Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(139,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.139");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.g (of order \(2\), degree \(1\), 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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.17 | ||
Character | \(\chi\) | \(=\) | 483.139 |
Dual form | 483.3.g.a.139.18 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.01661 | −1.00830 | −0.504152 | − | 0.863615i | \(-0.668195\pi\) | ||||
−0.504152 | + | 0.863615i | \(0.668195\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 0.0667068 | 0.0166767 | ||||||||
\(5\) | 2.33922i | 0.467844i | 0.972255 | + | 0.233922i | \(0.0751560\pi\) | ||||
−0.972255 | + | 0.233922i | \(0.924844\pi\) | |||||||
\(6\) | 3.49287i | 0.582145i | ||||||||
\(7\) | −5.55691 | + | 4.25685i | −0.793844 | + | 0.608122i | ||||
\(8\) | 7.93191 | 0.991489 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | − | 4.71728i | − | 0.471728i | ||||||
\(11\) | −12.1330 | −1.10300 | −0.551501 | − | 0.834174i | \(-0.685945\pi\) | ||||
−0.551501 | + | 0.834174i | \(0.685945\pi\) | |||||||
\(12\) | − | 0.115540i | − | 0.00962830i | ||||||
\(13\) | − | 13.3993i | − | 1.03071i | −0.856976 | − | 0.515356i | \(-0.827660\pi\) | ||
0.856976 | − | 0.515356i | \(-0.172340\pi\) | |||||||
\(14\) | 11.2061 | − | 8.58440i | 0.800436 | − | 0.613171i | ||||
\(15\) | 4.05164 | 0.270110 | ||||||||
\(16\) | −16.2624 | −1.01640 | ||||||||
\(17\) | 0.115332i | 0.00678426i | 0.999994 | + | 0.00339213i | \(0.00107975\pi\) | ||||
−0.999994 | + | 0.00339213i | \(0.998920\pi\) | |||||||
\(18\) | 6.04982 | 0.336101 | ||||||||
\(19\) | 27.1188i | 1.42731i | 0.700500 | + | 0.713653i | \(0.252960\pi\) | ||||
−0.700500 | + | 0.713653i | \(0.747040\pi\) | |||||||
\(20\) | 0.156042i | 0.00780209i | ||||||||
\(21\) | 7.37308 | + | 9.62485i | 0.351099 | + | 0.458326i | ||||
\(22\) | 24.4676 | 1.11216 | ||||||||
\(23\) | 4.79583 | 0.208514 | ||||||||
\(24\) | − | 13.7385i | − | 0.572436i | ||||||
\(25\) | 19.5281 | 0.781122 | ||||||||
\(26\) | 27.0211i | 1.03927i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −0.370684 | + | 0.283961i | −0.0132387 | + | 0.0101415i | ||||
\(29\) | 0.360599 | 0.0124345 | 0.00621723 | − | 0.999981i | \(-0.498021\pi\) | ||||
0.00621723 | + | 0.999981i | \(0.498021\pi\) | |||||||
\(30\) | −8.17058 | −0.272353 | ||||||||
\(31\) | − | 0.231242i | − | 0.00745943i | −0.999993 | − | 0.00372972i | \(-0.998813\pi\) | ||
0.999993 | − | 0.00372972i | \(-0.00118721\pi\) | |||||||
\(32\) | 1.06720 | 0.0333499 | ||||||||
\(33\) | 21.0150i | 0.636819i | ||||||||
\(34\) | − | 0.232580i | − | 0.00684060i | ||||||
\(35\) | −9.95770 | − | 12.9988i | −0.284506 | − | 0.371395i | ||||
\(36\) | −0.200120 | −0.00555890 | ||||||||
\(37\) | 66.3104 | 1.79217 | 0.896086 | − | 0.443880i | \(-0.146398\pi\) | ||||
0.896086 | + | 0.443880i | \(0.146398\pi\) | |||||||
\(38\) | − | 54.6880i | − | 1.43916i | ||||||
\(39\) | −23.2082 | −0.595082 | ||||||||
\(40\) | 18.5545i | 0.463862i | ||||||||
\(41\) | − | 55.2490i | − | 1.34754i | −0.738943 | − | 0.673768i | \(-0.764675\pi\) | ||
0.738943 | − | 0.673768i | \(-0.235325\pi\) | |||||||
\(42\) | −14.8686 | − | 19.4095i | −0.354015 | − | 0.462132i | ||||
\(43\) | −10.0786 | −0.234386 | −0.117193 | − | 0.993109i | \(-0.537390\pi\) | ||||
−0.117193 | + | 0.993109i | \(0.537390\pi\) | |||||||
\(44\) | −0.809355 | −0.0183944 | ||||||||
\(45\) | − | 7.01765i | − | 0.155948i | ||||||
\(46\) | −9.67131 | −0.210246 | ||||||||
\(47\) | − | 60.4153i | − | 1.28543i | −0.766104 | − | 0.642716i | \(-0.777807\pi\) | ||
0.766104 | − | 0.642716i | \(-0.222193\pi\) | |||||||
\(48\) | 28.1673i | 0.586818i | ||||||||
\(49\) | 12.7584 | − | 47.3099i | 0.260376 | − | 0.965507i | ||||
\(50\) | −39.3804 | −0.787609 | ||||||||
\(51\) | 0.199762 | 0.00391689 | ||||||||
\(52\) | − | 0.893822i | − | 0.0171889i | ||||||
\(53\) | −34.9684 | −0.659781 | −0.329891 | − | 0.944019i | \(-0.607012\pi\) | ||||
−0.329891 | + | 0.944019i | \(0.607012\pi\) | |||||||
\(54\) | − | 10.4786i | − | 0.194048i | ||||||
\(55\) | − | 28.3818i | − | 0.516033i | ||||||
\(56\) | −44.0769 | + | 33.7650i | −0.787087 | + | 0.602946i | ||||
\(57\) | 46.9711 | 0.824055 | ||||||||
\(58\) | −0.727187 | −0.0125377 | ||||||||
\(59\) | − | 43.3189i | − | 0.734218i | −0.930178 | − | 0.367109i | \(-0.880348\pi\) | ||
0.930178 | − | 0.367109i | \(-0.119652\pi\) | |||||||
\(60\) | 0.270272 | 0.00450454 | ||||||||
\(61\) | − | 19.6256i | − | 0.321732i | −0.986976 | − | 0.160866i | \(-0.948571\pi\) | ||
0.986976 | − | 0.160866i | \(-0.0514286\pi\) | |||||||
\(62\) | 0.466325i | 0.00752137i | ||||||||
\(63\) | 16.6707 | − | 12.7706i | 0.264615 | − | 0.202707i | ||||
\(64\) | 62.8974 | 0.982772 | ||||||||
\(65\) | 31.3438 | 0.482212 | ||||||||
\(66\) | − | 42.3791i | − | 0.642107i | ||||||
\(67\) | 115.924 | 1.73021 | 0.865107 | − | 0.501587i | \(-0.167250\pi\) | ||||
0.865107 | + | 0.501587i | \(0.167250\pi\) | |||||||
\(68\) | 0.00769346i | 0.000113139i | ||||||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | 20.0808 | + | 26.2135i | 0.286868 | + | 0.374479i | ||||
\(71\) | 5.79639 | 0.0816392 | 0.0408196 | − | 0.999167i | \(-0.487003\pi\) | ||||
0.0408196 | + | 0.999167i | \(0.487003\pi\) | |||||||
\(72\) | −23.7957 | −0.330496 | ||||||||
\(73\) | 17.7978i | 0.243806i | 0.992542 | + | 0.121903i | \(0.0388997\pi\) | ||||
−0.992542 | + | 0.121903i | \(0.961100\pi\) | |||||||
\(74\) | −133.722 | −1.80705 | ||||||||
\(75\) | − | 33.8236i | − | 0.450981i | ||||||
\(76\) | 1.80901i | 0.0238027i | ||||||||
\(77\) | 67.4221 | − | 51.6485i | 0.875612 | − | 0.670760i | ||||
\(78\) | 46.8019 | 0.600024 | ||||||||
\(79\) | 20.5579 | 0.260226 | 0.130113 | − | 0.991499i | \(-0.458466\pi\) | ||||
0.130113 | + | 0.991499i | \(0.458466\pi\) | |||||||
\(80\) | − | 38.0412i | − | 0.475516i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 111.416i | 1.35873i | ||||||||
\(83\) | − | 111.368i | − | 1.34179i | −0.741553 | − | 0.670894i | \(-0.765910\pi\) | ||
0.741553 | − | 0.670894i | \(-0.234090\pi\) | |||||||
\(84\) | 0.491835 | + | 0.642043i | 0.00585518 | + | 0.00764336i | ||||
\(85\) | −0.269788 | −0.00317397 | ||||||||
\(86\) | 20.3246 | 0.236333 | ||||||||
\(87\) | − | 0.624576i | − | 0.00717903i | ||||||
\(88\) | −96.2381 | −1.09361 | ||||||||
\(89\) | − | 26.8035i | − | 0.301163i | −0.988598 | − | 0.150581i | \(-0.951885\pi\) | ||
0.988598 | − | 0.150581i | \(-0.0481145\pi\) | |||||||
\(90\) | 14.1519i | 0.157243i | ||||||||
\(91\) | 57.0387 | + | 74.4585i | 0.626799 | + | 0.818225i | ||||
\(92\) | 0.319915 | 0.00347733 | ||||||||
\(93\) | −0.400524 | −0.00430671 | ||||||||
\(94\) | 121.834i | 1.29611i | ||||||||
\(95\) | −63.4368 | −0.667756 | ||||||||
\(96\) | − | 1.84844i | − | 0.0192546i | ||||||
\(97\) | − | 134.649i | − | 1.38814i | −0.719908 | − | 0.694069i | \(-0.755816\pi\) | ||
0.719908 | − | 0.694069i | \(-0.244184\pi\) | |||||||
\(98\) | −25.7288 | + | 95.4054i | −0.262538 | + | 0.973525i | ||||
\(99\) | 36.3991 | 0.367667 | ||||||||
\(100\) | 1.30265 | 0.0130265 | ||||||||
\(101\) | − | 54.2885i | − | 0.537510i | −0.963209 | − | 0.268755i | \(-0.913388\pi\) | ||
0.963209 | − | 0.268755i | \(-0.0866122\pi\) | |||||||
\(102\) | −0.402841 | −0.00394942 | ||||||||
\(103\) | 159.943i | 1.55284i | 0.630216 | + | 0.776420i | \(0.282966\pi\) | ||||
−0.630216 | + | 0.776420i | \(0.717034\pi\) | |||||||
\(104\) | − | 106.282i | − | 1.02194i | ||||||
\(105\) | −22.5146 | + | 17.2472i | −0.214425 | + | 0.164259i | ||||
\(106\) | 70.5176 | 0.665260 | ||||||||
\(107\) | 105.832 | 0.989089 | 0.494544 | − | 0.869152i | \(-0.335335\pi\) | ||||
0.494544 | + | 0.869152i | \(0.335335\pi\) | |||||||
\(108\) | 0.346619i | 0.00320943i | ||||||||
\(109\) | 199.718 | 1.83228 | 0.916140 | − | 0.400859i | \(-0.131288\pi\) | ||||
0.916140 | + | 0.400859i | \(0.131288\pi\) | |||||||
\(110\) | 57.2349i | 0.520318i | ||||||||
\(111\) | − | 114.853i | − | 1.03471i | ||||||
\(112\) | 90.3685 | − | 69.2265i | 0.806862 | − | 0.618094i | ||||
\(113\) | −41.4735 | −0.367022 | −0.183511 | − | 0.983018i | \(-0.558746\pi\) | ||||
−0.183511 | + | 0.983018i | \(0.558746\pi\) | |||||||
\(114\) | −94.7224 | −0.830898 | ||||||||
\(115\) | 11.2185i | 0.0975521i | ||||||||
\(116\) | 0.0240544 | 0.000207366 | ||||||||
\(117\) | 40.1978i | 0.343571i | ||||||||
\(118\) | 87.3571i | 0.740315i | ||||||||
\(119\) | −0.490953 | − | 0.640892i | −0.00412566 | − | 0.00538564i | ||||
\(120\) | 32.1373 | 0.267811 | ||||||||
\(121\) | 26.2104 | 0.216614 | ||||||||
\(122\) | 39.5772i | 0.324403i | ||||||||
\(123\) | −95.6941 | −0.778001 | ||||||||
\(124\) | − | 0.0154254i | − | 0.000124399i | ||||||
\(125\) | 104.161i | 0.833287i | ||||||||
\(126\) | −33.6183 | + | 25.7532i | −0.266812 | + | 0.204390i | ||||
\(127\) | 94.5345 | 0.744366 | 0.372183 | − | 0.928159i | \(-0.378609\pi\) | ||||
0.372183 | + | 0.928159i | \(0.378609\pi\) | |||||||
\(128\) | −131.108 | −1.02428 | ||||||||
\(129\) | 17.4567i | 0.135323i | ||||||||
\(130\) | −63.2082 | −0.486217 | ||||||||
\(131\) | 159.966i | 1.22112i | 0.791972 | + | 0.610558i | \(0.209055\pi\) | ||||
−0.791972 | + | 0.610558i | \(0.790945\pi\) | |||||||
\(132\) | 1.40184i | 0.0106200i | ||||||||
\(133\) | −115.441 | − | 150.697i | −0.867975 | − | 1.13306i | ||||
\(134\) | −233.774 | −1.74458 | ||||||||
\(135\) | −12.1549 | −0.0900365 | ||||||||
\(136\) | 0.914806i | 0.00672652i | ||||||||
\(137\) | 109.920 | 0.802338 | 0.401169 | − | 0.916004i | \(-0.368604\pi\) | ||||
0.401169 | + | 0.916004i | \(0.368604\pi\) | |||||||
\(138\) | 16.7512i | 0.121386i | ||||||||
\(139\) | 114.111i | 0.820939i | 0.911874 | + | 0.410470i | \(0.134635\pi\) | ||||
−0.911874 | + | 0.410470i | \(0.865365\pi\) | |||||||
\(140\) | −0.664246 | − | 0.867109i | −0.00474462 | − | 0.00619364i | ||||
\(141\) | −104.642 | −0.742145 | ||||||||
\(142\) | −11.6890 | −0.0823172 | ||||||||
\(143\) | 162.574i | 1.13688i | ||||||||
\(144\) | 48.7871 | 0.338800 | ||||||||
\(145\) | 0.843520i | 0.00581738i | ||||||||
\(146\) | − | 35.8913i | − | 0.245831i | ||||||
\(147\) | −81.9431 | − | 22.0983i | −0.557436 | − | 0.150328i | ||||
\(148\) | 4.42335 | 0.0298875 | ||||||||
\(149\) | −138.972 | −0.932701 | −0.466350 | − | 0.884600i | \(-0.654431\pi\) | ||||
−0.466350 | + | 0.884600i | \(0.654431\pi\) | |||||||
\(150\) | 68.2089i | 0.454726i | ||||||||
\(151\) | −220.090 | −1.45755 | −0.728775 | − | 0.684753i | \(-0.759910\pi\) | ||||
−0.728775 | + | 0.684753i | \(0.759910\pi\) | |||||||
\(152\) | 215.104i | 1.41516i | ||||||||
\(153\) | − | 0.345997i | − | 0.00226142i | ||||||
\(154\) | −135.964 | + | 104.155i | −0.882883 | + | 0.676330i | ||||
\(155\) | 0.540926 | 0.00348985 | ||||||||
\(156\) | −1.54815 | −0.00992401 | ||||||||
\(157\) | − | 137.787i | − | 0.877622i | −0.898579 | − | 0.438811i | \(-0.855400\pi\) | ||
0.898579 | − | 0.438811i | \(-0.144600\pi\) | |||||||
\(158\) | −41.4571 | −0.262387 | ||||||||
\(159\) | 60.5671i | 0.380925i | ||||||||
\(160\) | 2.49641i | 0.0156026i | ||||||||
\(161\) | −26.6500 | + | 20.4151i | −0.165528 | + | 0.126802i | ||||
\(162\) | −18.1495 | −0.112034 | ||||||||
\(163\) | −147.893 | −0.907318 | −0.453659 | − | 0.891175i | \(-0.649882\pi\) | ||||
−0.453659 | + | 0.891175i | \(0.649882\pi\) | |||||||
\(164\) | − | 3.68548i | − | 0.0224725i | ||||||
\(165\) | −49.1587 | −0.297932 | ||||||||
\(166\) | 224.586i | 1.35293i | ||||||||
\(167\) | 99.2846i | 0.594519i | 0.954797 | + | 0.297259i | \(0.0960726\pi\) | ||||
−0.954797 | + | 0.297259i | \(0.903927\pi\) | |||||||
\(168\) | 58.4826 | + | 76.3434i | 0.348111 | + | 0.454425i | ||||
\(169\) | −10.5404 | −0.0623692 | ||||||||
\(170\) | 0.544056 | 0.00320033 | ||||||||
\(171\) | − | 81.3564i | − | 0.475768i | ||||||
\(172\) | −0.672312 | −0.00390879 | ||||||||
\(173\) | − | 51.9594i | − | 0.300343i | −0.988660 | − | 0.150172i | \(-0.952017\pi\) | ||
0.988660 | − | 0.150172i | \(-0.0479826\pi\) | |||||||
\(174\) | 1.25952i | 0.00723865i | ||||||||
\(175\) | −108.516 | + | 83.1281i | −0.620089 | + | 0.475017i | ||||
\(176\) | 197.312 | 1.12109 | ||||||||
\(177\) | −75.0305 | −0.423901 | ||||||||
\(178\) | 54.0521i | 0.303663i | ||||||||
\(179\) | 305.827 | 1.70853 | 0.854265 | − | 0.519838i | \(-0.174008\pi\) | ||||
0.854265 | + | 0.519838i | \(0.174008\pi\) | |||||||
\(180\) | − | 0.468125i | − | 0.00260070i | ||||||
\(181\) | − | 83.0452i | − | 0.458813i | −0.973331 | − | 0.229407i | \(-0.926321\pi\) | ||
0.973331 | − | 0.229407i | \(-0.0736786\pi\) | |||||||
\(182\) | −115.025 | − | 150.154i | −0.632004 | − | 0.825020i | ||||
\(183\) | −33.9926 | −0.185752 | ||||||||
\(184\) | 38.0401 | 0.206740 | ||||||||
\(185\) | 155.114i | 0.838456i | ||||||||
\(186\) | 0.807699 | 0.00434247 | ||||||||
\(187\) | − | 1.39933i | − | 0.00748306i | ||||||
\(188\) | − | 4.03011i | − | 0.0214368i | ||||||
\(189\) | −22.1192 | − | 28.8745i | −0.117033 | − | 0.152775i | ||||
\(190\) | 127.927 | 0.673300 | ||||||||
\(191\) | 108.802 | 0.569646 | 0.284823 | − | 0.958580i | \(-0.408065\pi\) | ||||
0.284823 | + | 0.958580i | \(0.408065\pi\) | |||||||
\(192\) | − | 108.941i | − | 0.567404i | ||||||
\(193\) | −17.5365 | −0.0908628 | −0.0454314 | − | 0.998967i | \(-0.514466\pi\) | ||||
−0.0454314 | + | 0.998967i | \(0.514466\pi\) | |||||||
\(194\) | 271.535i | 1.39967i | ||||||||
\(195\) | − | 54.2891i | − | 0.278405i | ||||||
\(196\) | 0.851074 | − | 3.15589i | 0.00434222 | − | 0.0161015i | ||||
\(197\) | −344.079 | −1.74659 | −0.873297 | − | 0.487189i | \(-0.838022\pi\) | ||||
−0.873297 | + | 0.487189i | \(0.838022\pi\) | |||||||
\(198\) | −73.4027 | −0.370721 | ||||||||
\(199\) | − | 131.485i | − | 0.660730i | −0.943853 | − | 0.330365i | \(-0.892828\pi\) | ||
0.943853 | − | 0.330365i | \(-0.107172\pi\) | |||||||
\(200\) | 154.895 | 0.774474 | ||||||||
\(201\) | − | 200.787i | − | 0.998940i | ||||||
\(202\) | 109.479i | 0.541973i | ||||||||
\(203\) | −2.00382 | + | 1.53502i | −0.00987101 | + | 0.00756166i | ||||
\(204\) | 0.0133255 | 6.53209e−5 | ||||||||
\(205\) | 129.239 | 0.630436 | ||||||||
\(206\) | − | 322.541i | − | 1.56573i | ||||||
\(207\) | −14.3875 | −0.0695048 | ||||||||
\(208\) | 217.904i | 1.04762i | ||||||||
\(209\) | − | 329.033i | − | 1.57432i | ||||||
\(210\) | 45.4031 | − | 34.7809i | 0.216205 | − | 0.165623i | ||||
\(211\) | 159.966 | 0.758132 | 0.379066 | − | 0.925370i | \(-0.376245\pi\) | ||||
0.379066 | + | 0.925370i | \(0.376245\pi\) | |||||||
\(212\) | −2.33263 | −0.0110030 | ||||||||
\(213\) | − | 10.0396i | − | 0.0471344i | ||||||
\(214\) | −213.423 | −0.997302 | ||||||||
\(215\) | − | 23.5761i | − | 0.109656i | ||||||
\(216\) | 41.2154i | 0.190812i | ||||||||
\(217\) | 0.984365 | + | 1.28499i | 0.00453624 | + | 0.00592162i | ||||
\(218\) | −402.754 | −1.84749 | ||||||||
\(219\) | 30.8268 | 0.140762 | ||||||||
\(220\) | − | 1.89326i | − | 0.00860572i | ||||||
\(221\) | 1.54537 | 0.00699263 | ||||||||
\(222\) | 231.613i | 1.04330i | ||||||||
\(223\) | 374.032i | 1.67727i | 0.544691 | + | 0.838637i | \(0.316647\pi\) | ||||
−0.544691 | + | 0.838637i | \(0.683353\pi\) | |||||||
\(224\) | −5.93032 | + | 4.54290i | −0.0264746 | + | 0.0202808i | ||||
\(225\) | −58.5842 | −0.260374 | ||||||||
\(226\) | 83.6359 | 0.370070 | ||||||||
\(227\) | 31.6312i | 0.139345i | 0.997570 | + | 0.0696723i | \(0.0221954\pi\) | ||||
−0.997570 | + | 0.0696723i | \(0.977805\pi\) | |||||||
\(228\) | 3.13329 | 0.0137425 | ||||||||
\(229\) | 376.510i | 1.64415i | 0.569381 | + | 0.822074i | \(0.307183\pi\) | ||||
−0.569381 | + | 0.822074i | \(0.692817\pi\) | |||||||
\(230\) | − | 22.6233i | − | 0.0983622i | ||||||
\(231\) | −89.4578 | − | 116.779i | −0.387263 | − | 0.505535i | ||||
\(232\) | 2.86024 | 0.0123286 | ||||||||
\(233\) | 2.64982 | 0.0113726 | 0.00568632 | − | 0.999984i | \(-0.498190\pi\) | ||||
0.00568632 | + | 0.999984i | \(0.498190\pi\) | |||||||
\(234\) | − | 81.0632i | − | 0.346424i | ||||||
\(235\) | 141.325 | 0.601381 | ||||||||
\(236\) | − | 2.88966i | − | 0.0122443i | ||||||
\(237\) | − | 35.6073i | − | 0.150242i | ||||||
\(238\) | 0.990060 | + | 1.29243i | 0.00415991 | + | 0.00543037i | ||||
\(239\) | 153.415 | 0.641904 | 0.320952 | − | 0.947096i | \(-0.395997\pi\) | ||||
0.320952 | + | 0.947096i | \(0.395997\pi\) | |||||||
\(240\) | −65.8894 | −0.274539 | ||||||||
\(241\) | − | 155.790i | − | 0.646431i | −0.946325 | − | 0.323216i | \(-0.895236\pi\) | ||
0.946325 | − | 0.323216i | \(-0.104764\pi\) | |||||||
\(242\) | −52.8560 | −0.218413 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 1.30916i | − | 0.00536542i | ||||||
\(245\) | 110.668 | + | 29.8448i | 0.451706 | + | 0.121815i | ||||
\(246\) | 192.977 | 0.784461 | ||||||||
\(247\) | 363.372 | 1.47114 | ||||||||
\(248\) | − | 1.83419i | − | 0.00739594i | ||||||
\(249\) | −192.896 | −0.774682 | ||||||||
\(250\) | − | 210.052i | − | 0.840206i | ||||||
\(251\) | − | 313.684i | − | 1.24974i | −0.780729 | − | 0.624869i | \(-0.785152\pi\) | ||
0.780729 | − | 0.624869i | \(-0.214848\pi\) | |||||||
\(252\) | 1.11205 | − | 0.851883i | 0.00441290 | − | 0.00338049i | ||||
\(253\) | −58.1880 | −0.229992 | ||||||||
\(254\) | −190.639 | −0.750547 | ||||||||
\(255\) | 0.467286i | 0.00183249i | ||||||||
\(256\) | 12.8042 | 0.0500163 | ||||||||
\(257\) | 322.328i | 1.25419i | 0.778942 | + | 0.627097i | \(0.215757\pi\) | ||||
−0.778942 | + | 0.627097i | \(0.784243\pi\) | |||||||
\(258\) | − | 35.2032i | − | 0.136447i | ||||||
\(259\) | −368.481 | + | 282.273i | −1.42271 | + | 1.08986i | ||||
\(260\) | 2.09085 | 0.00804171 | ||||||||
\(261\) | −1.08180 | −0.00414482 | ||||||||
\(262\) | − | 322.589i | − | 1.23126i | ||||||
\(263\) | 289.840 | 1.10205 | 0.551026 | − | 0.834488i | \(-0.314236\pi\) | ||||
0.551026 | + | 0.834488i | \(0.314236\pi\) | |||||||
\(264\) | 166.689i | 0.631399i | ||||||||
\(265\) | − | 81.7987i | − | 0.308674i | ||||||
\(266\) | 232.799 | + | 303.896i | 0.875183 | + | 1.14247i | ||||
\(267\) | −46.4250 | −0.173876 | ||||||||
\(268\) | 7.73294 | 0.0288543 | ||||||||
\(269\) | − | 221.588i | − | 0.823749i | −0.911241 | − | 0.411874i | \(-0.864874\pi\) | ||
0.911241 | − | 0.411874i | \(-0.135126\pi\) | |||||||
\(270\) | 24.5117 | 0.0907842 | ||||||||
\(271\) | − | 321.439i | − | 1.18612i | −0.805157 | − | 0.593062i | \(-0.797919\pi\) | ||
0.805157 | − | 0.593062i | \(-0.202081\pi\) | |||||||
\(272\) | − | 1.87558i | − | 0.00689551i | ||||||
\(273\) | 128.966 | − | 98.7939i | 0.472403 | − | 0.361882i | ||||
\(274\) | −221.666 | −0.809000 | ||||||||
\(275\) | −236.934 | −0.861580 | ||||||||
\(276\) | − | 0.554108i | − | 0.00200764i | ||||||
\(277\) | 168.521 | 0.608379 | 0.304190 | − | 0.952611i | \(-0.401614\pi\) | ||||
0.304190 | + | 0.952611i | \(0.401614\pi\) | |||||||
\(278\) | − | 230.116i | − | 0.827756i | ||||||
\(279\) | 0.693727i | 0.00248648i | ||||||||
\(280\) | −78.9836 | − | 103.105i | −0.282084 | − | 0.368234i | ||||
\(281\) | 315.524 | 1.12286 | 0.561431 | − | 0.827524i | \(-0.310251\pi\) | ||||
0.561431 | + | 0.827524i | \(0.310251\pi\) | |||||||
\(282\) | 211.023 | 0.748307 | ||||||||
\(283\) | − | 330.149i | − | 1.16661i | −0.812255 | − | 0.583303i | \(-0.801760\pi\) | ||
0.812255 | − | 0.583303i | \(-0.198240\pi\) | |||||||
\(284\) | 0.386658 | 0.00136147 | ||||||||
\(285\) | 109.876i | 0.385529i | ||||||||
\(286\) | − | 327.847i | − | 1.14632i | ||||||
\(287\) | 235.187 | + | 307.014i | 0.819466 | + | 1.06973i | ||||
\(288\) | −3.20159 | −0.0111166 | ||||||||
\(289\) | 288.987 | 0.999954 | ||||||||
\(290\) | − | 1.70105i | − | 0.00586569i | ||||||
\(291\) | −233.220 | −0.801442 | ||||||||
\(292\) | 1.18724i | 0.00406588i | ||||||||
\(293\) | − | 359.896i | − | 1.22831i | −0.789184 | − | 0.614157i | \(-0.789496\pi\) | ||
0.789184 | − | 0.614157i | \(-0.210504\pi\) | |||||||
\(294\) | 165.247 | + | 44.5635i | 0.562065 | + | 0.151577i | ||||
\(295\) | 101.332 | 0.343499 | ||||||||
\(296\) | 525.968 | 1.77692 | ||||||||
\(297\) | − | 63.0451i | − | 0.212273i | ||||||
\(298\) | 280.253 | 0.940446 | ||||||||
\(299\) | − | 64.2606i | − | 0.214919i | ||||||
\(300\) | − | 2.25626i | − | 0.00752088i | ||||||
\(301\) | 56.0059 | − | 42.9031i | 0.186066 | − | 0.142535i | ||||
\(302\) | 443.835 | 1.46965 | ||||||||
\(303\) | −94.0304 | −0.310331 | ||||||||
\(304\) | − | 441.016i | − | 1.45071i | ||||||
\(305\) | 45.9086 | 0.150520 | ||||||||
\(306\) | 0.697741i | 0.00228020i | ||||||||
\(307\) | 192.798i | 0.628005i | 0.949422 | + | 0.314003i | \(0.101670\pi\) | ||||
−0.949422 | + | 0.314003i | \(0.898330\pi\) | |||||||
\(308\) | 4.49751 | − | 3.44531i | 0.0146023 | − | 0.0111861i | ||||
\(309\) | 277.029 | 0.896533 | ||||||||
\(310\) | −1.09084 | −0.00351883 | ||||||||
\(311\) | − | 481.302i | − | 1.54759i | −0.633434 | − | 0.773797i | \(-0.718355\pi\) | ||
0.633434 | − | 0.773797i | \(-0.281645\pi\) | |||||||
\(312\) | −184.085 | −0.590017 | ||||||||
\(313\) | 376.244i | 1.20206i | 0.799227 | + | 0.601029i | \(0.205242\pi\) | ||||
−0.799227 | + | 0.601029i | \(0.794758\pi\) | |||||||
\(314\) | 277.862i | 0.884909i | ||||||||
\(315\) | 29.8731 | + | 38.9964i | 0.0948353 | + | 0.123798i | ||||
\(316\) | 1.37135 | 0.00433971 | ||||||||
\(317\) | −223.316 | −0.704466 | −0.352233 | − | 0.935912i | \(-0.614578\pi\) | ||||
−0.352233 | + | 0.935912i | \(0.614578\pi\) | |||||||
\(318\) | − | 122.140i | − | 0.384088i | ||||||
\(319\) | −4.37516 | −0.0137152 | ||||||||
\(320\) | 147.131i | 0.459783i | ||||||||
\(321\) | − | 183.307i | − | 0.571051i | ||||||
\(322\) | 53.7426 | − | 41.1693i | 0.166902 | − | 0.127855i | ||||
\(323\) | −3.12768 | −0.00968321 | ||||||||
\(324\) | 0.600361 | 0.00185297 | ||||||||
\(325\) | − | 261.662i | − | 0.805113i | ||||||
\(326\) | 298.242 | 0.914853 | ||||||||
\(327\) | − | 345.923i | − | 1.05787i | ||||||
\(328\) | − | 438.230i | − | 1.33607i | ||||||
\(329\) | 257.179 | + | 335.722i | 0.781699 | + | 1.02043i | ||||
\(330\) | 99.1338 | 0.300406 | ||||||||
\(331\) | −81.3038 | −0.245631 | −0.122815 | − | 0.992430i | \(-0.539192\pi\) | ||||
−0.122815 | + | 0.992430i | \(0.539192\pi\) | |||||||
\(332\) | − | 7.42903i | − | 0.0223766i | ||||||
\(333\) | −198.931 | −0.597391 | ||||||||
\(334\) | − | 200.218i | − | 0.599455i | ||||||
\(335\) | 271.172i | 0.809470i | ||||||||
\(336\) | −119.904 | − | 156.523i | −0.356857 | − | 0.465842i | ||||
\(337\) | −486.946 | −1.44494 | −0.722472 | − | 0.691400i | \(-0.756994\pi\) | ||||
−0.722472 | + | 0.691400i | \(0.756994\pi\) | |||||||
\(338\) | 21.2559 | 0.0628871 | ||||||||
\(339\) | 71.8343i | 0.211901i | ||||||||
\(340\) | −0.0179967 | −5.29314e−5 | ||||||||
\(341\) | 2.80567i | 0.00822777i | ||||||||
\(342\) | 164.064i | 0.479719i | ||||||||
\(343\) | 130.494 | + | 317.207i | 0.380448 | + | 0.924802i | ||||
\(344\) | −79.9426 | −0.232391 | ||||||||
\(345\) | 19.4310 | 0.0563217 | ||||||||
\(346\) | 104.782i | 0.302837i | ||||||||
\(347\) | 28.4035 | 0.0818544 | 0.0409272 | − | 0.999162i | \(-0.486969\pi\) | ||||
0.0409272 | + | 0.999162i | \(0.486969\pi\) | |||||||
\(348\) | − | 0.0416635i | − | 0.000119723i | ||||||
\(349\) | − | 687.696i | − | 1.97048i | −0.171187 | − | 0.985239i | \(-0.554760\pi\) | ||
0.171187 | − | 0.985239i | \(-0.445240\pi\) | |||||||
\(350\) | 218.833 | − | 167.637i | 0.625238 | − | 0.478962i | ||||
\(351\) | 69.6246 | 0.198361 | ||||||||
\(352\) | −12.9483 | −0.0367851 | ||||||||
\(353\) | − | 3.12789i | − | 0.00886088i | −0.999990 | − | 0.00443044i | \(-0.998590\pi\) | ||
0.999990 | − | 0.00443044i | \(-0.00141026\pi\) | |||||||
\(354\) | 151.307 | 0.427421 | ||||||||
\(355\) | 13.5590i | 0.0381944i | ||||||||
\(356\) | − | 1.78797i | − | 0.00502240i | ||||||
\(357\) | −1.11006 | + | 0.850356i | −0.00310940 | + | 0.00238195i | ||||
\(358\) | −616.733 | −1.72272 | ||||||||
\(359\) | −464.707 | −1.29445 | −0.647224 | − | 0.762300i | \(-0.724070\pi\) | ||||
−0.647224 | + | 0.762300i | \(0.724070\pi\) | |||||||
\(360\) | − | 55.6634i | − | 0.154621i | ||||||
\(361\) | −374.429 | −1.03720 | ||||||||
\(362\) | 167.470i | 0.462623i | ||||||||
\(363\) | − | 45.3977i | − | 0.125062i | ||||||
\(364\) | 3.80487 | + | 4.96689i | 0.0104529 | + | 0.0136453i | ||||
\(365\) | −41.6330 | −0.114063 | ||||||||
\(366\) | 68.5497 | 0.187294 | ||||||||
\(367\) | 282.058i | 0.768550i | 0.923219 | + | 0.384275i | \(0.125549\pi\) | ||||
−0.923219 | + | 0.384275i | \(0.874451\pi\) | |||||||
\(368\) | −77.9916 | −0.211934 | ||||||||
\(369\) | 165.747i | 0.449179i | ||||||||
\(370\) | − | 312.805i | − | 0.845419i | ||||||
\(371\) | 194.316 | − | 148.855i | 0.523763 | − | 0.401227i | ||||
\(372\) | −0.0267176 | −7.18216e−5 | ||||||||
\(373\) | 193.560 | 0.518928 | 0.259464 | − | 0.965753i | \(-0.416454\pi\) | ||||
0.259464 | + | 0.965753i | \(0.416454\pi\) | |||||||
\(374\) | 2.82190i | 0.00754519i | ||||||||
\(375\) | 180.412 | 0.481098 | ||||||||
\(376\) | − | 479.209i | − | 1.27449i | ||||||
\(377\) | − | 4.83176i | − | 0.0128164i | ||||||
\(378\) | 44.6058 | + | 58.2286i | 0.118005 | + | 0.154044i | ||||
\(379\) | −170.530 | −0.449948 | −0.224974 | − | 0.974365i | \(-0.572230\pi\) | ||||
−0.224974 | + | 0.974365i | \(0.572230\pi\) | |||||||
\(380\) | −4.23166 | −0.0111360 | ||||||||
\(381\) | − | 163.739i | − | 0.429760i | ||||||
\(382\) | −219.412 | −0.574376 | ||||||||
\(383\) | 513.611i | 1.34102i | 0.741900 | + | 0.670510i | \(0.233925\pi\) | ||||
−0.741900 | + | 0.670510i | \(0.766075\pi\) | |||||||
\(384\) | 227.086i | 0.591370i | ||||||||
\(385\) | 120.817 | + | 157.715i | 0.313811 | + | 0.409649i | ||||
\(386\) | 35.3643 | 0.0916173 | ||||||||
\(387\) | 30.2358 | 0.0781287 | ||||||||
\(388\) | − | 8.98203i | − | 0.0231496i | ||||||
\(389\) | 486.118 | 1.24966 | 0.624830 | − | 0.780761i | \(-0.285168\pi\) | ||||
0.624830 | + | 0.780761i | \(0.285168\pi\) | |||||||
\(390\) | 109.480i | 0.280717i | ||||||||
\(391\) | 0.553115i | 0.00141462i | ||||||||
\(392\) | 101.199 | − | 375.257i | 0.258160 | − | 0.957290i | ||||
\(393\) | 277.069 | 0.705011 | ||||||||
\(394\) | 693.872 | 1.76110 | ||||||||
\(395\) | 48.0893i | 0.121745i | ||||||||
\(396\) | 2.42807 | 0.00613148 | ||||||||
\(397\) | − | 77.1778i | − | 0.194402i | −0.995265 | − | 0.0972012i | \(-0.969011\pi\) | ||
0.995265 | − | 0.0972012i | \(-0.0309890\pi\) | |||||||
\(398\) | 265.154i | 0.666217i | ||||||||
\(399\) | −261.014 | + | 199.949i | −0.654171 | + | 0.501126i | ||||
\(400\) | −317.573 | −0.793932 | ||||||||
\(401\) | −455.348 | −1.13553 | −0.567766 | − | 0.823190i | \(-0.692192\pi\) | ||||
−0.567766 | + | 0.823190i | \(0.692192\pi\) | |||||||
\(402\) | 404.908i | 1.00723i | ||||||||
\(403\) | −3.09848 | −0.00768853 | ||||||||
\(404\) | − | 3.62141i | − | 0.00896389i | ||||||
\(405\) | 21.0530i | 0.0519826i | ||||||||
\(406\) | 4.04091 | − | 3.09553i | 0.00995298 | − | 0.00762445i | ||||
\(407\) | −804.546 | −1.97677 | ||||||||
\(408\) | 1.58449 | 0.00388356 | ||||||||
\(409\) | − | 354.597i | − | 0.866986i | −0.901157 | − | 0.433493i | \(-0.857281\pi\) | ||
0.901157 | − | 0.433493i | \(-0.142719\pi\) | |||||||
\(410\) | −260.625 | −0.635671 | ||||||||
\(411\) | − | 190.387i | − | 0.463230i | ||||||
\(412\) | 10.6693i | 0.0258963i | ||||||||
\(413\) | 184.402 | + | 240.719i | 0.446494 | + | 0.582854i | ||||
\(414\) | 29.0139 | 0.0700820 | ||||||||
\(415\) | 260.515 | 0.627747 | ||||||||
\(416\) | − | 14.2997i | − | 0.0343742i | ||||||
\(417\) | 197.645 | 0.473970 | ||||||||
\(418\) | 663.531i | 1.58739i | ||||||||
\(419\) | − | 238.372i | − | 0.568908i | −0.958690 | − | 0.284454i | \(-0.908188\pi\) | ||
0.958690 | − | 0.284454i | \(-0.0918122\pi\) | |||||||
\(420\) | −1.50188 | + | 1.15051i | −0.00357590 | + | 0.00273931i | ||||
\(421\) | −81.3807 | −0.193303 | −0.0966517 | − | 0.995318i | \(-0.530813\pi\) | ||||
−0.0966517 | + | 0.995318i | \(0.530813\pi\) | |||||||
\(422\) | −322.589 | −0.764428 | ||||||||
\(423\) | 181.246i | 0.428477i | ||||||||
\(424\) | −277.366 | −0.654166 | ||||||||
\(425\) | 2.25222i | 0.00529934i | ||||||||
\(426\) | 20.2460i | 0.0475258i | ||||||||
\(427\) | 83.5434 | + | 109.058i | 0.195652 | + | 0.255405i | ||||
\(428\) | 7.05975 | 0.0164947 | ||||||||
\(429\) | 281.586 | 0.656377 | ||||||||
\(430\) | 47.5437i | 0.110567i | ||||||||
\(431\) | 256.291 | 0.594642 | 0.297321 | − | 0.954778i | \(-0.403907\pi\) | ||||
0.297321 | + | 0.954778i | \(0.403907\pi\) | |||||||
\(432\) | − | 84.5018i | − | 0.195606i | ||||||
\(433\) | − | 23.6575i | − | 0.0546362i | −0.999627 | − | 0.0273181i | \(-0.991303\pi\) | ||
0.999627 | − | 0.0273181i | \(-0.00869670\pi\) | |||||||
\(434\) | −1.98508 | − | 2.59133i | −0.00457391 | − | 0.00597080i | ||||
\(435\) | 1.46102 | 0.00335867 | ||||||||
\(436\) | 13.3226 | 0.0305564 | ||||||||
\(437\) | 130.057i | 0.297614i | ||||||||
\(438\) | −62.1655 | −0.141930 | ||||||||
\(439\) | − | 415.759i | − | 0.947059i | −0.880778 | − | 0.473529i | \(-0.842980\pi\) | ||
0.880778 | − | 0.473529i | \(-0.157020\pi\) | |||||||
\(440\) | − | 225.122i | − | 0.511640i | ||||||
\(441\) | −38.2753 | + | 141.930i | −0.0867921 | + | 0.321836i | ||||
\(442\) | −3.11641 | −0.00705069 | ||||||||
\(443\) | −842.902 | −1.90271 | −0.951357 | − | 0.308091i | \(-0.900310\pi\) | ||||
−0.951357 | + | 0.308091i | \(0.900310\pi\) | |||||||
\(444\) | − | 7.66147i | − | 0.0172556i | ||||||
\(445\) | 62.6992 | 0.140897 | ||||||||
\(446\) | − | 754.276i | − | 1.69120i | ||||||
\(447\) | 240.707i | 0.538495i | ||||||||
\(448\) | −349.515 | + | 267.745i | −0.780167 | + | 0.597645i | ||||
\(449\) | −214.674 | −0.478116 | −0.239058 | − | 0.971005i | \(-0.576839\pi\) | ||||
−0.239058 | + | 0.971005i | \(0.576839\pi\) | |||||||
\(450\) | 118.141 | 0.262536 | ||||||||
\(451\) | 670.338i | 1.48634i | ||||||||
\(452\) | −2.76657 | −0.00612072 | ||||||||
\(453\) | 381.207i | 0.841517i | ||||||||
\(454\) | − | 63.7878i | − | 0.140502i | ||||||
\(455\) | −174.175 | + | 133.426i | −0.382801 | + | 0.293244i | ||||
\(456\) | 372.571 | 0.817041 | ||||||||
\(457\) | −481.061 | −1.05265 | −0.526325 | − | 0.850283i | \(-0.676431\pi\) | ||||
−0.526325 | + | 0.850283i | \(0.676431\pi\) | |||||||
\(458\) | − | 759.273i | − | 1.65780i | ||||||
\(459\) | −0.599285 | −0.00130563 | ||||||||
\(460\) | 0.748350i | 0.00162685i | ||||||||
\(461\) | 422.982i | 0.917530i | 0.888558 | + | 0.458765i | \(0.151708\pi\) | ||||
−0.888558 | + | 0.458765i | \(0.848292\pi\) | |||||||
\(462\) | 180.401 | + | 235.496i | 0.390479 | + | 0.509733i | ||||
\(463\) | 642.954 | 1.38867 | 0.694335 | − | 0.719652i | \(-0.255699\pi\) | ||||
0.694335 | + | 0.719652i | \(0.255699\pi\) | |||||||
\(464\) | −5.86420 | −0.0126384 | ||||||||
\(465\) | − | 0.936912i | − | 0.00201486i | ||||||
\(466\) | −5.34366 | −0.0114671 | ||||||||
\(467\) | − | 10.6389i | − | 0.0227814i | −0.999935 | − | 0.0113907i | \(-0.996374\pi\) | ||
0.999935 | − | 0.0113907i | \(-0.00362585\pi\) | |||||||
\(468\) | 2.68147i | 0.00572963i | ||||||||
\(469\) | −644.181 | + | 493.473i | −1.37352 | + | 1.05218i | ||||
\(470\) | −284.996 | −0.606375 | ||||||||
\(471\) | −238.653 | −0.506695 | ||||||||
\(472\) | − | 343.601i | − | 0.727969i | ||||||
\(473\) | 122.284 | 0.258529 | ||||||||
\(474\) | 71.8059i | 0.151489i | ||||||||
\(475\) | 529.578i | 1.11490i | ||||||||
\(476\) | −0.0327499 | − | 0.0427518i | −6.88023e−5 | − | 8.98148e-5i | ||||
\(477\) | 104.905 | 0.219927 | ||||||||
\(478\) | −309.378 | −0.647234 | ||||||||
\(479\) | − | 201.028i | − | 0.419682i | −0.977736 | − | 0.209841i | \(-0.932705\pi\) | ||
0.977736 | − | 0.209841i | \(-0.0672946\pi\) | |||||||
\(480\) | 4.32391 | 0.00900814 | ||||||||
\(481\) | − | 888.511i | − | 1.84722i | ||||||
\(482\) | 314.167i | 0.651799i | ||||||||
\(483\) | 35.3601 | + | 46.1591i | 0.0732092 | + | 0.0955676i | ||||
\(484\) | 1.74841 | 0.00361241 | ||||||||
\(485\) | 314.974 | 0.649432 | ||||||||
\(486\) | 31.4358i | 0.0646827i | ||||||||
\(487\) | 326.372 | 0.670169 | 0.335085 | − | 0.942188i | \(-0.391235\pi\) | ||||
0.335085 | + | 0.942188i | \(0.391235\pi\) | |||||||
\(488\) | − | 155.669i | − | 0.318993i | ||||||
\(489\) | 256.158i | 0.523840i | ||||||||
\(490\) | −223.174 | − | 60.1852i | −0.455457 | − | 0.122827i | ||||
\(491\) | 334.331 | 0.680918 | 0.340459 | − | 0.940259i | \(-0.389417\pi\) | ||||
0.340459 | + | 0.940259i | \(0.389417\pi\) | |||||||
\(492\) | −6.38345 | −0.0129745 | ||||||||
\(493\) | 0.0415888i | 8.43586e-5i | ||||||||
\(494\) | −732.779 | −1.48336 | ||||||||
\(495\) | 85.1454i | 0.172011i | ||||||||
\(496\) | 3.76055i | 0.00758176i | ||||||||
\(497\) | −32.2100 | + | 24.6744i | −0.0648088 | + | 0.0496466i | ||||
\(498\) | 388.995 | 0.781115 | ||||||||
\(499\) | −492.699 | −0.987373 | −0.493687 | − | 0.869640i | \(-0.664351\pi\) | ||||
−0.493687 | + | 0.869640i | \(0.664351\pi\) | |||||||
\(500\) | 6.94824i | 0.0138965i | ||||||||
\(501\) | 171.966 | 0.343246 | ||||||||
\(502\) | 632.578i | 1.26012i | ||||||||
\(503\) | 671.425i | 1.33484i | 0.744681 | + | 0.667421i | \(0.232602\pi\) | ||||
−0.744681 | + | 0.667421i | \(0.767398\pi\) | |||||||
\(504\) | 132.231 | − | 101.295i | 0.262362 | − | 0.200982i | ||||
\(505\) | 126.993 | 0.251471 | ||||||||
\(506\) | 117.342 | 0.231902 | ||||||||
\(507\) | 18.2565i | 0.0360089i | ||||||||
\(508\) | 6.30609 | 0.0124136 | ||||||||
\(509\) | − | 714.776i | − | 1.40428i | −0.712041 | − | 0.702138i | \(-0.752229\pi\) | ||
0.712041 | − | 0.702138i | \(-0.247771\pi\) | |||||||
\(510\) | − | 0.942332i | − | 0.00184771i | ||||||
\(511\) | −75.7628 | − | 98.9010i | −0.148264 | − | 0.193544i | ||||
\(512\) | 498.612 | 0.973851 | ||||||||
\(513\) | −140.913 | −0.274685 | ||||||||
\(514\) | − | 650.008i | − | 1.26461i | ||||||
\(515\) | −374.140 | −0.726486 | ||||||||
\(516\) | 1.16448i | 0.00225674i | ||||||||
\(517\) | 733.021i | 1.41784i | ||||||||
\(518\) | 743.081 | − | 569.235i | 1.43452 | − | 1.09891i | ||||
\(519\) | −89.9963 | −0.173403 | ||||||||
\(520\) | 248.616 | 0.478108 | ||||||||
\(521\) | − | 662.096i | − | 1.27082i | −0.772176 | − | 0.635409i | \(-0.780832\pi\) | ||
0.772176 | − | 0.635409i | \(-0.219168\pi\) | |||||||
\(522\) | 2.18156 | 0.00417924 | ||||||||
\(523\) | 99.8558i | 0.190929i | 0.995433 | + | 0.0954644i | \(0.0304336\pi\) | ||||
−0.995433 | + | 0.0954644i | \(0.969566\pi\) | |||||||
\(524\) | 10.6708i | 0.0203642i | ||||||||
\(525\) | 143.982 | + | 187.955i | 0.274251 | + | 0.358009i | ||||
\(526\) | −584.493 | −1.11120 | ||||||||
\(527\) | 0.0266697 | 5.06067e−5 | ||||||||
\(528\) | − | 341.754i | − | 0.647262i | ||||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | 164.956i | 0.311238i | ||||||||
\(531\) | 129.957i | 0.244739i | ||||||||
\(532\) | −7.70068 | − | 10.0525i | −0.0144750 | − | 0.0188957i | ||||
\(533\) | −740.296 | −1.38892 | ||||||||
\(534\) | 93.6210 | 0.175320 | ||||||||
\(535\) | 247.565i | 0.462739i | ||||||||
\(536\) | 919.502 | 1.71549 | ||||||||
\(537\) | − | 529.708i | − | 0.986420i | ||||||
\(538\) | 446.857i | 0.830589i | ||||||||
\(539\) | −154.798 | + | 574.012i | −0.287196 | + | 1.06496i | ||||
\(540\) | −0.810817 | −0.00150151 | ||||||||
\(541\) | 1011.80 | 1.87024 | 0.935122 | − | 0.354327i | \(-0.115290\pi\) | ||||
0.935122 | + | 0.354327i | \(0.115290\pi\) | |||||||
\(542\) | 648.217i | 1.19597i | ||||||||
\(543\) | −143.839 | −0.264896 | ||||||||
\(544\) | 0.123083i | 0.000226255i | ||||||||
\(545\) | 467.185i | 0.857220i | ||||||||
\(546\) | −260.074 | + | 199.229i | −0.476325 | + | 0.364888i | ||||
\(547\) | −191.473 | −0.350042 | −0.175021 | − | 0.984565i | \(-0.555999\pi\) | ||||
−0.175021 | + | 0.984565i | \(0.555999\pi\) | |||||||
\(548\) | 7.33243 | 0.0133803 | ||||||||
\(549\) | 58.8769i | 0.107244i | ||||||||
\(550\) | 477.804 | 0.868734 | ||||||||
\(551\) | 9.77902i | 0.0177478i | ||||||||
\(552\) | − | 65.8874i | − | 0.119361i | ||||||
\(553\) | −114.238 | + | 87.5118i | −0.206579 | + | 0.158249i | ||||
\(554\) | −339.841 | −0.613431 | ||||||||
\(555\) | 268.666 | 0.484083 | ||||||||
\(556\) | 7.61195i | 0.0136906i | ||||||||
\(557\) | −108.847 | −0.195417 | −0.0977086 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977086 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(558\) | − | 1.39898i | − | 0.00250712i | ||||||
\(559\) | 135.046i | 0.241585i | ||||||||
\(560\) | 161.936 | + | 211.392i | 0.289171 | + | 0.377485i | ||||
\(561\) | −2.42371 | −0.00432034 | ||||||||
\(562\) | −636.288 | −1.13219 | ||||||||
\(563\) | 969.946i | 1.72282i | 0.507913 | + | 0.861409i | \(0.330417\pi\) | ||||
−0.507913 | + | 0.861409i | \(0.669583\pi\) | |||||||
\(564\) | −6.98036 | −0.0123765 | ||||||||
\(565\) | − | 97.0156i | − | 0.171709i | ||||||
\(566\) | 665.782i | 1.17629i | ||||||||
\(567\) | −50.0122 | + | 38.3117i | −0.0882049 | + | 0.0675691i | ||||
\(568\) | 45.9764 | 0.0809444 | ||||||||
\(569\) | −122.881 | −0.215959 | −0.107979 | − | 0.994153i | \(-0.534438\pi\) | ||||
−0.107979 | + | 0.994153i | \(0.534438\pi\) | |||||||
\(570\) | − | 221.576i | − | 0.388730i | ||||||
\(571\) | −752.698 | −1.31821 | −0.659105 | − | 0.752051i | \(-0.729065\pi\) | ||||
−0.659105 | + | 0.752051i | \(0.729065\pi\) | |||||||
\(572\) | 10.8448i | 0.0189594i | ||||||||
\(573\) | − | 188.451i | − | 0.328885i | ||||||
\(574\) | −474.279 | − | 619.126i | −0.826271 | − | 1.07862i | ||||
\(575\) | 93.6533 | 0.162875 | ||||||||
\(576\) | −188.692 | −0.327591 | ||||||||
\(577\) | 431.303i | 0.747493i | 0.927531 | + | 0.373746i | \(0.121927\pi\) | ||||
−0.927531 | + | 0.373746i | \(0.878073\pi\) | |||||||
\(578\) | −582.773 | −1.00826 | ||||||||
\(579\) | 30.3741i | 0.0524596i | ||||||||
\(580\) | 0.0562685i | 9.70147e-5i | ||||||||
\(581\) | 474.079 | + | 618.864i | 0.815971 | + | 1.06517i | ||||
\(582\) | 470.312 | 0.808097 | ||||||||
\(583\) | 424.273 | 0.727740 | ||||||||
\(584\) | 141.171i | 0.241731i | ||||||||
\(585\) | −94.0314 | −0.160737 | ||||||||
\(586\) | 725.769i | 1.23851i | ||||||||
\(587\) | − | 1045.67i | − | 1.78139i | −0.454604 | − | 0.890694i | \(-0.650219\pi\) | ||
0.454604 | − | 0.890694i | \(-0.349781\pi\) | |||||||
\(588\) | −5.46616 | − | 1.47410i | −0.00929619 | − | 0.00250698i | ||||
\(589\) | 6.27102 | 0.0106469 | ||||||||
\(590\) | −204.347 | −0.346351 | ||||||||
\(591\) | 595.962i | 1.00840i | ||||||||
\(592\) | −1078.36 | −1.82156 | ||||||||
\(593\) | − | 569.615i | − | 0.960564i | −0.877114 | − | 0.480282i | \(-0.840534\pi\) | ||
0.877114 | − | 0.480282i | \(-0.159466\pi\) | |||||||
\(594\) | 127.137i | 0.214036i | ||||||||
\(595\) | 1.49919 | − | 1.14845i | 0.00251964 | − | 0.00193016i | ||||
\(596\) | −9.27040 | −0.0155544 | ||||||||
\(597\) | −227.739 | −0.381473 | ||||||||
\(598\) | 129.588i | 0.216703i | ||||||||
\(599\) | 297.266 | 0.496270 | 0.248135 | − | 0.968725i | \(-0.420182\pi\) | ||||
0.248135 | + | 0.968725i | \(0.420182\pi\) | |||||||
\(600\) | − | 268.286i | − | 0.447143i | ||||||
\(601\) | − | 436.954i | − | 0.727045i | −0.931585 | − | 0.363523i | \(-0.881574\pi\) | ||
0.931585 | − | 0.363523i | \(-0.118426\pi\) | |||||||
\(602\) | −112.942 | + | 86.5188i | −0.187611 | + | 0.143719i | ||||
\(603\) | −347.773 | −0.576738 | ||||||||
\(604\) | −14.6815 | −0.0243071 | ||||||||
\(605\) | 61.3117i | 0.101342i | ||||||||
\(606\) | 189.623 | 0.312908 | ||||||||
\(607\) | − | 438.780i | − | 0.722867i | −0.932398 | − | 0.361433i | \(-0.882287\pi\) | ||
0.932398 | − | 0.361433i | \(-0.117713\pi\) | |||||||
\(608\) | 28.9411i | 0.0476005i | ||||||||
\(609\) | 2.65873 | + | 3.47071i | 0.00436573 | + | 0.00569903i | ||||
\(610\) | −92.5797 | −0.151770 | ||||||||
\(611\) | −809.521 | −1.32491 | ||||||||
\(612\) | − | 0.0230804i | − | 3.77130e-5i | ||||||
\(613\) | 466.673 | 0.761294 | 0.380647 | − | 0.924720i | \(-0.375701\pi\) | ||||
0.380647 | + | 0.924720i | \(0.375701\pi\) | |||||||
\(614\) | − | 388.797i | − | 0.633220i | ||||||
\(615\) | − | 223.849i | − | 0.363983i | ||||||
\(616\) | 534.786 | − | 409.671i | 0.868159 | − | 0.665051i | ||||
\(617\) | 1071.16 | 1.73608 | 0.868040 | − | 0.496494i | \(-0.165380\pi\) | ||||
0.868040 | + | 0.496494i | \(0.165380\pi\) | |||||||
\(618\) | −558.658 | −0.903977 | ||||||||
\(619\) | − | 797.671i | − | 1.28864i | −0.764754 | − | 0.644322i | \(-0.777140\pi\) | ||
0.764754 | − | 0.644322i | \(-0.222860\pi\) | |||||||
\(620\) | 0.0360835 | 5.81991e−5 | ||||||||
\(621\) | 24.9199i | 0.0401286i | ||||||||
\(622\) | 970.597i | 1.56044i | ||||||||
\(623\) | 114.098 | + | 148.944i | 0.183144 | + | 0.239076i | ||||
\(624\) | 377.421 | 0.604841 | ||||||||
\(625\) | 244.547 | 0.391275 | ||||||||
\(626\) | − | 758.737i | − | 1.21204i | ||||||
\(627\) | −569.902 | −0.908935 | ||||||||
\(628\) | − | 9.19130i | − | 0.0146358i | ||||||
\(629\) | 7.64774i | 0.0121586i | ||||||||
\(630\) | −60.2423 | − | 78.6405i | −0.0956228 | − | 0.124826i | ||||
\(631\) | 172.064 | 0.272684 | 0.136342 | − | 0.990662i | \(-0.456465\pi\) | ||||
0.136342 | + | 0.990662i | \(0.456465\pi\) | |||||||
\(632\) | 163.063 | 0.258011 | ||||||||
\(633\) | − | 277.069i | − | 0.437708i | ||||||
\(634\) | 450.340 | 0.710316 | ||||||||
\(635\) | 221.137i | 0.348247i | ||||||||
\(636\) | 4.04023i | 0.00635257i | ||||||||
\(637\) | −633.917 | − | 170.954i | −0.995161 | − | 0.268373i | ||||
\(638\) | 8.82298 | 0.0138291 | ||||||||
\(639\) | −17.3892 | −0.0272131 | ||||||||
\(640\) | − | 306.691i | − | 0.479204i | ||||||
\(641\) | 865.373 | 1.35004 | 0.675018 | − | 0.737801i | \(-0.264136\pi\) | ||||
0.675018 | + | 0.737801i | \(0.264136\pi\) | |||||||
\(642\) | 369.659i | 0.575793i | ||||||||
\(643\) | − | 542.527i | − | 0.843744i | −0.906655 | − | 0.421872i | \(-0.861373\pi\) | ||
0.906655 | − | 0.421872i | \(-0.138627\pi\) | |||||||
\(644\) | −1.77774 | + | 1.36183i | −0.00276046 | + | 0.00211464i | ||||
\(645\) | −40.8349 | −0.0633100 | ||||||||
\(646\) | 6.30730 | 0.00976362 | ||||||||
\(647\) | − | 788.734i | − | 1.21906i | −0.792762 | − | 0.609531i | \(-0.791358\pi\) | ||
0.792762 | − | 0.609531i | \(-0.208642\pi\) | |||||||
\(648\) | 71.3872 | 0.110165 | ||||||||
\(649\) | 525.589i | 0.809844i | ||||||||
\(650\) | 527.669i | 0.811799i | ||||||||
\(651\) | 2.22567 | − | 1.70497i | 0.00341885 | − | 0.00261900i | ||||
\(652\) | −9.86546 | −0.0151311 | ||||||||
\(653\) | 267.720 | 0.409985 | 0.204992 | − | 0.978764i | \(-0.434283\pi\) | ||||
0.204992 | + | 0.978764i | \(0.434283\pi\) | |||||||
\(654\) | 697.590i | 1.06665i | ||||||||
\(655\) | −374.196 | −0.571291 | ||||||||
\(656\) | 898.480i | 1.36963i | ||||||||
\(657\) | − | 53.3935i | − | 0.0812687i | ||||||
\(658\) | −518.629 | − | 677.020i | −0.788190 | − | 1.02891i | ||||
\(659\) | −939.789 | −1.42608 | −0.713042 | − | 0.701122i | \(-0.752683\pi\) | ||||
−0.713042 | + | 0.701122i | \(0.752683\pi\) | |||||||
\(660\) | −3.27922 | −0.00496852 | ||||||||
\(661\) | − | 220.558i | − | 0.333674i | −0.985984 | − | 0.166837i | \(-0.946645\pi\) | ||
0.985984 | − | 0.166837i | \(-0.0533553\pi\) | |||||||
\(662\) | 163.958 | 0.247671 | ||||||||
\(663\) | − | 2.67666i | − | 0.00403719i | ||||||
\(664\) | − | 883.365i | − | 1.33037i | ||||||
\(665\) | 352.512 | − | 270.041i | 0.530094 | − | 0.406077i | ||||
\(666\) | 401.166 | 0.602351 | ||||||||
\(667\) | 1.72937 | 0.00259276 | ||||||||
\(668\) | 6.62296i | 0.00991461i | ||||||||
\(669\) | 647.843 | 0.968375 | ||||||||
\(670\) | − | 546.848i | − | 0.816191i | ||||||
\(671\) | 238.118i | 0.354871i | ||||||||
\(672\) | 7.86854 | + | 10.2716i | 0.0117091 | + | 0.0152851i | ||||
\(673\) | 227.275 | 0.337704 | 0.168852 | − | 0.985641i | \(-0.445994\pi\) | ||||
0.168852 | + | 0.985641i | \(0.445994\pi\) | |||||||
\(674\) | 981.979 | 1.45694 | ||||||||
\(675\) | 101.471i | 0.150327i | ||||||||
\(676\) | −0.703116 | −0.00104011 | ||||||||
\(677\) | − | 808.648i | − | 1.19446i | −0.802071 | − | 0.597229i | \(-0.796268\pi\) | ||
0.802071 | − | 0.597229i | \(-0.203732\pi\) | |||||||
\(678\) | − | 144.862i | − | 0.213660i | ||||||
\(679\) | 573.183 | + | 748.234i | 0.844157 | + | 1.10197i | ||||
\(680\) | −2.13993 | −0.00314696 | ||||||||
\(681\) | 54.7869 | 0.0804507 | ||||||||
\(682\) | − | 5.65794i | − | 0.00829610i | ||||||
\(683\) | −799.836 | −1.17106 | −0.585532 | − | 0.810650i | \(-0.699114\pi\) | ||||
−0.585532 | + | 0.810650i | \(0.699114\pi\) | |||||||
\(684\) | − | 5.42702i | − | 0.00793425i | ||||||
\(685\) | 257.127i | 0.375369i | ||||||||
\(686\) | −263.154 | − | 639.683i | −0.383607 | − | 0.932482i | ||||
\(687\) | 652.134 | 0.949249 | ||||||||
\(688\) | 163.902 | 0.238230 | ||||||||
\(689\) | 468.551i | 0.680045i | ||||||||
\(690\) | −39.1847 | −0.0567894 | ||||||||
\(691\) | − | 497.520i | − | 0.719999i | −0.932952 | − | 0.360000i | \(-0.882777\pi\) | ||
0.932952 | − | 0.360000i | \(-0.117223\pi\) | |||||||
\(692\) | − | 3.46605i | − | 0.00500874i | ||||||
\(693\) | −202.266 | + | 154.945i | −0.291871 | + | 0.223587i | ||||
\(694\) | −57.2787 | −0.0825341 | ||||||||
\(695\) | −266.929 | −0.384071 | ||||||||
\(696\) | − | 4.95408i | − | 0.00711793i | ||||||
\(697\) | 6.37200 | 0.00914204 | ||||||||
\(698\) | 1386.81i | 1.98684i | ||||||||
\(699\) | − | 4.58963i | − | 0.00656599i | ||||||
\(700\) | −7.23873 | + | 5.54521i | −0.0103410 | + | 0.00792172i | ||||
\(701\) | 141.312 | 0.201586 | 0.100793 | − | 0.994907i | \(-0.467862\pi\) | ||||
0.100793 | + | 0.994907i | \(0.467862\pi\) | |||||||
\(702\) | −140.406 | −0.200008 | ||||||||
\(703\) | 1798.26i | 2.55798i | ||||||||
\(704\) | −763.136 | −1.08400 | ||||||||
\(705\) | − | 244.781i | − | 0.347208i | ||||||
\(706\) | 6.30773i | 0.00893446i | ||||||||
\(707\) | 231.098 | + | 301.676i | 0.326871 | + | 0.426699i | ||||
\(708\) | −5.00504 | −0.00706927 | ||||||||
\(709\) | 460.837 | 0.649982 | 0.324991 | − | 0.945717i | \(-0.394639\pi\) | ||||
0.324991 | + | 0.945717i | \(0.394639\pi\) | |||||||
\(710\) | − | 27.3432i | − | 0.0385115i | ||||||
\(711\) | −61.6736 | −0.0867420 | ||||||||
\(712\) | − | 212.603i | − | 0.298599i | ||||||
\(713\) | − | 1.10900i | − | 0.00155540i | ||||||
\(714\) | 2.23855 | − | 1.71483i | 0.00313522 | − | 0.00240173i | ||||
\(715\) | −380.295 | −0.531881 | ||||||||
\(716\) | 20.4007 | 0.0284926 | ||||||||
\(717\) | − | 265.723i | − | 0.370603i | ||||||
\(718\) | 937.132 | 1.30520 | ||||||||
\(719\) | − | 1300.87i | − | 1.80928i | −0.426178 | − | 0.904639i | \(-0.640140\pi\) | ||
0.426178 | − | 0.904639i | \(-0.359860\pi\) | |||||||
\(720\) | 114.124i | 0.158505i | ||||||||
\(721\) | −680.852 | − | 888.786i | −0.944316 | − | 1.23271i | ||||
\(722\) | 755.077 | 1.04581 | ||||||||
\(723\) | −269.836 | −0.373217 | ||||||||
\(724\) | − | 5.53968i | − | 0.00765149i | ||||||
\(725\) | 7.04180 | 0.00971283 | ||||||||
\(726\) | 91.5493i | 0.126101i | ||||||||
\(727\) | 327.305i | 0.450214i | 0.974334 | + | 0.225107i | \(0.0722731\pi\) | ||||
−0.974334 | + | 0.225107i | \(0.927727\pi\) | |||||||
\(728\) | 452.426 | + | 590.598i | 0.621464 | + | 0.811261i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 83.9575 | 0.115010 | ||||||||
\(731\) | − | 1.16239i | − | 0.00159014i | ||||||
\(732\) | −2.26754 | −0.00309773 | ||||||||
\(733\) | − | 1217.68i | − | 1.66123i | −0.556850 | − | 0.830613i | \(-0.687990\pi\) | ||
0.556850 | − | 0.830613i | \(-0.312010\pi\) | |||||||
\(734\) | − | 568.800i | − | 0.774932i | ||||||
\(735\) | 51.6926 | − | 191.683i | 0.0703301 | − | 0.260793i | ||||
\(736\) | 5.11810 | 0.00695394 | ||||||||
\(737\) | −1406.51 | −1.90843 | ||||||||
\(738\) | − | 334.247i | − | 0.452909i | ||||||
\(739\) | 73.9055 | 0.100007 | 0.0500037 | − | 0.998749i | \(-0.484077\pi\) | ||||
0.0500037 | + | 0.998749i | \(0.484077\pi\) | |||||||
\(740\) | 10.3472i | 0.0139827i | ||||||||
\(741\) | − | 629.379i | − | 0.849364i | ||||||
\(742\) | −391.860 | + | 300.183i | −0.528113 | + | 0.404559i | ||||
\(743\) | −923.482 | −1.24291 | −0.621455 | − | 0.783450i | \(-0.713458\pi\) | ||||
−0.621455 | + | 0.783450i | \(0.713458\pi\) | |||||||
\(744\) | −3.17692 | −0.00427005 | ||||||||
\(745\) | − | 325.087i | − | 0.436358i | ||||||
\(746\) | −390.335 | −0.523237 | ||||||||
\(747\) | 334.105i | 0.447263i | ||||||||
\(748\) | − | 0.0933449i | − | 0.000124793i | ||||||
\(749\) | −588.101 | + | 450.513i | −0.785182 | + | 0.601486i | ||||
\(750\) | −363.820 | −0.485093 | ||||||||
\(751\) | 484.296 | 0.644868 | 0.322434 | − | 0.946592i | \(-0.395499\pi\) | ||||
0.322434 | + | 0.946592i | \(0.395499\pi\) | |||||||
\(752\) | 982.497i | 1.30651i | ||||||||
\(753\) | −543.317 | −0.721537 | ||||||||
\(754\) | 9.74377i | 0.0129228i | ||||||||
\(755\) | − | 514.839i | − | 0.681906i | ||||||
\(756\) | −1.47550 | − | 1.92613i | −0.00195173 | − | 0.00254779i | ||||
\(757\) | 1119.03 | 1.47824 | 0.739121 | − | 0.673573i | \(-0.235241\pi\) | ||||
0.739121 | + | 0.673573i | \(0.235241\pi\) | |||||||
\(758\) | 343.893 | 0.453684 | ||||||||
\(759\) | 100.784i | 0.132786i | ||||||||
\(760\) | −503.175 | −0.662072 | ||||||||
\(761\) | 762.609i | 1.00211i | 0.865414 | + | 0.501057i | \(0.167055\pi\) | ||||
−0.865414 | + | 0.501057i | \(0.832945\pi\) | |||||||
\(762\) | 330.196i | 0.433329i | ||||||||
\(763\) | −1109.82 | + | 850.172i | −1.45454 | + | 1.11425i | ||||
\(764\) | 7.25785 | 0.00949981 | ||||||||
\(765\) | 0.809363 | 0.00105799 | ||||||||
\(766\) | − | 1035.75i | − | 1.35216i | ||||||
\(767\) | −580.441 | −0.756768 | ||||||||
\(768\) | − | 22.1775i | − | 0.0288769i | ||||||
\(769\) | − | 80.1758i | − | 0.104260i | −0.998640 | − | 0.0521299i | \(-0.983399\pi\) | ||
0.998640 | − | 0.0521299i | \(-0.0166010\pi\) | |||||||
\(770\) | −243.641 | − | 318.049i | −0.316416 | − | 0.413051i | ||||
\(771\) | 558.288 | 0.724109 | ||||||||
\(772\) | −1.16980 | −0.00151529 | ||||||||
\(773\) | − | 698.654i | − | 0.903822i | −0.892063 | − | 0.451911i | \(-0.850743\pi\) | ||
0.892063 | − | 0.451911i | \(-0.149257\pi\) | |||||||
\(774\) | −60.9738 | −0.0787775 | ||||||||
\(775\) | − | 4.51572i | − | 0.00582673i | ||||||
\(776\) | − | 1068.03i | − | 1.37632i | ||||||
\(777\) | 488.912 | + | 638.227i | 0.629230 | + | 0.821399i | ||||
\(778\) | −980.309 | −1.26004 | ||||||||
\(779\) | 1498.29 | 1.92335 | ||||||||
\(780\) | − | 3.62145i | − | 0.00464288i | ||||||
\(781\) | −70.3277 | −0.0900483 | ||||||||
\(782\) | − | 1.11542i | − | 0.00142636i | ||||||
\(783\) | 1.87373i | 0.00239301i | ||||||||
\(784\) | −207.482 | + | 769.371i | −0.264646 | + | 0.981340i | ||||
\(785\) | 322.313 | 0.410590 | ||||||||
\(786\) | −558.740 | −0.710866 | ||||||||
\(787\) | 1245.34i | 1.58239i | 0.611562 | + | 0.791197i | \(0.290542\pi\) | ||||
−0.611562 | + | 0.791197i | \(0.709458\pi\) | |||||||
\(788\) | −22.9524 | −0.0291274 | ||||||||
\(789\) | − | 502.017i | − | 0.636270i | ||||||
\(790\) | − | 96.9773i | − | 0.122756i | ||||||
\(791\) | 230.465 | − | 176.547i | 0.291359 | − | 0.223194i | ||||
\(792\) | 288.714 | 0.364538 | ||||||||
\(793\) | −262.969 | −0.331613 | ||||||||
\(794\) | 155.637i | 0.196017i | ||||||||
\(795\) | −141.680 | −0.178213 | ||||||||
\(796\) | − | 8.77096i | − | 0.0110188i | ||||||
\(797\) | − | 91.7211i | − | 0.115083i | −0.998343 | − | 0.0575415i | \(-0.981674\pi\) | ||
0.998343 | − | 0.0575415i | \(-0.0183261\pi\) | |||||||
\(798\) | 526.363 | − | 403.219i | 0.659603 | − | 0.505287i | ||||
\(799\) | 6.96785 | 0.00872071 | ||||||||
\(800\) | 20.8403 | 0.0260504 | ||||||||
\(801\) | 80.4104i | 0.100388i | ||||||||
\(802\) | 918.259 | 1.14496 | ||||||||
\(803\) | − | 215.942i | − | 0.268919i | ||||||
\(804\) | − | 13.3939i | − | 0.0166590i | ||||||
\(805\) | −47.7555 | − | 62.3401i | −0.0593236 | − | 0.0774412i | ||||
\(806\) | 6.24842 | 0.00775238 | ||||||||
\(807\) | −383.802 | −0.475592 | ||||||||
\(808\) | − | 430.611i | − | 0.532935i | ||||||
\(809\) | 480.075 | 0.593418 | 0.296709 | − | 0.954968i | \(-0.404111\pi\) | ||||
0.296709 | + | 0.954968i | \(0.404111\pi\) | |||||||
\(810\) | − | 42.4556i | − | 0.0524143i | ||||||
\(811\) | 324.813i | 0.400510i | 0.979744 | + | 0.200255i | \(0.0641770\pi\) | ||||
−0.979744 | + | 0.200255i | \(0.935823\pi\) | |||||||
\(812\) | −0.133668 | + | 0.102396i | −0.000164616 | + | 0.000126104i | ||||
\(813\) | −556.750 | −0.684809 | ||||||||
\(814\) | 1622.45 | 1.99319 | ||||||||
\(815\) | − | 345.954i | − | 0.424483i | ||||||
\(816\) | −3.24860 | −0.00398113 | ||||||||
\(817\) | − | 273.320i | − | 0.334541i | ||||||
\(818\) | 715.084i | 0.874185i | ||||||||
\(819\) | −171.116 | − | 223.375i | −0.208933 | − | 0.272742i | ||||
\(820\) | 8.62115 | 0.0105136 | ||||||||
\(821\) | 623.212 | 0.759089 | 0.379544 | − | 0.925174i | \(-0.376081\pi\) | ||||
0.379544 | + | 0.925174i | \(0.376081\pi\) | |||||||
\(822\) | 383.937i | 0.467077i | ||||||||
\(823\) | 173.202 | 0.210452 | 0.105226 | − | 0.994448i | \(-0.466443\pi\) | ||||
0.105226 | + | 0.994448i | \(0.466443\pi\) | |||||||
\(824\) | 1268.65i | 1.53962i | ||||||||
\(825\) | 410.383i | 0.497433i | ||||||||
\(826\) | −371.866 | − | 485.435i | −0.450201 | − | 0.587694i | ||||
\(827\) | −1124.73 | −1.36001 | −0.680006 | − | 0.733206i | \(-0.738023\pi\) | ||||
−0.680006 | + | 0.733206i | \(0.738023\pi\) | |||||||
\(828\) | −0.959744 | −0.00115911 | ||||||||
\(829\) | 1439.63i | 1.73659i | 0.496051 | + | 0.868293i | \(0.334783\pi\) | ||||
−0.496051 | + | 0.868293i | \(0.665217\pi\) | |||||||
\(830\) | −525.357 | −0.632960 | ||||||||
\(831\) | − | 291.887i | − | 0.351248i | ||||||
\(832\) | − | 842.779i | − | 1.01296i | ||||||
\(833\) | 5.45636 | + | 1.47146i | 0.00655025 | + | 0.00176646i | ||||
\(834\) | −398.573 | −0.477905 | ||||||||
\(835\) | −232.248 | −0.278142 | ||||||||
\(836\) | − | 21.9487i | − | 0.0262545i | ||||||
\(837\) | 1.20157 | 0.00143557 | ||||||||
\(838\) | 480.703i | 0.573632i | ||||||||
\(839\) | 1342.90i | 1.60060i | 0.599602 | + | 0.800298i | \(0.295326\pi\) | ||||
−0.599602 | + | 0.800298i | \(0.704674\pi\) | |||||||
\(840\) | −178.584 | + | 136.804i | −0.212600 | + | 0.162861i | ||||
\(841\) | −840.870 | −0.999845 | ||||||||
\(842\) | 164.113 | 0.194908 | ||||||||
\(843\) | − | 546.504i | − | 0.648284i | ||||||
\(844\) | 10.6708 | 0.0126431 | ||||||||
\(845\) | − | 24.6563i | − | 0.0291790i | ||||||
\(846\) | − | 365.502i | − | 0.432035i | ||||||
\(847\) | −145.648 | + | 111.574i | −0.171958 | + | 0.131728i | ||||
\(848\) | 568.669 | 0.670601 | ||||||||
\(849\) | −571.835 | −0.673540 | ||||||||
\(850\) | − | 4.54184i | − | 0.00534334i | ||||||
\(851\) | 318.013 | 0.373694 | ||||||||
\(852\) | − | 0.669712i | − | 0.000786047i | ||||||
\(853\) | 58.2855i | 0.0683301i | 0.999416 | + | 0.0341650i | \(0.0108772\pi\) | ||||
−0.999416 | + | 0.0341650i | \(0.989123\pi\) | |||||||
\(854\) | −168.474 | − | 219.927i | −0.197277 | − | 0.257526i | ||||
\(855\) | 190.310 | 0.222585 | ||||||||
\(856\) | 839.454 | 0.980670 | ||||||||
\(857\) | 325.688i | 0.380032i | 0.981781 | + | 0.190016i | \(0.0608540\pi\) | ||||
−0.981781 | + | 0.190016i | \(0.939146\pi\) | |||||||
\(858\) | −567.848 | −0.661828 | ||||||||
\(859\) | 389.076i | 0.452940i | 0.974018 | + | 0.226470i | \(0.0727186\pi\) | ||||
−0.974018 | + | 0.226470i | \(0.927281\pi\) | |||||||
\(860\) | − | 1.57268i | − | 0.00182870i | ||||||
\(861\) | 531.763 | − | 407.355i | 0.617611 | − | 0.473119i | ||||
\(862\) | −516.838 | −0.599580 | ||||||||
\(863\) | −757.604 | −0.877872 | −0.438936 | − | 0.898518i | \(-0.644645\pi\) | ||||
−0.438936 | + | 0.898518i | \(0.644645\pi\) | |||||||
\(864\) | 5.54532i | 0.00641820i | ||||||||
\(865\) | 121.544 | 0.140514 | ||||||||
\(866\) | 47.7078i | 0.0550898i | ||||||||
\(867\) | − | 500.540i | − | 0.577324i | ||||||
\(868\) | 0.0656638 | + | 0.0857177i | 7.56496e−5 | + | 9.87532e-5i | ||||
\(869\) | −249.429 | −0.287030 | ||||||||
\(870\) | −2.94630 | −0.00338656 | ||||||||
\(871\) | − | 1553.30i | − | 1.78335i | ||||||
\(872\) | 1584.15 | 1.81668 | ||||||||
\(873\) | 403.948i | 0.462713i | ||||||||
\(874\) | − | 262.274i | − | 0.300085i | ||||||
\(875\) | −443.397 | − | 578.812i | −0.506740 | − | 0.661499i | ||||
\(876\) | 2.05636 | 0.00234744 | ||||||||
\(877\) | 1016.23 | 1.15875 | 0.579377 | − | 0.815060i | \(-0.303296\pi\) | ||||
0.579377 | + | 0.815060i | \(0.303296\pi\) | |||||||
\(878\) | 838.422i | 0.954923i | ||||||||
\(879\) | −623.358 | −0.709167 | ||||||||
\(880\) | 461.555i | 0.524495i | ||||||||
\(881\) | 671.812i | 0.762556i | 0.924460 | + | 0.381278i | \(0.124516\pi\) | ||||
−0.924460 | + | 0.381278i | \(0.875484\pi\) | |||||||
\(882\) | 77.1863 | − | 286.216i | 0.0875128 | − | 0.324508i | ||||
\(883\) | 1262.79 | 1.43012 | 0.715058 | − | 0.699065i | \(-0.246400\pi\) | ||||
0.715058 | + | 0.699065i | \(0.246400\pi\) | |||||||
\(884\) | 0.103087 | 0.000116614 | ||||||||
\(885\) | − | 175.513i | − | 0.198319i | ||||||
\(886\) | 1699.80 | 1.91851 | ||||||||
\(887\) | − | 1304.28i | − | 1.47044i | −0.677829 | − | 0.735219i | \(-0.737079\pi\) | ||
0.677829 | − | 0.735219i | \(-0.262921\pi\) | |||||||
\(888\) | − | 911.003i | − | 1.02590i | ||||||
\(889\) | −525.319 | + | 402.419i | −0.590911 | + | 0.452665i | ||||
\(890\) | −126.440 | −0.142067 | ||||||||
\(891\) | −109.197 | −0.122556 | ||||||||
\(892\) | 24.9505i | 0.0279714i | ||||||||
\(893\) | 1638.39 | 1.83470 | ||||||||
\(894\) | − | 485.412i | − | 0.542967i | ||||||
\(895\) | 715.395i | 0.799325i | ||||||||
\(896\) | 728.556 | − | 558.108i | 0.813120 | − | 0.622888i | ||||
\(897\) | −111.303 | −0.124083 | ||||||||
\(898\) | 432.914 | 0.482087 | ||||||||
\(899\) | − | 0.0833858i | − | 9.27540e-5i | ||||||
\(900\) | −3.90796 | −0.00434218 | ||||||||
\(901\) | − | 4.03299i | − | 0.00447613i | ||||||
\(902\) | − | 1351.81i | − | 1.49868i | ||||||
\(903\) | −74.3104 | − | 97.0050i | −0.0822928 | − | 0.107425i | ||||
\(904\) | −328.964 | −0.363899 | ||||||||
\(905\) | 194.261 | 0.214653 | ||||||||
\(906\) | − | 768.746i | − | 0.848505i | ||||||
\(907\) | −1536.55 | −1.69410 | −0.847051 | − | 0.531512i | \(-0.821624\pi\) | ||||
−0.847051 | + | 0.531512i | \(0.821624\pi\) | |||||||
\(908\) | 2.11002i | 0.00232381i | ||||||||
\(909\) | 162.865i | 0.179170i | ||||||||
\(910\) | 351.242 | − | 269.068i | 0.385980 | − | 0.295679i | ||||
\(911\) | 1717.65 | 1.88546 | 0.942728 | − | 0.333561i | \(-0.108250\pi\) | ||||
0.942728 | + | 0.333561i | \(0.108250\pi\) | |||||||
\(912\) | −763.862 | −0.837568 | ||||||||
\(913\) | 1351.24i | 1.48000i | ||||||||
\(914\) | 970.112 | 1.06139 | ||||||||
\(915\) | − | 79.5161i | − | 0.0869028i | ||||||
\(916\) | 25.1158i | 0.0274190i | ||||||||
\(917\) | −680.952 | − | 888.917i | −0.742587 | − | 0.969375i | ||||
\(918\) | 1.20852 | 0.00131647 | ||||||||
\(919\) | 600.919 | 0.653883 | 0.326942 | − | 0.945044i | \(-0.393982\pi\) | ||||
0.326942 | + | 0.945044i | \(0.393982\pi\) | |||||||
\(920\) | 88.9841i | 0.0967218i | ||||||||
\(921\) | 333.935 | 0.362579 | ||||||||
\(922\) | − | 852.988i | − | 0.925150i | ||||||
\(923\) | − | 77.6673i | − | 0.0841466i | ||||||
\(924\) | −5.96744 | − | 7.78992i | −0.00645827 | − | 0.00843065i | ||||
\(925\) | 1294.91 | 1.39991 | ||||||||
\(926\) | −1296.59 | −1.40020 | ||||||||
\(927\) | − | 479.828i | − | 0.517613i | ||||||
\(928\) | 0.384831 | 0.000414688 | ||||||||
\(929\) | − | 145.356i | − | 0.156465i | −0.996935 | − | 0.0782323i | \(-0.975072\pi\) | ||
0.996935 | − | 0.0782323i | \(-0.0249276\pi\) | |||||||
\(930\) | 1.88938i | 0.00203160i | ||||||||
\(931\) | 1282.99 | + | 345.993i | 1.37807 | + | 0.371636i | ||||
\(932\) | 0.176761 | 0.000189658 | ||||||||
\(933\) | −833.639 | −0.893504 | ||||||||
\(934\) | 21.4545i | 0.0229705i | ||||||||
\(935\) | 3.27334 | 0.00350090 | ||||||||
\(936\) | 318.845i | 0.340647i | ||||||||
\(937\) | − | 55.3524i | − | 0.0590741i | −0.999564 | − | 0.0295370i | \(-0.990597\pi\) | ||
0.999564 | − | 0.0295370i | \(-0.00940330\pi\) | |||||||
\(938\) | 1299.06 | − | 995.141i | 1.38493 | − | 1.06092i | ||||
\(939\) | 651.674 | 0.694008 | ||||||||
\(940\) | 9.42731 | 0.0100291 | ||||||||
\(941\) | − | 748.881i | − | 0.795836i | −0.917421 | − | 0.397918i | \(-0.869733\pi\) | ||
0.917421 | − | 0.397918i | \(-0.130267\pi\) | |||||||
\(942\) | 481.270 | 0.510903 | ||||||||
\(943\) | − | 264.965i | − | 0.280981i | ||||||
\(944\) | 704.468i | 0.746258i | ||||||||
\(945\) | 67.5438 | − | 51.7417i | 0.0714749 | − | 0.0547532i | ||||
\(946\) | −246.599 | −0.260675 | ||||||||
\(947\) | 323.543 | 0.341650 | 0.170825 | − | 0.985301i | \(-0.445357\pi\) | ||||
0.170825 | + | 0.985301i | \(0.445357\pi\) | |||||||
\(948\) | − | 2.37525i | − | 0.00250553i | ||||||
\(949\) | 238.478 | 0.251294 | ||||||||
\(950\) | − | 1067.95i | − | 1.12416i | ||||||
\(951\) | 386.794i | 0.406724i | ||||||||
\(952\) | −3.89419 | − | 5.08349i | −0.00409054 | − | 0.00533980i | ||||
\(953\) | 848.969 | 0.890839 | 0.445419 | − | 0.895322i | \(-0.353055\pi\) | ||||
0.445419 | + | 0.895322i | \(0.353055\pi\) | |||||||
\(954\) | −211.553 | −0.221753 | ||||||||
\(955\) | 254.512i | 0.266505i | ||||||||
\(956\) | 10.2338 | 0.0107048 | ||||||||
\(957\) | 7.57800i | 0.00791849i | ||||||||
\(958\) | 405.394i | 0.423167i | ||||||||
\(959\) | −610.817 | + | 467.914i | −0.636931 | + | 0.487919i | ||||
\(960\) | 254.838 | 0.265456 | ||||||||
\(961\) | 960.947 | 0.999944 | ||||||||
\(962\) | 1791.78i | 1.86255i | ||||||||
\(963\) | −317.497 | −0.329696 | ||||||||
\(964\) | − | 10.3922i | − | 0.0107803i | ||||||
\(965\) | − | 41.0217i | − | 0.0425096i | ||||||
\(966\) | −71.3074 | − | 93.0849i | −0.0738172 | − | 0.0963612i | ||||
\(967\) | −78.0643 | −0.0807283 | −0.0403642 | − | 0.999185i | \(-0.512852\pi\) | ||||
−0.0403642 | + | 0.999185i | \(0.512852\pi\) | |||||||
\(968\) | 207.898 | 0.214771 | ||||||||
\(969\) | 5.41730i | 0.00559060i | ||||||||
\(970\) | −635.180 | −0.654824 | ||||||||
\(971\) | − | 22.2874i | − | 0.0229530i | −0.999934 | − | 0.0114765i | \(-0.996347\pi\) | ||
0.999934 | − | 0.0114765i | \(-0.00365317\pi\) | |||||||
\(972\) | − | 1.03986i | − | 0.00106981i | ||||||
\(973\) | −485.752 | − | 634.102i | −0.499231 | − | 0.651698i | ||||
\(974\) | −658.165 | −0.675734 | ||||||||
\(975\) | −453.211 | −0.464832 | ||||||||
\(976\) | 319.159i | 0.327008i | ||||||||
\(977\) | −1163.05 | −1.19043 | −0.595216 | − | 0.803566i | \(-0.702934\pi\) | ||||
−0.595216 | + | 0.803566i | \(0.702934\pi\) | |||||||
\(978\) | − | 516.570i | − | 0.528190i | ||||||
\(979\) | 325.207i | 0.332183i | ||||||||
\(980\) | 7.38231 | + | 1.99085i | 0.00753297 | + | 0.00203148i | ||||
\(981\) | −599.155 | −0.610760 | ||||||||
\(982\) | −674.214 | −0.686573 | ||||||||
\(983\) | 694.119i | 0.706123i | 0.935600 | + | 0.353062i | \(0.114859\pi\) | ||||
−0.935600 | + | 0.353062i | \(0.885141\pi\) | |||||||
\(984\) | −759.037 | −0.771379 | ||||||||
\(985\) | − | 804.875i | − | 0.817132i | ||||||
\(986\) | − | 0.0838682i | − | 8.50591e-5i | ||||||
\(987\) | 581.488 | − | 445.447i | 0.589147 | − | 0.451314i | ||||
\(988\) | 24.2394 | 0.0245338 | ||||||||
\(989\) | −48.3353 | −0.0488729 | ||||||||
\(990\) | − | 171.705i | − | 0.173439i | ||||||
\(991\) | −161.169 | −0.162632 | −0.0813162 | − | 0.996688i | \(-0.525912\pi\) | ||||
−0.0813162 | + | 0.996688i | \(0.525912\pi\) | |||||||
\(992\) | − | 0.246781i | − | 0.000248772i | ||||||
\(993\) | 140.822i | 0.141815i | ||||||||
\(994\) | 64.9549 | − | 49.7585i | 0.0653470 | − | 0.0500588i | ||||
\(995\) | 307.573 | 0.309118 | ||||||||
\(996\) | −12.8675 | −0.0129191 | ||||||||
\(997\) | 1338.45i | 1.34248i | 0.741241 | + | 0.671239i | \(0.234238\pi\) | ||||
−0.741241 | + | 0.671239i | \(0.765762\pi\) | |||||||
\(998\) | 993.581 | 0.995572 | ||||||||
\(999\) | 344.559i | 0.344904i |
(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 | 483.3.g.a.139.17 | ✓ | 60 | |
7.6 | odd | 2 | inner | 483.3.g.a.139.18 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.g.a.139.17 | ✓ | 60 | 1.1 | even | 1 | trivial | |
483.3.g.a.139.18 | yes | 60 | 7.6 | odd | 2 | inner |