Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(269,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 81 x^{14} + 4781 x^{12} - 127980 x^{10} + 2502300 x^{8} - 12798000 x^{6} + 47810000 x^{4} + \cdots + 100000000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{8}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.7 | ||
Root | \(1.59914 - 0.923267i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.269 |
Dual form | 1620.3.t.e.1349.7 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.55485 | − | 3.51612i | 0.710969 | − | 0.703223i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.42313 | + | 3.13104i | 0.774732 | + | 0.447292i | 0.834560 | − | 0.550917i | \(-0.185722\pi\) |
−0.0598278 | + | 0.998209i | \(0.519055\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.895275 | + | 0.516887i | 0.0813886 | + | 0.0469898i | 0.540142 | − | 0.841574i | \(-0.318371\pi\) |
−0.458753 | + | 0.888564i | \(0.651704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.59808 | + | 1.50000i | −0.199852 | + | 0.115385i | −0.596586 | − | 0.802549i | \(-0.703477\pi\) |
0.396734 | + | 0.917933i | \(0.370143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.7776 | 0.928092 | 0.464046 | − | 0.885811i | \(-0.346397\pi\) | ||||
0.464046 | + | 0.885811i | \(0.346397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.7863 | 0.988751 | 0.494375 | − | 0.869249i | \(-0.335397\pi\) | ||||
0.494375 | + | 0.869249i | \(0.335397\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −17.3282 | − | 30.0134i | −0.753401 | − | 1.30493i | −0.946165 | − | 0.323683i | \(-0.895079\pi\) |
0.192765 | − | 0.981245i | \(-0.438255\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.273852 | − | 24.9985i | 0.0109541 | − | 0.999940i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.68583 | + | 1.55066i | 0.0926147 | + | 0.0534711i | 0.545592 | − | 0.838051i | \(-0.316305\pi\) |
−0.452977 | + | 0.891522i | \(0.649638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.89313 | + | 15.4034i | 0.286875 | + | 0.496882i | 0.973062 | − | 0.230543i | \(-0.0740502\pi\) |
−0.686187 | + | 0.727425i | \(0.740717\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 30.2875 | − | 7.93797i | 0.865357 | − | 0.226799i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 43.3104i | 1.17055i | 0.810834 | + | 0.585276i | \(0.199014\pi\) | ||||
−0.810834 | + | 0.585276i | \(0.800986\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 40.0960 | − | 23.1494i | 0.977952 | − | 0.564621i | 0.0763006 | − | 0.997085i | \(-0.475689\pi\) |
0.901651 | + | 0.432464i | \(0.142356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.9596 | + | 10.3690i | 0.417664 | + | 0.241139i | 0.694077 | − | 0.719900i | \(-0.255813\pi\) |
−0.276413 | + | 0.961039i | \(0.589146\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −39.4439 | + | 68.3188i | −0.839232 | + | 1.45359i | 0.0513061 | + | 0.998683i | \(0.483662\pi\) |
−0.890538 | + | 0.454909i | \(0.849672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89313 | − | 8.47515i | −0.0998598 | − | 0.172962i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 44.2313 | 0.834554 | 0.417277 | − | 0.908779i | \(-0.362985\pi\) | ||||
0.417277 | + | 0.908779i | \(0.362985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | − | 1.31044i | 0.0909091 | − | 0.0238261i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 78.4015 | − | 45.2651i | 1.32884 | − | 0.767205i | 0.343719 | − | 0.939073i | \(-0.388313\pi\) |
0.985120 | + | 0.171867i | \(0.0549800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.39313 | + | 7.60913i | −0.0720185 | + | 0.124740i | −0.899786 | − | 0.436332i | \(-0.856277\pi\) |
0.827767 | + | 0.561072i | \(0.189611\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.96158 | + | 14.4674i | −0.0609475 | + | 0.222575i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −16.7233 | + | 9.65522i | −0.249602 | + | 0.144108i | −0.619582 | − | 0.784932i | \(-0.712698\pi\) |
0.369980 | + | 0.929040i | \(0.379365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 56.6366i | − | 0.797699i | −0.917016 | − | 0.398850i | \(-0.869410\pi\) | ||
0.917016 | − | 0.398850i | \(-0.130590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 109.310i | − | 1.49740i | −0.662907 | − | 0.748702i | \(-0.730678\pi\) | ||
0.662907 | − | 0.748702i | \(-0.269322\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.23679 | + | 5.60629i | 0.0420363 | + | 0.0728090i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.5000 | + | 33.7750i | −0.246835 | + | 0.427532i | −0.962646 | − | 0.270763i | \(-0.912724\pi\) |
0.715811 | + | 0.698294i | \(0.246057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −37.8932 | + | 65.6330i | −0.456545 | + | 0.790759i | −0.998776 | − | 0.0494706i | \(-0.984247\pi\) |
0.542231 | + | 0.840230i | \(0.317580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 56.0868 | − | 55.4757i | 0.659844 | − | 0.652656i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 90.5302i | − | 1.01719i | −0.861005 | − | 0.508597i | \(-0.830164\pi\) | ||
0.861005 | − | 0.508597i | \(-0.169836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.7863 | −0.206442 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 66.7823 | − | 66.0547i | 0.702971 | − | 0.695312i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.69287 | + | 4.44148i | 0.0793079 | + | 0.0457885i | 0.539130 | − | 0.842223i | \(-0.318753\pi\) |
−0.459822 | + | 0.888011i | \(0.652087\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 37.4102 | + | 21.5988i | 0.370398 | + | 0.213849i | 0.673632 | − | 0.739067i | \(-0.264733\pi\) |
−0.303234 | + | 0.952916i | \(0.598066\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −66.4151 | + | 38.3448i | −0.644807 | + | 0.372279i | −0.786464 | − | 0.617636i | \(-0.788090\pi\) |
0.141657 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 38.0287 | 0.355408 | 0.177704 | − | 0.984084i | \(-0.443133\pi\) | ||||
0.177704 | + | 0.984084i | \(0.443133\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −146.718 | −1.34603 | −0.673016 | − | 0.739628i | \(-0.735002\pi\) | ||||
−0.673016 | + | 0.739628i | \(0.735002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 93.1147 | + | 161.279i | 0.824024 | + | 1.42725i | 0.902663 | + | 0.430348i | \(0.141609\pi\) |
−0.0786394 | + | 0.996903i | \(0.525058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −167.130 | − | 45.7648i | −1.45330 | − | 0.397955i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 85.5637 | + | 49.4002i | 0.719023 | + | 0.415128i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.9657 | − | 103.864i | −0.495584 | − | 0.858377i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −86.9241 | − | 89.8287i | −0.695393 | − | 0.718630i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 161.242i | 1.26962i | 0.772668 | + | 0.634810i | \(0.218922\pi\) | ||||
−0.772668 | + | 0.634810i | \(0.781078\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 215.700 | − | 124.534i | 1.64656 | − | 0.950644i | 0.668139 | − | 0.744036i | \(-0.267091\pi\) |
0.978424 | − | 0.206608i | \(-0.0662423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 101.880 | + | 58.8206i | 0.766017 | + | 0.442260i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 122.984 | − | 213.014i | 0.897691 | − | 1.55485i | 0.0672525 | − | 0.997736i | \(-0.478577\pi\) |
0.830438 | − | 0.557110i | \(-0.188090\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 84.9657 | + | 147.165i | 0.611264 | + | 1.05874i | 0.991028 | + | 0.133656i | \(0.0426719\pi\) |
−0.379764 | + | 0.925083i | \(0.623995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.10132 | −0.0216876 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0000 | − | 3.93131i | 0.103448 | − | 0.0271125i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 140.879 | − | 81.3368i | 0.945499 | − | 0.545884i | 0.0538193 | − | 0.998551i | \(-0.482860\pi\) |
0.891680 | + | 0.452666i | \(0.149527\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 55.0725 | − | 95.3884i | 0.364719 | − | 0.631711i | −0.624012 | − | 0.781415i | \(-0.714498\pi\) |
0.988731 | + | 0.149703i | \(0.0478318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 85.7737 | + | 23.4873i | 0.553379 | + | 0.151531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 111.944 | − | 64.6310i | 0.713021 | − | 0.411663i | −0.0991578 | − | 0.995072i | \(-0.531615\pi\) |
0.812178 | + | 0.583409i | \(0.198282\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 217.022i | − | 1.34796i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 245.621i | − | 1.50688i | −0.657519 | − | 0.753438i | \(-0.728394\pi\) | ||
0.657519 | − | 0.753438i | \(-0.271606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 41.1300 | + | 71.2393i | 0.246288 | + | 0.426583i | 0.962493 | − | 0.271307i | \(-0.0874559\pi\) |
−0.716205 | + | 0.697890i | \(0.754123\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −80.0000 | + | 138.564i | −0.473373 | + | 0.819906i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 110.443 | − | 191.293i | 0.638398 | − | 1.10574i | −0.347386 | − | 0.937722i | \(-0.612931\pi\) |
0.985784 | − | 0.168016i | \(-0.0537360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 79.7565 | − | 134.713i | 0.455752 | − | 0.769786i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 149.234i | − | 0.833712i | −0.908973 | − | 0.416856i | \(-0.863132\pi\) | ||
0.908973 | − | 0.416856i | \(-0.136868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 137.931 | 0.762051 | 0.381026 | − | 0.924564i | \(-0.375571\pi\) | ||||
0.381026 | + | 0.924564i | \(0.375571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 152.285 | + | 153.962i | 0.823160 | + | 0.832227i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.1253 | + | 8.15522i | 0.0755361 | + | 0.0436108i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 174.708 | + | 100.868i | 0.914704 | + | 0.528105i | 0.881942 | − | 0.471359i | \(-0.156236\pi\) |
0.0327624 | + | 0.999463i | \(0.489570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −319.462 | + | 184.441i | −1.65524 | + | 0.955655i | −0.680378 | + | 0.732861i | \(0.738184\pi\) |
−0.974866 | + | 0.222794i | \(0.928482\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −170.181 | −0.863862 | −0.431931 | − | 0.901907i | \(-0.642168\pi\) | ||||
−0.431931 | + | 0.901907i | \(0.642168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 136.863 | 0.687752 | 0.343876 | − | 0.939015i | \(-0.388260\pi\) | ||||
0.343876 | + | 0.939015i | \(0.388260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.71038 | + | 16.8189i | 0.0478344 | + | 0.0828516i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 61.1390 | − | 223.275i | 0.298239 | − | 1.08915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.8189 | + | 9.71038i | 0.0804731 | + | 0.0464611i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9657 | + | 34.5815i | 0.0946240 | + | 0.163894i | 0.909452 | − | 0.415810i | \(-0.136502\pi\) |
−0.814828 | + | 0.579703i | \(0.803168\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 100.302 | − | 26.2879i | 0.466521 | − | 0.122269i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 111.379i | 0.513268i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40.9913 | + | 23.6663i | −0.185481 | + | 0.107087i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 268.181 | + | 154.835i | 1.20261 | + | 0.694326i | 0.961134 | − | 0.276082i | \(-0.0890361\pi\) |
0.241473 | + | 0.970408i | \(0.422369\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −53.6708 | + | 92.9605i | −0.236435 | + | 0.409518i | −0.959689 | − | 0.281065i | \(-0.909312\pi\) |
0.723254 | + | 0.690583i | \(0.242646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 44.4275 | + | 76.9506i | 0.194006 | + | 0.336029i | 0.946574 | − | 0.322486i | \(-0.104518\pi\) |
−0.752568 | + | 0.658515i | \(0.771185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −245.696 | −1.05449 | −0.527245 | − | 0.849713i | \(-0.676775\pi\) | ||||
−0.527245 | + | 0.849713i | \(0.676775\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 100.000 | + | 381.552i | 0.425532 | + | 1.62363i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 205.852 | − | 118.849i | 0.861304 | − | 0.497274i | −0.00314447 | − | 0.999995i | \(-0.501001\pi\) |
0.864449 | + | 0.502721i | \(0.167668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 80.5000 | − | 139.430i | 0.334025 | − | 0.578548i | −0.649272 | − | 0.760556i | \(-0.724926\pi\) |
0.983297 | + | 0.182008i | \(0.0582597\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −47.1939 | − | 12.9230i | −0.192628 | − | 0.0527471i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48.8081 | + | 28.1794i | −0.197604 | + | 0.114087i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 91.5640i | 0.364797i | 0.983225 | + | 0.182398i | \(0.0583861\pi\) | ||||
−0.983225 | + | 0.182398i | \(0.941614\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 35.8269i | − | 0.141608i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 124.534 | + | 215.700i | 0.484569 | + | 0.839299i | 0.999843 | − | 0.0177270i | \(-0.00564299\pi\) |
−0.515274 | + | 0.857026i | \(0.672310\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −135.607 | + | 234.878i | −0.523579 | + | 0.906865i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −98.0376 | + | 169.806i | −0.372767 | + | 0.645651i | −0.989990 | − | 0.141137i | \(-0.954924\pi\) |
0.617223 | + | 0.786788i | \(0.288257\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 157.236 | − | 155.523i | 0.593342 | − | 0.586878i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 166.809i | − | 0.620106i | −0.950719 | − | 0.310053i | \(-0.899653\pi\) | ||
0.950719 | − | 0.310053i | \(-0.100347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −89.9313 | −0.331850 | −0.165925 | − | 0.986138i | \(-0.553061\pi\) | ||||
−0.165925 | + | 0.986138i | \(0.553061\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1666 | − | 22.2390i | 0.0478785 | − | 0.0808690i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −364.436 | − | 210.407i | −1.31565 | − | 0.759593i | −0.332627 | − | 0.943059i | \(-0.607935\pi\) |
−0.983026 | + | 0.183466i | \(0.941268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −267.434 | − | 154.403i | −0.951724 | − | 0.549478i | −0.0581078 | − | 0.998310i | \(-0.518507\pi\) |
−0.893616 | + | 0.448832i | \(0.851840\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −51.2563 | + | 29.5929i | −0.181118 | + | 0.104568i | −0.587818 | − | 0.808993i | \(-0.700013\pi\) |
0.406700 | + | 0.913562i | \(0.366679\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 289.928 | 1.01020 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −40.0687 | −0.138646 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −113.680 | − | 196.899i | −0.387985 | − | 0.672010i | 0.604193 | − | 0.796838i | \(-0.293496\pi\) |
−0.992178 | + | 0.124828i | \(0.960162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 119.548 | − | 436.579i | 0.405247 | − | 1.47993i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 90.0401 | + | 51.9847i | 0.301137 | + | 0.173862i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 64.9313 | + | 112.464i | 0.215719 | + | 0.373636i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.1377 | + | 42.4960i | 0.0365170 | + | 0.139331i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 301.221i | − | 0.981177i | −0.871391 | − | 0.490589i | \(-0.836782\pi\) | ||
0.871391 | − | 0.490589i | \(-0.163218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 153.222 | − | 88.4627i | 0.492675 | − | 0.284446i | −0.233009 | − | 0.972475i | \(-0.574857\pi\) |
0.725683 | + | 0.688029i | \(0.241524\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 302.512 | + | 174.655i | 0.966491 | + | 0.558004i | 0.898165 | − | 0.439659i | \(-0.144901\pi\) |
0.0683264 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −185.958 | + | 322.089i | −0.586620 | + | 1.01606i | 0.408052 | + | 0.912959i | \(0.366208\pi\) |
−0.994671 | + | 0.103096i | \(0.967125\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.60303 | + | 2.77654i | 0.00502519 | + | 0.00870388i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 296.401 | 0.917651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 36.7863 | + | 65.3588i | 0.113188 | + | 0.201104i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −427.818 | + | 247.001i | −1.30036 | + | 0.750763i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −97.8970 | + | 169.563i | −0.295761 | + | 0.512273i | −0.975162 | − | 0.221494i | \(-0.928907\pi\) |
0.679400 | + | 0.733768i | \(0.262240\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.5000 | + | 93.1240i | −0.0761193 | + | 0.277982i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 408.048 | − | 235.587i | 1.21082 | − | 0.699070i | 0.247886 | − | 0.968789i | \(-0.420264\pi\) |
0.962939 | + | 0.269720i | \(0.0869310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.3870i | 0.0539208i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 368.125i | − | 1.07325i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −176.519 | − | 305.740i | −0.508700 | − | 0.881095i | −0.999949 | − | 0.0100755i | \(-0.996793\pi\) |
0.491249 | − | 0.871019i | \(-0.336541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −308.966 | + | 535.144i | −0.885288 | + | 1.53336i | −0.0399057 | + | 0.999203i | \(0.512706\pi\) |
−0.845383 | + | 0.534161i | \(0.820628\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.4967 | + | 45.8937i | −0.0750615 | + | 0.130010i | −0.901113 | − | 0.433584i | \(-0.857249\pi\) |
0.826051 | + | 0.563595i | \(0.190582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −199.141 | − | 201.335i | −0.560961 | − | 0.567139i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 618.426i | 1.72264i | 0.508067 | + | 0.861318i | \(0.330360\pi\) | ||||
−0.508067 | + | 0.861318i | \(0.669640\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.07636 | −0.0223722 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −384.348 | − | 388.582i | −1.05301 | − | 1.06461i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3364 | − | 10.5865i | −0.0499630 | − | 0.0288461i | 0.474810 | − | 0.880088i | \(-0.342517\pi\) |
−0.524773 | + | 0.851242i | \(0.675850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 239.872 | + | 138.490i | 0.646556 | + | 0.373289i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −500.821 | + | 289.149i | −1.34268 | + | 0.775198i | −0.987200 | − | 0.159485i | \(-0.949017\pi\) |
−0.355482 | + | 0.934683i | \(0.615683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.30397 | −0.0246790 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −675.657 | −1.78273 | −0.891367 | − | 0.453281i | \(-0.850253\pi\) | ||||
−0.891367 | + | 0.453281i | \(0.850253\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −83.9462 | − | 145.399i | −0.219181 | − | 0.379632i | 0.735377 | − | 0.677658i | \(-0.237005\pi\) |
−0.954558 | + | 0.298026i | \(0.903672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.2187 | + | 8.54855i | 0.0810875 | + | 0.0222040i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −586.221 | − | 338.455i | −1.50699 | − | 0.870063i | −0.999967 | − | 0.00813318i | \(-0.997411\pi\) |
−0.507027 | − | 0.861930i | \(-0.669256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −273.397 | − | 473.537i | −0.699225 | − | 1.21109i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 49.4373 | + | 188.629i | 0.125158 | + | 0.477542i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 63.8423i | − | 0.160812i | −0.996762 | − | 0.0804059i | \(-0.974378\pi\) | ||
0.996762 | − | 0.0804059i | \(-0.0256216\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −471.496 | + | 272.218i | −1.17580 | + | 0.678848i | −0.955039 | − | 0.296480i | \(-0.904187\pi\) |
−0.220760 | + | 0.975328i | \(0.570854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −46.2101 | − | 26.6794i | −0.114665 | − | 0.0662020i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.3866 | + | 38.7748i | −0.0550040 | + | 0.0952697i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 373.363 | + | 646.683i | 0.912867 | + | 1.58113i | 0.809994 | + | 0.586438i | \(0.199470\pi\) |
0.102873 | + | 0.994695i | \(0.467197\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 566.908 | 1.37266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 96.0687 | + | 366.552i | 0.231491 | + | 0.883258i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.8291 | − | 19.5312i | 0.0807377 | − | 0.0466139i | −0.459088 | − | 0.888391i | \(-0.651824\pi\) |
0.539825 | + | 0.841777i | \(0.318490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 179.966 | − | 311.710i | 0.427472 | − | 0.740403i | −0.569176 | − | 0.822216i | \(-0.692738\pi\) |
0.996648 | + | 0.0818128i | \(0.0260710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.32071 | − | 394.415i | 0.0101664 | − | 0.928036i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −47.6490 | + | 27.5102i | −0.111590 | + | 0.0644266i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 431.163i | 1.00038i | 0.865916 | + | 0.500189i | \(0.166736\pi\) | ||||
−0.865916 | + | 0.500189i | \(0.833264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.05602i | 0.0139862i | 0.999976 | + | 0.00699309i | \(0.00222599\pi\) | ||||
−0.999976 | + | 0.00699309i | \(0.997774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −325.532 | − | 563.839i | −0.744926 | − | 1.29025i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −246.641 | + | 427.195i | −0.561825 | + | 0.973110i | 0.435512 | + | 0.900183i | \(0.356567\pi\) |
−0.997337 | + | 0.0729268i | \(0.976766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.4053 | + | 21.4866i | −0.0280029 | + | 0.0485025i | −0.879687 | − | 0.475553i | \(-0.842248\pi\) |
0.851684 | + | 0.524055i | \(0.175581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −318.315 | − | 321.821i | −0.715314 | − | 0.723193i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 131.881i | 0.293722i | 0.989157 | + | 0.146861i | \(0.0469170\pi\) | ||||
−0.989157 | + | 0.146861i | \(0.953083\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.8626 | 0.106126 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −66.7823 | + | 66.0547i | −0.146774 | + | 0.145175i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −262.734 | − | 151.690i | −0.574910 | − | 0.331925i | 0.184198 | − | 0.982889i | \(-0.441031\pi\) |
−0.759108 | + | 0.650965i | \(0.774365\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −563.135 | − | 325.126i | −1.22155 | − | 0.705263i | −0.256302 | − | 0.966597i | \(-0.582504\pi\) |
−0.965248 | + | 0.261334i | \(0.915838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 624.973 | − | 360.828i | 1.34983 | − | 0.779327i | 0.361608 | − | 0.932330i | \(-0.382228\pi\) |
0.988226 | + | 0.153004i | \(0.0488946\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −341.445 | −0.731147 | −0.365573 | − | 0.930783i | \(-0.619127\pi\) | ||||
−0.365573 | + | 0.930783i | \(0.619127\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −120.924 | −0.257833 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.7192 | + | 18.5661i | 0.0226621 | + | 0.0392519i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.14465 | − | 469.628i | 0.0108308 | − | 0.988691i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 553.478 | + | 319.551i | 1.15549 | + | 0.667121i | 0.950218 | − | 0.311585i | \(-0.100860\pi\) |
0.205269 | + | 0.978706i | \(0.434193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −64.9657 | − | 112.524i | −0.135064 | − | 0.233937i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 42.9637 | − | 11.2602i | 0.0885850 | − | 0.0232170i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 411.931i | − | 0.845855i | −0.906164 | − | 0.422927i | \(-0.861003\pi\) | ||
0.906164 | − | 0.422927i | \(-0.138997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −508.714 | + | 293.706i | −1.03608 | + | 0.598180i | −0.918720 | − | 0.394910i | \(-0.870776\pi\) |
−0.117358 | + | 0.993090i | \(0.537443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 42.3758 | + | 24.4657i | 0.0859549 | + | 0.0496261i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 177.332 | − | 307.148i | 0.356804 | − | 0.618003i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 387.290 | + | 670.806i | 0.776132 | + | 1.34430i | 0.934156 | + | 0.356865i | \(0.116155\pi\) |
−0.158023 | + | 0.987435i | \(0.550512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −546.283 | −1.08605 | −0.543025 | − | 0.839717i | \(-0.682721\pi\) | ||||
−0.543025 | + | 0.839717i | \(0.682721\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 208.931 | − | 54.7583i | 0.413725 | − | 0.108432i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −603.422 | + | 348.386i | −1.18551 | + | 0.684452i | −0.957282 | − | 0.289157i | \(-0.906625\pi\) |
−0.228224 | + | 0.973609i | \(0.573292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 342.256 | − | 592.804i | 0.669776 | − | 1.16009i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −101.271 | + | 369.833i | −0.196642 | + | 0.718122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −70.6263 | + | 40.7761i | −0.136608 | + | 0.0788706i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 558.909i | 1.07276i | 0.843976 | + | 0.536381i | \(0.180209\pi\) | ||||
−0.843976 | + | 0.536381i | \(0.819791\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 402.669i | 0.769922i | 0.922933 | + | 0.384961i | \(0.125785\pi\) | ||||
−0.922933 | + | 0.384961i | \(0.874215\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 140.312 | + | 243.027i | 0.266246 | + | 0.461152i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −336.034 | + | 582.029i | −0.635226 | + | 1.10024i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −69.4483 | + | 120.288i | −0.130297 | + | 0.225681i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 135.186 | − | 133.713i | 0.252684 | − | 0.249931i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.1168i | − | 0.0187696i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 636.649 | 1.17680 | 0.588400 | − | 0.808570i | \(-0.299758\pi\) | ||||
0.588400 | + | 0.808570i | \(0.299758\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −521.558 | + | 515.876i | −0.956988 | + | 0.946562i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 257.866 | + | 148.879i | 0.471419 | + | 0.272174i | 0.716834 | − | 0.697244i | \(-0.245591\pi\) |
−0.245415 | + | 0.969418i | \(0.578924\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.4566 | + | 29.1311i | 0.0915728 | + | 0.0528696i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −211.502 | + | 122.111i | −0.382463 | + | 0.220815i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 391.067 | 0.702095 | 0.351047 | − | 0.936358i | \(-0.385826\pi\) | ||||
0.351047 | + | 0.936358i | \(0.385826\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.2137 | −0.111295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 205.108 | + | 355.258i | 0.364313 | + | 0.631009i | 0.988666 | − | 0.150134i | \(-0.0479705\pi\) |
−0.624353 | + | 0.781143i | \(0.714637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 898.085 | + | 245.921i | 1.58953 | + | 0.435259i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −538.450 | − | 310.874i | −0.946309 | − | 0.546352i | −0.0543766 | − | 0.998520i | \(-0.517317\pi\) |
−0.891932 | + | 0.452169i | \(0.850650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −198.324 | − | 343.508i | −0.347328 | − | 0.601590i | 0.638446 | − | 0.769667i | \(-0.279578\pi\) |
−0.985774 | + | 0.168077i | \(0.946244\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −755.034 | + | 424.960i | −1.31310 | + | 0.739061i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 571.601i | 0.990642i | 0.868710 | + | 0.495321i | \(0.164950\pi\) | ||||
−0.868710 | + | 0.495321i | \(0.835050\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −411.000 | + | 237.291i | −0.707400 | + | 0.408418i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.5992 | + | 22.8626i | 0.0679232 | + | 0.0392155i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 384.458 | − | 665.900i | 0.654953 | − | 1.13441i | −0.326952 | − | 0.945041i | \(-0.606022\pi\) |
0.981905 | − | 0.189372i | \(-0.0606451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 167.069 | + | 289.371i | 0.283648 | + | 0.491293i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −917.116 | −1.54657 | −0.773285 | − | 0.634059i | \(-0.781388\pi\) | ||||
−0.773285 | + | 0.634059i | \(0.781388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 477.863 | − | 125.242i | 0.803130 | − | 0.210490i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −765.405 | + | 441.907i | −1.27781 | + | 0.737741i | −0.976444 | − | 0.215769i | \(-0.930774\pi\) |
−0.301361 | + | 0.953510i | \(0.597441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 337.824 | − | 585.129i | 0.562104 | − | 0.973593i | −0.435209 | − | 0.900330i | \(-0.643325\pi\) |
0.997313 | − | 0.0732629i | \(-0.0233412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −578.365 | − | 158.373i | −0.955975 | − | 0.261773i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −595.109 | + | 343.587i | −0.980411 | + | 0.566040i | −0.902394 | − | 0.430912i | \(-0.858192\pi\) |
−0.0780166 | + | 0.996952i | \(0.524859\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 236.663i | − | 0.387338i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 193.896i | 0.316306i | 0.987415 | + | 0.158153i | \(0.0505539\pi\) | ||||
−0.987415 | + | 0.158153i | \(0.949446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 278.802 | + | 482.900i | 0.451867 | + | 0.782657i | 0.998502 | − | 0.0547139i | \(-0.0174247\pi\) |
−0.546635 | + | 0.837371i | \(0.684091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −513.324 | + | 889.104i | −0.829280 | + | 1.43636i | 0.0693235 | + | 0.997594i | \(0.477916\pi\) |
−0.898604 | + | 0.438761i | \(0.855417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 283.454 | − | 490.957i | 0.454983 | − | 0.788053i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −624.850 | − | 13.6918i | −0.999760 | − | 0.0219068i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 683.333i | 1.08638i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 145.794 | 0.231052 | 0.115526 | − | 0.993304i | \(-0.463145\pi\) | ||||
0.115526 | + | 0.993304i | \(0.463145\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 566.945 | + | 573.189i | 0.892826 | + | 0.902661i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.4255 | + | 14.6794i | 0.0399144 | + | 0.0230446i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 74.8204 | + | 43.1976i | 0.116724 | + | 0.0673909i | 0.557226 | − | 0.830361i | \(-0.311866\pi\) |
−0.440501 | + | 0.897752i | \(0.645199\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 163.857 | − | 94.6030i | 0.254832 | − | 0.147128i | −0.367143 | − | 0.930165i | \(-0.619664\pi\) |
0.621975 | + | 0.783037i | \(0.286331\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −801.554 | −1.23888 | −0.619439 | − | 0.785045i | \(-0.712640\pi\) | ||||
−0.619439 | + | 0.785045i | \(0.712640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 93.5879 | 0.144203 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −416.961 | − | 722.198i | −0.638531 | − | 1.10597i | −0.985755 | − | 0.168187i | \(-0.946209\pi\) |
0.347224 | − | 0.937782i | \(-0.387124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 328.902 | − | 1201.13i | 0.502141 | − | 1.83378i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −132.118 | − | 76.2784i | −0.200483 | − | 0.115749i | 0.396398 | − | 0.918079i | \(-0.370260\pi\) |
−0.596881 | + | 0.802330i | \(0.703593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 171.760 | + | 297.496i | 0.259848 | + | 0.450070i | 0.966201 | − | 0.257790i | \(-0.0829942\pi\) |
−0.706353 | + | 0.707860i | \(0.749661\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 568.989 | − | 149.125i | 0.855622 | − | 0.224248i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 107.481i | − | 0.161141i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.86612 | + | 4.54151i | −0.0117230 | + | 0.00676827i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −924.380 | − | 533.691i | −1.37352 | − | 0.793003i | −0.382152 | − | 0.924100i | \(-0.624817\pi\) |
−0.991370 | + | 0.131097i | \(0.958150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −62.5684 | + | 108.372i | −0.0924200 | + | 0.160076i | −0.908529 | − | 0.417822i | \(-0.862794\pi\) |
0.816109 | + | 0.577898i | \(0.196127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.8129 | + | 48.1734i | 0.0409616 | + | 0.0709476i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −675.334 | −0.988775 | −0.494388 | − | 0.869241i | \(-0.664608\pi\) | ||||
−0.494388 | + | 0.869241i | \(0.664608\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −311.794 | − | 1189.66i | −0.455174 | − | 1.73672i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −114.916 | + | 66.3470i | −0.166787 | + | 0.0962947i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −213.863 | + | 370.421i | −0.309497 | + | 0.536065i | −0.978252 | − | 0.207418i | \(-0.933494\pi\) |
0.668755 | + | 0.743483i | \(0.266827\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 819.488 | + | 224.399i | 1.17912 | + | 0.322876i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 632.617 | − | 365.242i | 0.907629 | − | 0.524020i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 410.708i | − | 0.585889i | −0.956129 | − | 0.292945i | \(-0.905365\pi\) | ||
0.956129 | − | 0.292945i | \(-0.0946352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 813.641i | 1.15738i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 135.253 | + | 234.266i | 0.191306 | + | 0.331352i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −395.462 | + | 684.960i | −0.557774 | + | 0.966093i | 0.439908 | + | 0.898043i | \(0.355011\pi\) |
−0.997682 | + | 0.0680501i | \(0.978322\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 308.204 | − | 533.825i | 0.432264 | − | 0.748703i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0247 | + | 10.9046i | −0.0154192 | + | 0.0152512i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 79.3797i | 0.110403i | 0.998475 | + | 0.0552014i | \(0.0175801\pi\) | ||||
−0.998475 | + | 0.0552014i | \(0.982420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −480.237 | −0.666070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.4997 | − | 66.7169i | 0.0544824 | − | 0.0920234i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1070.30 | + | 617.939i | 1.47222 | + | 0.849985i | 0.999512 | − | 0.0312360i | \(-0.00994433\pi\) |
0.472705 | + | 0.881221i | \(0.343278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 283.358 | + | 163.597i | 0.387631 | + | 0.223799i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1017.43 | − | 587.415i | 1.38804 | − | 0.801384i | 0.394944 | − | 0.918705i | \(-0.370764\pi\) |
0.993094 | + | 0.117321i | \(0.0374305\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.9626 | −0.0270863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −425.863 | −0.576269 | −0.288134 | − | 0.957590i | \(-0.593035\pi\) | ||||
−0.288134 | + | 0.957590i | \(0.593035\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 330.184 | + | 571.896i | 0.444394 | + | 0.769712i | 0.998010 | − | 0.0630597i | \(-0.0200858\pi\) |
−0.553616 | + | 0.832772i | \(0.686753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 214.815 | − | 784.488i | 0.288342 | − | 1.05300i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 206.234 | + | 119.070i | 0.275346 | + | 0.158971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.3626 | + | 66.4460i | 0.0510821 | + | 0.0884767i | 0.890436 | − | 0.455109i | \(-0.150400\pi\) |
−0.839354 | + | 0.543586i | \(0.817066\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −139.622 | − | 532.732i | −0.184930 | − | 0.705606i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 530.532i | 0.700835i | 0.936594 | + | 0.350417i | \(0.113960\pi\) | ||||
−0.936594 | + | 0.350417i | \(0.886040\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −635.078 | + | 366.662i | −0.834531 | + | 0.481817i | −0.855401 | − | 0.517966i | \(-0.826690\pi\) |
0.0208705 | + | 0.999782i | \(0.493356\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −795.668 | − | 459.379i | −1.04282 | − | 0.602070i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −135.795 | + | 235.204i | −0.177047 | + | 0.306655i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 122.637 | + | 212.414i | 0.159476 | + | 0.276221i | 0.934680 | − | 0.355490i | \(-0.115686\pi\) |
−0.775204 | + | 0.631712i | \(0.782353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1211.23 | 1.56692 | 0.783460 | − | 0.621443i | \(-0.213453\pi\) | ||||
0.783460 | + | 0.621443i | \(0.213453\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 387.496 | − | 218.097i | 0.499995 | − | 0.281415i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 753.254 | − | 434.892i | 0.966950 | − | 0.558269i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.2748 | − | 50.7054i | 0.0374837 | − | 0.0649236i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 170.694 | − | 623.362i | 0.217445 | − | 0.794092i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1041.88 | + | 601.528i | −1.32386 | + | 0.764330i | −0.984342 | − | 0.176269i | \(-0.943597\pi\) |
−0.339517 | + | 0.940600i | \(0.610264\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1166.18i | 1.47432i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.3588i | − | 0.0332393i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −507.170 | − | 878.445i | −0.636349 | − | 1.10219i | −0.986228 | − | 0.165394i | \(-0.947110\pi\) |
0.349878 | − | 0.936795i | \(-0.386223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −622.328 | + | 1077.90i | −0.778884 | + | 1.34907i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 56.5012 | − | 97.8629i | 0.0703626 | − | 0.121872i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −763.073 | − | 771.478i | −0.947917 | − | 0.958358i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 951.230i | − | 1.17581i | −0.808930 | − | 0.587905i | \(-0.799953\pi\) | ||
0.808930 | − | 0.587905i | \(-0.200047\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −404.580 | −0.498866 | −0.249433 | − | 0.968392i | \(-0.580244\pi\) | ||||
−0.249433 | + | 0.968392i | \(0.580244\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −863.632 | − | 873.144i | −1.05967 | − | 1.07134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 337.393 | + | 194.794i | 0.412966 | + | 0.238426i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1026.38 | − | 592.582i | −1.25016 | − | 0.721780i | −0.279019 | − | 0.960286i | \(-0.590009\pi\) |
−0.971141 | + | 0.238505i | \(0.923343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 578.564 | − | 334.034i | 0.702994 | − | 0.405874i | −0.105467 | − | 0.994423i | \(-0.533634\pi\) |
0.808462 | + | 0.588549i | \(0.200300\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −427.199 | −0.516564 | −0.258282 | − | 0.966070i | \(-0.583156\pi\) | ||||
−0.258282 | + | 0.966070i | \(0.583156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1143.52 | −1.37940 | −0.689698 | − | 0.724097i | \(-0.742257\pi\) | ||||
−0.689698 | + | 0.724097i | \(0.742257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −77.2017 | − | 133.717i | −0.0926791 | − | 0.160525i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 396.697 | + | 108.627i | 0.475086 | + | 0.130092i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 627.212 | + | 362.121i | 0.747571 | + | 0.431610i | 0.824816 | − | 0.565402i | \(-0.191279\pi\) |
−0.0772447 | + | 0.997012i | \(0.524612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −415.691 | − | 719.998i | −0.494282 | − | 0.856121i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 202.820 | + | 773.863i | 0.240023 | + | 0.915814i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 751.020i | − | 0.886683i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1299.89 | − | 750.493i | 1.52749 | − | 0.881895i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −423.187 | − | 244.327i | −0.496116 | − | 0.286433i | 0.230992 | − | 0.972956i | \(-0.425803\pi\) |
−0.727108 | + | 0.686523i | \(0.759136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −67.1598 | + | 116.324i | −0.0783662 | + | 0.135734i | −0.902545 | − | 0.430595i | \(-0.858304\pi\) |
0.824179 | + | 0.566329i | \(0.191637\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 660.691 | + | 1144.35i | 0.769140 | + | 1.33219i | 0.938030 | + | 0.346554i | \(0.112648\pi\) |
−0.168890 | + | 0.985635i | \(0.554018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 948.942 | 1.09959 | 0.549793 | − | 0.835301i | \(-0.314707\pi\) | ||||
0.549793 | + | 0.835301i | \(0.314707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −280.000 | − | 1068.35i | −0.323699 | − | 1.23508i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34.9157 | + | 20.1586i | −0.0401792 | + | 0.0231975i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.9657 | − | 50.1700i | 0.0332556 | − | 0.0576004i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −190.143 | − | 759.316i | −0.217306 | − | 0.867789i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.0452 | − | 27.1616i | 0.0536433 | − | 0.0309710i | −0.472938 | − | 0.881095i | \(-0.656807\pi\) |
0.526582 | + | 0.850124i | \(0.323473\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 762.713i | − | 0.865735i | −0.901458 | − | 0.432868i | \(-0.857502\pi\) | ||
0.901458 | − | 0.432868i | \(-0.142498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 95.0917i | − | 0.107692i | −0.998549 | − | 0.0538458i | \(-0.982852\pi\) | ||
0.998549 | − | 0.0538458i | \(-0.0171479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 336.387 | + | 582.640i | 0.379241 | + | 0.656865i | 0.990952 | − | 0.134216i | \(-0.0428517\pi\) |
−0.611711 | + | 0.791082i | \(0.709518\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −504.855 | + | 874.434i | −0.567891 | + | 0.983616i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −741.003 | + | 1283.46i | −0.829791 | + | 1.43724i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −524.726 | − | 530.505i | −0.586286 | − | 0.592743i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 55.1610i | 0.0613581i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 697.863 | 0.774542 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 490.324 | − | 484.983i | 0.541795 | − | 0.535892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 118.883 | + | 68.6374i | 0.131073 | + | 0.0756752i | 0.564103 | − | 0.825705i | \(-0.309222\pi\) |
−0.433030 | + | 0.901380i | \(0.642555\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1479.65 | + | 854.277i | 1.62420 | + | 0.937735i | 0.985778 | + | 0.168052i | \(0.0537477\pi\) |
0.638427 | + | 0.769683i | \(0.279586\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −67.8497 | + | 39.1731i | −0.0743151 | + | 0.0429059i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1559.69 | 1.70086 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 475.802 | 0.517738 | 0.258869 | − | 0.965912i | \(-0.416650\pi\) | ||||
0.258869 | + | 0.965912i | \(0.416650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 84.9550 | + | 147.146i | 0.0920422 | + | 0.159422i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1082.70 | + | 11.8606i | 1.17048 | + | 0.0128223i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −851.352 | − | 491.528i | −0.916418 | − | 0.529094i | −0.0339271 | − | 0.999424i | \(-0.510801\pi\) |
−0.882490 | + | 0.470330i | \(0.844135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −91.9236 | − | 159.216i | −0.0987365 | − | 0.171017i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 78.8878 | − | 20.6755i | 0.0843720 | − | 0.0221128i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 614.705i | 0.656035i | 0.944672 | + | 0.328018i | \(0.106381\pi\) | ||||
−0.944672 | + | 0.328018i | \(0.893619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1000.42 | − | 577.592i | 1.06314 | − | 0.613807i | 0.136844 | − | 0.990593i | \(-0.456304\pi\) |
0.926300 | + | 0.376786i | \(0.122971\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1389.59 | − | 802.277i | −1.47358 | − | 0.850771i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −706.076 | + | 1222.96i | −0.745592 | + | 1.29140i | 0.204325 | + | 0.978903i | \(0.434500\pi\) |
−0.949918 | + | 0.312501i | \(0.898833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 163.966 | + | 283.997i | 0.172777 | + | 0.299259i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −243.408 | −0.255412 | −0.127706 | − | 0.991812i | \(-0.540761\pi\) | ||||
−0.127706 | + | 0.991812i | \(0.540761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 975.725 | − | 255.725i | 1.02170 | − | 0.267775i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1333.91 | − | 770.134i | 1.39094 | − | 0.803060i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 322.324 | − | 558.282i | 0.335405 | − | 0.580939i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −487.120 | + | 1778.93i | −0.504788 | + | 1.84345i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −763.356 | + | 440.724i | −0.789407 | + | 0.455764i | −0.839754 | − | 0.542968i | \(-0.817301\pi\) |
0.0503470 | + | 0.998732i | \(0.483967\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1537.17i | − | 1.58308i | −0.611119 | − | 0.791538i | \(-0.709280\pi\) | ||
0.611119 | − | 0.791538i | \(-0.290720\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1064.12i | 1.09365i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −197.084 | − | 341.359i | −0.201724 | − | 0.349396i | 0.747360 | − | 0.664419i | \(-0.231321\pi\) |
−0.949084 | + | 0.315023i | \(0.897988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.7939 | − | 81.0495i | 0.0477977 | − | 0.0827880i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −364.434 | + | 631.219i | −0.370737 | + | 0.642135i | −0.989679 | − | 0.143301i | \(-0.954228\pi\) |
0.618942 | + | 0.785437i | \(0.287562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −604.967 | + | 598.376i | −0.614179 | + | 0.607488i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 718.702i | − | 0.726696i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −732.282 | −0.738933 | −0.369466 | − | 0.929244i | \(-0.620460\pi\) | ||||
−0.369466 | + | 0.929244i | \(0.620460\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 486.525 | − | 481.225i | 0.488970 | − | 0.483643i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −691.538 | − | 399.260i | −0.693619 | − | 0.400461i | 0.111348 | − | 0.993782i | \(-0.464483\pi\) |
−0.804966 | + | 0.593321i | \(0.797817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1620.3.t.e.269.7 | 16 | ||
3.2 | odd | 2 | inner | 1620.3.t.e.269.2 | 16 | ||
5.4 | even | 2 | inner | 1620.3.t.e.269.8 | 16 | ||
9.2 | odd | 6 | 540.3.b.c.269.3 | ✓ | 8 | ||
9.4 | even | 3 | inner | 1620.3.t.e.1349.1 | 16 | ||
9.5 | odd | 6 | inner | 1620.3.t.e.1349.8 | 16 | ||
9.7 | even | 3 | 540.3.b.c.269.6 | yes | 8 | ||
15.14 | odd | 2 | inner | 1620.3.t.e.269.1 | 16 | ||
36.7 | odd | 6 | 2160.3.c.n.1889.6 | 8 | |||
36.11 | even | 6 | 2160.3.c.n.1889.3 | 8 | |||
45.2 | even | 12 | 2700.3.g.o.701.4 | 4 | |||
45.4 | even | 6 | inner | 1620.3.t.e.1349.2 | 16 | ||
45.7 | odd | 12 | 2700.3.g.o.701.3 | 4 | |||
45.14 | odd | 6 | inner | 1620.3.t.e.1349.7 | 16 | ||
45.29 | odd | 6 | 540.3.b.c.269.5 | yes | 8 | ||
45.34 | even | 6 | 540.3.b.c.269.4 | yes | 8 | ||
45.38 | even | 12 | 2700.3.g.p.701.2 | 4 | |||
45.43 | odd | 12 | 2700.3.g.p.701.1 | 4 | |||
180.79 | odd | 6 | 2160.3.c.n.1889.4 | 8 | |||
180.119 | even | 6 | 2160.3.c.n.1889.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.3.b.c.269.3 | ✓ | 8 | 9.2 | odd | 6 | ||
540.3.b.c.269.4 | yes | 8 | 45.34 | even | 6 | ||
540.3.b.c.269.5 | yes | 8 | 45.29 | odd | 6 | ||
540.3.b.c.269.6 | yes | 8 | 9.7 | even | 3 | ||
1620.3.t.e.269.1 | 16 | 15.14 | odd | 2 | inner | ||
1620.3.t.e.269.2 | 16 | 3.2 | odd | 2 | inner | ||
1620.3.t.e.269.7 | 16 | 1.1 | even | 1 | trivial | ||
1620.3.t.e.269.8 | 16 | 5.4 | even | 2 | inner | ||
1620.3.t.e.1349.1 | 16 | 9.4 | even | 3 | inner | ||
1620.3.t.e.1349.2 | 16 | 45.4 | even | 6 | inner | ||
1620.3.t.e.1349.7 | 16 | 45.14 | odd | 6 | inner | ||
1620.3.t.e.1349.8 | 16 | 9.5 | odd | 6 | inner | ||
2160.3.c.n.1889.3 | 8 | 36.11 | even | 6 | |||
2160.3.c.n.1889.4 | 8 | 180.79 | odd | 6 | |||
2160.3.c.n.1889.5 | 8 | 180.119 | even | 6 | |||
2160.3.c.n.1889.6 | 8 | 36.7 | odd | 6 | |||
2700.3.g.o.701.3 | 4 | 45.7 | odd | 12 | |||
2700.3.g.o.701.4 | 4 | 45.2 | even | 12 | |||
2700.3.g.p.701.1 | 4 | 45.43 | odd | 12 | |||
2700.3.g.p.701.2 | 4 | 45.38 | even | 12 |