Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.8 | ||
Root | \(1.70042 + 0.329508i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.449 |
Dual form | 912.2.bn.o.65.8 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.70042 | − | 0.329508i | 0.981737 | − | 0.190242i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.87360 | + | 1.08173i | −0.837901 | + | 0.483763i | −0.856550 | − | 0.516063i | \(-0.827397\pi\) |
0.0186489 | + | 0.999826i | \(0.494064\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.41109 | −1.28927 | −0.644635 | − | 0.764490i | \(-0.722991\pi\) | ||||
−0.644635 | + | 0.764490i | \(0.722991\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.78285 | − | 1.12060i | 0.927616 | − | 0.373535i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.39878i | − | 0.723260i | −0.932322 | − | 0.361630i | \(-0.882220\pi\) | ||
0.932322 | − | 0.361630i | \(-0.117780\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.61325 | − | 2.66346i | −1.27948 | − | 0.738711i | −0.302731 | − | 0.953076i | \(-0.597898\pi\) |
−0.976754 | + | 0.214365i | \(0.931232\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82947 | + | 2.45676i | −0.730567 | + | 0.634332i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.15639 | + | 2.97704i | −1.25061 | + | 0.722039i | −0.971230 | − | 0.238142i | \(-0.923462\pi\) |
−0.279378 | + | 0.960181i | \(0.590128\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.09489 | − | 4.21915i | −0.251185 | − | 0.967939i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.80028 | + | 1.12398i | −1.26573 | + | 0.245273i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.01506 | + | 1.74074i | 0.628682 | + | 0.362970i | 0.780242 | − | 0.625478i | \(-0.215096\pi\) |
−0.151559 | + | 0.988448i | \(0.548429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.159737 | + | 0.276673i | −0.0319474 | + | 0.0553346i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.36276 | − | 2.82247i | 0.839613 | − | 0.543184i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.68230 | + | 8.10997i | −0.869481 | + | 1.50598i | −0.00695209 | + | 0.999976i | \(0.502213\pi\) |
−0.862528 | + | 0.506009i | \(0.831120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.72348i | − | 0.848362i | −0.905577 | − | 0.424181i | \(-0.860562\pi\) | ||
0.905577 | − | 0.424181i | \(-0.139438\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.790418 | − | 4.07893i | −0.137594 | − | 0.710051i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.39103 | − | 3.68986i | 1.08028 | − | 0.623701i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.54267i | − | 0.253613i | −0.991927 | − | 0.126807i | \(-0.959527\pi\) | ||
0.991927 | − | 0.126807i | \(-0.0404728\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.72209 | − | 3.00889i | −1.39665 | − | 0.481809i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.63304 | − | 8.02466i | −0.723559 | − | 1.25324i | −0.959564 | − | 0.281490i | \(-0.909171\pi\) |
0.236005 | − | 0.971752i | \(-0.424162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.248758 | − | 0.430862i | −0.0379353 | − | 0.0657058i | 0.846434 | − | 0.532493i | \(-0.178745\pi\) |
−0.884370 | + | 0.466787i | \(0.845411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00177 | + | 5.10985i | −0.596549 | + | 0.761731i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.18941 | − | 4.15081i | −1.04868 | − | 0.605458i | −0.126403 | − | 0.991979i | \(-0.540343\pi\) |
−0.922280 | + | 0.386521i | \(0.873677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.63553 | 0.662219 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.78706 | + | 6.76129i | −1.09041 | + | 0.946771i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.46423 | − | 7.73227i | 0.613209 | − | 1.06211i | −0.377487 | − | 0.926015i | \(-0.623212\pi\) |
0.990696 | − | 0.136094i | \(-0.0434549\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.59482 | + | 4.49437i | 0.349886 | + | 0.606020i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.25202 | − | 6.81354i | −0.430740 | − | 0.902476i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.192159 | + | 0.332829i | 0.0250169 | + | 0.0433306i | 0.878263 | − | 0.478178i | \(-0.158703\pi\) |
−0.853246 | + | 0.521509i | \(0.825369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.38846 | + | 2.40489i | −0.177775 | + | 0.307915i | −0.941118 | − | 0.338078i | \(-0.890223\pi\) |
0.763343 | + | 0.645993i | \(0.223556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.49255 | + | 3.82248i | −1.19595 | + | 0.481588i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.5245 | 1.42944 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.99235 | + | 2.88233i | 0.609912 | + | 0.352133i | 0.772931 | − | 0.634490i | \(-0.218790\pi\) |
−0.163019 | + | 0.986623i | \(0.552123\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.70045 | + | 1.96651i | 0.686253 | + | 0.236740i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.344463 | + | 0.596628i | 0.0408803 | + | 0.0708067i | 0.885742 | − | 0.464179i | \(-0.153650\pi\) |
−0.844861 | + | 0.534985i | \(0.820317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.06570 | + | 7.04199i | 0.475854 | + | 0.824203i | 0.999617 | − | 0.0276607i | \(-0.00880579\pi\) |
−0.523764 | + | 0.851864i | \(0.675472\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.180454 | + | 0.523095i | −0.0208370 | + | 0.0604018i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.18246i | 0.932478i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.09876 | − | 3.52112i | 0.686164 | − | 0.396157i | −0.116010 | − | 0.993248i | \(-0.537010\pi\) |
0.802173 | + | 0.597091i | \(0.203677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.48849 | − | 6.23695i | 0.720943 | − | 0.692994i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.73935i | − | 0.190919i | −0.995433 | − | 0.0954593i | \(-0.969568\pi\) | ||
0.995433 | − | 0.0954593i | \(-0.0304320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.44069 | − | 11.1556i | 0.698591 | − | 1.21000i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.28956 | + | 15.3332i | −0.567100 | + | 1.64389i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.86507 | + | 15.3547i | −0.939695 | + | 1.62760i | −0.173655 | + | 0.984806i | \(0.555558\pi\) |
−0.766040 | + | 0.642793i | \(0.777775\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.7362 | + | 9.08530i | 1.64960 | + | 0.952398i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.55643 | − | 8.03190i | −0.161394 | − | 0.832869i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.61535 | + | 6.72064i | 0.678721 | + | 0.689524i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.3326 | + | 7.12025i | −1.25219 | + | 0.722952i | −0.971544 | − | 0.236860i | \(-0.923882\pi\) |
−0.280645 | + | 0.959812i | \(0.590548\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.68808 | − | 6.67544i | −0.270163 | − | 0.670907i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.31911 | + | 5.38039i | 0.927286 | + | 0.535369i | 0.885952 | − | 0.463776i | \(-0.153506\pi\) |
0.0413340 | + | 0.999145i | \(0.486839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.9778i | 1.18021i | 0.807326 | + | 0.590105i | \(0.200914\pi\) | ||||
−0.807326 | + | 0.590105i | \(0.799086\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.65159 | − | 8.38021i | 0.941899 | − | 0.817825i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.9400 | −1.73433 | −0.867165 | − | 0.498021i | \(-0.834060\pi\) | ||||
−0.867165 | + | 0.498021i | \(0.834060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8910 | − | 8.01996i | 1.33051 | − | 0.768173i | 0.345136 | − | 0.938553i | \(-0.387833\pi\) |
0.985378 | + | 0.170380i | \(0.0544994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.508323 | − | 2.62318i | −0.0482478 | − | 0.248982i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.20466 | 0.583686 | 0.291843 | − | 0.956466i | \(-0.405732\pi\) | ||||
0.291843 | + | 0.956466i | \(0.405732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.53203 | −0.702365 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.8227 | − | 2.24238i | −1.46281 | − | 0.207308i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.5889 | − | 10.1550i | 1.61237 | − | 0.930904i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.24585 | 0.476895 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.5223 | − | 12.1187i | −0.948764 | − | 1.09270i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.5084i | − | 1.02935i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1594 | − | 9.90701i | −1.52265 | − | 0.879105i | −0.999641 | − | 0.0267797i | \(-0.991475\pi\) |
−0.523013 | − | 0.852325i | \(-0.675192\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.564966 | − | 0.650678i | −0.0497424 | − | 0.0572890i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.78152 | + | 1.02856i | −0.155652 | + | 0.0898656i | −0.575803 | − | 0.817589i | \(-0.695310\pi\) |
0.420151 | + | 0.907454i | \(0.361977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.73477 | + | 14.3919i | 0.323846 | + | 1.24794i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.12095 | + | 10.0075i | −0.440741 | + | 0.861309i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.98284 | − | 1.14479i | −0.169405 | − | 0.0978062i | 0.412900 | − | 0.910776i | \(-0.364516\pi\) |
−0.582305 | + | 0.812970i | \(0.697849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.07533 | − | 13.9869i | 0.684940 | − | 1.18635i | −0.288515 | − | 0.957475i | \(-0.593162\pi\) |
0.973456 | − | 0.228876i | \(-0.0735050\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5927 | − | 4.68914i | −1.14471 | − | 0.394897i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.38906 | + | 11.0662i | −0.534280 | + | 0.925400i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20.2598i | − | 1.68249i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.88235 | − | 1.52745i | 0.650125 | − | 0.125982i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.52225 | − | 1.45622i | 0.206631 | − | 0.119298i | −0.393114 | − | 0.919490i | \(-0.628602\pi\) |
0.599745 | + | 0.800192i | \(0.295269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.80176i | 0.553519i | 0.960939 | + | 0.276760i | \(0.0892606\pi\) | ||||
−0.960939 | + | 0.276760i | \(0.910739\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.0134 | + | 14.0629i | −0.890378 | + | 1.13692i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.10951 | + | 8.84994i | 0.410406 | + | 0.710844i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.154674 | + | 0.267903i | 0.0123443 | + | 0.0213810i | 0.872132 | − | 0.489271i | \(-0.162737\pi\) |
−0.859787 | + | 0.510652i | \(0.829404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.04321 | − | 14.6191i | 0.399953 | − | 1.15937i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2846 | − | 5.93783i | −0.810542 | − | 0.467967i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.0701 | 1.49368 | 0.746841 | − | 0.665002i | \(-0.231570\pi\) | ||||
0.746841 | + | 0.665002i | \(0.231570\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.89322 | + | 6.78729i | 0.458786 | + | 0.528390i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.09989 | + | 5.36917i | −0.239877 | + | 0.415479i | −0.960679 | − | 0.277662i | \(-0.910440\pi\) |
0.720802 | + | 0.693141i | \(0.243774\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.68804 | + | 13.3161i | 0.591388 | + | 1.02431i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.77491 | − | 10.5143i | −0.594562 | − | 0.804050i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.99652 | − | 5.19012i | −0.227821 | − | 0.394597i | 0.729341 | − | 0.684150i | \(-0.239827\pi\) |
−0.957162 | + | 0.289553i | \(0.906493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.544878 | − | 0.943756i | 0.0411889 | − | 0.0713413i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.436420 | + | 0.502630i | 0.0328034 | + | 0.0377800i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.68090 | −0.648841 | −0.324420 | − | 0.945913i | \(-0.605169\pi\) | ||||
−0.324420 | + | 0.945913i | \(0.605169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.974461 | + | 0.562605i | 0.0724311 | + | 0.0418181i | 0.535778 | − | 0.844359i | \(-0.320018\pi\) |
−0.463347 | + | 0.886177i | \(0.653352\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.56854 | + | 4.54683i | −0.115950 | + | 0.336112i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66875 | + | 2.89035i | 0.122689 | + | 0.212503i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.14128 | + | 12.3691i | 0.522222 | + | 0.904515i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.8818 | + | 9.62769i | −1.08249 | + | 0.700312i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.41621i | − | 0.102473i | −0.998687 | − | 0.0512367i | \(-0.983684\pi\) | ||
0.998687 | − | 0.0512367i | \(-0.0163163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.440846 | − | 0.254523i | 0.0317328 | − | 0.0183209i | −0.484050 | − | 0.875041i | \(-0.660835\pi\) |
0.515782 | + | 0.856720i | \(0.327501\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 19.5965 | − | 3.79743i | 1.40334 | − | 0.271940i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.04107i | − | 0.572903i | −0.958095 | − | 0.286451i | \(-0.907524\pi\) | ||
0.958095 | − | 0.286451i | \(-0.0924757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.24876 | + | 2.16291i | −0.0885221 | + | 0.153325i | −0.906887 | − | 0.421375i | \(-0.861548\pi\) |
0.818365 | + | 0.574700i | \(0.194881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.43883 | + | 3.25615i | 0.665764 | + | 0.229671i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.9717 | − | 27.6638i | 1.12100 | − | 1.94162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3610 | + | 10.0234i | 1.21254 | + | 0.700062i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3411 | + | 1.46554i | 0.718758 | + | 0.101862i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.1208 | + | 2.62640i | −0.700071 | + | 0.181672i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.71129 | − | 2.14271i | 0.255495 | − | 0.147510i | −0.366783 | − | 0.930307i | \(-0.619541\pi\) |
0.622278 | + | 0.782796i | \(0.286207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.782326 | + | 0.901014i | 0.0536041 | + | 0.0617364i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.932149 | + | 0.538176i | 0.0635720 | + | 0.0367033i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1122i | 1.09377i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.23378 | + | 10.6347i | 0.623961 | + | 0.718624i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.7169 | 2.13351 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.136033 | + | 0.0785386i | −0.00910943 | + | 0.00525933i | −0.504548 | − | 0.863384i | \(-0.668341\pi\) |
0.495438 | + | 0.868643i | \(0.335007\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.134483 | + | 0.948941i | −0.00896557 | + | 0.0632628i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.460625 | −0.0305727 | −0.0152864 | − | 0.999883i | \(-0.504866\pi\) | ||||
−0.0152864 | + | 0.999883i | \(0.504866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0794 | 0.666067 | 0.333033 | − | 0.942915i | \(-0.391928\pi\) | ||||
0.333033 | + | 0.942915i | \(0.391928\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.69619 | + | 13.9136i | 0.177396 | + | 0.915448i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.41962 | + | 1.39697i | −0.158515 | + | 0.0915185i | −0.577159 | − | 0.816632i | \(-0.695839\pi\) |
0.418644 | + | 0.908150i | \(0.362505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.9601 | 1.17159 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.21020 | − | 7.99697i | 0.598267 | − | 0.519459i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.5259i | − | 0.810233i | −0.914265 | − | 0.405117i | \(-0.867231\pi\) | ||
0.914265 | − | 0.405117i | \(-0.132769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1777 | − | 8.76287i | −0.977683 | − | 0.564466i | −0.0761135 | − | 0.997099i | \(-0.524251\pi\) |
−0.901570 | + | 0.432633i | \(0.857584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.97803 | − | 12.7434i | 0.575941 | − | 0.817492i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.68516 | + | 5.01438i | −0.554874 | + | 0.320357i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.18653 | + | 22.3802i | −0.393640 | + | 1.42402i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.573131 | − | 2.95762i | −0.0363207 | − | 0.187432i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.63458 | + | 4.98518i | 0.545010 | + | 0.314661i | 0.747107 | − | 0.664704i | \(-0.231442\pi\) |
−0.202097 | + | 0.979365i | \(0.564776\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.17566 | − | 7.23246i | 0.262522 | − | 0.454701i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.27601 | − | 21.0915i | 0.455641 | − | 1.32080i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.80570 | − | 13.5199i | 0.486906 | − | 0.843346i | −0.512981 | − | 0.858400i | \(-0.671459\pi\) |
0.999887 | + | 0.0150543i | \(0.00479212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.26218i | 0.326976i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.94205 | + | 27.8158i | −0.244006 | + | 1.72176i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.3095 | + | 11.7257i | −1.25234 | + | 0.723037i | −0.971573 | − | 0.236740i | \(-0.923921\pi\) |
−0.280764 | + | 0.959777i | \(0.590588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.3163i | 1.18659i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0148 | + | 29.0306i | −0.612896 | + | 1.77664i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.5518 | − | 21.7404i | −0.765299 | − | 1.32554i | −0.940088 | − | 0.340931i | \(-0.889258\pi\) |
0.174789 | − | 0.984606i | \(-0.444076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.23775 | − | 14.2682i | −0.500408 | − | 0.866731i | −1.00000 | 0.000470727i | \(-0.999850\pi\) | |
0.499592 | − | 0.866261i | \(-0.333483\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.7518 | + | 10.2636i | 1.80066 | + | 0.621182i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.663678 | + | 0.383175i | 0.0400213 | + | 0.0231063i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.8966 | −1.01522 | −0.507610 | − | 0.861587i | \(-0.669471\pi\) | ||||
−0.507610 | + | 0.861587i | \(0.669471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.29315 | − | 13.1447i | −0.316893 | − | 0.786955i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.36734 | + | 9.29650i | −0.320188 | + | 0.554583i | −0.980527 | − | 0.196386i | \(-0.937080\pi\) |
0.660338 | + | 0.750968i | \(0.270413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.1786 | − | 17.6298i | −0.605053 | − | 1.04798i | −0.992043 | − | 0.125899i | \(-0.959818\pi\) |
0.386990 | − | 0.922084i | \(-0.373515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.4634 | + | 9.24810i | 0.797502 | + | 0.547810i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.8037 | + | 27.3728i | 0.932864 | + | 1.61577i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.22558 | − | 15.9792i | 0.542681 | − | 0.939951i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.6245 | + | 16.1711i | −1.09179 | + | 0.947967i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.8101 | −0.806795 | −0.403397 | − | 0.915025i | \(-0.632171\pi\) | ||||
−0.403397 | + | 0.915025i | \(0.632171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.720059 | − | 0.415726i | −0.0419235 | − | 0.0242045i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.77048 | − | 10.4653i | −0.392863 | − | 0.607259i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.27280 | − | 16.0610i | −0.536260 | − | 0.928829i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.848536 | + | 1.46971i | 0.0489088 | + | 0.0847126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.6193 | + | 6.07819i | 1.01220 | + | 0.349183i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 6.00775i | − | 0.344003i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.0384379 | + | 0.0221921i | −0.00219377 | + | 0.00126657i | −0.501096 | − | 0.865391i | \(-0.667070\pi\) |
0.498903 | + | 0.866658i | \(0.333736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.94680 | + | 20.3673i | 0.224525 | + | 1.15866i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.5486i | − | 1.10850i | −0.832351 | − | 0.554248i | \(-0.813006\pi\) | ||
0.832351 | − | 0.554248i | \(-0.186994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1315 | + | 21.0124i | −0.685714 | + | 1.18769i | 0.287497 | + | 0.957781i | \(0.407177\pi\) |
−0.973212 | + | 0.229911i | \(0.926157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.6504 | − | 17.4302i | 0.769113 | − | 0.982078i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.90971 | + | 13.7000i | −0.444254 | + | 0.769470i | −0.998000 | − | 0.0632155i | \(-0.979864\pi\) |
0.553746 | + | 0.832686i | \(0.313198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.4541 | + | 11.2318i | 1.08922 | + | 0.628860i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.5056 | + | 5.91140i | −1.70266 | + | 0.329942i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.2063 | + | 18.4960i | 1.01302 | + | 1.02915i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.47382 | − | 0.850908i | 0.0817526 | − | 0.0471999i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.9778 | − | 18.2145i | 1.16008 | − | 1.00726i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.5237 | + | 14.1588i | 1.35204 | + | 0.780599i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.53614i | − | 0.469189i | −0.972093 | − | 0.234594i | \(-0.924624\pi\) | ||
0.972093 | − | 0.234594i | \(-0.0753762\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.72872 | − | 4.29302i | −0.0947334 | − | 0.235256i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4716 | −0.681395 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.61617 | + | 2.08780i | −0.196985 | + | 0.113729i | −0.595249 | − | 0.803542i | \(-0.702946\pi\) |
0.398263 | + | 0.917271i | \(0.369613\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.5505 | − | 2.04449i | 0.573026 | − | 0.111041i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.3306 | −0.613586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.06541 | 0.435491 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.8076 | + | 2.48187i | −0.689538 | + | 0.133619i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.14444 | + | 4.12484i | −0.383534 | + | 0.221433i | −0.679355 | − | 0.733810i | \(-0.737740\pi\) |
0.295821 | + | 0.955243i | \(0.404407\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0142 | 1.28545 | 0.642727 | − | 0.766096i | \(-0.277803\pi\) | ||||
0.642727 | + | 0.766096i | \(0.277803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.6440 | + | 1.40071i | −1.47553 | + | 0.0747646i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 28.6305i | − | 1.52385i | −0.647668 | − | 0.761923i | \(-0.724255\pi\) | ||
0.647668 | − | 0.761923i | \(-0.275745\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.29078 | − | 0.745230i | −0.0685073 | − | 0.0395527i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.5624 | − | 23.0634i | 1.40583 | − | 1.22064i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.22382 | − | 4.17068i | 0.381259 | − | 0.220120i | −0.297107 | − | 0.954844i | \(-0.596022\pi\) |
0.678366 | + | 0.734724i | \(0.262688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6024 | + | 9.23901i | −0.873812 | + | 0.486264i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.92014 | − | 1.72855i | 0.468186 | − | 0.0907254i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2350 | − | 8.79594i | −0.797437 | − | 0.460401i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7339 | + | 22.0558i | −0.664706 | + | 1.15130i | 0.314659 | + | 0.949205i | \(0.398110\pi\) |
−0.979365 | + | 0.202099i | \(0.935224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.8855 | − | 17.1396i | −1.13931 | − | 0.892252i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.2279 | + | 26.3755i | −0.790592 | + | 1.36935i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 20.8865i | − | 1.08146i | −0.841196 | − | 0.540731i | \(-0.818148\pi\) | ||
0.841196 | − | 0.540731i | \(-0.181852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.79212 | − | 19.5691i | −0.195824 | − | 1.01055i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 43.2012 | − | 24.9422i | 2.22497 | − | 1.28459i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 38.4960i | − | 1.97740i | −0.149893 | − | 0.988702i | \(-0.547893\pi\) | ||
0.149893 | − | 0.988702i | \(-0.452107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.4427 | − | 11.1919i | −1.66209 | − | 0.573377i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35991 | − | 7.55159i | −0.222781 | − | 0.385868i | 0.732870 | − | 0.680368i | \(-0.238180\pi\) |
−0.955651 | + | 0.294500i | \(0.904847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.85118 | − | 15.3307i | −0.451098 | − | 0.781324i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.17508 | − | 0.920263i | −0.0597328 | − | 0.0467796i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.3812 | + | 17.5406i | 1.54039 | + | 0.889343i | 0.998814 | + | 0.0486899i | \(0.0155046\pi\) |
0.541574 | + | 0.840653i | \(0.317829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.7291 | −1.04831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.69041 | + | 2.33601i | −0.135713 | + | 0.117836i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.61777 | + | 13.1944i | −0.383292 | + | 0.663881i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.21576 | − | 3.83781i | −0.111206 | − | 0.192614i | 0.805051 | − | 0.593206i | \(-0.202138\pi\) |
−0.916257 | + | 0.400592i | \(0.868805\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.0929 | + | 23.2416i | 0.555341 | + | 1.16354i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.7129 | + | 25.4834i | 0.734726 | + | 1.27258i | 0.954843 | + | 0.297109i | \(0.0960226\pi\) |
−0.220118 | + | 0.975473i | \(0.570644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5808 | + | 21.7906i | −0.626695 | + | 1.08547i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.41020 | + | 18.7043i | −0.268835 | + | 0.929426i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.70053 | −0.183428 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.64277 | − | 2.10316i | −0.180124 | − | 0.103994i | 0.407227 | − | 0.913327i | \(-0.366496\pi\) |
−0.587351 | + | 0.809333i | \(0.699829\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.74887 | − | 1.29326i | −0.184918 | − | 0.0637920i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.655471 | − | 1.13531i | −0.0322536 | − | 0.0558649i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.88150 | + | 3.25885i | 0.0923592 | + | 0.159971i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.12264 | − | 26.4444i | 0.446738 | − | 1.29499i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.54149i | − | 0.0753069i | −0.999291 | − | 0.0376534i | \(-0.988012\pi\) | ||
0.999291 | − | 0.0376534i | \(-0.0119883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.20580 | − | 1.27352i | 0.107504 | − | 0.0620676i | −0.445284 | − | 0.895389i | \(-0.646897\pi\) |
0.552788 | + | 0.833322i | \(0.313564\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.6585 | − | 3.49458i | −1.19894 | − | 0.169912i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.90218i | − | 0.0922692i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.73618 | − | 8.20330i | 0.229200 | − | 0.396985i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.21768 | + | 20.9224i | −0.348473 | + | 1.01014i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.82243 | + | 15.2809i | −0.424962 | + | 0.736055i | −0.996417 | − | 0.0845782i | \(-0.973046\pi\) |
0.571455 | + | 0.820633i | \(0.306379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8385 | + | 8.56702i | 0.713094 | + | 0.411705i | 0.812205 | − | 0.583372i | \(-0.198267\pi\) |
−0.0991119 | + | 0.995076i | \(0.531600\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.67579 | − | 34.4502i | −0.320080 | − | 1.65176i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.04330 | − | 14.6269i | 0.193417 | − | 0.699699i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.5109 | + | 14.1514i | −1.16984 | + | 0.675409i | −0.953643 | − | 0.300940i | \(-0.902700\pi\) |
−0.216200 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.9000 | − | 5.19460i | 0.614285 | − | 0.247362i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.5333 | − | 14.1643i | −1.16561 | − | 0.672966i | −0.212969 | − | 0.977059i | \(-0.568313\pi\) |
−0.952642 | + | 0.304093i | \(0.901647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 38.3583i | − | 1.81836i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.80904 | − | 3.30729i | 0.180161 | − | 0.156429i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.6491 | −1.21046 | −0.605228 | − | 0.796052i | \(-0.706918\pi\) | ||||
−0.605228 | + | 0.796052i | \(0.706918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.2494 | + | 11.1136i | −0.906419 | + | 0.523321i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.24124 | + | 11.5658i | 0.105303 | + | 0.543411i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −39.3112 | −1.84294 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7707 | −1.29906 | −0.649530 | − | 0.760336i | \(-0.725034\pi\) | ||||
−0.649530 | + | 0.760336i | \(0.725034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.0935 | + | 27.5419i | −0.657827 | + | 1.28554i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.23418 | + | 3.59931i | −0.290355 | + | 0.167636i | −0.638102 | − | 0.769952i | \(-0.720280\pi\) |
0.347747 | + | 0.937588i | \(0.386947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.54276 | −0.304068 | −0.152034 | − | 0.988375i | \(-0.548582\pi\) | ||||
−0.152034 | + | 0.988375i | \(0.548582\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.6044 | + | 13.3650i | 0.538143 | + | 0.619786i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.3832i | 1.35969i | 0.733354 | + | 0.679847i | \(0.237954\pi\) | ||||
−0.733354 | + | 0.679847i | \(0.762046\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.0293 | − | 9.83189i | −0.786342 | − | 0.453995i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.351286 | + | 0.404581i | 0.0161864 | + | 0.0186421i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.03354 | + | 0.596716i | −0.0475224 | + | 0.0274370i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.34222 | + | 0.371029i | 0.0615852 | + | 0.0170240i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.75845 | − | 26.5204i | 0.172088 | − | 1.21428i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.0915 | − | 19.1054i | −1.51199 | − | 0.872949i | −0.999902 | − | 0.0140167i | \(-0.995538\pi\) |
−0.512090 | − | 0.858932i | \(-0.671128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.10884 | + | 7.11672i | −0.187347 | + | 0.324494i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.4447 | − | 6.70793i | −0.884766 | − | 0.305221i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.4043 | − | 26.6811i | 0.699474 | − | 1.21152i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.9397i | − | 1.44733i | −0.690153 | − | 0.723663i | \(-0.742457\pi\) | ||
0.690153 | − | 0.723663i | \(-0.257543\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.4271 | − | 6.28374i | 1.46640 | − | 0.284161i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.95372 | − | 5.16943i | 0.404076 | − | 0.233293i | −0.284165 | − | 0.958775i | \(-0.591716\pi\) |
0.688241 | + | 0.725482i | \(0.258383\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 55.7576i | − | 2.51120i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.2574 | + | 9.59937i | 0.550930 | + | 0.431460i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.17499 | − | 2.03515i | −0.0527057 | − | 0.0912890i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.8210 | − | 25.6707i | −0.663479 | − | 1.14918i | −0.979695 | − | 0.200492i | \(-0.935746\pi\) |
0.316217 | − | 0.948687i | \(-0.397587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.50193 | + | 10.1513i | −0.156455 | + | 0.453526i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.2652 | + | 19.7830i | 1.52781 | + | 0.882082i | 0.999453 | + | 0.0330599i | \(0.0105252\pi\) |
0.528357 | + | 0.849022i | \(0.322808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.2804 | −1.03597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.4607 | + | 20.1096i | 0.775455 | + | 0.893100i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.22536 | + | 7.31853i | −0.187286 | + | 0.324388i | −0.944344 | − | 0.328959i | \(-0.893302\pi\) |
0.757059 | + | 0.653347i | \(0.226636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8685 | − | 24.0209i | −0.613504 | − | 1.06262i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.6852 | − | 15.3168i | −0.736668 | − | 0.676255i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.9567 | − | 22.4417i | −0.570942 | − | 0.988900i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.95688 | + | 17.2458i | −0.437903 | + | 0.758470i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.80552 | − | 7.83800i | −0.298729 | − | 0.344050i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.7517 | −1.12820 | −0.564101 | − | 0.825706i | \(-0.690777\pi\) | ||||
−0.564101 | + | 0.825706i | \(0.690777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7046 | − | 7.91236i | −0.599261 | − | 0.345983i | 0.169490 | − | 0.985532i | \(-0.445788\pi\) |
−0.768751 | + | 0.639549i | \(0.779121\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.615545 | − | 1.78432i | 0.0268646 | − | 0.0778742i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0620 | + | 24.3561i | 0.612551 | + | 1.06097i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.43963 | − | 9.42171i | −0.236506 | − | 0.409640i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.907718 | + | 0.710878i | 0.0393916 | + | 0.0308495i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.3597i | 2.13800i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.6126 | − | 19.4062i | 1.45320 | − | 0.839004i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.7612 | + | 2.86043i | −0.636991 | + | 0.123437i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 11.1196i | − | 0.478956i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.99608 | − | 6.92142i | 0.171805 | − | 0.297575i | −0.767246 | − | 0.641353i | \(-0.778373\pi\) |
0.939051 | + | 0.343778i | \(0.111707\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.84237 | + | 0.635572i | 0.0790639 | + | 0.0272750i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.3508 | + | 30.0525i | −0.743227 | + | 1.28731i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8767 | + | 18.9813i | 1.40570 | + | 0.811584i | 0.994970 | − | 0.100171i | \(-0.0319391\pi\) |
0.410734 | + | 0.911755i | \(0.365272\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.16895 | + | 8.24837i | −0.0498898 | + | 0.352032i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 39.3438 | + | 10.8758i | 1.67610 | + | 0.463323i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.8034 | + | 12.0109i | −0.884651 | + | 0.510753i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.78996 | + | 4.36494i | 0.160875 | + | 0.185282i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.79812 | − | 5.65695i | −0.415160 | − | 0.239693i | 0.277845 | − | 0.960626i | \(-0.410380\pi\) |
−0.693004 | + | 0.720934i | \(0.743713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.65023i | 0.112093i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.2189 | + | 18.6795i | 0.684761 | + | 0.788647i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.55642 | 0.149885 | 0.0749426 | − | 0.997188i | \(-0.476123\pi\) | ||||
0.0749426 | + | 0.997188i | \(0.476123\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.6251 | + | 6.71175i | −0.489071 | + | 0.282365i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.1328 | + | 21.2748i | −0.929491 | + | 0.893457i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.7017 | 1.11939 | 0.559697 | − | 0.828697i | \(-0.310918\pi\) | ||||
0.559697 | + | 0.828697i | \(0.310918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.8237 | −1.20624 | −0.603118 | − | 0.797652i | \(-0.706075\pi\) | ||||
−0.603118 | + | 0.797652i | \(0.706075\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.466653 | − | 2.40815i | −0.0194947 | − | 0.100602i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.963233 | + | 0.556123i | −0.0401696 | + | 0.0231919i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.6944 | −0.819890 | −0.409945 | − | 0.912110i | \(-0.634452\pi\) | ||||
−0.409945 | + | 0.912110i | \(0.634452\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.665755 | − | 0.578057i | 0.0276679 | − | 0.0240232i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.93308i | 0.246146i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5480 | − | 10.7087i | −0.768181 | − | 0.443509i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 32.0710 | − | 12.9145i | 1.32597 | − | 0.533947i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.7557 | − | 15.4474i | 1.10433 | − | 0.637582i | 0.166972 | − | 0.985962i | \(-0.446601\pi\) |
0.937354 | + | 0.348379i | \(0.113268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.9291 | + | 5.17169i | −0.821163 | + | 0.213096i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.64960 | − | 13.6732i | −0.108990 | − | 0.562440i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.5805 | + | 17.0783i | 1.21473 | + | 0.701323i | 0.963785 | − | 0.266679i | \(-0.0859263\pi\) |
0.250942 | + | 0.968002i | \(0.419260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.9698 | + | 38.0528i | −0.900673 | + | 1.56001i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.41071 | + | 4.08933i | −0.0577367 | + | 0.167365i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.08464 | − | 7.07481i | 0.166894 | − | 0.289069i | −0.770432 | − | 0.637522i | \(-0.779960\pi\) |
0.937326 | + | 0.348453i | \(0.113293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6875i | 0.435951i | 0.975954 | + | 0.217975i | \(0.0699453\pi\) | ||||
−0.975954 | + | 0.217975i | \(0.930055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.1229 | + | 2.42665i | 0.697298 | + | 0.0988208i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.82865 | + | 5.67457i | −0.399591 | + | 0.230704i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18.3048i | − | 0.742971i | −0.928439 | − | 0.371485i | \(-0.878849\pi\) | ||
0.928439 | − | 0.371485i | \(-0.121151\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.0432 | − | 52.3030i | 0.731146 | − | 2.11942i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.1110 | + | 38.2974i | 0.894516 | + | 1.54935i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9095 | + | 24.0920i | 0.561800 | + | 0.973067i | 0.997339 | + | 0.0728971i | \(0.0232245\pi\) |
−0.435539 | + | 0.900170i | \(0.643442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.8237 | + | 11.3233i | 1.32358 | + | 0.456601i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.62030 | − | 3.82223i | −0.266523 | − | 0.153877i | 0.360783 | − | 0.932650i | \(-0.382509\pi\) |
−0.627307 | + | 0.778772i | \(0.715843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.8851 | −1.64331 | −0.821656 | − | 0.569983i | \(-0.806950\pi\) | ||||
−0.821656 | + | 0.569983i | \(0.806950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0672 | − | 0.915457i | 0.725010 | − | 0.0367360i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.2395 | − | 52.3764i | 1.21152 | − | 2.09842i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.6503 | + | 20.1789i | 0.466011 | + | 0.807155i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.3442 | + | 7.80088i | −0.652724 | + | 0.311537i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.59259 | + | 7.95461i | 0.183119 | + | 0.317171i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.88883 | − | 5.00360i | 0.115003 | − | 0.199190i | −0.802778 | − | 0.596278i | \(-0.796646\pi\) |
0.917781 | + | 0.397087i | \(0.129979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.60470 | − | 4.86641i | 0.222767 | − | 0.193422i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.8667 | 1.70111 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.3849 | − | 12.3466i | −0.847299 | − | 0.489188i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.62717 | + | 1.27432i | 0.0643700 | + | 0.0504112i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.76090 | − | 15.1743i | −0.346035 | − | 0.599350i | 0.639506 | − | 0.768786i | \(-0.279139\pi\) |
−0.985541 | + | 0.169436i | \(0.945805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.7361 | + | 28.9878i | 0.660009 | + | 1.14317i | 0.980613 | + | 0.195955i | \(0.0627807\pi\) |
−0.320604 | + | 0.947213i | \(0.603886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.76238 | + | 0.607974i | 0.0693935 | + | 0.0239390i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 37.2892i | − | 1.46599i | −0.680234 | − | 0.732995i | \(-0.738122\pi\) | ||
0.680234 | − | 0.732995i | \(-0.261878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.798383 | − | 0.460947i | 0.0313393 | − | 0.0180937i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.30911 | + | 27.3975i | 0.208080 | + | 1.07379i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.4674i | 0.605285i | 0.953104 | + | 0.302643i | \(0.0978689\pi\) | ||||
−0.953104 | + | 0.302643i | \(0.902131\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.22524 | − | 3.85423i | 0.0869473 | − | 0.150597i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.2055 | + | 15.0408i | 0.749278 | + | 0.586796i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6487 | − | 39.2287i | 0.882268 | − | 1.52813i | 0.0334547 | − | 0.999440i | \(-0.489349\pi\) |
0.848813 | − | 0.528693i | \(-0.177318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.05122 | + | 4.07102i | 0.274261 | + | 0.158344i | 0.630822 | − | 0.775927i | \(-0.282718\pi\) |
−0.356562 | + | 0.934272i | \(0.616051\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 53.9321 | − | 10.4510i | 2.09455 | − | 0.405883i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.5656 | − | 22.9247i | −0.875055 | − | 0.888983i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.2348 | + | 16.3013i | −1.09325 | + | 0.631191i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.205434 | + | 0.178372i | −0.00794253 | + | 0.00689628i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.76881 | + | 3.33062i | 0.222702 | + | 0.128577i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.1954i | 1.12540i | 0.826662 | + | 0.562699i | \(0.190237\pi\) | ||||
−0.826662 | + | 0.562699i | \(0.809763\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0840059 | + | 1.65791i | 0.00323339 | + | 0.0638130i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.3867 | −1.62905 | −0.814527 | − | 0.580126i | \(-0.803003\pi\) | ||||
−0.814527 | + | 0.580126i | \(0.803003\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.0677 | − | 24.2878i | 1.61441 | − | 0.932080i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.783255 | + | 0.151780i | −0.0300144 | + | 0.00581621i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.4320 | −1.31750 | −0.658752 | − | 0.752360i | \(-0.728915\pi\) | ||||
−0.658752 | + | 0.752360i | \(0.728915\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.95341 | 0.189260 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.1392 | − | 3.32125i | 0.653903 | − | 0.126714i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.1892 | + | 23.7806i | −1.56918 | + | 0.905968i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0168 | −0.609308 | −0.304654 | − | 0.952463i | \(-0.598541\pi\) | ||||
−0.304654 | + | 0.952463i | \(0.598541\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.16930 | + | 22.7705i | 0.348313 | + | 0.864981i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 34.9412i | 1.32539i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.7795 | + | 27.5855i | 1.80978 | + | 1.04488i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.65406 | + | 3.17272i | −0.138209 | + | 0.120003i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.8208 | + | 13.7529i | −0.899699 | + | 0.519441i | −0.877102 | − | 0.480303i | \(-0.840527\pi\) |
−0.0225963 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.50875 | + | 1.68905i | −0.245482 | + | 0.0637039i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.5398 | − | 5.91802i | 1.15019 | − | 0.222886i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.7883 | − | 18.3530i | −1.19552 | − | 0.690236i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.3647 | + | 28.3445i | −0.614588 | + | 1.06450i | 0.375868 | + | 0.926673i | \(0.377345\pi\) |
−0.990457 | + | 0.137825i | \(0.955989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.0261 | − | 16.6330i | 0.488518 | − | 0.623787i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.22237 | − | 14.2416i | 0.307930 | − | 0.533350i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 27.6448i | − | 1.03386i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.12739 | − | 21.2993i | −0.154140 | − | 0.795436i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.0486 | − | 15.6165i | 1.00874 | − | 0.582398i | 0.0979190 | − | 0.995194i | \(-0.468781\pi\) |
0.910823 | + | 0.412797i | \(0.135448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 40.8574i | − | 1.52161i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.6959 | − | 9.89935i | −1.06721 | − | 0.368161i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.49587 | − | 2.59093i | −0.0555554 | − | 0.0962247i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.6620 | + | 27.1273i | 0.580870 | + | 1.00610i | 0.995377 | + | 0.0960497i | \(0.0306208\pi\) |
−0.414507 | + | 0.910046i | \(0.636046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.0673 | − | 24.6275i | 0.409901 | − | 0.912130i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.56539 | + | 1.48113i | 0.0948843 | + | 0.0547815i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.2383 | −0.969132 | −0.484566 | − | 0.874755i | \(-0.661023\pi\) | ||||
−0.484566 | + | 0.874755i | \(0.661023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.1161 | + | 11.3884i | −0.483795 | + | 0.420066i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.91408 | − | 11.9755i | 0.254684 | − | 0.441125i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.4088 | + | 24.9567i | 0.530035 | + | 0.918047i | 0.999386 | + | 0.0350355i | \(0.0111544\pi\) |
−0.469351 | + | 0.883011i | \(0.655512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.14524 | + | 40.0942i | −0.115543 | + | 1.47290i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.64272 | − | 16.7017i | −0.353757 | − | 0.612725i | 0.633147 | − | 0.774031i | \(-0.281763\pi\) |
−0.986904 | + | 0.161306i | \(0.948429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.15046 | + | 5.45676i | −0.115424 | + | 0.199920i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.94912 | − | 4.84035i | −0.0713147 | − | 0.177099i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 61.1951 | 2.23602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.7735 | + | 16.0350i | 1.01347 | + | 0.585127i | 0.912205 | − | 0.409733i | \(-0.134378\pi\) |
0.101263 | + | 0.994860i | \(0.467711\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.3251 | + | 5.63172i | 0.594918 | + | 0.205231i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.35764 | − | 12.7438i | −0.267772 | − | 0.463795i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.01914 | + | 8.69341i | 0.182424 | + | 0.315967i | 0.942705 | − | 0.333626i | \(-0.108272\pi\) |
−0.760282 | + | 0.649594i | \(0.774939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.71722 | − | 13.6741i | 0.171224 | − | 0.496339i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 20.1959i | − | 0.732101i | −0.930595 | − | 0.366051i | \(-0.880710\pi\) | ||
0.930595 | − | 0.366051i | \(-0.119290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.3834 | + | 27.3568i | −1.71539 | + | 0.990383i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.42245 | − | 38.2618i | 0.196049 | − | 1.38336i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.04723i | − | 0.0739212i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.6397 | − | 37.4810i | 0.780347 | − | 1.35160i | −0.151392 | − | 0.988474i | \(-0.548376\pi\) |
0.931740 | − | 0.363127i | \(-0.118291\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.81804 | − | 25.5615i | 0.317574 | − | 0.920574i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.63700 | + | 6.29947i | −0.130814 | + | 0.226576i | −0.923991 | − | 0.382415i | \(-0.875092\pi\) |
0.793177 | + | 0.608992i | \(0.208426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.30686 | + | 0.754516i | 0.0469438 | + | 0.0271030i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.73393 | + | 8.94792i | 0.0622045 | + | 0.321005i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.7846 | + | 28.3336i | −1.03131 | + | 1.01516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.43118 | − | 0.826292i | 0.0512116 | − | 0.0295670i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.46242 | + | 48.5975i | 0.0879998 | + | 1.73673i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.579595 | − | 0.334629i | −0.0206866 | − | 0.0119434i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 43.6380i | − | 1.55553i | −0.628558 | − | 0.777763i | \(-0.716355\pi\) | ||
0.628558 | − | 0.777763i | \(-0.283645\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.6709 | + | 26.6307i | −1.09191 | + | 0.948079i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1647 | −0.752529 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8107 | − | 7.39624i | 0.454920 | − | 0.262648i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.36488 | + | 32.8458i | 0.225739 | + | 1.16492i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.28414 | −0.116330 | −0.0581651 | − | 0.998307i | \(-0.518525\pi\) | ||||
−0.0581651 | + | 0.998307i | \(0.518525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 49.4285 | 1.74866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.46354 | + | 52.6642i | −0.263711 | + | 1.86080i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.8922 | − | 9.75272i | 0.596113 | − | 0.344166i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.6924 | 0.905539 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.5070 | − | 32.8319i | −1.00350 | − | 1.15574i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10.0754i | − | 0.354232i | −0.984190 | − | 0.177116i | \(-0.943323\pi\) | ||
0.984190 | − | 0.177116i | \(-0.0566768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6877 | + | 13.0988i | 0.796674 | + | 0.459960i | 0.842307 | − | 0.538998i | \(-0.181197\pi\) |
−0.0456327 | + | 0.998958i | \(0.514530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.7091 | − | 21.5475i | −0.656157 | − | 0.755704i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.7297 | + | 20.6286i | −1.25156 | + | 0.722588i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.54551 | + | 1.52129i | −0.0540704 | + | 0.0532233i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 53.9725 | + | 7.64896i | 1.88595 | + | 0.267276i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.26277 | + | 1.88376i | 0.113872 | + | 0.0657438i | 0.555854 | − | 0.831280i | \(-0.312391\pi\) |
−0.441983 | + | 0.897024i | \(0.645725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.17620 | + | 12.4295i | −0.250146 | + | 0.433266i | −0.963566 | − | 0.267471i | \(-0.913812\pi\) |
0.713419 | + | 0.700737i | \(0.247145\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.25479 | + | 0.432870i | 0.0436862 | + | 0.0150706i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.50448 | − | 16.4622i | 0.330503 | − | 0.572448i | −0.652107 | − | 0.758127i | \(-0.726115\pi\) |
0.982611 | + | 0.185678i | \(0.0594482\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13.1294i | − | 0.456004i | −0.973661 | − | 0.228002i | \(-0.926781\pi\) | ||
0.973661 | − | 0.228002i | \(-0.0732193\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.7314 | + | 5.56758i | −0.996680 | + | 0.193137i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.9026 | + | 13.8002i | −0.828177 | + | 0.478148i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 13.4129i | − | 0.464174i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.3319 | − | 20.6074i | −0.460817 | − | 0.712296i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.71399 | − | 13.3610i | −0.266317 | − | 0.461274i | 0.701591 | − | 0.712580i | \(-0.252473\pi\) |
−0.967908 | + | 0.251306i | \(0.919140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.3478 | − | 50.8319i | −1.01199 | − | 1.75282i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.06345 | + | 17.5765i | −0.208836 | + | 0.605368i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.8087 | − | 16.6327i | −0.991049 | − | 0.572183i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.8941 | −0.614847 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.1170 | − | 26.6241i | −0.793374 | − | 0.913738i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.68539 | − | 4.65123i | 0.0920540 | − | 0.159442i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.65239 | + | 9.79022i | 0.193534 | + | 0.335211i | 0.946419 | − | 0.322941i | \(-0.104672\pi\) |
−0.752885 | + | 0.658152i | \(0.771338\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.9407 | + | 11.2893i | 0.887154 | + | 0.386087i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.3851 | + | 38.7721i | 0.764659 | + | 1.32443i | 0.940427 | + | 0.339997i | \(0.110426\pi\) |
−0.175767 | + | 0.984432i | \(0.556241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4297 | + | 21.5289i | −0.424097 | + | 0.734558i | −0.996336 | − | 0.0855293i | \(-0.972742\pi\) |
0.572238 | + | 0.820087i | \(0.306075\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.8925 | + | 41.3378i | 1.22321 | + | 1.40879i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5718 | 0.632190 | 0.316095 | − | 0.948728i | \(-0.397628\pi\) | ||||
0.316095 | + | 0.948728i | \(0.397628\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.2286 | + | 6.48282i | 0.381783 | + | 0.220423i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.4221 | − | 30.2112i | 0.353952 | − | 1.02603i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.44639 | − | 14.6296i | −0.286524 | − | 0.496274i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.3540 | − | 26.5938i | −0.520249 | − | 0.901098i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.3409 | + | 33.6346i | −0.891503 | + | 1.13836i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39.2563i | 1.32710i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.9858 | − | 25.3952i | 1.48530 | − | 0.857536i | 0.485436 | − | 0.874272i | \(-0.338661\pi\) |
0.999860 | + | 0.0167363i | \(0.00532759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.4830 | + | 4.55055i | −0.792061 | + | 0.153486i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.8174i | − | 0.600282i | −0.953895 | − | 0.300141i | \(-0.902966\pi\) | ||
0.953895 | − | 0.300141i | \(-0.0970338\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.55094 | + | 7.88246i | −0.153151 | + | 0.265266i | −0.932384 | − | 0.361469i | \(-0.882276\pi\) |
0.779233 | + | 0.626734i | \(0.215609\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.36139 | − | 0.469643i | −0.0457625 | − | 0.0157869i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1470 | − | 33.1636i | 0.642894 | − | 1.11353i | −0.341890 | − | 0.939740i | \(-0.611067\pi\) |
0.984784 | − | 0.173785i | \(-0.0555998\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.5324 | + | 33.7937i | 1.96311 | + | 1.13340i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.9611 | − | 15.5645i | −0.501215 | − | 0.521429i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.64126 | + | 34.8779i | −0.322632 | + | 1.16714i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.2646 | − | 9.39035i | 0.543665 | − | 0.313885i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.0599 | − | 24.2549i | −0.703168 | − | 0.809847i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.3073 | + | 22.1167i | 1.27762 | + | 0.737634i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.1608i | 1.77104i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.92715 | + | 2.21952i | 0.0641315 | + | 0.0738610i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.43434 | −0.0809202 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.418757 | + | 0.241769i | −0.0139046 | + | 0.00802782i | −0.506936 | − | 0.861984i | \(-0.669222\pi\) |
0.493032 | + | 0.870011i | \(0.335889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.9630 | + | 4.52978i | 1.06014 | + | 0.150243i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4928 | 1.01027 | 0.505136 | − | 0.863039i | \(-0.331442\pi\) | ||||
0.505136 | + | 0.863039i | \(0.331442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.17232 | −0.138084 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.97961 | − | 10.2157i | −0.0654437 | − | 0.337721i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.07691 | − | 3.50851i | 0.200677 | − | 0.115861i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.6834 | 1.70488 | 0.852439 | − | 0.522827i | \(-0.175123\pi\) | ||||
0.852439 | + | 0.522827i | \(0.175123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0580481 | + | 0.0504016i | −0.00191275 | + | 0.00166079i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 3.66986i | − | 0.120795i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.426815 | + | 0.246422i | 0.0140336 | + | 0.00810230i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.4224 | + | 33.3325i | 0.440850 | + | 1.09478i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.520570 | + | 0.300551i | −0.0170793 | + | 0.00986077i | −0.508515 | − | 0.861053i | \(-0.669805\pi\) |
0.491436 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.07540 | − | 19.5580i | −0.166340 | − | 0.640988i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.44141 | − | 33.2407i | −0.210882 | − | 1.08825i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −26.7599 | − | 15.4498i | −0.875141 | − | 0.505263i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5574 | + | 47.7309i | −0.900262 | + | 1.55930i | −0.0731087 | + | 0.997324i | \(0.523292\pi\) |
−0.827154 | + | 0.561976i | \(0.810041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.7049 | + | 39.7274i | −0.447243 | + | 1.29645i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.5445 | − | 40.7802i | 0.767528 | − | 1.32940i | −0.171372 | − | 0.985206i | \(-0.554820\pi\) |
0.938900 | − | 0.344190i | \(-0.111847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 32.2597i | − | 1.05052i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.4680 | − | 34.1365i | 0.568234 | − | 1.11046i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.7806 | + | 11.9977i | −0.675280 | + | 0.389873i | −0.798074 | − | 0.602559i | \(-0.794148\pi\) |
0.122794 | + | 0.992432i | \(0.460815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 43.3153i | − | 1.40607i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.93555 | + | 25.9021i | −0.289755 | + | 0.839933i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.4045 | + | 31.8775i | 0.596180 | + | 1.03261i | 0.993379 | + | 0.114881i | \(0.0366488\pi\) |
−0.397199 | + | 0.917732i | \(0.630018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.53195 | + | 2.65342i | 0.0495728 | + | 0.0858626i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.7810 | + | 12.6885i | 1.18896 | + | 0.410161i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.76364 | + | 3.90499i | 0.218409 | + | 0.126099i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.68873 | 0.280281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −49.9244 | + | 20.1037i | −1.60879 | + | 0.647833i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.550647 | + | 0.953749i | −0.0177260 | + | 0.0307023i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.4881 | + | 45.8787i | 0.851799 | + | 1.47536i | 0.879583 | + | 0.475746i | \(0.157822\pi\) |
−0.0277835 | + | 0.999614i | \(0.508845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.0529 | + | 25.4519i | 1.19031 | + | 0.817633i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.19360 | − | 3.79943i | −0.0703961 | − | 0.121930i | 0.828679 | − | 0.559724i | \(-0.189093\pi\) |
−0.899075 | + | 0.437795i | \(0.855760\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.5457 | + | 47.7105i | −0.883073 | + | 1.52953i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.22572 | − | 1.93253i | 0.0712801 | − | 0.0618906i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.88126 | 0.188158 | 0.0940791 | − | 0.995565i | \(-0.470009\pi\) | ||||
0.0940791 | + | 0.995565i | \(0.470009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.8327 | + | 21.2654i | 1.17718 | + | 0.679644i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.6693 | − | 37.8846i | 0.947267 | − | 1.20956i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.7901 | − | 23.8852i | −0.439836 | − | 0.761819i | 0.557840 | − | 0.829948i | \(-0.311630\pi\) |
−0.997676 | + | 0.0681296i | \(0.978297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.69824 | + | 15.0658i | 0.277149 | + | 0.480036i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.3660 | + | 15.9951i | 1.47585 | + | 0.509129i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.73210i | − | 0.0550774i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3962 | − | 18.1266i | 0.997332 | − | 0.575810i | 0.0898745 | − | 0.995953i | \(-0.471353\pi\) |
0.907458 | + | 0.420143i | \(0.138020\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.81273 | − | 14.5150i | −0.0892593 | − | 0.460620i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.40326i | − | 0.171295i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.1181 | − | 31.3815i | 0.573806 | − | 0.993862i | −0.422364 | − | 0.906426i | \(-0.638800\pi\) |
0.996170 | − | 0.0874354i | \(-0.0278672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.35414 | − | 6.73030i | −0.137759 | − | 0.212937i |
(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 | 912.2.bn.o.449.8 | 16 | ||
3.2 | odd | 2 | 912.2.bn.n.449.7 | 16 | |||
4.3 | odd | 2 | 456.2.bf.c.449.1 | yes | 16 | ||
12.11 | even | 2 | 456.2.bf.d.449.2 | yes | 16 | ||
19.8 | odd | 6 | 912.2.bn.n.65.7 | 16 | |||
57.8 | even | 6 | inner | 912.2.bn.o.65.8 | 16 | ||
76.27 | even | 6 | 456.2.bf.d.65.2 | yes | 16 | ||
228.179 | odd | 6 | 456.2.bf.c.65.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.bf.c.65.1 | ✓ | 16 | 228.179 | odd | 6 | ||
456.2.bf.c.449.1 | yes | 16 | 4.3 | odd | 2 | ||
456.2.bf.d.65.2 | yes | 16 | 76.27 | even | 6 | ||
456.2.bf.d.449.2 | yes | 16 | 12.11 | even | 2 | ||
912.2.bn.n.65.7 | 16 | 19.8 | odd | 6 | |||
912.2.bn.n.449.7 | 16 | 3.2 | odd | 2 | |||
912.2.bn.o.65.8 | 16 | 57.8 | even | 6 | inner | ||
912.2.bn.o.449.8 | 16 | 1.1 | even | 1 | trivial |