Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,13,Mod(31,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.31");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.g (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(43.8717032293\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 4333x^{2} + 4332x + 18766224 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(-32.6599 + 56.5686i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.31 |
Dual form | 48.13.g.a.31.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 420.888i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −21286.8 | −1.36235 | −0.681176 | − | 0.732119i | \(-0.738531\pi\) | ||||
−0.681176 | + | 0.732119i | \(0.738531\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7111.90i | − 0.0604501i | −0.999543 | − | 0.0302251i | \(-0.990378\pi\) | ||||
0.999543 | − | 0.0302251i | \(-0.00962240\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −177147. | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.88540e6i | 1.06426i | 0.846663 | + | 0.532130i | \(0.178608\pi\) | ||||
−0.846663 | + | 0.532130i | \(0.821392\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.56106e6 | −1.77365 | −0.886824 | − | 0.462107i | \(-0.847093\pi\) | ||||
−0.886824 | + | 0.462107i | \(0.847093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 8.95935e6i | − 0.786555i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.77647e6 | 0.280744 | 0.140372 | − | 0.990099i | \(-0.455170\pi\) | ||||
0.140372 | + | 0.990099i | \(0.455170\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 645743.i | − 0.0137258i | −0.999976 | − | 0.00686291i | \(-0.997815\pi\) | ||||
0.999976 | − | 0.00686291i | \(-0.00218455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.99331e6 | 0.0349009 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 2.15694e8i | − 1.45704i | −0.685027 | − | 0.728518i | \(-0.740210\pi\) | ||||
0.685027 | − | 0.728518i | \(-0.259790\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.08985e8 | 0.856005 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 7.45591e7i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.66716e8 | −0.616513 | −0.308257 | − | 0.951303i | \(-0.599746\pi\) | ||||
−0.308257 | + | 0.951303i | \(0.599746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.03858e9i | 1.17022i | 0.810952 | + | 0.585112i | \(0.198950\pi\) | ||||
−0.810952 | + | 0.585112i | \(0.801050\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.93544e8 | −0.614451 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.51389e8i | 0.0823544i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.52823e9 | 1.37514 | 0.687570 | − | 0.726118i | \(-0.258678\pi\) | ||||
0.687570 | + | 0.726118i | \(0.258678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 3.60325e9i | − 1.02402i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.66160e9 | 1.19189 | 0.595945 | − | 0.803025i | \(-0.296778\pi\) | ||||
0.595945 | + | 0.803025i | \(0.296778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.86430e9i | 0.769502i | 0.923020 | + | 0.384751i | \(0.125713\pi\) | ||||
−0.923020 | + | 0.384751i | \(0.874287\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.77089e9 | 0.454118 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.89030e10i | − 1.75365i | −0.480811 | − | 0.876824i | \(-0.659658\pi\) | ||||
0.480811 | − | 0.876824i | \(-0.340342\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.37907e10 | 0.996346 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.85214e9i | 0.162087i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.61412e9 | 0.0728251 | 0.0364126 | − | 0.999337i | \(-0.488407\pi\) | ||||
0.0364126 | + | 0.999337i | \(0.488407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4.01341e10i | − 1.44990i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.71786e8 | 0.00792460 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.28375e10i | 0.304346i | 0.988354 | + | 0.152173i | \(0.0486271\pi\) | ||||
−0.988354 | + | 0.152173i | \(0.951373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.86920e10 | 0.751004 | 0.375502 | − | 0.926822i | \(-0.377470\pi\) | ||||
0.375502 | + | 0.926822i | \(0.377470\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.25985e9i | 0.0201500i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.82237e11 | 2.41633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.56544e11i | − 1.73056i | −0.501289 | − | 0.865280i | \(-0.667141\pi\) | ||||
0.501289 | − | 0.865280i | \(-0.332859\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.07829e10 | 0.841220 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 4.16779e10i | − 0.325354i | −0.986679 | − | 0.162677i | \(-0.947987\pi\) | ||||
0.986679 | − | 0.162677i | \(-0.0520128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00107e11 | 0.661497 | 0.330748 | − | 0.943719i | \(-0.392699\pi\) | ||||
0.330748 | + | 0.943719i | \(0.392699\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.79596e10i | 0.494214i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.34088e10 | 0.0643347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.99076e11i | 0.818947i | 0.912322 | + | 0.409473i | \(0.134288\pi\) | ||||
−0.912322 | + | 0.409473i | \(0.865712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.13811e10 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.30690e11i | − 0.705604i | −0.935698 | − | 0.352802i | \(-0.885229\pi\) | ||||
0.935698 | − | 0.352802i | \(-0.114771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.44249e11 | −0.382472 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.54347e11i | − 0.355944i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.73312e11 | −0.952375 | −0.476187 | − | 0.879344i | \(-0.657982\pi\) | ||||
−0.476187 | + | 0.879344i | \(0.657982\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.08854e10i | 0.107217i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.37126e11 | −0.675630 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.37458e10i | 0.0186994i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.29103e11 | 1.11541 | 0.557704 | − | 0.830040i | \(-0.311682\pi\) | ||||
0.557704 | + | 0.830040i | \(0.311682\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3.33993e11i | − 0.354754i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.30494e11 | −0.405545 | −0.202773 | − | 0.979226i | \(-0.564995\pi\) | ||||
−0.202773 | + | 0.979226i | \(0.564995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.24450e12i | 1.04225i | 0.853482 | + | 0.521123i | \(0.174487\pi\) | ||||
−0.853482 | + | 0.521123i | \(0.825513\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.37180e10 | −0.0475473 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.40478e11i | − 0.226875i | −0.993545 | − | 0.113437i | \(-0.963814\pi\) | ||||
0.993545 | − | 0.113437i | \(-0.0361861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.31888e12 | −1.97894 | −0.989470 | − | 0.144738i | \(-0.953766\pi\) | ||||
−0.989470 | + | 0.144738i | \(0.953766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.48499e12i | 0.793937i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.87063e12 | −1.85913 | −0.929567 | − | 0.368654i | \(-0.879819\pi\) | ||||
−0.929567 | + | 0.368654i | \(0.879819\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.59142e12i | 1.98500i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.51657e12 | 0.591216 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4.81935e10i | − 0.0169710i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.16314e11 | −0.132650 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.38290e12i | 0.688138i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.48339e11 | 0.196173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8.23613e12i | − 1.96291i | −0.191688 | − | 0.981456i | \(-0.561396\pi\) | ||||
0.191688 | − | 0.981456i | \(-0.438604\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.04733e12 | −0.444272 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.61593e12i | 0.319738i | 0.987138 | + | 0.159869i | \(0.0511072\pi\) | ||||
−0.987138 | + | 0.159869i | \(0.948893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.59246e9 | −0.000829727 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.58712e12i | 0.262185i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.29703e11 | −0.0649897 | −0.0324948 | − | 0.999472i | \(-0.510345\pi\) | ||||
−0.0324948 | + | 0.999472i | \(0.510345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1.70332e12i | − 0.236160i | −0.993004 | − | 0.118080i | \(-0.962326\pi\) | ||||
0.993004 | − | 0.118080i | \(-0.0376739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.95603e12 | 1.01247 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.61410e13i | − 1.88762i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.80621e12 | 0.839908 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.80435e12i | 0.575241i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.75418e12 | −0.525854 | −0.262927 | − | 0.964816i | \(-0.584688\pi\) | ||||
−0.262927 | + | 0.964816i | \(0.584688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.73435e13i | 1.46311i | 0.681785 | + | 0.731553i | \(0.261204\pi\) | ||||
−0.681785 | + | 0.731553i | \(0.738796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.20043e12 | −0.0935812 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.21080e13i | − 1.59426i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.18262e13 | 0.789672 | 0.394836 | − | 0.918752i | \(-0.370801\pi\) | ||||
0.394836 | + | 0.918752i | \(0.370801\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.79365e11i | 0.0420456i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.53399e12 | −0.0880780 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.72346e13i | 0.918917i | 0.888199 | + | 0.459458i | \(0.151956\pi\) | ||||
−0.888199 | + | 0.459458i | \(0.848044\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.68920e13 | 0.837099 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 3.25246e13i | − 1.49939i | −0.661785 | − | 0.749694i | \(-0.730201\pi\) | ||||
0.661785 | − | 0.749694i | \(-0.269799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.99937e13 | 2.14583 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14391e11i | 0.00457527i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.94963e13 | 1.10025 | 0.550125 | − | 0.835082i | \(-0.314580\pi\) | ||||
0.550125 | + | 0.835082i | \(0.314580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.48628e12i | − 0.0517456i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.40314e12 | −0.175714 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2.17325e13i | − 0.660682i | −0.943862 | − | 0.330341i | \(-0.892836\pi\) | ||||
0.943862 | − | 0.330341i | \(-0.107164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.24786e12 | −0.0354891 | −0.0177446 | − | 0.999843i | \(-0.505649\pi\) | ||||
−0.0177446 | + | 0.999843i | \(0.505649\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.62850e13i | 0.433592i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.51046e13 | −1.87343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.27764e13i | 0.298784i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.30257e11 | −0.0116336 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 6.52191e13i | − 1.34330i | −0.740866 | − | 0.671652i | \(-0.765585\pi\) | ||||
0.740866 | − | 0.671652i | \(-0.234415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.62613e13 | −0.314638 | −0.157319 | − | 0.987548i | \(-0.550285\pi\) | ||||
−0.157319 | + | 0.987548i | \(0.550285\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.67015e13i | 1.39507i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.69576e13 | −1.48768 | −0.743841 | − | 0.668356i | \(-0.766998\pi\) | ||||
−0.743841 | + | 0.668356i | \(0.766998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.03084e13i | 0.165986i | 0.996550 | + | 0.0829932i | \(0.0264480\pi\) | ||||
−0.996550 | + | 0.0829932i | \(0.973552\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.58874e13 | 0.999139 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.60805e12i | 0.0372683i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.20517e14 | −1.62378 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.82095e13i | 0.485678i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.21749e12 | 0.0146078 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.21337e14i | 1.37499i | 0.726189 | + | 0.687495i | \(0.241290\pi\) | ||||
−0.726189 | + | 0.687495i | \(0.758710\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.75417e13 | 0.187843 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 1.03545e14i | − 1.04833i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.38627e12 | 0.0707402 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.21339e13i | 0.381915i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.80137e13 | −0.497940 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.52486e14i | − 1.23994i | −0.784624 | − | 0.619972i | \(-0.787144\pi\) | ||||
0.784624 | − | 0.619972i | \(-0.212856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.70212e13 | −0.285335 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.60931e14i | 1.90709i | 0.301249 | + | 0.953545i | \(0.402596\pi\) | ||||
−0.301249 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11017e14 | 0.769798 | 0.384899 | − | 0.922959i | \(-0.374236\pi\) | ||||
0.384899 | + | 0.922959i | \(0.374236\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.64360e12i | 0.0371436i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.48696e14 | −0.929318 | −0.464659 | − | 0.885490i | \(-0.653823\pi\) | ||||
−0.464659 | + | 0.885490i | \(0.653823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.02383e14i | 2.38909i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.37887e13 | −0.472819 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 3.25593e14i | − 1.74698i | −0.486841 | − | 0.873491i | \(-0.661851\pi\) | ||||
0.486841 | − | 0.873491i | \(-0.338149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.46403e14 | −0.747220 | −0.373610 | − | 0.927586i | \(-0.621880\pi\) | ||||
−0.373610 | + | 0.927586i | \(0.621880\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.32079e13i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.93559e14 | −1.35737 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.52825e12i | 0.0243448i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.70949e13 | 0.407381 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4.56243e14i | − 1.82454i | −0.409589 | − | 0.912270i | \(-0.634328\pi\) | ||||
0.409589 | − | 0.912270i | \(-0.365672\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.06669e14 | 1.55067 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 6.07127e13i | − 0.220820i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.70340e14 | 1.63235 | 0.816175 | − | 0.577804i | \(-0.196090\pi\) | ||||
0.816175 | + | 0.577804i | \(0.196090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.50924e13i | − 0.0831274i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.49627e13 | 0.205504 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.42061e14i | 0.429280i | 0.976693 | + | 0.214640i | \(0.0688578\pi\) | ||||
−0.976693 | + | 0.214640i | \(0.931142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.43594e13 | −0.0992135 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.99212e14i | − 0.549854i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.94994e14 | 0.778573 | 0.389286 | − | 0.921117i | \(-0.372722\pi\) | ||||
0.389286 | + | 0.921117i | \(0.372722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 4.70773e14i | − 1.18849i | −0.804284 | − | 0.594246i | \(-0.797451\pi\) | ||||
0.804284 | − | 0.594246i | \(-0.202549\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.56259e13 | −0.0619019 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.94022e14i | 0.911012i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.15318e14 | 0.919395 | 0.459698 | − | 0.888075i | \(-0.347958\pi\) | ||||
0.459698 | + | 0.888075i | \(0.347958\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 1.83981e14i | − 0.390075i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.73345e14 | 1.36773 | 0.683864 | − | 0.729609i | \(-0.260298\pi\) | ||||
0.683864 | + | 0.729609i | \(0.260298\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.70518e14i | − 0.721259i | −0.932709 | − | 0.360629i | \(-0.882562\pi\) | ||||
0.932709 | − | 0.360629i | \(-0.117438\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.78544e12 | −0.0107961 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 4.02647e13i | − 0.0720499i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.36702e14 | −0.921183 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.91049e14i | 0.643981i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.56469e14 | 0.405350 | 0.202675 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202675 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2.73268e14i | − 0.414626i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.40574e14 | 0.204817 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.84657e15i | 2.58427i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.45944e13 | 0.0465165 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1.81190e14i | − 0.234142i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.23627e14 | −1.02313 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 8.24545e14i | − 0.984882i | −0.870346 | − | 0.492441i | \(-0.836105\pi\) | ||||
0.870346 | − | 0.492441i | \(-0.163895\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.23793e14 | −0.601740 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 7.97009e14i | − 0.880848i | −0.897790 | − | 0.440424i | \(-0.854828\pi\) | ||||
0.897790 | − | 0.440424i | \(-0.145172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.79978e14 | 0.191406 | 0.0957028 | − | 0.995410i | \(-0.469490\pi\) | ||||
0.0957028 | + | 0.995410i | \(0.469490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.68181e13i | − 0.0274515i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.63990e15 | 1.61608 | 0.808039 | − | 0.589130i | \(-0.200529\pi\) | ||||
0.808039 | + | 0.589130i | \(0.200529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 6.91408e14i | − 0.656131i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.43303e14 | 0.130986 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 4.37586e12i | − 0.00385343i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.78914e15 | −1.51825 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.39688e15i | − 1.14254i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.34436e14 | −0.106008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.09770e15i | 1.59505i | 0.603283 | + | 0.797527i | \(0.293859\pi\) | ||||
−0.603283 | + | 0.797527i | \(0.706141\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.25016e14 | −0.458380 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.33231e15i | 2.35763i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.36274e15 | −0.930321 | −0.465160 | − | 0.885226i | \(-0.654003\pi\) | ||||
−0.465160 | + | 0.885226i | \(0.654003\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.62910e15i | − 1.07337i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.95814e15 | −1.24542 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.96516e14i | − 0.120679i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.93247e15 | −1.14604 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.21109e15i | 1.26657i | 0.773917 | + | 0.633287i | \(0.218295\pi\) | ||||
−0.773917 | + | 0.633287i | \(0.781705\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.25554e14 | −0.456870 | −0.228435 | − | 0.973559i | \(-0.573361\pi\) | ||||
−0.228435 | + | 0.973559i | \(0.573361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.38305e14i | 0.341339i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.06854e14 | 0.468694 | 0.234347 | − | 0.972153i | \(-0.424705\pi\) | ||||
0.234347 | + | 0.972153i | \(0.424705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.87187e14i | 0.443246i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.02841e13 | 0.00979820 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 5.13417e14i | − 0.239830i | −0.992784 | − | 0.119915i | \(-0.961738\pi\) | ||||
0.992784 | − | 0.119915i | \(-0.0382622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.21290e15 | 0.999812 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.75222e14i | − 0.0765858i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.13096e15 | −0.901192 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.68311e14i | 0.273516i | 0.990605 | + | 0.136758i | \(0.0436682\pi\) | ||||
−0.990605 | + | 0.136758i | \(0.956332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00294e15 | −0.397297 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.14795e13i | − 0.00440229i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.11568e13 | 0.0338483 | 0.0169241 | − | 0.999857i | \(-0.494613\pi\) | ||||
0.0169241 | + | 0.999857i | \(0.494613\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.14967e14i | 0.113260i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.13948e15 | 1.09348 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3.53114e15i | − 1.19146i | −0.803184 | − | 0.595731i | \(-0.796863\pi\) | ||||
0.803184 | − | 0.595731i | \(-0.203137\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.46649e15 | 1.13329 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.41943e15i | 0.766515i | 0.923642 | + | 0.383257i | \(0.125198\pi\) | ||||
−0.923642 | + | 0.383257i | \(0.874802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.85430e14 | −0.0876465 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.61697e14i | − 0.256501i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.88362e15 | 1.40943 | 0.704717 | − | 0.709489i | \(-0.251074\pi\) | ||||
0.704717 | + | 0.709489i | \(0.251074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 1.46164e15i | − 0.409053i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.80125e14 | −0.184601 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.23768e15i | − 1.11569i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.63632e15 | −0.928792 | −0.464396 | − | 0.885628i | \(-0.653729\pi\) | ||||
−0.464396 | + | 0.885628i | \(0.653729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 1.93291e12i | 0 0.000479043i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.72304e14 | 0.0654919 | 0.0327459 | − | 0.999464i | \(-0.489575\pi\) | ||||
0.0327459 | + | 0.999464i | \(0.489575\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 8.89134e15i | − 2.07557i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.68001e14 | −0.151373 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.65214e15i | 1.46351i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.47132e15 | 0.314317 | 0.157158 | − | 0.987573i | \(-0.449767\pi\) | ||||
0.157158 | + | 0.987573i | \(0.449767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1.80857e14i | − 0.0375218i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.12988e13 | 0.0183977 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.91065e15i | 0.961281i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.16906e14 | 0.136347 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6.30146e15i | − 1.16455i | −0.812993 | − | 0.582273i | \(-0.802163\pi\) | ||||
0.812993 | − | 0.582273i | \(-0.197837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.25314e15 | 0.584266 | 0.292133 | − | 0.956378i | \(-0.405635\pi\) | ||||
0.292133 | + | 0.956378i | \(0.405635\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.34860e15i | 0.584550i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.41618e15 | 0.240318 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.75174e14i | − 0.0453983i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.79358e15 | 1.08982 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.03071e16i | − 1.60795i | −0.594660 | − | 0.803977i | \(-0.702713\pi\) | ||||
0.594660 | − | 0.803977i | \(-0.297287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.64406e15 | 1.46330 | 0.731648 | − | 0.681682i | \(-0.238751\pi\) | ||||
0.731648 | + | 0.681682i | \(0.238751\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.28554e15i | 0.484921i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.39283e14 | −0.0199990 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.83012e15i | 0.535087i | 0.963546 | + | 0.267544i | \(0.0862120\pi\) | ||||
−0.963546 | + | 0.267544i | \(0.913788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.44298e15 | −0.332115 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.98519e15i | − 0.924179i | −0.886833 | − | 0.462089i | \(-0.847100\pi\) | ||||
0.886833 | − | 0.462089i | \(-0.152900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00753e16 | 1.29747 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 2.42187e15i | − 0.303602i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.54024e15 | −0.798207 | −0.399103 | − | 0.916906i | \(-0.630679\pi\) | ||||
−0.399103 | + | 0.916906i | \(0.630679\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.06744e16i | 1.26848i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.29969e15 | −0.844725 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 1.29605e15i | − 0.146068i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.93711e15 | −0.432196 | −0.216098 | − | 0.976372i | \(-0.569333\pi\) | ||||
−0.216098 | + | 0.976372i | \(0.569333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 5.05247e14i | − 0.0540291i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.78296e15 | −0.706665 | −0.353333 | − | 0.935498i | \(-0.614952\pi\) | ||||
−0.353333 | + | 0.935498i | \(0.614952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.21932e16i | 1.23774i | 0.785492 | + | 0.618872i | \(0.212410\pi\) | ||||
−0.785492 | + | 0.618872i | \(0.787590\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.30499e15 | 0.920446 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.69994e14i | 0.0935121i | 0.998906 | + | 0.0467560i | \(0.0148883\pi\) | ||||
−0.998906 | + | 0.0467560i | \(0.985112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.11332e15 | −0.104613 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.97750e15i | 0.455917i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.17117e15 | −0.818951 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1.34951e14i | − 0.0117494i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.85937e14 | −0.0242750 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 6.76625e15i | − 0.560190i | −0.959972 | − | 0.280095i | \(-0.909634\pi\) | ||||
0.959972 | − | 0.280095i | \(-0.0903659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.02054e16 | −2.43901 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.45639e14i | − 0.0508518i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.97776e16 | −1.51958 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.15311e16i | 0.864367i | 0.901786 | + | 0.432184i | \(0.142257\pi\) | ||||
−0.901786 | + | 0.432184i | \(0.857743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.25385e15 | −0.530537 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.32213e16i | − 0.943596i | −0.881707 | − | 0.471798i | \(-0.843605\pi\) | ||||
0.881707 | − | 0.471798i | \(-0.156395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.48504e15 | −0.173082 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.10964e15i | 0.483299i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.96409e14 | −0.0196677 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.97689e15i | − 0.322370i | −0.986924 | − | 0.161185i | \(-0.948468\pi\) | ||||
0.986924 | − | 0.161185i | \(-0.0515316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.36892e16 | 0.865672 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.01640e16i | 0.627562i | 0.949495 | + | 0.313781i | \(0.101596\pi\) | ||||
−0.949495 | + | 0.313781i | \(0.898404\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.16383e15 | 0.552496 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.10417e16i | 1.23889i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.39231e16 | −0.800626 | −0.400313 | − | 0.916379i | \(-0.631099\pi\) | ||||
−0.400313 | + | 0.916379i | \(0.631099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 7.11951e14i | − 0.0399876i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.81460e13 | −0.00264153 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 2.64913e16i | − 1.41991i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.56397e16 | 1.86634 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.24147e16i | 0.635230i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.75513e16 | 0.877572 | 0.438786 | − | 0.898592i | \(-0.355409\pi\) | ||||
0.438786 | + | 0.898592i | \(0.355409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.65340e16i | − 0.807919i | −0.914777 | − | 0.403959i | \(-0.867634\pi\) | ||||
0.914777 | − | 0.403959i | \(-0.132366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.25559e14 | 0.0298753 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.03790e15i | 0.328533i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.46091e16 | −1.12295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.27412e15i | − 0.101449i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.84693e16 | −2.11399 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.24767e15i | 0.309083i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.14697e15 | 0.381445 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.60010e16i | 1.06037i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.40764e16 | −1.35916 | −0.679580 | − | 0.733602i | \(-0.737838\pi\) | ||||
−0.679580 | + | 0.733602i | \(0.737838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5.25211e14i | − 0.0204897i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.06482e16 | 2.69601 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.02110e16i | 1.12782i | 0.825835 | + | 0.563912i | \(0.190704\pi\) | ||||
−0.825835 | + | 0.563912i | \(0.809296\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.85417e15 | −0.250335 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.36805e14i | 0.00846215i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.41581e15 | 0.0495054 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 3.16107e16i | − 1.08162i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.86821e16 | 0.625596 | 0.312798 | − | 0.949820i | \(-0.398734\pi\) | ||||
0.312798 | + | 0.949820i | \(0.398734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 4.16436e16i | − 1.36483i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.37742e15 | −0.172503 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 1.77453e16i | − 0.557228i | −0.960403 | − | 0.278614i | \(-0.910125\pi\) | ||||
0.960403 | − | 0.278614i | \(-0.0898750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.23931e16 | 2.53280 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 2.23179e14i | − 0.00671668i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.04279e16 | −0.601935 | −0.300968 | − | 0.953634i | \(-0.597310\pi\) | ||||
−0.300968 | + | 0.953634i | \(0.597310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.67402e15i | 0.163709i | 0.996644 | + | 0.0818547i | \(0.0260844\pi\) | ||||
−0.996644 | + | 0.0818547i | \(0.973916\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.74500e16 | 0.775557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 4.50768e16i | − 1.24723i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.70028e16 | 0.460750 | 0.230375 | − | 0.973102i | \(-0.426005\pi\) | ||||
0.230375 | + | 0.973102i | \(0.426005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 6.84418e15i | − 0.181656i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.64065e15 | −0.0426538 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.04327e15i | 0.0775049i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.22828e16 | −0.805445 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3.27992e16i | − 0.801742i | −0.916134 | − | 0.400871i | \(-0.868708\pi\) | ||||
0.916134 | − | 0.400871i | \(-0.131292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.70655e14 | 0.0160623 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 3.65995e16i | − 0.858914i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.54880e16 | 1.50603 | 0.753015 | − | 0.658003i | \(-0.228599\pi\) | ||||
0.753015 | + | 0.658003i | \(0.228599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.02588e15i | 0.0231205i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.33868e15 | −0.0958322 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 1.46157e16i | − 0.316417i | −0.987406 | − | 0.158209i | \(-0.949428\pi\) | ||||
0.987406 | − | 0.158209i | \(-0.0505718\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.63481e16 | 0.771320 | 0.385660 | − | 0.922641i | \(-0.373974\pi\) | ||||
0.385660 | + | 0.922641i | \(0.373974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.77312e16i | 0.576853i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.86197e15 | 0.180717 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4.19339e16i | − 0.838364i | −0.907902 | − | 0.419182i | \(-0.862317\pi\) | ||||
0.907902 | − | 0.419182i | \(-0.137683\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.09770e15 | −0.0215169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.61829e17i | 3.11036i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.03819e16 | −0.384134 | −0.192067 | − | 0.981382i | \(-0.561519\pi\) | ||||
−0.192067 | + | 0.981382i | \(0.561519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 5.07243e16i | − 0.937487i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.74912e16 | −0.679545 | −0.339772 | − | 0.940508i | \(-0.610350\pi\) | ||||
−0.339772 | + | 0.940508i | \(0.610350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.18233e16i | 0.387951i | 0.981006 | + | 0.193975i | \(0.0621382\pi\) | ||||
−0.981006 | + | 0.193975i | \(0.937862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.60819e16 | −0.280407 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.36615e15i | 0.0575712i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.69516e16 | −1.12326 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.12426e14i | 0.00843384i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.39089e16 | 0.386062 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 4.54812e16i | − 0.720537i | −0.932849 | − | 0.360268i | \(-0.882685\pi\) | ||||
0.932849 | − | 0.360268i | \(-0.117315\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.10695e16 | −0.793851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.75320e17i | 2.67418i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.18063e17 | −1.76717 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.38311e15i | 0.108451i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.57002e16 | 1.09131 | 0.545656 | − | 0.838009i | \(-0.316281\pi\) | ||||
0.545656 | + | 0.838009i | \(0.316281\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.74737e16i | − 0.813212i | −0.913604 | − | 0.406606i | \(-0.866712\pi\) | ||||
0.913604 | − | 0.406606i | \(-0.133288\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.35810e16 | 0.605255 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.03250e16i | 0.686053i | 0.939326 | + | 0.343027i | \(0.111452\pi\) | ||||
−0.939326 | + | 0.343027i | \(0.888548\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.42038e16 | −0.323903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.10879e15i | 0.0408419i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.84738e15 | 0.0238275 | 0.0119137 | − | 0.999929i | \(-0.496208\pi\) | ||||
0.0119137 | + | 0.999929i | \(0.496208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 3.43979e16i | − 0.435596i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.77337e16 | −0.220499 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 8.93078e16i | − 1.09038i | −0.838313 | − | 0.545189i | \(-0.816458\pi\) | ||||
0.838313 | − | 0.545189i | \(-0.183542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.13618e16 | 0.136219 | 0.0681095 | − | 0.997678i | \(-0.478303\pi\) | ||||
0.0681095 | + | 0.997678i | \(0.478303\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.44173e16i | − 0.287486i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.77586e13 | 0.00113038 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.90984e16i | 0.898282i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.41797e16 | 0.715881 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.29500e16i | 0.799264i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.40873e17 | −1.51614 | −0.758069 | − | 0.652174i | \(-0.773857\pi\) | ||||
−0.758069 | + | 0.652174i | \(0.773857\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.55818e16i | − 0.164738i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.06344e17 | −1.10454 | −0.552268 | − | 0.833667i | \(-0.686238\pi\) | ||||
−0.552268 | + | 0.833667i | \(0.686238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 6.60769e15i | − 0.0674265i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09823e17 | −1.10106 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.82367e16i | 0.770702i | 0.922770 | + | 0.385351i | \(0.125920\pi\) | ||||
−0.922770 | + | 0.385351i | \(0.874080\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.14697e15 | 0.0885389 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.67258e16i | 0.444443i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.38186e16 | −0.129166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1.63249e17i | − 1.49963i | −0.661650 | − | 0.749813i | \(-0.730143\pi\) | ||||
0.661650 | − | 0.749813i | \(-0.269857\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.37533e15 | −0.0214449 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.62581e16i | 0.321733i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.83657e16 | 0.334616 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 6.25845e16i | − 0.536542i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.46995e17 | −1.23878 | −0.619391 | − | 0.785083i | \(-0.712620\pi\) | ||||
−0.619391 | + | 0.785083i | \(0.712620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.27833e15i | − 0.0188749i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.69358e17 | −1.37934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.06163e15i | 0.0245153i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.55937e16 | 0.437672 | 0.218836 | − | 0.975762i | \(-0.429774\pi\) | ||||
0.218836 | + | 0.975762i | \(0.429774\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 3.52657e16i | − 0.272982i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.24015e17 | 1.70506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.43590e17i | 2.57161i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.37038e17 | 1.00862 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.11386e16i | − 0.0806229i | −0.999187 | − | 0.0403115i | \(-0.987165\pi\) | ||||
0.999187 | − | 0.0403115i | \(-0.0128350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.85072e15 | 0.0630038 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.16194e16i | − 0.431408i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.66384e16 | −0.527738 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 4.35822e16i | − 0.295191i | −0.989048 | − | 0.147595i | \(-0.952847\pi\) | ||||
0.989048 | − | 0.147595i | \(-0.0471533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.55906e15 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.29628e16i | 0.216033i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.02849e17 | 0.663095 | 0.331547 | − | 0.943439i | \(-0.392429\pi\) | ||||
0.331547 | + | 0.943439i | \(0.392429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 1.23556e17i | − 0.783680i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.95148e17 | 1.84177 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.89187e16i | − 0.177546i | −0.996052 | − | 0.0887732i | \(-0.971705\pi\) | ||||
0.996052 | − | 0.0887732i | \(-0.0282946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.32677e15 | −0.0140555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.84464e17i | − 1.09642i | −0.836339 | − | 0.548212i | \(-0.815309\pi\) | ||||
0.836339 | − | 0.548212i | \(-0.184691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.22488e17 | 0.716399 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.08661e16i | 0.235201i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.42144e15 | −0.0137146 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1.07917e17i | − 0.601522i | −0.953700 | − | 0.300761i | \(-0.902759\pi\) | ||||
0.953700 | − | 0.300761i | \(-0.0972406\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.92027e17 | 1.05340 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 3.69188e17i | − 1.99327i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.20280e17 | 1.17058 | 0.585288 | − | 0.810825i | \(-0.300981\pi\) | ||||
0.585288 | + | 0.810825i | \(0.300981\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.71162e17i | 0.895277i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.15648e17 | 0.595430 | 0.297715 | − | 0.954655i | \(-0.403775\pi\) | ||||
0.297715 | + | 0.954655i | \(0.403775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.36035e16i | 0.119627i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.55533e16 | 0.127491 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.09902e17i | − 0.539803i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.40988e14 | −0.00455016 | −0.00227508 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227508 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.97961e17i | 0.942438i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.12581e17 | −0.996434 | −0.498217 | − | 0.867052i | \(-0.666012\pi\) | ||||
−0.498217 | + | 0.867052i | \(0.666012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17048e17i | 1.00172i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.05611e16 | 0.0479936 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 3.65594e15i | − 0.0163597i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.85796e16 | 0.346261 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.73421e16i | 0.118648i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.51741e17 | −1.07581 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.88757e17i | − 1.63617i | −0.575095 | − | 0.818087i | \(-0.695035\pi\) | ||||
0.575095 | − | 0.818087i | \(-0.304965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.97919e16 | −0.247845 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.75275e16i | 0.112385i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.31245e17 | −1.33202 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1.44615e16i | − 0.0572809i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.11775e16 | −0.0826276 | −0.0413138 | − | 0.999146i | \(-0.513154\pi\) | ||||
−0.0413138 | + | 0.999146i | \(0.513154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.28095e17i | − 0.492326i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.38459e16 | 0.317458 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.88742e17i | 0.704005i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.26537e16 | 0.119993 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.24159e17i | 0.449509i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.74837e17 | 0.980357 | 0.490179 | − | 0.871622i | \(-0.336932\pi\) | ||||
0.490179 | + | 0.871622i | \(0.336932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3.56743e17i | − 1.25381i | −0.779098 | − | 0.626903i | \(-0.784322\pi\) | ||||
0.779098 | − | 0.626903i | \(-0.215678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.98143e17 | 0.686176 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 3.66869e17i | − 1.25189i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.14109e15 | 0.0105620 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.07857e16i | − 0.0357391i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.70191e17 | −0.555748 | −0.277874 | − | 0.960617i | \(-0.589630\pi\) | ||||
−0.277874 | + | 0.960617i | \(0.589630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.53033e17i | 1.45791i | 0.684562 | + | 0.728955i | \(0.259994\pi\) | ||||
−0.684562 | + | 0.728955i | \(0.740006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.65839e17 | −0.525973 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 4.07186e17i | − 1.27280i | −0.771360 | − | 0.636399i | \(-0.780423\pi\) | ||||
0.771360 | − | 0.636399i | \(-0.219577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.99377e17 | 0.922342 | 0.461171 | − | 0.887311i | \(-0.347429\pi\) | ||||
0.461171 | + | 0.887311i | \(0.347429\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.74803e17i | 0.530813i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.34523e16 | 0.279718 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.92344e17i | 2.04269i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.74355e16 | 0.225210 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.54448e17i | 1.87631i | 0.346222 | + | 0.938153i | \(0.387464\pi\) | ||||
−0.346222 | + | 0.938153i | \(0.612536\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.19334e17 | −0.619911 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.83403e17i | 0.789659i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.06420e18 | −2.92337 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.96078e15i | 0.00801873i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.55947e17 | 0.416419 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 7.61017e17i | − 2.00363i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.94589e16 | 0.258196 | 0.129098 | − | 0.991632i | \(-0.458792\pi\) | ||||
0.129098 | + | 0.991632i | \(0.458792\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 2.43502e15i | − 0.00623313i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.81107e17 | 0.457142 | 0.228571 | − | 0.973527i | \(-0.426595\pi\) | ||||
0.228571 | + | 0.973527i | \(0.426595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.11062e17i | 0.525353i | 0.964884 | + | 0.262677i | \(0.0846052\pi\) | ||||
−0.964884 | + | 0.262677i | \(0.915395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.69470e16 | 0.0415980 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 3.64870e17i | − 0.883229i | −0.897205 | − | 0.441614i | \(-0.854406\pi\) | ||||
0.897205 | − | 0.441614i | \(-0.145594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.27881e17 | −1.49893 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.25892e17i | − 0.531845i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.75338e17 | −0.871573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.34018e18i | 3.06940i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.64588e17 | −0.371803 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5.32211e15i | − 0.0118587i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.20060e17 | 0.483663 | 0.241832 | − | 0.970318i | \(-0.422252\pi\) | ||||
0.241832 | + | 0.970318i | \(0.422252\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.07945e17i | 0.234029i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.23854e17 | −1.12035 | −0.560176 | − | 0.828373i | \(-0.689267\pi\) | ||||
−0.560176 | + | 0.828373i | \(0.689267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 5.19490e17i | − 1.09601i | −0.836476 | − | 0.548003i | \(-0.815388\pi\) | ||||
0.836476 | − | 0.548003i | \(-0.184612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.15015e17 | 0.239385 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.43189e17i | 1.32068i | 0.750968 | + | 0.660339i | \(0.229587\pi\) | ||||
−0.750968 | + | 0.660339i | \(0.770413\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.85745e16 | −0.118658 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.91659e16i | 0.118251i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.22065e16 | −0.0240703 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.62615e17i | 0.900081i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.77198e17 | −1.49203 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3.80864e17i | − 0.721459i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.09380e16 | 0.0204452 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.45604e16i | 0.0268563i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.65630e16 | 0.0483487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.20905e17i | − 1.47452i | −0.675612 | − | 0.737258i | \(-0.736120\pi\) | ||||
0.675612 | − | 0.737258i | \(-0.263880\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.62608e16 | 0.135182 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 7.92986e16i | − 0.138725i | −0.997592 | − | 0.0693625i | \(-0.977903\pi\) | ||||
0.997592 | − | 0.0693625i | \(-0.0220965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.34944e17 | 0.750946 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 3.46655e17i | − 0.590706i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.14923e16 | 0.0193282 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 7.38065e17i | − 1.22518i | −0.790399 | − | 0.612592i | \(-0.790127\pi\) | ||||
0.790399 | − | 0.612592i | \(-0.209873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.47041e17 | 0.568622 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.56807e17i | 0.577063i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.37349e17 | 1.17713 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.20459e17i | − 0.347415i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.11243e18 | 1.73052 | 0.865261 | − | 0.501322i | \(-0.167153\pi\) | ||||
0.865261 | + | 0.501322i | \(0.167153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 8.90526e15i | − 0.0136757i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.35452e17 | 0.508558 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2.71967e17i | − 0.407049i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.87919e17 | −0.573197 | −0.286598 | − | 0.958051i | \(-0.592525\pi\) | ||||
−0.286598 | + | 0.958051i | \(0.592525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.57508e16i | 0.110508i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.15087e17 | 0.453829 | 0.226914 | − | 0.973915i | \(-0.427136\pi\) | ||||
0.226914 | + | 0.973915i | \(0.427136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.22117e18i | − 1.73663i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.12874e16 | 0.0158491 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.79195e16i | 0.0525730i | 0.999654 | + | 0.0262865i | \(0.00836821\pi\) | ||||
−0.999654 | + | 0.0262865i | \(0.991632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.57023e17 | −1.17326 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.90215e17i | 0.933043i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.56690e17 | 0.876603 | 0.438302 | − | 0.898828i | \(-0.355580\pi\) | ||||
0.438302 | + | 0.898828i | \(0.355580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.38830e18i | 1.83005i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.91006e17 | 0.378817 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.05600e15i | 0.00392864i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.90984e17 | −0.369427 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.03146e16i | 0.0756249i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.46150e17 | 0.428647 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 6.24136e17i | − 0.763345i | −0.924298 | − | 0.381672i | \(-0.875348\pi\) | ||||
0.924298 | − | 0.381672i | \(-0.124652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.84175e15 | 0.00222478 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.04996e17i | 1.07977i | 0.841739 | + | 0.539885i | \(0.181532\pi\) | ||||
−0.841739 | + | 0.539885i | \(0.818468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.21138e16 | −0.0142759 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 7.53027e17i | − 0.876562i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.37695e17 | −0.158326 | −0.0791628 | − | 0.996862i | \(-0.525225\pi\) | ||||
−0.0791628 | + | 0.996862i | \(0.525225\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 8.92384e17i | − 1.01357i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.87930e17 | 0.659647 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.06312e18i | 1.17831i | 0.808018 | + | 0.589157i | \(0.200540\pi\) | ||||
−0.808018 | + | 0.589157i | \(0.799460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.85105e18 | 2.02675 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.65825e16i | − 0.0612039i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.04920e18 | 1.12119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 9.28788e17i | − 0.980561i | −0.871565 | − | 0.490281i | \(-0.836894\pi\) | ||||
0.871565 | − | 0.490281i | \(-0.163106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.82898e17 | −0.920905 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2.19432e17i | − 0.226132i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.52810e17 | −0.970142 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 2.63062e17i | − 0.264646i |
(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 | 48.13.g.a.31.3 | yes | 4 | |
3.2 | odd | 2 | 144.13.g.h.127.3 | 4 | |||
4.3 | odd | 2 | inner | 48.13.g.a.31.1 | ✓ | 4 | |
8.3 | odd | 2 | 192.13.g.c.127.4 | 4 | |||
8.5 | even | 2 | 192.13.g.c.127.2 | 4 | |||
12.11 | even | 2 | 144.13.g.h.127.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.13.g.a.31.1 | ✓ | 4 | 4.3 | odd | 2 | inner | |
48.13.g.a.31.3 | yes | 4 | 1.1 | even | 1 | trivial | |
144.13.g.h.127.3 | 4 | 3.2 | odd | 2 | |||
144.13.g.h.127.4 | 4 | 12.11 | even | 2 | |||
192.13.g.c.127.2 | 4 | 8.5 | even | 2 | |||
192.13.g.c.127.4 | 4 | 8.3 | odd | 2 |