Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(313,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.313");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.m (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: | \(16.0218395444\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.4 | ||
Root | \(0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.325 |
Dual form | 588.3.m.f.313.4 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 0.866025i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.65891 | − | 2.68982i | 0.931781 | − | 0.537964i | 0.0444067 | − | 0.999014i | \(-0.485860\pi\) |
0.887374 | + | 0.461049i | \(0.152527\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29579 | − | 7.44053i | 0.390527 | − | 0.676412i | −0.601992 | − | 0.798502i | \(-0.705626\pi\) |
0.992519 | + | 0.122090i | \(0.0389596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 21.0158i | − | 1.61660i | −0.588769 | − | 0.808301i | \(-0.700387\pi\) | ||
0.588769 | − | 0.808301i | \(-0.299613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.31781 | 0.621187 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.75120 | + | 2.74311i | 0.279483 | + | 0.161359i | 0.633189 | − | 0.773997i | \(-0.281746\pi\) |
−0.353707 | + | 0.935356i | \(0.615079\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.27088 | + | 3.62049i | −0.330046 | + | 0.190552i | −0.655862 | − | 0.754881i | \(-0.727695\pi\) |
0.325815 | + | 0.945433i | \(0.394361\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −14.0278 | − | 24.2969i | −0.609905 | − | 1.05639i | −0.991256 | − | 0.131956i | \(-0.957874\pi\) |
0.381350 | − | 0.924431i | \(-0.375459\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.97027 | − | 3.41261i | 0.0788107 | − | 0.136504i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.3447 | 1.39120 | 0.695599 | − | 0.718431i | \(-0.255139\pi\) | ||||
0.695599 | + | 0.718431i | \(0.255139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.0828 | + | 20.2550i | 1.13170 | + | 0.653388i | 0.944362 | − | 0.328907i | \(-0.106680\pi\) |
0.187340 | + | 0.982295i | \(0.440014\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.8874 | − | 7.44053i | 0.390527 | − | 0.225471i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.3185 | − | 57.7093i | −0.900500 | − | 1.55971i | −0.826846 | − | 0.562428i | \(-0.809867\pi\) |
−0.0736541 | − | 0.997284i | \(-0.523466\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.2002 | − | 31.5237i | 0.466673 | − | 0.808301i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.6357i | 0.820383i | 0.911999 | + | 0.410191i | \(0.134538\pi\) | ||||
−0.911999 | + | 0.410191i | \(0.865462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.932907 | 0.0216955 | 0.0108478 | − | 0.999941i | \(-0.496547\pi\) | ||||
0.0108478 | + | 0.999941i | \(0.496547\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.9767 | + | 8.06946i | 0.310594 | + | 0.179321i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −74.1789 | + | 42.8272i | −1.57827 | + | 0.911217i | −0.583173 | + | 0.812348i | \(0.698189\pi\) |
−0.995100 | + | 0.0988687i | \(0.968478\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.75120 | + | 8.22933i | 0.0931609 | + | 0.161359i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22.2977 | − | 38.6207i | 0.420711 | − | 0.728693i | −0.575298 | − | 0.817944i | \(-0.695114\pi\) |
0.996009 | + | 0.0892508i | \(0.0284473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 46.2197i | − | 0.840358i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.5418 | −0.220031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 55.1615 | + | 31.8475i | 0.934940 | + | 0.539788i | 0.888371 | − | 0.459127i | \(-0.151838\pi\) |
0.0465695 | + | 0.998915i | \(0.485171\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 27.7201 | − | 16.0042i | 0.454427 | − | 0.262364i | −0.255271 | − | 0.966870i | \(-0.582165\pi\) |
0.709698 | + | 0.704506i | \(0.248831\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −56.5288 | − | 97.9108i | −0.869674 | − | 1.50632i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.8671 | − | 41.3390i | 0.356225 | − | 0.617000i | −0.631102 | − | 0.775700i | \(-0.717397\pi\) |
0.987327 | + | 0.158700i | \(0.0507304\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 48.5938i | − | 0.704258i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.9676 | 0.210811 | 0.105405 | − | 0.994429i | \(-0.466386\pi\) | ||||
0.105405 | + | 0.994429i | \(0.466386\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 121.501 | + | 70.1488i | 1.66440 | + | 0.960942i | 0.970575 | + | 0.240798i | \(0.0774091\pi\) |
0.693825 | + | 0.720144i | \(0.255924\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.91081 | − | 3.41261i | 0.0788107 | − | 0.0455014i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61.1537 | + | 105.921i | 0.774098 | + | 1.34078i | 0.935300 | + | 0.353856i | \(0.115130\pi\) |
−0.161202 | + | 0.986921i | \(0.551537\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 33.1852i | 0.399822i | 0.979814 | + | 0.199911i | \(0.0640652\pi\) | ||||
−0.979814 | + | 0.199911i | \(0.935935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.5139 | 0.347222 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 60.5171 | + | 34.9396i | 0.695599 | + | 0.401604i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 31.2848 | − | 18.0623i | 0.351515 | − | 0.202947i | −0.313838 | − | 0.949477i | \(-0.601615\pi\) |
0.665352 | + | 0.746530i | \(0.268281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 35.0828 | + | 60.7651i | 0.377234 | + | 0.653388i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.4769 | + | 33.7351i | −0.205021 | + | 0.355106i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.2175i | 0.167191i | 0.996500 | + | 0.0835956i | \(0.0266404\pi\) | ||||
−0.996500 | + | 0.0835956i | \(0.973360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25.7748 | 0.260351 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −103.459 | − | 59.7322i | −1.02435 | − | 0.591407i | −0.108987 | − | 0.994043i | \(-0.534761\pi\) |
−0.915360 | + | 0.402636i | \(0.868094\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.73523 | + | 4.46594i | −0.0750994 | + | 0.0433586i | −0.537079 | − | 0.843532i | \(-0.680472\pi\) |
0.461980 | + | 0.886890i | \(0.347139\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −86.9279 | − | 150.564i | −0.812410 | − | 1.40714i | −0.911173 | − | 0.412025i | \(-0.864822\pi\) |
0.0987623 | − | 0.995111i | \(-0.468512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.1573 | − | 138.837i | 0.735388 | − | 1.27373i | −0.219165 | − | 0.975688i | \(-0.570333\pi\) |
0.954553 | − | 0.298042i | \(-0.0963334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 115.419i | − | 1.03981i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −81.4420 | −0.720725 | −0.360363 | − | 0.932812i | \(-0.617347\pi\) | ||||
−0.360363 | + | 0.932812i | \(0.617347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −130.709 | − | 75.4646i | −1.13660 | − | 0.656214i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 54.6007 | − | 31.5237i | 0.466673 | − | 0.269434i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.5923 | + | 40.8631i | 0.194978 | + | 0.337711i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −29.1294 | + | 50.4536i | −0.236824 | + | 0.410191i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 113.292i | 0.906339i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 117.172 | 0.922613 | 0.461307 | − | 0.887241i | \(-0.347381\pi\) | ||||
0.461307 | + | 0.887241i | \(0.347381\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.39936 | + | 0.807922i | 0.0108478 | + | 0.00626296i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −211.440 | + | 122.075i | −1.61404 | + | 0.931869i | −0.625625 | + | 0.780124i | \(0.715156\pi\) |
−0.988420 | + | 0.151745i | \(0.951511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.9767 | + | 24.2084i | 0.103531 | + | 0.179321i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −122.706 | + | 212.533i | −0.895663 | + | 1.55133i | −0.0626820 | + | 0.998034i | \(0.519965\pi\) |
−0.832981 | + | 0.553301i | \(0.813368\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 17.1371i | − | 0.123288i | −0.998098 | − | 0.0616441i | \(-0.980366\pi\) | ||
0.998098 | − | 0.0616441i | \(-0.0196344\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −148.358 | −1.05218 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −156.369 | − | 90.2797i | −1.09349 | − | 0.631326i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 187.962 | − | 108.520i | 1.29629 | − | 0.748414i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −67.1209 | − | 116.257i | −0.450476 | − | 0.780247i | 0.547940 | − | 0.836518i | \(-0.315412\pi\) |
−0.998416 | + | 0.0562707i | \(0.982079\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −99.5047 | + | 172.347i | −0.658971 | + | 1.14137i | 0.321911 | + | 0.946770i | \(0.395675\pi\) |
−0.980882 | + | 0.194602i | \(0.937659\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.4587i | 0.107573i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 217.930 | 1.40600 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −66.7004 | − | 38.5095i | −0.424843 | − | 0.245283i | 0.272304 | − | 0.962211i | \(-0.412214\pi\) |
−0.697147 | + | 0.716928i | \(0.745548\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 66.8931 | − | 38.6207i | 0.420711 | − | 0.242898i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 115.190 | + | 199.514i | 0.706684 | + | 1.22401i | 0.966080 | + | 0.258242i | \(0.0831432\pi\) |
−0.259396 | + | 0.965771i | \(0.583523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 40.0274 | − | 69.3295i | 0.242590 | − | 0.420179i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 229.231i | 1.37264i | 0.727298 | + | 0.686321i | \(0.240776\pi\) | ||||
−0.727298 | + | 0.686321i | \(0.759224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −272.665 | −1.61340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.8126 | − | 10.8615i | −0.110015 | − | 0.0635174i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −97.4044 | + | 56.2365i | −0.563031 | + | 0.325066i | −0.754361 | − | 0.656459i | \(-0.772053\pi\) |
0.191330 | + | 0.981526i | \(0.438720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 55.1615 | + | 95.5425i | 0.311647 | + | 0.539788i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −52.7470 | + | 91.3605i | −0.294676 | + | 0.510394i | −0.974909 | − | 0.222602i | \(-0.928545\pi\) |
0.680234 | + | 0.732995i | \(0.261878\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.2683i | 0.0843553i | 0.999110 | + | 0.0421776i | \(0.0134295\pi\) | ||||
−0.999110 | + | 0.0421776i | \(0.986570\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 55.4401 | 0.302951 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −310.456 | − | 179.242i | −1.67814 | − | 0.968874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 40.8204 | − | 23.5677i | 0.218291 | − | 0.126030i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 153.093 | + | 265.165i | 0.801534 | + | 1.38830i | 0.918606 | + | 0.395174i | \(0.129316\pi\) |
−0.117073 | + | 0.993123i | \(0.537351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.920499 | − | 1.59435i | 0.00476943 | − | 0.00826089i | −0.863631 | − | 0.504125i | \(-0.831815\pi\) |
0.868400 | + | 0.495864i | \(0.165149\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 195.822i | − | 1.00421i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −255.334 | −1.29611 | −0.648056 | − | 0.761593i | \(-0.724418\pi\) | ||||
−0.648056 | + | 0.761593i | \(0.724418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 31.7384 | + | 18.3242i | 0.159489 | + | 0.0920812i | 0.577620 | − | 0.816305i | \(-0.303981\pi\) |
−0.418131 | + | 0.908387i | \(0.637315\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 71.6012 | − | 41.3390i | 0.356225 | − | 0.205667i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 90.4740 | + | 156.706i | 0.441337 | + | 0.764417i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 42.0835 | − | 72.8907i | 0.203302 | − | 0.352129i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 62.2116i | 0.297663i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −126.571 | −0.599862 | −0.299931 | − | 0.953961i | \(-0.596964\pi\) | ||||
−0.299931 | + | 0.953961i | \(0.596964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.4513 | + | 12.9623i | 0.105405 | + | 0.0608558i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.34633 | − | 2.50935i | 0.0202155 | − | 0.0116714i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 121.501 | + | 210.446i | 0.554800 | + | 0.960942i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 57.6487 | − | 99.8505i | 0.260854 | − | 0.451812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 212.193i | − | 0.951536i | −0.879571 | − | 0.475768i | \(-0.842170\pi\) | ||
0.879571 | − | 0.475768i | \(-0.157830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.8216 | 0.0525405 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 91.3560 | + | 52.7444i | 0.402449 | + | 0.232354i | 0.687540 | − | 0.726146i | \(-0.258690\pi\) |
−0.285091 | + | 0.958500i | \(0.592024\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.05426 | − | 3.49543i | 0.0264378 | − | 0.0152639i | −0.486723 | − | 0.873556i | \(-0.661808\pi\) |
0.513161 | + | 0.858293i | \(0.328474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −168.023 | − | 291.024i | −0.721128 | − | 1.24903i | −0.960548 | − | 0.278115i | \(-0.910290\pi\) |
0.239419 | − | 0.970916i | \(-0.423043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −230.395 | + | 399.056i | −0.980404 | + | 1.69811i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 211.843i | 0.893851i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −232.382 | −0.972309 | −0.486155 | − | 0.873873i | \(-0.661601\pi\) | ||||
−0.486155 | + | 0.873873i | \(0.661601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 55.1958 | + | 31.8673i | 0.229028 | + | 0.132229i | 0.610124 | − | 0.792306i | \(-0.291120\pi\) |
−0.381095 | + | 0.924536i | \(0.624453\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 76.0876 | + | 131.788i | 0.308047 | + | 0.533553i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.7392 | + | 49.7778i | −0.115419 | + | 0.199911i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 415.450i | 1.65518i | 0.561334 | + | 0.827589i | \(0.310288\pi\) | ||||
−0.561334 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −241.043 | −0.952737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 44.2708 | + | 25.5598i | 0.173611 | + | 0.100234i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 230.014 | − | 132.799i | 0.894998 | − | 0.516727i | 0.0194240 | − | 0.999811i | \(-0.493817\pi\) |
0.875574 | + | 0.483084i | \(0.160483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 60.5171 | + | 104.819i | 0.231866 | + | 0.401604i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −78.1866 | + | 135.423i | −0.297288 | + | 0.514917i | −0.975514 | − | 0.219935i | \(-0.929415\pi\) |
0.678227 | + | 0.734853i | \(0.262749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 239.907i | − | 0.905310i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 62.5696 | 0.234343 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −288.266 | − | 166.431i | −1.07162 | − | 0.618701i | −0.142998 | − | 0.989723i | \(-0.545674\pi\) |
−0.928624 | + | 0.371022i | \(0.879008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −181.076 | + | 104.544i | −0.668178 | + | 0.385773i | −0.795386 | − | 0.606103i | \(-0.792732\pi\) |
0.127208 | + | 0.991876i | \(0.459398\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.9277 | − | 29.3197i | −0.0615554 | − | 0.106617i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 131.616 | − | 227.965i | 0.475146 | − | 0.822978i | −0.524448 | − | 0.851442i | \(-0.675728\pi\) |
0.999595 | + | 0.0284646i | \(0.00906180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 121.530i | 0.435592i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 391.519 | 1.39331 | 0.696653 | − | 0.717408i | \(-0.254672\pi\) | ||||
0.696653 | + | 0.717408i | \(0.254672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −94.7376 | − | 54.6968i | −0.334762 | − | 0.193275i | 0.323191 | − | 0.946334i | \(-0.395244\pi\) |
−0.657953 | + | 0.753059i | \(0.728578\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −58.4308 | + | 33.7351i | −0.205021 | + | 0.118369i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −129.451 | − | 224.215i | −0.447926 | − | 0.775831i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0448 | + | 24.3263i | −0.0482639 | + | 0.0835956i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 35.3685i | 0.120712i | 0.998177 | + | 0.0603558i | \(0.0192235\pi\) | ||||
−0.998177 | + | 0.0603558i | \(0.980776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 342.656 | 1.16155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 38.6622 | + | 22.3216i | 0.130176 | + | 0.0751569i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −510.619 | + | 294.806i | −1.70776 | + | 0.985974i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −103.459 | − | 179.196i | −0.341449 | − | 0.591407i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 86.0968 | − | 149.124i | 0.282284 | − | 0.488931i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 125.621i | 0.409189i | 0.978847 | + | 0.204594i | \(0.0655875\pi\) | ||||
−0.978847 | + | 0.204594i | \(0.934412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.4705 | −0.0500662 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 273.435 | + | 157.868i | 0.879211 | + | 0.507613i | 0.870398 | − | 0.492348i | \(-0.163861\pi\) |
0.00881288 | + | 0.999961i | \(0.497195\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −44.6909 | + | 25.8023i | −0.142782 | + | 0.0824355i | −0.569689 | − | 0.821860i | \(-0.692936\pi\) |
0.426907 | + | 0.904296i | \(0.359603\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.49696 | + | 4.32486i | 0.00787683 | + | 0.0136431i | 0.869937 | − | 0.493163i | \(-0.164159\pi\) |
−0.862060 | + | 0.506806i | \(0.830826\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 173.313 | − | 300.186i | 0.543300 | − | 0.941023i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 301.127i | − | 0.938091i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.7256 | −0.122990 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −71.7187 | − | 41.4068i | −0.220673 | − | 0.127406i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 240.472 | − | 138.837i | 0.735388 | − | 0.424577i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −227.390 | − | 393.851i | −0.686980 | − | 1.18988i | −0.972810 | − | 0.231603i | \(-0.925603\pi\) |
0.285831 | − | 0.958280i | \(-0.407731\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 99.9555 | − | 173.128i | 0.300167 | − | 0.519904i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 256.792i | − | 0.766545i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −183.824 | −0.545471 | −0.272736 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272736 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −122.163 | − | 70.5308i | −0.360363 | − | 0.208055i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 301.417 | − | 174.023i | 0.883920 | − | 0.510331i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −130.709 | − | 226.394i | −0.378865 | − | 0.656214i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −72.3882 | + | 125.380i | −0.208611 | + | 0.361326i | −0.951277 | − | 0.308337i | \(-0.900228\pi\) |
0.742666 | + | 0.669662i | \(0.233561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 187.069i | 0.536015i | 0.963417 | + | 0.268007i | \(0.0863651\pi\) | ||||
−0.963417 | + | 0.268007i | \(0.913635\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 109.201 | 0.311115 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 192.778 | + | 111.300i | 0.546113 | + | 0.315299i | 0.747553 | − | 0.664202i | \(-0.231229\pi\) |
−0.201440 | + | 0.979501i | \(0.564562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 69.7324 | − | 40.2600i | 0.196429 | − | 0.113409i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.4928 | − | 54.5472i | −0.0877237 | − | 0.151942i | 0.818825 | − | 0.574043i | \(-0.194626\pi\) |
−0.906549 | + | 0.422101i | \(0.861293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −154.284 | + | 267.228i | −0.427380 | + | 0.740243i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 81.7261i | 0.225141i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 754.750 | 2.06781 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 473.803 | + | 273.550i | 1.29102 | + | 0.745368i | 0.978834 | − | 0.204654i | \(-0.0656071\pi\) |
0.312181 | + | 0.950023i | \(0.398940\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −87.3881 | + | 50.4536i | −0.236824 | + | 0.136730i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2208 | + | 28.0953i | 0.0434875 | + | 0.0753226i | 0.886950 | − | 0.461866i | \(-0.152820\pi\) |
−0.843462 | + | 0.537188i | \(0.819486\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −98.1141 | + | 169.939i | −0.261637 | + | 0.453169i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 847.878i | − | 2.24901i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 508.859 | 1.34263 | 0.671317 | − | 0.741170i | \(-0.265729\pi\) | ||||
0.671317 | + | 0.741170i | \(0.265729\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 175.758 | + | 101.474i | 0.461307 | + | 0.266336i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.7625 | − | 13.1419i | 0.0594321 | − | 0.0343131i | −0.469990 | − | 0.882672i | \(-0.655742\pi\) |
0.529422 | + | 0.848359i | \(0.322409\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.39936 | + | 2.42376i | 0.00361592 | + | 0.00626296i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 180.064 | − | 311.880i | 0.462890 | − | 0.801749i | −0.536214 | − | 0.844082i | \(-0.680146\pi\) |
0.999104 | + | 0.0423337i | \(0.0134793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 153.919i | − | 0.393656i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −422.880 | −1.07603 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 569.819 | + | 328.985i | 1.44258 | + | 0.832874i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 494.494 | − | 285.496i | 1.24558 | − | 0.719134i | 0.275352 | − | 0.961343i | \(-0.411206\pi\) |
0.970224 | + | 0.242210i | \(0.0778722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.2007 | − | 59.2373i | −0.0852885 | − | 0.147724i | 0.820226 | − | 0.572040i | \(-0.193848\pi\) |
−0.905514 | + | 0.424316i | \(0.860515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 425.677 | − | 737.293i | 1.05627 | − | 1.82951i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 48.4168i | 0.119548i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −572.518 | −1.40668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3064 | + | 7.68246i | 0.0325340 | + | 0.0187835i | 0.516179 | − | 0.856481i | \(-0.327354\pi\) |
−0.483645 | + | 0.875264i | \(0.660687\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −368.118 | + | 212.533i | −0.895663 | + | 0.517112i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 89.2622 | + | 154.607i | 0.215090 | + | 0.372546i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.8411 | − | 25.7056i | 0.0355902 | − | 0.0616441i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 366.079i | − | 0.873696i | −0.899535 | − | 0.436848i | \(-0.856095\pi\) | ||
0.899535 | − | 0.436848i | \(-0.143905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 607.135 | 1.44213 | 0.721063 | − | 0.692870i | \(-0.243654\pi\) | ||||
0.721063 | + | 0.692870i | \(0.243654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −222.537 | − | 128.482i | −0.526091 | − | 0.303739i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.7223 | − | 10.8093i | 0.0440525 | − | 0.0254337i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −156.369 | − | 270.839i | −0.364497 | − | 0.631326i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 293.177 | − | 507.797i | 0.680224 | − | 1.17818i | −0.294688 | − | 0.955594i | \(-0.595216\pi\) |
0.974912 | − | 0.222590i | \(-0.0714510\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 518.769i | 1.19808i | 0.800719 | + | 0.599040i | \(0.204451\pi\) | ||||
−0.800719 | + | 0.599040i | \(0.795549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 375.924 | 0.864194 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 175.933 | + | 101.575i | 0.402594 | + | 0.232438i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −191.845 | + | 110.762i | −0.437005 | + | 0.252305i | −0.702326 | − | 0.711855i | \(-0.747855\pi\) |
0.265321 | + | 0.964160i | \(0.414522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 113.208 | + | 196.081i | 0.255548 | + | 0.442622i | 0.965044 | − | 0.262087i | \(-0.0844109\pi\) |
−0.709496 | + | 0.704709i | \(0.751078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 97.1686 | − | 168.301i | 0.218356 | − | 0.378205i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 232.514i | − | 0.520165i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −378.422 | −0.842810 | −0.421405 | − | 0.906873i | \(-0.638463\pi\) | ||||
−0.421405 | + | 0.906873i | \(0.638463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 250.268 | + | 144.492i | 0.554917 | + | 0.320382i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −298.514 | + | 172.347i | −0.658971 | + | 0.380457i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −219.077 | − | 379.452i | −0.479380 | − | 0.830311i | 0.520340 | − | 0.853959i | \(-0.325805\pi\) |
−0.999720 | + | 0.0236483i | \(0.992472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2536 | + | 24.6880i | −0.0310536 | + | 0.0537865i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 46.3981i | 0.100647i | 0.998733 | + | 0.0503234i | \(0.0160252\pi\) | ||||
−0.998733 | + | 0.0503234i | \(0.983975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 367.455 | 0.793639 | 0.396820 | − | 0.917897i | \(-0.370114\pi\) | ||||
0.396820 | + | 0.917897i | \(0.370114\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 326.895 | + | 188.733i | 0.702999 | + | 0.405877i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 458.530 | − | 264.733i | 0.981863 | − | 0.566879i | 0.0790311 | − | 0.996872i | \(-0.474817\pi\) |
0.902832 | + | 0.429993i | \(0.141484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −66.7004 | − | 115.528i | −0.141614 | − | 0.245283i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00758 | − | 6.94133i | 0.00847268 | − | 0.0146751i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.5334i | 0.0600702i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 133.786 | 0.280474 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 250.940 | + | 144.880i | 0.523883 | + | 0.302464i | 0.738522 | − | 0.674229i | \(-0.235524\pi\) |
−0.214639 | + | 0.976694i | \(0.568857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1212.81 | + | 700.216i | −2.52143 | + | 1.45575i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.6223 | + | 75.5560i | 0.0899428 | + | 0.155786i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −219.818 | + | 380.736i | −0.451372 | + | 0.781799i | −0.998472 | − | 0.0552685i | \(-0.982399\pi\) |
0.547100 | + | 0.837067i | \(0.315732\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 399.028i | 0.816009i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −320.561 | −0.652874 | −0.326437 | − | 0.945219i | \(-0.605848\pi\) | ||||
−0.326437 | + | 0.945219i | \(0.605848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 191.686 | + | 110.670i | 0.388815 | + | 0.224483i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 120.082 | − | 69.3295i | 0.242590 | − | 0.140060i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −385.986 | − | 668.548i | −0.773520 | − | 1.33978i | −0.935623 | − | 0.353002i | \(-0.885161\pi\) |
0.162103 | − | 0.986774i | \(-0.448172\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −198.520 | + | 343.847i | −0.396248 | + | 0.686321i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 101.632i | 0.202052i | 0.994884 | + | 0.101026i | \(0.0322126\pi\) | ||||
−0.994884 | + | 0.101026i | \(0.967787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −642.675 | −1.27262 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −408.998 | − | 236.135i | −0.806701 | − | 0.465749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 524.298 | − | 302.704i | 1.03006 | − | 0.594703i | 0.113055 | − | 0.993589i | \(-0.463937\pi\) |
0.917000 | + | 0.398886i | \(0.130603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.8126 | − | 32.5844i | −0.0366718 | − | 0.0635174i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.0252 | + | 41.6128i | −0.0466508 | + | 0.0808015i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 735.907i | 1.42342i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −194.809 | −0.375354 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 331.942 | + | 191.647i | 0.637124 | + | 0.367844i | 0.783506 | − | 0.621384i | \(-0.213429\pi\) |
−0.146382 | + | 0.989228i | \(0.546763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 388.061 | − | 224.047i | 0.741991 | − | 0.428389i | −0.0808018 | − | 0.996730i | \(-0.525748\pi\) |
0.822793 | + | 0.568341i | \(0.192415\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 111.124 | + | 192.472i | 0.210861 | + | 0.365221i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −129.059 | + | 223.538i | −0.243969 | + | 0.422566i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 191.085i | 0.359859i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 706.882 | 1.32623 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −809.978 | − | 467.641i | −1.51398 | − | 0.874095i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −158.241 | + | 91.3605i | −0.294676 | + | 0.170131i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 135.629 | + | 234.916i | 0.250700 | + | 0.434226i | 0.963719 | − | 0.266920i | \(-0.0860058\pi\) |
−0.713019 | + | 0.701145i | \(0.752672\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.2227 | + | 22.9025i | −0.0243513 | + | 0.0421776i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 862.435i | − | 1.58245i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −590.544 | −1.07961 | −0.539803 | − | 0.841791i | \(-0.681501\pi\) | ||||
−0.539803 | + | 0.841791i | \(0.681501\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 83.1602 | + | 48.0126i | 0.151476 | + | 0.0874546i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −252.997 | + | 146.068i | −0.459159 | + | 0.265096i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −310.456 | − | 537.725i | −0.559379 | − | 0.968874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −94.1473 | + | 163.068i | −0.169026 | + | 0.292761i | −0.938078 | − | 0.346425i | \(-0.887395\pi\) |
0.769052 | + | 0.639186i | \(0.220729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 19.6058i | − | 0.0350730i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 81.6408 | 0.145527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −176.805 | − | 102.078i | −0.314041 | − | 0.181312i | 0.334692 | − | 0.942327i | \(-0.391368\pi\) |
−0.648733 | + | 0.761016i | \(0.724701\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −379.430 | + | 219.064i | −0.671558 | + | 0.387724i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 330.456 | + | 572.367i | 0.580767 | + | 1.00592i | 0.995389 | + | 0.0959241i | \(0.0305806\pi\) |
−0.414622 | + | 0.909994i | \(0.636086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 266.989 | − | 462.438i | 0.467581 | − | 0.809874i | −0.531733 | − | 0.846912i | \(-0.678459\pi\) |
0.999314 | + | 0.0370381i | \(0.0117923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 530.329i | 0.925531i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −110.554 | −0.192268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.2750 | + | 26.7169i | 0.0801993 | + | 0.0463031i | 0.539563 | − | 0.841945i | \(-0.318589\pi\) |
−0.459364 | + | 0.888248i | \(0.651923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.76150 | − | 1.59435i | 0.00476943 | − | 0.00275363i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −191.573 | − | 331.813i | −0.328598 | − | 0.569148i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 169.586 | − | 293.732i | 0.289891 | − | 0.502107i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 413.063i | 0.703684i | 0.936059 | + | 0.351842i | \(0.114445\pi\) | ||||
−0.936059 | + | 0.351842i | \(0.885555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −293.333 | −0.498018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −383.001 | − | 221.126i | −0.648056 | − | 0.374155i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −106.047 | + | 61.2261i | −0.178831 | + | 0.103248i | −0.586743 | − | 0.809773i | \(-0.699590\pi\) |
0.407912 | + | 0.913021i | \(0.366257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.7384 | + | 54.9725i | 0.0531631 | + | 0.0920812i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 322.568 | − | 558.704i | 0.538511 | − | 0.932728i | −0.460474 | − | 0.887673i | \(-0.652320\pi\) |
0.998985 | − | 0.0450546i | \(-0.0143462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 683.488i | − | 1.13725i | −0.822596 | − | 0.568626i | \(-0.807475\pi\) | ||
0.822596 | − | 0.568626i | \(-0.192525\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 143.202 | 0.237483 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 219.829 | + | 126.918i | 0.363353 | + | 0.209782i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 222.788 | − | 128.627i | 0.367031 | − | 0.211905i | −0.305130 | − | 0.952311i | \(-0.598700\pi\) |
0.672161 | + | 0.740405i | \(0.265366\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 900.049 | + | 1558.93i | 1.47307 | + | 2.55144i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −442.856 | + | 767.050i | −0.722441 | + | 1.25130i | 0.237578 | + | 0.971369i | \(0.423647\pi\) |
−0.960019 | + | 0.279936i | \(0.909687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 313.411i | 0.509612i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.0724 | 0.0746717 | 0.0373358 | − | 0.999303i | \(-0.488113\pi\) | ||||
0.0373358 | + | 0.999303i | \(0.488113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −949.446 | − | 548.163i | −1.53384 | − | 0.885562i | −0.999180 | − | 0.0404930i | \(-0.987107\pi\) |
−0.534658 | − | 0.845069i | \(-0.679560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 126.250 | − | 72.8907i | 0.203302 | − | 0.117376i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 353.993 | + | 613.134i | 0.566388 | + | 0.981014i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −53.8768 | + | 93.3173i | −0.0859279 | + | 0.148831i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 365.585i | − | 0.581217i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 606.319 | 0.960886 | 0.480443 | − | 0.877026i | \(-0.340476\pi\) | ||||
0.480443 | + | 0.877026i | \(0.340476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −189.856 | − | 109.614i | −0.299931 | − | 0.173165i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 545.893 | − | 315.171i | 0.859674 | − | 0.496333i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.4513 | + | 38.8869i | 0.0351351 | + | 0.0608558i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −469.592 | + | 813.357i | −0.732593 | + | 1.26889i | 0.223178 | + | 0.974778i | \(0.428357\pi\) |
−0.955771 | + | 0.294111i | \(0.904977\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 992.960i | − | 1.54426i | −0.635464 | − | 0.772131i | \(-0.719191\pi\) | ||
0.635464 | − | 0.772131i | \(-0.280809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.69266 | 0.0134770 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −229.656 | − | 132.592i | −0.354955 | − | 0.204933i | 0.311910 | − | 0.950112i | \(-0.399031\pi\) |
−0.666865 | + | 0.745178i | \(0.732364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 473.925 | − | 273.620i | 0.730238 | − | 0.421603i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 567.071 | + | 982.196i | 0.868409 | + | 1.50413i | 0.863622 | + | 0.504139i | \(0.168190\pi\) |
0.00478648 | + | 0.999989i | \(0.498476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −656.719 | + | 1137.47i | −1.00262 | + | 1.73660i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 420.893i | 0.640628i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −924.147 | −1.40235 | −0.701174 | − | 0.712990i | \(-0.747340\pi\) | ||||
−0.701174 | + | 0.712990i | \(0.747340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −202.968 | − | 117.184i | −0.307062 | − | 0.177282i | 0.338549 | − | 0.940949i | \(-0.390064\pi\) |
−0.645611 | + | 0.763666i | \(0.723397\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 172.946 | − | 99.8505i | 0.260854 | − | 0.150604i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −565.948 | − | 980.251i | −0.848498 | − | 1.46964i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 183.764 | − | 318.289i | 0.274685 | − | 0.475768i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 275.003i | − | 0.409840i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −465.127 | −0.691125 | −0.345563 | − | 0.938396i | \(-0.612312\pi\) | ||||
−0.345563 | + | 0.938396i | \(0.612312\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.7324 | + | 10.2378i | 0.0262702 | + | 0.0151671i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1122.31 | − | 647.964i | 1.65776 | − | 0.957110i | 0.684020 | − | 0.729463i | \(-0.260230\pi\) |
0.973744 | − | 0.227647i | \(-0.0731032\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 91.3560 | + | 158.233i | 0.134150 | + | 0.232354i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.13060 | + | 14.0826i | −0.0119042 | + | 0.0206188i | −0.871916 | − | 0.489655i | \(-0.837123\pi\) |
0.860012 | + | 0.510274i | \(0.170456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1320.23i | 1.92734i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.1085 | 0.0176252 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −811.647 | − | 468.604i | −1.17801 | − | 0.680123i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −59.3542 | + | 34.2682i | −0.0858962 | + | 0.0495922i | −0.542333 | − | 0.840164i | \(-0.682459\pi\) |
0.456437 | + | 0.889756i | \(0.349125\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.0956 | − | 79.8400i | −0.0663246 | − | 0.114878i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −92.2664 | + | 159.810i | −0.132376 | + | 0.229283i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 582.048i | − | 0.832687i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 923.360 | 1.31720 | 0.658602 | − | 0.752491i | \(-0.271148\pi\) | ||||
0.658602 | + | 0.752491i | \(0.271148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 417.872 | + | 241.259i | 0.594413 | + | 0.343185i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −691.185 | + | 399.056i | −0.980404 | + | 0.566036i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 456.431 | + | 790.562i | 0.643768 | + | 1.11504i | 0.984585 | + | 0.174909i | \(0.0559631\pi\) |
−0.340817 | + | 0.940130i | \(0.610704\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −183.461 | + | 317.764i | −0.258033 | + | 0.446926i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1136.54i | − | 1.59402i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −971.345 | −1.35852 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −348.573 | − | 201.249i | −0.486155 | − | 0.280681i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 472.001 | − | 272.510i | 0.656469 | − | 0.379013i | −0.134461 | − | 0.990919i | \(-0.542930\pi\) |
0.790930 | + | 0.611906i | \(0.209597\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 55.1958 | + | 95.6019i | 0.0763427 | + | 0.132229i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 79.4899 | − | 137.681i | 0.109641 | − | 0.189904i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 750.292i | 1.03204i | 0.856577 | + | 0.516019i | \(0.172587\pi\) | ||||
−0.856577 | + | 0.516019i | \(0.827413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.43243 | + | 2.55907i | 0.00606352 | + | 0.00350078i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −802.458 | + | 463.299i | −1.09476 | + | 0.632059i | −0.934839 | − | 0.355071i | \(-0.884457\pi\) |
−0.159919 | + | 0.987130i | \(0.551123\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −205.056 | − | 355.167i | −0.278231 | − | 0.481910i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −244.073 | + | 422.748i | −0.330275 | + | 0.572054i | −0.982566 | − | 0.185915i | \(-0.940475\pi\) |
0.652290 | + | 0.757969i | \(0.273808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 263.575i | 0.355702i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1091.72 | −1.46935 | −0.734674 | − | 0.678421i | \(-0.762665\pi\) | ||||
−0.734674 | + | 0.678421i | \(0.762665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −625.420 | − | 361.086i | −0.839490 | − | 0.484680i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −86.2177 | + | 49.7778i | −0.115419 | + | 0.0666369i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 240.222 | + | 416.076i | 0.319869 | + | 0.554029i | 0.980460 | − | 0.196716i | \(-0.0630278\pi\) |
−0.660591 | + | 0.750746i | \(0.729694\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −359.790 | + | 623.175i | −0.477809 | + | 0.827589i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1070.60i | 1.41801i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 941.400 | 1.24359 | 0.621796 | − | 0.783179i | \(-0.286403\pi\) | ||||
0.621796 | + | 0.783179i | \(0.286403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −361.564 | − | 208.749i | −0.476369 | − | 0.275032i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1032.60 | + | 596.172i | −1.35690 | + | 0.783407i | −0.989205 | − | 0.146540i | \(-0.953186\pi\) |
−0.367695 | + | 0.929946i | \(0.619853\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 44.2708 | + | 76.6793i | 0.0578704 | + | 0.100234i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 669.301 | − | 1159.26i | 0.872622 | − | 1.51143i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 908.294i | − | 1.18114i | −0.806988 | − | 0.590568i | \(-0.798904\pi\) | ||
0.806988 | − | 0.590568i | \(-0.201096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 460.029 | 0.596665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1030.03 | − | 594.690i | −1.33251 | − | 0.769328i | −0.346830 | − | 0.937928i | \(-0.612742\pi\) |
−0.985685 | + | 0.168600i | \(0.946075\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 138.245 | − | 79.8158i | 0.178381 | − | 0.102988i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −121.778 | − | 210.925i | −0.156326 | − | 0.270764i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.2976 | − | 111.367i | 0.0823272 | − | 0.142595i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 209.637i | 0.267736i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −414.334 | −0.527814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −915.492 | − | 528.559i | −1.16327 | − | 0.671613i | −0.211183 | − | 0.977447i | \(-0.567731\pi\) |
−0.952085 | + | 0.305834i | \(0.901065\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −234.560 | + | 135.423i | −0.297288 | + | 0.171639i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −336.341 | − | 582.560i | −0.424138 | − | 0.734628i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 207.766 | − | 359.861i | 0.261340 | − | 0.452655i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1037.94i | 1.30231i | 0.758945 | + | 0.651154i | \(0.225715\pi\) | ||||
−0.758945 | + | 0.651154i | \(0.774285\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −469.919 | −0.588133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 93.8544 | + | 54.1869i | 0.117172 | + | 0.0676490i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1043.89 | − | 602.689i | 1.29999 | − | 0.750547i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −288.266 | − | 499.292i | −0.357207 | − | 0.618701i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −543.681 | + | 941.684i | −0.672041 | + | 1.16401i | 0.305283 | + | 0.952262i | \(0.401249\pi\) |
−0.977324 | + | 0.211748i | \(0.932084\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 926.995i | 1.14303i | 0.820593 | + | 0.571514i | \(0.193644\pi\) | ||||
−0.820593 | + | 0.571514i | \(0.806356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −362.153 | −0.445452 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1073.31 | + | 619.678i | 1.31695 | + | 0.760342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.85015 | + | 3.37758i | −0.00716052 | + | 0.00413413i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 215.150 | + | 372.651i | 0.262058 | + | 0.453898i | 0.966789 | − | 0.255577i | \(-0.0822654\pi\) |
−0.704730 | + | 0.709475i | \(0.748932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 522.368 | − | 904.767i | 0.634712 | − | 1.09935i | −0.351865 | − | 0.936051i | \(-0.614452\pi\) |
0.986576 | − | 0.163302i | \(-0.0522144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 58.6394i | − | 0.0710781i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −610.313 | −0.737984 | −0.368992 | − | 0.929433i | \(-0.620297\pi\) | ||||
−0.368992 | + | 0.929433i | \(0.620297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1224.47 | + | 706.950i | 1.47705 | + | 0.852775i | 0.999664 | − | 0.0259193i | \(-0.00825131\pi\) |
0.477385 | + | 0.878694i | \(0.341585\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 394.847 | − | 227.965i | 0.475146 | − | 0.274326i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 616.591 | + | 1067.97i | 0.738433 | + | 1.27900i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −105.248 | + | 182.295i | −0.125745 | + | 0.217796i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.3303i | 0.0552209i | 0.999619 | + | 0.0276105i | \(0.00878980\pi\) | ||||
−0.999619 | + | 0.0276105i | \(0.991210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 786.696 | 0.935430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 587.278 | + | 339.065i | 0.696653 | + | 0.402213i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1270.32 | + | 733.420i | −1.50334 | + | 0.867953i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −94.7376 | − | 164.090i | −0.111587 | − | 0.193275i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −934.772 | + | 1619.07i | −1.09844 | + | 1.90255i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 773.111i | 0.906343i | 0.891423 | + | 0.453172i | \(0.149708\pi\) | ||||
−0.891423 | + | 0.453172i | \(0.850292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −116.862 | −0.136680 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −379.457 | − | 219.080i | −0.442774 | − | 0.255636i | 0.262000 | − | 0.965068i | \(-0.415618\pi\) |
−0.704774 | + | 0.709432i | \(0.748951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 62.6499 | − | 36.1710i | 0.0729336 | − | 0.0421082i | −0.463090 | − | 0.886311i | \(-0.653259\pi\) |
0.536023 | + | 0.844203i | \(0.319926\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −213.247 | − | 369.355i | −0.247100 | − | 0.427990i | 0.715620 | − | 0.698490i | \(-0.246144\pi\) |
−0.962720 | + | 0.270500i | \(0.912811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −302.532 | + | 524.001i | −0.349748 | + | 0.605781i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 448.430i | − | 0.517221i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1050.82 | 1.20922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −868.773 | − | 501.586i | −0.997443 | − | 0.575874i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.1344 | + | 24.3263i | −0.0482639 | + | 0.0278652i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −208.243 | − | 360.687i | −0.237449 | − | 0.411273i | 0.722533 | − | 0.691337i | \(-0.242978\pi\) |
−0.959982 | + | 0.280063i | \(0.909645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.6300 | + | 53.0527i | −0.0348464 | + | 0.0603558i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1249.01i | − | 1.41771i | −0.705353 | − | 0.708857i | \(-0.749211\pi\) | ||
0.705353 | − | 0.708857i | \(-0.250789\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 81.5906 | 0.0924016 | 0.0462008 | − | 0.998932i | \(-0.485289\pi\) | ||||
0.0462008 | + | 0.998932i | \(0.485289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 513.984 | + | 296.749i | 0.580773 | + | 0.335309i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −794.777 | + | 458.865i | −0.896028 | + | 0.517322i | −0.875910 | − | 0.482475i | \(-0.839738\pi\) |
−0.0201189 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.6622 | + | 66.9648i | 0.0433919 | + | 0.0751569i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 310.111 | − | 537.128i | 0.347269 | − | 0.601487i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 567.520i | 0.634100i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1021.24 | −1.13850 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1415.40 | + | 817.184i | 1.57442 | + | 0.908992i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 211.882 | − | 122.330i | 0.235163 | − | 0.135771i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.0690 | + | 71.1336i | 0.0453801 | + | 0.0786007i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 725.700 | − | 1256.95i | 0.800110 | − | 1.38583i | −0.119433 | − | 0.992842i | \(-0.538108\pi\) |
0.919543 | − | 0.392989i | \(-0.128559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 358.393i | − | 0.394272i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −562.064 | −0.616975 | −0.308487 | − | 0.951228i | \(-0.599823\pi\) | ||||
−0.308487 | + | 0.951228i | \(0.599823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 246.916 | + | 142.557i | 0.270444 | + | 0.156141i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 258.290 | − | 149.124i | 0.282284 | − | 0.162977i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −269.079 | − | 466.059i | −0.292795 | − | 0.507137i | 0.681674 | − | 0.731656i | \(-0.261252\pi\) |
−0.974470 | + | 0.224519i | \(0.927919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −108.791 | + | 188.431i | −0.118123 | + | 0.204594i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 314.556i | − | 0.340797i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −262.586 | −0.283876 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.2057 | − | 13.3978i | −0.0250331 | − | 0.0144529i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 716.272 | − | 413.540i | 0.771014 | − | 0.445145i | −0.0622221 | − | 0.998062i | \(-0.519819\pi\) |
0.833236 | + | 0.552917i | \(0.186485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 273.435 | + | 473.603i | 0.293070 | + | 0.507613i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 126.786 | − | 219.599i | 0.135600 | − | 0.234865i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1501.10i | − | 1.60203i | −0.598644 | − | 0.801016i | \(-0.704293\pi\) | ||
0.598644 | − | 0.801016i | \(-0.295707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −89.3818 | −0.0951883 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 663.958 | + | 383.336i | 0.705587 | + | 0.407371i | 0.809425 | − | 0.587223i | \(-0.199779\pi\) |
−0.103838 | + | 0.994594i | \(0.533112\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 817.243 | − | 471.836i | 0.866642 | − | 0.500356i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −681.117 | − | 1179.73i | −0.719237 | − | 1.24576i | −0.961302 | − | 0.275495i | \(-0.911158\pi\) |
0.242065 | − | 0.970260i | \(-0.422175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1474.23 | − | 2553.45i | 1.55346 | − | 2.69067i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.64971i | 0.00909538i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1431.37 | 1.50196 | 0.750980 | − | 0.660325i | \(-0.229581\pi\) | ||||
0.750980 | + | 0.660325i | \(0.229581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1426.49 | + | 823.585i | 1.49371 | + | 0.862393i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 519.938 | − | 300.186i | 0.543300 | − | 0.313674i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 340.034 | + | 588.955i | 0.353833 | + | 0.612857i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 260.784 | − | 451.691i | 0.270803 | − | 0.469045i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 9.90391i | − | 0.0102631i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −426.276 | −0.440823 | −0.220411 | − | 0.975407i | \(-0.570740\pi\) | ||||
−0.220411 | + | 0.975407i | \(0.570740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −59.5884 | − | 34.4034i | −0.0614948 | − | 0.0355040i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1496.84 | + | 864.203i | −1.54155 | + | 0.890013i | −0.542807 | + | 0.839857i | \(0.682639\pi\) |
−0.998741 | + | 0.0501561i | \(0.984028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −71.7187 | − | 124.220i | −0.0735577 | − | 0.127406i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 356.160 | − | 616.887i | 0.364545 | − | 0.631410i | −0.624158 | − | 0.781298i | \(-0.714558\pi\) |
0.988703 | + | 0.149888i | \(0.0478914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 310.368i | − | 0.317025i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 480.944 | 0.490259 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −902.887 | − | 521.282i | −0.918502 | − | 0.530297i | −0.0353451 | − | 0.999375i | \(-0.511253\pi\) |
−0.883157 | + | 0.469078i | \(0.844586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1189.58 | + | 686.803i | −1.20769 | + | 0.697262i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.0867 | − | 22.6668i | −0.0132322 | − | 0.0229189i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −698.706 | + | 1210.19i | −0.705052 | + | 1.22119i | 0.261621 | + | 0.965171i | \(0.415743\pi\) |
−0.966673 | + | 0.256015i | \(0.917590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 787.703i | − | 0.793256i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 197.155 | 0.198146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 621.773 | + | 358.981i | 0.623644 | + | 0.360061i | 0.778286 | − | 0.627909i | \(-0.216089\pi\) |
−0.154642 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 299.867 | − | 173.128i | 0.300167 | − | 0.173301i |
(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 | 588.3.m.f.325.4 | 8 | ||
3.2 | odd | 2 | 1764.3.z.l.325.1 | 8 | |||
7.2 | even | 3 | 588.3.m.e.313.1 | 8 | |||
7.3 | odd | 6 | 588.3.d.c.97.5 | yes | 8 | ||
7.4 | even | 3 | 588.3.d.c.97.4 | ✓ | 8 | ||
7.5 | odd | 6 | inner | 588.3.m.f.313.4 | 8 | ||
7.6 | odd | 2 | 588.3.m.e.325.1 | 8 | |||
21.2 | odd | 6 | 1764.3.z.m.901.4 | 8 | |||
21.5 | even | 6 | 1764.3.z.l.901.1 | 8 | |||
21.11 | odd | 6 | 1764.3.d.h.685.2 | 8 | |||
21.17 | even | 6 | 1764.3.d.h.685.7 | 8 | |||
21.20 | even | 2 | 1764.3.z.m.325.4 | 8 | |||
28.3 | even | 6 | 2352.3.f.j.97.1 | 8 | |||
28.11 | odd | 6 | 2352.3.f.j.97.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.4 | ✓ | 8 | 7.4 | even | 3 | ||
588.3.d.c.97.5 | yes | 8 | 7.3 | odd | 6 | ||
588.3.m.e.313.1 | 8 | 7.2 | even | 3 | |||
588.3.m.e.325.1 | 8 | 7.6 | odd | 2 | |||
588.3.m.f.313.4 | 8 | 7.5 | odd | 6 | inner | ||
588.3.m.f.325.4 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.d.h.685.2 | 8 | 21.11 | odd | 6 | |||
1764.3.d.h.685.7 | 8 | 21.17 | even | 6 | |||
1764.3.z.l.325.1 | 8 | 3.2 | odd | 2 | |||
1764.3.z.l.901.1 | 8 | 21.5 | even | 6 | |||
1764.3.z.m.325.4 | 8 | 21.20 | even | 2 | |||
1764.3.z.m.901.4 | 8 | 21.2 | odd | 6 | |||
2352.3.f.j.97.1 | 8 | 28.3 | even | 6 | |||
2352.3.f.j.97.8 | 8 | 28.11 | odd | 6 |