Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(5,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.s (of order \(22\), degree \(10\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 125.2 | ||
Root | \(0.580057 - 0.814576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.125 |
Dual form | 804.2.s.a.521.2 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{15}{22}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.487975 | − | 1.66189i | 0.281733 | − | 0.959493i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.74514 | − | 4.27152i | 1.03757 | − | 1.61448i | 0.281995 | − | 0.959416i | \(-0.409004\pi\) |
0.755570 | − | 0.655068i | \(-0.227360\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.52376 | − | 1.62192i | −0.841254 | − | 0.540641i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.83933 | + | 0.983347i | −1.89689 | + | 0.272731i | −0.989162 | − | 0.146831i | \(-0.953093\pi\) |
−0.907726 | + | 0.419563i | \(0.862183\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.27844 | − | 4.67757i | 1.66979 | − | 1.07311i | 0.768542 | − | 0.639799i | \(-0.220983\pi\) |
0.901246 | − | 0.433308i | \(-0.142654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.75924 | − | 6.64652i | −1.25677 | − | 1.45039i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.711574 | + | 4.94911i | 0.142315 | + | 0.989821i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.92699 | + | 3.40276i | −0.755750 | + | 0.654861i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.72847 | − | 1.39874i | −1.74728 | − | 0.251222i | −0.806744 | − | 0.590901i | \(-0.798772\pi\) |
−0.940541 | + | 0.339680i | \(0.889681\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.43454 | 0.893432 | 0.446716 | − | 0.894676i | \(-0.352593\pi\) | ||||
0.446716 | + | 0.894676i | \(0.352593\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.70321 | + | 11.8461i | −0.272731 | + | 1.89689i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.85766 | + | 2.67510i | 0.893285 | + | 0.407949i | 0.808532 | − | 0.588453i | \(-0.200263\pi\) |
0.0847529 | + | 0.996402i | \(0.472990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.80220 | − | 17.0844i | −1.11460 | − | 2.44063i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.22191 | − | 14.3785i | −0.559205 | − | 1.90448i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00476 | − | 6.93617i | 1.02490 | − | 0.888085i | 0.0311325 | − | 0.999515i | \(-0.490089\pi\) |
0.993772 | + | 0.111430i | \(0.0355432\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.8562 | + | 6.32789i | −1.74571 | + | 0.797240i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.85294 | − | 7.67208i | −0.348542 | − | 0.937293i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.56926 | − | 2.96508i | −0.300709 | − | 0.347037i | 0.585206 | − | 0.810885i | \(-0.301014\pi\) |
−0.885915 | + | 0.463848i | \(0.846468\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.57211 | + | 1.23248i | 0.989821 | + | 0.142315i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.47911 | − | 0.212664i | 0.166413 | − | 0.0239266i | −0.0586047 | − | 0.998281i | \(-0.518665\pi\) |
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.73874 | + | 8.18669i | 0.415415 | + | 0.909632i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.5745 | + | 31.9138i | −1.52783 | + | 3.34547i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.07181 | + | 15.4851i | −0.733312 | + | 1.60573i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.35087i | 0.949437i | 0.880138 | + | 0.474718i | \(0.157450\pi\) | ||||
−0.880138 | + | 0.474718i | \(0.842550\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.66099 | − | 18.5076i | 0.262195 | − | 1.82361i | −0.254079 | − | 0.967183i | \(-0.581772\pi\) |
0.516274 | − | 0.856423i | \(-0.327319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.9764 | − | 1.72194i | 1.14713 | − | 0.164932i | 0.457578 | − | 0.889170i | \(-0.348717\pi\) |
0.689551 | + | 0.724238i | \(0.257808\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.65192 | − | 9.03160i | 0.251709 | − | 0.857242i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.8557 | + | 8.61113i | 1.74321 | + | 0.796099i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.56546 | + | 10.8880i | 0.142315 | + | 0.989821i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0480 | + | 7.10014i | 0.980354 | + | 0.630036i | 0.929559 | − | 0.368674i | \(-0.120188\pi\) |
0.0507955 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.30412 | − | 8.42940i | 0.643092 | − | 0.742168i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 43.9306i | − | 3.80926i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.9664 | + | 13.8350i | 1.35426 | + | 1.17347i | 0.967963 | + | 0.251093i | \(0.0807900\pi\) |
0.386293 | + | 0.922376i | \(0.373755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −32.1997 | + | 4.62962i | −2.65579 | + | 0.381845i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.52472 | + | 14.2871i | −0.530974 | + | 1.16267i | 0.434141 | + | 0.900845i | \(0.357052\pi\) |
−0.965115 | + | 0.261826i | \(0.915675\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.518645 | − | 0.152288i | −0.0413924 | − | 0.0121539i | 0.260971 | − | 0.965347i | \(-0.415957\pi\) |
−0.302363 | + | 0.953193i | \(0.597776\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25.3807 | 1.98797 | 0.993986 | − | 0.109509i | \(-0.0349277\pi\) | ||||
0.993986 | + | 0.109509i | \(0.0349277\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.3360 | − | 9.78834i | 2.56431 | − | 0.752949i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.9557 | −1.98488 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.0936 | + | 10.5465i | 1.74571 | + | 0.797240i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0635 | + | 6.47842i | 1.63996 | + | 0.481537i | 0.966282 | − | 0.257485i | \(-0.0828937\pi\) |
0.673682 | + | 0.739022i | \(0.264712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.62102 | − | 16.6877i | −0.563362 | − | 1.23359i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.75481 | + | 26.1153i | 0.273122 | + | 1.89961i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.89281 | − | 13.1648i | 0.136248 | − | 0.947623i | −0.800927 | − | 0.598762i | \(-0.795660\pi\) |
0.937175 | − | 0.348861i | \(-0.113431\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.13430 | + | 4.58494i | 0.505737 | + | 0.325018i | 0.768507 | − | 0.639841i | \(-0.221000\pi\) |
−0.262770 | + | 0.964858i | \(0.584636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.1423 | + | 0.997492i | −0.997522 | + | 0.0703577i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.6370 | − | 8.11495i | 1.90261 | − | 0.558656i | 0.914574 | − | 0.404419i | \(-0.132526\pi\) |
0.988034 | − | 0.154237i | \(-0.0492918\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.6808 | + | 37.7156i | −2.21852 | + | 2.56030i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.18138 | + | 2.82294i | −0.417699 | + | 0.190757i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.5868 | + | 8.39384i | −1.91431 | + | 0.562093i | −0.937509 | + | 0.347960i | \(0.886874\pi\) |
−0.976804 | + | 0.214133i | \(0.931307\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.23123 | − | 13.6445i | 0.415415 | − | 0.909632i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4823 | − | 3.52002i | −1.61783 | − | 0.232609i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
−0.890934 | + | 0.454133i | \(0.849949\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.368345 | − | 2.56189i | 0.0239266 | − | 0.166413i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.2681 | + | 22.2365i | 1.24116 | + | 1.43238i | 0.861889 | + | 0.507097i | \(0.169281\pi\) |
0.379276 | + | 0.925284i | \(0.376173\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4298 | − | 2.21847i | 0.989821 | − | 0.142315i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.1799 | + | 39.1486i | −2.87473 | + | 2.49097i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.9186 | − | 23.2137i | 0.926994 | − | 1.44243i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.36996 | + | 28.5055i | −0.508439 | + | 1.73158i | 0.159340 | + | 0.987224i | \(0.449063\pi\) |
−0.667779 | + | 0.744360i | \(0.732755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 45.9252 | + | 39.7944i | 2.77952 | + | 2.40847i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.9912 | − | 16.0609i | −1.50158 | − | 0.965005i | −0.994682 | − | 0.102998i | \(-0.967156\pi\) |
−0.506896 | − | 0.862007i | \(-0.669207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.2837 | + | 19.3089i | 1.33409 | + | 1.15599i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0217 | + | 7.08324i | −0.655174 | + | 0.421055i | −0.825554 | − | 0.564324i | \(-0.809137\pi\) |
0.170379 | + | 0.985379i | \(0.445501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1326 | − | 12.8477i | −0.654861 | − | 0.755750i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.5401 | + | 4.56299i | 0.910978 | + | 0.267487i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.5069 | − | 17.6776i | 1.58547 | − | 1.01892i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.98190 | − | 34.6498i | 0.284332 | − | 1.97757i | 0.0968945 | − | 0.995295i | \(-0.469109\pi\) |
0.187437 | − | 0.982277i | \(-0.439982\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −29.4591 | − | 13.4535i | −1.67587 | − | 0.765344i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.21722 | − | 10.9568i | −0.181848 | − | 0.619317i | −0.999075 | − | 0.0430013i | \(-0.986308\pi\) |
0.817227 | − | 0.576316i | \(-0.195510\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.73338 | − | 33.1488i | −0.539911 | − | 1.83877i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.98249 | − | 20.7437i | 0.164932 | − | 1.14713i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.91635 | + | 3.15859i | −0.380157 | + | 0.173612i | −0.596323 | − | 0.802745i | \(-0.703372\pi\) |
0.216166 | + | 0.976357i | \(0.430645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.7155 | − | 8.81440i | −0.751603 | − | 0.483026i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.2608 | + | 29.9704i | −1.04920 | + | 1.63259i | −0.321211 | + | 0.947008i | \(0.604090\pi\) |
−0.727993 | + | 0.685585i | \(0.759547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −59.2134 | − | 8.51361i | −3.19723 | − | 0.459692i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.88747 | + | 6.32267i | 0.154562 | + | 0.338445i | 0.971034 | − | 0.238941i | \(-0.0768002\pi\) |
−0.816472 | + | 0.577386i | \(0.804073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.5119 | − | 27.1342i | 1.25497 | − | 1.44831i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.2031 | − | 50.8077i | 1.22122 | − | 2.67409i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.8586 | + | 2.71146i | 0.989821 | + | 0.142315i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.17855 | − | 21.0422i | −0.322518 | − | 1.09839i | −0.948030 | − | 0.318180i | \(-0.896928\pi\) |
0.625513 | − | 0.780214i | \(-0.284890\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.3727i | − | 1.36553i | −0.730639 | − | 0.682764i | \(-0.760778\pi\) | ||
0.730639 | − | 0.682764i | \(-0.239222\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.2498 | + | 34.9075i | −0.526495 | + | 1.79308i | 0.0785782 | + | 0.996908i | \(0.474962\pi\) |
−0.605073 | + | 0.796170i | \(0.706856\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.1908 | − | 14.8959i | 0.880712 | − | 0.763142i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.4445 | − | 16.2520i | −0.530925 | − | 0.826135i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.13170 | − | 3.61417i | 0.157175 | − | 0.181390i | −0.671700 | − | 0.740823i | \(-0.734436\pi\) |
0.828876 | + | 0.559433i | \(0.188981\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −73.0078 | − | 21.4370i | −3.65496 | − | 1.07319i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 67.9116 | 3.38292 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6206 | + | 16.5260i | −0.525155 | + | 0.817157i | −0.997949 | − | 0.0640160i | \(-0.979609\pi\) |
0.472794 | + | 0.881173i | \(0.343245\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.7835 | − | 19.7833i | 1.50747 | − | 0.968794i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.4792 | + | 20.2304i | −1.53420 | + | 0.985971i | −0.545159 | + | 0.838333i | \(0.683531\pi\) |
−0.989041 | + | 0.147638i | \(0.952833\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.65379 | − | 53.2333i | −0.370393 | − | 2.57614i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.89621 | + | 0.560190i | 0.187240 | + | 0.0269210i | 0.235297 | − | 0.971924i | \(-0.424394\pi\) |
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.7279 | −0.798379 | −0.399190 | − | 0.916868i | \(-0.630708\pi\) | ||||
−0.399190 | + | 0.916868i | \(0.630708\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.01874 | + | 55.7716i | −0.381845 | + | 2.65579i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.5598 | + | 17.8151i | 0.965982 | + | 0.837028i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.39561 | + | 30.5722i | 0.205618 | + | 1.43011i | 0.787240 | + | 0.616647i | \(0.211509\pi\) |
−0.581622 | + | 0.813459i | \(0.697582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.3981 | − | 28.0731i | 1.50567 | − | 1.30467i | 0.695374 | − | 0.718648i | \(-0.255239\pi\) |
0.810296 | − | 0.586021i | \(-0.199307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.6032 | − | 8.87453i | −1.87488 | − | 0.409788i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.506172 | + | 0.787619i | −0.0233232 | + | 0.0362916i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.3289 | + | 32.6933i | 1.29982 | + | 1.50007i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.1686 | + | 5.34403i | −1.69474 | + | 0.243667i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.7159 | + | 17.2243i | −1.70907 | + | 0.780507i | −0.712157 | + | 0.702020i | \(0.752282\pi\) |
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.3852 | − | 42.1800i | 0.560076 | − | 1.90744i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.1112i | 1.61656i | 0.588798 | + | 0.808280i | \(0.299601\pi\) | ||||
−0.588798 | + | 0.808280i | \(0.700399\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 60.1773i | − | 2.67257i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.7184 | + | 2.83508i | −0.872290 | + | 0.125416i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.6657 | + | 43.1355i | −0.559205 | + | 1.90448i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.50714 | − | 17.4375i | −0.109629 | − | 0.762489i | −0.968269 | − | 0.249910i | \(-0.919599\pi\) |
0.858640 | − | 0.512579i | \(-0.171310\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.7962 | − | 33.2326i | 1.25677 | − | 1.45039i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.3488 | + | 12.4347i | 0.841254 | + | 0.540641i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.4478 | − | 25.5166i | −1.26606 | − | 1.09705i | −0.990751 | − | 0.135690i | \(-0.956675\pi\) |
−0.275307 | − | 0.961356i | \(-0.588780\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.5328 | − | 33.5058i | 0.924063 | − | 1.43787i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.1110 | + | 30.4239i | 1.50124 | + | 1.30083i | 0.826791 | + | 0.562510i | \(0.190164\pi\) |
0.674449 | + | 0.738321i | \(0.264381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.4520 | + | 4.52212i | −1.34234 | + | 0.192999i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.15197 | − | 6.90185i | 0.134035 | − | 0.293496i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.6930 | − | 12.5358i | −1.80572 | − | 0.530208i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 45.2330 | + | 6.50352i | 1.89961 | + | 0.273122i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.55660 | + | 0.750686i | −0.106990 | + | 0.0314152i | −0.334790 | − | 0.942293i | \(-0.608665\pi\) |
0.227799 | + | 0.973708i | \(0.426847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3689 | − | 10.6722i | −0.972859 | − | 0.444290i | −0.135400 | − | 0.990791i | \(-0.543232\pi\) |
−0.837458 | + | 0.546501i | \(0.815959\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.9548 | − | 9.56974i | −0.870852 | − | 0.397705i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −77.3508 | + | 35.3249i | −3.18718 | + | 1.45554i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.1010 | − | 9.61910i | 0.454335 | − | 0.393683i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1053 | − | 7.77957i | −0.493784 | − | 0.317335i | 0.269942 | − | 0.962877i | \(-0.412995\pi\) |
−0.763725 | + | 0.645541i | \(0.776632\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.24337 | + | 23.9897i | −0.213527 | + | 0.976937i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.12466 | − | 6.84205i | −0.126826 | − | 0.277710i | 0.835558 | − | 0.549402i | \(-0.185144\pi\) |
−0.962384 | + | 0.271691i | \(0.912417\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.3137 | − | 13.5989i | 1.87059 | − | 0.549256i | 0.872426 | − | 0.488746i | \(-0.162545\pi\) |
0.998168 | − | 0.0605099i | \(-0.0192727\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.5816 | − | 37.6012i | 1.30956 | − | 1.51132i | 0.643094 | − | 0.765787i | \(-0.277650\pi\) |
0.666471 | − | 0.745531i | \(-0.267804\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.9873 | + | 7.04331i | −0.959493 | + | 0.281733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.2997 | + | 5.07533i | 1.40526 | + | 0.202046i | 0.802869 | − | 0.596156i | \(-0.203306\pi\) |
0.602390 | + | 0.798202i | \(0.294215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 49.8895i | − | 1.98293i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 70.1617 | + | 109.174i | 2.77991 | + | 4.32562i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.68998 | + | 8.87471i | 0.303263 | + | 0.349984i | 0.886843 | − | 0.462072i | \(-0.152894\pi\) |
−0.583579 | + | 0.812056i | \(0.698348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.7318 | + | 72.7162i | 1.83157 | + | 2.84997i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.67506 | + | 11.6503i | 0.0653503 | + | 0.454521i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.4678 | + | 41.1848i | −1.02948 | + | 1.60190i | −0.257474 | + | 0.966285i | \(0.582890\pi\) |
−0.772005 | + | 0.635616i | \(0.780746\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 51.6041i | 1.99513i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2024 | + | 44.9633i | −0.508915 | + | 1.73321i | 0.157398 | + | 0.987535i | \(0.449689\pi\) |
−0.666314 | + | 0.745672i | \(0.732129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.6349 | − | 17.0138i | −0.755750 | − | 0.654861i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.9424 | + | 25.6694i | 1.53285 | + | 0.985103i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.7966 | + | 38.9692i | −0.678984 | + | 1.48677i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.9356 | + | 38.0098i | 1.25293 | + | 1.44596i | 0.846597 | + | 0.532234i | \(0.178648\pi\) |
0.406334 | + | 0.913725i | \(0.366807\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.5549 | − | 25.4204i | 1.49184 | − | 0.958749i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.05961 | − | 7.36976i | 0.0397945 | − | 0.276777i | −0.960202 | − | 0.279306i | \(-0.909896\pi\) |
0.999997 | + | 0.00252851i | \(0.000804851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.07785 | − | 1.86229i | −0.152931 | − | 0.0698413i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −71.7508 | − | 62.1724i | −2.67214 | − | 2.31542i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.3570 | − | 21.1705i | 1.72404 | − | 0.787341i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.9248 | − | 50.8293i | −0.553531 | − | 1.88515i | −0.456140 | − | 0.889908i | \(-0.650768\pi\) |
−0.0973917 | − | 0.995246i | \(-0.531050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.84250 | − | 26.7252i | 0.142315 | − | 0.989821i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.68418 | + | 3.96593i | −0.320757 | + | 0.146485i | −0.569286 | − | 0.822140i | \(-0.692780\pi\) |
0.248529 | + | 0.968625i | \(0.420053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.80151 | + | 5.91526i | −0.139841 | + | 0.217596i | −0.904109 | − | 0.427302i | \(-0.859464\pi\) |
0.764268 | + | 0.644899i | \(0.223100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 43.0141 | + | 94.1877i | 1.58016 | + | 3.46007i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.42864 | − | 5.31797i | −0.0886222 | − | 0.194056i | 0.860131 | − | 0.510073i | \(-0.170382\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.41166 | + | 11.6190i | −0.123999 | + | 0.422301i | −0.997971 | − | 0.0636752i | \(-0.979718\pi\) |
0.873972 | + | 0.485977i | \(0.161536\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.5215 | − | 55.8843i | 0.923940 | − | 2.02315i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.78000 | − | 9.46783i | −0.100250 | − | 0.341419i | 0.894060 | − | 0.447947i | \(-0.147845\pi\) |
−0.994310 | + | 0.106528i | \(0.966026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 49.1426i | − | 1.76525i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.2988 | − | 36.1207i | −1.12284 | − | 1.29582i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.9725 | − | 22.8217i | −1.78133 | − | 0.813504i | −0.975057 | − | 0.221955i | \(-0.928756\pi\) |
−0.806269 | − | 0.591549i | \(-0.798517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.9265 | + | 55.3102i | −1.70192 | + | 1.96412i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.1681 | + | 45.3865i | −1.02423 | + | 1.59374i | −0.242469 | + | 0.970159i | \(0.577957\pi\) |
−0.781763 | + | 0.623576i | \(0.785679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.2886 | + | 27.8199i | 1.51820 | + | 0.975687i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55.1476 | − | 7.92902i | 1.92937 | − | 0.277401i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 88.5443 | − | 56.9039i | 3.09399 | − | 1.98838i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.7721 | − | 16.5627i | 0.898359 | − | 0.577340i | −0.00794450 | − | 0.999968i | \(-0.502529\pi\) |
0.906303 | + | 0.422628i | \(0.138892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.76492 | + | 12.2753i | 0.0612980 | + | 0.426337i | 0.997244 | + | 0.0741933i | \(0.0236382\pi\) |
−0.935946 | + | 0.352144i | \(0.885453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.8865 | + | 33.6954i | −1.34896 | + | 1.16888i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.9632 | − | 27.6108i | 1.48503 | − | 0.954368i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.8059 | + | 23.2023i | 1.74571 | + | 0.797240i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.39324 | + | 21.7734i | 0.219415 | + | 0.747260i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.27773 | + | 13.7463i | 0.214945 | + | 0.470665i | 0.986136 | − | 0.165940i | \(-0.0530657\pi\) |
−0.771191 | + | 0.636604i | \(0.780338\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.30568 | − | 9.08120i | −0.0445492 | − | 0.309846i | −0.999897 | − | 0.0143623i | \(-0.995428\pi\) |
0.955348 | − | 0.295484i | \(-0.0954809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.7840 | + | 12.2318i | −0.909632 | + | 0.415415i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.0565 | + | 49.6664i | 0.916774 | + | 1.68288i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.1664 | − | 23.5994i | 0.513304 | − | 0.798717i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.9010 | − | 41.4319i | −1.21229 | − | 1.39906i | −0.892182 | − | 0.451676i | \(-0.850826\pi\) |
−0.320108 | − | 0.947381i | \(-0.603719\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.6982 | − | 7.72064i | 1.80709 | − | 0.259820i | 0.845434 | − | 0.534080i | \(-0.179342\pi\) |
0.961656 | + | 0.274260i | \(0.0884329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 60.6568 | − | 27.7010i | 2.03436 | − | 0.929063i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.9555 | − | 54.3396i | −0.530967 | − | 1.80831i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.57139 | + | 59.6153i | −0.284608 | + | 1.97949i | −0.130153 | + | 0.991494i | \(0.541547\pi\) |
−0.154455 | + | 0.988000i | \(0.549362\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2086 | + | 15.8849i | 0.336751 | + | 0.523995i | 0.967791 | − | 0.251755i | \(-0.0810079\pi\) |
−0.631040 | + | 0.775751i | \(0.717371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −55.1532 | − | 25.1876i | −1.81736 | − | 0.829961i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.86708 | + | 26.8961i | 0.127149 | + | 0.884338i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.7336 | + | 42.3928i | −1.20649 | + | 1.39236i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −136.701 | − | 87.8526i | −4.48021 | − | 2.87925i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.625795i | − | 0.0204438i | −0.999948 | − | 0.0102219i | \(-0.996746\pi\) | ||
0.999948 | − | 0.0102219i | \(-0.00325379\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.7790 | −0.645463 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.4877 | + | 17.7527i | 0.665059 | + | 0.576277i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.9424 | + | 18.4815i | 2.03040 | + | 0.596179i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.59871 | 0.0835688 | 0.0417844 | − | 0.999127i | \(-0.486696\pi\) | ||||
0.0417844 | + | 0.999127i | \(0.486696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 102.927 | − | 30.2220i | 3.29968 | − | 0.968872i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −59.8394 | −1.91639 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.0183 | − | 15.0790i | −1.05419 | − | 0.481435i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.0735 | + | 26.0646i | −1.81300 | + | 0.827970i | −0.872058 | + | 0.489402i | \(0.837215\pi\) |
−0.940942 | + | 0.338567i | \(0.890058\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.87423 | + | 13.0355i | 0.0594768 | + | 0.413670i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.86556 | − | 26.8856i | 0.122424 | − | 0.851474i | −0.832373 | − | 0.554215i | \(-0.813018\pi\) |
0.954797 | − | 0.297259i | \(-0.0960725\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.3414 | + | 18.4924i | −0.675211 | + | 0.585074i |
(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 | 804.2.s.a.125.2 | ✓ | 20 | |
3.2 | odd | 2 | CM | 804.2.s.a.125.2 | ✓ | 20 | |
67.52 | odd | 22 | inner | 804.2.s.a.521.2 | yes | 20 | |
201.119 | even | 22 | inner | 804.2.s.a.521.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.s.a.125.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
804.2.s.a.125.2 | ✓ | 20 | 3.2 | odd | 2 | CM | |
804.2.s.a.521.2 | yes | 20 | 67.52 | odd | 22 | inner | |
804.2.s.a.521.2 | yes | 20 | 201.119 | even | 22 | inner |