Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(17,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.bi (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.14 | ||
Character | \(\chi\) | \(=\) | 672.17 |
Dual form | 672.2.bi.c.593.14 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.390548 | − | 1.68745i | 0.225483 | − | 0.974247i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.54900 | + | 0.894317i | −0.692735 | + | 0.399951i | −0.804636 | − | 0.593769i | \(-0.797639\pi\) |
0.111901 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63573 | + | 0.230049i | −0.996213 | + | 0.0869505i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.69494 | − | 1.31806i | −0.898315 | − | 0.439353i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.501346 | − | 0.868358i | 0.151162 | − | 0.261820i | −0.780493 | − | 0.625164i | \(-0.785032\pi\) |
0.931655 | + | 0.363345i | \(0.118365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.47302 | 0.685891 | 0.342946 | − | 0.939355i | \(-0.388575\pi\) | ||||
0.342946 | + | 0.939355i | \(0.388575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.904151 | + | 2.96313i | 0.233451 | + | 0.765077i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.32963 | + | 5.76708i | −0.807553 | + | 1.39872i | 0.107001 | + | 0.994259i | \(0.465875\pi\) |
−0.914554 | + | 0.404464i | \(0.867458\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.85941 | − | 3.22059i | −0.426577 | − | 0.738854i | 0.569989 | − | 0.821652i | \(-0.306947\pi\) |
−0.996566 | + | 0.0827988i | \(0.973614\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.641185 | + | 4.53750i | −0.139918 | + | 0.990163i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.85244 | + | 3.95626i | −1.42883 | + | 0.824936i | −0.997029 | − | 0.0770314i | \(-0.975456\pi\) |
−0.431803 | + | 0.901968i | \(0.642123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.900394 | + | 1.55953i | −0.180079 | + | 0.311906i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.27666 | + | 4.03281i | −0.630593 | + | 0.776114i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.748403 | −0.138975 | −0.0694875 | − | 0.997583i | \(-0.522136\pi\) | ||||
−0.0694875 | + | 0.997583i | \(0.522136\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.87254 | − | 1.65846i | −0.515924 | − | 0.297869i | 0.219341 | − | 0.975648i | \(-0.429609\pi\) |
−0.735265 | + | 0.677779i | \(0.762942\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.26951 | − | 1.18513i | −0.220993 | − | 0.206305i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.87702 | − | 2.71353i | 0.655335 | − | 0.458670i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.22429 | + | 1.86155i | −0.530071 | + | 0.306036i | −0.741045 | − | 0.671455i | \(-0.765670\pi\) |
0.210975 | + | 0.977492i | \(0.432336\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.965832 | − | 4.17308i | 0.154657 | − | 0.668228i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.01044 | 0.313978 | 0.156989 | − | 0.987600i | \(-0.449821\pi\) | ||||
0.156989 | + | 0.987600i | \(0.449821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.19651i | 1.40245i | 0.712938 | + | 0.701227i | \(0.247364\pi\) | ||||
−0.712938 | + | 0.701227i | \(0.752636\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.35324 | − | 0.368459i | 0.798013 | − | 0.0549266i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.19840 | − | 2.07569i | −0.174805 | − | 0.302771i | 0.765289 | − | 0.643687i | \(-0.222596\pi\) |
−0.940094 | + | 0.340916i | \(0.889263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.89415 | − | 1.21270i | 0.984879 | − | 0.173242i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.43126 | + | 7.87089i | 1.18061 | + | 1.10214i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.33884 | − | 10.9792i | 0.870707 | − | 1.50811i | 0.00943963 | − | 0.999955i | \(-0.496995\pi\) |
0.861267 | − | 0.508153i | \(-0.169671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79345i | 0.241829i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.16075 | + | 1.87985i | −0.816012 | + | 0.248993i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.34922 | − | 4.24308i | −0.956787 | − | 0.552401i | −0.0616046 | − | 0.998101i | \(-0.519622\pi\) |
−0.895183 | + | 0.445699i | \(0.852955\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.02442 | − | 3.50640i | −0.259200 | − | 0.448948i | 0.706828 | − | 0.707386i | \(-0.250126\pi\) |
−0.966028 | + | 0.258438i | \(0.916792\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.40637 | + | 2.85408i | 0.933114 | + | 0.359580i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.83071 | + | 2.21166i | −0.475141 | + | 0.274323i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.89843 | + | 3.98281i | 0.842777 | + | 0.486577i | 0.858207 | − | 0.513303i | \(-0.171578\pi\) |
−0.0154303 | + | 0.999881i | \(0.504912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.99976 | + | 13.1082i | 0.481514 | + | 1.57804i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.46843i | 0.648984i | 0.945889 | + | 0.324492i | \(0.105193\pi\) | ||||
−0.945889 | + | 0.324492i | \(0.894807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.68546 | − | 3.28250i | −0.665433 | − | 0.384188i | 0.128911 | − | 0.991656i | \(-0.458852\pi\) |
−0.794344 | + | 0.607468i | \(0.792185\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.27997 | + | 2.12844i | 0.263268 | + | 0.245771i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.12165 | + | 2.40409i | −0.127824 | + | 0.273972i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.53988 | − | 4.39920i | −0.285759 | − | 0.494949i | 0.687034 | − | 0.726625i | \(-0.258912\pi\) |
−0.972793 | + | 0.231676i | \(0.925579\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.52545 | + | 7.10419i | 0.613938 | + | 0.789354i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.65457i | − | 0.620669i | −0.950627 | − | 0.310335i | \(-0.899559\pi\) | ||
0.950627 | − | 0.310335i | \(-0.100441\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.9110i | − | 1.29193i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.292288 | + | 1.26289i | −0.0313365 | + | 0.135396i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.39495 | − | 12.8084i | −0.783863 | − | 1.35769i | −0.929676 | − | 0.368379i | \(-0.879913\pi\) |
0.145812 | − | 0.989312i | \(-0.453420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.51821 | + | 0.568916i | −0.683294 | + | 0.0596386i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.92043 | + | 4.19955i | −0.406530 | + | 0.435473i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.76045 | + | 3.32580i | 0.591010 | + | 0.341220i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.75577i | − | 0.178271i | −0.996019 | − | 0.0891356i | \(-0.971590\pi\) | ||
0.996019 | − | 0.0891356i | \(-0.0284105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.49565 | + | 1.67937i | −0.250822 | + | 0.168783i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.6803 | − | 7.32100i | −1.26174 | − | 0.728467i | −0.288330 | − | 0.957531i | \(-0.593100\pi\) |
−0.973411 | + | 0.229064i | \(0.926433\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.54056 | − | 4.93089i | 0.841526 | − | 0.485855i | −0.0162566 | − | 0.999868i | \(-0.505175\pi\) |
0.857783 | + | 0.514013i | \(0.171842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.06476 | − | 7.60202i | −0.299090 | − | 0.741881i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.48110 | − | 6.02945i | −0.336531 | − | 0.582889i | 0.647247 | − | 0.762281i | \(-0.275920\pi\) |
−0.983778 | + | 0.179392i | \(0.942587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.36373 | + | 1.36470i | 0.226404 | + | 0.130715i | 0.608912 | − | 0.793238i | \(-0.291606\pi\) |
−0.382508 | + | 0.923952i | \(0.624939\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.88202 | + | 6.16785i | 0.178633 | + | 0.585426i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.531154i | 0.0499667i | 0.999688 | + | 0.0249834i | \(0.00795328\pi\) | ||||
−0.999688 | + | 0.0249834i | \(0.992047\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.07629 | − | 12.2565i | 0.659868 | − | 1.14292i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.66464 | − | 3.25958i | −0.616146 | − | 0.301348i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.44929 | − | 15.9665i | 0.682875 | − | 1.46364i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.99730 | + | 8.65558i | 0.454300 | + | 0.786871i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.785174 | − | 3.39251i | 0.0707967 | − | 0.305892i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1641i | − | 1.08799i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.52393 | 0.401434 | 0.200717 | − | 0.979649i | \(-0.435673\pi\) | ||||
0.200717 | + | 0.979649i | \(0.435673\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.5186 | + | 3.59168i | 1.36634 | + | 0.316230i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3927 | + | 7.73228i | −1.17013 | + | 0.675573i | −0.953710 | − | 0.300729i | \(-0.902770\pi\) |
−0.216416 | + | 0.976301i | \(0.569437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.64179 | + | 8.06085i | 0.489205 | + | 0.698964i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.46894 | − | 9.17720i | 0.126427 | − | 0.789847i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.71195 | + | 5.60719i | 0.829748 | + | 0.479055i | 0.853766 | − | 0.520657i | \(-0.174313\pi\) |
−0.0240187 | + | 0.999712i | \(0.507646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.9824 | −1.52525 | −0.762625 | − | 0.646840i | \(-0.776090\pi\) | ||||
−0.762625 | + | 0.646840i | \(0.776090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.97066 | + | 1.21158i | −0.334390 | + | 0.102033i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.23984 | − | 2.14746i | 0.103680 | − | 0.179580i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.15928 | − | 0.669310i | 0.0962728 | − | 0.0555831i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.646141 | − | 12.1071i | 0.0532928 | − | 0.998579i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.462495 | + | 0.801066i | 0.0378891 | + | 0.0656258i | 0.884348 | − | 0.466828i | \(-0.154603\pi\) |
−0.846459 | + | 0.532454i | \(0.821270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.56720 | + | 16.5709i | −0.778568 | + | 1.34852i | 0.154200 | + | 0.988040i | \(0.450720\pi\) |
−0.932767 | + | 0.360479i | \(0.882613\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.5745 | − | 11.1533i | 1.33997 | − | 0.901693i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.93277 | 0.476531 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.46873 | + | 9.47212i | −0.436452 | + | 0.755957i | −0.997413 | − | 0.0718851i | \(-0.977099\pi\) |
0.560961 | + | 0.827842i | \(0.310432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.0512 | − | 14.9844i | −1.27294 | − | 1.18834i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.1510 | − | 12.0040i | 1.35169 | − | 0.946050i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.21188 | − | 5.31848i | 0.721530 | − | 0.416576i | −0.0937855 | − | 0.995592i | \(-0.529897\pi\) |
0.815316 | + | 0.579017i | \(0.196563\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.02635 | + | 0.700429i | 0.235601 | + | 0.0545283i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.93040 | 0.613673 | 0.306836 | − | 0.951762i | \(-0.400730\pi\) | ||||
0.306836 | + | 0.951762i | \(0.400730\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.88419 | −0.529553 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.766076 | + | 11.1301i | 0.0585833 | + | 0.851141i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.69882 | + | 2.13552i | −0.281216 | + | 0.162360i | −0.633974 | − | 0.773354i | \(-0.718577\pi\) |
0.352758 | + | 0.935715i | \(0.385244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.01443 | − | 4.31763i | 0.152276 | − | 0.326382i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.0302 | + | 10.7443i | −0.753915 | + | 0.807590i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.77825 | − | 6.54412i | 0.282399 | − | 0.489130i | −0.689576 | − | 0.724214i | \(-0.742203\pi\) |
0.971975 | + | 0.235083i | \(0.0755363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00239 | 0.371824 | 0.185912 | − | 0.982566i | \(-0.440476\pi\) | ||||
0.185912 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.70749 | + | 2.04668i | −0.495832 | + | 0.151295i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.32963 | − | 5.76708i | 0.244799 | − | 0.424004i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.33859 | + | 5.78261i | 0.244142 | + | 0.422867i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.70864 | − | 11.3832i | 0.560721 | − | 0.828005i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4891 | + | 6.05587i | −0.758963 | + | 0.438188i | −0.828923 | − | 0.559362i | \(-0.811046\pi\) |
0.0699601 | + | 0.997550i | \(0.477713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.592437 | − | 1.02613i | 0.0426445 | − | 0.0738625i | −0.843915 | − | 0.536476i | \(-0.819755\pi\) |
0.886560 | + | 0.462614i | \(0.153088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.23598 | + | 7.32787i | 0.160122 | + | 0.524760i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.5111 | 1.39011 | 0.695054 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695054 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7632 | + | 7.36884i | 0.904760 | + | 0.522363i | 0.878741 | − | 0.477298i | \(-0.158384\pi\) |
0.0260186 | + | 0.999661i | \(0.491717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.41494 | − | 10.0852i | 0.664079 | − | 0.711358i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.97259 | − | 0.172170i | 0.138449 | − | 0.0120839i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.11418 | + | 1.79797i | −0.217503 | + | 0.125576i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.6815 | − | 1.62998i | 1.64598 | − | 0.113291i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.72883 | −0.257929 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.9240i | − | 1.02741i | −0.857967 | − | 0.513704i | \(-0.828273\pi\) | ||
0.857967 | − | 0.513704i | \(-0.171727\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.22768 | + | 2.13569i | 0.632270 | + | 0.146335i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.22459 | − | 14.2454i | −0.560913 | − | 0.971529i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.95278 | + | 3.71044i | 0.539870 | + | 0.251881i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.75949 | + | 8.31193i | −0.524338 | + | 0.561668i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.23422 | + | 14.2621i | −0.553894 | + | 0.959372i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.62187i | 0.510398i | 0.966889 | + | 0.255199i | \(0.0821410\pi\) | ||||
−0.966889 | + | 0.255199i | \(0.917859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.48206 | − | 3.01607i | 0.298804 | − | 0.201071i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6531 | + | 7.88264i | 0.906190 | + | 0.523189i | 0.879203 | − | 0.476446i | \(-0.158075\pi\) |
0.0269870 | + | 0.999636i | \(0.491409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.82193 | + | 15.2800i | 0.582970 | + | 1.00973i | 0.995125 | + | 0.0986198i | \(0.0314428\pi\) |
−0.412155 | + | 0.911114i | \(0.635224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.61871 | + | 2.83164i | 0.238094 | + | 0.186308i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.7079 | + | 9.06896i | −1.02906 | + | 0.594127i | −0.916715 | − | 0.399542i | \(-0.869169\pi\) |
−0.112344 | + | 0.993669i | \(0.535836\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.71266 | + | 2.14350i | 0.242187 | + | 0.139827i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.41536 | + | 2.56781i | −0.546637 | + | 0.166797i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.41040i | − | 0.349970i | −0.984571 | − | 0.174985i | \(-0.944012\pi\) | ||
0.984571 | − | 0.174985i | \(-0.0559877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6025 | − | 10.7401i | −1.19829 | − | 0.691834i | −0.238117 | − | 0.971236i | \(-0.576530\pi\) |
−0.960174 | + | 0.279403i | \(0.909863\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1459 | − | 6.54936i | 0.907459 | − | 0.420142i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.59453 | + | 8.04403i | −0.612972 | + | 0.513914i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.59834 | − | 7.96457i | −0.292586 | − | 0.506773i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.54177 | − | 2.20838i | −0.604685 | − | 0.139951i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.8553i | − | 1.25325i | −0.779319 | − | 0.626627i | \(-0.784435\pi\) | ||
0.779319 | − | 0.626627i | \(-0.215565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.93382i | 0.498795i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20.0991 | − | 4.65181i | −1.25865 | − | 0.291308i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.36616 | − | 7.56240i | −0.272353 | − | 0.471730i | 0.697111 | − | 0.716964i | \(-0.254469\pi\) |
−0.969464 | + | 0.245234i | \(0.921135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.07012 | − | 5.64828i | 0.501453 | − | 0.350967i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.01690 | + | 0.986439i | 0.124843 | + | 0.0610590i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.1429 | + | 9.89747i | 1.05708 | + | 0.610304i | 0.924623 | − | 0.380885i | \(-0.124381\pi\) |
0.132455 | + | 0.991189i | \(0.457714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.6757i | 1.39296i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.5016 | + | 7.47627i | −1.49947 | + | 0.457540i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.805574 | + | 0.465098i | 0.0491167 | + | 0.0283575i | 0.524357 | − | 0.851498i | \(-0.324306\pi\) |
−0.475241 | + | 0.879856i | \(0.657639\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.45646 | − | 4.30499i | 0.452948 | − | 0.261509i | −0.256127 | − | 0.966643i | \(-0.582446\pi\) |
0.709074 | + | 0.705134i | \(0.249113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.58566 | + | 11.2213i | −0.0959685 | + | 0.679144i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.902819 | + | 1.56373i | 0.0544420 | + | 0.0942964i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.5583 | − | 14.7561i | −1.53565 | − | 0.886607i | −0.999086 | − | 0.0427456i | \(-0.986390\pi\) |
−0.536562 | − | 0.843861i | \(-0.680277\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.55539 | + | 8.25565i | 0.332593 | + | 0.494253i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.3260i | 1.27220i | 0.771605 | + | 0.636102i | \(0.219454\pi\) | ||||
−0.771605 | + | 0.636102i | \(0.780546\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4247 | + | 18.0561i | −0.619684 | + | 1.07332i | 0.369860 | + | 0.929088i | \(0.379406\pi\) |
−0.989543 | + | 0.144236i | \(0.953928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.86184 | − | 8.42156i | 0.465695 | − | 0.498850i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.29898 | + | 0.462500i | −0.312789 | + | 0.0273005i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6728 | − | 23.6820i | −0.804284 | − | 1.39306i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.96276 | − | 0.685712i | −0.173680 | − | 0.0401972i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 13.1058i | − | 0.765652i | −0.923821 | − | 0.382826i | \(-0.874951\pi\) | ||
0.923821 | − | 0.382826i | \(-0.125049\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.1786 | 0.883733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.85918 | + | 4.86714i | 0.107880 | + | 0.282420i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.9462 | + | 9.78389i | −0.980023 | + | 0.565817i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.11565 | − | 24.2395i | −0.121944 | − | 1.39714i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.3061 | + | 18.5382i | −0.994208 | + | 1.06499i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.27166 | + | 3.62094i | 0.359114 | + | 0.207335i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.6425 | 1.06398 | 0.531992 | − | 0.846750i | \(-0.321444\pi\) | ||||
0.531992 | + | 0.846750i | \(0.321444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.98511 | − | 16.3375i | −0.283593 | − | 0.929406i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.92896 | + | 17.1975i | −0.563020 | + | 0.975179i | 0.434211 | + | 0.900811i | \(0.357027\pi\) |
−0.997231 | + | 0.0743677i | \(0.976306\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.33108 | − | 1.34585i | 0.131760 | − | 0.0760718i | −0.432671 | − | 0.901552i | \(-0.642429\pi\) |
0.564431 | + | 0.825480i | \(0.309096\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.0249 | + | 2.20267i | −0.790215 | + | 0.124106i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.35288 | + | 9.27147i | 0.300648 | + | 0.520737i | 0.976283 | − | 0.216499i | \(-0.0694638\pi\) |
−0.675635 | + | 0.737236i | \(0.736130\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.375209 | + | 0.649881i | −0.0210077 | + | 0.0363864i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.5339 | + | 3.51938i | −0.643760 | + | 0.196433i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.7645 | 1.37794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.22669 | + | 3.85674i | −0.123514 | + | 0.213933i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.22601 | − | 3.45569i | 0.178399 | − | 0.191100i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.63618 | + | 5.19528i | 0.200469 | + | 0.286425i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.8525 | + | 10.8845i | −1.03623 | + | 0.598266i | −0.918762 | − | 0.394811i | \(-0.870810\pi\) |
−0.117465 | + | 0.993077i | \(0.537477\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.1429 | − | 0.766958i | 0.610628 | − | 0.0420290i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.2476 | −0.778428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3104 | −0.616116 | −0.308058 | − | 0.951368i | \(-0.599679\pi\) | ||||
−0.308058 | + | 0.951368i | \(0.599679\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.896293 | + | 0.207441i | 0.0486799 | + | 0.0112667i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.88028 | + | 1.66293i | −0.155976 | + | 0.0900527i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8922 | + | 4.78234i | −0.966086 | + | 0.258222i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.9185 | − | 16.7276i | −0.964702 | − | 0.900585i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.94032 | + | 17.2171i | −0.533624 | + | 0.924265i | 0.465604 | + | 0.884993i | \(0.345837\pi\) |
−0.999229 | + | 0.0392715i | \(0.987496\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.45348 | 0.506033 | 0.253017 | − | 0.967462i | \(-0.418577\pi\) | ||||
0.253017 | + | 0.967462i | \(0.418577\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.10323 | + | 9.97319i | −0.432518 | + | 0.532330i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.48135 | + | 14.6901i | −0.451417 | + | 0.781877i | −0.998474 | − | 0.0552182i | \(-0.982415\pi\) |
0.547057 | + | 0.837095i | \(0.315748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.89051 | − | 8.47062i | −0.259561 | − | 0.449574i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.0332 | − | 18.8059i | −1.27197 | − | 0.995316i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.2162 | + | 10.5171i | −0.961413 | + | 0.555072i | −0.896608 | − | 0.442826i | \(-0.853976\pi\) |
−0.0648056 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.58521 | − | 4.47771i | 0.136064 | − | 0.235669i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5575 | − | 5.05225i | 0.869044 | − | 0.265174i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7424 | 0.614625 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.24875 | − | 0.720966i | −0.0651842 | − | 0.0376341i | 0.467054 | − | 0.884229i | \(-0.345315\pi\) |
−0.532238 | + | 0.846595i | \(0.678649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.41802 | − | 2.64988i | −0.282051 | − | 0.137947i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.1817 | + | 30.3964i | −0.736278 | + | 1.57810i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.8362 | − | 10.8751i | 0.975302 | − | 0.563091i | 0.0744535 | − | 0.997224i | \(-0.476279\pi\) |
0.900848 | + | 0.434134i | \(0.142945\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.5263 | − | 4.75068i | −1.05997 | − | 0.245324i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.85081 | −0.0953217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.82298i | 0.0936402i | 0.998903 | + | 0.0468201i | \(0.0149087\pi\) | ||||
−0.998903 | + | 0.0468201i | \(0.985091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.76681 | − | 7.63389i | 0.0905167 | − | 0.391096i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.81069 | + | 8.33236i | 0.245815 | + | 0.425763i | 0.962360 | − | 0.271777i | \(-0.0876112\pi\) |
−0.716546 | + | 0.697540i | \(0.754278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.412582 | − | 4.72705i | −0.0210271 | − | 0.240913i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.1215 | − | 24.7841i | 0.616172 | − | 1.25984i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0629 | + | 24.3576i | −0.713017 | + | 1.23498i | 0.250703 | + | 0.968064i | \(0.419338\pi\) |
−0.963719 | + | 0.266917i | \(0.913995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 52.6914i | − | 2.66472i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.81730 | + | 25.6193i | 0.394331 | + | 1.29232i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.86857 | + | 4.54292i | 0.395911 | + | 0.228579i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.42646 | − | 16.3271i | −0.473101 | − | 0.819434i | 0.526425 | − | 0.850221i | \(-0.323532\pi\) |
−0.999526 | + | 0.0307871i | \(0.990199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.8056 | − | 6.37206i | 0.791271 | − | 0.319002i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.22718 | + | 3.01791i | −0.261033 | + | 0.150707i | −0.624806 | − | 0.780780i | \(-0.714822\pi\) |
0.363773 | + | 0.931488i | \(0.381488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.10385 | − | 4.10141i | −0.353868 | − | 0.204306i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.9123 | − | 6.06290i | −0.740999 | − | 0.301268i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.73312i | 0.185044i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.6629 | + | 13.0844i | 1.12061 | + | 0.646984i | 0.941556 | − | 0.336856i | \(-0.109364\pi\) |
0.179052 | + | 0.983840i | \(0.442697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.2548 | − | 14.1985i | 0.653812 | − | 0.700360i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.3467 | + | 9.49292i | 1.00120 | + | 0.467116i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.05698 | + | 8.75894i | 0.248237 | + | 0.429959i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.02301 | + | 30.3444i | −0.343918 | + | 1.48597i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.51866i | 0.123045i | 0.998106 | + | 0.0615223i | \(0.0195955\pi\) | ||||
−0.998106 | + | 0.0615223i | \(0.980404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.4873i | 1.63207i | 0.578003 | + | 0.816034i | \(0.303832\pi\) | ||||
−0.578003 | + | 0.816034i | \(0.696168\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.493742 | + | 7.17345i | 0.0240066 | + | 0.348785i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.99595 | − | 10.3853i | −0.290846 | − | 0.503761i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.14247 | + | 8.77620i | 0.297255 | + | 0.424710i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.13951 | − | 2.93085i | −0.151577 | − | 0.141503i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0003 | + | 6.92836i | 0.578033 | + | 0.333727i | 0.760351 | − | 0.649512i | \(-0.225027\pi\) |
−0.182319 | + | 0.983240i | \(0.558360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.79368i | − | 0.470654i | −0.971916 | − | 0.235327i | \(-0.924384\pi\) | ||
0.971916 | − | 0.235327i | \(-0.0756161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.676669 | − | 2.21762i | −0.0324438 | − | 0.106327i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.4829 | + | 14.7126i | 1.21901 | + | 0.703798i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.99463 | + | 4.03835i | −0.333835 | + | 0.192740i | −0.657543 | − | 0.753417i | \(-0.728404\pi\) |
0.323707 | + | 0.946157i | \(0.395071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.1778 | − | 5.81875i | −0.960846 | − | 0.277083i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.84884 | + | 15.3266i | 0.420421 | + | 0.728191i | 0.995981 | − | 0.0895692i | \(-0.0285490\pi\) |
−0.575559 | + | 0.817760i | \(0.695216\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.9096 | + | 13.2269i | 1.08602 | + | 0.627014i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.53238 | − | 0.467581i | 0.0724791 | − | 0.0221158i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.4650i | − | 0.918609i | −0.888279 | − | 0.459305i | \(-0.848099\pi\) | ||
0.888279 | − | 0.459305i | \(-0.151901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00793 | − | 1.74578i | 0.0474614 | − | 0.0822056i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.2260 | + | 22.6159i | 1.13824 | + | 1.06259i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.58793 | − | 6.71059i | 0.449489 | − | 0.314597i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.75626 | + | 13.4342i | 0.362823 | + | 0.628427i | 0.988424 | − | 0.151715i | \(-0.0484797\pi\) |
−0.625601 | + | 0.780143i | \(0.715146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.3475 | − | 32.3245i | −0.576331 | − | 1.50878i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.857290i | 0.0399280i | 0.999801 | + | 0.0199640i | \(0.00635516\pi\) | ||||
−0.999801 | + | 0.0199640i | \(0.993645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.5731 | −1.74617 | −0.873086 | − | 0.487566i | \(-0.837885\pi\) | ||||
−0.873086 | + | 0.487566i | \(0.837885\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.31703 | − | 10.0112i | 0.107450 | − | 0.464259i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.69155 | − | 5.01807i | 0.402197 | − | 0.232208i | −0.285235 | − | 0.958458i | \(-0.592072\pi\) |
0.687431 | + | 0.726249i | \(0.258738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.0986 | − | 8.91063i | −0.881893 | − | 0.411455i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.8479 | + | 12.9275i | 0.638076 | + | 0.595668i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.98586 | + | 4.61064i | 0.367190 | + | 0.211997i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.69680 | 0.307270 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −31.5540 | + | 21.2333i | −1.44476 | + | 0.972208i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0594 | − | 19.1555i | 0.505318 | − | 0.875237i | −0.494663 | − | 0.869085i | \(-0.664708\pi\) |
0.999981 | − | 0.00615194i | \(-0.00195824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.97373 | + | 4.60364i | −0.363571 | + | 0.209908i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.5578 | − | 33.6296i | −0.616902 | − | 1.53020i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.57021 | + | 2.71969i | 0.0712997 | + | 0.123495i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2659 | + | 19.5131i | −0.510506 | + | 0.884223i | 0.489419 | + | 0.872049i | \(0.337209\pi\) |
−0.999926 | + | 0.0121746i | \(0.996125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.37696 | − | 17.6217i | −0.243155 | − | 0.796879i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1085 | 1.13313 | 0.566565 | − | 0.824017i | \(-0.308272\pi\) | ||||
0.566565 | + | 0.824017i | \(0.308272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.49190 | − | 4.31610i | 0.112230 | − | 0.194387i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.36387 | − | 4.83325i | 0.106248 | − | 0.217238i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.25801 | − | 14.4133i | −0.0564295 | − | 0.646526i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.19695 | + | 5.30986i | −0.411712 | + | 0.237702i | −0.691525 | − | 0.722353i | \(-0.743061\pi\) |
0.279813 | + | 0.960054i | \(0.409727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.09721 | − | 13.3821i | 0.138373 | − | 0.597869i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.3046 | 0.593223 | 0.296612 | − | 0.954998i | \(-0.404143\pi\) | ||||
0.296612 | + | 0.954998i | \(0.404143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.1892 | 1.16540 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.68861 | + | 11.6167i | −0.119405 | + | 0.515916i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.2595 | + | 11.6968i | −0.897985 | + | 0.518452i | −0.876546 | − | 0.481318i | \(-0.840158\pi\) |
−0.0214392 | + | 0.999770i | \(0.506825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7405 | + | 7.34385i | 0.696318 | + | 0.324873i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.0806 | + | 3.05413i | 0.842431 | + | 0.134843i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.81956 | + | 15.2759i | −0.388636 | + | 0.673138i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.40326 | −0.105695 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.15900 | + | 7.07558i | 0.0947695 | + | 0.310584i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.735700 | − | 1.27427i | 0.0322316 | − | 0.0558267i | −0.849460 | − | 0.527654i | \(-0.823072\pi\) |
0.881691 | + | 0.471827i | \(0.156405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.30372 | − | 9.18631i | −0.231915 | − | 0.401689i | 0.726456 | − | 0.687213i | \(-0.241166\pi\) |
−0.958372 | + | 0.285523i | \(0.907833\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.49904 | − | 5.08548i | −0.283641 | − | 0.221949i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.1290 | − | 11.0441i | 0.833272 | − | 0.481090i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.8039 | − | 34.3014i | 0.861040 | − | 1.49137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2131 | + | 21.1216i | 0.616797 | + | 0.916597i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.97185 | 0.215355 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.7845 | + | 6.22642i | 0.466254 | + | 0.269192i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.56725 | − | 8.93138i | −0.412857 | − | 0.385417i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.40331 | − | 6.59457i | 0.103518 | − | 0.284048i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0009 | + | 8.08343i | −0.601946 | + | 0.347534i | −0.769807 | − | 0.638277i | \(-0.779647\pi\) |
0.167861 | + | 0.985811i | \(0.446314\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.95367 | − | 8.44125i | 0.0838402 | − | 0.362249i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.88190 | −0.209118 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.4170i | − | 0.530914i | −0.964123 | − | 0.265457i | \(-0.914477\pi\) | ||
0.964123 | − | 0.265457i | \(-0.0855228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.834061 | + | 12.1178i | 0.0355969 | + | 0.517177i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.39159 | + | 2.41030i | 0.0592836 | + | 0.102682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.70648 | + | 11.0108i | 0.327713 | + | 0.468228i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.43126 | − | 7.87089i | −0.357887 | − | 0.334101i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.7167 | − | 18.5619i | 0.454081 | − | 0.786492i | −0.544554 | − | 0.838726i | \(-0.683301\pi\) |
0.998635 | + | 0.0522341i | \(0.0166342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.7431i | 0.961931i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.0617 | − | 3.37530i | 0.467026 | − | 0.142505i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.9430 | − | 10.3594i | −0.756205 | − | 0.436595i | 0.0717262 | − | 0.997424i | \(-0.477149\pi\) |
−0.827932 | + | 0.560829i | \(0.810483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.475020 | − | 0.822758i | −0.0199842 | − | 0.0346137i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.1979 | − | 17.4536i | −0.680248 | − | 0.732982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.8691 | − | 13.7808i | 1.00064 | − | 0.577722i | 0.0922056 | − | 0.995740i | \(-0.470608\pi\) |
0.908439 | + | 0.418018i | \(0.137275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.339940 | + | 0.196264i | 0.0142260 | + | 0.00821340i | 0.507096 | − | 0.861889i | \(-0.330719\pi\) |
−0.492870 | + | 0.870103i | \(0.664052\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.12246 | + | 20.0649i | 0.255770 | + | 0.838222i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 14.2488i | − | 0.594214i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.7927 | − | 7.38589i | −0.532569 | − | 0.307479i | 0.209493 | − | 0.977810i | \(-0.432819\pi\) |
−0.742062 | + | 0.670331i | \(0.766152\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.50016 | − | 1.40046i | −0.0623447 | − | 0.0582011i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.30083 | + | 14.9039i | 0.0539675 | + | 0.618319i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.35591 | − | 11.0088i | −0.263235 | − | 0.455936i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.2386 | − | 0.911205i | 0.547350 | − | 0.0376737i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.51421i | 0.145047i | 0.997367 | + | 0.0725236i | \(0.0231052\pi\) | ||||
−0.997367 | + | 0.0725236i | \(0.976895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3350i | 0.508256i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.62003 | − | 32.9239i | 0.313446 | − | 1.35431i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.8824 | + | 30.9732i | 0.734342 | + | 1.27192i | 0.955012 | + | 0.296568i | \(0.0958423\pi\) |
−0.220670 | + | 0.975349i | \(0.570824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.74011 | + | 31.3941i | 0.112334 | + | 1.28703i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.4192 | − | 18.6593i | 0.712919 | − | 0.763676i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.4819 | − | 20.4855i | −1.44975 | − | 0.837014i | −0.451284 | − | 0.892380i | \(-0.649034\pi\) |
−0.998466 | + | 0.0553669i | \(0.982367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1540i | 1.47475i | 0.675482 | + | 0.737377i | \(0.263936\pi\) | ||||
−0.675482 | + | 0.737377i | \(0.736064\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3413 | − | 19.8260i | −0.543300 | − | 0.807376i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.4817 | − | 8.93835i | −0.629419 | − | 0.363395i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.04038 | + | 5.21946i | −0.366938 | + | 0.211851i | −0.672120 | − | 0.740443i | \(-0.734616\pi\) |
0.305182 | + | 0.952294i | \(0.401283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.479865 | − | 3.39588i | 0.0194451 | − | 0.137608i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.96367 | − | 5.13323i | −0.119897 | − | 0.207668i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.37925 | − | 3.10571i | −0.217266 | − | 0.125439i | 0.387418 | − | 0.921904i | \(-0.373367\pi\) |
−0.604684 | + | 0.796466i | \(0.706700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.81774 | + | 5.95720i | 0.0732984 | + | 0.240217i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.4963i | − | 0.905669i | −0.891595 | − | 0.452834i | \(-0.850413\pi\) | ||
0.891595 | − | 0.452834i | \(-0.149587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.1624 | − | 24.5300i | 0.569235 | − | 0.985943i | −0.427407 | − | 0.904059i | \(-0.640573\pi\) |
0.996642 | − | 0.0818842i | \(-0.0260938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.49827 | − | 40.5978i | 0.260767 | − | 1.62914i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.4377 | + | 32.0584i | 0.898947 | + | 1.28439i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.37661 | + | 11.0446i | 0.255064 | + | 0.441785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.45629 | + | 6.29220i | −0.0581585 | + | 0.251286i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 24.7930i | − | 0.988563i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.51542 | −0.338993 | −0.169497 | − | 0.985531i | \(-0.554214\pi\) | ||||
−0.169497 | + | 0.985531i | \(0.554214\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.1834 | − | 5.82853i | −1.00095 | − | 0.231663i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.00758 | + | 4.04583i | −0.278087 | + | 0.160554i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0494 | − | 2.99902i | 0.675520 | − | 0.118825i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.20771 | − | 14.7371i | 0.285133 | − | 0.582992i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0793494 | + | 0.0458124i | 0.00313411 | + | 0.00180948i | 0.501566 | − | 0.865119i | \(-0.332757\pi\) |
−0.498432 | + | 0.866929i | \(0.666091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.89351 | −0.232417 | −0.116209 | − | 0.993225i | \(-0.537074\pi\) | ||||
−0.116209 | + | 0.993225i | \(0.537074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.2505 | + | 8.31503i | −1.07299 | + | 0.327404i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.05903 | − | 7.03045i | 0.159577 | − | 0.276396i | −0.775139 | − | 0.631791i | \(-0.782320\pi\) |
0.934716 | + | 0.355395i | \(0.115654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.36901 | + | 4.25450i | −0.289259 | + | 0.167004i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.36710 | − | 11.9708i | 0.367126 | − | 0.469172i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.7312 | − | 28.9792i | −0.654741 | − | 1.13404i | −0.981959 | − | 0.189095i | \(-0.939444\pi\) |
0.327218 | − | 0.944949i | \(-0.393889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8302 | − | 23.9547i | 0.540392 | − | 0.935986i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.9955 | + | 16.3399i | 0.428974 | + | 0.637481i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.5448 | −0.605540 | −0.302770 | − | 0.953064i | \(-0.597911\pi\) | ||||
−0.302770 | + | 0.953064i | \(0.597911\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4190 | − | 26.7065i | 0.599731 | − | 1.03876i | −0.393130 | − | 0.919483i | \(-0.628608\pi\) |
0.992861 | − | 0.119281i | \(-0.0380590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.8506 | + | 19.4648i | 0.809772 | + | 0.755952i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.9481 | − | 7.44072i | −0.618441 | − | 0.288539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.12838 | − | 2.96087i | 0.198572 | − | 0.114646i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.8615 | + | 2.97671i | 0.497254 | + | 0.115086i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.05974 | −0.156725 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.84855 | 0.148351 | 0.0741753 | − | 0.997245i | \(-0.476368\pi\) | ||||
0.0741753 | + | 0.997245i | \(0.476368\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.33899 | − | 8.74115i | −0.128518 | − | 0.336447i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.5497 | + | 18.7926i | −1.25099 | + | 0.722257i | −0.971305 | − | 0.237836i | \(-0.923562\pi\) |
−0.279680 | + | 0.960093i | \(0.590228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.403913 | + | 4.62773i | 0.0155008 | + | 0.177596i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.6337 | − | 19.9604i | 0.714046 | − | 0.764883i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.02051 | − | 1.76757i | 0.0390487 | − | 0.0676343i | −0.845841 | − | 0.533436i | \(-0.820901\pi\) |
0.884889 | + | 0.465802i | \(0.154234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.0584 | −0.766394 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.2296 | − | 8.91894i | 1.11518 | − | 0.340279i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.6761 | − | 27.1517i | 0.597210 | − | 1.03440i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7334 | + | 20.3229i | 0.446360 | + | 0.773119i | 0.998146 | − | 0.0608673i | \(-0.0193866\pi\) |
−0.551786 | + | 0.833986i | \(0.686053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.19151 | − | 5.00049i | 0.235196 | − | 0.189953i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.8548 | − | 16.0820i | 1.05659 | − | 0.610025i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.69401 | + | 11.5944i | −0.253554 | + | 0.439168i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.16868 | + | 30.0481i | 0.346791 | + | 1.13652i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.4603 | 0.583926 | 0.291963 | − | 0.956430i | \(-0.405692\pi\) | ||||
0.291963 | + | 0.956430i | \(0.405692\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9906 | + | 6.92275i | 0.452232 | + | 0.261096i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.06702 | − | 5.42777i | 0.190835 | − | 0.204421i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 35.1062 | + | 16.3791i | 1.32030 | + | 0.615999i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.7153 | − | 24.0843i | 1.56665 | − | 0.904505i | 0.570093 | − | 0.821580i | \(-0.306907\pi\) |
0.996556 | − | 0.0829254i | \(-0.0264263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.04643 | + | 15.2033i | 0.0392443 | + | 0.570169i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.2452 | 0.982891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.43523i | 0.165868i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.12976 | − | 2.11302i | −0.340957 | − | 0.0789123i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.49021 | − | 11.2414i | −0.242044 | − | 0.419232i | 0.719252 | − | 0.694749i | \(-0.244484\pi\) |
−0.961296 | + | 0.275517i | \(0.911151\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.3763 | + | 14.9613i | −0.796094 | + | 0.557186i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.3886 | + | 27.1961i | −0.944211 | + | 1.01143i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.673858 | − | 1.16716i | 0.0250264 | − | 0.0433471i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 12.0095i | − | 0.445406i | −0.974886 | − | 0.222703i | \(-0.928512\pi\) | ||
0.974886 | − | 0.222703i | \(-0.0714880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.52704 | − | 26.4282i | −0.204705 | − | 0.978824i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.0370 | − | 30.6209i | −1.96164 | − | 1.13256i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.29808 | − | 7.44449i | −0.158753 | − | 0.274968i | 0.775666 | − | 0.631143i | \(-0.217414\pi\) |
−0.934419 | + | 0.356175i | \(0.884081\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.82673 | + | 19.3318i | 0.362465 | + | 0.713065i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.91700 | − | 3.99353i | 0.254791 | − | 0.147104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.25350 | − | 1.30106i | −0.0828963 | − | 0.0478602i | 0.457979 | − | 0.888963i | \(-0.348574\pi\) |
−0.540875 | + | 0.841103i | \(0.681907\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.2356 | + | 4.64891i | −0.559695 | + | 0.170782i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.4061i | − | 0.491823i | −0.969292 | − | 0.245911i | \(-0.920913\pi\) | ||
0.969292 | − | 0.245911i | \(-0.0790872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.43281 | − | 0.827235i | −0.0524942 | − | 0.0303075i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.45305 | + | 15.2387i | −0.272693 | + | 0.557556i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5623 | + | 15.0912i | 0.385939 | + | 0.551420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.86182 | + | 13.6171i | 0.286882 | + | 0.496894i | 0.973064 | − | 0.230536i | \(-0.0740480\pi\) |
−0.686182 | + | 0.727430i | \(0.740715\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.5047 | − | 7.75445i | −1.22098 | − | 0.282588i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 34.2244i | − | 1.24555i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.7626i | − | 1.77231i | −0.463391 | − | 0.886154i | \(-0.653367\pi\) | ||
0.463391 | − | 0.886154i | \(-0.346633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.3879 | + | 3.09854i | 0.485950 | + | 0.112470i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7170 | + | 37.6149i | 0.787240 | + | 1.36354i | 0.927652 | + | 0.373447i | \(0.121824\pi\) |
−0.140411 | + | 0.990093i | \(0.544842\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.54411 | − | 3.05321i | −0.236913 | − | 0.110534i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.6993 | + | 32.0994i | −0.567611 | + | 1.16056i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.1747 | − | 10.4932i | −0.656252 | − | 0.378887i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 23.9226i | − | 0.862670i | −0.902192 | − | 0.431335i | \(-0.858043\pi\) | ||
0.902192 | − | 0.431335i | \(-0.141957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.4663 | + | 4.41417i | −0.520993 | + | 0.158972i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3402 | − | 8.27930i | −0.515780 | − | 0.297786i | 0.219427 | − | 0.975629i | \(-0.429581\pi\) |
−0.735206 | + | 0.677843i | \(0.762915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.17284 | − | 2.98654i | 0.185814 | − | 0.107280i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.37940 | − | 15.8238i | −0.228860 | − | 0.567676i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.73823 | − | 6.47480i | −0.133936 | − | 0.231984i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.74856 | + | 2.74158i | 0.169917 | + | 0.0981014i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.45226 | − | 3.01816i | 0.0876366 | − | 0.107860i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 19.5631i | − | 0.698237i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.81161 | + | 10.0660i | −0.207162 | + | 0.358814i | −0.950819 | − | 0.309746i | \(-0.899756\pi\) |
0.743658 | + | 0.668561i | \(0.233089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.3966 | − | 25.0623i | 0.832940 | − | 0.892242i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.122192 | − | 1.39998i | −0.00434463 | − | 0.0497775i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.00642 | − | 8.67137i | −0.177783 | − | 0.307930i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 38.2641 | + | 8.85597i | 1.35709 | + | 0.314089i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.35681i | − | 0.0834824i | −0.999128 | − | 0.0417412i | \(-0.986709\pi\) | ||
0.999128 | − | 0.0417412i | \(-0.0132905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9609 | 0.564657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.04672 | + | 44.2650i | 0.107651 | + | 1.56403i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.70077 | + | 3.29134i | −0.201176 | + | 0.116149i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.8316 | + | 33.9327i | −0.557991 | + | 1.19597i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.09944 | − | 1.17772i | 0.0387022 | − | 0.0414576i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.6070 | − | 22.8671i | −1.39251 | − | 0.803964i | −0.398914 | − | 0.916988i | \(-0.630613\pi\) |
−0.993592 | + | 0.113024i | \(0.963946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.844573 | 0.0296570 | 0.0148285 | − | 0.999890i | \(-0.495280\pi\) | ||||
0.0148285 | + | 0.999890i | \(0.495280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.35233 | − | 14.2637i | −0.152643 | − | 0.500249i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.51282 | + | 16.4767i | −0.333219 | + | 0.577153i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.6182 | − | 17.1000i | 1.03621 | − | 0.598255i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.3161 | + | 7.05818i | 0.640015 | + | 0.246633i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4890 | + | 32.0239i | 0.645272 | + | 1.11764i | 0.984239 | + | 0.176845i | \(0.0565892\pi\) |
−0.338967 | + | 0.940798i | \(0.610078\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.62518 | − | 6.27899i | 0.126366 | − | 0.218872i | −0.795900 | − | 0.605428i | \(-0.793002\pi\) |
0.922266 | + | 0.386556i | \(0.126335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.99130 | − | 0.912746i | 0.104144 | − | 0.0317777i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.4014 | 1.50921 | 0.754607 | − | 0.656176i | \(-0.227827\pi\) | ||||
0.754607 | + | 0.656176i | \(0.227827\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.7789 | + | 22.1338i | −0.443830 | + | 0.768737i | −0.997970 | − | 0.0636869i | \(-0.979714\pi\) |
0.554139 | + | 0.832424i | \(0.313047\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.8818 | + | 37.3652i | −1.21004 | + | 1.29619i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.9612 | + | 43.7970i | −0.553024 | + | 1.51748i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.2842 | + | 7.09229i | −0.425113 | + | 0.245439i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.1006 | − | 6.15019i | 0.556518 | − | 0.212582i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2288 | −0.663854 | −0.331927 | − | 0.943305i | \(-0.607699\pi\) | ||||
−0.331927 | + | 0.943305i | \(0.607699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4399 | −0.980686 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.9865 | + | 8.32884i | 1.23944 | + | 0.286860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6636 | − | 6.15665i | 0.366840 | − | 0.211795i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.1628 | − | 21.6642i | −0.520999 | − | 0.744389i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.3973 | + | 24.6429i | 0.905954 | + | 0.845741i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.7295 | − | 25.5123i | 0.504921 | − | 0.874549i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.5472 | −1.49103 | −0.745514 | − | 0.666489i | \(-0.767796\pi\) | ||||
−0.745514 | + | 0.666489i | \(0.767796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.1405 | − | 16.5555i | −0.380997 | − | 0.566185i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.41603 | + | 7.64878i | −0.150849 | + | 0.261277i | −0.931540 | − | 0.363640i | \(-0.881534\pi\) |
0.780691 | + | 0.624917i | \(0.214867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.94564 | − | 5.10200i | −0.100504 | − | 0.174078i | 0.811388 | − | 0.584507i | \(-0.198712\pi\) |
−0.911892 | + | 0.410429i | \(0.865379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.28906 | + | 9.12236i | −0.0439311 | + | 0.310889i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.80835 | − | 1.62140i | 0.0955974 | − | 0.0551932i | −0.451439 | − | 0.892302i | \(-0.649089\pi\) |
0.547037 | + | 0.837109i | \(0.315756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.81966 | − | 6.61584i | 0.129872 | − | 0.224945i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −45.3020 | + | 13.8232i | −1.53854 | + | 0.469460i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.09344 | −0.172783 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.0599 | + | 9.84955i | 0.578053 | + | 0.333739i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.31420 | + | 4.73170i | −0.0783240 | + | 0.160144i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.79835 | + | 32.0614i | 0.0946015 | + | 1.08387i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.1526 | + | 22.6048i | −1.32209 | + | 0.763309i | −0.984062 | − | 0.177828i | \(-0.943093\pi\) |
−0.338028 | + | 0.941136i | \(0.609760\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.1154 | − | 5.11847i | −0.745934 | − | 0.172642i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.1014 | −0.946759 | −0.473380 | − | 0.880859i | \(-0.656966\pi\) | ||||
−0.473380 | + | 0.880859i | \(0.656966\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.45102i | 0.183442i | 0.995785 | + | 0.0917208i | \(0.0292367\pi\) | ||||
−0.995785 | + | 0.0917208i | \(0.970763\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.92799 | − | 25.6131i | 0.199267 | − | 0.860975i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.3783 | + | 43.9566i | 0.852122 | + | 1.47592i | 0.879290 | + | 0.476287i | \(0.158018\pi\) |
−0.0271684 | + | 0.999631i | \(0.508649\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.9239 | + | 1.04073i | −0.399914 | + | 0.0349049i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.93914 | − | 1.23640i | 0.299472 | − | 0.0414211i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.45664 | + | 7.71912i | −0.149136 | + | 0.258311i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.5158i | 0.451783i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.89147 | + | 32.4168i | 0.330266 | + | 1.08237i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.14982 | + | 1.24120i | 0.0717005 | + | 0.0413963i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.2119 | + | 73.1132i | 1.40628 | + | 2.43575i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −41.7291 | − | 5.89666i | −1.38866 | − | 0.196228i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.74871 | + | 4.47372i | −0.257576 | + | 0.148711i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.66652 | + | 5.00362i | 0.287767 | + | 0.166142i | 0.636934 | − | 0.770918i | \(-0.280202\pi\) |
−0.349167 | + | 0.937060i | \(0.613536\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.5233 | + | 36.4431i | 0.813387 | + | 1.20874i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5940i | 0.483521i | 0.970336 | + | 0.241761i | \(0.0777249\pi\) | ||||
−0.970336 | + | 0.241761i | \(0.922275\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.91019 | − | 2.83490i | −0.162503 | − | 0.0938214i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.55953 | − | 9.16893i | 0.282969 | − | 0.303115i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.5208 | − | 23.4612i | 1.10695 | − | 0.774757i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.14316 | + | 1.98001i | 0.0377093 | + | 0.0653145i | 0.884264 | − | 0.466987i | \(-0.154661\pi\) |
−0.846555 | + | 0.532302i | \(0.821327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.28079 | − | 31.4582i | 0.239910 | − | 1.03658i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.5235i | 0.445132i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.70450i | − | 0.220443i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.5155 | + | 2.03153i | −0.969417 | + | 0.0667242i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.71753 | + | 16.8313i | 0.318822 | + | 0.552216i | 0.980242 | − | 0.197799i | \(-0.0633795\pi\) |
−0.661421 | + | 0.750015i | \(0.730046\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.7246 | − | 19.9483i | −0.548128 | − | 0.653780i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.1420 | + | 23.4710i | 0.823114 | + | 0.768407i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.3430 | − | 5.97152i | −0.338252 | − | 0.195290i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 21.6552i | − | 0.707445i | −0.935350 | − | 0.353723i | \(-0.884916\pi\) | ||
0.935350 | − | 0.353723i | \(-0.115084\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.36065 | − | 4.45918i | −0.0444030 | − | 0.145520i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.82024 | − | 3.36032i | −0.189735 | − | 0.109543i | 0.402124 | − | 0.915585i | \(-0.368272\pi\) |
−0.591858 | + | 0.806042i | \(0.701605\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.7764 | + | 7.95381i | −0.448622 | + | 0.259012i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.76053 | + | 24.5265i | −0.0572701 | + | 0.797849i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.5673 | − | 18.3031i | −0.343392 | − | 0.594772i | 0.641668 | − | 0.766982i | \(-0.278243\pi\) |
−0.985060 | + | 0.172210i | \(0.944909\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0602 | − | 8.11768i | −0.456414 | − | 0.263511i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.7357 | − | 5.41174i | 0.575118 | − | 0.175488i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.18327i | 0.0707230i | 0.999375 | + | 0.0353615i | \(0.0112583\pi\) | ||||
−0.999375 | + | 0.0353615i | \(0.988742\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8317 | − | 18.7611i | 0.350507 | − | 0.607096i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.950102 | + | 0.886955i | 0.0307124 | + | 0.0286712i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.8880 | − | 12.5448i | −0.868259 | − | 0.405094i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.99900 | − | 17.3188i | −0.322548 | − | 0.558670i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.43422 | + | 20.8373i | 0.0462170 | + | 0.671473i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.11931i | 0.0682229i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.1413 | 0.808490 | 0.404245 | − | 0.914651i | \(-0.367534\pi\) | ||||
0.404245 | + | 0.914651i | \(0.367534\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.67175 | − | 41.7888i | 0.310701 | − | 1.34245i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.0100 | − | 17.3263i | 0.963065 | − | 0.556026i | 0.0659503 | − | 0.997823i | \(-0.478992\pi\) |
0.897115 | + | 0.441797i | \(0.145659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.3969 | − | 4.13685i | 1.51947 | − | 0.132621i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.63841 | + | 5.26366i | 0.180574 | + | 0.168572i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.22538 | + | 1.86218i | 0.103189 | + | 0.0595763i | 0.550706 | − | 0.834699i | \(-0.314358\pi\) |
−0.447517 | + | 0.894275i | \(0.647692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.8297 | −0.473960 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.57137 | − | 6.79333i | −0.145953 | − | 0.216894i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.3018 | + | 47.2881i | −0.870792 | + | 1.50826i | −0.00961355 | + | 0.999954i | \(0.503060\pi\) |
−0.861179 | + | 0.508302i | \(0.830273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.2227 | + | 17.4491i | −0.962977 | + | 0.555975i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1869 | − | 4.10685i | 0.324251 | − | 0.130722i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.3837 | − | 63.0185i | −1.15694 | − | 2.00387i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1790 | − | 43.6114i | 0.799839 | − | 1.38536i | −0.119882 | − | 0.992788i | \(-0.538252\pi\) |
0.919721 | − | 0.392573i | \(-0.128415\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.0042 | + | 36.0635i | 0.349207 | + | 1.14444i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.3603 | −0.835679 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.7609 | + | 22.1025i | −0.404141 | + | 0.699993i | −0.994221 | − | 0.107352i | \(-0.965763\pi\) |
0.590080 | + | 0.807345i | \(0.299096\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.05765 | − | 19.1026i | 0.0967398 | − | 0.604380i |
(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 | 672.2.bi.c.17.14 | 48 | ||
3.2 | odd | 2 | inner | 672.2.bi.c.17.20 | 48 | ||
4.3 | odd | 2 | 168.2.ba.c.101.15 | yes | 48 | ||
7.5 | odd | 6 | inner | 672.2.bi.c.593.5 | 48 | ||
8.3 | odd | 2 | 168.2.ba.c.101.7 | yes | 48 | ||
8.5 | even | 2 | inner | 672.2.bi.c.17.11 | 48 | ||
12.11 | even | 2 | 168.2.ba.c.101.10 | yes | 48 | ||
21.5 | even | 6 | inner | 672.2.bi.c.593.11 | 48 | ||
24.5 | odd | 2 | inner | 672.2.bi.c.17.5 | 48 | ||
24.11 | even | 2 | 168.2.ba.c.101.18 | yes | 48 | ||
28.19 | even | 6 | 168.2.ba.c.5.18 | yes | 48 | ||
56.5 | odd | 6 | inner | 672.2.bi.c.593.20 | 48 | ||
56.19 | even | 6 | 168.2.ba.c.5.10 | yes | 48 | ||
84.47 | odd | 6 | 168.2.ba.c.5.7 | ✓ | 48 | ||
168.5 | even | 6 | inner | 672.2.bi.c.593.14 | 48 | ||
168.131 | odd | 6 | 168.2.ba.c.5.15 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.ba.c.5.7 | ✓ | 48 | 84.47 | odd | 6 | ||
168.2.ba.c.5.10 | yes | 48 | 56.19 | even | 6 | ||
168.2.ba.c.5.15 | yes | 48 | 168.131 | odd | 6 | ||
168.2.ba.c.5.18 | yes | 48 | 28.19 | even | 6 | ||
168.2.ba.c.101.7 | yes | 48 | 8.3 | odd | 2 | ||
168.2.ba.c.101.10 | yes | 48 | 12.11 | even | 2 | ||
168.2.ba.c.101.15 | yes | 48 | 4.3 | odd | 2 | ||
168.2.ba.c.101.18 | yes | 48 | 24.11 | even | 2 | ||
672.2.bi.c.17.5 | 48 | 24.5 | odd | 2 | inner | ||
672.2.bi.c.17.11 | 48 | 8.5 | even | 2 | inner | ||
672.2.bi.c.17.14 | 48 | 1.1 | even | 1 | trivial | ||
672.2.bi.c.17.20 | 48 | 3.2 | odd | 2 | inner | ||
672.2.bi.c.593.5 | 48 | 7.5 | odd | 6 | inner | ||
672.2.bi.c.593.11 | 48 | 21.5 | even | 6 | inner | ||
672.2.bi.c.593.14 | 48 | 168.5 | even | 6 | inner | ||
672.2.bi.c.593.20 | 48 | 56.5 | odd | 6 | inner |