Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (of order \(6\), degree \(2\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 959.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.959 |
Dual form | 1152.2.p.a.191.1 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | + | 2.44949i | −0.632456 | + | 1.09545i | 0.354593 | + | 0.935021i | \(0.384620\pi\) |
−0.987048 | + | 0.160424i | \(0.948714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50000 | − | 2.59808i | 1.35680 | − | 0.783349i | 0.367610 | − | 0.929980i | \(-0.380176\pi\) |
0.989191 | + | 0.146631i | \(0.0468429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | + | 2.44949i | 1.17670 | + | 0.679366i | 0.955248 | − | 0.295806i | \(-0.0955881\pi\) |
0.221449 | + | 0.975172i | \(0.428921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.89898i | − | 1.26491i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.73205i | − | 0.420084i | −0.977692 | − | 0.210042i | \(-0.932640\pi\) | ||
0.977692 | − | 0.210042i | \(-0.0673601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24264 | − | 7.34847i | 0.884652 | − | 1.53226i | 0.0385394 | − | 0.999257i | \(-0.487729\pi\) |
0.846112 | − | 0.533005i | \(-0.178937\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | + | 4.89898i | 0.525226 | + | 0.909718i | 0.999568 | + | 0.0293774i | \(0.00935245\pi\) |
−0.474343 | + | 0.880340i | \(0.657314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.50000 | + | 7.79423i | −0.783349 | + | 1.35680i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898i | 0.805387i | 0.915335 | + | 0.402694i | \(0.131926\pi\) | ||||
−0.915335 | + | 0.402694i | \(0.868074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.48528 | −1.35873 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | + | 2.59808i | 0.702782 | + | 0.405751i | 0.808383 | − | 0.588657i | \(-0.200343\pi\) |
−0.105601 | + | 0.994409i | \(0.533677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.50000 | − | 7.79423i | −0.686244 | − | 1.18861i | −0.973044 | − | 0.230618i | \(-0.925925\pi\) |
0.286801 | − | 0.957990i | \(-0.407408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.24264 | + | 7.34847i | 0.632456 | + | 1.09545i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.24264 | + | 7.34847i | 0.618853 | + | 1.07188i | 0.989695 | + | 0.143189i | \(0.0457356\pi\) |
−0.370843 | + | 0.928696i | \(0.620931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50000 | + | 2.59808i | 0.210042 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.65685 | 0.777029 | 0.388514 | − | 0.921443i | \(-0.372988\pi\) | ||||
0.388514 | + | 0.921443i | \(0.372988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.6969i | 1.98173i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.50000 | − | 2.59808i | 0.596040 | − | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | + | 2.59808i | 0.585850 | + | 0.338241i | 0.763455 | − | 0.645861i | \(-0.223502\pi\) |
−0.177605 | + | 0.984102i | \(0.556835\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.48528 | + | 4.89898i | −1.08643 | + | 0.627250i | −0.932623 | − | 0.360851i | \(-0.882486\pi\) |
−0.153806 | + | 0.988101i | \(0.549153\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.0000 | + | 6.92820i | −1.48842 | + | 0.859338i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | − | 2.59808i | 0.183254 | − | 0.317406i | −0.759733 | − | 0.650236i | \(-0.774670\pi\) |
0.942987 | + | 0.332830i | \(0.108004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.6969i | 1.76930i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48528 | 1.00702 | 0.503509 | − | 0.863990i | \(-0.332042\pi\) | ||||
0.503509 | + | 0.863990i | \(0.332042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | 0.585206 | 0.292603 | − | 0.956234i | \(-0.405479\pi\) | ||||
0.292603 | + | 0.956234i | \(0.405479\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.50000 | + | 2.59808i | 0.519615 | + | 0.300000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7279 | + | 7.34847i | −1.43200 | + | 0.826767i | −0.997274 | − | 0.0737937i | \(-0.976489\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.00000 | + | 5.19615i | −0.987878 | + | 0.570352i | −0.904639 | − | 0.426178i | \(-0.859860\pi\) |
−0.0832389 | + | 0.996530i | \(0.526526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24264 | + | 2.44949i | 0.460179 | + | 0.265684i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.48528 | − | 4.89898i | −0.909718 | − | 0.525226i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.8564i | − | 1.46878i | −0.678730 | − | 0.734388i | \(-0.737469\pi\) | ||
0.678730 | − | 0.734388i | \(-0.262531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.24264 | − | 7.34847i | 0.435286 | − | 0.753937i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.500000 | + | 0.866025i | 0.0507673 | + | 0.0879316i | 0.890292 | − | 0.455389i | \(-0.150500\pi\) |
−0.839525 | + | 0.543321i | \(0.817167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 15.5885i | − | 1.56670i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.41421 | + | 2.44949i | 0.140720 | + | 0.243733i | 0.927768 | − | 0.373158i | \(-0.121725\pi\) |
−0.787048 | + | 0.616891i | \(0.788392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7279 | + | 7.34847i | 1.25412 | + | 0.724066i | 0.971925 | − | 0.235291i | \(-0.0756043\pi\) |
0.282194 | + | 0.959357i | \(0.408938\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.19615i | − | 0.502331i | −0.967944 | − | 0.251166i | \(-0.919186\pi\) | ||
0.967944 | − | 0.251166i | \(-0.0808138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 9.79796i | − | 0.938474i | −0.883072 | − | 0.469237i | \(-0.844529\pi\) | ||
0.883072 | − | 0.469237i | \(-0.155471\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.24264 | − | 7.34847i | −0.402694 | − | 0.697486i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0000 | + | 6.92820i | 1.12887 | + | 0.651751i | 0.943649 | − | 0.330947i | \(-0.107368\pi\) |
0.185216 | + | 0.982698i | \(0.440702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | + | 20.7846i | 1.11901 | + | 1.93817i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7279 | − | 7.34847i | 1.17670 | − | 0.679366i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | − | 13.8564i | 0.727273 | − | 1.25967i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.00000 | −0.811503 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6969i | 1.30414i | 0.758158 | + | 0.652071i | \(0.226100\pi\) | ||||
−0.758158 | + | 0.652071i | \(0.773900\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.5000 | + | 7.79423i | 1.18861 | + | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | − | 5.19615i | −0.786334 | − | 0.453990i | 0.0523366 | − | 0.998630i | \(-0.483333\pi\) |
−0.838670 | + | 0.544640i | \(0.816666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.7279 | − | 7.34847i | −1.09545 | − | 0.632456i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.50000 | − | 4.33013i | 0.640768 | − | 0.369948i | −0.144142 | − | 0.989557i | \(-0.546042\pi\) |
0.784910 | + | 0.619609i | \(0.212709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50000 | + | 7.79423i | −0.381685 | + | 0.661098i | −0.991303 | − | 0.131597i | \(-0.957989\pi\) |
0.609618 | + | 0.792695i | \(0.291323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.7279 | − | 7.34847i | −1.07188 | − | 0.618853i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.4558 | 2.12872 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.0000 | −1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 12.1244i | − | 1.00000i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.41421 | + | 2.44949i | −0.115857 | + | 0.200670i | −0.918122 | − | 0.396298i | \(-0.870295\pi\) |
0.802265 | + | 0.596968i | \(0.203628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7279 | + | 7.34847i | −1.03578 | + | 0.598010i | −0.918636 | − | 0.395105i | \(-0.870708\pi\) |
−0.117147 | + | 0.993115i | \(0.537375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.50000 | − | 2.59808i | −0.363803 | − | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9706 | + | 9.79796i | 1.35440 | + | 0.781962i | 0.988862 | − | 0.148835i | \(-0.0475523\pi\) |
0.365536 | + | 0.930797i | \(0.380886\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.48528 | + | 4.89898i | −0.672927 | + | 0.388514i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.0000 | 1.87983 | 0.939913 | − | 0.341415i | \(-0.110906\pi\) | ||||
0.939913 | + | 0.341415i | \(0.110906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.7279 | − | 22.0454i | −0.990867 | − | 1.71623i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.24264 | − | 7.34847i | 0.328305 | − | 0.568642i | −0.653870 | − | 0.756607i | \(-0.726856\pi\) |
0.982176 | + | 0.187965i | \(0.0601892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.50000 | + | 9.52628i | 0.423077 | + | 0.732791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.50000 | + | 7.79423i | −0.344124 | + | 0.596040i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.82843 | − | 4.89898i | −0.215041 | − | 0.372463i | 0.738244 | − | 0.674534i | \(-0.235655\pi\) |
−0.953285 | + | 0.302071i | \(0.902322\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.00000 | −0.676481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 14.6969i | − | 1.09241i | −0.837650 | − | 0.546207i | \(-0.816071\pi\) | ||
0.837650 | − | 0.546207i | \(-0.183929\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.48528 | − | 14.6969i | 0.627250 | − | 1.08643i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.0000 | − | 6.92820i | −0.882258 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50000 | − | 7.79423i | −0.329073 | − | 0.569970i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.48528 | − | 14.6969i | −0.613973 | − | 1.06343i | −0.990564 | − | 0.137053i | \(-0.956237\pi\) |
0.376590 | − | 0.926380i | \(-0.377096\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.500000 | + | 0.866025i | −0.0359908 | + | 0.0623379i | −0.883460 | − | 0.468507i | \(-0.844792\pi\) |
0.847469 | + | 0.530845i | \(0.178125\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0000 | − | 20.7846i | 0.859338 | − | 1.48842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.3137 | −0.806068 | −0.403034 | − | 0.915185i | \(-0.632044\pi\) | ||||
−0.403034 | + | 0.915185i | \(0.632044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.19615i | 0.366508i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7279 | + | 7.34847i | −0.888957 | + | 0.513239i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7279 | − | 22.0454i | −0.884652 | − | 1.53226i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.5000 | + | 7.79423i | −0.933815 | + | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.7279 | + | 7.34847i | −0.872103 | + | 0.503509i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.4558 | 1.73607 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.50000 | + | 4.33013i | −0.506803 | + | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.24264 | − | 7.34847i | 0.285391 | − | 0.494312i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7279 | − | 7.34847i | 0.852325 | − | 0.492090i | −0.00910984 | − | 0.999959i | \(-0.502900\pi\) |
0.861435 | + | 0.507869i | \(0.169566\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.5000 | + | 7.79423i | −0.896026 | + | 0.517321i | −0.875909 | − | 0.482476i | \(-0.839737\pi\) |
−0.0201176 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.48528 | − | 4.89898i | −0.560723 | − | 0.323734i | 0.192713 | − | 0.981255i | \(-0.438272\pi\) |
−0.753436 | + | 0.657522i | \(0.771605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.5167i | 1.47512i | 0.675284 | + | 0.737558i | \(0.264021\pi\) | ||||
−0.675284 | + | 0.737558i | \(0.735979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7279 | − | 22.0454i | 0.826767 | − | 1.43200i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.24264 | − | 7.34847i | 0.274434 | − | 0.475333i | −0.695558 | − | 0.718470i | \(-0.744843\pi\) |
0.969992 | + | 0.243137i | \(0.0781763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | + | 6.06218i | 0.225455 | + | 0.390499i | 0.956456 | − | 0.291877i | \(-0.0942799\pi\) |
−0.731001 | + | 0.682376i | \(0.760947\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.89949 | − | 17.1464i | −0.632456 | − | 1.09545i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.7279 | − | 7.34847i | −0.809858 | − | 0.467572i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.00000 | − | 15.5885i | 0.570352 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.19615i | 0.327978i | 0.986462 | + | 0.163989i | \(0.0524362\pi\) | ||||
−0.986462 | + | 0.163989i | \(0.947564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 44.0908i | − | 2.77197i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.48528 | −0.531369 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | + | 0.866025i | 0.0935674 | + | 0.0540212i | 0.546054 | − | 0.837750i | \(-0.316129\pi\) |
−0.452486 | + | 0.891771i | \(0.649463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.9706 | 1.05045 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | + | 13.8564i | −0.491436 | + | 0.851192i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.0000 | + | 20.7846i | 0.734388 | + | 1.27200i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3137 | 0.689809 | 0.344904 | − | 0.938638i | \(-0.387911\pi\) | ||||
0.344904 | + | 0.938638i | \(0.387911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.3939i | 1.78555i | 0.450502 | + | 0.892775i | \(0.351245\pi\) | ||||
−0.450502 | + | 0.892775i | \(0.648755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.5000 | − | 7.79423i | −0.814081 | − | 0.470010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7279 | + | 7.34847i | −0.764747 | + | 0.441527i | −0.830997 | − | 0.556276i | \(-0.812230\pi\) |
0.0662507 | + | 0.997803i | \(0.478896\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0000 | − | 6.92820i | 0.715860 | − | 0.413302i | −0.0973670 | − | 0.995249i | \(-0.531042\pi\) |
0.813227 | + | 0.581947i | \(0.197709\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.0000 | − | 20.7846i | 0.713326 | − | 1.23552i | −0.250276 | − | 0.968175i | \(-0.580521\pi\) |
0.963602 | − | 0.267342i | \(-0.0861454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.6969i | 0.870572i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0000 | 0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50000 | − | 0.866025i | −0.0879316 | − | 0.0507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1421 | − | 24.4949i | 0.826192 | − | 1.43101i | −0.0748122 | − | 0.997198i | \(-0.523836\pi\) |
0.901005 | − | 0.433810i | \(-0.142831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7279 | + | 7.34847i | −0.741048 | + | 0.427844i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5000 | + | 23.3827i | 0.783349 | + | 1.35680i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.0000 | − | 20.7846i | 2.08193 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.24264 | − | 2.44949i | −0.243733 | − | 0.140720i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 27.7128i | − | 1.58683i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.00000 | −0.171219 | −0.0856095 | − | 0.996329i | \(-0.527284\pi\) | ||||
−0.0856095 | + | 0.996329i | \(0.527284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4558 | −1.44813 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.48528 | + | 14.6969i | −0.481156 | + | 0.833387i | −0.999766 | − | 0.0216240i | \(-0.993116\pi\) |
0.518610 | + | 0.855011i | \(0.326450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5000 | − | 25.1147i | −0.819588 | − | 1.41957i | −0.905986 | − | 0.423308i | \(-0.860869\pi\) |
0.0863973 | − | 0.996261i | \(-0.472465\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.89949 | − | 17.1464i | −0.556011 | − | 0.963039i | −0.997824 | − | 0.0659322i | \(-0.978998\pi\) |
0.441813 | − | 0.897107i | \(-0.354335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.4558 | + | 14.6969i | 1.42525 | + | 0.822871i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50000 | + | 7.79423i | 0.251166 | + | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.19615i | 0.289122i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 14.6969i | − | 0.815239i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.48528 | + | 14.6969i | 0.469237 | + | 0.812743i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | − | 20.7846i | −0.659580 | − | 1.14243i | −0.980725 | − | 0.195395i | \(-0.937401\pi\) |
0.321145 | − | 0.947030i | \(-0.395932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.7279 | + | 7.34847i | 0.697486 | + | 0.402694i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.24264 | + | 7.34847i | 0.231800 | + | 0.401490i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5000 | − | 19.9186i | 0.626445 | − | 1.08503i | −0.361815 | − | 0.932250i | \(-0.617843\pi\) |
0.988260 | − | 0.152784i | \(-0.0488240\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.0000 | −1.30350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −36.0000 | − | 20.7846i | −1.93817 | − | 1.11901i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.5000 | + | 18.1865i | 1.69101 | + | 0.976304i | 0.953705 | + | 0.300742i | \(0.0972344\pi\) |
0.737303 | + | 0.675562i | \(0.236099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4558 | + | 14.6969i | −1.36262 | + | 0.786709i | −0.989972 | − | 0.141264i | \(-0.954883\pi\) |
−0.372648 | + | 0.927973i | \(0.621550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.7279 | + | 22.0454i | −0.679366 | + | 1.17670i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.5000 | − | 12.9904i | 1.19755 | − | 0.691408i | 0.237545 | − | 0.971377i | \(-0.423657\pi\) |
0.960009 | + | 0.279968i | \(0.0903240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | + | 20.7846i | −0.636894 | + | 1.10313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.9706 | −0.895672 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.7128i | 1.45455i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.07107 | + | 12.2474i | −0.370117 | + | 0.641061i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7279 | + | 7.34847i | −0.664392 | + | 0.383587i | −0.793948 | − | 0.607985i | \(-0.791978\pi\) |
0.129556 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.5000 | − | 7.79423i | 0.702782 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7279 | + | 7.34847i | 0.659027 | + | 0.380489i | 0.791906 | − | 0.610643i | \(-0.209089\pi\) |
−0.132879 | + | 0.991132i | \(0.542422\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.48528 | − | 4.89898i | 0.438178 | − | 0.252982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.7128i | 1.42728i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0000 | −0.770498 | −0.385249 | − | 0.922813i | \(-0.625884\pi\) | ||||
−0.385249 | + | 0.922813i | \(0.625884\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.7279 | − | 22.0454i | −0.652071 | − | 1.12942i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.24264 | − | 7.34847i | 0.216789 | − | 0.375489i | −0.737036 | − | 0.675854i | \(-0.763775\pi\) |
0.953824 | + | 0.300365i | \(0.0971084\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.0000 | −1.37249 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3137 | + | 19.5959i | 0.573628 | + | 0.993552i | 0.996189 | + | 0.0872182i | \(0.0277977\pi\) |
−0.422561 | + | 0.906334i | \(0.638869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.7279 | − | 7.34847i | −0.643679 | − | 0.371628i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0000 | 0.907980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 41.5692i | − | 2.09157i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.89898i | 0.245873i | 0.992415 | + | 0.122936i | \(0.0392311\pi\) | ||||
−0.992415 | + | 0.122936i | \(0.960769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5000 | − | 6.06218i | −0.524345 | − | 0.302731i | 0.214366 | − | 0.976753i | \(-0.431232\pi\) |
−0.738711 | + | 0.674023i | \(0.764565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.4558 | 1.26491 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.7279 | + | 22.0454i | 0.630900 | + | 1.09275i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.50000 | + | 16.4545i | −0.469745 | + | 0.813622i | −0.999402 | − | 0.0345902i | \(-0.988987\pi\) |
0.529657 | + | 0.848212i | \(0.322321\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.50000 | + | 12.9904i | −0.369948 | + | 0.640768i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 29.3939i | − | 1.44289i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 15.5885i | − | 0.763370i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.00000 | + | 5.19615i | 0.439679 | + | 0.253849i | 0.703461 | − | 0.710734i | \(-0.251637\pi\) |
−0.263783 | + | 0.964582i | \(0.584970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.24264 | − | 2.44949i | 0.206774 | − | 0.119381i | −0.393037 | − | 0.919522i | \(-0.628576\pi\) |
0.599811 | + | 0.800142i | \(0.295242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.4558 | 1.23771 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.50000 | + | 2.59808i | −0.218282 | + | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −38.1838 | + | 22.0454i | −1.84353 | + | 1.06436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.9706 | −0.817443 | −0.408722 | − | 0.912659i | \(-0.634025\pi\) | ||||
−0.408722 | + | 0.912659i | \(0.634025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0000 | 1.48976 | 0.744882 | − | 0.667196i | \(-0.232506\pi\) | ||||
0.744882 | + | 0.667196i | \(0.232506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.0000 | − | 13.8564i | 1.15071 | − | 0.664364i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.7279 | + | 22.0454i | −0.608859 | + | 1.05457i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4558 | − | 14.6969i | 1.21494 | − | 0.701447i | 0.251110 | − | 0.967959i | \(-0.419205\pi\) |
0.963832 | + | 0.266512i | \(0.0858712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.5000 | + | 18.1865i | 0.500000 | + | 0.866025i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.50000 | − | 2.59808i | 0.213801 | − | 0.123438i | −0.389275 | − | 0.921121i | \(-0.627275\pi\) |
0.603077 | + | 0.797683i | \(0.293941\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.9411 | + | 19.5959i | 1.60896 | + | 0.928936i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.89898i | − | 0.231714i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.5885i | 0.735665i | 0.929892 | + | 0.367832i | \(0.119900\pi\) | ||||
−0.929892 | + | 0.367832i | \(0.880100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0000 | 1.27138 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.7279 | − | 22.0454i | 0.598010 | − | 1.03578i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5000 | + | 25.1147i | 0.678281 | + | 1.17482i | 0.975498 | + | 0.220008i | \(0.0706083\pi\) |
−0.297217 | + | 0.954810i | \(0.596058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.00000 | 0.420084 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41421 | + | 2.44949i | 0.0658665 | + | 0.114084i | 0.897078 | − | 0.441872i | \(-0.145686\pi\) |
−0.831212 | + | 0.555956i | \(0.812352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7279 | − | 7.34847i | −0.591517 | − | 0.341512i | 0.174180 | − | 0.984714i | \(-0.444272\pi\) |
−0.765697 | + | 0.643201i | \(0.777606\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.5885i | − | 0.721348i | −0.932692 | − | 0.360674i | \(-0.882547\pi\) | ||
0.932692 | − | 0.360674i | \(-0.117453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.9411 | −1.56392 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.5000 | − | 23.3827i | −1.86219 | − | 1.07514i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.50000 | + | 7.79423i | 0.206474 | + | 0.357624i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.48528 | − | 14.6969i | 0.388514 | − | 0.672927i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | + | 20.7846i | −0.547153 | + | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.82843 | −0.128432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.0000 | + | 20.7846i | −1.62798 | + | 0.939913i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | + | 2.59808i | 0.203082 | + | 0.117250i | 0.598092 | − | 0.801427i | \(-0.295926\pi\) |
−0.395010 | + | 0.918677i | \(0.629259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48528 | − | 4.89898i | 0.382158 | − | 0.220639i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 38.1838 | + | 22.0454i | 1.71623 | + | 0.990867i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.50000 | + | 2.59808i | −0.0671492 | + | 0.116306i | −0.897645 | − | 0.440719i | \(-0.854724\pi\) |
0.830496 | + | 0.557024i | \(0.188057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.6969i | 0.656611i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.9411 | −1.51336 | −0.756680 | − | 0.653785i | \(-0.773180\pi\) | ||||
−0.756680 | + | 0.653785i | \(0.773180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.5000 | − | 9.52628i | −0.732791 | − | 0.423077i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.65685 | + | 9.79796i | −0.250736 | + | 0.434287i | −0.963729 | − | 0.266884i | \(-0.914006\pi\) |
0.712993 | + | 0.701171i | \(0.247339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 15.5885i | − | 0.688247i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.0000 | + | 20.7846i | −1.58635 | + | 0.915879i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.1838 | + | 22.0454i | 1.67932 | + | 0.969556i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.48528 | + | 4.89898i | 0.372463 | + | 0.215041i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.3731i | 1.59353i | 0.604287 | + | 0.796766i | \(0.293458\pi\) | ||||
−0.604287 | + | 0.796766i | \(0.706542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0000 | −1.04945 | −0.524723 | − | 0.851273i | \(-0.675831\pi\) | ||||
−0.524723 | + | 0.851273i | \(0.675831\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.5000 | − | 42.4352i | −1.06522 | − | 1.84501i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.5000 | − | 7.79423i | 0.585850 | − | 0.338241i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.7279 | + | 22.0454i | 0.551308 | + | 0.954893i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7279 | + | 7.34847i | 0.550276 | + | 0.317702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.00000 | − | 15.5885i | −0.388379 | − | 0.672692i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.3731i | 1.56670i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.89898i | − | 0.210624i | −0.994439 | − | 0.105312i | \(-0.966416\pi\) | ||
0.994439 | − | 0.105312i | \(-0.0335841\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.7279 | + | 22.0454i | 0.546207 | + | 0.946059i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0000 | + | 13.8564i | 1.02805 | + | 0.593543i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.50000 | + | 2.59808i | 0.0641354 | + | 0.111086i | 0.896310 | − | 0.443428i | \(-0.146238\pi\) |
−0.832175 | + | 0.554513i | \(0.812904\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.3939i | 1.25450i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.48528 | − | 14.6969i | −0.361485 | − | 0.626111i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.0000 | 1.01874 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.3137 | −0.479377 | −0.239689 | − | 0.970850i | \(-0.577045\pi\) | ||||
−0.239689 | + | 0.970850i | \(0.577045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 44.0908i | − | 1.86484i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.5000 | + | 7.79423i | 0.569970 | + | 0.329073i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.5000 | − | 12.9904i | −0.948262 | − | 0.547479i | −0.0557214 | − | 0.998446i | \(-0.517746\pi\) |
−0.892541 | + | 0.450967i | \(0.851079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.9411 | + | 19.5959i | −1.42791 | + | 0.824406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.5000 | − | 16.4545i | 1.19478 | − | 0.689808i | 0.235395 | − | 0.971900i | \(-0.424362\pi\) |
0.959387 | + | 0.282092i | \(0.0910284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5000 | − | 28.5788i | 0.690504 | − | 1.19599i | −0.281170 | − | 0.959658i | \(-0.590722\pi\) |
0.971673 | − | 0.236329i | \(-0.0759443\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.4558 | + | 14.6969i | 1.06343 | + | 0.613973i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.4558 | −1.06158 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0000 | −1.29055 | −0.645273 | − | 0.763952i | \(-0.723257\pi\) | ||||
−0.645273 | + | 0.763952i | \(0.723257\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1.73205i | − | 0.0719816i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.4558 | − | 14.6969i | 1.05427 | − | 0.608685i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 41.5692i | 1.71868i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.50000 | + | 2.59808i | −0.185735 | + | 0.107234i | −0.589984 | − | 0.807415i | \(-0.700866\pi\) |
0.404249 | + | 0.914649i | \(0.367533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.9706 | − | 9.79796i | 0.698076 | − | 0.403034i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 27.7128i | − | 1.13803i | −0.822328 | − | 0.569014i | \(-0.807325\pi\) | ||
0.822328 | − | 0.569014i | \(-0.192675\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.24264 | − | 7.34847i | 0.173350 | − | 0.300250i | −0.766239 | − | 0.642555i | \(-0.777874\pi\) |
0.939589 | + | 0.342305i | \(0.111208\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50000 | + | 9.52628i | 0.224350 | + | 0.388585i | 0.956124 | − | 0.292962i | \(-0.0946409\pi\) |
−0.731774 | + | 0.681547i | \(0.761308\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.50000 | − | 7.79423i | −0.183254 | − | 0.317406i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.6274 | + | 39.1918i | 0.919935 | + | 1.59337i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.4558 | − | 14.6969i | −1.03322 | − | 0.596530i | −0.115315 | − | 0.993329i | \(-0.536788\pi\) |
−0.917906 | + | 0.396799i | \(0.870121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 41.5692i | 1.68171i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.6969i | − | 0.593604i | −0.954939 | − | 0.296802i | \(-0.904080\pi\) | ||
0.954939 | − | 0.296802i | \(-0.0959201\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.7279 | − | 22.0454i | 0.513239 | − | 0.888957i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.5000 | − | 11.2583i | −0.785040 | − | 0.453243i | 0.0531732 | − | 0.998585i | \(-0.483066\pi\) |
−0.838214 | + | 0.545342i | \(0.816400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.50000 | + | 7.79423i | 0.180870 | + | 0.313276i | 0.942177 | − | 0.335115i | \(-0.108775\pi\) |
−0.761307 | + | 0.648392i | \(0.775442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.1838 | + | 22.0454i | 1.53226 | + | 0.884652i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5000 | − | 26.8468i | 0.620000 | − | 1.07387i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.5000 | − | 23.3827i | 0.539138 | − | 0.933815i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.48528 | 0.338330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 44.0908i | − | 1.75523i | −0.479368 | − | 0.877614i | \(-0.659134\pi\) | ||
0.479368 | − | 0.877614i | \(-0.340866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36.0000 | − | 20.7846i | −1.42862 | − | 0.824812i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.6985 | + | 17.1464i | −1.17670 | + | 0.679366i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.7279 | − | 22.0454i | 0.503509 | − | 0.872103i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | − | 0.866025i | 0.0592464 | − | 0.0342059i | −0.470084 | − | 0.882622i | \(-0.655776\pi\) |
0.529331 | + | 0.848416i | \(0.322443\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.50000 | − | 2.59808i | 0.0591542 | − | 0.102458i | −0.834932 | − | 0.550353i | \(-0.814493\pi\) |
0.894086 | + | 0.447895i | \(0.147826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −38.1838 | + | 22.0454i | −1.50348 | + | 0.868037i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9706 | −0.667182 | −0.333591 | − | 0.942718i | \(-0.608260\pi\) | ||||
−0.333591 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.0000 | 1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.65685 | − | 9.79796i | 0.221370 | − | 0.383424i | −0.733854 | − | 0.679307i | \(-0.762281\pi\) |
0.955224 | + | 0.295883i | \(0.0956139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.4558 | − | 14.6969i | 0.994642 | − | 0.574257i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.50000 | − | 12.9904i | 0.292603 | − | 0.506803i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.00000 | − | 5.19615i | 0.350590 | − | 0.202413i | −0.314355 | − | 0.949306i | \(-0.601788\pi\) |
0.664945 | + | 0.746892i | \(0.268455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2132 | + | 12.2474i | 0.825098 | + | 0.476371i | 0.852171 | − | 0.523263i | \(-0.175285\pi\) |
−0.0270733 | + | 0.999633i | \(0.508619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.6969i | 0.570782i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0000 | 1.85857 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.7279 | + | 22.0454i | −0.492090 | + | 0.852325i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.4558 | + | 44.0908i | −0.982712 | + | 1.70211i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0000 | + | 32.9090i | 0.732396 | + | 1.26855i | 0.955856 | + | 0.293834i | \(0.0949314\pi\) |
−0.223460 | + | 0.974713i | \(0.571735\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.5000 | − | 7.79423i | 0.519615 | − | 0.300000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.1421 | − | 24.4949i | −0.543526 | − | 0.941415i | −0.998698 | − | 0.0510117i | \(-0.983755\pi\) |
0.455172 | − | 0.890404i | \(-0.349578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5000 | − | 23.3827i | 0.517321 | − | 0.896026i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.19615i | 0.198825i | 0.995046 | + | 0.0994126i | \(0.0316964\pi\) | ||||
−0.995046 | + | 0.0994126i | \(0.968304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.4949i | 0.935902i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.9706 | 0.647467 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.0000 | + | 13.8564i | 0.914327 | + | 0.527887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | + | 20.7846i | 0.456502 | + | 0.790684i | 0.998773 | − | 0.0495194i | \(-0.0157690\pi\) |
−0.542272 | + | 0.840203i | \(0.682436\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.7279 | − | 22.0454i | −0.482798 | − | 0.836230i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.50000 | − | 7.79423i | 0.170450 | − | 0.295227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.5000 | − | 33.7750i | −0.737558 | − | 1.27749i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.7696 | 1.38877 | 0.694383 | − | 0.719605i | \(-0.255677\pi\) | ||||
0.694383 | + | 0.719605i | \(0.255677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 14.6969i | − | 0.554306i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.0000 | − | 20.7846i | 1.35584 | − | 0.782794i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.4264 | + | 24.4949i | −1.59336 | + | 0.919925i | −0.600632 | + | 0.799526i | \(0.705084\pi\) |
−0.992726 | + | 0.120399i | \(0.961583\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.0908i | 1.65353i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0000 | + | 62.3538i | −1.34632 | + | 2.33190i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.6969i | 0.548867i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.4558 | −0.949343 | −0.474671 | − | 0.880163i | \(-0.657433\pi\) | ||||
−0.474671 | + | 0.880163i | \(0.657433\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.5000 | − | 6.06218i | −0.390499 | − | 0.225455i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.48528 | − | 14.6969i | 0.315135 | − | 0.545831i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.7279 | + | 7.34847i | −0.472052 | + | 0.272540i | −0.717099 | − | 0.696972i | \(-0.754530\pi\) |
0.245046 | + | 0.969511i | \(0.421197\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5000 | + | 7.79423i | −0.499316 | + | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.6985 | + | 17.1464i | 1.09545 | + | 0.632456i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 15.5885i | − | 0.574208i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.0000 | 0.993211 | 0.496606 | − | 0.867976i | \(-0.334580\pi\) | ||||
0.496606 | + | 0.867976i | \(0.334580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.4558 | 0.935144 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.48528 | + | 14.6969i | −0.311295 | + | 0.539178i | −0.978643 | − | 0.205568i | \(-0.934096\pi\) |
0.667348 | + | 0.744746i | \(0.267429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.00000 | − | 6.92820i | −0.146549 | − | 0.253830i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.1769i | 1.14070i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.7279 | − | 7.34847i | −0.464448 | − | 0.268149i | 0.249464 | − | 0.968384i | \(-0.419745\pi\) |
−0.713913 | + | 0.700235i | \(0.753079\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.50000 | − | 7.79423i | −0.163989 | − | 0.284037i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 41.5692i | − | 1.51286i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.3939i | − | 1.06834i | −0.845378 | − | 0.534169i | \(-0.820624\pi\) | ||
0.845378 | − | 0.534169i | \(-0.179376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.1838 | + | 66.1362i | 1.38598 | + | 2.40059i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0000 | − | 6.92820i | −0.435000 | − | 0.251147i | 0.266475 | − | 0.963842i | \(-0.414141\pi\) |
−0.701474 | + | 0.712695i | \(0.747474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.7279 | − | 7.34847i | 0.460179 | − | 0.265684i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.7279 | + | 22.0454i | 0.459579 | + | 0.796014i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.0000 | − | 22.5167i | 0.468792 | − | 0.811972i | −0.530572 | − | 0.847640i | \(-0.678023\pi\) |
0.999364 | + | 0.0356685i | \(0.0113561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00000 | −0.108042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.1421 | 0.508657 | 0.254329 | − | 0.967118i | \(-0.418146\pi\) | ||||
0.254329 | + | 0.967118i | \(0.418146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.5000 | − | 7.79423i | −0.483688 | − | 0.279257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.1838 | − | 22.0454i | 1.36632 | − | 0.788847i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.4558 | + | 14.6969i | −0.909718 | + | 0.525226i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.0000 | + | 27.7128i | −1.71319 | + | 0.989113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0000 | − | 20.7846i | 0.427754 | − | 0.740891i | −0.568919 | − | 0.822393i | \(-0.692638\pi\) |
0.996673 | + | 0.0815020i | \(0.0259717\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.0000 | −1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 27.7128i | − | 0.982872i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.41421 | − | 2.44949i | 0.0500940 | − | 0.0867654i | −0.839891 | − | 0.542755i | \(-0.817381\pi\) |
0.889985 | + | 0.455990i | \(0.150715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.7279 | − | 7.34847i | 0.450282 | − | 0.259970i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.0000 | − | 20.7846i | −1.27200 | − | 0.734388i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.5000 | − | 12.9904i | 0.794008 | − | 0.458421i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.9706 | + | 9.79796i | −0.597392 | + | 0.344904i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.66025i | 0.304478i | 0.988344 | + | 0.152239i | \(0.0486484\pi\) | ||||
−0.988344 | + | 0.152239i | \(0.951352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.0000 | −1.15879 | −0.579393 | − | 0.815048i | \(-0.696710\pi\) | ||||
−0.579393 | + | 0.815048i | \(0.696710\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.4558 | − | 44.0908i | −0.892775 | − | 1.54633i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.9411 | + | 58.7878i | −1.18891 | + | 2.05925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5000 | + | 23.3827i | 0.472305 | + | 0.818057i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.82843 | − | 4.89898i | −0.0987128 | − | 0.170976i | 0.812439 | − | 0.583046i | \(-0.198139\pi\) |
−0.911152 | + | 0.412070i | \(0.864806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.7279 | + | 7.34847i | 0.443667 | + | 0.256152i | 0.705152 | − | 0.709056i | \(-0.250879\pi\) |
−0.261485 | + | 0.965208i | \(0.584212\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 27.0000 | 0.940019 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.3923i | 0.361376i | 0.983540 | + | 0.180688i | \(0.0578324\pi\) | ||||
−0.983540 | + | 0.180688i | \(0.942168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.7279 | − | 22.0454i | 0.441527 | − | 0.764747i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5000 | + | 6.06218i | 0.363803 | + | 0.210042i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | + | 20.7846i | 0.415277 | + | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.48528 | − | 14.6969i | −0.292944 | − | 0.507395i | 0.681560 | − | 0.731762i | \(-0.261302\pi\) |
−0.974505 | + | 0.224367i | \(0.927968\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.50000 | + | 2.59808i | −0.0517241 | + | 0.0895888i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.0000 | + | 20.7846i | −0.413302 | + | 0.715860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.1127 | −1.07031 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.5692i | 1.42665i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000 | + | 20.7846i | 1.23406 | + | 0.712487i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7279 | − | 7.34847i | 0.435796 | − | 0.251607i | −0.266017 | − | 0.963968i | \(-0.585708\pi\) |
0.701813 | + | 0.712362i | \(0.252374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.7279 | − | 22.0454i | −0.435286 | − | 0.753937i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0000 | − | 6.92820i | 0.409912 | − | 0.236663i | −0.280840 | − | 0.959755i | \(-0.590613\pi\) |
0.690752 | + | 0.723092i | \(0.257280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.50000 | − | 12.9904i | 0.255897 | − | 0.443226i | −0.709242 | − | 0.704965i | \(-0.750963\pi\) |
0.965139 | + | 0.261739i | \(0.0842960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.48528 | −0.288842 | −0.144421 | − | 0.989516i | \(-0.546132\pi\) | ||||
−0.144421 | + | 0.989516i | \(0.546132\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.0000 | 0.544016 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.0000 | + | 12.1244i | −0.713197 | + | 0.411765i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.1838 | + | 66.1362i | −1.29530 | + | 2.24352i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.7279 | − | 7.34847i | 0.431269 | − | 0.248993i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | 0.101535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.9706 | − | 9.79796i | −0.573055 | − | 0.330854i | 0.185313 | − | 0.982679i | \(-0.440670\pi\) |
−0.758369 | + | 0.651826i | \(0.774003\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.9898i | 1.65238i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.5692i | − | 1.40050i | −0.713896 | − | 0.700251i | \(-0.753071\pi\) | ||
0.713896 | − | 0.700251i | \(-0.246929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.0000 | −1.51437 | −0.757185 | − | 0.653200i | \(-0.773426\pi\) | ||||
−0.757185 | + | 0.653200i | \(0.773426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.7279 | − | 22.0454i | 0.427844 | − | 0.741048i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7279 | + | 22.0454i | −0.427362 | + | 0.740212i | −0.996638 | − | 0.0819342i | \(-0.973890\pi\) |
0.569276 | + | 0.822147i | \(0.307224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.5000 | − | 23.3827i | −1.35680 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.7279 | − | 22.0454i | −0.425924 | − | 0.737721i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.4558 | − | 14.6969i | −0.850895 | − | 0.491264i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | + | 62.3538i | −1.20201 | + | 2.08193i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.79796i | − | 0.326417i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.0000 | + | 20.7846i | 1.19668 | + | 0.690904i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.50000 | − | 12.9904i | −0.249033 | − | 0.431339i | 0.714224 | − | 0.699917i | \(-0.246780\pi\) |
−0.963258 | + | 0.268578i | \(0.913446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.48528 | 0.281439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9706 | − | 29.3939i | −0.562260 | − | 0.973863i | −0.997299 | − | 0.0734510i | \(-0.976599\pi\) |
0.435039 | − | 0.900412i | \(-0.356735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.0000 | + | 46.7654i | −0.893570 | + | 1.54771i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.0000 | + | 41.5692i | 0.793416 | + | 1.37424i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.6969i | − | 0.484807i | −0.970175 | − | 0.242404i | \(-0.922064\pi\) | ||
0.970175 | − | 0.242404i | \(-0.0779358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.50000 | − | 2.59808i | 0.148280 | − | 0.0856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.0000 | + | 20.7846i | 1.18495 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.7279 | − | 7.34847i | 0.418491 | − | 0.241616i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38.1838 | − | 22.0454i | 1.25412 | − | 0.724066i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0000 | + | 13.8564i | −0.787414 | + | 0.454614i | −0.839052 | − | 0.544052i | \(-0.816889\pi\) |
0.0516371 | + | 0.998666i | \(0.483556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.5000 | − | 18.1865i | 0.344124 | − | 0.596040i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 29.3939i | − | 0.962312i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.4558 | 0.832495 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.5000 | + | 25.1147i | 1.41957 | + | 0.819588i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.1421 | − | 24.4949i | 0.461020 | − | 0.798511i | −0.537992 | − | 0.842950i | \(-0.680817\pi\) |
0.999012 | + | 0.0444393i | \(0.0141501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.1838 | − | 22.0454i | 1.24343 | − | 0.717897i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5000 | − | 7.79423i | 0.438691 | − | 0.253278i | −0.264351 | − | 0.964426i | \(-0.585158\pi\) |
0.703042 | + | 0.711148i | \(0.251824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.2132 | + | 12.2474i | 0.688610 | + | 0.397569i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.6985 | + | 17.1464i | 0.963039 | + | 0.556011i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0526i | 0.617173i | 0.951196 | + | 0.308586i | \(0.0998559\pi\) | ||||
−0.951196 | + | 0.308586i | \(0.900144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.0000 | 1.55324 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −50.9117 | −1.64574 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | − | 26.8468i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.5000 | − | 7.79423i | −0.435031 | − | 0.251166i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.41421 | − | 2.44949i | −0.0455251 | − | 0.0788519i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.4558 | − | 14.6969i | −0.818605 | − | 0.472622i | 0.0313303 | − | 0.999509i | \(-0.490026\pi\) |
−0.849935 | + | 0.526887i | \(0.823359\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.50000 | − | 7.79423i | −0.144561 | − | 0.250387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 51.9615i | − | 1.66752i | −0.552124 | − | 0.833762i | \(-0.686182\pi\) | ||
0.552124 | − | 0.833762i | \(-0.313818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.7279 | + | 22.0454i | 0.407620 | + | 0.706018i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.5000 | + | 7.79423i | 0.431903 | + | 0.249359i | 0.700157 | − | 0.713989i | \(-0.253113\pi\) |
−0.268254 | + | 0.963348i | \(0.586447\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.0000 | − | 62.3538i | −1.15056 | − | 1.99284i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.4558 | − | 14.6969i | −0.812743 | − | 0.469237i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.7279 | − | 22.0454i | −0.405958 | − | 0.703139i | 0.588475 | − | 0.808516i | \(-0.299729\pi\) |
−0.994432 | + | 0.105376i | \(0.966395\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | − | 27.7128i | 0.509802 | − | 0.883004i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −76.3675 | −2.42835 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.0000 | + | 20.7846i | 1.14243 | + | 0.659580i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.48528 | − | 4.89898i | 0.268732 | − | 0.155152i | −0.359580 | − | 0.933114i | \(-0.617080\pi\) |
0.628311 | + | 0.777962i | \(0.283747\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.4558 | −0.805387 |
(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 | 1152.2.p.a.959.1 | yes | 4 | |
3.2 | odd | 2 | 3456.2.p.a.2879.2 | 4 | |||
4.3 | odd | 2 | 1152.2.p.b.959.1 | yes | 4 | ||
8.3 | odd | 2 | inner | 1152.2.p.a.959.2 | yes | 4 | |
8.5 | even | 2 | 1152.2.p.b.959.2 | yes | 4 | ||
9.2 | odd | 6 | inner | 1152.2.p.a.191.2 | yes | 4 | |
9.7 | even | 3 | 3456.2.p.a.575.1 | 4 | |||
12.11 | even | 2 | 3456.2.p.b.2879.2 | 4 | |||
24.5 | odd | 2 | 3456.2.p.b.2879.1 | 4 | |||
24.11 | even | 2 | 3456.2.p.a.2879.1 | 4 | |||
36.7 | odd | 6 | 3456.2.p.b.575.1 | 4 | |||
36.11 | even | 6 | 1152.2.p.b.191.2 | yes | 4 | ||
72.11 | even | 6 | inner | 1152.2.p.a.191.1 | ✓ | 4 | |
72.29 | odd | 6 | 1152.2.p.b.191.1 | yes | 4 | ||
72.43 | odd | 6 | 3456.2.p.a.575.2 | 4 | |||
72.61 | even | 6 | 3456.2.p.b.575.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.a.191.1 | ✓ | 4 | 72.11 | even | 6 | inner | |
1152.2.p.a.191.2 | yes | 4 | 9.2 | odd | 6 | inner | |
1152.2.p.a.959.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.2.p.a.959.2 | yes | 4 | 8.3 | odd | 2 | inner | |
1152.2.p.b.191.1 | yes | 4 | 72.29 | odd | 6 | ||
1152.2.p.b.191.2 | yes | 4 | 36.11 | even | 6 | ||
1152.2.p.b.959.1 | yes | 4 | 4.3 | odd | 2 | ||
1152.2.p.b.959.2 | yes | 4 | 8.5 | even | 2 | ||
3456.2.p.a.575.1 | 4 | 9.7 | even | 3 | |||
3456.2.p.a.575.2 | 4 | 72.43 | odd | 6 | |||
3456.2.p.a.2879.1 | 4 | 24.11 | even | 2 | |||
3456.2.p.a.2879.2 | 4 | 3.2 | odd | 2 | |||
3456.2.p.b.575.1 | 4 | 36.7 | odd | 6 | |||
3456.2.p.b.575.2 | 4 | 72.61 | even | 6 | |||
3456.2.p.b.2879.1 | 4 | 24.5 | odd | 2 | |||
3456.2.p.b.2879.2 | 4 | 12.11 | even | 2 |