Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(559,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.p (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.9 | ||
Root | \(-1.40199 - 0.185533i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.559 |
Dual form | 672.2.p.a.559.1 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.84444 | −1.71929 | −0.859644 | − | 0.510894i | \(-0.829314\pi\) | ||||
−0.859644 | + | 0.510894i | \(0.829314\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62140 | − | 2.09071i | 0.612831 | − | 0.790214i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.54637 | 1.37078 | 0.685391 | − | 0.728175i | \(-0.259631\pi\) | ||||
0.685391 | + | 0.728175i | \(0.259631\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.81625 | 0.503738 | 0.251869 | − | 0.967761i | \(-0.418955\pi\) | ||||
0.251869 | + | 0.967761i | \(0.418955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.84444i | − | 0.992631i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.49124i | 0.846751i | 0.905954 | + | 0.423375i | \(0.139155\pi\) | ||||
−0.905954 | + | 0.423375i | \(0.860845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.68700i | 0.387025i | 0.981098 | + | 0.193513i | \(0.0619881\pi\) | ||||
−0.981098 | + | 0.193513i | \(0.938012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.09071 | + | 1.62140i | 0.456230 | + | 0.353818i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.00632i | 1.04389i | 0.852979 | + | 0.521945i | \(0.174793\pi\) | ||||
−0.852979 | + | 0.521945i | \(0.825207\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.77975 | 1.95595 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.81625i | 0.337270i | 0.985679 | + | 0.168635i | \(0.0539359\pi\) | ||||
−0.985679 | + | 0.168635i | \(0.946064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.34329 | 0.959683 | 0.479842 | − | 0.877355i | \(-0.340694\pi\) | ||||
0.479842 | + | 0.877355i | \(0.340694\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54637i | 0.791422i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.23338 | + | 8.03761i | −1.05363 | + | 1.35860i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.42654i | 0.234522i | 0.993101 | + | 0.117261i | \(0.0374114\pi\) | ||||
−0.993101 | + | 0.117261i | \(0.962589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.81625i | 0.290833i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.97551i | 1.40174i | 0.713290 | + | 0.700869i | \(0.247204\pi\) | ||||
−0.713290 | + | 0.700869i | \(0.752796\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.03761 | 1.22572 | 0.612862 | − | 0.790190i | \(-0.290018\pi\) | ||||
0.612862 | + | 0.790190i | \(0.290018\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.84444 | 0.573096 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.83580 | 0.705374 | 0.352687 | − | 0.935741i | \(-0.385268\pi\) | ||||
0.352687 | + | 0.935741i | \(0.385268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74213 | − | 6.77975i | −0.248876 | − | 0.968535i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.49124 | −0.488872 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.87263i | − | 0.806668i | −0.915053 | − | 0.403334i | \(-0.867851\pi\) | ||
0.915053 | − | 0.403334i | \(-0.132149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.4783 | −2.35677 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.68700 | −0.223449 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.46675i | − | 1.10228i | −0.834414 | − | 0.551139i | \(-0.814194\pi\) | ||
0.834414 | − | 0.551139i | \(-0.185806\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.01955 | −0.386613 | −0.193307 | − | 0.981138i | \(-0.561921\pi\) | ||||
−0.193307 | + | 0.981138i | \(0.561921\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.62140 | + | 2.09071i | −0.204277 | + | 0.263405i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.98249 | −0.866071 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.42914 | 0.541105 | 0.270553 | − | 0.962705i | \(-0.412794\pi\) | ||||
0.270553 | + | 0.962705i | \(0.412794\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.00632 | −0.602690 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.47928i | 0.175558i | 0.996140 | + | 0.0877791i | \(0.0279769\pi\) | ||||
−0.996140 | + | 0.0877791i | \(0.972023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.98249i | 0.817238i | 0.912705 | + | 0.408619i | \(0.133990\pi\) | ||||
−0.912705 | + | 0.408619i | \(0.866010\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.77975i | 1.12927i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.37148 | − | 9.50514i | 0.840058 | − | 1.08321i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.97813i | − | 0.335065i | −0.985867 | − | 0.167533i | \(-0.946420\pi\) | ||
0.985867 | − | 0.167533i | \(-0.0535800\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5770i | 1.16098i | 0.814268 | + | 0.580489i | \(0.197138\pi\) | ||||
−0.814268 | + | 0.580489i | \(0.802862\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.4219i | − | 1.45581i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.81625 | −0.194723 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.9580i | − | 1.69154i | −0.533544 | − | 0.845772i | \(-0.679140\pi\) | ||
0.533544 | − | 0.845772i | \(-0.320860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.94487 | − | 3.79726i | 0.308707 | − | 0.398061i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.34329i | 0.554073i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.48559i | − | 0.665408i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.6085i | − | 1.17866i | −0.807892 | − | 0.589331i | \(-0.799391\pi\) | ||
0.807892 | − | 0.589331i | \(-0.200609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.54637 | −0.456928 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5333 | 1.14761 | 0.573805 | − | 0.818992i | \(-0.305467\pi\) | ||||
0.573805 | + | 0.818992i | \(0.305467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.14230 | 0.112555 | 0.0562773 | − | 0.998415i | \(-0.482077\pi\) | ||||
0.0562773 | + | 0.998415i | \(0.482077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.03761 | − | 6.23338i | −0.784391 | − | 0.608315i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0796192 | −0.00769707 | −0.00384854 | − | 0.999993i | \(-0.501225\pi\) | ||||
−0.00384854 | + | 0.999993i | \(0.501225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.1081i | 1.92601i | 0.269489 | + | 0.963004i | \(0.413145\pi\) | ||||
−0.269489 | + | 0.963004i | \(0.586855\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.42654 | −0.135401 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.98249 | 0.468713 | 0.234356 | − | 0.972151i | \(-0.424702\pi\) | ||||
0.234356 | + | 0.972151i | \(0.424702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 19.2465i | − | 1.79475i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.81625 | −0.167913 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.29918 | + | 5.66070i | 0.669114 | + | 0.518915i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.66949 | 0.879045 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.97551 | −0.809294 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.3755 | −1.64355 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.38471i | 0.477816i | 0.971042 | + | 0.238908i | \(0.0767894\pi\) | ||||
−0.971042 | + | 0.238908i | \(0.923211\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.03761i | 0.707673i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.0927i | − | 1.14392i | −0.820282 | − | 0.571959i | \(-0.806184\pi\) | ||
0.820282 | − | 0.571959i | \(-0.193816\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.52704 | + | 2.73531i | 0.305833 | + | 0.237181i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.84444i | 0.330877i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.5595 | −1.67108 | −0.835540 | − | 0.549429i | \(-0.814845\pi\) | ||||
−0.835540 | + | 0.549429i | \(0.814845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.5910i | − | 1.23759i | −0.785553 | − | 0.618795i | \(-0.787621\pi\) | ||
0.785553 | − | 0.618795i | \(-0.212379\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.83580i | 0.407248i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.25737 | 0.690516 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.98249i | − | 0.579864i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.77975 | − | 1.74213i | 0.559184 | − | 0.143689i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.3973i | 1.50717i | 0.657352 | + | 0.753584i | \(0.271676\pi\) | ||||
−0.657352 | + | 0.753584i | \(0.728324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.88759i | 0.804641i | 0.915499 | + | 0.402320i | \(0.131796\pi\) | ||||
−0.915499 | + | 0.402320i | \(0.868204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.49124i | − | 0.282250i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.5420 | −1.64997 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3582 | 0.986294 | 0.493147 | − | 0.869946i | \(-0.335846\pi\) | ||||
0.493147 | + | 0.869946i | \(0.335846\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.87263 | 0.465730 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4668 | + | 8.11723i | 0.824896 | + | 0.639728i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.57086 | 0.279692 | 0.139846 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139846 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 17.4783i | − | 1.36068i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.5788 | −1.51505 | −0.757525 | − | 0.652806i | \(-0.773592\pi\) | ||||
−0.757525 | + | 0.652806i | \(0.773592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.70122 | −0.746248 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 1.68700i | − | 0.129008i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.49424 | −0.417719 | −0.208860 | − | 0.977946i | \(-0.566975\pi\) | ||||
−0.208860 | + | 0.977946i | \(0.566975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.8569 | − | 20.4466i | 1.19867 | − | 1.54562i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.46675 | 0.636400 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.0306 | −0.749725 | −0.374862 | − | 0.927080i | \(-0.622310\pi\) | ||||
−0.374862 | + | 0.927080i | \(0.622310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2481 | −1.80235 | −0.901174 | − | 0.433458i | \(-0.857293\pi\) | ||||
−0.901174 | + | 0.433458i | \(0.857293\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.01955i | − | 0.223211i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.48426i | − | 0.403211i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8725i | 1.16071i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.09071 | − | 1.62140i | −0.152077 | − | 0.117939i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.49422i | − | 0.614620i | −0.951609 | − | 0.307310i | \(-0.900571\pi\) | ||
0.951609 | − | 0.307310i | \(-0.0994288\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2955 | −0.813067 | −0.406533 | − | 0.913636i | \(-0.633262\pi\) | ||||
−0.406533 | + | 0.913636i | \(0.633262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 6.98249i | − | 0.500026i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.38473i | 0.169905i | 0.996385 | + | 0.0849526i | \(0.0270739\pi\) | ||||
−0.996385 | + | 0.0849526i | \(0.972926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.46338 | 0.174624 | 0.0873120 | − | 0.996181i | \(-0.472172\pi\) | ||||
0.0873120 | + | 0.996181i | \(0.472172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.42914i | 0.312407i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.79726 | + | 2.94487i | 0.266515 | + | 0.206690i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 34.5058i | − | 2.40999i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 5.00632i | − | 0.347963i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.66975i | 0.530528i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0376150 | 0.00258952 | 0.00129476 | − | 0.999999i | \(-0.499588\pi\) | ||||
0.00129476 | + | 0.999999i | \(0.499588\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.47928 | −0.101359 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.9002 | −2.10737 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.66361 | − | 11.1713i | 0.588124 | − | 0.758355i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.98249 | −0.471833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.34099i | 0.426541i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.9144 | 0.864812 | 0.432406 | − | 0.901679i | \(-0.357665\pi\) | ||||
0.432406 | + | 0.901679i | \(0.357665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.77975 | −0.651983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1.48426i | − | 0.0985141i | −0.998786 | − | 0.0492571i | \(-0.984315\pi\) | ||
0.998786 | − | 0.0492571i | \(-0.0156854\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.66934 | −0.308559 | −0.154279 | − | 0.988027i | \(-0.549306\pi\) | ||||
−0.154279 | + | 0.988027i | \(0.549306\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.50514 | + | 7.37148i | 0.625392 | + | 0.485008i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.35650 | −0.547452 | −0.273726 | − | 0.961808i | \(-0.588256\pi\) | ||||
−0.273726 | + | 0.961808i | \(0.588256\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5910 | −1.21274 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.97813 | 0.193450 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.8547i | − | 1.28430i | −0.766580 | − | 0.642148i | \(-0.778043\pi\) | ||
0.766580 | − | 0.642148i | \(-0.221957\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.57701i | − | 0.423662i | −0.977306 | − | 0.211831i | \(-0.932057\pi\) | ||
0.977306 | − | 0.211831i | \(-0.0679427\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.69753 | + | 26.0644i | 0.427889 | + | 1.66519i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.06403i | 0.194960i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.5770 | −0.670291 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.85827i | 0.306652i | 0.988176 | + | 0.153326i | \(0.0489984\pi\) | ||||
−0.988176 | + | 0.153326i | \(0.951002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.7606i | 1.43094i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.4219 | 0.840511 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.20998i | − | 0.574503i | −0.957855 | − | 0.287251i | \(-0.907259\pi\) | ||
0.957855 | − | 0.287251i | \(-0.0927415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.98249 | + | 2.31300i | 0.185323 | + | 0.143723i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.81625i | − | 0.112423i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.90849i | 0.241008i | 0.992713 | + | 0.120504i | \(0.0384511\pi\) | ||||
−0.992713 | + | 0.120504i | \(0.961549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.5770i | 1.38689i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9580 | 0.976613 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.24872 | 0.563905 | 0.281952 | − | 0.959428i | \(-0.409018\pi\) | ||||
0.281952 | + | 0.959428i | \(0.409018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.5201 | −1.00352 | −0.501762 | − | 0.865006i | \(-0.667315\pi\) | ||||
−0.501762 | + | 0.865006i | \(0.667315\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.79726 | + | 2.94487i | 0.229821 | + | 0.178232i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 44.4624 | 2.68118 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.26465i | − | 0.196154i | −0.995179 | − | 0.0980769i | \(-0.968731\pi\) | ||
0.995179 | − | 0.0980769i | \(-0.0312691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.34329 | −0.319894 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1680 | 1.14347 | 0.571733 | − | 0.820440i | \(-0.306271\pi\) | ||||
0.571733 | + | 0.820440i | \(0.306271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.2780i | 1.20540i | 0.797968 | + | 0.602700i | \(0.205908\pi\) | ||||
−0.797968 | + | 0.602700i | \(0.794092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.48559 | 0.384173 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.7652 | + | 14.5529i | 1.10767 | + | 0.859029i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.81122 | 0.283013 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.6085 | 0.680501 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.07037 | 0.296214 | 0.148107 | − | 0.988971i | \(-0.452682\pi\) | ||||
0.148107 | + | 0.988971i | \(0.452682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.5500i | 1.89513i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.54637i | − | 0.263807i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.09274i | 0.525847i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.0322 | − | 16.8043i | 0.751162 | − | 0.968585i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.5333i | 0.662573i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.6085 | 0.664700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.2465i | 0.870164i | 0.900391 | + | 0.435082i | \(0.143281\pi\) | ||||
−0.900391 | + | 0.435082i | \(0.856719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.14230i | 0.0649834i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.91481 | 0.505513 | 0.252756 | − | 0.967530i | \(-0.418663\pi\) | ||||
0.252756 | + | 0.967530i | \(0.418663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9335i | 1.40932i | 0.709543 | + | 0.704662i | \(0.248902\pi\) | ||||
−0.709543 | + | 0.704662i | \(0.751098\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.23338 | − | 8.03761i | 0.351211 | − | 0.452868i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 16.1127i | − | 0.904980i | −0.891769 | − | 0.452490i | \(-0.850536\pi\) | ||
0.891769 | − | 0.452490i | \(-0.149464\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.25737i | 0.462324i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 0.0796192i | − | 0.00444391i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.88974 | −0.327714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.7625 | 0.985287 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.1081 | −1.11198 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.84076 | − | 10.1103i | 0.432275 | − | 0.557396i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.3802 | −1.23012 | −0.615062 | − | 0.788479i | \(-0.710869\pi\) | ||||
−0.615062 | + | 0.788479i | \(0.710869\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.42654i | − | 0.0781741i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.0276 | −0.930315 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.22051 | 0.120959 | 0.0604795 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604795 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.98249i | 0.270612i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.2926 | 1.31552 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9992 | − | 7.35038i | −0.917869 | − | 0.396883i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.2465 | 1.03620 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4186 | 0.935080 | 0.467540 | − | 0.883972i | \(-0.345140\pi\) | ||||
0.467540 | + | 0.883972i | \(0.345140\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.0839 | −1.55683 | −0.778413 | − | 0.627753i | \(-0.783975\pi\) | ||||
−0.778413 | + | 0.627753i | \(0.783975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.81625i | − | 0.0969445i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.02449i | 0.373876i | 0.982372 | + | 0.186938i | \(0.0598563\pi\) | ||||
−0.982372 | + | 0.186938i | \(0.940144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.68700i | − | 0.301835i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.66070 | + | 7.29918i | −0.299596 | + | 0.386313i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.1509i | − | 0.588521i | −0.955725 | − | 0.294260i | \(-0.904927\pi\) | ||
0.955725 | − | 0.294260i | \(-0.0950733\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.1540 | 0.850211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.66949i | 0.507517i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 26.8438i | − | 1.40507i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.42880 | 0.335581 | 0.167790 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167790 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 8.97551i | − | 0.467246i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.2780 | − | 9.52188i | −0.637440 | − | 0.494351i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.75527i | 0.0908842i | 0.998967 | + | 0.0454421i | \(0.0144697\pi\) | ||||
−0.998967 | + | 0.0454421i | \(0.985530\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 18.3755i | − | 0.948905i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.29878i | 0.169896i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0061 | 0.976280 | 0.488140 | − | 0.872765i | \(-0.337676\pi\) | ||||
0.488140 | + | 0.872765i | \(0.337676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.38471 | −0.275867 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.4936 | 1.45595 | 0.727977 | − | 0.685602i | \(-0.240461\pi\) | ||||
0.727977 | + | 0.685602i | \(0.240461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.3392 | + | 36.5420i | −1.44430 | + | 1.86235i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.03761 | −0.408575 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 29.3858i | − | 1.48992i | −0.667110 | − | 0.744960i | \(-0.732469\pi\) | ||
0.667110 | − | 0.744960i | \(-0.267531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.4783 | −0.883914 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.0927 | 0.660442 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.4492i | 0.576074i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.5442 | 0.780143 | 0.390071 | − | 0.920785i | \(-0.372450\pi\) | ||||
0.390071 | + | 0.920785i | \(0.372450\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.73531 | + | 3.52704i | −0.136937 | + | 0.176573i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.5595 | −0.777004 | −0.388502 | − | 0.921448i | \(-0.627007\pi\) | ||||
−0.388502 | + | 0.921448i | \(0.627007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.70478 | 0.483429 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.84444 | −0.191032 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.48559i | 0.321479i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.3565i | − | 0.907670i | −0.891086 | − | 0.453835i | \(-0.850055\pi\) | ||
0.891086 | − | 0.453835i | \(-0.149945\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 19.5595i | − | 0.964799i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.7015 | − | 13.7280i | −0.871035 | − | 0.675510i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 40.6627i | − | 1.99605i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.5910 | 0.714523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 21.1680i | − | 1.03412i | −0.855948 | − | 0.517062i | \(-0.827026\pi\) | ||
0.855948 | − | 0.517062i | \(-0.172974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.20597i | 0.107512i | 0.998554 | + | 0.0537561i | \(0.0171193\pi\) | ||||
−0.998554 | + | 0.0537561i | \(0.982881\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.83580 | −0.235125 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.1435i | 1.65620i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.89589 | + | 6.31300i | −0.236929 | + | 0.305507i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.25737i | 0.398669i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.4255i | − | 0.839358i | −0.907673 | − | 0.419679i | \(-0.862143\pi\) | ||
0.907673 | − | 0.419679i | \(-0.137857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.18549i | 0.105028i | 0.998620 | + | 0.0525139i | \(0.0167234\pi\) | ||||
−0.998620 | + | 0.0525139i | \(0.983277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.98249 | 0.334785 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.44568 | −0.404012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.5128 | 1.31311 | 0.656556 | − | 0.754277i | \(-0.272013\pi\) | ||||
0.656556 | + | 0.754277i | \(0.272013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.74213 | + | 6.77975i | 0.0829587 | + | 0.322845i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.37840 | −0.160513 | −0.0802563 | − | 0.996774i | \(-0.525574\pi\) | ||||
−0.0802563 | + | 0.996774i | \(0.525574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 61.3496i | 2.90825i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.3973 | −0.870163 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.76553 | 0.0833206 | 0.0416603 | − | 0.999132i | \(-0.486735\pi\) | ||||
0.0416603 | + | 0.999132i | \(0.486735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.8060i | 1.92148i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.88759 | −0.464560 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3214 | + | 14.5984i | −0.530755 | + | 0.684381i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.4178 | −1.14222 | −0.571108 | − | 0.820875i | \(-0.693486\pi\) | ||||
−0.571108 | + | 0.820875i | \(0.693486\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.49124 | 0.162957 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.77884 | −0.362297 | −0.181148 | − | 0.983456i | \(-0.557981\pi\) | ||||
−0.181148 | + | 0.983456i | \(0.557981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.5615i | − | 0.769678i | −0.922984 | − | 0.384839i | \(-0.874257\pi\) | ||
0.922984 | − | 0.384839i | \(-0.125743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 20.5420i | − | 0.952612i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.1103i | 0.652945i | 0.945207 | + | 0.326472i | \(0.105860\pi\) | ||||
−0.945207 | + | 0.326472i | \(0.894140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.18140 | − | 9.26004i | 0.331606 | − | 0.427589i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.3582i | 0.569437i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.5420 | 1.68020 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.4985i | 0.757002i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.87263i | 0.268889i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.74757 | 0.399687 | 0.199843 | − | 0.979828i | \(-0.435957\pi\) | ||||
0.199843 | + | 0.979828i | \(0.435957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.59097i | 0.118138i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.11723 | + | 10.4668i | −0.369347 | + | 0.476254i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.6281i | 2.02646i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.0252i | 1.40589i | 0.711246 | + | 0.702943i | \(0.248131\pi\) | ||||
−0.711246 | + | 0.702943i | \(0.751869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.57086i | 0.161480i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0446 | 0.994859 | 0.497429 | − | 0.867505i | \(-0.334277\pi\) | ||||
0.497429 | + | 0.867505i | \(0.334277\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.34099 | −0.285584 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.4783 | 0.785590 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.09274 | + | 2.39850i | 0.138728 | + | 0.107587i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.6409 | −1.81934 | −0.909668 | − | 0.415337i | \(-0.863664\pi\) | ||||
−0.909668 | + | 0.415337i | \(0.863664\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 19.5788i | − | 0.874715i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.1848 | 1.47964 | 0.739818 | − | 0.672807i | \(-0.234912\pi\) | ||||
0.739818 | + | 0.672807i | \(0.234912\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.3392 | −1.97307 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.70122i | − | 0.430846i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.5240 | −1.57457 | −0.787287 | − | 0.616586i | \(-0.788515\pi\) | ||||
−0.787287 | + | 0.616586i | \(0.788515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5984 | + | 11.3214i | 0.645793 | + | 0.500829i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.68700 | 0.0744831 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.39152 | −0.193514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.9853 | 0.966914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.49424i | − | 0.241170i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.4737i | − | 1.15984i | −0.814675 | − | 0.579918i | \(-0.803085\pi\) | ||
0.814675 | − | 0.579918i | \(-0.196915\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 41.7100i | − | 1.82385i | −0.410358 | − | 0.911924i | \(-0.634596\pi\) | ||
0.410358 | − | 0.911924i | \(-0.365404\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.4466 | + | 15.8569i | 0.892363 | + | 0.692051i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.6547i | 0.812613i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.06320 | −0.0897043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.46675i | 0.367426i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.3018i | 0.706110i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.306091 | 0.0132335 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 10.0306i | − | 0.432854i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.92038 | − | 30.8232i | −0.341155 | − | 1.32765i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.3187i | − | 0.443637i | −0.975088 | − | 0.221818i | \(-0.928801\pi\) | ||
0.975088 | − | 0.221818i | \(-0.0711992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 24.2481i | − | 1.04059i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 77.3045i | − | 3.31136i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6461 | −0.840006 | −0.420003 | − | 0.907523i | \(-0.637971\pi\) | ||||
−0.420003 | + | 0.907523i | \(0.637971\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.01955 | 0.128871 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.06403 | −0.130532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.22640 | − | 4.82873i | −0.264773 | − | 0.205339i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.48426 | 0.232794 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 30.0989i | − | 1.27533i | −0.770314 | − | 0.637665i | \(-0.779900\pi\) | ||
0.770314 | − | 0.637665i | \(-0.220100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5984 | 0.617445 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.8725 | −0.670137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.35650i | 0.267894i | 0.990988 | + | 0.133947i | \(0.0427653\pi\) | ||||
−0.990988 | + | 0.133947i | \(0.957235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.1549 | −0.805852 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.62140 | − | 2.09071i | 0.0680923 | − | 0.0878015i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.7589 | −1.58294 | −0.791469 | − | 0.611210i | \(-0.790683\pi\) | ||||
−0.791469 | + | 0.611210i | \(0.790683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.0324 | 1.21497 | 0.607484 | − | 0.794332i | \(-0.292179\pi\) | ||||
0.607484 | + | 0.794332i | \(0.292179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.49422 | 0.354851 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.9605i | 2.04179i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.4060i | 1.59886i | 0.600758 | + | 0.799431i | \(0.294866\pi\) | ||||
−0.600758 | + | 0.799431i | \(0.705134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 11.2955i | − | 0.469424i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.1134 | + | 17.1495i | 0.917420 | + | 0.711483i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 26.6992i | − | 1.10577i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.98249 | 0.288690 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 0.157054i | − | 0.00648231i | −0.999995 | − | 0.00324116i | \(-0.998968\pi\) | ||
0.999995 | − | 0.00324116i | \(-0.00103169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.01416i | 0.371422i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.38473 | −0.0980948 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.5927i | 1.54375i | 0.635776 | + | 0.771874i | \(0.280680\pi\) | ||||
−0.635776 | + | 0.771874i | \(0.719320\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.0613 | − | 21.7622i | −1.15040 | − | 0.892165i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.46338i | 0.100819i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 18.7569i | − | 0.766387i | −0.923668 | − | 0.383194i | \(-0.874824\pi\) | ||
0.923668 | − | 0.383194i | \(-0.125176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.44051i | 0.0995503i | 0.998760 | + | 0.0497751i | \(0.0158505\pi\) | ||||
−0.998760 | + | 0.0497751i | \(0.984150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.42914 | −0.180368 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.1738 | −1.51133 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.4839 | −1.64319 | −0.821596 | − | 0.570070i | \(-0.806916\pi\) | ||||
−0.821596 | + | 0.570070i | \(0.806916\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.94487 | + | 3.79726i | −0.119332 | + | 0.153873i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.78304 | 0.355324 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 8.57378i | − | 0.346292i | −0.984896 | − | 0.173146i | \(-0.944607\pi\) | ||
0.984896 | − | 0.173146i | \(-0.0553932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.5058 | 1.39141 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.3390 | 1.26166 | 0.630830 | − | 0.775921i | \(-0.282715\pi\) | ||||
0.630830 | + | 0.775921i | \(0.282715\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 41.5595i | − | 1.67042i | −0.549933 | − | 0.835209i | \(-0.685347\pi\) | ||
0.549933 | − | 0.835209i | \(-0.314653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.00632 | 0.200897 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −33.3635 | − | 25.8743i | −1.33668 | − | 1.03663i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7447 | 0.869789 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.66975 | −0.306300 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.98041 | −0.198582 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 48.0528i | − | 1.91295i | −0.291814 | − | 0.956475i | \(-0.594259\pi\) | ||
0.291814 | − | 0.956475i | \(-0.405741\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0376150i | 0.00149506i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 20.7012i | − | 0.821503i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.16416 | − | 12.3137i | −0.125368 | − | 0.487888i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1.47928i | − | 0.0585194i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9335 | −1.06381 | −0.531905 | − | 0.846804i | \(-0.678524\pi\) | ||||
−0.531905 | + | 0.846804i | \(0.678524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.2780i | 0.799685i | 0.916584 | + | 0.399843i | \(0.130935\pi\) | ||||
−0.916584 | + | 0.399843i | \(0.869065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 30.9002i | − | 1.21669i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.3928 | −0.644466 | −0.322233 | − | 0.946660i | \(-0.604433\pi\) | ||||
−0.322233 | + | 0.946660i | \(0.604433\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 38.4930i | − | 1.51098i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.1713 | + | 8.66361i | 0.437837 | + | 0.339553i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.4567i | − | 1.07447i | −0.843434 | − | 0.537233i | \(-0.819470\pi\) | ||
0.843434 | − | 0.537233i | \(-0.180530\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 50.3343i | 1.96672i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.98249i | − | 0.272413i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.1059 | −1.32858 | −0.664288 | − | 0.747477i | \(-0.731265\pi\) | ||||
−0.664288 | + | 0.747477i | \(0.731265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.0551 | −1.63575 | −0.817877 | − | 0.575393i | \(-0.804849\pi\) | ||||
−0.817877 | + | 0.575393i | \(0.804849\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.34099 | −0.246263 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.5595 | − | 10.5157i | −0.525815 | − | 0.407783i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.09274 | −0.352072 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.9144i | 0.499300i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.7280 | −0.529963 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.0405 | 1.65909 | 0.829544 | − | 0.558441i | \(-0.188600\pi\) | ||||
0.829544 | + | 0.558441i | \(0.188600\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 9.77975i | − | 0.376423i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.91811 | 0.227451 | 0.113726 | − | 0.993512i | \(-0.463722\pi\) | ||||
0.113726 | + | 0.993512i | \(0.463722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.2700 | − | 18.8220i | −0.931395 | − | 0.722321i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.48426 | 0.0568772 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.50261 | 0.0574958 | 0.0287479 | − | 0.999587i | \(-0.490848\pi\) | ||||
0.0287479 | + | 0.999587i | \(0.490848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 75.1954 | 2.87307 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.66934i | − | 0.178146i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 10.6662i | − | 0.406350i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.62599i | 0.328148i | 0.986448 | + | 0.164074i | \(0.0524636\pi\) | ||||
−0.986448 | + | 0.164074i | \(0.947536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.37148 | + | 9.50514i | −0.280019 | + | 0.361070i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 56.0941i | 2.12777i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.3357 | −1.18692 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 8.35650i | − | 0.316072i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 10.4065i | − | 0.393050i | −0.980499 | − | 0.196525i | \(-0.937034\pi\) | ||
0.980499 | − | 0.196525i | \(-0.0629656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.40659 | −0.0907661 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 18.5910i | − | 0.700176i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.7001 | − | 24.1128i | 0.703291 | − | 0.906857i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 34.8737i | − | 1.30971i | −0.755755 | − | 0.654855i | \(-0.772730\pi\) | ||
0.755755 | − | 0.654855i | \(-0.227270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.97813i | 0.111688i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.7502i | 1.00180i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.7450 | −1.18719 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.8547 | 0.741489 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.74757 | 0.326229 | 0.163115 | − | 0.986607i | \(-0.447846\pi\) | ||||
0.163115 | + | 0.986607i | \(0.447846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.85213 | − | 2.38823i | 0.0689769 | − | 0.0889422i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.57701 | 0.244602 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.7625i | 0.659683i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.7851 | −0.882140 | −0.441070 | − | 0.897473i | \(-0.645401\pi\) | ||||
−0.441070 | + | 0.897473i | \(0.645401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.0613i | 1.03788i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.79132 | −0.176971 | −0.0884857 | − | 0.996077i | \(-0.528203\pi\) | ||||
−0.0884857 | + | 0.996077i | \(0.528203\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.0644 | + | 6.69753i | −0.961398 | + | 0.247042i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.1365 | 0.741738 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.7563 | −0.506035 | −0.253018 | − | 0.967462i | \(-0.581423\pi\) | ||||
−0.253018 | + | 0.967462i | \(0.581423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.06403 | −0.112560 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.5310i | − | 0.423033i | −0.977374 | − | 0.211517i | \(-0.932160\pi\) | ||
0.977374 | − | 0.211517i | \(-0.0678402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 70.7275i | − | 2.59125i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 10.5770i | − | 0.386992i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.129094 | + | 0.166461i | −0.00471701 | + | 0.00608234i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.8541i | 1.49079i | 0.666625 | + | 0.745393i | \(0.267738\pi\) | ||||
−0.666625 | + | 0.745393i | \(0.732262\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.85827 | −0.177045 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 38.0123i | − | 1.38341i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.8196i | 1.01112i | 0.862791 | + | 0.505561i | \(0.168714\pi\) | ||||
−0.862791 | + | 0.505561i | \(0.831286\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.7606 | −0.826156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.4737i | 0.959672i | 0.877358 | + | 0.479836i | \(0.159304\pi\) | ||||
−0.877358 | + | 0.479836i | \(0.840696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.0402 | + | 32.6033i | 1.52196 | + | 1.18032i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.4219i | 0.485269i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.3778i | − | 0.555259i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.5945i | − | 1.13933i | −0.821878 | − | 0.569664i | \(-0.807073\pi\) | ||
0.821878 | − | 0.569664i | \(-0.192927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.20998 | 0.331689 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.5413 | 1.20640 | 0.603199 | − | 0.797591i | \(-0.293893\pi\) | ||||
0.603199 | + | 0.797591i | \(0.293893\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 52.2560 | 1.87709 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.31300 | + | 2.98249i | −0.0829782 | + | 0.106996i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.1417 | −0.542509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.72535i | 0.240652i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.81625 | 0.0649076 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −47.5105 | −1.69572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.03147i | − | 0.0367679i | −0.999831 | − | 0.0183840i | \(-0.994148\pi\) | ||
0.999831 | − | 0.0183840i | \(-0.00585213\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.90849 | −0.139146 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.07860 | − | 10.4169i | 0.287242 | − | 0.370384i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.48426 | −0.194752 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.5770 | −0.800724 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.2199 | 0.787070 | 0.393535 | − | 0.919310i | \(-0.371252\pi\) | ||||
0.393535 | + | 0.919310i | \(0.371252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8830i | 0.597276i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.9580i | 0.563848i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.7450i | 1.12026i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.2388 | − | 31.2062i | −1.41823 | − | 1.09988i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.24872i | 0.325570i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −52.4790 | −1.84506 | −0.922532 | − | 0.385920i | \(-0.873884\pi\) | ||||
−0.922532 | + | 0.385920i | \(0.873884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.40548i | 0.154697i | 0.997004 | + | 0.0773487i | \(0.0246455\pi\) | ||||
−0.997004 | + | 0.0773487i | \(0.975355\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.5201i | − | 0.579384i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.7280 | −0.480870 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5595i | 0.474387i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.94487 | + | 3.79726i | −0.102902 | + | 0.132687i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2067i | 0.740119i | 0.929008 | + | 0.370060i | \(0.120663\pi\) | ||||
−0.929008 | + | 0.370060i | \(0.879337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.3609i | 1.02346i | 0.859148 | + | 0.511728i | \(0.170994\pi\) | ||||
−0.859148 | + | 0.511728i | \(0.829006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 44.4624i | 1.54798i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.2161 | 0.981171 | 0.490585 | − | 0.871393i | \(-0.336783\pi\) | ||||
0.490585 | + | 0.871393i | \(0.336783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.77173 | −0.339386 | −0.169693 | − | 0.985497i | \(-0.554278\pi\) | ||||
−0.169693 | + | 0.985497i | \(0.554278\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.26465 | 0.113249 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.6698 | − | 6.08221i | 0.820108 | − | 0.210736i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 75.2694 | 2.60481 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.34329i | − | 0.184691i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.0785 | 1.21104 | 0.605522 | − | 0.795828i | \(-0.292964\pi\) | ||||
0.605522 | + | 0.795828i | \(0.292964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.7012 | 0.886249 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.1680i | 0.660180i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.2958 | 1.28301 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.6781 | − | 20.2161i | 0.538706 | − | 0.694633i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.2780 | −0.695938 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.14173 | −0.244815 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.3536 | 0.628416 | 0.314208 | − | 0.949354i | \(-0.398261\pi\) | ||||
0.314208 | + | 0.949354i | \(0.398261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.48559i | 0.221803i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.62775i | 0.260559i | 0.991477 | + | 0.130279i | \(0.0415874\pi\) | ||||
−0.991477 | + | 0.130279i | \(0.958413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 13.9075i | − | 0.474518i | −0.971446 | − | 0.237259i | \(-0.923751\pi\) | ||
0.971446 | − | 0.237259i | \(-0.0762491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.5529 | + | 18.7652i | −0.495961 | + | 0.639516i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 13.3074i | − | 0.452989i | −0.974012 | − | 0.226494i | \(-0.927274\pi\) | ||
0.974012 | − | 0.226494i | \(-0.0727265\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1223 | 0.718179 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.81122i | 0.163398i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.5397i | − | 0.459302i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.04444 | 0.272575 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.6085i | 0.392887i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −29.7940 | + | 38.4178i | −1.00722 | + | 1.29876i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.0885i | 0.847179i | 0.905854 | + | 0.423589i | \(0.139230\pi\) | ||||
−0.905854 | + | 0.423589i | \(0.860770\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.07037i | 0.171019i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.29180i | − | 0.178285i | −0.996019 | − | 0.0891426i | \(-0.971587\pi\) | ||
0.996019 | − | 0.0891426i | \(-0.0284127\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.5219 | 0.724269 | 0.362134 | − | 0.932126i | \(-0.382048\pi\) | ||||
0.362134 | + | 0.932126i | \(0.382048\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.5500 | −1.09415 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7656 | 0.495780 | 0.247890 | − | 0.968788i | \(-0.420263\pi\) | ||||
0.247890 | + | 0.968788i | \(0.420263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.2579 | + | 8.73076i | 0.377577 | + | 0.292820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.54637 | 0.152309 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.15802i | 0.272998i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.5622 | 1.28899 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.09274 | −0.303598 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.70478i | 0.323672i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.5028 | 0.683047 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.8043 | + | 13.0322i | 0.559213 | + | 0.433684i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 93.2205 | 3.09875 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.8609 | −1.55599 | −0.777995 | − | 0.628271i | \(-0.783763\pi\) | ||||
−0.777995 | + | 0.628271i | \(0.783763\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.5333 | −0.382536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54.6440i | − | 1.81044i | −0.424945 | − | 0.905219i | \(-0.639707\pi\) | ||
0.424945 | − | 0.905219i | \(-0.360293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0870i | 1.59145i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.6085i | 0.383764i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.3731 | − | 21.2286i | −0.903940 | − | 0.701029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.6186i | − | 0.944041i | −0.881588 | − | 0.472020i | \(-0.843525\pi\) | ||
0.881588 | − | 0.472020i | \(-0.156475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.2465 | −0.502389 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.68675i | 0.0884353i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.9512i | 0.458714i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.14230 | −0.0375182 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29.6885i | − | 0.974048i | −0.873389 | − | 0.487024i | \(-0.838082\pi\) | ||
0.873389 | − | 0.487024i | \(-0.161918\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4375 | − | 2.93899i | 0.374848 | − | 0.0963214i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.91481i | 0.291858i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 61.0209i | − | 1.99560i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.4055i | 1.05864i | 0.848422 | + | 0.529320i | \(0.177553\pi\) | ||||
−0.848422 | + | 0.529320i | \(0.822447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.9335 | −0.813674 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5656 | −0.344429 | −0.172214 | − | 0.985060i | \(-0.555092\pi\) | ||||
−0.172214 | + | 0.985060i | \(0.555092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.9342 | −1.46326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.03761 | + | 6.23338i | 0.261464 | + | 0.202772i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.44186 | 0.111845 | 0.0559226 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559226 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6820i | 0.411674i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1127 | 0.522491 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.5559 | −1.24895 | −0.624475 | − | 0.781045i | \(-0.714687\pi\) | ||||
−0.624475 | + | 0.781045i | \(0.714687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.6555i | 1.05671i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.25737 | −0.266923 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.7137 | + | 40.8932i | −1.02409 | + | 1.32051i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.44924 | −0.0790077 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0796192 | 0.00256569 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.4248 | 1.39790 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0322i | 0.322614i | 0.986904 | + | 0.161307i | \(0.0515709\pi\) | ||||
−0.986904 | + | 0.161307i | \(0.948429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.88974i | − | 0.189206i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.4807i | 0.913989i | 0.889469 | + | 0.456995i | \(0.151074\pi\) | ||||
−0.889469 | + | 0.456995i | \(0.848926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.5055 | − | 23.6578i | −0.977960 | − | 0.758433i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.7625i | 0.568856i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.98249 | 0.287375 | 0.143688 | − | 0.989623i | \(-0.454104\pi\) | ||||
0.143688 | + | 0.989623i | \(0.454104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 72.5510i | − | 2.31874i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 20.1081i | − | 0.642002i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1768 | −0.356484 | −0.178242 | − | 0.983987i | \(-0.557041\pi\) | ||||
−0.178242 | + | 0.983987i | \(0.557041\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.16797i | − | 0.292116i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1103 | + | 7.84076i | 0.321813 | + | 0.249574i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.2388i | 1.27952i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5500i | 0.684559i | 0.939598 | + | 0.342279i | \(0.111199\pi\) | ||||
−0.939598 | + | 0.342279i | \(0.888801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 22.3802i | − | 0.710213i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.47031 | −0.300229 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.2116 | −1.21017 | −0.605087 | − | 0.796159i | \(-0.706862\pi\) | ||||
−0.605087 | + | 0.796159i | \(0.706862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.42654 | 0.0451338 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 672.2.p.a.559.9 | 16 | ||
3.2 | odd | 2 | 2016.2.p.g.559.15 | 16 | |||
4.3 | odd | 2 | 168.2.p.a.139.7 | yes | 16 | ||
7.6 | odd | 2 | inner | 672.2.p.a.559.8 | 16 | ||
8.3 | odd | 2 | inner | 672.2.p.a.559.16 | 16 | ||
8.5 | even | 2 | 168.2.p.a.139.5 | ✓ | 16 | ||
12.11 | even | 2 | 504.2.p.g.307.10 | 16 | |||
21.20 | even | 2 | 2016.2.p.g.559.1 | 16 | |||
24.5 | odd | 2 | 504.2.p.g.307.11 | 16 | |||
24.11 | even | 2 | 2016.2.p.g.559.2 | 16 | |||
28.27 | even | 2 | 168.2.p.a.139.8 | yes | 16 | ||
56.13 | odd | 2 | 168.2.p.a.139.6 | yes | 16 | ||
56.27 | even | 2 | inner | 672.2.p.a.559.1 | 16 | ||
84.83 | odd | 2 | 504.2.p.g.307.9 | 16 | |||
168.83 | odd | 2 | 2016.2.p.g.559.16 | 16 | |||
168.125 | even | 2 | 504.2.p.g.307.12 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.p.a.139.5 | ✓ | 16 | 8.5 | even | 2 | ||
168.2.p.a.139.6 | yes | 16 | 56.13 | odd | 2 | ||
168.2.p.a.139.7 | yes | 16 | 4.3 | odd | 2 | ||
168.2.p.a.139.8 | yes | 16 | 28.27 | even | 2 | ||
504.2.p.g.307.9 | 16 | 84.83 | odd | 2 | |||
504.2.p.g.307.10 | 16 | 12.11 | even | 2 | |||
504.2.p.g.307.11 | 16 | 24.5 | odd | 2 | |||
504.2.p.g.307.12 | 16 | 168.125 | even | 2 | |||
672.2.p.a.559.1 | 16 | 56.27 | even | 2 | inner | ||
672.2.p.a.559.8 | 16 | 7.6 | odd | 2 | inner | ||
672.2.p.a.559.9 | 16 | 1.1 | even | 1 | trivial | ||
672.2.p.a.559.16 | 16 | 8.3 | odd | 2 | inner | ||
2016.2.p.g.559.1 | 16 | 21.20 | even | 2 | |||
2016.2.p.g.559.2 | 16 | 24.11 | even | 2 | |||
2016.2.p.g.559.15 | 16 | 3.2 | odd | 2 | |||
2016.2.p.g.559.16 | 16 | 168.83 | odd | 2 |