Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.6007640023\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 200) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.4.c.g.49.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.00000i | 0.962250i | 0.876652 | + | 0.481125i | \(0.159772\pi\) | ||||
−0.876652 | + | 0.481125i | \(0.840228\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.00000i | − 0.107990i | −0.998541 | − | 0.0539949i | \(-0.982805\pi\) | ||||
0.998541 | − | 0.0539949i | \(-0.0171955\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.0000 | −1.06899 | −0.534497 | − | 0.845170i | \(-0.679499\pi\) | ||||
−0.534497 | + | 0.845170i | \(0.679499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 84.0000i | − 1.79211i | −0.443945 | − | 0.896054i | \(-0.646421\pi\) | ||||
0.443945 | − | 0.896054i | \(-0.353579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 61.0000i | − 0.870275i | −0.900364 | − | 0.435137i | \(-0.856700\pi\) | ||||
0.900364 | − | 0.435137i | \(-0.143300\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 151.000 | 1.82325 | 0.911626 | − | 0.411021i | \(-0.134828\pi\) | ||||
0.911626 | + | 0.411021i | \(0.134828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.0000 | 0.103913 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 58.0000i | − 0.525819i | −0.964821 | − | 0.262909i | \(-0.915318\pi\) | ||||
0.964821 | − | 0.262909i | \(-0.0846821\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 145.000i | 1.03353i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −192.000 | −1.22943 | −0.614716 | − | 0.788749i | \(-0.710729\pi\) | ||||
−0.614716 | + | 0.788749i | \(0.710729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.0000 | 0.104287 | 0.0521435 | − | 0.998640i | \(-0.483395\pi\) | ||||
0.0521435 | + | 0.998640i | \(0.483395\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 195.000i | − 1.02864i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 138.000i | − 0.613164i | −0.951844 | − | 0.306582i | \(-0.900815\pi\) | ||||
0.951844 | − | 0.306582i | \(-0.0991853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 420.000 | 1.72446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 229.000 | 0.872288 | 0.436144 | − | 0.899877i | \(-0.356344\pi\) | ||||
0.436144 | + | 0.899877i | \(0.356344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 164.000i | − 0.581622i | −0.956780 | − | 0.290811i | \(-0.906075\pi\) | ||||
0.956780 | − | 0.290811i | \(-0.0939252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 212.000i | 0.657944i | 0.944340 | + | 0.328972i | \(0.106702\pi\) | ||||
−0.944340 | + | 0.328972i | \(0.893298\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 339.000 | 0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 305.000 | 0.837422 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 578.000i | − 1.49801i | −0.662566 | − | 0.749004i | \(-0.730532\pi\) | ||||
0.662566 | − | 0.749004i | \(-0.269468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 755.000i | 1.75442i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −336.000 | −0.741415 | −0.370707 | − | 0.928750i | \(-0.620885\pi\) | ||||
−0.370707 | + | 0.928750i | \(0.620885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 858.000 | 1.80091 | 0.900456 | − | 0.434947i | \(-0.143233\pi\) | ||||
0.900456 | + | 0.434947i | \(0.143233\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.00000i | − 0.00799925i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 209.000i | 0.381096i | 0.981678 | + | 0.190548i | \(0.0610264\pi\) | ||||
−0.981678 | + | 0.190548i | \(0.938974\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 290.000 | 0.505970 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 780.000 | 1.30379 | 0.651894 | − | 0.758310i | \(-0.273975\pi\) | ||||
0.651894 | + | 0.758310i | \(0.273975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 403.000i | 0.646131i | 0.946377 | + | 0.323066i | \(0.104713\pi\) | ||||
−0.946377 | + | 0.323066i | \(0.895287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 78.0000i | 0.115441i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −230.000 | −0.327557 | −0.163779 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163779 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1293.00i | − 1.70994i | −0.518676 | − | 0.854971i | \(-0.673575\pi\) | ||||
0.518676 | − | 0.854971i | \(-0.326425\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 960.000i | − 1.18302i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1369.00 | 1.63049 | 0.815246 | − | 0.579115i | \(-0.196602\pi\) | ||||
0.815246 | + | 0.579115i | \(0.196602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −168.000 | −0.193530 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 90.0000i | 0.100350i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 382.000i | 0.399858i | 0.979810 | + | 0.199929i | \(0.0640711\pi\) | ||||
−0.979810 | + | 0.199929i | \(0.935929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −78.0000 | −0.0791848 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −794.000 | −0.782237 | −0.391119 | − | 0.920340i | \(-0.627912\pi\) | ||||
−0.391119 | + | 0.920340i | \(0.627912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1348.00i | − 1.28954i | −0.764378 | − | 0.644769i | \(-0.776954\pi\) | ||||
0.764378 | − | 0.644769i | \(-0.223046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 775.000i | 0.700206i | 0.936711 | + | 0.350103i | \(0.113853\pi\) | ||||
−0.936711 | + | 0.350103i | \(0.886147\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −446.000 | −0.391918 | −0.195959 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195959 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 690.000 | 0.590017 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 231.000i | 0.192307i | 0.995367 | + | 0.0961533i | \(0.0306539\pi\) | ||||
−0.995367 | + | 0.0961533i | \(0.969346\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 168.000i | − 0.132749i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −122.000 | −0.0939809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 190.000 | 0.142750 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1145.00i | 0.839359i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2386.00i | − 1.66711i | −0.552435 | − | 0.833556i | \(-0.686301\pi\) | ||||
0.552435 | − | 0.833556i | \(-0.313699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 820.000 | 0.559666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2452.00 | −1.63536 | −0.817680 | − | 0.575673i | \(-0.804740\pi\) | ||||
−0.817680 | + | 0.575673i | \(0.804740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 302.000i | − 0.196893i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1125.00i | − 0.701571i | −0.936456 | − | 0.350786i | \(-0.885915\pi\) | ||||
0.936456 | − | 0.350786i | \(-0.114085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1377.00 | −0.840256 | −0.420128 | − | 0.907465i | \(-0.638015\pi\) | ||||
−0.420128 | + | 0.907465i | \(0.638015\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1060.00 | −0.633107 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3276.00i | 1.91575i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1695.00i | 0.951029i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1920.00 | −1.05565 | −0.527827 | − | 0.849352i | \(-0.676993\pi\) | ||||
−0.527827 | + | 0.849352i | \(0.676993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1854.00 | −0.999181 | −0.499591 | − | 0.866262i | \(-0.666516\pi\) | ||||
−0.499591 | + | 0.866262i | \(0.666516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 122.000i | − 0.0644648i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 634.000i | − 0.322285i | −0.986931 | − | 0.161142i | \(-0.948482\pi\) | ||||
0.986931 | − | 0.161142i | \(-0.0515178\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2890.00 | 1.44146 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −116.000 | −0.0567831 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 103.000i | 0.0494944i | 0.999694 | + | 0.0247472i | \(0.00787808\pi\) | ||||
−0.999694 | + | 0.0247472i | \(0.992122\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 44.0000i | − 0.0203882i | −0.999948 | − | 0.0101941i | \(-0.996755\pi\) | ||||
0.999948 | − | 0.0101941i | \(-0.00324493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4859.00 | −2.21165 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 302.000 | 0.135056 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1128.00i | 0.495724i | 0.968795 | + | 0.247862i | \(0.0797280\pi\) | ||||
−0.968795 | + | 0.247862i | \(0.920272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1680.00i | − 0.713427i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2245.00 | −0.937426 | −0.468713 | − | 0.883351i | \(-0.655282\pi\) | ||||
−0.468713 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3050.00 | 1.25251 | 0.626256 | − | 0.779617i | \(-0.284586\pi\) | ||||
0.626256 | + | 0.779617i | \(0.284586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4290.00i | 1.73293i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2379.00i | 0.930319i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 290.000 | 0.111611 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4222.00 | 1.59944 | 0.799720 | − | 0.600373i | \(-0.204981\pi\) | ||||
0.799720 | + | 0.600373i | \(0.204981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3357.00i | 1.25203i | 0.779810 | + | 0.626016i | \(0.215316\pi\) | ||||
−0.779810 | + | 0.626016i | \(0.784684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 166.000i | − 0.0600356i | −0.999549 | − | 0.0300178i | \(-0.990444\pi\) | ||||
0.999549 | − | 0.0300178i | \(-0.00955640\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3372.00 | 1.20118 | 0.600590 | − | 0.799557i | \(-0.294932\pi\) | ||||
0.600590 | + | 0.799557i | \(0.294932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1045.00 | −0.366710 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 384.000i | 0.132766i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 116.000i | − 0.0389496i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5889.00 | −1.94905 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5601.00 | −1.82743 | −0.913717 | − | 0.406350i | \(-0.866801\pi\) | ||||
−0.913717 | + | 0.406350i | \(0.866801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3900.00i | 1.25457i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 36.0000i | − 0.0112619i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2015.00 | −0.621740 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5124.00 | −1.55963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 828.000i | 0.248641i | 0.992242 | + | 0.124321i | \(0.0396751\pi\) | ||||
−0.992242 | + | 0.124321i | \(0.960325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2388.00i | 0.698225i | 0.937081 | + | 0.349113i | \(0.113517\pi\) | ||||
−0.937081 | + | 0.349113i | \(0.886483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2844.00 | 0.820685 | 0.410342 | − | 0.911932i | \(-0.365409\pi\) | ||||
0.410342 | + | 0.911932i | \(0.365409\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −390.000 | −0.111083 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 5962.00i | − 1.67632i | −0.545421 | − | 0.838162i | \(-0.683630\pi\) | ||||
0.545421 | − | 0.838162i | \(-0.316370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1150.00i | − 0.315192i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4320.00 | −1.16919 | −0.584597 | − | 0.811324i | \(-0.698748\pi\) | ||||
−0.584597 | + | 0.811324i | \(0.698748\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3857.00 | 1.03092 | 0.515459 | − | 0.856914i | \(-0.327621\pi\) | ||||
0.515459 | + | 0.856914i | \(0.327621\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 560.000i | 0.147835i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 12684.0i | − 3.26746i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6465.00 | 1.64539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 287.000 | 0.0721724 | 0.0360862 | − | 0.999349i | \(-0.488511\pi\) | ||||
0.0360862 | + | 0.999349i | \(0.488511\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2262.00i | 0.562098i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2130.00i | 0.516987i | 0.966013 | + | 0.258494i | \(0.0832261\pi\) | ||||
−0.966013 | + | 0.258494i | \(0.916774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −276.000 | −0.0662155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −384.000 | −0.0910690 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 3066.00i | − 0.718850i | −0.933174 | − | 0.359425i | \(-0.882973\pi\) | ||||
0.933174 | − | 0.359425i | \(-0.117027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6845.00i | 1.56894i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3744.00 | 0.848609 | 0.424304 | − | 0.905520i | \(-0.360519\pi\) | ||||
0.424304 | + | 0.905520i | \(0.360519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3346.00 | 0.750019 | 0.375009 | − | 0.927021i | \(-0.377640\pi\) | ||||
0.375009 | + | 0.927021i | \(0.377640\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 840.000i | − 0.186224i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7040.00i | 1.52705i | 0.645779 | + | 0.763525i | \(0.276533\pi\) | ||||
−0.645779 | + | 0.763525i | \(0.723467\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 36.0000 | 0.00772496 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3010.00 | −0.639009 | −0.319505 | − | 0.947585i | \(-0.603516\pi\) | ||||
−0.319505 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6001.00i | − 1.26050i | −0.776391 | − | 0.630252i | \(-0.782952\pi\) | ||||
0.776391 | − | 0.630252i | \(-0.217048\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 458.000i | − 0.0941982i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1192.00 | 0.242622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1910.00 | −0.384764 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4802.00i | − 0.957460i | −0.877962 | − | 0.478730i | \(-0.841097\pi\) | ||||
0.877962 | − | 0.478730i | \(-0.158903\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5655.00i | − 1.10484i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4872.00 | −0.942325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −328.000 | −0.0628093 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 3970.00i | − 0.752708i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6149.00i | − 1.14313i | −0.820556 | − | 0.571567i | \(-0.806336\pi\) | ||||
0.820556 | − | 0.571567i | \(-0.193664\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6740.00 | 1.24086 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 878.000 | 0.160086 | 0.0800431 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800431 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4042.00i | 0.729928i | 0.931022 | + | 0.364964i | \(0.118919\pi\) | ||||
−0.931022 | + | 0.364964i | \(0.881081\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3844.00i | 0.681074i | 0.940231 | + | 0.340537i | \(0.110609\pi\) | ||||
−0.940231 | + | 0.340537i | \(0.889391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7488.00 | 1.31426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3875.00 | −0.673774 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9211.00i | − 1.58673i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 2230.00i | − 0.377123i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 424.000 | 0.0710513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2717.00 | 0.451178 | 0.225589 | − | 0.974223i | \(-0.427569\pi\) | ||||
0.225589 | + | 0.974223i | \(0.427569\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 276.000i | − 0.0454195i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1603.00i | − 0.259113i | −0.991572 | − | 0.129556i | \(-0.958645\pi\) | ||||
0.991572 | − | 0.129556i | \(-0.0413553\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1155.00 | −0.185047 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −702.000 | −0.111482 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1364.00i | − 0.214720i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11607.0i | 1.79567i | 0.440335 | + | 0.897833i | \(0.354860\pi\) | ||||
−0.440335 | + | 0.897833i | \(0.645140\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4030.00 | −0.618112 | −0.309056 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309056 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12180.0 | 1.85219 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 2106.00i | − 0.317538i | −0.987316 | − | 0.158769i | \(-0.949247\pi\) | ||||
0.987316 | − | 0.158769i | \(-0.0507526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 610.000i | − 0.0904331i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7394.00 | 1.08702 | 0.543510 | − | 0.839402i | \(-0.317095\pi\) | ||||
0.543510 | + | 0.839402i | \(0.317095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15942.0 | 2.32425 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 950.000i | 0.137361i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6940.00i | 0.987098i | 0.869718 | + | 0.493549i | \(0.164301\pi\) | ||||
−0.869718 | + | 0.493549i | \(0.835699\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 458.000 | 0.0646139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1156.00 | −0.161770 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 7486.00i | − 1.03917i | −0.854419 | − | 0.519585i | \(-0.826087\pi\) | ||||
0.854419 | − | 0.519585i | \(-0.173913\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16128.0i | 2.20327i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1285.00 | 0.174158 | 0.0870792 | − | 0.996201i | \(-0.472247\pi\) | ||||
0.0870792 | + | 0.996201i | \(0.472247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11930.0 | 1.60418 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9622.00i | 1.28371i | 0.766826 | + | 0.641855i | \(0.221835\pi\) | ||||
−0.766826 | + | 0.641855i | \(0.778165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 328.000i | − 0.0430831i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1974.00 | −0.257290 | −0.128645 | − | 0.991691i | \(-0.541063\pi\) | ||||
−0.128645 | + | 0.991691i | \(0.541063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3538.00 | −0.457607 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 12260.0i | − 1.57363i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8084.00i | − 1.02198i | −0.859588 | − | 0.510988i | \(-0.829280\pi\) | ||||
0.859588 | − | 0.510988i | \(-0.170720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1510.00 | 0.189460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5667.00 | −0.705727 | −0.352863 | − | 0.935675i | \(-0.614792\pi\) | ||||
−0.352863 | + | 0.935675i | \(0.614792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1512.00i | − 0.186894i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5382.00i | 0.655469i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4835.00 | 0.584536 | 0.292268 | − | 0.956336i | \(-0.405590\pi\) | ||||
0.292268 | + | 0.956336i | \(0.405590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5625.00 | 0.675087 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 672.000i | 0.0800653i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 6885.00i | − 0.808537i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4619.00 | 0.538551 | 0.269276 | − | 0.963063i | \(-0.413216\pi\) | ||||
0.269276 | + | 0.963063i | \(0.413216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7476.00 | 0.865458 | 0.432729 | − | 0.901524i | \(-0.357551\pi\) | ||||
0.432729 | + | 0.901524i | \(0.357551\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 424.000i | 0.0487366i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1716.00i | − 0.194480i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16380.0 | −1.84344 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7810.00 | −0.872841 | −0.436420 | − | 0.899743i | \(-0.643754\pi\) | ||||
−0.436420 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2029.00i | 0.225191i | 0.993641 | + | 0.112595i | \(0.0359164\pi\) | ||||
−0.993641 | + | 0.112595i | \(0.964084\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8758.00i | − 0.958700i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3208.00 | 0.348769 | 0.174384 | − | 0.984678i | \(-0.444206\pi\) | ||||
0.174384 | + | 0.984678i | \(0.444206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 678.000 | 0.0732102 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13227.0i | 1.41859i | 0.704914 | + | 0.709293i | \(0.250986\pi\) | ||||
−0.704914 | + | 0.709293i | \(0.749014\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 9600.00i | − 1.01580i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3617.00 | −0.380171 | −0.190086 | − | 0.981768i | \(-0.560877\pi\) | ||||
−0.190086 | + | 0.981768i | \(0.560877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8931.00 | −0.932471 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 9270.00i | − 0.961463i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6215.00i | 0.636161i | 0.948064 | + | 0.318080i | \(0.103038\pi\) | ||||
−0.948064 | + | 0.318080i | \(0.896962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8845.00 | 0.899454 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7108.00 | −0.718118 | −0.359059 | − | 0.933315i | \(-0.616902\pi\) | ||||
−0.359059 | + | 0.933315i | \(0.616902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 3364.00i | − 0.337664i | −0.985645 | − | 0.168832i | \(-0.946000\pi\) | ||||
0.985645 | − | 0.168832i | \(-0.0539995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18964.0i | 1.87912i | 0.342384 | + | 0.939560i | \(0.388766\pi\) | ||||
−0.342384 | + | 0.939560i | \(0.611234\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 418.000 | 0.0411545 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3170.00 | 0.310119 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6396.00i | 0.621751i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1156.00i | − 0.110964i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10926.0 | −1.04222 | −0.521108 | − | 0.853491i | \(-0.674481\pi\) | ||||
−0.521108 | + | 0.853491i | \(0.674481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11592.0 | −1.09886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 580.000i | − 0.0546396i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4350.00i | 0.404758i | 0.979307 | + | 0.202379i | \(0.0648673\pi\) | ||||
−0.979307 | + | 0.202379i | \(0.935133\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −515.000 | −0.0476260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1324.00 | 0.121693 | 0.0608465 | − | 0.998147i | \(-0.480620\pi\) | ||||
0.0608465 | + | 0.998147i | \(0.480620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11712.0i | 1.06994i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 1560.00i | − 0.140796i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9068.00 | 0.813506 | 0.406753 | − | 0.913538i | \(-0.366661\pi\) | ||||
0.406753 | + | 0.913538i | \(0.366661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 220.000 | 0.0196185 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 19836.0i | − 1.75834i | −0.476511 | − | 0.879169i | \(-0.658099\pi\) | ||||
0.476511 | − | 0.879169i | \(-0.341901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 24295.0i | − 2.12816i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2682.00 | −0.233551 | −0.116776 | − | 0.993158i | \(-0.537256\pi\) | ||||
−0.116776 | + | 0.993158i | \(0.537256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 806.000 | 0.0697756 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21895.0i | 1.88438i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 8268.00i | − 0.703339i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5640.00 | −0.477011 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3035.00 | −0.255213 | −0.127606 | − | 0.991825i | \(-0.540729\pi\) | ||||
−0.127606 | + | 0.991825i | \(0.540729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7701.00i | 0.643865i | 0.946763 | + | 0.321932i | \(0.104332\pi\) | ||||
−0.946763 | + | 0.321932i | \(0.895668\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1098.00i | − 0.0907583i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8803.00 | 0.723514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −672.000 | −0.0549196 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 19236.0i | − 1.56323i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 11225.0i | − 0.902038i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13221.0 | −1.05653 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18112.0 | −1.43936 | −0.719682 | − | 0.694304i | \(-0.755712\pi\) | ||||
−0.719682 | + | 0.694304i | \(0.755712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15250.0i | 1.20523i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 19541.0i | − 1.52745i | −0.645544 | − | 0.763723i | \(-0.723369\pi\) | ||||
0.645544 | − | 0.763723i | \(-0.276631\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1716.00 | 0.133401 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28992.0 | −2.24156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 460.000i | 0.0353729i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13508.0i | 1.02756i | 0.857921 | + | 0.513781i | \(0.171756\pi\) | ||||
−0.857921 | + | 0.513781i | \(0.828244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13776.0 | −1.04233 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11895.0 | −0.895200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8712.00i | − 0.652162i | −0.945342 | − | 0.326081i | \(-0.894272\pi\) | ||||
0.945342 | − | 0.326081i | \(-0.105728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1342.00i | 0.0993981i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9623.00 | 0.708993 | 0.354497 | − | 0.935057i | \(-0.384652\pi\) | ||||
0.354497 | + | 0.935057i | \(0.384652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −604.000 | −0.0442673 | −0.0221336 | − | 0.999755i | \(-0.507046\pi\) | ||||
−0.0221336 | + | 0.999755i | \(0.507046\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21110.0i | 1.53906i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3629.00i | 0.261832i | 0.991393 | + | 0.130916i | \(0.0417919\pi\) | ||||
−0.991393 | + | 0.130916i | \(0.958208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16785.0 | −1.20477 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2586.00 | −0.184656 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22542.0i | 1.60136i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 9219.00i | − 0.648226i | −0.946018 | − | 0.324113i | \(-0.894934\pi\) | ||||
0.946018 | − | 0.324113i | \(-0.105066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2718.00 | 0.190141 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 830.000 | 0.0577693 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19111.0i | 1.32343i | 0.749755 | + | 0.661716i | \(0.230171\pi\) | ||||
−0.749755 | + | 0.661716i | \(0.769829\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16860.0i | 1.15584i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17086.0 | −1.16547 | −0.582734 | − | 0.812663i | \(-0.698017\pi\) | ||||
−0.582734 | + | 0.812663i | \(0.698017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9035.00 | 0.613220 | 0.306610 | − | 0.951835i | \(-0.400805\pi\) | ||||
0.306610 | + | 0.951835i | \(0.400805\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 418.000i | 0.0282293i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14784.0i | 0.988573i | 0.869299 | + | 0.494287i | \(0.164571\pi\) | ||||
−0.869299 | + | 0.494287i | \(0.835429\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1920.00 | −0.127754 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17808.0 | 1.17911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17846.0i | 1.17585i | 0.808917 | + | 0.587923i | \(0.200054\pi\) | ||||
−0.808917 | + | 0.587923i | \(0.799946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11618.0i | 0.758060i | 0.925384 | + | 0.379030i | \(0.123742\pi\) | ||||
−0.925384 | + | 0.379030i | \(0.876258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9556.00 | −0.620498 | −0.310249 | − | 0.950655i | \(-0.600412\pi\) | ||||
−0.310249 | + | 0.950655i | \(0.600412\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8410.00 | 0.543449 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2738.00i | − 0.176076i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 29445.0i | − 1.87547i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8418.00 | −0.533621 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19394.0 | 1.22355 | 0.611777 | − | 0.791030i | \(-0.290455\pi\) | ||||
0.611777 | + | 0.791030i | \(0.290455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 28005.0i | − 1.75845i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 28476.0i | − 1.77121i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1560.00 | 0.0965769 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12138.0 | 0.747929 | 0.373964 | − | 0.927443i | \(-0.377998\pi\) | ||||
0.373964 | + | 0.927443i | \(0.377998\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27036.0i | 1.65816i | 0.559131 | + | 0.829079i | \(0.311135\pi\) | ||||
−0.559131 | + | 0.829079i | \(0.688865\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17556.0i | 1.06677i | 0.845874 | + | 0.533383i | \(0.179080\pi\) | ||||
−0.845874 | + | 0.533383i | \(0.820920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13104.0 | 0.792569 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 180.000 | 0.0108368 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17262.0i | 1.03448i | 0.855841 | + | 0.517239i | \(0.173040\pi\) | ||||
−0.855841 | + | 0.517239i | \(0.826960\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 806.000i | 0.0478616i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10517.0 | 0.621675 | 0.310838 | − | 0.950463i | \(-0.399390\pi\) | ||||
0.310838 | + | 0.950463i | \(0.399390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1408.00 | 0.0828515 | 0.0414258 | − | 0.999142i | \(-0.486810\pi\) | ||||
0.0414258 | + | 0.999142i | \(0.486810\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 25620.0i | − 1.50075i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11136.0i | 0.646458i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4140.00 | −0.239255 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33462.0 | −1.92517 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9626.00i | 0.551345i | 0.961252 | + | 0.275672i | \(0.0889005\pi\) | ||||
−0.961252 | + | 0.275672i | \(0.911100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28464.0i | 1.61589i | 0.589255 | + | 0.807947i | \(0.299421\pi\) | ||||
−0.589255 | + | 0.807947i | \(0.700579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 764.000 | 0.0431806 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11940.0 | −0.671868 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 3963.00i | − 0.222020i | −0.993819 | − | 0.111010i | \(-0.964591\pi\) | ||||
0.993819 | − | 0.111010i | \(-0.0354086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14220.0i | 0.789704i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −48552.0 | −2.68459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31781.0 | 1.74965 | 0.874824 | − | 0.484442i | \(-0.160977\pi\) | ||||
0.874824 | + | 0.484442i | \(0.160977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 156.000i | 0.00855115i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 13969.0i | − 0.759130i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29810.0 | 1.61304 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28004.0 | −1.50884 | −0.754420 | − | 0.656392i | \(-0.772082\pi\) | ||||
−0.754420 | + | 0.656392i | \(0.772082\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 20838.0i | − 1.11795i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1588.00i | 0.0844737i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35228.0 | 1.86603 | 0.933015 | − | 0.359837i | \(-0.117168\pi\) | ||||
0.933015 | + | 0.359837i | \(0.117168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −460.000 | −0.0242635 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1044.00i | − 0.0548361i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 21600.0i | − 1.12506i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8658.00 | −0.449081 | −0.224540 | − | 0.974465i | \(-0.572088\pi\) | ||||
−0.224540 | + | 0.974465i | \(0.572088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2696.00 | −0.139257 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19285.0i | 0.992001i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 5728.00i | − 0.292214i | −0.989269 | − | 0.146107i | \(-0.953326\pi\) | ||||
0.989269 | − | 0.146107i | \(-0.0466744\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20917.0 | −1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10004.0 | −0.506171 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 21460.0i | − 1.08137i | −0.841226 | − | 0.540684i | \(-0.818165\pi\) | ||||
0.841226 | − | 0.540684i | \(-0.181835\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 8151.00i | − 0.407389i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29164.0 | 1.45171 | 0.725856 | − | 0.687847i | \(-0.241444\pi\) | ||||
0.725856 | + | 0.687847i | \(0.241444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 63420.0 | 3.14412 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29478.0i | 1.45551i | 0.685838 | + | 0.727754i | \(0.259436\pi\) | ||||
−0.685838 | + | 0.727754i | \(0.740564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2586.00i | − 0.126662i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1550.00 | 0.0756152 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −576.000 | −0.0279874 | −0.0139937 | − | 0.999902i | \(-0.504454\pi\) | ||||
−0.0139937 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1435.00i | 0.0694480i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2880.00i | 0.138277i | 0.997607 | + | 0.0691383i | \(0.0220250\pi\) | ||||
−0.997607 | + | 0.0691383i | \(0.977975\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11310.0 | −0.540879 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20789.0 | 0.990277 | 0.495138 | − | 0.868814i | \(-0.335117\pi\) | ||||
0.495138 | + | 0.868814i | \(0.335117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 892.000i | 0.0423232i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28224.0i | 1.32870i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26421.0 | −1.23897 | −0.619484 | − | 0.785010i | \(-0.712658\pi\) | ||||
−0.619484 | + | 0.785010i | \(0.712658\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10650.0 | −0.497471 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 32504.0i | − 1.51240i | −0.654339 | − | 0.756202i | \(-0.727053\pi\) | ||||
0.654339 | − | 0.756202i | \(-0.272947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1380.00i | − 0.0637159i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34579.0 | 1.59040 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30420.0 | −1.39374 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 27840.0i | − 1.27065i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 996.000i | − 0.0451125i | −0.999746 | − | 0.0225563i | \(-0.992820\pi\) | ||||
0.999746 | − | 0.0225563i | \(-0.00718049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15330.0 | 0.691714 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 462.000 | 0.0207672 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 72072.0i | − 3.22743i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15134.0i | 0.672615i | 0.941752 | + | 0.336307i | \(0.109178\pi\) | ||||
−0.941752 | + | 0.336307i | \(0.890822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12932.0 | 0.572592 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2738.00 | 0.120777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 15717.0i | − 0.690711i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18720.0i | 0.816574i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36942.0 | 1.60545 | 0.802727 | − | 0.596347i | \(-0.203382\pi\) | ||||
0.802727 | + | 0.596347i | \(0.203382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11748.0 | 0.508666 | 0.254333 | − | 0.967117i | \(-0.418144\pi\) | ||||
0.254333 | + | 0.967117i | \(0.418144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16730.0i | 0.721706i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 24764.0i | − 1.06044i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −336.000 | −0.0143355 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1198.00 | −0.0509263 | −0.0254631 | − | 0.999676i | \(-0.508106\pi\) | ||||
−0.0254631 | + | 0.999676i | \(0.508106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6788.00i | − 0.287503i | −0.989614 | − | 0.143751i | \(-0.954083\pi\) | ||||
0.989614 | − | 0.143751i | \(-0.0459166\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 33011.0i | − 1.38803i | −0.719958 | − | 0.694017i | \(-0.755839\pi\) | ||||
0.719958 | − | 0.694017i | \(-0.244161\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17732.0 | −0.742892 | −0.371446 | − | 0.928454i | \(-0.621138\pi\) | ||||
−0.371446 | + | 0.928454i | \(0.621138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35200.0 | −1.46940 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 20679.0i | − 0.860126i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2610.00i | 0.107784i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8480.00 | 0.348942 | 0.174471 | − | 0.984662i | \(-0.444179\pi\) | ||||
0.174471 | + | 0.984662i | \(0.444179\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12475.0 | 0.511501 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 15050.0i | − 0.614887i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 380.000i | − 0.0154155i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30005.0 | 1.21292 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8004.00 | −0.322413 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 30014.0i | − 1.20476i | −0.798210 | − | 0.602380i | \(-0.794219\pi\) | ||||
0.798210 | − | 0.602380i | \(-0.205781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21643.0i | 0.862673i | 0.902191 | + | 0.431337i | \(0.141958\pi\) | ||||
−0.902191 | + | 0.431337i | \(0.858042\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2799.00 | 0.111177 | 0.0555883 | − | 0.998454i | \(-0.482297\pi\) | ||||
0.0555883 | + | 0.998454i | \(0.482297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2290.00 | 0.0906423 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 19384.0i | − 0.764588i | −0.924041 | − | 0.382294i | \(-0.875134\pi\) | ||||
0.924041 | − | 0.382294i | \(-0.124866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5960.00i | 0.233463i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8970.00 | 0.350157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17556.0 | 0.682965 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 764.000i | 0.0296191i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5132.00i | 0.197600i | 0.995107 | + | 0.0988001i | \(0.0315004\pi\) | ||||
−0.995107 | + | 0.0988001i | \(0.968500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24010.0 | 0.921316 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4430.00 | 0.169410 | 0.0847052 | − | 0.996406i | \(-0.473005\pi\) | ||||
0.0847052 | + | 0.996406i | \(0.473005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24317.0i | 0.926764i | 0.886159 | + | 0.463382i | \(0.153364\pi\) | ||||
−0.886159 | + | 0.463382i | \(0.846636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26100.0i | 0.987996i | 0.869463 | + | 0.493998i | \(0.164465\pi\) | ||||
−0.869463 | + | 0.493998i | \(0.835535\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4772.00 | −0.180031 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26169.0 | 0.983944 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32012.0i | 1.19960i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 24360.0i | − 0.906752i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3456.00 | −0.128214 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35258.0 | −1.30368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1640.00i | − 0.0604383i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 24356.0i | − 0.891651i | −0.895120 | − | 0.445826i | \(-0.852910\pi\) | ||||
0.895120 | − | 0.445826i | \(-0.147090\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1588.00 | −0.0579435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29900.0 | 1.08741 | 0.543705 | − | 0.839276i | \(-0.317021\pi\) | ||||
0.543705 | + | 0.839276i | \(0.317021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50427.0i | 1.82792i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4904.00i | 0.176602i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34838.0 | −1.25049 | −0.625245 | − | 0.780429i | \(-0.715001\pi\) | ||||
−0.625245 | + | 0.780429i | \(0.715001\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30745.0 | 1.09998 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 65520.0i | − 2.33653i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2696.00i | − 0.0955213i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26334.0 | −0.930022 | −0.465011 | − | 0.885305i | \(-0.653950\pi\) | ||||
−0.465011 | + | 0.885305i | \(0.653950\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 51189.0 | 1.80199 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4390.00i | 0.154043i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30949.0i | 1.07904i | 0.841973 | + | 0.539520i | \(0.181394\pi\) | ||||
−0.841973 | + | 0.539520i | \(0.818606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20210.0 | −0.702373 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25276.0 | 0.875637 | 0.437818 | − | 0.899063i | \(-0.355751\pi\) | ||||
0.437818 | + | 0.899063i | \(0.355751\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 13282.0i | − 0.458665i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1216.00i | 0.0417262i | 0.999782 | + | 0.0208631i | \(0.00664141\pi\) | ||||
−0.999782 | + | 0.0208631i | \(0.993359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33852.0 | 1.15794 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19220.0 | −0.655364 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6033.00i | 0.205066i | 0.994730 | + | 0.102533i | \(0.0326947\pi\) | ||||
−0.994730 | + | 0.102533i | \(0.967305\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37440.0i | 1.26464i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2250.00 | −0.0757626 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29467.0 | −0.989124 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1550.00i | 0.0518671i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41792.0i | 1.38980i | 0.719105 | + | 0.694902i | \(0.244552\pi\) | ||||
−0.719105 | + | 0.694902i | \(0.755448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46055.0 | 1.52683 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2105.00 | 0.0695702 | 0.0347851 | − | 0.999395i | \(-0.488925\pi\) | ||||
0.0347851 | + | 0.999395i | \(0.488925\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2754.00i | 0.0907391i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30119.0i | 0.986277i | 0.869951 | + | 0.493138i | \(0.164150\pi\) | ||||
−0.869951 | + | 0.493138i | \(0.835850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53391.0 | −1.74299 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −892.000 | −0.0290310 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18438.0i | 0.598251i | 0.954214 | + | 0.299126i | \(0.0966949\pi\) | ||||
−0.954214 | + | 0.299126i | \(0.903305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2120.00i | 0.0683691i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9512.00 | −0.305828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2230.00 | 0.0714816 | 0.0357408 | − | 0.999361i | \(-0.488621\pi\) | ||||
0.0357408 | + | 0.999361i | \(0.488621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13585.0i | 0.434146i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 6804.00i | − 0.216133i | −0.994144 | − | 0.108067i | \(-0.965534\pi\) | ||||
0.994144 | − | 0.108067i | \(-0.0344660\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20010.0 | 0.633722 |
(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 | 400.4.c.g.49.2 | 2 | ||
4.3 | odd | 2 | 200.4.c.d.49.1 | 2 | |||
5.2 | odd | 4 | 400.4.a.q.1.1 | 1 | |||
5.3 | odd | 4 | 400.4.a.f.1.1 | 1 | |||
5.4 | even | 2 | inner | 400.4.c.g.49.1 | 2 | ||
12.11 | even | 2 | 1800.4.f.c.649.2 | 2 | |||
20.3 | even | 4 | 200.4.a.h.1.1 | yes | 1 | ||
20.7 | even | 4 | 200.4.a.c.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 200.4.c.d.49.2 | 2 | |||
40.3 | even | 4 | 1600.4.a.m.1.1 | 1 | |||
40.13 | odd | 4 | 1600.4.a.bo.1.1 | 1 | |||
40.27 | even | 4 | 1600.4.a.bn.1.1 | 1 | |||
40.37 | odd | 4 | 1600.4.a.n.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.a.t.1.1 | 1 | |||
60.47 | odd | 4 | 1800.4.a.p.1.1 | 1 | |||
60.59 | even | 2 | 1800.4.f.c.649.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.4.a.c.1.1 | ✓ | 1 | 20.7 | even | 4 | ||
200.4.a.h.1.1 | yes | 1 | 20.3 | even | 4 | ||
200.4.c.d.49.1 | 2 | 4.3 | odd | 2 | |||
200.4.c.d.49.2 | 2 | 20.19 | odd | 2 | |||
400.4.a.f.1.1 | 1 | 5.3 | odd | 4 | |||
400.4.a.q.1.1 | 1 | 5.2 | odd | 4 | |||
400.4.c.g.49.1 | 2 | 5.4 | even | 2 | inner | ||
400.4.c.g.49.2 | 2 | 1.1 | even | 1 | trivial | ||
1600.4.a.m.1.1 | 1 | 40.3 | even | 4 | |||
1600.4.a.n.1.1 | 1 | 40.37 | odd | 4 | |||
1600.4.a.bn.1.1 | 1 | 40.27 | even | 4 | |||
1600.4.a.bo.1.1 | 1 | 40.13 | odd | 4 | |||
1800.4.a.p.1.1 | 1 | 60.47 | odd | 4 | |||
1800.4.a.t.1.1 | 1 | 60.23 | odd | 4 | |||
1800.4.f.c.649.1 | 2 | 60.59 | even | 2 | |||
1800.4.f.c.649.2 | 2 | 12.11 | even | 2 |