Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,12,Mod(1,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("273.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(209.757688293\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 26640 x^{14} - 38138 x^{13} + 279954048 x^{12} + 940095168 x^{11} + \cdots + 45\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{12}\cdot 5\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-65.6788\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −69.6788 | −1.53970 | −0.769849 | − | 0.638226i | \(-0.779669\pi\) | ||||
−0.769849 | + | 0.638226i | \(0.779669\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 2807.14 | 1.37067 | ||||||||
\(5\) | −8533.64 | −1.22123 | −0.610617 | − | 0.791926i | \(-0.709079\pi\) | ||||
−0.610617 | + | 0.791926i | \(0.709079\pi\) | |||||||
\(6\) | 16932.0 | 0.888945 | ||||||||
\(7\) | 16807.0 | 0.377964 | ||||||||
\(8\) | −52895.7 | −0.570723 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 594614. | 1.88033 | ||||||||
\(11\) | −896472. | −1.67833 | −0.839165 | − | 0.543877i | \(-0.816956\pi\) | ||||
−0.839165 | + | 0.543877i | \(0.816956\pi\) | |||||||
\(12\) | −682134. | −0.791358 | ||||||||
\(13\) | −371293. | −0.277350 | ||||||||
\(14\) | −1.17109e6 | −0.581951 | ||||||||
\(15\) | 2.07367e6 | 0.705080 | ||||||||
\(16\) | −2.06330e6 | −0.491930 | ||||||||
\(17\) | 6.97736e6 | 1.19185 | 0.595926 | − | 0.803039i | \(-0.296785\pi\) | ||||
0.595926 | + | 0.803039i | \(0.296785\pi\) | |||||||
\(18\) | −4.11446e6 | −0.513233 | ||||||||
\(19\) | 8.73840e6 | 0.809631 | 0.404815 | − | 0.914398i | \(-0.367336\pi\) | ||||
0.404815 | + | 0.914398i | \(0.367336\pi\) | |||||||
\(20\) | −2.39551e7 | −1.67391 | ||||||||
\(21\) | −4.08410e6 | −0.218218 | ||||||||
\(22\) | 6.24651e7 | 2.58412 | ||||||||
\(23\) | −2.99957e7 | −0.971754 | −0.485877 | − | 0.874027i | \(-0.661500\pi\) | ||||
−0.485877 | + | 0.874027i | \(0.661500\pi\) | |||||||
\(24\) | 1.28537e7 | 0.329507 | ||||||||
\(25\) | 2.39948e7 | 0.491414 | ||||||||
\(26\) | 2.58713e7 | 0.427036 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 4.71795e7 | 0.518065 | ||||||||
\(29\) | −2.58336e7 | −0.233882 | −0.116941 | − | 0.993139i | \(-0.537309\pi\) | ||||
−0.116941 | + | 0.993139i | \(0.537309\pi\) | |||||||
\(30\) | −1.44491e8 | −1.08561 | ||||||||
\(31\) | −1.03902e8 | −0.651833 | −0.325917 | − | 0.945398i | \(-0.605673\pi\) | ||||
−0.325917 | + | 0.945398i | \(0.605673\pi\) | |||||||
\(32\) | 2.52099e8 | 1.32815 | ||||||||
\(33\) | 2.17843e8 | 0.968984 | ||||||||
\(34\) | −4.86174e8 | −1.83509 | ||||||||
\(35\) | −1.43425e8 | −0.461583 | ||||||||
\(36\) | 1.65759e8 | 0.456891 | ||||||||
\(37\) | −2.97829e7 | −0.0706086 | −0.0353043 | − | 0.999377i | \(-0.511240\pi\) | ||||
−0.0353043 | + | 0.999377i | \(0.511240\pi\) | |||||||
\(38\) | −6.08881e8 | −1.24659 | ||||||||
\(39\) | 9.02242e7 | 0.160128 | ||||||||
\(40\) | 4.51393e8 | 0.696987 | ||||||||
\(41\) | −4.22760e8 | −0.569879 | −0.284939 | − | 0.958546i | \(-0.591973\pi\) | ||||
−0.284939 | + | 0.958546i | \(0.591973\pi\) | |||||||
\(42\) | 2.84575e8 | 0.335990 | ||||||||
\(43\) | 3.51751e8 | 0.364887 | 0.182443 | − | 0.983216i | \(-0.441599\pi\) | ||||
0.182443 | + | 0.983216i | \(0.441599\pi\) | |||||||
\(44\) | −2.51652e9 | −2.30044 | ||||||||
\(45\) | −5.03903e8 | −0.407078 | ||||||||
\(46\) | 2.09007e9 | 1.49621 | ||||||||
\(47\) | 1.85963e8 | 0.118274 | 0.0591370 | − | 0.998250i | \(-0.481165\pi\) | ||||
0.0591370 | + | 0.998250i | \(0.481165\pi\) | |||||||
\(48\) | 5.01383e8 | 0.284016 | ||||||||
\(49\) | 2.82475e8 | 0.142857 | ||||||||
\(50\) | −1.67193e9 | −0.756629 | ||||||||
\(51\) | −1.69550e9 | −0.688116 | ||||||||
\(52\) | −1.04227e9 | −0.380156 | ||||||||
\(53\) | −3.89621e9 | −1.27975 | −0.639874 | − | 0.768480i | \(-0.721014\pi\) | ||||
−0.639874 | + | 0.768480i | \(0.721014\pi\) | |||||||
\(54\) | 9.99815e8 | 0.296315 | ||||||||
\(55\) | 7.65017e9 | 2.04963 | ||||||||
\(56\) | −8.89019e8 | −0.215713 | ||||||||
\(57\) | −2.12343e9 | −0.467440 | ||||||||
\(58\) | 1.80006e9 | 0.360107 | ||||||||
\(59\) | −6.93019e9 | −1.26200 | −0.630999 | − | 0.775783i | \(-0.717355\pi\) | ||||
−0.630999 | + | 0.775783i | \(0.717355\pi\) | |||||||
\(60\) | 5.82108e9 | 0.966434 | ||||||||
\(61\) | 3.21359e9 | 0.487165 | 0.243582 | − | 0.969880i | \(-0.421677\pi\) | ||||
0.243582 | + | 0.969880i | \(0.421677\pi\) | |||||||
\(62\) | 7.23980e9 | 1.00363 | ||||||||
\(63\) | 9.92437e8 | 0.125988 | ||||||||
\(64\) | −1.33403e10 | −1.55302 | ||||||||
\(65\) | 3.16848e9 | 0.338710 | ||||||||
\(66\) | −1.51790e10 | −1.49194 | ||||||||
\(67\) | 1.07796e10 | 0.975421 | 0.487711 | − | 0.873005i | \(-0.337832\pi\) | ||||
0.487711 | + | 0.873005i | \(0.337832\pi\) | |||||||
\(68\) | 1.95864e10 | 1.63364 | ||||||||
\(69\) | 7.28896e9 | 0.561042 | ||||||||
\(70\) | 9.99367e9 | 0.710699 | ||||||||
\(71\) | 1.05896e10 | 0.696562 | 0.348281 | − | 0.937390i | \(-0.386765\pi\) | ||||
0.348281 | + | 0.937390i | \(0.386765\pi\) | |||||||
\(72\) | −3.12344e9 | −0.190241 | ||||||||
\(73\) | −1.93948e10 | −1.09499 | −0.547495 | − | 0.836809i | \(-0.684418\pi\) | ||||
−0.547495 | + | 0.836809i | \(0.684418\pi\) | |||||||
\(74\) | 2.07524e9 | 0.108716 | ||||||||
\(75\) | −5.83074e9 | −0.283718 | ||||||||
\(76\) | 2.45299e10 | 1.10974 | ||||||||
\(77\) | −1.50670e10 | −0.634349 | ||||||||
\(78\) | −6.28671e9 | −0.246549 | ||||||||
\(79\) | −4.97021e9 | −0.181730 | −0.0908648 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908648 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(80\) | 1.76075e10 | 0.600762 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 2.94574e10 | 0.877441 | ||||||||
\(83\) | 1.40537e9 | 0.0391616 | 0.0195808 | − | 0.999808i | \(-0.493767\pi\) | ||||
0.0195808 | + | 0.999808i | \(0.493767\pi\) | |||||||
\(84\) | −1.14646e10 | −0.299105 | ||||||||
\(85\) | −5.95423e10 | −1.45553 | ||||||||
\(86\) | −2.45096e10 | −0.561816 | ||||||||
\(87\) | 6.27757e9 | 0.135032 | ||||||||
\(88\) | 4.74196e10 | 0.957862 | ||||||||
\(89\) | −6.73546e10 | −1.27856 | −0.639282 | − | 0.768973i | \(-0.720768\pi\) | ||||
−0.639282 | + | 0.768973i | \(0.720768\pi\) | |||||||
\(90\) | 3.51113e10 | 0.626778 | ||||||||
\(91\) | −6.24032e9 | −0.104828 | ||||||||
\(92\) | −8.42021e10 | −1.33196 | ||||||||
\(93\) | 2.52483e10 | 0.376336 | ||||||||
\(94\) | −1.29577e10 | −0.182106 | ||||||||
\(95\) | −7.45703e10 | −0.988749 | ||||||||
\(96\) | −6.12601e10 | −0.766806 | ||||||||
\(97\) | 9.77987e10 | 1.15635 | 0.578174 | − | 0.815914i | \(-0.303766\pi\) | ||||
0.578174 | + | 0.815914i | \(0.303766\pi\) | |||||||
\(98\) | −1.96825e10 | −0.219957 | ||||||||
\(99\) | −5.29358e10 | −0.559443 | ||||||||
\(100\) | 6.73567e10 | 0.673567 | ||||||||
\(101\) | −5.47424e10 | −0.518270 | −0.259135 | − | 0.965841i | \(-0.583437\pi\) | ||||
−0.259135 | + | 0.965841i | \(0.583437\pi\) | |||||||
\(102\) | 1.18140e11 | 1.05949 | ||||||||
\(103\) | 1.95398e11 | 1.66079 | 0.830397 | − | 0.557172i | \(-0.188114\pi\) | ||||
0.830397 | + | 0.557172i | \(0.188114\pi\) | |||||||
\(104\) | 1.96398e10 | 0.158290 | ||||||||
\(105\) | 3.48522e10 | 0.266495 | ||||||||
\(106\) | 2.71483e11 | 1.97043 | ||||||||
\(107\) | 3.50218e10 | 0.241395 | 0.120697 | − | 0.992689i | \(-0.461487\pi\) | ||||
0.120697 | + | 0.992689i | \(0.461487\pi\) | |||||||
\(108\) | −4.02793e10 | −0.263786 | ||||||||
\(109\) | 1.88052e11 | 1.17066 | 0.585331 | − | 0.810795i | \(-0.300965\pi\) | ||||
0.585331 | + | 0.810795i | \(0.300965\pi\) | |||||||
\(110\) | −5.33055e11 | −3.15582 | ||||||||
\(111\) | 7.23725e9 | 0.0407659 | ||||||||
\(112\) | −3.46779e10 | −0.185932 | ||||||||
\(113\) | 2.38260e11 | 1.21652 | 0.608260 | − | 0.793738i | \(-0.291868\pi\) | ||||
0.608260 | + | 0.793738i | \(0.291868\pi\) | |||||||
\(114\) | 1.47958e11 | 0.719718 | ||||||||
\(115\) | 2.55972e11 | 1.18674 | ||||||||
\(116\) | −7.25185e10 | −0.320575 | ||||||||
\(117\) | −2.19245e10 | −0.0924500 | ||||||||
\(118\) | 4.82887e11 | 1.94310 | ||||||||
\(119\) | 1.17269e11 | 0.450478 | ||||||||
\(120\) | −1.09688e11 | −0.402406 | ||||||||
\(121\) | 5.18351e11 | 1.81679 | ||||||||
\(122\) | −2.23919e11 | −0.750087 | ||||||||
\(123\) | 1.02731e11 | 0.329020 | ||||||||
\(124\) | −2.91668e11 | −0.893450 | ||||||||
\(125\) | 2.11918e11 | 0.621103 | ||||||||
\(126\) | −6.91518e10 | −0.193984 | ||||||||
\(127\) | −1.08959e11 | −0.292647 | −0.146323 | − | 0.989237i | \(-0.546744\pi\) | ||||
−0.146323 | + | 0.989237i | \(0.546744\pi\) | |||||||
\(128\) | 4.13238e11 | 1.06303 | ||||||||
\(129\) | −8.54754e10 | −0.210668 | ||||||||
\(130\) | −2.20776e11 | −0.521511 | ||||||||
\(131\) | 1.96232e11 | 0.444404 | 0.222202 | − | 0.975001i | \(-0.428676\pi\) | ||||
0.222202 | + | 0.975001i | \(0.428676\pi\) | |||||||
\(132\) | 6.11515e11 | 1.32816 | ||||||||
\(133\) | 1.46866e11 | 0.306012 | ||||||||
\(134\) | −7.51111e11 | −1.50185 | ||||||||
\(135\) | 1.22448e11 | 0.235027 | ||||||||
\(136\) | −3.69073e11 | −0.680218 | ||||||||
\(137\) | 1.01527e12 | 1.79728 | 0.898642 | − | 0.438683i | \(-0.144555\pi\) | ||||
0.898642 | + | 0.438683i | \(0.144555\pi\) | |||||||
\(138\) | −5.07886e11 | −0.863836 | ||||||||
\(139\) | 1.92508e11 | 0.314678 | 0.157339 | − | 0.987545i | \(-0.449708\pi\) | ||||
0.157339 | + | 0.987545i | \(0.449708\pi\) | |||||||
\(140\) | −4.02613e11 | −0.632679 | ||||||||
\(141\) | −4.51891e10 | −0.0682855 | ||||||||
\(142\) | −7.37873e11 | −1.07250 | ||||||||
\(143\) | 3.32854e11 | 0.465485 | ||||||||
\(144\) | −1.21836e11 | −0.163977 | ||||||||
\(145\) | 2.20455e11 | 0.285624 | ||||||||
\(146\) | 1.35141e12 | 1.68595 | ||||||||
\(147\) | −6.86415e10 | −0.0824786 | ||||||||
\(148\) | −8.36047e10 | −0.0967813 | ||||||||
\(149\) | 6.90195e11 | 0.769923 | 0.384961 | − | 0.922933i | \(-0.374215\pi\) | ||||
0.384961 | + | 0.922933i | \(0.374215\pi\) | |||||||
\(150\) | 4.06279e11 | 0.436840 | ||||||||
\(151\) | −4.33411e10 | −0.0449290 | −0.0224645 | − | 0.999748i | \(-0.507151\pi\) | ||||
−0.0224645 | + | 0.999748i | \(0.507151\pi\) | |||||||
\(152\) | −4.62224e11 | −0.462075 | ||||||||
\(153\) | 4.12006e11 | 0.397284 | ||||||||
\(154\) | 1.04985e12 | 0.976706 | ||||||||
\(155\) | 8.86666e11 | 0.796041 | ||||||||
\(156\) | 2.53272e11 | 0.219483 | ||||||||
\(157\) | 1.52920e12 | 1.27943 | 0.639714 | − | 0.768613i | \(-0.279053\pi\) | ||||
0.639714 | + | 0.768613i | \(0.279053\pi\) | |||||||
\(158\) | 3.46318e11 | 0.279809 | ||||||||
\(159\) | 9.46778e11 | 0.738863 | ||||||||
\(160\) | −2.15132e12 | −1.62198 | ||||||||
\(161\) | −5.04138e11 | −0.367288 | ||||||||
\(162\) | −2.42955e11 | −0.171078 | ||||||||
\(163\) | 2.42450e12 | 1.65040 | 0.825202 | − | 0.564838i | \(-0.191061\pi\) | ||||
0.825202 | + | 0.564838i | \(0.191061\pi\) | |||||||
\(164\) | −1.18674e12 | −0.781117 | ||||||||
\(165\) | −1.85899e12 | −1.18336 | ||||||||
\(166\) | −9.79244e10 | −0.0602971 | ||||||||
\(167\) | −2.70780e12 | −1.61315 | −0.806577 | − | 0.591129i | \(-0.798682\pi\) | ||||
−0.806577 | + | 0.591129i | \(0.798682\pi\) | |||||||
\(168\) | 2.16032e11 | 0.124542 | ||||||||
\(169\) | 1.37858e11 | 0.0769231 | ||||||||
\(170\) | 4.14883e12 | 2.24108 | ||||||||
\(171\) | 5.15994e11 | 0.269877 | ||||||||
\(172\) | 9.87412e11 | 0.500140 | ||||||||
\(173\) | 1.97019e12 | 0.966616 | 0.483308 | − | 0.875450i | \(-0.339435\pi\) | ||||
0.483308 | + | 0.875450i | \(0.339435\pi\) | |||||||
\(174\) | −4.37414e11 | −0.207908 | ||||||||
\(175\) | 4.03281e11 | 0.185737 | ||||||||
\(176\) | 1.84969e12 | 0.825620 | ||||||||
\(177\) | 1.68404e12 | 0.728615 | ||||||||
\(178\) | 4.69319e12 | 1.96860 | ||||||||
\(179\) | −8.09414e11 | −0.329215 | −0.164607 | − | 0.986359i | \(-0.552636\pi\) | ||||
−0.164607 | + | 0.986359i | \(0.552636\pi\) | |||||||
\(180\) | −1.41452e12 | −0.557971 | ||||||||
\(181\) | 2.39624e12 | 0.916850 | 0.458425 | − | 0.888733i | \(-0.348414\pi\) | ||||
0.458425 | + | 0.888733i | \(0.348414\pi\) | |||||||
\(182\) | 4.34818e11 | 0.161404 | ||||||||
\(183\) | −7.80902e11 | −0.281265 | ||||||||
\(184\) | 1.58665e12 | 0.554603 | ||||||||
\(185\) | 2.54157e11 | 0.0862297 | ||||||||
\(186\) | −1.75927e12 | −0.579444 | ||||||||
\(187\) | −6.25501e12 | −2.00032 | ||||||||
\(188\) | 5.22025e11 | 0.162115 | ||||||||
\(189\) | −2.41162e11 | −0.0727393 | ||||||||
\(190\) | 5.19597e12 | 1.52238 | ||||||||
\(191\) | −2.02981e12 | −0.577791 | −0.288896 | − | 0.957361i | \(-0.593288\pi\) | ||||
−0.288896 | + | 0.957361i | \(0.593288\pi\) | |||||||
\(192\) | 3.24170e12 | 0.896635 | ||||||||
\(193\) | −2.71671e12 | −0.730261 | −0.365130 | − | 0.930956i | \(-0.618976\pi\) | ||||
−0.365130 | + | 0.930956i | \(0.618976\pi\) | |||||||
\(194\) | −6.81450e12 | −1.78043 | ||||||||
\(195\) | −7.69940e11 | −0.195554 | ||||||||
\(196\) | 7.92947e11 | 0.195810 | ||||||||
\(197\) | 5.51146e12 | 1.32343 | 0.661717 | − | 0.749754i | \(-0.269828\pi\) | ||||
0.661717 | + | 0.749754i | \(0.269828\pi\) | |||||||
\(198\) | 3.68850e12 | 0.861374 | ||||||||
\(199\) | −4.57352e12 | −1.03886 | −0.519432 | − | 0.854512i | \(-0.673857\pi\) | ||||
−0.519432 | + | 0.854512i | \(0.673857\pi\) | |||||||
\(200\) | −1.26922e12 | −0.280461 | ||||||||
\(201\) | −2.61945e12 | −0.563160 | ||||||||
\(202\) | 3.81438e12 | 0.797980 | ||||||||
\(203\) | −4.34186e11 | −0.0883990 | ||||||||
\(204\) | −4.75950e12 | −0.943181 | ||||||||
\(205\) | 3.60768e12 | 0.695955 | ||||||||
\(206\) | −1.36151e13 | −2.55712 | ||||||||
\(207\) | −1.77122e12 | −0.323918 | ||||||||
\(208\) | 7.66090e11 | 0.136437 | ||||||||
\(209\) | −7.83373e12 | −1.35883 | ||||||||
\(210\) | −2.42846e12 | −0.410322 | ||||||||
\(211\) | 9.73284e12 | 1.60209 | 0.801044 | − | 0.598606i | \(-0.204279\pi\) | ||||
0.801044 | + | 0.598606i | \(0.204279\pi\) | |||||||
\(212\) | −1.09372e13 | −1.75412 | ||||||||
\(213\) | −2.57328e12 | −0.402160 | ||||||||
\(214\) | −2.44028e12 | −0.371675 | ||||||||
\(215\) | −3.00171e12 | −0.445612 | ||||||||
\(216\) | 7.58996e11 | 0.109836 | ||||||||
\(217\) | −1.74629e12 | −0.246370 | ||||||||
\(218\) | −1.31032e13 | −1.80247 | ||||||||
\(219\) | 4.71294e12 | 0.632192 | ||||||||
\(220\) | 2.14751e13 | 2.80938 | ||||||||
\(221\) | −2.59065e12 | −0.330560 | ||||||||
\(222\) | −5.04283e11 | −0.0627672 | ||||||||
\(223\) | −9.59844e12 | −1.16553 | −0.582766 | − | 0.812640i | \(-0.698029\pi\) | ||||
−0.582766 | + | 0.812640i | \(0.698029\pi\) | |||||||
\(224\) | 4.23703e12 | 0.501993 | ||||||||
\(225\) | 1.41687e12 | 0.163805 | ||||||||
\(226\) | −1.66017e13 | −1.87307 | ||||||||
\(227\) | −1.62487e13 | −1.78928 | −0.894638 | − | 0.446791i | \(-0.852567\pi\) | ||||
−0.894638 | + | 0.446791i | \(0.852567\pi\) | |||||||
\(228\) | −5.96076e12 | −0.640708 | ||||||||
\(229\) | −1.10665e13 | −1.16122 | −0.580612 | − | 0.814181i | \(-0.697186\pi\) | ||||
−0.580612 | + | 0.814181i | \(0.697186\pi\) | |||||||
\(230\) | −1.78359e13 | −1.82722 | ||||||||
\(231\) | 3.66128e12 | 0.366241 | ||||||||
\(232\) | 1.36649e12 | 0.133482 | ||||||||
\(233\) | 9.50085e12 | 0.906368 | 0.453184 | − | 0.891417i | \(-0.350288\pi\) | ||||
0.453184 | + | 0.891417i | \(0.350288\pi\) | |||||||
\(234\) | 1.52767e12 | 0.142345 | ||||||||
\(235\) | −1.58694e12 | −0.144440 | ||||||||
\(236\) | −1.94540e13 | −1.72979 | ||||||||
\(237\) | 1.20776e12 | 0.104922 | ||||||||
\(238\) | −8.17113e12 | −0.693600 | ||||||||
\(239\) | −8.95973e12 | −0.743201 | −0.371601 | − | 0.928393i | \(-0.621191\pi\) | ||||
−0.371601 | + | 0.928393i | \(0.621191\pi\) | |||||||
\(240\) | −4.27862e12 | −0.346850 | ||||||||
\(241\) | −2.13370e13 | −1.69060 | −0.845299 | − | 0.534293i | \(-0.820578\pi\) | ||||
−0.845299 | + | 0.534293i | \(0.820578\pi\) | |||||||
\(242\) | −3.61181e13 | −2.79731 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 9.02098e12 | 0.667743 | ||||||||
\(245\) | −2.41054e12 | −0.174462 | ||||||||
\(246\) | −7.15815e12 | −0.506591 | ||||||||
\(247\) | −3.24451e12 | −0.224551 | ||||||||
\(248\) | 5.49600e12 | 0.372017 | ||||||||
\(249\) | −3.41505e11 | −0.0226100 | ||||||||
\(250\) | −1.47662e13 | −0.956312 | ||||||||
\(251\) | 5.02959e12 | 0.318659 | 0.159330 | − | 0.987225i | \(-0.449067\pi\) | ||||
0.159330 | + | 0.987225i | \(0.449067\pi\) | |||||||
\(252\) | 2.78590e12 | 0.172688 | ||||||||
\(253\) | 2.68903e13 | 1.63092 | ||||||||
\(254\) | 7.59215e12 | 0.450588 | ||||||||
\(255\) | 1.44688e13 | 0.840351 | ||||||||
\(256\) | −1.47300e12 | −0.0837302 | ||||||||
\(257\) | 1.00594e13 | 0.559679 | 0.279840 | − | 0.960047i | \(-0.409719\pi\) | ||||
0.279840 | + | 0.960047i | \(0.409719\pi\) | |||||||
\(258\) | 5.95582e12 | 0.324365 | ||||||||
\(259\) | −5.00562e11 | −0.0266876 | ||||||||
\(260\) | 8.89435e12 | 0.464260 | ||||||||
\(261\) | −1.52545e12 | −0.0779606 | ||||||||
\(262\) | −1.36732e13 | −0.684248 | ||||||||
\(263\) | 3.66706e13 | 1.79705 | 0.898527 | − | 0.438919i | \(-0.144638\pi\) | ||||
0.898527 | + | 0.438919i | \(0.144638\pi\) | |||||||
\(264\) | −1.15230e13 | −0.553022 | ||||||||
\(265\) | 3.32488e13 | 1.56287 | ||||||||
\(266\) | −1.02335e13 | −0.471166 | ||||||||
\(267\) | 1.63672e13 | 0.738179 | ||||||||
\(268\) | 3.02599e13 | 1.33698 | ||||||||
\(269\) | 2.37943e13 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(270\) | −8.53205e12 | −0.361870 | ||||||||
\(271\) | 4.13886e13 | 1.72008 | 0.860042 | − | 0.510223i | \(-0.170437\pi\) | ||||
0.860042 | + | 0.510223i | \(0.170437\pi\) | |||||||
\(272\) | −1.43964e13 | −0.586308 | ||||||||
\(273\) | 1.51640e12 | 0.0605228 | ||||||||
\(274\) | −7.07425e13 | −2.76727 | ||||||||
\(275\) | −2.15107e13 | −0.824754 | ||||||||
\(276\) | 2.04611e13 | 0.769005 | ||||||||
\(277\) | 1.81620e12 | 0.0669150 | 0.0334575 | − | 0.999440i | \(-0.489348\pi\) | ||||
0.0334575 | + | 0.999440i | \(0.489348\pi\) | |||||||
\(278\) | −1.34137e13 | −0.484509 | ||||||||
\(279\) | −6.13534e12 | −0.217278 | ||||||||
\(280\) | 7.58656e12 | 0.263436 | ||||||||
\(281\) | −5.02144e13 | −1.70979 | −0.854896 | − | 0.518800i | \(-0.826379\pi\) | ||||
−0.854896 | + | 0.518800i | \(0.826379\pi\) | |||||||
\(282\) | 3.14872e12 | 0.105139 | ||||||||
\(283\) | 1.48728e13 | 0.487043 | 0.243521 | − | 0.969896i | \(-0.421697\pi\) | ||||
0.243521 | + | 0.969896i | \(0.421697\pi\) | |||||||
\(284\) | 2.97265e13 | 0.954758 | ||||||||
\(285\) | 1.81206e13 | 0.570854 | ||||||||
\(286\) | −2.31929e13 | −0.716706 | ||||||||
\(287\) | −7.10532e12 | −0.215394 | ||||||||
\(288\) | 1.48862e13 | 0.442716 | ||||||||
\(289\) | 1.44117e13 | 0.420511 | ||||||||
\(290\) | −1.53610e13 | −0.439776 | ||||||||
\(291\) | −2.37651e13 | −0.667618 | ||||||||
\(292\) | −5.44439e13 | −1.50087 | ||||||||
\(293\) | −3.58573e12 | −0.0970076 | −0.0485038 | − | 0.998823i | \(-0.515445\pi\) | ||||
−0.0485038 | + | 0.998823i | \(0.515445\pi\) | |||||||
\(294\) | 4.78286e12 | 0.126992 | ||||||||
\(295\) | 5.91397e13 | 1.54120 | ||||||||
\(296\) | 1.57539e12 | 0.0402980 | ||||||||
\(297\) | 1.28634e13 | 0.322995 | ||||||||
\(298\) | −4.80919e13 | −1.18545 | ||||||||
\(299\) | 1.11372e13 | 0.269516 | ||||||||
\(300\) | −1.63677e13 | −0.388884 | ||||||||
\(301\) | 5.91187e12 | 0.137914 | ||||||||
\(302\) | 3.01996e12 | 0.0691771 | ||||||||
\(303\) | 1.33024e13 | 0.299223 | ||||||||
\(304\) | −1.80300e13 | −0.398282 | ||||||||
\(305\) | −2.74236e13 | −0.594943 | ||||||||
\(306\) | −2.87081e13 | −0.611698 | ||||||||
\(307\) | 3.08147e13 | 0.644907 | 0.322454 | − | 0.946585i | \(-0.395492\pi\) | ||||
0.322454 | + | 0.946585i | \(0.395492\pi\) | |||||||
\(308\) | −4.22952e13 | −0.869484 | ||||||||
\(309\) | −4.74817e13 | −0.958860 | ||||||||
\(310\) | −6.17818e13 | −1.22566 | ||||||||
\(311\) | −6.43609e13 | −1.25441 | −0.627206 | − | 0.778853i | \(-0.715802\pi\) | ||||
−0.627206 | + | 0.778853i | \(0.715802\pi\) | |||||||
\(312\) | −4.77248e12 | −0.0913889 | ||||||||
\(313\) | −5.65228e13 | −1.06348 | −0.531740 | − | 0.846907i | \(-0.678462\pi\) | ||||
−0.531740 | + | 0.846907i | \(0.678462\pi\) | |||||||
\(314\) | −1.06553e14 | −1.96993 | ||||||||
\(315\) | −8.46909e12 | −0.153861 | ||||||||
\(316\) | −1.39521e13 | −0.249092 | ||||||||
\(317\) | −2.88898e13 | −0.506896 | −0.253448 | − | 0.967349i | \(-0.581565\pi\) | ||||
−0.253448 | + | 0.967349i | \(0.581565\pi\) | |||||||
\(318\) | −6.59704e13 | −1.13763 | ||||||||
\(319\) | 2.31591e13 | 0.392531 | ||||||||
\(320\) | 1.13841e14 | 1.89660 | ||||||||
\(321\) | −8.51030e12 | −0.139369 | ||||||||
\(322\) | 3.51277e13 | 0.565513 | ||||||||
\(323\) | 6.09710e13 | 0.964960 | ||||||||
\(324\) | 9.78788e12 | 0.152297 | ||||||||
\(325\) | −8.90911e12 | −0.136294 | ||||||||
\(326\) | −1.68936e14 | −2.54112 | ||||||||
\(327\) | −4.56965e13 | −0.675881 | ||||||||
\(328\) | 2.23622e13 | 0.325243 | ||||||||
\(329\) | 3.12549e12 | 0.0447034 | ||||||||
\(330\) | 1.29532e14 | 1.82201 | ||||||||
\(331\) | −9.09171e13 | −1.25774 | −0.628871 | − | 0.777510i | \(-0.716483\pi\) | ||||
−0.628871 | + | 0.777510i | \(0.716483\pi\) | |||||||
\(332\) | 3.94506e12 | 0.0536778 | ||||||||
\(333\) | −1.75865e12 | −0.0235362 | ||||||||
\(334\) | 1.88676e14 | 2.48377 | ||||||||
\(335\) | −9.19894e13 | −1.19122 | ||||||||
\(336\) | 8.42674e12 | 0.107348 | ||||||||
\(337\) | −1.09634e13 | −0.137398 | −0.0686989 | − | 0.997637i | \(-0.521885\pi\) | ||||
−0.0686989 | + | 0.997637i | \(0.521885\pi\) | |||||||
\(338\) | −9.60582e12 | −0.118438 | ||||||||
\(339\) | −5.78971e13 | −0.702358 | ||||||||
\(340\) | −1.67143e14 | −1.99506 | ||||||||
\(341\) | 9.31457e13 | 1.09399 | ||||||||
\(342\) | −3.59538e13 | −0.415529 | ||||||||
\(343\) | 4.74756e12 | 0.0539949 | ||||||||
\(344\) | −1.86061e13 | −0.208250 | ||||||||
\(345\) | −6.22013e13 | −0.685164 | ||||||||
\(346\) | −1.37280e14 | −1.48830 | ||||||||
\(347\) | 8.11014e13 | 0.865399 | 0.432700 | − | 0.901538i | \(-0.357561\pi\) | ||||
0.432700 | + | 0.901538i | \(0.357561\pi\) | |||||||
\(348\) | 1.76220e13 | 0.185084 | ||||||||
\(349\) | 1.60423e14 | 1.65854 | 0.829272 | − | 0.558846i | \(-0.188756\pi\) | ||||
0.829272 | + | 0.558846i | \(0.188756\pi\) | |||||||
\(350\) | −2.81001e13 | −0.285979 | ||||||||
\(351\) | 5.32765e12 | 0.0533761 | ||||||||
\(352\) | −2.26000e14 | −2.22907 | ||||||||
\(353\) | −6.62141e13 | −0.642968 | −0.321484 | − | 0.946915i | \(-0.604182\pi\) | ||||
−0.321484 | + | 0.946915i | \(0.604182\pi\) | |||||||
\(354\) | −1.17342e14 | −1.12185 | ||||||||
\(355\) | −9.03680e13 | −0.850666 | ||||||||
\(356\) | −1.89074e14 | −1.75249 | ||||||||
\(357\) | −2.84963e13 | −0.260083 | ||||||||
\(358\) | 5.63990e13 | 0.506891 | ||||||||
\(359\) | −2.92551e13 | −0.258930 | −0.129465 | − | 0.991584i | \(-0.541326\pi\) | ||||
−0.129465 | + | 0.991584i | \(0.541326\pi\) | |||||||
\(360\) | 2.66543e13 | 0.232329 | ||||||||
\(361\) | −4.01307e13 | −0.344498 | ||||||||
\(362\) | −1.66967e14 | −1.41167 | ||||||||
\(363\) | −1.25959e14 | −1.04892 | ||||||||
\(364\) | −1.75174e13 | −0.143685 | ||||||||
\(365\) | 1.65508e14 | 1.33724 | ||||||||
\(366\) | 5.44123e13 | 0.433063 | ||||||||
\(367\) | −1.50824e14 | −1.18252 | −0.591259 | − | 0.806482i | \(-0.701369\pi\) | ||||
−0.591259 | + | 0.806482i | \(0.701369\pi\) | |||||||
\(368\) | 6.18903e13 | 0.478035 | ||||||||
\(369\) | −2.49635e13 | −0.189960 | ||||||||
\(370\) | −1.77093e13 | −0.132768 | ||||||||
\(371\) | −6.54835e13 | −0.483699 | ||||||||
\(372\) | 7.08754e13 | 0.515834 | ||||||||
\(373\) | −2.04928e13 | −0.146962 | −0.0734808 | − | 0.997297i | \(-0.523411\pi\) | ||||
−0.0734808 | + | 0.997297i | \(0.523411\pi\) | |||||||
\(374\) | 4.35842e14 | 3.07989 | ||||||||
\(375\) | −5.14962e13 | −0.358594 | ||||||||
\(376\) | −9.83667e12 | −0.0675017 | ||||||||
\(377\) | 9.59184e12 | 0.0648671 | ||||||||
\(378\) | 1.68039e13 | 0.111997 | ||||||||
\(379\) | 2.04954e14 | 1.34629 | 0.673147 | − | 0.739509i | \(-0.264942\pi\) | ||||
0.673147 | + | 0.739509i | \(0.264942\pi\) | |||||||
\(380\) | −2.09329e14 | −1.35525 | ||||||||
\(381\) | 2.64771e13 | 0.168960 | ||||||||
\(382\) | 1.41434e14 | 0.889625 | ||||||||
\(383\) | 1.00545e14 | 0.623402 | 0.311701 | − | 0.950180i | \(-0.399101\pi\) | ||||
0.311701 | + | 0.950180i | \(0.399101\pi\) | |||||||
\(384\) | −1.00417e14 | −0.613741 | ||||||||
\(385\) | 1.28576e14 | 0.774689 | ||||||||
\(386\) | 1.89297e14 | 1.12438 | ||||||||
\(387\) | 2.07705e13 | 0.121629 | ||||||||
\(388\) | 2.74534e14 | 1.58497 | ||||||||
\(389\) | −6.01083e13 | −0.342146 | −0.171073 | − | 0.985258i | \(-0.554723\pi\) | ||||
−0.171073 | + | 0.985258i | \(0.554723\pi\) | |||||||
\(390\) | 5.36485e13 | 0.301094 | ||||||||
\(391\) | −2.09291e14 | −1.15819 | ||||||||
\(392\) | −1.49417e13 | −0.0815319 | ||||||||
\(393\) | −4.76844e13 | −0.256577 | ||||||||
\(394\) | −3.84032e14 | −2.03769 | ||||||||
\(395\) | 4.24139e13 | 0.221934 | ||||||||
\(396\) | −1.48598e14 | −0.766813 | ||||||||
\(397\) | −1.41729e14 | −0.721293 | −0.360646 | − | 0.932703i | \(-0.617444\pi\) | ||||
−0.360646 | + | 0.932703i | \(0.617444\pi\) | |||||||
\(398\) | 3.18678e14 | 1.59954 | ||||||||
\(399\) | −3.56885e13 | −0.176676 | ||||||||
\(400\) | −4.95086e13 | −0.241741 | ||||||||
\(401\) | −1.34314e14 | −0.646884 | −0.323442 | − | 0.946248i | \(-0.604840\pi\) | ||||
−0.323442 | + | 0.946248i | \(0.604840\pi\) | |||||||
\(402\) | 1.82520e14 | 0.867096 | ||||||||
\(403\) | 3.85783e13 | 0.180786 | ||||||||
\(404\) | −1.53669e14 | −0.710378 | ||||||||
\(405\) | −2.97549e13 | −0.135693 | ||||||||
\(406\) | 3.02535e13 | 0.136108 | ||||||||
\(407\) | 2.66996e13 | 0.118505 | ||||||||
\(408\) | 8.96847e13 | 0.392724 | ||||||||
\(409\) | 1.73873e14 | 0.751199 | 0.375600 | − | 0.926782i | \(-0.377437\pi\) | ||||
0.375600 | + | 0.926782i | \(0.377437\pi\) | |||||||
\(410\) | −2.51379e14 | −1.07156 | ||||||||
\(411\) | −2.46710e14 | −1.03766 | ||||||||
\(412\) | 5.48509e14 | 2.27640 | ||||||||
\(413\) | −1.16476e14 | −0.476991 | ||||||||
\(414\) | 1.23416e14 | 0.498736 | ||||||||
\(415\) | −1.19929e13 | −0.0478255 | ||||||||
\(416\) | −9.36026e13 | −0.368362 | ||||||||
\(417\) | −4.67793e13 | −0.181679 | ||||||||
\(418\) | 5.45845e14 | 2.09218 | ||||||||
\(419\) | 3.03381e14 | 1.14766 | 0.573828 | − | 0.818976i | \(-0.305458\pi\) | ||||
0.573828 | + | 0.818976i | \(0.305458\pi\) | |||||||
\(420\) | 9.78350e13 | 0.365278 | ||||||||
\(421\) | 3.70294e13 | 0.136457 | 0.0682284 | − | 0.997670i | \(-0.478265\pi\) | ||||
0.0682284 | + | 0.997670i | \(0.478265\pi\) | |||||||
\(422\) | −6.78173e14 | −2.46673 | ||||||||
\(423\) | 1.09810e13 | 0.0394247 | ||||||||
\(424\) | 2.06093e14 | 0.730383 | ||||||||
\(425\) | 1.67420e14 | 0.585692 | ||||||||
\(426\) | 1.79303e14 | 0.619206 | ||||||||
\(427\) | 5.40108e13 | 0.184131 | ||||||||
\(428\) | 9.83110e13 | 0.330873 | ||||||||
\(429\) | −8.08835e13 | −0.268748 | ||||||||
\(430\) | 2.09156e14 | 0.686109 | ||||||||
\(431\) | −2.62477e14 | −0.850094 | −0.425047 | − | 0.905171i | \(-0.639742\pi\) | ||||
−0.425047 | + | 0.905171i | \(0.639742\pi\) | |||||||
\(432\) | 2.96062e13 | 0.0946720 | ||||||||
\(433\) | 3.32199e12 | 0.0104885 | 0.00524427 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524427 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(434\) | 1.21679e14 | 0.379335 | ||||||||
\(435\) | −5.35705e13 | −0.164905 | ||||||||
\(436\) | 5.27886e14 | 1.60459 | ||||||||
\(437\) | −2.62114e14 | −0.786761 | ||||||||
\(438\) | −3.28392e14 | −0.973386 | ||||||||
\(439\) | 3.33043e14 | 0.974866 | 0.487433 | − | 0.873160i | \(-0.337933\pi\) | ||||
0.487433 | + | 0.873160i | \(0.337933\pi\) | |||||||
\(440\) | −4.04661e14 | −1.16977 | ||||||||
\(441\) | 1.66799e13 | 0.0476190 | ||||||||
\(442\) | 1.80513e14 | 0.508963 | ||||||||
\(443\) | −5.42968e14 | −1.51201 | −0.756003 | − | 0.654568i | \(-0.772850\pi\) | ||||
−0.756003 | + | 0.654568i | \(0.772850\pi\) | |||||||
\(444\) | 2.03160e13 | 0.0558767 | ||||||||
\(445\) | 5.74779e14 | 1.56143 | ||||||||
\(446\) | 6.68808e14 | 1.79457 | ||||||||
\(447\) | −1.67717e14 | −0.444515 | ||||||||
\(448\) | −2.24211e14 | −0.586985 | ||||||||
\(449\) | 2.68562e14 | 0.694528 | 0.347264 | − | 0.937767i | \(-0.387111\pi\) | ||||
0.347264 | + | 0.937767i | \(0.387111\pi\) | |||||||
\(450\) | −9.87258e13 | −0.252210 | ||||||||
\(451\) | 3.78992e14 | 0.956444 | ||||||||
\(452\) | 6.68828e14 | 1.66745 | ||||||||
\(453\) | 1.05319e13 | 0.0259398 | ||||||||
\(454\) | 1.13219e15 | 2.75495 | ||||||||
\(455\) | 5.32526e13 | 0.128020 | ||||||||
\(456\) | 1.12320e14 | 0.266779 | ||||||||
\(457\) | −2.97540e14 | −0.698241 | −0.349121 | − | 0.937078i | \(-0.613520\pi\) | ||||
−0.349121 | + | 0.937078i | \(0.613520\pi\) | |||||||
\(458\) | 7.71102e14 | 1.78793 | ||||||||
\(459\) | −1.00118e14 | −0.229372 | ||||||||
\(460\) | 7.18550e14 | 1.62663 | ||||||||
\(461\) | 7.77771e14 | 1.73979 | 0.869895 | − | 0.493237i | \(-0.164186\pi\) | ||||
0.869895 | + | 0.493237i | \(0.164186\pi\) | |||||||
\(462\) | −2.55114e14 | −0.563902 | ||||||||
\(463\) | −3.15118e14 | −0.688301 | −0.344151 | − | 0.938914i | \(-0.611833\pi\) | ||||
−0.344151 | + | 0.938914i | \(0.611833\pi\) | |||||||
\(464\) | 5.33026e13 | 0.115053 | ||||||||
\(465\) | −2.15460e14 | −0.459595 | ||||||||
\(466\) | −6.62008e14 | −1.39553 | ||||||||
\(467\) | −2.77897e12 | −0.00578951 | −0.00289475 | − | 0.999996i | \(-0.500921\pi\) | ||||
−0.00289475 | + | 0.999996i | \(0.500921\pi\) | |||||||
\(468\) | −6.15450e13 | −0.126719 | ||||||||
\(469\) | 1.81173e14 | 0.368675 | ||||||||
\(470\) | 1.10576e14 | 0.222394 | ||||||||
\(471\) | −3.71595e14 | −0.738678 | ||||||||
\(472\) | 3.66577e14 | 0.720252 | ||||||||
\(473\) | −3.15335e14 | −0.612400 | ||||||||
\(474\) | −8.41553e13 | −0.161548 | ||||||||
\(475\) | 2.09676e14 | 0.397864 | ||||||||
\(476\) | 3.29189e14 | 0.617457 | ||||||||
\(477\) | −2.30067e14 | −0.426583 | ||||||||
\(478\) | 6.24303e14 | 1.14431 | ||||||||
\(479\) | −6.67118e14 | −1.20881 | −0.604404 | − | 0.796678i | \(-0.706589\pi\) | ||||
−0.604404 | + | 0.796678i | \(0.706589\pi\) | |||||||
\(480\) | 5.22771e14 | 0.936450 | ||||||||
\(481\) | 1.10582e13 | 0.0195833 | ||||||||
\(482\) | 1.48674e15 | 2.60301 | ||||||||
\(483\) | 1.22506e14 | 0.212054 | ||||||||
\(484\) | 1.45508e15 | 2.49022 | ||||||||
\(485\) | −8.34578e14 | −1.41217 | ||||||||
\(486\) | 5.90381e13 | 0.0987717 | ||||||||
\(487\) | −9.81062e14 | −1.62288 | −0.811441 | − | 0.584434i | \(-0.801317\pi\) | ||||
−0.811441 | + | 0.584434i | \(0.801317\pi\) | |||||||
\(488\) | −1.69985e14 | −0.278036 | ||||||||
\(489\) | −5.89153e14 | −0.952861 | ||||||||
\(490\) | 1.67964e14 | 0.268619 | ||||||||
\(491\) | 9.80830e13 | 0.155112 | 0.0775560 | − | 0.996988i | \(-0.475288\pi\) | ||||
0.0775560 | + | 0.996988i | \(0.475288\pi\) | |||||||
\(492\) | 2.88379e14 | 0.450978 | ||||||||
\(493\) | −1.80251e14 | −0.278752 | ||||||||
\(494\) | 2.26073e14 | 0.345741 | ||||||||
\(495\) | 4.51735e14 | 0.683211 | ||||||||
\(496\) | 2.14382e14 | 0.320656 | ||||||||
\(497\) | 1.77980e14 | 0.263276 | ||||||||
\(498\) | 2.37956e13 | 0.0348126 | ||||||||
\(499\) | 6.25519e14 | 0.905081 | 0.452540 | − | 0.891744i | \(-0.350518\pi\) | ||||
0.452540 | + | 0.891744i | \(0.350518\pi\) | |||||||
\(500\) | 5.94884e14 | 0.851329 | ||||||||
\(501\) | 6.57995e14 | 0.931355 | ||||||||
\(502\) | −3.50456e14 | −0.490639 | ||||||||
\(503\) | 1.22254e15 | 1.69293 | 0.846467 | − | 0.532441i | \(-0.178725\pi\) | ||||
0.846467 | + | 0.532441i | \(0.178725\pi\) | |||||||
\(504\) | −5.24957e13 | −0.0719044 | ||||||||
\(505\) | 4.67152e14 | 0.632929 | ||||||||
\(506\) | −1.87369e15 | −2.51113 | ||||||||
\(507\) | −3.34996e13 | −0.0444116 | ||||||||
\(508\) | −3.05863e14 | −0.401123 | ||||||||
\(509\) | −8.89866e14 | −1.15445 | −0.577227 | − | 0.816584i | \(-0.695865\pi\) | ||||
−0.577227 | + | 0.816584i | \(0.695865\pi\) | |||||||
\(510\) | −1.00817e15 | −1.29389 | ||||||||
\(511\) | −3.25969e14 | −0.413867 | ||||||||
\(512\) | −7.43676e14 | −0.934111 | ||||||||
\(513\) | −1.25386e14 | −0.155813 | ||||||||
\(514\) | −7.00926e14 | −0.861737 | ||||||||
\(515\) | −1.66746e15 | −2.02822 | ||||||||
\(516\) | −2.39941e14 | −0.288756 | ||||||||
\(517\) | −1.66711e14 | −0.198503 | ||||||||
\(518\) | 3.48785e13 | 0.0410908 | ||||||||
\(519\) | −4.78756e14 | −0.558076 | ||||||||
\(520\) | −1.67599e14 | −0.193309 | ||||||||
\(521\) | 5.21685e14 | 0.595389 | 0.297694 | − | 0.954661i | \(-0.403782\pi\) | ||||
0.297694 | + | 0.954661i | \(0.403782\pi\) | |||||||
\(522\) | 1.06292e14 | 0.120036 | ||||||||
\(523\) | 3.05092e14 | 0.340935 | 0.170468 | − | 0.985363i | \(-0.445472\pi\) | ||||
0.170468 | + | 0.985363i | \(0.445472\pi\) | |||||||
\(524\) | 5.50850e14 | 0.609132 | ||||||||
\(525\) | −9.79972e13 | −0.107235 | ||||||||
\(526\) | −2.55516e15 | −2.76692 | ||||||||
\(527\) | −7.24965e14 | −0.776889 | ||||||||
\(528\) | −4.49476e14 | −0.476672 | ||||||||
\(529\) | −5.30669e13 | −0.0556951 | ||||||||
\(530\) | −2.31674e15 | −2.40635 | ||||||||
\(531\) | −4.09221e14 | −0.420666 | ||||||||
\(532\) | 4.12274e14 | 0.419442 | ||||||||
\(533\) | 1.56968e14 | 0.158056 | ||||||||
\(534\) | −1.14044e15 | −1.13657 | ||||||||
\(535\) | −2.98863e14 | −0.294800 | ||||||||
\(536\) | −5.70196e14 | −0.556696 | ||||||||
\(537\) | 1.96688e14 | 0.190072 | ||||||||
\(538\) | −1.65796e15 | −1.58588 | ||||||||
\(539\) | −2.53231e14 | −0.239761 | ||||||||
\(540\) | 3.43729e14 | 0.322145 | ||||||||
\(541\) | 1.13529e15 | 1.05323 | 0.526613 | − | 0.850105i | \(-0.323462\pi\) | ||||
0.526613 | + | 0.850105i | \(0.323462\pi\) | |||||||
\(542\) | −2.88391e15 | −2.64841 | ||||||||
\(543\) | −5.82287e14 | −0.529344 | ||||||||
\(544\) | 1.75899e15 | 1.58295 | ||||||||
\(545\) | −1.60476e15 | −1.42965 | ||||||||
\(546\) | −1.05661e14 | −0.0931868 | ||||||||
\(547\) | 7.88321e14 | 0.688292 | 0.344146 | − | 0.938916i | \(-0.388168\pi\) | ||||
0.344146 | + | 0.938916i | \(0.388168\pi\) | |||||||
\(548\) | 2.84999e15 | 2.46349 | ||||||||
\(549\) | 1.89759e14 | 0.162388 | ||||||||
\(550\) | 1.49884e15 | 1.26987 | ||||||||
\(551\) | −2.25744e14 | −0.189358 | ||||||||
\(552\) | −3.85555e14 | −0.320200 | ||||||||
\(553\) | −8.35343e13 | −0.0686873 | ||||||||
\(554\) | −1.26550e14 | −0.103029 | ||||||||
\(555\) | −6.17601e13 | −0.0497847 | ||||||||
\(556\) | 5.40395e14 | 0.431320 | ||||||||
\(557\) | 7.96205e14 | 0.629247 | 0.314624 | − | 0.949217i | \(-0.398122\pi\) | ||||
0.314624 | + | 0.949217i | \(0.398122\pi\) | |||||||
\(558\) | 4.27503e14 | 0.334542 | ||||||||
\(559\) | −1.30603e14 | −0.101201 | ||||||||
\(560\) | 2.95929e14 | 0.227067 | ||||||||
\(561\) | 1.51997e15 | 1.15489 | ||||||||
\(562\) | 3.49888e15 | 2.63256 | ||||||||
\(563\) | 1.39446e15 | 1.03898 | 0.519492 | − | 0.854475i | \(-0.326121\pi\) | ||||
0.519492 | + | 0.854475i | \(0.326121\pi\) | |||||||
\(564\) | −1.26852e14 | −0.0935970 | ||||||||
\(565\) | −2.03322e15 | −1.48566 | ||||||||
\(566\) | −1.03632e15 | −0.749899 | ||||||||
\(567\) | 5.86024e13 | 0.0419961 | ||||||||
\(568\) | −5.60146e14 | −0.397544 | ||||||||
\(569\) | −1.12310e14 | −0.0789407 | −0.0394704 | − | 0.999221i | \(-0.512567\pi\) | ||||
−0.0394704 | + | 0.999221i | \(0.512567\pi\) | |||||||
\(570\) | −1.26262e15 | −0.878944 | ||||||||
\(571\) | −1.55142e15 | −1.06962 | −0.534811 | − | 0.844972i | \(-0.679617\pi\) | ||||
−0.534811 | + | 0.844972i | \(0.679617\pi\) | |||||||
\(572\) | 9.34367e14 | 0.638027 | ||||||||
\(573\) | 4.93243e14 | 0.333588 | ||||||||
\(574\) | 4.95090e14 | 0.331642 | ||||||||
\(575\) | −7.19741e14 | −0.477533 | ||||||||
\(576\) | −7.87732e14 | −0.517672 | ||||||||
\(577\) | 1.01495e15 | 0.660658 | 0.330329 | − | 0.943866i | \(-0.392840\pi\) | ||||
0.330329 | + | 0.943866i | \(0.392840\pi\) | |||||||
\(578\) | −1.00419e15 | −0.647460 | ||||||||
\(579\) | 6.60160e14 | 0.421616 | ||||||||
\(580\) | 6.18847e14 | 0.391498 | ||||||||
\(581\) | 2.36200e13 | 0.0148017 | ||||||||
\(582\) | 1.65592e15 | 1.02793 | ||||||||
\(583\) | 3.49284e15 | 2.14784 | ||||||||
\(584\) | 1.02590e15 | 0.624936 | ||||||||
\(585\) | 1.87096e14 | 0.112903 | ||||||||
\(586\) | 2.49849e14 | 0.149362 | ||||||||
\(587\) | −1.86828e14 | −0.110645 | −0.0553226 | − | 0.998469i | \(-0.517619\pi\) | ||||
−0.0553226 | + | 0.998469i | \(0.517619\pi\) | |||||||
\(588\) | −1.92686e14 | −0.113051 | ||||||||
\(589\) | −9.07941e14 | −0.527744 | ||||||||
\(590\) | −4.12078e15 | −2.37298 | ||||||||
\(591\) | −1.33928e15 | −0.764085 | ||||||||
\(592\) | 6.14512e13 | 0.0347345 | ||||||||
\(593\) | −9.63033e13 | −0.0539312 | −0.0269656 | − | 0.999636i | \(-0.508584\pi\) | ||||
−0.0269656 | + | 0.999636i | \(0.508584\pi\) | |||||||
\(594\) | −8.96306e14 | −0.497314 | ||||||||
\(595\) | −1.00073e15 | −0.550139 | ||||||||
\(596\) | 1.93747e15 | 1.05531 | ||||||||
\(597\) | 1.11137e15 | 0.599789 | ||||||||
\(598\) | −7.76027e14 | −0.414973 | ||||||||
\(599\) | −3.14151e15 | −1.66453 | −0.832264 | − | 0.554380i | \(-0.812956\pi\) | ||||
−0.832264 | + | 0.554380i | \(0.812956\pi\) | |||||||
\(600\) | 3.08421e14 | 0.161924 | ||||||||
\(601\) | 1.48261e15 | 0.771288 | 0.385644 | − | 0.922648i | \(-0.373979\pi\) | ||||
0.385644 | + | 0.922648i | \(0.373979\pi\) | |||||||
\(602\) | −4.11932e14 | −0.212346 | ||||||||
\(603\) | 6.36526e14 | 0.325140 | ||||||||
\(604\) | −1.21664e14 | −0.0615829 | ||||||||
\(605\) | −4.42342e15 | −2.21873 | ||||||||
\(606\) | −9.26895e14 | −0.460714 | ||||||||
\(607\) | 2.41052e15 | 1.18733 | 0.593666 | − | 0.804711i | \(-0.297680\pi\) | ||||
0.593666 | + | 0.804711i | \(0.297680\pi\) | |||||||
\(608\) | 2.20294e15 | 1.07531 | ||||||||
\(609\) | 1.05507e14 | 0.0510372 | ||||||||
\(610\) | 1.91084e15 | 0.916032 | ||||||||
\(611\) | −6.90469e13 | −0.0328033 | ||||||||
\(612\) | 1.15656e15 | 0.544546 | ||||||||
\(613\) | −3.43178e15 | −1.60135 | −0.800676 | − | 0.599097i | \(-0.795526\pi\) | ||||
−0.800676 | + | 0.599097i | \(0.795526\pi\) | |||||||
\(614\) | −2.14713e15 | −0.992963 | ||||||||
\(615\) | −8.76665e14 | −0.401810 | ||||||||
\(616\) | 7.96981e14 | 0.362038 | ||||||||
\(617\) | 1.08854e15 | 0.490092 | 0.245046 | − | 0.969512i | \(-0.421197\pi\) | ||||
0.245046 | + | 0.969512i | \(0.421197\pi\) | |||||||
\(618\) | 3.30847e15 | 1.47636 | ||||||||
\(619\) | 1.12768e15 | 0.498754 | 0.249377 | − | 0.968406i | \(-0.419774\pi\) | ||||
0.249377 | + | 0.968406i | \(0.419774\pi\) | |||||||
\(620\) | 2.48899e15 | 1.09111 | ||||||||
\(621\) | 4.30406e14 | 0.187014 | ||||||||
\(622\) | 4.48459e15 | 1.93142 | ||||||||
\(623\) | −1.13203e15 | −0.483251 | ||||||||
\(624\) | −1.86160e14 | −0.0787718 | ||||||||
\(625\) | −2.98006e15 | −1.24993 | ||||||||
\(626\) | 3.93844e15 | 1.63744 | ||||||||
\(627\) | 1.90360e15 | 0.784519 | ||||||||
\(628\) | 4.29267e15 | 1.75368 | ||||||||
\(629\) | −2.07806e14 | −0.0841550 | ||||||||
\(630\) | 5.90116e14 | 0.236900 | ||||||||
\(631\) | 4.31662e14 | 0.171784 | 0.0858919 | − | 0.996304i | \(-0.472626\pi\) | ||||
0.0858919 | + | 0.996304i | \(0.472626\pi\) | |||||||
\(632\) | 2.62903e14 | 0.103717 | ||||||||
\(633\) | −2.36508e15 | −0.924965 | ||||||||
\(634\) | 2.01301e15 | 0.780467 | ||||||||
\(635\) | 9.29819e14 | 0.357390 | ||||||||
\(636\) | 2.65774e15 | 1.01274 | ||||||||
\(637\) | −1.04881e14 | −0.0396214 | ||||||||
\(638\) | −1.61370e15 | −0.604379 | ||||||||
\(639\) | 6.25307e14 | 0.232187 | ||||||||
\(640\) | −3.52643e15 | −1.29821 | ||||||||
\(641\) | 2.80860e15 | 1.02511 | 0.512555 | − | 0.858654i | \(-0.328699\pi\) | ||||
0.512555 | + | 0.858654i | \(0.328699\pi\) | |||||||
\(642\) | 5.92988e14 | 0.214587 | ||||||||
\(643\) | 5.14744e15 | 1.84685 | 0.923424 | − | 0.383781i | \(-0.125378\pi\) | ||||
0.923424 | + | 0.383781i | \(0.125378\pi\) | |||||||
\(644\) | −1.41518e15 | −0.503432 | ||||||||
\(645\) | 7.29416e14 | 0.257274 | ||||||||
\(646\) | −4.24838e15 | −1.48575 | ||||||||
\(647\) | −4.79076e15 | −1.66123 | −0.830617 | − | 0.556844i | \(-0.812012\pi\) | ||||
−0.830617 | + | 0.556844i | \(0.812012\pi\) | |||||||
\(648\) | −1.84436e14 | −0.0634137 | ||||||||
\(649\) | 6.21272e15 | 2.11805 | ||||||||
\(650\) | 6.20776e14 | 0.209851 | ||||||||
\(651\) | 4.24348e14 | 0.142242 | ||||||||
\(652\) | 6.80590e15 | 2.26216 | ||||||||
\(653\) | −4.82004e15 | −1.58865 | −0.794324 | − | 0.607494i | \(-0.792175\pi\) | ||||
−0.794324 | + | 0.607494i | \(0.792175\pi\) | |||||||
\(654\) | 3.18408e15 | 1.04065 | ||||||||
\(655\) | −1.67457e15 | −0.542722 | ||||||||
\(656\) | 8.72282e14 | 0.280340 | ||||||||
\(657\) | −1.14524e15 | −0.364996 | ||||||||
\(658\) | −2.17780e14 | −0.0688297 | ||||||||
\(659\) | −2.71767e15 | −0.851779 | −0.425890 | − | 0.904775i | \(-0.640039\pi\) | ||||
−0.425890 | + | 0.904775i | \(0.640039\pi\) | |||||||
\(660\) | −5.21844e15 | −1.62199 | ||||||||
\(661\) | −5.37344e14 | −0.165632 | −0.0828160 | − | 0.996565i | \(-0.526391\pi\) | ||||
−0.0828160 | + | 0.996565i | \(0.526391\pi\) | |||||||
\(662\) | 6.33499e15 | 1.93654 | ||||||||
\(663\) | 6.29527e14 | 0.190849 | ||||||||
\(664\) | −7.43380e13 | −0.0223505 | ||||||||
\(665\) | −1.25330e15 | −0.373712 | ||||||||
\(666\) | 1.22541e14 | 0.0362387 | ||||||||
\(667\) | 7.74898e14 | 0.227275 | ||||||||
\(668\) | −7.60116e15 | −2.21110 | ||||||||
\(669\) | 2.33242e15 | 0.672920 | ||||||||
\(670\) | 6.40971e15 | 1.83412 | ||||||||
\(671\) | −2.88089e15 | −0.817623 | ||||||||
\(672\) | −1.02960e15 | −0.289826 | ||||||||
\(673\) | −4.27385e15 | −1.19326 | −0.596632 | − | 0.802515i | \(-0.703495\pi\) | ||||
−0.596632 | + | 0.802515i | \(0.703495\pi\) | |||||||
\(674\) | 7.63915e14 | 0.211551 | ||||||||
\(675\) | −3.44299e14 | −0.0945726 | ||||||||
\(676\) | 3.86988e14 | 0.105436 | ||||||||
\(677\) | −1.08439e15 | −0.293053 | −0.146527 | − | 0.989207i | \(-0.546809\pi\) | ||||
−0.146527 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(678\) | 4.03420e15 | 1.08142 | ||||||||
\(679\) | 1.64370e15 | 0.437058 | ||||||||
\(680\) | 3.14953e15 | 0.830705 | ||||||||
\(681\) | 3.94844e15 | 1.03304 | ||||||||
\(682\) | −6.49028e15 | −1.68442 | ||||||||
\(683\) | −4.17016e15 | −1.07359 | −0.536796 | − | 0.843712i | \(-0.680366\pi\) | ||||
−0.536796 | + | 0.843712i | \(0.680366\pi\) | |||||||
\(684\) | 1.44846e15 | 0.369913 | ||||||||
\(685\) | −8.66391e15 | −2.19490 | ||||||||
\(686\) | −3.30804e14 | −0.0831359 | ||||||||
\(687\) | 2.68916e15 | 0.670432 | ||||||||
\(688\) | −7.25768e14 | −0.179499 | ||||||||
\(689\) | 1.44663e15 | 0.354938 | ||||||||
\(690\) | 4.33411e15 | 1.05495 | ||||||||
\(691\) | −1.29754e15 | −0.313323 | −0.156661 | − | 0.987652i | \(-0.550073\pi\) | ||||
−0.156661 | + | 0.987652i | \(0.550073\pi\) | |||||||
\(692\) | 5.53059e15 | 1.32491 | ||||||||
\(693\) | −8.89692e14 | −0.211450 | ||||||||
\(694\) | −5.65105e15 | −1.33245 | ||||||||
\(695\) | −1.64279e15 | −0.384296 | ||||||||
\(696\) | −3.32057e14 | −0.0770658 | ||||||||
\(697\) | −2.94975e15 | −0.679211 | ||||||||
\(698\) | −1.11781e16 | −2.55366 | ||||||||
\(699\) | −2.30871e15 | −0.523292 | ||||||||
\(700\) | 1.13206e15 | 0.254584 | ||||||||
\(701\) | 1.60609e15 | 0.358361 | 0.179180 | − | 0.983816i | \(-0.442655\pi\) | ||||
0.179180 | + | 0.983816i | \(0.442655\pi\) | |||||||
\(702\) | −3.71224e14 | −0.0821830 | ||||||||
\(703\) | −2.60255e14 | −0.0571669 | ||||||||
\(704\) | 1.19592e16 | 2.60647 | ||||||||
\(705\) | 3.85627e14 | 0.0833926 | ||||||||
\(706\) | 4.61372e15 | 0.989977 | ||||||||
\(707\) | −9.20055e14 | −0.195888 | ||||||||
\(708\) | 4.72732e15 | 0.998693 | ||||||||
\(709\) | −6.62938e15 | −1.38969 | −0.694847 | − | 0.719158i | \(-0.744528\pi\) | ||||
−0.694847 | + | 0.719158i | \(0.744528\pi\) | |||||||
\(710\) | 6.29674e15 | 1.30977 | ||||||||
\(711\) | −2.93486e14 | −0.0605765 | ||||||||
\(712\) | 3.56277e15 | 0.729706 | ||||||||
\(713\) | 3.11663e15 | 0.633421 | ||||||||
\(714\) | 1.98559e15 | 0.400450 | ||||||||
\(715\) | −2.84045e15 | −0.568466 | ||||||||
\(716\) | −2.27214e15 | −0.451245 | ||||||||
\(717\) | 2.17721e15 | 0.429088 | ||||||||
\(718\) | 2.03846e15 | 0.398674 | ||||||||
\(719\) | 8.59398e15 | 1.66796 | 0.833979 | − | 0.551795i | \(-0.186057\pi\) | ||||
0.833979 | + | 0.551795i | \(0.186057\pi\) | |||||||
\(720\) | 1.03970e15 | 0.200254 | ||||||||
\(721\) | 3.28406e15 | 0.627721 | ||||||||
\(722\) | 2.79626e15 | 0.530423 | ||||||||
\(723\) | 5.18490e15 | 0.976067 | ||||||||
\(724\) | 6.72658e15 | 1.25670 | ||||||||
\(725\) | −6.19873e14 | −0.114933 | ||||||||
\(726\) | 8.77670e15 | 1.61503 | ||||||||
\(727\) | −4.63477e15 | −0.846426 | −0.423213 | − | 0.906030i | \(-0.639098\pi\) | ||||
−0.423213 | + | 0.906030i | \(0.639098\pi\) | |||||||
\(728\) | 3.30086e14 | 0.0598281 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −1.15324e16 | −2.05894 | ||||||||
\(731\) | 2.45429e15 | 0.434891 | ||||||||
\(732\) | −2.19210e15 | −0.385522 | ||||||||
\(733\) | 9.26638e15 | 1.61748 | 0.808739 | − | 0.588168i | \(-0.200151\pi\) | ||||
0.808739 | + | 0.588168i | \(0.200151\pi\) | |||||||
\(734\) | 1.05093e16 | 1.82072 | ||||||||
\(735\) | 5.85761e14 | 0.100726 | ||||||||
\(736\) | −7.56189e15 | −1.29063 | ||||||||
\(737\) | −9.66364e15 | −1.63708 | ||||||||
\(738\) | 1.73943e15 | 0.292480 | ||||||||
\(739\) | −1.35050e15 | −0.225398 | −0.112699 | − | 0.993629i | \(-0.535950\pi\) | ||||
−0.112699 | + | 0.993629i | \(0.535950\pi\) | |||||||
\(740\) | 7.13452e14 | 0.118193 | ||||||||
\(741\) | 7.88415e14 | 0.129645 | ||||||||
\(742\) | 4.56282e15 | 0.744751 | ||||||||
\(743\) | −1.24892e15 | −0.202347 | −0.101173 | − | 0.994869i | \(-0.532260\pi\) | ||||
−0.101173 | + | 0.994869i | \(0.532260\pi\) | |||||||
\(744\) | −1.33553e15 | −0.214784 | ||||||||
\(745\) | −5.88987e15 | −0.940256 | ||||||||
\(746\) | 1.42792e15 | 0.226277 | ||||||||
\(747\) | 8.29856e13 | 0.0130539 | ||||||||
\(748\) | −1.75587e16 | −2.74178 | ||||||||
\(749\) | 5.88612e14 | 0.0912386 | ||||||||
\(750\) | 3.58819e15 | 0.552127 | ||||||||
\(751\) | 9.42935e15 | 1.44033 | 0.720165 | − | 0.693803i | \(-0.244066\pi\) | ||||
0.720165 | + | 0.693803i | \(0.244066\pi\) | |||||||
\(752\) | −3.83699e14 | −0.0581825 | ||||||||
\(753\) | −1.22219e15 | −0.183978 | ||||||||
\(754\) | −6.68348e14 | −0.0998758 | ||||||||
\(755\) | 3.69857e14 | 0.0548688 | ||||||||
\(756\) | −6.76975e14 | −0.0997017 | ||||||||
\(757\) | −3.10111e15 | −0.453408 | −0.226704 | − | 0.973964i | \(-0.572795\pi\) | ||||
−0.226704 | + | 0.973964i | \(0.572795\pi\) | |||||||
\(758\) | −1.42809e16 | −2.07289 | ||||||||
\(759\) | −6.53435e15 | −0.941613 | ||||||||
\(760\) | 3.94445e15 | 0.564302 | ||||||||
\(761\) | 7.93065e15 | 1.12640 | 0.563201 | − | 0.826320i | \(-0.309570\pi\) | ||||
0.563201 | + | 0.826320i | \(0.309570\pi\) | |||||||
\(762\) | −1.84489e15 | −0.260147 | ||||||||
\(763\) | 3.16058e15 | 0.442468 | ||||||||
\(764\) | −5.69794e15 | −0.791963 | ||||||||
\(765\) | −3.51591e15 | −0.485177 | ||||||||
\(766\) | −7.00587e15 | −0.959851 | ||||||||
\(767\) | 2.57313e15 | 0.350015 | ||||||||
\(768\) | 3.57939e14 | 0.0483417 | ||||||||
\(769\) | −8.90447e15 | −1.19402 | −0.597012 | − | 0.802232i | \(-0.703646\pi\) | ||||
−0.597012 | + | 0.802232i | \(0.703646\pi\) | |||||||
\(770\) | −8.95905e15 | −1.19279 | ||||||||
\(771\) | −2.44443e15 | −0.323131 | ||||||||
\(772\) | −7.62618e15 | −1.00095 | ||||||||
\(773\) | −2.52946e15 | −0.329640 | −0.164820 | − | 0.986324i | \(-0.552704\pi\) | ||||
−0.164820 | + | 0.986324i | \(0.552704\pi\) | |||||||
\(774\) | −1.44726e15 | −0.187272 | ||||||||
\(775\) | −2.49312e15 | −0.320320 | ||||||||
\(776\) | −5.17313e15 | −0.659955 | ||||||||
\(777\) | 1.21636e14 | 0.0154081 | ||||||||
\(778\) | 4.18827e15 | 0.526802 | ||||||||
\(779\) | −3.69424e15 | −0.461391 | ||||||||
\(780\) | −2.16133e15 | −0.268040 | ||||||||
\(781\) | −9.49331e15 | −1.16906 | ||||||||
\(782\) | 1.45831e16 | 1.78326 | ||||||||
\(783\) | 3.70684e14 | 0.0450106 | ||||||||
\(784\) | −5.82832e14 | −0.0702757 | ||||||||
\(785\) | −1.30496e16 | −1.56248 | ||||||||
\(786\) | 3.32259e15 | 0.395051 | ||||||||
\(787\) | −2.31157e15 | −0.272926 | −0.136463 | − | 0.990645i | \(-0.543574\pi\) | ||||
−0.136463 | + | 0.990645i | \(0.543574\pi\) | |||||||
\(788\) | 1.54714e16 | 1.81399 | ||||||||
\(789\) | −8.91095e15 | −1.03753 | ||||||||
\(790\) | −2.95535e15 | −0.341712 | ||||||||
\(791\) | 4.00443e15 | 0.459801 | ||||||||
\(792\) | 2.80008e15 | 0.319287 | ||||||||
\(793\) | −1.19318e15 | −0.135115 | ||||||||
\(794\) | 9.87552e15 | 1.11057 | ||||||||
\(795\) | −8.07946e15 | −0.902325 | ||||||||
\(796\) | −1.28385e16 | −1.42394 | ||||||||
\(797\) | −4.55532e15 | −0.501763 | −0.250881 | − | 0.968018i | \(-0.580720\pi\) | ||||
−0.250881 | + | 0.968018i | \(0.580720\pi\) | |||||||
\(798\) | 2.48673e15 | 0.272028 | ||||||||
\(799\) | 1.29753e15 | 0.140965 | ||||||||
\(800\) | 6.04907e15 | 0.652670 | ||||||||
\(801\) | −3.97722e15 | −0.426188 | ||||||||
\(802\) | 9.35882e15 | 0.996007 | ||||||||
\(803\) | 1.73869e16 | 1.83775 | ||||||||
\(804\) | −7.35315e15 | −0.771907 | ||||||||
\(805\) | 4.30213e15 | 0.448545 | ||||||||
\(806\) | −2.68809e15 | −0.278356 | ||||||||
\(807\) | −5.78202e15 | −0.594668 | ||||||||
\(808\) | 2.89564e15 | 0.295789 | ||||||||
\(809\) | 8.22276e15 | 0.834259 | 0.417129 | − | 0.908847i | \(-0.363036\pi\) | ||||
0.417129 | + | 0.908847i | \(0.363036\pi\) | |||||||
\(810\) | 2.07329e15 | 0.208926 | ||||||||
\(811\) | 5.02418e15 | 0.502864 | 0.251432 | − | 0.967875i | \(-0.419098\pi\) | ||||
0.251432 | + | 0.967875i | \(0.419098\pi\) | |||||||
\(812\) | −1.21882e15 | −0.121166 | ||||||||
\(813\) | −1.00574e16 | −0.993091 | ||||||||
\(814\) | −1.86039e15 | −0.182461 | ||||||||
\(815\) | −2.06898e16 | −2.01553 | ||||||||
\(816\) | 3.49833e15 | 0.338505 | ||||||||
\(817\) | 3.07374e15 | 0.295424 | ||||||||
\(818\) | −1.21153e16 | −1.15662 | ||||||||
\(819\) | −3.68485e14 | −0.0349428 | ||||||||
\(820\) | 1.01272e16 | 0.953927 | ||||||||
\(821\) | 3.09589e15 | 0.289666 | 0.144833 | − | 0.989456i | \(-0.453735\pi\) | ||||
0.144833 | + | 0.989456i | \(0.453735\pi\) | |||||||
\(822\) | 1.71904e16 | 1.59769 | ||||||||
\(823\) | −6.68332e14 | −0.0617012 | −0.0308506 | − | 0.999524i | \(-0.509822\pi\) | ||||
−0.0308506 | + | 0.999524i | \(0.509822\pi\) | |||||||
\(824\) | −1.03357e16 | −0.947854 | ||||||||
\(825\) | 5.22710e15 | 0.476172 | ||||||||
\(826\) | 8.11589e15 | 0.734422 | ||||||||
\(827\) | −4.06670e15 | −0.365563 | −0.182781 | − | 0.983154i | \(-0.558510\pi\) | ||||
−0.182781 | + | 0.983154i | \(0.558510\pi\) | |||||||
\(828\) | −4.97205e15 | −0.443985 | ||||||||
\(829\) | −4.83804e15 | −0.429161 | −0.214580 | − | 0.976706i | \(-0.568838\pi\) | ||||
−0.214580 | + | 0.976706i | \(0.568838\pi\) | |||||||
\(830\) | 8.35651e14 | 0.0736369 | ||||||||
\(831\) | −4.41335e14 | −0.0386334 | ||||||||
\(832\) | 4.95317e15 | 0.430729 | ||||||||
\(833\) | 1.97093e15 | 0.170265 | ||||||||
\(834\) | 3.25953e15 | 0.279732 | ||||||||
\(835\) | 2.31074e16 | 1.97004 | ||||||||
\(836\) | −2.19904e16 | −1.86251 | ||||||||
\(837\) | 1.49089e15 | 0.125445 | ||||||||
\(838\) | −2.11392e16 | −1.76704 | ||||||||
\(839\) | −5.75907e15 | −0.478257 | −0.239129 | − | 0.970988i | \(-0.576862\pi\) | ||||
−0.239129 | + | 0.970988i | \(0.576862\pi\) | |||||||
\(840\) | −1.84353e15 | −0.152095 | ||||||||
\(841\) | −1.15331e16 | −0.945299 | ||||||||
\(842\) | −2.58017e15 | −0.210102 | ||||||||
\(843\) | 1.22021e16 | 0.987149 | ||||||||
\(844\) | 2.73214e16 | 2.19594 | ||||||||
\(845\) | −1.17643e15 | −0.0939411 | ||||||||
\(846\) | −7.65140e14 | −0.0607021 | ||||||||
\(847\) | 8.71193e15 | 0.686682 | ||||||||
\(848\) | 8.03906e15 | 0.629547 | ||||||||
\(849\) | −3.61409e15 | −0.281194 | ||||||||
\(850\) | −1.16657e16 | −0.901790 | ||||||||
\(851\) | 8.93360e14 | 0.0686142 | ||||||||
\(852\) | −7.22355e15 | −0.551230 | ||||||||
\(853\) | −1.54688e16 | −1.17283 | −0.586417 | − | 0.810009i | \(-0.699462\pi\) | ||||
−0.586417 | + | 0.810009i | \(0.699462\pi\) | |||||||
\(854\) | −3.76341e15 | −0.283506 | ||||||||
\(855\) | −4.40330e15 | −0.329583 | ||||||||
\(856\) | −1.85250e15 | −0.137770 | ||||||||
\(857\) | 3.67451e15 | 0.271522 | 0.135761 | − | 0.990742i | \(-0.456652\pi\) | ||||
0.135761 | + | 0.990742i | \(0.456652\pi\) | |||||||
\(858\) | 5.63587e15 | 0.413791 | ||||||||
\(859\) | −9.25548e15 | −0.675206 | −0.337603 | − | 0.941289i | \(-0.609616\pi\) | ||||
−0.337603 | + | 0.941289i | \(0.609616\pi\) | |||||||
\(860\) | −8.42621e15 | −0.610789 | ||||||||
\(861\) | 1.72659e15 | 0.124358 | ||||||||
\(862\) | 1.82891e16 | 1.30889 | ||||||||
\(863\) | 1.04164e16 | 0.740728 | 0.370364 | − | 0.928887i | \(-0.379233\pi\) | ||||
0.370364 | + | 0.928887i | \(0.379233\pi\) | |||||||
\(864\) | −3.61735e15 | −0.255602 | ||||||||
\(865\) | −1.68129e16 | −1.18047 | ||||||||
\(866\) | −2.31472e14 | −0.0161492 | ||||||||
\(867\) | −3.50204e15 | −0.242782 | ||||||||
\(868\) | −4.90207e15 | −0.337692 | ||||||||
\(869\) | 4.45566e15 | 0.305002 | ||||||||
\(870\) | 3.73273e15 | 0.253905 | ||||||||
\(871\) | −4.00240e15 | −0.270533 | ||||||||
\(872\) | −9.94712e15 | −0.668124 | ||||||||
\(873\) | 5.77491e15 | 0.385449 | ||||||||
\(874\) | 1.82638e16 | 1.21138 | ||||||||
\(875\) | 3.56171e15 | 0.234755 | ||||||||
\(876\) | 1.32299e16 | 0.866528 | ||||||||
\(877\) | −6.19237e15 | −0.403050 | −0.201525 | − | 0.979483i | \(-0.564590\pi\) | ||||
−0.201525 | + | 0.979483i | \(0.564590\pi\) | |||||||
\(878\) | −2.32060e16 | −1.50100 | ||||||||
\(879\) | 8.71332e14 | 0.0560073 | ||||||||
\(880\) | −1.57846e16 | −1.00828 | ||||||||
\(881\) | −1.08017e16 | −0.685683 | −0.342842 | − | 0.939393i | \(-0.611389\pi\) | ||||
−0.342842 | + | 0.939393i | \(0.611389\pi\) | |||||||
\(882\) | −1.16223e15 | −0.0733190 | ||||||||
\(883\) | 2.71395e16 | 1.70145 | 0.850723 | − | 0.525615i | \(-0.176165\pi\) | ||||
0.850723 | + | 0.525615i | \(0.176165\pi\) | |||||||
\(884\) | −7.27230e15 | −0.453090 | ||||||||
\(885\) | −1.43709e16 | −0.889810 | ||||||||
\(886\) | 3.78333e16 | 2.32803 | ||||||||
\(887\) | −2.60367e16 | −1.59223 | −0.796114 | − | 0.605146i | \(-0.793115\pi\) | ||||
−0.796114 | + | 0.605146i | \(0.793115\pi\) | |||||||
\(888\) | −3.82820e14 | −0.0232661 | ||||||||
\(889\) | −1.83128e15 | −0.110610 | ||||||||
\(890\) | −4.00500e16 | −2.40412 | ||||||||
\(891\) | −3.12581e15 | −0.186481 | ||||||||
\(892\) | −2.69441e16 | −1.59756 | ||||||||
\(893\) | 1.62502e15 | 0.0957582 | ||||||||
\(894\) | 1.16863e16 | 0.684419 | ||||||||
\(895\) | 6.90724e15 | 0.402048 | ||||||||
\(896\) | 6.94530e15 | 0.401788 | ||||||||
\(897\) | −2.70634e15 | −0.155605 | ||||||||
\(898\) | −1.87131e16 | −1.06936 | ||||||||
\(899\) | 2.68418e15 | 0.152452 | ||||||||
\(900\) | 3.97735e15 | 0.224522 | ||||||||
\(901\) | −2.71852e16 | −1.52527 | ||||||||
\(902\) | −2.64077e16 | −1.47264 | ||||||||
\(903\) | −1.43658e15 | −0.0796248 | ||||||||
\(904\) | −1.26029e16 | −0.694297 | ||||||||
\(905\) | −2.04486e16 | −1.11969 | ||||||||
\(906\) | −7.33849e14 | −0.0399394 | ||||||||
\(907\) | −2.29470e16 | −1.24133 | −0.620664 | − | 0.784077i | \(-0.713137\pi\) | ||||
−0.620664 | + | 0.784077i | \(0.713137\pi\) | |||||||
\(908\) | −4.56124e16 | −2.45251 | ||||||||
\(909\) | −3.23248e15 | −0.172757 | ||||||||
\(910\) | −3.71058e15 | −0.197112 | ||||||||
\(911\) | −1.26887e14 | −0.00669989 | −0.00334994 | − | 0.999994i | \(-0.501066\pi\) | ||||
−0.00334994 | + | 0.999994i | \(0.501066\pi\) | |||||||
\(912\) | 4.38128e15 | 0.229948 | ||||||||
\(913\) | −1.25987e15 | −0.0657261 | ||||||||
\(914\) | 2.07322e16 | 1.07508 | ||||||||
\(915\) | 6.66393e15 | 0.343490 | ||||||||
\(916\) | −3.10652e16 | −1.59166 | ||||||||
\(917\) | 3.29807e15 | 0.167969 | ||||||||
\(918\) | 6.97607e15 | 0.353164 | ||||||||
\(919\) | −1.75468e16 | −0.883006 | −0.441503 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441503 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(920\) | −1.35399e16 | −0.677300 | ||||||||
\(921\) | −7.48798e15 | −0.372337 | ||||||||
\(922\) | −5.41942e16 | −2.67875 | ||||||||
\(923\) | −3.93186e15 | −0.193192 | ||||||||
\(924\) | 1.02777e16 | 0.501997 | ||||||||
\(925\) | −7.14636e14 | −0.0346981 | ||||||||
\(926\) | 2.19571e16 | 1.05978 | ||||||||
\(927\) | 1.15381e16 | 0.553598 | ||||||||
\(928\) | −6.51263e15 | −0.310629 | ||||||||
\(929\) | −1.89078e16 | −0.896509 | −0.448254 | − | 0.893906i | \(-0.647954\pi\) | ||||
−0.448254 | + | 0.893906i | \(0.647954\pi\) | |||||||
\(930\) | 1.50130e16 | 0.707637 | ||||||||
\(931\) | 2.46838e15 | 0.115662 | ||||||||
\(932\) | 2.66702e16 | 1.24233 | ||||||||
\(933\) | 1.56397e16 | 0.724235 | ||||||||
\(934\) | 1.93636e14 | 0.00891410 | ||||||||
\(935\) | 5.33780e16 | 2.44286 | ||||||||
\(936\) | 1.15971e15 | 0.0527634 | ||||||||
\(937\) | 1.03996e16 | 0.470380 | 0.235190 | − | 0.971949i | \(-0.424429\pi\) | ||||
0.235190 | + | 0.971949i | \(0.424429\pi\) | |||||||
\(938\) | −1.26239e16 | −0.567648 | ||||||||
\(939\) | 1.37350e16 | 0.614001 | ||||||||
\(940\) | −4.45477e15 | −0.197980 | ||||||||
\(941\) | −1.27405e16 | −0.562917 | −0.281459 | − | 0.959573i | \(-0.590818\pi\) | ||||
−0.281459 | + | 0.959573i | \(0.590818\pi\) | |||||||
\(942\) | 2.58923e16 | 1.13734 | ||||||||
\(943\) | 1.26810e16 | 0.553781 | ||||||||
\(944\) | 1.42991e16 | 0.620815 | ||||||||
\(945\) | 2.05799e15 | 0.0888317 | ||||||||
\(946\) | 2.19721e16 | 0.942912 | ||||||||
\(947\) | −3.55556e16 | −1.51699 | −0.758496 | − | 0.651678i | \(-0.774065\pi\) | ||||
−0.758496 | + | 0.651678i | \(0.774065\pi\) | |||||||
\(948\) | 3.39035e15 | 0.143813 | ||||||||
\(949\) | 7.20116e15 | 0.303695 | ||||||||
\(950\) | −1.46100e16 | −0.612590 | ||||||||
\(951\) | 7.02023e15 | 0.292657 | ||||||||
\(952\) | −6.20301e15 | −0.257098 | ||||||||
\(953\) | 1.67046e16 | 0.688374 | 0.344187 | − | 0.938901i | \(-0.388155\pi\) | ||||
0.344187 | + | 0.938901i | \(0.388155\pi\) | |||||||
\(954\) | 1.60308e16 | 0.656809 | ||||||||
\(955\) | 1.73216e16 | 0.705619 | ||||||||
\(956\) | −2.51512e16 | −1.01869 | ||||||||
\(957\) | −5.62767e15 | −0.226628 | ||||||||
\(958\) | 4.64840e16 | 1.86120 | ||||||||
\(959\) | 1.70636e16 | 0.679309 | ||||||||
\(960\) | −2.76635e16 | −1.09500 | ||||||||
\(961\) | −1.46128e16 | −0.575113 | ||||||||
\(962\) | −7.70522e14 | −0.0301524 | ||||||||
\(963\) | 2.06800e15 | 0.0804649 | ||||||||
\(964\) | −5.98960e16 | −2.31726 | ||||||||
\(965\) | 2.31834e16 | 0.891820 | ||||||||
\(966\) | −8.53604e15 | −0.326499 | ||||||||
\(967\) | −4.25554e16 | −1.61849 | −0.809243 | − | 0.587474i | \(-0.800122\pi\) | ||||
−0.809243 | + | 0.587474i | \(0.800122\pi\) | |||||||
\(968\) | −2.74186e16 | −1.03688 | ||||||||
\(969\) | −1.48159e16 | −0.557120 | ||||||||
\(970\) | 5.81524e16 | 2.17432 | ||||||||
\(971\) | −3.37519e16 | −1.25485 | −0.627425 | − | 0.778677i | \(-0.715891\pi\) | ||||
−0.627425 | + | 0.778677i | \(0.715891\pi\) | |||||||
\(972\) | −2.37845e15 | −0.0879287 | ||||||||
\(973\) | 3.23547e15 | 0.118937 | ||||||||
\(974\) | 6.83592e16 | 2.49875 | ||||||||
\(975\) | 2.16491e15 | 0.0786892 | ||||||||
\(976\) | −6.63061e15 | −0.239651 | ||||||||
\(977\) | −3.92325e16 | −1.41002 | −0.705012 | − | 0.709196i | \(-0.749058\pi\) | ||||
−0.705012 | + | 0.709196i | \(0.749058\pi\) | |||||||
\(978\) | 4.10515e16 | 1.46712 | ||||||||
\(979\) | 6.03815e16 | 2.14585 | ||||||||
\(980\) | −6.76672e15 | −0.239130 | ||||||||
\(981\) | 1.11043e16 | 0.390220 | ||||||||
\(982\) | −6.83431e15 | −0.238826 | ||||||||
\(983\) | −2.36974e15 | −0.0823485 | −0.0411742 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411742 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(984\) | −5.43401e15 | −0.187779 | ||||||||
\(985\) | −4.70328e16 | −1.61622 | ||||||||
\(986\) | 1.25596e16 | 0.429195 | ||||||||
\(987\) | −7.59493e14 | −0.0258095 | ||||||||
\(988\) | −9.10777e15 | −0.307786 | ||||||||
\(989\) | −1.05510e16 | −0.354580 | ||||||||
\(990\) | −3.14763e16 | −1.05194 | ||||||||
\(991\) | 4.33811e16 | 1.44177 | 0.720884 | − | 0.693056i | \(-0.243736\pi\) | ||||
0.720884 | + | 0.693056i | \(0.243736\pi\) | |||||||
\(992\) | −2.61937e16 | −0.865731 | ||||||||
\(993\) | 2.20928e16 | 0.726157 | ||||||||
\(994\) | −1.24014e16 | −0.405365 | ||||||||
\(995\) | 3.90288e16 | 1.26870 | ||||||||
\(996\) | −9.58650e14 | −0.0309909 | ||||||||
\(997\) | −1.80200e16 | −0.579338 | −0.289669 | − | 0.957127i | \(-0.593545\pi\) | ||||
−0.289669 | + | 0.957127i | \(0.593545\pi\) | |||||||
\(998\) | −4.35854e16 | −1.39355 | ||||||||
\(999\) | 4.27352e14 | 0.0135886 |
(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 | 273.12.a.c.1.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.12.a.c.1.4 | ✓ | 16 | 1.1 | even | 1 | trivial |