Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,5,Mod(296,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.296");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(54.8894503975\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 296.16 | ||
Character | \(\chi\) | \(=\) | 531.296 |
Dual form | 531.5.b.a.296.61 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/531\mathbb{Z}\right)^\times\).
\(n\) | \(119\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.40748i | − 1.35187i | −0.736961 | − | 0.675935i | \(-0.763740\pi\) | ||||
0.736961 | − | 0.675935i | \(-0.236260\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −13.2409 | −0.827554 | ||||||||
\(5\) | 5.33509i | 0.213403i | 0.994291 | + | 0.106702i | \(0.0340290\pi\) | ||||
−0.994291 | + | 0.106702i | \(0.965971\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −40.2707 | −0.821851 | −0.410926 | − | 0.911669i | \(-0.634794\pi\) | ||||
−0.410926 | + | 0.911669i | \(0.634794\pi\) | |||||||
\(8\) | − 14.9200i | − 0.233125i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 28.8494 | 0.288494 | ||||||||
\(11\) | 236.242i | 1.95242i | 0.216836 | + | 0.976208i | \(0.430426\pi\) | ||||
−0.216836 | + | 0.976208i | \(0.569574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 228.643 | 1.35292 | 0.676460 | − | 0.736480i | \(-0.263513\pi\) | ||||
0.676460 | + | 0.736480i | \(0.263513\pi\) | |||||||
\(14\) | 217.763i | 1.11104i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −292.533 | −1.14271 | ||||||||
\(17\) | − 143.085i | − 0.495105i | −0.968874 | − | 0.247552i | \(-0.920374\pi\) | ||||
0.968874 | − | 0.247552i | \(-0.0796262\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −422.626 | −1.17071 | −0.585355 | − | 0.810777i | \(-0.699045\pi\) | ||||
−0.585355 | + | 0.810777i | \(0.699045\pi\) | |||||||
\(20\) | − 70.6411i | − 0.176603i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1277.48 | 2.63941 | ||||||||
\(23\) | − 486.101i | − 0.918906i | −0.888202 | − | 0.459453i | \(-0.848045\pi\) | ||||
0.888202 | − | 0.459453i | \(-0.151955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 596.537 | 0.954459 | ||||||||
\(26\) | − 1236.38i | − 1.82897i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 533.219 | 0.680126 | ||||||||
\(29\) | − 464.257i | − 0.552030i | −0.961153 | − | 0.276015i | \(-0.910986\pi\) | ||||
0.961153 | − | 0.276015i | \(-0.0890139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1107.45 | 1.15239 | 0.576196 | − | 0.817312i | \(-0.304537\pi\) | ||||
0.576196 | + | 0.817312i | \(0.304537\pi\) | |||||||
\(32\) | 1343.15i | 1.31167i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −773.731 | −0.669318 | ||||||||
\(35\) | − 214.848i | − 0.175386i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.3545 | −0.0440865 | −0.0220433 | − | 0.999757i | \(-0.507017\pi\) | ||||
−0.0220433 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(38\) | 2285.34i | 1.58265i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 79.5994 | 0.0497496 | ||||||||
\(41\) | − 404.305i | − 0.240514i | −0.992743 | − | 0.120257i | \(-0.961628\pi\) | ||||
0.992743 | − | 0.120257i | \(-0.0383719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1540.56 | 0.833186 | 0.416593 | − | 0.909093i | \(-0.363224\pi\) | ||||
0.416593 | + | 0.909093i | \(0.363224\pi\) | |||||||
\(44\) | − 3128.05i | − 1.61573i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2628.58 | −1.24224 | ||||||||
\(47\) | − 1125.85i | − 0.509666i | −0.966985 | − | 0.254833i | \(-0.917979\pi\) | ||||
0.966985 | − | 0.254833i | \(-0.0820205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −779.269 | −0.324560 | ||||||||
\(50\) | − 3225.76i | − 1.29030i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3027.44 | −1.11961 | ||||||||
\(53\) | − 5199.94i | − 1.85117i | −0.378537 | − | 0.925586i | \(-0.623573\pi\) | ||||
0.378537 | − | 0.925586i | \(-0.376427\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1260.37 | −0.416652 | ||||||||
\(56\) | 600.838i | 0.191594i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2510.46 | −0.746273 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −126.227 | −0.0339229 | −0.0169614 | − | 0.999856i | \(-0.505399\pi\) | ||||
−0.0169614 | + | 0.999856i | \(0.505399\pi\) | |||||||
\(62\) | − 5988.51i | − 1.55788i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2582.52 | 0.630499 | ||||||||
\(65\) | 1219.83i | 0.288718i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5064.97 | 1.12831 | 0.564153 | − | 0.825670i | \(-0.309203\pi\) | ||||
0.564153 | + | 0.825670i | \(0.309203\pi\) | |||||||
\(68\) | 1894.57i | 0.409726i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1161.79 | −0.237099 | ||||||||
\(71\) | − 3201.77i | − 0.635147i | −0.948234 | − | 0.317573i | \(-0.897132\pi\) | ||||
0.948234 | − | 0.317573i | \(-0.102868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4567.64 | 0.857128 | 0.428564 | − | 0.903511i | \(-0.359020\pi\) | ||||
0.428564 | + | 0.903511i | \(0.359020\pi\) | |||||||
\(74\) | 326.366i | 0.0595993i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5595.94 | 0.968825 | ||||||||
\(77\) | − 9513.65i | − 1.60460i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 71.8464 | 0.0115120 | 0.00575600 | − | 0.999983i | \(-0.498168\pi\) | ||||
0.00575600 | + | 0.999983i | \(0.498168\pi\) | |||||||
\(80\) | − 1560.69i | − 0.243858i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2186.27 | −0.325144 | ||||||||
\(83\) | − 4147.02i | − 0.601977i | −0.953628 | − | 0.300989i | \(-0.902683\pi\) | ||||
0.953628 | − | 0.300989i | \(-0.0973166\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 763.372 | 0.105657 | ||||||||
\(86\) | − 8330.56i | − 1.12636i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3524.73 | 0.455156 | ||||||||
\(89\) | − 7286.37i | − 0.919880i | −0.887950 | − | 0.459940i | \(-0.847871\pi\) | ||||
0.887950 | − | 0.459940i | \(-0.152129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9207.63 | −1.11190 | ||||||||
\(92\) | 6436.40i | 0.760444i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6088.03 | −0.689003 | ||||||||
\(95\) | − 2254.75i | − 0.249833i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11003.2 | −1.16944 | −0.584718 | − | 0.811237i | \(-0.698795\pi\) | ||||
−0.584718 | + | 0.811237i | \(0.698795\pi\) | |||||||
\(98\) | 4213.88i | 0.438763i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7898.66 | −0.789866 | ||||||||
\(101\) | − 13790.2i | − 1.35185i | −0.736971 | − | 0.675924i | \(-0.763745\pi\) | ||||
0.736971 | − | 0.675924i | \(-0.236255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 845.921 | 0.0797361 | 0.0398681 | − | 0.999205i | \(-0.487306\pi\) | ||||
0.0398681 | + | 0.999205i | \(0.487306\pi\) | |||||||
\(104\) | − 3411.35i | − 0.315399i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28118.6 | −2.50255 | ||||||||
\(107\) | 9260.27i | 0.808828i | 0.914576 | + | 0.404414i | \(0.132525\pi\) | ||||
−0.914576 | + | 0.404414i | \(0.867475\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16263.0 | −1.36883 | −0.684413 | − | 0.729094i | \(-0.739941\pi\) | ||||
−0.684413 | + | 0.729094i | \(0.739941\pi\) | |||||||
\(110\) | 6815.45i | 0.563260i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11780.5 | 0.939136 | ||||||||
\(113\) | − 7683.57i | − 0.601737i | −0.953666 | − | 0.300868i | \(-0.902724\pi\) | ||||
0.953666 | − | 0.300868i | \(-0.0972765\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2593.39 | 0.196098 | ||||||||
\(116\) | 6147.17i | 0.456835i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2450.60 | 0.175999 | ||||||||
\(119\) | 5762.15i | 0.406903i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −41169.4 | −2.81193 | ||||||||
\(122\) | 682.570i | 0.0458593i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14663.6 | −0.953666 | ||||||||
\(125\) | 6517.00i | 0.417088i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 27830.1 | 1.72547 | 0.862734 | − | 0.505658i | \(-0.168750\pi\) | ||||
0.862734 | + | 0.505658i | \(0.168750\pi\) | |||||||
\(128\) | 7525.45i | 0.459317i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6596.22 | 0.390309 | ||||||||
\(131\) | 21420.2i | 1.24819i | 0.781348 | + | 0.624095i | \(0.214532\pi\) | ||||
−0.781348 | + | 0.624095i | \(0.785468\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17019.5 | 0.962149 | ||||||||
\(134\) | − 27388.7i | − 1.52532i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2134.83 | −0.115421 | ||||||||
\(137\) | − 5082.92i | − 0.270814i | −0.990790 | − | 0.135407i | \(-0.956766\pi\) | ||||
0.990790 | − | 0.135407i | \(-0.0432343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6781.40 | 0.350986 | 0.175493 | − | 0.984481i | \(-0.443848\pi\) | ||||
0.175493 | + | 0.984481i | \(0.443848\pi\) | |||||||
\(140\) | 2844.77i | 0.145141i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17313.5 | −0.858636 | ||||||||
\(143\) | 54015.2i | 2.64146i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2476.85 | 0.117805 | ||||||||
\(146\) | − 24699.4i | − 1.15873i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 799.146 | 0.0364840 | ||||||||
\(149\) | − 36064.7i | − 1.62446i | −0.583335 | − | 0.812232i | \(-0.698252\pi\) | ||||
0.583335 | − | 0.812232i | \(-0.301748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7344.83 | 0.322127 | 0.161064 | − | 0.986944i | \(-0.448508\pi\) | ||||
0.161064 | + | 0.986944i | \(0.448508\pi\) | |||||||
\(152\) | 6305.57i | 0.272921i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −51444.9 | −2.16921 | ||||||||
\(155\) | 5908.33i | 0.245924i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9876.14 | 0.400671 | 0.200336 | − | 0.979727i | \(-0.435797\pi\) | ||||
0.200336 | + | 0.979727i | \(0.435797\pi\) | |||||||
\(158\) | − 388.508i | − 0.0155627i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7165.82 | −0.279915 | ||||||||
\(161\) | 19575.6i | 0.755204i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −36136.4 | −1.36010 | −0.680049 | − | 0.733167i | \(-0.738041\pi\) | ||||
−0.680049 | + | 0.733167i | \(0.738041\pi\) | |||||||
\(164\) | 5353.35i | 0.199039i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22424.9 | −0.813795 | ||||||||
\(167\) | − 22251.4i | − 0.797856i | −0.916982 | − | 0.398928i | \(-0.869382\pi\) | ||||
0.916982 | − | 0.398928i | \(-0.130618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23716.8 | 0.830390 | ||||||||
\(170\) | − 4127.92i | − 0.142835i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −20398.4 | −0.689507 | ||||||||
\(173\) | 24165.7i | 0.807436i | 0.914884 | + | 0.403718i | \(0.132282\pi\) | ||||
−0.914884 | + | 0.403718i | \(0.867718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24023.0 | −0.784423 | ||||||||
\(176\) | − 69108.8i | − 2.23104i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −39400.9 | −1.24356 | ||||||||
\(179\) | 47777.0i | 1.49112i | 0.666437 | + | 0.745561i | \(0.267818\pi\) | ||||
−0.666437 | + | 0.745561i | \(0.732182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 55467.3 | 1.69309 | 0.846545 | − | 0.532317i | \(-0.178678\pi\) | ||||
0.846545 | + | 0.532317i | \(0.178678\pi\) | |||||||
\(182\) | 49790.1i | 1.50314i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7252.62 | −0.214220 | ||||||||
\(185\) | − 321.996i | − 0.00940822i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33802.8 | 0.966651 | ||||||||
\(188\) | 14907.3i | 0.421776i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12192.5 | −0.337743 | ||||||||
\(191\) | − 26889.8i | − 0.737089i | −0.929610 | − | 0.368545i | \(-0.879856\pi\) | ||||
0.929610 | − | 0.368545i | \(-0.120144\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 43456.7 | 1.16665 | 0.583327 | − | 0.812238i | \(-0.301751\pi\) | ||||
0.583327 | + | 0.812238i | \(0.301751\pi\) | |||||||
\(194\) | 59499.7i | 1.58093i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10318.2 | 0.268591 | ||||||||
\(197\) | − 8804.71i | − 0.226873i | −0.993545 | − | 0.113436i | \(-0.963814\pi\) | ||||
0.993545 | − | 0.113436i | \(-0.0361858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 62780.3 | 1.58532 | 0.792661 | − | 0.609663i | \(-0.208695\pi\) | ||||
0.792661 | + | 0.609663i | \(0.208695\pi\) | |||||||
\(200\) | − 8900.32i | − 0.222508i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −74570.3 | −1.82752 | ||||||||
\(203\) | 18696.0i | 0.453687i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2157.00 | 0.0513266 | ||||||||
\(206\) | − 4574.30i | − 0.107793i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −66885.8 | −1.54599 | ||||||||
\(209\) | − 99842.2i | − 2.28571i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13469.2 | 0.302536 | 0.151268 | − | 0.988493i | \(-0.451664\pi\) | ||||
0.151268 | + | 0.988493i | \(0.451664\pi\) | |||||||
\(212\) | 68851.7i | 1.53194i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 50074.8 | 1.09343 | ||||||||
\(215\) | 8219.03i | 0.177805i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44597.7 | −0.947095 | ||||||||
\(218\) | 87942.0i | 1.85048i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16688.4 | 0.344802 | ||||||||
\(221\) | − 32715.5i | − 0.669837i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20730.4 | 0.416868 | 0.208434 | − | 0.978036i | \(-0.433163\pi\) | ||||
0.208434 | + | 0.978036i | \(0.433163\pi\) | |||||||
\(224\) | − 54089.6i | − 1.07800i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −41548.8 | −0.813470 | ||||||||
\(227\) | − 26973.0i | − 0.523453i | −0.965142 | − | 0.261727i | \(-0.915708\pi\) | ||||
0.965142 | − | 0.261727i | \(-0.0842919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −97728.9 | −1.86360 | −0.931798 | − | 0.362977i | \(-0.881760\pi\) | ||||
−0.931798 | + | 0.362977i | \(0.881760\pi\) | |||||||
\(230\) | − 14023.7i | − 0.265099i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6926.71 | −0.128692 | ||||||||
\(233\) | − 46974.8i | − 0.865273i | −0.901568 | − | 0.432637i | \(-0.857583\pi\) | ||||
0.901568 | − | 0.432637i | \(-0.142417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6006.52 | 0.108764 | ||||||||
\(236\) | − 6000.60i | − 0.107738i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 31158.7 | 0.550080 | ||||||||
\(239\) | − 36154.4i | − 0.632944i | −0.948602 | − | 0.316472i | \(-0.897502\pi\) | ||||
0.948602 | − | 0.316472i | \(-0.102498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 41569.2 | 0.715711 | 0.357856 | − | 0.933777i | \(-0.383508\pi\) | ||||
0.357856 | + | 0.933777i | \(0.383508\pi\) | |||||||
\(242\) | 222623.i | 3.80136i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1671.35 | 0.0280730 | ||||||||
\(245\) | − 4157.47i | − 0.0692623i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −96630.7 | −1.58388 | ||||||||
\(248\) | − 16523.1i | − 0.268651i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 35240.6 | 0.563849 | ||||||||
\(251\) | − 37383.6i | − 0.593381i | −0.954974 | − | 0.296690i | \(-0.904117\pi\) | ||||
0.954974 | − | 0.296690i | \(-0.0958829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 114838. | 1.79409 | ||||||||
\(254\) | − 150491.i | − 2.33261i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 82014.1 | 1.25144 | ||||||||
\(257\) | 13617.3i | 0.206170i | 0.994673 | + | 0.103085i | \(0.0328714\pi\) | ||||
−0.994673 | + | 0.103085i | \(0.967129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2430.52 | 0.0362326 | ||||||||
\(260\) | − 16151.6i | − 0.238929i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 115829. | 1.68739 | ||||||||
\(263\) | − 109111.i | − 1.57746i | −0.614738 | − | 0.788731i | \(-0.710738\pi\) | ||||
0.614738 | − | 0.788731i | \(-0.289262\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27742.1 | 0.395047 | ||||||||
\(266\) | − 92032.4i | − 1.30070i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −67064.6 | −0.933735 | ||||||||
\(269\) | − 114932.i | − 1.58832i | −0.607709 | − | 0.794160i | \(-0.707911\pi\) | ||||
0.607709 | − | 0.794160i | \(-0.292089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6066.71 | 0.0826065 | 0.0413033 | − | 0.999147i | \(-0.486849\pi\) | ||||
0.0413033 | + | 0.999147i | \(0.486849\pi\) | |||||||
\(272\) | 41857.2i | 0.565760i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −27485.8 | −0.366106 | ||||||||
\(275\) | 140927.i | 1.86350i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 510.178 | 0.00664908 | 0.00332454 | − | 0.999994i | \(-0.498942\pi\) | ||||
0.00332454 | + | 0.999994i | \(0.498942\pi\) | |||||||
\(278\) | − 36670.3i | − 0.474487i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3205.52 | −0.0408868 | ||||||||
\(281\) | 119073.i | 1.50799i | 0.656878 | + | 0.753997i | \(0.271877\pi\) | ||||
−0.656878 | + | 0.753997i | \(0.728123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 39843.2 | 0.497487 | 0.248743 | − | 0.968569i | \(-0.419982\pi\) | ||||
0.248743 | + | 0.968569i | \(0.419982\pi\) | |||||||
\(284\) | 42394.3i | 0.525618i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 292086. | 3.57091 | ||||||||
\(287\) | 16281.6i | 0.197667i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 63047.6 | 0.754871 | ||||||||
\(290\) | − 13393.5i | − 0.159257i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −60479.4 | −0.709320 | ||||||||
\(293\) | 34537.5i | 0.402306i | 0.979560 | + | 0.201153i | \(0.0644688\pi\) | ||||
−0.979560 | + | 0.201153i | \(0.935531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2417.79 | −0.0277828 | ||||||||
\(296\) | 900.488i | 0.0102777i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −195019. | −2.19606 | ||||||||
\(299\) | − 111144.i | − 1.24321i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −62039.5 | −0.684755 | ||||||||
\(302\) | − 39717.0i | − 0.435474i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 123632. | 1.33778 | ||||||||
\(305\) | − 673.432i | − 0.00723926i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 101616. | 1.07816 | 0.539080 | − | 0.842255i | \(-0.318772\pi\) | ||||
0.539080 | + | 0.842255i | \(0.318772\pi\) | |||||||
\(308\) | 125969.i | 1.32789i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 31949.2 | 0.332458 | ||||||||
\(311\) | − 160917.i | − 1.66372i | −0.554985 | − | 0.831860i | \(-0.687276\pi\) | ||||
0.554985 | − | 0.831860i | \(-0.312724\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 177997. | 1.81687 | 0.908437 | − | 0.418022i | \(-0.137276\pi\) | ||||
0.908437 | + | 0.418022i | \(0.137276\pi\) | |||||||
\(314\) | − 53405.1i | − 0.541656i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −951.309 | −0.00952681 | ||||||||
\(317\) | 31885.4i | 0.317303i | 0.987335 | + | 0.158651i | \(0.0507146\pi\) | ||||
−0.987335 | + | 0.158651i | \(0.949285\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 109677. | 1.07779 | ||||||||
\(320\) | 13778.0i | 0.134551i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 105855. | 1.02094 | ||||||||
\(323\) | 60471.6i | 0.579624i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 136394. | 1.29131 | ||||||||
\(326\) | 195407.i | 1.83868i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6032.22 | −0.0560699 | ||||||||
\(329\) | 45338.9i | 0.418870i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 183181. | 1.67195 | 0.835975 | − | 0.548767i | \(-0.184903\pi\) | ||||
0.835975 | + | 0.548767i | \(0.184903\pi\) | |||||||
\(332\) | 54910.2i | 0.498169i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −120324. | −1.07860 | ||||||||
\(335\) | 27022.0i | 0.240785i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −48086.1 | −0.423408 | −0.211704 | − | 0.977334i | \(-0.567901\pi\) | ||||
−0.211704 | + | 0.977334i | \(0.567901\pi\) | |||||||
\(338\) | − 128248.i | − 1.12258i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10107.7 | −0.0874369 | ||||||||
\(341\) | 261626.i | 2.24995i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 128072. | 1.08859 | ||||||||
\(344\) | − 22985.1i | − 0.194236i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 130676. | 1.09155 | ||||||||
\(347\) | 89342.6i | 0.741993i | 0.928634 | + | 0.370996i | \(0.120984\pi\) | ||||
−0.928634 | + | 0.370996i | \(0.879016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −152276. | −1.25020 | −0.625102 | − | 0.780543i | \(-0.714943\pi\) | ||||
−0.625102 | + | 0.780543i | \(0.714943\pi\) | |||||||
\(350\) | 129904.i | 1.06044i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −317309. | −2.56092 | ||||||||
\(353\) | 4377.51i | 0.0351300i | 0.999846 | + | 0.0175650i | \(0.00559140\pi\) | ||||
−0.999846 | + | 0.0175650i | \(0.994409\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17081.7 | 0.135542 | ||||||||
\(356\) | 96477.9i | 0.761251i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 258354. | 2.01580 | ||||||||
\(359\) | 84682.0i | 0.657056i | 0.944494 | + | 0.328528i | \(0.106553\pi\) | ||||
−0.944494 | + | 0.328528i | \(0.893447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48291.9 | 0.370561 | ||||||||
\(362\) | − 299939.i | − 2.28884i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 121917. | 0.920156 | ||||||||
\(365\) | 24368.7i | 0.182914i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −62433.7 | −0.463540 | −0.231770 | − | 0.972771i | \(-0.574452\pi\) | ||||
−0.231770 | + | 0.972771i | \(0.574452\pi\) | |||||||
\(368\) | 142201.i | 1.05004i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1741.19 | −0.0127187 | ||||||||
\(371\) | 209405.i | 1.52139i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 93463.9 | 0.671778 | 0.335889 | − | 0.941901i | \(-0.390963\pi\) | ||||
0.335889 | + | 0.941901i | \(0.390963\pi\) | |||||||
\(374\) | − 182788.i | − 1.30679i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16797.7 | −0.118816 | ||||||||
\(377\) | − 106149.i | − 0.746852i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −194054. | −1.35097 | −0.675483 | − | 0.737376i | \(-0.736065\pi\) | ||||
−0.675483 | + | 0.737376i | \(0.736065\pi\) | |||||||
\(380\) | 29854.8i | 0.206751i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −145406. | −0.996449 | ||||||||
\(383\) | − 234963.i | − 1.60177i | −0.598816 | − | 0.800887i | \(-0.704362\pi\) | ||||
0.598816 | − | 0.800887i | \(-0.295638\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 50756.1 | 0.342426 | ||||||||
\(386\) | − 234991.i | − 1.57716i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 145692. | 0.967771 | ||||||||
\(389\) | 13392.4i | 0.0885032i | 0.999020 | + | 0.0442516i | \(0.0140903\pi\) | ||||
−0.999020 | + | 0.0442516i | \(0.985910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −69553.9 | −0.454955 | ||||||||
\(392\) | 11626.7i | 0.0756630i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −47611.3 | −0.306703 | ||||||||
\(395\) | 383.307i | 0.00245670i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −244261. | −1.54979 | −0.774894 | − | 0.632091i | \(-0.782197\pi\) | ||||
−0.774894 | + | 0.632091i | \(0.782197\pi\) | |||||||
\(398\) | − 339483.i | − 2.14315i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −174507. | −1.09067 | ||||||||
\(401\) | − 47912.6i | − 0.297962i | −0.988840 | − | 0.148981i | \(-0.952401\pi\) | ||||
0.988840 | − | 0.148981i | \(-0.0475993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 253211. | 1.55909 | ||||||||
\(404\) | 182594.i | 1.11873i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 101098. | 0.613325 | ||||||||
\(407\) | − 14258.3i | − 0.0860753i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −50042.1 | −0.299150 | −0.149575 | − | 0.988750i | \(-0.547791\pi\) | ||||
−0.149575 | + | 0.988750i | \(0.547791\pi\) | |||||||
\(410\) | − 11663.9i | − 0.0693869i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11200.7 | −0.0659860 | ||||||||
\(413\) | − 18250.2i | − 0.106996i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22124.7 | 0.128464 | ||||||||
\(416\) | 307102.i | 1.77458i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −539895. | −3.08999 | ||||||||
\(419\) | 236589.i | 1.34762i | 0.738906 | + | 0.673809i | \(0.235343\pi\) | ||||
−0.738906 | + | 0.673809i | \(0.764657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −100454. | −0.566767 | −0.283383 | − | 0.959007i | \(-0.591457\pi\) | ||||
−0.283383 | + | 0.959007i | \(0.591457\pi\) | |||||||
\(422\) | − 72834.5i | − 0.408989i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −77583.0 | −0.431554 | ||||||||
\(425\) | − 85355.7i | − 0.472557i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5083.25 | 0.0278796 | ||||||||
\(428\) | − 122614.i | − 0.669349i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 44444.3 | 0.240369 | ||||||||
\(431\) | − 45004.6i | − 0.242271i | −0.992636 | − | 0.121136i | \(-0.961346\pi\) | ||||
0.992636 | − | 0.121136i | \(-0.0386536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 81854.8 | 0.436584 | 0.218292 | − | 0.975883i | \(-0.429951\pi\) | ||||
0.218292 | + | 0.975883i | \(0.429951\pi\) | |||||||
\(434\) | 241161.i | 1.28035i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 215336. | 1.13278 | ||||||||
\(437\) | 205439.i | 1.07577i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 203970. | 1.05837 | 0.529185 | − | 0.848506i | \(-0.322498\pi\) | ||||
0.529185 | + | 0.848506i | \(0.322498\pi\) | |||||||
\(440\) | 18804.7i | 0.0971319i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −176908. | −0.905533 | ||||||||
\(443\) | − 13039.6i | − 0.0664443i | −0.999448 | − | 0.0332222i | \(-0.989423\pi\) | ||||
0.999448 | − | 0.0332222i | \(-0.0105769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38873.4 | 0.196306 | ||||||||
\(446\) | − 112099.i | − 0.563552i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −104000. | −0.518176 | ||||||||
\(449\) | 132025.i | 0.654884i | 0.944871 | + | 0.327442i | \(0.106187\pi\) | ||||
−0.944871 | + | 0.327442i | \(0.893813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 95513.9 | 0.469584 | ||||||||
\(452\) | 101737.i | 0.497970i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −145856. | −0.707641 | ||||||||
\(455\) | − 49123.5i | − 0.237283i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −416478. | −1.99416 | −0.997078 | − | 0.0763845i | \(-0.975662\pi\) | ||||
−0.997078 | + | 0.0763845i | \(0.975662\pi\) | |||||||
\(458\) | 528467.i | 2.51934i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −34338.8 | −0.162281 | ||||||||
\(461\) | 240078.i | 1.12967i | 0.825205 | + | 0.564833i | \(0.191060\pi\) | ||||
−0.825205 | + | 0.564833i | \(0.808940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 256699. | 1.19746 | 0.598731 | − | 0.800950i | \(-0.295672\pi\) | ||||
0.598731 | + | 0.800950i | \(0.295672\pi\) | |||||||
\(464\) | 135811.i | 0.630809i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −254016. | −1.16974 | ||||||||
\(467\) | − 117445.i | − 0.538520i | −0.963068 | − | 0.269260i | \(-0.913221\pi\) | ||||
0.963068 | − | 0.269260i | \(-0.0867791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −203970. | −0.927301 | ||||||||
\(470\) | − 32480.1i | − 0.147036i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6761.55 | 0.0303502 | ||||||||
\(473\) | 363946.i | 1.62673i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −252112. | −1.11739 | ||||||||
\(476\) | − 76295.8i | − 0.336734i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −195504. | −0.855659 | ||||||||
\(479\) | − 374316.i | − 1.63143i | −0.578456 | − | 0.815714i | \(-0.696344\pi\) | ||||
0.578456 | − | 0.815714i | \(-0.303656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13799.7 | −0.0596455 | ||||||||
\(482\) | − 224785.i | − 0.967549i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 545119. | 2.32702 | ||||||||
\(485\) | − 58703.1i | − 0.249562i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 109835. | 0.463107 | 0.231553 | − | 0.972822i | \(-0.425619\pi\) | ||||
0.231553 | + | 0.972822i | \(0.425619\pi\) | |||||||
\(488\) | 1883.30i | 0.00790826i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22481.4 | −0.0936336 | ||||||||
\(491\) | 222390.i | 0.922471i | 0.887278 | + | 0.461236i | \(0.152594\pi\) | ||||
−0.887278 | + | 0.461236i | \(0.847406\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −66428.4 | −0.273313 | ||||||||
\(494\) | 522529.i | 2.14119i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −323966. | −1.31685 | ||||||||
\(497\) | 128938.i | 0.521996i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −111625. | −0.448292 | −0.224146 | − | 0.974556i | \(-0.571959\pi\) | ||||
−0.224146 | + | 0.974556i | \(0.571959\pi\) | |||||||
\(500\) | − 86290.8i | − 0.345163i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −202151. | −0.802174 | ||||||||
\(503\) | 139370.i | 0.550850i | 0.961323 | + | 0.275425i | \(0.0888186\pi\) | ||||
−0.961323 | + | 0.275425i | \(0.911181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 73571.9 | 0.288489 | ||||||||
\(506\) | − 620983.i | − 2.42537i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −368494. | −1.42792 | ||||||||
\(509\) | − 12592.1i | − 0.0486030i | −0.999705 | − | 0.0243015i | \(-0.992264\pi\) | ||||
0.999705 | − | 0.0243015i | \(-0.00773616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −183942. | −0.704432 | ||||||||
\(512\) | − 323082.i | − 1.23246i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 73635.5 | 0.278715 | ||||||||
\(515\) | 4513.06i | 0.0170160i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 265974. | 0.995080 | ||||||||
\(518\) | − 13143.0i | − 0.0489818i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18199.9 | 0.0673072 | ||||||||
\(521\) | − 44155.3i | − 0.162670i | −0.996687 | − | 0.0813350i | \(-0.974082\pi\) | ||||
0.996687 | − | 0.0813350i | \(-0.0259184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 140348. | 0.513102 | 0.256551 | − | 0.966531i | \(-0.417414\pi\) | ||||
0.256551 | + | 0.966531i | \(0.417414\pi\) | |||||||
\(524\) | − 283622.i | − 1.03295i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −590018. | −2.13252 | ||||||||
\(527\) | − 158460.i | − 0.570555i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43546.6 | 0.155612 | ||||||||
\(530\) | − 150015.i | − 0.534052i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −225352. | −0.796231 | ||||||||
\(533\) | − 92441.6i | − 0.325397i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49404.3 | −0.172607 | ||||||||
\(536\) | − 75569.2i | − 0.263036i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −621495. | −2.14720 | ||||||||
\(539\) | − 184096.i | − 0.633677i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 335690. | 1.14695 | 0.573474 | − | 0.819224i | \(-0.305595\pi\) | ||||
0.573474 | + | 0.819224i | \(0.305595\pi\) | |||||||
\(542\) | − 32805.6i | − 0.111673i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 192185. | 0.649414 | ||||||||
\(545\) | − 86764.6i | − 0.292112i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25995.2 | 0.0868798 | 0.0434399 | − | 0.999056i | \(-0.486168\pi\) | ||||
0.0434399 | + | 0.999056i | \(0.486168\pi\) | |||||||
\(548\) | 67302.2i | 0.224114i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 762062. | 2.51921 | ||||||||
\(551\) | 196207.i | 0.646267i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2893.31 | −0.00946116 | ||||||||
\(554\) | − 2758.78i | − 0.00898870i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −89791.6 | −0.290460 | ||||||||
\(557\) | − 375672.i | − 1.21087i | −0.795894 | − | 0.605437i | \(-0.792999\pi\) | ||||
0.795894 | − | 0.605437i | \(-0.207001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 352239. | 1.12723 | ||||||||
\(560\) | 62850.1i | 0.200415i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 643884. | 2.03861 | ||||||||
\(563\) | − 5956.29i | − 0.0187914i | −0.999956 | − | 0.00939570i | \(-0.997009\pi\) | ||||
0.999956 | − | 0.00939570i | \(-0.00299079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40992.5 | 0.128413 | ||||||||
\(566\) | − 215452.i | − 0.672538i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −47770.4 | −0.148068 | ||||||||
\(569\) | 598655.i | 1.84907i | 0.381103 | + | 0.924533i | \(0.375544\pi\) | ||||
−0.381103 | + | 0.924533i | \(0.624456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −291238. | −0.893257 | −0.446629 | − | 0.894719i | \(-0.647375\pi\) | ||||
−0.446629 | + | 0.894719i | \(0.647375\pi\) | |||||||
\(572\) | − 715208.i | − 2.18595i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 88042.7 | 0.267220 | ||||||||
\(575\) | − 289977.i | − 0.877058i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −97573.3 | −0.293075 | −0.146538 | − | 0.989205i | \(-0.546813\pi\) | ||||
−0.146538 | + | 0.989205i | \(0.546813\pi\) | |||||||
\(578\) | − 340929.i | − 1.02049i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −32795.7 | −0.0974901 | ||||||||
\(581\) | 167004.i | 0.494736i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.22845e6 | 3.61426 | ||||||||
\(584\) | − 68149.0i | − 0.199818i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 186761. | 0.543865 | ||||||||
\(587\) | 610947.i | 1.77308i | 0.462656 | + | 0.886538i | \(0.346896\pi\) | ||||
−0.462656 | + | 0.886538i | \(0.653104\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −468037. | −1.34912 | ||||||||
\(590\) | 13074.2i | 0.0375587i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17655.7 | 0.0503781 | ||||||||
\(593\) | 289519.i | 0.823319i | 0.911338 | + | 0.411660i | \(0.135051\pi\) | ||||
−0.911338 | + | 0.411660i | \(0.864949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30741.6 | −0.0868344 | ||||||||
\(596\) | 477528.i | 1.34433i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −601008. | −1.68065 | ||||||||
\(599\) | 666953.i | 1.85884i | 0.369025 | + | 0.929420i | \(0.379692\pi\) | ||||
−0.369025 | + | 0.929420i | \(0.620308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 267999. | 0.741965 | 0.370983 | − | 0.928640i | \(-0.379021\pi\) | ||||
0.370983 | + | 0.928640i | \(0.379021\pi\) | |||||||
\(602\) | 335478.i | 0.925701i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −97251.8 | −0.266578 | ||||||||
\(605\) | − 219642.i | − 0.600075i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −651200. | −1.76741 | −0.883704 | − | 0.468046i | \(-0.844958\pi\) | ||||
−0.883704 | + | 0.468046i | \(0.844958\pi\) | |||||||
\(608\) | − 567650.i | − 1.53558i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3641.57 | −0.00978654 | ||||||||
\(611\) | − 257419.i | − 0.689537i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −123203. | −0.327868 | −0.163934 | − | 0.986471i | \(-0.552418\pi\) | ||||
−0.163934 | + | 0.986471i | \(0.552418\pi\) | |||||||
\(614\) | − 549484.i | − 1.45753i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −141943. | −0.374071 | ||||||||
\(617\) | − 427945.i | − 1.12413i | −0.827092 | − | 0.562067i | \(-0.810006\pi\) | ||||
0.827092 | − | 0.562067i | \(-0.189994\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −67763.5 | −0.176854 | −0.0884269 | − | 0.996083i | \(-0.528184\pi\) | ||||
−0.0884269 | + | 0.996083i | \(0.528184\pi\) | |||||||
\(620\) | − 78231.4i | − 0.203516i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −870154. | −2.24913 | ||||||||
\(623\) | 293427.i | 0.756005i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 338067. | 0.865451 | ||||||||
\(626\) | − 962517.i | − 2.45618i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −130769. | −0.331577 | ||||||||
\(629\) | 8635.84i | 0.0218275i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −479812. | −1.20507 | −0.602536 | − | 0.798092i | \(-0.705843\pi\) | ||||
−0.602536 | + | 0.798092i | \(0.705843\pi\) | |||||||
\(632\) | − 1071.95i | − 0.00268373i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 172420. | 0.428952 | ||||||||
\(635\) | 148476.i | 0.368221i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −178175. | −0.439104 | ||||||||
\(638\) | − 593077.i | − 1.45704i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −40148.9 | −0.0980198 | ||||||||
\(641\) | 499820.i | 1.21646i | 0.793761 | + | 0.608230i | \(0.208120\pi\) | ||||
−0.793761 | + | 0.608230i | \(0.791880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −512244. | −1.23895 | −0.619476 | − | 0.785015i | \(-0.712655\pi\) | ||||
−0.619476 | + | 0.785015i | \(0.712655\pi\) | |||||||
\(644\) | − 259198.i | − 0.624972i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 326999. | 0.783577 | ||||||||
\(647\) | − 246169.i | − 0.588063i | −0.955796 | − | 0.294032i | \(-0.905003\pi\) | ||||
0.955796 | − | 0.294032i | \(-0.0949971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −107062. | −0.254183 | ||||||||
\(650\) | − 737549.i | − 1.74568i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 478477. | 1.12555 | ||||||||
\(653\) | 232200.i | 0.544549i | 0.962220 | + | 0.272274i | \(0.0877758\pi\) | ||||
−0.962220 | + | 0.272274i | \(0.912224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −114279. | −0.266368 | ||||||||
\(656\) | 118273.i | 0.274838i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 245169. | 0.566258 | ||||||||
\(659\) | − 254880.i | − 0.586902i | −0.955974 | − | 0.293451i | \(-0.905196\pi\) | ||||
0.955974 | − | 0.293451i | \(-0.0948037\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −735421. | −1.68319 | −0.841595 | − | 0.540109i | \(-0.818383\pi\) | ||||
−0.841595 | + | 0.540109i | \(0.818383\pi\) | |||||||
\(662\) | − 990546.i | − 2.26026i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −61873.5 | −0.140336 | ||||||||
\(665\) | 90800.3i | 0.205326i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −225676. | −0.507264 | ||||||||
\(668\) | 294628.i | 0.660269i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 146121. | 0.325510 | ||||||||
\(671\) | − 29820.2i | − 0.0662315i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 678968. | 1.49906 | 0.749530 | − | 0.661971i | \(-0.230280\pi\) | ||||
0.749530 | + | 0.661971i | \(0.230280\pi\) | |||||||
\(674\) | 260025.i | 0.572393i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −314030. | −0.687193 | ||||||||
\(677\) | 574807.i | 1.25414i | 0.778965 | + | 0.627068i | \(0.215745\pi\) | ||||
−0.778965 | + | 0.627068i | \(0.784255\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 443108. | 0.961102 | ||||||||
\(680\) | − 11389.5i | − 0.0246313i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.41474e6 | 3.04164 | ||||||||
\(683\) | 415608.i | 0.890928i | 0.895300 | + | 0.445464i | \(0.146961\pi\) | ||||
−0.895300 | + | 0.445464i | \(0.853039\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27117.8 | 0.0577927 | ||||||||
\(686\) | − 692546.i | − 1.47164i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −450666. | −0.952089 | ||||||||
\(689\) | − 1.18893e6i | − 2.50449i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −77705.9 | −0.162741 | −0.0813706 | − | 0.996684i | \(-0.525930\pi\) | ||||
−0.0813706 | + | 0.996684i | \(0.525930\pi\) | |||||||
\(692\) | − 319975.i | − 0.668197i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 483118. | 1.00308 | ||||||||
\(695\) | 36179.3i | 0.0749016i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57850.1 | −0.119080 | ||||||||
\(698\) | 823430.i | 1.69011i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 318085. | 0.649153 | ||||||||
\(701\) | − 754544.i | − 1.53549i | −0.640753 | − | 0.767747i | \(-0.721378\pi\) | ||||
0.640753 | − | 0.767747i | \(-0.278622\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25507.4 | 0.0516125 | ||||||||
\(704\) | 610101.i | 1.23100i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23671.3 | 0.0474912 | ||||||||
\(707\) | 555342.i | 1.11102i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −312848. | −0.622360 | −0.311180 | − | 0.950351i | \(-0.600724\pi\) | ||||
−0.311180 | + | 0.950351i | \(0.600724\pi\) | |||||||
\(710\) | − 92369.2i | − 0.183236i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −108713. | −0.214447 | ||||||||
\(713\) | − 538332.i | − 1.05894i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −288176. | −0.563697 | ||||||||
\(716\) | − 632609.i | − 1.23398i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 457917. | 0.888255 | ||||||||
\(719\) | 518853.i | 1.00366i | 0.864966 | + | 0.501830i | \(0.167340\pi\) | ||||
−0.864966 | + | 0.501830i | \(0.832660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34065.8 | −0.0655313 | ||||||||
\(722\) | − 261137.i | − 0.500951i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −734436. | −1.40112 | ||||||||
\(725\) | − 276946.i | − 0.526890i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 352533. | 0.667007 | 0.333504 | − | 0.942749i | \(-0.391769\pi\) | ||||
0.333504 | + | 0.942749i | \(0.391769\pi\) | |||||||
\(728\) | 137378.i | 0.259211i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 131773. | 0.247276 | ||||||||
\(731\) | − 220432.i | − 0.412515i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 242825. | 0.451944 | 0.225972 | − | 0.974134i | \(-0.427444\pi\) | ||||
0.225972 | + | 0.974134i | \(0.427444\pi\) | |||||||
\(734\) | 337609.i | 0.626645i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 652907. | 1.20530 | ||||||||
\(737\) | 1.19656e6i | 2.20292i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −919000. | −1.68278 | −0.841388 | − | 0.540431i | \(-0.818261\pi\) | ||||
−0.841388 | + | 0.540431i | \(0.818261\pi\) | |||||||
\(740\) | 4263.51i | 0.00778581i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.13236e6 | 2.05672 | ||||||||
\(743\) | − 563145.i | − 1.02010i | −0.860145 | − | 0.510050i | \(-0.829627\pi\) | ||||
0.860145 | − | 0.510050i | \(-0.170373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 192408. | 0.346666 | ||||||||
\(746\) | − 505404.i | − 0.908157i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −447578. | −0.799956 | ||||||||
\(749\) | − 372918.i | − 0.664736i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 105723. | 0.187451 | 0.0937255 | − | 0.995598i | \(-0.470122\pi\) | ||||
0.0937255 | + | 0.995598i | \(0.470122\pi\) | |||||||
\(752\) | 329349.i | 0.582400i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −574000. | −1.00965 | ||||||||
\(755\) | 39185.3i | 0.0687431i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −318147. | −0.555184 | −0.277592 | − | 0.960699i | \(-0.589536\pi\) | ||||
−0.277592 | + | 0.960699i | \(0.589536\pi\) | |||||||
\(758\) | 1.04934e6i | 1.82633i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −33640.8 | −0.0582423 | ||||||||
\(761\) | − 864313.i | − 1.49246i | −0.665690 | − | 0.746228i | \(-0.731863\pi\) | ||||
0.665690 | − | 0.746228i | \(-0.268137\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 654924. | 1.12497 | ||||||||
\(764\) | 356044.i | 0.609981i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.27056e6 | −2.16539 | ||||||||
\(767\) | 103618.i | 0.176135i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.13314e6 | 1.91615 | 0.958077 | − | 0.286512i | \(-0.0924958\pi\) | ||||
0.958077 | + | 0.286512i | \(0.0924958\pi\) | |||||||
\(770\) | − 274463.i | − 0.462916i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −575404. | −0.965469 | ||||||||
\(773\) | − 995777.i | − 1.66649i | −0.552903 | − | 0.833246i | \(-0.686480\pi\) | ||||
0.552903 | − | 0.833246i | \(-0.313520\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 660634. | 1.09991 | ||||||||
\(776\) | 164168.i | 0.272624i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 72419.1 | 0.119645 | ||||||||
\(779\) | 170870.i | 0.281573i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 756395. | 1.24007 | ||||||||
\(782\) | 376112.i | 0.615040i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 227962. | 0.370878 | ||||||||
\(785\) | 52690.1i | 0.0855046i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.08294e6 | −1.74845 | −0.874225 | − | 0.485521i | \(-0.838630\pi\) | ||||
−0.874225 | + | 0.485521i | \(0.838630\pi\) | |||||||
\(788\) | 116582.i | 0.187750i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2072.73 | 0.00332114 | ||||||||
\(791\) | 309423.i | 0.494538i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28861.0 | −0.0458949 | ||||||||
\(794\) | 1.32083e6i | 2.09511i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −831265. | −1.31194 | ||||||||
\(797\) | 1.09994e6i | 1.73161i | 0.500378 | + | 0.865807i | \(0.333194\pi\) | ||||
−0.500378 | + | 0.865807i | \(0.666806\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −161093. | −0.252338 | ||||||||
\(800\) | 801238.i | 1.25193i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −259086. | −0.402806 | ||||||||
\(803\) | 1.07907e6i | 1.67347i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −104438. | −0.161163 | ||||||||
\(806\) | − 1.36923e6i | − 2.10769i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −205750. | −0.315149 | ||||||||
\(809\) | 1.06036e6i | 1.62015i | 0.586328 | + | 0.810074i | \(0.300573\pi\) | ||||
−0.586328 | + | 0.810074i | \(0.699427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32747.6 | −0.0497895 | −0.0248948 | − | 0.999690i | \(-0.507925\pi\) | ||||
−0.0248948 | + | 0.999690i | \(0.507925\pi\) | |||||||
\(812\) | − 247551.i | − 0.375450i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −77101.4 | −0.116363 | ||||||||
\(815\) | − 192791.i | − 0.290249i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −651082. | −0.975419 | ||||||||
\(818\) | 270602.i | 0.404412i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28560.6 | −0.0424755 | ||||||||
\(821\) | − 286009.i | − 0.424319i | −0.977235 | − | 0.212160i | \(-0.931950\pi\) | ||||
0.977235 | − | 0.212160i | \(-0.0680497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 68867.6 | 0.101675 | 0.0508376 | − | 0.998707i | \(-0.483811\pi\) | ||||
0.0508376 | + | 0.998707i | \(0.483811\pi\) | |||||||
\(824\) | − 12621.1i | − 0.0185885i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −98687.6 | −0.144645 | ||||||||
\(827\) | 214757.i | 0.314005i | 0.987598 | + | 0.157002i | \(0.0501830\pi\) | ||||
−0.987598 | + | 0.157002i | \(0.949817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −891503. | −1.29722 | −0.648610 | − | 0.761121i | \(-0.724649\pi\) | ||||
−0.648610 | + | 0.761121i | \(0.724649\pi\) | |||||||
\(830\) | − 119639.i | − 0.173667i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 590476. | 0.853013 | ||||||||
\(833\) | 111502.i | 0.160691i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 118713. | 0.170265 | ||||||||
\(836\) | 1.32200e6i | 1.89155i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.27935e6 | 1.82180 | ||||||||
\(839\) | 716368.i | 1.01768i | 0.860860 | + | 0.508841i | \(0.169926\pi\) | ||||
−0.860860 | + | 0.508841i | \(0.830074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 491746. | 0.695263 | ||||||||
\(842\) | 543205.i | 0.766195i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −178344. | −0.250365 | ||||||||
\(845\) | 126531.i | 0.177208i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.65792e6 | 2.31099 | ||||||||
\(848\) | 1.52116e6i | 2.11535i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −461559. | −0.638836 | ||||||||
\(851\) | 29338.4i | 0.0405114i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −206839. | −0.284273 | −0.142136 | − | 0.989847i | \(-0.545397\pi\) | ||||
−0.142136 | + | 0.989847i | \(0.545397\pi\) | |||||||
\(854\) | − 27487.6i | − 0.0376895i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 138163. | 0.188558 | ||||||||
\(857\) | 141720.i | 0.192960i | 0.995335 | + | 0.0964802i | \(0.0307585\pi\) | ||||
−0.995335 | + | 0.0964802i | \(0.969242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −587558. | −0.796277 | −0.398139 | − | 0.917325i | \(-0.630344\pi\) | ||||
−0.398139 | + | 0.917325i | \(0.630344\pi\) | |||||||
\(860\) | − 108827.i | − 0.147143i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −243362. | −0.327520 | ||||||||
\(863\) | − 1.10938e6i | − 1.48957i | −0.667307 | − | 0.744783i | \(-0.732553\pi\) | ||||
0.667307 | − | 0.744783i | \(-0.267447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −128926. | −0.172310 | ||||||||
\(866\) | − 442628.i | − 0.590206i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 590513. | 0.783772 | ||||||||
\(869\) | 16973.2i | 0.0224762i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.15807e6 | 1.52651 | ||||||||
\(872\) | 242644.i | 0.319107i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.11091e6 | 1.45430 | ||||||||
\(875\) | − 262444.i | − 0.342785i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 299446. | 0.389332 | 0.194666 | − | 0.980870i | \(-0.437638\pi\) | ||||
0.194666 | + | 0.980870i | \(0.437638\pi\) | |||||||
\(878\) | − 1.10297e6i | − 1.43078i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 368701. | 0.476112 | ||||||||
\(881\) | − 743364.i | − 0.957745i | −0.877884 | − | 0.478872i | \(-0.841046\pi\) | ||||
0.877884 | − | 0.478872i | \(-0.158954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 294544. | 0.377771 | 0.188886 | − | 0.981999i | \(-0.439512\pi\) | ||||
0.188886 | + | 0.981999i | \(0.439512\pi\) | |||||||
\(884\) | 433181.i | 0.554326i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −70511.6 | −0.0898241 | ||||||||
\(887\) | − 441410.i | − 0.561041i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) | ||||
0.959848 | − | 0.280521i | \(-0.0905071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.12074e6 | −1.41808 | ||||||||
\(890\) | − 210207.i | − 0.265380i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −274489. | −0.344981 | ||||||||
\(893\) | 475815.i | 0.596671i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −254895. | −0.318211 | ||||||||
\(896\) | − 303055.i | − 0.377490i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 713924. | 0.885318 | ||||||||
\(899\) | − 514141.i | − 0.636155i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −744035. | −0.916524 | ||||||||
\(902\) | − 516490.i | − 0.634817i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −114639. | −0.140280 | ||||||||
\(905\) | 295923.i | 0.361311i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −887819. | −1.07922 | −0.539610 | − | 0.841915i | \(-0.681428\pi\) | ||||
−0.539610 | + | 0.841915i | \(0.681428\pi\) | |||||||
\(908\) | 357146.i | 0.433186i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −265634. | −0.320776 | ||||||||
\(911\) | 1.25649e6i | 1.51399i | 0.653422 | + | 0.756994i | \(0.273333\pi\) | ||||
−0.653422 | + | 0.756994i | \(0.726667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 979702. | 1.17531 | ||||||||
\(914\) | 2.25210e6i | 2.69584i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.29401e6 | 1.54223 | ||||||||
\(917\) | − 862607.i | − 1.02583i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −700226. | −0.829101 | −0.414550 | − | 0.910026i | \(-0.636061\pi\) | ||||
−0.414550 | + | 0.910026i | \(0.636061\pi\) | |||||||
\(920\) | − 38693.4i | − 0.0457152i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.29822e6 | 1.52716 | ||||||||
\(923\) | − 732064.i | − 0.859302i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36003.7 | −0.0420788 | ||||||||
\(926\) | − 1.38809e6i | − 1.61881i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 623567. | 0.724081 | ||||||||
\(929\) | 1.28131e6i | 1.48464i | 0.670043 | + | 0.742322i | \(0.266276\pi\) | ||||
−0.670043 | + | 0.742322i | \(0.733724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 329340. | 0.379966 | ||||||||
\(932\) | 621987.i | 0.716060i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −635083. | −0.728009 | ||||||||
\(935\) | 180341.i | 0.206287i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.20550e6 | −1.37305 | −0.686525 | − | 0.727106i | \(-0.740865\pi\) | ||||
−0.686525 | + | 0.727106i | \(0.740865\pi\) | |||||||
\(938\) | 1.10296e6i | 1.25359i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −79531.5 | −0.0900085 | ||||||||
\(941\) | 404760.i | 0.457107i | 0.973531 | + | 0.228554i | \(0.0733996\pi\) | ||||
−0.973531 | + | 0.228554i | \(0.926600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −196533. | −0.221010 | ||||||||
\(944\) | − 132572.i | − 0.148768i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.96803e6 | 2.19912 | ||||||||
\(947\) | 111370.i | 0.124185i | 0.998070 | + | 0.0620925i | \(0.0197774\pi\) | ||||
−0.998070 | + | 0.0620925i | \(0.980223\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.04436e6 | 1.15962 | ||||||||
\(950\) | 1.36329e6i | 1.51057i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 85971.1 | 0.0948590 | ||||||||
\(953\) | 848130.i | 0.933849i | 0.884297 | + | 0.466925i | \(0.154638\pi\) | ||||
−0.884297 | + | 0.466925i | \(0.845362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 143459. | 0.157297 | ||||||||
\(956\) | 478716.i | 0.523796i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.02411e6 | −2.20548 | ||||||||
\(959\) | 204693.i | 0.222569i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 302921. | 0.328006 | ||||||||
\(962\) | 74621.4i | 0.0806330i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −550412. | −0.592290 | ||||||||
\(965\) | 231845.i | 0.248968i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.22760e6 | −1.31282 | −0.656408 | − | 0.754406i | \(-0.727925\pi\) | ||||
−0.656408 | + | 0.754406i | \(0.727925\pi\) | |||||||
\(968\) | 614247.i | 0.655530i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −317436. | −0.337375 | ||||||||
\(971\) | 863529.i | 0.915880i | 0.888983 | + | 0.457940i | \(0.151413\pi\) | ||||
−0.888983 | + | 0.457940i | \(0.848587\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −273092. | −0.288458 | ||||||||
\(974\) | − 593928.i | − 0.626060i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36925.6 | 0.0387639 | ||||||||
\(977\) | − 1.55838e6i | − 1.63262i | −0.577613 | − | 0.816311i | \(-0.696016\pi\) | ||||
0.577613 | − | 0.816311i | \(-0.303984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.72135e6 | 1.79599 | ||||||||
\(980\) | 55048.5i | 0.0573183i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.20257e6 | 1.24706 | ||||||||
\(983\) | 1.35456e6i | 1.40182i | 0.713251 | + | 0.700909i | \(0.247222\pi\) | ||||
−0.713251 | + | 0.700909i | \(0.752778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46973.9 | 0.0484155 | ||||||||
\(986\) | 359210.i | 0.369483i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.27947e6 | 1.31074 | ||||||||
\(989\) | − 748869.i | − 0.765620i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 79523.9 | 0.0809749 | 0.0404874 | − | 0.999180i | \(-0.487109\pi\) | ||||
0.0404874 | + | 0.999180i | \(0.487109\pi\) | |||||||
\(992\) | 1.48747e6i | 1.51156i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 697229. | 0.705671 | ||||||||
\(995\) | 334938.i | 0.338313i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.29801e6 | −1.30583 | −0.652917 | − | 0.757430i | \(-0.726455\pi\) | ||||
−0.652917 | + | 0.757430i | \(0.726455\pi\) | |||||||
\(998\) | 603611.i | 0.606033i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.5.b.a.296.16 | ✓ | 76 | |
3.2 | odd | 2 | inner | 531.5.b.a.296.61 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
531.5.b.a.296.16 | ✓ | 76 | 1.1 | even | 1 | trivial | |
531.5.b.a.296.61 | yes | 76 | 3.2 | odd | 2 | inner |