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: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 61.2715 | 1.35392 | 0.676961 | − | 0.736019i | \(-0.263296\pi\) | ||||
0.676961 | + | 0.736019i | \(0.263296\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 1706.20 | 0.833106 | ||||||||
\(5\) | −4729.37 | −0.676812 | −0.338406 | − | 0.941000i | \(-0.609888\pi\) | ||||
−0.338406 | + | 0.941000i | \(0.609888\pi\) | |||||||
\(6\) | 14889.0 | 0.781688 | ||||||||
\(7\) | 60563.4 | 1.36198 | 0.680990 | − | 0.732293i | \(-0.261550\pi\) | ||||
0.680990 | + | 0.732293i | \(0.261550\pi\) | |||||||
\(8\) | −20942.5 | −0.225961 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −289776. | −0.916351 | ||||||||
\(11\) | 473617. | 0.886681 | 0.443341 | − | 0.896353i | \(-0.353793\pi\) | ||||
0.443341 | + | 0.896353i | \(0.353793\pi\) | |||||||
\(12\) | 414607. | 0.480994 | ||||||||
\(13\) | 610625. | 0.456128 | 0.228064 | − | 0.973646i | \(-0.426761\pi\) | ||||
0.228064 | + | 0.973646i | \(0.426761\pi\) | |||||||
\(14\) | 3.71081e6 | 1.84402 | ||||||||
\(15\) | −1.14924e6 | −0.390758 | ||||||||
\(16\) | −4.77748e6 | −1.13904 | ||||||||
\(17\) | 1.14809e7 | 1.96112 | 0.980562 | − | 0.196208i | \(-0.0628628\pi\) | ||||
0.980562 | + | 0.196208i | \(0.0628628\pi\) | |||||||
\(18\) | 3.61802e6 | 0.451308 | ||||||||
\(19\) | −7.38886e6 | −0.684594 | −0.342297 | − | 0.939592i | \(-0.611205\pi\) | ||||
−0.342297 | + | 0.939592i | \(0.611205\pi\) | |||||||
\(20\) | −8.06926e6 | −0.563856 | ||||||||
\(21\) | 1.47169e7 | 0.786340 | ||||||||
\(22\) | 2.90192e7 | 1.20050 | ||||||||
\(23\) | −2.70104e7 | −0.875042 | −0.437521 | − | 0.899208i | \(-0.644143\pi\) | ||||
−0.437521 | + | 0.899208i | \(0.644143\pi\) | |||||||
\(24\) | −5.08902e6 | −0.130459 | ||||||||
\(25\) | −2.64612e7 | −0.541926 | ||||||||
\(26\) | 3.74140e7 | 0.617562 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 1.03333e8 | 1.13467 | ||||||||
\(29\) | 1.49323e7 | 0.135187 | 0.0675937 | − | 0.997713i | \(-0.478468\pi\) | ||||
0.0675937 | + | 0.997713i | \(0.478468\pi\) | |||||||
\(30\) | −7.04155e7 | −0.529055 | ||||||||
\(31\) | −8.45122e6 | −0.0530188 | −0.0265094 | − | 0.999649i | \(-0.508439\pi\) | ||||
−0.0265094 | + | 0.999649i | \(0.508439\pi\) | |||||||
\(32\) | −2.49833e8 | −1.31621 | ||||||||
\(33\) | 1.15089e8 | 0.511926 | ||||||||
\(34\) | 7.03450e8 | 2.65521 | ||||||||
\(35\) | −2.86426e8 | −0.921804 | ||||||||
\(36\) | 1.00750e8 | 0.277702 | ||||||||
\(37\) | 7.46727e8 | 1.77032 | 0.885161 | − | 0.465285i | \(-0.154048\pi\) | ||||
0.885161 | + | 0.465285i | \(0.154048\pi\) | |||||||
\(38\) | −4.52727e8 | −0.926887 | ||||||||
\(39\) | 1.48382e8 | 0.263345 | ||||||||
\(40\) | 9.90447e7 | 0.152933 | ||||||||
\(41\) | 1.73357e7 | 0.0233685 | 0.0116843 | − | 0.999932i | \(-0.496281\pi\) | ||||
0.0116843 | + | 0.999932i | \(0.496281\pi\) | |||||||
\(42\) | 9.01727e8 | 1.06464 | ||||||||
\(43\) | −1.74521e7 | −0.0181039 | −0.00905195 | − | 0.999959i | \(-0.502881\pi\) | ||||
−0.00905195 | + | 0.999959i | \(0.502881\pi\) | |||||||
\(44\) | 8.08086e8 | 0.738700 | ||||||||
\(45\) | −2.79264e8 | −0.225604 | ||||||||
\(46\) | −1.65497e9 | −1.18474 | ||||||||
\(47\) | 4.85876e8 | 0.309021 | 0.154510 | − | 0.987991i | \(-0.450620\pi\) | ||||
0.154510 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(48\) | −1.16093e9 | −0.657625 | ||||||||
\(49\) | 1.69060e9 | 0.854990 | ||||||||
\(50\) | −1.62132e9 | −0.733725 | ||||||||
\(51\) | 2.78985e9 | 1.13226 | ||||||||
\(52\) | 1.04185e9 | 0.380003 | ||||||||
\(53\) | −5.23306e8 | −0.171885 | −0.0859427 | − | 0.996300i | \(-0.527390\pi\) | ||||
−0.0859427 | + | 0.996300i | \(0.527390\pi\) | |||||||
\(54\) | 8.79180e8 | 0.260563 | ||||||||
\(55\) | −2.23991e9 | −0.600116 | ||||||||
\(56\) | −1.26835e9 | −0.307754 | ||||||||
\(57\) | −1.79549e9 | −0.395250 | ||||||||
\(58\) | 9.14922e8 | 0.183033 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −1.96083e9 | −0.325543 | ||||||||
\(61\) | 5.78647e9 | 0.877202 | 0.438601 | − | 0.898682i | \(-0.355474\pi\) | ||||
0.438601 | + | 0.898682i | \(0.355474\pi\) | |||||||
\(62\) | −5.17819e8 | −0.0717834 | ||||||||
\(63\) | 3.57621e9 | 0.453993 | ||||||||
\(64\) | −5.52340e9 | −0.643008 | ||||||||
\(65\) | −2.88787e9 | −0.308713 | ||||||||
\(66\) | 7.05167e9 | 0.693108 | ||||||||
\(67\) | 1.56316e10 | 1.41446 | 0.707230 | − | 0.706983i | \(-0.249944\pi\) | ||||
0.707230 | + | 0.706983i | \(0.249944\pi\) | |||||||
\(68\) | 1.95887e10 | 1.63383 | ||||||||
\(69\) | −6.56354e9 | −0.505205 | ||||||||
\(70\) | −1.75498e10 | −1.24805 | ||||||||
\(71\) | 2.68417e10 | 1.76559 | 0.882794 | − | 0.469761i | \(-0.155660\pi\) | ||||
0.882794 | + | 0.469761i | \(0.155660\pi\) | |||||||
\(72\) | −1.23663e9 | −0.0753203 | ||||||||
\(73\) | 1.19612e10 | 0.675305 | 0.337652 | − | 0.941271i | \(-0.390367\pi\) | ||||
0.337652 | + | 0.941271i | \(0.390367\pi\) | |||||||
\(74\) | 4.57531e10 | 2.39688 | ||||||||
\(75\) | −6.43007e9 | −0.312881 | ||||||||
\(76\) | −1.26069e10 | −0.570339 | ||||||||
\(77\) | 2.86838e10 | 1.20764 | ||||||||
\(78\) | 9.09159e9 | 0.356549 | ||||||||
\(79\) | 9.69640e9 | 0.354537 | 0.177268 | − | 0.984163i | \(-0.443274\pi\) | ||||
0.177268 | + | 0.984163i | \(0.443274\pi\) | |||||||
\(80\) | 2.25945e10 | 0.770916 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 1.06219e9 | 0.0316392 | ||||||||
\(83\) | 2.95177e10 | 0.822534 | 0.411267 | − | 0.911515i | \(-0.365086\pi\) | ||||
0.411267 | + | 0.911515i | \(0.365086\pi\) | |||||||
\(84\) | 2.51100e10 | 0.655105 | ||||||||
\(85\) | −5.42972e10 | −1.32731 | ||||||||
\(86\) | −1.06932e9 | −0.0245113 | ||||||||
\(87\) | 3.62854e9 | 0.0780505 | ||||||||
\(88\) | −9.91872e9 | −0.200355 | ||||||||
\(89\) | 1.71396e10 | 0.325353 | 0.162677 | − | 0.986679i | \(-0.447987\pi\) | ||||
0.162677 | + | 0.986679i | \(0.447987\pi\) | |||||||
\(90\) | −1.71110e10 | −0.305450 | ||||||||
\(91\) | 3.69815e10 | 0.621237 | ||||||||
\(92\) | −4.60853e10 | −0.729003 | ||||||||
\(93\) | −2.05365e9 | −0.0306104 | ||||||||
\(94\) | 2.97704e10 | 0.418390 | ||||||||
\(95\) | 3.49446e10 | 0.463341 | ||||||||
\(96\) | −6.07095e10 | −0.759915 | ||||||||
\(97\) | 7.11706e10 | 0.841504 | 0.420752 | − | 0.907176i | \(-0.361766\pi\) | ||||
0.420752 | + | 0.907176i | \(0.361766\pi\) | |||||||
\(98\) | 1.03585e11 | 1.15759 | ||||||||
\(99\) | 2.79666e10 | 0.295560 | ||||||||
\(100\) | −4.51482e10 | −0.451482 | ||||||||
\(101\) | −1.82667e11 | −1.72939 | −0.864693 | − | 0.502300i | \(-0.832487\pi\) | ||||
−0.864693 | + | 0.502300i | \(0.832487\pi\) | |||||||
\(102\) | 1.70938e11 | 1.53299 | ||||||||
\(103\) | 7.44821e10 | 0.633064 | 0.316532 | − | 0.948582i | \(-0.397482\pi\) | ||||
0.316532 | + | 0.948582i | \(0.397482\pi\) | |||||||
\(104\) | −1.27880e10 | −0.103067 | ||||||||
\(105\) | −6.96016e10 | −0.532204 | ||||||||
\(106\) | −3.20638e10 | −0.232719 | ||||||||
\(107\) | −6.75408e10 | −0.465538 | −0.232769 | − | 0.972532i | \(-0.574779\pi\) | ||||
−0.232769 | + | 0.972532i | \(0.574779\pi\) | |||||||
\(108\) | 2.44821e10 | 0.160331 | ||||||||
\(109\) | −1.13770e11 | −0.708241 | −0.354120 | − | 0.935200i | \(-0.615220\pi\) | ||||
−0.354120 | + | 0.935200i | \(0.615220\pi\) | |||||||
\(110\) | −1.37243e11 | −0.812511 | ||||||||
\(111\) | 1.81455e11 | 1.02210 | ||||||||
\(112\) | −2.89340e11 | −1.55135 | ||||||||
\(113\) | 2.57366e11 | 1.31407 | 0.657037 | − | 0.753858i | \(-0.271809\pi\) | ||||
0.657037 | + | 0.753858i | \(0.271809\pi\) | |||||||
\(114\) | −1.10013e11 | −0.535138 | ||||||||
\(115\) | 1.27742e11 | 0.592238 | ||||||||
\(116\) | 2.54774e10 | 0.112626 | ||||||||
\(117\) | 3.60568e10 | 0.152043 | ||||||||
\(118\) | 4.38045e10 | 0.176266 | ||||||||
\(119\) | 6.95319e11 | 2.67101 | ||||||||
\(120\) | 2.40679e10 | 0.0882959 | ||||||||
\(121\) | −6.09987e10 | −0.213797 | ||||||||
\(122\) | 3.54546e11 | 1.18766 | ||||||||
\(123\) | 4.21258e9 | 0.0134918 | ||||||||
\(124\) | −1.44195e10 | −0.0441703 | ||||||||
\(125\) | 3.56071e11 | 1.04359 | ||||||||
\(126\) | 2.19120e11 | 0.614672 | ||||||||
\(127\) | −1.05426e11 | −0.283157 | −0.141578 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141578 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(128\) | 1.73232e11 | 0.445628 | ||||||||
\(129\) | −4.24087e9 | −0.0104523 | ||||||||
\(130\) | −1.76944e11 | −0.417973 | ||||||||
\(131\) | −7.87487e11 | −1.78341 | −0.891706 | − | 0.452616i | \(-0.850491\pi\) | ||||
−0.891706 | + | 0.452616i | \(0.850491\pi\) | |||||||
\(132\) | 1.96365e11 | 0.426488 | ||||||||
\(133\) | −4.47494e11 | −0.932403 | ||||||||
\(134\) | 9.57770e11 | 1.91507 | ||||||||
\(135\) | −6.78612e10 | −0.130253 | ||||||||
\(136\) | −2.40438e11 | −0.443138 | ||||||||
\(137\) | −4.11607e11 | −0.728651 | −0.364325 | − | 0.931272i | \(-0.618700\pi\) | ||||
−0.364325 | + | 0.931272i | \(0.618700\pi\) | |||||||
\(138\) | −4.02158e11 | −0.684009 | ||||||||
\(139\) | 5.12086e11 | 0.837070 | 0.418535 | − | 0.908201i | \(-0.362544\pi\) | ||||
0.418535 | + | 0.908201i | \(0.362544\pi\) | |||||||
\(140\) | −4.88701e11 | −0.767961 | ||||||||
\(141\) | 1.18068e11 | 0.178413 | ||||||||
\(142\) | 1.64463e12 | 2.39047 | ||||||||
\(143\) | 2.89203e11 | 0.404440 | ||||||||
\(144\) | −2.82105e11 | −0.379680 | ||||||||
\(145\) | −7.06201e10 | −0.0914965 | ||||||||
\(146\) | 7.32883e11 | 0.914310 | ||||||||
\(147\) | 4.10815e11 | 0.493629 | ||||||||
\(148\) | 1.27407e12 | 1.47487 | ||||||||
\(149\) | 4.29777e11 | 0.479423 | 0.239711 | − | 0.970844i | \(-0.422947\pi\) | ||||
0.239711 | + | 0.970844i | \(0.422947\pi\) | |||||||
\(150\) | −3.93981e11 | −0.423617 | ||||||||
\(151\) | 1.87094e9 | 0.00193948 | 0.000969742 | − | 1.00000i | \(-0.499691\pi\) | ||||
0.000969742 | 1.00000i | \(0.499691\pi\) | ||||||||
\(152\) | 1.54741e11 | 0.154691 | ||||||||
\(153\) | 6.77933e11 | 0.653708 | ||||||||
\(154\) | 1.75750e12 | 1.63505 | ||||||||
\(155\) | 3.99689e10 | 0.0358838 | ||||||||
\(156\) | 2.53170e11 | 0.219395 | ||||||||
\(157\) | −1.79317e12 | −1.50029 | −0.750143 | − | 0.661276i | \(-0.770015\pi\) | ||||
−0.750143 | + | 0.661276i | \(0.770015\pi\) | |||||||
\(158\) | 5.94113e11 | 0.480015 | ||||||||
\(159\) | −1.27163e11 | −0.0992380 | ||||||||
\(160\) | 1.18155e12 | 0.890827 | ||||||||
\(161\) | −1.63584e12 | −1.19179 | ||||||||
\(162\) | 2.13641e11 | 0.150436 | ||||||||
\(163\) | −7.95760e11 | −0.541689 | −0.270845 | − | 0.962623i | \(-0.587303\pi\) | ||||
−0.270845 | + | 0.962623i | \(0.587303\pi\) | |||||||
\(164\) | 2.95783e10 | 0.0194685 | ||||||||
\(165\) | −5.44298e11 | −0.346477 | ||||||||
\(166\) | 1.80860e12 | 1.11365 | ||||||||
\(167\) | −5.42394e11 | −0.323128 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(168\) | −3.08208e11 | −0.177682 | ||||||||
\(169\) | −1.41930e12 | −0.791947 | ||||||||
\(170\) | −3.32687e12 | −1.79708 | ||||||||
\(171\) | −4.36305e11 | −0.228198 | ||||||||
\(172\) | −2.97769e10 | −0.0150825 | ||||||||
\(173\) | −6.92367e10 | −0.0339690 | −0.0169845 | − | 0.999856i | \(-0.505407\pi\) | ||||
−0.0169845 | + | 0.999856i | \(0.505407\pi\) | |||||||
\(174\) | 2.22326e11 | 0.105674 | ||||||||
\(175\) | −1.60258e12 | −0.738092 | ||||||||
\(176\) | −2.26270e12 | −1.00997 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.05017e12 | 0.440503 | ||||||||
\(179\) | −1.98227e12 | −0.806254 | −0.403127 | − | 0.915144i | \(-0.632077\pi\) | ||||
−0.403127 | + | 0.915144i | \(0.632077\pi\) | |||||||
\(180\) | −4.76481e11 | −0.187952 | ||||||||
\(181\) | −2.29475e12 | −0.878018 | −0.439009 | − | 0.898483i | \(-0.644670\pi\) | ||||
−0.439009 | + | 0.898483i | \(0.644670\pi\) | |||||||
\(182\) | 2.26592e12 | 0.841107 | ||||||||
\(183\) | 1.40611e12 | 0.506453 | ||||||||
\(184\) | 5.65666e11 | 0.197725 | ||||||||
\(185\) | −3.53154e12 | −1.19817 | ||||||||
\(186\) | −1.25830e11 | −0.0414442 | ||||||||
\(187\) | 5.43753e12 | 1.73889 | ||||||||
\(188\) | 8.29003e11 | 0.257447 | ||||||||
\(189\) | 8.69018e11 | 0.262113 | ||||||||
\(190\) | 2.14111e12 | 0.627328 | ||||||||
\(191\) | 3.35774e12 | 0.955793 | 0.477896 | − | 0.878416i | \(-0.341399\pi\) | ||||
0.477896 | + | 0.878416i | \(0.341399\pi\) | |||||||
\(192\) | −1.34219e12 | −0.371241 | ||||||||
\(193\) | −3.15457e12 | −0.847960 | −0.423980 | − | 0.905672i | \(-0.639367\pi\) | ||||
−0.423980 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(194\) | 4.36074e12 | 1.13933 | ||||||||
\(195\) | −7.01753e11 | −0.178235 | ||||||||
\(196\) | 2.88450e12 | 0.712298 | ||||||||
\(197\) | 9.04203e11 | 0.217121 | 0.108560 | − | 0.994090i | \(-0.465376\pi\) | ||||
0.108560 | + | 0.994090i | \(0.465376\pi\) | |||||||
\(198\) | 1.71356e12 | 0.400166 | ||||||||
\(199\) | −1.92290e12 | −0.436781 | −0.218391 | − | 0.975861i | \(-0.570081\pi\) | ||||
−0.218391 | + | 0.975861i | \(0.570081\pi\) | |||||||
\(200\) | 5.54164e11 | 0.122454 | ||||||||
\(201\) | 3.79847e12 | 0.816639 | ||||||||
\(202\) | −1.11923e13 | −2.34146 | ||||||||
\(203\) | 9.04347e11 | 0.184123 | ||||||||
\(204\) | 4.76004e12 | 0.943290 | ||||||||
\(205\) | −8.19870e10 | −0.0158161 | ||||||||
\(206\) | 4.56364e12 | 0.857119 | ||||||||
\(207\) | −1.59494e12 | −0.291681 | ||||||||
\(208\) | −2.91725e12 | −0.519548 | ||||||||
\(209\) | −3.49949e12 | −0.607016 | ||||||||
\(210\) | −4.26460e12 | −0.720563 | ||||||||
\(211\) | 9.34786e12 | 1.53872 | 0.769359 | − | 0.638817i | \(-0.220576\pi\) | ||||
0.769359 | + | 0.638817i | \(0.220576\pi\) | |||||||
\(212\) | −8.92867e11 | −0.143199 | ||||||||
\(213\) | 6.52254e12 | 1.01936 | ||||||||
\(214\) | −4.13833e12 | −0.630303 | ||||||||
\(215\) | 8.25376e10 | 0.0122529 | ||||||||
\(216\) | −3.00502e11 | −0.0434862 | ||||||||
\(217\) | −5.11834e11 | −0.0722106 | ||||||||
\(218\) | −6.97085e12 | −0.958903 | ||||||||
\(219\) | 2.90658e12 | 0.389887 | ||||||||
\(220\) | −3.82174e12 | −0.499961 | ||||||||
\(221\) | 7.01050e12 | 0.894523 | ||||||||
\(222\) | 1.11180e13 | 1.38384 | ||||||||
\(223\) | −2.48981e12 | −0.302335 | −0.151168 | − | 0.988508i | \(-0.548303\pi\) | ||||
−0.151168 | + | 0.988508i | \(0.548303\pi\) | |||||||
\(224\) | −1.51308e13 | −1.79265 | ||||||||
\(225\) | −1.56251e12 | −0.180642 | ||||||||
\(226\) | 1.57692e13 | 1.77916 | ||||||||
\(227\) | 1.29486e12 | 0.142587 | 0.0712934 | − | 0.997455i | \(-0.477287\pi\) | ||||
0.0712934 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(228\) | −3.06347e12 | −0.329286 | ||||||||
\(229\) | 1.63443e12 | 0.171503 | 0.0857516 | − | 0.996317i | \(-0.472671\pi\) | ||||
0.0857516 | + | 0.996317i | \(0.472671\pi\) | |||||||
\(230\) | 7.82697e12 | 0.801845 | ||||||||
\(231\) | 6.97017e12 | 0.697232 | ||||||||
\(232\) | −3.12718e11 | −0.0305471 | ||||||||
\(233\) | 4.27341e12 | 0.407677 | 0.203839 | − | 0.979004i | \(-0.434658\pi\) | ||||
0.203839 | + | 0.979004i | \(0.434658\pi\) | |||||||
\(234\) | 2.20926e12 | 0.205854 | ||||||||
\(235\) | −2.29789e12 | −0.209149 | ||||||||
\(236\) | 1.21981e12 | 0.108461 | ||||||||
\(237\) | 2.35622e12 | 0.204692 | ||||||||
\(238\) | 4.26033e13 | 3.61635 | ||||||||
\(239\) | 2.31396e13 | 1.91941 | 0.959703 | − | 0.281015i | \(-0.0906712\pi\) | ||||
0.959703 | + | 0.281015i | \(0.0906712\pi\) | |||||||
\(240\) | 5.49045e12 | 0.445088 | ||||||||
\(241\) | −6.20913e12 | −0.491968 | −0.245984 | − | 0.969274i | \(-0.579111\pi\) | ||||
−0.245984 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(242\) | −3.73749e12 | −0.289464 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 9.87288e12 | 0.730802 | ||||||||
\(245\) | −7.99545e12 | −0.578668 | ||||||||
\(246\) | 2.58111e11 | 0.0182669 | ||||||||
\(247\) | −4.51183e12 | −0.312262 | ||||||||
\(248\) | 1.76990e11 | 0.0119802 | ||||||||
\(249\) | 7.17281e12 | 0.474890 | ||||||||
\(250\) | 2.18170e13 | 1.41295 | ||||||||
\(251\) | −6.70656e12 | −0.424907 | −0.212454 | − | 0.977171i | \(-0.568145\pi\) | ||||
−0.212454 | + | 0.977171i | \(0.568145\pi\) | |||||||
\(252\) | 6.10173e12 | 0.378225 | ||||||||
\(253\) | −1.27926e13 | −0.775883 | ||||||||
\(254\) | −6.45961e12 | −0.383372 | ||||||||
\(255\) | −1.31942e13 | −0.766324 | ||||||||
\(256\) | 2.19261e13 | 1.24635 | ||||||||
\(257\) | 9.09638e12 | 0.506100 | 0.253050 | − | 0.967453i | \(-0.418566\pi\) | ||||
0.253050 | + | 0.967453i | \(0.418566\pi\) | |||||||
\(258\) | −2.59845e11 | −0.0141516 | ||||||||
\(259\) | 4.52243e13 | 2.41114 | ||||||||
\(260\) | −4.92729e12 | −0.257191 | ||||||||
\(261\) | 8.81734e11 | 0.0450625 | ||||||||
\(262\) | −4.82506e13 | −2.41460 | ||||||||
\(263\) | −1.91000e13 | −0.936004 | −0.468002 | − | 0.883728i | \(-0.655026\pi\) | ||||
−0.468002 | + | 0.883728i | \(0.655026\pi\) | |||||||
\(264\) | −2.41025e12 | −0.115675 | ||||||||
\(265\) | 2.47491e12 | 0.116334 | ||||||||
\(266\) | −2.74187e13 | −1.26240 | ||||||||
\(267\) | 4.16492e12 | 0.187843 | ||||||||
\(268\) | 2.66706e13 | 1.17840 | ||||||||
\(269\) | −6.78130e12 | −0.293546 | −0.146773 | − | 0.989170i | \(-0.546889\pi\) | ||||
−0.146773 | + | 0.989170i | \(0.546889\pi\) | |||||||
\(270\) | −4.15796e12 | −0.176352 | ||||||||
\(271\) | −2.78714e13 | −1.15832 | −0.579160 | − | 0.815214i | \(-0.696619\pi\) | ||||
−0.579160 | + | 0.815214i | \(0.696619\pi\) | |||||||
\(272\) | −5.48496e13 | −2.23380 | ||||||||
\(273\) | 8.98651e12 | 0.358671 | ||||||||
\(274\) | −2.52198e13 | −0.986537 | ||||||||
\(275\) | −1.25325e13 | −0.480515 | ||||||||
\(276\) | −1.11987e13 | −0.420890 | ||||||||
\(277\) | 1.40144e13 | 0.516341 | 0.258171 | − | 0.966099i | \(-0.416880\pi\) | ||||
0.258171 | + | 0.966099i | \(0.416880\pi\) | |||||||
\(278\) | 3.13763e13 | 1.13333 | ||||||||
\(279\) | −4.99036e11 | −0.0176729 | ||||||||
\(280\) | 5.99848e12 | 0.208292 | ||||||||
\(281\) | −3.57219e13 | −1.21633 | −0.608164 | − | 0.793812i | \(-0.708094\pi\) | ||||
−0.608164 | + | 0.793812i | \(0.708094\pi\) | |||||||
\(282\) | 7.23421e12 | 0.241558 | ||||||||
\(283\) | −8.91205e12 | −0.291845 | −0.145923 | − | 0.989296i | \(-0.546615\pi\) | ||||
−0.145923 | + | 0.989296i | \(0.546615\pi\) | |||||||
\(284\) | 4.57974e13 | 1.47092 | ||||||||
\(285\) | 8.49155e12 | 0.267510 | ||||||||
\(286\) | 1.77199e13 | 0.547580 | ||||||||
\(287\) | 1.04991e12 | 0.0318275 | ||||||||
\(288\) | −1.47524e13 | −0.438737 | ||||||||
\(289\) | 9.75381e13 | 2.84601 | ||||||||
\(290\) | −4.32700e12 | −0.123879 | ||||||||
\(291\) | 1.72945e13 | 0.485843 | ||||||||
\(292\) | 2.04083e13 | 0.562601 | ||||||||
\(293\) | 3.66862e13 | 0.992501 | 0.496250 | − | 0.868179i | \(-0.334710\pi\) | ||||
0.496250 | + | 0.868179i | \(0.334710\pi\) | |||||||
\(294\) | 2.51713e13 | 0.668335 | ||||||||
\(295\) | −3.38114e12 | −0.0881134 | ||||||||
\(296\) | −1.56383e13 | −0.400023 | ||||||||
\(297\) | 6.79588e12 | 0.170642 | ||||||||
\(298\) | 2.63331e13 | 0.649101 | ||||||||
\(299\) | −1.64933e13 | −0.399131 | ||||||||
\(300\) | −1.09710e13 | −0.260663 | ||||||||
\(301\) | −1.05696e12 | −0.0246572 | ||||||||
\(302\) | 1.14635e11 | 0.00262591 | ||||||||
\(303\) | −4.43880e13 | −0.998462 | ||||||||
\(304\) | 3.53001e13 | 0.779779 | ||||||||
\(305\) | −2.73663e13 | −0.593701 | ||||||||
\(306\) | 4.15380e13 | 0.885070 | ||||||||
\(307\) | −5.80115e13 | −1.21410 | −0.607048 | − | 0.794665i | \(-0.707646\pi\) | ||||
−0.607048 | + | 0.794665i | \(0.707646\pi\) | |||||||
\(308\) | 4.89404e13 | 1.00609 | ||||||||
\(309\) | 1.80992e13 | 0.365499 | ||||||||
\(310\) | 2.44896e12 | 0.0485838 | ||||||||
\(311\) | 5.93629e11 | 0.0115700 | 0.00578500 | − | 0.999983i | \(-0.498159\pi\) | ||||
0.00578500 | + | 0.999983i | \(0.498159\pi\) | |||||||
\(312\) | −3.10749e12 | −0.0595058 | ||||||||
\(313\) | 2.75783e13 | 0.518888 | 0.259444 | − | 0.965758i | \(-0.416461\pi\) | ||||
0.259444 | + | 0.965758i | \(0.416461\pi\) | |||||||
\(314\) | −1.09870e14 | −2.03127 | ||||||||
\(315\) | −1.69132e13 | −0.307268 | ||||||||
\(316\) | 1.65440e13 | 0.295367 | ||||||||
\(317\) | −1.86608e13 | −0.327420 | −0.163710 | − | 0.986509i | \(-0.552346\pi\) | ||||
−0.163710 | + | 0.986509i | \(0.552346\pi\) | |||||||
\(318\) | −7.79150e12 | −0.134361 | ||||||||
\(319\) | 7.07217e12 | 0.119868 | ||||||||
\(320\) | 2.61222e13 | 0.435195 | ||||||||
\(321\) | −1.64124e13 | −0.268779 | ||||||||
\(322\) | −1.00231e14 | −1.61359 | ||||||||
\(323\) | −8.48305e13 | −1.34257 | ||||||||
\(324\) | 5.94916e12 | 0.0925674 | ||||||||
\(325\) | −1.61579e13 | −0.247187 | ||||||||
\(326\) | −4.87574e13 | −0.733405 | ||||||||
\(327\) | −2.76460e13 | −0.408903 | ||||||||
\(328\) | −3.63053e11 | −0.00528037 | ||||||||
\(329\) | 2.94263e13 | 0.420880 | ||||||||
\(330\) | −3.33500e13 | −0.469103 | ||||||||
\(331\) | −4.90147e13 | −0.678067 | −0.339034 | − | 0.940774i | \(-0.610100\pi\) | ||||
−0.339034 | + | 0.940774i | \(0.610100\pi\) | |||||||
\(332\) | 5.03632e13 | 0.685258 | ||||||||
\(333\) | 4.40935e13 | 0.590107 | ||||||||
\(334\) | −3.32333e13 | −0.437490 | ||||||||
\(335\) | −7.39274e13 | −0.957324 | ||||||||
\(336\) | −7.03097e13 | −0.895672 | ||||||||
\(337\) | 1.01087e14 | 1.26687 | 0.633435 | − | 0.773796i | \(-0.281644\pi\) | ||||
0.633435 | + | 0.773796i | \(0.281644\pi\) | |||||||
\(338\) | −8.69625e13 | −1.07224 | ||||||||
\(339\) | 6.25400e13 | 0.758681 | ||||||||
\(340\) | −9.26420e13 | −1.10579 | ||||||||
\(341\) | −4.00264e12 | −0.0470108 | ||||||||
\(342\) | −2.67331e13 | −0.308962 | ||||||||
\(343\) | −1.73654e13 | −0.197500 | ||||||||
\(344\) | 3.65491e11 | 0.00409077 | ||||||||
\(345\) | 3.10414e13 | 0.341929 | ||||||||
\(346\) | −4.24224e12 | −0.0459914 | ||||||||
\(347\) | −6.59289e13 | −0.703499 | −0.351750 | − | 0.936094i | \(-0.614413\pi\) | ||||
−0.351750 | + | 0.936094i | \(0.614413\pi\) | |||||||
\(348\) | 6.19102e12 | 0.0650244 | ||||||||
\(349\) | 7.85864e13 | 0.812471 | 0.406235 | − | 0.913768i | \(-0.366841\pi\) | ||||
0.406235 | + | 0.913768i | \(0.366841\pi\) | |||||||
\(350\) | −9.81926e13 | −0.999320 | ||||||||
\(351\) | 8.76181e12 | 0.0877818 | ||||||||
\(352\) | −1.18325e14 | −1.16706 | ||||||||
\(353\) | 1.17523e13 | 0.114120 | 0.0570602 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570602 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(354\) | 1.06445e13 | 0.101767 | ||||||||
\(355\) | −1.26944e14 | −1.19497 | ||||||||
\(356\) | 2.92436e13 | 0.271054 | ||||||||
\(357\) | 1.68963e14 | 1.54211 | ||||||||
\(358\) | −1.21457e14 | −1.09161 | ||||||||
\(359\) | 1.51873e14 | 1.34419 | 0.672095 | − | 0.740465i | \(-0.265395\pi\) | ||||
0.672095 | + | 0.740465i | \(0.265395\pi\) | |||||||
\(360\) | 5.84849e12 | 0.0509777 | ||||||||
\(361\) | −6.18950e13 | −0.531332 | ||||||||
\(362\) | −1.40603e14 | −1.18877 | ||||||||
\(363\) | −1.48227e13 | −0.123436 | ||||||||
\(364\) | 6.30980e13 | 0.517557 | ||||||||
\(365\) | −5.65690e13 | −0.457054 | ||||||||
\(366\) | 8.61546e13 | 0.685698 | ||||||||
\(367\) | −2.15723e14 | −1.69135 | −0.845674 | − | 0.533700i | \(-0.820801\pi\) | ||||
−0.845674 | + | 0.533700i | \(0.820801\pi\) | |||||||
\(368\) | 1.29042e14 | 0.996707 | ||||||||
\(369\) | 1.02366e12 | 0.00778950 | ||||||||
\(370\) | −2.16383e14 | −1.62224 | ||||||||
\(371\) | −3.16932e13 | −0.234104 | ||||||||
\(372\) | −3.50394e12 | −0.0255017 | ||||||||
\(373\) | 7.11762e13 | 0.510430 | 0.255215 | − | 0.966884i | \(-0.417854\pi\) | ||||
0.255215 | + | 0.966884i | \(0.417854\pi\) | |||||||
\(374\) | 3.33166e14 | 2.35433 | ||||||||
\(375\) | 8.65252e13 | 0.602519 | ||||||||
\(376\) | −1.01755e13 | −0.0698266 | ||||||||
\(377\) | 9.11801e12 | 0.0616627 | ||||||||
\(378\) | 5.32461e13 | 0.354881 | ||||||||
\(379\) | −1.39102e14 | −0.913730 | −0.456865 | − | 0.889536i | \(-0.651028\pi\) | ||||
−0.456865 | + | 0.889536i | \(0.651028\pi\) | |||||||
\(380\) | 5.96226e13 | 0.386012 | ||||||||
\(381\) | −2.56185e13 | −0.163481 | ||||||||
\(382\) | 2.05734e14 | 1.29407 | ||||||||
\(383\) | −2.19166e14 | −1.35888 | −0.679438 | − | 0.733733i | \(-0.737776\pi\) | ||||
−0.679438 | + | 0.733733i | \(0.737776\pi\) | |||||||
\(384\) | 4.20953e13 | 0.257283 | ||||||||
\(385\) | −1.35656e14 | −0.817347 | ||||||||
\(386\) | −1.93286e14 | −1.14807 | ||||||||
\(387\) | −1.03053e12 | −0.00603463 | ||||||||
\(388\) | 1.21432e14 | 0.701063 | ||||||||
\(389\) | −3.18027e14 | −1.81026 | −0.905131 | − | 0.425133i | \(-0.860227\pi\) | ||||
−0.905131 | + | 0.425133i | \(0.860227\pi\) | |||||||
\(390\) | −4.29975e13 | −0.241317 | ||||||||
\(391\) | −3.10103e14 | −1.71607 | ||||||||
\(392\) | −3.54053e13 | −0.193194 | ||||||||
\(393\) | −1.91359e14 | −1.02965 | ||||||||
\(394\) | 5.54019e13 | 0.293965 | ||||||||
\(395\) | −4.58578e13 | −0.239955 | ||||||||
\(396\) | 4.77167e13 | 0.246233 | ||||||||
\(397\) | −3.67489e14 | −1.87024 | −0.935118 | − | 0.354337i | \(-0.884707\pi\) | ||||
−0.935118 | + | 0.354337i | \(0.884707\pi\) | |||||||
\(398\) | −1.17819e14 | −0.591368 | ||||||||
\(399\) | −1.08741e14 | −0.538323 | ||||||||
\(400\) | 1.26418e14 | 0.617275 | ||||||||
\(401\) | −1.15345e14 | −0.555527 | −0.277764 | − | 0.960649i | \(-0.589593\pi\) | ||||
−0.277764 | + | 0.960649i | \(0.589593\pi\) | |||||||
\(402\) | 2.32738e14 | 1.10567 | ||||||||
\(403\) | −5.16053e12 | −0.0241834 | ||||||||
\(404\) | −3.11667e14 | −1.44076 | ||||||||
\(405\) | −1.64903e13 | −0.0752013 | ||||||||
\(406\) | 5.54108e13 | 0.249288 | ||||||||
\(407\) | 3.53662e14 | 1.56971 | ||||||||
\(408\) | −5.84264e13 | −0.255846 | ||||||||
\(409\) | −9.55715e13 | −0.412905 | −0.206453 | − | 0.978457i | \(-0.566192\pi\) | ||||
−0.206453 | + | 0.978457i | \(0.566192\pi\) | |||||||
\(410\) | −5.02347e12 | −0.0214138 | ||||||||
\(411\) | −1.00020e14 | −0.420687 | ||||||||
\(412\) | 1.27082e14 | 0.527409 | ||||||||
\(413\) | 4.32982e13 | 0.177315 | ||||||||
\(414\) | −9.77244e13 | −0.394913 | ||||||||
\(415\) | −1.39600e14 | −0.556701 | ||||||||
\(416\) | −1.52555e14 | −0.600360 | ||||||||
\(417\) | 1.24437e14 | 0.483282 | ||||||||
\(418\) | −2.14419e14 | −0.821853 | ||||||||
\(419\) | −4.36834e14 | −1.65249 | −0.826246 | − | 0.563310i | \(-0.809528\pi\) | ||||
−0.826246 | + | 0.563310i | \(0.809528\pi\) | |||||||
\(420\) | −1.18754e14 | −0.443383 | ||||||||
\(421\) | −4.67891e14 | −1.72422 | −0.862111 | − | 0.506720i | \(-0.830858\pi\) | ||||
−0.862111 | + | 0.506720i | \(0.830858\pi\) | |||||||
\(422\) | 5.72758e14 | 2.08330 | ||||||||
\(423\) | 2.86905e13 | 0.103007 | ||||||||
\(424\) | 1.09593e13 | 0.0388394 | ||||||||
\(425\) | −3.03797e14 | −1.06278 | ||||||||
\(426\) | 3.99646e14 | 1.38014 | ||||||||
\(427\) | 3.50448e14 | 1.19473 | ||||||||
\(428\) | −1.15238e14 | −0.387843 | ||||||||
\(429\) | 7.02762e13 | 0.233503 | ||||||||
\(430\) | 5.05721e12 | 0.0165895 | ||||||||
\(431\) | −4.38864e13 | −0.142136 | −0.0710682 | − | 0.997471i | \(-0.522641\pi\) | ||||
−0.0710682 | + | 0.997471i | \(0.522641\pi\) | |||||||
\(432\) | −6.85516e13 | −0.219208 | ||||||||
\(433\) | 9.84065e13 | 0.310699 | 0.155350 | − | 0.987860i | \(-0.450350\pi\) | ||||
0.155350 | + | 0.987860i | \(0.450350\pi\) | |||||||
\(434\) | −3.13609e13 | −0.0977675 | ||||||||
\(435\) | −1.71607e13 | −0.0528255 | ||||||||
\(436\) | −1.94114e14 | −0.590040 | ||||||||
\(437\) | 1.99576e14 | 0.599048 | ||||||||
\(438\) | 1.78090e14 | 0.527877 | ||||||||
\(439\) | −3.97742e14 | −1.16425 | −0.582125 | − | 0.813099i | \(-0.697778\pi\) | ||||
−0.582125 | + | 0.813099i | \(0.697778\pi\) | |||||||
\(440\) | 4.69092e13 | 0.135603 | ||||||||
\(441\) | 9.98280e13 | 0.284997 | ||||||||
\(442\) | 4.29544e14 | 1.21112 | ||||||||
\(443\) | 5.19038e14 | 1.44537 | 0.722684 | − | 0.691179i | \(-0.242908\pi\) | ||||
0.722684 | + | 0.691179i | \(0.242908\pi\) | |||||||
\(444\) | 3.09598e14 | 0.851514 | ||||||||
\(445\) | −8.10593e13 | −0.220203 | ||||||||
\(446\) | −1.52554e14 | −0.409339 | ||||||||
\(447\) | 1.04436e14 | 0.276795 | ||||||||
\(448\) | −3.34516e14 | −0.875764 | ||||||||
\(449\) | 6.11715e14 | 1.58195 | 0.790977 | − | 0.611845i | \(-0.209573\pi\) | ||||
0.790977 | + | 0.611845i | \(0.209573\pi\) | |||||||
\(450\) | −9.57373e13 | −0.244575 | ||||||||
\(451\) | 8.21050e12 | 0.0207204 | ||||||||
\(452\) | 4.39119e14 | 1.09476 | ||||||||
\(453\) | 4.54638e11 | 0.00111976 | ||||||||
\(454\) | 7.93379e13 | 0.193052 | ||||||||
\(455\) | −1.74899e14 | −0.420461 | ||||||||
\(456\) | 3.76021e13 | 0.0893111 | ||||||||
\(457\) | −6.05954e14 | −1.42200 | −0.711001 | − | 0.703191i | \(-0.751758\pi\) | ||||
−0.711001 | + | 0.703191i | \(0.751758\pi\) | |||||||
\(458\) | 1.00144e14 | 0.232202 | ||||||||
\(459\) | 1.64738e14 | 0.377419 | ||||||||
\(460\) | 2.17954e14 | 0.493398 | ||||||||
\(461\) | 6.00121e14 | 1.34241 | 0.671203 | − | 0.741274i | \(-0.265778\pi\) | ||||
0.671203 | + | 0.741274i | \(0.265778\pi\) | |||||||
\(462\) | 4.27073e14 | 0.943999 | ||||||||
\(463\) | −1.51514e14 | −0.330947 | −0.165473 | − | 0.986214i | \(-0.552915\pi\) | ||||
−0.165473 | + | 0.986214i | \(0.552915\pi\) | |||||||
\(464\) | −7.13385e13 | −0.153984 | ||||||||
\(465\) | 9.71245e12 | 0.0207175 | ||||||||
\(466\) | 2.61838e14 | 0.551964 | ||||||||
\(467\) | 7.37741e14 | 1.53695 | 0.768477 | − | 0.639877i | \(-0.221015\pi\) | ||||
0.768477 | + | 0.639877i | \(0.221015\pi\) | |||||||
\(468\) | 6.15202e13 | 0.126668 | ||||||||
\(469\) | 9.46700e14 | 1.92647 | ||||||||
\(470\) | −1.40795e14 | −0.283171 | ||||||||
\(471\) | −4.35741e14 | −0.866190 | ||||||||
\(472\) | −1.49723e13 | −0.0294176 | ||||||||
\(473\) | −8.26563e12 | −0.0160524 | ||||||||
\(474\) | 1.44369e14 | 0.277137 | ||||||||
\(475\) | 1.95518e14 | 0.370999 | ||||||||
\(476\) | 1.18636e15 | 2.22524 | ||||||||
\(477\) | −3.09007e13 | −0.0572951 | ||||||||
\(478\) | 1.41780e15 | 2.59873 | ||||||||
\(479\) | 7.42160e14 | 1.34478 | 0.672391 | − | 0.740196i | \(-0.265267\pi\) | ||||
0.672391 | + | 0.740196i | \(0.265267\pi\) | |||||||
\(480\) | 2.87118e14 | 0.514319 | ||||||||
\(481\) | 4.55970e14 | 0.807493 | ||||||||
\(482\) | −3.80443e14 | −0.666087 | ||||||||
\(483\) | −3.97510e14 | −0.688080 | ||||||||
\(484\) | −1.04076e14 | −0.178115 | ||||||||
\(485\) | −3.36592e14 | −0.569540 | ||||||||
\(486\) | 5.19147e13 | 0.0868542 | ||||||||
\(487\) | −8.43286e14 | −1.39497 | −0.697486 | − | 0.716598i | \(-0.745698\pi\) | ||||
−0.697486 | + | 0.716598i | \(0.745698\pi\) | |||||||
\(488\) | −1.21183e14 | −0.198213 | ||||||||
\(489\) | −1.93370e14 | −0.312744 | ||||||||
\(490\) | −4.89893e14 | −0.783471 | ||||||||
\(491\) | 4.18548e14 | 0.661908 | 0.330954 | − | 0.943647i | \(-0.392630\pi\) | ||||
0.330954 | + | 0.943647i | \(0.392630\pi\) | |||||||
\(492\) | 7.18752e12 | 0.0112401 | ||||||||
\(493\) | 1.71435e14 | 0.265119 | ||||||||
\(494\) | −2.76447e14 | −0.422779 | ||||||||
\(495\) | −1.32264e14 | −0.200039 | ||||||||
\(496\) | 4.03755e13 | 0.0603906 | ||||||||
\(497\) | 1.62562e15 | 2.40470 | ||||||||
\(498\) | 4.39489e14 | 0.642964 | ||||||||
\(499\) | −1.56784e14 | −0.226856 | −0.113428 | − | 0.993546i | \(-0.536183\pi\) | ||||
−0.113428 | + | 0.993546i | \(0.536183\pi\) | |||||||
\(500\) | 6.07529e14 | 0.869425 | ||||||||
\(501\) | −1.31802e14 | −0.186558 | ||||||||
\(502\) | −4.10921e14 | −0.575292 | ||||||||
\(503\) | 4.68877e14 | 0.649285 | 0.324642 | − | 0.945837i | \(-0.394756\pi\) | ||||
0.324642 | + | 0.945837i | \(0.394756\pi\) | |||||||
\(504\) | −7.48947e13 | −0.102585 | ||||||||
\(505\) | 8.63898e14 | 1.17047 | ||||||||
\(506\) | −7.83823e14 | −1.05049 | ||||||||
\(507\) | −3.44889e14 | −0.457231 | ||||||||
\(508\) | −1.79878e14 | −0.235900 | ||||||||
\(509\) | −2.30249e14 | −0.298710 | −0.149355 | − | 0.988784i | \(-0.547720\pi\) | ||||
−0.149355 | + | 0.988784i | \(0.547720\pi\) | |||||||
\(510\) | −8.08430e14 | −1.03754 | ||||||||
\(511\) | 7.24412e14 | 0.919752 | ||||||||
\(512\) | 9.88667e14 | 1.24184 | ||||||||
\(513\) | −1.06022e14 | −0.131750 | ||||||||
\(514\) | 5.57349e14 | 0.685220 | ||||||||
\(515\) | −3.52253e14 | −0.428465 | ||||||||
\(516\) | −7.23578e12 | −0.00870787 | ||||||||
\(517\) | 2.30119e14 | 0.274003 | ||||||||
\(518\) | 2.77096e15 | 3.26450 | ||||||||
\(519\) | −1.68245e13 | −0.0196120 | ||||||||
\(520\) | 6.04792e13 | 0.0697570 | ||||||||
\(521\) | 1.35492e14 | 0.154634 | 0.0773172 | − | 0.997007i | \(-0.475365\pi\) | ||||
0.0773172 | + | 0.997007i | \(0.475365\pi\) | |||||||
\(522\) | 5.40252e13 | 0.0610111 | ||||||||
\(523\) | −5.15997e14 | −0.576617 | −0.288309 | − | 0.957538i | \(-0.593093\pi\) | ||||
−0.288309 | + | 0.957538i | \(0.593093\pi\) | |||||||
\(524\) | −1.34361e15 | −1.48577 | ||||||||
\(525\) | −3.89427e14 | −0.426138 | ||||||||
\(526\) | −1.17029e15 | −1.26728 | ||||||||
\(527\) | −9.70272e13 | −0.103977 | ||||||||
\(528\) | −5.49835e14 | −0.583104 | ||||||||
\(529\) | −2.23246e14 | −0.234302 | ||||||||
\(530\) | 1.51641e14 | 0.157507 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −7.63516e14 | −0.776791 | ||||||||
\(533\) | 1.05856e13 | 0.0106590 | ||||||||
\(534\) | 2.55191e14 | 0.254324 | ||||||||
\(535\) | 3.19425e14 | 0.315082 | ||||||||
\(536\) | −3.27364e14 | −0.319613 | ||||||||
\(537\) | −4.81693e14 | −0.465491 | ||||||||
\(538\) | −4.15501e14 | −0.397438 | ||||||||
\(539\) | 8.00695e14 | 0.758104 | ||||||||
\(540\) | −1.15785e14 | −0.108514 | ||||||||
\(541\) | −2.46913e14 | −0.229065 | −0.114532 | − | 0.993420i | \(-0.536537\pi\) | ||||
−0.114532 | + | 0.993420i | \(0.536537\pi\) | |||||||
\(542\) | −1.70773e15 | −1.56827 | ||||||||
\(543\) | −5.57624e14 | −0.506924 | ||||||||
\(544\) | −2.86830e15 | −2.58125 | ||||||||
\(545\) | 5.38059e14 | 0.479346 | ||||||||
\(546\) | 5.50618e14 | 0.485613 | ||||||||
\(547\) | −5.16101e14 | −0.450613 | −0.225307 | − | 0.974288i | \(-0.572338\pi\) | ||||
−0.225307 | + | 0.974288i | \(0.572338\pi\) | |||||||
\(548\) | −7.02284e14 | −0.607044 | ||||||||
\(549\) | 3.41685e14 | 0.292401 | ||||||||
\(550\) | −7.67884e14 | −0.650580 | ||||||||
\(551\) | −1.10332e14 | −0.0925484 | ||||||||
\(552\) | 1.37457e14 | 0.114157 | ||||||||
\(553\) | 5.87246e14 | 0.482872 | ||||||||
\(554\) | 8.58686e14 | 0.699086 | ||||||||
\(555\) | −8.58165e14 | −0.691766 | ||||||||
\(556\) | 8.73722e14 | 0.697368 | ||||||||
\(557\) | 5.88335e14 | 0.464966 | 0.232483 | − | 0.972600i | \(-0.425315\pi\) | ||||
0.232483 | + | 0.972600i | \(0.425315\pi\) | |||||||
\(558\) | −3.05767e13 | −0.0239278 | ||||||||
\(559\) | −1.06567e13 | −0.00825769 | ||||||||
\(560\) | 1.36840e15 | 1.04997 | ||||||||
\(561\) | 1.32132e15 | 1.00395 | ||||||||
\(562\) | −2.18874e15 | −1.64681 | ||||||||
\(563\) | 7.94570e14 | 0.592019 | 0.296010 | − | 0.955185i | \(-0.404344\pi\) | ||||
0.296010 | + | 0.955185i | \(0.404344\pi\) | |||||||
\(564\) | 2.01448e14 | 0.148637 | ||||||||
\(565\) | −1.21718e15 | −0.889382 | ||||||||
\(566\) | −5.46055e14 | −0.395136 | ||||||||
\(567\) | 2.11171e14 | 0.151331 | ||||||||
\(568\) | −5.62132e14 | −0.398954 | ||||||||
\(569\) | −2.31308e15 | −1.62582 | −0.812912 | − | 0.582387i | \(-0.802119\pi\) | ||||
−0.812912 | + | 0.582387i | \(0.802119\pi\) | |||||||
\(570\) | 5.20290e14 | 0.362188 | ||||||||
\(571\) | 1.61932e15 | 1.11644 | 0.558219 | − | 0.829694i | \(-0.311485\pi\) | ||||
0.558219 | + | 0.829694i | \(0.311485\pi\) | |||||||
\(572\) | 4.93438e14 | 0.336941 | ||||||||
\(573\) | 8.15931e14 | 0.551827 | ||||||||
\(574\) | 6.43296e13 | 0.0430919 | ||||||||
\(575\) | 7.14729e14 | 0.474207 | ||||||||
\(576\) | −3.26151e14 | −0.214336 | ||||||||
\(577\) | −3.95780e14 | −0.257625 | −0.128812 | − | 0.991669i | \(-0.541116\pi\) | ||||
−0.128812 | + | 0.991669i | \(0.541116\pi\) | |||||||
\(578\) | 5.97631e15 | 3.85328 | ||||||||
\(579\) | −7.66561e14 | −0.489570 | ||||||||
\(580\) | −1.20492e14 | −0.0762263 | ||||||||
\(581\) | 1.78769e15 | 1.12027 | ||||||||
\(582\) | 1.05966e15 | 0.657794 | ||||||||
\(583\) | −2.47847e14 | −0.152407 | ||||||||
\(584\) | −2.50498e14 | −0.152592 | ||||||||
\(585\) | −1.70526e14 | −0.102904 | ||||||||
\(586\) | 2.24782e15 | 1.34377 | ||||||||
\(587\) | −2.50811e15 | −1.48538 | −0.742690 | − | 0.669636i | \(-0.766450\pi\) | ||||
−0.742690 | + | 0.669636i | \(0.766450\pi\) | |||||||
\(588\) | 7.00933e14 | 0.411245 | ||||||||
\(589\) | 6.24449e13 | 0.0362963 | ||||||||
\(590\) | −2.07168e14 | −0.119299 | ||||||||
\(591\) | 2.19721e14 | 0.125355 | ||||||||
\(592\) | −3.56747e15 | −2.01647 | ||||||||
\(593\) | −8.43239e14 | −0.472226 | −0.236113 | − | 0.971726i | \(-0.575874\pi\) | ||||
−0.236113 | + | 0.971726i | \(0.575874\pi\) | |||||||
\(594\) | 4.16394e14 | 0.231036 | ||||||||
\(595\) | −3.28842e15 | −1.80777 | ||||||||
\(596\) | 7.33286e14 | 0.399410 | ||||||||
\(597\) | −4.67264e14 | −0.252176 | ||||||||
\(598\) | −1.01057e15 | −0.540392 | ||||||||
\(599\) | −2.42799e15 | −1.28647 | −0.643234 | − | 0.765669i | \(-0.722408\pi\) | ||||
−0.643234 | + | 0.765669i | \(0.722408\pi\) | |||||||
\(600\) | 1.34662e14 | 0.0706989 | ||||||||
\(601\) | −6.07393e14 | −0.315980 | −0.157990 | − | 0.987441i | \(-0.550501\pi\) | ||||
−0.157990 | + | 0.987441i | \(0.550501\pi\) | |||||||
\(602\) | −6.47616e13 | −0.0333839 | ||||||||
\(603\) | 9.23028e14 | 0.471487 | ||||||||
\(604\) | 3.19220e12 | 0.00161580 | ||||||||
\(605\) | 2.88485e14 | 0.144700 | ||||||||
\(606\) | −2.71972e15 | −1.35184 | ||||||||
\(607\) | 8.52930e13 | 0.0420122 | 0.0210061 | − | 0.999779i | \(-0.493313\pi\) | ||||
0.0210061 | + | 0.999779i | \(0.493313\pi\) | |||||||
\(608\) | 1.84598e15 | 0.901070 | ||||||||
\(609\) | 2.19756e14 | 0.106303 | ||||||||
\(610\) | −1.67678e15 | −0.803825 | ||||||||
\(611\) | 2.96688e14 | 0.140953 | ||||||||
\(612\) | 1.15669e15 | 0.544609 | ||||||||
\(613\) | 4.05440e15 | 1.89188 | 0.945942 | − | 0.324336i | \(-0.105141\pi\) | ||||
0.945942 | + | 0.324336i | \(0.105141\pi\) | |||||||
\(614\) | −3.55445e15 | −1.64379 | ||||||||
\(615\) | −1.99229e13 | −0.00913142 | ||||||||
\(616\) | −6.00711e14 | −0.272880 | ||||||||
\(617\) | −4.21114e15 | −1.89597 | −0.947985 | − | 0.318314i | \(-0.896883\pi\) | ||||
−0.947985 | + | 0.318314i | \(0.896883\pi\) | |||||||
\(618\) | 1.10896e15 | 0.494858 | ||||||||
\(619\) | 2.48051e15 | 1.09709 | 0.548545 | − | 0.836121i | \(-0.315182\pi\) | ||||
0.548545 | + | 0.836121i | \(0.315182\pi\) | |||||||
\(620\) | 6.81950e13 | 0.0298950 | ||||||||
\(621\) | −3.87570e14 | −0.168402 | ||||||||
\(622\) | 3.63726e13 | 0.0156649 | ||||||||
\(623\) | 1.03803e15 | 0.443125 | ||||||||
\(624\) | −7.08892e14 | −0.299961 | ||||||||
\(625\) | −3.91939e14 | −0.164391 | ||||||||
\(626\) | 1.68977e15 | 0.702534 | ||||||||
\(627\) | −8.50376e14 | −0.350461 | ||||||||
\(628\) | −3.05951e15 | −1.24990 | ||||||||
\(629\) | 8.57306e15 | 3.47182 | ||||||||
\(630\) | −1.03630e15 | −0.416017 | ||||||||
\(631\) | −2.87235e15 | −1.14308 | −0.571539 | − | 0.820575i | \(-0.693653\pi\) | ||||
−0.571539 | + | 0.820575i | \(0.693653\pi\) | |||||||
\(632\) | −2.03067e14 | −0.0801115 | ||||||||
\(633\) | 2.27153e15 | 0.888379 | ||||||||
\(634\) | −1.14338e15 | −0.443301 | ||||||||
\(635\) | 4.98598e14 | 0.191644 | ||||||||
\(636\) | −2.16967e14 | −0.0826759 | ||||||||
\(637\) | 1.03232e15 | 0.389985 | ||||||||
\(638\) | 4.33323e14 | 0.162292 | ||||||||
\(639\) | 1.58498e15 | 0.588529 | ||||||||
\(640\) | −8.19276e14 | −0.301606 | ||||||||
\(641\) | 1.27809e15 | 0.466491 | 0.233246 | − | 0.972418i | \(-0.425065\pi\) | ||||
0.233246 | + | 0.972418i | \(0.425065\pi\) | |||||||
\(642\) | −1.00561e15 | −0.363905 | ||||||||
\(643\) | −3.85741e15 | −1.38400 | −0.691999 | − | 0.721898i | \(-0.743270\pi\) | ||||
−0.691999 | + | 0.721898i | \(0.743270\pi\) | |||||||
\(644\) | −2.79108e15 | −0.992887 | ||||||||
\(645\) | 2.00566e13 | 0.00707424 | ||||||||
\(646\) | −5.19769e15 | −1.81774 | ||||||||
\(647\) | 4.09141e15 | 1.41873 | 0.709364 | − | 0.704842i | \(-0.248982\pi\) | ||||
0.709364 | + | 0.704842i | \(0.248982\pi\) | |||||||
\(648\) | −7.30219e13 | −0.0251068 | ||||||||
\(649\) | 3.38600e14 | 0.115436 | ||||||||
\(650\) | −9.90019e14 | −0.334673 | ||||||||
\(651\) | −1.24376e14 | −0.0416908 | ||||||||
\(652\) | −1.35773e15 | −0.451285 | ||||||||
\(653\) | 1.20118e15 | 0.395900 | 0.197950 | − | 0.980212i | \(-0.436572\pi\) | ||||
0.197950 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(654\) | −1.69392e15 | −0.553623 | ||||||||
\(655\) | 3.72432e15 | 1.20703 | ||||||||
\(656\) | −8.28211e13 | −0.0266177 | ||||||||
\(657\) | 7.06298e14 | 0.225102 | ||||||||
\(658\) | 1.80300e15 | 0.569839 | ||||||||
\(659\) | −8.71415e14 | −0.273121 | −0.136561 | − | 0.990632i | \(-0.543605\pi\) | ||||
−0.136561 | + | 0.990632i | \(0.543605\pi\) | |||||||
\(660\) | −9.28682e14 | −0.288652 | ||||||||
\(661\) | −1.76923e15 | −0.545350 | −0.272675 | − | 0.962106i | \(-0.587908\pi\) | ||||
−0.272675 | + | 0.962106i | \(0.587908\pi\) | |||||||
\(662\) | −3.00321e15 | −0.918051 | ||||||||
\(663\) | 1.70355e15 | 0.516453 | ||||||||
\(664\) | −6.18175e14 | −0.185860 | ||||||||
\(665\) | 2.11637e15 | 0.631061 | ||||||||
\(666\) | 2.70167e15 | 0.798959 | ||||||||
\(667\) | −4.03327e14 | −0.118295 | ||||||||
\(668\) | −9.25434e14 | −0.269200 | ||||||||
\(669\) | −6.05023e14 | −0.174553 | ||||||||
\(670\) | −4.52965e15 | −1.29614 | ||||||||
\(671\) | 2.74057e15 | 0.777798 | ||||||||
\(672\) | −3.67677e15 | −1.03499 | ||||||||
\(673\) | −2.82172e15 | −0.787828 | −0.393914 | − | 0.919147i | \(-0.628879\pi\) | ||||
−0.393914 | + | 0.919147i | \(0.628879\pi\) | |||||||
\(674\) | 6.19378e15 | 1.71524 | ||||||||
\(675\) | −3.79689e14 | −0.104294 | ||||||||
\(676\) | −2.42161e15 | −0.659777 | ||||||||
\(677\) | 5.77021e15 | 1.55939 | 0.779694 | − | 0.626161i | \(-0.215375\pi\) | ||||
0.779694 | + | 0.626161i | \(0.215375\pi\) | |||||||
\(678\) | 3.83192e15 | 1.02720 | ||||||||
\(679\) | 4.31033e15 | 1.14611 | ||||||||
\(680\) | 1.13712e15 | 0.299921 | ||||||||
\(681\) | 3.14650e14 | 0.0823226 | ||||||||
\(682\) | −2.45248e14 | −0.0636490 | ||||||||
\(683\) | 2.28597e15 | 0.588513 | 0.294256 | − | 0.955727i | \(-0.404928\pi\) | ||||
0.294256 | + | 0.955727i | \(0.404928\pi\) | |||||||
\(684\) | −7.44424e14 | −0.190113 | ||||||||
\(685\) | 1.94664e15 | 0.493159 | ||||||||
\(686\) | −1.06401e15 | −0.267400 | ||||||||
\(687\) | 3.97168e14 | 0.0990175 | ||||||||
\(688\) | 8.33773e13 | 0.0206211 | ||||||||
\(689\) | −3.19544e14 | −0.0784017 | ||||||||
\(690\) | 1.90195e15 | 0.462945 | ||||||||
\(691\) | 6.69541e15 | 1.61677 | 0.808384 | − | 0.588656i | \(-0.200343\pi\) | ||||
0.808384 | + | 0.588656i | \(0.200343\pi\) | |||||||
\(692\) | −1.18132e14 | −0.0282998 | ||||||||
\(693\) | 1.69375e15 | 0.402547 | ||||||||
\(694\) | −4.03957e15 | −0.952484 | ||||||||
\(695\) | −2.42184e15 | −0.566539 | ||||||||
\(696\) | −7.59906e13 | −0.0176364 | ||||||||
\(697\) | 1.99029e14 | 0.0458286 | ||||||||
\(698\) | 4.81511e15 | 1.10002 | ||||||||
\(699\) | 1.03844e15 | 0.235373 | ||||||||
\(700\) | −2.73433e15 | −0.614909 | ||||||||
\(701\) | −5.28166e15 | −1.17848 | −0.589239 | − | 0.807959i | \(-0.700572\pi\) | ||||
−0.589239 | + | 0.807959i | \(0.700572\pi\) | |||||||
\(702\) | 5.36849e14 | 0.118850 | ||||||||
\(703\) | −5.51746e15 | −1.21195 | ||||||||
\(704\) | −2.61597e15 | −0.570143 | ||||||||
\(705\) | −5.58387e14 | −0.120752 | ||||||||
\(706\) | 7.20084e14 | 0.154510 | ||||||||
\(707\) | −1.10629e16 | −2.35539 | ||||||||
\(708\) | 2.96413e14 | 0.0626201 | ||||||||
\(709\) | −5.09324e14 | −0.106768 | −0.0533838 | − | 0.998574i | \(-0.517001\pi\) | ||||
−0.0533838 | + | 0.998574i | \(0.517001\pi\) | |||||||
\(710\) | −7.77807e15 | −1.61790 | ||||||||
\(711\) | 5.72562e14 | 0.118179 | ||||||||
\(712\) | −3.58945e14 | −0.0735171 | ||||||||
\(713\) | 2.28271e14 | 0.0463937 | ||||||||
\(714\) | 1.03526e16 | 2.08790 | ||||||||
\(715\) | −1.36774e15 | −0.273730 | ||||||||
\(716\) | −3.38216e15 | −0.671696 | ||||||||
\(717\) | 5.62292e15 | 1.10817 | ||||||||
\(718\) | 9.30548e15 | 1.81993 | ||||||||
\(719\) | 6.03395e15 | 1.17110 | 0.585549 | − | 0.810637i | \(-0.300879\pi\) | ||||
0.585549 | + | 0.810637i | \(0.300879\pi\) | |||||||
\(720\) | 1.33418e15 | 0.256972 | ||||||||
\(721\) | 4.51089e15 | 0.862220 | ||||||||
\(722\) | −3.79240e15 | −0.719382 | ||||||||
\(723\) | −1.50882e15 | −0.284038 | ||||||||
\(724\) | −3.91531e15 | −0.731482 | ||||||||
\(725\) | −3.95125e14 | −0.0732615 | ||||||||
\(726\) | −9.08209e14 | −0.167122 | ||||||||
\(727\) | −1.44703e15 | −0.264264 | −0.132132 | − | 0.991232i | \(-0.542182\pi\) | ||||
−0.132132 | + | 0.991232i | \(0.542182\pi\) | |||||||
\(728\) | −7.74485e14 | −0.140375 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −3.46607e15 | −0.618816 | ||||||||
\(731\) | −2.00366e14 | −0.0355040 | ||||||||
\(732\) | 2.39911e15 | 0.421929 | ||||||||
\(733\) | −5.16246e15 | −0.901125 | −0.450562 | − | 0.892745i | \(-0.648777\pi\) | ||||
−0.450562 | + | 0.892745i | \(0.648777\pi\) | |||||||
\(734\) | −1.32177e16 | −2.28995 | ||||||||
\(735\) | −1.94289e15 | −0.334094 | ||||||||
\(736\) | 6.74811e15 | 1.15174 | ||||||||
\(737\) | 7.40337e15 | 1.25418 | ||||||||
\(738\) | 6.27211e13 | 0.0105464 | ||||||||
\(739\) | 9.92866e15 | 1.65709 | 0.828545 | − | 0.559923i | \(-0.189169\pi\) | ||||
0.828545 | + | 0.559923i | \(0.189169\pi\) | |||||||
\(740\) | −6.02553e15 | −0.998207 | ||||||||
\(741\) | −1.09637e15 | −0.180285 | ||||||||
\(742\) | −1.94189e15 | −0.316959 | ||||||||
\(743\) | −3.22833e15 | −0.523046 | −0.261523 | − | 0.965197i | \(-0.584225\pi\) | ||||
−0.261523 | + | 0.965197i | \(0.584225\pi\) | |||||||
\(744\) | 4.30085e13 | 0.00691676 | ||||||||
\(745\) | −2.03257e15 | −0.324479 | ||||||||
\(746\) | 4.36108e15 | 0.691083 | ||||||||
\(747\) | 1.74299e15 | 0.274178 | ||||||||
\(748\) | 9.27752e15 | 1.44868 | ||||||||
\(749\) | −4.09050e15 | −0.634054 | ||||||||
\(750\) | 5.30153e15 | 0.815764 | ||||||||
\(751\) | 4.74253e15 | 0.724419 | 0.362210 | − | 0.932097i | \(-0.382022\pi\) | ||||
0.362210 | + | 0.932097i | \(0.382022\pi\) | |||||||
\(752\) | −2.32126e15 | −0.351987 | ||||||||
\(753\) | −1.62969e15 | −0.245320 | ||||||||
\(754\) | 5.58675e14 | 0.0834866 | ||||||||
\(755\) | −8.84835e12 | −0.00131267 | ||||||||
\(756\) | 1.48272e15 | 0.218368 | ||||||||
\(757\) | 7.08211e15 | 1.03546 | 0.517732 | − | 0.855543i | \(-0.326776\pi\) | ||||
0.517732 | + | 0.855543i | \(0.326776\pi\) | |||||||
\(758\) | −8.52299e15 | −1.23712 | ||||||||
\(759\) | −3.10860e15 | −0.447956 | ||||||||
\(760\) | −7.31828e14 | −0.104697 | ||||||||
\(761\) | 9.54792e14 | 0.135610 | 0.0678052 | − | 0.997699i | \(-0.478400\pi\) | ||||
0.0678052 | + | 0.997699i | \(0.478400\pi\) | |||||||
\(762\) | −1.56968e15 | −0.221340 | ||||||||
\(763\) | −6.89028e15 | −0.964610 | ||||||||
\(764\) | 5.72898e15 | 0.796277 | ||||||||
\(765\) | −3.20619e15 | −0.442437 | ||||||||
\(766\) | −1.34286e16 | −1.83981 | ||||||||
\(767\) | 4.36551e14 | 0.0593828 | ||||||||
\(768\) | 5.32804e15 | 0.719583 | ||||||||
\(769\) | −4.67556e15 | −0.626959 | −0.313479 | − | 0.949595i | \(-0.601495\pi\) | ||||
−0.313479 | + | 0.949595i | \(0.601495\pi\) | |||||||
\(770\) | −8.31188e15 | −1.10662 | ||||||||
\(771\) | 2.21042e15 | 0.292197 | ||||||||
\(772\) | −5.38234e15 | −0.706441 | ||||||||
\(773\) | −7.06977e15 | −0.921336 | −0.460668 | − | 0.887573i | \(-0.652390\pi\) | ||||
−0.460668 | + | 0.887573i | \(0.652390\pi\) | |||||||
\(774\) | −6.31423e13 | −0.00817043 | ||||||||
\(775\) | 2.23630e14 | 0.0287323 | ||||||||
\(776\) | −1.49049e15 | −0.190147 | ||||||||
\(777\) | 1.09895e16 | 1.39207 | ||||||||
\(778\) | −1.94860e16 | −2.45095 | ||||||||
\(779\) | −1.28091e14 | −0.0159979 | ||||||||
\(780\) | −1.19733e15 | −0.148489 | ||||||||
\(781\) | 1.27127e16 | 1.56551 | ||||||||
\(782\) | −1.90005e16 | −2.32342 | ||||||||
\(783\) | 2.14261e14 | 0.0260168 | ||||||||
\(784\) | −8.07679e15 | −0.973868 | ||||||||
\(785\) | 8.48057e15 | 1.01541 | ||||||||
\(786\) | −1.17249e16 | −1.39407 | ||||||||
\(787\) | −1.64678e15 | −0.194436 | −0.0972178 | − | 0.995263i | \(-0.530994\pi\) | ||||
−0.0972178 | + | 0.995263i | \(0.530994\pi\) | |||||||
\(788\) | 1.54275e15 | 0.180885 | ||||||||
\(789\) | −4.64131e15 | −0.540402 | ||||||||
\(790\) | −2.80978e15 | −0.324880 | ||||||||
\(791\) | 1.55870e16 | 1.78974 | ||||||||
\(792\) | −5.85690e14 | −0.0667851 | ||||||||
\(793\) | 3.53336e15 | 0.400116 | ||||||||
\(794\) | −2.25166e16 | −2.53215 | ||||||||
\(795\) | 6.01403e14 | 0.0671655 | ||||||||
\(796\) | −3.28085e15 | −0.363885 | ||||||||
\(797\) | 7.50082e15 | 0.826205 | 0.413103 | − | 0.910685i | \(-0.364445\pi\) | ||||
0.413103 | + | 0.910685i | \(0.364445\pi\) | |||||||
\(798\) | −6.66274e15 | −0.728848 | ||||||||
\(799\) | 5.57828e15 | 0.606028 | ||||||||
\(800\) | 6.61089e15 | 0.713289 | ||||||||
\(801\) | 1.01207e15 | 0.108451 | ||||||||
\(802\) | −7.06737e15 | −0.752141 | ||||||||
\(803\) | 5.66504e15 | 0.598780 | ||||||||
\(804\) | 6.48096e15 | 0.680348 | ||||||||
\(805\) | 7.73651e15 | 0.806617 | ||||||||
\(806\) | −3.16194e14 | −0.0327424 | ||||||||
\(807\) | −1.64786e15 | −0.169479 | ||||||||
\(808\) | 3.82550e15 | 0.390774 | ||||||||
\(809\) | 1.32814e16 | 1.34749 | 0.673747 | − | 0.738962i | \(-0.264684\pi\) | ||||
0.673747 | + | 0.738962i | \(0.264684\pi\) | |||||||
\(810\) | −1.01039e15 | −0.101817 | ||||||||
\(811\) | −1.09505e16 | −1.09602 | −0.548011 | − | 0.836471i | \(-0.684615\pi\) | ||||
−0.548011 | + | 0.836471i | \(0.684615\pi\) | |||||||
\(812\) | 1.54300e15 | 0.153394 | ||||||||
\(813\) | −6.77276e15 | −0.668756 | ||||||||
\(814\) | 2.16694e16 | 2.12527 | ||||||||
\(815\) | 3.76344e15 | 0.366622 | ||||||||
\(816\) | −1.33284e16 | −1.28968 | ||||||||
\(817\) | 1.28951e14 | 0.0123938 | ||||||||
\(818\) | −5.85582e15 | −0.559042 | ||||||||
\(819\) | 2.18372e15 | 0.207079 | ||||||||
\(820\) | −1.39886e14 | −0.0131765 | ||||||||
\(821\) | 5.80101e15 | 0.542770 | 0.271385 | − | 0.962471i | \(-0.412518\pi\) | ||||
0.271385 | + | 0.962471i | \(0.412518\pi\) | |||||||
\(822\) | −6.12841e15 | −0.569577 | ||||||||
\(823\) | −2.90427e15 | −0.268126 | −0.134063 | − | 0.990973i | \(-0.542802\pi\) | ||||
−0.134063 | + | 0.990973i | \(0.542802\pi\) | |||||||
\(824\) | −1.55984e15 | −0.143048 | ||||||||
\(825\) | −3.04539e15 | −0.277426 | ||||||||
\(826\) | 2.65295e15 | 0.240070 | ||||||||
\(827\) | −1.16091e16 | −1.04356 | −0.521780 | − | 0.853080i | \(-0.674732\pi\) | ||||
−0.521780 | + | 0.853080i | \(0.674732\pi\) | |||||||
\(828\) | −2.72129e15 | −0.243001 | ||||||||
\(829\) | 1.34670e16 | 1.19460 | 0.597300 | − | 0.802018i | \(-0.296240\pi\) | ||||
0.597300 | + | 0.802018i | \(0.296240\pi\) | |||||||
\(830\) | −8.55352e15 | −0.753729 | ||||||||
\(831\) | 3.40551e15 | 0.298110 | ||||||||
\(832\) | −3.37273e15 | −0.293294 | ||||||||
\(833\) | 1.94095e16 | 1.67674 | ||||||||
\(834\) | 7.62444e15 | 0.654327 | ||||||||
\(835\) | 2.56518e15 | 0.218697 | ||||||||
\(836\) | −5.97084e15 | −0.505709 | ||||||||
\(837\) | −1.21266e14 | −0.0102035 | ||||||||
\(838\) | −2.67655e16 | −2.23735 | ||||||||
\(839\) | −9.41707e15 | −0.782033 | −0.391016 | − | 0.920384i | \(-0.627876\pi\) | ||||
−0.391016 | + | 0.920384i | \(0.627876\pi\) | |||||||
\(840\) | 1.45763e15 | 0.120257 | ||||||||
\(841\) | −1.19775e16 | −0.981724 | ||||||||
\(842\) | −2.86684e16 | −2.33446 | ||||||||
\(843\) | −8.68043e15 | −0.702247 | ||||||||
\(844\) | 1.59493e16 | 1.28192 | ||||||||
\(845\) | 6.71238e15 | 0.535999 | ||||||||
\(846\) | 1.75791e15 | 0.139463 | ||||||||
\(847\) | −3.69429e15 | −0.291187 | ||||||||
\(848\) | 2.50009e15 | 0.195784 | ||||||||
\(849\) | −2.16563e15 | −0.168497 | ||||||||
\(850\) | −1.86141e16 | −1.43893 | ||||||||
\(851\) | −2.01694e16 | −1.54910 | ||||||||
\(852\) | 1.11288e16 | 0.849237 | ||||||||
\(853\) | −1.51177e16 | −1.14621 | −0.573107 | − | 0.819481i | \(-0.694262\pi\) | ||||
−0.573107 | + | 0.819481i | \(0.694262\pi\) | |||||||
\(854\) | 2.14725e16 | 1.61757 | ||||||||
\(855\) | 2.06345e15 | 0.154447 | ||||||||
\(856\) | 1.41447e15 | 0.105193 | ||||||||
\(857\) | −1.03947e16 | −0.768098 | −0.384049 | − | 0.923313i | \(-0.625471\pi\) | ||||
−0.384049 | + | 0.923313i | \(0.625471\pi\) | |||||||
\(858\) | 4.30593e15 | 0.316146 | ||||||||
\(859\) | 9.82183e15 | 0.716522 | 0.358261 | − | 0.933621i | \(-0.383370\pi\) | ||||
0.358261 | + | 0.933621i | \(0.383370\pi\) | |||||||
\(860\) | 1.40826e14 | 0.0102080 | ||||||||
\(861\) | 2.55128e14 | 0.0183756 | ||||||||
\(862\) | −2.68899e15 | −0.192442 | ||||||||
\(863\) | 1.10779e16 | 0.787767 | 0.393883 | − | 0.919160i | \(-0.371131\pi\) | ||||
0.393883 | + | 0.919160i | \(0.371131\pi\) | |||||||
\(864\) | −3.58484e15 | −0.253305 | ||||||||
\(865\) | 3.27446e14 | 0.0229906 | ||||||||
\(866\) | 6.02952e15 | 0.420663 | ||||||||
\(867\) | 2.37018e16 | 1.64314 | ||||||||
\(868\) | −8.73293e14 | −0.0601591 | ||||||||
\(869\) | 4.59238e15 | 0.314361 | ||||||||
\(870\) | −1.05146e15 | −0.0715216 | ||||||||
\(871\) | 9.54503e15 | 0.645175 | ||||||||
\(872\) | 2.38262e15 | 0.160035 | ||||||||
\(873\) | 4.20256e15 | 0.280501 | ||||||||
\(874\) | 1.22284e16 | 0.811064 | ||||||||
\(875\) | 2.15649e16 | 1.42135 | ||||||||
\(876\) | 4.95921e15 | 0.324818 | ||||||||
\(877\) | −9.39677e15 | −0.611619 | −0.305809 | − | 0.952093i | \(-0.598927\pi\) | ||||
−0.305809 | + | 0.952093i | \(0.598927\pi\) | |||||||
\(878\) | −2.43702e16 | −1.57630 | ||||||||
\(879\) | 8.91475e15 | 0.573020 | ||||||||
\(880\) | 1.07011e16 | 0.683556 | ||||||||
\(881\) | −1.50679e16 | −0.956499 | −0.478250 | − | 0.878224i | \(-0.658729\pi\) | ||||
−0.478250 | + | 0.878224i | \(0.658729\pi\) | |||||||
\(882\) | 6.11661e15 | 0.385864 | ||||||||
\(883\) | 1.69609e14 | 0.0106332 | 0.00531661 | − | 0.999986i | \(-0.498308\pi\) | ||||
0.00531661 | + | 0.999986i | \(0.498308\pi\) | |||||||
\(884\) | 1.19613e16 | 0.745233 | ||||||||
\(885\) | −8.21617e14 | −0.0508723 | ||||||||
\(886\) | 3.18022e16 | 1.95692 | ||||||||
\(887\) | 2.98957e16 | 1.82822 | 0.914110 | − | 0.405466i | \(-0.132891\pi\) | ||||
0.914110 | + | 0.405466i | \(0.132891\pi\) | |||||||
\(888\) | −3.80011e15 | −0.230954 | ||||||||
\(889\) | −6.38495e15 | −0.385654 | ||||||||
\(890\) | −4.96663e15 | −0.298138 | ||||||||
\(891\) | 1.65140e15 | 0.0985201 | ||||||||
\(892\) | −4.24811e15 | −0.251877 | ||||||||
\(893\) | −3.59007e15 | −0.211554 | ||||||||
\(894\) | 6.39894e15 | 0.374759 | ||||||||
\(895\) | 9.37490e15 | 0.545682 | ||||||||
\(896\) | 1.04915e16 | 0.606937 | ||||||||
\(897\) | −4.00786e15 | −0.230438 | ||||||||
\(898\) | 3.74807e16 | 2.14184 | ||||||||
\(899\) | −1.26196e14 | −0.00716748 | ||||||||
\(900\) | −2.66595e15 | −0.150494 | ||||||||
\(901\) | −6.00801e15 | −0.337089 | ||||||||
\(902\) | 5.03070e14 | 0.0280538 | ||||||||
\(903\) | −2.56841e14 | −0.0142358 | ||||||||
\(904\) | −5.38989e15 | −0.296930 | ||||||||
\(905\) | 1.08527e16 | 0.594253 | ||||||||
\(906\) | 2.78564e13 | 0.00151607 | ||||||||
\(907\) | 2.56344e16 | 1.38670 | 0.693350 | − | 0.720601i | \(-0.256134\pi\) | ||||
0.693350 | + | 0.720601i | \(0.256134\pi\) | |||||||
\(908\) | 2.20929e15 | 0.118790 | ||||||||
\(909\) | −1.07863e16 | −0.576462 | ||||||||
\(910\) | −1.07163e16 | −0.569271 | ||||||||
\(911\) | 2.70877e14 | 0.0143028 | 0.00715140 | − | 0.999974i | \(-0.497724\pi\) | ||||
0.00715140 | + | 0.999974i | \(0.497724\pi\) | |||||||
\(912\) | 8.57794e15 | 0.450206 | ||||||||
\(913\) | 1.39801e16 | 0.729325 | ||||||||
\(914\) | −3.71277e16 | −1.92528 | ||||||||
\(915\) | −6.65002e15 | −0.342773 | ||||||||
\(916\) | 2.78868e15 | 0.142880 | ||||||||
\(917\) | −4.76929e16 | −2.42897 | ||||||||
\(918\) | 1.00937e16 | 0.510996 | ||||||||
\(919\) | −7.84005e13 | −0.00394533 | −0.00197267 | − | 0.999998i | \(-0.500628\pi\) | ||||
−0.00197267 | + | 0.999998i | \(0.500628\pi\) | |||||||
\(920\) | −2.67524e15 | −0.133823 | ||||||||
\(921\) | −1.40968e16 | −0.700959 | ||||||||
\(922\) | 3.67704e16 | 1.81751 | ||||||||
\(923\) | 1.63902e16 | 0.805333 | ||||||||
\(924\) | 1.18925e16 | 0.580869 | ||||||||
\(925\) | −1.97593e16 | −0.959383 | ||||||||
\(926\) | −9.28351e15 | −0.448076 | ||||||||
\(927\) | 4.39810e15 | 0.211021 | ||||||||
\(928\) | −3.73057e15 | −0.177935 | ||||||||
\(929\) | −9.20590e15 | −0.436495 | −0.218248 | − | 0.975893i | \(-0.570034\pi\) | ||||
−0.218248 | + | 0.975893i | \(0.570034\pi\) | |||||||
\(930\) | 5.95097e14 | 0.0280499 | ||||||||
\(931\) | −1.24916e16 | −0.585321 | ||||||||
\(932\) | 7.29130e15 | 0.339639 | ||||||||
\(933\) | 1.44252e14 | 0.00667994 | ||||||||
\(934\) | 4.52025e16 | 2.08092 | ||||||||
\(935\) | −2.57161e16 | −1.17690 | ||||||||
\(936\) | −7.55120e14 | −0.0343557 | ||||||||
\(937\) | 4.14539e16 | 1.87498 | 0.937491 | − | 0.348009i | \(-0.113142\pi\) | ||||
0.937491 | + | 0.348009i | \(0.113142\pi\) | |||||||
\(938\) | 5.80058e16 | 2.60829 | ||||||||
\(939\) | 6.70153e15 | 0.299580 | ||||||||
\(940\) | −3.92066e15 | −0.174243 | ||||||||
\(941\) | −4.25852e15 | −0.188155 | −0.0940774 | − | 0.995565i | \(-0.529990\pi\) | ||||
−0.0940774 | + | 0.995565i | \(0.529990\pi\) | |||||||
\(942\) | −2.66985e16 | −1.17275 | ||||||||
\(943\) | −4.68246e14 | −0.0204484 | ||||||||
\(944\) | −3.41554e15 | −0.148290 | ||||||||
\(945\) | −4.10991e15 | −0.177401 | ||||||||
\(946\) | −5.06448e14 | −0.0217337 | ||||||||
\(947\) | −3.04814e16 | −1.30050 | −0.650249 | − | 0.759721i | \(-0.725336\pi\) | ||||
−0.650249 | + | 0.759721i | \(0.725336\pi\) | |||||||
\(948\) | 4.02019e15 | 0.170530 | ||||||||
\(949\) | 7.30383e15 | 0.308025 | ||||||||
\(950\) | 1.19797e16 | 0.502304 | ||||||||
\(951\) | −4.53458e15 | −0.189036 | ||||||||
\(952\) | −1.45617e16 | −0.603545 | ||||||||
\(953\) | 1.69177e16 | 0.697156 | 0.348578 | − | 0.937280i | \(-0.386665\pi\) | ||||
0.348578 | + | 0.937280i | \(0.386665\pi\) | |||||||
\(954\) | −1.89334e15 | −0.0775731 | ||||||||
\(955\) | −1.58800e16 | −0.646892 | ||||||||
\(956\) | 3.94808e16 | 1.59907 | ||||||||
\(957\) | 1.71854e15 | 0.0692059 | ||||||||
\(958\) | 4.54733e16 | 1.82073 | ||||||||
\(959\) | −2.49283e16 | −0.992408 | ||||||||
\(960\) | 6.34769e15 | 0.251260 | ||||||||
\(961\) | −2.53371e16 | −0.997189 | ||||||||
\(962\) | 2.79380e16 | 1.09328 | ||||||||
\(963\) | −3.98822e15 | −0.155179 | ||||||||
\(964\) | −1.05940e16 | −0.409862 | ||||||||
\(965\) | 1.49191e16 | 0.573909 | ||||||||
\(966\) | −2.43561e16 | −0.931607 | ||||||||
\(967\) | −3.55367e16 | −1.35155 | −0.675774 | − | 0.737109i | \(-0.736191\pi\) | ||||
−0.675774 | + | 0.737109i | \(0.736191\pi\) | |||||||
\(968\) | 1.27747e15 | 0.0483097 | ||||||||
\(969\) | −2.06138e16 | −0.775135 | ||||||||
\(970\) | −2.06235e16 | −0.771113 | ||||||||
\(971\) | −4.75504e16 | −1.76786 | −0.883930 | − | 0.467619i | \(-0.845112\pi\) | ||||
−0.883930 | + | 0.467619i | \(0.845112\pi\) | |||||||
\(972\) | 1.44565e15 | 0.0534438 | ||||||||
\(973\) | 3.10137e16 | 1.14007 | ||||||||
\(974\) | −5.16695e16 | −1.88869 | ||||||||
\(975\) | −3.92637e15 | −0.142714 | ||||||||
\(976\) | −2.76447e16 | −0.999168 | ||||||||
\(977\) | 3.50019e16 | 1.25797 | 0.628987 | − | 0.777416i | \(-0.283470\pi\) | ||||
0.628987 | + | 0.777416i | \(0.283470\pi\) | |||||||
\(978\) | −1.18481e16 | −0.423432 | ||||||||
\(979\) | 8.11759e15 | 0.288484 | ||||||||
\(980\) | −1.36418e16 | −0.482092 | ||||||||
\(981\) | −6.71799e15 | −0.236080 | ||||||||
\(982\) | 2.56451e16 | 0.896172 | ||||||||
\(983\) | −1.49287e14 | −0.00518772 | −0.00259386 | − | 0.999997i | \(-0.500826\pi\) | ||||
−0.00259386 | + | 0.999997i | \(0.500826\pi\) | |||||||
\(984\) | −8.82220e13 | −0.00304862 | ||||||||
\(985\) | −4.27631e15 | −0.146950 | ||||||||
\(986\) | 1.05041e16 | 0.358951 | ||||||||
\(987\) | 7.15059e15 | 0.242995 | ||||||||
\(988\) | −7.69809e15 | −0.260148 | ||||||||
\(989\) | 4.71390e14 | 0.0158417 | ||||||||
\(990\) | −8.10404e15 | −0.270837 | ||||||||
\(991\) | 8.63362e15 | 0.286938 | 0.143469 | − | 0.989655i | \(-0.454174\pi\) | ||||
0.143469 | + | 0.989655i | \(0.454174\pi\) | |||||||
\(992\) | 2.11140e15 | 0.0697840 | ||||||||
\(993\) | −1.19106e16 | −0.391482 | ||||||||
\(994\) | 9.96045e16 | 3.25577 | ||||||||
\(995\) | 9.09408e15 | 0.295619 | ||||||||
\(996\) | 1.22383e16 | 0.395634 | ||||||||
\(997\) | 3.53290e16 | 1.13582 | 0.567909 | − | 0.823092i | \(-0.307753\pi\) | ||||
0.567909 | + | 0.823092i | \(0.307753\pi\) | |||||||
\(998\) | −9.60642e15 | −0.307145 | ||||||||
\(999\) | 1.07147e16 | 0.340699 |
(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.d.1.22 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.22 | ✓ | 28 | 1.1 | even | 1 | trivial |