Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(449,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.c (of order \(2\), degree \(1\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.32 | ||
Character | \(\chi\) | \(=\) | 1050.449 |
Dual form | 1050.3.c.c.449.31 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 2.92855 | + | 0.650833i | 0.976184 | + | 0.216944i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.14160 | + | 0.920417i | 0.690266 | + | 0.153403i | ||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 8.15283 | + | 3.81200i | 0.905870 | + | 0.423555i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 7.97556i | − | 0.725051i | −0.931974 | − | 0.362526i | \(-0.881915\pi\) | ||
0.931974 | − | 0.362526i | \(-0.118085\pi\) | |||||||
\(12\) | 5.85710 | + | 1.30167i | 0.488092 | + | 0.108472i | ||||
\(13\) | − | 5.79363i | − | 0.445664i | −0.974857 | − | 0.222832i | \(-0.928470\pi\) | ||
0.974857 | − | 0.222832i | \(-0.0715301\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −9.35782 | −0.550460 | −0.275230 | − | 0.961378i | \(-0.588754\pi\) | ||||
−0.275230 | + | 0.961378i | \(0.588754\pi\) | |||||||
\(18\) | 11.5298 | + | 5.39098i | 0.640547 | + | 0.299499i | ||||
\(19\) | 22.7979 | 1.19989 | 0.599946 | − | 0.800041i | \(-0.295189\pi\) | ||||
0.599946 | + | 0.800041i | \(0.295189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.72194 | + | 7.74822i | −0.0819972 | + | 0.368963i | ||||
\(22\) | − | 11.2792i | − | 0.512689i | ||||||
\(23\) | 34.9882 | 1.52123 | 0.760613 | − | 0.649205i | \(-0.224898\pi\) | ||||
0.760613 | + | 0.649205i | \(0.224898\pi\) | |||||||
\(24\) | 8.28320 | + | 1.84083i | 0.345133 | + | 0.0767014i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 8.19343i | − | 0.315132i | ||||||
\(27\) | 21.3950 | + | 16.4698i | 0.792408 | + | 0.609991i | ||||
\(28\) | 5.29150i | 0.188982i | ||||||||
\(29\) | 15.5858i | 0.537442i | 0.963218 | + | 0.268721i | \(0.0866010\pi\) | ||||
−0.963218 | + | 0.268721i | \(0.913399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 25.5869 | 0.825384 | 0.412692 | − | 0.910871i | \(-0.364589\pi\) | ||||
0.412692 | + | 0.910871i | \(0.364589\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 5.19076 | − | 23.3569i | 0.157296 | − | 0.707783i | ||||
\(34\) | −13.2340 | −0.389234 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.3057 | + | 7.62399i | 0.452935 | + | 0.211778i | ||||
\(37\) | − | 38.4908i | − | 1.04029i | −0.854078 | − | 0.520145i | \(-0.825878\pi\) | ||
0.854078 | − | 0.520145i | \(-0.174122\pi\) | |||||||
\(38\) | 32.2412 | 0.848451 | ||||||||
\(39\) | 3.77068 | − | 16.9669i | 0.0966842 | − | 0.435050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.1062i | 0.856249i | 0.903720 | + | 0.428125i | \(0.140826\pi\) | ||||
−0.903720 | + | 0.428125i | \(0.859174\pi\) | |||||||
\(42\) | −2.43519 | + | 10.9576i | −0.0579808 | + | 0.260896i | ||||
\(43\) | 59.0951i | 1.37431i | 0.726513 | + | 0.687153i | \(0.241140\pi\) | ||||
−0.726513 | + | 0.687153i | \(0.758860\pi\) | |||||||
\(44\) | − | 15.9511i | − | 0.362526i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 49.4808 | 1.07567 | ||||||||
\(47\) | 1.03517 | 0.0220249 | 0.0110124 | − | 0.999939i | \(-0.496495\pi\) | ||||
0.0110124 | + | 0.999939i | \(0.496495\pi\) | |||||||
\(48\) | 11.7142 | + | 2.60333i | 0.244046 | + | 0.0542361i | ||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −27.4049 | − | 6.09038i | −0.537351 | − | 0.119419i | ||||
\(52\) | − | 11.5873i | − | 0.222832i | ||||||
\(53\) | −41.5179 | −0.783357 | −0.391679 | − | 0.920102i | \(-0.628105\pi\) | ||||
−0.391679 | + | 0.920102i | \(0.628105\pi\) | |||||||
\(54\) | 30.2571 | + | 23.2918i | 0.560317 | + | 0.431329i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 66.7650 | + | 14.8377i | 1.17131 | + | 0.260310i | ||||
\(58\) | 22.0417i | 0.380029i | ||||||||
\(59\) | 55.1602i | 0.934919i | 0.884014 | + | 0.467460i | \(0.154831\pi\) | ||||
−0.884014 | + | 0.467460i | \(0.845169\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −94.7726 | −1.55365 | −0.776824 | − | 0.629717i | \(-0.783171\pi\) | ||||
−0.776824 | + | 0.629717i | \(0.783171\pi\) | |||||||
\(62\) | 36.1853 | 0.583635 | ||||||||
\(63\) | −10.0856 | + | 21.5704i | −0.160089 | + | 0.342387i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.34084 | − | 33.0316i | 0.111225 | − | 0.500478i | ||||
\(67\) | − | 77.1064i | − | 1.15084i | −0.817857 | − | 0.575421i | \(-0.804838\pi\) | ||
0.817857 | − | 0.575421i | \(-0.195162\pi\) | |||||||
\(68\) | −18.7156 | −0.275230 | ||||||||
\(69\) | 102.465 | + | 22.7715i | 1.48500 | + | 0.330021i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 18.0046i | − | 0.253586i | −0.991929 | − | 0.126793i | \(-0.959532\pi\) | ||
0.991929 | − | 0.126793i | \(-0.0404684\pi\) | |||||||
\(72\) | 23.0597 | + | 10.7820i | 0.320274 | + | 0.149749i | ||||
\(73\) | 33.2022i | 0.454825i | 0.973799 | + | 0.227412i | \(0.0730266\pi\) | ||||
−0.973799 | + | 0.227412i | \(0.926973\pi\) | |||||||
\(74\) | − | 54.4342i | − | 0.735597i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 45.5959 | 0.599946 | ||||||||
\(77\) | 21.1014 | 0.274044 | ||||||||
\(78\) | 5.33255 | − | 23.9949i | 0.0683660 | − | 0.307627i | ||||
\(79\) | 54.9427 | 0.695478 | 0.347739 | − | 0.937591i | \(-0.386950\pi\) | ||||
0.347739 | + | 0.937591i | \(0.386950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 51.9374 | + | 62.1571i | 0.641202 | + | 0.767372i | ||||
\(82\) | 49.6477i | 0.605460i | ||||||||
\(83\) | −78.6593 | −0.947703 | −0.473851 | − | 0.880605i | \(-0.657137\pi\) | ||||
−0.473851 | + | 0.880605i | \(0.657137\pi\) | |||||||
\(84\) | −3.44388 | + | 15.4964i | −0.0409986 | + | 0.184481i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 83.5731i | 0.971781i | ||||||||
\(87\) | −10.1438 | + | 45.6439i | −0.116595 | + | 0.524643i | ||||
\(88\) | − | 22.5583i | − | 0.256344i | ||||||
\(89\) | − | 120.028i | − | 1.34863i | −0.738442 | − | 0.674317i | \(-0.764438\pi\) | ||
0.738442 | − | 0.674317i | \(-0.235562\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.3285 | 0.168445 | ||||||||
\(92\) | 69.9764 | 0.760613 | ||||||||
\(93\) | 74.9326 | + | 16.6528i | 0.805727 | + | 0.179062i | ||||
\(94\) | 1.46395 | 0.0155739 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.5664 | + | 3.68167i | 0.172567 | + | 0.0383507i | ||||
\(97\) | − | 24.5127i | − | 0.252708i | −0.991985 | − | 0.126354i | \(-0.959672\pi\) | ||
0.991985 | − | 0.126354i | \(-0.0403276\pi\) | |||||||
\(98\) | −9.89949 | −0.101015 | ||||||||
\(99\) | 30.4028 | − | 65.0234i | 0.307099 | − | 0.656802i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 158.695i | − | 1.57124i | −0.618709 | − | 0.785620i | \(-0.712344\pi\) | ||
0.618709 | − | 0.785620i | \(-0.287656\pi\) | |||||||
\(102\) | −38.7563 | − | 8.61310i | −0.379964 | − | 0.0844421i | ||||
\(103\) | 177.505i | 1.72335i | 0.507461 | + | 0.861674i | \(0.330584\pi\) | ||||
−0.507461 | + | 0.861674i | \(0.669416\pi\) | |||||||
\(104\) | − | 16.3869i | − | 0.157566i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −58.7152 | −0.553917 | ||||||||
\(107\) | −210.992 | −1.97189 | −0.985946 | − | 0.167064i | \(-0.946571\pi\) | ||||
−0.985946 | + | 0.167064i | \(0.946571\pi\) | |||||||
\(108\) | 42.7900 | + | 32.9395i | 0.396204 | + | 0.304996i | ||||
\(109\) | 98.5237 | 0.903887 | 0.451943 | − | 0.892047i | \(-0.350731\pi\) | ||||
0.451943 | + | 0.892047i | \(0.350731\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.0511 | − | 112.722i | 0.225685 | − | 1.01552i | ||||
\(112\) | 10.5830i | 0.0944911i | ||||||||
\(113\) | −102.830 | −0.910000 | −0.455000 | − | 0.890492i | \(-0.650361\pi\) | ||||
−0.455000 | + | 0.890492i | \(0.650361\pi\) | |||||||
\(114\) | 94.4199 | + | 20.9836i | 0.828245 | + | 0.184067i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 31.1717i | 0.268721i | ||||||||
\(117\) | 22.0853 | − | 47.2345i | 0.188763 | − | 0.403713i | ||||
\(118\) | 78.0084i | 0.661088i | ||||||||
\(119\) | − | 24.7585i | − | 0.208054i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 57.3904 | 0.474301 | ||||||||
\(122\) | −134.029 | −1.09860 | ||||||||
\(123\) | −22.8483 | + | 102.810i | −0.185758 | + | 0.835857i | ||||
\(124\) | 51.1738 | 0.412692 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −14.2632 | + | 30.5051i | −0.113200 | + | 0.242104i | ||||
\(127\) | − | 157.688i | − | 1.24164i | −0.783954 | − | 0.620819i | \(-0.786800\pi\) | ||
0.783954 | − | 0.620819i | \(-0.213200\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | −38.4611 | + | 173.063i | −0.298148 | + | 1.34158i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 250.120i | − | 1.90932i | −0.297705 | − | 0.954658i | \(-0.596221\pi\) | ||
0.297705 | − | 0.954658i | \(-0.403779\pi\) | |||||||
\(132\) | 10.3815 | − | 46.7137i | 0.0786479 | − | 0.353892i | ||||
\(133\) | 60.3177i | 0.453516i | ||||||||
\(134\) | − | 109.045i | − | 0.813768i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −26.4679 | −0.194617 | ||||||||
\(137\) | −191.896 | −1.40070 | −0.700350 | − | 0.713800i | \(-0.746973\pi\) | ||||
−0.700350 | + | 0.713800i | \(0.746973\pi\) | |||||||
\(138\) | 144.907 | + | 32.2037i | 1.05005 | + | 0.233360i | ||||
\(139\) | −21.4645 | −0.154421 | −0.0772103 | − | 0.997015i | \(-0.524601\pi\) | ||||
−0.0772103 | + | 0.997015i | \(0.524601\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.03155 | + | 0.673722i | 0.0215003 | + | 0.00477817i | ||||
\(142\) | − | 25.4624i | − | 0.179313i | ||||||
\(143\) | −46.2074 | −0.323129 | ||||||||
\(144\) | 32.6113 | + | 15.2480i | 0.226468 | + | 0.105889i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 46.9550i | 0.321610i | ||||||||
\(147\) | −20.4999 | − | 4.55583i | −0.139455 | − | 0.0309920i | ||||
\(148\) | − | 76.9815i | − | 0.520145i | ||||||
\(149\) | 66.8671i | 0.448772i | 0.974500 | + | 0.224386i | \(0.0720377\pi\) | ||||
−0.974500 | + | 0.224386i | \(0.927962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −64.4712 | −0.426962 | −0.213481 | − | 0.976947i | \(-0.568480\pi\) | ||||
−0.213481 | + | 0.976947i | \(0.568480\pi\) | |||||||
\(152\) | 64.4823 | 0.424226 | ||||||||
\(153\) | −76.2928 | − | 35.6720i | −0.498646 | − | 0.233150i | ||||
\(154\) | 29.8418 | 0.193778 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.54137 | − | 33.9339i | 0.0483421 | − | 0.217525i | ||||
\(157\) | 207.257i | 1.32011i | 0.751217 | + | 0.660056i | \(0.229467\pi\) | ||||
−0.751217 | + | 0.660056i | \(0.770533\pi\) | |||||||
\(158\) | 77.7008 | 0.491777 | ||||||||
\(159\) | −121.587 | − | 27.0212i | −0.764701 | − | 0.169945i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 92.5701i | 0.574970i | ||||||||
\(162\) | 73.4505 | + | 87.9035i | 0.453398 | + | 0.542614i | ||||
\(163\) | 236.067i | 1.44826i | 0.689662 | + | 0.724132i | \(0.257759\pi\) | ||||
−0.689662 | + | 0.724132i | \(0.742241\pi\) | |||||||
\(164\) | 70.2124i | 0.428125i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −111.241 | −0.670127 | ||||||||
\(167\) | −109.647 | −0.656568 | −0.328284 | − | 0.944579i | \(-0.606470\pi\) | ||||
−0.328284 | + | 0.944579i | \(0.606470\pi\) | |||||||
\(168\) | −4.87039 | + | 21.9153i | −0.0289904 | + | 0.130448i | ||||
\(169\) | 135.434 | 0.801384 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 185.868 | + | 86.9057i | 1.08695 | + | 0.508220i | ||||
\(172\) | 118.190i | 0.687153i | ||||||||
\(173\) | 46.7105 | 0.270003 | 0.135001 | − | 0.990845i | \(-0.456896\pi\) | ||||
0.135001 | + | 0.990845i | \(0.456896\pi\) | |||||||
\(174\) | −14.3455 | + | 64.5502i | −0.0824452 | + | 0.370978i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 31.9023i | − | 0.181263i | ||||||
\(177\) | −35.9001 | + | 161.540i | −0.202825 | + | 0.912653i | ||||
\(178\) | − | 169.746i | − | 0.953629i | ||||||
\(179\) | − | 293.828i | − | 1.64150i | −0.571289 | − | 0.820749i | \(-0.693556\pi\) | ||
0.571289 | − | 0.820749i | \(-0.306444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −129.626 | −0.716168 | −0.358084 | − | 0.933689i | \(-0.616570\pi\) | ||||
−0.358084 | + | 0.933689i | \(0.616570\pi\) | |||||||
\(182\) | 21.6778 | 0.119109 | ||||||||
\(183\) | −277.546 | − | 61.6811i | −1.51665 | − | 0.337055i | ||||
\(184\) | 98.9616 | 0.537835 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 105.971 | + | 23.5506i | 0.569735 | + | 0.126616i | ||||
\(187\) | 74.6339i | 0.399112i | ||||||||
\(188\) | 2.07034 | 0.0110124 | ||||||||
\(189\) | −43.5749 | + | 56.6059i | −0.230555 | + | 0.299502i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.24400i | − | 0.0379267i | −0.999820 | − | 0.0189633i | \(-0.993963\pi\) | ||
0.999820 | − | 0.0189633i | \(-0.00603658\pi\) | |||||||
\(192\) | 23.4284 | + | 5.20666i | 0.122023 | + | 0.0271180i | ||||
\(193\) | − | 313.671i | − | 1.62524i | −0.582793 | − | 0.812620i | \(-0.698040\pi\) | ||
0.582793 | − | 0.812620i | \(-0.301960\pi\) | |||||||
\(194\) | − | 34.6662i | − | 0.178692i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −94.5137 | −0.479765 | −0.239882 | − | 0.970802i | \(-0.577109\pi\) | ||||
−0.239882 | + | 0.970802i | \(0.577109\pi\) | |||||||
\(198\) | 42.9961 | − | 91.9570i | 0.217152 | − | 0.464429i | ||||
\(199\) | 185.816 | 0.933747 | 0.466874 | − | 0.884324i | \(-0.345380\pi\) | ||||
0.466874 | + | 0.884324i | \(0.345380\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 50.1834 | − | 225.810i | 0.249669 | − | 1.12343i | ||||
\(202\) | − | 224.429i | − | 1.11104i | ||||||
\(203\) | −41.2362 | −0.203134 | ||||||||
\(204\) | −54.8098 | − | 12.1808i | −0.268675 | − | 0.0597096i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 251.030i | 1.21859i | ||||||||
\(207\) | 285.253 | + | 133.375i | 1.37803 | + | 0.644323i | ||||
\(208\) | − | 23.1745i | − | 0.111416i | ||||||
\(209\) | − | 181.826i | − | 0.869983i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 375.709 | 1.78061 | 0.890306 | − | 0.455363i | \(-0.150491\pi\) | ||||
0.890306 | + | 0.455363i | \(0.150491\pi\) | |||||||
\(212\) | −83.0359 | −0.391679 | ||||||||
\(213\) | 11.7180 | − | 52.7275i | 0.0550141 | − | 0.247547i | ||||
\(214\) | −298.388 | −1.39434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 60.5143 | + | 46.5835i | 0.280159 | + | 0.215664i | ||||
\(217\) | 67.6966i | 0.311966i | ||||||||
\(218\) | 139.334 | 0.639145 | ||||||||
\(219\) | −21.6091 | + | 97.2344i | −0.0986717 | + | 0.443993i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 54.2158i | 0.245320i | ||||||||
\(222\) | 35.4275 | − | 159.413i | 0.159584 | − | 0.718078i | ||||
\(223\) | − | 19.6107i | − | 0.0879404i | −0.999033 | − | 0.0439702i | \(-0.985999\pi\) | ||
0.999033 | − | 0.0439702i | \(-0.0140007\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −145.424 | −0.643467 | ||||||||
\(227\) | −250.934 | −1.10543 | −0.552717 | − | 0.833369i | \(-0.686409\pi\) | ||||
−0.552717 | + | 0.833369i | \(0.686409\pi\) | |||||||
\(228\) | 133.530 | + | 29.6753i | 0.585657 | + | 0.130155i | ||||
\(229\) | −296.680 | −1.29555 | −0.647773 | − | 0.761833i | \(-0.724299\pi\) | ||||
−0.647773 | + | 0.761833i | \(0.724299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 61.7964 | + | 13.7335i | 0.267517 | + | 0.0594522i | ||||
\(232\) | 44.0834i | 0.190015i | ||||||||
\(233\) | −157.483 | −0.675891 | −0.337946 | − | 0.941166i | \(-0.609732\pi\) | ||||
−0.337946 | + | 0.941166i | \(0.609732\pi\) | |||||||
\(234\) | 31.2333 | − | 66.7996i | 0.133476 | − | 0.285469i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 110.320i | 0.467460i | ||||||||
\(237\) | 160.903 | + | 35.7586i | 0.678914 | + | 0.150880i | ||||
\(238\) | − | 35.0138i | − | 0.147117i | ||||||
\(239\) | − | 78.7765i | − | 0.329609i | −0.986326 | − | 0.164804i | \(-0.947301\pi\) | ||
0.986326 | − | 0.164804i | \(-0.0526993\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −148.348 | −0.615553 | −0.307777 | − | 0.951459i | \(-0.599585\pi\) | ||||
−0.307777 | + | 0.951459i | \(0.599585\pi\) | |||||||
\(242\) | 81.1623 | 0.335381 | ||||||||
\(243\) | 111.647 | + | 215.833i | 0.459454 | + | 0.888201i | ||||
\(244\) | −189.545 | −0.776824 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −32.3124 | + | 145.396i | −0.131351 | + | 0.591040i | ||||
\(247\) | − | 132.083i | − | 0.534748i | ||||||
\(248\) | 72.3707 | 0.291817 | ||||||||
\(249\) | −230.358 | − | 51.1941i | −0.925132 | − | 0.205599i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 223.217i | 0.889310i | 0.895702 | + | 0.444655i | \(0.146674\pi\) | ||||
−0.895702 | + | 0.444655i | \(0.853326\pi\) | |||||||
\(252\) | −20.1712 | + | 43.1407i | −0.0800444 | + | 0.171193i | ||||
\(253\) | − | 279.051i | − | 1.10297i | ||||||
\(254\) | − | 223.004i | − | 0.877970i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 359.930 | 1.40051 | 0.700254 | − | 0.713894i | \(-0.253070\pi\) | ||||
0.700254 | + | 0.713894i | \(0.253070\pi\) | |||||||
\(258\) | −54.3922 | + | 244.748i | −0.210822 | + | 0.948637i | ||||
\(259\) | 101.837 | 0.393193 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −59.4131 | + | 127.069i | −0.227637 | + | 0.486853i | ||||
\(262\) | − | 353.724i | − | 1.35009i | ||||||
\(263\) | 228.402 | 0.868447 | 0.434224 | − | 0.900805i | \(-0.357023\pi\) | ||||
0.434224 | + | 0.900805i | \(0.357023\pi\) | |||||||
\(264\) | 14.6817 | − | 66.0632i | 0.0556124 | − | 0.250239i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 85.3021i | 0.320685i | ||||||||
\(267\) | 78.1185 | − | 351.510i | 0.292579 | − | 1.31652i | ||||
\(268\) | − | 154.213i | − | 0.575421i | ||||||
\(269\) | 283.528i | 1.05401i | 0.849863 | + | 0.527003i | \(0.176684\pi\) | ||||
−0.849863 | + | 0.527003i | \(0.823316\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −290.789 | −1.07302 | −0.536512 | − | 0.843893i | \(-0.680258\pi\) | ||||
−0.536512 | + | 0.843893i | \(0.680258\pi\) | |||||||
\(272\) | −37.4313 | −0.137615 | ||||||||
\(273\) | 44.8903 | + | 9.97629i | 0.164433 | + | 0.0365432i | ||||
\(274\) | −271.382 | −0.990444 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 204.930 | + | 45.5430i | 0.742498 | + | 0.165011i | ||||
\(277\) | 267.470i | 0.965596i | 0.875732 | + | 0.482798i | \(0.160379\pi\) | ||||
−0.875732 | + | 0.482798i | \(0.839621\pi\) | |||||||
\(278\) | −30.3553 | −0.109192 | ||||||||
\(279\) | 208.606 | + | 97.5372i | 0.747691 | + | 0.349596i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 212.689i | − | 0.756900i | −0.925622 | − | 0.378450i | \(-0.876457\pi\) | ||
0.925622 | − | 0.378450i | \(-0.123543\pi\) | |||||||
\(282\) | 4.28725 | + | 0.952787i | 0.0152030 | + | 0.00337868i | ||||
\(283\) | − | 249.746i | − | 0.882496i | −0.897385 | − | 0.441248i | \(-0.854536\pi\) | ||
0.897385 | − | 0.441248i | \(-0.145464\pi\) | |||||||
\(284\) | − | 36.0092i | − | 0.126793i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −65.3472 | −0.228487 | ||||||||
\(287\) | −92.8823 | −0.323632 | ||||||||
\(288\) | 46.1194 | + | 21.5639i | 0.160137 | + | 0.0748747i | ||||
\(289\) | −201.431 | −0.696993 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.9537 | − | 71.7868i | 0.0548237 | − | 0.246690i | ||||
\(292\) | 66.4044i | 0.227412i | ||||||||
\(293\) | −312.196 | −1.06552 | −0.532758 | − | 0.846268i | \(-0.678844\pi\) | ||||
−0.532758 | + | 0.846268i | \(0.678844\pi\) | |||||||
\(294\) | −28.9912 | − | 6.44292i | −0.0986095 | − | 0.0219147i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 108.868i | − | 0.367798i | ||||||
\(297\) | 131.356 | − | 170.637i | 0.442275 | − | 0.574537i | ||||
\(298\) | 94.5643i | 0.317330i | ||||||||
\(299\) | − | 202.709i | − | 0.677955i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −156.351 | −0.519439 | ||||||||
\(302\) | −91.1760 | −0.301907 | ||||||||
\(303\) | 103.284 | − | 464.748i | 0.340872 | − | 1.53382i | ||||
\(304\) | 91.1918 | 0.299973 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −107.894 | − | 50.4478i | −0.352596 | − | 0.164862i | ||||
\(307\) | 155.259i | 0.505729i | 0.967502 | + | 0.252864i | \(0.0813727\pi\) | ||||
−0.967502 | + | 0.252864i | \(0.918627\pi\) | |||||||
\(308\) | 42.2027 | 0.137022 | ||||||||
\(309\) | −115.526 | + | 519.832i | −0.373871 | + | 1.68231i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 338.149i | 1.08730i | 0.839313 | + | 0.543649i | \(0.182958\pi\) | ||||
−0.839313 | + | 0.543649i | \(0.817042\pi\) | |||||||
\(312\) | 10.6651 | − | 47.9897i | 0.0341830 | − | 0.153813i | ||||
\(313\) | 32.5551i | 0.104010i | 0.998647 | + | 0.0520050i | \(0.0165612\pi\) | ||||
−0.998647 | + | 0.0520050i | \(0.983439\pi\) | |||||||
\(314\) | 293.106i | 0.933460i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 109.885 | 0.347739 | ||||||||
\(317\) | 156.813 | 0.494679 | 0.247340 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247340 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(318\) | −171.951 | − | 38.2138i | −0.540725 | − | 0.120169i | ||||
\(319\) | 124.306 | 0.389673 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −617.902 | − | 137.321i | −1.92493 | − | 0.427791i | ||||
\(322\) | 130.914i | 0.406565i | ||||||||
\(323\) | −213.339 | −0.660493 | ||||||||
\(324\) | 103.875 | + | 124.314i | 0.320601 | + | 0.383686i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 333.849i | 1.02408i | ||||||||
\(327\) | 288.532 | + | 64.1225i | 0.882360 | + | 0.196093i | ||||
\(328\) | 99.2954i | 0.302730i | ||||||||
\(329\) | 2.73880i | 0.00832462i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 62.7666 | 0.189627 | 0.0948136 | − | 0.995495i | \(-0.469775\pi\) | ||||
0.0948136 | + | 0.995495i | \(0.469775\pi\) | |||||||
\(332\) | −157.319 | −0.473851 | ||||||||
\(333\) | 146.727 | − | 313.809i | 0.440620 | − | 0.942369i | ||||
\(334\) | −155.064 | −0.464263 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.88777 | + | 30.9929i | −0.0204993 | + | 0.0922407i | ||||
\(337\) | − | 429.763i | − | 1.27526i | −0.770342 | − | 0.637631i | \(-0.779914\pi\) | ||
0.770342 | − | 0.637631i | \(-0.220086\pi\) | |||||||
\(338\) | 191.532 | 0.566664 | ||||||||
\(339\) | −301.143 | − | 66.9251i | −0.888327 | − | 0.197419i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 204.070i | − | 0.598446i | ||||||
\(342\) | 262.857 | + | 122.903i | 0.768587 | + | 0.359366i | ||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | 167.146i | 0.485890i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 66.0586 | 0.190921 | ||||||||
\(347\) | −611.203 | −1.76139 | −0.880695 | − | 0.473683i | \(-0.842924\pi\) | ||||
−0.880695 | + | 0.473683i | \(0.842924\pi\) | |||||||
\(348\) | −20.2875 | + | 91.2878i | −0.0582975 | + | 0.262321i | ||||
\(349\) | 229.756 | 0.658327 | 0.329163 | − | 0.944273i | \(-0.393233\pi\) | ||||
0.329163 | + | 0.944273i | \(0.393233\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 95.4197 | − | 123.955i | 0.271851 | − | 0.353148i | ||||
\(352\) | − | 45.1166i | − | 0.128172i | ||||||
\(353\) | −434.601 | −1.23117 | −0.615583 | − | 0.788072i | \(-0.711079\pi\) | ||||
−0.615583 | + | 0.788072i | \(0.711079\pi\) | |||||||
\(354\) | −50.7704 | + | 228.452i | −0.143419 | + | 0.645343i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 240.057i | − | 0.674317i | ||||||
\(357\) | 16.1136 | − | 72.5065i | 0.0451362 | − | 0.203099i | ||||
\(358\) | − | 415.536i | − | 1.16071i | ||||||
\(359\) | − | 185.884i | − | 0.517782i | −0.965907 | − | 0.258891i | \(-0.916643\pi\) | ||
0.965907 | − | 0.258891i | \(-0.0833570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 158.746 | 0.439740 | ||||||||
\(362\) | −183.320 | −0.506408 | ||||||||
\(363\) | 168.071 | + | 37.3516i | 0.463005 | + | 0.102897i | ||||
\(364\) | 30.6570 | 0.0842225 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −392.510 | − | 87.2303i | −1.07243 | − | 0.238334i | ||||
\(367\) | 418.446i | 1.14018i | 0.821582 | + | 0.570090i | \(0.193092\pi\) | ||||
−0.821582 | + | 0.570090i | \(0.806908\pi\) | |||||||
\(368\) | 139.953 | 0.380307 | ||||||||
\(369\) | −133.825 | + | 286.215i | −0.362669 | + | 0.775651i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 109.846i | − | 0.296081i | ||||||
\(372\) | 149.865 | + | 33.3056i | 0.402863 | + | 0.0895312i | ||||
\(373\) | 597.593i | 1.60213i | 0.598581 | + | 0.801063i | \(0.295732\pi\) | ||||
−0.598581 | + | 0.801063i | \(0.704268\pi\) | |||||||
\(374\) | 105.548i | 0.282215i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.92790 | 0.00778697 | ||||||||
\(377\) | 90.2985 | 0.239519 | ||||||||
\(378\) | −61.6242 | + | 80.0528i | −0.163027 | + | 0.211780i | ||||
\(379\) | −563.466 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 102.629 | − | 461.797i | 0.269366 | − | 1.21207i | ||||
\(382\) | − | 10.2446i | − | 0.0268182i | ||||||
\(383\) | 108.726 | 0.283881 | 0.141940 | − | 0.989875i | \(-0.454666\pi\) | ||||
0.141940 | + | 0.989875i | \(0.454666\pi\) | |||||||
\(384\) | 33.1328 | + | 7.36333i | 0.0862833 | + | 0.0191753i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 443.598i | − | 1.14922i | ||||||
\(387\) | −225.270 | + | 481.793i | −0.582094 | + | 1.24494i | ||||
\(388\) | − | 49.0254i | − | 0.126354i | ||||||
\(389\) | 128.348i | 0.329944i | 0.986298 | + | 0.164972i | \(0.0527534\pi\) | ||||
−0.986298 | + | 0.164972i | \(0.947247\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −327.414 | −0.837375 | ||||||||
\(392\) | −19.7990 | −0.0505076 | ||||||||
\(393\) | 162.787 | − | 732.490i | 0.414215 | − | 1.86384i | ||||
\(394\) | −133.663 | −0.339245 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 60.8056 | − | 130.047i | 0.153550 | − | 0.328401i | ||||
\(397\) | 165.453i | 0.416758i | 0.978048 | + | 0.208379i | \(0.0668188\pi\) | ||||
−0.978048 | + | 0.208379i | \(0.933181\pi\) | |||||||
\(398\) | 262.783 | 0.660259 | ||||||||
\(399\) | −39.2567 | + | 176.643i | −0.0983878 | + | 0.442715i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 397.048i | 0.990144i | 0.868852 | + | 0.495072i | \(0.164858\pi\) | ||||
−0.868852 | + | 0.495072i | \(0.835142\pi\) | |||||||
\(402\) | 70.9700 | − | 319.344i | 0.176542 | − | 0.794387i | ||||
\(403\) | − | 148.241i | − | 0.367844i | ||||||
\(404\) | − | 317.391i | − | 0.785620i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −58.3168 | −0.143638 | ||||||||
\(407\) | −306.985 | −0.754264 | ||||||||
\(408\) | −77.5127 | − | 17.2262i | −0.189982 | − | 0.0422211i | ||||
\(409\) | −590.813 | −1.44453 | −0.722265 | − | 0.691616i | \(-0.756899\pi\) | ||||
−0.722265 | + | 0.691616i | \(0.756899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −561.977 | − | 124.892i | −1.36734 | − | 0.303874i | ||||
\(412\) | 355.010i | 0.861674i | ||||||||
\(413\) | −145.940 | −0.353366 | ||||||||
\(414\) | 403.409 | + | 188.621i | 0.974417 | + | 0.455605i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 32.7737i | − | 0.0787829i | ||||||
\(417\) | −62.8598 | − | 13.9698i | −0.150743 | − | 0.0335007i | ||||
\(418\) | − | 257.141i | − | 0.615171i | ||||||
\(419\) | 275.411i | 0.657305i | 0.944451 | + | 0.328653i | \(0.106595\pi\) | ||||
−0.944451 | + | 0.328653i | \(0.893405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 570.120 | 1.35420 | 0.677102 | − | 0.735890i | \(-0.263236\pi\) | ||||
0.677102 | + | 0.735890i | \(0.263236\pi\) | |||||||
\(422\) | 531.333 | 1.25908 | ||||||||
\(423\) | 8.43956 | + | 3.94606i | 0.0199517 | + | 0.00932875i | ||||
\(424\) | −117.430 | −0.276959 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16.5718 | − | 74.5679i | 0.0389008 | − | 0.175042i | ||||
\(427\) | − | 250.745i | − | 0.587224i | ||||||
\(428\) | −421.985 | −0.985946 | ||||||||
\(429\) | −135.321 | − | 30.0733i | −0.315433 | − | 0.0701010i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 650.331i | − | 1.50889i | −0.656365 | − | 0.754444i | \(-0.727907\pi\) | ||
0.656365 | − | 0.754444i | \(-0.272093\pi\) | |||||||
\(432\) | 85.5801 | + | 65.8790i | 0.198102 | + | 0.152498i | ||||
\(433\) | 635.503i | 1.46767i | 0.679325 | + | 0.733837i | \(0.262273\pi\) | ||||
−0.679325 | + | 0.733837i | \(0.737727\pi\) | |||||||
\(434\) | 95.7374i | 0.220593i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 197.047 | 0.451943 | ||||||||
\(437\) | 797.659 | 1.82531 | ||||||||
\(438\) | −30.5599 | + | 137.510i | −0.0697714 | + | 0.313950i | ||||
\(439\) | 341.898 | 0.778810 | 0.389405 | − | 0.921067i | \(-0.372681\pi\) | ||||
0.389405 | + | 0.921067i | \(0.372681\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −57.0698 | − | 26.6840i | −0.129410 | − | 0.0605079i | ||||
\(442\) | 76.6726i | 0.173468i | ||||||||
\(443\) | −254.231 | −0.573884 | −0.286942 | − | 0.957948i | \(-0.592639\pi\) | ||||
−0.286942 | + | 0.957948i | \(0.592639\pi\) | |||||||
\(444\) | 50.1021 | − | 225.444i | 0.112843 | − | 0.507758i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 27.7337i | − | 0.0621833i | ||||||
\(447\) | −43.5193 | + | 195.824i | −0.0973586 | + | 0.438084i | ||||
\(448\) | 21.1660i | 0.0472456i | ||||||||
\(449\) | − | 73.2691i | − | 0.163183i | −0.996666 | − | 0.0815915i | \(-0.974000\pi\) | ||
0.996666 | − | 0.0815915i | \(-0.0260003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 279.992 | 0.620825 | ||||||||
\(452\) | −205.660 | −0.455000 | ||||||||
\(453\) | −188.807 | − | 41.9600i | −0.416793 | − | 0.0926269i | ||||
\(454\) | −354.874 | −0.781660 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 188.840 | + | 41.9672i | 0.414122 | + | 0.0920334i | ||||
\(457\) | − | 201.124i | − | 0.440097i | −0.975489 | − | 0.220049i | \(-0.929378\pi\) | ||
0.975489 | − | 0.220049i | \(-0.0706216\pi\) | |||||||
\(458\) | −419.569 | −0.916089 | ||||||||
\(459\) | −200.211 | − | 154.121i | −0.436189 | − | 0.335776i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 500.367i | 1.08539i | 0.839929 | + | 0.542697i | \(0.182597\pi\) | ||||
−0.839929 | + | 0.542697i | \(0.817403\pi\) | |||||||
\(462\) | 87.3933 | + | 19.4220i | 0.189163 | + | 0.0420391i | ||||
\(463\) | − | 601.585i | − | 1.29932i | −0.760225 | − | 0.649660i | \(-0.774911\pi\) | ||
0.760225 | − | 0.649660i | \(-0.225089\pi\) | |||||||
\(464\) | 62.3433i | 0.134361i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −222.714 | −0.477927 | ||||||||
\(467\) | −271.025 | −0.580353 | −0.290176 | − | 0.956973i | \(-0.593714\pi\) | ||||
−0.290176 | + | 0.956973i | \(0.593714\pi\) | |||||||
\(468\) | 44.1706 | − | 94.4690i | 0.0943816 | − | 0.201857i | ||||
\(469\) | 204.004 | 0.434977 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −134.890 | + | 606.964i | −0.286391 | + | 1.28867i | ||||
\(472\) | 156.017i | 0.330544i | ||||||||
\(473\) | 471.317 | 0.996442 | ||||||||
\(474\) | 227.551 | + | 50.5702i | 0.480065 | + | 0.106688i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 49.5170i | − | 0.104027i | ||||||
\(477\) | −338.489 | − | 158.266i | −0.709620 | − | 0.331795i | ||||
\(478\) | − | 111.407i | − | 0.233069i | ||||||
\(479\) | − | 203.003i | − | 0.423807i | −0.977291 | − | 0.211903i | \(-0.932034\pi\) | ||
0.977291 | − | 0.211903i | \(-0.0679662\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −223.001 | −0.463620 | ||||||||
\(482\) | −209.796 | −0.435262 | ||||||||
\(483\) | −60.2477 | + | 271.096i | −0.124736 | + | 0.561276i | ||||
\(484\) | 114.781 | 0.237150 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 157.893 | + | 305.234i | 0.324883 | + | 0.628053i | ||||
\(487\) | − | 795.875i | − | 1.63424i | −0.576468 | − | 0.817120i | \(-0.695569\pi\) | ||
0.576468 | − | 0.817120i | \(-0.304431\pi\) | |||||||
\(488\) | −268.057 | −0.549298 | ||||||||
\(489\) | −153.640 | + | 691.334i | −0.314193 | + | 1.41377i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.1374i | 0.0837830i | 0.999122 | + | 0.0418915i | \(0.0133384\pi\) | ||||
−0.999122 | + | 0.0418915i | \(0.986662\pi\) | |||||||
\(492\) | −45.6966 | + | 205.621i | −0.0928792 | + | 0.417928i | ||||
\(493\) | − | 145.849i | − | 0.295841i | ||||||
\(494\) | − | 186.793i | − | 0.378124i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 102.348 | 0.206346 | ||||||||
\(497\) | 47.6357 | 0.0958466 | ||||||||
\(498\) | −325.775 | − | 72.3994i | −0.654167 | − | 0.145380i | ||||
\(499\) | −590.508 | −1.18338 | −0.591692 | − | 0.806164i | \(-0.701540\pi\) | ||||
−0.591692 | + | 0.806164i | \(0.701540\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −321.106 | − | 71.3618i | −0.640931 | − | 0.142439i | ||||
\(502\) | 315.676i | 0.628837i | ||||||||
\(503\) | 276.575 | 0.549850 | 0.274925 | − | 0.961466i | \(-0.411347\pi\) | ||||
0.274925 | + | 0.961466i | \(0.411347\pi\) | |||||||
\(504\) | −28.5264 | + | 61.0102i | −0.0565999 | + | 0.121052i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 394.637i | − | 0.779916i | ||||||
\(507\) | 396.625 | + | 88.1448i | 0.782298 | + | 0.173856i | ||||
\(508\) | − | 315.376i | − | 0.620819i | ||||||
\(509\) | − | 311.610i | − | 0.612201i | −0.951999 | − | 0.306100i | \(-0.900976\pi\) | ||
0.951999 | − | 0.306100i | \(-0.0990243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −87.8448 | −0.171908 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 487.762 | + | 375.477i | 0.950804 | + | 0.731923i | ||||
\(514\) | 509.019 | 0.990309 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −76.9221 | + | 346.126i | −0.149074 | + | 0.670788i | ||||
\(517\) | − | 8.25606i | − | 0.0159692i | ||||||
\(518\) | 144.019 | 0.278029 | ||||||||
\(519\) | 136.794 | + | 30.4007i | 0.263572 | + | 0.0585756i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 435.399i | 0.835698i | 0.908516 | + | 0.417849i | \(0.137216\pi\) | ||||
−0.908516 | + | 0.417849i | \(0.862784\pi\) | |||||||
\(522\) | −84.0229 | + | 179.702i | −0.160963 | + | 0.344257i | ||||
\(523\) | 619.746i | 1.18498i | 0.805577 | + | 0.592491i | \(0.201856\pi\) | ||||
−0.805577 | + | 0.592491i | \(0.798144\pi\) | |||||||
\(524\) | − | 500.241i | − | 0.954658i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 323.009 | 0.614085 | ||||||||
\(527\) | −239.438 | −0.454341 | ||||||||
\(528\) | 20.7630 | − | 93.4274i | 0.0393239 | − | 0.176946i | ||||
\(529\) | 695.175 | 1.31413 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −210.271 | + | 449.712i | −0.395990 | + | 0.846916i | ||||
\(532\) | 120.635i | 0.226758i | ||||||||
\(533\) | 203.392 | 0.381599 | ||||||||
\(534\) | 110.476 | − | 497.110i | 0.206884 | − | 0.930917i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 218.090i | − | 0.406884i | ||||||
\(537\) | 191.233 | − | 860.491i | 0.356114 | − | 1.60240i | ||||
\(538\) | 400.969i | 0.745295i | ||||||||
\(539\) | 55.8289i | 0.103579i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 709.366 | 1.31121 | 0.655606 | − | 0.755103i | \(-0.272413\pi\) | ||||
0.655606 | + | 0.755103i | \(0.272413\pi\) | |||||||
\(542\) | −411.238 | −0.758742 | ||||||||
\(543\) | −379.618 | − | 84.3652i | −0.699112 | − | 0.155369i | ||||
\(544\) | −52.9359 | −0.0973086 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 63.4845 | + | 14.1086i | 0.116272 | + | 0.0258399i | ||||
\(547\) | 306.448i | 0.560234i | 0.959966 | + | 0.280117i | \(0.0903733\pi\) | ||||
−0.959966 | + | 0.280117i | \(0.909627\pi\) | |||||||
\(548\) | −383.792 | −0.700350 | ||||||||
\(549\) | −772.665 | − | 361.273i | −1.40740 | − | 0.658056i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 355.325i | 0.644873i | ||||||||
\(552\) | 289.814 | + | 64.4075i | 0.525026 | + | 0.116680i | ||||
\(553\) | 145.365i | 0.262866i | ||||||||
\(554\) | 378.260i | 0.682780i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −42.9289 | −0.0772103 | ||||||||
\(557\) | 259.701 | 0.466250 | 0.233125 | − | 0.972447i | \(-0.425105\pi\) | ||||
0.233125 | + | 0.972447i | \(0.425105\pi\) | |||||||
\(558\) | 295.013 | + | 137.938i | 0.528697 | + | 0.247201i | ||||
\(559\) | 342.375 | 0.612478 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.5742 | + | 218.569i | −0.0865851 | + | 0.389607i | ||||
\(562\) | − | 300.787i | − | 0.535209i | ||||||
\(563\) | −1066.78 | −1.89481 | −0.947407 | − | 0.320032i | \(-0.896306\pi\) | ||||
−0.947407 | + | 0.320032i | \(0.896306\pi\) | |||||||
\(564\) | 6.06309 | + | 1.34744i | 0.0107502 | + | 0.00238909i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 353.195i | − | 0.624019i | ||||||
\(567\) | −164.452 | + | 137.413i | −0.290039 | + | 0.242352i | ||||
\(568\) | − | 50.9248i | − | 0.0896563i | ||||||
\(569\) | 294.913i | 0.518301i | 0.965837 | + | 0.259150i | \(0.0834425\pi\) | ||||
−0.965837 | + | 0.259150i | \(0.916557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 183.465 | 0.321304 | 0.160652 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160652 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(572\) | −92.4149 | −0.161564 | ||||||||
\(573\) | 4.71463 | − | 21.2144i | 0.00822798 | − | 0.0370234i | ||||
\(574\) | −131.355 | −0.228842 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 65.2227 | + | 30.4960i | 0.113234 | + | 0.0529444i | ||||
\(577\) | − | 740.634i | − | 1.28359i | −0.766874 | − | 0.641797i | \(-0.778189\pi\) | ||
0.766874 | − | 0.641797i | \(-0.221811\pi\) | |||||||
\(578\) | −284.867 | −0.492849 | ||||||||
\(579\) | 204.148 | − | 918.603i | 0.352587 | − | 1.58653i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 208.113i | − | 0.358198i | ||||||
\(582\) | 22.5619 | − | 101.522i | 0.0387662 | − | 0.174436i | ||||
\(583\) | 331.129i | 0.567974i | ||||||||
\(584\) | 93.9101i | 0.160805i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −441.512 | −0.753433 | ||||||||
\(587\) | −694.040 | −1.18235 | −0.591175 | − | 0.806543i | \(-0.701336\pi\) | ||||
−0.591175 | + | 0.806543i | \(0.701336\pi\) | |||||||
\(588\) | −40.9997 | − | 9.11166i | −0.0697274 | − | 0.0154960i | ||||
\(589\) | 583.329 | 0.990371 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −276.788 | − | 61.5126i | −0.468339 | − | 0.104082i | ||||
\(592\) | − | 153.963i | − | 0.260073i | ||||||
\(593\) | 428.653 | 0.722855 | 0.361427 | − | 0.932400i | \(-0.382290\pi\) | ||||
0.361427 | + | 0.932400i | \(0.382290\pi\) | |||||||
\(594\) | 185.765 | − | 241.318i | 0.312736 | − | 0.406259i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 133.734i | 0.224386i | ||||||||
\(597\) | 544.171 | + | 120.935i | 0.911509 | + | 0.202571i | ||||
\(598\) | − | 286.673i | − | 0.479387i | ||||||
\(599\) | − | 1068.82i | − | 1.78433i | −0.451705 | − | 0.892167i | \(-0.649184\pi\) | ||
0.451705 | − | 0.892167i | \(-0.350816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 259.767 | 0.432224 | 0.216112 | − | 0.976369i | \(-0.430662\pi\) | ||||
0.216112 | + | 0.976369i | \(0.430662\pi\) | |||||||
\(602\) | −221.114 | −0.367299 | ||||||||
\(603\) | 293.929 | − | 628.636i | 0.487445 | − | 1.04251i | ||||
\(604\) | −128.942 | −0.213481 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 146.066 | − | 657.252i | 0.241033 | − | 1.08457i | ||||
\(607\) | 1147.06i | 1.88972i | 0.327479 | + | 0.944858i | \(0.393801\pi\) | ||||
−0.327479 | + | 0.944858i | \(0.606199\pi\) | |||||||
\(608\) | 128.965 | 0.212113 | ||||||||
\(609\) | −120.762 | − | 26.8379i | −0.198296 | − | 0.0440688i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.99739i | − | 0.00981569i | ||||||
\(612\) | −152.586 | − | 71.3440i | −0.249323 | − | 0.116575i | ||||
\(613\) | − | 166.678i | − | 0.271905i | −0.990715 | − | 0.135952i | \(-0.956591\pi\) | ||
0.990715 | − | 0.135952i | \(-0.0434094\pi\) | |||||||
\(614\) | 219.569i | 0.357604i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 59.6837 | 0.0968890 | ||||||||
\(617\) | 319.900 | 0.518477 | 0.259238 | − | 0.965813i | \(-0.416528\pi\) | ||||
0.259238 | + | 0.965813i | \(0.416528\pi\) | |||||||
\(618\) | −163.379 | + | 735.154i | −0.264367 | + | 1.18957i | ||||
\(619\) | 917.131 | 1.48163 | 0.740817 | − | 0.671707i | \(-0.234439\pi\) | ||||
0.740817 | + | 0.671707i | \(0.234439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 748.574 | + | 576.247i | 1.20543 | + | 0.927935i | ||||
\(622\) | 478.216i | 0.768835i | ||||||||
\(623\) | 317.565 | 0.509736 | ||||||||
\(624\) | 15.0827 | − | 67.8678i | 0.0241710 | − | 0.108762i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 46.0399i | 0.0735461i | ||||||||
\(627\) | 118.339 | − | 532.488i | 0.188738 | − | 0.849263i | ||||
\(628\) | 414.515i | 0.660056i | ||||||||
\(629\) | 360.190i | 0.572639i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 695.889 | 1.10283 | 0.551417 | − | 0.834229i | \(-0.314087\pi\) | ||||
0.551417 | + | 0.834229i | \(0.314087\pi\) | |||||||
\(632\) | 155.402 | 0.245889 | ||||||||
\(633\) | 1100.28 | + | 244.524i | 1.73820 | + | 0.386294i | ||||
\(634\) | 221.767 | 0.349791 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −243.175 | − | 54.0425i | −0.382350 | − | 0.0849725i | ||||
\(637\) | 40.5554i | 0.0636662i | ||||||||
\(638\) | 175.795 | 0.275541 | ||||||||
\(639\) | 68.6335 | − | 146.789i | 0.107408 | − | 0.229716i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 75.7558i | − | 0.118184i | −0.998253 | − | 0.0590919i | \(-0.981180\pi\) | ||
0.998253 | − | 0.0590919i | \(-0.0188205\pi\) | |||||||
\(642\) | −873.846 | − | 194.201i | −1.36113 | − | 0.302494i | ||||
\(643\) | 1173.40i | 1.82488i | 0.409215 | + | 0.912438i | \(0.365803\pi\) | ||||
−0.409215 | + | 0.912438i | \(0.634197\pi\) | |||||||
\(644\) | 185.140i | 0.287485i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −301.707 | −0.467039 | ||||||||
\(647\) | 322.830 | 0.498964 | 0.249482 | − | 0.968379i | \(-0.419740\pi\) | ||||
0.249482 | + | 0.968379i | \(0.419740\pi\) | |||||||
\(648\) | 146.901 | + | 175.807i | 0.226699 | + | 0.271307i | ||||
\(649\) | 439.934 | 0.677864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44.0592 | + | 198.253i | −0.0676792 | + | 0.304536i | ||||
\(652\) | 472.134i | 0.724132i | ||||||||
\(653\) | 1056.82 | 1.61841 | 0.809206 | − | 0.587526i | \(-0.199898\pi\) | ||||
0.809206 | + | 0.587526i | \(0.199898\pi\) | |||||||
\(654\) | 408.045 | + | 90.6828i | 0.623923 | + | 0.138659i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 140.425i | 0.214062i | ||||||||
\(657\) | −126.567 | + | 270.692i | −0.192643 | + | 0.412012i | ||||
\(658\) | 3.87325i | 0.00588640i | ||||||||
\(659\) | − | 808.670i | − | 1.22712i | −0.789649 | − | 0.613559i | \(-0.789737\pi\) | ||
0.789649 | − | 0.613559i | \(-0.210263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1068.86 | 1.61703 | 0.808515 | − | 0.588476i | \(-0.200272\pi\) | ||||
0.808515 | + | 0.588476i | \(0.200272\pi\) | |||||||
\(662\) | 88.7654 | 0.134087 | ||||||||
\(663\) | −35.2854 | + | 158.774i | −0.0532208 | + | 0.239478i | ||||
\(664\) | −222.482 | −0.335064 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 207.503 | − | 443.793i | 0.311566 | − | 0.666355i | ||||
\(667\) | 545.320i | 0.817572i | ||||||||
\(668\) | −219.294 | −0.328284 | ||||||||
\(669\) | 12.7633 | − | 57.4310i | 0.0190782 | − | 0.0858460i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 755.865i | 1.12647i | ||||||||
\(672\) | −9.74078 | + | 43.8306i | −0.0144952 | + | 0.0652240i | ||||
\(673\) | − | 1159.59i | − | 1.72302i | −0.507744 | − | 0.861508i | \(-0.669521\pi\) | ||
0.507744 | − | 0.861508i | \(-0.330479\pi\) | |||||||
\(674\) | − | 607.777i | − | 0.901747i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 270.868 | 0.400692 | ||||||||
\(677\) | −202.423 | −0.298999 | −0.149500 | − | 0.988762i | \(-0.547766\pi\) | ||||
−0.149500 | + | 0.988762i | \(0.547766\pi\) | |||||||
\(678\) | −425.880 | − | 94.6464i | −0.628142 | − | 0.139596i | ||||
\(679\) | 64.8546 | 0.0955148 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −734.872 | − | 163.316i | −1.07911 | − | 0.239818i | ||||
\(682\) | − | 288.599i | − | 0.423165i | ||||||
\(683\) | 432.740 | 0.633587 | 0.316794 | − | 0.948494i | \(-0.397394\pi\) | ||||
0.316794 | + | 0.948494i | \(0.397394\pi\) | |||||||
\(684\) | 371.736 | + | 173.811i | 0.543473 | + | 0.254110i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | −868.843 | − | 193.089i | −1.26469 | − | 0.281061i | ||||
\(688\) | 236.381i | 0.343576i | ||||||||
\(689\) | 240.539i | 0.349114i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −507.481 | −0.734415 | −0.367208 | − | 0.930139i | \(-0.619686\pi\) | ||||
−0.367208 | + | 0.930139i | \(0.619686\pi\) | |||||||
\(692\) | 93.4210 | 0.135001 | ||||||||
\(693\) | 172.036 | + | 80.4383i | 0.248248 | + | 0.116073i | ||||
\(694\) | −864.371 | −1.24549 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −28.6909 | + | 129.100i | −0.0412226 | + | 0.185489i | ||||
\(697\) | − | 328.518i | − | 0.471331i | ||||||
\(698\) | 324.924 | 0.465507 | ||||||||
\(699\) | −461.196 | − | 102.495i | −0.659794 | − | 0.146631i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 465.228i | − | 0.663663i | −0.943339 | − | 0.331831i | \(-0.892333\pi\) | ||
0.943339 | − | 0.331831i | \(-0.107667\pi\) | |||||||
\(702\) | 134.944 | − | 175.299i | 0.192228 | − | 0.249713i | ||||
\(703\) | − | 877.510i | − | 1.24824i | ||||||
\(704\) | − | 63.8045i | − | 0.0906314i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −614.619 | −0.870566 | ||||||||
\(707\) | 419.868 | 0.593873 | ||||||||
\(708\) | −71.8002 | + | 323.079i | −0.101413 | + | 0.456327i | ||||
\(709\) | 902.795 | 1.27334 | 0.636668 | − | 0.771138i | \(-0.280312\pi\) | ||||
0.636668 | + | 0.771138i | \(0.280312\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 447.939 | + | 209.442i | 0.630013 | + | 0.294573i | ||||
\(712\) | − | 339.492i | − | 0.476814i | ||||||
\(713\) | 895.240 | 1.25560 | ||||||||
\(714\) | 22.7881 | − | 102.540i | 0.0319161 | − | 0.143613i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 587.656i | − | 0.820749i | ||||||
\(717\) | 51.2703 | − | 230.701i | 0.0715067 | − | 0.321759i | ||||
\(718\) | − | 262.879i | − | 0.366127i | ||||||
\(719\) | 1105.81i | 1.53798i | 0.639262 | + | 0.768989i | \(0.279240\pi\) | ||||
−0.639262 | + | 0.768989i | \(0.720760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −469.634 | −0.651365 | ||||||||
\(722\) | 224.501 | 0.310943 | ||||||||
\(723\) | −434.446 | − | 96.5500i | −0.600893 | − | 0.133541i | ||||
\(724\) | −259.253 | −0.358084 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 237.688 | + | 52.8231i | 0.327394 | + | 0.0727591i | ||||
\(727\) | 215.564i | 0.296512i | 0.988949 | + | 0.148256i | \(0.0473660\pi\) | ||||
−0.988949 | + | 0.148256i | \(0.952634\pi\) | |||||||
\(728\) | 43.3555 | 0.0595543 | ||||||||
\(729\) | 186.494 | + | 704.742i | 0.255822 | + | 0.966724i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 553.002i | − | 0.756501i | ||||||
\(732\) | −555.093 | − | 123.362i | −0.758323 | − | 0.168528i | ||||
\(733\) | 1068.10i | 1.45716i | 0.684963 | + | 0.728578i | \(0.259819\pi\) | ||||
−0.684963 | + | 0.728578i | \(0.740181\pi\) | |||||||
\(734\) | 591.772i | 0.806229i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 197.923 | 0.268917 | ||||||||
\(737\) | −614.967 | −0.834419 | ||||||||
\(738\) | −189.257 | + | 404.769i | −0.256446 | + | 0.548468i | ||||
\(739\) | 156.720 | 0.212071 | 0.106035 | − | 0.994362i | \(-0.466184\pi\) | ||||
0.106035 | + | 0.994362i | \(0.466184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 85.9638 | − | 386.811i | 0.116011 | − | 0.522012i | ||||
\(742\) | − | 155.346i | − | 0.209361i | ||||||
\(743\) | 423.464 | 0.569938 | 0.284969 | − | 0.958537i | \(-0.408017\pi\) | ||||
0.284969 | + | 0.958537i | \(0.408017\pi\) | |||||||
\(744\) | 211.941 | + | 47.1012i | 0.284867 | + | 0.0633081i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 845.124i | 1.13287i | ||||||||
\(747\) | −641.296 | − | 299.849i | −0.858496 | − | 0.401404i | ||||
\(748\) | 149.268i | 0.199556i | ||||||||
\(749\) | − | 558.234i | − | 0.745305i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1305.05 | −1.73776 | −0.868878 | − | 0.495026i | \(-0.835158\pi\) | ||||
−0.868878 | + | 0.495026i | \(0.835158\pi\) | |||||||
\(752\) | 4.14068 | 0.00550622 | ||||||||
\(753\) | −145.277 | + | 653.702i | −0.192931 | + | 0.868130i | ||||
\(754\) | 127.701 | 0.169365 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −87.1498 | + | 113.212i | −0.115277 | + | 0.149751i | ||||
\(757\) | − | 59.6912i | − | 0.0788523i | −0.999222 | − | 0.0394261i | \(-0.987447\pi\) | ||
0.999222 | − | 0.0394261i | \(-0.0125530\pi\) | |||||||
\(758\) | −796.861 | −1.05127 | ||||||||
\(759\) | 181.615 | − | 817.214i | 0.239282 | − | 1.07670i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 899.617i | 1.18215i | 0.806616 | + | 0.591075i | \(0.201296\pi\) | ||||
−0.806616 | + | 0.591075i | \(0.798704\pi\) | |||||||
\(762\) | 145.139 | − | 653.080i | 0.190471 | − | 0.857060i | ||||
\(763\) | 260.669i | 0.341637i | ||||||||
\(764\) | − | 14.4880i | − | 0.0189633i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 153.762 | 0.200734 | ||||||||
\(767\) | 319.578 | 0.416660 | ||||||||
\(768\) | 46.8568 | + | 10.4133i | 0.0610115 | + | 0.0135590i | ||||
\(769\) | 268.385 | 0.349005 | 0.174503 | − | 0.984657i | \(-0.444168\pi\) | ||||
0.174503 | + | 0.984657i | \(0.444168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1054.08 | + | 234.255i | 1.36715 | + | 0.303832i | ||||
\(772\) | − | 627.343i | − | 0.812620i | ||||||
\(773\) | −80.8488 | −0.104591 | −0.0522955 | − | 0.998632i | \(-0.516654\pi\) | ||||
−0.0522955 | + | 0.998632i | \(0.516654\pi\) | |||||||
\(774\) | −318.581 | + | 681.358i | −0.411603 | + | 0.880307i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 69.3324i | − | 0.0893459i | ||||||
\(777\) | 298.235 | + | 66.2789i | 0.383829 | + | 0.0853010i | ||||
\(778\) | 181.512i | 0.233306i | ||||||||
\(779\) | 800.350i | 1.02741i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −143.597 | −0.183863 | ||||||||
\(782\) | −463.033 | −0.592113 | ||||||||
\(783\) | −256.695 | + | 333.459i | −0.327835 | + | 0.425874i | ||||
\(784\) | −28.0000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 230.215 | − | 1035.90i | 0.292894 | − | 1.31794i | ||||
\(787\) | − | 592.703i | − | 0.753117i | −0.926393 | − | 0.376559i | \(-0.877107\pi\) | ||
0.926393 | − | 0.376559i | \(-0.122893\pi\) | |||||||
\(788\) | −189.027 | −0.239882 | ||||||||
\(789\) | 668.886 | + | 148.651i | 0.847764 | + | 0.188405i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 272.062i | − | 0.343948i | ||||||
\(792\) | 85.9922 | − | 183.914i | 0.108576 | − | 0.232215i | ||||
\(793\) | 549.077i | 0.692405i | ||||||||
\(794\) | 233.986i | 0.294693i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 371.632 | 0.466874 | ||||||||
\(797\) | 463.874 | 0.582025 | 0.291012 | − | 0.956719i | \(-0.406008\pi\) | ||||
0.291012 | + | 0.956719i | \(0.406008\pi\) | |||||||
\(798\) | −55.5174 | + | 249.812i | −0.0695707 | + | 0.313047i | ||||
\(799\) | −9.68693 | −0.0121238 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 457.548 | − | 978.572i | 0.571221 | − | 1.22169i | ||||
\(802\) | 561.510i | 0.700138i | ||||||||
\(803\) | 264.806 | 0.329771 | ||||||||
\(804\) | 100.367 | − | 451.620i | 0.124834 | − | 0.561717i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 209.644i | − | 0.260105i | ||||||
\(807\) | −184.529 | + | 830.326i | −0.228661 | + | 1.02890i | ||||
\(808\) | − | 448.858i | − | 0.555518i | ||||||
\(809\) | 454.905i | 0.562305i | 0.959663 | + | 0.281152i | \(0.0907166\pi\) | ||||
−0.959663 | + | 0.281152i | \(0.909283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 349.822 | 0.431346 | 0.215673 | − | 0.976466i | \(-0.430805\pi\) | ||||
0.215673 | + | 0.976466i | \(0.430805\pi\) | |||||||
\(812\) | −82.4725 | −0.101567 | ||||||||
\(813\) | −851.591 | − | 189.255i | −1.04747 | − | 0.232786i | ||||
\(814\) | −434.143 | −0.533345 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −109.620 | − | 24.3615i | −0.134338 | − | 0.0298548i | ||||
\(817\) | 1347.25i | 1.64902i | ||||||||
\(818\) | −835.536 | −1.02144 | ||||||||
\(819\) | 124.971 | + | 58.4322i | 0.152589 | + | 0.0713458i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 779.459i | 0.949402i | 0.880147 | + | 0.474701i | \(0.157444\pi\) | ||||
−0.880147 | + | 0.474701i | \(0.842556\pi\) | |||||||
\(822\) | −794.755 | − | 176.624i | −0.966856 | − | 0.214871i | ||||
\(823\) | − | 931.372i | − | 1.13168i | −0.824516 | − | 0.565839i | \(-0.808552\pi\) | ||
0.824516 | − | 0.565839i | \(-0.191448\pi\) | |||||||
\(824\) | 502.060i | 0.609296i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −206.391 | −0.249868 | ||||||||
\(827\) | −197.854 | −0.239243 | −0.119621 | − | 0.992820i | \(-0.538168\pi\) | ||||
−0.119621 | + | 0.992820i | \(0.538168\pi\) | |||||||
\(828\) | 570.506 | + | 266.750i | 0.689017 | + | 0.322162i | ||||
\(829\) | 767.502 | 0.925816 | 0.462908 | − | 0.886406i | \(-0.346806\pi\) | ||||
0.462908 | + | 0.886406i | \(0.346806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −174.078 | + | 783.300i | −0.209481 | + | 0.942599i | ||||
\(832\) | − | 46.3490i | − | 0.0557080i | ||||||
\(833\) | 65.5048 | 0.0786372 | ||||||||
\(834\) | −88.8972 | − | 19.7563i | −0.106591 | − | 0.0236886i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 363.653i | − | 0.434991i | ||||||
\(837\) | 547.432 | + | 421.410i | 0.654041 | + | 0.503477i | ||||
\(838\) | 389.490i | 0.464785i | ||||||||
\(839\) | − | 789.441i | − | 0.940931i | −0.882418 | − | 0.470466i | \(-0.844086\pi\) | ||
0.882418 | − | 0.470466i | \(-0.155914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 598.082 | 0.711156 | ||||||||
\(842\) | 806.271 | 0.957566 | ||||||||
\(843\) | 138.425 | − | 622.870i | 0.164205 | − | 0.738874i | ||||
\(844\) | 751.418 | 0.890306 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.9353 | + | 5.58057i | 0.0141080 | + | 0.00659642i | ||||
\(847\) | 151.841i | 0.179269i | ||||||||
\(848\) | −166.072 | −0.195839 | ||||||||
\(849\) | 162.543 | − | 731.395i | 0.191452 | − | 0.861478i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1346.72i | − | 1.58252i | ||||||
\(852\) | 23.4360 | − | 105.455i | 0.0275070 | − | 0.123773i | ||||
\(853\) | − | 167.784i | − | 0.196699i | −0.995152 | − | 0.0983493i | \(-0.968644\pi\) | ||
0.995152 | − | 0.0983493i | \(-0.0313563\pi\) | |||||||
\(854\) | − | 354.606i | − | 0.415230i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −596.777 | −0.697169 | ||||||||
\(857\) | 873.473 | 1.01922 | 0.509611 | − | 0.860405i | \(-0.329789\pi\) | ||||
0.509611 | + | 0.860405i | \(0.329789\pi\) | |||||||
\(858\) | −191.373 | − | 42.5301i | −0.223045 | − | 0.0495689i | ||||
\(859\) | −480.534 | −0.559411 | −0.279705 | − | 0.960086i | \(-0.590237\pi\) | ||||
−0.279705 | + | 0.960086i | \(0.590237\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −272.011 | − | 60.4509i | −0.315924 | − | 0.0702101i | ||||
\(862\) | − | 919.706i | − | 1.06694i | ||||||
\(863\) | −263.159 | −0.304936 | −0.152468 | − | 0.988308i | \(-0.548722\pi\) | ||||
−0.152468 | + | 0.988308i | \(0.548722\pi\) | |||||||
\(864\) | 121.029 | + | 93.1670i | 0.140079 | + | 0.107832i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 898.737i | 1.03780i | ||||||||
\(867\) | −589.901 | − | 131.098i | −0.680394 | − | 0.151209i | ||||
\(868\) | 135.393i | 0.155983i | ||||||||
\(869\) | − | 438.199i | − | 0.504257i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −446.726 | −0.512888 | ||||||||
\(872\) | 278.667 | 0.319572 | ||||||||
\(873\) | 93.4424 | − | 199.848i | 0.107036 | − | 0.228921i | ||||
\(874\) | 1128.06 | 1.29069 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −43.2182 | + | 194.469i | −0.0493358 | + | 0.221996i | ||||
\(877\) | 982.305i | 1.12007i | 0.828468 | + | 0.560037i | \(0.189213\pi\) | ||||
−0.828468 | + | 0.560037i | \(0.810787\pi\) | |||||||
\(878\) | 483.517 | 0.550702 | ||||||||
\(879\) | −914.282 | − | 203.187i | −1.04014 | − | 0.231158i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 651.840i | − | 0.739886i | −0.929054 | − | 0.369943i | \(-0.879377\pi\) | ||
0.929054 | − | 0.369943i | \(-0.120623\pi\) | |||||||
\(882\) | −80.7089 | − | 37.7368i | −0.0915067 | − | 0.0427855i | ||||
\(883\) | 811.043i | 0.918509i | 0.888305 | + | 0.459254i | \(0.151883\pi\) | ||||
−0.888305 | + | 0.459254i | \(0.848117\pi\) | |||||||
\(884\) | 108.432i | 0.122660i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −359.536 | −0.405797 | ||||||||
\(887\) | 795.521 | 0.896867 | 0.448433 | − | 0.893816i | \(-0.351982\pi\) | ||||
0.448433 | + | 0.893816i | \(0.351982\pi\) | |||||||
\(888\) | 70.8551 | − | 318.826i | 0.0797918 | − | 0.359039i | ||||
\(889\) | 417.203 | 0.469295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 495.738 | − | 414.230i | 0.556384 | − | 0.464904i | ||||
\(892\) | − | 39.2214i | − | 0.0439702i | ||||||
\(893\) | 23.5997 | 0.0264275 | ||||||||
\(894\) | −61.5456 | + | 276.937i | −0.0688429 | + | 0.309772i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 131.929 | − | 593.643i | 0.147079 | − | 0.661809i | ||||
\(898\) | − | 103.618i | − | 0.115388i | ||||||
\(899\) | 398.793i | 0.443596i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 388.518 | 0.431207 | ||||||||
\(902\) | 395.968 | 0.438989 | ||||||||
\(903\) | −457.882 | − | 101.758i | −0.507068 | − | 0.112689i | ||||
\(904\) | −290.847 | −0.321733 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −267.014 | − | 59.3404i | −0.294717 | − | 0.0654971i | ||||
\(907\) | − | 855.003i | − | 0.942672i | −0.881954 | − | 0.471336i | \(-0.843772\pi\) | ||
0.881954 | − | 0.471336i | \(-0.156228\pi\) | |||||||
\(908\) | −501.867 | −0.552717 | ||||||||
\(909\) | 604.946 | − | 1293.82i | 0.665507 | − | 1.42334i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1234.06i | 1.35462i | 0.735696 | + | 0.677312i | \(0.236855\pi\) | ||||
−0.735696 | + | 0.677312i | \(0.763145\pi\) | |||||||
\(912\) | 267.060 | + | 59.3506i | 0.292829 | + | 0.0650774i | ||||
\(913\) | 627.352i | 0.687133i | ||||||||
\(914\) | − | 284.433i | − | 0.311196i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −593.360 | −0.647773 | ||||||||
\(917\) | 661.756 | 0.721653 | ||||||||
\(918\) | −283.141 | − | 217.960i | −0.308432 | − | 0.237429i | ||||
\(919\) | 1390.69 | 1.51326 | 0.756632 | − | 0.653842i | \(-0.226844\pi\) | ||||
0.756632 | + | 0.653842i | \(0.226844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −101.048 | + | 454.683i | −0.109715 | + | 0.493684i | ||||
\(922\) | 707.625i | 0.767490i | ||||||||
\(923\) | −104.312 | −0.113014 | ||||||||
\(924\) | 123.593 | + | 27.4669i | 0.133758 | + | 0.0297261i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 850.770i | − | 0.918758i | ||||||
\(927\) | −676.648 | + | 1447.17i | −0.729933 | + | 1.56113i | ||||
\(928\) | 88.1668i | 0.0950073i | ||||||||
\(929\) | 934.368i | 1.00578i | 0.864351 | + | 0.502889i | \(0.167730\pi\) | ||||
−0.864351 | + | 0.502889i | \(0.832270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −159.586 | −0.171413 | ||||||||
\(932\) | −314.965 | −0.337946 | ||||||||
\(933\) | −220.079 | + | 990.288i | −0.235883 | + | 1.06140i | ||||
\(934\) | −383.287 | −0.410372 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 62.4666 | − | 133.599i | 0.0667378 | − | 0.142734i | ||||
\(937\) | − | 229.679i | − | 0.245122i | −0.992461 | − | 0.122561i | \(-0.960889\pi\) | ||
0.992461 | − | 0.122561i | \(-0.0391107\pi\) | |||||||
\(938\) | 288.506 | 0.307575 | ||||||||
\(939\) | −21.1879 | + | 95.3393i | −0.0225644 | + | 0.101533i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 688.683i | − | 0.731863i | −0.930642 | − | 0.365932i | \(-0.880750\pi\) | ||
0.930642 | − | 0.365932i | \(-0.119250\pi\) | |||||||
\(942\) | −190.763 | + | 858.377i | −0.202509 | + | 0.911228i | ||||
\(943\) | 1228.30i | 1.30255i | ||||||||
\(944\) | 220.641i | 0.233730i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 666.543 | 0.704591 | ||||||||
\(947\) | 897.803 | 0.948049 | 0.474025 | − | 0.880512i | \(-0.342801\pi\) | ||||
0.474025 | + | 0.880512i | \(0.342801\pi\) | |||||||
\(948\) | 321.805 | + | 71.5171i | 0.339457 | + | 0.0754400i | ||||
\(949\) | 192.361 | 0.202699 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 459.236 | + | 102.059i | 0.482898 | + | 0.107318i | ||||
\(952\) | − | 70.0275i | − | 0.0735584i | ||||||
\(953\) | −809.558 | −0.849483 | −0.424742 | − | 0.905315i | \(-0.639635\pi\) | ||||
−0.424742 | + | 0.905315i | \(0.639635\pi\) | |||||||
\(954\) | −478.695 | − | 223.822i | −0.501777 | − | 0.234614i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 157.553i | − | 0.164804i | ||||||
\(957\) | 364.036 | + | 80.9023i | 0.380393 | + | 0.0845374i | ||||
\(958\) | − | 287.090i | − | 0.299677i | ||||||
\(959\) | − | 507.709i | − | 0.529415i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −306.310 | −0.318741 | ||||||||
\(962\) | −315.371 | −0.327829 | ||||||||
\(963\) | −1720.19 | − | 804.302i | −1.78628 | − | 0.835205i | ||||
\(964\) | −296.697 | −0.307777 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −85.2031 | + | 383.388i | −0.0882019 | + | 0.396882i | ||||
\(967\) | − | 952.817i | − | 0.985333i | −0.870218 | − | 0.492667i | \(-0.836022\pi\) | ||
0.870218 | − | 0.492667i | \(-0.163978\pi\) | |||||||
\(968\) | 162.325 | 0.167691 | ||||||||
\(969\) | −624.775 | − | 138.848i | −0.644762 | − | 0.143290i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 755.094i | − | 0.777646i | −0.921313 | − | 0.388823i | \(-0.872882\pi\) | ||
0.921313 | − | 0.388823i | \(-0.127118\pi\) | |||||||
\(972\) | 223.295 | + | 431.666i | 0.229727 | + | 0.444101i | ||||
\(973\) | − | 56.7897i | − | 0.0583655i | ||||||
\(974\) | − | 1125.54i | − | 1.15558i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −379.090 | −0.388412 | ||||||||
\(977\) | 1865.83 | 1.90975 | 0.954876 | − | 0.297006i | \(-0.0959881\pi\) | ||||
0.954876 | + | 0.297006i | \(0.0959881\pi\) | |||||||
\(978\) | −217.280 | + | 977.694i | −0.222168 | + | 0.999687i | ||||
\(979\) | −957.295 | −0.977829 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 803.247 | + | 375.572i | 0.818804 | + | 0.382846i | ||||
\(982\) | 58.1771i | 0.0592435i | ||||||||
\(983\) | 1469.42 | 1.49483 | 0.747417 | − | 0.664356i | \(-0.231294\pi\) | ||||
0.747417 | + | 0.664356i | \(0.231294\pi\) | |||||||
\(984\) | −64.6247 | + | 290.792i | −0.0656755 | + | 0.295520i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 206.262i | − | 0.209191i | ||||||
\(987\) | −1.78250 | + | 8.02072i | −0.00180598 | + | 0.00812636i | ||||
\(988\) | − | 264.166i | − | 0.267374i | ||||||
\(989\) | 2067.63i | 2.09063i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1075.76 | 1.08553 | 0.542764 | − | 0.839885i | \(-0.317378\pi\) | ||||
0.542764 | + | 0.839885i | \(0.317378\pi\) | |||||||
\(992\) | 144.741 | 0.145909 | ||||||||
\(993\) | 183.815 | + | 40.8506i | 0.185111 | + | 0.0411385i | ||||
\(994\) | 67.3671 | 0.0677738 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −460.716 | − | 102.388i | −0.462566 | − | 0.102799i | ||||
\(997\) | − | 1114.55i | − | 1.11791i | −0.829199 | − | 0.558953i | \(-0.811203\pi\) | ||
0.829199 | − | 0.558953i | \(-0.188797\pi\) | |||||||
\(998\) | −835.105 | −0.836779 | ||||||||
\(999\) | 633.934 | − | 823.511i | 0.634568 | − | 0.824335i |
(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 | 1050.3.c.c.449.32 | 32 | ||
3.2 | odd | 2 | inner | 1050.3.c.c.449.2 | 32 | ||
5.2 | odd | 4 | 210.3.e.a.71.14 | yes | 16 | ||
5.3 | odd | 4 | 1050.3.e.d.701.3 | 16 | |||
5.4 | even | 2 | inner | 1050.3.c.c.449.1 | 32 | ||
15.2 | even | 4 | 210.3.e.a.71.6 | ✓ | 16 | ||
15.8 | even | 4 | 1050.3.e.d.701.11 | 16 | |||
15.14 | odd | 2 | inner | 1050.3.c.c.449.31 | 32 | ||
20.7 | even | 4 | 1680.3.l.c.1121.6 | 16 | |||
60.47 | odd | 4 | 1680.3.l.c.1121.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.e.a.71.6 | ✓ | 16 | 15.2 | even | 4 | ||
210.3.e.a.71.14 | yes | 16 | 5.2 | odd | 4 | ||
1050.3.c.c.449.1 | 32 | 5.4 | even | 2 | inner | ||
1050.3.c.c.449.2 | 32 | 3.2 | odd | 2 | inner | ||
1050.3.c.c.449.31 | 32 | 15.14 | odd | 2 | inner | ||
1050.3.c.c.449.32 | 32 | 1.1 | even | 1 | trivial | ||
1050.3.e.d.701.3 | 16 | 5.3 | odd | 4 | |||
1050.3.e.d.701.11 | 16 | 15.8 | even | 4 | |||
1680.3.l.c.1121.5 | 16 | 60.47 | odd | 4 | |||
1680.3.l.c.1121.6 | 16 | 20.7 | even | 4 |