Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 103x^{6} + 239x^{4} + 197x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.6 | ||
Root | \(1.84717i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.v.4049.5 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.724570i | 0.418331i | 0.977880 | + | 0.209165i | \(0.0670747\pi\) | ||||
−0.977880 | + | 0.209165i | \(0.932925\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.33840i | − 0.883833i | −0.897056 | − | 0.441916i | \(-0.854299\pi\) | ||||
0.897056 | − | 0.441916i | \(-0.145701\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.47500 | 0.825000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.62783 | −0.792321 | −0.396160 | − | 0.918181i | \(-0.629658\pi\) | ||||
−0.396160 | + | 0.918181i | \(0.629658\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.29631i | 1.19158i | 0.803140 | + | 0.595791i | \(0.203161\pi\) | ||||
−0.803140 | + | 0.595791i | \(0.796839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.85404i | 1.66235i | 0.556011 | + | 0.831175i | \(0.312331\pi\) | ||||
−0.556011 | + | 0.831175i | \(0.687669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.87303 | −0.659118 | −0.329559 | − | 0.944135i | \(-0.606900\pi\) | ||||
−0.329559 | + | 0.944135i | \(0.606900\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.69433 | 0.369734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.96702i | 0.763453i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.03711 | 0.935368 | 0.467684 | − | 0.883896i | \(-0.345088\pi\) | ||||
0.467684 | + | 0.883896i | \(0.345088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.31504 | −1.31382 | −0.656910 | − | 0.753969i | \(-0.728137\pi\) | ||||
−0.656910 | + | 0.753969i | \(0.728137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.90405i | − 0.331452i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.24142i | − 1.51928i | −0.650344 | − | 0.759640i | \(-0.725375\pi\) | ||||
0.650344 | − | 0.759640i | \(-0.274625\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.11297 | −0.498475 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.95078 | −1.08553 | −0.542765 | − | 0.839885i | \(-0.682623\pi\) | ||||
−0.542765 | + | 0.839885i | \(0.682623\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.01520i | − 1.06981i | −0.844913 | − | 0.534904i | \(-0.820348\pi\) | ||||
0.844913 | − | 0.534904i | \(-0.179652\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.74690i | 0.692406i | 0.938160 | + | 0.346203i | \(0.112529\pi\) | ||||
−0.938160 | + | 0.346203i | \(0.887471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.53188 | 0.218840 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.96623 | −0.695412 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.3849i | 1.70120i | 0.525817 | + | 0.850598i | \(0.323760\pi\) | ||||
−0.525817 | + | 0.850598i | \(0.676240\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 2.08171i | − 0.275729i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.14073 | 0.278699 | 0.139349 | − | 0.990243i | \(-0.455499\pi\) | ||||
0.139349 | + | 0.990243i | \(0.455499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.30567 | −0.295210 | −0.147605 | − | 0.989046i | \(-0.547156\pi\) | ||||
−0.147605 | + | 0.989046i | \(0.547156\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 5.78754i | − 0.729162i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.98376i | − 0.242355i | −0.992631 | − | 0.121178i | \(-0.961333\pi\) | ||||
0.992631 | − | 0.121178i | \(-0.0386671\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.724570 | 0.0872279 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.87990 | −0.816494 | −0.408247 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408247 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 13.2518i | − 1.55101i | −0.631342 | − | 0.775505i | \(-0.717496\pi\) | ||||
0.631342 | − | 0.775505i | \(-0.282504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.14492i | 0.700279i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.6578 | −1.87415 | −0.937076 | − | 0.349126i | \(-0.886478\pi\) | ||||
−0.937076 | + | 0.349126i | \(0.886478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.55062 | 0.505624 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 9.09450i | − 0.998251i | −0.866530 | − | 0.499126i | \(-0.833655\pi\) | ||||
0.866530 | − | 0.499126i | \(-0.166345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.64974i | 0.391293i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.676383 | −0.0716965 | −0.0358482 | − | 0.999357i | \(-0.511413\pi\) | ||||
−0.0358482 | + | 0.999357i | \(0.511413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0465 | 1.05316 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 5.30026i | − 0.549611i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0759i | 1.53073i | 0.643597 | + | 0.765365i | \(0.277441\pi\) | ||||
−0.643597 | + | 0.765365i | \(0.722559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.50388 | −0.653664 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7713 | −1.07178 | −0.535892 | − | 0.844286i | \(-0.680025\pi\) | ||||
−0.535892 | + | 0.844286i | \(0.680025\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4501i | 1.62088i | 0.585824 | + | 0.810438i | \(0.300771\pi\) | ||||
−0.585824 | + | 0.810438i | \(0.699229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.21143i | 0.697155i | 0.937280 | + | 0.348578i | \(0.113335\pi\) | ||||
−0.937280 | + | 0.348578i | \(0.886665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6581 | −1.78712 | −0.893560 | − | 0.448943i | \(-0.851801\pi\) | ||||
−0.893560 | + | 0.448943i | \(0.851801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.69605 | 0.635561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.722608i | 0.0679772i | 0.999422 | + | 0.0339886i | \(0.0108210\pi\) | ||||
−0.999422 | + | 0.0339886i | \(0.989179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.6334i | 0.983054i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.0275 | 1.46924 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.09450 | −0.372228 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.03633i | − 0.454110i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1029i | 1.69510i | 0.530712 | + | 0.847552i | \(0.321924\pi\) | ||||
−0.530712 | + | 0.847552i | \(0.678076\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.08300 | 0.447534 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.25213 | 0.808362 | 0.404181 | − | 0.914679i | \(-0.367557\pi\) | ||||
0.404181 | + | 0.914679i | \(0.367557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.71829i | 0.582550i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.5484i | 1.75557i | 0.479058 | + | 0.877783i | \(0.340978\pi\) | ||||
−0.479058 | + | 0.877783i | \(0.659022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.48875 | 0.465550 | 0.232775 | − | 0.972531i | \(-0.425219\pi\) | ||||
0.232775 | + | 0.972531i | \(0.425219\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.43946 | −0.289655 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 11.2900i | − 0.944115i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.10995i | 0.0915473i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.51461 | −0.451775 | −0.225887 | − | 0.974153i | \(-0.572528\pi\) | ||||
−0.225887 | + | 0.974153i | \(0.572528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.5363 | 1.34570 | 0.672851 | − | 0.739778i | \(-0.265069\pi\) | ||||
0.672851 | + | 0.739778i | \(0.265069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.9638i | 1.37144i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.6888i | 1.09249i | 0.837626 | + | 0.546244i | \(0.183943\pi\) | ||||
−0.837626 | + | 0.546244i | \(0.816057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.97372 | −0.711662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.33840 | −0.184292 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18.8266i | − 1.47462i | −0.675556 | − | 0.737308i | \(-0.736097\pi\) | ||||
0.675556 | − | 0.737308i | \(-0.263903\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.68830i | 0.285409i | 0.989765 | + | 0.142705i | \(0.0455799\pi\) | ||||
−0.989765 | + | 0.142705i | \(0.954420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.45825 | −0.419866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.11074 | −0.543772 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 7.94698i | − 0.604198i | −0.953277 | − | 0.302099i | \(-0.902313\pi\) | ||||
0.953277 | − | 0.302099i | \(-0.0976873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.55111i | 0.116588i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.72373 | −0.427811 | −0.213906 | − | 0.976854i | \(-0.568619\pi\) | ||||
−0.213906 | + | 0.976854i | \(0.568619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.19348 | −0.163040 | −0.0815199 | − | 0.996672i | \(-0.525977\pi\) | ||||
−0.0815199 | + | 0.996672i | \(0.525977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1.67062i | − 0.123495i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 18.0113i | − 1.31711i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.27648 | 0.674765 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.4643 | −1.04660 | −0.523302 | − | 0.852148i | \(-0.675300\pi\) | ||||
−0.523302 | + | 0.852148i | \(0.675300\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7400i | 1.27696i | 0.769640 | + | 0.638478i | \(0.220436\pi\) | ||||
−0.769640 | + | 0.638478i | \(0.779564\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 24.0847i | − 1.71596i | −0.513679 | − | 0.857982i | \(-0.671718\pi\) | ||||
0.513679 | − | 0.857982i | \(-0.328282\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.78754 | −0.552044 | −0.276022 | − | 0.961151i | \(-0.589016\pi\) | ||||
−0.276022 | + | 0.961151i | \(0.589016\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.43738 | 0.101385 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 11.7788i | − 0.826709i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.47500i | − 0.172024i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.54983 | 0.522233 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.5419 | 1.13879 | 0.569394 | − | 0.822065i | \(-0.307178\pi\) | ||||
0.569394 | + | 0.822065i | \(0.307178\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 4.98497i | − 0.341565i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.1055i | 1.16120i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.60187 | 0.648834 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.4471 | −1.98082 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.4323i | 1.43521i | 0.696449 | + | 0.717606i | \(0.254762\pi\) | ||||
−0.696449 | + | 0.717606i | \(0.745238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.6739i | 1.23943i | 0.784827 | + | 0.619715i | \(0.212752\pi\) | ||||
−0.784827 | + | 0.619715i | \(0.787248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.85981 | 0.122900 | 0.0614499 | − | 0.998110i | \(-0.480428\pi\) | ||||
0.0614499 | + | 0.998110i | \(0.480428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.45243 | −0.292948 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.39803i | 0.353637i | 0.984244 | + | 0.176818i | \(0.0565805\pi\) | ||||
−0.984244 | + | 0.176818i | \(0.943420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 12.0698i | − 0.784015i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.1817 | −1.37013 | −0.685065 | − | 0.728482i | \(-0.740226\pi\) | ||||
−0.685065 | + | 0.728482i | \(0.740226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.8152 | −1.92057 | −0.960283 | − | 0.279028i | \(-0.909988\pi\) | ||||
−0.960283 | + | 0.279028i | \(0.909988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1983i | 0.974971i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 12.3434i | − 0.785392i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.58960 | 0.417599 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.0212 | −0.885013 | −0.442506 | − | 0.896765i | \(-0.645911\pi\) | ||||
−0.442506 | + | 0.896765i | \(0.645911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.62783i | 0.165210i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.14991i | 0.445999i | 0.974819 | + | 0.222999i | \(0.0715848\pi\) | ||||
−0.974819 | + | 0.222999i | \(0.928415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.6101 | −1.34279 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4668 | 0.771678 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 16.6723i | − 1.02806i | −0.857772 | − | 0.514030i | \(-0.828152\pi\) | ||||
0.857772 | − | 0.514030i | \(-0.171848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 0.490087i | − 0.0299928i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7884 | 0.718752 | 0.359376 | − | 0.933193i | \(-0.382990\pi\) | ||||
0.359376 | + | 0.933193i | \(0.382990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.37717 | −0.508877 | −0.254438 | − | 0.967089i | \(-0.581891\pi\) | ||||
−0.254438 | + | 0.967089i | \(0.581891\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.27938i | 0.440568i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.99879i | 0.240264i | 0.992758 | + | 0.120132i | \(0.0383318\pi\) | ||||
−0.992758 | + | 0.120132i | \(0.961668\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.1047 | −1.08390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.9478 | 1.30930 | 0.654648 | − | 0.755934i | \(-0.272817\pi\) | ||||
0.654648 | + | 0.755934i | \(0.272817\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6297i | 0.631868i | 0.948781 | + | 0.315934i | \(0.102318\pi\) | ||||
−0.948781 | + | 0.315934i | \(0.897682\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.2537i | 0.959427i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.9779 | −1.76341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.9236 | −0.640351 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 28.5108i | − 1.66562i | −0.553558 | − | 0.832810i | \(-0.686730\pi\) | ||||
0.553558 | − | 0.832810i | \(-0.313270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 10.4247i | − 0.604900i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.29631 | 0.248462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.4044 | −0.945532 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 7.80456i | − 0.448360i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 0.391652i | − 0.0223528i | −0.999938 | − | 0.0111764i | \(-0.996442\pi\) | ||||
0.999938 | − | 0.0111764i | \(-0.00355763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.9192 | −0.678062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5240 | 1.27722 | 0.638609 | − | 0.769531i | \(-0.279510\pi\) | ||||
0.638609 | + | 0.769531i | \(0.279510\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 22.0468i | − 1.24616i | −0.782160 | − | 0.623078i | \(-0.785882\pi\) | ||||
0.782160 | − | 0.623078i | \(-0.214118\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.01192i | 0.337663i | 0.985645 | + | 0.168831i | \(0.0539994\pi\) | ||||
−0.985645 | + | 0.168831i | \(0.946001\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.2367 | −0.741112 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.22518 | −0.291641 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 19.6919i | − 1.09568i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 13.5191i | − 0.747607i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1002 | 0.611971 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.5619 | −1.51494 | −0.757469 | − | 0.652871i | \(-0.773564\pi\) | ||||
−0.757469 | + | 0.652871i | \(0.773564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 22.8725i | − 1.25341i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8095i | 0.643306i | 0.946858 | + | 0.321653i | \(0.104239\pi\) | ||||
−0.946858 | + | 0.321653i | \(0.895761\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.523580 | −0.0284370 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.2227 | 1.04097 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 19.9510i | − 1.07725i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 28.8288i | − 1.54761i | −0.633423 | − | 0.773806i | \(-0.718351\pi\) | ||||
0.633423 | − | 0.773806i | \(-0.281649\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1403 | 1.39926 | 0.699629 | − | 0.714506i | \(-0.253349\pi\) | ||||
0.699629 | + | 0.714506i | \(0.253349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.0435 | −0.909716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.8004i | 1.26677i | 0.773839 | + | 0.633383i | \(0.218334\pi\) | ||||
−0.773839 | + | 0.633383i | \(0.781666\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.6130i | 0.614628i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.0102 | −1.53110 | −0.765551 | − | 0.643375i | \(-0.777534\pi\) | ||||
−0.765551 | + | 0.643375i | \(0.777534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.7457 | −0.565564 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.96675i | − 0.155714i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.84461i | 0.148487i | 0.997240 | + | 0.0742437i | \(0.0236543\pi\) | ||||
−0.997240 | + | 0.0742437i | \(0.976346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.2032 | −0.895562 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.9609 | 1.50357 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.65308i | − 0.240928i | −0.992718 | − | 0.120464i | \(-0.961562\pi\) | ||||
0.992718 | − | 0.120464i | \(-0.0384382\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.6410i | 1.11457i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8607 | −1.07154 | −0.535772 | − | 0.844363i | \(-0.679979\pi\) | ||||
−0.535772 | + | 0.844363i | \(0.679979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.8413 | −0.709114 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 10.7116i | − 0.547337i | −0.961824 | − | 0.273669i | \(-0.911763\pi\) | ||||
0.961824 | − | 0.273669i | \(-0.0882372\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 17.3626i | − 0.882592i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.28523 | −0.166568 | −0.0832839 | − | 0.996526i | \(-0.526541\pi\) | ||||
−0.0832839 | + | 0.996526i | \(0.526541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.85404 | 0.346624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.70381i | 0.338163i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00319i | 0.301292i | 0.988588 | + | 0.150646i | \(0.0481353\pi\) | ||||
−0.988588 | + | 0.150646i | \(0.951865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.86787 | −0.243698 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.9420 | −1.14567 | −0.572835 | − | 0.819671i | \(-0.694156\pi\) | ||||
−0.572835 | + | 0.819671i | \(0.694156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 31.4277i | − 1.56552i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2849i | 1.20376i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.04425 | 0.447210 | 0.223605 | − | 0.974680i | \(-0.428218\pi\) | ||||
0.223605 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.8887 | −0.734407 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.00588i | − 0.246323i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.97698i | 0.194754i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.1921 | 1.37727 | 0.688637 | − | 0.725106i | \(-0.258209\pi\) | ||||
0.688637 | + | 0.725106i | \(0.258209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.14897 | −0.445893 | −0.222947 | − | 0.974831i | \(-0.571568\pi\) | ||||
−0.222947 | + | 0.974831i | \(0.571568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.7486i | 0.571235i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.39157i | 0.260916i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.18037 | 0.394952 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.5005 | 1.56549 | 0.782747 | − | 0.622340i | \(-0.213818\pi\) | ||||
0.782747 | + | 0.622340i | \(0.213818\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 0.555560i | − 0.0266985i | −0.999911 | − | 0.0133492i | \(-0.995751\pi\) | ||||
0.999911 | − | 0.0133492i | \(-0.00424932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.87303i | 0.137436i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.8680 | 1.23461 | 0.617305 | − | 0.786724i | \(-0.288224\pi\) | ||||
0.617305 | + | 0.786724i | \(0.288224\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.79140 | 0.180543 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.2965i | 1.43943i | 0.694270 | + | 0.719715i | \(0.255728\pi\) | ||||
−0.694270 | + | 0.719715i | \(0.744272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.99572i | − 0.188991i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.6573 | 1.49400 | 0.747001 | − | 0.664823i | \(-0.231493\pi\) | ||||
0.747001 | + | 0.664823i | \(0.231493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2655 | 0.860088 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9817i | 0.562949i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.34455i | 0.343564i | 0.985135 | + | 0.171782i | \(0.0549524\pi\) | ||||
−0.985135 | + | 0.171782i | \(0.945048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.1901 | −1.26913 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6987 | 0.731163 | 0.365581 | − | 0.930779i | \(-0.380870\pi\) | ||||
0.365581 | + | 0.930779i | \(0.380870\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.82421i | − 0.0847782i | −0.999101 | − | 0.0423891i | \(-0.986503\pi\) | ||||
0.999101 | − | 0.0423891i | \(-0.0134969\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.43722i | − 0.0665067i | −0.999447 | − | 0.0332533i | \(-0.989413\pi\) | ||||
0.999447 | − | 0.0332533i | \(-0.0105868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.63884 | −0.214202 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.91852 | −0.457021 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.4348i | 0.847632i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.6526i | 1.40349i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.5858 | −1.21474 | −0.607368 | − | 0.794420i | \(-0.707775\pi\) | ||||
−0.607368 | + | 0.794420i | \(0.707775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.7040 | 1.81035 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.69433i | − 0.0770949i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 33.8112i | − 1.53213i | −0.642762 | − | 0.766066i | \(-0.722212\pi\) | ||||
0.642762 | − | 0.766066i | \(-0.277788\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.6412 | 0.616877 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.4820 | 1.01460 | 0.507298 | − | 0.861770i | \(-0.330644\pi\) | ||||
0.507298 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.5246i | 1.55491i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.0880i | 0.721644i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.6152 | −1.01240 | −0.506198 | − | 0.862417i | \(-0.668949\pi\) | ||||
−0.506198 | + | 0.862417i | \(0.668949\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.67243 | −0.119395 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.3142i | 0.727414i | 0.931513 | + | 0.363707i | \(0.118489\pi\) | ||||
−0.931513 | + | 0.363707i | \(0.881511\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 3.95488i | − 0.175643i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.01935 | 0.355451 | 0.177726 | − | 0.984080i | \(-0.443126\pi\) | ||||
0.177726 | + | 0.984080i | \(0.443126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.9881 | −1.37083 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 11.3973i | − 0.503205i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 12.4740i | − 0.548608i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.75814 | 0.252754 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0130 | 0.789162 | 0.394581 | − | 0.918861i | \(-0.370890\pi\) | ||||
0.394581 | + | 0.918861i | \(0.370890\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.91940i | − 0.0839294i | −0.999119 | − | 0.0419647i | \(-0.986638\pi\) | ||||
0.999119 | − | 0.0419647i | \(-0.0133617\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 50.1376i | − 2.18403i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.29830 | 0.229927 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 29.8627i | − 1.29350i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 4.14724i | − 0.178967i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.02552 | −0.173391 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.0297 | −1.80700 | −0.903500 | − | 0.428589i | \(-0.859011\pi\) | ||||
−0.903500 | + | 0.428589i | \(0.859011\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.58933i | − 0.0682045i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0750i | 1.54246i | 0.636559 | + | 0.771228i | \(0.280357\pi\) | ||||
−0.636559 | + | 0.771228i | \(0.719643\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.70652 | −0.243548 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.4718 | −0.616518 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.9527i | 1.65644i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.9500i | 1.35377i | 0.736091 | + | 0.676883i | \(0.236670\pi\) | ||||
−0.736091 | + | 0.676883i | \(0.763330\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.1395 | 1.27476 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.0504 | 0.550989 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 6.26575i | − 0.264070i | −0.991245 | − | 0.132035i | \(-0.957849\pi\) | ||||
0.991245 | − | 0.132035i | \(-0.0421511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 10.6412i | − 0.446887i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.7997 | 0.536593 | 0.268296 | − | 0.963336i | \(-0.413539\pi\) | ||||
0.268296 | + | 0.963336i | \(0.413539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7690 | 0.576217 | 0.288108 | − | 0.957598i | \(-0.406974\pi\) | ||||
0.288108 | + | 0.957598i | \(0.406974\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 10.4804i | − 0.437826i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 13.5830i | − 0.565470i | −0.959198 | − | 0.282735i | \(-0.908758\pi\) | ||||
0.959198 | − | 0.282735i | \(-0.0912416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.8539 | −0.534190 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.2666 | −0.882287 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 32.5454i | − 1.34789i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 19.3233i | − 0.797557i | −0.917047 | − | 0.398778i | \(-0.869434\pi\) | ||||
0.917047 | − | 0.398778i | \(-0.130566\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.0163 | 0.865962 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.4511 | 0.717840 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 25.1344i | − 1.03215i | −0.856545 | − | 0.516073i | \(-0.827393\pi\) | ||||
0.856545 | − | 0.516073i | \(-0.172607\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.64262i | − 0.230937i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.88678 | −0.0770918 | −0.0385459 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385459 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.2105 | 0.538866 | 0.269433 | − | 0.963019i | \(-0.413164\pi\) | ||||
0.269433 | + | 0.963019i | \(0.413164\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.90982i | − 0.199943i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50465i | 0.142249i | 0.997467 | + | 0.0711246i | \(0.0226588\pi\) | ||||
−0.997467 | + | 0.0711246i | \(0.977341\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.53455 | 0.345838 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.3941 | −0.825058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.59433i | 0.306732i | 0.988169 | + | 0.153366i | \(0.0490114\pi\) | ||||
−0.988169 | + | 0.153366i | \(0.950989\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 13.4277i | − 0.540579i | −0.962779 | − | 0.270290i | \(-0.912881\pi\) | ||||
0.962779 | − | 0.270290i | \(-0.0871195\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.0584 | 1.81105 | 0.905525 | − | 0.424292i | \(-0.139477\pi\) | ||||
0.905525 | + | 0.424292i | \(0.139477\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.96702 | 0.159191 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.58166i | 0.0633677i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.47038i | 0.218466i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 63.3411 | 2.52557 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9030 | −0.593280 | −0.296640 | − | 0.954989i | \(-0.595866\pi\) | ||||
−0.296640 | + | 0.954989i | \(0.595866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.9857i | 0.476390i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.58142i | 0.260765i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.0278 | −0.673608 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.7852 | 1.49243 | 0.746213 | − | 0.665707i | \(-0.231870\pi\) | ||||
0.746213 | + | 0.665707i | \(0.231870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.8777i | 0.744465i | 0.928140 | + | 0.372232i | \(0.121408\pi\) | ||||
−0.928140 | + | 0.372232i | \(0.878592\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.5272i | 0.807009i | 0.914978 | + | 0.403505i | \(0.132208\pi\) | ||||
−0.914978 | + | 0.403505i | \(0.867792\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.62547 | −0.220819 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.3941 | −0.485764 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.07302i | 0.120256i | 0.998191 | + | 0.0601282i | \(0.0191509\pi\) | ||||
−0.998191 | + | 0.0601282i | \(0.980849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 32.7983i | − 1.27958i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.4014 | 0.794725 | 0.397363 | − | 0.917662i | \(-0.369925\pi\) | ||||
0.397363 | + | 0.917662i | \(0.369925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.17682 | −0.162460 | −0.0812298 | − | 0.996695i | \(-0.525885\pi\) | ||||
−0.0812298 | + | 0.996695i | \(0.525885\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 21.3365i | − 0.828639i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.03711i | − 0.195038i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.5292 | −0.600393 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.05890 | 0.233901 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.0529i | 1.73666i | 0.495984 | + | 0.868331i | \(0.334807\pi\) | ||||
−0.495984 | + | 0.868331i | \(0.665193\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 16.5395i | − 0.635665i | −0.948147 | − | 0.317833i | \(-0.897045\pi\) | ||||
0.948147 | − | 0.317833i | \(-0.102955\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.2536 | 1.35291 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.5305 | −0.518492 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.9328i | 1.03055i | 0.857024 | + | 0.515277i | \(0.172311\pi\) | ||||
−0.857024 | + | 0.515277i | \(0.827689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.34756i | 0.0514128i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53.2093 | −2.02711 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.1583 | 1.67986 | 0.839931 | − | 0.542693i | \(-0.182595\pi\) | ||||
0.839931 | + | 0.542693i | \(0.182595\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.2087i | 0.577730i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 47.6410i | − 1.80453i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.91125 | −0.147937 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.6476 | −0.591002 | −0.295501 | − | 0.955342i | \(-0.595487\pi\) | ||||
−0.295501 | + | 0.955342i | \(0.595487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.5508i | 1.00138i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.1876i | 0.947279i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.79068 | −0.330141 | −0.165070 | − | 0.986282i | \(-0.552785\pi\) | ||||
−0.165070 | + | 0.986282i | \(0.552785\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.2281 | −1.54617 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.31504i | 0.273951i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 15.3476i | − 0.573167i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.3081 | −1.46594 | −0.732972 | − | 0.680259i | \(-0.761867\pi\) | ||||
−0.732972 | + | 0.680259i | \(0.761867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.4669 | 1.43258 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 21.6032i | − 0.803431i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 16.1156i | − 0.597695i | −0.954301 | − | 0.298848i | \(-0.903398\pi\) | ||||
0.954301 | − | 0.298848i | \(-0.0966022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.63962 | 0.0977638 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.0825 | 1.77840 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.66306i | − 0.356913i | −0.983948 | − | 0.178457i | \(-0.942890\pi\) | ||||
0.983948 | − | 0.178457i | \(-0.0571104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.21300i | 0.192023i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.3518 | −0.895796 | −0.447898 | − | 0.894085i | \(-0.647827\pi\) | ||||
−0.447898 | + | 0.894085i | \(0.647827\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.94366 | 0.328553 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32.0702i | − 1.17654i | −0.808664 | − | 0.588271i | \(-0.799809\pi\) | ||||
0.808664 | − | 0.588271i | \(-0.200191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 22.5089i | − 0.823557i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.8632 | 0.616168 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.88705 | 0.0688596 | 0.0344298 | − | 0.999407i | \(-0.489038\pi\) | ||||
0.0344298 | + | 0.999407i | \(0.489038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 10.1594i | − 0.370228i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.13762i | 0.186730i | 0.995632 | + | 0.0933651i | \(0.0297624\pi\) | ||||
−0.995632 | + | 0.0933651i | \(0.970238\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.90405 | −0.0691125 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.4855 | 1.43135 | 0.715674 | − | 0.698435i | \(-0.246120\pi\) | ||||
0.715674 | + | 0.698435i | \(0.246120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.6301i | 1.57952i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.19722i | 0.332092i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.32121 | 0.0476439 | 0.0238220 | − | 0.999716i | \(-0.492417\pi\) | ||||
0.0238220 | + | 0.999716i | \(0.492417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.18061 | −0.186575 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.7473i | 1.21381i | 0.794776 | + | 0.606903i | \(0.207588\pi\) | ||||
−0.794776 | + | 0.606903i | \(0.792412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 15.6581i | − 0.561730i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.9698 | 0.715492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0792 | 0.646926 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.9823i | 0.714110i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.1800i | 0.469816i | 0.972018 | + | 0.234908i | \(0.0754789\pi\) | ||||
−0.972018 | + | 0.234908i | \(0.924521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.0803 | 0.430069 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.68975 | 0.0600805 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 9.90584i | − 0.351767i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 21.0017i | − 0.743919i | −0.928249 | − | 0.371959i | \(-0.878686\pi\) | ||||
0.928249 | − | 0.371959i | \(-0.121314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.5354 | −1.15102 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.67405 | −0.0591496 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.8236i | 1.22890i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.54153i | 0.300676i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.45831 | −0.156746 | −0.0783729 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783729 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.9804 | 0.982525 | 0.491263 | − | 0.871012i | \(-0.336536\pi\) | ||||
0.491263 | + | 0.871012i | \(0.336536\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.06984i | − 0.212879i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.1549i | 0.705130i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.8651 | 0.868855 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.0587 | 1.01416 | 0.507078 | − | 0.861900i | \(-0.330726\pi\) | ||||
0.507078 | + | 0.861900i | \(0.330726\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6.83168i | − 0.238138i | −0.992886 | − | 0.119069i | \(-0.962009\pi\) | ||||
0.992886 | − | 0.119069i | \(-0.0379909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 31.5165i | − 1.09594i | −0.836499 | − | 0.547968i | \(-0.815402\pi\) | ||||
0.836499 | − | 0.547968i | \(-0.184598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.9202 | 0.796052 | 0.398026 | − | 0.917374i | \(-0.369695\pi\) | ||||
0.398026 | + | 0.917374i | \(0.369695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.89741 | −0.100510 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.4996i | 0.363788i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 29.0189i | − 1.00304i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.6003 | −0.676676 | −0.338338 | − | 0.941025i | \(-0.609865\pi\) | ||||
−0.338338 | + | 0.941025i | \(0.609865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.62750 | −0.125086 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.9027i | 0.547718i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.57459i | 0.328987i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.70193 | −0.264330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.24142 | −0.316792 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 9.76951i | − 0.334502i | −0.985914 | − | 0.167251i | \(-0.946511\pi\) | ||||
0.985914 | − | 0.167251i | \(-0.0534890\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.5308i | 0.906273i | 0.891441 | + | 0.453137i | \(0.149695\pi\) | ||||
−0.891441 | + | 0.453137i | \(0.850305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.1341 | −1.26700 | −0.633499 | − | 0.773744i | \(-0.718382\pi\) | ||||
−0.633499 | + | 0.773744i | \(0.718382\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.7770 | −0.401358 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.15457i | 0.209504i | 0.994498 | + | 0.104752i | \(0.0334049\pi\) | ||||
−0.994498 | + | 0.104752i | \(0.966595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 21.7211i | − 0.737687i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.7739 | 1.48493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.52286 | 0.288786 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 37.3129i | 1.26285i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 22.0440i | − 0.744373i | −0.928158 | − | 0.372186i | \(-0.878608\pi\) | ||||
0.928158 | − | 0.372186i | \(-0.121392\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.6581 | 0.696780 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.0196 | 0.371260 | 0.185630 | − | 0.982620i | \(-0.440567\pi\) | ||||
0.185630 | + | 0.982620i | \(0.440567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 33.8860i | − 1.14035i | −0.821522 | − | 0.570177i | \(-0.806875\pi\) | ||||
0.821522 | − | 0.570177i | \(-0.193125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 3.89387i | − 0.130743i | −0.997861 | − | 0.0653717i | \(-0.979177\pi\) | ||||
0.997861 | − | 0.0653717i | \(-0.0208233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.6701 | 1.49819 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.9582 | −0.400616 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 13.6380i | − 0.456377i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.11297i | 0.103939i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.8467 | −1.22891 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −84.8866 | −2.82798 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 11.8861i | − 0.395545i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 30.5048i | − 1.01289i | −0.862271 | − | 0.506447i | \(-0.830959\pi\) | ||||
0.862271 | − | 0.506447i | \(-0.169041\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.6590 | −0.884222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.8042 | −0.523616 | −0.261808 | − | 0.965120i | \(-0.584319\pi\) | ||||
−0.261808 | + | 0.965120i | \(0.584319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.8988i | 0.790935i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 21.6352i | − 0.714457i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.2196 | 1.35971 | 0.679855 | − | 0.733347i | \(-0.262043\pi\) | ||||
0.679855 | + | 0.733347i | \(0.262043\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.283779 | 0.00935085 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 29.5582i | − 0.972919i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.7140i | 1.33722i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.3600 | −0.438326 | −0.219163 | − | 0.975688i | \(-0.570333\pi\) | ||||
−0.219163 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.40113 | −0.144241 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.3202i | 0.534299i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 16.6980i | − 0.545501i | −0.962085 | − | 0.272751i | \(-0.912067\pi\) | ||||
0.962085 | − | 0.272751i | \(-0.0879334\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9744 | 0.521305 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.3650 | 0.533482 | 0.266741 | − | 0.963768i | \(-0.414053\pi\) | ||||
0.266741 | + | 0.963768i | \(0.414053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.95078i | 0.226349i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.88894i | 0.256356i | 0.991751 | + | 0.128178i | \(0.0409129\pi\) | ||||
−0.991751 | + | 0.128178i | \(0.959087\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.9339 | 1.84815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.35605 | −0.141255 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 2.26143i | − 0.0732549i | −0.999329 | − | 0.0366275i | \(-0.988339\pi\) | ||||
0.999329 | − | 0.0366275i | \(-0.0116615\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.59090i | − 0.310030i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 48.0504 | 1.55163 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.5099 | 0.726125 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.8483i | 0.575153i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.1416i | 0.744182i | 0.928196 | + | 0.372091i | \(0.121359\pi\) | ||||
−0.928196 | + | 0.372091i | \(0.878641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.2681 | 0.458358 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9414 | −0.896683 | −0.448341 | − | 0.893862i | \(-0.647985\pi\) | ||||
−0.448341 | + | 0.893862i | \(0.647985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12.8349i | − 0.411468i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.62964i | 0.308079i | 0.988065 | + | 0.154040i | \(0.0492284\pi\) | ||||
−0.988065 | + | 0.154040i | \(0.950772\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.77742 | 0.0568066 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.1787 | −1.47437 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 23.3104i | − 0.743487i | −0.928336 | − | 0.371743i | \(-0.878760\pi\) | ||||
0.928336 | − | 0.371743i | \(-0.121240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.04283i | 0.256006i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.01520 | −0.223071 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.62769 | −0.0834712 | −0.0417356 | − | 0.999129i | \(-0.513289\pi\) | ||||
−0.0417356 | + | 0.999129i | \(0.513289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 19.9705i | − 0.633745i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.4056i | 0.741264i | 0.928780 | + | 0.370632i | \(0.120859\pi\) | ||||
−0.928780 | + | 0.370632i | \(0.879141\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.6609 | 1.15990 |
(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 | 4600.2.e.v.4049.6 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bc.1.4 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bg.1.2 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.v.4049.5 | 10 | ||
20.3 | even | 4 | 9200.2.a.cs.1.4 | 5 | |||
20.7 | even | 4 | 9200.2.a.cw.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.4 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bg.1.2 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.v.4049.5 | 10 | 5.4 | even | 2 | inner | ||
4600.2.e.v.4049.6 | 10 | 1.1 | even | 1 | trivial | ||
9200.2.a.cs.1.4 | 5 | 20.3 | even | 4 | |||
9200.2.a.cw.1.2 | 5 | 20.7 | even | 4 |