | 1.08468e13 | 1.15862 | ||||||||
\(764\) | −3.64186e12 | −0.386726 | ||||||||
\(765\) | −2.66937e12 | −0.281794 | ||||||||
\(766\) | −1.38269e13 | −1.45110 | ||||||||
\(767\) | 8.84710e10 | 0.00923043 | ||||||||
\(768\) | −5.92243e12 | −0.614292 | ||||||||
\(769\) | −3.26322e12 | −0.336494 | −0.168247 | − | 0.985745i | \(-0.553811\pi\) | ||||
−0.168247 | + | 0.985745i | \(0.553811\pi\) | |||||||
\(770\) | 2.76449e12 | 0.283405 | ||||||||
\(771\) | −6.65072e12 | −0.677835 | ||||||||
\(772\) | 1.93082e12 | 0.195643 | ||||||||
\(773\) | 1.21642e12 | 0.122539 | 0.0612697 | − | 0.998121i | \(-0.480485\pi\) | ||||
0.0612697 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(774\) | −2.73116e12 | −0.273535 | ||||||||
\(775\) | −1.31539e12 | −0.130978 | ||||||||
\(776\) | 1.12480e12 | 0.111352 | ||||||||
\(777\) | −1.30632e12 | −0.128574 | ||||||||
\(778\) | −1.19160e13 | −1.16606 | ||||||||
\(779\) | −5.15121e12 | −0.501176 | ||||||||
\(780\) | 8.51436e11 | 0.0823619 | ||||||||
\(781\) | −1.84314e12 | −0.177267 | ||||||||
\(782\) | 8.75884e11 | 0.0837561 | ||||||||
\(783\) | −4.75129e12 | −0.451735 | ||||||||
\(784\) | 1.97446e12 | 0.186649 | ||||||||
\(785\) | 1.23175e13 | 1.15773 | ||||||||
\(786\) | 6.67793e11 | 0.0624081 | ||||||||
\(787\) | −2.95303e12 | −0.274398 | −0.137199 | − | 0.990544i | \(-0.543810\pi\) | ||||
−0.137199 | + | 0.990544i | \(0.543810\pi\) | |||||||
\(788\) | 1.62417e12 | 0.150060 | ||||||||
\(789\) | 9.69910e12 | 0.891015 | ||||||||
\(790\) | 1.72544e12 | 0.157608 | ||||||||
\(791\) | −5.87854e12 | −0.533919 | ||||||||
\(792\) | 4.16557e12 | 0.376194 | ||||||||
\(793\) | 1.32832e12 | 0.119282 | ||||||||
\(794\) | −1.64023e13 | −1.46458 | ||||||||
\(795\) | 1.01607e13 | 0.902135 | ||||||||
\(796\) | 4.74455e11 | 0.0418877 | ||||||||
\(797\) | 1.70002e13 | 1.49242 | 0.746211 | − | 0.665710i | \(-0.231871\pi\) | ||||
0.746211 | + | 0.665710i | \(0.231871\pi\) | |||||||
\(798\) | 1.78660e12 | 0.155961 | ||||||||
\(799\) | 9.01143e12 | 0.782228 | ||||||||
\(800\) | −2.06375e12 | −0.178136 | ||||||||
\(801\) | −1.14034e11 | −0.00978789 | ||||||||
\(802\) | 1.34040e13 | 1.14406 | ||||||||
\(803\) | 7.42160e12 | 0.629909 | ||||||||
\(804\) | 5.21332e12 | 0.440009 | ||||||||
\(805\) | −1.62679e12 | −0.136537 | ||||||||
\(806\) | 1.91137e12 | 0.159528 | ||||||||
\(807\) | 6.97800e12 | 0.579162 | ||||||||
\(808\) | 1.22635e12 | 0.101219 | ||||||||
\(809\) | 2.92170e12 | 0.239810 | 0.119905 | − | 0.992785i | \(-0.461741\pi\) | ||||
0.119905 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(810\) | 1.52250e10 | 0.00124272 | ||||||||
\(811\) | 1.76690e13 | 1.43423 | 0.717115 | − | 0.696955i | \(-0.245462\pi\) | ||||
0.717115 | + | 0.696955i | \(0.245462\pi\) | |||||||
\(812\) | 1.71009e12 | 0.138044 | ||||||||
\(813\) | 9.86989e12 | 0.792327 | ||||||||
\(814\) | 1.50433e12 | 0.120098 | ||||||||
\(815\) | 4.53166e12 | 0.359789 | ||||||||
\(816\) | 1.73916e12 | 0.137320 | ||||||||
\(817\) | −3.21041e12 | −0.252093 | ||||||||
\(818\) | −1.52784e13 | −1.19313 | ||||||||
\(819\) | 2.21949e12 | 0.172376 | ||||||||
\(820\) | 5.29350e12 | 0.408866 | ||||||||
\(821\) | −2.28315e13 | −1.75384 | −0.876922 | − | 0.480633i | \(-0.840407\pi\) | ||||
−0.876922 | + | 0.480633i | \(0.840407\pi\) | |||||||
\(822\) | −2.22317e12 | −0.169844 | ||||||||
\(823\) | −1.72245e13 | −1.30872 | −0.654362 | − | 0.756181i | \(-0.727063\pi\) | ||||
−0.654362 | + | 0.756181i | \(0.727063\pi\) | |||||||
\(824\) | 5.72791e12 | 0.432837 | ||||||||
\(825\) | −1.09092e12 | −0.0819880 | ||||||||
\(826\) | −1.90770e11 | −0.0142594 | ||||||||
\(827\) | 2.12680e13 | 1.58107 | 0.790535 | − | 0.612416i | \(-0.209802\pi\) | ||||
0.790535 | + | 0.612416i | \(0.209802\pi\) | |||||||
\(828\) | −7.10644e11 | −0.0525431 | ||||||||
\(829\) | −2.26060e13 | −1.66237 | −0.831185 | − | 0.555996i | \(-0.812337\pi\) | ||||
−0.831185 | + | 0.555996i | \(0.812337\pi\) | |||||||
\(830\) | 1.57189e13 | 1.14966 | ||||||||
\(831\) | 1.05342e13 | 0.766297 | ||||||||
\(832\) | 5.18959e12 | 0.375472 | ||||||||
\(833\) | 3.18650e12 | 0.229304 | ||||||||
\(834\) | −1.22686e12 | −0.0878105 | ||||||||
\(835\) | −2.26629e13 | −1.61334 | ||||||||
\(836\) | 1.41955e12 | 0.100513 | ||||||||
\(837\) | −7.90086e12 | −0.556429 | ||||||||
\(838\) | −1.44941e13 | −1.01530 | ||||||||
\(839\) | 2.52979e13 | 1.76261 | 0.881305 | − | 0.472548i | \(-0.156666\pi\) | ||||
0.881305 | + | 0.472548i | \(0.156666\pi\) | |||||||
\(840\) | −6.33285e12 | −0.438877 | ||||||||
\(841\) | −1.15501e13 | −0.796168 | ||||||||
\(842\) | −4.15887e12 | −0.285148 | ||||||||
\(843\) | −5.05101e12 | −0.344472 | ||||||||
\(844\) | −3.05298e12 | −0.207101 | ||||||||
\(845\) | 1.11559e13 | 0.752750 | ||||||||
\(846\) | 1.05968e13 | 0.711225 | ||||||||
\(847\) | 7.66660e12 | 0.511832 | ||||||||
\(848\) | 1.06739e13 | 0.708829 | ||||||||
\(849\) | 9.01225e12 | 0.595317 | ||||||||
\(850\) | 1.43980e12 | 0.0946055 | ||||||||
\(851\) | −8.85237e11 | −0.0578597 | ||||||||
\(852\) | 1.22406e12 | 0.0795840 | ||||||||
\(853\) | 1.73877e13 | 1.12453 | 0.562266 | − | 0.826957i | \(-0.309930\pi\) | ||||
0.562266 | + | 0.826957i | \(0.309930\pi\) | |||||||
\(854\) | −2.86427e12 | −0.184269 | ||||||||
\(855\) | −3.68978e12 | −0.236131 | ||||||||
\(856\) | −4.37278e12 | −0.278372 | ||||||||
\(857\) | −5.92067e12 | −0.374936 | −0.187468 | − | 0.982271i | \(-0.560028\pi\) | ||||
−0.187468 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(858\) | 1.58519e12 | 0.0998596 | ||||||||
\(859\) | −1.22656e13 | −0.768633 | −0.384316 | − | 0.923201i | \(-0.625563\pi\) | ||||
−0.384316 | + | 0.923201i | \(0.625563\pi\) | |||||||
\(860\) | 3.29909e12 | 0.205661 | ||||||||
\(861\) | −8.55811e12 | −0.530718 | ||||||||
\(862\) | 2.17536e13 | 1.34199 | ||||||||
\(863\) | −1.24413e13 | −0.763512 | −0.381756 | − | 0.924263i | \(-0.624681\pi\) | ||||
−0.381756 | + | 0.924263i | \(0.624681\pi\) | |||||||
\(864\) | −1.23958e13 | −0.756768 | ||||||||
\(865\) | −2.81700e13 | −1.71086 | ||||||||
\(866\) | −2.88102e12 | −0.174067 | ||||||||
\(867\) | −7.48685e12 | −0.450001 | ||||||||
\(868\) | 2.84368e12 | 0.170036 | ||||||||
\(869\) | −2.21644e12 | −0.131846 | ||||||||
\(870\) | −3.17466e12 | −0.187872 | ||||||||
\(871\) | −1.10339e13 | −0.649599 | ||||||||
\(872\) | 2.86142e13 | 1.67594 | ||||||||
\(873\) | 1.08879e12 | 0.0634426 | ||||||||
\(874\) | 1.21071e12 | 0.0701839 | ||||||||
\(875\) | −1.40282e13 | −0.809030 | ||||||||
\(876\) | −4.92883e12 | −0.282798 | ||||||||
\(877\) | −2.81673e13 | −1.60786 | −0.803929 | − | 0.594726i | \(-0.797261\pi\) | ||||
−0.803929 | + | 0.594726i | \(0.797261\pi\) | |||||||
\(878\) | −2.56696e13 | −1.45779 | ||||||||
\(879\) | −7.38154e11 | −0.0417058 | ||||||||
\(880\) | 3.71980e12 | 0.209097 | ||||||||
\(881\) | −1.04783e13 | −0.586003 | −0.293001 | − | 0.956112i | \(-0.594654\pi\) | ||||
−0.293001 | + | 0.956112i | \(0.594654\pi\) | |||||||
\(882\) | 3.74709e12 | 0.208490 | ||||||||
\(883\) | −1.07155e13 | −0.593183 | −0.296591 | − | 0.955004i | \(-0.595850\pi\) | ||||
−0.296591 | + | 0.955004i | \(0.595850\pi\) | |||||||
\(884\) | 1.44350e12 | 0.0795026 | ||||||||
\(885\) | −2.44352e11 | −0.0133897 | ||||||||
\(886\) | −2.16634e13 | −1.18107 | ||||||||
\(887\) | 3.90674e12 | 0.211913 | 0.105957 | − | 0.994371i | \(-0.466210\pi\) | ||||
0.105957 | + | 0.994371i | \(0.466210\pi\) | |||||||
\(888\) | −3.44610e12 | −0.185982 | ||||||||
\(889\) | −2.24537e13 | −1.20567 | ||||||||
\(890\) | −1.99644e11 | −0.0106660 | ||||||||
\(891\) | −1.95575e10 | −0.00103959 | ||||||||
\(892\) | −6.89489e12 | −0.364658 | ||||||||
\(893\) | 1.24562e13 | 0.655473 | ||||||||
\(894\) | 1.10570e13 | 0.578918 | ||||||||
\(895\) | −1.59809e13 | −0.832527 | ||||||||
\(896\) | −2.62521e11 | −0.0136075 | ||||||||
\(897\) | −9.32820e11 | −0.0481096 | ||||||||
\(898\) | 2.20199e13 | 1.12998 | ||||||||
\(899\) | 4.91719e12 | 0.251072 | ||||||||
\(900\) | −1.16817e12 | −0.0593493 | ||||||||
\(901\) | 1.72261e13 | 0.870816 | ||||||||
\(902\) | 9.85539e12 | 0.495729 | ||||||||
\(903\) | −5.33370e12 | −0.266953 | ||||||||
\(904\) | −1.55078e13 | −0.772310 | ||||||||
\(905\) | −1.25798e12 | −0.0623382 | ||||||||
\(906\) | −1.18459e13 | −0.584103 | ||||||||
\(907\) | 1.35226e13 | 0.663481 | 0.331741 | − | 0.943371i | \(-0.392364\pi\) | ||||
0.331741 | + | 0.943371i | \(0.392364\pi\) | |||||||
\(908\) | 1.14965e13 | 0.561277 | ||||||||
\(909\) | 1.18709e12 | 0.0576694 | ||||||||
\(910\) | 3.88575e12 | 0.187840 | ||||||||
\(911\) | 3.63077e13 | 1.74649 | 0.873246 | − | 0.487280i | \(-0.162011\pi\) | ||||
0.873246 | + | 0.487280i | \(0.162011\pi\) | |||||||
\(912\) | 2.40399e12 | 0.115068 | ||||||||
\(913\) | −2.01920e13 | −0.961746 | ||||||||
\(914\) | 4.43740e11 | 0.0210315 | ||||||||
\(915\) | −3.66875e12 | −0.173031 | ||||||||
\(916\) | 1.18459e13 | 0.555955 | ||||||||
\(917\) | −2.10277e12 | −0.0982039 | ||||||||
\(918\) | 8.64808e12 | 0.401909 | ||||||||
\(919\) | 3.11569e13 | 1.44090 | 0.720450 | − | 0.693506i | \(-0.243935\pi\) | ||||
0.720450 | + | 0.693506i | \(0.243935\pi\) | |||||||
\(920\) | −4.29152e12 | −0.197499 | ||||||||
\(921\) | −1.54770e13 | −0.708792 | ||||||||
\(922\) | 2.17708e13 | 0.992169 | ||||||||
\(923\) | −2.59070e12 | −0.117492 | ||||||||
\(924\) | 2.35840e12 | 0.106437 | ||||||||
\(925\) | −1.45517e12 | −0.0653546 | ||||||||
\(926\) | 1.24815e13 | 0.557851 | ||||||||
\(927\) | 5.54455e12 | 0.246608 | ||||||||
\(928\) | 7.71467e12 | 0.341469 | ||||||||
\(929\) | 8.29345e12 | 0.365312 | 0.182656 | − | 0.983177i | \(-0.441530\pi\) | ||||
0.182656 | + | 0.983177i | \(0.441530\pi\) | |||||||
\(930\) | −5.27911e12 | −0.231413 | ||||||||
\(931\) | 4.40460e12 | 0.192147 | ||||||||
\(932\) | 4.60305e12 | 0.199836 | ||||||||
\(933\) | 1.28097e13 | 0.553443 | ||||||||
\(934\) | −8.29128e12 | −0.356501 | ||||||||
\(935\) | 6.00324e12 | 0.256882 | ||||||||
\(936\) | 5.85510e12 | 0.249341 | ||||||||
\(937\) | 2.53064e13 | 1.07251 | 0.536257 | − | 0.844055i | \(-0.319838\pi\) | ||||
0.536257 | + | 0.844055i | \(0.319838\pi\) | |||||||
\(938\) | 2.37923e13 | 1.00352 | ||||||||
\(939\) | 2.14228e13 | 0.899250 | ||||||||
\(940\) | −1.28003e13 | −0.534743 | ||||||||
\(941\) | −8.22803e12 | −0.342092 | −0.171046 | − | 0.985263i | \(-0.554715\pi\) | ||||
−0.171046 | + | 0.985263i | \(0.554715\pi\) | |||||||
\(942\) | −1.52300e13 | −0.630188 | ||||||||
\(943\) | −5.79948e12 | −0.238829 | ||||||||
\(944\) | −2.56694e11 | −0.0105206 | ||||||||
\(945\) | −1.60622e13 | −0.655180 | ||||||||
\(946\) | 6.14221e12 | 0.249353 | ||||||||
\(947\) | −2.37452e12 | −0.0959405 | −0.0479702 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479702 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(948\) | 1.47198e12 | 0.0591923 | ||||||||
\(949\) | 1.04318e13 | 0.417503 | ||||||||
\(950\) | 1.99019e12 | 0.0792753 | ||||||||
\(951\) | 3.66089e12 | 0.145136 | ||||||||
\(952\) | −1.07365e13 | −0.423641 | ||||||||
\(953\) | −4.17617e13 | −1.64006 | −0.820031 | − | 0.572318i | \(-0.806044\pi\) | ||||
−0.820031 | + | 0.572318i | \(0.806044\pi\) | |||||||
\(954\) | 2.02567e13 | 0.791772 | ||||||||
\(955\) | −2.12888e13 | −0.828203 | ||||||||
\(956\) | −5.45585e12 | −0.211253 | ||||||||
\(957\) | 4.07806e12 | 0.157163 | ||||||||
\(958\) | 4.61223e12 | 0.176916 | ||||||||
\(959\) | 7.00038e12 | 0.267262 | ||||||||
\(960\) | −1.43334e13 | −0.544662 | ||||||||
\(961\) | −1.82629e13 | −0.690740 | ||||||||
\(962\) | 2.11448e12 | 0.0796005 | ||||||||
\(963\) | −4.23280e12 | −0.158602 | ||||||||
\(964\) | 1.49441e13 | 0.557345 | ||||||||
\(965\) | 1.12868e13 | 0.418983 | ||||||||
\(966\) | 2.01144e12 | 0.0743208 | ||||||||
\(967\) | 3.67341e11 | 0.0135098 | 0.00675492 | − | 0.999977i | \(-0.497850\pi\) | ||||
0.00675492 | + | 0.999977i | \(0.497850\pi\) | |||||||
\(968\) | 2.02247e13 | 0.740362 | ||||||||
\(969\) | 3.87970e12 | 0.141365 | ||||||||
\(970\) | 1.90619e12 | 0.0691342 | ||||||||
\(971\) | −3.92627e12 | −0.141741 | −0.0708703 | − | 0.997486i | \(-0.522578\pi\) | ||||
−0.0708703 | + | 0.997486i | \(0.522578\pi\) | |||||||
\(972\) | −1.13553e13 | −0.408037 | ||||||||
\(973\) | 3.86316e12 | 0.138177 | ||||||||
\(974\) | −2.50942e13 | −0.893425 | ||||||||
\(975\) | −1.53339e12 | −0.0543415 | ||||||||
\(976\) | −3.85405e12 | −0.135955 | ||||||||
\(977\) | −3.19527e13 | −1.12197 | −0.560986 | − | 0.827826i | \(-0.689578\pi\) | ||||
−0.560986 | + | 0.827826i | \(0.689578\pi\) | |||||||
\(978\) | −5.60318e12 | −0.195844 | ||||||||
\(979\) | 2.56456e11 | 0.00892258 | ||||||||
\(980\) | −4.52627e12 | −0.156756 | ||||||||
\(981\) | 2.76982e13 | 0.954864 | ||||||||
\(982\) | 8.03497e11 | 0.0275729 | ||||||||
\(983\) | −2.07291e12 | −0.0708091 | −0.0354045 | − | 0.999373i | \(-0.511272\pi\) | ||||
−0.0354045 | + | 0.999373i | \(0.511272\pi\) | |||||||
\(984\) | −2.25766e13 | −0.767679 | ||||||||
\(985\) | 9.49424e12 | 0.321364 | ||||||||
\(986\) | −5.38223e12 | −0.181349 | ||||||||
\(987\) | 2.06945e13 | 0.694109 | ||||||||
\(988\) | 1.99530e12 | 0.0666197 | ||||||||
\(989\) | −3.61443e12 | −0.120132 | ||||||||
\(990\) | 7.05936e12 | 0.233565 | ||||||||
\(991\) | −1.25112e13 | −0.412066 | −0.206033 | − | 0.978545i | \(-0.566055\pi\) | ||||
−0.206033 | + | 0.978545i | \(0.566055\pi\) | |||||||
\(992\) | 1.28286e13 | 0.420608 | ||||||||
\(993\) | 2.84666e13 | 0.929103 | ||||||||
\(994\) | 5.58633e12 | 0.181505 | ||||||||
\(995\) | 2.77347e12 | 0.0897056 | ||||||||
\(996\) | 1.34099e13 | 0.431776 | ||||||||
\(997\) | −1.53878e13 | −0.493227 | −0.246614 | − | 0.969114i | \(-0.579318\pi\) | ||||
−0.246614 | + | 0.969114i | \(0.579318\pi\) | |||||||
\(998\) | 5.74858e12 | 0.183431 | ||||||||
\(999\) | −8.74042e12 | −0.277644 |
(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 | 23.10.a.a.1.5 | ✓ | 7 | |
3.2 | odd | 2 | 207.10.a.b.1.3 | 7 | |||
4.3 | odd | 2 | 368.10.a.f.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.10.a.a.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial | |
207.10.a.b.1.3 | 7 | 3.2 | odd | 2 | |||
368.10.a.f.1.3 | 7 | 4.3 | odd | 2 |