Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,3,Mod(65,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 13]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.bc (of order \(18\), degree \(6\), 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: | \(11.7711474204\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 401.5 | ||
Character | \(\chi\) | \(=\) | 432.401 |
Dual form | 432.3.bc.a.209.5 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{11}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.94744 | + | 0.559079i | 0.982482 | + | 0.186360i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.15614 | + | 1.08549i | 1.23123 | + | 0.217099i | 0.751153 | − | 0.660128i | \(-0.229498\pi\) |
0.480076 | + | 0.877227i | \(0.340609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.21846 | − | 5.21791i | 0.888352 | − | 0.745415i | −0.0795272 | − | 0.996833i | \(-0.525341\pi\) |
0.967879 | + | 0.251417i | \(0.0808966\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.37486 | + | 3.29571i | 0.930540 | + | 0.366190i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.99059 | − | 1.40896i | 0.726417 | − | 0.128087i | 0.201802 | − | 0.979426i | \(-0.435320\pi\) |
0.524615 | + | 0.851339i | \(0.324209\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.12402 | + | 3.32087i | −0.701848 | + | 0.255452i | −0.668200 | − | 0.743982i | \(-0.732935\pi\) |
−0.0336483 | + | 0.999434i | \(0.510713\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 17.5380 | + | 6.64120i | 1.16920 | + | 0.442747i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.0143 | − | 7.51380i | −0.765546 | − | 0.441988i | 0.0657372 | − | 0.997837i | \(-0.479060\pi\) |
−0.831284 | + | 0.555849i | \(0.812393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.93226 | − | 15.4711i | −0.470119 | − | 0.814270i | 0.529297 | − | 0.848437i | \(-0.322456\pi\) |
−0.999416 | + | 0.0341664i | \(0.989122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.2458 | − | 11.9029i | 1.01170 | − | 0.566804i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.9268 | + | 20.1726i | −0.735949 | + | 0.877070i | −0.996076 | − | 0.0885045i | \(-0.971791\pi\) |
0.260127 | + | 0.965575i | \(0.416236\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.2275 | + | 4.81440i | 0.529099 | + | 0.192576i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 22.8419 | + | 14.3961i | 0.845996 | + | 0.533190i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.18906 | − | 14.2568i | 0.178933 | − | 0.491615i | −0.817507 | − | 0.575919i | \(-0.804644\pi\) |
0.996440 | + | 0.0843038i | \(0.0268666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.0755 | − | 21.0408i | −0.808886 | − | 0.678736i | 0.141456 | − | 0.989945i | \(-0.454822\pi\) |
−0.950342 | + | 0.311209i | \(0.899266\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.3395 | + | 0.314547i | 0.737562 | + | 0.00953171i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 43.9457 | − | 25.3721i | 1.25559 | − | 0.724917i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.8096 | + | 27.3831i | −0.427287 | + | 0.740083i | −0.996631 | − | 0.0820163i | \(-0.973864\pi\) |
0.569344 | + | 0.822100i | \(0.307197\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −28.7492 | + | 4.68704i | −0.737159 | + | 0.120181i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65018 | + | 15.5238i | 0.137809 | + | 0.378628i | 0.989330 | − | 0.145693i | \(-0.0465413\pi\) |
−0.851520 | + | 0.524321i | \(0.824319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14.5559 | + | 82.5505i | 0.338509 | + | 1.91978i | 0.389385 | + | 0.921075i | \(0.372688\pi\) |
−0.0508761 | + | 0.998705i | \(0.516201\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 47.9794 | + | 29.3797i | 1.06621 | + | 0.652882i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.46562 | − | 10.0889i | −0.180120 | − | 0.214658i | 0.668429 | − | 0.743776i | \(-0.266967\pi\) |
−0.848548 | + | 0.529118i | \(0.822523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.93393 | − | 16.6391i | 0.0598761 | − | 0.339574i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −34.1581 | − | 29.4225i | −0.669766 | − | 0.576912i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 25.7140i | − | 0.485169i | −0.970130 | − | 0.242585i | \(-0.922005\pi\) | ||
0.970130 | − | 0.242585i | \(-0.0779952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 50.7206 | 0.922193 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.6778 | − | 50.5941i | −0.310136 | − | 0.887617i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22.3660 | + | 3.94373i | 0.379085 | + | 0.0668428i | 0.359944 | − | 0.932974i | \(-0.382796\pi\) |
0.0191407 | + | 0.999817i | \(0.493907\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26.1131 | − | 21.9115i | 0.428084 | − | 0.359205i | −0.403144 | − | 0.915137i | \(-0.632083\pi\) |
0.831228 | + | 0.555931i | \(0.187638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 69.2755 | − | 23.2050i | 1.09961 | − | 0.368334i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −59.7736 | + | 10.5397i | −0.919593 | + | 0.162149i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.61567 | − | 2.77188i | 0.113667 | − | 0.0413713i | −0.284561 | − | 0.958658i | \(-0.591848\pi\) |
0.398227 | + | 0.917287i | \(0.369625\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −61.1690 | + | 49.9942i | −0.886507 | + | 0.724554i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35.7557 | − | 20.6436i | −0.503601 | − | 0.290754i | 0.226598 | − | 0.973988i | \(-0.427240\pi\) |
−0.730199 | + | 0.683234i | \(0.760573\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.4046 | + | 69.9827i | 0.553487 | + | 0.958668i | 0.998020 | + | 0.0629050i | \(0.0200365\pi\) |
−0.444532 | + | 0.895763i | \(0.646630\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 36.2956 | + | 21.5854i | 0.483941 | + | 0.287805i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 42.3374 | − | 50.4557i | 0.549836 | − | 0.655269i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −25.9652 | − | 9.45057i | −0.328674 | − | 0.119627i | 0.172412 | − | 0.985025i | \(-0.444844\pi\) |
−0.501086 | + | 0.865397i | \(0.667066\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59.2766 | + | 55.2022i | 0.731810 | + | 0.681508i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.01607 | − | 16.5290i | 0.0724827 | − | 0.199145i | −0.898161 | − | 0.439667i | \(-0.855096\pi\) |
0.970644 | + | 0.240522i | \(0.0773187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −71.9616 | − | 60.3830i | −0.846607 | − | 0.710388i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.2652 | − | 39.1201i | 0.267416 | − | 0.449657i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 24.4986 | − | 14.1443i | 0.275265 | − | 0.158924i | −0.356013 | − | 0.934481i | \(-0.615864\pi\) |
0.631278 | + | 0.775557i | \(0.282531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39.4094 | + | 68.2590i | −0.433070 | + | 0.750099i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −62.1451 | − | 76.0358i | −0.668227 | − | 0.817589i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.1945 | − | 104.938i | −0.402047 | − | 1.10461i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 29.2825 | + | 166.069i | 0.301881 | + | 1.71205i | 0.637834 | + | 0.770174i | \(0.279831\pi\) |
−0.335953 | + | 0.941879i | \(0.609058\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 71.5636 | + | 14.5348i | 0.722865 | + | 0.146816i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44.8847 | − | 53.4915i | −0.444403 | − | 0.529619i | 0.496617 | − | 0.867970i | \(-0.334575\pi\) |
−0.941020 | + | 0.338351i | \(0.890131\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1315 | + | 68.8014i | −0.117782 | + | 0.667974i | 0.867553 | + | 0.497344i | \(0.165691\pi\) |
−0.985335 | + | 0.170630i | \(0.945420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 143.713 | − | 50.2137i | 1.36869 | − | 0.478226i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 121.432i | − | 1.13488i | −0.823416 | − | 0.567438i | \(-0.807935\pi\) | ||
0.823416 | − | 0.567438i | \(-0.192065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −119.633 | −1.09755 | −0.548777 | − | 0.835969i | \(-0.684907\pi\) | ||||
−0.548777 | + | 0.835969i | \(0.684907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −61.9073 | + | 71.8713i | −0.557723 | + | 0.647489i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 122.474 | + | 21.5955i | 1.08384 | + | 0.191111i | 0.686914 | − | 0.726738i | \(-0.258965\pi\) |
0.396929 | + | 0.917849i | \(0.370076\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −126.101 | + | 105.811i | −1.09653 | + | 0.920100i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −87.3571 | − | 2.25826i | −0.746642 | − | 0.0193013i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −120.135 | + | 21.1831i | −1.00954 | + | 0.178009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −51.8384 | + | 18.8676i | −0.428417 | + | 0.155931i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.97461 | + | 48.9143i | 0.0648342 | + | 0.397677i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −59.1363 | − | 34.1424i | −0.473091 | − | 0.273139i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −58.7300 | − | 101.723i | −0.462441 | − | 0.800971i | 0.536641 | − | 0.843811i | \(-0.319693\pi\) |
−0.999082 | + | 0.0428396i | \(0.986360\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.24957 | + | 251.451i | −0.0251905 | + | 1.94923i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.02933 | + | 3.61022i | −0.0231247 | + | 0.0275589i | −0.777483 | − | 0.628904i | \(-0.783504\pi\) |
0.754358 | + | 0.656463i | \(0.227948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −136.272 | − | 49.5989i | −1.02460 | − | 0.372924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 124.991 | + | 113.419i | 0.925859 | + | 0.840143i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 75.5147 | − | 207.475i | 0.551202 | − | 1.51442i | −0.280869 | − | 0.959746i | \(-0.590623\pi\) |
0.832071 | − | 0.554669i | \(-0.187155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 27.3980 | + | 22.9896i | 0.197108 | + | 0.165393i | 0.736000 | − | 0.676982i | \(-0.236712\pi\) |
−0.538892 | + | 0.842375i | \(0.681157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.3114 | − | 34.4695i | −0.136961 | − | 0.244465i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −68.2274 | + | 39.3911i | −0.477114 | + | 0.275462i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 47.4203 | − | 82.1344i | 0.327037 | − | 0.566444i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.9502 | − | 47.4026i | 0.122110 | − | 0.322467i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −57.3691 | − | 157.620i | −0.385028 | − | 1.05786i | −0.969211 | − | 0.246233i | \(-0.920807\pi\) |
0.584183 | − | 0.811622i | \(-0.301415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.5375 | + | 82.4463i | 0.0962748 | + | 0.546002i | 0.994349 | + | 0.106158i | \(0.0338550\pi\) |
−0.898074 | + | 0.439844i | \(0.855034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −84.2296 | − | 105.818i | −0.550520 | − | 0.691623i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −131.528 | − | 156.750i | −0.848571 | − | 1.01129i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9271 | + | 73.3133i | −0.0823383 | + | 0.466963i | 0.915561 | + | 0.402179i | \(0.131747\pi\) |
−0.997899 | + | 0.0647844i | \(0.979364\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.3761 | − | 75.7905i | 0.0904159 | − | 0.476670i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 213.765i | 1.32773i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −254.830 | −1.56337 | −0.781687 | − | 0.623670i | \(-0.785641\pi\) | ||||
−0.781687 | + | 0.623670i | \(0.785641\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 149.496 | + | 28.3568i | 0.906038 | + | 0.171859i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 156.190 | + | 27.5405i | 0.935269 | + | 0.164913i | 0.620457 | − | 0.784241i | \(-0.286947\pi\) |
0.314813 | + | 0.949154i | \(0.398058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −57.2419 | + | 48.0317i | −0.338710 | + | 0.284211i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.8181 | − | 159.007i | −0.139287 | − | 0.929864i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −293.553 | + | 51.7613i | −1.69684 | + | 0.299198i | −0.936587 | − | 0.350434i | \(-0.886034\pi\) |
−0.760249 | + | 0.649632i | \(0.774923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 107.376 | − | 39.0815i | 0.613575 | − | 0.223323i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 63.7177 | + | 24.1283i | 0.359987 | + | 0.136318i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.3997 | − | 14.6645i | −0.141898 | − | 0.0819248i | 0.427370 | − | 0.904077i | \(-0.359440\pi\) |
−0.569268 | + | 0.822152i | \(0.692773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −41.7019 | − | 72.2299i | −0.230397 | − | 0.399060i | 0.727528 | − | 0.686078i | \(-0.240669\pi\) |
−0.957925 | + | 0.287018i | \(0.907336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 89.2173 | − | 49.9837i | 0.487526 | − | 0.273135i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −127.050 | + | 151.413i | −0.686759 | + | 0.818448i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −114.578 | − | 41.7031i | −0.612719 | − | 0.223011i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 217.159 | − | 29.6651i | 1.14899 | − | 0.156958i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −53.6797 | + | 147.484i | −0.281046 | + | 0.772166i | 0.716193 | + | 0.697902i | \(0.245883\pi\) |
−0.997239 | + | 0.0742641i | \(0.976339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31.7673 | − | 26.6559i | −0.164598 | − | 0.138114i | 0.556769 | − | 0.830668i | \(-0.312041\pi\) |
−0.721366 | + | 0.692554i | \(0.756485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −182.072 | − | 2.35296i | −0.933702 | − | 0.0120665i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −182.437 | + | 105.330i | −0.926074 | + | 0.534669i | −0.885568 | − | 0.464510i | \(-0.846230\pi\) |
−0.0405063 | + | 0.999179i | \(0.512897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −87.7654 | + | 152.014i | −0.441032 | + | 0.763890i | −0.997766 | − | 0.0668004i | \(-0.978721\pi\) |
0.556734 | + | 0.830691i | \(0.312054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.9965 | − | 3.91220i | 0.119385 | − | 0.0194637i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −42.1229 | − | 115.732i | −0.207502 | − | 0.570107i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.9324 | + | 101.700i | 0.0874751 | + | 0.496096i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −208.243 | + | 113.157i | −1.00600 | + | 0.546652i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −93.1722 | − | 111.038i | −0.445800 | − | 0.531284i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 45.2968 | − | 256.891i | 0.214677 | − | 1.21749i | −0.666789 | − | 0.745246i | \(-0.732332\pi\) |
0.881466 | − | 0.472247i | \(-0.156557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −93.8465 | − | 80.8360i | −0.440594 | − | 0.379512i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 523.993i | 2.43718i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −265.720 | −1.22452 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 79.9643 | + | 228.860i | 0.365134 | + | 1.04502i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 143.695 | + | 25.3373i | 0.650204 | + | 0.114648i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 298.157 | − | 250.184i | 1.33703 | − | 1.12190i | 0.354650 | − | 0.934999i | \(-0.384600\pi\) |
0.982379 | − | 0.186901i | \(-0.0598445\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 94.9113 | + | 83.9138i | 0.421828 | + | 0.372950i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 343.139 | − | 60.5046i | 1.51162 | − | 0.266540i | 0.644489 | − | 0.764614i | \(-0.277070\pi\) |
0.867135 | + | 0.498074i | \(0.165959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 342.540 | − | 124.675i | 1.49581 | − | 0.544430i | 0.540838 | − | 0.841127i | \(-0.318107\pi\) |
0.954972 | + | 0.296696i | \(0.0958849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 152.996 | − | 125.045i | 0.662319 | − | 0.541323i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 164.260 | + | 94.8353i | 0.704976 | + | 0.407018i | 0.809198 | − | 0.587536i | \(-0.199902\pi\) |
−0.104222 | + | 0.994554i | \(0.533235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −41.1641 | − | 71.2983i | −0.175166 | − | 0.303397i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −71.2475 | − | 42.3716i | −0.300622 | − | 0.178783i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 196.756 | − | 234.485i | 0.823249 | − | 0.981110i | −0.176746 | − | 0.984256i | \(-0.556557\pi\) |
0.999995 | + | 0.00314661i | \(0.00100160\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 277.120 | + | 100.864i | 1.14988 | + | 0.418521i | 0.845471 | − | 0.534021i | \(-0.179320\pi\) |
0.304406 | + | 0.952542i | \(0.401542\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 143.852 | + | 195.846i | 0.591984 | + | 0.805949i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 36.1234 | − | 99.2481i | 0.147442 | − | 0.405094i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 132.876 | + | 111.496i | 0.537959 | + | 0.451401i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.9730 | − | 45.3549i | 0.108325 | − | 0.182148i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −158.404 | + | 91.4547i | −0.631092 | + | 0.364361i | −0.781175 | − | 0.624312i | \(-0.785379\pi\) |
0.150083 | + | 0.988673i | \(0.452046\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −106.833 | + | 185.040i | −0.422265 | + | 0.731384i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −178.344 | − | 218.208i | −0.699388 | − | 0.855716i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −91.7859 | − | 252.180i | −0.357144 | − | 0.981244i | −0.980016 | − | 0.198920i | \(-0.936256\pi\) |
0.622872 | − | 0.782324i | \(-0.285966\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 44.5708 | + | 252.774i | 0.172088 | + | 0.975961i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 90.4440 | − | 102.297i | 0.346529 | − | 0.391944i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −226.246 | − | 269.629i | −0.860250 | − | 1.02521i | −0.999390 | − | 0.0349337i | \(-0.988878\pi\) |
0.139139 | − | 0.990273i | \(-0.455566\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.9123 | − | 158.299i | 0.105330 | − | 0.597354i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 80.1160 | − | 27.9928i | 0.300060 | − | 0.104842i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 164.243i | 0.610570i | 0.952261 | + | 0.305285i | \(0.0987518\pi\) | ||||
−0.952261 | + | 0.305285i | \(0.901248\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 128.850 | 0.475462 | 0.237731 | − | 0.971331i | \(-0.423596\pi\) | ||||
0.237731 | + | 0.971331i | \(0.423596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −154.319 | + | 179.157i | −0.565272 | + | 0.656252i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 112.479 | + | 19.8330i | 0.409013 | + | 0.0721200i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 115.074 | − | 96.5583i | 0.415428 | − | 0.348586i | −0.410992 | − | 0.911639i | \(-0.634818\pi\) |
0.826421 | + | 0.563053i | \(0.190373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −140.659 | − | 258.855i | −0.504155 | − | 0.927797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 453.995 | − | 80.0516i | 1.61564 | − | 0.284881i | 0.708501 | − | 0.705710i | \(-0.249372\pi\) |
0.907140 | + | 0.420828i | \(0.138261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −64.7049 | + | 23.5506i | −0.228639 | + | 0.0832178i | −0.453799 | − | 0.891104i | \(-0.649932\pi\) |
0.225160 | + | 0.974322i | \(0.427709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −53.9072 | − | 330.654i | −0.189148 | − | 1.16019i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 116.137 | + | 67.0517i | 0.404658 | + | 0.233630i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −31.5856 | − | 54.7078i | −0.109293 | − | 0.189300i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.53725 | + | 505.851i | −0.0224648 | + | 1.73832i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 328.314 | − | 391.270i | 1.12053 | − | 1.33539i | 0.184755 | − | 0.982785i | \(-0.440851\pi\) |
0.935772 | − | 0.352607i | \(-0.114705\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 133.407 | + | 48.5563i | 0.452228 | + | 0.164598i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 202.804 | + | 82.8503i | 0.682841 | + | 0.278957i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 87.4501 | − | 240.267i | 0.292475 | − | 0.803569i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 521.256 | + | 437.386i | 1.73175 | + | 1.45311i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −102.389 | − | 182.757i | −0.337919 | − | 0.603160i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 184.541 | − | 106.545i | 0.605053 | − | 0.349327i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3017 | − | 45.5559i | 0.0856734 | − | 0.148391i | −0.820005 | − | 0.572357i | \(-0.806029\pi\) |
0.905678 | + | 0.423966i | \(0.139363\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −74.2224 | + | 196.006i | −0.240202 | + | 0.634323i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 121.357 | + | 333.427i | 0.390217 | + | 1.07211i | 0.966903 | + | 0.255146i | \(0.0821234\pi\) |
−0.576686 | + | 0.816966i | \(0.695654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.2161 | + | 165.693i | 0.0933421 | + | 0.529369i | 0.995243 | + | 0.0974258i | \(0.0310609\pi\) |
−0.901901 | + | 0.431943i | \(0.857828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 451.658 | − | 67.6554i | 1.43384 | − | 0.214779i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 327.814 | + | 390.674i | 1.03411 | + | 1.23241i | 0.972157 | + | 0.234330i | \(0.0752898\pi\) |
0.0619572 | + | 0.998079i | \(0.480266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.3764 | − | 121.232i | 0.0670107 | − | 0.380037i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 67.8898 | − | 357.913i | 0.211495 | − | 1.11499i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 268.461i | 0.831149i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −136.676 | −0.420541 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −352.613 | − | 66.8845i | −1.07833 | − | 0.204540i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −105.286 | − | 18.5648i | −0.320019 | − | 0.0564280i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 259.951 | − | 218.125i | 0.785350 | − | 0.658987i | −0.159240 | − | 0.987240i | \(-0.550904\pi\) |
0.944590 | + | 0.328253i | \(0.106460\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −222.650 | + | 177.226i | −0.668619 | + | 0.532209i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 49.8920 | − | 8.79731i | 0.148931 | − | 0.0262606i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 64.1227 | − | 23.3388i | 0.190275 | − | 0.0692545i | −0.245125 | − | 0.969491i | \(-0.578829\pi\) |
0.435400 | + | 0.900237i | \(0.356607\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 348.913 | + | 132.124i | 1.02924 | + | 0.389748i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −230.013 | − | 132.798i | −0.674526 | − | 0.389438i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 130.305 | + | 225.695i | 0.379897 | + | 0.658002i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −430.833 | + | 241.373i | −1.24879 | + | 0.699632i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 111.265 | − | 132.600i | 0.320648 | − | 0.382134i | −0.581510 | − | 0.813539i | \(-0.697538\pi\) |
0.902158 | + | 0.431406i | \(0.141982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −431.866 | − | 157.186i | −1.23744 | − | 0.450390i | −0.361299 | − | 0.932450i | \(-0.617667\pi\) |
−0.876138 | + | 0.482060i | \(0.839889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −256.218 | − | 55.4956i | −0.729965 | − | 0.158107i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −137.578 | + | 377.991i | −0.389738 | + | 1.07080i | 0.577381 | + | 0.816475i | \(0.304075\pi\) |
−0.967119 | + | 0.254322i | \(0.918148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −197.709 | − | 165.897i | −0.556926 | − | 0.467316i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −365.935 | − | 4.72908i | −1.02503 | − | 0.0132467i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 197.249 | − | 113.882i | 0.549439 | − | 0.317219i | −0.199457 | − | 0.979907i | \(-0.563918\pi\) |
0.748896 | + | 0.662688i | \(0.230584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.9294 | − | 36.2507i | 0.0579761 | − | 0.100418i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −163.339 | + | 26.6296i | −0.449971 | + | 0.0733597i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 172.770 | + | 474.683i | 0.473343 | + | 1.30050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 40.8884 | + | 231.890i | 0.111413 | + | 0.631852i | 0.988464 | + | 0.151456i | \(0.0483960\pi\) |
−0.877052 | + | 0.480396i | \(0.840493\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.84223 | + | 148.631i | −0.0104126 | + | 0.402793i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −134.173 | − | 159.901i | −0.361653 | − | 0.431001i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 113.349 | − | 642.835i | 0.303885 | − | 1.72342i | −0.324822 | − | 0.945775i | \(-0.605304\pi\) |
0.628707 | − | 0.777642i | \(-0.283585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −155.213 | − | 133.695i | −0.413901 | − | 0.356519i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 147.312i | 0.390748i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −625.053 | −1.64922 | −0.824608 | − | 0.565705i | \(-0.808604\pi\) | ||||
−0.824608 | + | 0.565705i | \(0.808604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −116.232 | − | 332.659i | −0.305071 | − | 0.873119i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −104.921 | − | 18.5004i | −0.273945 | − | 0.0483039i | 0.0349879 | − | 0.999388i | \(-0.488861\pi\) |
−0.308933 | + | 0.951084i | \(0.599972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 315.404 | − | 264.656i | 0.819232 | − | 0.687417i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −150.159 | + | 739.321i | −0.388007 | + | 1.91039i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −584.613 | + | 103.083i | −1.50286 | + | 0.264995i | −0.863672 | − | 0.504054i | \(-0.831841\pi\) |
−0.639190 | + | 0.769049i | \(0.720730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 371.864 | − | 135.347i | 0.951058 | − | 0.346157i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.9472 | + | 8.94729i | −0.0278555 | + | 0.0227666i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −149.587 | − | 86.3642i | −0.378702 | − | 0.218643i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −187.410 | − | 324.603i | −0.472064 | − | 0.817640i | 0.527425 | − | 0.849602i | \(-0.323158\pi\) |
−0.999489 | + | 0.0319623i | \(0.989824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −373.924 | − | 222.377i | −0.937153 | − | 0.557335i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −176.385 | + | 210.207i | −0.439862 | + | 0.524207i | −0.939741 | − | 0.341889i | \(-0.888933\pi\) |
0.499879 | + | 0.866095i | \(0.333378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 298.663 | + | 108.704i | 0.741099 | + | 0.269738i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 304.994 | + | 404.177i | 0.753071 | + | 0.997968i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −87.7467 | + | 241.082i | −0.215594 | + | 0.592339i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −422.454 | − | 354.481i | −1.03289 | − | 0.866701i | −0.0417017 | − | 0.999130i | \(-0.513278\pi\) |
−0.991193 | + | 0.132429i | \(0.957722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 338.570 | − | 569.302i | 0.823772 | − | 1.38516i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 159.660 | − | 92.1798i | 0.386586 | − | 0.223196i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.9779 | − | 95.2245i | 0.132477 | − | 0.229457i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 67.9010 | + | 83.0783i | 0.162832 | + | 0.199228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.9567 | + | 82.3055i | 0.0714958 | + | 0.196433i | 0.970294 | − | 0.241930i | \(-0.0777805\pi\) |
−0.898798 | + | 0.438363i | \(0.855558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 51.4449 | + | 291.759i | 0.122197 | + | 0.693013i | 0.982933 | + | 0.183962i | \(0.0588924\pi\) |
−0.860736 | + | 0.509051i | \(0.829996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −37.6482 | − | 112.394i | −0.0890029 | − | 0.265706i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −135.972 | − | 162.045i | −0.319933 | − | 0.381281i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.0512 | − | 272.512i | 0.112532 | − | 0.638201i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −223.119 | + | 77.9586i | −0.520091 | + | 0.181722i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 586.175i | 1.36003i | 0.733196 | + | 0.680017i | \(0.238028\pi\) | ||||
−0.733196 | + | 0.680017i | \(0.761972\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 415.367 | 0.959277 | 0.479639 | − | 0.877466i | \(-0.340768\pi\) | ||||
0.479639 | + | 0.877466i | \(0.340768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 185.688 | − | 215.575i | 0.426870 | − | 0.495575i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 463.288 | + | 81.6902i | 1.06016 | + | 0.186934i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −256.133 | + | 214.921i | −0.583447 | + | 0.489570i | −0.886077 | − | 0.463538i | \(-0.846580\pi\) |
0.302630 | + | 0.953108i | \(0.402135\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 79.4090 | − | 129.681i | 0.180066 | − | 0.294062i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −444.780 | + | 78.4268i | −1.00402 | + | 0.177036i | −0.651402 | − | 0.758732i | \(-0.725819\pi\) |
−0.352616 | + | 0.935768i | \(0.614708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 166.170 | − | 60.4810i | 0.373416 | − | 0.135912i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −80.9702 | − | 496.651i | −0.181141 | − | 1.11108i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −165.422 | − | 95.5067i | −0.368424 | − | 0.212710i | 0.304346 | − | 0.952562i | \(-0.401562\pi\) |
−0.672770 | + | 0.739852i | \(0.734896\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.0206 | + | 116.083i | 0.148604 | + | 0.257390i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.24547 | + | 251.133i | −0.00716438 | + | 0.554378i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −316.704 | + | 377.434i | −0.696054 | + | 0.829525i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 362.489 | + | 131.935i | 0.793192 | + | 0.288698i | 0.706662 | − | 0.707551i | \(-0.250200\pi\) |
0.0865297 | + | 0.996249i | \(0.472422\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −189.101 | − | 358.985i | −0.411985 | − | 0.782102i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 148.113 | − | 406.937i | 0.321286 | − | 0.882727i | −0.668947 | − | 0.743310i | \(-0.733255\pi\) |
0.990234 | − | 0.139417i | \(-0.0445229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −423.513 | − | 355.369i | −0.914714 | − | 0.767536i | 0.0582960 | − | 0.998299i | \(-0.481433\pi\) |
−0.973010 | + | 0.230763i | \(0.925878\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −300.038 | − | 535.545i | −0.645242 | − | 1.15171i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 186.467 | − | 107.657i | 0.399286 | − | 0.230528i | −0.286890 | − | 0.957964i | \(-0.592621\pi\) |
0.686176 | + | 0.727436i | \(0.259288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.8943 | − | 56.9747i | 0.0701372 | − | 0.121481i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −79.0898 | + | 208.860i | −0.167919 | + | 0.443439i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 232.620 | + | 639.119i | 0.491798 | + | 1.35120i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.6669 | − | 247.647i | −0.0919304 | − | 0.521363i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 84.7457 | − | 215.351i | 0.177664 | − | 0.451469i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 145.585 | + | 173.501i | 0.303935 | + | 0.362216i | 0.896295 | − | 0.443457i | \(-0.146248\pi\) |
−0.592360 | + | 0.805673i | \(0.701804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.3117 | − | 302.346i | 0.110835 | − | 0.628577i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −119.512 | + | 630.061i | −0.247436 | + | 1.30447i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1054.13i | 2.17347i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 443.130 | 0.909919 | 0.454959 | − | 0.890512i | \(-0.349654\pi\) | ||||
0.454959 | + | 0.890512i | \(0.349654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −751.098 | − | 142.470i | −1.53599 | − | 0.291350i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 657.316 | + | 115.902i | 1.33873 | + | 0.236054i | 0.796735 | − | 0.604329i | \(-0.206559\pi\) |
0.541993 | + | 0.840383i | \(0.317670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −174.655 | + | 146.553i | −0.354270 | + | 0.297268i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 424.778 | + | 167.160i | 0.858138 | + | 0.337698i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −330.061 | + | 58.1987i | −0.664108 | + | 0.117100i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −54.0177 | + | 19.6608i | −0.108252 | + | 0.0394005i | −0.395578 | − | 0.918432i | \(-0.629456\pi\) |
0.287326 | + | 0.957833i | \(0.407234\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 444.964 | + | 168.497i | 0.888152 | + | 0.336321i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −423.202 | − | 244.336i | −0.841356 | − | 0.485757i | 0.0163686 | − | 0.999866i | \(-0.494789\pi\) |
−0.857725 | + | 0.514109i | \(0.828123\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −218.252 | − | 378.024i | −0.432182 | − | 0.748562i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −195.571 | + | 109.568i | −0.385741 | + | 0.216110i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 182.714 | − | 217.750i | 0.358966 | − | 0.427799i | −0.556093 | − | 0.831120i | \(-0.687700\pi\) |
0.915058 | + | 0.403322i | \(0.132144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 616.418 | + | 224.358i | 1.20630 | + | 0.439056i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.6946 | − | 481.980i | 0.0364417 | − | 0.939532i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −149.367 | + | 410.382i | −0.290033 | + | 0.796859i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −81.8602 | − | 68.6889i | −0.158337 | − | 0.132860i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −894.169 | − | 11.5556i | −1.72287 | − | 0.0222651i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.1966 | − | 20.3207i | 0.0675558 | − | 0.0390033i | −0.465842 | − | 0.884868i | \(-0.654248\pi\) |
0.533397 | + | 0.845865i | \(0.320915\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 174.951 | − | 303.024i | 0.334514 | − | 0.579395i | −0.648877 | − | 0.760893i | \(-0.724761\pi\) |
0.983391 | + | 0.181498i | \(0.0580946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 338.333 | − | 55.1592i | 0.644444 | − | 0.105065i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 168.243 | + | 462.243i | 0.319246 | + | 0.877122i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.5567 | − | 161.953i | −0.0539825 | − | 0.306150i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 174.315 | + | 106.740i | 0.328276 | + | 0.201017i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −103.105 | − | 122.876i | −0.193442 | − | 0.230536i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 131.813 | − | 747.550i | 0.246380 | − | 1.39729i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −66.6656 | − | 57.4233i | −0.124145 | − | 0.106934i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 137.090i | − | 0.254342i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 145.531 | 0.269003 | 0.134501 | − | 0.990913i | \(-0.457057\pi\) | ||||
0.134501 | + | 0.990913i | \(0.457057\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −82.5320 | − | 236.208i | −0.151993 | − | 0.435006i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −736.481 | − | 129.861i | −1.35134 | − | 0.238278i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −372.320 | + | 312.413i | −0.680657 | + | 0.571139i | −0.916198 | − | 0.400725i | \(-0.868758\pi\) |
0.235541 | + | 0.971864i | \(0.424314\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 290.908 | − | 97.4448i | 0.529887 | − | 0.177495i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −266.919 | + | 47.0651i | −0.484427 | + | 0.0854176i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −210.776 | + | 76.7162i | −0.381150 | + | 0.138727i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −459.126 | + | 375.250i | −0.827254 | + | 0.676126i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.82805 | + | 1.63278i | 0.00507730 | + | 0.00293138i | 0.502537 | − | 0.864556i | \(-0.332400\pi\) |
−0.497459 | + | 0.867487i | \(0.665734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −406.948 | − | 704.855i | −0.727993 | − | 1.26092i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −314.398 | − | 186.976i | −0.560425 | − | 0.333291i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 427.292 | − | 509.227i | 0.758956 | − | 0.904489i | −0.238825 | − | 0.971063i | \(-0.576762\pi\) |
0.997781 | + | 0.0665739i | \(0.0212068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 730.527 | + | 265.890i | 1.29297 | + | 0.470602i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 656.649 | + | 33.9726i | 1.15811 | + | 0.0599164i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9713 | − | 71.3556i | 0.0456438 | − | 0.125405i | −0.914776 | − | 0.403960i | \(-0.867633\pi\) |
0.960420 | + | 0.278555i | \(0.0898555\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 225.287 | + | 189.038i | 0.394548 | + | 0.331065i | 0.818382 | − | 0.574675i | \(-0.194871\pi\) |
−0.423834 | + | 0.905740i | \(0.639316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −240.673 | + | 404.689i | −0.420023 | + | 0.706264i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −321.018 | + | 185.340i | −0.558292 | + | 0.322330i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −529.296 | + | 916.768i | −0.917325 | + | 1.58885i | −0.113864 | + | 0.993496i | \(0.536323\pi\) |
−0.803461 | + | 0.595357i | \(0.797011\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −78.7297 | − | 96.3274i | −0.135975 | − | 0.166369i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −48.8362 | − | 134.176i | −0.0840554 | − | 0.230940i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.2299 | − | 205.470i | −0.0621438 | − | 0.352435i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −535.331 | − | 108.728i | −0.915096 | − | 0.185859i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −89.2844 | − | 106.405i | −0.152103 | − | 0.181269i | 0.684612 | − | 0.728907i | \(-0.259971\pi\) |
−0.836715 | + | 0.547638i | \(0.815527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −101.545 | + | 575.888i | −0.172402 | + | 0.977738i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −596.609 | + | 208.457i | −1.00949 | + | 0.352720i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 145.309i | − | 0.245040i | −0.992466 | − | 0.122520i | \(-0.960902\pi\) | ||
0.992466 | − | 0.122520i | \(-0.0390975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −762.563 | −1.28162 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −343.672 | + | 398.986i | −0.575664 | + | 0.668318i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6235 | + | 3.98914i | 0.0377688 | + | 0.00665966i | 0.192501 | − | 0.981297i | \(-0.438340\pi\) |
−0.154732 | + | 0.987957i | \(0.549451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −710.406 | + | 596.102i | −1.18204 | + | 0.991849i | −0.182077 | + | 0.983284i | \(0.558282\pi\) |
−0.999963 | + | 0.00856516i | \(0.997274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 72.9155 | + | 1.88493i | 0.120921 | + | 0.00312592i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −339.605 | + | 59.8816i | −0.561331 | + | 0.0989779i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 492.373 | − | 179.209i | 0.811158 | − | 0.295237i | 0.0970557 | − | 0.995279i | \(-0.469057\pi\) |
0.714102 | + | 0.700042i | \(0.246835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −59.4517 | − | 364.663i | −0.0976219 | − | 0.598789i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 110.745 | + | 63.9384i | 0.181251 | + | 0.104646i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.0848 | − | 60.7687i | −0.0572346 | − | 0.0991333i | 0.835988 | − | 0.548747i | \(-0.184895\pi\) |
−0.893223 | + | 0.449614i | \(0.851562\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.00337 | + | 309.780i | −0.00650954 | + | 0.503707i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 427.172 | − | 509.083i | 0.692337 | − | 0.825095i | −0.299299 | − | 0.954159i | \(-0.596753\pi\) |
0.991636 | + | 0.129064i | \(0.0411974\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −912.210 | − | 332.017i | −1.47368 | − | 0.536377i | −0.524585 | − | 0.851358i | \(-0.675780\pi\) |
−0.949098 | + | 0.314981i | \(0.898002\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −677.048 | + | 217.100i | −1.09025 | + | 0.349597i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 78.5400 | − | 215.787i | 0.126067 | − | 0.346367i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −596.569 | − | 500.581i | −0.954510 | − | 0.800929i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −212.541 | − | 379.370i | −0.338981 | − | 0.605056i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 411.502 | − | 237.581i | 0.654216 | − | 0.377712i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −94.6588 | + | 163.954i | −0.150014 | + | 0.259832i | −0.931232 | − | 0.364426i | \(-0.881265\pi\) |
0.781218 | + | 0.624258i | \(0.214599\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 277.132 | − | 731.848i | 0.437808 | − | 1.15616i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −251.130 | − | 689.974i | −0.395480 | − | 1.08657i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.4872 | + | 161.559i | 0.0447209 | + | 0.253625i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −231.414 | − | 290.727i | −0.362150 | − | 0.454972i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −445.262 | − | 530.643i | −0.694637 | − | 0.827836i | 0.297271 | − | 0.954793i | \(-0.403923\pi\) |
−0.991908 | + | 0.126957i | \(0.959479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −184.867 | + | 1048.43i | −0.287506 | + | 1.63053i | 0.408687 | + | 0.912675i | \(0.365987\pi\) |
−0.696193 | + | 0.717854i | \(0.745124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −292.953 | + | 1544.44i | −0.454191 | + | 2.39448i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 352.755i | 0.545217i | 0.962125 | + | 0.272608i | \(0.0878863\pi\) | ||||
−0.962125 | + | 0.272608i | \(0.912114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 184.274 | 0.283935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −783.195 | − | 148.558i | −1.20306 | − | 0.228200i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 461.316 | + | 81.3425i | 0.706457 | + | 0.124567i | 0.515322 | − | 0.856996i | \(-0.327672\pi\) |
0.191135 | + | 0.981564i | \(0.438783\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.5679 | + | 18.9367i | −0.0344548 | + | 0.0289110i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 107.740 | + | 719.257i | 0.163988 | + | 1.09476i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 84.6349 | − | 14.9234i | 0.128429 | − | 0.0226455i | −0.109064 | − | 0.994035i | \(-0.534785\pi\) |
0.237493 | + | 0.971389i | \(0.423674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −115.687 | + | 42.1068i | −0.175019 | + | 0.0637016i | −0.428043 | − | 0.903758i | \(-0.640797\pi\) |
0.253024 | + | 0.967460i | \(0.418575\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 409.368 | + | 155.017i | 0.617447 | + | 0.233812i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −785.070 | − | 453.260i | −1.18056 | − | 0.681594i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 199.763 | + | 346.000i | 0.299495 | + | 0.518741i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1018.67 | − | 570.709i | 1.52268 | − | 0.853078i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 177.787 | − | 211.878i | 0.264958 | − | 0.315765i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 598.221 | + | 217.735i | 0.888887 | + | 0.323528i | 0.745791 | − | 0.666180i | \(-0.232072\pi\) |
0.143096 | + | 0.989709i | \(0.454294\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 232.832 | + | 300.394i | 0.344936 | + | 0.445029i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 56.5391 | − | 155.340i | 0.0835141 | − | 0.229453i | −0.890906 | − | 0.454188i | \(-0.849929\pi\) |
0.974420 | + | 0.224735i | \(0.0721516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1048.63 | + | 879.901i | 1.54437 | + | 1.29588i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1045.21 | + | 13.5075i | 1.53481 | + | 0.0198348i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1129.58 | − | 652.163i | 1.65385 | − | 0.954851i | 0.678383 | − | 0.734709i | \(-0.262681\pi\) |
0.975468 | − | 0.220142i | \(-0.0706522\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 690.092 | − | 1195.27i | 1.00743 | − | 1.74493i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1079.32 | − | 175.964i | 1.57107 | − | 0.256134i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 85.3928 | + | 234.615i | 0.123937 | + | 0.340515i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 62.8288 | + | 356.320i | 0.0909245 | + | 0.515658i | 0.995920 | + | 0.0902378i | \(0.0287627\pi\) |
−0.904996 | + | 0.425421i | \(0.860126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 520.857 | − | 283.028i | 0.751597 | − | 0.408410i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 143.711 | + | 171.268i | 0.206778 | + | 0.246428i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.1093 | − | 244.485i | 0.0618498 | − | 0.350767i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 431.125 | + | 371.356i | 0.616775 | + | 0.531267i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 893.344i | 1.27438i | 0.770705 | + | 0.637192i | \(0.219904\pi\) | ||||
−0.770705 | + | 0.637192i | \(0.780096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 564.863 | 0.803504 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −81.4675 | − | 233.162i | −0.115557 | − | 0.330726i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −558.228 | − | 98.4307i | −0.789573 | − | 0.139223i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −529.040 | + | 443.917i | −0.746178 | + | 0.626118i | −0.934489 | − | 0.355992i | \(-0.884143\pi\) |
0.188311 | + | 0.982109i | \(0.439699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −186.309 | − | 164.721i | −0.262038 | − | 0.231675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 848.896 | − | 149.683i | 1.19060 | − | 0.209935i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −462.776 | + | 168.437i | −0.647239 | + | 0.235576i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 711.025 | − | 581.130i | 0.991666 | − | 0.810502i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −417.508 | − | 241.049i | −0.580679 | − | 0.335255i | 0.180724 | − | 0.983534i | \(-0.442156\pi\) |
−0.761403 | + | 0.648279i | \(0.775489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 283.560 | + | 491.140i | 0.393287 | + | 0.681192i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 760.406 | + | 452.222i | 1.05174 | + | 0.625480i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 137.276 | − | 163.600i | 0.189347 | − | 0.225655i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 324.225 | + | 118.008i | 0.445977 | + | 0.162322i | 0.555239 | − | 0.831691i | \(-0.312627\pi\) |
−0.109263 | + | 0.994013i | \(0.534849\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 314.503 | + | 657.669i | 0.431418 | + | 0.902152i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 430.834 | − | 1183.71i | 0.589376 | − | 1.61930i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 413.108 | + | 346.639i | 0.563585 | + | 0.472904i | 0.879510 | − | 0.475880i | \(-0.157870\pi\) |
−0.315925 | + | 0.948784i | \(0.602315\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 161.959 | − | 272.333i | 0.220353 | − | 0.370521i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56.9482 | − | 32.8791i | 0.0772704 | − | 0.0446121i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 368.737 | − | 638.671i | 0.498968 | − | 0.864237i | −0.501032 | − | 0.865429i | \(-0.667046\pi\) |
0.999999 | + | 0.00119161i | \(0.000379300\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 329.309 | + | 402.917i | 0.444412 | + | 0.543747i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 356.128 | + | 978.454i | 0.479311 | + | 1.31690i | 0.910079 | + | 0.414434i | \(0.136020\pi\) |
−0.430768 | + | 0.902463i | \(0.641757\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −182.077 | − | 1032.61i | −0.244398 | − | 1.38605i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 104.858 | − | 118.601i | 0.140373 | − | 0.158770i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −633.619 | − | 755.118i | −0.845953 | − | 1.00817i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.8554 | + | 237.374i | −0.0557329 | + | 0.316077i | −0.999911 | − | 0.0133592i | \(-0.995748\pi\) |
0.944178 | + | 0.329436i | \(0.106859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −518.018 | + | 180.997i | −0.687939 | + | 0.240368i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 523.331i | 0.693154i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7615 | 0.0432781 | 0.0216391 | − | 0.999766i | \(-0.493112\pi\) | ||||
0.0216391 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −418.336 | + | 485.668i | −0.551168 | + | 0.639879i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 314.502 | + | 55.4551i | 0.413274 | + | 0.0728714i | 0.376420 | − | 0.926449i | \(-0.377155\pi\) |
0.0368545 | + | 0.999321i | \(0.488266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −743.936 | + | 624.236i | −0.975014 | + | 0.818134i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −403.664 | − | 742.863i | −0.527665 | − | 0.971063i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −217.164 | + | 38.2920i | −0.283135 | + | 0.0499243i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 447.488 | − | 162.872i | 0.581910 | − | 0.211798i | −0.0342578 | − | 0.999413i | \(-0.510907\pi\) |
0.616167 | + | 0.787615i | \(0.288685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −129.546 | − | 794.601i | −0.168023 | − | 1.03061i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1122.62 | + | 648.147i | 1.45229 | + | 0.838482i | 0.998611 | − | 0.0526817i | \(-0.0167769\pi\) |
0.453682 | + | 0.891164i | \(0.350110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −230.386 | − | 399.040i | −0.297272 | − | 0.514890i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.95035 | + | 769.955i | −0.0128061 | + | 0.990934i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 189.701 | − | 226.077i | 0.243519 | − | 0.290214i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −314.795 | − | 114.576i | −0.403066 | − | 0.146704i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 323.771 | − | 250.951i | 0.413501 | − | 0.320499i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −159.162 | + | 437.295i | −0.202754 | + | 0.557063i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −659.528 | − | 553.410i | −0.838028 | − | 0.703189i | 0.119091 | − | 0.992883i | \(-0.462002\pi\) |
−0.957119 | + | 0.289694i | \(0.906446\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −516.103 | − | 921.207i | −0.654123 | − | 1.16756i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 874.285 | − | 504.769i | 1.10529 | − | 0.638140i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −165.492 | + | 286.640i | −0.208690 | + | 0.361462i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 170.772 | − | 450.972i | 0.214807 | − | 0.567260i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −198.415 | − | 545.140i | −0.248952 | − | 0.683990i | −0.999725 | − | 0.0234300i | \(-0.992541\pi\) |
0.750774 | − | 0.660560i | \(-0.229681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.3678 | + | 194.909i | 0.0430135 | + | 0.243942i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 251.788 | − | 37.7161i | 0.314342 | − | 0.0470863i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 421.459 | + | 502.275i | 0.524855 | + | 0.625498i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −232.041 | + | 1315.97i | −0.288249 | + | 1.63474i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −91.8250 | + | 484.098i | −0.113786 | + | 0.599874i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 661.323i | − | 0.817457i | −0.912656 | − | 0.408729i | \(-0.865972\pi\) | ||
0.912656 | − | 0.408729i | \(-0.134028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 168.725 | 0.208045 | 0.104023 | − | 0.994575i | \(-0.466829\pi\) | ||||
0.104023 | + | 0.994575i | \(0.466829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 379.779 | + | 72.0374i | 0.467133 | + | 0.0886069i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1568.77 | − | 276.617i | −1.92487 | − | 0.339407i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1147.13 | − | 962.559i | 1.40408 | − | 1.17816i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −555.010 | + | 441.778i | −0.677668 | + | 0.539412i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 149.275 | − | 26.3213i | 0.181822 | − | 0.0320600i | −0.0819959 | − | 0.996633i | \(-0.526129\pi\) |
0.263817 | + | 0.964573i | \(0.415018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 211.263 | − | 76.8935i | 0.256699 | − | 0.0934307i | −0.210465 | − | 0.977601i | \(-0.567498\pi\) |
0.467164 | + | 0.884171i | \(0.345276\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 320.436 | + | 121.341i | 0.388407 | + | 0.147080i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −292.855 | − | 169.080i | −0.354117 | − | 0.204449i | 0.312380 | − | 0.949957i | \(-0.398874\pi\) |
−0.666497 | + | 0.745508i | \(0.732207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 401.806 | + | 695.949i | 0.484688 | + | 0.839504i | 0.999845 | − | 0.0175917i | \(-0.00559990\pi\) |
−0.515157 | + | 0.857096i | \(0.672267\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 393.157 | − | 220.265i | 0.473113 | − | 0.265060i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −163.206 | + | 194.502i | −0.195926 | + | 0.233495i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 931.633 | + | 339.087i | 1.11573 | + | 0.406092i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −269.865 | − | 841.601i | −0.322419 | − | 1.00550i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −292.066 | + | 802.443i | −0.348111 | + | 0.956428i | 0.634853 | + | 0.772633i | \(0.281061\pi\) |
−0.982965 | + | 0.183795i | \(0.941162\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 467.912 | + | 392.625i | 0.556376 | + | 0.466855i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1382.88 | + | 17.8714i | 1.64043 | + | 0.0211997i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −404.527 | + | 233.554i | −0.478731 | + | 0.276395i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −223.906 | + | 387.816i | −0.264351 | + | 0.457870i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −203.881 | + | 33.2391i | −0.240142 | + | 0.0391509i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −284.781 | − | 782.430i | −0.334643 | − | 0.919424i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −138.765 | − | 786.975i | −0.162679 | − | 0.922596i | −0.951426 | − | 0.307878i | \(-0.900381\pi\) |
0.788747 | − | 0.614718i | \(-0.210730\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.9729 | − | 1004.72i | 0.0303777 | − | 1.17511i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 998.416 | + | 1189.87i | 1.16501 | + | 1.38841i | 0.906397 | + | 0.422427i | \(0.138822\pi\) |
0.258616 | + | 0.965980i | \(0.416734\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.90592 | − | 27.8228i | 0.00571119 | − | 0.0323898i | −0.981819 | − | 0.189820i | \(-0.939210\pi\) |
0.987530 | + | 0.157430i | \(0.0503208\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 304.820 | + | 262.561i | 0.354030 | + | 0.304949i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 951.550i | − | 1.10261i | −0.834305 | − | 0.551304i | \(-0.814131\pi\) | ||
0.834305 | − | 0.551304i | \(-0.185869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1863.34 | −2.15415 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −62.5107 | − | 178.907i | −0.0721000 | − | 0.206352i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −220.793 | − | 38.9318i | −0.254077 | − | 0.0448006i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.2805 | + | 50.5813i | −0.0692084 | + | 0.0580727i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −302.079 | + | 1487.31i | −0.346024 | + | 1.70368i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −545.889 | + | 96.2549i | −0.623873 | + | 0.110006i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 214.431 | − | 78.0465i | 0.244505 | − | 0.0889926i | −0.216861 | − | 0.976203i | \(-0.569582\pi\) |
0.461366 | + | 0.887210i | \(0.347360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1186.44 | − | 969.692i | 1.34976 | − | 1.10318i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1343.36 | − | 775.592i | −1.52482 | − | 0.880354i | −0.999568 | − | 0.0294054i | \(-0.990639\pi\) |
−0.525250 | − | 0.850948i | \(-0.676028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 781.794 | + | 1354.11i | 0.885384 | + | 1.53353i | 0.845272 | + | 0.534336i | \(0.179438\pi\) |
0.0401121 | + | 0.999195i | \(0.487228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 366.064 | + | 217.702i | 0.413632 | + | 0.245991i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −451.340 | + | 537.886i | −0.508839 | + | 0.606411i | −0.957904 | − | 0.287088i | \(-0.907313\pi\) |
0.449065 | + | 0.893499i | \(0.351757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −895.993 | − | 326.115i | −1.00787 | − | 0.366833i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 551.433 | + | 357.580i | 0.618892 | + | 0.401324i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −80.4701 | + | 221.090i | −0.0901121 | + | 0.247581i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −140.446 | − | 117.848i | −0.156923 | − | 0.131674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 392.083 | − | 659.283i | 0.437104 | − | 0.734986i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −430.094 | + | 248.315i | −0.478413 | + | 0.276212i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −193.210 | + | 334.649i | −0.214439 | + | 0.371419i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1291.84 | + | 1580.59i | 1.43061 | + | 1.75038i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −178.318 | − | 489.924i | −0.197036 | − | 0.541353i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −280.357 | − | 1589.99i | −0.309104 | − | 1.75302i | −0.603528 | − | 0.797341i | \(-0.706239\pi\) |
0.294424 | − | 0.955675i | \(-0.404872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −199.611 | − | 595.911i | −0.219594 | − | 0.655568i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 394.005 | + | 469.556i | 0.432497 | + | 0.515430i | 0.937641 | − | 0.347605i | \(-0.113005\pi\) |
−0.505144 | + | 0.863035i | \(0.668561\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.7833 | − | 140.553i | 0.0271449 | − | 0.153946i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 603.491 | − | 210.862i | 0.659554 | − | 0.230450i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.2568i | 0.0417195i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −628.091 | −0.683451 | −0.341725 | − | 0.939800i | \(-0.611011\pi\) | ||||
−0.341725 | + | 0.939800i | \(0.611011\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 102.992 | − | 119.569i | 0.111827 | − | 0.129825i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 394.790 | + | 69.6122i | 0.427725 | + | 0.0754195i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −340.955 | + | 286.095i | −0.368600 | + | 0.309292i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −328.349 | + | 536.220i | −0.354206 | + | 0.578446i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1234.51 | − | 217.678i | 1.32886 | − | 0.234314i | 0.536260 | − | 0.844053i | \(-0.319837\pi\) |
0.792603 | + | 0.609738i | \(0.208726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −283.633 | + | 103.234i | −0.304654 | + | 0.110885i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 171.282 | + | 1050.61i | 0.183583 | + | 1.12605i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −660.093 | − | 381.105i | −0.705981 | − | 0.407599i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 460.132 | + | 796.972i | 0.491070 | + | 0.850557i | 0.999947 | − | 0.0102815i | \(-0.00327275\pi\) |
−0.508878 | + | 0.860839i | \(0.669939\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.52243 | + | 504.704i | −0.00694614 | + | 0.537491i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −439.314 | + | 523.554i | −0.466859 | + | 0.556381i | −0.947176 | − | 0.320714i | \(-0.896077\pi\) |
0.480317 | + | 0.877095i | \(0.340522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −408.794 | − | 148.789i | −0.433504 | − | 0.157783i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1369.06 | + | 53.1020i | 1.44874 | + | 0.0561926i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 287.907 | − | 791.018i | 0.304020 | − | 0.835288i | −0.689771 | − | 0.724027i | \(-0.742289\pi\) |
0.993791 | − | 0.111261i | \(-0.0354889\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −601.056 | − | 504.346i | −0.633357 | − | 0.531450i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 747.797 | + | 1334.76i | 0.786327 | + | 1.40354i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1277.52 | − | 737.576i | 1.34052 | − | 0.773952i | 0.353640 | − | 0.935382i | \(-0.384944\pi\) |
0.986884 | + | 0.161430i | \(0.0516105\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −490.553 | + | 849.662i | −0.513668 | + | 0.889698i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 130.784 | − | 345.373i | 0.136660 | − | 0.360891i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −613.000 | − | 1684.20i | −0.639207 | − | 1.75621i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.1872 | + | 108.816i | 0.0199659 | + | 0.113232i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 400.203 | − | 1016.97i | 0.415580 | − | 1.05605i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −166.629 | − | 198.581i | −0.172673 | − | 0.205783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.3919 | + | 319.814i | −0.0583163 | + | 0.330728i | −0.999983 | − | 0.00581841i | \(-0.998148\pi\) |
0.941667 | + | 0.336547i | \(0.109259\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −150.091 | + | 791.274i | −0.154892 | + | 0.816588i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1203.37i | 1.23931i | 0.784873 | + | 0.619657i | \(0.212728\pi\) | ||||
−0.784873 | + | 0.619657i | \(0.787272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 290.331 | 0.298387 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −402.844 | − | 76.4125i | −0.413174 | − | 0.0783718i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 186.452 | + | 32.8765i | 0.190841 | + | 0.0336505i | 0.268252 | − | 0.963349i | \(-0.413554\pi\) |
−0.0774104 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 175.829 | − | 147.538i | 0.179601 | − | 0.150703i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1001.91 | − | 394.277i | −1.02132 | − | 0.401913i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1245.48 | − | 219.613i | 1.26702 | − | 0.223411i | 0.500562 | − | 0.865701i | \(-0.333127\pi\) |
0.766462 | + | 0.642290i | \(0.222016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1237.44 | + | 450.391i | −1.25628 | + | 0.457250i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −299.946 | − | 113.582i | −0.303897 | − | 0.115078i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1911.64 | − | 1103.69i | −1.93291 | − | 1.11596i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −697.271 | − | 1207.71i | −0.703604 | − | 1.21868i | −0.967193 | − | 0.254043i | \(-0.918240\pi\) |
0.263589 | − | 0.964635i | \(-0.415094\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 888.140 | − | 497.578i | 0.894401 | − | 0.501085i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −705.307 | + | 840.552i | −0.708851 | + | 0.844776i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −947.882 | − | 345.001i | −0.950734 | − | 0.346039i | −0.180338 | − | 0.983605i | \(-0.557719\pi\) |
−0.770396 | + | 0.637566i | \(0.779941\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −755.332 | + | 397.884i | −0.756088 | + | 0.398282i |
(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 | 432.3.bc.a.401.5 | 30 | ||
4.3 | odd | 2 | 27.3.f.a.23.5 | yes | 30 | ||
12.11 | even | 2 | 81.3.f.a.17.1 | 30 | |||
27.20 | odd | 18 | inner | 432.3.bc.a.209.5 | 30 | ||
36.7 | odd | 6 | 243.3.f.d.215.1 | 30 | |||
36.11 | even | 6 | 243.3.f.a.215.5 | 30 | |||
36.23 | even | 6 | 243.3.f.b.134.1 | 30 | |||
36.31 | odd | 6 | 243.3.f.c.134.5 | 30 | |||
108.7 | odd | 18 | 81.3.f.a.62.1 | 30 | |||
108.11 | even | 18 | 243.3.f.d.26.1 | 30 | |||
108.43 | odd | 18 | 243.3.f.a.26.5 | 30 | |||
108.47 | even | 18 | 27.3.f.a.20.5 | ✓ | 30 | ||
108.67 | odd | 18 | 729.3.b.a.728.26 | 30 | |||
108.79 | odd | 18 | 243.3.f.b.107.1 | 30 | |||
108.83 | even | 18 | 243.3.f.c.107.5 | 30 | |||
108.95 | even | 18 | 729.3.b.a.728.5 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.20.5 | ✓ | 30 | 108.47 | even | 18 | ||
27.3.f.a.23.5 | yes | 30 | 4.3 | odd | 2 | ||
81.3.f.a.17.1 | 30 | 12.11 | even | 2 | |||
81.3.f.a.62.1 | 30 | 108.7 | odd | 18 | |||
243.3.f.a.26.5 | 30 | 108.43 | odd | 18 | |||
243.3.f.a.215.5 | 30 | 36.11 | even | 6 | |||
243.3.f.b.107.1 | 30 | 108.79 | odd | 18 | |||
243.3.f.b.134.1 | 30 | 36.23 | even | 6 | |||
243.3.f.c.107.5 | 30 | 108.83 | even | 18 | |||
243.3.f.c.134.5 | 30 | 36.31 | odd | 6 | |||
243.3.f.d.26.1 | 30 | 108.11 | even | 18 | |||
243.3.f.d.215.1 | 30 | 36.7 | odd | 6 | |||
432.3.bc.a.209.5 | 30 | 27.20 | odd | 18 | inner | ||
432.3.bc.a.401.5 | 30 | 1.1 | even | 1 | trivial | ||
729.3.b.a.728.5 | 30 | 108.95 | even | 18 | |||
729.3.b.a.728.26 | 30 | 108.67 | odd | 18 |