Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,5,Mod(37,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.37");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.b (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: | \(3.92805859719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 450x^{6} + 68229x^{4} + 4001228x^{2} + 77475204 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.6 | ||
Root | \(-8.07810i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.37 |
Dual form | 38.5.b.a.37.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | − | 6.66389i | − | 0.740432i | −0.928946 | − | 0.370216i | \(-0.879284\pi\) | ||
0.928946 | − | 0.370216i | \(-0.120716\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 26.7027 | 1.06811 | 0.534054 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534054 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(6\) | 18.8483 | 0.523565 | ||||||||
\(7\) | 51.4469 | 1.04994 | 0.524969 | − | 0.851121i | \(-0.324077\pi\) | ||||
0.524969 | + | 0.851121i | \(0.324077\pi\) | |||||||
\(8\) | − | 22.6274i | − | 0.353553i | ||||||
\(9\) | 36.5926 | 0.451760 | ||||||||
\(10\) | 75.5266i | 0.755266i | ||||||||
\(11\) | −25.0891 | −0.207348 | −0.103674 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103674 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(12\) | 53.3111i | 0.370216i | ||||||||
\(13\) | 53.2531i | 0.315107i | 0.987510 | + | 0.157553i | \(0.0503606\pi\) | ||||
−0.987510 | + | 0.157553i | \(0.949639\pi\) | |||||||
\(14\) | 145.514i | 0.742418i | ||||||||
\(15\) | − | 177.944i | − | 0.790862i | ||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | −24.4913 | −0.0847451 | −0.0423726 | − | 0.999102i | \(-0.513492\pi\) | ||||
−0.0423726 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(18\) | 103.499i | 0.319443i | ||||||||
\(19\) | −78.0101 | − | 352.470i | −0.216094 | − | 0.976372i | ||||
\(20\) | −213.622 | −0.534054 | ||||||||
\(21\) | − | 342.837i | − | 0.777408i | ||||||
\(22\) | − | 70.9628i | − | 0.146617i | ||||||
\(23\) | −612.242 | −1.15736 | −0.578679 | − | 0.815555i | \(-0.696432\pi\) | ||||
−0.578679 | + | 0.815555i | \(0.696432\pi\) | |||||||
\(24\) | −150.787 | −0.261782 | ||||||||
\(25\) | 88.0343 | 0.140855 | ||||||||
\(26\) | −150.622 | −0.222814 | ||||||||
\(27\) | − | 783.624i | − | 1.07493i | ||||||
\(28\) | −411.576 | −0.524969 | ||||||||
\(29\) | 1345.96i | 1.60043i | 0.599713 | + | 0.800215i | \(0.295282\pi\) | ||||
−0.599713 | + | 0.800215i | \(0.704718\pi\) | |||||||
\(30\) | 503.301 | 0.559224 | ||||||||
\(31\) | 912.680i | 0.949719i | 0.880062 | + | 0.474860i | \(0.157501\pi\) | ||||
−0.880062 | + | 0.474860i | \(0.842499\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 167.191i | 0.153527i | ||||||||
\(34\) | − | 69.2720i | − | 0.0599238i | ||||||
\(35\) | 1373.77 | 1.12145 | ||||||||
\(36\) | −292.741 | −0.225880 | ||||||||
\(37\) | − | 325.059i | − | 0.237443i | −0.992928 | − | 0.118721i | \(-0.962120\pi\) | ||
0.992928 | − | 0.118721i | \(-0.0378795\pi\) | |||||||
\(38\) | 996.937 | − | 220.646i | 0.690400 | − | 0.152802i | ||||
\(39\) | 354.872 | 0.233315 | ||||||||
\(40\) | − | 604.213i | − | 0.377633i | ||||||
\(41\) | 51.7494i | 0.0307849i | 0.999882 | + | 0.0153924i | \(0.00489976\pi\) | ||||
−0.999882 | + | 0.0153924i | \(0.995100\pi\) | |||||||
\(42\) | 969.689 | 0.549710 | ||||||||
\(43\) | −2545.26 | −1.37656 | −0.688280 | − | 0.725445i | \(-0.741634\pi\) | ||||
−0.688280 | + | 0.725445i | \(0.741634\pi\) | |||||||
\(44\) | 200.713 | 0.103674 | ||||||||
\(45\) | 977.121 | 0.482529 | ||||||||
\(46\) | − | 1731.68i | − | 0.818376i | ||||||
\(47\) | 2998.19 | 1.35726 | 0.678630 | − | 0.734480i | \(-0.262574\pi\) | ||||
0.678630 | + | 0.734480i | \(0.262574\pi\) | |||||||
\(48\) | − | 426.489i | − | 0.185108i | ||||||
\(49\) | 245.788 | 0.102369 | ||||||||
\(50\) | 248.999i | 0.0995994i | ||||||||
\(51\) | 163.208i | 0.0627480i | ||||||||
\(52\) | − | 426.024i | − | 0.157553i | ||||||
\(53\) | 4067.86i | 1.44815i | 0.689720 | + | 0.724077i | \(0.257734\pi\) | ||||
−0.689720 | + | 0.724077i | \(0.742266\pi\) | |||||||
\(54\) | 2216.42 | 0.760090 | ||||||||
\(55\) | −669.948 | −0.221470 | ||||||||
\(56\) | − | 1164.11i | − | 0.371209i | ||||||
\(57\) | −2348.82 | + | 519.851i | −0.722938 | + | 0.160003i | ||||
\(58\) | −3806.96 | −1.13168 | ||||||||
\(59\) | − | 1078.88i | − | 0.309933i | −0.987920 | − | 0.154966i | \(-0.950473\pi\) | ||
0.987920 | − | 0.154966i | \(-0.0495269\pi\) | |||||||
\(60\) | 1423.55i | 0.395431i | ||||||||
\(61\) | −6530.89 | −1.75514 | −0.877572 | − | 0.479445i | \(-0.840838\pi\) | ||||
−0.877572 | + | 0.479445i | \(0.840838\pi\) | |||||||
\(62\) | −2581.45 | −0.671553 | ||||||||
\(63\) | 1882.58 | 0.474320 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 1422.00i | 0.336568i | ||||||||
\(66\) | −472.888 | −0.108560 | ||||||||
\(67\) | − | 7386.18i | − | 1.64540i | −0.568478 | − | 0.822698i | \(-0.692468\pi\) | ||
0.568478 | − | 0.822698i | \(-0.307532\pi\) | |||||||
\(68\) | 195.931 | 0.0423726 | ||||||||
\(69\) | 4079.92i | 0.856945i | ||||||||
\(70\) | 3885.62i | 0.792983i | ||||||||
\(71\) | − | 5806.02i | − | 1.15176i | −0.817535 | − | 0.575879i | \(-0.804660\pi\) | ||
0.817535 | − | 0.575879i | \(-0.195340\pi\) | |||||||
\(72\) | − | 827.995i | − | 0.159721i | ||||||
\(73\) | 3629.56 | 0.681096 | 0.340548 | − | 0.940227i | \(-0.389387\pi\) | ||||
0.340548 | + | 0.940227i | \(0.389387\pi\) | |||||||
\(74\) | 919.405 | 0.167897 | ||||||||
\(75\) | − | 586.651i | − | 0.104293i | ||||||
\(76\) | 624.081 | + | 2819.76i | 0.108047 | + | 0.488186i | ||||
\(77\) | −1290.76 | −0.217703 | ||||||||
\(78\) | 1003.73i | 0.164979i | ||||||||
\(79\) | − | 3903.16i | − | 0.625407i | −0.949851 | − | 0.312703i | \(-0.898765\pi\) | ||
0.949851 | − | 0.312703i | \(-0.101235\pi\) | |||||||
\(80\) | 1708.97 | 0.267027 | ||||||||
\(81\) | −2257.99 | −0.344153 | ||||||||
\(82\) | −146.369 | −0.0217682 | ||||||||
\(83\) | −997.967 | −0.144864 | −0.0724319 | − | 0.997373i | \(-0.523076\pi\) | ||||
−0.0724319 | + | 0.997373i | \(0.523076\pi\) | |||||||
\(84\) | 2742.69i | 0.388704i | ||||||||
\(85\) | −653.985 | −0.0905169 | ||||||||
\(86\) | − | 7199.08i | − | 0.973375i | ||||||
\(87\) | 8969.34 | 1.18501 | ||||||||
\(88\) | 567.702i | 0.0733087i | ||||||||
\(89\) | 6152.85i | 0.776777i | 0.921496 | + | 0.388389i | \(0.126968\pi\) | ||||
−0.921496 | + | 0.388389i | \(0.873032\pi\) | |||||||
\(90\) | 2763.71i | 0.341199i | ||||||||
\(91\) | 2739.71i | 0.330843i | ||||||||
\(92\) | 4897.94 | 0.578679 | ||||||||
\(93\) | 6082.00 | 0.703203 | ||||||||
\(94\) | 8480.16i | 0.959728i | ||||||||
\(95\) | −2083.08 | − | 9411.91i | −0.230812 | − | 1.04287i | ||||
\(96\) | 1206.29 | 0.130891 | ||||||||
\(97\) | − | 5023.58i | − | 0.533912i | −0.963709 | − | 0.266956i | \(-0.913982\pi\) | ||
0.963709 | − | 0.266956i | \(-0.0860178\pi\) | |||||||
\(98\) | 695.195i | 0.0723860i | ||||||||
\(99\) | −918.076 | −0.0936717 | ||||||||
\(100\) | −704.274 | −0.0704274 | ||||||||
\(101\) | 15793.7 | 1.54825 | 0.774123 | − | 0.633035i | \(-0.218191\pi\) | ||||
0.774123 | + | 0.633035i | \(0.218191\pi\) | |||||||
\(102\) | −461.621 | −0.0443695 | ||||||||
\(103\) | 13068.7i | 1.23185i | 0.787806 | + | 0.615924i | \(0.211217\pi\) | ||||
−0.787806 | + | 0.615924i | \(0.788783\pi\) | |||||||
\(104\) | 1204.98 | 0.111407 | ||||||||
\(105\) | − | 9154.67i | − | 0.830355i | ||||||
\(106\) | −11505.7 | −1.02400 | ||||||||
\(107\) | 8273.09i | 0.722604i | 0.932449 | + | 0.361302i | \(0.117668\pi\) | ||||
−0.932449 | + | 0.361302i | \(0.882332\pi\) | |||||||
\(108\) | 6268.99i | 0.537465i | ||||||||
\(109\) | − | 14219.6i | − | 1.19683i | −0.801186 | − | 0.598416i | \(-0.795797\pi\) | ||
0.801186 | − | 0.598416i | \(-0.204203\pi\) | |||||||
\(110\) | − | 1894.90i | − | 0.156603i | ||||||
\(111\) | −2166.16 | −0.175810 | ||||||||
\(112\) | 3292.60 | 0.262484 | ||||||||
\(113\) | 20747.4i | 1.62483i | 0.583080 | + | 0.812414i | \(0.301847\pi\) | ||||
−0.583080 | + | 0.812414i | \(0.698153\pi\) | |||||||
\(114\) | −1470.36 | − | 6643.48i | −0.113139 | − | 0.511194i | ||||
\(115\) | −16348.5 | −1.23618 | ||||||||
\(116\) | − | 10767.7i | − | 0.800215i | ||||||
\(117\) | 1948.67i | 0.142353i | ||||||||
\(118\) | 3051.52 | 0.219155 | ||||||||
\(119\) | −1260.00 | −0.0889771 | ||||||||
\(120\) | −4026.41 | −0.279612 | ||||||||
\(121\) | −14011.5 | −0.957007 | ||||||||
\(122\) | − | 18472.1i | − | 1.24107i | ||||||
\(123\) | 344.852 | 0.0227941 | ||||||||
\(124\) | − | 7301.44i | − | 0.474860i | ||||||
\(125\) | −14338.4 | −0.917660 | ||||||||
\(126\) | 5324.73i | 0.335395i | ||||||||
\(127\) | 11117.8i | 0.689305i | 0.938730 | + | 0.344653i | \(0.112003\pi\) | ||||
−0.938730 | + | 0.344653i | \(0.887997\pi\) | |||||||
\(128\) | − | 1448.15i | − | 0.0883883i | ||||||
\(129\) | 16961.3i | 1.01925i | ||||||||
\(130\) | −4022.02 | −0.237990 | ||||||||
\(131\) | 223.317 | 0.0130130 | 0.00650652 | − | 0.999979i | \(-0.497929\pi\) | ||||
0.00650652 | + | 0.999979i | \(0.497929\pi\) | |||||||
\(132\) | − | 1337.53i | − | 0.0767637i | ||||||
\(133\) | −4013.38 | − | 18133.5i | −0.226886 | − | 1.02513i | ||||
\(134\) | 20891.3 | 1.16347 | ||||||||
\(135\) | − | 20924.9i | − | 1.14814i | ||||||
\(136\) | 554.176i | 0.0299619i | ||||||||
\(137\) | 18953.1 | 1.00981 | 0.504903 | − | 0.863176i | \(-0.331528\pi\) | ||||
0.504903 | + | 0.863176i | \(0.331528\pi\) | |||||||
\(138\) | −11539.7 | −0.605952 | ||||||||
\(139\) | −11115.5 | −0.575309 | −0.287655 | − | 0.957734i | \(-0.592875\pi\) | ||||
−0.287655 | + | 0.957734i | \(0.592875\pi\) | |||||||
\(140\) | −10990.2 | −0.560723 | ||||||||
\(141\) | − | 19979.6i | − | 1.00496i | ||||||
\(142\) | 16421.9 | 0.814416 | ||||||||
\(143\) | − | 1336.07i | − | 0.0653368i | ||||||
\(144\) | 2341.92 | 0.112940 | ||||||||
\(145\) | 35940.8i | 1.70943i | ||||||||
\(146\) | 10265.9i | 0.481608i | ||||||||
\(147\) | − | 1637.91i | − | 0.0757975i | ||||||
\(148\) | 2600.47i | 0.118721i | ||||||||
\(149\) | −19727.7 | −0.888597 | −0.444299 | − | 0.895879i | \(-0.646547\pi\) | ||||
−0.444299 | + | 0.895879i | \(0.646547\pi\) | |||||||
\(150\) | 1659.30 | 0.0737466 | ||||||||
\(151\) | − | 770.565i | − | 0.0337952i | −0.999857 | − | 0.0168976i | \(-0.994621\pi\) | ||
0.999857 | − | 0.0168976i | \(-0.00537894\pi\) | |||||||
\(152\) | −7975.50 | + | 1765.17i | −0.345200 | + | 0.0764009i | ||||
\(153\) | −896.201 | −0.0382845 | ||||||||
\(154\) | − | 3650.82i | − | 0.153939i | ||||||
\(155\) | 24371.0i | 1.01440i | ||||||||
\(156\) | −2838.98 | −0.116658 | ||||||||
\(157\) | 46244.5 | 1.87612 | 0.938061 | − | 0.346470i | \(-0.112620\pi\) | ||||
0.938061 | + | 0.346470i | \(0.112620\pi\) | |||||||
\(158\) | 11039.8 | 0.442229 | ||||||||
\(159\) | 27107.8 | 1.07226 | ||||||||
\(160\) | 4833.71i | 0.188817i | ||||||||
\(161\) | −31498.0 | −1.21515 | ||||||||
\(162\) | − | 6386.55i | − | 0.243353i | ||||||
\(163\) | 32951.9 | 1.24024 | 0.620119 | − | 0.784507i | \(-0.287084\pi\) | ||||
0.620119 | + | 0.784507i | \(0.287084\pi\) | |||||||
\(164\) | − | 413.995i | − | 0.0153924i | ||||||
\(165\) | 4464.46i | 0.163984i | ||||||||
\(166\) | − | 2822.68i | − | 0.102434i | ||||||
\(167\) | 48049.1i | 1.72287i | 0.507870 | + | 0.861434i | \(0.330433\pi\) | ||||
−0.507870 | + | 0.861434i | \(0.669567\pi\) | |||||||
\(168\) | −7757.51 | −0.274855 | ||||||||
\(169\) | 25725.1 | 0.900708 | ||||||||
\(170\) | − | 1849.75i | − | 0.0640051i | ||||||
\(171\) | −2854.59 | − | 12897.8i | −0.0976228 | − | 0.441086i | ||||
\(172\) | 20362.1 | 0.688280 | ||||||||
\(173\) | − | 46219.6i | − | 1.54431i | −0.635436 | − | 0.772153i | \(-0.719180\pi\) | ||
0.635436 | − | 0.772153i | \(-0.280820\pi\) | |||||||
\(174\) | 25369.1i | 0.837929i | ||||||||
\(175\) | 4529.10 | 0.147889 | ||||||||
\(176\) | −1605.70 | −0.0518371 | ||||||||
\(177\) | −7189.51 | −0.229484 | ||||||||
\(178\) | −17402.9 | −0.549264 | ||||||||
\(179\) | − | 39826.5i | − | 1.24299i | −0.783420 | − | 0.621493i | \(-0.786527\pi\) | ||
0.783420 | − | 0.621493i | \(-0.213473\pi\) | |||||||
\(180\) | −7816.96 | −0.241264 | ||||||||
\(181\) | − | 51844.5i | − | 1.58251i | −0.611488 | − | 0.791254i | \(-0.709429\pi\) | ||
0.611488 | − | 0.791254i | \(-0.290571\pi\) | |||||||
\(182\) | −7749.06 | −0.233941 | ||||||||
\(183\) | 43521.1i | 1.29957i | ||||||||
\(184\) | 13853.5i | 0.409188i | ||||||||
\(185\) | − | 8679.95i | − | 0.253614i | ||||||
\(186\) | 17202.5i | 0.497239i | ||||||||
\(187\) | 614.467 | 0.0175718 | ||||||||
\(188\) | −23985.5 | −0.678630 | ||||||||
\(189\) | − | 40315.1i | − | 1.12861i | ||||||
\(190\) | 26620.9 | − | 5891.84i | 0.737421 | − | 0.163209i | ||||
\(191\) | −38958.8 | −1.06792 | −0.533960 | − | 0.845509i | \(-0.679297\pi\) | ||||
−0.533960 | + | 0.845509i | \(0.679297\pi\) | |||||||
\(192\) | 3411.91i | 0.0925540i | ||||||||
\(193\) | − | 43058.1i | − | 1.15595i | −0.816053 | − | 0.577977i | \(-0.803842\pi\) | ||
0.816053 | − | 0.577977i | \(-0.196158\pi\) | |||||||
\(194\) | 14208.8 | 0.377533 | ||||||||
\(195\) | 9476.05 | 0.249206 | ||||||||
\(196\) | −1966.31 | −0.0511846 | ||||||||
\(197\) | 26311.0 | 0.677962 | 0.338981 | − | 0.940793i | \(-0.389918\pi\) | ||||
0.338981 | + | 0.940793i | \(0.389918\pi\) | |||||||
\(198\) | − | 2596.71i | − | 0.0662359i | ||||||
\(199\) | −11773.1 | −0.297293 | −0.148647 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148647 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(200\) | − | 1991.99i | − | 0.0497997i | ||||||
\(201\) | −49220.7 | −1.21830 | ||||||||
\(202\) | 44671.2i | 1.09478i | ||||||||
\(203\) | 69245.7i | 1.68035i | ||||||||
\(204\) | − | 1305.66i | − | 0.0313740i | ||||||
\(205\) | 1381.85i | 0.0328816i | ||||||||
\(206\) | −36963.8 | −0.871048 | ||||||||
\(207\) | −22403.5 | −0.522848 | ||||||||
\(208\) | 3408.20i | 0.0787767i | ||||||||
\(209\) | 1957.21 | + | 8843.18i | 0.0448068 | + | 0.202449i | ||||
\(210\) | 25893.3 | 0.587150 | ||||||||
\(211\) | 12495.7i | 0.280670i | 0.990104 | + | 0.140335i | \(0.0448179\pi\) | ||||
−0.990104 | + | 0.140335i | \(0.955182\pi\) | |||||||
\(212\) | − | 32542.9i | − | 0.724077i | ||||||
\(213\) | −38690.7 | −0.852799 | ||||||||
\(214\) | −23399.8 | −0.510958 | ||||||||
\(215\) | −67965.3 | −1.47032 | ||||||||
\(216\) | −17731.4 | −0.380045 | ||||||||
\(217\) | 46954.6i | 0.997146i | ||||||||
\(218\) | 40219.0 | 0.846288 | ||||||||
\(219\) | − | 24187.0i | − | 0.504305i | ||||||
\(220\) | 5359.58 | 0.110735 | ||||||||
\(221\) | − | 1304.24i | − | 0.0267038i | ||||||
\(222\) | − | 6126.82i | − | 0.124317i | ||||||
\(223\) | − | 59706.5i | − | 1.20064i | −0.799761 | − | 0.600319i | \(-0.795040\pi\) | ||
0.799761 | − | 0.600319i | \(-0.204960\pi\) | |||||||
\(224\) | 9312.89i | 0.185605i | ||||||||
\(225\) | 3221.40 | 0.0636326 | ||||||||
\(226\) | −58682.6 | −1.14893 | ||||||||
\(227\) | 57964.2i | 1.12489i | 0.826836 | + | 0.562443i | \(0.190138\pi\) | ||||
−0.826836 | + | 0.562443i | \(0.809862\pi\) | |||||||
\(228\) | 18790.6 | − | 4158.80i | 0.361469 | − | 0.0800016i | ||||
\(229\) | 40157.9 | 0.765773 | 0.382886 | − | 0.923795i | \(-0.374930\pi\) | ||||
0.382886 | + | 0.923795i | \(0.374930\pi\) | |||||||
\(230\) | − | 46240.6i | − | 0.874114i | ||||||
\(231\) | 8601.48i | 0.161194i | ||||||||
\(232\) | 30455.6 | 0.565838 | ||||||||
\(233\) | 71740.1 | 1.32145 | 0.660724 | − | 0.750629i | \(-0.270249\pi\) | ||||
0.660724 | + | 0.750629i | \(0.270249\pi\) | |||||||
\(234\) | −5511.66 | −0.100659 | ||||||||
\(235\) | 80059.7 | 1.44970 | ||||||||
\(236\) | 8631.00i | 0.154966i | ||||||||
\(237\) | −26010.2 | −0.463071 | ||||||||
\(238\) | − | 3563.83i | − | 0.0629163i | ||||||
\(239\) | 44178.4 | 0.773417 | 0.386709 | − | 0.922202i | \(-0.373612\pi\) | ||||
0.386709 | + | 0.922202i | \(0.373612\pi\) | |||||||
\(240\) | − | 11388.4i | − | 0.197715i | ||||||
\(241\) | 33823.7i | 0.582353i | 0.956669 | + | 0.291177i | \(0.0940467\pi\) | ||||
−0.956669 | + | 0.291177i | \(0.905953\pi\) | |||||||
\(242\) | − | 39630.6i | − | 0.676706i | ||||||
\(243\) | − | 48426.6i | − | 0.820108i | ||||||
\(244\) | 52247.1 | 0.877572 | ||||||||
\(245\) | 6563.22 | 0.109341 | ||||||||
\(246\) | 975.390i | 0.0161179i | ||||||||
\(247\) | 18770.1 | − | 4154.27i | 0.307662 | − | 0.0680928i | ||||
\(248\) | 20651.6 | 0.335777 | ||||||||
\(249\) | 6650.34i | 0.107262i | ||||||||
\(250\) | − | 40555.2i | − | 0.648884i | ||||||
\(251\) | −64952.8 | −1.03098 | −0.515490 | − | 0.856896i | \(-0.672390\pi\) | ||||
−0.515490 | + | 0.856896i | \(0.672390\pi\) | |||||||
\(252\) | −15060.6 | −0.237160 | ||||||||
\(253\) | 15360.6 | 0.239976 | ||||||||
\(254\) | −31445.9 | −0.487412 | ||||||||
\(255\) | 4358.08i | 0.0670217i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − | 1155.59i | − | 0.0174959i | −0.999962 | − | 0.00874796i | \(-0.997215\pi\) | ||
0.999962 | − | 0.00874796i | \(-0.00278460\pi\) | |||||||
\(258\) | −47973.9 | −0.720718 | ||||||||
\(259\) | − | 16723.3i | − | 0.249300i | ||||||
\(260\) | − | 11376.0i | − | 0.168284i | ||||||
\(261\) | 49252.2i | 0.723011i | ||||||||
\(262\) | 631.635i | 0.00920161i | ||||||||
\(263\) | 6732.94 | 0.0973404 | 0.0486702 | − | 0.998815i | \(-0.484502\pi\) | ||||
0.0486702 | + | 0.998815i | \(0.484502\pi\) | |||||||
\(264\) | 3783.11 | 0.0542801 | ||||||||
\(265\) | 108623.i | 1.54678i | ||||||||
\(266\) | 51289.4 | − | 11351.6i | 0.724877 | − | 0.160432i | ||||
\(267\) | 41001.9 | 0.575151 | ||||||||
\(268\) | 59089.5i | 0.822698i | ||||||||
\(269\) | 22231.5i | 0.307230i | 0.988131 | + | 0.153615i | \(0.0490915\pi\) | ||||
−0.988131 | + | 0.153615i | \(0.950908\pi\) | |||||||
\(270\) | 59184.5 | 0.811859 | ||||||||
\(271\) | −46597.6 | −0.634490 | −0.317245 | − | 0.948344i | \(-0.602758\pi\) | ||||
−0.317245 | + | 0.948344i | \(0.602758\pi\) | |||||||
\(272\) | −1567.45 | −0.0211863 | ||||||||
\(273\) | 18257.1 | 0.244966 | ||||||||
\(274\) | 53607.3i | 0.714041i | ||||||||
\(275\) | −2208.70 | −0.0292060 | ||||||||
\(276\) | − | 32639.3i | − | 0.428473i | ||||||
\(277\) | 105817. | 1.37910 | 0.689548 | − | 0.724240i | \(-0.257809\pi\) | ||||
0.689548 | + | 0.724240i | \(0.257809\pi\) | |||||||
\(278\) | − | 31439.5i | − | 0.406805i | ||||||
\(279\) | 33397.3i | 0.429045i | ||||||||
\(280\) | − | 31084.9i | − | 0.396491i | ||||||
\(281\) | − | 20298.2i | − | 0.257067i | −0.991705 | − | 0.128533i | \(-0.958973\pi\) | ||
0.991705 | − | 0.128533i | \(-0.0410269\pi\) | |||||||
\(282\) | 56510.8 | 0.710614 | ||||||||
\(283\) | −55710.6 | −0.695609 | −0.347804 | − | 0.937567i | \(-0.613073\pi\) | ||||
−0.347804 | + | 0.937567i | \(0.613073\pi\) | |||||||
\(284\) | 46448.1i | 0.575879i | ||||||||
\(285\) | −62720.0 | + | 13881.4i | −0.772176 | + | 0.170901i | ||||
\(286\) | 3778.99 | 0.0462001 | ||||||||
\(287\) | 2662.35i | 0.0323222i | ||||||||
\(288\) | 6623.96i | 0.0798607i | ||||||||
\(289\) | −82921.2 | −0.992818 | ||||||||
\(290\) | −101656. | −1.20875 | ||||||||
\(291\) | −33476.6 | −0.395326 | ||||||||
\(292\) | −29036.5 | −0.340548 | ||||||||
\(293\) | − | 84053.1i | − | 0.979081i | −0.871980 | − | 0.489541i | \(-0.837164\pi\) | ||
0.871980 | − | 0.489541i | \(-0.162836\pi\) | |||||||
\(294\) | 4632.70 | 0.0535969 | ||||||||
\(295\) | − | 28808.9i | − | 0.331042i | ||||||
\(296\) | −7355.24 | −0.0839486 | ||||||||
\(297\) | 19660.4i | 0.222885i | ||||||||
\(298\) | − | 55798.5i | − | 0.628333i | ||||||
\(299\) | − | 32603.8i | − | 0.364691i | ||||||
\(300\) | 4693.21i | 0.0521467i | ||||||||
\(301\) | −130946. | −1.44530 | ||||||||
\(302\) | 2179.49 | 0.0238968 | ||||||||
\(303\) | − | 105247.i | − | 1.14637i | ||||||
\(304\) | −4992.64 | − | 22558.1i | −0.0540236 | − | 0.244093i | ||||
\(305\) | −174392. | −1.87468 | ||||||||
\(306\) | − | 2534.84i | − | 0.0270712i | ||||||
\(307\) | 10396.7i | 0.110311i | 0.998478 | + | 0.0551555i | \(0.0175655\pi\) | ||||
−0.998478 | + | 0.0551555i | \(0.982435\pi\) | |||||||
\(308\) | 10326.1 | 0.108851 | ||||||||
\(309\) | 87088.2 | 0.912100 | ||||||||
\(310\) | −68931.7 | −0.717291 | ||||||||
\(311\) | 118107. | 1.22111 | 0.610557 | − | 0.791973i | \(-0.290946\pi\) | ||||
0.610557 | + | 0.791973i | \(0.290946\pi\) | |||||||
\(312\) | − | 8029.85i | − | 0.0824894i | ||||||
\(313\) | −8391.17 | −0.0856513 | −0.0428257 | − | 0.999083i | \(-0.513636\pi\) | ||||
−0.0428257 | + | 0.999083i | \(0.513636\pi\) | |||||||
\(314\) | 130799.i | 1.32662i | ||||||||
\(315\) | 50269.9 | 0.506625 | ||||||||
\(316\) | 31225.3i | 0.312703i | ||||||||
\(317\) | − | 143474.i | − | 1.42776i | −0.700270 | − | 0.713878i | \(-0.746937\pi\) | ||
0.700270 | − | 0.713878i | \(-0.253063\pi\) | |||||||
\(318\) | 76672.4i | 0.758202i | ||||||||
\(319\) | − | 33769.0i | − | 0.331847i | ||||||
\(320\) | −13671.8 | −0.133514 | ||||||||
\(321\) | 55131.0 | 0.535039 | ||||||||
\(322\) | − | 89089.8i | − | 0.859244i | ||||||
\(323\) | 1910.57 | + | 8632.47i | 0.0183129 | + | 0.0827428i | ||||
\(324\) | 18063.9 | 0.172076 | ||||||||
\(325\) | 4688.09i | 0.0443843i | ||||||||
\(326\) | 93202.1i | 0.876981i | ||||||||
\(327\) | −94757.6 | −0.886173 | ||||||||
\(328\) | 1170.96 | 0.0108841 | ||||||||
\(329\) | 154248. | 1.42504 | ||||||||
\(330\) | −12627.4 | −0.115954 | ||||||||
\(331\) | 16943.3i | 0.154647i | 0.997006 | + | 0.0773237i | \(0.0246375\pi\) | ||||
−0.997006 | + | 0.0773237i | \(0.975363\pi\) | |||||||
\(332\) | 7983.73 | 0.0724319 | ||||||||
\(333\) | − | 11894.7i | − | 0.107267i | ||||||
\(334\) | −135903. | −1.21825 | ||||||||
\(335\) | − | 197231.i | − | 1.75746i | ||||||
\(336\) | − | 21941.6i | − | 0.194352i | ||||||
\(337\) | 217168.i | 1.91221i | 0.293021 | + | 0.956106i | \(0.405339\pi\) | ||||
−0.293021 | + | 0.956106i | \(0.594661\pi\) | |||||||
\(338\) | 72761.6i | 0.636897i | ||||||||
\(339\) | 138259. | 1.20308 | ||||||||
\(340\) | 5231.88 | 0.0452585 | ||||||||
\(341\) | − | 22898.4i | − | 0.196923i | ||||||
\(342\) | 36480.5 | − | 8074.00i | 0.311895 | − | 0.0690298i | ||||
\(343\) | −110879. | −0.942456 | ||||||||
\(344\) | 57592.7i | 0.486688i | ||||||||
\(345\) | 108945.i | 0.915310i | ||||||||
\(346\) | 130729. | 1.09199 | ||||||||
\(347\) | 64555.0 | 0.536131 | 0.268066 | − | 0.963401i | \(-0.413616\pi\) | ||||
0.268066 | + | 0.963401i | \(0.413616\pi\) | |||||||
\(348\) | −71754.8 | −0.592505 | ||||||||
\(349\) | −113275. | −0.930001 | −0.465001 | − | 0.885310i | \(-0.653946\pi\) | ||||
−0.465001 | + | 0.885310i | \(0.653946\pi\) | |||||||
\(350\) | 12810.2i | 0.104573i | ||||||||
\(351\) | 41730.4 | 0.338718 | ||||||||
\(352\) | − | 4541.62i | − | 0.0366543i | ||||||
\(353\) | 27685.3 | 0.222178 | 0.111089 | − | 0.993810i | \(-0.464566\pi\) | ||||
0.111089 | + | 0.993810i | \(0.464566\pi\) | |||||||
\(354\) | − | 20335.0i | − | 0.162270i | ||||||
\(355\) | − | 155036.i | − | 1.23020i | ||||||
\(356\) | − | 49222.8i | − | 0.388389i | ||||||
\(357\) | 8396.53i | 0.0658815i | ||||||||
\(358\) | 112646. | 0.878923 | ||||||||
\(359\) | 65336.2 | 0.506950 | 0.253475 | − | 0.967342i | \(-0.418426\pi\) | ||||
0.253475 | + | 0.967342i | \(0.418426\pi\) | |||||||
\(360\) | − | 22109.7i | − | 0.170600i | ||||||
\(361\) | −118150. | + | 54992.5i | −0.906606 | + | 0.421977i | ||||
\(362\) | 146638. | 1.11900 | ||||||||
\(363\) | 93371.3i | 0.708599i | ||||||||
\(364\) | − | 21917.7i | − | 0.165421i | ||||||
\(365\) | 96919.1 | 0.727484 | ||||||||
\(366\) | −123096. | −0.918931 | ||||||||
\(367\) | 177298. | 1.31635 | 0.658176 | − | 0.752864i | \(-0.271328\pi\) | ||||
0.658176 | + | 0.752864i | \(0.271328\pi\) | |||||||
\(368\) | −39183.5 | −0.289340 | ||||||||
\(369\) | 1893.64i | 0.0139074i | ||||||||
\(370\) | 24550.6 | 0.179332 | ||||||||
\(371\) | 209279.i | 1.52047i | ||||||||
\(372\) | −48656.0 | −0.351601 | ||||||||
\(373\) | − | 15381.6i | − | 0.110557i | −0.998471 | − | 0.0552783i | \(-0.982395\pi\) | ||
0.998471 | − | 0.0552783i | \(-0.0176046\pi\) | |||||||
\(374\) | 1737.97i | 0.0124251i | ||||||||
\(375\) | 95549.8i | 0.679465i | ||||||||
\(376\) | − | 67841.3i | − | 0.479864i | ||||||
\(377\) | −71676.6 | −0.504307 | ||||||||
\(378\) | 114028. | 0.798047 | ||||||||
\(379\) | − | 232626.i | − | 1.61949i | −0.586780 | − | 0.809746i | \(-0.699605\pi\) | ||
0.586780 | − | 0.809746i | \(-0.300395\pi\) | |||||||
\(380\) | 16664.6 | + | 75295.3i | 0.115406 | + | 0.521436i | ||||
\(381\) | 74087.8 | 0.510384 | ||||||||
\(382\) | − | 110192.i | − | 0.755134i | ||||||
\(383\) | 52033.6i | 0.354721i | 0.984146 | + | 0.177360i | \(0.0567558\pi\) | ||||
−0.984146 | + | 0.177360i | \(0.943244\pi\) | |||||||
\(384\) | −9650.34 | −0.0654456 | ||||||||
\(385\) | −34466.8 | −0.232530 | ||||||||
\(386\) | 121787. | 0.817383 | ||||||||
\(387\) | −93137.6 | −0.621875 | ||||||||
\(388\) | 40188.6i | 0.266956i | ||||||||
\(389\) | 57687.6 | 0.381227 | 0.190613 | − | 0.981665i | \(-0.438952\pi\) | ||||
0.190613 | + | 0.981665i | \(0.438952\pi\) | |||||||
\(390\) | 26802.3i | 0.176215i | ||||||||
\(391\) | 14994.6 | 0.0980804 | ||||||||
\(392\) | − | 5561.56i | − | 0.0361930i | ||||||
\(393\) | − | 1488.16i | − | 0.00963527i | ||||||
\(394\) | 74418.9i | 0.479392i | ||||||||
\(395\) | − | 104225.i | − | 0.668002i | ||||||
\(396\) | 7344.61 | 0.0468358 | ||||||||
\(397\) | 16914.2 | 0.107317 | 0.0536586 | − | 0.998559i | \(-0.482912\pi\) | ||||
0.0536586 | + | 0.998559i | \(0.482912\pi\) | |||||||
\(398\) | − | 33299.4i | − | 0.210218i | ||||||
\(399\) | −120840. | + | 26744.7i | −0.759039 | + | 0.167993i | ||||
\(400\) | 5634.19 | 0.0352137 | ||||||||
\(401\) | 23481.6i | 0.146029i | 0.997331 | + | 0.0730144i | \(0.0232619\pi\) | ||||
−0.997331 | + | 0.0730144i | \(0.976738\pi\) | |||||||
\(402\) | − | 139217.i | − | 0.861471i | ||||||
\(403\) | −48603.0 | −0.299263 | ||||||||
\(404\) | −126349. | −0.774123 | ||||||||
\(405\) | −60294.3 | −0.367592 | ||||||||
\(406\) | −195856. | −1.18819 | ||||||||
\(407\) | 8155.45i | 0.0492333i | ||||||||
\(408\) | 3692.97 | 0.0221848 | ||||||||
\(409\) | 310776.i | 1.85781i | 0.370321 | + | 0.928904i | \(0.379248\pi\) | ||||
−0.370321 | + | 0.928904i | \(0.620752\pi\) | |||||||
\(410\) | −3908.46 | −0.0232508 | ||||||||
\(411\) | − | 126301.i | − | 0.747693i | ||||||
\(412\) | − | 104549.i | − | 0.615924i | ||||||
\(413\) | − | 55504.9i | − | 0.325410i | ||||||
\(414\) | − | 63366.7i | − | 0.369710i | ||||||
\(415\) | −26648.4 | −0.154730 | ||||||||
\(416\) | −9639.83 | −0.0557035 | ||||||||
\(417\) | 74072.8i | 0.425977i | ||||||||
\(418\) | −25012.3 | + | 5535.81i | −0.143153 | + | 0.0316832i | ||||
\(419\) | −271562. | −1.54682 | −0.773411 | − | 0.633905i | \(-0.781451\pi\) | ||||
−0.773411 | + | 0.633905i | \(0.781451\pi\) | |||||||
\(420\) | 73237.3i | 0.415178i | ||||||||
\(421\) | − | 322467.i | − | 1.81937i | −0.415299 | − | 0.909685i | \(-0.636323\pi\) | ||
0.415299 | − | 0.909685i | \(-0.363677\pi\) | |||||||
\(422\) | −35343.2 | −0.198464 | ||||||||
\(423\) | 109711. | 0.613156 | ||||||||
\(424\) | 92045.2 | 0.512000 | ||||||||
\(425\) | −2156.08 | −0.0119368 | ||||||||
\(426\) | − | 109434.i | − | 0.603020i | ||||||
\(427\) | −335994. | −1.84279 | ||||||||
\(428\) | − | 66184.7i | − | 0.361302i | ||||||
\(429\) | −8903.44 | −0.0483775 | ||||||||
\(430\) | − | 192235.i | − | 1.03967i | ||||||
\(431\) | 157951.i | 0.850290i | 0.905125 | + | 0.425145i | \(0.139777\pi\) | ||||
−0.905125 | + | 0.425145i | \(0.860223\pi\) | |||||||
\(432\) | − | 50151.9i | − | 0.268732i | ||||||
\(433\) | − | 36946.7i | − | 0.197061i | −0.995134 | − | 0.0985304i | \(-0.968586\pi\) | ||
0.995134 | − | 0.0985304i | \(-0.0314142\pi\) | |||||||
\(434\) | −132808. | −0.705089 | ||||||||
\(435\) | 239506. | 1.26572 | ||||||||
\(436\) | 113756.i | 0.598416i | ||||||||
\(437\) | 47761.1 | + | 215797.i | 0.250099 | + | 1.13001i | ||||
\(438\) | 68411.1 | 0.356598 | ||||||||
\(439\) | 194377.i | 1.00859i | 0.863531 | + | 0.504296i | \(0.168248\pi\) | ||||
−0.863531 | + | 0.504296i | \(0.831752\pi\) | |||||||
\(440\) | 15159.2i | 0.0783016i | ||||||||
\(441\) | 8994.03 | 0.0462463 | ||||||||
\(442\) | 3688.94 | 0.0188824 | ||||||||
\(443\) | 30671.7 | 0.156290 | 0.0781449 | − | 0.996942i | \(-0.475100\pi\) | ||||
0.0781449 | + | 0.996942i | \(0.475100\pi\) | |||||||
\(444\) | 17329.3 | 0.0879051 | ||||||||
\(445\) | 164298.i | 0.829682i | ||||||||
\(446\) | 168875. | 0.848979 | ||||||||
\(447\) | 131464.i | 0.657946i | ||||||||
\(448\) | −26340.8 | −0.131242 | ||||||||
\(449\) | − | 236846.i | − | 1.17483i | −0.809287 | − | 0.587413i | \(-0.800146\pi\) | ||
0.809287 | − | 0.587413i | \(-0.199854\pi\) | |||||||
\(450\) | 9111.50i | 0.0449951i | ||||||||
\(451\) | − | 1298.35i | − | 0.00638319i | ||||||
\(452\) | − | 165980.i | − | 0.812414i | ||||||
\(453\) | −5134.96 | −0.0250231 | ||||||||
\(454\) | −163948. | −0.795414 | ||||||||
\(455\) | 73157.6i | 0.353376i | ||||||||
\(456\) | 11762.9 | + | 53147.8i | 0.0565697 | + | 0.255597i | ||||
\(457\) | −82060.7 | −0.392919 | −0.196459 | − | 0.980512i | \(-0.562944\pi\) | ||||
−0.196459 | + | 0.980512i | \(0.562944\pi\) | |||||||
\(458\) | 113584.i | 0.541483i | ||||||||
\(459\) | 19192.0i | 0.0910951i | ||||||||
\(460\) | 130788. | 0.618092 | ||||||||
\(461\) | −16781.0 | −0.0789614 | −0.0394807 | − | 0.999220i | \(-0.512570\pi\) | ||||
−0.0394807 | + | 0.999220i | \(0.512570\pi\) | |||||||
\(462\) | −24328.7 | −0.113981 | ||||||||
\(463\) | 100169. | 0.467274 | 0.233637 | − | 0.972324i | \(-0.424937\pi\) | ||||
0.233637 | + | 0.972324i | \(0.424937\pi\) | |||||||
\(464\) | 86141.6i | 0.400108i | ||||||||
\(465\) | 162406. | 0.751097 | ||||||||
\(466\) | 202912.i | 0.934405i | ||||||||
\(467\) | −216772. | −0.993960 | −0.496980 | − | 0.867762i | \(-0.665558\pi\) | ||||
−0.496980 | + | 0.867762i | \(0.665558\pi\) | |||||||
\(468\) | − | 15589.3i | − | 0.0711764i | ||||||
\(469\) | − | 379997.i | − | 1.72756i | ||||||
\(470\) | 226443.i | 1.02509i | ||||||||
\(471\) | − | 308168.i | − | 1.38914i | ||||||
\(472\) | −24412.2 | −0.109578 | ||||||||
\(473\) | 63858.4 | 0.285427 | ||||||||
\(474\) | − | 73568.1i | − | 0.327441i | ||||||
\(475\) | −6867.56 | − | 31029.5i | −0.0304379 | − | 0.137527i | ||||
\(476\) | 10080.0 | 0.0444885 | ||||||||
\(477\) | 148854.i | 0.654218i | ||||||||
\(478\) | 124955.i | 0.546889i | ||||||||
\(479\) | 91676.2 | 0.399563 | 0.199782 | − | 0.979840i | \(-0.435977\pi\) | ||||
0.199782 | + | 0.979840i | \(0.435977\pi\) | |||||||
\(480\) | 32211.3 | 0.139806 | ||||||||
\(481\) | 17310.4 | 0.0748198 | ||||||||
\(482\) | −95667.8 | −0.411786 | ||||||||
\(483\) | 209899.i | 0.899739i | ||||||||
\(484\) | 112092. | 0.478503 | ||||||||
\(485\) | − | 134143.i | − | 0.570276i | ||||||
\(486\) | 136971. | 0.579904 | ||||||||
\(487\) | 107326.i | 0.452528i | 0.974066 | + | 0.226264i | \(0.0726512\pi\) | ||||
−0.974066 | + | 0.226264i | \(0.927349\pi\) | |||||||
\(488\) | 147777.i | 0.620537i | ||||||||
\(489\) | − | 219588.i | − | 0.918313i | ||||||
\(490\) | 18563.6i | 0.0773160i | ||||||||
\(491\) | 211818. | 0.878619 | 0.439310 | − | 0.898336i | \(-0.355223\pi\) | ||||
0.439310 | + | 0.898336i | \(0.355223\pi\) | |||||||
\(492\) | −2758.82 | −0.0113971 | ||||||||
\(493\) | − | 32964.4i | − | 0.135629i | ||||||
\(494\) | 11750.1 | + | 53089.9i | 0.0481489 | + | 0.217550i | ||||
\(495\) | −24515.1 | −0.100051 | ||||||||
\(496\) | 58411.5i | 0.237430i | ||||||||
\(497\) | − | 298702.i | − | 1.20928i | ||||||
\(498\) | −18810.0 | −0.0758456 | ||||||||
\(499\) | 145489. | 0.584291 | 0.292146 | − | 0.956374i | \(-0.405631\pi\) | ||||
0.292146 | + | 0.956374i | \(0.405631\pi\) | |||||||
\(500\) | 114707. | 0.458830 | ||||||||
\(501\) | 320194. | 1.27567 | ||||||||
\(502\) | − | 183714.i | − | 0.729013i | ||||||
\(503\) | −33735.6 | −0.133338 | −0.0666689 | − | 0.997775i | \(-0.521237\pi\) | ||||
−0.0666689 | + | 0.997775i | \(0.521237\pi\) | |||||||
\(504\) | − | 42597.8i | − | 0.167697i | ||||||
\(505\) | 421733. | 1.65369 | ||||||||
\(506\) | 43446.4i | 0.169689i | ||||||||
\(507\) | − | 171429.i | − | 0.666913i | ||||||
\(508\) | − | 88942.4i | − | 0.344653i | ||||||
\(509\) | − | 128247.i | − | 0.495009i | −0.968887 | − | 0.247505i | \(-0.920389\pi\) | ||
0.968887 | − | 0.247505i | \(-0.0796105\pi\) | |||||||
\(510\) | −12326.5 | −0.0473915 | ||||||||
\(511\) | 186730. | 0.715108 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | −276204. | + | 61130.6i | −1.04953 | + | 0.232286i | ||||
\(514\) | 3268.50 | 0.0123715 | ||||||||
\(515\) | 348969.i | 1.31575i | ||||||||
\(516\) | − | 135691.i | − | 0.509625i | ||||||
\(517\) | −75222.0 | −0.281426 | ||||||||
\(518\) | 47300.6 | 0.176282 | ||||||||
\(519\) | −308002. | −1.14345 | ||||||||
\(520\) | 32176.2 | 0.118995 | ||||||||
\(521\) | − | 38092.9i | − | 0.140336i | −0.997535 | − | 0.0701680i | \(-0.977646\pi\) | ||
0.997535 | − | 0.0701680i | \(-0.0223535\pi\) | |||||||
\(522\) | −139306. | −0.511246 | ||||||||
\(523\) | 96329.4i | 0.352173i | 0.984375 | + | 0.176086i | \(0.0563438\pi\) | ||||
−0.984375 | + | 0.176086i | \(0.943656\pi\) | |||||||
\(524\) | −1786.53 | −0.00650652 | ||||||||
\(525\) | − | 30181.4i | − | 0.109502i | ||||||
\(526\) | 19043.6i | 0.0688301i | ||||||||
\(527\) | − | 22352.8i | − | 0.0804841i | ||||||
\(528\) | 10700.2i | 0.0383818i | ||||||||
\(529\) | 94999.8 | 0.339478 | ||||||||
\(530\) | −307232. | −1.09374 | ||||||||
\(531\) | − | 39478.8i | − | 0.140015i | ||||||
\(532\) | 32107.0 | + | 145068.i | 0.113443 | + | 0.512565i | ||||
\(533\) | −2755.81 | −0.00970053 | ||||||||
\(534\) | 115971.i | 0.406693i | ||||||||
\(535\) | 220914.i | 0.771819i | ||||||||
\(536\) | −167130. | −0.581735 | ||||||||
\(537\) | −265399. | −0.920346 | ||||||||
\(538\) | −62880.1 | −0.217244 | ||||||||
\(539\) | −6166.62 | −0.0212261 | ||||||||
\(540\) | 167399.i | 0.574071i | ||||||||
\(541\) | −163021. | −0.556993 | −0.278496 | − | 0.960437i | \(-0.589836\pi\) | ||||
−0.278496 | + | 0.960437i | \(0.589836\pi\) | |||||||
\(542\) | − | 131798.i | − | 0.448652i | ||||||
\(543\) | −345486. | −1.17174 | ||||||||
\(544\) | − | 4433.41i | − | 0.0149810i | ||||||
\(545\) | − | 379701.i | − | 1.27835i | ||||||
\(546\) | 51638.9i | 0.173217i | ||||||||
\(547\) | 450817.i | 1.50670i | 0.657621 | + | 0.753349i | \(0.271563\pi\) | ||||
−0.657621 | + | 0.753349i | \(0.728437\pi\) | |||||||
\(548\) | −151624. | −0.504903 | ||||||||
\(549\) | −238982. | −0.792904 | ||||||||
\(550\) | − | 6247.16i | − | 0.0206518i | ||||||
\(551\) | 474412. | − | 104999.i | 1.56262 | − | 0.345844i | ||||
\(552\) | 92318.0 | 0.302976 | ||||||||
\(553\) | − | 200806.i | − | 0.656638i | ||||||
\(554\) | 299295.i | 0.975168i | ||||||||
\(555\) | −57842.2 | −0.187784 | ||||||||
\(556\) | 88924.4 | 0.287655 | ||||||||
\(557\) | −270930. | −0.873268 | −0.436634 | − | 0.899639i | \(-0.643829\pi\) | ||||
−0.436634 | + | 0.899639i | \(0.643829\pi\) | |||||||
\(558\) | −94461.9 | −0.303381 | ||||||||
\(559\) | − | 135543.i | − | 0.433764i | ||||||
\(560\) | 87921.4 | 0.280362 | ||||||||
\(561\) | − | 4094.74i | − | 0.0130107i | ||||||
\(562\) | 57412.1 | 0.181774 | ||||||||
\(563\) | − | 59429.1i | − | 0.187492i | −0.995596 | − | 0.0937459i | \(-0.970116\pi\) | ||
0.995596 | − | 0.0937459i | \(-0.0298841\pi\) | |||||||
\(564\) | 159837.i | 0.502480i | ||||||||
\(565\) | 554013.i | 1.73549i | ||||||||
\(566\) | − | 157573.i | − | 0.491870i | ||||||
\(567\) | −116166. | −0.361339 | ||||||||
\(568\) | −131375. | −0.407208 | ||||||||
\(569\) | − | 364145.i | − | 1.12473i | −0.826888 | − | 0.562367i | \(-0.809891\pi\) | ||
0.826888 | − | 0.562367i | \(-0.190109\pi\) | |||||||
\(570\) | −39262.6 | − | 177399.i | −0.120845 | − | 0.546011i | ||||
\(571\) | 410057. | 1.25769 | 0.628843 | − | 0.777532i | \(-0.283529\pi\) | ||||
0.628843 | + | 0.777532i | \(0.283529\pi\) | |||||||
\(572\) | 10688.6i | 0.0326684i | ||||||||
\(573\) | 259617.i | 0.790723i | ||||||||
\(574\) | −7530.26 | −0.0228553 | ||||||||
\(575\) | −53898.3 | −0.163020 | ||||||||
\(576\) | −18735.4 | −0.0564700 | ||||||||
\(577\) | −44617.5 | −0.134015 | −0.0670075 | − | 0.997752i | \(-0.521345\pi\) | ||||
−0.0670075 | + | 0.997752i | \(0.521345\pi\) | |||||||
\(578\) | − | 234536.i | − | 0.702029i | ||||||
\(579\) | −286935. | −0.855906 | ||||||||
\(580\) | − | 287527.i | − | 0.854717i | ||||||
\(581\) | −51342.3 | −0.152098 | ||||||||
\(582\) | − | 94686.0i | − | 0.279537i | ||||||
\(583\) | − | 102059.i | − | 0.300272i | ||||||
\(584\) | − | 82127.6i | − | 0.240804i | ||||||
\(585\) | 52034.7i | 0.152048i | ||||||||
\(586\) | 237738. | 0.692315 | ||||||||
\(587\) | −371422. | −1.07793 | −0.538966 | − | 0.842328i | \(-0.681185\pi\) | ||||
−0.538966 | + | 0.842328i | \(0.681185\pi\) | |||||||
\(588\) | 13103.3i | 0.0378987i | ||||||||
\(589\) | 321693. | − | 71198.3i | 0.927280 | − | 0.205229i | ||||
\(590\) | 81483.9 | 0.234082 | ||||||||
\(591\) | − | 175334.i | − | 0.501985i | ||||||
\(592\) | − | 20803.8i | − | 0.0593606i | ||||||
\(593\) | −327963. | −0.932644 | −0.466322 | − | 0.884615i | \(-0.654421\pi\) | ||||
−0.466322 | + | 0.884615i | \(0.654421\pi\) | |||||||
\(594\) | −55608.1 | −0.157603 | ||||||||
\(595\) | −33645.5 | −0.0950372 | ||||||||
\(596\) | 157822. | 0.444299 | ||||||||
\(597\) | 78454.7i | 0.220125i | ||||||||
\(598\) | 92217.4 | 0.257876 | ||||||||
\(599\) | 81737.2i | 0.227806i | 0.993492 | + | 0.113903i | \(0.0363354\pi\) | ||||
−0.993492 | + | 0.113903i | \(0.963665\pi\) | |||||||
\(600\) | −13274.4 | −0.0368733 | ||||||||
\(601\) | 75524.8i | 0.209093i | 0.994520 | + | 0.104547i | \(0.0333392\pi\) | ||||
−0.994520 | + | 0.104547i | \(0.966661\pi\) | |||||||
\(602\) | − | 370371.i | − | 1.02198i | ||||||
\(603\) | − | 270279.i | − | 0.743325i | ||||||
\(604\) | 6164.52i | 0.0168976i | ||||||||
\(605\) | −374146. | −1.02219 | ||||||||
\(606\) | 297684. | 0.810607 | ||||||||
\(607\) | 97397.5i | 0.264345i | 0.991227 | + | 0.132172i | \(0.0421952\pi\) | ||||
−0.991227 | + | 0.132172i | \(0.957805\pi\) | |||||||
\(608\) | 63804.0 | − | 14121.3i | 0.172600 | − | 0.0382005i | ||||
\(609\) | 461445. | 1.24419 | ||||||||
\(610\) | − | 493256.i | − | 1.32560i | ||||||
\(611\) | 159663.i | 0.427682i | ||||||||
\(612\) | 7169.61 | 0.0191422 | ||||||||
\(613\) | 185283. | 0.493078 | 0.246539 | − | 0.969133i | \(-0.420707\pi\) | ||||
0.246539 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(614\) | −29406.3 | −0.0780017 | ||||||||
\(615\) | 9208.49 | 0.0243466 | ||||||||
\(616\) | 29206.6i | 0.0769695i | ||||||||
\(617\) | 628408. | 1.65071 | 0.825357 | − | 0.564612i | \(-0.190974\pi\) | ||||
0.825357 | + | 0.564612i | \(0.190974\pi\) | |||||||
\(618\) | 246323.i | 0.644952i | ||||||||
\(619\) | 203791. | 0.531867 | 0.265933 | − | 0.963991i | \(-0.414320\pi\) | ||||
0.265933 | + | 0.963991i | \(0.414320\pi\) | |||||||
\(620\) | − | 194968.i | − | 0.507201i | ||||||
\(621\) | 479768.i | 1.24408i | ||||||||
\(622\) | 334058.i | 0.863458i | ||||||||
\(623\) | 316545.i | 0.815568i | ||||||||
\(624\) | 22711.8 | 0.0583288 | ||||||||
\(625\) | −437896. | −1.12101 | ||||||||
\(626\) | − | 23733.8i | − | 0.0605646i | ||||||
\(627\) | 58930.0 | − | 13042.6i | 0.149900 | − | 0.0331764i | ||||
\(628\) | −369956. | −0.938061 | ||||||||
\(629\) | 7961.13i | 0.0201221i | ||||||||
\(630\) | 142185.i | 0.358238i | ||||||||
\(631\) | 496722. | 1.24754 | 0.623771 | − | 0.781607i | \(-0.285600\pi\) | ||||
0.623771 | + | 0.781607i | \(0.285600\pi\) | |||||||
\(632\) | −88318.5 | −0.221115 | ||||||||
\(633\) | 83270.0 | 0.207817 | ||||||||
\(634\) | 405805. | 1.00958 | ||||||||
\(635\) | 296875.i | 0.736252i | ||||||||
\(636\) | −216862. | −0.536130 | ||||||||
\(637\) | 13089.0i | 0.0322572i | ||||||||
\(638\) | 95513.2 | 0.234651 | ||||||||
\(639\) | − | 212457.i | − | 0.520319i | ||||||
\(640\) | − | 38669.6i | − | 0.0944083i | ||||||
\(641\) | 44345.5i | 0.107928i | 0.998543 | + | 0.0539639i | \(0.0171856\pi\) | ||||
−0.998543 | + | 0.0539639i | \(0.982814\pi\) | |||||||
\(642\) | 155934.i | 0.378330i | ||||||||
\(643\) | 139327. | 0.336987 | 0.168494 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168494 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(644\) | 251984. | 0.607577 | ||||||||
\(645\) | 452913.i | 1.08867i | ||||||||
\(646\) | −24416.3 | + | 5403.91i | −0.0585080 | + | 0.0129492i | ||||
\(647\) | −617612. | −1.47539 | −0.737696 | − | 0.675133i | \(-0.764086\pi\) | ||||
−0.737696 | + | 0.675133i | \(0.764086\pi\) | |||||||
\(648\) | 51092.4i | 0.121676i | ||||||||
\(649\) | 27068.1i | 0.0642640i | ||||||||
\(650\) | −13259.9 | −0.0313845 | ||||||||
\(651\) | 312900. | 0.738319 | ||||||||
\(652\) | −263615. | −0.620119 | ||||||||
\(653\) | 570062. | 1.33689 | 0.668446 | − | 0.743761i | \(-0.266960\pi\) | ||||
0.668446 | + | 0.743761i | \(0.266960\pi\) | |||||||
\(654\) | − | 268015.i | − | 0.626619i | ||||||
\(655\) | 5963.16 | 0.0138993 | ||||||||
\(656\) | 3311.96i | 0.00769622i | ||||||||
\(657\) | 132815. | 0.307692 | ||||||||
\(658\) | 436278.i | 1.00765i | ||||||||
\(659\) | 716546.i | 1.64996i | 0.565162 | + | 0.824980i | \(0.308814\pi\) | ||||
−0.565162 | + | 0.824980i | \(0.691186\pi\) | |||||||
\(660\) | − | 35715.7i | − | 0.0819919i | ||||||
\(661\) | 187692.i | 0.429579i | 0.976660 | + | 0.214790i | \(0.0689066\pi\) | ||||
−0.976660 | + | 0.214790i | \(0.931093\pi\) | |||||||
\(662\) | −47923.0 | −0.109352 | ||||||||
\(663\) | −8691.30 | −0.0197723 | ||||||||
\(664\) | 22581.4i | 0.0512171i | ||||||||
\(665\) | −107168. | − | 484214.i | −0.242338 | − | 1.09495i | ||||
\(666\) | 33643.4 | 0.0758493 | ||||||||
\(667\) | − | 824055.i | − | 1.85227i | ||||||
\(668\) | − | 384393.i | − | 0.861434i | ||||||
\(669\) | −397877. | −0.888990 | ||||||||
\(670\) | 557854. | 1.24271 | ||||||||
\(671\) | 163854. | 0.363926 | ||||||||
\(672\) | 62060.1 | 0.137428 | ||||||||
\(673\) | − | 504263.i | − | 1.11334i | −0.830734 | − | 0.556669i | \(-0.812079\pi\) | ||
0.830734 | − | 0.556669i | \(-0.187921\pi\) | |||||||
\(674\) | −614244. | −1.35214 | ||||||||
\(675\) | − | 68985.8i | − | 0.151409i | ||||||
\(676\) | −205801. | −0.450354 | ||||||||
\(677\) | 689926.i | 1.50531i | 0.658417 | + | 0.752653i | \(0.271226\pi\) | ||||
−0.658417 | + | 0.752653i | \(0.728774\pi\) | |||||||
\(678\) | 391055.i | 0.850703i | ||||||||
\(679\) | − | 258448.i | − | 0.560574i | ||||||
\(680\) | 14798.0i | 0.0320026i | ||||||||
\(681\) | 386267. | 0.832901 | ||||||||
\(682\) | 64766.3 | 0.139245 | ||||||||
\(683\) | − | 226300.i | − | 0.485113i | −0.970137 | − | 0.242556i | \(-0.922014\pi\) | ||
0.970137 | − | 0.242556i | \(-0.0779859\pi\) | |||||||
\(684\) | 22836.7 | + | 103182.i | 0.0488114 | + | 0.220543i | ||||
\(685\) | 506098. | 1.07858 | ||||||||
\(686\) | − | 313613.i | − | 0.666417i | ||||||
\(687\) | − | 267608.i | − | 0.567003i | ||||||
\(688\) | −162897. | −0.344140 | ||||||||
\(689\) | −216626. | −0.456323 | ||||||||
\(690\) | −308142. | −0.647222 | ||||||||
\(691\) | −921891. | −1.93074 | −0.965370 | − | 0.260886i | \(-0.915985\pi\) | ||||
−0.965370 | + | 0.260886i | \(0.915985\pi\) | |||||||
\(692\) | 369756.i | 0.772153i | ||||||||
\(693\) | −47232.2 | −0.0983494 | ||||||||
\(694\) | 182589.i | 0.379102i | ||||||||
\(695\) | −296815. | −0.614492 | ||||||||
\(696\) | − | 202953.i | − | 0.418964i | ||||||
\(697\) | − | 1267.41i | − | 0.00260887i | ||||||
\(698\) | − | 320390.i | − | 0.657610i | ||||||
\(699\) | − | 478068.i | − | 0.978443i | ||||||
\(700\) | −36232.8 | −0.0739444 | ||||||||
\(701\) | −561368. | −1.14238 | −0.571191 | − | 0.820817i | \(-0.693519\pi\) | ||||
−0.571191 | + | 0.820817i | \(0.693519\pi\) | |||||||
\(702\) | 118031.i | 0.239510i | ||||||||
\(703\) | −114574. | + | 25357.9i | −0.231832 | + | 0.0513100i | ||||
\(704\) | 12845.6 | 0.0259185 | ||||||||
\(705\) | − | 533509.i | − | 1.07341i | ||||||
\(706\) | 78306.0i | 0.157103i | ||||||||
\(707\) | 812536. | 1.62556 | ||||||||
\(708\) | 57516.1 | 0.114742 | ||||||||
\(709\) | −287728. | −0.572386 | −0.286193 | − | 0.958172i | \(-0.592390\pi\) | ||||
−0.286193 | + | 0.958172i | \(0.592390\pi\) | |||||||
\(710\) | 438509. | 0.869885 | ||||||||
\(711\) | − | 142827.i | − | 0.282534i | ||||||
\(712\) | 139223. | 0.274632 | ||||||||
\(713\) | − | 558782.i | − | 1.09917i | ||||||
\(714\) | −23749.0 | −0.0465853 | ||||||||
\(715\) | − | 35676.8i | − | 0.0697868i | ||||||
\(716\) | 318612.i | 0.621493i | ||||||||
\(717\) | − | 294400.i | − | 0.572663i | ||||||
\(718\) | 184799.i | 0.358468i | ||||||||
\(719\) | −805860. | −1.55884 | −0.779420 | − | 0.626502i | \(-0.784486\pi\) | ||||
−0.779420 | + | 0.626502i | \(0.784486\pi\) | |||||||
\(720\) | 62535.7 | 0.120632 | ||||||||
\(721\) | 672344.i | 1.29336i | ||||||||
\(722\) | −155542. | − | 334178.i | −0.298383 | − | 0.641068i | ||||
\(723\) | 225397. | 0.431193 | ||||||||
\(724\) | 414756.i | 0.791254i | ||||||||
\(725\) | 118491.i | 0.225428i | ||||||||
\(726\) | −264094. | −0.501055 | ||||||||
\(727\) | −348604. | −0.659575 | −0.329787 | − | 0.944055i | \(-0.606977\pi\) | ||||
−0.329787 | + | 0.944055i | \(0.606977\pi\) | |||||||
\(728\) | 61992.5 | 0.116970 | ||||||||
\(729\) | −505606. | −0.951387 | ||||||||
\(730\) | 274129.i | 0.514409i | ||||||||
\(731\) | 62336.8 | 0.116657 | ||||||||
\(732\) | − | 348169.i | − | 0.649783i | ||||||
\(733\) | 238795. | 0.444443 | 0.222222 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222222 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(734\) | 501475.i | 0.930801i | ||||||||
\(735\) | − | 43736.6i | − | 0.0809599i | ||||||
\(736\) | − | 110828.i | − | 0.204594i | ||||||
\(737\) | 185313.i | 0.341170i | ||||||||
\(738\) | −5356.03 | −0.00983401 | ||||||||
\(739\) | 502122. | 0.919433 | 0.459717 | − | 0.888066i | \(-0.347951\pi\) | ||||
0.459717 | + | 0.888066i | \(0.347951\pi\) | |||||||
\(740\) | 69439.6i | 0.126807i | ||||||||
\(741\) | −27683.6 | − | 125082.i | −0.0504181 | − | 0.227803i | ||||
\(742\) | −591931. | −1.07514 | ||||||||
\(743\) | 411861.i | 0.746058i | 0.927820 | + | 0.373029i | \(0.121681\pi\) | ||||
−0.927820 | + | 0.373029i | \(0.878319\pi\) | |||||||
\(744\) | − | 137620.i | − | 0.248620i | ||||||
\(745\) | −526784. | −0.949118 | ||||||||
\(746\) | 43505.8 | 0.0781753 | ||||||||
\(747\) | −36518.2 | −0.0654437 | ||||||||
\(748\) | −4915.73 | −0.00878588 | ||||||||
\(749\) | 425625.i | 0.758689i | ||||||||
\(750\) | −270256. | −0.480454 | ||||||||
\(751\) | − | 876407.i | − | 1.55391i | −0.629556 | − | 0.776955i | \(-0.716763\pi\) | ||
0.629556 | − | 0.776955i | \(-0.283237\pi\) | |||||||
\(752\) | 191884. | 0.339315 | ||||||||
\(753\) | 432838.i | 0.763371i | ||||||||
\(754\) | − | 202732.i | − | 0.356599i | ||||||
\(755\) | − | 20576.2i | − | 0.0360970i | ||||||
\(756\) | 322520.i | 0.564305i | ||||||||
\(757\) | −447975. | −0.781739 | −0.390870 | − | 0.920446i | \(-0.627826\pi\) | ||||
−0.390870 | + | 0.920446i | \(0.627826\pi\) | |||||||
\(758\) | 657964. | 1.14515 | ||||||||
\(759\) | − | 102362.i | − | 0.177686i | ||||||
\(760\) | −212967. | + | 47134.7i | −0.368711 | + | 0.0816044i | ||||
\(761\) | 527400. | 0.910690 | 0.455345 | − | 0.890315i | \(-0.349516\pi\) | ||||
0.455345 | + | 0.890315i | \(0.349516\pi\) | |||||||
\(762\) | 209552.i | 0.360896i | ||||||||
\(763\) | − | 731553.i | − | 1.25660i | ||||||
\(764\) | 311671. | 0.533960 | ||||||||
\(765\) | −23931.0 | −0.0408919 | ||||||||
\(766\) | −147173. | −0.250825 | ||||||||
\(767\) | 57453.4 | 0.0976619 | ||||||||
\(768\) | − | 27295.3i | − | 0.0462770i | ||||||
\(769\) | 549287. | 0.928852 | 0.464426 | − | 0.885612i | \(-0.346261\pi\) | ||||
0.464426 | + | 0.885612i | \(0.346261\pi\) | |||||||
\(770\) | − | 97486.7i | − | 0.164424i | ||||||
\(771\) | −7700.71 | −0.0129545 | ||||||||
\(772\) | 344465.i | 0.577977i | ||||||||
\(773\) | 1.03569e6i | 1.73329i | 0.498927 | + | 0.866644i | \(0.333728\pi\) | ||||
−0.498927 | + | 0.866644i | \(0.666272\pi\) | |||||||
\(774\) | − | 263433.i | − | 0.439732i | ||||||
\(775\) | 80347.2i | 0.133773i | ||||||||
\(776\) | −113671. | −0.188766 | ||||||||
\(777\) | −111442. | −0.184590 | ||||||||
\(778\) | 163165.i | 0.269568i | ||||||||
\(779\) | 18240.1 | − | 4036.98i | 0.0300575 | − | 0.00665244i | ||||
\(780\) | −75808.4 | −0.124603 | ||||||||
\(781\) | 145668.i | 0.238815i | ||||||||
\(782\) | 42411.2i | 0.0693533i | ||||||||
\(783\) | 1.05473e6 | 1.72035 | ||||||||
\(784\) | 15730.5 | 0.0255923 | ||||||||
\(785\) | 1.23485e6 | 2.00390 | ||||||||
\(786\) | 4209.15 | 0.00681317 | ||||||||
\(787\) | − | 1.04115e6i | − | 1.68098i | −0.541824 | − | 0.840492i | \(-0.682266\pi\) | ||
0.541824 | − | 0.840492i | \(-0.317734\pi\) | |||||||
\(788\) | −210488. | −0.338981 | ||||||||
\(789\) | − | 44867.6i | − | 0.0720740i | ||||||
\(790\) | 294793. | 0.472349 | ||||||||
\(791\) | 1.06739e6i | 1.70597i | ||||||||
\(792\) | 20773.7i | 0.0331179i | ||||||||
\(793\) | − | 347790.i | − | 0.553058i | ||||||
\(794\) | 47840.5i | 0.0758847i | ||||||||
\(795\) | 723851. | 1.14529 | ||||||||
\(796\) | 94184.8 | 0.148647 | ||||||||
\(797\) | − | 476576.i | − | 0.750266i | −0.926971 | − | 0.375133i | \(-0.877597\pi\) | ||
0.926971 | − | 0.375133i | \(-0.122403\pi\) | |||||||
\(798\) | −75645.5 | − | 341787.i | −0.118789 | − | 0.536722i | ||||
\(799\) | −73429.7 | −0.115021 | ||||||||
\(800\) | 15935.9i | 0.0248999i | ||||||||
\(801\) | 225149.i | 0.350917i | ||||||||
\(802\) | −66415.9 | −0.103258 | ||||||||
\(803\) | −91062.5 | −0.141224 | ||||||||
\(804\) | 393766. | 0.609152 | ||||||||
\(805\) | −841082. | −1.29792 | ||||||||
\(806\) | − | 137470.i | − | 0.211611i | ||||||
\(807\) | 148148. | 0.227483 | ||||||||
\(808\) | − | 357370.i | − | 0.547388i | ||||||
\(809\) | −1.00569e6 | −1.53663 | −0.768314 | − | 0.640074i | \(-0.778904\pi\) | ||||
−0.768314 | + | 0.640074i | \(0.778904\pi\) | |||||||
\(810\) | − | 170538.i | − | 0.259927i | ||||||
\(811\) | 257961.i | 0.392205i | 0.980583 | + | 0.196102i | \(0.0628285\pi\) | ||||
−0.980583 | + | 0.196102i | \(0.937171\pi\) | |||||||
\(812\) | − | 553965.i | − | 0.840176i | ||||||
\(813\) | 310521.i | 0.469797i | ||||||||
\(814\) | −23067.1 | −0.0348132 | ||||||||
\(815\) | 879905. | 1.32471 | ||||||||
\(816\) | 10445.3i | 0.0156870i | ||||||||
\(817\) | 198556. | + | 897129.i | 0.297467 | + | 1.34404i | ||||
\(818\) | −879007. | −1.31367 | ||||||||
\(819\) | 100253.i | 0.149461i | ||||||||
\(820\) | − | 11054.8i | − | 0.0164408i | ||||||
\(821\) | −65320.9 | −0.0969094 | −0.0484547 | − | 0.998825i | \(-0.515430\pi\) | ||||
−0.0484547 | + | 0.998825i | \(0.515430\pi\) | |||||||
\(822\) | 357233. | 0.528699 | ||||||||
\(823\) | −109324. | −0.161404 | −0.0807020 | − | 0.996738i | \(-0.525716\pi\) | ||||
−0.0807020 | + | 0.996738i | \(0.525716\pi\) | |||||||
\(824\) | 295710. | 0.435524 | ||||||||
\(825\) | 14718.6i | 0.0216251i | ||||||||
\(826\) | 156991. | 0.230100 | ||||||||
\(827\) | − | 988603.i | − | 1.44548i | −0.691122 | − | 0.722738i | \(-0.742883\pi\) | ||
0.691122 | − | 0.722738i | \(-0.257117\pi\) | |||||||
\(828\) | 179228. | 0.261424 | ||||||||
\(829\) | 467829.i | 0.680735i | 0.940292 | + | 0.340368i | \(0.110552\pi\) | ||||
−0.940292 | + | 0.340368i | \(0.889448\pi\) | |||||||
\(830\) | − | 75373.1i | − | 0.109411i | ||||||
\(831\) | − | 705151.i | − | 1.02113i | ||||||
\(832\) | − | 27265.6i | − | 0.0393884i | ||||||
\(833\) | −6019.69 | −0.00867529 | ||||||||
\(834\) | −209509. | −0.301211 | ||||||||
\(835\) | 1.28304e6i | 1.84021i | ||||||||
\(836\) | −15657.6 | − | 70745.4i | −0.0224034 | − | 0.101225i | ||||
\(837\) | 715198. | 1.02088 | ||||||||
\(838\) | − | 768092.i | − | 1.09377i | ||||||
\(839\) | 657894.i | 0.934613i | 0.884095 | + | 0.467306i | \(0.154776\pi\) | ||||
−0.884095 | + | 0.467306i | \(0.845224\pi\) | |||||||
\(840\) | −207147. | −0.293575 | ||||||||
\(841\) | −1.10433e6 | −1.56138 | ||||||||
\(842\) | 912074. | 1.28649 | ||||||||
\(843\) | −135265. | −0.190340 | ||||||||
\(844\) | − | 99965.6i | − | 0.140335i | ||||||
\(845\) | 686930. | 0.962053 | ||||||||
\(846\) | 310311.i | 0.433567i | ||||||||
\(847\) | −720851. | −1.00480 | ||||||||
\(848\) | 260343.i | 0.362038i | ||||||||
\(849\) | 371249.i | 0.515051i | ||||||||
\(850\) | − | 6098.31i | − | 0.00844057i | ||||||
\(851\) | 199015.i | 0.274806i | ||||||||
\(852\) | 309525. | 0.426400 | ||||||||
\(853\) | −226576. | −0.311398 | −0.155699 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155699 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(854\) | − | 950336.i | − | 1.30305i | ||||||
\(855\) | −76225.2 | − | 344406.i | −0.104272 | − | 0.471128i | ||||
\(856\) | 187199. | 0.255479 | ||||||||
\(857\) | 183273.i | 0.249539i | 0.992186 | + | 0.124769i | \(0.0398191\pi\) | ||||
−0.992186 | + | 0.124769i | \(0.960181\pi\) | |||||||
\(858\) | − | 25182.7i | − | 0.0342081i | ||||||
\(859\) | 565839. | 0.766843 | 0.383421 | − | 0.923574i | \(-0.374746\pi\) | ||||
0.383421 | + | 0.923574i | \(0.374746\pi\) | |||||||
\(860\) | 543723. | 0.735158 | ||||||||
\(861\) | 17741.6 | 0.0239324 | ||||||||
\(862\) | −446752. | −0.601246 | ||||||||
\(863\) | − | 247431.i | − | 0.332225i | −0.986107 | − | 0.166113i | \(-0.946878\pi\) | ||
0.986107 | − | 0.166113i | \(-0.0531216\pi\) | |||||||
\(864\) | 141851. | 0.190023 | ||||||||
\(865\) | − | 1.23419e6i | − | 1.64949i | ||||||
\(866\) | 104501. | 0.139343 | ||||||||
\(867\) | 552578.i | 0.735115i | ||||||||
\(868\) | − | 375637.i | − | 0.498573i | ||||||
\(869\) | 97927.0i | 0.129677i | ||||||||
\(870\) | 677424.i | 0.894999i | ||||||||
\(871\) | 393337. | 0.518476 | ||||||||
\(872\) | −321752. | −0.423144 | ||||||||
\(873\) | − | 183826.i | − | 0.241200i | ||||||
\(874\) | −610367. | + | 135089.i | −0.799040 | + | 0.176846i | ||||
\(875\) | −737669. | −0.963486 | ||||||||
\(876\) | 193496.i | 0.252153i | ||||||||
\(877\) | − | 58891.6i | − | 0.0765692i | −0.999267 | − | 0.0382846i | \(-0.987811\pi\) | ||
0.999267 | − | 0.0382846i | \(-0.0121893\pi\) | |||||||
\(878\) | −549780. | −0.713182 | ||||||||
\(879\) | −560121. | −0.724943 | ||||||||
\(880\) | −42876.7 | −0.0553676 | ||||||||
\(881\) | −844161. | −1.08761 | −0.543806 | − | 0.839211i | \(-0.683017\pi\) | ||||
−0.543806 | + | 0.839211i | \(0.683017\pi\) | |||||||
\(882\) | 25439.0i | 0.0327011i | ||||||||
\(883\) | −1.34541e6 | −1.72558 | −0.862788 | − | 0.505565i | \(-0.831284\pi\) | ||||
−0.862788 | + | 0.505565i | \(0.831284\pi\) | |||||||
\(884\) | 10433.9i | 0.0133519i | ||||||||
\(885\) | −191979. | −0.245114 | ||||||||
\(886\) | 86752.7i | 0.110514i | ||||||||
\(887\) | 268542.i | 0.341323i | 0.985330 | + | 0.170661i | \(0.0545904\pi\) | ||||
−0.985330 | + | 0.170661i | \(0.945410\pi\) | |||||||
\(888\) | 49014.5i | 0.0621583i | ||||||||
\(889\) | 571977.i | 0.723727i | ||||||||
\(890\) | −464704. | −0.586674 | ||||||||
\(891\) | 56650.9 | 0.0713594 | ||||||||
\(892\) | 477652.i | 0.600319i | ||||||||
\(893\) | −233889. | − | 1.05677e6i | −0.293296 | − | 1.32519i | ||||
\(894\) | −371835. | −0.465238 | ||||||||
\(895\) | − | 1.06348e6i | − | 1.32764i | ||||||
\(896\) | − | 74503.1i | − | 0.0928023i | ||||||
\(897\) | −217268. | −0.270029 | ||||||||
\(898\) | 669902. | 0.830728 | ||||||||
\(899\) | −1.22843e6 | −1.51996 | ||||||||
\(900\) | −25771.2 | −0.0318163 | ||||||||
\(901\) | − | 99627.4i | − | 0.122724i | ||||||
\(902\) | 3672.28 | 0.00451360 | ||||||||
\(903\) | 872609.i | 1.07015i | ||||||||
\(904\) | 469461. | 0.574464 | ||||||||
\(905\) | − | 1.38439e6i | − | 1.69029i | ||||||
\(906\) | − | 14523.9i | − | 0.0176940i | ||||||
\(907\) | 1.24035e6i | 1.50775i | 0.657017 | + | 0.753876i | \(0.271818\pi\) | ||||
−0.657017 | + | 0.753876i | \(0.728182\pi\) | |||||||
\(908\) | − | 463714.i | − | 0.562443i | ||||||
\(909\) | 577931. | 0.699436 | ||||||||
\(910\) | −206921. | −0.249874 | ||||||||
\(911\) | − | 191069.i | − | 0.230226i | −0.993352 | − | 0.115113i | \(-0.963277\pi\) | ||
0.993352 | − | 0.115113i | \(-0.0367229\pi\) | |||||||
\(912\) | −150325. | + | 33270.4i | −0.180734 | + | 0.0400008i | ||||
\(913\) | 25038.1 | 0.0300372 | ||||||||
\(914\) | − | 232103.i | − | 0.277836i | ||||||
\(915\) | 1.16213e6i | 1.38808i | ||||||||
\(916\) | −321263. | −0.382886 | ||||||||
\(917\) | 11489.0 | 0.0136629 | ||||||||
\(918\) | −54283.2 | −0.0644139 | ||||||||
\(919\) | 830092. | 0.982868 | 0.491434 | − | 0.870915i | \(-0.336473\pi\) | ||||
0.491434 | + | 0.870915i | \(0.336473\pi\) | |||||||
\(920\) | 369925.i | 0.437057i | ||||||||
\(921\) | 69282.5 | 0.0816779 | ||||||||
\(922\) | − | 47463.7i | − | 0.0558342i | ||||||
\(923\) | 309188. | 0.362927 | ||||||||
\(924\) | − | 68811.8i | − | 0.0805971i | ||||||
\(925\) | − | 28616.3i | − | 0.0334449i | ||||||
\(926\) | 283321.i | 0.330413i | ||||||||
\(927\) | 478216.i | 0.556500i | ||||||||
\(928\) | −243645. | −0.282919 | ||||||||
\(929\) | 1.18305e6 | 1.37080 | 0.685399 | − | 0.728168i | \(-0.259628\pi\) | ||||
0.685399 | + | 0.728168i | \(0.259628\pi\) | |||||||
\(930\) | 459353.i | 0.531106i | ||||||||
\(931\) | −19174.0 | − | 86633.2i | −0.0221214 | − | 0.0999505i | ||||
\(932\) | −573921. | −0.660724 | ||||||||
\(933\) | − | 787054.i | − | 0.904152i | ||||||
\(934\) | − | 613123.i | − | 0.702836i | ||||||
\(935\) | 16407.9 | 0.0187685 | ||||||||
\(936\) | 44093.3 | 0.0503293 | ||||||||
\(937\) | 1.14337e6 | 1.30229 | 0.651144 | − | 0.758954i | \(-0.274289\pi\) | ||||
0.651144 | + | 0.758954i | \(0.274289\pi\) | |||||||
\(938\) | 1.07479e6 | 1.22157 | ||||||||
\(939\) | 55917.9i | 0.0634190i | ||||||||
\(940\) | −640478. | −0.724851 | ||||||||
\(941\) | 1.12716e6i | 1.27294i | 0.771302 | + | 0.636469i | \(0.219606\pi\) | ||||
−0.771302 | + | 0.636469i | \(0.780394\pi\) | |||||||
\(942\) | 871632. | 0.982271 | ||||||||
\(943\) | − | 31683.2i | − | 0.0356291i | ||||||
\(944\) | − | 69048.0i | − | 0.0774832i | ||||||
\(945\) | − | 1.07652e6i | − | 1.20548i | ||||||
\(946\) | 180619.i | 0.201828i | ||||||||
\(947\) | 1.01859e6 | 1.13579 | 0.567897 | − | 0.823099i | \(-0.307757\pi\) | ||||
0.567897 | + | 0.823099i | \(0.307757\pi\) | |||||||
\(948\) | 208082. | 0.231536 | ||||||||
\(949\) | 193285.i | 0.214618i | ||||||||
\(950\) | 87764.6 | − | 19424.4i | 0.0972461 | − | 0.0215229i | ||||
\(951\) | −956093. | −1.05716 | ||||||||
\(952\) | 28510.6i | 0.0314582i | ||||||||
\(953\) | 18352.7i | 0.0202076i | 0.999949 | + | 0.0101038i | \(0.00321619\pi\) | ||||
−0.999949 | + | 0.0101038i | \(0.996784\pi\) | |||||||
\(954\) | −421021. | −0.462602 | ||||||||
\(955\) | −1.04031e6 | −1.14066 | ||||||||
\(956\) | −353427. | −0.386709 | ||||||||
\(957\) | −225033. | −0.245710 | ||||||||
\(958\) | 259299.i | 0.282534i | ||||||||
\(959\) | 975077. | 1.06023 | ||||||||
\(960\) | 91107.3i | 0.0988577i | ||||||||
\(961\) | 90535.6 | 0.0980331 | ||||||||
\(962\) | 48961.1i | 0.0529056i | ||||||||
\(963\) | 302734.i | 0.326444i | ||||||||
\(964\) | − | 270589.i | − | 0.291177i | ||||||
\(965\) | − | 1.14977e6i | − | 1.23468i | ||||||
\(966\) | −593685. | −0.636212 | ||||||||
\(967\) | 301406. | 0.322329 | 0.161164 | − | 0.986928i | \(-0.448475\pi\) | ||||
0.161164 | + | 0.986928i | \(0.448475\pi\) | |||||||
\(968\) | 317045.i | 0.338353i | ||||||||
\(969\) | 57525.9 | − | 12731.8i | 0.0612654 | − | 0.0135595i | ||||
\(970\) | 379414. | 0.403246 | ||||||||
\(971\) | − | 796081.i | − | 0.844342i | −0.906516 | − | 0.422171i | \(-0.861268\pi\) | ||
0.906516 | − | 0.422171i | \(-0.138732\pi\) | |||||||
\(972\) | 387413.i | 0.410054i | ||||||||
\(973\) | −571861. | −0.604039 | ||||||||
\(974\) | −303562. | −0.319985 | ||||||||
\(975\) | 31240.9 | 0.0328636 | ||||||||
\(976\) | −417977. | −0.438786 | ||||||||
\(977\) | − | 664866.i | − | 0.696538i | −0.937395 | − | 0.348269i | \(-0.886770\pi\) | ||
0.937395 | − | 0.348269i | \(-0.113230\pi\) | |||||||
\(978\) | 621088. | 0.649345 | ||||||||
\(979\) | − | 154370.i | − | 0.161063i | ||||||
\(980\) | −52505.7 | −0.0546707 | ||||||||
\(981\) | − | 520330.i | − | 0.540681i | ||||||
\(982\) | 599113.i | 0.621278i | ||||||||
\(983\) | 1.05287e6i | 1.08960i | 0.838566 | + | 0.544801i | \(0.183395\pi\) | ||||
−0.838566 | + | 0.544801i | \(0.816605\pi\) | |||||||
\(984\) | − | 7803.12i | − | 0.00805894i | ||||||
\(985\) | 702576. | 0.724137 | ||||||||
\(986\) | 93237.5 | 0.0959040 | ||||||||
\(987\) | − | 1.02789e6i | − | 1.05514i | ||||||
\(988\) | −150161. | + | 33234.2i | −0.153831 | + | 0.0340464i | ||||
\(989\) | 1.55832e6 | 1.59317 | ||||||||
\(990\) | − | 69339.2i | − | 0.0707471i | ||||||
\(991\) | − | 1.85377e6i | − | 1.88759i | −0.330529 | − | 0.943796i | \(-0.607227\pi\) | ||
0.330529 | − | 0.943796i | \(-0.392773\pi\) | |||||||
\(992\) | −165213. | −0.167888 | ||||||||
\(993\) | 112908. | 0.114506 | ||||||||
\(994\) | 844856. | 0.855087 | ||||||||
\(995\) | −314374. | −0.317541 | ||||||||
\(996\) | − | 53202.7i | − | 0.0536309i | ||||||
\(997\) | 494751. | 0.497733 | 0.248867 | − | 0.968538i | \(-0.419942\pi\) | ||||
0.248867 | + | 0.968538i | \(0.419942\pi\) | |||||||
\(998\) | 411505.i | 0.413156i | ||||||||
\(999\) | −254724. | −0.255234 |
(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 | 38.5.b.a.37.6 | yes | 8 | |
3.2 | odd | 2 | 342.5.d.a.37.2 | 8 | |||
4.3 | odd | 2 | 304.5.e.e.113.5 | 8 | |||
19.18 | odd | 2 | inner | 38.5.b.a.37.3 | ✓ | 8 | |
57.56 | even | 2 | 342.5.d.a.37.6 | 8 | |||
76.75 | even | 2 | 304.5.e.e.113.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.b.a.37.3 | ✓ | 8 | 19.18 | odd | 2 | inner | |
38.5.b.a.37.6 | yes | 8 | 1.1 | even | 1 | trivial | |
304.5.e.e.113.4 | 8 | 76.75 | even | 2 | |||
304.5.e.e.113.5 | 8 | 4.3 | odd | 2 | |||
342.5.d.a.37.2 | 8 | 3.2 | odd | 2 | |||
342.5.d.a.37.6 | 8 | 57.56 | even | 2 |