Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(559,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.p (of order \(2\), degree \(1\), not 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.6 | ||
Root | \(-0.474920 - 1.33209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.559 |
Dual form | 672.2.p.a.559.14 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58069 | 0.706908 | 0.353454 | − | 0.935452i | \(-0.385007\pi\) | ||||
0.353454 | + | 0.935452i | \(0.385007\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37995 | − | 1.15578i | 0.899537 | − | 0.436844i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.26057 | 0.681588 | 0.340794 | − | 0.940138i | \(-0.389304\pi\) | ||||
0.340794 | + | 0.940138i | \(0.389304\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.548664 | 0.152172 | 0.0760860 | − | 0.997101i | \(-0.475758\pi\) | ||||
0.0760860 | + | 0.997101i | \(0.475758\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.58069i | − | 0.408134i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.433635i | 0.105172i | 0.998616 | + | 0.0525860i | \(0.0167464\pi\) | ||||
−0.998616 | + | 0.0525860i | \(0.983254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.02255i | 1.38167i | 0.723014 | + | 0.690834i | \(0.242756\pi\) | ||||
−0.723014 | + | 0.690834i | \(0.757244\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.15578 | − | 2.37995i | −0.252212 | − | 0.519348i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.24028i | − | 1.71822i | −0.511794 | − | 0.859108i | \(-0.671019\pi\) | ||
0.511794 | − | 0.859108i | \(-0.328981\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.50141 | −0.500281 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.548664i | − | 0.101884i | −0.998702 | − | 0.0509422i | \(-0.983778\pi\) | ||
0.998702 | − | 0.0509422i | \(-0.0162224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.50941 | 1.34873 | 0.674365 | − | 0.738398i | \(-0.264418\pi\) | ||||
0.674365 | + | 0.738398i | \(0.264418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.26057i | − | 0.393515i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.76198 | − | 1.82694i | 0.635890 | − | 0.308809i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.21124i | − | 0.692324i | −0.938175 | − | 0.346162i | \(-0.887485\pi\) | ||
0.938175 | − | 0.346162i | \(-0.112515\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.548664i | − | 0.0878565i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.09032i | 1.10732i | 0.832742 | + | 0.553661i | \(0.186770\pi\) | ||||
−0.832742 | + | 0.553661i | \(0.813230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.82694 | 0.278605 | 0.139303 | − | 0.990250i | \(-0.455514\pi\) | ||||
0.139303 | + | 0.990250i | \(0.455514\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.58069 | −0.235636 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.5839 | −1.68968 | −0.844840 | − | 0.535018i | \(-0.820305\pi\) | ||||
−0.844840 | + | 0.535018i | \(0.820305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.32834 | − | 5.50141i | 0.618334 | − | 0.785915i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.433635 | 0.0607210 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.71005i | − | 0.509615i | −0.966992 | − | 0.254807i | \(-0.917988\pi\) | ||
0.966992 | − | 0.254807i | \(-0.0820121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.57327 | 0.481820 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.02255 | 0.797706 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.5240i | − | 1.50029i | −0.661273 | − | 0.750145i | \(-0.729983\pi\) | ||
0.661273 | − | 0.750145i | \(-0.270017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.1325 | 1.55341 | 0.776706 | − | 0.629864i | \(-0.216889\pi\) | ||||
0.776706 | + | 0.629864i | \(0.216889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.37995 | + | 1.15578i | −0.299846 | + | 0.145615i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.867270 | 0.107572 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.35089 | −1.14239 | −0.571196 | − | 0.820813i | \(-0.693521\pi\) | ||||
−0.571196 | + | 0.820813i | \(0.693521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.24028 | −0.992013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.27953i | − | 0.151852i | −0.997113 | − | 0.0759262i | \(-0.975809\pi\) | ||
0.997113 | − | 0.0759262i | \(-0.0241913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.867270i | 0.101506i | 0.998711 | + | 0.0507531i | \(0.0161622\pi\) | ||||
−0.998711 | + | 0.0507531i | \(0.983838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.50141i | 0.288837i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.38005 | − | 2.61272i | 0.613114 | − | 0.297748i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3696i | 1.16668i | 0.812230 | + | 0.583338i | \(0.198253\pi\) | ||||
−0.812230 | + | 0.583338i | \(0.801747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.13554i | 0.673463i | 0.941601 | + | 0.336732i | \(0.109321\pi\) | ||||
−0.941601 | + | 0.336732i | \(0.890679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.685444i | 0.0743469i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.548664 | −0.0588229 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.95759i | − | 0.843503i | −0.906712 | − | 0.421751i | \(-0.861416\pi\) | ||
0.906712 | − | 0.421751i | \(-0.138584\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30579 | − | 0.634135i | 0.136884 | − | 0.0664754i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 7.50941i | − | 0.778689i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.51981i | 0.976712i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.1778i | 1.94721i | 0.228233 | + | 0.973607i | \(0.426705\pi\) | ||||
−0.228233 | + | 0.973607i | \(0.573295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.26057 | −0.227196 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.74208 | −0.471855 | −0.235927 | − | 0.971771i | \(-0.575813\pi\) | ||||
−0.235927 | + | 0.971771i | \(0.575813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.01040 | 0.198090 | 0.0990452 | − | 0.995083i | \(-0.468421\pi\) | ||||
0.0990452 | + | 0.995083i | \(0.468421\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.82694 | − | 3.76198i | −0.178291 | − | 0.367131i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.7845 | −1.71929 | −0.859647 | − | 0.510888i | \(-0.829317\pi\) | ||||
−0.859647 | + | 0.510888i | \(0.829317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0432i | 1.15353i | 0.816909 | + | 0.576766i | \(0.195686\pi\) | ||||
−0.816909 | + | 0.576766i | \(0.804314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.21124 | −0.399713 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.86727 | −0.269730 | −0.134865 | − | 0.990864i | \(-0.543060\pi\) | ||||
−0.134865 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.0254i | − | 1.21462i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.548664 | −0.0507240 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.501187 | + | 1.03203i | 0.0459437 | + | 0.0946061i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.88982 | −0.535438 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.09032 | 0.639312 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8574 | −1.06056 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9928i | 1.33039i | 0.746669 | + | 0.665196i | \(0.231652\pi\) | ||||
−0.746669 | + | 0.665196i | \(0.768348\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1.82694i | − | 0.160853i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.52114i | 0.744496i | 0.928133 | + | 0.372248i | \(0.121413\pi\) | ||||
−0.928133 | + | 0.372248i | \(0.878587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.96075 | + | 14.3334i | 0.603573 | + | 1.24286i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.58069i | 0.136045i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.00281 | 0.427419 | 0.213709 | − | 0.976897i | \(-0.431445\pi\) | ||||
0.213709 | + | 0.976897i | \(0.431445\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3106i | 1.21381i | 0.794776 | + | 0.606903i | \(0.207588\pi\) | ||||
−0.794776 | + | 0.606903i | \(0.792412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5839i | 0.975538i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.24029 | 0.103719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.867270i | − | 0.0720229i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.50141 | − | 4.32834i | −0.453748 | − | 0.356996i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.4553i | 1.51192i | 0.654619 | + | 0.755959i | \(0.272829\pi\) | ||||
−0.654619 | + | 0.755959i | \(0.727171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.5334i | − | 1.18271i | −0.806411 | − | 0.591356i | \(-0.798593\pi\) | ||
0.806411 | − | 0.591356i | \(-0.201407\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 0.433635i | − | 0.0350573i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8701 | 0.953428 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.80975 | 0.463669 | 0.231834 | − | 0.972755i | \(-0.425527\pi\) | ||||
0.231834 | + | 0.972755i | \(0.425527\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.71005 | −0.294226 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.52395 | − | 19.6115i | −0.750593 | − | 1.54560i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3509 | 1.35903 | 0.679513 | − | 0.733663i | \(-0.262191\pi\) | ||||
0.679513 | + | 0.733663i | \(0.262191\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 3.57327i | − | 0.278179i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.823767 | 0.0637450 | 0.0318725 | − | 0.999492i | \(-0.489853\pi\) | ||||
0.0318725 | + | 0.999492i | \(0.489853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6990 | −0.976844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 6.02255i | − | 0.460556i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.5230 | −1.48430 | −0.742152 | − | 0.670231i | \(-0.766195\pi\) | ||||
−0.742152 | + | 0.670231i | \(0.766195\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.95322 | + | 2.89108i | −0.450021 | + | 0.218545i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.5240 | −0.866193 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.39611 | 0.328581 | 0.164290 | − | 0.986412i | \(-0.447467\pi\) | ||||
0.164290 | + | 0.986412i | \(0.447467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.14738 | −0.605590 | −0.302795 | − | 0.953056i | \(-0.597920\pi\) | ||||
−0.302795 | + | 0.953056i | \(0.597920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.1325i | − | 0.896863i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.65668i | − | 0.489409i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.980263i | 0.0716839i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.15578 | + | 2.37995i | 0.0840707 | + | 0.173116i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.420123i | − | 0.0303990i | −0.999884 | − | 0.0151995i | \(-0.995162\pi\) | ||
0.999884 | − | 0.0151995i | \(-0.00483834\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1553 | −0.802974 | −0.401487 | − | 0.915865i | \(-0.631507\pi\) | ||||
−0.401487 | + | 0.915865i | \(0.631507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 0.867270i | − | 0.0621065i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.95035i | − | 0.352698i | −0.984328 | − | 0.176349i | \(-0.943571\pi\) | ||
0.984328 | − | 0.176349i | \(-0.0564287\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0851 | 0.856687 | 0.428343 | − | 0.903616i | \(-0.359097\pi\) | ||||
0.428343 | + | 0.903616i | \(0.359097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.35089i | 0.659561i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.634135 | − | 1.30579i | −0.0445076 | − | 0.0916488i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.2076i | 0.782775i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.24028i | 0.572739i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.6144i | 0.941728i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.17306 | −0.424971 | −0.212486 | − | 0.977164i | \(-0.568156\pi\) | ||||
−0.212486 | + | 0.977164i | \(0.568156\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.27953 | −0.0876720 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.88783 | 0.196948 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.8720 | − | 8.67923i | 1.21323 | − | 0.589185i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.867270 | 0.0586047 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.237920i | 0.0160042i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.4078 | −1.23268 | −0.616340 | − | 0.787480i | \(-0.711385\pi\) | ||||
−0.616340 | + | 0.787480i | \(0.711385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.50141 | 0.166760 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 10.6567i | − | 0.707309i | −0.935376 | − | 0.353654i | \(-0.884939\pi\) | ||
0.935376 | − | 0.353654i | \(-0.115061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.97114 | −0.592830 | −0.296415 | − | 0.955059i | \(-0.595791\pi\) | ||||
−0.296415 | + | 0.955059i | \(0.595791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.61272 | − | 5.38005i | −0.171905 | − | 0.353981i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9124 | 0.976942 | 0.488471 | − | 0.872580i | \(-0.337555\pi\) | ||||
0.488471 | + | 0.872580i | \(0.337555\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.3106 | −1.19445 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.3696 | 0.673580 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1370i | 0.849759i | 0.905250 | + | 0.424880i | \(0.139684\pi\) | ||||
−0.905250 | + | 0.424880i | \(0.860316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.1355i | − | 0.652888i | −0.945217 | − | 0.326444i | \(-0.894150\pi\) | ||
0.945217 | − | 0.326444i | \(-0.105850\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.84179 | − | 8.69604i | 0.437106 | − | 0.555570i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.30435i | 0.210251i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.13554 | 0.388824 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.7018i | 1.43292i | 0.697626 | + | 0.716462i | \(0.254240\pi\) | ||||
−0.697626 | + | 0.716462i | \(0.745760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.6277i | − | 1.17112i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.685444 | 0.0429242 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.1326i | 1.00632i | 0.864192 | + | 0.503162i | \(0.167830\pi\) | ||||
−0.864192 | + | 0.503162i | \(0.832170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.86727 | − | 10.0225i | −0.302437 | − | 0.622771i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.548664i | 0.0339614i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 15.0581i | − | 0.928519i | −0.885699 | − | 0.464260i | \(-0.846320\pi\) | ||
0.885699 | − | 0.464260i | \(-0.153680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.86446i | − | 0.360251i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.95759 | −0.486996 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.76288 | −0.534282 | −0.267141 | − | 0.963657i | \(-0.586079\pi\) | ||||
−0.267141 | + | 0.963657i | \(0.586079\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.31238 | 0.261958 | 0.130979 | − | 0.991385i | \(-0.458188\pi\) | ||||
0.130979 | + | 0.991385i | \(0.458188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.634135 | − | 1.30579i | −0.0383796 | − | 0.0790302i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.65460 | −0.340985 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 25.5528i | − | 1.53532i | −0.640857 | − | 0.767661i | \(-0.721421\pi\) | ||
0.640857 | − | 0.767661i | \(-0.278579\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.50941 | −0.449577 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.17501 | 0.129751 | 0.0648753 | − | 0.997893i | \(-0.479335\pi\) | ||||
0.0648753 | + | 0.997893i | \(0.479335\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.2880i | − | 0.730446i | −0.930920 | − | 0.365223i | \(-0.880993\pi\) | ||
0.930920 | − | 0.365223i | \(-0.119007\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.51981 | 0.563905 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.19485 | + | 16.8746i | 0.483727 | + | 0.996077i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8120 | 0.988939 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.1778 | 1.12422 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8790 | 1.45345 | 0.726724 | − | 0.686929i | \(-0.241042\pi\) | ||||
0.726724 | + | 0.686929i | \(0.241042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 18.2158i | − | 1.06057i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.26057i | 0.131172i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 4.52114i | − | 0.261464i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.34802 | − | 2.11154i | 0.250616 | − | 0.121707i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.74208i | 0.272426i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.1778 | 1.09812 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.0254i | 0.971689i | 0.874045 | + | 0.485844i | \(0.161488\pi\) | ||||
−0.874045 | + | 0.485844i | \(0.838512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.01040i | − | 0.114368i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2983 | 1.32113 | 0.660564 | − | 0.750770i | \(-0.270317\pi\) | ||||
0.660564 | + | 0.750770i | \(0.270317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0479i | 0.850558i | 0.905062 | + | 0.425279i | \(0.139824\pi\) | ||||
−0.905062 | + | 0.425279i | \(0.860176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.76198 | + | 1.82694i | −0.211963 | + | 0.102936i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 22.4761i | − | 1.26238i | −0.775627 | − | 0.631192i | \(-0.782566\pi\) | ||
0.775627 | − | 0.631192i | \(-0.217434\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.24029i | − | 0.0694431i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.7845i | 0.992635i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.61159 | −0.145313 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.37243 | −0.0761288 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0432 | 0.665992 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.5690 | + | 13.3884i | −1.51993 | + | 0.738127i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5315 | 1.29341 | 0.646705 | − | 0.762740i | \(-0.276147\pi\) | ||||
0.646705 | + | 0.762740i | \(0.276147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.21124i | 0.230775i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.7809 | −0.807567 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.77682 | 0.478104 | 0.239052 | − | 0.971007i | \(-0.423163\pi\) | ||||
0.239052 | + | 0.971007i | \(0.423163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.86727i | 0.155729i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9756 | 0.919278 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.94283 | − | 18.0957i | 0.212893 | − | 0.977076i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.0254 | −0.701262 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.00489 | 0.214994 | 0.107497 | − | 0.994205i | \(-0.465716\pi\) | ||||
0.107497 | + | 0.994205i | \(0.465716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.43649 | 0.183951 | 0.0919756 | − | 0.995761i | \(-0.470682\pi\) | ||||
0.0919756 | + | 0.995761i | \(0.470682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.548664i | 0.0292855i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 23.0903i | − | 1.22897i | −0.788927 | − | 0.614487i | \(-0.789363\pi\) | ||
0.788927 | − | 0.614487i | \(-0.210637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2.02255i | − | 0.107346i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.03203 | − | 0.501187i | 0.0546208 | − | 0.0265256i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.8882i | − | 1.15522i | −0.816315 | − | 0.577608i | \(-0.803986\pi\) | ||
0.816315 | − | 0.577608i | \(-0.196014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2711 | −0.909004 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.88982i | 0.309135i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.37089i | 0.0717556i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.9276 | −1.45781 | −0.728905 | − | 0.684614i | \(-0.759971\pi\) | ||||
−0.728905 | + | 0.684614i | \(0.759971\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.09032i | − | 0.369107i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.28801 | − | 8.82975i | −0.222622 | − | 0.458418i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.2403i | − | 0.789111i | −0.918872 | − | 0.394555i | \(-0.870899\pi\) | ||
0.918872 | − | 0.394555i | \(-0.129101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.8574i | 0.612315i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.301032i | − | 0.0155039i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4864 | −0.590018 | −0.295009 | − | 0.955494i | \(-0.595323\pi\) | ||||
−0.295009 | + | 0.955494i | \(0.595323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.9928 | 0.768102 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.4746 | 1.14840 | 0.574198 | − | 0.818716i | \(-0.305314\pi\) | ||||
0.574198 | + | 0.818716i | \(0.305314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.50422 | − | 4.12992i | 0.433415 | − | 0.210480i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.82694 | −0.0928684 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.5907i | 1.04399i | 0.852949 | + | 0.521994i | \(0.174812\pi\) | ||||
−0.852949 | + | 0.521994i | \(0.825188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.57327 | 0.180708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.52114 | 0.429835 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.3912i | 0.824732i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.8778 | −1.34896 | −0.674479 | − | 0.738294i | \(-0.735632\pi\) | ||||
−0.674479 | + | 0.738294i | \(0.735632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.3334 | − | 6.96075i | 0.717566 | − | 0.348473i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.00281 | 0.449579 | 0.224789 | − | 0.974407i | \(-0.427831\pi\) | ||||
0.224789 | + | 0.974407i | \(0.427831\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.12014 | 0.205239 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.58069 | 0.0785453 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.51981i | − | 0.471879i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.91237i | − | 0.242901i | −0.992597 | − | 0.121450i | \(-0.961245\pi\) | ||
0.992597 | − | 0.121450i | \(-0.0387545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.00281i | − | 0.246770i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3192 | − | 27.4265i | −0.655393 | − | 1.34957i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.69841i | 0.476076i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.3106 | 0.700791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.17501i | 0.203963i | 0.994786 | + | 0.101981i | \(0.0325182\pi\) | ||||
−0.994786 | + | 0.101981i | \(0.967482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.11391i | 0.151763i | 0.997117 | + | 0.0758814i | \(0.0241770\pi\) | ||||
−0.997117 | + | 0.0758814i | \(0.975823\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5839 | 0.563227 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.08470i | − | 0.0526155i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.8748 | − | 14.0225i | 1.39735 | − | 0.678599i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 1.24029i | − | 0.0598820i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 0.641564i | − | 0.0309030i | −0.999881 | − | 0.0154515i | \(-0.995081\pi\) | ||
0.999881 | − | 0.0154515i | \(-0.00491857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.95772i | 0.334366i | 0.985926 | + | 0.167183i | \(0.0534671\pi\) | ||||
−0.985926 | + | 0.167183i | \(0.946533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.867270 | −0.0415824 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 49.6275 | 2.37400 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.4055 | −0.830717 | −0.415359 | − | 0.909658i | \(-0.636344\pi\) | ||||
−0.415359 | + | 0.909658i | \(0.636344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.32834 | + | 5.50141i | −0.206111 | + | 0.261972i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0856 | −0.859271 | −0.429635 | − | 0.903002i | \(-0.641358\pi\) | ||||
−0.429635 | + | 0.903002i | \(0.641358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.5785i | − | 0.596279i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.4553 | 0.872906 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.2229 | −1.00157 | −0.500786 | − | 0.865571i | \(-0.666956\pi\) | ||||
−0.500786 | + | 0.865571i | \(0.666956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0282i | 0.754737i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.5334 | −0.682839 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.06406 | − | 1.00237i | 0.0967647 | − | 0.0469920i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.7046 | 1.29597 | 0.647983 | − | 0.761655i | \(-0.275613\pi\) | ||||
0.647983 | + | 0.761655i | \(0.275613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.433635 | −0.0202403 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.5438 | −1.09654 | −0.548272 | − | 0.836300i | \(-0.684714\pi\) | ||||
−0.548272 | + | 0.836300i | \(0.684714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26.8145i | − | 1.24618i | −0.782151 | − | 0.623089i | \(-0.785878\pi\) | ||
0.782151 | − | 0.623089i | \(-0.214122\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 11.8701i | − | 0.550462i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 17.3884i | − | 0.804640i | −0.915499 | − | 0.402320i | \(-0.868204\pi\) | ||
0.915499 | − | 0.402320i | \(-0.131796\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.2547 | + | 10.8076i | −1.02762 | + | 0.499048i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 5.80975i | − | 0.267699i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.12992 | 0.189894 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 15.0648i | − | 0.691222i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.71005i | 0.169872i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.6003 | −1.16971 | −0.584854 | − | 0.811139i | \(-0.698848\pi\) | ||||
−0.584854 | + | 0.811139i | \(0.698848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 2.31056i | − | 0.105352i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.6115 | + | 9.52395i | −0.892352 | + | 0.433355i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.3143i | 1.37650i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.940673i | 0.0426260i | 0.999773 | + | 0.0213130i | \(0.00678464\pi\) | ||||
−0.999773 | + | 0.0213130i | \(0.993215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 17.3509i | − | 0.784634i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0500 | 1.08536 | 0.542680 | − | 0.839939i | \(-0.317410\pi\) | ||||
0.542680 | + | 0.839939i | \(0.317410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.237920 | 0.0107154 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.57327 | −0.160607 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.47886 | − | 3.04522i | −0.0663358 | − | 0.136597i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.8354 | 1.20132 | 0.600658 | − | 0.799506i | \(-0.294905\pi\) | ||||
0.600658 | + | 0.799506i | \(0.294905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 0.823767i | − | 0.0368032i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.13297 | 0.0505166 | 0.0252583 | − | 0.999681i | \(-0.491959\pi\) | ||||
0.0252583 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.49578 | −0.333558 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6990i | 0.563981i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.7937 | 0.522745 | 0.261373 | − | 0.965238i | \(-0.415825\pi\) | ||||
0.261373 | + | 0.965238i | \(0.415825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00237 | + | 2.06406i | 0.0443424 | + | 0.0913087i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.02255 | −0.265902 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.17783 | 0.140032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.1862 | −1.15167 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.5230i | 0.856964i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.6991i | 0.643979i | 0.946743 | + | 0.321990i | \(0.104352\pi\) | ||||
−0.946743 | + | 0.321990i | \(0.895648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.69507i | − | 0.336482i | −0.985746 | − | 0.168241i | \(-0.946191\pi\) | ||
0.985746 | − | 0.168241i | \(-0.0538086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.89108 | + | 5.95322i | 0.126177 | + | 0.259820i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.25634i | 0.141849i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.9022 | −1.95227 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.5240i | 0.500097i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.89020i | 0.168503i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.1119 | −1.21538 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4.39611i | − | 0.189706i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.78452 | − | 12.4363i | 0.421449 | − | 0.535670i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 11.6313i | − | 0.500071i | −0.968237 | − | 0.250035i | \(-0.919558\pi\) | ||
0.968237 | − | 0.250035i | \(-0.0804422\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.14738i | 0.349637i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.0367i | 0.815441i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0048 | −0.898099 | −0.449049 | − | 0.893507i | \(-0.648237\pi\) | ||||
−0.449049 | + | 0.893507i | \(0.648237\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.1325 | −0.517804 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.30435 | 0.140770 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.9850 | + | 24.6792i | 0.509655 | + | 1.04947i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.65668 | −0.282560 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.7501i | 1.47241i | 0.676760 | + | 0.736204i | \(0.263383\pi\) | ||||
−0.676760 | + | 0.736204i | \(0.736617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00237 | 0.0423959 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.980263 | 0.0413867 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.9124i | 0.712771i | 0.934339 | + | 0.356386i | \(0.115991\pi\) | ||||
−0.934339 | + | 0.356386i | \(0.884009\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.53228 | −0.190674 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37995 | − | 1.15578i | 0.0999486 | − | 0.0485382i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.4856 | −0.858800 | −0.429400 | − | 0.903114i | \(-0.641275\pi\) | ||||
−0.429400 | + | 0.903114i | \(0.641275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.0132 | −1.92559 | −0.962796 | − | 0.270229i | \(-0.912901\pi\) | ||||
−0.962796 | + | 0.270229i | \(0.912901\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.420123 | −0.0175509 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.6123i | 0.859591i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 35.8191i | − | 1.49117i | −0.666411 | − | 0.745585i | \(-0.732170\pi\) | ||
0.666411 | − | 0.745585i | \(-0.267830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.1553i | 0.463598i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.09134 | + | 14.6023i | 0.294198 | + | 0.605805i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.38684i | − | 0.347347i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.867270 | −0.0358572 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 30.4007i | − | 1.25477i | −0.778708 | − | 0.627387i | \(-0.784125\pi\) | ||
0.778708 | − | 0.627387i | \(-0.215875\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.2258i | 1.86350i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.95035 | −0.203630 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.3065i | 0.957084i | 0.878065 | + | 0.478542i | \(0.158835\pi\) | ||||
−0.878065 | + | 0.478542i | \(0.841165\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.792224 | + | 1.63132i | 0.0324780 | + | 0.0668778i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 12.0851i | − | 0.494608i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.9547i | 0.815329i | 0.913132 | + | 0.407664i | \(0.133657\pi\) | ||||
−0.913132 | + | 0.407664i | \(0.866343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 27.0028i | − | 1.10147i | −0.834681 | − | 0.550734i | \(-0.814348\pi\) | ||
0.834681 | − | 0.550734i | \(-0.185652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.35089 | 0.380798 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.31000 | −0.378505 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.63416 | −0.0663283 | −0.0331642 | − | 0.999450i | \(-0.510558\pi\) | ||||
−0.0331642 | + | 0.999450i | \(0.510558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.30579 | + | 0.634135i | −0.0529134 | + | 0.0256965i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.35565 | −0.257122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.3500i | − | 0.660369i | −0.943916 | − | 0.330184i | \(-0.892889\pi\) | ||
0.943916 | − | 0.330184i | \(-0.107111\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.2076 | 0.451935 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.220365 | 0.00887154 | 0.00443577 | − | 0.999990i | \(-0.498588\pi\) | ||||
0.00443577 | + | 0.999990i | \(0.498588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9972i | 0.683175i | 0.939850 | + | 0.341587i | \(0.110965\pi\) | ||||
−0.939850 | + | 0.341587i | \(0.889035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.24028 | 0.330671 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.19723 | − | 18.9387i | −0.368479 | − | 0.758762i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.23595 | −0.249438 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.6144 | 0.543707 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.82614 | 0.0728130 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8402i | 0.550971i | 0.961305 | + | 0.275485i | \(0.0888386\pi\) | ||||
−0.961305 | + | 0.275485i | \(0.911161\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.17306i | 0.245357i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.6990i | 0.940465i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.37480 | − | 3.01842i | 0.0940932 | − | 0.119594i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.27953i | 0.0506175i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0479 | 0.515361 | 0.257681 | − | 0.966230i | \(-0.417042\pi\) | ||||
0.257681 | + | 0.966230i | \(0.417042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.2880i | − | 0.484592i | −0.970202 | − | 0.242296i | \(-0.922100\pi\) | ||
0.970202 | − | 0.242296i | \(-0.0779005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.88783i | − | 0.113708i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.8638 | −1.25269 | −0.626347 | − | 0.779544i | \(-0.715451\pi\) | ||||
−0.626347 | + | 0.779544i | \(0.715451\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 26.0507i | − | 1.02258i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.67923 | − | 17.8720i | −0.340166 | − | 0.700460i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.6007i | 0.571371i | 0.958323 | + | 0.285686i | \(0.0922213\pi\) | ||||
−0.958323 | + | 0.285686i | \(0.907779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.4693i | 0.526290i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 0.867270i | − | 0.0338354i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.25776 | −0.282722 | −0.141361 | − | 0.989958i | \(-0.545148\pi\) | ||||
−0.141361 | + | 0.989958i | \(0.545148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.6031 | −0.606891 | −0.303446 | − | 0.952849i | \(-0.598137\pi\) | ||||
−0.303446 | + | 0.952849i | \(0.598137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.237920 | 0.00924004 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.0028 | + | 22.6567i | 0.426671 | + | 0.878588i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.52114 | −0.175059 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.4078i | 0.711688i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.4265 | 1.05879 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.19475 | 0.354432 | 0.177216 | − | 0.984172i | \(-0.443291\pi\) | ||||
0.177216 | + | 0.984172i | \(0.443291\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 2.50141i | − | 0.0962791i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.1669 | 0.544480 | 0.272240 | − | 0.962229i | \(-0.412236\pi\) | ||||
0.272240 | + | 0.962229i | \(0.412236\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.1654 | + | 45.6423i | 0.850629 | + | 1.75159i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.6567 | −0.408365 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.9201 | 1.37444 | 0.687222 | − | 0.726448i | \(-0.258830\pi\) | ||||
0.687222 | + | 0.726448i | \(0.258830\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.90791 | 0.302146 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.97114i | 0.342270i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.03557i | − | 0.0775491i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.0451i | − | 0.914719i | −0.889282 | − | 0.457359i | \(-0.848795\pi\) | ||
0.889282 | − | 0.457359i | \(-0.151205\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.38005 | + | 2.61272i | −0.204371 | + | 0.0992492i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.6206i | 0.858049i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.07461 | −0.116459 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 14.9124i | − | 0.564037i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.3211i | − | 1.48514i | −0.669771 | − | 0.742568i | \(-0.733608\pi\) | ||
0.669771 | − | 0.742568i | \(-0.266392\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.3624 | 0.956561 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.3106i | 0.689615i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.2859 | + | 5.48081i | −0.424451 | + | 0.206127i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8578i | 1.42178i | 0.703304 | + | 0.710890i | \(0.251707\pi\) | ||||
−0.703304 | + | 0.710890i | \(0.748293\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.3696i | − | 0.388892i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 61.8796i | − | 2.31741i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.96053 | 0.0733195 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.1370 | 0.490609 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.6003 | −0.954731 | −0.477365 | − | 0.878705i | \(-0.658408\pi\) | ||||
−0.477365 | + | 0.878705i | \(0.658408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.78465 | − | 2.32358i | 0.178190 | − | 0.0865346i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.1355 | −0.376945 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.37243i | 0.0509708i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.11772 | 0.0785420 | 0.0392710 | − | 0.999229i | \(-0.487496\pi\) | ||||
0.0392710 | + | 0.999229i | \(0.487496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.792224i | 0.0293014i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4120 | 0.753936 | 0.376968 | − | 0.926226i | \(-0.376967\pi\) | ||||
0.376968 | + | 0.926226i | \(0.376967\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.69604 | − | 6.84179i | −0.320758 | − | 0.252363i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.1384 | −0.778641 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.3932 | −0.676604 | −0.338302 | − | 0.941038i | \(-0.609853\pi\) | ||||
−0.338302 | + | 0.941038i | \(0.609853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.30435 | 0.121389 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3812i | 1.22464i | 0.790611 | + | 0.612319i | \(0.209763\pi\) | ||||
−0.790611 | + | 0.612319i | \(0.790237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.1722i | 1.06879i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.13554i | − | 0.224488i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.3263 | + | 20.5550i | −1.54657 | + | 0.751064i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.83899i | 0.359030i | 0.983755 | + | 0.179515i | \(0.0574528\pi\) | ||||
−0.983755 | + | 0.179515i | \(0.942547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.7018 | 0.827299 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 22.9729i | − | 0.836068i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 23.9363i | − | 0.869980i | −0.900435 | − | 0.434990i | \(-0.856752\pi\) | ||
0.900435 | − | 0.434990i | \(-0.143248\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.6277 | −0.676144 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 14.6991i | − | 0.532842i | −0.963857 | − | 0.266421i | \(-0.914159\pi\) | ||
0.963857 | − | 0.266421i | \(-0.0858411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.9193 | + | 28.6623i | 0.503914 | + | 1.03765i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 0.685444i | − | 0.0247823i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.32278i | − | 0.228302i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.7317i | 0.819727i | 0.912147 | + | 0.409864i | \(0.134424\pi\) | ||||
−0.912147 | + | 0.409864i | \(0.865576\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.1326 | 0.581002 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.21267 | 0.295389 | 0.147695 | − | 0.989033i | \(-0.452815\pi\) | ||||
0.147695 | + | 0.989033i | \(0.452815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.7841 | −0.674744 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.0225 | + | 4.86727i | −0.359557 | + | 0.174612i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.7018 | −1.52995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.89247i | − | 0.103501i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.548664 | 0.0196076 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.18345 | 0.327771 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.3134i | 0.902324i | 0.892442 | + | 0.451162i | \(0.148990\pi\) | ||||
−0.892442 | + | 0.451162i | \(0.851010\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.0581 | −0.536081 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.82396 | + | 3.31394i | −0.242632 | + | 0.117830i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.65668 | 0.236386 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.86446 | −0.207991 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2767 | 0.364021 | 0.182010 | − | 0.983297i | \(-0.441740\pi\) | ||||
0.182010 | + | 0.983297i | \(0.441740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.02317i | − | 0.177707i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.95759i | 0.281168i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.96053i | 0.0691854i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.0545 | − | 30.9997i | −0.530600 | − | 1.09260i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.76288i | 0.308468i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.4968 | 1.00189 | 0.500947 | − | 0.865478i | \(-0.332985\pi\) | ||||
0.500947 | + | 0.865478i | \(0.332985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.2683i | − | 0.465912i | −0.972487 | − | 0.232956i | \(-0.925160\pi\) | ||
0.972487 | − | 0.232956i | \(-0.0748398\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 4.31238i | − | 0.151242i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.4265 | 0.960707 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0028i | 0.384940i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.30579 | + | 0.634135i | −0.0456281 | + | 0.0221585i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 50.5926i | − | 1.76570i | −0.469659 | − | 0.882848i | \(-0.655623\pi\) | ||
0.469659 | − | 0.882848i | \(-0.344377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.5730i | − | 0.682274i | −0.940014 | − | 0.341137i | \(-0.889188\pi\) | ||
0.940014 | − | 0.341137i | \(-0.110812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.65460i | 0.196868i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.64617 | 0.161563 | 0.0807816 | − | 0.996732i | \(-0.474258\pi\) | ||||
0.0807816 | + | 0.996732i | \(0.474258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2382 | 0.772364 | 0.386182 | − | 0.922423i | \(-0.373794\pi\) | ||||
0.386182 | + | 0.922423i | \(0.373794\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.5528 | −0.886418 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.38560 | + | 1.87692i | 0.0826562 | + | 0.0650314i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.30212 | 0.0450619 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.50941i | 0.259563i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.5297 | −1.26115 | −0.630573 | − | 0.776130i | \(-0.717180\pi\) | ||||
−0.630573 | + | 0.776130i | \(0.717180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6990 | 0.989620 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2.17501i | − | 0.0749115i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −20.0732 | −0.690539 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0175 | + | 6.80734i | −0.481646 | + | 0.233903i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.2880 | −0.421723 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.7018 | −1.18956 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.1702 | 1.44388 | 0.721940 | − | 0.691956i | \(-0.243251\pi\) | ||||
0.721940 | + | 0.691956i | \(0.243251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 9.51981i | − | 0.325571i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.5720i | 1.28343i | 0.766941 | + | 0.641717i | \(0.221778\pi\) | ||||
−0.766941 | + | 0.641717i | \(0.778222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7543i | 0.435170i | 0.976041 | + | 0.217585i | \(0.0698180\pi\) | ||||
−0.976041 | + | 0.217585i | \(0.930182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.8746 | − | 8.19485i | 0.575085 | − | 0.279280i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 51.1449i | − | 1.74099i | −0.492175 | − | 0.870496i | \(-0.663798\pi\) | ||
0.492175 | − | 0.870496i | \(-0.336202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.8599 | −1.04927 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.8120i | − | 0.570964i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.4413i | 0.795192i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.13050 | −0.173840 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 19.1778i | − | 0.649071i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.2201 | + | 13.7046i | −0.954014 | + | 0.463300i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.8694i | 0.468335i | 0.972196 | + | 0.234168i | \(0.0752365\pi\) | ||||
−0.972196 | + | 0.234168i | \(0.924764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 24.8790i | − | 0.839149i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.92202i | − | 0.199518i | −0.995012 | − | 0.0997589i | \(-0.968193\pi\) | ||
0.995012 | − | 0.0997589i | \(-0.0318071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.17025 | 0.106688 | 0.0533438 | − | 0.998576i | \(-0.483012\pi\) | ||||
0.0533438 | + | 0.998576i | \(0.483012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.2158 | −0.612319 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.9010 | 1.67551 | 0.837756 | − | 0.546045i | \(-0.183867\pi\) | ||||
0.837756 | + | 0.546045i | \(0.183867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.3283 | + | 35.6820i | 0.581174 | + | 1.19674i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.26057 | 0.0757320 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 69.7644i | − | 2.33458i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.94891 | 0.232276 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.52114 | −0.150957 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.12014i | − | 0.137414i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60881 | 0.0535972 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.11154 | − | 4.34802i | −0.0702676 | − | 0.144693i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.8785 | −0.428096 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.60938 | 0.0866431 | 0.0433216 | − | 0.999061i | \(-0.486206\pi\) | ||||
0.0433216 | + | 0.999061i | \(0.486206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.74208 | 0.157285 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 42.9082i | − | 1.42161i | −0.703388 | − | 0.710807i | \(-0.748330\pi\) | ||
0.703388 | − | 0.710807i | \(-0.251670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8698i | 0.459024i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 19.1778i | − | 0.633999i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.84857 | + | 20.2799i | 0.325229 | + | 0.669702i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4217i | 0.805598i | 0.915288 | + | 0.402799i | \(0.131963\pi\) | ||||
−0.915288 | + | 0.402799i | \(0.868037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.0254 | 0.561005 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.702033i | − | 0.0231077i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5340i | 0.346356i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.01040 | −0.0660301 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 32.9150i | − | 1.07991i | −0.841695 | − | 0.539954i | \(-0.818442\pi\) | ||
0.841695 | − | 0.539954i | \(-0.181558\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.1325 | + | 26.0676i | 1.08587 | + | 0.854332i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 23.2983i | − | 0.762753i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.54950i | 0.0506739i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.2683i | − | 1.34818i | −0.738651 | − | 0.674088i | \(-0.764537\pi\) | ||
0.738651 | − | 0.674088i | \(-0.235463\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.0479 | 0.491070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.4508 | −1.74245 | −0.871223 | − | 0.490887i | \(-0.836673\pi\) | ||||
−0.871223 | + | 0.490887i | \(0.836673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.4262 | 1.90262 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.82694 | + | 3.76198i | 0.0594302 | + | 0.122377i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.2631 | 1.79581 | 0.897905 | − | 0.440189i | \(-0.145089\pi\) | ||||
0.897905 | + | 0.440189i | \(0.145089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.475840i | 0.0154464i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.4761 | −0.728838 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.5760 | −0.731309 | −0.365654 | − | 0.930751i | \(-0.619155\pi\) | ||||
−0.365654 | + | 0.930751i | \(0.619155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.664086i | − | 0.0214893i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.24029 | −0.0400930 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.9064 | − | 5.78215i | 0.384479 | − | 0.186715i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.3912 | 0.819072 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.7845 | 0.573098 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.6331 | −0.567629 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.2911i | − | 0.781150i | −0.920571 | − | 0.390575i | \(-0.872276\pi\) | ||
0.920571 | − | 0.390575i | \(-0.127724\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.61159i | 0.0838963i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.9221i | − | 0.799790i | −0.916561 | − | 0.399895i | \(-0.869047\pi\) | ||
0.916561 | − | 0.399895i | \(-0.130953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.5399 | + | 34.0584i | 0.530244 | + | 1.09186i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.37243i | 0.0439530i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.13273 | 0.0362392 | 0.0181196 | − | 0.999836i | \(-0.494232\pi\) | ||||
0.0181196 | + | 0.999836i | \(0.494232\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 17.9887i | − | 0.574921i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 12.0432i | − | 0.384511i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.8218 | 0.377056 | 0.188528 | − | 0.982068i | \(-0.439628\pi\) | ||||
0.188528 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.82499i | − | 0.249325i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.3884 | + | 27.5690i | 0.426158 | + | 0.877532i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 15.0545i | − | 0.478704i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 52.1176i | − | 1.65557i | −0.561045 | − | 0.827785i | \(-0.689600\pi\) | ||
0.561045 | − | 0.827785i | \(-0.310400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 23.5315i | − | 0.746750i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.1028 | 0.605599 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.2326 | −0.830796 | −0.415398 | − | 0.909640i | \(-0.636358\pi\) | ||||
−0.415398 | + | 0.909640i | \(0.636358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.21124 | 0.133238 |
(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 | 672.2.p.a.559.6 | 16 | ||
3.2 | odd | 2 | 2016.2.p.g.559.5 | 16 | |||
4.3 | odd | 2 | 168.2.p.a.139.14 | yes | 16 | ||
7.6 | odd | 2 | inner | 672.2.p.a.559.11 | 16 | ||
8.3 | odd | 2 | inner | 672.2.p.a.559.3 | 16 | ||
8.5 | even | 2 | 168.2.p.a.139.16 | yes | 16 | ||
12.11 | even | 2 | 504.2.p.g.307.3 | 16 | |||
21.20 | even | 2 | 2016.2.p.g.559.11 | 16 | |||
24.5 | odd | 2 | 504.2.p.g.307.2 | 16 | |||
24.11 | even | 2 | 2016.2.p.g.559.12 | 16 | |||
28.27 | even | 2 | 168.2.p.a.139.13 | ✓ | 16 | ||
56.13 | odd | 2 | 168.2.p.a.139.15 | yes | 16 | ||
56.27 | even | 2 | inner | 672.2.p.a.559.14 | 16 | ||
84.83 | odd | 2 | 504.2.p.g.307.4 | 16 | |||
168.83 | odd | 2 | 2016.2.p.g.559.6 | 16 | |||
168.125 | even | 2 | 504.2.p.g.307.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.p.a.139.13 | ✓ | 16 | 28.27 | even | 2 | ||
168.2.p.a.139.14 | yes | 16 | 4.3 | odd | 2 | ||
168.2.p.a.139.15 | yes | 16 | 56.13 | odd | 2 | ||
168.2.p.a.139.16 | yes | 16 | 8.5 | even | 2 | ||
504.2.p.g.307.1 | 16 | 168.125 | even | 2 | |||
504.2.p.g.307.2 | 16 | 24.5 | odd | 2 | |||
504.2.p.g.307.3 | 16 | 12.11 | even | 2 | |||
504.2.p.g.307.4 | 16 | 84.83 | odd | 2 | |||
672.2.p.a.559.3 | 16 | 8.3 | odd | 2 | inner | ||
672.2.p.a.559.6 | 16 | 1.1 | even | 1 | trivial | ||
672.2.p.a.559.11 | 16 | 7.6 | odd | 2 | inner | ||
672.2.p.a.559.14 | 16 | 56.27 | even | 2 | inner | ||
2016.2.p.g.559.5 | 16 | 3.2 | odd | 2 | |||
2016.2.p.g.559.6 | 16 | 168.83 | odd | 2 | |||
2016.2.p.g.559.11 | 16 | 21.20 | even | 2 | |||
2016.2.p.g.559.12 | 16 | 24.11 | even | 2 |