Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.8 | ||
Character | \(\chi\) | \(=\) | 3150.1349 |
Dual form | 3150.2.bp.h.899.8 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22849 | + | 2.34325i | 0.464326 | + | 0.885664i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.03986 | + | 1.17771i | −0.615040 | + | 0.355093i | −0.774935 | − | 0.632041i | \(-0.782218\pi\) |
0.159896 | + | 0.987134i | \(0.448884\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64698 | 1.28884 | 0.644420 | − | 0.764672i | \(-0.277099\pi\) | ||||
0.644420 | + | 0.764672i | \(0.277099\pi\) | |||||||
\(14\) | 2.64356 | + | 0.107718i | 0.706520 | + | 0.0287888i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.95097 | + | 2.28109i | −0.958250 | + | 0.553246i | −0.895634 | − | 0.444792i | \(-0.853278\pi\) |
−0.0626158 | + | 0.998038i | \(0.519944\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.491268 | − | 0.283634i | −0.112705 | − | 0.0650700i | 0.442588 | − | 0.896725i | \(-0.354060\pi\) |
−0.555293 | + | 0.831655i | \(0.687394\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.35542i | 0.502178i | ||||||||
\(23\) | −2.91324 | + | 5.04588i | −0.607453 | + | 1.05214i | 0.384206 | + | 0.923247i | \(0.374475\pi\) |
−0.991659 | + | 0.128891i | \(0.958858\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.32349 | − | 4.02440i | 0.455674 | − | 0.789250i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.41507 | − | 2.23553i | 0.267422 | − | 0.422475i | ||||
\(29\) | 2.55339i | 0.474153i | 0.971491 | + | 0.237077i | \(0.0761893\pi\) | ||||
−0.971491 | + | 0.237077i | \(0.923811\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.89659 | + | 1.09500i | −0.340638 | + | 0.196667i | −0.660554 | − | 0.750778i | \(-0.729679\pi\) |
0.319916 | + | 0.947446i | \(0.396345\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.56218i | 0.782408i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.02554 | − | 4.63355i | −1.31939 | − | 0.761750i | −0.335760 | − | 0.941948i | \(-0.608993\pi\) |
−0.983630 | + | 0.180197i | \(0.942326\pi\) | |||||||
\(38\) | −0.491268 | + | 0.283634i | −0.0796942 | + | 0.0460114i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.68451 | −1.35629 | −0.678147 | − | 0.734927i | \(-0.737217\pi\) | ||||
−0.678147 | + | 0.734927i | \(0.737217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.57695i | − | 1.00298i | −0.865165 | − | 0.501488i | \(-0.832786\pi\) | ||
0.865165 | − | 0.501488i | \(-0.167214\pi\) | |||||||
\(44\) | 2.03986 | + | 1.17771i | 0.307520 | + | 0.177547i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.91324 | + | 5.04588i | 0.429534 | + | 0.743975i | ||||
\(47\) | −5.46663 | − | 3.15616i | −0.797391 | − | 0.460374i | 0.0451673 | − | 0.998979i | \(-0.485618\pi\) |
−0.842558 | + | 0.538606i | \(0.818951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.98161 | + | 5.75732i | −0.568802 | + | 0.822475i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.32349 | − | 4.02440i | −0.322210 | − | 0.558084i | ||||
\(53\) | 6.07533 | + | 10.5228i | 0.834511 | + | 1.44542i | 0.894428 | + | 0.447212i | \(0.147583\pi\) |
−0.0599168 | + | 0.998203i | \(0.519084\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.22849 | − | 2.34325i | −0.164164 | − | 0.313130i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.21130 | + | 1.27670i | 0.290359 | + | 0.167639i | ||||
\(59\) | 1.67739 | + | 2.90532i | 0.218377 | + | 0.378241i | 0.954312 | − | 0.298812i | \(-0.0965903\pi\) |
−0.735935 | + | 0.677053i | \(0.763257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.85523 | − | 3.95787i | −0.877722 | − | 0.506753i | −0.00781543 | − | 0.999969i | \(-0.502488\pi\) |
−0.869907 | + | 0.493216i | \(0.835821\pi\) | |||||||
\(62\) | 2.18999i | 0.278130i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46657 | − | 2.00143i | 0.423509 | − | 0.244513i | −0.273068 | − | 0.961995i | \(-0.588039\pi\) |
0.696578 | + | 0.717481i | \(0.254705\pi\) | |||||||
\(68\) | 3.95097 | + | 2.28109i | 0.479125 | + | 0.276623i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.02720i | − | 0.240585i | −0.992738 | − | 0.120292i | \(-0.961617\pi\) | ||
0.992738 | − | 0.120292i | \(-0.0383832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.10801 | + | 7.11528i | 0.480806 | + | 0.832780i | 0.999757 | − | 0.0220235i | \(-0.00701086\pi\) |
−0.518952 | + | 0.854804i | \(0.673678\pi\) | |||||||
\(74\) | −8.02554 | + | 4.63355i | −0.932950 | + | 0.538639i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.567267i | 0.0650700i | ||||||||
\(77\) | −5.26562 | − | 3.33308i | −0.600073 | − | 0.379839i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.13212 | + | 7.15704i | −0.464900 | + | 0.805230i | −0.999197 | − | 0.0400666i | \(-0.987243\pi\) |
0.534297 | + | 0.845297i | \(0.320576\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.34226 | + | 7.52101i | −0.479522 | + | 0.830556i | ||||
\(83\) | − | 0.171637i | − | 0.0188396i | −0.999956 | − | 0.00941978i | \(-0.997002\pi\) | ||
0.999956 | − | 0.00941978i | \(-0.00299845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.69581 | − | 3.28848i | −0.614195 | − | 0.354606i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.03986 | − | 1.17771i | 0.217449 | − | 0.125544i | ||||
\(89\) | −2.72938 | + | 4.72742i | −0.289313 | + | 0.501105i | −0.973646 | − | 0.228065i | \(-0.926760\pi\) |
0.684333 | + | 0.729170i | \(0.260094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.70878 | + | 10.8890i | 0.598443 | + | 1.14148i | ||||
\(92\) | 5.82648 | 0.607453 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.46663 | + | 3.15616i | −0.563840 | + | 0.325533i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8564 | −1.10230 | −0.551151 | − | 0.834406i | \(-0.685811\pi\) | ||||
−0.551151 | + | 0.834406i | \(0.685811\pi\) | |||||||
\(98\) | 2.99518 | + | 6.32684i | 0.302559 | + | 0.639107i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.74827 | + | 9.95630i | 0.571975 | + | 0.990689i | 0.996363 | + | 0.0852090i | \(0.0271558\pi\) |
−0.424388 | + | 0.905480i | \(0.639511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.68690 | − | 16.7782i | 0.954478 | − | 1.65320i | 0.218920 | − | 0.975743i | \(-0.429747\pi\) |
0.735558 | − | 0.677462i | \(-0.236920\pi\) | |||||||
\(104\) | −4.64698 | −0.455674 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.1507 | 1.18018 | ||||||||
\(107\) | 5.36029 | − | 9.28430i | 0.518199 | − | 0.897547i | −0.481577 | − | 0.876404i | \(-0.659936\pi\) |
0.999776 | − | 0.0211436i | \(-0.00673071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.41186 | + | 9.37362i | 0.518363 | + | 0.897830i | 0.999772 | + | 0.0213347i | \(0.00679157\pi\) |
−0.481410 | + | 0.876496i | \(0.659875\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.64356 | − | 0.107718i | −0.249793 | − | 0.0101784i | ||||
\(113\) | −18.4343 | −1.73415 | −0.867076 | − | 0.498176i | \(-0.834003\pi\) | ||||
−0.867076 | + | 0.498176i | \(0.834003\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.21130 | − | 1.27670i | 0.205314 | − | 0.118538i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.35478 | 0.308832 | ||||||||
\(119\) | −10.1989 | − | 6.45578i | −0.934931 | − | 0.591801i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.72599 | + | 4.72156i | −0.247817 | + | 0.429232i | ||||
\(122\) | −6.85523 | + | 3.95787i | −0.620643 | + | 0.358329i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.89659 | + | 1.09500i | 0.170319 | + | 0.0983337i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.04880i | − | 0.359273i | −0.983733 | − | 0.179637i | \(-0.942508\pi\) | ||
0.983733 | − | 0.179637i | \(-0.0574922\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.14129 | + | 12.3691i | −0.623937 | + | 1.08069i | 0.364808 | + | 0.931083i | \(0.381134\pi\) |
−0.988745 | + | 0.149608i | \(0.952199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0611049 | − | 1.49960i | 0.00529846 | − | 0.130032i | ||||
\(134\) | − | 4.00285i | − | 0.345794i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.95097 | − | 2.28109i | 0.338792 | − | 0.195602i | ||||
\(137\) | 2.61421 | + | 4.52794i | 0.223347 | + | 0.386848i | 0.955822 | − | 0.293945i | \(-0.0949684\pi\) |
−0.732475 | + | 0.680794i | \(0.761635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4726i | 1.65164i | 0.563933 | + | 0.825820i | \(0.309288\pi\) | ||||
−0.563933 | + | 0.825820i | \(0.690712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.75561 | − | 1.01360i | −0.147328 | − | 0.0850596i | ||||
\(143\) | −9.47917 | + | 5.47280i | −0.792688 | + | 0.457659i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.21601 | 0.679962 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.26709i | 0.761750i | ||||||||
\(149\) | 4.79814 | + | 2.77021i | 0.393079 | + | 0.226944i | 0.683493 | − | 0.729957i | \(-0.260460\pi\) |
−0.290414 | + | 0.956901i | \(0.593793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.23984 | + | 7.34362i | 0.345033 | + | 0.597615i | 0.985360 | − | 0.170488i | \(-0.0545343\pi\) |
−0.640327 | + | 0.768103i | \(0.721201\pi\) | |||||||
\(152\) | 0.491268 | + | 0.283634i | 0.0398471 | + | 0.0230057i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.51934 | + | 2.89362i | −0.444761 | + | 0.233174i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.560470 | + | 0.970763i | 0.0447304 | + | 0.0774753i | 0.887524 | − | 0.460762i | \(-0.152424\pi\) |
−0.842793 | + | 0.538237i | \(0.819090\pi\) | |||||||
\(158\) | 4.13212 | + | 7.15704i | 0.328734 | + | 0.569384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.4026 | − | 0.627617i | −1.21390 | − | 0.0494631i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.81534 | + | 3.35749i | 0.455493 | + | 0.262979i | 0.710147 | − | 0.704053i | \(-0.248628\pi\) |
−0.254654 | + | 0.967032i | \(0.581962\pi\) | |||||||
\(164\) | 4.34226 | + | 7.52101i | 0.339073 | + | 0.587292i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.148642 | − | 0.0858183i | −0.0115368 | − | 0.00666079i | ||||
\(167\) | − | 2.80110i | − | 0.216756i | −0.994110 | − | 0.108378i | \(-0.965434\pi\) | ||
0.994110 | − | 0.108378i | \(-0.0345657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.59442 | 0.661109 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.69581 | + | 3.28848i | −0.434301 | + | 0.250744i | ||||
\(173\) | 11.9515 | + | 6.90018i | 0.908653 | + | 0.524611i | 0.879998 | − | 0.474978i | \(-0.157544\pi\) |
0.0286558 | + | 0.999589i | \(0.490877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.35542i | − | 0.177547i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.72938 | + | 4.72742i | 0.204575 | + | 0.354335i | ||||
\(179\) | 2.31980 | − | 1.33933i | 0.173390 | − | 0.100107i | −0.410794 | − | 0.911728i | \(-0.634748\pi\) |
0.584183 | + | 0.811622i | \(0.301415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.88082i | 0.511447i | 0.966750 | + | 0.255724i | \(0.0823137\pi\) | ||||
−0.966750 | + | 0.255724i | \(0.917686\pi\) | |||||||
\(182\) | 12.2846 | + | 0.500563i | 0.910592 | + | 0.0371042i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.91324 | − | 5.04588i | 0.214767 | − | 0.371987i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.37293 | − | 9.30619i | 0.392908 | − | 0.680536i | ||||
\(188\) | 6.31233i | 0.460374i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.65356 | − | 4.99614i | −0.626150 | − | 0.361508i | 0.153110 | − | 0.988209i | \(-0.451071\pi\) |
−0.779260 | + | 0.626701i | \(0.784405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.7620 | − | 12.5643i | 1.56646 | − | 0.904398i | 0.569887 | − | 0.821723i | \(-0.306987\pi\) |
0.996577 | − | 0.0826753i | \(-0.0263464\pi\) | |||||||
\(194\) | −5.42821 | + | 9.40193i | −0.389723 | + | 0.675019i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.97679 | + | 0.569517i | 0.498342 | + | 0.0406798i | ||||
\(197\) | −20.0811 | −1.43072 | −0.715359 | − | 0.698757i | \(-0.753737\pi\) | ||||
−0.715359 | + | 0.698757i | \(0.753737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3028 | − | 5.94834i | 0.730348 | − | 0.421667i | −0.0882014 | − | 0.996103i | \(-0.528112\pi\) |
0.818550 | + | 0.574436i | \(0.194779\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.4965 | 0.808894 | ||||||||
\(203\) | −5.98323 | + | 3.13683i | −0.419941 | + | 0.220162i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.68690 | − | 16.7782i | −0.674918 | − | 1.16899i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.32349 | + | 4.02440i | −0.161105 | + | 0.279042i | ||||
\(209\) | 1.33615 | 0.0924237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.78640 | −0.467195 | −0.233597 | − | 0.972333i | \(-0.575050\pi\) | ||||
−0.233597 | + | 0.972333i | \(0.575050\pi\) | |||||||
\(212\) | 6.07533 | − | 10.5228i | 0.417256 | − | 0.722708i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.36029 | − | 9.28430i | −0.366422 | − | 0.634662i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.89580 | − | 3.09899i | −0.332348 | − | 0.210373i | ||||
\(218\) | 10.8237 | 0.733075 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3601 | + | 10.6002i | −1.23503 | + | 0.713045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.7684 | 1.92648 | 0.963239 | − | 0.268646i | \(-0.0865763\pi\) | ||||
0.963239 | + | 0.268646i | \(0.0865763\pi\) | |||||||
\(224\) | −1.41507 | + | 2.23553i | −0.0945480 | + | 0.149368i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.21714 | + | 15.9646i | −0.613115 | + | 1.06195i | ||||
\(227\) | 1.82186 | − | 1.05185i | 0.120921 | − | 0.0698140i | −0.438319 | − | 0.898819i | \(-0.644426\pi\) |
0.559241 | + | 0.829005i | \(0.311093\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0269 | + | 8.09841i | 0.926920 | + | 0.535158i | 0.885836 | − | 0.463998i | \(-0.153585\pi\) |
0.0410842 | + | 0.999156i | \(0.486919\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2.55339i | − | 0.167639i | ||||||
\(233\) | 4.00569 | − | 6.93805i | 0.262421 | − | 0.454527i | −0.704464 | − | 0.709740i | \(-0.748812\pi\) |
0.966885 | + | 0.255213i | \(0.0821457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.67739 | − | 2.90532i | 0.109189 | − | 0.189120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.6903 | + | 5.60460i | −0.692950 | + | 0.363293i | ||||
\(239\) | − | 15.6233i | − | 1.01059i | −0.862947 | − | 0.505294i | \(-0.831384\pi\) | ||
0.862947 | − | 0.505294i | \(-0.168616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.54491 | + | 2.04665i | −0.228348 | + | 0.131837i | −0.609809 | − | 0.792548i | \(-0.708754\pi\) |
0.381462 | + | 0.924385i | \(0.375421\pi\) | |||||||
\(242\) | 2.72599 | + | 4.72156i | 0.175233 | + | 0.303513i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.91574i | 0.506753i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.28291 | − | 1.31804i | −0.145258 | − | 0.0838648i | ||||
\(248\) | 1.89659 | − | 1.09500i | 0.120434 | − | 0.0695324i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9413 | 1.25869 | 0.629343 | − | 0.777128i | \(-0.283324\pi\) | ||||
0.629343 | + | 0.777128i | \(0.283324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.7238i | − | 0.862810i | ||||||
\(254\) | −3.50637 | − | 2.02440i | −0.220009 | − | 0.127022i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 17.6188 | + | 10.1722i | 1.09903 | + | 0.634527i | 0.935967 | − | 0.352088i | \(-0.114528\pi\) |
0.163067 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.998233 | − | 24.4981i | 0.0620272 | − | 1.52224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.14129 | + | 12.3691i | 0.441190 | + | 0.764164i | ||||
\(263\) | −1.80801 | − | 3.13156i | −0.111487 | − | 0.193100i | 0.804883 | − | 0.593433i | \(-0.202228\pi\) |
−0.916370 | + | 0.400333i | \(0.868895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.26814 | − | 0.802720i | −0.0777548 | − | 0.0492179i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.46657 | − | 2.00143i | −0.211755 | − | 0.122257i | ||||
\(269\) | −10.6172 | − | 18.3896i | −0.647345 | − | 1.12123i | −0.983755 | − | 0.179518i | \(-0.942546\pi\) |
0.336410 | − | 0.941716i | \(-0.390787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9957 | − | 10.9672i | −1.15390 | − | 0.666207i | −0.204069 | − | 0.978956i | \(-0.565417\pi\) |
−0.949836 | + | 0.312749i | \(0.898750\pi\) | |||||||
\(272\) | − | 4.56218i | − | 0.276623i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.22842 | 0.315860 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.59880 | − | 4.96452i | 0.516652 | − | 0.298289i | −0.218912 | − | 0.975745i | \(-0.570251\pi\) |
0.735564 | + | 0.677456i | \(0.236917\pi\) | |||||||
\(278\) | 16.8637 | + | 9.73628i | 1.01142 | + | 0.583943i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0696i | 0.660358i | 0.943918 | + | 0.330179i | \(0.107109\pi\) | ||||
−0.943918 | + | 0.330179i | \(0.892891\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3387 | + | 19.6392i | 0.674014 | + | 1.16743i | 0.976756 | + | 0.214354i | \(0.0687646\pi\) |
−0.302742 | + | 0.953072i | \(0.597902\pi\) | |||||||
\(284\) | −1.75561 | + | 1.01360i | −0.104176 | + | 0.0601462i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.9456i | 0.647227i | ||||||||
\(287\) | −10.6689 | − | 20.3500i | −0.629763 | − | 1.20122i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.90675 | − | 3.30259i | 0.112162 | − | 0.194270i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.10801 | − | 7.11528i | 0.240403 | − | 0.416390i | ||||
\(293\) | − | 12.3248i | − | 0.720020i | −0.932949 | − | 0.360010i | \(-0.882773\pi\) | ||
0.932949 | − | 0.360010i | \(-0.117227\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.02554 | + | 4.63355i | 0.466475 | + | 0.269319i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.79814 | − | 2.77021i | 0.277949 | − | 0.160474i | ||||
\(299\) | −13.5378 | + | 23.4481i | −0.782909 | + | 1.35604i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4114 | − | 8.07974i | 0.888300 | − | 0.465708i | ||||
\(302\) | 8.47968 | 0.487951 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.491268 | − | 0.283634i | 0.0281761 | − | 0.0162675i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.06274 | −0.460165 | −0.230082 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230082 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(308\) | −0.253721 | + | 6.22670i | −0.0144571 | + | 0.354799i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.2215 | + | 22.9003i | 0.749721 | + | 1.29855i | 0.947956 | + | 0.318400i | \(0.103146\pi\) |
−0.198236 | + | 0.980154i | \(0.563521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.26650 | + | 14.3180i | −0.467250 | + | 0.809301i | −0.999300 | − | 0.0374122i | \(-0.988089\pi\) |
0.532050 | + | 0.846713i | \(0.321422\pi\) | |||||||
\(314\) | 1.12094 | 0.0632583 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.26424 | 0.464900 | ||||||||
\(317\) | −6.13038 | + | 10.6181i | −0.344317 | + | 0.596374i | −0.985229 | − | 0.171240i | \(-0.945223\pi\) |
0.640913 | + | 0.767614i | \(0.278556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.00716 | − | 5.20856i | −0.168369 | − | 0.291623i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.24485 | + | 13.0253i | −0.459468 | + | 0.725870i | ||||
\(323\) | 2.58798 | 0.143999 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.81534 | − | 3.35749i | 0.322082 | − | 0.185954i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.68451 | 0.479522 | ||||||||
\(329\) | 0.679951 | − | 16.6870i | 0.0374869 | − | 0.919984i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1942 | + | 29.7812i | −0.945077 | + | 1.63692i | −0.189479 | + | 0.981885i | \(0.560680\pi\) |
−0.755598 | + | 0.655036i | \(0.772654\pi\) | |||||||
\(332\) | −0.148642 | + | 0.0858183i | −0.00815777 | + | 0.00470989i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.42583 | − | 1.40055i | −0.132735 | − | 0.0766348i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9536i | 1.30484i | 0.757860 | + | 0.652418i | \(0.226245\pi\) | ||||
−0.757860 | + | 0.652418i | \(0.773755\pi\) | |||||||
\(338\) | 4.29721 | − | 7.44298i | 0.233737 | − | 0.404845i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.57918 | − | 4.46727i | 0.139671 | − | 0.241916i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3822 | − | 2.25708i | −0.992546 | − | 0.121871i | ||||
\(344\) | 6.57695i | 0.354606i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.9515 | − | 6.90018i | 0.642515 | − | 0.370956i | ||||
\(347\) | −14.3501 | − | 24.8552i | −0.770355 | − | 1.33429i | −0.937368 | − | 0.348340i | \(-0.886746\pi\) |
0.167013 | − | 0.985955i | \(-0.446588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.57176i | 0.191192i | 0.995420 | + | 0.0955960i | \(0.0304757\pi\) | ||||
−0.995420 | + | 0.0955960i | \(0.969524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.03986 | − | 1.17771i | −0.108725 | − | 0.0627722i | ||||
\(353\) | −10.8597 | + | 6.26984i | −0.578003 | + | 0.333710i | −0.760339 | − | 0.649526i | \(-0.774967\pi\) |
0.182337 | + | 0.983236i | \(0.441634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.45875 | 0.289313 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.67867i | − | 0.141572i | ||||||
\(359\) | −13.6940 | − | 7.90624i | −0.722742 | − | 0.417275i | 0.0930190 | − | 0.995664i | \(-0.470348\pi\) |
−0.815761 | + | 0.578389i | \(0.803682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.33910 | − | 16.1758i | −0.491532 | − | 0.851358i | ||||
\(362\) | 5.95896 | + | 3.44041i | 0.313196 | + | 0.180824i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.57578 | − | 10.3885i | 0.344664 | − | 0.544503i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8317 | + | 30.8855i | 0.930809 | + | 1.61221i | 0.781942 | + | 0.623351i | \(0.214229\pi\) |
0.148867 | + | 0.988857i | \(0.452437\pi\) | |||||||
\(368\) | −2.91324 | − | 5.04588i | −0.151863 | − | 0.263035i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.1940 | + | 27.1632i | −0.892667 | + | 1.41024i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.9717 | − | 11.5306i | −1.03409 | − | 0.597034i | −0.115939 | − | 0.993256i | \(-0.536988\pi\) |
−0.918155 | + | 0.396222i | \(0.870321\pi\) | |||||||
\(374\) | −5.37293 | − | 9.30619i | −0.277828 | − | 0.481212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.46663 | + | 3.15616i | 0.281920 | + | 0.162767i | ||||
\(377\) | 11.8656i | 0.611108i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.20110 | −0.421262 | −0.210631 | − | 0.977566i | \(-0.567552\pi\) | ||||
−0.210631 | + | 0.977566i | \(0.567552\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.65356 | + | 4.99614i | −0.442755 | + | 0.255625i | ||||
\(383\) | −4.01207 | − | 2.31637i | −0.205007 | − | 0.118361i | 0.393982 | − | 0.919118i | \(-0.371097\pi\) |
−0.598989 | + | 0.800757i | \(0.704431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 25.1286i | − | 1.27901i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.42821 | + | 9.40193i | 0.275575 | + | 0.477311i | ||||
\(389\) | 29.0194 | − | 16.7544i | 1.47134 | − | 0.849480i | 0.471860 | − | 0.881673i | \(-0.343583\pi\) |
0.999482 | + | 0.0321938i | \(0.0102494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 26.5815i | − | 1.34428i | ||||||
\(392\) | 3.98161 | − | 5.75732i | 0.201102 | − | 0.290789i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0405 | + | 17.3907i | −0.505835 | + | 0.876132i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.28081 | − | 16.0748i | 0.465790 | − | 0.806772i | −0.533447 | − | 0.845834i | \(-0.679103\pi\) |
0.999237 | + | 0.0390613i | \(0.0124368\pi\) | |||||||
\(398\) | − | 11.8967i | − | 0.596327i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.1377 | − | 7.00770i | −0.606128 | − | 0.349948i | 0.165321 | − | 0.986240i | \(-0.447134\pi\) |
−0.771448 | + | 0.636292i | \(0.780467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.81342 | + | 5.08843i | −0.439028 | + | 0.253473i | ||||
\(404\) | 5.74827 | − | 9.95630i | 0.285987 | − | 0.495345i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.275047 | + | 6.75005i | −0.0136503 | + | 0.334999i | ||||
\(407\) | 21.8279 | 1.08197 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.6162 | + | 11.9028i | −1.01941 | + | 0.588555i | −0.913932 | − | 0.405868i | \(-0.866969\pi\) |
−0.105474 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −19.3738 | −0.954478 | ||||||||
\(413\) | −4.74723 | + | 7.49970i | −0.233596 | + | 0.369036i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.32349 | + | 4.02440i | 0.113918 | + | 0.197313i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.668077 | − | 1.15714i | 0.0326767 | − | 0.0565977i | ||||
\(419\) | −18.1374 | −0.886068 | −0.443034 | − | 0.896505i | \(-0.646098\pi\) | ||||
−0.443034 | + | 0.896505i | \(0.646098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.98092 | 0.388966 | 0.194483 | − | 0.980906i | \(-0.437697\pi\) | ||||
0.194483 | + | 0.980906i | \(0.437697\pi\) | |||||||
\(422\) | −3.39320 | + | 5.87719i | −0.165178 | + | 0.286097i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.07533 | − | 10.5228i | −0.295044 | − | 0.511032i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.852667 | − | 20.9257i | 0.0412635 | − | 1.01267i | ||||
\(428\) | −10.7206 | −0.518199 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.1353 | − | 15.6666i | 1.30706 | − | 0.754632i | 0.325456 | − | 0.945557i | \(-0.394482\pi\) |
0.981605 | + | 0.190925i | \(0.0611488\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.21564 | −0.250648 | −0.125324 | − | 0.992116i | \(-0.539997\pi\) | ||||
−0.125324 | + | 0.992116i | \(0.539997\pi\) | |||||||
\(434\) | −5.13170 | + | 2.69039i | −0.246329 | + | 0.129143i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.41186 | − | 9.37362i | 0.259181 | − | 0.448915i | ||||
\(437\) | 2.86236 | − | 1.65259i | 0.136925 | − | 0.0790539i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.91887 | + | 5.14931i | 0.425675 | + | 0.245763i | 0.697502 | − | 0.716583i | \(-0.254295\pi\) |
−0.271828 | + | 0.962346i | \(0.587628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.2004i | 1.00840i | ||||||||
\(443\) | 20.7828 | − | 35.9968i | 0.987419 | − | 1.71026i | 0.356768 | − | 0.934193i | \(-0.383879\pi\) |
0.630651 | − | 0.776067i | \(-0.282788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.3842 | − | 24.9142i | 0.681113 | − | 1.17972i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.22849 | + | 2.34325i | 0.0580408 | + | 0.110708i | ||||
\(449\) | − | 23.7838i | − | 1.12242i | −0.827672 | − | 0.561212i | \(-0.810335\pi\) | ||
0.827672 | − | 0.561212i | \(-0.189665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7152 | − | 10.2279i | 0.834174 | − | 0.481611i | ||||
\(452\) | 9.21714 | + | 15.9646i | 0.433538 | + | 0.750910i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.10371i | − | 0.0987319i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.2595 | − | 9.38745i | −0.760589 | − | 0.439126i | 0.0689182 | − | 0.997622i | \(-0.478045\pi\) |
−0.829507 | + | 0.558496i | \(0.811379\pi\) | |||||||
\(458\) | 14.0269 | − | 8.09841i | 0.655432 | − | 0.378414i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.4662 | 0.813484 | 0.406742 | − | 0.913543i | \(-0.366665\pi\) | ||||
0.406742 | + | 0.913543i | \(0.366665\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.99345i | − | 0.139117i | −0.997578 | − | 0.0695586i | \(-0.977841\pi\) | ||
0.997578 | − | 0.0695586i | \(-0.0221591\pi\) | |||||||
\(464\) | −2.21130 | − | 1.27670i | −0.102657 | − | 0.0592692i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00569 | − | 6.93805i | −0.185560 | − | 0.321399i | ||||
\(467\) | −22.0058 | − | 12.7050i | −1.01831 | − | 0.587920i | −0.104694 | − | 0.994505i | \(-0.533386\pi\) |
−0.913613 | + | 0.406585i | \(0.866720\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.94849 | + | 5.66430i | 0.413203 | + | 0.261553i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.67739 | − | 2.90532i | −0.0772081 | − | 0.133728i | ||||
\(473\) | 7.74575 | + | 13.4160i | 0.356150 | + | 0.616870i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.491429 | + | 12.0604i | −0.0225246 | + | 0.552787i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.5302 | − | 7.81165i | −0.618856 | − | 0.357297i | ||||
\(479\) | 11.8516 | + | 20.5276i | 0.541514 | + | 0.937929i | 0.998817 | + | 0.0486188i | \(0.0154819\pi\) |
−0.457304 | + | 0.889311i | \(0.651185\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.2945 | − | 21.5320i | −1.70048 | − | 0.981774i | ||||
\(482\) | 4.09331i | 0.186445i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.45198 | 0.247817 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.84683 | − | 5.10772i | 0.400888 | − | 0.231453i | −0.285979 | − | 0.958236i | \(-0.592319\pi\) |
0.686867 | + | 0.726783i | \(0.258985\pi\) | |||||||
\(488\) | 6.85523 | + | 3.95787i | 0.310322 | + | 0.179164i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.25910i | 0.101952i | 0.998700 | + | 0.0509758i | \(0.0162331\pi\) | ||||
−0.998700 | + | 0.0509758i | \(0.983767\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.82452 | − | 10.0884i | −0.262323 | − | 0.454357i | ||||
\(494\) | −2.28291 | + | 1.31804i | −0.102713 | + | 0.0593014i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.18999i | − | 0.0983337i | ||||||
\(497\) | 4.75024 | − | 2.49041i | 0.213077 | − | 0.111710i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6811 | − | 30.6246i | 0.791517 | − | 1.37095i | −0.133511 | − | 0.991047i | \(-0.542625\pi\) |
0.925028 | − | 0.379900i | \(-0.124042\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.97066 | − | 17.2697i | 0.445012 | − | 0.770784i | ||||
\(503\) | − | 30.7297i | − | 1.37017i | −0.728464 | − | 0.685084i | \(-0.759766\pi\) | ||
0.728464 | − | 0.685084i | \(-0.240234\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.8852 | − | 6.86191i | −0.528361 | − | 0.305049i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.50637 | + | 2.02440i | −0.155570 | + | 0.0898183i | ||||
\(509\) | −1.03925 | + | 1.80003i | −0.0460637 | + | 0.0797847i | −0.888138 | − | 0.459577i | \(-0.848001\pi\) |
0.842074 | + | 0.539362i | \(0.181334\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.6262 | + | 18.3671i | −0.514313 | + | 0.812514i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.6188 | − | 10.1722i | 0.777134 | − | 0.448679i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.8682 | 0.653903 | ||||||||
\(518\) | −20.7169 | − | 13.1135i | −0.910246 | − | 0.576176i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.86182 | + | 8.42093i | 0.213000 | + | 0.368927i | 0.952652 | − | 0.304062i | \(-0.0983431\pi\) |
−0.739652 | + | 0.672990i | \(0.765010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.695001 | + | 1.20378i | −0.0303903 | + | 0.0526375i | −0.880821 | − | 0.473450i | \(-0.843008\pi\) |
0.850430 | + | 0.526088i | \(0.176342\pi\) | |||||||
\(524\) | 14.2826 | 0.623937 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.61602 | −0.157666 | ||||||||
\(527\) | 4.99558 | − | 8.65259i | 0.217611 | − | 0.376913i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.47394 | − | 9.48114i | −0.237997 | − | 0.412224i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.32925 | + | 0.696883i | −0.0576302 | + | 0.0302137i | ||||
\(533\) | −40.3568 | −1.74805 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.46657 | + | 2.00143i | −0.149733 | + | 0.0864485i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21.2345 | −0.915484 | ||||||||
\(539\) | 1.34145 | − | 16.4333i | 0.0577805 | − | 0.707832i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.5510 | + | 39.0594i | −0.969541 | + | 1.67930i | −0.272658 | + | 0.962111i | \(0.587903\pi\) |
−0.696884 | + | 0.717184i | \(0.745431\pi\) | |||||||
\(542\) | −18.9957 | + | 10.9672i | −0.815934 | + | 0.471080i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.95097 | − | 2.28109i | −0.169396 | − | 0.0978010i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1372i | 0.476193i | 0.971242 | + | 0.238096i | \(0.0765234\pi\) | ||||
−0.971242 | + | 0.238096i | \(0.923477\pi\) | |||||||
\(548\) | 2.61421 | − | 4.52794i | 0.111673 | − | 0.193424i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.724228 | − | 1.25440i | 0.0308532 | − | 0.0534393i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.8470 | − | 0.890207i | −0.929029 | − | 0.0378555i | ||||
\(554\) | − | 9.92903i | − | 0.421844i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8637 | − | 9.73628i | 0.715181 | − | 0.412910i | ||||
\(557\) | −13.7214 | − | 23.7662i | −0.581395 | − | 1.00701i | −0.995314 | − | 0.0966925i | \(-0.969174\pi\) |
0.413919 | − | 0.910314i | \(-0.364160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 30.5630i | − | 1.29268i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.58656 | + | 5.53481i | 0.404385 | + | 0.233472i | ||||
\(563\) | 28.8238 | − | 16.6414i | 1.21478 | − | 0.701352i | 0.250981 | − | 0.967992i | \(-0.419247\pi\) |
0.963796 | + | 0.266640i | \(0.0859136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.6773 | 0.953200 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.02720i | 0.0850596i | ||||||||
\(569\) | 24.6215 | + | 14.2152i | 1.03219 | + | 0.595932i | 0.917610 | − | 0.397482i | \(-0.130116\pi\) |
0.114575 | + | 0.993415i | \(0.463449\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0784 | − | 24.3845i | −0.589162 | − | 1.02046i | −0.994343 | − | 0.106221i | \(-0.966125\pi\) |
0.405181 | − | 0.914237i | \(-0.367209\pi\) | |||||||
\(572\) | 9.47917 | + | 5.47280i | 0.396344 | + | 0.228829i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −22.9580 | − | 0.935478i | −0.958249 | − | 0.0390461i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.02540 | + | 1.77604i | 0.0426879 | + | 0.0739377i | 0.886580 | − | 0.462575i | \(-0.153075\pi\) |
−0.843892 | + | 0.536513i | \(0.819741\pi\) | |||||||
\(578\) | −1.90675 | − | 3.30259i | −0.0793103 | − | 0.137370i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.402187 | − | 0.210854i | 0.0166855 | − | 0.00874771i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.7856 | − | 14.3100i | −1.02652 | − | 0.592659i | ||||
\(584\) | −4.10801 | − | 7.11528i | −0.169991 | − | 0.294432i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.6735 | − | 6.16238i | −0.440920 | − | 0.254565i | ||||
\(587\) | 36.2336i | 1.49552i | 0.663968 | + | 0.747761i | \(0.268871\pi\) | ||||
−0.663968 | + | 0.747761i | \(0.731129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.24231 | 0.0511886 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.02554 | − | 4.63355i | 0.329848 | − | 0.190438i | ||||
\(593\) | 30.1239 | + | 17.3920i | 1.23704 | + | 0.714205i | 0.968488 | − | 0.249061i | \(-0.0801219\pi\) |
0.268551 | + | 0.963265i | \(0.413455\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.54041i | − | 0.226944i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.5378 | + | 23.4481i | 0.553601 | + | 0.958864i | ||||
\(599\) | −31.6459 | + | 18.2708i | −1.29302 | + | 0.746524i | −0.979188 | − | 0.202956i | \(-0.934945\pi\) |
−0.313829 | + | 0.949479i | \(0.601612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 45.5137i | − | 1.85654i | −0.371902 | − | 0.928272i | \(-0.621294\pi\) | ||
0.371902 | − | 0.928272i | \(-0.378706\pi\) | |||||||
\(602\) | 0.708456 | − | 17.3866i | 0.0288745 | − | 0.708623i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.23984 | − | 7.34362i | 0.172517 | − | 0.298807i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.3836 | − | 31.8414i | 0.746169 | − | 1.29240i | −0.203478 | − | 0.979080i | \(-0.565224\pi\) |
0.949647 | − | 0.313323i | \(-0.101442\pi\) | |||||||
\(608\) | − | 0.567267i | − | 0.0230057i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.4033 | − | 14.6666i | −1.02771 | − | 0.593348i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3288 | + | 16.3557i | −1.14419 | + | 0.660599i | −0.947465 | − | 0.319860i | \(-0.896364\pi\) |
−0.196726 | + | 0.980459i | \(0.563031\pi\) | |||||||
\(614\) | −4.03137 | + | 6.98254i | −0.162693 | + | 0.281792i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.26562 | + | 3.33308i | 0.212158 | + | 0.134294i | ||||
\(617\) | 20.5530 | 0.827435 | 0.413717 | − | 0.910405i | \(-0.364230\pi\) | ||||
0.413717 | + | 0.910405i | \(0.364230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9593 | + | 8.63675i | −0.601265 | + | 0.347140i | −0.769539 | − | 0.638600i | \(-0.779514\pi\) |
0.168274 | + | 0.985740i | \(0.446181\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.4429 | 1.06027 | ||||||||
\(623\) | −14.4305 | − | 0.588006i | −0.578147 | − | 0.0235580i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.26650 | + | 14.3180i | 0.330396 | + | 0.572262i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.560470 | − | 0.970763i | 0.0223652 | − | 0.0387377i | ||||
\(629\) | 42.2782 | 1.68574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.7501 | 1.30376 | 0.651880 | − | 0.758322i | \(-0.273981\pi\) | ||||
0.651880 | + | 0.758322i | \(0.273981\pi\) | |||||||
\(632\) | 4.13212 | − | 7.15704i | 0.164367 | − | 0.284692i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.13038 | + | 10.6181i | 0.243469 | + | 0.421700i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.5025 | + | 26.7542i | −0.733095 | + | 1.06004i | ||||
\(638\) | −6.01432 | −0.238109 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9300 | + | 10.9292i | −0.747688 | + | 0.431678i | −0.824858 | − | 0.565340i | \(-0.808745\pi\) |
0.0771698 | + | 0.997018i | \(0.475412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.13643 | 0.163125 | 0.0815624 | − | 0.996668i | \(-0.474009\pi\) | ||||
0.0815624 | + | 0.996668i | \(0.474009\pi\) | |||||||
\(644\) | 7.15779 | + | 13.6529i | 0.282056 | + | 0.537999i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.29399 | − | 2.24125i | 0.0509113 | − | 0.0881809i | ||||
\(647\) | −26.6816 | + | 15.4046i | −1.04896 | + | 0.605618i | −0.922358 | − | 0.386335i | \(-0.873741\pi\) |
−0.126603 | + | 0.991953i | \(0.540407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.84327 | − | 3.95096i | −0.268622 | − | 0.155089i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.71498i | − | 0.262979i | ||||||
\(653\) | −3.45110 | + | 5.97747i | −0.135052 | + | 0.233917i | −0.925617 | − | 0.378461i | \(-0.876453\pi\) |
0.790565 | + | 0.612378i | \(0.209787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.34226 | − | 7.52101i | 0.169537 | − | 0.293646i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.1114 | − | 8.93235i | −0.550119 | − | 0.348219i | ||||
\(659\) | 11.0895i | 0.431985i | 0.976395 | + | 0.215992i | \(0.0692986\pi\) | ||||
−0.976395 | + | 0.215992i | \(0.930701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7077 | − | 7.91416i | 0.533169 | − | 0.307825i | −0.209137 | − | 0.977886i | \(-0.567065\pi\) |
0.742306 | + | 0.670061i | \(0.233732\pi\) | |||||||
\(662\) | 17.1942 | + | 29.7812i | 0.668270 | + | 1.15748i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.171637i | 0.00666079i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.8841 | − | 7.43865i | −0.498875 | − | 0.288026i | ||||
\(668\) | −2.42583 | + | 1.40055i | −0.0938581 | + | 0.0541890i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.6449 | 0.719779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.8980i | 1.07539i | 0.843139 | + | 0.537695i | \(0.180705\pi\) | ||||
−0.843139 | + | 0.537695i | \(0.819295\pi\) | |||||||
\(674\) | 20.7444 | + | 11.9768i | 0.799045 | + | 0.461329i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.29721 | − | 7.44298i | −0.165277 | − | 0.286269i | ||||
\(677\) | 26.9749 | + | 15.5739i | 1.03673 | + | 0.598555i | 0.918905 | − | 0.394479i | \(-0.129075\pi\) |
0.117823 | + | 0.993035i | \(0.462408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3370 | − | 25.4393i | −0.511828 | − | 0.976269i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.57918 | − | 4.46727i | −0.0987620 | − | 0.171061i | ||||
\(683\) | −12.5960 | − | 21.8168i | −0.481971 | − | 0.834798i | 0.517815 | − | 0.855493i | \(-0.326746\pi\) |
−0.999786 | + | 0.0206948i | \(0.993412\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.1458 | + | 14.7909i | −0.425548 | + | 0.564720i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.69581 | + | 3.28848i | 0.217151 | + | 0.125372i | ||||
\(689\) | 28.2319 | + | 48.8992i | 1.07555 | + | 1.86291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2549 | − | 15.7356i | −1.03683 | − | 0.598612i | −0.117894 | − | 0.993026i | \(-0.537614\pi\) |
−0.918933 | + | 0.394414i | \(0.870948\pi\) | |||||||
\(692\) | − | 13.8004i | − | 0.524611i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.7003 | −1.08945 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.3122 | − | 19.8102i | 1.29967 | − | 0.750363i | ||||
\(698\) | 3.09324 | + | 1.78588i | 0.117081 | + | 0.0675966i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.19395i | 0.196173i | 0.995178 | + | 0.0980864i | \(0.0312721\pi\) | ||||
−0.995178 | + | 0.0980864i | \(0.968728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.62846 | + | 4.55262i | 0.0991342 | + | 0.171705i | ||||
\(704\) | −2.03986 | + | 1.17771i | −0.0768800 | + | 0.0443867i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.5397i | 0.471937i | ||||||||
\(707\) | −16.2684 | + | 25.7009i | −0.611835 | + | 0.966581i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.9440 | − | 31.0800i | 0.673903 | − | 1.16723i | −0.302885 | − | 0.953027i | \(-0.597950\pi\) |
0.976788 | − | 0.214207i | \(-0.0687167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.72938 | − | 4.72742i | 0.102288 | − | 0.177167i | ||||
\(713\) | − | 12.7600i | − | 0.477864i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.31980 | − | 1.33933i | −0.0866948 | − | 0.0500533i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.6940 | + | 7.90624i | −0.511056 | + | 0.295058i | ||||
\(719\) | 13.0548 | − | 22.6115i | 0.486861 | − | 0.843268i | −0.513025 | − | 0.858374i | \(-0.671475\pi\) |
0.999886 | + | 0.0151058i | \(0.00480851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.2157 | + | 2.08691i | 1.90737 | + | 0.0777204i | ||||
\(722\) | −18.6782 | −0.695131 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.95896 | − | 3.44041i | 0.221463 | − | 0.127862i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0193 | 0.705386 | 0.352693 | − | 0.935739i | \(-0.385266\pi\) | ||||
0.352693 | + | 0.935739i | \(0.385266\pi\) | |||||||
\(728\) | −5.70878 | − | 10.8890i | −0.211581 | − | 0.403574i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0026 | + | 25.9853i | 0.554892 | + | 0.961101i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.41992 | − | 7.65553i | 0.163254 | − | 0.282763i | −0.772780 | − | 0.634674i | \(-0.781134\pi\) |
0.936034 | + | 0.351910i | \(0.114468\pi\) | |||||||
\(734\) | 35.6635 | 1.31636 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.82648 | −0.214767 | ||||||||
\(737\) | −4.71421 | + | 8.16524i | −0.173650 | + | 0.300771i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.20546 | − | 14.2123i | −0.301843 | − | 0.522807i | 0.674711 | − | 0.738082i | \(-0.264268\pi\) |
−0.976553 | + | 0.215276i | \(0.930935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.9270 | + | 28.4720i | 0.547987 | + | 1.04524i | ||||
\(743\) | −47.4829 | −1.74198 | −0.870989 | − | 0.491302i | \(-0.836521\pi\) | ||||
−0.870989 | + | 0.491302i | \(0.836521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19.9717 | + | 11.5306i | −0.731214 | + | 0.422167i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.7459 | −0.392908 | ||||||||
\(749\) | 28.3405 | + | 1.15480i | 1.03554 | + | 0.0421955i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.4048 | − | 30.1459i | 0.635109 | − | 1.10004i | −0.351383 | − | 0.936232i | \(-0.614289\pi\) |
0.986492 | − | 0.163809i | \(-0.0523781\pi\) | |||||||
\(752\) | 5.46663 | − | 3.15616i | 0.199348 | − | 0.115093i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.2759 | + | 5.93279i | 0.374226 | + | 0.216059i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.68581i | − | 0.352037i | −0.984387 | − | 0.176018i | \(-0.943678\pi\) | ||
0.984387 | − | 0.176018i | \(-0.0563218\pi\) | |||||||
\(758\) | −4.10055 | + | 7.10236i | −0.148939 | + | 0.257969i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2236 | − | 38.4924i | 0.805605 | − | 1.39535i | −0.110277 | − | 0.993901i | \(-0.535174\pi\) |
0.915882 | − | 0.401448i | \(-0.131493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3163 | + | 24.1968i | −0.554487 | + | 0.875982i | ||||
\(764\) | 9.99228i | 0.361508i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.01207 | + | 2.31637i | −0.144962 | + | 0.0836939i | ||||
\(767\) | 7.79479 | + | 13.5010i | 0.281454 | + | 0.487492i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.0290i | 1.47954i | 0.672858 | + | 0.739771i | \(0.265066\pi\) | ||||
−0.672858 | + | 0.739771i | \(0.734934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.7620 | − | 12.5643i | −0.783232 | − | 0.452199i | ||||
\(773\) | −30.3059 | + | 17.4971i | −1.09003 | + | 0.629327i | −0.933583 | − | 0.358360i | \(-0.883336\pi\) |
−0.156443 | + | 0.987687i | \(0.550003\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.8564 | 0.389723 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 33.5087i | − | 1.20135i | ||||||
\(779\) | 4.26642 | + | 2.46322i | 0.152860 | + | 0.0882540i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.38746 | + | 4.13521i | 0.0854301 | + | 0.147969i | ||||
\(782\) | −23.0202 | − | 13.2907i | −0.823201 | − | 0.475276i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.99518 | − | 6.32684i | −0.106971 | − | 0.225959i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1509 | + | 19.3139i | 0.397485 | + | 0.688465i | 0.993415 | − | 0.114572i | \(-0.0365496\pi\) |
−0.595930 | + | 0.803037i | \(0.703216\pi\) | |||||||
\(788\) | 10.0405 | + | 17.3907i | 0.357679 | + | 0.619519i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6464 | − | 43.1961i | −0.805212 | − | 1.53588i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.8561 | − | 18.3921i | −1.13124 | − | 0.653124i | ||||
\(794\) | −9.28081 | − | 16.0748i | −0.329363 | − | 0.570474i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.3028 | − | 5.94834i | −0.365174 | − | 0.210833i | ||||
\(797\) | 49.1382i | 1.74057i | 0.492553 | + | 0.870283i | \(0.336064\pi\) | ||||
−0.492553 | + | 0.870283i | \(0.663936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.7980 | 1.01880 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.1377 | + | 7.00770i | −0.428597 | + | 0.247451i | ||||
\(803\) | −16.7595 | − | 9.67609i | −0.591429 | − | 0.341462i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.1769i | 0.358465i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.74827 | − | 9.95630i | −0.202224 | − | 0.350262i | ||||
\(809\) | 32.5217 | − | 18.7764i | 1.14340 | − | 0.660144i | 0.196132 | − | 0.980578i | \(-0.437162\pi\) |
0.947271 | + | 0.320434i | \(0.103829\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.3972i | 1.13762i | 0.822469 | + | 0.568810i | \(0.192596\pi\) | ||||
−0.822469 | + | 0.568810i | \(0.807404\pi\) | |||||||
\(812\) | 5.70819 | + | 3.61322i | 0.200318 | + | 0.126799i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.9140 | − | 18.9035i | 0.382534 | − | 0.662569i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.86544 | + | 3.23104i | −0.0652636 | + | 0.113040i | ||||
\(818\) | 23.8056i | 0.832342i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.8756 | + | 9.74316i | 0.588964 | + | 0.340039i | 0.764688 | − | 0.644401i | \(-0.222893\pi\) |
−0.175724 | + | 0.984440i | \(0.556227\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.9370 | + | 14.3974i | −0.869250 | + | 0.501861i | −0.867099 | − | 0.498136i | \(-0.834018\pi\) |
−0.00215079 | + | 0.999998i | \(0.500685\pi\) | |||||||
\(824\) | −9.68690 | + | 16.7782i | −0.337459 | + | 0.584496i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.12132 | + | 7.86107i | 0.143399 | + | 0.273522i | ||||
\(827\) | −32.2720 | −1.12221 | −0.561104 | − | 0.827745i | \(-0.689623\pi\) | ||||
−0.561104 | + | 0.827745i | \(0.689623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.2675 | + | 27.2899i | −1.64167 | + | 0.947817i | −0.661426 | + | 0.750011i | \(0.730048\pi\) |
−0.980241 | + | 0.197806i | \(0.936618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.64698 | 0.161105 | ||||||||
\(833\) | 2.59824 | − | 31.8294i | 0.0900237 | − | 1.10282i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.668077 | − | 1.15714i | −0.0231059 | − | 0.0400206i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.06868 | + | 15.7074i | −0.313272 | + | 0.542604i | ||||
\(839\) | −47.8295 | −1.65126 | −0.825629 | − | 0.564213i | \(-0.809180\pi\) | ||||
−0.825629 | + | 0.564213i | \(0.809180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4802 | 0.775179 | ||||||||
\(842\) | 3.99046 | − | 6.91168i | 0.137520 | − | 0.238192i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.39320 | + | 5.87719i | 0.116799 | + | 0.202301i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.4126 | − | 0.587277i | −0.495224 | − | 0.0201791i | ||||
\(848\) | −12.1507 | −0.417256 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.7606 | − | 26.9973i | 1.60293 | − | 0.925455i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.9274 | −0.374148 | −0.187074 | − | 0.982346i | \(-0.559900\pi\) | ||||
−0.187074 | + | 0.982346i | \(0.559900\pi\) | |||||||
\(854\) | −17.6959 | − | 11.2013i | −0.605540 | − | 0.383300i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.36029 | + | 9.28430i | −0.183211 | + | 0.317331i | ||||
\(857\) | 19.3778 | − | 11.1878i | 0.661932 | − | 0.382167i | −0.131081 | − | 0.991372i | \(-0.541845\pi\) |
0.793013 | + | 0.609205i | \(0.208511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2119 | − | 16.2881i | −0.962577 | − | 0.555744i | −0.0656116 | − | 0.997845i | \(-0.520900\pi\) |
−0.896965 | + | 0.442101i | \(0.854233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 31.3331i | − | 1.06721i | ||||||
\(863\) | 20.9504 | − | 36.2871i | 0.713160 | − | 1.23523i | −0.250506 | − | 0.968115i | \(-0.580597\pi\) |
0.963665 | − | 0.267113i | \(-0.0860698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.60782 | + | 4.51688i | −0.0886174 | + | 0.153490i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.235902 | + | 5.78938i | −0.00800703 | + | 0.196504i | ||||
\(869\) | − | 19.4658i | − | 0.660331i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1091 | − | 9.30059i | 0.545836 | − | 0.315138i | ||||
\(872\) | −5.41186 | − | 9.37362i | −0.183269 | − | 0.317431i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.30517i | − | 0.111799i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.7637 | − | 29.3084i | −1.71417 | − | 0.989675i | −0.928749 | − | 0.370710i | \(-0.879114\pi\) |
−0.785419 | − | 0.618965i | \(-0.787552\pi\) | |||||||
\(878\) | 8.91887 | − | 5.14931i | 0.300997 | − | 0.173781i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.97791 | −0.167710 | −0.0838550 | − | 0.996478i | \(-0.526723\pi\) | ||||
−0.0838550 | + | 0.996478i | \(0.526723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.8600i | − | 0.701995i | −0.936376 | − | 0.350998i | \(-0.885843\pi\) | ||
0.936376 | − | 0.350998i | \(-0.114157\pi\) | |||||||
\(884\) | 18.3601 | + | 10.6002i | 0.617515 | + | 0.356523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.7828 | − | 35.9968i | −0.698211 | − | 1.20934i | ||||
\(887\) | 43.1470 | + | 24.9109i | 1.44873 | + | 0.836427i | 0.998406 | − | 0.0564371i | \(-0.0179740\pi\) |
0.450327 | + | 0.892864i | \(0.351307\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.48735 | − | 4.97392i | 0.318195 | − | 0.166820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.3842 | − | 24.9142i | −0.481619 | − | 0.834189i | ||||
\(893\) | 1.79039 | + | 3.10104i | 0.0599130 | + | 0.103772i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.64356 | + | 0.107718i | 0.0883151 | + | 0.00359861i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.5973 | − | 11.8919i | −0.687342 | − | 0.396837i | ||||
\(899\) | −2.79596 | − | 4.84275i | −0.0932505 | − | 0.161515i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0069 | − | 27.7168i | −1.59934 | − | 0.923379i | ||||
\(902\) | − | 20.4557i | − | 0.681100i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.4343 | 0.613115 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3149 | − | 18.0797i | 1.03980 | − | 0.600326i | 0.120020 | − | 0.992771i | \(-0.461704\pi\) |
0.919775 | + | 0.392445i | \(0.128371\pi\) | |||||||
\(908\) | −1.82186 | − | 1.05185i | −0.0604607 | − | 0.0349070i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.05205i | − | 0.0679873i | −0.999422 | − | 0.0339937i | \(-0.989177\pi\) | ||
0.999422 | − | 0.0339937i | \(-0.0108226\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.202138 | + | 0.350114i | 0.00668980 | + | 0.0115871i | ||||
\(914\) | −16.2595 | + | 9.38745i | −0.537818 | + | 0.310509i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 16.1968i | − | 0.535158i | ||||||
\(917\) | −37.7568 | − | 1.53849i | −1.24684 | − | 0.0508054i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.696500 | − | 1.20637i | 0.0229754 | − | 0.0397946i | −0.854309 | − | 0.519765i | \(-0.826019\pi\) |
0.877285 | + | 0.479971i | \(0.159353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.73312 | − | 15.1262i | 0.287610 | − | 0.498155i | ||||
\(923\) | − | 9.42038i | − | 0.310076i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.59240 | − | 1.49672i | −0.0851916 | − | 0.0491854i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.21130 | + | 1.27670i | −0.0725896 | + | 0.0419096i | ||||
\(929\) | −16.5276 | + | 28.6266i | −0.542252 | + | 0.939208i | 0.456522 | + | 0.889712i | \(0.349095\pi\) |
−0.998774 | + | 0.0494960i | \(0.984238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.58901 | − | 1.69907i | 0.117625 | − | 0.0556847i | ||||
\(932\) | −8.01137 | −0.262421 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.0058 | + | 12.7050i | −0.720051 | + | 0.415722i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.53551 | −0.0828314 | −0.0414157 | − | 0.999142i | \(-0.513187\pi\) | ||||
−0.0414157 | + | 0.999142i | \(0.513187\pi\) | |||||||
\(938\) | 9.37967 | − | 4.91747i | 0.306257 | − | 0.160561i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8858 | + | 32.7112i | 0.615659 | + | 1.06635i | 0.990268 | + | 0.139171i | \(0.0444436\pi\) |
−0.374609 | + | 0.927183i | \(0.622223\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3001 | − | 43.8210i | 0.823884 | − | 1.42701i | ||||
\(944\) | −3.35478 | −0.109189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.4915 | 0.503672 | ||||||||
\(947\) | 28.2981 | − | 49.0138i | 0.919566 | − | 1.59274i | 0.119491 | − | 0.992835i | \(-0.461874\pi\) |
0.800075 | − | 0.599900i | \(-0.204793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.0898 | + | 33.0645i | 0.619682 | + | 1.07332i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.1989 | + | 6.45578i | 0.330548 | + | 0.209233i | ||||
\(953\) | 34.3234 | 1.11184 | 0.555922 | − | 0.831234i | \(-0.312365\pi\) | ||||
0.555922 | + | 0.831234i | \(0.312365\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.5302 | + | 7.81165i | −0.437597 | + | 0.252647i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.7032 | 0.765816 | ||||||||
\(959\) | −7.39855 | + | 11.6883i | −0.238912 | + | 0.377434i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.1020 | + | 22.6933i | −0.422644 | + | 0.732041i | ||||
\(962\) | −37.2945 | + | 21.5320i | −1.20242 | + | 0.694219i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.54491 | + | 2.04665i | 0.114174 | + | 0.0659183i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 0.903990i | − | 0.0290703i | −0.999894 | − | 0.0145352i | \(-0.995373\pi\) | ||
0.999894 | − | 0.0145352i | \(-0.00462685\pi\) | |||||||
\(968\) | 2.72599 | − | 4.72156i | 0.0876167 | − | 0.151757i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2293 | − | 36.7703i | 0.681282 | − | 1.18001i | −0.293308 | − | 0.956018i | \(-0.594756\pi\) |
0.974590 | − | 0.223997i | \(-0.0719105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.6290 | + | 23.9219i | −1.46280 | + | 0.766901i | ||||
\(974\) | − | 10.2154i | − | 0.327324i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.85523 | − | 3.95787i | 0.219431 | − | 0.126688i | ||||
\(977\) | 3.07196 | + | 5.32079i | 0.0982807 | + | 0.170227i | 0.910973 | − | 0.412466i | \(-0.135332\pi\) |
−0.812692 | + | 0.582693i | \(0.801999\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.8577i | − | 0.410933i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.95643 | + | 1.12955i | 0.0624323 | + | 0.0360453i | ||||
\(983\) | −34.2830 | + | 19.7933i | −1.09346 | + | 0.631309i | −0.934495 | − | 0.355976i | \(-0.884149\pi\) |
−0.158964 | + | 0.987284i | \(0.550815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.6490 | −0.370981 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.63608i | 0.0838648i | ||||||||
\(989\) | 33.1865 | + | 19.1602i | 1.05527 | + | 0.609260i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.4602 | + | 33.7060i | 0.618172 | + | 1.07071i | 0.989819 | + | 0.142331i | \(0.0454599\pi\) |
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(992\) | −1.89659 | − | 1.09500i | −0.0602168 | − | 0.0347662i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.218366 | − | 5.35903i | 0.00692616 | − | 0.169978i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.7111 | + | 18.5522i | 0.339225 | + | 0.587555i | 0.984287 | − | 0.176575i | \(-0.0565018\pi\) |
−0.645062 | + | 0.764130i | \(0.723168\pi\) | |||||||
\(998\) | −17.6811 | − | 30.6246i | −0.559687 | − | 0.969406i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bp.h.1349.8 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.g.1349.8 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.e.1601.11 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.d.1601.2 | yes | 24 | ||
5.4 | even | 2 | 3150.2.bp.g.1349.5 | 24 | |||
7.3 | odd | 6 | inner | 3150.2.bp.h.899.5 | 24 | ||
15.2 | even | 4 | 3150.2.bf.e.1601.2 | yes | 24 | ||
15.8 | even | 4 | 3150.2.bf.d.1601.11 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.h.1349.5 | 24 | ||
21.17 | even | 6 | 3150.2.bp.g.899.5 | 24 | |||
35.3 | even | 12 | 3150.2.bf.d.1151.11 | yes | 24 | ||
35.17 | even | 12 | 3150.2.bf.e.1151.2 | yes | 24 | ||
35.24 | odd | 6 | 3150.2.bp.g.899.8 | 24 | |||
105.17 | odd | 12 | 3150.2.bf.e.1151.11 | yes | 24 | ||
105.38 | odd | 12 | 3150.2.bf.d.1151.2 | ✓ | 24 | ||
105.59 | even | 6 | inner | 3150.2.bp.h.899.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.2 | ✓ | 24 | 105.38 | odd | 12 | ||
3150.2.bf.d.1151.11 | yes | 24 | 35.3 | even | 12 | ||
3150.2.bf.d.1601.2 | yes | 24 | 5.3 | odd | 4 | ||
3150.2.bf.d.1601.11 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bf.e.1151.2 | yes | 24 | 35.17 | even | 12 | ||
3150.2.bf.e.1151.11 | yes | 24 | 105.17 | odd | 12 | ||
3150.2.bf.e.1601.2 | yes | 24 | 15.2 | even | 4 | ||
3150.2.bf.e.1601.11 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bp.g.899.5 | 24 | 21.17 | even | 6 | |||
3150.2.bp.g.899.8 | 24 | 35.24 | odd | 6 | |||
3150.2.bp.g.1349.5 | 24 | 5.4 | even | 2 | |||
3150.2.bp.g.1349.8 | 24 | 3.2 | odd | 2 | |||
3150.2.bp.h.899.5 | 24 | 7.3 | odd | 6 | inner | ||
3150.2.bp.h.899.8 | 24 | 105.59 | even | 6 | inner | ||
3150.2.bp.h.1349.5 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.h.1349.8 | 24 | 1.1 | even | 1 | trivial |