Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −64.1897 | −1.41841 | −0.709203 | − | 0.705005i | \(-0.750945\pi\) | ||||
−0.709203 | + | 0.705005i | \(0.750945\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 2072.32 | 1.01187 | ||||||||
\(5\) | −6307.39 | −0.902640 | −0.451320 | − | 0.892362i | \(-0.649047\pi\) | ||||
−0.451320 | + | 0.892362i | \(0.649047\pi\) | |||||||
\(6\) | 15598.1 | 0.818917 | ||||||||
\(7\) | 84626.9 | 1.90313 | 0.951566 | − | 0.307444i | \(-0.0994737\pi\) | ||||
0.951566 | + | 0.307444i | \(0.0994737\pi\) | |||||||
\(8\) | −1560.87 | −0.0168412 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 404869. | 1.28031 | ||||||||
\(11\) | −902806. | −1.69019 | −0.845094 | − | 0.534618i | \(-0.820455\pi\) | ||||
−0.845094 | + | 0.534618i | \(0.820455\pi\) | |||||||
\(12\) | −503573. | −0.584205 | ||||||||
\(13\) | −1.37458e6 | −1.02679 | −0.513394 | − | 0.858153i | \(-0.671612\pi\) | ||||
−0.513394 | + | 0.858153i | \(0.671612\pi\) | |||||||
\(14\) | −5.43217e6 | −2.69941 | ||||||||
\(15\) | 1.53270e6 | 0.521139 | ||||||||
\(16\) | −4.14391e6 | −0.987986 | ||||||||
\(17\) | 6.10500e6 | 1.04284 | 0.521419 | − | 0.853301i | \(-0.325403\pi\) | ||||
0.521419 | + | 0.853301i | \(0.325403\pi\) | |||||||
\(18\) | −3.79034e6 | −0.472802 | ||||||||
\(19\) | 1.53727e7 | 1.42431 | 0.712155 | − | 0.702022i | \(-0.247719\pi\) | ||||
0.712155 | + | 0.702022i | \(0.247719\pi\) | |||||||
\(20\) | −1.30709e7 | −0.913357 | ||||||||
\(21\) | −2.05643e7 | −1.09877 | ||||||||
\(22\) | 5.79509e7 | 2.39737 | ||||||||
\(23\) | 5.45940e7 | 1.76865 | 0.884324 | − | 0.466873i | \(-0.154619\pi\) | ||||
0.884324 | + | 0.466873i | \(0.154619\pi\) | |||||||
\(24\) | 379292. | 0.00972326 | ||||||||
\(25\) | −9.04497e6 | −0.185241 | ||||||||
\(26\) | 8.82338e7 | 1.45640 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 1.75374e8 | 1.92573 | ||||||||
\(29\) | 3.20407e7 | 0.290076 | 0.145038 | − | 0.989426i | \(-0.453669\pi\) | ||||
0.145038 | + | 0.989426i | \(0.453669\pi\) | |||||||
\(30\) | −9.83833e7 | −0.739187 | ||||||||
\(31\) | 2.01437e8 | 1.26372 | 0.631860 | − | 0.775083i | \(-0.282292\pi\) | ||||
0.631860 | + | 0.775083i | \(0.282292\pi\) | |||||||
\(32\) | 2.69193e8 | 1.41821 | ||||||||
\(33\) | 2.19382e8 | 0.975830 | ||||||||
\(34\) | −3.91878e8 | −1.47917 | ||||||||
\(35\) | −5.33774e8 | −1.71784 | ||||||||
\(36\) | 1.22368e8 | 0.337291 | ||||||||
\(37\) | 6.20122e8 | 1.47017 | 0.735085 | − | 0.677975i | \(-0.237142\pi\) | ||||
0.735085 | + | 0.677975i | \(0.237142\pi\) | |||||||
\(38\) | −9.86768e8 | −2.02025 | ||||||||
\(39\) | 3.34023e8 | 0.592817 | ||||||||
\(40\) | 9.84503e6 | 0.0152015 | ||||||||
\(41\) | −1.18981e9 | −1.60386 | −0.801932 | − | 0.597415i | \(-0.796194\pi\) | ||||
−0.801932 | + | 0.597415i | \(0.796194\pi\) | |||||||
\(42\) | 1.32002e9 | 1.55851 | ||||||||
\(43\) | −2.91907e8 | −0.302808 | −0.151404 | − | 0.988472i | \(-0.548380\pi\) | ||||
−0.151404 | + | 0.988472i | \(0.548380\pi\) | |||||||
\(44\) | −1.87090e9 | −1.71026 | ||||||||
\(45\) | −3.72445e8 | −0.300880 | ||||||||
\(46\) | −3.50437e9 | −2.50866 | ||||||||
\(47\) | 6.14694e7 | 0.0390950 | 0.0195475 | − | 0.999809i | \(-0.493777\pi\) | ||||
0.0195475 | + | 0.999809i | \(0.493777\pi\) | |||||||
\(48\) | 1.00697e9 | 0.570414 | ||||||||
\(49\) | 5.18438e9 | 2.62191 | ||||||||
\(50\) | 5.80594e8 | 0.262747 | ||||||||
\(51\) | −1.48352e9 | −0.602083 | ||||||||
\(52\) | −2.84856e9 | −1.03898 | ||||||||
\(53\) | −3.65243e9 | −1.19968 | −0.599839 | − | 0.800120i | \(-0.704769\pi\) | ||||
−0.599839 | + | 0.800120i | \(0.704769\pi\) | |||||||
\(54\) | 9.21052e8 | 0.272972 | ||||||||
\(55\) | 5.69435e9 | 1.52563 | ||||||||
\(56\) | −1.32092e8 | −0.0320510 | ||||||||
\(57\) | −3.73556e9 | −0.822326 | ||||||||
\(58\) | −2.05668e9 | −0.411446 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | 3.17623e9 | 0.527327 | ||||||||
\(61\) | 1.13062e10 | 1.71397 | 0.856987 | − | 0.515338i | \(-0.172333\pi\) | ||||
0.856987 | + | 0.515338i | \(0.172333\pi\) | |||||||
\(62\) | −1.29302e10 | −1.79247 | ||||||||
\(63\) | 4.99713e9 | 0.634377 | ||||||||
\(64\) | −8.79269e9 | −1.02360 | ||||||||
\(65\) | 8.67000e9 | 0.926821 | ||||||||
\(66\) | −1.40821e10 | −1.38412 | ||||||||
\(67\) | −8.11606e9 | −0.734402 | −0.367201 | − | 0.930142i | \(-0.619684\pi\) | ||||
−0.367201 | + | 0.930142i | \(0.619684\pi\) | |||||||
\(68\) | 1.26515e10 | 1.05522 | ||||||||
\(69\) | −1.32663e10 | −1.02113 | ||||||||
\(70\) | 3.42628e10 | 2.43660 | ||||||||
\(71\) | −1.75527e10 | −1.15458 | −0.577290 | − | 0.816539i | \(-0.695890\pi\) | ||||
−0.577290 | + | 0.816539i | \(0.695890\pi\) | |||||||
\(72\) | −9.21680e7 | −0.00561373 | ||||||||
\(73\) | −1.78971e10 | −1.01043 | −0.505215 | − | 0.862994i | \(-0.668587\pi\) | ||||
−0.505215 | + | 0.862994i | \(0.668587\pi\) | |||||||
\(74\) | −3.98055e10 | −2.08530 | ||||||||
\(75\) | 2.19793e9 | 0.106949 | ||||||||
\(76\) | 3.18571e10 | 1.44122 | ||||||||
\(77\) | −7.64017e10 | −3.21665 | ||||||||
\(78\) | −2.14408e10 | −0.840855 | ||||||||
\(79\) | 2.32461e10 | 0.849963 | 0.424982 | − | 0.905202i | \(-0.360281\pi\) | ||||
0.424982 | + | 0.905202i | \(0.360281\pi\) | |||||||
\(80\) | 2.61373e10 | 0.891795 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 7.63737e10 | 2.27493 | ||||||||
\(83\) | 8.67597e9 | 0.241762 | 0.120881 | − | 0.992667i | \(-0.461428\pi\) | ||||
0.120881 | + | 0.992667i | \(0.461428\pi\) | |||||||
\(84\) | −4.26158e10 | −1.11182 | ||||||||
\(85\) | −3.85066e10 | −0.941307 | ||||||||
\(86\) | 1.87374e10 | 0.429505 | ||||||||
\(87\) | −7.78588e9 | −0.167476 | ||||||||
\(88\) | 1.40917e9 | 0.0284648 | ||||||||
\(89\) | 7.88055e10 | 1.49593 | 0.747966 | − | 0.663737i | \(-0.231031\pi\) | ||||
0.747966 | + | 0.663737i | \(0.231031\pi\) | |||||||
\(90\) | 2.39071e10 | 0.426770 | ||||||||
\(91\) | −1.16326e11 | −1.95412 | ||||||||
\(92\) | 1.13136e11 | 1.78965 | ||||||||
\(93\) | −4.89493e10 | −0.729609 | ||||||||
\(94\) | −3.94570e9 | −0.0554525 | ||||||||
\(95\) | −9.69615e10 | −1.28564 | ||||||||
\(96\) | −6.54139e10 | −0.818801 | ||||||||
\(97\) | −6.50540e10 | −0.769183 | −0.384592 | − | 0.923087i | \(-0.625658\pi\) | ||||
−0.384592 | + | 0.923087i | \(0.625658\pi\) | |||||||
\(98\) | −3.32784e11 | −3.71893 | ||||||||
\(99\) | −5.33098e10 | −0.563396 | ||||||||
\(100\) | −1.87440e10 | −0.187440 | ||||||||
\(101\) | −8.59215e10 | −0.813457 | −0.406728 | − | 0.913549i | \(-0.633330\pi\) | ||||
−0.406728 | + | 0.913549i | \(0.633330\pi\) | |||||||
\(102\) | 9.52264e10 | 0.853998 | ||||||||
\(103\) | −4.71359e10 | −0.400633 | −0.200317 | − | 0.979731i | \(-0.564197\pi\) | ||||
−0.200317 | + | 0.979731i | \(0.564197\pi\) | |||||||
\(104\) | 2.14554e9 | 0.0172923 | ||||||||
\(105\) | 1.29707e11 | 0.991797 | ||||||||
\(106\) | 2.34449e11 | 1.70163 | ||||||||
\(107\) | 6.98844e10 | 0.481692 | 0.240846 | − | 0.970563i | \(-0.422575\pi\) | ||||
0.240846 | + | 0.970563i | \(0.422575\pi\) | |||||||
\(108\) | −2.97355e10 | −0.194735 | ||||||||
\(109\) | −8.79549e9 | −0.0547538 | −0.0273769 | − | 0.999625i | \(-0.508715\pi\) | ||||
−0.0273769 | + | 0.999625i | \(0.508715\pi\) | |||||||
\(110\) | −3.65519e11 | −2.16396 | ||||||||
\(111\) | −1.50690e11 | −0.848803 | ||||||||
\(112\) | −3.50686e11 | −1.88027 | ||||||||
\(113\) | −1.78906e10 | −0.0913468 | −0.0456734 | − | 0.998956i | \(-0.514543\pi\) | ||||
−0.0456734 | + | 0.998956i | \(0.514543\pi\) | |||||||
\(114\) | 2.39785e11 | 1.16639 | ||||||||
\(115\) | −3.44345e11 | −1.59645 | ||||||||
\(116\) | 6.63984e10 | 0.293521 | ||||||||
\(117\) | −8.11675e10 | −0.342263 | ||||||||
\(118\) | 4.58908e10 | 0.184661 | ||||||||
\(119\) | 5.16647e11 | 1.98466 | ||||||||
\(120\) | −2.39234e9 | −0.00877661 | ||||||||
\(121\) | 5.29748e11 | 1.85673 | ||||||||
\(122\) | −7.25745e11 | −2.43111 | ||||||||
\(123\) | 2.89125e11 | 0.925991 | ||||||||
\(124\) | 4.17442e11 | 1.27872 | ||||||||
\(125\) | 3.65028e11 | 1.06985 | ||||||||
\(126\) | −3.20764e11 | −0.899804 | ||||||||
\(127\) | −4.11217e10 | −0.110446 | −0.0552231 | − | 0.998474i | \(-0.517587\pi\) | ||||
−0.0552231 | + | 0.998474i | \(0.517587\pi\) | |||||||
\(128\) | 1.30926e10 | 0.0336800 | ||||||||
\(129\) | 7.09334e10 | 0.174827 | ||||||||
\(130\) | −5.56525e11 | −1.31461 | ||||||||
\(131\) | −7.36528e11 | −1.66800 | −0.834002 | − | 0.551762i | \(-0.813956\pi\) | ||||
−0.834002 | + | 0.551762i | \(0.813956\pi\) | |||||||
\(132\) | 4.54629e11 | 0.987417 | ||||||||
\(133\) | 1.30094e12 | 2.71065 | ||||||||
\(134\) | 5.20967e11 | 1.04168 | ||||||||
\(135\) | 9.05041e10 | 0.173713 | ||||||||
\(136\) | −9.52914e9 | −0.0175626 | ||||||||
\(137\) | −5.15534e11 | −0.912628 | −0.456314 | − | 0.889819i | \(-0.650831\pi\) | ||||
−0.456314 | + | 0.889819i | \(0.650831\pi\) | |||||||
\(138\) | 8.51562e11 | 1.44838 | ||||||||
\(139\) | 3.25513e11 | 0.532092 | 0.266046 | − | 0.963960i | \(-0.414283\pi\) | ||||
0.266046 | + | 0.963960i | \(0.414283\pi\) | |||||||
\(140\) | −1.10615e12 | −1.73824 | ||||||||
\(141\) | −1.49371e10 | −0.0225715 | ||||||||
\(142\) | 1.12671e12 | 1.63766 | ||||||||
\(143\) | 1.24098e12 | 1.73547 | ||||||||
\(144\) | −2.44694e11 | −0.329329 | ||||||||
\(145\) | −2.02093e11 | −0.261835 | ||||||||
\(146\) | 1.14881e12 | 1.43320 | ||||||||
\(147\) | −1.25980e12 | −1.51376 | ||||||||
\(148\) | 1.28509e12 | 1.48763 | ||||||||
\(149\) | 1.16267e12 | 1.29697 | 0.648485 | − | 0.761227i | \(-0.275403\pi\) | ||||
0.648485 | + | 0.761227i | \(0.275403\pi\) | |||||||
\(150\) | −1.41084e11 | −0.151697 | ||||||||
\(151\) | 7.93846e11 | 0.822930 | 0.411465 | − | 0.911425i | \(-0.365017\pi\) | ||||
0.411465 | + | 0.911425i | \(0.365017\pi\) | |||||||
\(152\) | −2.39948e10 | −0.0239871 | ||||||||
\(153\) | 3.60494e11 | 0.347613 | ||||||||
\(154\) | 4.90420e12 | 4.56251 | ||||||||
\(155\) | −1.27054e12 | −1.14068 | ||||||||
\(156\) | 6.92201e11 | 0.599856 | ||||||||
\(157\) | −1.68630e12 | −1.41087 | −0.705436 | − | 0.708774i | \(-0.749249\pi\) | ||||
−0.705436 | + | 0.708774i | \(0.749249\pi\) | |||||||
\(158\) | −1.49216e12 | −1.20559 | ||||||||
\(159\) | 8.87541e11 | 0.692635 | ||||||||
\(160\) | −1.69791e12 | −1.28013 | ||||||||
\(161\) | 4.62012e12 | 3.36597 | ||||||||
\(162\) | −2.23816e11 | −0.157601 | ||||||||
\(163\) | −6.34506e11 | −0.431921 | −0.215960 | − | 0.976402i | \(-0.569288\pi\) | ||||
−0.215960 | + | 0.976402i | \(0.569288\pi\) | |||||||
\(164\) | −2.46567e12 | −1.62291 | ||||||||
\(165\) | −1.38373e12 | −0.880823 | ||||||||
\(166\) | −5.56908e11 | −0.342917 | ||||||||
\(167\) | −1.56788e12 | −0.934056 | −0.467028 | − | 0.884242i | \(-0.654675\pi\) | ||||
−0.467028 | + | 0.884242i | \(0.654675\pi\) | |||||||
\(168\) | 3.20983e10 | 0.0185047 | ||||||||
\(169\) | 9.73062e10 | 0.0542955 | ||||||||
\(170\) | 2.47173e12 | 1.33516 | ||||||||
\(171\) | 9.07741e11 | 0.474770 | ||||||||
\(172\) | −6.04924e11 | −0.306404 | ||||||||
\(173\) | −1.63986e12 | −0.804550 | −0.402275 | − | 0.915519i | \(-0.631780\pi\) | ||||
−0.402275 | + | 0.915519i | \(0.631780\pi\) | |||||||
\(174\) | 4.99773e11 | 0.237548 | ||||||||
\(175\) | −7.65447e11 | −0.352538 | ||||||||
\(176\) | 3.74115e12 | 1.66988 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | −5.05850e12 | −2.12184 | ||||||||
\(179\) | −2.22928e12 | −0.906718 | −0.453359 | − | 0.891328i | \(-0.649775\pi\) | ||||
−0.453359 | + | 0.891328i | \(0.649775\pi\) | |||||||
\(180\) | −7.71824e11 | −0.304452 | ||||||||
\(181\) | 1.95784e12 | 0.749111 | 0.374555 | − | 0.927205i | \(-0.377795\pi\) | ||||
0.374555 | + | 0.927205i | \(0.377795\pi\) | |||||||
\(182\) | 7.46695e12 | 2.77173 | ||||||||
\(183\) | −2.74742e12 | −0.989564 | ||||||||
\(184\) | −8.52143e10 | −0.0297861 | ||||||||
\(185\) | −3.91135e12 | −1.32703 | ||||||||
\(186\) | 3.14204e12 | 1.03488 | ||||||||
\(187\) | −5.51164e12 | −1.76259 | ||||||||
\(188\) | 1.27384e11 | 0.0395592 | ||||||||
\(189\) | −1.21430e12 | −0.366258 | ||||||||
\(190\) | 6.22393e12 | 1.82356 | ||||||||
\(191\) | −1.00786e12 | −0.286891 | −0.143446 | − | 0.989658i | \(-0.545818\pi\) | ||||
−0.143446 | + | 0.989658i | \(0.545818\pi\) | |||||||
\(192\) | 2.13662e12 | 0.590978 | ||||||||
\(193\) | 3.80074e12 | 1.02165 | 0.510826 | − | 0.859684i | \(-0.329340\pi\) | ||||
0.510826 | + | 0.859684i | \(0.329340\pi\) | |||||||
\(194\) | 4.17580e12 | 1.09101 | ||||||||
\(195\) | −2.10681e12 | −0.535100 | ||||||||
\(196\) | 1.07437e13 | 2.65304 | ||||||||
\(197\) | −2.35828e12 | −0.566280 | −0.283140 | − | 0.959079i | \(-0.591376\pi\) | ||||
−0.283140 | + | 0.959079i | \(0.591376\pi\) | |||||||
\(198\) | 3.42194e12 | 0.799124 | ||||||||
\(199\) | −1.25177e12 | −0.284336 | −0.142168 | − | 0.989843i | \(-0.545407\pi\) | ||||
−0.142168 | + | 0.989843i | \(0.545407\pi\) | |||||||
\(200\) | 1.41181e10 | 0.00311968 | ||||||||
\(201\) | 1.97220e12 | 0.424007 | ||||||||
\(202\) | 5.51528e12 | 1.15381 | ||||||||
\(203\) | 2.71150e12 | 0.552054 | ||||||||
\(204\) | −3.07431e12 | −0.609232 | ||||||||
\(205\) | 7.50461e12 | 1.44771 | ||||||||
\(206\) | 3.02564e12 | 0.568260 | ||||||||
\(207\) | 3.22372e12 | 0.589550 | ||||||||
\(208\) | 5.69613e12 | 1.01445 | ||||||||
\(209\) | −1.38786e13 | −2.40735 | ||||||||
\(210\) | −8.32586e12 | −1.40677 | ||||||||
\(211\) | −4.10909e12 | −0.676382 | −0.338191 | − | 0.941077i | \(-0.609815\pi\) | ||||
−0.338191 | + | 0.941077i | \(0.609815\pi\) | |||||||
\(212\) | −7.56900e12 | −1.21392 | ||||||||
\(213\) | 4.26532e12 | 0.666597 | ||||||||
\(214\) | −4.48586e12 | −0.683235 | ||||||||
\(215\) | 1.84117e12 | 0.273327 | ||||||||
\(216\) | 2.23968e10 | 0.00324109 | ||||||||
\(217\) | 1.70470e13 | 2.40503 | ||||||||
\(218\) | 5.64580e11 | 0.0776631 | ||||||||
\(219\) | 4.34899e12 | 0.583372 | ||||||||
\(220\) | 1.18005e13 | 1.54375 | ||||||||
\(221\) | −8.39181e12 | −1.07077 | ||||||||
\(222\) | 9.67272e12 | 1.20395 | ||||||||
\(223\) | 9.53747e12 | 1.15813 | 0.579064 | − | 0.815282i | \(-0.303418\pi\) | ||||
0.579064 | + | 0.815282i | \(0.303418\pi\) | |||||||
\(224\) | 2.27810e13 | 2.69903 | ||||||||
\(225\) | −5.34096e11 | −0.0617470 | ||||||||
\(226\) | 1.14839e12 | 0.129567 | ||||||||
\(227\) | 9.82918e12 | 1.08237 | 0.541184 | − | 0.840904i | \(-0.317976\pi\) | ||||
0.541184 | + | 0.840904i | \(0.317976\pi\) | |||||||
\(228\) | −7.74127e12 | −0.832090 | ||||||||
\(229\) | −4.90493e12 | −0.514681 | −0.257340 | − | 0.966321i | \(-0.582846\pi\) | ||||
−0.257340 | + | 0.966321i | \(0.582846\pi\) | |||||||
\(230\) | 2.21034e13 | 2.26442 | ||||||||
\(231\) | 1.85656e13 | 1.85713 | ||||||||
\(232\) | −5.00114e10 | −0.00488523 | ||||||||
\(233\) | 1.38224e13 | 1.31863 | 0.659317 | − | 0.751865i | \(-0.270845\pi\) | ||||
0.659317 | + | 0.751865i | \(0.270845\pi\) | |||||||
\(234\) | 5.21012e12 | 0.485468 | ||||||||
\(235\) | −3.87711e11 | −0.0352887 | ||||||||
\(236\) | −1.48155e12 | −0.131735 | ||||||||
\(237\) | −5.64879e12 | −0.490727 | ||||||||
\(238\) | −3.31634e13 | −2.81505 | ||||||||
\(239\) | −2.29756e12 | −0.190581 | −0.0952904 | − | 0.995450i | \(-0.530378\pi\) | ||||
−0.0952904 | + | 0.995450i | \(0.530378\pi\) | |||||||
\(240\) | −6.35136e12 | −0.514878 | ||||||||
\(241\) | −4.33916e12 | −0.343805 | −0.171903 | − | 0.985114i | \(-0.554991\pi\) | ||||
−0.171903 | + | 0.985114i | \(0.554991\pi\) | |||||||
\(242\) | −3.40044e13 | −2.63360 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 2.34301e13 | 1.73433 | ||||||||
\(245\) | −3.26999e13 | −2.36664 | ||||||||
\(246\) | −1.85588e13 | −1.31343 | ||||||||
\(247\) | −2.11310e13 | −1.46247 | ||||||||
\(248\) | −3.14418e11 | −0.0212825 | ||||||||
\(249\) | −2.10826e12 | −0.139581 | ||||||||
\(250\) | −2.34310e13 | −1.51748 | ||||||||
\(251\) | 8.15418e12 | 0.516624 | 0.258312 | − | 0.966062i | \(-0.416834\pi\) | ||||
0.258312 | + | 0.966062i | \(0.416834\pi\) | |||||||
\(252\) | 1.03556e13 | 0.641910 | ||||||||
\(253\) | −4.92878e13 | −2.98935 | ||||||||
\(254\) | 2.63959e12 | 0.156658 | ||||||||
\(255\) | 9.35711e12 | 0.543464 | ||||||||
\(256\) | 1.71670e13 | 0.975832 | ||||||||
\(257\) | 1.34438e13 | 0.747982 | 0.373991 | − | 0.927432i | \(-0.377989\pi\) | ||||
0.373991 | + | 0.927432i | \(0.377989\pi\) | |||||||
\(258\) | −4.55319e12 | −0.247975 | ||||||||
\(259\) | 5.24790e13 | 2.79793 | ||||||||
\(260\) | 1.79670e13 | 0.937825 | ||||||||
\(261\) | 1.89197e12 | 0.0966921 | ||||||||
\(262\) | 4.72775e13 | 2.36590 | ||||||||
\(263\) | 2.31137e13 | 1.13270 | 0.566348 | − | 0.824166i | \(-0.308356\pi\) | ||||
0.566348 | + | 0.824166i | \(0.308356\pi\) | |||||||
\(264\) | −3.42427e11 | −0.0164341 | ||||||||
\(265\) | 2.30373e13 | 1.08288 | ||||||||
\(266\) | −8.35070e13 | −3.84480 | ||||||||
\(267\) | −1.91497e13 | −0.863676 | ||||||||
\(268\) | −1.68190e13 | −0.743122 | ||||||||
\(269\) | 2.85981e13 | 1.23794 | 0.618970 | − | 0.785415i | \(-0.287550\pi\) | ||||
0.618970 | + | 0.785415i | \(0.287550\pi\) | |||||||
\(270\) | −5.80943e12 | −0.246396 | ||||||||
\(271\) | −7.95747e12 | −0.330707 | −0.165354 | − | 0.986234i | \(-0.552877\pi\) | ||||
−0.165354 | + | 0.986234i | \(0.552877\pi\) | |||||||
\(272\) | −2.52986e13 | −1.03031 | ||||||||
\(273\) | 2.82673e13 | 1.12821 | ||||||||
\(274\) | 3.30919e13 | 1.29448 | ||||||||
\(275\) | 8.16586e12 | 0.313092 | ||||||||
\(276\) | −2.74920e13 | −1.03325 | ||||||||
\(277\) | −1.29393e13 | −0.476729 | −0.238365 | − | 0.971176i | \(-0.576611\pi\) | ||||
−0.238365 | + | 0.971176i | \(0.576611\pi\) | |||||||
\(278\) | −2.08946e13 | −0.754722 | ||||||||
\(279\) | 1.18947e13 | 0.421240 | ||||||||
\(280\) | 8.33154e11 | 0.0289305 | ||||||||
\(281\) | 1.93697e13 | 0.659536 | 0.329768 | − | 0.944062i | \(-0.393029\pi\) | ||||
0.329768 | + | 0.944062i | \(0.393029\pi\) | |||||||
\(282\) | 9.58806e11 | 0.0320155 | ||||||||
\(283\) | 5.69672e13 | 1.86552 | 0.932759 | − | 0.360499i | \(-0.117394\pi\) | ||||
0.932759 | + | 0.360499i | \(0.117394\pi\) | |||||||
\(284\) | −3.63748e13 | −1.16829 | ||||||||
\(285\) | 2.35616e13 | 0.742265 | ||||||||
\(286\) | −7.96580e13 | −2.46159 | ||||||||
\(287\) | −1.00690e14 | −3.05237 | ||||||||
\(288\) | 1.58956e13 | 0.472735 | ||||||||
\(289\) | 2.99918e12 | 0.0875115 | ||||||||
\(290\) | 1.29723e13 | 0.371388 | ||||||||
\(291\) | 1.58081e13 | 0.444088 | ||||||||
\(292\) | −3.70884e13 | −1.02243 | ||||||||
\(293\) | −4.46407e13 | −1.20770 | −0.603849 | − | 0.797098i | \(-0.706367\pi\) | ||||
−0.603849 | + | 0.797098i | \(0.706367\pi\) | |||||||
\(294\) | 8.08664e13 | 2.14713 | ||||||||
\(295\) | 4.50931e12 | 0.117514 | ||||||||
\(296\) | −9.67932e11 | −0.0247594 | ||||||||
\(297\) | 1.29543e13 | 0.325277 | ||||||||
\(298\) | −7.46311e13 | −1.83963 | ||||||||
\(299\) | −7.50437e13 | −1.81603 | ||||||||
\(300\) | 4.55480e12 | 0.108219 | ||||||||
\(301\) | −2.47032e13 | −0.576285 | ||||||||
\(302\) | −5.09567e13 | −1.16725 | ||||||||
\(303\) | 2.08789e13 | 0.469649 | ||||||||
\(304\) | −6.37030e13 | −1.40720 | ||||||||
\(305\) | −7.13129e13 | −1.54710 | ||||||||
\(306\) | −2.31400e13 | −0.493056 | ||||||||
\(307\) | 6.66583e13 | 1.39506 | 0.697530 | − | 0.716556i | \(-0.254282\pi\) | ||||
0.697530 | + | 0.716556i | \(0.254282\pi\) | |||||||
\(308\) | −1.58328e14 | −3.25484 | ||||||||
\(309\) | 1.14540e13 | 0.231306 | ||||||||
\(310\) | 8.15558e13 | 1.61795 | ||||||||
\(311\) | −6.84643e13 | −1.33439 | −0.667194 | − | 0.744884i | \(-0.732505\pi\) | ||||
−0.667194 | + | 0.744884i | \(0.732505\pi\) | |||||||
\(312\) | −5.21367e11 | −0.00998374 | ||||||||
\(313\) | 1.48075e13 | 0.278603 | 0.139302 | − | 0.990250i | \(-0.455514\pi\) | ||||
0.139302 | + | 0.990250i | \(0.455514\pi\) | |||||||
\(314\) | 1.08243e14 | 2.00119 | ||||||||
\(315\) | −3.15188e13 | −0.572614 | ||||||||
\(316\) | 4.81732e13 | 0.860055 | ||||||||
\(317\) | 8.34508e13 | 1.46421 | 0.732107 | − | 0.681190i | \(-0.238537\pi\) | ||||
0.732107 | + | 0.681190i | \(0.238537\pi\) | |||||||
\(318\) | −5.69710e13 | −0.982437 | ||||||||
\(319\) | −2.89265e13 | −0.490284 | ||||||||
\(320\) | 5.54589e13 | 0.923946 | ||||||||
\(321\) | −1.69819e13 | −0.278105 | ||||||||
\(322\) | −2.96564e14 | −4.77431 | ||||||||
\(323\) | 9.38503e13 | 1.48533 | ||||||||
\(324\) | 7.22572e12 | 0.112430 | ||||||||
\(325\) | 1.24330e13 | 0.190203 | ||||||||
\(326\) | 4.07288e13 | 0.612639 | ||||||||
\(327\) | 2.13730e12 | 0.0316121 | ||||||||
\(328\) | 1.85715e12 | 0.0270110 | ||||||||
\(329\) | 5.20196e12 | 0.0744029 | ||||||||
\(330\) | 8.88210e13 | 1.24936 | ||||||||
\(331\) | −4.81979e13 | −0.666767 | −0.333383 | − | 0.942791i | \(-0.608190\pi\) | ||||
−0.333383 | + | 0.942791i | \(0.608190\pi\) | |||||||
\(332\) | 1.79793e13 | 0.244633 | ||||||||
\(333\) | 3.66176e13 | 0.490057 | ||||||||
\(334\) | 1.00642e14 | 1.32487 | ||||||||
\(335\) | 5.11911e13 | 0.662901 | ||||||||
\(336\) | 8.52168e13 | 1.08557 | ||||||||
\(337\) | 7.78671e13 | 0.975865 | 0.487932 | − | 0.872881i | \(-0.337751\pi\) | ||||
0.487932 | + | 0.872881i | \(0.337751\pi\) | |||||||
\(338\) | −6.24605e12 | −0.0770130 | ||||||||
\(339\) | 4.34741e12 | 0.0527391 | ||||||||
\(340\) | −7.97979e13 | −0.952484 | ||||||||
\(341\) | −1.81859e14 | −2.13592 | ||||||||
\(342\) | −5.82676e13 | −0.673417 | ||||||||
\(343\) | 2.71403e14 | 3.08671 | ||||||||
\(344\) | 4.55630e11 | 0.00509965 | ||||||||
\(345\) | 8.36759e13 | 0.921713 | ||||||||
\(346\) | 1.05262e14 | 1.14118 | ||||||||
\(347\) | −9.04895e13 | −0.965575 | −0.482788 | − | 0.875737i | \(-0.660376\pi\) | ||||
−0.482788 | + | 0.875737i | \(0.660376\pi\) | |||||||
\(348\) | −1.61348e13 | −0.169464 | ||||||||
\(349\) | 7.98190e13 | 0.825214 | 0.412607 | − | 0.910909i | \(-0.364618\pi\) | ||||
0.412607 | + | 0.910909i | \(0.364618\pi\) | |||||||
\(350\) | 4.91338e13 | 0.500042 | ||||||||
\(351\) | 1.97237e13 | 0.197606 | ||||||||
\(352\) | −2.43029e14 | −2.39703 | ||||||||
\(353\) | 5.16894e13 | 0.501927 | 0.250964 | − | 0.967996i | \(-0.419253\pi\) | ||||
0.250964 | + | 0.967996i | \(0.419253\pi\) | |||||||
\(354\) | −1.11515e13 | −0.106614 | ||||||||
\(355\) | 1.10712e14 | 1.04217 | ||||||||
\(356\) | 1.63310e14 | 1.51369 | ||||||||
\(357\) | −1.25545e14 | −1.14584 | ||||||||
\(358\) | 1.43097e14 | 1.28609 | ||||||||
\(359\) | 1.14657e14 | 1.01480 | 0.507399 | − | 0.861711i | \(-0.330607\pi\) | ||||
0.507399 | + | 0.861711i | \(0.330607\pi\) | |||||||
\(360\) | 5.81339e11 | 0.00506718 | ||||||||
\(361\) | 1.19829e14 | 1.02866 | ||||||||
\(362\) | −1.25673e14 | −1.06254 | ||||||||
\(363\) | −1.28729e14 | −1.07199 | ||||||||
\(364\) | −2.41065e14 | −1.97732 | ||||||||
\(365\) | 1.12884e14 | 0.912054 | ||||||||
\(366\) | 1.76356e14 | 1.40360 | ||||||||
\(367\) | −2.83999e12 | −0.0222666 | −0.0111333 | − | 0.999938i | \(-0.503544\pi\) | ||||
−0.0111333 | + | 0.999938i | \(0.503544\pi\) | |||||||
\(368\) | −2.26233e14 | −1.74740 | ||||||||
\(369\) | −7.02573e13 | −0.534621 | ||||||||
\(370\) | 2.51068e14 | 1.88227 | ||||||||
\(371\) | −3.09094e14 | −2.28315 | ||||||||
\(372\) | −1.01438e14 | −0.738272 | ||||||||
\(373\) | −7.99288e13 | −0.573198 | −0.286599 | − | 0.958051i | \(-0.592525\pi\) | ||||
−0.286599 | + | 0.958051i | \(0.592525\pi\) | |||||||
\(374\) | 3.53790e14 | 2.50007 | ||||||||
\(375\) | −8.87018e13 | −0.617676 | ||||||||
\(376\) | −9.59460e10 | −0.000658406 0 | ||||||||
\(377\) | −4.40424e13 | −0.297847 | ||||||||
\(378\) | 7.79457e13 | 0.519502 | ||||||||
\(379\) | −1.32898e14 | −0.872974 | −0.436487 | − | 0.899711i | \(-0.643778\pi\) | ||||
−0.436487 | + | 0.899711i | \(0.643778\pi\) | |||||||
\(380\) | −2.00935e14 | −1.30090 | ||||||||
\(381\) | 9.99258e12 | 0.0637662 | ||||||||
\(382\) | 6.46944e13 | 0.406928 | ||||||||
\(383\) | −3.98305e13 | −0.246958 | −0.123479 | − | 0.992347i | \(-0.539405\pi\) | ||||
−0.123479 | + | 0.992347i | \(0.539405\pi\) | |||||||
\(384\) | −3.18151e12 | −0.0194452 | ||||||||
\(385\) | 4.81895e14 | 2.90348 | ||||||||
\(386\) | −2.43968e14 | −1.44912 | ||||||||
\(387\) | −1.72368e13 | −0.100936 | ||||||||
\(388\) | −1.34813e14 | −0.778316 | ||||||||
\(389\) | 1.63688e14 | 0.931736 | 0.465868 | − | 0.884854i | \(-0.345742\pi\) | ||||
0.465868 | + | 0.884854i | \(0.345742\pi\) | |||||||
\(390\) | 1.35236e14 | 0.758989 | ||||||||
\(391\) | 3.33296e14 | 1.84441 | ||||||||
\(392\) | −8.09216e12 | −0.0441561 | ||||||||
\(393\) | 1.78976e14 | 0.963022 | ||||||||
\(394\) | 1.51377e14 | 0.803214 | ||||||||
\(395\) | −1.46622e14 | −0.767211 | ||||||||
\(396\) | −1.10475e14 | −0.570085 | ||||||||
\(397\) | 2.15879e13 | 0.109866 | 0.0549328 | − | 0.998490i | \(-0.482506\pi\) | ||||
0.0549328 | + | 0.998490i | \(0.482506\pi\) | |||||||
\(398\) | 8.03505e13 | 0.403303 | ||||||||
\(399\) | −3.16129e14 | −1.56500 | ||||||||
\(400\) | 3.74816e13 | 0.183015 | ||||||||
\(401\) | 6.97618e13 | 0.335988 | 0.167994 | − | 0.985788i | \(-0.446271\pi\) | ||||
0.167994 | + | 0.985788i | \(0.446271\pi\) | |||||||
\(402\) | −1.26595e14 | −0.601414 | ||||||||
\(403\) | −2.76891e14 | −1.29757 | ||||||||
\(404\) | −1.78057e14 | −0.823115 | ||||||||
\(405\) | −2.19925e13 | −0.100293 | ||||||||
\(406\) | −1.74050e14 | −0.783036 | ||||||||
\(407\) | −5.59850e14 | −2.48486 | ||||||||
\(408\) | 2.31558e12 | 0.0101398 | ||||||||
\(409\) | −1.49949e14 | −0.647838 | −0.323919 | − | 0.946085i | \(-0.605001\pi\) | ||||
−0.323919 | + | 0.946085i | \(0.605001\pi\) | |||||||
\(410\) | −4.81719e14 | −2.05344 | ||||||||
\(411\) | 1.25275e14 | 0.526906 | ||||||||
\(412\) | −9.76805e13 | −0.405390 | ||||||||
\(413\) | −6.05018e13 | −0.247767 | ||||||||
\(414\) | −2.06930e14 | −0.836220 | ||||||||
\(415\) | −5.47227e13 | −0.218224 | ||||||||
\(416\) | −3.70027e14 | −1.45620 | ||||||||
\(417\) | −7.90996e13 | −0.307203 | ||||||||
\(418\) | 8.90860e14 | 3.41460 | ||||||||
\(419\) | −8.76706e13 | −0.331647 | −0.165824 | − | 0.986155i | \(-0.553028\pi\) | ||||
−0.165824 | + | 0.986155i | \(0.553028\pi\) | |||||||
\(420\) | 2.68794e14 | 1.00357 | ||||||||
\(421\) | 1.73321e14 | 0.638705 | 0.319352 | − | 0.947636i | \(-0.396535\pi\) | ||||
0.319352 | + | 0.947636i | \(0.396535\pi\) | |||||||
\(422\) | 2.63761e14 | 0.959384 | ||||||||
\(423\) | 3.62971e12 | 0.0130317 | ||||||||
\(424\) | 5.70099e12 | 0.0202040 | ||||||||
\(425\) | −5.52196e13 | −0.193176 | ||||||||
\(426\) | −2.73789e14 | −0.945505 | ||||||||
\(427\) | 9.56812e14 | 3.26192 | ||||||||
\(428\) | 1.44823e14 | 0.487411 | ||||||||
\(429\) | −3.01558e14 | −1.00197 | ||||||||
\(430\) | −1.18184e14 | −0.387688 | ||||||||
\(431\) | 1.13774e14 | 0.368484 | 0.184242 | − | 0.982881i | \(-0.441017\pi\) | ||||
0.184242 | + | 0.982881i | \(0.441017\pi\) | |||||||
\(432\) | 5.94606e13 | 0.190138 | ||||||||
\(433\) | 2.00411e14 | 0.632758 | 0.316379 | − | 0.948633i | \(-0.397533\pi\) | ||||
0.316379 | + | 0.948633i | \(0.397533\pi\) | |||||||
\(434\) | −1.09424e15 | −3.41130 | ||||||||
\(435\) | 4.91086e13 | 0.151170 | ||||||||
\(436\) | −1.82270e13 | −0.0554039 | ||||||||
\(437\) | 8.39256e14 | 2.51911 | ||||||||
\(438\) | −2.79160e14 | −0.827458 | ||||||||
\(439\) | −4.94116e14 | −1.44635 | −0.723176 | − | 0.690664i | \(-0.757318\pi\) | ||||
−0.723176 | + | 0.690664i | \(0.757318\pi\) | |||||||
\(440\) | −8.88816e12 | −0.0256934 | ||||||||
\(441\) | 3.06132e14 | 0.873971 | ||||||||
\(442\) | 5.38668e14 | 1.51879 | ||||||||
\(443\) | −1.92652e14 | −0.536479 | −0.268240 | − | 0.963352i | \(-0.586442\pi\) | ||||
−0.268240 | + | 0.963352i | \(0.586442\pi\) | |||||||
\(444\) | −3.12277e14 | −0.858882 | ||||||||
\(445\) | −4.97057e14 | −1.35029 | ||||||||
\(446\) | −6.12207e14 | −1.64269 | ||||||||
\(447\) | −2.82528e14 | −0.748806 | ||||||||
\(448\) | −7.44098e14 | −1.94805 | ||||||||
\(449\) | 7.18393e14 | 1.85783 | 0.928917 | − | 0.370287i | \(-0.120741\pi\) | ||||
0.928917 | + | 0.370287i | \(0.120741\pi\) | |||||||
\(450\) | 3.42835e13 | 0.0875823 | ||||||||
\(451\) | 1.07417e15 | 2.71083 | ||||||||
\(452\) | −3.70750e13 | −0.0924314 | ||||||||
\(453\) | −1.92905e14 | −0.475119 | ||||||||
\(454\) | −6.30932e14 | −1.53524 | ||||||||
\(455\) | 7.33715e14 | 1.76386 | ||||||||
\(456\) | 5.83074e12 | 0.0138490 | ||||||||
\(457\) | 2.86012e14 | 0.671189 | 0.335595 | − | 0.942006i | \(-0.391063\pi\) | ||||
0.335595 | + | 0.942006i | \(0.391063\pi\) | |||||||
\(458\) | 3.14846e14 | 0.730026 | ||||||||
\(459\) | −8.76001e13 | −0.200694 | ||||||||
\(460\) | −7.13593e14 | −1.61541 | ||||||||
\(461\) | −2.80949e14 | −0.628451 | −0.314226 | − | 0.949348i | \(-0.601745\pi\) | ||||
−0.314226 | + | 0.949348i | \(0.601745\pi\) | |||||||
\(462\) | −1.19172e15 | −2.63417 | ||||||||
\(463\) | −5.41341e14 | −1.18243 | −0.591215 | − | 0.806514i | \(-0.701352\pi\) | ||||
−0.591215 | + | 0.806514i | \(0.701352\pi\) | |||||||
\(464\) | −1.32774e14 | −0.286591 | ||||||||
\(465\) | 3.08742e14 | 0.658574 | ||||||||
\(466\) | −8.87253e14 | −1.87036 | ||||||||
\(467\) | −3.33665e14 | −0.695133 | −0.347567 | − | 0.937655i | \(-0.612992\pi\) | ||||
−0.347567 | + | 0.937655i | \(0.612992\pi\) | |||||||
\(468\) | −1.68205e14 | −0.346327 | ||||||||
\(469\) | −6.86837e14 | −1.39766 | ||||||||
\(470\) | 2.48871e13 | 0.0500536 | ||||||||
\(471\) | 4.09772e14 | 0.814567 | ||||||||
\(472\) | 1.11591e12 | 0.00219254 | ||||||||
\(473\) | 2.63536e14 | 0.511803 | ||||||||
\(474\) | 3.62594e14 | 0.696049 | ||||||||
\(475\) | −1.39045e14 | −0.263841 | ||||||||
\(476\) | 1.07066e15 | 2.00822 | ||||||||
\(477\) | −2.15673e14 | −0.399893 | ||||||||
\(478\) | 1.47480e14 | 0.270321 | ||||||||
\(479\) | 6.72462e14 | 1.21849 | 0.609245 | − | 0.792982i | \(-0.291473\pi\) | ||||
0.609245 | + | 0.792982i | \(0.291473\pi\) | |||||||
\(480\) | 4.12591e14 | 0.739083 | ||||||||
\(481\) | −8.52407e14 | −1.50956 | ||||||||
\(482\) | 2.78530e14 | 0.487655 | ||||||||
\(483\) | −1.12269e15 | −1.94335 | ||||||||
\(484\) | 1.09781e15 | 1.87878 | ||||||||
\(485\) | 4.10321e14 | 0.694295 | ||||||||
\(486\) | 5.43872e13 | 0.0909907 | ||||||||
\(487\) | −2.16358e14 | −0.357901 | −0.178950 | − | 0.983858i | \(-0.557270\pi\) | ||||
−0.178950 | + | 0.983858i | \(0.557270\pi\) | |||||||
\(488\) | −1.76476e13 | −0.0288654 | ||||||||
\(489\) | 1.54185e14 | 0.249370 | ||||||||
\(490\) | 2.09900e15 | 3.35686 | ||||||||
\(491\) | 5.66577e14 | 0.896006 | 0.448003 | − | 0.894032i | \(-0.352135\pi\) | ||||
0.448003 | + | 0.894032i | \(0.352135\pi\) | |||||||
\(492\) | 5.99158e14 | 0.936986 | ||||||||
\(493\) | 1.95608e14 | 0.302503 | ||||||||
\(494\) | 1.35639e15 | 2.07437 | ||||||||
\(495\) | 3.36246e14 | 0.508544 | ||||||||
\(496\) | −8.34739e14 | −1.24854 | ||||||||
\(497\) | −1.48543e15 | −2.19732 | ||||||||
\(498\) | 1.35329e14 | 0.197983 | ||||||||
\(499\) | −4.60728e14 | −0.666641 | −0.333320 | − | 0.942814i | \(-0.608169\pi\) | ||||
−0.333320 | + | 0.942814i | \(0.608169\pi\) | |||||||
\(500\) | 7.56454e14 | 1.08255 | ||||||||
\(501\) | 3.80996e14 | 0.539278 | ||||||||
\(502\) | −5.23414e14 | −0.732782 | ||||||||
\(503\) | 5.36485e14 | 0.742906 | 0.371453 | − | 0.928452i | \(-0.378860\pi\) | ||||
0.371453 | + | 0.928452i | \(0.378860\pi\) | |||||||
\(504\) | −7.79989e12 | −0.0106837 | ||||||||
\(505\) | 5.41940e14 | 0.734258 | ||||||||
\(506\) | 3.16377e15 | 4.24011 | ||||||||
\(507\) | −2.36454e13 | −0.0313475 | ||||||||
\(508\) | −8.52173e13 | −0.111758 | ||||||||
\(509\) | 1.27284e15 | 1.65131 | 0.825653 | − | 0.564179i | \(-0.190807\pi\) | ||||
0.825653 | + | 0.564179i | \(0.190807\pi\) | |||||||
\(510\) | −6.00630e14 | −0.770852 | ||||||||
\(511\) | −1.51457e15 | −1.92298 | ||||||||
\(512\) | −1.12876e15 | −1.41781 | ||||||||
\(513\) | −2.20581e14 | −0.274109 | ||||||||
\(514\) | −8.62956e14 | −1.06094 | ||||||||
\(515\) | 2.97304e14 | 0.361628 | ||||||||
\(516\) | 1.46996e14 | 0.176902 | ||||||||
\(517\) | −5.54950e13 | −0.0660778 | ||||||||
\(518\) | −3.36861e15 | −3.96860 | ||||||||
\(519\) | 3.98486e14 | 0.464507 | ||||||||
\(520\) | −1.35328e13 | −0.0156088 | ||||||||
\(521\) | 4.23962e14 | 0.483860 | 0.241930 | − | 0.970294i | \(-0.422220\pi\) | ||||
0.241930 | + | 0.970294i | \(0.422220\pi\) | |||||||
\(522\) | −1.21445e14 | −0.137149 | ||||||||
\(523\) | 1.41638e15 | 1.58278 | 0.791390 | − | 0.611312i | \(-0.209358\pi\) | ||||
0.791390 | + | 0.611312i | \(0.209358\pi\) | |||||||
\(524\) | −1.52632e15 | −1.68781 | ||||||||
\(525\) | 1.86004e14 | 0.203538 | ||||||||
\(526\) | −1.48366e15 | −1.60662 | ||||||||
\(527\) | 1.22978e15 | 1.31785 | ||||||||
\(528\) | −9.09100e14 | −0.964106 | ||||||||
\(529\) | 2.02769e15 | 2.12812 | ||||||||
\(530\) | −1.47876e15 | −1.53596 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 2.69596e15 | 2.74284 | ||||||||
\(533\) | 1.63549e15 | 1.64683 | ||||||||
\(534\) | 1.22922e15 | 1.22504 | ||||||||
\(535\) | −4.40788e14 | −0.434795 | ||||||||
\(536\) | 1.26681e13 | 0.0123682 | ||||||||
\(537\) | 5.41714e14 | 0.523494 | ||||||||
\(538\) | −1.83570e15 | −1.75590 | ||||||||
\(539\) | −4.68049e15 | −4.43152 | ||||||||
\(540\) | 1.87553e14 | 0.175776 | ||||||||
\(541\) | 3.05136e14 | 0.283079 | 0.141540 | − | 0.989933i | \(-0.454795\pi\) | ||||
0.141540 | + | 0.989933i | \(0.454795\pi\) | |||||||
\(542\) | 5.10788e14 | 0.469077 | ||||||||
\(543\) | −4.75756e14 | −0.432499 | ||||||||
\(544\) | 1.64343e15 | 1.47896 | ||||||||
\(545\) | 5.54766e13 | 0.0494230 | ||||||||
\(546\) | −1.81447e15 | −1.60026 | ||||||||
\(547\) | −5.80672e14 | −0.506991 | −0.253496 | − | 0.967337i | \(-0.581580\pi\) | ||||
−0.253496 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(548\) | −1.06835e15 | −0.923464 | ||||||||
\(549\) | 6.67623e14 | 0.571325 | ||||||||
\(550\) | −5.24164e14 | −0.444091 | ||||||||
\(551\) | 4.92551e14 | 0.413159 | ||||||||
\(552\) | 2.07071e13 | 0.0171970 | ||||||||
\(553\) | 1.96724e15 | 1.61759 | ||||||||
\(554\) | 8.30569e14 | 0.676195 | ||||||||
\(555\) | 9.50458e14 | 0.766164 | ||||||||
\(556\) | 6.74566e14 | 0.538410 | ||||||||
\(557\) | 1.27295e15 | 1.00602 | 0.503011 | − | 0.864280i | \(-0.332225\pi\) | ||||
0.503011 | + | 0.864280i | \(0.332225\pi\) | |||||||
\(558\) | −7.63515e14 | −0.597489 | ||||||||
\(559\) | 4.01249e14 | 0.310920 | ||||||||
\(560\) | 2.21191e15 | 1.69720 | ||||||||
\(561\) | 1.33933e15 | 1.01763 | ||||||||
\(562\) | −1.24334e15 | −0.935490 | ||||||||
\(563\) | 1.15682e15 | 0.861923 | 0.430961 | − | 0.902370i | \(-0.358175\pi\) | ||||
0.430961 | + | 0.902370i | \(0.358175\pi\) | |||||||
\(564\) | −3.09543e13 | −0.0228395 | ||||||||
\(565\) | 1.12843e14 | 0.0824532 | ||||||||
\(566\) | −3.65671e15 | −2.64606 | ||||||||
\(567\) | 2.95076e14 | 0.211459 | ||||||||
\(568\) | 2.73976e13 | 0.0194445 | ||||||||
\(569\) | 2.09256e15 | 1.47082 | 0.735412 | − | 0.677620i | \(-0.236989\pi\) | ||||
0.735412 | + | 0.677620i | \(0.236989\pi\) | |||||||
\(570\) | −1.51241e15 | −1.05283 | ||||||||
\(571\) | −2.47949e14 | −0.170948 | −0.0854740 | − | 0.996340i | \(-0.527240\pi\) | ||||
−0.0854740 | + | 0.996340i | \(0.527240\pi\) | |||||||
\(572\) | 2.57170e15 | 1.75607 | ||||||||
\(573\) | 2.44910e14 | 0.165637 | ||||||||
\(574\) | 6.46327e15 | 4.32949 | ||||||||
\(575\) | −4.93801e14 | −0.327626 | ||||||||
\(576\) | −5.19200e14 | −0.341201 | ||||||||
\(577\) | 3.09646e14 | 0.201557 | 0.100778 | − | 0.994909i | \(-0.467867\pi\) | ||||
0.100778 | + | 0.994909i | \(0.467867\pi\) | |||||||
\(578\) | −1.92517e14 | −0.124127 | ||||||||
\(579\) | −9.23579e14 | −0.589851 | ||||||||
\(580\) | −4.18800e14 | −0.264943 | ||||||||
\(581\) | 7.34220e14 | 0.460105 | ||||||||
\(582\) | −1.01472e15 | −0.629897 | ||||||||
\(583\) | 3.29744e15 | 2.02768 | ||||||||
\(584\) | 2.79350e13 | 0.0170168 | ||||||||
\(585\) | 5.11955e14 | 0.308940 | ||||||||
\(586\) | 2.86547e15 | 1.71301 | ||||||||
\(587\) | −2.08360e15 | −1.23397 | −0.616986 | − | 0.786974i | \(-0.711647\pi\) | ||||
−0.616986 | + | 0.786974i | \(0.711647\pi\) | |||||||
\(588\) | −2.61071e15 | −1.53174 | ||||||||
\(589\) | 3.09663e15 | 1.79993 | ||||||||
\(590\) | −2.89451e14 | −0.166682 | ||||||||
\(591\) | 5.73062e14 | 0.326942 | ||||||||
\(592\) | −2.56973e15 | −1.45251 | ||||||||
\(593\) | 2.43608e15 | 1.36424 | 0.682119 | − | 0.731241i | \(-0.261059\pi\) | ||||
0.682119 | + | 0.731241i | \(0.261059\pi\) | |||||||
\(594\) | −8.31532e14 | −0.461374 | ||||||||
\(595\) | −3.25870e15 | −1.79143 | ||||||||
\(596\) | 2.40941e15 | 1.31237 | ||||||||
\(597\) | 3.04179e14 | 0.164161 | ||||||||
\(598\) | 4.81703e15 | 2.57586 | ||||||||
\(599\) | −6.60050e14 | −0.349727 | −0.174863 | − | 0.984593i | \(-0.555948\pi\) | ||||
−0.174863 | + | 0.984593i | \(0.555948\pi\) | |||||||
\(600\) | −3.43069e12 | −0.00180115 | ||||||||
\(601\) | 3.71095e14 | 0.193052 | 0.0965261 | − | 0.995330i | \(-0.469227\pi\) | ||||
0.0965261 | + | 0.995330i | \(0.469227\pi\) | |||||||
\(602\) | 1.58569e15 | 0.817405 | ||||||||
\(603\) | −4.79245e14 | −0.244801 | ||||||||
\(604\) | 1.64510e15 | 0.832701 | ||||||||
\(605\) | −3.34133e15 | −1.67596 | ||||||||
\(606\) | −1.34021e15 | −0.666153 | ||||||||
\(607\) | −2.04336e15 | −1.00648 | −0.503242 | − | 0.864146i | \(-0.667859\pi\) | ||||
−0.503242 | + | 0.864146i | \(0.667859\pi\) | |||||||
\(608\) | 4.13822e15 | 2.01997 | ||||||||
\(609\) | −6.58895e14 | −0.318728 | ||||||||
\(610\) | 4.57755e15 | 2.19442 | ||||||||
\(611\) | −8.44945e13 | −0.0401423 | ||||||||
\(612\) | 7.47059e14 | 0.351740 | ||||||||
\(613\) | −2.66338e15 | −1.24280 | −0.621399 | − | 0.783494i | \(-0.713435\pi\) | ||||
−0.621399 | + | 0.783494i | \(0.713435\pi\) | |||||||
\(614\) | −4.27877e15 | −1.97876 | ||||||||
\(615\) | −1.82362e15 | −0.835837 | ||||||||
\(616\) | 1.19253e14 | 0.0541722 | ||||||||
\(617\) | −3.42504e15 | −1.54205 | −0.771024 | − | 0.636806i | \(-0.780255\pi\) | ||||
−0.771024 | + | 0.636806i | \(0.780255\pi\) | |||||||
\(618\) | −7.35230e14 | −0.328085 | ||||||||
\(619\) | 3.05390e15 | 1.35069 | 0.675347 | − | 0.737500i | \(-0.263994\pi\) | ||||
0.675347 | + | 0.737500i | \(0.263994\pi\) | |||||||
\(620\) | −2.63297e15 | −1.15423 | ||||||||
\(621\) | −7.83364e14 | −0.340377 | ||||||||
\(622\) | 4.39470e15 | 1.89270 | ||||||||
\(623\) | 6.66906e15 | 2.84696 | ||||||||
\(624\) | −1.38416e15 | −0.585695 | ||||||||
\(625\) | −1.86073e15 | −0.780445 | ||||||||
\(626\) | −9.50486e14 | −0.395173 | ||||||||
\(627\) | 3.37249e15 | 1.38989 | ||||||||
\(628\) | −3.49455e15 | −1.42762 | ||||||||
\(629\) | 3.78585e15 | 1.53315 | ||||||||
\(630\) | 2.02319e15 | 0.812199 | ||||||||
\(631\) | 2.34415e15 | 0.932877 | 0.466438 | − | 0.884554i | \(-0.345537\pi\) | ||||
0.466438 | + | 0.884554i | \(0.345537\pi\) | |||||||
\(632\) | −3.62841e13 | −0.0143144 | ||||||||
\(633\) | 9.98509e14 | 0.390509 | ||||||||
\(634\) | −5.35668e15 | −2.07685 | ||||||||
\(635\) | 2.59371e14 | 0.0996932 | ||||||||
\(636\) | 1.83927e15 | 0.700859 | ||||||||
\(637\) | −7.12633e15 | −2.69215 | ||||||||
\(638\) | 1.85678e15 | 0.695421 | ||||||||
\(639\) | −1.03647e15 | −0.384860 | ||||||||
\(640\) | −8.25803e13 | −0.0304009 | ||||||||
\(641\) | 1.76636e14 | 0.0644703 | 0.0322351 | − | 0.999480i | \(-0.489737\pi\) | ||||
0.0322351 | + | 0.999480i | \(0.489737\pi\) | |||||||
\(642\) | 1.09006e15 | 0.394466 | ||||||||
\(643\) | 5.68123e14 | 0.203837 | 0.101918 | − | 0.994793i | \(-0.467502\pi\) | ||||
0.101918 | + | 0.994793i | \(0.467502\pi\) | |||||||
\(644\) | 9.57434e15 | 3.40594 | ||||||||
\(645\) | −4.47405e14 | −0.157805 | ||||||||
\(646\) | −6.02422e15 | −2.10679 | ||||||||
\(647\) | −4.50332e15 | −1.56156 | −0.780782 | − | 0.624804i | \(-0.785179\pi\) | ||||
−0.780782 | + | 0.624804i | \(0.785179\pi\) | |||||||
\(648\) | −5.44243e12 | −0.00187124 | ||||||||
\(649\) | 6.45438e14 | 0.220044 | ||||||||
\(650\) | −7.98072e14 | −0.269785 | ||||||||
\(651\) | −4.14242e15 | −1.38854 | ||||||||
\(652\) | −1.31490e15 | −0.437049 | ||||||||
\(653\) | 1.31034e15 | 0.431879 | 0.215939 | − | 0.976407i | \(-0.430719\pi\) | ||||
0.215939 | + | 0.976407i | \(0.430719\pi\) | |||||||
\(654\) | −1.37193e14 | −0.0448388 | ||||||||
\(655\) | 4.64557e15 | 1.50561 | ||||||||
\(656\) | 4.93048e15 | 1.58459 | ||||||||
\(657\) | −1.05680e15 | −0.336810 | ||||||||
\(658\) | −3.33912e14 | −0.105533 | ||||||||
\(659\) | −4.17876e15 | −1.30972 | −0.654858 | − | 0.755752i | \(-0.727272\pi\) | ||||
−0.654858 | + | 0.755752i | \(0.727272\pi\) | |||||||
\(660\) | −2.86752e15 | −0.891282 | ||||||||
\(661\) | −9.57421e14 | −0.295117 | −0.147559 | − | 0.989053i | \(-0.547142\pi\) | ||||
−0.147559 | + | 0.989053i | \(0.547142\pi\) | |||||||
\(662\) | 3.09381e15 | 0.945745 | ||||||||
\(663\) | 2.03921e15 | 0.618212 | ||||||||
\(664\) | −1.35421e13 | −0.00407156 | ||||||||
\(665\) | −8.20554e15 | −2.44674 | ||||||||
\(666\) | −2.35047e15 | −0.695099 | ||||||||
\(667\) | 1.74923e15 | 0.513043 | ||||||||
\(668\) | −3.24915e15 | −0.945147 | ||||||||
\(669\) | −2.31761e15 | −0.668645 | ||||||||
\(670\) | −3.28594e15 | −0.940262 | ||||||||
\(671\) | −1.02074e16 | −2.89694 | ||||||||
\(672\) | −5.53577e15 | −1.55829 | ||||||||
\(673\) | 4.38576e15 | 1.22451 | 0.612255 | − | 0.790660i | \(-0.290263\pi\) | ||||
0.612255 | + | 0.790660i | \(0.290263\pi\) | |||||||
\(674\) | −4.99827e15 | −1.38417 | ||||||||
\(675\) | 1.29785e14 | 0.0356496 | ||||||||
\(676\) | 2.01649e14 | 0.0549401 | ||||||||
\(677\) | 1.46162e15 | 0.395001 | 0.197500 | − | 0.980303i | \(-0.436718\pi\) | ||||
0.197500 | + | 0.980303i | \(0.436718\pi\) | |||||||
\(678\) | −2.79059e14 | −0.0748054 | ||||||||
\(679\) | −5.50532e15 | −1.46386 | ||||||||
\(680\) | 6.01040e13 | 0.0158527 | ||||||||
\(681\) | −2.38849e15 | −0.624906 | ||||||||
\(682\) | 1.16735e16 | 3.02960 | ||||||||
\(683\) | 7.08973e14 | 0.182522 | 0.0912612 | − | 0.995827i | \(-0.470910\pi\) | ||||
0.0912612 | + | 0.995827i | \(0.470910\pi\) | |||||||
\(684\) | 1.88113e15 | 0.480407 | ||||||||
\(685\) | 3.25167e15 | 0.823775 | ||||||||
\(686\) | −1.74212e16 | −4.37821 | ||||||||
\(687\) | 1.19190e15 | 0.297151 | ||||||||
\(688\) | 1.20964e15 | 0.299170 | ||||||||
\(689\) | 5.02056e15 | 1.23182 | ||||||||
\(690\) | −5.37113e15 | −1.30736 | ||||||||
\(691\) | −6.30474e15 | −1.52243 | −0.761216 | − | 0.648499i | \(-0.775397\pi\) | ||||
−0.761216 | + | 0.648499i | \(0.775397\pi\) | |||||||
\(692\) | −3.39831e15 | −0.814102 | ||||||||
\(693\) | −4.51144e15 | −1.07222 | ||||||||
\(694\) | 5.80849e15 | 1.36958 | ||||||||
\(695\) | −2.05314e15 | −0.480288 | ||||||||
\(696\) | 1.21528e13 | 0.00282049 | ||||||||
\(697\) | −7.26382e15 | −1.67257 | ||||||||
\(698\) | −5.12356e15 | −1.17049 | ||||||||
\(699\) | −3.35883e15 | −0.761314 | ||||||||
\(700\) | −1.58625e15 | −0.356724 | ||||||||
\(701\) | 3.31122e15 | 0.738820 | 0.369410 | − | 0.929267i | \(-0.379560\pi\) | ||||
0.369410 | + | 0.929267i | \(0.379560\pi\) | |||||||
\(702\) | −1.26606e15 | −0.280285 | ||||||||
\(703\) | 9.53294e15 | 2.09398 | ||||||||
\(704\) | 7.93810e15 | 1.73008 | ||||||||
\(705\) | 9.42139e13 | 0.0203739 | ||||||||
\(706\) | −3.31793e15 | −0.711937 | ||||||||
\(707\) | −7.27127e15 | −1.54812 | ||||||||
\(708\) | 3.60017e14 | 0.0760571 | ||||||||
\(709\) | 2.87126e15 | 0.601892 | 0.300946 | − | 0.953641i | \(-0.402698\pi\) | ||||
0.300946 | + | 0.953641i | \(0.402698\pi\) | |||||||
\(710\) | −7.10657e15 | −1.47822 | ||||||||
\(711\) | 1.37266e15 | 0.283321 | ||||||||
\(712\) | −1.23005e14 | −0.0251933 | ||||||||
\(713\) | 1.09973e16 | 2.23508 | ||||||||
\(714\) | 8.05871e15 | 1.62527 | ||||||||
\(715\) | −7.82733e15 | −1.56650 | ||||||||
\(716\) | −4.61977e15 | −0.917484 | ||||||||
\(717\) | 5.58308e14 | 0.110032 | ||||||||
\(718\) | −7.35978e15 | −1.43940 | ||||||||
\(719\) | 7.29124e14 | 0.141512 | 0.0707558 | − | 0.997494i | \(-0.477459\pi\) | ||||
0.0707558 | + | 0.997494i | \(0.477459\pi\) | |||||||
\(720\) | 1.54338e15 | 0.297265 | ||||||||
\(721\) | −3.98896e15 | −0.762458 | ||||||||
\(722\) | −7.69179e15 | −1.45906 | ||||||||
\(723\) | 1.05442e15 | 0.198496 | ||||||||
\(724\) | 4.05727e15 | 0.758005 | ||||||||
\(725\) | −2.89807e14 | −0.0537340 | ||||||||
\(726\) | 8.26306e15 | 1.52051 | ||||||||
\(727\) | 3.25997e15 | 0.595352 | 0.297676 | − | 0.954667i | \(-0.403788\pi\) | ||||
0.297676 | + | 0.954667i | \(0.403788\pi\) | |||||||
\(728\) | 1.81571e14 | 0.0329096 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −7.24597e15 | −1.29366 | ||||||||
\(731\) | −1.78209e15 | −0.315780 | ||||||||
\(732\) | −5.69352e15 | −1.00131 | ||||||||
\(733\) | −8.09179e15 | −1.41245 | −0.706224 | − | 0.707988i | \(-0.749603\pi\) | ||||
−0.706224 | + | 0.707988i | \(0.749603\pi\) | |||||||
\(734\) | 1.82298e14 | 0.0315831 | ||||||||
\(735\) | 7.94607e15 | 1.36638 | ||||||||
\(736\) | 1.46963e16 | 2.50831 | ||||||||
\(737\) | 7.32723e15 | 1.24128 | ||||||||
\(738\) | 4.50979e15 | 0.758310 | ||||||||
\(739\) | −3.12675e15 | −0.521853 | −0.260927 | − | 0.965359i | \(-0.584028\pi\) | ||||
−0.260927 | + | 0.965359i | \(0.584028\pi\) | |||||||
\(740\) | −8.10556e15 | −1.34279 | ||||||||
\(741\) | 5.13482e15 | 0.844356 | ||||||||
\(742\) | 1.98406e16 | 3.23843 | ||||||||
\(743\) | −2.31503e15 | −0.375075 | −0.187537 | − | 0.982257i | \(-0.560051\pi\) | ||||
−0.187537 | + | 0.982257i | \(0.560051\pi\) | |||||||
\(744\) | 7.64036e13 | 0.0122875 | ||||||||
\(745\) | −7.33338e15 | −1.17070 | ||||||||
\(746\) | 5.13060e15 | 0.813027 | ||||||||
\(747\) | 5.12307e14 | 0.0805874 | ||||||||
\(748\) | −1.14219e16 | −1.78352 | ||||||||
\(749\) | 5.91410e15 | 0.916724 | ||||||||
\(750\) | 5.69374e15 | 0.876115 | ||||||||
\(751\) | 9.42887e15 | 1.44026 | 0.720129 | − | 0.693840i | \(-0.244083\pi\) | ||||
0.720129 | + | 0.693840i | \(0.244083\pi\) | |||||||
\(752\) | −2.54724e14 | −0.0386253 | ||||||||
\(753\) | −1.98147e15 | −0.298273 | ||||||||
\(754\) | 2.82707e15 | 0.422468 | ||||||||
\(755\) | −5.00710e15 | −0.742810 | ||||||||
\(756\) | −2.51642e15 | −0.370607 | ||||||||
\(757\) | 1.92231e15 | 0.281058 | 0.140529 | − | 0.990077i | \(-0.455120\pi\) | ||||
0.140529 | + | 0.990077i | \(0.455120\pi\) | |||||||
\(758\) | 8.53065e15 | 1.23823 | ||||||||
\(759\) | 1.19769e16 | 1.72590 | ||||||||
\(760\) | 1.51345e14 | 0.0216517 | ||||||||
\(761\) | −5.23339e15 | −0.743306 | −0.371653 | − | 0.928372i | \(-0.621209\pi\) | ||||
−0.371653 | + | 0.928372i | \(0.621209\pi\) | |||||||
\(762\) | −6.41421e14 | −0.0904463 | ||||||||
\(763\) | −7.44335e14 | −0.104204 | ||||||||
\(764\) | −2.08861e15 | −0.290298 | ||||||||
\(765\) | −2.27378e15 | −0.313769 | ||||||||
\(766\) | 2.55671e15 | 0.350286 | ||||||||
\(767\) | 9.82720e14 | 0.133677 | ||||||||
\(768\) | −4.17159e15 | −0.563397 | ||||||||
\(769\) | −2.22888e15 | −0.298877 | −0.149438 | − | 0.988771i | \(-0.547747\pi\) | ||||
−0.149438 | + | 0.988771i | \(0.547747\pi\) | |||||||
\(770\) | −3.09327e16 | −4.11831 | ||||||||
\(771\) | −3.26685e15 | −0.431848 | ||||||||
\(772\) | 7.87633e15 | 1.03378 | ||||||||
\(773\) | −6.35866e15 | −0.828664 | −0.414332 | − | 0.910126i | \(-0.635985\pi\) | ||||
−0.414332 | + | 0.910126i | \(0.635985\pi\) | |||||||
\(774\) | 1.10643e15 | 0.143168 | ||||||||
\(775\) | −1.82199e15 | −0.234093 | ||||||||
\(776\) | 1.01541e14 | 0.0129540 | ||||||||
\(777\) | −1.27524e16 | −1.61539 | ||||||||
\(778\) | −1.05071e16 | −1.32158 | ||||||||
\(779\) | −1.82906e16 | −2.28440 | ||||||||
\(780\) | −4.36598e15 | −0.541454 | ||||||||
\(781\) | 1.58467e16 | 1.95146 | ||||||||
\(782\) | −2.13942e16 | −2.61613 | ||||||||
\(783\) | −4.59748e14 | −0.0558252 | ||||||||
\(784\) | −2.14836e16 | −2.59041 | ||||||||
\(785\) | 1.06362e16 | 1.27351 | ||||||||
\(786\) | −1.14884e16 | −1.36596 | ||||||||
\(787\) | −4.68159e15 | −0.552755 | −0.276378 | − | 0.961049i | \(-0.589134\pi\) | ||||
−0.276378 | + | 0.961049i | \(0.589134\pi\) | |||||||
\(788\) | −4.88710e15 | −0.573003 | ||||||||
\(789\) | −5.61664e15 | −0.653962 | ||||||||
\(790\) | 9.41162e15 | 1.08822 | ||||||||
\(791\) | −1.51402e15 | −0.173845 | ||||||||
\(792\) | 8.32099e13 | 0.00948826 | ||||||||
\(793\) | −1.55413e16 | −1.75989 | ||||||||
\(794\) | −1.38572e15 | −0.155834 | ||||||||
\(795\) | −5.59807e15 | −0.625200 | ||||||||
\(796\) | −2.59406e15 | −0.287712 | ||||||||
\(797\) | 9.28783e15 | 1.02304 | 0.511521 | − | 0.859271i | \(-0.329082\pi\) | ||||
0.511521 | + | 0.859271i | \(0.329082\pi\) | |||||||
\(798\) | 2.02922e16 | 2.21980 | ||||||||
\(799\) | 3.75271e14 | 0.0407697 | ||||||||
\(800\) | −2.43484e15 | −0.262710 | ||||||||
\(801\) | 4.65339e15 | 0.498644 | ||||||||
\(802\) | −4.47799e15 | −0.476567 | ||||||||
\(803\) | 1.61576e16 | 1.70782 | ||||||||
\(804\) | 4.08703e15 | 0.429042 | ||||||||
\(805\) | −2.91409e16 | −3.03826 | ||||||||
\(806\) | 1.77736e16 | 1.84048 | ||||||||
\(807\) | −6.94933e15 | −0.714725 | ||||||||
\(808\) | 1.34113e14 | 0.0136996 | ||||||||
\(809\) | 6.57580e15 | 0.667163 | 0.333581 | − | 0.942721i | \(-0.391743\pi\) | ||||
0.333581 | + | 0.942721i | \(0.391743\pi\) | |||||||
\(810\) | 1.41169e15 | 0.142257 | ||||||||
\(811\) | 8.94290e15 | 0.895084 | 0.447542 | − | 0.894263i | \(-0.352299\pi\) | ||||
0.447542 | + | 0.894263i | \(0.352299\pi\) | |||||||
\(812\) | 5.61909e15 | 0.558609 | ||||||||
\(813\) | 1.93367e15 | 0.190934 | ||||||||
\(814\) | 3.59366e16 | 3.52454 | ||||||||
\(815\) | 4.00208e15 | 0.389869 | ||||||||
\(816\) | 6.14756e15 | 0.594849 | ||||||||
\(817\) | −4.48739e15 | −0.431293 | ||||||||
\(818\) | 9.62521e15 | 0.918897 | ||||||||
\(819\) | −6.86895e15 | −0.651372 | ||||||||
\(820\) | 1.55519e16 | 1.46490 | ||||||||
\(821\) | −6.28129e15 | −0.587708 | −0.293854 | − | 0.955850i | \(-0.594938\pi\) | ||||
−0.293854 | + | 0.955850i | \(0.594938\pi\) | |||||||
\(822\) | −8.04134e15 | −0.747366 | ||||||||
\(823\) | 1.30428e16 | 1.20413 | 0.602063 | − | 0.798449i | \(-0.294346\pi\) | ||||
0.602063 | + | 0.798449i | \(0.294346\pi\) | |||||||
\(824\) | 7.35731e13 | 0.00674714 | ||||||||
\(825\) | −1.98430e15 | −0.180764 | ||||||||
\(826\) | 3.88359e15 | 0.351434 | ||||||||
\(827\) | 3.68427e15 | 0.331185 | 0.165593 | − | 0.986194i | \(-0.447046\pi\) | ||||
0.165593 | + | 0.986194i | \(0.447046\pi\) | |||||||
\(828\) | 6.68057e15 | 0.596550 | ||||||||
\(829\) | 8.52482e15 | 0.756198 | 0.378099 | − | 0.925765i | \(-0.376578\pi\) | ||||
0.378099 | + | 0.925765i | \(0.376578\pi\) | |||||||
\(830\) | 3.51263e15 | 0.309530 | ||||||||
\(831\) | 3.14425e15 | 0.275240 | ||||||||
\(832\) | 1.20862e16 | 1.05103 | ||||||||
\(833\) | 3.16506e16 | 2.73423 | ||||||||
\(834\) | 5.07738e15 | 0.435739 | ||||||||
\(835\) | 9.88925e15 | 0.843117 | ||||||||
\(836\) | −2.87608e16 | −2.43594 | ||||||||
\(837\) | −2.89041e15 | −0.243203 | ||||||||
\(838\) | 5.62755e15 | 0.470410 | ||||||||
\(839\) | 1.13665e16 | 0.943920 | 0.471960 | − | 0.881620i | \(-0.343547\pi\) | ||||
0.471960 | + | 0.881620i | \(0.343547\pi\) | |||||||
\(840\) | −2.02456e14 | −0.0167030 | ||||||||
\(841\) | −1.11739e16 | −0.915856 | ||||||||
\(842\) | −1.11254e16 | −0.905942 | ||||||||
\(843\) | −4.70684e15 | −0.380784 | ||||||||
\(844\) | −8.51534e15 | −0.684413 | ||||||||
\(845\) | −6.13748e14 | −0.0490093 | ||||||||
\(846\) | −2.32990e14 | −0.0184842 | ||||||||
\(847\) | 4.48309e16 | 3.53361 | ||||||||
\(848\) | 1.51354e16 | 1.18527 | ||||||||
\(849\) | −1.38430e16 | −1.07706 | ||||||||
\(850\) | 3.54453e15 | 0.274002 | ||||||||
\(851\) | 3.38549e16 | 2.60022 | ||||||||
\(852\) | 8.83909e15 | 0.674512 | ||||||||
\(853\) | −2.38523e16 | −1.80847 | −0.904235 | − | 0.427035i | \(-0.859558\pi\) | ||||
−0.904235 | + | 0.427035i | \(0.859558\pi\) | |||||||
\(854\) | −6.14175e16 | −4.62672 | ||||||||
\(855\) | −5.72548e15 | −0.428547 | ||||||||
\(856\) | −1.09081e14 | −0.00811227 | ||||||||
\(857\) | −1.55491e16 | −1.14897 | −0.574486 | − | 0.818514i | \(-0.694798\pi\) | ||||
−0.574486 | + | 0.818514i | \(0.694798\pi\) | |||||||
\(858\) | 1.93569e16 | 1.42120 | ||||||||
\(859\) | 2.58000e16 | 1.88216 | 0.941080 | − | 0.338184i | \(-0.109813\pi\) | ||||
0.941080 | + | 0.338184i | \(0.109813\pi\) | |||||||
\(860\) | 3.81549e15 | 0.276572 | ||||||||
\(861\) | 2.44677e16 | 1.76228 | ||||||||
\(862\) | −7.30313e15 | −0.522660 | ||||||||
\(863\) | 6.23324e15 | 0.443256 | 0.221628 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221628 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(864\) | −3.86263e15 | −0.272934 | ||||||||
\(865\) | 1.03432e16 | 0.726219 | ||||||||
\(866\) | −1.28643e16 | −0.897507 | ||||||||
\(867\) | −7.28802e14 | −0.0505248 | ||||||||
\(868\) | 3.53268e16 | 2.43358 | ||||||||
\(869\) | −2.09867e16 | −1.43660 | ||||||||
\(870\) | −3.15226e15 | −0.214421 | ||||||||
\(871\) | 1.11562e16 | 0.754076 | ||||||||
\(872\) | 1.37286e13 | 0.000922119 0 | ||||||||
\(873\) | −3.84138e15 | −0.256394 | ||||||||
\(874\) | −5.38716e16 | −3.57311 | ||||||||
\(875\) | 3.08912e16 | 2.03606 | ||||||||
\(876\) | 9.01248e15 | 0.590298 | ||||||||
\(877\) | 2.58853e16 | 1.68483 | 0.842413 | − | 0.538832i | \(-0.181134\pi\) | ||||
0.842413 | + | 0.538832i | \(0.181134\pi\) | |||||||
\(878\) | 3.17171e16 | 2.05151 | ||||||||
\(879\) | 1.08477e16 | 0.697265 | ||||||||
\(880\) | −2.35969e16 | −1.50730 | ||||||||
\(881\) | −1.51066e16 | −0.958955 | −0.479478 | − | 0.877554i | \(-0.659174\pi\) | ||||
−0.479478 | + | 0.877554i | \(0.659174\pi\) | |||||||
\(882\) | −1.96505e16 | −1.23964 | ||||||||
\(883\) | 1.59585e16 | 1.00048 | 0.500240 | − | 0.865887i | \(-0.333245\pi\) | ||||
0.500240 | + | 0.865887i | \(0.333245\pi\) | |||||||
\(884\) | −1.73905e16 | −1.08349 | ||||||||
\(885\) | −1.09576e15 | −0.0678466 | ||||||||
\(886\) | 1.23663e16 | 0.760945 | ||||||||
\(887\) | 7.58241e15 | 0.463690 | 0.231845 | − | 0.972753i | \(-0.425524\pi\) | ||||
0.231845 | + | 0.972753i | \(0.425524\pi\) | |||||||
\(888\) | 2.35208e14 | 0.0142949 | ||||||||
\(889\) | −3.48000e15 | −0.210194 | ||||||||
\(890\) | 3.19059e16 | 1.91525 | ||||||||
\(891\) | −3.14789e15 | −0.187799 | ||||||||
\(892\) | 1.97647e16 | 1.17188 | ||||||||
\(893\) | 9.44950e14 | 0.0556834 | ||||||||
\(894\) | 1.81354e16 | 1.06211 | ||||||||
\(895\) | 1.40609e16 | 0.818440 | ||||||||
\(896\) | 1.10799e15 | 0.0640975 | ||||||||
\(897\) | 1.82356e16 | 1.04848 | ||||||||
\(898\) | −4.61134e16 | −2.63516 | ||||||||
\(899\) | 6.45419e15 | 0.366575 | ||||||||
\(900\) | −1.10682e15 | −0.0624801 | ||||||||
\(901\) | −2.22981e16 | −1.25107 | ||||||||
\(902\) | −6.89507e16 | −3.84506 | ||||||||
\(903\) | 6.00287e15 | 0.332718 | ||||||||
\(904\) | 2.79249e13 | 0.00153839 | ||||||||
\(905\) | −1.23489e16 | −0.676177 | ||||||||
\(906\) | 1.23825e16 | 0.673911 | ||||||||
\(907\) | 1.27789e16 | 0.691279 | 0.345639 | − | 0.938367i | \(-0.387662\pi\) | ||||
0.345639 | + | 0.938367i | \(0.387662\pi\) | |||||||
\(908\) | 2.03692e16 | 1.09522 | ||||||||
\(909\) | −5.07358e15 | −0.271152 | ||||||||
\(910\) | −4.70969e16 | −2.50187 | ||||||||
\(911\) | −2.17665e16 | −1.14931 | −0.574655 | − | 0.818396i | \(-0.694864\pi\) | ||||
−0.574655 | + | 0.818396i | \(0.694864\pi\) | |||||||
\(912\) | 1.54798e16 | 0.812447 | ||||||||
\(913\) | −7.83272e15 | −0.408623 | ||||||||
\(914\) | −1.83590e16 | −0.952018 | ||||||||
\(915\) | 1.73290e16 | 0.893220 | ||||||||
\(916\) | −1.01646e16 | −0.520792 | ||||||||
\(917\) | −6.23300e16 | −3.17443 | ||||||||
\(918\) | 5.62303e15 | 0.284666 | ||||||||
\(919\) | −1.17338e16 | −0.590476 | −0.295238 | − | 0.955424i | \(-0.595399\pi\) | ||||
−0.295238 | + | 0.955424i | \(0.595399\pi\) | |||||||
\(920\) | 5.37480e14 | 0.0268862 | ||||||||
\(921\) | −1.61980e16 | −0.805438 | ||||||||
\(922\) | 1.80340e16 | 0.891399 | ||||||||
\(923\) | 2.41276e16 | 1.18551 | ||||||||
\(924\) | 3.84738e16 | 1.87918 | ||||||||
\(925\) | −5.60899e15 | −0.272336 | ||||||||
\(926\) | 3.47485e16 | 1.67717 | ||||||||
\(927\) | −2.78333e15 | −0.133544 | ||||||||
\(928\) | 8.62513e15 | 0.411388 | ||||||||
\(929\) | 3.02918e16 | 1.43628 | 0.718138 | − | 0.695900i | \(-0.244995\pi\) | ||||
0.718138 | + | 0.695900i | \(0.244995\pi\) | |||||||
\(930\) | −1.98181e16 | −0.934125 | ||||||||
\(931\) | 7.96978e16 | 3.73442 | ||||||||
\(932\) | 2.86443e16 | 1.33429 | ||||||||
\(933\) | 1.66368e16 | 0.770409 | ||||||||
\(934\) | 2.14179e16 | 0.985980 | ||||||||
\(935\) | 3.47640e16 | 1.59099 | ||||||||
\(936\) | 1.26692e14 | 0.00576411 | ||||||||
\(937\) | −4.00930e16 | −1.81343 | −0.906715 | − | 0.421743i | \(-0.861418\pi\) | ||||
−0.906715 | + | 0.421743i | \(0.861418\pi\) | |||||||
\(938\) | 4.40878e16 | 1.98245 | ||||||||
\(939\) | −3.59821e15 | −0.160852 | ||||||||
\(940\) | −8.03461e14 | −0.0357077 | ||||||||
\(941\) | −1.61072e16 | −0.711667 | −0.355834 | − | 0.934549i | \(-0.615803\pi\) | ||||
−0.355834 | + | 0.934549i | \(0.615803\pi\) | |||||||
\(942\) | −2.63031e16 | −1.15539 | ||||||||
\(943\) | −6.49566e16 | −2.83667 | ||||||||
\(944\) | 2.96258e15 | 0.128625 | ||||||||
\(945\) | 7.65908e15 | 0.330599 | ||||||||
\(946\) | −1.69163e16 | −0.725944 | ||||||||
\(947\) | −1.00119e16 | −0.427162 | −0.213581 | − | 0.976925i | \(-0.568513\pi\) | ||||
−0.213581 | + | 0.976925i | \(0.568513\pi\) | |||||||
\(948\) | −1.17061e16 | −0.496553 | ||||||||
\(949\) | 2.46009e16 | 1.03750 | ||||||||
\(950\) | 8.92528e15 | 0.374233 | ||||||||
\(951\) | −2.02785e16 | −0.845364 | ||||||||
\(952\) | −8.06421e14 | −0.0334240 | ||||||||
\(953\) | 7.97340e15 | 0.328574 | 0.164287 | − | 0.986413i | \(-0.447468\pi\) | ||||
0.164287 | + | 0.986413i | \(0.447468\pi\) | |||||||
\(954\) | 1.38440e16 | 0.567210 | ||||||||
\(955\) | 6.35698e15 | 0.258960 | ||||||||
\(956\) | −4.76128e15 | −0.192844 | ||||||||
\(957\) | 7.02914e15 | 0.283065 | ||||||||
\(958\) | −4.31651e16 | −1.72831 | ||||||||
\(959\) | −4.36280e16 | −1.73685 | ||||||||
\(960\) | −1.34765e16 | −0.533440 | ||||||||
\(961\) | 1.51685e16 | 0.596987 | ||||||||
\(962\) | 5.47157e16 | 2.14116 | ||||||||
\(963\) | 4.12660e15 | 0.160564 | ||||||||
\(964\) | −8.99212e15 | −0.347887 | ||||||||
\(965\) | −2.39727e16 | −0.922184 | ||||||||
\(966\) | 7.20650e16 | 2.75645 | ||||||||
\(967\) | 1.81277e16 | 0.689440 | 0.344720 | − | 0.938706i | \(-0.387974\pi\) | ||||
0.344720 | + | 0.938706i | \(0.387974\pi\) | |||||||
\(968\) | −8.26869e14 | −0.0312696 | ||||||||
\(969\) | −2.28056e16 | −0.857553 | ||||||||
\(970\) | −2.63384e16 | −0.984792 | ||||||||
\(971\) | −3.66253e16 | −1.36168 | −0.680841 | − | 0.732431i | \(-0.738386\pi\) | ||||
−0.680841 | + | 0.732431i | \(0.738386\pi\) | |||||||
\(972\) | −1.75585e15 | −0.0649117 | ||||||||
\(973\) | 2.75471e16 | 1.01264 | ||||||||
\(974\) | 1.38879e16 | 0.507649 | ||||||||
\(975\) | −3.02122e15 | −0.109814 | ||||||||
\(976\) | −4.68521e16 | −1.69338 | ||||||||
\(977\) | 4.10970e16 | 1.47703 | 0.738516 | − | 0.674236i | \(-0.235527\pi\) | ||||
0.738516 | + | 0.674236i | \(0.235527\pi\) | |||||||
\(978\) | −9.89709e15 | −0.353707 | ||||||||
\(979\) | −7.11461e16 | −2.52840 | ||||||||
\(980\) | −6.77645e16 | −2.39474 | ||||||||
\(981\) | −5.19365e14 | −0.0182513 | ||||||||
\(982\) | −3.63684e16 | −1.27090 | ||||||||
\(983\) | 3.22372e16 | 1.12024 | 0.560122 | − | 0.828410i | \(-0.310754\pi\) | ||||
0.560122 | + | 0.828410i | \(0.310754\pi\) | |||||||
\(984\) | −4.51287e14 | −0.0155948 | ||||||||
\(985\) | 1.48746e16 | 0.511147 | ||||||||
\(986\) | −1.25560e16 | −0.429072 | ||||||||
\(987\) | −1.26408e15 | −0.0429565 | ||||||||
\(988\) | −4.37900e16 | −1.47983 | ||||||||
\(989\) | −1.59364e16 | −0.535562 | ||||||||
\(990\) | −2.15835e16 | −0.721321 | ||||||||
\(991\) | −5.59817e15 | −0.186055 | −0.0930274 | − | 0.995664i | \(-0.529654\pi\) | ||||
−0.0930274 | + | 0.995664i | \(0.529654\pi\) | |||||||
\(992\) | 5.42255e16 | 1.79221 | ||||||||
\(993\) | 1.17121e16 | 0.384958 | ||||||||
\(994\) | 9.53495e16 | 3.11669 | ||||||||
\(995\) | 7.89538e15 | 0.256653 | ||||||||
\(996\) | −4.36898e15 | −0.141239 | ||||||||
\(997\) | −4.95070e16 | −1.59163 | −0.795817 | − | 0.605538i | \(-0.792958\pi\) | ||||
−0.795817 | + | 0.605538i | \(0.792958\pi\) | |||||||
\(998\) | 2.95740e16 | 0.945567 | ||||||||
\(999\) | −8.89808e15 | −0.282934 |
(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 | 177.12.a.c.1.6 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.6 | ✓ | 27 | 1.1 | even | 1 | trivial |