Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,4,Mod(49,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("144.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.49627504083\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.97 |
Dual form | 144.4.i.c.49.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.55842 | + | 3.78651i | −0.684819 | + | 0.728714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.31386 | − | 4.00772i | −0.206958 | − | 0.358462i | 0.743797 | − | 0.668406i | \(-0.233023\pi\) |
−0.950755 | + | 0.309944i | \(0.899690\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.05842 | − | 10.4935i | 0.327124 | − | 0.566595i | −0.654816 | − | 0.755788i | \(-0.727254\pi\) |
0.981940 | + | 0.189193i | \(0.0605872\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.67527 | − | 26.9480i | −0.0620469 | − | 0.998073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.01087 | − | 8.67909i | 0.137349 | − | 0.237895i | −0.789144 | − | 0.614209i | \(-0.789475\pi\) |
0.926492 | + | 0.376314i | \(0.122809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 24.2921 | + | 42.0752i | 0.518263 | + | 0.897658i | 0.999775 | + | 0.0212183i | \(0.00675450\pi\) |
−0.481512 | + | 0.876440i | \(0.659912\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 23.4090 | + | 5.49972i | 0.402944 | + | 0.0946681i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 75.3505 | 1.07501 | 0.537506 | − | 0.843260i | \(-0.319367\pi\) | ||||
0.537506 | + | 0.843260i | \(0.319367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116.052 | 1.40127 | 0.700633 | − | 0.713522i | \(-0.252901\pi\) | ||||
0.700633 | + | 0.713522i | \(0.252901\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.1753 | + | 60.2805i | 0.188865 | + | 0.626395i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.0367 | − | 32.9725i | −0.172584 | − | 0.298923i | 0.766739 | − | 0.641959i | \(-0.221878\pi\) |
−0.939322 | + | 0.343036i | \(0.888545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 51.7921 | − | 89.7066i | 0.414337 | − | 0.717653i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 108.000 | + | 89.5489i | 0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.3139 | − | 19.5962i | 0.0724459 | − | 0.125480i | −0.827527 | − | 0.561426i | \(-0.810253\pi\) |
0.899973 | + | 0.435946i | \(0.143586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 15.0584 | + | 26.0820i | 0.0872443 | + | 0.151112i | 0.906345 | − | 0.422538i | \(-0.138861\pi\) |
−0.819101 | + | 0.573649i | \(0.805527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.0326 | + | 49.8576i | 0.0792983 | + | 0.263003i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −56.0733 | −0.270804 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 130.103 | 0.578077 | 0.289038 | − | 0.957318i | \(-0.406665\pi\) | ||||
0.289038 | + | 0.957318i | \(0.406665\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −245.759 | − | 57.7390i | −1.00905 | − | 0.237068i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −173.742 | − | 300.930i | −0.661803 | − | 1.14628i | −0.980142 | − | 0.198299i | \(-0.936458\pi\) |
0.318339 | − | 0.947977i | \(-0.396875\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.3832 | − | 23.1803i | 0.0474631 | − | 0.0822085i | −0.841318 | − | 0.540541i | \(-0.818220\pi\) |
0.888781 | + | 0.458332i | \(0.151553\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −104.124 | + | 69.0678i | −0.344930 | + | 0.228801i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 230.439 | − | 399.132i | 0.715169 | − | 1.23871i | −0.247725 | − | 0.968830i | \(-0.579683\pi\) |
0.962894 | − | 0.269879i | \(-0.0869837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 98.0910 | + | 169.899i | 0.285980 | + | 0.495331i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −268.129 | + | 285.315i | −0.736188 | + | 0.783375i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −438.310 | −1.13597 | −0.567985 | − | 0.823039i | \(-0.692277\pi\) | ||||
−0.567985 | + | 0.823039i | \(0.692277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −46.3778 | −0.113702 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −412.961 | + | 439.430i | −0.959613 | + | 1.02112i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.18487 | + | 7.24841i | 0.00923430 | + | 0.0159943i | 0.870606 | − | 0.491982i | \(-0.163727\pi\) |
−0.861371 | + | 0.507976i | \(0.830394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 41.0448 | − | 71.0916i | 0.0861515 | − | 0.149219i | −0.819730 | − | 0.572750i | \(-0.805876\pi\) |
0.905881 | + | 0.423532i | \(0.139210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −292.928 | − | 145.683i | −0.585801 | − | 0.291338i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 112.417 | − | 194.712i | 0.214517 | − | 0.371555i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 341.785 | + | 591.989i | 0.623220 | + | 1.07945i | 0.988882 | + | 0.148701i | \(0.0475091\pi\) |
−0.365663 | + | 0.930747i | \(0.619158\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 192.591 | + | 45.2475i | 0.336018 | + | 0.0789444i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1097.61 | −1.83468 | −0.917339 | − | 0.398107i | \(-0.869667\pi\) | ||||
−0.917339 | + | 0.398107i | \(0.869667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 470.464 | 0.754297 | 0.377149 | − | 0.926153i | \(-0.376905\pi\) | ||||
0.377149 | + | 0.926153i | \(0.376905\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 155.376 | + | 515.325i | 0.239218 | + | 0.793395i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −60.7160 | − | 105.163i | −0.0898601 | − | 0.155642i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 243.017 | − | 420.919i | 0.346096 | − | 0.599456i | −0.639456 | − | 0.768828i | \(-0.720840\pi\) |
0.985552 | + | 0.169371i | \(0.0541737\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −723.387 | + | 90.2901i | −0.992300 | + | 0.123855i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 49.5829 | − | 85.8802i | 0.0655715 | − | 0.113573i | −0.831376 | − | 0.555711i | \(-0.812446\pi\) |
0.896947 | + | 0.442137i | \(0.145780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −174.351 | − | 301.984i | −0.222482 | − | 0.385350i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 33.9416 | + | 112.571i | 0.0418267 | + | 0.138723i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.80426 | 0.0104859 | 0.00524297 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524297 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 588.687 | 0.678145 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −152.344 | − | 35.7918i | −0.169864 | − | 0.0399079i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −268.527 | − | 465.103i | −0.290003 | − | 0.502300i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −330.486 | + | 572.419i | −0.345936 | + | 0.599179i | −0.985523 | − | 0.169540i | \(-0.945772\pi\) |
0.639587 | + | 0.768719i | \(0.279105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −242.278 | − | 120.493i | −0.245959 | − | 0.122323i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 282.561 | − | 489.410i | 0.278375 | − | 0.482160i | −0.692606 | − | 0.721316i | \(-0.743537\pi\) |
0.970981 | + | 0.239156i | \(0.0768708\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −485.591 | − | 841.068i | −0.464531 | − | 0.804592i | 0.534649 | − | 0.845074i | \(-0.320444\pi\) |
−0.999180 | + | 0.0404826i | \(0.987110\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 199.533 | − | 212.322i | 0.185451 | − | 0.197338i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 563.845 | 0.509430 | 0.254715 | − | 0.967016i | \(-0.418018\pi\) | ||||
0.254715 | + | 0.967016i | \(0.418018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 225.484 | 0.198142 | 0.0990709 | − | 0.995080i | \(-0.468413\pi\) | ||||
0.0990709 | + | 0.995080i | \(0.468413\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −462.962 | + | 492.637i | −0.395878 | + | 0.421252i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 345.531 | + | 598.478i | 0.287654 | + | 0.498231i | 0.973249 | − | 0.229752i | \(-0.0737915\pi\) |
−0.685596 | + | 0.727983i | \(0.740458\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −88.0964 | + | 152.587i | −0.0714350 | + | 0.123729i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1093.14 | − | 725.110i | 0.863772 | − | 0.572961i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 456.505 | − | 790.690i | 0.351662 | − | 0.609096i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 615.282 | + | 1065.70i | 0.462271 | + | 0.800676i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1757.72 | + | 412.960i | 1.28852 | + | 0.302726i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1057.82 | −0.756917 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 895.897 | 0.625968 | 0.312984 | − | 0.949758i | \(-0.398671\pi\) | ||||
0.312984 | + | 0.949758i | \(0.398671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 40.1495 | + | 133.161i | 0.0274028 | + | 0.0908849i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 827.428 | + | 1433.15i | 0.551853 | + | 0.955837i | 0.998141 | + | 0.0609476i | \(0.0194122\pi\) |
−0.446288 | + | 0.894889i | \(0.647254\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 703.090 | − | 1217.79i | 0.458388 | − | 0.793951i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 108.990 | − | 640.037i | 0.0694843 | − | 0.408042i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1325.55 | − | 2295.91i | 0.826635 | − | 1.43177i | −0.0740277 | − | 0.997256i | \(-0.523585\pi\) |
0.900663 | − | 0.434518i | \(-0.143081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 317.084 | + | 549.206i | 0.193487 | + | 0.335130i | 0.946404 | − | 0.322986i | \(-0.104687\pi\) |
−0.752916 | + | 0.658116i | \(0.771354\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 691.316 | + | 2292.84i | 0.412903 | + | 1.36944i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 486.899 | 0.284731 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −104.715 | −0.0599730 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −992.372 | − | 233.149i | −0.556799 | − | 0.130815i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1703.16 | + | 2949.96i | 0.936432 | + | 1.62195i | 0.772060 | + | 0.635550i | \(0.219227\pi\) |
0.164372 | + | 0.986398i | \(0.447440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −875.159 | + | 1515.82i | −0.471652 | + | 0.816925i | −0.999474 | − | 0.0324302i | \(-0.989675\pi\) |
0.527822 | + | 0.849355i | \(0.323009\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −126.232 | − | 2030.54i | −0.0667011 | − | 1.07294i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 69.6861 | − | 120.700i | 0.0361118 | − | 0.0625474i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1089.29 | − | 1886.70i | −0.553723 | − | 0.959076i | −0.998002 | − | 0.0631876i | \(-0.979873\pi\) |
0.444279 | − | 0.895889i | \(-0.353460\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1559.69 | − | 1659.66i | 0.777934 | − | 0.827797i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −461.329 | −0.225825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2188.41 | −1.05159 | −0.525797 | − | 0.850610i | \(-0.676233\pi\) | ||||
−0.525797 | + | 0.850610i | \(0.676233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 165.032 | − | 175.610i | 0.0778650 | − | 0.0828559i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 960.520 | + | 1663.67i | 0.445074 | + | 0.770890i | 0.998057 | − | 0.0623020i | \(-0.0198442\pi\) |
−0.552984 | + | 0.833192i | \(0.686511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.7132 | + | 141.531i | −0.0371931 | + | 0.0644203i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −194.417 | − | 3127.36i | −0.0869442 | − | 1.39857i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1584.91 | + | 2745.15i | −0.696525 | + | 1.20642i | 0.273139 | + | 0.961974i | \(0.411938\pi\) |
−0.969664 | + | 0.244442i | \(0.921395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −627.557 | − | 1086.96i | −0.271079 | − | 0.469523i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −42.3377 | − | 9.94685i | −0.0179791 | − | 0.00422402i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1368.78 | −0.571551 | −0.285776 | − | 0.958297i | \(-0.592251\pi\) | ||||
−0.285776 | + | 0.958297i | \(0.592251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3951.44 | −1.62270 | −0.811350 | − | 0.584561i | \(-0.801267\pi\) | ||||
−0.811350 | + | 0.584561i | \(0.801267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 123.134 | + | 408.390i | 0.0497396 | + | 0.164968i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −301.040 | − | 521.417i | −0.119637 | − | 0.207218i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 377.572 | − | 653.974i | 0.147651 | − | 0.255740i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1593.99 | − | 590.773i | 0.613469 | − | 0.227367i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1201.29 | + | 2080.70i | −0.455092 | + | 0.788243i | −0.998693 | − | 0.0511008i | \(-0.983727\pi\) |
0.543601 | + | 0.839344i | \(0.317060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 667.535 | + | 1156.20i | 0.248965 | + | 0.431220i | 0.963239 | − | 0.268646i | \(-0.0865763\pi\) |
−0.714274 | + | 0.699866i | \(0.753243\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 337.251 | + | 1118.54i | 0.123852 | + | 0.410769i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2630.89 | −0.951487 | −0.475743 | − | 0.879584i | \(-0.657821\pi\) | ||||
−0.475743 | + | 0.879584i | \(0.657821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2477.34 | −0.882483 | −0.441241 | − | 0.897388i | \(-0.645462\pi\) | ||||
−0.441241 | + | 0.897388i | \(0.645462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3457.79 | − | 812.376i | −1.21340 | − | 0.285078i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −137.088 | − | 237.444i | −0.0473976 | − | 0.0820950i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −804.028 | + | 1392.62i | −0.273931 | + | 0.474462i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −856.650 | + | 568.238i | −0.287639 | + | 0.190798i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 581.520 | − | 1007.22i | 0.192462 | − | 0.333354i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1392.36 | − | 2411.65i | −0.454286 | − | 0.786847i | 0.544361 | − | 0.838851i | \(-0.316772\pi\) |
−0.998647 | + | 0.0520047i | \(0.983439\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3905.75 | − | 4156.10i | 1.25642 | − | 1.33696i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −123.867 | −0.0392914 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 364.921 | 0.114159 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1674.11 | + | 1781.42i | −0.516557 | + | 0.549667i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1830.42 | + | 3170.39i | 0.557138 | + | 0.964992i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.5288 | + | 37.2890i | −0.00646491 | + | 0.0111976i | −0.869240 | − | 0.494391i | \(-0.835391\pi\) |
0.862775 | + | 0.505588i | \(0.168725\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2504.18 | − | 1245.41i | −0.741978 | − | 0.369010i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 341.630 | − | 591.721i | 0.0998889 | − | 0.173013i | −0.811750 | − | 0.584006i | \(-0.801485\pi\) |
0.911639 | + | 0.410993i | \(0.134818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2147.15 | − | 3718.98i | −0.619598 | − | 1.07317i | −0.989559 | − | 0.144127i | \(-0.953962\pi\) |
0.369962 | − | 0.929047i | \(-0.379371\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 614.254 | + | 144.313i | 0.174957 | + | 0.0411045i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3466.34 | 0.974625 | 0.487313 | − | 0.873228i | \(-0.337977\pi\) | ||||
0.487313 | + | 0.873228i | \(0.337977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2132.81 | −0.592040 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 729.052 | + | 2417.99i | 0.199819 | + | 0.662724i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2821.69 | + | 4887.30i | 0.763681 | + | 1.32273i | 0.940941 | + | 0.338570i | \(0.109943\pi\) |
−0.177261 | + | 0.984164i | \(0.556724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3294.71 | + | 5706.61i | −0.880627 | + | 1.52529i | −0.0299825 | + | 0.999550i | \(0.509545\pi\) |
−0.850645 | + | 0.525741i | \(0.823788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2232.23 | − | 3060.40i | 0.589291 | − | 0.807921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 453.938 | − | 786.243i | 0.118372 | − | 0.205025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2819.14 | + | 4882.89i | 0.726225 | + | 1.25786i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 148.749 | + | 493.344i | 0.0378577 | + | 0.125560i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4135.47 | −1.03996 | −0.519978 | − | 0.854180i | \(-0.674060\pi\) | ||||
−0.519978 | + | 0.854180i | \(0.674060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −381.562 | −0.0948165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1763.88 | + | 414.407i | 0.433170 | + | 0.101769i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1672.31 | + | 2896.53i | 0.405898 | + | 0.703036i | 0.994426 | − | 0.105441i | \(-0.0336254\pi\) |
−0.588527 | + | 0.808477i | \(0.700292\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 788.220 | − | 1365.24i | 0.189103 | − | 0.327536i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −547.031 | − | 272.057i | −0.129733 | − | 0.0645207i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3260.75 | − | 5647.78i | 0.764511 | − | 1.32417i | −0.175994 | − | 0.984391i | \(-0.556314\pi\) |
0.940505 | − | 0.339780i | \(-0.110353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1014.19 | + | 1756.62i | 0.235098 | + | 0.407202i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.3293 | + | 33.3374i | −0.00718097 | + | 0.00764125i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2904.99 | −0.658441 | −0.329220 | − | 0.944253i | \(-0.606786\pi\) | ||||
−0.329220 | + | 0.944253i | \(0.606786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1335.38 | 0.299331 | 0.149665 | − | 0.988737i | \(-0.452180\pi\) | ||||
0.149665 | + | 0.988737i | \(0.452180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2094.80 | + | 2229.07i | −0.464406 | + | 0.494174i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −519.048 | − | 899.017i | −0.113817 | − | 0.197137i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4187.82 | − | 7253.51i | 0.908381 | − | 1.57336i | 0.0920685 | − | 0.995753i | \(-0.470652\pi\) |
0.816313 | − | 0.577610i | \(-0.196015\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 677.629 | − | 449.488i | 0.145407 | − | 0.0964522i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2589.67 | − | 4485.43i | 0.549774 | − | 0.952237i | −0.448516 | − | 0.893775i | \(-0.648047\pi\) |
0.998290 | − | 0.0584616i | \(-0.0186195\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1540.03 | − | 2667.42i | −0.323482 | − | 0.560288i | 0.657722 | − | 0.753261i | \(-0.271520\pi\) |
−0.981204 | + | 0.192973i | \(0.938187\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2716.65 | + | 638.252i | 0.564632 | + | 0.132655i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4210.40 | −0.865966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 764.703 | 0.155649 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −991.459 | − | 3288.30i | −0.199726 | − | 0.662417i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1824.45 | − | 3160.04i | −0.363773 | − | 0.630073i | 0.624806 | − | 0.780780i | \(-0.285178\pi\) |
−0.988578 | + | 0.150708i | \(0.951845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.3664 | − | 33.5436i | 0.00382222 | − | 0.00662028i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1318.38 | − | 488.624i | 0.257576 | − | 0.0954640i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 924.882 | − | 1601.94i | 0.178887 | − | 0.309842i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −162.162 | − | 280.872i | −0.0310526 | − | 0.0537847i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 847.684 | + | 2811.45i | 0.160720 | + | 0.533048i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −379.887 | −0.0713190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3439.25 | 0.639376 | 0.319688 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319688 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4912.65 | + | 1154.18i | 0.904436 | + | 0.212489i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3587.66 | + | 6214.02i | 0.654141 | + | 1.13301i | 0.982108 | + | 0.188316i | \(0.0603030\pi\) |
−0.327968 | + | 0.944689i | \(0.606364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2428.65 | − | 4206.54i | 0.438579 | − | 0.759642i | −0.559001 | − | 0.829167i | \(-0.688815\pi\) |
0.997580 | + | 0.0695253i | \(0.0221485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 93.9378 | + | 1511.06i | 0.0168025 | + | 0.270282i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3773.97 | + | 6536.70i | −0.668666 | + | 1.15816i | 0.309611 | + | 0.950863i | \(0.399801\pi\) |
−0.978277 | + | 0.207300i | \(0.933532\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −113.385 | − | 196.388i | −0.0199007 | − | 0.0344690i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2006.40 | + | 2135.00i | −0.348867 | + | 0.371228i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8744.55 | 1.50638 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5032.56 | 0.858942 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −802.367 | + | 853.797i | −0.135691 | + | 0.144389i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2792.19 | − | 4836.22i | −0.467898 | − | 0.810423i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1564.86 | + | 2710.41i | −0.259856 | + | 0.450084i | −0.966203 | − | 0.257782i | \(-0.917008\pi\) |
0.706347 | + | 0.707866i | \(0.250342\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −217.957 | − | 3506.02i | −0.0358679 | − | 0.576963i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1581.69 | − | 2739.56i | 0.257960 | − | 0.446801i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4614.99 | + | 7993.39i | 0.745978 | + | 1.29207i | 0.949737 | + | 0.313050i | \(0.101351\pi\) |
−0.203759 | + | 0.979021i | \(0.565316\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3495.69 | − | 821.280i | −0.560058 | − | 0.131581i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 301.823 | 0.0479315 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6533.19 | 1.02845 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −264.289 | − | 876.548i | −0.0412430 | − | 0.136788i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4052.20 | − | 7018.61i | −0.626897 | − | 1.08582i | −0.988171 | − | 0.153358i | \(-0.950991\pi\) |
0.361273 | − | 0.932460i | \(-0.382342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1538.21 | + | 2664.26i | −0.235927 | + | 0.408638i | −0.959542 | − | 0.281566i | \(-0.909146\pi\) |
0.723615 | + | 0.690204i | \(0.242479\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1144.24 | + | 6719.45i | −0.174002 | + | 1.02182i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3075.04 | − | 5326.13i | 0.463649 | − | 0.803063i | −0.535491 | − | 0.844541i | \(-0.679873\pi\) |
0.999139 | + | 0.0414780i | \(0.0132067\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2539.71 | + | 4398.91i | 0.379701 | + | 0.657662i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1369.52 | + | 4542.17i | 0.203032 | + | 0.673381i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3307.94 | −0.486313 | −0.243156 | − | 0.969987i | \(-0.578183\pi\) | ||||
−0.243156 | + | 0.969987i | \(0.578183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6608.97 | 0.963548 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6224.71 | − | 1462.44i | −0.900035 | − | 0.211455i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1088.59 | − | 1885.49i | −0.156108 | − | 0.270387i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1474.65 | − | 2554.16i | 0.209744 | − | 0.363287i | −0.741890 | − | 0.670522i | \(-0.766070\pi\) |
0.951634 | + | 0.307235i | \(0.0994037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7818.38 | + | 5186.13i | −1.10300 | + | 0.731650i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2655.46 | + | 4599.40i | −0.371603 | + | 0.643636i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −581.790 | − | 1007.69i | −0.0807612 | − | 0.139883i | 0.822816 | − | 0.568308i | \(-0.192402\pi\) |
−0.903577 | + | 0.428425i | \(0.859068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3764.18 | − | 4005.46i | 0.518351 | − | 0.551576i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1099.35 | 0.150184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4016.67 | 0.544387 | 0.272193 | − | 0.962243i | \(-0.412251\pi\) | ||||
0.272193 | + | 0.962243i | \(0.412251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3187.98 | + | 3392.32i | −0.428675 | + | 0.456152i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5401.65 | − | 9355.93i | −0.720656 | − | 1.24821i | −0.960737 | − | 0.277460i | \(-0.910507\pi\) |
0.240081 | − | 0.970753i | \(-0.422826\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −280.977 | + | 486.666i | −0.0371945 | + | 0.0644228i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −647.083 | − | 321.816i | −0.0849950 | − | 0.0422708i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1032.29 | + | 1787.99i | −0.134549 | + | 0.233045i | −0.925425 | − | 0.378931i | \(-0.876292\pi\) |
0.790876 | + | 0.611976i | \(0.209625\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1434.42 | − | 2484.49i | −0.185529 | − | 0.321346i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8370.96 | − | 1966.68i | −1.07445 | − | 0.252432i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2249.23 | −0.286509 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7937.61 | −1.00347 | −0.501735 | − | 0.865022i | \(-0.667305\pi\) | ||||
−0.501735 | + | 0.865022i | \(0.667305\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2109.27 | + | 6995.65i | 0.264650 | + | 0.877746i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1289.10 | − | 2232.79i | −0.160536 | − | 0.278056i | 0.774525 | − | 0.632543i | \(-0.217989\pi\) |
−0.935061 | + | 0.354487i | \(0.884656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −731.602 | + | 1267.17i | −0.0904310 | + | 0.156631i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2035.67 | + | 2690.22i | 0.249762 | + | 0.330069i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 651.931 | − | 1129.18i | 0.0793981 | − | 0.137521i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2922.88 | − | 5062.57i | −0.353367 | − | 0.612049i | 0.633470 | − | 0.773767i | \(-0.281630\pi\) |
−0.986837 | + | 0.161718i | \(0.948297\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3976.64 | + | 13189.0i | 0.477258 | + | 1.58289i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 101.415 | 0.0120830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −458.912 | −0.0542822 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3207.89 | − | 753.665i | −0.376717 | − | 0.0885063i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4370.66 | − | 7570.20i | −0.509596 | − | 0.882646i | −0.999938 | − | 0.0111158i | \(-0.996462\pi\) |
0.490343 | − | 0.871530i | \(-0.336872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −528.254 | + | 914.963i | −0.0611533 | + | 0.105921i | −0.894981 | − | 0.446104i | \(-0.852811\pi\) |
0.833828 | + | 0.552024i | \(0.186145\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11141.8 | − | 5541.21i | −1.28070 | − | 0.636933i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3902.56 | − | 6759.44i | 0.445417 | − | 0.771484i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −497.333 | − | 861.406i | −0.0563645 | − | 0.0976261i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1732.59 | + | 1843.65i | −0.194989 | + | 0.207487i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9868.64 | −1.10291 | −0.551457 | − | 0.834203i | \(-0.685928\pi\) | ||||
−0.551457 | + | 0.834203i | \(0.685928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 477.948 | 0.0530456 | 0.0265228 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265228 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 372.619 | − | 396.503i | 0.0410706 | − | 0.0437031i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2209.24 | − | 3826.51i | −0.241835 | − | 0.418871i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −526.239 | + | 911.473i | −0.0572119 | + | 0.0990939i | −0.893213 | − | 0.449634i | \(-0.851554\pi\) |
0.836001 | + | 0.548728i | \(0.184888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4414.10 | − | 2927.98i | 0.476633 | − | 0.316162i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5249.35 | + | 9092.14i | −0.562989 | + | 0.975126i | 0.434245 | + | 0.900795i | \(0.357015\pi\) |
−0.997234 | + | 0.0743307i | \(0.976318\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.3718 | − | 35.2850i | −0.00217015 | − | 0.00375881i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17230.6 | − | 4048.18i | −1.82322 | − | 0.428349i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7329.40 | −0.770369 | −0.385184 | − | 0.922840i | \(-0.625862\pi\) | ||||
−0.385184 | + | 0.922840i | \(0.625862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3482.39 | −0.363591 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2625.48 | − | 8707.72i | −0.272308 | − | 0.903144i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1362.14 | − | 2359.30i | −0.140347 | − | 0.243089i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3572.20 | + | 6187.23i | −0.365646 | + | 0.633318i | −0.988880 | − | 0.148718i | \(-0.952485\pi\) |
0.623233 | + | 0.782036i | \(0.285819\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8137.86 | + | 6747.55i | 0.827544 | + | 0.686163i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2859.34 | + | 4952.53i | −0.288878 | + | 0.500352i | −0.973542 | − | 0.228507i | \(-0.926616\pi\) |
0.684664 | + | 0.728859i | \(0.259949\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 394.233 | + | 682.831i | 0.0395714 | + | 0.0685397i | 0.885133 | − | 0.465339i | \(-0.154067\pi\) |
−0.845561 | + | 0.533878i | \(0.820734\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 209.058 | + | 693.368i | 0.0208491 | + | 0.0691488i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17068.0 | 1.69125 | 0.845626 | − | 0.533776i | \(-0.179228\pi\) | ||||
0.845626 | + | 0.533776i | \(0.179228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8282.72 | 0.815481 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11020.1 | + | 2589.08i | 1.07809 | + | 0.253288i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −134.123 | − | 232.307i | −0.0130380 | − | 0.0225824i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6010.56 | − | 10410.6i | 0.580596 | − | 1.00562i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 734.285 | + | 11811.6i | 0.0704834 | + | 1.13378i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 758.994 | − | 1314.62i | 0.0723994 | − | 0.125399i | −0.827553 | − | 0.561388i | \(-0.810268\pi\) |
0.899952 | + | 0.435988i | \(0.143601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3160.48 | + | 5474.11i | 0.299596 | + | 0.518915i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1641.60 | − | 1746.82i | 0.154649 | − | 0.164562i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3058.80 | 0.286377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12737.3 | −1.18518 | −0.592591 | − | 0.805503i | \(-0.701895\pi\) | ||||
−0.592591 | + | 0.805503i | \(0.701895\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7787.30 | − | 8286.44i | 0.720151 | − | 0.766310i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2823.85 | + | 4891.05i | 0.259549 | + | 0.449552i | 0.966121 | − | 0.258089i | \(-0.0830928\pi\) |
−0.706572 | + | 0.707641i | \(0.749759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 852.505 | − | 1476.58i | 0.0778801 | − | 0.134892i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 77.6952 | + | 1249.79i | 0.00705483 | + | 0.113482i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6649.78 | + | 11517.7i | −0.600167 | + | 1.03952i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5423.14 | + | 9393.15i | 0.486519 | + | 0.842676i | 0.999880 | − | 0.0154970i | \(-0.00493306\pi\) |
−0.513361 | + | 0.858173i | \(0.671600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9717.43 | − | 2283.02i | −0.866553 | − | 0.203589i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12345.7 | 1.09437 | 0.547186 | − | 0.837011i | \(-0.315699\pi\) | ||||
0.547186 | + | 0.837011i | \(0.315699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2615.23 | −0.230448 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −245.140 | − | 813.036i | −0.0214734 | − | 0.0712193i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2947.87 | + | 5105.87i | 0.256704 | + | 0.444624i | 0.965357 | − | 0.260933i | \(-0.0840302\pi\) |
−0.708653 | + | 0.705557i | \(0.750697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2850.27 | − | 4936.82i | 0.246749 | − | 0.427381i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12533.6 | + | 10392.3i | 1.07870 | + | 0.894407i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2247.18 | + | 3892.23i | −0.192277 | + | 0.333033i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2309.40 | − | 4000.00i | −0.196455 | − | 0.340270i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4754.74 | − | 15769.7i | −0.402139 | − | 1.33374i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5211.51 | 0.438235 | 0.219118 | − | 0.975698i | \(-0.429682\pi\) | ||||
0.219118 | + | 0.975698i | \(0.429682\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9809.86 | 0.820182 | 0.410091 | − | 0.912045i | \(-0.365497\pi\) | ||||
0.410091 | + | 0.912045i | \(0.365497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6348.90 | + | 1491.62i | 0.527788 | + | 0.123999i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1134.66 | + | 1965.29i | 0.0937886 | + | 0.162447i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5358.71 | − | 9281.56i | 0.440430 | − | 0.762847i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 188.319 | − | 124.917i | 0.0153905 | − | 0.0102089i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8441.11 | − | 14620.4i | 0.685976 | − | 1.18814i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1304.66 | − | 2259.73i | −0.105430 | − | 0.182611i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4870.71 | − | 5182.91i | 0.391409 | − | 0.416497i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1966.09 | 0.157116 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8084.25 | 0.642456 | 0.321228 | − | 0.947002i | \(-0.395904\pi\) | ||||
0.321228 | + | 0.947002i | \(0.395904\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14060.9 | − | 14962.2i | 1.11125 | − | 1.18248i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −521.738 | − | 903.677i | −0.0410070 | − | 0.0710262i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12033.6 | + | 20842.7i | −0.940617 | + | 1.62920i | −0.176319 | + | 0.984333i | \(0.556419\pi\) |
−0.764298 | + | 0.644863i | \(0.776914\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1984.54 | − | 986.976i | −0.154277 | − | 0.0767270i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1312.99 | − | 2274.17i | 0.101516 | − | 0.175831i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2944.60 | − | 5100.20i | −0.226433 | − | 0.392193i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3045.58 | + | 715.531i | 0.232933 | + | 0.0547254i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4582.37 | 0.348584 | 0.174292 | − | 0.984694i | \(-0.444236\pi\) | ||||
0.174292 | + | 0.984694i | \(0.444236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1300.42 | 0.0983934 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1132.72 | + | 3756.79i | 0.0852466 | + | 0.282731i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1547.66 | − | 2680.62i | −0.115854 | − | 0.200666i | 0.802267 | − | 0.596966i | \(-0.203627\pi\) |
−0.918121 | + | 0.396300i | \(0.870294\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1599.02 | − | 2769.59i | 0.119064 | − | 0.206226i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3435.13 | + | 8137.87i | −0.254430 | + | 0.602749i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10282.5 | + | 17809.9i | −0.757586 | + | 1.31218i | 0.186492 | + | 0.982456i | \(0.440288\pi\) |
−0.944078 | + | 0.329721i | \(0.893045\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −584.992 | − | 1013.24i | −0.0428742 | − | 0.0742602i | 0.843792 | − | 0.536670i | \(-0.180318\pi\) |
−0.886666 | + | 0.462410i | \(0.846985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3603.88 | − | 11952.7i | −0.262748 | − | 0.871435i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3943.80 | −0.286031 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13073.0 | −0.943214 | −0.471607 | − | 0.881809i | \(-0.656326\pi\) | ||||
−0.471607 | + | 0.881809i | \(0.656326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6753.35 | − | 1586.64i | −0.484731 | − | 0.113883i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −600.789 | − | 1040.60i | −0.0429000 | − | 0.0743050i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2196.31 | + | 3804.13i | −0.156024 | + | 0.270242i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5435.42 | − | 2703.22i | −0.384149 | − | 0.191050i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7273.91 | + | 12598.8i | −0.511459 | + | 0.885873i | 0.488453 | + | 0.872590i | \(0.337561\pi\) |
−0.999912 | + | 0.0132825i | \(0.995772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1747.55 | + | 3026.85i | 0.122252 | + | 0.211747i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9361.80 | − | 9961.87i | 0.651596 | − | 0.693361i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19018.0 | 1.31699 | 0.658494 | − | 0.752586i | \(-0.271194\pi\) | ||||
0.658494 | + | 0.752586i | \(0.271194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4225.16 | −0.291117 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8815.43 | − | 9380.47i | 0.604341 | − | 0.643077i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5587.20 | + | 9677.32i | 0.381113 | + | 0.660108i | 0.991222 | − | 0.132210i | \(-0.0422074\pi\) |
−0.610108 | + | 0.792318i | \(0.708874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2294.27 | + | 3973.79i | −0.155716 | + | 0.269708i | −0.933319 | − | 0.359047i | \(-0.883102\pi\) |
0.777604 | + | 0.628755i | \(0.216435\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15380.3 | − | 10202.2i | 1.03870 | − | 0.688995i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2847.35 | − | 4931.76i | 0.191341 | − | 0.331413i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5744.99 | − | 9950.61i | −0.384155 | − | 0.665375i | 0.607497 | − | 0.794322i | \(-0.292174\pi\) |
−0.991652 | + | 0.128947i | \(0.958840\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1386.90 | + | 325.840i | 0.0922825 | + | 0.0216809i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22391.4 | 1.48258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22966.9 | −1.51326 | −0.756628 | − | 0.653846i | \(-0.773154\pi\) | ||||
−0.756628 | + | 0.653846i | \(0.773154\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2412.08 | − | 7999.98i | −0.158154 | − | 0.524537i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4248.31 | + | 7358.29i | 0.277197 | + | 0.480120i | 0.970687 | − | 0.240347i | \(-0.0772612\pi\) |
−0.693490 | + | 0.720466i | \(0.743928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7169.94 | − | 12418.7i | 0.465564 | − | 0.806381i | −0.533662 | − | 0.845698i | \(-0.679185\pi\) |
0.999227 | + | 0.0393163i | \(0.0125180\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 896.688 | − | 5265.74i | 0.0579434 | − | 0.340269i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 53.3399 | − | 92.3874i | 0.00343021 | − | 0.00594129i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4026.36 | − | 6973.86i | −0.257687 | − | 0.446327i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1744.56 | + | 5786.05i | 0.111118 | + | 0.368537i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9803.34 | 0.621439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17834.3 | −1.12516 | −0.562578 | − | 0.826744i | \(-0.690190\pi\) | ||||
−0.562578 | + | 0.826744i | \(0.690190\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14086.3 | + | 3309.46i | 0.884489 | + | 0.207803i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2072.98 | − | 3590.51i | −0.129549 | − | 0.224386i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4765.68 | + | 8254.39i | −0.296425 | + | 0.513424i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1838.79 | + | 29578.3i | 0.113836 | + | 1.83114i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13173.0 | + | 22816.3i | −0.811705 | + | 1.40591i | 0.0999654 | + | 0.994991i | \(0.468127\pi\) |
−0.911670 | + | 0.410923i | \(0.865207\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10782.5 | − | 18675.9i | −0.661309 | − | 1.14542i | −0.980272 | − | 0.197653i | \(-0.936668\pi\) |
0.318963 | − | 0.947767i | \(-0.396665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 440.771 | − | 469.023i | 0.0269075 | − | 0.0286322i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4186.32 | −0.254376 | −0.127188 | − | 0.991879i | \(-0.540595\pi\) | ||||
−0.127188 | + | 0.991879i | \(0.540595\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 83.8794 | 0.00507328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1298.54 | + | 1381.78i | −0.0781781 | + | 0.0831891i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1402.57 | − | 2429.33i | −0.0840534 | − | 0.145585i | 0.820934 | − | 0.571023i | \(-0.193453\pi\) |
−0.904987 | + | 0.425438i | \(0.860120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3829.10 | − | 6632.20i | 0.228420 | − | 0.395636i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −788.153 | − | 12678.1i | −0.0468018 | − | 0.752844i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9536.15 | + | 16517.1i | −0.563696 | + | 0.976350i | 0.433474 | + | 0.901166i | \(0.357288\pi\) |
−0.997170 | + | 0.0751839i | \(0.976046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12256.5 | + | 21228.9i | 0.721216 | + | 1.24918i | 0.960513 | + | 0.278237i | \(0.0897500\pi\) |
−0.239296 | + | 0.970947i | \(0.576917\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18518.1 | − | 4350.66i | −1.08474 | − | 0.254850i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6507.40 | −0.379468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −861.513 | −0.0500119 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −64.5864 | − | 214.209i | −0.00373252 | − | 0.0123794i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −411.340 | − | 712.462i | −0.0236656 | − | 0.0409900i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1773.32 | − | 3071.49i | 0.101570 | − | 0.175924i | −0.810762 | − | 0.585376i | \(-0.800947\pi\) |
0.912332 | + | 0.409452i | \(0.134280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13626.7 | − | 5050.38i | 0.777023 | − | 0.287984i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8937.50 | + | 15480.2i | −0.507380 | + | 0.878807i | 0.492584 | + | 0.870265i | \(0.336052\pi\) |
−0.999964 | + | 0.00854232i | \(0.997281\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4004.45 | + | 6935.91i | 0.226328 | + | 0.392012i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1024.89 | + | 3399.18i | 0.0576709 | + | 0.191273i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2857.23 | −0.160072 | −0.0800358 | − | 0.996792i | \(-0.525503\pi\) | ||||
−0.0800358 | + | 0.996792i | \(0.525503\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12268.5 | −0.684315 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21722.4 | + | 5103.48i | 1.20635 | + | 0.283421i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10647.5 | − | 18441.9i | −0.588732 | − | 1.01971i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7813.79 | + | 13533.9i | −0.430175 | + | 0.745084i | −0.996888 | − | 0.0788308i | \(-0.974881\pi\) |
0.566714 | + | 0.823915i | \(0.308215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2732.22 | + | 1812.35i | −0.149767 | + | 0.0993441i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1467.38 | − | 2541.57i | 0.0800874 | − | 0.138716i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13091.5 | − | 22675.2i | −0.711445 | − | 1.23226i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12334.7 | + | 13125.3i | −0.667442 | + | 0.710223i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17562.6 | 0.946264 | 0.473132 | − | 0.880992i | \(-0.343123\pi\) | ||||
0.473132 | + | 0.880992i | \(0.343123\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15098.7 | 0.810039 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7589.44 | − | 8075.91i | 0.405440 | − | 0.431427i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3423.75 | − | 5930.11i | −0.182126 | − | 0.315452i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10001.8 | + | 17323.6i | −0.529795 | + | 0.917632i | 0.469601 | + | 0.882879i | \(0.344398\pi\) |
−0.999396 | + | 0.0347532i | \(0.988935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11750.0 | − | 5843.68i | −0.619775 | − | 0.308235i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 573.324 | − | 993.027i | 0.0301138 | − | 0.0521587i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1126.62 | − | 1951.36i | −0.0589273 | − | 0.102065i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28546.6 | − | 6706.75i | −1.48688 | − | 0.349328i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25504.1 | −1.32287 | −0.661435 | − | 0.750002i | \(-0.730052\pi\) | ||||
−0.661435 | + | 0.750002i | \(0.730052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11767.7 | −0.607837 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9884.14 | − | 32782.0i | −0.508430 | − | 1.68627i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1171.94 | − | 2029.85i | −0.0600340 | − | 0.103982i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11954.9 | + | 20706.5i | −0.609879 | + | 1.05634i | 0.381380 | + | 0.924418i | \(0.375449\pi\) |
−0.991260 | + | 0.131924i | \(0.957885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3645.00 | + | 19342.6i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1008.43 | − | 1746.65i | 0.0510233 | − | 0.0883750i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4252.77 | + | 7366.02i | 0.214297 | + | 0.371173i | 0.953055 | − | 0.302798i | \(-0.0979206\pi\) |
−0.738758 | + | 0.673971i | \(0.764587\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1361.81 | + | 4516.62i | 0.0683418 | + | 0.226664i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6850.57 | 0.342394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25802.5 | −1.28438 | −0.642192 | − | 0.766544i | \(-0.721975\pi\) | ||||
−0.642192 | + | 0.766544i | \(0.721975\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28520.8 | − | 6700.70i | −1.41395 | − | 0.332195i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13668.8 | + | 23675.0i | 0.674911 | + | 1.16898i | 0.976495 | + | 0.215541i | \(0.0691514\pi\) |
−0.301584 | + | 0.953440i | \(0.597515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7881.75 | − | 13651.6i | 0.387604 | − | 0.671350i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2397.36 | − | 1192.29i | −0.117423 | − | 0.0583983i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3416.01 | − | 5916.71i | 0.166647 | − | 0.288641i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1668.32 | + | 2889.61i | 0.0810623 | + | 0.140404i | 0.903706 | − | 0.428153i | \(-0.140835\pi\) |
−0.822644 | + | 0.568557i | \(0.807502\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14715.8 | − | 15659.0i | 0.712181 | − | 0.757830i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8099.98 | 0.390448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33149.5 | 1.59160 | 0.795798 | − | 0.605562i | \(-0.207052\pi\) | ||||
0.795798 | + | 0.605562i | \(0.207052\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1357.76 | − | 1444.79i | 0.0649321 | − | 0.0690940i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5498.42 | + | 9523.54i | 0.261915 | + | 0.453651i | 0.966751 | − | 0.255720i | \(-0.0823125\pi\) |
−0.704836 | + | 0.709371i | \(0.748979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1366.08 | − | 2366.12i | 0.0648169 | − | 0.112266i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7845.77 | + | 5204.30i | −0.370803 | + | 0.245963i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −203.319 | + | 352.158i | −0.00957159 | + | 0.0165785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16642.5 | − | 28825.6i | −0.780420 | − | 1.35173i | −0.931697 | − | 0.363236i | \(-0.881672\pi\) |
0.151277 | − | 0.988491i | \(-0.451661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16918.5 | − | 3974.85i | −0.790279 | − | 0.185669i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7242.46 | −0.336990 | −0.168495 | − | 0.985703i | \(-0.553891\pi\) | ||||
−0.168495 | + | 0.985703i | \(0.553891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3119.63 | 0.144594 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2364.66 | + | 7842.69i | 0.109179 | + | 0.362104i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20163.0 | − | 34923.4i | −0.927362 | − | 1.60624i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5499.98 | + | 9526.24i | −0.251991 | + | 0.436461i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2976.71 | − | 1103.24i | 0.135861 | − | 0.0503534i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5040.91 | + | 8731.11i | −0.229195 | + | 0.396977i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8707.15 | + | 15081.2i | 0.394379 | + | 0.683084i | 0.993022 | − | 0.117932i | \(-0.0376264\pi\) |
−0.598643 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9782.25 | + | 32444.0i | 0.441391 | + | 1.46393i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8373.50 | 0.376394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3988.26 | 0.178597 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10260.4 | − | 2410.58i | −0.457733 | − | 0.107540i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14566.5 | − | 25229.9i | −0.647391 | − | 1.12131i | −0.983744 | − | 0.179578i | \(-0.942527\pi\) |
0.336353 | − | 0.941736i | \(-0.390807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17363.7 | − | 30074.8i | 0.768815 | − | 1.33163i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.7495 | − | 237.257i | −0.000650620 | − | 0.0104657i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2357.44 | − | 4083.20i | 0.103602 | − | 0.179443i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1067.45 | + | 1848.88i | 0.0467362 | + | 0.0809495i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10337.2 | − | 10999.8i | 0.450912 | − | 0.479815i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36440.1 | −1.58364 | −0.791820 | − | 0.610754i | \(-0.790866\pi\) | ||||
−0.791820 | + | 0.610754i | \(0.790866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18922.0 | 0.819286 | 0.409643 | − | 0.912246i | \(-0.365653\pi\) | ||||
0.409643 | + | 0.912246i | \(0.365653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4751.85 | + | 5056.43i | −0.204987 | + | 0.218126i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5063.68 | + | 8770.55i | 0.217636 | + | 0.376956i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1553.14 | − | 2690.11i | 0.0665084 | − | 0.115196i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −986.208 | − | 15863.9i | −0.0420768 | − | 0.676839i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8955.36 | − | 15511.1i | 0.380687 | − | 0.659369i | −0.610474 | − | 0.792037i | \(-0.709021\pi\) |
0.991161 | + | 0.132667i | \(0.0423542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8762.22 | + | 15176.6i | 0.371120 | + | 0.642799i | 0.989738 | − | 0.142893i | \(-0.0456405\pi\) |
−0.618618 | + | 0.785692i | \(0.712307\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5251.12 | + | 1233.70i | 0.221601 | + | 0.0520631i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17643.9 | 0.741885 | 0.370943 | − | 0.928656i | \(-0.379035\pi\) | ||||
0.370943 | + | 0.928656i | \(0.379035\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45178.6 | 1.89278 | 0.946391 | − | 0.323023i | \(-0.104699\pi\) | ||||
0.946391 | + | 0.323023i | \(0.104699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12563.5 | + | 41668.3i | 0.524454 | + | 1.73942i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7391.21 | + | 12802.0i | 0.307431 | + | 0.532487i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4445.02 | − | 7699.00i | 0.184223 | − | 0.319084i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −709.300 | + | 4165.32i | −0.0292915 | + | 0.172012i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13388.0 | − | 23188.7i | 0.550901 | − | 0.954188i | −0.447309 | − | 0.894379i | \(-0.647618\pi\) |
0.998210 | − | 0.0598087i | \(-0.0190491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11938.5 | + | 20678.1i | 0.489503 | + | 0.847844i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7769.00 | + | 25766.9i | 0.317412 | + | 1.05274i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 756.291 | 0.0307896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14910.6 | 0.604879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15580.3 | + | 3660.45i | 0.629816 | + | 0.147970i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2476.73 | − | 4289.83i | −0.0997665 | − | 0.172801i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3955.88 | − | 6851.78i | 0.158789 | − | 0.275030i | −0.775644 | − | 0.631171i | \(-0.782575\pi\) |
0.934432 | + | 0.356141i | \(0.115908\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12083.7 | + | 8015.43i | −0.483339 | + | 0.320611i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −924.149 | + | 1600.67i | −0.0368359 | + | 0.0638016i | −0.883856 | − | 0.467760i | \(-0.845061\pi\) |
0.847020 | + | 0.531561i | \(0.178395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9427.10 | − | 16328.2i | −0.374445 | − | 0.648558i | 0.615799 | − | 0.787904i | \(-0.288833\pi\) |
−0.990244 | + | 0.139345i | \(0.955500\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14982.4 | − | 15942.7i | 0.593030 | − | 0.631041i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2086.03 | −0.0822821 | −0.0411410 | − | 0.999153i | \(-0.513099\pi\) | ||||
−0.0411410 | + | 0.999153i | \(0.513099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14669.1 | 0.576605 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2721.13 | + | 2895.55i | −0.106591 | + | 0.113423i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2435.46 | − | 4218.34i | −0.0950717 | − | 0.164669i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16605.4 | + | 28761.3i | −0.645983 | + | 1.11888i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15979.2 | + | 7946.98i | 0.619489 | + | 0.308092i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6408.74 | + | 11100.3i | −0.247606 | + | 0.428866i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12388.6 | + | 21457.7i | 0.477005 | + | 0.826197i | 0.999653 | − | 0.0263520i | \(-0.00838907\pi\) |
−0.522648 | + | 0.852549i | \(0.675056\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18457.6 | + | 4336.46i | 0.708261 | + | 0.166399i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3741.26 | 0.143072 | 0.0715359 | − | 0.997438i | \(-0.477210\pi\) | ||||
0.0715359 | + | 0.997438i | \(0.477210\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14131.6 | −0.538580 | −0.269290 | − | 0.963059i | \(-0.586789\pi\) | ||||
−0.269290 | + | 0.963059i | \(0.586789\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 58.0992 | + | 192.693i | 0.00220676 | + | 0.00731900i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13311.3 | + | 23055.8i | 0.503888 | + | 0.872759i | 0.999990 | + | 0.00449496i | \(0.00143080\pi\) |
−0.496102 | + | 0.868264i | \(0.665236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5427.72 | − | 9401.09i | 0.204769 | − | 0.354671i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2841.17 | + | 6730.77i | −0.106827 | + | 0.253074i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26742.8 | − | 46319.9i | 1.00214 | − | 1.73576i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3167.17 | + | 5485.70i | 0.118287 | + | 0.204879i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2774.65 | + | 9202.46i | 0.103281 | + | 0.342543i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 681.475 | 0.0252820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33026.9 | −1.22118 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1640.56 | + | 385.436i | 0.0604591 | + | 0.0142043i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9143.09 | + | 15836.3i | 0.335830 | + | 0.581675i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26309.7 | − | 45569.7i | 0.963174 | − | 1.66827i | 0.248731 | − | 0.968572i | \(-0.419986\pi\) |
0.714443 | − | 0.699694i | \(-0.246680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13662.0 | − | 6794.56i | −0.498503 | − | 0.247922i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5090.22 | − | 8816.52i | 0.185122 | − | 0.320641i | −0.758495 | − | 0.651678i | \(-0.774065\pi\) |
0.943618 | + | 0.331037i | \(0.107399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −496.908 | − | 860.670i | −0.0180123 | − | 0.0311983i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1351.80 | − | 1438.45i | 0.0488406 | − | 0.0519711i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20051.6 | 0.722097 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45618.2 | 1.63744 | 0.818718 | − | 0.574195i | \(-0.194685\pi\) | ||||
0.818718 | + | 0.574195i | \(0.194685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12238.3 | + | 13022.7i | −0.437857 | + | 0.465922i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26663.2 | − | 46182.1i | −0.950846 | − | 1.64691i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6738.32 | − | 11671.1i | 0.239518 | − | 0.414858i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21851.6 | + | 14494.7i | −0.774219 | + | 0.513558i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6600.20 | − | 11431.9i | 0.233095 | − | 0.403733i | −0.725622 | − | 0.688093i | \(-0.758448\pi\) |
0.958717 | + | 0.284361i | \(0.0917813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11383.6 | + | 19717.0i | 0.400734 | + | 0.694091i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36295.8 | − | 8527.38i | −1.27360 | − | 0.299222i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3494.59 | −0.122230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13468.1 | −0.469565 | −0.234783 | − | 0.972048i | \(-0.575438\pi\) | ||||
−0.234783 | + | 0.972048i | \(0.575438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7285.95 | + | 24164.8i | 0.253214 | + | 0.839816i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6942.05 | − | 12024.0i | −0.240493 | − | 0.416547i | 0.720362 | − | 0.693599i | \(-0.243976\pi\) |
−0.960855 | + | 0.277052i | \(0.910643\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6614.93 | + | 11457.4i | −0.228432 | + | 0.395657i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6055.92 | − | 5021.30i | −0.208465 | − | 0.172850i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2638.32 | − | 4569.70i | 0.0905320 | − | 0.156806i | −0.817203 | − | 0.576350i | \(-0.804477\pi\) |
0.907735 | + | 0.419544i | \(0.137810\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11428.6 | + | 19794.9i | 0.390924 | + | 0.677101i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11321.9 | − | 37550.5i | −0.386054 | − | 1.28040i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26131.4 | −0.888225 | −0.444112 | − | 0.895971i | \(-0.646481\pi\) | ||||
−0.444112 | + | 0.895971i | \(0.646481\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11118.5 | 0.376740 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1147.09 | + | 269.500i | 0.0387464 | + | 0.00910312i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16061.4 | − | 27819.2i | −0.540825 | − | 0.936736i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14442.0 | − | 25014.3i | 0.484777 | − | 0.839658i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −944.591 | − | 15194.5i | −0.0316085 | − | 0.508448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3089.16 | − | 5350.59i | 0.103050 | − | 0.178489i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1998.77 | − | 3461.96i | −0.0664695 | − | 0.115128i | 0.830875 | − | 0.556458i | \(-0.187840\pi\) |
−0.897345 | + | 0.441330i | \(0.854507\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −31116.8 | + | 33111.3i | −1.03159 | + | 1.09772i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41785.1 | −1.38100 | −0.690499 | − | 0.723334i | \(-0.742609\pi\) | ||||
−0.690499 | + | 0.723334i | \(0.742609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7684.12 | 0.253177 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17908.0 | + | 19055.8i | −0.588219 | + | 0.625923i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6122.55 | − | 10604.6i | −0.200489 | − | 0.347257i | 0.748197 | − | 0.663476i | \(-0.230920\pi\) |
−0.948686 | + | 0.316220i | \(0.897586\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.1170 | − | 76.4129i | 0.00144023 | − | 0.00249455i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −377.746 | − | 6076.34i | −0.0122941 | − | 0.197760i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21891.5 | − | 37917.3i | 0.710307 | − | 1.23029i | −0.254435 | − | 0.967090i | \(-0.581889\pi\) |
0.964742 | − | 0.263198i | \(-0.0847773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6087.50 | + | 10543.9i | 0.196918 | + | 0.341071i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28248.2 | + | 6636.65i | 0.910992 | + | 0.214029i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1019.08 | −0.0327654 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5178.38 | −0.165991 | −0.0829953 | − | 0.996550i | \(-0.526449\pi\) | ||||
−0.0829953 | + | 0.996550i | \(0.526449\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4694.57 | − | 15570.1i | −0.150028 | − | 0.497587i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5732.22 | + | 9928.50i | 0.182637 | + | 0.316336i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12860.5 | + | 22275.0i | −0.408520 | + | 0.707578i | −0.994724 | − | 0.102586i | \(-0.967288\pi\) |
0.586204 | + | 0.810164i | \(0.300622\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14051.1 | + | 11650.6i | 0.445004 | + | 0.368977i |
(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 | 144.4.i.c.97.1 | 4 | ||
3.2 | odd | 2 | 432.4.i.c.289.1 | 4 | |||
4.3 | odd | 2 | 9.4.c.a.7.1 | yes | 4 | ||
9.2 | odd | 6 | 1296.4.a.i.1.2 | 2 | |||
9.4 | even | 3 | inner | 144.4.i.c.49.1 | 4 | ||
9.5 | odd | 6 | 432.4.i.c.145.1 | 4 | |||
9.7 | even | 3 | 1296.4.a.u.1.1 | 2 | |||
12.11 | even | 2 | 27.4.c.a.19.2 | 4 | |||
20.3 | even | 4 | 225.4.k.b.124.4 | 8 | |||
20.7 | even | 4 | 225.4.k.b.124.1 | 8 | |||
20.19 | odd | 2 | 225.4.e.b.151.2 | 4 | |||
36.7 | odd | 6 | 81.4.a.d.1.2 | 2 | |||
36.11 | even | 6 | 81.4.a.a.1.1 | 2 | |||
36.23 | even | 6 | 27.4.c.a.10.2 | 4 | |||
36.31 | odd | 6 | 9.4.c.a.4.1 | ✓ | 4 | ||
180.67 | even | 12 | 225.4.k.b.49.4 | 8 | |||
180.79 | odd | 6 | 2025.4.a.g.1.1 | 2 | |||
180.103 | even | 12 | 225.4.k.b.49.1 | 8 | |||
180.119 | even | 6 | 2025.4.a.n.1.2 | 2 | |||
180.139 | odd | 6 | 225.4.e.b.76.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.4.c.a.4.1 | ✓ | 4 | 36.31 | odd | 6 | ||
9.4.c.a.7.1 | yes | 4 | 4.3 | odd | 2 | ||
27.4.c.a.10.2 | 4 | 36.23 | even | 6 | |||
27.4.c.a.19.2 | 4 | 12.11 | even | 2 | |||
81.4.a.a.1.1 | 2 | 36.11 | even | 6 | |||
81.4.a.d.1.2 | 2 | 36.7 | odd | 6 | |||
144.4.i.c.49.1 | 4 | 9.4 | even | 3 | inner | ||
144.4.i.c.97.1 | 4 | 1.1 | even | 1 | trivial | ||
225.4.e.b.76.2 | 4 | 180.139 | odd | 6 | |||
225.4.e.b.151.2 | 4 | 20.19 | odd | 2 | |||
225.4.k.b.49.1 | 8 | 180.103 | even | 12 | |||
225.4.k.b.49.4 | 8 | 180.67 | even | 12 | |||
225.4.k.b.124.1 | 8 | 20.7 | even | 4 | |||
225.4.k.b.124.4 | 8 | 20.3 | even | 4 | |||
432.4.i.c.145.1 | 4 | 9.5 | odd | 6 | |||
432.4.i.c.289.1 | 4 | 3.2 | odd | 2 | |||
1296.4.a.i.1.2 | 2 | 9.2 | odd | 6 | |||
1296.4.a.u.1.1 | 2 | 9.7 | even | 3 | |||
2025.4.a.g.1.1 | 2 | 180.79 | odd | 6 | |||
2025.4.a.n.1.2 | 2 | 180.119 | even | 6 |