Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,5,Mod(113,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.113");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.4244687775\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 996 x^{18} + 408854 x^{16} + 89661524 x^{14} + 11414409521 x^{12} + 861580608848 x^{10} + \cdots + 34\!\cdots\!64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{50} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.2 | ||
Root | \(-14.8343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 304.113 |
Dual form | 304.5.e.f.113.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 14.8343i | − | 1.64826i | −0.566402 | − | 0.824129i | \(-0.691665\pi\) | ||
0.566402 | − | 0.824129i | \(-0.308335\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −45.4605 | −1.81842 | −0.909209 | − | 0.416339i | \(-0.863313\pi\) | ||||
−0.909209 | + | 0.416339i | \(0.863313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.86483 | 0.0584658 | 0.0292329 | − | 0.999573i | \(-0.490694\pi\) | ||||
0.0292329 | + | 0.999573i | \(0.490694\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −139.057 | −1.71675 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −100.724 | −0.832430 | −0.416215 | − | 0.909266i | \(-0.636644\pi\) | ||||
−0.416215 | + | 0.909266i | \(0.636644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 53.2006i | − | 0.314797i | −0.987535 | − | 0.157398i | \(-0.949689\pi\) | ||
0.987535 | − | 0.157398i | \(-0.0503106\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 674.375i | 2.99722i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −145.257 | −0.502620 | −0.251310 | − | 0.967907i | \(-0.580861\pi\) | ||||
−0.251310 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 336.954 | − | 129.548i | 0.933391 | − | 0.358860i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 42.4977i | − | 0.0963668i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −828.203 | −1.56560 | −0.782801 | − | 0.622272i | \(-0.786210\pi\) | ||||
−0.782801 | + | 0.622272i | \(0.786210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1441.65 | 2.30665 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 861.237i | 1.18139i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 152.947i | − | 0.181864i | −0.995857 | − | 0.0909319i | \(-0.971015\pi\) | ||
0.995857 | − | 0.0909319i | \(-0.0289846\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1072.35i | 1.11587i | 0.829885 | + | 0.557935i | \(0.188406\pi\) | ||||
−0.829885 | + | 0.557935i | \(0.811594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1494.17i | 1.37206i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −130.236 | −0.106315 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1201.35i | 0.877537i | 0.898600 | + | 0.438769i | \(0.144585\pi\) | ||||
−0.898600 | + | 0.438769i | \(0.855415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −789.195 | −0.518866 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3018.54i | − | 1.79568i | −0.440318 | − | 0.897842i | \(-0.645134\pi\) | ||
0.440318 | − | 0.897842i | \(-0.354866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2469.37 | 1.33551 | 0.667757 | − | 0.744379i | \(-0.267255\pi\) | ||||
0.667757 | + | 0.744379i | \(0.267255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6321.60 | 3.12178 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2268.18 | 1.02679 | 0.513395 | − | 0.858153i | \(-0.328388\pi\) | ||||
0.513395 | + | 0.858153i | \(0.328388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2392.79 | −0.996582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2154.79i | 0.828447i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4530.72i | − | 1.61293i | −0.591282 | − | 0.806465i | \(-0.701378\pi\) | ||
0.591282 | − | 0.806465i | \(-0.298622\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4578.96 | 1.51371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1921.76 | − | 4998.49i | −0.591494 | − | 1.53847i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1580.60i | 0.454064i | 0.973887 | + | 0.227032i | \(0.0729022\pi\) | ||||
−0.973887 | + | 0.227032i | \(0.927098\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2849.06 | 0.765671 | 0.382836 | − | 0.923816i | \(-0.374948\pi\) | ||||
0.382836 | + | 0.923816i | \(0.374948\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −398.374 | −0.100371 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2418.52i | 0.572432i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 6810.56i | − | 1.51717i | −0.651576 | − | 0.758584i | \(-0.725892\pi\) | ||
0.651576 | − | 0.758584i | \(-0.274108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12285.8i | 2.58052i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6602.83i | 1.30982i | 0.755705 | + | 0.654912i | \(0.227294\pi\) | ||||
−0.755705 | + | 0.654912i | \(0.772706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4523.72 | −0.848888 | −0.424444 | − | 0.905454i | \(-0.639530\pi\) | ||||
−0.424444 | + | 0.905454i | \(0.639530\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 21386.0i | − | 3.80195i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −288.557 | −0.0486687 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1691.70i | 0.271063i | 0.990773 | + | 0.135531i | \(0.0432742\pi\) | ||||
−0.990773 | + | 0.135531i | \(0.956726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1512.24 | 0.230489 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6627.75 | 0.962077 | 0.481039 | − | 0.876699i | \(-0.340260\pi\) | ||||
0.481039 | + | 0.876699i | \(0.340260\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6603.46 | 0.913973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2268.87 | −0.299758 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1262.43i | − | 0.159377i | −0.996820 | − | 0.0796886i | \(-0.974607\pi\) | ||
0.996820 | − | 0.0796886i | \(-0.0253926\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 152.410i | − | 0.0184048i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15907.6 | 1.83924 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15318.1 | + | 5889.33i | −1.69730 | + | 0.652558i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15824.6i | 1.68185i | 0.541149 | + | 0.840927i | \(0.317990\pi\) | ||||
−0.541149 | + | 0.840927i | \(0.682010\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14006.4 | 1.42908 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1728.80 | −0.169474 | −0.0847370 | − | 0.996403i | \(-0.527005\pi\) | ||||
−0.0847370 | + | 0.996403i | \(0.527005\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18702.4i | 1.76288i | 0.472299 | + | 0.881439i | \(0.343424\pi\) | ||||
−0.472299 | + | 0.881439i | \(0.656576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1931.97i | 0.175235i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5713.61i | 0.499049i | 0.968368 | + | 0.249524i | \(0.0802743\pi\) | ||||
−0.968368 | + | 0.249524i | \(0.919726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13528.3i | 1.13865i | 0.822112 | + | 0.569326i | \(0.192796\pi\) | ||||
−0.822112 | + | 0.569326i | \(0.807204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17821.2 | 1.44641 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14367.9i | 1.12522i | 0.826723 | + | 0.562609i | \(0.190202\pi\) | ||||
−0.826723 | + | 0.562609i | \(0.809798\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 37650.5 | 2.84692 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7397.92i | 0.540428i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −416.136 | −0.0293861 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4495.66 | −0.307060 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −44778.1 | −2.95975 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −37125.5 | −2.37603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3564.00i | 0.220968i | 0.993878 | + | 0.110484i | \(0.0352401\pi\) | ||||
−0.993878 | + | 0.110484i | \(0.964760\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 36631.4i | − | 2.20127i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7223.20 | −0.420908 | −0.210454 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210454 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 965.315 | − | 371.134i | 0.0545715 | − | 0.0209810i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 39152.2i | − | 2.14827i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7261.51 | −0.386888 | −0.193444 | − | 0.981111i | \(-0.561966\pi\) | ||||
−0.193444 | + | 0.981111i | \(0.561966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7455.27 | −0.385864 | −0.192932 | − | 0.981212i | \(-0.561800\pi\) | ||||
−0.192932 | + | 0.981212i | \(0.561800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 33646.9i | − | 1.69241i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5358.58i | 0.262046i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6953.06i | 0.330705i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 35495.5i | 1.64262i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15653.0 | −0.705058 | −0.352529 | − | 0.935801i | \(-0.614678\pi\) | ||||
−0.352529 | + | 0.935801i | \(0.614678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15060.9i | 0.660536i | 0.943887 | + | 0.330268i | \(0.107139\pi\) | ||||
−0.943887 | + | 0.330268i | \(0.892861\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20199.0 | 0.862874 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 48749.6i | − | 2.02912i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9569.26 | −0.388221 | −0.194110 | − | 0.980980i | \(-0.562182\pi\) | ||||
−0.194110 | + | 0.980980i | \(0.562182\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −67210.1 | −2.65852 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2372.66 | −0.0915342 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11904.1 | −0.448045 | −0.224022 | − | 0.974584i | \(-0.571919\pi\) | ||||
−0.224022 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 67925.8i | − | 2.49498i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19033.2i | 0.682461i | 0.939980 | + | 0.341231i | \(0.110844\pi\) | ||||
−0.939980 | + | 0.341231i | \(0.889156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25730.7 | 0.900903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −46855.9 | + | 18014.6i | −1.60240 | + | 0.616074i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 27328.5i | 0.913112i | 0.889695 | + | 0.456556i | \(0.150917\pi\) | ||||
−0.889695 | + | 0.456556i | \(0.849083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4130.09 | 0.134860 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23447.1 | 0.748414 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3468.70i | − | 0.108258i | −0.998534 | − | 0.0541291i | \(-0.982762\pi\) | ||
0.998534 | − | 0.0541291i | \(-0.0172383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 42357.6i | − | 1.29293i | −0.762945 | − | 0.646464i | \(-0.776247\pi\) | ||
0.762945 | − | 0.646464i | \(-0.223753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 42263.9i | − | 1.26202i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 54613.9i | − | 1.59573i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14630.9 | 0.418396 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2467.29i | 0.0690712i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23795.4 | 0.652270 | 0.326135 | − | 0.945323i | \(-0.394254\pi\) | ||||
0.326135 | + | 0.945323i | \(0.394254\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 36775.1i | − | 0.987277i | −0.869667 | − | 0.493639i | \(-0.835667\pi\) | ||
0.869667 | − | 0.493639i | \(-0.164333\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 35877.2 | 0.943515 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 67966.3 | 1.75130 | 0.875651 | − | 0.482944i | \(-0.160433\pi\) | ||||
0.875651 | + | 0.482944i | \(0.160433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9109.02 | 0.230020 | 0.115010 | − | 0.993364i | \(-0.463310\pi\) | ||||
0.115010 | + | 0.993364i | \(0.463310\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −101030. | −2.50068 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 438.168i | − | 0.0106328i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 137224.i | 3.26531i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 115168. | 2.68775 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33939.4 | + | 13048.6i | −0.776983 | + | 0.298726i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 71608.1i | − | 1.60841i | −0.594351 | − | 0.804206i | \(-0.702591\pi\) | ||
0.594351 | − | 0.804206i | \(-0.297409\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 97948.4 | 2.15893 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −112259. | −2.42852 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3072.10i | 0.0652403i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 67106.4i | 1.39919i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7727.77i | 0.158223i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 30553.2i | − | 0.614393i | −0.951646 | − | 0.307197i | \(-0.900609\pi\) | ||
0.951646 | − | 0.307197i | \(-0.0993909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −200472. | −3.95994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 95469.6i | 1.85274i | 0.376620 | + | 0.926368i | \(0.377086\pi\) | ||||
−0.376620 | + | 0.926368i | \(0.622914\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −84302.1 | −1.60756 | −0.803781 | − | 0.594926i | \(-0.797181\pi\) | ||||
−0.803781 | + | 0.594926i | \(0.797181\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4280.55i | 0.0802186i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −55650.0 | −1.02507 | −0.512534 | − | 0.858667i | \(-0.671293\pi\) | ||||
−0.512534 | + | 0.858667i | \(0.671293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −103112. | −1.86713 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25095.3 | 0.446782 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 36259.9 | 0.634791 | 0.317395 | − | 0.948293i | \(-0.397192\pi\) | ||||
0.317395 | + | 0.948293i | \(0.397192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37725.4i | 0.649531i | 0.945795 | + | 0.324766i | \(0.105285\pi\) | ||||
−0.945795 | + | 0.324766i | \(0.894715\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 47327.1i | 0.801489i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 108777. | 1.81220 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6892.06 | − | 17926.2i | −0.112968 | − | 0.293828i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 98318.2i | − | 1.58575i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 47956.5 | 0.761203 | 0.380601 | − | 0.924739i | \(-0.375717\pi\) | ||||
0.380601 | + | 0.924739i | \(0.375717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 83420.0 | 1.30325 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 97957.8i | − | 1.50646i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2340.34i | − | 0.0354334i | −0.999843 | − | 0.0177167i | \(-0.994360\pi\) | ||
0.999843 | − | 0.0177167i | \(-0.00563969\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3441.65i | 0.0513060i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21268.4i | 0.312215i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −96120.0 | −1.38964 | −0.694820 | − | 0.719183i | \(-0.744516\pi\) | ||||
−0.694820 | + | 0.719183i | \(0.744516\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 205969.i | 2.93298i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18727.2 | −0.262695 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 44228.9i | 0.611226i | 0.952156 | + | 0.305613i | \(0.0988614\pi\) | ||||
−0.952156 | + | 0.305613i | \(0.901139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 121267. | 1.65122 | 0.825610 | − | 0.564241i | \(-0.190831\pi\) | ||||
0.825610 | + | 0.564241i | \(0.190831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2260.91 | −0.0303359 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −145209. | −1.92012 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −53311.7 | −0.694805 | −0.347402 | − | 0.937716i | \(-0.612936\pi\) | ||||
−0.347402 | + | 0.937716i | \(0.612936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 149118.i | − | 1.91567i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 91196.0i | − | 1.15495i | −0.816408 | − | 0.577475i | \(-0.804038\pi\) | ||
0.816408 | − | 0.577475i | \(-0.195962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19894.3 | −0.248403 | −0.124201 | − | 0.992257i | \(-0.539637\pi\) | ||||
−0.124201 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 87364.3 | + | 227234.i | 1.07558 | + | 2.79758i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8647.60i | − | 0.104986i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −62421.4 | −0.747373 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 234747. | 2.77213 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 55158.5i | 0.642505i | 0.946993 | + | 0.321253i | \(0.104104\pi\) | ||||
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 71854.7i | − | 0.825678i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 86747.3i | − | 0.983429i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44060.9i | 0.492846i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7074.30 | 0.0780819 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25645.6i | 0.279337i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −129520. | −1.39231 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 124990.i | 1.32617i | 0.748545 | + | 0.663084i | \(0.230753\pi\) | ||||
−0.748545 | + | 0.663084i | \(0.769247\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 277437. | 2.90568 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 40835.5 | 0.422199 | 0.211099 | − | 0.977465i | \(-0.432296\pi\) | ||||
0.211099 | + | 0.977465i | \(0.432296\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 99556.2 | 1.01620 | 0.508100 | − | 0.861298i | \(-0.330348\pi\) | ||||
0.508100 | + | 0.861298i | \(0.330348\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18110.3 | 0.182517 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 95876.3i | − | 0.954097i | −0.878877 | − | 0.477049i | \(-0.841707\pi\) | ||
0.878877 | − | 0.477049i | \(-0.158293\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15405.5i | 0.151389i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 84757.5 | 0.822561 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48945.0 | + | 18817.8i | −0.469141 | + | 0.180370i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 76696.9i | − | 0.726124i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 200683. | 1.87679 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6497.94 | 0.0600321 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 143098.i | − | 1.30610i | −0.757315 | − | 0.653050i | \(-0.773489\pi\) | ||
0.757315 | − | 0.653050i | \(-0.226511\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 167056.i | − | 1.50652i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 309611.i | 2.75885i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 218865.i | 1.92715i | 0.267433 | + | 0.963576i | \(0.413825\pi\) | ||||
−0.267433 | + | 0.963576i | \(0.586175\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 213138. | 1.85465 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 108012.i | − | 0.928884i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13733.4 | −0.116732 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 558520.i | − | 4.69246i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 121057. | 1.00538 | 0.502692 | − | 0.864466i | \(-0.332343\pi\) | ||||
0.502692 | + | 0.864466i | \(0.332343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −232555. | −1.90931 | −0.954653 | − | 0.297722i | \(-0.903773\pi\) | ||||
−0.954653 | + | 0.297722i | \(0.903773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 45818.3 | 0.371899 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 142311. | 1.14206 | 0.571030 | − | 0.820929i | \(-0.306544\pi\) | ||||
0.571030 | + | 0.820929i | \(0.306544\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 300168.i | − | 2.38181i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6173.10i | 0.0484358i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −74343.0 | −0.576834 | −0.288417 | − | 0.957505i | \(-0.593129\pi\) | ||||
−0.288417 | + | 0.957505i | \(0.593129\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 96755.4 | − | 87303.8i | 0.742439 | − | 0.669914i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 66690.1i | 0.506114i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 205651. | 1.54363 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −84813.8 | −0.629701 | −0.314850 | − | 0.949141i | \(-0.601954\pi\) | ||||
−0.314850 | + | 0.949141i | \(0.601954\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 419750.i | 3.08275i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 12979.7i | − | 0.0943012i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 120963.i | 0.869433i | 0.900567 | + | 0.434717i | \(0.143151\pi\) | ||||
−0.900567 | + | 0.434717i | \(0.856849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 550731.i | 3.91631i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8136.90 | −0.0572501 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25901.6i | 0.180322i | 0.995927 | + | 0.0901608i | \(0.0287381\pi\) | ||||
−0.995927 | + | 0.0901608i | \(0.971262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 52869.4 | 0.364212 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 118419.i | − | 0.807280i | −0.914918 | − | 0.403640i | \(-0.867745\pi\) | ||
0.914918 | − | 0.403640i | \(-0.132255\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13117.9 | 0.0885001 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −343383. | −2.29275 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 45823.7 | 0.302824 | 0.151412 | − | 0.988471i | \(-0.451618\pi\) | ||||
0.151412 | + | 0.988471i | \(0.451618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 120302. | 0.786902 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 107151.i | 0.693765i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 76905.6i | − | 0.492906i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −112423. | −0.713304 | −0.356652 | − | 0.934237i | \(-0.616082\pi\) | ||||
−0.356652 | + | 0.934237i | \(0.616082\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5505.52 | − | 14319.8i | −0.0345822 | − | 0.0899479i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 155180.i | − | 0.965043i | −0.875884 | − | 0.482522i | \(-0.839721\pi\) | ||
0.875884 | − | 0.482522i | \(-0.160279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 57049.7 | 0.351272 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −68747.2 | −0.419126 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 121005.i | − | 0.730489i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2674.57i | − | 0.0159885i | −0.999968 | − | 0.00799424i | \(-0.997455\pi\) | ||
0.999968 | − | 0.00799424i | \(-0.00254467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 107720.i | 0.637692i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4528.13i | 0.0265472i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −301301. | −1.74946 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 110594.i | 0.636003i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −47400.1 | −0.269992 | −0.134996 | − | 0.990846i | \(-0.543102\pi\) | ||||
−0.134996 | + | 0.990846i | \(0.543102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 101396.i | − | 0.572081i | −0.958218 | − | 0.286040i | \(-0.907661\pi\) | ||
0.958218 | − | 0.286040i | \(-0.0923391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −315406. | −1.76274 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −209411. | −1.15937 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8162.07 | 0.0447656 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 79490.9 | 0.431920 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 99089.3i | − | 0.533424i | −0.963776 | − | 0.266712i | \(-0.914063\pi\) | ||
0.963776 | − | 0.266712i | \(-0.0859372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 256640.i | − | 1.36883i | −0.729094 | − | 0.684414i | \(-0.760058\pi\) | ||
0.729094 | − | 0.684414i | \(-0.239942\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 103144. | 0.545086 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −279067. | + | 107292.i | −1.46132 | + | 0.561832i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 135549.i | − | 0.703345i | −0.936123 | − | 0.351673i | \(-0.885613\pi\) | ||
0.936123 | − | 0.351673i | \(-0.114387\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 332735. | 1.71089 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −211491. | −1.07767 | −0.538834 | − | 0.842412i | \(-0.681135\pi\) | ||||
−0.538834 | + | 0.842412i | \(0.681135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57390.5i | 0.289814i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 232201.i | 1.16212i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 242635.i | 1.20354i | 0.798669 | + | 0.601770i | \(0.205538\pi\) | ||||
−0.798669 | + | 0.601770i | \(0.794462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 304040.i | 1.49478i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 223418. | 1.08873 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6928.65i | 0.0334677i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 84466.2 | 0.404437 | 0.202218 | − | 0.979340i | \(-0.435185\pi\) | ||||
0.202218 | + | 0.979340i | \(0.435185\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 125101.i | − | 0.593792i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −314530. | −1.48000 | −0.739998 | − | 0.672609i | \(-0.765174\pi\) | ||||
−0.739998 | + | 0.672609i | \(0.765174\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 230478. | 1.07514 | 0.537572 | − | 0.843218i | \(-0.319342\pi\) | ||||
0.537572 | + | 0.843218i | \(0.319342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −723167. | −3.34451 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −117986. | −0.541000 | −0.270500 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270500 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 19511.1i | − | 0.0887025i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 141953.i | 0.639888i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −248725. | −1.11172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 485772. | − | 186764.i | 2.15300 | − | 0.827763i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 630028.i | 2.76900i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 190455. | 0.830081 | 0.415040 | − | 0.909803i | \(-0.363767\pi\) | ||||
0.415040 | + | 0.909803i | \(0.363767\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 63912.5 | 0.276246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35196.8i | 0.150872i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 719392.i | − | 3.05831i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 176874.i | 0.745774i | 0.927877 | + | 0.372887i | \(0.121632\pi\) | ||||
−0.927877 | + | 0.372887i | \(0.878368\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 176589.i | 0.738493i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −85636.3 | −0.355218 | −0.177609 | − | 0.984101i | \(-0.556836\pi\) | ||||
−0.177609 | + | 0.984101i | \(0.556836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22216.7i | 0.0914083i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −636737. | −2.59866 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18915.9i | 0.0765800i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 399577. | 1.60472 | 0.802361 | − | 0.596839i | \(-0.203577\pi\) | ||||
0.802361 | + | 0.596839i | \(0.203577\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 282344. | 1.12487 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 377058. | 1.49029 | 0.745147 | − | 0.666900i | \(-0.232379\pi\) | ||||
0.745147 | + | 0.666900i | \(0.232379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 78592.3 | 0.308175 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 381697.i | − | 1.48492i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 439558.i | 1.69661i | 0.529511 | + | 0.848303i | \(0.322375\pi\) | ||||
−0.529511 | + | 0.848303i | \(0.677625\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12959.7 | −0.0496310 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 111572. | + | 290197.i | 0.423955 | + | 1.10270i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 850218.i | − | 3.20565i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −228460. | −0.854731 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 405400. | 1.50504 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 188374.i | − | 0.693977i | −0.937869 | − | 0.346988i | \(-0.887204\pi\) | ||
0.937869 | − | 0.346988i | \(-0.112796\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 120335.i | − | 0.439936i | −0.975507 | − | 0.219968i | \(-0.929405\pi\) | ||
0.975507 | − | 0.219968i | \(-0.0705952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 61267.0i | − | 0.222284i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 155767.i | − | 0.560858i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 406080. | 1.45111 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 219793.i | − | 0.779516i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −160588. | −0.565275 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 259743.i | − | 0.907480i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −51455.8 | −0.178437 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 241012. | 0.829585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −73485.7 | −0.251078 | −0.125539 | − | 0.992089i | \(-0.540066\pi\) | ||||
−0.125539 | + | 0.992089i | \(0.540066\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −628346. | −2.13108 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 615004.i | − | 2.07054i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 192601.i | 0.643700i | 0.946791 | + | 0.321850i | \(0.104305\pi\) | ||||
−0.946791 | + | 0.321850i | \(0.895695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −396182. | −1.31447 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19814.1 | − | 51536.3i | −0.0652637 | − | 0.169750i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4846.44i | 0.0158479i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −810160. | −2.63018 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −234775. | −0.756730 | −0.378365 | − | 0.925656i | \(-0.623514\pi\) | ||||
−0.378365 | + | 0.925656i | \(0.623514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 131372.i | − | 0.420415i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 217039.i | − | 0.689624i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43274.1i | 0.136525i | 0.997667 | + | 0.0682623i | \(0.0217455\pi\) | ||||
−0.997667 | + | 0.0682623i | \(0.978255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 653172.i | − | 2.04612i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4332.31 | 0.0134758 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 369293.i | 1.14064i | 0.821424 | + | 0.570318i | \(0.193180\pi\) | ||||
−0.821424 | + | 0.570318i | \(0.806820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 56108.0 | 0.172089 | 0.0860444 | − | 0.996291i | \(-0.472577\pi\) | ||||
0.0860444 | + | 0.996291i | \(0.472577\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 352989.i | − | 1.07511i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.19398e6 | −3.61129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 82362.1 | 0.247386 | 0.123693 | − | 0.992321i | \(-0.460526\pi\) | ||||
0.123693 | + | 0.992321i | \(0.460526\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −545534. | −1.62729 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18987.4 | 0.0562486 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 456352.i | 1.34265i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 336313.i | − | 0.982724i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −172458. | −0.500502 | −0.250251 | − | 0.968181i | \(-0.580513\pi\) | ||||
−0.250251 | + | 0.968181i | \(0.580513\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 138921. | + | 361333.i | 0.400441 | + | 1.04154i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1.00823e6i | − | 2.88660i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −379651. | −1.07963 | −0.539815 | − | 0.841784i | \(-0.681506\pi\) | ||||
−0.539815 | + | 0.841784i | \(0.681506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18917.8 | 0.0534362 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 135126.i | − | 0.379132i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 425819.i | 1.18678i | 0.804914 | + | 0.593391i | \(0.202211\pi\) | ||||
−0.804914 | + | 0.593391i | \(0.797789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 571193.i | 1.58137i | 0.612222 | + | 0.790686i | \(0.290276\pi\) | ||||
−0.612222 | + | 0.790686i | \(0.709724\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 947057.i | 2.60460i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 204375. | 0.558363 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 287559.i | 0.780458i | 0.920718 | + | 0.390229i | \(0.127604\pi\) | ||||
−0.920718 | + | 0.390229i | \(0.872396\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6499.92 | −0.0175256 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 120668.i | − | 0.323230i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 338076. | 0.899692 | 0.449846 | − | 0.893106i | \(-0.351479\pi\) | ||||
0.449846 | + | 0.893106i | \(0.351479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.03563e6 | 5.38206 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −91953.9 | −0.241546 | −0.120773 | − | 0.992680i | \(-0.538537\pi\) | ||||
−0.120773 | + | 0.992680i | \(0.538537\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −309424. | −0.807557 | −0.403778 | − | 0.914857i | \(-0.632303\pi\) | ||||
−0.403778 | + | 0.914857i | \(0.632303\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 713279.i | − | 1.84959i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3616.63i | − | 0.00931812i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 786708. | 2.01397 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 193568. | + | 503468.i | 0.492377 | + | 1.28067i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 174504.i | − | 0.441068i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 347970. | 0.873944 | 0.436972 | − | 0.899475i | \(-0.356051\pi\) | ||||
0.436972 | + | 0.899475i | \(0.356051\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.06226e6 | −2.65108 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 162021.i | − | 0.401813i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 127298.i | 0.313720i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 918170.i | − | 2.24865i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 196909.i | − | 0.479237i | −0.970867 | − | 0.239619i | \(-0.922978\pi\) | ||
0.970867 | − | 0.239619i | \(-0.0770224\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 458651. | 1.10933 | 0.554665 | − | 0.832074i | \(-0.312847\pi\) | ||||
0.554665 | + | 0.832074i | \(0.312847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.66528e6i | 4.00283i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −455186. | −1.08738 | −0.543689 | − | 0.839287i | \(-0.682973\pi\) | ||||
−0.543689 | + | 0.839287i | \(0.682973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 159204.i | − | 0.377977i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45572.5 | 0.107533 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −196893. | −0.461747 | −0.230873 | − | 0.972984i | \(-0.574158\pi\) | ||||
−0.230873 | + | 0.972984i | \(0.574158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 328370. | 0.765387 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 629056. | 1.45733 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 697104.i | 1.60519i | 0.596524 | + | 0.802595i | \(0.296548\pi\) | ||||
−0.596524 | + | 0.802595i | \(0.703452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 326279.i | − | 0.746770i | −0.927676 | − | 0.373385i | \(-0.878197\pi\) | ||
0.927676 | − | 0.373385i | \(-0.121803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 114636. | 0.260792 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −43883.7 | + | 16871.9i | −0.0992338 | + | 0.0381523i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 126672.i | 0.284726i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −453235. | −1.01268 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −286969. | −0.637368 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 257251.i | − | 0.567972i | −0.958828 | − | 0.283986i | \(-0.908343\pi\) | ||
0.958828 | − | 0.283986i | \(-0.0916569\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.24161e6i | 2.72506i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 365636.i | − | 0.797759i | −0.917003 | − | 0.398879i | \(-0.869399\pi\) | ||
0.917003 | − | 0.398879i | \(-0.130601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45334.6i | 0.0983310i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41623e6 | 3.05379 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 135949.i | 0.291429i | 0.989327 | + | 0.145715i | \(0.0465481\pi\) | ||||
−0.989327 | + | 0.145715i | \(0.953452\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 330112. | 0.703525 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.25056e6i | 2.64967i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −241037. | −0.507744 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −166089. | −0.347844 | −0.173922 | − | 0.984759i | \(-0.555644\pi\) | ||||
−0.173922 | + | 0.984759i | \(0.555644\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 40125.9 | 0.0835522 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 338920. | 0.701662 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 438465.i | 0.902546i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 825529.i | 1.68958i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 72123.3 | 0.146771 | 0.0733854 | − | 0.997304i | \(-0.476620\pi\) | ||||
0.0733854 | + | 0.997304i | \(0.476620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 155633. | + | 404800.i | 0.314913 | + | 0.819086i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.52960e6i | 3.07752i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4952.73 | −0.00990844 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −566782. | −1.12752 | −0.563759 | − | 0.825939i | \(-0.690645\pi\) | ||||
−0.563759 | + | 0.825939i | \(0.690645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 235243.i | − | 0.465348i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 888125.i | − | 1.74701i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 243604.i | − | 0.476510i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 537891.i | − | 1.04630i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −425756. | −0.823574 | −0.411787 | − | 0.911280i | \(-0.635095\pi\) | ||||
−0.411787 | + | 0.911280i | \(0.635095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 53579.0i | 0.103068i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 559631. | 1.07059 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 220497.i | − | 0.419496i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −363837. | −0.688395 | −0.344197 | − | 0.938897i | \(-0.611849\pi\) | ||||
−0.344197 | + | 0.938897i | \(0.611849\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 824557. | 1.55155 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −358693. | −0.671256 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 117252. | 0.218229 | 0.109115 | − | 0.994029i | \(-0.465198\pi\) | ||||
0.109115 | + | 0.994029i | \(0.465198\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 1.61364e6i | − | 2.98698i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 685988.i | 1.26294i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 326297. | 0.597481 | 0.298740 | − | 0.954334i | \(-0.403434\pi\) | ||||
0.298740 | + | 0.954334i | \(0.403434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −265923. | + | 102239.i | −0.484305 | + | 0.186200i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 179042.i | − | 0.324323i | −0.986764 | − | 0.162161i | \(-0.948154\pi\) | ||
0.986764 | − | 0.162161i | \(-0.0518465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 711592. | 1.28209 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −921635. | −1.65165 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16368.5i | 0.0291773i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 407455.i | − | 0.722436i | −0.932481 | − | 0.361218i | \(-0.882361\pi\) | ||
0.932481 | − | 0.361218i | \(-0.117639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 711402.i | − | 1.25466i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 684674.i | − | 1.20113i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 714736. | 1.24725 | 0.623626 | − | 0.781723i | \(-0.285659\pi\) | ||||
0.623626 | + | 0.781723i | \(0.285659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.23748e6i | − | 2.14810i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 419311. | 0.724047 | 0.362024 | − | 0.932169i | \(-0.382086\pi\) | ||||
0.362024 | + | 0.932169i | \(0.382086\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38756.3i | 0.0665722i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −918257. | −1.56907 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 84088.7 | 0.142938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −460066. | −0.777978 | −0.388989 | − | 0.921242i | \(-0.627176\pi\) | ||||
−0.388989 | + | 0.921242i | \(0.627176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34717.3 | −0.0584034 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 757267.i | 1.26733i | 0.773608 | + | 0.633665i | \(0.218450\pi\) | ||||
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.54596e6i | 2.57392i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51054.6 | 0.0845654 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −391048. | − | 1.01711e6i | −0.644399 | − | 1.67608i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 665064.i | − | 1.09034i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 131724. | 0.214853 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 435023. | 0.705948 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 332574.i | − | 0.536957i | −0.963286 | − | 0.268478i | \(-0.913479\pi\) | ||
0.963286 | − | 0.268478i | \(-0.0865208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.42588e6i | 2.29049i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41161.6i | 0.0657868i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 151572.i | − | 0.241031i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.05540e6 | 4.83431 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 388000.i | 0.610823i | 0.952220 | + | 0.305412i | \(0.0987940\pi\) | ||||
−0.952220 | + | 0.305412i | \(0.901206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −329469. | −0.516085 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 175549.i | 0.273611i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 455648. | 0.706640 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 107862. | 0.166448 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 656106. | 1.00746 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −864221. | −1.32047 | −0.660234 | − | 0.751060i | \(-0.729543\pi\) | ||||
−0.660234 | + | 0.751060i | \(0.729543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 61653.6i | 0.0937382i | 0.998901 | + | 0.0468691i | \(0.0149244\pi\) | ||||
−0.998901 | + | 0.0468691i | \(0.985076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.79892e6i | − | 2.72164i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 541166. | 0.814733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 832063. | − | 319902.i | 1.24656 | − | 0.479263i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21193.8i | 0.0315966i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 84273.1 | 0.125027 | 0.0625134 | − | 0.998044i | \(-0.480088\pi\) | ||||
0.0625134 | + | 0.998044i | \(0.480088\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −983646. | −1.45224 | −0.726121 | − | 0.687567i | \(-0.758679\pi\) | ||||
−0.726121 | + | 0.687567i | \(0.758679\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.15408e6i | 3.16486i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 361582.i | − | 0.528684i | −0.964429 | − | 0.264342i | \(-0.914845\pi\) | ||
0.964429 | − | 0.264342i | \(-0.0851548\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 411606.i | − | 0.598925i | −0.954108 | − | 0.299462i | \(-0.903193\pi\) | ||
0.954108 | − | 0.299462i | \(-0.0968073\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 790843.i | 1.14522i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 347570. | 0.500902 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 865256.i | − | 1.24100i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −923548. | −1.31828 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 626506.i | − | 0.890023i | −0.895525 | − | 0.445012i | \(-0.853200\pi\) | ||
0.895525 | − | 0.445012i | \(-0.146800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 683888. | 0.966926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.35283e6 | −1.90366 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.16973e6 | −1.63822 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12879.3 | −0.0179525 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 295119.i | 0.409432i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 994961.i | − | 1.37387i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.43364e6 | −1.97034 | −0.985172 | − | 0.171570i | \(-0.945116\pi\) | ||||
−0.985172 | + | 0.171570i | \(0.945116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.13009e6 | − | 818953.i | 2.91384 | − | 1.12028i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.13615e6i | 1.54695i | 0.633828 | + | 0.773474i | \(0.281483\pi\) | ||||
−0.633828 | + | 0.773474i | \(0.718517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −270468. | −0.366548 | −0.183274 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183274 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −128281. | −0.173044 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 104658.i | 0.140525i | 0.997529 | + | 0.0702623i | \(0.0223836\pi\) | ||||
−0.997529 | + | 0.0702623i | \(0.977616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.24237e6i | − | 1.66042i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 925979.i | 1.23186i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 170395.i | − | 0.225641i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −362326. | −0.477599 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.20052e6i | − | 2.88733i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −106358. | −0.138917 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.18104e6i | − | 1.53556i | −0.640717 | − | 0.767778i | \(-0.721363\pi\) | ||
0.640717 | − | 0.767778i | \(-0.278637\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 818238. | 1.05901 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 648093. | 0.834998 | 0.417499 | − | 0.908677i | \(-0.362907\pi\) | ||||
0.417499 | + | 0.908677i | \(0.362907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −617809. | −0.792379 | −0.396190 | − | 0.918169i | \(-0.629668\pi\) | ||||
−0.396190 | + | 0.918169i | \(0.629668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.06591e6 | −1.36093 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 895467.i | 1.13816i | 0.822283 | + | 0.569079i | \(0.192700\pi\) | ||||
−0.822283 | + | 0.569079i | \(0.807300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10210.2i | 0.0129191i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −152319. | −0.191866 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 764272. | − | 293839.i | 0.958397 | − | 0.368474i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 157689.i | 0.196859i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 653614. | 0.812337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 164013. | 0.202936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 658119.i | 0.810690i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 104942.i | − | 0.128699i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.92560e6i | 2.35108i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 356161.i | 0.432944i | 0.976289 | + | 0.216472i | \(0.0694551\pi\) | ||||
−0.976289 | + | 0.216472i | \(0.930545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 240403. | 0.290945 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 551857.i | 0.664952i | 0.943112 | + | 0.332476i | \(0.107884\pi\) | ||||
−0.943112 | + | 0.332476i | \(0.892116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −667574. | −0.800862 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.92134e6i | 2.29489i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20693.2 | −0.0246087 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −276649. | −0.327566 | −0.163783 | − | 0.986496i | \(-0.552370\pi\) | ||||
−0.163783 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.85414e6 | 2.18587 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 351274. | 0.412328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.73193e6i | 2.02417i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.60070e6i | − | 3.02643i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 277351. | 0.321365 | 0.160682 | − | 0.987006i | \(-0.448630\pi\) | ||||
0.160682 | + | 0.987006i | \(0.448630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −806262. | + | 309983.i | −0.930201 | + | 0.357633i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 605767.i | − | 0.695892i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −665127. | −0.760819 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −130928. | −0.149126 | −0.0745631 | − | 0.997216i | \(-0.523756\pi\) | ||||
−0.0745631 | + | 0.997216i | \(0.523756\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1.47685e6i | − | 1.67496i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 271511.i | − | 0.306626i | −0.988178 | − | 0.153313i | \(-0.951006\pi\) | ||
0.988178 | − | 0.153313i | \(-0.0489943\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.49997e6i | 2.81133i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 112164.i | − | 0.125600i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 939290. | 1.04737 | 0.523684 | − | 0.851912i | \(-0.324557\pi\) | ||||
0.523684 | + | 0.851912i | \(0.324557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 240665.i | 0.267227i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.42226e6 | −1.57260 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.37941e6i | 1.51882i | 0.650611 | + | 0.759411i | \(0.274513\pi\) | ||||
−0.650611 | + | 0.759411i | \(0.725487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.08175e6 | −1.18610 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 228530. | 0.249528 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20803.0 | −0.0226197 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −226415. | −0.245165 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 794518.i | − | 0.856744i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.67181e6i | 1.79528i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −849703. | −0.908687 | −0.454343 | − | 0.890827i | \(-0.650126\pi\) | ||||
−0.454343 | + | 0.890827i | \(0.650126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 279150. | + | 726066.i | 0.297296 | + | 0.773265i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 267402.i | 0.283613i | 0.989894 | + | 0.141806i | \(0.0452910\pi\) | ||||
−0.989894 | + | 0.141806i | \(0.954709\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21358.1 | −0.0225598 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.13775e6 | −1.19684 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 169611.i | 0.177690i | 0.996045 | + | 0.0888451i | \(0.0283176\pi\) | ||||
−0.996045 | + | 0.0888451i | \(0.971682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 127157.i | 0.132670i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.88121e6i | − | 1.95478i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.42103e6i | 1.47060i | 0.677740 | + | 0.735302i | \(0.262960\pi\) | ||||
−0.677740 | + | 0.735302i | \(0.737040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.08978e6 | −3.18460 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 96392.5i | − | 0.0989484i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.04514e6 | −2.09088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.43454e6i | 1.46071i | 0.683067 | + | 0.730356i | \(0.260646\pi\) | ||||
−0.683067 | + | 0.730356i | \(0.739354\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.12276e6 | −2.15279 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −414100. | −0.418272 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 425661. | 0.428226 | 0.214113 | − | 0.976809i | \(-0.431314\pi\) | ||||
0.214113 | + | 0.976809i | \(0.431314\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.03465e6 | −1.03672 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 304.5.e.f.113.2 | 20 | ||
4.3 | odd | 2 | 152.5.e.a.113.19 | yes | 20 | ||
12.11 | even | 2 | 1368.5.o.a.721.19 | 20 | |||
19.18 | odd | 2 | inner | 304.5.e.f.113.19 | 20 | ||
76.75 | even | 2 | 152.5.e.a.113.2 | ✓ | 20 | ||
228.227 | odd | 2 | 1368.5.o.a.721.20 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.5.e.a.113.2 | ✓ | 20 | 76.75 | even | 2 | ||
152.5.e.a.113.19 | yes | 20 | 4.3 | odd | 2 | ||
304.5.e.f.113.2 | 20 | 1.1 | even | 1 | trivial | ||
304.5.e.f.113.19 | 20 | 19.18 | odd | 2 | inner | ||
1368.5.o.a.721.19 | 20 | 12.11 | even | 2 | |||
1368.5.o.a.721.20 | 20 | 228.227 | odd | 2 |