Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(235,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.235");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.c (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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 177) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.26 | ||
Character | \(\chi\) | \(=\) | 531.235 |
Dual form | 531.5.c.d.235.15 |
$q$-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 \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33963i | 0.584908i | 0.956280 | + | 0.292454i | \(0.0944718\pi\) | ||||
−0.956280 | + | 0.292454i | \(0.905528\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.5261 | 0.657883 | ||||||||
\(5\) | −30.0439 | −1.20176 | −0.600878 | − | 0.799341i | \(-0.705182\pi\) | ||||
−0.600878 | + | 0.799341i | \(0.705182\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −41.7287 | −0.851607 | −0.425803 | − | 0.904816i | \(-0.640008\pi\) | ||||
−0.425803 | + | 0.904816i | \(0.640008\pi\) | |||||||
\(8\) | 62.0613i | 0.969708i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 70.2916i | − | 0.702916i | ||||||
\(11\) | 117.370i | 0.970001i | 0.874514 | + | 0.485000i | \(0.161181\pi\) | ||||
−0.874514 | + | 0.485000i | \(0.838819\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 118.348i | 0.700284i | 0.936697 | + | 0.350142i | \(0.113867\pi\) | ||||
−0.936697 | + | 0.350142i | \(0.886133\pi\) | |||||||
\(14\) | − | 97.6298i | − | 0.498111i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 23.2175 | 0.0906934 | ||||||||
\(17\) | −263.868 | −0.913040 | −0.456520 | − | 0.889713i | \(-0.650904\pi\) | ||||
−0.456520 | + | 0.889713i | \(0.650904\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 373.890 | 1.03571 | 0.517854 | − | 0.855469i | \(-0.326731\pi\) | ||||
0.517854 | + | 0.855469i | \(0.326731\pi\) | |||||||
\(20\) | −316.246 | −0.790615 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −274.603 | −0.567361 | ||||||||
\(23\) | 503.177i | 0.951185i | 0.879666 | + | 0.475592i | \(0.157766\pi\) | ||||
−0.879666 | + | 0.475592i | \(0.842234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 277.635 | 0.444217 | ||||||||
\(26\) | −276.891 | −0.409601 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −439.242 | −0.560258 | ||||||||
\(29\) | 549.815 | 0.653763 | 0.326882 | − | 0.945065i | \(-0.394002\pi\) | ||||
0.326882 | + | 0.945065i | \(0.394002\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 450.839i | − | 0.469135i | −0.972100 | − | 0.234568i | \(-0.924633\pi\) | ||
0.972100 | − | 0.234568i | \(-0.0753674\pi\) | |||||||
\(32\) | 1047.30i | 1.02276i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 617.355i | − | 0.534044i | ||||||
\(35\) | 1253.69 | 1.02342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1430.88i | − | 1.04520i | −0.852577 | − | 0.522601i | \(-0.824962\pi\) | ||
0.852577 | − | 0.522601i | \(-0.175038\pi\) | |||||||
\(38\) | 874.765i | 0.605793i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1864.56i | − | 1.16535i | ||||||
\(41\) | −1441.61 | −0.857591 | −0.428796 | − | 0.903401i | \(-0.641062\pi\) | ||||
−0.428796 | + | 0.903401i | \(0.641062\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3202.06i | − | 1.73178i | −0.500236 | − | 0.865889i | \(-0.666753\pi\) | ||
0.500236 | − | 0.865889i | \(-0.333247\pi\) | |||||||
\(44\) | 1235.45i | 0.638147i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1177.25 | −0.556355 | ||||||||
\(47\) | − | 967.133i | − | 0.437815i | −0.975746 | − | 0.218907i | \(-0.929751\pi\) | ||
0.975746 | − | 0.218907i | \(-0.0702493\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −659.713 | −0.274766 | ||||||||
\(50\) | 649.564i | 0.259826i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1245.75i | 0.460705i | ||||||||
\(53\) | −1662.12 | −0.591713 | −0.295856 | − | 0.955232i | \(-0.595605\pi\) | ||||
−0.295856 | + | 0.955232i | \(0.595605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3526.26i | − | 1.16570i | ||||||
\(56\) | − | 2589.74i | − | 0.825810i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1286.36i | 0.382391i | ||||||||
\(59\) | 34.3306 | − | 3480.83i | 0.00986228 | − | 0.999951i | ||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1712.94i | 0.460343i | 0.973150 | + | 0.230172i | \(0.0739288\pi\) | ||||
−0.973150 | + | 0.230172i | \(0.926071\pi\) | |||||||
\(62\) | 1054.80 | 0.274401 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2078.82 | −0.507524 | ||||||||
\(65\) | − | 3555.63i | − | 0.841570i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5062.54i | − | 1.12777i | −0.825854 | − | 0.563883i | \(-0.809307\pi\) | ||
0.825854 | − | 0.563883i | \(-0.190693\pi\) | |||||||
\(68\) | −2777.51 | −0.600673 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2933.18i | 0.598608i | ||||||||
\(71\) | −6150.31 | −1.22006 | −0.610028 | − | 0.792380i | \(-0.708842\pi\) | ||||
−0.610028 | + | 0.792380i | \(0.708842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4170.58i | 0.782619i | 0.920259 | + | 0.391309i | \(0.127978\pi\) | ||||
−0.920259 | + | 0.391309i | \(0.872022\pi\) | |||||||
\(74\) | 3347.74 | 0.611347 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3935.62 | 0.681374 | ||||||||
\(77\) | − | 4897.71i | − | 0.826059i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5990.22 | −0.959818 | −0.479909 | − | 0.877318i | \(-0.659330\pi\) | ||||
−0.479909 | + | 0.877318i | \(0.659330\pi\) | |||||||
\(80\) | −697.544 | −0.108991 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3372.84i | − | 0.501612i | ||||||
\(83\) | 2937.78i | 0.426445i | 0.977004 | + | 0.213222i | \(0.0683959\pi\) | ||||
−0.977004 | + | 0.213222i | \(0.931604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7927.64 | 1.09725 | ||||||||
\(86\) | 7491.63 | 1.01293 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7284.15 | −0.940618 | ||||||||
\(89\) | 3877.47i | 0.489518i | 0.969584 | + | 0.244759i | \(0.0787088\pi\) | ||||
−0.969584 | + | 0.244759i | \(0.921291\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4938.51i | − | 0.596367i | ||||||
\(92\) | 5296.50i | 0.625769i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2262.73 | 0.256081 | ||||||||
\(95\) | −11233.1 | −1.24467 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2340.59i | − | 0.248760i | −0.992235 | − | 0.124380i | \(-0.960306\pi\) | ||
0.992235 | − | 0.124380i | \(-0.0396942\pi\) | |||||||
\(98\) | − | 1543.48i | − | 0.160713i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2922.43 | 0.292243 | ||||||||
\(101\) | − | 18031.3i | − | 1.76761i | −0.467860 | − | 0.883803i | \(-0.654975\pi\) | ||
0.467860 | − | 0.883803i | \(-0.345025\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12277.9i | 1.15731i | 0.815572 | + | 0.578656i | \(0.196423\pi\) | ||||
−0.815572 | + | 0.578656i | \(0.803577\pi\) | |||||||
\(104\) | −7344.83 | −0.679071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 3888.75i | − | 0.346097i | ||||||
\(107\) | −7815.43 | −0.682630 | −0.341315 | − | 0.939949i | \(-0.610872\pi\) | ||||
−0.341315 | + | 0.939949i | \(0.610872\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4707.99i | 0.396262i | 0.980176 | + | 0.198131i | \(0.0634872\pi\) | ||||
−0.980176 | + | 0.198131i | \(0.936513\pi\) | |||||||
\(110\) | 8250.13 | 0.681829 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −968.837 | −0.0772351 | ||||||||
\(113\) | − | 8859.89i | − | 0.693860i | −0.937891 | − | 0.346930i | \(-0.887224\pi\) | ||
0.937891 | − | 0.346930i | \(-0.112776\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 15117.4i | − | 1.14309i | ||||||
\(116\) | 5787.42 | 0.430100 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8143.86 | + | 80.3209i | 0.584879 | + | 0.00576852i | ||||
\(119\) | 11010.9 | 0.777551 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 865.256 | 0.0590981 | ||||||||
\(122\) | −4007.64 | −0.269258 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4745.59i | − | 0.308636i | ||||||
\(125\) | 10436.2 | 0.667916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7759.81 | −0.481109 | −0.240554 | − | 0.970636i | \(-0.577329\pi\) | ||||
−0.240554 | + | 0.970636i | \(0.577329\pi\) | |||||||
\(128\) | 11893.2i | 0.725901i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8318.87 | 0.492241 | ||||||||
\(131\) | − | 26570.9i | − | 1.54833i | −0.632984 | − | 0.774165i | \(-0.718170\pi\) | ||
0.632984 | − | 0.774165i | \(-0.281830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15602.0 | −0.882015 | ||||||||
\(134\) | 11844.5 | 0.659639 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 16376.0i | − | 0.885382i | ||||||
\(137\) | 6370.46 | 0.339414 | 0.169707 | − | 0.985495i | \(-0.445718\pi\) | ||||
0.169707 | + | 0.985495i | \(0.445718\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 26487.6 | 1.37092 | 0.685461 | − | 0.728109i | \(-0.259601\pi\) | ||||
0.685461 | + | 0.728109i | \(0.259601\pi\) | |||||||
\(140\) | 13196.5 | 0.673293 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 14389.4i | − | 0.713620i | ||||||
\(143\) | −13890.5 | −0.679276 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16518.6 | −0.785664 | ||||||||
\(146\) | −9757.60 | −0.457760 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 15061.7i | − | 0.687621i | ||||||
\(149\) | − | 37732.0i | − | 1.69956i | −0.527136 | − | 0.849781i | \(-0.676734\pi\) | ||
0.527136 | − | 0.849781i | \(-0.323266\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 19425.6i | − | 0.851961i | −0.904732 | − | 0.425981i | \(-0.859929\pi\) | ||
0.904732 | − | 0.425981i | \(-0.140071\pi\) | |||||||
\(152\) | 23204.1i | 1.00433i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11458.8 | 0.483168 | ||||||||
\(155\) | 13545.0i | 0.563786i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 40542.8i | 1.64480i | 0.568907 | + | 0.822402i | \(0.307366\pi\) | ||||
−0.568907 | + | 0.822402i | \(0.692634\pi\) | |||||||
\(158\) | − | 14014.9i | − | 0.561405i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 31465.0i | − | 1.22910i | ||||||
\(161\) | − | 20996.9i | − | 0.810036i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6024.65 | −0.226755 | −0.113377 | − | 0.993552i | \(-0.536167\pi\) | ||||
−0.113377 | + | 0.993552i | \(0.536167\pi\) | |||||||
\(164\) | −15174.6 | −0.564195 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6873.32 | −0.249431 | ||||||||
\(167\) | 38348.4 | 1.37504 | 0.687519 | − | 0.726167i | \(-0.258700\pi\) | ||||
0.687519 | + | 0.726167i | \(0.258700\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14554.8 | 0.509602 | ||||||||
\(170\) | 18547.7i | 0.641790i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 33705.3i | − | 1.13931i | ||||||
\(173\) | 6642.40i | 0.221938i | 0.993824 | + | 0.110969i | \(0.0353955\pi\) | ||||
−0.993824 | + | 0.110969i | \(0.964604\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11585.4 | −0.378298 | ||||||||
\(176\) | 2725.04i | 0.0879727i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9071.85 | −0.286323 | ||||||||
\(179\) | − | 15505.0i | − | 0.483910i | −0.970287 | − | 0.241955i | \(-0.922211\pi\) | ||
0.970287 | − | 0.241955i | \(-0.0777887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7207.84 | −0.220013 | −0.110006 | − | 0.993931i | \(-0.535087\pi\) | ||||
−0.110006 | + | 0.993931i | \(0.535087\pi\) | |||||||
\(182\) | 11554.3 | 0.348819 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −31227.8 | −0.922372 | ||||||||
\(185\) | 42989.3i | 1.25608i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 30970.3i | − | 0.885649i | ||||||
\(188\) | − | 10180.2i | − | 0.288031i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 26281.3i | − | 0.728015i | ||||||
\(191\) | − | 24422.5i | − | 0.669459i | −0.942314 | − | 0.334729i | \(-0.891355\pi\) | ||
0.942314 | − | 0.334729i | \(-0.108645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42315.7 | −1.13602 | −0.568011 | − | 0.823021i | \(-0.692287\pi\) | ||||
−0.568011 | + | 0.823021i | \(0.692287\pi\) | |||||||
\(194\) | 5476.11 | 0.145502 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6944.23 | −0.180764 | ||||||||
\(197\) | 3081.53 | 0.0794024 | 0.0397012 | − | 0.999212i | \(-0.487359\pi\) | ||||
0.0397012 | + | 0.999212i | \(0.487359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 71081.9 | 1.79495 | 0.897476 | − | 0.441064i | \(-0.145399\pi\) | ||||
0.897476 | + | 0.441064i | \(0.145399\pi\) | |||||||
\(200\) | 17230.4i | 0.430761i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 42186.7 | 1.03389 | ||||||||
\(203\) | −22943.1 | −0.556749 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 43311.6 | 1.03062 | ||||||||
\(206\) | −28725.8 | −0.676920 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2747.74i | 0.0635111i | ||||||||
\(209\) | 43883.5i | 1.00464i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 31417.1i | 0.705670i | 0.935686 | + | 0.352835i | \(0.114782\pi\) | ||||
−0.935686 | + | 0.352835i | \(0.885218\pi\) | |||||||
\(212\) | −17495.7 | −0.389278 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 18285.2i | − | 0.399275i | ||||||
\(215\) | 96202.3i | 2.08117i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18812.9i | 0.399519i | ||||||||
\(218\) | −11015.0 | −0.231777 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 37117.8i | − | 0.766897i | ||||||
\(221\) | − | 31228.3i | − | 0.639387i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −55061.3 | −1.10723 | −0.553613 | − | 0.832774i | \(-0.686751\pi\) | ||||
−0.553613 | + | 0.832774i | \(0.686751\pi\) | |||||||
\(224\) | − | 43702.6i | − | 0.870986i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20728.9 | 0.405844 | ||||||||
\(227\) | 23259.5i | 0.451386i | 0.974198 | + | 0.225693i | \(0.0724646\pi\) | ||||
−0.974198 | + | 0.225693i | \(0.927535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16859.6i | 0.321496i | 0.986995 | + | 0.160748i | \(0.0513907\pi\) | ||||
−0.986995 | + | 0.160748i | \(0.948609\pi\) | |||||||
\(230\) | 35369.1 | 0.668603 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 34122.3i | 0.633960i | ||||||||
\(233\) | 56400.3i | 1.03889i | 0.854504 | + | 0.519445i | \(0.173861\pi\) | ||||
−0.854504 | + | 0.519445i | \(0.826139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29056.4i | 0.526147i | ||||||||
\(236\) | 361.368 | − | 36639.7i | 0.00648823 | − | 0.657851i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 25761.4i | 0.454795i | ||||||||
\(239\) | −17569.0 | −0.307575 | −0.153788 | − | 0.988104i | \(-0.549147\pi\) | ||||
−0.153788 | + | 0.988104i | \(0.549147\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 97271.4 | 1.67475 | 0.837377 | − | 0.546625i | \(-0.184088\pi\) | ||||
0.837377 | + | 0.546625i | \(0.184088\pi\) | |||||||
\(242\) | 2024.38i | 0.0345670i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18030.6i | 0.302852i | ||||||||
\(245\) | 19820.3 | 0.330202 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44249.2i | 0.725289i | ||||||||
\(248\) | 27979.7 | 0.454924 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24416.8i | 0.390669i | ||||||||
\(251\) | 41339.8 | 0.656177 | 0.328089 | − | 0.944647i | \(-0.393596\pi\) | ||||
0.328089 | + | 0.944647i | \(0.393596\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −59057.9 | −0.922650 | ||||||||
\(254\) | − | 18155.1i | − | 0.281404i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −61086.7 | −0.932109 | ||||||||
\(257\) | 14776.8 | 0.223725 | 0.111863 | − | 0.993724i | \(-0.464318\pi\) | ||||
0.111863 | + | 0.993724i | \(0.464318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 59708.9i | 0.890102i | ||||||||
\(260\) | − | 37427.1i | − | 0.553655i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 62166.1 | 0.905630 | ||||||||
\(263\) | −46511.4 | −0.672431 | −0.336216 | − | 0.941785i | \(-0.609147\pi\) | ||||
−0.336216 | + | 0.941785i | \(0.609147\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 49936.6 | 0.711094 | ||||||||
\(266\) | − | 36502.8i | − | 0.515897i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 53289.0i | − | 0.741939i | ||||||
\(269\) | 52167.3i | 0.720931i | 0.932773 | + | 0.360465i | \(0.117382\pi\) | ||||
−0.932773 | + | 0.360465i | \(0.882618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −118272. | −1.61044 | −0.805220 | − | 0.592977i | \(-0.797953\pi\) | ||||
−0.805220 | + | 0.592977i | \(0.797953\pi\) | |||||||
\(272\) | −6126.37 | −0.0828066 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14904.5i | 0.198526i | ||||||||
\(275\) | 32586.1i | 0.430891i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −116769. | −1.52184 | −0.760919 | − | 0.648847i | \(-0.775252\pi\) | ||||
−0.760919 | + | 0.648847i | \(0.775252\pi\) | |||||||
\(278\) | 61971.2i | 0.801863i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 77805.9i | 0.992422i | ||||||||
\(281\) | −148473. | −1.88034 | −0.940169 | − | 0.340710i | \(-0.889333\pi\) | ||||
−0.940169 | + | 0.340710i | \(0.889333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30655.6i | 0.382769i | 0.981515 | + | 0.191385i | \(0.0612978\pi\) | ||||
−0.981515 | + | 0.191385i | \(0.938702\pi\) | |||||||
\(284\) | −64738.9 | −0.802655 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 32498.7i | − | 0.397314i | ||||||
\(287\) | 60156.6 | 0.730331 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13894.4 | −0.166359 | ||||||||
\(290\) | − | 38647.4i | − | 0.459541i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 43900.0i | 0.514872i | ||||||||
\(293\) | −77404.6 | −0.901636 | −0.450818 | − | 0.892616i | \(-0.648868\pi\) | ||||
−0.450818 | + | 0.892616i | \(0.648868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1031.42 | + | 104578.i | −0.0118520 | + | 1.20170i | ||||
\(296\) | 88802.5 | 1.01354 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 88278.8 | 0.994086 | ||||||||
\(299\) | −59550.0 | −0.666100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 133618.i | 1.47479i | ||||||||
\(302\) | 45448.7 | 0.498319 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8680.80 | 0.0939318 | ||||||||
\(305\) | − | 51463.3i | − | 0.553220i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −124048. | −1.31617 | −0.658085 | − | 0.752943i | \(-0.728633\pi\) | ||||
−0.658085 | + | 0.752943i | \(0.728633\pi\) | |||||||
\(308\) | − | 51553.9i | − | 0.543451i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −31690.2 | −0.329762 | ||||||||
\(311\) | 3890.57 | 0.0402247 | 0.0201123 | − | 0.999798i | \(-0.493598\pi\) | ||||
0.0201123 | + | 0.999798i | \(0.493598\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18870.8i | − | 0.192620i | −0.995351 | − | 0.0963099i | \(-0.969296\pi\) | ||
0.995351 | − | 0.0963099i | \(-0.0307040\pi\) | |||||||
\(314\) | −94855.1 | −0.962058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −63053.9 | −0.631448 | ||||||||
\(317\) | 31502.4 | 0.313491 | 0.156745 | − | 0.987639i | \(-0.449900\pi\) | ||||
0.156745 | + | 0.987639i | \(0.449900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 64531.9i | 0.634151i | ||||||||
\(320\) | 62455.8 | 0.609920 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 49125.1 | 0.473796 | ||||||||
\(323\) | −98657.8 | −0.945642 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32857.6i | 0.311078i | ||||||||
\(326\) | − | 14095.4i | − | 0.132631i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 89468.3i | − | 0.831614i | ||||||
\(329\) | 40357.2i | 0.372846i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4457.32 | 0.0406834 | 0.0203417 | − | 0.999793i | \(-0.493525\pi\) | ||||
0.0203417 | + | 0.999793i | \(0.493525\pi\) | |||||||
\(332\) | 30923.4i | 0.280551i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 89721.1i | 0.804270i | ||||||||
\(335\) | 152099.i | 1.35530i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 46555.0i | 0.409927i | 0.978770 | + | 0.204964i | \(0.0657076\pi\) | ||||
−0.978770 | + | 0.204964i | \(0.934292\pi\) | |||||||
\(338\) | 34052.7i | 0.298070i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 83447.3 | 0.721863 | ||||||||
\(341\) | 52915.0 | 0.455061 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 127720. | 1.08560 | ||||||||
\(344\) | 198724. | 1.67932 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15540.8 | −0.129814 | ||||||||
\(347\) | − | 173485.i | − | 1.44080i | −0.693560 | − | 0.720399i | \(-0.743959\pi\) | ||
0.693560 | − | 0.720399i | \(-0.256041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 160924.i | − | 1.32120i | −0.750737 | − | 0.660601i | \(-0.770301\pi\) | ||
0.750737 | − | 0.660601i | \(-0.229699\pi\) | |||||||
\(350\) | − | 27105.5i | − | 0.221269i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −122922. | −0.992074 | ||||||||
\(353\) | − | 109289.i | − | 0.877055i | −0.898718 | − | 0.438527i | \(-0.855500\pi\) | ||
0.898718 | − | 0.438527i | \(-0.144500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 184779. | 1.46621 | ||||||||
\(356\) | 40814.8i | 0.322045i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 36275.9 | 0.283043 | ||||||||
\(359\) | −127764. | −0.991336 | −0.495668 | − | 0.868512i | \(-0.665077\pi\) | ||||
−0.495668 | + | 0.868512i | \(0.665077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9472.92 | 0.0726891 | ||||||||
\(362\) | − | 16863.7i | − | 0.128687i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 51983.4i | − | 0.392339i | ||||||
\(365\) | − | 125300.i | − | 0.940516i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 131014.i | 0.972718i | 0.873759 | + | 0.486359i | \(0.161675\pi\) | ||||
−0.873759 | + | 0.486359i | \(0.838325\pi\) | |||||||
\(368\) | 11682.5i | 0.0862662i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −100579. | −0.734690 | ||||||||
\(371\) | 69358.2 | 0.503907 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 162049. | 1.16474 | 0.582369 | − | 0.812924i | \(-0.302126\pi\) | ||||
0.582369 | + | 0.812924i | \(0.302126\pi\) | |||||||
\(374\) | 72459.0 | 0.518023 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 60021.6 | 0.424553 | ||||||||
\(377\) | 65069.5i | 0.457820i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −170314. | −1.18569 | −0.592847 | − | 0.805315i | \(-0.701996\pi\) | ||||
−0.592847 | + | 0.805315i | \(0.701996\pi\) | |||||||
\(380\) | −118241. | −0.818845 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 57139.7 | 0.391572 | ||||||||
\(383\) | −197908. | −1.34916 | −0.674582 | − | 0.738200i | \(-0.735676\pi\) | ||||
−0.674582 | + | 0.738200i | \(0.735676\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 147146.i | 0.992722i | ||||||||
\(386\) | − | 99003.0i | − | 0.664468i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 24637.3i | − | 0.163655i | ||||||
\(389\) | 130696. | 0.863699 | 0.431849 | − | 0.901946i | \(-0.357861\pi\) | ||||
0.431849 | + | 0.901946i | \(0.357861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 132772.i | − | 0.868470i | ||||||
\(392\) | − | 40942.7i | − | 0.266443i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7209.64i | 0.0464431i | ||||||||
\(395\) | 179970. | 1.15347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 35127.3i | − | 0.222876i | −0.993771 | − | 0.111438i | \(-0.964454\pi\) | ||
0.993771 | − | 0.111438i | \(-0.0355457\pi\) | |||||||
\(398\) | 166305.i | 1.04988i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6446.00 | 0.0402875 | ||||||||
\(401\) | 177132.i | 1.10156i | 0.834650 | + | 0.550780i | \(0.185670\pi\) | ||||
−0.834650 | + | 0.550780i | \(0.814330\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 53355.9 | 0.328528 | ||||||||
\(404\) | − | 189800.i | − | 1.16288i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 53678.3i | − | 0.325647i | ||||||
\(407\) | 167943. | 1.01385 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 194928.i | 1.16527i | 0.812733 | + | 0.582636i | \(0.197979\pi\) | ||||
−0.812733 | + | 0.582636i | \(0.802021\pi\) | |||||||
\(410\) | 101333.i | 0.602815i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 129239.i | 0.761376i | ||||||||
\(413\) | −1432.57 | + | 145251.i | −0.00839878 | + | 0.851565i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 88262.3i | − | 0.512483i | ||||||
\(416\) | −123946. | −0.716219 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −102671. | −0.587620 | ||||||||
\(419\) | 86241.5i | 0.491234i | 0.969367 | + | 0.245617i | \(0.0789906\pi\) | ||||
−0.969367 | + | 0.245617i | \(0.921009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 51752.7i | 0.291990i | 0.989285 | + | 0.145995i | \(0.0466384\pi\) | ||||
−0.989285 | + | 0.145995i | \(0.953362\pi\) | |||||||
\(422\) | −73504.5 | −0.412752 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 103153.i | − | 0.573789i | ||||||
\(425\) | −73259.2 | −0.405587 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 71478.7i | − | 0.392031i | ||||||
\(428\) | −82266.2 | −0.449091 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −225078. | −1.21729 | ||||||||
\(431\) | 184933.i | 0.995545i | 0.867308 | + | 0.497773i | \(0.165849\pi\) | ||||
−0.867308 | + | 0.497773i | \(0.834151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −201660. | −1.07558 | −0.537790 | − | 0.843079i | \(-0.680741\pi\) | ||||
−0.537790 | + | 0.843079i | \(0.680741\pi\) | |||||||
\(434\) | −44015.3 | −0.233681 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 49556.9i | 0.260694i | ||||||||
\(437\) | 188133.i | 0.985149i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 264954. | 1.37480 | 0.687402 | − | 0.726277i | \(-0.258751\pi\) | ||||
0.687402 | + | 0.726277i | \(0.258751\pi\) | |||||||
\(440\) | 218844. | 1.13039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 73062.7 | 0.373982 | ||||||||
\(443\) | 377029.i | 1.92117i | 0.277978 | + | 0.960587i | \(0.410336\pi\) | ||||
−0.277978 | + | 0.960587i | \(0.589664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 116494.i | − | 0.588281i | ||||||
\(446\) | − | 128823.i | − | 0.647625i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 86746.5 | 0.432211 | ||||||||
\(449\) | −108089. | −0.536155 | −0.268078 | − | 0.963397i | \(-0.586388\pi\) | ||||
−0.268078 | + | 0.963397i | \(0.586388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 169202.i | − | 0.831864i | ||||||
\(452\) | − | 93260.4i | − | 0.456479i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −54418.5 | −0.264019 | ||||||||
\(455\) | 148372.i | 0.716687i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 265515.i | − | 1.27132i | −0.771968 | − | 0.635662i | \(-0.780727\pi\) | ||
0.771968 | − | 0.635662i | \(-0.219273\pi\) | |||||||
\(458\) | −39445.2 | −0.188046 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 159128.i | − | 0.752021i | ||||||
\(461\) | −216820. | −1.02023 | −0.510114 | − | 0.860107i | \(-0.670397\pi\) | ||||
−0.510114 | + | 0.860107i | \(0.670397\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 245917.i | − | 1.14716i | −0.819148 | − | 0.573582i | \(-0.805553\pi\) | ||
0.819148 | − | 0.573582i | \(-0.194447\pi\) | |||||||
\(464\) | 12765.3 | 0.0592920 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −131956. | −0.607654 | ||||||||
\(467\) | − | 198167.i | − | 0.908651i | −0.890836 | − | 0.454326i | \(-0.849880\pi\) | ||
0.890836 | − | 0.454326i | \(-0.150120\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 211254.i | 0.960414i | ||||||||
\(470\) | −67981.3 | −0.307747 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 216025. | + | 2130.60i | 0.969661 | + | 0.00956353i | ||||
\(473\) | 375826. | 1.67983 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 103805. | 0.460078 | ||||||||
\(476\) | 115902. | 0.511538 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 41105.0i | − | 0.179903i | ||||||
\(479\) | 419986. | 1.83048 | 0.915238 | − | 0.402915i | \(-0.132003\pi\) | ||||
0.915238 | + | 0.402915i | \(0.132003\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 169342. | 0.731939 | ||||||||
\(482\) | 227579.i | 0.979577i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9107.80 | 0.0388797 | ||||||||
\(485\) | 70320.3i | 0.298949i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −336768. | −1.41995 | −0.709975 | − | 0.704227i | \(-0.751294\pi\) | ||||
−0.709975 | + | 0.704227i | \(0.751294\pi\) | |||||||
\(488\) | −106307. | −0.446399 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 46372.3i | 0.193137i | ||||||||
\(491\) | −279399. | −1.15894 | −0.579471 | − | 0.814993i | \(-0.696741\pi\) | ||||
−0.579471 | + | 0.814993i | \(0.696741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −145079. | −0.596912 | ||||||||
\(494\) | −103527. | −0.424227 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 10467.4i | − | 0.0425474i | ||||||
\(497\) | 256644. | 1.03901 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23800.2 | 0.0955826 | 0.0477913 | − | 0.998857i | \(-0.484782\pi\) | ||||
0.0477913 | + | 0.998857i | \(0.484782\pi\) | |||||||
\(500\) | 109853. | 0.439410 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 96719.9i | 0.383803i | ||||||||
\(503\) | − | 25529.1i | − | 0.100902i | −0.998727 | − | 0.0504509i | \(-0.983934\pi\) | ||
0.998727 | − | 0.0504509i | \(-0.0160659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 541732.i | 2.12423i | ||||||||
\(506\) | − | 138174.i | − | 0.539665i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −81680.7 | −0.316513 | ||||||||
\(509\) | − | 6537.03i | − | 0.0252316i | −0.999920 | − | 0.0126158i | \(-0.995984\pi\) | ||
0.999920 | − | 0.0126158i | \(-0.00401584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 174033.i | − | 0.666483i | ||||||
\(512\) | 47370.3i | 0.180703i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34572.3i | 0.130859i | ||||||||
\(515\) | − | 368877.i | − | 1.39081i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 113513. | 0.424681 | ||||||||
\(518\) | −139697. | −0.520627 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 220667. | 0.816078 | ||||||||
\(521\) | 307294. | 1.13208 | 0.566042 | − | 0.824376i | \(-0.308474\pi\) | ||||
0.566042 | + | 0.824376i | \(0.308474\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −92199.8 | −0.337075 | −0.168537 | − | 0.985695i | \(-0.553904\pi\) | ||||
−0.168537 | + | 0.985695i | \(0.553904\pi\) | |||||||
\(524\) | − | 279689.i | − | 1.01862i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 108819.i | − | 0.393310i | ||||||
\(527\) | 118962.i | 0.428339i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26654.1 | 0.0952472 | ||||||||
\(530\) | 116833.i | 0.415924i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −164228. | −0.580263 | ||||||||
\(533\) | − | 170612.i | − | 0.600557i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 234806. | 0.820354 | ||||||||
\(536\) | 314188. | 1.09360 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −122052. | −0.421678 | ||||||||
\(539\) | − | 77430.6i | − | 0.266523i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 234603.i | 0.801564i | 0.916173 | + | 0.400782i | \(0.131262\pi\) | ||||
−0.916173 | + | 0.400782i | \(0.868738\pi\) | |||||||
\(542\) | − | 276713.i | − | 0.941958i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 276350.i | − | 0.933816i | ||||||
\(545\) | − | 141446.i | − | 0.476210i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −246372. | −0.823411 | −0.411706 | − | 0.911317i | \(-0.635067\pi\) | ||||
−0.411706 | + | 0.911317i | \(0.635067\pi\) | |||||||
\(548\) | 67056.3 | 0.223295 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −76239.4 | −0.252031 | ||||||||
\(551\) | 205570. | 0.677107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 249964. | 0.817387 | ||||||||
\(554\) | − | 273197.i | − | 0.890134i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 278812. | 0.901907 | ||||||||
\(557\) | −567300. | −1.82853 | −0.914266 | − | 0.405115i | \(-0.867231\pi\) | ||||
−0.914266 | + | 0.405115i | \(0.867231\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 378957. | 1.21274 | ||||||||
\(560\) | 29107.6 | 0.0928177 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 347373.i | − | 1.09982i | ||||||
\(563\) | − | 327570.i | − | 1.03344i | −0.856153 | − | 0.516722i | \(-0.827152\pi\) | ||
0.856153 | − | 0.516722i | \(-0.172848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 266186.i | 0.833850i | ||||||||
\(566\) | −71722.8 | −0.223885 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 381696.i | − | 1.18310i | ||||||
\(569\) | − | 379301.i | − | 1.17154i | −0.810476 | − | 0.585772i | \(-0.800791\pi\) | ||
0.810476 | − | 0.585772i | \(-0.199209\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 580504.i | − | 1.78046i | −0.455509 | − | 0.890231i | \(-0.650543\pi\) | ||
0.455509 | − | 0.890231i | \(-0.349457\pi\) | |||||||
\(572\) | −146213. | −0.446884 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 140744.i | 0.427176i | ||||||||
\(575\) | 139700.i | 0.422532i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34030.7 | −0.102216 | −0.0511080 | − | 0.998693i | \(-0.516275\pi\) | ||||
−0.0511080 | + | 0.998693i | \(0.516275\pi\) | |||||||
\(578\) | − | 32507.8i | − | 0.0973044i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −173877. | −0.516875 | ||||||||
\(581\) | − | 122590.i | − | 0.363163i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 195083.i | − | 0.573962i | ||||||
\(584\) | −258831. | −0.758912 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 181098.i | − | 0.527374i | ||||||
\(587\) | − | 360445.i | − | 1.04607i | −0.852310 | − | 0.523037i | \(-0.824799\pi\) | ||
0.852310 | − | 0.523037i | \(-0.175201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 168564.i | − | 0.485886i | ||||||
\(590\) | −244673. | − | 2413.15i | −0.702882 | − | 0.00693235i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 33221.5i | − | 0.0947930i | ||||||
\(593\) | −203460. | −0.578589 | −0.289294 | − | 0.957240i | \(-0.593421\pi\) | ||||
−0.289294 | + | 0.957240i | \(0.593421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −330810. | −0.934426 | ||||||||
\(596\) | − | 397172.i | − | 1.11811i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 139325.i | − | 0.389607i | ||||||
\(599\) | −68798.6 | −0.191746 | −0.0958729 | − | 0.995394i | \(-0.530564\pi\) | ||||
−0.0958729 | + | 0.995394i | \(0.530564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 549707.i | − | 1.52189i | −0.648818 | − | 0.760943i | \(-0.724737\pi\) | ||
0.648818 | − | 0.760943i | \(-0.275263\pi\) | |||||||
\(602\) | −312616. | −0.862618 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 204476.i | − | 0.560491i | ||||||
\(605\) | −25995.7 | −0.0710215 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −350392. | −0.950991 | −0.475495 | − | 0.879718i | \(-0.657731\pi\) | ||||
−0.475495 | + | 0.879718i | \(0.657731\pi\) | |||||||
\(608\) | 391576.i | 1.05928i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 120405. | 0.323583 | ||||||||
\(611\) | 114458. | 0.306595 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 450003.i | 1.19755i | 0.800917 | + | 0.598776i | \(0.204346\pi\) | ||||
−0.800917 | + | 0.598776i | \(0.795654\pi\) | |||||||
\(614\) | − | 290226.i | − | 0.769838i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 303958. | 0.801037 | ||||||||
\(617\) | −165810. | −0.435552 | −0.217776 | − | 0.975999i | \(-0.569880\pi\) | ||||
−0.217776 | + | 0.975999i | \(0.569880\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −286451. | −0.747599 | −0.373799 | − | 0.927510i | \(-0.621945\pi\) | ||||
−0.373799 | + | 0.927510i | \(0.621945\pi\) | |||||||
\(620\) | 142576.i | 0.370905i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9102.49i | 0.0235277i | ||||||||
\(623\) | − | 161802.i | − | 0.416877i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −487066. | −1.24689 | ||||||||
\(626\) | 44150.6 | 0.112665 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 426758.i | 1.08209i | ||||||||
\(629\) | 377565.i | 0.954312i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 94171.7 | 0.236517 | 0.118258 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118258 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(632\) | − | 371761.i | − | 0.930743i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 73703.9i | 0.183363i | ||||||||
\(635\) | 233135. | 0.578175 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 78075.7i | − | 0.192414i | ||||||
\(638\) | −150981. | −0.370920 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 357317.i | − | 0.872356i | ||||||
\(641\) | −739487. | −1.79976 | −0.899880 | − | 0.436137i | \(-0.856346\pi\) | ||||
−0.899880 | + | 0.436137i | \(0.856346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 446727. | 1.08049 | 0.540244 | − | 0.841508i | \(-0.318332\pi\) | ||||
0.540244 | + | 0.841508i | \(0.318332\pi\) | |||||||
\(644\) | − | 221016.i | − | 0.532909i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 230823.i | − | 0.553113i | ||||||
\(647\) | 370357. | 0.884732 | 0.442366 | − | 0.896835i | \(-0.354139\pi\) | ||||
0.442366 | + | 0.896835i | \(0.354139\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 408546. | + | 4029.38i | 0.969954 | + | 0.00956642i | ||||
\(650\) | −76874.6 | −0.181952 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −63416.2 | −0.149178 | ||||||||
\(653\) | 339613. | 0.796449 | 0.398224 | − | 0.917288i | \(-0.369627\pi\) | ||||
0.398224 | + | 0.917288i | \(0.369627\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 798293.i | 1.86071i | ||||||||
\(656\) | −33470.6 | −0.0777779 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −94421.0 | −0.218081 | ||||||||
\(659\) | − | 387109.i | − | 0.891378i | −0.895188 | − | 0.445689i | \(-0.852959\pi\) | ||
0.895188 | − | 0.445689i | \(-0.147041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −367793. | −0.841784 | −0.420892 | − | 0.907111i | \(-0.638283\pi\) | ||||
−0.420892 | + | 0.907111i | \(0.638283\pi\) | |||||||
\(662\) | 10428.5i | 0.0237961i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −182322. | −0.413527 | ||||||||
\(665\) | 468744. | 1.05997 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 276654.i | 0.621850i | ||||||||
\(668\) | 403660. | 0.904614 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −355854. | −0.792725 | ||||||||
\(671\) | −201048. | −0.446533 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 356274.i | 0.786600i | 0.919410 | + | 0.393300i | \(0.128667\pi\) | ||||
−0.919410 | + | 0.393300i | \(0.871333\pi\) | |||||||
\(674\) | −108922. | −0.239770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 153205. | 0.335259 | ||||||||
\(677\) | −427232. | −0.932152 | −0.466076 | − | 0.884745i | \(-0.654333\pi\) | ||||
−0.466076 | + | 0.884745i | \(0.654333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 97669.7i | 0.211846i | ||||||||
\(680\) | 492000.i | 1.06401i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 123802.i | 0.266169i | ||||||||
\(683\) | 816072.i | 1.74939i | 0.484673 | + | 0.874695i | \(0.338939\pi\) | ||||
−0.484673 | + | 0.874695i | \(0.661061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −191393. | −0.407893 | ||||||||
\(686\) | 298817.i | 0.634975i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 74343.8i | − | 0.157061i | ||||||
\(689\) | − | 196709.i | − | 0.414367i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 101566.i | − | 0.212712i | −0.994328 | − | 0.106356i | \(-0.966082\pi\) | ||
0.994328 | − | 0.106356i | \(-0.0339183\pi\) | |||||||
\(692\) | 69918.7i | 0.146010i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 405891. | 0.842733 | ||||||||
\(695\) | −795790. | −1.64751 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 380396. | 0.783015 | ||||||||
\(698\) | 376502. | 0.772782 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −121949. | −0.248876 | ||||||||
\(701\) | − | 265473.i | − | 0.540236i | −0.962827 | − | 0.270118i | \(-0.912937\pi\) | ||
0.962827 | − | 0.270118i | \(-0.0870628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 534993.i | − | 1.08252i | ||||||
\(704\) | − | 243991.i | − | 0.492299i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 255696. | 0.512996 | ||||||||
\(707\) | 752425.i | 1.50530i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −380605. | −0.757150 | −0.378575 | − | 0.925571i | \(-0.623586\pi\) | ||||
−0.378575 | + | 0.925571i | \(0.623586\pi\) | |||||||
\(710\) | 432315.i | 0.857597i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −240641. | −0.474689 | ||||||||
\(713\) | 226852. | 0.446234 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 417325. | 0.816324 | ||||||||
\(716\) | − | 163207.i | − | 0.318356i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 298921.i | − | 0.579840i | ||||||
\(719\) | 356832.i | 0.690249i | 0.938557 | + | 0.345124i | \(0.112163\pi\) | ||||
−0.938557 | + | 0.345124i | \(0.887837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 512342.i | − | 0.985575i | ||||||
\(722\) | 22163.1i | 0.0425164i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −75870.6 | −0.144743 | ||||||||
\(725\) | 152648. | 0.290413 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 84925.0 | 0.160682 | 0.0803409 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803409 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(728\) | 306491. | 0.578302 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 293156. | 0.550115 | ||||||||
\(731\) | 844922.i | 1.58118i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −359849. | −0.669750 | −0.334875 | − | 0.942263i | \(-0.608694\pi\) | ||||
−0.334875 | + | 0.942263i | \(0.608694\pi\) | |||||||
\(734\) | −306525. | −0.568950 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −526978. | −0.972830 | ||||||||
\(737\) | 594191. | 1.09393 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 813633.i | 1.48984i | 0.667154 | + | 0.744920i | \(0.267512\pi\) | ||||
−0.667154 | + | 0.744920i | \(0.732488\pi\) | |||||||
\(740\) | 452511.i | 0.826353i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 162273.i | 0.294739i | ||||||||
\(743\) | 407788. | 0.738680 | 0.369340 | − | 0.929294i | \(-0.379584\pi\) | ||||
0.369340 | + | 0.929294i | \(0.379584\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.13361e6i | 2.04246i | ||||||||
\(746\) | 379135.i | 0.681265i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 325997.i | − | 0.582654i | ||||||
\(749\) | 326128. | 0.581332 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 726139.i | − | 1.28748i | −0.765245 | − | 0.643739i | \(-0.777382\pi\) | ||
0.765245 | − | 0.643739i | \(-0.222618\pi\) | |||||||
\(752\) | − | 22454.4i | − | 0.0397069i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −152239. | −0.267782 | ||||||||
\(755\) | 583620.i | 1.02385i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 226073. | 0.394508 | 0.197254 | − | 0.980352i | \(-0.436798\pi\) | ||||
0.197254 | + | 0.980352i | \(0.436798\pi\) | |||||||
\(758\) | − | 398472.i | − | 0.693521i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 697142.i | − | 1.20696i | ||||||
\(761\) | 32895.1 | 0.0568018 | 0.0284009 | − | 0.999597i | \(-0.490958\pi\) | ||||
0.0284009 | + | 0.999597i | \(0.490958\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 196458.i | − | 0.337459i | ||||||
\(764\) | − | 257075.i | − | 0.440426i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 463031.i | − | 0.789137i | ||||||
\(767\) | 411949. | + | 4062.96i | 0.700250 | + | 0.00690639i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 954320.i | 1.61377i | 0.590710 | + | 0.806884i | \(0.298848\pi\) | ||||
−0.590710 | + | 0.806884i | \(0.701152\pi\) | |||||||
\(770\) | −344268. | −0.580650 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −445420. | −0.747370 | ||||||||
\(773\) | 430986.i | 0.721280i | 0.932705 | + | 0.360640i | \(0.117442\pi\) | ||||
−0.932705 | + | 0.360640i | \(0.882558\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 125169.i | − | 0.208398i | ||||||
\(776\) | 145260. | 0.241225 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 305780.i | 0.505184i | ||||||||
\(779\) | −539004. | −0.888213 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 721862.i | − | 1.18346i | ||||||
\(782\) | 310639. | 0.507974 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15316.9 | −0.0249195 | ||||||||
\(785\) | − | 1.21806e6i | − | 1.97665i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 449468. | 0.725687 | 0.362844 | − | 0.931850i | \(-0.381806\pi\) | ||||
0.362844 | + | 0.931850i | \(0.381806\pi\) | |||||||
\(788\) | 32436.6 | 0.0522375 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 421062.i | 0.674671i | ||||||||
\(791\) | 369712.i | 0.590895i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −202723. | −0.322371 | ||||||||
\(794\) | 82184.9 | 0.130362 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 748217. | 1.18087 | ||||||||
\(797\) | 300325.i | 0.472797i | 0.971656 | + | 0.236398i | \(0.0759671\pi\) | ||||
−0.971656 | + | 0.236398i | \(0.924033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 255196.i | 0.399742i | ||||||||
\(800\) | 290768.i | 0.454325i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −414424. | −0.644311 | ||||||||
\(803\) | −489501. | −0.759141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 630830.i | 0.973465i | ||||||||
\(806\) | 124833.i | 0.192158i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.11905e6 | 1.71406 | ||||||||
\(809\) | − | 676692.i | − | 1.03394i | −0.856005 | − | 0.516968i | \(-0.827060\pi\) | ||
0.856005 | − | 0.516968i | \(-0.172940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 435345.i | 0.661899i | 0.943648 | + | 0.330950i | \(0.107369\pi\) | ||||
−0.943648 | + | 0.330950i | \(0.892631\pi\) | |||||||
\(812\) | −241502. | −0.366276 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 392924.i | 0.593007i | ||||||||
\(815\) | 181004. | 0.272504 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.19722e6i | − | 1.79362i | ||||||
\(818\) | −456059. | −0.681576 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 455904. | 0.678024 | ||||||||
\(821\) | − | 1.03403e6i | − | 1.53408i | −0.641599 | − | 0.767040i | \(-0.721729\pi\) | ||
0.641599 | − | 0.767040i | \(-0.278271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.06922e6i | 1.57858i | 0.614020 | + | 0.789291i | \(0.289551\pi\) | ||||
−0.614020 | + | 0.789291i | \(0.710449\pi\) | |||||||
\(824\) | −761984. | −1.12226 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −339833. | − | 3351.69i | −0.498087 | − | 0.00491251i | ||||
\(827\) | −344792. | −0.504135 | −0.252067 | − | 0.967710i | \(-0.581110\pi\) | ||||
−0.252067 | + | 0.967710i | \(0.581110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 71136.1 | 0.103510 | 0.0517549 | − | 0.998660i | \(-0.483519\pi\) | ||||
0.0517549 | + | 0.998660i | \(0.483519\pi\) | |||||||
\(830\) | 206501. | 0.299755 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 246024.i | − | 0.355411i | ||||||
\(833\) | 174077. | 0.250872 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.15214e6 | −1.65246 | ||||||||
\(836\) | 461924.i | 0.660934i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −201773. | −0.287326 | ||||||||
\(839\) | 708706.i | 1.00680i | 0.864054 | + | 0.503399i | \(0.167917\pi\) | ||||
−0.864054 | + | 0.503399i | \(0.832083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −404984. | −0.572593 | ||||||||
\(842\) | −121082. | −0.170787 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 330701.i | 0.464248i | ||||||||
\(845\) | −437281. | −0.612418 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36106.0 | −0.0503284 | ||||||||
\(848\) | −38590.3 | −0.0536644 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 171400.i | − | 0.237231i | ||||||
\(851\) | 719987. | 0.994181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.25574e6 | 1.72584 | 0.862922 | − | 0.505337i | \(-0.168632\pi\) | ||||
0.862922 | + | 0.505337i | \(0.168632\pi\) | |||||||
\(854\) | 167234. | 0.229302 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 485036.i | − | 0.661952i | ||||||
\(857\) | − | 799600.i | − | 1.08871i | −0.838856 | − | 0.544353i | \(-0.816775\pi\) | ||
0.838856 | − | 0.544353i | \(-0.183225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 853825.i | − | 1.15713i | −0.815636 | − | 0.578565i | \(-0.803613\pi\) | ||
0.815636 | − | 0.578565i | \(-0.196387\pi\) | |||||||
\(860\) | 1.01264e6i | 1.36917i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −432676. | −0.582302 | ||||||||
\(863\) | − | 365706.i | − | 0.491033i | −0.969392 | − | 0.245516i | \(-0.921043\pi\) | ||
0.969392 | − | 0.245516i | \(-0.0789575\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 199563.i | − | 0.266716i | ||||||
\(866\) | − | 471809.i | − | 0.629115i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 198027.i | 0.262837i | ||||||||
\(869\) | − | 703073.i | − | 0.931024i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 599142. | 0.789757 | ||||||||
\(872\) | −292184. | −0.384259 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −440161. | −0.576221 | ||||||||
\(875\) | −435489. | −0.568802 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 538704. | 0.700408 | 0.350204 | − | 0.936674i | \(-0.386112\pi\) | ||||
0.350204 | + | 0.936674i | \(0.386112\pi\) | |||||||
\(878\) | 619894.i | 0.804134i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 81870.8i | − | 0.105722i | ||||||
\(881\) | 131412.i | 0.169311i | 0.996410 | + | 0.0846554i | \(0.0269789\pi\) | ||||
−0.996410 | + | 0.0846554i | \(0.973021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 152864. | 0.196058 | 0.0980289 | − | 0.995184i | \(-0.468746\pi\) | ||||
0.0980289 | + | 0.995184i | \(0.468746\pi\) | |||||||
\(884\) | − | 328713.i | − | 0.420642i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −882108. | −1.12371 | ||||||||
\(887\) | − | 437411.i | − | 0.555959i | −0.960587 | − | 0.277980i | \(-0.910335\pi\) | ||
0.960587 | − | 0.277980i | \(-0.0896648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 323807. | 0.409716 | ||||||||
\(890\) | 272554. | 0.344090 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −579582. | −0.728426 | ||||||||
\(893\) | − | 361602.i | − | 0.453448i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 465830.i | 0.581542i | ||||||||
\(896\) | − | 496286.i | − | 0.618182i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 252889.i | − | 0.313601i | ||||||
\(899\) | − | 247878.i | − | 0.306703i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 438581. | 0.540257 | ||||||||
\(902\) | 395870. | 0.486564 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 549857. | 0.672841 | ||||||||
\(905\) | 216551. | 0.264402 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.20250e6 | 1.46174 | 0.730870 | − | 0.682517i | \(-0.239115\pi\) | ||||
0.730870 | + | 0.682517i | \(0.239115\pi\) | |||||||
\(908\) | 244832.i | 0.296959i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −347136. | −0.419196 | ||||||||
\(911\) | 1.26490e6 | 1.52412 | 0.762059 | − | 0.647508i | \(-0.224189\pi\) | ||||
0.762059 | + | 0.647508i | \(0.224189\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −344807. | −0.413652 | ||||||||
\(914\) | 621206. | 0.743607 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 177466.i | 0.211507i | ||||||||
\(917\) | 1.10877e6i | 1.31857i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 831045.i | 0.983996i | 0.870596 | + | 0.491998i | \(0.163733\pi\) | ||||
−0.870596 | + | 0.491998i | \(0.836267\pi\) | |||||||
\(920\) | 938205. | 1.10847 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 507279.i | − | 0.596740i | ||||||
\(923\) | − | 727876.i | − | 0.854386i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 397264.i | − | 0.464297i | ||||||
\(926\) | 575354. | 0.670985 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 575822.i | 0.668640i | ||||||||
\(929\) | − | 1.33453e6i | − | 1.54631i | −0.634217 | − | 0.773155i | \(-0.718677\pi\) | ||
0.634217 | − | 0.773155i | \(-0.281323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −246660. | −0.284577 | ||||||||
\(932\) | 593677.i | 0.683468i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 463637. | 0.531477 | ||||||||
\(935\) | 930468.i | 1.06433i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.31851e6i | 1.50177i | 0.660431 | + | 0.750887i | \(0.270374\pi\) | ||||
−0.660431 | + | 0.750887i | \(0.729626\pi\) | |||||||
\(938\) | −494255. | −0.561753 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 305852.i | 0.346143i | ||||||||
\(941\) | 1.26151e6i | 1.42466i | 0.701842 | + | 0.712332i | \(0.252361\pi\) | ||||
−0.701842 | + | 0.712332i | \(0.747639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 725385.i | − | 0.815728i | ||||||
\(944\) | 797.070 | − | 80816.2i | 0.000894443 | − | 0.0906890i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 879294.i | 0.982543i | ||||||||
\(947\) | −1.34445e6 | −1.49914 | −0.749572 | − | 0.661923i | \(-0.769741\pi\) | ||||
−0.749572 | + | 0.661923i | \(0.769741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −493579. | −0.548055 | ||||||||
\(950\) | 242866.i | 0.269103i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 683351.i | 0.753997i | ||||||||
\(953\) | −654376. | −0.720513 | −0.360256 | − | 0.932853i | \(-0.617311\pi\) | ||||
−0.360256 | + | 0.932853i | \(0.617311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 733748.i | 0.804526i | ||||||||
\(956\) | −184934. | −0.202349 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 982612.i | 1.07066i | ||||||||
\(959\) | −265831. | −0.289047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 720265. | 0.779912 | ||||||||
\(962\) | 396198.i | 0.428117i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.02389e6 | 1.10179 | ||||||||
\(965\) | 1.27133e6 | 1.36522 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.67352e6i | 1.78969i | 0.446373 | + | 0.894847i | \(0.352716\pi\) | ||||
−0.446373 | + | 0.894847i | \(0.647284\pi\) | |||||||
\(968\) | 53698.9i | 0.0573080i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −164524. | −0.174858 | ||||||||
\(971\) | 1.34581e6 | 1.42740 | 0.713700 | − | 0.700451i | \(-0.247018\pi\) | ||||
0.713700 | + | 0.700451i | \(0.247018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.10529e6 | −1.16749 | ||||||||
\(974\) | − | 787913.i | − | 0.830539i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39770.1i | 0.0417501i | ||||||||
\(977\) | − | 108100.i | − | 0.113250i | −0.998396 | − | 0.0566248i | \(-0.981966\pi\) | ||
0.998396 | − | 0.0566248i | \(-0.0180339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −455099. | −0.474833 | ||||||||
\(980\) | 208632. | 0.217234 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 653690.i | − | 0.677874i | ||||||
\(983\) | 412747.i | 0.427147i | 0.976927 | + | 0.213573i | \(0.0685103\pi\) | ||||
−0.976927 | + | 0.213573i | \(0.931490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −92581.1 | −0.0954223 | ||||||||
\(986\) | − | 339431.i | − | 0.349138i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 465772.i | 0.477155i | ||||||||
\(989\) | 1.61120e6 | 1.64724 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.11405e6i | 1.13438i | 0.823588 | + | 0.567188i | \(0.191969\pi\) | ||||
−0.823588 | + | 0.567188i | \(0.808031\pi\) | |||||||
\(992\) | 472164. | 0.479810 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 600453.i | 0.607724i | ||||||||
\(995\) | −2.13558e6 | −2.15709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −289466. | −0.291210 | −0.145605 | − | 0.989343i | \(-0.546513\pi\) | ||||
−0.145605 | + | 0.989343i | \(0.546513\pi\) | |||||||
\(998\) | 55683.6i | 0.0559070i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.5.c.d.235.26 | 40 | ||
3.2 | odd | 2 | 177.5.c.a.58.15 | ✓ | 40 | ||
59.58 | odd | 2 | inner | 531.5.c.d.235.15 | 40 | ||
177.176 | even | 2 | 177.5.c.a.58.26 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.15 | ✓ | 40 | 3.2 | odd | 2 | ||
177.5.c.a.58.26 | yes | 40 | 177.176 | even | 2 | ||
531.5.c.d.235.15 | 40 | 59.58 | odd | 2 | inner | ||
531.5.c.d.235.26 | 40 | 1.1 | even | 1 | trivial |