Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3456,2,Mod(1153,3456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3456.1153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3456 = 2^{7} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3456.i (of order \(3\), degree \(2\), 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: | \(27.5962989386\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.2 | ||
Root | \(1.73202 + 0.0102491i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3456.2305 |
Dual form | 3456.2.i.l.1153.2 |
$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).
\(n\) | \(2053\) | \(2431\) | \(2945\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.551563 | + | 0.955334i | −0.246666 | + | 0.427238i | −0.962599 | − | 0.270931i | \(-0.912668\pi\) |
0.715933 | + | 0.698169i | \(0.246002\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62490 | − | 2.81442i | −0.614156 | − | 1.06375i | −0.990532 | − | 0.137282i | \(-0.956163\pi\) |
0.376376 | − | 0.926467i | \(-0.377170\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.28869 | − | 2.23208i | −0.388555 | − | 0.672997i | 0.603701 | − | 0.797211i | \(-0.293692\pi\) |
−0.992255 | + | 0.124215i | \(0.960359\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58731 | − | 2.74930i | 0.440241 | − | 0.762520i | −0.557466 | − | 0.830200i | \(-0.688226\pi\) |
0.997707 | + | 0.0676799i | \(0.0215597\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.71601 | −1.14380 | −0.571900 | − | 0.820323i | \(-0.693794\pi\) | ||||
−0.571900 | + | 0.820323i | \(0.693794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.75569 | −1.32045 | −0.660223 | − | 0.751070i | \(-0.729538\pi\) | ||||
−0.660223 | + | 0.751070i | \(0.729538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.35397 | + | 4.07719i | −0.490836 | + | 0.850152i | −0.999944 | − | 0.0105499i | \(-0.996642\pi\) |
0.509109 | + | 0.860702i | \(0.329975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.89156 | + | 3.27627i | 0.378312 | + | 0.655255i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.66250 | + | 6.34363i | 0.680108 | + | 1.17798i | 0.974947 | + | 0.222435i | \(0.0714006\pi\) |
−0.294839 | + | 0.955547i | \(0.595266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.93135 | + | 5.07724i | −0.526485 | + | 0.911899i | 0.473039 | + | 0.881042i | \(0.343157\pi\) |
−0.999524 | + | 0.0308575i | \(0.990176\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.58494 | 0.605966 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0714979 | −0.0117542 | −0.00587709 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587709 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.63887 | − | 2.83861i | 0.255949 | − | 0.443317i | −0.709204 | − | 0.705004i | \(-0.750945\pi\) |
0.965153 | + | 0.261687i | \(0.0842787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.12088 | − | 3.67347i | −0.323431 | − | 0.560198i | 0.657763 | − | 0.753225i | \(-0.271503\pi\) |
−0.981193 | + | 0.193027i | \(0.938170\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.72803 | + | 8.18919i | 0.689654 | + | 1.19452i | 0.971950 | + | 0.235188i | \(0.0755706\pi\) |
−0.282296 | + | 0.959327i | \(0.591096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.78062 | + | 3.08413i | −0.254375 | + | 0.440590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.42812 | 0.882970 | 0.441485 | − | 0.897269i | \(-0.354452\pi\) | ||||
0.441485 | + | 0.897269i | \(0.354452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.84317 | 0.383373 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.19606 | − | 7.26779i | 0.546281 | − | 0.946186i | −0.452244 | − | 0.891894i | \(-0.649377\pi\) |
0.998525 | − | 0.0542918i | \(-0.0172901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.66250 | + | 8.07568i | 0.596971 | + | 1.03398i | 0.993265 | + | 0.115861i | \(0.0369628\pi\) |
−0.396294 | + | 0.918124i | \(0.629704\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75100 | + | 3.03283i | 0.217185 | + | 0.376176i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09975 | − | 10.5651i | 0.745203 | − | 1.29073i | −0.204897 | − | 0.978783i | \(-0.565686\pi\) |
0.950100 | − | 0.311945i | \(-0.100981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.335627 | 0.0398316 | 0.0199158 | − | 0.999802i | \(-0.493660\pi\) | ||||
0.0199158 | + | 0.999802i | \(0.493660\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.8664 | 1.73998 | 0.869989 | − | 0.493071i | \(-0.164126\pi\) | ||||
0.869989 | + | 0.493071i | \(0.164126\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.18800 | + | 7.25382i | −0.477266 | + | 0.826650i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85985 | + | 8.41750i | 0.546776 | + | 0.947043i | 0.998493 | + | 0.0548820i | \(0.0174783\pi\) |
−0.451717 | + | 0.892161i | \(0.649188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.07022 | + | 5.31778i | 0.337000 | + | 0.583702i | 0.983867 | − | 0.178901i | \(-0.0572543\pi\) |
−0.646867 | + | 0.762603i | \(0.723921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.60117 | − | 4.50537i | 0.282137 | − | 0.488676i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.42812 | −0.469379 | −0.234690 | − | 0.972070i | \(-0.575407\pi\) | ||||
−0.234690 | + | 0.972070i | \(0.575407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3169 | −1.08151 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.17462 | − | 5.49861i | 0.325709 | − | 0.564145i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.39456 | + | 11.0757i | 0.649270 | + | 1.12457i | 0.983298 | + | 0.182005i | \(0.0582586\pi\) |
−0.334028 | + | 0.942563i | \(0.608408\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.80137 | − | 6.58417i | −0.378250 | − | 0.655149i | 0.612557 | − | 0.790426i | \(-0.290141\pi\) |
−0.990808 | + | 0.135277i | \(0.956808\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.62490 | − | 9.74262i | 0.554238 | − | 0.959969i | −0.443724 | − | 0.896163i | \(-0.646343\pi\) |
0.997962 | − | 0.0638053i | \(-0.0203237\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.81493 | 0.272130 | 0.136065 | − | 0.990700i | \(-0.456554\pi\) | ||||
0.136065 | + | 0.990700i | \(0.456554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6539 | −1.49937 | −0.749685 | − | 0.661795i | \(-0.769795\pi\) | ||||
−0.749685 | + | 0.661795i | \(0.769795\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1828 | + | 17.6370i | −0.957913 | + | 1.65915i | −0.230355 | + | 0.973107i | \(0.573989\pi\) |
−0.727557 | + | 0.686047i | \(0.759344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.59672 | − | 4.49765i | −0.242145 | − | 0.419408i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.66306 | + | 13.2728i | 0.702472 | + | 1.21672i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.17855 | − | 3.77337i | 0.198050 | − | 0.343033i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.68887 | −0.866599 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.09888 | 0.274981 | 0.137491 | − | 0.990503i | \(-0.456096\pi\) | ||||
0.137491 | + | 0.990503i | \(0.456096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.251085 | + | 0.434893i | −0.0219374 | + | 0.0379968i | −0.876786 | − | 0.480881i | \(-0.840317\pi\) |
0.854848 | + | 0.518878i | \(0.173650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.35244 | + | 16.1989i | 0.810960 | + | 1.40462i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.88868 | + | 8.46744i | 0.417668 | + | 0.723423i | 0.995704 | − | 0.0925885i | \(-0.0295141\pi\) |
−0.578036 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.188498 | + | 0.326488i | −0.0159882 | + | 0.0276924i | −0.873909 | − | 0.486090i | \(-0.838423\pi\) |
0.857921 | + | 0.513782i | \(0.171756\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.18221 | −0.684231 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.08038 | −0.671039 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.83712 | + | 8.37814i | −0.396272 | + | 0.686364i | −0.993263 | − | 0.115885i | \(-0.963030\pi\) |
0.596990 | + | 0.802248i | \(0.296363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.42915 | + | 14.5997i | 0.685954 | + | 1.18811i | 0.973136 | + | 0.230232i | \(0.0739484\pi\) |
−0.287181 | + | 0.957876i | \(0.592718\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.23364 | − | 5.60083i | −0.259732 | − | 0.449870i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.36262 | + | 7.55628i | −0.348175 | + | 0.603057i | −0.985925 | − | 0.167187i | \(-0.946532\pi\) |
0.637750 | + | 0.770243i | \(0.279865\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2999 | 1.20580 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2063 | −0.956067 | −0.478034 | − | 0.878342i | \(-0.658650\pi\) | ||||
−0.478034 | + | 0.878342i | \(0.658650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3806 | + | 19.7118i | −0.880657 | + | 1.52534i | −0.0300447 | + | 0.999549i | \(0.509565\pi\) |
−0.850612 | + | 0.525794i | \(0.823768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.46088 | + | 2.53033i | 0.112376 | + | 0.194640i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.9797 | + | 20.7494i | 0.910798 | + | 1.57755i | 0.812939 | + | 0.582348i | \(0.197866\pi\) |
0.0978588 | + | 0.995200i | \(0.468801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.14720 | − | 10.6473i | 0.464684 | − | 0.804857i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.9992 | −0.822121 | −0.411061 | − | 0.911608i | \(-0.634842\pi\) | ||||
−0.411061 | + | 0.911608i | \(0.634842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.2168 | 1.65136 | 0.825679 | − | 0.564140i | \(-0.190792\pi\) | ||||
0.825679 | + | 0.564140i | \(0.190792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0394356 | − | 0.0683044i | 0.00289936 | − | 0.00502184i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.07748 | + | 10.5265i | 0.444429 | + | 0.769774i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.48760 | − | 9.50479i | −0.397068 | − | 0.687743i | 0.596294 | − | 0.802766i | \(-0.296639\pi\) |
−0.993363 | + | 0.115023i | \(0.963306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.11682 | + | 12.3267i | −0.512280 | + | 0.887294i | 0.487619 | + | 0.873057i | \(0.337866\pi\) |
−0.999899 | + | 0.0142378i | \(0.995468\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.15037 | −0.580690 | −0.290345 | − | 0.956922i | \(-0.593770\pi\) | ||||
−0.290345 | + | 0.956922i | \(0.593770\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.09200 | 0.431850 | 0.215925 | − | 0.976410i | \(-0.430723\pi\) | ||||
0.215925 | + | 0.976410i | \(0.430723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.9024 | − | 20.6156i | 0.835385 | − | 1.44693i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.80788 | + | 3.13135i | 0.126268 | + | 0.218703i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.41730 | + | 12.8471i | 0.513066 | + | 0.888656i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.01985 | − | 5.23054i | 0.207895 | − | 0.360085i | −0.743156 | − | 0.669118i | \(-0.766672\pi\) |
0.951051 | + | 0.309033i | \(0.100005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.67918 | 0.319118 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.0526 | 1.29338 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.48578 | + | 12.9657i | −0.503548 | + | 0.872170i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5391 | + | 18.2542i | 0.705749 | + | 1.22239i | 0.966420 | + | 0.256966i | \(0.0827228\pi\) |
−0.260671 | + | 0.965428i | \(0.583944\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9946 | − | 25.9713i | −0.995224 | − | 1.72378i | −0.582155 | − | 0.813078i | \(-0.697790\pi\) |
−0.413069 | − | 0.910700i | \(-0.635543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.53170 | − | 16.5094i | 0.629873 | − | 1.09097i | −0.357704 | − | 0.933835i | \(-0.616440\pi\) |
0.987577 | − | 0.157136i | \(-0.0502262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.91098 | −0.518266 | −0.259133 | − | 0.965842i | \(-0.583437\pi\) | ||||
−0.259133 | + | 0.965842i | \(0.583437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4312 | −0.680457 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.96685 | + | 5.13873i | −0.191910 | + | 0.332397i | −0.945883 | − | 0.324508i | \(-0.894801\pi\) |
0.753973 | + | 0.656905i | \(0.228135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2494 | − | 24.6808i | −0.917888 | − | 1.58983i | −0.802618 | − | 0.596494i | \(-0.796560\pi\) |
−0.115270 | − | 0.993334i | \(-0.536773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.96425 | − | 3.40218i | −0.125491 | − | 0.217357i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.13607 | + | 15.8241i | −0.581314 | + | 1.00687i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6924 | −0.990498 | −0.495249 | − | 0.868751i | \(-0.664923\pi\) | ||||
−0.495249 | + | 0.868751i | \(0.664923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.1341 | 0.762866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5645 | + | 20.0304i | −0.721377 | + | 1.24946i | 0.239071 | + | 0.971002i | \(0.423157\pi\) |
−0.960448 | + | 0.278459i | \(0.910176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.116177 | + | 0.201225i | 0.00721890 | + | 0.0125035i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0737 | − | 20.9122i | −0.744494 | − | 1.28950i | −0.950431 | − | 0.310936i | \(-0.899358\pi\) |
0.205937 | − | 0.978565i | \(-0.433976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.54551 | + | 6.14100i | −0.217799 | + | 0.377239i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.45599 | 0.576542 | 0.288271 | − | 0.957549i | \(-0.406920\pi\) | ||||
0.288271 | + | 0.957549i | \(0.406920\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5750 | −0.946115 | −0.473057 | − | 0.881032i | \(-0.656850\pi\) | ||||
−0.473057 | + | 0.881032i | \(0.656850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.87526 | − | 8.44420i | 0.293989 | − | 0.509205i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.87862 | + | 4.98592i | 0.172960 | + | 0.299575i | 0.939453 | − | 0.342677i | \(-0.111334\pi\) |
−0.766494 | + | 0.642252i | \(0.778000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.99712 | − | 10.3873i | −0.357758 | − | 0.619656i | 0.629828 | − | 0.776735i | \(-0.283126\pi\) |
−0.987586 | + | 0.157079i | \(0.949792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.604018 | + | 1.04619i | −0.0359051 | + | 0.0621895i | −0.883420 | − | 0.468583i | \(-0.844765\pi\) |
0.847514 | + | 0.530772i | \(0.178098\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6520 | −0.628771 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.24075 | 0.308279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4657 | − | 18.1272i | 0.611415 | − | 1.05900i | −0.379587 | − | 0.925156i | \(-0.623934\pi\) |
0.991002 | − | 0.133846i | \(-0.0427328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.62878 | + | 8.01728i | 0.269498 | + | 0.466784i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.47295 | + | 12.9435i | 0.432172 | + | 0.748544i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.89244 | + | 11.9381i | −0.397274 | + | 0.688098i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.2866 | −0.589011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.12445 | 0.292468 | 0.146234 | − | 0.989250i | \(-0.453285\pi\) | ||||
0.146234 | + | 0.989250i | \(0.453285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.70739 | − | 8.15344i | 0.266931 | − | 0.462339i | −0.701136 | − | 0.713027i | \(-0.747324\pi\) |
0.968068 | + | 0.250688i | \(0.0806569\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.48986 | − | 16.4369i | −0.536398 | − | 0.929069i | −0.999094 | − | 0.0425521i | \(-0.986451\pi\) |
0.462696 | − | 0.886517i | \(-0.346882\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.2294 | − | 24.6461i | −0.799205 | − | 1.38426i | −0.920135 | − | 0.391602i | \(-0.871921\pi\) |
0.120930 | − | 0.992661i | \(-0.461412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.43965 | − | 16.3499i | 0.528519 | − | 0.915421i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.1439 | 1.51033 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0100 | 0.666193 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.3652 | − | 26.6133i | 0.847110 | − | 1.46724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.837151 | + | 1.44999i | 0.0460140 | + | 0.0796986i | 0.888115 | − | 0.459621i | \(-0.152015\pi\) |
−0.842101 | + | 0.539320i | \(0.818681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.72878 | + | 11.6546i | 0.367633 | + | 0.636758i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.1064 | + | 26.1651i | −0.822899 | + | 1.42530i | 0.0806146 | + | 0.996745i | \(0.474312\pi\) |
−0.903514 | + | 0.428558i | \(0.859022\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1104 | 0.818273 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.1753 | −0.603408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.46076 | + | 14.6545i | −0.454197 | + | 0.786693i | −0.998642 | − | 0.0521042i | \(-0.983407\pi\) |
0.544444 | + | 0.838797i | \(0.316741\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.92436 | + | 15.4574i | 0.477710 | + | 0.827418i | 0.999674 | − | 0.0255500i | \(-0.00813369\pi\) |
−0.521964 | + | 0.852968i | \(0.674800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.93593 | + | 12.0134i | 0.369162 | + | 0.639407i | 0.989435 | − | 0.144979i | \(-0.0463114\pi\) |
−0.620273 | + | 0.784386i | \(0.712978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.185119 | + | 0.320636i | −0.00982510 | + | 0.0170176i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.333139 | 0.0175824 | 0.00879120 | − | 0.999961i | \(-0.497202\pi\) | ||||
0.00879120 | + | 0.999961i | \(0.497202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1280 | 0.743577 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.19974 | + | 14.2024i | −0.429194 | + | 0.743386i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.5763 | + | 18.3188i | 0.552081 | + | 0.956232i | 0.998124 | + | 0.0612208i | \(0.0194994\pi\) |
−0.446043 | + | 0.895011i | \(0.647167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4451 | − | 18.0914i | −0.542281 | − | 0.939258i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33750 | − | 7.51278i | 0.224587 | − | 0.388997i | −0.731608 | − | 0.681725i | \(-0.761230\pi\) |
0.956196 | + | 0.292729i | \(0.0945632\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.2541 | 1.19765 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2538 | 0.732168 | 0.366084 | − | 0.930582i | \(-0.380698\pi\) | ||||
0.366084 | + | 0.930582i | \(0.380698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.11696 | + | 8.86283i | −0.261464 | + | 0.452869i | −0.966631 | − | 0.256172i | \(-0.917539\pi\) |
0.705167 | + | 0.709041i | \(0.250872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.61988 | − | 8.00187i | −0.235451 | − | 0.407813i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.62675 | − | 2.81761i | −0.0824793 | − | 0.142858i | 0.821835 | − | 0.569726i | \(-0.192951\pi\) |
−0.904314 | + | 0.426867i | \(0.859617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.1013 | − | 19.2281i | 0.561418 | − | 0.972405i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7220 | −0.539484 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.8709 | −1.54936 | −0.774682 | − | 0.632351i | \(-0.782090\pi\) | ||||
−0.774682 | + | 0.632351i | \(0.782090\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.01000 | − | 3.48143i | 0.100375 | − | 0.173854i | −0.811464 | − | 0.584402i | \(-0.801329\pi\) |
0.911839 | + | 0.410548i | \(0.134662\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.30592 | + | 16.1183i | 0.463561 | + | 0.802911i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0921386 | + | 0.159589i | 0.00456714 | + | 0.00791052i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.33949 | + | 5.78416i | −0.165127 | + | 0.286008i | −0.936700 | − | 0.350132i | \(-0.886137\pi\) |
0.771573 | + | 0.636140i | \(0.219470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.2728 | −1.34201 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.77367 | −0.332507 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.0507 | + | 29.5327i | −0.832982 | + | 1.44277i | 0.0626815 | + | 0.998034i | \(0.480035\pi\) |
−0.895663 | + | 0.444733i | \(0.853299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.34688 | + | 16.1893i | 0.455539 | + | 0.789017i | 0.998719 | − | 0.0505996i | \(-0.0161132\pi\) |
−0.543180 | + | 0.839616i | \(0.682780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.92060 | − | 15.4509i | −0.432713 | − | 0.749481i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.1522 | − | 26.2444i | 0.733267 | − | 1.27006i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.49967 | 0.313078 | 0.156539 | − | 0.987672i | \(-0.449966\pi\) | ||||
0.156539 | + | 0.987672i | \(0.449966\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.3266 | 1.36129 | 0.680645 | − | 0.732613i | \(-0.261700\pi\) | ||||
0.680645 | + | 0.732613i | \(0.261700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.5487 | − | 23.4670i | 0.648122 | − | 1.12258i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.82047 | + | 6.61724i | 0.182341 | + | 0.315824i | 0.942677 | − | 0.333706i | \(-0.108299\pi\) |
−0.760336 | + | 0.649530i | \(0.774966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.94625 | + | 12.0313i | 0.330026 | + | 0.571623i | 0.982517 | − | 0.186175i | \(-0.0596090\pi\) |
−0.652490 | + | 0.757797i | \(0.726276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.44238 | − | 4.23033i | 0.115780 | − | 0.200537i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.8869 | −0.560976 | −0.280488 | − | 0.959857i | \(-0.590496\pi\) | ||||
−0.280488 | + | 0.959857i | \(0.590496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.44800 | −0.397801 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.69042 | − | 9.85610i | 0.266771 | − | 0.462061i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.860741 | + | 1.49085i | 0.0402638 | + | 0.0697389i | 0.885455 | − | 0.464725i | \(-0.153847\pi\) |
−0.845191 | + | 0.534464i | \(0.820514\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.8265 | + | 27.4123i | 0.737113 | + | 1.27672i | 0.953790 | + | 0.300474i | \(0.0971447\pi\) |
−0.216677 | + | 0.976243i | \(0.569522\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.71702 | − | 2.97396i | 0.0797966 | − | 0.138212i | −0.823366 | − | 0.567511i | \(-0.807906\pi\) |
0.903162 | + | 0.429300i | \(0.141240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.5333 | 0.718797 | 0.359398 | − | 0.933184i | \(-0.382982\pi\) | ||||
0.359398 | + | 0.933184i | \(0.382982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.6460 | −1.83068 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.46631 | + | 9.46792i | −0.251341 | + | 0.435335i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8872 | − | 18.8572i | −0.499540 | − | 0.865228i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6927 | + | 28.9126i | 0.762710 | + | 1.32105i | 0.941449 | + | 0.337156i | \(0.109465\pi\) |
−0.178739 | + | 0.983897i | \(0.557202\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.113489 | + | 0.196569i | −0.00517467 | + | 0.00896280i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.1080 | −0.640612 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.0794 | −0.909883 | −0.454941 | − | 0.890521i | \(-0.650340\pi\) | ||||
−0.454941 | + | 0.890521i | \(0.650340\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.10538 | − | 3.64663i | 0.0950146 | − | 0.164570i | −0.814600 | − | 0.580023i | \(-0.803044\pi\) |
0.909615 | + | 0.415453i | \(0.136377\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.2724 | − | 29.9166i | −0.777908 | − | 1.34738i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.545361 | − | 0.944593i | −0.0244628 | − | 0.0423708i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.24770 | + | 9.08928i | −0.234919 | + | 0.406892i | −0.959249 | − | 0.282561i | \(-0.908816\pi\) |
0.724330 | + | 0.689453i | \(0.242149\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.5118 | 1.53881 | 0.769403 | − | 0.638764i | \(-0.220554\pi\) | ||||
0.769403 | + | 0.638764i | \(0.220554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.38677 | 0.373206 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.62702 | − | 4.55013i | 0.116440 | − | 0.201681i | −0.801914 | − | 0.597439i | \(-0.796185\pi\) |
0.918355 | + | 0.395758i | \(0.129518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.1564 | − | 41.8402i | −1.06862 | − | 1.85090i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.20497 | + | 10.7473i | 0.273424 | + | 0.473584i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1859 | − | 21.1066i | 0.535937 | − | 0.928269i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.9218 | 0.566113 | 0.283056 | − | 0.959103i | \(-0.408652\pi\) | ||||
0.283056 | + | 0.959103i | \(0.408652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.10475 | 0.223215 | 0.111607 | − | 0.993752i | \(-0.464400\pi\) | ||||
0.111607 | + | 0.993752i | \(0.464400\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.8243 | − | 23.9443i | 0.602194 | − | 1.04303i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.417694 | + | 0.723468i | 0.0181606 | + | 0.0314551i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.20281 | − | 9.01153i | −0.225359 | − | 0.390333i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.55261 | + | 2.68920i | −0.0671252 | + | 0.116264i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.17869 | 0.395354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.9746 | −1.63266 | −0.816328 | − | 0.577589i | \(-0.803994\pi\) | ||||
−0.816328 | + | 0.577589i | \(0.803994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.63410 | − | 14.9547i | 0.369844 | − | 0.640589i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.9350 | + | 27.6003i | 0.681332 | + | 1.18010i | 0.974575 | + | 0.224063i | \(0.0719323\pi\) |
−0.293243 | + | 0.956038i | \(0.594734\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.0802 | − | 36.5120i | −0.898046 | − | 1.55546i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.7936 | − | 27.3553i | 0.671611 | − | 1.16326i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.5906 | 0.491111 | 0.245555 | − | 0.969383i | \(-0.421030\pi\) | ||||
0.245555 | + | 0.969383i | \(0.421030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4660 | −0.569550 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.25138 | + | 2.16745i | −0.0527392 | + | 0.0913470i | −0.891190 | − | 0.453631i | \(-0.850129\pi\) |
0.838451 | + | 0.544978i | \(0.183462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2328 | − | 19.4559i | −0.472569 | − | 0.818514i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.9597 | − | 22.4469i | −0.543301 | − | 0.941024i | −0.998712 | − | 0.0507432i | \(-0.983841\pi\) |
0.455411 | − | 0.890281i | \(-0.349492\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.03679 | − | 8.72398i | 0.210783 | − | 0.365087i | −0.741177 | − | 0.671310i | \(-0.765732\pi\) |
0.951960 | + | 0.306223i | \(0.0990653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.8106 | −0.742755 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4726 | −0.977177 | −0.488588 | − | 0.872514i | \(-0.662488\pi\) | ||||
−0.488588 | + | 0.872514i | \(0.662488\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.97762 | − | 17.2818i | 0.413942 | − | 0.716968i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.28385 | − | 14.3481i | −0.343082 | − | 0.594236i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.4138 | + | 21.5012i | 0.512370 | + | 0.887451i | 0.999897 | + | 0.0143435i | \(0.00456582\pi\) |
−0.487527 | + | 0.873108i | \(0.662101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.8719 | − | 29.2230i | 0.695195 | − | 1.20411i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.70977 | 0.316602 | 0.158301 | − | 0.987391i | \(-0.449398\pi\) | ||||
0.158301 | + | 0.987391i | \(0.449398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.9066 | −0.693104 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.7176 | + | 25.4916i | −0.601344 | + | 1.04156i | 0.391274 | + | 0.920274i | \(0.372035\pi\) |
−0.992618 | + | 0.121284i | \(0.961299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.76388 | − | 3.05514i | −0.0719503 | − | 0.124622i | 0.827806 | − | 0.561015i | \(-0.189589\pi\) |
−0.899756 | + | 0.436393i | \(0.856256\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.40322 | + | 4.16250i | 0.0977047 | + | 0.169230i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3211 | − | 23.0728i | 0.540687 | − | 0.936497i | −0.458178 | − | 0.888860i | \(-0.651498\pi\) |
0.998865 | − | 0.0476362i | \(-0.0151688\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.0194 | 1.21446 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.706406 | 0.0285315 | 0.0142657 | − | 0.999898i | \(-0.495459\pi\) | ||||
0.0142657 | + | 0.999898i | \(0.495459\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.58480 | + | 14.8693i | −0.345611 | + | 0.598616i | −0.985465 | − | 0.169881i | \(-0.945662\pi\) |
0.639853 | + | 0.768497i | \(0.278995\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.17800 | + | 7.23651i | 0.167928 | + | 0.290860i | 0.937691 | − | 0.347470i | \(-0.112959\pi\) |
−0.769763 | + | 0.638330i | \(0.779626\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.19526 | + | 12.4626i | 0.288272 | + | 0.499302i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.11377 | + | 7.12526i | −0.164551 | + | 0.285010i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.337185 | 0.0134444 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.9865 | −0.954889 | −0.477444 | − | 0.878662i | \(-0.658437\pi\) | ||||
−0.477444 | + | 0.878662i | \(0.658437\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.70923 | + | 2.96047i | −0.0678286 | + | 0.117483i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.65281 | + | 9.79095i | 0.223972 | + | 0.387932i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.58068 | − | 11.3981i | −0.259921 | − | 0.450197i | 0.706299 | − | 0.707913i | \(-0.250363\pi\) |
−0.966221 | + | 0.257716i | \(0.917030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.85931 | + | 13.6127i | −0.309941 | + | 0.536834i | −0.978349 | − | 0.206961i | \(-0.933643\pi\) |
0.668408 | + | 0.743795i | \(0.266976\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.5146 | −0.924455 | −0.462228 | − | 0.886761i | \(-0.652950\pi\) | ||||
−0.462228 | + | 0.886761i | \(0.652950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.6297 | −0.849040 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1340 | − | 22.7487i | 0.513971 | − | 0.890224i | −0.485897 | − | 0.874016i | \(-0.661507\pi\) |
0.999869 | − | 0.0162084i | \(-0.00515952\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.276979 | − | 0.479741i | −0.0108224 | − | 0.0187450i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.2710 | + | 22.9860i | 0.516963 | + | 0.895406i | 0.999806 | + | 0.0196993i | \(0.00627088\pi\) |
−0.482843 | + | 0.875707i | \(0.660396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.981745 | − | 1.70043i | 0.0381855 | − | 0.0661392i | −0.846301 | − | 0.532705i | \(-0.821176\pi\) |
0.884487 | + | 0.466566i | \(0.154509\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.6338 | −0.800145 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.4856 | −1.33529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0170 | − | 20.8141i | 0.463912 | − | 0.803519i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9859 | − | 32.8846i | −0.731854 | − | 1.26761i | −0.956090 | − | 0.293073i | \(-0.905322\pi\) |
0.224236 | − | 0.974535i | \(-0.428011\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.5894 | + | 23.5375i | 0.522282 | + | 0.904619i | 0.999664 | + | 0.0259229i | \(0.00825242\pi\) |
−0.477382 | + | 0.878696i | \(0.658414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7811 | − | 35.9939i | 0.797505 | − | 1.38132i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.9121 | −1.79504 | −0.897520 | − | 0.440974i | \(-0.854633\pi\) | ||||
−0.897520 | + | 0.440974i | \(0.854633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.7857 | −0.412099 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.2034 | − | 17.6728i | 0.388719 | − | 0.673282i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6750 | + | 21.9538i | 0.482181 | + | 0.835161i | 0.999791 | − | 0.0204552i | \(-0.00651153\pi\) |
−0.517610 | + | 0.855617i | \(0.673178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.207937 | − | 0.360157i | −0.00788750 | − | 0.0136616i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.72895 | + | 13.3869i | −0.292755 | + | 0.507066i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.2840 | 1.67258 | 0.836292 | − | 0.548284i | \(-0.184719\pi\) | ||||
0.836292 | + | 0.548284i | \(0.184719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.411520 | 0.0155208 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.3537 | + | 21.3973i | −0.464609 | + | 0.804727i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.80457 | − | 13.5179i | −0.293107 | − | 0.507676i | 0.681436 | − | 0.731878i | \(-0.261356\pi\) |
−0.974543 | + | 0.224202i | \(0.928022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8006 | − | 23.9033i | −0.516836 | − | 0.895185i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.51300 | − | 7.81675i | 0.168777 | − | 0.292330i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.1560 | 0.788985 | 0.394493 | − | 0.918899i | \(-0.370920\pi\) | ||||
0.394493 | + | 0.918899i | \(0.370920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.5597 | −1.36155 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.8556 | + | 23.9987i | −0.514586 | + | 0.891289i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.9909 | + | 22.5009i | 0.481805 | + | 0.834511i | 0.999782 | − | 0.0208834i | \(-0.00664789\pi\) |
−0.517977 | + | 0.855395i | \(0.673315\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0021 | + | 17.3241i | 0.369940 | + | 0.640755i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.41447 | + | 9.37814i | −0.199988 | + | 0.346390i | −0.948524 | − | 0.316704i | \(-0.897424\pi\) |
0.748536 | + | 0.663094i | \(0.230757\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.4427 | −1.15821 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.4520 | 0.421270 | 0.210635 | − | 0.977565i | \(-0.432447\pi\) | ||||
0.210635 | + | 0.977565i | \(0.432447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0077 | − | 41.5826i | 0.880758 | − | 1.52552i | 0.0302573 | − | 0.999542i | \(-0.490367\pi\) |
0.850500 | − | 0.525975i | \(-0.176299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.33595 | − | 9.24213i | −0.195494 | − | 0.338605i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.57399 | − | 7.92239i | −0.167130 | − | 0.289478i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5881 | + | 39.1238i | −0.824253 | + | 1.42765i | 0.0782360 | + | 0.996935i | \(0.475071\pi\) |
−0.902489 | + | 0.430713i | \(0.858262\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.5968 | −0.676807 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.5457 | −0.601365 | −0.300682 | − | 0.953724i | \(-0.597214\pi\) | ||||
−0.300682 | + | 0.953724i | \(0.597214\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.6826 | − | 35.8234i | 0.749745 | − | 1.29860i | −0.198200 | − | 0.980162i | \(-0.563509\pi\) |
0.947945 | − | 0.318435i | \(-0.103157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.4361 | + | 44.0565i | 0.920847 | + | 1.59495i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.3209 | − | 23.0725i | −0.480990 | − | 0.833100i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.22518 | + | 5.58617i | −0.116303 | + | 0.201443i | −0.918300 | − | 0.395886i | \(-0.870438\pi\) |
0.801997 | + | 0.597328i | \(0.203771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.949001 | −0.0341332 | −0.0170666 | − | 0.999854i | \(-0.505433\pi\) | ||||
−0.0170666 | + | 0.999854i | \(0.505433\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.1792 | −0.796702 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.43285 | + | 16.3382i | −0.337967 | + | 0.585376i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.432519 | − | 0.749145i | −0.0154767 | − | 0.0268065i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.81251 | − | 8.33552i | −0.171766 | − | 0.297507i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.6992 | − | 30.6559i | 0.630909 | − | 1.09277i | −0.356458 | − | 0.934312i | \(-0.616016\pi\) |
0.987366 | − | 0.158454i | \(-0.0506511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 66.1840 | 2.35323 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.6033 | 1.05125 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.42624 | + | 2.47032i | −0.0505200 | + | 0.0875032i | −0.890180 | − | 0.455610i | \(-0.849421\pi\) |
0.839660 | + | 0.543113i | \(0.182755\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.2974 | − | 38.6203i | −0.788826 | − | 1.36629i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.1582 | − | 33.1829i | −0.676077 | − | 1.17100i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.43883 | + | 14.6165i | −0.297430 | + | 0.515164i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.18770 | 0.0769155 | 0.0384577 | − | 0.999260i | \(-0.487756\pi\) | ||||
0.0384577 | + | 0.999260i | \(0.487756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.54428 | −0.264915 | −0.132458 | − | 0.991189i | \(-0.542287\pi\) | ||||
−0.132458 | + | 0.991189i | \(0.542287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.73251 | − | 11.6610i | 0.235830 | − | 0.408469i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.2071 | + | 21.1433i | 0.427073 | + | 0.739712i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.5333 | − | 32.1006i | −0.646815 | − | 1.12032i | −0.983879 | − | 0.178835i | \(-0.942767\pi\) |
0.337064 | − | 0.941482i | \(-0.390566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.9008 | + | 37.9334i | −0.763416 | + | 1.32227i | 0.177665 | + | 0.984091i | \(0.443146\pi\) |
−0.941080 | + | 0.338184i | \(0.890188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4192 | 0.431859 | 0.215929 | − | 0.976409i | \(-0.430722\pi\) | ||||
0.215929 | + | 0.976409i | \(0.430722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.1889 | 0.527532 | 0.263766 | − | 0.964587i | \(-0.415035\pi\) | ||||
0.263766 | + | 0.964587i | \(0.415035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.39744 | − | 14.5448i | 0.290954 | − | 0.503947i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.5542 | − | 21.7445i | −0.434457 | − | 0.752501i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.7428 | − | 42.8557i | −0.854215 | − | 1.47954i | −0.877372 | − | 0.479811i | \(-0.840705\pi\) |
0.0231569 | − | 0.999732i | \(-0.492628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.3278 | + | 21.3523i | −0.425095 | + | 0.736286i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.22308 | −0.110877 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.1598 | −0.486535 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.168304 | − | 0.291510i | 0.00576937 | − | 0.00999284i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.36674 | + | 11.0275i | 0.217993 | + | 0.377575i | 0.954194 | − | 0.299188i | \(-0.0967157\pi\) |
−0.736201 | + | 0.676763i | \(0.763382\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.6560 | + | 18.4567i | 0.364001 | + | 0.630467i | 0.988615 | − | 0.150466i | \(-0.0480773\pi\) |
−0.624615 | + | 0.780933i | \(0.714744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.26681 | − | 10.8544i | 0.213821 | − | 0.370348i | −0.739086 | − | 0.673611i | \(-0.764743\pi\) |
0.952907 | + | 0.303262i | \(0.0980759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.1767 | −1.67399 | −0.836997 | − | 0.547207i | \(-0.815691\pi\) | ||||
−0.836997 | + | 0.547207i | \(0.815691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.4302 | −0.898653 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.5257 | − | 21.6951i | 0.424905 | − | 0.735956i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.3644 | − | 33.5401i | −0.656137 | − | 1.13646i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.7435 | + | 27.2685i | 0.532227 | + | 0.921844i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.06962 | − | 1.85264i | 0.0361185 | − | 0.0625591i | −0.847401 | − | 0.530953i | \(-0.821834\pi\) |
0.883520 | + | 0.468394i | \(0.155167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.40791 | 0.249579 | 0.124789 | − | 0.992183i | \(-0.460174\pi\) | ||||
0.124789 | + | 0.992183i | \(0.460174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.0800 | −0.339221 | −0.169610 | − | 0.985511i | \(-0.554251\pi\) | ||||
−0.169610 | + | 0.985511i | \(0.554251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.6871 | + | 28.9028i | −0.560297 | + | 0.970462i | 0.437174 | + | 0.899377i | \(0.355980\pi\) |
−0.997470 | + | 0.0710852i | \(0.977354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.03538 | − | 8.72154i | −0.168881 | − | 0.292511i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.2131 | − | 47.1344i | −0.910651 | − | 1.57729i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.06676 | − | 10.5079i | 0.202790 | − | 0.351242i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42.9442 | −1.43227 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.3151 | −1.00994 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.2539 | + | 21.2244i | −0.407334 | + | 0.705524i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5436 | + | 42.5107i | 0.814955 | + | 1.41154i | 0.909360 | + | 0.416010i | \(0.136572\pi\) |
−0.0944045 | + | 0.995534i | \(0.530095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.31861 | − | 12.6762i | −0.242476 | − | 0.419981i | 0.718943 | − | 0.695069i | \(-0.244626\pi\) |
−0.961419 | + | 0.275088i | \(0.911293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.91313 | − | 13.7059i | 0.261886 | − | 0.453600i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.63196 | 0.0538920 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.03261 | 0.166011 | 0.0830053 | − | 0.996549i | \(-0.473548\pi\) | ||||
0.0830053 | + | 0.996549i | \(0.473548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.532744 | − | 0.922740i | 0.0175355 | − | 0.0303724i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.135242 | − | 0.234247i | −0.00444674 | − | 0.00770198i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.75518 | − | 15.1644i | −0.287248 | − | 0.497528i | 0.685904 | − | 0.727692i | \(-0.259407\pi\) |
−0.973152 | + | 0.230164i | \(0.926074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.2487 | − | 17.7513i | 0.335888 | − | 0.581776i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.4084 | −0.438503 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.7518 | −0.775936 | −0.387968 | − | 0.921673i | \(-0.626823\pi\) | ||||
−0.387968 | + | 0.921673i | \(0.626823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.97367 | − | 3.41849i | 0.0643397 | − | 0.111440i | −0.832061 | − | 0.554684i | \(-0.812839\pi\) |
0.896401 | + | 0.443244i | \(0.146173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.71571 | + | 13.3640i | 0.251258 | + | 0.435191i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.45686 | + | 9.45155i | 0.177324 | + | 0.307134i | 0.940963 | − | 0.338509i | \(-0.109923\pi\) |
−0.763639 | + | 0.645643i | \(0.776589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.5976 | − | 40.8722i | 0.766010 | − | 1.32677i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.6348 | 1.67261 | 0.836307 | − | 0.548261i | \(-0.184710\pi\) | ||||
0.836307 | + | 0.548261i | \(0.184710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.1070 | 0.391774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.8873 | − | 27.5176i | 0.513027 | − | 0.888588i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.68558 | − | 2.91951i | −0.0543735 | − | 0.0941776i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.85074 | − | 13.5979i | −0.252724 | − | 0.437731i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.2718 | − | 22.9875i | 0.426793 | − | 0.739228i | −0.569793 | − | 0.821788i | \(-0.692976\pi\) |
0.996586 | + | 0.0825607i | \(0.0263098\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.9365 | 0.639792 | 0.319896 | − | 0.947453i | \(-0.396352\pi\) | ||||
0.319896 | + | 0.947453i | \(0.396352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22517 | 0.0392770 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.9725 | − | 39.7895i | 0.734956 | − | 1.27298i | −0.219787 | − | 0.975548i | \(-0.570536\pi\) |
0.954743 | − | 0.297433i | \(-0.0961303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.70647 | + | 9.88390i | 0.182380 | + | 0.315891i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0873 | + | 27.8640i | 0.513105 | + | 0.888725i | 0.999884 | + | 0.0151995i | \(0.00483833\pi\) |
−0.486779 | + | 0.873525i | \(0.661828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.49544 | − | 7.78633i | 0.143237 | − | 0.248093i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.9699 | 0.635005 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.32904 | 0.296347 | 0.148173 | − | 0.988961i | \(-0.452661\pi\) | ||||
0.148173 | + | 0.988961i | \(0.452661\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.36012 | + | 5.81990i | −0.106523 | + | 0.184503i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.13466 | − | 15.8217i | −0.289297 | − | 0.501078i | 0.684345 | − | 0.729159i | \(-0.260088\pi\) |
−0.973642 | + | 0.228081i | \(0.926755\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3456.2.i.l.2305.2 | 12 | ||
3.2 | odd | 2 | 1152.2.i.k.769.4 | yes | 12 | ||
4.3 | odd | 2 | 3456.2.i.k.2305.2 | 12 | |||
8.3 | odd | 2 | 3456.2.i.i.2305.5 | 12 | |||
8.5 | even | 2 | 3456.2.i.j.2305.5 | 12 | |||
9.2 | odd | 6 | 1152.2.i.k.385.4 | yes | 12 | ||
9.7 | even | 3 | inner | 3456.2.i.l.1153.2 | 12 | ||
12.11 | even | 2 | 1152.2.i.i.769.3 | yes | 12 | ||
24.5 | odd | 2 | 1152.2.i.j.769.3 | yes | 12 | ||
24.11 | even | 2 | 1152.2.i.l.769.4 | yes | 12 | ||
36.7 | odd | 6 | 3456.2.i.k.1153.2 | 12 | |||
36.11 | even | 6 | 1152.2.i.i.385.3 | ✓ | 12 | ||
72.11 | even | 6 | 1152.2.i.l.385.4 | yes | 12 | ||
72.29 | odd | 6 | 1152.2.i.j.385.3 | yes | 12 | ||
72.43 | odd | 6 | 3456.2.i.i.1153.5 | 12 | |||
72.61 | even | 6 | 3456.2.i.j.1153.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.i.385.3 | ✓ | 12 | 36.11 | even | 6 | ||
1152.2.i.i.769.3 | yes | 12 | 12.11 | even | 2 | ||
1152.2.i.j.385.3 | yes | 12 | 72.29 | odd | 6 | ||
1152.2.i.j.769.3 | yes | 12 | 24.5 | odd | 2 | ||
1152.2.i.k.385.4 | yes | 12 | 9.2 | odd | 6 | ||
1152.2.i.k.769.4 | yes | 12 | 3.2 | odd | 2 | ||
1152.2.i.l.385.4 | yes | 12 | 72.11 | even | 6 | ||
1152.2.i.l.769.4 | yes | 12 | 24.11 | even | 2 | ||
3456.2.i.i.1153.5 | 12 | 72.43 | odd | 6 | |||
3456.2.i.i.2305.5 | 12 | 8.3 | odd | 2 | |||
3456.2.i.j.1153.5 | 12 | 72.61 | even | 6 | |||
3456.2.i.j.2305.5 | 12 | 8.5 | even | 2 | |||
3456.2.i.k.1153.2 | 12 | 36.7 | odd | 6 | |||
3456.2.i.k.2305.2 | 12 | 4.3 | odd | 2 | |||
3456.2.i.l.1153.2 | 12 | 9.7 | even | 3 | inner | ||
3456.2.i.l.2305.2 | 12 | 1.1 | even | 1 | trivial |