Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(89,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("840.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.da (of order \(6\), degree \(2\), 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: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.3 | ||
Character | \(\chi\) | \(=\) | 840.89 |
Dual form | 840.2.da.a.689.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.65401 | − | 0.514040i | −0.954946 | − | 0.296781i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.955903 | + | 2.02145i | −0.427493 | + | 0.904019i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.96308 | − | 1.77379i | −0.741973 | − | 0.670430i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.47153 | + | 1.70046i | 0.823842 | + | 0.566819i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.95951 | + | 2.28602i | −1.19384 | + | 0.689262i | −0.959175 | − | 0.282815i | \(-0.908732\pi\) |
−0.234663 | + | 0.972077i | \(0.575399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57517 | 0.436873 | 0.218437 | − | 0.975851i | \(-0.429904\pi\) | ||||
0.218437 | + | 0.975851i | \(0.429904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.62018 | − | 2.85213i | 0.676528 | − | 0.736417i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.06751 | − | 2.34838i | 0.986516 | − | 0.569565i | 0.0822846 | − | 0.996609i | \(-0.473778\pi\) |
0.904231 | + | 0.427044i | \(0.140445\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0201141 | + | 0.0116129i | 0.00461449 | + | 0.00266418i | 0.502305 | − | 0.864690i | \(-0.332485\pi\) |
−0.497691 | + | 0.867354i | \(0.665819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.33516 | + | 3.94297i | 0.509573 | + | 0.860427i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0964144 | + | 0.166995i | −0.0201038 | + | 0.0348208i | −0.875902 | − | 0.482489i | \(-0.839733\pi\) |
0.855798 | + | 0.517309i | \(0.173066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.17250 | − | 3.86461i | −0.634500 | − | 0.772923i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.21384 | − | 4.08305i | −0.618503 | − | 0.785782i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.98429i | − | 0.925560i | −0.886473 | − | 0.462780i | \(-0.846852\pi\) | ||
0.886473 | − | 0.462780i | \(-0.153148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.92678 | − | 3.42183i | 1.06448 | − | 0.614579i | 0.137813 | − | 0.990458i | \(-0.455993\pi\) |
0.926668 | + | 0.375880i | \(0.122659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.72419 | − | 1.74577i | 1.34461 | − | 0.303900i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.46213 | − | 2.27269i | 0.923269 | − | 0.384154i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.79834 | − | 1.03827i | −0.295645 | − | 0.170691i | 0.344840 | − | 0.938662i | \(-0.387933\pi\) |
−0.640485 | + | 0.767971i | \(0.721267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.60535 | − | 0.809699i | −0.417190 | − | 0.129656i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.85645 | 0.914624 | 0.457312 | − | 0.889306i | \(-0.348812\pi\) | ||||
0.457312 | + | 0.889306i | \(0.348812\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.60899i | − | 1.00786i | −0.863744 | − | 0.503931i | \(-0.831887\pi\) | ||
0.863744 | − | 0.503931i | \(-0.168113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.79993 | + | 3.37059i | −0.864602 | + | 0.502458i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.93457 | + | 2.84898i | 0.719781 | + | 0.415566i | 0.814672 | − | 0.579922i | \(-0.196917\pi\) |
−0.0948910 | + | 0.995488i | \(0.530250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.707338 | + | 6.96417i | 0.101048 | + | 0.994882i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.93487 | + | 1.79339i | −1.11110 | + | 0.251124i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.13922 | − | 8.90140i | −0.705927 | − | 1.22270i | −0.966356 | − | 0.257208i | \(-0.917197\pi\) |
0.260429 | − | 0.965493i | \(-0.416136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.836172 | − | 10.1892i | −0.112749 | − | 1.37391i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0272995 | − | 0.0295473i | −0.00361591 | − | 0.00391364i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.24724 | + | 2.16029i | 0.162377 | + | 0.281246i | 0.935721 | − | 0.352741i | \(-0.114750\pi\) |
−0.773343 | + | 0.633987i | \(0.781417\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.02451 | + | 4.63295i | 1.02743 | + | 0.593189i | 0.916248 | − | 0.400611i | \(-0.131202\pi\) |
0.111185 | + | 0.993800i | \(0.464535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.83554 | − | 7.72210i | −0.231256 | − | 0.972893i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.50571 | + | 3.18412i | −0.186760 | + | 0.394941i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.87567 | − | 3.39232i | 0.717827 | − | 0.414438i | −0.0961254 | − | 0.995369i | \(-0.530645\pi\) |
0.813952 | + | 0.580932i | \(0.197312\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.245313 | − | 0.226651i | 0.0295322 | − | 0.0272855i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.0928i | − | 1.55383i | −0.629603 | − | 0.776917i | \(-0.716782\pi\) | ||
0.629603 | − | 0.776917i | \(-0.283218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.23510 | − | 12.5316i | −0.846804 | − | 1.46671i | −0.884045 | − | 0.467402i | \(-0.845190\pi\) |
0.0372407 | − | 0.999306i | \(-0.488143\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.26080 | + | 8.02292i | 0.376524 | + | 0.926407i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.8277 | + | 2.53570i | 1.34790 | + | 0.288970i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.60158 | − | 11.4343i | 0.742736 | − | 1.28646i | −0.208509 | − | 0.978020i | \(-0.566861\pi\) |
0.951245 | − | 0.308436i | \(-0.0998055\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.21688 | + | 8.40545i | 0.357431 | + | 0.933939i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.02664i | 0.112688i | 0.998411 | + | 0.0563442i | \(0.0179444\pi\) | ||||
−0.998411 | + | 0.0563442i | \(0.982056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.858979 | + | 10.4671i | 0.0931694 | + | 1.13531i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.56212 | + | 8.24409i | −0.274689 | + | 0.883859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.594890 | − | 1.03038i | 0.0630583 | − | 0.109220i | −0.832773 | − | 0.553615i | \(-0.813248\pi\) |
0.895831 | + | 0.444395i | \(0.146581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.09218 | − | 2.79402i | −0.324148 | − | 0.292893i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.5619 | + | 2.61315i | −1.19892 | + | 0.270971i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0427019 | + | 0.0295588i | −0.00438113 | + | 0.00303267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.721802 | −0.0732879 | −0.0366440 | − | 0.999328i | \(-0.511667\pi\) | ||||
−0.0366440 | + | 0.999328i | \(0.511667\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.6733 | − | 1.08301i | −1.37422 | − | 0.108847i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.55211 | + | 13.0806i | 0.751463 | + | 1.30157i | 0.947114 | + | 0.320899i | \(0.103985\pi\) |
−0.195650 | + | 0.980674i | \(0.562682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.17456 | − | 3.76645i | 0.214266 | − | 0.371120i | −0.738779 | − | 0.673947i | \(-0.764597\pi\) |
0.953045 | + | 0.302828i | \(0.0979307\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.2027 | + | 0.951300i | −0.995681 | + | 0.0928374i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.53479 | + | 11.3186i | −0.631742 | + | 1.09421i | 0.355453 | + | 0.934694i | \(0.384327\pi\) |
−0.987195 | + | 0.159516i | \(0.949007\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.63655 | − | 6.29868i | −0.348318 | − | 0.603304i | 0.637633 | − | 0.770340i | \(-0.279914\pi\) |
−0.985951 | + | 0.167036i | \(0.946580\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.44076 | + | 2.64173i | 0.231667 | + | 0.250742i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9519 | −1.31249 | −0.656243 | − | 0.754550i | \(-0.727855\pi\) | ||||
−0.656243 | + | 0.754550i | \(0.727855\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.245408 | − | 0.354527i | −0.0228844 | − | 0.0330598i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.89307 | + | 2.67851i | 0.359914 | + | 0.247628i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.1504 | − | 2.60486i | −1.11382 | − | 0.238787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.95181 | − | 8.57679i | 0.450165 | − | 0.779708i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.68666 | − | 3.01045i | −0.873417 | − | 0.271443i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8447 | − | 2.71885i | 0.969981 | − | 0.243181i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.98070i | 0.885644i | 0.896610 | + | 0.442822i | \(0.146023\pi\) | ||||
−0.896610 | + | 0.442822i | \(0.853977\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.39728 | + | 10.9314i | −0.299114 | + | 0.962453i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.23882 | + | 10.8060i | −0.545088 | + | 0.944121i | 0.453513 | + | 0.891250i | \(0.350171\pi\) |
−0.998601 | + | 0.0528709i | \(0.983163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0188867 | − | 0.0584751i | −0.00163768 | − | 0.00507044i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.3258 | − | 2.59361i | 0.974768 | − | 0.223222i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.56853 | − | 6.18087i | −0.304880 | − | 0.528067i | 0.672355 | − | 0.740229i | \(-0.265283\pi\) |
−0.977235 | + | 0.212162i | \(0.931950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.40154i | − | 0.797428i | −0.917075 | − | 0.398714i | \(-0.869457\pi\) | ||
0.917075 | − | 0.398714i | \(-0.130543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.69736 | − | 7.24881i | −0.564020 | − | 0.610460i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.23689 | + | 3.60087i | −0.521555 | + | 0.301120i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0755 | + | 4.76450i | 0.836723 | + | 0.395670i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.40991 | − | 11.8824i | 0.198766 | − | 0.980047i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.18404 | − | 0.683607i | −0.0970005 | − | 0.0560033i | 0.450715 | − | 0.892668i | \(-0.351169\pi\) |
−0.547716 | + | 0.836665i | \(0.684502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4085 | + | 19.7601i | 0.928411 | + | 1.60806i | 0.785981 | + | 0.618251i | \(0.212158\pi\) |
0.142431 | + | 0.989805i | \(0.454508\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.0463 | + | 1.11255i | 1.13557 | + | 0.0899446i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.25162 | + | 15.2516i | 0.100533 | + | 1.22504i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6334 | + | 20.1496i | 0.928443 | + | 1.60811i | 0.785929 | + | 0.618317i | \(0.212185\pi\) |
0.142514 | + | 0.989793i | \(0.454481\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.92468 | + | 17.3648i | 0.311247 | + | 1.37712i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.485482 | − | 0.156804i | 0.0382614 | − | 0.0123579i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5250 | + | 11.2727i | 1.52931 | + | 0.882950i | 0.999391 | + | 0.0349039i | \(0.0111125\pi\) |
0.529923 | + | 0.848046i | \(0.322221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.85459 | + | 17.2828i | −0.300080 | + | 1.34547i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.56225i | 0.198273i | 0.995074 | + | 0.0991364i | \(0.0316080\pi\) | ||||
−0.995074 | + | 0.0991364i | \(0.968392\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5188 | −0.809142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0299653 | + | 0.0629047i | 0.00229150 | + | 0.00481044i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.0147 | − | 10.9782i | −1.44566 | − | 0.834654i | −0.447444 | − | 0.894312i | \(-0.647666\pi\) |
−0.998219 | + | 0.0596581i | \(0.980999\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.627152 | + | 13.2139i | −0.0474083 | + | 0.998876i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.952485 | − | 4.21429i | −0.0715931 | − | 0.316765i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.32644 | − | 3.07522i | 0.398117 | − | 0.229853i | −0.287554 | − | 0.957764i | \(-0.592842\pi\) |
0.685671 | + | 0.727911i | \(0.259509\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.8923i | − | 1.62725i | −0.581393 | − | 0.813623i | \(-0.697492\pi\) | ||
0.581393 | − | 0.813623i | \(-0.302508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8911 | − | 11.7879i | −0.805096 | − | 0.871386i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.81785 | − | 2.64276i | 0.280694 | − | 0.194300i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7369 | + | 18.5968i | −0.785159 | + | 1.35994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.933459 | + | 13.7160i | −0.0678991 | + | 0.997692i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.72916 | − | 3.88508i | −0.486905 | − | 0.281115i | 0.236385 | − | 0.971660i | \(-0.424037\pi\) |
−0.723290 | + | 0.690545i | \(0.757371\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.48274 | − | 4.32016i | 0.538620 | − | 0.310972i | −0.205900 | − | 0.978573i | \(-0.566012\pi\) |
0.744519 | + | 0.667601i | \(0.232679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.12723 | − | 4.49259i | 0.295557 | − | 0.321721i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0102 | 0.713196 | 0.356598 | − | 0.934258i | \(-0.383937\pi\) | ||||
0.356598 | + | 0.934258i | \(0.383937\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4751 | − | 9.51189i | 1.16789 | − | 0.674280i | 0.214705 | − | 0.976679i | \(-0.431121\pi\) |
0.953181 | + | 0.302399i | \(0.0977875\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.4622 | + | 2.59062i | −0.808483 | + | 0.182728i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.84108 | + | 9.78454i | −0.620522 | + | 0.686740i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.59820 | + | 11.8385i | −0.390995 | + | 0.826838i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.522258 | + | 0.248783i | −0.0362994 | + | 0.0172916i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.106189 | −0.00734527 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.9031 | −1.57671 | −0.788356 | − | 0.615220i | \(-0.789067\pi\) | ||||
−0.788356 | + | 0.615220i | \(0.789067\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.73024 | + | 21.6557i | −0.461148 | + | 1.48383i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.3597 | + | 6.31755i | 0.911126 | + | 0.430853i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.7043 | − | 3.79555i | −1.20185 | − | 0.257659i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.52524 | + | 24.4465i | 0.373361 | + | 1.65194i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.40701 | − | 3.69909i | 0.430982 | − | 0.248828i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.13076 | −0.0757211 | −0.0378605 | − | 0.999283i | \(-0.512054\pi\) | ||||
−0.0378605 | + | 0.999283i | \(0.512054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.26930 | − | 14.9462i | −0.0846202 | − | 0.996413i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0771562 | + | 0.0445462i | −0.00512104 | + | 0.00295663i | −0.502558 | − | 0.864543i | \(-0.667608\pi\) |
0.497437 | + | 0.867500i | \(0.334274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.76866 | + | 4.48524i | 0.513368 | + | 0.296393i | 0.734217 | − | 0.678915i | \(-0.237550\pi\) |
−0.220849 | + | 0.975308i | \(0.570883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.2598 | − | 10.2740i | −1.20141 | − | 0.675981i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.0036 | + | 19.0589i | −0.720873 | + | 1.24859i | 0.239778 | + | 0.970828i | \(0.422925\pi\) |
−0.960650 | + | 0.277760i | \(0.910408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4760 | + | 7.25163i | −0.683380 | + | 0.473044i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.7968 | + | 15.5190i | −1.09107 | + | 1.00807i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.9277i | − | 1.74181i | −0.491450 | − | 0.870906i | \(-0.663533\pi\) | ||
0.491450 | − | 0.870906i | \(-0.336467\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5893 | − | 8.42312i | 0.939778 | − | 0.542581i | 0.0498872 | − | 0.998755i | \(-0.484114\pi\) |
0.889891 | + | 0.456174i | \(0.150780\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00003 | − | 15.5563i | −0.0641520 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7539 | − | 5.22722i | −0.942589 | − | 0.333955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0316831 | + | 0.0182922i | 0.00201595 | + | 0.00116391i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.527734 | − | 1.69808i | 0.0334438 | − | 0.107611i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.43606 | 0.532479 | 0.266240 | − | 0.963907i | \(-0.414219\pi\) | ||||
0.266240 | + | 0.963907i | \(0.414219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.881623i | − | 0.0554271i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.95973 | − | 17.7542i | 0.247968 | − | 1.11181i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.2289 | − | 8.79239i | −0.949951 | − | 0.548454i | −0.0568852 | − | 0.998381i | \(-0.518117\pi\) |
−0.893066 | + | 0.449926i | \(0.851450\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68860 | + | 5.22808i | 0.104925 | + | 0.324857i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.47558 | − | 12.3188i | 0.524625 | − | 0.762515i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.53721 | + | 7.85868i | 0.279776 | + | 0.484587i | 0.971329 | − | 0.237739i | \(-0.0764064\pi\) |
−0.691553 | + | 0.722326i | \(0.743073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.9063 | − | 1.87980i | 1.40712 | − | 0.115475i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.51361 | + | 1.39847i | −0.0926317 | + | 0.0855848i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.1072 | − | 22.7023i | −0.799158 | − | 1.38418i | −0.920165 | − | 0.391531i | \(-0.871945\pi\) |
0.121006 | − | 0.992652i | \(-0.461388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0011 | − | 10.9703i | −1.15424 | − | 0.666399i | −0.204321 | − | 0.978904i | \(-0.565499\pi\) |
−0.949916 | + | 0.312505i | \(0.898832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.67827 | + | 6.21085i | 0.222619 | + | 0.375898i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.3961 | + | 8.04956i | 1.29024 | + | 0.485407i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.6278 | − | 11.9094i | 1.23940 | − | 0.715569i | 0.270430 | − | 0.962740i | \(-0.412834\pi\) |
0.968972 | + | 0.247171i | \(0.0795009\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.4669 | + | 1.62111i | 1.22532 | + | 0.0970531i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.605728i | 0.0361347i | 0.999837 | + | 0.0180674i | \(0.00575133\pi\) | ||||
−0.999837 | + | 0.0180674i | \(0.994249\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3583 | − | 26.6013i | −0.912955 | − | 1.58128i | −0.809869 | − | 0.586611i | \(-0.800462\pi\) |
−0.103086 | − | 0.994672i | \(-0.532872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0858240 | − | 0.0269402i | 0.00508378 | − | 0.00159580i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4967 | − | 10.3881i | −0.678627 | − | 0.613191i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.52975 | − | 4.38165i | 0.148809 | − | 0.257744i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.19387 | + | 0.371035i | 0.0699860 | + | 0.0217505i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 22.7443i | − | 1.32874i | −0.747405 | − | 0.664369i | \(-0.768700\pi\) | ||
0.747405 | − | 0.664369i | \(-0.231300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.55916 | + | 0.456212i | −0.323667 | + | 0.0265617i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.0592 | + | 8.81995i | 1.28000 | + | 0.511786i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.151869 | + | 0.263045i | −0.00878281 | + | 0.0152123i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.7230 | + | 12.9740i | −0.675700 | + | 0.747806i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.76733 | − | 25.5177i | −0.331324 | − | 1.46595i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.0359 | + | 11.7925i | −0.975474 | + | 0.675235i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.56762 | −0.260688 | −0.130344 | − | 0.991469i | \(-0.541608\pi\) | ||||
−0.130344 | + | 0.991469i | \(0.541608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.53286 | + | 5.11195i | −0.314754 | + | 0.290809i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.15556 | − | 10.6617i | −0.349050 | − | 0.604572i | 0.637031 | − | 0.770838i | \(-0.280162\pi\) |
−0.986081 | + | 0.166266i | \(0.946829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.33440 | + | 5.77536i | −0.188472 | + | 0.326442i | −0.944741 | − | 0.327818i | \(-0.893687\pi\) |
0.756269 | + | 0.654261i | \(0.227020\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.3644 | + | 3.67113i | 0.978374 | + | 0.206845i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.81329 | − | 8.33686i | 0.270341 | − | 0.468245i | −0.698608 | − | 0.715505i | \(-0.746197\pi\) |
0.968949 | + | 0.247260i | \(0.0795301\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.3942 | + | 19.7353i | 0.637953 | + | 1.10497i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.6268 | − | 15.3620i | 0.928020 | − | 0.857422i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.109086 | 0.00606969 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.99722 | − | 6.08742i | −0.277196 | − | 0.337669i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.77713 | + | 12.2874i | 0.153575 | + | 0.679497i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.63345 | − | 14.3456i | −0.255451 | − | 0.790901i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97347 | + | 10.3464i | −0.328332 | + | 0.568687i | −0.982181 | − | 0.187938i | \(-0.939820\pi\) |
0.653849 | + | 0.756625i | \(0.273153\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.67910 | − | 5.62411i | −0.146814 | − | 0.308200i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.24083 | + | 15.1201i | 0.0677937 | + | 0.826098i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.59087i | 0.467975i | 0.972240 | + | 0.233987i | \(0.0751774\pi\) | ||||
−0.972240 | + | 0.233987i | \(0.924823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.0767 | + | 7.17184i | 1.25335 | + | 0.389521i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.6448 | + | 27.0975i | −0.847212 | + | 1.46741i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9644 | − | 14.9259i | 0.592023 | − | 0.805921i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.223667 | + | 0.712543i | 0.0120418 | + | 0.0383620i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0394 | + | 19.1207i | 0.592624 | + | 1.02646i | 0.993877 | + | 0.110488i | \(0.0352414\pi\) |
−0.401253 | + | 0.915967i | \(0.631425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.44889i | 0.0775573i | 0.999248 | + | 0.0387787i | \(0.0123467\pi\) | ||||
−0.999248 | + | 0.0387787i | \(0.987653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.06233 | − | 6.43148i | −0.270207 | − | 0.343287i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.4981 | − | 10.1026i | 0.931332 | − | 0.537705i | 0.0440991 | − | 0.999027i | \(-0.485958\pi\) |
0.887232 | + | 0.461323i | \(0.152625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.4665 | + | 12.5155i | 1.40470 | + | 0.664253i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.7579 | + | 10.5542i | 0.992771 | + | 0.558590i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.81277 | + | 3.93336i | 0.359564 | + | 0.207595i | 0.668890 | − | 0.743362i | \(-0.266770\pi\) |
−0.309325 | + | 0.950956i | \(0.600103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49973 | − | 16.4540i | −0.499986 | − | 0.866001i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.5992 | + | 11.6407i | −0.661286 | + | 0.610979i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.2479 | − | 2.64642i | 1.68793 | − | 0.138520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.75729 | − | 15.1681i | −0.457127 | − | 0.791767i | 0.541681 | − | 0.840584i | \(-0.317788\pi\) |
−0.998808 | + | 0.0488172i | \(0.984455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.4744 | + | 9.95866i | 0.753506 | + | 0.518427i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.70052 | + | 26.5900i | −0.295956 | + | 1.38049i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.6990 | − | 10.2185i | −0.916418 | − | 0.529094i | −0.0339275 | − | 0.999424i | \(-0.510802\pi\) |
−0.882491 | + | 0.470330i | \(0.844135\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.3349 | − | 1.07760i | −0.998451 | − | 0.0556471i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.85110i | − | 0.404352i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3214 | −1.14657 | −0.573286 | − | 0.819355i | \(-0.694332\pi\) | ||||
−0.573286 | + | 0.819355i | \(0.694332\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.13048 | − | 16.5082i | 0.262842 | − | 0.845741i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.403621 | − | 0.233031i | −0.0206241 | − | 0.0119073i | 0.489653 | − | 0.871918i | \(-0.337124\pi\) |
−0.510277 | + | 0.860010i | \(0.670457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.4320 | + | 21.4853i | −0.837450 | + | 1.09499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.2383 | − | 16.3343i | 0.571276 | − | 0.830319i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1455 | + | 8.16690i | −0.717205 | + | 0.414078i | −0.813723 | − | 0.581253i | \(-0.802563\pi\) |
0.0965184 | + | 0.995331i | \(0.469229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.905669i | 0.0458017i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.8738 | − | 14.6662i | 0.800727 | − | 0.739812i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.8033 | + | 24.2748i | 0.845467 | + | 1.22140i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.37186 | − | 16.2325i | 0.470360 | − | 0.814688i | −0.529065 | − | 0.848581i | \(-0.677457\pi\) |
0.999425 | + | 0.0338935i | \(0.0107907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.00118031 | + | 0.106427i | 5.90896e−5 | + | 0.00532803i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.15425 | − | 1.82111i | −0.157516 | − | 0.0909417i | 0.419170 | − | 0.907908i | \(-0.362321\pi\) |
−0.576686 | + | 0.816966i | \(0.695654\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.33568 | − | 5.38996i | 0.465043 | − | 0.268493i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.0662 | − | 1.53204i | −0.997098 | − | 0.0761275i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.49405 | 0.470603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.51215 | + | 1.45039i | −0.124218 | + | 0.0717171i | −0.560821 | − | 0.827937i | \(-0.689515\pi\) |
0.436604 | + | 0.899654i | \(0.356181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.72518 | + | 12.0576i | 0.134423 | + | 0.594758i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.38347 | − | 6.45317i | 0.0680759 | − | 0.317540i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07530 | − | 0.981369i | −0.101872 | − | 0.0481735i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.83276 | + | 15.5503i | −0.236662 | + | 0.761500i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8585 | 0.774736 | 0.387368 | − | 0.921925i | \(-0.373384\pi\) | ||||
0.387368 | + | 0.921925i | \(0.373384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.26063 | 0.451335 | 0.225668 | − | 0.974204i | \(-0.427544\pi\) | ||||
0.225668 | + | 0.974204i | \(0.427544\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.35136 | + | 15.4323i | 0.357435 | + | 0.750346i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.9797 | − | 8.26912i | −1.06617 | − | 0.401111i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.53484 | − | 23.3286i | −0.364637 | − | 1.12895i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.1669 | − | 2.74988i | 0.587424 | − | 0.132766i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.1009 | − | 7.56382i | 0.631050 | − | 0.364337i | −0.150109 | − | 0.988669i | \(-0.547962\pi\) |
0.781158 | + | 0.624333i | \(0.214629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.69681 | 0.129601 | 0.0648003 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0648003 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.2158 | − | 13.0597i | −0.681598 | − | 0.626167i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.00387858 | + | 0.00223930i | −0.000185537 | + | 0.000107120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.77101 | + | 4.48659i | 0.370890 | + | 0.214133i | 0.673847 | − | 0.738871i | \(-0.264641\pi\) |
−0.302957 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.0941 | + | 18.4149i | −0.480670 | + | 0.876901i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.1374 | − | 33.1469i | 0.909244 | − | 1.57486i | 0.0941261 | − | 0.995560i | \(-0.469994\pi\) |
0.815117 | − | 0.579296i | \(-0.196672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.51420 | + | 2.18748i | 0.0717801 | + | 0.103697i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.60702 | + | 1.73934i | 0.0760095 | + | 0.0822680i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.746605i | − | 0.0352345i | −0.999845 | − | 0.0176172i | \(-0.994392\pi\) | ||
0.999845 | − | 0.0176172i | \(-0.00560803\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.1887 | + | 13.3880i | −1.09191 | + | 0.630416i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.71235 | − | 38.5479i | −0.409342 | − | 1.81114i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.60378 | − | 3.57986i | 0.403351 | − | 0.167827i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.35184 | − | 2.51254i | −0.203571 | − | 0.117531i | 0.394749 | − | 0.918789i | \(-0.370831\pi\) |
−0.598320 | + | 0.801257i | \(0.704165\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.6608 | − | 9.06052i | −1.05772 | − | 0.422909i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5502 | 1.23656 | 0.618282 | − | 0.785956i | \(-0.287829\pi\) | ||||
0.618282 | + | 0.785956i | \(0.287829\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.30452i | 0.432418i | 0.976347 | + | 0.216209i | \(0.0693692\pi\) | ||||
−0.976347 | + | 0.216209i | \(0.930631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.76974 | − | 25.8698i | 0.267565 | − | 1.19968i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.45358 | + | 5.45803i | 0.437460 | + | 0.252567i | 0.702520 | − | 0.711664i | \(-0.252058\pi\) |
−0.265060 | + | 0.964232i | \(0.585392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5516 | − | 3.76282i | −0.810460 | − | 0.173751i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.88406 | − | 39.3077i | −0.409356 | − | 1.81120i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.1083 | + | 26.1684i | 0.694681 | + | 1.20322i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0189327 | − | 0.114575i | −0.000868691 | − | 0.00525706i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.43473 | − | 30.7391i | 0.111479 | − | 1.40745i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.01995 | + | 15.6230i | 0.412132 | + | 0.713834i | 0.995123 | − | 0.0986452i | \(-0.0314509\pi\) |
−0.582991 | + | 0.812479i | \(0.698118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.83269 | − | 1.63545i | −0.129159 | − | 0.0745702i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.883598 | + | 0.00979939i | −0.0402051 | + | 0.000445888i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.689973 | − | 1.45909i | 0.0313301 | − | 0.0662537i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.4337 | − | 18.1482i | 1.42440 | − | 0.822375i | 0.427725 | − | 0.903909i | \(-0.359315\pi\) |
0.996671 | + | 0.0815333i | \(0.0259817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.4999 | − | 28.6819i | −1.19837 | − | 1.29704i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.9137i | − | 0.582786i | −0.956603 | − | 0.291393i | \(-0.905881\pi\) | ||
0.956603 | − | 0.291393i | \(-0.0941187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7050 | − | 20.2736i | −0.527166 | − | 0.913079i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.2596 | − | 26.6046i | 0.685869 | − | 1.19579i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.2239 | + | 25.7022i | −1.04174 | + | 1.15290i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.7602 | + | 20.3692i | −0.526458 | + | 0.911852i | 0.473067 | + | 0.881027i | \(0.343147\pi\) |
−0.999525 | + | 0.0308254i | \(0.990186\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.31710 | − | 4.23800i | 0.0588436 | − | 0.189340i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.11496i | 0.228065i | 0.993477 | + | 0.114032i | \(0.0363768\pi\) | ||||
−0.993477 | + | 0.114032i | \(0.963623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.6609 | + | 2.76238i | −1.49789 | + | 0.122924i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.3983 | + | 5.40711i | 0.772686 | + | 0.240138i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6297 | − | 27.0714i | 0.692774 | − | 1.19992i | −0.278151 | − | 0.960537i | \(-0.589722\pi\) |
0.970925 | − | 0.239382i | \(-0.0769450\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.02530 | + | 37.4340i | −0.355018 | + | 1.65598i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0172275 | − | 0.119449i | −0.000760612 | − | 0.00527379i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.53502 | + | 7.99613i | 0.243902 | + | 0.352351i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.0513 | −1.14574 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.8074 | + | 27.9324i | 1.13282 | + | 1.22609i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.97790 | + | 17.2822i | 0.437140 | + | 0.757148i | 0.997468 | − | 0.0711229i | \(-0.0226582\pi\) |
−0.560328 | + | 0.828271i | \(0.689325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.2872 | + | 26.4783i | −0.668464 | + | 1.15781i | 0.309870 | + | 0.950779i | \(0.399714\pi\) |
−0.978334 | + | 0.207034i | \(0.933619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.82978 | − | 21.5336i | 0.341720 | − | 0.939802i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0715 | − | 27.8366i | 0.700085 | − | 1.21258i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4814 | + | 19.8864i | 0.499192 | + | 0.864625i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.590887 | + | 7.46010i | −0.0256423 | + | 0.323741i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.22490 | 0.399575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6333 | − | 24.0292i | −0.719121 | − | 1.03887i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.3908 | + | 2.34846i | −0.448396 | + | 0.101343i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.7210 | − | 25.9577i | −0.806369 | − | 1.11808i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.1289 | − | 34.8642i | 0.865407 | − | 1.49893i | −0.00123544 | − | 0.999999i | \(-0.500393\pi\) |
0.866642 | − | 0.498930i | \(-0.166273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.2535 | + | 36.2103i | −0.482936 | + | 1.55393i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.2086 | − | 1.33016i | 0.694302 | − | 0.0569778i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0498i | 0.557967i | 0.960296 | + | 0.278984i | \(0.0899975\pi\) | ||||
−0.960296 | + | 0.278984i | \(0.910002\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.9546 | + | 25.0958i | 0.510212 | + | 1.07106i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0578820 | − | 0.100254i | 0.00246585 | − | 0.00427098i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.2414 | + | 10.7365i | −1.41357 | + | 0.456564i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.67326 | + | 2.40864i | −0.325712 | + | 0.102241i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.7291 | − | 25.5116i | −0.624093 | − | 1.08096i | −0.988716 | − | 0.149805i | \(-0.952135\pi\) |
0.364623 | − | 0.931155i | \(-0.381198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.4103i | − | 0.440308i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.3185 | − | 25.2403i | 1.15339 | − | 1.06564i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.8141 | + | 19.5226i | −1.42509 | + | 0.822778i | −0.996728 | − | 0.0808279i | \(-0.974244\pi\) |
−0.428365 | + | 0.903606i | \(0.640910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.3367 | − | 28.2031i | 0.561078 | − | 1.18651i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.59452 | − | 22.2066i | 0.360936 | − | 0.932591i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.8770 | − | 18.4042i | −1.33635 | − | 0.771543i | −0.350088 | − | 0.936717i | \(-0.613848\pi\) |
−0.986265 | + | 0.165174i | \(0.947182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.27778 | + | 5.67728i | 0.137171 | + | 0.237587i | 0.926425 | − | 0.376480i | \(-0.122866\pi\) |
−0.789254 | + | 0.614067i | \(0.789532\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.13304 | + | 9.88504i | 0.381538 | + | 0.412953i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.951245 | − | 0.157186i | 0.0396696 | − | 0.00655512i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.50501 | + | 9.53496i | 0.229177 | + | 0.396945i | 0.957564 | − | 0.288220i | \(-0.0930633\pi\) |
−0.728388 | + | 0.685165i | \(0.759730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.5973 | + | 3.29918i | −0.606643 | + | 0.137109i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.82105 | − | 2.01537i | 0.0755497 | − | 0.0836118i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.6976 | + | 23.4968i | 1.68552 | + | 0.973137i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.13586 | + | 5.30924i | −0.377721 | + | 0.219510i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.2051i | 0.875227i | 0.899163 | + | 0.437614i | \(0.144176\pi\) | ||||
−0.899163 | + | 0.437614i | \(0.855824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.158949 | 0.00654938 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.5570 | − | 5.14563i | −0.681064 | − | 0.211663i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.8813 | + | 18.9841i | 1.35027 | + | 0.779582i | 0.988288 | − | 0.152601i | \(-0.0487651\pi\) |
0.361987 | + | 0.932183i | \(0.382098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.8801 | − | 22.0713i | 0.692019 | − | 0.904836i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.1395 | + | 7.26395i | −1.31538 | + | 0.297294i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.8018 | + | 12.0099i | −0.849937 | + | 0.490711i | −0.860629 | − | 0.509232i | \(-0.829930\pi\) |
0.0106928 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.3360i | 1.56376i | 0.623431 | + | 0.781878i | \(0.285738\pi\) | ||||
−0.623431 | + | 0.781878i | \(0.714262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2904 | + | 1.60712i | 0.826287 | + | 0.0654472i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.6041 | + | 18.2084i | 0.512429 | + | 0.740277i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.2254 | + | 24.6391i | −0.577390 | + | 1.00007i | 0.418388 | + | 0.908268i | \(0.362595\pi\) |
−0.995777 | + | 0.0917998i | \(0.970738\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.6529 | − | 11.6391i | 0.796377 | − | 0.471640i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.77278 | + | 4.48762i | 0.314453 | + | 0.181550i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.287485 | + | 0.165979i | −0.0116114 | + | 0.00670384i | −0.505794 | − | 0.862654i | \(-0.668801\pi\) |
0.494183 | + | 0.869358i | \(0.335467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.3450 | − | 16.7034i | 0.618769 | − | 0.673545i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.89790 | −0.156924 | −0.0784618 | − | 0.996917i | \(-0.525001\pi\) | ||||
−0.0784618 | + | 0.996917i | \(0.525001\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.6297 | + | 21.1482i | −1.47227 | + | 0.850018i | −0.999514 | − | 0.0311740i | \(-0.990075\pi\) |
−0.472760 | + | 0.881191i | \(0.656742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.991707 | − | 0.143029i | 0.0397958 | − | 0.00573956i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.99549 | + | 0.967505i | −0.120012 | + | 0.0387623i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.87048 | + | 24.5210i | −0.194819 | + | 0.980839i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.175639 | + | 0.0545855i | 0.00701433 | + | 0.00217994i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.75301 | −0.388878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1993 | 0.963360 | 0.481680 | − | 0.876347i | \(-0.340027\pi\) | ||||
0.481680 | + | 0.876347i | \(0.340027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.8820 | + | 11.7731i | 1.50567 | + | 0.467938i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.1755 | − | 9.54057i | −0.800638 | − | 0.378606i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.11418 | + | 10.9697i | 0.0441453 | + | 0.434637i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.2638 | − | 32.3593i | 0.880743 | − | 1.28011i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.8431 | − | 14.3432i | 0.981243 | − | 0.566521i | 0.0785980 | − | 0.996906i | \(-0.474956\pi\) |
0.902645 | + | 0.430385i | \(0.141622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.7651 | 1.33157 | 0.665783 | − | 0.746145i | \(-0.268098\pi\) | ||||
0.665783 | + | 0.746145i | \(0.268098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.8497 | − | 17.3168i | −0.742207 | − | 0.681846i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.78572 | − | 2.18568i | 0.148832 | − | 0.0859281i | −0.423735 | − | 0.905786i | \(-0.639281\pi\) |
0.572567 | + | 0.819858i | \(0.305948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.87696 | − | 5.70246i | −0.387704 | − | 0.223841i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.3321 | + | 15.3786i | 1.07123 | + | 0.602736i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.10337 | − | 3.64315i | 0.0823113 | − | 0.142567i | −0.821931 | − | 0.569587i | \(-0.807103\pi\) |
0.904242 | + | 0.427020i | \(0.140436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.8800 | − | 22.9409i | −0.620482 | − | 0.896375i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.42766 | − | 43.2751i | 0.133726 | − | 1.68832i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 41.3660i | − | 1.61139i | −0.592329 | − | 0.805696i | \(-0.701791\pi\) | ||
0.592329 | − | 0.805696i | \(-0.298209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.42328 | + | 3.70848i | −0.249837 | + | 0.144243i | −0.619689 | − | 0.784847i | \(-0.712741\pi\) |
0.369853 | + | 0.929090i | \(0.379408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.4988 | + | 2.82489i | −0.485412 | + | 0.109710i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.136258 | + | 0.0177181i | 0.00528387 | + | 0.000687077i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.832350 | + | 0.480557i | 0.0322287 | + | 0.0186073i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.87029 | + | 0.581254i | 0.0723095 | + | 0.0224726i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.3642 | −1.63545 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.5806i | 0.600587i | 0.953847 | + | 0.300293i | \(0.0970846\pi\) | ||||
−0.953847 | + | 0.300293i | \(0.902915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.58350 | + | 25.3737i | −0.214909 | + | 0.976634i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.1207 | − | 6.42051i | −0.427401 | − | 0.246760i | 0.270838 | − | 0.962625i | \(-0.412699\pi\) |
−0.698239 | + | 0.715865i | \(0.746033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.41695 | + | 1.28033i | 0.0543777 | + | 0.0491344i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.150516 | − | 0.0340186i | 0.00576779 | − | 0.00130360i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.1628 | − | 26.2628i | −0.580190 | − | 1.00492i | −0.995456 | − | 0.0952184i | \(-0.969645\pi\) |
0.415267 | − | 0.909700i | \(-0.363688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.9055 | − | 1.30528i | 0.607716 | − | 0.0498722i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5439 | − | 11.4121i | −0.402274 | − | 0.435397i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.09514 | − | 14.0212i | −0.308400 | − | 0.534165i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.57027 | + | 4.94805i | 0.326028 | + | 0.188233i | 0.654076 | − | 0.756429i | \(-0.273057\pi\) |
−0.328048 | + | 0.944661i | \(0.606391\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.9207 | + | 26.3796i | 0.946661 | + | 1.00208i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.0047 | + | 8.98695i | 0.720890 | + | 0.340895i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.8212 | − | 13.7532i | 0.902291 | − | 0.520938i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.9972 | − | 25.8673i | 1.05895 | − | 0.978392i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.88682i | 0.373420i | 0.982415 | + | 0.186710i | \(0.0597825\pi\) | ||||
−0.982415 | + | 0.186710i | \(0.940217\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0241146 | − | 0.0417678i | −0.000909501 | − | 0.00157530i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.0551 | − | 6.60921i | 0.792982 | − | 0.248917i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.37694 | − | 39.0742i | 0.315047 | − | 1.46953i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.5650 | + | 46.0119i | −0.997670 | + | 1.72801i | −0.439745 | + | 0.898123i | \(0.644931\pi\) |
−0.557925 | + | 0.829891i | \(0.688402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.7595 | − | 17.0344i | 1.34109 | − | 0.638840i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.31965i | 0.0494214i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.31711 | − | 16.0496i | −0.0492572 | − | 0.600222i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.8419 | + | 44.5389i | −0.516937 | + | 1.66333i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.10194 | + | 5.37272i | −0.115683 | + | 0.200369i | −0.918053 | − | 0.396459i | \(-0.870239\pi\) |
0.802370 | + | 0.596827i | \(0.203572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9497 | + | 3.53662i | −0.407789 | + | 0.131711i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.4607 | + | 6.43250i | −1.05846 | + | 0.239227i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.2624 | + | 15.8127i | −0.715386 | + | 0.587268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6957 | −0.841735 | −0.420868 | − | 0.907122i | \(-0.638274\pi\) | ||||
−0.420868 | + | 0.907122i | \(0.638274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.34252 | + | 26.2445i | −0.234908 | + | 0.972018i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5204 | − | 26.8821i | −0.574043 | − | 0.994271i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.48996 | + | 11.2409i | −0.239712 | + | 0.415193i | −0.960632 | − | 0.277825i | \(-0.910386\pi\) |
0.720920 | + | 0.693019i | \(0.243720\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.7161 | + | 16.2300i | 0.801010 | + | 0.598651i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.5098 | + | 26.8638i | −0.571312 | + | 0.989542i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.2551 | − | 45.4752i | −0.965811 | − | 1.67283i | −0.707420 | − | 0.706794i | \(-0.750141\pi\) |
−0.258391 | − | 0.966040i | \(-0.583192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0430013 | − | 0.0465420i | −0.00157969 | − | 0.00170976i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.0232 | −0.771265 | −0.385632 | − | 0.922652i | \(-0.626017\pi\) | ||||
−0.385632 | + | 0.922652i | \(0.626017\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.51370 | − | 1.74002i | 0.0920950 | − | 0.0637493i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.74576 | + | 2.53737i | −0.0638740 | + | 0.0928375i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.9051 | − | 10.6279i | 1.20233 | − | 0.388336i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.73267 | − | 13.3934i | 0.282169 | − | 0.488731i | −0.689750 | − | 0.724048i | \(-0.742279\pi\) |
0.971919 | + | 0.235317i | \(0.0756128\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.9534 | − | 4.33647i | −0.508489 | − | 0.158030i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50.8495 | + | 4.17296i | −1.85060 | + | 0.151869i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5557i | 1.03788i | 0.854812 | + | 0.518938i | \(0.173672\pi\) | ||||
−0.854812 | + | 0.518938i | \(0.826328\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.453189 | + | 1.45822i | −0.0164497 | + | 0.0529299i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.6618 | + | 42.7156i | −0.893991 | + | 1.54844i | −0.0589430 | + | 0.998261i | \(0.518773\pi\) |
−0.835048 | + | 0.550177i | \(0.814560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.03372 | + | 18.8153i | −0.146031 | + | 0.681158i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.6758 | + | 27.3303i | −0.566761 | + | 0.988129i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.96462 | + | 3.40282i | 0.0709383 | + | 0.122869i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.85691i | 0.139084i | 0.997579 | + | 0.0695419i | \(0.0221538\pi\) | ||||
−0.997579 | + | 0.0695419i | \(0.977846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6691 | + | 22.3710i | 0.744381 | + | 0.805671i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.1407 | − | 14.5150i | 0.904247 | − | 0.522067i | 0.0256713 | − | 0.999670i | \(-0.491828\pi\) |
0.878576 | + | 0.477603i | \(0.158494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.0268 | − | 12.0490i | −1.15044 | − | 0.432812i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.105528 | − | 9.51533i | −0.00378580 | − | 0.341360i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.117797 | + | 0.0680103i | 0.00422052 | + | 0.00243672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.9305 | + | 51.8412i | 1.07100 | + | 1.85503i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.3511 | + | 16.0187i | −0.727288 | + | 0.572461i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −51.8516 | + | 4.25520i | −1.85066 | + | 0.151875i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5679 | − | 20.0362i | −0.412352 | − | 0.714215i | 0.582794 | − | 0.812620i | \(-0.301959\pi\) |
−0.995146 | + | 0.0984048i | \(0.968626\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.46494 | − | 15.3307i | −0.123355 | − | 0.545786i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.3887 | + | 24.7478i | 0.973829 | + | 0.879930i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6400 | + | 7.29768i | 0.448858 | + | 0.259148i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.8536 | − | 8.66553i | −1.37800 | − | 0.307335i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.9627i | 1.02591i | 0.858415 | + | 0.512956i | \(0.171450\pi\) | ||||
−0.858415 | + | 0.512956i | \(0.828550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.7619 | 0.946767 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.22241 | − | 1.53503i | 0.113858 | − | 0.0542375i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 57.2949 | + | 33.0792i | 2.02189 | + | 1.16734i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.147102 | + | 1.13127i | −0.00518466 | + | 0.0398719i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0096 | + | 44.2875i | 0.352354 | + | 1.55899i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.47318 | − | 0.850541i | 0.0517943 | − | 0.0299034i | −0.473879 | − | 0.880590i | \(-0.657147\pi\) |
0.525674 | + | 0.850686i | \(0.323813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.26175i | 0.0443059i | 0.999755 | + | 0.0221529i | \(0.00705208\pi\) | ||||
−0.999755 | + | 0.0221529i | \(0.992948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.7890 | + | 27.9124i | 0.904459 | + | 0.978930i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.4512 | + | 28.6931i | −1.45197 | + | 1.00507i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0767494 | − | 0.132934i | 0.00268512 | − | 0.00465077i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.89128 | − | 12.1636i | −0.101030 | − | 0.425031i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.4002 | − | 11.2007i | −0.677072 | − | 0.390908i | 0.121679 | − | 0.992569i | \(-0.461172\pi\) |
−0.798751 | + | 0.601662i | \(0.794505\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.3644 | + | 10.6027i | −0.640144 | + | 0.369587i | −0.784670 | − | 0.619914i | \(-0.787168\pi\) |
0.144526 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −31.2517 | − | 24.3126i | −1.08805 | − | 0.846455i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.3474 | −1.36824 | −0.684122 | − | 0.729368i | \(-0.739814\pi\) | ||||
−0.684122 | + | 0.729368i | \(0.739814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5440 | − | 11.8611i | 0.713521 | − | 0.411952i | −0.0988421 | − | 0.995103i | \(-0.531514\pi\) |
0.812364 | + | 0.583151i | \(0.198181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.2405 | + | 9.09489i | −1.39593 | + | 0.315498i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.2316 | + | 26.6657i | 0.666335 | + | 0.923912i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.17946 | − | 2.44926i | −0.179242 | − | 0.0847602i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.0192 | − | 13.2021i | −1.14131 | − | 0.456332i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.8614 | −0.478550 | −0.239275 | − | 0.970952i | \(-0.576910\pi\) | ||||
−0.239275 | + | 0.970952i | \(0.576910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.15685 | 0.143340 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.311368 | − | 1.00188i | 0.0107241 | − | 0.0345067i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0550 | − | 21.2633i | 0.345902 | − | 0.731480i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.9342 | + | 8.05342i | −0.856750 | + | 0.276719i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.7287 | + | 51.8937i | 0.402527 | + | 1.78099i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.346771 | − | 0.200209i | 0.0118872 | − | 0.00686306i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.4548 | −0.803078 | −0.401539 | − | 0.915842i | \(-0.631524\pi\) | ||||
−0.401539 | + | 0.915842i | \(0.631524\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.155802 | 0.000442496i | −0.00532833 | 1.51331e-5i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.7019 | + | 23.4993i | −1.39035 | + | 0.802720i | −0.993354 | − | 0.115100i | \(-0.963281\pi\) |
−0.396997 | + | 0.917820i | \(0.629948\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.8802 | + | 12.0552i | 0.712424 | + | 0.411318i | 0.811958 | − | 0.583716i | \(-0.198402\pi\) |
−0.0995342 | + | 0.995034i | \(0.531735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6757 | + | 23.0918i | 0.466068 | + | 0.786968i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.82464 | + | 4.89242i | −0.0961519 | + | 0.166540i | −0.910089 | − | 0.414413i | \(-0.863987\pi\) |
0.813937 | + | 0.580953i | \(0.197320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.3680 | − | 27.9432i | 1.37255 | − | 0.950098i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.43658 | + | 5.94692i | −0.218598 | + | 0.201968i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.3655i | 2.04776i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.25516 | − | 5.34347i | 0.313599 | − | 0.181057i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.78395 | − | 1.22740i | −0.0603777 | − | 0.0415410i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.1117 | − | 13.8989i | −0.882736 | − | 0.469870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.425057 | + | 0.245407i | 0.0143531 | + | 0.00828679i | 0.507159 | − | 0.861852i | \(-0.330696\pi\) |
−0.492806 | + | 0.870139i | \(0.664029\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.6915 | + | 37.6195i | −0.394344 | + | 1.26887i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.5907 | 0.929555 | 0.464778 | − | 0.885427i | \(-0.346134\pi\) | ||||
0.464778 | + | 0.885427i | \(0.346134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.5174i | 1.06064i | 0.847796 | + | 0.530322i | \(0.177929\pi\) | ||||
−0.847796 | + | 0.530322i | \(0.822071\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.42944 | + | 2.10305i | 0.316967 | + | 0.0706932i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.19558 | − | 5.30907i | −0.308757 | − | 0.178261i | 0.337613 | − | 0.941285i | \(-0.390381\pi\) |
−0.646370 | + | 0.763024i | \(0.723714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.7037 | − | 19.5929i | 0.593762 | − | 0.657124i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.9524 | − | 25.9276i | −1.07044 | − | 0.868608i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0661696 | + | 0.114609i | 0.00221428 | + | 0.00383525i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.12484 | + | 13.7067i | 0.0375993 | + | 0.458166i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.386409 | − | 0.357013i | 0.0129018 | − | 0.0119203i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.0554 | − | 29.5408i | −0.568829 | − | 0.985241i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.8077 | − | 24.1377i | −1.39282 | − | 0.804142i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.0591 | − | 15.4330i | 0.867192 | − | 0.513579i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 44.2542 | + | 20.9269i | 1.47106 | + | 0.695635i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.0167 | − | 21.9489i | 1.26232 | − | 0.728803i | 0.288800 | − | 0.957390i | \(-0.406744\pi\) |
0.973523 | + | 0.228587i | \(0.0734106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.57784 | + | 45.1712i | −0.118670 | + | 1.49823i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.18050i | 0.271032i | 0.990775 | + | 0.135516i | \(0.0432692\pi\) | ||||
−0.990775 | + | 0.135516i | \(0.956731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.34693 | − | 4.06499i | −0.0776719 | − | 0.134532i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 34.2395 | − | 10.7478i | 1.13192 | − | 0.355311i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.4148 | − | 10.1466i | 1.03741 | − | 0.335069i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.15414 | + | 8.92723i | −0.170019 | + | 0.294482i | −0.938426 | − | 0.345479i | \(-0.887716\pi\) |
0.768407 | + | 0.639961i | \(0.221050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.55490 | + | 2.34794i | 0.248942 | + | 0.0773671i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 20.6234i | − | 0.678828i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.69271 | + | 10.2438i | 0.0556560 | + | 0.336814i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.7792 | − | 5.61113i | 0.386879 | − | 0.184294i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.9667 | − | 39.7794i | 0.753512 | − | 1.30512i | −0.192599 | − | 0.981278i | \(-0.561692\pi\) |
0.946111 | − | 0.323843i | \(-0.104975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0666466 | + | 0.148292i | −0.00218425 | + | 0.00486008i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.70082 | + | 20.7989i | 0.153898 | + | 0.680925i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.3291 | − | 39.4808i | −0.893758 | − | 1.29116i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.3541 | 1.64500 | 0.822499 | − | 0.568767i | \(-0.192579\pi\) | ||||
0.822499 | + | 0.568767i | \(0.192579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.48391 | − | 7.83850i | 0.276862 | − | 0.255800i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.96200 | − | 8.59443i | −0.161757 | − | 0.280171i | 0.773742 | − | 0.633501i | \(-0.218383\pi\) |
−0.935499 | + | 0.353330i | \(0.885049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.564646 | + | 0.977996i | −0.0183874 | + | 0.0318479i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −26.8339 | − | 14.9981i | −0.872906 | − | 0.487888i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.97339 | − | 6.88211i | 0.129118 | − | 0.223638i | −0.794217 | − | 0.607634i | \(-0.792119\pi\) |
0.923335 | + | 0.383995i | \(0.125452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.3965 | − | 19.7393i | −0.369946 | − | 0.640765i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.2467 | + | 11.3151i | −0.397127 | + | 0.366916i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.8058 | −1.38662 | −0.693308 | − | 0.720641i | \(-0.743848\pi\) | ||||
−0.693308 | + | 0.720641i | \(0.743848\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.2859 | − | 9.88888i | 0.462281 | − | 0.319997i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.70143 | − | 38.4996i | −0.281277 | − | 1.24452i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.95827 | + | 18.4633i | −0.127819 | + | 0.596212i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.91782 | − | 13.7141i | 0.255414 | − | 0.442389i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.3977 | + | 16.8621i | −1.14068 | + | 0.543372i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.58021 | + | 19.2556i | 0.0508688 | + | 0.619861i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9826i | 0.771227i | 0.922660 | + | 0.385613i | \(0.126010\pi\) | ||||
−0.922660 | + | 0.385613i | \(0.873990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.180429 | − | 0.0560744i | −0.00579622 | − | 0.00180137i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.893834 | − | 1.54817i | 0.0286845 | − | 0.0496830i | −0.851327 | − | 0.524636i | \(-0.824202\pi\) |
0.880011 | + | 0.474953i | \(0.157535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.6764 | + | 18.4559i | −0.534619 | + | 0.591670i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.13630 | + | 12.6374i | 0.164493 | + | 0.404722i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.56427 | + | 14.8337i | 0.273995 | + | 0.474574i | 0.969881 | − | 0.243579i | \(-0.0783214\pi\) |
−0.695886 | + | 0.718152i | \(0.744988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.43974i | 0.173855i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.72283 | − | 21.7512i | 0.0550057 | − | 0.694461i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.1805 | − | 27.2397i | 1.50483 | − | 0.868811i | 0.504841 | − | 0.863212i | \(-0.331551\pi\) |
0.999984 | − | 0.00559883i | \(-0.00178217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.56876 | + | 20.2351i | −0.304886 | + | 0.644743i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.289565 | + | 26.1097i | 0.00921696 | + | 0.831080i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.10367 | + | 0.637202i | 0.0350945 | + | 0.0202618i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.6055 | − | 20.1013i | −0.368661 | − | 0.638540i | 0.620695 | − | 0.784052i | \(-0.286850\pi\) |
−0.989357 | + | 0.145512i | \(0.953517\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.1986 | − | 14.0424i | 0.482314 | − | 0.445623i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.47922 | + | 42.3959i | 0.110299 | + | 1.34404i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.30773 | + | 5.72916i | 0.104757 | + | 0.181444i | 0.913639 | − | 0.406527i | \(-0.133260\pi\) |
−0.808882 | + | 0.587971i | \(0.799927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.54026 | + | 10.6795i | 0.0487316 | + | 0.337885i |
(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 | 840.2.da.a.89.3 | ✓ | 48 | |
3.2 | odd | 2 | 840.2.da.b.89.13 | yes | 48 | ||
5.4 | even | 2 | 840.2.da.b.89.22 | yes | 48 | ||
7.3 | odd | 6 | inner | 840.2.da.a.689.12 | yes | 48 | |
15.14 | odd | 2 | inner | 840.2.da.a.89.12 | yes | 48 | |
21.17 | even | 6 | 840.2.da.b.689.22 | yes | 48 | ||
35.24 | odd | 6 | 840.2.da.b.689.13 | yes | 48 | ||
105.59 | even | 6 | inner | 840.2.da.a.689.3 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.da.a.89.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
840.2.da.a.89.12 | yes | 48 | 15.14 | odd | 2 | inner | |
840.2.da.a.689.3 | yes | 48 | 105.59 | even | 6 | inner | |
840.2.da.a.689.12 | yes | 48 | 7.3 | odd | 6 | inner | |
840.2.da.b.89.13 | yes | 48 | 3.2 | odd | 2 | ||
840.2.da.b.89.22 | yes | 48 | 5.4 | even | 2 | ||
840.2.da.b.689.13 | yes | 48 | 35.24 | odd | 6 | ||
840.2.da.b.689.22 | yes | 48 | 21.17 | even | 6 |