Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [704,5,Mod(65,704)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(704, 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("704.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 704.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: | \(72.7724540110\) |
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 | 65.3 | ||
Root | \(-11.2580 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 704.65 |
Dual form | 704.5.h.i.65.4 |
$q$-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 \(\left(\mathbb{Z}/704\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(321\) | \(639\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 11.2580 | 1.25089 | 0.625443 | − | 0.780270i | \(-0.284918\pi\) | ||||
0.625443 | + | 0.780270i | \(0.284918\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.2580 | 0.770319 | 0.385160 | − | 0.922850i | \(-0.374146\pi\) | ||||
0.385160 | + | 0.922850i | \(0.374146\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 33.9411i | − | 0.692676i | −0.938110 | − | 0.346338i | \(-0.887425\pi\) | ||
0.938110 | − | 0.346338i | \(-0.112575\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 45.7420 | 0.564716 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.03190 | + | 120.983i | −0.0167926 | + | 0.999859i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.2602i | 0.427575i | 0.976880 | + | 0.213788i | \(0.0685801\pi\) | ||||
−0.976880 | + | 0.213788i | \(0.931420\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 216.806 | 0.963581 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 517.873i | 1.79195i | 0.444107 | + | 0.895974i | \(0.353521\pi\) | ||||
−0.444107 | + | 0.895974i | \(0.646479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 411.672i | 1.14036i | 0.821518 | + | 0.570182i | \(0.193127\pi\) | ||||
−0.821518 | + | 0.570182i | \(0.806873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 382.108i | − | 0.866459i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −967.641 | −1.82919 | −0.914594 | − | 0.404373i | \(-0.867490\pi\) | ||||
−0.914594 | + | 0.404373i | \(0.867490\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −254.130 | −0.406609 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −396.933 | −0.544490 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 640.503i | 0.761597i | 0.924658 | + | 0.380799i | \(0.124351\pi\) | ||||
−0.924658 | + | 0.380799i | \(0.875649\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 716.487 | 0.745564 | 0.372782 | − | 0.927919i | \(-0.378404\pi\) | ||||
0.372782 | + | 0.927919i | \(0.378404\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −22.8751 | + | 1362.02i | −0.0210056 | + | 1.25071i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 653.637i | − | 0.533582i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1209.64 | −0.883590 | −0.441795 | − | 0.897116i | \(-0.645658\pi\) | ||||
−0.441795 | + | 0.897116i | \(0.645658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 813.504i | 0.534848i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 966.781i | − | 0.575122i | −0.957762 | − | 0.287561i | \(-0.907156\pi\) | ||
0.957762 | − | 0.287561i | \(-0.0928445\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2720.75i | 1.47147i | 0.677269 | + | 0.735736i | \(0.263163\pi\) | ||||
−0.677269 | + | 0.735736i | \(0.736837\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 880.899 | 0.435012 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −177.085 | −0.0801651 | −0.0400826 | − | 0.999196i | \(-0.512762\pi\) | ||||
−0.0400826 | + | 0.999196i | \(0.512762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1249.00 | 0.520200 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5830.20i | 2.24152i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4023.28 | 1.43228 | 0.716140 | − | 0.697956i | \(-0.245907\pi\) | ||||
0.716140 | + | 0.697956i | \(0.245907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −39.1304 | + | 2329.89i | −0.0129357 | + | 0.770210i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4634.59i | 1.42647i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1988.02 | 0.571107 | 0.285554 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285554 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2396.69i | − | 0.644097i | −0.946723 | − | 0.322049i | \(-0.895629\pi\) | ||
0.946723 | − | 0.322049i | \(-0.104371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1552.54i | − | 0.391165i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1391.59i | 0.329370i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2007.13 | 0.447122 | 0.223561 | − | 0.974690i | \(-0.428232\pi\) | ||||
0.223561 | + | 0.974690i | \(0.428232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10893.7 | −2.28811 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4255.04 | 0.844086 | 0.422043 | − | 0.906576i | \(-0.361313\pi\) | ||||
0.422043 | + | 0.906576i | \(0.361313\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1288.68i | − | 0.241824i | −0.992663 | − | 0.120912i | \(-0.961418\pi\) | ||
0.992663 | − | 0.120912i | \(-0.0385819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2860.99 | −0.508621 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4106.30 | + | 68.9651i | 0.692578 | + | 0.0116318i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1480.23i | − | 0.237178i | −0.992943 | − | 0.118589i | \(-0.962163\pi\) | ||
0.992943 | − | 0.118589i | \(-0.0378371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8173.77 | −1.24581 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10124.2i | − | 1.46963i | −0.678270 | − | 0.734813i | \(-0.737270\pi\) | ||
0.678270 | − | 0.734813i | \(-0.262730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9973.18i | 1.38037i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7210.77i | 0.952672i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5133.72 | 0.648115 | 0.324058 | − | 0.946037i | \(-0.394953\pi\) | ||||
0.324058 | + | 0.946037i | \(0.394953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2452.59 | 0.296171 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8066.19 | 0.932615 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7927.96i | 0.878444i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2239.34 | 0.238000 | 0.119000 | − | 0.992894i | \(-0.462031\pi\) | ||||
0.119000 | + | 0.992894i | \(0.462031\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −92.9434 | + | 5534.00i | −0.00948305 | + | 0.564637i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15580.0i | 1.52730i | 0.645629 | + | 0.763651i | \(0.276595\pi\) | ||||
−0.645629 | + | 0.763651i | \(0.723405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9119.47 | −0.859597 | −0.429799 | − | 0.902925i | \(-0.641415\pi\) | ||||
−0.429799 | + | 0.902925i | \(0.641415\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 7358.63i | − | 0.667450i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11204.9i | − | 0.978684i | −0.872092 | − | 0.489342i | \(-0.837237\pi\) | ||
0.872092 | − | 0.489342i | \(-0.162763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10286.3i | 0.865776i | 0.901448 | + | 0.432888i | \(0.142505\pi\) | ||||
−0.901448 | + | 0.432888i | \(0.857495\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13618.0 | −1.10527 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17026.9 | 1.33345 | 0.666727 | − | 0.745302i | \(-0.267695\pi\) | ||||
0.666727 | + | 0.745302i | \(0.267695\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18634.8 | −1.40906 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3305.33i | 0.241459i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17577.2 | 1.24124 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14632.7 | − | 491.651i | −0.999436 | − | 0.0335805i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 10884.0i | − | 0.719413i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16930.3 | −1.08354 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 27813.0i | − | 1.72441i | −0.506558 | − | 0.862206i | \(-0.669082\pi\) | ||
0.506558 | − | 0.862206i | \(-0.330918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 30630.1i | 1.84064i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6310.74i | 0.367738i | 0.982951 | + | 0.183869i | \(0.0588621\pi\) | ||||
−0.982951 | + | 0.183869i | \(0.941138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13972.6 | 0.789903 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7644.13 | −0.419431 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14207.1 | −0.756944 | −0.378472 | − | 0.925613i | \(-0.623550\pi\) | ||||
−0.378472 | + | 0.925613i | \(0.623550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 27772.6i | − | 1.43743i | −0.695306 | − | 0.718714i | \(-0.744731\pi\) | ||
0.695306 | − | 0.718714i | \(-0.255269\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1993.62 | −0.100277 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8742.26 | − | 146.826i | −0.427515 | − | 0.00718010i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12334.8i | 0.586673i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14061.2 | 0.650711 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23436.8i | 1.05567i | 0.849348 | + | 0.527833i | \(0.176995\pi\) | ||||
−0.849348 | + | 0.527833i | \(0.823005\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6556.14i | − | 0.287538i | −0.989611 | − | 0.143769i | \(-0.954078\pi\) | ||
0.989611 | − | 0.143769i | \(-0.0459222\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 23688.6i | 1.01194i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13798.1 | 0.574322 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2315.17 | −0.0939254 | −0.0469627 | − | 0.998897i | \(-0.514954\pi\) | ||||
−0.0469627 | + | 0.998897i | \(0.514954\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 45293.9 | 1.79162 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32842.8i | 1.26704i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21728.0 | 0.817796 | 0.408898 | − | 0.912580i | \(-0.365913\pi\) | ||||
0.408898 | + | 0.912580i | \(0.365913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −440.529 | + | 26229.8i | −0.0161810 | + | 0.963446i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 26470.6i | − | 0.949143i | −0.880217 | − | 0.474571i | \(-0.842603\pi\) | ||
0.880217 | − | 0.474571i | \(-0.157397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23339.5 | 0.817179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18830.7i | 0.643982i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6136.89i | − | 0.205048i | −0.994731 | − | 0.102524i | \(-0.967308\pi\) | ||
0.994731 | − | 0.102524i | \(-0.0326919\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8625.47i | 0.281648i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22381.1 | 0.714390 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8164.31 | 0.254808 | 0.127404 | − | 0.991851i | \(-0.459335\pi\) | ||||
0.127404 | + | 0.991851i | \(0.459335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10130.6 | 0.309228 | 0.154614 | − | 0.987975i | \(-0.450587\pi\) | ||||
0.154614 | + | 0.987975i | \(0.450587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 26981.8i | − | 0.805692i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −23295.1 | −0.680647 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −62653.8 | − | 1052.27i | −1.79170 | − | 0.0300915i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13472.4i | 0.377155i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13853.6 | 0.379749 | 0.189875 | − | 0.981808i | \(-0.439192\pi\) | ||||
0.189875 | + | 0.981808i | \(0.439192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 55752.8i | 1.49676i | 0.663270 | + | 0.748380i | \(0.269168\pi\) | ||||
−0.663270 | + | 0.748380i | \(0.730832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15666.4i | 0.412004i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 38577.9i | 0.994046i | 0.867737 | + | 0.497023i | \(0.165574\pi\) | ||||
−0.867737 | + | 0.497023i | \(0.834426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −43741.2 | −1.10455 | −0.552275 | − | 0.833662i | \(-0.686240\pi\) | ||||
−0.552275 | + | 0.833662i | \(0.686240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22596.2 | 0.559299 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21739.4 | 0.527540 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 18618.2i | − | 0.443028i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −44261.8 | −1.03297 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −49805.2 | − | 836.477i | −1.14020 | − | 0.0191497i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 40460.8i | 0.908803i | 0.890797 | + | 0.454402i | \(0.150147\pi\) | ||||
−0.890797 | + | 0.454402i | \(0.849853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 47903.1 | 1.05586 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 52396.2i | 1.13350i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 24318.4i | − | 0.516434i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 14507.9i | − | 0.302494i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37421.6 | −0.766193 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12067.6 | 0.242667 | 0.121334 | − | 0.992612i | \(-0.461283\pi\) | ||||
0.121334 | + | 0.992612i | \(0.461283\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11624.4 | −0.229619 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 38616.4i | 0.749411i | 0.927144 | + | 0.374705i | \(0.122256\pi\) | ||||
−0.927144 | + | 0.374705i | \(0.877744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −74080.9 | −1.41265 | −0.706326 | − | 0.707887i | \(-0.749649\pi\) | ||||
−0.706326 | + | 0.707887i | \(0.749649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 46228.6 | + | 776.408i | 0.866337 | + | 0.0145501i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 51719.5i | 0.952670i | 0.879264 | + | 0.476335i | \(0.158035\pi\) | ||||
−0.879264 | + | 0.476335i | \(0.841965\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3410.29 | −0.0617527 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 16664.4i | − | 0.296683i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16911.3i | 0.296062i | 0.988983 | + | 0.148031i | \(0.0472935\pi\) | ||||
−0.988983 | + | 0.148031i | \(0.952706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 59892.0i | 1.03118i | 0.856835 | + | 0.515590i | \(0.172427\pi\) | ||||
−0.856835 | + | 0.515590i | \(0.827573\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59868.5 | −1.01388 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24053.2 | 0.400720 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29747.5 | −0.487592 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 113979.i | − | 1.83833i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19186.2 | 0.304538 | 0.152269 | − | 0.988339i | \(-0.451342\pi\) | ||||
0.152269 | + | 0.988339i | \(0.451342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1966.15 | − | 117068.i | 0.0307168 | − | 1.82893i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 112278.i | 1.72669i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 30625.1 | 0.463672 | 0.231836 | − | 0.972755i | \(-0.425527\pi\) | ||||
0.231836 | + | 0.972755i | \(0.425527\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 41056.4i | 0.612042i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29297.9i | 0.430086i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 73815.1i | − | 1.06717i | −0.845746 | − | 0.533585i | \(-0.820844\pi\) | ||
0.845746 | − | 0.533585i | \(-0.179156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 77480.2 | 1.10331 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 57795.3 | 0.810718 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 87292.0 | 1.20634 | 0.603170 | − | 0.797612i | \(-0.293904\pi\) | ||||
0.603170 | + | 0.797612i | \(0.293904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4518.78i | − | 0.0615294i | −0.999527 | − | 0.0307647i | \(-0.990206\pi\) | ||
0.999527 | − | 0.0307647i | \(-0.00979425\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 27611.2 | 0.370477 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 516.369 | − | 30745.4i | 0.00682801 | − | 0.406551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4641.04i | − | 0.0604861i | −0.999543 | − | 0.0302431i | \(-0.990372\pi\) | ||
0.999543 | − | 0.0302431i | \(-0.00962813\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32773.6 | 0.421032 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 58621.1i | − | 0.742406i | −0.928552 | − | 0.371203i | \(-0.878945\pi\) | ||
0.928552 | − | 0.371203i | \(-0.121055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 90326.0i | 1.12782i | 0.825836 | + | 0.563910i | \(0.190704\pi\) | ||||
−0.825836 | + | 0.563910i | \(0.809296\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 89252.8i | 1.09883i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32813.6 | −0.398373 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −184671. | −2.21108 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25210.4 | 0.297710 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 77687.4i | 0.904931i | 0.891782 | + | 0.452465i | \(0.149455\pi\) | ||||
−0.891782 | + | 0.452465i | \(0.850545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38285.3 | 0.439935 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 806.531 | − | 48022.2i | 0.00914341 | − | 0.544414i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 69922.0i | − | 0.782116i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 92345.3 | 1.01925 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 175399.i | 1.91048i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 46155.3i | − | 0.496160i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 60487.2i | − | 0.641781i | −0.947116 | − | 0.320890i | \(-0.896018\pi\) | ||
0.947116 | − | 0.320890i | \(-0.103982\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −102667. | −1.07526 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32106.2 | 0.331947 | 0.165973 | − | 0.986130i | \(-0.446923\pi\) | ||||
0.165973 | + | 0.986130i | \(0.446923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 111475. | 1.13786 | 0.568932 | − | 0.822384i | \(-0.307357\pi\) | ||||
0.568932 | + | 0.822384i | \(0.307357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 29898.7i | − | 0.301322i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −139267. | −1.38589 | −0.692945 | − | 0.720990i | \(-0.743687\pi\) | ||||
−0.692945 | + | 0.720990i | \(0.743687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −77490.0 | − | 1301.44i | −0.761490 | − | 0.0127892i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 126145.i | − | 1.22422i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −213194. | −2.04347 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 18363.5i | − | 0.173856i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 115803.i | 1.08299i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6010.46i | 0.0555285i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 60223.2 | 0.549677 | 0.274839 | − | 0.961490i | \(-0.411376\pi\) | ||||
0.274839 | + | 0.961490i | \(0.411376\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −55331.2 | −0.498978 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38653.3 | 0.344427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 85639.9i | 0.754078i | 0.926197 | + | 0.377039i | \(0.123058\pi\) | ||||
−0.926197 | + | 0.377039i | \(0.876942\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 191688. | 1.66800 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1455.83 | + | 86682.7i | −0.0125200 | + | 0.745459i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 123885.i | − | 1.05301i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −209790. | −1.76257 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 99499.7i | − | 0.826348i | −0.910652 | − | 0.413174i | \(-0.864420\pi\) | ||
0.910652 | − | 0.413174i | \(-0.135580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 47515.3i | 0.390106i | 0.980793 | + | 0.195053i | \(0.0624878\pi\) | ||||
−0.980793 | + | 0.195053i | \(0.937512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 28682.5i | − | 0.232811i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 167482. | 1.34406 | 0.672030 | − | 0.740524i | \(-0.265423\pi\) | ||||
0.672030 | + | 0.740524i | \(0.265423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 81943.4 | 0.650216 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 197884. | 1.55265 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5063.91i | − | 0.0392914i | −0.999807 | − | 0.0196457i | \(-0.993746\pi\) | ||
0.999807 | − | 0.0196457i | \(-0.00625382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39152.4 | −0.300431 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −164735. | − | 5535.00i | −1.25018 | − | 0.0420053i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 24817.4i | − | 0.186282i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 264021. | 1.96023 | 0.980115 | − | 0.198429i | \(-0.0635841\pi\) | ||||
0.980115 | + | 0.198429i | \(0.0635841\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 44222.5i | − | 0.324781i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 136555.i | − | 0.992106i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 270510.i | − | 1.94431i | −0.234339 | − | 0.972155i | \(-0.575293\pi\) | ||
0.234339 | − | 0.972155i | \(-0.424707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −190601. | −1.35538 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46282.9 | −0.325640 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38850.0 | 0.270466 | 0.135233 | − | 0.990814i | \(-0.456822\pi\) | ||||
0.135233 | + | 0.990814i | \(0.456822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 313118.i | − | 2.15704i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −243070. | −1.65704 | −0.828522 | − | 0.559956i | \(-0.810818\pi\) | ||||
−0.828522 | + | 0.559956i | \(0.810818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 79079.0 | + | 1328.13i | 0.533506 | + | 0.00896022i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 124453.i | 0.830964i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 142544. | 0.941995 | 0.470998 | − | 0.882135i | \(-0.343894\pi\) | ||||
0.470998 | + | 0.882135i | \(0.343894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 501115.i | − | 3.27781i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 71046.2i | 0.459998i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 28506.2i | − | 0.182703i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 73860.0 | 0.468628 | 0.234314 | − | 0.972161i | \(-0.424716\pi\) | ||||
0.234314 | + | 0.972161i | \(0.424716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 157303. | 0.988079 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 225776. | 1.40407 | 0.702034 | − | 0.712143i | \(-0.252275\pi\) | ||||
0.702034 | + | 0.712143i | \(0.252275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 51773.5i | 0.318785i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −157410. | −0.959673 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2457.86 | − | 146345.i | 0.0148378 | − | 0.883466i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 97972.9i | 0.585679i | 0.956162 | + | 0.292839i | \(0.0946001\pi\) | ||||
−0.956162 | + | 0.292839i | \(0.905400\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −159943. | −0.946851 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 67475.8i | − | 0.395592i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 194973.i | − | 1.13208i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 312663.i | − | 1.79806i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 64572.5 | 0.367807 | 0.183903 | − | 0.982944i | \(-0.441127\pi\) | ||||
0.183903 | + | 0.982944i | \(0.441127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −203272. | −1.14687 | −0.573434 | − | 0.819252i | \(-0.694389\pi\) | ||||
−0.573434 | + | 0.819252i | \(0.694389\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8100.21 | −0.0452706 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 131607.i | − | 0.728621i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −81346.2 | −0.446151 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −98420.1 | − | 1652.96i | −0.534773 | − | 0.00898149i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11113.4i | 0.0598266i | 0.999552 | + | 0.0299133i | \(0.00952311\pi\) | ||||
−0.999552 | + | 0.0299133i | \(0.990477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −288512. | −1.53882 | −0.769409 | − | 0.638756i | \(-0.779449\pi\) | ||||
−0.769409 | + | 0.638756i | \(0.779449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 138865.i | 0.733861i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 398350.i | − | 2.08594i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 107467.i | 0.557630i | 0.960345 | + | 0.278815i | \(0.0899417\pi\) | ||||
−0.960345 | + | 0.278815i | \(0.910058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 57131.8 | 0.293765 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 130812. | 0.666563 | 0.333281 | − | 0.942827i | \(-0.391844\pi\) | ||||
0.333281 | + | 0.942827i | \(0.391844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 98865.0 | 0.499255 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 263851.i | 1.32052i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −158898. | −0.788181 | −0.394090 | − | 0.919072i | \(-0.628940\pi\) | ||||
−0.394090 | + | 0.919072i | \(0.628940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 116964. | + | 1964.41i | 0.575041 | + | 0.00965780i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 73808.9i | − | 0.359677i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 47232.0 | 0.228146 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 291561.i | − | 1.39604i | −0.716079 | − | 0.698019i | \(-0.754065\pi\) | ||
0.716079 | − | 0.698019i | \(-0.245935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 205561.i | − | 0.975698i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 62731.9i | 0.295180i | 0.989049 | + | 0.147590i | \(0.0471515\pi\) | ||||
−0.989049 | + | 0.147590i | \(0.952848\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −170883. | −0.797146 | −0.398573 | − | 0.917137i | \(-0.630494\pi\) | ||||
−0.398573 | + | 0.917137i | \(0.630494\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 155339. | 0.718411 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −94559.0 | −0.433580 | −0.216790 | − | 0.976218i | \(-0.569559\pi\) | ||||
−0.216790 | + | 0.976218i | \(0.569559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 68124.3i | − | 0.309711i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26064.1 | −0.117490 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −329164. | − | 5528.30i | −1.47126 | − | 0.0247098i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 104618.i | − | 0.463682i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 184033. | 0.808832 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 154781.i | 0.674600i | 0.941397 | + | 0.337300i | \(0.109514\pi\) | ||||
−0.941397 | + | 0.337300i | \(0.890486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 87408.6i | − | 0.377802i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 369744.i | 1.58492i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43125.1 | 0.183336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 205330. | 0.865754 | 0.432877 | − | 0.901453i | \(-0.357498\pi\) | ||||
0.432877 | + | 0.901453i | \(0.357498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 244614. | 1.02297 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 180799.i | − | 0.749950i | −0.927035 | − | 0.374975i | \(-0.877651\pi\) | ||
0.927035 | − | 0.374975i | \(-0.122349\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −331699. | −1.36474 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1789.90 | + | 106574.i | −0.00730498 | + | 0.434950i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 144421.i | − | 0.584678i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −198403. | −0.796797 | −0.398399 | − | 0.917212i | \(-0.630434\pi\) | ||||
−0.398399 | + | 0.917212i | \(0.630434\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 298006.i | − | 1.18727i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 278604.i | − | 1.10116i | −0.834781 | − | 0.550582i | \(-0.814406\pi\) | ||
0.834781 | − | 0.550582i | \(-0.185594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 300040.i | 1.17651i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 262755. | 1.02220 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 195175. | 0.753336 | 0.376668 | − | 0.926348i | \(-0.377070\pi\) | ||||
0.376668 | + | 0.926348i | \(0.377070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43739.2 | −0.167506 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 163406.i | − | 0.620917i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −175622. | −0.662164 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 359.819 | − | 21424.2i | 0.00134618 | − | 0.0801538i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 69089.0i | − | 0.256492i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2617.52 | −0.00964304 | −0.00482152 | − | 0.999988i | \(-0.501535\pi\) | ||||
−0.00482152 | + | 0.999988i | \(0.501535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 309803.i | − | 1.13261i | −0.824194 | − | 0.566307i | \(-0.808372\pi\) | ||
0.824194 | − | 0.566307i | \(-0.191628\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 97105.3i | 0.352310i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 371049.i | 1.33601i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 656488. | 2.34593 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 90936.2 | 0.322513 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 69859.8 | 0.245908 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 215785.i | − | 0.753899i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 91913.7 | 0.318736 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2537.85 | + | 151108.i | −0.00873551 | + | 0.520127i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 197545.i | 0.674948i | 0.941335 | + | 0.337474i | \(0.109573\pi\) | ||||
−0.941335 | + | 0.337474i | \(0.890427\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 114050. | 0.386809 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 198093.i | 0.666923i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 440541.i | 1.47235i | 0.676790 | + | 0.736176i | \(0.263370\pi\) | ||||
−0.676790 | + | 0.736176i | \(0.736630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 109629.i | − | 0.363732i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −263677. | −0.868498 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −50240.6 | −0.164288 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −262256. | −0.851411 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 422793.i | 1.36275i | 0.731933 | + | 0.681376i | \(0.238618\pi\) | ||||
−0.731933 | + | 0.681376i | \(0.761382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −196602. | −0.629165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −705355. | − | 11846.4i | −2.24121 | − | 0.0376410i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 52520.6i | 0.165696i | 0.996562 | + | 0.0828482i | \(0.0264017\pi\) | ||||
−0.996562 | + | 0.0828482i | \(0.973598\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 327903. | 1.02718 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 277427.i | 0.862944i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 140197.i | − | 0.433025i | −0.976280 | − | 0.216513i | \(-0.930532\pi\) | ||
0.976280 | − | 0.216513i | \(-0.0694683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 207548.i | − | 0.636569i | −0.947995 | − | 0.318284i | \(-0.896893\pi\) | ||
0.947995 | − | 0.318284i | \(-0.103107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 155964. | 0.475023 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 245907. | 0.743764 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −273572. | −0.821712 | −0.410856 | − | 0.911700i | \(-0.634770\pi\) | ||||
−0.410856 | + | 0.911700i | \(0.634770\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 627664.i | 1.87228i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −343628. | −1.01797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8174.91 | + | 486748.i | −0.0240517 | + | 1.43208i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 63654.0i | 0.186000i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 576701. | 1.67369 | 0.836843 | − | 0.547442i | \(-0.184398\pi\) | ||||
0.836843 | + | 0.547442i | \(0.184398\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 294957.i | 0.850214i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 434309.i | 1.24344i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 671956.i | − | 1.91087i | −0.295202 | − | 0.955435i | \(-0.595387\pi\) | ||
0.295202 | − | 0.955435i | \(-0.404613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 338501. | 0.956150 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −492438. | −1.38167 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 582984. | 1.62481 | 0.812406 | − | 0.583092i | \(-0.198157\pi\) | ||||
0.812406 | + | 0.583092i | \(0.198157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 377092.i | 1.04399i | 0.852947 | + | 0.521997i | \(0.174813\pi\) | ||||
−0.852947 | + | 0.521997i | \(0.825187\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 91810.2 | 0.252497 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −281797. | − | 9468.21i | −0.769885 | − | 0.0258677i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 465535.i | 1.26350i | 0.775173 | + | 0.631750i | \(0.217663\pi\) | ||||
−0.775173 | + | 0.631750i | \(0.782337\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 244742. | 0.659893 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 12796.2i | − | 0.0342766i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 623300.i | 1.65873i | 0.558705 | + | 0.829366i | \(0.311298\pi\) | ||||
−0.558705 | + | 0.829366i | \(0.688702\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 209604.i | − | 0.554177i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 197189. | 0.517980 | 0.258990 | − | 0.965880i | \(-0.416610\pi\) | ||||
0.258990 | + | 0.965880i | \(0.416610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −214900. | −0.560861 | −0.280431 | − | 0.959874i | \(-0.590477\pi\) | ||||
−0.280431 | + | 0.959874i | \(0.590477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 384089. | 0.995976 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 174244.i | − | 0.448934i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −167211. | −0.428061 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −560706. | − | 9417.04i | −1.42626 | − | 0.0239541i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 626437.i | − | 1.58335i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40334.6 | −0.101302 | −0.0506511 | − | 0.998716i | \(-0.516130\pi\) | ||||
−0.0506511 | + | 0.998716i | \(0.516130\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 455507.i | 1.13681i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 535623.i | − | 1.32835i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 90253.1i | 0.222425i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 194634. | 0.476669 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19965.1 | −0.0485909 | −0.0242954 | − | 0.999705i | \(-0.507734\pi\) | ||||
−0.0242954 | + | 0.999705i | \(0.507734\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21885.5 | −0.0529340 | −0.0264670 | − | 0.999650i | \(-0.508426\pi\) | ||||
−0.0264670 | + | 0.999650i | \(0.508426\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 589875.i | 1.41788i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −345969. | −0.826472 | −0.413236 | − | 0.910624i | \(-0.635602\pi\) | ||||
−0.413236 | + | 0.910624i | \(0.635602\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4039.47 | + | 240517.i | −0.00959037 | + | 0.571027i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 273776.i | − | 0.646000i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −380939. | −0.893366 | −0.446683 | − | 0.894692i | \(-0.647395\pi\) | ||||
−0.446683 | + | 0.894692i | \(0.647395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 121532.i | 0.283275i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 58946.8i | − | 0.136562i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 149577.i | 0.344424i | 0.985060 | + | 0.172212i | \(0.0550914\pi\) | ||||
−0.985060 | + | 0.172212i | \(0.944909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 637662. | 1.45945 | 0.729723 | − | 0.683743i | \(-0.239649\pi\) | ||||
0.729723 | + | 0.683743i | \(0.239649\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −421292. | −0.958420 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 269084. | 0.608477 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 619777.i | − | 1.39311i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 135857. | 0.303549 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 289958. | + | 4869.84i | 0.644006 | + | 0.0108161i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 165463.i | − | 0.365318i | −0.983176 | − | 0.182659i | \(-0.941530\pi\) | ||
0.983176 | − | 0.182659i | \(-0.0584704\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 100873. | 0.221394 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 420292.i | 0.917009i | 0.888692 | + | 0.458504i | \(0.151615\pi\) | ||||
−0.888692 | + | 0.458504i | \(0.848385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 76005.7i | − | 0.164857i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 434742.i | 0.937428i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −265281. | −0.568677 | −0.284338 | − | 0.958724i | \(-0.591774\pi\) | ||||
−0.284338 | + | 0.958724i | \(0.591774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −273600. | −0.583089 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −834001. | −1.76707 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 290723.i | 0.612408i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 72314.2 | 0.151449 | 0.0757247 | − | 0.997129i | \(-0.475873\pi\) | ||||
0.0757247 | + | 0.997129i | \(0.475873\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 187830. | + | 3154.60i | 0.391110 | + | 0.00656868i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 534843.i | − | 1.10728i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 500669. | 1.03059 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 582257.i | 1.19168i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 142549.i | − | 0.290088i | −0.989425 | − | 0.145044i | \(-0.953668\pi\) | ||
0.989425 | − | 0.145044i | \(-0.0463324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 497972.i | − | 1.00761i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38393.0 | −0.0772456 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 528803. | 1.05793 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 588664. | 1.17105 | 0.585525 | − | 0.810654i | \(-0.300888\pi\) | ||||
0.585525 | + | 0.810654i | \(0.300888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 67708.7i | − | 0.133938i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −693302. | −1.36378 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −168358. | − | 2827.57i | −0.329323 | − | 0.00553097i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 190387.i | 0.370340i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −133520. | −0.258280 | −0.129140 | − | 0.991626i | \(-0.541222\pi\) | ||||
−0.129140 | + | 0.991626i | \(0.541222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 309525.i | 0.595422i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 674263.i | 1.28989i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 162771.i | − | 0.309672i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 224313. | 0.424410 | 0.212205 | − | 0.977225i | \(-0.431936\pi\) | ||||
0.212205 | + | 0.977225i | \(0.431936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11922.8 | −0.0224348 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.40900e6 | −2.63680 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 297252.i | − | 0.553243i | −0.960979 | − | 0.276622i | \(-0.910785\pi\) | ||
0.960979 | − | 0.276622i | \(-0.0892149\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 270790. | 0.501255 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4078.30 | + | 242829.i | −0.00750834 | + | 0.447059i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 268988.i | 0.492543i | 0.969201 | + | 0.246272i | \(0.0792056\pi\) | ||||
−0.969201 | + | 0.246272i | \(0.920794\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −334896. | −0.609922 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 133653.i | − | 0.242104i | −0.992646 | − | 0.121052i | \(-0.961373\pi\) | ||
0.992646 | − | 0.121052i | \(-0.0386267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 451346.i | 0.813200i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 463104.i | − | 0.829921i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −380309. | −0.677911 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 201267. | 0.356856 | 0.178428 | − | 0.983953i | \(-0.442899\pi\) | ||||
0.178428 | + | 0.983953i | \(0.442899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 215998. | 0.380942 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 126258.i | − | 0.221496i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −835429. | −1.45787 | −0.728934 | − | 0.684584i | \(-0.759984\pi\) | ||||
−0.728934 | + | 0.684584i | \(0.759984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22134.9 | − | 1.31795e6i | 0.0384233 | − | 2.28778i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 345963.i | − | 0.597393i | −0.954348 | − | 0.298696i | \(-0.903448\pi\) | ||
0.954348 | − | 0.298696i | \(-0.0965518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 349128. | 0.599702 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 456194.i | 0.779518i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 143655.i | 0.244191i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.05669e6i | 1.78688i | 0.449183 | + | 0.893440i | \(0.351715\pi\) | ||||
−0.449183 | + | 0.893440i | \(0.648285\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 344776. | 0.580001 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 224559. | 0.375813 | 0.187907 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187907 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −182081. | −0.303153 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 462212.i | 0.765595i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 397996. | 0.655849 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8645.83 | + | 514787.i | −0.0141744 | + | 0.843967i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 254237.i | − | 0.414682i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44585.4 | −0.0723525 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 227376.i | − | 0.367109i | −0.983010 | − | 0.183554i | \(-0.941240\pi\) | ||
0.983010 | − | 0.183554i | \(-0.0587603\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 831008.i | − | 1.33491i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 577911.i | − | 0.923651i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 173185. | 0.275400 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 872270. | 1.38012 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 972019. | 1.53023 | 0.765117 | − | 0.643891i | \(-0.222681\pi\) | ||||
0.765117 | + | 0.643891i | \(0.222681\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 91707.4i | − | 0.143652i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 234827. | 0.366001 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 155908. | + | 2618.47i | 0.241790 | + | 0.00406085i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 632486.i | 0.976021i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 982732. | 1.50900 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56475.6i | 0.0862906i | 0.999069 | + | 0.0431453i | \(0.0137378\pi\) | ||||
−0.999069 | + | 0.0431453i | \(0.986262\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 224590.i | − | 0.341467i | −0.985317 | − | 0.170733i | \(-0.945386\pi\) | ||
0.985317 | − | 0.170733i | \(-0.0546137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 50872.3i | − | 0.0769663i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 418438. | 0.629964 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.12006e6 | −1.67801 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 112187. | 0.167253 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 719097.i | − | 1.06684i | −0.845849 | − | 0.533422i | \(-0.820906\pi\) | ||
0.845849 | − | 0.533422i | \(-0.179094\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52447.6 | 0.0774330 | 0.0387165 | − | 0.999250i | \(-0.487673\pi\) | ||||
0.0387165 | + | 0.999250i | \(0.487673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5813.26 | − | 346131.i | 0.00854107 | − | 0.508549i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 121409.i | 0.177517i | 0.996053 | + | 0.0887586i | \(0.0282900\pi\) | ||||
−0.996053 | + | 0.0887586i | \(0.971710\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −555136. | −0.807774 | −0.403887 | − | 0.914809i | \(-0.632341\pi\) | ||||
−0.403887 | + | 0.914809i | \(0.632341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 52248.7i | − | 0.0756612i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 646823.i | 0.932171i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 509771.i | − | 0.731143i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −284398. | −0.405952 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −728123. | −1.03438 | −0.517191 | − | 0.855870i | \(-0.673022\pi\) | ||||
−0.517191 | + | 0.855870i | \(0.673022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 297036. | 0.419969 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 659955.i | − | 0.928665i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 449471. | 0.629489 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16687.2 | + | 496652.i | −0.0232604 | + | 0.692285i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.01689e6i | 1.41078i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17049e6 | 1.61625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 560810.i | 0.770757i | 0.922759 | + | 0.385379i | \(0.125929\pi\) | ||||
−0.922759 | + | 0.385379i | \(0.874071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 362641.i | 0.496072i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.02077e6i | − | 1.38984i | −0.719086 | − | 0.694921i | \(-0.755439\pi\) | ||
0.719086 | − | 0.694921i | \(-0.244561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −350246. | −0.474665 | −0.237332 | − | 0.971428i | \(-0.576273\pi\) | ||||
−0.237332 | + | 0.971428i | \(0.576273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −369415. | −0.498320 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −516997. | −0.694170 | −0.347085 | − | 0.937834i | \(-0.612829\pi\) | ||||
−0.347085 | + | 0.937834i | \(0.612829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 118184.i | − | 0.157953i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.07903e6 | −2.76581 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 179082. | + | 3007.68i | 0.237145 | + | 0.00398284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 145036.i | 0.191178i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 102432. | 0.134402 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 574632.i | 0.750540i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 657406.i | 0.854741i | 0.904077 | + | 0.427371i | \(0.140560\pi\) | ||||
−0.904077 | + | 0.427371i | \(0.859440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 874603.i | 1.13197i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 869395. | 1.12012 | 0.560061 | − | 0.828452i | \(-0.310778\pi\) | ||||
0.560061 | + | 0.828452i | \(0.310778\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −955758. | −1.22582 | −0.612910 | − | 0.790153i | \(-0.710001\pi\) | ||||
−0.612910 | + | 0.790153i | \(0.710001\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 431015. | 0.550308 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 436265.i | 0.554503i | 0.960797 | + | 0.277251i | \(0.0894235\pi\) | ||||
−0.960797 | + | 0.277251i | \(0.910577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −944006. | −1.19446 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16608.3 | − | 988887.i | 0.0209204 | − | 1.24564i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 72900.7i | − | 0.0914174i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 157228. | 0.196284 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 787180.i | − | 0.978338i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 458912.i | 0.567819i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.08355e6i | 2.56657i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.03962e6 | 1.27497 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 195095. | 0.238204 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 707203. | 0.859666 | 0.429833 | − | 0.902909i | \(-0.358573\pi\) | ||||
0.429833 | + | 0.902909i | \(0.358573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 712661.i | 0.862493i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 132785. | 0.159998 | 0.0799989 | − | 0.996795i | \(-0.474508\pi\) | ||||
0.0799989 | + | 0.996795i | \(0.474508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.22486e6 | + | 20571.5i | 1.46942 | + | 0.0246788i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 519615.i | − | 0.620640i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 214194. | 0.254723 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 964589.i | − | 1.14212i | −0.820909 | − | 0.571059i | \(-0.806533\pi\) | ||
0.820909 | − | 0.571059i | \(-0.193467\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 680963.i | − | 0.802795i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 307470.i | 0.360911i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 307405. | 0.359275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −417143. | −0.485429 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 634849. | 0.735596 | 0.367798 | − | 0.929906i | \(-0.380112\pi\) | ||||
0.367798 | + | 0.929906i | \(0.380112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 514178.i | 0.593217i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 361451. | 0.415228 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.20659e6 | − | 20264.6i | −1.38018 | − | 0.0231800i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3331.90i | 0.00379501i | 0.999998 | + | 0.00189750i | \(0.000603995\pi\) | ||||
−0.999998 | + | 0.00189750i | \(0.999396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.25499e6 | 1.42334 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.13619e6i | − | 1.28313i | −0.767069 | − | 0.641564i | \(-0.778286\pi\) | ||
0.767069 | − | 0.641564i | \(-0.221714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 935496.i | 1.05201i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 259451.i | 0.290530i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −156679. | −0.174707 | −0.0873536 | − | 0.996177i | \(-0.527841\pi\) | ||||
−0.0873536 | + | 0.996177i | \(0.527841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 93120.3 | 0.103398 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.56786e6 | −1.73359 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 343607.i | 0.378334i | 0.981945 | + | 0.189167i | \(0.0605788\pi\) | ||||
−0.981945 | + | 0.189167i | \(0.939421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 266793. | 0.292528 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −872380. | − | 14651.6i | −0.952537 | − | 0.0159978i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 482205.i | 0.524317i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −410168. | −0.444135 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 512537.i | − | 0.552679i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.07369e6i | 1.15298i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 395609.i | 0.423071i | 0.977370 | + | 0.211536i | \(0.0678464\pi\) | ||||
−0.977370 | + | 0.211536i | \(0.932154\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.40013e6 | −2.55615 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.28188e6 | −1.35960 | −0.679799 | − | 0.733398i | \(-0.737933\pi\) | ||||
−0.679799 | + | 0.733398i | \(0.737933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −942632. | −0.995672 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 206736.i | − | 0.217474i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.02959e6 | −1.07863 | −0.539316 | − | 0.842103i | \(-0.681317\pi\) | ||||
−0.539316 | + | 0.842103i | \(0.681317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10431.2 | + | 621092.i | −0.0108835 | + | 0.648024i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 470515.i | 0.488918i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.35529e6 | 1.40257 | 0.701284 | − | 0.712882i | \(-0.252610\pi\) | ||||
0.701284 | + | 0.712882i | \(0.252610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 742933.i | 0.765732i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 67665.6i | 0.0694598i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.63271e6i | − | 2.69160i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47967.0 | −0.0488422 | −0.0244211 | − | 0.999702i | \(-0.507774\pi\) | ||||
−0.0244211 | + | 0.999702i | \(0.507774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 677991. | 0.687584 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −842368. | −0.850855 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.71845e6i | 1.72881i | 0.502798 | + | 0.864404i | \(0.332304\pi\) | ||||
−0.502798 | + | 0.864404i | \(0.667696\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 480145. | 0.481106 |
(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 | 704.5.h.i.65.3 | 4 | ||
4.3 | odd | 2 | 704.5.h.j.65.2 | 4 | |||
8.3 | odd | 2 | 176.5.h.e.65.4 | 4 | |||
8.5 | even | 2 | 22.5.b.a.21.1 | ✓ | 4 | ||
11.10 | odd | 2 | inner | 704.5.h.i.65.4 | 4 | ||
24.5 | odd | 2 | 198.5.d.a.109.4 | 4 | |||
40.13 | odd | 4 | 550.5.c.a.549.2 | 8 | |||
40.29 | even | 2 | 550.5.d.a.351.4 | 4 | |||
40.37 | odd | 4 | 550.5.c.a.549.7 | 8 | |||
44.43 | even | 2 | 704.5.h.j.65.1 | 4 | |||
88.21 | odd | 2 | 22.5.b.a.21.3 | yes | 4 | ||
88.43 | even | 2 | 176.5.h.e.65.3 | 4 | |||
264.197 | even | 2 | 198.5.d.a.109.2 | 4 | |||
440.109 | odd | 2 | 550.5.d.a.351.2 | 4 | |||
440.197 | even | 4 | 550.5.c.a.549.3 | 8 | |||
440.373 | even | 4 | 550.5.c.a.549.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.5.b.a.21.1 | ✓ | 4 | 8.5 | even | 2 | ||
22.5.b.a.21.3 | yes | 4 | 88.21 | odd | 2 | ||
176.5.h.e.65.3 | 4 | 88.43 | even | 2 | |||
176.5.h.e.65.4 | 4 | 8.3 | odd | 2 | |||
198.5.d.a.109.2 | 4 | 264.197 | even | 2 | |||
198.5.d.a.109.4 | 4 | 24.5 | odd | 2 | |||
550.5.c.a.549.2 | 8 | 40.13 | odd | 4 | |||
550.5.c.a.549.3 | 8 | 440.197 | even | 4 | |||
550.5.c.a.549.6 | 8 | 440.373 | even | 4 | |||
550.5.c.a.549.7 | 8 | 40.37 | odd | 4 | |||
550.5.d.a.351.2 | 4 | 440.109 | odd | 2 | |||
550.5.d.a.351.4 | 4 | 40.29 | even | 2 | |||
704.5.h.i.65.3 | 4 | 1.1 | even | 1 | trivial | ||
704.5.h.i.65.4 | 4 | 11.10 | odd | 2 | inner | ||
704.5.h.j.65.1 | 4 | 44.43 | even | 2 | |||
704.5.h.j.65.2 | 4 | 4.3 | odd | 2 |