Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(82,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bc (of order \(12\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 418.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.418 |
Dual form | 525.2.bc.a.157.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63896 | − | 0.189469i | −0.997433 | − | 0.0716124i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | −1.93185 | + | 0.517638i | −0.557678 | + | 0.149429i | ||||
\(13\) | −1.41421 | + | 1.41421i | −0.392232 | + | 0.392232i | −0.875482 | − | 0.483250i | \(-0.839456\pi\) |
0.483250 | + | 0.875482i | \(0.339456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 1.55291 | − | 5.79555i | 0.376637 | − | 1.40563i | −0.474301 | − | 0.880363i | \(-0.657299\pi\) |
0.850938 | − | 0.525266i | \(-0.176034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73205 | + | 3.00000i | −0.397360 | + | 0.688247i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) |
0.596040 | + | 0.802955i | \(0.296740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | + | 0.866025i | 0.545545 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −4.76028 | + | 2.31079i | −0.899608 | + | 0.436698i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | + | 2.59808i | −0.808224 | + | 0.466628i | −0.846339 | − | 0.532645i | \(-0.821198\pi\) |
0.0381148 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.55291 | + | 5.79555i | 0.270328 | + | 1.00888i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | −2.24144 | − | 8.36516i | −0.368490 | − | 1.37522i | −0.862627 | − | 0.505840i | \(-0.831183\pi\) |
0.494137 | − | 0.869384i | \(-0.335484\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.73205 | − | 1.00000i | 0.277350 | − | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.3923i | − | 1.62301i | −0.584349 | − | 0.811503i | \(-0.698650\pi\) | ||
0.584349 | − | 0.811503i | \(-0.301350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.67423 | + | 3.67423i | 0.560316 | + | 0.560316i | 0.929397 | − | 0.369082i | \(-0.120328\pi\) |
−0.369082 | + | 0.929397i | \(0.620328\pi\) | |||||||
\(44\) | −10.3923 | − | 6.00000i | −1.56670 | − | 0.904534i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.79555 | + | 1.55291i | −0.845369 | + | 0.226516i | −0.655407 | − | 0.755276i | \(-0.727503\pi\) |
−0.189961 | + | 0.981792i | \(0.560836\pi\) | |||||||
\(48\) | −2.82843 | + | 2.82843i | −0.408248 | + | 0.408248i | ||||
\(49\) | 6.92820 | + | 1.00000i | 0.989743 | + | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | + | 5.19615i | −0.420084 | + | 0.727607i | ||||
\(52\) | −1.03528 | + | 3.86370i | −0.143567 | + | 0.535799i | ||||
\(53\) | 2.68973 | − | 10.0382i | 0.369462 | − | 1.37885i | −0.491807 | − | 0.870704i | \(-0.663664\pi\) |
0.861270 | − | 0.508148i | \(-0.169670\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.44949 | − | 2.44949i | 0.324443 | − | 0.324443i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.19615 | + | 9.00000i | 0.676481 | + | 1.17170i | 0.976034 | + | 0.217620i | \(0.0698294\pi\) |
−0.299552 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.50000 | + | 4.33013i | 0.960277 | + | 0.554416i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.19067 | − | 1.48356i | −0.275999 | − | 0.186911i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34607 | + | 0.896575i | 0.408787 | + | 0.109534i | 0.457352 | − | 0.889286i | \(-0.348798\pi\) |
−0.0485648 | + | 0.998820i | \(0.515465\pi\) | |||||||
\(68\) | −3.10583 | − | 11.5911i | −0.376637 | − | 1.40563i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.965926 | + | 0.258819i | 0.113053 | + | 0.0302925i | 0.314902 | − | 0.949124i | \(-0.398028\pi\) |
−0.201849 | + | 0.979417i | \(0.564695\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.92820i | 0.794719i | ||||||||
\(77\) | 6.93237 | + | 14.2808i | 0.790017 | + | 1.62745i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.33013 | − | 2.50000i | −0.487177 | − | 0.281272i | 0.236225 | − | 0.971698i | \(-0.424090\pi\) |
−0.723403 | + | 0.690426i | \(0.757423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.24264 | − | 4.24264i | 0.465690 | − | 0.465690i | −0.434825 | − | 0.900515i | \(-0.643190\pi\) |
0.900515 | + | 0.434825i | \(0.143190\pi\) | |||||||
\(84\) | 5.19615 | − | 1.00000i | 0.566947 | − | 0.109109i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.19615 | + | 9.00000i | −0.550791 | + | 0.953998i | 0.447427 | + | 0.894321i | \(0.352341\pi\) |
−0.998218 | + | 0.0596775i | \(0.980993\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 3.46410i | 0.419314 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.01910 | − | 1.34486i | 0.520456 | − | 0.139456i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.19239 | + | 9.19239i | 0.933346 | + | 0.933346i | 0.997913 | − | 0.0645677i | \(-0.0205669\pi\) |
−0.0645677 | + | 0.997913i | \(0.520567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 6.00000i | − | 0.603023i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.81173 | + | 6.76148i | 0.178515 | + | 0.666228i | 0.995926 | + | 0.0901732i | \(0.0287421\pi\) |
−0.817411 | + | 0.576055i | \(0.804591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(108\) | −1.93185 | − | 0.517638i | −0.185893 | − | 0.0498097i | ||||
\(109\) | 8.66025 | − | 5.00000i | 0.829502 | − | 0.478913i | −0.0241802 | − | 0.999708i | \(-0.507698\pi\) |
0.853682 | + | 0.520794i | \(0.174364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.66025i | 0.821995i | ||||||||
\(112\) | −5.93426 | + | 8.76268i | −0.560734 | + | 0.827996i | ||||
\(113\) | 7.34847 | + | 7.34847i | 0.691286 | + | 0.691286i | 0.962515 | − | 0.271229i | \(-0.0874301\pi\) |
−0.271229 | + | 0.962515i | \(0.587430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.93185 | + | 0.517638i | −0.178600 | + | 0.0478557i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.19615 | + | 15.0000i | −0.476331 | + | 1.37505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.68973 | + | 10.0382i | −0.242524 | + | 0.905114i | ||||
\(124\) | −5.19615 | + | 9.00000i | −0.466628 | + | 0.808224i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.57321 | − | 8.57321i | 0.760750 | − | 0.760750i | −0.215708 | − | 0.976458i | \(-0.569206\pi\) |
0.976458 | + | 0.215708i | \(0.0692060\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.59808 | − | 4.50000i | −0.228748 | − | 0.396203i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.00000 | + | 5.19615i | 0.786334 | + | 0.453990i | 0.838670 | − | 0.544640i | \(-0.183334\pi\) |
−0.0523366 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(132\) | 8.48528 | + | 8.48528i | 0.738549 | + | 0.738549i | ||||
\(133\) | 5.13922 | − | 7.58871i | 0.445627 | − | 0.658024i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.0764 | + | 5.37945i | 1.71524 | + | 0.459598i | 0.976700 | − | 0.214610i | \(-0.0688480\pi\) |
0.738542 | + | 0.674207i | \(0.235515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.73205 | −0.146911 | −0.0734553 | − | 0.997299i | \(-0.523403\pi\) | ||||
−0.0734553 | + | 0.997299i | \(0.523403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5911 | + | 3.10583i | 0.969297 | + | 0.259722i | ||||
\(144\) | 3.46410 | − | 2.00000i | 0.288675 | − | 0.166667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.43331 | − | 2.75908i | −0.530611 | − | 0.227565i | ||||
\(148\) | −12.2474 | − | 12.2474i | −1.00673 | − | 1.00673i | ||||
\(149\) | −10.3923 | − | 6.00000i | −0.851371 | − | 0.491539i | 0.00974235 | − | 0.999953i | \(-0.496899\pi\) |
−0.861113 | + | 0.508413i | \(0.830232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | − | 4.33013i | −0.203447 | − | 0.352381i | 0.746190 | − | 0.665733i | \(-0.231881\pi\) |
−0.949637 | + | 0.313353i | \(0.898548\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.24264 | − | 4.24264i | 0.342997 | − | 0.342997i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 3.46410i | 0.160128 | − | 0.277350i | ||||
\(157\) | 1.81173 | − | 6.76148i | 0.144592 | − | 0.539625i | −0.855181 | − | 0.518329i | \(-0.826554\pi\) |
0.999773 | − | 0.0212957i | \(-0.00677914\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.19615 | + | 9.00000i | −0.412082 | + | 0.713746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.36516 | − | 2.24144i | 0.655210 | − | 0.175563i | 0.0841267 | − | 0.996455i | \(-0.473190\pi\) |
0.571083 | + | 0.820892i | \(0.306523\pi\) | |||||||
\(164\) | −10.3923 | − | 18.0000i | −0.811503 | − | 1.40556i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.48528 | − | 8.48528i | −0.656611 | − | 0.656611i | 0.297966 | − | 0.954577i | \(-0.403692\pi\) |
−0.954577 | + | 0.297966i | \(0.903692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000i | 0.692308i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 1.73205i | −0.229416 | + | 0.132453i | ||||
\(172\) | 10.0382 | + | 2.68973i | 0.765405 | + | 0.205090i | ||||
\(173\) | −4.65874 | − | 17.3867i | −0.354198 | − | 1.32188i | −0.881491 | − | 0.472200i | \(-0.843460\pi\) |
0.527294 | − | 0.849683i | \(-0.323207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.0000 | −1.80907 | ||||||||
\(177\) | −2.68973 | − | 10.0382i | −0.202172 | − | 0.754517i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7846 | − | 12.0000i | 1.55351 | − | 0.896922i | 0.555663 | − | 0.831408i | \(-0.312464\pi\) |
0.997852 | − | 0.0655145i | \(-0.0208689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.19615i | − | 0.386227i | −0.981176 | − | 0.193113i | \(-0.938141\pi\) | ||
0.981176 | − | 0.193113i | \(-0.0618586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.12372 | − | 6.12372i | −0.452679 | − | 0.452679i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.7733 | + | 9.31749i | −2.54288 | + | 0.681362i | ||||
\(188\) | −8.48528 | + | 8.48528i | −0.618853 | + | 0.618853i | ||||
\(189\) | 1.73205 | + | 2.00000i | 0.125988 | + | 0.145479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | −2.07055 | + | 7.72741i | −0.149429 | + | 0.557678i | ||||
\(193\) | −4.03459 | + | 15.0573i | −0.290416 | + | 1.08385i | 0.654374 | + | 0.756171i | \(0.272932\pi\) |
−0.944790 | + | 0.327677i | \(0.893734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0000 | − | 5.19615i | 0.928571 | − | 0.371154i | ||||
\(197\) | −7.34847 | + | 7.34847i | −0.523557 | + | 0.523557i | −0.918644 | − | 0.395087i | \(-0.870714\pi\) |
0.395087 | + | 0.918644i | \(0.370714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.52628 | − | 16.5000i | −0.675300 | − | 1.16965i | −0.976381 | − | 0.216055i | \(-0.930681\pi\) |
0.301081 | − | 0.953599i | \(-0.402653\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.00000 | − | 1.73205i | −0.211604 | − | 0.122169i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.0000i | 0.840168i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.07055 | + | 7.72741i | 0.143567 | + | 0.535799i | ||||
\(209\) | 20.7846 | 1.43770 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.00000 | 0.481900 | 0.240950 | − | 0.970538i | \(-0.422541\pi\) | ||||
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(212\) | −5.37945 | − | 20.0764i | −0.369462 | − | 1.37885i | ||||
\(213\) | 5.79555 | + | 1.55291i | 0.397105 | + | 0.106404i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.3676 | − | 6.00361i | 0.839565 | − | 0.407551i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.866025 | − | 0.500000i | −0.0585206 | − | 0.0337869i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.53553 | − | 3.53553i | 0.236757 | − | 0.236757i | −0.578749 | − | 0.815506i | \(-0.696459\pi\) |
0.815506 | + | 0.578749i | \(0.196459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.55291 | − | 5.79555i | 0.103071 | − | 0.384664i | −0.895049 | − | 0.445969i | \(-0.852859\pi\) |
0.998119 | + | 0.0613041i | \(0.0195260\pi\) | |||||||
\(228\) | 1.79315 | − | 6.69213i | 0.118754 | − | 0.443197i | ||||
\(229\) | −3.46410 | + | 6.00000i | −0.228914 | + | 0.396491i | −0.957487 | − | 0.288478i | \(-0.906851\pi\) |
0.728572 | + | 0.684969i | \(0.240184\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 15.5885i | −0.197386 | − | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.0764 | + | 5.37945i | −1.31525 | + | 0.352420i | −0.847196 | − | 0.531281i | \(-0.821711\pi\) |
−0.468052 | + | 0.883701i | \(0.655044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.0000 | + | 10.3923i | 1.17170 | + | 0.676481i | ||||
\(237\) | 3.53553 | + | 3.53553i | 0.229658 | + | 0.229658i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 18.0000i | − | 1.16432i | −0.813073 | − | 0.582162i | \(-0.802207\pi\) | ||
0.813073 | − | 0.582162i | \(-0.197793\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5000 | − | 9.52628i | 1.06286 | − | 0.613642i | 0.136637 | − | 0.990621i | \(-0.456371\pi\) |
0.926222 | + | 0.376980i | \(0.123037\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 17.3205 | 1.10883 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.79315 | − | 6.69213i | −0.114095 | − | 0.425810i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.19615 | + | 3.00000i | −0.329293 | + | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.7846i | − | 1.31191i | −0.754799 | − | 0.655956i | \(-0.772265\pi\) | ||
0.754799 | − | 0.655956i | \(-0.227735\pi\) | |||||||
\(252\) | −5.27792 | − | 0.378937i | −0.332478 | − | 0.0238708i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 5.79555 | − | 1.55291i | 0.361517 | − | 0.0968681i | −0.0734884 | − | 0.997296i | \(-0.523413\pi\) |
0.435005 | + | 0.900428i | \(0.356747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.33013 | + | 22.5000i | 0.269061 | + | 1.39808i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.06918 | + | 30.1146i | −0.497567 | + | 1.85694i | 0.0175838 | + | 0.999845i | \(0.494403\pi\) |
−0.515151 | + | 0.857100i | \(0.672264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.34847 | − | 7.34847i | 0.449719 | − | 0.449719i | ||||
\(268\) | 6.69213 | − | 1.79315i | 0.408787 | − | 0.109534i | ||||
\(269\) | 10.3923 | + | 18.0000i | 0.633630 | + | 1.09748i | 0.986804 | + | 0.161922i | \(0.0517692\pi\) |
−0.353174 | + | 0.935558i | \(0.614898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.0000 | − | 15.5885i | −1.64013 | − | 0.946931i | −0.980785 | − | 0.195094i | \(-0.937499\pi\) |
−0.659349 | − | 0.751837i | \(-0.729168\pi\) | |||||||
\(272\) | −16.9706 | − | 16.9706i | −1.02899 | − | 1.02899i | ||||
\(273\) | −4.76028 | + | 2.31079i | −0.288105 | + | 0.139855i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3843 | − | 3.58630i | −0.804182 | − | 0.215480i | −0.166763 | − | 0.985997i | \(-0.553331\pi\) |
−0.637419 | + | 0.770517i | \(0.719998\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.19615 | −0.311086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.4548 | − | 4.14110i | −0.918693 | − | 0.246163i | −0.231667 | − | 0.972795i | \(-0.574418\pi\) |
−0.687027 | + | 0.726632i | \(0.741084\pi\) | |||||||
\(284\) | −10.3923 | + | 6.00000i | −0.616670 | + | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.96902 | + | 27.4249i | −0.116227 | + | 1.61884i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4545 | − | 9.50000i | −0.967911 | − | 0.558824i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.50000 | − | 11.2583i | −0.381037 | − | 0.659975i | ||||
\(292\) | 1.93185 | − | 0.517638i | 0.113053 | − | 0.0302925i | ||||
\(293\) | −12.7279 | + | 12.7279i | −0.743573 | + | 0.743573i | −0.973264 | − | 0.229691i | \(-0.926229\pi\) |
0.229691 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.55291 | + | 5.79555i | −0.0901092 | + | 0.336292i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.00000 | − | 10.3923i | −0.518751 | − | 0.599002i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.92820 | + | 12.0000i | 0.397360 | + | 0.688247i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.94975 | − | 4.94975i | −0.282497 | − | 0.282497i | 0.551607 | − | 0.834104i | \(-0.314015\pi\) |
−0.834104 | + | 0.551607i | \(0.814015\pi\) | |||||||
\(308\) | 26.2880 | + | 17.8028i | 1.49790 | + | 1.01441i | ||||
\(309\) | − | 7.00000i | − | 0.398216i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000 | − | 10.3923i | 1.02069 | − | 0.589294i | 0.106384 | − | 0.994325i | \(-0.466073\pi\) |
0.914303 | + | 0.405032i | \(0.132739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.91756 | − | 18.3526i | −0.277957 | − | 1.03735i | −0.953834 | − | 0.300335i | \(-0.902902\pi\) |
0.675877 | − | 0.737015i | \(-0.263765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −2.68973 | − | 10.0382i | −0.151070 | − | 0.563801i | −0.999410 | − | 0.0343491i | \(-0.989064\pi\) |
0.848340 | − | 0.529452i | \(-0.177602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6969 | + | 14.6969i | 0.817760 | + | 0.817760i | ||||
\(324\) | 1.73205 | + | 1.00000i | 0.0962250 | + | 0.0555556i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.65926 | + | 2.58819i | −0.534158 | + | 0.143127i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.5885 | − | 3.00000i | 0.859419 | − | 0.165395i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50000 | − | 4.33013i | 0.137412 | − | 0.238005i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.926516 | + | 0.376254i | \(0.122788\pi\) | |||||||
\(332\) | 3.10583 | − | 11.5911i | 0.170454 | − | 0.636145i | ||||
\(333\) | 2.24144 | − | 8.36516i | 0.122830 | − | 0.458408i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.00000 | − | 6.92820i | 0.436436 | − | 0.377964i | ||||
\(337\) | 18.3712 | − | 18.3712i | 1.00074 | − | 1.00074i | 0.000741840 | − | 1.00000i | \(-0.499764\pi\) |
1.00000 | 0.000741840i | \(-0.000236135\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.19615 | − | 9.00000i | −0.282216 | − | 0.488813i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.0000 | + | 15.5885i | 1.46213 | + | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | − | 3.95164i | −0.976972 | − | 0.213368i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.0382 | − | 2.68973i | −0.538879 | − | 0.144392i | −0.0208935 | − | 0.999782i | \(-0.506651\pi\) |
−0.517985 | + | 0.855390i | \(0.673318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.7846 | −1.11257 | −0.556287 | − | 0.830990i | \(-0.687775\pi\) | ||||
−0.556287 | + | 0.830990i | \(0.687775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.7733 | − | 9.31749i | −1.85080 | − | 0.495920i | −0.851215 | − | 0.524817i | \(-0.824134\pi\) |
−0.999582 | + | 0.0288971i | \(0.990800\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.7846i | 1.10158i | ||||||||
\(357\) | 8.90138 | − | 13.1440i | 0.471111 | − | 0.695656i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5885 | + | 9.00000i | 0.822727 | + | 0.475002i | 0.851356 | − | 0.524588i | \(-0.175781\pi\) |
−0.0286287 | + | 0.999590i | \(0.509114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.50000 | + | 6.06218i | 0.184211 | + | 0.319062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.6777 | − | 17.6777i | 0.927837 | − | 0.927837i | ||||
\(364\) | 3.46410 | − | 10.0000i | 0.181568 | − | 0.524142i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.39992 | + | 16.4207i | −0.229674 | + | 0.857156i | 0.750804 | + | 0.660526i | \(0.229666\pi\) |
−0.980478 | + | 0.196630i | \(0.937000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.19615 | − | 9.00000i | 0.270501 | − | 0.468521i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.00000 | + | 25.9808i | −0.467257 | + | 1.34885i | ||||
\(372\) | 7.34847 | − | 7.34847i | 0.381000 | − | 0.381000i | ||||
\(373\) | 6.69213 | − | 1.79315i | 0.346505 | − | 0.0928458i | −0.0813690 | − | 0.996684i | \(-0.525929\pi\) |
0.427874 | + | 0.903838i | \(0.359263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 28.0000i | − | 1.43826i | −0.694874 | − | 0.719132i | \(-0.744540\pi\) | ||
0.694874 | − | 0.719132i | \(-0.255460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5000 | + | 6.06218i | −0.537931 | + | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.21166 | + | 23.1822i | 0.317401 | + | 1.18456i | 0.921733 | + | 0.387824i | \(0.126773\pi\) |
−0.604333 | + | 0.796732i | \(0.706560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.34486 | + | 5.01910i | 0.0683632 | + | 0.255135i | ||||
\(388\) | 25.1141 | + | 6.72930i | 1.27497 | + | 0.341628i | ||||
\(389\) | −5.19615 | + | 3.00000i | −0.263455 | + | 0.152106i | −0.625910 | − | 0.779895i | \(-0.715272\pi\) |
0.362454 | + | 0.932002i | \(0.381939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.34847 | − | 7.34847i | −0.370681 | − | 0.370681i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.00000 | − | 10.3923i | −0.301511 | − | 0.522233i | ||||
\(397\) | 6.76148 | − | 1.81173i | 0.339349 | − | 0.0909283i | −0.0851201 | − | 0.996371i | \(-0.527127\pi\) |
0.424469 | + | 0.905442i | \(0.360461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | + | 6.00000i | −0.346844 | + | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.68973 | − | 10.0382i | 0.133985 | − | 0.500038i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.7423 | + | 36.7423i | −1.82125 | + | 1.82125i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.46410 | − | 6.00000i | −0.171289 | − | 0.296681i | 0.767582 | − | 0.640951i | \(-0.221460\pi\) |
−0.938871 | + | 0.344270i | \(0.888126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | − | 10.3923i | −0.887875 | − | 0.512615i | ||||
\(412\) | 9.89949 | + | 9.89949i | 0.487713 | + | 0.487713i | ||||
\(413\) | −12.0072 | − | 24.7351i | −0.590836 | − | 1.21714i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.67303 | + | 0.448288i | 0.0819288 | + | 0.0219527i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.0000 | 1.51085 | 0.755424 | − | 0.655237i | \(-0.227431\pi\) | ||||
0.755424 | + | 0.655237i | \(0.227431\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.79555 | − | 1.55291i | −0.281790 | − | 0.0755053i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.9718 | − | 12.8480i | −0.918108 | − | 0.621760i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.3923 | − | 6.00000i | −0.501745 | − | 0.289683i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | −3.86370 | + | 1.03528i | −0.185893 | + | 0.0498097i | ||||
\(433\) | 20.5061 | − | 20.5061i | 0.985460 | − | 0.985460i | −0.0144357 | − | 0.999896i | \(-0.504595\pi\) |
0.999896 | + | 0.0144357i | \(0.00459518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.0000 | − | 17.3205i | 0.478913 | − | 0.829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.33013 | − | 7.50000i | 0.206666 | − | 0.357955i | −0.743996 | − | 0.668184i | \(-0.767072\pi\) |
0.950662 | + | 0.310228i | \(0.100405\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0382 | − | 2.68973i | 0.476929 | − | 0.127793i | −0.0123433 | − | 0.999924i | \(-0.503929\pi\) |
0.489272 | + | 0.872131i | \(0.337262\pi\) | |||||||
\(444\) | 8.66025 | + | 15.0000i | 0.410997 | + | 0.711868i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.48528 | + | 8.48528i | 0.401340 | + | 0.401340i | ||||
\(448\) | −1.51575 | + | 21.1117i | −0.0716124 | + | 0.997433i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −54.0000 | + | 31.1769i | −2.54276 | + | 1.46806i | ||||
\(452\) | 20.0764 | + | 5.37945i | 0.944314 | + | 0.253028i | ||||
\(453\) | 1.29410 | + | 4.82963i | 0.0608019 | + | 0.226916i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.93117 | + | 18.4034i | 0.230670 | + | 0.860873i | 0.980053 | + | 0.198736i | \(0.0636836\pi\) |
−0.749383 | + | 0.662137i | \(0.769650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.19615 | + | 3.00000i | −0.242536 | + | 0.140028i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 31.1769i | − | 1.45205i | −0.687666 | − | 0.726027i | \(-0.741365\pi\) | ||
0.687666 | − | 0.726027i | \(-0.258635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.22474 | + | 1.22474i | 0.0569187 | + | 0.0569187i | 0.734993 | − | 0.678074i | \(-0.237185\pi\) |
−0.678074 | + | 0.734993i | \(0.737185\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.9778 | − | 7.76457i | 1.34093 | − | 0.359302i | 0.484152 | − | 0.874984i | \(-0.339128\pi\) |
0.856780 | + | 0.515683i | \(0.172462\pi\) | |||||||
\(468\) | −2.82843 | + | 2.82843i | −0.130744 | + | 0.130744i | ||||
\(469\) | −8.66025 | − | 3.00000i | −0.399893 | − | 0.138527i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | + | 6.06218i | −0.161271 | + | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.06918 | − | 30.1146i | 0.371021 | − | 1.38467i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.00000 | + | 31.1769i | 0.275010 | + | 1.42899i | ||||
\(477\) | 7.34847 | − | 7.34847i | 0.336463 | − | 0.336463i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.3923 | − | 18.0000i | −0.474837 | − | 0.822441i | 0.524748 | − | 0.851258i | \(-0.324159\pi\) |
−0.999585 | + | 0.0288165i | \(0.990826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.0000 | + | 8.66025i | 0.683941 | + | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 50.0000i | 2.27273i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.1337 | + | 9.41404i | 1.59206 | + | 0.426591i | 0.942632 | − | 0.333833i | \(-0.108342\pi\) |
0.649427 | + | 0.760424i | \(0.275009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.66025 | −0.391630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 5.37945 | + | 20.0764i | 0.242524 | + | 0.905114i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.7846i | 0.933257i | ||||||||
\(497\) | 15.8338 | + | 1.13681i | 0.710241 | + | 0.0509930i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3205 | + | 10.0000i | 0.775372 | + | 0.447661i | 0.834788 | − | 0.550572i | \(-0.185590\pi\) |
−0.0594153 | + | 0.998233i | \(0.518924\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | + | 25.4558i | −1.13502 | + | 1.13502i | −0.145690 | + | 0.989330i | \(0.546540\pi\) |
−0.989330 | + | 0.145690i | \(0.953460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.32937 | − | 8.69333i | 0.103451 | − | 0.386084i | ||||
\(508\) | 6.27603 | − | 23.4225i | 0.278454 | − | 1.03920i | ||||
\(509\) | −5.19615 | + | 9.00000i | −0.230315 | + | 0.398918i | −0.957901 | − | 0.287099i | \(-0.907309\pi\) |
0.727586 | + | 0.686017i | \(0.240642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.50000 | − | 0.866025i | −0.110593 | − | 0.0383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.34607 | − | 0.896575i | 0.147732 | − | 0.0395848i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.00000 | − | 5.19615i | −0.396203 | − | 0.228748i | ||||
\(517\) | 25.4558 | + | 25.4558i | 1.11955 | + | 1.11955i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0000i | 0.790112i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 5.19615i | −0.394297 | + | 0.227648i | −0.684020 | − | 0.729463i | \(-0.739770\pi\) |
0.289723 | + | 0.957110i | \(0.406437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.81173 | + | 6.76148i | 0.0792216 | + | 0.295659i | 0.994157 | − | 0.107941i | \(-0.0344256\pi\) |
−0.914936 | + | 0.403599i | \(0.867759\pi\) | |||||||
\(524\) | 20.7846 | 0.907980 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.06918 | + | 30.1146i | 0.351499 | + | 1.31181i | ||||
\(528\) | 23.1822 | + | 6.21166i | 1.00888 | + | 0.270328i | ||||
\(529\) | −19.9186 | + | 11.5000i | −0.866025 | + | 0.500000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923i | 0.450988i | ||||||||
\(532\) | 1.31268 | − | 18.2832i | 0.0569118 | − | 0.792679i | ||||
\(533\) | 14.6969 | + | 14.6969i | 0.636595 | + | 0.636595i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.1822 | + | 6.21166i | −1.00039 | + | 0.268053i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.5885 | − | 39.0000i | −0.671442 | − | 1.67985i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.34486 | + | 5.01910i | −0.0577136 | + | 0.215390i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.0454 | + | 22.0454i | −0.942594 | + | 0.942594i | −0.998439 | − | 0.0558458i | \(-0.982214\pi\) |
0.0558458 | + | 0.998439i | \(0.482214\pi\) | |||||||
\(548\) | 40.1528 | − | 10.7589i | 1.71524 | − | 0.459598i | ||||
\(549\) | 4.33013 | + | 7.50000i | 0.184805 | + | 0.320092i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9534 | + | 7.41782i | 0.465784 | + | 0.315438i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00000 | + | 1.73205i | −0.127228 | + | 0.0734553i | ||||
\(557\) | −10.0382 | − | 2.68973i | −0.425332 | − | 0.113967i | 0.0398021 | − | 0.999208i | \(-0.487327\pi\) |
−0.465134 | + | 0.885240i | \(0.653994\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.3923 | −0.439548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.79555 | − | 1.55291i | −0.244254 | − | 0.0654475i | 0.134615 | − | 0.990898i | \(-0.457020\pi\) |
−0.378869 | + | 0.925450i | \(0.623687\pi\) | |||||||
\(564\) | 10.3923 | − | 6.00000i | 0.437595 | − | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.15539 | − | 2.38014i | −0.0485220 | − | 0.0999565i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.7846 | + | 12.0000i | 0.871336 | + | 0.503066i | 0.867792 | − | 0.496928i | \(-0.165539\pi\) |
0.00354413 | + | 0.999994i | \(0.498872\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | 23.1822 | − | 6.21166i | 0.969297 | − | 0.259722i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | −1.81173 | + | 6.76148i | −0.0754234 | + | 0.281484i | −0.993329 | − | 0.115315i | \(-0.963212\pi\) |
0.917906 | + | 0.396799i | \(0.129879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.79423 | − | 13.5000i | 0.323917 | − | 0.561041i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.0000 | + | 10.3923i | −0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −60.2292 | + | 16.1384i | −2.49444 | + | 0.668383i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.7279 | − | 12.7279i | −0.525338 | − | 0.525338i | 0.393841 | − | 0.919179i | \(-0.371146\pi\) |
−0.919179 | + | 0.393841i | \(0.871146\pi\) | |||||||
\(588\) | −13.9019 | + | 1.65445i | −0.573305 | + | 0.0682284i | ||||
\(589\) | − | 18.0000i | − | 0.741677i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 5.19615i | 0.370211 | − | 0.213741i | ||||
\(592\) | −33.4607 | − | 8.96575i | −1.37522 | − | 0.368490i | ||||
\(593\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.0000 | −0.983078 | ||||||||
\(597\) | 4.93117 | + | 18.4034i | 0.201819 | + | 0.753199i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.3923 | − | 6.00000i | 0.424618 | − | 0.245153i | −0.272433 | − | 0.962175i | \(-0.587828\pi\) |
0.697051 | + | 0.717021i | \(0.254495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6410i | 1.41304i | 0.707695 | + | 0.706518i | \(0.249735\pi\) | ||||
−0.707695 | + | 0.706518i | \(0.750265\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.44949 | + | 2.44949i | 0.0997509 | + | 0.0997509i | ||||
\(604\) | −8.66025 | − | 5.00000i | −0.352381 | − | 0.203447i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1481 | − | 6.47048i | 0.980143 | − | 0.262629i | 0.267038 | − | 0.963686i | \(-0.413955\pi\) |
0.713105 | + | 0.701057i | \(0.247288\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | − | 10.3923i | 0.242734 | − | 0.420428i | ||||
\(612\) | 3.10583 | − | 11.5911i | 0.125546 | − | 0.468543i | ||||
\(613\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.34847 | + | 7.34847i | −0.295838 | + | 0.295838i | −0.839381 | − | 0.543543i | \(-0.817082\pi\) |
0.543543 | + | 0.839381i | \(0.317082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3827 | + | 40.5000i | 0.939829 | + | 1.62783i | 0.765787 | + | 0.643094i | \(0.222350\pi\) |
0.174042 | + | 0.984738i | \(0.444317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.4176 | − | 22.7661i | 0.617695 | − | 0.912105i | ||||
\(624\) | − | 8.00000i | − | 0.320256i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.0764 | − | 5.37945i | −0.801774 | − | 0.214835i | ||||
\(628\) | −3.62347 | − | 13.5230i | −0.144592 | − | 0.539625i | ||||
\(629\) | −51.9615 | −2.07184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.76148 | − | 1.81173i | −0.268745 | − | 0.0720099i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 20.7846i | 0.824163i | ||||||||
\(637\) | −11.2122 | + | 8.38375i | −0.444242 | + | 0.332176i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.19615 | − | 3.00000i | −0.205557 | − | 0.118678i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | + | 15.5885i | 0.355479 | + | 0.615707i | 0.987200 | − | 0.159489i | \(-0.0509845\pi\) |
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5061 | − | 20.5061i | 0.808682 | − | 0.808682i | −0.175753 | − | 0.984434i | \(-0.556236\pi\) |
0.984434 | + | 0.175753i | \(0.0562359\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.65874 | − | 17.3867i | 0.183154 | − | 0.683540i | −0.811864 | − | 0.583846i | \(-0.801547\pi\) |
0.995018 | − | 0.0996938i | \(-0.0317863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.1769 | − | 54.0000i | 1.22380 | − | 2.11969i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.5000 | + | 2.59808i | −0.529107 | + | 0.101827i | ||||
\(652\) | 12.2474 | − | 12.2474i | 0.479647 | − | 0.479647i | ||||
\(653\) | −10.0382 | + | 2.68973i | −0.392825 | + | 0.105257i | −0.449824 | − | 0.893117i | \(-0.648513\pi\) |
0.0569993 | + | 0.998374i | \(0.481847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.0000 | − | 20.7846i | −1.40556 | − | 0.811503i | ||||
\(657\) | 0.707107 | + | 0.707107i | 0.0275869 | + | 0.0275869i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.00000i | − | 0.233727i | −0.993148 | − | 0.116863i | \(-0.962716\pi\) | ||
0.993148 | − | 0.116863i | \(-0.0372840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.5000 | − | 21.6506i | 1.45858 | − | 0.842112i | 0.459639 | − | 0.888106i | \(-0.347979\pi\) |
0.998942 | + | 0.0459936i | \(0.0146454\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.10583 | − | 11.5911i | −0.120620 | − | 0.450161i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −23.1822 | − | 6.21166i | −0.896947 | − | 0.240336i | ||||
\(669\) | −4.33013 | + | 2.50000i | −0.167412 | + | 0.0966556i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 51.9615i | − | 2.00595i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.57321 | − | 8.57321i | −0.330473 | − | 0.330473i | 0.522293 | − | 0.852766i | \(-0.325077\pi\) |
−0.852766 | + | 0.522293i | \(0.825077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00000 | + | 15.5885i | 0.346154 | + | 0.599556i | ||||
\(677\) | 46.3644 | − | 12.4233i | 1.78193 | − | 0.477467i | 0.790997 | − | 0.611820i | \(-0.209562\pi\) |
0.990933 | + | 0.134354i | \(0.0428958\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.5167 | − | 26.0000i | −0.864110 | − | 0.997788i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.00000 | + | 5.19615i | −0.114960 | + | 0.199117i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.06918 | − | 30.1146i | 0.308759 | − | 1.15230i | −0.620903 | − | 0.783888i | \(-0.713234\pi\) |
0.929661 | − | 0.368415i | \(-0.120099\pi\) | |||||||
\(684\) | −3.46410 | + | 6.00000i | −0.132453 | + | 0.229416i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.89898 | − | 4.89898i | 0.186908 | − | 0.186908i | ||||
\(688\) | 20.0764 | − | 5.37945i | 0.765405 | − | 0.205090i | ||||
\(689\) | 10.3923 | + | 18.0000i | 0.395915 | + | 0.685745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5000 | + | 6.06218i | 0.399439 | + | 0.230616i | 0.686242 | − | 0.727373i | \(-0.259259\pi\) |
−0.286803 | + | 0.957990i | \(0.592593\pi\) | |||||||
\(692\) | −25.4558 | − | 25.4558i | −0.967686 | − | 0.967686i | ||||
\(693\) | −1.13681 | + | 15.8338i | −0.0431839 | + | 0.601474i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60.2292 | − | 16.1384i | −2.28134 | − | 0.611284i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.7846 | 0.786146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9778 | + | 7.76457i | 1.09292 | + | 0.292846i | ||||
\(704\) | −41.5692 | + | 24.0000i | −1.56670 | + | 0.904534i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −14.6969 | − | 14.6969i | −0.552345 | − | 0.552345i | ||||
\(709\) | 26.8468 | + | 15.5000i | 1.00825 | + | 0.582115i | 0.910679 | − | 0.413114i | \(-0.135559\pi\) |
0.0975728 | + | 0.995228i | \(0.468892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | − | 4.33013i | −0.0937573 | − | 0.162392i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.0000 | − | 41.5692i | 0.896922 | − | 1.55351i | ||||
\(717\) | −4.65874 | + | 17.3867i | −0.173984 | + | 0.649317i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.50000 | − | 18.1865i | −0.130347 | − | 0.677302i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.4034 | + | 4.93117i | −0.684428 | + | 0.183392i | ||||
\(724\) | −5.19615 | − | 9.00000i | −0.193113 | − | 0.334482i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2843 | − | 28.2843i | −1.04901 | − | 1.04901i | −0.998736 | − | 0.0502699i | \(-0.983992\pi\) |
−0.0502699 | − | 0.998736i | \(-0.516008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.0000 | − | 15.5885i | 0.998631 | − | 0.576560i | ||||
\(732\) | −16.7303 | − | 4.48288i | −0.618371 | − | 0.165692i | ||||
\(733\) | 12.1645 | + | 45.3985i | 0.449306 | + | 1.67683i | 0.704310 | + | 0.709892i | \(0.251256\pi\) |
−0.255004 | + | 0.966940i | \(0.582077\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.37945 | − | 20.0764i | −0.198155 | − | 0.739523i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.866025 | − | 0.500000i | 0.0318573 | − | 0.0183928i | −0.483987 | − | 0.875075i | \(-0.660812\pi\) |
0.515844 | + | 0.856683i | \(0.327478\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.92820i | 0.254514i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.79555 | − | 1.55291i | 0.212048 | − | 0.0568182i | ||||
\(748\) | −50.9117 | + | 50.9117i | −1.86152 | + | 1.86152i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.50000 | + | 9.52628i | −0.200698 | + | 0.347619i | −0.948753 | − | 0.316017i | \(-0.897654\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(752\) | −6.21166 | + | 23.1822i | −0.226516 | + | 0.845369i | ||||
\(753\) | −5.37945 | + | 20.0764i | −0.196038 | + | 0.731624i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.00000 | + | 1.73205i | 0.181848 | + | 0.0629941i | ||||
\(757\) | 20.8207 | − | 20.8207i | 0.756740 | − | 0.756740i | −0.218988 | − | 0.975728i | \(-0.570275\pi\) |
0.975728 | + | 0.218988i | \(0.0702755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | − | 10.3923i | −0.652499 | − | 0.376721i | 0.136914 | − | 0.990583i | \(-0.456282\pi\) |
−0.789413 | + | 0.613862i | \(0.789615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.8014 | + | 11.5539i | −0.861668 | + | 0.418281i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.0764 | − | 5.37945i | −0.724916 | − | 0.194241i | ||||
\(768\) | 4.14110 | + | 15.4548i | 0.149429 | + | 0.557678i | ||||
\(769\) | −5.19615 | −0.187378 | −0.0936890 | − | 0.995602i | \(-0.529866\pi\) | ||||
−0.0936890 | + | 0.995602i | \(0.529866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 8.06918 | + | 30.1146i | 0.290416 | + | 1.08385i | ||||
\(773\) | 23.1822 | + | 6.21166i | 0.833806 | + | 0.223418i | 0.650374 | − | 0.759614i | \(-0.274612\pi\) |
0.183433 | + | 0.983032i | \(0.441279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.64085 | − | 22.8541i | 0.0588651 | − | 0.819884i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.1769 | + | 18.0000i | 1.11703 | + | 0.644917i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | + | 31.1769i | 0.644091 | + | 1.11560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17.3205 | − | 22.0000i | 0.618590 | − | 0.785714i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.84701 | − | 10.6252i | 0.101485 | − | 0.378747i | −0.896438 | − | 0.443170i | \(-0.853854\pi\) |
0.997923 | + | 0.0644227i | \(0.0205206\pi\) | |||||||
\(788\) | −5.37945 | + | 20.0764i | −0.191635 | + | 0.715192i | ||||
\(789\) | 15.5885 | − | 27.0000i | 0.554964 | − | 0.961225i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | − | 20.7846i | −0.640006 | − | 0.739016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.7303 | + | 4.48288i | −0.594111 | + | 0.159192i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.0000 | − | 19.0526i | −1.16965 | − | 0.675300i | ||||
\(797\) | −8.48528 | − | 8.48528i | −0.300564 | − | 0.300564i | 0.540670 | − | 0.841235i | \(-0.318171\pi\) |
−0.841235 | + | 0.540670i | \(0.818171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000i | 1.27359i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | + | 5.19615i | −0.317999 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.55291 | − | 5.79555i | −0.0548012 | − | 0.204521i | ||||
\(804\) | −6.92820 | −0.244339 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.37945 | − | 20.0764i | −0.189366 | − | 0.706722i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.7846 | + | 12.0000i | −0.730748 | + | 0.421898i | −0.818696 | − | 0.574228i | \(-0.805302\pi\) |
0.0879478 | + | 0.996125i | \(0.471969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 39.8372i | − | 1.39887i | −0.714695 | − | 0.699436i | \(-0.753435\pi\) | ||
0.714695 | − | 0.699436i | \(-0.246565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0454 | + | 22.0454i | 0.773166 | + | 0.773166i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.0000 | + | 20.7846i | 0.420084 | + | 0.727607i | ||||
\(817\) | −17.3867 | + | 4.65874i | −0.608282 | + | 0.162989i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.19615 | − | 1.00000i | 0.181568 | − | 0.0349428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | − | 20.7846i | 0.418803 | − | 0.725388i | −0.577016 | − | 0.816733i | \(-0.695783\pi\) |
0.995819 | + | 0.0913446i | \(0.0291165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3106 | + | 38.4797i | −0.359406 | + | 1.34132i | 0.515443 | + | 0.856924i | \(0.327627\pi\) |
−0.874849 | + | 0.484396i | \(0.839039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.0454 | + | 22.0454i | −0.766594 | + | 0.766594i | −0.977505 | − | 0.210911i | \(-0.932357\pi\) |
0.210911 | + | 0.977505i | \(0.432357\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.33013 | − | 7.50000i | −0.150392 | − | 0.260486i | 0.780980 | − | 0.624556i | \(-0.214720\pi\) |
−0.931371 | + | 0.364070i | \(0.881387\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | + | 6.92820i | 0.416275 | + | 0.240337i | ||||
\(832\) | 11.3137 | + | 11.3137i | 0.392232 | + | 0.392232i | ||||
\(833\) | 16.5545 | − | 38.5999i | 0.573578 | − | 1.33741i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 36.0000 | − | 20.7846i | 1.24509 | − | 0.718851i | ||||
\(837\) | 5.01910 | + | 1.34486i | 0.173485 | + | 0.0464853i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.1769 | −1.07635 | −0.538173 | − | 0.842834i | \(-0.680885\pi\) | ||||
−0.538173 | + | 0.842834i | \(0.680885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.79555 | + | 1.55291i | 0.199610 | + | 0.0534852i | ||||
\(844\) | 12.1244 | − | 7.00000i | 0.417338 | − | 0.240950i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.0891 | − | 54.7668i | 1.27440 | − | 1.88181i | ||||
\(848\) | −29.3939 | − | 29.3939i | −1.00939 | − | 1.00939i | ||||
\(849\) | 13.8564 | + | 8.00000i | 0.475551 | + | 0.274559i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 11.5911 | − | 3.10583i | 0.397105 | − | 0.106404i | ||||
\(853\) | 13.4350 | − | 13.4350i | 0.460007 | − | 0.460007i | −0.438651 | − | 0.898658i | \(-0.644544\pi\) |
0.898658 | + | 0.438651i | \(0.144544\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.21166 | + | 23.1822i | −0.212186 | + | 0.791890i | 0.774952 | + | 0.632020i | \(0.217774\pi\) |
−0.987138 | + | 0.159869i | \(0.948893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.19615 | + | 9.00000i | −0.177290 | + | 0.307076i | −0.940952 | − | 0.338541i | \(-0.890067\pi\) |
0.763661 | + | 0.645617i | \(0.223400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.00000 | − | 25.9808i | 0.306719 | − | 0.885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.1146 | + | 8.06918i | −1.02511 | + | 0.274678i | −0.731931 | − | 0.681379i | \(-0.761381\pi\) |
−0.293181 | + | 0.956057i | \(0.594714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4350 | + | 13.4350i | 0.456278 | + | 0.456278i | ||||
\(868\) | 15.4176 | − | 22.7661i | 0.523309 | − | 0.772732i | ||||
\(869\) | 30.0000i | 1.01768i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | + | 3.46410i | −0.203302 | + | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.36465 | + | 12.5570i | 0.113876 | + | 0.424991i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 5.82774 | + | 21.7494i | 0.196789 | + | 0.734426i | 0.991797 | + | 0.127827i | \(0.0408001\pi\) |
−0.795008 | + | 0.606599i | \(0.792533\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5885 | − | 9.00000i | 0.525786 | − | 0.303562i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.3923i | − | 0.350126i | −0.984557 | − | 0.175063i | \(-0.943987\pi\) | ||
0.984557 | − | 0.175063i | \(-0.0560129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.44949 | − | 2.44949i | −0.0824319 | − | 0.0824319i | 0.664689 | − | 0.747121i | \(-0.268564\pi\) |
−0.747121 | + | 0.664689i | \(0.768564\pi\) | |||||||
\(884\) | 20.7846 | + | 12.0000i | 0.699062 | + | 0.403604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.3867 | − | 4.65874i | 0.583787 | − | 0.156425i | 0.0451749 | − | 0.998979i | \(-0.485615\pi\) |
0.538612 | + | 0.842554i | \(0.318949\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.2487 | + | 21.0000i | −0.813276 | + | 0.704317i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | − | 5.19615i | 0.100504 | − | 0.174078i | ||||
\(892\) | 2.58819 | − | 9.65926i | 0.0866590 | − | 0.323416i | ||||
\(893\) | 5.37945 | − | 20.0764i | 0.180017 | − | 0.671831i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.0000 | − | 31.1769i | −1.79900 | − | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00361 | + | 12.3676i | 0.199787 | + | 0.411567i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.67303 | − | 0.448288i | −0.0555521 | − | 0.0148851i | 0.230936 | − | 0.972969i | \(-0.425821\pi\) |
−0.286488 | + | 0.958084i | \(0.592488\pi\) | |||||||
\(908\) | −3.10583 | − | 11.5911i | −0.103071 | − | 0.384664i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | −3.58630 | − | 13.3843i | −0.118754 | − | 0.443197i | ||||
\(913\) | −34.7733 | − | 9.31749i | −1.15083 | − | 0.308364i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | −22.7661 | − | 15.4176i | −0.751803 | − | 0.509136i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.6506 | + | 12.5000i | 0.714189 | + | 0.412337i | 0.812610 | − | 0.582808i | \(-0.198046\pi\) |
−0.0984214 | + | 0.995145i | \(0.531379\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.50000 | + | 6.06218i | 0.115329 | + | 0.199756i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.48528 | − | 8.48528i | 0.279296 | − | 0.279296i | ||||
\(924\) | −20.7846 | − | 24.0000i | −0.683763 | − | 0.789542i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.81173 | + | 6.76148i | −0.0595051 | + | 0.222076i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.19615 | − | 9.00000i | 0.170480 | − | 0.295280i | −0.768108 | − | 0.640321i | \(-0.778801\pi\) |
0.938588 | + | 0.345040i | \(0.112135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0000 | + | 19.0526i | −0.491605 | + | 0.624422i | ||||
\(932\) | −29.3939 | + | 29.3939i | −0.962828 | + | 0.962828i | ||||
\(933\) | −20.0764 | + | 5.37945i | −0.657272 | + | 0.176115i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.5061 | − | 20.5061i | −0.669905 | − | 0.669905i | 0.287789 | − | 0.957694i | \(-0.407080\pi\) |
−0.957694 | + | 0.287789i | \(0.907080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0000i | 0.620042i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0000 | + | 15.5885i | −0.880175 | + | 0.508169i | −0.870716 | − | 0.491786i | \(-0.836344\pi\) |
−0.00945879 | + | 0.999955i | \(0.503011\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 41.5692 | 1.35296 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.68973 | + | 10.0382i | 0.0874044 | + | 0.326198i | 0.995759 | − | 0.0920040i | \(-0.0293273\pi\) |
−0.908354 | + | 0.418202i | \(0.862661\pi\) | |||||||
\(948\) | 9.65926 | + | 2.58819i | 0.313718 | + | 0.0840605i | ||||
\(949\) | −1.73205 | + | 1.00000i | −0.0562247 | + | 0.0324614i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.3923i | 0.336994i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.0000 | − | 31.1769i | −0.582162 | − | 1.00833i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.9615 | − | 18.0000i | −1.67793 | − | 0.581250i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | + | 3.46410i | −0.0645161 | + | 0.111745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.0526 | − | 33.0000i | 0.613642 | − | 1.06286i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.6186 | + | 30.6186i | −0.984628 | + | 0.984628i | −0.999884 | − | 0.0152551i | \(-0.995144\pi\) |
0.0152551 | + | 0.999884i | \(0.495144\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.3923 | − | 18.0000i | −0.333849 | − | 0.578243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | + | 10.3923i | 0.577647 | + | 0.333505i | 0.760198 | − | 0.649692i | \(-0.225102\pi\) |
−0.182550 | + | 0.983196i | \(0.558435\pi\) | |||||||
\(972\) | −1.41421 | − | 1.41421i | −0.0453609 | − | 0.0453609i | ||||
\(973\) | 4.57081 | + | 0.328169i | 0.146533 | + | 0.0105206i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.0000 | − | 17.3205i | 0.960277 | − | 0.554416i | ||||
\(977\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.3538 | 1.99284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.5689 | + | 10.8704i | 1.29395 | + | 0.346712i | 0.839158 | − | 0.543888i | \(-0.183048\pi\) |
0.454788 | + | 0.890600i | \(0.349715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.8338 | − | 1.13681i | −0.503994 | − | 0.0361851i | ||||
\(988\) | −9.79796 | − | 9.79796i | −0.311715 | − | 0.311715i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.5000 | + | 25.1147i | 0.460608 | + | 0.797796i | 0.998991 | − | 0.0449040i | \(-0.0142982\pi\) |
−0.538384 | + | 0.842700i | \(0.680965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.53553 | + | 3.53553i | −0.112197 | + | 0.112197i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | + | 10.3923i | −0.190117 | + | 0.329293i | ||||
\(997\) | −1.29410 | + | 4.82963i | −0.0409844 | + | 0.152956i | −0.983386 | − | 0.181529i | \(-0.941896\pi\) |
0.942401 | + | 0.334484i | \(0.108562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.33013 | + | 7.50000i | −0.136999 | + | 0.237289i |
(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 | 525.2.bc.a.418.1 | yes | 8 | |
5.2 | odd | 4 | inner | 525.2.bc.a.82.1 | ✓ | 8 | |
5.3 | odd | 4 | inner | 525.2.bc.a.82.2 | yes | 8 | |
5.4 | even | 2 | inner | 525.2.bc.a.418.2 | yes | 8 | |
7.3 | odd | 6 | inner | 525.2.bc.a.493.1 | yes | 8 | |
35.3 | even | 12 | inner | 525.2.bc.a.157.2 | yes | 8 | |
35.17 | even | 12 | inner | 525.2.bc.a.157.1 | yes | 8 | |
35.24 | odd | 6 | inner | 525.2.bc.a.493.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bc.a.82.1 | ✓ | 8 | 5.2 | odd | 4 | inner | |
525.2.bc.a.82.2 | yes | 8 | 5.3 | odd | 4 | inner | |
525.2.bc.a.157.1 | yes | 8 | 35.17 | even | 12 | inner | |
525.2.bc.a.157.2 | yes | 8 | 35.3 | even | 12 | inner | |
525.2.bc.a.418.1 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.bc.a.418.2 | yes | 8 | 5.4 | even | 2 | inner | |
525.2.bc.a.493.1 | yes | 8 | 7.3 | odd | 6 | inner | |
525.2.bc.a.493.2 | yes | 8 | 35.24 | odd | 6 | inner |