Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(127,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, 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("128.127");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.205520896.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 12x^{6} - 12x^{5} - 8x^{4} + 12x^{3} + 12x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{39} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.6 | ||
Root | \(-0.550501 + 0.228025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.127 |
Dual form | 128.5.c.b.127.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.05664i | 0.784071i | 0.919950 | + | 0.392036i | \(0.128229\pi\) | ||||
−0.919950 | + | 0.392036i | \(0.871771\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.50277 | −0.380111 | −0.190055 | − | 0.981773i | \(-0.560867\pi\) | ||||
−0.190055 | + | 0.981773i | \(0.560867\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.49140i | 0.132478i | 0.997804 | + | 0.0662388i | \(0.0210999\pi\) | ||||
−0.997804 | + | 0.0662388i | \(0.978900\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 31.2038 | 0.385232 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 128.436i | 1.06145i | 0.847543 | + | 0.530727i | \(0.178081\pi\) | ||||
−0.847543 | + | 0.530727i | \(0.821919\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −220.919 | −1.30721 | −0.653606 | − | 0.756835i | \(-0.726744\pi\) | ||||
−0.653606 | + | 0.756835i | \(0.726744\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 67.0576i | − 0.298034i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −382.628 | −1.32397 | −0.661986 | − | 0.749516i | \(-0.730286\pi\) | ||||
−0.661986 | + | 0.749516i | \(0.730286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 77.3763i | 0.214339i | 0.994241 | + | 0.107169i | \(0.0341787\pi\) | ||||
−0.994241 | + | 0.107169i | \(0.965821\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −45.8075 | −0.103872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 951.968i | − 1.79956i | −0.436342 | − | 0.899781i | \(-0.643726\pi\) | ||||
0.436342 | − | 0.899781i | \(-0.356274\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −534.697 | −0.855516 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 791.782i | 1.08612i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −561.558 | −0.667726 | −0.333863 | − | 0.942622i | \(-0.608352\pi\) | ||||
−0.333863 | + | 0.942622i | \(0.608352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 321.171i | − 0.334205i | −0.985940 | − | 0.167102i | \(-0.946559\pi\) | ||||
0.985940 | − | 0.167102i | \(-0.0534410\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −906.325 | −0.832255 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 61.6862i | − 0.0503561i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1090.63 | −0.796659 | −0.398330 | − | 0.917242i | \(-0.630410\pi\) | ||||
−0.398330 | + | 0.917242i | \(0.630410\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 1558.94i | − 1.02495i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −437.095 | −0.260021 | −0.130011 | − | 0.991513i | \(-0.541501\pi\) | ||||
−0.130011 | + | 0.991513i | \(0.541501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2558.67i | 1.38381i | 0.721988 | + | 0.691906i | \(0.243229\pi\) | ||||
−0.721988 | + | 0.691906i | \(0.756771\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −296.523 | −0.146431 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3832.88i | 1.73512i | 0.497332 | + | 0.867560i | \(0.334313\pi\) | ||||
−0.497332 | + | 0.867560i | \(0.665687\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2358.86 | 0.982450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2700.07i | − 1.03809i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1524.58 | −0.542747 | −0.271373 | − | 0.962474i | \(-0.587478\pi\) | ||||
−0.271373 | + | 0.962474i | \(0.587478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1220.50i | − 0.403470i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −546.017 | −0.168057 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1757.10i | 0.504770i | 0.967627 | + | 0.252385i | \(0.0812149\pi\) | ||||
−0.967627 | + | 0.252385i | \(0.918785\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4766.53 | 1.28098 | 0.640490 | − | 0.767966i | \(-0.278731\pi\) | ||||
0.640490 | + | 0.767966i | \(0.278731\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 202.556i | 0.0510346i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2099.34 | 0.496885 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6919.35i | − 1.54140i | −0.637198 | − | 0.770700i | \(-0.719907\pi\) | ||||
0.637198 | − | 0.770700i | \(-0.280093\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6717.70 | 1.41098 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 337.001i | 0.0668521i | 0.999441 | + | 0.0334260i | \(0.0106418\pi\) | ||||
−0.999441 | + | 0.0334260i | \(0.989358\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4239.85 | 0.795619 | 0.397809 | − | 0.917468i | \(-0.369771\pi\) | ||||
0.397809 | + | 0.917468i | \(0.369771\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3773.17i | − 0.670785i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −833.728 | −0.140619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11095.6i | 1.77785i | 0.458050 | + | 0.888926i | \(0.348548\pi\) | ||||
−0.458050 | + | 0.888926i | \(0.651452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3059.81 | −0.466364 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3972.05i | − 0.576579i | −0.957543 | − | 0.288289i | \(-0.906913\pi\) | ||||
0.957543 | − | 0.288289i | \(-0.0930865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3636.02 | 0.503256 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3962.71i | − 0.523545i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5526.64 | 0.697720 | 0.348860 | − | 0.937175i | \(-0.386569\pi\) | ||||
0.348860 | + | 0.937175i | \(0.386569\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1434.07i | − 0.173176i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2266.39 | 0.262040 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 735.289i | − 0.0814724i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4730.94 | 0.502810 | 0.251405 | − | 0.967882i | \(-0.419107\pi\) | ||||
0.251405 | + | 0.967882i | \(0.419107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4007.69i | 0.408906i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1509.47 | −0.147973 | −0.0739865 | − | 0.997259i | \(-0.523572\pi\) | ||||
−0.0739865 | + | 0.997259i | \(0.523572\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11777.5i | 1.11014i | 0.831803 | + | 0.555071i | \(0.187309\pi\) | ||||
−0.831803 | + | 0.555071i | \(0.812691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 435.298 | 0.0394828 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6628.96i | 0.578999i | 0.957178 | + | 0.289500i | \(0.0934889\pi\) | ||||
−0.957178 | + | 0.289500i | \(0.906511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13286.3 | −1.11828 | −0.559142 | − | 0.829072i | \(-0.688869\pi\) | ||||
−0.559142 | + | 0.829072i | \(0.688869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 7696.16i | − 0.624638i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1399.22 | −0.109579 | −0.0547896 | − | 0.998498i | \(-0.517449\pi\) | ||||
−0.0547896 | + | 0.998498i | \(0.517449\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9046.33i | 0.684033i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6893.51 | −0.503580 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 2483.79i | − 0.175397i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1854.76 | −0.126683 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3084.43i | − 0.203875i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11020.3 | 0.705301 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 18940.8i | − 1.17433i | −0.809467 | − | 0.587165i | \(-0.800244\pi\) | ||||
0.809467 | − | 0.587165i | \(-0.199756\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18055.6 | −1.08501 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16937.9i | 0.987001i | 0.869746 | + | 0.493500i | \(0.164283\pi\) | ||||
−0.869746 | + | 0.493500i | \(0.835717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −502.280 | −0.0283951 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 7524.12i | − 0.412846i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −32620.9 | −1.73802 | −0.869010 | − | 0.494795i | \(-0.835243\pi\) | ||||
−0.869010 | + | 0.494795i | \(0.835243\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 16900.2i | − 0.874705i | −0.899290 | − | 0.437353i | \(-0.855916\pi\) | ||||
0.899290 | − | 0.437353i | \(-0.144084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27047.3 | −1.36046 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 28373.9i | − 1.38754i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5336.35 | 0.253810 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16645.6i | 0.770310i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −33124.9 | −1.49205 | −0.746023 | − | 0.665920i | \(-0.768039\pi\) | ||||
−0.746023 | + | 0.665920i | \(0.768039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22546.4i | 0.988833i | 0.869225 | + | 0.494416i | \(0.164618\pi\) | ||||
−0.869225 | + | 0.494416i | \(0.835382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11939.5 | −0.510037 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3052.01i | 0.127035i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 49129.2 | 1.99315 | 0.996576 | − | 0.0826841i | \(-0.0263492\pi\) | ||||
0.996576 | + | 0.0826841i | \(0.0263492\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 10758.4i | − 0.425552i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6179.60 | 0.238401 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8068.82i | 0.303693i | 0.988404 | + | 0.151847i | \(0.0485220\pi\) | ||||
−0.988404 | + | 0.151847i | \(0.951478\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8612.60 | 0.316349 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 15371.0i | − 0.551149i | −0.961280 | − | 0.275575i | \(-0.911132\pi\) | ||||
0.961280 | − | 0.275575i | \(-0.0888681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20244.1 | 0.708801 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2414.44i | 0.0825702i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −43716.8 | −1.46068 | −0.730341 | − | 0.683083i | \(-0.760639\pi\) | ||||
−0.730341 | + | 0.683083i | \(0.760639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3470.93i | − 0.113337i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12399.2 | −0.395775 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 28396.2i | 0.886246i | 0.896461 | + | 0.443123i | \(0.146129\pi\) | ||||
−0.896461 | + | 0.443123i | \(0.853871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6646.43 | 0.202876 | 0.101438 | − | 0.994842i | \(-0.467656\pi\) | ||||
0.101438 | + | 0.994842i | \(0.467656\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33635.7i | 1.00438i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10364.0 | 0.302819 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 49143.1i | − 1.40533i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5139.77 | −0.143887 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 39571.8i | 1.08472i | 0.840145 | + | 0.542362i | \(0.182470\pi\) | ||||
−0.840145 | + | 0.542362i | \(0.817530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 31206.5 | 0.837781 | 0.418890 | − | 0.908037i | \(-0.362419\pi\) | ||||
0.418890 | + | 0.908037i | \(0.362419\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14814.3i | 0.389593i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 39072.5 | 1.00679 | 0.503394 | − | 0.864057i | \(-0.332084\pi\) | ||||
0.503394 | + | 0.864057i | \(0.332084\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 45057.3i | 1.13778i | 0.822413 | + | 0.568891i | \(0.192627\pi\) | ||||
−0.822413 | + | 0.568891i | \(0.807373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 48827.3 | 1.20857 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3645.30i | − 0.0884587i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4153.62 | 0.0988368 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 29705.0i | − 0.693249i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9937.89 | −0.227511 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 88509.2i | − 1.98803i | −0.109228 | − | 0.994017i | \(-0.534838\pi\) | ||||
0.109228 | − | 0.994017i | \(-0.465162\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2378.10 | −0.0524168 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 24314.4i | − 0.526001i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2084.85 | 0.0442746 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29919.1i | 0.623822i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 84529.7 | 1.73071 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 63144.7i | 1.26978i | 0.772604 | + | 0.634888i | \(0.218954\pi\) | ||||
−0.772604 | + | 0.634888i | \(0.781046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16684.6 | −0.329572 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 79318.8i | − 1.53930i | −0.638464 | − | 0.769652i | \(-0.720430\pi\) | ||||
0.638464 | − | 0.769652i | \(-0.279570\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 73199.3 | 1.39584 | 0.697921 | − | 0.716175i | \(-0.254109\pi\) | ||||
0.697921 | + | 0.716175i | \(0.254109\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 5883.32i | − 0.110255i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15770.0 | −0.290482 | −0.145241 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145241 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 36423.0i | − 0.659538i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −78297.5 | −1.39396 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3598.13i | 0.0629913i | 0.999504 | + | 0.0314957i | \(0.0100270\pi\) | ||||
−0.999504 | + | 0.0314957i | \(0.989973\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 66204.6 | 1.13987 | 0.569933 | − | 0.821691i | \(-0.306969\pi\) | ||||
0.569933 | + | 0.821691i | \(0.306969\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 42542.4i | 0.720459i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22415.7 | −0.373440 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 17093.9i | − 0.280186i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28029.3 | 0.452079 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 42650.1i | 0.676975i | 0.940971 | + | 0.338488i | \(0.109915\pi\) | ||||
−0.940971 | + | 0.338488i | \(0.890085\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 122267. | 1.91015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 25658.1i | 0.394589i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −49938.6 | −0.756084 | −0.378042 | − | 0.925789i | \(-0.623402\pi\) | ||||
−0.378042 | + | 0.925789i | \(0.623402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7079.69i | − 0.105539i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17522.8 | −0.257230 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 87275.8i | − 1.26178i | −0.775874 | − | 0.630888i | \(-0.782691\pi\) | ||||
0.775874 | − | 0.630888i | \(-0.217309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14487.7 | 0.206304 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 38999.5i | 0.547062i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −110723. | −1.53015 | −0.765073 | − | 0.643943i | \(-0.777297\pi\) | ||||
−0.765073 | + | 0.643943i | \(0.777297\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 82671.9i | 1.12569i | 0.826562 | + | 0.562846i | \(0.190294\pi\) | ||||
−0.826562 | + | 0.562846i | \(0.809706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10119.7 | 0.135782 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 68674.3i | − 0.908090i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −46204.8 | −0.602181 | −0.301091 | − | 0.953596i | \(-0.597351\pi\) | ||||
−0.301091 | + | 0.953596i | \(0.597351\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 10021.7i | − 0.128746i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −84998.0 | −1.07646 | −0.538228 | − | 0.842800i | \(-0.680906\pi\) | ||||
−0.538228 | + | 0.842800i | \(0.680906\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31233.9i | 0.389990i | 0.980804 | + | 0.194995i | \(0.0624690\pi\) | ||||
−0.980804 | + | 0.194995i | \(0.937531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5188.67 | 0.0638802 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2837.36i | − 0.0344469i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 62883.2 | 0.752903 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 33384.5i | 0.394239i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −108954. | −1.26914 | −0.634570 | − | 0.772866i | \(-0.718823\pi\) | ||||
−0.634570 | + | 0.772866i | \(0.718823\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 16697.3i | − 0.191868i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −101693. | −1.15287 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 210308.i | 2.35241i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16609.3 | −0.183324 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 10651.8i | − 0.116021i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −45295.2 | −0.486915 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 49054.1i | 0.520474i | 0.965545 | + | 0.260237i | \(0.0838006\pi\) | ||||
−0.965545 | + | 0.260237i | \(0.916199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −83109.5 | −0.870430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 116875.i | − 1.20837i | −0.796845 | − | 0.604184i | \(-0.793499\pi\) | ||||
0.796845 | − | 0.604184i | \(-0.206501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 44685.2 | 0.456116 | 0.228058 | − | 0.973648i | \(-0.426762\pi\) | ||||
0.228058 | + | 0.973648i | \(0.426762\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1924.85i | − 0.0193988i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2512.62 | −0.0250039 | −0.0125019 | − | 0.999922i | \(-0.503980\pi\) | ||||
−0.0125019 | + | 0.999922i | \(0.503980\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 72124.2i | − 0.708760i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −46778.2 | −0.453977 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 29606.3i | − 0.283779i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 118125. | 1.11834 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 93756.9i | − 0.876814i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24880.8 | −0.229864 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 137925.i | − 1.25889i | −0.777046 | − | 0.629444i | \(-0.783283\pi\) | ||||
0.777046 | − | 0.629444i | \(-0.216717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −34031.7 | −0.306899 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 65752.9i | 0.585903i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −150041. | −1.32115 | −0.660574 | − | 0.750761i | \(-0.729687\pi\) | ||||
−0.660574 | + | 0.750761i | \(0.729687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 9873.78i | − 0.0859180i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41249.8 | 0.354742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30898.2i | 0.262630i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −63836.7 | −0.536330 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 142965.i | 1.18733i | 0.804714 | + | 0.593663i | \(0.202319\pi\) | ||||
−0.804714 | + | 0.593663i | \(0.797681\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −64364.5 | −0.528440 | −0.264220 | − | 0.964462i | \(-0.585115\pi\) | ||||
−0.264220 | + | 0.964462i | \(0.585115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 174919.i | − 1.41979i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17129.7 | 0.137467 | 0.0687337 | − | 0.997635i | \(-0.478104\pi\) | ||||
0.0687337 | + | 0.997635i | \(0.478104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 3202.44i | − 0.0254112i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17527.2 | 0.137523 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29116.6i | 0.225919i | 0.993600 | + | 0.112959i | \(0.0360330\pi\) | ||||
−0.993600 | + | 0.112959i | \(0.963967\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 124334. | 0.954059 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 13088.4i | − 0.0993282i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40290.3 | −0.302423 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4255.09i | 0.0315919i | 0.999875 | + | 0.0157960i | \(0.00502822\pi\) | ||||
−0.999875 | + | 0.0157960i | \(0.994972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13639.1 | −0.100169 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9896.63i | − 0.0719017i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 696.069 | 0.00500305 | 0.00250152 | − | 0.999997i | \(-0.499204\pi\) | ||||
0.00250152 | + | 0.999997i | \(0.499204\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 77766.5i | 0.553006i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 124059. | 0.872860 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 169548.i | − 1.18036i | −0.807272 | − | 0.590179i | \(-0.799057\pi\) | ||||
0.807272 | − | 0.590179i | \(-0.200943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 133658. | 0.920758 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 57233.5i | 0.390169i | 0.980786 | + | 0.195084i | \(0.0624981\pi\) | ||||
−0.980786 | + | 0.195084i | \(0.937502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7922.72 | 0.0534506 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 79840.2i | 0.533089i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23301.7 | 0.153988 | 0.0769941 | − | 0.997032i | \(-0.475468\pi\) | ||||
0.0769941 | + | 0.997032i | \(0.475468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 364250.i | 2.38257i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −119525. | −0.773879 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 105439.i | − 0.675781i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −42551.3 | −0.269980 | −0.134990 | − | 0.990847i | \(-0.543100\pi\) | ||||
−0.134990 | + | 0.990847i | \(0.543100\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 3544.41i | − 0.0222637i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 171821. | 1.06853 | 0.534266 | − | 0.845317i | \(-0.320588\pi\) | ||||
0.534266 | + | 0.845317i | \(0.320588\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 70952.6i | 0.436876i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29076.7 | 0.177270 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 140076.i | − 0.845616i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 91529.4 | 0.547160 | 0.273580 | − | 0.961849i | \(-0.411792\pi\) | ||||
0.273580 | + | 0.961849i | \(0.411792\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 230194.i | − 1.36273i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11406.1 | −0.0668706 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 37745.5i | 0.219164i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 119259. | 0.685831 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 65318.4i | 0.372056i | 0.982544 | + | 0.186028i | \(0.0595614\pi\) | ||||
−0.982544 | + | 0.186028i | \(0.940439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 108601. | 0.612729 | 0.306364 | − | 0.951914i | \(-0.400887\pi\) | ||||
0.306364 | + | 0.951914i | \(0.400887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 119601.i | 0.668425i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 204590. | 1.13268 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30941.4i | 0.169701i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 200224. | 1.08793 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 193826.i | 1.04342i | 0.853124 | + | 0.521708i | \(0.174705\pi\) | ||||
−0.853124 | + | 0.521708i | \(0.825295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 197671. | 1.05431 | 0.527154 | − | 0.849770i | \(-0.323259\pi\) | ||||
0.527154 | + | 0.849770i | \(0.323259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 37656.7i | 0.199005i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 73659.8 | 0.385716 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 168788.i | 0.875815i | 0.899020 | + | 0.437908i | \(0.144280\pi\) | ||||
−0.899020 | + | 0.437908i | \(0.855720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 73605.5 | 0.378471 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 33462.6i | − 0.170511i | −0.996359 | − | 0.0852555i | \(-0.972829\pi\) | ||||
0.996359 | − | 0.0852555i | \(-0.0271707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −52518.4 | −0.265211 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 233751.i | − 1.16987i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −245538. | −1.21794 | −0.608969 | − | 0.793194i | \(-0.708417\pi\) | ||||
−0.608969 | + | 0.793194i | \(0.708417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 56138.7i | − 0.276000i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −159102. | −0.775315 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13627.6i | 0.0658261i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −133704. | −0.640196 | −0.320098 | − | 0.947385i | \(-0.603716\pi\) | ||||
−0.320098 | + | 0.947385i | \(0.603716\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 302958.i | − 1.43799i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 275191. | 1.29489 | 0.647445 | − | 0.762112i | \(-0.275838\pi\) | ||||
0.647445 | + | 0.762112i | \(0.275838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 345853.i | − 1.61335i | −0.590994 | − | 0.806676i | \(-0.701264\pi\) | ||||
0.590994 | − | 0.806676i | \(-0.298736\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21536.9 | −0.0996042 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 95388.2i | − 0.437382i | −0.975794 | − | 0.218691i | \(-0.929821\pi\) | ||||
0.975794 | − | 0.218691i | \(-0.0701786\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44916.2 | 0.204201 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 346687.i | 1.56277i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −328624. | −1.46885 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 41372.9i | − 0.183370i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −47572.6 | −0.209084 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13002.6i | 0.0566707i | 0.999598 | + | 0.0283354i | \(0.00902063\pi\) | ||||
−0.999598 | + | 0.0283354i | \(0.990979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 240940. | 1.04140 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 43607.2i | 0.186924i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −44957.0 | −0.191123 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 140830.i | − 0.593794i | −0.954909 | − | 0.296897i | \(-0.904048\pi\) | ||||
0.954909 | − | 0.296897i | \(-0.0959519\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −56938.8 | −0.238117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 19020.5i | − 0.0788969i | −0.999222 | − | 0.0394484i | \(-0.987440\pi\) | ||||
0.999222 | − | 0.0394484i | \(-0.0125601\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 214868. | 0.884051 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 38084.1i | − 0.155430i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2187.61 | −0.00885640 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 288185.i | 1.15736i | 0.815553 | + | 0.578682i | \(0.196433\pi\) | ||||
−0.815553 | + | 0.578682i | \(0.803567\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 108468. | 0.432140 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 128399.i | − 0.507486i | −0.967272 | − | 0.253743i | \(-0.918338\pi\) | ||||
0.967272 | − | 0.253743i | \(-0.0816618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14344.2 | 0.0562461 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 142855.i | 0.555750i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −452490. | −1.74652 | −0.873259 | − | 0.487256i | \(-0.837998\pi\) | ||||
−0.873259 | + | 0.487256i | \(0.837998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27522.6i | 0.105402i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −61265.2 | −0.232798 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 111919.i | − 0.421976i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −492279. | −1.84175 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 308493.i | − 1.14528i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 233443. | 0.860015 | 0.430008 | − | 0.902825i | \(-0.358511\pi\) | ||||
0.430008 | + | 0.902825i | \(0.358511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 235862.i | 0.862293i | 0.902282 | + | 0.431146i | \(0.141891\pi\) | ||||
−0.902282 | + | 0.431146i | \(0.858109\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24493.1 | 0.0888640 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 122889.i | 0.442478i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −626402. | −2.23842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 54828.4i | 0.194454i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 96562.6 | 0.339902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 62993.5i | − 0.220084i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −200382. | −0.694880 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 302962.i | 1.04282i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −335400. | −1.14596 | −0.572978 | − | 0.819571i | \(-0.694212\pi\) | ||||
−0.572978 | + | 0.819571i | \(0.694212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46901.5i | 0.159070i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 126257. | 0.425072 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 333389.i | 1.11423i | 0.830434 | + | 0.557117i | \(0.188092\pi\) | ||||
−0.830434 | + | 0.557117i | \(0.811908\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 148734. | 0.493475 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 43451.3i | − 0.143120i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −72025.8 | −0.235525 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 73134.8i | 0.237431i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −144667. | −0.466294 | −0.233147 | − | 0.972441i | \(-0.574902\pi\) | ||||
−0.233147 | + | 0.972441i | \(0.574902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 565257.i | − 1.80893i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 346785. | 1.10188 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 333299.i | − 1.05152i | −0.850634 | − | 0.525759i | \(-0.823781\pi\) | ||||
0.850634 | − | 0.525759i | \(-0.176219\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13296.4 | 0.0416523 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 19862.5i | − 0.0617827i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 303109. | 0.936212 | 0.468106 | − | 0.883672i | \(-0.344937\pi\) | ||||
0.468106 | + | 0.883672i | \(0.344937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24945.5i | 0.0765102i | 0.999268 | + | 0.0382551i | \(0.0121799\pi\) | ||||
−0.999268 | + | 0.0382551i | \(0.987820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −279244. | −0.850501 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 509015.i | 1.53955i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −532837. | −1.60045 | −0.800226 | − | 0.599698i | \(-0.795287\pi\) | ||||
−0.800226 | + | 0.599698i | \(0.795287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 220213.i | 0.656880i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25784.2 | 0.0763837 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 195810.i | − 0.576100i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 65507.4 | 0.191416 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 624244.i | 1.81167i | 0.423634 | + | 0.905833i | \(0.360754\pi\) | ||||
−0.423634 | + | 0.905833i | \(0.639246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24851.0 | 0.0716330 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 275720.i | 0.789394i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −158609. | −0.451045 | −0.225522 | − | 0.974238i | \(-0.572409\pi\) | ||||
−0.225522 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23602.9i | 0.0666701i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −317953. | −0.892102 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 514165.i | − 1.43301i | −0.697583 | − | 0.716504i | \(-0.745741\pi\) | ||||
0.697583 | − | 0.716504i | \(-0.254259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −407561. | −1.12835 | −0.564175 | − | 0.825655i | \(-0.690806\pi\) | ||||
−0.564175 | + | 0.825655i | \(0.690806\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 215910.i | − 0.593797i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17625.4 | 0.0481534 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 177651.i | 0.482158i | 0.970505 | + | 0.241079i | \(0.0775013\pi\) | ||||
−0.970505 | + | 0.241079i | \(0.922499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25723.5 | 0.0693579 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 846755.i | − 2.26817i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −132291. | −0.352055 | −0.176028 | − | 0.984385i | \(-0.556325\pi\) | ||||
−0.176028 | + | 0.984385i | \(0.556325\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29310.6i | 0.0774951i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −351562. | −0.923488 | −0.461744 | − | 0.887013i | \(-0.652776\pi\) | ||||
−0.461744 | + | 0.887013i | \(0.652776\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 318145.i | − 0.830318i | −0.909749 | − | 0.415159i | \(-0.863726\pi\) | ||||
0.909749 | − | 0.415159i | \(-0.136274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 753751. | 1.95454 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35875.6i | 0.0924322i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 229462. | 0.587423 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 70128.1i | − 0.178384i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 417304. | 1.05475 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 260248.i | − 0.653626i | −0.945089 | − | 0.326813i | \(-0.894025\pi\) | ||||
0.945089 | − | 0.326813i | \(-0.105975\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 624578. | 1.55876 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 179990.i | 0.446375i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −521117. | −1.28427 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10515.7i | 0.0257536i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26771.0 | 0.0651550 | 0.0325775 | − | 0.999469i | \(-0.489628\pi\) | ||||
0.0325775 | + | 0.999469i | \(0.489628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5813.96i | 0.0140621i | 0.999975 | + | 0.00703105i | \(0.00223807\pi\) | ||||
−0.999975 | + | 0.00703105i | \(0.997762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 171578. | 0.412423 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 150358.i | − 0.359185i | −0.983741 | − | 0.179592i | \(-0.942522\pi\) | ||||
0.983741 | − | 0.179592i | \(-0.0574779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −225675. | −0.535789 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14712.0i | 0.0347144i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 807136. | 1.89287 | 0.946434 | − | 0.322898i | \(-0.104657\pi\) | ||||
0.946434 | + | 0.322898i | \(0.104657\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 160957.i | − 0.375169i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 132300. | 0.306498 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 327592.i | − 0.754331i | −0.926146 | − | 0.377166i | \(-0.876899\pi\) | ||||
0.926146 | − | 0.377166i | \(-0.123101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 482222. | 1.10368 | 0.551842 | − | 0.833949i | \(-0.313925\pi\) | ||||
0.551842 | + | 0.833949i | \(0.313925\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 596496.i | 1.35700i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4773.05 | 0.0107933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 534585.i | 1.20161i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −445589. | −0.995595 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 612193.i | 1.35970i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 350805. | 0.774526 | 0.387263 | − | 0.921969i | \(-0.373421\pi\) | ||||
0.387263 | + | 0.921969i | \(0.373421\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 423364.i | − 0.929194i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −468433. | −1.02204 | −0.511022 | − | 0.859567i | \(-0.670733\pi\) | ||||
−0.511022 | + | 0.859567i | \(0.670733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30710.4i | 0.0666110i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 559724. | 1.20692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 254774.i | − 0.546153i | −0.961992 | − | 0.273076i | \(-0.911959\pi\) | ||||
0.961992 | − | 0.273076i | \(-0.0880412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 309989. | 0.660640 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 516541.i | 1.09444i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 336807. | 0.709485 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 416717.i | − 0.872741i | −0.899767 | − | 0.436371i | \(-0.856264\pi\) | ||||
0.899767 | − | 0.436371i | \(-0.143736\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −26015.5 | −0.0541709 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 160598.i | 0.332485i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 167245. | 0.344261 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 111283.i | − 0.227759i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 554976. | 1.12938 | 0.564688 | − | 0.825305i | \(-0.308997\pi\) | ||||
0.564688 | + | 0.825305i | \(0.308997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 84388.6i | − 0.170755i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 257024. | 0.517125 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 9798.58i | − 0.0196031i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −208869. | −0.415511 | −0.207755 | − | 0.978181i | \(-0.566616\pi\) | ||||
−0.207755 | + | 0.978181i | \(0.566616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 346224.i | 0.684886i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −305744. | −0.601422 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 269630.i | 0.527420i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25390.7 | −0.0493897 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 245345.i | 0.474590i | 0.971438 | + | 0.237295i | \(0.0762608\pi\) | ||||
−0.971438 | + | 0.237295i | \(0.923739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −76452.3 | −0.147069 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 467182.i | 0.893737i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 300264. | 0.571251 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 462973.i | − 0.875965i | −0.898983 | − | 0.437983i | \(-0.855693\pi\) | ||||
0.898983 | − | 0.437983i | \(-0.144307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −548051. | −1.03125 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 979018.i | − 1.83213i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −275737. | −0.513201 | −0.256600 | − | 0.966518i | \(-0.582602\pi\) | ||||
−0.256600 | + | 0.966518i | \(0.582602\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 158180.i | − 0.292803i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 888692. | 1.63612 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 751459.i | 1.37599i | 0.725714 | + | 0.687997i | \(0.241510\pi\) | ||||
−0.725714 | + | 0.687997i | \(0.758490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 120625. | 0.219686 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 33291.6i | − 0.0603055i | −0.999545 | − | 0.0301527i | \(-0.990401\pi\) | ||||
0.999545 | − | 0.0301527i | \(-0.00959937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 314778. | 0.567143 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 123943.i | − 0.222117i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43031.2 | −0.0767044 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 356855.i | 0.632721i | 0.948639 | + | 0.316361i | \(0.102461\pi\) | ||||
−0.948639 | + | 0.316361i | \(0.897539\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −300967. | −0.530797 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 214253.i | − 0.375866i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −622463. | −1.08623 | −0.543115 | − | 0.839658i | \(-0.682755\pi\) | ||||
−0.543115 | + | 0.839658i | \(0.682755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 862793.i | 1.49769i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 967703. | 1.67099 | 0.835493 | − | 0.549502i | \(-0.185182\pi\) | ||||
0.835493 | + | 0.549502i | \(0.185182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 86246.9i | − 0.148147i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 113458. | 0.193871 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 388177.i | − 0.659841i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.06634e6 | −1.80320 | −0.901600 | − | 0.432572i | \(-0.857606\pi\) | ||||
−0.901600 | + | 0.432572i | \(0.857606\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 352399.i | − 0.592823i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 314448. | 0.526247 | 0.263123 | − | 0.964762i | \(-0.415247\pi\) | ||||
0.263123 | + | 0.964762i | \(0.415247\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 171729.i | 0.285917i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 49958.8 | 0.0827504 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 33820.8i | − 0.0557326i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43283.0 | −0.0709603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 444632.i | − 0.725232i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −466863. | −0.757618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 505795.i | 0.816629i | 0.912841 | + | 0.408315i | \(0.133883\pi\) | ||||
−0.912841 | + | 0.408315i | \(0.866117\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 615874. | 0.989323 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 9082.88i | − 0.0145168i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.05302e6 | −1.67451 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 102234.i | 0.161757i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −324326. | −0.510581 | −0.255290 | − | 0.966864i | \(-0.582171\pi\) | ||||
−0.255290 | + | 0.966864i | \(0.582171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.46657e6i | − 2.29725i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 172452. | 0.268784 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 544549.i | 0.844512i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −58723.3 | −0.0906189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 781332.i | − 1.19974i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35692.7 | −0.0545359 | −0.0272679 | − | 0.999628i | \(-0.508681\pi\) | ||||
−0.0272679 | + | 0.999628i | \(0.508681\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 448798.i | − 0.682353i | −0.939999 | − | 0.341177i | \(-0.889175\pi\) | ||||
0.939999 | − | 0.341177i | \(-0.110825\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −583386. | −0.882622 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 76676.2i | − 0.115437i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −197980. | −0.296604 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 44748.5i | − 0.0667130i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 389526. | 0.577897 | 0.288949 | − | 0.957345i | \(-0.406694\pi\) | ||||
0.288949 | + | 0.957345i | \(0.406694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 538138.i | − 0.794500i | −0.917711 | − | 0.397250i | \(-0.869965\pi\) | ||||
0.917711 | − | 0.397250i | \(-0.130035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 484610. | 0.712007 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.07219e6i | 1.56769i | 0.620956 | + | 0.783845i | \(0.286744\pi\) | ||||
−0.620956 | + | 0.783845i | \(0.713256\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −193379. | −0.281385 | −0.140693 | − | 0.990053i | \(-0.544933\pi\) | ||||
−0.140693 | + | 0.990053i | \(0.544933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 326050.i | − 0.472153i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −902567. | −1.30074 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 146067.i | 0.209498i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 254297. | 0.362986 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 744976.i | 1.05832i | 0.848521 | + | 0.529161i | \(0.177493\pi\) | ||||
−0.848521 | + | 0.529161i | \(0.822507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −391934. | −0.554141 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 599800.i | − 0.844018i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −192375. | −0.269423 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 12040.0i | − 0.0167826i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −220406. | −0.305780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.03824e6i | 1.43364i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.23891e6 | −1.70271 | −0.851355 | − | 0.524589i | \(-0.824219\pi\) | ||||
−0.851355 | + | 0.524589i | \(0.824219\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 22943.8i | − 0.0313858i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −726182. | −0.988744 | −0.494372 | − | 0.869251i | \(-0.664602\pi\) | ||||
−0.494372 | + | 0.869251i | \(0.664602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 656830.i | − 0.890156i | −0.895492 | − | 0.445078i | \(-0.853176\pi\) | ||||
0.895492 | − | 0.445078i | \(-0.146824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20022.2 | 0.0270089 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 273884.i | − 0.367743i | −0.982950 | − | 0.183872i | \(-0.941137\pi\) | ||||
0.982950 | − | 0.183872i | \(-0.0588631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 415430. | 0.555221 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 443744.i | 0.590329i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.42507e6 | −1.88711 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.52861e6i | 2.01494i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 147623. | 0.193699 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 71537.4i | 0.0934366i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −213538. | −0.277636 | −0.138818 | − | 0.990318i | \(-0.544330\pi\) | ||||
−0.138818 | + | 0.990318i | \(0.544330\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 768852.i | − 0.995096i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.04959e6 | 1.35228 | 0.676140 | − | 0.736773i | \(-0.263651\pi\) | ||||
0.676140 | + | 0.736773i | \(0.263651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 783260.i | 1.00458i | 0.864699 | + | 0.502290i | \(0.167509\pi\) | ||||
−0.864699 | + | 0.502290i | \(0.832491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 117827. | 0.150438 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 653199.i | − 0.830230i | −0.909769 | − | 0.415115i | \(-0.863741\pi\) | ||||
0.909769 | − | 0.415115i | \(-0.136259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 122952. | 0.155572 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 392989.i | − 0.495023i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −296574. | −0.371904 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 269842.i | − 0.336871i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.48406e6 | −1.84445 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 180356.i | 0.223157i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 583345. | 0.718582 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 117206.i | − 0.143739i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −63159.5 | −0.0771155 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.12141e6i | 1.36317i | 0.731741 | + | 0.681583i | \(0.238708\pi\) | ||||
−0.731741 | + | 0.681583i | \(0.761292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −47101.3 | −0.0570040 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 87118.2i | − 0.104972i | −0.998622 | − | 0.0524859i | \(-0.983286\pi\) | ||||
0.998622 | − | 0.0524859i | \(-0.0167144\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 510154. | 0.612011 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 319632.i | − 0.381776i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −109951. | −0.130755 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 262218.i | 0.310478i | 0.987877 | + | 0.155239i | \(0.0496148\pi\) | ||||
−0.987877 | + | 0.155239i | \(0.950385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −346157. | −0.408088 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 74449.9i | − 0.0873898i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 583155. | 0.681555 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 367503.i | 0.427662i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 780426. | 0.904274 | 0.452137 | − | 0.891948i | \(-0.350662\pi\) | ||||
0.452137 | + | 0.891948i | \(0.350662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 182520.i | 0.210577i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 824742. | 0.947447 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 466996.i | 0.534183i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −122296. | −0.139294 | −0.0696471 | − | 0.997572i | \(-0.522187\pi\) | ||||
−0.0696471 | + | 0.997572i | \(0.522187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 315328.i | 0.357627i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −368852. | −0.416556 | −0.208278 | − | 0.978070i | \(-0.566786\pi\) | ||||
−0.208278 | + | 0.978070i | \(0.566786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 416101.i | 0.467924i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 48842.1 | 0.0546928 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.28300e6i | − 1.43063i | −0.698801 | − | 0.715317i | \(-0.746283\pi\) | ||||
0.698801 | − | 0.715317i | \(-0.253717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −936663. | −1.04004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 17730.6i | − 0.0196048i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 640178. | 0.704880 | 0.352440 | − | 0.935834i | \(-0.385352\pi\) | ||||
0.352440 | + | 0.935834i | \(0.385352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 376042.i | − 0.412315i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 508954. | 0.555719 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 211755.i | − 0.230249i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 820370. | 0.888307 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 206849.i | 0.223049i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −296548. | −0.318449 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.34359e6i | − 1.43686i | −0.695599 | − | 0.718430i | \(-0.744861\pi\) | ||||
0.695599 | − | 0.718430i | \(-0.255139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 208921. | 0.222503 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.07804e6i | − 1.14340i | −0.820463 | − | 0.571699i | \(-0.806284\pi\) | ||||
0.820463 | − | 0.571699i | \(-0.193716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 109706. | 0.115879 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 833563.i | 0.876858i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.48550e6 | −1.55626 | −0.778132 | − | 0.628101i | \(-0.783833\pi\) | ||||
−0.778132 | + | 0.628101i | \(0.783833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 709818.i | 0.740597i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −414584. | −0.430799 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.05481e6i | 1.09161i | 0.837912 | + | 0.545805i | \(0.183776\pi\) | ||||
−0.837912 | + | 0.545805i | \(0.816224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −371297. | −0.382691 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 175575.i | − 0.180230i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.43577e6 | 2.49025 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 818767.i | 0.833706i | 0.908974 | + | 0.416853i | \(0.136867\pi\) | ||||
−0.908974 | + | 0.416853i | \(0.863133\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 973288. | 0.987058 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 428169.i | − 0.432483i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.77533e6 | 1.78603 | 0.893014 | − | 0.450029i | \(-0.148586\pi\) | ||||
0.893014 | + | 0.450029i | \(0.148586\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 863539.i | − 0.865268i |
(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 | 128.5.c.b.127.6 | yes | 8 | |
3.2 | odd | 2 | 1152.5.g.a.127.6 | 8 | |||
4.3 | odd | 2 | inner | 128.5.c.b.127.3 | yes | 8 | |
8.3 | odd | 2 | 128.5.c.a.127.6 | yes | 8 | ||
8.5 | even | 2 | 128.5.c.a.127.3 | ✓ | 8 | ||
12.11 | even | 2 | 1152.5.g.a.127.5 | 8 | |||
16.3 | odd | 4 | 256.5.d.g.127.6 | 8 | |||
16.5 | even | 4 | 256.5.d.g.127.5 | 8 | |||
16.11 | odd | 4 | 256.5.d.h.127.3 | 8 | |||
16.13 | even | 4 | 256.5.d.h.127.4 | 8 | |||
24.5 | odd | 2 | 1152.5.g.b.127.4 | 8 | |||
24.11 | even | 2 | 1152.5.g.b.127.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.5.c.a.127.3 | ✓ | 8 | 8.5 | even | 2 | ||
128.5.c.a.127.6 | yes | 8 | 8.3 | odd | 2 | ||
128.5.c.b.127.3 | yes | 8 | 4.3 | odd | 2 | inner | |
128.5.c.b.127.6 | yes | 8 | 1.1 | even | 1 | trivial | |
256.5.d.g.127.5 | 8 | 16.5 | even | 4 | |||
256.5.d.g.127.6 | 8 | 16.3 | odd | 4 | |||
256.5.d.h.127.3 | 8 | 16.11 | odd | 4 | |||
256.5.d.h.127.4 | 8 | 16.13 | even | 4 | |||
1152.5.g.a.127.5 | 8 | 12.11 | even | 2 | |||
1152.5.g.a.127.6 | 8 | 3.2 | odd | 2 | |||
1152.5.g.b.127.3 | 8 | 24.11 | even | 2 | |||
1152.5.g.b.127.4 | 8 | 24.5 | odd | 2 |