Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(193,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.r (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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 193.3 | ||
Character | \(\chi\) | \(=\) | 1152.193 |
Dual form | 1152.2.r.g.961.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.37296 | + | 1.05593i | −0.792676 | + | 0.609643i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.35903 | − | 1.93934i | −1.50221 | − | 0.867299i | −0.999997 | − | 0.00255286i | \(-0.999187\pi\) |
−0.502209 | − | 0.864746i | \(-0.667479\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.14978 | + | 1.99147i | 0.434575 | + | 0.752707i | 0.997261 | − | 0.0739645i | \(-0.0235651\pi\) |
−0.562686 | + | 0.826671i | \(0.690232\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.770012 | − | 2.89950i | 0.256671 | − | 0.966499i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.60542 | + | 2.08159i | −1.08708 | + | 0.627624i | −0.932797 | − | 0.360403i | \(-0.882639\pi\) |
−0.154280 | + | 0.988027i | \(0.549306\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.846691 | + | 0.488838i | 0.234830 | + | 0.135579i | 0.612798 | − | 0.790239i | \(-0.290044\pi\) |
−0.377968 | + | 0.925819i | \(0.623377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.65962 | − | 0.884289i | 1.71951 | − | 0.228322i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.79209 | −1.64732 | −0.823662 | − | 0.567082i | \(-0.808072\pi\) | ||||
−0.823662 | + | 0.567082i | \(0.808072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.729224i | − | 0.167296i | −0.996495 | − | 0.0836478i | \(-0.973343\pi\) | ||
0.996495 | − | 0.0836478i | \(-0.0266571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.68146 | − | 1.52012i | −0.803360 | − | 0.331717i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.94585 | − | 5.10236i | 0.614251 | − | 1.06391i | −0.376264 | − | 0.926513i | \(-0.622791\pi\) |
0.990515 | − | 0.137402i | \(-0.0438753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.02208 | + | 8.69849i | 1.00442 | + | 1.73970i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.00448 | + | 4.79396i | 0.385763 | + | 0.922598i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.32630 | − | 2.49779i | 0.803374 | − | 0.463828i | −0.0412755 | − | 0.999148i | \(-0.513142\pi\) |
0.844650 | + | 0.535320i | \(0.179809\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.53163 | − | 2.65287i | 0.275089 | − | 0.476469i | −0.695068 | − | 0.718944i | \(-0.744626\pi\) |
0.970158 | + | 0.242475i | \(0.0779592\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.75206 | − | 6.66502i | 0.479073 | − | 1.16023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 8.91924i | − | 1.50763i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.11690i | 0.183618i | 0.995777 | + | 0.0918089i | \(0.0292649\pi\) | ||||
−0.995777 | + | 0.0918089i | \(0.970735\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.67865 | + | 0.222897i | −0.268799 | + | 0.0356921i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12603 | + | 5.41445i | −0.488204 | + | 0.845594i | −0.999908 | − | 0.0135675i | \(-0.995681\pi\) |
0.511704 | + | 0.859162i | \(0.329015\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.80283 | − | 2.77291i | 0.732424 | − | 0.422865i | −0.0868842 | − | 0.996218i | \(-0.527691\pi\) |
0.819308 | + | 0.573353i | \(0.194358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.20961 | + | 8.24620i | −1.22382 | + | 1.22927i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.86355 | + | 8.42391i | 0.709421 | + | 1.22875i | 0.965072 | + | 0.261985i | \(0.0843770\pi\) |
−0.255651 | + | 0.966769i | \(0.582290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.856020 | − | 1.48267i | 0.122289 | − | 0.211810i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.32523 | − | 7.17199i | 1.30579 | − | 1.00428i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.81170i | − | 0.935660i | −0.883819 | − | 0.467830i | \(-0.845036\pi\) | ||
0.883819 | − | 0.467830i | \(-0.154964\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.1477 | 2.17735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.770012 | + | 1.00119i | 0.101991 | + | 0.132611i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6458 | + | 6.14633i | 1.38596 | + | 0.800184i | 0.992857 | − | 0.119311i | \(-0.0380686\pi\) |
0.393102 | + | 0.919495i | \(0.371402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8032 | − | 6.23724i | 1.38321 | − | 0.798597i | 0.390672 | − | 0.920530i | \(-0.372243\pi\) |
0.992538 | + | 0.121933i | \(0.0389093\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.65962 | − | 1.80032i | 0.839033 | − | 0.226819i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.89604 | − | 3.28404i | −0.235175 | − | 0.407336i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0524343 | − | 0.0302730i | −0.00640587 | − | 0.00369843i | 0.496794 | − | 0.867869i | \(-0.334511\pi\) |
−0.503200 | + | 0.864170i | \(0.667844\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.34323 | + | 10.1159i | 0.161706 | + | 1.21781i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7904 | 1.51794 | 0.758968 | − | 0.651128i | \(-0.225704\pi\) | ||||
0.758968 | + | 0.651128i | \(0.225704\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.71204 | −0.200379 | −0.100190 | − | 0.994968i | \(-0.531945\pi\) | ||||
−0.100190 | + | 0.994968i | \(0.531945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.0801 | − | 6.63966i | −1.85677 | − | 0.766682i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.29088 | − | 4.78674i | −0.944833 | − | 0.545500i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.77427 | − | 10.0013i | −0.649657 | − | 1.12524i | −0.983205 | − | 0.182505i | \(-0.941579\pi\) |
0.333548 | − | 0.942733i | \(-0.391754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.81416 | − | 4.46529i | −0.868240 | − | 0.496144i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.35637 | + | 3.66985i | −0.697702 | + | 0.402818i | −0.806491 | − | 0.591246i | \(-0.798636\pi\) |
0.108789 | + | 0.994065i | \(0.465303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.8149 | + | 13.1722i | 2.47462 | + | 1.42872i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.30232 | + | 7.99764i | −0.354046 | + | 0.857437i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3321 | 1.09520 | 0.547601 | − | 0.836740i | \(-0.315541\pi\) | ||||
0.547601 | + | 0.836740i | \(0.315541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.24822i | 0.235677i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.698385 | + | 5.25957i | 0.0724191 | + | 0.545392i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.41421 | + | 2.44949i | −0.145095 | + | 0.251312i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.66606 | − | 8.08185i | −0.473766 | − | 0.820587i | 0.525783 | − | 0.850619i | \(-0.323772\pi\) |
−0.999549 | + | 0.0300318i | \(0.990439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.25935 | + | 12.0568i | 0.327577 | + | 1.21175i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.29357 | − | 3.05624i | 0.526730 | − | 0.304108i | −0.212954 | − | 0.977062i | \(-0.568308\pi\) |
0.739684 | + | 0.672955i | \(0.234975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.39242 | + | 9.33994i | −0.531331 | + | 0.920292i | 0.468000 | + | 0.883728i | \(0.344975\pi\) |
−0.999331 | + | 0.0365638i | \(0.988359\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.41812 | + | 12.2457i | 0.919114 | + | 1.19506i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.608132i | − | 0.0587904i | −0.999568 | − | 0.0293952i | \(-0.990642\pi\) | ||
0.999568 | − | 0.0293952i | \(-0.00935813\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8475i | 1.42213i | 0.703124 | + | 0.711067i | \(0.251788\pi\) | ||||
−0.703124 | + | 0.711067i | \(0.748212\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.17938 | − | 1.53346i | −0.111941 | − | 0.145549i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.98205 | − | 10.3612i | 0.562744 | − | 0.974701i | −0.434512 | − | 0.900666i | \(-0.643079\pi\) |
0.997256 | − | 0.0740351i | \(-0.0235877\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.7904 | + | 11.4260i | −1.84546 | + | 1.06548i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.06935 | − | 2.07857i | 0.191311 | − | 0.192164i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.80939 | − | 13.5263i | −0.715886 | − | 1.23995i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.16606 | − | 5.48377i | 0.287823 | − | 0.498524i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.42539 | − | 10.7347i | −0.128523 | − | 0.967913i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 19.5646i | − | 1.74992i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.48528 | 0.752947 | 0.376473 | − | 0.926427i | \(-0.377137\pi\) | ||||
0.376473 | + | 0.926427i | \(0.377137\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.66606 | + | 8.87855i | −0.322778 | + | 0.781713i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.69741 | + | 3.86675i | 0.585155 | + | 0.337839i | 0.763179 | − | 0.646187i | \(-0.223637\pi\) |
−0.178024 | + | 0.984026i | \(0.556971\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.45223 | − | 0.838446i | 0.125924 | − | 0.0727025i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.56399 | − | 19.9904i | 0.220673 | − | 1.72050i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.91812 | + | 6.78638i | 0.334748 | + | 0.579800i | 0.983436 | − | 0.181254i | \(-0.0580156\pi\) |
−0.648689 | + | 0.761054i | \(0.724682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.33004 | − | 1.92260i | −0.282450 | − | 0.163073i | 0.352082 | − | 0.935969i | \(-0.385474\pi\) |
−0.634532 | + | 0.772897i | \(0.718807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.5725 | − | 6.43007i | −1.31144 | − | 0.541510i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.07024 | −0.340371 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.3763 | −1.60911 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.390323 | + | 2.93954i | 0.0321933 | + | 0.242449i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.32361 | − | 4.22829i | −0.599973 | − | 0.346395i | 0.169058 | − | 0.985606i | \(-0.445928\pi\) |
−0.769031 | + | 0.639211i | \(0.779261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.71101 | − | 4.69560i | −0.220619 | − | 0.382123i | 0.734377 | − | 0.678741i | \(-0.237474\pi\) |
−0.954996 | + | 0.296619i | \(0.904141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.22999 | + | 19.6936i | −0.422819 | + | 1.59214i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2896 | + | 5.94071i | −0.826482 | + | 0.477169i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.50734 | + | 2.02496i | 0.279916 | + | 0.161610i | 0.633386 | − | 0.773836i | \(-0.281665\pi\) |
−0.353469 | + | 0.935446i | \(0.614998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.19270 | + | 9.35216i | 0.570418 | + | 0.741675i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5483 | 1.06775 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.39102i | 0.735562i | 0.929913 | + | 0.367781i | \(0.119882\pi\) | ||||
−0.929913 | + | 0.367781i | \(0.880118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.1700 | + | 17.0508i | −1.72593 | + | 1.32741i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.92681 | + | 13.7296i | −0.613395 | + | 1.06243i | 0.377269 | + | 0.926104i | \(0.376863\pi\) |
−0.990664 | + | 0.136328i | \(0.956470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.02208 | − | 10.4305i | −0.463237 | − | 0.802349i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.11438 | − | 0.561511i | −0.161691 | − | 0.0429398i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.21073 | + | 1.85371i | −0.244107 | + | 0.140935i | −0.617063 | − | 0.786914i | \(-0.711678\pi\) |
0.372956 | + | 0.927849i | \(0.378344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5485 | + | 20.0027i | −0.872988 | + | 1.51206i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.1063 | + | 2.80257i | −1.58644 | + | 0.210654i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 22.1833i | − | 1.65806i | −0.559206 | − | 0.829029i | \(-0.688894\pi\) | ||
0.559206 | − | 0.829029i | \(-0.311106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.1998i | − | 1.50144i | −0.660620 | − | 0.750720i | \(-0.729707\pi\) | ||
0.660620 | − | 0.750720i | \(-0.270293\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.24623 | + | 19.9709i | −0.609579 | + | 1.47629i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.16606 | − | 3.75172i | 0.159252 | − | 0.275832i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.4884 | − | 14.1384i | 1.79077 | − | 1.03390i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.24234 | + | 9.50387i | −0.526803 | + | 0.691304i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.27776 | − | 10.8734i | −0.454243 | − | 0.786772i | 0.544401 | − | 0.838825i | \(-0.316757\pi\) |
−0.998644 | + | 0.0520530i | \(0.983424\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.66606 | − | 6.34979i | 0.263888 | − | 0.457068i | −0.703383 | − | 0.710811i | \(-0.748328\pi\) |
0.967272 | + | 0.253742i | \(0.0816616\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.07091 | + | 2.50675i | 0.434747 | + | 0.179512i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 25.5059i | − | 1.81722i | −0.417647 | − | 0.908609i | \(-0.637145\pi\) | ||
0.417647 | − | 0.908609i | \(-0.362855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.6876 | −1.46650 | −0.733252 | − | 0.679957i | \(-0.761998\pi\) | ||||
−0.733252 | + | 0.679957i | \(0.761998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.103956 | − | 0.0138037i | 0.00733250 | − | 0.000973637i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.94857 | + | 5.74381i | 0.698253 | + | 0.403137i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 21.0009 | − | 12.1249i | 1.46677 | − | 0.846838i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.5259 | − | 12.4703i | −0.870612 | − | 0.866749i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.51795 | + | 2.62916i | 0.104999 | + | 0.181863i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.18585 | + | 3.57140i | 0.425851 | + | 0.245865i | 0.697578 | − | 0.716509i | \(-0.254261\pi\) |
−0.271726 | + | 0.962375i | \(0.587595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.5606 | + | 13.5058i | −1.20323 | + | 0.925400i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.5105 | −1.46700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.04415 | 0.478188 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.35055 | − | 1.80780i | 0.158836 | − | 0.122160i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.75080 | − | 3.32023i | −0.386841 | − | 0.223343i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.32915 | − | 4.03421i | −0.155972 | − | 0.270151i | 0.777441 | − | 0.628956i | \(-0.216518\pi\) |
−0.933412 | + | 0.358805i | \(0.883184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29.0883 | − | 7.86355i | 1.93922 | − | 0.524237i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.39503 | − | 4.84688i | 0.557198 | − | 0.321698i | −0.194822 | − | 0.980839i | \(-0.562413\pi\) |
0.752020 | + | 0.659140i | \(0.229080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.26619 | + | 1.88574i | 0.215836 | + | 0.124613i | 0.604021 | − | 0.796969i | \(-0.293564\pi\) |
−0.388185 | + | 0.921582i | \(0.626898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4375 | − | 2.18263i | 1.08151 | − | 0.143606i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.95585 | 0.128132 | 0.0640659 | − | 0.997946i | \(-0.479593\pi\) | ||||
0.0640659 | + | 0.997946i | \(0.479593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 37.7283i | − | 2.46112i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.4886 | + | 7.63414i | 1.20096 | + | 0.495891i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.78125 | − | 11.7455i | 0.438643 | − | 0.759751i | −0.558942 | − | 0.829206i | \(-0.688793\pi\) |
0.997585 | + | 0.0694552i | \(0.0221261\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.21204 | − | 2.09932i | −0.0780744 | − | 0.135229i | 0.824345 | − | 0.566088i | \(-0.191544\pi\) |
−0.902419 | + | 0.430859i | \(0.858210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4435 | − | 2.12058i | 0.990704 | − | 0.136035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.75080 | + | 3.32023i | −0.367405 | + | 0.212122i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.356472 | − | 0.617428i | 0.0226818 | − | 0.0392860i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.85189 | − | 11.7504i | 0.307476 | − | 0.744654i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.7914i | 1.43858i | 0.694708 | + | 0.719291i | \(0.255533\pi\) | ||||
−0.694708 | + | 0.719291i | \(0.744467\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.5282i | 1.54208i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −45.2327 | + | 6.00617i | −2.83258 | + | 0.376121i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.78796 | − | 3.09684i | 0.111530 | − | 0.193175i | −0.804857 | − | 0.593468i | \(-0.797758\pi\) |
0.916387 | + | 0.400293i | \(0.131092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.22429 | + | 1.28419i | −0.138210 | + | 0.0797958i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.91103 | − | 14.4674i | −0.242087 | − | 0.895511i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0802 | + | 22.6555i | 0.806558 | + | 1.39700i | 0.915234 | + | 0.402923i | \(0.132006\pi\) |
−0.108676 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.2102 | + | 22.8808i | −0.811497 | + | 1.40555i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.1855 | + | 10.9100i | −0.868140 | + | 0.667682i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 14.5691i | − | 0.888291i | −0.895955 | − | 0.444146i | \(-0.853507\pi\) | ||
0.895955 | − | 0.444146i | \(-0.146493\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3714 | 0.751512 | 0.375756 | − | 0.926719i | \(-0.377383\pi\) | ||||
0.375756 | + | 0.926719i | \(0.377383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.37397 | − | 3.08670i | −0.143679 | − | 0.186816i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.2134 | − | 20.9078i | −2.18375 | − | 1.26079i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0771 | + | 5.81802i | −0.605474 | + | 0.349571i | −0.771192 | − | 0.636602i | \(-0.780339\pi\) |
0.165718 | + | 0.986173i | \(0.447006\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.51260 | − | 6.48370i | −0.389899 | − | 0.388169i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.89604 | − | 8.48020i | −0.292073 | − | 0.505886i | 0.682226 | − | 0.731141i | \(-0.261012\pi\) |
−0.974300 | + | 0.225255i | \(0.927679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0400 | + | 8.68335i | 0.894036 | + | 0.516172i | 0.875260 | − | 0.483652i | \(-0.160690\pi\) |
0.0187752 | + | 0.999824i | \(0.494023\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.644845 | − | 4.85635i | −0.0381973 | − | 0.287666i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.3770 | −0.848646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.1325 | 1.71367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.9402 | + | 6.16897i | 0.875808 | + | 0.361631i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.14526 | + | 2.97062i | 0.300589 | + | 0.173545i | 0.642708 | − | 0.766112i | \(-0.277811\pi\) |
−0.342118 | + | 0.939657i | \(0.611144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.8396 | − | 41.2915i | −1.38800 | − | 2.40408i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.2061 | − | 13.1117i | −0.998398 | − | 0.760821i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.98845 | − | 2.88008i | 0.288489 | − | 0.166559i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0444 | + | 6.37647i | 0.636587 | + | 0.367534i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.04065 | + | 9.78574i | −0.232129 | + | 0.562176i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −48.3845 | −2.77049 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.3867i | 1.67718i | 0.544759 | + | 0.838592i | \(0.316621\pi\) | ||||
−0.544759 | + | 0.838592i | \(0.683379\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.45880 | − | 18.5174i | −0.139876 | − | 1.05342i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.18849 | + | 12.4508i | −0.407622 | + | 0.706021i | −0.994623 | − | 0.103565i | \(-0.966975\pi\) |
0.587001 | + | 0.809586i | \(0.300308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.50000 | + | 4.33013i | 0.141308 | + | 0.244753i | 0.927990 | − | 0.372606i | \(-0.121536\pi\) |
−0.786681 | + | 0.617359i | \(0.788202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.8613 | − | 6.86792i | −1.45712 | − | 0.386964i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.54007 | + | 1.46651i | −0.142665 | + | 0.0823675i | −0.569633 | − | 0.821899i | \(-0.692915\pi\) |
0.426969 | + | 0.904266i | \(0.359581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.3988 | + | 18.0112i | −0.582219 | + | 1.00843i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.642147 | + | 0.834939i | 0.0358412 | + | 0.0466017i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.95296i | 0.275590i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.81992i | 0.544711i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.6780 | − | 20.3850i | −0.866994 | − | 1.12729i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.1840 | + | 19.3713i | −0.616594 | + | 1.06797i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.2381 | + | 6.48830i | −0.617700 | + | 0.356629i | −0.775973 | − | 0.630766i | \(-0.782741\pi\) |
0.158273 | + | 0.987395i | \(0.449407\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.23846 | + | 0.860029i | 0.177466 | + | 0.0471293i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.117419 | + | 0.203376i | 0.00641529 | + | 0.0111116i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.54415 | + | 11.3348i | −0.356483 | + | 0.617446i | −0.987371 | − | 0.158428i | \(-0.949357\pi\) |
0.630888 | + | 0.775874i | \(0.282691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.72766 | + | 20.5421i | 0.148146 | + | 1.11570i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.7529i | 0.690610i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0338 | 1.08173 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.1063 | − | 36.5847i | 0.813293 | − | 1.96965i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.1842 | − | 7.03455i | −0.654082 | − | 0.377634i | 0.135936 | − | 0.990718i | \(-0.456596\pi\) |
−0.790018 | + | 0.613083i | \(0.789929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.81396 | + | 1.04729i | −0.0970990 | + | 0.0560601i | −0.547763 | − | 0.836633i | \(-0.684521\pi\) |
0.450664 | + | 0.892694i | \(0.351187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.646290 | + | 5.03887i | −0.0344964 | + | 0.268955i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0901 | + | 20.9407i | 0.643493 | + | 1.11456i | 0.984647 | + | 0.174555i | \(0.0558488\pi\) |
−0.341154 | + | 0.940007i | \(0.610818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.9633 | − | 24.8049i | −2.28025 | − | 1.31650i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.0048 | + | 10.3248i | 1.32339 | + | 0.546444i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.469676 | −0.0247886 | −0.0123943 | − | 0.999923i | \(-0.503945\pi\) | ||||
−0.0123943 | + | 0.999923i | \(0.503945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4682 | 0.972012 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.44364 | + | 10.8721i | 0.0757714 | + | 0.570638i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.75080 | + | 3.32023i | 0.301011 | + | 0.173789i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.71101 | − | 4.69560i | −0.141513 | − | 0.245109i | 0.786553 | − | 0.617522i | \(-0.211864\pi\) |
−0.928067 | + | 0.372414i | \(0.878530\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.2921 | + | 13.2331i | 0.691958 | + | 0.688888i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5653 | − | 7.83195i | 0.704277 | − | 0.406615i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6141 | + | 10.1695i | 0.912025 | + | 0.526558i | 0.881082 | − | 0.472963i | \(-0.156816\pi\) |
0.0309430 | + | 0.999521i | \(0.490149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.6590 | + | 26.8614i | 1.06682 | + | 1.38712i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.88406 | 0.251542 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7646i | 0.963873i | 0.876206 | + | 0.481937i | \(0.160066\pi\) | ||||
−0.876206 | + | 0.481937i | \(0.839934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.6499 | + | 8.95989i | −0.596843 | + | 0.459029i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.68500 | − | 11.5788i | 0.341587 | − | 0.591647i | −0.643140 | − | 0.765748i | \(-0.722369\pi\) |
0.984728 | + | 0.174102i | \(0.0557021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.5662 | + | 32.1576i | 0.946223 | + | 1.63891i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.34182 | − | 16.0610i | −0.220707 | − | 0.816424i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0089 | − | 8.66542i | 0.760984 | − | 0.439354i | −0.0686651 | − | 0.997640i | \(-0.521874\pi\) |
0.829649 | + | 0.558286i | \(0.188541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.0084 | + | 34.6556i | −1.01187 | + | 1.75261i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.2783 | + | 1.76314i | −0.669800 | + | 0.0889385i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 44.7931i | 2.25379i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.6228i | − | 1.33616i | −0.744090 | − | 0.668080i | \(-0.767117\pi\) | ||
0.744090 | − | 0.668080i | \(-0.232883\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.10851 | + | 2.68461i | −0.0554947 | + | 0.134399i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.71021 | + | 13.3545i | −0.385029 | + | 0.666890i | −0.991773 | − | 0.128007i | \(-0.959142\pi\) |
0.606744 | + | 0.794897i | \(0.292475\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.59364 | − | 1.49744i | 0.129198 | − | 0.0745927i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.5883 | + | 30.1534i | 0.873971 | + | 1.49833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.32494 | − | 4.02691i | −0.115243 | − | 0.199607i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.50000 | − | 4.33013i | 0.123617 | − | 0.214111i | −0.797574 | − | 0.603220i | \(-0.793884\pi\) |
0.921192 | + | 0.389109i | \(0.127217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5454 | − | 5.18013i | −0.618817 | − | 0.255517i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.2677i | 1.39096i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.4683 | 1.39746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.60212 | − | 0.876654i | 0.323307 | − | 0.0429300i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.39624 | − | 0.806118i | −0.0682107 | − | 0.0393815i | 0.465507 | − | 0.885044i | \(-0.345872\pi\) |
−0.533717 | + | 0.845663i | \(0.679205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5487 | − | 11.2864i | 0.952744 | − | 0.550067i | 0.0588116 | − | 0.998269i | \(-0.481269\pi\) |
0.893932 | + | 0.448202i | \(0.147936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.1701 | − | 7.61533i | 1.36968 | − | 0.370270i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.1104 | − | 59.0809i | −1.65460 | − | 2.86585i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.8426 | + | 14.3429i | 1.20222 | + | 0.694101i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.58826 | − | 4.29790i | 0.269804 | − | 0.207505i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.7834 | 0.567586 | 0.283793 | − | 0.958886i | \(-0.408407\pi\) | ||||
0.283793 | + | 0.958886i | \(0.408407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.28796 | 0.109952 | 0.0549762 | − | 0.998488i | \(-0.482492\pi\) | ||||
0.0549762 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.6027 | − | 20.4600i | 1.27550 | − | 0.980983i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.72076 | − | 2.14818i | −0.177988 | − | 0.102762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.71736 | − | 13.3669i | −0.368329 | − | 0.637965i | 0.620975 | − | 0.783830i | \(-0.286737\pi\) |
−0.989304 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.63985 | − | 3.62370i | −0.173326 | − | 0.172557i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.8566 | − | 10.3095i | 0.848393 | − | 0.489820i | −0.0117155 | − | 0.999931i | \(-0.503729\pi\) |
0.860108 | + | 0.510112i | \(0.170396\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.7059 | − | 20.0375i | −1.64522 | − | 0.949867i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.5198 | − | 1.92799i | 0.686762 | − | 0.0911908i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.95218 | 0.139322 | 0.0696611 | − | 0.997571i | \(-0.477808\pi\) | ||||
0.0696611 | + | 0.997571i | \(0.477808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 26.0285i | − | 1.22563i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.68033 | + | 3.58421i | 0.407838 | + | 0.168401i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.36006 | − | 7.55185i | 0.204403 | − | 0.354036i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.37810 | − | 11.0472i | −0.298355 | − | 0.516766i | 0.677405 | − | 0.735610i | \(-0.263105\pi\) |
−0.975760 | + | 0.218845i | \(0.929771\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.6146 | − | 32.5610i | −0.635476 | − | 1.51982i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.6141 | − | 10.1695i | 0.820372 | − | 0.473642i | −0.0301727 | − | 0.999545i | \(-0.509606\pi\) |
0.850545 | + | 0.525903i | \(0.176272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.24686 | + | 7.35577i | −0.197368 | + | 0.341852i | −0.947674 | − | 0.319239i | \(-0.896573\pi\) |
0.750306 | + | 0.661091i | \(0.229906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.85419 | − | 19.0215i | 0.364229 | − | 0.882100i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.8773i | − | 0.503342i | −0.967813 | − | 0.251671i | \(-0.919020\pi\) | ||
0.967813 | − | 0.251671i | \(-0.0809801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.139229i | − | 0.00642899i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.95365 | + | 0.923331i | −0.320407 | + | 0.0425449i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.5442 | + | 19.9951i | −0.530801 | + | 0.919374i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.34315 | − | 3.66222i | 0.291044 | − | 0.168034i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.7505 | − | 5.24509i | −0.904314 | − | 0.240156i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.66514 | − | 15.0085i | −0.395920 | − | 0.685754i | 0.597298 | − | 0.802020i | \(-0.296241\pi\) |
−0.993218 | + | 0.116265i | \(0.962908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.545984 | + | 0.945673i | −0.0248947 | + | 0.0431190i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.6012 | + | 14.3061i | −0.846383 | + | 0.650949i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.1963i | 1.64359i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.2953 | 1.46344 | 0.731720 | − | 0.681605i | \(-0.238718\pi\) | ||||
0.731720 | + | 0.681605i | \(0.238718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.91629 | − | 12.8935i | −0.448430 | − | 0.583062i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2245 | + | 11.0993i | 0.867591 | + | 0.500904i | 0.866547 | − | 0.499096i | \(-0.166334\pi\) |
0.00104378 | + | 0.999999i | \(0.499668\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.3846 | + | 16.9652i | −1.32342 | + | 0.764075i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.4339 | − | 46.8201i | 0.558862 | − | 2.10441i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.7061 | + | 25.4717i | 0.659658 | + | 1.14256i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0686 | + | 12.1639i | 0.943158 | + | 0.544532i | 0.890949 | − | 0.454104i | \(-0.150040\pi\) |
0.0522091 | + | 0.998636i | \(0.483374\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.61442 | − | 27.2204i | −0.161480 | − | 1.21612i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.36573 | −0.150070 | −0.0750352 | − | 0.997181i | \(-0.523907\pi\) | ||||
−0.0750352 | + | 0.997181i | \(0.523907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.7084 | −1.05501 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.2820 | + | 7.96176i | 0.856343 | + | 0.353594i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.753847 | + | 0.435234i | 0.0334137 | + | 0.0192914i | 0.516614 | − | 0.856219i | \(-0.327192\pi\) |
−0.483200 | + | 0.875510i | \(0.660526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.96847 | − | 3.40948i | −0.0870798 | − | 0.150827i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.49587 | − | 1.46172i | 0.154347 | − | 0.0645364i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 36.2266 | − | 20.9155i | 1.59634 | − | 0.921645i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.0703 | − | 20.2479i | −1.54239 | − | 0.890500i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.45079 | − | 5.93538i | 0.107578 | − | 0.260534i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.9558 | 0.874282 | 0.437141 | − | 0.899393i | \(-0.355991\pi\) | ||||
0.437141 | + | 0.899393i | \(0.355991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.1185i | − | 0.661085i | −0.943791 | − | 0.330543i | \(-0.892768\pi\) | ||
0.943791 | − | 0.330543i | \(-0.107232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.26584 | − | 39.6573i | −0.229820 | − | 1.73078i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.4030 | + | 18.0185i | −0.453161 | + | 0.784898i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.85602 | − | 10.1429i | −0.254610 | − | 0.440997i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.0186 | − | 26.1346i | 1.12911 | − | 1.13414i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.29357 | + | 3.05624i | −0.229290 | + | 0.132381i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.17938 | + | 2.04274i | −0.0509888 | + | 0.0883153i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.4241 | + | 30.4567i | 1.01082 | + | 1.31430i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.12754i | 0.307005i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.0537i | − | 0.518230i | −0.965846 | − | 0.259115i | \(-0.916569\pi\) | ||
0.965846 | − | 0.259115i | \(-0.0834309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.3297 | + | 27.7334i | 0.915343 | + | 1.19016i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.7944 | − | 49.8733i | 1.23342 | − | 2.13634i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.4510 | + | 14.1168i | −1.04545 | + | 0.603591i | −0.921372 | − | 0.388682i | \(-0.872931\pi\) |
−0.124078 | + | 0.992272i | \(0.539597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.76626 | − | 36.1267i | −0.416814 | − | 1.54185i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.82145 | − | 3.15484i | −0.0775964 | − | 0.134401i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.2783 | − | 22.9986i | 0.564649 | − | 0.978001i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.987665 | + | 7.43815i | 0.0419241 | + | 0.315732i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4351i | 0.865864i | 0.901427 | + | 0.432932i | \(0.142521\pi\) | ||||
−0.901427 | + | 0.432932i | \(0.857479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.42202 | 0.229327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.6923 | + | 45.2694i | −0.789188 | + | 1.91128i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.8436 | − | 13.7661i | −1.00489 | − | 0.580173i | −0.0951975 | − | 0.995458i | \(-0.530348\pi\) |
−0.909691 | + | 0.415286i | \(0.863682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.1878 | + | 23.2025i | −1.69072 | + | 0.976135i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0920369 | − | 20.6958i | −0.00386518 | − | 0.869142i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.25619 | + | 14.3001i | 0.346118 | + | 0.599493i | 0.985556 | − | 0.169349i | \(-0.0541665\pi\) |
−0.639439 | + | 0.768842i | \(0.720833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.5817 | − | 23.4298i | −1.69829 | − | 0.980508i | −0.947384 | − | 0.320100i | \(-0.896283\pi\) |
−0.750907 | − | 0.660408i | \(-0.770383\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.1007 | + | 8.29980i | 0.839717 | + | 0.346729i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 59.1771 | 2.46785 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.95218 | 0.206162 | 0.103081 | − | 0.994673i | \(-0.467130\pi\) | ||||
0.103081 | + | 0.994673i | \(0.467130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.67163 | + | 12.5891i | 0.0694704 | + | 0.523185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6168 | − | 8.43903i | −0.606408 | − | 0.350110i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1792 | + | 24.5591i | 0.587242 | + | 1.01713i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.9821 | + | 2.96882i | −0.454052 | + | 0.122746i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.06698 | − | 1.19337i | 0.0853135 | − | 0.0492558i | −0.456736 | − | 0.889602i | \(-0.650982\pi\) |
0.542050 | + | 0.840346i | \(0.317648\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.93453 | − | 1.11690i | −0.0797111 | − | 0.0460212i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.9325 | + | 35.0184i | 1.10785 | + | 1.44047i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.4287 | 1.04423 | 0.522115 | − | 0.852875i | \(-0.325143\pi\) | ||||
0.522115 | + | 0.852875i | \(0.325143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 60.5803i | 2.48355i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.4031 | − | 21.8447i | 1.16246 | − | 0.894044i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.3108 | − | 40.3754i | 0.952452 | − | 1.64970i | 0.212358 | − | 0.977192i | \(-0.431886\pi\) |
0.740094 | − | 0.672503i | \(-0.234781\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7102 | − | 30.6750i | −0.722414 | − | 1.25126i | −0.960029 | − | 0.279899i | \(-0.909699\pi\) |
0.237615 | − | 0.971359i | \(-0.423634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.128151 | + | 0.128723i | −0.00521873 | + | 0.00524199i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.2698 | + | 12.2801i | −0.864740 | + | 0.499258i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.8754 | − | 20.5688i | 0.482009 | − | 0.834863i | −0.517778 | − | 0.855515i | \(-0.673241\pi\) |
0.999787 | + | 0.0206517i | \(0.00657410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.7240 | + | 2.61903i | −0.799258 | + | 0.106128i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.50994i | 0.384731i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.5983i | 0.872345i | 0.899863 | + | 0.436173i | \(0.143666\pi\) | ||||
−0.899863 | + | 0.436173i | \(0.856334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.0302 | + | 38.8224i | −0.646402 | + | 1.56547i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.17018 | − | 7.22297i | 0.167885 | − | 0.290786i | −0.769791 | − | 0.638296i | \(-0.779640\pi\) |
0.937676 | + | 0.347510i | \(0.112973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.0809 | − | 17.9446i | 1.24925 | − | 0.721253i | 0.278287 | − | 0.960498i | \(-0.410233\pi\) |
0.970959 | + | 0.239245i | \(0.0768999\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.3654 | + | 3.89469i | 1.21852 | + | 0.156289i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8796 | + | 20.5761i | 0.475948 | + | 0.824365i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8321 | + | 22.2259i | −0.513284 | + | 0.889035i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.86029 | − | 2.00687i | −0.194101 | − | 0.0801467i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.58611i | − | 0.302478i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.5824 | 1.25727 | 0.628637 | − | 0.777699i | \(-0.283613\pi\) | ||||
0.628637 | + | 0.777699i | \(0.283613\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.2641 | + | 1.62847i | −0.487452 | + | 0.0647257i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.5024 | − | 16.4558i | −1.13108 | − | 0.653030i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.44957 | − | 0.836909i | 0.0574340 | − | 0.0331596i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.84873 | − | 37.0856i | 0.389610 | − | 1.46708i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.6242 | + | 37.4542i | 0.854105 | + | 1.47935i | 0.877473 | + | 0.479625i | \(0.159227\pi\) |
−0.0233688 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9211 | + | 6.30532i | 0.430688 | + | 0.248658i | 0.699640 | − | 0.714496i | \(-0.253344\pi\) |
−0.268952 | + | 0.963154i | \(0.586677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29.5329 | − | 22.7136i | 1.16286 | − | 0.894348i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.3641 | 1.46893 | 0.734467 | − | 0.678644i | \(-0.237432\pi\) | ||||
0.734467 | + | 0.678644i | \(0.237432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.1766 | −2.00886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.67130 | + | 7.43815i | −0.379048 | + | 0.291524i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.7270 | + | 12.5441i | 0.850244 | + | 0.490888i | 0.860733 | − | 0.509057i | \(-0.170006\pi\) |
−0.0104893 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9979 | − | 25.9771i | −0.586016 | − | 1.01501i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.31829 | + | 4.96405i | −0.0514314 | + | 0.193666i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.0292 | + | 20.2241i | −1.36455 | + | 0.787821i | −0.990225 | − | 0.139479i | \(-0.955457\pi\) |
−0.374320 | + | 0.927299i | \(0.622124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.8592 | − | 19.5486i | −1.31697 | − | 0.760354i | −0.333731 | − | 0.942668i | \(-0.608308\pi\) |
−0.983240 | + | 0.182315i | \(0.941641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.4015 | − | 1.51394i | 0.442799 | − | 0.0587965i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.50413 | −0.252219 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 29.4324i | − | 1.13963i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.45768 | + | 3.07936i | 0.288331 | + | 0.119055i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.9668 | + | 44.9758i | −1.00244 | + | 1.73627i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.26405 | − | 12.5817i | −0.280009 | − | 0.484989i | 0.691378 | − | 0.722493i | \(-0.257004\pi\) |
−0.971387 | + | 0.237504i | \(0.923671\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.6336 | + | 41.5116i | −1.21758 | + | 1.59778i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.9668 | + | 23.6522i | −1.57448 | + | 0.909027i | −0.578871 | + | 0.815419i | \(0.696507\pi\) |
−0.995609 | + | 0.0936076i | \(0.970160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.7299 | − | 18.5847i | 0.411774 | − | 0.713214i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.40803 | + | 15.5191i | −0.245556 | + | 0.594695i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.97962i | − | 0.114012i | −0.998374 | − | 0.0570059i | \(-0.981845\pi\) | ||
0.998374 | − | 0.0570059i | \(-0.0181554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 30.3943i | − | 1.16130i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.47554 | + | 0.859847i | −0.247057 | + | 0.0328052i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.32982 | − | 5.76741i | 0.126856 | − | 0.219721i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.27507 | + | 4.77761i | −0.314798 | + | 0.181749i | −0.649072 | − | 0.760727i | \(-0.724842\pi\) |
0.334273 | + | 0.942476i | \(0.391509\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.2632 | + | 20.3535i | −0.769736 | + | 0.773166i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.45714 | + | 12.9161i | 0.282865 | + | 0.489937i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.2323 | − | 36.7754i | 0.804230 | − | 1.39297i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.68529 | + | 2.06524i | −0.101567 | + | 0.0781147i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.7403i | 0.556734i | 0.960475 | + | 0.278367i | \(0.0897931\pi\) | ||||
−0.960475 | + | 0.278367i | \(0.910207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.814473 | 0.0307184 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 39.8385 | + | 51.7992i | 1.50041 | + | 1.95087i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.1729 | + | 7.02800i | 0.457808 | + | 0.264315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5013 | − | 7.79495i | 0.507050 | − | 0.292746i | −0.224570 | − | 0.974458i | \(-0.572098\pi\) |
0.731620 | + | 0.681712i | \(0.238764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.4451 | + | 9.04134i | −1.25429 | + | 0.339077i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.02391 | − | 15.6299i | −0.337948 | − | 0.585343i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.6721 | + | 7.89358i | 0.511307 | + | 0.295203i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.09207 | + | 23.2865i | 0.115476 | + | 0.869652i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.7089 | −1.40630 | −0.703152 | − | 0.711039i | \(-0.748225\pi\) | ||||
−0.703152 | + | 0.711039i | \(0.748225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.8003 | −0.923613 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.88081 | + | 1.60243i | 0.144329 | + | 0.0595951i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 43.4540 | + | 25.0882i | 1.61384 | + | 0.931752i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.83754 | + | 15.3071i | 0.327766 | + | 0.567708i | 0.982068 | − | 0.188526i | \(-0.0603709\pi\) |
−0.654302 | + | 0.756233i | \(0.727038\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.9641 | + | 19.2188i | −0.702374 | + | 0.711808i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.6212 | + | 18.8339i | −1.20654 | + | 0.696596i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.02969 | + | 2.32654i | 0.148840 | + | 0.0859328i | 0.572570 | − | 0.819856i | \(-0.305946\pi\) |
−0.423730 | + | 0.905788i | \(0.639280\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.38966 | − | 10.6310i | 0.161915 | − | 0.392130i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.252064 | 0.00928489 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.1901i | − | 1.51520i | −0.652718 | − | 0.757601i | \(-0.726371\pi\) | ||
0.652718 | − | 0.757601i | \(-0.273629\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.162542 | + | 1.22411i | 0.00597113 | + | 0.0449689i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.91901 | − | 6.78793i | 0.143775 | − | 0.249025i | −0.785141 | − | 0.619318i | \(-0.787409\pi\) |
0.928915 | + | 0.370293i | \(0.120743\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.4002 | + | 28.4059i | 0.600856 | + | 1.04071i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.74624 | + | 21.2561i | 0.210244 | + | 0.777720i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.21108 | − | 0.699217i | 0.0442519 | − | 0.0255489i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0295971 | + | 0.0512637i | −0.00108001 | + | 0.00187064i | −0.866565 | − | 0.499064i | \(-0.833677\pi\) |
0.865485 | + | 0.500935i | \(0.167010\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.0662 | − | 31.2916i | −0.877022 | − | 1.14033i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.0303i | 0.765370i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35.2826i | − | 1.28237i | −0.767387 | − | 0.641185i | \(-0.778443\pi\) | ||
0.767387 | − | 0.641185i | \(-0.221557\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.9001 | − | 33.6761i | −0.940115 | − | 1.22237i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.4443 | − | 31.9465i | 0.668606 | − | 1.15806i | −0.309688 | − | 0.950838i | \(-0.600225\pi\) |
0.978294 | − | 0.207222i | \(-0.0664421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.5685 | + | 17.0714i | −1.07045 | + | 0.618025i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 55.7604 | − | 56.0089i | 2.01602 | − | 2.02501i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00911 | + | 10.4081i | 0.216976 | + | 0.375814i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.52208 | − | 14.7607i | 0.307314 | − | 0.532283i | −0.670460 | − | 0.741946i | \(-0.733903\pi\) |
0.977774 | + | 0.209662i | \(0.0672365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.815263 | + | 6.13978i | 0.0293610 | + | 0.221119i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.1463i | 1.15622i | 0.815958 | + | 0.578112i | \(0.196210\pi\) | ||||
−0.815958 | + | 0.578112i | \(0.803790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.7679 | 1.10522 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.69782 | − | 4.11183i | 0.0609091 | − | 0.147511i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.94835 | + | 2.27958i | 0.141464 | + | 0.0816744i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.1147 | + | 26.6243i | −1.65011 | + | 0.952693i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.6463 | + | 15.7333i | 0.737839 | + | 0.562264i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.85419 | − | 13.6039i | −0.280328 | − | 0.485542i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.85559 | − | 4.53543i | −0.280022 | − | 0.161671i | 0.353412 | − | 0.935468i | \(-0.385022\pi\) |
−0.633433 | + | 0.773797i | \(0.718355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.8812 | − | 17.2932i | −1.49101 | − | 0.615656i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.5121 | 0.978219 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.1960 | 0.433092 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.02351 | − | 45.3633i | −0.213632 | − | 1.60887i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.5519 | + | 24.5673i | 1.50726 | + | 0.870220i | 0.999964 | + | 0.00845051i | \(0.00268991\pi\) |
0.507301 | + | 0.861769i | \(0.330643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.0336 | − | 57.2160i | −1.16865 | − | 2.02415i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.95585 | − | 29.9579i | 0.281106 | − | 1.05851i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.17263 | − | 3.56377i | 0.217827 | − | 0.125763i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.5091 | − | 26.2747i | −1.60399 | − | 0.926062i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3840 | + | 20.0027i | 0.541541 | + | 0.704127i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.7203 | 1.50197 | 0.750983 | − | 0.660322i | \(-0.229580\pi\) | ||||
0.750983 | + | 0.660322i | \(0.229580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9697i | 0.736346i | 0.929757 | + | 0.368173i | \(0.120017\pi\) | ||||
−0.929757 | + | 0.368173i | \(0.879983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.9854 | + | 13.0634i | −0.595706 | + | 0.458154i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.2124 | − | 31.5448i | 0.637952 | − | 1.10496i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.02208 | − | 3.50234i | −0.0707435 | − | 0.122531i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.51870 | + | 1.73116i | 0.227782 | + | 0.0604915i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9020 | − | 17.8413i | 1.07849 | − | 0.622664i | 0.147998 | − | 0.988988i | \(-0.452717\pi\) |
0.930488 | + | 0.366323i | \(0.119384\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.2721 | + | 29.9161i | −0.602066 | + | 1.04281i | 0.390442 | + | 0.920628i | \(0.372322\pi\) |
−0.992508 | + | 0.122181i | \(0.961011\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 71.7967 | − | 9.53343i | 2.49964 | − | 0.331911i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 55.0950i | − | 1.91584i | −0.287034 | − | 0.957920i | \(-0.592669\pi\) | ||
0.287034 | − | 0.957920i | \(-0.407331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.70301i | 0.302268i | 0.988513 | + | 0.151134i | \(0.0482925\pi\) | ||||
−0.988513 | + | 0.151134i | \(0.951707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.69198 | − | 18.6286i | 0.266832 | − | 0.646220i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.81416 | + | 10.0704i | −0.201449 | + | 0.348920i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 53.2529 | − | 30.7456i | 1.84289 | − | 1.06399i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.7879 | + | 2.02496i | 0.545708 | + | 0.0699930i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.6617 | − | 37.5192i | −0.747845 | − | 1.29531i | −0.948854 | − | 0.315717i | \(-0.897755\pi\) |
0.201008 | − | 0.979590i | \(-0.435578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.02208 | + | 3.50234i | −0.0697268 | + | 0.120770i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.6766 | + | 6.47304i | 0.539930 | + | 0.222943i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.7154i | 1.60706i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5610 | 0.500324 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.8183 | + | 3.95938i | −1.02336 | + | 0.135886i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.69884 | + | 3.29023i | 0.195354 | + | 0.112788i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.846691 | + | 0.488838i | −0.0289902 | + | 0.0167375i | −0.514425 | − | 0.857535i | \(-0.671995\pi\) |
0.485435 | + | 0.874273i | \(0.338661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.01333 | + | 5.98664i | 0.205651 | + | 0.204739i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.64398 | + | 2.84746i | 0.0561573 | + | 0.0972673i | 0.892737 | − | 0.450577i | \(-0.148782\pi\) |
−0.836580 | + | 0.547845i | \(0.815449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.2664 | + | 19.7837i | 1.16915 | + | 0.675012i | 0.953481 | − | 0.301454i | \(-0.0974718\pi\) |
0.215674 | + | 0.976465i | \(0.430805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.7389 | − | 15.1811i | 0.672701 | − | 0.517371i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.2687 | −0.689953 | −0.344977 | − | 0.938611i | \(-0.612113\pi\) | ||||
−0.344977 | + | 0.938611i | \(0.612113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.3799 | 0.488932 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.9976 | + | 30.7619i | −1.35839 | + | 1.04473i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.6374 | + | 24.0394i | 1.41245 | + | 0.815480i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0295971 | − | 0.0512637i | −0.00100286 | − | 0.00173700i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.0262 | + | 7.30610i | −0.914698 | + | 0.247274i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.9625 | − | 22.4950i | 1.31717 | − | 0.760470i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.57746 | + | 1.48810i | 0.0870345 | + | 0.0502494i | 0.542886 | − | 0.839807i | \(-0.317332\pi\) |
−0.455851 | + | 0.890056i | \(0.650665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.2010 | + | 1.35452i | −0.344071 | + | 0.0456870i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.3404 | −1.59494 | −0.797469 | − | 0.603360i | \(-0.793828\pi\) | ||||
−0.797469 | + | 0.603360i | \(0.793828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31.9403i | − | 1.07488i | −0.843303 | − | 0.537438i | \(-0.819392\pi\) | ||
0.843303 | − | 0.537438i | \(-0.180608\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 76.3318 | + | 31.5183i | 2.56586 | + | 1.05948i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.71101 | − | 4.69560i | 0.0910267 | − | 0.157663i | −0.816917 | − | 0.576756i | \(-0.804318\pi\) |
0.907943 | + | 0.419093i | \(0.137652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.75619 | + | 16.8982i | 0.327212 | + | 0.566748i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.4683 | − | 0.166626i | 1.25524 | − | 0.00558219i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.14292 | − | 3.54662i | 0.205565 | − | 0.118683i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.0210 | + | 74.5145i | −1.43803 | + | 2.49074i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.80774 | + | 9.22168i | −0.127137 | + | 0.307903i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 15.3028i | − | 0.510377i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.2657i | 1.54133i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.8966 | + | 2.90751i | −0.728672 | + | 0.0967557i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.1743 | + | 67.8519i | −1.30220 | + | 2.25547i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.06588 | − | 3.50214i | 0.201414 | − | 0.116287i | −0.395901 | − | 0.918293i | \(-0.629568\pi\) |
0.597315 | + | 0.802007i | \(0.296234\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.78546 | − | 17.7020i | −0.158724 | − | 0.587139i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.88341 | + | 4.99421i | 0.0955315 | + | 0.165465i | 0.909830 | − | 0.414980i | \(-0.136212\pi\) |
−0.814299 | + | 0.580446i | \(0.802878\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.2783 | − | 26.4627i | 0.505637 | − | 0.875789i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 66.4298 | − | 51.0908i | 2.19610 | − | 1.68901i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.7836i | 0.587267i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.3629 | −1.49638 | −0.748191 | − | 0.663483i | \(-0.769077\pi\) | ||||
−0.748191 | + | 0.663483i | \(0.769077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.0303 | − | 40.3466i | −1.02248 | − | 1.32946i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.8295 | + | 6.25241i | 0.356457 | + | 0.205801i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.71538 | + | 5.60918i | −0.319440 | + | 0.184429i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.9289 | + | 22.8272i | 0.753084 | + | 0.749743i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.0202 | − | 22.5517i | −0.427180 | − | 0.739898i | 0.569441 | − | 0.822032i | \(-0.307160\pi\) |
−0.996621 | + | 0.0821342i | \(0.973826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.08120 | − | 0.624231i | −0.0354349 | − | 0.0204583i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.27776 | − | 24.6850i | −0.107309 | − | 0.808150i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −109.676 | −3.58680 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.7562 | 0.514732 | 0.257366 | − | 0.966314i | \(-0.417145\pi\) | ||||
0.257366 | + | 0.966314i | \(0.417145\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.00471 | − | 3.30524i | −0.261224 | − | 0.107862i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.9521 | − | 19.6022i | −1.10681 | − | 0.639015i | −0.168806 | − | 0.985649i | \(-0.553991\pi\) |
−0.938000 | + | 0.346635i | \(0.887324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.4176 | + | 31.9003i | 0.599760 | + | 1.03882i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 42.7585 | − | 17.8785i | 1.39093 | − | 0.581586i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.5295 | + | 20.5129i | −1.15455 | + | 0.666581i | −0.949992 | − | 0.312273i | \(-0.898910\pi\) |
−0.204560 | + | 0.978854i | \(0.565576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.44957 | − | 0.836909i | −0.0470550 | − | 0.0271672i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.93887 | − | 4.69560i | 0.0628721 | − | 0.152265i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.13612 | −0.166375 | −0.0831876 | − | 0.996534i | \(-0.526510\pi\) | ||||
−0.0831876 | + | 0.996534i | \(0.526510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.6988i | 1.57586i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.74157 | − | 35.7090i | −0.153273 | − | 1.15431i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00994 | + | 15.6057i | −0.290946 | + | 0.503933i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.8082 | + | 18.7204i | 0.348652 | + | 0.603882i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.76328 | − | 0.468269i | −0.0568208 | − | 0.0150898i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24.6288 | + | 14.2195i | −0.792830 | + | 0.457740i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.89445 | + | 11.9415i | −0.221711 | + | 0.384014i | −0.955328 | − | 0.295549i | \(-0.904497\pi\) |
0.733617 | + | 0.679563i | \(0.237831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.22999 | − | 6.80019i | −0.168011 | − | 0.218453i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 37.0596i | − | 1.18930i | −0.803985 | − | 0.594650i | \(-0.797291\pi\) | ||
0.803985 | − | 0.594650i | \(-0.202709\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.84224i | − | 0.283469i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.3692 | − | 13.4823i | −0.332079 | − | 0.431779i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.419953 | − | 0.727379i | 0.0134355 | − | 0.0232709i | −0.859230 | − | 0.511590i | \(-0.829057\pi\) |
0.872665 | + | 0.488319i | \(0.162390\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.2516 | + | 21.5072i | −1.19057 | + | 0.687375i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.0503 | + | 11.4328i | 1.37449 | + | 0.365020i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.8627 | + | 37.8674i | 0.697313 | + | 1.20778i | 0.969395 | + | 0.245507i | \(0.0789546\pi\) |
−0.272082 | + | 0.962274i | \(0.587712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.4646 | + | 85.6751i | −1.57607 | + | 2.72984i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.09962 | − | 38.4054i | −0.162323 | − | 1.22246i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 32.6743i | − | 1.03898i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.7973 | −0.438287 | −0.219143 | − | 0.975693i | \(-0.570326\pi\) | ||||
−0.219143 | + | 0.975693i | \(0.570326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.57815 | − | 20.7748i | 0.272219 | − | 0.659268i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.4903 | + | 40.1202i | 2.20299 | + | 1.27190i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.6848 | − | 27.5308i | 1.51019 | − | 0.871911i | 0.510264 | − | 0.860018i | \(-0.329548\pi\) |
0.999929 | − | 0.0118930i | \(-0.00378575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.35439 | + | 2.23881i | −0.169405 | + | 0.0708329i |
(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 | 1152.2.r.g.193.3 | ✓ | 24 | |
3.2 | odd | 2 | 3456.2.r.h.577.11 | 24 | |||
4.3 | odd | 2 | inner | 1152.2.r.g.193.9 | yes | 24 | |
8.3 | odd | 2 | inner | 1152.2.r.g.193.4 | yes | 24 | |
8.5 | even | 2 | inner | 1152.2.r.g.193.10 | yes | 24 | |
9.2 | odd | 6 | 3456.2.r.h.2881.1 | 24 | |||
9.7 | even | 3 | inner | 1152.2.r.g.961.10 | yes | 24 | |
12.11 | even | 2 | 3456.2.r.h.577.12 | 24 | |||
24.5 | odd | 2 | 3456.2.r.h.577.1 | 24 | |||
24.11 | even | 2 | 3456.2.r.h.577.2 | 24 | |||
36.7 | odd | 6 | inner | 1152.2.r.g.961.4 | yes | 24 | |
36.11 | even | 6 | 3456.2.r.h.2881.2 | 24 | |||
72.11 | even | 6 | 3456.2.r.h.2881.12 | 24 | |||
72.29 | odd | 6 | 3456.2.r.h.2881.11 | 24 | |||
72.43 | odd | 6 | inner | 1152.2.r.g.961.9 | yes | 24 | |
72.61 | even | 6 | inner | 1152.2.r.g.961.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.r.g.193.3 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1152.2.r.g.193.4 | yes | 24 | 8.3 | odd | 2 | inner | |
1152.2.r.g.193.9 | yes | 24 | 4.3 | odd | 2 | inner | |
1152.2.r.g.193.10 | yes | 24 | 8.5 | even | 2 | inner | |
1152.2.r.g.961.3 | yes | 24 | 72.61 | even | 6 | inner | |
1152.2.r.g.961.4 | yes | 24 | 36.7 | odd | 6 | inner | |
1152.2.r.g.961.9 | yes | 24 | 72.43 | odd | 6 | inner | |
1152.2.r.g.961.10 | yes | 24 | 9.7 | even | 3 | inner | |
3456.2.r.h.577.1 | 24 | 24.5 | odd | 2 | |||
3456.2.r.h.577.2 | 24 | 24.11 | even | 2 | |||
3456.2.r.h.577.11 | 24 | 3.2 | odd | 2 | |||
3456.2.r.h.577.12 | 24 | 12.11 | even | 2 | |||
3456.2.r.h.2881.1 | 24 | 9.2 | odd | 6 | |||
3456.2.r.h.2881.2 | 24 | 36.11 | even | 6 | |||
3456.2.r.h.2881.11 | 24 | 72.29 | odd | 6 | |||
3456.2.r.h.2881.12 | 24 | 72.11 | even | 6 |