Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(149,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.u (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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 749.2 | ||
Character | \(\chi\) | \(=\) | 900.749 |
Dual form | 900.3.u.c.149.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.87949 | + | 0.841761i | −0.959829 | + | 0.280587i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.3705 | + | 5.98742i | 1.48150 | + | 0.855345i | 0.999780 | − | 0.0209794i | \(-0.00667844\pi\) |
0.481721 | + | 0.876324i | \(0.340012\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.58288 | − | 4.84768i | 0.842542 | − | 0.538631i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.43429 | + | 4.29219i | 0.675845 | + | 0.390199i | 0.798288 | − | 0.602277i | \(-0.205740\pi\) |
−0.122443 | + | 0.992476i | \(0.539073\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4628 | − | 8.35009i | 1.11252 | − | 0.642314i | 0.173040 | − | 0.984915i | \(-0.444641\pi\) |
0.939481 | + | 0.342601i | \(0.111308\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.1715 | 1.30420 | 0.652102 | − | 0.758131i | \(-0.273887\pi\) | ||||
0.652102 | + | 0.758131i | \(0.273887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.9572 | −1.41880 | −0.709400 | − | 0.704806i | \(-0.751034\pi\) | ||||
−0.709400 | + | 0.704806i | \(0.751034\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −34.9017 | − | 8.51119i | −1.66199 | − | 0.405295i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.3998 | − | 33.6015i | −0.843472 | − | 1.46094i | −0.886942 | − | 0.461881i | \(-0.847175\pi\) |
0.0434704 | − | 0.999055i | \(-0.486159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.7542 | + | 20.3418i | −0.657563 | + | 0.753400i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.44943 | − | 4.87828i | −0.291360 | − | 0.168217i | 0.347195 | − | 0.937793i | \(-0.387134\pi\) |
−0.638555 | + | 0.769576i | \(0.720467\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.01648 | + | 10.4208i | 0.194080 | + | 0.336156i | 0.946598 | − | 0.322415i | \(-0.104495\pi\) |
−0.752519 | + | 0.658571i | \(0.771161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −25.0199 | − | 6.10140i | −0.758180 | − | 0.184891i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 25.0544i | − | 0.677147i | −0.940940 | − | 0.338574i | \(-0.890056\pi\) | ||
0.940940 | − | 0.338574i | \(-0.109944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −34.6166 | + | 36.2181i | −0.887604 | + | 0.928670i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.8030 | − | 20.0935i | 0.848854 | − | 0.490086i | −0.0114101 | − | 0.999935i | \(-0.503632\pi\) |
0.860264 | + | 0.509849i | \(0.170299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 67.8113 | + | 39.1509i | 1.57701 | + | 0.910485i | 0.995274 | + | 0.0971043i | \(0.0309580\pi\) |
0.581732 | + | 0.813381i | \(0.302375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 37.1715 | − | 64.3830i | 0.790883 | − | 1.36985i | −0.134537 | − | 0.990909i | \(-0.542955\pi\) |
0.925421 | − | 0.378942i | \(-0.123712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.1983 | + | 81.7498i | 0.963231 | + | 1.66836i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −63.8424 | + | 18.6631i | −1.25181 | + | 0.365943i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0311 | 0.245869 | 0.122934 | − | 0.992415i | \(-0.460770\pi\) | ||||
0.122934 | + | 0.992415i | \(0.460770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 77.6229 | − | 22.6915i | 1.36181 | − | 0.398097i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −32.9009 | + | 18.9954i | −0.557643 | + | 0.321955i | −0.752199 | − | 0.658936i | \(-0.771007\pi\) |
0.194556 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.56537 | + | 7.90745i | −0.0748421 | + | 0.129630i | −0.901018 | − | 0.433783i | \(-0.857179\pi\) |
0.826175 | + | 0.563413i | \(0.190512\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 107.663 | − | 4.87104i | 1.70894 | − | 0.0773180i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20.8770 | + | 12.0533i | −0.311597 | + | 0.179901i | −0.647641 | − | 0.761946i | \(-0.724244\pi\) |
0.336044 | + | 0.941846i | \(0.390911\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 84.1460 | + | 80.4251i | 1.21951 | + | 1.16558i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 43.7125i | − | 0.615668i | −0.951440 | − | 0.307834i | \(-0.900396\pi\) | ||
0.951440 | − | 0.307834i | \(-0.0996042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.68710i | − | 0.105303i | −0.998613 | − | 0.0526514i | \(-0.983233\pi\) | ||
0.998613 | − | 0.0526514i | \(-0.0167672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 51.3982 | + | 89.0244i | 0.667510 | + | 1.15616i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −19.3250 | + | 33.4718i | −0.244620 | + | 0.423694i | −0.962025 | − | 0.272963i | \(-0.911997\pi\) |
0.717405 | + | 0.696657i | \(0.245330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34.0001 | − | 73.5187i | 0.419754 | − | 0.907638i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −42.1875 | + | 73.0708i | −0.508283 | + | 0.880372i | 0.491671 | + | 0.870781i | \(0.336386\pi\) |
−0.999954 | + | 0.00959062i | \(0.996947\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.4364 | + | 6.93454i | 0.326855 | + | 0.0797074i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 61.5351i | − | 0.691406i | −0.938344 | − | 0.345703i | \(-0.887640\pi\) | ||
0.938344 | − | 0.345703i | \(-0.112360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 199.982 | 2.19760 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.0962 | − | 24.9422i | −0.280604 | − | 0.268196i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 54.2630 | + | 31.3288i | 0.559413 | + | 0.322977i | 0.752910 | − | 0.658124i | \(-0.228650\pi\) |
−0.193497 | + | 0.981101i | \(0.561983\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 77.1805 | − | 3.49189i | 0.779601 | − | 0.0352716i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36.0279 | − | 20.8007i | −0.356712 | − | 0.205948i | 0.310925 | − | 0.950434i | \(-0.399361\pi\) |
−0.667638 | + | 0.744486i | \(0.732694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4144 | − | 7.74480i | 0.130237 | − | 0.0751923i | −0.433466 | − | 0.901170i | \(-0.642710\pi\) |
0.563703 | + | 0.825978i | \(0.309376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 195.752 | 1.82946 | 0.914729 | − | 0.404067i | \(-0.132404\pi\) | ||||
0.914729 | + | 0.404067i | \(0.132404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 86.4249 | 0.792889 | 0.396444 | − | 0.918059i | \(-0.370244\pi\) | ||||
0.396444 | + | 0.918059i | \(0.370244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.0899 | + | 72.1439i | 0.189999 | + | 0.649945i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 50.9210 | + | 88.1977i | 0.450628 | + | 0.780511i | 0.998425 | − | 0.0561004i | \(-0.0178667\pi\) |
−0.547797 | + | 0.836611i | \(0.684533\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 69.1909 | − | 133.429i | 0.591375 | − | 1.14041i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 229.929 | + | 132.750i | 1.93218 | + | 1.11554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.6542 | − | 40.9703i | −0.195489 | − | 0.338598i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −83.3008 | + | 87.1548i | −0.677243 | + | 0.708576i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 93.7585i | 0.738256i | 0.929379 | + | 0.369128i | \(0.120344\pi\) | ||||
−0.929379 | + | 0.369128i | \(0.879656\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −228.217 | − | 55.6535i | −1.76913 | − | 0.431422i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −119.315 | + | 68.8867i | −0.910804 | + | 0.525853i | −0.880690 | − | 0.473694i | \(-0.842920\pi\) |
−0.0301140 | + | 0.999546i | \(0.509587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −279.560 | − | 161.404i | −2.10196 | − | 1.21356i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 47.8412 | − | 82.8634i | 0.349206 | − | 0.604842i | −0.636903 | − | 0.770944i | \(-0.719785\pi\) |
0.986109 | + | 0.166102i | \(0.0531180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 40.8322 | + | 70.7235i | 0.293757 | + | 0.508802i | 0.974695 | − | 0.223539i | \(-0.0717610\pi\) |
−0.680938 | + | 0.732341i | \(0.738428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −52.8398 | + | 216.679i | −0.374750 | + | 1.53673i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 143.361 | 1.00252 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −204.721 | − | 195.668i | −1.39266 | − | 1.33107i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −85.2595 | + | 49.2246i | −0.572211 | + | 0.330366i | −0.758032 | − | 0.652217i | \(-0.773839\pi\) |
0.185821 | + | 0.982584i | \(0.440506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −92.5938 | + | 160.377i | −0.613204 | + | 1.06210i | 0.377492 | + | 0.926013i | \(0.376786\pi\) |
−0.990697 | + | 0.136088i | \(0.956547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 168.123 | − | 107.480i | 1.09885 | − | 0.702484i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −160.367 | + | 92.5876i | −1.02144 | + | 0.589730i | −0.914522 | − | 0.404537i | \(-0.867433\pi\) |
−0.106921 | + | 0.994267i | \(0.534099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −37.5227 | + | 10.9690i | −0.235992 | + | 0.0689876i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 464.620i | − | 2.88584i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 180.426i | 1.10691i | 0.832880 | + | 0.553454i | \(0.186691\pi\) | ||||
−0.832880 | + | 0.553454i | \(0.813309\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 83.1659 | + | 144.047i | 0.497999 | + | 0.862560i | 0.999997 | − | 0.00230886i | \(-0.000734932\pi\) |
−0.501998 | + | 0.864869i | \(0.667402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 54.9479 | − | 95.1725i | 0.325135 | − | 0.563151i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −204.413 | + | 130.680i | −1.19540 | + | 0.764210i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 75.4211 | − | 130.633i | 0.435960 | − | 0.755105i | −0.561414 | − | 0.827535i | \(-0.689742\pi\) |
0.997373 | + | 0.0724307i | \(0.0230756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 78.7482 | − | 82.3916i | 0.444905 | − | 0.465489i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 181.881i | − | 1.01610i | −0.861329 | − | 0.508048i | \(-0.830367\pi\) | ||
0.861329 | − | 0.508048i | \(-0.169633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 120.345 | 0.664887 | 0.332444 | − | 0.943123i | \(-0.392127\pi\) | ||||
0.332444 | + | 0.943123i | \(0.392127\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.48973 | − | 26.6123i | 0.0354630 | − | 0.145423i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 164.829 | + | 95.1641i | 0.881439 | + | 0.508899i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −305.915 | + | 104.653i | −1.61860 | + | 0.553719i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.73186 | + | 3.30929i | 0.0300098 | + | 0.0173261i | 0.514930 | − | 0.857232i | \(-0.327818\pi\) |
−0.484920 | + | 0.874558i | \(0.661151\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 147.954 | − | 85.4213i | 0.766601 | − | 0.442597i | −0.0650597 | − | 0.997881i | \(-0.520724\pi\) |
0.831661 | + | 0.555284i | \(0.187390\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −200.181 | −1.01615 | −0.508074 | − | 0.861313i | \(-0.669642\pi\) | ||||
−0.508074 | + | 0.861313i | \(0.669642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −96.3228 | −0.484034 | −0.242017 | − | 0.970272i | \(-0.577809\pi\) | ||||
−0.242017 | + | 0.970272i | \(0.577809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.9690 | − | 52.2808i | 0.248602 | − | 0.260104i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −58.4166 | − | 101.181i | −0.287767 | − | 0.498426i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −309.996 | − | 160.752i | −1.49756 | − | 0.776580i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −200.408 | − | 115.705i | −0.958889 | − | 0.553615i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 163.796 | + | 283.703i | 0.776284 | + | 1.34456i | 0.934070 | + | 0.357089i | \(0.116231\pi\) |
−0.157787 | + | 0.987473i | \(0.550436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 36.7954 | + | 125.869i | 0.172749 | + | 0.590936i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 144.093i | 0.664021i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.47070 | + | 22.1349i | 0.0295466 | + | 0.101073i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 320.661 | − | 185.134i | 1.45095 | − | 0.837709i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 46.7687 | + | 27.0019i | 0.209725 | + | 0.121085i | 0.601184 | − | 0.799111i | \(-0.294696\pi\) |
−0.391459 | + | 0.920196i | \(0.628029\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −114.956 | + | 199.109i | −0.506413 | + | 0.877133i | 0.493559 | + | 0.869712i | \(0.335696\pi\) |
−0.999972 | + | 0.00742111i | \(0.997638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.83249 | − | 15.2983i | −0.0385698 | − | 0.0668049i | 0.846096 | − | 0.533030i | \(-0.178947\pi\) |
−0.884666 | + | 0.466225i | \(0.845614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −222.938 | − | 213.079i | −0.965098 | − | 0.922422i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −399.853 | −1.71611 | −0.858054 | − | 0.513560i | \(-0.828326\pi\) | ||||
−0.858054 | + | 0.513560i | \(0.828326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.4707 | − | 112.649i | 0.115910 | − | 0.475311i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 97.0062 | − | 56.0066i | 0.405884 | − | 0.234337i | −0.283136 | − | 0.959080i | \(-0.591375\pi\) |
0.689020 | + | 0.724743i | \(0.258041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6167 | − | 32.2451i | 0.0772478 | − | 0.133797i | −0.824814 | − | 0.565405i | \(-0.808720\pi\) |
0.902062 | + | 0.431607i | \(0.142053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −36.0175 | + | 240.316i | −0.148220 | + | 0.988954i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −389.876 | + | 225.095i | −1.57845 | + | 0.911316i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 59.9700 | − | 245.918i | 0.240844 | − | 0.987623i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 426.106i | − | 1.69763i | −0.528686 | − | 0.848817i | \(-0.677315\pi\) | ||
0.528686 | − | 0.848817i | \(-0.322685\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 333.071i | − | 1.31649i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −77.8523 | − | 134.844i | −0.302927 | − | 0.524685i | 0.673870 | − | 0.738850i | \(-0.264631\pi\) |
−0.976798 | + | 0.214164i | \(0.931297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 150.011 | − | 259.827i | 0.579195 | − | 1.00319i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −87.7194 | + | 3.96871i | −0.336090 | + | 0.0152058i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 142.667 | − | 247.107i | 0.542461 | − | 0.939569i | −0.456301 | − | 0.889825i | \(-0.650826\pi\) |
0.998762 | − | 0.0497440i | \(-0.0158405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 51.7979 | + | 177.190i | 0.193999 | + | 0.663631i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 112.337i | 0.417611i | 0.977957 | + | 0.208806i | \(0.0669576\pi\) | ||||
−0.977957 | + | 0.208806i | \(0.933042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 39.2503 | 0.144835 | 0.0724175 | − | 0.997374i | \(-0.476929\pi\) | ||||
0.0724175 | + | 0.997374i | \(0.476929\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −575.845 | + | 168.337i | −2.10932 | + | 0.616618i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −409.507 | − | 236.429i | −1.47836 | − | 0.853534i | −0.478663 | − | 0.877999i | \(-0.658878\pi\) |
−0.999701 | + | 0.0244650i | \(0.992212\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 96.1391 | + | 49.8540i | 0.344584 | + | 0.178688i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 104.091 | + | 60.0971i | 0.370431 | + | 0.213869i | 0.673647 | − | 0.739053i | \(-0.264727\pi\) |
−0.303216 | + | 0.952922i | \(0.598060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 181.872 | − | 105.004i | 0.642658 | − | 0.371039i | −0.142980 | − | 0.989726i | \(-0.545668\pi\) |
0.785638 | + | 0.618687i | \(0.212335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 481.233 | 1.67677 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 202.574 | 0.700947 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −182.621 | − | 44.5343i | −0.627564 | − | 0.153039i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 70.4835 | + | 122.081i | 0.240558 | + | 0.416659i | 0.960873 | − | 0.276988i | \(-0.0893362\pi\) |
−0.720315 | + | 0.693647i | \(0.756003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −219.301 | + | 75.0223i | −0.738386 | + | 0.252600i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −561.151 | − | 323.981i | −1.87676 | − | 1.08355i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 468.825 | + | 812.028i | 1.55756 | + | 2.69777i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 121.251 | + | 29.5685i | 0.400169 | + | 0.0975858i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 83.3870i | 0.271619i | 0.990735 | + | 0.135809i | \(0.0433635\pi\) | ||||
−0.990735 | + | 0.135809i | \(0.956637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.1073 | + | 33.5928i | −0.103907 | + | 0.108714i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −354.823 | + | 204.857i | −1.14091 | + | 0.658704i | −0.946656 | − | 0.322247i | \(-0.895562\pi\) |
−0.194254 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 201.134 | + | 116.125i | 0.642602 | + | 0.371007i | 0.785616 | − | 0.618714i | \(-0.212346\pi\) |
−0.143014 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 156.512 | − | 271.087i | 0.493730 | − | 0.855165i | −0.506244 | − | 0.862390i | \(-0.668967\pi\) |
0.999974 | + | 0.00722536i | \(0.00229992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.8770 | − | 72.5331i | −0.131276 | − | 0.227377i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −563.665 | + | 164.776i | −1.75597 | + | 0.513322i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −597.681 | −1.85041 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −248.859 | + | 72.7491i | −0.761037 | + | 0.222474i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 770.975 | − | 445.123i | 2.34339 | − | 1.35296i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −39.3215 | + | 68.1068i | −0.118796 | + | 0.205761i | −0.919291 | − | 0.393579i | \(-0.871237\pi\) |
0.800495 | + | 0.599340i | \(0.204570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −121.456 | − | 189.985i | −0.364732 | − | 0.570525i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −116.656 | + | 67.3515i | −0.346161 | + | 0.199856i | −0.662993 | − | 0.748626i | \(-0.730714\pi\) |
0.316832 | + | 0.948482i | \(0.397381\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −220.868 | − | 211.101i | −0.651527 | − | 0.622716i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 103.295i | 0.302919i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 543.617i | 1.58489i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −35.3923 | − | 61.3013i | −0.101995 | − | 0.176661i | 0.810511 | − | 0.585723i | \(-0.199189\pi\) |
−0.912507 | + | 0.409062i | \(0.865856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −182.024 | + | 315.274i | −0.521557 | + | 0.903364i | 0.478128 | + | 0.878290i | \(0.341315\pi\) |
−0.999686 | + | 0.0250738i | \(0.992018\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −86.9193 | + | 442.448i | −0.247633 | + | 1.26053i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.46473 | − | 7.73314i | 0.0126480 | − | 0.0219069i | −0.859632 | − | 0.510913i | \(-0.829307\pi\) |
0.872280 | + | 0.489007i | \(0.162641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −773.822 | − | 188.706i | −2.16757 | − | 0.528587i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 320.413i | − | 0.892516i | −0.894904 | − | 0.446258i | \(-0.852756\pi\) | ||
0.894904 | − | 0.446258i | \(-0.147244\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 365.692 | 1.01300 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 102.599 | + | 98.0622i | 0.282642 | + | 0.270144i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −115.412 | − | 66.6334i | −0.314475 | − | 0.181562i | 0.334452 | − | 0.942413i | \(-0.391449\pi\) |
−0.648927 | + | 0.760850i | \(0.724782\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 166.500 | − | 321.081i | 0.451220 | − | 0.870137i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 135.139 | + | 78.0223i | 0.364255 | + | 0.210303i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −619.796 | + | 357.839i | −1.66165 | + | 0.959355i | −0.689725 | + | 0.724071i | \(0.742269\pi\) |
−0.971927 | + | 0.235284i | \(0.924398\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −162.936 | −0.432192 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −45.4400 | −0.119894 | −0.0599472 | − | 0.998202i | \(-0.519093\pi\) | ||||
−0.0599472 | + | 0.998202i | \(0.519093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −78.9222 | − | 269.976i | −0.207145 | − | 0.708599i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 349.952 | + | 606.135i | 0.913713 | + | 1.58260i | 0.808775 | + | 0.588118i | \(0.200131\pi\) |
0.104938 | + | 0.994479i | \(0.466536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 703.995 | − | 31.8510i | 1.81911 | − | 0.0823024i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 98.3531 | + | 56.7842i | 0.252836 | + | 0.145975i | 0.621062 | − | 0.783761i | \(-0.286702\pi\) |
−0.368226 | + | 0.929736i | \(0.620035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −430.123 | − | 744.995i | −1.10006 | − | 1.90536i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 285.581 | − | 298.793i | 0.726668 | − | 0.760288i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 614.028i | 1.54667i | 0.633998 | + | 0.773335i | \(0.281413\pi\) | ||||
−0.633998 | + | 0.773335i | \(0.718587\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 940.853 | + | 229.438i | 2.35803 | + | 0.575033i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 639.856 | − | 369.421i | 1.59565 | − | 0.921250i | 0.603339 | − | 0.797484i | \(-0.293836\pi\) |
0.992312 | − | 0.123765i | \(-0.0394969\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 174.030 | + | 100.476i | 0.431836 | + | 0.249321i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 107.538 | − | 186.262i | 0.264222 | − | 0.457646i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 274.589 | + | 475.602i | 0.671366 | + | 1.16284i | 0.977517 | + | 0.210857i | \(0.0676255\pi\) |
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −68.0069 | + | 278.875i | −0.165467 | + | 0.678528i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −454.933 | −1.10153 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −177.108 | − | 169.276i | −0.424720 | − | 0.405938i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −168.477 | + | 97.2700i | −0.402092 | + | 0.232148i | −0.687386 | − | 0.726292i | \(-0.741242\pi\) |
0.285294 | + | 0.958440i | \(0.407909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 301.120 | − | 521.555i | 0.715249 | − | 1.23885i | −0.247615 | − | 0.968859i | \(-0.579647\pi\) |
0.962863 | − | 0.269989i | \(-0.0870200\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.2407 | − | 668.404i | −0.0714911 | − | 1.58015i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −94.6904 | + | 54.6695i | −0.221757 | + | 0.128032i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −412.805 | + | 120.675i | −0.962249 | + | 0.281294i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 148.264i | − | 0.344001i | −0.985097 | − | 0.172000i | \(-0.944977\pi\) | ||
0.985097 | − | 0.172000i | \(-0.0550231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 405.637i | − | 0.936805i | −0.883515 | − | 0.468402i | \(-0.844830\pi\) | ||
0.883515 | − | 0.468402i | \(-0.155170\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 522.966 | + | 905.803i | 1.19672 | + | 2.07278i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 55.5992 | − | 96.3007i | 0.126650 | − | 0.219364i | −0.795727 | − | 0.605656i | \(-0.792911\pi\) |
0.922377 | + | 0.386292i | \(0.126244\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 754.196 | + | 391.097i | 1.71019 | + | 0.886841i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 155.408 | − | 269.175i | 0.350808 | − | 0.607618i | −0.635583 | − | 0.772033i | \(-0.719240\pi\) |
0.986391 | + | 0.164415i | \(0.0525735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 204.068 | − | 213.510i | 0.456528 | − | 0.477650i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 371.254i | 0.826846i | 0.910539 | + | 0.413423i | \(0.135667\pi\) | ||||
−0.910539 | + | 0.413423i | \(0.864333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 344.981 | 0.764924 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 131.623 | − | 539.746i | 0.290559 | − | 1.19149i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −226.691 | − | 130.880i | −0.496041 | − | 0.286390i | 0.231036 | − | 0.972945i | \(-0.425788\pi\) |
−0.727077 | + | 0.686556i | \(0.759122\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −393.637 | + | 451.007i | −0.857596 | + | 0.982586i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −360.223 | − | 207.975i | −0.781394 | − | 0.451138i | 0.0555299 | − | 0.998457i | \(-0.482315\pi\) |
−0.836924 | + | 0.547319i | \(0.815649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 116.882 | − | 67.4817i | 0.252444 | − | 0.145749i | −0.368439 | − | 0.929652i | \(-0.620108\pi\) |
0.620883 | + | 0.783903i | \(0.286774\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −342.345 | −0.733073 | −0.366537 | − | 0.930404i | \(-0.619457\pi\) | ||||
−0.366537 | + | 0.930404i | \(0.619457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −288.673 | −0.615508 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 383.836 | − | 401.595i | 0.814939 | − | 0.852643i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 336.086 | + | 582.118i | 0.710541 | + | 1.23069i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 98.8129 | − | 63.1703i | 0.207155 | − | 0.132433i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −302.469 | − | 174.630i | −0.631458 | − | 0.364573i | 0.149858 | − | 0.988707i | \(-0.452118\pi\) |
−0.781317 | + | 0.624135i | \(0.785452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −209.207 | − | 362.357i | −0.434941 | − | 0.753340i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 391.099 | + | 1337.87i | 0.809728 | + | 2.76991i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 744.059i | − | 1.52784i | −0.645310 | − | 0.763921i | \(-0.723272\pi\) | ||
0.645310 | − | 0.763921i | \(-0.276728\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −151.876 | − | 519.534i | −0.310584 | − | 1.06244i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −663.655 | + | 383.162i | −1.35164 | + | 0.780370i | −0.988479 | − | 0.151357i | \(-0.951636\pi\) |
−0.363161 | + | 0.931726i | \(0.618302\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −187.336 | − | 108.159i | −0.379993 | − | 0.219389i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 261.725 | − | 453.320i | 0.526609 | − | 0.912113i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −444.348 | − | 769.633i | −0.890477 | − | 1.54235i | −0.839305 | − | 0.543661i | \(-0.817038\pi\) |
−0.0511717 | − | 0.998690i | \(-0.516296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −360.728 | − | 344.777i | −0.720017 | − | 0.688178i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −188.524 | −0.374800 | −0.187400 | − | 0.982284i | \(-0.560006\pi\) | ||||
−0.187400 | + | 0.982284i | \(0.560006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −78.1091 | + | 320.301i | −0.154061 | + | 0.631757i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 67.0370 | − | 38.7038i | 0.131703 | − | 0.0760389i | −0.432701 | − | 0.901538i | \(-0.642439\pi\) |
0.564404 | + | 0.825499i | \(0.309106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.0259 | − | 79.7191i | 0.0900702 | − | 0.156006i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 478.604 | − | 548.358i | 0.932951 | − | 1.06892i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 552.688 | − | 319.094i | 1.06903 | − | 0.617204i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −107.212 | + | 439.643i | −0.206574 | + | 0.847096i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 558.234i | 1.07147i | 0.844387 | + | 0.535734i | \(0.179965\pi\) | ||||
−0.844387 | + | 0.535734i | \(0.820035\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 927.119i | − | 1.77269i | −0.463022 | − | 0.886347i | \(-0.653235\pi\) | ||
0.463022 | − | 0.886347i | \(-0.346765\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 133.394 | + | 231.045i | 0.253120 | + | 0.438416i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −488.208 | + | 845.601i | −0.922888 | + | 1.59849i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −157.400 | + | 303.533i | −0.296423 | + | 0.571624i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 335.565 | − | 581.216i | 0.629579 | − | 1.09046i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 153.100 | + | 523.724i | 0.285103 | + | 0.975278i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 810.336i | 1.50341i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −870.887 | −1.60977 | −0.804886 | − | 0.593429i | \(-0.797774\pi\) | ||||
−0.804886 | + | 0.593429i | \(0.797774\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −346.531 | + | 101.301i | −0.638178 | + | 0.186559i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −151.801 | − | 87.6421i | −0.277515 | − | 0.160223i | 0.354783 | − | 0.934949i | \(-0.384555\pi\) |
−0.632298 | + | 0.774725i | \(0.717888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.71414 | + | 82.0927i | 0.00676528 | + | 0.149531i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 227.773 | + | 131.505i | 0.413382 | + | 0.238666i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −400.820 | + | 231.413i | −0.724809 | + | 0.418469i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.6793 | −0.0461029 | −0.0230515 | − | 0.999734i | \(-0.507338\pi\) | ||||
−0.0230515 | + | 0.999734i | \(0.507338\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1307.65 | 2.33927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −554.728 | − | 135.277i | −0.988821 | − | 0.241136i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 249.991 | + | 432.998i | 0.444035 | + | 0.769090i | 0.997984 | − | 0.0634596i | \(-0.0202134\pi\) |
−0.553950 | + | 0.832550i | \(0.686880\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 792.785 | − | 558.854i | 1.39821 | − | 0.985632i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 163.726 | + | 94.5273i | 0.287744 | + | 0.166129i | 0.636924 | − | 0.770927i | \(-0.280207\pi\) |
−0.349180 | + | 0.937056i | \(0.613540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 491.393 | + | 851.117i | 0.860583 | + | 1.49057i | 0.871367 | + | 0.490631i | \(0.163234\pi\) |
−0.0107848 | + | 0.999942i | \(0.503433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.2905 | − | 4.70420i | −0.0336657 | − | 0.00820978i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 348.901i | 0.604681i | 0.953200 | + | 0.302341i | \(0.0977680\pi\) | ||||
−0.953200 | + | 0.302341i | \(0.902232\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −354.127 | + | 370.511i | −0.611619 | + | 0.639916i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −875.011 | + | 505.188i | −1.50604 | + | 0.869514i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 96.8766 | + | 55.9318i | 0.166169 | + | 0.0959378i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −282.746 | + | 489.730i | −0.481679 | + | 0.834292i | −0.999779 | − | 0.0210277i | \(-0.993306\pi\) |
0.518100 | + | 0.855320i | \(0.326640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −162.187 | − | 280.917i | −0.275361 | − | 0.476939i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 576.419 | − | 168.505i | 0.975328 | − | 0.285118i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 664.718 | 1.12094 | 0.560471 | − | 0.828174i | \(-0.310620\pi\) | ||||
0.560471 | + | 0.828174i | \(0.310620\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 277.360 | − | 81.0807i | 0.464590 | − | 0.135814i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −728.790 | + | 420.767i | −1.21668 | + | 0.702449i | −0.964206 | − | 0.265155i | \(-0.914577\pi\) |
−0.252472 | + | 0.967604i | \(0.581243\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −412.452 | + | 714.388i | −0.686276 | + | 1.18866i | 0.286758 | + | 0.958003i | \(0.407422\pi\) |
−0.973034 | + | 0.230662i | \(0.925911\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −99.8770 | + | 192.604i | −0.165633 | + | 0.319409i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 789.319 | − | 455.713i | 1.30036 | − | 0.750763i | 0.319895 | − | 0.947453i | \(-0.396352\pi\) |
0.980466 | + | 0.196690i | \(0.0630192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 253.380 | + | 242.175i | 0.416059 | + | 0.397660i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1241.54i | − | 2.03198i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 222.488i | 0.362949i | 0.983396 | + | 0.181475i | \(0.0580870\pi\) | ||||
−0.983396 | + | 0.181475i | \(0.941913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −355.212 | − | 615.245i | −0.575708 | − | 0.997156i | −0.995964 | − | 0.0897507i | \(-0.971393\pi\) |
0.420256 | − | 0.907406i | \(-0.361940\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 160.056 | − | 277.226i | 0.258573 | − | 0.447861i | −0.707287 | − | 0.706926i | \(-0.750081\pi\) |
0.965860 | + | 0.259065i | \(0.0834145\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1027.94 | + | 201.941i | 1.65530 | + | 0.325186i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 368.436 | − | 638.151i | 0.591391 | − | 1.02432i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 674.468 | + | 164.477i | 1.07571 | + | 0.262324i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 555.494i | − | 0.883138i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1051.94 | −1.66711 | −0.833553 | − | 0.552439i | \(-0.813697\pi\) | ||||
−0.833553 | + | 0.552439i | \(0.813697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −710.458 | − | 679.041i | −1.12237 | − | 1.07273i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1365.24 | + | 788.220i | 2.14323 | + | 1.23739i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −211.904 | − | 331.466i | −0.331618 | − | 0.518726i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 762.966 | + | 440.499i | 1.19027 | + | 0.687205i | 0.958369 | − | 0.285533i | \(-0.0921705\pi\) |
0.231906 | + | 0.972738i | \(0.425504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 707.819 | − | 408.659i | 1.10081 | − | 0.635551i | 0.164374 | − | 0.986398i | \(-0.447440\pi\) |
0.936433 | + | 0.350847i | \(0.114106\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −299.497 | −0.462901 | −0.231451 | − | 0.972847i | \(-0.574347\pi\) | ||||
−0.231451 | + | 0.972847i | \(0.574347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −326.127 | −0.502507 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −121.291 | − | 414.912i | −0.186316 | − | 0.637346i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −377.726 | − | 654.241i | −0.578447 | − | 1.00190i | −0.995658 | − | 0.0930902i | \(-0.970326\pi\) |
0.417210 | − | 0.908810i | \(-0.363008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.2646 | − | 58.2903i | −0.0567193 | − | 0.0887219i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 538.168 | + | 310.712i | 0.816644 | + | 0.471490i | 0.849258 | − | 0.527978i | \(-0.177050\pi\) |
−0.0326137 | + | 0.999468i | \(0.510383\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8919 | + | 43.1140i | 0.0376580 | + | 0.0652255i | 0.884240 | − | 0.467033i | \(-0.154677\pi\) |
−0.846582 | + | 0.532258i | \(0.821344\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −767.500 | + | 803.009i | −1.15762 | + | 1.21118i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 378.552i | 0.567544i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −157.399 | − | 38.3836i | −0.235275 | − | 0.0573746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −67.8805 | + | 39.1908i | −0.101163 | + | 0.0584066i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 210.090 | + | 121.295i | 0.312169 | + | 0.180231i | 0.647897 | − | 0.761728i | \(-0.275649\pi\) |
−0.335728 | + | 0.941959i | \(0.608982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 408.572 | − | 707.668i | 0.603504 | − | 1.04530i | −0.388782 | − | 0.921330i | \(-0.627104\pi\) |
0.992286 | − | 0.123970i | \(-0.0395628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 375.157 | + | 649.791i | 0.552514 | + | 0.956982i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 163.411 | − | 670.098i | 0.239958 | − | 0.983990i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −911.627 | −1.33474 | −0.667369 | − | 0.744727i | \(-0.732580\pi\) | ||||
−0.667369 | + | 0.744727i | \(0.732580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.3106 | + | 36.6165i | 0.0557650 | + | 0.0532991i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 188.465 | − | 108.810i | 0.273534 | − | 0.157925i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 197.429 | − | 341.957i | 0.285715 | − | 0.494872i | −0.687068 | − | 0.726594i | \(-0.741102\pi\) |
0.972782 | + | 0.231721i | \(0.0744357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 821.308 | + | 425.899i | 1.18515 | + | 0.614573i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 771.634 | − | 445.503i | 1.10708 | − | 0.639172i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1151.37 | − | 336.581i | 1.64717 | − | 0.481517i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1256.28i | − | 1.79213i | −0.443925 | − | 0.896064i | \(-0.646414\pi\) | ||
0.443925 | − | 0.896064i | \(-0.353586\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 675.398i | 0.960737i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −249.085 | − | 431.428i | −0.352313 | − | 0.610224i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −211.556 | + | 366.426i | −0.298387 | + | 0.516821i | −0.975767 | − | 0.218812i | \(-0.929782\pi\) |
0.677380 | + | 0.735633i | \(0.263115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.7217 | + | 347.494i | 0.0221122 | + | 0.488740i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 233.437 | − | 404.325i | 0.327402 | − | 0.567076i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −232.184 | + | 242.926i | −0.323827 | + | 0.338809i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1290.42i | 1.79474i | 0.441283 | + | 0.897368i | \(0.354523\pi\) | ||||
−0.441283 | + | 0.897368i | \(0.645477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 185.485 | 0.257261 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.4639 | + | 108.520i | −0.0366029 | + | 0.150097i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 959.948 | + | 554.226i | 1.32042 | + | 0.762347i | 0.983796 | − | 0.179291i | \(-0.0573803\pi\) |
0.336628 | + | 0.941638i | \(0.390714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −98.5766 | − | 722.304i | −0.135222 | − | 0.990815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1503.47 | + | 868.032i | 2.05674 | + | 1.18746i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −397.974 | + | 229.770i | −0.542939 | + | 0.313466i | −0.746269 | − | 0.665644i | \(-0.768157\pi\) |
0.203330 | + | 0.979110i | \(0.434823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −206.941 | −0.280788 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −620.936 | −0.840238 | −0.420119 | − | 0.907469i | \(-0.638012\pi\) | ||||
−0.420119 | + | 0.907469i | \(0.638012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 933.166 | − | 976.340i | 1.25933 | − | 1.31760i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −254.499 | − | 440.805i | −0.342529 | − | 0.593278i | 0.642373 | − | 0.766392i | \(-0.277950\pi\) |
−0.984902 | + | 0.173115i | \(0.944617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.3214 | + | 758.598i | 0.0459457 | + | 1.01553i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2030.05 | + | 1172.05i | 2.71035 | + | 1.56482i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −416.456 | − | 721.324i | −0.554536 | − | 0.960484i | −0.997939 | − | 0.0641621i | \(-0.979563\pi\) |
0.443404 | − | 0.896322i | \(-0.353771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 358.680 | + | 1226.97i | 0.476334 | + | 1.62944i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1174.63i | − | 1.55169i | −0.630924 | − | 0.775845i | \(-0.717324\pi\) | ||
0.630924 | − | 0.775845i | \(-0.282676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 280.366 | + | 959.074i | 0.369389 | + | 1.26360i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −594.035 | + | 342.966i | −0.780598 | + | 0.450678i | −0.836642 | − | 0.547750i | \(-0.815485\pi\) |
0.0560442 | + | 0.998428i | \(0.482151\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 896.270 | + | 517.462i | 1.17467 | + | 0.678194i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −317.226 | + | 549.451i | −0.413593 | + | 0.716364i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −196.412 | − | 340.196i | −0.255412 | − | 0.442387i | 0.709595 | − | 0.704610i | \(-0.248878\pi\) |
−0.965007 | + | 0.262223i | \(0.915545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 337.681 | + | 322.749i | 0.437978 | + | 0.418611i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 250.268 | 0.323761 | 0.161881 | − | 0.986810i | \(-0.448244\pi\) | ||||
0.161881 | + | 0.986810i | \(0.448244\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −213.243 | + | 874.443i | −0.274444 | + | 1.12541i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −938.192 | + | 541.666i | −1.20435 | + | 0.695335i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 187.622 | − | 324.971i | 0.240233 | − | 0.416096i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 249.246 | − | 85.2666i | 0.318322 | − | 0.108897i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −466.707 | + | 269.454i | −0.593021 | + | 0.342381i | −0.766291 | − | 0.642494i | \(-0.777900\pi\) |
0.173270 | + | 0.984874i | \(0.444567\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −202.803 | + | 831.632i | −0.257038 | + | 1.05403i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1219.54i | 1.54177i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 152.485i | 0.192289i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 120.351 | + | 208.455i | 0.151006 | + | 0.261549i | 0.931597 | − | 0.363492i | \(-0.118416\pi\) |
−0.780592 | + | 0.625041i | \(0.785082\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 824.147 | − | 1427.46i | 1.03147 | − | 1.78656i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −298.302 | − | 466.613i | −0.372413 | − | 0.582538i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.9945 | − | 57.1481i | 0.0410890 | − | 0.0711683i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −94.5613 | − | 323.474i | −0.117176 | − | 0.400835i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 608.095i | − | 0.751662i | −0.926688 | − | 0.375831i | \(-0.877357\pi\) | ||
0.926688 | − | 0.375831i | \(-0.122643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1166.65 | −1.43853 | −0.719266 | − | 0.694735i | \(-0.755522\pi\) | ||||
−0.719266 | + | 0.694735i | \(0.755522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −113.021 | + | 33.0394i | −0.139017 | + | 0.0406388i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1828.00 | − | 1055.40i | −2.23746 | − | 1.29180i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1516.44 | − | 969.447i | 1.85157 | − | 1.18370i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 351.855 | + | 203.143i | 0.428568 | + | 0.247434i | 0.698737 | − | 0.715379i | \(-0.253746\pi\) |
−0.270168 | + | 0.962813i | \(0.587079\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 585.761 | − | 338.189i | 0.711738 | − | 0.410922i | −0.0999661 | − | 0.994991i | \(-0.531873\pi\) |
0.811704 | + | 0.584069i | \(0.198540\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −351.096 | −0.424542 | −0.212271 | − | 0.977211i | \(-0.568086\pi\) | ||||
−0.212271 | + | 0.977211i | \(0.568086\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0890 | −0.0290579 | −0.0145290 | − | 0.999894i | \(-0.504625\pi\) | ||||
−0.0145290 | + | 0.999894i | \(0.504625\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1378.19 | + | 336.087i | 1.65847 | + | 0.404436i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1046.46 | + | 1812.51i | 1.25625 | + | 2.17589i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −318.796 | − | 62.6279i | −0.380880 | − | 0.0748242i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1078.79 | − | 622.840i | −1.28581 | − | 0.742361i | −0.307903 | − | 0.951418i | \(-0.599627\pi\) |
−0.977903 | + | 0.209057i | \(0.932960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −372.905 | − | 645.890i | −0.443406 | − | 0.768002i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −350.316 | − | 85.4288i | −0.415559 | − | 0.101339i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 566.511i | − | 0.668844i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −435.310 | + | 455.451i | −0.512733 | + | 0.536455i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −841.867 | + | 486.052i | −0.989268 | + | 0.571154i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −651.823 | − | 376.330i | −0.764154 | − | 0.441185i | 0.0666312 | − | 0.997778i | \(-0.478775\pi\) |
−0.830785 | + | 0.556593i | \(0.812108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −236.059 | + | 408.865i | −0.275448 | + | 0.477089i | −0.970248 | − | 0.242113i | \(-0.922159\pi\) |
0.694800 | + | 0.719203i | \(0.255493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 73.2644 | + | 126.898i | 0.0852904 | + | 0.147727i | 0.905515 | − | 0.424314i | \(-0.139485\pi\) |
−0.820225 | + | 0.572042i | \(0.806152\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1385.70 | + | 405.083i | −1.60941 | + | 0.470480i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 784.829 | 0.909419 | 0.454709 | − | 0.890640i | \(-0.349743\pi\) | ||||
0.454709 | + | 0.890640i | \(0.349743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −583.308 | + | 170.519i | −0.672789 | + | 0.196677i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −287.335 | + | 165.893i | −0.330650 | + | 0.190901i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −201.293 | + | 348.649i | −0.231105 | + | 0.400286i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 563.342 | − | 25.4874i | 0.645294 | − | 0.0291952i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1418.00 | − | 818.684i | 1.61688 | − | 0.933505i | 0.629156 | − | 0.777279i | \(-0.283401\pi\) |
0.987721 | − | 0.156226i | \(-0.0499327\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −305.719 | − | 292.200i | −0.347804 | − | 0.332424i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1368.39i | 1.55323i | 0.629977 | + | 0.776614i | \(0.283064\pi\) | ||||
−0.629977 | + | 0.776614i | \(0.716936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 623.608i | − | 0.706238i | −0.935578 | − | 0.353119i | \(-0.885121\pi\) | ||
0.935578 | − | 0.353119i | \(-0.114879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −687.672 | − | 1191.08i | −0.775278 | − | 1.34282i | −0.934638 | − | 0.355601i | \(-0.884276\pi\) |
0.159360 | − | 0.987221i | \(-0.449057\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −561.371 | + | 972.323i | −0.631463 | + | 1.09373i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 568.322 | − | 400.625i | 0.637848 | − | 0.449635i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1002.04 | + | 1735.59i | −1.12211 | + | 1.94354i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1888.54 | + | 460.543i | 2.10540 | + | 0.513426i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 117.400i | − | 0.130590i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 288.918 | 0.320663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2033.51 | − | 1943.59i | −2.25195 | − | 2.15237i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −545.676 | − | 315.046i | −0.601627 | − | 0.347349i | 0.168054 | − | 0.985778i | \(-0.446252\pi\) |
−0.769681 | + | 0.638428i | \(0.779585\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −374.031 | + | 16.9223i | −0.411475 | + | 0.0186164i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0956 | − | 13.9116i | −0.0264496 | − | 0.0152707i | 0.486717 | − | 0.873560i | \(-0.338194\pi\) |
−0.513167 | + | 0.858289i | \(0.671528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −627.268 | + | 362.153i | −0.687040 | + | 0.396663i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1649.81 | −1.79914 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1574.63 | −1.71342 | −0.856709 | − | 0.515800i | \(-0.827495\pi\) | ||||
−0.856709 | + | 0.515800i | \(0.827495\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −70.1919 | − | 240.112i | −0.0762127 | − | 0.260708i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −365.003 | − | 632.203i | −0.395453 | − | 0.684944i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 64.1754 | − | 123.757i | 0.0692291 | − | 0.133502i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −771.004 | − | 445.139i | −0.829929 | − | 0.479160i | 0.0238995 | − | 0.999714i | \(-0.492392\pi\) |
−0.853828 | + | 0.520555i | \(0.825725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1272.33 | − | 2203.75i | −1.36663 | − | 2.36708i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 849.267 | − | 888.559i | 0.910254 | − | 0.952368i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 943.059i | − | 1.00647i | −0.864151 | − | 0.503233i | \(-0.832144\pi\) | ||
0.864151 | − | 0.503233i | \(-0.167856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −676.913 | − | 165.073i | −0.720888 | − | 0.175797i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1341.95 | + | 774.773i | −1.42608 | + | 0.823350i | −0.996809 | − | 0.0798230i | \(-0.974564\pi\) |
−0.429276 | + | 0.903173i | \(0.641231\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1350.35 | − | 779.623i | −1.43197 | − | 0.826747i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −246.504 | + | 426.957i | −0.260299 | + | 0.450852i | −0.966321 | − | 0.257338i | \(-0.917155\pi\) |
0.706022 | + | 0.708190i | \(0.250488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64.1879 | − | 111.177i | −0.0676374 | − | 0.117151i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −222.484 | + | 912.338i | −0.233948 | + | 0.959346i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1588.42 | −1.66675 | −0.833377 | − | 0.552706i | \(-0.813595\pi\) | ||||
−0.833377 | + | 0.552706i | \(0.813595\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 181.640 | + | 173.608i | 0.189801 | + | 0.181408i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 992.275 | − | 572.891i | 1.03470 | − | 0.597383i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 408.104 | − | 706.857i | 0.424666 | − | 0.735543i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1484.36 | − | 948.943i | 1.54140 | − | 0.985403i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −544.974 | + | 314.641i | −0.563572 | + | 0.325378i | −0.754578 | − | 0.656210i | \(-0.772158\pi\) |
0.191006 | + | 0.981589i | \(0.438825\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1721.01 | − | 503.104i | 1.77607 | − | 0.519200i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 547.967i | 0.564332i | 0.959366 | + | 0.282166i | \(0.0910529\pi\) | ||||
−0.959366 | + | 0.282166i | \(0.908947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 977.918i | 1.00505i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 883.292 | + | 1529.91i | 0.904086 | + | 1.56592i | 0.822140 | + | 0.569285i | \(0.192780\pi\) |
0.0819454 | + | 0.996637i | \(0.473887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 264.120 | − | 457.470i | 0.269786 | − | 0.467283i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 655.349 | − | 418.960i | 0.668042 | − | 0.427074i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 765.891 | − | 1326.56i | 0.779136 | − | 1.34950i | −0.153304 | − | 0.988179i | \(-0.548991\pi\) |
0.932440 | − | 0.361324i | \(-0.117675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1845.33 | + | 1930.70i | −1.86963 | + | 1.95613i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3038.08i | − | 3.07187i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1431.39 | 1.44439 | 0.722193 | − | 0.691692i | \(-0.243134\pi\) | ||||
0.722193 | + | 0.691692i | \(0.243134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 55.8960 | − | 229.212i | 0.0562900 | − | 0.230828i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 72.5120 | + | 41.8648i | 0.0727302 | + | 0.0419908i | 0.535924 | − | 0.844266i | \(-0.319963\pi\) |
−0.463194 | + | 0.886257i | \(0.653297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 509.652 | + | 444.822i | 0.510162 | + | 0.445267i |
(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 | 900.3.u.c.749.2 | 24 | ||
3.2 | odd | 2 | 2700.3.u.c.2249.12 | 24 | |||
5.2 | odd | 4 | 180.3.o.b.101.4 | yes | 12 | ||
5.3 | odd | 4 | 900.3.p.c.101.3 | 12 | |||
5.4 | even | 2 | inner | 900.3.u.c.749.11 | 24 | ||
9.4 | even | 3 | 2700.3.u.c.449.1 | 24 | |||
9.5 | odd | 6 | inner | 900.3.u.c.149.11 | 24 | ||
15.2 | even | 4 | 540.3.o.b.521.1 | 12 | |||
15.8 | even | 4 | 2700.3.p.c.1601.6 | 12 | |||
15.14 | odd | 2 | 2700.3.u.c.2249.1 | 24 | |||
20.7 | even | 4 | 720.3.bs.b.641.3 | 12 | |||
45.2 | even | 12 | 1620.3.g.b.161.6 | 12 | |||
45.4 | even | 6 | 2700.3.u.c.449.12 | 24 | |||
45.7 | odd | 12 | 1620.3.g.b.161.12 | 12 | |||
45.13 | odd | 12 | 2700.3.p.c.2501.6 | 12 | |||
45.14 | odd | 6 | inner | 900.3.u.c.149.2 | 24 | ||
45.22 | odd | 12 | 540.3.o.b.341.1 | 12 | |||
45.23 | even | 12 | 900.3.p.c.401.3 | 12 | |||
45.32 | even | 12 | 180.3.o.b.41.4 | ✓ | 12 | ||
60.47 | odd | 4 | 2160.3.bs.b.1601.3 | 12 | |||
180.67 | even | 12 | 2160.3.bs.b.881.3 | 12 | |||
180.167 | odd | 12 | 720.3.bs.b.401.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.b.41.4 | ✓ | 12 | 45.32 | even | 12 | ||
180.3.o.b.101.4 | yes | 12 | 5.2 | odd | 4 | ||
540.3.o.b.341.1 | 12 | 45.22 | odd | 12 | |||
540.3.o.b.521.1 | 12 | 15.2 | even | 4 | |||
720.3.bs.b.401.3 | 12 | 180.167 | odd | 12 | |||
720.3.bs.b.641.3 | 12 | 20.7 | even | 4 | |||
900.3.p.c.101.3 | 12 | 5.3 | odd | 4 | |||
900.3.p.c.401.3 | 12 | 45.23 | even | 12 | |||
900.3.u.c.149.2 | 24 | 45.14 | odd | 6 | inner | ||
900.3.u.c.149.11 | 24 | 9.5 | odd | 6 | inner | ||
900.3.u.c.749.2 | 24 | 1.1 | even | 1 | trivial | ||
900.3.u.c.749.11 | 24 | 5.4 | even | 2 | inner | ||
1620.3.g.b.161.6 | 12 | 45.2 | even | 12 | |||
1620.3.g.b.161.12 | 12 | 45.7 | odd | 12 | |||
2160.3.bs.b.881.3 | 12 | 180.67 | even | 12 | |||
2160.3.bs.b.1601.3 | 12 | 60.47 | odd | 4 | |||
2700.3.p.c.1601.6 | 12 | 15.8 | even | 4 | |||
2700.3.p.c.2501.6 | 12 | 45.13 | odd | 12 | |||
2700.3.u.c.449.1 | 24 | 9.4 | even | 3 | |||
2700.3.u.c.449.12 | 24 | 45.4 | even | 6 | |||
2700.3.u.c.2249.1 | 24 | 15.14 | odd | 2 | |||
2700.3.u.c.2249.12 | 24 | 3.2 | odd | 2 |