Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(9,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("280.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.bg (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: | \(2.23581125660\) |
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 | 9.2 | ||
Character | \(\chi\) | \(=\) | 280.9 |
Dual form | 280.2.bg.a.249.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.20343 | + | 1.27215i | −1.27215 | + | 0.734478i | −0.975393 | − | 0.220474i | \(-0.929240\pi\) |
−0.296760 | + | 0.954952i | \(0.595906\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.474541 | − | 2.18513i | −0.212221 | − | 0.977222i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64391 | + | 0.0988222i | 0.999302 | + | 0.0373513i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.73675 | − | 3.00813i | 0.578915 | − | 1.00271i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.95614 | + | 3.38814i | 0.589799 | + | 1.02156i | 0.994258 | + | 0.107006i | \(0.0341264\pi\) |
−0.404459 | + | 0.914556i | \(0.632540\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47349i | 0.963373i | 0.876344 | + | 0.481687i | \(0.159976\pi\) | ||||
−0.876344 | + | 0.481687i | \(0.840024\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.82544 | + | 4.21111i | 0.987726 | + | 1.08730i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.40168 | − | 2.54131i | 1.06756 | − | 0.616358i | 0.140049 | − | 0.990145i | \(-0.455274\pi\) |
0.927515 | + | 0.373787i | \(0.121941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.62594 | + | 4.54826i | −0.602432 | + | 1.04344i | 0.390019 | + | 0.920807i | \(0.372468\pi\) |
−0.992452 | + | 0.122637i | \(0.960865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.95139 | + | 3.14570i | −1.29870 | + | 0.686449i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.21157 | + | 3.00890i | 1.08669 | + | 0.627399i | 0.932692 | − | 0.360673i | \(-0.117453\pi\) |
0.153994 | + | 0.988072i | \(0.450786\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.54962 | + | 2.07387i | −0.909924 | + | 0.414775i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.20471i | 0.231846i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2660 | 1.90635 | 0.953175 | − | 0.302419i | \(-0.0977942\pi\) | ||||
0.953175 | + | 0.302419i | \(0.0977942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.02175 | − | 1.76973i | −0.183512 | − | 0.317852i | 0.759562 | − | 0.650435i | \(-0.225413\pi\) |
−0.943074 | + | 0.332583i | \(0.892080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.62046 | − | 4.97702i | −1.50063 | − | 0.866389i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.03870 | − | 5.82418i | −0.175573 | − | 0.984466i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.350741 | + | 0.202501i | 0.0576615 | + | 0.0332909i | 0.528554 | − | 0.848900i | \(-0.322735\pi\) |
−0.470892 | + | 0.882191i | \(0.656068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.41881 | − | 7.65361i | −0.707576 | − | 1.22556i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.57534 | −0.402200 | −0.201100 | − | 0.979571i | \(-0.564452\pi\) | ||||
−0.201100 | + | 0.979571i | \(0.564452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.15769i | − | 0.939038i | −0.882922 | − | 0.469519i | \(-0.844427\pi\) | ||
0.882922 | − | 0.469519i | \(-0.155573\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.39733 | − | 2.36754i | −1.10273 | − | 0.352932i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.416173 | − | 0.240278i | −0.0607051 | − | 0.0350481i | 0.469340 | − | 0.883017i | \(-0.344492\pi\) |
−0.530045 | + | 0.847969i | \(0.677825\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98047 | + | 0.522553i | 0.997210 | + | 0.0746504i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.46587 | + | 11.1992i | −0.905403 | + | 1.56820i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.403939 | − | 0.233214i | 0.0554852 | − | 0.0320344i | −0.472001 | − | 0.881598i | \(-0.656468\pi\) |
0.527486 | + | 0.849564i | \(0.323135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.47526 | − | 5.88224i | 0.873124 | − | 0.793162i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 13.3624i | − | 1.76989i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.15565 | − | 8.92984i | −0.671208 | − | 1.16257i | −0.977562 | − | 0.210649i | \(-0.932442\pi\) |
0.306354 | − | 0.951918i | \(-0.400891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.04044 | + | 6.99825i | −0.517325 | + | 0.896034i | 0.482472 | + | 0.875911i | \(0.339739\pi\) |
−0.999798 | + | 0.0201223i | \(0.993594\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.88906 | − | 7.78159i | 0.615964 | − | 0.980388i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.59005 | − | 1.64832i | 0.941429 | − | 0.204448i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.59547 | + | 2.07585i | −0.439257 | + | 0.253605i | −0.703282 | − | 0.710911i | \(-0.748283\pi\) |
0.264026 | + | 0.964516i | \(0.414950\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.3111 | −1.84324 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.28658 | −0.508724 | −0.254362 | − | 0.967109i | \(-0.581865\pi\) | ||||
−0.254362 | + | 0.967109i | \(0.581865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.16976 | − | 2.40741i | 0.488034 | − | 0.281767i | −0.235724 | − | 0.971820i | \(-0.575746\pi\) |
0.723759 | + | 0.690053i | \(0.242413\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.38650 | − | 10.3575i | 0.852920 | − | 1.19598i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.83703 | + | 9.15122i | 0.551231 | + | 1.04288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.33197 | + | 10.9673i | −0.712403 | + | 1.23392i | 0.251550 | + | 0.967844i | \(0.419060\pi\) |
−0.963953 | + | 0.266073i | \(0.914274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.67766 | + | 6.36990i | 0.408629 | + | 0.707767i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.42280i | 0.924522i | 0.886744 | + | 0.462261i | \(0.152962\pi\) | ||||
−0.886744 | + | 0.462261i | \(0.847038\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.64188 | − | 8.41230i | −0.828878 | − | 0.912442i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.6205 | + | 13.0599i | −2.42517 | + | 1.40017i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.19298 | − | 2.06629i | 0.126455 | − | 0.219027i | −0.795846 | − | 0.605500i | \(-0.792973\pi\) |
0.922301 | + | 0.386473i | \(0.126307\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.343258 | + | 9.18358i | −0.0359832 | + | 0.962701i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.50272 | + | 2.59965i | 0.466911 | + | 0.269571i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.1847 | + | 3.57969i | 1.14752 | + | 0.367269i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.32080i | − | 0.134107i | −0.997749 | − | 0.0670537i | \(-0.978640\pi\) | ||
0.997749 | − | 0.0670537i | \(-0.0213599\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.5893 | 1.36577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.87583 | − | 6.71314i | −0.385660 | − | 0.667982i | 0.606201 | − | 0.795312i | \(-0.292693\pi\) |
−0.991860 | + | 0.127330i | \(0.959359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.90841 | − | 1.10182i | −0.188041 | − | 0.108565i | 0.403024 | − | 0.915189i | \(-0.367959\pi\) |
−0.591065 | + | 0.806624i | \(0.701292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.69796 | + | 11.5118i | 0.946424 | + | 1.12344i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.37347 | − | 5.41177i | −0.906167 | − | 0.523176i | −0.0269713 | − | 0.999636i | \(-0.508586\pi\) |
−0.879196 | + | 0.476460i | \(0.841920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.52166 | − | 9.56380i | −0.528880 | − | 0.916046i | −0.999433 | − | 0.0336747i | \(-0.989279\pi\) |
0.470553 | − | 0.882372i | \(-0.344054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.03045 | −0.0978057 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.29167i | 0.685942i | 0.939346 | + | 0.342971i | \(0.111433\pi\) | ||||
−0.939346 | + | 0.342971i | \(0.888567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.10174 | − | 12.8158i | 0.382490 | − | 1.19508i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.4487 | + | 6.03257i | 0.965985 | + | 0.557712i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.8888 | − | 6.28400i | 1.08984 | − | 0.576053i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.15298 | + | 3.72908i | −0.195726 | + | 0.339007i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.67458 | − | 3.27622i | 0.511660 | − | 0.295407i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.69067 | + | 8.95739i | 0.598432 | + | 0.801174i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.66305i | − | 0.679986i | −0.940428 | − | 0.339993i | \(-0.889575\pi\) | ||
0.940428 | − | 0.339993i | \(-0.110425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.83352 | + | 13.5680i | 0.689703 | + | 1.19460i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.60596 | − | 14.9060i | 0.751906 | − | 1.30234i | −0.194991 | − | 0.980805i | \(-0.562468\pi\) |
0.946898 | − | 0.321535i | \(-0.104199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.39221 | + | 11.7657i | −0.640986 | + | 1.02021i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.63245 | − | 0.571684i | 0.226565 | − | 0.0492027i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.55592 | − | 2.63036i | 0.389239 | − | 0.224727i | −0.292592 | − | 0.956238i | \(-0.594518\pi\) |
0.681830 | + | 0.731510i | \(0.261184\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2148 | 1.29050 | 0.645250 | − | 0.763971i | \(-0.276753\pi\) | ||||
0.645250 | + | 0.763971i | \(0.276753\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.22268 | 0.102968 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.7687 | + | 6.79464i | −0.984146 | + | 0.568197i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.87165 | − | 22.4326i | −0.404568 | − | 1.86293i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.0458 | + | 7.72881i | −1.32343 | + | 0.637462i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.508607 | + | 0.880934i | −0.0416667 | + | 0.0721689i | −0.886107 | − | 0.463481i | \(-0.846600\pi\) |
0.844440 | + | 0.535650i | \(0.179933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.62914 | − | 11.4820i | −0.539472 | − | 0.934392i | −0.998932 | − | 0.0461942i | \(-0.985291\pi\) |
0.459461 | − | 0.888198i | \(-0.348043\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 17.6544i | − | 1.42728i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.38222 | + | 3.07247i | −0.271667 | + | 0.246787i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3912 | + | 8.88611i | −1.22835 | + | 0.709189i | −0.966685 | − | 0.255970i | \(-0.917605\pi\) |
−0.261666 | + | 0.965158i | \(0.584272\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.593368 | + | 1.02774i | −0.0470571 | + | 0.0815053i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.4815 | + | 8.47026i | 1.06249 | + | 0.667550i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.52838 | − | 1.45976i | −0.198038 | − | 0.114337i | 0.397702 | − | 0.917515i | \(-0.369808\pi\) |
−0.595740 | + | 0.803177i | \(0.703141\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.78470 | + | 21.1987i | −0.528188 | + | 1.65031i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.21710i | 0.713240i | 0.934249 | + | 0.356620i | \(0.116071\pi\) | ||||
−0.934249 | + | 0.356620i | \(0.883929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.934854 | 0.0719118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.12118 | + | 15.7984i | 0.697514 | + | 1.20813i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.7757 | + | 10.8402i | 1.42749 | + | 0.824162i | 0.996922 | − | 0.0783961i | \(-0.0249799\pi\) |
0.430568 | + | 0.902558i | \(0.358313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2337 | + | 5.03352i | −0.924782 | + | 0.380498i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.7202 | + | 13.1175i | 1.70776 | + | 0.985975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.4983 | − | 21.6476i | −0.934164 | − | 1.61802i | −0.776117 | − | 0.630588i | \(-0.782814\pi\) |
−0.158047 | − | 0.987432i | \(-0.550520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.17900 | −0.310623 | −0.155311 | − | 0.987866i | \(-0.549638\pi\) | ||||
−0.155311 | + | 0.987866i | \(0.549638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 20.5602i | − | 1.51986i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.276050 | − | 0.862512i | 0.0202956 | − | 0.0634131i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.2206 | + | 9.94232i | 1.25930 | + | 0.727055i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.119052 | + | 3.18513i | −0.00865975 | + | 0.231684i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.48585 | − | 7.76972i | 0.324585 | − | 0.562197i | −0.656844 | − | 0.754027i | \(-0.728109\pi\) |
0.981428 | + | 0.191830i | \(0.0614422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7806 | + | 9.11092i | −1.13591 | + | 0.655818i | −0.945415 | − | 0.325870i | \(-0.894343\pi\) |
−0.190496 | + | 0.981688i | \(0.561010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.6272 | + | 13.2877i | −1.04748 | + | 0.951549i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 23.5632i | − | 1.67881i | −0.543509 | − | 0.839403i | \(-0.682905\pi\) | ||
0.543509 | − | 0.839403i | \(-0.317095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3582 | + | 17.9409i | 0.734271 | + | 1.27180i | 0.955042 | + | 0.296470i | \(0.0958094\pi\) |
−0.220771 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.28159 | − | 9.14798i | 0.372534 | − | 0.645249i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.1424 | + | 1.01451i | 1.90502 | + | 0.0712046i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22210 | + | 5.62745i | 0.0853554 | + | 0.393038i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.1023 | − | 10.4514i | 1.25820 | − | 0.726422i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.5469 | −1.42126 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.69865 | 0.529997 | 0.264998 | − | 0.964249i | \(-0.414629\pi\) | ||||
0.264998 | + | 0.964249i | \(0.414629\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.44520 | − | 5.45319i | 0.647174 | − | 0.373646i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.4554 | + | 2.92208i | −0.917648 | + | 0.199284i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.52653 | − | 4.77996i | −0.171512 | − | 0.324485i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.12520 | + | 10.6092i | −0.413903 | + | 0.716900i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.82722 | + | 15.2892i | 0.593783 | + | 1.02846i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7136i | 0.851366i | 0.904872 | + | 0.425683i | \(0.139966\pi\) | ||||
−0.904872 | + | 0.425683i | \(0.860034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.66305 | + | 17.2877i | −0.110870 | + | 1.15251i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.28633 | − | 5.36146i | 0.616355 | − | 0.355853i | −0.159093 | − | 0.987264i | \(-0.550857\pi\) |
0.775449 | + | 0.631411i | \(0.217524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.3946 | + | 21.4681i | −0.819059 | + | 1.41865i | 0.0873173 | + | 0.996181i | \(0.472171\pi\) |
−0.906376 | + | 0.422471i | \(0.861163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.2998 | − | 14.0107i | −1.46722 | − | 0.921835i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.7059 | − | 11.3772i | −1.29098 | − | 0.745345i | −0.312148 | − | 0.950034i | \(-0.601048\pi\) |
−0.978827 | + | 0.204689i | \(0.934382\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.327548 | + | 1.02342i | −0.0213669 | + | 0.0667603i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 32.2210i | − | 2.09298i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.49071 | 0.0964258 | 0.0482129 | − | 0.998837i | \(-0.484647\pi\) | ||||
0.0482129 | + | 0.998837i | \(0.484647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0839 | − | 22.6619i | −0.842806 | − | 1.45978i | −0.887513 | − | 0.460783i | \(-0.847569\pi\) |
0.0447069 | − | 0.999000i | \(-0.485765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.3369 | − | 11.1642i | −1.24046 | − | 0.716182i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.17067 | − | 15.5012i | −0.138679 | − | 0.990337i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.7984 | − | 9.12118i | −1.00523 | − | 0.580367i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.7151 | − | 18.5591i | −0.679041 | − | 1.17613i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.90277 | 0.309460 | 0.154730 | − | 0.987957i | \(-0.450549\pi\) | ||||
0.154730 | + | 0.987957i | \(0.450549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.5433i | 1.48016i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.5401 | + | 8.81430i | 1.72463 | + | 0.551973i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6866 | + | 6.16993i | 0.666614 | + | 0.384870i | 0.794792 | − | 0.606882i | \(-0.207580\pi\) |
−0.128179 | + | 0.991751i | \(0.540913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.907315 | + | 0.570053i | 0.0563778 | + | 0.0354214i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.8295 | − | 30.8815i | 1.10362 | − | 1.91152i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.4285 | + | 10.0623i | −1.07469 | + | 0.620471i | −0.929458 | − | 0.368927i | \(-0.879725\pi\) |
−0.145229 | + | 0.989398i | \(0.546392\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.701290 | − | 0.771990i | −0.0430799 | − | 0.0474230i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.07059i | 0.371514i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.46972 | − | 12.9379i | −0.455437 | − | 0.788840i | 0.543276 | − | 0.839554i | \(-0.317184\pi\) |
−0.998713 | + | 0.0507142i | \(0.983850\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90466 | − | 5.03102i | 0.176446 | − | 0.305613i | −0.764215 | − | 0.644962i | \(-0.776873\pi\) |
0.940661 | + | 0.339349i | \(0.110207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.9266 | − | 20.6721i | −0.661306 | − | 1.25113i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.9263 | − | 11.3580i | −0.960390 | − | 0.684910i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4639 | − | 12.9695i | 1.34972 | − | 0.779263i | 0.361513 | − | 0.932367i | \(-0.382260\pi\) |
0.988210 | + | 0.153104i | \(0.0489271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.09809 | −0.424952 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8840 | −0.887904 | −0.443952 | − | 0.896051i | \(-0.646424\pi\) | ||||
−0.443952 | + | 0.896051i | \(0.646424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.41378 | − | 4.85770i | 0.500147 | − | 0.288760i | −0.228627 | − | 0.973514i | \(-0.573424\pi\) |
0.728774 | + | 0.684754i | \(0.240090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −29.1986 | + | 6.34101i | −1.72958 | + | 0.375609i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.80894 | − | 0.254500i | −0.401919 | − | 0.0150227i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.41651 | − | 7.64961i | 0.259794 | − | 0.449977i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.68027 | + | 2.91031i | 0.0984989 | + | 0.170605i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.08596i | − | 0.472387i | −0.971706 | − | 0.236194i | \(-0.924100\pi\) | ||
0.971706 | − | 0.236194i | \(-0.0758999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.0663 | + | 15.5034i | −0.993640 | + | 0.902640i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.08172 | + | 2.35658i | −0.236845 | + | 0.136743i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4514 | + | 18.1023i | −0.604419 | + | 1.04688i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.608516 | − | 16.2803i | 0.0350743 | − | 0.938383i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.0803 | + | 9.86130i | 0.981236 | + | 0.566517i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.2095 | + | 5.50794i | 0.985411 | + | 0.315384i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.81809i | − | 0.503275i | −0.967822 | − | 0.251637i | \(-0.919031\pi\) | ||
0.967822 | − | 0.251637i | \(-0.0809690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.60673 | 0.318956 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.83219 | − | 8.36960i | −0.274009 | − | 0.474597i | 0.695876 | − | 0.718162i | \(-0.255016\pi\) |
−0.969885 | + | 0.243565i | \(0.921683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5441 | − | 13.5932i | −1.33079 | − | 0.768334i | −0.345372 | − | 0.938466i | \(-0.612247\pi\) |
−0.985421 | + | 0.170132i | \(0.945581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.3239 | − | 6.99057i | −1.08878 | − | 0.393874i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5294 | − | 6.07913i | −0.591388 | − | 0.341438i | 0.174258 | − | 0.984700i | \(-0.444247\pi\) |
−0.765646 | + | 0.643262i | \(0.777581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.0818 | + | 34.7827i | 1.12436 | + | 1.94745i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.5384 | 1.53704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.6933i | 1.48526i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.20358 | − | 15.8031i | −0.399583 | − | 0.876597i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.3332 | + | 14.0488i | 1.34563 | + | 0.776901i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.07658 | − | 0.676399i | −0.0593537 | − | 0.0372911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.71473 | − | 2.96999i | 0.0942499 | − | 0.163246i | −0.815045 | − | 0.579397i | \(-0.803288\pi\) |
0.909295 | + | 0.416151i | \(0.136621\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.21830 | − | 0.703384i | 0.0667623 | − | 0.0385452i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.24220 | + | 6.87151i | 0.341048 | + | 0.375431i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.39770i | − | 0.0761375i | −0.999275 | − | 0.0380687i | \(-0.987879\pi\) | ||
0.999275 | − | 0.0380687i | \(-0.0121206\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.27611 | − | 16.0667i | −0.503809 | − | 0.872623i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.99738 | − | 6.92367i | 0.216470 | − | 0.374938i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4041 | + | 2.07141i | 0.993726 | + | 0.111845i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.26576 | + | 33.4568i | 0.391175 | + | 1.80126i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.99906 | − | 1.73151i | 0.160998 | − | 0.0929522i | −0.417336 | − | 0.908752i | \(-0.637036\pi\) |
0.578334 | + | 0.815800i | \(0.303703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.2360 | 1.02968 | 0.514838 | − | 0.857287i | \(-0.327852\pi\) | ||||
0.514838 | + | 0.857287i | \(0.327852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.18454 | −0.223354 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.9520 | − | 8.63257i | 0.795817 | − | 0.459465i | −0.0461892 | − | 0.998933i | \(-0.514708\pi\) |
0.842006 | + | 0.539467i | \(0.181374\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.03416 | + | 9.36675i | 0.107962 | + | 0.497136i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.2019 | + | 28.9707i | −0.963345 | + | 1.53329i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.433817 | − | 0.751393i | 0.0228960 | − | 0.0396570i | −0.854350 | − | 0.519697i | \(-0.826045\pi\) |
0.877246 | + | 0.480040i | \(0.159378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.29113 | − | 7.43246i | −0.225849 | − | 0.391182i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.9557i | − | 0.575025i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.23925 | − | 7.96908i | −0.378920 | − | 0.417121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.2880 | − | 8.24920i | 0.745830 | − | 0.430605i | −0.0783555 | − | 0.996925i | \(-0.524967\pi\) |
0.824185 | + | 0.566321i | \(0.191634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.47270 | + | 7.74695i | −0.232840 | + | 0.403290i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.09102 | − | 0.576678i | 0.0566430 | − | 0.0299396i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6557 | + | 10.1935i | 0.914179 | + | 0.527801i | 0.881773 | − | 0.471673i | \(-0.156350\pi\) |
0.0324054 | + | 0.999475i | \(0.489683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.1376 | − | 11.2255i | −1.34974 | − | 0.579680i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 35.6589i | 1.83653i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.1652 | −0.676251 | −0.338126 | − | 0.941101i | \(-0.609793\pi\) | ||||
−0.338126 | + | 0.941101i | \(0.609793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.74857 | + | 16.8850i | 0.499434 | + | 0.865046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.49608 | − | 2.59581i | −0.229739 | − | 0.132640i | 0.380713 | − | 0.924693i | \(-0.375679\pi\) |
−0.610452 | + | 0.792054i | \(0.709012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.7013 | − | 14.9122i | 0.902141 | − | 0.759996i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.5231 | − | 10.6943i | −0.941584 | − | 0.543624i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.5709 | + | 26.9697i | 0.789478 | + | 1.36742i | 0.926287 | + | 0.376819i | \(0.122982\pi\) |
−0.136809 | + | 0.990597i | \(0.543685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.5862 | 1.54681 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 43.7924i | 2.20903i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.9698 | + | 8.63177i | 1.35700 | + | 0.434312i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0826 | − | 7.55325i | −0.656598 | − | 0.379087i | 0.134382 | − | 0.990930i | \(-0.457095\pi\) |
−0.790979 | + | 0.611843i | \(0.790429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.32050 | − | 35.3289i | 0.0661077 | − | 1.76866i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.12353 | + | 14.0704i | −0.405670 | + | 0.702641i | −0.994399 | − | 0.105690i | \(-0.966295\pi\) |
0.588729 | + | 0.808330i | \(0.299628\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.14713 | − | 3.54905i | 0.306210 | − | 0.176791i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.1739 | − | 11.0590i | 0.604925 | − | 0.549525i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.58448i | 0.0785397i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.6603 | + | 28.8565i | 0.823798 | + | 1.42686i | 0.902834 | + | 0.429989i | \(0.141482\pi\) |
−0.0790359 | + | 0.996872i | \(0.525184\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.69245 | + | 11.5917i | −0.330114 | + | 0.571774i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.7486 | − | 24.1191i | −0.627316 | − | 1.18683i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4049 | − | 3.99697i | 0.903463 | − | 0.196203i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.5247 | + | 19.3555i | −1.64171 | + | 0.947844i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.3290 | −0.553457 | −0.276729 | − | 0.960948i | \(-0.589250\pi\) | ||||
−0.276729 | + | 0.960948i | \(0.589250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5047 | 0.609440 | 0.304720 | − | 0.952442i | \(-0.401437\pi\) | ||||
0.304720 | + | 0.952442i | \(0.401437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.44558 | + | 0.834603i | −0.0702863 | + | 0.0405798i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.7556 | + | 20.6905i | −0.715752 | + | 1.00364i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3741 | + | 18.1034i | −0.550432 | + | 0.876086i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.2877 | − | 29.9431i | 0.834656 | − | 1.44567i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.57356 | + | 4.45754i | 0.123964 | + | 0.214712i | 0.921328 | − | 0.388787i | \(-0.127106\pi\) |
−0.797363 | + | 0.603499i | \(0.793773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.88420i | 0.0905491i | 0.998975 | + | 0.0452745i | \(0.0144163\pi\) | ||||
−0.998975 | + | 0.0452745i | \(0.985584\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39.2721 | + | 43.2313i | 1.88295 | + | 2.07278i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.3705 | + | 15.8024i | −1.30931 | + | 0.755930i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.29522 | − | 9.17159i | 0.252727 | − | 0.437736i | −0.711549 | − | 0.702637i | \(-0.752006\pi\) |
0.964276 | + | 0.264901i | \(0.0853392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.6952 | − | 20.0906i | 0.652153 | − | 0.956697i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.0886 | − | 12.1755i | −1.00195 | − | 0.578476i | −0.0931250 | − | 0.995654i | \(-0.529686\pi\) |
−0.908825 | + | 0.417179i | \(0.863019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.08125 | − | 1.62627i | −0.240874 | − | 0.0770926i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.58811i | − | 0.122413i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.2506 | −0.955684 | −0.477842 | − | 0.878446i | \(-0.658581\pi\) | ||||
−0.477842 | + | 0.878446i | \(0.658581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.03772 | − | 8.72559i | −0.237217 | − | 0.410872i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.2137 | + | 16.8666i | 1.37258 | + | 0.792460i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.2302 | − | 3.60793i | 0.948409 | − | 0.169142i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.6159 | − | 9.59321i | −0.777261 | − | 0.448752i | 0.0581979 | − | 0.998305i | \(-0.481465\pi\) |
−0.835459 | + | 0.549553i | \(0.814798\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.06154 | + | 5.30274i | 0.142900 | + | 0.247511i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.4096 | −0.624548 | −0.312274 | − | 0.949992i | \(-0.601091\pi\) | ||||
−0.312274 | + | 0.949992i | \(0.601091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.7864i | − | 0.826604i | −0.910594 | − | 0.413302i | \(-0.864375\pi\) | ||
0.910594 | − | 0.413302i | \(-0.135625\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.54385 | − | 11.0727i | 0.164342 | − | 0.513484i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1723 | + | 7.60500i | 0.609539 | + | 0.351918i | 0.772785 | − | 0.634668i | \(-0.218863\pi\) |
−0.163246 | + | 0.986585i | \(0.552196\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.71122 | + | 5.13303i | −0.448423 | + | 0.237021i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.6090 | − | 39.1599i | 1.04177 | − | 1.80439i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.8631 | − | 12.0453i | 0.959286 | − | 0.553844i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.51451 | − | 26.1387i | 0.115374 | − | 1.19933i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.62013i | − | 0.0741809i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.28422 | − | 10.8846i | −0.287133 | − | 0.497329i | 0.685991 | − | 0.727610i | \(-0.259369\pi\) |
−0.973124 | + | 0.230281i | \(0.926036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.703384 | + | 1.21830i | −0.0320716 | + | 0.0555496i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −40.4811 | − | 1.51308i | −1.84196 | − | 0.0688475i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.88614 | + | 0.626777i | −0.131053 | + | 0.0284605i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9425 | + | 6.89503i | −0.541169 | + | 0.312444i | −0.745552 | − | 0.666447i | \(-0.767814\pi\) |
0.204384 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.42816 | 0.335913 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4423 | 1.23845 | 0.619226 | − | 0.785213i | \(-0.287447\pi\) | ||||
0.619226 | + | 0.785213i | \(0.287447\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.1877 | − | 26.0891i | 2.03515 | − | 1.17499i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.44868 | − | 29.6944i | −0.289847 | − | 1.33466i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.3333 | − | 0.423609i | −0.508369 | − | 0.0190015i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.86895 | + | 17.0935i | −0.441795 | + | 0.765211i | −0.997823 | − | 0.0659525i | \(-0.978991\pi\) |
0.556028 | + | 0.831164i | \(0.312325\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7256 | − | 20.3093i | −0.523859 | − | 0.907351i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.00417i | 0.223125i | 0.993757 | + | 0.111562i | \(0.0355855\pi\) | ||||
−0.993757 | + | 0.111562i | \(0.964415\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.8299 | + | 11.6549i | −0.570921 | + | 0.518635i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.05989 | + | 1.18928i | −0.0914828 | + | 0.0528176i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.3796 | − | 19.7100i | 0.504392 | − | 0.873632i | −0.495595 | − | 0.868553i | \(-0.665050\pi\) |
0.999987 | − | 0.00507852i | \(-0.00161655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.2624 | − | 5.95291i | 0.498218 | − | 0.263341i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.47933 | − | 3.16349i | −0.241918 | − | 0.139672i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.50200 | + | 4.69298i | −0.0661862 | + | 0.206797i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.88007i | − | 0.0826854i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −55.1614 | −2.42131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.76856 | + | 15.1876i | 0.384158 | + | 0.665381i | 0.991652 | − | 0.128943i | \(-0.0411586\pi\) |
−0.607494 | + | 0.794324i | \(0.707825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9425 | + | 6.89503i | 0.522211 | + | 0.301499i | 0.737839 | − | 0.674977i | \(-0.235846\pi\) |
−0.215628 | + | 0.976476i | \(0.569180\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.5528 | − | 26.6542i | 0.896996 | − | 1.16328i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.99484 | − | 5.19317i | −0.391821 | − | 0.226218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.60694 | + | 11.4436i | 0.287258 | + | 0.497546i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.8162 | −1.55429 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.94541i | − | 0.387469i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.37735 | + | 23.0504i | −0.318951 | + | 0.996555i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 55.0782 | + | 31.7994i | 2.37680 | + | 1.37225i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.8843 | + | 24.6730i | 0.511893 | + | 1.06274i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.0000 | + | 39.8372i | −0.988849 | + | 1.71274i | −0.365454 | + | 0.930829i | \(0.619086\pi\) |
−0.623395 | + | 0.781907i | \(0.714247\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.20815 | − | 5.31633i | 0.395160 | − | 0.228146i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.2779 | + | 16.6040i | −0.782941 | + | 0.711237i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.4411i | − | 1.13054i | −0.824906 | − | 0.565270i | \(-0.808772\pi\) | ||
0.824906 | − | 0.565270i | \(-0.191228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.0344 | + | 24.3084i | 0.598975 | + | 1.03746i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.9579 | + | 46.6925i | −1.14845 | + | 1.98917i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.8249 | + | 28.3708i | −0.757994 | + | 1.20645i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.488990 | + | 2.25166i | 0.0207565 | + | 0.0955778i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.4720 | − | 15.8609i | 1.16402 | − | 0.672050i | 0.211759 | − | 0.977322i | \(-0.432081\pi\) |
0.952265 | + | 0.305272i | \(0.0987473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.3887 | 0.904644 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.5926 | −2.13602 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.9483 | + | 10.3624i | −0.756429 | + | 0.436724i | −0.828012 | − | 0.560710i | \(-0.810528\pi\) |
0.0715834 | + | 0.997435i | \(0.477195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.9333 | − | 3.46020i | 0.670318 | − | 0.145572i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.09391 | + | 17.2049i | 0.381908 | + | 0.722536i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.2727 | − | 36.8454i | 0.891799 | − | 1.54464i | 0.0540816 | − | 0.998537i | \(-0.482777\pi\) |
0.837717 | − | 0.546104i | \(-0.183890\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0531 | − | 26.0727i | −0.629952 | − | 1.09111i | −0.987561 | − | 0.157238i | \(-0.949741\pi\) |
0.357608 | − | 0.933872i | \(-0.383592\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.8267i | 0.953601i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −29.9507 | − | 2.88122i | −1.24903 | − | 0.120155i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.89257 | − | 5.13413i | 0.370202 | − | 0.213736i | −0.303344 | − | 0.952881i | \(-0.598103\pi\) |
0.673547 | + | 0.739144i | \(0.264770\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.1810 | − | 40.1506i | 0.963368 | − | 1.66860i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.832360 | + | 22.2691i | −0.0345321 | + | 0.923877i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.58032 | + | 0.912400i | 0.0654503 | + | 0.0377877i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.22363 | − | 25.6946i | 0.340005 | − | 1.06234i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 41.5546i | − | 1.71514i | −0.514367 | − | 0.857570i | \(-0.671973\pi\) | ||
0.514367 | − | 0.857570i | \(-0.328027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7322 | 0.442214 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.9760 | + | 51.9199i | 1.23305 | + | 2.13570i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.7242 | − | 11.9651i | −0.851041 | − | 0.491349i | 0.00996069 | − | 0.999950i | \(-0.496829\pi\) |
−0.861002 | + | 0.508601i | \(0.830163\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.3731 | − | 22.9965i | −0.794219 | − | 0.942765i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −45.6471 | − | 26.3544i | −1.86821 | − | 1.07861i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.54134 | + | 7.86583i | 0.185554 | + | 0.321389i | 0.943763 | − | 0.330623i | \(-0.107259\pi\) |
−0.758209 | + | 0.652012i | \(0.773925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.8162 | −1.21623 | −0.608114 | − | 0.793850i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793850i | \(0.708074\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4209i | 0.587263i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.17022 | + | 2.93496i | 0.372822 | + | 0.119323i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5990 | + | 7.27401i | 0.511376 | + | 0.295243i | 0.733399 | − | 0.679798i | \(-0.237933\pi\) |
−0.222023 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −61.0970 | + | 32.2938i | −2.47577 | + | 1.30861i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.834603 | − | 1.44558i | 0.0337644 | − | 0.0584817i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.93982 | − | 5.16141i | 0.361076 | − | 0.208467i | −0.308477 | − | 0.951232i | \(-0.599819\pi\) |
0.669553 | + | 0.742765i | \(0.266486\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.85180 | − | 10.8450i | −0.397263 | − | 0.437313i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.0906i | − | 0.527008i | −0.964658 | − | 0.263504i | \(-0.915122\pi\) | ||
0.964658 | − | 0.263504i | \(-0.0848782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.2794 | − | 28.1968i | −0.654325 | − | 1.13332i | −0.982063 | − | 0.188556i | \(-0.939619\pi\) |
0.327737 | − | 0.944769i | \(-0.393714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.62485 | + | 6.27842i | −0.145460 | + | 0.251944i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.35831 | − | 5.34519i | 0.134548 | − | 0.214151i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.3981 | − | 18.8707i | 0.655924 | − | 0.754827i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 45.2736 | − | 26.1387i | 1.80805 | − | 1.04388i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.05847 | 0.0820764 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2537 | −0.527620 | −0.263810 | − | 0.964575i | \(-0.584979\pi\) | ||||
−0.263810 | + | 0.964575i | \(0.584979\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.9635 | + | 9.79386i | −0.674237 | + | 0.389271i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.7448 | + | 3.63644i | −0.664497 | + | 0.144308i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.81508 | + | 24.2466i | −0.0719162 | + | 0.960685i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.44470 | + | 12.8946i | −0.294508 | + | 0.510103i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.351536 | − | 0.608879i | −0.0138848 | − | 0.0240493i | 0.858999 | − | 0.511976i | \(-0.171086\pi\) |
−0.872884 | + | 0.487927i | \(0.837753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.64163i | 0.183048i | 0.995803 | + | 0.0915240i | \(0.0291738\pi\) | ||||
−0.995803 | + | 0.0915240i | \(0.970826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.9307 | − | 23.5559i | 1.02102 | − | 0.927512i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.4230 | + | 6.01770i | −0.409769 | + | 0.236580i | −0.690691 | − | 0.723150i | \(-0.742693\pi\) |
0.280921 | + | 0.959731i | \(0.409360\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.1704 | − | 34.9361i | 0.791756 | − | 1.37136i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.6479 | + | 7.31819i | 0.456516 | + | 0.286823i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.8018 | − | 9.12319i | −0.618373 | − | 0.357018i | 0.157862 | − | 0.987461i | \(-0.449540\pi\) |
−0.776235 | + | 0.630443i | \(0.782873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.6554 | − | 11.7317i | −1.43225 | − | 0.458395i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 16.7243i | − | 0.652476i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4231 | −1.14616 | −0.573081 | − | 0.819499i | \(-0.694252\pi\) | ||||
−0.573081 | + | 0.819499i | \(0.694252\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.64783 | + | 14.9785i | 0.336361 | + | 0.582595i | 0.983745 | − | 0.179569i | \(-0.0574703\pi\) |
−0.647384 | + | 0.762164i | \(0.724137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −38.9004 | − | 22.4591i | −1.51077 | − | 0.872241i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.2175 | + | 10.5697i | 1.13301 | + | 0.409874i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.5020 | + | 30.8894i | 2.07161 | + | 1.19604i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.1737 | − | 28.0136i | −0.625309 | − | 1.08307i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.6147 | −1.22047 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.7525i | − | 1.10833i | −0.832407 | − | 0.554164i | \(-0.813038\pi\) | ||
0.832407 | − | 0.554164i | \(-0.186962\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.49841 | − | 5.48097i | −0.0961639 | − | 0.210962i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.75096 | − | 2.74297i | −0.182594 | − | 0.105421i | 0.405917 | − | 0.913910i | \(-0.366952\pi\) |
−0.588511 | + | 0.808489i | \(0.700286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.130525 | − | 3.49208i | 0.00500908 | − | 0.134014i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6412 | + | 23.6273i | −0.522732 | + | 0.905398i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.85256 | + | 5.68838i | −0.376998 | + | 0.217660i | −0.676511 | − | 0.736432i | \(-0.736509\pi\) |
0.299514 | + | 0.954092i | \(0.403176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.90967 | − | 8.70708i | −0.302213 | − | 0.332681i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 63.0714i | − | 2.40632i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.810067 | + | 1.40308i | 0.0308611 | + | 0.0534530i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6631 | − | 39.2536i | 0.862144 | − | 1.49328i | −0.00771164 | − | 0.999970i | \(-0.502455\pi\) |
0.869855 | − | 0.493307i | \(-0.164212\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 35.9288 | + | 1.34292i | 1.36482 | + | 0.0510134i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.22004 | − | 33.2463i | −0.273872 | − | 1.26110i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.3358 | + | 6.54472i | −0.429374 | + | 0.247899i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 57.8941 | 2.18976 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.87634 | 0.184177 | 0.0920884 | − | 0.995751i | \(-0.470646\pi\) | ||||
0.0920884 | + | 0.995751i | \(0.470646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.84205 | + | 1.06351i | −0.0694743 | + | 0.0401110i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.580213 | − | 2.67172i | −0.0218521 | − | 0.100623i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.58392 | − | 18.1319i | −0.360441 | − | 0.681921i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4443 | + | 21.5542i | −0.467357 | + | 0.809485i | −0.999304 | − | 0.0372918i | \(-0.988127\pi\) |
0.531948 | + | 0.846777i | \(0.321460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.9941 | + | 38.0948i | 0.824842 | + | 1.42867i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 12.2974i | − | 0.460541i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.4319 | + | 22.4918i | 0.764111 | + | 0.841145i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.28467 | + | 1.89641i | −0.122668 | + | 0.0708226i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.71787 | + | 4.70748i | −0.101359 | + | 0.175559i | −0.912245 | − | 0.409645i | \(-0.865653\pi\) |
0.810886 | + | 0.585205i | \(0.198986\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.93676 | − | 3.10170i | −0.183855 | − | 0.115513i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 57.6589 | + | 33.2894i | 2.14436 | + | 1.23804i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −46.7065 | + | 21.2904i | −1.73463 | + | 0.790706i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17.1112i | − | 0.634621i | −0.948322 | − | 0.317310i | \(-0.897220\pi\) | ||
0.948322 | − | 0.317310i | \(-0.102780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.7441 | 1.28682 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.6486 | − | 27.1041i | −0.578784 | − | 1.00248i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.80474 | − | 3.92872i | −0.251339 | − | 0.145111i | 0.369038 | − | 0.929414i | \(-0.379687\pi\) |
−0.620377 | + | 0.784304i | \(0.713020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.5029 | + | 31.3945i | 0.903802 | + | 1.15800i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.0665 | − | 8.12130i | −0.518146 | − | 0.299152i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.5055 | + | 44.1768i | 0.938234 | + | 1.62507i | 0.768763 | + | 0.639534i | \(0.220873\pi\) |
0.169471 | + | 0.985535i | \(0.445794\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 46.4142 | 1.70507 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.82733i | 0.250470i | 0.992127 | + | 0.125235i | \(0.0399686\pi\) | ||||
−0.992127 | + | 0.125235i | \(0.960031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.16631 | + | 0.693336i | 0.0793676 | + | 0.0254019i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.3369 | + | 14.6283i | 0.927028 | + | 0.535220i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.2478 | − | 15.2345i | −0.885994 | − | 0.556657i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.1785 | + | 28.0220i | −0.590361 | + | 1.02254i | 0.403822 | + | 0.914837i | \(0.367681\pi\) |
−0.994184 | + | 0.107698i | \(0.965652\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.8029 | + | 6.23708i | −0.393681 | + | 0.227292i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.9439 | + | 19.9342i | −0.798621 | + | 0.725481i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1180i | 1.05831i | 0.848524 | + | 0.529156i | \(0.177491\pi\) | ||||
−0.848524 | + | 0.529156i | \(0.822509\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.9507 | − | 51.8762i | −1.08714 | − | 1.88299i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.0865 | + | 24.3986i | −0.510636 | + | 0.884447i | 0.489288 | + | 0.872122i | \(0.337257\pi\) |
−0.999924 | + | 0.0123251i | \(0.996077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.6536 | − | 25.8315i | −0.494295 | − | 0.935161i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.5773 | + | 8.37776i | −1.39477 | + | 0.302899i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.0177 | − | 17.9081i | 1.11999 | − | 0.646624i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.5017 | −0.595065 | −0.297532 | − | 0.954712i | \(-0.596164\pi\) | ||||
−0.297532 | + | 0.954712i | \(0.596164\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.3964 | −1.13071 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.0120 | + | 9.24453i | −0.575912 | + | 0.332503i | −0.759507 | − | 0.650499i | \(-0.774560\pi\) |
0.183595 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.31877 | + | 5.93260i | 0.298819 | + | 0.213105i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.72440 | − | 0.101831i | −0.0977374 | − | 0.00365317i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.76268 | − | 11.7133i | 0.242298 | − | 0.419673i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.38516 | − | 14.5235i | −0.300045 | − | 0.519693i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.3675i | 0.441980i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.7211 | + | 29.4150i | 0.953717 | + | 1.04987i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.6350 | + | 7.87216i | −0.486035 | + | 0.280612i | −0.722928 | − | 0.690923i | \(-0.757204\pi\) |
0.236893 | + | 0.971536i | \(0.423871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.6017 | − | 44.3434i | 0.911444 | − | 1.57867i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.720579 | + | 19.2785i | −0.0256208 | + | 0.685464i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.3084 | − | 14.0344i | −0.863215 | − | 0.498377i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.52733 | + | 0.808881i | 0.0896353 | + | 0.0286881i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.9307i | 1.06020i | 0.847935 | + | 0.530100i | \(0.177846\pi\) | ||||
−0.847935 | + | 0.530100i | \(0.822154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.44248 | −0.0864088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.14379 | − | 7.17726i | −0.146414 | − | 0.253596i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.3133 | + | 9.41849i | 0.575684 | + | 0.332371i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.1111 | − | 33.4785i | 0.426860 | − | 1.17996i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.9181 | + | 19.0052i | 1.15877 | + | 0.669016i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.58329 | + | 4.47439i | 0.0908236 | + | 0.157311i | 0.907858 | − | 0.419278i | \(-0.137717\pi\) |
−0.817034 | + | 0.576589i | \(0.804383\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.4698 | −1.35086 | −0.675430 | − | 0.737425i | \(-0.736042\pi\) | ||||
−0.675430 | + | 0.737425i | \(0.736042\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.7807i | 0.518381i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.98995 | + | 6.21757i | −0.0697050 | + | 0.217792i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0068 | + | 16.1697i | 0.979833 | + | 0.565707i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.0293 | + | 16.9821i | 0.944479 | + | 0.593403i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.84776 | − | 3.20041i | 0.0644872 | − | 0.111695i | −0.831979 | − | 0.554807i | \(-0.812792\pi\) |
0.896466 | + | 0.443112i | \(0.146126\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.7220 | + | 21.2015i | −1.28005 | + | 0.739037i | −0.976857 | − | 0.213892i | \(-0.931386\pi\) |
−0.303193 | + | 0.952929i | \(0.598053\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 49.5415 | + | 4.76583i | 1.72481 | + | 0.165925i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.0950i | 1.39424i | 0.716954 | + | 0.697120i | \(0.245536\pi\) | ||||
−0.716954 | + | 0.697120i | \(0.754464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.9132 | + | 46.6151i | 0.934734 | + | 1.61901i | 0.775107 | + | 0.631830i | \(0.217696\pi\) |
0.159628 | + | 0.987177i | \(0.448971\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.9984 | + | 57.1549i | −1.14470 | + | 1.98268i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32.0537 | − | 15.4394i | 1.11060 | − | 0.534944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.1406 | − | 4.37389i | 0.696994 | − | 0.151365i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.13200 | − | 1.23091i | 0.0736928 | − | 0.0425466i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.1002 | 0.866556 | 0.433278 | − | 0.901260i | \(-0.357357\pi\) | ||||
0.433278 | + | 0.901260i | \(0.357357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 76.3910 | 2.63417 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.7959 | − | 18.9347i | 1.12955 | − | 0.652146i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.443627 | − | 2.04278i | −0.0152612 | − | 0.0702738i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.06080 | + | 9.64657i | −0.208252 | + | 0.331460i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.3595 | + | 21.4072i | −0.424176 | + | 0.734694i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.21861 | + | 2.11069i | 0.0417733 | + | 0.0723535i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.7320i | 0.915286i | 0.889136 | + | 0.457643i | \(0.151306\pi\) | ||||
−0.889136 | + | 0.457643i | \(0.848694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 30.1931 | − | 27.4280i | 1.03258 | − | 0.938017i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.3473 | + | 23.2945i | −1.37824 | + | 0.795726i | −0.991947 | − | 0.126651i | \(-0.959577\pi\) |
−0.386291 | + | 0.922377i | \(0.626244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.32674 | + | 16.1544i | −0.318224 | + | 0.551180i | −0.980118 | − | 0.198418i | \(-0.936420\pi\) |
0.661893 | + | 0.749598i | \(0.269753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.3268 | − | 8.10124i | 0.522336 | − | 0.276090i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.4360 | + | 8.91196i | 0.525447 | + | 0.303367i | 0.739160 | − | 0.673530i | \(-0.235223\pi\) |
−0.213714 | + | 0.976896i | \(0.568556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7773 | − | 46.1715i | 0.502445 | − | 1.56988i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.4739i | 0.763253i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.5450 | −1.68070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.21043 | − | 12.4888i | −0.244316 | − | 0.423168i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.97316 | − | 2.29390i | −0.134471 | − | 0.0776368i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.8043 | + | 24.3437i | 0.568090 | + | 0.822967i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1915 | + | 13.3896i | 0.783123 | + | 0.452136i | 0.837536 | − | 0.546382i | \(-0.183995\pi\) |
−0.0544130 | + | 0.998519i | \(0.517329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.2866 | + | 17.8169i | 0.346958 | + | 0.600949i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.5843 | 0.592429 | 0.296215 | − | 0.955121i | \(-0.404276\pi\) | ||||
0.296215 | + | 0.955121i | \(0.404276\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 18.9638i | − | 0.638182i | −0.947724 | − | 0.319091i | \(-0.896622\pi\) | ||
0.947724 | − | 0.319091i | \(-0.103378\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17.8819 | − | 55.8716i | 0.601093 | − | 1.87810i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.66950 | − | 5.58269i | −0.324670 | − | 0.187448i | 0.328802 | − | 0.944399i | \(-0.393355\pi\) |
−0.653472 | + | 0.756950i | \(0.726688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.757280 | − | 20.2604i | 0.0253983 | − | 0.679511i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.3881 | + | 24.9209i | −0.482018 | + | 0.834881i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.18569 | − | 1.26191i | 0.0731415 | − | 0.0422282i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.3720 | + | 37.5831i | −1.38291 | + | 1.25626i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 53.1830i | − | 1.77573i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.4893 | − | 18.1680i | −0.349838 | − | 0.605938i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.18534 | − | 2.05307i | 0.0394893 | − | 0.0683975i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.3703 | + | 36.6468i | 0.644602 | + | 1.21953i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.98311 | + | 9.13168i | 0.0659208 | + | 0.303547i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.0516 | + | 19.0823i | −1.09746 | + | 0.633619i | −0.935553 | − | 0.353187i | \(-0.885098\pi\) |
−0.161907 | + | 0.986806i | \(0.551765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.9253 | −0.893057 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.0251 | 1.55801 | 0.779006 | − | 0.627016i | \(-0.215724\pi\) | ||||
0.779006 | + | 0.627016i | \(0.215724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.5376 | + | 16.4762i | −0.944457 | + | 0.545282i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −44.9268 | + | 9.75668i | −1.48524 | + | 0.322546i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.2264 | − | 38.5595i | 0.800026 | − | 1.27335i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6939 | − | 21.9865i | 0.418734 | − | 0.725269i | −0.577078 | − | 0.816689i | \(-0.695807\pi\) |
0.995812 | + | 0.0914199i | \(0.0291405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.2180 | + | 19.4301i | 0.369644 | + | 0.640243i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 14.8894i | − | 0.490091i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.01570 | − | 0.193908i | −0.0662758 | − | 0.00637565i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.62883 | + | 3.82716i | −0.217719 | + | 0.125700i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.82355 | − | 6.62257i | 0.125446 | − | 0.217280i | −0.796461 | − | 0.604690i | \(-0.793297\pi\) |
0.921907 | + | 0.387410i | \(0.126630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7070 | + | 30.3768i | −0.678645 | + | 0.995560i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.2948 | + | 12.2946i | 0.697161 | + | 0.402506i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.5534 | − | 42.3474i | 0.443244 | − | 1.38491i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.40923i | − | 0.0460375i | −0.999735 | − | 0.0230188i | \(-0.992672\pi\) | ||
0.999735 | − | 0.0230188i | \(-0.00732774\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 69.1706 | 2.25730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2051 | − | 45.3885i | −0.854260 | − | 1.47962i | −0.877330 | − | 0.479888i | \(-0.840677\pi\) |
0.0230692 | − | 0.999734i | \(-0.492656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.4215 | − | 7.74892i | −0.437065 | − | 0.252340i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.01644 | − | 1.25133i | 0.228245 | − | 0.0407059i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.3388 | − | 16.3614i | −0.920888 | − | 0.531675i | −0.0369700 | − | 0.999316i | \(-0.511771\pi\) |
−0.883918 | + | 0.467641i | \(0.845104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.36214 | + | 14.4836i | 0.271446 | + | 0.470159i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.9344 | 1.00312 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 41.7747i | − | 1.35322i | −0.736344 | − | 0.676608i | \(-0.763449\pi\) | ||
0.736344 | − | 0.676608i | \(-0.236551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.1066 | − | 6.11513i | −0.618275 | − | 0.197881i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −88.4977 | − | 51.0942i | −2.86072 | − | 1.65164i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.3054 | − | 6.50420i | 0.397361 | − | 0.210032i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.4120 | − | 23.2303i | 0.432647 | − | 0.749366i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.5587 | + | 18.7978i | −1.04919 | + | 0.605749i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.3971 | + | 30.1592i | 0.881944 | + | 0.970858i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.47375i | 0.208182i | 0.994568 | + | 0.104091i | \(0.0331933\pi\) | ||||
−0.994568 | + | 0.104091i | \(0.966807\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.9580 | − | 58.8169i | −1.09089 | − | 1.88947i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.5872 | − | 28.7298i | 0.532308 | − | 0.921984i | −0.466981 | − | 0.884267i | \(-0.654658\pi\) |
0.999288 | − | 0.0377164i | \(-0.0120083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.2264 | + | 1.50356i | 1.28960 | + | 0.0482018i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 35.9765 | + | 25.6570i | 1.15217 | + | 0.821680i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.7026 | + | 20.0356i | −1.11023 | + | 0.640994i | −0.938890 | − | 0.344217i | \(-0.888144\pi\) |
−0.171344 | + | 0.985211i | \(0.554811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.33452 | 0.298333 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.3589 | −1.22471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.737954 | − | 0.426058i | 0.0235371 | − | 0.0135891i | −0.488185 | − | 0.872740i | \(-0.662341\pi\) |
0.511722 | + | 0.859151i | \(0.329008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.4887 | + | 11.1817i | −1.64057 | + | 0.356279i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.23265 | + | 0.120828i | 0.102896 | + | 0.00384600i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5279 | − | 32.0912i | 0.589151 | − | 1.02044i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.51380 | + | 4.35403i | 0.0798535 | + | 0.138310i | 0.903187 | − | 0.429248i | \(-0.141221\pi\) |
−0.823333 | + | 0.567558i | \(0.807888\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.72558i | 0.276898i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.2878 | − | 31.1477i | 1.08700 | − | 0.987448i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.4079 | + | 13.5146i | −0.741336 | + | 0.428011i | −0.822555 | − | 0.568686i | \(-0.807452\pi\) |
0.0812187 | + | 0.996696i | \(0.474119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.243954 | + | 0.422541i | −0.00771837 | + | 0.0133686i |
(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 | 280.2.bg.a.9.2 | ✓ | 24 | |
4.3 | odd | 2 | 560.2.bw.f.289.11 | 24 | |||
5.2 | odd | 4 | 1400.2.q.n.401.6 | 12 | |||
5.3 | odd | 4 | 1400.2.q.o.401.1 | 12 | |||
5.4 | even | 2 | inner | 280.2.bg.a.9.11 | yes | 24 | |
7.2 | even | 3 | 1960.2.g.f.1569.2 | 12 | |||
7.4 | even | 3 | inner | 280.2.bg.a.249.11 | yes | 24 | |
7.5 | odd | 6 | 1960.2.g.e.1569.11 | 12 | |||
20.19 | odd | 2 | 560.2.bw.f.289.2 | 24 | |||
28.11 | odd | 6 | 560.2.bw.f.529.2 | 24 | |||
35.2 | odd | 12 | 9800.2.a.cx.1.1 | 6 | |||
35.4 | even | 6 | inner | 280.2.bg.a.249.2 | yes | 24 | |
35.9 | even | 6 | 1960.2.g.f.1569.11 | 12 | |||
35.12 | even | 12 | 9800.2.a.cw.1.6 | 6 | |||
35.18 | odd | 12 | 1400.2.q.o.1201.1 | 12 | |||
35.19 | odd | 6 | 1960.2.g.e.1569.2 | 12 | |||
35.23 | odd | 12 | 9800.2.a.cv.1.6 | 6 | |||
35.32 | odd | 12 | 1400.2.q.n.1201.6 | 12 | |||
35.33 | even | 12 | 9800.2.a.cy.1.1 | 6 | |||
140.39 | odd | 6 | 560.2.bw.f.529.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
280.2.bg.a.9.11 | yes | 24 | 5.4 | even | 2 | inner | |
280.2.bg.a.249.2 | yes | 24 | 35.4 | even | 6 | inner | |
280.2.bg.a.249.11 | yes | 24 | 7.4 | even | 3 | inner | |
560.2.bw.f.289.2 | 24 | 20.19 | odd | 2 | |||
560.2.bw.f.289.11 | 24 | 4.3 | odd | 2 | |||
560.2.bw.f.529.2 | 24 | 28.11 | odd | 6 | |||
560.2.bw.f.529.11 | 24 | 140.39 | odd | 6 | |||
1400.2.q.n.401.6 | 12 | 5.2 | odd | 4 | |||
1400.2.q.n.1201.6 | 12 | 35.32 | odd | 12 | |||
1400.2.q.o.401.1 | 12 | 5.3 | odd | 4 | |||
1400.2.q.o.1201.1 | 12 | 35.18 | odd | 12 | |||
1960.2.g.e.1569.2 | 12 | 35.19 | odd | 6 | |||
1960.2.g.e.1569.11 | 12 | 7.5 | odd | 6 | |||
1960.2.g.f.1569.2 | 12 | 7.2 | even | 3 | |||
1960.2.g.f.1569.11 | 12 | 35.9 | even | 6 | |||
9800.2.a.cv.1.6 | 6 | 35.23 | odd | 12 | |||
9800.2.a.cw.1.6 | 6 | 35.12 | even | 12 | |||
9800.2.a.cx.1.1 | 6 | 35.2 | odd | 12 | |||
9800.2.a.cy.1.1 | 6 | 35.33 | even | 12 |