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 | 82.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.82 |
Dual form | 525.2.bc.a.493.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | 0.258819 | − | 0.965926i | 0.149429 | − | 0.557678i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.189469 | + | 2.63896i | −0.0716124 | + | 0.997433i | ||||
\(8\) | 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 | \(-0.526448\pi\) | |||||||
\(12\) | 0.517638 | + | 1.93185i | 0.149429 | + | 0.557678i | ||||
\(13\) | −1.41421 | − | 1.41421i | −0.392232 | − | 0.392232i | 0.483250 | − | 0.875482i | \(-0.339456\pi\) |
−0.875482 | + | 0.483250i | \(0.839456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −5.79555 | − | 1.55291i | −1.40563 | − | 0.376637i | −0.525266 | − | 0.850938i | \(-0.676034\pi\) |
−0.880363 | + | 0.474301i | \(0.842701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205 | − | 3.00000i | 0.397360 | − | 0.688247i | −0.596040 | − | 0.802955i | \(-0.703260\pi\) |
0.993399 | + | 0.114708i | \(0.0365932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | + | 0.866025i | 0.545545 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −2.31079 | − | 4.76028i | −0.436698 | − | 0.899608i | ||||
\(29\) | 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 | ||||||||
\(33\) | −5.79555 | + | 1.55291i | −1.00888 | + | 0.270328i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | −8.36516 | + | 2.24144i | −1.37522 | + | 0.368490i | −0.869384 | − | 0.494137i | \(-0.835484\pi\) |
−0.505840 | + | 0.862627i | \(0.668817\pi\) | |||||||
\(38\) | 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 | \(-0.879672\pi\) |
0.369082 | + | 0.929397i | \(0.379672\pi\) | |||||||
\(44\) | 10.3923 | + | 6.00000i | 1.56670 | + | 0.904534i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.55291 | + | 5.79555i | 0.226516 | + | 0.845369i | 0.981792 | + | 0.189961i | \(0.0608363\pi\) |
−0.755276 | + | 0.655407i | \(0.772497\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | 3.86370 | + | 1.03528i | 0.535799 | + | 0.143567i | ||||
\(53\) | 10.0382 | + | 2.68973i | 1.37885 | + | 0.369462i | 0.870704 | − | 0.491807i | \(-0.163664\pi\) |
0.508148 | + | 0.861270i | \(0.330330\pi\) | |||||||
\(54\) | 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 | \(-0.930171\pi\) |
0.299552 | − | 0.954080i | \(-0.403163\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 1.48356 | − | 2.19067i | 0.186911 | − | 0.275999i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.896575 | − | 3.34607i | 0.109534 | − | 0.408787i | −0.889286 | − | 0.457352i | \(-0.848798\pi\) |
0.998820 | + | 0.0485648i | \(0.0154647\pi\) | |||||||
\(68\) | 11.5911 | − | 3.10583i | 1.40563 | − | 0.376637i | ||||
\(69\) | 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 | ||||||||
\(73\) | −0.258819 | + | 0.965926i | −0.0302925 | + | 0.113053i | −0.979417 | − | 0.201849i | \(-0.935305\pi\) |
0.949124 | + | 0.314902i | \(0.101972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.92820i | 0.794719i | ||||||||
\(77\) | 14.2808 | − | 6.93237i | 1.62745 | − | 0.790017i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.33013 | + | 2.50000i | 0.487177 | + | 0.281272i | 0.723403 | − | 0.690426i | \(-0.242577\pi\) |
−0.236225 | + | 0.971698i | \(0.575910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.24264 | + | 4.24264i | 0.465690 | + | 0.465690i | 0.900515 | − | 0.434825i | \(-0.143190\pi\) |
−0.434825 | + | 0.900515i | \(0.643190\pi\) | |||||||
\(84\) | −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 | \(-0.647659\pi\) |
0.998218 | − | 0.0596775i | \(-0.0190072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 3.46410i | 0.419314 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.34486 | + | 5.01910i | 0.139456 | + | 0.520456i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.19239 | − | 9.19239i | 0.933346 | − | 0.933346i | −0.0645677 | − | 0.997913i | \(-0.520567\pi\) |
0.997913 | + | 0.0645677i | \(0.0205669\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | −6.76148 | + | 1.81173i | −0.666228 | + | 0.178515i | −0.576055 | − | 0.817411i | \(-0.695409\pi\) |
−0.0901732 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(108\) | 0.517638 | − | 1.93185i | 0.0498097 | − | 0.185893i | ||||
\(109\) | −8.66025 | + | 5.00000i | −0.829502 | + | 0.478913i | −0.853682 | − | 0.520794i | \(-0.825636\pi\) |
0.0241802 | + | 0.999708i | \(0.492302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.66025i | 0.821995i | ||||||||
\(112\) | 8.76268 | + | 5.93426i | 0.827996 | + | 0.560734i | ||||
\(113\) | −7.34847 | + | 7.34847i | −0.691286 | + | 0.691286i | −0.962515 | − | 0.271229i | \(-0.912570\pi\) |
0.271229 | + | 0.962515i | \(0.412570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.517638 | + | 1.93185i | 0.0478557 | + | 0.178600i | ||||
\(118\) | 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 | ||||||||
\(123\) | −10.0382 | − | 2.68973i | −0.905114 | − | 0.242524i | ||||
\(124\) | 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 | \(-0.430794\pi\) |
−0.976458 | + | 0.215708i | \(0.930794\pi\) | |||||||
\(128\) | 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 | ||||
\(133\) | 7.58871 | + | 5.13922i | 0.658024 | + | 0.445627i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.37945 | − | 20.0764i | 0.459598 | − | 1.71524i | −0.214610 | − | 0.976700i | \(-0.568848\pi\) |
0.674207 | − | 0.738542i | \(-0.264485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.73205 | 0.146911 | 0.0734553 | − | 0.997299i | \(-0.476597\pi\) | ||||
0.0734553 | + | 0.997299i | \(0.476597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.10583 | + | 11.5911i | −0.259722 | + | 0.969297i | ||||
\(144\) | −3.46410 | + | 2.00000i | −0.288675 | + | 0.166667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.75908 | + | 6.43331i | −0.227565 | + | 0.530611i | ||||
\(148\) | 12.2474 | − | 12.2474i | 1.00673 | − | 1.00673i | ||||
\(149\) | 10.3923 | + | 6.00000i | 0.851371 | + | 0.491539i | 0.861113 | − | 0.508413i | \(-0.169768\pi\) |
−0.00974235 | + | 0.999953i | \(0.503101\pi\) | |||||||
\(150\) | 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 | ||||
\(157\) | −6.76148 | − | 1.81173i | −0.539625 | − | 0.144592i | −0.0212957 | − | 0.999773i | \(-0.506779\pi\) |
−0.518329 | + | 0.855181i | \(0.673446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.19615 | − | 9.00000i | 0.412082 | − | 0.713746i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.24144 | + | 8.36516i | 0.175563 | + | 0.655210i | 0.996455 | + | 0.0841267i | \(0.0268101\pi\) |
−0.820892 | + | 0.571083i | \(0.806523\pi\) | |||||||
\(164\) | 10.3923 | + | 18.0000i | 0.811503 | + | 1.40556i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.48528 | + | 8.48528i | −0.656611 | + | 0.656611i | −0.954577 | − | 0.297966i | \(-0.903692\pi\) |
0.297966 | + | 0.954577i | \(0.403692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.00000i | − | 0.692308i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 1.73205i | −0.229416 | + | 0.132453i | ||||
\(172\) | 2.68973 | − | 10.0382i | 0.205090 | − | 0.765405i | ||||
\(173\) | 17.3867 | − | 4.65874i | 1.32188 | − | 0.354198i | 0.472200 | − | 0.881491i | \(-0.343460\pi\) |
0.849683 | + | 0.527294i | \(0.176793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −24.0000 | −1.80907 | ||||||||
\(177\) | −10.0382 | + | 2.68973i | −0.754517 | + | 0.202172i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.7846 | + | 12.0000i | −1.55351 | + | 0.896922i | −0.555663 | + | 0.831408i | \(0.687536\pi\) |
−0.997852 | + | 0.0655145i | \(0.979131\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | 9.31749 | + | 34.7733i | 0.681362 | + | 2.54288i | ||||
\(188\) | −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 | \(0.166667\pi\) | |||||||
\(192\) | 7.72741 | + | 2.07055i | 0.557678 | + | 0.149429i | ||||
\(193\) | −15.0573 | − | 4.03459i | −1.08385 | − | 0.290416i | −0.327677 | − | 0.944790i | \(-0.606266\pi\) |
−0.756171 | + | 0.654374i | \(0.772932\pi\) | |||||||
\(194\) | 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 | \(-0.129286\pi\) |
−0.395087 | + | 0.918644i | \(0.629286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.52628 | + | 16.5000i | 0.675300 | + | 1.16965i | 0.976381 | + | 0.216055i | \(0.0693192\pi\) |
−0.301081 | + | 0.953599i | \(0.597347\pi\) | |||||||
\(200\) | 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 | ||||||||
\(208\) | −7.72741 | + | 2.07055i | −0.535799 | + | 0.143567i | ||||
\(209\) | −20.7846 | −1.43770 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.00000 | 0.481900 | 0.240950 | − | 0.970538i | \(-0.422541\pi\) | ||||
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(212\) | −20.0764 | + | 5.37945i | −1.37885 | + | 0.369462i | ||||
\(213\) | −1.55291 | + | 5.79555i | −0.106404 | + | 0.397105i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00361 | − | 12.3676i | −0.407551 | − | 0.839565i | ||||
\(218\) | 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 | 0.815506 | − | 0.578749i | \(-0.196459\pi\) |
−0.578749 | + | 0.815506i | \(0.696459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.79555 | − | 1.55291i | −0.384664 | − | 0.103071i | 0.0613041 | − | 0.998119i | \(-0.480474\pi\) |
−0.445969 | + | 0.895049i | \(0.647141\pi\) | |||||||
\(228\) | 6.69213 | + | 1.79315i | 0.443197 | + | 0.118754i | ||||
\(229\) | 3.46410 | − | 6.00000i | 0.228914 | − | 0.396491i | −0.728572 | − | 0.684969i | \(-0.759816\pi\) |
0.957487 | + | 0.288478i | \(0.0931491\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | − | 15.5885i | −0.197386 | − | 1.02565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.37945 | − | 20.0764i | −0.352420 | − | 1.31525i | −0.883701 | − | 0.468052i | \(-0.844956\pi\) |
0.531281 | − | 0.847196i | \(-0.321711\pi\) | |||||||
\(234\) | 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 | \(0.197793\pi\) | ||||
−0.813073 | + | 0.582162i | \(0.802207\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 0.965926 | − | 0.258819i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | −17.3205 | −1.10883 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.69213 | + | 1.79315i | −0.425810 | + | 0.114095i | ||||
\(248\) | 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 | \(-0.227735\pi\) | |||||||
\(252\) | −0.378937 | + | 5.27792i | −0.0238708 | + | 0.332478i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −1.55291 | − | 5.79555i | −0.0968681 | − | 0.361517i | 0.900428 | − | 0.435005i | \(-0.143253\pi\) |
−0.997296 | + | 0.0734884i | \(0.976587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.33013 | − | 22.5000i | −0.269061 | − | 1.39808i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.1146 | − | 8.06918i | −1.85694 | − | 0.497567i | −0.857100 | − | 0.515151i | \(-0.827736\pi\) |
−0.999845 | + | 0.0175838i | \(0.994403\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.34847 | − | 7.34847i | −0.449719 | − | 0.449719i | ||||
\(268\) | 1.79315 | + | 6.69213i | 0.109534 | + | 0.408787i | ||||
\(269\) | −10.3923 | − | 18.0000i | −0.633630 | − | 1.09748i | −0.986804 | − | 0.161922i | \(-0.948231\pi\) |
0.353174 | − | 0.935558i | \(-0.385102\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | −2.31079 | − | 4.76028i | −0.139855 | − | 0.288105i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.58630 | + | 13.3843i | −0.215480 | + | 0.804182i | 0.770517 | + | 0.637419i | \(0.219998\pi\) |
−0.985997 | + | 0.166763i | \(0.946669\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 4.14110 | − | 15.4548i | 0.246163 | − | 0.918693i | −0.726632 | − | 0.687027i | \(-0.758916\pi\) |
0.972795 | − | 0.231667i | \(-0.0744178\pi\) | |||||||
\(284\) | 10.3923 | − | 6.00000i | 0.616670 | − | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.4249 | + | 1.96902i | 1.61884 | + | 0.116227i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4545 | + | 9.50000i | 0.967911 | + | 0.558824i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.50000 | − | 11.2583i | −0.381037 | − | 0.659975i | ||||
\(292\) | −0.517638 | − | 1.93185i | −0.0302925 | − | 0.113053i | ||||
\(293\) | −12.7279 | − | 12.7279i | −0.743573 | − | 0.743573i | 0.229691 | − | 0.973264i | \(-0.426229\pi\) |
−0.973264 | + | 0.229691i | \(0.926229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.79555 | + | 1.55291i | 0.336292 | + | 0.0901092i | ||||
\(298\) | 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 | −0.834104 | − | 0.551607i | \(-0.814015\pi\) |
0.551607 | + | 0.834104i | \(0.314015\pi\) | |||||||
\(308\) | −17.8028 | + | 26.2880i | −1.01441 | + | 1.49790i | ||||
\(309\) | 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 | ||||||||
\(313\) | 18.3526 | − | 4.91756i | 1.03735 | − | 0.277957i | 0.300335 | − | 0.953834i | \(-0.402902\pi\) |
0.737015 | + | 0.675877i | \(0.236235\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −10.0382 | + | 2.68973i | −0.563801 | + | 0.151070i | −0.529452 | − | 0.848340i | \(-0.677602\pi\) |
−0.0343491 | + | 0.999410i | \(0.510936\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 2.58819 | + | 9.65926i | 0.143127 | + | 0.534158i | ||||
\(328\) | 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 | \(0.122788\pi\) | |||||||
\(332\) | −11.5911 | − | 3.10583i | −0.636145 | − | 0.170454i | ||||
\(333\) | 8.36516 | + | 2.24144i | 0.458408 | + | 0.122830i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.00000 | − | 6.92820i | 0.436436 | − | 0.377964i | ||||
\(337\) | −18.3712 | − | 18.3712i | −1.00074 | − | 1.00074i | −1.00000 | 0.000741840i | \(-0.999764\pi\) | |
−0.000741840 | − | 1.00000i | \(-0.500236\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 3.95164 | − | 18.0938i | 0.213368 | − | 0.976972i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.68973 | + | 10.0382i | −0.144392 | + | 0.538879i | 0.855390 | + | 0.517985i | \(0.173318\pi\) |
−0.999782 | + | 0.0208935i | \(0.993349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.7846 | 1.11257 | 0.556287 | − | 0.830990i | \(-0.312225\pi\) | ||||
0.556287 | + | 0.830990i | \(0.312225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.31749 | − | 34.7733i | 0.495920 | − | 1.85080i | −0.0288971 | − | 0.999582i | \(-0.509200\pi\) |
0.524817 | − | 0.851215i | \(-0.324134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.7846i | 1.10158i | ||||||||
\(357\) | −13.1440 | − | 8.90138i | −0.695656 | − | 0.471111i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.5885 | − | 9.00000i | −0.822727 | − | 0.475002i | 0.0286287 | − | 0.999590i | \(-0.490886\pi\) |
−0.851356 | + | 0.524588i | \(0.824219\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 16.4207 | + | 4.39992i | 0.857156 | + | 0.229674i | 0.660526 | − | 0.750804i | \(-0.270334\pi\) |
0.196630 | + | 0.980478i | \(0.437000\pi\) | |||||||
\(368\) | 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 | ||||
\(373\) | 1.79315 | + | 6.69213i | 0.0928458 | + | 0.346505i | 0.996684 | − | 0.0813690i | \(-0.0259292\pi\) |
−0.903838 | + | 0.427874i | \(0.859263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000i | 1.43826i | 0.694874 | + | 0.719132i | \(0.255460\pi\) | ||||
−0.694874 | + | 0.719132i | \(0.744540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5000 | + | 6.06218i | −0.537931 | + | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.1822 | + | 6.21166i | −1.18456 | + | 0.317401i | −0.796732 | − | 0.604333i | \(-0.793440\pi\) |
−0.387824 | + | 0.921733i | \(0.626773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.01910 | − | 1.34486i | 0.255135 | − | 0.0683632i | ||||
\(388\) | −6.72930 | + | 25.1141i | −0.341628 | + | 1.27497i | ||||
\(389\) | 5.19615 | − | 3.00000i | 0.263455 | − | 0.152106i | −0.362454 | − | 0.932002i | \(-0.618061\pi\) |
0.625910 | + | 0.779895i | \(0.284728\pi\) | |||||||
\(390\) | 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 | ||||
\(397\) | −1.81173 | − | 6.76148i | −0.0909283 | − | 0.339349i | 0.905442 | − | 0.424469i | \(-0.139539\pi\) |
−0.996371 | + | 0.0851201i | \(0.972873\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 10.0382 | + | 2.68973i | 0.500038 | + | 0.133985i | ||||
\(404\) | 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 | 0.938871 | − | 0.344270i | \(-0.111874\pi\) |
−0.767582 | + | 0.640951i | \(0.778540\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | − | 10.3923i | −0.887875 | − | 0.512615i | ||||
\(412\) | 9.89949 | − | 9.89949i | 0.487713 | − | 0.487713i | ||||
\(413\) | 24.7351 | − | 12.0072i | 1.21714 | − | 0.590836i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.448288 | − | 1.67303i | 0.0219527 | − | 0.0819288i | ||||
\(418\) | 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 | ||||||||
\(423\) | 1.55291 | − | 5.79555i | 0.0755053 | − | 0.281790i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8480 | + | 18.9718i | −0.621760 | + | 0.918108i | ||||
\(428\) | 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 | \(0.740007\pi\) | |||||||
\(432\) | 1.03528 | + | 3.86370i | 0.0498097 | + | 0.185893i | ||||
\(433\) | 20.5061 | + | 20.5061i | 0.985460 | + | 0.985460i | 0.999896 | − | 0.0144357i | \(-0.00459518\pi\) |
−0.0144357 | + | 0.999896i | \(0.504595\pi\) | |||||||
\(434\) | 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 | −0.950662 | − | 0.310228i | \(-0.899595\pi\) |
0.743996 | + | 0.668184i | \(0.232928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.68973 | + | 10.0382i | 0.127793 | + | 0.476929i | 0.999924 | − | 0.0123433i | \(-0.00392908\pi\) |
−0.872131 | + | 0.489272i | \(0.837262\pi\) | |||||||
\(444\) | −8.66025 | − | 15.0000i | −0.410997 | − | 0.711868i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.48528 | − | 8.48528i | 0.401340 | − | 0.401340i | ||||
\(448\) | −21.1117 | − | 1.51575i | −0.997433 | − | 0.0716124i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −54.0000 | + | 31.1769i | −2.54276 | + | 1.46806i | ||||
\(452\) | 5.37945 | − | 20.0764i | 0.253028 | − | 0.944314i | ||||
\(453\) | −4.82963 | + | 1.29410i | −0.226916 | + | 0.0608019i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.4034 | − | 4.93117i | 0.860873 | − | 0.230670i | 0.198736 | − | 0.980053i | \(-0.436316\pi\) |
0.662137 | + | 0.749383i | \(0.269650\pi\) | |||||||
\(458\) | 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 | \(-0.762815\pi\) |
0.678074 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.76457 | − | 28.9778i | −0.359302 | − | 1.34093i | −0.874984 | − | 0.484152i | \(-0.839128\pi\) |
0.515683 | − | 0.856780i | \(-0.327538\pi\) | |||||||
\(468\) | −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 | ||||||||
\(473\) | 30.1146 | + | 8.06918i | 1.38467 | + | 0.371021i | ||||
\(474\) | 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 | 0.999585 | − | 0.0288165i | \(-0.00917385\pi\) |
−0.524748 | + | 0.851258i | \(0.675841\pi\) | |||||||
\(480\) | 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 | ||||||||
\(487\) | 9.41404 | − | 35.1337i | 0.426591 | − | 1.59206i | −0.333833 | − | 0.942632i | \(-0.608342\pi\) |
0.760424 | − | 0.649427i | \(-0.224991\pi\) | |||||||
\(488\) | 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 | \(0.412720\pi\) | |||||||
\(492\) | 20.0764 | − | 5.37945i | 0.905114 | − | 0.242524i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.7846i | 0.933257i | ||||||||
\(497\) | 1.13681 | − | 15.8338i | 0.0509930 | − | 0.710241i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3205 | − | 10.0000i | −0.775372 | − | 0.447661i | 0.0594153 | − | 0.998233i | \(-0.481076\pi\) |
−0.834788 | + | 0.550572i | \(0.814410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | + | 10.3923i | 0.268060 | + | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | − | 25.4558i | −1.13502 | − | 1.13502i | −0.989330 | − | 0.145690i | \(-0.953460\pi\) |
−0.145690 | − | 0.989330i | \(-0.546540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.69333 | − | 2.32937i | −0.386084 | − | 0.103451i | ||||
\(508\) | 23.4225 | + | 6.27603i | 1.03920 | + | 0.278454i | ||||
\(509\) | 5.19615 | − | 9.00000i | 0.230315 | − | 0.398918i | −0.727586 | − | 0.686017i | \(-0.759358\pi\) |
0.957901 | + | 0.287099i | \(0.0926909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.50000 | − | 0.866025i | −0.110593 | − | 0.0383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.896575 | + | 3.34607i | 0.0395848 | + | 0.147732i | ||||
\(514\) | 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 | ||||||||
\(523\) | −6.76148 | + | 1.81173i | −0.295659 | + | 0.0792216i | −0.403599 | − | 0.914936i | \(-0.632241\pi\) |
0.107941 | + | 0.994157i | \(0.465574\pi\) | |||||||
\(524\) | −20.7846 | −0.907980 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.1146 | − | 8.06918i | 1.31181 | − | 0.351499i | ||||
\(528\) | −6.21166 | + | 23.1822i | −0.270328 | + | 1.00888i | ||||
\(529\) | 19.9186 | − | 11.5000i | 0.866025 | − | 0.500000i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3923i | 0.450988i | ||||||||
\(532\) | −18.2832 | − | 1.31268i | −0.792679 | − | 0.0569118i | ||||
\(533\) | −14.6969 | + | 14.6969i | −0.636595 | + | 0.636595i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.21166 | + | 23.1822i | 0.268053 | + | 1.00039i | ||||
\(538\) | 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 | ||||||||
\(543\) | −5.01910 | − | 1.34486i | −0.215390 | − | 0.0577136i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0454 | + | 22.0454i | 0.942594 | + | 0.942594i | 0.998439 | − | 0.0558458i | \(-0.0177855\pi\) |
−0.0558458 | + | 0.998439i | \(0.517786\pi\) | |||||||
\(548\) | 10.7589 | + | 40.1528i | 0.459598 | + | 1.71524i | ||||
\(549\) | −4.33013 | − | 7.50000i | −0.184805 | − | 0.320092i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.41782 | + | 10.9534i | −0.315438 | + | 0.465784i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00000 | + | 1.73205i | −0.127228 | + | 0.0734553i | ||||
\(557\) | −2.68973 | + | 10.0382i | −0.113967 | + | 0.425332i | −0.999208 | − | 0.0398021i | \(-0.987327\pi\) |
0.885240 | + | 0.465134i | \(0.153994\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.3923 | 0.439548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.55291 | − | 5.79555i | 0.0654475 | − | 0.244254i | −0.925450 | − | 0.378869i | \(-0.876313\pi\) |
0.990898 | + | 0.134615i | \(0.0429798\pi\) | |||||||
\(564\) | −10.3923 | + | 6.00000i | −0.437595 | + | 0.252646i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.38014 | + | 1.15539i | −0.0999565 | + | 0.0485220i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.7846 | − | 12.0000i | −0.871336 | − | 0.503066i | −0.00354413 | − | 0.999994i | \(-0.501128\pi\) |
−0.867792 | + | 0.496928i | \(0.834461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | −6.21166 | − | 23.1822i | −0.259722 | − | 0.969297i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.00000 | − | 6.92820i | 0.166667 | − | 0.288675i | ||||
\(577\) | 6.76148 | + | 1.81173i | 0.281484 | + | 0.0754234i | 0.396799 | − | 0.917906i | \(-0.370121\pi\) |
−0.115315 | + | 0.993329i | \(0.536788\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | −16.1384 | − | 60.2292i | −0.668383 | − | 2.49444i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.7279 | + | 12.7279i | −0.525338 | + | 0.525338i | −0.919179 | − | 0.393841i | \(-0.871146\pi\) |
0.393841 | + | 0.919179i | \(0.371146\pi\) | |||||||
\(588\) | −1.65445 | − | 13.9019i | −0.0682284 | − | 0.573305i | ||||
\(589\) | 18.0000i | 0.741677i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 5.19615i | 0.370211 | − | 0.213741i | ||||
\(592\) | −8.96575 | + | 33.4607i | −0.368490 | + | 1.37522i | ||||
\(593\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.0000 | −0.983078 | ||||||||
\(597\) | 18.4034 | − | 4.93117i | 0.753199 | − | 0.201819i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.3923 | + | 6.00000i | −0.424618 | + | 0.245153i | −0.697051 | − | 0.717021i | \(-0.745505\pi\) |
0.272433 | + | 0.962175i | \(0.412172\pi\) | |||||||
\(600\) | 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 | ||||||||
\(607\) | −6.47048 | − | 24.1481i | −0.262629 | − | 0.980143i | −0.963686 | − | 0.267038i | \(-0.913955\pi\) |
0.701057 | − | 0.713105i | \(-0.252712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | − | 10.3923i | 0.242734 | − | 0.420428i | ||||
\(612\) | −11.5911 | − | 3.10583i | −0.468543 | − | 0.125546i | ||||
\(613\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.34847 | + | 7.34847i | 0.295838 | + | 0.295838i | 0.839381 | − | 0.543543i | \(-0.182918\pi\) |
−0.543543 | + | 0.839381i | \(0.682918\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.3827 | − | 40.5000i | −0.939829 | − | 1.62783i | −0.765787 | − | 0.643094i | \(-0.777650\pi\) |
−0.174042 | − | 0.984738i | \(-0.555683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.7661 | + | 15.4176i | 0.912105 | + | 0.617695i | ||||
\(624\) | 8.00000i | 0.320256i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.37945 | + | 20.0764i | −0.214835 | + | 0.801774i | ||||
\(628\) | 13.5230 | − | 3.62347i | 0.539625 | − | 0.144592i | ||||
\(629\) | 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 | ||||||||
\(633\) | 1.81173 | − | 6.76148i | 0.0720099 | − | 0.268745i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 20.7846i | 0.824163i | ||||||||
\(637\) | 8.38375 | + | 11.2122i | 0.332176 | + | 0.444242i | ||||
\(638\) | 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 | 0.984434 | − | 0.175753i | \(-0.0562359\pi\) |
−0.175753 | + | 0.984434i | \(0.556236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.3867 | − | 4.65874i | −0.683540 | − | 0.183154i | −0.0996938 | − | 0.995018i | \(-0.531786\pi\) |
−0.583846 | + | 0.811864i | \(0.698453\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | −2.68973 | − | 10.0382i | −0.105257 | − | 0.392825i | 0.893117 | − | 0.449824i | \(-0.148513\pi\) |
−0.998374 | + | 0.0569993i | \(0.981847\pi\) | |||||||
\(654\) | 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 | \(0.0372840\pi\) | ||||
−0.993148 | + | 0.116863i | \(0.962716\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 11.5911 | − | 3.10583i | 0.450161 | − | 0.120620i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.21166 | − | 23.1822i | 0.240336 | − | 0.896947i | ||||
\(669\) | 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 | \(-0.674923\pi\) |
0.852766 | + | 0.522293i | \(0.174923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00000 | + | 15.5885i | 0.346154 | + | 0.599556i | ||||
\(677\) | −12.4233 | − | 46.3644i | −0.477467 | − | 1.78193i | −0.611820 | − | 0.790997i | \(-0.709562\pi\) |
0.134354 | − | 0.990933i | \(-0.457104\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 30.1146 | + | 8.06918i | 1.15230 | + | 0.308759i | 0.783888 | − | 0.620903i | \(-0.213234\pi\) |
0.368415 | + | 0.929661i | \(0.379901\pi\) | |||||||
\(684\) | 3.46410 | − | 6.00000i | 0.132453 | − | 0.229416i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.89898 | − | 4.89898i | −0.186908 | − | 0.186908i | ||||
\(688\) | 5.37945 | + | 20.0764i | 0.205090 | + | 0.765405i | ||||
\(689\) | −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 | ||||
\(693\) | −15.8338 | − | 1.13681i | −0.601474 | − | 0.0431839i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.1384 | + | 60.2292i | −0.611284 | + | 2.28134i | ||||
\(698\) | 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 | ||||||||
\(703\) | −7.76457 | + | 28.9778i | −0.292846 | + | 1.09292i | ||||
\(704\) | 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 | −0.0975728 | − | 0.995228i | \(-0.531108\pi\) |
−0.910679 | + | 0.413114i | \(0.864441\pi\) | |||||||
\(710\) | 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 | ||||
\(717\) | 17.3867 | + | 4.65874i | 0.649317 | + | 0.173984i | ||||
\(718\) | 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 | ||||||||
\(723\) | −4.93117 | − | 18.4034i | −0.183392 | − | 0.684428i | ||||
\(724\) | 5.19615 | + | 9.00000i | 0.193113 | + | 0.334482i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2843 | + | 28.2843i | −1.04901 | + | 1.04901i | −0.0502699 | + | 0.998736i | \(0.516008\pi\) |
−0.998736 | + | 0.0502699i | \(0.983992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.0000 | − | 15.5885i | 0.998631 | − | 0.576560i | ||||
\(732\) | −4.48288 | + | 16.7303i | −0.165692 | + | 0.618371i | ||||
\(733\) | −45.3985 | + | 12.1645i | −1.67683 | + | 0.449306i | −0.966940 | − | 0.255004i | \(-0.917923\pi\) |
−0.709892 | + | 0.704310i | \(0.751256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.0764 | + | 5.37945i | −0.739523 | + | 0.198155i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.866025 | + | 0.500000i | −0.0318573 | + | 0.0183928i | −0.515844 | − | 0.856683i | \(-0.672522\pi\) |
0.483987 | + | 0.875075i | \(0.339188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.92820i | 0.254514i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.55291 | − | 5.79555i | −0.0568182 | − | 0.212048i | ||||
\(748\) | −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 | \(0.230988\pi\) | |||||||
\(752\) | 23.1822 | + | 6.21166i | 0.845369 | + | 0.226516i | ||||
\(753\) | −20.0764 | − | 5.37945i | −0.731624 | − | 0.196038i | ||||
\(754\) | 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 | \(-0.429725\pi\) |
−0.975728 | + | 0.218988i | \(0.929725\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −11.5539 | − | 23.8014i | −0.418281 | − | 0.861668i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.37945 | + | 20.0764i | −0.194241 | + | 0.724916i | ||||
\(768\) | −15.4548 | + | 4.14110i | −0.557678 | + | 0.149429i | ||||
\(769\) | 5.19615 | 0.187378 | 0.0936890 | − | 0.995602i | \(-0.470134\pi\) | ||||
0.0936890 | + | 0.995602i | \(0.470134\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 30.1146 | − | 8.06918i | 1.08385 | − | 0.290416i | ||||
\(773\) | −6.21166 | + | 23.1822i | −0.223418 | + | 0.833806i | 0.759614 | + | 0.650374i | \(0.225388\pi\) |
−0.983032 | + | 0.183433i | \(0.941279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.8541 | − | 1.64085i | −0.819884 | − | 0.0588651i | ||||
\(778\) | 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 | ||||||||
\(787\) | −10.6252 | − | 2.84701i | −0.378747 | − | 0.101485i | 0.0644227 | − | 0.997923i | \(-0.479479\pi\) |
−0.443170 | + | 0.896438i | \(0.646146\pi\) | |||||||
\(788\) | −20.0764 | − | 5.37945i | −0.715192 | − | 0.191635i | ||||
\(789\) | −15.5885 | + | 27.0000i | −0.554964 | + | 0.961225i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | − | 20.7846i | −0.640006 | − | 0.739016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.48288 | − | 16.7303i | −0.159192 | − | 0.594111i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.0000 | − | 19.0526i | −1.16965 | − | 0.675300i | ||||
\(797\) | −8.48528 | + | 8.48528i | −0.300564 | + | 0.300564i | −0.841235 | − | 0.540670i | \(-0.818171\pi\) |
0.540670 | + | 0.841235i | \(0.318171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36.0000i | − | 1.27359i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | + | 5.19615i | −0.317999 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.79555 | − | 1.55291i | 0.204521 | − | 0.0548012i | ||||
\(804\) | 6.92820 | 0.244339 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.0764 | + | 5.37945i | −0.706722 | + | 0.189366i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.7846 | − | 12.0000i | 0.730748 | − | 0.421898i | −0.0879478 | − | 0.996125i | \(-0.528031\pi\) |
0.818696 | + | 0.574228i | \(0.194698\pi\) | |||||||
\(810\) | 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 | ||||
\(817\) | 4.65874 | + | 17.3867i | 0.162989 | + | 0.608282i | ||||
\(818\) | 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 | ||||||||
\(823\) | −38.4797 | − | 10.3106i | −1.34132 | − | 0.359406i | −0.484396 | − | 0.874849i | \(-0.660961\pi\) |
−0.856924 | + | 0.515443i | \(0.827627\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0454 | + | 22.0454i | 0.766594 | + | 0.766594i | 0.977505 | − | 0.210911i | \(-0.0676431\pi\) |
−0.210911 | + | 0.977505i | \(0.567643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.33013 | + | 7.50000i | 0.150392 | + | 0.260486i | 0.931371 | − | 0.364070i | \(-0.118613\pi\) |
−0.780980 | + | 0.624556i | \(0.785280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | + | 6.92820i | 0.416275 | + | 0.240337i | ||||
\(832\) | 11.3137 | − | 11.3137i | 0.392232 | − | 0.392232i | ||||
\(833\) | 38.5999 | + | 16.5545i | 1.33741 | + | 0.573578i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 36.0000 | − | 20.7846i | 1.24509 | − | 0.718851i | ||||
\(837\) | 1.34486 | − | 5.01910i | 0.0464853 | − | 0.173485i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.1769 | 1.07635 | 0.538173 | − | 0.842834i | \(-0.319115\pi\) | ||||
0.538173 | + | 0.842834i | \(0.319115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.55291 | + | 5.79555i | −0.0534852 | + | 0.199610i | ||||
\(844\) | −12.1244 | + | 7.00000i | −0.417338 | + | 0.240950i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −54.7668 | − | 37.0891i | −1.88181 | − | 1.27440i | ||||
\(848\) | 29.3939 | − | 29.3939i | 1.00939 | − | 1.00939i | ||||
\(849\) | −13.8564 | − | 8.00000i | −0.475551 | − | 0.274559i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −3.10583 | − | 11.5911i | −0.106404 | − | 0.397105i | ||||
\(853\) | 13.4350 | + | 13.4350i | 0.460007 | + | 0.460007i | 0.898658 | − | 0.438651i | \(-0.144544\pi\) |
−0.438651 | + | 0.898658i | \(0.644544\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.1822 | + | 6.21166i | 0.791890 | + | 0.212186i | 0.632020 | − | 0.774952i | \(-0.282226\pi\) |
0.159869 | + | 0.987138i | \(0.448893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.19615 | − | 9.00000i | 0.177290 | − | 0.307076i | −0.763661 | − | 0.645617i | \(-0.776600\pi\) |
0.940952 | + | 0.338541i | \(0.109933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.00000 | − | 25.9808i | 0.306719 | − | 0.885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.06918 | − | 30.1146i | −0.274678 | − | 1.02511i | −0.956057 | − | 0.293181i | \(-0.905286\pi\) |
0.681379 | − | 0.731931i | \(-0.261381\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.4350 | − | 13.4350i | 0.456278 | − | 0.456278i | ||||
\(868\) | 22.7661 | + | 15.4176i | 0.772732 | + | 0.523309i | ||||
\(869\) | − | 30.0000i | − | 1.01768i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | + | 3.46410i | −0.203302 | + | 0.117377i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.5570 | + | 3.36465i | −0.424991 | + | 0.113876i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 21.7494 | − | 5.82774i | 0.734426 | − | 0.196789i | 0.127827 | − | 0.991797i | \(-0.459200\pi\) |
0.606599 | + | 0.795008i | \(0.292533\pi\) | |||||||
\(878\) | 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 | \(-0.731436\pi\) |
0.747121 | + | 0.664689i | \(0.231436\pi\) | |||||||
\(884\) | −20.7846 | − | 12.0000i | −0.699062 | − | 0.403604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.65874 | − | 17.3867i | −0.156425 | − | 0.583787i | −0.998979 | − | 0.0451749i | \(-0.985615\pi\) |
0.842554 | − | 0.538612i | \(-0.181051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.2487 | − | 21.0000i | 0.813276 | − | 0.704317i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | − | 5.19615i | 0.100504 | − | 0.174078i | ||||
\(892\) | −9.65926 | − | 2.58819i | −0.323416 | − | 0.0866590i | ||||
\(893\) | 20.0764 | + | 5.37945i | 0.671831 | + | 0.180017i | ||||
\(894\) | 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 | ||||||||
\(903\) | −12.3676 | + | 6.00361i | −0.411567 | + | 0.199787i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.448288 | + | 1.67303i | −0.0148851 | + | 0.0555521i | −0.972969 | − | 0.230936i | \(-0.925821\pi\) |
0.958084 | + | 0.286488i | \(0.0924879\pi\) | |||||||
\(908\) | 11.5911 | − | 3.10583i | 0.384664 | − | 0.103071i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | −13.3843 | + | 3.58630i | −0.443197 | + | 0.118754i | ||||
\(913\) | 9.31749 | − | 34.7733i | 0.308364 | − | 1.15083i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | −15.4176 | + | 22.7661i | −0.509136 | + | 0.751803i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.6506 | − | 12.5000i | −0.714189 | − | 0.412337i | 0.0984214 | − | 0.995145i | \(-0.468621\pi\) |
−0.812610 | + | 0.582808i | \(0.801954\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | 6.76148 | + | 1.81173i | 0.222076 | + | 0.0595051i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.19615 | + | 9.00000i | −0.170480 | + | 0.295280i | −0.938588 | − | 0.345040i | \(-0.887865\pi\) |
0.768108 | + | 0.640321i | \(0.221199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0000 | + | 19.0526i | −0.491605 | + | 0.624422i | ||||
\(932\) | 29.3939 | + | 29.3939i | 0.962828 | + | 0.962828i | ||||
\(933\) | −5.37945 | − | 20.0764i | −0.176115 | − | 0.657272i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.5061 | + | 20.5061i | −0.669905 | + | 0.669905i | −0.957694 | − | 0.287789i | \(-0.907080\pi\) |
0.287789 | + | 0.957694i | \(0.407080\pi\) | |||||||
\(938\) | 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 | ||||||||
\(947\) | 10.0382 | − | 2.68973i | 0.326198 | − | 0.0874044i | −0.0920040 | − | 0.995759i | \(-0.529327\pi\) |
0.418202 | + | 0.908354i | \(0.362661\pi\) | |||||||
\(948\) | −2.58819 | + | 9.65926i | −0.0840605 | + | 0.313718i | ||||
\(949\) | 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 | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 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 | \(-0.00485605\pi\) |
−0.0152551 | + | 0.999884i | \(0.504856\pi\) | |||||||
\(968\) | 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 | ||||
\(973\) | −0.328169 | + | 4.57081i | −0.0105206 | + | 0.146533i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.0000 | − | 17.3205i | 0.960277 | − | 0.554416i | ||||
\(977\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.3538 | −1.99284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.8704 | + | 40.5689i | −0.346712 | + | 1.29395i | 0.543888 | + | 0.839158i | \(0.316952\pi\) |
−0.890600 | + | 0.454788i | \(0.849715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.13681 | + | 15.8338i | −0.0361851 | + | 0.503994i | ||||
\(988\) | 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 | ||||
\(997\) | 4.82963 | + | 1.29410i | 0.152956 | + | 0.0409844i | 0.334484 | − | 0.942401i | \(-0.391438\pi\) |
−0.181529 | + | 0.983386i | \(0.558104\pi\) | |||||||
\(998\) | 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.82.2 | yes | 8 | |
5.2 | odd | 4 | inner | 525.2.bc.a.418.1 | yes | 8 | |
5.3 | odd | 4 | inner | 525.2.bc.a.418.2 | yes | 8 | |
5.4 | even | 2 | inner | 525.2.bc.a.82.1 | ✓ | 8 | |
7.3 | odd | 6 | inner | 525.2.bc.a.157.2 | yes | 8 | |
35.3 | even | 12 | inner | 525.2.bc.a.493.2 | yes | 8 | |
35.17 | even | 12 | inner | 525.2.bc.a.493.1 | yes | 8 | |
35.24 | odd | 6 | inner | 525.2.bc.a.157.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bc.a.82.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
525.2.bc.a.82.2 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.bc.a.157.1 | yes | 8 | 35.24 | odd | 6 | inner | |
525.2.bc.a.157.2 | yes | 8 | 7.3 | odd | 6 | inner | |
525.2.bc.a.418.1 | yes | 8 | 5.2 | odd | 4 | inner | |
525.2.bc.a.418.2 | yes | 8 | 5.3 | odd | 4 | inner | |
525.2.bc.a.493.1 | yes | 8 | 35.17 | even | 12 | inner | |
525.2.bc.a.493.2 | yes | 8 | 35.3 | even | 12 | inner |