Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.4244687775\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 38) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Root | \(-8.07810i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.e.113.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 6.66389i | − | 0.740432i | −0.928946 | − | 0.370216i | \(-0.879284\pi\) | ||
0.928946 | − | 0.370216i | \(-0.120716\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 26.7027 | 1.06811 | 0.534054 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534054 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −51.4469 | −1.04994 | −0.524969 | − | 0.851121i | \(-0.675923\pi\) | ||||
−0.524969 | + | 0.851121i | \(0.675923\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 36.5926 | 0.451760 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.0891 | 0.207348 | 0.103674 | − | 0.994611i | \(-0.466940\pi\) | ||||
0.103674 | + | 0.994611i | \(0.466940\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 53.2531i | − | 0.315107i | −0.987510 | − | 0.157553i | \(-0.949639\pi\) | ||
0.987510 | − | 0.157553i | \(-0.0503606\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 177.944i | − | 0.790862i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24.4913 | −0.0847451 | −0.0423726 | − | 0.999102i | \(-0.513492\pi\) | ||||
−0.0423726 | + | 0.999102i | \(0.513492\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 78.0101 | − | 352.470i | 0.216094 | − | 0.976372i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 342.837i | 0.777408i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 612.242 | 1.15736 | 0.578679 | − | 0.815555i | \(-0.303568\pi\) | ||||
0.578679 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 88.0343 | 0.140855 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 783.624i | − | 1.07493i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1345.96i | − | 1.60043i | −0.599713 | − | 0.800215i | \(-0.704718\pi\) | ||
0.599713 | − | 0.800215i | \(-0.295282\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 912.680i | 0.949719i | 0.880062 | + | 0.474860i | \(0.157501\pi\) | ||||
−0.880062 | + | 0.474860i | \(0.842499\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 167.191i | − | 0.153527i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1373.77 | −1.12145 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 325.059i | 0.237443i | 0.992928 | + | 0.118721i | \(0.0378795\pi\) | ||||
−0.992928 | + | 0.118721i | \(0.962120\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −354.872 | −0.233315 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 51.7494i | − | 0.0307849i | −0.999882 | − | 0.0153924i | \(-0.995100\pi\) | ||
0.999882 | − | 0.0153924i | \(-0.00489976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2545.26 | 1.37656 | 0.688280 | − | 0.725445i | \(-0.258366\pi\) | ||||
0.688280 | + | 0.725445i | \(0.258366\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 977.121 | 0.482529 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2998.19 | −1.35726 | −0.678630 | − | 0.734480i | \(-0.737426\pi\) | ||||
−0.678630 | + | 0.734480i | \(0.737426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 245.788 | 0.102369 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 163.208i | 0.0627480i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4067.86i | − | 1.44815i | −0.689720 | − | 0.724077i | \(-0.742266\pi\) | ||
0.689720 | − | 0.724077i | \(-0.257734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 669.948 | 0.221470 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2348.82 | − | 519.851i | −0.722938 | − | 0.160003i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1078.88i | − | 0.309933i | −0.987920 | − | 0.154966i | \(-0.950473\pi\) | ||
0.987920 | − | 0.154966i | \(-0.0495269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6530.89 | −1.75514 | −0.877572 | − | 0.479445i | \(-0.840838\pi\) | ||||
−0.877572 | + | 0.479445i | \(0.840838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1882.58 | −0.474320 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1422.00i | − | 0.336568i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7386.18i | − | 1.64540i | −0.568478 | − | 0.822698i | \(-0.692468\pi\) | ||
0.568478 | − | 0.822698i | \(-0.307532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4079.92i | − | 0.856945i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5806.02i | − | 1.15176i | −0.817535 | − | 0.575879i | \(-0.804660\pi\) | ||
0.817535 | − | 0.575879i | \(-0.195340\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3629.56 | 0.681096 | 0.340548 | − | 0.940227i | \(-0.389387\pi\) | ||||
0.340548 | + | 0.940227i | \(0.389387\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 586.651i | − | 0.104293i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1290.76 | −0.217703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3903.16i | − | 0.625407i | −0.949851 | − | 0.312703i | \(-0.898765\pi\) | ||
0.949851 | − | 0.312703i | \(-0.101235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2257.99 | −0.344153 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 997.967 | 0.144864 | 0.0724319 | − | 0.997373i | \(-0.476924\pi\) | ||||
0.0724319 | + | 0.997373i | \(0.476924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −653.985 | −0.0905169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8969.34 | −1.18501 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6152.85i | − | 0.776777i | −0.921496 | − | 0.388389i | \(-0.873032\pi\) | ||
0.921496 | − | 0.388389i | \(-0.126968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2739.71i | 0.330843i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6082.00 | 0.703203 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2083.08 | − | 9411.91i | 0.230812 | − | 1.04287i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5023.58i | 0.533912i | 0.963709 | + | 0.266956i | \(0.0860178\pi\) | ||||
−0.963709 | + | 0.266956i | \(0.913982\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 918.076 | 0.0936717 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15793.7 | 1.54825 | 0.774123 | − | 0.633035i | \(-0.218191\pi\) | ||||
0.774123 | + | 0.633035i | \(0.218191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13068.7i | 1.23185i | 0.787806 | + | 0.615924i | \(0.211217\pi\) | ||||
−0.787806 | + | 0.615924i | \(0.788783\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9154.67i | 0.830355i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8273.09i | 0.722604i | 0.932449 | + | 0.361302i | \(0.117668\pi\) | ||||
−0.932449 | + | 0.361302i | \(0.882332\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14219.6i | 1.19683i | 0.801186 | + | 0.598416i | \(0.204203\pi\) | ||||
−0.801186 | + | 0.598416i | \(0.795797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2166.16 | 0.175810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 20747.4i | − | 1.62483i | −0.583080 | − | 0.812414i | \(-0.698153\pi\) | ||
0.583080 | − | 0.812414i | \(-0.301847\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16348.5 | 1.23618 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1948.67i | − | 0.142353i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1260.00 | 0.0889771 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14011.5 | −0.957007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −344.852 | −0.0227941 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14338.4 | −0.917660 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11117.8i | 0.689305i | 0.938730 | + | 0.344653i | \(0.112003\pi\) | ||||
−0.938730 | + | 0.344653i | \(0.887997\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 16961.3i | − | 1.01925i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −223.317 | −0.0130130 | −0.00650652 | − | 0.999979i | \(-0.502071\pi\) | ||||
−0.00650652 | + | 0.999979i | \(0.502071\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4013.38 | + | 18133.5i | −0.226886 | + | 1.02513i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 20924.9i | − | 1.14814i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18953.1 | 1.00981 | 0.504903 | − | 0.863176i | \(-0.331528\pi\) | ||||
0.504903 | + | 0.863176i | \(0.331528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11115.5 | 0.575309 | 0.287655 | − | 0.957734i | \(-0.407125\pi\) | ||||
0.287655 | + | 0.957734i | \(0.407125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19979.6i | 1.00496i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1336.07i | − | 0.0653368i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 35940.8i | − | 1.70943i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1637.91i | − | 0.0757975i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19727.7 | −0.888597 | −0.444299 | − | 0.895879i | \(-0.646547\pi\) | ||||
−0.444299 | + | 0.895879i | \(0.646547\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 770.565i | − | 0.0337952i | −0.999857 | − | 0.0168976i | \(-0.994621\pi\) | ||
0.999857 | − | 0.0168976i | \(-0.00537894\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −896.201 | −0.0382845 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24371.0i | 1.01440i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 46244.5 | 1.87612 | 0.938061 | − | 0.346470i | \(-0.112620\pi\) | ||||
0.938061 | + | 0.346470i | \(0.112620\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27107.8 | −1.07226 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31498.0 | −1.21515 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −32951.9 | −1.24024 | −0.620119 | − | 0.784507i | \(-0.712916\pi\) | ||||
−0.620119 | + | 0.784507i | \(0.712916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 4464.46i | − | 0.163984i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 48049.1i | 1.72287i | 0.507870 | + | 0.861434i | \(0.330433\pi\) | ||||
−0.507870 | + | 0.861434i | \(0.669567\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25725.1 | 0.900708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2854.59 | − | 12897.8i | 0.0976228 | − | 0.441086i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 46219.6i | 1.54431i | 0.635436 | + | 0.772153i | \(0.280820\pi\) | ||||
−0.635436 | + | 0.772153i | \(0.719180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4529.10 | −0.147889 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7189.51 | −0.229484 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 39826.5i | − | 1.24299i | −0.783420 | − | 0.621493i | \(-0.786527\pi\) | ||
0.783420 | − | 0.621493i | \(-0.213473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 51844.5i | 1.58251i | 0.611488 | + | 0.791254i | \(0.290571\pi\) | ||||
−0.611488 | + | 0.791254i | \(0.709429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 43521.1i | 1.29957i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8679.95i | 0.253614i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −614.467 | −0.0175718 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 40315.1i | 1.12861i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 38958.8 | 1.06792 | 0.533960 | − | 0.845509i | \(-0.320703\pi\) | ||||
0.533960 | + | 0.845509i | \(0.320703\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 43058.1i | 1.15595i | 0.816053 | + | 0.577977i | \(0.196158\pi\) | ||||
−0.816053 | + | 0.577977i | \(0.803842\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9476.05 | −0.249206 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26311.0 | 0.677962 | 0.338981 | − | 0.940793i | \(-0.389918\pi\) | ||||
0.338981 | + | 0.940793i | \(0.389918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11773.1 | 0.297293 | 0.148647 | − | 0.988890i | \(-0.452508\pi\) | ||||
0.148647 | + | 0.988890i | \(0.452508\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −49220.7 | −1.21830 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 69245.7i | 1.68035i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1381.85i | − | 0.0328816i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22403.5 | 0.522848 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1957.21 | − | 8843.18i | 0.0448068 | − | 0.202449i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12495.7i | 0.280670i | 0.990104 | + | 0.140335i | \(0.0448179\pi\) | ||||
−0.990104 | + | 0.140335i | \(0.955182\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −38690.7 | −0.852799 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 67965.3 | 1.47032 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 46954.6i | − | 0.997146i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 24187.0i | − | 0.504305i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1304.24i | 0.0267038i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 59706.5i | − | 1.20064i | −0.799761 | − | 0.600319i | \(-0.795040\pi\) | ||
0.799761 | − | 0.600319i | \(-0.204960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3221.40 | 0.0636326 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 57964.2i | 1.12489i | 0.826836 | + | 0.562443i | \(0.190138\pi\) | ||||
−0.826836 | + | 0.562443i | \(0.809862\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 40157.9 | 0.765773 | 0.382886 | − | 0.923795i | \(-0.374930\pi\) | ||||
0.382886 | + | 0.923795i | \(0.374930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8601.48i | 0.161194i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 71740.1 | 1.32145 | 0.660724 | − | 0.750629i | \(-0.270249\pi\) | ||||
0.660724 | + | 0.750629i | \(0.270249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −80059.7 | −1.44970 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26010.2 | −0.463071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −44178.4 | −0.773417 | −0.386709 | − | 0.922202i | \(-0.626388\pi\) | ||||
−0.386709 | + | 0.922202i | \(0.626388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 33823.7i | − | 0.582353i | −0.956669 | − | 0.291177i | \(-0.905953\pi\) | ||
0.956669 | − | 0.291177i | \(-0.0940467\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 48426.6i | − | 0.820108i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6563.22 | 0.109341 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18770.1 | − | 4154.27i | −0.307662 | − | 0.0680928i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6650.34i | − | 0.107262i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 64952.8 | 1.03098 | 0.515490 | − | 0.856896i | \(-0.327610\pi\) | ||||
0.515490 | + | 0.856896i | \(0.327610\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15360.6 | 0.239976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4358.08i | 0.0670217i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1155.59i | 0.0174959i | 0.999962 | + | 0.00874796i | \(0.00278460\pi\) | ||||
−0.999962 | + | 0.00874796i | \(0.997215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16723.3i | − | 0.249300i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 49252.2i | − | 0.723011i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6732.94 | −0.0973404 | −0.0486702 | − | 0.998815i | \(-0.515498\pi\) | ||||
−0.0486702 | + | 0.998815i | \(0.515498\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 108623.i | − | 1.54678i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −41001.9 | −0.575151 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 22231.5i | − | 0.307230i | −0.988131 | − | 0.153615i | \(-0.950908\pi\) | ||
0.988131 | − | 0.153615i | \(-0.0490915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46597.6 | 0.634490 | 0.317245 | − | 0.948344i | \(-0.397242\pi\) | ||||
0.317245 | + | 0.948344i | \(0.397242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18257.1 | 0.244966 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2208.70 | 0.0292060 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 105817. | 1.37910 | 0.689548 | − | 0.724240i | \(-0.257809\pi\) | ||||
0.689548 | + | 0.724240i | \(0.257809\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33397.3i | 0.429045i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20298.2i | 0.257067i | 0.991705 | + | 0.128533i | \(0.0410269\pi\) | ||||
−0.991705 | + | 0.128533i | \(0.958973\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 55710.6 | 0.695609 | 0.347804 | − | 0.937567i | \(-0.386927\pi\) | ||||
0.347804 | + | 0.937567i | \(0.386927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −62720.0 | − | 13881.4i | −0.772176 | − | 0.170901i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2662.35i | 0.0323222i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −82921.2 | −0.992818 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33476.6 | 0.395326 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 84053.1i | 0.979081i | 0.871980 | + | 0.489541i | \(0.162836\pi\) | ||||
−0.871980 | + | 0.489541i | \(0.837164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 28808.9i | − | 0.331042i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 19660.4i | − | 0.222885i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 32603.8i | − | 0.364691i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −130946. | −1.44530 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 105247.i | − | 1.14637i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −174392. | −1.87468 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10396.7i | 0.110311i | 0.998478 | + | 0.0551555i | \(0.0175655\pi\) | ||||
−0.998478 | + | 0.0551555i | \(0.982435\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 87088.2 | 0.912100 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −118107. | −1.22111 | −0.610557 | − | 0.791973i | \(-0.709054\pi\) | ||||
−0.610557 | + | 0.791973i | \(0.709054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8391.17 | −0.0856513 | −0.0428257 | − | 0.999083i | \(-0.513636\pi\) | ||||
−0.0428257 | + | 0.999083i | \(0.513636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −50269.9 | −0.506625 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 143474.i | 1.42776i | 0.700270 | + | 0.713878i | \(0.253063\pi\) | ||||
−0.700270 | + | 0.713878i | \(0.746937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 33769.0i | − | 0.331847i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 55131.0 | 0.535039 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1910.57 | + | 8632.47i | −0.0183129 | + | 0.0827428i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4688.09i | − | 0.0443843i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 94757.6 | 0.886173 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 154248. | 1.42504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16943.3i | 0.154647i | 0.997006 | + | 0.0773237i | \(0.0246375\pi\) | ||||
−0.997006 | + | 0.0773237i | \(0.975363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11894.7i | 0.107267i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 197231.i | − | 1.75746i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 217168.i | − | 1.91221i | −0.293021 | − | 0.956106i | \(-0.594661\pi\) | ||
0.293021 | − | 0.956106i | \(-0.405339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −138259. | −1.20308 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22898.4i | 0.196923i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 110879. | 0.942456 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 108945.i | − | 0.915310i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −64555.0 | −0.536131 | −0.268066 | − | 0.963401i | \(-0.586384\pi\) | ||||
−0.268066 | + | 0.963401i | \(0.586384\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −113275. | −0.930001 | −0.465001 | − | 0.885310i | \(-0.653946\pi\) | ||||
−0.465001 | + | 0.885310i | \(0.653946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −41730.4 | −0.338718 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27685.3 | 0.222178 | 0.111089 | − | 0.993810i | \(-0.464566\pi\) | ||||
0.111089 | + | 0.993810i | \(0.464566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 155036.i | − | 1.23020i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 8396.53i | − | 0.0658815i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −65336.2 | −0.506950 | −0.253475 | − | 0.967342i | \(-0.581574\pi\) | ||||
−0.253475 | + | 0.967342i | \(0.581574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −118150. | − | 54992.5i | −0.906606 | − | 0.421977i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 93371.3i | 0.708599i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 96919.1 | 0.727484 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −177298. | −1.31635 | −0.658176 | − | 0.752864i | \(-0.728672\pi\) | ||||
−0.658176 | + | 0.752864i | \(0.728672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1893.64i | − | 0.0139074i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 209279.i | 1.52047i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15381.6i | 0.110557i | 0.998471 | + | 0.0552783i | \(0.0176046\pi\) | ||||
−0.998471 | + | 0.0552783i | \(0.982395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 95549.8i | 0.679465i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −71676.6 | −0.504307 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 232626.i | − | 1.61949i | −0.586780 | − | 0.809746i | \(-0.699605\pi\) | ||
0.586780 | − | 0.809746i | \(-0.300395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 74087.8 | 0.510384 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 52033.6i | 0.354721i | 0.984146 | + | 0.177360i | \(0.0567558\pi\) | ||||
−0.984146 | + | 0.177360i | \(0.943244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −34466.8 | −0.232530 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 93137.6 | 0.621875 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 57687.6 | 0.381227 | 0.190613 | − | 0.981665i | \(-0.438952\pi\) | ||||
0.190613 | + | 0.981665i | \(0.438952\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14994.6 | −0.0980804 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1488.16i | 0.00963527i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 104225.i | − | 0.668002i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16914.2 | 0.107317 | 0.0536586 | − | 0.998559i | \(-0.482912\pi\) | ||||
0.0536586 | + | 0.998559i | \(0.482912\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 120840. | + | 26744.7i | 0.759039 | + | 0.167993i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 23481.6i | − | 0.146029i | −0.997331 | − | 0.0730144i | \(-0.976738\pi\) | ||
0.997331 | − | 0.0730144i | \(-0.0232619\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48603.0 | 0.299263 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −60294.3 | −0.367592 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8155.45i | 0.0492333i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 310776.i | − | 1.85781i | −0.370321 | − | 0.928904i | \(-0.620752\pi\) | ||
0.370321 | − | 0.928904i | \(-0.379248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 126301.i | − | 0.747693i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 55504.9i | 0.325410i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26648.4 | 0.154730 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 74072.8i | − | 0.425977i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 271562. | 1.54682 | 0.773411 | − | 0.633905i | \(-0.218549\pi\) | ||||
0.773411 | + | 0.633905i | \(0.218549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 322467.i | 1.81937i | 0.415299 | + | 0.909685i | \(0.363677\pi\) | ||||
−0.415299 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −109711. | −0.613156 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2156.08 | −0.0119368 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 335994. | 1.84279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8903.44 | −0.0483775 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 157951.i | 0.850290i | 0.905125 | + | 0.425145i | \(0.139777\pi\) | ||||
−0.905125 | + | 0.425145i | \(0.860223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36946.7i | 0.197061i | 0.995134 | + | 0.0985304i | \(0.0314142\pi\) | ||||
−0.995134 | + | 0.0985304i | \(0.968586\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −239506. | −1.26572 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 47761.1 | − | 215797.i | 0.250099 | − | 1.13001i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 194377.i | 1.00859i | 0.863531 | + | 0.504296i | \(0.168248\pi\) | ||||
−0.863531 | + | 0.504296i | \(0.831752\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8994.03 | 0.0462463 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30671.7 | −0.156290 | −0.0781449 | − | 0.996942i | \(-0.524900\pi\) | ||||
−0.0781449 | + | 0.996942i | \(0.524900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 164298.i | − | 0.829682i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 131464.i | 0.657946i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 236846.i | 1.17483i | 0.809287 | + | 0.587413i | \(0.199854\pi\) | ||||
−0.809287 | + | 0.587413i | \(0.800146\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1298.35i | − | 0.00638319i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5134.96 | −0.0250231 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 73157.6i | 0.353376i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −82060.7 | −0.392919 | −0.196459 | − | 0.980512i | \(-0.562944\pi\) | ||||
−0.196459 | + | 0.980512i | \(0.562944\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19192.0i | 0.0910951i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16781.0 | −0.0789614 | −0.0394807 | − | 0.999220i | \(-0.512570\pi\) | ||||
−0.0394807 | + | 0.999220i | \(0.512570\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −100169. | −0.467274 | −0.233637 | − | 0.972324i | \(-0.575063\pi\) | ||||
−0.233637 | + | 0.972324i | \(0.575063\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 162406. | 0.751097 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 216772. | 0.993960 | 0.496980 | − | 0.867762i | \(-0.334442\pi\) | ||||
0.496980 | + | 0.867762i | \(0.334442\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 379997.i | 1.72756i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 308168.i | − | 1.38914i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 63858.4 | 0.285427 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6867.56 | − | 31029.5i | 0.0304379 | − | 0.137527i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 148854.i | − | 0.654218i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −91676.2 | −0.399563 | −0.199782 | − | 0.979840i | \(-0.564023\pi\) | ||||
−0.199782 | + | 0.979840i | \(0.564023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17310.4 | 0.0748198 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 209899.i | 0.899739i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 134143.i | 0.570276i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 107326.i | 0.452528i | 0.974066 | + | 0.226264i | \(0.0726512\pi\) | ||||
−0.974066 | + | 0.226264i | \(0.927349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 219588.i | 0.918313i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −211818. | −0.878619 | −0.439310 | − | 0.898336i | \(-0.644777\pi\) | ||||
−0.439310 | + | 0.898336i | \(0.644777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32964.4i | 0.135629i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24515.1 | 0.100051 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 298702.i | 1.20928i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −145489. | −0.584291 | −0.292146 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292146 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 320194. | 1.27567 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33735.6 | 0.133338 | 0.0666689 | − | 0.997775i | \(-0.478763\pi\) | ||||
0.0666689 | + | 0.997775i | \(0.478763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 421733. | 1.65369 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 171429.i | − | 0.666913i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 128247.i | 0.495009i | 0.968887 | + | 0.247505i | \(0.0796105\pi\) | ||||
−0.968887 | + | 0.247505i | \(0.920389\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −186730. | −0.715108 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −276204. | − | 61130.6i | −1.04953 | − | 0.232286i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 348969.i | 1.31575i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −75222.0 | −0.281426 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 308002. | 1.14345 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38092.9i | 0.140336i | 0.997535 | + | 0.0701680i | \(0.0223535\pi\) | ||||
−0.997535 | + | 0.0701680i | \(0.977646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 96329.4i | 0.352173i | 0.984375 | + | 0.176086i | \(0.0563438\pi\) | ||||
−0.984375 | + | 0.176086i | \(0.943656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30181.4i | 0.109502i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 22352.8i | − | 0.0804841i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 94999.8 | 0.339478 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 39478.8i | − | 0.140015i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2755.81 | −0.00970053 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 220914.i | 0.771819i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −265399. | −0.920346 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6166.62 | 0.0212261 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −163021. | −0.556993 | −0.278496 | − | 0.960437i | \(-0.589836\pi\) | ||||
−0.278496 | + | 0.960437i | \(0.589836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 345486. | 1.17174 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 379701.i | 1.27835i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 450817.i | 1.50670i | 0.657621 | + | 0.753349i | \(0.271563\pi\) | ||||
−0.657621 | + | 0.753349i | \(0.728437\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −238982. | −0.792904 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −474412. | − | 104999.i | −1.56262 | − | 0.345844i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 200806.i | 0.656638i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 57842.2 | 0.187784 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −270930. | −0.873268 | −0.436634 | − | 0.899639i | \(-0.643829\pi\) | ||||
−0.436634 | + | 0.899639i | \(0.643829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 135543.i | − | 0.433764i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4094.74i | 0.0130107i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 59429.1i | − | 0.187492i | −0.995596 | − | 0.0937459i | \(-0.970116\pi\) | ||
0.995596 | − | 0.0937459i | \(-0.0298841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 554013.i | − | 1.73549i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 116166. | 0.361339 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 364145.i | 1.12473i | 0.826888 | + | 0.562367i | \(0.190109\pi\) | ||||
−0.826888 | + | 0.562367i | \(0.809891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −410057. | −1.25769 | −0.628843 | − | 0.777532i | \(-0.716471\pi\) | ||||
−0.628843 | + | 0.777532i | \(0.716471\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 259617.i | − | 0.790723i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 53898.3 | 0.163020 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44617.5 | −0.134015 | −0.0670075 | − | 0.997752i | \(-0.521345\pi\) | ||||
−0.0670075 | + | 0.997752i | \(0.521345\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 286935. | 0.855906 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −51342.3 | −0.152098 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 102059.i | − | 0.300272i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 52034.7i | − | 0.152048i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 371422. | 1.07793 | 0.538966 | − | 0.842328i | \(-0.318815\pi\) | ||||
0.538966 | + | 0.842328i | \(0.318815\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 321693. | + | 71198.3i | 0.927280 | + | 0.205229i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 175334.i | − | 0.501985i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −327963. | −0.932644 | −0.466322 | − | 0.884615i | \(-0.654421\pi\) | ||||
−0.466322 | + | 0.884615i | \(0.654421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 33645.5 | 0.0950372 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 78454.7i | − | 0.220125i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 81737.2i | 0.227806i | 0.993492 | + | 0.113903i | \(0.0363354\pi\) | ||||
−0.993492 | + | 0.113903i | \(0.963665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 75524.8i | − | 0.209093i | −0.994520 | − | 0.104547i | \(-0.966661\pi\) | ||
0.994520 | − | 0.104547i | \(-0.0333392\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 270279.i | − | 0.743325i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −374146. | −1.02219 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 97397.5i | 0.264345i | 0.991227 | + | 0.132172i | \(0.0421952\pi\) | ||||
−0.991227 | + | 0.132172i | \(0.957805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 461445. | 1.24419 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 159663.i | 0.427682i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 185283. | 0.493078 | 0.246539 | − | 0.969133i | \(-0.420707\pi\) | ||||
0.246539 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9208.49 | −0.0243466 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 628408. | 1.65071 | 0.825357 | − | 0.564612i | \(-0.190974\pi\) | ||||
0.825357 | + | 0.564612i | \(0.190974\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −203791. | −0.531867 | −0.265933 | − | 0.963991i | \(-0.585680\pi\) | ||||
−0.265933 | + | 0.963991i | \(0.585680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 479768.i | − | 1.24408i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 316545.i | 0.815568i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −437896. | −1.12101 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −58930.0 | − | 13042.6i | −0.149900 | − | 0.0331764i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7961.13i | − | 0.0201221i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −496722. | −1.24754 | −0.623771 | − | 0.781607i | \(-0.714400\pi\) | ||||
−0.623771 | + | 0.781607i | \(0.714400\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 83270.0 | 0.207817 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 296875.i | 0.736252i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 13089.0i | − | 0.0322572i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 212457.i | − | 0.520319i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 44345.5i | − | 0.107928i | −0.998543 | − | 0.0539639i | \(-0.982814\pi\) | ||
0.998543 | − | 0.0539639i | \(-0.0171856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −139327. | −0.336987 | −0.168494 | − | 0.985703i | \(-0.553890\pi\) | ||||
−0.168494 | + | 0.985703i | \(0.553890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 452913.i | − | 1.08867i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 617612. | 1.47539 | 0.737696 | − | 0.675133i | \(-0.235914\pi\) | ||||
0.737696 | + | 0.675133i | \(0.235914\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27068.1i | − | 0.0642640i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −312900. | −0.738319 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 570062. | 1.33689 | 0.668446 | − | 0.743761i | \(-0.266960\pi\) | ||||
0.668446 | + | 0.743761i | \(0.266960\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5963.16 | −0.0138993 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 132815. | 0.307692 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 716546.i | 1.64996i | 0.565162 | + | 0.824980i | \(0.308814\pi\) | ||||
−0.565162 | + | 0.824980i | \(0.691186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 187692.i | − | 0.429579i | −0.976660 | − | 0.214790i | \(-0.931093\pi\) | ||
0.976660 | − | 0.214790i | \(-0.0689066\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8691.30 | 0.0197723 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −107168. | + | 484214.i | −0.242338 | + | 1.09495i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 824055.i | − | 1.85227i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −397877. | −0.888990 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −163854. | −0.363926 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 504263.i | 1.11334i | 0.830734 | + | 0.556669i | \(0.187921\pi\) | ||||
−0.830734 | + | 0.556669i | \(0.812079\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 68985.8i | − | 0.151409i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 689926.i | − | 1.50531i | −0.658417 | − | 0.752653i | \(-0.728774\pi\) | ||
0.658417 | − | 0.752653i | \(-0.271226\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 258448.i | − | 0.560574i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 386267. | 0.832901 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 226300.i | − | 0.485113i | −0.970137 | − | 0.242556i | \(-0.922014\pi\) | ||
0.970137 | − | 0.242556i | \(-0.0779859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 506098. | 1.07858 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 267608.i | − | 0.567003i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −216626. | −0.456323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 921891. | 1.93074 | 0.965370 | − | 0.260886i | \(-0.0840148\pi\) | ||||
0.965370 | + | 0.260886i | \(0.0840148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −47232.2 | −0.0983494 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 296815. | 0.614492 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1267.41i | 0.00260887i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 478068.i | − | 0.978443i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −561368. | −1.14238 | −0.571191 | − | 0.820817i | \(-0.693519\pi\) | ||||
−0.571191 | + | 0.820817i | \(0.693519\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 114574. | + | 25357.9i | 0.231832 | + | 0.0513100i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 533509.i | 1.07341i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −812536. | −1.62556 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −287728. | −0.572386 | −0.286193 | − | 0.958172i | \(-0.592390\pi\) | ||||
−0.286193 | + | 0.958172i | \(0.592390\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 142827.i | − | 0.282534i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 558782.i | 1.09917i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 35676.8i | − | 0.0697868i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 294400.i | 0.572663i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 805860. | 1.55884 | 0.779420 | − | 0.626502i | \(-0.215514\pi\) | ||||
0.779420 | + | 0.626502i | \(0.215514\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 672344.i | − | 1.29336i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −225397. | −0.431193 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 118491.i | − | 0.225428i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 348604. | 0.659575 | 0.329787 | − | 0.944055i | \(-0.393023\pi\) | ||||
0.329787 | + | 0.944055i | \(0.393023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −505606. | −0.951387 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62336.8 | −0.116657 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 238795. | 0.444443 | 0.222222 | − | 0.974996i | \(-0.428669\pi\) | ||||
0.222222 | + | 0.974996i | \(0.428669\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 43736.6i | − | 0.0809599i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 185313.i | − | 0.341170i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −502122. | −0.919433 | −0.459717 | − | 0.888066i | \(-0.652049\pi\) | ||||
−0.459717 | + | 0.888066i | \(0.652049\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27683.6 | + | 125082.i | −0.0504181 | + | 0.227803i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 411861.i | 0.746058i | 0.927820 | + | 0.373029i | \(0.121681\pi\) | ||||
−0.927820 | + | 0.373029i | \(0.878319\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −526784. | −0.949118 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36518.2 | 0.0654437 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 425625.i | − | 0.758689i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 876407.i | − | 1.55391i | −0.629556 | − | 0.776955i | \(-0.716763\pi\) | ||
0.629556 | − | 0.776955i | \(-0.283237\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 432838.i | − | 0.763371i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 20576.2i | − | 0.0360970i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −447975. | −0.781739 | −0.390870 | − | 0.920446i | \(-0.627826\pi\) | ||||
−0.390870 | + | 0.920446i | \(0.627826\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 102362.i | − | 0.177686i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 527400. | 0.910690 | 0.455345 | − | 0.890315i | \(-0.349516\pi\) | ||||
0.455345 | + | 0.890315i | \(0.349516\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 731553.i | − | 1.25660i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −23931.0 | −0.0408919 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −57453.4 | −0.0976619 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 549287. | 0.928852 | 0.464426 | − | 0.885612i | \(-0.346261\pi\) | ||||
0.464426 | + | 0.885612i | \(0.346261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7700.71 | 0.0129545 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.03569e6i | − | 1.73329i | −0.498927 | − | 0.866644i | \(-0.666272\pi\) | ||
0.498927 | − | 0.866644i | \(-0.333728\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 80347.2i | 0.133773i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −111442. | −0.184590 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18240.1 | − | 4036.98i | −0.0300575 | − | 0.00665244i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 145668.i | − | 0.238815i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.05473e6 | −1.72035 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.23485e6 | 2.00390 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.04115e6i | − | 1.68098i | −0.541824 | − | 0.840492i | \(-0.682266\pi\) | ||
0.541824 | − | 0.840492i | \(-0.317734\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44867.6i | 0.0720740i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.06739e6i | 1.70597i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 347790.i | 0.553058i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −723851. | −1.14529 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 476576.i | 0.750266i | 0.926971 | + | 0.375133i | \(0.122403\pi\) | ||||
−0.926971 | + | 0.375133i | \(0.877597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73429.7 | 0.115021 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 225149.i | − | 0.350917i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 91062.5 | 0.141224 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −841082. | −1.29792 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −148148. | −0.227483 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.00569e6 | −1.53663 | −0.768314 | − | 0.640074i | \(-0.778904\pi\) | ||||
−0.768314 | + | 0.640074i | \(0.778904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 257961.i | 0.392205i | 0.980583 | + | 0.196102i | \(0.0628285\pi\) | ||||
−0.980583 | + | 0.196102i | \(0.937171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 310521.i | − | 0.469797i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −879905. | −1.32471 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 198556. | − | 897129.i | 0.297467 | − | 1.34404i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 100253.i | 0.149461i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −65320.9 | −0.0969094 | −0.0484547 | − | 0.998825i | \(-0.515430\pi\) | ||||
−0.0484547 | + | 0.998825i | \(0.515430\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 109324. | 0.161404 | 0.0807020 | − | 0.996738i | \(-0.474284\pi\) | ||||
0.0807020 | + | 0.996738i | \(0.474284\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14718.6i | − | 0.0216251i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 988603.i | − | 1.44548i | −0.691122 | − | 0.722738i | \(-0.742883\pi\) | ||
0.691122 | − | 0.722738i | \(-0.257117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 467829.i | − | 0.680735i | −0.940292 | − | 0.340368i | \(-0.889448\pi\) | ||
0.940292 | − | 0.340368i | \(-0.110552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 705151.i | − | 1.02113i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6019.69 | −0.00867529 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.28304e6i | 1.84021i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 715198. | 1.02088 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 657894.i | 0.934613i | 0.884095 | + | 0.467306i | \(0.154776\pi\) | ||||
−0.884095 | + | 0.467306i | \(0.845224\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.10433e6 | −1.56138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 135265. | 0.190340 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 686930. | 0.962053 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 720851. | 1.00480 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 371249.i | − | 0.515051i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 199015.i | 0.274806i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −226576. | −0.311398 | −0.155699 | − | 0.987805i | \(-0.549763\pi\) | ||||
−0.155699 | + | 0.987805i | \(0.549763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 76225.2 | − | 344406.i | 0.104272 | − | 0.471128i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 183273.i | − | 0.249539i | −0.992186 | − | 0.124769i | \(-0.960181\pi\) | ||
0.992186 | − | 0.124769i | \(-0.0398191\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −565839. | −0.766843 | −0.383421 | − | 0.923574i | \(-0.625254\pi\) | ||||
−0.383421 | + | 0.923574i | \(0.625254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17741.6 | 0.0239324 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 247431.i | − | 0.332225i | −0.986107 | − | 0.166113i | \(-0.946878\pi\) | ||
0.986107 | − | 0.166113i | \(-0.0531216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.23419e6i | 1.64949i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 552578.i | 0.735115i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 97927.0i | − | 0.129677i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −393337. | −0.518476 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 183826.i | 0.241200i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 737669. | 0.963486 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58891.6i | 0.0765692i | 0.999267 | + | 0.0382846i | \(0.0121893\pi\) | ||||
−0.999267 | + | 0.0382846i | \(0.987811\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 560121. | 0.724943 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −844161. | −1.08761 | −0.543806 | − | 0.839211i | \(-0.683017\pi\) | ||||
−0.543806 | + | 0.839211i | \(0.683017\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.34541e6 | 1.72558 | 0.862788 | − | 0.505565i | \(-0.168716\pi\) | ||||
0.862788 | + | 0.505565i | \(0.168716\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −191979. | −0.245114 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 268542.i | 0.341323i | 0.985330 | + | 0.170661i | \(0.0545904\pi\) | ||||
−0.985330 | + | 0.170661i | \(0.945410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 571977.i | − | 0.723727i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −56650.9 | −0.0713594 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −233889. | + | 1.05677e6i | −0.293296 | + | 1.32519i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.06348e6i | − | 1.32764i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −217268. | −0.270029 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.22843e6 | 1.51996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 99627.4i | 0.122724i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 872609.i | 1.07015i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.38439e6i | 1.69029i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.24035e6i | 1.50775i | 0.657017 | + | 0.753876i | \(0.271818\pi\) | ||||
−0.657017 | + | 0.753876i | \(0.728182\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 577931. | 0.699436 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 191069.i | − | 0.230226i | −0.993352 | − | 0.115113i | \(-0.963277\pi\) | ||
0.993352 | − | 0.115113i | \(-0.0367229\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25038.1 | 0.0300372 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.16213e6i | 1.38808i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11489.0 | 0.0136629 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −830092. | −0.982868 | −0.491434 | − | 0.870915i | \(-0.663527\pi\) | ||||
−0.491434 | + | 0.870915i | \(0.663527\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 69282.5 | 0.0816779 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −309188. | −0.362927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28616.3i | 0.0334449i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 478216.i | 0.556500i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.18305e6 | 1.37080 | 0.685399 | − | 0.728168i | \(-0.259628\pi\) | ||||
0.685399 | + | 0.728168i | \(0.259628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19174.0 | − | 86633.2i | 0.0221214 | − | 0.0999505i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 787054.i | 0.904152i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16407.9 | −0.0187685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.14337e6 | 1.30229 | 0.651144 | − | 0.758954i | \(-0.274289\pi\) | ||||
0.651144 | + | 0.758954i | \(0.274289\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55917.9i | 0.0634190i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.12716e6i | − | 1.27294i | −0.771302 | − | 0.636469i | \(-0.780394\pi\) | ||
0.771302 | − | 0.636469i | \(-0.219606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 31683.2i | − | 0.0356291i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.07652e6i | 1.20548i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.01859e6 | −1.13579 | −0.567897 | − | 0.823099i | \(-0.692243\pi\) | ||||
−0.567897 | + | 0.823099i | \(0.692243\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 193285.i | − | 0.214618i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 956093. | 1.05716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18352.7i | − | 0.0202076i | −0.999949 | − | 0.0101038i | \(-0.996784\pi\) | ||
0.999949 | − | 0.0101038i | \(-0.00321619\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.04031e6 | 1.14066 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −225033. | −0.245710 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −975077. | −1.06023 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 90535.6 | 0.0980331 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 302734.i | 0.326444i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.14977e6i | 1.23468i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −301406. | −0.322329 | −0.161164 | − | 0.986928i | \(-0.551525\pi\) | ||||
−0.161164 | + | 0.986928i | \(0.551525\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 57525.9 | + | 12731.8i | 0.0612654 | + | 0.0135595i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 796081.i | − | 0.844342i | −0.906516 | − | 0.422171i | \(-0.861268\pi\) | ||
0.906516 | − | 0.422171i | \(-0.138732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −571861. | −0.604039 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −31240.9 | −0.0328636 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 664866.i | 0.696538i | 0.937395 | + | 0.348269i | \(0.113230\pi\) | ||||
−0.937395 | + | 0.348269i | \(0.886770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 154370.i | − | 0.161063i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 520330.i | 0.540681i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.05287e6i | 1.08960i | 0.838566 | + | 0.544801i | \(0.183395\pi\) | ||||
−0.838566 | + | 0.544801i | \(0.816605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 702576. | 0.724137 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.02789e6i | − | 1.05514i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.55832e6 | 1.59317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.85377e6i | − | 1.88759i | −0.330529 | − | 0.943796i | \(-0.607227\pi\) | ||
0.330529 | − | 0.943796i | \(-0.392773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 112908. | 0.114506 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 314374. | 0.317541 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 494751. | 0.497733 | 0.248867 | − | 0.968538i | \(-0.419942\pi\) | ||||
0.248867 | + | 0.968538i | \(0.419942\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 304.5.e.e.113.4 | 8 | ||
4.3 | odd | 2 | 38.5.b.a.37.3 | ✓ | 8 | ||
12.11 | even | 2 | 342.5.d.a.37.6 | 8 | |||
19.18 | odd | 2 | inner | 304.5.e.e.113.5 | 8 | ||
76.75 | even | 2 | 38.5.b.a.37.6 | yes | 8 | ||
228.227 | odd | 2 | 342.5.d.a.37.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.b.a.37.3 | ✓ | 8 | 4.3 | odd | 2 | ||
38.5.b.a.37.6 | yes | 8 | 76.75 | even | 2 | ||
304.5.e.e.113.4 | 8 | 1.1 | even | 1 | trivial | ||
304.5.e.e.113.5 | 8 | 19.18 | odd | 2 | inner | ||
342.5.d.a.37.2 | 8 | 228.227 | odd | 2 | |||
342.5.d.a.37.6 | 8 | 12.11 | even | 2 |