Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, 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("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.10 | ||
Character | \(\chi\) | \(=\) | 1728.1601 |
Dual form | 1728.3.q.k.449.10 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.41309 | − | 3.12525i | 1.08262 | − | 0.625050i | 0.151017 | − | 0.988531i | \(-0.451745\pi\) |
0.931602 | + | 0.363481i | \(0.118412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.74855 | − | 6.49268i | 0.535507 | − | 0.927525i | −0.463632 | − | 0.886028i | \(-0.653454\pi\) |
0.999139 | − | 0.0414972i | \(-0.0132128\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.17688 | − | 3.56622i | −0.561534 | − | 0.324202i | 0.192227 | − | 0.981351i | \(-0.438429\pi\) |
−0.753761 | + | 0.657149i | \(0.771762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.888802 | + | 1.53945i | 0.0683694 | + | 0.118419i | 0.898184 | − | 0.439620i | \(-0.144887\pi\) |
−0.829814 | + | 0.558040i | \(0.811554\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.7791i | 0.869362i | 0.900585 | + | 0.434681i | \(0.143139\pi\) | ||||
−0.900585 | + | 0.434681i | \(0.856861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.9460 | 1.04979 | 0.524896 | − | 0.851167i | \(-0.324104\pi\) | ||||
0.524896 | + | 0.851167i | \(0.324104\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.8716 | − | 12.0502i | 0.907462 | − | 0.523923i | 0.0278482 | − | 0.999612i | \(-0.491134\pi\) |
0.879614 | + | 0.475689i | \(0.157801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.03438 | − | 12.1839i | 0.281375 | − | 0.487356i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.1279 | + | 23.1679i | 1.38372 | + | 0.798891i | 0.992598 | − | 0.121447i | \(-0.0387535\pi\) |
0.391123 | + | 0.920339i | \(0.372087\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.1547 | + | 24.5167i | 0.456603 | + | 0.790860i | 0.998779 | − | 0.0494054i | \(-0.0157326\pi\) |
−0.542176 | + | 0.840265i | \(0.682399\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 46.8606i | − | 1.33887i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −63.0770 | −1.70478 | −0.852391 | − | 0.522904i | \(-0.824849\pi\) | ||||
−0.852391 | + | 0.522904i | \(0.824849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 28.0185 | − | 16.1765i | 0.683378 | − | 0.394549i | −0.117748 | − | 0.993043i | \(-0.537568\pi\) |
0.801127 | + | 0.598495i | \(0.204234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 38.8176 | − | 67.2341i | 0.902736 | − | 1.56358i | 0.0788077 | − | 0.996890i | \(-0.474889\pi\) |
0.823928 | − | 0.566694i | \(-0.191778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 38.4719 | + | 22.2118i | 0.818551 | + | 0.472591i | 0.849917 | − | 0.526917i | \(-0.176652\pi\) |
−0.0313654 | + | 0.999508i | \(0.509986\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.60324 | − | 6.24099i | −0.0735354 | − | 0.127367i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 42.2846i | − | 0.797823i | −0.916990 | − | 0.398911i | \(-0.869388\pi\) | ||
0.916990 | − | 0.398911i | \(-0.130612\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −44.5813 | −0.810570 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 93.8917 | − | 54.2084i | 1.59138 | − | 0.918786i | 0.598314 | − | 0.801262i | \(-0.295838\pi\) |
0.993070 | − | 0.117524i | \(-0.0374957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 25.3858 | − | 43.9695i | 0.416161 | − | 0.720812i | −0.579389 | − | 0.815051i | \(-0.696709\pi\) |
0.995550 | + | 0.0942396i | \(0.0300420\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.62233 | + | 5.55546i | 0.148036 | + | 0.0854686i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −56.9484 | − | 98.6376i | −0.849977 | − | 1.47220i | −0.881228 | − | 0.472691i | \(-0.843283\pi\) |
0.0312514 | − | 0.999512i | \(-0.490051\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 85.2129i | 1.20018i | 0.799932 | + | 0.600091i | \(0.204869\pi\) | ||||
−0.799932 | + | 0.600091i | \(0.795131\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −94.5357 | −1.29501 | −0.647505 | − | 0.762061i | \(-0.724188\pi\) | ||||
−0.647505 | + | 0.762061i | \(0.724188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −46.3086 | + | 26.7363i | −0.601411 | + | 0.347225i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −35.6059 | + | 61.6712i | −0.450707 | + | 0.780648i | −0.998430 | − | 0.0560122i | \(-0.982161\pi\) |
0.547723 | + | 0.836660i | \(0.315495\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −94.9037 | − | 54.7927i | −1.14342 | − | 0.660153i | −0.196144 | − | 0.980575i | \(-0.562842\pi\) |
−0.947275 | + | 0.320422i | \(0.896175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 46.1885 | + | 80.0009i | 0.543395 | + | 0.941187i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 29.6936i | − | 0.333635i | −0.985988 | − | 0.166818i | \(-0.946651\pi\) | ||
0.985988 | − | 0.166818i | \(-0.0533491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3269 | 0.146449 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 107.970 | − | 62.3363i | 1.13652 | − | 0.656172i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −62.4793 | + | 108.217i | −0.644116 | + | 1.11564i | 0.340389 | + | 0.940285i | \(0.389441\pi\) |
−0.984505 | + | 0.175357i | \(0.943892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −34.0989 | − | 19.6870i | −0.337613 | − | 0.194921i | 0.321603 | − | 0.946875i | \(-0.395778\pi\) |
−0.659216 | + | 0.751954i | \(0.729112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −74.7230 | − | 129.424i | −0.725466 | − | 1.25654i | −0.958782 | − | 0.284143i | \(-0.908291\pi\) |
0.233316 | − | 0.972401i | \(-0.425042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.420211i | − | 0.00392721i | −0.999998 | − | 0.00196360i | \(-0.999375\pi\) | ||
0.999998 | − | 0.00196360i | \(-0.000625035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −64.4616 | −0.591391 | −0.295695 | − | 0.955282i | \(-0.595551\pi\) | ||||
−0.295695 | + | 0.955282i | \(0.595551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −22.4718 | + | 12.9741i | −0.198865 | + | 0.114815i | −0.596126 | − | 0.802891i | \(-0.703294\pi\) |
0.397261 | + | 0.917706i | \(0.369961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 75.3200 | − | 130.458i | 0.654957 | − | 1.13442i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 95.9562 | + | 55.4004i | 0.806355 | + | 0.465549i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35.0641 | − | 60.7329i | −0.289786 | − | 0.501925i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 68.3258i | 0.546606i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0916 | −0.0952097 | −0.0476049 | − | 0.998866i | \(-0.515159\pi\) | ||||
−0.0476049 | + | 0.998866i | \(0.515159\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −45.4518 | + | 26.2416i | −0.346960 | + | 0.200318i | −0.663346 | − | 0.748313i | \(-0.730864\pi\) |
0.316385 | + | 0.948631i | \(0.397531\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 74.7687 | − | 129.503i | 0.562171 | − | 0.973708i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 121.224 | + | 69.9888i | 0.884848 | + | 0.510867i | 0.872254 | − | 0.489053i | \(-0.162658\pi\) |
0.0125942 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.9656 | − | 34.5814i | −0.143637 | − | 0.248787i | 0.785226 | − | 0.619209i | \(-0.212547\pi\) |
−0.928864 | + | 0.370422i | \(0.879213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 12.6787i | − | 0.0886619i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 289.621 | 1.99739 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.26226 | + | 1.88347i | −0.0218944 | + | 0.0126407i | −0.510907 | − | 0.859636i | \(-0.670690\pi\) |
0.489013 | + | 0.872277i | \(0.337357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 74.8795 | − | 129.695i | 0.495891 | − | 0.858908i | −0.504098 | − | 0.863646i | \(-0.668175\pi\) |
0.999989 | + | 0.00473848i | \(0.00150831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 153.241 | + | 88.4739i | 0.988654 | + | 0.570800i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 58.9507 | + | 102.106i | 0.375482 | + | 0.650354i | 0.990399 | − | 0.138238i | \(-0.0441439\pi\) |
−0.614917 | + | 0.788592i | \(0.710811\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 180.684i | − | 1.12226i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −111.960 | −0.686874 | −0.343437 | − | 0.939176i | \(-0.611591\pi\) | ||||
−0.343437 | + | 0.939176i | \(0.611591\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.33677 | + | 0.771783i | −0.00800460 | + | 0.00462146i | −0.503997 | − | 0.863705i | \(-0.668138\pi\) |
0.495992 | + | 0.868327i | \(0.334804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.9201 | − | 143.622i | 0.490651 | − | 0.849833i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 46.0581 | + | 26.5917i | 0.266232 | + | 0.153709i | 0.627174 | − | 0.778879i | \(-0.284211\pi\) |
−0.360942 | + | 0.932588i | \(0.617545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −52.7374 | − | 91.3439i | −0.301357 | − | 0.521965i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 239.444i | − | 1.33768i | −0.743407 | − | 0.668839i | \(-0.766792\pi\) | ||
0.743407 | − | 0.668839i | \(-0.233208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −61.1557 | −0.337877 | −0.168938 | − | 0.985627i | \(-0.554034\pi\) | ||||
−0.168938 | + | 0.985627i | \(0.554034\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −341.441 | + | 197.131i | −1.84563 | + | 1.06557i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 52.7057 | − | 91.2890i | 0.281849 | − | 0.488176i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28.9063 | − | 16.6891i | −0.151342 | − | 0.0873773i | 0.422417 | − | 0.906402i | \(-0.361182\pi\) |
−0.573759 | + | 0.819024i | \(0.694515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.2796 | + | 36.8573i | 0.110257 | + | 0.190971i | 0.915874 | − | 0.401466i | \(-0.131499\pi\) |
−0.805617 | + | 0.592437i | \(0.798166\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 203.372i | − | 1.03235i | −0.856484 | − | 0.516173i | \(-0.827356\pi\) | ||
0.856484 | − | 0.516173i | \(-0.172644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 128.160 | 0.644022 | 0.322011 | − | 0.946736i | \(-0.395641\pi\) | ||||
0.322011 | + | 0.946736i | \(0.395641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 300.843 | − | 173.692i | 1.48198 | − | 0.855624i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 101.111 | − | 175.130i | 0.493225 | − | 0.854291i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −123.204 | − | 71.1320i | −0.589494 | − | 0.340344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −97.2675 | − | 168.472i | −0.460983 | − | 0.798446i | 0.538027 | − | 0.842928i | \(-0.319170\pi\) |
−0.999010 | + | 0.0444812i | \(0.985837\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 485.259i | − | 2.25702i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 212.238 | 0.978057 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.7518 | + | 13.1357i | −0.102949 | + | 0.0594377i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 95.1454 | − | 164.797i | 0.426661 | − | 0.738998i | −0.569913 | − | 0.821705i | \(-0.693023\pi\) |
0.996574 | + | 0.0827067i | \(0.0263565\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 320.930 | + | 185.289i | 1.41379 | + | 0.816252i | 0.995743 | − | 0.0921738i | \(-0.0293815\pi\) |
0.418047 | + | 0.908426i | \(0.362715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 203.685 | + | 352.793i | 0.889455 | + | 1.54058i | 0.840521 | + | 0.541779i | \(0.182249\pi\) |
0.0489338 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5267i | 0.0923895i | 0.998932 | + | 0.0461947i | \(0.0147095\pi\) | ||||
−0.998932 | + | 0.0461947i | \(0.985291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 277.669 | 1.18157 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 172.020 | − | 99.3155i | 0.719747 | − | 0.415546i | −0.0949125 | − | 0.995486i | \(-0.530257\pi\) |
0.814660 | + | 0.579939i | \(0.196924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −138.940 | + | 240.652i | −0.576516 | + | 0.998556i | 0.419359 | + | 0.907821i | \(0.362255\pi\) |
−0.995875 | + | 0.0907351i | \(0.971078\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −39.0093 | − | 22.5220i | −0.159222 | − | 0.0919267i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.7281 | + | 30.7059i | 0.0717736 | + | 0.124315i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 128.325i | 0.511253i | 0.966776 | + | 0.255627i | \(0.0822817\pi\) | ||||
−0.966776 | + | 0.255627i | \(0.917718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −171.895 | −0.679428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −62.3584 | + | 36.0026i | −0.242640 | + | 0.140088i | −0.616389 | − | 0.787442i | \(-0.711405\pi\) |
0.373750 | + | 0.927530i | \(0.378072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −236.447 | + | 409.538i | −0.912923 | + | 1.58123i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 113.783 | + | 65.6926i | 0.432634 | + | 0.249782i | 0.700468 | − | 0.713683i | \(-0.252975\pi\) |
−0.267834 | + | 0.963465i | \(0.586308\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −132.150 | − | 228.890i | −0.498679 | − | 0.863737i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 38.8284i | − | 0.144344i | −0.997392 | − | 0.0721718i | \(-0.977007\pi\) | ||
0.997392 | − | 0.0721718i | \(-0.0229930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.802525 | −0.00296135 | −0.00148067 | − | 0.999999i | \(-0.500471\pi\) | ||||
−0.00148067 | + | 0.999999i | \(0.500471\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −86.9009 | + | 50.1723i | −0.316003 | + | 0.182445i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −61.1932 | + | 105.990i | −0.220914 | + | 0.382635i | −0.955086 | − | 0.296329i | \(-0.904237\pi\) |
0.734172 | + | 0.678964i | \(0.237571\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 254.139 | + | 146.727i | 0.904408 | + | 0.522160i | 0.878628 | − | 0.477508i | \(-0.158460\pi\) |
0.0257801 | + | 0.999668i | \(0.491793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 90.6191 | + | 156.957i | 0.320209 | + | 0.554618i | 0.980531 | − | 0.196364i | \(-0.0629136\pi\) |
−0.660322 | + | 0.750983i | \(0.729580\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 242.554i | − | 0.845134i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 70.5768 | 0.244210 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −290.545 | + | 167.746i | −0.991622 | + | 0.572513i | −0.905759 | − | 0.423794i | \(-0.860698\pi\) |
−0.0858631 | + | 0.996307i | \(0.527365\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 338.829 | − | 586.870i | 1.14857 | − | 1.98939i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.1015 | + | 21.4205i | 0.124085 | + | 0.0716406i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −291.020 | − | 504.061i | −0.966843 | − | 1.67462i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 317.348i | − | 1.04049i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −289.210 | −0.942053 | −0.471027 | − | 0.882119i | \(-0.656116\pi\) | ||||
−0.471027 | + | 0.882119i | \(0.656116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6987 | − | 13.6824i | 0.0762016 | − | 0.0439950i | −0.461415 | − | 0.887184i | \(-0.652658\pi\) |
0.537617 | + | 0.843189i | \(0.319325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −293.572 | + | 508.481i | −0.937928 | + | 1.62454i | −0.168601 | + | 0.985684i | \(0.553925\pi\) |
−0.769327 | + | 0.638855i | \(0.779408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 326.081 | + | 188.263i | 1.02865 | + | 0.593889i | 0.916596 | − | 0.399814i | \(-0.130925\pi\) |
0.112049 | + | 0.993703i | \(0.464259\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −165.243 | − | 286.210i | −0.518004 | − | 0.897210i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 294.785i | 0.912648i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.0087 | 0.0769497 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 288.428 | − | 166.524i | 0.876680 | − | 0.506151i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.48388 | + | 2.57015i | −0.00448301 | + | 0.00776480i | −0.868258 | − | 0.496113i | \(-0.834760\pi\) |
0.863775 | + | 0.503877i | \(0.168094\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −616.534 | − | 355.956i | −1.84040 | − | 1.06256i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −329.235 | − | 570.251i | −0.976958 | − | 1.69214i | −0.673317 | − | 0.739354i | \(-0.735131\pi\) |
−0.303641 | − | 0.952786i | \(-0.598202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 201.915i | − | 0.592126i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 313.330 | 0.913499 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −255.949 | + | 147.772i | −0.737606 | + | 0.425857i | −0.821198 | − | 0.570643i | \(-0.806694\pi\) |
0.0835920 | + | 0.996500i | \(0.473361\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −106.379 | + | 184.254i | −0.304811 | + | 0.527949i | −0.977219 | − | 0.212232i | \(-0.931927\pi\) |
0.672408 | + | 0.740181i | \(0.265260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 124.287 | + | 71.7570i | 0.352087 | + | 0.203278i | 0.665604 | − | 0.746305i | \(-0.268174\pi\) |
−0.313517 | + | 0.949583i | \(0.601507\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 266.312 | + | 461.265i | 0.750173 | + | 1.29934i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 270.973i | 0.754799i | 0.926051 | + | 0.377400i | \(0.123182\pi\) | ||||
−0.926051 | + | 0.377400i | \(0.876818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.8443 | 0.102062 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −511.731 | + | 295.448i | −1.40200 | + | 0.809446i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −200.855 | + | 347.892i | −0.547290 | + | 0.947934i | 0.451169 | + | 0.892438i | \(0.351007\pi\) |
−0.998459 | + | 0.0554953i | \(0.982326\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −274.540 | − | 158.506i | −0.740001 | − | 0.427240i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 146.890 | + | 254.422i | 0.393808 | + | 0.682095i | 0.992948 | − | 0.118549i | \(-0.0378241\pi\) |
−0.599140 | + | 0.800644i | \(0.704491\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 82.3665i | 0.218479i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −280.802 | −0.740903 | −0.370452 | − | 0.928852i | \(-0.620797\pi\) | ||||
−0.370452 | + | 0.928852i | \(0.620797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −546.665 | + | 315.617i | −1.42732 | + | 0.824066i | −0.996909 | − | 0.0785646i | \(-0.974966\pi\) |
−0.430416 | + | 0.902631i | \(0.641633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −167.115 | + | 289.452i | −0.434066 | + | 0.751824i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 378.049 | + | 218.267i | 0.971849 | + | 0.561097i | 0.899799 | − | 0.436304i | \(-0.143713\pi\) |
0.0720497 | + | 0.997401i | \(0.477046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 178.092 | + | 308.465i | 0.455479 | + | 0.788913i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 445.109i | 1.12686i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 405.382 | 1.02111 | 0.510557 | − | 0.859844i | \(-0.329439\pi\) | ||||
0.510557 | + | 0.859844i | \(0.329439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 66.9595 | − | 38.6591i | 0.166981 | − | 0.0964068i | −0.414180 | − | 0.910195i | \(-0.635932\pi\) |
0.581162 | + | 0.813788i | \(0.302598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.1614 | + | 43.5809i | −0.0624353 | + | 0.108141i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 389.619 | + | 224.946i | 0.957294 | + | 0.552694i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 85.3306 | + | 147.797i | 0.208632 | + | 0.361362i | 0.951284 | − | 0.308316i | \(-0.0997655\pi\) |
−0.742652 | + | 0.669678i | \(0.766432\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 812.811i | − | 1.96807i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −684.964 | −1.65051 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −123.529 | + | 71.3195i | −0.294819 | + | 0.170214i | −0.640113 | − | 0.768281i | \(-0.721112\pi\) |
0.345294 | + | 0.938494i | \(0.387779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 307.819 | − | 533.158i | 0.731162 | − | 1.26641i | −0.225226 | − | 0.974307i | \(-0.572312\pi\) |
0.956387 | − | 0.292102i | \(-0.0943548\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 180.068 | + | 103.962i | 0.423689 | + | 0.244617i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −190.320 | − | 329.644i | −0.445714 | − | 0.772000i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 405.961i | 0.941905i | 0.882159 | + | 0.470953i | \(0.156090\pi\) | ||||
−0.882159 | + | 0.470953i | \(0.843910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 50.1302 | 0.115774 | 0.0578870 | − | 0.998323i | \(-0.481564\pi\) | ||||
0.0578870 | + | 0.998323i | \(0.481564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 416.306 | − | 240.354i | 0.952646 | − | 0.550010i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −363.552 | + | 629.690i | −0.828136 | + | 1.43437i | 0.0713624 | + | 0.997450i | \(0.477265\pi\) |
−0.899499 | + | 0.436924i | \(0.856068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 324.072 | + | 187.103i | 0.731540 | + | 0.422355i | 0.818985 | − | 0.573815i | \(-0.194537\pi\) |
−0.0874454 | + | 0.996169i | \(0.527870\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −92.7998 | − | 160.734i | −0.208539 | − | 0.361200i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 225.368i | 0.501934i | 0.967996 | + | 0.250967i | \(0.0807486\pi\) | ||||
−0.967996 | + | 0.250967i | \(0.919251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −230.756 | −0.511654 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 72.1396 | − | 41.6498i | 0.158549 | − | 0.0915380i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 390.263 | − | 675.955i | 0.853966 | − | 1.47911i | −0.0236344 | − | 0.999721i | \(-0.507524\pi\) |
0.877601 | − | 0.479392i | \(-0.159143\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 474.085 | + | 273.713i | 1.02838 | + | 0.593738i | 0.916521 | − | 0.399986i | \(-0.130985\pi\) |
0.111863 | + | 0.993724i | \(0.464318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 174.664 | + | 302.526i | 0.377243 | + | 0.653404i | 0.990660 | − | 0.136355i | \(-0.0435388\pi\) |
−0.613417 | + | 0.789759i | \(0.710205\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 499.358i | − | 1.06929i | −0.845077 | − | 0.534645i | \(-0.820445\pi\) | ||
0.845077 | − | 0.534645i | \(-0.179555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −853.896 | −1.82067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −479.543 | + | 276.865i | −1.01383 | + | 0.585337i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 140.308 | − | 243.020i | 0.295385 | − | 0.511622i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −571.640 | − | 330.036i | −1.19340 | − | 0.689011i | −0.234326 | − | 0.972158i | \(-0.575288\pi\) |
−0.959076 | + | 0.283147i | \(0.908621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −56.0629 | − | 97.1038i | −0.116555 | − | 0.201879i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 781.053i | 1.61042i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 217.861 | 0.447352 | 0.223676 | − | 0.974664i | \(-0.428194\pi\) | ||||
0.223676 | + | 0.974664i | \(0.428194\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −132.712 | + | 76.6214i | −0.270289 | + | 0.156052i | −0.629019 | − | 0.777390i | \(-0.716543\pi\) |
0.358730 | + | 0.933441i | \(0.383210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −342.401 | + | 593.056i | −0.694526 | + | 1.20295i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 553.260 | + | 319.425i | 1.11320 | + | 0.642706i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 153.693 | + | 266.204i | 0.308002 | + | 0.533476i | 0.977925 | − | 0.208955i | \(-0.0670062\pi\) |
−0.669923 | + | 0.742431i | \(0.733673\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 797.972i | 1.58643i | 0.608945 | + | 0.793213i | \(0.291593\pi\) | ||||
−0.608945 | + | 0.793213i | \(0.708407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −246.107 | −0.487341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 260.405 | − | 150.345i | 0.511602 | − | 0.295373i | −0.221890 | − | 0.975072i | \(-0.571223\pi\) |
0.733492 | + | 0.679698i | \(0.237889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −354.372 | + | 613.790i | −0.693487 | + | 1.20115i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −808.965 | − | 467.056i | −1.57081 | − | 0.906905i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −158.424 | − | 274.399i | −0.306430 | − | 0.530752i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 928.990i | − | 1.78309i | −0.452932 | − | 0.891545i | \(-0.649622\pi\) | ||
0.452932 | − | 0.891545i | \(-0.350378\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 519.086 | 0.992516 | 0.496258 | − | 0.868175i | \(-0.334707\pi\) | ||||
0.496258 | + | 0.868175i | \(0.334707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −362.335 | + | 209.194i | −0.687543 | + | 0.396953i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.9164 | − | 44.8885i | 0.0489913 | − | 0.0848554i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.8058 | + | 28.7554i | 0.0934443 | + | 0.0539501i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.31326 | − | 2.27464i | −0.00245470 | − | 0.00425167i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 51.3997i | 0.0953613i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 109.959 | 0.203251 | 0.101625 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101625 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −348.937 | + | 201.459i | −0.640251 | + | 0.369649i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −489.119 | + | 847.180i | −0.894185 | + | 1.54877i | −0.0593757 | + | 0.998236i | \(0.518911\pi\) |
−0.834810 | + | 0.550539i | \(0.814422\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 800.392 | + | 462.107i | 1.45262 | + | 0.838669i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 266.941 | + | 462.355i | 0.482714 | + | 0.836084i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 322.002i | − | 0.578100i | −0.957314 | − | 0.289050i | \(-0.906661\pi\) | ||
0.957314 | − | 0.289050i | \(-0.0933394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 138.005 | 0.246878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −174.603 | + | 100.807i | −0.310129 | + | 0.179053i | −0.646984 | − | 0.762503i | \(-0.723970\pi\) |
0.336855 | + | 0.941556i | \(0.390637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −81.0945 | + | 140.460i | −0.143530 | + | 0.248601i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 123.786 | + | 71.4677i | 0.217549 | + | 0.125602i | 0.604815 | − | 0.796366i | \(-0.293247\pi\) |
−0.387266 | + | 0.921968i | \(0.626580\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.7205 | + | 79.1902i | 0.0800709 | + | 0.138687i | 0.903280 | − | 0.429051i | \(-0.141152\pi\) |
−0.823209 | + | 0.567738i | \(0.807819\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 339.064i | − | 0.589676i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 404.739 | 0.701455 | 0.350727 | − | 0.936478i | \(-0.385934\pi\) | ||||
0.350727 | + | 0.936478i | \(0.385934\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −711.503 | + | 410.786i | −1.22462 | + | 0.707033i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −150.796 | + | 261.187i | −0.258656 | + | 0.448005i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −702.845 | − | 405.788i | −1.19735 | − | 0.691291i | −0.237387 | − | 0.971415i | \(-0.576291\pi\) |
−0.959964 | + | 0.280125i | \(0.909624\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 282.330 | + | 489.010i | 0.479338 | + | 0.830238i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 95.3026i | − | 0.160713i | −0.996766 | − | 0.0803563i | \(-0.974394\pi\) | ||
0.996766 | − | 0.0803563i | \(-0.0256058\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 692.560 | 1.16397 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 381.733 | − | 220.393i | 0.637283 | − | 0.367936i | −0.146284 | − | 0.989243i | \(-0.546731\pi\) |
0.783567 | + | 0.621307i | \(0.213398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 90.4814 | − | 156.718i | 0.150551 | − | 0.260763i | −0.780879 | − | 0.624682i | \(-0.785228\pi\) |
0.931430 | + | 0.363920i | \(0.118562\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −379.611 | − | 219.168i | −0.627456 | − | 0.362262i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 277.996 | + | 481.504i | 0.457984 | + | 0.793252i | 0.998854 | − | 0.0478542i | \(-0.0152383\pi\) |
−0.540870 | + | 0.841106i | \(0.681905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 78.9674i | 0.129243i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 335.352 | 0.547067 | 0.273534 | − | 0.961862i | \(-0.411808\pi\) | ||||
0.273534 | + | 0.961862i | \(0.411808\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1020.64 | + | 589.268i | −1.65420 | + | 0.955053i | −0.678884 | + | 0.734246i | \(0.737536\pi\) |
−0.975317 | + | 0.220808i | \(0.929131\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 449.292 | − | 778.197i | 0.725835 | − | 1.25718i | −0.232794 | − | 0.972526i | \(-0.574787\pi\) |
0.958629 | − | 0.284658i | \(-0.0918800\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −192.791 | − | 111.308i | −0.309455 | − | 0.178664i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 389.395 | + | 674.451i | 0.623031 | + | 1.07912i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 932.224i | − | 1.48207i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 431.017 | 0.683070 | 0.341535 | − | 0.939869i | \(-0.389053\pi\) | ||||
0.341535 | + | 0.939869i | \(0.389053\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −65.4531 | + | 37.7894i | −0.103076 | + | 0.0595108i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.40513 | − | 11.0940i | 0.0100551 | − | 0.0174160i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −775.987 | − | 448.016i | −1.21059 | − | 0.698933i | −0.247701 | − | 0.968837i | \(-0.579675\pi\) |
−0.962887 | + | 0.269903i | \(0.913008\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 110.854 | + | 192.004i | 0.172401 | + | 0.298607i | 0.939259 | − | 0.343210i | \(-0.111514\pi\) |
−0.766858 | + | 0.641817i | \(0.778181\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 536.838i | 0.829734i | 0.909882 | + | 0.414867i | \(0.136172\pi\) | ||||
−0.909882 | + | 0.414867i | \(0.863828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −773.276 | −1.19149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −483.774 | + | 279.307i | −0.740848 | + | 0.427729i | −0.822378 | − | 0.568942i | \(-0.807353\pi\) |
0.0815296 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −164.023 | + | 284.096i | −0.250417 | + | 0.433735i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −933.150 | − | 538.755i | −1.41601 | − | 0.817534i | −0.420064 | − | 0.907494i | \(-0.637993\pi\) |
−0.995945 | + | 0.0899606i | \(0.971326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −147.880 | − | 256.135i | −0.223721 | − | 0.387496i | 0.732214 | − | 0.681075i | \(-0.238487\pi\) |
−0.955935 | + | 0.293579i | \(0.905154\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 934.683i | − | 1.40554i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1116.71 | 1.67423 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −313.610 | + | 181.063i | −0.467377 | + | 0.269840i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 283.724 | − | 491.424i | 0.421580 | − | 0.730199i | −0.574514 | − | 0.818495i | \(-0.694809\pi\) |
0.996094 | + | 0.0882963i | \(0.0281422\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −813.905 | − | 469.908i | −1.20222 | − | 0.694104i | −0.241174 | − | 0.970482i | \(-0.577533\pi\) |
−0.961049 | + | 0.276378i | \(0.910866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 468.413 | + | 811.315i | 0.689857 | + | 1.19487i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 14.2541i | − | 0.0208699i | −0.999946 | − | 0.0104349i | \(-0.996678\pi\) | ||
0.999946 | − | 0.0104349i | \(-0.00332161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 874.930 | 1.27727 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 65.0950 | − | 37.5826i | 0.0944775 | − | 0.0545466i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 83.1353 | − | 143.995i | 0.120312 | − | 0.208386i | −0.799579 | − | 0.600561i | \(-0.794944\pi\) |
0.919891 | + | 0.392175i | \(0.128277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −216.151 | − | 124.795i | −0.311009 | − | 0.179561i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 239.075 | + | 414.090i | 0.343006 | + | 0.594103i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 506.174i | 0.722074i | 0.932551 | + | 0.361037i | \(0.117577\pi\) | ||||
−0.932551 | + | 0.361037i | \(0.882423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1258.14 | −1.78967 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −255.643 | + | 147.595i | −0.361588 | + | 0.208763i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 259.993 | − | 450.321i | 0.366704 | − | 0.635150i | −0.622344 | − | 0.782744i | \(-0.713819\pi\) |
0.989048 | + | 0.147594i | \(0.0471528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 590.863 | + | 341.135i | 0.828700 | + | 0.478450i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.6240 | − | 68.6307i | −0.0554181 | − | 0.0959870i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 467.630i | 0.650390i | 0.945647 | + | 0.325195i | \(0.105430\pi\) | ||||
−0.945647 | + | 0.325195i | \(0.894570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1120.41 | −1.55397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 564.549 | − | 325.943i | 0.778689 | − | 0.449576i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 262.371 | − | 454.439i | 0.360895 | − | 0.625088i | −0.627214 | − | 0.778847i | \(-0.715805\pi\) |
0.988108 | + | 0.153759i | \(0.0491380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 993.663 | + | 573.692i | 1.35932 | + | 0.784804i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 329.348 | + | 570.447i | 0.449315 | + | 0.778236i | 0.998342 | − | 0.0575688i | \(-0.0183349\pi\) |
−0.549027 | + | 0.835805i | \(0.685002\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 812.363i | 1.10226i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1209.27 | −1.63637 | −0.818183 | − | 0.574957i | \(-0.805019\pi\) | ||||
−0.818183 | + | 0.574957i | \(0.805019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −339.650 | + | 196.097i | −0.457134 | + | 0.263926i | −0.710838 | − | 0.703355i | \(-0.751684\pi\) |
0.253704 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.7726 | + | 20.3908i | −0.0158022 | + | 0.0273701i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.72829 | − | 1.57518i | −0.00364258 | − | 0.00210305i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 558.493 | + | 967.339i | 0.743666 | + | 1.28807i | 0.950815 | + | 0.309758i | \(0.100248\pi\) |
−0.207149 | + | 0.978309i | \(0.566419\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 936.069i | − | 1.23983i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 623.892 | 0.824164 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 832.456 | − | 480.619i | 1.09390 | − | 0.631562i | 0.159286 | − | 0.987233i | \(-0.449081\pi\) |
0.934611 | + | 0.355671i | \(0.115748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −241.638 | + | 418.528i | −0.316694 | + | 0.548530i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 166.902 | + | 96.3610i | 0.217604 | + | 0.125634i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −109.653 | − | 189.924i | −0.142592 | − | 0.246976i | 0.785880 | − | 0.618379i | \(-0.212210\pi\) |
−0.928472 | + | 0.371403i | \(0.878877\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 761.394i | 0.984986i | 0.870316 | + | 0.492493i | \(0.163914\pi\) | ||||
−0.870316 | + | 0.492493i | \(0.836086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 398.278 | 0.513907 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 558.858 | − | 322.657i | 0.717405 | − | 0.414194i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 303.888 | − | 526.349i | 0.389101 | − | 0.673943i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 638.211 | + | 368.471i | 0.813007 | + | 0.469390i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −263.023 | − | 455.569i | −0.334210 | − | 0.578868i | 0.649123 | − | 0.760684i | \(-0.275136\pi\) |
−0.983333 | + | 0.181815i | \(0.941803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 194.536i | 0.245937i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 90.2518 | 0.113811 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1230.12 | + | 710.212i | −1.54344 | + | 0.891107i | −0.544824 | + | 0.838551i | \(0.683403\pi\) |
−0.998618 | + | 0.0525560i | \(0.983263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −328.271 | + | 568.582i | −0.410852 | + | 0.711617i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 583.935 | + | 337.135i | 0.727192 | + | 0.419845i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −564.681 | − | 978.057i | −0.701468 | − | 1.21498i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 749.612i | − | 0.926590i | −0.886204 | − | 0.463295i | \(-0.846667\pi\) | ||
0.886204 | − | 0.463295i | \(-0.153333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −238.446 | −0.294015 | −0.147008 | − | 0.989135i | \(-0.546964\pi\) | ||||
−0.147008 | + | 0.989135i | \(0.546964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −606.052 | + | 349.905i | −0.743623 | + | 0.429331i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 774.258 | − | 1341.05i | 0.947684 | − | 1.64144i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 937.937 | + | 541.518i | 1.14243 | + | 0.659583i | 0.947032 | − | 0.321140i | \(-0.104066\pi\) |
0.195400 | + | 0.980724i | \(0.437399\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −787.881 | − | 1364.65i | −0.957328 | − | 1.65814i | −0.728949 | − | 0.684568i | \(-0.759991\pi\) |
−0.228379 | − | 0.973572i | \(-0.573343\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 124.799i | 0.150906i | 0.997149 | + | 0.0754529i | \(0.0240403\pi\) | ||||
−0.997149 | + | 0.0754529i | \(0.975960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −426.486 | −0.514458 | −0.257229 | − | 0.966350i | \(-0.582810\pi\) | ||||
−0.257229 | + | 0.966350i | \(0.582810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 92.2365 | − | 53.2528i | 0.110728 | − | 0.0639289i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.82403 | + | 8.35547i | −0.00577728 | + | 0.0100065i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −430.710 | − | 248.671i | −0.513362 | − | 0.296389i | 0.220853 | − | 0.975307i | \(-0.429116\pi\) |
−0.734214 | + | 0.678918i | \(0.762449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 652.999 | + | 1131.03i | 0.776455 | + | 1.34486i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1036.58i | − | 1.22673i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −525.759 | −0.620730 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1316.52 | + | 760.092i | −1.54703 | + | 0.893176i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −767.481 | + | 1329.32i | −0.899743 | + | 1.55840i | −0.0719203 | + | 0.997410i | \(0.522913\pi\) |
−0.827823 | + | 0.560990i | \(0.810421\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1055.08 | − | 609.149i | −1.23113 | − | 0.710792i | −0.263863 | − | 0.964560i | \(-0.584997\pi\) |
−0.967265 | + | 0.253768i | \(0.918330\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 289.720 | + | 501.811i | 0.337276 | + | 0.584180i | 0.983919 | − | 0.178613i | \(-0.0571610\pi\) |
−0.646643 | + | 0.762793i | \(0.723828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1361.09i | − | 1.57716i | −0.614934 | − | 0.788579i | \(-0.710817\pi\) | ||
0.614934 | − | 0.788579i | \(-0.289183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 332.422 | 0.384303 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 439.866 | − | 253.957i | 0.506175 | − | 0.292240i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 101.232 | − | 175.339i | 0.116225 | − | 0.201307i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 443.617 | + | 256.122i | 0.506991 | + | 0.292711i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −150.947 | − | 261.448i | −0.172118 | − | 0.298117i | 0.767042 | − | 0.641597i | \(-0.221728\pi\) |
−0.939160 | + | 0.343480i | \(0.888394\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1170.94i | 1.32911i | 0.747240 | + | 0.664554i | \(0.231378\pi\) | ||||
−0.747240 | + | 0.664554i | \(0.768622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1339.68 | −1.51719 | −0.758597 | − | 0.651560i | \(-0.774115\pi\) | ||||
−0.758597 | + | 0.651560i | \(0.774115\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.4375 | + | 8.33547i | −0.0162767 | + | 0.00939738i | −0.508116 | − | 0.861288i | \(-0.669658\pi\) |
0.491840 | + | 0.870686i | \(0.336325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.3261 | + | 78.5071i | −0.0509855 | + | 0.0883094i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 767.362 | + | 443.037i | 0.859308 | + | 0.496122i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −748.323 | − | 1296.13i | −0.836115 | − | 1.44819i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1311.74i | 1.45911i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 624.930 | 0.693596 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −331.042 | + | 191.127i | −0.365792 | + | 0.211190i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −225.668 | + | 390.868i | −0.248807 | + | 0.430946i | −0.963195 | − | 0.268803i | \(-0.913372\pi\) |
0.714388 | + | 0.699750i | \(0.246705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1243.11 | + | 717.711i | 1.36456 | + | 0.787827i | 0.990227 | − | 0.139468i | \(-0.0445392\pi\) |
0.374331 | + | 0.927295i | \(0.377873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 390.806 | + | 676.895i | 0.428046 | + | 0.741397i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 393.472i | 0.429086i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 380.633 | 0.414181 | 0.207091 | − | 0.978322i | \(-0.433600\pi\) | ||||
0.207091 | + | 0.978322i | \(0.433600\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −131.181 | + | 75.7374i | −0.142125 | + | 0.0820557i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −443.707 | + | 768.523i | −0.479683 | + | 0.830836i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 856.635 | + | 494.578i | 0.922104 | + | 0.532377i | 0.884306 | − | 0.466908i | \(-0.154632\pi\) |
0.0377985 | + | 0.999285i | \(0.487965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −71.8703 | − | 124.483i | −0.0771969 | − | 0.133709i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 658.874i | − | 0.704678i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −549.202 | −0.586128 | −0.293064 | − | 0.956093i | \(-0.594675\pi\) | ||||
−0.293064 | + | 0.956093i | \(0.594675\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 405.479 | − | 234.103i | 0.430902 | − | 0.248781i | −0.268829 | − | 0.963188i | \(-0.586637\pi\) |
0.699731 | + | 0.714407i | \(0.253303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 389.861 | − | 675.259i | 0.413427 | − | 0.716076i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 260.869 | + | 150.613i | 0.275469 | + | 0.159042i | 0.631370 | − | 0.775482i | \(-0.282493\pi\) |
−0.355902 | + | 0.934523i | \(0.615826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −84.0235 | − | 145.533i | −0.0885390 | − | 0.153354i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 319.384i | 0.335135i | 0.985861 | + | 0.167567i | \(0.0535912\pi\) | ||||
−0.985861 | + | 0.167567i | \(0.946409\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −208.630 | −0.218461 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 908.829 | − | 524.713i | 0.947685 | − | 0.547146i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79.7892 | − | 138.199i | 0.0830272 | − | 0.143807i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 230.377 | + | 133.008i | 0.238732 | + | 0.137832i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −302.086 | − | 523.229i | −0.312395 | − | 0.541085i | 0.666485 | − | 0.745518i | \(-0.267798\pi\) |
−0.978880 | + | 0.204434i | \(0.934465\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 465.068i | 0.478958i | 0.970902 | + | 0.239479i | \(0.0769766\pi\) | ||||
−0.970902 | + | 0.239479i | \(0.923023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −299.368 | −0.307675 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 332.512 | − | 191.976i | 0.340340 | − | 0.196495i | −0.320083 | − | 0.947390i | \(-0.603711\pi\) |
0.660422 | + | 0.750894i | \(0.270377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −105.894 | + | 183.413i | −0.108165 | + | 0.187348i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −586.197 | − | 338.441i | −0.596335 | − | 0.344294i | 0.171264 | − | 0.985225i | \(-0.445215\pi\) |
−0.767598 | + | 0.640931i | \(0.778548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −635.589 | − | 1100.87i | −0.645268 | − | 1.11764i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1871.05i | − | 1.89186i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1097.79 | 1.10776 | 0.553878 | − | 0.832598i | \(-0.313147\pi\) | ||||
0.553878 | + | 0.832598i | \(0.313147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 693.744 | − | 400.533i | 0.697230 | − | 0.402546i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 90.7127 | − | 157.119i | 0.0909857 | − | 0.157592i | −0.816940 | − | 0.576722i | \(-0.804332\pi\) |
0.907926 | + | 0.419130i | \(0.137665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.q.k.1601.10 | 24 | ||
3.2 | odd | 2 | 576.3.q.l.65.1 | 24 | |||
4.3 | odd | 2 | inner | 1728.3.q.k.1601.9 | 24 | ||
8.3 | odd | 2 | 864.3.q.a.737.3 | 24 | |||
8.5 | even | 2 | 864.3.q.a.737.4 | 24 | |||
9.4 | even | 3 | 576.3.q.l.257.1 | 24 | |||
9.5 | odd | 6 | inner | 1728.3.q.k.449.10 | 24 | ||
12.11 | even | 2 | 576.3.q.l.65.12 | 24 | |||
24.5 | odd | 2 | 288.3.q.b.65.12 | yes | 24 | ||
24.11 | even | 2 | 288.3.q.b.65.1 | ✓ | 24 | ||
36.23 | even | 6 | inner | 1728.3.q.k.449.9 | 24 | ||
36.31 | odd | 6 | 576.3.q.l.257.12 | 24 | |||
72.5 | odd | 6 | 864.3.q.a.449.4 | 24 | |||
72.11 | even | 6 | 2592.3.e.i.161.20 | 24 | |||
72.13 | even | 6 | 288.3.q.b.257.12 | yes | 24 | ||
72.29 | odd | 6 | 2592.3.e.i.161.6 | 24 | |||
72.43 | odd | 6 | 2592.3.e.i.161.19 | 24 | |||
72.59 | even | 6 | 864.3.q.a.449.3 | 24 | |||
72.61 | even | 6 | 2592.3.e.i.161.5 | 24 | |||
72.67 | odd | 6 | 288.3.q.b.257.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.3.q.b.65.1 | ✓ | 24 | 24.11 | even | 2 | ||
288.3.q.b.65.12 | yes | 24 | 24.5 | odd | 2 | ||
288.3.q.b.257.1 | yes | 24 | 72.67 | odd | 6 | ||
288.3.q.b.257.12 | yes | 24 | 72.13 | even | 6 | ||
576.3.q.l.65.1 | 24 | 3.2 | odd | 2 | |||
576.3.q.l.65.12 | 24 | 12.11 | even | 2 | |||
576.3.q.l.257.1 | 24 | 9.4 | even | 3 | |||
576.3.q.l.257.12 | 24 | 36.31 | odd | 6 | |||
864.3.q.a.449.3 | 24 | 72.59 | even | 6 | |||
864.3.q.a.449.4 | 24 | 72.5 | odd | 6 | |||
864.3.q.a.737.3 | 24 | 8.3 | odd | 2 | |||
864.3.q.a.737.4 | 24 | 8.5 | even | 2 | |||
1728.3.q.k.449.9 | 24 | 36.23 | even | 6 | inner | ||
1728.3.q.k.449.10 | 24 | 9.5 | odd | 6 | inner | ||
1728.3.q.k.1601.9 | 24 | 4.3 | odd | 2 | inner | ||
1728.3.q.k.1601.10 | 24 | 1.1 | even | 1 | trivial | ||
2592.3.e.i.161.5 | 24 | 72.61 | even | 6 | |||
2592.3.e.i.161.6 | 24 | 72.29 | odd | 6 | |||
2592.3.e.i.161.19 | 24 | 72.43 | odd | 6 | |||
2592.3.e.i.161.20 | 24 | 72.11 | even | 6 |