Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(19,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.325 |
Dual form | 882.3.n.e.19.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 1.22474i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.250000 | + | 0.433013i | ||||
\(5\) | 7.24264 | − | 4.18154i | 1.44853 | − | 0.836308i | 0.450134 | − | 0.892961i | \(-0.351376\pi\) |
0.998394 | + | 0.0566528i | \(0.0180428\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.2426 | + | 5.91359i | 1.02426 | + | 0.591359i | ||||
\(11\) | 3.00000 | − | 5.19615i | 0.272727 | − | 0.472377i | −0.696832 | − | 0.717234i | \(-0.745408\pi\) |
0.969559 | + | 0.244857i | \(0.0787410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 17.8639i | − | 1.37414i | −0.726590 | − | 0.687072i | \(-0.758896\pi\) | ||
0.726590 | − | 0.687072i | \(-0.241104\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −16.2426 | − | 9.37769i | −0.955449 | − | 0.551629i | −0.0606799 | − | 0.998157i | \(-0.519327\pi\) |
−0.894770 | + | 0.446528i | \(0.852660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.7426 | − | 8.51167i | 0.775928 | − | 0.447983i | −0.0590569 | − | 0.998255i | \(-0.518809\pi\) |
0.834985 | + | 0.550272i | \(0.185476\pi\) | |||||||
\(20\) | 16.7262i | 0.836308i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.48528 | 0.385695 | ||||||||
\(23\) | 6.72792 | + | 11.6531i | 0.292518 | + | 0.506657i | 0.974405 | − | 0.224802i | \(-0.0721734\pi\) |
−0.681886 | + | 0.731458i | \(0.738840\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.4706 | − | 38.9202i | 0.898823 | − | 1.55681i | ||||
\(26\) | 21.8787 | − | 12.6317i | 0.841488 | − | 0.485833i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −12.7721 | − | 7.37396i | −0.412003 | − | 0.237870i | 0.279647 | − | 0.960103i | \(-0.409782\pi\) |
−0.691650 | + | 0.722233i | \(0.743116\pi\) | |||||||
\(32\) | 2.82843 | − | 4.89898i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 26.5241i | − | 0.780121i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.98528 | − | 5.17066i | −0.0806833 | − | 0.139748i | 0.822860 | − | 0.568244i | \(-0.192377\pi\) |
−0.903544 | + | 0.428496i | \(0.859044\pi\) | |||||||
\(38\) | 20.8492 | + | 12.0373i | 0.548664 | + | 0.316771i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.4853 | + | 11.8272i | −0.512132 | + | 0.295680i | ||||
\(41\) | − | 35.2354i | − | 0.859399i | −0.902972 | − | 0.429700i | \(-0.858619\pi\) | ||
0.902972 | − | 0.429700i | \(-0.141381\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15.4853 | 0.360123 | 0.180061 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180061 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(44\) | 6.00000 | + | 10.3923i | 0.136364 | + | 0.236189i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.51472 | + | 16.4800i | −0.206842 | + | 0.358260i | ||||
\(47\) | −28.7574 | + | 16.6031i | −0.611859 | + | 0.353257i | −0.773693 | − | 0.633561i | \(-0.781592\pi\) |
0.161834 | + | 0.986818i | \(0.448259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 63.5563 | 1.27113 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 30.9411 | + | 17.8639i | 0.595022 | + | 0.343536i | ||||
\(53\) | −17.2721 | + | 29.9161i | −0.325888 | + | 0.564455i | −0.981692 | − | 0.190477i | \(-0.938997\pi\) |
0.655803 | + | 0.754932i | \(0.272330\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 50.1785i | − | 0.912336i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −24.0000 | − | 41.5692i | −0.413793 | − | 0.716711i | ||||
\(59\) | 23.6985 | + | 13.6823i | 0.401669 | + | 0.231904i | 0.687204 | − | 0.726465i | \(-0.258838\pi\) |
−0.285535 | + | 0.958368i | \(0.592171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.9706 | − | 20.1903i | 0.573288 | − | 0.330988i | −0.185174 | − | 0.982706i | \(-0.559285\pi\) |
0.758461 | + | 0.651718i | \(0.225951\pi\) | |||||||
\(62\) | − | 20.8567i | − | 0.336399i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −74.6985 | − | 129.382i | −1.14921 | − | 1.99049i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 57.1985 | − | 99.0707i | 0.853709 | − | 1.47867i | −0.0241291 | − | 0.999709i | \(-0.507681\pi\) |
0.877838 | − | 0.478958i | \(-0.158985\pi\) | |||||||
\(68\) | 32.4853 | − | 18.7554i | 0.477725 | − | 0.275814i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −18.6030 | −0.262015 | −0.131007 | − | 0.991381i | \(-0.541821\pi\) | ||||
−0.131007 | + | 0.991381i | \(0.541821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 101.353 | + | 58.5161i | 1.38839 | + | 0.801590i | 0.993134 | − | 0.116979i | \(-0.0373210\pi\) |
0.395260 | + | 0.918569i | \(0.370654\pi\) | |||||||
\(74\) | 4.22183 | − | 7.31242i | 0.0570517 | − | 0.0988164i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.0467i | 0.447983i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 44.1690 | + | 76.5030i | 0.559102 | + | 0.968393i | 0.997572 | + | 0.0696469i | \(0.0221873\pi\) |
−0.438470 | + | 0.898746i | \(0.644479\pi\) | |||||||
\(80\) | −28.9706 | − | 16.7262i | −0.362132 | − | 0.209077i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 43.1543 | − | 24.9152i | 0.526272 | − | 0.303843i | ||||
\(83\) | − | 75.7601i | − | 0.912772i | −0.889782 | − | 0.456386i | \(-0.849144\pi\) | ||
0.889782 | − | 0.456386i | \(-0.150856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −156.853 | −1.84533 | ||||||||
\(86\) | 10.9497 | + | 18.9655i | 0.127323 | + | 0.220529i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.48528 | + | 14.6969i | −0.0964237 | + | 0.167011i | ||||
\(89\) | −18.0000 | + | 10.3923i | −0.202247 | + | 0.116767i | −0.597703 | − | 0.801717i | \(-0.703920\pi\) |
0.395456 | + | 0.918485i | \(0.370587\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −26.9117 | −0.292518 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −40.6690 | − | 23.4803i | −0.432649 | − | 0.249790i | ||||
\(95\) | 71.1838 | − | 123.294i | 0.749303 | − | 1.29783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 30.5826i | 0.315284i | 0.987496 | + | 0.157642i | \(0.0503892\pi\) | ||||
−0.987496 | + | 0.157642i | \(0.949611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 44.9411 | + | 77.8403i | 0.449411 | + | 0.778403i | ||||
\(101\) | 110.823 | + | 63.9839i | 1.09726 | + | 0.633504i | 0.935500 | − | 0.353326i | \(-0.114949\pi\) |
0.161761 | + | 0.986830i | \(0.448283\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 70.1102 | − | 40.4781i | 0.680681 | − | 0.392992i | −0.119430 | − | 0.992843i | \(-0.538107\pi\) |
0.800112 | + | 0.599851i | \(0.204774\pi\) | |||||||
\(104\) | 50.5266i | 0.485833i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −48.8528 | −0.460876 | ||||||||
\(107\) | 84.7279 | + | 146.753i | 0.791850 | + | 1.37152i | 0.924820 | + | 0.380404i | \(0.124215\pi\) |
−0.132971 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −89.4706 | + | 154.968i | −0.820831 | + | 1.42172i | 0.0842335 | + | 0.996446i | \(0.473156\pi\) |
−0.905064 | + | 0.425275i | \(0.860177\pi\) | |||||||
\(110\) | 61.4558 | − | 35.4815i | 0.558689 | − | 0.322560i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3970 | 0.153955 | 0.0769777 | − | 0.997033i | \(-0.475473\pi\) | ||||
0.0769777 | + | 0.997033i | \(0.475473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 97.4558 | + | 56.2662i | 0.847442 | + | 0.489271i | ||||
\(116\) | 33.9411 | − | 58.7878i | 0.292596 | − | 0.506791i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 38.6995i | 0.327962i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 42.5000 | + | 73.6122i | 0.351240 | + | 0.608365i | ||||
\(122\) | 49.4558 | + | 28.5533i | 0.405376 | + | 0.234044i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.5442 | − | 14.7479i | 0.206001 | − | 0.118935i | ||||
\(125\) | − | 166.769i | − | 1.33415i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 167.426 | 1.31832 | 0.659159 | − | 0.752004i | \(-0.270912\pi\) | ||||
0.659159 | + | 0.752004i | \(0.270912\pi\) | |||||||
\(128\) | 5.65685 | + | 9.79796i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 105.640 | − | 182.973i | 0.812612 | − | 1.40749i | ||||
\(131\) | −1.54416 | + | 0.891519i | −0.0117874 | + | 0.00680549i | −0.505882 | − | 0.862603i | \(-0.668833\pi\) |
0.494095 | + | 0.869408i | \(0.335500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 161.782 | 1.20733 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 45.9411 | + | 26.5241i | 0.337802 | + | 0.195030i | ||||
\(137\) | 50.4853 | − | 87.4431i | 0.368506 | − | 0.638271i | −0.620826 | − | 0.783948i | \(-0.713203\pi\) |
0.989332 | + | 0.145677i | \(0.0465362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 140.542i | − | 1.01110i | −0.862799 | − | 0.505548i | \(-0.831290\pi\) | ||
0.862799 | − | 0.505548i | \(-0.168710\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.1543 | − | 22.7840i | −0.0926361 | − | 0.160450i | ||||
\(143\) | −92.8234 | − | 53.5916i | −0.649115 | − | 0.374766i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −245.823 | + | 141.926i | −1.69533 | + | 0.978801i | ||||
\(146\) | 165.508i | 1.13362i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.9411 | 0.0806833 | ||||||||
\(149\) | 91.4558 | + | 158.406i | 0.613798 | + | 1.06313i | 0.990594 | + | 0.136833i | \(0.0436922\pi\) |
−0.376797 | + | 0.926296i | \(0.622974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 144.397 | − | 250.103i | 0.956271 | − | 1.65631i | 0.224840 | − | 0.974396i | \(-0.427814\pi\) |
0.731432 | − | 0.681915i | \(-0.238852\pi\) | |||||||
\(152\) | −41.6985 | + | 24.0746i | −0.274332 | + | 0.158386i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −123.338 | −0.795730 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −162.000 | − | 93.5307i | −1.03185 | − | 0.595737i | −0.114334 | − | 0.993442i | \(-0.536473\pi\) |
−0.917513 | + | 0.397705i | \(0.869807\pi\) | |||||||
\(158\) | −62.4645 | + | 108.192i | −0.395345 | + | 0.684757i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 47.3087i | − | 0.295680i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.02944 | − | 13.9074i | −0.0492604 | − | 0.0853214i | 0.840344 | − | 0.542054i | \(-0.182353\pi\) |
−0.889604 | + | 0.456732i | \(0.849020\pi\) | |||||||
\(164\) | 61.0294 | + | 35.2354i | 0.372131 | + | 0.214850i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 92.7868 | − | 53.5705i | 0.558957 | − | 0.322714i | ||||
\(167\) | 176.117i | 1.05459i | 0.849681 | + | 0.527297i | \(0.176794\pi\) | ||||
−0.849681 | + | 0.527297i | \(0.823206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −150.118 | −0.888271 | ||||||||
\(170\) | −110.912 | − | 192.105i | −0.652422 | − | 1.13003i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −15.4853 | + | 26.8213i | −0.0900307 | + | 0.155938i | ||||
\(173\) | −200.184 | + | 115.576i | −1.15713 | + | 0.668070i | −0.950615 | − | 0.310373i | \(-0.899546\pi\) |
−0.206517 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.0000 | −0.136364 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −25.4558 | − | 14.6969i | −0.143010 | − | 0.0825671i | ||||
\(179\) | −42.6396 | + | 73.8540i | −0.238210 | + | 0.412592i | −0.960201 | − | 0.279311i | \(-0.909894\pi\) |
0.721991 | + | 0.691903i | \(0.243227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.58655i | − | 0.0308649i | −0.999881 | − | 0.0154325i | \(-0.995087\pi\) | ||
0.999881 | − | 0.0154325i | \(-0.00491250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.0294 | − | 32.9600i | −0.103421 | − | 0.179130i | ||||
\(185\) | −43.2426 | − | 24.9662i | −0.233744 | − | 0.134952i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −97.4558 | + | 56.2662i | −0.521154 | + | 0.300889i | ||||
\(188\) | − | 66.4123i | − | 0.353257i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 201.338 | 1.05967 | ||||||||
\(191\) | 92.6985 | + | 160.558i | 0.485332 | + | 0.840620i | 0.999858 | − | 0.0168547i | \(-0.00536527\pi\) |
−0.514526 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −113.897 | + | 197.275i | −0.590140 | + | 1.02215i | 0.404073 | + | 0.914727i | \(0.367594\pi\) |
−0.994213 | + | 0.107425i | \(0.965739\pi\) | |||||||
\(194\) | −37.4558 | + | 21.6251i | −0.193071 | + | 0.111470i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −123.161 | −0.625185 | −0.312593 | − | 0.949887i | \(-0.601197\pi\) | ||||
−0.312593 | + | 0.949887i | \(0.601197\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.39697 | − | 3.11594i | −0.0271205 | − | 0.0156580i | 0.486378 | − | 0.873748i | \(-0.338318\pi\) |
−0.513499 | + | 0.858090i | \(0.671651\pi\) | |||||||
\(200\) | −63.5563 | + | 110.083i | −0.317782 | + | 0.550414i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 180.974i | 0.895910i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −147.338 | − | 255.197i | −0.718722 | − | 1.24486i | ||||
\(206\) | 99.1508 | + | 57.2447i | 0.481314 | + | 0.277887i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −61.8823 | + | 35.7277i | −0.297511 | + | 0.171768i | ||||
\(209\) | − | 102.140i | − | 0.488708i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −124.912 | −0.591999 | −0.295999 | − | 0.955188i | \(-0.595653\pi\) | ||||
−0.295999 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(212\) | −34.5442 | − | 59.8322i | −0.162944 | − | 0.282228i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −119.823 | + | 207.540i | −0.559922 | + | 0.969814i | ||||
\(215\) | 112.154 | − | 64.7523i | 0.521648 | − | 0.301174i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −253.061 | −1.16083 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 86.9117 | + | 50.1785i | 0.395053 | + | 0.228084i | ||||
\(221\) | −167.522 | + | 290.156i | −0.758017 | + | 1.31292i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 228.631i | − | 1.02525i | −0.858613 | − | 0.512625i | \(-0.828673\pi\) | ||
0.858613 | − | 0.512625i | \(-0.171327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3015 | + | 21.3068i | 0.0544315 | + | 0.0942781i | ||||
\(227\) | −146.823 | − | 84.7685i | −0.646799 | − | 0.373430i | 0.140430 | − | 0.990091i | \(-0.455152\pi\) |
−0.787229 | + | 0.616661i | \(0.788485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30.0442 | + | 17.3460i | −0.131197 | + | 0.0757467i | −0.564162 | − | 0.825664i | \(-0.690801\pi\) |
0.432965 | + | 0.901411i | \(0.357467\pi\) | |||||||
\(230\) | 159.145i | 0.691934i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.0000 | 0.413793 | ||||||||
\(233\) | −127.243 | − | 220.391i | −0.546106 | − | 0.945883i | −0.998536 | − | 0.0540833i | \(-0.982776\pi\) |
0.452431 | − | 0.891800i | \(-0.350557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −138.853 | + | 240.500i | −0.590863 | + | 1.02340i | ||||
\(236\) | −47.3970 | + | 27.3647i | −0.200835 | + | 0.115952i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −197.147 | −0.824884 | −0.412442 | − | 0.910984i | \(-0.635324\pi\) | ||||
−0.412442 | + | 0.910984i | \(0.635324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −76.6173 | − | 44.2350i | −0.317914 | − | 0.183548i | 0.332548 | − | 0.943086i | \(-0.392092\pi\) |
−0.650462 | + | 0.759538i | \(0.725425\pi\) | |||||||
\(242\) | −60.1041 | + | 104.103i | −0.248364 | + | 0.430179i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 80.7611i | 0.330988i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −152.051 | − | 263.361i | −0.615592 | − | 1.06624i | ||||
\(248\) | 36.1249 | + | 20.8567i | 0.145665 | + | 0.0840997i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 204.250 | − | 117.924i | 0.816999 | − | 0.471695i | ||||
\(251\) | 215.903i | 0.860172i | 0.902788 | + | 0.430086i | \(0.141517\pi\) | ||||
−0.902788 | + | 0.430086i | \(0.858483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 80.7351 | 0.319111 | ||||||||
\(254\) | 118.388 | + | 205.055i | 0.466096 | + | 0.807302i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.72792 | + | 2.15232i | −0.0145055 | + | 0.00837477i | −0.507235 | − | 0.861808i | \(-0.669332\pi\) |
0.492730 | + | 0.870182i | \(0.335999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 298.794 | 1.14921 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.18377 | − | 1.26080i | −0.00833499 | − | 0.00481221i | ||||
\(263\) | 141.338 | − | 244.805i | 0.537407 | − | 0.930817i | −0.461635 | − | 0.887070i | \(-0.652737\pi\) |
0.999043 | − | 0.0437468i | \(-0.0139295\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 288.896i | 1.09017i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 114.397 | + | 198.141i | 0.426854 | + | 0.739333i | ||||
\(269\) | −330.765 | − | 190.967i | −1.22961 | − | 0.709914i | −0.262660 | − | 0.964888i | \(-0.584600\pi\) |
−0.966948 | + | 0.254974i | \(0.917933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 73.0294 | − | 42.1636i | 0.269481 | − | 0.155585i | −0.359171 | − | 0.933272i | \(-0.616940\pi\) |
0.628652 | + | 0.777687i | \(0.283607\pi\) | |||||||
\(272\) | 75.0215i | 0.275814i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 142.794 | 0.521146 | ||||||||
\(275\) | −134.823 | − | 233.521i | −0.490267 | − | 0.849167i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 68.5589 | − | 118.747i | 0.247505 | − | 0.428691i | −0.715328 | − | 0.698789i | \(-0.753723\pi\) |
0.962833 | + | 0.270098i | \(0.0870560\pi\) | |||||||
\(278\) | 172.128 | − | 99.3784i | 0.619167 | − | 0.357476i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 325.103 | 1.15695 | 0.578474 | − | 0.815701i | \(-0.303648\pi\) | ||||
0.578474 | + | 0.815701i | \(0.303648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −168.507 | − | 97.2876i | −0.595432 | − | 0.343773i | 0.171811 | − | 0.985130i | \(-0.445038\pi\) |
−0.767242 | + | 0.641357i | \(0.778372\pi\) | |||||||
\(284\) | 18.6030 | − | 32.2214i | 0.0655036 | − | 0.113456i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 151.580i | − | 0.530000i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.3823 | + | 54.3557i | 0.108589 | + | 0.188082i | ||||
\(290\) | −347.647 | − | 200.714i | −1.19878 | − | 0.692117i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −202.706 | + | 117.032i | −0.694197 | + | 0.400795i | ||||
\(293\) | 239.702i | 0.818095i | 0.912513 | + | 0.409048i | \(0.134139\pi\) | ||||
−0.912513 | + | 0.409048i | \(0.865861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 228.853 | 0.775772 | ||||||||
\(296\) | 8.44365 | + | 14.6248i | 0.0285258 | + | 0.0494082i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −129.338 | + | 224.020i | −0.434020 | + | 0.751745i | ||||
\(299\) | 208.169 | − | 120.187i | 0.696219 | − | 0.401962i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 408.416 | 1.35237 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −58.9706 | − | 34.0467i | −0.193982 | − | 0.111996i | ||||
\(305\) | 168.853 | − | 292.462i | 0.553616 | − | 0.958891i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 540.272i | 1.75984i | 0.475120 | + | 0.879921i | \(0.342405\pi\) | ||||
−0.475120 | + | 0.879921i | \(0.657595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −87.2132 | − | 151.058i | −0.281333 | − | 0.487283i | ||||
\(311\) | 350.044 | + | 202.098i | 1.12554 | + | 0.649832i | 0.942810 | − | 0.333330i | \(-0.108172\pi\) |
0.182732 | + | 0.983163i | \(0.441506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 113.706 | − | 65.6482i | 0.363278 | − | 0.209739i | −0.307240 | − | 0.951632i | \(-0.599405\pi\) |
0.670518 | + | 0.741893i | \(0.266072\pi\) | |||||||
\(314\) | − | 264.545i | − | 0.842500i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −176.676 | −0.559102 | ||||||||
\(317\) | −46.9706 | − | 81.3554i | −0.148172 | − | 0.256642i | 0.782380 | − | 0.622802i | \(-0.214006\pi\) |
−0.930552 | + | 0.366160i | \(0.880672\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −101.823 | + | 176.363i | −0.319196 | + | 0.552863i | ||||
\(320\) | 57.9411 | − | 33.4523i | 0.181066 | − | 0.104539i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −319.279 | −0.988481 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −695.265 | − | 401.411i | −2.13928 | − | 1.23511i | ||||
\(326\) | 11.3553 | − | 19.6680i | 0.0348323 | − | 0.0603314i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 99.6607i | 0.303843i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 130.684 | + | 226.351i | 0.394815 | + | 0.683840i | 0.993078 | − | 0.117460i | \(-0.0374754\pi\) |
−0.598263 | + | 0.801300i | \(0.704142\pi\) | |||||||
\(332\) | 131.220 | + | 75.7601i | 0.395242 | + | 0.228193i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −215.698 | + | 124.534i | −0.645804 | + | 0.372855i | ||||
\(335\) | − | 956.711i | − | 2.85585i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 136.265 | 0.404347 | 0.202173 | − | 0.979350i | \(-0.435200\pi\) | ||||
0.202173 | + | 0.979350i | \(0.435200\pi\) | |||||||
\(338\) | −106.149 | − | 183.856i | −0.314051 | − | 0.543952i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 156.853 | − | 271.677i | 0.461332 | − | 0.799050i | ||||
\(341\) | −76.6325 | + | 44.2438i | −0.224729 | + | 0.129747i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −43.7990 | −0.127323 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −283.103 | − | 163.449i | −0.818216 | − | 0.472397i | ||||
\(347\) | −161.095 | + | 279.026i | −0.464252 | + | 0.804108i | −0.999167 | − | 0.0407975i | \(-0.987010\pi\) |
0.534915 | + | 0.844906i | \(0.320343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 346.495i | 0.992821i | 0.868088 | + | 0.496411i | \(0.165349\pi\) | ||||
−0.868088 | + | 0.496411i | \(0.834651\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.9706 | − | 29.3939i | −0.0482118 | − | 0.0835053i | ||||
\(353\) | −537.448 | − | 310.296i | −1.52252 | − | 0.879025i | −0.999646 | − | 0.0266116i | \(-0.991528\pi\) |
−0.522869 | − | 0.852413i | \(-0.675138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −134.735 | + | 77.7893i | −0.379535 | + | 0.219125i | ||||
\(356\) | − | 41.5692i | − | 0.116767i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −120.603 | −0.336880 | ||||||||
\(359\) | 10.1177 | + | 17.5245i | 0.0281831 | + | 0.0488146i | 0.879773 | − | 0.475394i | \(-0.157695\pi\) |
−0.851590 | + | 0.524209i | \(0.824361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.6030 | + | 61.6663i | −0.0986234 | + | 0.170821i | ||||
\(362\) | 6.84210 | − | 3.95029i | 0.0189008 | − | 0.0109124i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 978.749 | 2.68151 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 269.831 | + | 155.787i | 0.735234 | + | 0.424488i | 0.820334 | − | 0.571885i | \(-0.193788\pi\) |
−0.0850998 | + | 0.996372i | \(0.527121\pi\) | |||||||
\(368\) | 26.9117 | − | 46.6124i | 0.0731296 | − | 0.126664i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 70.6149i | − | 0.190851i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 340.691 | + | 590.094i | 0.913380 | + | 1.58202i | 0.809255 | + | 0.587457i | \(0.199871\pi\) |
0.104125 | + | 0.994564i | \(0.466796\pi\) | |||||||
\(374\) | −137.823 | − | 79.5724i | −0.368512 | − | 0.212760i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 81.3381 | − | 46.9606i | 0.216325 | − | 0.124895i | ||||
\(377\) | 606.320i | 1.60828i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −624.779 | −1.64849 | −0.824246 | − | 0.566231i | \(-0.808401\pi\) | ||||
−0.824246 | + | 0.566231i | \(0.808401\pi\) | |||||||
\(380\) | 142.368 | + | 246.588i | 0.374651 | + | 0.648915i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −131.095 | + | 227.064i | −0.343182 | + | 0.594408i | ||||
\(383\) | 119.772 | − | 69.1502i | 0.312720 | − | 0.180549i | −0.335423 | − | 0.942068i | \(-0.608879\pi\) |
0.648143 | + | 0.761519i | \(0.275546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −322.149 | −0.834584 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −52.9706 | − | 30.5826i | −0.136522 | − | 0.0788211i | ||||
\(389\) | −281.787 | + | 488.069i | −0.724388 | + | 1.25468i | 0.234838 | + | 0.972035i | \(0.424544\pi\) |
−0.959226 | + | 0.282642i | \(0.908789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 252.370i | − | 0.645446i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −87.0883 | − | 150.841i | −0.221036 | − | 0.382846i | ||||
\(395\) | 639.801 | + | 369.389i | 1.61975 | + | 0.935163i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 392.603 | − | 226.669i | 0.988923 | − | 0.570955i | 0.0839711 | − | 0.996468i | \(-0.473240\pi\) |
0.904952 | + | 0.425513i | \(0.139906\pi\) | |||||||
\(398\) | − | 8.81321i | − | 0.0221438i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −179.765 | −0.449411 | ||||||||
\(401\) | −137.875 | − | 238.807i | −0.343828 | − | 0.595528i | 0.641312 | − | 0.767280i | \(-0.278390\pi\) |
−0.985140 | + | 0.171752i | \(0.945057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −131.727 | + | 228.159i | −0.326867 | + | 0.566151i | ||||
\(404\) | −221.647 | + | 127.968i | −0.548631 | + | 0.316752i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.8234 | −0.0880181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 377.441 | + | 217.916i | 0.922839 | + | 0.532801i | 0.884540 | − | 0.466465i | \(-0.154473\pi\) |
0.0382993 | + | 0.999266i | \(0.487806\pi\) | |||||||
\(410\) | 208.368 | − | 360.903i | 0.508213 | − | 0.880252i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 161.913i | 0.392992i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −316.794 | − | 548.703i | −0.763359 | − | 1.32218i | ||||
\(416\) | −87.5147 | − | 50.5266i | −0.210372 | − | 0.121458i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 125.095 | − | 72.2239i | 0.299271 | − | 0.172784i | ||||
\(419\) | 301.257i | 0.718991i | 0.933147 | + | 0.359496i | \(0.117051\pi\) | ||||
−0.933147 | + | 0.359496i | \(0.882949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −203.794 | −0.484071 | −0.242036 | − | 0.970267i | \(-0.577815\pi\) | ||||
−0.242036 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(422\) | −88.3259 | − | 152.985i | −0.209303 | − | 0.362524i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48.8528 | − | 84.6156i | 0.115219 | − | 0.199565i | ||||
\(425\) | −729.963 | + | 421.444i | −1.71756 | + | 0.991633i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −338.912 | −0.791850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 158.610 | + | 91.5736i | 0.368861 | + | 0.212962i | ||||
\(431\) | −197.860 | + | 342.703i | −0.459072 | + | 0.795136i | −0.998912 | − | 0.0466317i | \(-0.985151\pi\) |
0.539840 | + | 0.841767i | \(0.318485\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 44.2685i | − | 0.102237i | −0.998693 | − | 0.0511184i | \(-0.983721\pi\) | ||
0.998693 | − | 0.0511184i | \(-0.0162786\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −178.941 | − | 309.935i | −0.410415 | − | 0.710860i | ||||
\(437\) | 198.375 | + | 114.532i | 0.453947 | + | 0.262086i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −344.558 | + | 198.931i | −0.784871 | + | 0.453146i | −0.838154 | − | 0.545434i | \(-0.816365\pi\) |
0.0532827 | + | 0.998579i | \(0.483032\pi\) | |||||||
\(440\) | 141.926i | 0.322560i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −473.823 | −1.07200 | ||||||||
\(443\) | −59.2721 | − | 102.662i | −0.133797 | − | 0.231743i | 0.791340 | − | 0.611376i | \(-0.209384\pi\) |
−0.925137 | + | 0.379633i | \(0.876050\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −86.9117 | + | 150.535i | −0.195307 | + | 0.338282i | ||||
\(446\) | 280.014 | − | 161.666i | 0.627835 | − | 0.362481i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −713.897 | −1.58997 | −0.794985 | − | 0.606629i | \(-0.792521\pi\) | ||||
−0.794985 | + | 0.606629i | \(0.792521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −183.088 | − | 105.706i | −0.405961 | − | 0.234382i | ||||
\(452\) | −17.3970 | + | 30.1324i | −0.0384889 | + | 0.0666647i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 239.762i | − | 0.528109i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 62.5883 | + | 108.406i | 0.136955 | + | 0.237213i | 0.926342 | − | 0.376682i | \(-0.122935\pi\) |
−0.789388 | + | 0.613895i | \(0.789602\pi\) | |||||||
\(458\) | −42.4889 | − | 24.5310i | −0.0927704 | − | 0.0535610i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −194.912 | + | 112.532i | −0.423721 | + | 0.244635i | ||||
\(461\) | − | 655.767i | − | 1.42249i | −0.702945 | − | 0.711244i | \(-0.748132\pi\) | ||
0.702945 | − | 0.711244i | \(-0.251868\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 869.396 | 1.87775 | 0.938873 | − | 0.344265i | \(-0.111872\pi\) | ||||
0.938873 | + | 0.344265i | \(0.111872\pi\) | |||||||
\(464\) | 67.8823 | + | 117.576i | 0.146298 | + | 0.253395i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 179.948 | − | 311.680i | 0.386155 | − | 0.668840i | ||||
\(467\) | −231.551 | + | 133.686i | −0.495827 | + | 0.286266i | −0.726989 | − | 0.686649i | \(-0.759081\pi\) |
0.231162 | + | 0.972915i | \(0.425747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −392.735 | −0.835607 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −67.0294 | − | 38.6995i | −0.142012 | − | 0.0819904i | ||||
\(473\) | 46.4558 | − | 80.4639i | 0.0982153 | − | 0.170114i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 765.048i | − | 1.61063i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −139.404 | − | 241.455i | −0.291640 | − | 0.505136i | ||||
\(479\) | 235.331 | + | 135.868i | 0.491296 | + | 0.283650i | 0.725112 | − | 0.688631i | \(-0.241788\pi\) |
−0.233816 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −92.3680 | + | 53.3287i | −0.192033 | + | 0.110870i | ||||
\(482\) | − | 125.116i | − | 0.259576i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −170.000 | −0.351240 | ||||||||
\(485\) | 127.882 | + | 221.499i | 0.263675 | + | 0.456698i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 280.757 | − | 486.285i | 0.576503 | − | 0.998532i | −0.419374 | − | 0.907814i | \(-0.637750\pi\) |
0.995877 | − | 0.0907186i | \(-0.0289164\pi\) | |||||||
\(488\) | −98.9117 | + | 57.1067i | −0.202688 | + | 0.117022i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 406.441 | 0.827781 | 0.413891 | − | 0.910327i | \(-0.364170\pi\) | ||||
0.413891 | + | 0.910327i | \(0.364170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 551.294 | + | 318.289i | 1.11824 | + | 0.645618i | ||||
\(494\) | 215.033 | − | 372.448i | 0.435289 | − | 0.753944i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 58.9917i | 0.118935i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 185.713 | + | 321.665i | 0.372171 | + | 0.644619i | 0.989899 | − | 0.141773i | \(-0.0452802\pi\) |
−0.617728 | + | 0.786391i | \(0.711947\pi\) | |||||||
\(500\) | 288.853 | + | 166.769i | 0.577706 | + | 0.333538i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −264.426 | + | 152.667i | −0.526746 | + | 0.304117i | ||||
\(503\) | − | 64.6292i | − | 0.128488i | −0.997934 | − | 0.0642438i | \(-0.979536\pi\) | ||
0.997934 | − | 0.0642438i | \(-0.0204635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1070.21 | 2.11922 | ||||||||
\(506\) | 57.0883 | + | 98.8799i | 0.112823 | + | 0.195415i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −167.426 | + | 289.991i | −0.329580 | + | 0.570849i | ||||
\(509\) | 871.889 | − | 503.385i | 1.71294 | − | 0.988969i | 0.782410 | − | 0.622764i | \(-0.213990\pi\) |
0.930534 | − | 0.366205i | \(-0.119343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.27208 | − | 3.04384i | −0.0102570 | − | 0.00592186i | ||||
\(515\) | 338.522 | − | 586.337i | 0.657324 | − | 1.13852i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 199.237i | 0.385371i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 211.279 | + | 365.946i | 0.406306 | + | 0.703743i | ||||
\(521\) | −322.294 | − | 186.077i | −0.618607 | − | 0.357153i | 0.157719 | − | 0.987484i | \(-0.449586\pi\) |
−0.776327 | + | 0.630331i | \(0.782919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 551.904 | − | 318.642i | 1.05527 | − | 0.609258i | 0.131147 | − | 0.991363i | \(-0.458134\pi\) |
0.924119 | + | 0.382105i | \(0.124801\pi\) | |||||||
\(524\) | − | 3.56608i | − | 0.00680549i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 399.765 | 0.760009 | ||||||||
\(527\) | 138.302 | + | 239.545i | 0.262432 | + | 0.454545i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 173.970 | − | 301.325i | 0.328866 | − | 0.569613i | ||||
\(530\) | −353.823 | + | 204.280i | −0.667591 | + | 0.385434i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −629.440 | −1.18094 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1227.31 | + | 708.586i | 2.29403 | + | 1.32446i | ||||
\(536\) | −161.782 | + | 280.214i | −0.301832 | + | 0.522788i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 540.136i | − | 1.00397i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −110.412 | − | 191.239i | −0.204088 | − | 0.353491i | 0.745754 | − | 0.666222i | \(-0.232090\pi\) |
−0.949842 | + | 0.312731i | \(0.898756\pi\) | |||||||
\(542\) | 103.279 | + | 59.6283i | 0.190552 | + | 0.110015i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −91.8823 | + | 53.0482i | −0.168901 | + | 0.0975152i | ||||
\(545\) | 1496.50i | 2.74587i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −160.676 | −0.293741 | −0.146870 | − | 0.989156i | \(-0.546920\pi\) | ||||
−0.146870 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(548\) | 100.971 | + | 174.886i | 0.184253 | + | 0.319135i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 190.669 | − | 330.248i | 0.346671 | − | 0.600452i | ||||
\(551\) | −500.382 | + | 288.896i | −0.908134 | + | 0.524311i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 193.914 | 0.350025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 243.426 | + | 140.542i | 0.437817 | + | 0.252774i | ||||
\(557\) | −237.177 | + | 410.802i | −0.425811 | + | 0.737526i | −0.996496 | − | 0.0836431i | \(-0.973344\pi\) |
0.570685 | + | 0.821169i | \(0.306678\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 276.627i | − | 0.494860i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 229.882 | + | 398.168i | 0.409043 | + | 0.708484i | ||||
\(563\) | −430.301 | − | 248.434i | −0.764300 | − | 0.441269i | 0.0665378 | − | 0.997784i | \(-0.478805\pi\) |
−0.830837 | + | 0.556515i | \(0.812138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 126.000 | − | 72.7461i | 0.223009 | − | 0.128754i | ||||
\(566\) | − | 275.171i | − | 0.486168i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 52.6173 | 0.0926361 | ||||||||
\(569\) | 392.647 | + | 680.084i | 0.690065 | + | 1.19523i | 0.971816 | + | 0.235740i | \(0.0757512\pi\) |
−0.281752 | + | 0.959487i | \(0.590915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 357.521 | − | 619.245i | 0.626132 | − | 1.08449i | −0.362189 | − | 0.932105i | \(-0.617970\pi\) |
0.988321 | − | 0.152388i | \(-0.0486963\pi\) | |||||||
\(572\) | 185.647 | − | 107.183i | 0.324557 | − | 0.187383i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 604.721 | 1.05169 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −669.117 | − | 386.315i | −1.15965 | − | 0.669524i | −0.208429 | − | 0.978038i | \(-0.566835\pi\) |
−0.951220 | + | 0.308514i | \(0.900168\pi\) | |||||||
\(578\) | −44.3812 | + | 76.8705i | −0.0767841 | + | 0.132994i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 567.705i | − | 0.978801i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 103.632 | + | 179.497i | 0.177757 | + | 0.307885i | ||||
\(584\) | −286.669 | − | 165.508i | −0.490872 | − | 0.283405i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −293.574 | + | 169.495i | −0.500979 | + | 0.289240i | ||||
\(587\) | 436.477i | 0.743572i | 0.928318 | + | 0.371786i | \(0.121254\pi\) | ||||
−0.928318 | + | 0.371786i | \(0.878746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −251.059 | −0.426246 | ||||||||
\(590\) | 161.823 | + | 280.286i | 0.274277 | + | 0.475062i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.9411 | + | 20.6826i | −0.0201708 | + | 0.0349369i | ||||
\(593\) | 722.397 | − | 417.076i | 1.21821 | − | 0.703332i | 0.253673 | − | 0.967290i | \(-0.418361\pi\) |
0.964534 | + | 0.263958i | \(0.0850279\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −365.823 | −0.613798 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 294.396 | + | 169.970i | 0.492301 | + | 0.284230i | ||||
\(599\) | 436.794 | − | 756.549i | 0.729205 | − | 1.26302i | −0.228014 | − | 0.973658i | \(-0.573223\pi\) |
0.957220 | − | 0.289363i | \(-0.0934434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 198.982i | 0.331085i | 0.986203 | + | 0.165542i | \(0.0529375\pi\) | ||||
−0.986203 | + | 0.165542i | \(0.947063\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 288.794 | + | 500.206i | 0.478136 | + | 0.828155i | ||||
\(605\) | 615.624 | + | 355.431i | 1.01756 | + | 0.587489i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −137.654 | + | 79.4748i | −0.226778 | + | 0.130930i | −0.609085 | − | 0.793105i | \(-0.708463\pi\) |
0.382307 | + | 0.924035i | \(0.375130\pi\) | |||||||
\(608\) | − | 96.2985i | − | 0.158386i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 477.588 | 0.782931 | ||||||||
\(611\) | 296.595 | + | 513.718i | 0.485426 | + | 0.840782i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 357.368 | − | 618.979i | 0.582981 | − | 1.00975i | −0.412143 | − | 0.911119i | \(-0.635219\pi\) |
0.995124 | − | 0.0986338i | \(-0.0314473\pi\) | |||||||
\(614\) | −661.695 | + | 382.030i | −1.07768 | + | 0.622198i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 639.381 | 1.03627 | 0.518137 | − | 0.855298i | \(-0.326626\pi\) | ||||
0.518137 | + | 0.855298i | \(0.326626\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −148.978 | − | 86.0126i | −0.240676 | − | 0.138954i | 0.374812 | − | 0.927101i | \(-0.377707\pi\) |
−0.615487 | + | 0.788147i | \(0.711041\pi\) | |||||||
\(620\) | 123.338 | − | 213.628i | 0.198932 | − | 0.344561i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 571.619i | 0.919002i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −135.588 | − | 234.846i | −0.216941 | − | 0.375753i | ||||
\(626\) | 160.805 | + | 92.8406i | 0.256876 | + | 0.148308i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 324.000 | − | 187.061i | 0.515924 | − | 0.297869i | ||||
\(629\) | 111.980i | 0.178029i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1141.06 | −1.80833 | −0.904166 | − | 0.427180i | \(-0.859507\pi\) | ||||
−0.904166 | + | 0.427180i | \(0.859507\pi\) | |||||||
\(632\) | −124.929 | − | 216.383i | −0.197672 | − | 0.342379i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 66.4264 | − | 115.054i | 0.104774 | − | 0.181473i | ||||
\(635\) | 1212.61 | − | 700.100i | 1.90962 | − | 1.10252i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −288.000 | −0.451411 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 81.9411 | + | 47.3087i | 0.128033 | + | 0.0739199i | ||||
\(641\) | 114.551 | − | 198.409i | 0.178707 | − | 0.309530i | −0.762731 | − | 0.646716i | \(-0.776142\pi\) |
0.941438 | + | 0.337186i | \(0.109475\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 707.670i | 1.10058i | 0.834975 | + | 0.550288i | \(0.185482\pi\) | ||||
−0.834975 | + | 0.550288i | \(0.814518\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −225.765 | − | 391.036i | −0.349481 | − | 0.605318i | ||||
\(647\) | 1021.37 | + | 589.687i | 1.57862 | + | 0.911417i | 0.995052 | + | 0.0993530i | \(0.0316773\pi\) |
0.583568 | + | 0.812064i | \(0.301656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 142.191 | − | 82.0940i | 0.219092 | − | 0.126493i | ||||
\(650\) | − | 1135.36i | − | 1.74671i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.1177 | 0.0492604 | ||||||||
\(653\) | −77.3818 | − | 134.029i | −0.118502 | − | 0.205252i | 0.800672 | − | 0.599103i | \(-0.204476\pi\) |
−0.919174 | + | 0.393851i | \(0.871143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.45584 | + | 12.9139i | −0.0113830 | + | 0.0197159i | ||||
\(656\) | −122.059 | + | 70.4707i | −0.186065 | + | 0.107425i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −591.308 | −0.897280 | −0.448640 | − | 0.893712i | \(-0.648092\pi\) | ||||
−0.448640 | + | 0.893712i | \(0.648092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −140.441 | − | 81.0837i | −0.212468 | − | 0.122668i | 0.389990 | − | 0.920819i | \(-0.372478\pi\) |
−0.602458 | + | 0.798151i | \(0.705812\pi\) | |||||||
\(662\) | −184.815 | + | 320.109i | −0.279176 | + | 0.483548i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 214.282i | 0.322714i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −228.353 | − | 395.519i | −0.342359 | − | 0.592983i | ||||
\(668\) | −305.044 | − | 176.117i | −0.456652 | − | 0.263648i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1171.73 | − | 676.497i | 1.74885 | − | 1.00970i | ||||
\(671\) | − | 242.283i | − | 0.361078i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.3238 | 0.0628883 | 0.0314441 | − | 0.999506i | \(-0.489989\pi\) | ||||
0.0314441 | + | 0.999506i | \(0.489989\pi\) | |||||||
\(674\) | 96.3539 | + | 166.890i | 0.142958 | + | 0.247611i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 150.118 | − | 260.012i | 0.222068 | − | 0.384632i | ||||
\(677\) | 430.721 | − | 248.677i | 0.636220 | − | 0.367322i | −0.146937 | − | 0.989146i | \(-0.546941\pi\) |
0.783157 | + | 0.621824i | \(0.213608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 443.647 | 0.652422 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −108.375 | − | 62.5701i | −0.158907 | − | 0.0917451i | ||||
\(683\) | 608.080 | − | 1053.23i | 0.890308 | − | 1.54206i | 0.0508015 | − | 0.998709i | \(-0.483822\pi\) |
0.839506 | − | 0.543350i | \(-0.182844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 844.425i | − | 1.23274i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.9706 | − | 53.6426i | −0.0450154 | − | 0.0779689i | ||||
\(689\) | 534.418 | + | 308.546i | 0.775642 | + | 0.447817i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 932.182 | − | 538.196i | 1.34903 | − | 0.778865i | 0.360921 | − | 0.932596i | \(-0.382462\pi\) |
0.988113 | + | 0.153731i | \(0.0491290\pi\) | |||||||
\(692\) | − | 462.305i | − | 0.668070i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −455.647 | −0.656552 | ||||||||
\(695\) | −587.683 | − | 1017.90i | −0.845588 | − | 1.46460i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −330.426 | + | 572.315i | −0.474069 | + | 0.821112i | ||||
\(698\) | −424.368 | + | 245.009i | −0.607976 | + | 0.351015i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 695.897 | 0.992720 | 0.496360 | − | 0.868117i | \(-0.334670\pi\) | ||||
0.496360 | + | 0.868117i | \(0.334670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −88.0219 | − | 50.8194i | −0.125209 | − | 0.0722894i | ||||
\(704\) | 24.0000 | − | 41.5692i | 0.0340909 | − | 0.0590472i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 877.649i | − | 1.24313i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −127.412 | − | 220.684i | −0.179707 | − | 0.311261i | 0.762073 | − | 0.647491i | \(-0.224182\pi\) |
−0.941780 | + | 0.336229i | \(0.890848\pi\) | |||||||
\(710\) | −190.544 | − | 110.011i | −0.268372 | − | 0.154945i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 50.9117 | − | 29.3939i | 0.0715052 | − | 0.0412835i | ||||
\(713\) | − | 198.446i | − | 0.278325i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −896.382 | −1.25368 | ||||||||
\(716\) | −85.2792 | − | 147.708i | −0.119105 | − | 0.206296i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.3087 | + | 24.7833i | −0.0199285 | + | 0.0345172i | ||||
\(719\) | −964.925 | + | 557.100i | −1.34204 | + | 0.774826i | −0.987106 | − | 0.160066i | \(-0.948829\pi\) |
−0.354931 | + | 0.934892i | \(0.615496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −100.701 | −0.139474 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.67619 | + | 5.58655i | 0.0133649 | + | 0.00771623i | ||||
\(725\) | −762.676 | + | 1320.99i | −1.05197 | + | 1.82206i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 398.345i | − | 0.547930i | −0.961740 | − | 0.273965i | \(-0.911665\pi\) | ||
0.961740 | − | 0.273965i | \(-0.0883353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 692.080 | + | 1198.72i | 0.948055 | + | 1.64208i | ||||
\(731\) | −251.522 | − | 145.216i | −0.344079 | − | 0.198654i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −818.514 | + | 472.569i | −1.11666 | + | 0.644706i | −0.940547 | − | 0.339663i | \(-0.889687\pi\) |
−0.176116 | + | 0.984369i | \(0.556354\pi\) | |||||||
\(734\) | 440.632i | 0.600316i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 76.1177 | 0.103421 | ||||||||
\(737\) | −343.191 | − | 594.424i | −0.465659 | − | 0.806546i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −96.3162 | + | 166.825i | −0.130333 | + | 0.225744i | −0.923805 | − | 0.382863i | \(-0.874938\pi\) |
0.793472 | + | 0.608607i | \(0.208271\pi\) | |||||||
\(740\) | 86.4853 | − | 49.9323i | 0.116872 | − | 0.0674761i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 911.616 | 1.22694 | 0.613470 | − | 0.789718i | \(-0.289773\pi\) | ||||
0.613470 | + | 0.789718i | \(0.289773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1324.76 | + | 764.853i | 1.77821 | + | 1.02665i | ||||
\(746\) | −481.810 | + | 834.519i | −0.645858 | + | 1.11866i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 225.065i | − | 0.300889i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 195.831 | + | 339.189i | 0.260760 | + | 0.451650i | 0.966444 | − | 0.256877i | \(-0.0826935\pi\) |
−0.705684 | + | 0.708527i | \(0.749360\pi\) | |||||||
\(752\) | 115.029 | + | 66.4123i | 0.152965 | + | 0.0883142i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −742.587 | + | 428.733i | −0.984863 | + | 0.568611i | ||||
\(755\) | − | 2415.21i | − | 3.19895i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −152.823 | −0.201879 | −0.100940 | − | 0.994893i | \(-0.532185\pi\) | ||||
−0.100940 | + | 0.994893i | \(0.532185\pi\) | |||||||
\(758\) | −441.785 | − | 765.195i | −0.582830 | − | 1.00949i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −201.338 | + | 348.728i | −0.264919 | + | 0.458852i | ||||
\(761\) | −109.331 | + | 63.1223i | −0.143667 | + | 0.0829465i | −0.570111 | − | 0.821568i | \(-0.693100\pi\) |
0.426443 | + | 0.904514i | \(0.359766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −370.794 | −0.485332 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 169.383 | + | 97.7931i | 0.221126 | + | 0.127667i | ||||
\(767\) | 244.419 | − | 423.347i | 0.318669 | − | 0.551951i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 369.148i | − | 0.480037i | −0.970768 | − | 0.240018i | \(-0.922847\pi\) | ||
0.970768 | − | 0.240018i | \(-0.0771535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −227.794 | − | 394.551i | −0.295070 | − | 0.511076i | ||||
\(773\) | −1215.65 | − | 701.853i | −1.57263 | − | 0.907961i | −0.995845 | − | 0.0910674i | \(-0.970972\pi\) |
−0.576789 | − | 0.816893i | \(-0.695695\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −573.992 | + | 331.394i | −0.740634 | + | 0.427605i | ||||
\(776\) | − | 86.5006i | − | 0.111470i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −797.013 | −1.02444 | ||||||||
\(779\) | −299.912 | − | 519.462i | −0.384996 | − | 0.666832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −55.8091 | + | 96.6642i | −0.0714585 | + | 0.123770i | ||||
\(782\) | 309.088 | − | 178.452i | 0.395254 | − | 0.228200i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1564.41 | −1.99288 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −196.161 | − | 113.253i | −0.249251 | − | 0.143905i | 0.370170 | − | 0.928964i | \(-0.379299\pi\) |
−0.619421 | + | 0.785059i | \(0.712633\pi\) | |||||||
\(788\) | 123.161 | − | 213.322i | 0.156296 | − | 0.270713i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1044.79i | 1.32252i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −360.676 | − | 624.709i | −0.454825 | − | 0.787780i | ||||
\(794\) | 555.224 | + | 320.559i | 0.699274 | + | 0.403726i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.7939 | − | 6.23188i | 0.0135602 | − | 0.00782900i | ||||
\(797\) | 688.414i | 0.863756i | 0.901932 | + | 0.431878i | \(0.142149\pi\) | ||||
−0.901932 | + | 0.431878i | \(0.857851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 622.794 | 0.779467 | ||||||||
\(800\) | −127.113 | − | 220.166i | −0.158891 | − | 0.275207i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 194.985 | − | 337.724i | 0.243123 | − | 0.421102i | ||||
\(803\) | 608.117 | − | 351.096i | 0.757306 | − | 0.437231i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −372.582 | −0.462260 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −313.456 | − | 180.974i | −0.387940 | − | 0.223977i | ||||
\(809\) | 12.6396 | − | 21.8924i | 0.0156237 | − | 0.0270611i | −0.858108 | − | 0.513470i | \(-0.828360\pi\) |
0.873732 | + | 0.486408i | \(0.161693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1527.62i | 1.88362i | 0.336145 | + | 0.941810i | \(0.390877\pi\) | ||||
−0.336145 | + | 0.941810i | \(0.609123\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.3310 | − | 43.8745i | −0.0311191 | − | 0.0538999i | ||||
\(815\) | −116.309 | − | 67.1508i | −0.142710 | − | 0.0823937i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 228.294 | − | 131.806i | 0.279430 | − | 0.161329i | ||||
\(818\) | 616.359i | 0.753495i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 589.352 | 0.718722 | ||||||||
\(821\) | −58.3310 | − | 101.032i | −0.0710487 | − | 0.123060i | 0.828312 | − | 0.560266i | \(-0.189301\pi\) |
−0.899361 | + | 0.437206i | \(0.855968\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −62.9554 | + | 109.042i | −0.0764950 | + | 0.132493i | −0.901735 | − | 0.432288i | \(-0.857706\pi\) |
0.825240 | + | 0.564782i | \(0.191040\pi\) | |||||||
\(824\) | −198.302 | + | 114.489i | −0.240657 | + | 0.138943i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1434.40 | 1.73446 | 0.867229 | − | 0.497910i | \(-0.165899\pi\) | ||||
0.867229 | + | 0.497910i | \(0.165899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.3225 | + | 18.6614i | 0.0389898 | + | 0.0225107i | 0.519368 | − | 0.854551i | \(-0.326167\pi\) |
−0.480378 | + | 0.877061i | \(0.659501\pi\) | |||||||
\(830\) | 448.014 | − | 775.984i | 0.539776 | − | 0.934920i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 142.911i | − | 0.171768i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 736.441 | + | 1275.55i | 0.881965 | + | 1.52761i | ||||
\(836\) | 176.912 | + | 102.140i | 0.211617 | + | 0.122177i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −368.963 | + | 213.021i | −0.440290 | + | 0.254202i | ||||
\(839\) | − | 3.07370i | − | 0.00366353i | −0.999998 | − | 0.00183177i | \(-0.999417\pi\) | ||
0.999998 | − | 0.00183177i | \(-0.000583069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | −144.104 | − | 249.596i | −0.171145 | − | 0.296432i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 124.912 | − | 216.353i | 0.148000 | − | 0.256343i | ||||
\(845\) | −1087.25 | + | 627.723i | −1.28669 | + | 0.742868i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 138.177 | 0.162944 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1032.32 | − | 596.012i | −1.21450 | − | 0.701191i | ||||
\(851\) | 40.1695 | − | 69.5756i | 0.0472027 | − | 0.0817574i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 155.257i | − | 0.182013i | −0.995850 | − | 0.0910063i | \(-0.970992\pi\) | ||
0.995850 | − | 0.0910063i | \(-0.0290083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −239.647 | − | 415.080i | −0.279961 | − | 0.484907i | ||||
\(857\) | −1388.98 | − | 801.931i | −1.62075 | − | 0.935742i | −0.986719 | − | 0.162436i | \(-0.948065\pi\) |
−0.634033 | − | 0.773306i | \(-0.718602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −545.367 | + | 314.868i | −0.634886 | + | 0.366551i | −0.782642 | − | 0.622472i | \(-0.786128\pi\) |
0.147756 | + | 0.989024i | \(0.452795\pi\) | |||||||
\(860\) | 259.009i | 0.301174i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −559.632 | −0.649226 | ||||||||
\(863\) | 514.706 | + | 891.496i | 0.596414 | + | 1.03302i | 0.993346 | + | 0.115172i | \(0.0367418\pi\) |
−0.396931 | + | 0.917848i | \(0.629925\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −966.573 | + | 1674.15i | −1.11743 | + | 1.93544i | ||||
\(866\) | 54.2176 | − | 31.3026i | 0.0626070 | − | 0.0361462i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 530.029 | 0.609929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1769.79 | − | 1021.79i | −2.03190 | − | 1.17312i | ||||
\(872\) | 253.061 | − | 438.314i | 0.290208 | − | 0.502654i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 323.944i | 0.370646i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −324.220 | − | 561.566i | −0.369693 | − | 0.640326i | 0.619825 | − | 0.784740i | \(-0.287204\pi\) |
−0.989517 | + | 0.144414i | \(0.953870\pi\) | |||||||
\(878\) | −487.279 | − | 281.331i | −0.554988 | − | 0.320422i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −173.823 | + | 100.357i | −0.197527 | + | 0.114042i | ||||
\(881\) | 363.857i | 0.413005i | 0.978446 | + | 0.206502i | \(0.0662082\pi\) | ||||
−0.978446 | + | 0.206502i | \(0.933792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1536.16 | 1.73971 | 0.869853 | − | 0.493312i | \(-0.164214\pi\) | ||||
0.869853 | + | 0.493312i | \(0.164214\pi\) | |||||||
\(884\) | −335.044 | − | 580.313i | −0.379009 | − | 0.656462i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.8234 | − | 145.186i | 0.0946088 | − | 0.163867i | ||||
\(887\) | 974.720 | − | 562.755i | 1.09890 | − | 0.634447i | 0.162964 | − | 0.986632i | \(-0.447894\pi\) |
0.935931 | + | 0.352185i | \(0.114561\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −245.823 | −0.276206 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 396.000 | + | 228.631i | 0.443946 | + | 0.256312i | ||||
\(893\) | −282.640 | + | 489.546i | −0.316506 | + | 0.548204i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 713.197i | 0.796868i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −504.801 | − | 874.341i | −0.562139 | − | 0.973654i | ||||
\(899\) | 433.499 | + | 250.281i | 0.482201 | + | 0.278399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 561.088 | − | 323.944i | 0.622740 | − | 0.359539i | ||||
\(902\) | − | 298.982i | − | 0.331466i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49.2061 | −0.0544315 | ||||||||
\(905\) | −23.3604 | − | 40.4614i | −0.0258126 | − | 0.0447087i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −117.448 | + | 203.426i | −0.129491 | + | 0.224285i | −0.923479 | − | 0.383648i | \(-0.874668\pi\) |
0.793989 | + | 0.607933i | \(0.208001\pi\) | |||||||
\(908\) | 293.647 | − | 169.537i | 0.323400 | − | 0.186715i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −224.278 | −0.246189 | −0.123095 | − | 0.992395i | \(-0.539282\pi\) | ||||
−0.123095 | + | 0.992395i | \(0.539282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −393.661 | − | 227.280i | −0.431173 | − | 0.248938i | ||||
\(914\) | −88.5132 | + | 153.309i | −0.0968416 | + | 0.167735i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 69.3840i | − | 0.0757467i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 466.081 | + | 807.276i | 0.507161 | + | 0.878428i | 0.999966 | + | 0.00828836i | \(0.00263830\pi\) |
−0.492805 | + | 0.870140i | \(0.664028\pi\) | |||||||
\(920\) | −275.647 | − | 159.145i | −0.299616 | − | 0.172983i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 803.147 | − | 463.697i | 0.871092 | − | 0.502925i | ||||
\(923\) | 332.322i | 0.360046i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −268.324 | −0.290080 | ||||||||
\(926\) | 614.756 | + | 1064.79i | 0.663883 | + | 1.14988i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −96.0000 | + | 166.277i | −0.103448 | + | 0.179178i | ||||
\(929\) | −618.390 | + | 357.028i | −0.665651 | + | 0.384314i | −0.794427 | − | 0.607360i | \(-0.792229\pi\) |
0.128776 | + | 0.991674i | \(0.458895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 508.971 | 0.546106 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −327.463 | − | 189.061i | −0.350603 | − | 0.202421i | ||||
\(935\) | −470.558 | + | 815.031i | −0.503271 | + | 0.871691i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1723.25i | − | 1.83912i | −0.392952 | − | 0.919559i | \(-0.628546\pi\) | ||
0.392952 | − | 0.919559i | \(-0.371454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −277.706 | − | 481.000i | −0.295432 | − | 0.511702i | ||||
\(941\) | 835.508 | + | 482.381i | 0.887893 | + | 0.512625i | 0.873253 | − | 0.487267i | \(-0.162006\pi\) |
0.0146405 | + | 0.999893i | \(0.495340\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 410.601 | − | 237.061i | 0.435420 | − | 0.251390i | ||||
\(944\) | − | 109.459i | − | 0.115952i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 131.397 | 0.138897 | ||||||||
\(947\) | 725.881 | + | 1257.26i | 0.766506 | + | 1.32763i | 0.939447 | + | 0.342695i | \(0.111340\pi\) |
−0.172940 | + | 0.984932i | \(0.555327\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1045.32 | − | 1810.55i | 1.10150 | − | 1.90785i | ||||
\(950\) | 936.988 | − | 540.971i | 0.986304 | − | 0.569443i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1147.43 | −1.20401 | −0.602007 | − | 0.798491i | \(-0.705632\pi\) | ||||
−0.602007 | + | 0.798491i | \(0.705632\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1342.76 | + | 775.245i | 1.40604 | + | 0.811775i | ||||
\(956\) | 197.147 | − | 341.469i | 0.206221 | − | 0.357185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 384.294i | 0.401142i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −371.749 | − | 643.889i | −0.386836 | − | 0.670020i | ||||
\(962\) | −130.628 | − | 75.4181i | −0.135788 | − | 0.0783972i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 153.235 | − | 88.4701i | 0.158957 | − | 0.0917739i | ||||
\(965\) | 1905.06i | 1.97415i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 412.190 | 0.426257 | 0.213128 | − | 0.977024i | \(-0.431635\pi\) | ||||
0.213128 | + | 0.977024i | \(0.431635\pi\) | |||||||
\(968\) | −120.208 | − | 208.207i | −0.124182 | − | 0.215089i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −180.853 | + | 313.246i | −0.186446 | + | 0.322934i | ||||
\(971\) | 869.595 | − | 502.061i | 0.895566 | − | 0.517056i | 0.0198073 | − | 0.999804i | \(-0.493695\pi\) |
0.875759 | + | 0.482748i | \(0.160361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 794.101 | 0.815298 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −139.882 | − | 80.7611i | −0.143322 | − | 0.0827470i | ||||
\(977\) | −794.117 | + | 1375.45i | −0.812812 | + | 1.40783i | 0.0980772 | + | 0.995179i | \(0.468731\pi\) |
−0.910889 | + | 0.412652i | \(0.864603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 124.708i | 0.127383i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 287.397 | + | 497.786i | 0.292665 | + | 0.506911i | ||||
\(983\) | 721.861 | + | 416.767i | 0.734345 | + | 0.423974i | 0.820009 | − | 0.572350i | \(-0.193968\pi\) |
−0.0856648 | + | 0.996324i | \(0.527301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −892.014 | + | 515.005i | −0.905598 | + | 0.522847i | ||||
\(986\) | 900.259i | 0.913041i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 608.205 | 0.615592 | ||||||||
\(989\) | 104.184 | + | 180.452i | 0.105343 | + | 0.182459i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.4483 | + | 57.9341i | −0.0337520 | + | 0.0584602i | −0.882408 | − | 0.470485i | \(-0.844079\pi\) |
0.848656 | + | 0.528945i | \(0.177412\pi\) | |||||||
\(992\) | −72.2498 | + | 41.7134i | −0.0728324 | + | 0.0420498i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52.1177 | −0.0523796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1268.65 | − | 732.453i | −1.27246 | − | 0.734657i | −0.297012 | − | 0.954874i | \(-0.595990\pi\) |
−0.975451 | + | 0.220217i | \(0.929323\pi\) | |||||||
\(998\) | −262.638 | + | 454.903i | −0.263164 | + | 0.455814i | ||||
\(999\) | 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 | 882.3.n.e.325.2 | 4 | ||
3.2 | odd | 2 | 294.3.g.a.31.1 | 4 | |||
7.2 | even | 3 | 126.3.n.a.19.2 | 4 | |||
7.3 | odd | 6 | 882.3.c.b.685.1 | 4 | |||
7.4 | even | 3 | 882.3.c.b.685.2 | 4 | |||
7.5 | odd | 6 | inner | 882.3.n.e.19.2 | 4 | ||
7.6 | odd | 2 | 126.3.n.a.73.2 | 4 | |||
21.2 | odd | 6 | 42.3.g.a.19.1 | ✓ | 4 | ||
21.5 | even | 6 | 294.3.g.a.19.1 | 4 | |||
21.11 | odd | 6 | 294.3.c.a.97.4 | 4 | |||
21.17 | even | 6 | 294.3.c.a.97.3 | 4 | |||
21.20 | even | 2 | 42.3.g.a.31.1 | yes | 4 | ||
28.23 | odd | 6 | 1008.3.cg.h.145.1 | 4 | |||
28.27 | even | 2 | 1008.3.cg.h.577.1 | 4 | |||
84.11 | even | 6 | 2352.3.f.e.97.1 | 4 | |||
84.23 | even | 6 | 336.3.bh.e.145.2 | 4 | |||
84.59 | odd | 6 | 2352.3.f.e.97.4 | 4 | |||
84.83 | odd | 2 | 336.3.bh.e.241.2 | 4 | |||
105.2 | even | 12 | 1050.3.q.a.649.1 | 8 | |||
105.23 | even | 12 | 1050.3.q.a.649.4 | 8 | |||
105.44 | odd | 6 | 1050.3.p.a.901.2 | 4 | |||
105.62 | odd | 4 | 1050.3.q.a.199.4 | 8 | |||
105.83 | odd | 4 | 1050.3.q.a.199.1 | 8 | |||
105.104 | even | 2 | 1050.3.p.a.451.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.1 | ✓ | 4 | 21.2 | odd | 6 | ||
42.3.g.a.31.1 | yes | 4 | 21.20 | even | 2 | ||
126.3.n.a.19.2 | 4 | 7.2 | even | 3 | |||
126.3.n.a.73.2 | 4 | 7.6 | odd | 2 | |||
294.3.c.a.97.3 | 4 | 21.17 | even | 6 | |||
294.3.c.a.97.4 | 4 | 21.11 | odd | 6 | |||
294.3.g.a.19.1 | 4 | 21.5 | even | 6 | |||
294.3.g.a.31.1 | 4 | 3.2 | odd | 2 | |||
336.3.bh.e.145.2 | 4 | 84.23 | even | 6 | |||
336.3.bh.e.241.2 | 4 | 84.83 | odd | 2 | |||
882.3.c.b.685.1 | 4 | 7.3 | odd | 6 | |||
882.3.c.b.685.2 | 4 | 7.4 | even | 3 | |||
882.3.n.e.19.2 | 4 | 7.5 | odd | 6 | inner | ||
882.3.n.e.325.2 | 4 | 1.1 | even | 1 | trivial | ||
1008.3.cg.h.145.1 | 4 | 28.23 | odd | 6 | |||
1008.3.cg.h.577.1 | 4 | 28.27 | even | 2 | |||
1050.3.p.a.451.2 | 4 | 105.104 | even | 2 | |||
1050.3.p.a.901.2 | 4 | 105.44 | odd | 6 | |||
1050.3.q.a.199.1 | 8 | 105.83 | odd | 4 | |||
1050.3.q.a.199.4 | 8 | 105.62 | odd | 4 | |||
1050.3.q.a.649.1 | 8 | 105.2 | even | 12 | |||
1050.3.q.a.649.4 | 8 | 105.23 | even | 12 | |||
2352.3.f.e.97.1 | 4 | 84.11 | even | 6 | |||
2352.3.f.e.97.4 | 4 | 84.59 | odd | 6 |