Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.d.361.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.50000 | + | 2.59808i | −0.530330 | + | 0.918559i | 0.469044 | + | 0.883175i | \(0.344599\pi\) |
−0.999374 | + | 0.0353837i | \(0.988735\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.0625000 | − | 0.108253i | ||||
\(5\) | 9.00000 | − | 15.5885i | 0.804984 | − | 1.39427i | −0.111317 | − | 0.993785i | \(-0.535507\pi\) |
0.916302 | − | 0.400489i | \(-0.131160\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 27.0000 | + | 46.7654i | 0.853815 | + | 1.47885i | ||||
\(11\) | −18.0000 | − | 31.1769i | −0.493382 | − | 0.854563i | 0.506589 | − | 0.862188i | \(-0.330906\pi\) |
−0.999971 | + | 0.00762479i | \(0.997573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.0000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 35.5000 | − | 61.4878i | 0.554688 | − | 0.960747i | ||||
\(17\) | −21.0000 | − | 36.3731i | −0.299603 | − | 0.518927i | 0.676442 | − | 0.736496i | \(-0.263521\pi\) |
−0.976045 | + | 0.217568i | \(0.930187\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −62.0000 | + | 107.387i | −0.748620 | + | 1.29665i | 0.199865 | + | 0.979824i | \(0.435950\pi\) |
−0.948484 | + | 0.316824i | \(0.897384\pi\) | |||||||
\(20\) | −18.0000 | −0.201246 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 108.000 | 1.04662 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −99.5000 | − | 172.339i | −0.796000 | − | 1.37871i | ||||
\(26\) | −51.0000 | + | 88.3346i | −0.384689 | + | 0.666301i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −102.000 | −0.653135 | −0.326568 | − | 0.945174i | \(-0.605892\pi\) | ||||
−0.326568 | + | 0.945174i | \(0.605892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −80.0000 | − | 138.564i | −0.463498 | − | 0.802801i | 0.535635 | − | 0.844450i | \(-0.320072\pi\) |
−0.999132 | + | 0.0416484i | \(0.986739\pi\) | |||||||
\(32\) | 22.5000 | + | 38.9711i | 0.124296 | + | 0.215287i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 126.000 | 0.635554 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −199.000 | + | 344.678i | −0.884200 | + | 1.53148i | −0.0375721 | + | 0.999294i | \(0.511962\pi\) |
−0.846628 | + | 0.532185i | \(0.821371\pi\) | |||||||
\(38\) | −186.000 | − | 322.161i | −0.794031 | − | 1.37530i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −189.000 | + | 327.358i | −0.747088 | + | 1.29399i | ||||
\(41\) | −318.000 | −1.21130 | −0.605649 | − | 0.795732i | \(-0.707087\pi\) | ||||
−0.605649 | + | 0.795732i | \(0.707087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −268.000 | −0.950456 | −0.475228 | − | 0.879863i | \(-0.657634\pi\) | ||||
−0.475228 | + | 0.879863i | \(0.657634\pi\) | |||||||
\(44\) | −18.0000 | + | 31.1769i | −0.0616728 | + | 0.106820i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120.000 | + | 207.846i | −0.372421 | + | 0.645053i | −0.989937 | − | 0.141506i | \(-0.954806\pi\) |
0.617516 | + | 0.786558i | \(0.288139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 597.000 | 1.68857 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −17.0000 | − | 29.4449i | −0.0453361 | − | 0.0785244i | ||||
\(53\) | −249.000 | − | 431.281i | −0.645335 | − | 1.11775i | −0.984224 | − | 0.176927i | \(-0.943384\pi\) |
0.338888 | − | 0.940827i | \(-0.389949\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −648.000 | −1.58866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 153.000 | − | 265.004i | 0.346377 | − | 0.599943i | ||||
\(59\) | 66.0000 | + | 114.315i | 0.145635 | + | 0.252247i | 0.929610 | − | 0.368546i | \(-0.120144\pi\) |
−0.783975 | + | 0.620793i | \(0.786811\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 199.000 | − | 344.678i | 0.417694 | − | 0.723467i | −0.578013 | − | 0.816028i | \(-0.696172\pi\) |
0.995707 | + | 0.0925602i | \(0.0295051\pi\) | |||||||
\(62\) | 480.000 | 0.983227 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 306.000 | − | 530.008i | 0.583917 | − | 1.01137i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −46.0000 | − | 79.6743i | −0.0838775 | − | 0.145280i | 0.821035 | − | 0.570878i | \(-0.193397\pi\) |
−0.904912 | + | 0.425598i | \(0.860064\pi\) | |||||||
\(68\) | −21.0000 | + | 36.3731i | −0.0374504 | + | 0.0648659i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 720.000 | 1.20350 | 0.601748 | − | 0.798686i | \(-0.294471\pi\) | ||||
0.601748 | + | 0.798686i | \(0.294471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −251.000 | − | 434.745i | −0.402429 | − | 0.697028i | 0.591589 | − | 0.806239i | \(-0.298501\pi\) |
−0.994019 | + | 0.109212i | \(0.965167\pi\) | |||||||
\(74\) | −597.000 | − | 1034.03i | −0.937836 | − | 1.62438i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 124.000 | 0.187155 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 512.000 | − | 886.810i | 0.729171 | − | 1.26296i | −0.228063 | − | 0.973646i | \(-0.573239\pi\) |
0.957234 | − | 0.289315i | \(-0.0934274\pi\) | |||||||
\(80\) | −639.000 | − | 1106.78i | −0.893030 | − | 1.54677i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 477.000 | − | 826.188i | 0.642388 | − | 1.11265i | ||||
\(83\) | −204.000 | −0.269782 | −0.134891 | − | 0.990860i | \(-0.543068\pi\) | ||||
−0.134891 | + | 0.990860i | \(0.543068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −756.000 | −0.964703 | ||||||||
\(86\) | 402.000 | − | 696.284i | 0.504056 | − | 0.873050i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 378.000 | + | 654.715i | 0.457897 | + | 0.793101i | ||||
\(89\) | −177.000 | + | 306.573i | −0.210809 | + | 0.365131i | −0.951968 | − | 0.306198i | \(-0.900943\pi\) |
0.741159 | + | 0.671329i | \(0.234276\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −360.000 | − | 623.538i | −0.395012 | − | 0.684182i | ||||
\(95\) | 1116.00 | + | 1932.97i | 1.20525 | + | 2.08756i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 286.000 | 0.299370 | 0.149685 | − | 0.988734i | \(-0.452174\pi\) | ||||
0.149685 | + | 0.988734i | \(0.452174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −99.5000 | + | 172.339i | −0.0995000 | + | 0.172339i | ||||
\(101\) | −207.000 | − | 358.535i | −0.203933 | − | 0.353223i | 0.745859 | − | 0.666104i | \(-0.232039\pi\) |
−0.949792 | + | 0.312881i | \(0.898706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 28.0000 | − | 48.4974i | 0.0267857 | − | 0.0463941i | −0.852322 | − | 0.523018i | \(-0.824806\pi\) |
0.879107 | + | 0.476624i | \(0.158140\pi\) | |||||||
\(104\) | −714.000 | −0.673206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1494.00 | 1.36896 | ||||||||
\(107\) | 6.00000 | − | 10.3923i | 0.00542095 | − | 0.00938936i | −0.863302 | − | 0.504687i | \(-0.831608\pi\) |
0.868723 | + | 0.495298i | \(0.164941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −739.000 | − | 1279.99i | −0.649389 | − | 1.12477i | −0.983269 | − | 0.182159i | \(-0.941692\pi\) |
0.333880 | − | 0.942615i | \(-0.391642\pi\) | |||||||
\(110\) | 972.000 | − | 1683.55i | 0.842514 | − | 1.45928i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −402.000 | −0.334664 | −0.167332 | − | 0.985901i | \(-0.553515\pi\) | ||||
−0.167332 | + | 0.985901i | \(0.553515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 51.0000 | + | 88.3346i | 0.0408210 | + | 0.0707040i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −396.000 | −0.308939 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5000 | − | 30.3109i | 0.0131480 | − | 0.0227730i | ||||
\(122\) | 597.000 | + | 1034.03i | 0.443031 | + | 0.767353i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −80.0000 | + | 138.564i | −0.0579372 | + | 0.100350i | ||||
\(125\) | −1332.00 | −0.953102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1280.00 | 0.894344 | 0.447172 | − | 0.894448i | \(-0.352431\pi\) | ||||
0.447172 | + | 0.894448i | \(0.352431\pi\) | |||||||
\(128\) | −829.500 | + | 1436.74i | −0.572798 | + | 0.992115i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 918.000 | + | 1590.02i | 0.619338 | + | 1.07272i | ||||
\(131\) | −882.000 | + | 1527.67i | −0.588250 | + | 1.01888i | 0.406212 | + | 0.913779i | \(0.366849\pi\) |
−0.994462 | + | 0.105099i | \(0.966484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 276.000 | 0.177931 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 441.000 | + | 763.834i | 0.278055 | + | 0.481605i | ||||
\(137\) | −1179.00 | − | 2042.09i | −0.735246 | − | 1.27348i | −0.954615 | − | 0.297842i | \(-0.903733\pi\) |
0.219369 | − | 0.975642i | \(-0.429600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 52.0000 | 0.0317308 | 0.0158654 | − | 0.999874i | \(-0.494950\pi\) | ||||
0.0158654 | + | 0.999874i | \(0.494950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1080.00 | + | 1870.61i | −0.638251 | + | 1.10548i | ||||
\(143\) | −612.000 | − | 1060.02i | −0.357888 | − | 0.619881i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −918.000 | + | 1590.02i | −0.525764 | + | 0.910650i | ||||
\(146\) | 1506.00 | 0.853681 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 398.000 | 0.221050 | ||||||||
\(149\) | −873.000 | + | 1512.08i | −0.479993 | + | 0.831372i | −0.999737 | − | 0.0229501i | \(-0.992694\pi\) |
0.519744 | + | 0.854322i | \(0.326027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 116.000 | + | 200.918i | 0.0625162 | + | 0.108281i | 0.895590 | − | 0.444881i | \(-0.146754\pi\) |
−0.833073 | + | 0.553163i | \(0.813421\pi\) | |||||||
\(152\) | 1302.00 | − | 2255.13i | 0.694777 | − | 1.20339i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2880.00 | −1.49243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 847.000 | + | 1467.05i | 0.430560 | + | 0.745752i | 0.996922 | − | 0.0784048i | \(-0.0249827\pi\) |
−0.566361 | + | 0.824157i | \(0.691649\pi\) | |||||||
\(158\) | 1536.00 | + | 2660.43i | 0.773403 | + | 1.33957i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 810.000 | 0.400226 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1466.00 | − | 2539.19i | 0.704454 | − | 1.22015i | −0.262434 | − | 0.964950i | \(-0.584525\pi\) |
0.966888 | − | 0.255200i | \(-0.0821413\pi\) | |||||||
\(164\) | 159.000 | + | 275.396i | 0.0757062 | + | 0.131127i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 306.000 | − | 530.008i | 0.143074 | − | 0.247811i | ||||
\(167\) | 1176.00 | 0.544920 | 0.272460 | − | 0.962167i | \(-0.412163\pi\) | ||||
0.272460 | + | 0.962167i | \(0.412163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | 1134.00 | − | 1964.15i | 0.511611 | − | 0.886136i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 134.000 | + | 232.095i | 0.0594035 | + | 0.102890i | ||||
\(173\) | −435.000 | + | 753.442i | −0.191170 | + | 0.331116i | −0.945638 | − | 0.325220i | \(-0.894562\pi\) |
0.754468 | + | 0.656337i | \(0.227895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2556.00 | −1.09469 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −531.000 | − | 919.719i | −0.223596 | − | 0.387280i | ||||
\(179\) | −1158.00 | − | 2005.71i | −0.483536 | − | 0.837509i | 0.516285 | − | 0.856417i | \(-0.327315\pi\) |
−0.999821 | + | 0.0189075i | \(0.993981\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 106.000 | 0.0435299 | 0.0217650 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217650 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3582.00 | + | 6204.21i | 1.42353 | + | 2.46563i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −756.000 | + | 1309.43i | −0.295637 | + | 0.512059i | ||||
\(188\) | 240.000 | 0.0931053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6696.00 | −2.55673 | ||||||||
\(191\) | −564.000 | + | 976.877i | −0.213663 | + | 0.370075i | −0.952858 | − | 0.303416i | \(-0.901873\pi\) |
0.739195 | + | 0.673491i | \(0.235206\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2017.00 | − | 3493.55i | −0.752263 | − | 1.30296i | −0.946723 | − | 0.322048i | \(-0.895629\pi\) |
0.194460 | − | 0.980910i | \(-0.437705\pi\) | |||||||
\(194\) | −429.000 | + | 743.050i | −0.158765 | + | 0.274989i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1314.00 | 0.475221 | 0.237611 | − | 0.971360i | \(-0.423636\pi\) | ||||
0.237611 | + | 0.971360i | \(0.423636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2548.00 | + | 4413.27i | 0.907653 | + | 1.57210i | 0.817316 | + | 0.576190i | \(0.195461\pi\) |
0.0903369 | + | 0.995911i | \(0.471206\pi\) | |||||||
\(200\) | 2089.50 | + | 3619.12i | 0.738750 | + | 1.27955i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1242.00 | 0.432608 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2862.00 | + | 4957.13i | −0.975077 | + | 1.68888i | ||||
\(206\) | 84.0000 | + | 145.492i | 0.0284105 | + | 0.0492084i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1207.00 | − | 2090.59i | 0.402358 | − | 0.696904i | ||||
\(209\) | 4464.00 | 1.47742 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3076.00 | −1.00360 | −0.501802 | − | 0.864982i | \(-0.667330\pi\) | ||||
−0.501802 | + | 0.864982i | \(0.667330\pi\) | |||||||
\(212\) | −249.000 | + | 431.281i | −0.0806669 | + | 0.139719i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000 | + | 31.1769i | 0.00574979 | + | 0.00995893i | ||||
\(215\) | −2412.00 | + | 4177.71i | −0.765102 | + | 1.32520i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4434.00 | 1.37756 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 324.000 | + | 561.184i | 0.0992913 | + | 0.171977i | ||||
\(221\) | −714.000 | − | 1236.68i | −0.217325 | − | 0.376418i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1888.00 | 0.566950 | 0.283475 | − | 0.958980i | \(-0.408513\pi\) | ||||
0.283475 | + | 0.958980i | \(0.408513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 603.000 | − | 1044.43i | 0.177482 | − | 0.307408i | ||||
\(227\) | 2358.00 | + | 4084.18i | 0.689454 | + | 1.19417i | 0.972015 | + | 0.234919i | \(0.0754826\pi\) |
−0.282561 | + | 0.959249i | \(0.591184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −845.000 | + | 1463.58i | −0.243839 | + | 0.422342i | −0.961805 | − | 0.273737i | \(-0.911740\pi\) |
0.717965 | + | 0.696079i | \(0.245074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2142.00 | 0.606160 | ||||||||
\(233\) | 69.0000 | − | 119.512i | 0.0194006 | − | 0.0336028i | −0.856162 | − | 0.516707i | \(-0.827158\pi\) |
0.875563 | + | 0.483104i | \(0.160491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2160.00 | + | 3741.23i | 0.599587 | + | 1.03851i | ||||
\(236\) | 66.0000 | − | 114.315i | 0.0182044 | − | 0.0315309i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1896.00 | −0.513147 | −0.256573 | − | 0.966525i | \(-0.582594\pi\) | ||||
−0.256573 | + | 0.966525i | \(0.582594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1799.00 | − | 3115.96i | −0.480846 | − | 0.832849i | 0.518913 | − | 0.854827i | \(-0.326337\pi\) |
−0.999758 | + | 0.0219782i | \(0.993004\pi\) | |||||||
\(242\) | 52.5000 | + | 90.9327i | 0.0139456 | + | 0.0241544i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −398.000 | −0.104424 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2108.00 | + | 3651.16i | −0.543032 | + | 0.940558i | ||||
\(248\) | 1680.00 | + | 2909.85i | 0.430162 | + | 0.745062i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1998.00 | − | 3460.64i | 0.505458 | − | 0.875480i | ||||
\(251\) | −3060.00 | −0.769504 | −0.384752 | − | 0.923020i | \(-0.625713\pi\) | ||||
−0.384752 | + | 0.923020i | \(0.625713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1920.00 | + | 3325.54i | −0.474297 | + | 0.821507i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −756.500 | − | 1310.30i | −0.184692 | − | 0.319897i | ||||
\(257\) | 3411.00 | − | 5908.03i | 0.827908 | − | 1.43398i | −0.0717686 | − | 0.997421i | \(-0.522864\pi\) |
0.899676 | − | 0.436557i | \(-0.143802\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −612.000 | −0.145979 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2646.00 | − | 4583.01i | −0.623933 | − | 1.08068i | ||||
\(263\) | 1296.00 | + | 2244.74i | 0.303858 | + | 0.526298i | 0.977007 | − | 0.213209i | \(-0.0683917\pi\) |
−0.673148 | + | 0.739508i | \(0.735058\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8964.00 | −2.07794 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −46.0000 | + | 79.6743i | −0.0104847 | + | 0.0181600i | ||||
\(269\) | −4107.00 | − | 7113.53i | −0.930886 | − | 1.61234i | −0.781811 | − | 0.623515i | \(-0.785704\pi\) |
−0.149074 | − | 0.988826i | \(-0.547629\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2672.00 | + | 4628.04i | −0.598939 | + | 1.03739i | 0.394039 | + | 0.919094i | \(0.371077\pi\) |
−0.992978 | + | 0.118299i | \(0.962256\pi\) | |||||||
\(272\) | −2982.00 | −0.664744 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7074.00 | 1.55969 | ||||||||
\(275\) | −3582.00 | + | 6204.21i | −0.785464 | + | 1.36046i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3257.00 | + | 5641.29i | 0.706477 | + | 1.22365i | 0.966156 | + | 0.257959i | \(0.0830500\pi\) |
−0.259679 | + | 0.965695i | \(0.583617\pi\) | |||||||
\(278\) | −78.0000 | + | 135.100i | −0.0168278 | + | 0.0291466i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6618.00 | −1.40497 | −0.702485 | − | 0.711698i | \(-0.747926\pi\) | ||||
−0.702485 | + | 0.711698i | \(0.747926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1630.00 | + | 2823.24i | 0.342380 | + | 0.593019i | 0.984874 | − | 0.173271i | \(-0.0554338\pi\) |
−0.642494 | + | 0.766290i | \(0.722100\pi\) | |||||||
\(284\) | −360.000 | − | 623.538i | −0.0752186 | − | 0.130282i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3672.00 | 0.759195 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1574.50 | − | 2727.11i | 0.320476 | − | 0.555081i | ||||
\(290\) | −2754.00 | − | 4770.07i | −0.557657 | − | 0.965890i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −251.000 | + | 434.745i | −0.0503036 | + | 0.0871285i | ||||
\(293\) | 5118.00 | 1.02047 | 0.510233 | − | 0.860036i | \(-0.329559\pi\) | ||||
0.510233 | + | 0.860036i | \(0.329559\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2376.00 | 0.468936 | ||||||||
\(296\) | 4179.00 | − | 7238.24i | 0.820606 | − | 1.42133i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2619.00 | − | 4536.24i | −0.509109 | − | 0.881803i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −696.000 | −0.132617 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4402.00 | + | 7624.49i | 0.830500 | + | 1.43847i | ||||
\(305\) | −3582.00 | − | 6204.21i | −0.672475 | − | 1.16476i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −452.000 | −0.0840293 | −0.0420147 | − | 0.999117i | \(-0.513378\pi\) | ||||
−0.0420147 | + | 0.999117i | \(0.513378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4320.00 | − | 7482.46i | 0.791482 | − | 1.37089i | ||||
\(311\) | −2508.00 | − | 4343.98i | −0.457285 | − | 0.792041i | 0.541531 | − | 0.840681i | \(-0.317845\pi\) |
−0.998816 | + | 0.0486397i | \(0.984511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2701.00 | − | 4678.27i | 0.487762 | − | 0.844829i | −0.512139 | − | 0.858903i | \(-0.671147\pi\) |
0.999901 | + | 0.0140739i | \(0.00448001\pi\) | |||||||
\(314\) | −5082.00 | −0.913356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1024.00 | −0.182293 | ||||||||
\(317\) | 5043.00 | − | 8734.73i | 0.893511 | − | 1.54761i | 0.0578751 | − | 0.998324i | \(-0.481567\pi\) |
0.835636 | − | 0.549283i | \(-0.185099\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1836.00 | + | 3180.05i | 0.322245 | + | 0.558145i | ||||
\(320\) | 3897.00 | − | 6749.80i | 0.680778 | − | 1.17914i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5208.00 | 0.897154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3383.00 | − | 5859.53i | −0.577400 | − | 1.00009i | ||||
\(326\) | 4398.00 | + | 7617.56i | 0.747186 | + | 1.29416i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6678.00 | 1.12418 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4022.00 | − | 6966.31i | 0.667883 | − | 1.15681i | −0.310613 | − | 0.950537i | \(-0.600534\pi\) |
0.978495 | − | 0.206270i | \(-0.0661325\pi\) | |||||||
\(332\) | 102.000 | + | 176.669i | 0.0168614 | + | 0.0292048i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1764.00 | + | 3055.34i | −0.288987 | + | 0.500541i | ||||
\(335\) | −1656.00 | −0.270080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4178.00 | 0.675342 | 0.337671 | − | 0.941264i | \(-0.390361\pi\) | ||||
0.337671 | + | 0.941264i | \(0.390361\pi\) | |||||||
\(338\) | 1561.50 | − | 2704.60i | 0.251285 | − | 0.435239i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 378.000 | + | 654.715i | 0.0602939 | + | 0.104432i | ||||
\(341\) | −2880.00 | + | 4988.31i | −0.457363 | + | 0.792176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5628.00 | 0.882097 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1305.00 | − | 2260.33i | −0.202767 | − | 0.351202i | ||||
\(347\) | 78.0000 | + | 135.100i | 0.0120670 | + | 0.0209007i | 0.871996 | − | 0.489513i | \(-0.162826\pi\) |
−0.859929 | + | 0.510414i | \(0.829492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12418.0 | 1.90464 | 0.952321 | − | 0.305097i | \(-0.0986888\pi\) | ||||
0.952321 | + | 0.305097i | \(0.0986888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 810.000 | − | 1402.96i | 0.122651 | − | 0.212438i | ||||
\(353\) | 3915.00 | + | 6780.98i | 0.590296 | + | 1.02242i | 0.994192 | + | 0.107618i | \(0.0343222\pi\) |
−0.403897 | + | 0.914805i | \(0.632344\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6480.00 | − | 11223.7i | 0.968796 | − | 1.67800i | ||||
\(356\) | 354.000 | 0.0527021 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6948.00 | 1.02574 | ||||||||
\(359\) | −4656.00 | + | 8064.43i | −0.684497 | + | 1.18558i | 0.289098 | + | 0.957299i | \(0.406645\pi\) |
−0.973595 | + | 0.228283i | \(0.926689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4258.50 | − | 7375.94i | −0.620863 | − | 1.07537i | ||||
\(362\) | −159.000 | + | 275.396i | −0.0230852 | + | 0.0399848i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9036.00 | −1.29580 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1880.00 | − | 3256.26i | −0.267398 | − | 0.463148i | 0.700791 | − | 0.713367i | \(-0.252831\pi\) |
−0.968189 | + | 0.250219i | \(0.919497\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −21492.0 | −3.01977 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2935.00 | + | 5083.57i | −0.407422 | + | 0.705676i | −0.994600 | − | 0.103782i | \(-0.966906\pi\) |
0.587178 | + | 0.809458i | \(0.300239\pi\) | |||||||
\(374\) | −2268.00 | − | 3928.29i | −0.313571 | − | 0.543121i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2520.00 | − | 4364.77i | 0.345636 | − | 0.598659i | ||||
\(377\) | −3468.00 | −0.473769 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1852.00 | −0.251005 | −0.125502 | − | 0.992093i | \(-0.540054\pi\) | ||||
−0.125502 | + | 0.992093i | \(0.540054\pi\) | |||||||
\(380\) | 1116.00 | − | 1932.97i | 0.150657 | − | 0.260945i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1692.00 | − | 2930.63i | −0.226624 | − | 0.392524i | ||||
\(383\) | −1080.00 | + | 1870.61i | −0.144087 | + | 0.249566i | −0.929032 | − | 0.369999i | \(-0.879358\pi\) |
0.784945 | + | 0.619566i | \(0.212691\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12102.0 | 1.59579 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −143.000 | − | 247.683i | −0.0187106 | − | 0.0324078i | ||||
\(389\) | −3393.00 | − | 5876.85i | −0.442241 | − | 0.765985i | 0.555614 | − | 0.831440i | \(-0.312483\pi\) |
−0.997855 | + | 0.0654557i | \(0.979150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1971.00 | + | 3413.87i | −0.252024 | + | 0.436519i | ||||
\(395\) | −9216.00 | − | 15962.6i | −1.17394 | − | 2.03333i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3257.00 | + | 5641.29i | −0.411748 | + | 0.713169i | −0.995081 | − | 0.0990641i | \(-0.968415\pi\) |
0.583333 | + | 0.812233i | \(0.301748\pi\) | |||||||
\(398\) | −15288.0 | −1.92542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14129.0 | −1.76612 | ||||||||
\(401\) | 1665.00 | − | 2883.86i | 0.207347 | − | 0.359135i | −0.743531 | − | 0.668701i | \(-0.766850\pi\) |
0.950878 | + | 0.309566i | \(0.100184\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2720.00 | − | 4711.18i | −0.336211 | − | 0.582334i | ||||
\(404\) | −207.000 | + | 358.535i | −0.0254917 | + | 0.0441529i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14328.0 | 1.74499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2699.00 | − | 4674.81i | −0.326301 | − | 0.565169i | 0.655474 | − | 0.755218i | \(-0.272469\pi\) |
−0.981775 | + | 0.190048i | \(0.939136\pi\) | |||||||
\(410\) | −8586.00 | − | 14871.4i | −1.03423 | − | 1.79133i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −56.0000 | −0.00669641 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1836.00 | + | 3180.05i | −0.217170 | + | 0.376150i | ||||
\(416\) | 765.000 | + | 1325.02i | 0.0901616 | + | 0.156164i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6696.00 | + | 11597.8i | −0.783522 | + | 1.35710i | ||||
\(419\) | 13092.0 | 1.52646 | 0.763229 | − | 0.646128i | \(-0.223613\pi\) | ||||
0.763229 | + | 0.646128i | \(0.223613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −322.000 | −0.0372763 | −0.0186381 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186381 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(422\) | 4614.00 | − | 7991.68i | 0.532242 | − | 0.921870i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5229.00 | + | 9056.89i | 0.598921 | + | 1.03736i | ||||
\(425\) | −4179.00 | + | 7238.24i | −0.476968 | + | 0.826132i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.00135524 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7236.00 | − | 12533.1i | −0.811514 | − | 1.40558i | ||||
\(431\) | 1308.00 | + | 2265.52i | 0.146181 | + | 0.253193i | 0.929813 | − | 0.368032i | \(-0.119968\pi\) |
−0.783632 | + | 0.621226i | \(0.786635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4322.00 | −0.479681 | −0.239841 | − | 0.970812i | \(-0.577095\pi\) | ||||
−0.239841 | + | 0.970812i | \(0.577095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −739.000 | + | 1279.99i | −0.0811736 | + | 0.140597i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4508.00 | + | 7808.09i | −0.490103 | + | 0.848883i | −0.999935 | − | 0.0113909i | \(-0.996374\pi\) |
0.509832 | + | 0.860274i | \(0.329707\pi\) | |||||||
\(440\) | 13608.0 | 1.47440 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4284.00 | 0.461016 | ||||||||
\(443\) | −2634.00 | + | 4562.22i | −0.282495 | + | 0.489295i | −0.971999 | − | 0.234987i | \(-0.924495\pi\) |
0.689504 | + | 0.724282i | \(0.257829\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3186.00 | + | 5518.31i | 0.339395 | + | 0.587850i | ||||
\(446\) | −2832.00 | + | 4905.17i | −0.300671 | + | 0.520777i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5310.00 | 0.558117 | 0.279058 | − | 0.960274i | \(-0.409978\pi\) | ||||
0.279058 | + | 0.960274i | \(0.409978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5724.00 | + | 9914.26i | 0.597633 | + | 1.03513i | ||||
\(452\) | 201.000 | + | 348.142i | 0.0209165 | + | 0.0362284i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14148.0 | −1.46255 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7885.00 | + | 13657.2i | −0.807100 | + | 1.39794i | 0.107764 | + | 0.994177i | \(0.465631\pi\) |
−0.914864 | + | 0.403762i | \(0.867702\pi\) | |||||||
\(458\) | −2535.00 | − | 4390.75i | −0.258631 | − | 0.447961i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5370.00 | −0.542529 | −0.271264 | − | 0.962505i | \(-0.587442\pi\) | ||||
−0.271264 | + | 0.962505i | \(0.587442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3328.00 | −0.334050 | −0.167025 | − | 0.985953i | \(-0.553416\pi\) | ||||
−0.167025 | + | 0.985953i | \(0.553416\pi\) | |||||||
\(464\) | −3621.00 | + | 6271.76i | −0.362286 | + | 0.627498i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 207.000 | + | 358.535i | 0.0205774 | + | 0.0356412i | ||||
\(467\) | −2274.00 | + | 3938.68i | −0.225328 | + | 0.390280i | −0.956418 | − | 0.292002i | \(-0.905679\pi\) |
0.731090 | + | 0.682281i | \(0.239012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12960.0 | −1.27192 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1386.00 | − | 2400.62i | −0.135161 | − | 0.234105i | ||||
\(473\) | 4824.00 | + | 8355.41i | 0.468938 | + | 0.812225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24676.0 | 2.38361 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2844.00 | − | 4925.95i | 0.272137 | − | 0.471355i | ||||
\(479\) | 4032.00 | + | 6983.63i | 0.384607 | + | 0.666159i | 0.991715 | − | 0.128461i | \(-0.0410036\pi\) |
−0.607108 | + | 0.794620i | \(0.707670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6766.00 | + | 11719.1i | −0.641378 | + | 1.11090i | ||||
\(482\) | 10794.0 | 1.02003 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −35.0000 | −0.00328700 | ||||||||
\(485\) | 2574.00 | − | 4458.30i | 0.240988 | − | 0.417404i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8308.00 | − | 14389.9i | −0.773042 | − | 1.33895i | −0.935888 | − | 0.352296i | \(-0.885401\pi\) |
0.162847 | − | 0.986651i | \(-0.447932\pi\) | |||||||
\(488\) | −4179.00 | + | 7238.24i | −0.387653 | + | 0.671434i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7140.00 | 0.656260 | 0.328130 | − | 0.944633i | \(-0.393582\pi\) | ||||
0.328130 | + | 0.944633i | \(0.393582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2142.00 | + | 3710.05i | 0.195681 | + | 0.338930i | ||||
\(494\) | −6324.00 | − | 10953.5i | −0.575972 | − | 0.997613i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11360.0 | −1.02839 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4562.00 | − | 7901.62i | 0.409265 | − | 0.708868i | −0.585543 | − | 0.810642i | \(-0.699119\pi\) |
0.994808 | + | 0.101774i | \(0.0324519\pi\) | |||||||
\(500\) | 666.000 | + | 1153.55i | 0.0595689 | + | 0.103176i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4590.00 | − | 7950.11i | 0.408091 | − | 0.706834i | ||||
\(503\) | −6552.00 | −0.580794 | −0.290397 | − | 0.956906i | \(-0.593787\pi\) | ||||
−0.290397 | + | 0.956906i | \(0.593787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7452.00 | −0.656653 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −640.000 | − | 1108.51i | −0.0558965 | − | 0.0968155i | ||||
\(509\) | −1395.00 | + | 2416.21i | −0.121478 | + | 0.210406i | −0.920351 | − | 0.391094i | \(-0.872097\pi\) |
0.798873 | + | 0.601500i | \(0.205430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10233.0 | + | 17724.1i | 0.878129 | + | 1.52096i | ||||
\(515\) | −504.000 | − | 872.954i | −0.0431241 | − | 0.0746931i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8640.00 | 0.734984 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6426.00 | + | 11130.2i | −0.541921 | + | 0.938634i | ||||
\(521\) | 7431.00 | + | 12870.9i | 0.624871 | + | 1.08231i | 0.988566 | + | 0.150791i | \(0.0481820\pi\) |
−0.363694 | + | 0.931518i | \(0.618485\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8830.00 | − | 15294.0i | 0.738258 | − | 1.27870i | −0.215021 | − | 0.976609i | \(-0.568982\pi\) |
0.953279 | − | 0.302091i | \(-0.0976846\pi\) | |||||||
\(524\) | 1764.00 | 0.147062 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7776.00 | −0.644581 | ||||||||
\(527\) | −3360.00 | + | 5819.69i | −0.277730 | + | 0.481043i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6083.50 | + | 10536.9i | 0.500000 | + | 0.866025i | ||||
\(530\) | 13446.0 | − | 23289.2i | 1.10199 | − | 1.90871i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10812.0 | −0.878649 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −108.000 | − | 187.061i | −0.00872756 | − | 0.0151166i | ||||
\(536\) | 966.000 | + | 1673.16i | 0.0778449 | + | 0.134831i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24642.0 | 1.97471 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9917.00 | − | 17176.7i | 0.788106 | − | 1.36504i | −0.139021 | − | 0.990290i | \(-0.544395\pi\) |
0.927126 | − | 0.374749i | \(-0.122271\pi\) | |||||||
\(542\) | −8016.00 | − | 13884.1i | −0.635271 | − | 1.10032i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 945.000 | − | 1636.79i | 0.0744789 | − | 0.129001i | ||||
\(545\) | −26604.0 | −2.09099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20972.0 | 1.63930 | 0.819651 | − | 0.572863i | \(-0.194167\pi\) | ||||
0.819651 | + | 0.572863i | \(0.194167\pi\) | |||||||
\(548\) | −1179.00 | + | 2042.09i | −0.0919058 | + | 0.159186i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −10746.0 | − | 18612.6i | −0.833111 | − | 1.44299i | ||||
\(551\) | 6324.00 | − | 10953.5i | 0.488950 | − | 0.846886i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19542.0 | −1.49866 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.0000 | − | 45.0333i | −0.00198318 | − | 0.00343496i | ||||
\(557\) | 10587.0 | + | 18337.2i | 0.805360 | + | 1.39492i | 0.916048 | + | 0.401069i | \(0.131361\pi\) |
−0.110688 | + | 0.993855i | \(0.535305\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9112.00 | −0.689439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9927.00 | − | 17194.1i | 0.745098 | − | 1.29055i | ||||
\(563\) | 8886.00 | + | 15391.0i | 0.665187 | + | 1.15214i | 0.979235 | + | 0.202730i | \(0.0649815\pi\) |
−0.314048 | + | 0.949407i | \(0.601685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3618.00 | + | 6266.56i | −0.269399 | + | 0.466613i | ||||
\(566\) | −9780.00 | −0.726297 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15120.0 | −1.11694 | ||||||||
\(569\) | 4125.00 | − | 7144.71i | 0.303917 | − | 0.526400i | −0.673102 | − | 0.739549i | \(-0.735039\pi\) |
0.977020 | + | 0.213149i | \(0.0683720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10378.0 | − | 17975.2i | −0.760606 | − | 1.31741i | −0.942539 | − | 0.334097i | \(-0.891569\pi\) |
0.181933 | − | 0.983311i | \(-0.441765\pi\) | |||||||
\(572\) | −612.000 | + | 1060.02i | −0.0447360 | + | 0.0774851i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.00000 | + | 1.73205i | 7.21500e−5 | + | 0.000124967i | 0.866061 | − | 0.499938i | \(-0.166644\pi\) |
−0.865989 | + | 0.500062i | \(0.833310\pi\) | |||||||
\(578\) | 4723.50 | + | 8181.34i | 0.339916 | + | 0.588753i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1836.00 | 0.131441 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8964.00 | + | 15526.1i | −0.636794 | + | 1.10296i | ||||
\(584\) | 5271.00 | + | 9129.64i | 0.373485 | + | 0.646896i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7677.00 | + | 13297.0i | −0.541184 | + | 0.937359i | ||||
\(587\) | 26364.0 | 1.85376 | 0.926881 | − | 0.375354i | \(-0.122479\pi\) | ||||
0.926881 | + | 0.375354i | \(0.122479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19840.0 | 1.38793 | ||||||||
\(590\) | −3564.00 | + | 6173.03i | −0.248691 | + | 0.430745i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14129.0 | + | 24472.1i | 0.980909 | + | 1.69898i | ||||
\(593\) | −1149.00 | + | 1990.13i | −0.0795679 | + | 0.137816i | −0.903064 | − | 0.429507i | \(-0.858687\pi\) |
0.823496 | + | 0.567323i | \(0.192021\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1746.00 | 0.119998 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1536.00 | + | 2660.43i | 0.104773 | + | 0.181473i | 0.913646 | − | 0.406512i | \(-0.133255\pi\) |
−0.808872 | + | 0.587984i | \(0.799922\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24554.0 | −1.66652 | −0.833260 | − | 0.552881i | \(-0.813528\pi\) | ||||
−0.833260 | + | 0.552881i | \(0.813528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 116.000 | − | 200.918i | 0.00781452 | − | 0.0135352i | ||||
\(605\) | −315.000 | − | 545.596i | −0.0211679 | − | 0.0366639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8416.00 | − | 14576.9i | 0.562759 | − | 0.974728i | −0.434495 | − | 0.900674i | \(-0.643073\pi\) |
0.997254 | − | 0.0740535i | \(-0.0235935\pi\) | |||||||
\(608\) | −5580.00 | −0.372202 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21492.0 | 1.42653 | ||||||||
\(611\) | −4080.00 | + | 7066.77i | −0.270146 | + | 0.467906i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1241.00 | + | 2149.48i | 0.0817676 | + | 0.141626i | 0.904009 | − | 0.427513i | \(-0.140610\pi\) |
−0.822242 | + | 0.569139i | \(0.807277\pi\) | |||||||
\(614\) | 678.000 | − | 1174.33i | 0.0445633 | − | 0.0771859i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15798.0 | 1.03080 | 0.515400 | − | 0.856950i | \(-0.327643\pi\) | ||||
0.515400 | + | 0.856950i | \(0.327643\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7730.00 | − | 13388.8i | −0.501930 | − | 0.869369i | −0.999998 | − | 0.00223050i | \(-0.999290\pi\) |
0.498067 | − | 0.867138i | \(-0.334043\pi\) | |||||||
\(620\) | 1440.00 | + | 2494.15i | 0.0932771 | + | 0.161561i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15048.0 | 0.970048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 449.500 | − | 778.557i | 0.0287680 | − | 0.0498276i | ||||
\(626\) | 8103.00 | + | 14034.8i | 0.517350 | + | 0.896076i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 847.000 | − | 1467.05i | 0.0538200 | − | 0.0932190i | ||||
\(629\) | 16716.0 | 1.05964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7720.00 | −0.487050 | −0.243525 | − | 0.969895i | \(-0.578304\pi\) | ||||
−0.243525 | + | 0.969895i | \(0.578304\pi\) | |||||||
\(632\) | −10752.0 | + | 18623.0i | −0.676727 | + | 1.17213i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15129.0 | + | 26204.2i | 0.947712 | + | 1.64149i | ||||
\(635\) | 11520.0 | − | 19953.2i | 0.719933 | − | 1.24696i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11016.0 | −0.683586 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14931.0 | + | 25861.3i | 0.922187 | + | 1.59727i | ||||
\(641\) | −8631.00 | − | 14949.3i | −0.531832 | − | 0.921159i | −0.999310 | − | 0.0371545i | \(-0.988171\pi\) |
0.467478 | − | 0.884005i | \(-0.345163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12220.0 | 0.749471 | 0.374735 | − | 0.927132i | \(-0.377734\pi\) | ||||
0.374735 | + | 0.927132i | \(0.377734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7812.00 | + | 13530.8i | −0.475788 | + | 0.824089i | ||||
\(647\) | −6780.00 | − | 11743.3i | −0.411977 | − | 0.713566i | 0.583129 | − | 0.812380i | \(-0.301828\pi\) |
−0.995106 | + | 0.0988143i | \(0.968495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2376.00 | − | 4115.35i | 0.143707 | − | 0.248909i | ||||
\(650\) | 20298.0 | 1.22485 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2932.00 | −0.176113 | ||||||||
\(653\) | 11547.0 | − | 20000.0i | 0.691989 | − | 1.19856i | −0.279196 | − | 0.960234i | \(-0.590068\pi\) |
0.971185 | − | 0.238326i | \(-0.0765988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15876.0 | + | 27498.0i | 0.947064 | + | 1.64036i | ||||
\(656\) | −11289.0 | + | 19553.1i | −0.671892 | + | 1.16375i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22548.0 | −1.33285 | −0.666423 | − | 0.745574i | \(-0.732175\pi\) | ||||
−0.666423 | + | 0.745574i | \(0.732175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8731.00 | + | 15122.5i | 0.513762 | + | 0.889862i | 0.999873 | + | 0.0159643i | \(0.00508182\pi\) |
−0.486111 | + | 0.873897i | \(0.661585\pi\) | |||||||
\(662\) | 12066.0 | + | 20898.9i | 0.708396 | + | 1.22698i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4284.00 | 0.250379 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −588.000 | − | 1018.45i | −0.0340575 | − | 0.0589893i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2484.00 | − | 4302.41i | 0.143232 | − | 0.248085i | ||||
\(671\) | −14328.0 | −0.824331 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22462.0 | −1.28655 | −0.643274 | − | 0.765636i | \(-0.722424\pi\) | ||||
−0.643274 | + | 0.765636i | \(0.722424\pi\) | |||||||
\(674\) | −6267.00 | + | 10854.8i | −0.358154 | + | 0.620341i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 520.500 | + | 901.532i | 0.0296142 | + | 0.0512934i | ||||
\(677\) | 12777.0 | − | 22130.4i | 0.725347 | − | 1.25634i | −0.233484 | − | 0.972361i | \(-0.575013\pi\) |
0.958831 | − | 0.283977i | \(-0.0916541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15876.0 | 0.895319 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8640.00 | − | 14964.9i | −0.485107 | − | 0.840229i | ||||
\(683\) | 4638.00 | + | 8033.25i | 0.259836 | + | 0.450050i | 0.966198 | − | 0.257802i | \(-0.0829981\pi\) |
−0.706362 | + | 0.707851i | \(0.749665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42444.0 | −2.36745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9514.00 | + | 16478.7i | −0.527206 | + | 0.913148i | ||||
\(689\) | −8466.00 | − | 14663.5i | −0.468112 | − | 0.810793i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13690.0 | − | 23711.8i | 0.753679 | − | 1.30541i | −0.192349 | − | 0.981326i | \(-0.561611\pi\) |
0.946028 | − | 0.324084i | \(-0.105056\pi\) | |||||||
\(692\) | 870.000 | 0.0477925 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −468.000 | −0.0255980 | ||||||||
\(695\) | 468.000 | − | 810.600i | 0.0255428 | − | 0.0442414i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6678.00 | + | 11566.6i | 0.362909 | + | 0.628576i | ||||
\(698\) | −18627.0 | + | 32262.9i | −1.01009 | + | 1.74953i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25830.0 | −1.39171 | −0.695853 | − | 0.718184i | \(-0.744973\pi\) | ||||
−0.695853 | + | 0.718184i | \(0.744973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24676.0 | − | 42740.1i | −1.32386 | − | 2.29299i | ||||
\(704\) | −7794.00 | − | 13499.6i | −0.417255 | − | 0.722707i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23490.0 | −1.25221 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3113.00 | − | 5391.87i | 0.164896 | − | 0.285608i | −0.771722 | − | 0.635959i | \(-0.780605\pi\) |
0.936618 | + | 0.350351i | \(0.113938\pi\) | |||||||
\(710\) | 19440.0 | + | 33671.1i | 1.02756 | + | 1.77979i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3717.00 | − | 6438.03i | 0.195647 | − | 0.338870i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22032.0 | −1.15238 | ||||||||
\(716\) | −1158.00 | + | 2005.71i | −0.0604420 | + | 0.104689i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13968.0 | − | 24193.3i | −0.726018 | − | 1.25750i | ||||
\(719\) | 7536.00 | − | 13052.7i | 0.390884 | − | 0.677030i | −0.601683 | − | 0.798735i | \(-0.705503\pi\) |
0.992566 | + | 0.121705i | \(0.0388361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25551.0 | 1.31705 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −53.0000 | − | 91.7987i | −0.00272062 | − | 0.00471225i | ||||
\(725\) | 10149.0 | + | 17578.6i | 0.519896 | + | 0.900486i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32920.0 | 1.67942 | 0.839708 | − | 0.543038i | \(-0.182726\pi\) | ||||
0.839708 | + | 0.543038i | \(0.182726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13554.0 | − | 23476.2i | 0.687200 | − | 1.19027i | ||||
\(731\) | 5628.00 | + | 9747.98i | 0.284759 | + | 0.493218i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3473.00 | + | 6015.41i | −0.175004 | + | 0.303116i | −0.940163 | − | 0.340726i | \(-0.889327\pi\) |
0.765158 | + | 0.643842i | \(0.222661\pi\) | |||||||
\(734\) | 11280.0 | 0.567238 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1656.00 | + | 2868.28i | −0.0827674 | + | 0.143357i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1178.00 | + | 2040.36i | 0.0586379 | + | 0.101564i | 0.893854 | − | 0.448358i | \(-0.147991\pi\) |
−0.835216 | + | 0.549922i | \(0.814658\pi\) | |||||||
\(740\) | 3582.00 | − | 6204.21i | 0.177942 | − | 0.308204i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23520.0 | 1.16133 | 0.580663 | − | 0.814144i | \(-0.302793\pi\) | ||||
0.580663 | + | 0.814144i | \(0.302793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15714.0 | + | 27217.4i | 0.772774 | + | 1.33848i | ||||
\(746\) | −8805.00 | − | 15250.7i | −0.432137 | − | 0.748483i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1512.00 | 0.0739094 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1504.00 | + | 2605.00i | −0.0730782 | + | 0.126575i | −0.900249 | − | 0.435376i | \(-0.856616\pi\) |
0.827171 | + | 0.561951i | \(0.189949\pi\) | |||||||
\(752\) | 8520.00 | + | 14757.1i | 0.413155 | + | 0.715605i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5202.00 | − | 9010.13i | 0.251254 | − | 0.435185i | ||||
\(755\) | 4176.00 | 0.201298 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20770.0 | −0.997224 | −0.498612 | − | 0.866825i | \(-0.666157\pi\) | ||||
−0.498612 | + | 0.866825i | \(0.666157\pi\) | |||||||
\(758\) | 2778.00 | − | 4811.64i | 0.133115 | − | 0.230563i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23436.0 | − | 40592.3i | −1.11857 | − | 1.93742i | ||||
\(761\) | −5769.00 | + | 9992.20i | −0.274804 | + | 0.475975i | −0.970086 | − | 0.242763i | \(-0.921946\pi\) |
0.695281 | + | 0.718738i | \(0.255280\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1128.00 | 0.0534157 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3240.00 | − | 5611.84i | −0.152828 | − | 0.264705i | ||||
\(767\) | 2244.00 | + | 3886.72i | 0.105640 | + | 0.182974i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8498.00 | −0.398499 | −0.199249 | − | 0.979949i | \(-0.563850\pi\) | ||||
−0.199249 | + | 0.979949i | \(0.563850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2017.00 | + | 3493.55i | −0.0940329 | + | 0.162870i | ||||
\(773\) | 16161.0 | + | 27991.7i | 0.751967 | + | 1.30245i | 0.946868 | + | 0.321623i | \(0.104228\pi\) |
−0.194901 | + | 0.980823i | \(0.562438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15920.0 | + | 27574.2i | −0.737888 | + | 1.27806i | ||||
\(776\) | −6006.00 | −0.277839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20358.0 | 0.938136 | ||||||||
\(779\) | 19716.0 | − | 34149.1i | 0.906802 | − | 1.57063i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12960.0 | − | 22447.4i | −0.593784 | − | 1.02846i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30492.0 | 1.38638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13114.0 | + | 22714.1i | 0.593982 | + | 1.02881i | 0.993690 | + | 0.112164i | \(0.0357782\pi\) |
−0.399708 | + | 0.916643i | \(0.630888\pi\) | |||||||
\(788\) | −657.000 | − | 1137.96i | −0.0297013 | − | 0.0514442i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 55296.0 | 2.49031 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6766.00 | − | 11719.1i | 0.302986 | − | 0.524787i | ||||
\(794\) | −9771.00 | − | 16923.9i | −0.436725 | − | 0.756430i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2548.00 | − | 4413.27i | 0.113457 | − | 0.196513i | ||||
\(797\) | −43338.0 | −1.92611 | −0.963056 | − | 0.269302i | \(-0.913207\pi\) | ||||
−0.963056 | + | 0.269302i | \(0.913207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10080.0 | 0.446314 | ||||||||
\(800\) | 4477.50 | − | 7755.26i | 0.197879 | − | 0.342737i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4995.00 | + | 8651.59i | 0.219925 | + | 0.380921i | ||||
\(803\) | −9036.00 | + | 15650.8i | −0.397103 | + | 0.687802i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16320.0 | 0.713210 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4347.00 | + | 7529.22i | 0.189266 | + | 0.327818i | ||||
\(809\) | −14451.0 | − | 25029.9i | −0.628022 | − | 1.08777i | −0.987948 | − | 0.154786i | \(-0.950531\pi\) |
0.359926 | − | 0.932981i | \(-0.382802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27164.0 | −1.17615 | −0.588075 | − | 0.808807i | \(-0.700114\pi\) | ||||
−0.588075 | + | 0.808807i | \(0.700114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21492.0 | + | 37225.2i | −0.925423 | + | 1.60288i | ||||
\(815\) | −26388.0 | − | 45705.4i | −1.13415 | − | 1.96440i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16616.0 | − | 28779.8i | 0.711530 | − | 1.23241i | ||||
\(818\) | 16194.0 | 0.692188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5724.00 | 0.243769 | ||||||||
\(821\) | −8601.00 | + | 14897.4i | −0.365624 | + | 0.633279i | −0.988876 | − | 0.148742i | \(-0.952478\pi\) |
0.623252 | + | 0.782021i | \(0.285811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2996.00 | + | 5189.22i | 0.126894 | + | 0.219787i | 0.922472 | − | 0.386064i | \(-0.126166\pi\) |
−0.795578 | + | 0.605852i | \(0.792832\pi\) | |||||||
\(824\) | −588.000 | + | 1018.45i | −0.0248592 | + | 0.0430573i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25884.0 | −1.08836 | −0.544181 | − | 0.838968i | \(-0.683159\pi\) | ||||
−0.544181 | + | 0.838968i | \(0.683159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −737.000 | − | 1276.52i | −0.0308770 | − | 0.0534806i | 0.850174 | − | 0.526502i | \(-0.176497\pi\) |
−0.881051 | + | 0.473021i | \(0.843163\pi\) | |||||||
\(830\) | −5508.00 | − | 9540.14i | −0.230344 | − | 0.398967i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14722.0 | 0.613454 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10584.0 | − | 18332.0i | 0.438652 | − | 0.759768i | ||||
\(836\) | −2232.00 | − | 3865.94i | −0.0923389 | − | 0.159936i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19638.0 | + | 34014.0i | −0.809527 | + | 1.40214i | ||||
\(839\) | 33528.0 | 1.37964 | 0.689818 | − | 0.723983i | \(-0.257690\pi\) | ||||
0.689818 | + | 0.723983i | \(0.257690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | 483.000 | − | 836.581i | 0.0197687 | − | 0.0342405i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1538.00 | + | 2663.89i | 0.0627253 | + | 0.108643i | ||||
\(845\) | −9369.00 | + | 16227.6i | −0.381424 | + | 0.660646i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35358.0 | −1.43184 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12537.0 | − | 21714.7i | −0.505901 | − | 0.876246i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1190.00 | −0.0477665 | −0.0238832 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238832 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −126.000 | + | 218.238i | −0.00503106 | + | 0.00871406i | ||||
\(857\) | −17289.0 | − | 29945.4i | −0.689126 | − | 1.19360i | −0.972121 | − | 0.234480i | \(-0.924661\pi\) |
0.282995 | − | 0.959121i | \(-0.408672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22202.0 | + | 38455.0i | −0.881865 | + | 1.52744i | −0.0326009 | + | 0.999468i | \(0.510379\pi\) |
−0.849265 | + | 0.527967i | \(0.822954\pi\) | |||||||
\(860\) | 4824.00 | 0.191276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7848.00 | −0.310097 | ||||||||
\(863\) | −19164.0 | + | 33193.0i | −0.755910 | + | 1.30927i | 0.189011 | + | 0.981975i | \(0.439472\pi\) |
−0.944921 | + | 0.327299i | \(0.893862\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7830.00 | + | 13562.0i | 0.307778 | + | 0.533087i | ||||
\(866\) | 6483.00 | − | 11228.9i | 0.254390 | − | 0.440616i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36864.0 | −1.43904 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1564.00 | − | 2708.93i | −0.0608428 | − | 0.105383i | ||||
\(872\) | 15519.0 | + | 26879.7i | 0.602683 | + | 1.04388i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19421.0 | − | 33638.2i | 0.747777 | − | 1.29519i | −0.201109 | − | 0.979569i | \(-0.564454\pi\) |
0.948886 | − | 0.315619i | \(-0.102212\pi\) | |||||||
\(878\) | −13524.0 | − | 23424.3i | −0.519832 | − | 0.900376i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −23004.0 | + | 39844.1i | −0.881210 | + | 1.52630i | ||||
\(881\) | −35046.0 | −1.34022 | −0.670108 | − | 0.742264i | \(-0.733752\pi\) | ||||
−0.670108 | + | 0.742264i | \(0.733752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14204.0 | 0.541339 | 0.270670 | − | 0.962672i | \(-0.412755\pi\) | ||||
0.270670 | + | 0.962672i | \(0.412755\pi\) | |||||||
\(884\) | −714.000 | + | 1236.68i | −0.0271656 | + | 0.0470523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7902.00 | − | 13686.7i | −0.299631 | − | 0.518976i | ||||
\(887\) | 13068.0 | − | 22634.4i | 0.494679 | − | 0.856810i | −0.505302 | − | 0.862943i | \(-0.668619\pi\) |
0.999981 | + | 0.00613301i | \(0.00195221\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −19116.0 | −0.719966 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −944.000 | − | 1635.06i | −0.0354344 | − | 0.0613741i | ||||
\(893\) | −14880.0 | − | 25772.9i | −0.557604 | − | 0.965798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41688.0 | −1.55696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7965.00 | + | 13795.8i | −0.295986 | + | 0.512663i | ||||
\(899\) | 8160.00 | + | 14133.5i | 0.302727 | + | 0.524338i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10458.0 | + | 18113.8i | −0.386689 | + | 0.669764i | ||||
\(902\) | −34344.0 | −1.26777 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8442.00 | 0.310594 | ||||||||
\(905\) | 954.000 | − | 1652.38i | 0.0350409 | − | 0.0606927i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4526.00 | + | 7839.26i | 0.165693 | + | 0.286988i | 0.936901 | − | 0.349595i | \(-0.113681\pi\) |
−0.771208 | + | 0.636583i | \(0.780347\pi\) | |||||||
\(908\) | 2358.00 | − | 4084.18i | 0.0861817 | − | 0.149271i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5016.00 | −0.182423 | −0.0912116 | − | 0.995832i | \(-0.529074\pi\) | ||||
−0.0912116 | + | 0.995832i | \(0.529074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3672.00 | + | 6360.09i | 0.133106 | + | 0.230546i | ||||
\(914\) | −23655.0 | − | 40971.7i | −0.856059 | − | 1.48274i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1690.00 | 0.0609598 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22276.0 | + | 38583.2i | −0.799584 | + | 1.38492i | 0.120304 | + | 0.992737i | \(0.461613\pi\) |
−0.919887 | + | 0.392182i | \(0.871720\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8055.00 | − | 13951.7i | 0.287719 | − | 0.498345i | ||||
\(923\) | 24480.0 | 0.872989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 79202.0 | 2.81529 | ||||||||
\(926\) | 4992.00 | − | 8646.40i | 0.177157 | − | 0.306845i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2295.00 | − | 3975.06i | −0.0811822 | − | 0.140612i | ||||
\(929\) | −12117.0 | + | 20987.3i | −0.427929 | + | 0.741194i | −0.996689 | − | 0.0813090i | \(-0.974090\pi\) |
0.568760 | + | 0.822503i | \(0.307423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −138.000 | −0.00485015 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6822.00 | − | 11816.1i | −0.238996 | − | 0.413954i | ||||
\(935\) | 13608.0 | + | 23569.7i | 0.475967 | + | 0.824399i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13894.0 | 0.484415 | 0.242208 | − | 0.970224i | \(-0.422128\pi\) | ||||
0.242208 | + | 0.970224i | \(0.422128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2160.00 | − | 3741.23i | 0.0749483 | − | 0.129814i | ||||
\(941\) | −23379.0 | − | 40493.6i | −0.809919 | − | 1.40282i | −0.912920 | − | 0.408139i | \(-0.866178\pi\) |
0.103001 | − | 0.994681i | \(-0.467156\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 9372.00 | 0.323128 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28944.0 | −0.994768 | ||||||||
\(947\) | 6906.00 | − | 11961.5i | 0.236974 | − | 0.410452i | −0.722870 | − | 0.690984i | \(-0.757178\pi\) |
0.959845 | + | 0.280532i | \(0.0905109\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8534.00 | − | 14781.3i | −0.291913 | − | 0.505608i | ||||
\(950\) | −37014.0 | + | 64110.1i | −1.26410 | + | 2.18948i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58518.0 | 1.98907 | 0.994535 | − | 0.104402i | \(-0.0332930\pi\) | ||||
0.994535 | + | 0.104402i | \(0.0332930\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10152.0 | + | 17583.8i | 0.343991 | + | 0.595809i | ||||
\(956\) | 948.000 | + | 1641.98i | 0.0320717 | + | 0.0555498i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24192.0 | −0.815875 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2095.50 | − | 3629.51i | 0.0703400 | − | 0.121833i | ||||
\(962\) | −20298.0 | − | 35157.2i | −0.680285 | − | 1.17829i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1799.00 | + | 3115.96i | −0.0601057 | + | 0.104106i | ||||
\(965\) | −72612.0 | −2.42224 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19640.0 | 0.653133 | 0.326567 | − | 0.945174i | \(-0.394108\pi\) | ||||
0.326567 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(968\) | −367.500 | + | 636.529i | −0.0122024 | + | 0.0211351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7722.00 | + | 13374.9i | 0.255607 | + | 0.442724i | ||||
\(971\) | 29154.0 | − | 50496.2i | 0.963539 | − | 1.66890i | 0.250049 | − | 0.968233i | \(-0.419553\pi\) |
0.713490 | − | 0.700665i | \(-0.247113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 49848.0 | 1.63987 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14129.0 | − | 24472.1i | −0.463379 | − | 0.802597i | ||||
\(977\) | −11775.0 | − | 20394.9i | −0.385584 | − | 0.667851i | 0.606266 | − | 0.795262i | \(-0.292667\pi\) |
−0.991850 | + | 0.127411i | \(0.959333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12744.0 | 0.416037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10710.0 | + | 18550.3i | −0.348034 | + | 0.602813i | ||||
\(983\) | −7884.00 | − | 13655.5i | −0.255809 | − | 0.443075i | 0.709306 | − | 0.704901i | \(-0.249009\pi\) |
−0.965115 | + | 0.261826i | \(0.915675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11826.0 | − | 20483.2i | 0.382546 | − | 0.662589i | ||||
\(986\) | −12852.0 | −0.415102 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4216.00 | 0.135758 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17632.0 | − | 30539.5i | −0.565186 | − | 0.978930i | −0.997032 | − | 0.0769832i | \(-0.975471\pi\) |
0.431847 | − | 0.901947i | \(-0.357862\pi\) | |||||||
\(992\) | 3600.00 | − | 6235.38i | 0.115222 | − | 0.199570i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 91728.0 | 2.92259 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14669.0 | − | 25407.5i | −0.465970 | − | 0.807083i | 0.533275 | − | 0.845942i | \(-0.320961\pi\) |
−0.999245 | + | 0.0388586i | \(0.987628\pi\) | |||||||
\(998\) | 13686.0 | + | 23704.8i | 0.434091 | + | 0.751868i | ||||
\(999\) | 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 | 441.4.e.d.226.1 | 2 | ||
3.2 | odd | 2 | 147.4.e.g.79.1 | 2 | |||
7.2 | even | 3 | 441.4.a.j.1.1 | 1 | |||
7.3 | odd | 6 | 441.4.e.b.361.1 | 2 | |||
7.4 | even | 3 | inner | 441.4.e.d.361.1 | 2 | ||
7.5 | odd | 6 | 63.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 441.4.e.b.226.1 | 2 | |||
21.2 | odd | 6 | 147.4.a.c.1.1 | 1 | |||
21.5 | even | 6 | 21.4.a.a.1.1 | ✓ | 1 | ||
21.11 | odd | 6 | 147.4.e.g.67.1 | 2 | |||
21.17 | even | 6 | 147.4.e.i.67.1 | 2 | |||
21.20 | even | 2 | 147.4.e.i.79.1 | 2 | |||
28.19 | even | 6 | 1008.4.a.v.1.1 | 1 | |||
35.19 | odd | 6 | 1575.4.a.b.1.1 | 1 | |||
84.23 | even | 6 | 2352.4.a.r.1.1 | 1 | |||
84.47 | odd | 6 | 336.4.a.f.1.1 | 1 | |||
105.47 | odd | 12 | 525.4.d.c.274.1 | 2 | |||
105.68 | odd | 12 | 525.4.d.c.274.2 | 2 | |||
105.89 | even | 6 | 525.4.a.g.1.1 | 1 | |||
168.5 | even | 6 | 1344.4.a.ba.1.1 | 1 | |||
168.131 | odd | 6 | 1344.4.a.n.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.a.1.1 | ✓ | 1 | 21.5 | even | 6 | ||
63.4.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
147.4.a.c.1.1 | 1 | 21.2 | odd | 6 | |||
147.4.e.g.67.1 | 2 | 21.11 | odd | 6 | |||
147.4.e.g.79.1 | 2 | 3.2 | odd | 2 | |||
147.4.e.i.67.1 | 2 | 21.17 | even | 6 | |||
147.4.e.i.79.1 | 2 | 21.20 | even | 2 | |||
336.4.a.f.1.1 | 1 | 84.47 | odd | 6 | |||
441.4.a.j.1.1 | 1 | 7.2 | even | 3 | |||
441.4.e.b.226.1 | 2 | 7.6 | odd | 2 | |||
441.4.e.b.361.1 | 2 | 7.3 | odd | 6 | |||
441.4.e.d.226.1 | 2 | 1.1 | even | 1 | trivial | ||
441.4.e.d.361.1 | 2 | 7.4 | even | 3 | inner | ||
525.4.a.g.1.1 | 1 | 105.89 | even | 6 | |||
525.4.d.c.274.1 | 2 | 105.47 | odd | 12 | |||
525.4.d.c.274.2 | 2 | 105.68 | odd | 12 | |||
1008.4.a.v.1.1 | 1 | 28.19 | even | 6 | |||
1344.4.a.n.1.1 | 1 | 168.131 | odd | 6 | |||
1344.4.a.ba.1.1 | 1 | 168.5 | even | 6 | |||
1575.4.a.b.1.1 | 1 | 35.19 | odd | 6 | |||
2352.4.a.r.1.1 | 1 | 84.23 | even | 6 |