Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(109,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.o (of order \(10\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 229.3 | ||
Character | \(\chi\) | \(=\) | 300.229 |
Dual form | 300.2.o.a.169.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.99921 | − | 1.00158i | 0.894074 | − | 0.447919i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.80992i | 1.44001i | 0.693968 | + | 0.720006i | \(0.255861\pi\) | ||||
−0.693968 | + | 0.720006i | \(0.744139\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0589397 | − | 0.181398i | 0.0177710 | − | 0.0546935i | −0.941778 | − | 0.336236i | \(-0.890846\pi\) |
0.959549 | + | 0.281542i | \(0.0908460\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59724 | − | 0.518974i | 0.442994 | − | 0.143937i | −0.0790227 | − | 0.996873i | \(-0.525180\pi\) |
0.522016 | + | 0.852935i | \(0.325180\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.364813 | + | 2.20611i | −0.0941944 | + | 0.569615i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.70572 | + | 3.72410i | 0.656233 | + | 0.903227i | 0.999349 | − | 0.0360656i | \(-0.0114825\pi\) |
−0.343116 | + | 0.939293i | \(0.611483\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.13682 | + | 1.55249i | −0.490221 | + | 0.356166i | −0.805269 | − | 0.592909i | \(-0.797979\pi\) |
0.315049 | + | 0.949076i | \(0.397979\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.08229 | − | 2.23941i | −0.672610 | − | 0.488680i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.04461 | + | 1.96401i | 1.26039 | + | 0.409525i | 0.861632 | − | 0.507533i | \(-0.169442\pi\) |
0.398755 | + | 0.917057i | \(0.369442\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.99369 | − | 4.00473i | 0.598737 | − | 0.800946i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.03878 | + | 1.48126i | 0.378593 | + | 0.275064i | 0.760765 | − | 0.649027i | \(-0.224824\pi\) |
−0.382172 | + | 0.924091i | \(0.624824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.03331 | + | 2.20383i | −0.544798 | + | 0.395819i | −0.825864 | − | 0.563870i | \(-0.809312\pi\) |
0.281066 | + | 0.959688i | \(0.409312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.112110 | + | 0.154306i | 0.0195158 | + | 0.0268612i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.81593 | + | 7.61682i | 0.645009 | + | 1.28748i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.2820 | + | 3.66574i | −1.85474 | + | 0.602643i | −0.858839 | + | 0.512245i | \(0.828814\pi\) |
−0.995906 | + | 0.0903980i | \(0.971186\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.518974 | + | 1.59724i | −0.0831023 | + | 0.255763i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.22169 | − | 6.83765i | −0.346969 | − | 1.06786i | −0.960521 | − | 0.278207i | \(-0.910260\pi\) |
0.613552 | − | 0.789655i | \(-0.289740\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.22619i | − | 1.40698i | −0.710705 | − | 0.703491i | \(-0.751624\pi\) | ||
0.710705 | − | 0.703491i | \(-0.248376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.57035 | − | 1.59186i | −0.234093 | − | 0.237300i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.67353 | − | 3.67980i | 0.389975 | − | 0.536754i | −0.568218 | − | 0.822878i | \(-0.692367\pi\) |
0.958193 | + | 0.286124i | \(0.0923670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.51545 | −1.07364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60324 | −0.644583 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.54285 | − | 7.62908i | 0.761369 | − | 1.04793i | −0.235730 | − | 0.971819i | \(-0.575748\pi\) |
0.997099 | − | 0.0761162i | \(-0.0242520\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0638510 | − | 0.421685i | −0.00860967 | − | 0.0568600i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.64126i | − | 0.349843i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.20656 | − | 6.79109i | −0.287269 | − | 0.884124i | −0.985709 | − | 0.168456i | \(-0.946122\pi\) |
0.698440 | − | 0.715669i | \(-0.253878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.94497 | − | 9.06368i | 0.377064 | − | 1.16049i | −0.565011 | − | 0.825084i | \(-0.691128\pi\) |
0.942075 | − | 0.335402i | \(-0.108872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.62344 | − | 1.17733i | 0.456511 | − | 0.148329i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.67342 | − | 2.63729i | 0.331597 | − | 0.327116i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.55709 | + | 4.89591i | 0.434567 | + | 0.598131i | 0.968994 | − | 0.247084i | \(-0.0794724\pi\) |
−0.534427 | + | 0.845215i | \(0.679472\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.14185 | + | 3.73577i | −0.619006 | + | 0.449734i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7586 | − | 7.81655i | −1.27681 | − | 0.927654i | −0.277355 | − | 0.960768i | \(-0.589458\pi\) |
−0.999452 | + | 0.0331133i | \(0.989458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.95645 | − | 1.61045i | −0.580109 | − | 0.188489i | 0.00424038 | − | 0.999991i | \(-0.498650\pi\) |
−0.584349 | + | 0.811502i | \(0.698650\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.48025 | + | 4.77586i | 0.170924 | + | 0.551469i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.691110 | + | 0.224555i | 0.0787593 | + | 0.0255904i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.51740 | − | 1.82900i | −0.283230 | − | 0.205779i | 0.437095 | − | 0.899415i | \(-0.356007\pi\) |
−0.720325 | + | 0.693637i | \(0.756007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.74988 | − | 3.78488i | −0.301838 | − | 0.415445i | 0.630976 | − | 0.775802i | \(-0.282655\pi\) |
−0.932814 | + | 0.360358i | \(0.882655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.13928 | + | 4.73528i | 0.991294 | + | 0.513613i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.39673 | + | 0.778746i | −0.256957 | + | 0.0834904i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.30840 | + | 13.2599i | −0.456690 | + | 1.40555i | 0.412451 | + | 0.910980i | \(0.364673\pi\) |
−0.869140 | + | 0.494566i | \(0.835327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.97725 | + | 6.08534i | 0.207272 | + | 0.637917i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.74937i | − | 0.388792i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.71702 | + | 5.24395i | −0.278760 | + | 0.538018i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.93527 | + | 5.41643i | −0.399566 | + | 0.549955i | −0.960635 | − | 0.277814i | \(-0.910390\pi\) |
0.561069 | + | 0.827769i | \(0.310390\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.190733 | −0.0191694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5147 | 1.04625 | 0.523127 | − | 0.852255i | \(-0.324765\pi\) | ||||
0.523127 | + | 0.852255i | \(0.324765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.62055 | + | 10.4888i | −0.750875 | + | 1.03349i | 0.247044 | + | 0.969004i | \(0.420541\pi\) |
−0.997919 | + | 0.0644861i | \(0.979459\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.40508 | − | 1.38991i | −0.820252 | − | 0.135641i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.64606i | 0.932520i | 0.884648 | + | 0.466260i | \(0.154399\pi\) | ||||
−0.884648 | + | 0.466260i | \(0.845601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31798 | − | 19.4447i | −0.605153 | − | 1.86247i | −0.495738 | − | 0.868472i | \(-0.665102\pi\) |
−0.109414 | − | 0.993996i | \(-0.534898\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.66574 | − | 11.2820i | 0.347936 | − | 1.07084i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.84623 | − | 1.24972i | 0.361823 | − | 0.117564i | −0.122463 | − | 0.992473i | \(-0.539079\pi\) |
0.484286 | + | 0.874910i | \(0.339079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.0515 | − | 2.12767i | 1.31031 | − | 0.198406i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.987147 | − | 1.35869i | −0.0912617 | − | 0.125611i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.1885 | + | 10.3086i | −1.30066 | + | 0.944984i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.86976 | + | 6.44425i | 0.806341 | + | 0.585841i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.83765 | + | 2.22169i | 0.616530 | + | 0.200323i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.97396 | − | 11.0047i | 0.176556 | − | 0.984291i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9338 | + | 5.17719i | 1.41389 | + | 0.459401i | 0.913656 | − | 0.406488i | \(-0.133247\pi\) |
0.500236 | + | 0.865889i | \(0.333247\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.46415 | + | 5.42302i | 0.657181 | + | 0.477470i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.67583 | − | 1.94410i | 0.233788 | − | 0.169857i | −0.464723 | − | 0.885456i | \(-0.653846\pi\) |
0.698511 | + | 0.715599i | \(0.253846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.91486 | − | 8.14111i | −0.512884 | − | 0.705924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.21087 | − | 0.334767i | 0.190281 | − | 0.0288121i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.99642 | + | 0.648677i | −0.170566 | + | 0.0554202i | −0.393055 | − | 0.919515i | \(-0.628582\pi\) |
0.222489 | + | 0.974935i | \(0.428582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.10525 | − | 12.6347i | 0.348203 | − | 1.07166i | −0.611643 | − | 0.791134i | \(-0.709491\pi\) |
0.959847 | − | 0.280525i | \(-0.0905087\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.40556 | + | 4.32586i | 0.118369 | + | 0.364303i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.320323i | − | 0.0267868i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.55956 | + | 0.919357i | 0.461696 | + | 0.0763484i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.41747 | − | 6.08013i | 0.364347 | − | 0.501481i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.79913 | 0.229313 | 0.114657 | − | 0.993405i | \(-0.463423\pi\) | ||||
0.114657 | + | 0.993405i | \(0.463423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.71330 | −0.546320 | −0.273160 | − | 0.961969i | \(-0.588069\pi\) | ||||
−0.273160 | + | 0.961969i | \(0.588069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.70572 | − | 3.72410i | 0.218744 | − | 0.301076i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.85692 | + | 7.44401i | −0.309795 | + | 0.597917i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9495i | 1.11329i | 0.830750 | + | 0.556646i | \(0.187912\pi\) | ||||
−0.830750 | + | 0.556646i | \(0.812088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.91405 | + | 8.96852i | 0.231099 | + | 0.711250i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.48272 | + | 23.0294i | −0.589721 | + | 1.81497i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.44065 | + | 2.74253i | −0.661123 | + | 0.214812i | −0.620312 | − | 0.784355i | \(-0.712994\pi\) |
−0.0408107 | + | 0.999167i | \(0.512994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.378681 | + | 0.196204i | 0.0294803 | + | 0.0152744i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.4563 | − | 19.8973i | −1.11866 | − | 1.53970i | −0.808003 | − | 0.589178i | \(-0.799452\pi\) |
−0.310655 | − | 0.950523i | \(-0.600548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.23539 | + | 5.98336i | −0.633492 | + | 0.460259i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.13682 | + | 1.55249i | 0.163407 | + | 0.118722i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.1062 | + | 5.23322i | 1.22453 | + | 0.397874i | 0.848730 | − | 0.528826i | \(-0.177368\pi\) |
0.375801 | + | 0.926701i | \(0.377368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.2577 | + | 11.4057i | 1.15337 | + | 0.862189i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.79109 | + | 2.20656i | 0.510449 | + | 0.165855i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9328 | + | 8.66966i | 0.891897 | + | 0.648001i | 0.936372 | − | 0.351010i | \(-0.114162\pi\) |
−0.0444751 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.89013 | − | 6.45906i | 0.660798 | − | 0.480098i | −0.206134 | − | 0.978524i | \(-0.566088\pi\) |
0.866932 | + | 0.498426i | \(0.166088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.60166 | + | 7.71003i | 0.414087 | + | 0.569941i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.8835 | + | 18.6283i | −1.38834 | + | 1.36958i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.835018 | − | 0.271314i | 0.0610625 | − | 0.0198404i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.17733 | + | 3.62344i | −0.0856380 | + | 0.263567i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.42739 | − | 22.8591i | −0.537427 | − | 1.65403i | −0.738346 | − | 0.674422i | \(-0.764393\pi\) |
0.200919 | − | 0.979608i | \(-0.435607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50843i | 0.540469i | 0.962795 | + | 0.270234i | \(0.0871012\pi\) | ||||
−0.962795 | + | 0.270234i | \(0.912899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.562219 | + | 3.71300i | 0.0402613 | + | 0.265894i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.37799 | − | 10.1549i | 0.525660 | − | 0.723509i | −0.460801 | − | 0.887503i | \(-0.652438\pi\) |
0.986461 | + | 0.163995i | \(0.0524380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7618 | 1.40088 | 0.700440 | − | 0.713711i | \(-0.252987\pi\) | ||||
0.700440 | + | 0.713711i | \(0.252987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.05168 | −0.426852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.64349 | + | 7.76760i | −0.396095 | + | 0.545178i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.2901 | − | 11.4447i | −0.788532 | − | 0.799333i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.35567i | − | 0.441750i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.155675 | + | 0.479118i | 0.0107683 | + | 0.0331413i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.47579 | + | 10.6974i | −0.239283 | + | 0.736437i | 0.757241 | + | 0.653135i | \(0.226547\pi\) |
−0.996524 | + | 0.0833021i | \(0.973453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.6474 | − | 4.10941i | 0.866589 | − | 0.281572i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.24075 | − | 18.4451i | −0.630214 | − | 1.25795i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.39639 | − | 11.5566i | −0.569984 | − | 0.784516i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.21621 | − | 3.06326i | 0.284905 | − | 0.206996i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.25438 | + | 4.54407i | 0.420715 | + | 0.305668i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.91605 | − | 2.24716i | −0.463133 | − | 0.150481i | 0.0681508 | − | 0.997675i | \(-0.478290\pi\) |
−0.531284 | + | 0.847194i | \(0.678290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.73382 | − | 1.60963i | −0.315588 | − | 0.107309i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.00583 | − | 2.92617i | −0.597738 | − | 0.194217i | −0.00550660 | − | 0.999985i | \(-0.501753\pi\) |
−0.592231 | + | 0.805768i | \(0.701753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1755 | + | 12.4787i | 1.13499 | + | 0.824617i | 0.986413 | − | 0.164284i | \(-0.0525315\pi\) |
0.148575 | + | 0.988901i | \(0.452531\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.587893 | + | 0.427129i | −0.0386805 | + | 0.0281030i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.16700 | − | 5.73538i | −0.272989 | − | 0.375737i | 0.650407 | − | 0.759586i | \(-0.274598\pi\) |
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.65935 | − | 10.0344i | 0.108244 | − | 0.654575i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.95939 | − | 0.961563i | 0.192233 | − | 0.0624602i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.18395 | − | 19.0323i | 0.400007 | − | 1.23109i | −0.524987 | − | 0.851110i | \(-0.675930\pi\) |
0.924993 | − | 0.379983i | \(-0.124070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.43498 | + | 19.8048i | 0.414513 | + | 1.27574i | 0.912686 | + | 0.408662i | \(0.134005\pi\) |
−0.498172 | + | 0.867078i | \(0.665995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.0250 | + | 7.52731i | −0.959910 | + | 0.480902i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.60731 | + | 3.58865i | −0.165899 | + | 0.228340i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.67837 | 0.296480 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.7741 | −1.87932 | −0.939662 | − | 0.342104i | \(-0.888861\pi\) | ||||
−0.939662 | + | 0.342104i | \(0.888861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.712534 | − | 0.980719i | 0.0447966 | − | 0.0616573i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.20285 | + | 4.61050i | −0.576305 | + | 0.288721i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2853i | 1.32774i | 0.747849 | + | 0.663869i | \(0.231087\pi\) | ||||
−0.747849 | + | 0.663869i | \(0.768913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.9661 | − | 42.9834i | −0.867814 | − | 2.67086i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.778746 | − | 2.39673i | 0.0482032 | − | 0.148354i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.7951 | + | 6.75674i | −1.28228 | + | 0.416638i | −0.869383 | − | 0.494139i | \(-0.835483\pi\) |
−0.412898 | + | 0.910777i | \(0.635483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.44021 | − | 20.8037i | 0.211331 | − | 1.27796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.19506 | − | 11.2795i | −0.501530 | − | 0.690297i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.69018 | + | 2.68108i | −0.224995 | + | 0.163468i | −0.694572 | − | 0.719423i | \(-0.744406\pi\) |
0.469578 | + | 0.882891i | \(0.344406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4519 | + | 7.59377i | 0.634909 | + | 0.461288i | 0.858097 | − | 0.513487i | \(-0.171646\pi\) |
−0.223188 | + | 0.974775i | \(0.571646\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.08534 | − | 1.97725i | −0.368301 | − | 0.119668i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.550002 | − | 0.779085i | −0.0331663 | − | 0.0469806i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.40278 | − | 2.73023i | −0.504874 | − | 0.164044i | 0.0454957 | − | 0.998965i | \(-0.485513\pi\) |
−0.550370 | + | 0.834921i | \(0.685513\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.03331 | + | 2.20383i | 0.181599 | + | 0.131940i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0247151 | + | 0.0179566i | −0.00147438 | + | 0.00107120i | −0.588522 | − | 0.808481i | \(-0.700290\pi\) |
0.587048 | + | 0.809552i | \(0.300290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.82560 | + | 3.88910i | 0.167964 | + | 0.231183i | 0.884699 | − | 0.466163i | \(-0.154364\pi\) |
−0.716735 | + | 0.697346i | \(0.754364\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.64542 | − | 5.28043i | −0.156701 | − | 0.312786i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.0509 | − | 8.46444i | 1.53773 | − | 0.499640i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.29473 | + | 3.98478i | −0.0761607 | + | 0.234399i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.06889 | − | 6.36739i | −0.121281 | − | 0.373263i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9705i | 0.874587i | 0.899319 | + | 0.437294i | \(0.144063\pi\) | ||||
−0.899319 | + | 0.437294i | \(0.855937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.2132 | − | 11.3668i | −0.652856 | − | 0.661799i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.112110 | − | 0.154306i | 0.00650528 | − | 0.00895375i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.6739 | 0.617290 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.1510 | 2.02607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.18040 | + | 8.50659i | −0.355055 | + | 0.488691i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.19037 | − | 21.0698i | −0.182680 | − | 1.20645i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.47622i | 0.255472i | 0.991808 | + | 0.127736i | \(0.0407710\pi\) | ||||
−0.991808 | + | 0.127736i | \(0.959229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00636 | − | 12.3303i | −0.227914 | − | 0.701446i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0915043 | − | 0.281621i | 0.00518873 | − | 0.0159693i | −0.948429 | − | 0.316991i | \(-0.897328\pi\) |
0.953617 | + | 0.301021i | \(0.0973276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1214 | + | 6.53785i | −1.13733 | + | 0.369541i | −0.816357 | − | 0.577547i | \(-0.804010\pi\) |
−0.320973 | + | 0.947088i | \(0.604010\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.06484 | − | 5.98289i | 0.341715 | − | 0.337098i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.2334 | − | 20.9670i | −0.855594 | − | 1.17762i | −0.982602 | − | 0.185723i | \(-0.940537\pi\) |
0.127008 | − | 0.991902i | \(-0.459463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.388863 | − | 0.282526i | 0.0217722 | − | 0.0158184i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.80383 | − | 5.66981i | −0.435567 | − | 0.316458i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.5633 | − | 3.75714i | −0.643398 | − | 0.209053i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.70328 | − | 7.95014i | 0.149951 | − | 0.440995i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.4447 | + | 6.31798i | 1.07530 | + | 0.349385i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.0197 | + | 10.1859i | 0.772932 | + | 0.561568i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.48400 | − | 1.80473i | 0.136533 | − | 0.0991969i | −0.517423 | − | 0.855730i | \(-0.673108\pi\) |
0.653955 | + | 0.756533i | \(0.273108\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.97264 | + | 9.59702i | 0.382098 | + | 0.525913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0150 | + | 6.22526i | 0.656450 | + | 0.340122i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.8694 | + | 8.73038i | −1.46367 | + | 0.475574i | −0.929188 | − | 0.369607i | \(-0.879492\pi\) |
−0.534479 | + | 0.845182i | \(0.679492\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.24972 | + | 3.84623i | −0.0678753 | + | 0.208899i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.220987 | + | 0.680128i | 0.0119671 | + | 0.0368310i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.96383i | − | 0.106037i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.53797 | + | 12.6186i | −0.351993 | + | 0.679360i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.9869 | − | 24.7568i | 0.965586 | − | 1.32901i | 0.0213401 | − | 0.999772i | \(-0.493207\pi\) |
0.944245 | − | 0.329242i | \(-0.106793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1178 | 0.862764 | 0.431382 | − | 0.902169i | \(-0.358026\pi\) | ||||
0.431382 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67943 | 0.0896416 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.253341 | − | 0.348695i | 0.0134840 | − | 0.0185591i | −0.802222 | − | 0.597026i | \(-0.796349\pi\) |
0.815706 | + | 0.578467i | \(0.196349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.3375 | − | 4.85140i | −1.55707 | − | 0.257486i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 17.5380i | − | 0.928207i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.70871 | − | 17.5696i | −0.301294 | − | 0.927288i | −0.981034 | − | 0.193835i | \(-0.937907\pi\) |
0.679740 | − | 0.733453i | \(-0.262093\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.71555 | + | 11.4353i | −0.195555 | + | 0.601857i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.4270 | + | 3.38795i | −0.547277 | + | 0.177821i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.5220 | + | 1.74465i | −0.603088 | + | 0.0913189i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.03990 | − | 8.31320i | −0.315280 | − | 0.433946i | 0.621739 | − | 0.783225i | \(-0.286427\pi\) |
−0.937019 | + | 0.349279i | \(0.886427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.81645 | + | 4.22590i | −0.302792 | + | 0.219992i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.0662 | + | 21.1178i | 1.50904 | + | 1.09638i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9266 | − | 4.52503i | −0.721092 | − | 0.234297i | −0.0745954 | − | 0.997214i | \(-0.523767\pi\) |
−0.646497 | + | 0.762917i | \(0.723767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.74273 | + | 8.06537i | 0.399833 | + | 0.416494i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.02516 | + | 1.30785i | 0.207306 | + | 0.0673579i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.66061 | − | 6.29230i | −0.444866 | − | 0.323214i | 0.342700 | − | 0.939445i | \(-0.388659\pi\) |
−0.787565 | + | 0.616231i | \(0.788659\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5541 | + | 9.84760i | −0.694396 | + | 0.504508i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.4690 | + | 21.2912i | 0.790428 | + | 1.08793i | 0.994055 | + | 0.108882i | \(0.0347270\pi\) |
−0.203627 | + | 0.979049i | \(0.565273\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.60658 | − | 0.243267i | 0.0818791 | − | 0.0123980i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.77463 | + | 2.85105i | −0.446040 | + | 0.144927i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0901650 | + | 0.277499i | −0.00457155 | + | 0.0140698i | −0.953316 | − | 0.301974i | \(-0.902355\pi\) |
0.948745 | + | 0.316043i | \(0.102355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.04082 | + | 27.8248i | 0.457214 | + | 1.40716i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.30750i | 0.166841i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.86471 | − | 1.13518i | −0.345401 | − | 0.0571173i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.18504 | − | 1.63106i | 0.0594753 | − | 0.0818608i | −0.778243 | − | 0.627963i | \(-0.783889\pi\) |
0.837719 | + | 0.546102i | \(0.183889\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0630 | 0.503778 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.88760 | 0.493763 | 0.246882 | − | 0.969046i | \(-0.420594\pi\) | ||||
0.246882 | + | 0.969046i | \(0.420594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.70118 | + | 5.09424i | −0.184369 | + | 0.253762i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.02868 | + | 1.98540i | −0.0511157 | + | 0.0986553i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.26258i | 0.112152i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6440 | + | 35.8367i | 0.575761 | + | 1.77201i | 0.633573 | + | 0.773683i | \(0.281587\pi\) |
−0.0578124 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.648677 | − | 1.99642i | 0.0319969 | − | 0.0984762i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.8735 | − | 8.40680i | 1.27315 | − | 0.413672i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.28843 | − | 4.81256i | −0.455951 | − | 0.236239i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.80866 | + | 10.7477i | 0.382392 | + | 0.526317i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6641 | + | 9.20102i | −0.618682 | + | 0.449499i | −0.852461 | − | 0.522791i | \(-0.824891\pi\) |
0.233779 | + | 0.972290i | \(0.424891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7531 | − | 8.53916i | −0.572813 | − | 0.416173i | 0.263313 | − | 0.964711i | \(-0.415185\pi\) |
−0.836126 | + | 0.548537i | \(0.815185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.32586 | − | 1.40556i | −0.210331 | − | 0.0683406i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.0141 | + | 0.313121i | 1.11635 | + | 0.0151886i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.5318 | + | 11.2201i | 1.67111 | + | 0.542978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.259147 | + | 0.188281i | 0.0125117 | + | 0.00909030i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2150 | − | 7.42161i | 0.492038 | − | 0.357486i | −0.313930 | − | 0.949446i | \(-0.601646\pi\) |
0.805967 | + | 0.591960i | \(0.201646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.05145 | − | 2.82358i | −0.0985864 | − | 0.135693i | 0.756874 | − | 0.653561i | \(-0.226726\pi\) |
−0.855460 | + | 0.517868i | \(0.826726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.01160 | + | 3.95739i | −0.192342 | + | 0.189742i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.9654 | + | 5.18746i | −0.763727 | + | 0.248150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.04528 | − | 18.6055i | 0.288526 | − | 0.887991i | −0.696794 | − | 0.717271i | \(-0.745391\pi\) |
0.985320 | − | 0.170719i | \(-0.0546092\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.32240 | + | 7.14762i | 0.110591 | + | 0.340363i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.77485i | 0.131837i | 0.997825 | + | 0.0659185i | \(0.0209977\pi\) | ||||
−0.997825 | + | 0.0659185i | \(0.979002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.66741 | + | 30.8245i | 0.221257 | + | 1.46122i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.64529 | + | 2.26454i | −0.0778194 | + | 0.107109i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.4261 | 1.81344 | 0.906721 | − | 0.421732i | \(-0.138578\pi\) | ||||
0.906721 | + | 0.421732i | \(0.138578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37128 | −0.0645710 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.94598 | − | 5.43117i | 0.185398 | − | 0.255179i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.0479 | + | 10.1855i | 0.471051 | + | 0.477504i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.0296i | − | 1.68539i | −0.538389 | − | 0.842696i | \(-0.680967\pi\) | ||
0.538389 | − | 0.842696i | \(-0.319033\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.42248 | + | 4.37794i | 0.0663957 | + | 0.204345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.265011 | − | 0.815619i | 0.0123428 | − | 0.0379871i | −0.944695 | − | 0.327949i | \(-0.893643\pi\) |
0.957038 | + | 0.289962i | \(0.0936426\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.89742 | − | 3.21587i | 0.459972 | − | 0.149454i | −0.0698596 | − | 0.997557i | \(-0.522255\pi\) |
0.529832 | + | 0.848103i | \(0.322255\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.75529 | − | 7.49579i | −0.174147 | − | 0.347609i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0910 | + | 16.6419i | 0.559506 | + | 0.770094i | 0.991264 | − | 0.131895i | \(-0.0421063\pi\) |
−0.431757 | + | 0.901990i | \(0.642106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.6530 | + | 13.5522i | −0.861316 | + | 0.625782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2854 | − | 8.19931i | −0.520003 | − | 0.377804i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.67361 | − | 0.543789i | −0.0769527 | − | 0.0250034i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.179663 | + | 13.2051i | −0.00824351 | + | 0.605890i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.96852 | − | 2.91405i | −0.410640 | − | 0.133425i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.8384 | + | 18.7727i | 1.18059 | + | 0.857747i | 0.992238 | − | 0.124355i | \(-0.0396861\pi\) |
0.188350 | + | 0.982102i | \(0.439686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1176 | + | 11.7101i | −0.734898 | + | 0.533934i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.2330 | − | 19.5900i | −0.647623 | − | 0.891376i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.44245 | + | 14.7701i | −0.110906 | + | 0.670674i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.9140 | + | 4.84587i | −0.675820 | + | 0.219587i | −0.626764 | − | 0.779209i | \(-0.715621\pi\) |
−0.0490554 | + | 0.998796i | \(0.515621\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.74253 | − | 8.44065i | 0.124022 | − | 0.381699i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.09354 | + | 15.6763i | 0.229868 | + | 0.707462i | 0.997761 | + | 0.0668834i | \(0.0213055\pi\) |
−0.767892 | + | 0.640579i | \(0.778694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6005i | 0.522461i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.381315 | + | 0.191034i | −0.0171388 | + | 0.00858633i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.7804 | − | 40.9892i | 1.33583 | − | 1.83862i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4339 | −0.556618 | −0.278309 | − | 0.960492i | \(-0.589774\pi\) | ||||
−0.278309 | + | 0.960492i | \(0.589774\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5944 | 1.09880 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.54703 | + | 3.50569i | −0.113567 | + | 0.156311i | −0.862016 | − | 0.506881i | \(-0.830799\pi\) |
0.748450 | + | 0.663191i | \(0.230799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.0211 | − | 10.5313i | 0.935428 | − | 0.468637i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 10.1795i | − | 0.452088i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.32995 | − | 13.3262i | −0.191922 | − | 0.590674i | −0.999999 | − | 0.00159734i | \(-0.999492\pi\) |
0.808077 | − | 0.589077i | \(-0.200508\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.13568 | − | 18.8837i | 0.271426 | − | 0.835364i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.51198 | + | 0.816193i | −0.110907 | + | 0.0360358i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.72975 | + | 28.6019i | −0.208418 | + | 1.26035i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.509930 | − | 0.701859i | −0.0224267 | − | 0.0308677i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.7007 | + | 9.95417i | −0.601396 | + | 0.436940i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.56002 | − | 1.13342i | −0.0683458 | − | 0.0496561i | 0.553088 | − | 0.833123i | \(-0.313449\pi\) |
−0.621434 | + | 0.783467i | \(0.713449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.86306 | + | 0.605344i | 0.0814659 | + | 0.0264699i | 0.349466 | − | 0.936949i | \(-0.386363\pi\) |
−0.268001 | + | 0.963419i | \(0.586363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −18.1956 | + | 5.63962i | −0.794122 | + | 0.246133i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.4145 | − | 5.33341i | −0.715029 | − | 0.232327i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0725 | + | 10.2243i | 0.611849 | + | 0.444534i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.77684 | + | 4.19712i | −0.250694 | + | 0.182140i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.09712 | − | 9.76835i | −0.307410 | − | 0.423114i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.66128 | + | 19.2845i | 0.417693 | + | 0.833742i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.0278 | + | 4.55791i | −0.605345 | + | 0.196688i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.442958 | + | 1.36329i | −0.0190796 | + | 0.0587209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6961 | − | 32.9191i | −0.459860 | − | 1.41530i | −0.865333 | − | 0.501197i | \(-0.832893\pi\) |
0.405473 | − | 0.914107i | \(-0.367107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9888i | 0.471575i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.1064 | − | 32.5462i | −1.37529 | − | 1.39413i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.37482 | − | 12.9033i | 0.400838 | − | 0.551706i | −0.560116 | − | 0.828414i | \(-0.689243\pi\) |
0.960954 | + | 0.276708i | \(0.0892434\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.53012 | −0.406735 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65617 | −0.283562 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.96834 | − | 9.59110i | 0.296324 | − | 0.407855i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.97119 | − | 26.2266i | −0.168568 | − | 1.11326i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0343i | 1.82342i | 0.410831 | + | 0.911711i | \(0.365239\pi\) | ||||
−0.410831 | + | 0.911711i | \(0.634761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.78815 | − | 14.7364i | −0.202517 | − | 0.623284i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.271314 | + | 0.835018i | −0.0114549 | + | 0.0352545i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.9331 | − | 5.82682i | 0.755791 | − | 0.245571i | 0.0943197 | − | 0.995542i | \(-0.469932\pi\) |
0.661471 | + | 0.749971i | \(0.269932\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.43774 | − | 6.35075i | 0.270838 | − | 0.267178i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.23941 | − | 3.08229i | −0.0940465 | − | 0.129444i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.7119 | + | 14.3215i | −0.826364 | + | 0.600389i | −0.918528 | − | 0.395355i | \(-0.870621\pi\) |
0.0921644 | + | 0.995744i | \(0.470621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.4096 | − | 9.01612i | −0.519327 | − | 0.377313i | 0.297023 | − | 0.954870i | \(-0.404006\pi\) |
−0.816350 | + | 0.577557i | \(0.804006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.8591 | + | 7.42739i | 0.954955 | + | 0.310284i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.9610 | − | 18.3274i | 1.08265 | − | 0.764304i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6382 | + | 4.43133i | 0.567767 | + | 0.184479i | 0.578813 | − | 0.815460i | \(-0.303516\pi\) |
−0.0110462 | + | 0.999939i | \(0.503516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.07445 | − | 4.41335i | −0.252446 | − | 0.183412i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4201 | − | 10.4768i | 0.598245 | − | 0.434651i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05720 | − | 1.45512i | −0.0437849 | − | 0.0602648i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.33435 | − | 1.72760i | −0.137858 | − | 0.0714277i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.1788 | − | 3.30729i | 0.420123 | − | 0.136506i | −0.0913234 | − | 0.995821i | \(-0.529110\pi\) |
0.511447 | + | 0.859315i | \(0.329110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.06021 | − | 9.41837i | 0.126094 | − | 0.388077i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.87884 | + | 11.9378i | 0.159554 | + | 0.491057i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 23.5756i | − | 0.968135i | −0.875031 | − | 0.484067i | \(-0.839159\pi\) | ||
0.875031 | − | 0.484067i | \(-0.160841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.0410 | + | 34.8199i | −0.739609 | + | 1.42748i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.6157 | + | 15.9877i | −0.475400 | + | 0.654332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8055 | −0.564078 | −0.282039 | − | 0.959403i | \(-0.591011\pi\) | ||||
−0.282039 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.61536 | 0.392219 | 0.196109 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196109 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.55709 | − | 4.89591i | 0.144856 | − | 0.199377i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.1869 | + | 3.99967i | 0.983338 | + | 0.162610i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.7884i | 0.965539i | 0.875747 | + | 0.482770i | \(0.160369\pi\) | ||||
−0.875747 | + | 0.482770i | \(0.839631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.96696 | − | 9.13136i | −0.120227 | − | 0.370021i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.36054 | − | 7.26500i | 0.0954973 | − | 0.293911i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2850 | + | 4.96640i | −0.617356 | + | 0.200591i | −0.600966 | − | 0.799275i | \(-0.705217\pi\) |
−0.0163900 | + | 0.999866i | \(0.505217\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.8951 | − | 2.40682i | 0.640952 | − | 0.0970522i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.49341 | + | 7.56104i | 0.221157 | + | 0.304396i | 0.905150 | − | 0.425092i | \(-0.139758\pi\) |
−0.683994 | + | 0.729488i | \(0.739758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9480 | + | 10.8604i | −0.600813 | + | 0.436516i | −0.846167 | − | 0.532917i | \(-0.821096\pi\) |
0.245354 | + | 0.969433i | \(0.421096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.14185 | + | 3.73577i | 0.206335 | + | 0.149911i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −50.5191 | − | 16.4146i | −2.02400 | − | 0.657639i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.07570 | − | 23.9778i | −0.283028 | − | 0.959112i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.479118 | − | 0.155675i | −0.0191341 | − | 0.00621706i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.1774 | − | 32.0968i | −1.76147 | − | 1.27978i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2030 | + | 22.6703i | −1.24217 | + | 0.902491i | −0.997741 | − | 0.0671762i | \(-0.978601\pi\) |
−0.244431 | + | 0.969667i | \(0.578601\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.61134 | − | 9.09973i | −0.262777 | − | 0.361682i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.0403 | − | 5.60860i | 1.46990 | − | 0.222570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0040 | + | 3.90032i | −0.475614 | + | 0.154536i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.10941 | + | 12.6474i | −0.162566 | + | 0.500325i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.96965 | − | 12.2173i | −0.156792 | − | 0.482556i | 0.841546 | − | 0.540185i | \(-0.181646\pi\) |
−0.998338 | + | 0.0576293i | \(0.981646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1030i | 0.792784i | 0.918081 | + | 0.396392i | \(0.129738\pi\) | ||||
−0.918081 | + | 0.396392i | \(0.870262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.3540 | + | 3.36584i | 0.801437 | + | 0.132530i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.0350 | + | 31.7050i | −0.905600 | + | 1.24645i | 0.0630466 | + | 0.998011i | \(0.479918\pi\) |
−0.968647 | + | 0.248441i | \(0.920082\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.36194 | −0.0534609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2848 | 0.559865 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.2762 | − | 21.0259i | 0.597804 | − | 0.822806i | −0.397701 | − | 0.917515i | \(-0.630192\pi\) |
0.995505 | + | 0.0947087i | \(0.0301920\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.40237 | − | 6.56671i | 0.132942 | − | 0.256583i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.21152i | 0.203321i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.98499 | + | 6.10917i | 0.0773242 | + | 0.237980i | 0.982246 | − | 0.187599i | \(-0.0600706\pi\) |
−0.904921 | + | 0.425579i | \(0.860071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.67091 | − | 20.5310i | 0.259468 | − | 0.798562i | −0.733448 | − | 0.679746i | \(-0.762090\pi\) |
0.992916 | − | 0.118816i | \(-0.0379098\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.35247 | + | 2.38896i | −0.285546 | + | 0.0927796i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.9790 | − | 10.3516i | −0.774753 | − | 0.401418i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.41443 | + | 12.9578i | 0.364528 | + | 0.501730i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.88314 | − | 4.27435i | 0.227455 | − | 0.165256i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.47055 | − | 1.06842i | −0.0567701 | − | 0.0412459i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.64965 | + | 1.83568i | 0.217778 | + | 0.0707604i | 0.415874 | − | 0.909422i | \(-0.363476\pi\) |
−0.198096 | + | 0.980183i | \(0.563476\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.08469 | − | 2.88362i | 0.157220 | − | 0.110991i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.3587 | − | 11.4888i | −1.35895 | − | 0.441549i | −0.463256 | − | 0.886225i | \(-0.653319\pi\) |
−0.895691 | + | 0.444676i | \(0.853319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.6361 | − | 14.9930i | −0.791942 | − | 0.575380i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.66082 | − | 5.56591i | 0.293563 | − | 0.213286i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.5106 | + | 36.4886i | 1.01440 | + | 1.39620i | 0.916058 | + | 0.401046i | \(0.131353\pi\) |
0.0983404 | + | 0.995153i | \(0.468647\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.34157 | + | 3.29641i | −0.127675 | + | 0.125949i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.1910 | + | 6.56045i | −0.770334 | + | 0.250297i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.89395 | − | 15.0620i | 0.186445 | − | 0.573818i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.82903 | − | 27.1730i | −0.335872 | − | 1.03371i | −0.966291 | − | 0.257453i | \(-0.917117\pi\) |
0.630419 | − | 0.776255i | \(-0.282883\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.726676i | − | 0.0276041i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.44734 | − | 29.3711i | −0.168697 | − | 1.11411i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.4528 | − | 26.7745i | 0.736829 | − | 1.01416i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.08932 | 0.268143 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.2636 | −1.67181 | −0.835907 | − | 0.548871i | \(-0.815058\pi\) | ||||
−0.835907 | + | 0.548871i | \(0.815058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.4165 | − | 25.3482i | 0.694593 | − | 0.956025i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.14269 | + | 7.24054i | 0.269009 | + | 0.272694i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.0602i | 1.50662i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.25711 | − | 16.1797i | −0.197435 | − | 0.607643i | −0.999940 | − | 0.0109965i | \(-0.996500\pi\) |
0.802505 | − | 0.596646i | \(-0.203500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.961563 | + | 2.95939i | −0.0360614 | + | 0.110986i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.6635 | + | 7.36381i | −0.848754 | + | 0.275777i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.320828 | − | 0.640393i | −0.0119983 | − | 0.0239494i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.7626 | + | 16.1898i | 0.439282 | + | 0.604619i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.71076 | − | 4.87565i | 0.250269 | − | 0.181831i | −0.455577 | − | 0.890196i | \(-0.650567\pi\) |
0.705846 | + | 0.708365i | \(0.250567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.9614 | − | 29.0336i | −1.48824 | − | 1.08127i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.8048 | − | 6.43498i | −0.736549 | − | 0.239319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.0355 | − | 3.73034i | 0.446989 | − | 0.138541i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.09791 | + | 2.30625i | 0.263247 | + | 0.0855342i | 0.437667 | − | 0.899137i | \(-0.355805\pi\) |
−0.174420 | + | 0.984671i | \(0.555805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.3593 | − | 24.9635i | 1.27082 | − | 0.923308i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.06525 | + | 9.72449i | 0.260961 | + | 0.359182i | 0.919312 | − | 0.393529i | \(-0.128746\pi\) |
−0.658351 | + | 0.752711i | \(0.728746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.74174 | − | 16.5799i | 0.101130 | − | 0.611559i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.09776 | − | 0.356684i | 0.0404365 | − | 0.0131386i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.82848 | + | 24.0936i | −0.287975 | + | 0.886297i | 0.697516 | + | 0.716570i | \(0.254289\pi\) |
−0.985491 | + | 0.169728i | \(0.945711\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.37074 | − | 4.21871i | −0.0503555 | − | 0.154978i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.0959i | − | 0.773935i | −0.922093 | − | 0.386968i | \(-0.873523\pi\) | ||
0.922093 | − | 0.386968i | \(-0.126477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.59605 | − | 2.80354i | 0.205023 | − | 0.102714i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.74988 | + | 3.78488i | −0.100613 | + | 0.138482i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.7507 | −1.34284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3897 | −1.25490 | −0.627449 | − | 0.778658i | \(-0.715901\pi\) | ||||
−0.627449 | + | 0.778658i | \(0.715901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.5008 | − | 24.0877i | 0.637764 | − | 0.877806i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.4213 | + | 6.72389i | −0.488451 | + | 0.244707i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33.9762i | − | 1.23488i | −0.786616 | − | 0.617442i | \(-0.788169\pi\) | ||
0.786616 | − | 0.617442i | \(-0.211831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.374601 | + | 1.15290i | 0.0135972 | + | 0.0418478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.13686 | + | 12.7319i | −0.149961 | + | 0.461533i | −0.997616 | − | 0.0690159i | \(-0.978014\pi\) |
0.847654 | + | 0.530549i | \(0.178014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 74.0828 | − | 24.0710i | 2.68198 | − | 0.871427i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.67932 | − | 10.1552i | 0.0607161 | − | 0.367164i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.04879 | − | 9.70183i | −0.254517 | − | 0.350313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.80948 | + | 3.49429i | −0.173434 | + | 0.126007i | −0.671116 | − | 0.741352i | \(-0.734185\pi\) |
0.497682 | + | 0.867360i | \(0.334185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.2201 | − | 12.5112i | −0.620168 | − | 0.450579i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.4278 | + | 10.5364i | 1.16635 | + | 0.378969i | 0.827278 | − | 0.561793i | \(-0.189888\pi\) |
0.339068 | + | 0.940762i | \(0.389888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.255039 | + | 18.7451i | −0.00916127 | + | 0.673345i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 42.9834 | + | 13.9661i | 1.54202 | + | 0.501032i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.3628 | + | 11.1617i | 0.550428 | + | 0.399909i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.05201 | + | 1.49087i | −0.0734267 | + | 0.0533476i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.48126 | + | 2.03878i | 0.0529360 | + | 0.0728602i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.9715 | + | 27.8880i | 0.498665 | + | 0.995365i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.87644 | + | 0.609693i | −0.0668879 | + | 0.0217332i | −0.342270 | − | 0.939602i | \(-0.611196\pi\) |
0.275382 | + | 0.961335i | \(0.411196\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.75674 | − | 20.7951i | 0.240546 | − | 0.740325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.76132 | + | 14.6538i | 0.169293 | + | 0.521030i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.0052i | − | 0.568361i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.8085 | + | 15.0113i | 0.525202 | + | 0.532397i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3698 | + | 23.9075i | −0.615269 | + | 0.846845i | −0.996998 | − | 0.0774291i | \(-0.975329\pi\) |
0.381729 | + | 0.924274i | \(0.375329\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9378 | 0.740725 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9423 | 0.492626 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.584264 | + | 0.804170i | −0.0206182 | + | 0.0283785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.10624 | + | 53.5352i | 0.285707 | + | 1.88687i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.56132i | − | 0.160566i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.45516 | − | 7.55621i | −0.0863189 | − | 0.265662i | 0.898575 | − | 0.438819i | \(-0.144603\pi\) |
−0.984894 | + | 0.173157i | \(0.944603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.71747 | − | 17.5966i | 0.200768 | − | 0.617899i | −0.799093 | − | 0.601207i | \(-0.794687\pi\) |
0.999861 | − | 0.0166920i | \(-0.00531347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2870 | + | 3.99228i | −0.430923 | + | 0.140015i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.1278 | + | 13.9369i | −0.494874 | + | 0.488187i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.3236 | + | 19.7147i | 0.501119 | + | 0.689731i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.17650 | − | 3.76094i | 0.180881 | − | 0.131418i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4784 | + | 9.06610i | 0.435500 | + | 0.316409i | 0.783844 | − | 0.620958i | \(-0.213256\pi\) |
−0.348345 | + | 0.937367i | \(0.613256\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.5494 | + | 12.8504i | 1.37860 | + | 0.447936i | 0.902210 | − | 0.431296i | \(-0.141944\pi\) |
0.476394 | + | 0.879232i | \(0.341944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.953576 | + | 0.0129740i | 0.0331992 | + | 0.000451696i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.1783 | − | 10.7803i | −1.15372 | − | 0.374867i | −0.331177 | − | 0.943569i | \(-0.607446\pi\) |
−0.822544 | + | 0.568702i | \(0.807446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.7079 | + | 27.3964i | 1.30965 | + | 0.951516i | 1.00000 | 0.000664954i | \(0.000211661\pi\) | |
0.309649 | + | 0.950851i | \(0.399788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.14783 | − | 5.19320i | 0.247956 | − | 0.180150i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.3347 | − | 27.9883i | −0.704555 | − | 0.969737i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.8298 | − | 25.2999i | −1.68982 | − | 0.875538i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.56587 | + | 1.15862i | −0.123254 | + | 0.0400478i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.1009 | + | 40.3203i | −0.452292 | + | 1.39201i | 0.421992 | + | 0.906599i | \(0.361331\pi\) |
−0.874285 | + | 0.485414i | \(0.838669\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.99899 | − | 21.5407i | −0.241345 | − | 0.742782i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.0305495i | − | 0.00105218i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.4715 | + | 20.2104i | −0.360230 | + | 0.695258i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.5521 | + | 33.7930i | −0.843619 | + | 1.16114i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.80719 | −0.164982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −75.3946 | −2.58449 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.20116 | − | 3.02964i | 0.0753663 | − | 0.103733i | −0.769670 | − | 0.638442i | \(-0.779579\pi\) |
0.845036 | + | 0.534710i | \(0.179579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.82690 | + | 0.963566i | 0.199276 | + | 0.0329532i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9648i | 1.36517i | 0.730806 | + | 0.682586i | \(0.239145\pi\) | ||||
−0.730806 | + | 0.682586i | \(0.760855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3383 | + | 53.3617i | 0.591574 | + | 1.82068i | 0.571091 | + | 0.820887i | \(0.306520\pi\) |
0.0204824 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.46444 | + | 26.0509i | −0.288467 | + | 0.887811i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.6827 | − | 5.74547i | 0.601927 | − | 0.195578i | 0.00782756 | − | 0.999969i | \(-0.497508\pi\) |
0.594100 | + | 0.804391i | \(0.297508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.4411 | − | 5.66929i | 1.27304 | − | 0.192762i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.46273 | − | 3.38965i | −0.0836386 | − | 0.115119i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.480152 | + | 0.348851i | −0.0162880 | + | 0.0118339i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.22236 | + | 5.97389i | 0.278604 | + | 0.202418i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.36739 | + | 2.06889i | 0.215504 | + | 0.0700214i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.9270 | + | 7.52062i | 1.41739 | + | 0.254243i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.3467 | + | 3.36186i | 0.349385 | + | 0.113522i | 0.478452 | − | 0.878114i | \(-0.341198\pi\) |
−0.129067 | + | 0.991636i | \(0.541198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.1114 | − | 8.79945i | −0.408508 | − | 0.296798i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.5016 | + | 19.9811i | −0.926552 | + | 0.673180i | −0.945146 | − | 0.326647i | \(-0.894081\pi\) |
0.0185939 | + | 0.999827i | \(0.494081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.96658 | + | 12.3414i | 0.301749 | + | 0.415322i | 0.932786 | − | 0.360431i | \(-0.117370\pi\) |
−0.631037 | + | 0.775753i | \(0.717370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.7869 | − | 2.39043i | 0.530669 | − | 0.0803533i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.1095 | − | 8.80840i | 0.910247 | − | 0.295757i | 0.183787 | − | 0.982966i | \(-0.441164\pi\) |
0.726460 | + | 0.687209i | \(0.241164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.7247 | + | 60.7063i | −0.661544 | + | 2.03602i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0589397 | + | 0.181398i | 0.00197455 | + | 0.00607705i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0137i | 0.402024i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.5394 | + | 5.38089i | 1.08767 | + | 0.179863i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.27398 | + | 8.63540i | −0.209482 | + | 0.288327i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.44871 | −0.315132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4089 | 1.44616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.6612 | + | 28.4378i | −0.687563 | + | 0.946350i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.3040 | − | 21.8172i | 0.375757 | − | 0.725227i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.1919i | − | 0.736868i | −0.929654 | − | 0.368434i | \(-0.879894\pi\) | ||
0.929654 | − | 0.368434i | \(-0.120106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.24923 | − | 10.0001i | −0.107770 | − | 0.331682i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5476 | − | 38.6174i | 0.415719 | − | 1.27945i | −0.495887 | − | 0.868387i | \(-0.665157\pi\) |
0.911606 | − | 0.411064i | \(-0.134843\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.848645 | + | 0.275742i | −0.0280861 | + | 0.00912572i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.9211 | + | 9.80347i | 0.625512 | + | 0.324093i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.40686 | + | 10.1947i | 0.244596 | + | 0.336658i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1543 | − | 7.37751i | 0.334958 | − | 0.243361i | −0.407573 | − | 0.913173i | \(-0.633625\pi\) |
0.742532 | + | 0.669811i | \(0.233625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.62134 | − | 2.63106i | −0.119327 | − | 0.0866963i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.2406 | − | 6.90148i | −0.699141 | − | 0.227165i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.0944 | + | 56.1553i | −0.627820 | + | 1.84637i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.3303 | + | 4.00636i | 0.404980 | + | 0.131586i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.6390 | − | 33.1587i | −1.49737 | − | 1.08790i | −0.971415 | − | 0.237388i | \(-0.923709\pi\) |
−0.525953 | − | 0.850513i | \(-0.676291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.0592 | − | 11.6677i | 0.526319 | − | 0.382393i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.174051 | + | 0.239561i | 0.00569819 | + | 0.00784288i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.39763 | − | 1.37875i | 0.0457075 | − | 0.0450899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.0630 | − | 13.0173i | 1.30880 | − | 0.425255i | 0.430166 | − | 0.902750i | \(-0.358455\pi\) |
0.878635 | + | 0.477494i | \(0.158455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.53785 | − | 20.1214i | 0.213355 | − | 0.656638i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.51260 | − | 29.2768i | −0.310102 | − | 0.954395i | −0.977724 | − | 0.209895i | \(-0.932688\pi\) |
0.667622 | − | 0.744500i | \(-0.267312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45.6943i | − | 1.48801i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.27543 | + | 8.42321i | 0.0414898 | + | 0.274007i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.435973 | − | 0.600065i | 0.0141672 | − | 0.0194995i | −0.801875 | − | 0.597492i | \(-0.796164\pi\) |
0.816042 | + | 0.577993i | \(0.196164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.75241 | −0.284115 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9166 | 0.840405 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.1037 | + | 31.7995i | −0.748401 | + | 1.03009i | 0.249690 | + | 0.968326i | \(0.419671\pi\) |
−0.998091 | + | 0.0617601i | \(0.980329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.7441 | − | 38.2611i | −1.22137 | − | 1.23810i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.480661i | 0.0155376i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.47140 | − | 7.60620i | −0.0798058 | − | 0.245617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.23543 | + | 16.1130i | −0.168885 | + | 0.519774i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.17395 | − | 2.98080i | 0.295626 | − | 0.0960548i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.52028 | + | 15.0109i | 0.242086 | + | 0.483219i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.6718 | − | 39.4633i | −0.922022 | − | 1.26905i | −0.962891 | − | 0.269890i | \(-0.913013\pi\) |
0.0408691 | − | 0.999165i | \(-0.486987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.83631 | − | 7.14650i | 0.315988 | − | 0.229579i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.5659 | + | 36.0118i | 1.59065 | + | 1.15567i | 0.903011 | + | 0.429616i | \(0.141351\pi\) |
0.687635 | + | 0.726056i | \(0.258649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.1370 | + | 15.6407i | 1.54320 | + | 0.501417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.84286 | + | 6.85997i | 0.155096 | + | 0.219695i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6181 | + | 3.45004i | 0.339704 | + | 0.110377i | 0.473901 | − | 0.880578i | \(-0.342845\pi\) |
−0.134197 | + | 0.990955i | \(0.542845\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.15138 | + | 1.56307i | 0.0687583 | + | 0.0499559i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.5407 | + | 12.0175i | −0.528103 | + | 0.383690i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.2257 | − | 25.0855i | −0.581310 | − | 0.800104i | 0.412528 | − | 0.910945i | \(-0.364646\pi\) |
−0.993838 | + | 0.110840i | \(0.964646\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.57920 | − | 27.6915i | 0.145906 | − | 0.882323i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.4812 | + | 5.35506i | −0.524602 | + | 0.170453i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.1203 | − | 55.7687i | 0.576194 | − | 1.77334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.13378 | + | 28.1109i | 0.290144 | + | 0.892972i | 0.984809 | + | 0.173639i | \(0.0555526\pi\) |
−0.694665 | + | 0.719333i | \(0.744447\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.07039i | 0.0974358i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.5081 | − | 19.7930i | 1.25249 | − | 0.627481i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.7701 | + | 43.7278i | −1.00617 | + | 1.38487i | −0.0847083 | + | 0.996406i | \(0.526996\pi\) |
−0.921462 | + | 0.388469i | \(0.873004\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8626 | −0.375315 |
(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 | 300.2.o.a.229.3 | yes | 24 | |
3.2 | odd | 2 | 900.2.w.c.829.1 | 24 | |||
5.2 | odd | 4 | 1500.2.m.d.601.2 | 24 | |||
5.3 | odd | 4 | 1500.2.m.c.601.5 | 24 | |||
5.4 | even | 2 | 1500.2.o.c.649.4 | 24 | |||
25.6 | even | 5 | 1500.2.o.c.349.4 | 24 | |||
25.8 | odd | 20 | 1500.2.m.c.901.5 | 24 | |||
25.9 | even | 10 | 7500.2.d.g.1249.15 | 24 | |||
25.12 | odd | 20 | 7500.2.a.m.1.3 | 12 | |||
25.13 | odd | 20 | 7500.2.a.n.1.10 | 12 | |||
25.16 | even | 5 | 7500.2.d.g.1249.10 | 24 | |||
25.17 | odd | 20 | 1500.2.m.d.901.2 | 24 | |||
25.19 | even | 10 | inner | 300.2.o.a.169.3 | ✓ | 24 | |
75.44 | odd | 10 | 900.2.w.c.469.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.3 | ✓ | 24 | 25.19 | even | 10 | inner | |
300.2.o.a.229.3 | yes | 24 | 1.1 | even | 1 | trivial | |
900.2.w.c.469.1 | 24 | 75.44 | odd | 10 | |||
900.2.w.c.829.1 | 24 | 3.2 | odd | 2 | |||
1500.2.m.c.601.5 | 24 | 5.3 | odd | 4 | |||
1500.2.m.c.901.5 | 24 | 25.8 | odd | 20 | |||
1500.2.m.d.601.2 | 24 | 5.2 | odd | 4 | |||
1500.2.m.d.901.2 | 24 | 25.17 | odd | 20 | |||
1500.2.o.c.349.4 | 24 | 25.6 | even | 5 | |||
1500.2.o.c.649.4 | 24 | 5.4 | even | 2 | |||
7500.2.a.m.1.3 | 12 | 25.12 | odd | 20 | |||
7500.2.a.n.1.10 | 12 | 25.13 | odd | 20 | |||
7500.2.d.g.1249.10 | 24 | 25.16 | even | 5 | |||
7500.2.d.g.1249.15 | 24 | 25.9 | even | 10 |