Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (of order \(2\), degree \(1\), 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1919698923024.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 2x^{6} + 12x^{5} - 36x^{4} + 48x^{3} + 32x^{2} - 192x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(-1.97436 - 0.319229i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.3.d.i.163.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97436 | + | 0.319229i | −0.987179 | + | 0.159615i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.79619 | − | 1.26055i | 0.949046 | − | 0.315136i | ||||
\(5\) | −2.71218 | −0.542435 | −0.271218 | − | 0.962518i | \(-0.587426\pi\) | ||||
−0.271218 | + | 0.962518i | \(0.587426\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.5967i | 1.65668i | 0.560227 | + | 0.828339i | \(0.310714\pi\) | ||||
−0.560227 | + | 0.828339i | \(0.689286\pi\) | |||||||
\(8\) | −7.09263 | + | 3.70062i | −0.886579 | + | 0.462578i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.35481 | − | 0.865806i | 0.535481 | − | 0.0865806i | ||||
\(11\) | − | 9.87064i | − | 0.897331i | −0.893700 | − | 0.448665i | \(-0.851899\pi\) | ||
0.893700 | − | 0.448665i | \(-0.148101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.592371 | −0.0455670 | −0.0227835 | − | 0.999740i | \(-0.507253\pi\) | ||||
−0.0227835 | + | 0.999740i | \(0.507253\pi\) | |||||||
\(14\) | −3.70202 | − | 22.8961i | −0.264430 | − | 1.63544i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.8220 | − | 9.57053i | 0.801378 | − | 0.598158i | ||||
\(17\) | −8.87968 | −0.522334 | −0.261167 | − | 0.965294i | \(-0.584107\pi\) | ||||
−0.261167 | + | 0.965294i | \(0.584107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 14.0989i | − | 0.742046i | −0.928624 | − | 0.371023i | \(-0.879007\pi\) | ||
0.928624 | − | 0.371023i | \(-0.120993\pi\) | |||||||
\(20\) | −10.2959 | + | 3.41882i | −0.514796 | + | 0.170941i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.15100 | + | 19.4882i | 0.143227 | + | 0.885826i | ||||
\(23\) | 21.1026i | 0.917506i | 0.888564 | + | 0.458753i | \(0.151704\pi\) | ||||
−0.888564 | + | 0.458753i | \(0.848296\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17.6441 | −0.705764 | ||||||||
\(26\) | 1.16955 | − | 0.189102i | 0.0449828 | − | 0.00727316i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.6182 | + | 44.0234i | 0.522080 | + | 1.57226i | ||||
\(29\) | −20.3528 | −0.701819 | −0.350910 | − | 0.936409i | \(-0.614128\pi\) | ||||
−0.350910 | + | 0.936409i | \(0.614128\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 16.5534i | − | 0.533980i | −0.963699 | − | 0.266990i | \(-0.913971\pi\) | ||
0.963699 | − | 0.266990i | \(-0.0860291\pi\) | |||||||
\(32\) | −22.2601 | + | 22.9888i | −0.695629 | + | 0.718401i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 17.5317 | − | 2.83465i | 0.515637 | − | 0.0833721i | ||||
\(35\) | − | 31.4524i | − | 0.898641i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.6557 | −1.09880 | −0.549401 | − | 0.835559i | \(-0.685144\pi\) | ||||
−0.549401 | + | 0.835559i | \(0.685144\pi\) | |||||||
\(38\) | 4.50077 | + | 27.8363i | 0.118441 | + | 0.732533i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 19.2365 | − | 10.0367i | 0.480912 | − | 0.250919i | ||||
\(41\) | −42.4355 | −1.03501 | −0.517506 | − | 0.855680i | \(-0.673139\pi\) | ||||
−0.517506 | + | 0.855680i | \(0.673139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 37.2258i | − | 0.865716i | −0.901462 | − | 0.432858i | \(-0.857505\pi\) | ||
0.901462 | − | 0.432858i | \(-0.142495\pi\) | |||||||
\(44\) | −12.4424 | − | 37.4708i | −0.282782 | − | 0.851609i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.73658 | − | 41.6642i | −0.146447 | − | 0.905743i | ||||
\(47\) | 1.81442i | 0.0386047i | 0.999814 | + | 0.0193024i | \(0.00614451\pi\) | ||||
−0.999814 | + | 0.0193024i | \(0.993855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −85.4845 | −1.74458 | ||||||||
\(50\) | 34.8358 | − | 5.63251i | 0.696716 | − | 0.112650i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.24875 | + | 0.746711i | −0.0432452 | + | 0.0143598i | ||||
\(53\) | −21.1005 | −0.398122 | −0.199061 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199061 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.7709i | 0.486744i | ||||||||
\(56\) | −42.9152 | − | 82.2514i | −0.766343 | − | 1.46878i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 40.1836 | − | 6.49719i | 0.692822 | − | 0.112021i | ||||
\(59\) | − | 88.5516i | − | 1.50087i | −0.660942 | − | 0.750437i | \(-0.729843\pi\) | ||
0.660942 | − | 0.750437i | \(-0.270157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −72.9851 | −1.19648 | −0.598238 | − | 0.801318i | \(-0.704132\pi\) | ||||
−0.598238 | + | 0.801318i | \(0.704132\pi\) | |||||||
\(62\) | 5.28433 | + | 32.6823i | 0.0852311 | + | 0.527134i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.6108 | − | 52.4943i | 0.572043 | − | 0.820223i | ||||
\(65\) | 1.60661 | 0.0247171 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.2378i | 0.660265i | 0.943935 | + | 0.330133i | \(0.107094\pi\) | ||||
−0.943935 | + | 0.330133i | \(0.892906\pi\) | |||||||
\(68\) | −33.7089 | + | 11.1932i | −0.495719 | + | 0.164606i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 10.0405 | + | 62.0984i | 0.143436 | + | 0.887120i | ||||
\(71\) | 111.798i | 1.57462i | 0.616557 | + | 0.787310i | \(0.288527\pi\) | ||||
−0.616557 | + | 0.787310i | \(0.711473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.2003 | −1.04384 | −0.521920 | − | 0.852995i | \(-0.674784\pi\) | ||||
−0.521920 | + | 0.852995i | \(0.674784\pi\) | |||||||
\(74\) | 80.2690 | − | 12.9785i | 1.08472 | − | 0.175385i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.7723 | − | 53.5220i | −0.233846 | − | 0.704236i | ||||
\(77\) | 114.467 | 1.48659 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.58903i | − | 0.121380i | −0.998157 | − | 0.0606901i | \(-0.980670\pi\) | ||
0.998157 | − | 0.0606901i | \(-0.0193301\pi\) | |||||||
\(80\) | −34.7757 | + | 25.9570i | −0.434696 | + | 0.324462i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 83.7828 | − | 13.5466i | 1.02174 | − | 0.165203i | ||||
\(83\) | 85.0141i | 1.02427i | 0.858906 | + | 0.512133i | \(0.171145\pi\) | ||||
−0.858906 | + | 0.512133i | \(0.828855\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.0833 | 0.283332 | ||||||||
\(86\) | 11.8836 | + | 73.4971i | 0.138181 | + | 0.854617i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 36.5275 | + | 70.0088i | 0.415085 | + | 0.795554i | ||||
\(89\) | 64.7845 | 0.727916 | 0.363958 | − | 0.931415i | \(-0.381425\pi\) | ||||
0.363958 | + | 0.931415i | \(0.381425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.86958i | − | 0.0754898i | ||||||
\(92\) | 26.6008 | + | 80.1095i | 0.289140 | + | 0.870756i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.579216 | − | 3.58232i | −0.00616188 | − | 0.0381098i | ||||
\(95\) | 38.2387i | 0.402512i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.18278 | 0.0740492 | 0.0370246 | − | 0.999314i | \(-0.488212\pi\) | ||||
0.0370246 | + | 0.999314i | \(0.488212\pi\) | |||||||
\(98\) | 168.777 | − | 27.2892i | 1.72222 | − | 0.278461i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −66.9803 | + | 22.2412i | −0.669803 | + | 0.222412i | ||||
\(101\) | 111.007 | 1.09908 | 0.549542 | − | 0.835466i | \(-0.314802\pi\) | ||||
0.549542 | + | 0.835466i | \(0.314802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 91.9295i | − | 0.892520i | −0.894903 | − | 0.446260i | \(-0.852756\pi\) | ||
0.894903 | − | 0.446260i | \(-0.147244\pi\) | |||||||
\(104\) | 4.20147 | − | 2.19214i | 0.0403987 | − | 0.0210783i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 41.6599 | − | 6.73588i | 0.393018 | − | 0.0635460i | ||||
\(107\) | − | 107.741i | − | 1.00693i | −0.864016 | − | 0.503465i | \(-0.832058\pi\) | ||
0.864016 | − | 0.503465i | \(-0.167942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 86.5562 | 0.794093 | 0.397047 | − | 0.917798i | \(-0.370035\pi\) | ||||
0.397047 | + | 0.917798i | \(0.370035\pi\) | |||||||
\(110\) | −8.54606 | − | 52.8554i | −0.0776915 | − | 0.480504i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 110.987 | + | 148.694i | 0.990956 | + | 1.32763i | ||||
\(113\) | 4.70397 | 0.0416280 | 0.0208140 | − | 0.999783i | \(-0.493374\pi\) | ||||
0.0208140 | + | 0.999783i | \(0.493374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 57.2341i | − | 0.497688i | ||||||
\(116\) | −77.2628 | + | 25.6556i | −0.666059 | + | 0.221169i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 28.2682 | + | 174.833i | 0.239561 | + | 1.48163i | ||||
\(119\) | − | 102.975i | − | 0.865339i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.5705 | 0.194797 | ||||||||
\(122\) | 144.099 | − | 23.2990i | 1.18114 | − | 0.190975i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.8663 | − | 62.8398i | −0.168277 | − | 0.506772i | ||||
\(125\) | 115.658 | 0.925267 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.37118i | − | 0.0659148i | −0.999457 | − | 0.0329574i | \(-0.989507\pi\) | ||
0.999457 | − | 0.0329574i | \(-0.0104926\pi\) | |||||||
\(128\) | −55.5251 | + | 115.330i | −0.433790 | + | 0.901014i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.17203 | + | 0.512878i | −0.0244003 | + | 0.00394522i | ||||
\(131\) | 132.868i | 1.01426i | 0.861870 | + | 0.507129i | \(0.169293\pi\) | ||||
−0.861870 | + | 0.507129i | \(0.830707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 163.501 | 1.22933 | ||||||||
\(134\) | −14.1220 | − | 87.3413i | −0.105388 | − | 0.651800i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 62.9803 | − | 32.8603i | 0.463090 | − | 0.241620i | ||||
\(137\) | −45.1159 | −0.329313 | −0.164656 | − | 0.986351i | \(-0.552652\pi\) | ||||
−0.164656 | + | 0.986351i | \(0.552652\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 150.970i | 1.08611i | 0.839696 | + | 0.543056i | \(0.182733\pi\) | ||||
−0.839696 | + | 0.543056i | \(0.817267\pi\) | |||||||
\(140\) | −39.6472 | − | 119.399i | −0.283195 | − | 0.852852i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −35.6892 | − | 220.729i | −0.251332 | − | 1.55443i | ||||
\(143\) | 5.84708i | 0.0408887i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55.2003 | 0.380692 | ||||||||
\(146\) | 150.447 | − | 24.3254i | 1.03046 | − | 0.166612i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −154.337 | + | 51.2484i | −1.04281 | + | 0.346273i | ||||
\(149\) | −142.783 | −0.958274 | −0.479137 | − | 0.877740i | \(-0.659050\pi\) | ||||
−0.479137 | + | 0.877740i | \(0.659050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 254.065i | 1.68255i | 0.540606 | + | 0.841276i | \(0.318195\pi\) | ||||
−0.540606 | + | 0.841276i | \(0.681805\pi\) | |||||||
\(152\) | 52.1746 | + | 99.9981i | 0.343254 | + | 0.657882i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −226.000 | + | 36.5413i | −1.46753 | + | 0.237281i | ||||
\(155\) | 44.8957i | 0.289650i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.30722 | −0.0338039 | −0.0169020 | − | 0.999857i | \(-0.505380\pi\) | ||||
−0.0169020 | + | 0.999857i | \(0.505380\pi\) | |||||||
\(158\) | 3.06110 | + | 18.9322i | 0.0193740 | + | 0.119824i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 60.3734 | − | 62.3498i | 0.377334 | − | 0.389686i | ||||
\(161\) | −244.722 | −1.52001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 59.5534i | − | 0.365359i | −0.983173 | − | 0.182679i | \(-0.941523\pi\) | ||
0.983173 | − | 0.182679i | \(-0.0584770\pi\) | |||||||
\(164\) | −161.093 | + | 53.4918i | −0.982273 | + | 0.326170i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −27.1390 | − | 167.848i | −0.163488 | − | 1.01113i | ||||
\(167\) | 99.0080i | 0.592862i | 0.955054 | + | 0.296431i | \(0.0957965\pi\) | ||||
−0.955054 | + | 0.296431i | \(0.904203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.649 | −0.997924 | ||||||||
\(170\) | −47.5490 | + | 7.68808i | −0.279700 | + | 0.0452240i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −46.9248 | − | 141.316i | −0.272819 | − | 0.821605i | ||||
\(173\) | −38.5929 | −0.223081 | −0.111540 | − | 0.993760i | \(-0.535578\pi\) | ||||
−0.111540 | + | 0.993760i | \(0.535578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 204.614i | − | 1.16922i | ||||||
\(176\) | −94.4673 | − | 126.562i | −0.536746 | − | 0.719101i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −127.908 | + | 20.6811i | −0.718584 | + | 0.116186i | ||||
\(179\) | − | 36.4264i | − | 0.203499i | −0.994810 | − | 0.101750i | \(-0.967556\pi\) | ||
0.994810 | − | 0.101750i | \(-0.0324441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.5921 | −0.102719 | −0.0513594 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513594 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(182\) | 2.19297 | + | 13.5630i | 0.0120493 | + | 0.0745220i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −78.0929 | − | 149.673i | −0.424418 | − | 0.813441i | ||||
\(185\) | 110.265 | 0.596030 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 87.6481i | 0.468706i | ||||||||
\(188\) | 2.28716 | + | 6.88788i | 0.0121658 | + | 0.0366377i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.2069 | − | 75.4968i | −0.0642468 | − | 0.397352i | ||||
\(191\) | − | 282.870i | − | 1.48099i | −0.672059 | − | 0.740497i | \(-0.734590\pi\) | ||
0.672059 | − | 0.740497i | \(-0.265410\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 303.085 | 1.57039 | 0.785193 | − | 0.619251i | \(-0.212564\pi\) | ||||
0.785193 | + | 0.619251i | \(0.212564\pi\) | |||||||
\(194\) | −14.1814 | + | 2.29295i | −0.0730999 | + | 0.0118193i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −324.515 | + | 107.757i | −1.65569 | + | 0.549782i | ||||
\(197\) | 139.184 | 0.706520 | 0.353260 | − | 0.935525i | \(-0.385073\pi\) | ||||
0.353260 | + | 0.935525i | \(0.385073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.2337i | − | 0.0564505i | −0.999602 | − | 0.0282253i | \(-0.991014\pi\) | ||
0.999602 | − | 0.0282253i | \(-0.00898558\pi\) | |||||||
\(200\) | 125.143 | − | 65.2942i | 0.625715 | − | 0.326471i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −219.169 | + | 35.4368i | −1.08499 | + | 0.175430i | ||||
\(203\) | − | 236.026i | − | 1.16269i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 115.092 | 0.561427 | ||||||||
\(206\) | 29.3466 | + | 181.502i | 0.142459 | + | 0.881077i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.59541 | + | 5.66930i | −0.0365164 | + | 0.0272563i | ||||
\(209\) | −139.165 | −0.665861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 129.346i | 0.613012i | 0.951869 | + | 0.306506i | \(0.0991599\pi\) | ||||
−0.951869 | + | 0.306506i | \(0.900840\pi\) | |||||||
\(212\) | −80.1012 | + | 26.5981i | −0.377836 | + | 0.125463i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 34.3942 | + | 212.720i | 0.160721 | + | 0.994020i | ||||
\(215\) | 100.963i | 0.469595i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 191.966 | 0.884634 | ||||||||
\(218\) | −170.893 | + | 27.6313i | −0.783913 | + | 0.126749i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 33.7460 | + | 101.627i | 0.153391 | + | 0.461943i | ||||
\(221\) | 5.26006 | 0.0238012 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 241.574i | − | 1.08329i | −0.840606 | − | 0.541647i | \(-0.817801\pi\) | ||
0.840606 | − | 0.541647i | \(-0.182199\pi\) | |||||||
\(224\) | −266.596 | − | 258.145i | −1.19016 | − | 1.15243i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.28732 | + | 1.50164i | −0.0410943 | + | 0.00664444i | ||||
\(227\) | 381.871i | 1.68225i | 0.540840 | + | 0.841126i | \(0.318107\pi\) | ||||
−0.540840 | + | 0.841126i | \(0.681893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −149.328 | −0.652089 | −0.326044 | − | 0.945354i | \(-0.605716\pi\) | ||||
−0.326044 | + | 0.945354i | \(0.605716\pi\) | |||||||
\(230\) | 18.2708 | + | 113.001i | 0.0794382 | + | 0.491307i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 144.355 | − | 75.3179i | 0.622218 | − | 0.324646i | ||||
\(233\) | −218.934 | −0.939631 | −0.469816 | − | 0.882765i | \(-0.655680\pi\) | ||||
−0.469816 | + | 0.882765i | \(0.655680\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.92103i | − | 0.0209406i | ||||||
\(236\) | −111.623 | − | 336.158i | −0.472980 | − | 1.42440i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 32.8727 | + | 203.310i | 0.138121 | + | 0.854245i | ||||
\(239\) | − | 252.018i | − | 1.05447i | −0.849720 | − | 0.527235i | \(-0.823229\pi\) | ||
0.849720 | − | 0.527235i | \(-0.176771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 452.027 | 1.87563 | 0.937816 | − | 0.347133i | \(-0.112845\pi\) | ||||
0.937816 | + | 0.347133i | \(0.112845\pi\) | |||||||
\(242\) | −46.5366 | + | 7.52439i | −0.192300 | + | 0.0310925i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −277.065 | + | 92.0011i | −1.13551 | + | 0.377053i | ||||
\(245\) | 231.849 | 0.946323 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.35177i | 0.0338128i | ||||||||
\(248\) | 61.2579 | + | 117.407i | 0.247008 | + | 0.473416i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −228.351 | + | 36.9215i | −0.913404 | + | 0.147686i | ||||
\(251\) | 139.429i | 0.555492i | 0.960655 | + | 0.277746i | \(0.0895874\pi\) | ||||
−0.960655 | + | 0.277746i | \(0.910413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 208.297 | 0.823306 | ||||||||
\(254\) | 2.67232 | + | 16.5277i | 0.0105210 | + | 0.0650697i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 72.8098 | − | 245.428i | 0.284413 | − | 0.958702i | ||||
\(257\) | −470.615 | −1.83119 | −0.915594 | − | 0.402104i | \(-0.868279\pi\) | ||||
−0.915594 | + | 0.402104i | \(0.868279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 471.474i | − | 1.82036i | ||||||
\(260\) | 6.09901 | − | 2.02521i | 0.0234577 | − | 0.00778928i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.4152 | − | 262.328i | −0.161890 | − | 1.00125i | ||||
\(263\) | 25.6376i | 0.0974814i | 0.998811 | + | 0.0487407i | \(0.0155208\pi\) | ||||
−0.998811 | + | 0.0487407i | \(0.984479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 57.2282 | 0.215955 | ||||||||
\(266\) | −322.810 | + | 52.1943i | −1.21357 | + | 0.196219i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 55.7638 | + | 167.935i | 0.208074 | + | 0.626622i | ||||
\(269\) | 8.15075 | 0.0303002 | 0.0151501 | − | 0.999885i | \(-0.495177\pi\) | ||||
0.0151501 | + | 0.999885i | \(0.495177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 401.979i | 1.48332i | 0.670777 | + | 0.741659i | \(0.265961\pi\) | ||||
−0.670777 | + | 0.741659i | \(0.734039\pi\) | |||||||
\(272\) | −113.856 | + | 84.9832i | −0.418587 | + | 0.312438i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 89.0749 | − | 14.4023i | 0.325091 | − | 0.0525632i | ||||
\(275\) | 174.158i | 0.633304i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −112.404 | −0.405791 | −0.202896 | − | 0.979200i | \(-0.565035\pi\) | ||||
−0.202896 | + | 0.979200i | \(0.565035\pi\) | |||||||
\(278\) | −48.1939 | − | 298.068i | −0.173359 | − | 1.07219i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 116.394 | + | 223.080i | 0.415691 | + | 0.796716i | ||||
\(281\) | −537.734 | −1.91365 | −0.956823 | − | 0.290673i | \(-0.906121\pi\) | ||||
−0.956823 | + | 0.290673i | \(0.906121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 141.223i | 0.499021i | 0.968372 | + | 0.249510i | \(0.0802696\pi\) | ||||
−0.968372 | + | 0.249510i | \(0.919730\pi\) | |||||||
\(284\) | 140.927 | + | 424.406i | 0.496220 | + | 1.49439i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.86656 | − | 11.5442i | −0.00652643 | − | 0.0403644i | ||||
\(287\) | − | 492.113i | − | 1.71468i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −210.151 | −0.727167 | ||||||||
\(290\) | −108.985 | + | 17.6215i | −0.375811 | + | 0.0607639i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −289.270 | + | 96.0540i | −0.990652 | + | 0.328952i | ||||
\(293\) | 460.581 | 1.57195 | 0.785975 | − | 0.618259i | \(-0.212162\pi\) | ||||
0.785975 | + | 0.618259i | \(0.212162\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 240.168i | 0.814127i | ||||||||
\(296\) | 288.356 | − | 150.451i | 0.974175 | − | 0.508282i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 281.904 | − | 45.5804i | 0.945988 | − | 0.152954i | ||||
\(299\) | − | 12.5006i | − | 0.0418080i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 431.698 | 1.43421 | ||||||||
\(302\) | −81.1051 | − | 501.616i | −0.268560 | − | 1.66098i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −134.934 | − | 180.777i | −0.443861 | − | 0.594660i | ||||
\(305\) | 197.948 | 0.649011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 210.322i | 0.685089i | 0.939502 | + | 0.342545i | \(0.111289\pi\) | ||||
−0.939502 | + | 0.342545i | \(0.888711\pi\) | |||||||
\(308\) | 434.539 | − | 144.291i | 1.41084 | − | 0.468478i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.3320 | − | 88.6403i | −0.0462324 | − | 0.285936i | ||||
\(311\) | − | 128.164i | − | 0.412104i | −0.978541 | − | 0.206052i | \(-0.933938\pi\) | ||
0.978541 | − | 0.206052i | \(-0.0660616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.24281 | 0.0231400 | 0.0115700 | − | 0.999933i | \(-0.496317\pi\) | ||||
0.0115700 | + | 0.999933i | \(0.496317\pi\) | |||||||
\(314\) | 10.4784 | − | 1.69422i | 0.0333705 | − | 0.00539560i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0874 | − | 36.4017i | −0.0382513 | − | 0.115195i | ||||
\(317\) | 240.291 | 0.758015 | 0.379007 | − | 0.925394i | \(-0.376266\pi\) | ||||
0.379007 | + | 0.925394i | \(0.376266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 200.895i | 0.629764i | ||||||||
\(320\) | −99.2949 | + | 142.374i | −0.310297 | + | 0.444918i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 483.169 | − | 78.1224i | 1.50052 | − | 0.242616i | ||||
\(323\) | 125.194i | 0.387596i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.4518 | 0.0321595 | ||||||||
\(326\) | 19.0112 | + | 117.580i | 0.0583166 | + | 0.360674i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 300.979 | − | 157.038i | 0.917619 | − | 0.478773i | ||||
\(329\) | −21.0414 | −0.0639556 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 427.684i | 1.29210i | 0.763297 | + | 0.646048i | \(0.223579\pi\) | ||||
−0.763297 | + | 0.646048i | \(0.776421\pi\) | |||||||
\(332\) | 107.164 | + | 322.729i | 0.322784 | + | 0.972076i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −31.6062 | − | 195.477i | −0.0946295 | − | 0.585261i | ||||
\(335\) | − | 119.981i | − | 0.358151i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −304.883 | −0.904698 | −0.452349 | − | 0.891841i | \(-0.649414\pi\) | ||||
−0.452349 | + | 0.891841i | \(0.649414\pi\) | |||||||
\(338\) | 332.974 | − | 53.8377i | 0.985130 | − | 0.159283i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 91.4245 | − | 30.3581i | 0.268896 | − | 0.0892884i | ||||
\(341\) | −163.393 | −0.479157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 423.102i | − | 1.23353i | ||||||
\(344\) | 137.759 | + | 264.029i | 0.400461 | + | 0.767525i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 76.1963 | − | 12.3200i | 0.220221 | − | 0.0356069i | ||||
\(347\) | 169.055i | 0.487191i | 0.969877 | + | 0.243595i | \(0.0783269\pi\) | ||||
−0.969877 | + | 0.243595i | \(0.921673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −214.596 | −0.614888 | −0.307444 | − | 0.951566i | \(-0.599474\pi\) | ||||
−0.307444 | + | 0.951566i | \(0.599474\pi\) | |||||||
\(350\) | 65.3188 | + | 403.982i | 0.186625 | + | 1.15423i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 226.915 | + | 219.722i | 0.644644 | + | 0.624209i | ||||
\(353\) | 551.791 | 1.56315 | 0.781574 | − | 0.623813i | \(-0.214417\pi\) | ||||
0.781574 | + | 0.623813i | \(0.214417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 303.216i | − | 0.854130i | ||||||
\(356\) | 245.934 | − | 81.6639i | 0.690826 | − | 0.229393i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6284 | + | 71.9188i | 0.0324815 | + | 0.200890i | ||||
\(359\) | 554.828i | 1.54548i | 0.634721 | + | 0.772741i | \(0.281115\pi\) | ||||
−0.634721 | + | 0.772741i | \(0.718885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 162.222 | 0.449367 | ||||||||
\(362\) | 36.7075 | − | 5.93514i | 0.101402 | − | 0.0163954i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.65942 | − | 26.0782i | −0.0237896 | − | 0.0716434i | ||||
\(365\) | 206.669 | 0.566216 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 168.173i | 0.458237i | 0.973399 | + | 0.229118i | \(0.0735843\pi\) | ||||
−0.973399 | + | 0.229118i | \(0.926416\pi\) | |||||||
\(368\) | 201.963 | + | 270.579i | 0.548814 | + | 0.735269i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −217.704 | + | 35.2000i | −0.588388 | + | 0.0951350i | ||||
\(371\) | − | 244.697i | − | 0.659560i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −343.397 | −0.920637 | −0.460318 | − | 0.887754i | \(-0.652265\pi\) | ||||
−0.460318 | + | 0.887754i | \(0.652265\pi\) | |||||||
\(374\) | −27.9798 | − | 173.049i | −0.0748124 | − | 0.462697i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.71449 | − | 12.8690i | −0.0178577 | − | 0.0342261i | ||||
\(377\) | 12.0564 | 0.0319798 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 602.392i | − | 1.58943i | −0.606986 | − | 0.794713i | \(-0.707621\pi\) | ||
0.606986 | − | 0.794713i | \(-0.292379\pi\) | |||||||
\(380\) | 48.2016 | + | 145.161i | 0.126846 | + | 0.382003i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 90.3004 | + | 558.487i | 0.236388 | + | 1.46201i | ||||
\(383\) | 364.610i | 0.951984i | 0.879450 | + | 0.475992i | \(0.157911\pi\) | ||||
−0.879450 | + | 0.475992i | \(0.842089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −310.456 | −0.806378 | ||||||||
\(386\) | −598.398 | + | 96.7534i | −1.55025 | + | 0.250657i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.2672 | − | 9.05422i | 0.0702762 | − | 0.0233356i | ||||
\(389\) | −214.651 | −0.551802 | −0.275901 | − | 0.961186i | \(-0.588976\pi\) | ||||
−0.275901 | + | 0.961186i | \(0.588976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 187.385i | − | 0.479244i | ||||||
\(392\) | 606.310 | − | 316.346i | 1.54671 | − | 0.807005i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −274.800 | + | 44.4317i | −0.697462 | + | 0.112771i | ||||
\(395\) | 26.0071i | 0.0658409i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −684.628 | −1.72450 | −0.862251 | − | 0.506480i | \(-0.830946\pi\) | ||||
−0.862251 | + | 0.506480i | \(0.830946\pi\) | |||||||
\(398\) | 3.58611 | + | 22.1793i | 0.00901033 | + | 0.0557268i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −226.233 | + | 168.863i | −0.565584 | + | 0.422158i | ||||
\(401\) | −190.384 | −0.474772 | −0.237386 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237386 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.80575i | 0.0243319i | ||||||||
\(404\) | 421.405 | − | 139.930i | 1.04308 | − | 0.346361i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 75.3463 | + | 466.000i | 0.185582 | + | 1.14778i | ||||
\(407\) | 401.298i | 0.985990i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −377.956 | −0.924099 | −0.462049 | − | 0.886854i | \(-0.652886\pi\) | ||||
−0.462049 | + | 0.886854i | \(0.652886\pi\) | |||||||
\(410\) | −227.234 | + | 36.7409i | −0.554229 | + | 0.0896119i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −115.881 | − | 348.982i | −0.281266 | − | 0.847043i | ||||
\(413\) | 1026.91 | 2.48647 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 230.573i | − | 0.555598i | ||||||
\(416\) | 13.1863 | − | 13.6179i | 0.0316977 | − | 0.0327354i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 274.762 | − | 44.4255i | 0.657324 | − | 0.106281i | ||||
\(419\) | 308.681i | 0.736709i | 0.929685 | + | 0.368355i | \(0.120079\pi\) | ||||
−0.929685 | + | 0.368355i | \(0.879921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −353.669 | −0.840069 | −0.420034 | − | 0.907508i | \(-0.637982\pi\) | ||||
−0.420034 | + | 0.907508i | \(0.637982\pi\) | |||||||
\(422\) | −41.2909 | − | 255.374i | −0.0978457 | − | 0.605153i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 149.658 | − | 78.0848i | 0.352966 | − | 0.184162i | ||||
\(425\) | 156.674 | 0.368644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 846.390i | − | 1.98218i | ||||||
\(428\) | −135.813 | − | 409.007i | −0.317320 | − | 0.955623i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −32.2303 | − | 199.337i | −0.0749542 | − | 0.463575i | ||||
\(431\) | − | 472.777i | − | 1.09693i | −0.836174 | − | 0.548465i | \(-0.815213\pi\) | ||
0.836174 | − | 0.548465i | \(-0.184787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 61.4188 | 0.141845 | 0.0709224 | − | 0.997482i | \(-0.477406\pi\) | ||||
0.0709224 | + | 0.997482i | \(0.477406\pi\) | |||||||
\(434\) | −379.009 | + | 61.2810i | −0.873292 | + | 0.141200i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 328.583 | − | 109.108i | 0.753632 | − | 0.250248i | ||||
\(437\) | 297.524 | 0.680832 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 409.165i | − | 0.932038i | −0.884775 | − | 0.466019i | \(-0.845688\pi\) | ||
0.884775 | − | 0.466019i | \(-0.154312\pi\) | |||||||
\(440\) | −99.0691 | − | 189.876i | −0.225157 | − | 0.431537i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.3853 | + | 1.67917i | −0.0234960 | + | 0.00379902i | ||||
\(443\) | − | 772.271i | − | 1.74328i | −0.490151 | − | 0.871638i | \(-0.663058\pi\) | ||
0.490151 | − | 0.871638i | \(-0.336942\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −175.707 | −0.394848 | ||||||||
\(446\) | 77.1176 | + | 476.954i | 0.172909 | + | 1.06940i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 608.763 | + | 424.566i | 1.35885 | + | 0.947692i | ||||
\(449\) | −789.037 | −1.75732 | −0.878660 | − | 0.477448i | \(-0.841562\pi\) | ||||
−0.878660 | + | 0.477448i | \(0.841562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 418.865i | 0.928747i | ||||||||
\(452\) | 17.8571 | − | 5.92957i | 0.0395069 | − | 0.0131185i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −121.904 | − | 753.950i | −0.268512 | − | 1.66068i | ||||
\(455\) | 18.6315i | 0.0409484i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −276.331 | −0.604662 | −0.302331 | − | 0.953203i | \(-0.597765\pi\) | ||||
−0.302331 | + | 0.953203i | \(0.597765\pi\) | |||||||
\(458\) | 294.828 | − | 47.6700i | 0.643728 | − | 0.104083i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −72.1462 | − | 217.271i | −0.156840 | − | 0.472329i | ||||
\(461\) | 588.083 | 1.27567 | 0.637834 | − | 0.770174i | \(-0.279831\pi\) | ||||
0.637834 | + | 0.770174i | \(0.279831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 782.061i | 1.68912i | 0.535464 | + | 0.844558i | \(0.320137\pi\) | ||||
−0.535464 | + | 0.844558i | \(0.679863\pi\) | |||||||
\(464\) | −260.964 | + | 194.787i | −0.562422 | + | 0.419799i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 432.254 | − | 69.8901i | 0.927585 | − | 0.149979i | ||||
\(467\) | − | 663.203i | − | 1.42014i | −0.704133 | − | 0.710068i | \(-0.748664\pi\) | ||
0.704133 | − | 0.710068i | \(-0.251336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −513.014 | −1.09385 | ||||||||
\(470\) | 1.57094 | + | 9.71589i | 0.00334242 | + | 0.0206721i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 327.696 | + | 628.063i | 0.694271 | + | 1.33064i | ||||
\(473\) | −367.442 | −0.776834 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 248.762i | 0.523709i | ||||||||
\(476\) | −129.805 | − | 390.914i | −0.272700 | − | 0.821247i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 80.4516 | + | 497.574i | 0.168309 | + | 1.04095i | ||||
\(479\) | 648.962i | 1.35483i | 0.735602 | + | 0.677414i | \(0.236899\pi\) | ||||
−0.735602 | + | 0.677414i | \(0.763101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0833 | 0.0500691 | ||||||||
\(482\) | −892.464 | + | 144.300i | −1.85159 | + | 0.299378i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 89.4779 | − | 29.7117i | 0.184872 | − | 0.0613878i | ||||
\(485\) | −19.4810 | −0.0401669 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 282.104i | 0.579269i | 0.957137 | + | 0.289635i | \(0.0935338\pi\) | ||||
−0.957137 | + | 0.289635i | \(0.906466\pi\) | |||||||
\(488\) | 517.656 | − | 270.090i | 1.06077 | − | 0.553464i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −457.754 | + | 74.0130i | −0.934191 | + | 0.151047i | ||||
\(491\) | − | 753.942i | − | 1.53552i | −0.640735 | − | 0.767762i | \(-0.721370\pi\) | ||
0.640735 | − | 0.767762i | \(-0.278630\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 180.726 | 0.366584 | ||||||||
\(494\) | −2.66613 | − | 16.4894i | −0.00539702 | − | 0.0333793i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.425 | − | 212.248i | −0.319405 | − | 0.427920i | ||||
\(497\) | −1296.49 | −2.60864 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 515.192i | 1.03245i | 0.856454 | + | 0.516224i | \(0.172663\pi\) | ||||
−0.856454 | + | 0.516224i | \(0.827337\pi\) | |||||||
\(500\) | 439.061 | − | 145.793i | 0.878121 | − | 0.291585i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −44.5096 | − | 275.282i | −0.0886646 | − | 0.548370i | ||||
\(503\) | 523.660i | 1.04107i | 0.853839 | + | 0.520537i | \(0.174268\pi\) | ||||
−0.853839 | + | 0.520537i | \(0.825732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −301.072 | −0.596182 | ||||||||
\(506\) | −411.252 | + | 66.4943i | −0.812751 | + | 0.131412i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.5523 | − | 31.7785i | −0.0207722 | − | 0.0625562i | ||||
\(509\) | 535.371 | 1.05181 | 0.525905 | − | 0.850544i | \(-0.323727\pi\) | ||||
0.525905 | + | 0.850544i | \(0.323727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 883.675i | − | 1.72931i | ||||||
\(512\) | −65.4050 | + | 507.805i | −0.127744 | + | 0.991807i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 929.163 | − | 150.234i | 1.80771 | − | 0.292284i | ||||
\(515\) | 249.329i | 0.484134i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.9095 | 0.0346412 | ||||||||
\(518\) | 150.508 | + | 930.859i | 0.290556 | + | 1.79702i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.3951 | + | 5.94548i | −0.0219137 | + | 0.0114336i | ||||
\(521\) | 177.268 | 0.340246 | 0.170123 | − | 0.985423i | \(-0.445584\pi\) | ||||
0.170123 | + | 0.985423i | \(0.445584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 444.206i | 0.849343i | 0.905347 | + | 0.424672i | \(0.139610\pi\) | ||||
−0.905347 | + | 0.424672i | \(0.860390\pi\) | |||||||
\(524\) | 167.486 | + | 504.390i | 0.319629 | + | 0.962577i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.18427 | − | 50.6178i | −0.0155595 | − | 0.0962316i | ||||
\(527\) | 146.989i | 0.278916i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 83.6788 | 0.158183 | ||||||||
\(530\) | −112.989 | + | 18.2689i | −0.213187 | + | 0.0344696i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 620.681 | − | 206.101i | 1.16669 | − | 0.387407i | ||||
\(533\) | 25.1375 | 0.0471623 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 292.214i | 0.546194i | ||||||||
\(536\) | −163.707 | − | 313.762i | −0.305424 | − | 0.585377i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.0925 | + | 2.60196i | −0.0299117 | + | 0.00483635i | ||||
\(539\) | 843.787i | 1.56547i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 571.163 | 1.05575 | 0.527877 | − | 0.849321i | \(-0.322988\pi\) | ||||
0.527877 | + | 0.849321i | \(0.322988\pi\) | |||||||
\(542\) | −128.323 | − | 793.651i | −0.236759 | − | 1.46430i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 197.663 | − | 204.133i | 0.363351 | − | 0.375245i | ||||
\(545\) | −234.756 | −0.430744 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 161.514i | 0.295272i | 0.989042 | + | 0.147636i | \(0.0471664\pi\) | ||||
−0.989042 | + | 0.147636i | \(0.952834\pi\) | |||||||
\(548\) | −171.268 | + | 56.8706i | −0.312533 | + | 0.103779i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −55.5965 | − | 343.851i | −0.101085 | − | 0.625184i | ||||
\(551\) | 286.951i | 0.520782i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 111.202 | 0.201088 | ||||||||
\(554\) | 221.926 | − | 35.8827i | 0.400589 | − | 0.0647702i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 190.304 | + | 573.109i | 0.342274 | + | 1.03077i | ||||
\(557\) | −568.917 | −1.02139 | −0.510697 | − | 0.859761i | \(-0.670613\pi\) | ||||
−0.510697 | + | 0.859761i | \(0.670613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0515i | 0.0394481i | ||||||||
\(560\) | −301.017 | − | 403.285i | −0.537530 | − | 0.720151i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1061.68 | − | 171.660i | 1.88911 | − | 0.305446i | ||||
\(563\) | − | 289.283i | − | 0.513825i | −0.966435 | − | 0.256912i | \(-0.917295\pi\) | ||
0.966435 | − | 0.256912i | \(-0.0827051\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7580 | −0.0225805 | ||||||||
\(566\) | −45.0824 | − | 278.824i | −0.0796510 | − | 0.492623i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −413.723 | − | 792.942i | −0.728385 | − | 1.39603i | ||||
\(569\) | 446.234 | 0.784243 | 0.392121 | − | 0.919913i | \(-0.371741\pi\) | ||||
0.392121 | + | 0.919913i | \(0.371741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 429.994i | − | 0.753054i | −0.926406 | − | 0.376527i | \(-0.877118\pi\) | ||
0.926406 | − | 0.376527i | \(-0.122882\pi\) | |||||||
\(572\) | 7.37051 | + | 22.1966i | 0.0128855 | + | 0.0388052i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 157.097 | + | 971.608i | 0.273688 | + | 1.69270i | ||||
\(575\) | − | 372.337i | − | 0.647542i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 50.9694 | 0.0883353 | 0.0441676 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441676 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(578\) | 414.914 | − | 67.0864i | 0.717845 | − | 0.116067i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 209.551 | − | 69.5825i | 0.361294 | − | 0.119970i | ||||
\(581\) | −985.887 | −1.69688 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 208.275i | 0.357247i | ||||||||
\(584\) | 540.460 | − | 281.989i | 0.925446 | − | 0.482857i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −909.353 | + | 147.031i | −1.55180 | + | 0.250906i | ||||
\(587\) | − | 743.363i | − | 1.26638i | −0.773998 | − | 0.633188i | \(-0.781746\pi\) | ||
0.773998 | − | 0.633188i | \(-0.218254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −233.384 | −0.396238 | ||||||||
\(590\) | −76.6685 | − | 474.177i | −0.129947 | − | 0.803690i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −521.289 | + | 389.097i | −0.880556 | + | 0.657258i | ||||
\(593\) | −382.547 | −0.645104 | −0.322552 | − | 0.946552i | \(-0.604541\pi\) | ||||
−0.322552 | + | 0.946552i | \(0.604541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 279.287i | 0.469391i | ||||||||
\(596\) | −542.030 | + | 179.984i | −0.909446 | + | 0.301987i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.99055 | + | 24.6806i | 0.00667316 | + | 0.0412720i | ||||
\(599\) | − | 988.710i | − | 1.65060i | −0.564694 | − | 0.825301i | \(-0.691006\pi\) | ||
0.564694 | − | 0.825301i | \(-0.308994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 526.560 | 0.876140 | 0.438070 | − | 0.898941i | \(-0.355662\pi\) | ||||
0.438070 | + | 0.898941i | \(0.355662\pi\) | |||||||
\(602\) | −852.327 | + | 137.811i | −1.41583 | + | 0.228921i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 320.261 | + | 964.479i | 0.530233 | + | 1.59682i | ||||
\(605\) | −63.9273 | −0.105665 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 516.880i | − | 0.851531i | −0.904833 | − | 0.425766i | \(-0.860005\pi\) | ||
0.904833 | − | 0.425766i | \(-0.139995\pi\) | |||||||
\(608\) | 324.117 | + | 313.843i | 0.533087 | + | 0.516189i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −390.821 | + | 63.1909i | −0.640691 | + | 0.103592i | ||||
\(611\) | − | 1.07481i | − | 0.00175910i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 762.957 | 1.24463 | 0.622314 | − | 0.782768i | \(-0.286193\pi\) | ||||
0.622314 | + | 0.782768i | \(0.286193\pi\) | |||||||
\(614\) | −67.1411 | − | 415.252i | −0.109350 | − | 0.676306i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −811.874 | + | 423.600i | −1.31798 | + | 0.687663i | ||||
\(617\) | −121.834 | −0.197461 | −0.0987307 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987307 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 306.775i | 0.495598i | 0.968811 | + | 0.247799i | \(0.0797072\pi\) | ||||
−0.968811 | + | 0.247799i | \(0.920293\pi\) | |||||||
\(620\) | 56.5931 | + | 170.433i | 0.0912793 | + | 0.274891i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40.9138 | + | 253.042i | 0.0657778 | + | 0.406820i | ||||
\(623\) | 751.290i | 1.20592i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 127.416 | 0.203866 | ||||||||
\(626\) | −14.2999 | + | 2.31212i | −0.0228433 | + | 0.00369348i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.1472 | + | 6.68999i | −0.0320815 | + | 0.0106529i | ||||
\(629\) | 361.010 | 0.573942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1071.11i | − | 1.69749i | −0.528805 | − | 0.848744i | \(-0.677360\pi\) | ||
0.528805 | − | 0.848744i | \(-0.322640\pi\) | |||||||
\(632\) | 35.4854 | + | 68.0114i | 0.0561478 | + | 0.107613i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −474.420 | + | 76.7078i | −0.748296 | + | 0.120990i | ||||
\(635\) | 22.7041i | 0.0357545i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 50.6386 | 0.0794954 | ||||||||
\(638\) | −64.1315 | − | 396.638i | −0.100520 | − | 0.621690i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 150.594 | − | 312.795i | 0.235303 | − | 0.488742i | ||||
\(641\) | −1054.52 | −1.64511 | −0.822557 | − | 0.568682i | \(-0.807454\pi\) | ||||
−0.822557 | + | 0.568682i | \(0.807454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.5759i | 0.0755458i | 0.999286 | + | 0.0377729i | \(0.0120263\pi\) | ||||
−0.999286 | + | 0.0377729i | \(0.987974\pi\) | |||||||
\(644\) | −929.010 | + | 308.483i | −1.44256 | + | 0.479011i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.9654 | − | 247.177i | −0.0618660 | − | 0.382627i | ||||
\(647\) | − | 539.373i | − | 0.833653i | −0.908986 | − | 0.416826i | \(-0.863142\pi\) | ||
0.908986 | − | 0.416826i | \(-0.136858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −874.061 | −1.34678 | ||||||||
\(650\) | −20.6357 | + | 3.33654i | −0.0317472 | + | 0.00513313i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −75.0699 | − | 226.076i | −0.115138 | − | 0.346742i | ||||
\(653\) | 552.915 | 0.846730 | 0.423365 | − | 0.905959i | \(-0.360849\pi\) | ||||
0.423365 | + | 0.905959i | \(0.360849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 360.361i | − | 0.550169i | ||||||
\(656\) | −544.109 | + | 406.130i | −0.829435 | + | 0.619100i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 41.5433 | − | 6.71703i | 0.0631357 | − | 0.0102082i | ||||
\(659\) | − | 847.738i | − | 1.28640i | −0.765698 | − | 0.643200i | \(-0.777606\pi\) | ||
0.765698 | − | 0.643200i | \(-0.222394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 718.893 | 1.08758 | 0.543792 | − | 0.839220i | \(-0.316988\pi\) | ||||
0.543792 | + | 0.839220i | \(0.316988\pi\) | |||||||
\(662\) | −136.529 | − | 844.401i | −0.206237 | − | 1.27553i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −314.605 | − | 602.973i | −0.473803 | − | 0.908093i | ||||
\(665\) | −443.444 | −0.666833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 429.497i | − | 0.643923i | ||||||
\(668\) | 124.804 | + | 375.853i | 0.186833 | + | 0.562654i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38.3013 | + | 236.885i | 0.0571662 | + | 0.353560i | ||||
\(671\) | 720.409i | 1.07364i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −576.975 | −0.857318 | −0.428659 | − | 0.903466i | \(-0.641014\pi\) | ||||
−0.428659 | + | 0.903466i | \(0.641014\pi\) | |||||||
\(674\) | 601.949 | − | 97.3277i | 0.893100 | − | 0.144403i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −640.223 | + | 212.590i | −0.947076 | + | 0.314482i | ||||
\(677\) | 202.042 | 0.298437 | 0.149219 | − | 0.988804i | \(-0.452324\pi\) | ||||
0.149219 | + | 0.988804i | \(0.452324\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 83.2968i | 0.122676i | ||||||||
\(680\) | −170.814 | + | 89.1231i | −0.251196 | + | 0.131063i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 322.596 | − | 52.1597i | 0.473014 | − | 0.0764805i | ||||
\(683\) | 568.249i | 0.831990i | 0.909367 | + | 0.415995i | \(0.136567\pi\) | ||||
−0.909367 | + | 0.415995i | \(0.863433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 122.362 | 0.178631 | ||||||||
\(686\) | 135.067 | + | 835.355i | 0.196890 | + | 1.21772i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −356.271 | − | 477.311i | −0.517835 | − | 0.693766i | ||||
\(689\) | 12.4993 | 0.0181412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 405.734i | − | 0.587170i | −0.955933 | − | 0.293585i | \(-0.905152\pi\) | ||
0.955933 | − | 0.293585i | \(-0.0948483\pi\) | |||||||
\(692\) | −146.506 | + | 48.6482i | −0.211714 | + | 0.0703008i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53.9673 | − | 333.775i | −0.0777627 | − | 0.480945i | ||||
\(695\) | − | 409.456i | − | 0.589146i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 376.813 | 0.540621 | ||||||||
\(698\) | 423.689 | − | 68.5053i | 0.607005 | − | 0.0981451i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −257.925 | − | 776.753i | −0.368465 | − | 1.10965i | ||||
\(701\) | 83.5164 | 0.119139 | 0.0595695 | − | 0.998224i | \(-0.481027\pi\) | ||||
0.0595695 | + | 0.998224i | \(0.481027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 573.200i | 0.815363i | ||||||||
\(704\) | −518.152 | − | 361.372i | −0.736012 | − | 0.513312i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1089.43 | + | 176.148i | −1.54311 | + | 0.249501i | ||||
\(707\) | 1287.33i | 1.82083i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 347.815 | 0.490572 | 0.245286 | − | 0.969451i | \(-0.421118\pi\) | ||||
0.245286 | + | 0.969451i | \(0.421118\pi\) | |||||||
\(710\) | 96.7955 | + | 598.657i | 0.136332 | + | 0.843180i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −459.493 | + | 239.743i | −0.645355 | + | 0.336718i | ||||
\(713\) | 349.320 | 0.489930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 15.8583i | − | 0.0221795i | ||||||
\(716\) | −45.9172 | − | 138.281i | −0.0641301 | − | 0.193130i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −177.117 | − | 1095.43i | −0.246682 | − | 1.52567i | ||||
\(719\) | − | 536.277i | − | 0.745865i | −0.927858 | − | 0.372933i | \(-0.878352\pi\) | ||
0.927858 | − | 0.372933i | \(-0.121648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1066.08 | 1.47862 | ||||||||
\(722\) | −320.284 | + | 51.7859i | −0.443606 | + | 0.0717256i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −70.5791 | + | 23.4362i | −0.0974849 | + | 0.0323704i | ||||
\(725\) | 359.106 | 0.495319 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 941.145i | 1.29456i | 0.762252 | + | 0.647280i | \(0.224094\pi\) | ||||
−0.762252 | + | 0.647280i | \(0.775906\pi\) | |||||||
\(728\) | 25.4217 | + | 48.7233i | 0.0349199 | + | 0.0669277i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −408.038 | + | 65.9747i | −0.558956 | + | 0.0903763i | ||||
\(731\) | 330.553i | 0.452193i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −622.126 | −0.848740 | −0.424370 | − | 0.905489i | \(-0.639504\pi\) | ||||
−0.424370 | + | 0.905489i | \(0.639504\pi\) | |||||||
\(734\) | −53.6857 | − | 332.033i | −0.0731412 | − | 0.452362i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −485.125 | − | 469.747i | −0.659137 | − | 0.638244i | ||||
\(737\) | 436.655 | 0.592477 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 444.439i | 0.601406i | 0.953718 | + | 0.300703i | \(0.0972213\pi\) | ||||
−0.953718 | + | 0.300703i | \(0.902779\pi\) | |||||||
\(740\) | 418.588 | − | 138.995i | 0.565660 | − | 0.187831i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 78.1143 | + | 483.119i | 0.105275 | + | 0.651104i | ||||
\(743\) | 76.4724i | 0.102924i | 0.998675 | + | 0.0514619i | \(0.0163881\pi\) | ||||
−0.998675 | + | 0.0514619i | \(0.983612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 387.252 | 0.519801 | ||||||||
\(746\) | 677.990 | − | 109.622i | 0.908833 | − | 0.146947i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 110.484 | + | 332.728i | 0.147706 | + | 0.444824i | ||||
\(749\) | 1249.45 | 1.66816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1095.84i | 1.45917i | 0.683888 | + | 0.729587i | \(0.260288\pi\) | ||||
−0.683888 | + | 0.729587i | \(0.739712\pi\) | |||||||
\(752\) | 17.3650 | + | 23.2646i | 0.0230917 | + | 0.0309370i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.8036 | + | 3.84875i | −0.0315698 | + | 0.00510444i | ||||
\(755\) | − | 689.070i | − | 0.912676i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −346.346 | −0.457525 | −0.228762 | − | 0.973482i | \(-0.573468\pi\) | ||||
−0.228762 | + | 0.973482i | \(0.573468\pi\) | |||||||
\(758\) | 192.301 | + | 1189.34i | 0.253696 | + | 1.56905i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −141.507 | − | 271.213i | −0.186193 | − | 0.356859i | ||||
\(761\) | 213.130 | 0.280065 | 0.140033 | − | 0.990147i | \(-0.455279\pi\) | ||||
0.140033 | + | 0.990147i | \(0.455279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1003.77i | 1.31556i | ||||||||
\(764\) | −356.571 | − | 1073.83i | −0.466715 | − | 1.40553i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −116.394 | − | 719.871i | −0.151951 | − | 0.939779i | ||||
\(767\) | 52.4554i | 0.0683903i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 541.572 | 0.704254 | 0.352127 | − | 0.935952i | \(-0.385458\pi\) | ||||
0.352127 | + | 0.935952i | \(0.385458\pi\) | |||||||
\(770\) | 612.951 | − | 99.1065i | 0.796040 | − | 0.128710i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1150.56 | − | 382.052i | 1.49037 | − | 0.494886i | ||||
\(773\) | 1255.73 | 1.62449 | 0.812245 | − | 0.583317i | \(-0.198245\pi\) | ||||
0.812245 | + | 0.583317i | \(0.198245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 292.070i | 0.376864i | ||||||||
\(776\) | −50.9448 | + | 26.5808i | −0.0656505 | + | 0.0342535i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 423.798 | − | 68.5229i | 0.544728 | − | 0.0880757i | ||||
\(779\) | 598.292i | 0.768026i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1103.52 | 1.41296 | ||||||||
\(782\) | 59.8186 | + | 369.964i | 0.0764944 | + | 0.473100i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1096.09 | + | 818.133i | −1.39807 | + | 1.04354i | ||||
\(785\) | 14.3941 | 0.0183364 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 992.405i | − | 1.26100i | −0.776190 | − | 0.630499i | \(-0.782850\pi\) | ||
0.776190 | − | 0.630499i | \(-0.217150\pi\) | |||||||
\(788\) | 528.370 | − | 175.448i | 0.670520 | − | 0.222650i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.30224 | − | 51.3474i | −0.0105092 | − | 0.0649967i | ||||
\(791\) | 54.5507i | 0.0689643i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.2342 | 0.0545198 | ||||||||
\(794\) | 1351.70 | − | 218.553i | 1.70239 | − | 0.275256i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.1605 | − | 42.6451i | −0.0177896 | − | 0.0535742i | ||||
\(797\) | −638.524 | −0.801159 | −0.400580 | − | 0.916262i | \(-0.631191\pi\) | ||||
−0.400580 | + | 0.916262i | \(0.631191\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 16.1115i | − | 0.0201646i | ||||||
\(800\) | 392.760 | − | 405.617i | 0.490950 | − | 0.507022i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 375.885 | − | 60.7760i | 0.468685 | − | 0.0757805i | ||||
\(803\) | 752.146i | 0.936669i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 663.729 | 0.824508 | ||||||||
\(806\) | −3.13028 | − | 19.3601i | −0.00388372 | − | 0.0240199i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −787.335 | + | 410.797i | −0.974424 | + | 0.508412i | ||||
\(809\) | −174.260 | −0.215401 | −0.107701 | − | 0.994183i | \(-0.534349\pi\) | ||||
−0.107701 | + | 0.994183i | \(0.534349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1182.19i | − | 1.45770i | −0.684675 | − | 0.728849i | \(-0.740056\pi\) | ||
0.684675 | − | 0.728849i | \(-0.259944\pi\) | |||||||
\(812\) | −297.521 | − | 895.998i | −0.366406 | − | 1.10345i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −128.106 | − | 792.306i | −0.157378 | − | 0.973349i | ||||
\(815\) | 161.519i | 0.198183i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −524.842 | −0.642402 | ||||||||
\(818\) | 746.222 | − | 120.655i | 0.912251 | − | 0.147500i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 436.912 | − | 145.079i | 0.532820 | − | 0.176926i | ||||
\(821\) | −587.909 | −0.716089 | −0.358045 | − | 0.933705i | \(-0.616556\pi\) | ||||
−0.358045 | + | 0.933705i | \(0.616556\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 113.247i | − | 0.137603i | −0.997630 | − | 0.0688015i | \(-0.978082\pi\) | ||
0.997630 | − | 0.0688015i | \(-0.0219175\pi\) | |||||||
\(824\) | 340.197 | + | 652.022i | 0.412860 | + | 0.791289i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2027.49 | + | 327.820i | −2.45459 | + | 0.396876i | ||||
\(827\) | 800.560i | 0.968030i | 0.875060 | + | 0.484015i | \(0.160822\pi\) | ||||
−0.875060 | + | 0.484015i | \(0.839178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1162.87 | 1.40274 | 0.701369 | − | 0.712798i | \(-0.252573\pi\) | ||||
0.701369 | + | 0.712798i | \(0.252573\pi\) | |||||||
\(830\) | 73.6057 | + | 455.234i | 0.0886816 | + | 0.548475i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.6872 | + | 31.0961i | −0.0260663 | + | 0.0373751i | ||||
\(833\) | 759.075 | 0.911255 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 268.527i | − | 0.321589i | ||||||
\(836\) | −528.296 | + | 175.424i | −0.631933 | + | 0.209837i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −98.5400 | − | 609.447i | −0.117590 | − | 0.727264i | ||||
\(839\) | − | 1565.68i | − | 1.86613i | −0.359707 | − | 0.933065i | \(-0.617123\pi\) | ||
0.359707 | − | 0.933065i | \(-0.382877\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −426.765 | −0.507450 | ||||||||
\(842\) | 698.269 | − | 112.901i | 0.829298 | − | 0.134087i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 163.046 | + | 491.020i | 0.193182 | + | 0.581777i | ||||
\(845\) | 457.406 | 0.541309 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 273.341i | 0.322717i | ||||||||
\(848\) | −270.551 | + | 201.943i | −0.319046 | + | 0.238140i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −309.330 | + | 50.0149i | −0.363918 | + | 0.0588410i | ||||
\(851\) | − | 857.943i | − | 1.00816i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 137.618 | 0.161334 | 0.0806668 | − | 0.996741i | \(-0.474295\pi\) | ||||
0.0806668 | + | 0.996741i | \(0.474295\pi\) | |||||||
\(854\) | 270.192 | + | 1671.08i | 0.316384 | + | 1.95676i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 398.711 | + | 764.170i | 0.465783 | + | 0.892722i | ||||
\(857\) | 768.979 | 0.897291 | 0.448646 | − | 0.893710i | \(-0.351907\pi\) | ||||
0.448646 | + | 0.893710i | \(0.351907\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 205.945i | − | 0.239749i | −0.992789 | − | 0.119875i | \(-0.961751\pi\) | ||
0.992789 | − | 0.119875i | \(-0.0382493\pi\) | |||||||
\(860\) | 127.268 | + | 383.274i | 0.147987 | + | 0.445668i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 150.924 | + | 933.430i | 0.175086 | + | 1.08287i | ||||
\(863\) | 772.757i | 0.895431i | 0.894176 | + | 0.447716i | \(0.147762\pi\) | ||||
−0.894176 | + | 0.447716i | \(0.852238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 104.671 | 0.121007 | ||||||||
\(866\) | −121.263 | + | 19.6067i | −0.140026 | + | 0.0226405i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 728.737 | − | 241.981i | 0.839558 | − | 0.278780i | ||||
\(869\) | −94.6498 | −0.108918 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 26.2052i | − | 0.0300863i | ||||||
\(872\) | −613.911 | + | 320.312i | −0.704026 | + | 0.367330i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −587.418 | + | 94.9782i | −0.672103 | + | 0.108671i | ||||
\(875\) | 1341.26i | 1.53287i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 400.193 | 0.456320 | 0.228160 | − | 0.973624i | \(-0.426729\pi\) | ||||
0.228160 | + | 0.973624i | \(0.426729\pi\) | |||||||
\(878\) | 130.617 | + | 807.838i | 0.148767 | + | 0.920089i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 256.212 | + | 343.258i | 0.291150 | + | 0.390066i | ||||
\(881\) | −728.323 | −0.826700 | −0.413350 | − | 0.910572i | \(-0.635641\pi\) | ||||
−0.413350 | + | 0.910572i | \(0.635641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 383.413i | 0.434216i | 0.976148 | + | 0.217108i | \(0.0696625\pi\) | ||||
−0.976148 | + | 0.217108i | \(0.930338\pi\) | |||||||
\(884\) | 19.9682 | − | 6.63055i | 0.0225884 | − | 0.00750062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 246.531 | + | 1524.74i | 0.278252 | + | 1.72093i | ||||
\(887\) | − | 1450.20i | − | 1.63495i | −0.575968 | − | 0.817473i | \(-0.695375\pi\) | ||
0.575968 | − | 0.817473i | \(-0.304625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 97.0784 | 0.109200 | ||||||||
\(890\) | 346.909 | − | 56.0909i | 0.389785 | − | 0.0630234i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −304.516 | − | 917.061i | −0.341385 | − | 1.02810i | ||||
\(893\) | 25.5813 | 0.0286465 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 98.7949i | 0.110385i | ||||||||
\(896\) | −1337.45 | − | 643.910i | −1.49269 | − | 0.718650i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1557.84 | − | 251.884i | 1.73479 | − | 0.280494i | ||||
\(899\) | 336.907i | 0.374758i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 187.365 | 0.207952 | ||||||||
\(902\) | −133.714 | − | 826.990i | −0.148242 | − | 0.916840i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.3635 | + | 17.4076i | −0.0369065 | + | 0.0192562i | ||||
\(905\) | 50.4251 | 0.0557183 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 615.790i | − | 0.678931i | −0.940619 | − | 0.339465i | \(-0.889754\pi\) | ||
0.940619 | − | 0.339465i | \(-0.110246\pi\) | |||||||
\(908\) | 481.366 | + | 1449.65i | 0.530139 | + | 1.59653i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.94772 | − | 36.7853i | −0.00653596 | − | 0.0404234i | ||||
\(911\) | 262.153i | 0.287764i | 0.989595 | + | 0.143882i | \(0.0459586\pi\) | ||||
−0.989595 | + | 0.143882i | \(0.954041\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 839.143 | 0.919106 | ||||||||
\(914\) | 545.576 | − | 88.2128i | 0.596910 | − | 0.0965129i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −566.878 | + | 188.235i | −0.618862 | + | 0.205497i | ||||
\(917\) | −1540.83 | −1.68030 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 566.458i | − | 0.616385i | −0.951324 | − | 0.308193i | \(-0.900276\pi\) | ||
0.951324 | − | 0.308193i | \(-0.0997241\pi\) | |||||||
\(920\) | 211.802 | + | 405.940i | 0.230219 | + | 0.441239i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1161.09 | + | 187.733i | −1.25931 | + | 0.203615i | ||||
\(923\) | − | 66.2259i | − | 0.0717507i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 717.333 | 0.775495 | ||||||||
\(926\) | −249.657 | − | 1544.07i | −0.269608 | − | 1.66746i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 453.055 | − | 467.886i | 0.488206 | − | 0.504188i | ||||
\(929\) | −597.491 | −0.643155 | −0.321577 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321577 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1205.24i | 1.29456i | ||||||||
\(932\) | −831.114 | + | 275.976i | −0.891754 | + | 0.296112i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 211.714 | + | 1309.40i | 0.226674 | + | 1.40193i | ||||
\(935\) | − | 237.717i | − | 0.254243i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 457.785 | 0.488564 | 0.244282 | − | 0.969704i | \(-0.421448\pi\) | ||||
0.244282 | + | 0.969704i | \(0.421448\pi\) | |||||||
\(938\) | 1012.87 | − | 163.769i | 1.07982 | − | 0.174594i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.20319 | − | 18.6812i | −0.00659914 | − | 0.0198736i | ||||
\(941\) | 1355.72 | 1.44072 | 0.720360 | − | 0.693601i | \(-0.243977\pi\) | ||||
0.720360 | + | 0.693601i | \(0.243977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 895.500i | − | 0.949629i | ||||||
\(944\) | −847.486 | − | 1135.41i | −0.897760 | − | 1.20277i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 725.463 | − | 117.298i | 0.766874 | − | 0.123994i | ||||
\(947\) | − | 655.783i | − | 0.692484i | −0.938145 | − | 0.346242i | \(-0.887458\pi\) | ||
0.938145 | − | 0.346242i | \(-0.112542\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.1388 | 0.0475646 | ||||||||
\(950\) | −79.4121 | − | 491.145i | −0.0835917 | − | 0.516995i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 381.073 | + | 730.366i | 0.400287 | + | 0.767191i | ||||
\(953\) | 554.778 | 0.582139 | 0.291069 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291069 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 767.193i | 0.803344i | ||||||||
\(956\) | −317.680 | − | 956.708i | −0.332302 | − | 1.00074i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −207.168 | − | 1281.28i | −0.216250 | − | 1.33746i | ||||
\(959\) | − | 523.197i | − | 0.545566i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 686.985 | 0.714865 | ||||||||
\(962\) | −47.5490 | + | 7.68808i | −0.0494272 | + | 0.00799177i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1715.98 | − | 569.801i | 1.78006 | − | 0.591080i | ||||
\(965\) | −822.019 | −0.851833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 579.659i | − | 0.599441i | −0.954027 | − | 0.299720i | \(-0.903107\pi\) | ||
0.954027 | − | 0.299720i | \(-0.0968934\pi\) | |||||||
\(968\) | −167.177 | + | 87.2255i | −0.172703 | + | 0.0901090i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.4624 | − | 6.21889i | 0.0396520 | − | 0.00641123i | ||||
\(971\) | − | 260.660i | − | 0.268445i | −0.990951 | − | 0.134223i | \(-0.957146\pi\) | ||
0.990951 | − | 0.134223i | \(-0.0428537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1750.76 | −1.79934 | ||||||||
\(974\) | −90.0559 | − | 556.975i | −0.0924598 | − | 0.571843i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −935.818 | + | 698.506i | −0.958830 | + | 0.715682i | ||||
\(977\) | −1277.91 | −1.30799 | −0.653995 | − | 0.756499i | \(-0.726908\pi\) | ||||
−0.653995 | + | 0.756499i | \(0.726908\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 639.465i | − | 0.653182i | ||||||
\(980\) | 880.143 | − | 292.257i | 0.898105 | − | 0.298221i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 240.680 | + | 1488.55i | 0.245092 | + | 1.51584i | ||||
\(983\) | 436.852i | 0.444407i | 0.975000 | + | 0.222204i | \(0.0713250\pi\) | ||||
−0.975000 | + | 0.222204i | \(0.928675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −377.493 | −0.383241 | ||||||||
\(986\) | −356.818 | + | 57.6930i | −0.361884 | + | 0.0585122i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.5278 | + | 31.7049i | 0.0106557 | + | 0.0320899i | ||||
\(989\) | 785.562 | 0.794300 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1344.50i | 1.35671i | 0.734734 | + | 0.678356i | \(0.237307\pi\) | ||||
−0.734734 | + | 0.678356i | \(0.762693\pi\) | |||||||
\(992\) | 380.543 | + | 368.481i | 0.383612 | + | 0.371452i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2559.74 | − | 413.879i | 2.57520 | − | 0.416377i | ||||
\(995\) | 30.4677i | 0.0306208i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1884.79 | −1.89047 | −0.945233 | − | 0.326396i | \(-0.894166\pi\) | ||||
−0.945233 | + | 0.326396i | \(0.894166\pi\) | |||||||
\(998\) | −164.464 | − | 1017.17i | −0.164794 | − | 1.01921i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.3.d.i.163.2 | 8 | ||
3.2 | odd | 2 | 324.3.d.g.163.7 | 8 | |||
4.3 | odd | 2 | inner | 324.3.d.i.163.1 | 8 | ||
9.2 | odd | 6 | 108.3.f.c.91.2 | 16 | |||
9.4 | even | 3 | 36.3.f.c.7.6 | ✓ | 16 | ||
9.5 | odd | 6 | 108.3.f.c.19.3 | 16 | |||
9.7 | even | 3 | 36.3.f.c.31.7 | yes | 16 | ||
12.11 | even | 2 | 324.3.d.g.163.8 | 8 | |||
36.7 | odd | 6 | 36.3.f.c.31.6 | yes | 16 | ||
36.11 | even | 6 | 108.3.f.c.91.3 | 16 | |||
36.23 | even | 6 | 108.3.f.c.19.2 | 16 | |||
36.31 | odd | 6 | 36.3.f.c.7.7 | yes | 16 | ||
72.5 | odd | 6 | 1728.3.o.g.127.5 | 16 | |||
72.11 | even | 6 | 1728.3.o.g.1279.5 | 16 | |||
72.13 | even | 6 | 576.3.o.g.511.3 | 16 | |||
72.29 | odd | 6 | 1728.3.o.g.1279.6 | 16 | |||
72.43 | odd | 6 | 576.3.o.g.319.3 | 16 | |||
72.59 | even | 6 | 1728.3.o.g.127.6 | 16 | |||
72.61 | even | 6 | 576.3.o.g.319.6 | 16 | |||
72.67 | odd | 6 | 576.3.o.g.511.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.6 | ✓ | 16 | 9.4 | even | 3 | ||
36.3.f.c.7.7 | yes | 16 | 36.31 | odd | 6 | ||
36.3.f.c.31.6 | yes | 16 | 36.7 | odd | 6 | ||
36.3.f.c.31.7 | yes | 16 | 9.7 | even | 3 | ||
108.3.f.c.19.2 | 16 | 36.23 | even | 6 | |||
108.3.f.c.19.3 | 16 | 9.5 | odd | 6 | |||
108.3.f.c.91.2 | 16 | 9.2 | odd | 6 | |||
108.3.f.c.91.3 | 16 | 36.11 | even | 6 | |||
324.3.d.g.163.7 | 8 | 3.2 | odd | 2 | |||
324.3.d.g.163.8 | 8 | 12.11 | even | 2 | |||
324.3.d.i.163.1 | 8 | 4.3 | odd | 2 | inner | ||
324.3.d.i.163.2 | 8 | 1.1 | even | 1 | trivial | ||
576.3.o.g.319.3 | 16 | 72.43 | odd | 6 | |||
576.3.o.g.319.6 | 16 | 72.61 | even | 6 | |||
576.3.o.g.511.3 | 16 | 72.13 | even | 6 | |||
576.3.o.g.511.6 | 16 | 72.67 | odd | 6 | |||
1728.3.o.g.127.5 | 16 | 72.5 | odd | 6 | |||
1728.3.o.g.127.6 | 16 | 72.59 | even | 6 | |||
1728.3.o.g.1279.5 | 16 | 72.11 | even | 6 | |||
1728.3.o.g.1279.6 | 16 | 72.29 | odd | 6 |