Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,2,Mod(2204,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.2204");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.g (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: | \(17.6070136457\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 315) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2204.22 | ||
Character | \(\chi\) | \(=\) | 2205.2204 |
Dual form | 2205.2.g.b.2204.23 |
$q$-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 \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(1081\) | \(1226\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56937 | 1.81682 | 0.908411 | − | 0.418079i | \(-0.137297\pi\) | ||||
0.908411 | + | 0.418079i | \(0.137297\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.60168 | 2.30084 | ||||||||
\(5\) | 0.884697 | − | 2.05361i | 0.395648 | − | 0.918402i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.68468 | 2.36339 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.27312 | − | 5.27649i | 0.718822 | − | 1.66857i | ||||
\(11\) | 5.63712i | 1.69966i | 0.527060 | + | 0.849828i | \(0.323294\pi\) | ||||
−0.527060 | + | 0.849828i | \(0.676706\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.53537 | 0.980535 | 0.490267 | − | 0.871572i | \(-0.336899\pi\) | ||||
0.490267 | + | 0.871572i | \(0.336899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.97209 | 1.99302 | ||||||||
\(17\) | − | 5.34283i | − | 1.29583i | −0.761714 | − | 0.647914i | \(-0.775642\pi\) | ||
0.761714 | − | 0.647914i | \(-0.224358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.44270i | 0.330979i | 0.986212 | + | 0.165489i | \(0.0529204\pi\) | ||||
−0.986212 | + | 0.165489i | \(0.947080\pi\) | |||||||
\(20\) | 4.07109 | − | 9.45005i | 0.910323 | − | 2.11310i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.4839i | 3.08797i | ||||||||
\(23\) | 2.99860 | 0.625251 | 0.312626 | − | 0.949876i | \(-0.398791\pi\) | ||||
0.312626 | + | 0.949876i | \(0.398791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.43462 | − | 3.63364i | −0.686925 | − | 0.726729i | ||||
\(26\) | 9.08368 | 1.78146 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.19404i | − | 0.407423i | −0.979031 | − | 0.203712i | \(-0.934699\pi\) | ||
0.979031 | − | 0.203712i | \(-0.0653005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52304i | 0.273546i | 0.990602 | + | 0.136773i | \(0.0436731\pi\) | ||||
−0.990602 | + | 0.136773i | \(0.956327\pi\) | |||||||
\(32\) | 7.11391 | 1.25757 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 13.7277i | − | 2.35429i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.09314i | 0.179712i | 0.995955 | + | 0.0898558i | \(0.0286406\pi\) | ||||
−0.995955 | + | 0.0898558i | \(0.971359\pi\) | |||||||
\(38\) | 3.70684i | 0.601329i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.91392 | − | 13.7277i | 0.935073 | − | 2.17055i | ||||
\(41\) | −6.52058 | −1.01834 | −0.509172 | − | 0.860665i | \(-0.670048\pi\) | ||||
−0.509172 | + | 0.860665i | \(0.670048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.486125i | − | 0.0741333i | −0.999313 | − | 0.0370667i | \(-0.988199\pi\) | ||
0.999313 | − | 0.0370667i | \(-0.0118014\pi\) | |||||||
\(44\) | 25.9402i | 3.91064i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.70452 | 1.13597 | ||||||||
\(47\) | 4.25632i | 0.620849i | 0.950598 | + | 0.310424i | \(0.100471\pi\) | ||||
−0.950598 | + | 0.310424i | \(0.899529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.82483 | − | 9.33618i | −1.24802 | − | 1.32034i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.2686 | 2.25605 | ||||||||
\(53\) | 4.02204 | 0.552469 | 0.276235 | − | 0.961090i | \(-0.410913\pi\) | ||||
0.276235 | + | 0.961090i | \(0.410913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5764 | + | 4.98714i | 1.56097 | + | 0.672466i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 5.63731i | − | 0.740216i | ||||||
\(59\) | −11.4196 | −1.48670 | −0.743350 | − | 0.668903i | \(-0.766764\pi\) | ||||
−0.743350 | + | 0.668903i | \(0.766764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.00854i | − | 0.897352i | −0.893695 | − | 0.448676i | \(-0.851896\pi\) | ||
0.893695 | − | 0.448676i | \(-0.148104\pi\) | |||||||
\(62\) | 3.91326i | 0.496984i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.33411 | 0.291764 | ||||||||
\(65\) | 3.12773 | − | 7.26027i | 0.387947 | − | 0.900525i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.48980i | 0.304177i | 0.988367 | + | 0.152089i | \(0.0485999\pi\) | ||||
−0.988367 | + | 0.152089i | \(0.951400\pi\) | |||||||
\(68\) | − | 24.5860i | − | 2.98149i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.13849i | − | 0.965861i | −0.875659 | − | 0.482930i | \(-0.839572\pi\) | ||
0.875659 | − | 0.482930i | \(-0.160428\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.13802 | −0.367277 | −0.183639 | − | 0.982994i | \(-0.558788\pi\) | ||||
−0.183639 | + | 0.982994i | \(0.558788\pi\) | |||||||
\(74\) | 2.80869i | 0.326504i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.63886i | 0.761529i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.8050 | 1.44068 | 0.720340 | − | 0.693622i | \(-0.243986\pi\) | ||||
0.720340 | + | 0.693622i | \(0.243986\pi\) | |||||||
\(80\) | 7.05288 | − | 16.3716i | 0.788536 | − | 1.83040i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.7538 | −1.85015 | ||||||||
\(83\) | 6.77241i | 0.743368i | 0.928359 | + | 0.371684i | \(0.121220\pi\) | ||||
−0.928359 | + | 0.371684i | \(0.878780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9721 | − | 4.72679i | −1.19009 | − | 0.512692i | ||||
\(86\) | − | 1.24904i | − | 0.134687i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 37.6824i | 4.01695i | ||||||||
\(89\) | −10.3303 | −1.09501 | −0.547503 | − | 0.836804i | \(-0.684421\pi\) | ||||
−0.547503 | + | 0.836804i | \(0.684421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.7986 | 1.43860 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.9361i | 1.12797i | ||||||||
\(95\) | 2.96275 | + | 1.27635i | 0.303972 | + | 0.130951i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7321 | −1.49582 | −0.747908 | − | 0.663802i | \(-0.768942\pi\) | ||||
−0.747908 | + | 0.663802i | \(0.768942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.8050 | − | 16.7209i | −1.58050 | − | 1.67209i | ||||
\(101\) | 14.9337 | 1.48595 | 0.742977 | − | 0.669317i | \(-0.233413\pi\) | ||||
0.742977 | + | 0.669317i | \(0.233413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.91510 | 0.385767 | 0.192883 | − | 0.981222i | \(-0.438216\pi\) | ||||
0.192883 | + | 0.981222i | \(0.438216\pi\) | |||||||
\(104\) | 23.6328 | 2.31739 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.3341 | 1.00374 | ||||||||
\(107\) | −14.8220 | −1.43290 | −0.716450 | − | 0.697638i | \(-0.754234\pi\) | ||||
−0.716450 | + | 0.697638i | \(0.754234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0386 | 1.05731 | 0.528655 | − | 0.848837i | \(-0.322697\pi\) | ||||
0.528655 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(110\) | 29.7442 | + | 12.8138i | 2.83600 | + | 1.22175i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.54314 | −0.709599 | −0.354799 | − | 0.934942i | \(-0.615451\pi\) | ||||
−0.354799 | + | 0.934942i | \(0.615451\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.65285 | − | 6.15795i | 0.247380 | − | 0.574232i | ||||
\(116\) | − | 10.0963i | − | 0.937416i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.3411 | −2.70107 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.7771 | −1.88883 | ||||||||
\(122\) | − | 18.0076i | − | 1.63033i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.00854i | 0.629385i | ||||||||
\(125\) | −10.5007 | + | 3.83871i | −0.939210 | + | 0.343344i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.93715i | − | 0.349366i | −0.984625 | − | 0.174683i | \(-0.944110\pi\) | ||
0.984625 | − | 0.174683i | \(-0.0558900\pi\) | |||||||
\(128\) | −8.23062 | −0.727491 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.03630 | − | 18.6543i | 0.704830 | − | 1.63609i | ||||
\(131\) | −3.94799 | −0.344937 | −0.172469 | − | 0.985015i | \(-0.555174\pi\) | ||||
−0.172469 | + | 0.985015i | \(0.555174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.39722i | 0.552635i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 35.7152i | − | 3.06255i | ||||||
\(137\) | 5.66125 | 0.483673 | 0.241837 | − | 0.970317i | \(-0.422250\pi\) | ||||
0.241837 | + | 0.970317i | \(0.422250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.3015i | 1.97640i | 0.153158 | + | 0.988202i | \(0.451056\pi\) | ||||
−0.153158 | + | 0.988202i | \(0.548944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 20.9108i | − | 1.75480i | ||||||
\(143\) | 19.9293i | 1.66657i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50571 | − | 1.94106i | −0.374179 | − | 0.161196i | ||||
\(146\) | −8.06275 | −0.667278 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.03030i | 0.413488i | ||||||||
\(149\) | − | 4.67568i | − | 0.383046i | −0.981488 | − | 0.191523i | \(-0.938657\pi\) | ||
0.981488 | − | 0.191523i | \(-0.0613427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.86085 | 0.151434 | 0.0757170 | − | 0.997129i | \(-0.475875\pi\) | ||||
0.0757170 | + | 0.997129i | \(0.475875\pi\) | |||||||
\(152\) | 9.64401i | 0.782233i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.12773 | + | 1.34743i | 0.251225 | + | 0.108228i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.56796 | 0.524180 | 0.262090 | − | 0.965043i | \(-0.415588\pi\) | ||||
0.262090 | + | 0.965043i | \(0.415588\pi\) | |||||||
\(158\) | 32.9009 | 2.61746 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.29365 | − | 14.6092i | 0.497557 | − | 1.15496i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7752i | 1.47059i | 0.677747 | + | 0.735295i | \(0.262956\pi\) | ||||
−0.677747 | + | 0.735295i | \(0.737044\pi\) | |||||||
\(164\) | −30.0056 | −2.34304 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.4008i | 1.35057i | ||||||||
\(167\) | − | 4.80581i | − | 0.371884i | −0.982561 | − | 0.185942i | \(-0.940466\pi\) | ||
0.982561 | − | 0.185942i | \(-0.0595337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.501166 | −0.0385512 | ||||||||
\(170\) | −28.1914 | − | 12.1449i | −2.16218 | − | 0.931470i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.23699i | − | 0.170569i | ||||||
\(173\) | − | 3.36378i | − | 0.255743i | −0.991791 | − | 0.127872i | \(-0.959185\pi\) | ||
0.991791 | − | 0.127872i | \(-0.0408145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 44.9396i | 3.38745i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −26.5423 | −1.98943 | ||||||||
\(179\) | 11.1288i | 0.831805i | 0.909409 | + | 0.415903i | \(0.136534\pi\) | ||||
−0.909409 | + | 0.415903i | \(0.863466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.19549i | − | 0.163190i | −0.996666 | − | 0.0815949i | \(-0.973999\pi\) | ||
0.996666 | − | 0.0815949i | \(-0.0260014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20.0447 | 1.47771 | ||||||||
\(185\) | 2.24489 | + | 0.967100i | 0.165048 | + | 0.0711026i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.1182 | 2.20246 | ||||||||
\(188\) | 19.5862i | 1.42847i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.61241 | + | 3.27943i | 0.552262 | + | 0.237915i | ||||
\(191\) | − | 9.95413i | − | 0.720256i | −0.932903 | − | 0.360128i | \(-0.882733\pi\) | ||
0.932903 | − | 0.360128i | \(-0.117267\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9494i | 1.79590i | 0.440102 | + | 0.897948i | \(0.354942\pi\) | ||||
−0.440102 | + | 0.897948i | \(0.645058\pi\) | |||||||
\(194\) | −37.8522 | −2.71763 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1023 | −1.36098 | −0.680492 | − | 0.732755i | \(-0.738234\pi\) | ||||
−0.680492 | + | 0.732755i | \(0.738234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.84327i | 0.130666i | 0.997864 | + | 0.0653329i | \(0.0208109\pi\) | ||||
−0.997864 | + | 0.0653329i | \(0.979189\pi\) | |||||||
\(200\) | −22.9594 | − | 24.2898i | −1.62347 | − | 1.71755i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 38.3701 | 2.69971 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.76873 | + | 13.3907i | −0.402906 | + | 0.935249i | ||||
\(206\) | 10.0594 | 0.700869 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 28.1843 | 1.95423 | ||||||||
\(209\) | −8.13269 | −0.562550 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.77713 | −0.673085 | −0.336543 | − | 0.941668i | \(-0.609258\pi\) | ||||
−0.336543 | + | 0.941668i | \(0.609258\pi\) | |||||||
\(212\) | 18.5081 | 1.27114 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −38.0833 | −2.60332 | ||||||||
\(215\) | −0.998310 | − | 0.430073i | −0.0680842 | − | 0.0293307i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 28.3624 | 1.92094 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 53.2711 | + | 22.9492i | 3.59154 | + | 1.54724i | ||||
\(221\) | − | 18.8889i | − | 1.27060i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.84782 | 0.525529 | 0.262765 | − | 0.964860i | \(-0.415366\pi\) | ||||
0.262765 | + | 0.964860i | \(0.415366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.3811 | −1.28921 | ||||||||
\(227\) | 0.549482i | 0.0364704i | 0.999834 | + | 0.0182352i | \(0.00580476\pi\) | ||||
−0.999834 | + | 0.0182352i | \(0.994195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.4582i | 1.41800i | 0.705210 | + | 0.708998i | \(0.250853\pi\) | ||||
−0.705210 | + | 0.708998i | \(0.749147\pi\) | |||||||
\(230\) | 6.81617 | − | 15.8221i | 0.449445 | − | 1.04328i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 14.6665i | − | 0.962902i | ||||||
\(233\) | 18.7664 | 1.22943 | 0.614713 | − | 0.788751i | \(-0.289272\pi\) | ||||
0.614713 | + | 0.788751i | \(0.289272\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.74083 | + | 3.76556i | 0.570189 | + | 0.245638i | ||||
\(236\) | −52.5491 | −3.42066 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 7.35866i | − | 0.475992i | −0.971266 | − | 0.237996i | \(-0.923509\pi\) | ||
0.971266 | − | 0.237996i | \(-0.0764905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5358i | 1.77374i | 0.462022 | + | 0.886868i | \(0.347124\pi\) | ||||
−0.462022 | + | 0.886868i | \(0.652876\pi\) | |||||||
\(242\) | −53.3842 | −3.43167 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 32.2511i | − | 2.06466i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.10049i | 0.324536i | ||||||||
\(248\) | 10.1810i | 0.646497i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.9802 | + | 9.86307i | −1.70638 | + | 0.623795i | ||||
\(251\) | −22.4204 | −1.41516 | −0.707582 | − | 0.706631i | \(-0.750214\pi\) | ||||
−0.707582 | + | 0.706631i | \(0.750214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.9035i | 1.06271i | ||||||||
\(254\) | − | 10.1160i | − | 0.634735i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −25.8158 | −1.61349 | ||||||||
\(257\) | − | 17.1275i | − | 1.06838i | −0.845364 | − | 0.534191i | \(-0.820616\pi\) | ||
0.845364 | − | 0.534191i | \(-0.179384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.3928 | − | 33.4094i | 0.892604 | − | 2.07196i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.1439 | −0.626689 | ||||||||
\(263\) | 1.61764 | 0.0997481 | 0.0498741 | − | 0.998756i | \(-0.484118\pi\) | ||||
0.0498741 | + | 0.998756i | \(0.484118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.55828 | − | 8.25969i | 0.218583 | − | 0.507389i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11.4572i | 0.699863i | ||||||||
\(269\) | −11.6810 | −0.712201 | −0.356101 | − | 0.934448i | \(-0.615894\pi\) | ||||
−0.356101 | + | 0.934448i | \(0.615894\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.83773i | − | 0.354617i | −0.984155 | − | 0.177308i | \(-0.943261\pi\) | ||
0.984155 | − | 0.177308i | \(-0.0567390\pi\) | |||||||
\(272\) | − | 42.5936i | − | 2.58261i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5459 | 0.878748 | ||||||||
\(275\) | 20.4833 | − | 19.3614i | 1.23519 | − | 1.16754i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.6000i | − | 0.997395i | −0.866776 | − | 0.498698i | \(-0.833812\pi\) | ||
0.866776 | − | 0.498698i | \(-0.166188\pi\) | |||||||
\(278\) | 59.8701i | 3.59077i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.4255i | − | 1.21848i | −0.792984 | − | 0.609242i | \(-0.791474\pi\) | ||
0.792984 | − | 0.609242i | \(-0.208526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.63286 | −0.394283 | −0.197141 | − | 0.980375i | \(-0.563166\pi\) | ||||
−0.197141 | + | 0.980375i | \(0.563166\pi\) | |||||||
\(284\) | − | 37.4507i | − | 2.22229i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.2058i | 3.02786i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.5459 | −0.679168 | ||||||||
\(290\) | −11.5768 | − | 4.98731i | −0.679816 | − | 0.292865i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.4402 | −0.845047 | ||||||||
\(293\) | 16.3716i | 0.956437i | 0.878241 | + | 0.478219i | \(0.158717\pi\) | ||||
−0.878241 | + | 0.478219i | \(0.841283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1028 | + | 23.4513i | −0.588210 | + | 1.36539i | ||||
\(296\) | 7.30732i | 0.424729i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 12.0136i | − | 0.695927i | ||||||
\(299\) | 10.6012 | 0.613081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.78122 | 0.275129 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.5014i | 0.659648i | ||||||||
\(305\) | −14.3928 | − | 6.20043i | −0.824130 | − | 0.355036i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.5071 | 1.45576 | 0.727882 | − | 0.685702i | \(-0.240505\pi\) | ||||
0.727882 | + | 0.685702i | \(0.240505\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.03630 | + | 3.46205i | 0.456431 | + | 0.196631i | ||||
\(311\) | −31.0360 | −1.75989 | −0.879946 | − | 0.475073i | \(-0.842422\pi\) | ||||
−0.879946 | + | 0.475073i | \(0.842422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0469 | 0.850501 | 0.425251 | − | 0.905076i | \(-0.360186\pi\) | ||||
0.425251 | + | 0.905076i | \(0.360186\pi\) | |||||||
\(314\) | 16.8755 | 0.952341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 58.9247 | 3.31477 | ||||||||
\(317\) | −15.5812 | −0.875129 | −0.437564 | − | 0.899187i | \(-0.644159\pi\) | ||||
−0.437564 | + | 0.899187i | \(0.644159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.3681 | 0.692480 | ||||||||
\(320\) | 2.06498 | − | 4.79335i | 0.115436 | − | 0.267956i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.70812 | 0.428891 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1427 | − | 12.8463i | −0.673554 | − | 0.712583i | ||||
\(326\) | 48.2406i | 2.67180i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −43.5880 | −2.40675 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6682 | 0.751273 | 0.375637 | − | 0.926767i | \(-0.377424\pi\) | ||||
0.375637 | + | 0.926767i | \(0.377424\pi\) | |||||||
\(332\) | 31.1644i | 1.71037i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 12.3479i | − | 0.675647i | ||||||
\(335\) | 5.11307 | + | 2.20271i | 0.279357 | + | 0.120347i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.8443i | − | 1.24441i | −0.782855 | − | 0.622204i | \(-0.786237\pi\) | ||
0.782855 | − | 0.622204i | \(-0.213763\pi\) | |||||||
\(338\) | −1.28768 | −0.0700406 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −50.4900 | − | 21.7512i | −2.73821 | − | 1.17962i | ||||
\(341\) | −8.58556 | −0.464934 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3.24959i | − | 0.175206i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 8.64280i | − | 0.464640i | ||||||
\(347\) | 19.6248 | 1.05352 | 0.526758 | − | 0.850015i | \(-0.323407\pi\) | ||||
0.526758 | + | 0.850015i | \(0.323407\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.14050i | − | 0.328693i | −0.986403 | − | 0.164347i | \(-0.947448\pi\) | ||
0.986403 | − | 0.164347i | \(-0.0525516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 40.1020i | 2.13744i | ||||||||
\(353\) | − | 24.0041i | − | 1.27761i | −0.769369 | − | 0.638805i | \(-0.779429\pi\) | ||
0.769369 | − | 0.638805i | \(-0.220571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.7133 | − | 7.20009i | −0.887049 | − | 0.382141i | ||||
\(356\) | −47.5366 | −2.51943 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.5940i | 1.51124i | ||||||||
\(359\) | − | 16.9508i | − | 0.894631i | −0.894376 | − | 0.447315i | \(-0.852380\pi\) | ||
0.894376 | − | 0.447315i | \(-0.147620\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.9186 | 0.890453 | ||||||||
\(362\) | − | 5.64104i | − | 0.296487i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.77620 | + | 6.44427i | −0.145313 | + | 0.337308i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0036 | 1.82717 | 0.913587 | − | 0.406642i | \(-0.133300\pi\) | ||||
0.913587 | + | 0.406642i | \(0.133300\pi\) | |||||||
\(368\) | 23.9051 | 1.24614 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.76796 | + | 2.48484i | 0.299862 | + | 0.129181i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.99153i | 0.310229i | 0.987896 | + | 0.155115i | \(0.0495747\pi\) | ||||
−0.987896 | + | 0.155115i | \(0.950425\pi\) | |||||||
\(374\) | 77.3849 | 4.00148 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.4522i | 1.46731i | ||||||||
\(377\) | − | 7.75675i | − | 0.399493i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.12842 | −0.160696 | −0.0803481 | − | 0.996767i | \(-0.525603\pi\) | ||||
−0.0803481 | + | 0.996767i | \(0.525603\pi\) | |||||||
\(380\) | 13.6336 | + | 5.87337i | 0.699390 | + | 0.301298i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 25.5759i | − | 1.30858i | ||||||
\(383\) | − | 16.9659i | − | 0.866917i | −0.901173 | − | 0.433459i | \(-0.857293\pi\) | ||
0.901173 | − | 0.433459i | \(-0.142707\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 64.1043i | 3.26282i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −67.7923 | −3.44163 | ||||||||
\(389\) | − | 0.449473i | − | 0.0227892i | −0.999935 | − | 0.0113946i | \(-0.996373\pi\) | ||
0.999935 | − | 0.0113946i | \(-0.00362709\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.0210i | − | 0.810218i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −49.0810 | −2.47267 | ||||||||
\(395\) | 11.3286 | − | 26.2965i | 0.570002 | − | 1.32312i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7326 | 1.14092 | 0.570459 | − | 0.821326i | \(-0.306765\pi\) | ||||
0.570459 | + | 0.821326i | \(0.306765\pi\) | |||||||
\(398\) | 4.73604i | 0.237396i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −27.3811 | − | 28.9677i | −1.36906 | − | 1.44839i | ||||
\(401\) | − | 9.71458i | − | 0.485123i | −0.970136 | − | 0.242562i | \(-0.922012\pi\) | ||
0.970136 | − | 0.242562i | \(-0.0779876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.38451i | 0.268221i | ||||||||
\(404\) | 68.7199 | 3.41894 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.16218 | −0.305448 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.06026i | 0.200767i | 0.994949 | + | 0.100383i | \(0.0320069\pi\) | ||||
−0.994949 | + | 0.100383i | \(0.967993\pi\) | |||||||
\(410\) | −14.8220 | + | 34.4058i | −0.732008 | + | 1.69918i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.0161 | 0.887587 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9079 | + | 5.99153i | 0.682711 | + | 0.294112i | ||||
\(416\) | 25.1503 | 1.23310 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.8959 | −1.02205 | ||||||||
\(419\) | −20.9314 | −1.02257 | −0.511283 | − | 0.859412i | \(-0.670830\pi\) | ||||
−0.511283 | + | 0.859412i | \(0.670830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.7795 | −0.963992 | −0.481996 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481996 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(422\) | −25.1211 | −1.22288 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.8860 | 1.30570 | ||||||||
\(425\) | −19.4139 | + | 18.3506i | −0.941715 | + | 0.890136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −68.2062 | −3.29687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.56503 | − | 1.10502i | −0.123697 | − | 0.0532887i | ||||
\(431\) | 10.6596i | 0.513454i | 0.966484 | + | 0.256727i | \(0.0826442\pi\) | ||||
−0.966484 | + | 0.256727i | \(0.917356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.2351 | −1.02050 | −0.510248 | − | 0.860028i | \(-0.670446\pi\) | ||||
−0.510248 | + | 0.860028i | \(0.670446\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 50.7963 | 2.43270 | ||||||||
\(437\) | 4.32609i | 0.206945i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 21.4436i | − | 1.02345i | −0.859150 | − | 0.511725i | \(-0.829007\pi\) | ||
0.859150 | − | 0.511725i | \(-0.170993\pi\) | |||||||
\(440\) | 77.3849 | + | 33.3375i | 3.68918 | + | 1.58930i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 48.5326i | − | 2.30846i | ||||||
\(443\) | 0.170970 | 0.00812304 | 0.00406152 | − | 0.999992i | \(-0.498707\pi\) | ||||
0.00406152 | + | 0.999992i | \(0.498707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.13915 | + | 21.2143i | −0.433237 | + | 1.00566i | ||||
\(446\) | 20.1640 | 0.954792 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.38752i | − | 0.443025i | −0.975158 | − | 0.221512i | \(-0.928901\pi\) | ||
0.975158 | − | 0.221512i | \(-0.0710993\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.7573i | − | 1.73083i | ||||||
\(452\) | −34.7111 | −1.63267 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.41182i | 0.0662602i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.8925i | − | 0.790196i | −0.918639 | − | 0.395098i | \(-0.870711\pi\) | ||
0.918639 | − | 0.395098i | \(-0.129289\pi\) | |||||||
\(458\) | 55.1341i | 2.57625i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.2076 | − | 28.3369i | 0.569181 | − | 1.32122i | ||||
\(461\) | 31.0360 | 1.44549 | 0.722746 | − | 0.691113i | \(-0.242880\pi\) | ||||
0.722746 | + | 0.691113i | \(0.242880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.9434i | − | 0.555055i | −0.960718 | − | 0.277528i | \(-0.910485\pi\) | ||
0.960718 | − | 0.277528i | \(-0.0895150\pi\) | |||||||
\(464\) | − | 17.4911i | − | 0.812004i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 48.2178 | 2.23365 | ||||||||
\(467\) | − | 34.5606i | − | 1.59928i | −0.600483 | − | 0.799638i | \(-0.705025\pi\) | ||
0.600483 | − | 0.799638i | \(-0.294975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 22.4584 | + | 9.67512i | 1.03593 | + | 0.446280i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −76.3362 | −3.51366 | ||||||||
\(473\) | 2.74034 | 0.126001 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.24227 | − | 4.95514i | 0.240532 | − | 0.227357i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 18.9071i | − | 0.864793i | ||||||
\(479\) | 2.97230 | 0.135808 | 0.0679040 | − | 0.997692i | \(-0.478369\pi\) | ||||
0.0679040 | + | 0.997692i | \(0.478369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.86467i | 0.176214i | ||||||||
\(482\) | 70.7498i | 3.22256i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −95.6097 | −4.34589 | ||||||||
\(485\) | −13.0334 | + | 30.2539i | −0.591817 | + | 1.37376i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.7124i | − | 1.02920i | −0.857431 | − | 0.514598i | \(-0.827941\pi\) | ||
0.857431 | − | 0.514598i | \(-0.172059\pi\) | |||||||
\(488\) | − | 46.8499i | − | 2.12079i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0036i | 0.586846i | 0.955983 | + | 0.293423i | \(0.0947944\pi\) | ||||
−0.955983 | + | 0.293423i | \(0.905206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7224 | −0.527950 | ||||||||
\(494\) | 13.1051i | 0.589624i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.1418i | 0.545184i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.6077 | −0.967295 | −0.483648 | − | 0.875263i | \(-0.660688\pi\) | ||||
−0.483648 | + | 0.875263i | \(0.660688\pi\) | |||||||
\(500\) | −48.3208 | + | 17.6645i | −2.16097 | + | 0.789980i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −57.6064 | −2.57110 | ||||||||
\(503\) | − | 32.4125i | − | 1.44520i | −0.691265 | − | 0.722601i | \(-0.742946\pi\) | ||
0.691265 | − | 0.722601i | \(-0.257054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2118 | − | 30.6679i | 0.587915 | − | 1.36470i | ||||
\(506\) | 43.4313i | 1.93076i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 18.1175i | − | 0.803835i | ||||||
\(509\) | 36.5604 | 1.62051 | 0.810255 | − | 0.586077i | \(-0.199329\pi\) | ||||
0.810255 | + | 0.586077i | \(0.199329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −49.8691 | −2.20392 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 44.0068i | − | 1.94106i | ||||||
\(515\) | 3.46368 | − | 8.04010i | 0.152628 | − | 0.354289i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.9934 | −1.05523 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 20.9079 | − | 48.5326i | 0.916871 | − | 2.12830i | ||||
\(521\) | 18.8722 | 0.826804 | 0.413402 | − | 0.910549i | \(-0.364340\pi\) | ||||
0.413402 | + | 0.910549i | \(0.364340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.2248 | −1.23418 | −0.617092 | − | 0.786891i | \(-0.711690\pi\) | ||||
−0.617092 | + | 0.786891i | \(0.711690\pi\) | |||||||
\(524\) | −18.1674 | −0.793645 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.15633 | 0.181225 | ||||||||
\(527\) | 8.13735 | 0.354468 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0084 | −0.609061 | ||||||||
\(530\) | 9.14255 | − | 21.2222i | 0.397127 | − | 0.921835i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.0527 | −0.998521 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1130 | + | 30.4387i | −0.566924 | + | 1.31598i | ||||
\(536\) | 16.6435i | 0.718890i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30.0128 | −1.29394 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.4537 | 1.22332 | 0.611661 | − | 0.791120i | \(-0.290502\pi\) | ||||
0.611661 | + | 0.791120i | \(0.290502\pi\) | |||||||
\(542\) | − | 14.9993i | − | 0.644275i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 38.0084i | − | 1.62960i | ||||||
\(545\) | 9.76584 | − | 22.6690i | 0.418323 | − | 0.971035i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.9338i | 0.937820i | 0.883246 | + | 0.468910i | \(0.155353\pi\) | ||||
−0.883246 | + | 0.468910i | \(0.844647\pi\) | |||||||
\(548\) | 26.0513 | 1.11285 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 52.6292 | − | 49.7466i | 2.24412 | − | 2.12120i | ||||
\(551\) | 3.16535 | 0.134848 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 42.6515i | − | 1.81209i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 107.226i | 4.54739i | ||||||||
\(557\) | 24.4336 | 1.03529 | 0.517643 | − | 0.855597i | \(-0.326810\pi\) | ||||
0.517643 | + | 0.855597i | \(0.326810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.71863i | − | 0.0726903i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 52.4808i | − | 2.21377i | ||||||
\(563\) | 21.3140i | 0.898279i | 0.893462 | + | 0.449139i | \(0.148269\pi\) | ||||
−0.893462 | + | 0.449139i | \(0.851731\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.67339 | + | 15.4907i | −0.280752 | + | 0.651697i | ||||
\(566\) | −17.0423 | −0.716341 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 54.4032i | − | 2.28271i | ||||||
\(569\) | 27.9099i | 1.17004i | 0.811018 | + | 0.585022i | \(0.198914\pi\) | ||||
−0.811018 | + | 0.585022i | \(0.801086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.3872 | −1.94124 | −0.970622 | − | 0.240609i | \(-0.922653\pi\) | ||||
−0.970622 | + | 0.240609i | \(0.922653\pi\) | |||||||
\(572\) | 91.7083i | 3.83451i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.2991 | − | 10.8958i | −0.429501 | − | 0.454388i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4333 | 1.35022 | 0.675108 | − | 0.737719i | \(-0.264097\pi\) | ||||
0.675108 | + | 0.737719i | \(0.264097\pi\) | |||||||
\(578\) | −29.6656 | −1.23393 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.7338 | − | 8.93214i | −0.860925 | − | 0.370887i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6727i | 0.939007i | ||||||||
\(584\) | −20.9767 | −0.868021 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.0647i | 1.73768i | ||||||||
\(587\) | 0.790380i | 0.0326225i | 0.999867 | + | 0.0163112i | \(0.00519226\pi\) | ||||
−0.999867 | + | 0.0163112i | \(0.994808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.19729 | −0.0905379 | ||||||||
\(590\) | −25.9580 | + | 60.2552i | −1.06867 | + | 2.48067i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.71464i | 0.358170i | ||||||||
\(593\) | 20.2848i | 0.832998i | 0.909136 | + | 0.416499i | \(0.136743\pi\) | ||||
−0.909136 | + | 0.416499i | \(0.863257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 21.5160i | − | 0.881328i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27.2383 | 1.11386 | ||||||||
\(599\) | 10.1357i | 0.414135i | 0.978327 | + | 0.207068i | \(0.0663920\pi\) | ||||
−0.978327 | + | 0.207068i | \(0.933608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.6657i | 1.45483i | 0.686196 | + | 0.727417i | \(0.259279\pi\) | ||||
−0.686196 | + | 0.727417i | \(0.740721\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.56305 | 0.348425 | ||||||||
\(605\) | −18.3815 | + | 42.6681i | −0.747312 | + | 1.73471i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.2665 | 1.06613 | 0.533063 | − | 0.846076i | \(-0.321041\pi\) | ||||
0.533063 | + | 0.846076i | \(0.321041\pi\) | |||||||
\(608\) | 10.2633i | 0.416230i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −36.9805 | − | 15.9312i | −1.49730 | − | 0.645036i | ||||
\(611\) | 15.0477i | 0.608764i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.8819i | 1.04536i | 0.852528 | + | 0.522681i | \(0.175068\pi\) | ||||
−0.852528 | + | 0.522681i | \(0.824932\pi\) | |||||||
\(614\) | 65.5371 | 2.64486 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.1754 | 0.651198 | 0.325599 | − | 0.945508i | \(-0.394434\pi\) | ||||
0.325599 | + | 0.945508i | \(0.394434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.10962i | 0.245566i | 0.992434 | + | 0.122783i | \(0.0391820\pi\) | ||||
−0.992434 | + | 0.122783i | \(0.960818\pi\) | |||||||
\(620\) | 14.3928 | + | 6.20043i | 0.578029 | + | 0.249015i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −79.7432 | −3.19741 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.40672 | + | 24.9604i | −0.0562687 | + | 0.998416i | ||||
\(626\) | 38.6611 | 1.54521 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.2236 | 1.20605 | ||||||||
\(629\) | 5.84048 | 0.232875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.89949 | 0.0756174 | 0.0378087 | − | 0.999285i | \(-0.487962\pi\) | ||||
0.0378087 | + | 0.999285i | \(0.487962\pi\) | |||||||
\(632\) | 85.5976 | 3.40489 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −40.0340 | −1.58995 | ||||||||
\(635\) | −8.08537 | − | 3.48318i | −0.320858 | − | 0.138226i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31.7782 | 1.25811 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.28160 | + | 16.9025i | −0.287831 | + | 0.668129i | ||||
\(641\) | − | 11.3453i | − | 0.448113i | −0.974576 | − | 0.224057i | \(-0.928070\pi\) | ||
0.974576 | − | 0.224057i | \(-0.0719300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.2255 | 0.718742 | 0.359371 | − | 0.933195i | \(-0.382991\pi\) | ||||
0.359371 | + | 0.933195i | \(0.382991\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.8050 | 0.779219 | ||||||||
\(647\) | − | 24.5411i | − | 0.964812i | −0.875948 | − | 0.482406i | \(-0.839763\pi\) | ||
0.875948 | − | 0.482406i | \(-0.160237\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 64.3734i | − | 2.52688i | ||||||
\(650\) | −31.1990 | − | 33.0069i | −1.22373 | − | 1.29464i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 86.3976i | 3.38359i | ||||||||
\(653\) | −8.75313 | −0.342536 | −0.171268 | − | 0.985224i | \(-0.554786\pi\) | ||||
−0.171268 | + | 0.985224i | \(0.554786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.49277 | + | 8.10762i | −0.136474 | + | 0.316791i | ||||
\(656\) | −51.9827 | −2.02958 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.51324i | 0.0979020i | 0.998801 | + | 0.0489510i | \(0.0155878\pi\) | ||||
−0.998801 | + | 0.0489510i | \(0.984412\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.8826i | − | 1.55125i | −0.631192 | − | 0.775626i | \(-0.717434\pi\) | ||
0.631192 | − | 0.775626i | \(-0.282566\pi\) | |||||||
\(662\) | 35.1188 | 1.36493 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.2714i | 1.75687i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.57906i | − | 0.254742i | ||||||
\(668\) | − | 22.1148i | − | 0.855646i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.1374 | + | 5.65960i | 0.507541 | + | 0.218649i | ||||
\(671\) | 39.5080 | 1.52519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.0634i | − | 1.39014i | −0.718941 | − | 0.695071i | \(-0.755373\pi\) | ||
0.718941 | − | 0.695071i | \(-0.244627\pi\) | |||||||
\(674\) | − | 58.6955i | − | 2.26087i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.30620 | −0.0887001 | ||||||||
\(677\) | − | 7.90377i | − | 0.303767i | −0.988398 | − | 0.151883i | \(-0.951466\pi\) | ||
0.988398 | − | 0.151883i | \(-0.0485338\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −73.3450 | − | 31.5971i | −2.81265 | − | 1.21169i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.0595 | −0.844702 | ||||||||
\(683\) | 25.2861 | 0.967545 | 0.483772 | − | 0.875194i | \(-0.339266\pi\) | ||||
0.483772 | + | 0.875194i | \(0.339266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.00849 | − | 11.6260i | 0.191365 | − | 0.444206i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 3.87543i | − | 0.147749i | ||||||
\(689\) | 14.2194 | 0.541715 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1704i | 0.577111i | 0.957463 | + | 0.288555i | \(0.0931749\pi\) | ||||
−0.957463 | + | 0.288555i | \(0.906825\pi\) | |||||||
\(692\) | − | 15.4790i | − | 0.588424i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 50.4235 | 1.91405 | ||||||||
\(695\) | 47.8521 | + | 20.6147i | 1.81513 | + | 0.781961i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.8384i | 1.31960i | ||||||||
\(698\) | − | 15.7772i | − | 0.597177i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.6815i | 1.30990i | 0.755671 | + | 0.654951i | \(0.227311\pi\) | ||||
−0.755671 | + | 0.654951i | \(0.772689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.57708 | −0.0594807 | ||||||||
\(704\) | 13.1577i | 0.495898i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 61.6755i | − | 2.32119i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.4621 | 1.29425 | 0.647126 | − | 0.762383i | \(-0.275971\pi\) | ||||
0.647126 | + | 0.762383i | \(0.275971\pi\) | |||||||
\(710\) | −42.9426 | − | 18.4997i | −1.61161 | − | 0.694282i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −69.0545 | −2.58793 | ||||||||
\(713\) | 4.56699i | 0.171035i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.9270 | + | 17.6314i | 1.53058 | + | 0.659376i | ||||
\(716\) | 51.2112i | 1.91385i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 43.5530i | − | 1.62538i | ||||||
\(719\) | −26.9650 | −1.00562 | −0.502812 | − | 0.864396i | \(-0.667701\pi\) | ||||
−0.502812 | + | 0.864396i | \(0.667701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 43.4702 | 1.61779 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.1030i | − | 0.375473i | ||||||
\(725\) | −7.97237 | + | 7.53571i | −0.296086 | + | 0.279869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.4196 | −0.386442 | −0.193221 | − | 0.981155i | \(-0.561894\pi\) | ||||
−0.193221 | + | 0.981155i | \(0.561894\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.13308 | + | 16.5577i | −0.264007 | + | 0.612829i | ||||
\(731\) | −2.59728 | −0.0960640 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.7082 | 0.838748 | 0.419374 | − | 0.907814i | \(-0.362250\pi\) | ||||
0.419374 | + | 0.907814i | \(0.362250\pi\) | |||||||
\(734\) | 89.9374 | 3.31965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.3318 | 0.786300 | ||||||||
\(737\) | −14.0353 | −0.516996 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7795 | 1.09546 | 0.547728 | − | 0.836657i | \(-0.315493\pi\) | ||||
0.547728 | + | 0.836657i | \(0.315493\pi\) | |||||||
\(740\) | 10.3303 | + | 4.45029i | 0.379748 | + | 0.163596i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.8044 | 1.27685 | 0.638424 | − | 0.769684i | \(-0.279586\pi\) | ||||
0.638424 | + | 0.769684i | \(0.279586\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.60201 | − | 4.13656i | −0.351791 | − | 0.151552i | ||||
\(746\) | 15.3945i | 0.563632i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 138.594 | 5.06751 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.49044 | 0.273330 | 0.136665 | − | 0.990617i | \(-0.456362\pi\) | ||||
0.136665 | + | 0.990617i | \(0.456362\pi\) | |||||||
\(752\) | 33.9318i | 1.23737i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 19.9300i | − | 0.725807i | ||||||
\(755\) | 1.64629 | − | 3.82146i | 0.0599146 | − | 0.139077i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.66139i | − | 0.0967300i | −0.998830 | − | 0.0483650i | \(-0.984599\pi\) | ||
0.998830 | − | 0.0483650i | \(-0.0154011\pi\) | |||||||
\(758\) | −8.03808 | −0.291956 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 19.8050 | + | 8.53203i | 0.718404 | + | 0.309489i | ||||
\(761\) | 5.56959 | 0.201897 | 0.100949 | − | 0.994892i | \(-0.467812\pi\) | ||||
0.100949 | + | 0.994892i | \(0.467812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 45.8057i | − | 1.65719i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 43.5917i | − | 1.57503i | ||||||
\(767\) | −40.3724 | −1.45776 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.5002i | 0.414709i | 0.978266 | + | 0.207355i | \(0.0664854\pi\) | ||||
−0.978266 | + | 0.207355i | \(0.933515\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 114.809i | 4.13207i | ||||||||
\(773\) | − | 25.3743i | − | 0.912650i | −0.889813 | − | 0.456325i | \(-0.849165\pi\) | ||
0.889813 | − | 0.456325i | \(-0.150835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.53418 | − | 5.23107i | 0.198794 | − | 0.187906i | ||||
\(776\) | −98.4793 | −3.53520 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1.15486i | − | 0.0414039i | ||||||
\(779\) | − | 9.40726i | − | 0.337050i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.8776 | 1.64163 | ||||||||
\(782\) | − | 41.1640i | − | 1.47202i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.81065 | − | 13.4880i | 0.207391 | − | 0.481408i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.9934 | 0.855273 | 0.427636 | − | 0.903951i | \(-0.359346\pi\) | ||||
0.427636 | + | 0.903951i | \(0.359346\pi\) | |||||||
\(788\) | −87.9028 | −3.13141 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 29.1073 | − | 67.5656i | 1.03559 | − | 2.40388i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 24.7778i | − | 0.879885i | ||||||
\(794\) | 58.4086 | 2.07284 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.48212i | 0.300641i | ||||||||
\(797\) | 28.1188i | 0.996020i | 0.867171 | + | 0.498010i | \(0.165936\pi\) | ||||
−0.867171 | + | 0.498010i | \(0.834064\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7408 | 0.804513 | ||||||||
\(800\) | −24.4336 | − | 25.8494i | −0.863859 | − | 0.913915i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 24.9604i | − | 0.881382i | ||||||
\(803\) | − | 17.6894i | − | 0.624245i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.8348i | 0.487310i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 99.8268 | 3.51189 | ||||||||
\(809\) | 28.0566i | 0.986417i | 0.869911 | + | 0.493209i | \(0.164176\pi\) | ||||
−0.869911 | + | 0.493209i | \(0.835824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.4980i | − | 1.52742i | −0.645559 | − | 0.763710i | \(-0.723376\pi\) | ||
0.645559 | − | 0.763710i | \(-0.276624\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.8329 | −0.554944 | ||||||||
\(815\) | 38.5570 | + | 16.6104i | 1.35059 | + | 0.581836i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.701333 | 0.0245365 | ||||||||
\(818\) | 10.4323i | 0.364757i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −26.5459 | + | 61.6198i | −0.927022 | + | 2.15186i | ||||
\(821\) | − | 36.4741i | − | 1.27295i | −0.771295 | − | 0.636477i | \(-0.780391\pi\) | ||
0.771295 | − | 0.636477i | \(-0.219609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 46.1045i | − | 1.60710i | −0.595235 | − | 0.803551i | \(-0.702941\pi\) | ||
0.595235 | − | 0.803551i | \(-0.297059\pi\) | |||||||
\(824\) | 26.1712 | 0.911718 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.1533 | 0.700800 | 0.350400 | − | 0.936600i | \(-0.386046\pi\) | ||||
0.350400 | + | 0.936600i | \(0.386046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.08776i | 0.246168i | 0.992396 | + | 0.123084i | \(0.0392785\pi\) | ||||
−0.992396 | + | 0.123084i | \(0.960722\pi\) | |||||||
\(830\) | 35.7345 | + | 15.3945i | 1.24036 | + | 0.534350i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.25194 | 0.286085 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.86925 | − | 4.25168i | −0.341539 | − | 0.147135i | ||||
\(836\) | −37.4240 | −1.29434 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −53.7806 | −1.85782 | ||||||||
\(839\) | −33.0805 | −1.14206 | −0.571032 | − | 0.820928i | \(-0.693457\pi\) | ||||
−0.571032 | + | 0.820928i | \(0.693457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1862 | 0.834006 | ||||||||
\(842\) | −50.8208 | −1.75140 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −44.9912 | −1.54866 | ||||||||
\(845\) | −0.443379 | + | 1.02920i | −0.0152527 | + | 0.0354055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.0640 | 1.10108 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −49.8817 | + | 47.1496i | −1.71093 | + | 1.61722i | ||||
\(851\) | 3.27790i | 0.112365i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.1187 | 1.30516 | 0.652580 | − | 0.757719i | \(-0.273686\pi\) | ||||
0.652580 | + | 0.757719i | \(0.273686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −99.0806 | −3.38651 | ||||||||
\(857\) | − | 7.03613i | − | 0.240350i | −0.992753 | − | 0.120175i | \(-0.961654\pi\) | ||
0.992753 | − | 0.120175i | \(-0.0383455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.6740i | − | 0.875984i | −0.898979 | − | 0.437992i | \(-0.855690\pi\) | ||
0.898979 | − | 0.437992i | \(-0.144310\pi\) | |||||||
\(860\) | −4.59390 | − | 1.97906i | −0.156651 | − | 0.0674853i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.3885i | 0.932855i | ||||||||
\(863\) | 50.9858 | 1.73558 | 0.867788 | − | 0.496934i | \(-0.165541\pi\) | ||||
0.867788 | + | 0.496934i | \(0.165541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.90788 | − | 2.97592i | −0.234875 | − | 0.101184i | ||||
\(866\) | −54.5610 | −1.85406 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 72.1835i | 2.44866i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.80235i | 0.298256i | ||||||||
\(872\) | 73.7898 | 2.49884 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.1153i | 0.375982i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 38.5532i | − | 1.30185i | −0.759142 | − | 0.650925i | \(-0.774381\pi\) | ||
0.759142 | − | 0.650925i | \(-0.225619\pi\) | |||||||
\(878\) | − | 55.0967i | − | 1.85942i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 92.2885 | + | 39.7580i | 3.11104 | + | 1.34024i | ||||
\(881\) | 34.4764 | 1.16154 | 0.580770 | − | 0.814068i | \(-0.302752\pi\) | ||||
0.580770 | + | 0.814068i | \(0.302752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5869i | 0.861068i | 0.902574 | + | 0.430534i | \(0.141675\pi\) | ||||
−0.902574 | + | 0.430534i | \(0.858325\pi\) | |||||||
\(884\) | − | 86.9206i | − | 2.92346i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.439286 | 0.0147581 | ||||||||
\(887\) | 23.7956i | 0.798979i | 0.916738 | + | 0.399489i | \(0.130813\pi\) | ||||
−0.916738 | + | 0.399489i | \(0.869187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −23.4819 | + | 54.5075i | −0.787114 | + | 1.82710i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.1132 | 1.20916 | ||||||||
\(893\) | −6.14061 | −0.205488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.8542 | + | 9.84561i | 0.763932 | + | 0.329102i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 24.1201i | − | 0.804897i | ||||||
\(899\) | 3.34161 | 0.111449 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 21.4891i | − | 0.715904i | ||||||
\(902\) | − | 94.4432i | − | 3.14461i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50.4235 | −1.67706 | ||||||||
\(905\) | −4.50869 | − | 1.94235i | −0.149874 | − | 0.0645658i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.7755i | 1.28752i | 0.765227 | + | 0.643760i | \(0.222626\pi\) | ||||
−0.765227 | + | 0.643760i | \(0.777374\pi\) | |||||||
\(908\) | 2.52854i | 0.0839125i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4438i | 1.04178i | 0.853624 | + | 0.520889i | \(0.174400\pi\) | ||||
−0.853624 | + | 0.520889i | \(0.825600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.1769 | −1.26347 | ||||||||
\(914\) | − | 43.4030i | − | 1.43564i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 98.7437i | 3.26258i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.9744 | 0.922791 | 0.461396 | − | 0.887195i | \(-0.347349\pi\) | ||||
0.461396 | + | 0.887195i | \(0.347349\pi\) | |||||||
\(920\) | 17.7335 | − | 41.1640i | 0.584655 | − | 1.35714i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 79.7432 | 2.62620 | ||||||||
\(923\) | − | 28.7726i | − | 0.947060i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.97209 | − | 3.75454i | 0.130602 | − | 0.123448i | ||||
\(926\) | − | 30.6870i | − | 1.00844i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 15.6082i | − | 0.512365i | ||||||
\(929\) | −22.4904 | −0.737885 | −0.368943 | − | 0.929452i | \(-0.620280\pi\) | ||||
−0.368943 | + | 0.929452i | \(0.620280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 86.3568 | 2.82871 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 88.7992i | − | 2.90560i | ||||||
\(935\) | 26.6455 | − | 61.8510i | 0.871400 | − | 2.02274i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0994 | −1.04864 | −0.524321 | − | 0.851521i | \(-0.675681\pi\) | ||||
−0.524321 | + | 0.851521i | \(0.675681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 40.2225 | + | 17.3279i | 1.31191 | + | 0.565173i | ||||
\(941\) | −10.2182 | −0.333105 | −0.166552 | − | 0.986033i | \(-0.553264\pi\) | ||||
−0.166552 | + | 0.986033i | \(0.553264\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.5526 | −0.636721 | ||||||||
\(944\) | −91.0378 | −2.96303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.04097 | 0.228922 | ||||||||
\(947\) | 10.2991 | 0.334675 | 0.167337 | − | 0.985900i | \(-0.446483\pi\) | ||||
0.167337 | + | 0.985900i | \(0.446483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0941 | −0.360128 | ||||||||
\(950\) | 13.4693 | − | 12.7316i | 0.437003 | − | 0.413068i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.930159 | 0.0301308 | 0.0150654 | − | 0.999887i | \(-0.495204\pi\) | ||||
0.0150654 | + | 0.999887i | \(0.495204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.4419 | − | 8.80639i | −0.661484 | − | 0.284968i | ||||
\(956\) | − | 33.8622i | − | 1.09518i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.63696 | 0.246739 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.6803 | 0.925173 | ||||||||
\(962\) | 9.92977i | 0.320149i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 126.711i | 4.08108i | ||||||||
\(965\) | 51.2363 | + | 22.0726i | 1.64935 | + | 0.710543i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.22117i | − | 0.135744i | −0.997694 | − | 0.0678719i | \(-0.978379\pi\) | ||
0.997694 | − | 0.0678719i | \(-0.0216209\pi\) | |||||||
\(968\) | −138.889 | −4.46405 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −33.4877 | + | 77.7337i | −1.07523 | + | 2.49588i | ||||
\(971\) | 4.57870 | 0.146938 | 0.0734688 | − | 0.997298i | \(-0.476593\pi\) | ||||
0.0734688 | + | 0.997298i | \(0.476593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 58.3566i | − | 1.86987i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 55.8727i | − | 1.78844i | ||||||
\(977\) | −45.5111 | −1.45603 | −0.728015 | − | 0.685562i | \(-0.759557\pi\) | ||||
−0.728015 | + | 0.685562i | \(0.759557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 58.2329i | − | 1.86113i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.4112i | 1.06619i | ||||||||
\(983\) | 10.5166i | 0.335428i | 0.985836 | + | 0.167714i | \(0.0536385\pi\) | ||||
−0.985836 | + | 0.167714i | \(0.946362\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8998 | + | 39.2287i | −0.538471 | + | 1.24993i | ||||
\(986\) | −30.1192 | −0.959192 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.4708i | 0.746706i | ||||||||
\(989\) | − | 1.45769i | − | 0.0463520i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.9079 | −0.886523 | −0.443262 | − | 0.896392i | \(-0.646179\pi\) | ||||
−0.443262 | + | 0.896392i | \(0.646179\pi\) | |||||||
\(992\) | 10.8348i | 0.344004i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.78535 | + | 1.63073i | 0.120004 | + | 0.0516977i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.9134 | −1.23240 | −0.616201 | − | 0.787589i | \(-0.711329\pi\) | ||||
−0.616201 | + | 0.787589i | \(0.711329\pi\) | |||||||
\(998\) | −55.5184 | −1.75740 | ||||||||
\(999\) | 0 | 0 |
(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 | 2205.2.g.b.2204.22 | 24 | ||
3.2 | odd | 2 | inner | 2205.2.g.b.2204.4 | 24 | ||
5.4 | even | 2 | inner | 2205.2.g.b.2204.2 | 24 | ||
7.4 | even | 3 | 315.2.bb.b.89.1 | ✓ | 24 | ||
7.5 | odd | 6 | 315.2.bb.b.269.2 | yes | 24 | ||
7.6 | odd | 2 | inner | 2205.2.g.b.2204.21 | 24 | ||
15.14 | odd | 2 | inner | 2205.2.g.b.2204.24 | 24 | ||
21.5 | even | 6 | 315.2.bb.b.269.11 | yes | 24 | ||
21.11 | odd | 6 | 315.2.bb.b.89.12 | yes | 24 | ||
21.20 | even | 2 | inner | 2205.2.g.b.2204.3 | 24 | ||
35.4 | even | 6 | 315.2.bb.b.89.11 | yes | 24 | ||
35.12 | even | 12 | 1575.2.bk.i.1151.12 | 24 | |||
35.18 | odd | 12 | 1575.2.bk.i.26.11 | 24 | |||
35.19 | odd | 6 | 315.2.bb.b.269.12 | yes | 24 | ||
35.32 | odd | 12 | 1575.2.bk.i.26.1 | 24 | |||
35.33 | even | 12 | 1575.2.bk.i.1151.2 | 24 | |||
35.34 | odd | 2 | inner | 2205.2.g.b.2204.1 | 24 | ||
105.32 | even | 12 | 1575.2.bk.i.26.12 | 24 | |||
105.47 | odd | 12 | 1575.2.bk.i.1151.1 | 24 | |||
105.53 | even | 12 | 1575.2.bk.i.26.2 | 24 | |||
105.68 | odd | 12 | 1575.2.bk.i.1151.11 | 24 | |||
105.74 | odd | 6 | 315.2.bb.b.89.2 | yes | 24 | ||
105.89 | even | 6 | 315.2.bb.b.269.1 | yes | 24 | ||
105.104 | even | 2 | inner | 2205.2.g.b.2204.23 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bb.b.89.1 | ✓ | 24 | 7.4 | even | 3 | ||
315.2.bb.b.89.2 | yes | 24 | 105.74 | odd | 6 | ||
315.2.bb.b.89.11 | yes | 24 | 35.4 | even | 6 | ||
315.2.bb.b.89.12 | yes | 24 | 21.11 | odd | 6 | ||
315.2.bb.b.269.1 | yes | 24 | 105.89 | even | 6 | ||
315.2.bb.b.269.2 | yes | 24 | 7.5 | odd | 6 | ||
315.2.bb.b.269.11 | yes | 24 | 21.5 | even | 6 | ||
315.2.bb.b.269.12 | yes | 24 | 35.19 | odd | 6 | ||
1575.2.bk.i.26.1 | 24 | 35.32 | odd | 12 | |||
1575.2.bk.i.26.2 | 24 | 105.53 | even | 12 | |||
1575.2.bk.i.26.11 | 24 | 35.18 | odd | 12 | |||
1575.2.bk.i.26.12 | 24 | 105.32 | even | 12 | |||
1575.2.bk.i.1151.1 | 24 | 105.47 | odd | 12 | |||
1575.2.bk.i.1151.2 | 24 | 35.33 | even | 12 | |||
1575.2.bk.i.1151.11 | 24 | 105.68 | odd | 12 | |||
1575.2.bk.i.1151.12 | 24 | 35.12 | even | 12 | |||
2205.2.g.b.2204.1 | 24 | 35.34 | odd | 2 | inner | ||
2205.2.g.b.2204.2 | 24 | 5.4 | even | 2 | inner | ||
2205.2.g.b.2204.3 | 24 | 21.20 | even | 2 | inner | ||
2205.2.g.b.2204.4 | 24 | 3.2 | odd | 2 | inner | ||
2205.2.g.b.2204.21 | 24 | 7.6 | odd | 2 | inner | ||
2205.2.g.b.2204.22 | 24 | 1.1 | even | 1 | trivial | ||
2205.2.g.b.2204.23 | 24 | 105.104 | even | 2 | inner | ||
2205.2.g.b.2204.24 | 24 | 15.14 | odd | 2 | inner |