Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,5,Mod(65,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, 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("176.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.h (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: | \(18.1931135028\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{553})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 271x^{2} + 272x + 19602 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(12.2580 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.65 |
Dual form | 176.5.h.e.65.1 |
$q$-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 \(\left(\mathbb{Z}/176\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(133\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −12.2580 | −1.36200 | −0.680999 | − | 0.732285i | \(-0.738454\pi\) | ||||
−0.680999 | + | 0.732285i | \(0.738454\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.25798 | 0.170319 | 0.0851595 | − | 0.996367i | \(-0.472860\pi\) | ||||
0.0851595 | + | 0.996367i | \(0.472860\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 33.9411i | 0.692676i | 0.938110 | + | 0.346338i | \(0.112575\pi\) | ||||
−0.938110 | + | 0.346338i | \(0.887425\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 69.2580 | 0.855037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 92.0319 | − | 78.5565i | 0.760594 | − | 0.649228i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 326.819i | 1.93384i | 0.255083 | + | 0.966919i | \(0.417897\pi\) | ||||
−0.255083 | + | 0.966919i | \(0.582103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −52.1942 | −0.231974 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 280.285i | − | 0.969844i | −0.874557 | − | 0.484922i | \(-0.838848\pi\) | ||
0.874557 | − | 0.484922i | \(-0.161152\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.5926i | 0.0348825i | 0.999848 | + | 0.0174412i | \(0.00555200\pi\) | ||||
−0.999848 | + | 0.0174412i | \(0.994448\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 416.050i | − | 0.943423i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −184.641 | −0.349037 | −0.174519 | − | 0.984654i | \(-0.555837\pi\) | ||||
−0.174519 | + | 0.984654i | \(0.555837\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −606.870 | −0.970991 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 143.933 | 0.197440 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1039.58i | − | 1.23613i | −0.786128 | − | 0.618063i | \(-0.787918\pi\) | ||
0.786128 | − | 0.618063i | \(-0.212082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1492.51 | −1.55308 | −0.776542 | − | 0.630066i | \(-0.783028\pi\) | ||||
−0.776542 | + | 0.630066i | \(0.783028\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1128.12 | + | 962.944i | −1.03593 | + | 0.884246i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 144.520i | 0.117976i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1400.64 | −1.02311 | −0.511554 | − | 0.859251i | \(-0.670930\pi\) | ||||
−0.511554 | + | 0.859251i | \(0.670930\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4006.14i | − | 2.63388i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2563.10i | − | 1.52475i | −0.647138 | − | 0.762373i | \(-0.724034\pi\) | ||
0.647138 | − | 0.762373i | \(-0.275966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 870.960i | − | 0.471044i | −0.971869 | − | 0.235522i | \(-0.924320\pi\) | ||
0.971869 | − | 0.235522i | \(-0.0756799\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 294.899 | 0.145629 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3021.08 | −1.36763 | −0.683813 | − | 0.729658i | \(-0.739679\pi\) | ||||
−0.683813 | + | 0.729658i | \(0.739679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1249.00 | 0.520200 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3435.73i | 1.32093i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −260.724 | −0.0928173 | −0.0464087 | − | 0.998923i | \(-0.514778\pi\) | ||||
−0.0464087 | + | 0.998923i | \(0.514778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 391.870 | − | 334.492i | 0.129544 | − | 0.110576i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 154.359i | − | 0.0475098i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −293.024 | −0.0841780 | −0.0420890 | − | 0.999114i | \(-0.513401\pi\) | ||||
−0.0420890 | + | 0.999114i | \(0.513401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3593.92i | 0.965849i | 0.875662 | + | 0.482924i | \(0.160425\pi\) | ||||
−0.875662 | + | 0.482924i | \(0.839575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2350.69i | 0.592263i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1391.59i | 0.329370i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2359.87 | 0.525701 | 0.262850 | − | 0.964837i | \(-0.415337\pi\) | ||||
0.262850 | + | 0.964837i | \(0.415337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2263.32 | 0.475388 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2494.04 | 0.494751 | 0.247375 | − | 0.968920i | \(-0.420432\pi\) | ||||
0.247375 | + | 0.968920i | \(0.420432\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4481.31i | − | 0.840929i | −0.907309 | − | 0.420465i | \(-0.861867\pi\) | ||
0.907309 | − | 0.420465i | \(-0.138133\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7438.99 | 1.32249 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2666.30 | + | 3123.67i | 0.449704 | + | 0.526845i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9693.98i | − | 1.55327i | −0.629949 | − | 0.776637i | \(-0.716924\pi\) | ||
0.629949 | − | 0.776637i | \(-0.283076\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7374.23 | −1.12395 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6237.99i | 0.905500i | 0.891638 | + | 0.452750i | \(0.149557\pi\) | ||||
−0.891638 | + | 0.452750i | \(0.850443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1193.45i | − | 0.165183i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12743.2i | 1.68360i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9516.72 | −1.20145 | −0.600727 | − | 0.799454i | \(-0.705122\pi\) | ||||
−0.600727 | + | 0.799454i | \(0.705122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11092.6 | −1.33952 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18295.2 | 2.11530 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 53.6188i | 0.00594115i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6401.66 | 0.680376 | 0.340188 | − | 0.940357i | \(-0.389509\pi\) | ||||
0.340188 | + | 0.940357i | \(0.389509\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6373.94 | − | 5440.67i | 0.650336 | − | 0.555113i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.9343i | − | 0.00156203i | −1.00000 | 0.000781015i | \(-0.999751\pi\) | |||
1.00000 | 0.000781015i | \(-0.000248605\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12891.5 | −1.21514 | −0.607572 | − | 0.794265i | \(-0.707856\pi\) | ||||
−0.607572 | + | 0.794265i | \(0.707856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1771.53i | − | 0.160683i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10805.9i | − | 0.943827i | −0.881645 | − | 0.471913i | \(-0.843564\pi\) | ||
0.881645 | − | 0.471913i | \(-0.156436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8470.43i | 0.712939i | 0.934307 | + | 0.356470i | \(0.116020\pi\) | ||||
−0.934307 | + | 0.356470i | \(0.883980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17169.0 | 1.39347 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1009.87 | −0.0790874 | −0.0395437 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395437 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −786.196 | −0.0594477 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22634.8i | 1.65350i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9513.19 | 0.671788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2298.74 | − | 14459.4i | 0.157007 | − | 0.987597i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31418.4i | 2.07670i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5245.27 | −0.335697 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7859.09i | 0.487264i | 0.969868 | + | 0.243632i | \(0.0783390\pi\) | ||||
−0.969868 | + | 0.243632i | \(0.921661\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10676.2i | 0.641560i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 24418.3i | − | 1.42290i | −0.702738 | − | 0.711448i | \(-0.748040\pi\) | ||
0.702738 | − | 0.711448i | \(-0.251960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −427.406 | −0.0241622 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 612.865 | 0.0336277 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2895.91 | −0.154292 | −0.0771462 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771462 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14602.9i | − | 0.755807i | −0.925845 | − | 0.377903i | \(-0.876645\pi\) | ||
0.925845 | − | 0.377903i | \(-0.123355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37032.4 | 1.86270 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25673.7 | + | 30077.7i | 1.25550 | + | 1.47087i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4426.52i | − | 0.210536i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15310.2 | −0.708511 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9469.08i | − | 0.426516i | −0.976996 | − | 0.213258i | \(-0.931593\pi\) | ||
0.976996 | − | 0.213258i | \(-0.0684075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15335.9i | 0.672597i | 0.941755 | + | 0.336298i | \(0.109175\pi\) | ||||
−0.941755 | + | 0.336298i | \(0.890825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 19412.0i | − | 0.829253i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6355.09 | −0.264520 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4810.17 | −0.195147 | −0.0975733 | − | 0.995228i | \(-0.531108\pi\) | ||||
−0.0975733 | + | 0.995228i | \(0.531108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3195.95 | 0.126417 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6266.92i | − | 0.241770i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9875.98 | 0.371711 | 0.185855 | − | 0.982577i | \(-0.440494\pi\) | ||||
0.185855 | + | 0.982577i | \(0.440494\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4803.53 | + | 4100.19i | −0.176438 | + | 0.150604i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 13437.3i | − | 0.481812i | −0.970548 | − | 0.240906i | \(-0.922555\pi\) | ||
0.970548 | − | 0.240906i | \(-0.0774445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −78249.5 | −2.73973 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 872.136i | 0.0298258i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 37664.1i | 1.25845i | 0.777223 | + | 0.629225i | \(0.216627\pi\) | ||||
−0.777223 | + | 0.629225i | \(0.783373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 20597.8i | − | 0.672582i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3591.88 | 0.114650 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −53941.3 | −1.68351 | −0.841755 | − | 0.539860i | \(-0.818477\pi\) | ||||
−0.841755 | + | 0.539860i | \(0.818477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23379.6 | 0.713642 | 0.356821 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356821 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 44054.2i | − | 1.31548i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5963.87 | −0.174255 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22018.2 | − | 25795.2i | −0.629650 | − | 0.737658i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4885.26i | 0.136762i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −46611.4 | −1.27769 | −0.638844 | − | 0.769336i | \(-0.720587\pi\) | ||||
−0.638844 | + | 0.769336i | \(0.720587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 57585.6i | − | 1.54596i | −0.634428 | − | 0.772982i | \(-0.718764\pi\) | ||
0.634428 | − | 0.772982i | \(-0.281236\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 17058.0i | − | 0.448600i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 39775.2i | − | 1.02490i | −0.858718 | − | 0.512448i | \(-0.828739\pi\) | ||
0.858718 | − | 0.512448i | \(-0.171261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18905.2 | −0.477393 | −0.238697 | − | 0.971094i | \(-0.576720\pi\) | ||||
−0.238697 | + | 0.971094i | \(0.576720\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28927.2 | −0.716003 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 35284.6 | 0.856235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 10913.6i | − | 0.259693i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12787.8 | −0.298440 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 989.228 | + | 1158.92i | 0.0226466 | + | 0.0265314i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 30974.3i | − | 0.695723i | −0.937546 | − | 0.347862i | \(-0.886908\pi\) | ||
0.937546 | − | 0.347862i | \(-0.113092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −30571.9 | −0.673849 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3708.52i | − | 0.0802277i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 50657.6i | − | 1.07578i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 54931.8i | 1.14534i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 91602.4 | 1.87552 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19890.6 | 0.399980 | 0.199990 | − | 0.979798i | \(-0.435909\pi\) | ||||
0.199990 | + | 0.979798i | \(0.435909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −42030.6 | −0.830233 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 76528.9i | 1.48516i | 0.669757 | + | 0.742581i | \(0.266398\pi\) | ||||
−0.669757 | + | 0.742581i | \(0.733602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −56079.9 | −1.06939 | −0.534695 | − | 0.845045i | \(-0.679574\pi\) | ||||
−0.534695 | + | 0.845045i | \(0.679574\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32683.4 | − | 38289.8i | −0.612496 | − | 0.717562i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3353.39i | − | 0.0617693i | −0.999523 | − | 0.0308847i | \(-0.990168\pi\) | ||
0.999523 | − | 0.0308847i | \(-0.00983246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12863.7 | −0.232933 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 118829.i | 2.11555i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8629.71i | 0.151078i | 0.997143 | + | 0.0755388i | \(0.0240677\pi\) | ||||
−0.997143 | + | 0.0755388i | \(0.975932\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101396.i | 1.74577i | 0.487924 | + | 0.872886i | \(0.337754\pi\) | ||||
−0.487924 | + | 0.872886i | \(0.662246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 78734.5 | 1.33338 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5318.21 | 0.0886000 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4115.49 | −0.0674570 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 76465.1i | − | 1.23329i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 81244.8 | 1.28958 | 0.644790 | − | 0.764360i | \(-0.276945\pi\) | ||||
0.644790 | + | 0.764360i | \(0.276945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16992.8 | + | 14504.7i | −0.265476 | + | 0.226605i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14629.2i | 0.224979i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 56962.9 | 0.862434 | 0.431217 | − | 0.902248i | \(-0.358084\pi\) | ||||
0.431217 | + | 0.902248i | \(0.358084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 47539.1i | − | 0.708683i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 71999.4i | − | 1.05693i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6000.71i | − | 0.0867543i | −0.999059 | − | 0.0433772i | \(-0.986188\pi\) | ||
0.999059 | − | 0.0433772i | \(-0.0138117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1110.16 | −0.0158086 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 116656. | 1.63638 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24832.0 | 0.343169 | 0.171584 | − | 0.985169i | \(-0.445111\pi\) | ||||
0.171584 | + | 0.985169i | \(0.445111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 65976.9i | 0.898367i | 0.893440 | + | 0.449183i | \(0.148285\pi\) | ||||
−0.893440 | + | 0.449183i | \(0.851715\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 135973. | 1.82443 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −55851.4 | + | 47673.6i | −0.738530 | + | 0.630394i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 31675.1i | − | 0.412818i | −0.978466 | − | 0.206409i | \(-0.933822\pi\) | ||
0.978466 | − | 0.206409i | \(-0.0661778\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −103368. | −1.32794 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 130542.i | 1.65325i | 0.562753 | + | 0.826625i | \(0.309742\pi\) | ||||
−0.562753 | + | 0.826625i | \(0.690258\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 77156.4i | 0.963384i | 0.876341 | + | 0.481692i | \(0.159978\pi\) | ||||
−0.876341 | + | 0.481692i | \(0.840022\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 657.258i | − | 0.00809182i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 86994.4 | 1.05615 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4961.32 | 0.0594020 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −78471.4 | −0.926671 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 73563.5i | 0.856894i | 0.903567 | + | 0.428447i | \(0.140939\pi\) | ||||
−0.903567 | + | 0.428447i | \(0.859061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1247.69 | −0.0143371 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13246.5 | − | 11306.9i | 0.150171 | − | 0.128183i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 60344.1i | − | 0.674982i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29561.3 | 0.326281 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 195.322i | 0.00212748i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15302.8i | 0.164502i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14140.6i | 0.150034i | 0.997182 | + | 0.0750171i | \(0.0239011\pi\) | ||||
−0.997182 | + | 0.0750171i | \(0.976099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 158023. | 1.65502 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 115950. | 1.19881 | 0.599406 | − | 0.800445i | \(-0.295404\pi\) | ||||
0.599406 | + | 0.800445i | \(0.295404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −167682. | −1.71159 | −0.855793 | − | 0.517318i | \(-0.826930\pi\) | ||||
−0.855793 | + | 0.517318i | \(0.826930\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10009.2i | 0.100874i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −43569.8 | −0.433577 | −0.216789 | − | 0.976219i | \(-0.569558\pi\) | ||||
−0.216789 | + | 0.976219i | \(0.569558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −81666.0 | − | 95674.7i | −0.802527 | − | 0.940191i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 132458.i | 1.28549i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3529.51 | 0.0338305 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 198336.i | − | 1.87774i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 103830.i | − | 0.971021i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 102539.i | − | 0.947321i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13167.8 | 0.120187 | 0.0600934 | − | 0.998193i | \(-0.480860\pi\) | ||||
0.0600934 | + | 0.998193i | \(0.480860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −97005.2 | −0.874795 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10048.3 | 0.0895368 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 41741.2i | 0.367540i | 0.982969 | + | 0.183770i | \(0.0588302\pi\) | ||||
−0.982969 | + | 0.183770i | \(0.941170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12378.9 | 0.107717 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −137359. | + | 117247.i | −1.18127 | + | 1.00830i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 123885.i | 1.05301i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9637.17 | 0.0809676 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8110.63i | − | 0.0673590i | −0.999433 | − | 0.0336795i | \(-0.989277\pi\) | ||
0.999433 | − | 0.0336795i | \(-0.0107225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16786.2i | − | 0.137817i | −0.997623 | − | 0.0689083i | \(-0.978048\pi\) | ||
0.997623 | − | 0.0689083i | \(-0.0219516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 47040.1i | 0.381816i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 116711. | 0.936618 | 0.468309 | − | 0.883565i | \(-0.344863\pi\) | ||||
0.468309 | + | 0.883565i | \(0.344863\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10619.6 | 0.0842655 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −116612. | −0.914973 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35393.9i | 0.274625i | 0.990528 | + | 0.137312i | \(0.0438464\pi\) | ||||
−0.990528 | + | 0.137312i | \(0.956154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130162. | 0.998783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28177.9 | + | 177243.i | −0.213843 | + | 1.34511i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 19081.3i | − | 0.143226i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 91892.5 | 0.682257 | 0.341128 | − | 0.940017i | \(-0.389191\pi\) | ||||
0.341128 | + | 0.940017i | \(0.389191\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 177515.i | − | 1.30371i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8849.26i | − | 0.0642923i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35452.4i | 0.254817i | 0.991850 | + | 0.127408i | \(0.0406659\pi\) | ||||
−0.991850 | + | 0.127408i | \(0.959334\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 64296.4 | 0.457219 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 339755. | 2.39047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −217027. | −1.51090 | −0.755449 | − | 0.655207i | \(-0.772581\pi\) | ||||
−0.755449 | + | 0.655207i | \(0.772581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 96336.5i | − | 0.663653i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 199025. | 1.35678 | 0.678390 | − | 0.734702i | \(-0.262678\pi\) | ||||
0.678390 | + | 0.734702i | \(0.262678\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11353.0 | + | 13300.5i | 0.0765932 | + | 0.0897318i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 60320.9i | − | 0.402760i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −141391. | −0.934380 | −0.467190 | − | 0.884157i | \(-0.654734\pi\) | ||||
−0.467190 | + | 0.884157i | \(0.654734\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51752.1i | 0.338512i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 299319.i | 1.93798i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 41276.7i | − | 0.264552i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 109000. | 0.691585 | 0.345793 | − | 0.938311i | \(-0.387610\pi\) | ||||
0.345793 | + | 0.938311i | \(0.387610\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5239.13 | 0.0329089 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −262604. | −1.63310 | −0.816549 | − | 0.577277i | \(-0.804115\pi\) | ||||
−0.816549 | + | 0.577277i | \(0.804115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 487781.i | − | 3.00341i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31399.3 | −0.191430 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −128903. | + | 110029.i | −0.778170 | + | 0.664230i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 132695.i | − | 0.793244i | −0.917982 | − | 0.396622i | \(-0.870182\pi\) | ||
0.917982 | − | 0.396622i | \(-0.129818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35498.0 | 0.210146 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9945.55i | − | 0.0583081i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26561.2i | 0.154224i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 179003.i | 1.02941i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −54888.5 | −0.312646 | −0.156323 | − | 0.987706i | \(-0.549964\pi\) | ||||
−0.156323 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20412.0 | 0.115165 | 0.0575826 | − | 0.998341i | \(-0.481661\pi\) | ||||
0.0575826 | + | 0.998341i | \(0.481661\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −209234. | −1.16937 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 170096.i | 0.941710i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −121982. | −0.669020 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −314708. | − | 368692.i | −1.70999 | − | 2.00332i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 157298.i | 0.846776i | 0.905949 | + | 0.423388i | \(0.139159\pi\) | ||||
−0.905949 | + | 0.423388i | \(0.860841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −134223. | −0.715900 | −0.357950 | − | 0.933741i | \(-0.616524\pi\) | ||||
−0.357950 | + | 0.933741i | \(0.616524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 54260.1i | 0.286749i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2325.10i | − | 0.0121753i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 304612.i | − | 1.58059i | −0.612729 | − | 0.790293i | \(-0.709928\pi\) | ||
0.612729 | − | 0.790293i | \(-0.290072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 86503.2 | 0.444790 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 116115. | 0.591671 | 0.295835 | − | 0.955239i | \(-0.404402\pi\) | ||||
0.295835 | + | 0.955239i | \(0.404402\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40522.0 | −0.204631 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 116072.i | 0.580913i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 156051. | 0.774059 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −201348. | − | 235887.i | −0.989906 | − | 1.15971i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 187987.i | − | 0.916075i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −47232.0 | −0.228146 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 154609.i | 0.740290i | 0.928974 | + | 0.370145i | \(0.120692\pi\) | ||||
−0.928974 | + | 0.370145i | \(0.879308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 40342.4i | − | 0.191486i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 324927.i | − | 1.52892i | −0.644674 | − | 0.764458i | \(-0.723007\pi\) | ||
0.644674 | − | 0.764458i | \(-0.276993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 135116. | 0.630295 | 0.315147 | − | 0.949043i | \(-0.397946\pi\) | ||||
0.315147 | + | 0.949043i | \(0.397946\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 77900.5 | 0.360275 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −217618. | −0.997840 | −0.498920 | − | 0.866648i | \(-0.666270\pi\) | ||||
−0.498920 | + | 0.866648i | \(0.666270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 80096.6i | 0.364140i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 58962.9 | 0.265789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −68419.6 | − | 80156.1i | −0.305814 | − | 0.358273i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7642.05i | − | 0.0338706i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18057.2 | −0.0793622 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2332.66i | − | 0.0101667i | −0.999987 | − | 0.00508335i | \(-0.998382\pi\) | ||
0.999987 | − | 0.00508335i | \(-0.00161809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 457754.i | − | 1.97853i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 76819.7i | 0.329290i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27258.1 | 0.115881 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −307695. | −1.29737 | −0.648683 | − | 0.761059i | \(-0.724680\pi\) | ||||
−0.648683 | + | 0.761059i | \(0.724680\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −121060. | −0.506269 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 165203.i | 0.685258i | 0.939471 | + | 0.342629i | \(0.111317\pi\) | ||||
−0.939471 | + | 0.342629i | \(0.888683\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −291379. | −1.19885 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27140.1 | − | 23166.2i | 0.110765 | − | 0.0945464i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 84650.5i | 0.342702i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −271209. | −1.08919 | −0.544594 | − | 0.838700i | \(-0.683316\pi\) | ||||
−0.544594 | + | 0.838700i | \(0.683316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 164713.i | 0.656226i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 242593.i | − | 0.958831i | −0.877588 | − | 0.479415i | \(-0.840849\pi\) | ||
0.877588 | − | 0.479415i | \(-0.159151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 67.8477i | − | 0.000266043i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 959180. | 3.73151 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −231272. | −0.892663 | −0.446331 | − | 0.894868i | \(-0.647270\pi\) | ||||
−0.446331 | + | 0.894868i | \(0.647270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 152101. | 0.582491 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1812.49i | 0.00688718i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −54891.6 | −0.206962 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −278036. | + | 237326.i | −1.04021 | + | 0.887900i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 461686.i | − | 1.71400i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19525.5 | −0.0719327 | −0.0359664 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359664 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 493543.i | 1.80435i | 0.431366 | + | 0.902177i | \(0.358032\pi\) | ||||
−0.431366 | + | 0.902177i | \(0.641968\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 252488.i | 0.916056i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 418329.i | 1.50625i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −245749. | −0.878173 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20294.2 | −0.0719753 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 837668. | 2.94861 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 46011.1i | − | 0.160752i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 661211. | 2.29293 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 114948. | − | 98117.1i | 0.395661 | − | 0.337728i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 211511.i | 0.722669i | 0.932436 | + | 0.361334i | \(0.117679\pi\) | ||||
−0.932436 | + | 0.361334i | \(0.882321\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −286587. | −0.971978 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36066.9i | 0.121427i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 271731.i | 0.908163i | 0.890960 | + | 0.454082i | \(0.150033\pi\) | ||||
−0.890960 | + | 0.454082i | \(0.849967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 248908.i | 0.825836i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13091.0 | 0.0431191 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 329025. | 1.07592 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 73105.0 | 0.237335 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 420797.i | − | 1.35632i | −0.734914 | − | 0.678160i | \(-0.762777\pi\) | ||
0.734914 | − | 0.678160i | \(-0.237223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 284646. | 0.910922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 269899. | + | 316196.i | 0.857581 | + | 1.00469i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 199781.i | 0.630285i | 0.949044 | + | 0.315142i | \(0.102052\pi\) | ||||
−0.949044 | + | 0.315142i | \(0.897948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4299.99 | −0.0134701 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 250290.i | − | 0.778532i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 393771.i | 1.21624i | 0.793845 | + | 0.608120i | \(0.208076\pi\) | ||||
−0.793845 | + | 0.608120i | \(0.791924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 152076.i | − | 0.466431i | −0.972425 | − | 0.233215i | \(-0.925075\pi\) | ||
0.972425 | − | 0.233215i | \(-0.0749247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 571361. | 1.74021 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 112053. | 0.338912 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −260379. | −0.782086 | −0.391043 | − | 0.920372i | \(-0.627886\pi\) | ||||
−0.391043 | + | 0.920372i | \(0.627886\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 705883.i | 2.10560i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −211724. | −0.627218 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23994.9 | + | 20481.6i | −0.0705963 | + | 0.0602596i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 96378.4i | 0.281623i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 197623. | 0.573538 | 0.286769 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286769 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 18794.6i | − | 0.0541754i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 487563.i | 1.39590i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 103667.i | − | 0.294803i | −0.989077 | − | 0.147401i | \(-0.952909\pi\) | ||
0.989077 | − | 0.147401i | \(-0.0470909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40506.9 | 0.114418 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 231740. | 0.650208 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −204660. | −0.570399 | −0.285199 | − | 0.958468i | \(-0.592060\pi\) | ||||
−0.285199 | + | 0.958468i | \(0.592060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 140115.i | − | 0.387913i | −0.981010 | − | 0.193957i | \(-0.937868\pi\) | ||
0.981010 | − | 0.193957i | \(-0.0621321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 163440. | 0.449493 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9787.99 | − | 61567.8i | 0.0267413 | − | 0.168207i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 69648.7i | − | 0.189032i | −0.995523 | − | 0.0945160i | \(-0.969870\pi\) | ||
0.995523 | − | 0.0945160i | \(-0.0301304\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −432518. | −1.16619 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 987347.i | − | 2.64477i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 619709.i | − | 1.64917i | −0.565735 | − | 0.824587i | \(-0.691407\pi\) | ||
0.565735 | − | 0.824587i | \(-0.308593\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 133779.i | 0.353701i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −284417. | −0.747112 | −0.373556 | − | 0.927608i | \(-0.621862\pi\) | ||||
−0.373556 | + | 0.927608i | \(0.621862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 231315. | 0.603702 | 0.301851 | − | 0.953355i | \(-0.402395\pi\) | ||||
0.301851 | + | 0.953355i | \(0.402395\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26576.0 | −0.0689138 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 323008.i | − | 0.832219i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 356959. | 0.913816 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12125.9 | − | 14206.0i | −0.0308447 | − | 0.0361357i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 392577.i | 0.992256i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −311488. | −0.782316 | −0.391158 | − | 0.920324i | \(-0.627925\pi\) | ||||
−0.391158 | + | 0.920324i | \(0.627925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 379682.i | 0.947573i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33463.8i | 0.0829904i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 408197.i | 1.00598i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 172732. | 0.423030 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −297618. | −0.724341 | −0.362170 | − | 0.932112i | \(-0.617964\pi\) | ||||
−0.362170 | + | 0.932112i | \(0.617964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 121820. | 0.294645 | 0.147322 | − | 0.989089i | \(-0.452935\pi\) | ||||
0.147322 | + | 0.989089i | \(0.452935\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 45459.0i | 0.109270i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 377550. | 0.901917 | 0.450958 | − | 0.892545i | \(-0.351082\pi\) | ||||
0.450958 | + | 0.892545i | \(0.351082\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26967.5 | + | 23018.9i | −0.0640253 | + | 0.0546507i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 620959.i | 1.46521i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −558170. | −1.30900 | −0.654501 | − | 0.756061i | \(-0.727121\pi\) | ||||
−0.654501 | + | 0.756061i | \(0.727121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 103973.i | − | 0.242346i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 310367.i | − | 0.719025i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 357653.i | − | 0.823551i | −0.911285 | − | 0.411776i | \(-0.864909\pi\) | ||
0.911285 | − | 0.411776i | \(-0.135091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 290959. | 0.665931 | 0.332965 | − | 0.942939i | \(-0.391951\pi\) | ||||
0.332965 | + | 0.942939i | \(0.391951\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.12286e6 | −2.55446 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1819.88 | −0.00411529 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 191949.i | 0.431454i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −243818. | −0.544771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 282326. | + | 330756.i | 0.627056 | + | 0.734619i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 465570.i | − | 1.02791i | −0.857817 | − | 0.513955i | \(-0.828180\pi\) | ||
0.857817 | − | 0.513955i | \(-0.171820\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −87348.8 | −0.191712 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 361627.i | − | 0.789012i | −0.918893 | − | 0.394506i | \(-0.870916\pi\) | ||
0.918893 | − | 0.394506i | \(-0.129084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 217280.i | 0.471280i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 938089.i | − | 2.02279i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −673707. | −1.44421 | −0.722103 | − | 0.691785i | \(-0.756825\pi\) | ||||
−0.722103 | + | 0.691785i | \(0.756825\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12330.7 | −0.0262789 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 687426. | 1.45651 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 85209.4i | − | 0.179494i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −66171.2 | −0.138584 | −0.0692920 | − | 0.997596i | \(-0.522074\pi\) | ||||
−0.0692920 | + | 0.997596i | \(0.522074\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 184662. | + | 216339.i | 0.384514 | + | 0.450472i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 62179.0i | − | 0.128728i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −718397. | −1.47877 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41105.8i | 0.0841297i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 439863.i | 0.895121i | 0.894254 | + | 0.447560i | \(0.147707\pi\) | ||||
−0.894254 | + | 0.447560i | \(0.852293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 17637.6i | − | 0.0356885i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 157683. | 0.317254 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 540.827 | 0.00108198 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 511529. | 1.01760 | 0.508801 | − | 0.860884i | \(-0.330089\pi\) | ||||
0.508801 | + | 0.860884i | \(0.330089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 671386.i | − | 1.32811i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 275579. | 0.542084 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 109318. | + | 128070.i | 0.213836 | + | 0.250517i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 105783.i | − | 0.205767i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −683729. | −1.32259 | −0.661297 | − | 0.750124i | \(-0.729994\pi\) | ||||
−0.661297 | + | 0.750124i | \(0.729994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 437551.i | − | 0.841701i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1.24291e6i | − | 2.37774i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 630891.i | 1.20027i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −258952. | −0.489949 | −0.244974 | − | 0.969530i | \(-0.578780\pi\) | ||||
−0.244974 | + | 0.969530i | \(0.578780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −367813. | −0.692105 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −244117. | −0.456839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 474044.i | 0.882288i | 0.897436 | + | 0.441144i | \(0.145427\pi\) | ||||
−0.897436 | + | 0.441144i | \(0.854573\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −65190.5 | −0.120673 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 217183. | − | 185383.i | 0.399845 | − | 0.341299i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 758640.i | − | 1.38914i | −0.719424 | − | 0.694571i | \(-0.755594\pi\) | ||
0.719424 | − | 0.694571i | \(-0.244406\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50447.5 | 0.0918763 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 579823.i | 1.05031i | 0.851006 | + | 0.525156i | \(0.175993\pi\) | ||||
−0.851006 | + | 0.525156i | \(0.824007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 40319.1i | − | 0.0726438i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 432030.i | 0.774236i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 366763. | 0.653766 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 844322. | 1.49702 | 0.748511 | − | 0.663122i | \(-0.230769\pi\) | ||||
0.748511 | + | 0.663122i | \(0.230769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −995897. | −1.75640 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 65299.8i | 0.114556i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 801567. | 1.39877 | 0.699387 | − | 0.714743i | \(-0.253456\pi\) | ||||
0.699387 | + | 0.714743i | \(0.253456\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 208298. | − | 177799.i | 0.361577 | − | 0.308635i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6823.03i | 0.0117817i | 0.999983 | + | 0.00589085i | \(0.00187513\pi\) | ||||
−0.999983 | + | 0.00589085i | \(0.998125\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −287496. | −0.493836 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 82655.7i | − | 0.141237i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 95765.6i | − | 0.162787i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 375862.i | 0.635588i | 0.948160 | + | 0.317794i | \(0.102942\pi\) | ||||
−0.948160 | + | 0.317794i | \(0.897058\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −698250. | −1.17463 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −857421. | −1.43494 | −0.717472 | − | 0.696587i | \(-0.754701\pi\) | ||||
−0.717472 | + | 0.696587i | \(0.754701\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 905761. | 1.50803 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 582734.i | 0.965224i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32276.0 | 0.0531868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 229531. | − | 195923.i | 0.376305 | − | 0.321206i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 149631.i | − | 0.244060i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20481.6 | −0.0332372 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.02294e6i | 1.65158i | 0.563976 | + | 0.825791i | \(0.309271\pi\) | ||||
−0.563976 | + | 0.825791i | \(0.690729\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 73556.6i | 0.118159i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 34276.0i | − | 0.0547820i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.17456e6 | −1.86780 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13608.3 | 0.0215312 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 865636. | 1.36276 | 0.681379 | − | 0.731931i | \(-0.261381\pi\) | ||||
0.681379 | + | 0.731931i | \(0.261381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 846765.i | 1.32638i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −659109. | −1.02729 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −352036. | − | 412424.i | −0.545954 | − | 0.639606i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 26684.4i | − | 0.0411780i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −304390. | −0.467395 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 886947.i | − | 1.35519i | −0.735435 | − | 0.677596i | \(-0.763022\pi\) | ||
0.735435 | − | 0.677596i | \(-0.236978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 608105.i | − | 0.924563i | −0.886733 | − | 0.462282i | \(-0.847031\pi\) | ||
0.886733 | − | 0.462282i | \(-0.152969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 808744.i | − | 1.22357i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42051.7 | 0.0633094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10967.6 | 0.0164312 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −768251. | −1.14534 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 102607.i | − | 0.152227i | −0.997099 | − | 0.0761133i | \(-0.975749\pi\) | ||
0.997099 | − | 0.0761133i | \(-0.0242511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −338801. | −0.500202 | −0.250101 | − | 0.968220i | \(-0.580464\pi\) | ||||
−0.250101 | + | 0.968220i | \(0.580464\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 684625. | − | 584382.i | 1.00588 | − | 0.858595i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 303788.i | 0.444181i | 0.975026 | + | 0.222090i | \(0.0712880\pi\) | ||||
−0.975026 | + | 0.222090i | \(0.928712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 923889. | 1.34435 | 0.672173 | − | 0.740394i | \(-0.265361\pi\) | ||||
0.672173 | + | 0.740394i | \(0.265361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 388273.i | 0.562258i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 350076.i | − | 0.504513i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 57215.5i | − | 0.0820617i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −214823. | −0.306640 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44067.7 | 0.0626032 | 0.0313016 | − | 0.999510i | \(-0.490035\pi\) | ||||
0.0313016 | + | 0.999510i | \(0.490035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −373450. | −0.528009 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.60018e6i | − | 2.25172i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −333184. | −0.466628 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 490769. | + | 78021.9i | 0.684085 | + | 0.108755i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 945782.i | − | 1.31213i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 258614. | 0.357103 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.02952e6i | 1.41494i | 0.706746 | + | 0.707468i | \(0.250163\pi\) | ||||
−0.706746 | + | 0.707468i | \(0.749837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3713.53i | 0.00507990i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 571557.i | 0.778212i | 0.921193 | + | 0.389106i | \(0.127216\pi\) | ||||
−0.921193 | + | 0.389106i | \(0.872784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 479749. | 0.650172 | 0.325086 | − | 0.945685i | \(-0.394607\pi\) | ||||
0.325086 | + | 0.945685i | \(0.394607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.06637e6 | −1.43848 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 220319. | 0.295822 | 0.147911 | − | 0.989001i | \(-0.452745\pi\) | ||||
0.147911 | + | 0.989001i | \(0.452745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 160373.i | 0.214338i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −60815.7 | −0.0809054 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −761526. | − | 892156.i | −1.00843 | − | 1.18141i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 771250.i | 1.01662i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 443366. | 0.581747 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 178030.i | − | 0.232530i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.23303e6i | 1.60315i | 0.597893 | + | 0.801576i | \(0.296005\pi\) | ||||
−0.597893 | + | 0.801576i | \(0.703995\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 901740.i | − | 1.16709i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 227150. | 0.292659 | 0.146329 | − | 0.989236i | \(-0.453254\pi\) | ||||
0.146329 | + | 0.989236i | \(0.453254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 136322. | 0.174842 | 0.0874210 | − | 0.996171i | \(-0.472137\pi\) | ||||
0.0874210 | + | 0.996171i | \(0.472137\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15294.1 | 0.0195271 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 852106.i | − | 1.08304i | −0.840686 | − | 0.541522i | \(-0.817848\pi\) | ||
0.840686 | − | 0.541522i | \(-0.182152\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −266746. | −0.337516 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −678664. | + | 579294.i | −0.854869 | + | 0.729699i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 38043.2i | − | 0.0477061i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −229681. | −0.286734 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 739696.i | 0.919324i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.55159e6i | 1.91981i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73077.0i | 0.0900183i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −362362. | −0.444393 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 99549.8 | 0.121547 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 945937. | 1.14987 | 0.574934 | − | 0.818200i | \(-0.305028\pi\) | ||||
0.574934 | + | 0.818200i | \(0.305028\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1103.57i | − | 0.00133559i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13013.5 | 0.0156803 | 0.00784017 | − | 0.999969i | \(-0.497504\pi\) | ||||
0.00784017 | + | 0.999969i | \(0.497504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 490035. | + | 574094.i | 0.587875 | + | 0.688718i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 187582.i | − | 0.224052i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 828786. | 0.985607 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 809716.i | − | 0.958742i | −0.877612 | − | 0.479371i | \(-0.840865\pi\) | ||
0.877612 | − | 0.479371i | \(-0.159135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 173335.i | − | 0.204346i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 815099.i | 0.956768i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 850003. | 0.993429 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −892837. | −1.03899 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 731171. | 0.847203 | 0.423601 | − | 0.905849i | \(-0.360766\pi\) | ||||
0.423601 | + | 0.905849i | \(0.360766\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15728.1i | 0.0181458i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.42131e6 | −1.63278 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −93753.0 | − | 109835.i | −0.107241 | − | 0.125637i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 637069.i | 0.725617i | 0.931864 | + | 0.362809i | \(0.118182\pi\) | ||||
−0.931864 | + | 0.362809i | \(0.881818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.05545e6 | 2.33118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 77429.7i | 0.0874437i | 0.999044 | + | 0.0437218i | \(0.0139215\pi\) | ||||
−0.999044 | + | 0.0437218i | \(0.986078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 473252.i | 0.532193i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20801.3i | 0.0232931i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −362138. | −0.403807 | −0.201904 | − | 0.979405i | \(-0.564713\pi\) | ||||
−0.201904 | + | 0.979405i | \(0.564713\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.46458e6 | 1.62622 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 534077. | 0.590531 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.11862e6i | − | 1.23168i | −0.787873 | − | 0.615838i | \(-0.788818\pi\) | ||
0.787873 | − | 0.615838i | \(-0.211182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −198470. | −0.217615 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.00106e6 | + | 1.17278e6i | 1.09304 | + | 1.28054i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 98290.6i | − | 0.106875i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.30407e6 | 1.41207 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 748393.i | − | 0.807006i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 245198.i | − | 0.263307i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 104836.i | 0.112113i | 0.998428 | + | 0.0560565i | \(0.0178527\pi\) | ||||
−0.998428 | + | 0.0560565i | \(0.982147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43264.6 | −0.0460771 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.63144e6 | 1.73034 | 0.865170 | − | 0.501478i | \(-0.167210\pi\) | ||||
0.865170 | + | 0.501478i | \(0.167210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 495640. | 0.523529 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.43120e6i | 2.55748i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4386.95 | 0.00459593 | 0.00229796 | − | 0.999997i | \(-0.499269\pi\) | ||||
0.00229796 | + | 0.999997i | \(0.499269\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −875842. | + | 747600.i | −0.913819 | + | 0.780017i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 586645.i | 0.609589i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −147531. | −0.152678 | −0.0763388 | − | 0.997082i | \(-0.524323\pi\) | ||||
−0.0763388 | + | 0.997082i | \(0.524323\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 169362.i | − | 0.174559i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.25692e6i | 1.29025i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 160815.i | 0.164412i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −373627. | −0.380444 | −0.190222 | − | 0.981741i | \(-0.560921\pi\) | ||||
−0.190222 | + | 0.981741i | \(0.560921\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −161410. | −0.163694 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −80498.1 | −0.0813092 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 71451.7i | − | 0.0718824i | −0.999354 | − | 0.0359412i | \(-0.988557\pi\) | ||
0.999354 | − | 0.0359412i | \(-0.0114429\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −201598. | −0.202002 |
(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 | 176.5.h.e.65.2 | 4 | ||
4.3 | odd | 2 | 22.5.b.a.21.2 | ✓ | 4 | ||
8.3 | odd | 2 | 704.5.h.i.65.1 | 4 | |||
8.5 | even | 2 | 704.5.h.j.65.4 | 4 | |||
11.10 | odd | 2 | inner | 176.5.h.e.65.1 | 4 | ||
12.11 | even | 2 | 198.5.d.a.109.3 | 4 | |||
20.3 | even | 4 | 550.5.c.a.549.4 | 8 | |||
20.7 | even | 4 | 550.5.c.a.549.5 | 8 | |||
20.19 | odd | 2 | 550.5.d.a.351.3 | 4 | |||
44.43 | even | 2 | 22.5.b.a.21.4 | yes | 4 | ||
88.21 | odd | 2 | 704.5.h.j.65.3 | 4 | |||
88.43 | even | 2 | 704.5.h.i.65.2 | 4 | |||
132.131 | odd | 2 | 198.5.d.a.109.1 | 4 | |||
220.43 | odd | 4 | 550.5.c.a.549.8 | 8 | |||
220.87 | odd | 4 | 550.5.c.a.549.1 | 8 | |||
220.219 | even | 2 | 550.5.d.a.351.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.b.a.21.2 | ✓ | 4 | 4.3 | odd | 2 | ||
22.5.b.a.21.4 | yes | 4 | 44.43 | even | 2 | ||
176.5.h.e.65.1 | 4 | 11.10 | odd | 2 | inner | ||
176.5.h.e.65.2 | 4 | 1.1 | even | 1 | trivial | ||
198.5.d.a.109.1 | 4 | 132.131 | odd | 2 | |||
198.5.d.a.109.3 | 4 | 12.11 | even | 2 | |||
550.5.c.a.549.1 | 8 | 220.87 | odd | 4 | |||
550.5.c.a.549.4 | 8 | 20.3 | even | 4 | |||
550.5.c.a.549.5 | 8 | 20.7 | even | 4 | |||
550.5.c.a.549.8 | 8 | 220.43 | odd | 4 | |||
550.5.d.a.351.1 | 4 | 220.219 | even | 2 | |||
550.5.d.a.351.3 | 4 | 20.19 | odd | 2 | |||
704.5.h.i.65.1 | 4 | 8.3 | odd | 2 | |||
704.5.h.i.65.2 | 4 | 88.43 | even | 2 | |||
704.5.h.j.65.3 | 4 | 88.21 | odd | 2 | |||
704.5.h.j.65.4 | 4 | 8.5 | even | 2 |