Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(769,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.e (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: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 308) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(-0.707107 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.769 |
Dual form | 1232.2.e.b.769.3 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 2.23607i | − | 1.29099i | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||
0.763763 | − | 0.645497i | \(-0.223350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.12132 | + | 1.58114i | −0.801784 | + | 0.597614i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 3.16228i | 0.301511 | − | 0.953463i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82843 | 0.784465 | 0.392232 | − | 0.919866i | \(-0.371703\pi\) | ||||
0.392232 | + | 0.919866i | \(0.371703\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.00000 | 1.29099 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.65685 | −1.37199 | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | 0.324443 | 0.162221 | − | 0.986754i | \(-0.448134\pi\) | ||||
0.162221 | + | 0.986754i | \(0.448134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.53553 | + | 4.74342i | 0.771517 | + | 1.03510i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.00000 | 1.04257 | 0.521286 | − | 0.853382i | \(-0.325452\pi\) | ||||
0.521286 | + | 0.853382i | \(0.325452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.23607i | − | 0.430331i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 9.48683i | − | 1.76166i | −0.473432 | − | 0.880830i | \(-0.656985\pi\) | ||
0.473432 | − | 0.880830i | \(-0.343015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.23607i | − | 0.401610i | −0.979631 | − | 0.200805i | \(-0.935644\pi\) | ||
0.979631 | − | 0.200805i | \(-0.0643557\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.07107 | − | 2.23607i | −1.23091 | − | 0.389249i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.53553 | − | 4.74342i | −0.597614 | − | 0.801784i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0000 | 1.80839 | 0.904194 | − | 0.427121i | \(-0.140472\pi\) | ||||
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.32456i | − | 1.01274i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.89949 | 1.54604 | 0.773021 | − | 0.634381i | \(-0.218745\pi\) | ||||
0.773021 | + | 0.634381i | \(0.218745\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16228i | 0.482243i | 0.970495 | + | 0.241121i | \(0.0775152\pi\) | ||||
−0.970495 | + | 0.241121i | \(0.922485\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 4.47214i | − | 0.666667i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.47214i | − | 0.652328i | −0.945313 | − | 0.326164i | \(-0.894244\pi\) | ||
0.945313 | − | 0.326164i | \(-0.105756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | − | 6.70820i | 0.285714 | − | 0.958315i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.6491i | 1.77123i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.07107 | + | 2.23607i | 0.953463 | + | 0.301511i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.16228i | − | 0.418854i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.23607i | 0.291111i | 0.989350 | + | 0.145556i | \(0.0464970\pi\) | ||||
−0.989350 | + | 0.145556i | \(0.953503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.24264 | −0.543214 | −0.271607 | − | 0.962408i | \(-0.587555\pi\) | ||||
−0.271607 | + | 0.962408i | \(0.587555\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.24264 | − | 3.16228i | 0.534522 | − | 0.398410i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.32456i | 0.784465i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00000 | −1.09952 | −0.549762 | − | 0.835321i | \(-0.685282\pi\) | ||||
−0.549762 | + | 0.835321i | \(0.685282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 11.1803i | − | 1.34595i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | 0.118678 | 0.0593391 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593391 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.24264 | −0.496564 | −0.248282 | − | 0.968688i | \(-0.579866\pi\) | ||||
−0.248282 | + | 0.968688i | \(0.579866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.87868 | + | 8.28934i | 0.328056 | + | 0.944658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.32456i | − | 0.711568i | −0.934568 | − | 0.355784i | \(-0.884214\pi\) | ||
0.934568 | − | 0.355784i | \(-0.115786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.41421 | 0.155230 | 0.0776151 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776151 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 12.6491i | − | 1.37199i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.2132 | −2.27429 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.70820i | − | 0.711068i | −0.934663 | − | 0.355534i | \(-0.884299\pi\) | ||
0.934663 | − | 0.355534i | \(-0.115701\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 4.47214i | −0.628971 | + | 0.468807i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.00000 | −0.518476 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.16228i | 0.324443i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.6525i | − | 1.58927i | −0.607089 | − | 0.794634i | \(-0.707663\pi\) | ||
0.607089 | − | 0.794634i | \(-0.292337\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | + | 6.32456i | −0.201008 | + | 0.635642i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24264 | −0.422159 | −0.211079 | − | 0.977469i | \(-0.567698\pi\) | ||||
−0.211079 | + | 0.977469i | \(0.567698\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.47214i | 0.440653i | 0.975426 | + | 0.220326i | \(0.0707122\pi\) | ||||
−0.975426 | + | 0.220326i | \(0.929288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.6066 | + | 7.90569i | −1.03510 | + | 0.771517i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.32456i | 0.611418i | 0.952125 | + | 0.305709i | \(0.0988934\pi\) | ||||
−0.952125 | + | 0.305709i | \(0.901107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8114i | 1.51446i | 0.653150 | + | 0.757228i | \(0.273447\pi\) | ||||
−0.653150 | + | 0.757228i | \(0.726553\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 24.5967i | − | 2.33462i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | −0.282216 | −0.141108 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141108 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.1803i | 1.04257i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.65685 | −0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0000 | − | 8.94427i | 1.10004 | − | 0.819920i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | − | 6.32456i | −0.818182 | − | 0.574960i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 22.1359i | − | 1.99593i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803i | 1.00000i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8114i | 1.40303i | 0.712653 | + | 0.701517i | \(0.247494\pi\) | ||||
−0.712653 | + | 0.701517i | \(0.752506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.07107 | 0.622573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.1421 | −1.23560 | −0.617802 | − | 0.786334i | \(-0.711977\pi\) | ||||
−0.617802 | + | 0.786334i | \(0.711977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 2.23607i | −0.260133 | + | 0.193892i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | 0.768922 | 0.384461 | − | 0.923141i | \(-0.374387\pi\) | ||||
0.384461 | + | 0.923141i | \(0.374387\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.6274 | 1.91923 | 0.959616 | − | 0.281312i | \(-0.0907697\pi\) | ||||
0.959616 | + | 0.281312i | \(0.0907697\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0000 | −0.842152 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.82843 | − | 8.94427i | 0.236525 | − | 0.747958i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.2132 | 1.76166 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.0000 | − | 4.47214i | −1.23718 | − | 0.368856i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.32456i | − | 0.518128i | −0.965860 | − | 0.259064i | \(-0.916586\pi\) | ||
0.965860 | − | 0.259064i | \(-0.0834140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.6491i | − | 1.02937i | −0.857379 | − | 0.514685i | \(-0.827909\pi\) | ||
0.857379 | − | 0.514685i | \(-0.172091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.3137 | 0.914659 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | 0.401610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.70820i | 0.535373i | 0.963506 | + | 0.267686i | \(0.0862591\pi\) | ||||
−0.963506 | + | 0.267686i | \(0.913741\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 17.8885i | − | 1.41865i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6066 | + | 7.90569i | −0.835917 | + | 0.623056i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00000 | − | 15.8114i | 0.389249 | − | 1.23091i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.41421 | −0.109435 | −0.0547176 | − | 0.998502i | \(-0.517426\pi\) | ||||
−0.0547176 | + | 0.998502i | \(0.517426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.7279 | 0.967686 | 0.483843 | − | 0.875155i | \(-0.339241\pi\) | ||||
0.483843 | + | 0.875155i | \(0.339241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.00000 | 0.375823 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0000 | 0.971666 | 0.485833 | − | 0.874052i | \(-0.338516\pi\) | ||||
0.485833 | + | 0.874052i | \(0.338516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1246i | 1.49585i | 0.663783 | + | 0.747925i | \(0.268950\pi\) | ||||
−0.663783 | + | 0.747925i | \(0.731050\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.48683i | 0.701287i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.5967i | 1.80839i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.65685 | + | 17.8885i | −0.413670 | + | 1.30814i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.53553 | + | 4.74342i | 0.257172 | + | 0.345033i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 15.8114i | − | 1.13813i | −0.822293 | − | 0.569064i | \(-0.807306\pi\) | ||
0.822293 | − | 0.569064i | \(-0.192694\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.1421 | 1.01274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6491i | 0.901212i | 0.892723 | + | 0.450606i | \(0.148792\pi\) | ||||
−0.892723 | + | 0.450606i | \(0.851208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.8885i | 1.26809i | 0.773298 | + | 0.634043i | \(0.218606\pi\) | ||||
−0.773298 | + | 0.634043i | \(0.781394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.1246i | 1.41948i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.0000 | + | 20.1246i | 1.05279 | + | 1.41247i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.1359i | 1.54604i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.0000 | −0.695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.41421 | − | 4.47214i | 0.0978232 | − | 0.309344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.48683i | − | 0.653101i | −0.945180 | − | 0.326550i | \(-0.894114\pi\) | ||
0.945180 | − | 0.326550i | \(-0.105886\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2.23607i | − | 0.153213i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.07107 | −0.482243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.53553 | + | 4.74342i | 0.240008 | + | 0.322004i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.48683i | 0.641061i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0000 | −1.07628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1246i | 1.34764i | 0.738894 | + | 0.673822i | \(0.235348\pi\) | ||||
−0.738894 | + | 0.673822i | \(0.764652\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 29.6985 | 1.97116 | 0.985579 | − | 0.169217i | \(-0.0541238\pi\) | ||||
0.985579 | + | 0.169217i | \(0.0541238\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.1803i | − | 0.738818i | −0.929267 | − | 0.369409i | \(-0.879560\pi\) | ||
0.929267 | − | 0.369409i | \(-0.120440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.5355 | − | 6.43692i | 1.21955 | − | 0.423518i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.48683i | − | 0.621503i | −0.950491 | − | 0.310752i | \(-0.899419\pi\) | ||
0.950491 | − | 0.310752i | \(-0.100581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0000 | 0.652328 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1421 | −0.918630 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.8114i | − | 1.02275i | −0.859357 | − | 0.511377i | \(-0.829136\pi\) | ||
0.859357 | − | 0.511377i | \(-0.170864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9706 | −1.09317 | −0.546585 | − | 0.837404i | \(-0.684072\pi\) | ||||
−0.546585 | + | 0.837404i | \(0.684072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.8885i | 1.14755i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.0000 | + | 4.47214i | 0.958315 | + | 0.285714i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.16228i | − | 0.200401i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.5967i | 1.55253i | 0.630405 | + | 0.776266i | \(0.282889\pi\) | ||||
−0.630405 | + | 0.776266i | \(0.717111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.00000 | − | 15.8114i | 0.314347 | − | 0.994053i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −28.2843 | −1.77123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.4164i | − | 0.836893i | −0.908242 | − | 0.418446i | \(-0.862575\pi\) | ||
0.908242 | − | 0.418446i | \(-0.137425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.3345 | + | 17.3925i | −1.44994 | + | 1.08072i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.9737i | 1.17444i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.6491i | − | 0.779978i | −0.920820 | − | 0.389989i | \(-0.872479\pi\) | ||
0.920820 | − | 0.389989i | \(-0.127521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.8885i | 1.09888i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0000 | −0.917985 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.8885i | − | 1.09068i | −0.838214 | − | 0.545342i | \(-0.816400\pi\) | ||
0.838214 | − | 0.545342i | \(-0.183600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9706 | 1.03089 | 0.515444 | − | 0.856923i | \(-0.327627\pi\) | ||||
0.515444 | + | 0.856923i | \(0.327627\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.0000 | + | 13.4164i | 0.605228 | + | 0.811998i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 22.1359i | − | 1.33002i | −0.746834 | − | 0.665010i | \(-0.768427\pi\) | ||
0.746834 | − | 0.665010i | \(-0.231573\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.47214i | 0.267740i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.16228i | − | 0.188646i | −0.995542 | − | 0.0943228i | \(-0.969931\pi\) | ||
0.995542 | − | 0.0943228i | \(-0.0300686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528 | 0.504398 | 0.252199 | − | 0.967675i | \(-0.418846\pi\) | ||||
0.252199 | + | 0.967675i | \(0.418846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.07107 | 0.418854 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.0000 | + | 15.6525i | −1.23959 | + | 0.923936i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000 | 0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.0000 | −2.05174 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.5563 | 0.908812 | 0.454406 | − | 0.890795i | \(-0.349852\pi\) | ||||
0.454406 | + | 0.890795i | \(0.349852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.00000 | −0.291111 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.07107 | − | 2.23607i | −0.410305 | − | 0.129750i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.1421 | 0.817861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.00000 | − | 6.70820i | −0.288195 | − | 0.386654i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.48683i | 0.545004i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.48683i | − | 0.543214i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.7990 | −1.12999 | −0.564994 | − | 0.825095i | \(-0.691122\pi\) | ||||
−0.564994 | + | 0.825095i | \(0.691122\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 22.3607i | − | 1.26796i | −0.773350 | − | 0.633979i | \(-0.781421\pi\) | ||
0.773350 | − | 0.633979i | \(-0.218579\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1246i | 1.13751i | 0.822507 | + | 0.568755i | \(0.192575\pi\) | ||||
−0.822507 | + | 0.568755i | \(0.807425\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.07107 | + | 9.48683i | 0.398410 | + | 0.534522i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.0000 | −0.842484 | −0.421242 | − | 0.906948i | \(-0.638406\pi\) | ||||
−0.421242 | + | 0.906948i | \(0.638406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.0000 | − | 9.48683i | −1.67968 | − | 0.531161i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.1421 | 0.789337 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 35.3553 | 1.95515 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.07107 | + | 9.48683i | 0.389841 | + | 0.523026i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | 0.0549650 | 0.0274825 | − | 0.999622i | \(-0.491251\pi\) | ||||
0.0274825 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.0000 | −1.20559 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 20.1246i | − | 1.09952i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2982i | 1.37808i | 0.724722 | + | 0.689041i | \(0.241968\pi\) | ||||
−0.724722 | + | 0.689041i | \(0.758032\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.70820i | 0.364340i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.07107 | − | 2.23607i | −0.382920 | − | 0.121090i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.36396 | + | 17.3925i | 0.343622 | + | 0.939108i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.0000 | 1.34595 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.16228i | 0.169760i | 0.996391 | + | 0.0848800i | \(0.0270507\pi\) | ||||
−0.996391 | + | 0.0848800i | \(0.972949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.6274 | −1.21122 | −0.605609 | − | 0.795762i | \(-0.707070\pi\) | ||||
−0.605609 | + | 0.795762i | \(0.707070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 6.32456i | − | 0.337580i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.1803i | − | 0.595069i | −0.954711 | − | 0.297535i | \(-0.903836\pi\) | ||
0.954711 | − | 0.297535i | \(-0.0961644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.23607i | 0.118678i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.0000 | − | 26.8328i | −1.05851 | − | 1.42014i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.2982i | 1.33519i | 0.744525 | + | 0.667595i | \(0.232676\pi\) | ||||
−0.744525 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.1421 | + | 20.1246i | −0.742270 | + | 1.05627i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.48683i | − | 0.496564i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.70820i | 0.350165i | 0.984554 | + | 0.175083i | \(0.0560193\pi\) | ||||
−0.984554 | + | 0.175083i | \(0.943981\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.7990 | −1.03069 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9706 | + | 12.6491i | −0.881068 | + | 0.656709i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.7851i | 1.80110i | 0.434751 | + | 0.900551i | \(0.356837\pi\) | ||||
−0.434751 | + | 0.900551i | \(0.643163\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.0000 | 1.29099 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 26.8328i | − | 1.38196i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0000 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.3553 | 1.81131 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 15.6525i | − | 0.799804i | −0.916558 | − | 0.399902i | \(-0.869044\pi\) | ||
0.916558 | − | 0.399902i | \(-0.130956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.5355 | + | 6.43692i | −0.944658 | + | 0.328056i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 6.32456i | − | 0.321495i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.0000 | −0.861934 | −0.430967 | − | 0.902368i | \(-0.641828\pi\) | ||||
−0.430967 | + | 0.902368i | \(0.641828\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.2843 | −1.43040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.6228i | 1.59516i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.1421 | 0.711568 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.8885i | 0.897800i | 0.893582 | + | 0.448900i | \(0.148184\pi\) | ||||
−0.893582 | + | 0.448900i | \(0.851816\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.00000 | + | 6.70820i | 0.250313 | + | 0.335830i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0000 | −1.19850 | −0.599251 | − | 0.800561i | \(-0.704535\pi\) | ||||
−0.599251 | + | 0.800561i | \(0.704535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.32456i | − | 0.315049i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 24.5967i | − | 1.22222i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.0000 | − | 34.7851i | 0.545250 | − | 1.72423i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.65685 | 0.279713 | 0.139857 | − | 0.990172i | \(-0.455336\pi\) | ||||
0.139857 | + | 0.990172i | \(0.455336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 20.1246i | − | 0.992674i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.53553 | − | 4.74342i | −0.173972 | − | 0.233408i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.16228i | 0.155230i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 50.5964i | − | 2.47772i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 31.3050i | − | 1.52935i | −0.644418 | − | 0.764673i | \(-0.722900\pi\) | ||
0.644418 | − | 0.764673i | \(-0.277100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.0000 | −1.75453 | −0.877266 | − | 0.480004i | \(-0.840635\pi\) | ||||
−0.877266 | + | 0.480004i | \(0.840635\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.94427i | 0.434885i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.00000 | − | 6.70820i | 0.435541 | − | 0.324633i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.0000 | − | 6.32456i | −0.965609 | − | 0.305352i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8114i | 0.761608i | 0.924656 | + | 0.380804i | \(0.124353\pi\) | ||||
−0.924656 | + | 0.380804i | \(0.875647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5967i | 1.18204i | 0.806655 | + | 0.591022i | \(0.201275\pi\) | ||||
−0.806655 | + | 0.591022i | \(0.798725\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 47.4342i | − | 2.27429i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.07107 | 0.338255 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8701 | 1.28244 | 0.641219 | − | 0.767358i | \(-0.278429\pi\) | ||||
0.641219 | + | 0.767358i | \(0.278429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.00000 | + | 13.4164i | −0.190476 | + | 0.638877i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.0000 | −1.28281 | −0.641404 | − | 0.767203i | \(-0.721648\pi\) | ||||
−0.641404 | + | 0.767203i | \(0.721648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0000 | 0.711068 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1421 | −0.668900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0000 | 1.74614 | 0.873069 | − | 0.487597i | \(-0.162126\pi\) | ||||
0.873069 | + | 0.487597i | \(0.162126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.89949 | − | 31.3050i | 0.466149 | − | 1.47409i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −28.2843 | −1.32891 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.0000 | − | 13.4164i | −0.468807 | − | 0.628971i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9737i | 0.887551i | 0.896138 | + | 0.443775i | \(0.146361\pi\) | ||||
−0.896138 | + | 0.443775i | \(0.853639\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.6491i | 0.590410i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.89949 | −0.461065 | −0.230533 | − | 0.973065i | \(-0.574047\pi\) | ||||
−0.230533 | + | 0.973065i | \(0.574047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.00000 | 0.325318 | 0.162659 | − | 0.986682i | \(-0.447993\pi\) | ||||
0.162659 | + | 0.986682i | \(0.447993\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 11.1803i | − | 0.518476i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.70820i | 0.310419i | 0.987882 | + | 0.155209i | \(0.0496052\pi\) | ||||
−0.987882 | + | 0.155209i | \(0.950395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.0919 | − | 14.2302i | 0.881581 | − | 0.657092i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.0000 | 0.691164 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000 | + | 3.16228i | 0.459800 | + | 0.145402i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.0000 | −0.732590 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.7990 | −0.904639 | −0.452319 | − | 0.891856i | \(-0.649403\pi\) | ||||
−0.452319 | + | 0.891856i | \(0.649403\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.1127 | 1.41862 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.6777 | + | 23.7171i | 0.804362 | + | 1.07916i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.0000 | 1.58927 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.0000 | 0.951601 | 0.475800 | − | 0.879553i | \(-0.342158\pi\) | ||||
0.475800 | + | 0.879553i | \(0.342158\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3607i | 1.01118i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.48683i | − | 0.428135i | −0.976819 | − | 0.214067i | \(-0.931329\pi\) | ||
0.976819 | − | 0.214067i | \(-0.0686712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 53.6656i | 2.41698i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.1421 | − | 4.47214i | −0.635642 | − | 0.201008i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.12132 | + | 1.58114i | −0.0951542 | + | 0.0709238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | −0.358129 | −0.179065 | − | 0.983837i | \(-0.557307\pi\) | ||||
−0.179065 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.16228i | 0.141280i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.5269 | −1.45030 | −0.725152 | − | 0.688589i | \(-0.758230\pi\) | ||||
−0.725152 | + | 0.688589i | \(0.758230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9.48683i | − | 0.422159i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.1803i | 0.496536i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.23607i | − | 0.0991120i | −0.998771 | − | 0.0495560i | \(-0.984219\pi\) | ||
0.998771 | − | 0.0495560i | \(-0.0157806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.00000 | − | 6.70820i | 0.398137 | − | 0.296753i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.16228i | − | 0.139618i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0000 | −0.440653 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1421 | − | 4.47214i | −0.621970 | − | 0.196684i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 28.4605i | − | 1.24928i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.23607i | − | 0.0979639i | −0.998800 | − | 0.0489820i | \(-0.984402\pi\) | ||
0.998800 | − | 0.0489820i | \(-0.0155977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.82843 | −0.123678 | −0.0618392 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618392 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.6491i | 0.551004i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.47214i | − | 0.194074i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.0000 | 1.21281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.1421 | −0.611418 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 29.0689i | − | 1.25441i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.2132 | − | 13.0328i | −0.827571 | − | 0.561361i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.6228i | 1.35957i | 0.733412 | + | 0.679785i | \(0.237927\pi\) | ||||
−0.733412 | + | 0.679785i | \(0.762073\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.0000 | 1.93113 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.3553 | −1.51446 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.2719i | 1.89293i | 0.322808 | + | 0.946465i | \(0.395373\pi\) | ||||
−0.322808 | + | 0.946465i | \(0.604627\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.48528 | 0.362143 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.4164i | − | 0.571558i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | + | 13.4164i | 0.425243 | + | 0.570524i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 55.0000 | 2.33462 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 12.6491i | − | 0.535960i | −0.963424 | − | 0.267980i | \(-0.913644\pi\) | ||
0.963424 | − | 0.267980i | \(-0.0863561\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.94427i | 0.378302i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | + | 12.6491i | 1.68880 | + | 0.534046i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.5980 | 1.66886 | 0.834428 | − | 0.551117i | \(-0.185798\pi\) | ||||
0.834428 | + | 0.551117i | \(0.185798\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.70820i | − | 0.282216i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.3345 | − | 17.3925i | 0.979958 | − | 0.730417i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 9.48683i | − | 0.397709i | −0.980029 | − | 0.198854i | \(-0.936278\pi\) | ||
0.980029 | − | 0.198854i | \(-0.0637221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6491i | 0.529349i | 0.964338 | + | 0.264674i | \(0.0852645\pi\) | ||||
−0.964338 | + | 0.264674i | \(0.914736\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.70820i | − | 0.280239i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 29.0689i | − | 1.21015i | −0.796167 | − | 0.605077i | \(-0.793142\pi\) | ||
0.796167 | − | 0.605077i | \(-0.206858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −35.3553 | −1.46932 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00000 | + | 2.23607i | −0.124461 | + | 0.0927677i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000 | − | 25.2982i | 0.331326 | − | 1.04775i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 12.6491i | − | 0.522976i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.4164i | 0.553754i | 0.960905 | + | 0.276877i | \(0.0892995\pi\) | ||||
−0.960905 | + | 0.276877i | \(0.910700\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 3.16228i | − | 0.130299i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.2843 | 1.16346 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.41421 | 0.0580748 | 0.0290374 | − | 0.999578i | \(-0.490756\pi\) | ||||
0.0290374 | + | 0.999578i | \(0.490756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.0000 | + | 26.8328i | 0.819920 | + | 1.10004i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.0000 | 1.63709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.2132 | 0.865305 | 0.432652 | − | 0.901561i | \(-0.357578\pi\) | ||||
0.432652 | + | 0.901561i | \(0.357578\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.0000 | 0.733017 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.1421 | − | 20.1246i | 0.574960 | − | 0.818182i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.4558 | −1.03322 | −0.516610 | − | 0.856221i | \(-0.672806\pi\) | ||||
−0.516610 | + | 0.856221i | \(0.672806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.0000 | − | 33.5410i | 1.82349 | − | 1.35915i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 12.6491i | − | 0.511728i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 18.9737i | − | 0.766339i | −0.923678 | − | 0.383170i | \(-0.874832\pi\) | ||
0.923678 | − | 0.383170i | \(-0.125168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 49.4975 | 1.99593 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.0000 | −0.966204 | −0.483102 | − | 0.875564i | \(-0.660490\pi\) | ||||
−0.483102 | + | 0.875564i | \(0.660490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.0689i | − | 1.16838i | −0.811618 | − | 0.584189i | \(-0.801413\pi\) | ||
0.811618 | − | 0.584189i | \(-0.198587\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 11.1803i | − | 0.448652i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.6066 | + | 14.2302i | 0.424945 | + | 0.570123i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.0000 | − | 3.16228i | −0.399362 | − | 0.126289i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −62.2254 | −2.48109 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.0000 | −0.517522 | −0.258761 | − | 0.965941i | \(-0.583314\pi\) | ||||
−0.258761 | + | 0.965941i | \(0.583314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.2132 | −0.843149 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.3553 | −1.40303 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.65685 | − | 18.9737i | 0.224133 | − | 0.751764i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0000 | −0.434474 | −0.217237 | − | 0.976119i | \(-0.569704\pi\) | ||||
−0.217237 | + | 0.976119i | \(0.569704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.1803i | − | 0.440910i | −0.975397 | − | 0.220455i | \(-0.929246\pi\) | ||
0.975397 | − | 0.220455i | \(-0.0707541\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.8114i | 0.622573i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.0132i | 1.49445i | 0.664570 | + | 0.747226i | \(0.268615\pi\) | ||||
−0.664570 | + | 0.747226i | \(0.731385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.07107 | + | 2.23607i | 0.277564 | + | 0.0877733i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.6066 | − | 7.90569i | 0.415705 | − | 0.309849i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.0000 | 1.05659 | 0.528296 | − | 0.849060i | \(-0.322831\pi\) | ||||
0.528296 | + | 0.849060i | \(0.322831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 31.6228i | − | 1.23560i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.48528 | 0.331042 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 18.9737i | − | 0.739109i | −0.929209 | − | 0.369555i | \(-0.879510\pi\) | ||
0.929209 | − | 0.369555i | \(-0.120490\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.70820i | − | 0.260919i | −0.991454 | − | 0.130459i | \(-0.958355\pi\) | ||
0.991454 | − | 0.130459i | \(-0.0416452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.7771i | 1.38947i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.00000 | − | 6.70820i | −0.193892 | − | 0.260133i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 47.4342i | − | 1.83666i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.0000 | 1.73980 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.24264 | + | 13.4164i | −0.163785 | + | 0.517935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.48683i | 0.365691i | 0.983142 | + | 0.182845i | \(0.0585307\pi\) | ||||
−0.983142 | + | 0.182845i | \(0.941469\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6274 | 0.869642 | 0.434821 | − | 0.900517i | \(-0.356812\pi\) | ||||
0.434821 | + | 0.900517i | \(0.356812\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.7487 | + | 33.2039i | 0.949769 | + | 1.27425i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 66.4078i | − | 2.54475i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0000 | −1.14792 | −0.573959 | − | 0.818884i | \(-0.694593\pi\) | ||||
−0.573959 | + | 0.818884i | \(0.694593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.1246i | 0.768922i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.0000 | −0.953809 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.6274 | 0.862036 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.70820i | − | 0.255192i | −0.991826 | − | 0.127596i | \(-0.959274\pi\) | ||
0.991826 | − | 0.127596i | \(-0.0407261\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.75736 | − | 16.5787i | −0.218704 | − | 0.629772i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 50.5964i | 1.91923i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −56.0000 | −2.12115 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.2132 | −0.802357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.48683i | 0.358313i | 0.983821 | + | 0.179156i | \(0.0573368\pi\) | ||||
−0.983821 | + | 0.179156i | \(0.942663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5563 | 0.586719 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 22.3607i | − | 0.842152i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.00000 | − | 6.70820i | 0.338480 | − | 0.252288i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0000 | 0.488225 | 0.244113 | − | 0.969747i | \(-0.421503\pi\) | ||||
0.244113 | + | 0.969747i | \(0.421503\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.6491i | 0.474379i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 11.1803i | − | 0.418707i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.0000 | + | 6.32456i | 0.747958 | + | 0.236525i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.3553 | −1.32037 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.1803i | 0.416956i | 0.978027 | + | 0.208478i | \(0.0668510\pi\) | ||||
−0.978027 | + | 0.208478i | \(0.933149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.07107 | − | 9.48683i | −0.263340 | − | 0.353308i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.9473i | 1.41128i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.70820i | 0.248794i | 0.992233 | + | 0.124397i | \(0.0396996\pi\) | ||||
−0.992233 | + | 0.124397i | \(0.960300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 17.8885i | − | 0.661632i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.9117 | 1.88047 | 0.940233 | − | 0.340532i | \(-0.110607\pi\) | ||||
0.940233 | + | 0.340532i | \(0.110607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.0000 | − | 33.5410i | 0.368856 | − | 1.23718i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.00000 | + | 28.4605i | −0.331519 | + | 1.04836i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37.9473i | − | 1.39592i | −0.716139 | − | 0.697958i | \(-0.754092\pi\) | ||
0.716139 | − | 0.697958i | \(-0.245908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 8.94427i | − | 0.328576i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.9737i | − | 0.696076i | −0.937480 | − | 0.348038i | \(-0.886848\pi\) | ||
0.937480 | − | 0.348038i | \(-0.113152\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1421 | 0.518128 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.82843 | −0.103487 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.0000 | − | 13.4164i | −0.365392 | − | 0.490225i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0000 | −1.13121 | −0.565603 | − | 0.824678i | \(-0.691357\pi\) | ||||
−0.565603 | + | 0.824678i | \(0.691357\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 55.0000 | 2.00431 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.2843 | 1.02937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0000 | 0.726912 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −35.3553 | − | 11.1803i | −1.28332 | − | 0.405821i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.2548 | −1.64049 | −0.820243 | − | 0.572015i | \(-0.806162\pi\) | ||||
−0.820243 | + | 0.572015i | \(0.806162\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25.0000 | − | 33.5410i | −0.905061 | − | 1.21427i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 25.2982i | 0.914659i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.32456i | 0.228366i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.4264 | −1.52994 | −0.764968 | − | 0.644069i | \(-0.777245\pi\) | ||||
−0.764968 | + | 0.644069i | \(0.777245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.0000 | −1.08042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 44.7214i | − | 1.60852i | −0.594281 | − | 0.804258i | \(-0.702563\pi\) | ||
0.594281 | − | 0.804258i | \(-0.297437\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38.8909 | + | 52.1776i | 1.39520 | + | 1.87186i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.0000 | 0.501602 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.00000 | − | 3.16228i | 0.0357828 | − | 0.113155i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.2132 | −0.758098 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.0000 | −0.535373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5563 | 0.554524 | 0.277262 | − | 0.960794i | \(-0.410573\pi\) | ||||
0.277262 | + | 0.960794i | \(0.410573\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.2843 | −1.00695 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.36396 | − | 4.74342i | 0.226276 | − | 0.168656i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | −0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.0000 | 1.41865 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.5410i | 1.18808i | 0.804434 | + | 0.594042i | \(0.202469\pi\) | ||||
−0.804434 | + | 0.594042i | \(0.797531\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.2982i | 0.894987i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4164i | 0.474045i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.24264 | + | 13.4164i | −0.149720 | + | 0.473455i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.6777 | − | 23.7171i | −0.623056 | − | 0.835917i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.0000 | −1.40807 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 28.4605i | − | 1.00062i | −0.865847 | − | 0.500309i | \(-0.833220\pi\) | ||
0.865847 | − | 0.500309i | \(-0.166780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 37.9473i | − | 1.33087i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 22.3607i | − | 0.783260i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.47214i | 0.156460i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000 | − | 8.94427i | 0.419314 | − | 0.312538i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.32456i | 0.220729i | 0.993891 | + | 0.110364i | \(0.0352017\pi\) | ||||
−0.993891 | + | 0.110364i | \(0.964798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.0000 | −1.22002 | −0.610012 | − | 0.792392i | \(-0.708835\pi\) | ||||
−0.610012 | + | 0.792392i | \(0.708835\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.9473i | 1.31956i | 0.751460 | + | 0.659779i | \(0.229350\pi\) | ||||
−0.751460 | + | 0.659779i | \(0.770650\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6525i | 0.543633i | 0.962349 | + | 0.271816i | \(0.0876244\pi\) | ||||
−0.962349 | + | 0.271816i | \(0.912376\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49.4975 | −1.71705 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.3137 | + | 37.9473i | −0.391997 | + | 1.31480i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.16228i | − | 0.109435i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00000 | −0.172825 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 29.0689i | − | 1.00357i | −0.864993 | − | 0.501785i | \(-0.832677\pi\) | ||
0.864993 | − | 0.501785i | \(-0.167323\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −61.0000 | −2.10345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.07107 | −0.243541 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 11.1803i | − | 0.384615i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.0919 | − | 0.813842i | 0.999609 | − | 0.0279639i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 18.9737i | − | 0.651175i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.0000 | 1.88538 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.2548 | 1.54950 | 0.774748 | − | 0.632270i | \(-0.217877\pi\) | ||||
0.774748 | + | 0.632270i | \(0.217877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.32456i | − | 0.216295i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.7990 | 0.676321 | 0.338160 | − | 0.941089i | \(-0.390195\pi\) | ||||
0.338160 | + | 0.941089i | \(0.390195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 46.9574i | − | 1.60217i | −0.598553 | − | 0.801083i | \(-0.704257\pi\) | ||
0.598553 | − | 0.801083i | \(-0.295743\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.0000 | + | 46.9574i | 1.19280 | + | 1.60030i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.0000 | 0.612727 | 0.306364 | − | 0.951915i | \(-0.400888\pi\) | ||||
0.306364 | + | 0.951915i | \(0.400888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.4605i | 0.967686i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 33.5410i | − | 1.13911i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0000 | − | 6.32456i | −0.678454 | − | 0.214546i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.4558 | −0.862538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.3050i | 1.05951i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.6777 | − | 23.7171i | −0.597614 | − | 0.801784i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.7851i | 1.17461i | 0.809366 | + | 0.587304i | \(0.199811\pi\) | ||||
−0.809366 | + | 0.587304i | \(0.800189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 34.7851i | − | 1.17327i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.4853i | − | 1.43137i | −0.698425 | − | 0.715683i | \(-0.746116\pi\) | ||
0.698425 | − | 0.715683i | \(-0.253884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0000 | 1.07689 | 0.538443 | − | 0.842662i | \(-0.319013\pi\) | ||||
0.538443 | + | 0.842662i | \(0.319013\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.1803i | 0.375823i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.7696 | 1.23460 | 0.617300 | − | 0.786728i | \(-0.288226\pi\) | ||||
0.617300 | + | 0.786728i | \(0.288226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.0000 | − | 33.5410i | −0.838473 | − | 1.12493i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.0000 | + | 34.7851i | −0.368514 | + | 1.16534i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.32456i | − | 0.211643i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.0689i | 0.971666i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 31.6228i | − | 1.05585i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.2132 | −0.707500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.2548 | −1.50766 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.0000 | + | 11.1803i | −0.499169 | + | 0.372058i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −45.0000 | −1.49585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | −0.332045 | −0.166022 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166022 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.48528 | 0.281439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.41421 | − | 4.47214i | 0.0468036 | − | 0.148006i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.2132 | −0.701287 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.0000 | − | 22.3607i | 0.990687 | − | 0.738415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.16228i | − | 0.104314i | −0.998639 | − | 0.0521570i | \(-0.983390\pi\) | ||
0.998639 | − | 0.0521570i | \(-0.0166096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.2719i | 1.45881i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.82843 | 0.0930988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 8.94427i | − | 0.293768i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 17.8885i | − | 0.586904i | −0.955974 | − | 0.293452i | \(-0.905196\pi\) | ||
0.955974 | − | 0.293452i | \(-0.0948041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | − | 9.48683i | 0.0926980 | − | 0.310918i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.0000 | −1.63693 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.0000 | − | 12.6491i | −1.30814 | − | 0.413670i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.65685 | 0.184801 | 0.0924007 | − | 0.995722i | \(-0.470546\pi\) | ||||
0.0924007 | + | 0.995722i | \(0.470546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.0000 | 1.46852 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.2843 | 0.922041 | 0.461020 | − | 0.887390i | \(-0.347483\pi\) | ||||
0.461020 | + | 0.887390i | \(0.347483\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.4975 | 1.61186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.6066 | + | 7.90569i | −0.345033 | + | 0.257172i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 61.0000 | 1.98223 | 0.991117 | − | 0.132994i | \(-0.0424591\pi\) | ||||
0.991117 | + | 0.132994i | \(0.0424591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.5410i | 1.08764i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.48683i | 0.307309i | 0.988125 | + | 0.153654i | \(0.0491042\pi\) | ||||
−0.988125 | + | 0.153654i | \(0.950896\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.70820i | 0.217072i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.2132 | + | 67.0820i | −0.685725 | + | 2.16845i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.0919 | + | 14.2302i | −0.616509 | + | 0.459519i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.0000 | 0.838710 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 12.6491i | − | 0.407612i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.3553 | 1.13813 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4342i | 1.52538i | 0.646764 | + | 0.762690i | \(0.276122\pi\) | ||||
−0.646764 | + | 0.762690i | \(0.723878\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.8885i | 0.574663i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.0689i | 0.932865i | 0.884557 | + | 0.466432i | \(0.154461\pi\) | ||||
−0.884557 | + | 0.466432i | \(0.845539\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.0000 | + | 35.7771i | −1.53881 | + | 1.14696i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0000 | −0.671850 | −0.335925 | − | 0.941889i | \(-0.609049\pi\) | ||||
−0.335925 | + | 0.941889i | \(0.609049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.2132 | − | 6.70820i | −0.677977 | − | 0.214395i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 31.6228i | − | 1.00964i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.23607i | 0.0713195i | 0.999364 | + | 0.0356597i | \(0.0113533\pi\) | ||||
−0.999364 | + | 0.0356597i | \(0.988647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.2843 | −0.901212 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.2132 | − | 15.8114i | 0.675224 | − | 0.503282i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.8114i | 0.502773i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.23607i | − | 0.0709595i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.0000 | −1.26809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7279 | −0.403097 | −0.201549 | − | 0.979479i | \(-0.564597\pi\) | ||||
−0.201549 | + | 0.979479i | \(0.564597\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 24.5967i | − | 0.778207i |
(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 | 1232.2.e.b.769.1 | 4 | ||
4.3 | odd | 2 | 308.2.c.a.153.4 | yes | 4 | ||
7.6 | odd | 2 | inner | 1232.2.e.b.769.4 | 4 | ||
11.10 | odd | 2 | inner | 1232.2.e.b.769.2 | 4 | ||
12.11 | even | 2 | 2772.2.i.c.1693.2 | 4 | |||
28.3 | even | 6 | 2156.2.q.b.901.2 | 8 | |||
28.11 | odd | 6 | 2156.2.q.b.901.4 | 8 | |||
28.19 | even | 6 | 2156.2.q.b.2089.3 | 8 | |||
28.23 | odd | 6 | 2156.2.q.b.2089.1 | 8 | |||
28.27 | even | 2 | 308.2.c.a.153.1 | ✓ | 4 | ||
44.43 | even | 2 | 308.2.c.a.153.3 | yes | 4 | ||
77.76 | even | 2 | inner | 1232.2.e.b.769.3 | 4 | ||
84.83 | odd | 2 | 2772.2.i.c.1693.3 | 4 | |||
132.131 | odd | 2 | 2772.2.i.c.1693.1 | 4 | |||
308.87 | odd | 6 | 2156.2.q.b.901.1 | 8 | |||
308.131 | odd | 6 | 2156.2.q.b.2089.4 | 8 | |||
308.219 | even | 6 | 2156.2.q.b.2089.2 | 8 | |||
308.263 | even | 6 | 2156.2.q.b.901.3 | 8 | |||
308.307 | odd | 2 | 308.2.c.a.153.2 | yes | 4 | ||
924.923 | even | 2 | 2772.2.i.c.1693.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.c.a.153.1 | ✓ | 4 | 28.27 | even | 2 | ||
308.2.c.a.153.2 | yes | 4 | 308.307 | odd | 2 | ||
308.2.c.a.153.3 | yes | 4 | 44.43 | even | 2 | ||
308.2.c.a.153.4 | yes | 4 | 4.3 | odd | 2 | ||
1232.2.e.b.769.1 | 4 | 1.1 | even | 1 | trivial | ||
1232.2.e.b.769.2 | 4 | 11.10 | odd | 2 | inner | ||
1232.2.e.b.769.3 | 4 | 77.76 | even | 2 | inner | ||
1232.2.e.b.769.4 | 4 | 7.6 | odd | 2 | inner | ||
2156.2.q.b.901.1 | 8 | 308.87 | odd | 6 | |||
2156.2.q.b.901.2 | 8 | 28.3 | even | 6 | |||
2156.2.q.b.901.3 | 8 | 308.263 | even | 6 | |||
2156.2.q.b.901.4 | 8 | 28.11 | odd | 6 | |||
2156.2.q.b.2089.1 | 8 | 28.23 | odd | 6 | |||
2156.2.q.b.2089.2 | 8 | 308.219 | even | 6 | |||
2156.2.q.b.2089.3 | 8 | 28.19 | even | 6 | |||
2156.2.q.b.2089.4 | 8 | 308.131 | odd | 6 | |||
2772.2.i.c.1693.1 | 4 | 132.131 | odd | 2 | |||
2772.2.i.c.1693.2 | 4 | 12.11 | even | 2 | |||
2772.2.i.c.1693.3 | 4 | 84.83 | odd | 2 | |||
2772.2.i.c.1693.4 | 4 | 924.923 | even | 2 |