Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (of order \(4\), 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Root | \(-1.62580 - 1.16481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.97 |
Dual form | 128.4.e.a.33.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.756776 | − | 0.756776i | 0.145642 | − | 0.145642i | −0.630526 | − | 0.776168i | \(-0.717161\pi\) |
0.776168 | + | 0.630526i | \(0.217161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.22587 | − | 8.22587i | −0.735744 | − | 0.735744i | 0.236007 | − | 0.971751i | \(-0.424161\pi\) |
−0.971751 | + | 0.236007i | \(0.924161\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.67171i | − | 0.144259i | −0.997395 | − | 0.0721293i | \(-0.977021\pi\) | ||
0.997395 | − | 0.0721293i | \(-0.0229794\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 25.8546i | 0.957577i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −45.2213 | − | 45.2213i | −1.23952 | − | 1.23952i | −0.960197 | − | 0.279323i | \(-0.909890\pi\) |
−0.279323 | − | 0.960197i | \(-0.590110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.3968 | + | 35.3968i | −0.755176 | + | 0.755176i | −0.975440 | − | 0.220264i | \(-0.929308\pi\) |
0.220264 | + | 0.975440i | \(0.429308\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.4503 | −0.214310 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −72.4991 | −1.03433 | −0.517165 | − | 0.855886i | \(-0.673013\pi\) | ||||
−0.517165 | + | 0.855886i | \(0.673013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.4427 | − | 19.4427i | 0.234761 | − | 0.234761i | −0.579916 | − | 0.814676i | \(-0.696915\pi\) |
0.814676 | + | 0.579916i | \(0.196915\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.02188 | − | 2.02188i | −0.0210100 | − | 0.0210100i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 139.462i | − | 1.26434i | −0.774830 | − | 0.632170i | \(-0.782165\pi\) | ||
0.774830 | − | 0.632170i | \(-0.217835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.3299i | 0.0826390i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 39.9991 | + | 39.9991i | 0.285105 | + | 0.285105i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −66.0434 | + | 66.0434i | −0.422895 | + | 0.422895i | −0.886199 | − | 0.463304i | \(-0.846664\pi\) |
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −188.682 | −1.09317 | −0.546584 | − | 0.837404i | \(-0.684072\pi\) | ||||
−0.546584 | + | 0.837404i | \(0.684072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −68.4447 | −0.361051 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −21.9771 | + | 21.9771i | −0.106137 | + | 0.106137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 84.0653 | + | 84.0653i | 0.373520 | + | 0.373520i | 0.868758 | − | 0.495237i | \(-0.164919\pi\) |
−0.495237 | + | 0.868758i | \(0.664919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 53.5748i | 0.219970i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 104.629i | − | 0.398545i | −0.979944 | − | 0.199272i | \(-0.936142\pi\) | ||
0.979944 | − | 0.199272i | \(-0.0638578\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −31.4857 | − | 31.4857i | −0.111663 | − | 0.111663i | 0.649067 | − | 0.760731i | \(-0.275159\pi\) |
−0.760731 | + | 0.649067i | \(0.775159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 212.676 | − | 212.676i | 0.704532 | − | 0.704532i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 488.151 | 1.51498 | 0.757491 | − | 0.652846i | \(-0.226425\pi\) | ||||
0.757491 | + | 0.652846i | \(0.226425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 335.862 | 0.979189 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −54.8656 | + | 54.8656i | −0.150641 | + | 0.150641i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −149.560 | − | 149.560i | −0.387617 | − | 0.387617i | 0.486220 | − | 0.873837i | \(-0.338376\pi\) |
−0.873837 | + | 0.486220i | \(0.838376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 743.968i | 1.82394i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 29.4275i | − | 0.0683819i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 284.698 | + | 284.698i | 0.628212 | + | 0.628212i | 0.947618 | − | 0.319406i | \(-0.103483\pi\) |
−0.319406 | + | 0.947618i | \(0.603483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 228.069 | − | 228.069i | 0.478709 | − | 0.478709i | −0.426010 | − | 0.904719i | \(-0.640081\pi\) |
0.904719 | + | 0.426010i | \(0.140081\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 69.0758 | 0.138139 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 582.338 | 1.11123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 139.151 | − | 139.151i | 0.253730 | − | 0.253730i | −0.568768 | − | 0.822498i | \(-0.692580\pi\) |
0.822498 | + | 0.568768i | \(0.192580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −105.541 | − | 105.541i | −0.184140 | − | 0.184140i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 453.655i | − | 0.758294i | −0.925336 | − | 0.379147i | \(-0.876217\pi\) | ||
0.925336 | − | 0.379147i | \(-0.123783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 259.747i | 0.416454i | 0.978081 | + | 0.208227i | \(0.0667692\pi\) | ||||
−0.978081 | + | 0.208227i | \(0.933231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.81740 | + | 7.81740i | 0.0120357 | + | 0.0120357i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −120.818 | + | 120.818i | −0.178811 | + | 0.178811i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −323.190 | −0.460275 | −0.230138 | − | 0.973158i | \(-0.573918\pi\) | ||||
−0.230138 | + | 0.973158i | \(0.573918\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −637.533 | −0.874531 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −563.897 | + | 563.897i | −0.745732 | + | 0.745732i | −0.973674 | − | 0.227943i | \(-0.926800\pi\) |
0.227943 | + | 0.973674i | \(0.426800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 596.368 | + | 596.368i | 0.761002 | + | 0.761002i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 99.9602i | 0.123182i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 866.853i | − | 1.03243i | −0.856459 | − | 0.516215i | \(-0.827341\pi\) | ||
0.856459 | − | 0.516215i | \(-0.172659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 94.5697 | + | 94.5697i | 0.108941 | + | 0.108941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −142.790 | + | 142.790i | −0.159211 | + | 0.159211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −319.866 | −0.345448 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −936.077 | −0.979837 | −0.489919 | − | 0.871768i | \(-0.662974\pi\) | ||||
−0.489919 | + | 0.871768i | \(0.662974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1169.18 | − | 1169.18i | 1.18694 | − | 1.18694i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.58844 | + | 1.58844i | 0.00156491 | + | 0.00156491i | 0.707889 | − | 0.706324i | \(-0.249648\pi\) |
−0.706324 | + | 0.707889i | \(0.749648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1388.28i | − | 1.32807i | −0.747700 | − | 0.664036i | \(-0.768842\pi\) | ||
0.747700 | − | 0.664036i | \(-0.231158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 33.2635i | 0.0309160i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −821.526 | − | 821.526i | −0.742243 | − | 0.742243i | 0.230767 | − | 0.973009i | \(-0.425877\pi\) |
−0.973009 | + | 0.230767i | \(0.925877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −532.797 | + | 532.797i | −0.468190 | + | 0.468190i | −0.901328 | − | 0.433138i | \(-0.857406\pi\) |
0.433138 | + | 0.901328i | \(0.357406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 127.237 | 0.108800 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −67.2680 | −0.0560003 | −0.0280002 | − | 0.999608i | \(-0.508914\pi\) | ||||
−0.0280002 | + | 0.999608i | \(0.508914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1147.19 | + | 1147.19i | −0.930230 | + | 0.930230i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −915.168 | − | 915.168i | −0.723140 | − | 0.723140i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 193.696i | 0.149211i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2758.92i | 2.07282i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −79.1808 | − | 79.1808i | −0.0580447 | − | 0.0580447i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −943.262 | + | 943.262i | −0.674943 | + | 0.674943i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1903.59 | −1.33005 | −0.665026 | − | 0.746820i | \(-0.731579\pi\) | ||||
−0.665026 | + | 0.746820i | \(0.731579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −47.6552 | −0.0325257 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 918.430 | − | 918.430i | 0.612546 | − | 0.612546i | −0.331062 | − | 0.943609i | \(-0.607407\pi\) |
0.943609 | + | 0.331062i | \(0.107407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −51.9451 | − | 51.9451i | −0.0338662 | − | 0.0338662i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 658.054i | − | 0.419528i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 477.234i | − | 0.297612i | −0.988866 | − | 0.148806i | \(-0.952457\pi\) | ||
0.988866 | − | 0.148806i | \(-0.0475430\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1513.89 | − | 1513.89i | −0.923788 | − | 0.923788i | 0.0735064 | − | 0.997295i | \(-0.476581\pi\) |
−0.997295 | + | 0.0735064i | \(0.976581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 369.421 | − | 369.421i | 0.220644 | − | 0.220644i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3201.37 | 1.87211 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1086.53 | 0.622285 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 254.172 | − | 254.172i | 0.142611 | − | 0.142611i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −375.353 | − | 375.353i | −0.206377 | − | 0.206377i | 0.596349 | − | 0.802725i | \(-0.296618\pi\) |
−0.802725 | + | 0.596349i | \(0.796618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2997.52i | 1.61546i | 0.589553 | + | 0.807730i | \(0.299304\pi\) | ||||
−0.589553 | + | 0.807730i | \(0.700696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1874.43i | − | 0.990451i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1552.07 | + | 1552.07i | 0.804293 | + | 0.804293i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1509.01 | − | 1509.01i | 0.767082 | − | 0.767082i | −0.210510 | − | 0.977592i | \(-0.567512\pi\) |
0.977592 | + | 0.210510i | \(0.0675125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −226.368 | −0.112906 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −372.601 | −0.182392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1425.19 | + | 1425.19i | −0.684844 | + | 0.684844i | −0.961088 | − | 0.276244i | \(-0.910910\pi\) |
0.276244 | + | 0.961088i | \(0.410910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 563.017 | + | 563.017i | 0.265641 | + | 0.265641i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 792.415i | − | 0.367179i | −0.983003 | − | 0.183590i | \(-0.941228\pi\) | ||
0.983003 | − | 0.183590i | \(-0.0587717\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 308.861i | − | 0.140583i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 502.682 | + | 502.682i | 0.224802 | + | 0.224802i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 773.594 | − | 773.594i | 0.339972 | − | 0.339972i | −0.516384 | − | 0.856357i | \(-0.672722\pi\) |
0.856357 | + | 0.516384i | \(0.172722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.5984 | 0.0119214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 430.905 | 0.182988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 426.050 | − | 426.050i | 0.177902 | − | 0.177902i | −0.612539 | − | 0.790441i | \(-0.709852\pi\) |
0.790441 | + | 0.612539i | \(0.209852\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2618.06 | + | 2618.06i | 1.07513 | + | 1.07513i | 0.996938 | + | 0.0781951i | \(0.0249157\pi\) |
0.0781951 | + | 0.996938i | \(0.475084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 345.194i | − | 0.139440i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1383.02i | − | 0.549631i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3278.50 | + | 3278.50i | 1.28207 | + | 1.28207i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 106.866 | − | 106.866i | 0.0411288 | − | 0.0411288i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3216.39 | −1.21848 | −0.609240 | − | 0.792986i | \(-0.708525\pi\) | ||||
−0.609240 | + | 0.792986i | \(0.708525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2852.57 | 1.06390 | 0.531950 | − | 0.846776i | \(-0.321459\pi\) | ||||
0.531950 | + | 0.846776i | \(0.321459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 440.700 | − | 440.700i | 0.161842 | − | 0.161842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1609.02 | − | 1609.02i | −0.581918 | − | 0.581918i | 0.353512 | − | 0.935430i | \(-0.384987\pi\) |
−0.935430 | + | 0.353512i | \(0.884987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 747.136i | 0.266146i | 0.991106 | + | 0.133073i | \(0.0424845\pi\) | ||||
−0.991106 | + | 0.133073i | \(0.957516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 210.612i | − | 0.0739074i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 176.449 | + | 176.449i | 0.0610062 | + | 0.0610062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −860.666 | + | 860.666i | −0.293227 | + | 0.293227i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3605.73 | 1.21070 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1758.44 | −0.581981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2227.13 | + | 2227.13i | −0.726645 | + | 0.726645i | −0.969950 | − | 0.243305i | \(-0.921769\pi\) |
0.243305 | + | 0.969950i | \(0.421769\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −343.315 | − | 343.315i | −0.110439 | − | 0.110439i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 517.995i | 0.164311i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 504.102i | 0.157699i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 196.570 | + | 196.570i | 0.0606530 | + | 0.0606530i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2566.23 | − | 2566.23i | 0.781102 | − | 0.781102i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 358.053 | 0.107520 | 0.0537601 | − | 0.998554i | \(-0.482879\pi\) | ||||
0.0537601 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −267.075 | −0.0791332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3455.40 | − | 3455.40i | 1.01032 | − | 1.01032i | 0.0103741 | − | 0.999946i | \(-0.496698\pi\) |
0.999946 | − | 0.0103741i | \(-0.00330223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1430.03 | + | 1430.03i | 0.412659 | + | 0.412659i | 0.882664 | − | 0.470005i | \(-0.155748\pi\) |
−0.470005 | + | 0.882664i | \(0.655748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 182.864i | 0.0520847i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 926.479i | 0.260496i | 0.991481 | + | 0.130248i | \(0.0415774\pi\) | ||||
−0.991481 | + | 0.130248i | \(0.958423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4015.47 | − | 4015.47i | −1.11464 | − | 1.11464i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −244.583 | + | 244.583i | −0.0670352 | + | 0.0670352i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 792.472 | 0.214480 | 0.107240 | − | 0.994233i | \(-0.465799\pi\) | ||||
0.107240 | + | 0.994233i | \(0.465799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1449.01 | 0.387299 | 0.193650 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1562.44 | + | 1562.44i | −0.412473 | + | 0.412473i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2762.76 | − | 2762.76i | −0.720433 | − | 0.720433i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1376.42i | 0.354572i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 853.487i | 0.217219i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3580.04 | − | 3580.04i | −0.900280 | − | 0.900280i | 0.0951802 | − | 0.995460i | \(-0.469657\pi\) |
−0.995460 | + | 0.0951802i | \(0.969657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6306.64 | + | 6306.64i | −1.56717 | + | 1.56717i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 902.634 | 0.221667 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4708.87 | −1.14292 | −0.571461 | − | 0.820629i | \(-0.693623\pi\) | ||||
−0.571461 | + | 0.820629i | \(0.693623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 224.598 | − | 224.598i | 0.0538835 | − | 0.0538835i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1707.53 | − | 1707.53i | −0.404955 | − | 0.404955i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2967.82i | − | 0.695830i | −0.937526 | − | 0.347915i | \(-0.886890\pi\) | ||
0.937526 | − | 0.347915i | \(-0.113110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2460.53i | 0.570374i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −656.013 | − | 656.013i | −0.150365 | − | 0.150365i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 663.633 | − | 663.633i | 0.150418 | − | 0.150418i | −0.627887 | − | 0.778305i | \(-0.716080\pi\) |
0.778305 | + | 0.627887i | \(0.216080\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8058.74 | −1.80640 | −0.903199 | − | 0.429223i | \(-0.858788\pi\) | ||||
−0.903199 | + | 0.429223i | \(0.858788\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 143.136 | 0.0317326 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 467.130 | − | 467.130i | 0.102433 | − | 0.102433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −482.477 | − | 482.477i | −0.104654 | − | 0.104654i | 0.652841 | − | 0.757495i | \(-0.273577\pi\) |
−0.757495 | + | 0.652841i | \(0.773577\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4878.29i | − | 1.04679i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5899.10i | 1.25235i | 0.779682 | + | 0.626175i | \(0.215381\pi\) | ||||
−0.779682 | + | 0.626175i | \(0.784619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −679.897 | − | 679.897i | −0.142812 | − | 0.142812i | 0.632086 | − | 0.774898i | \(-0.282199\pi\) |
−0.774898 | + | 0.632086i | \(0.782199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −242.067 | + | 242.067i | −0.0503116 | + | 0.0503116i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −279.538 | −0.0574935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 343.118 | 0.0698388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −708.401 | + | 708.401i | −0.142705 | + | 0.142705i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3552.87 | + | 3552.87i | 0.708398 | + | 0.708398i | 0.966198 | − | 0.257800i | \(-0.0829976\pi\) |
−0.257800 | + | 0.966198i | \(0.582998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4683.78i | − | 0.924407i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3617.62i | − | 0.706786i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4936.50 | + | 4936.50i | 0.954799 | + | 0.954799i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −84.1205 | + | 84.1205i | −0.0161084 | + | 0.0161084i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.40419 | 0.000455831 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3752.13 | −0.704415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2735.56 | − | 2735.56i | 0.508556 | − | 0.508556i | −0.405527 | − | 0.914083i | \(-0.632912\pi\) |
0.914083 | + | 0.405527i | \(0.132912\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1050.62 | − | 1050.62i | −0.193423 | − | 0.193423i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5796.70i | 1.05692i | 0.848960 | + | 0.528458i | \(0.177229\pi\) | ||||
−0.848960 | + | 0.528458i | \(0.822771\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8362.62i | − | 1.51017i | −0.655627 | − | 0.755085i | \(-0.727596\pi\) | ||
0.655627 | − | 0.755085i | \(-0.272404\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −568.209 | − | 568.209i | −0.101635 | − | 0.101635i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 344.406 | − | 344.406i | 0.0610214 | − | 0.0610214i | −0.675938 | − | 0.736959i | \(-0.736261\pi\) |
0.736959 | + | 0.675938i | \(0.236261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5973.13 | 1.04837 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1243.42 | −0.216203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1409.58 | + | 1409.58i | −0.242820 | + | 0.242820i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −365.644 | − | 365.644i | −0.0624071 | − | 0.0624071i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 806.416i | 0.136376i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 1304.20i | − | 0.218549i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2687.86 | + | 2687.86i | 0.446339 | + | 0.446339i | 0.894135 | − | 0.447797i | \(-0.147791\pi\) |
−0.447797 | + | 0.894135i | \(0.647791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2173.47 | + | 2173.47i | −0.357675 | + | 0.357675i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2289.27 | −0.373361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1795.31 | −0.290199 | −0.145099 | − | 0.989417i | \(-0.546350\pi\) | ||||
−0.145099 | + | 0.989417i | \(0.546350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −50.9068 | + | 50.9068i | −0.00815598 | + | 0.00815598i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8532.42 | + | 8532.42i | 1.35500 | + | 1.35500i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1813.72i | − | 0.285515i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1736.34i | 0.270960i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1967.33 | − | 1967.33i | −0.304357 | − | 0.304357i | 0.538359 | − | 0.842716i | \(-0.319045\pi\) |
−0.842716 | + | 0.538359i | \(0.819045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7363.37 | − | 7363.37i | 1.12938 | − | 1.12938i | 0.139097 | − | 0.990279i | \(-0.455580\pi\) |
0.990279 | − | 0.139097i | \(-0.0444200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2831.68 | −0.430609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10644.3 | 1.60493 | 0.802466 | − | 0.596698i | \(-0.203521\pi\) | ||||
0.802466 | + | 0.596698i | \(0.203521\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3731.70 | + | 3731.70i | −0.557911 | + | 0.557911i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 146.585 | + | 146.585i | 0.0217313 | + | 0.0217313i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7459.42i | 1.09664i | 0.836269 | + | 0.548319i | \(0.184732\pi\) | ||||
−0.836269 | + | 0.548319i | \(0.815268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6102.96i | 0.889775i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2087.89 | + | 2087.89i | 0.301889 | + | 0.301889i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2136.65 | − | 2136.65i | 0.306403 | − | 0.306403i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6251.35 | 0.889149 | 0.444574 | − | 0.895742i | \(-0.353355\pi\) | ||||
0.444574 | + | 0.895742i | \(0.353355\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2705.14 | 0.381637 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −399.582 | + | 399.582i | −0.0559171 | + | 0.0559171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8911.86 | − | 8911.86i | −1.23710 | − | 1.23710i | −0.961180 | − | 0.275921i | \(-0.911017\pi\) |
−0.275921 | − | 0.961180i | \(-0.588983\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1427.68i | 0.196600i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4675.45i | − | 0.638721i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1184.03 | + | 1184.03i | 0.160473 | + | 0.160473i | 0.782776 | − | 0.622303i | \(-0.213803\pi\) |
−0.622303 | + | 0.782776i | \(0.713803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1440.59 | + | 1440.59i | −0.193711 | + | 0.193711i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2880.38 | 0.384283 | 0.192142 | − | 0.981367i | \(-0.438457\pi\) | ||||
0.192142 | + | 0.981367i | \(0.438457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1987.66 | 0.263119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 814.050 | − | 814.050i | 0.106926 | − | 0.106926i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9244.24 | − | 9244.24i | −1.20489 | − | 1.20489i | −0.972662 | − | 0.232226i | \(-0.925399\pi\) |
−0.232226 | − | 0.972662i | \(-0.574601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10110.9i | 1.30774i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1390.09i | − | 0.178424i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2658.52 | + | 2658.52i | 0.338645 | + | 0.338645i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4257.80 | − | 4257.80i | 0.538270 | − | 0.538270i | −0.384751 | − | 0.923020i | \(-0.625713\pi\) |
0.923020 | + | 0.384751i | \(0.125713\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −78.6216 | −0.00986467 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12722.6 | 1.58437 | 0.792187 | − | 0.610278i | \(-0.208942\pi\) | ||||
0.792187 | + | 0.610278i | \(0.208942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6678.72 | − | 6678.72i | 0.825535 | − | 0.825535i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5244.26 | + | 5244.26i | 0.643431 | + | 0.643431i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7603.08i | − | 0.925972i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 232.991i | − | 0.0281678i | −0.999901 | − | 0.0140839i | \(-0.995517\pi\) | ||
0.999901 | − | 0.0140839i | \(-0.00448320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −361.159 | − | 361.159i | −0.0433447 | − | 0.0433447i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 760.629 | − | 760.629i | 0.0906250 | − | 0.0906250i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9277.08 | 1.09734 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2291.35 | −0.269084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6125.69 | + | 6125.69i | −0.714223 | + | 0.714223i | −0.967416 | − | 0.253193i | \(-0.918519\pi\) |
0.253193 | + | 0.967416i | \(0.418519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8308.44 | + | 8308.44i | 0.961825 | + | 0.961825i | 0.999298 | − | 0.0374725i | \(-0.0119307\pi\) |
−0.0374725 | + | 0.999298i | \(0.511931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12620.9i | 1.45071i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 748.907i | − | 0.0854760i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −609.333 | − | 609.333i | −0.0690579 | − | 0.0690579i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2422.72 | − | 2422.72i | 0.272657 | − | 0.272657i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8737.57 | −0.976506 | −0.488253 | − | 0.872702i | \(-0.662366\pi\) | ||||
−0.488253 | + | 0.872702i | \(0.662366\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11627.5 | −1.29049 | −0.645247 | − | 0.763974i | \(-0.723245\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 822.260 | − | 822.260i | 0.0906306 | − | 0.0906306i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2711.51 | − | 2711.51i | −0.296817 | − | 0.296817i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 17631.8i | − | 1.91690i | −0.285261 | − | 0.958450i | \(-0.592080\pi\) | ||
0.285261 | − | 0.958450i | \(-0.407920\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8683.57i | 0.937649i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4549.81 | − | 4549.81i | −0.487964 | − | 0.487964i | 0.419699 | − | 0.907663i | \(-0.362136\pi\) |
−0.907663 | + | 0.419699i | \(0.862136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7130.62 | + | 7130.62i | −0.759604 | + | 0.759604i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −568.116 | −0.0601140 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12926.5 | −1.35867 | −0.679334 | − | 0.733830i | \(-0.737731\pi\) | ||||
−0.679334 | + | 0.733830i | \(0.737731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4731.46 | + | 4731.46i | −0.494004 | + | 0.494004i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2268.45 | + | 2268.45i | 0.235278 | + | 0.235278i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1555.84i | − | 0.160305i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9320.32i | − | 0.954018i | −0.878898 | − | 0.477009i | \(-0.841721\pi\) | ||
0.878898 | − | 0.477009i | \(-0.158279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2899.90 | − | 2899.90i | −0.294892 | − | 0.294892i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12885.0 | + | 12885.0i | −1.30177 | + | 1.30177i | −0.374566 | + | 0.927200i | \(0.622208\pi\) |
−0.927200 | + | 0.374566i | \(0.877792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7038.37 | −0.706482 | −0.353241 | − | 0.935532i | \(-0.614920\pi\) | ||||
−0.353241 | + | 0.935532i | \(0.614920\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2349.14 | 0.234277 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6001.76 | − | 6001.76i | 0.594707 | − | 0.594707i | −0.344192 | − | 0.938899i | \(-0.611847\pi\) |
0.938899 | + | 0.344192i | \(0.111847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −371.769 | − | 371.769i | −0.0366028 | − | 0.0366028i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2283.96i | − | 0.223438i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2847.65i | 0.276818i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 200.840 | + | 200.840i | 0.0194004 | + | 0.0194004i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3866.82 | − | 3866.82i | 0.371173 | − | 0.371173i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 587.317 | 0.0560234 | 0.0280117 | − | 0.999608i | \(-0.491082\pi\) | ||||
0.0280117 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5951.28 | −0.564148 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −281.975 | + | 281.975i | −0.0265638 | + | 0.0265638i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7700.05 | + | 7700.05i | 0.720910 | + | 0.720910i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8366.45i | − | 0.778481i | −0.921136 | − | 0.389240i | \(-0.872738\pi\) | ||
0.921136 | − | 0.389240i | \(-0.127262\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2157.10i | 0.199483i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1529.30 | + | 1529.30i | 0.140563 | + | 0.140563i | 0.773887 | − | 0.633324i | \(-0.218310\pi\) |
−0.633324 | + | 0.773887i | \(0.718310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4788.09 | − | 4788.09i | 0.437413 | − | 0.437413i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19235.0 | −1.74656 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1212.03 | −0.109390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11364.5 | − | 11364.5i | 1.01952 | − | 1.01952i | 0.0197191 | − | 0.999806i | \(-0.493723\pi\) |
0.999806 | − | 0.0197191i | \(-0.00627718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −599.681 | − | 599.681i | −0.0534766 | − | 0.0534766i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12570.2i | − | 1.11427i | −0.830421 | − | 0.557137i | \(-0.811900\pi\) | ||
0.830421 | − | 0.557137i | \(-0.188100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 26.1326i | − | 0.00230274i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −233.738 | − | 233.738i | −0.0204747 | − | 0.0204747i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11880.4 | + | 11880.4i | −1.03456 | + | 1.03456i | −0.0351750 | + | 0.999381i | \(0.511199\pi\) |
−0.999381 | + | 0.0351750i | \(0.988801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 693.968 | 0.0600770 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1555.38 | 0.133863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11419.8 | + | 11419.8i | −0.977122 | + | 0.977122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22074.8 | − | 22074.8i | −1.87785 | − | 1.87785i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1170.87i | − | 0.0990283i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6612.98i | 0.556085i | 0.960569 | + | 0.278042i | \(0.0896856\pi\) | ||||
−0.960569 | + | 0.278042i | \(0.910314\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5129.30 | + | 5129.30i | 0.428850 | + | 0.428850i | 0.888236 | − | 0.459387i | \(-0.151931\pi\) |
−0.459387 | + | 0.888236i | \(0.651931\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.8858 | − | 20.8858i | 0.00173625 | − | 0.00173625i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13679.3 | 1.13070 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7282.60 | −0.598553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7360.75 | + | 7360.75i | −0.601562 | + | 0.601562i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3703.53 | + | 3703.53i | 0.300972 | + | 0.300972i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13515.5i | 1.09220i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 644.849i | − | 0.0518199i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15188.1 | − | 15188.1i | −1.21372 | − | 1.21372i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10968.5 | − | 10968.5i | 0.871672 | − | 0.871672i | −0.120983 | − | 0.992655i | \(-0.538605\pi\) |
0.992655 | + | 0.120983i | \(0.0386047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3962.57 | 0.313168 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8765.44 | 0.688936 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13088.8 | − | 13088.8i | 1.02311 | − | 1.02311i | 0.0233784 | − | 0.999727i | \(-0.492558\pi\) |
0.999727 | − | 0.0233784i | \(-0.00744226\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5896.63 | + | 5896.63i | 0.458401 | + | 0.458401i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2568.12i | 0.198558i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 863.469i | 0.0663986i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1046.64 | − | 1046.64i | −0.0800491 | − | 0.0800491i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5049.87 | + | 5049.87i | −0.384147 | + | 0.384147i | −0.872594 | − | 0.488447i | \(-0.837564\pi\) |
0.488447 | + | 0.872594i | \(0.337564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2228.98 | 0.168651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4962.18 | 0.373446 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3249.06 | + | 3249.06i | −0.243217 | + | 0.243217i | −0.818180 | − | 0.574962i | \(-0.805017\pi\) |
0.574962 | + | 0.818180i | \(0.305017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 553.338 | + | 553.338i | 0.0412019 | + | 0.0412019i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1703.30i | 0.126159i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2806.05i | − | 0.206741i | −0.994643 | − | 0.103371i | \(-0.967037\pi\) | ||
0.994643 | − | 0.103371i | \(-0.0329628\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12038.8 | − | 12038.8i | −0.882324 | − | 0.882324i | 0.111446 | − | 0.993770i | \(-0.464452\pi\) |
−0.993770 | + | 0.111446i | \(0.964452\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2434.08 | + | 2434.08i | −0.177461 | + | 0.177461i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1440.62 | 0.104484 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7206.84 | 0.519973 | 0.259987 | − | 0.965612i | \(-0.416282\pi\) | ||||
0.259987 | + | 0.965612i | \(0.416282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2158.76 | − | 2158.76i | 0.154948 | − | 0.154948i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1506.57 | + | 1506.57i | 0.107578 | + | 0.107578i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13526.6i | 0.960918i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15056.1i | 1.06409i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10377.0 | + | 10377.0i | 0.729647 | + | 0.729647i | 0.970549 | − | 0.240903i | \(-0.0774435\pi\) |
−0.240903 | + | 0.970549i | \(0.577443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3668.48 | + | 3668.48i | −0.256633 | + | 0.256633i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2435.33 | −0.169503 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4758.60 | −0.329531 | −0.164766 | − | 0.986333i | \(-0.552687\pi\) | ||||
−0.164766 | + | 0.986333i | \(0.552687\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1593.32 | − | 1593.32i | 0.109781 | − | 0.109781i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 565.414 | + | 565.414i | 0.0387619 | + | 0.0387619i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14256.4i | 0.972455i | 0.873832 | + | 0.486227i | \(0.161627\pi\) | ||||
−0.873832 | + | 0.486227i | \(0.838373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10385.2i | − | 0.704862i | −0.935838 | − | 0.352431i | \(-0.885355\pi\) | ||
0.935838 | − | 0.352431i | \(-0.114645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3597.68 | + | 3597.68i | 0.242966 | + | 0.242966i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22694.5 | − | 22694.5i | 1.52506 | − | 1.52506i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16243.6 | 1.08618 | 0.543088 | − | 0.839676i | \(-0.317255\pi\) | ||||
0.543088 | + | 0.839676i | \(0.317255\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 267.064 | 0.0177701 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17279.0 | + | 17279.0i | −1.14408 | + | 1.14408i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 500.502 | + | 500.502i | 0.0329773 | + | 0.0329773i | 0.723403 | − | 0.690426i | \(-0.242577\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1302.66i | 0.0854121i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11575.9i | − | 0.755316i | −0.925945 | − | 0.377658i | \(-0.876729\pi\) | ||
0.925945 | − | 0.377658i | \(-0.123271\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18356.1 | + | 18356.1i | 1.19191 | + | 1.19191i | 0.976530 | + | 0.215380i | \(0.0690992\pi\) |
0.215380 | + | 0.976530i | \(0.430901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5578.34 | − | 5578.34i | 0.360469 | − | 0.360469i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2315.98 | −0.148937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16809.5 | 1.07581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1330.75 | + | 1330.75i | −0.0847607 | + | 0.0847607i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6094.66 | − | 6094.66i | −0.386343 | − | 0.386343i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10224.8i | − | 0.645079i | −0.946556 | − | 0.322539i | \(-0.895463\pi\) | ||
0.946556 | − | 0.322539i | \(-0.104537\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3370.88i | 0.211660i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15658.7 | + | 15658.7i | 0.978578 | + | 0.978578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11888.4 | + | 11888.4i | −0.739461 | + | 0.739461i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11729.0 | 0.726125 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19804.4 | 1.22032 | 0.610162 | − | 0.792277i | \(-0.291104\pi\) | ||||
0.610162 | + | 0.792277i | \(0.291104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15680.7 | − | 15680.7i | 0.961723 | − | 0.961723i | −0.0375712 | − | 0.999294i | \(-0.511962\pi\) |
0.999294 | + | 0.0375712i | \(0.0119621\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 392.006 | + | 392.006i | 0.0239306 | + | 0.0239306i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9232.26i | − | 0.560985i | −0.959856 | − | 0.280493i | \(-0.909502\pi\) | ||
0.959856 | − | 0.280493i | \(-0.0904978\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25748.8i | − | 1.55736i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 381.492 | + | 381.492i | 0.0229675 | + | 0.0229675i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19697.9 | − | 19697.9i | 1.18046 | − | 1.18046i | 0.200833 | − | 0.979626i | \(-0.435635\pi\) |
0.979626 | − | 0.200833i | \(-0.0643648\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15109.8 | −0.901355 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6715.66 | −0.398786 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3888.06 | − | 3888.06i | 0.229829 | − | 0.229829i | −0.582792 | − | 0.812621i | \(-0.698040\pi\) |
0.812621 | + | 0.582792i | \(0.198040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8110.20 | + | 8110.20i | 0.477232 | + | 0.477232i | 0.904245 | − | 0.427013i | \(-0.140434\pi\) |
−0.427013 | + | 0.904245i | \(0.640434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3884.13i | − | 0.227522i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 854.587i | 0.0498338i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9210.54 | + | 9210.54i | 0.534683 | + | 0.534683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 270.966 | − | 270.966i | 0.0156594 | − | 0.0156594i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20627.1 | −1.18674 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28428.2 | −1.62827 | −0.814135 | − | 0.580676i | \(-0.802788\pi\) | ||||
−0.814135 | + | 0.580676i | \(0.802788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −413.186 | + | 413.186i | −0.0235608 | + | 0.0235608i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16967.4 | + | 16967.4i | 0.963235 | + | 0.963235i | 0.999348 | − | 0.0361128i | \(-0.0114975\pi\) |
−0.0361128 | + | 0.999348i | \(0.511498\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2500.92i | 0.141350i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 5229.92i | − | 0.294289i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9550.16 | − | 9550.16i | −0.535032 | − | 0.535032i | 0.387034 | − | 0.922066i | \(-0.373500\pi\) |
−0.922066 | + | 0.387034i | \(0.873500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3925.66 | + | 3925.66i | −0.218966 | + | 0.218966i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2164.42 | 0.120201 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10587.9 | 0.585439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20859.7 | + | 20859.7i | −1.14839 | + | 1.14839i | −0.161527 | + | 0.986868i | \(0.551642\pi\) |
−0.986868 | + | 0.161527i | \(0.948358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3123.70 | − | 3123.70i | −0.171226 | − | 0.171226i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24906.1i | 1.35934i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7585.52i | 0.412227i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 701.137 | + | 701.137i | 0.0379391 | + | 0.0379391i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23495.4 | + | 23495.4i | −1.26592 | + | 1.26592i | −0.317740 | + | 0.948178i | \(0.602924\pi\) |
−0.948178 | + | 0.317740i | \(0.897076\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3268.91 | 0.175376 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6077.62 | −0.324676 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.24384 | − | 4.24384i | 0.000225751 | − | 0.000225751i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4559.45 | − | 4559.45i | −0.241515 | − | 0.241515i | 0.575962 | − | 0.817477i | \(-0.304628\pi\) |
−0.817477 | + | 0.575962i | \(0.804628\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8355.95i | − | 0.440749i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26313.9i | 1.38214i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26334.1 | − | 26334.1i | −1.37740 | − | 1.37740i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 599.724 | − | 599.724i | 0.0312372 | − | 0.0312372i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6494.67 | 0.336871 | 0.168436 | − | 0.985713i | \(-0.446128\pi\) | ||||
0.168436 | + | 0.985713i | \(0.446128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3709.08 | −0.191586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1096.58 | − | 1096.58i | 0.0564069 | − | 0.0564069i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −682.221 | − | 682.221i | −0.0349476 | − | 0.0349476i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24866.4i | − | 1.26856i | −0.773103 | − | 0.634280i | \(-0.781296\pi\) | ||
0.773103 | − | 0.634280i | \(-0.218704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 14848.5i | − | 0.754384i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2282.68 | + | 2282.68i | 0.115497 | + | 0.115497i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14914.3 | − | 14914.3i | 0.751533 | − | 0.751533i | −0.223232 | − | 0.974765i | \(-0.571661\pi\) |
0.974765 | + | 0.223232i | \(0.0716607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4181.58 | −0.209850 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12585.1 | −0.629008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8451.86 | − | 8451.86i | 0.420713 | − | 0.420713i | −0.464737 | − | 0.885449i | \(-0.653851\pi\) |
0.885449 | + | 0.464737i | \(0.153851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1041.64 | + | 1041.64i | 0.0516404 | + | 0.0516404i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5622.43i | − | 0.277614i | −0.990319 | − | 0.138807i | \(-0.955673\pi\) | ||
0.990319 | − | 0.138807i | \(-0.0443267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6175.21i | 0.303681i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14579.3 | − | 14579.3i | −0.714095 | − | 0.714095i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2194.88 | + | 2194.88i | −0.107075 | + | 0.107075i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32314.9 | 1.57016 | 0.785079 | − | 0.619396i | \(-0.212622\pi\) | ||||
0.785079 | + | 0.619396i | \(0.212622\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5418.58 | −0.262236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24657.2 | − | 24657.2i | 1.18857 | − | 1.18857i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12692.8 | − | 12692.8i | −0.609418 | − | 0.609418i | 0.333376 | − | 0.942794i | \(-0.391812\pi\) |
−0.942794 | + | 0.333376i | \(0.891812\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9545.42i | 0.456491i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13108.2i | 0.624404i | 0.950016 | + | 0.312202i | \(0.101067\pi\) | ||||
−0.950016 | + | 0.312202i | \(0.898933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1423.48 | + | 1423.48i | 0.0675404 | + | 0.0675404i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15418.8 | + | 15418.8i | −0.728718 | + | 0.728718i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20154.8 | −0.948822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23661.2 | 1.10955 | 0.554776 | − | 0.832000i | \(-0.312804\pi\) | ||||
0.554776 | + | 0.832000i | \(0.312804\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3563.56 | + | 3563.56i | −0.166457 | + | 0.166457i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21370.5 | − | 21370.5i | −0.994362 | − | 0.994362i | 0.00562228 | − | 0.999984i | \(-0.498210\pi\) |
−0.999984 | + | 0.00562228i | \(0.998210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1949.06i | − | 0.0903384i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 339.940i | − | 0.0156954i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2034.27 | − | 2034.27i | −0.0935627 | − | 0.0935627i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20514.8 | + | 20514.8i | −0.939921 | + | 0.939921i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5283.35 | −0.241139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24825.8 | −1.12875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20890.9 | + | 20890.9i | −0.946226 | + | 0.946226i | −0.998626 | − | 0.0524002i | \(-0.983313\pi\) |
0.0524002 | + | 0.998626i | \(0.483313\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2245.97 | − | 2245.97i | −0.101342 | − | 0.101342i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 179.720i | 0.00807853i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16145.8i | 0.723020i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1862.07 | + | 1862.07i | 0.0830702 | + | 0.0830702i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6834.83 | − | 6834.83i | 0.303767 | − | 0.303767i | −0.538719 | − | 0.842486i | \(-0.681092\pi\) |
0.842486 | + | 0.538719i | \(0.181092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35390.5 | −1.56699 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22412.1 | 0.988631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11746.1 | − | 11746.1i | 0.516203 | − | 0.516203i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3064.97 | + | 3064.97i | 0.134194 | + | 0.134194i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1004.44i | − | 0.0438142i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15807.0i | 0.686952i | 0.939162 | + | 0.343476i | \(0.111604\pi\) | ||||
−0.939162 | + | 0.343476i | \(0.888396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11522.7 | − | 11522.7i | −0.498910 | − | 0.498910i | 0.412189 | − | 0.911099i | \(-0.364764\pi\) |
−0.911099 | + | 0.412189i | \(0.864764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6098.66 | + | 6098.66i | −0.263087 | + | 0.263087i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23446.9 | 1.00774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1224.33 | −0.0524284 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2445.06 | + | 2445.06i | −0.104319 | + | 0.104319i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −308.824 | − | 308.824i | −0.0131279 | − | 0.0131279i | 0.700512 | − | 0.713640i | \(-0.252955\pi\) |
−0.713640 | + | 0.700512i | \(0.752955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5633.49i | − | 0.238604i | −0.992858 | − | 0.119302i | \(-0.961934\pi\) | ||
0.992858 | − | 0.119302i | \(-0.0380656\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 707.026i | − | 0.0298369i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15835.5 | − | 15835.5i | −0.665844 | − | 0.665844i | 0.290908 | − | 0.956751i | \(-0.406043\pi\) |
−0.956751 | + | 0.290908i | \(0.906043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6200.19 | − | 6200.19i | 0.259761 | − | 0.259761i | −0.565196 | − | 0.824957i | \(-0.691199\pi\) |
0.824957 | + | 0.565196i | \(0.191199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −730.253 | −0.0304840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24349.7 | −1.01281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6518.30 | + | 6518.30i | −0.270150 | + | 0.270150i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7547.09 | − | 7547.09i | −0.311668 | − | 0.311668i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 30644.3i | − | 1.26098i | −0.776199 | − | 0.630488i | \(-0.782855\pi\) | ||
0.776199 | − | 0.630488i | \(-0.217145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15665.5i | 0.642319i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4464.29 | + | 4464.29i | 0.182394 | + | 0.182394i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2540.65 | + | 2540.65i | −0.103433 | + | 0.103433i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7371.03 | 0.299022 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1029.06 | −0.0415986 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11723.9 | − | 11723.9i | 0.472256 | − | 0.472256i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30801.0 | + | 30801.0i | 1.23635 | + | 1.23635i | 0.961482 | + | 0.274869i | \(0.0886346\pi\) |
0.274869 | + | 0.961482i | \(0.411365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8270.00i | − | 0.330793i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 41788.5i | − | 1.66566i | −0.553533 | − | 0.832828i | \(-0.686721\pi\) | ||
0.553533 | − | 0.832828i | \(-0.313279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11914.5 | + | 11914.5i | 0.473243 | + | 0.473243i | 0.902963 | − | 0.429719i | \(-0.141388\pi\) |
−0.429719 | + | 0.902963i | \(0.641388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −211.548 | + | 211.548i | −0.00837344 | + | 0.00837344i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27636.7 | −1.09011 | −0.545054 | − | 0.838401i | \(-0.683491\pi\) | ||||
−0.545054 | + | 0.838401i | \(0.683491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12727.0 | −0.500266 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 259.664 | − | 259.664i | 0.0101714 | − | 0.0101714i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14615.1 | + | 14615.1i | 0.570520 | + | 0.570520i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9850.95i | 0.383223i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 24201.9i | − | 0.938270i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2520.12 | + | 2520.12i | 0.0973663 | + | 0.0973663i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11918.3 | − | 11918.3i | 0.458896 | − | 0.458896i | −0.439397 | − | 0.898293i | \(-0.644808\pi\) |
0.898293 | + | 0.439397i | \(0.144808\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5377.45 | 0.206344 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13330.0 | −0.509759 | −0.254880 | − | 0.966973i | \(-0.582036\pi\) | ||||
−0.254880 | + | 0.966973i | \(0.582036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25172.1 | + | 25172.1i | −0.959353 | + | 0.959353i | −0.999206 | − | 0.0398530i | \(-0.987311\pi\) |
0.0398530 | + | 0.999206i | \(0.487311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3544.57 | − | 3544.57i | −0.134632 | − | 0.134632i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48821.3i | 1.84810i | 0.382278 | + | 0.924048i | \(0.375140\pi\) | ||||
−0.382278 | + | 0.924048i | \(0.624860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5085.84i | 0.191871i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28830.0 | + | 28830.0i | 1.08400 | + | 1.08400i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9490.96 | − | 9490.96i | 0.355658 | − | 0.355658i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7009.27 | −0.261781 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7471.64 | 0.278117 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12461.2 | − | 12461.2i | 0.462296 | − | 0.462296i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10843.0 | + | 10843.0i | 0.400924 | + | 0.400924i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 127.321i | 0.00469210i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 43071.7i | − | 1.58205i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5320.20 | + | 5320.20i | 0.194768 | + | 0.194768i | 0.797753 | − | 0.602985i | \(-0.206022\pi\) |
−0.602985 | + | 0.797753i | \(0.706022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.0685 | + | 41.0685i | −0.00149852 | + | 0.00149852i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26016.0 | 0.946155 | 0.473077 | − | 0.881021i | \(-0.343143\pi\) | ||||
0.473077 | + | 0.881021i | \(0.343143\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51000.2 | 1.84870 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2839.52 | + | 2839.52i | −0.102592 | + | 0.102592i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2453.77 | − | 2453.77i | −0.0883650 | − | 0.0883650i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24082.1i | 0.864413i | 0.901775 | + | 0.432206i | \(0.142265\pi\) | ||||
−0.901775 | + | 0.432206i | \(0.857735\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 4140.41i | − | 0.148134i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16057.9 | + | 16057.9i | 0.572646 | + | 0.572646i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −868.385 | + | 868.385i | −0.0308674 | + | 0.0308674i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35893.5 | 1.27173 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9324.93 | 0.329323 | 0.164661 | − | 0.986350i | \(-0.447347\pi\) | ||||
0.164661 | + | 0.986350i | \(0.447347\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6530.06 | − | 6530.06i | 0.229875 | − | 0.229875i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4386.80 | + | 4386.80i | 0.153931 | + | 0.153931i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 53937.0i | − | 1.88656i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15535.2i | 0.541636i | 0.962631 | + | 0.270818i | \(0.0872941\pi\) | ||||
−0.962631 | + | 0.270818i | \(0.912706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6328.63 | − | 6328.63i | −0.219944 | − | 0.219944i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34024.8 | − | 34024.8i | 1.17872 | − | 1.17872i | 0.198651 | − | 0.980070i | \(-0.436344\pi\) |
0.980070 | − | 0.198651i | \(-0.0636559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14591.8 | −0.503896 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1758.13 | −0.0605205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3816.02 | + | 3816.02i | −0.130944 | + | 0.130944i | −0.769541 | − | 0.638597i | \(-0.779515\pi\) |
0.638597 | + | 0.769541i | \(0.279515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9194.21 | − | 9194.21i | −0.314496 | − | 0.314496i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 521.277i | − | 0.0177745i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21759.7i | 0.739629i | 0.929106 | + | 0.369815i | \(0.120579\pi\) | ||||
−0.929106 | + | 0.369815i | \(0.879421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26457.6 | + | 26457.6i | 0.896489 | + | 0.896489i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4520.32 | − | 4520.32i | 0.152687 | − | 0.152687i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1275.03 | −0.0429331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5809.78 | 0.195018 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21240.2 | − | 21240.2i | 0.710754 | − | 0.710754i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23464.9 | − | 23464.9i | −0.782759 | − | 0.782759i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19338.5i | 0.643108i | 0.946891 | + | 0.321554i | \(0.104205\pi\) | ||||
−0.946891 | + | 0.321554i | \(0.895795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2133.47i | 0.0707294i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4184.92 | + | 4184.92i | 0.138311 | + | 0.138311i | 0.772873 | − | 0.634561i | \(-0.218819\pi\) |
−0.634561 | + | 0.772873i | \(0.718819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4044.67 | + | 4044.67i | −0.133264 | + | 0.133264i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −553.421 | −0.0181781 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17841.9 | 0.584249 | 0.292125 | − | 0.956380i | \(-0.405638\pi\) | ||||
0.292125 | + | 0.956380i | \(0.405638\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39200.2 | + | 39200.2i | −1.27972 | + | 1.27972i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13775.2 | − | 13775.2i | −0.448328 | − | 0.448328i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 61512.0i | 1.99586i | 0.0643304 | + | 0.997929i | \(0.479509\pi\) | ||||
−0.0643304 | + | 0.997929i | \(0.520491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26471.2i | 0.856286i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −986.984 | − | 986.984i | −0.0318298 | − | 0.0318298i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4391.05 | + | 4391.05i | −0.141180 | + | 0.141180i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1827.73 | −0.0585870 | −0.0292935 | − | 0.999571i | \(-0.509326\pi\) | ||||
−0.0292935 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4068.21 | 0.130011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6145.84 | − | 6145.84i | 0.195815 | − | 0.195815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25017.0 | + | 25017.0i | 0.794681 | + | 0.794681i | 0.982251 | − | 0.187570i | \(-0.0600611\pi\) |
−0.187570 | + | 0.982251i | \(0.560061\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6725.07i | 0.212985i |
(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 | 128.4.e.a.97.3 | 10 | ||
4.3 | odd | 2 | 128.4.e.b.97.3 | 10 | |||
8.3 | odd | 2 | 16.4.e.a.5.3 | ✓ | 10 | ||
8.5 | even | 2 | 64.4.e.a.49.3 | 10 | |||
16.3 | odd | 4 | 128.4.e.b.33.3 | 10 | |||
16.5 | even | 4 | 64.4.e.a.17.3 | 10 | |||
16.11 | odd | 4 | 16.4.e.a.13.3 | yes | 10 | ||
16.13 | even | 4 | inner | 128.4.e.a.33.3 | 10 | ||
24.5 | odd | 2 | 576.4.k.a.433.2 | 10 | |||
24.11 | even | 2 | 144.4.k.a.37.3 | 10 | |||
32.3 | odd | 8 | 1024.4.a.n.1.5 | 10 | |||
32.5 | even | 8 | 1024.4.b.k.513.6 | 10 | |||
32.11 | odd | 8 | 1024.4.b.j.513.6 | 10 | |||
32.13 | even | 8 | 1024.4.a.m.1.5 | 10 | |||
32.19 | odd | 8 | 1024.4.a.n.1.6 | 10 | |||
32.21 | even | 8 | 1024.4.b.k.513.5 | 10 | |||
32.27 | odd | 8 | 1024.4.b.j.513.5 | 10 | |||
32.29 | even | 8 | 1024.4.a.m.1.6 | 10 | |||
48.5 | odd | 4 | 576.4.k.a.145.2 | 10 | |||
48.11 | even | 4 | 144.4.k.a.109.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.3 | ✓ | 10 | 8.3 | odd | 2 | ||
16.4.e.a.13.3 | yes | 10 | 16.11 | odd | 4 | ||
64.4.e.a.17.3 | 10 | 16.5 | even | 4 | |||
64.4.e.a.49.3 | 10 | 8.5 | even | 2 | |||
128.4.e.a.33.3 | 10 | 16.13 | even | 4 | inner | ||
128.4.e.a.97.3 | 10 | 1.1 | even | 1 | trivial | ||
128.4.e.b.33.3 | 10 | 16.3 | odd | 4 | |||
128.4.e.b.97.3 | 10 | 4.3 | odd | 2 | |||
144.4.k.a.37.3 | 10 | 24.11 | even | 2 | |||
144.4.k.a.109.3 | 10 | 48.11 | even | 4 | |||
576.4.k.a.145.2 | 10 | 48.5 | odd | 4 | |||
576.4.k.a.433.2 | 10 | 24.5 | odd | 2 | |||
1024.4.a.m.1.5 | 10 | 32.13 | even | 8 | |||
1024.4.a.m.1.6 | 10 | 32.29 | even | 8 | |||
1024.4.a.n.1.5 | 10 | 32.3 | odd | 8 | |||
1024.4.a.n.1.6 | 10 | 32.19 | odd | 8 | |||
1024.4.b.j.513.5 | 10 | 32.27 | odd | 8 | |||
1024.4.b.j.513.6 | 10 | 32.11 | odd | 8 | |||
1024.4.b.k.513.5 | 10 | 32.21 | even | 8 | |||
1024.4.b.k.513.6 | 10 | 32.5 | even | 8 |