Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,4,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, 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("64.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.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: | \(3.77612224037\) |
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 | 17.3 | ||
Root | \(-1.62580 + 1.16481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 64.17 |
Dual form | 64.4.e.a.49.3 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | \(-0.282839\pi\) |
−0.776168 | + | 0.630526i | \(0.782839\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.22587 | − | 8.22587i | 0.735744 | − | 0.735744i | −0.236007 | − | 0.971751i | \(-0.575839\pi\) |
0.971751 | + | 0.236007i | \(0.0758389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.67171i | 0.144259i | 0.997395 | + | 0.0721293i | \(0.0229794\pi\) | ||||
−0.997395 | + | 0.0721293i | \(0.977021\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 25.8546i | − | 0.957577i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 45.2213 | − | 45.2213i | 1.23952 | − | 1.23952i | 0.279323 | − | 0.960197i | \(-0.409890\pi\) |
0.960197 | − | 0.279323i | \(-0.0901099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 35.3968 | + | 35.3968i | 0.755176 | + | 0.755176i | 0.975440 | − | 0.220264i | \(-0.0706918\pi\) |
−0.220264 | + | 0.975440i | \(0.570692\pi\) | |||||||
\(14\) | 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 | \(-0.303085\pi\) |
−0.814676 | + | 0.579916i | \(0.803085\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.02188 | − | 2.02188i | 0.0210100 | − | 0.0210100i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 139.462i | 1.26434i | 0.774830 | + | 0.632170i | \(0.217835\pi\) | ||||
−0.774830 | + | 0.632170i | \(0.782165\pi\) | |||||||
\(24\) | 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 | \(-0.153336\pi\) |
−0.463304 | + | 0.886199i | \(0.653336\pi\) | |||||||
\(30\) | 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 | \(-0.835081\pi\) |
0.495237 | + | 0.868758i | \(0.335081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 53.5748i | − | 0.219970i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 104.629i | 0.398545i | 0.979944 | + | 0.199272i | \(0.0638578\pi\) | ||||
−0.979944 | + | 0.199272i | \(0.936142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.4857 | − | 31.4857i | 0.111663 | − | 0.111663i | −0.649067 | − | 0.760731i | \(-0.724841\pi\) |
0.760731 | + | 0.649067i | \(0.224841\pi\) | |||||||
\(44\) | 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 | \(-0.661624\pi\) |
0.873837 | + | 0.486220i | \(0.161624\pi\) | |||||||
\(54\) | 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 | \(-0.896517\pi\) |
0.319406 | + | 0.947618i | \(0.396517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −228.069 | − | 228.069i | −0.478709 | − | 0.478709i | 0.426010 | − | 0.904719i | \(-0.359919\pi\) |
−0.904719 | + | 0.426010i | \(0.859919\pi\) | |||||||
\(62\) | 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 | \(-0.307420\pi\) |
−0.822498 | + | 0.568768i | \(0.807420\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 105.541 | − | 105.541i | 0.184140 | − | 0.184140i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 453.655i | 0.758294i | 0.925336 | + | 0.379147i | \(0.123783\pi\) | ||||
−0.925336 | + | 0.379147i | \(0.876217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 259.747i | − | 0.416454i | −0.978081 | − | 0.208227i | \(-0.933231\pi\) | ||
0.978081 | − | 0.208227i | \(-0.0667692\pi\) | |||||||
\(74\) | 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 | \(-0.0732000\pi\) |
−0.227943 | + | 0.973674i | \(0.573200\pi\) | |||||||
\(84\) | 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 | \(0.172659\pi\) | ||||
−0.856459 | + | 0.516215i | \(0.827341\pi\) | |||||||
\(90\) | 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 | \(-0.750352\pi\) |
0.706324 | + | 0.707889i | \(0.250352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1388.28i | 1.32807i | 0.747700 | + | 0.664036i | \(0.231158\pi\) | ||||
−0.747700 | + | 0.664036i | \(0.768842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 33.2635i | − | 0.0309160i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 821.526 | − | 821.526i | 0.742243 | − | 0.742243i | −0.230767 | − | 0.973009i | \(-0.574123\pi\) |
0.973009 | + | 0.230767i | \(0.0741234\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 532.797 | + | 532.797i | 0.468190 | + | 0.468190i | 0.901328 | − | 0.433138i | \(-0.142594\pi\) |
−0.433138 | + | 0.901328i | \(0.642594\pi\) | |||||||
\(110\) | 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 | \(-0.392593\pi\) |
−0.943609 | + | 0.331062i | \(0.892593\pi\) | |||||||
\(132\) | 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 | \(0.0475430\pi\) | ||||
−0.988866 | + | 0.148806i | \(0.952457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1513.89 | − | 1513.89i | 0.923788 | − | 0.923788i | −0.0735064 | − | 0.997295i | \(-0.523419\pi\) |
0.997295 | + | 0.0735064i | \(0.0234189\pi\) | |||||||
\(140\) | 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 | \(-0.703382\pi\) |
0.802725 | + | 0.596349i | \(0.203382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2997.52i | − | 1.61546i | −0.589553 | − | 0.807730i | \(-0.700696\pi\) | ||
0.589553 | − | 0.807730i | \(-0.299304\pi\) | |||||||
\(152\) | 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 | \(-0.432488\pi\) |
−0.977592 | + | 0.210510i | \(0.932488\pi\) | |||||||
\(158\) | 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 | \(-0.0890898\pi\) |
−0.276244 | + | 0.961088i | \(0.589090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −563.017 | + | 563.017i | −0.265641 | + | 0.265641i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 792.415i | 0.367179i | 0.983003 | + | 0.183590i | \(0.0587717\pi\) | ||||
−0.983003 | + | 0.183590i | \(0.941228\pi\) | |||||||
\(168\) | 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 | \(-0.327278\pi\) |
−0.856357 | + | 0.516384i | \(0.827278\pi\) | |||||||
\(174\) | 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 | \(-0.290148\pi\) |
−0.790441 | + | 0.612539i | \(0.790148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2618.06 | + | 2618.06i | −1.07513 | + | 1.07513i | −0.0781951 | + | 0.996938i | \(0.524916\pi\) |
−0.996938 | + | 0.0781951i | \(0.975084\pi\) | |||||||
\(182\) | 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 | \(-0.615013\pi\) |
0.935430 | + | 0.353512i | \(0.115013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 747.136i | − | 0.266146i | −0.991106 | − | 0.133073i | \(-0.957516\pi\) | ||
0.991106 | − | 0.133073i | \(-0.0424845\pi\) | |||||||
\(200\) | 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 | \(-0.0782315\pi\) |
−0.243305 | + | 0.969950i | \(0.578231\pi\) | |||||||
\(212\) | 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 | −0.999946 | − | 0.0103741i | \(-0.996698\pi\) |
−0.0103741 | − | 0.999946i | \(-0.503302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1430.03 | + | 1430.03i | −0.412659 | + | 0.412659i | −0.882664 | − | 0.470005i | \(-0.844252\pi\) |
0.470005 | + | 0.882664i | \(0.344252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 182.864i | − | 0.0520847i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 926.479i | − | 0.260496i | −0.991481 | − | 0.130248i | \(-0.958423\pi\) | ||
0.991481 | − | 0.130248i | \(-0.0415774\pi\) | |||||||
\(234\) | 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 | \(-0.530343\pi\) |
0.995460 | + | 0.0951802i | \(0.0303427\pi\) | |||||||
\(252\) | 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 | \(0.113110\pi\) | ||||
−0.937526 | + | 0.347915i | \(0.886890\pi\) | |||||||
\(264\) | 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 | \(-0.283920\pi\) |
−0.778305 | + | 0.627887i | \(0.783920\pi\) | |||||||
\(270\) | 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 | \(-0.726423\pi\) |
0.757495 | + | 0.652841i | \(0.226423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4878.29i | 1.04679i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5899.10i | − | 1.25235i | −0.779682 | − | 0.626175i | \(-0.784619\pi\) | ||
0.779682 | − | 0.626175i | \(-0.215381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 679.897 | − | 679.897i | 0.142812 | − | 0.142812i | −0.632086 | − | 0.774898i | \(-0.717801\pi\) |
0.774898 | + | 0.632086i | \(0.217801\pi\) | |||||||
\(284\) | 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 | \(-0.917002\pi\) |
0.257800 | + | 0.966198i | \(0.417002\pi\) | |||||||
\(294\) | 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 | \(-0.367088\pi\) |
−0.914083 | + | 0.405527i | \(0.867088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1050.62 | − | 1050.62i | 0.193423 | − | 0.193423i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5796.70i | − | 1.05692i | −0.848960 | − | 0.528458i | \(-0.822771\pi\) | ||
0.848960 | − | 0.528458i | \(-0.177229\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8362.62i | 1.51017i | 0.655627 | + | 0.755085i | \(0.272404\pi\) | ||||
−0.655627 | + | 0.755085i | \(0.727596\pi\) | |||||||
\(314\) | 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 | \(-0.263739\pi\) |
−0.736959 | + | 0.675938i | \(0.763739\pi\) | |||||||
\(318\) | 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 | \(-0.852209\pi\) |
0.447797 | + | 0.894135i | \(0.352209\pi\) | |||||||
\(332\) | 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 | \(-0.680955\pi\) |
0.842716 | + | 0.538359i | \(0.180955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7363.37 | − | 7363.37i | −1.12938 | − | 1.12938i | −0.990279 | − | 0.139097i | \(-0.955580\pi\) |
−0.139097 | − | 0.990279i | \(-0.544420\pi\) | |||||||
\(350\) | 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 | \(-0.815268\pi\) | ||
0.836269 | − | 0.548319i | \(-0.184732\pi\) | |||||||
\(360\) | 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 | 0.275921 | − | 0.961180i | \(-0.411017\pi\) |
0.961180 | − | 0.275921i | \(-0.0889827\pi\) | |||||||
\(374\) | 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 | \(-0.786197\pi\) |
0.622303 | + | 0.782776i | \(0.286197\pi\) | |||||||
\(380\) | 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 | 0.232226 | − | 0.972662i | \(-0.425399\pi\) |
0.972662 | − | 0.232226i | \(-0.0746009\pi\) | |||||||
\(390\) | 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 | \(-0.374287\pi\) |
−0.923020 | + | 0.384751i | \(0.874287\pi\) | |||||||
\(398\) | 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 | \(0.00448320\pi\) | ||||
−0.999901 | + | 0.0140839i | \(0.995517\pi\) | |||||||
\(410\) | 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 | \(-0.0814807\pi\) |
−0.253193 | + | 0.967416i | \(0.581481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8308.44 | + | 8308.44i | −0.961825 | + | 0.961825i | −0.999298 | − | 0.0374725i | \(-0.988069\pi\) |
0.0374725 | + | 0.999298i | \(0.488069\pi\) | |||||||
\(422\) | 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 | \(0.407920\pi\) | ||||
−0.285261 | + | 0.958450i | \(0.592080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 8683.57i | − | 0.937649i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4549.81 | − | 4549.81i | 0.487964 | − | 0.487964i | −0.419699 | − | 0.907663i | \(-0.637864\pi\) |
0.907663 | + | 0.419699i | \(0.137864\pi\) | |||||||
\(444\) | 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 | \(0.158279\pi\) | ||||
−0.878898 | + | 0.477009i | \(0.841721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2899.90 | − | 2899.90i | 0.294892 | − | 0.294892i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12885.0 | + | 12885.0i | 1.30177 | + | 1.30177i | 0.927200 | + | 0.374566i | \(0.122208\pi\) |
0.374566 | + | 0.927200i | \(0.377792\pi\) | |||||||
\(462\) | 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 | \(-0.388153\pi\) |
−0.938899 | + | 0.344192i | \(0.888153\pi\) | |||||||
\(468\) | 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 | \(0.127262\pi\) | ||||
−0.921136 | + | 0.389240i | \(0.872738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2157.10i | − | 0.199483i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1529.30 | + | 1529.30i | −0.140563 | + | 0.140563i | −0.773887 | − | 0.633324i | \(-0.781690\pi\) |
0.633324 | + | 0.773887i | \(0.281690\pi\) | |||||||
\(492\) | 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 | −0.999806 | − | 0.0197191i | \(-0.993723\pi\) |
−0.0197191 | − | 0.999806i | \(-0.506277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 599.681 | − | 599.681i | 0.0534766 | − | 0.0534766i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12570.2i | 1.11427i | 0.830421 | + | 0.557137i | \(0.188100\pi\) | ||||
−0.830421 | + | 0.557137i | \(0.811900\pi\) | |||||||
\(504\) | 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 | 0.999381 | + | 0.0351750i | \(0.0111989\pi\) |
0.0351750 | + | 0.999381i | \(0.488801\pi\) | |||||||
\(510\) | 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 | \(-0.910314\pi\) | ||
0.960569 | − | 0.278042i | \(-0.0896856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5129.30 | + | 5129.30i | −0.428850 | + | 0.428850i | −0.888236 | − | 0.459387i | \(-0.848069\pi\) |
0.459387 | + | 0.888236i | \(0.348069\pi\) | |||||||
\(524\) | 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 | \(-0.461395\pi\) |
−0.992655 | + | 0.120983i | \(0.961395\pi\) | |||||||
\(542\) | 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 | −0.999727 | − | 0.0233784i | \(-0.992558\pi\) |
−0.0233784 | − | 0.999727i | \(-0.507442\pi\) | |||||||
\(548\) | 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 | \(-0.162436\pi\) |
−0.488447 | + | 0.872594i | \(0.662436\pi\) | |||||||
\(558\) | 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 | \(-0.194983\pi\) |
−0.574962 | + | 0.818180i | \(0.694983\pi\) | |||||||
\(564\) | 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 | \(0.0329628\pi\) | ||||
−0.994643 | + | 0.103371i | \(0.967037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12038.8 | − | 12038.8i | 0.882324 | − | 0.882324i | −0.111446 | − | 0.993770i | \(-0.535548\pi\) |
0.993770 | + | 0.111446i | \(0.0355483\pi\) | |||||||
\(572\) | 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 | \(-0.922557\pi\) |
0.240903 | + | 0.970549i | \(0.422557\pi\) | |||||||
\(588\) | 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 | \(-0.838373\pi\) | ||
0.873832 | − | 0.486227i | \(-0.161627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10385.2i | 0.704862i | 0.935838 | + | 0.352431i | \(0.114645\pi\) | ||||
−0.935838 | + | 0.352431i | \(0.885355\pi\) | |||||||
\(602\) | 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 | \(-0.757423\pi\) |
0.690426 | + | 0.723403i | \(0.257423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1302.66i | − | 0.0854121i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11575.9i | 0.755316i | 0.925945 | + | 0.377658i | \(0.123271\pi\) | ||||
−0.925945 | + | 0.377658i | \(0.876729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18356.1 | + | 18356.1i | −1.19191 | + | 1.19191i | −0.215380 | + | 0.976530i | \(0.569099\pi\) |
−0.976530 | + | 0.215380i | \(0.930901\pi\) | |||||||
\(620\) | 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 | \(0.104537\pi\) | ||||
−0.946556 | + | 0.322539i | \(0.895463\pi\) | |||||||
\(632\) | 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 | \(-0.488038\pi\) |
−0.999294 | + | 0.0375712i | \(0.988038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −392.006 | + | 392.006i | −0.0239306 | + | 0.0239306i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9232.26i | 0.560985i | 0.959856 | + | 0.280493i | \(0.0904978\pi\) | ||||
−0.959856 | + | 0.280493i | \(0.909502\pi\) | |||||||
\(648\) | 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 | −0.979626 | − | 0.200833i | \(-0.935635\pi\) |
−0.200833 | − | 0.979626i | \(-0.564365\pi\) | |||||||
\(654\) | 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 | \(-0.301960\pi\) |
−0.812621 | + | 0.582792i | \(0.801960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8110.20 | + | 8110.20i | −0.477232 | + | 0.477232i | −0.904245 | − | 0.427013i | \(-0.859566\pi\) |
0.427013 | + | 0.904245i | \(0.359566\pi\) | |||||||
\(662\) | 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 | \(-0.988502\pi\) |
0.0361128 | + | 0.999348i | \(0.488502\pi\) | |||||||
\(678\) | 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 | \(-0.626500\pi\) |
0.922066 | + | 0.387034i | \(0.126500\pi\) | |||||||
\(684\) | 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 | 0.986868 | + | 0.161527i | \(0.0516418\pi\) |
0.161527 | + | 0.986868i | \(0.448358\pi\) | |||||||
\(692\) | 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 | 0.948178 | + | 0.317740i | \(0.102924\pi\) |
0.317740 | + | 0.948178i | \(0.397076\pi\) | |||||||
\(702\) | 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 | \(-0.695372\pi\) |
0.817477 | + | 0.575962i | \(0.195372\pi\) | |||||||
\(710\) | 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 | \(0.218704\pi\) | ||||
−0.773103 | + | 0.634280i | \(0.781296\pi\) | |||||||
\(728\) | 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 | \(-0.428339\pi\) |
−0.974765 | + | 0.223232i | \(0.928339\pi\) | |||||||
\(734\) | 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 | \(-0.346149\pi\) |
−0.885449 | + | 0.464737i | \(0.846149\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1041.64 | + | 1041.64i | −0.0516404 | + | 0.0516404i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5622.43i | 0.277614i | 0.990319 | + | 0.138807i | \(0.0443267\pi\) | ||||
−0.990319 | + | 0.138807i | \(0.955673\pi\) | |||||||
\(744\) | 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 | \(-0.608188\pi\) |
0.942794 | + | 0.333376i | \(0.108188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 9545.42i | − | 0.456491i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 13108.2i | − | 0.624404i | −0.950016 | − | 0.312202i | \(-0.898933\pi\) | ||
0.950016 | − | 0.312202i | \(-0.101067\pi\) | |||||||
\(762\) | 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 | \(-0.501790\pi\) |
0.999984 | + | 0.00562228i | \(0.00178964\pi\) | |||||||
\(774\) | 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 | \(-0.0166872\pi\) |
−0.0524002 | + | 0.998626i | \(0.516687\pi\) | |||||||
\(788\) | 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 | \(-0.318908\pi\) |
−0.842486 | + | 0.538719i | \(0.818908\pi\) | |||||||
\(798\) | 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 | \(-0.888396\pi\) | ||
0.939162 | − | 0.343476i | \(-0.111604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11522.7 | − | 11522.7i | 0.498910 | − | 0.498910i | −0.412189 | − | 0.911099i | \(-0.635236\pi\) |
0.911099 | + | 0.412189i | \(0.135236\pi\) | |||||||
\(812\) | 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 | \(-0.747045\pi\) |
0.713640 | + | 0.700512i | \(0.247045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5633.49i | 0.238604i | 0.992858 | + | 0.119302i | \(0.0380656\pi\) | ||||
−0.992858 | + | 0.119302i | \(0.961934\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 707.026i | 0.0298369i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15835.5 | − | 15835.5i | 0.665844 | − | 0.665844i | −0.290908 | − | 0.956751i | \(-0.593957\pi\) |
0.956751 | + | 0.290908i | \(0.0939572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6200.19 | − | 6200.19i | −0.259761 | − | 0.259761i | 0.565196 | − | 0.824957i | \(-0.308801\pi\) |
−0.824957 | + | 0.565196i | \(0.808801\pi\) | |||||||
\(830\) | 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 | \(0.217145\pi\) | ||||
−0.776199 | + | 0.630488i | \(0.782855\pi\) | |||||||
\(840\) | 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 | −0.274869 | + | 0.961482i | \(0.588635\pi\) |
−0.961482 | + | 0.274869i | \(0.911365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8270.00i | 0.330793i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41788.5i | 1.66566i | 0.553533 | + | 0.832828i | \(0.313279\pi\) | ||||
−0.553533 | + | 0.832828i | \(0.686721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11914.5 | + | 11914.5i | −0.473243 | + | 0.473243i | −0.902963 | − | 0.429719i | \(-0.858612\pi\) |
0.429719 | + | 0.902963i | \(0.358612\pi\) | |||||||
\(860\) | 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 | \(-0.355192\pi\) |
−0.898293 | + | 0.439397i | \(0.855192\pi\) | |||||||
\(878\) | 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 | \(-0.0126890\pi\) |
−0.0398530 | + | 0.999206i | \(0.512689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3544.57 | − | 3544.57i | 0.134632 | − | 0.134632i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 48821.3i | − | 1.84810i | −0.382278 | − | 0.924048i | \(-0.624860\pi\) | ||
0.382278 | − | 0.924048i | \(-0.375140\pi\) | |||||||
\(888\) | 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 | \(-0.793978\pi\) |
0.602985 | + | 0.797753i | \(0.293978\pi\) | |||||||
\(908\) | 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 | \(-0.857735\pi\) | ||
0.901775 | − | 0.432206i | \(-0.142265\pi\) | |||||||
\(920\) | 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 | \(-0.912706\pi\) | ||
0.962631 | − | 0.270818i | \(-0.0872941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6328.63 | − | 6328.63i | 0.219944 | − | 0.219944i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34024.8 | − | 34024.8i | −1.17872 | − | 1.17872i | −0.980070 | − | 0.198651i | \(-0.936344\pi\) |
−0.198651 | − | 0.980070i | \(-0.563656\pi\) | |||||||
\(942\) | 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 | \(-0.220485\pi\) |
−0.638597 | + | 0.769541i | \(0.720485\pi\) | |||||||
\(948\) | 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 | \(-0.879421\pi\) | ||
0.929106 | − | 0.369815i | \(-0.120579\pi\) | |||||||
\(954\) | 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 | \(-0.895795\pi\) | ||
0.946891 | − | 0.321554i | \(-0.104205\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2133.47i | − | 0.0707294i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4184.92 | + | 4184.92i | −0.138311 | + | 0.138311i | −0.772873 | − | 0.634561i | \(-0.781181\pi\) |
0.634561 | + | 0.772873i | \(0.281181\pi\) | |||||||
\(972\) | 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 | \(-0.520491\pi\) | ||
0.0643304 | − | 0.997929i | \(-0.479509\pi\) | |||||||
\(984\) | 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 | \(-0.939939\pi\) |
0.187570 | + | 0.982251i | \(0.439939\pi\) | |||||||
\(998\) | 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 | 64.4.e.a.17.3 | 10 | ||
3.2 | odd | 2 | 576.4.k.a.145.2 | 10 | |||
4.3 | odd | 2 | 16.4.e.a.13.3 | yes | 10 | ||
8.3 | odd | 2 | 128.4.e.b.33.3 | 10 | |||
8.5 | even | 2 | 128.4.e.a.33.3 | 10 | |||
12.11 | even | 2 | 144.4.k.a.109.3 | 10 | |||
16.3 | odd | 4 | 128.4.e.b.97.3 | 10 | |||
16.5 | even | 4 | inner | 64.4.e.a.49.3 | 10 | ||
16.11 | odd | 4 | 16.4.e.a.5.3 | ✓ | 10 | ||
16.13 | even | 4 | 128.4.e.a.97.3 | 10 | |||
32.3 | odd | 8 | 1024.4.b.j.513.6 | 10 | |||
32.5 | even | 8 | 1024.4.a.m.1.6 | 10 | |||
32.11 | odd | 8 | 1024.4.a.n.1.6 | 10 | |||
32.13 | even | 8 | 1024.4.b.k.513.6 | 10 | |||
32.19 | odd | 8 | 1024.4.b.j.513.5 | 10 | |||
32.21 | even | 8 | 1024.4.a.m.1.5 | 10 | |||
32.27 | odd | 8 | 1024.4.a.n.1.5 | 10 | |||
32.29 | even | 8 | 1024.4.b.k.513.5 | 10 | |||
48.5 | odd | 4 | 576.4.k.a.433.2 | 10 | |||
48.11 | even | 4 | 144.4.k.a.37.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.3 | ✓ | 10 | 16.11 | odd | 4 | ||
16.4.e.a.13.3 | yes | 10 | 4.3 | odd | 2 | ||
64.4.e.a.17.3 | 10 | 1.1 | even | 1 | trivial | ||
64.4.e.a.49.3 | 10 | 16.5 | even | 4 | inner | ||
128.4.e.a.33.3 | 10 | 8.5 | even | 2 | |||
128.4.e.a.97.3 | 10 | 16.13 | even | 4 | |||
128.4.e.b.33.3 | 10 | 8.3 | odd | 2 | |||
128.4.e.b.97.3 | 10 | 16.3 | odd | 4 | |||
144.4.k.a.37.3 | 10 | 48.11 | even | 4 | |||
144.4.k.a.109.3 | 10 | 12.11 | even | 2 | |||
576.4.k.a.145.2 | 10 | 3.2 | odd | 2 | |||
576.4.k.a.433.2 | 10 | 48.5 | odd | 4 | |||
1024.4.a.m.1.5 | 10 | 32.21 | even | 8 | |||
1024.4.a.m.1.6 | 10 | 32.5 | even | 8 | |||
1024.4.a.n.1.5 | 10 | 32.27 | odd | 8 | |||
1024.4.a.n.1.6 | 10 | 32.11 | odd | 8 | |||
1024.4.b.j.513.5 | 10 | 32.19 | odd | 8 | |||
1024.4.b.j.513.6 | 10 | 32.3 | odd | 8 | |||
1024.4.b.k.513.5 | 10 | 32.29 | even | 8 | |||
1024.4.b.k.513.6 | 10 | 32.13 | even | 8 |