Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.11 | ||
Character | \(\chi\) | \(=\) | 1323.667 |
Dual form | 1323.2.g.h.361.11 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.08816 | + | 1.88474i | 0.769442 | + | 1.33271i | 0.937866 | + | 0.346998i | \(0.112799\pi\) |
−0.168424 | + | 0.985715i | \(0.553868\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.36816 | + | 2.36973i | −0.684082 | + | 1.18487i | ||||
\(5\) | −1.26829 | −0.567196 | −0.283598 | − | 0.958943i | \(-0.591528\pi\) | ||||
−0.283598 | + | 0.958943i | \(0.591528\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.60248 | −0.566563 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.38010 | − | 2.39040i | −0.436425 | − | 0.755910i | ||||
\(11\) | 5.47733 | 1.65148 | 0.825739 | − | 0.564053i | \(-0.190759\pi\) | ||||
0.825739 | + | 0.564053i | \(0.190759\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.37268 | + | 4.10960i | 0.658062 | + | 1.13980i | 0.981117 | + | 0.193417i | \(0.0619570\pi\) |
−0.323054 | + | 0.946380i | \(0.604710\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.992580 | + | 1.71920i | 0.248145 | + | 0.429800i | ||||
\(17\) | −2.40822 | − | 4.17116i | −0.584079 | − | 1.01165i | −0.994990 | − | 0.0999785i | \(-0.968123\pi\) |
0.410911 | − | 0.911676i | \(-0.365211\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.69059 | + | 4.66025i | −0.617265 | + | 1.06913i | 0.372718 | + | 0.927945i | \(0.378426\pi\) |
−0.989983 | + | 0.141189i | \(0.954907\pi\) | |||||||
\(20\) | 1.73523 | − | 3.00550i | 0.388009 | − | 0.672051i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.96019 | + | 10.3233i | 1.27072 | + | 2.20095i | ||||
\(23\) | 5.17631 | 1.07934 | 0.539668 | − | 0.841878i | \(-0.318550\pi\) | ||||
0.539668 | + | 0.841878i | \(0.318550\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.39144 | −0.678288 | ||||||||
\(26\) | −5.16368 | + | 8.94376i | −1.01268 | + | 1.75402i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.01656 | + | 3.49278i | −0.374466 | + | 0.648594i | −0.990247 | − | 0.139324i | \(-0.955507\pi\) |
0.615781 | + | 0.787917i | \(0.288841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.732093 | − | 1.26802i | 0.131488 | − | 0.227744i | −0.792763 | − | 0.609531i | \(-0.791358\pi\) |
0.924250 | + | 0.381787i | \(0.124691\pi\) | |||||||
\(32\) | −3.76264 | + | 6.51709i | −0.665148 | + | 1.15207i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.24103 | − | 9.07773i | 0.898830 | − | 1.55682i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.959170 | + | 1.66133i | −0.157687 | + | 0.273121i | −0.934034 | − | 0.357184i | \(-0.883737\pi\) |
0.776347 | + | 0.630305i | \(0.217070\pi\) | |||||||
\(38\) | −11.7111 | −1.89980 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.03241 | 0.321352 | ||||||||
\(41\) | 1.94808 | + | 3.37418i | 0.304239 | + | 0.526958i | 0.977092 | − | 0.212819i | \(-0.0682644\pi\) |
−0.672852 | + | 0.739777i | \(0.734931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66016 | + | 2.87549i | −0.253173 | + | 0.438508i | −0.964398 | − | 0.264457i | \(-0.914807\pi\) |
0.711225 | + | 0.702964i | \(0.248141\pi\) | |||||||
\(44\) | −7.49389 | + | 12.9798i | −1.12975 | + | 1.95678i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.63263 | + | 9.75600i | 0.830486 | + | 1.43844i | ||||
\(47\) | 1.57773 | + | 2.73271i | 0.230135 | + | 0.398606i | 0.957848 | − | 0.287276i | \(-0.0927498\pi\) |
−0.727712 | + | 0.685882i | \(0.759416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.69042 | − | 6.39199i | −0.521904 | − | 0.903964i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −12.9849 | −1.80068 | ||||||||
\(53\) | −3.57149 | − | 6.18601i | −0.490582 | − | 0.849714i | 0.509359 | − | 0.860554i | \(-0.329883\pi\) |
−0.999941 | + | 0.0108405i | \(0.996549\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.94684 | −0.936712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.77732 | −1.15252 | ||||||||
\(59\) | 0.154341 | − | 0.267327i | 0.0200935 | − | 0.0348030i | −0.855804 | − | 0.517301i | \(-0.826937\pi\) |
0.875897 | + | 0.482498i | \(0.160270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.17143 | − | 8.95719i | −0.662134 | − | 1.14685i | −0.980054 | − | 0.198732i | \(-0.936318\pi\) |
0.317920 | − | 0.948118i | \(-0.397016\pi\) | |||||||
\(62\) | 3.18652 | 0.404689 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4070 | −1.55088 | ||||||||
\(65\) | −3.00924 | − | 5.21216i | −0.373250 | − | 0.646489i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.23655 | + | 3.87382i | −0.273238 | + | 0.473262i | −0.969689 | − | 0.244342i | \(-0.921428\pi\) |
0.696451 | + | 0.717604i | \(0.254761\pi\) | |||||||
\(68\) | 13.1794 | 1.59823 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.96688 | 0.233426 | 0.116713 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116713 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.27515 | + | 9.13683i | 0.617409 | + | 1.06938i | 0.989957 | + | 0.141371i | \(0.0451512\pi\) |
−0.372547 | + | 0.928013i | \(0.621516\pi\) | |||||||
\(74\) | −4.17491 | −0.485323 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.36235 | − | 12.7520i | −0.844520 | − | 1.46275i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50822 | + | 7.80846i | 0.507214 | + | 0.878520i | 0.999965 | + | 0.00835000i | \(0.00265792\pi\) |
−0.492751 | + | 0.870170i | \(0.664009\pi\) | |||||||
\(80\) | −1.25888 | − | 2.18044i | −0.140747 | − | 0.243781i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.23963 | + | 7.34326i | −0.468189 | + | 0.810927i | ||||
\(83\) | 5.08023 | − | 8.79921i | 0.557627 | − | 0.965839i | −0.440066 | − | 0.897965i | \(-0.645045\pi\) |
0.997694 | − | 0.0678739i | \(-0.0216216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.05432 | + | 5.29023i | 0.331287 | + | 0.573806i | ||||
\(86\) | −7.22607 | −0.779207 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.77732 | −0.935666 | ||||||||
\(89\) | 2.59776 | − | 4.49945i | 0.275362 | − | 0.476941i | −0.694864 | − | 0.719141i | \(-0.744536\pi\) |
0.970226 | + | 0.242200i | \(0.0778690\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.08205 | + | 12.2665i | −0.738354 | + | 1.27887i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.43363 | + | 5.94722i | −0.354152 | + | 0.613409i | ||||
\(95\) | 3.41245 | − | 5.91054i | 0.350110 | − | 0.606409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.48521 | + | 4.30451i | −0.252335 | + | 0.437057i | −0.964168 | − | 0.265291i | \(-0.914532\pi\) |
0.711833 | + | 0.702348i | \(0.247865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.64005 | − | 8.03680i | 0.464005 | − | 0.803680i | ||||
\(101\) | −0.00533808 | −0.000531159 | −0.000265580 | − | 1.00000i | \(-0.500085\pi\) | ||||
−0.000265580 | 1.00000i | \(0.500085\pi\) | ||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0348 | 1.28436 | 0.642180 | − | 0.766554i | \(-0.278030\pi\) | ||||
0.642180 | + | 0.766554i | \(0.278030\pi\) | |||||||
\(104\) | −3.80217 | − | 6.58555i | −0.372834 | − | 0.645767i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.77268 | − | 13.4627i | 0.754950 | − | 1.30761i | ||||
\(107\) | 4.71081 | − | 8.15936i | 0.455411 | − | 0.788795i | −0.543301 | − | 0.839538i | \(-0.682826\pi\) |
0.998712 | + | 0.0507430i | \(0.0161589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.44513 | − | 14.6274i | −0.808896 | − | 1.40105i | −0.913629 | − | 0.406549i | \(-0.866732\pi\) |
0.104732 | − | 0.994500i | \(-0.466601\pi\) | |||||||
\(110\) | −7.55924 | − | 13.0930i | −0.720746 | − | 1.24837i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.07313 | + | 5.32281i | 0.289095 | + | 0.500728i | 0.973594 | − | 0.228286i | \(-0.0733122\pi\) |
−0.684499 | + | 0.729014i | \(0.739979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.56506 | −0.612195 | ||||||||
\(116\) | −5.51797 | − | 9.55741i | −0.512331 | − | 0.887383i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.671790 | 0.0618432 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.0012 | 1.72738 | ||||||||
\(122\) | 11.2546 | − | 19.4936i | 1.01895 | − | 1.76487i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00325 | + | 3.46973i | 0.179897 | + | 0.311591i | ||||
\(125\) | 10.6428 | 0.951919 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.9305 | −1.23613 | −0.618065 | − | 0.786127i | \(-0.712083\pi\) | ||||
−0.618065 | + | 0.786127i | \(0.712083\pi\) | |||||||
\(128\) | −5.97551 | − | 10.3499i | −0.528165 | − | 0.914809i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.54905 | − | 11.3433i | 0.574389 | − | 0.994871i | ||||
\(131\) | 0.179156 | 0.0156529 | 0.00782645 | − | 0.999969i | \(-0.497509\pi\) | ||||
0.00782645 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.73486 | −0.840964 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.85913 | + | 6.68420i | 0.330917 | + | 0.573166i | ||||
\(137\) | −3.15206 | −0.269299 | −0.134649 | − | 0.990893i | \(-0.542991\pi\) | ||||
−0.134649 | + | 0.990893i | \(0.542991\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.42857 | + | 16.3308i | 0.799721 | + | 1.38516i | 0.919798 | + | 0.392392i | \(0.128352\pi\) |
−0.120077 | + | 0.992765i | \(0.538314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.14027 | + | 3.70706i | 0.179608 | + | 0.311090i | ||||
\(143\) | 12.9959 | + | 22.5096i | 1.08677 | + | 1.88235i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.55758 | − | 4.42986i | 0.212396 | − | 0.367880i | ||||
\(146\) | −11.4804 | + | 19.8846i | −0.950122 | + | 1.64566i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.62461 | − | 4.54595i | −0.215741 | − | 0.373675i | ||||
\(149\) | 21.2740 | 1.74284 | 0.871418 | − | 0.490541i | \(-0.163201\pi\) | ||||
0.871418 | + | 0.490541i | \(0.163201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.36561 | 0.518026 | 0.259013 | − | 0.965874i | \(-0.416603\pi\) | ||||
0.259013 | + | 0.965874i | \(0.416603\pi\) | |||||||
\(152\) | 4.31163 | − | 7.46796i | 0.349719 | − | 0.605731i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.928506 | + | 1.60822i | −0.0745794 | + | 0.129175i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.697976 | + | 1.20893i | −0.0557045 | + | 0.0964830i | −0.892533 | − | 0.450982i | \(-0.851074\pi\) |
0.836828 | + | 0.547465i | \(0.184407\pi\) | |||||||
\(158\) | −9.81128 | + | 16.9936i | −0.780543 | + | 1.35194i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.77212 | − | 8.26556i | 0.377269 | − | 0.653450i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.53086 | − | 16.5079i | 0.746515 | − | 1.29300i | −0.202969 | − | 0.979185i | \(-0.565059\pi\) |
0.949484 | − | 0.313816i | \(-0.101608\pi\) | |||||||
\(164\) | −10.6612 | −0.832499 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.1123 | 1.71625 | ||||||||
\(167\) | −0.872003 | − | 1.51035i | −0.0674776 | − | 0.116875i | 0.830313 | − | 0.557298i | \(-0.188162\pi\) |
−0.897790 | + | 0.440423i | \(0.854828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.75919 | + | 8.24317i | −0.366092 | + | 0.634090i | ||||
\(170\) | −6.64715 | + | 11.5132i | −0.509813 | + | 0.883022i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.54276 | − | 7.86828i | −0.346382 | − | 0.599951i | ||||
\(173\) | −5.03794 | − | 8.72598i | −0.383028 | − | 0.663424i | 0.608466 | − | 0.793580i | \(-0.291785\pi\) |
−0.991493 | + | 0.130157i | \(0.958452\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.43669 | + | 9.41662i | 0.409806 | + | 0.709805i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.3071 | 0.847500 | ||||||||
\(179\) | −9.27118 | − | 16.0582i | −0.692961 | − | 1.20024i | −0.970863 | − | 0.239634i | \(-0.922973\pi\) |
0.277902 | − | 0.960609i | \(-0.410361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.80982 | −0.654829 | −0.327414 | − | 0.944881i | \(-0.606177\pi\) | ||||
−0.327414 | + | 0.944881i | \(0.606177\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.29494 | −0.611511 | ||||||||
\(185\) | 1.21651 | − | 2.10705i | 0.0894393 | − | 0.154913i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.1906 | − | 22.8468i | −0.964593 | − | 1.67072i | ||||
\(188\) | −8.63437 | −0.629726 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.8531 | 1.07756 | ||||||||
\(191\) | 2.45469 | + | 4.25165i | 0.177615 | + | 0.307639i | 0.941063 | − | 0.338231i | \(-0.109828\pi\) |
−0.763448 | + | 0.645869i | \(0.776495\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.88380 | − | 8.45899i | 0.351544 | − | 0.608892i | −0.634976 | − | 0.772531i | \(-0.718990\pi\) |
0.986520 | + | 0.163640i | \(0.0523235\pi\) | |||||||
\(194\) | −10.8172 | −0.776629 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.31445 | −0.236145 | −0.118073 | − | 0.993005i | \(-0.537672\pi\) | ||||
−0.118073 | + | 0.993005i | \(0.537672\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.54432 | − | 9.60304i | −0.393026 | − | 0.680742i | 0.599821 | − | 0.800134i | \(-0.295239\pi\) |
−0.992847 | + | 0.119393i | \(0.961905\pi\) | |||||||
\(200\) | 5.43472 | 0.384293 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.00580866 | − | 0.0100609i | −0.000408696 | − | 0.000707883i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.47073 | − | 4.27943i | −0.172563 | − | 0.298889i | ||||
\(206\) | 14.1839 | + | 24.5673i | 0.988240 | + | 1.71168i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.71014 | + | 8.15821i | −0.326590 | + | 0.565670i | ||||
\(209\) | −14.7373 | + | 25.5257i | −1.01940 | + | 1.76565i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.66118 | − | 6.34135i | −0.252046 | − | 0.436557i | 0.712043 | − | 0.702136i | \(-0.247770\pi\) |
−0.964089 | + | 0.265579i | \(0.914437\pi\) | |||||||
\(212\) | 19.5456 | 1.34240 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.5044 | 1.40165 | ||||||||
\(215\) | 2.10557 | − | 3.64695i | 0.143599 | − | 0.248720i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.3792 | − | 31.8337i | 1.24480 | − | 2.15605i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.50442 | − | 16.4621i | 0.640788 | − | 1.10988i | ||||
\(221\) | 11.4278 | − | 19.7936i | 0.768720 | − | 1.33146i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.02765 | − | 3.51199i | 0.135782 | − | 0.235181i | −0.790114 | − | 0.612960i | \(-0.789979\pi\) |
0.925896 | + | 0.377779i | \(0.123312\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.68808 | + | 11.5841i | −0.444884 | + | 0.770562i | ||||
\(227\) | −1.33417 | −0.0885522 | −0.0442761 | − | 0.999019i | \(-0.514098\pi\) | ||||
−0.0442761 | + | 0.999019i | \(0.514098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.9966 | −1.05709 | −0.528544 | − | 0.848906i | \(-0.677262\pi\) | ||||
−0.528544 | + | 0.848906i | \(0.677262\pi\) | |||||||
\(230\) | −7.14381 | − | 12.3734i | −0.471049 | − | 0.815880i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.23150 | − | 5.59712i | 0.212158 | − | 0.367469i | ||||
\(233\) | 4.06542 | − | 7.04151i | 0.266334 | − | 0.461305i | −0.701578 | − | 0.712593i | \(-0.747521\pi\) |
0.967912 | + | 0.251288i | \(0.0808542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.00102 | − | 3.46586i | −0.130532 | − | 0.226088i | ||||
\(236\) | 0.422329 | + | 0.731495i | 0.0274913 | + | 0.0476163i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0509 | − | 19.1407i | −0.714823 | − | 1.23811i | −0.963028 | − | 0.269403i | \(-0.913174\pi\) |
0.248204 | − | 0.968708i | \(-0.420160\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5947 | 1.77753 | 0.888765 | − | 0.458362i | \(-0.151564\pi\) | ||||
0.888765 | + | 0.458362i | \(0.151564\pi\) | |||||||
\(242\) | 20.6762 | + | 35.8122i | 1.32912 | + | 2.30210i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.3015 | 1.81182 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.5356 | −1.62479 | ||||||||
\(248\) | −1.17317 | + | 2.03198i | −0.0744961 | + | 0.129031i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.5810 | + | 20.0589i | 0.732447 | + | 1.26863i | ||||
\(251\) | 16.5610 | 1.04532 | 0.522661 | − | 0.852541i | \(-0.324939\pi\) | ||||
0.522661 | + | 0.852541i | \(0.324939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3524 | 1.78250 | ||||||||
\(254\) | −15.1585 | − | 26.2553i | −0.951130 | − | 1.64741i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.597516 | − | 1.03493i | 0.0373448 | − | 0.0646831i | ||||
\(257\) | −2.06573 | −0.128857 | −0.0644285 | − | 0.997922i | \(-0.520522\pi\) | ||||
−0.0644285 | + | 0.997922i | \(0.520522\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.4686 | 1.02134 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.194949 | + | 0.337662i | 0.0120440 | + | 0.0208608i | ||||
\(263\) | −10.1296 | −0.624620 | −0.312310 | − | 0.949980i | \(-0.601103\pi\) | ||||
−0.312310 | + | 0.949980i | \(0.601103\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.52969 | + | 7.84565i | 0.278257 | + | 0.481954i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.11994 | − | 10.6000i | −0.373835 | − | 0.647501i | ||||
\(269\) | −7.54972 | − | 13.0765i | −0.460315 | − | 0.797289i | 0.538662 | − | 0.842522i | \(-0.318930\pi\) |
−0.998976 | + | 0.0452336i | \(0.985597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.4026 | − | 24.9459i | 0.874893 | − | 1.51536i | 0.0180156 | − | 0.999838i | \(-0.494265\pi\) |
0.856877 | − | 0.515521i | \(-0.172402\pi\) | |||||||
\(272\) | 4.78070 | − | 8.28041i | 0.289872 | − | 0.502074i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.42993 | − | 5.94082i | −0.207210 | − | 0.358898i | ||||
\(275\) | −18.5760 | −1.12018 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.69963 | −0.162205 | −0.0811026 | − | 0.996706i | \(-0.525844\pi\) | ||||
−0.0811026 | + | 0.996706i | \(0.525844\pi\) | |||||||
\(278\) | −20.5195 | + | 35.5408i | −1.23068 | + | 2.13160i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.46312 | − | 4.26626i | 0.146938 | − | 0.254503i | −0.783157 | − | 0.621825i | \(-0.786392\pi\) |
0.930094 | + | 0.367321i | \(0.119725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.79079 | + | 3.10173i | −0.106451 | + | 0.184379i | −0.914330 | − | 0.404969i | \(-0.867282\pi\) |
0.807879 | + | 0.589348i | \(0.200615\pi\) | |||||||
\(284\) | −2.69102 | + | 4.66098i | −0.159682 | + | 0.276578i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.2832 | + | 48.9879i | −1.67242 | + | 2.89672i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.09903 | + | 5.36768i | −0.182296 | + | 0.315746i | ||||
\(290\) | 11.1322 | 0.653704 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.8691 | −1.68944 | ||||||||
\(293\) | −12.1955 | − | 21.1232i | −0.712469 | − | 1.23403i | −0.963928 | − | 0.266164i | \(-0.914244\pi\) |
0.251459 | − | 0.967868i | \(-0.419090\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.195750 | + | 0.339048i | −0.0113970 | + | 0.0197401i | ||||
\(296\) | 1.53705 | − | 2.66225i | 0.0893394 | − | 0.154740i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 23.1494 | + | 40.0960i | 1.34101 | + | 2.32270i | ||||
\(299\) | 12.2817 | + | 21.2726i | 0.710270 | + | 1.23022i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.92678 | + | 11.9975i | 0.398591 | + | 0.690380i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.6825 | −0.612685 | ||||||||
\(305\) | 6.55887 | + | 11.3603i | 0.375560 | + | 0.650489i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9025 | −1.36419 | −0.682094 | − | 0.731265i | \(-0.738930\pi\) | ||||
−0.682094 | + | 0.731265i | \(0.738930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.04143 | −0.229538 | ||||||||
\(311\) | −6.47082 | + | 11.2078i | −0.366926 | + | 0.635535i | −0.989083 | − | 0.147357i | \(-0.952923\pi\) |
0.622157 | + | 0.782893i | \(0.286257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4340 | + | 23.2684i | 0.759336 | + | 1.31521i | 0.943189 | + | 0.332255i | \(0.107810\pi\) |
−0.183853 | + | 0.982954i | \(0.558857\pi\) | |||||||
\(314\) | −3.03802 | −0.171446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.6719 | −1.38790 | ||||||||
\(317\) | 4.15584 | + | 7.19813i | 0.233415 | + | 0.404287i | 0.958811 | − | 0.284045i | \(-0.0916765\pi\) |
−0.725396 | + | 0.688332i | \(0.758343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0454 | + | 19.1311i | −0.618422 | + | 1.07114i | ||||
\(320\) | 15.7357 | 0.879654 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.9182 | 1.44212 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.04680 | − | 13.9375i | −0.446356 | − | 0.773111i | ||||
\(326\) | 41.4842 | 2.29760 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.12177 | − | 5.40706i | −0.172371 | − | 0.298555i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.19889 | − | 10.7368i | −0.340722 | − | 0.590147i | 0.643845 | − | 0.765156i | \(-0.277338\pi\) |
−0.984567 | + | 0.175009i | \(0.944005\pi\) | |||||||
\(332\) | 13.9012 | + | 24.0775i | 0.762926 | + | 1.32143i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.89775 | − | 3.28700i | 0.103840 | − | 0.179857i | ||||
\(335\) | 2.83659 | − | 4.91312i | 0.154980 | − | 0.268433i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9588 | − | 22.4454i | −0.705913 | − | 1.22268i | −0.966361 | − | 0.257189i | \(-0.917204\pi\) |
0.260448 | − | 0.965488i | \(-0.416130\pi\) | |||||||
\(338\) | −20.7150 | −1.12675 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.7152 | −0.906511 | ||||||||
\(341\) | 4.00992 | − | 6.94538i | 0.217149 | − | 0.376113i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.66038 | − | 4.60792i | 0.143438 | − | 0.248442i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.9641 | − | 18.9904i | 0.589435 | − | 1.02093i | ||||
\(347\) | −8.42415 | + | 14.5911i | −0.452232 | + | 0.783289i | −0.998524 | − | 0.0543058i | \(-0.982705\pi\) |
0.546292 | + | 0.837595i | \(0.316039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5503 | − | 26.9340i | 0.832390 | − | 1.44174i | −0.0637477 | − | 0.997966i | \(-0.520305\pi\) |
0.896138 | − | 0.443776i | \(-0.146361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.6092 | + | 35.6963i | −1.09848 | + | 1.90262i | ||||
\(353\) | −2.65938 | −0.141544 | −0.0707722 | − | 0.997493i | \(-0.522546\pi\) | ||||
−0.0707722 | + | 0.997493i | \(0.522546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.49457 | −0.132398 | ||||||||
\(356\) | 7.10833 | + | 12.3120i | 0.376741 | + | 0.652534i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1770 | − | 34.9476i | 1.06639 | − | 1.84704i | ||||
\(359\) | −16.2715 | + | 28.1830i | −0.858775 | + | 1.48744i | 0.0143230 | + | 0.999897i | \(0.495441\pi\) |
−0.873098 | + | 0.487545i | \(0.837893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.97859 | − | 8.62318i | −0.262031 | − | 0.453852i | ||||
\(362\) | −9.58646 | − | 16.6042i | −0.503853 | − | 0.872699i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.69042 | − | 11.5881i | −0.350192 | − | 0.606551i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1536 | 0.738809 | 0.369405 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369405 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(368\) | 5.13790 | + | 8.89911i | 0.267832 | + | 0.463898i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.29499 | 0.275273 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.67628 | 0.138573 | 0.0692863 | − | 0.997597i | \(-0.477928\pi\) | ||||
0.0692863 | + | 0.997597i | \(0.477928\pi\) | |||||||
\(374\) | 28.7069 | − | 49.7217i | 1.48440 | − | 2.57105i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.52828 | − | 4.37911i | −0.130386 | − | 0.225835i | ||||
\(377\) | −19.1386 | −0.985687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.312929 | −0.0160741 | −0.00803705 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803705 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(380\) | 9.33759 | + | 16.1732i | 0.479008 | + | 0.829667i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.34218 | + | 9.25292i | −0.273330 | + | 0.473421i | ||||
\(383\) | 8.98880 | 0.459306 | 0.229653 | − | 0.973273i | \(-0.426241\pi\) | ||||
0.229653 | + | 0.973273i | \(0.426241\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.2573 | 1.08197 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.80036 | − | 11.7786i | −0.345236 | − | 0.597966i | ||||
\(389\) | 26.9869 | 1.36829 | 0.684144 | − | 0.729347i | \(-0.260176\pi\) | ||||
0.684144 | + | 0.729347i | \(0.260176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4657 | − | 21.5912i | −0.630417 | − | 1.09191i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.60664 | − | 6.24689i | −0.181700 | − | 0.314714i | ||||
\(395\) | −5.71772 | − | 9.90339i | −0.287690 | − | 0.498293i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.7503 | + | 25.5482i | −0.740295 | + | 1.28223i | 0.212066 | + | 0.977255i | \(0.431981\pi\) |
−0.952361 | + | 0.304973i | \(0.901352\pi\) | |||||||
\(398\) | 12.0662 | − | 20.8992i | 0.604822 | − | 1.04758i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.36628 | − | 5.83056i | −0.168314 | − | 0.291528i | ||||
\(401\) | 34.2784 | 1.71178 | 0.855891 | − | 0.517156i | \(-0.173009\pi\) | ||||
0.855891 | + | 0.517156i | \(0.173009\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.94808 | 0.346109 | ||||||||
\(404\) | 0.00730338 | − | 0.0126498i | 0.000363357 | − | 0.000629352i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.25369 | + | 9.09966i | −0.260416 | + | 0.451054i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.49225 | + | 9.51286i | −0.271574 | + | 0.470381i | −0.969265 | − | 0.246018i | \(-0.920878\pi\) |
0.697691 | + | 0.716399i | \(0.254211\pi\) | |||||||
\(410\) | 5.37708 | − | 9.31338i | 0.265555 | − | 0.459955i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.8338 | + | 30.8890i | −0.878608 | + | 1.52179i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.44320 | + | 11.1599i | −0.316284 | + | 0.547820i | ||||
\(416\) | −35.7102 | −1.75083 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −64.1458 | −3.13747 | ||||||||
\(419\) | 3.33207 | + | 5.77132i | 0.162782 | + | 0.281947i | 0.935866 | − | 0.352357i | \(-0.114620\pi\) |
−0.773083 | + | 0.634305i | \(0.781286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0430 | + | 29.5193i | −0.830625 | + | 1.43868i | 0.0669186 | + | 0.997758i | \(0.478683\pi\) |
−0.897543 | + | 0.440926i | \(0.854650\pi\) | |||||||
\(422\) | 7.96787 | − | 13.8008i | 0.387870 | − | 0.671810i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.72325 | + | 9.91297i | 0.277946 | + | 0.481416i | ||||
\(425\) | 8.16733 | + | 14.1462i | 0.396174 | + | 0.686193i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.8903 | + | 22.3267i | 0.623077 | + | 1.07920i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.16474 | 0.441963 | ||||||||
\(431\) | 1.12969 | + | 1.95669i | 0.0544155 | + | 0.0942504i | 0.891950 | − | 0.452134i | \(-0.149337\pi\) |
−0.837535 | + | 0.546384i | \(0.816004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.3904 | 1.65270 | 0.826348 | − | 0.563160i | \(-0.190415\pi\) | ||||
0.826348 | + | 0.563160i | \(0.190415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 46.2173 | 2.21341 | ||||||||
\(437\) | −13.9274 | + | 24.1229i | −0.666236 | + | 1.15395i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.99569 | − | 5.18869i | −0.142977 | − | 0.247643i | 0.785640 | − | 0.618684i | \(-0.212334\pi\) |
−0.928616 | + | 0.371042i | \(0.879001\pi\) | |||||||
\(440\) | 11.1322 | 0.530706 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 49.7411 | 2.36594 | ||||||||
\(443\) | −19.7190 | − | 34.1543i | −0.936879 | − | 1.62272i | −0.771249 | − | 0.636534i | \(-0.780368\pi\) |
−0.165630 | − | 0.986188i | \(-0.552966\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.29471 | + | 5.70661i | −0.156184 | + | 0.270519i | ||||
\(446\) | 8.82560 | 0.417904 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.45092 | −0.115666 | −0.0578330 | − | 0.998326i | \(-0.518419\pi\) | ||||
−0.0578330 | + | 0.998326i | \(0.518419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.6703 | + | 18.4815i | 0.502444 | + | 0.870259i | ||||
\(452\) | −16.8182 | −0.791060 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.45179 | − | 2.51457i | −0.0681358 | − | 0.118015i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.51058 | − | 9.54461i | −0.257774 | − | 0.446478i | 0.707871 | − | 0.706342i | \(-0.249656\pi\) |
−0.965645 | + | 0.259864i | \(0.916322\pi\) | |||||||
\(458\) | −17.4068 | − | 30.1495i | −0.813368 | − | 1.40879i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.98208 | − | 15.5574i | 0.418792 | − | 0.725369i | ||||
\(461\) | −14.6540 | + | 25.3814i | −0.682503 | + | 1.18213i | 0.291711 | + | 0.956506i | \(0.405775\pi\) |
−0.974215 | + | 0.225624i | \(0.927558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.593566 | + | 1.02809i | 0.0275853 | + | 0.0477792i | 0.879489 | − | 0.475920i | \(-0.157885\pi\) |
−0.851903 | + | 0.523699i | \(0.824552\pi\) | |||||||
\(464\) | −8.00639 | −0.371687 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.6952 | 0.819715 | ||||||||
\(467\) | 11.0573 | − | 19.1519i | 0.511673 | − | 0.886243i | −0.488236 | − | 0.872712i | \(-0.662359\pi\) |
0.999908 | − | 0.0135313i | \(-0.00430729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.35483 | − | 7.54280i | 0.200874 | − | 0.347923i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.247329 | + | 0.428387i | −0.0113842 | + | 0.0197181i | ||||
\(473\) | −9.09327 | + | 15.7500i | −0.418109 | + | 0.724186i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.12499 | − | 15.8050i | 0.418683 | − | 0.725181i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.0502 | − | 41.6562i | 1.10003 | − | 1.90531i | ||||
\(479\) | 25.1428 | 1.14880 | 0.574402 | − | 0.818573i | \(-0.305234\pi\) | ||||
0.574402 | + | 0.818573i | \(0.305234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.10321 | −0.415071 | ||||||||
\(482\) | 30.0273 | + | 52.0088i | 1.36771 | + | 2.36894i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.9967 | + | 45.0276i | −1.18167 | + | 2.04671i | ||||
\(485\) | 3.15197 | − | 5.45937i | 0.143123 | − | 0.247897i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.78904 | − | 11.7590i | −0.307641 | − | 0.532849i | 0.670205 | − | 0.742176i | \(-0.266206\pi\) |
−0.977846 | + | 0.209327i | \(0.932873\pi\) | |||||||
\(488\) | 8.28713 | + | 14.3537i | 0.375141 | + | 0.649763i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.25177 | − | 12.5604i | −0.327268 | − | 0.566844i | 0.654701 | − | 0.755888i | \(-0.272795\pi\) |
−0.981969 | + | 0.189044i | \(0.939461\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.4253 | 0.874870 | ||||||||
\(494\) | −27.7868 | − | 48.1281i | −1.25019 | − | 2.16538i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.90664 | 0.130512 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9915 | 0.626345 | 0.313172 | − | 0.949696i | \(-0.398608\pi\) | ||||
0.313172 | + | 0.949696i | \(0.398608\pi\) | |||||||
\(500\) | −14.5611 | + | 25.2205i | −0.651191 | + | 1.12790i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.0209 | + | 31.2132i | 0.804314 | + | 1.39311i | ||||
\(503\) | −28.4011 | −1.26634 | −0.633171 | − | 0.774012i | \(-0.718247\pi\) | ||||
−0.633171 | + | 0.774012i | \(0.718247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.00677023 | 0.000301271 | ||||||||
\(506\) | 30.8518 | + | 53.4369i | 1.37153 | + | 2.37556i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.0592 | − | 33.0115i | 0.845615 | − | 1.46465i | ||||
\(509\) | 3.45993 | 0.153359 | 0.0766794 | − | 0.997056i | \(-0.475568\pi\) | ||||
0.0766794 | + | 0.997056i | \(0.475568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.3013 | −0.941392 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.24784 | − | 3.89337i | −0.0991480 | − | 0.171729i | ||||
\(515\) | −16.5319 | −0.728484 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.64174 | + | 14.9679i | 0.380063 | + | 0.658289i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.82225 | + | 8.35239i | 0.211470 | + | 0.366276i | ||||
\(521\) | 3.56797 | + | 6.17991i | 0.156316 | + | 0.270747i | 0.933537 | − | 0.358480i | \(-0.116705\pi\) |
−0.777222 | + | 0.629227i | \(0.783372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.53235 | − | 11.3144i | 0.285640 | − | 0.494743i | −0.687124 | − | 0.726540i | \(-0.741127\pi\) |
0.972764 | + | 0.231797i | \(0.0744606\pi\) | |||||||
\(524\) | −0.245114 | + | 0.424551i | −0.0107079 | + | 0.0185466i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0226 | − | 19.0917i | −0.480609 | − | 0.832439i | ||||
\(527\) | −7.05216 | −0.307197 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.79420 | 0.164965 | ||||||||
\(530\) | −9.85801 | + | 17.0746i | −0.428205 | + | 0.741672i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.24434 | + | 16.0117i | −0.400417 | + | 0.693542i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.97467 | + | 10.3484i | −0.258308 | + | 0.447402i | ||||
\(536\) | 3.58403 | − | 6.20772i | 0.154807 | − | 0.268133i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.4305 | − | 28.4585i | 0.708371 | − | 1.22693i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.46788 | + | 4.27450i | −0.106103 | + | 0.183775i | −0.914188 | − | 0.405290i | \(-0.867171\pi\) |
0.808086 | + | 0.589065i | \(0.200504\pi\) | |||||||
\(542\) | 62.6889 | 2.69272 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 36.2451 | 1.55399 | ||||||||
\(545\) | 10.7109 | + | 18.5518i | 0.458803 | + | 0.794670i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.559964 | − | 0.969887i | 0.0239423 | − | 0.0414694i | −0.853806 | − | 0.520591i | \(-0.825712\pi\) |
0.877748 | + | 0.479122i | \(0.159045\pi\) | |||||||
\(548\) | 4.31254 | − | 7.46954i | 0.184223 | − | 0.319083i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.2136 | − | 35.0110i | −0.861912 | − | 1.49288i | ||||
\(551\) | −10.8515 | − | 18.7953i | −0.462289 | − | 0.800708i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.93762 | − | 5.08811i | −0.124808 | − | 0.216173i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −51.5993 | −2.18830 | ||||||||
\(557\) | −5.47832 | − | 9.48873i | −0.232124 | − | 0.402050i | 0.726309 | − | 0.687368i | \(-0.241234\pi\) |
−0.958433 | + | 0.285318i | \(0.907901\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7561 | −0.666413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.7210 | 0.452240 | ||||||||
\(563\) | −2.38048 | + | 4.12311i | −0.100325 | + | 0.173768i | −0.911819 | − | 0.410593i | \(-0.865322\pi\) |
0.811493 | + | 0.584361i | \(0.198655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.89761 | − | 6.75087i | −0.163974 | − | 0.284011i | ||||
\(566\) | −7.79462 | −0.327632 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.15189 | −0.132250 | ||||||||
\(569\) | 1.74988 | + | 3.03088i | 0.0733588 | + | 0.127061i | 0.900371 | − | 0.435122i | \(-0.143295\pi\) |
−0.827013 | + | 0.562183i | \(0.809962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.53051 | + | 6.11501i | −0.147747 | + | 0.255905i | −0.930394 | − | 0.366560i | \(-0.880535\pi\) |
0.782647 | + | 0.622465i | \(0.213869\pi\) | |||||||
\(572\) | −71.1223 | −2.97377 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.5552 | −0.732101 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.44149 | − | 11.1570i | −0.268163 | − | 0.464472i | 0.700225 | − | 0.713923i | \(-0.253083\pi\) |
−0.968387 | + | 0.249451i | \(0.919750\pi\) | |||||||
\(578\) | −13.4889 | −0.561064 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.99838 | + | 12.1216i | 0.290592 | + | 0.503320i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.5623 | − | 33.8828i | −0.810186 | − | 1.40328i | ||||
\(584\) | −8.45333 | − | 14.6416i | −0.349801 | − | 0.605874i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.5412 | − | 45.9707i | 1.09641 | − | 1.89903i | ||||
\(587\) | 19.5044 | − | 33.7826i | 0.805034 | − | 1.39436i | −0.111235 | − | 0.993794i | \(-0.535481\pi\) |
0.916268 | − | 0.400565i | \(-0.131186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.93953 | + | 6.82347i | 0.162326 | + | 0.281156i | ||||
\(590\) | −0.852024 | −0.0350773 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.80821 | −0.156517 | ||||||||
\(593\) | 20.1513 | − | 34.9031i | 0.827515 | − | 1.43330i | −0.0724676 | − | 0.997371i | \(-0.523087\pi\) |
0.899982 | − | 0.435927i | \(-0.143579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.1064 | + | 50.4137i | −1.19224 | + | 2.06503i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26.7288 | + | 46.2957i | −1.09302 | + | 1.89317i | ||||
\(599\) | −6.39103 | + | 11.0696i | −0.261130 | + | 0.452291i | −0.966543 | − | 0.256506i | \(-0.917429\pi\) |
0.705412 | + | 0.708797i | \(0.250762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.86311 | + | 8.42316i | −0.198371 | + | 0.343588i | −0.948000 | − | 0.318270i | \(-0.896898\pi\) |
0.749630 | + | 0.661858i | \(0.230232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.70921 | + | 15.0848i | −0.354373 | + | 0.613792i | ||||
\(605\) | −24.0990 | −0.979762 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.4873 | 1.68392 | 0.841959 | − | 0.539541i | \(-0.181402\pi\) | ||||
0.841959 | + | 0.539541i | \(0.181402\pi\) | |||||||
\(608\) | −20.2475 | − | 35.0697i | −0.821145 | − | 1.42226i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2742 | + | 24.7236i | −0.577943 | + | 1.00103i | ||||
\(611\) | −7.48688 | + | 12.9677i | −0.302887 | + | 0.524615i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.64783 | − | 13.2464i | −0.308893 | − | 0.535018i | 0.669228 | − | 0.743057i | \(-0.266625\pi\) |
−0.978120 | + | 0.208039i | \(0.933292\pi\) | |||||||
\(614\) | −26.0096 | − | 45.0500i | −1.04966 | − | 1.81807i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.66563 | + | 4.61700i | 0.107314 | + | 0.185873i | 0.914681 | − | 0.404176i | \(-0.132442\pi\) |
−0.807367 | + | 0.590049i | \(0.799108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.6841 | −0.509817 | −0.254908 | − | 0.966965i | \(-0.582045\pi\) | ||||
−0.254908 | + | 0.966965i | \(0.582045\pi\) | |||||||
\(620\) | −2.54070 | − | 4.40062i | −0.102037 | − | 0.176733i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28.1650 | −1.12931 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.45909 | 0.138363 | ||||||||
\(626\) | −29.2366 | + | 50.6393i | −1.16853 | + | 2.02395i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.90989 | − | 3.30803i | −0.0762129 | − | 0.132005i | ||||
\(629\) | 9.23957 | 0.368406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.123764 | 0.00492698 | 0.00246349 | − | 0.999997i | \(-0.499216\pi\) | ||||
0.00246349 | + | 0.999997i | \(0.499216\pi\) | |||||||
\(632\) | −7.22433 | − | 12.5129i | −0.287369 | − | 0.497737i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.04441 | + | 15.6654i | −0.359199 | + | 0.622151i | ||||
\(635\) | 17.6679 | 0.701128 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −48.0763 | −1.90336 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.57868 | + | 13.1267i | 0.299573 | + | 0.518876i | ||||
\(641\) | −5.93177 | −0.234291 | −0.117145 | − | 0.993115i | \(-0.537374\pi\) | ||||
−0.117145 | + | 0.993115i | \(0.537374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.4140 | − | 40.5542i | −0.923358 | − | 1.59930i | −0.794180 | − | 0.607682i | \(-0.792100\pi\) |
−0.129178 | − | 0.991621i | \(-0.541234\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.2030 | + | 48.8490i | 1.10963 | + | 1.92194i | ||||
\(647\) | −19.5701 | − | 33.8964i | −0.769379 | − | 1.33260i | −0.937900 | − | 0.346905i | \(-0.887233\pi\) |
0.168521 | − | 0.985698i | \(-0.446101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.845379 | − | 1.46424i | 0.0331840 | − | 0.0574764i | ||||
\(650\) | 17.5123 | − | 30.3322i | 0.686890 | − | 1.18973i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26.0796 | + | 45.1711i | 1.02135 | + | 1.76904i | ||||
\(653\) | −43.3281 | −1.69556 | −0.847779 | − | 0.530350i | \(-0.822061\pi\) | ||||
−0.847779 | + | 0.530350i | \(0.822061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.227221 | −0.00887827 | ||||||||
\(656\) | −3.86726 | + | 6.69828i | −0.150991 | + | 0.261524i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.43895 | + | 5.95643i | −0.133962 | + | 0.232030i | −0.925201 | − | 0.379478i | \(-0.876103\pi\) |
0.791238 | + | 0.611508i | \(0.209437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.3835 | + | 33.5733i | −0.753932 | + | 1.30585i | 0.191971 | + | 0.981401i | \(0.438512\pi\) |
−0.945903 | + | 0.324449i | \(0.894821\pi\) | |||||||
\(662\) | 13.4907 | − | 23.3666i | 0.524331 | − | 0.908168i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.14097 | + | 14.1006i | −0.315931 | + | 0.547209i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.4383 | + | 18.0797i | −0.404174 | + | 0.700050i | ||||
\(668\) | 4.77217 | 0.184641 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.3466 | 0.476991 | ||||||||
\(671\) | −28.3257 | − | 49.0615i | −1.09350 | − | 1.89400i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.9897 | − | 31.1591i | 0.693452 | − | 1.20109i | −0.277248 | − | 0.960798i | \(-0.589422\pi\) |
0.970700 | − | 0.240295i | \(-0.0772443\pi\) | |||||||
\(674\) | 28.2025 | − | 48.8481i | 1.08632 | − | 1.88156i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0227 | − | 22.5560i | −0.500874 | − | 0.867539i | ||||
\(677\) | 2.23329 | + | 3.86817i | 0.0858322 | + | 0.148666i | 0.905746 | − | 0.423822i | \(-0.139312\pi\) |
−0.819913 | + | 0.572488i | \(0.805978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.89449 | − | 8.47750i | −0.187695 | − | 0.325097i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.4536 | 0.668335 | ||||||||
\(683\) | −13.3356 | − | 23.0980i | −0.510274 | − | 0.883821i | −0.999929 | − | 0.0119046i | \(-0.996211\pi\) |
0.489655 | − | 0.871916i | \(-0.337123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.99773 | 0.152745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.59138 | −0.251294 | ||||||||
\(689\) | 16.9480 | − | 29.3548i | 0.645668 | − | 1.11833i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.5220 | + | 35.5452i | 0.780694 | + | 1.35220i | 0.931538 | + | 0.363644i | \(0.118468\pi\) |
−0.150844 | + | 0.988558i | \(0.548199\pi\) | |||||||
\(692\) | 27.5709 | 1.04809 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.6671 | −1.39187 | ||||||||
\(695\) | −11.9582 | − | 20.7121i | −0.453599 | − | 0.785656i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.38281 | − | 16.2515i | 0.355399 | − | 0.615570i | ||||
\(698\) | 67.6847 | 2.56190 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.63355 | −0.363854 | −0.181927 | − | 0.983312i | \(-0.558233\pi\) | ||||
−0.181927 | + | 0.983312i | \(0.558233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.16148 | − | 8.93994i | −0.194669 | − | 0.337176i | ||||
\(704\) | −67.9575 | −2.56125 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.89382 | − | 5.01224i | −0.108910 | − | 0.188638i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.07131 | + | 8.78376i | 0.190457 | + | 0.329881i | 0.945402 | − | 0.325907i | \(-0.105670\pi\) |
−0.754945 | + | 0.655788i | \(0.772336\pi\) | |||||||
\(710\) | −2.71448 | − | 4.70162i | −0.101873 | − | 0.176449i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.16286 | + | 7.21029i | −0.156010 | + | 0.270217i | ||||
\(713\) | 3.78954 | − | 6.56368i | 0.141919 | − | 0.245812i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4826 | − | 28.5487i | −0.616415 | − | 1.06766i | ||||
\(716\) | 50.7380 | 1.89617 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −70.8235 | −2.64311 | ||||||||
\(719\) | −20.6844 | + | 35.8264i | −0.771397 | + | 1.33610i | 0.165400 | + | 0.986227i | \(0.447109\pi\) |
−0.936797 | + | 0.349873i | \(0.886225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.8350 | − | 18.7667i | 0.403236 | − | 0.698425i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.0533 | − | 20.8769i | 0.447957 | − | 0.775884i | ||||
\(725\) | 6.83904 | − | 11.8456i | 0.253996 | − | 0.439934i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.86372 | + | 8.42422i | −0.180386 | + | 0.312437i | −0.942012 | − | 0.335580i | \(-0.891068\pi\) |
0.761626 | + | 0.648016i | \(0.224401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.5604 | − | 25.2194i | 0.538906 | − | 0.933412i | ||||
\(731\) | 15.9921 | 0.591491 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.9108 | 1.06784 | 0.533922 | − | 0.845534i | \(-0.320718\pi\) | ||||
0.533922 | + | 0.845534i | \(0.320718\pi\) | |||||||
\(734\) | 15.4013 | + | 26.6758i | 0.568471 | + | 0.984621i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.4766 | + | 33.7345i | −0.717918 | + | 1.24347i | ||||
\(737\) | −12.2503 | + | 21.2182i | −0.451247 | + | 0.781582i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.67467 | + | 11.5609i | 0.245532 | + | 0.425273i | 0.962281 | − | 0.272058i | \(-0.0877041\pi\) |
−0.716749 | + | 0.697331i | \(0.754371\pi\) | |||||||
\(740\) | 3.32876 | + | 5.76558i | 0.122368 | + | 0.211947i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9100 | − | 34.4851i | −0.730425 | − | 1.26513i | −0.956702 | − | 0.291071i | \(-0.905988\pi\) |
0.226276 | − | 0.974063i | \(-0.427345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.9816 | −0.988530 | ||||||||
\(746\) | 2.91221 | + | 5.04410i | 0.106624 | + | 0.184678i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 72.1877 | 2.63944 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.4345 | −1.40250 | −0.701248 | − | 0.712917i | \(-0.747374\pi\) | ||||
−0.701248 | + | 0.712917i | \(0.747374\pi\) | |||||||
\(752\) | −3.13204 | + | 5.42486i | −0.114214 | + | 0.197824i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.8258 | − | 36.0713i | −0.758429 | − | 1.31364i | ||||
\(755\) | −8.07344 | −0.293823 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.66698 | −0.205970 | −0.102985 | − | 0.994683i | \(-0.532839\pi\) | ||||
−0.102985 | + | 0.994683i | \(0.532839\pi\) | |||||||
\(758\) | −0.340516 | − | 0.589791i | −0.0123681 | − | 0.0214222i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.46839 | + | 9.47153i | −0.198359 | + | 0.343569i | ||||
\(761\) | −52.3321 | −1.89704 | −0.948519 | − | 0.316719i | \(-0.897419\pi\) | ||||
−0.948519 | + | 0.316719i | \(0.897419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.4337 | −0.486014 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.78121 | + | 16.9416i | 0.353410 | + | 0.612123i | ||||
\(767\) | 1.46481 | 0.0528912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.17360 | + | 2.03274i | 0.0423212 | + | 0.0733025i | 0.886410 | − | 0.462901i | \(-0.153191\pi\) |
−0.844089 | + | 0.536203i | \(0.819858\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.3637 | + | 23.1466i | 0.480970 | + | 0.833064i | ||||
\(773\) | 18.1814 | + | 31.4912i | 0.653941 | + | 1.13266i | 0.982158 | + | 0.188057i | \(0.0602189\pi\) |
−0.328217 | + | 0.944602i | \(0.606448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.48285 | + | 4.30042i | −0.0891866 | + | 0.154476i | ||||
\(776\) | 3.98251 | − | 6.89790i | 0.142964 | − | 0.247620i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.3659 | + | 50.8633i | 1.05282 | + | 1.82354i | ||||
\(779\) | −20.9660 | −0.751185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.7733 | 0.385497 | ||||||||
\(782\) | 27.1292 | − | 46.9892i | 0.970139 | − | 1.68033i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.885235 | − | 1.53327i | 0.0315954 | − | 0.0547248i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8846 | − | 27.5129i | 0.566224 | − | 0.980729i | −0.430711 | − | 0.902490i | \(-0.641737\pi\) |
0.996935 | − | 0.0782386i | \(-0.0249296\pi\) | |||||||
\(788\) | 4.53472 | − | 7.85437i | 0.161543 | − | 0.279800i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.4435 | − | 21.5528i | 0.442721 | − | 0.766816i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5403 | − | 42.5050i | 0.871451 | − | 1.50940i | ||||
\(794\) | −64.2024 | −2.27846 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.3422 | 1.07545 | ||||||||
\(797\) | 7.45306 | + | 12.9091i | 0.264001 | + | 0.457263i | 0.967301 | − | 0.253630i | \(-0.0816245\pi\) |
−0.703301 | + | 0.710893i | \(0.748291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.59903 | − | 13.1619i | 0.268834 | − | 0.465635i | ||||
\(800\) | 12.7608 | − | 22.1023i | 0.451162 | − | 0.781436i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 37.3002 | + | 64.6059i | 1.31712 | + | 2.28131i | ||||
\(803\) | 28.8937 | + | 50.0454i | 1.01964 | + | 1.76606i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.56059 | + | 13.0953i | 0.266311 | + | 0.461263i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.00855418 | 0.000300935 | ||||||||
\(809\) | 23.9018 | + | 41.3992i | 0.840344 | + | 1.45552i | 0.889604 | + | 0.456733i | \(0.150980\pi\) |
−0.0492597 | + | 0.998786i | \(0.515686\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.1131 | −1.12764 | −0.563821 | − | 0.825897i | \(-0.690669\pi\) | ||||
−0.563821 | + | 0.825897i | \(0.690669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.8673 | −0.801500 | ||||||||
\(815\) | −12.0879 | + | 20.9368i | −0.423420 | + | 0.733385i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.93366 | − | 15.4735i | −0.312549 | − | 0.541351i | ||||
\(818\) | −23.9057 | −0.835843 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5215 | 0.472190 | ||||||||
\(821\) | 23.5535 | + | 40.7958i | 0.822023 | + | 1.42378i | 0.904174 | + | 0.427165i | \(0.140488\pi\) |
−0.0821512 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8955 | + | 29.2639i | −0.588941 | + | 1.02008i | 0.405431 | + | 0.914126i | \(0.367122\pi\) |
−0.994372 | + | 0.105950i | \(0.966212\pi\) | |||||||
\(824\) | −20.8881 | −0.727670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.98023 | −0.103633 | −0.0518164 | − | 0.998657i | \(-0.516501\pi\) | ||||
−0.0518164 | + | 0.998657i | \(0.516501\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.03978 | − | 5.26506i | −0.105576 | − | 0.182863i | 0.808397 | − | 0.588637i | \(-0.200335\pi\) |
−0.913973 | + | 0.405774i | \(0.867002\pi\) | |||||||
\(830\) | −28.0448 | −0.973450 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −29.4379 | − | 50.9880i | −1.02058 | − | 1.76769i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.10595 | + | 1.91557i | 0.0382731 | + | 0.0662909i | ||||
\(836\) | −40.3260 | − | 69.8467i | −1.39471 | − | 2.41570i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.25163 | + | 12.5602i | −0.250503 | + | 0.433885i | ||||
\(839\) | −1.85858 | + | 3.21915i | −0.0641653 | + | 0.111138i | −0.896323 | − | 0.443401i | \(-0.853772\pi\) |
0.832158 | + | 0.554538i | \(0.187105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.36697 | + | 11.0279i | 0.219551 | + | 0.380273i | ||||
\(842\) | −74.1817 | −2.55647 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0364 | 0.689681 | ||||||||
\(845\) | 6.03604 | − | 10.4547i | 0.207646 | − | 0.359653i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.08999 | − | 12.2802i | 0.243471 | − | 0.421705i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.7747 | + | 30.7866i | −0.609666 | + | 1.05597i | ||||
\(851\) | −4.96496 | + | 8.59957i | −0.170197 | + | 0.294789i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.553861 | + | 0.959315i | −0.0189638 | + | 0.0328463i | −0.875352 | − | 0.483487i | \(-0.839370\pi\) |
0.856388 | + | 0.516333i | \(0.172703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.54899 | + | 13.0752i | −0.258019 | + | 0.446902i | ||||
\(857\) | 38.5195 | 1.31580 | 0.657900 | − | 0.753105i | \(-0.271445\pi\) | ||||
0.657900 | + | 0.753105i | \(0.271445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8874 | −1.19034 | −0.595171 | − | 0.803599i | \(-0.702916\pi\) | ||||
−0.595171 | + | 0.803599i | \(0.702916\pi\) | |||||||
\(860\) | 5.76153 | + | 9.97926i | 0.196467 | + | 0.340290i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.45857 | + | 4.25836i | −0.0837391 | + | 0.145040i | ||||
\(863\) | 1.07924 | − | 1.86931i | 0.0367379 | − | 0.0636319i | −0.847072 | − | 0.531478i | \(-0.821637\pi\) |
0.883810 | + | 0.467847i | \(0.154970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.38957 | + | 11.0671i | 0.217252 | + | 0.376291i | ||||
\(866\) | 37.4221 | + | 64.8169i | 1.27165 | + | 2.20257i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.6930 | + | 42.7695i | 0.837652 | + | 1.45086i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.2264 | −0.719231 | ||||||||
\(872\) | 13.5332 | + | 23.4401i | 0.458291 | + | 0.793783i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −60.6205 | −2.05052 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.8790 | 0.637499 | 0.318749 | − | 0.947839i | \(-0.396737\pi\) | ||||
0.318749 | + | 0.947839i | \(0.396737\pi\) | |||||||
\(878\) | 6.51956 | − | 11.2922i | 0.220025 | − | 0.381094i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.89530 | − | 11.9430i | −0.232440 | − | 0.402599i | ||||
\(881\) | 18.7203 | 0.630704 | 0.315352 | − | 0.948975i | \(-0.397877\pi\) | ||||
0.315352 | + | 0.948975i | \(0.397877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.3717 | −0.449993 | −0.224996 | − | 0.974360i | \(-0.572237\pi\) | ||||
−0.224996 | + | 0.974360i | \(0.572237\pi\) | |||||||
\(884\) | 31.2704 | + | 54.1618i | 1.05174 | + | 1.82166i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.9147 | − | 74.3305i | 1.44175 | − | 2.49718i | ||||
\(887\) | −41.2568 | −1.38527 | −0.692633 | − | 0.721290i | \(-0.743550\pi\) | ||||
−0.692633 | + | 0.721290i | \(0.743550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.3406 | −0.480699 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.54832 | + | 9.60997i | 0.185772 | + | 0.321766i | ||||
\(893\) | −16.9801 | −0.568218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.7585 | + | 20.3664i | 0.393045 | + | 0.680774i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.66698 | − | 4.61934i | −0.0889982 | − | 0.154149i | ||||
\(899\) | 2.95262 | + | 5.11408i | 0.0984753 | + | 0.170564i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.2019 | + | 29.7945i | −0.573078 | + | 0.992599i | ||||
\(902\) | −23.2219 | + | 40.2215i | −0.773204 | + | 1.33923i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.92463 | − | 8.52971i | −0.163791 | − | 0.283694i | ||||
\(905\) | 11.1734 | 0.371416 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.69037 | 0.122537 | 0.0612684 | − | 0.998121i | \(-0.480485\pi\) | ||||
0.0612684 | + | 0.998121i | \(0.480485\pi\) | |||||||
\(908\) | 1.82537 | − | 3.16163i | 0.0605770 | − | 0.104922i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.43831 | − | 5.95533i | 0.113916 | − | 0.197309i | −0.803430 | − | 0.595400i | \(-0.796994\pi\) |
0.917346 | + | 0.398091i | \(0.130327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.8261 | − | 48.1962i | 0.920909 | − | 1.59506i | ||||
\(914\) | 11.9927 | − | 20.7720i | 0.396685 | − | 0.687078i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.8860 | − | 37.9077i | 0.723135 | − | 1.25251i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.6473 | + | 32.2981i | −0.615119 | + | 1.06542i | 0.375245 | + | 0.926926i | \(0.377559\pi\) |
−0.990364 | + | 0.138491i | \(0.955775\pi\) | |||||||
\(920\) | 10.5204 | 0.346847 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −63.7832 | −2.10059 | ||||||||
\(923\) | 4.66677 | + | 8.08309i | 0.153609 | + | 0.266058i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.25297 | − | 5.63431i | 0.106957 | − | 0.185255i | ||||
\(926\) | −1.29178 | + | 2.23743i | −0.0424506 | + | 0.0735267i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.1752 | − | 26.2842i | −0.498150 | − | 0.862821i | ||||
\(929\) | −8.98933 | − | 15.5700i | −0.294930 | − | 0.510834i | 0.680038 | − | 0.733177i | \(-0.261963\pi\) |
−0.974969 | + | 0.222342i | \(0.928630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.1243 | + | 19.2679i | 0.364389 | + | 0.631141i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 48.1284 | 1.57481 | ||||||||
\(935\) | 16.7295 | + | 28.9764i | 0.547113 | + | 0.947628i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7312 | 1.13462 | 0.567310 | − | 0.823504i | \(-0.307984\pi\) | ||||
0.567310 | + | 0.823504i | \(0.307984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.9509 | 0.357178 | ||||||||
\(941\) | 21.6512 | − | 37.5010i | 0.705810 | − | 1.22250i | −0.260588 | − | 0.965450i | \(-0.583917\pi\) |
0.966398 | − | 0.257049i | \(-0.0827501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0839 | + | 17.4658i | 0.328376 | + | 0.568764i | ||||
\(944\) | 0.612785 | 0.0199444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.5796 | −1.28684 | ||||||||
\(947\) | 19.1295 | + | 33.1333i | 0.621626 | + | 1.07669i | 0.989183 | + | 0.146687i | \(0.0468611\pi\) |
−0.367557 | + | 0.930001i | \(0.619806\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.0325 | + | 43.3575i | −0.812588 | + | 1.40744i | ||||
\(950\) | 39.7176 | 1.28861 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.8757 | 1.55085 | 0.775423 | − | 0.631442i | \(-0.217537\pi\) | ||||
0.775423 | + | 0.631442i | \(0.217537\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.11326 | − | 5.39233i | −0.100743 | − | 0.174492i | ||||
\(956\) | 60.4778 | 1.95599 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.3593 | + | 47.3877i | 0.883939 | + | 1.53103i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4281 | + | 24.9902i | 0.465422 | + | 0.806134i | ||||
\(962\) | −9.90570 | − | 17.1572i | −0.319373 | − | 0.553170i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.7541 | + | 65.3920i | −1.21598 | + | 2.10613i | ||||
\(965\) | −6.19407 | + | 10.7284i | −0.199394 | + | 0.345361i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5575 | + | 26.9463i | 0.500294 | + | 0.866535i | 1.00000 | 0.000339469i | \(0.000108056\pi\) | |
−0.499706 | + | 0.866195i | \(0.666559\pi\) | |||||||
\(968\) | −30.4490 | −0.978668 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.7193 | 0.440501 | ||||||||
\(971\) | 15.1312 | − | 26.2080i | 0.485583 | − | 0.841055i | −0.514279 | − | 0.857623i | \(-0.671941\pi\) |
0.999863 | + | 0.0165676i | \(0.00527387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 14.7751 | − | 25.5911i | 0.473423 | − | 0.819993i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.2661 | − | 17.7815i | 0.328611 | − | 0.569170i | ||||
\(977\) | 19.1101 | − | 33.0996i | 0.611385 | − | 1.05895i | −0.379622 | − | 0.925142i | \(-0.623946\pi\) |
0.991007 | − | 0.133808i | \(-0.0427207\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.2288 | − | 24.6450i | 0.454754 | − | 0.787657i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.7821 | − | 27.3354i | 0.503627 | − | 0.872308i | ||||
\(983\) | −37.3929 | −1.19265 | −0.596324 | − | 0.802744i | \(-0.703372\pi\) | ||||
−0.596324 | + | 0.802744i | \(0.703372\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.20369 | 0.133941 | ||||||||
\(986\) | 21.1377 | + | 36.6116i | 0.673162 | + | 1.16595i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 34.9370 | − | 60.5126i | 1.11149 | − | 1.92516i | ||||
\(989\) | −8.59353 | + | 14.8844i | −0.273258 | + | 0.473297i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.9299 | + | 20.6631i | 0.378965 | + | 0.656386i | 0.990912 | − | 0.134512i | \(-0.0429468\pi\) |
−0.611947 | + | 0.790899i | \(0.709613\pi\) | |||||||
\(992\) | 5.50921 | + | 9.54223i | 0.174918 | + | 0.302966i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.03180 | + | 12.1794i | 0.222923 | + | 0.386114i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.6826 | −1.63681 | −0.818403 | − | 0.574645i | \(-0.805140\pi\) | ||||
−0.818403 | + | 0.574645i | \(0.805140\pi\) | |||||||
\(998\) | 15.2249 | + | 26.3703i | 0.481936 | + | 0.834738i | ||||
\(999\) | 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 | 1323.2.g.h.667.11 | 24 | ||
3.2 | odd | 2 | 441.2.g.h.79.1 | 24 | |||
7.2 | even | 3 | 1323.2.f.h.883.12 | 24 | |||
7.3 | odd | 6 | 1323.2.h.h.802.1 | 24 | |||
7.4 | even | 3 | 1323.2.h.h.802.2 | 24 | |||
7.5 | odd | 6 | 1323.2.f.h.883.11 | 24 | |||
7.6 | odd | 2 | inner | 1323.2.g.h.667.12 | 24 | ||
9.4 | even | 3 | 1323.2.h.h.226.2 | 24 | |||
9.5 | odd | 6 | 441.2.h.h.373.11 | 24 | |||
21.2 | odd | 6 | 441.2.f.h.295.2 | yes | 24 | ||
21.5 | even | 6 | 441.2.f.h.295.1 | yes | 24 | ||
21.11 | odd | 6 | 441.2.h.h.214.11 | 24 | |||
21.17 | even | 6 | 441.2.h.h.214.12 | 24 | |||
21.20 | even | 2 | 441.2.g.h.79.2 | 24 | |||
63.2 | odd | 6 | 3969.2.a.bh.1.12 | 12 | |||
63.4 | even | 3 | inner | 1323.2.g.h.361.11 | 24 | ||
63.5 | even | 6 | 441.2.f.h.148.1 | ✓ | 24 | ||
63.13 | odd | 6 | 1323.2.h.h.226.1 | 24 | |||
63.16 | even | 3 | 3969.2.a.bi.1.1 | 12 | |||
63.23 | odd | 6 | 441.2.f.h.148.2 | yes | 24 | ||
63.31 | odd | 6 | inner | 1323.2.g.h.361.12 | 24 | ||
63.32 | odd | 6 | 441.2.g.h.67.1 | 24 | |||
63.40 | odd | 6 | 1323.2.f.h.442.11 | 24 | |||
63.41 | even | 6 | 441.2.h.h.373.12 | 24 | |||
63.47 | even | 6 | 3969.2.a.bh.1.11 | 12 | |||
63.58 | even | 3 | 1323.2.f.h.442.12 | 24 | |||
63.59 | even | 6 | 441.2.g.h.67.2 | 24 | |||
63.61 | odd | 6 | 3969.2.a.bi.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.1 | ✓ | 24 | 63.5 | even | 6 | ||
441.2.f.h.148.2 | yes | 24 | 63.23 | odd | 6 | ||
441.2.f.h.295.1 | yes | 24 | 21.5 | even | 6 | ||
441.2.f.h.295.2 | yes | 24 | 21.2 | odd | 6 | ||
441.2.g.h.67.1 | 24 | 63.32 | odd | 6 | |||
441.2.g.h.67.2 | 24 | 63.59 | even | 6 | |||
441.2.g.h.79.1 | 24 | 3.2 | odd | 2 | |||
441.2.g.h.79.2 | 24 | 21.20 | even | 2 | |||
441.2.h.h.214.11 | 24 | 21.11 | odd | 6 | |||
441.2.h.h.214.12 | 24 | 21.17 | even | 6 | |||
441.2.h.h.373.11 | 24 | 9.5 | odd | 6 | |||
441.2.h.h.373.12 | 24 | 63.41 | even | 6 | |||
1323.2.f.h.442.11 | 24 | 63.40 | odd | 6 | |||
1323.2.f.h.442.12 | 24 | 63.58 | even | 3 | |||
1323.2.f.h.883.11 | 24 | 7.5 | odd | 6 | |||
1323.2.f.h.883.12 | 24 | 7.2 | even | 3 | |||
1323.2.g.h.361.11 | 24 | 63.4 | even | 3 | inner | ||
1323.2.g.h.361.12 | 24 | 63.31 | odd | 6 | inner | ||
1323.2.g.h.667.11 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.g.h.667.12 | 24 | 7.6 | odd | 2 | inner | ||
1323.2.h.h.226.1 | 24 | 63.13 | odd | 6 | |||
1323.2.h.h.226.2 | 24 | 9.4 | even | 3 | |||
1323.2.h.h.802.1 | 24 | 7.3 | odd | 6 | |||
1323.2.h.h.802.2 | 24 | 7.4 | even | 3 | |||
3969.2.a.bh.1.11 | 12 | 63.47 | even | 6 | |||
3969.2.a.bh.1.12 | 12 | 63.2 | odd | 6 | |||
3969.2.a.bi.1.1 | 12 | 63.16 | even | 3 | |||
3969.2.a.bi.1.2 | 12 | 63.61 | odd | 6 |