Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(3497,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.3497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.c (of order \(2\), degree \(1\), 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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3497.10 | ||
Character | \(\chi\) | \(=\) | 4028.3497 |
Dual form | 4028.2.c.a.3497.73 |
$q$-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 \(\left(\mathbb{Z}/4028\mathbb{Z}\right)^\times\).
\(n\) | \(2015\) | \(2281\) | \(2757\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.57074i | − | 1.48422i | −0.670281 | − | 0.742108i | \(-0.733826\pi\) | ||
0.670281 | − | 0.742108i | \(-0.266174\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.44297i | 1.09253i | 0.837613 | + | 0.546264i | \(0.183950\pi\) | ||||
−0.837613 | + | 0.546264i | \(0.816050\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.60312 | 1.36185 | 0.680925 | − | 0.732353i | \(-0.261578\pi\) | ||||
0.680925 | + | 0.732353i | \(0.261578\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.60868 | −1.20289 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.948707 | −0.286046 | −0.143023 | − | 0.989719i | \(-0.545682\pi\) | ||||
−0.143023 | + | 0.989719i | \(0.545682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.15492 | −0.875016 | −0.437508 | − | 0.899214i | \(-0.644139\pi\) | ||||
−0.437508 | + | 0.899214i | \(0.644139\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.28022 | 1.62155 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.26887 | −1.76296 | −0.881480 | − | 0.472221i | \(-0.843452\pi\) | ||||
−0.881480 | + | 0.472221i | \(0.843452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 9.26266i | − | 2.02128i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.89346i | 1.43739i | 0.695327 | + | 0.718693i | \(0.255259\pi\) | ||||
−0.695327 | + | 0.718693i | \(0.744741\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.968083 | −0.193617 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.56476i | 0.301139i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.36961 | −1.18281 | −0.591404 | − | 0.806376i | \(-0.701426\pi\) | ||||
−0.591404 | + | 0.806376i | \(0.701426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.80776i | − | 0.504289i | −0.967690 | − | 0.252145i | \(-0.918864\pi\) | ||
0.967690 | − | 0.252145i | \(-0.0811359\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.43887i | 0.424554i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.80229i | 1.48786i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1740 | 1.83699 | 0.918495 | − | 0.395433i | \(-0.129405\pi\) | ||||
0.918495 | + | 0.395433i | \(0.129405\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.11046i | 1.29871i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92669i | 1.08177i | 0.841097 | + | 0.540884i | \(0.181910\pi\) | ||||
−0.841097 | + | 0.540884i | \(0.818090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.16676 | −0.635425 | −0.317712 | − | 0.948187i | \(-0.602915\pi\) | ||||
−0.317712 | + | 0.948187i | \(0.602915\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 8.81589i | − | 1.31420i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.62489 | −0.820474 | −0.410237 | − | 0.911979i | \(-0.634554\pi\) | ||||
−0.410237 | + | 0.911979i | \(0.634554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.98244 | 0.854635 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.6863i | 2.61661i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.24654 | + | 0.698304i | 0.995389 | + | 0.0959195i | ||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.31766i | − | 0.312513i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.57074 | 0.340502 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.58150 | −0.596460 | −0.298230 | − | 0.954494i | \(-0.596396\pi\) | ||||
−0.298230 | + | 0.954494i | \(0.596396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.5043i | − | 1.47297i | −0.676451 | − | 0.736487i | \(-0.736483\pi\) | ||
0.676451 | − | 0.736487i | \(-0.263517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.0025 | −1.63816 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7.70735i | − | 0.955980i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.84596i | 1.08071i | 0.841439 | + | 0.540353i | \(0.181709\pi\) | ||||
−0.841439 | + | 0.540353i | \(0.818291\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 17.7213 | 2.13339 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.8529i | 1.52536i | 0.646777 | + | 0.762679i | \(0.276116\pi\) | ||||
−0.646777 | + | 0.762679i | \(0.723884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.65387i | 0.544694i | 0.962199 | + | 0.272347i | \(0.0877998\pi\) | ||||
−0.962199 | + | 0.272347i | \(0.912200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.48869i | 0.287369i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.41830 | −0.389551 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.29138i | − | 0.932853i | −0.884560 | − | 0.466427i | \(-0.845541\pi\) | ||
0.884560 | − | 0.466427i | \(-0.154459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.80345 | −0.755939 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.5520i | 1.48753i | 0.668442 | + | 0.743764i | \(0.266961\pi\) | ||||
−0.668442 | + | 0.743764i | \(0.733039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 17.7576i | − | 1.92608i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.3746i | 1.75554i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.4473 | −1.10741 | −0.553706 | − | 0.832712i | \(-0.686787\pi\) | ||||
−0.553706 | + | 0.832712i | \(0.686787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3675 | −1.19164 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.21802 | −0.748474 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.44297 | −0.250643 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.9611 | −1.62060 | −0.810300 | − | 0.586016i | \(-0.800696\pi\) | ||||
−0.810300 | + | 0.586016i | \(0.800696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.42358 | 0.344083 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.15664i | 0.513104i | 0.966530 | + | 0.256552i | \(0.0825866\pi\) | ||||
−0.966530 | + | 0.256552i | \(0.917413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.888961i | − | 0.0875919i | −0.999040 | − | 0.0437960i | \(-0.986055\pi\) | ||
0.999040 | − | 0.0437960i | \(-0.0139451\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 22.6284 | 2.20830 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.55582 | 0.440428 | 0.220214 | − | 0.975452i | \(-0.429324\pi\) | ||||
0.220214 | + | 0.975452i | \(0.429324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.1576i | 1.54762i | 0.633419 | + | 0.773809i | \(0.281651\pi\) | ||||
−0.633419 | + | 0.773809i | \(0.718349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 28.7253i | − | 2.72649i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.11319 | −0.104720 | −0.0523602 | − | 0.998628i | \(-0.516674\pi\) | ||||
−0.0523602 | + | 0.998628i | \(0.516674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.8405 | −1.57038 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.3851 | 1.05255 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.1906 | −2.40089 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1000 | −0.918178 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.8067 | 1.60558 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.84984i | 0.880996i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2788i | 1.08957i | 0.838576 | + | 0.544784i | \(0.183389\pi\) | ||||
−0.838576 | + | 0.544784i | \(0.816611\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7116i | 0.943107i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.7383 | −1.89928 | −0.949642 | − | 0.313337i | \(-0.898553\pi\) | ||||
−0.949642 | + | 0.313337i | \(0.898553\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.60312i | 0.312430i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.82267 | −0.329003 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.6929i | − | 1.08443i | −0.840240 | − | 0.542214i | \(-0.817586\pi\) | ||
0.840240 | − | 0.542214i | \(-0.182414\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.58144i | 0.812687i | 0.913720 | + | 0.406343i | \(0.133196\pi\) | ||||
−0.913720 | + | 0.406343i | \(0.866804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.4601i | 1.21776i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.99309 | 0.250295 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.5608i | − | 1.29225i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 15.3793i | − | 1.26846i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.0973 | 1.40066 | 0.700332 | − | 0.713817i | \(-0.253035\pi\) | ||||
0.700332 | + | 0.713817i | \(0.253035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8359i | 1.12595i | 0.826475 | + | 0.562974i | \(0.190343\pi\) | ||||
−0.826475 | + | 0.562974i | \(0.809657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 26.2311 | 2.12066 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.85927 | 0.550950 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.0964i | − | 1.52406i | −0.647541 | − | 0.762031i | \(-0.724202\pi\) | ||
0.647541 | − | 0.762031i | \(-0.275798\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.79516 | − | 18.6289i | 0.142365 | − | 1.47737i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.8379i | 1.95750i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8464 | 1.16286 | 0.581428 | − | 0.813598i | \(-0.302494\pi\) | ||||
0.581428 | + | 0.813598i | \(0.302494\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.95809 | −0.463837 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.0043i | − | 1.47060i | −0.677742 | − | 0.735299i | \(-0.737042\pi\) | ||
0.677742 | − | 0.735299i | \(-0.262958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.04650 | −0.234346 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 3.60868i | − | 0.275963i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.4866i | 1.63360i | 0.576923 | + | 0.816798i | \(0.304253\pi\) | ||||
−0.576923 | + | 0.816798i | \(0.695747\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.48812 | −0.263677 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.7778i | 0.885275i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.72190i | 0.278188i | 0.990279 | + | 0.139094i | \(0.0444190\pi\) | ||||
−0.990279 | + | 0.139094i | \(0.955581\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.11585i | 0.528917i | 0.964397 | + | 0.264459i | \(0.0851933\pi\) | ||||
−0.964397 | + | 0.264459i | \(0.914807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.5745 | −2.18621 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.2976i | 2.00696i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.89603 | 0.504287 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.63803i | 0.410106i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 9.99012i | − | 0.722859i | −0.932399 | − | 0.361430i | \(-0.882289\pi\) | ||
0.932399 | − | 0.361430i | \(-0.117711\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.5860i | 1.04992i | 0.851126 | + | 0.524962i | \(0.175920\pi\) | ||||
−0.851126 | + | 0.524962i | \(0.824080\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.8136 | −1.41888 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0710 | 0.860023 | 0.430011 | − | 0.902824i | \(-0.358510\pi\) | ||||
0.430011 | + | 0.902824i | \(0.358510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.40006 | 0.170136 | 0.0850679 | − | 0.996375i | \(-0.472889\pi\) | ||||
0.0850679 | + | 0.996375i | \(0.472889\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.7406 | 1.60400 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.9505 | −1.61081 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.9217 | −1.18186 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 24.8763i | − | 1.72902i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.948707i | − | 0.0656234i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.93651 | −0.133315 | −0.0666573 | − | 0.997776i | \(-0.521233\pi\) | ||||
−0.0666573 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 33.0414 | 2.26396 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 10.1793i | − | 0.694219i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 10.1167i | − | 0.686766i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.9639 | 0.808443 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.9327 | 1.54262 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.85826 | −0.392298 | −0.196149 | − | 0.980574i | \(-0.562844\pi\) | ||||
−0.196149 | + | 0.980574i | \(0.562844\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.49351 | 0.232900 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.75394 | 0.182785 | 0.0913927 | − | 0.995815i | \(-0.470868\pi\) | ||||
0.0913927 | + | 0.995815i | \(0.470868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5488 | −1.62223 | −0.811116 | − | 0.584886i | \(-0.801139\pi\) | ||||
−0.811116 | + | 0.584886i | \(0.801139\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.78755i | 0.578178i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 21.7655i | − | 1.42590i | −0.701214 | − | 0.712951i | \(-0.747358\pi\) | ||
0.701214 | − | 0.712951i | \(-0.252642\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.7414i | − | 0.896390i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.3150 | −1.38456 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.1693i | − | 1.17527i | −0.809125 | − | 0.587636i | \(-0.800059\pi\) | ||
0.809125 | − | 0.587636i | \(-0.199941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0911 | 1.55184 | 0.775921 | − | 0.630831i | \(-0.217286\pi\) | ||||
0.775921 | + | 0.630831i | \(0.217286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.1842i | 1.42312i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.6149i | 0.933712i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.15492i | − | 0.200743i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.8387 | 2.20781 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2126i | 0.770856i | 0.922738 | + | 0.385428i | \(0.125946\pi\) | ||||
−0.922738 | + | 0.385428i | \(0.874054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.53987i | − | 0.411158i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −45.6501 | −2.85872 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.45904i | − | 0.590039i | −0.955491 | − | 0.295019i | \(-0.904674\pi\) | ||
0.955491 | − | 0.295019i | \(-0.0953261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 40.2611 | 2.50170 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.9859 | 1.42279 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.16668i | − | 0.441916i | −0.975283 | − | 0.220958i | \(-0.929082\pi\) | ||
0.975283 | − | 0.220958i | \(-0.0709184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.70593 | + | 17.7031i | −0.104795 | + | 1.08749i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.8573i | 1.64364i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.56790 | −0.522394 | −0.261197 | − | 0.965285i | \(-0.584117\pi\) | ||||
−0.261197 | + | 0.965285i | \(0.584117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5952 | −1.06883 | −0.534415 | − | 0.845222i | \(-0.679468\pi\) | ||||
−0.534415 | + | 0.845222i | \(0.679468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.2229i | 1.76865i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.918427 | 0.0553832 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5039i | 0.931537i | 0.884907 | + | 0.465768i | \(0.154222\pi\) | ||||
−0.884907 | + | 0.465768i | \(0.845778\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.1323i | 0.606607i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7959 | −1.59851 | −0.799255 | − | 0.600992i | \(-0.794772\pi\) | ||||
−0.799255 | + | 0.600992i | \(0.794772\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.6246i | − | 0.750454i | −0.926933 | − | 0.375227i | \(-0.877565\pi\) | ||
0.926933 | − | 0.375227i | \(-0.122435\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.28022i | 0.372008i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.9577i | 1.47320i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.8365 | 2.10803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.0317i | 2.40532i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.83415 | −0.340835 | −0.170417 | − | 0.985372i | \(-0.554512\pi\) | ||||
−0.170417 | + | 0.985372i | \(0.554512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.1924i | − | 0.651649i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.48450i | − | 0.0861396i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 21.7483i | − | 1.25774i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0133 | −0.865353 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.2563 | 0.761557 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.1046 | 1.60927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.0926 | 1.77455 | 0.887276 | − | 0.461240i | \(-0.152595\pi\) | ||||
0.887276 | + | 0.461240i | \(0.152595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.28528 | −0.130005 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.31053 | 0.471247 | 0.235623 | − | 0.971844i | \(-0.424287\pi\) | ||||
0.235623 | + | 0.971844i | \(0.424287\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.49511i | 0.0845085i | 0.999107 | + | 0.0422543i | \(0.0134540\pi\) | ||||
−0.999107 | + | 0.0422543i | \(0.986546\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 31.7647i | − | 1.78974i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0874 | 0.566566 | 0.283283 | − | 0.959036i | \(-0.408576\pi\) | ||||
0.283283 | + | 0.959036i | \(0.408576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.04290 | 0.338337 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 11.7118i | − | 0.653690i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.26887i | − | 0.404451i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.05422 | 0.169418 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 41.5370 | 2.29700 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.2671 | −1.11736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.9475 | 1.15138 | 0.575688 | − | 0.817669i | \(-0.304734\pi\) | ||||
0.575688 | + | 0.817669i | \(0.304734\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40.3233 | −2.20971 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.6104 | −1.18070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.92030i | − | 0.322500i | −0.986914 | − | 0.161250i | \(-0.948448\pi\) | ||
0.986914 | − | 0.161250i | \(-0.0515525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.86172i | 0.155427i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.66374i | 0.144250i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.66637 | −0.197965 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 43.2925i | 2.33079i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.8245 | 1.81579 | 0.907897 | − | 0.419193i | \(-0.137687\pi\) | ||||
0.907897 | + | 0.419193i | \(0.137687\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 35.3581i | − | 1.89268i | −0.323178 | − | 0.946338i | \(-0.604751\pi\) | ||
0.323178 | − | 0.946338i | \(-0.395249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.93670i | − | 0.263502i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.04080i | 0.374744i | 0.982289 | + | 0.187372i | \(0.0599969\pi\) | ||||
−0.982289 | + | 0.187372i | \(0.940003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.3992 | −1.66650 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 67.3291i | 3.56343i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.4866i | 1.08124i | 0.841267 | + | 0.540620i | \(0.181810\pi\) | ||||
−0.841267 | + | 0.540620i | \(0.818190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.9643i | 1.36277i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.3692 | −0.595093 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.6024 | −1.49303 | −0.746516 | − | 0.665368i | \(-0.768275\pi\) | ||||
−0.746516 | + | 0.665368i | \(0.768275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 24.9962i | − | 1.30125i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 26.1101 | + | 2.51607i | 1.35557 | + | 0.130628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8995i | 0.719690i | 0.933012 | + | 0.359845i | \(0.117170\pi\) | ||||
−0.933012 | + | 0.359845i | \(0.882830\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.3213 | 1.30759 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.0956 | 1.03498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.8767i | − | 1.27783i | −0.769278 | − | 0.638915i | \(-0.779384\pi\) | ||
0.769278 | − | 0.638915i | \(-0.220616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 31.5656 | 1.61715 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 11.9379i | − | 0.609998i | −0.952353 | − | 0.304999i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304999i | \(-0.0986562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 8.35079i | − | 0.425596i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.0365 | 0.764349 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.34772i | − | 0.372544i | −0.982498 | − | 0.186272i | \(-0.940359\pi\) | ||
0.982498 | − | 0.186272i | \(-0.0596406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 50.1077i | − | 2.53406i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 55.8834i | 2.81895i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.2556 | 1.01917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.8014i | 1.09418i | 0.837073 | + | 0.547091i | \(0.184265\pi\) | ||||
−0.837073 | + | 0.547091i | \(0.815735\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.26266 | 0.463713 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.9816i | 0.947897i | 0.880553 | + | 0.473948i | \(0.157172\pi\) | ||||
−0.880553 | + | 0.473948i | \(0.842828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.85826i | 0.441261i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 16.6206i | − | 0.825885i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.6008 | −0.525463 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.1676 | 1.59058 | 0.795292 | − | 0.606226i | \(-0.207317\pi\) | ||||
0.795292 | + | 0.606226i | \(0.207317\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.6301 | −1.60952 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.5077 | −0.812289 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.1071 | −1.62517 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.6313 | 1.20620 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.6421i | 1.44811i | 0.689741 | + | 0.724056i | \(0.257725\pi\) | ||||
−0.689741 | + | 0.724056i | \(0.742275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.8937i | 1.11577i | 0.829917 | + | 0.557886i | \(0.188388\pi\) | ||||
−0.829917 | + | 0.557886i | \(0.811612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.2984 | 0.986943 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.03687 | 0.341338 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 41.4513i | − | 2.00597i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 7.69445i | − | 0.371491i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.7222 | 1.67251 | 0.836255 | − | 0.548341i | \(-0.184740\pi\) | ||||
0.836255 | + | 0.548341i | \(0.184740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.1939 | 1.45102 | 0.725512 | − | 0.688209i | \(-0.241603\pi\) | ||||
0.725512 | + | 0.688209i | \(0.241603\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40.0026 | −1.91798 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.89346 | −0.329759 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7509 | 1.18130 | 0.590648 | − | 0.806930i | \(-0.298872\pi\) | ||||
0.590648 | + | 0.806930i | \(0.298872\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.5887 | −1.02804 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.6006i | 0.551159i | 0.961278 | + | 0.275580i | \(0.0888698\pi\) | ||||
−0.961278 | + | 0.275580i | \(0.911130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 25.5224i | − | 1.20988i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 43.9526i | − | 2.07889i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4105 | −0.491303 | −0.245652 | − | 0.969358i | \(-0.579002\pi\) | ||||
−0.245652 | + | 0.969358i | \(0.579002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6.57140i | − | 0.309435i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.5684 | 1.67115 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 27.7705i | − | 1.30190i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 25.7431i | − | 1.20421i | −0.798417 | − | 0.602105i | \(-0.794329\pi\) | ||
0.798417 | − | 0.602105i | \(-0.205671\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 11.3741i | − | 0.530896i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.85631 | −0.319330 | −0.159665 | − | 0.987171i | \(-0.551041\pi\) | ||||
−0.159665 | + | 0.987171i | \(0.551041\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.8067i | 1.52466i | 0.647190 | + | 0.762329i | \(0.275944\pi\) | ||||
−0.647190 | + | 0.762329i | \(0.724056\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 17.6334i | − | 0.817728i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.8687 | −1.38216 | −0.691078 | − | 0.722780i | \(-0.742864\pi\) | ||||
−0.691078 | + | 0.722780i | \(0.742864\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.8730i | 1.47176i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −49.0919 | −2.26204 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.95303 | 0.181761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.968083i | − | 0.0444187i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.1505 | − | 2.51996i | −1.19735 | − | 0.115381i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 10.9833i | − | 0.501841i | −0.968008 | − | 0.250921i | \(-0.919267\pi\) | ||
0.968008 | − | 0.250921i | \(-0.0807333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.2530 | −1.60740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 63.8518 | 2.90536 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 38.9923i | − | 1.77055i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4742 | −0.973088 | −0.486544 | − | 0.873656i | \(-0.661743\pi\) | ||||
−0.486544 | + | 0.873656i | \(0.661743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 38.1661i | − | 1.72593i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.52728i | 0.0689252i | 0.999406 | + | 0.0344626i | \(0.0109720\pi\) | ||||
−0.999406 | + | 0.0344626i | \(0.989028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.2999 | 2.08524 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.36370i | 0.375920i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.3105i | 2.07731i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.54485i | 0.158689i | 0.996847 | + | 0.0793446i | \(0.0252827\pi\) | ||||
−0.996847 | + | 0.0793446i | \(0.974717\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −48.8551 | −2.18269 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 28.6581i | − | 1.27780i | −0.769289 | − | 0.638901i | \(-0.779390\pi\) | ||
0.769289 | − | 0.638901i | \(-0.220610\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.5975 | −0.560581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.83175i | 0.347820i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7.91923i | − | 0.351014i | −0.984478 | − | 0.175507i | \(-0.943844\pi\) | ||
0.984478 | − | 0.175507i | \(-0.0561564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.7684i | 0.741791i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.56476 | −0.0690860 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.17170 | 0.0956966 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.33637 | 0.234693 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55.2364 | 2.42461 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3321 | −0.671712 | −0.335856 | − | 0.941913i | \(-0.609025\pi\) | ||||
−0.335856 | + | 0.941913i | \(0.609025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8157 | −0.953934 | −0.476967 | − | 0.878921i | \(-0.658264\pi\) | ||||
−0.476967 | + | 0.878921i | \(0.658264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.96703i | 0.391353i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4093i | 0.889042i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.5198 | −1.06608 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.5332 | 0.717478 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21.8531i | − | 0.946564i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.1297i | 0.481180i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.56802 | 0.412891 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.67559 | −0.244465 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.96480 | 0.127467 | 0.0637335 | − | 0.997967i | \(-0.479699\pi\) | ||||
0.0637335 | + | 0.997967i | \(0.479699\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.2930 | 0.785027 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.4725 | −1.69082 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9037 | −1.06481 | −0.532403 | − | 0.846491i | \(-0.678711\pi\) | ||||
−0.532403 | + | 0.846491i | \(0.678711\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 41.5154i | 1.77183i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.36961i | − | 0.271355i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 29.8748i | − | 1.27041i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 70.1750 | 2.97876 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.9872i | − | 0.635030i | −0.948253 | − | 0.317515i | \(-0.897152\pi\) | ||
0.948253 | − | 0.317515i | \(-0.102848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.1458 | 0.556007 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 17.7279i | − | 0.748471i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.6862i | 1.12469i | 0.826903 | + | 0.562345i | \(0.190101\pi\) | ||||
−0.826903 | + | 0.562345i | \(0.809899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.71949i | − | 0.114410i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.5136 | −1.02948 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17.8067i | − | 0.746494i | −0.927732 | − | 0.373247i | \(-0.878244\pi\) | ||
0.927732 | − | 0.373247i | \(-0.121756\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.9075i | − | 0.665708i | −0.942978 | − | 0.332854i | \(-0.891988\pi\) | ||
0.942978 | − | 0.332854i | \(-0.108012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.6819 | −1.07288 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.67345i | − | 0.278302i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.8577 | 1.78419 | 0.892094 | − | 0.451849i | \(-0.149235\pi\) | ||||
0.892094 | + | 0.451849i | \(0.149235\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37.4968 | 1.55831 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.8295i | 2.02579i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.87484 | − | 0.662486i | −0.284727 | − | 0.0274374i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.8134i | 1.14994i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.3378 | −1.87129 | −0.935647 | − | 0.352938i | \(-0.885183\pi\) | ||||
−0.935647 | + | 0.352938i | \(0.885183\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.80776 | 0.115692 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 31.0313i | − | 1.27646i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.2727 | 0.668238 | 0.334119 | − | 0.942531i | \(-0.391561\pi\) | ||||
0.334119 | + | 0.942531i | \(0.391561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 63.9827i | − | 2.62304i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 6.16992i | − | 0.252518i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.6092 | −0.719494 | −0.359747 | − | 0.933050i | \(-0.617137\pi\) | ||||
−0.359747 | + | 0.933050i | \(0.617137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.9394i | − | 1.26204i | −0.775765 | − | 0.631022i | \(-0.782636\pi\) | ||
0.775765 | − | 0.631022i | \(-0.217364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 31.9223i | − | 1.29997i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 24.6738i | − | 1.00313i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.1792 | −0.616104 | −0.308052 | − | 0.951370i | \(-0.599677\pi\) | ||||
−0.308052 | + | 0.951370i | \(0.599677\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 58.9996i | 2.39078i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.7460 | 0.717928 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 35.9950i | − | 1.45383i | −0.686730 | − | 0.726913i | \(-0.740954\pi\) | ||
0.686730 | − | 0.726913i | \(-0.259046\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 43.5012i | 1.75414i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.671258i | − | 0.0270238i | −0.999909 | − | 0.0135119i | \(-0.995699\pi\) | ||
0.999909 | − | 0.0135119i | \(-0.00430111\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4141 | 1.26264 | 0.631320 | − | 0.775523i | \(-0.282514\pi\) | ||||
0.631320 | + | 0.775523i | \(0.282514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.7866 | −0.432853 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −37.6429 | −1.50813 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.9032 | −1.15613 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.43887 | −0.0973993 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −81.2222 | −3.23854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.73742i | − | 0.188594i | −0.995544 | − | 0.0942968i | \(-0.969940\pi\) | ||
0.995544 | − | 0.0942968i | \(-0.0300603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.97825i | 0.197868i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.9967 | −1.19038 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.8741 | −0.747820 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 46.3820i | − | 1.83484i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 42.6838i | − | 1.68591i | −0.537986 | − | 0.842954i | \(-0.680815\pi\) | ||
0.537986 | − | 0.842954i | \(-0.319185\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.8484 | −1.01936 | −0.509682 | − | 0.860363i | \(-0.670237\pi\) | ||||
−0.509682 | + | 0.860363i | \(0.670237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.1682 | −1.03037 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.5257 | −1.63254 | −0.816272 | − | 0.577668i | \(-0.803963\pi\) | ||||
−0.816272 | + | 0.577668i | \(0.803963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.34650 | 0.170615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.0074 | −1.01931 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.03265 | 0.353475 | 0.176737 | − | 0.984258i | \(-0.443446\pi\) | ||||
0.176737 | + | 0.984258i | \(0.443446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 53.1059i | − | 2.07502i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 16.7943i | − | 0.655209i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27.7419i | − | 1.08067i | −0.841450 | − | 0.540335i | \(-0.818298\pi\) | ||
0.841450 | − | 0.540335i | \(-0.181702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.8006 | 0.731260 | 0.365630 | − | 0.930760i | \(-0.380854\pi\) | ||||
0.365630 | + | 0.930760i | \(0.380854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 58.9539i | − | 2.28958i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.80229 | −0.341338 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 43.9087i | − | 1.70015i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.0600i | 0.582255i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9142i | 0.421338i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.60508 | −0.216060 | −0.108030 | − | 0.994148i | \(-0.534454\pi\) | ||||
−0.108030 | + | 0.994148i | \(0.534454\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.51482i | − | 0.0583055i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 40.8171i | − | 1.56873i | −0.620301 | − | 0.784364i | \(-0.712990\pi\) | ||
0.620301 | − | 0.784364i | \(-0.287010\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −57.5095 | −2.20701 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 7.07965i | − | 0.271293i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9164 | −1.29778 | −0.648888 | − | 0.760884i | \(-0.724766\pi\) | ||||
−0.648888 | + | 0.760884i | \(0.724766\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.0083 | 1.18477 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 63.1085i | 2.40774i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.8622 | − | 2.20309i | −0.870982 | − | 0.0839311i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.7868i | 1.47552i | 0.675064 | + | 0.737759i | \(0.264116\pi\) | ||||
−0.675064 | + | 0.737759i | \(0.735884\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.3356 | 0.468589 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.4071 | −0.887883 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 50.3492i | − | 1.90711i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −55.9532 | −2.11635 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.1597i | 1.47904i | 0.673134 | + | 0.739520i | \(0.264948\pi\) | ||||
−0.673134 | + | 0.739520i | \(0.735052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1740i | 0.421434i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35.3255 | −1.33044 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.5800i | 0.698771i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.27467i | − | 0.122983i | −0.998108 | − | 0.0614913i | \(-0.980414\pi\) | ||
0.998108 | − | 0.0614913i | \(-0.0195857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.9210i | 1.12212i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.3552 | 0.724859 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.31202i | 0.273454i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.7084 | −1.74436 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 22.2113i | − | 0.828341i | −0.910199 | − | 0.414170i | \(-0.864072\pi\) | ||
0.910199 | − | 0.414170i | \(-0.135928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.20303i | − | 0.119287i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 61.9317i | − | 2.30327i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.16632 | 0.229011 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1898 | −0.377920 | −0.188960 | − | 0.981985i | \(-0.560512\pi\) | ||||
−0.188960 | + | 0.981985i | \(0.560512\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.6193 | 1.35627 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.2876 | 1.12023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.3091 | 0.750132 | 0.375066 | − | 0.926998i | \(-0.377620\pi\) | ||||
0.375066 | + | 0.926998i | \(0.377620\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 37.5711 | 1.38583 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8.39222i | − | 0.309131i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.9263i | − | 0.916929i | −0.888713 | − | 0.458464i | \(-0.848400\pi\) | ||
0.888713 | − | 0.458464i | \(-0.151600\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.11046 | −0.297945 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0233 | 0.624523 | 0.312262 | − | 0.949996i | \(-0.398913\pi\) | ||||
0.312262 | + | 0.949996i | \(0.398913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.7681i | 1.53027i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 48.9050i | − | 1.78934i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.4152 | 0.599797 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.83424 | 0.139914 | 0.0699568 | − | 0.997550i | \(-0.477714\pi\) | ||||
0.0699568 | + | 0.997550i | \(0.477714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.3955 | 1.14412 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.8006 | −1.23013 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0335 | −1.12793 | −0.563965 | − | 0.825798i | \(-0.690725\pi\) | ||||
−0.563965 | + | 0.825798i | \(0.690725\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.8123 | −0.610248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.3119i | − | 0.373806i | −0.982378 | − | 0.186903i | \(-0.940155\pi\) | ||
0.982378 | − | 0.186903i | \(-0.0598450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.2177i | 2.10762i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 64.0816i | 2.31687i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.4542 | 0.521912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.9935i | 0.757044i | 0.925592 | + | 0.378522i | \(0.123568\pi\) | ||||
−0.925592 | + | 0.378522i | \(0.876432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.3167 | −0.875744 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.05916i | − | 0.325835i | −0.986640 | − | 0.162918i | \(-0.947909\pi\) | ||
0.986640 | − | 0.162918i | \(-0.0520905\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.71815i | 0.0976388i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 103.501i | − | 3.71307i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.92669 | −0.248175 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 12.1936i | − | 0.436322i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.96695i | − | 0.356190i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.6519 | 1.66508 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 23.4232i | − | 0.834948i | −0.908689 | − | 0.417474i | \(-0.862916\pi\) | ||
0.908689 | − | 0.417474i | \(-0.137084\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.4236 | −0.655899 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.01096 | −0.142613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.2951i | 1.28888i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 45.5099 | + | 4.38551i | 1.61407 | + | 0.155538i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.5691i | 1.96836i | 0.177176 | + | 0.984179i | \(0.443304\pi\) | ||||
−0.177176 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.8866 | 1.44646 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.7010 | 1.33210 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 4.41515i | − | 0.155807i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −60.6783 | −2.13863 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.0258i | 0.775346i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.6779i | 1.07858i | 0.842121 | + | 0.539289i | \(0.181307\pi\) | ||||
−0.842121 | + | 0.539289i | \(0.818693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.7290 | 0.763010 | 0.381505 | − | 0.924367i | \(-0.375406\pi\) | ||||
0.381505 | + | 0.924367i | \(0.375406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.2325i | 1.58637i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.2691i | 1.27045i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.16676i | − | 0.145776i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.0218 | 1.43342 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.69953i | 0.233815i | 0.993143 | + | 0.116908i | \(0.0372982\pi\) | ||||
−0.993143 | + | 0.116908i | \(0.962702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.4208 | −1.16497 | −0.582487 | − | 0.812840i | \(-0.697920\pi\) | ||||
−0.582487 | + | 0.812840i | \(0.697920\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.36103i | − | 0.0822006i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.1652i | − | 0.562119i | −0.959690 | − | 0.281059i | \(-0.909314\pi\) | ||
0.959690 | − | 0.281059i | \(-0.0906858\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.0835i | 0.766992i | 0.923543 | + | 0.383496i | \(0.125280\pi\) | ||||
−0.923543 | + | 0.383496i | \(0.874720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 39.8563 | 1.38260 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43.4856 | −1.50669 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.4269 | 1.60667 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.39349 | 0.151861 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.4795 | 1.25941 | 0.629706 | − | 0.776833i | \(-0.283175\pi\) | ||||
0.629706 | + | 0.776833i | \(0.283175\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5720 | 0.399034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 68.8852i | 2.37253i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.44250i | − | 0.256030i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.3913 | −1.25042 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.4545 | −1.11384 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77.0274i | 2.64046i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6039i | 0.876661i | 0.898814 | + | 0.438330i | \(0.144430\pi\) | ||||
−0.898814 | + | 0.438330i | \(0.855570\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.81589 | 0.301497 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.2444 | 1.06729 | 0.533644 | − | 0.845709i | \(-0.320822\pi\) | ||||
0.533644 | + | 0.845709i | \(0.320822\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.4493 | −1.58483 | −0.792415 | − | 0.609983i | \(-0.791176\pi\) | ||||
−0.792415 | + | 0.609983i | \(0.791176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 64.1596 | 2.18655 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.2303 | 0.756728 | 0.378364 | − | 0.925657i | \(-0.376487\pi\) | ||||
0.378364 | + | 0.925657i | \(0.376487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.4911 | −1.78475 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 92.1262i | − | 3.12877i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.86609i | 0.266839i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 27.9083i | − | 0.945635i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 57.5984 | 1.94941 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 35.4901i | 1.19978i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.8793 | −1.07649 | −0.538244 | − | 0.842789i | \(-0.680912\pi\) | ||||
−0.538244 | + | 0.842789i | \(0.680912\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.9981i | 0.505872i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.55656i | 0.0524418i | 0.999656 | + | 0.0262209i | \(0.00834732\pi\) | ||||
−0.999656 | + | 0.0262209i | \(0.991653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.37840i | 0.0463869i | 0.999731 | + | 0.0231934i | \(0.00738336\pi\) | ||||
−0.999731 | + | 0.0231934i | \(0.992617\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.7728 | −0.967187 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 7.54983i | − | 0.253499i | −0.991935 | − | 0.126749i | \(-0.959546\pi\) | ||
0.991935 | − | 0.126749i | \(-0.0404544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.2420i | 1.48383i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.45448 | 0.216233 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 5.62489i | − | 0.188230i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.09247 | −0.303928 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −55.9091 | −1.86675 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.8844i | 0.596477i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.6742 | − | 5.07589i | −1.75483 | − | 0.169102i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.5953i | 1.28437i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.3838 | −0.577857 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3016 | −0.474876 | −0.237438 | − | 0.971403i | \(-0.576308\pi\) | ||||
−0.237438 | + | 0.971403i | \(0.576308\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 18.6087i | − | 0.617211i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.3908 | −0.543051 | −0.271526 | − | 0.962431i | \(-0.587528\pi\) | ||||
−0.271526 | + | 0.962431i | \(0.587528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.8569i | − | 0.425501i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 72.2495i | − | 2.38850i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −78.3256 | −2.58654 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.06505i | − | 0.266042i | −0.991113 | − | 0.133021i | \(-0.957532\pi\) | ||
0.991113 | − | 0.133021i | \(-0.0424677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 79.9310i | − | 2.63382i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 40.5498i | − | 1.33471i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8173 | −0.355672 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.20798i | 0.105364i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.4599 | −0.507223 | −0.253611 | − | 0.967306i | \(-0.581618\pi\) | ||||
−0.253611 | + | 0.967306i | \(0.581618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.98244i | 0.196067i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 21.3642i | − | 0.699432i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.8468i | 0.550948i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.4639 | −0.929874 | −0.464937 | − | 0.885344i | \(-0.653923\pi\) | ||||
−0.464937 | + | 0.885344i | \(0.653923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.84353 | 0.125429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.6180 | 1.65010 | 0.825051 | − | 0.565059i | \(-0.191147\pi\) | ||||
0.825051 | + | 0.565059i | \(0.191147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7489 | −1.55492 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.7735 | −0.448052 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.7460 | −0.739145 | −0.369573 | − | 0.929202i | \(-0.620496\pi\) | ||||
−0.369573 | + | 0.929202i | \(0.620496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 14.6826i | − | 0.476616i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 25.9321i | − | 0.840906i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.5790 | −0.601834 | −0.300917 | − | 0.953650i | \(-0.597293\pi\) | ||||
−0.300917 | + | 0.953650i | \(0.597293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.4055 | 0.789744 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 15.5347i | − | 0.502165i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 45.7340i | − | 1.47683i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.1165 | 0.745692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.4405 | −0.529788 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.6331 | −1.14707 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.93218 | −0.126450 | −0.0632252 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632252 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.6863 | −0.600292 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5985 | 1.36705 | 0.683526 | − | 0.729926i | \(-0.260446\pi\) | ||||
0.683526 | + | 0.729926i | \(0.260446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.5230i | 1.10676i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 7.85160i | − | 0.251452i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4273i | 0.525557i | 0.964856 | + | 0.262779i | \(0.0846388\pi\) | ||||
−0.964856 | + | 0.262779i | \(0.915361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.91143 | 0.316771 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 58.3077i | − | 1.86162i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.71022 | 0.182128 | 0.0910638 | − | 0.995845i | \(-0.470973\pi\) | ||||
0.0910638 | + | 0.995845i | \(0.470973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.4890i | 0.939598i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 52.1014i | 1.65841i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 28.7234i | − | 0.913351i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.61664 | 0.178418 | 0.0892092 | − | 0.996013i | \(-0.471566\pi\) | ||||
0.0892092 | + | 0.996013i | \(0.471566\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 53.8504i | − | 1.70889i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.86326i | 0.185878i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.0475 | −1.23665 | −0.618323 | − | 0.785924i | \(-0.712188\pi\) | ||||
−0.618323 | + | 0.785924i | \(0.712188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.4846i | 0.553189i |
(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 | 4028.2.c.a.3497.10 | ✓ | 82 | |
53.52 | even | 2 | inner | 4028.2.c.a.3497.73 | yes | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.c.a.3497.10 | ✓ | 82 | 1.1 | even | 1 | trivial | |
4028.2.c.a.3497.73 | yes | 82 | 53.52 | even | 2 | inner |