Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,48,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 48, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 48);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 48 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(13.9907662655\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-906006.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02978e7 | −1.71097 | −0.855486 | − | 0.517825i | \(-0.826742\pi\) | ||||
−0.855486 | + | 0.517825i | \(0.826742\pi\) | |||||||
\(3\) | −2.01642e10 | −0.123661 | −0.0618303 | − | 0.998087i | \(-0.519694\pi\) | ||||
−0.0618303 | + | 0.998087i | \(0.519694\pi\) | |||||||
\(4\) | 2.71261e14 | 1.92743 | ||||||||
\(5\) | −3.11682e16 | −1.16927 | −0.584637 | − | 0.811295i | \(-0.698763\pi\) | ||||
−0.584637 | + | 0.811295i | \(0.698763\pi\) | |||||||
\(6\) | 4.09288e17 | 0.211580 | ||||||||
\(7\) | −1.26592e20 | −1.74824 | −0.874122 | − | 0.485707i | \(-0.838562\pi\) | ||||
−0.874122 | + | 0.485707i | \(0.838562\pi\) | |||||||
\(8\) | −2.64934e21 | −1.58680 | ||||||||
\(9\) | −2.61822e22 | −0.984708 | ||||||||
\(10\) | 6.32644e23 | 2.00060 | ||||||||
\(11\) | −1.78518e23 | −0.0601110 | −0.0300555 | − | 0.999548i | \(-0.509568\pi\) | ||||
−0.0300555 | + | 0.999548i | \(0.509568\pi\) | |||||||
\(12\) | −5.46976e24 | −0.238347 | ||||||||
\(13\) | −1.12359e26 | −0.746346 | −0.373173 | − | 0.927762i | \(-0.621730\pi\) | ||||
−0.373173 | + | 0.927762i | \(0.621730\pi\) | |||||||
\(14\) | 2.56953e27 | 2.99120 | ||||||||
\(15\) | 6.28481e26 | 0.144593 | ||||||||
\(16\) | 1.55990e28 | 0.787550 | ||||||||
\(17\) | 4.31126e28 | 0.523667 | 0.261833 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261833 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(18\) | 5.31440e29 | 1.68481 | ||||||||
\(19\) | −7.19841e29 | −0.640511 | −0.320256 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320256 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(20\) | −8.45472e30 | −2.25369 | ||||||||
\(21\) | 2.55262e30 | 0.216189 | ||||||||
\(22\) | 3.62352e30 | 0.102848 | ||||||||
\(23\) | 8.88061e30 | 0.0886826 | 0.0443413 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443413 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(24\) | 5.34218e31 | 0.196225 | ||||||||
\(25\) | 2.60913e32 | 0.367202 | ||||||||
\(26\) | 2.28064e33 | 1.27698 | ||||||||
\(27\) | 1.06408e33 | 0.245430 | ||||||||
\(28\) | −3.43395e34 | −3.36961 | ||||||||
\(29\) | 2.84937e34 | 1.22573 | 0.612866 | − | 0.790187i | \(-0.290017\pi\) | ||||
0.612866 | + | 0.790187i | \(0.290017\pi\) | |||||||
\(30\) | −1.27568e34 | −0.247395 | ||||||||
\(31\) | 1.11855e35 | 1.00382 | 0.501911 | − | 0.864919i | \(-0.332630\pi\) | ||||
0.501911 | + | 0.864919i | \(0.332630\pi\) | |||||||
\(32\) | 5.62362e34 | 0.239327 | ||||||||
\(33\) | 3.59967e33 | 0.00743336 | ||||||||
\(34\) | −8.75090e35 | −0.895980 | ||||||||
\(35\) | 3.94564e36 | 2.04418 | ||||||||
\(36\) | −7.10222e36 | −1.89795 | ||||||||
\(37\) | −9.87647e36 | −1.38631 | −0.693156 | − | 0.720787i | \(-0.743780\pi\) | ||||
−0.693156 | + | 0.720787i | \(0.743780\pi\) | |||||||
\(38\) | 1.46112e37 | 1.09590 | ||||||||
\(39\) | 2.26563e36 | 0.0922935 | ||||||||
\(40\) | 8.25752e37 | 1.85541 | ||||||||
\(41\) | −3.56038e37 | −0.447791 | −0.223896 | − | 0.974613i | \(-0.571877\pi\) | ||||
−0.223896 | + | 0.974613i | \(0.571877\pi\) | |||||||
\(42\) | −5.18125e37 | −0.369893 | ||||||||
\(43\) | −3.37056e38 | −1.38418 | −0.692091 | − | 0.721811i | \(-0.743310\pi\) | ||||
−0.692091 | + | 0.721811i | \(0.743310\pi\) | |||||||
\(44\) | −4.84250e37 | −0.115860 | ||||||||
\(45\) | 8.16052e38 | 1.15139 | ||||||||
\(46\) | −1.80256e38 | −0.151734 | ||||||||
\(47\) | −1.22952e39 | −0.624361 | −0.312181 | − | 0.950023i | \(-0.601059\pi\) | ||||
−0.312181 | + | 0.950023i | \(0.601059\pi\) | |||||||
\(48\) | −3.14542e38 | −0.0973889 | ||||||||
\(49\) | 1.07822e40 | 2.05635 | ||||||||
\(50\) | −5.29595e39 | −0.628273 | ||||||||
\(51\) | −8.69331e38 | −0.0647569 | ||||||||
\(52\) | −3.04787e40 | −1.43853 | ||||||||
\(53\) | −1.08443e39 | −0.0327129 | −0.0163565 | − | 0.999866i | \(-0.505207\pi\) | ||||
−0.0163565 | + | 0.999866i | \(0.505207\pi\) | |||||||
\(54\) | −2.15985e40 | −0.419924 | ||||||||
\(55\) | 5.56408e39 | 0.0702863 | ||||||||
\(56\) | 3.35385e41 | 2.77412 | ||||||||
\(57\) | 1.45150e40 | 0.0792060 | ||||||||
\(58\) | −5.78358e41 | −2.09719 | ||||||||
\(59\) | −1.45567e40 | −0.0353216 | −0.0176608 | − | 0.999844i | \(-0.505622\pi\) | ||||
−0.0176608 | + | 0.999844i | \(0.505622\pi\) | |||||||
\(60\) | 1.70483e41 | 0.278693 | ||||||||
\(61\) | 4.79341e41 | 0.531366 | 0.265683 | − | 0.964060i | \(-0.414403\pi\) | ||||
0.265683 | + | 0.964060i | \(0.414403\pi\) | |||||||
\(62\) | −2.27041e42 | −1.71751 | ||||||||
\(63\) | 3.31446e42 | 1.72151 | ||||||||
\(64\) | −3.33684e42 | −1.19703 | ||||||||
\(65\) | 3.50203e42 | 0.872683 | ||||||||
\(66\) | −7.30652e40 | −0.0127183 | ||||||||
\(67\) | 3.35317e42 | 0.409919 | 0.204959 | − | 0.978770i | \(-0.434294\pi\) | ||||
0.204959 | + | 0.978770i | \(0.434294\pi\) | |||||||
\(68\) | 1.16948e43 | 1.00933 | ||||||||
\(69\) | −1.79070e41 | −0.0109665 | ||||||||
\(70\) | −8.00876e43 | −3.49753 | ||||||||
\(71\) | 9.20990e42 | 0.288193 | 0.144097 | − | 0.989564i | \(-0.453972\pi\) | ||||
0.144097 | + | 0.989564i | \(0.453972\pi\) | |||||||
\(72\) | 6.93656e43 | 1.56254 | ||||||||
\(73\) | −5.22911e43 | −0.851805 | −0.425903 | − | 0.904769i | \(-0.640043\pi\) | ||||
−0.425903 | + | 0.904769i | \(0.640043\pi\) | |||||||
\(74\) | 2.00470e44 | 2.37194 | ||||||||
\(75\) | −5.26110e42 | −0.0454085 | ||||||||
\(76\) | −1.95265e44 | −1.23454 | ||||||||
\(77\) | 2.25989e43 | 0.105089 | ||||||||
\(78\) | −4.59873e43 | −0.157912 | ||||||||
\(79\) | −7.68215e43 | −0.195545 | −0.0977724 | − | 0.995209i | \(-0.531172\pi\) | ||||
−0.0977724 | + | 0.995209i | \(0.531172\pi\) | |||||||
\(80\) | −4.86194e44 | −0.920862 | ||||||||
\(81\) | 6.74698e44 | 0.954358 | ||||||||
\(82\) | 7.22677e44 | 0.766158 | ||||||||
\(83\) | −1.71031e45 | −1.36377 | −0.681884 | − | 0.731460i | \(-0.738839\pi\) | ||||
−0.681884 | + | 0.731460i | \(0.738839\pi\) | |||||||
\(84\) | 6.92428e44 | 0.416688 | ||||||||
\(85\) | −1.34374e45 | −0.612310 | ||||||||
\(86\) | 6.84147e45 | 2.36830 | ||||||||
\(87\) | −5.74552e44 | −0.151575 | ||||||||
\(88\) | 4.72955e44 | 0.0953844 | ||||||||
\(89\) | −9.70124e45 | −1.50024 | −0.750122 | − | 0.661299i | \(-0.770005\pi\) | ||||
−0.750122 | + | 0.661299i | \(0.770005\pi\) | |||||||
\(90\) | −1.65640e46 | −1.97000 | ||||||||
\(91\) | 1.42238e46 | 1.30479 | ||||||||
\(92\) | 2.40897e45 | 0.170929 | ||||||||
\(93\) | −2.25547e45 | −0.124133 | ||||||||
\(94\) | 2.49565e46 | 1.06827 | ||||||||
\(95\) | 2.24361e46 | 0.748933 | ||||||||
\(96\) | −1.13396e45 | −0.0295953 | ||||||||
\(97\) | 5.35657e46 | 1.09585 | 0.547925 | − | 0.836528i | \(-0.315418\pi\) | ||||
0.547925 | + | 0.836528i | \(0.315418\pi\) | |||||||
\(98\) | −2.18854e47 | −3.51837 | ||||||||
\(99\) | 4.67400e45 | 0.0591918 | ||||||||
\(100\) | 7.07756e46 | 0.707756 | ||||||||
\(101\) | 1.46056e47 | 1.15602 | 0.578011 | − | 0.816029i | \(-0.303829\pi\) | ||||
0.578011 | + | 0.816029i | \(0.303829\pi\) | |||||||
\(102\) | 1.76455e46 | 0.110797 | ||||||||
\(103\) | −3.94670e47 | −1.97042 | −0.985212 | − | 0.171342i | \(-0.945190\pi\) | ||||
−0.985212 | + | 0.171342i | \(0.945190\pi\) | |||||||
\(104\) | 2.97678e47 | 1.18430 | ||||||||
\(105\) | −7.95606e46 | −0.252784 | ||||||||
\(106\) | 2.20115e46 | 0.0559709 | ||||||||
\(107\) | 5.84600e47 | 1.19218 | 0.596088 | − | 0.802919i | \(-0.296721\pi\) | ||||
0.596088 | + | 0.802919i | \(0.296721\pi\) | |||||||
\(108\) | 2.88645e47 | 0.473049 | ||||||||
\(109\) | −7.05835e47 | −0.931494 | −0.465747 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465747 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(110\) | −1.12938e47 | −0.120258 | ||||||||
\(111\) | 1.99151e47 | 0.171432 | ||||||||
\(112\) | −1.97471e48 | −1.37683 | ||||||||
\(113\) | −6.63621e47 | −0.375471 | −0.187736 | − | 0.982220i | \(-0.560115\pi\) | ||||
−0.187736 | + | 0.982220i | \(0.560115\pi\) | |||||||
\(114\) | −2.94622e47 | −0.135519 | ||||||||
\(115\) | −2.76792e47 | −0.103694 | ||||||||
\(116\) | 7.72923e48 | 2.36251 | ||||||||
\(117\) | 2.94181e48 | 0.734933 | ||||||||
\(118\) | 2.95468e47 | 0.0604342 | ||||||||
\(119\) | −5.45771e48 | −0.915497 | ||||||||
\(120\) | −1.66506e48 | −0.229441 | ||||||||
\(121\) | −8.78788e48 | −0.996387 | ||||||||
\(122\) | −9.72955e48 | −0.909152 | ||||||||
\(123\) | 7.17921e47 | 0.0553741 | ||||||||
\(124\) | 3.03420e49 | 1.93479 | ||||||||
\(125\) | 1.40141e49 | 0.739914 | ||||||||
\(126\) | −6.72760e49 | −2.94546 | ||||||||
\(127\) | 1.84983e49 | 0.672580 | 0.336290 | − | 0.941758i | \(-0.390828\pi\) | ||||
0.336290 | + | 0.941758i | \(0.390828\pi\) | |||||||
\(128\) | 5.98158e49 | 1.80876 | ||||||||
\(129\) | 6.79645e48 | 0.171169 | ||||||||
\(130\) | −7.10834e49 | −1.49314 | ||||||||
\(131\) | 3.62008e49 | 0.635100 | 0.317550 | − | 0.948242i | \(-0.397140\pi\) | ||||
0.317550 | + | 0.948242i | \(0.397140\pi\) | |||||||
\(132\) | 9.76452e47 | 0.0143273 | ||||||||
\(133\) | 9.11260e49 | 1.11977 | ||||||||
\(134\) | −6.80618e49 | −0.701360 | ||||||||
\(135\) | −3.31656e49 | −0.286975 | ||||||||
\(136\) | −1.14220e50 | −0.830956 | ||||||||
\(137\) | −2.09650e50 | −1.28399 | −0.641994 | − | 0.766709i | \(-0.721893\pi\) | ||||
−0.641994 | + | 0.766709i | \(0.721893\pi\) | |||||||
\(138\) | 3.63472e48 | 0.0187635 | ||||||||
\(139\) | −1.18819e50 | −0.517653 | −0.258826 | − | 0.965924i | \(-0.583336\pi\) | ||||
−0.258826 | + | 0.965924i | \(0.583336\pi\) | |||||||
\(140\) | 1.07030e51 | 3.94000 | ||||||||
\(141\) | 2.47923e49 | 0.0772089 | ||||||||
\(142\) | −1.86940e50 | −0.493091 | ||||||||
\(143\) | 2.00582e49 | 0.0448636 | ||||||||
\(144\) | −4.08417e50 | −0.775507 | ||||||||
\(145\) | −8.88096e50 | −1.43322 | ||||||||
\(146\) | 1.06139e51 | 1.45742 | ||||||||
\(147\) | −2.17414e50 | −0.254290 | ||||||||
\(148\) | −2.67910e51 | −2.67202 | ||||||||
\(149\) | 1.81480e51 | 1.54508 | 0.772540 | − | 0.634966i | \(-0.218986\pi\) | ||||
0.772540 | + | 0.634966i | \(0.218986\pi\) | |||||||
\(150\) | 1.06788e50 | 0.0776926 | ||||||||
\(151\) | 1.57042e51 | 0.977366 | 0.488683 | − | 0.872461i | \(-0.337477\pi\) | ||||
0.488683 | + | 0.872461i | \(0.337477\pi\) | |||||||
\(152\) | 1.90710e51 | 1.01637 | ||||||||
\(153\) | −1.12878e51 | −0.515659 | ||||||||
\(154\) | −4.58708e50 | −0.179804 | ||||||||
\(155\) | −3.48633e51 | −1.17374 | ||||||||
\(156\) | 6.14579e50 | 0.177889 | ||||||||
\(157\) | 3.70380e51 | 0.922584 | 0.461292 | − | 0.887248i | \(-0.347386\pi\) | ||||
0.461292 | + | 0.887248i | \(0.347386\pi\) | |||||||
\(158\) | 1.55930e51 | 0.334572 | ||||||||
\(159\) | 2.18667e49 | 0.00404530 | ||||||||
\(160\) | −1.75278e51 | −0.279839 | ||||||||
\(161\) | −1.12421e51 | −0.155039 | ||||||||
\(162\) | −1.36948e52 | −1.63288 | ||||||||
\(163\) | 4.02579e51 | 0.415377 | 0.207688 | − | 0.978195i | \(-0.433406\pi\) | ||||
0.207688 | + | 0.978195i | \(0.433406\pi\) | |||||||
\(164\) | −9.65793e51 | −0.863085 | ||||||||
\(165\) | −1.12195e50 | −0.00869164 | ||||||||
\(166\) | 3.47155e52 | 2.33337 | ||||||||
\(167\) | 1.17072e52 | 0.683308 | 0.341654 | − | 0.939826i | \(-0.389013\pi\) | ||||
0.341654 | + | 0.939826i | \(0.389013\pi\) | |||||||
\(168\) | −6.76277e51 | −0.343049 | ||||||||
\(169\) | −1.00394e52 | −0.442968 | ||||||||
\(170\) | 2.72750e52 | 1.04765 | ||||||||
\(171\) | 1.88470e52 | 0.630717 | ||||||||
\(172\) | −9.14302e52 | −2.66791 | ||||||||
\(173\) | −2.17798e52 | −0.554587 | −0.277293 | − | 0.960785i | \(-0.589437\pi\) | ||||
−0.277293 | + | 0.960785i | \(0.589437\pi\) | |||||||
\(174\) | 1.16621e52 | 0.259340 | ||||||||
\(175\) | −3.30295e52 | −0.641959 | ||||||||
\(176\) | −2.78471e51 | −0.0473404 | ||||||||
\(177\) | 2.93523e50 | 0.00436788 | ||||||||
\(178\) | 1.96913e53 | 2.56688 | ||||||||
\(179\) | −9.95625e52 | −1.13776 | −0.568879 | − | 0.822421i | \(-0.692623\pi\) | ||||
−0.568879 | + | 0.822421i | \(0.692623\pi\) | |||||||
\(180\) | 2.21363e53 | 2.21923 | ||||||||
\(181\) | −6.46484e52 | −0.568998 | −0.284499 | − | 0.958676i | \(-0.591827\pi\) | ||||
−0.284499 | + | 0.958676i | \(0.591827\pi\) | |||||||
\(182\) | −2.88711e53 | −2.23247 | ||||||||
\(183\) | −9.66552e51 | −0.0657090 | ||||||||
\(184\) | −2.35278e52 | −0.140722 | ||||||||
\(185\) | 3.07832e53 | 1.62098 | ||||||||
\(186\) | 4.57810e52 | 0.212388 | ||||||||
\(187\) | −7.69638e51 | −0.0314781 | ||||||||
\(188\) | −3.33521e53 | −1.20341 | ||||||||
\(189\) | −1.34704e53 | −0.429072 | ||||||||
\(190\) | −4.55403e53 | −1.28140 | ||||||||
\(191\) | 7.79937e53 | 1.93988 | 0.969942 | − | 0.243337i | \(-0.0782421\pi\) | ||||
0.969942 | + | 0.243337i | \(0.0782421\pi\) | |||||||
\(192\) | 6.72846e52 | 0.148026 | ||||||||
\(193\) | 6.70136e52 | 0.130487 | 0.0652433 | − | 0.997869i | \(-0.479218\pi\) | ||||
0.0652433 | + | 0.997869i | \(0.479218\pi\) | |||||||
\(194\) | −1.08726e54 | −1.87497 | ||||||||
\(195\) | −7.06157e52 | −0.107916 | ||||||||
\(196\) | 2.92478e54 | 3.96348 | ||||||||
\(197\) | −1.22925e54 | −1.47804 | −0.739019 | − | 0.673685i | \(-0.764711\pi\) | ||||
−0.739019 | + | 0.673685i | \(0.764711\pi\) | |||||||
\(198\) | −9.48717e52 | −0.101276 | ||||||||
\(199\) | 1.40028e54 | 1.32790 | 0.663952 | − | 0.747775i | \(-0.268878\pi\) | ||||
0.663952 | + | 0.747775i | \(0.268878\pi\) | |||||||
\(200\) | −6.91248e53 | −0.582678 | ||||||||
\(201\) | −6.76139e52 | −0.0506908 | ||||||||
\(202\) | −2.96460e54 | −1.97792 | ||||||||
\(203\) | −3.60707e54 | −2.14288 | ||||||||
\(204\) | −2.35816e53 | −0.124814 | ||||||||
\(205\) | 1.10971e54 | 0.523591 | ||||||||
\(206\) | 8.01092e54 | 3.37134 | ||||||||
\(207\) | −2.32514e53 | −0.0873265 | ||||||||
\(208\) | −1.75270e54 | −0.587785 | ||||||||
\(209\) | 1.28505e53 | 0.0385018 | ||||||||
\(210\) | 1.61490e54 | 0.432506 | ||||||||
\(211\) | 7.49292e53 | 0.179479 | 0.0897394 | − | 0.995965i | \(-0.471397\pi\) | ||||
0.0897394 | + | 0.995965i | \(0.471397\pi\) | |||||||
\(212\) | −2.94164e53 | −0.0630518 | ||||||||
\(213\) | −1.85710e53 | −0.0356381 | ||||||||
\(214\) | −1.18661e55 | −2.03978 | ||||||||
\(215\) | 1.05054e55 | 1.61849 | ||||||||
\(216\) | −2.81912e54 | −0.389449 | ||||||||
\(217\) | −1.41600e55 | −1.75493 | ||||||||
\(218\) | 1.43269e55 | 1.59376 | ||||||||
\(219\) | 1.05441e54 | 0.105335 | ||||||||
\(220\) | 1.50932e54 | 0.135472 | ||||||||
\(221\) | −4.84410e54 | −0.390836 | ||||||||
\(222\) | −4.04232e54 | −0.293316 | ||||||||
\(223\) | 7.65012e54 | 0.499464 | 0.249732 | − | 0.968315i | \(-0.419658\pi\) | ||||
0.249732 | + | 0.968315i | \(0.419658\pi\) | |||||||
\(224\) | −7.11905e54 | −0.418402 | ||||||||
\(225\) | −6.83128e54 | −0.361587 | ||||||||
\(226\) | 1.34700e55 | 0.642421 | ||||||||
\(227\) | 1.58232e55 | 0.680277 | 0.340138 | − | 0.940375i | \(-0.389526\pi\) | ||||
0.340138 | + | 0.940375i | \(0.389526\pi\) | |||||||
\(228\) | 3.93736e54 | 0.152664 | ||||||||
\(229\) | 2.86045e55 | 1.00069 | 0.500347 | − | 0.865825i | \(-0.333206\pi\) | ||||
0.500347 | + | 0.865825i | \(0.333206\pi\) | |||||||
\(230\) | 5.61827e54 | 0.177418 | ||||||||
\(231\) | −4.55689e53 | −0.0129953 | ||||||||
\(232\) | −7.54894e55 | −1.94500 | ||||||||
\(233\) | −3.61119e55 | −0.840980 | −0.420490 | − | 0.907297i | \(-0.638142\pi\) | ||||
−0.420490 | + | 0.907297i | \(0.638142\pi\) | |||||||
\(234\) | −5.97122e55 | −1.25745 | ||||||||
\(235\) | 3.83219e55 | 0.730050 | ||||||||
\(236\) | −3.94866e54 | −0.0680798 | ||||||||
\(237\) | 1.54904e54 | 0.0241812 | ||||||||
\(238\) | 1.10779e56 | 1.56639 | ||||||||
\(239\) | 5.47124e55 | 0.701027 | 0.350514 | − | 0.936558i | \(-0.386007\pi\) | ||||
0.350514 | + | 0.936558i | \(0.386007\pi\) | |||||||
\(240\) | 9.80370e54 | 0.113874 | ||||||||
\(241\) | −8.92529e55 | −0.940204 | −0.470102 | − | 0.882612i | \(-0.655783\pi\) | ||||
−0.470102 | + | 0.882612i | \(0.655783\pi\) | |||||||
\(242\) | 1.78374e56 | 1.70479 | ||||||||
\(243\) | −4.18975e55 | −0.363447 | ||||||||
\(244\) | 1.30027e56 | 1.02417 | ||||||||
\(245\) | −3.36060e56 | −2.40444 | ||||||||
\(246\) | −1.45722e55 | −0.0947436 | ||||||||
\(247\) | 8.08808e55 | 0.478043 | ||||||||
\(248\) | −2.96343e56 | −1.59287 | ||||||||
\(249\) | 3.44871e55 | 0.168644 | ||||||||
\(250\) | −2.84456e56 | −1.26597 | ||||||||
\(251\) | 1.98048e56 | 0.802487 | 0.401244 | − | 0.915971i | \(-0.368578\pi\) | ||||
0.401244 | + | 0.915971i | \(0.368578\pi\) | |||||||
\(252\) | 8.99084e56 | 3.31808 | ||||||||
\(253\) | −1.58535e54 | −0.00533080 | ||||||||
\(254\) | −3.75474e56 | −1.15077 | ||||||||
\(255\) | 2.70955e55 | 0.0757186 | ||||||||
\(256\) | −7.44508e56 | −1.89771 | ||||||||
\(257\) | −1.71029e55 | −0.0397778 | −0.0198889 | − | 0.999802i | \(-0.506331\pi\) | ||||
−0.0198889 | + | 0.999802i | \(0.506331\pi\) | |||||||
\(258\) | −1.37953e56 | −0.292865 | ||||||||
\(259\) | 1.25028e57 | 2.42361 | ||||||||
\(260\) | 9.49967e56 | 1.68203 | ||||||||
\(261\) | −7.46028e56 | −1.20699 | ||||||||
\(262\) | −7.34794e56 | −1.08664 | ||||||||
\(263\) | 3.32579e56 | 0.449712 | 0.224856 | − | 0.974392i | \(-0.427809\pi\) | ||||
0.224856 | + | 0.974392i | \(0.427809\pi\) | |||||||
\(264\) | −9.53676e54 | −0.0117953 | ||||||||
\(265\) | 3.37998e55 | 0.0382504 | ||||||||
\(266\) | −1.84965e57 | −1.91590 | ||||||||
\(267\) | 1.95618e56 | 0.185521 | ||||||||
\(268\) | 9.09585e56 | 0.790088 | ||||||||
\(269\) | −1.74613e57 | −1.38963 | −0.694815 | − | 0.719189i | \(-0.744514\pi\) | ||||
−0.694815 | + | 0.719189i | \(0.744514\pi\) | |||||||
\(270\) | 6.73187e56 | 0.491007 | ||||||||
\(271\) | 1.96258e56 | 0.131235 | 0.0656174 | − | 0.997845i | \(-0.479098\pi\) | ||||
0.0656174 | + | 0.997845i | \(0.479098\pi\) | |||||||
\(272\) | 6.72516e56 | 0.412414 | ||||||||
\(273\) | −2.86811e56 | −0.161352 | ||||||||
\(274\) | 4.25542e57 | 2.19687 | ||||||||
\(275\) | −4.65777e55 | −0.0220729 | ||||||||
\(276\) | −4.85748e55 | −0.0211372 | ||||||||
\(277\) | 1.40234e57 | 0.560503 | 0.280252 | − | 0.959927i | \(-0.409582\pi\) | ||||
0.280252 | + | 0.959927i | \(0.409582\pi\) | |||||||
\(278\) | 2.41176e57 | 0.885690 | ||||||||
\(279\) | −2.92862e57 | −0.988472 | ||||||||
\(280\) | −1.04533e58 | −3.24371 | ||||||||
\(281\) | −3.15409e57 | −0.900068 | −0.450034 | − | 0.893011i | \(-0.648588\pi\) | ||||
−0.450034 | + | 0.893011i | \(0.648588\pi\) | |||||||
\(282\) | −5.03228e56 | −0.132102 | ||||||||
\(283\) | 6.43417e57 | 1.55422 | 0.777108 | − | 0.629368i | \(-0.216686\pi\) | ||||
0.777108 | + | 0.629368i | \(0.216686\pi\) | |||||||
\(284\) | 2.49829e57 | 0.555472 | ||||||||
\(285\) | −4.52406e56 | −0.0926135 | ||||||||
\(286\) | −4.07136e56 | −0.0767604 | ||||||||
\(287\) | 4.50715e57 | 0.782848 | ||||||||
\(288\) | −1.47239e57 | −0.235667 | ||||||||
\(289\) | −4.91926e57 | −0.725773 | ||||||||
\(290\) | 1.80264e58 | 2.45219 | ||||||||
\(291\) | −1.08011e57 | −0.135513 | ||||||||
\(292\) | −1.41845e58 | −1.64179 | ||||||||
\(293\) | −7.47274e57 | −0.798162 | −0.399081 | − | 0.916916i | \(-0.630671\pi\) | ||||
−0.399081 | + | 0.916916i | \(0.630671\pi\) | |||||||
\(294\) | 4.41301e57 | 0.435083 | ||||||||
\(295\) | 4.53705e56 | 0.0413006 | ||||||||
\(296\) | 2.61661e58 | 2.19981 | ||||||||
\(297\) | −1.89958e56 | −0.0147531 | ||||||||
\(298\) | −3.68363e58 | −2.64359 | ||||||||
\(299\) | −9.97819e56 | −0.0661879 | ||||||||
\(300\) | −1.42713e57 | −0.0875215 | ||||||||
\(301\) | 4.26685e58 | 2.41989 | ||||||||
\(302\) | −3.18760e58 | −1.67225 | ||||||||
\(303\) | −2.94510e57 | −0.142954 | ||||||||
\(304\) | −1.12288e58 | −0.504435 | ||||||||
\(305\) | −1.49402e58 | −0.621312 | ||||||||
\(306\) | 2.29118e58 | 0.882278 | ||||||||
\(307\) | −2.04451e58 | −0.729183 | −0.364592 | − | 0.931168i | \(-0.618791\pi\) | ||||
−0.364592 | + | 0.931168i | \(0.618791\pi\) | |||||||
\(308\) | 6.13022e57 | 0.202551 | ||||||||
\(309\) | 7.95820e57 | 0.243664 | ||||||||
\(310\) | 7.07646e58 | 2.00824 | ||||||||
\(311\) | 3.46247e58 | 0.910997 | 0.455499 | − | 0.890236i | \(-0.349461\pi\) | ||||
0.455499 | + | 0.890236i | \(0.349461\pi\) | |||||||
\(312\) | −6.00243e57 | −0.146452 | ||||||||
\(313\) | 7.50527e58 | 1.69853 | 0.849267 | − | 0.527963i | \(-0.177044\pi\) | ||||
0.849267 | + | 0.527963i | \(0.177044\pi\) | |||||||
\(314\) | −7.51789e58 | −1.57852 | ||||||||
\(315\) | −1.03306e59 | −2.01292 | ||||||||
\(316\) | −2.08387e58 | −0.376898 | ||||||||
\(317\) | −9.59709e58 | −1.61156 | −0.805781 | − | 0.592213i | \(-0.798254\pi\) | ||||
−0.805781 | + | 0.592213i | \(0.798254\pi\) | |||||||
\(318\) | −4.43844e56 | −0.00692139 | ||||||||
\(319\) | −5.08663e57 | −0.0736800 | ||||||||
\(320\) | 1.04003e59 | 1.39966 | ||||||||
\(321\) | −1.17880e58 | −0.147425 | ||||||||
\(322\) | 2.28190e58 | 0.265267 | ||||||||
\(323\) | −3.10342e58 | −0.335414 | ||||||||
\(324\) | 1.83019e59 | 1.83946 | ||||||||
\(325\) | −2.93160e58 | −0.274060 | ||||||||
\(326\) | −8.17144e58 | −0.710698 | ||||||||
\(327\) | 1.42326e58 | 0.115189 | ||||||||
\(328\) | 9.43265e58 | 0.710556 | ||||||||
\(329\) | 1.55647e59 | 1.09154 | ||||||||
\(330\) | 2.27731e57 | 0.0148712 | ||||||||
\(331\) | −9.45783e58 | −0.575219 | −0.287610 | − | 0.957748i | \(-0.592861\pi\) | ||||
−0.287610 | + | 0.957748i | \(0.592861\pi\) | |||||||
\(332\) | −4.63942e59 | −2.62856 | ||||||||
\(333\) | 2.58588e59 | 1.36511 | ||||||||
\(334\) | −2.37630e59 | −1.16912 | ||||||||
\(335\) | −1.04512e59 | −0.479307 | ||||||||
\(336\) | 3.98184e58 | 0.170259 | ||||||||
\(337\) | 4.62637e59 | 1.84475 | 0.922375 | − | 0.386295i | \(-0.126245\pi\) | ||||
0.922375 | + | 0.386295i | \(0.126245\pi\) | |||||||
\(338\) | 2.03778e59 | 0.757906 | ||||||||
\(339\) | 1.33814e58 | 0.0464310 | ||||||||
\(340\) | −3.64505e59 | −1.18018 | ||||||||
\(341\) | −1.99682e58 | −0.0603408 | ||||||||
\(342\) | −3.82552e59 | −1.07914 | ||||||||
\(343\) | −7.01170e59 | −1.84677 | ||||||||
\(344\) | 8.92975e59 | 2.19642 | ||||||||
\(345\) | 5.58129e57 | 0.0128229 | ||||||||
\(346\) | 4.42080e59 | 0.948883 | ||||||||
\(347\) | 4.68114e59 | 0.938878 | 0.469439 | − | 0.882965i | \(-0.344456\pi\) | ||||
0.469439 | + | 0.882965i | \(0.344456\pi\) | |||||||
\(348\) | −1.55854e59 | −0.292149 | ||||||||
\(349\) | −1.32904e59 | −0.232884 | −0.116442 | − | 0.993197i | \(-0.537149\pi\) | ||||
−0.116442 | + | 0.993197i | \(0.537149\pi\) | |||||||
\(350\) | 6.70424e59 | 1.09837 | ||||||||
\(351\) | −1.19560e59 | −0.183176 | ||||||||
\(352\) | −1.00392e58 | −0.0143862 | ||||||||
\(353\) | −7.06798e59 | −0.947523 | −0.473762 | − | 0.880653i | \(-0.657104\pi\) | ||||
−0.473762 | + | 0.880653i | \(0.657104\pi\) | |||||||
\(354\) | −5.95787e57 | −0.00747333 | ||||||||
\(355\) | −2.87056e59 | −0.336977 | ||||||||
\(356\) | −2.63157e60 | −2.89161 | ||||||||
\(357\) | 1.10050e59 | 0.113211 | ||||||||
\(358\) | 2.02090e60 | 1.94667 | ||||||||
\(359\) | 8.86439e59 | 0.799704 | 0.399852 | − | 0.916580i | \(-0.369061\pi\) | ||||
0.399852 | + | 0.916580i | \(0.369061\pi\) | |||||||
\(360\) | −2.16200e60 | −1.82704 | ||||||||
\(361\) | −7.44875e59 | −0.589745 | ||||||||
\(362\) | 1.31222e60 | 0.973541 | ||||||||
\(363\) | 1.77200e59 | 0.123214 | ||||||||
\(364\) | 3.85836e60 | 2.51490 | ||||||||
\(365\) | 1.62982e60 | 0.995994 | ||||||||
\(366\) | 1.96188e59 | 0.112426 | ||||||||
\(367\) | −1.87716e60 | −1.00890 | −0.504451 | − | 0.863440i | \(-0.668305\pi\) | ||||
−0.504451 | + | 0.863440i | \(0.668305\pi\) | |||||||
\(368\) | 1.38529e59 | 0.0698420 | ||||||||
\(369\) | 9.32186e59 | 0.440943 | ||||||||
\(370\) | −6.24829e60 | −2.77345 | ||||||||
\(371\) | 1.37280e59 | 0.0571901 | ||||||||
\(372\) | −6.11822e59 | −0.239258 | ||||||||
\(373\) | −2.92907e59 | −0.107541 | −0.0537703 | − | 0.998553i | \(-0.517124\pi\) | ||||
−0.0537703 | + | 0.998553i | \(0.517124\pi\) | |||||||
\(374\) | 1.56219e59 | 0.0538582 | ||||||||
\(375\) | −2.82584e59 | −0.0914982 | ||||||||
\(376\) | 3.25742e60 | 0.990739 | ||||||||
\(377\) | −3.20153e60 | −0.914820 | ||||||||
\(378\) | 2.73420e60 | 0.734130 | ||||||||
\(379\) | 1.26439e60 | 0.319051 | 0.159525 | − | 0.987194i | \(-0.449004\pi\) | ||||
0.159525 | + | 0.987194i | \(0.449004\pi\) | |||||||
\(380\) | 6.08605e60 | 1.44352 | ||||||||
\(381\) | −3.73003e59 | −0.0831716 | ||||||||
\(382\) | −1.58310e61 | −3.31909 | ||||||||
\(383\) | 7.65652e60 | 1.50959 | 0.754797 | − | 0.655958i | \(-0.227735\pi\) | ||||
0.754797 | + | 0.655958i | \(0.227735\pi\) | |||||||
\(384\) | −1.20614e60 | −0.223673 | ||||||||
\(385\) | −7.04368e59 | −0.122877 | ||||||||
\(386\) | −1.36023e60 | −0.223259 | ||||||||
\(387\) | 8.82487e60 | 1.36301 | ||||||||
\(388\) | 1.45303e61 | 2.11217 | ||||||||
\(389\) | −7.85479e60 | −1.07478 | −0.537389 | − | 0.843335i | \(-0.680589\pi\) | ||||
−0.537389 | + | 0.843335i | \(0.680589\pi\) | |||||||
\(390\) | 1.43334e60 | 0.184642 | ||||||||
\(391\) | 3.82867e59 | 0.0464401 | ||||||||
\(392\) | −2.85656e61 | −3.26303 | ||||||||
\(393\) | −7.29959e59 | −0.0785368 | ||||||||
\(394\) | 2.49511e61 | 2.52888 | ||||||||
\(395\) | 2.39439e60 | 0.228645 | ||||||||
\(396\) | 1.26788e60 | 0.114088 | ||||||||
\(397\) | −1.21556e61 | −1.03086 | −0.515430 | − | 0.856932i | \(-0.672368\pi\) | ||||
−0.515430 | + | 0.856932i | \(0.672368\pi\) | |||||||
\(398\) | −2.84225e61 | −2.27201 | ||||||||
\(399\) | −1.83748e60 | −0.138471 | ||||||||
\(400\) | 4.06999e60 | 0.289190 | ||||||||
\(401\) | 1.13229e61 | 0.758692 | 0.379346 | − | 0.925255i | \(-0.376149\pi\) | ||||
0.379346 | + | 0.925255i | \(0.376149\pi\) | |||||||
\(402\) | 1.37241e60 | 0.0867305 | ||||||||
\(403\) | −1.25680e61 | −0.749198 | ||||||||
\(404\) | 3.96193e61 | 2.22815 | ||||||||
\(405\) | −2.10291e61 | −1.11591 | ||||||||
\(406\) | 7.32154e61 | 3.66640 | ||||||||
\(407\) | 1.76313e60 | 0.0833327 | ||||||||
\(408\) | 2.30316e60 | 0.102757 | ||||||||
\(409\) | −1.93004e61 | −0.812958 | −0.406479 | − | 0.913660i | \(-0.633244\pi\) | ||||
−0.406479 | + | 0.913660i | \(0.633244\pi\) | |||||||
\(410\) | −2.25245e61 | −0.895849 | ||||||||
\(411\) | 4.22742e60 | 0.158779 | ||||||||
\(412\) | −1.07059e62 | −3.79785 | ||||||||
\(413\) | 1.84276e60 | 0.0617507 | ||||||||
\(414\) | 4.71951e60 | 0.149413 | ||||||||
\(415\) | 5.33073e61 | 1.59462 | ||||||||
\(416\) | −6.31866e60 | −0.178621 | ||||||||
\(417\) | 2.39589e60 | 0.0640132 | ||||||||
\(418\) | −2.60835e60 | −0.0658755 | ||||||||
\(419\) | −3.12082e60 | −0.0745141 | −0.0372571 | − | 0.999306i | \(-0.511862\pi\) | ||||
−0.0372571 | + | 0.999306i | \(0.511862\pi\) | |||||||
\(420\) | −2.15817e61 | −0.487223 | ||||||||
\(421\) | 6.12499e61 | 1.30760 | 0.653802 | − | 0.756666i | \(-0.273173\pi\) | ||||
0.653802 | + | 0.756666i | \(0.273173\pi\) | |||||||
\(422\) | −1.52089e61 | −0.307084 | ||||||||
\(423\) | 3.21916e61 | 0.614814 | ||||||||
\(424\) | 2.87303e60 | 0.0519090 | ||||||||
\(425\) | 1.12487e61 | 0.192292 | ||||||||
\(426\) | 3.76950e60 | 0.0609759 | ||||||||
\(427\) | −6.06807e61 | −0.928957 | ||||||||
\(428\) | 1.58579e62 | 2.29783 | ||||||||
\(429\) | −4.04456e59 | −0.00554786 | ||||||||
\(430\) | −2.13236e62 | −2.76919 | ||||||||
\(431\) | −7.83169e61 | −0.963030 | −0.481515 | − | 0.876438i | \(-0.659913\pi\) | ||||
−0.481515 | + | 0.876438i | \(0.659913\pi\) | |||||||
\(432\) | 1.65987e61 | 0.193288 | ||||||||
\(433\) | 2.94510e61 | 0.324814 | 0.162407 | − | 0.986724i | \(-0.448074\pi\) | ||||
0.162407 | + | 0.986724i | \(0.448074\pi\) | |||||||
\(434\) | 2.87416e62 | 3.00263 | ||||||||
\(435\) | 1.79077e61 | 0.177232 | ||||||||
\(436\) | −1.91466e62 | −1.79539 | ||||||||
\(437\) | −6.39262e60 | −0.0568022 | ||||||||
\(438\) | −2.14021e61 | −0.180225 | ||||||||
\(439\) | −8.39024e60 | −0.0669666 | −0.0334833 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334833 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(440\) | −1.47412e61 | −0.111530 | ||||||||
\(441\) | −2.82301e62 | −2.02491 | ||||||||
\(442\) | 9.83245e61 | 0.668711 | ||||||||
\(443\) | −7.70512e61 | −0.496926 | −0.248463 | − | 0.968641i | \(-0.579925\pi\) | ||||
−0.248463 | + | 0.968641i | \(0.579925\pi\) | |||||||
\(444\) | 5.40220e61 | 0.330423 | ||||||||
\(445\) | 3.02370e62 | 1.75420 | ||||||||
\(446\) | −1.55280e62 | −0.854569 | ||||||||
\(447\) | −3.65939e61 | −0.191065 | ||||||||
\(448\) | 4.22417e62 | 2.09270 | ||||||||
\(449\) | 1.71627e62 | 0.806857 | 0.403429 | − | 0.915011i | \(-0.367818\pi\) | ||||
0.403429 | + | 0.915011i | \(0.367818\pi\) | |||||||
\(450\) | 1.38660e62 | 0.618666 | ||||||||
\(451\) | 6.35592e60 | 0.0269172 | ||||||||
\(452\) | −1.80015e62 | −0.723693 | ||||||||
\(453\) | −3.16662e61 | −0.120862 | ||||||||
\(454\) | −3.21175e62 | −1.16394 | ||||||||
\(455\) | −4.43329e62 | −1.52566 | ||||||||
\(456\) | −3.84552e61 | −0.125684 | ||||||||
\(457\) | 4.06573e62 | 1.26214 | 0.631070 | − | 0.775726i | \(-0.282616\pi\) | ||||
0.631070 | + | 0.775726i | \(0.282616\pi\) | |||||||
\(458\) | −5.80608e62 | −1.71216 | ||||||||
\(459\) | 4.58755e61 | 0.128524 | ||||||||
\(460\) | −7.50831e61 | −0.199863 | ||||||||
\(461\) | 2.67924e62 | 0.677704 | 0.338852 | − | 0.940840i | \(-0.389961\pi\) | ||||
0.338852 | + | 0.940840i | \(0.389961\pi\) | |||||||
\(462\) | 9.24946e60 | 0.0222346 | ||||||||
\(463\) | −5.44459e62 | −1.24397 | −0.621987 | − | 0.783027i | \(-0.713675\pi\) | ||||
−0.621987 | + | 0.783027i | \(0.713675\pi\) | |||||||
\(464\) | 4.44474e62 | 0.965325 | ||||||||
\(465\) | 7.02989e61 | 0.145146 | ||||||||
\(466\) | 7.32990e62 | 1.43889 | ||||||||
\(467\) | 4.82071e62 | 0.899839 | 0.449919 | − | 0.893069i | \(-0.351453\pi\) | ||||
0.449919 | + | 0.893069i | \(0.351453\pi\) | |||||||
\(468\) | 7.98001e62 | 1.41653 | ||||||||
\(469\) | −4.24484e62 | −0.716637 | ||||||||
\(470\) | −7.77849e62 | −1.24910 | ||||||||
\(471\) | −7.46841e61 | −0.114087 | ||||||||
\(472\) | 3.85656e61 | 0.0560484 | ||||||||
\(473\) | 6.01705e61 | 0.0832045 | ||||||||
\(474\) | −3.14421e61 | −0.0413733 | ||||||||
\(475\) | −1.87816e62 | −0.235197 | ||||||||
\(476\) | −1.48047e63 | −1.76455 | ||||||||
\(477\) | 2.83928e61 | 0.0322127 | ||||||||
\(478\) | −1.11054e63 | −1.19944 | ||||||||
\(479\) | 1.74319e63 | 1.79251 | 0.896253 | − | 0.443543i | \(-0.146279\pi\) | ||||
0.896253 | + | 0.443543i | \(0.146279\pi\) | |||||||
\(480\) | 3.53434e61 | 0.0346050 | ||||||||
\(481\) | 1.10971e63 | 1.03467 | ||||||||
\(482\) | 1.81163e63 | 1.60866 | ||||||||
\(483\) | 2.26688e61 | 0.0191722 | ||||||||
\(484\) | −2.38381e63 | −1.92046 | ||||||||
\(485\) | −1.66955e63 | −1.28135 | ||||||||
\(486\) | 8.50425e62 | 0.621847 | ||||||||
\(487\) | −2.19497e63 | −1.52932 | −0.764661 | − | 0.644433i | \(-0.777093\pi\) | ||||
−0.764661 | + | 0.644433i | \(0.777093\pi\) | |||||||
\(488\) | −1.26994e63 | −0.843173 | ||||||||
\(489\) | −8.11767e61 | −0.0513657 | ||||||||
\(490\) | 6.82127e63 | 4.11394 | ||||||||
\(491\) | −4.81659e62 | −0.276901 | −0.138451 | − | 0.990369i | \(-0.544212\pi\) | ||||
−0.138451 | + | 0.990369i | \(0.544212\pi\) | |||||||
\(492\) | 1.94744e62 | 0.106730 | ||||||||
\(493\) | 1.22844e63 | 0.641875 | ||||||||
\(494\) | −1.64170e63 | −0.817918 | ||||||||
\(495\) | −1.45680e62 | −0.0692114 | ||||||||
\(496\) | 1.74483e63 | 0.790560 | ||||||||
\(497\) | −1.16590e63 | −0.503832 | ||||||||
\(498\) | −7.00010e62 | −0.288546 | ||||||||
\(499\) | −2.59805e63 | −1.02161 | −0.510805 | − | 0.859696i | \(-0.670653\pi\) | ||||
−0.510805 | + | 0.859696i | \(0.670653\pi\) | |||||||
\(500\) | 3.80149e63 | 1.42613 | ||||||||
\(501\) | −2.36066e62 | −0.0844983 | ||||||||
\(502\) | −4.01993e63 | −1.37303 | ||||||||
\(503\) | 5.26346e63 | 1.71563 | 0.857816 | − | 0.513958i | \(-0.171821\pi\) | ||||
0.857816 | + | 0.513958i | \(0.171821\pi\) | |||||||
\(504\) | −8.78112e63 | −2.73170 | ||||||||
\(505\) | −4.55229e63 | −1.35171 | ||||||||
\(506\) | 3.21790e61 | 0.00912086 | ||||||||
\(507\) | 2.02437e62 | 0.0547777 | ||||||||
\(508\) | 5.01787e63 | 1.29635 | ||||||||
\(509\) | −1.22138e63 | −0.301289 | −0.150644 | − | 0.988588i | \(-0.548135\pi\) | ||||
−0.150644 | + | 0.988588i | \(0.548135\pi\) | |||||||
\(510\) | −5.49977e62 | −0.129552 | ||||||||
\(511\) | 6.61963e63 | 1.48916 | ||||||||
\(512\) | 6.69351e63 | 1.43817 | ||||||||
\(513\) | −7.65972e62 | −0.157201 | ||||||||
\(514\) | 3.47150e62 | 0.0680587 | ||||||||
\(515\) | 1.23012e64 | 2.30397 | ||||||||
\(516\) | 1.84361e63 | 0.329915 | ||||||||
\(517\) | 2.19492e62 | 0.0375310 | ||||||||
\(518\) | −2.53779e64 | −4.14673 | ||||||||
\(519\) | 4.39171e62 | 0.0685805 | ||||||||
\(520\) | −9.27808e63 | −1.38478 | ||||||||
\(521\) | −9.22332e62 | −0.131583 | −0.0657916 | − | 0.997833i | \(-0.520957\pi\) | ||||
−0.0657916 | + | 0.997833i | \(0.520957\pi\) | |||||||
\(522\) | 1.51427e64 | 2.06512 | ||||||||
\(523\) | −1.18236e64 | −1.54155 | −0.770777 | − | 0.637105i | \(-0.780132\pi\) | ||||
−0.770777 | + | 0.637105i | \(0.780132\pi\) | |||||||
\(524\) | 9.81987e63 | 1.22411 | ||||||||
\(525\) | 6.66012e62 | 0.0793850 | ||||||||
\(526\) | −6.75060e63 | −0.769444 | ||||||||
\(527\) | 4.82238e63 | 0.525668 | ||||||||
\(528\) | 5.61514e61 | 0.00585414 | ||||||||
\(529\) | −9.94900e63 | −0.992135 | ||||||||
\(530\) | −6.86059e62 | −0.0654453 | ||||||||
\(531\) | 3.81126e62 | 0.0347814 | ||||||||
\(532\) | 2.47190e64 | 2.15828 | ||||||||
\(533\) | 4.00041e63 | 0.334207 | ||||||||
\(534\) | −3.97060e63 | −0.317422 | ||||||||
\(535\) | −1.82209e64 | −1.39398 | ||||||||
\(536\) | −8.88369e63 | −0.650460 | ||||||||
\(537\) | 2.00760e63 | 0.140696 | ||||||||
\(538\) | 3.54426e64 | 2.37762 | ||||||||
\(539\) | −1.92481e63 | −0.123610 | ||||||||
\(540\) | −8.99654e63 | −0.553124 | ||||||||
\(541\) | −1.28271e64 | −0.755077 | −0.377539 | − | 0.925994i | \(-0.623229\pi\) | ||||
−0.377539 | + | 0.925994i | \(0.623229\pi\) | |||||||
\(542\) | −3.98360e63 | −0.224539 | ||||||||
\(543\) | 1.30358e63 | 0.0703627 | ||||||||
\(544\) | 2.42449e63 | 0.125328 | ||||||||
\(545\) | 2.19996e64 | 1.08917 | ||||||||
\(546\) | 5.82161e63 | 0.276068 | ||||||||
\(547\) | 3.21410e64 | 1.46001 | 0.730007 | − | 0.683440i | \(-0.239517\pi\) | ||||
0.730007 | + | 0.683440i | \(0.239517\pi\) | |||||||
\(548\) | −5.68699e64 | −2.47479 | ||||||||
\(549\) | −1.25502e64 | −0.523240 | ||||||||
\(550\) | 9.45422e62 | 0.0377661 | ||||||||
\(551\) | −2.05109e64 | −0.785095 | ||||||||
\(552\) | 4.74418e62 | 0.0174018 | ||||||||
\(553\) | 9.72498e63 | 0.341860 | ||||||||
\(554\) | −2.84643e64 | −0.959006 | ||||||||
\(555\) | −6.20717e63 | −0.200451 | ||||||||
\(556\) | −3.22310e64 | −0.997738 | ||||||||
\(557\) | −1.16869e64 | −0.346819 | −0.173409 | − | 0.984850i | \(-0.555478\pi\) | ||||
−0.173409 | + | 0.984850i | \(0.555478\pi\) | |||||||
\(558\) | 5.94444e64 | 1.69125 | ||||||||
\(559\) | 3.78713e64 | 1.03308 | ||||||||
\(560\) | 6.15482e64 | 1.60989 | ||||||||
\(561\) | 1.55191e62 | 0.00389260 | ||||||||
\(562\) | 6.40209e64 | 1.53999 | ||||||||
\(563\) | 9.31800e63 | 0.214969 | 0.107484 | − | 0.994207i | \(-0.465720\pi\) | ||||
0.107484 | + | 0.994207i | \(0.465720\pi\) | |||||||
\(564\) | 6.72519e63 | 0.148815 | ||||||||
\(565\) | 2.06839e64 | 0.439029 | ||||||||
\(566\) | −1.30599e65 | −2.65922 | ||||||||
\(567\) | −8.54113e64 | −1.66845 | ||||||||
\(568\) | −2.44002e64 | −0.457306 | ||||||||
\(569\) | 7.98965e64 | 1.43678 | 0.718388 | − | 0.695642i | \(-0.244880\pi\) | ||||
0.718388 | + | 0.695642i | \(0.244880\pi\) | |||||||
\(570\) | 9.18283e63 | 0.158459 | ||||||||
\(571\) | −7.20740e64 | −1.19352 | −0.596761 | − | 0.802419i | \(-0.703546\pi\) | ||||
−0.596761 | + | 0.802419i | \(0.703546\pi\) | |||||||
\(572\) | 5.44100e63 | 0.0864713 | ||||||||
\(573\) | −1.57268e64 | −0.239887 | ||||||||
\(574\) | −9.14850e64 | −1.33943 | ||||||||
\(575\) | 2.31707e63 | 0.0325645 | ||||||||
\(576\) | 8.73658e64 | 1.17873 | ||||||||
\(577\) | 3.11163e64 | 0.403047 | 0.201523 | − | 0.979484i | \(-0.435411\pi\) | ||||
0.201523 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(578\) | 9.98500e64 | 1.24178 | ||||||||
\(579\) | −1.35127e63 | −0.0161360 | ||||||||
\(580\) | −2.40906e65 | −2.76242 | ||||||||
\(581\) | 2.16512e65 | 2.38420 | ||||||||
\(582\) | 2.19238e64 | 0.231860 | ||||||||
\(583\) | 1.93591e62 | 0.00196641 | ||||||||
\(584\) | 1.38537e65 | 1.35165 | ||||||||
\(585\) | −9.16910e64 | −0.859338 | ||||||||
\(586\) | 1.51680e65 | 1.36563 | ||||||||
\(587\) | −1.26293e65 | −1.09241 | −0.546205 | − | 0.837652i | \(-0.683928\pi\) | ||||
−0.546205 | + | 0.837652i | \(0.683928\pi\) | |||||||
\(588\) | −5.89759e64 | −0.490126 | ||||||||
\(589\) | −8.05180e64 | −0.642959 | ||||||||
\(590\) | −9.20919e63 | −0.0706642 | ||||||||
\(591\) | 2.47869e64 | 0.182775 | ||||||||
\(592\) | −1.54063e65 | −1.09179 | ||||||||
\(593\) | −1.16829e65 | −0.795726 | −0.397863 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397863 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(594\) | 3.85573e63 | 0.0252421 | ||||||||
\(595\) | 1.70107e65 | 1.07047 | ||||||||
\(596\) | 4.92284e65 | 2.97803 | ||||||||
\(597\) | −2.82354e64 | −0.164209 | ||||||||
\(598\) | 2.02535e64 | 0.113246 | ||||||||
\(599\) | −2.64716e65 | −1.42315 | −0.711573 | − | 0.702612i | \(-0.752017\pi\) | ||||
−0.711573 | + | 0.702612i | \(0.752017\pi\) | |||||||
\(600\) | 1.39384e64 | 0.0720543 | ||||||||
\(601\) | −1.04245e65 | −0.518208 | −0.259104 | − | 0.965849i | \(-0.583427\pi\) | ||||
−0.259104 | + | 0.965849i | \(0.583427\pi\) | |||||||
\(602\) | −8.66075e65 | −4.14036 | ||||||||
\(603\) | −8.77934e64 | −0.403650 | ||||||||
\(604\) | 4.25994e65 | 1.88380 | ||||||||
\(605\) | 2.73902e65 | 1.16505 | ||||||||
\(606\) | 5.97788e64 | 0.244591 | ||||||||
\(607\) | 2.13825e65 | 0.841635 | 0.420818 | − | 0.907145i | \(-0.361743\pi\) | ||||
0.420818 | + | 0.907145i | \(0.361743\pi\) | |||||||
\(608\) | −4.04811e64 | −0.153292 | ||||||||
\(609\) | 7.27336e64 | 0.264989 | ||||||||
\(610\) | 3.03252e65 | 1.06305 | ||||||||
\(611\) | 1.38148e65 | 0.465990 | ||||||||
\(612\) | −3.06196e65 | −0.993895 | ||||||||
\(613\) | −9.41515e64 | −0.294108 | −0.147054 | − | 0.989129i | \(-0.546979\pi\) | ||||
−0.147054 | + | 0.989129i | \(0.546979\pi\) | |||||||
\(614\) | 4.14989e65 | 1.24761 | ||||||||
\(615\) | −2.23763e64 | −0.0647475 | ||||||||
\(616\) | −5.98723e64 | −0.166755 | ||||||||
\(617\) | 3.62608e65 | 0.972156 | 0.486078 | − | 0.873916i | \(-0.338427\pi\) | ||||
0.486078 | + | 0.873916i | \(0.338427\pi\) | |||||||
\(618\) | −1.61534e65 | −0.416902 | ||||||||
\(619\) | −1.97673e65 | −0.491154 | −0.245577 | − | 0.969377i | \(-0.578977\pi\) | ||||
−0.245577 | + | 0.969377i | \(0.578977\pi\) | |||||||
\(620\) | −9.45706e65 | −2.26231 | ||||||||
\(621\) | 9.44972e63 | 0.0217654 | ||||||||
\(622\) | −7.02804e65 | −1.55869 | ||||||||
\(623\) | 1.22810e66 | 2.62279 | ||||||||
\(624\) | 3.53417e64 | 0.0726858 | ||||||||
\(625\) | −6.22185e65 | −1.23236 | ||||||||
\(626\) | −1.52340e66 | −2.90615 | ||||||||
\(627\) | −2.59119e63 | −0.00476115 | ||||||||
\(628\) | 1.00470e66 | 1.77821 | ||||||||
\(629\) | −4.25801e65 | −0.725966 | ||||||||
\(630\) | 2.09687e66 | 3.44405 | ||||||||
\(631\) | −1.83594e65 | −0.290515 | −0.145257 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145257 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(632\) | 2.03526e65 | 0.310291 | ||||||||
\(633\) | −1.51089e64 | −0.0221945 | ||||||||
\(634\) | 1.94799e66 | 2.75734 | ||||||||
\(635\) | −5.76558e65 | −0.786431 | ||||||||
\(636\) | 5.93158e63 | 0.00779701 | ||||||||
\(637\) | −1.21148e66 | −1.53475 | ||||||||
\(638\) | 1.03247e65 | 0.126064 | ||||||||
\(639\) | −2.41136e65 | −0.283786 | ||||||||
\(640\) | −1.86435e66 | −2.11494 | ||||||||
\(641\) | 9.34817e64 | 0.102226 | 0.0511132 | − | 0.998693i | \(-0.483723\pi\) | ||||
0.0511132 | + | 0.998693i | \(0.483723\pi\) | |||||||
\(642\) | 2.39270e65 | 0.252240 | ||||||||
\(643\) | 6.98717e65 | 0.710139 | 0.355070 | − | 0.934840i | \(-0.384457\pi\) | ||||
0.355070 | + | 0.934840i | \(0.384457\pi\) | |||||||
\(644\) | −3.04955e65 | −0.298826 | ||||||||
\(645\) | −2.11833e65 | −0.200143 | ||||||||
\(646\) | 6.29925e65 | 0.573885 | ||||||||
\(647\) | 8.30387e65 | 0.729508 | 0.364754 | − | 0.931104i | \(-0.381153\pi\) | ||||
0.364754 | + | 0.931104i | \(0.381153\pi\) | |||||||
\(648\) | −1.78750e66 | −1.51438 | ||||||||
\(649\) | 2.59863e63 | 0.00212321 | ||||||||
\(650\) | 5.95049e65 | 0.468909 | ||||||||
\(651\) | 2.85524e65 | 0.217015 | ||||||||
\(652\) | 1.09204e66 | 0.800609 | ||||||||
\(653\) | −7.01610e65 | −0.496176 | −0.248088 | − | 0.968737i | \(-0.579802\pi\) | ||||
−0.248088 | + | 0.968737i | \(0.579802\pi\) | |||||||
\(654\) | −2.88889e65 | −0.197085 | ||||||||
\(655\) | −1.12831e66 | −0.742606 | ||||||||
\(656\) | −5.55385e65 | −0.352658 | ||||||||
\(657\) | 1.36910e66 | 0.838780 | ||||||||
\(658\) | −3.15929e66 | −1.86759 | ||||||||
\(659\) | 2.56897e66 | 1.46539 | 0.732693 | − | 0.680559i | \(-0.238263\pi\) | ||||
0.732693 | + | 0.680559i | \(0.238263\pi\) | |||||||
\(660\) | −3.04342e64 | −0.0167525 | ||||||||
\(661\) | 1.01472e66 | 0.539028 | 0.269514 | − | 0.962996i | \(-0.413137\pi\) | ||||
0.269514 | + | 0.962996i | \(0.413137\pi\) | |||||||
\(662\) | 1.91973e66 | 0.984185 | ||||||||
\(663\) | 9.76774e64 | 0.0483311 | ||||||||
\(664\) | 4.53120e66 | 2.16403 | ||||||||
\(665\) | −2.84023e66 | −1.30932 | ||||||||
\(666\) | −5.24875e66 | −2.33567 | ||||||||
\(667\) | 2.53041e65 | 0.108701 | ||||||||
\(668\) | 3.17572e66 | 1.31703 | ||||||||
\(669\) | −1.54258e65 | −0.0617640 | ||||||||
\(670\) | 2.12136e66 | 0.820082 | ||||||||
\(671\) | −8.55710e64 | −0.0319409 | ||||||||
\(672\) | 1.43550e65 | 0.0517398 | ||||||||
\(673\) | 1.27088e66 | 0.442334 | 0.221167 | − | 0.975236i | \(-0.429013\pi\) | ||||
0.221167 | + | 0.975236i | \(0.429013\pi\) | |||||||
\(674\) | −9.39049e66 | −3.15632 | ||||||||
\(675\) | 2.77634e65 | 0.0901225 | ||||||||
\(676\) | −2.72331e66 | −0.853789 | ||||||||
\(677\) | 2.17082e66 | 0.657341 | 0.328671 | − | 0.944445i | \(-0.393399\pi\) | ||||
0.328671 | + | 0.944445i | \(0.393399\pi\) | |||||||
\(678\) | −2.71612e65 | −0.0794421 | ||||||||
\(679\) | −6.78098e66 | −1.91581 | ||||||||
\(680\) | 3.56003e66 | 0.971616 | ||||||||
\(681\) | −3.19061e65 | −0.0841234 | ||||||||
\(682\) | 4.05309e65 | 0.103241 | ||||||||
\(683\) | 7.17341e64 | 0.0176538 | 0.00882692 | − | 0.999961i | \(-0.497190\pi\) | ||||
0.00882692 | + | 0.999961i | \(0.497190\pi\) | |||||||
\(684\) | 5.11247e66 | 1.21566 | ||||||||
\(685\) | 6.53440e66 | 1.50133 | ||||||||
\(686\) | 1.42322e67 | 3.15976 | ||||||||
\(687\) | −5.76787e65 | −0.123746 | ||||||||
\(688\) | −5.25774e66 | −1.09011 | ||||||||
\(689\) | 1.21846e65 | 0.0244151 | ||||||||
\(690\) | −1.13288e65 | −0.0219396 | ||||||||
\(691\) | −4.47891e66 | −0.838374 | −0.419187 | − | 0.907900i | \(-0.637685\pi\) | ||||
−0.419187 | + | 0.907900i | \(0.637685\pi\) | |||||||
\(692\) | −5.90801e66 | −1.06893 | ||||||||
\(693\) | −5.91690e65 | −0.103482 | ||||||||
\(694\) | −9.50166e66 | −1.60639 | ||||||||
\(695\) | 3.70338e66 | 0.605278 | ||||||||
\(696\) | 1.52218e66 | 0.240519 | ||||||||
\(697\) | −1.53497e66 | −0.234493 | ||||||||
\(698\) | 2.69765e66 | 0.398459 | ||||||||
\(699\) | 7.28166e65 | 0.103996 | ||||||||
\(700\) | −8.95962e66 | −1.23733 | ||||||||
\(701\) | −3.84070e66 | −0.512905 | −0.256452 | − | 0.966557i | \(-0.582554\pi\) | ||||
−0.256452 | + | 0.966557i | \(0.582554\pi\) | |||||||
\(702\) | 2.42680e66 | 0.313409 | ||||||||
\(703\) | 7.10949e66 | 0.887949 | ||||||||
\(704\) | 5.95686e65 | 0.0719548 | ||||||||
\(705\) | −7.72730e65 | −0.0902784 | ||||||||
\(706\) | 1.43464e67 | 1.62119 | ||||||||
\(707\) | −1.84895e67 | −2.02101 | ||||||||
\(708\) | 7.96216e64 | 0.00841878 | ||||||||
\(709\) | 6.56172e64 | 0.00671168 | 0.00335584 | − | 0.999994i | \(-0.498932\pi\) | ||||
0.00335584 | + | 0.999994i | \(0.498932\pi\) | |||||||
\(710\) | 5.82659e66 | 0.576558 | ||||||||
\(711\) | 2.01136e66 | 0.192555 | ||||||||
\(712\) | 2.57019e67 | 2.38059 | ||||||||
\(713\) | 9.93343e65 | 0.0890216 | ||||||||
\(714\) | −2.23377e66 | −0.193701 | ||||||||
\(715\) | −6.25176e65 | −0.0524579 | ||||||||
\(716\) | −2.70075e67 | −2.19294 | ||||||||
\(717\) | −1.10323e66 | −0.0866894 | ||||||||
\(718\) | −1.79927e67 | −1.36827 | ||||||||
\(719\) | −2.12438e67 | −1.56352 | −0.781760 | − | 0.623580i | \(-0.785678\pi\) | ||||
−0.781760 | + | 0.623580i | \(0.785678\pi\) | |||||||
\(720\) | 1.27296e67 | 0.906780 | ||||||||
\(721\) | 4.99620e67 | 3.44478 | ||||||||
\(722\) | 1.51193e67 | 1.00904 | ||||||||
\(723\) | 1.79971e66 | 0.116266 | ||||||||
\(724\) | −1.75366e67 | −1.09670 | ||||||||
\(725\) | 7.43437e66 | 0.450092 | ||||||||
\(726\) | −3.59677e66 | −0.210815 | ||||||||
\(727\) | 2.27873e67 | 1.29311 | 0.646554 | − | 0.762868i | \(-0.276209\pi\) | ||||
0.646554 | + | 0.762868i | \(0.276209\pi\) | |||||||
\(728\) | −3.76836e67 | −2.07045 | ||||||||
\(729\) | −1.70946e67 | −0.909414 | ||||||||
\(730\) | −3.30816e67 | −1.70412 | ||||||||
\(731\) | −1.45314e67 | −0.724850 | ||||||||
\(732\) | −2.62188e66 | −0.126649 | ||||||||
\(733\) | −2.32774e66 | −0.108891 | −0.0544454 | − | 0.998517i | \(-0.517339\pi\) | ||||
−0.0544454 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(734\) | 3.81022e67 | 1.72620 | ||||||||
\(735\) | 6.77639e66 | 0.297335 | ||||||||
\(736\) | 4.99412e65 | 0.0212242 | ||||||||
\(737\) | −5.98601e65 | −0.0246406 | ||||||||
\(738\) | −1.89213e67 | −0.754442 | ||||||||
\(739\) | −1.90706e65 | −0.00736579 | −0.00368290 | − | 0.999993i | \(-0.501172\pi\) | ||||
−0.00368290 | + | 0.999993i | \(0.501172\pi\) | |||||||
\(740\) | 8.35028e67 | 3.12432 | ||||||||
\(741\) | −1.63090e66 | −0.0591151 | ||||||||
\(742\) | −2.78648e66 | −0.0978507 | ||||||||
\(743\) | 3.96691e67 | 1.34963 | 0.674816 | − | 0.737986i | \(-0.264223\pi\) | ||||
0.674816 | + | 0.737986i | \(0.264223\pi\) | |||||||
\(744\) | 5.97551e66 | 0.196975 | ||||||||
\(745\) | −5.65639e67 | −1.80662 | ||||||||
\(746\) | 5.94536e66 | 0.183999 | ||||||||
\(747\) | 4.47798e67 | 1.34291 | ||||||||
\(748\) | −2.08773e66 | −0.0606718 | ||||||||
\(749\) | −7.40056e67 | −2.08421 | ||||||||
\(750\) | 5.73582e66 | 0.156551 | ||||||||
\(751\) | −4.47498e67 | −1.18373 | −0.591865 | − | 0.806037i | \(-0.701608\pi\) | ||||
−0.591865 | + | 0.806037i | \(0.701608\pi\) | |||||||
\(752\) | −1.91793e67 | −0.491716 | ||||||||
\(753\) | −3.99348e66 | −0.0992360 | ||||||||
\(754\) | 6.49838e67 | 1.56523 | ||||||||
\(755\) | −4.89471e67 | −1.14281 | ||||||||
\(756\) | −3.65401e67 | −0.827004 | ||||||||
\(757\) | 1.35751e67 | 0.297845 | 0.148922 | − | 0.988849i | \(-0.452420\pi\) | ||||
0.148922 | + | 0.988849i | \(0.452420\pi\) | |||||||
\(758\) | −2.56643e67 | −0.545887 | ||||||||
\(759\) | 3.19673e64 | 0.000659210 0 | ||||||||
\(760\) | −5.94410e67 | −1.18841 | ||||||||
\(761\) | 3.22776e67 | 0.625693 | 0.312846 | − | 0.949804i | \(-0.398717\pi\) | ||||
0.312846 | + | 0.949804i | \(0.398717\pi\) | |||||||
\(762\) | 7.57112e66 | 0.142304 | ||||||||
\(763\) | 8.93529e67 | 1.62848 | ||||||||
\(764\) | 2.11567e68 | 3.73899 | ||||||||
\(765\) | 3.51822e67 | 0.602947 | ||||||||
\(766\) | −1.55410e68 | −2.58288 | ||||||||
\(767\) | 1.63558e66 | 0.0263621 | ||||||||
\(768\) | 1.50124e67 | 0.234672 | ||||||||
\(769\) | −6.92939e67 | −1.05057 | −0.525287 | − | 0.850925i | \(-0.676042\pi\) | ||||
−0.525287 | + | 0.850925i | \(0.676042\pi\) | |||||||
\(770\) | 1.42971e67 | 0.210240 | ||||||||
\(771\) | 3.44865e65 | 0.00491894 | ||||||||
\(772\) | 1.81782e67 | 0.251504 | ||||||||
\(773\) | 1.00550e68 | 1.34947 | 0.674733 | − | 0.738062i | \(-0.264259\pi\) | ||||
0.674733 | + | 0.738062i | \(0.264259\pi\) | |||||||
\(774\) | −1.79125e68 | −2.33208 | ||||||||
\(775\) | 2.91845e67 | 0.368606 | ||||||||
\(776\) | −1.41914e68 | −1.73890 | ||||||||
\(777\) | −2.52109e67 | −0.299705 | ||||||||
\(778\) | 1.59435e68 | 1.83892 | ||||||||
\(779\) | 2.56291e67 | 0.286815 | ||||||||
\(780\) | −1.91553e67 | −0.208001 | ||||||||
\(781\) | −1.64413e66 | −0.0173236 | ||||||||
\(782\) | −7.77133e66 | −0.0794578 | ||||||||
\(783\) | 3.03197e67 | 0.300831 | ||||||||
\(784\) | 1.68191e68 | 1.61948 | ||||||||
\(785\) | −1.15441e68 | −1.07875 | ||||||||
\(786\) | 1.48165e67 | 0.134374 | ||||||||
\(787\) | −2.41454e66 | −0.0212534 | −0.0106267 | − | 0.999944i | \(-0.503383\pi\) | ||||
−0.0106267 | + | 0.999944i | \(0.503383\pi\) | |||||||
\(788\) | −3.33449e68 | −2.84881 | ||||||||
\(789\) | −6.70618e66 | −0.0556116 | ||||||||
\(790\) | −4.86007e67 | −0.391206 | ||||||||
\(791\) | 8.40090e67 | 0.656415 | ||||||||
\(792\) | −1.23830e67 | −0.0939258 | ||||||||
\(793\) | −5.38584e67 | −0.396583 | ||||||||
\(794\) | 2.46732e68 | 1.76377 | ||||||||
\(795\) | −6.81544e65 | −0.00473006 | ||||||||
\(796\) | 3.79841e68 | 2.55944 | ||||||||
\(797\) | −2.29036e68 | −1.49842 | −0.749210 | − | 0.662332i | \(-0.769567\pi\) | ||||
−0.749210 | + | 0.662332i | \(0.769567\pi\) | |||||||
\(798\) | 3.72967e67 | 0.236921 | ||||||||
\(799\) | −5.30079e67 | −0.326957 | ||||||||
\(800\) | 1.46728e67 | 0.0878815 | ||||||||
\(801\) | 2.54000e68 | 1.47730 | ||||||||
\(802\) | −2.29830e68 | −1.29810 | ||||||||
\(803\) | 9.33490e66 | 0.0512029 | ||||||||
\(804\) | −1.83410e67 | −0.0977028 | ||||||||
\(805\) | 3.50397e67 | 0.181283 | ||||||||
\(806\) | 2.55102e68 | 1.28186 | ||||||||
\(807\) | 3.52094e67 | 0.171842 | ||||||||
\(808\) | −3.86952e68 | −1.83438 | ||||||||
\(809\) | 7.74628e66 | 0.0356700 | 0.0178350 | − | 0.999841i | \(-0.494323\pi\) | ||||
0.0178350 | + | 0.999841i | \(0.494323\pi\) | |||||||
\(810\) | 4.26844e68 | 1.90929 | ||||||||
\(811\) | −2.32748e68 | −1.01134 | −0.505669 | − | 0.862727i | \(-0.668754\pi\) | ||||
−0.505669 | + | 0.862727i | \(0.668754\pi\) | |||||||
\(812\) | −9.78458e68 | −4.13024 | ||||||||
\(813\) | −3.95739e66 | −0.0162286 | ||||||||
\(814\) | −3.57875e67 | −0.142580 | ||||||||
\(815\) | −1.25476e68 | −0.485689 | ||||||||
\(816\) | −1.35607e67 | −0.0509993 | ||||||||
\(817\) | 2.42626e68 | 0.886584 | ||||||||
\(818\) | 3.91754e68 | 1.39095 | ||||||||
\(819\) | −3.72410e68 | −1.28484 | ||||||||
\(820\) | 3.01020e68 | 1.00918 | ||||||||
\(821\) | 4.26945e68 | 1.39094 | 0.695470 | − | 0.718556i | \(-0.255196\pi\) | ||||
0.695470 | + | 0.718556i | \(0.255196\pi\) | |||||||
\(822\) | −8.58071e67 | −0.271666 | ||||||||
\(823\) | 1.89793e68 | 0.583961 | 0.291981 | − | 0.956424i | \(-0.405686\pi\) | ||||
0.291981 | + | 0.956424i | \(0.405686\pi\) | |||||||
\(824\) | 1.04562e69 | 3.12667 | ||||||||
\(825\) | 9.39201e65 | 0.00272955 | ||||||||
\(826\) | −3.74038e67 | −0.105654 | ||||||||
\(827\) | −8.12864e67 | −0.223171 | −0.111586 | − | 0.993755i | \(-0.535593\pi\) | ||||
−0.111586 | + | 0.993755i | \(0.535593\pi\) | |||||||
\(828\) | −6.30721e67 | −0.168316 | ||||||||
\(829\) | −6.84615e68 | −1.77589 | −0.887943 | − | 0.459953i | \(-0.847866\pi\) | ||||
−0.887943 | + | 0.459953i | \(0.847866\pi\) | |||||||
\(830\) | −1.08202e69 | −2.72835 | ||||||||
\(831\) | −2.82770e67 | −0.0693122 | ||||||||
\(832\) | 3.74925e68 | 0.893400 | ||||||||
\(833\) | 4.64848e68 | 1.07684 | ||||||||
\(834\) | −4.86312e67 | −0.109525 | ||||||||
\(835\) | −3.64893e68 | −0.798975 | ||||||||
\(836\) | 3.48583e67 | 0.0742094 | ||||||||
\(837\) | 1.19024e68 | 0.246368 | ||||||||
\(838\) | 6.33456e67 | 0.127492 | ||||||||
\(839\) | −4.43097e67 | −0.0867147 | −0.0433574 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433574 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(840\) | 2.10783e68 | 0.401118 | ||||||||
\(841\) | 2.71501e68 | 0.502418 | ||||||||
\(842\) | −1.24324e69 | −2.23727 | ||||||||
\(843\) | 6.35996e67 | 0.111303 | ||||||||
\(844\) | 2.03254e68 | 0.345933 | ||||||||
\(845\) | 3.12911e68 | 0.517951 | ||||||||
\(846\) | −6.53417e68 | −1.05193 | ||||||||
\(847\) | 1.11247e69 | 1.74193 | ||||||||
\(848\) | −1.69161e67 | −0.0257630 | ||||||||
\(849\) | −1.29740e68 | −0.192195 | ||||||||
\(850\) | −2.28322e68 | −0.329006 | ||||||||
\(851\) | −8.77091e67 | −0.122942 | ||||||||
\(852\) | −5.03760e67 | −0.0686899 | ||||||||
\(853\) | 1.15923e69 | 1.53768 | 0.768842 | − | 0.639439i | \(-0.220833\pi\) | ||||
0.768842 | + | 0.639439i | \(0.220833\pi\) | |||||||
\(854\) | 1.23168e69 | 1.58942 | ||||||||
\(855\) | −5.87428e68 | −0.737481 | ||||||||
\(856\) | −1.54881e69 | −1.89175 | ||||||||
\(857\) | −1.19885e69 | −1.42467 | −0.712334 | − | 0.701840i | \(-0.752362\pi\) | ||||
−0.712334 | + | 0.701840i | \(0.752362\pi\) | |||||||
\(858\) | 8.20956e66 | 0.00949223 | ||||||||
\(859\) | −1.22015e69 | −1.37269 | −0.686345 | − | 0.727276i | \(-0.740786\pi\) | ||||
−0.686345 | + | 0.727276i | \(0.740786\pi\) | |||||||
\(860\) | 2.84971e69 | 3.11952 | ||||||||
\(861\) | −9.08830e67 | −0.0968074 | ||||||||
\(862\) | 1.58966e69 | 1.64772 | ||||||||
\(863\) | 5.27188e68 | 0.531755 | 0.265878 | − | 0.964007i | \(-0.414338\pi\) | ||||
0.265878 | + | 0.964007i | \(0.414338\pi\) | |||||||
\(864\) | 5.98401e67 | 0.0587381 | ||||||||
\(865\) | 6.78835e68 | 0.648464 | ||||||||
\(866\) | −5.97789e68 | −0.555748 | ||||||||
\(867\) | 9.91930e67 | 0.0897495 | ||||||||
\(868\) | −3.84105e69 | −3.38249 | ||||||||
\(869\) | 1.37140e67 | 0.0117544 | ||||||||
\(870\) | −3.63487e68 | −0.303240 | ||||||||
\(871\) | −3.76760e68 | −0.305941 | ||||||||
\(872\) | 1.87000e69 | 1.47810 | ||||||||
\(873\) | −1.40247e69 | −1.07909 | ||||||||
\(874\) | 1.29756e68 | 0.0971871 | ||||||||
\(875\) | −1.77408e69 | −1.29355 | ||||||||
\(876\) | 2.86020e68 | 0.203025 | ||||||||
\(877\) | −1.25938e69 | −0.870296 | −0.435148 | − | 0.900359i | \(-0.643304\pi\) | ||||
−0.435148 | + | 0.900359i | \(0.643304\pi\) | |||||||
\(878\) | 1.70303e68 | 0.114578 | ||||||||
\(879\) | 1.50682e68 | 0.0987011 | ||||||||
\(880\) | 8.67943e67 | 0.0553539 | ||||||||
\(881\) | 1.05379e69 | 0.654365 | 0.327182 | − | 0.944961i | \(-0.393901\pi\) | ||||
0.327182 | + | 0.944961i | \(0.393901\pi\) | |||||||
\(882\) | 5.73008e69 | 3.46456 | ||||||||
\(883\) | 1.51174e69 | 0.890021 | 0.445010 | − | 0.895525i | \(-0.353200\pi\) | ||||
0.445010 | + | 0.895525i | \(0.353200\pi\) | |||||||
\(884\) | −1.31402e69 | −0.753309 | ||||||||
\(885\) | −9.14859e66 | −0.00510725 | ||||||||
\(886\) | 1.56397e69 | 0.850227 | ||||||||
\(887\) | 2.55796e69 | 1.35422 | 0.677108 | − | 0.735883i | \(-0.263233\pi\) | ||||
0.677108 | + | 0.735883i | \(0.263233\pi\) | |||||||
\(888\) | −5.27619e68 | −0.272029 | ||||||||
\(889\) | −2.34173e69 | −1.17583 | ||||||||
\(890\) | −6.13743e69 | −3.00138 | ||||||||
\(891\) | −1.20446e68 | −0.0573674 | ||||||||
\(892\) | 2.07518e69 | 0.962680 | ||||||||
\(893\) | 8.85059e68 | 0.399911 | ||||||||
\(894\) | 7.42774e68 | 0.326908 | ||||||||
\(895\) | 3.10318e69 | 1.33035 | ||||||||
\(896\) | −7.57219e69 | −3.16216 | ||||||||
\(897\) | 2.01202e67 | 0.00818483 | ||||||||
\(898\) | −3.48364e69 | −1.38051 | ||||||||
\(899\) | 3.18717e69 | 1.23042 | ||||||||
\(900\) | −1.85306e69 | −0.696933 | ||||||||
\(901\) | −4.67527e67 | −0.0171307 | ||||||||
\(902\) | −1.29011e68 | −0.0460546 | ||||||||
\(903\) | −8.60376e68 | −0.299244 | ||||||||
\(904\) | 1.75816e69 | 0.595799 | ||||||||
\(905\) | 2.01497e69 | 0.665315 | ||||||||
\(906\) | 6.42753e68 | 0.206791 | ||||||||
\(907\) | −1.67267e69 | −0.524373 | −0.262186 | − | 0.965017i | \(-0.584443\pi\) | ||||
−0.262186 | + | 0.965017i | \(0.584443\pi\) | |||||||
\(908\) | 4.29221e69 | 1.31118 | ||||||||
\(909\) | −3.82406e69 | −1.13835 | ||||||||
\(910\) | 8.99858e69 | 2.61037 | ||||||||
\(911\) | −2.16759e68 | −0.0612767 | −0.0306383 | − | 0.999531i | \(-0.509754\pi\) | ||||
−0.0306383 | + | 0.999531i | \(0.509754\pi\) | |||||||
\(912\) | 2.26420e68 | 0.0623787 | ||||||||
\(913\) | 3.05322e68 | 0.0819775 | ||||||||
\(914\) | −8.25251e69 | −2.15949 | ||||||||
\(915\) | 3.01257e68 | 0.0768318 | ||||||||
\(916\) | 7.75931e69 | 1.92876 | ||||||||
\(917\) | −4.58272e69 | −1.11031 | ||||||||
\(918\) | −9.31170e68 | −0.219900 | ||||||||
\(919\) | −1.42756e69 | −0.328610 | −0.164305 | − | 0.986410i | \(-0.552538\pi\) | ||||
−0.164305 | + | 0.986410i | \(0.552538\pi\) | |||||||
\(920\) | 7.33318e68 | 0.164543 | ||||||||
\(921\) | 4.12258e68 | 0.0901712 | ||||||||
\(922\) | −5.43826e69 | −1.15953 | ||||||||
\(923\) | −1.03482e69 | −0.215092 | ||||||||
\(924\) | −1.23611e68 | −0.0250475 | ||||||||
\(925\) | −2.57690e69 | −0.509057 | ||||||||
\(926\) | 1.10513e70 | 2.12841 | ||||||||
\(927\) | 1.03333e70 | 1.94029 | ||||||||
\(928\) | 1.60238e69 | 0.293351 | ||||||||
\(929\) | 8.84307e68 | 0.157846 | 0.0789231 | − | 0.996881i | \(-0.474852\pi\) | ||||
0.0789231 | + | 0.996881i | \(0.474852\pi\) | |||||||
\(930\) | −1.42691e69 | −0.248340 | ||||||||
\(931\) | −7.76144e69 | −1.31712 | ||||||||
\(932\) | −9.79575e69 | −1.62093 | ||||||||
\(933\) | −6.98179e68 | −0.112654 | ||||||||
\(934\) | −9.78496e69 | −1.53960 | ||||||||
\(935\) | 2.39882e68 | 0.0368066 | ||||||||
\(936\) | −7.79387e69 | −1.16619 | ||||||||
\(937\) | −4.16313e69 | −0.607491 | −0.303746 | − | 0.952753i | \(-0.598237\pi\) | ||||
−0.303746 | + | 0.952753i | \(0.598237\pi\) | |||||||
\(938\) | 8.61607e69 | 1.22615 | ||||||||
\(939\) | −1.51338e69 | −0.210042 | ||||||||
\(940\) | 1.03953e70 | 1.40712 | ||||||||
\(941\) | 1.24869e70 | 1.64853 | 0.824266 | − | 0.566203i | \(-0.191588\pi\) | ||||
0.824266 | + | 0.566203i | \(0.191588\pi\) | |||||||
\(942\) | 1.51592e69 | 0.195200 | ||||||||
\(943\) | −3.16183e68 | −0.0397113 | ||||||||
\(944\) | −2.27070e68 | −0.0278175 | ||||||||
\(945\) | 4.19849e69 | 0.501702 | ||||||||
\(946\) | −1.22133e69 | −0.142361 | ||||||||
\(947\) | −6.06340e69 | −0.689433 | −0.344716 | − | 0.938707i | \(-0.612025\pi\) | ||||
−0.344716 | + | 0.938707i | \(0.612025\pi\) | |||||||
\(948\) | 4.20196e68 | 0.0466075 | ||||||||
\(949\) | 5.87539e69 | 0.635741 | ||||||||
\(950\) | 3.81224e69 | 0.402416 | ||||||||
\(951\) | 1.93518e69 | 0.199287 | ||||||||
\(952\) | 1.44593e70 | 1.45271 | ||||||||
\(953\) | −3.62312e69 | −0.355140 | −0.177570 | − | 0.984108i | \(-0.556824\pi\) | ||||
−0.177570 | + | 0.984108i | \(0.556824\pi\) | |||||||
\(954\) | −5.76310e68 | −0.0551150 | ||||||||
\(955\) | −2.43092e70 | −2.26826 | ||||||||
\(956\) | 1.48414e70 | 1.35118 | ||||||||
\(957\) | 1.02568e68 | 0.00911131 | ||||||||
\(958\) | −3.53829e70 | −3.06693 | ||||||||
\(959\) | 2.65400e70 | 2.24472 | ||||||||
\(960\) | −2.09714e69 | −0.173083 | ||||||||
\(961\) | 9.50929e67 | 0.00765858 | ||||||||
\(962\) | −2.25247e70 | −1.77029 | ||||||||
\(963\) | −1.53061e70 | −1.17394 | ||||||||
\(964\) | −2.42109e70 | −1.81217 | ||||||||
\(965\) | −2.08869e69 | −0.152575 | ||||||||
\(966\) | −4.60126e68 | −0.0328031 | ||||||||
\(967\) | 2.47757e70 | 1.72387 | 0.861933 | − | 0.507023i | \(-0.169254\pi\) | ||||
0.861933 | + | 0.507023i | \(0.169254\pi\) | |||||||
\(968\) | 2.32821e70 | 1.58107 | ||||||||
\(969\) | 6.25780e68 | 0.0414775 | ||||||||
\(970\) | 3.38880e70 | 2.19235 | ||||||||
\(971\) | −1.69313e70 | −1.06915 | −0.534574 | − | 0.845122i | \(-0.679528\pi\) | ||||
−0.534574 | + | 0.845122i | \(0.679528\pi\) | |||||||
\(972\) | −1.13652e70 | −0.700517 | ||||||||
\(973\) | 1.50415e70 | 0.904983 | ||||||||
\(974\) | 4.45530e70 | 2.61663 | ||||||||
\(975\) | 5.91133e68 | 0.0338904 | ||||||||
\(976\) | 7.47726e69 | 0.418477 | ||||||||
\(977\) | −1.88519e70 | −1.02999 | −0.514994 | − | 0.857193i | \(-0.672206\pi\) | ||||
−0.514994 | + | 0.857193i | \(0.672206\pi\) | |||||||
\(978\) | 1.64771e69 | 0.0878853 | ||||||||
\(979\) | 1.73185e69 | 0.0901812 | ||||||||
\(980\) | −9.11602e70 | −4.63439 | ||||||||
\(981\) | 1.84803e70 | 0.917250 | ||||||||
\(982\) | 9.77660e69 | 0.473770 | ||||||||
\(983\) | 1.50691e69 | 0.0712982 | 0.0356491 | − | 0.999364i | \(-0.488650\pi\) | ||||
0.0356491 | + | 0.999364i | \(0.488650\pi\) | |||||||
\(984\) | −1.90202e69 | −0.0878678 | ||||||||
\(985\) | 3.83136e70 | 1.72823 | ||||||||
\(986\) | −2.49345e70 | −1.09823 | ||||||||
\(987\) | −3.13850e69 | −0.134980 | ||||||||
\(988\) | 2.19398e70 | 0.921393 | ||||||||
\(989\) | −2.99326e69 | −0.122753 | ||||||||
\(990\) | 2.95698e69 | 0.118419 | ||||||||
\(991\) | −3.55474e70 | −1.39020 | −0.695099 | − | 0.718914i | \(-0.744639\pi\) | ||||
−0.695099 | + | 0.718914i | \(0.744639\pi\) | |||||||
\(992\) | 6.29032e69 | 0.240242 | ||||||||
\(993\) | 1.90709e69 | 0.0711319 | ||||||||
\(994\) | 2.36651e70 | 0.862043 | ||||||||
\(995\) | −4.36441e70 | −1.55268 | ||||||||
\(996\) | 9.35501e69 | 0.325050 | ||||||||
\(997\) | −1.08915e70 | −0.369618 | −0.184809 | − | 0.982774i | \(-0.559167\pi\) | ||||
−0.184809 | + | 0.982774i | \(0.559167\pi\) | |||||||
\(998\) | 5.27347e70 | 1.74795 | ||||||||
\(999\) | −1.05094e70 | −0.340243 |
(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 | 1.48.a.a.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 9.48.a.c.1.4 | 4 | |||
4.3 | odd | 2 | 16.48.a.d.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.48.a.a.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.48.a.c.1.4 | 4 | 3.2 | odd | 2 | |||
16.48.a.d.1.3 | 4 | 4.3 | odd | 2 |