Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.217 |
Dual form | 324.4.e.f.109.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 1.50000 | + | 2.59808i | 0.134164 | + | 0.232379i | 0.925278 | − | 0.379290i | \(-0.123832\pi\) |
−0.791114 | + | 0.611669i | \(0.790498\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 3.46410i | 0.107990 | − | 0.187044i | −0.806966 | − | 0.590598i | \(-0.798892\pi\) |
0.914956 | + | 0.403554i | \(0.132225\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | + | 20.7846i | −0.328921 | + | 0.569709i | −0.982298 | − | 0.187324i | \(-0.940018\pi\) |
0.653377 | + | 0.757033i | \(0.273352\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.5000 | + | 21.6506i | 0.266683 | + | 0.461908i | 0.968003 | − | 0.250938i | \(-0.0807391\pi\) |
−0.701320 | + | 0.712846i | \(0.747406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 21.0000 | 0.299603 | 0.149801 | − | 0.988716i | \(-0.452137\pi\) | ||||
0.149801 | + | 0.988716i | \(0.452137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −52.0000 | −0.627875 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 84.0000 | + | 145.492i | 0.761531 | + | 1.31901i | 0.942061 | + | 0.335441i | \(0.108885\pi\) |
−0.180530 | + | 0.983569i | \(0.557781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 58.0000 | − | 100.459i | 0.464000 | − | 0.803672i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −88.5000 | + | 153.286i | −0.566691 | + | 0.981538i | 0.430199 | + | 0.902734i | \(0.358443\pi\) |
−0.996890 | + | 0.0788035i | \(0.974890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 62.0000 | + | 107.387i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.0000 | 0.0579534 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −265.000 | −1.17745 | −0.588726 | − | 0.808333i | \(-0.700370\pi\) | ||||
−0.588726 | + | 0.808333i | \(0.700370\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 213.000 | + | 368.927i | 0.811342 | + | 1.40529i | 0.911925 | + | 0.410356i | \(0.134596\pi\) |
−0.100583 | + | 0.994929i | \(0.532071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 80.0000 | − | 138.564i | 0.283718 | − | 0.491414i | −0.688579 | − | 0.725161i | \(-0.741765\pi\) |
0.972298 | + | 0.233747i | \(0.0750986\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −270.000 | + | 467.654i | −0.837948 | + | 1.45137i | 0.0536598 | + | 0.998559i | \(0.482911\pi\) |
−0.891608 | + | 0.452809i | \(0.850422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 163.500 | + | 283.190i | 0.476676 | + | 0.825628i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 258.000 | 0.668661 | 0.334330 | − | 0.942456i | \(-0.391490\pi\) | ||||
0.334330 | + | 0.942456i | \(0.391490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −72.0000 | −0.176518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 264.000 | + | 457.261i | 0.582540 | + | 1.00899i | 0.995177 | + | 0.0980937i | \(0.0312745\pi\) |
−0.412637 | + | 0.910896i | \(0.635392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 252.500 | − | 437.343i | 0.529989 | − | 0.917967i | −0.469399 | − | 0.882986i | \(-0.655529\pi\) |
0.999388 | − | 0.0349814i | \(-0.0111372\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −37.5000 | + | 64.9519i | −0.0715585 | + | 0.123943i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 122.000 | + | 211.310i | 0.222458 | + | 0.385308i | 0.955554 | − | 0.294817i | \(-0.0952587\pi\) |
−0.733096 | + | 0.680125i | \(0.761925\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −204.000 | −0.340991 | −0.170495 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170495 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −397.000 | −0.636511 | −0.318256 | − | 0.948005i | \(-0.603097\pi\) | ||||
−0.318256 | + | 0.948005i | \(0.603097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 48.0000 | + | 83.1384i | 0.0710404 | + | 0.123046i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −100.000 | + | 173.205i | −0.142416 | + | 0.246672i | −0.928406 | − | 0.371567i | \(-0.878820\pi\) |
0.785990 | + | 0.618239i | \(0.212154\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −270.000 | + | 467.654i | −0.357064 | + | 0.618454i | −0.987469 | − | 0.157813i | \(-0.949556\pi\) |
0.630405 | + | 0.776267i | \(0.282889\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31.5000 | + | 54.5596i | 0.0401959 | + | 0.0696214i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 453.000 | 0.539527 | 0.269764 | − | 0.962927i | \(-0.413054\pi\) | ||||
0.269764 | + | 0.962927i | \(0.413054\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 100.000 | 0.115196 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −78.0000 | − | 135.100i | −0.0842382 | − | 0.145905i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −145.000 | + | 251.147i | −0.151779 | + | 0.262888i | −0.931881 | − | 0.362763i | \(-0.881833\pi\) |
0.780103 | + | 0.625651i | \(0.215167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 687.000 | − | 1189.92i | 0.676822 | − | 1.17229i | −0.299110 | − | 0.954219i | \(-0.596690\pi\) |
0.975933 | − | 0.218072i | \(-0.0699768\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −634.000 | − | 1098.12i | −0.606504 | − | 1.05050i | −0.991812 | − | 0.127707i | \(-0.959238\pi\) |
0.385308 | − | 0.922788i | \(-0.374095\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1164.00 | −1.05166 | −0.525832 | − | 0.850588i | \(-0.676246\pi\) | ||||
−0.525832 | + | 0.850588i | \(0.676246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 587.000 | 0.515820 | 0.257910 | − | 0.966169i | \(-0.416966\pi\) | ||||
0.257910 | + | 0.966169i | \(0.416966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −616.500 | − | 1067.81i | −0.513234 | − | 0.888947i | −0.999882 | − | 0.0153493i | \(-0.995114\pi\) |
0.486648 | − | 0.873598i | \(-0.338219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −252.000 | + | 436.477i | −0.204340 | + | 0.353928i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 42.0000 | − | 72.7461i | 0.0323541 | − | 0.0560389i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 377.500 | + | 653.849i | 0.283621 | + | 0.491247i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 723.000 | 0.517337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1496.00 | 1.04526 | 0.522632 | − | 0.852558i | \(-0.324950\pi\) | ||||
0.522632 | + | 0.852558i | \(0.324950\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1002.00 | − | 1735.51i | −0.668284 | − | 1.15750i | −0.978384 | − | 0.206797i | \(-0.933696\pi\) |
0.310100 | − | 0.950704i | \(-0.399637\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −104.000 | + | 180.133i | −0.0678041 | + | 0.117440i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1387.50 | − | 2403.22i | 0.865271 | − | 1.49869i | −0.00150687 | − | 0.999999i | \(-0.500480\pi\) |
0.866778 | − | 0.498694i | \(-0.166187\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1006.00 | − | 1742.44i | −0.613869 | − | 1.06325i | −0.990582 | − | 0.136922i | \(-0.956279\pi\) |
0.376713 | − | 0.926330i | \(-0.377054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −600.000 | −0.350871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −531.000 | −0.304118 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1072.50 | − | 1857.62i | −0.589682 | − | 1.02136i | −0.994274 | − | 0.106862i | \(-0.965920\pi\) |
0.404592 | − | 0.914497i | \(-0.367414\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1588.00 | + | 2750.50i | −0.855825 | + | 1.48233i | 0.0200521 | + | 0.999799i | \(0.493617\pi\) |
−0.875877 | + | 0.482534i | \(0.839717\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −186.000 | + | 322.161i | −0.0963863 | + | 0.166946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −257.500 | − | 446.003i | −0.130896 | − | 0.226719i | 0.793126 | − | 0.609058i | \(-0.208452\pi\) |
−0.924022 | + | 0.382338i | \(0.875119\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 672.000 | 0.328950 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3272.00 | 1.57229 | 0.786144 | − | 0.618044i | \(-0.212075\pi\) | ||||
0.786144 | + | 0.618044i | \(0.212075\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −342.000 | − | 592.361i | −0.158472 | − | 0.274481i | 0.775846 | − | 0.630922i | \(-0.217323\pi\) |
−0.934318 | + | 0.356441i | \(0.883990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 786.000 | − | 1361.39i | 0.357761 | − | 0.619660i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1561.50 | − | 2704.60i | 0.686235 | − | 1.18859i | −0.286812 | − | 0.957987i | \(-0.592596\pi\) |
0.973047 | − | 0.230607i | \(-0.0740711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −232.000 | − | 401.836i | −0.100215 | − | 0.173577i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2892.00 | −1.20759 | −0.603794 | − | 0.797140i | \(-0.706345\pi\) | ||||
−0.603794 | + | 0.797140i | \(0.706345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1426.00 | −0.585601 | −0.292800 | − | 0.956174i | \(-0.594587\pi\) | ||||
−0.292800 | + | 0.956174i | \(0.594587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −397.500 | − | 688.490i | −0.157972 | − | 0.273615i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −252.000 | + | 436.477i | −0.0985458 | + | 0.170686i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −798.000 | + | 1382.18i | −0.302310 | + | 0.523617i | −0.976659 | − | 0.214796i | \(-0.931091\pi\) |
0.674349 | + | 0.738413i | \(0.264425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −557.500 | − | 965.618i | −0.207926 | − | 0.360138i | 0.743135 | − | 0.669142i | \(-0.233338\pi\) |
−0.951061 | + | 0.309003i | \(0.900005\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1245.00 | 0.450267 | 0.225133 | − | 0.974328i | \(-0.427718\pi\) | ||||
0.225133 | + | 0.974328i | \(0.427718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −700.000 | −0.249355 | −0.124678 | − | 0.992197i | \(-0.539790\pi\) | ||||
−0.124678 | + | 0.992197i | \(0.539790\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 354.000 | + | 613.146i | 0.122394 | + | 0.211992i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −639.000 | + | 1106.78i | −0.217706 | + | 0.377078i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 624.000 | − | 1080.80i | 0.206521 | − | 0.357706i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −352.000 | − | 609.682i | −0.114847 | − | 0.198921i | 0.802872 | − | 0.596152i | \(-0.203304\pi\) |
−0.917719 | + | 0.397231i | \(0.869971\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 480.000 | 0.152259 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 496.000 | 0.155164 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 262.500 | + | 454.663i | 0.0798989 | + | 0.138389i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 440.000 | − | 762.102i | 0.132128 | − | 0.228853i | −0.792369 | − | 0.610043i | \(-0.791152\pi\) |
0.924497 | + | 0.381190i | \(0.124486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1962.00 | + | 3398.28i | −0.573667 | + | 0.993621i | 0.422518 | + | 0.906355i | \(0.361146\pi\) |
−0.996185 | + | 0.0872664i | \(0.972187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3072.50 | + | 5321.73i | 0.886622 | + | 1.53567i | 0.843843 | + | 0.536590i | \(0.180288\pi\) |
0.0427795 | + | 0.999085i | \(0.486379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3885.00 | 1.09234 | 0.546169 | − | 0.837675i | \(-0.316086\pi\) | ||||
0.546169 | + | 0.837675i | \(0.316086\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1620.00 | −0.449690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2430.00 | + | 4208.88i | 0.657672 | + | 1.13912i | 0.981217 | + | 0.192909i | \(0.0617921\pi\) |
−0.323545 | + | 0.946213i | \(0.604875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2274.50 | − | 3939.55i | 0.607940 | − | 1.05298i | −0.383640 | − | 0.923483i | \(-0.625330\pi\) |
0.991580 | − | 0.129499i | \(-0.0413370\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −490.500 | + | 849.571i | −0.127906 | + | 0.221539i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −650.000 | − | 1125.83i | −0.167443 | − | 0.290020i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4800.00 | −1.20706 | −0.603532 | − | 0.797338i | \(-0.706241\pi\) | ||||
−0.603532 | + | 0.797338i | \(0.706241\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4032.00 | −1.00194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1255.50 | + | 2174.59i | 0.304731 | + | 0.527810i | 0.977201 | − | 0.212314i | \(-0.0681000\pi\) |
−0.672470 | + | 0.740124i | \(0.734767\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −530.000 | + | 917.987i | −0.127153 | + | 0.220235i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2274.00 | + | 3938.68i | −0.533159 | + | 0.923459i | 0.466091 | + | 0.884737i | \(0.345662\pi\) |
−0.999250 | + | 0.0387218i | \(0.987671\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 387.000 | + | 670.304i | 0.0897103 | + | 0.155383i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2517.00 | 0.570499 | 0.285249 | − | 0.958453i | \(-0.407924\pi\) | ||||
0.285249 | + | 0.958453i | \(0.407924\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4040.00 | 0.905581 | 0.452791 | − | 0.891617i | \(-0.350429\pi\) | ||||
0.452791 | + | 0.891617i | \(0.350429\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1392.00 | + | 2411.01i | 0.305239 | + | 0.528690i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3545.00 | − | 6140.12i | 0.768947 | − | 1.33186i | −0.169187 | − | 0.985584i | \(-0.554114\pi\) |
0.938134 | − | 0.346272i | \(-0.112553\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1582.50 | + | 2740.97i | −0.335957 | + | 0.581895i | −0.983668 | − | 0.179991i | \(-0.942393\pi\) |
0.647711 | + | 0.761886i | \(0.275726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3374.00 | + | 5843.94i | 0.708705 | + | 1.22751i | 0.965338 | + | 0.261004i | \(0.0840535\pi\) |
−0.256633 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1704.00 | 0.350467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4472.00 | −0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3247.50 | + | 5624.83i | 0.647512 | + | 1.12152i | 0.983715 | + | 0.179734i | \(0.0575237\pi\) |
−0.336203 | + | 0.941789i | \(0.609143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −792.000 | + | 1371.78i | −0.156312 | + | 0.270740i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2100.00 | + | 3637.31i | −0.406174 | + | 0.703515i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −320.000 | − | 554.256i | −0.0612774 | − | 0.106136i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1515.00 | 0.284422 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8980.00 | −1.66943 | −0.834716 | − | 0.550681i | \(-0.814368\pi\) | ||||
−0.834716 | + | 0.550681i | \(0.814368\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1932.00 | + | 3346.32i | 0.352263 | + | 0.610137i | 0.986646 | − | 0.162882i | \(-0.0520791\pi\) |
−0.634383 | + | 0.773019i | \(0.718746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2747.50 | + | 4758.81i | −0.496159 | + | 0.859373i | −0.999990 | − | 0.00442912i | \(-0.998590\pi\) |
0.503831 | + | 0.863802i | \(0.331923\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −442.500 | + | 766.432i | −0.0784015 | + | 0.135795i | −0.902560 | − | 0.430563i | \(-0.858315\pi\) |
0.824159 | + | 0.566359i | \(0.191648\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2124.00 | − | 3678.88i | −0.372794 | − | 0.645698i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1092.00 | −0.188113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2900.00 | 0.494963 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1080.00 | + | 1870.61i | 0.180980 | + | 0.313466i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5462.00 | − | 9460.46i | 0.907005 | − | 1.57098i | 0.0888021 | − | 0.996049i | \(-0.471696\pi\) |
0.818203 | − | 0.574930i | \(-0.194971\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −366.000 | + | 633.931i | −0.0596917 | + | 0.103389i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3935.00 | + | 6815.62i | 0.636063 | + | 1.10169i | 0.986289 | + | 0.165028i | \(0.0527713\pi\) |
−0.350226 | + | 0.936665i | \(0.613895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2976.00 | −0.472608 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2680.00 | 0.421885 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2358.00 | − | 4084.18i | −0.364796 | − | 0.631845i | 0.623948 | − | 0.781466i | \(-0.285528\pi\) |
−0.988743 | + | 0.149622i | \(0.952194\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 821.000 | − | 1422.01i | 0.125923 | − | 0.218105i | −0.796170 | − | 0.605073i | \(-0.793144\pi\) |
0.922093 | + | 0.386968i | \(0.126477\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1545.00 | − | 2676.02i | 0.232952 | − | 0.403485i | −0.725724 | − | 0.687986i | \(-0.758495\pi\) |
0.958676 | + | 0.284502i | \(0.0918282\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −306.000 | − | 530.008i | −0.0457487 | − | 0.0792391i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5688.00 | 0.836215 | 0.418107 | − | 0.908398i | \(-0.362694\pi\) | ||||
0.418107 | + | 0.908398i | \(0.362694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4155.00 | −0.605773 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −595.500 | − | 1031.44i | −0.0853970 | − | 0.147912i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3388.00 | + | 5868.19i | −0.481886 | + | 0.834651i | −0.999784 | − | 0.0207914i | \(-0.993381\pi\) |
0.517898 | + | 0.855442i | \(0.326715\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 516.000 | − | 893.738i | 0.0722086 | − | 0.125069i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3079.00 | − | 5332.98i | −0.427412 | − | 0.740299i | 0.569231 | − | 0.822178i | \(-0.307241\pi\) |
−0.996642 | + | 0.0818791i | \(0.973908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4425.00 | −0.604507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7484.00 | 1.01432 | 0.507160 | − | 0.861852i | \(-0.330695\pi\) | ||||
0.507160 | + | 0.861852i | \(0.330695\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2310.00 | + | 4001.04i | 0.308187 | + | 0.533795i | 0.977966 | − | 0.208765i | \(-0.0669445\pi\) |
−0.669779 | + | 0.742560i | \(0.733611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −144.000 | + | 249.415i | −0.0190621 | + | 0.0330166i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −465.000 | + | 805.404i | −0.0606078 | + | 0.104976i | −0.894737 | − | 0.446593i | \(-0.852637\pi\) |
0.834129 | + | 0.551569i | \(0.185971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1764.00 | + | 3055.34i | 0.228157 | + | 0.395179i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −600.000 | −0.0764285 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1919.00 | 0.242599 | 0.121300 | − | 0.992616i | \(-0.461294\pi\) | ||||
0.121300 | + | 0.992616i | \(0.461294\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5002.50 | − | 8664.58i | −0.622975 | − | 1.07902i | −0.988929 | − | 0.148391i | \(-0.952591\pi\) |
0.365954 | − | 0.930633i | \(-0.380743\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1550.00 | + | 2684.68i | −0.191591 | + | 0.331845i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3180.00 | − | 5507.92i | 0.387289 | − | 0.670805i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3827.50 | − | 6629.42i | −0.462733 | − | 0.801477i | 0.536363 | − | 0.843987i | \(-0.319798\pi\) |
−0.999096 | + | 0.0425106i | \(0.986464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2112.00 | 0.251634 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1620.00 | −0.191621 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7020.00 | − | 12159.0i | −0.818495 | − | 1.41768i | −0.906791 | − | 0.421581i | \(-0.861475\pi\) |
0.0882958 | − | 0.996094i | \(-0.471858\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5609.50 | + | 9715.94i | −0.649383 | + | 1.12476i | 0.333887 | + | 0.942613i | \(0.391639\pi\) |
−0.983270 | + | 0.182152i | \(0.941694\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1218.00 | − | 2109.64i | 0.139016 | − | 0.240782i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1010.00 | − | 1749.37i | −0.114467 | − | 0.198262i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1884.00 | 0.210555 | 0.105277 | − | 0.994443i | \(-0.466427\pi\) | ||||
0.105277 | + | 0.994443i | \(0.466427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17507.0 | 1.94303 | 0.971516 | − | 0.236975i | \(-0.0761558\pi\) | ||||
0.971516 | + | 0.236975i | \(0.0761558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4368.00 | − | 7565.60i | −0.478146 | − | 0.828173i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1754.00 | − | 3038.02i | 0.190692 | − | 0.330288i | −0.754788 | − | 0.655969i | \(-0.772260\pi\) |
0.945480 | + | 0.325681i | \(0.105593\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6210.00 | − | 10756.0i | 0.666018 | − | 1.15358i | −0.312990 | − | 0.949756i | \(-0.601331\pi\) |
0.979008 | − | 0.203821i | \(-0.0653360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 679.500 | + | 1176.93i | 0.0723851 | + | 0.125375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8658.00 | −0.910014 | −0.455007 | − | 0.890488i | \(-0.650363\pi\) | ||||
−0.455007 | + | 0.890488i | \(0.650363\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10224.0 | −1.06747 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 150.000 | + | 259.808i | 0.0154552 | + | 0.0267692i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −167.500 | + | 290.119i | −0.0171451 | + | 0.0296962i | −0.874471 | − | 0.485078i | \(-0.838791\pi\) |
0.857326 | + | 0.514775i | \(0.172124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 123.000 | − | 213.042i | 0.0124266 | − | 0.0215236i | −0.859745 | − | 0.510723i | \(-0.829378\pi\) |
0.872172 | + | 0.489200i | \(0.162711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7156.00 | − | 12394.6i | −0.718288 | − | 1.24411i | −0.961677 | − | 0.274183i | \(-0.911593\pi\) |
0.243389 | − | 0.969929i | \(-0.421741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8184.00 | −0.810943 | −0.405471 | − | 0.914108i | \(-0.632893\pi\) | ||||
−0.405471 | + | 0.914108i | \(0.632893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 976.000 | 0.0960927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1920.00 | + | 3325.54i | 0.186642 | + | 0.323274i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3016.00 | + | 5223.87i | −0.291334 | + | 0.504605i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9054.00 | − | 15682.0i | 0.863649 | − | 1.49588i | −0.00473362 | − | 0.999989i | \(-0.501507\pi\) |
0.868383 | − | 0.495895i | \(-0.165160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3312.50 | − | 5737.42i | −0.314006 | − | 0.543875i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −870.000 | −0.0814529 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13700.0 | 1.27476 | 0.637378 | − | 0.770551i | \(-0.280019\pi\) | ||||
0.637378 | + | 0.770551i | \(0.280019\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10068.0 | − | 17438.3i | −0.925382 | − | 1.60281i | −0.790946 | − | 0.611886i | \(-0.790411\pi\) |
−0.134436 | − | 0.990922i | \(-0.542922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1858.50 | + | 3219.02i | −0.169782 | + | 0.294071i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −408.000 | + | 706.677i | −0.0368235 | + | 0.0637802i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6704.00 | + | 11611.7i | 0.601427 | + | 1.04170i | 0.992605 | + | 0.121388i | \(0.0387344\pi\) |
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21600.0 | 1.91470 | 0.957352 | − | 0.288923i | \(-0.0932972\pi\) | ||||
0.957352 | + | 0.288923i | \(0.0932972\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4122.00 | 0.363221 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2973.00 | − | 5149.39i | −0.258892 | − | 0.448414i | 0.707054 | − | 0.707160i | \(-0.250024\pi\) |
−0.965945 | + | 0.258746i | \(0.916691\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −794.000 | + | 1375.25i | −0.0687368 | + | 0.119056i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1902.00 | − | 3294.36i | 0.162742 | − | 0.281877i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6480.00 | − | 11223.7i | −0.551238 | − | 0.954772i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8970.00 | −0.754286 | −0.377143 | − | 0.926155i | \(-0.623093\pi\) | ||||
−0.377143 | + | 0.926155i | \(0.623093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12520.0 | −1.04677 | −0.523386 | − | 0.852096i | \(-0.675331\pi\) | ||||
−0.523386 | + | 0.852096i | \(0.675331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1302.00 | + | 2255.13i | 0.107621 | + | 0.186404i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8028.50 | + | 13905.8i | −0.659859 | + | 1.14291i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5325.00 | + | 9223.17i | −0.432742 | + | 0.749531i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1746.00 | − | 3024.16i | −0.141096 | − | 0.244385i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7848.00 | −0.627156 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3911.00 | 0.310808 | 0.155404 | − | 0.987851i | \(-0.450332\pi\) | ||||
0.155404 | + | 0.987851i | \(0.450332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 880.500 | + | 1525.07i | 0.0692045 | + | 0.119866i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8510.00 | − | 14739.8i | 0.665194 | − | 1.15215i | −0.314038 | − | 0.949410i | \(-0.601682\pi\) |
0.979233 | − | 0.202740i | \(-0.0649847\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4602.00 | − | 7970.90i | 0.355811 | − | 0.616283i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 400.000 | + | 692.820i | 0.0307590 | + | 0.0532762i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13875.0 | −1.05548 | −0.527740 | − | 0.849406i | \(-0.676961\pi\) | ||||
−0.527740 | + | 0.849406i | \(0.676961\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4000.00 | 0.302651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 270.000 | + | 467.654i | 0.0202116 | + | 0.0350076i | 0.875954 | − | 0.482394i | \(-0.160233\pi\) |
−0.855743 | + | 0.517402i | \(0.826899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1849.50 | − | 3203.43i | 0.137715 | − | 0.238530i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6256.50 | + | 10836.6i | −0.460960 | + | 0.798406i | −0.999009 | − | 0.0445076i | \(-0.985828\pi\) |
0.538049 | + | 0.842913i | \(0.319161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10208.0 | + | 17680.8i | 0.748146 | + | 1.29583i | 0.948710 | + | 0.316147i | \(0.102389\pi\) |
−0.200564 | + | 0.979681i | \(0.564277\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19488.0 | 1.41340 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1801.00 | −0.129942 | −0.0649711 | − | 0.997887i | \(-0.520696\pi\) | ||||
−0.0649711 | + | 0.997887i | \(0.520696\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1080.00 | + | 1870.61i | 0.0771187 | + | 0.133573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3096.00 | + | 5362.43i | −0.219937 | + | 0.380942i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2760.00 | + | 4780.46i | −0.194067 | + | 0.336134i | −0.946594 | − | 0.322427i | \(-0.895501\pi\) |
0.752527 | + | 0.658561i | \(0.228835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3224.00 | − | 5584.13i | −0.225539 | − | 0.390645i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11937.0 | 0.826634 | 0.413317 | − | 0.910587i | \(-0.364370\pi\) | ||||
0.413317 | + | 0.910587i | \(0.364370\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 252.000 | 0.0173630 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8094.00 | + | 14019.2i | 0.552107 | + | 0.956277i | 0.998122 | + | 0.0612516i | \(0.0195092\pi\) |
−0.446016 | + | 0.895025i | \(0.647157\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5970.50 | − | 10341.2i | 0.405228 | − | 0.701875i | −0.589120 | − | 0.808045i | \(-0.700526\pi\) |
0.994348 | + | 0.106171i | \(0.0338589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1132.50 | + | 1961.55i | −0.0761036 | + | 0.131815i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6230.00 | + | 10790.7i | 0.416586 | + | 0.721549i | 0.995594 | − | 0.0937737i | \(-0.0298930\pi\) |
−0.579007 | + | 0.815322i | \(0.696560\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13500.0 | −0.893865 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4670.00 | 0.307699 | 0.153850 | − | 0.988094i | \(-0.450833\pi\) | ||||
0.153850 | + | 0.988094i | \(0.450833\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4717.50 | + | 8170.95i | 0.307811 | + | 0.533144i | 0.977883 | − | 0.209152i | \(-0.0670702\pi\) |
−0.670072 | + | 0.742296i | \(0.733737\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6980.00 | − | 12089.7i | 0.453231 | − | 0.785019i | −0.545354 | − | 0.838206i | \(-0.683605\pi\) |
0.998585 | + | 0.0531872i | \(0.0169380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 906.000 | − | 1569.24i | 0.0582634 | − | 0.100915i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6165.50 | − | 10679.0i | −0.394592 | − | 0.683453i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5565.00 | −0.352768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18904.0 | −1.19264 | −0.596320 | − | 0.802747i | \(-0.703371\pi\) | ||||
−0.596320 | + | 0.802747i | \(0.703371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2244.00 | + | 3886.72i | 0.140237 | + | 0.242897i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4087.50 | + | 7079.76i | −0.254243 | + | 0.440361i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10690.5 | + | 18516.5i | −0.658735 | + | 1.14096i | 0.322208 | + | 0.946669i | \(0.395575\pi\) |
−0.980943 | + | 0.194294i | \(0.937758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 710.000 | + | 1229.76i | 0.0435454 | + | 0.0754228i | 0.886977 | − | 0.461814i | \(-0.152801\pi\) |
−0.843431 | + | 0.537237i | \(0.819468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21204.0 | 1.28843 | 0.644216 | − | 0.764844i | \(-0.277184\pi\) | ||||
0.644216 | + | 0.764844i | \(0.277184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12672.0 | −0.766440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11595.0 | + | 20083.1i | 0.694866 | + | 1.20354i | 0.970226 | + | 0.242202i | \(0.0778696\pi\) |
−0.275360 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3006.00 | − | 5206.54i | 0.179319 | − | 0.310590i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4902.00 | + | 8490.51i | −0.289765 | + | 0.501887i | −0.973753 | − | 0.227606i | \(-0.926910\pi\) |
0.683989 | + | 0.729492i | \(0.260244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15120.5 | + | 26189.5i | 0.889742 | + | 1.54108i | 0.840181 | + | 0.542307i | \(0.182449\pi\) |
0.0495612 | + | 0.998771i | \(0.484218\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −624.000 | −0.0363875 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29736.0 | −1.72621 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6060.00 | + | 10496.2i | 0.348649 | + | 0.603878i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −401.500 | + | 695.418i | −0.0229966 | + | 0.0398312i | −0.877295 | − | 0.479952i | \(-0.840654\pi\) |
0.854298 | + | 0.519783i | \(0.173987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7233.00 | + | 12527.9i | −0.410616 | + | 0.711207i | −0.994957 | − | 0.100301i | \(-0.968020\pi\) |
0.584342 | + | 0.811508i | \(0.301353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 580.000 | + | 1004.59i | 0.0327811 | + | 0.0567785i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7020.00 | 0.393284 | 0.196642 | − | 0.980475i | \(-0.436996\pi\) | ||||
0.196642 | + | 0.980475i | \(0.436996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8325.00 | 0.464353 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3225.00 | + | 5585.86i | 0.178320 | + | 0.308860i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12230.0 | − | 21183.0i | 0.673301 | − | 1.16619i | −0.303661 | − | 0.952780i | \(-0.598209\pi\) |
0.976962 | − | 0.213412i | \(-0.0684576\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3018.00 | − | 5227.33i | 0.164718 | − | 0.285301i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4473.00 | + | 7747.46i | 0.243080 | + | 0.421027i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27651.0 | −1.48982 | −0.744910 | − | 0.667165i | \(-0.767508\pi\) | ||||
−0.744910 | + | 0.667165i | \(0.767508\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13780.0 | 0.739292 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2748.00 | − | 4759.68i | −0.146180 | − | 0.253191i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2460.50 | − | 4261.71i | 0.130333 | − | 0.225743i | −0.793472 | − | 0.608607i | \(-0.791729\pi\) |
0.923805 | + | 0.382864i | \(0.125062\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10416.0 | + | 18041.0i | −0.547100 | + | 0.947605i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −900.000 | − | 1558.85i | −0.0470743 | − | 0.0815350i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20232.0 | 1.04941 | 0.524705 | − | 0.851284i | \(-0.324176\pi\) | ||||
0.524705 | + | 0.851284i | \(0.324176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5072.00 | −0.261985 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10266.0 | + | 17781.2i | 0.525889 | + | 0.910867i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3250.00 | + | 5629.17i | −0.165799 | + | 0.287172i | −0.936939 | − | 0.349494i | \(-0.886354\pi\) |
0.771140 | + | 0.636666i | \(0.219687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1680.00 | − | 2909.85i | 0.0850028 | − | 0.147229i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6859.00 | − | 11880.1i | −0.345625 | − | 0.598640i | 0.639842 | − | 0.768506i | \(-0.279000\pi\) |
−0.985467 | + | 0.169867i | \(0.945666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5856.00 | −0.292685 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13588.0 | −0.676377 | −0.338189 | − | 0.941078i | \(-0.609814\pi\) | ||||
−0.338189 | + | 0.941078i | \(0.609814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17046.0 | + | 29524.5i | 0.841665 | + | 1.45781i | 0.888486 | + | 0.458903i | \(0.151758\pi\) |
−0.0468213 | + | 0.998903i | \(0.514909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3217.50 | − | 5572.87i | 0.158228 | − | 0.274059i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2328.00 | + | 4032.21i | −0.113569 | + | 0.196707i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 470.000 | + | 814.064i | 0.0228369 | + | 0.0395547i | 0.877218 | − | 0.480092i | \(-0.159397\pi\) |
−0.854381 | + | 0.519647i | \(0.826063\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9528.00 | −0.459284 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5410.00 | −0.259749 | −0.129874 | − | 0.991530i | \(-0.541457\pi\) | ||||
−0.129874 | + | 0.991530i | \(0.541457\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3424.50 | − | 5931.41i | −0.163125 | − | 0.282541i | 0.772863 | − | 0.634573i | \(-0.218824\pi\) |
−0.935988 | + | 0.352032i | \(0.885491\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1174.00 | − | 2033.43i | 0.0557033 | − | 0.0964810i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6600.00 | + | 11431.5i | −0.310707 | + | 0.538160i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4566.50 | + | 7909.41i | 0.214138 | + | 0.370898i | 0.953006 | − | 0.302953i | \(-0.0979724\pi\) |
−0.738868 | + | 0.673851i | \(0.764639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37845.0 | 1.76092 | 0.880459 | − | 0.474122i | \(-0.157234\pi\) | ||||
0.880459 | + | 0.474122i | \(0.157234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14384.0 | 0.666695 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11076.0 | − | 19184.2i | −0.509421 | − | 0.882343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2448.00 | − | 4240.06i | 0.112159 | − | 0.194265i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 772.500 | − | 1338.01i | 0.0351232 | − | 0.0608352i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16988.0 | + | 29424.1i | 0.769450 | + | 1.33273i | 0.937862 | + | 0.347009i | \(0.112803\pi\) |
−0.168412 | + | 0.985717i | \(0.553864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4932.00 | −0.221696 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12625.0 | 0.565355 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11902.5 | − | 20615.7i | −0.528994 | − | 0.916244i | −0.999428 | − | 0.0338094i | \(-0.989236\pi\) |
0.470434 | − | 0.882435i | \(-0.344097\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5670.00 | + | 9820.73i | −0.251052 | + | 0.434834i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4764.00 | − | 8251.49i | 0.209362 | − | 0.362626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1008.00 | + | 1745.91i | 0.0441333 | + | 0.0764412i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6567.00 | −0.285394 | −0.142697 | − | 0.989766i | \(-0.545577\pi\) | ||||
−0.142697 | + | 0.989766i | \(0.545577\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8656.00 | −0.374788 | −0.187394 | − | 0.982285i | \(-0.560004\pi\) | ||||
−0.187394 | + | 0.982285i | \(0.560004\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4908.00 | + | 8500.91i | 0.210944 | + | 0.365367i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4160.00 | + | 7205.33i | −0.178140 | + | 0.308547i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2995.50 | − | 5188.36i | 0.127337 | − | 0.220554i | −0.795307 | − | 0.606207i | \(-0.792690\pi\) |
0.922644 | + | 0.385653i | \(0.126024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22906.0 | − | 39674.4i | −0.970174 | − | 1.68039i | −0.695021 | − | 0.718990i | \(-0.744605\pi\) |
−0.275153 | − | 0.961400i | \(-0.588729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35160.0 | −1.47840 | −0.739198 | − | 0.673489i | \(-0.764795\pi\) | ||||
−0.739198 | + | 0.673489i | \(0.764795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9898.00 | −0.414682 | −0.207341 | − | 0.978269i | \(-0.566481\pi\) | ||||
−0.207341 | + | 0.978269i | \(0.566481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3433.50 | + | 5947.00i | 0.142814 | + | 0.247360i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1026.00 | − | 1777.08i | 0.0425224 | − | 0.0736509i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2016.00 | − | 3491.81i | 0.0829560 | − | 0.143684i | −0.821562 | − | 0.570119i | \(-0.806897\pi\) |
0.904518 | + | 0.426435i | \(0.140231\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3470.00 | − | 6010.22i | −0.142277 | − | 0.246431i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4716.00 | 0.191994 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3020.00 | 0.122513 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22260.0 | − | 38555.5i | −0.896666 | − | 1.55307i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9319.00 | + | 16141.0i | −0.374064 | + | 0.647898i | −0.990186 | − | 0.139753i | \(-0.955369\pi\) |
0.616123 | + | 0.787650i | \(0.288703\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18787.5 | − | 32540.9i | 0.748855 | − | 1.29705i | −0.199517 | − | 0.979894i | \(-0.563937\pi\) |
0.948372 | − | 0.317161i | \(-0.102729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3134.00 | + | 5428.25i | 0.124483 | + | 0.215610i | 0.921531 | − | 0.388306i | \(-0.126940\pi\) |
−0.797048 | + | 0.603916i | \(0.793606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44832.0 | 1.76837 | 0.884183 | − | 0.467142i | \(-0.154716\pi\) | ||||
0.884183 | + | 0.467142i | \(0.154716\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9369.00 | 0.368272 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2400.00 | − | 4156.92i | −0.0936875 | − | 0.162271i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3050.00 | + | 5282.75i | −0.118651 | + | 0.205510i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1446.00 | − | 2504.55i | 0.0558671 | − | 0.0967647i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7247.50 | − | 12553.0i | −0.279054 | − | 0.483336i | 0.692096 | − | 0.721806i | \(-0.256688\pi\) |
−0.971150 | + | 0.238469i | \(0.923354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25986.0 | −0.993746 | −0.496873 | − | 0.867823i | \(-0.665519\pi\) | ||||
−0.496873 | + | 0.867823i | \(0.665519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34868.0 | 1.32888 | 0.664440 | − | 0.747341i | \(-0.268670\pi\) | ||||
0.664440 | + | 0.747341i | \(0.268670\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3360.00 | − | 5819.69i | −0.127190 | − | 0.220300i | 0.795397 | − | 0.606089i | \(-0.207263\pi\) |
−0.922587 | + | 0.385789i | \(0.873929\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2992.00 | − | 5182.30i | 0.112878 | − | 0.195510i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14040.0 | − | 24318.0i | 0.526126 | − | 0.911277i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4338.00 | − | 7513.64i | −0.162015 | − | 0.280618i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21948.0 | −0.814246 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5418.00 | 0.200333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2139.00 | − | 3704.86i | −0.0785666 | − | 0.136081i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8648.00 | − | 14978.8i | 0.316596 | − | 0.548360i | −0.663180 | − | 0.748460i | \(-0.730794\pi\) |
0.979775 | + | 0.200101i | \(0.0641269\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7128.00 | + | 12346.1i | −0.259233 | + | 0.449005i | −0.966037 | − | 0.258405i | \(-0.916803\pi\) |
0.706804 | + | 0.707410i | \(0.250136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6480.00 | − | 11223.7i | −0.234892 | − | 0.406845i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8016.00 | −0.288671 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15752.0 | 0.565409 | 0.282704 | − | 0.959207i | \(-0.408768\pi\) | ||||
0.282704 | + | 0.959207i | \(0.408768\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2550.00 | − | 4416.73i | −0.0909364 | − | 0.157506i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15370.0 | + | 26621.6i | −0.546338 | + | 0.946285i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15781.5 | − | 27334.4i | 0.557346 | − | 0.965351i | −0.440371 | − | 0.897816i | \(-0.645153\pi\) |
0.997717 | − | 0.0675353i | \(-0.0215135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8502.00 | − | 14725.9i | −0.299293 | − | 0.518391i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1512.00 | −0.0528852 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3901.00 | −0.136009 | −0.0680043 | − | 0.997685i | \(-0.521663\pi\) | ||||
−0.0680043 | + | 0.997685i | \(0.521663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26722.5 | − | 46284.7i | −0.925748 | − | 1.60344i | −0.790354 | − | 0.612650i | \(-0.790103\pi\) |
−0.135394 | − | 0.990792i | \(-0.543230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35784.0 | + | 61979.7i | −1.23572 | + | 2.14034i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4518.00 | − | 7825.41i | 0.155032 | − | 0.268523i | −0.778039 | − | 0.628216i | \(-0.783785\pi\) |
0.933071 | + | 0.359693i | \(0.117119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4962.50 | − | 8595.30i | −0.169747 | − | 0.294010i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25065.0 | 0.851978 | 0.425989 | − | 0.904728i | \(-0.359926\pi\) | ||||
0.425989 | + | 0.904728i | \(0.359926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4788.00 | −0.162237 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5550.00 | − | 9612.88i | −0.186881 | − | 0.323687i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7207.50 | − | 12483.8i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1672.50 | − | 2896.85i | 0.0557924 | − | 0.0966353i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7222.00 | − | 12508.9i | −0.240169 | − | 0.415986i | 0.720593 | − | 0.693358i | \(-0.243870\pi\) |
−0.960762 | + | 0.277373i | \(0.910536\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50004.0 | −1.65263 | −0.826316 | − | 0.563207i | \(-0.809567\pi\) | ||||
−0.826316 | + | 0.563207i | \(0.809567\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8048.00 | −0.265167 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22695.0 | − | 39308.9i | −0.743170 | − | 1.28721i | −0.951045 | − | 0.309053i | \(-0.899988\pi\) |
0.207874 | − | 0.978156i | \(-0.433345\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5436.00 | + | 9415.43i | −0.177462 | + | 0.307373i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17976.0 | − | 31135.3i | 0.583261 | − | 1.01024i | −0.411829 | − | 0.911261i | \(-0.635110\pi\) |
0.995090 | − | 0.0989762i | \(-0.0315568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1867.50 | + | 3234.60i | 0.0604096 | + | 0.104633i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26880.0 | 0.864241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14156.0 | 0.453764 | 0.226882 | − | 0.973922i | \(-0.427147\pi\) | ||||
0.226882 | + | 0.973922i | \(0.427147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1050.00 | − | 1818.65i | −0.0334545 | − | 0.0579449i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25770.5 | − | 44635.8i | 0.818616 | − | 1.41788i | −0.0880865 | − | 0.996113i | \(-0.528075\pi\) |
0.906702 | − | 0.421771i | \(-0.138591\pi\) | |||||||
\(998\) | 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 | 324.4.e.f.217.1 | 2 | ||
3.2 | odd | 2 | 324.4.e.c.217.1 | 2 | |||
9.2 | odd | 6 | 324.4.a.b.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 324.4.e.f.109.1 | 2 | ||
9.5 | odd | 6 | 324.4.e.c.109.1 | 2 | |||
9.7 | even | 3 | 324.4.a.a.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 1296.4.a.d.1.1 | 1 | |||
36.11 | even | 6 | 1296.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.4.a.a.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
324.4.a.b.1.1 | yes | 1 | 9.2 | odd | 6 | ||
324.4.e.c.109.1 | 2 | 9.5 | odd | 6 | |||
324.4.e.c.217.1 | 2 | 3.2 | odd | 2 | |||
324.4.e.f.109.1 | 2 | 9.4 | even | 3 | inner | ||
324.4.e.f.217.1 | 2 | 1.1 | even | 1 | trivial | ||
1296.4.a.d.1.1 | 1 | 36.7 | odd | 6 | |||
1296.4.a.e.1.1 | 1 | 36.11 | even | 6 |