Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,3,Mod(137,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.137");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bh (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.86650266188\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.6 | ||
Character | \(\chi\) | \(=\) | 252.149 |
Dual form | 252.3.bh.a.137.6 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.40238 | + | 2.65204i | −0.467459 | + | 0.884015i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.97157 | − | 4.02504i | 1.39431 | − | 0.805008i | 0.400525 | − | 0.916286i | \(-0.368828\pi\) |
0.993789 | + | 0.111278i | \(0.0354945\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23048 | − | 6.89100i | 0.175783 | − | 0.984429i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.06667 | − | 7.43834i | −0.562964 | − | 0.826482i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.6393 | − | 9.60669i | −1.51266 | − | 0.873335i | −0.999890 | − | 0.0148098i | \(-0.995286\pi\) |
−0.512771 | − | 0.858526i | \(-0.671381\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.782606 | − | 1.35551i | 0.0602005 | − | 0.104270i | −0.834354 | − | 0.551228i | \(-0.814159\pi\) |
0.894555 | + | 0.446958i | \(0.147493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.897800 | + | 24.1335i | 0.0598533 | + | 1.60890i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.39721 | − | 4.84813i | 0.493953 | − | 0.285184i | −0.232260 | − | 0.972654i | \(-0.574612\pi\) |
0.726213 | + | 0.687470i | \(0.241279\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.84871 | − | 10.1303i | 0.307827 | − | 0.533172i | −0.670060 | − | 0.742307i | \(-0.733732\pi\) |
0.977887 | + | 0.209135i | \(0.0670649\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.5496 | + | 12.9271i | 0.788078 | + | 0.615575i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.79731 | + | 1.03768i | −0.0781439 | + | 0.0451164i | −0.538563 | − | 0.842585i | \(-0.681033\pi\) |
0.460419 | + | 0.887702i | \(0.347699\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.9019 | − | 34.4710i | 0.796075 | − | 1.37884i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.8322 | − | 3.00568i | 0.993784 | − | 0.111321i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.2492 | − | 23.2379i | 1.38790 | − | 0.801306i | 0.394823 | − | 0.918757i | \(-0.370806\pi\) |
0.993079 | + | 0.117451i | \(0.0374725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.3494 | −0.720949 | −0.360474 | − | 0.932769i | \(-0.617385\pi\) | ||||
−0.360474 | + | 0.932769i | \(0.617385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.8119 | − | 30.6559i | 1.47915 | − | 0.928966i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.1582 | − | 52.9938i | −0.547376 | − | 1.51411i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.6213 | + | 53.0376i | −0.827603 | + | 1.43345i | 0.0723114 | + | 0.997382i | \(0.476962\pi\) |
−0.899914 | + | 0.436068i | \(0.856371\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.49737 | + | 3.97645i | 0.0640352 | + | 0.101960i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.9545 | + | 28.2639i | 1.19401 | + | 0.689363i | 0.959214 | − | 0.282682i | \(-0.0912240\pi\) |
0.234797 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21.6300 | + | 37.4643i | 0.503023 | + | 0.871262i | 0.999994 | + | 0.00349442i | \(0.00111231\pi\) |
−0.496971 | + | 0.867767i | \(0.665554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −65.2622 | − | 31.4633i | −1.45027 | − | 0.699185i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.35293i | 0.135169i | 0.997714 | + | 0.0675844i | \(0.0215292\pi\) | ||||
−0.997714 | + | 0.0675844i | \(0.978471\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −45.9718 | − | 16.9585i | −0.938201 | − | 0.346091i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.08139 | + | 29.0687i | 0.0212038 | + | 0.569974i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.3510 | − | 31.9569i | 1.04436 | − | 0.602960i | 0.123293 | − | 0.992370i | \(-0.460654\pi\) |
0.921065 | + | 0.389410i | \(0.127321\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −154.669 | −2.81217 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.6638 | + | 29.7175i | 0.327435 | + | 0.521359i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 32.0773i | 0.543683i | 0.962342 | + | 0.271842i | \(0.0876327\pi\) | ||||
−0.962342 | + | 0.271842i | \(0.912367\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −74.5416 | −1.22199 | −0.610997 | − | 0.791633i | \(-0.709231\pi\) | ||||
−0.610997 | + | 0.791633i | \(0.709231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −57.4920 | + | 25.7617i | −0.912572 | + | 0.408916i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 12.6001i | − | 0.193847i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.76192 | 0.0710734 | 0.0355367 | − | 0.999368i | \(-0.488686\pi\) | ||||
0.0355367 | + | 0.999368i | \(0.488686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.231458 | − | 6.22176i | −0.00335446 | − | 0.0901704i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 33.1772i | − | 0.467284i | −0.972323 | − | 0.233642i | \(-0.924936\pi\) | ||
0.972323 | − | 0.233642i | \(-0.0750644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.60726 | + | 11.4441i | 0.0905104 | + | 0.156769i | 0.907726 | − | 0.419563i | \(-0.137817\pi\) |
−0.817216 | + | 0.576332i | \(0.804483\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 63.5088 | + | 101.122i | 0.846784 | + | 1.34829i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −86.6740 | + | 102.840i | −1.12564 | + | 1.33559i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46.2460 | 0.585393 | 0.292696 | − | 0.956205i | \(-0.405448\pi\) | ||||
0.292696 | + | 0.956205i | \(0.405448\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29.6577 | + | 75.3752i | −0.366144 | + | 0.930558i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 81.0445 | − | 46.7910i | 0.976439 | − | 0.563748i | 0.0752462 | − | 0.997165i | \(-0.476026\pi\) |
0.901193 | + | 0.433417i | \(0.142692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 39.0278 | − | 67.5982i | 0.459151 | − | 0.795273i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.18329 | + | 139.331i | 0.0595781 | + | 1.60150i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −55.9009 | − | 32.2744i | −0.628099 | − | 0.362633i | 0.151916 | − | 0.988393i | \(-0.451456\pi\) |
−0.780016 | + | 0.625760i | \(0.784789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.37786 | − | 7.06087i | −0.0920644 | − | 0.0775920i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 31.3423 | − | 59.2716i | 0.337014 | − | 0.637329i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 94.1651i | − | 0.991212i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −96.6875 | − | 167.468i | −0.996779 | − | 1.72647i | −0.567846 | − | 0.823135i | \(-0.692223\pi\) |
−0.428933 | − | 0.903337i | \(-0.641110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.8480 | + | 172.442i | 0.129777 | + | 1.74184i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −58.3858 | − | 33.7091i | −0.578077 | − | 0.333753i | 0.182292 | − | 0.983245i | \(-0.441649\pi\) |
−0.760369 | + | 0.649491i | \(0.774982\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 40.1420 | + | 69.5280i | 0.389728 | + | 0.675029i | 0.992413 | − | 0.122951i | \(-0.0392357\pi\) |
−0.602685 | + | 0.797979i | \(0.705902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 167.409 | + | 23.5091i | 1.59437 | + | 0.223896i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 108.086 | + | 62.4035i | 1.01015 | + | 0.583210i | 0.911236 | − | 0.411886i | \(-0.135130\pi\) |
0.0989143 | + | 0.995096i | \(0.468463\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.8079 | + | 139.963i | 0.741357 | + | 1.28407i | 0.951878 | + | 0.306478i | \(0.0991506\pi\) |
−0.210521 | + | 0.977589i | \(0.567516\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −97.7155 | − | 155.588i | −0.880320 | − | 1.40169i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28.7804 | + | 16.6164i | 0.254694 | + | 0.147048i | 0.621912 | − | 0.783087i | \(-0.286356\pi\) |
−0.367218 | + | 0.930135i | \(0.619690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.35338 | + | 14.4685i | −0.0726381 | + | 0.125813i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.0480 | + | 1.04666i | −0.120068 | + | 0.00894577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.0759 | − | 63.8307i | −0.193915 | − | 0.536393i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 124.077 | + | 214.908i | 1.02543 | + | 1.77610i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −143.610 | + | 90.1927i | −1.16756 | + | 0.733274i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 119.171i | − | 0.953370i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −194.763 | −1.53357 | −0.766785 | − | 0.641904i | \(-0.778145\pi\) | ||||
−0.766785 | + | 0.641904i | \(0.778145\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −129.690 | + | 4.82465i | −1.00535 | + | 0.0374004i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −101.363 | + | 58.5218i | −0.773761 | + | 0.446731i | −0.834215 | − | 0.551440i | \(-0.814079\pi\) |
0.0604533 | + | 0.998171i | \(0.480745\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −62.6109 | − | 52.7686i | −0.470759 | − | 0.396756i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 174.964 | − | 128.955i | 1.29603 | − | 0.955221i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −69.1202 | − | 39.9066i | −0.504527 | − | 0.291289i | 0.226054 | − | 0.974115i | \(-0.427417\pi\) |
−0.730581 | + | 0.682826i | \(0.760751\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −37.9101 | + | 65.6622i | −0.272734 | + | 0.472390i | −0.969561 | − | 0.244850i | \(-0.921261\pi\) |
0.696827 | + | 0.717240i | \(0.254595\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.8483 | − | 8.90922i | −0.119491 | − | 0.0631859i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −26.0440 | + | 15.0365i | −0.182126 | + | 0.105150i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 187.067 | − | 324.009i | 1.29011 | − | 2.23454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 109.445 | − | 98.1371i | 0.744521 | − | 0.667599i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 94.3571 | − | 54.4771i | 0.633269 | − | 0.365618i | −0.148748 | − | 0.988875i | \(-0.547524\pi\) |
0.782017 | + | 0.623257i | \(0.214191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −81.7169 | + | 141.538i | −0.541172 | + | 0.937337i | 0.457665 | + | 0.889125i | \(0.348686\pi\) |
−0.998837 | + | 0.0482125i | \(0.984648\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −78.6079 | − | 37.8974i | −0.513777 | − | 0.247695i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −155.811 | + | 89.9573i | −1.00523 | + | 0.580369i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.5130 | −0.200720 | −0.100360 | − | 0.994951i | \(-0.531999\pi\) | ||||
−0.100360 | + | 0.994951i | \(0.531999\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.12811 | + | 191.609i | 0.0448309 | + | 1.20509i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.93908 | + | 13.6621i | 0.0306775 | + | 0.0848578i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 149.467 | − | 258.884i | 0.916974 | − | 1.58824i | 0.112988 | − | 0.993596i | \(-0.463958\pi\) |
0.803986 | − | 0.594648i | \(-0.202709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 216.905 | − | 410.189i | 1.31457 | − | 2.48600i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 226.397 | + | 130.710i | 1.35567 | + | 0.782695i | 0.989037 | − | 0.147671i | \(-0.0471776\pi\) |
0.366632 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 83.2751 | + | 144.237i | 0.492752 | + | 0.853471i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −104.986 | + | 7.82205i | −0.613952 | + | 0.0457430i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 192.482i | − | 1.11261i | −0.830977 | − | 0.556307i | \(-0.812218\pi\) | ||
0.830977 | − | 0.556307i | \(-0.187782\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −213.051 | − | 179.560i | −1.21744 | − | 1.02606i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −85.0705 | − | 44.9845i | −0.480624 | − | 0.254150i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 303.708 | − | 175.346i | 1.69669 | − | 0.979585i | 0.747831 | − | 0.663889i | \(-0.231095\pi\) |
0.948860 | − | 0.315696i | \(-0.102238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 227.913 | 1.25919 | 0.629594 | − | 0.776925i | \(-0.283221\pi\) | ||||
0.629594 | + | 0.776925i | \(0.283221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 104.535 | − | 197.688i | 0.571232 | − | 1.08026i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 493.008i | 2.66491i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −186.298 | −0.996246 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.3043 | − | 188.599i | 0.0651023 | − | 0.997879i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 187.619i | 0.982298i | 0.871076 | + | 0.491149i | \(0.163423\pi\) | ||||
−0.871076 | + | 0.491149i | \(0.836577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35.8113 | −0.185551 | −0.0927753 | − | 0.995687i | \(-0.529574\pi\) | ||||
−0.0927753 | + | 0.995687i | \(0.529574\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 33.4160 | + | 17.6701i | 0.171364 | + | 0.0906157i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 110.071i | 0.558736i | 0.960184 | + | 0.279368i | \(0.0901250\pi\) | ||||
−0.960184 | + | 0.279368i | \(0.909875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 34.5156 | + | 59.7829i | 0.173445 | + | 0.300416i | 0.939622 | − | 0.342214i | \(-0.111177\pi\) |
−0.766177 | + | 0.642630i | \(0.777843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.67801 | + | 12.6288i | −0.0332239 | + | 0.0628300i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −110.606 | − | 305.951i | −0.544859 | − | 1.50715i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 455.053 | 2.21977 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.8250 | + | 8.11142i | 0.0812800 | + | 0.0391856i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −194.637 | + | 112.373i | −0.931275 | + | 0.537672i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 122.482 | − | 212.145i | 0.580484 | − | 1.00543i | −0.414938 | − | 0.909849i | \(-0.636197\pi\) |
0.995422 | − | 0.0955775i | \(-0.0304698\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 87.9874 | + | 46.5270i | 0.413086 | + | 0.218436i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 301.590 | + | 174.123i | 1.40274 | + | 0.809875i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.5005 | + | 154.010i | −0.126730 | + | 0.709723i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −39.6162 | + | 1.47377i | −0.180896 | + | 0.00672956i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.1767i | − | 0.0686729i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −50.2344 | − | 87.0085i | −0.225266 | − | 0.390173i | 0.731133 | − | 0.682235i | \(-0.238992\pi\) |
−0.956399 | + | 0.292062i | \(0.905659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −357.243 | + | 26.6167i | −1.58775 | + | 0.118297i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −144.520 | − | 83.4386i | −0.636651 | − | 0.367571i | 0.146672 | − | 0.989185i | \(-0.453144\pi\) |
−0.783323 | + | 0.621614i | \(0.786477\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 138.765 | + | 240.347i | 0.605959 | + | 1.04955i | 0.991899 | + | 0.127027i | \(0.0405436\pi\) |
−0.385941 | + | 0.922524i | \(0.626123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −151.188 | − | 374.084i | −0.654492 | − | 1.61941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −41.2378 | − | 23.8087i | −0.176986 | − | 0.102183i | 0.408890 | − | 0.912584i | \(-0.365916\pi\) |
−0.585876 | + | 0.810401i | \(0.699249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.5708 | + | 44.2899i | 0.108812 | + | 0.188468i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −64.8544 | + | 122.646i | −0.273647 | + | 0.517496i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 199.849 | + | 115.383i | 0.836187 | + | 0.482773i | 0.855966 | − | 0.517032i | \(-0.172963\pi\) |
−0.0197796 | + | 0.999804i | \(0.506296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −148.738 | + | 257.623i | −0.617172 | + | 1.06897i | 0.372827 | + | 0.927901i | \(0.378388\pi\) |
−0.989999 | + | 0.141073i | \(0.954945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −158.307 | − | 184.358i | −0.651470 | − | 0.758675i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −388.754 | + | 66.8111i | −1.58675 | + | 0.272699i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.15447 | − | 15.8560i | −0.0370626 | − | 0.0641943i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.4369 | + | 280.552i | 0.0419154 | + | 1.12672i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 85.2548i | − | 0.339661i | −0.985473 | − | 0.169830i | \(-0.945678\pi\) | ||
0.985473 | − | 0.169830i | \(-0.0543220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39.8746 | 0.157607 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 124.542 | + | 198.302i | 0.488398 | + | 0.777654i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 62.1430 | − | 35.8783i | 0.241802 | − | 0.139604i | −0.374203 | − | 0.927347i | \(-0.622084\pi\) |
0.616004 | + | 0.787743i | \(0.288750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 327.804 | + | 276.273i | 1.26565 | + | 1.06669i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −376.780 | − | 181.648i | −1.44360 | − | 0.695970i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −295.596 | − | 170.662i | −1.12394 | − | 0.648906i | −0.181534 | − | 0.983385i | \(-0.558106\pi\) |
−0.942403 | + | 0.334479i | \(0.891440\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 257.255 | − | 445.580i | 0.970775 | − | 1.68143i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 163.987 | − | 102.991i | 0.614184 | − | 0.385733i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −182.681 | + | 105.471i | −0.679111 | + | 0.392085i | −0.799520 | − | 0.600639i | \(-0.794913\pi\) |
0.120409 | + | 0.992724i | \(0.461579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −129.425 | + | 224.171i | −0.477584 | + | 0.827199i | −0.999670 | − | 0.0256934i | \(-0.991821\pi\) |
0.522086 | + | 0.852893i | \(0.325154\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.4747 | − | 12.3165i | 0.111629 | − | 0.0451152i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −662.305 | + | 382.382i | −2.40838 | + | 1.39048i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 204.629 | − | 354.427i | 0.738731 | − | 1.27952i | −0.214336 | − | 0.976760i | \(-0.568759\pi\) |
0.953067 | − | 0.302760i | \(-0.0979080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 113.237 | + | 166.242i | 0.405868 | + | 0.595851i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −277.104 | + | 159.986i | −0.986134 | + | 0.569344i | −0.904116 | − | 0.427286i | \(-0.859470\pi\) |
−0.0820173 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 123.768 | 0.437341 | 0.218671 | − | 0.975799i | \(-0.429828\pi\) | ||||
0.218671 | + | 0.975799i | \(0.429828\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 249.730 | + | 132.055i | 0.876246 | + | 0.463351i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 255.004 | − | 302.567i | 0.888515 | − | 1.05424i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −97.4913 | + | 168.860i | −0.337340 | + | 0.584290i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 579.724 | − | 21.5665i | 1.99218 | − | 0.0741118i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0474 | + | 9.26498i | 0.0547693 | + | 0.0316211i | 0.527135 | − | 0.849782i | \(-0.323266\pi\) |
−0.472365 | + | 0.881403i | \(0.656600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129.112 | + | 223.629i | 0.437669 | + | 0.758066i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −475.343 | − | 207.756i | −1.60048 | − | 0.699515i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.24837i | 0.0108641i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 284.782 | − | 102.953i | 0.946118 | − | 0.342038i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 171.277 | − | 107.569i | 0.565270 | − | 0.355013i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −519.672 | + | 300.033i | −1.70384 | + | 0.983714i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 363.739 | 1.18482 | 0.592408 | − | 0.805638i | \(-0.298177\pi\) | ||||
0.592408 | + | 0.805638i | \(0.298177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −240.685 | + | 8.95382i | −0.778917 | + | 0.0289768i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 150.188i | − | 0.482921i | −0.970411 | − | 0.241460i | \(-0.922374\pi\) | ||
0.970411 | − | 0.241460i | \(-0.0776264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −234.215 | −0.748290 | −0.374145 | − | 0.927370i | \(-0.622064\pi\) | ||||
−0.374145 | + | 0.927370i | \(0.622064\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −297.118 | + | 411.007i | −0.943231 | + | 1.30479i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 392.685i | 1.23875i | 0.785094 | + | 0.619377i | \(0.212615\pi\) | ||||
−0.785094 | + | 0.619377i | \(0.787385\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −892.956 | −2.79923 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −317.074 | + | 199.136i | −0.987770 | + | 0.620360i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 113.421i | − | 0.351149i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.1506 | − | 53.9545i | −0.0958481 | − | 0.166014i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −484.512 | + | 18.0245i | −1.48169 | + | 0.0551208i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 43.7781 | + | 7.81716i | 0.133064 | + | 0.0237604i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 152.027 | 0.459295 | 0.229648 | − | 0.973274i | \(-0.426243\pi\) | ||||
0.229648 | + | 0.973274i | \(0.426243\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 549.660 | − | 40.9529i | 1.65063 | − | 0.122982i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.1981 | − | 19.1669i | 0.0990987 | − | 0.0572147i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −142.286 | + | 246.447i | −0.422214 | + | 0.731295i | −0.996156 | − | 0.0876006i | \(-0.972080\pi\) |
0.573942 | + | 0.818896i | \(0.305413\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −84.4284 | + | 53.0245i | −0.249051 | + | 0.156414i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 371.878 | + | 214.704i | 1.09055 | + | 0.629630i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −173.428 | + | 295.925i | −0.505622 | + | 0.862755i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.6564 | − | 42.4438i | −0.0772651 | − | 0.123026i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 133.781i | 0.385537i | 0.981244 | + | 0.192768i | \(0.0617466\pi\) | ||||
−0.981244 | + | 0.192768i | \(0.938253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −231.018 | − | 400.135i | −0.661943 | − | 1.14652i | −0.980105 | − | 0.198482i | \(-0.936399\pi\) |
0.318162 | − | 0.948036i | \(-0.396934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.9248 | − | 38.7236i | 0.0482188 | − | 0.110324i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 557.892 | + | 322.099i | 1.58043 | + | 0.912462i | 0.994796 | + | 0.101888i | \(0.0324883\pi\) |
0.585636 | + | 0.810575i | \(0.300845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −133.539 | − | 231.297i | −0.376168 | − | 0.651541i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 201.643 | + | 28.3165i | 0.564826 | + | 0.0793180i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 157.335 | + | 90.8373i | 0.438259 | + | 0.253029i | 0.702859 | − | 0.711329i | \(-0.251907\pi\) |
−0.264600 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 112.085 | + | 194.137i | 0.310485 | + | 0.537776i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −743.947 | + | 27.6758i | −2.04944 | + | 0.0762420i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 92.1260 | + | 53.1889i | 0.252400 | + | 0.145723i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 281.621 | − | 487.782i | 0.767360 | − | 1.32911i | −0.171630 | − | 0.985161i | \(-0.554903\pi\) |
0.938990 | − | 0.343945i | \(-0.111763\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.8000 | − | 507.343i | −0.102439 | − | 1.37491i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −152.107 | − | 420.746i | −0.409991 | − | 1.13409i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0770 | + | 38.2385i | 0.0591877 | + | 0.102516i | 0.894101 | − | 0.447865i | \(-0.147816\pi\) |
−0.834913 | + | 0.550381i | \(0.814482\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 316.047 | + | 167.123i | 0.842793 | + | 0.445662i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 72.7444i | − | 0.192956i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 106.066 | 0.279857 | 0.139928 | − | 0.990162i | \(-0.455313\pi\) | ||||
0.139928 | + | 0.990162i | \(0.455313\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 273.132 | − | 516.521i | 0.716881 | − | 1.35570i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 271.781 | − | 156.913i | 0.709612 | − | 0.409695i | −0.101305 | − | 0.994855i | \(-0.532302\pi\) |
0.810917 | + | 0.585161i | \(0.198969\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −190.317 | + | 1065.83i | −0.494331 | + | 2.76838i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 169.080 | − | 350.710i | 0.436898 | − | 0.906228i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 53.2693 | + | 30.7550i | 0.136939 | + | 0.0790618i | 0.566904 | − | 0.823784i | \(-0.308141\pi\) |
−0.429965 | + | 0.902845i | \(0.641474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0616 | + | 17.4272i | −0.0257330 | + | 0.0445708i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.0535 | − | 350.888i | −0.0332150 | − | 0.892845i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 322.407 | − | 186.142i | 0.816221 | − | 0.471245i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −65.6615 | + | 113.729i | −0.165394 | + | 0.286471i | −0.936795 | − | 0.349878i | \(-0.886223\pi\) |
0.771401 | + | 0.636349i | \(0.219556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 227.749 | − | 92.0455i | 0.570799 | − | 0.230690i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −181.577 | + | 104.834i | −0.452811 | + | 0.261431i | −0.709017 | − | 0.705192i | \(-0.750861\pi\) |
0.256206 | + | 0.966622i | \(0.417528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.4908 | + | 30.2949i | −0.0434015 | + | 0.0751735i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 96.6276 | + | 644.857i | 0.238587 | + | 1.59224i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1019.03 | − | 588.338i | 2.50376 | − | 1.44555i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 272.976 | 0.667423 | 0.333711 | − | 0.942675i | \(-0.391699\pi\) | ||||
0.333711 | + | 0.942675i | \(0.391699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 202.767 | − | 127.346i | 0.493350 | − | 0.309844i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 221.045 | + | 39.4705i | 0.535218 | + | 0.0955702i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 376.672 | − | 652.414i | 0.907642 | − | 1.57208i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −120.975 | − | 192.622i | −0.290107 | − | 0.461924i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 93.8050 | + | 54.1584i | 0.223878 | + | 0.129256i | 0.607745 | − | 0.794132i | \(-0.292074\pi\) |
−0.383866 | + | 0.923389i | \(0.625408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −268.137 | − | 464.427i | −0.636905 | − | 1.10315i | −0.986108 | − | 0.166104i | \(-0.946881\pi\) |
0.349203 | − | 0.937047i | \(-0.386452\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 47.2553 | − | 32.1882i | 0.111715 | − | 0.0760951i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 385.947i | − | 0.908112i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −91.7220 | + | 513.666i | −0.214806 | + | 1.20297i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.35395 | − | 90.1566i | −0.00781806 | − | 0.210155i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −235.401 | + | 135.909i | −0.546173 | + | 0.315333i | −0.747577 | − | 0.664175i | \(-0.768783\pi\) |
0.201404 | + | 0.979508i | \(0.435450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −428.323 | −0.989199 | −0.494600 | − | 0.869121i | \(-0.664685\pi\) | ||||
−0.494600 | + | 0.869121i | \(0.664685\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 596.947 | + | 950.492i | 1.37229 | + | 2.18504i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.2763i | 0.0555521i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −306.579 | −0.698358 | −0.349179 | − | 0.937056i | \(-0.613539\pi\) | ||||
−0.349179 | + | 0.937056i | \(0.613539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 106.781 | + | 427.877i | 0.242135 | + | 0.970243i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 290.777i | 0.656381i | 0.944612 | + | 0.328191i | \(0.106439\pi\) | ||||
−0.944612 | + | 0.328191i | \(0.893561\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −519.622 | −1.16769 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.1513 | + | 326.637i | 0.0271842 | + | 0.730731i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 278.892i | 0.621140i | 0.950550 | + | 0.310570i | \(0.100520\pi\) | ||||
−0.950550 | + | 0.310570i | \(0.899480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −543.044 | − | 940.580i | −1.20409 | − | 2.08554i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −260.767 | − | 415.207i | −0.575644 | − | 0.916571i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −86.8272 | − | 15.5041i | −0.190829 | − | 0.0340750i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 443.216 | 0.969838 | 0.484919 | − | 0.874559i | \(-0.338849\pi\) | ||||
0.484919 | + | 0.874559i | \(0.338849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 210.743 | − | 155.325i | 0.459136 | − | 0.338399i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 134.497 | − | 77.6519i | 0.291751 | − | 0.168442i | −0.346980 | − | 0.937872i | \(-0.612793\pi\) |
0.638731 | + | 0.769430i | \(0.279460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 201.958 | − | 349.802i | 0.436195 | − | 0.755511i | −0.561198 | − | 0.827682i | \(-0.689659\pi\) |
0.997392 | + | 0.0721704i | \(0.0229925\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.0653 | − | 539.370i | −0.0431512 | − | 1.15994i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −358.548 | − | 207.008i | −0.767769 | − | 0.443272i | 0.0643092 | − | 0.997930i | \(-0.479516\pi\) |
−0.832078 | + | 0.554658i | \(0.812849\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.85945 | − | 32.8144i | 0.0124935 | − | 0.0699668i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.1931 | − | 83.5738i | 0.0938282 | − | 0.177439i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 831.171i | − | 1.75723i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −232.800 | − | 403.222i | −0.490106 | − | 0.848889i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −518.151 | − | 249.804i | −1.08627 | − | 0.523698i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −721.242 | − | 416.409i | −1.50572 | − | 0.869330i | −0.999978 | − | 0.00664795i | \(-0.997884\pi\) |
−0.505746 | − | 0.862682i | \(-0.668783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.9288 | + | 83.0151i | 0.0996441 | + | 0.172589i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −43.1590 | − | 6.06077i | −0.0893560 | − | 0.0125482i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1348.13 | − | 778.342i | −2.77965 | − | 1.60483i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 90.7601 | + | 157.201i | 0.186366 | + | 0.322795i | 0.944036 | − | 0.329843i | \(-0.106996\pi\) |
−0.757670 | + | 0.652638i | \(0.773662\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 476.963 | + | 759.445i | 0.975384 | + | 1.55306i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −213.443 | − | 123.232i | −0.434712 | − | 0.250981i | 0.266640 | − | 0.963796i | \(-0.414086\pi\) |
−0.701352 | + | 0.712815i | \(0.747420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 225.320 | − | 390.266i | 0.457039 | − | 0.791615i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 783.658 | + | 1150.48i | 1.58315 | + | 2.32420i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −228.624 | − | 40.8239i | −0.460008 | − | 0.0821406i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 463.819 | + | 803.358i | 0.929497 | + | 1.60994i | 0.784164 | + | 0.620554i | \(0.213092\pi\) |
0.145333 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −664.143 | + | 417.109i | −1.32563 | + | 0.832552i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 569.020i | − | 1.13125i | −0.824662 | − | 0.565626i | \(-0.808634\pi\) | ||
0.824662 | − | 0.565626i | \(-0.191366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −542.721 | −1.07470 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −499.305 | + | 18.5748i | −0.984822 | + | 0.0366367i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 547.002 | − | 315.812i | 1.07466 | − | 0.620456i | 0.145210 | − | 0.989401i | \(-0.453614\pi\) |
0.929451 | + | 0.368945i | \(0.120281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 86.9915 | − | 31.4489i | 0.170238 | − | 0.0615438i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 126.485 | − | 289.396i | 0.246560 | − | 0.564125i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 559.705 | + | 323.146i | 1.08681 | + | 0.627468i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 61.0307 | − | 105.708i | 0.118048 | − | 0.204465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 510.472 | + | 269.933i | 0.983568 | + | 0.520102i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 278.992 | − | 161.076i | 0.535494 | − | 0.309168i | −0.207757 | − | 0.978181i | \(-0.566616\pi\) |
0.743251 | + | 0.669013i | \(0.233283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −204.092 | + | 353.498i | −0.390233 | + | 0.675904i | −0.992480 | − | 0.122406i | \(-0.960939\pi\) |
0.602247 | + | 0.798310i | \(0.294272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 774.979 | − | 313.211i | 1.47615 | − | 0.596591i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −187.673 | + | 108.353i | −0.356115 | + | 0.205603i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −262.346 | + | 454.397i | −0.495929 | + | 0.858974i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 238.602 | − | 162.525i | 0.449344 | − | 0.306074i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 76.6241 | − | 44.2389i | 0.143760 | − | 0.0829999i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1004.71 | 1.87795 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.1115 | + | 1051.35i | 0.0728334 | + | 1.95782i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 602.023 | + | 723.814i | 1.11693 | + | 1.34288i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −182.747 | + | 316.528i | −0.337795 | + | 0.585079i | −0.984018 | − | 0.178070i | \(-0.943015\pi\) |
0.646222 | + | 0.763149i | \(0.276348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −319.620 | + | 604.435i | −0.588619 | + | 1.11314i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1126.72 | + | 650.510i | 2.06737 | + | 1.19360i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −294.880 | − | 510.747i | −0.539086 | − | 0.933724i | −0.998954 | − | 0.0457367i | \(-0.985436\pi\) |
0.459868 | − | 0.887987i | \(-0.347897\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 377.678 | + | 554.465i | 0.687938 | + | 1.00996i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 543.646i | − | 0.986653i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.9048 | − | 318.681i | 0.102902 | − | 0.576277i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1307.48 | − | 691.383i | −2.35582 | − | 1.24574i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 426.103 | − | 246.011i | 0.764996 | − | 0.441671i | −0.0660907 | − | 0.997814i | \(-0.521053\pi\) |
0.831087 | + | 0.556143i | \(0.187719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 67.7111 | 0.121129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 261.260 | − | 494.070i | 0.465704 | − | 0.880696i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 21.1519i | − | 0.0375699i | −0.999824 | − | 0.0187850i | \(-0.994020\pi\) | ||
0.999824 | − | 0.0187850i | \(-0.00597979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 267.526 | 0.473498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 482.918 | + | 297.119i | 0.851707 | + | 0.524019i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 154.080i | 0.270791i | 0.990792 | + | 0.135396i | \(0.0432306\pi\) | ||||
−0.990792 | + | 0.135396i | \(0.956769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.1693 | 0.0791056 | 0.0395528 | − | 0.999217i | \(-0.487407\pi\) | ||||
0.0395528 | + | 0.999217i | \(0.487407\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −497.574 | − | 263.113i | −0.868366 | − | 0.459184i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 82.6069i | 0.143664i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.1264 | + | 22.7356i | 0.0227494 | + | 0.0394032i | 0.877176 | − | 0.480169i | \(-0.159425\pi\) |
−0.854427 | + | 0.519572i | \(0.826091\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 50.2209 | − | 94.9730i | 0.0867373 | − | 0.164029i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −222.714 | − | 616.053i | −0.383328 | − | 1.06033i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1228.00 | −2.10635 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −93.7236 | + | 63.8404i | −0.160211 | + | 0.109129i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 606.599 | − | 350.220i | 1.03339 | − | 0.596627i | 0.115434 | − | 0.993315i | \(-0.463174\pi\) |
0.917953 | + | 0.396688i | \(0.129841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −130.715 | + | 226.405i | −0.221927 | + | 0.384389i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −291.913 | − | 154.361i | −0.493931 | − | 0.261186i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −679.184 | − | 392.127i | −1.14534 | − | 0.661260i | −0.197589 | − | 0.980285i | \(-0.563311\pi\) |
−0.947746 | + | 0.319025i | \(0.896645\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −417.796 | − | 352.119i | −0.702179 | − | 0.591797i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −206.951 | + | 7.69885i | −0.346651 | + | 0.0128959i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 518.783i | − | 0.866081i | −0.901374 | − | 0.433041i | \(-0.857441\pi\) | ||
0.901374 | − | 0.433041i | \(-0.142559\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.71229 | + | 2.96577i | 0.00284907 | + | 0.00493473i | 0.867446 | − | 0.497531i | \(-0.165760\pi\) |
−0.864597 | + | 0.502465i | \(0.832426\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.1271 | − | 35.4208i | −0.0400118 | − | 0.0587409i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1730.02 | + | 998.829i | 2.85954 | + | 1.65096i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −219.639 | − | 380.425i | −0.361843 | − | 0.626730i | 0.626421 | − | 0.779485i | \(-0.284519\pi\) |
−0.988264 | + | 0.152754i | \(0.951186\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 966.507 | + | 135.726i | 1.58704 | + | 0.222866i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.61149 | + | 4.97184i | 0.0140941 | + | 0.00813722i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 56.2801 | + | 97.4800i | 0.0918109 | + | 0.159021i | 0.908273 | − | 0.418378i | \(-0.137401\pi\) |
−0.816462 | + | 0.577399i | \(0.804068\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −638.156 | + | 1206.82i | −1.03765 | + | 1.96231i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −259.198 | − | 149.648i | −0.420094 | − | 0.242541i | 0.275024 | − | 0.961437i | \(-0.411314\pi\) |
−0.695117 | + | 0.718896i | \(0.744648\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −143.491 | + | 248.533i | −0.231811 | + | 0.401508i | −0.958341 | − | 0.285627i | \(-0.907798\pi\) |
0.726530 | + | 0.687134i | \(0.241132\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −45.1068 | + | 33.2453i | −0.0726358 | + | 0.0535351i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −291.188 | + | 345.500i | −0.467396 | + | 0.554575i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8780 | + | 30.9655i | 0.0286047 | + | 0.0495449i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.0653 | − | 673.775i | −0.0399766 | − | 1.07460i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 593.824i | 0.944077i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −263.760 | −0.418003 | −0.209001 | − | 0.977915i | \(-0.567021\pi\) | ||||
−0.209001 | + | 0.977915i | \(0.567021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 390.852 | + | 622.335i | 0.617460 | + | 0.983152i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1357.81 | + | 783.930i | −2.13828 | + | 1.23454i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −58.9653 | + | 49.0436i | −0.0925672 | + | 0.0769916i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −246.783 | + | 168.098i | −0.386202 | + | 0.263064i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −104.470 | − | 60.3156i | −0.162979 | − | 0.0940960i | 0.416292 | − | 0.909231i | \(-0.363329\pi\) |
−0.579271 | + | 0.815135i | \(0.696663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −477.894 | + | 827.737i | −0.743226 | + | 1.28730i | 0.207794 | + | 0.978173i | \(0.433372\pi\) |
−0.951019 | + | 0.309132i | \(0.899962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −884.726 | + | 555.644i | −1.37167 | + | 0.861463i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −340.484 | + | 196.578i | −0.526250 | + | 0.303831i | −0.739488 | − | 0.673170i | \(-0.764932\pi\) |
0.213238 | + | 0.977000i | \(0.431599\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 308.157 | − | 533.743i | 0.474818 | − | 0.822409i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −369.875 | − | 288.913i | −0.568164 | − | 0.443798i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −600.236 | + | 346.547i | −0.919198 | + | 0.530699i | −0.883379 | − | 0.468659i | \(-0.844737\pi\) |
−0.0358191 | + | 0.999358i | \(0.511404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −471.105 | + | 815.978i | −0.719244 | + | 1.24577i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 51.6483 | − | 107.131i | 0.0786123 | − | 0.163060i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −120.779 | + | 69.7321i | −0.183277 | + | 0.105815i | −0.588831 | − | 0.808256i | \(-0.700412\pi\) |
0.405554 | + | 0.914071i | \(0.367078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −202.532 | −0.306402 | −0.153201 | − | 0.988195i | \(-0.548958\pi\) | ||||
−0.153201 | + | 0.988195i | \(0.548958\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 40.2493 | + | 21.2835i | 0.0607078 | + | 0.0321018i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −648.892 | − | 115.868i | −0.975778 | − | 0.174238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.2268 | + | 83.5313i | −0.0723040 | + | 0.125234i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 301.198 | − | 11.2050i | 0.450221 | − | 0.0167488i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1240.32 | + | 716.098i | 1.84846 | + | 1.06721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −319.572 | − | 553.515i | −0.474847 | − | 0.822459i | 0.524738 | − | 0.851264i | \(-0.324163\pi\) |
−0.999585 | + | 0.0288047i | \(0.990830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 430.402 | − | 984.752i | 0.637632 | − | 1.45889i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 344.793i | 0.509295i | 0.967034 | + | 0.254647i | \(0.0819594\pi\) | ||||
−0.967034 | + | 0.254647i | \(0.918041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1272.99 | + | 460.208i | −1.87480 | + | 0.677774i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 423.954 | − | 266.261i | 0.622547 | − | 0.390985i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −392.616 | + | 226.677i | −0.574840 | + | 0.331884i | −0.759080 | − | 0.650997i | \(-0.774351\pi\) |
0.184240 | + | 0.982881i | \(0.441018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −642.502 | −0.937959 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −832.012 | + | 30.9520i | −1.21108 | + | 0.0450538i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 100.039i | − | 0.145194i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.6872 | −0.0313852 | −0.0156926 | − | 0.999877i | \(-0.504995\pi\) | ||||
−0.0156926 | + | 0.999877i | \(0.504995\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1204.11 | + | 123.652i | 1.73753 | + | 0.178429i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 610.358i | 0.878213i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 548.108 | 0.786381 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 120.973 | − | 75.9757i | 0.173065 | − | 0.108692i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 988.932i | − | 1.41074i | −0.708837 | − | 0.705372i | \(-0.750780\pi\) | ||
0.708837 | − | 0.705372i | \(-0.249220\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 358.190 | + | 620.403i | 0.509516 | + | 0.882508i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −153.319 | + | 5.70367i | −0.217473 | + | 0.00809031i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −304.132 | + | 360.858i | −0.430172 | + | 0.510408i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 657.215 | 0.926960 | 0.463480 | − | 0.886107i | \(-0.346601\pi\) | ||||
0.463480 | + | 0.886107i | \(0.346601\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −234.313 | − | 343.993i | −0.329555 | − | 0.483816i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.1688 | − | 23.1915i | 0.0563378 | − | 0.0325266i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −121.045 | + | 209.656i | −0.169294 | + | 0.293225i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −586.263 | + | 368.197i | −0.817661 | + | 0.513525i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 490.350 | + | 283.104i | 0.681988 | + | 0.393746i | 0.800604 | − | 0.599194i | \(-0.204512\pi\) |
−0.118615 | + | 0.992940i | \(0.537846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 528.511 | − | 191.066i | 0.733025 | − | 0.265001i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −474.639 | − | 755.745i | −0.656485 | − | 1.04529i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1849.91i | − | 2.55160i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 61.6116 | + | 106.714i | 0.0847478 | + | 0.146787i | 0.905284 | − | 0.424807i | \(-0.139658\pi\) |
−0.820536 | + | 0.571595i | \(0.806325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 710.932 | − | 161.298i | 0.975215 | − | 0.221259i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 363.263 | + | 209.730i | 0.496940 | + | 0.286908i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −518.567 | − | 898.184i | −0.707458 | − | 1.22535i | −0.965797 | − | 0.259299i | \(-0.916509\pi\) |
0.258339 | − | 0.966054i | \(-0.416825\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 367.995 | − | 1124.69i | 0.500673 | − | 1.53019i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −79.2349 | − | 45.7463i | −0.107510 | − | 0.0620709i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 536.011 | + | 928.397i | 0.725319 | + | 1.25629i | 0.958843 | + | 0.283938i | \(0.0916409\pi\) |
−0.233524 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 54.8888 | − | 2.04194i | 0.0740740 | − | 0.00275565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −645.464 | − | 372.659i | −0.868727 | − | 0.501560i | −0.00180187 | − | 0.999998i | \(-0.500574\pi\) |
−0.866925 | + | 0.498439i | \(0.833907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 438.545 | − | 759.582i | 0.588651 | − | 1.01957i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −758.673 | − | 365.761i | −1.01563 | − | 0.489640i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 563.020 | − | 668.035i | 0.751696 | − | 0.891902i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.18917 | + | 5.52381i | 0.00424657 | + | 0.00735527i | 0.868141 | − | 0.496318i | \(-0.165315\pi\) |
−0.863894 | + | 0.503673i | \(0.831982\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 226.099 | + | 119.559i | 0.300265 | + | 0.158777i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1315.66i | 1.74259i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1187.30 | 1.56843 | 0.784216 | − | 0.620488i | \(-0.213066\pi\) | ||||
0.784216 | + | 0.620488i | \(0.213066\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −55.9192 | + | 105.749i | −0.0736748 | + | 0.139327i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 234.723 | − | 135.518i | 0.308441 | − | 0.178078i | −0.337788 | − | 0.941222i | \(-0.609679\pi\) |
0.646228 | + | 0.763144i | \(0.276345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1063.92 | − | 384.625i | 1.39439 | − | 0.504096i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −700.559 | + | 52.1957i | −0.915764 | + | 0.0682297i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.4812 | + | 25.1039i | 0.0566900 | + | 0.0327300i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.4068 | + | 21.4892i | −0.0161337 | + | 0.0279443i | −0.873980 | − | 0.485963i | \(-0.838469\pi\) |
0.857846 | + | 0.513907i | \(0.171802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.00279 | + | 215.121i | 0.0103798 | + | 0.279015i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −780.685 | + | 450.729i | −1.00994 | + | 0.583090i | −0.911175 | − | 0.412020i | \(-0.864823\pi\) |
−0.0987672 | + | 0.995111i | \(0.531490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −444.795 | + | 770.408i | −0.573929 | + | 0.994075i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1192.39 | + | 481.910i | −1.53461 | + | 0.620219i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 572.641 | − | 330.614i | 0.735097 | − | 0.424409i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −318.723 | + | 552.044i | −0.408096 | + | 0.706843i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1010.13 | − | 744.499i | 1.29007 | − | 0.950828i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −219.695 | + | 126.841i | −0.279866 | + | 0.161581i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 778.855 | 0.989651 | 0.494825 | − | 0.868992i | \(-0.335232\pi\) | ||||
0.494825 | + | 0.868992i | \(0.335232\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 867.140 | − | 544.599i | 1.09904 | − | 0.690240i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 149.917 | − | 177.880i | 0.189529 | − | 0.224880i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.3367 | + | 101.042i | −0.0735646 | + | 0.127418i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 820.927 | + | 1307.12i | 1.03261 | + | 1.64418i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 492.791 | + | 284.513i | 0.618307 | + | 0.356980i | 0.776210 | − | 0.630475i | \(-0.217140\pi\) |
−0.157903 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.7999 | + | 53.3469i | 0.0385480 | + | 0.0667671i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 43.1637 | + | 579.333i | 0.0538872 | + | 0.723262i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 253.896i | − | 0.316184i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 89.4237 | + | 75.3663i | 0.111085 | + | 0.0936228i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.5257 | − | 632.388i | −0.0291520 | − | 0.783628i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −888.209 | + | 512.808i | −1.09791 | + | 0.633878i | −0.935671 | − | 0.352873i | \(-0.885205\pi\) |
−0.162238 | + | 0.986752i | \(0.551871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −276.040 | −0.340370 | −0.170185 | − | 0.985412i | \(-0.554437\pi\) | ||||
−0.170185 | + | 0.985412i | \(0.554437\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −413.008 | − | 657.614i | −0.508005 | − | 0.808873i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2406.44i | − | 2.95268i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 506.030 | 0.619376 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.0732 | + | 98.0925i | −0.0122994 | + | 0.119771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 203.452i | 0.247810i | 0.992294 | + | 0.123905i | \(0.0395418\pi\) | ||||
−0.992294 | + | 0.123905i | \(0.960458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 820.361 | 0.996794 | 0.498397 | − | 0.866949i | \(-0.333922\pi\) | ||||
0.498397 | + | 0.866949i | \(0.333922\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −85.2918 | − | 2292.71i | −0.103384 | − | 2.77904i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1580.90i | 1.91161i | 0.293998 | + | 0.955806i | \(0.405014\pi\) | ||||
−0.293998 | + | 0.955806i | \(0.594986\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.7377 | + | 89.6124i | 0.0624098 | + | 0.108097i | 0.895542 | − | 0.444977i | \(-0.146788\pi\) |
−0.833132 | + | 0.553074i | \(0.813455\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 652.989 | + | 1039.72i | 0.785788 | + | 1.25117i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −468.252 | + | 80.4736i | −0.562127 | + | 0.0966069i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2104.45 | 2.52030 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −599.684 | + | 67.1751i | −0.716468 | + | 0.0802570i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1258.61 | + | 726.657i | −1.50013 | + | 0.866099i | −0.500127 | + | 0.865952i | \(0.666713\pi\) |
−1.00000 | 0.000147057i | \(0.999953\pi\) | ||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 659.496 | − | 1142.28i | 0.784181 | − | 1.35824i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.6854 | − | 959.251i | −0.0423315 | − | 1.13790i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1161.12 | + | 670.371i | 1.37410 | + | 0.793338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1633.60 | − | 590.575i | 1.92869 | − | 0.697255i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −173.569 | + | 328.237i | −0.204439 | + | 0.386616i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 127.100i | − | 0.149354i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.3396 | − | 90.6549i | −0.0613595 | − | 0.106278i | 0.833714 | − | 0.552197i | \(-0.186210\pi\) |
−0.895073 | + | 0.445919i | \(0.852877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −700.432 | + | 477.104i | −0.819218 | + | 0.558016i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −195.478 | − | 112.859i | −0.228096 | − | 0.131691i | 0.381598 | − | 0.924329i | \(-0.375374\pi\) |
−0.609693 | + | 0.792637i | \(0.708707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −291.619 | − | 505.099i | −0.339486 | − | 0.588008i | 0.644850 | − | 0.764309i | \(-0.276920\pi\) |
−0.984336 | + | 0.176302i | \(0.943587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 444.810 | + | 1100.59i | 0.516620 | + | 1.27828i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 306.120 | + | 176.739i | 0.354716 | + | 0.204796i | 0.666761 | − | 0.745272i | \(-0.267680\pi\) |
−0.312044 | + | 0.950068i | \(0.601014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −774.749 | − | 1341.90i | −0.895664 | − | 1.55133i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −311.104 | − | 495.356i | −0.358828 | − | 0.571345i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −769.500 | − | 444.271i | −0.885500 | − | 0.511244i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72671 | − | 6.45485i | 0.00427865 | − | 0.00741084i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −755.797 | + | 1567.70i | −0.865747 | + | 1.79576i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −821.209 | − | 146.638i | −0.938525 | − | 0.167586i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −458.091 | − | 793.437i | −0.522339 | − | 0.904718i | −0.999662 | − | 0.0259898i | \(-0.991726\pi\) |
0.477323 | − | 0.878728i | \(-0.341607\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −47.0757 | + | 29.5654i | −0.0535559 | + | 0.0336353i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1041.09i | − | 1.18172i | −0.806775 | − | 0.590859i | \(-0.798789\pi\) | ||
0.806775 | − | 0.590859i | \(-0.201211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 247.115 | 0.279858 | 0.139929 | − | 0.990162i | \(-0.455313\pi\) | ||||
0.139929 | + | 0.990162i | \(0.455313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −774.139 | + | 28.7990i | −0.874734 | + | 0.0325413i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −933.499 | + | 538.956i | −1.05242 | + | 0.607616i | −0.923327 | − | 0.384016i | \(-0.874541\pi\) |
−0.129096 | + | 0.991632i | \(0.541207\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −239.652 | + | 1342.11i | −0.269575 | + | 1.50969i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1217.59 | − | 969.277i | 1.36654 | − | 1.08785i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.3569 | + | 37.1565i | 0.0720682 | + | 0.0416086i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1411.55 | − | 2444.87i | 1.57715 | − | 2.73170i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.61482 | − | 4.55544i | −0.00960403 | − | 0.00507853i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −899.545 | + | 519.353i | −1.00061 | + | 0.577700i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 309.862 | − | 536.697i | 0.343909 | − | 0.595669i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −126.335 | + | 899.633i | −0.139905 | + | 0.996271i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1588.91 | − | 917.358i | 1.75570 | − | 1.01366i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 433.640 | − | 751.087i | 0.478104 | − | 0.828100i | −0.521581 | − | 0.853202i | \(-0.674658\pi\) |
0.999685 | + | 0.0251017i | \(0.00799095\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.0824 | + | 605.086i | 0.0495956 | + | 0.665661i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 987.899 | − | 570.364i | 1.08441 | − | 0.626085i | 0.152328 | − | 0.988330i | \(-0.451323\pi\) |
0.932083 | + | 0.362245i | \(0.117990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1798.03 | −1.96936 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −66.9235 | − | 1798.95i | −0.0731404 | − | 1.96607i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 278.549 | + | 770.501i | 0.303761 | + | 0.840241i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 308.533 | − | 534.394i | 0.335726 | − | 0.581495i | −0.647898 | − | 0.761727i | \(-0.724352\pi\) |
0.983624 | + | 0.180232i | \(0.0576849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −510.099 | + | 964.651i | −0.553853 | + | 1.04739i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −44.9721 | − | 25.9647i | −0.0487239 | − | 0.0281307i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1218.84 | + | 2111.10i | 1.31767 | + | 2.28227i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 313.786 | − | 650.865i | 0.338496 | − | 0.702120i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 532.241i | 0.572918i | 0.958093 | + | 0.286459i | \(0.0924782\pi\) | ||||
−0.958093 | + | 0.286459i | \(0.907522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −440.670 | + | 366.521i | −0.473329 | + | 0.393686i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 398.306 | + | 210.621i | 0.426909 | + | 0.225746i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1298.79 | + | 749.856i | −1.38908 | + | 0.801985i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1506.24 | −1.60751 | −0.803755 | − | 0.594960i | \(-0.797168\pi\) | ||||
−0.803755 | + | 0.594960i | \(0.797168\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 328.458 | − | 621.148i | 0.349795 | − | 0.661499i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 204.118i | 0.216916i | 0.994101 | + | 0.108458i | \(0.0345913\pi\) | ||||
−0.994101 | + | 0.108458i | \(0.965409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −117.315 | −0.124406 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −673.338 | − | 1364.36i | −0.712527 | − | 1.44376i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 497.276i | 0.525106i | 0.964918 | + | 0.262553i | \(0.0845645\pi\) | ||||
−0.964918 | + | 0.262553i | \(0.915435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.6835 | 0.0217951 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1041.42 | − | 550.693i | −1.09508 | − | 0.579067i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 582.144i | 0.610854i | 0.952215 | + | 0.305427i | \(0.0987992\pi\) | ||||
−0.952215 | + | 0.305427i | \(0.901201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 755.174 | + | 1308.00i | 0.790758 | + | 1.36963i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1252.26 | − | 2368.16i | 1.30853 | − | 2.47456i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −360.047 | + | 427.203i | −0.375441 | + | 0.445468i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −461.504 | −0.480233 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −83.4583 | − | 1120.16i | −0.0866649 | − | 1.16320i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −249.661 | + | 144.142i | −0.258716 | + | 0.149370i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −239.897 | + | 415.514i | −0.248084 | + | 0.429694i | −0.962994 | − | 0.269522i | \(-0.913134\pi\) |
0.714910 | + | 0.699216i | \(0.246468\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 300.798 | + | 159.059i | 0.310421 | + | 0.164148i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 311.099 | + | 179.613i | 0.320391 | + | 0.184978i | 0.651567 | − | 0.758591i | \(-0.274112\pi\) |
−0.331176 | + | 0.943569i | \(0.607445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 405.831 | + | 342.034i | 0.417092 | + | 0.351526i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 186.775 | − | 6.94827i | 0.191564 | − | 0.00712643i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.86558i | 0.0100978i | 0.999987 | + | 0.00504892i | \(0.00160713\pi\) | ||||
−0.999987 | + | 0.00504892i | \(0.998393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 620.100 | + | 1074.04i | 0.633401 | + | 1.09708i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 631.667 | − | 1310.22i | 0.643901 | − | 1.33560i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 177.778 | + | 102.640i | 0.180853 | + | 0.104415i | 0.587693 | − | 0.809084i | \(-0.300036\pi\) |
−0.406840 | + | 0.913499i | \(0.633370\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 443.040 | + | 767.368i | 0.449787 | + | 0.779054i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −82.1249 | + | 105.139i | −0.0832066 | + | 0.106524i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −77.7516 | − | 44.8899i | −0.0786164 | − | 0.0453892i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −204.103 | − | 353.517i | −0.205957 | − | 0.356728i | 0.744480 | − | 0.667645i | \(-0.232697\pi\) |
−0.950437 | + | 0.310917i | \(0.899364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −213.199 | + | 403.182i | −0.214702 | + | 0.406024i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 481.257 | + | 277.854i | 0.483675 | + | 0.279250i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 325.326 | − | 563.482i | 0.326305 | − | 0.565177i | −0.655471 | − | 0.755221i | \(-0.727530\pi\) |
0.981776 | + | 0.190044i | \(0.0608630\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −662.222 | + | 1515.15i | −0.662885 | + | 1.51667i |
(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 | 252.3.bh.a.149.6 | yes | 32 | |
3.2 | odd | 2 | 756.3.bh.a.233.2 | 32 | |||
7.4 | even | 3 | 252.3.m.a.221.16 | yes | 32 | ||
9.2 | odd | 6 | 252.3.m.a.65.16 | ✓ | 32 | ||
9.7 | even | 3 | 756.3.m.a.737.15 | 32 | |||
21.11 | odd | 6 | 756.3.m.a.557.2 | 32 | |||
63.11 | odd | 6 | inner | 252.3.bh.a.137.6 | yes | 32 | |
63.25 | even | 3 | 756.3.bh.a.305.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.3.m.a.65.16 | ✓ | 32 | 9.2 | odd | 6 | ||
252.3.m.a.221.16 | yes | 32 | 7.4 | even | 3 | ||
252.3.bh.a.137.6 | yes | 32 | 63.11 | odd | 6 | inner | |
252.3.bh.a.149.6 | yes | 32 | 1.1 | even | 1 | trivial | |
756.3.m.a.557.2 | 32 | 21.11 | odd | 6 | |||
756.3.m.a.737.15 | 32 | 9.7 | even | 3 | |||
756.3.bh.a.233.2 | 32 | 3.2 | odd | 2 | |||
756.3.bh.a.305.2 | 32 | 63.25 | even | 3 |