Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,3,Mod(29,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 17]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.bc (of order \(18\), degree \(6\), 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: | \(10.3542500457\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.3 | ||
Character | \(\chi\) | \(=\) | 380.29 |
Dual form | 380.3.bc.a.249.3 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.70131 | + | 3.10577i | −1.23377 | + | 1.03526i | −0.235786 | + | 0.971805i | \(0.575766\pi\) |
−0.997985 | + | 0.0634514i | \(0.979789\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.40108 | + | 2.37286i | −0.880217 | + | 0.474572i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.39353 | − | 3.11396i | −0.770505 | − | 0.444851i | 0.0625499 | − | 0.998042i | \(-0.480077\pi\) |
−0.833055 | + | 0.553191i | \(0.813410\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.49107 | − | 14.1276i | 0.276786 | − | 1.56973i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.50250 | − | 9.53061i | −0.500227 | − | 0.866419i | −1.00000 | 0.000262521i | \(-0.999916\pi\) | |
0.499773 | − | 0.866157i | \(-0.333417\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.18533 | + | 1.83371i | 0.168102 | + | 0.141055i | 0.722958 | − | 0.690892i | \(-0.242782\pi\) |
−0.554856 | + | 0.831947i | \(0.687226\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.92023 | − | 22.4514i | 0.594682 | − | 1.49676i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −10.0440 | + | 1.77103i | −0.590824 | + | 0.104178i | −0.461064 | − | 0.887367i | \(-0.652532\pi\) |
−0.129761 | + | 0.991545i | \(0.541421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.50913 | + | 17.8502i | 0.342586 | + | 0.939487i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 29.6344 | − | 5.22534i | 1.41116 | − | 0.248826i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 11.1915 | + | 30.7484i | 0.486588 | + | 1.33689i | 0.903751 | + | 0.428058i | \(0.140802\pi\) |
−0.417164 | + | 0.908831i | \(0.636976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.7391 | − | 20.8863i | 0.549563 | − | 0.835452i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.9140 | + | 22.3677i | 0.478297 | + | 0.828434i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 35.2028 | + | 6.20721i | 1.21389 | + | 0.214042i | 0.743694 | − | 0.668520i | \(-0.233072\pi\) |
0.470197 | + | 0.882562i | \(0.344183\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −32.0389 | − | 18.4977i | −1.03351 | − | 0.596699i | −0.115524 | − | 0.993305i | \(-0.536855\pi\) |
−0.917989 | + | 0.396605i | \(0.870188\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 49.9664 | + | 18.1863i | 1.51413 | + | 0.551099i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 31.1264 | + | 0.906694i | 0.889325 | + | 0.0259056i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.2462 | 0.520166 | 0.260083 | − | 0.965586i | \(-0.416250\pi\) | ||||
0.260083 | + | 0.965586i | \(0.416250\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.7837 | −0.353427 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.3488 | + | 24.2508i | 0.496313 | + | 0.591483i | 0.954811 | − | 0.297212i | \(-0.0960569\pi\) |
−0.458498 | + | 0.888695i | \(0.651613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.3688 | − | 44.9730i | 0.380671 | − | 1.04588i | −0.590404 | − | 0.807108i | \(-0.701031\pi\) |
0.971075 | − | 0.238777i | \(-0.0767463\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 22.5593 | + | 68.0876i | 0.501318 | + | 1.51306i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −73.4155 | − | 12.9451i | −1.56203 | − | 0.275428i | −0.675241 | − | 0.737598i | \(-0.735960\pi\) |
−0.886792 | + | 0.462169i | \(0.847071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.10654 | − | 8.84478i | −0.104215 | − | 0.180506i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 31.6756 | − | 37.7495i | 0.621090 | − | 0.740187i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 68.3938 | − | 24.8933i | 1.29045 | − | 0.469685i | 0.396574 | − | 0.918003i | \(-0.370199\pi\) |
0.893874 | + | 0.448318i | \(0.147977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.8318 | + | 28.8884i | 0.851487 | + | 0.525243i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −79.5311 | − | 45.8535i | −1.39528 | − | 0.804447i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.75422 | + | 0.309316i | −0.0297325 | + | 0.00524264i | −0.188495 | − | 0.982074i | \(-0.560361\pi\) |
0.158762 | + | 0.987317i | \(0.449250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 99.4120 | − | 36.1830i | 1.62971 | − | 0.593164i | 0.644509 | − | 0.764596i | \(-0.277062\pi\) |
0.985196 | + | 0.171432i | \(0.0548395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −57.4283 | + | 68.4404i | −0.911561 | + | 1.08636i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.9690 | − | 2.88483i | −0.214907 | − | 0.0443820i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.73000 | + | 15.4826i | −0.0407463 | + | 0.231084i | −0.998379 | − | 0.0569071i | \(-0.981876\pi\) |
0.957633 | + | 0.287991i | \(0.0929872\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −136.921 | − | 79.0513i | −1.98436 | − | 1.14567i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.4037 | − | 80.7861i | 0.414137 | − | 1.13783i | −0.540833 | − | 0.841130i | \(-0.681891\pi\) |
0.954970 | − | 0.296702i | \(-0.0958869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.964646 | + | 1.14962i | 0.0132143 | + | 0.0157482i | 0.772611 | − | 0.634880i | \(-0.218950\pi\) |
−0.759397 | + | 0.650628i | \(0.774506\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.0154 | + | 119.977i | 0.186872 | + | 1.59970i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 68.5382i | 0.890107i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.0023 | + | 27.4131i | 0.291168 | + | 0.347001i | 0.891722 | − | 0.452584i | \(-0.149498\pi\) |
−0.600554 | + | 0.799584i | \(0.705053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.05556 | + | 1.47610i | 0.0500687 | + | 0.0182235i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −96.0430 | − | 55.4504i | −1.15714 | − | 0.668077i | −0.206526 | − | 0.978441i | \(-0.566216\pi\) |
−0.950618 | + | 0.310364i | \(0.899549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40.0021 | − | 31.6275i | 0.470613 | − | 0.372088i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −149.575 | + | 86.3571i | −1.71925 | + | 0.992610i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.32264 | + | 11.1103i | −0.104749 | + | 0.124835i | −0.815872 | − | 0.578233i | \(-0.803742\pi\) |
0.711123 | + | 0.703068i | \(0.248187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.07655 | − | 16.6952i | −0.0667753 | − | 0.183464i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 176.036 | − | 31.0398i | 1.89286 | − | 0.333762i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −71.0033 | − | 63.1152i | −0.747404 | − | 0.664370i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.0891 | − | 96.9169i | −0.176176 | − | 0.999143i | −0.936778 | − | 0.349925i | \(-0.886207\pi\) |
0.760602 | − | 0.649218i | \(-0.224904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −148.352 | + | 53.9955i | −1.49850 | + | 0.545410i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6708 | − | 8.95385i | −0.105651 | − | 0.0886520i | 0.588432 | − | 0.808547i | \(-0.299746\pi\) |
−0.694083 | + | 0.719895i | \(0.744190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.5158 | − | 35.5344i | −0.199182 | − | 0.344994i | 0.749081 | − | 0.662478i | \(-0.230495\pi\) |
−0.948264 | + | 0.317484i | \(0.897162\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −118.024 | + | 93.3154i | −1.12404 | + | 0.888718i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 22.8431 | − | 39.5654i | 0.213487 | − | 0.369770i | −0.739317 | − | 0.673358i | \(-0.764851\pi\) |
0.952803 | + | 0.303588i | \(0.0981846\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 28.7117 | − | 78.8848i | 0.263410 | − | 0.723714i | −0.735521 | − | 0.677501i | \(-0.763063\pi\) |
0.998932 | − | 0.0462122i | \(-0.0147150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −71.2360 | + | 59.7741i | −0.641766 | + | 0.538506i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −100.441 | −0.888859 | −0.444430 | − | 0.895814i | \(-0.646594\pi\) | ||||
−0.444430 | + | 0.895814i | \(0.646594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −122.217 | − | 108.771i | −1.06275 | − | 0.945831i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31.3497 | − | 26.3055i | 0.267946 | − | 0.224833i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 59.6876 | + | 21.7245i | 0.501577 | + | 0.182559i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0550269 | + | 0.0953094i | −0.000454768 | + | 0.000787681i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −150.635 | − | 26.5610i | −1.22467 | − | 0.215943i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9066 | + | 124.523i | −0.0872526 | + | 0.996186i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −97.0632 | − | 81.4457i | −0.764277 | − | 0.641304i | 0.174960 | − | 0.984576i | \(-0.444021\pi\) |
−0.939236 | + | 0.343271i | \(0.888465\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 79.0897 | + | 217.297i | 0.613098 | + | 1.68447i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44.6821 | + | 253.405i | 0.341085 | + | 1.93439i | 0.355964 | + | 0.934500i | \(0.384153\pi\) |
−0.0148787 | + | 0.999889i | \(0.504736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4777 | − | 116.545i | 0.153968 | − | 0.876278i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −109.911 | − | 67.7991i | −0.814157 | − | 0.502216i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 36.1609 | + | 99.3513i | 0.263948 | + | 0.725192i | 0.998892 | + | 0.0470637i | \(0.0149864\pi\) |
−0.734944 | + | 0.678128i | \(0.762791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 177.969 | + | 149.334i | 1.28035 | + | 1.07434i | 0.993195 | + | 0.116460i | \(0.0371546\pi\) |
0.287157 | + | 0.957884i | \(0.407290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 311.938 | − | 180.098i | 2.21233 | − | 1.27729i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.45159 | − | 30.9175i | 0.0381230 | − | 0.216206i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −169.660 | + | 56.2129i | −1.17007 | + | 0.387675i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 46.3707 | + | 16.8776i | 0.315447 | + | 0.114813i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −99.6722 | + | 83.6349i | −0.668941 | + | 0.561308i | −0.912752 | − | 0.408515i | \(-0.866047\pi\) |
0.243811 | + | 0.969823i | \(0.421602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 83.6396i | − | 0.553905i | −0.960884 | − | 0.276952i | \(-0.910676\pi\) | ||
0.960884 | − | 0.276952i | \(-0.0893244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 146.309i | 0.956270i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 184.898 | + | 5.38599i | 1.19289 | + | 0.0347483i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 48.8046 | − | 134.090i | 0.310857 | − | 0.854074i | −0.681627 | − | 0.731700i | \(-0.738727\pi\) |
0.992484 | − | 0.122374i | \(-0.0390506\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −175.834 | + | 304.553i | −1.10587 | + | 1.91543i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 35.3875 | − | 200.693i | 0.219798 | − | 1.24654i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 121.449 | − | 70.1187i | 0.745087 | − | 0.430176i | −0.0788290 | − | 0.996888i | \(-0.525118\pi\) |
0.823916 | + | 0.566712i | \(0.191785\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −263.060 | + | 38.5238i | −1.59430 | + | 0.233478i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 272.922 | − | 99.3354i | 1.63426 | − | 0.594823i | 0.648240 | − | 0.761436i | \(-0.275505\pi\) |
0.986022 | + | 0.166613i | \(0.0532832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27.9334 | − | 158.418i | −0.165286 | − | 0.937385i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 268.395 | − | 47.4919i | 1.56956 | − | 0.277731i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.5180 | − | 76.6642i | −0.0781385 | − | 0.443146i | −0.998627 | − | 0.0523768i | \(-0.983320\pi\) |
0.920489 | − | 0.390769i | \(-0.127791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −139.141 | + | 69.8681i | −0.795093 | + | 0.399246i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.53224 | − | 6.59307i | 0.0312556 | − | 0.0372490i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −117.256 | + | 67.6978i | −0.655061 | + | 0.378200i | −0.790393 | − | 0.612601i | \(-0.790123\pi\) |
0.135331 | + | 0.990800i | \(0.456790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −338.236 | − | 59.6401i | −1.86871 | − | 0.329503i | −0.879485 | − | 0.475927i | \(-0.842113\pi\) |
−0.989222 | + | 0.146424i | \(0.953224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −255.579 | + | 442.675i | −1.39661 | + | 2.41899i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −84.7039 | + | 45.6684i | −0.457859 | + | 0.246856i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.1462 | + | 85.9805i | 0.385808 | + | 0.459789i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 160.855i | − | 0.851083i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 149.468 | 0.782558 | 0.391279 | − | 0.920272i | \(-0.372033\pi\) | ||||
0.391279 | + | 0.920272i | \(0.372033\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 71.4194 | − | 59.9280i | 0.370049 | − | 0.310508i | −0.438732 | − | 0.898618i | \(-0.644572\pi\) |
0.808781 | + | 0.588110i | \(0.200128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 60.6631 | − | 32.7067i | 0.311093 | − | 0.167727i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 136.779 | + | 78.9693i | 0.694309 | + | 0.400859i | 0.805224 | − | 0.592970i | \(-0.202045\pi\) |
−0.110915 | + | 0.993830i | \(0.535378\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2690 | − | 86.5949i | 0.0767288 | − | 0.435150i | −0.922108 | − | 0.386932i | \(-0.873535\pi\) |
0.998837 | − | 0.0482180i | \(-0.0153542\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.9808 | − | 65.7847i | −0.188959 | − | 0.327287i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −170.539 | − | 143.099i | −0.840092 | − | 0.704921i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −147.101 | − | 58.4449i | −0.717564 | − | 0.285097i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 462.280 | − | 81.5124i | 2.23324 | − | 0.393780i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 134.307 | − | 160.257i | 0.642618 | − | 0.766780i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 312.360 | − | 55.0775i | 1.48038 | − | 0.261031i | 0.625649 | − | 0.780105i | \(-0.284834\pi\) |
0.854729 | + | 0.519074i | \(0.173723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 142.071 | + | 390.336i | 0.666998 | + | 1.83256i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 34.6740 | + | 236.771i | 0.161275 | + | 1.10126i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 115.202 | + | 199.536i | 0.530885 | + | 0.919519i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.14091 | − | 1.25914i | −0.0326069 | − | 0.00574948i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.1970 | − | 14.5475i | −0.114014 | − | 0.0658258i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −310.807 | − | 113.124i | −1.39375 | − | 0.507284i | −0.467435 | − | 0.884028i | \(-0.654822\pi\) |
−0.926318 | + | 0.376743i | \(0.877044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −260.848 | − | 246.129i | −1.15932 | − | 1.09391i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.57972 | 0.0245803 | 0.0122901 | − | 0.999924i | \(-0.496088\pi\) | ||||
0.0122901 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −244.828 | −1.06912 | −0.534559 | − | 0.845131i | \(-0.679522\pi\) | ||||
−0.534559 | + | 0.845131i | \(0.679522\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −212.864 | − | 253.681i | −0.921489 | − | 1.09819i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.3000 | − | 50.2789i | 0.0785408 | − | 0.215789i | −0.894208 | − | 0.447653i | \(-0.852260\pi\) |
0.972748 | + | 0.231864i | \(0.0744823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 353.825 | − | 117.232i | 1.50564 | − | 0.498860i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −170.277 | − | 30.0245i | −0.718470 | − | 0.126686i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −187.445 | − | 324.665i | −0.784290 | − | 1.35843i | −0.929422 | − | 0.369018i | \(-0.879694\pi\) |
0.145132 | − | 0.989412i | \(-0.453639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 112.767 | − | 134.391i | 0.467914 | − | 0.557639i | −0.479544 | − | 0.877518i | \(-0.659198\pi\) |
0.947458 | + | 0.319879i | \(0.103642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −238.029 | + | 86.6355i | −0.979543 | + | 0.356525i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 43.4617 | + | 26.8095i | 0.177395 | + | 0.109427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.5076 | + | 50.9445i | −0.0749294 | + | 0.206253i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 527.701 | − | 93.0480i | 2.11928 | − | 0.373687i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 290.782 | − | 105.836i | 1.15849 | − | 0.421657i | 0.309935 | − | 0.950758i | \(-0.399693\pi\) |
0.848559 | + | 0.529100i | \(0.177471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 231.470 | − | 275.855i | 0.914902 | − | 1.09034i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −49.8327 | + | 241.301i | −0.195422 | + | 0.946277i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −78.4041 | + | 444.652i | −0.305075 | + | 1.73016i | 0.318079 | + | 0.948064i | \(0.396962\pi\) |
−0.623154 | + | 0.782099i | \(0.714149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −103.805 | − | 59.9317i | −0.400791 | − | 0.231397i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 175.386 | − | 481.868i | 0.671976 | − | 1.84624i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.9739 | + | 38.1050i | 0.121574 | + | 0.144886i | 0.823398 | − | 0.567464i | \(-0.192075\pi\) |
−0.701824 | + | 0.712350i | \(0.747631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −241.938 | + | 271.846i | −0.912975 | + | 1.02584i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 70.0766i | − | 0.262459i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −121.517 | − | 144.819i | −0.451737 | − | 0.538359i | 0.491325 | − | 0.870976i | \(-0.336513\pi\) |
−0.943062 | + | 0.332617i | \(0.892068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −161.727 | − | 58.8637i | −0.596778 | − | 0.217209i | 0.0259301 | − | 0.999664i | \(-0.491745\pi\) |
−0.622708 | + | 0.782454i | \(0.713968\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 74.3426 | + | 42.9217i | 0.272317 | + | 0.157223i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −274.659 | − | 16.0149i | −0.998758 | − | 0.0582360i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 309.467 | − | 178.671i | 1.11721 | − | 0.645021i | 0.176523 | − | 0.984297i | \(-0.443515\pi\) |
0.940687 | + | 0.339275i | \(0.110182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −341.139 | + | 406.553i | −1.22272 | + | 1.45718i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 155.851 | + | 428.198i | 0.554631 | + | 1.52384i | 0.827318 | + | 0.561734i | \(0.189866\pi\) |
−0.272686 | + | 0.962103i | \(0.587912\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 353.971 | − | 62.4146i | 1.25078 | − | 0.220546i | 0.491250 | − | 0.871018i | \(-0.336540\pi\) |
0.759530 | + | 0.650472i | \(0.225429\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 458.827 | + | 13.0890i | 1.60992 | + | 0.0459262i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.2362 | − | 194.163i | −0.119290 | − | 0.676526i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −173.826 | + | 63.2673i | −0.601473 | + | 0.218918i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 364.253 | + | 305.645i | 1.25173 | + | 1.05033i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 69.1119 | + | 119.705i | 0.235877 | + | 0.408551i | 0.959527 | − | 0.281616i | \(-0.0908705\pi\) |
−0.723650 | + | 0.690167i | \(0.757537\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.98650 | − | 5.52384i | 0.0236830 | − | 0.0187249i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 142.119 | − | 246.157i | 0.478514 | − | 0.828811i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.9265 | + | 87.7175i | −0.106778 | + | 0.293369i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −228.330 | + | 191.592i | −0.758572 | + | 0.636517i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 67.3045 | 0.222127 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −351.663 | + | 395.135i | −1.15299 | + | 1.29553i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 161.450 | − | 135.473i | 0.525895 | − | 0.441279i | −0.340786 | − | 0.940141i | \(-0.610693\pi\) |
0.866681 | + | 0.498862i | \(0.166249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 186.297 | + | 67.8065i | 0.602903 | + | 0.219439i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 265.110 | − | 459.184i | 0.852444 | − | 1.47648i | −0.0265526 | − | 0.999647i | \(-0.508453\pi\) |
0.878996 | − | 0.476828i | \(-0.158214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 411.512 | + | 72.5606i | 1.31473 | + | 0.231823i | 0.786666 | − | 0.617379i | \(-0.211806\pi\) |
0.528068 | + | 0.849202i | \(0.322917\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 90.3474 | − | 437.482i | 0.286817 | − | 1.38883i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 102.814 | + | 86.2708i | 0.324333 | + | 0.272148i | 0.790386 | − | 0.612609i | \(-0.209880\pi\) |
−0.466053 | + | 0.884757i | \(0.654324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −134.545 | − | 369.660i | −0.421772 | − | 1.15881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.3316 | + | 217.389i | 0.119413 | + | 0.677225i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −96.9911 | − | 167.760i | −0.300282 | − | 0.519381i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 68.3238 | − | 20.4500i | 0.210227 | − | 0.0629230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 138.727 | + | 381.149i | 0.424241 | + | 1.16559i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 355.658 | + | 298.433i | 1.08103 | + | 0.907091i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −77.0531 | + | 44.4866i | −0.232789 | + | 0.134401i | −0.611858 | − | 0.790968i | \(-0.709578\pi\) |
0.379069 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 47.9436 | − | 271.901i | 0.143975 | − | 0.816521i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.7231 | − | 74.6182i | −0.0738002 | − | 0.222741i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −239.236 | − | 87.0749i | −0.709900 | − | 0.258383i | −0.0382682 | − | 0.999268i | \(-0.512184\pi\) |
−0.671632 | + | 0.740885i | \(0.734406\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 371.764 | − | 311.947i | 1.09665 | − | 0.920197i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 407.134i | 1.19394i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 368.774i | 1.07514i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 790.178 | + | 23.0175i | 2.29037 | + | 0.0667173i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −101.149 | + | 277.905i | −0.291496 | + | 0.800879i | 0.704352 | + | 0.709851i | \(0.251238\pi\) |
−0.995848 | + | 0.0910283i | \(0.970985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −65.4118 | + | 113.297i | −0.187426 | + | 0.324632i | −0.944391 | − | 0.328823i | \(-0.893348\pi\) |
0.756965 | + | 0.653455i | \(0.226681\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.7945 | + | 72.5614i | −0.0364517 | + | 0.206728i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 197.288 | − | 113.904i | 0.558888 | − | 0.322674i | −0.193811 | − | 0.981039i | \(-0.562085\pi\) |
0.752699 | + | 0.658365i | \(0.228751\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 62.2857 | + | 425.317i | 0.175453 | + | 1.19808i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −288.394 | + | 104.967i | −0.807826 | + | 0.294025i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 46.7510 | + | 265.138i | 0.130226 | + | 0.738547i | 0.978066 | + | 0.208295i | \(0.0667914\pi\) |
−0.847840 | + | 0.530252i | \(0.822097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −276.262 | + | 232.379i | −0.765270 | + | 0.643709i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0923373 | − | 0.523671i | −0.000254373 | − | 0.00144262i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.97338 | − | 2.77061i | −0.0191051 | − | 0.00759070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −131.716 | + | 156.973i | −0.358899 | + | 0.427719i | −0.915036 | − | 0.403371i | \(-0.867838\pi\) |
0.556138 | + | 0.831090i | \(0.312283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 393.295 | − | 227.069i | 1.06584 | − | 0.615364i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −446.401 | − | 78.7125i | −1.20324 | − | 0.212163i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 144.014 | − | 249.440i | 0.386098 | − | 0.668741i | −0.605823 | − | 0.795599i | \(-0.707156\pi\) |
0.991921 | + | 0.126859i | \(0.0404895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −346.372 | − | 494.773i | −0.923659 | − | 1.31939i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 65.5476 | + | 78.1166i | 0.173866 | + | 0.207206i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 374.063i | 0.986975i | 0.869753 | + | 0.493487i | \(0.164278\pi\) | ||||
−0.869753 | + | 0.493487i | \(0.835722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 612.212 | 1.60686 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.66590 | − | 3.91515i | 0.0121825 | − | 0.0102223i | −0.636676 | − | 0.771131i | \(-0.719691\pi\) |
0.648859 | + | 0.760909i | \(0.275247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −162.632 | − | 301.642i | −0.422420 | − | 0.783487i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −594.584 | − | 343.283i | −1.53639 | − | 0.887037i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.4427 | − | 172.649i | 0.0782589 | − | 0.443828i | −0.920350 | − | 0.391096i | \(-0.872096\pi\) |
0.998609 | − | 0.0527320i | \(-0.0167929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −166.864 | − | 289.017i | −0.426763 | − | 0.739174i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −952.400 | − | 799.158i | −2.42341 | − | 2.03348i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −166.282 | − | 66.0660i | −0.420968 | − | 0.167256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.0745 | + | 4.06865i | −0.0581221 | + | 0.0102485i | −0.202634 | − | 0.979255i | \(-0.564950\pi\) |
0.144511 | + | 0.989503i | \(0.453839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 286.168 | + | 494.969i | 0.717212 | + | 1.24052i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −673.256 | + | 118.713i | −1.67894 | + | 0.296043i | −0.930264 | − | 0.366890i | \(-0.880423\pi\) |
−0.748679 | + | 0.662933i | \(0.769311\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.0962 | − | 99.1736i | −0.0895688 | − | 0.246088i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.3515 | + | 3.12682i | −0.0527197 | + | 0.00772055i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −105.902 | − | 183.428i | −0.260201 | − | 0.450682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −152.896 | − | 26.9598i | −0.373830 | − | 0.0659163i | −0.0164231 | − | 0.999865i | \(-0.505228\pi\) |
−0.357407 | + | 0.933949i | \(0.616339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −442.405 | − | 255.423i | −1.07641 | − | 0.621466i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.4246 | + | 3.79425i | 0.0252412 | + | 0.00918706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 554.269 | + | 16.1456i | 1.33559 | + | 0.0389050i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1122.51 | −2.69188 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −660.535 | −1.57646 | −0.788228 | − | 0.615384i | \(-0.789001\pi\) | ||||
−0.788228 | + | 0.615384i | \(0.789001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −416.428 | − | 496.280i | −0.989141 | − | 1.17881i | −0.983881 | − | 0.178826i | \(-0.942770\pi\) |
−0.00525979 | − | 0.999986i | \(-0.501674\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −365.767 | + | 1004.94i | −0.864697 | + | 2.37573i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −101.005 | + | 234.115i | −0.237659 | + | 0.550858i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −648.854 | − | 114.411i | −1.51957 | − | 0.267940i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 75.8446 | + | 131.367i | 0.176794 | + | 0.306216i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −136.428 | + | 162.589i | −0.316539 | + | 0.377236i | −0.900730 | − | 0.434380i | \(-0.856967\pi\) |
0.584191 | + | 0.811616i | \(0.301412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 465.015 | − | 169.252i | 1.07394 | − | 0.390881i | 0.256290 | − | 0.966600i | \(-0.417500\pi\) |
0.817648 | + | 0.575718i | \(0.195278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 453.378 | − | 734.985i | 1.04225 | − | 1.68962i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −476.020 | + | 399.917i | −1.08929 | + | 0.915142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −183.802 | + | 32.4092i | −0.418683 | + | 0.0738251i | −0.379021 | − | 0.925388i | \(-0.623739\pi\) |
−0.0396619 | + | 0.999213i | \(0.512628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −137.676 | + | 50.1100i | −0.312191 | + | 0.113628i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −69.7156 | + | 83.0838i | −0.157371 | + | 0.187548i | −0.838969 | − | 0.544179i | \(-0.816841\pi\) |
0.681597 | + | 0.731727i | \(0.261286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.6666 | − | 71.0186i | 0.0329586 | − | 0.159592i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 109.167 | − | 619.118i | 0.244222 | − | 1.38505i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.26444 | − | 3.61678i | −0.0139520 | − | 0.00805518i | 0.493008 | − | 0.870025i | \(-0.335897\pi\) |
−0.506960 | + | 0.861970i | \(0.669231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 119.155 | − | 327.377i | 0.264203 | − | 0.725891i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 259.765 | + | 309.576i | 0.573433 | + | 0.683391i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 66.3588 | + | 59.0581i | 0.145843 | + | 0.129798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 212.758i | − | 0.465554i | −0.972530 | − | 0.232777i | \(-0.925219\pi\) | ||
0.972530 | − | 0.232777i | \(-0.0747812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −169.322 | − | 201.791i | −0.368894 | − | 0.439631i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 170.351 | + | 62.0025i | 0.369524 | + | 0.134496i | 0.520106 | − | 0.854102i | \(-0.325892\pi\) |
−0.150582 | + | 0.988598i | \(0.548115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −389.839 | − | 225.074i | −0.841986 | − | 0.486121i | 0.0159531 | − | 0.999873i | \(-0.494922\pi\) |
−0.857939 | + | 0.513752i | \(0.828255\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −701.094 | + | 554.316i | −1.50773 | + | 1.19208i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −599.198 | + | 345.947i | −1.28308 | + | 0.740786i | −0.977410 | − | 0.211351i | \(-0.932214\pi\) |
−0.305670 | + | 0.952138i | \(0.598880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 62.9365 | − | 75.0048i | 0.134193 | − | 0.159925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 235.810 | + | 647.883i | 0.500659 | + | 1.37555i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −518.690 | + | 91.4591i | −1.09660 | + | 0.193360i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 462.255 | + | 109.294i | 0.973169 | + | 0.230093i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −181.308 | − | 1028.25i | −0.380101 | − | 2.15566i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 639.439 | − | 232.737i | 1.33495 | − | 0.485880i | 0.426728 | − | 0.904380i | \(-0.359666\pi\) |
0.908217 | + | 0.418500i | \(0.137444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.0592 | + | 35.2918i | 0.0874411 | + | 0.0733718i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 492.325 | + | 852.732i | 1.01931 | + | 1.76549i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 305.180 | + | 385.989i | 0.629238 | + | 0.795854i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 418.424 | − | 724.731i | 0.859186 | − | 1.48815i | −0.0135198 | − | 0.999909i | \(-0.504304\pi\) |
0.872706 | − | 0.488246i | \(-0.162363\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −231.749 | + | 636.724i | −0.473924 | + | 1.30209i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −245.424 | + | 205.935i | −0.499845 | + | 0.419420i | −0.857539 | − | 0.514419i | \(-0.828008\pi\) |
0.357694 | + | 0.933839i | \(0.383563\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −364.571 | −0.739495 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 524.784 | − | 589.656i | 1.06017 | − | 1.19122i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −410.154 | + | 344.160i | −0.825260 | + | 0.692476i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6903 | + | 9.35050i | 0.0514835 | + | 0.0187385i | 0.367634 | − | 0.929971i | \(-0.380168\pi\) |
−0.316150 | + | 0.948709i | \(0.602390\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −701.656 | + | 1215.30i | −1.40051 | + | 2.42576i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 520.504 | + | 91.7789i | 1.03480 | + | 0.182463i | 0.665151 | − | 0.746709i | \(-0.268367\pi\) |
0.369648 | + | 0.929172i | \(0.379478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 68.2093 | + | 14.0864i | 0.135068 | + | 0.0278938i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 595.400 | + | 499.600i | 1.17436 | + | 0.985404i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −302.530 | − | 831.194i | −0.594361 | − | 1.63299i | −0.762320 | − | 0.647200i | \(-0.775940\pi\) |
0.167959 | − | 0.985794i | \(-0.446282\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.62298 | − | 9.20438i | −0.00317609 | − | 0.0180125i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −315.210 | + | 376.113i | −0.614445 | + | 0.733163i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 174.610 | + | 107.709i | 0.339048 | + | 0.209143i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 280.594 | + | 770.925i | 0.542735 | + | 1.49115i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 288.135 | + | 241.774i | 0.555174 | + | 0.465847i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 624.692 | − | 360.666i | 1.19903 | − | 0.692257i | 0.238687 | − | 0.971097i | \(-0.423283\pi\) |
0.960338 | + | 0.278839i | \(0.0899496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 168.483 | − | 955.513i | 0.322147 | − | 1.82698i | −0.206865 | − | 0.978370i | \(-0.566326\pi\) |
0.529011 | − | 0.848615i | \(-0.322563\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 298.011 | − | 690.744i | 0.567640 | − | 1.31570i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 354.559 | + | 129.049i | 0.672788 | + | 0.244875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −414.979 | + | 348.209i | −0.784460 | + | 0.658240i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.5534i | 0.0481231i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 90.3098i | 0.169437i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.65125 | + | 228.334i | −0.0124322 | + | 0.426793i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 223.747 | − | 614.741i | 0.416662 | − | 1.14477i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −56.1974 | + | 97.3368i | −0.104262 | + | 0.180588i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −138.020 | + | 782.748i | −0.255119 | + | 1.44685i | 0.540647 | + | 0.841250i | \(0.318180\pi\) |
−0.795766 | + | 0.605604i | \(0.792932\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1437.15 | − | 829.736i | 2.64668 | − | 1.52806i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 60.8198 | + | 415.307i | 0.111596 | + | 0.762032i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −552.475 | + | 201.084i | −1.01001 | + | 0.367613i | −0.793436 | − | 0.608653i | \(-0.791710\pi\) |
−0.216573 | + | 0.976266i | \(0.569488\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −263.536 | − | 1494.59i | −0.480029 | − | 2.72238i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 118.340 | + | 668.783i | 0.214772 | + | 1.21376i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.7005 | − | 219.481i | −0.0699828 | − | 0.396892i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 171.680 | − | 432.104i | 0.309334 | − | 0.778566i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.14290 | + | 9.70434i | −0.0146192 | + | 0.0174225i | −0.773305 | − | 0.634035i | \(-0.781398\pi\) |
0.758685 | + | 0.651457i | \(0.225842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 118.239 | − | 68.2652i | 0.211518 | − | 0.122120i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −534.071 | − | 94.1711i | −0.951998 | − | 0.167863i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 421.700 | − | 730.406i | 0.749023 | − | 1.29735i | −0.199268 | − | 0.979945i | \(-0.563857\pi\) |
0.948291 | − | 0.317401i | \(-0.102810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 442.050 | − | 238.333i | 0.782389 | − | 0.421828i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.2773 | − | 20.5903i | −0.0304714 | − | 0.0363144i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 166.474i | − | 0.292572i | −0.989242 | − | 0.146286i | \(-0.953268\pi\) | ||
0.989242 | − | 0.146286i | \(-0.0467320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −310.342 | −0.543506 | −0.271753 | − | 0.962367i | \(-0.587603\pi\) | ||||
−0.271753 | + | 0.962367i | \(0.587603\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −553.229 | + | 464.215i | −0.965496 | + | 0.810148i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 795.983 | + | 188.706i | 1.38432 | + | 0.328184i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −91.4934 | − | 52.8238i | −0.158567 | − | 0.0915490i | 0.418617 | − | 0.908163i | \(-0.362515\pi\) |
−0.577184 | + | 0.816614i | \(0.695848\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −78.2230 | + | 443.625i | −0.135100 | + | 0.766191i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 345.341 | + | 598.147i | 0.594390 | + | 1.02951i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −613.585 | − | 514.859i | −1.05246 | − | 0.883120i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −75.5533 | + | 190.161i | −0.129151 | + | 0.325062i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 149.284 | − | 26.3228i | 0.254317 | − | 0.0448430i | −0.0450359 | − | 0.998985i | \(-0.514340\pi\) |
0.299353 | + | 0.954142i | \(0.403229\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 121.643 | − | 692.306i | 0.206524 | − | 1.17539i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −751.522 | + | 132.514i | −1.27161 | + | 0.224219i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 285.051 | + | 783.171i | 0.480693 | + | 1.32069i | 0.908900 | + | 0.417013i | \(0.136923\pi\) |
−0.428207 | + | 0.903681i | \(0.640855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −314.239 | + | 46.0189i | −0.528133 | + | 0.0773427i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 212.428 | + | 367.937i | 0.355827 | + | 0.616310i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 54.8231 | + | 9.66679i | 0.0915243 | + | 0.0161382i | 0.219223 | − | 0.975675i | \(-0.429648\pi\) |
−0.127698 | + | 0.991813i | \(0.540759\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 244.702 | + | 141.279i | 0.407157 | + | 0.235072i | 0.689568 | − | 0.724221i | \(-0.257801\pi\) |
−0.282410 | + | 0.959294i | \(0.591134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 211.931 | + | 77.1366i | 0.351461 | + | 0.127921i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0160222 | − | 0.550036i | 2.64830e−5 | − | 0.000909150i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1205.30 | 1.98566 | 0.992832 | − | 0.119520i | \(-0.0381356\pi\) | ||||
0.992832 | + | 0.119520i | \(0.0381356\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1075.65 | 1.76626 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −136.699 | − | 162.912i | −0.223731 | − | 0.266632i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −238.707 | + | 655.843i | −0.389408 | + | 1.06989i | 0.577861 | + | 0.816136i | \(0.303888\pi\) |
−0.967269 | + | 0.253755i | \(0.918334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 725.982 | − | 240.538i | 1.18046 | − | 0.391119i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.3727 | − | 3.76858i | −0.0346396 | − | 0.00610790i | 0.156302 | − | 0.987709i | \(-0.450043\pi\) |
−0.190941 | + | 0.981601i | \(0.561154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 523.107 | + | 906.048i | 0.845084 | + | 1.46373i | 0.885548 | + | 0.464547i | \(0.153783\pi\) |
−0.0404644 | + | 0.999181i | \(0.512884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −543.245 | + | 647.415i | −0.874791 | + | 1.04254i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 84.8790 | − | 30.8934i | 0.136242 | − | 0.0495881i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −247.475 | − | 573.917i | −0.395961 | − | 0.918267i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.608107 | + | 1010.29i | 0.000969867 | + | 1.61131i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −193.309 | + | 34.0855i | −0.307327 | + | 0.0541900i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1056.66 | − | 384.593i | 1.67458 | − | 0.609498i | 0.682030 | − | 0.731324i | \(-0.261097\pi\) |
0.992551 | + | 0.121827i | \(0.0388752\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −985.083 | + | 1173.98i | −1.55621 | + | 1.85462i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 620.442 | + | 128.132i | 0.977074 | + | 0.201783i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.05929 | − | 28.6927i | 0.00794237 | − | 0.0450434i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1068.06 | − | 616.647i | −1.67146 | − | 0.965019i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −190.149 | + | 522.430i | −0.296644 | + | 0.815023i | 0.698411 | + | 0.715697i | \(0.253891\pi\) |
−0.995055 | + | 0.0993261i | \(0.968331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8161 | + | 25.9994i | 0.0339287 | + | 0.0404346i | 0.782742 | − | 0.622346i | \(-0.213820\pi\) |
−0.748813 | + | 0.662781i | \(0.769376\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −863.696 | − | 768.674i | −1.33906 | − | 1.19174i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 855.878i | − | 1.32284i | −0.750015 | − | 0.661421i | \(-0.769954\pi\) | ||
0.750015 | − | 0.661421i | \(-0.230046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.6006 | + | 15.0168i | 0.0194153 | + | 0.0231383i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1046.11 | − | 380.753i | −1.60693 | − | 0.584874i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −487.866 | − | 281.670i | −0.747115 | − | 0.431347i | 0.0775355 | − | 0.996990i | \(-0.475295\pi\) |
−0.824651 | + | 0.565643i | \(0.808628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −797.944 | − | 1009.23i | −1.21824 | − | 1.54081i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.6444 | − | 10.7643i | 0.0283780 | − | 0.0163841i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 360.097 | − | 429.147i | 0.546429 | − | 0.651209i | −0.420187 | − | 0.907437i | \(-0.638036\pi\) |
0.966616 | + | 0.256229i | \(0.0824800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −204.329 | − | 561.390i | −0.309122 | − | 0.849305i | −0.992828 | − | 0.119548i | \(-0.961855\pi\) |
0.683707 | − | 0.729757i | \(-0.260367\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 138.443 | − | 24.4113i | 0.208813 | − | 0.0368194i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 186.421 | + | 561.515i | 0.280332 | + | 0.844384i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 203.111 | + | 1151.90i | 0.304515 | + | 1.72699i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1501.73 | − | 546.586i | 2.24474 | − | 0.817019i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −891.861 | − | 748.360i | −1.32915 | − | 1.11529i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −568.787 | − | 985.168i | −0.845152 | − | 1.46385i | −0.885489 | − | 0.464660i | \(-0.846177\pi\) |
0.0403372 | − | 0.999186i | \(-0.487157\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 644.606 | + | 37.5859i | 0.954972 | + | 0.0556829i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 455.681 | − | 789.262i | 0.673088 | − | 1.16582i | −0.303936 | − | 0.952692i | \(-0.598301\pi\) |
0.977024 | − | 0.213130i | \(-0.0683658\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −209.625 | + | 575.939i | −0.308725 | + | 0.848216i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.6523 | + | 17.3293i | −0.0303264 | + | 0.0254469i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 661.708 | 0.968826 | 0.484413 | − | 0.874839i | \(-0.339033\pi\) | ||||
0.484413 | + | 0.874839i | \(0.339033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −394.894 | − | 351.449i | −0.576487 | − | 0.513064i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 906.184 | − | 760.379i | 1.31905 | − | 1.10681i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 195.110 | + | 71.0142i | 0.283179 | + | 0.103069i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.8141 | − | 88.0125i | 0.0735370 | − | 0.127370i | −0.826912 | − | 0.562331i | \(-0.809905\pi\) |
0.900449 | + | 0.434961i | \(0.143238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 968.279 | + | 170.734i | 1.39723 | + | 0.246369i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1137.60 | − | 234.935i | −1.63684 | − | 0.338036i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −247.333 | − | 207.537i | −0.354853 | − | 0.297757i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 88.4205 | + | 242.933i | 0.126496 | + | 0.347544i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −168.097 | − | 953.327i | −0.239797 | − | 1.35995i | −0.832273 | − | 0.554366i | \(-0.812961\pi\) |
0.592477 | − | 0.805588i | \(-0.298150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 125.276 | + | 343.549i | 0.178202 | + | 0.488689i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −945.520 | + | 1532.81i | −1.34116 | + | 2.17420i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.6713 | + | 81.5213i | 0.0419679 | + | 0.115306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 88.1291 | + | 73.9491i | 0.124301 | + | 0.104301i | 0.702819 | − | 0.711369i | \(-0.251924\pi\) |
−0.578518 | + | 0.815669i | \(0.696369\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 444.581 | − | 256.679i | 0.625289 | − | 0.361011i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 210.211 | − | 1192.16i | 0.294826 | − | 1.67204i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 49.3700 | + | 149.006i | 0.0690489 | + | 0.208401i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1702.13 | + | 619.524i | 2.37396 | + | 0.864050i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 508.673 | − | 426.827i | 0.707473 | − | 0.593640i | −0.216416 | − | 0.976301i | \(-0.569437\pi\) |
0.923889 | + | 0.382661i | \(0.124992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 255.541i | 0.354426i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 847.652i | 1.17241i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 613.300 | − | 649.976i | 0.845932 | − | 0.896519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −58.6097 | + | 161.029i | −0.0806186 | + | 0.221498i | −0.973453 | − | 0.228888i | \(-0.926491\pi\) |
0.892834 | + | 0.450385i | \(0.148713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 592.529 | − | 1026.29i | 0.812796 | − | 1.40780i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −84.7603 | + | 480.699i | −0.115951 | + | 0.657591i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 948.075 | − | 547.371i | 1.29342 | − | 0.746755i | 0.314159 | − | 0.949370i | \(-0.398278\pi\) |
0.979258 | + | 0.202616i | \(0.0649443\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −244.130 | + | 35.7516i | −0.332149 | + | 0.0486417i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 162.581 | − | 59.1745i | 0.220598 | − | 0.0802910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −134.060 | − | 760.292i | −0.181407 | − | 1.02881i | −0.930485 | − | 0.366330i | \(-0.880614\pi\) |
0.749078 | − | 0.662482i | \(-0.230497\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −89.7196 | − | 246.042i | −0.121079 | − | 0.332040i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −205.976 | − | 1168.15i | −0.277222 | − | 1.57221i | −0.731814 | − | 0.681505i | \(-0.761326\pi\) |
0.454591 | − | 0.890700i | \(-0.349785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 240.212 | − | 604.592i | 0.322432 | − | 0.811533i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1022.63 | + | 1218.72i | −1.36898 | + | 1.63149i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −246.410 | + | 142.265i | −0.328985 | + | 0.189940i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1403.24 | + | 247.429i | 1.86849 | + | 0.329466i | 0.989172 | − | 0.146762i | \(-0.0468850\pi\) |
0.879322 | + | 0.476228i | \(0.157996\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −747.573 | + | 1294.83i | −0.992793 | + | 1.71957i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 198.465 | + | 368.105i | 0.262868 | + | 0.487556i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 242.035 | + | 288.446i | 0.319730 | + | 0.381039i | 0.901839 | − | 0.432071i | \(-0.142217\pi\) |
−0.582110 | + | 0.813110i | \(0.697773\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1739.92i | 2.29238i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −147.483 | −0.193802 | −0.0969009 | − | 0.995294i | \(-0.530893\pi\) | ||||
−0.0969009 | + | 0.995294i | \(0.530893\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −400.501 | + | 336.061i | −0.524904 | + | 0.440446i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −347.171 | − | 643.919i | −0.453819 | − | 0.841725i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.40074 | − | 2.54077i | −0.00573760 | − | 0.00331260i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.1475 | − | 159.632i | 0.0366027 | − | 0.207584i | −0.961022 | − | 0.276473i | \(-0.910834\pi\) |
0.997624 | + | 0.0688889i | \(0.0219454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1090.79 | − | 1889.30i | −1.41477 | − | 2.45046i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −951.125 | − | 798.088i | −1.23043 | − | 1.03246i | −0.998211 | − | 0.0597932i | \(-0.980956\pi\) |
−0.232222 | − | 0.972663i | \(-0.574600\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −826.533 | + | 415.034i | −1.06649 | + | 0.535527i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 570.348 | − | 100.568i | 0.734038 | − | 0.129431i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −300.430 | + | 521.083i | −0.385660 | + | 0.668913i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −931.735 | + | 164.290i | −1.19300 | + | 0.210358i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 315.769 | + | 867.568i | 0.403281 | + | 1.10800i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 103.382 | + | 705.946i | 0.131697 | + | 0.899294i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 347.181 | + | 601.335i | 0.441145 | + | 0.764085i | 0.997775 | − | 0.0666752i | \(-0.0212391\pi\) |
−0.556630 | + | 0.830761i | \(0.687906\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −236.691 | − | 41.7350i | −0.299989 | − | 0.0528961i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 541.732 | + | 312.769i | 0.684870 | + | 0.395410i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 283.597 | + | 103.221i | 0.357626 | + | 0.130165i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 51.1977 | − | 1757.59i | 0.0643997 | − | 2.21081i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 223.303 | 0.280179 | 0.140089 | − | 0.990139i | \(-0.455261\pi\) | ||||
0.140089 | + | 0.990139i | \(0.455261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 760.312 | 0.951580 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 133.738 | + | 159.383i | 0.166964 | + | 0.198980i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.64862 | − | 15.5195i | 0.00703439 | − | 0.0193268i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 320.472 | + | 967.235i | 0.398102 | + | 1.20153i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 899.547 | + | 158.614i | 1.11468 | + | 0.196548i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −413.014 | − | 715.361i | −0.510524 | − | 0.884253i | −0.999926 | − | 0.0121948i | \(-0.996118\pi\) |
0.489402 | − | 0.872058i | \(-0.337215\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −546.655 | + | 651.478i | −0.674051 | + | 0.803302i | −0.989329 | − | 0.145697i | \(-0.953458\pi\) |
0.315279 | + | 0.948999i | \(0.397902\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 781.419 | − | 284.413i | 0.961154 | − | 0.349832i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −368.126 | + | 596.780i | −0.451689 | + | 0.732246i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 909.327 | − | 0.547336i | 1.11301 | − | 0.000669934i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −251.000 | + | 44.2580i | −0.306471 | + | 0.0540391i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −199.975 | + | 72.7850i | −0.243575 | + | 0.0886541i | −0.460923 | − | 0.887440i | \(-0.652482\pi\) |
0.217348 | + | 0.976094i | \(0.430259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −138.657 | + | 165.245i | −0.168478 | + | 0.200784i | −0.843676 | − | 0.536852i | \(-0.819613\pi\) |
0.675199 | + | 0.737636i | \(0.264058\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1066.34 | − | 793.750i | 1.29253 | − | 0.962121i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.9515 | − | 209.562i | 0.0446813 | − | 0.253401i | −0.954283 | − | 0.298905i | \(-0.903379\pi\) |
0.998964 | + | 0.0455048i | \(0.0144896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1416.47 | + | 817.797i | 1.70864 | + | 0.986486i | 0.936245 | + | 0.351348i | \(0.114277\pi\) |
0.772399 | + | 0.635138i | \(0.219057\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −590.524 | + | 1622.45i | −0.710618 | + | 1.95241i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 66.9545 | + | 79.7932i | 0.0803775 | + | 0.0957902i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −965.443 | + | 1084.79i | −1.15622 | + | 1.29915i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 955.517i | − | 1.14160i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −676.349 | − | 806.041i | −0.806137 | − | 0.960717i | 0.193656 | − | 0.981070i | \(-0.437965\pi\) |
−0.999793 | + | 0.0203528i | \(0.993521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 410.429 | + | 149.384i | 0.488025 | + | 0.177627i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1906.74 | − | 1100.86i | −2.26185 | − | 1.30588i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 498.841 | + | 630.929i | 0.590344 | + | 0.746661i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.593579 | − | 0.342703i | 0.000700801 | − | 0.000404608i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1116.31 | + | 1330.37i | −1.31485 | + | 1.56698i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 215.394 | + | 591.789i | 0.253107 | + | 0.695405i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −457.367 | + | 80.6462i | −0.536187 | + | 0.0945442i | −0.435183 | − | 0.900342i | \(-0.643316\pi\) |
−0.101003 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1068.54 | + | 845.880i | −1.24975 | + | 0.989334i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.4066 | + | 200.801i | 0.0413146 | + | 0.234307i | 0.998472 | − | 0.0552616i | \(-0.0175993\pi\) |
−0.957157 | + | 0.289569i | \(0.906488\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 642.546 | − | 233.868i | 0.748017 | − | 0.272256i | 0.0602457 | − | 0.998184i | \(-0.480812\pi\) |
0.687771 | + | 0.725928i | \(0.258589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 729.744 | + | 612.328i | 0.847554 | + | 0.711182i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 606.102 | + | 1049.80i | 0.702320 | + | 1.21645i | 0.967650 | + | 0.252296i | \(0.0811856\pi\) |
−0.265331 | + | 0.964157i | \(0.585481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 241.407 | + | 305.329i | 0.279083 | + | 0.352982i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 446.889 | − | 774.034i | 0.515443 | − | 0.892773i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 134.693 | − | 370.066i | 0.154998 | − | 0.425853i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.3565 | + | 28.8286i | −0.0394449 | + | 0.0330982i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1411.77 | −1.61715 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 446.585 | − | 637.658i | 0.510383 | − | 0.728752i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 433.920 | − | 364.102i | 0.494778 | − | 0.415168i | −0.360957 | − | 0.932583i | \(-0.617550\pi\) |
0.855735 | + | 0.517414i | \(0.173105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −627.582 | − | 228.421i | −0.713973 | − | 0.259865i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 309.992 | − | 536.922i | 0.351864 | − | 0.609446i | −0.634712 | − | 0.772748i | \(-0.718881\pi\) |
0.986576 | + | 0.163303i | \(0.0522148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1323.69 | + | 233.403i | 1.49909 | + | 0.264329i | 0.862176 | − | 0.506609i | \(-0.169101\pi\) |
0.636910 | + | 0.770938i | \(0.280212\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.70344 | + | 42.1439i | −0.00983439 | + | 0.0476202i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1174.09 | − | 985.177i | −1.32366 | − | 1.11068i | −0.985514 | − | 0.169591i | \(-0.945755\pi\) |
−0.338148 | − | 0.941093i | \(-0.609800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 269.895 | + | 741.530i | 0.303594 | + | 0.834117i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.24757 | − | 46.7743i | −0.00925653 | − | 0.0524964i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −246.797 | − | 1394.75i | −0.276369 | − | 1.56187i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 355.416 | − | 576.176i | 0.397113 | − | 0.643772i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −154.260 | − | 423.826i | −0.171973 | − | 0.472493i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1013.04 | − | 850.043i | −1.12685 | − | 0.945543i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −642.861 | + | 371.156i | −0.713497 | + | 0.411938i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 250.081 | − | 1418.28i | 0.276945 | − | 1.57063i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1630.12 | − | 540.105i | 1.80124 | − | 0.596801i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1257.80 | − | 457.803i | −1.38677 | − | 0.504744i | −0.462548 | − | 0.886594i | \(-0.653065\pi\) |
−0.924224 | + | 0.381851i | \(0.875287\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −153.078 | + | 128.448i | −0.168403 | + | 0.141307i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 658.221i | 0.722526i | 0.932464 | + | 0.361263i | \(0.117654\pi\) | ||||
−0.932464 | + | 0.361263i | \(0.882346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1220.46i | 1.33676i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 74.4172 | − | 2554.70i | 0.0813302 | − | 2.79203i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 548.098 | − | 1505.89i | 0.597708 | − | 1.64219i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −370.964 | + | 642.529i | −0.403661 | + | 0.699161i | −0.994165 | − | 0.107874i | \(-0.965596\pi\) |
0.590504 | + | 0.807035i | \(0.298929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −176.830 | + | 1002.85i | −0.191998 | + | 1.08887i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 212.395 | − | 122.626i | 0.230114 | − | 0.132856i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 264.424 | − | 401.981i | 0.285864 | − | 0.434574i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −553.121 | + | 201.320i | −0.596679 | + | 0.217173i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −227.922 | − | 1292.61i | −0.245341 | − | 1.39140i | −0.819699 | − | 0.572794i | \(-0.805860\pi\) |
0.574358 | − | 0.818604i | \(-0.305252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 124.642 | − | 148.725i | 0.133880 | − | 0.159747i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 444.865 | + | 2522.95i | 0.476811 | + | 2.70413i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −521.541 | − | 207.214i | −0.557798 | − | 0.221620i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −720.434 | + | 858.580i | −0.768873 | + | 0.916308i | −0.998374 | − | 0.0570008i | \(-0.981846\pi\) |
0.229501 | + | 0.973309i | \(0.426291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1748.49 | + | 1009.49i | −1.86208 | + | 1.07507i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 495.539 | + | 87.3769i | 0.526609 | + | 0.0928554i | 0.430631 | − | 0.902528i | \(-0.358291\pi\) |
0.0959781 | + | 0.995383i | \(0.469402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −517.940 | + | 897.098i | −0.549247 | + | 0.951324i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 381.686 | + | 707.935i | 0.403900 | + | 0.749138i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −299.919 | − | 357.430i | −0.316704 | − | 0.377434i | 0.584083 | − | 0.811694i | \(-0.301454\pi\) |
−0.900787 | + | 0.434260i | \(0.857010\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.28118i | 0.00451125i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −648.482 | −0.681895 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −587.190 | + | 492.711i | −0.616149 | + | 0.517011i | −0.896590 | − | 0.442861i | \(-0.853964\pi\) |
0.280441 | + | 0.959871i | \(0.409519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −657.823 | + | 354.668i | −0.688820 | + | 0.371380i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1646.07 | + | 950.360i | 1.72003 | + | 0.993062i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 114.341 | − | 648.458i | 0.119229 | − | 0.676182i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 203.828 | + | 353.041i | 0.212100 | + | 0.367368i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −502.059 | − | 421.278i | −0.521349 | − | 0.437464i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −172.122 | + | 433.217i | −0.178365 | + | 0.448929i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −833.913 | + | 147.041i | −0.862371 | + | 0.152059i | −0.587305 | − | 0.809366i | \(-0.699811\pi\) |
−0.275067 | + | 0.961425i | \(0.588700\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 880.019 | + | 319.701i | 0.908172 | + | 0.329929i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 894.877 | − | 157.791i | 0.921603 | − | 0.162504i | 0.307335 | − | 0.951601i | \(-0.400563\pi\) |
0.614268 | + | 0.789098i | \(0.289452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −494.863 | − | 1359.62i | −0.508595 | − | 1.39735i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −189.375 | + | 287.890i | −0.194231 | + | 0.295272i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −207.038 | − | 358.601i | −0.211912 | − | 0.367043i | 0.740401 | − | 0.672166i | \(-0.234636\pi\) |
−0.952313 | + | 0.305123i | \(0.901302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 157.186 | + | 27.7161i | 0.160557 | + | 0.0283106i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1042.93 | − | 602.135i | −1.06313 | − | 0.613797i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 751.916 | + | 273.675i | 0.764919 | + | 0.278408i | 0.694870 | − | 0.719136i | \(-0.255462\pi\) |
0.0700495 | + | 0.997544i | \(0.477684\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −789.358 | − | 22.9936i | −0.801379 | − | 0.0233437i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2243.27 | −2.27281 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1566.04 | 1.58346 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 153.532 | + | 182.973i | 0.154927 | + | 0.184635i | 0.837925 | − | 0.545786i | \(-0.183769\pi\) |
−0.682998 | + | 0.730420i | \(0.739324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 147.032 | − | 403.968i | 0.148069 | − | 0.406816i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 138.277 | + | 417.343i | 0.138972 | + | 0.419440i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1577.80 | − | 278.208i | −1.58255 | − | 0.279046i | −0.687895 | − | 0.725810i | \(-0.741465\pi\) |
−0.894651 | + | 0.446765i | \(0.852576\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 248.545 | + | 430.493i | 0.248794 | + | 0.430924i |
(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 | 380.3.bc.a.29.3 | ✓ | 120 | |
5.4 | even | 2 | inner | 380.3.bc.a.29.18 | yes | 120 | |
19.2 | odd | 18 | inner | 380.3.bc.a.249.18 | yes | 120 | |
95.59 | odd | 18 | inner | 380.3.bc.a.249.3 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.3.bc.a.29.3 | ✓ | 120 | 1.1 | even | 1 | trivial | |
380.3.bc.a.29.18 | yes | 120 | 5.4 | even | 2 | inner | |
380.3.bc.a.249.3 | yes | 120 | 95.59 | odd | 18 | inner | |
380.3.bc.a.249.18 | yes | 120 | 19.2 | odd | 18 | inner |