Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,4,Mod(145,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.145");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.k (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: | \(33.9851001633\) |
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: | \(\Z[a_1, \ldots, a_{25}]\) |
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 | 433.2 | ||
Root | \(-1.62580 - 1.16481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.433 |
Dual form | 576.4.k.a.145.2 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −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 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | −0.220264 | − | 0.975440i | \(-0.570692\pi\) |
0.975440 | + | 0.220264i | \(0.0706918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 72.4991 | 1.03433 | 0.517165 | − | 0.855886i | \(-0.326987\pi\) | ||||
0.517165 | + | 0.855886i | \(0.326987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.4427 | + | 19.4427i | −0.234761 | + | 0.234761i | −0.814676 | − | 0.579916i | \(-0.803085\pi\) |
0.579916 | + | 0.814676i | \(0.303085\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −21.9771 | + | 21.9771i | −0.106137 | + | 0.106137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −84.0653 | − | 84.0653i | −0.373520 | − | 0.373520i | 0.495237 | − | 0.868758i | \(-0.335081\pi\) |
−0.868758 | + | 0.495237i | \(0.835081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 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 | 0.760731 | − | 0.649067i | \(-0.224841\pi\) |
−0.649067 | + | 0.760731i | \(0.724841\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −488.151 | −1.51498 | −0.757491 | − | 0.652846i | \(-0.773575\pi\) | ||||
−0.757491 | + | 0.652846i | \(0.773575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 335.862 | 0.979189 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | −0.904719 | − | 0.426010i | \(-0.859919\pi\) |
0.426010 | + | 0.904719i | \(0.359919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −582.338 | −1.11123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −139.151 | + | 139.151i | −0.253730 | + | 0.253730i | −0.822498 | − | 0.568768i | \(-0.807420\pi\) |
0.568768 | + | 0.822498i | \(0.307420\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(0.0667692\pi\) | ||||
−0.978081 | + | 0.208227i | \(0.933231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | −0.433138 | − | 0.901328i | \(-0.642594\pi\) |
0.901328 | + | 0.433138i | \(0.142594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 67.2680 | 0.0560003 | 0.0280002 | − | 0.999608i | \(-0.491086\pi\) | ||||
0.0280002 | + | 0.999608i | \(0.491086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1147.19 | − | 1147.19i | 0.930230 | − | 0.930230i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 193.696i | − | 0.149211i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2758.92i | 2.07282i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 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 | 0.997295 | − | 0.0735064i | \(-0.0234189\pi\) |
−0.0735064 | + | 0.997295i | \(0.523419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3201.37 | −1.87211 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1086.53 | 0.622285 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1552.07 | + | 1552.07i | 0.804293 | + | 0.804293i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1509.01 | + | 1509.01i | −0.767082 | + | 0.767082i | −0.977592 | − | 0.210510i | \(-0.932488\pi\) |
0.210510 | + | 0.977592i | \(0.432488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 372.601 | 0.182392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1425.19 | − | 1425.19i | 0.684844 | − | 0.684844i | −0.276244 | − | 0.961088i | \(-0.589090\pi\) |
0.961088 | + | 0.276244i | \(0.0890898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | \(-0.975084\pi\) |
−0.0781951 | − | 0.996938i | \(-0.524916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1383.02i | 0.549631i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3278.50 | − | 3278.50i | −1.28207 | − | 1.28207i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3216.39 | 1.21848 | 0.609240 | − | 0.792986i | \(-0.291475\pi\) | ||||
0.609240 | + | 0.792986i | \(0.291475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2852.57 | 1.06390 | 0.531950 | − | 0.846776i | \(-0.321459\pi\) | ||||
0.531950 | + | 0.846776i | \(0.321459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1758.44 | 0.581981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2227.13 | − | 2227.13i | 0.726645 | − | 0.726645i | −0.243305 | − | 0.969950i | \(-0.578231\pi\) |
0.969950 | + | 0.243305i | \(0.0782315\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 517.995i | − | 0.164311i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 504.102i | 0.157699i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | 0.470005 | − | 0.882664i | \(-0.344252\pi\) |
−0.882664 | + | 0.470005i | \(0.844252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −792.472 | −0.214480 | −0.107240 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107240 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1449.01 | 0.387299 | 0.193650 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2762.76 | − | 2762.76i | −0.720433 | − | 0.720433i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1376.42i | 0.354572i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4708.87 | 1.14292 | 0.571461 | − | 0.820629i | \(-0.306377\pi\) | ||||
0.571461 | + | 0.820629i | \(0.306377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −224.598 | + | 224.598i | −0.0538835 | + | 0.0538835i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 467.130 | − | 467.130i | 0.102433 | − | 0.102433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 482.477 | + | 482.477i | 0.104654 | + | 0.104654i | 0.757495 | − | 0.652841i | \(-0.226423\pi\) |
−0.652841 | + | 0.757495i | \(0.726423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 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 | 0.774898 | − | 0.632086i | \(-0.217801\pi\) |
−0.632086 | + | 0.774898i | \(0.717801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 279.538 | 0.0574935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 343.118 | 0.0698388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3752.13 | 0.704415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2735.56 | + | 2735.56i | −0.508556 | + | 0.508556i | −0.914083 | − | 0.405527i | \(-0.867088\pi\) |
0.405527 | + | 0.914083i | \(0.367088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.727596\pi\) | ||
0.655627 | − | 0.755085i | \(-0.272404\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 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 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1304.20i | 0.218549i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2687.86 | − | 2687.86i | −0.446339 | − | 0.446339i | 0.447797 | − | 0.894135i | \(-0.352209\pi\) |
−0.894135 | + | 0.447797i | \(0.852209\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8532.42 | + | 8532.42i | 1.35500 | + | 1.35500i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1813.72i | − | 0.285515i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | \(0.544420\pi\) |
−0.990279 | + | 0.139097i | \(0.955580\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10644.3 | −1.60493 | −0.802466 | − | 0.596698i | \(-0.796479\pi\) | ||||
−0.802466 | + | 0.596698i | \(0.796479\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3731.70 | − | 3731.70i | 0.557911 | − | 0.557911i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | \(0.0889827\pi\) |
0.275921 | + | 0.961180i | \(0.411017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4675.45i | 0.638721i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1184.03 | − | 1184.03i | −0.160473 | − | 0.160473i | 0.622303 | − | 0.782776i | \(-0.286197\pi\) |
−0.782776 | + | 0.622303i | \(0.786197\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2880.38 | −0.384283 | −0.192142 | − | 0.981367i | \(-0.561543\pi\) | ||||
−0.192142 | + | 0.981367i | \(0.561543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1987.66 | 0.263119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2658.52 | + | 2658.52i | 0.338645 | + | 0.338645i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4257.80 | + | 4257.80i | −0.538270 | + | 0.538270i | −0.923020 | − | 0.384751i | \(-0.874287\pi\) |
0.384751 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12722.6 | −1.58437 | −0.792187 | − | 0.610278i | \(-0.791058\pi\) | ||||
−0.792187 | + | 0.610278i | \(0.791058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6678.72 | + | 6678.72i | −0.825535 | + | 0.825535i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 760.629 | − | 760.629i | 0.0906250 | − | 0.0906250i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9277.08 | 1.09734 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | 0.0374725 | − | 0.999298i | \(-0.488069\pi\) |
−0.999298 | + | 0.0374725i | \(0.988069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 748.907i | 0.0854760i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 609.333 | + | 609.333i | 0.0690579 | + | 0.0690579i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8737.57 | 0.976506 | 0.488253 | − | 0.872702i | \(-0.337634\pi\) | ||||
0.488253 | + | 0.872702i | \(0.337634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11627.5 | −1.29049 | −0.645247 | − | 0.763974i | \(-0.723245\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723245\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12926.5 | 1.35867 | 0.679334 | − | 0.733830i | \(-0.262269\pi\) | ||||
0.679334 | + | 0.733830i | \(0.262269\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4731.46 | − | 4731.46i | 0.494004 | − | 0.494004i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2847.65i | − | 0.276818i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −200.840 | − | 200.840i | −0.0194004 | − | 0.0194004i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −587.317 | −0.0560234 | −0.0280117 | − | 0.999608i | \(-0.508918\pi\) | ||||
−0.0280117 | + | 0.999608i | \(0.508918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5951.28 | −0.564148 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1212.03 | 0.109390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11364.5 | + | 11364.5i | −1.01952 | + | 1.01952i | −0.0197191 | + | 0.999806i | \(0.506277\pi\) |
−0.999806 | + | 0.0197191i | \(0.993723\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 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 | 0.459387 | − | 0.888236i | \(-0.348069\pi\) |
−0.888236 | + | 0.459387i | \(0.848069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13679.3 | −1.13070 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7282.60 | −0.598553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3703.53 | + | 3703.53i | 0.300972 | + | 0.300972i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13515.5i | 1.09220i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15188.1 | − | 15188.1i | −1.21372 | − | 1.21372i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10968.5 | + | 10968.5i | −0.871672 | + | 0.871672i | −0.992655 | − | 0.120983i | \(-0.961395\pi\) |
0.120983 | + | 0.992655i | \(0.461395\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8765.44 | −0.688936 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13088.8 | + | 13088.8i | −1.02311 | + | 1.02311i | −0.0233784 | + | 0.999727i | \(0.507442\pi\) |
−0.999727 | + | 0.0233784i | \(0.992558\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2568.12i | − | 0.198558i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 863.469i | 0.0663986i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | 0.993770 | − | 0.111446i | \(-0.0355483\pi\) |
−0.111446 | + | 0.993770i | \(0.535548\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1506.57 | + | 1506.57i | 0.107578 | + | 0.107578i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13526.6i | 0.960918i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4758.60 | 0.329531 | 0.164766 | − | 0.986333i | \(-0.447313\pi\) | ||||
0.164766 | + | 0.986333i | \(0.447313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1593.32 | + | 1593.32i | −0.109781 | + | 0.109781i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | \(-0.885355\pi\) | ||
0.935838 | − | 0.352431i | \(-0.114645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17279.0 | + | 17279.0i | −1.14408 | + | 1.14408i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −500.502 | − | 500.502i | −0.0329773 | − | 0.0329773i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.723403 | + | 0.690426i | \(0.757423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 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 | −0.976530 | − | 0.215380i | \(-0.930901\pi\) |
−0.215380 | − | 0.976530i | \(-0.569099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2315.98 | 0.148937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16809.5 | 1.07581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19804.4 | −1.22032 | −0.610162 | − | 0.792277i | \(-0.708896\pi\) | ||||
−0.610162 | + | 0.792277i | \(0.708896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15680.7 | + | 15680.7i | −0.961723 | + | 0.961723i | −0.999294 | − | 0.0375712i | \(-0.988038\pi\) |
0.0375712 | + | 0.999294i | \(0.488038\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 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 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | 0.427013 | − | 0.904245i | \(-0.359566\pi\) |
−0.904245 | + | 0.427013i | \(0.859566\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 854.587i | − | 0.0498338i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9210.54 | − | 9210.54i | −0.534683 | − | 0.534683i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10587.9 | −0.585439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20859.7 | − | 20859.7i | 1.14839 | − | 1.14839i | 0.161527 | − | 0.986868i | \(-0.448358\pi\) |
0.986868 | − | 0.161527i | \(-0.0516418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 24906.1i | − | 1.35934i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7585.52i | 0.412227i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.24384 | − | 4.24384i | 0.000225751 | − | 0.000225751i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4559.45 | + | 4559.45i | 0.241515 | + | 0.241515i | 0.817477 | − | 0.575962i | \(-0.195372\pi\) |
−0.575962 | + | 0.817477i | \(0.695372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 26313.9i | − | 1.38214i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26334.1 | + | 26334.1i | 1.37740 | + | 1.37740i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6494.67 | −0.336871 | −0.168436 | − | 0.985713i | \(-0.553872\pi\) | ||||
−0.168436 | + | 0.985713i | \(0.553872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3709.08 | −0.191586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2282.68 | + | 2282.68i | 0.115497 | + | 0.115497i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14914.3 | + | 14914.3i | −0.751533 | + | 0.751533i | −0.974765 | − | 0.223232i | \(-0.928339\pi\) |
0.223232 | + | 0.974765i | \(0.428339\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12585.1 | 0.629008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8451.86 | + | 8451.86i | −0.420713 | + | 0.420713i | −0.885449 | − | 0.464737i | \(-0.846149\pi\) |
0.464737 | + | 0.885449i | \(0.346149\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24657.2 | − | 24657.2i | 1.18857 | − | 1.18857i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12692.8 | + | 12692.8i | 0.609418 | + | 0.609418i | 0.942794 | − | 0.333376i | \(-0.108188\pi\) |
−0.333376 | + | 0.942794i | \(0.608188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 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 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24825.8 | 1.12875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20890.9 | − | 20890.9i | 0.946226 | − | 0.946226i | −0.0524002 | − | 0.998626i | \(-0.516687\pi\) |
0.998626 | + | 0.0524002i | \(0.0166872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 179.720i | − | 0.00807853i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16145.8i | 0.723020i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | 0.911099 | − | 0.412189i | \(-0.135236\pi\) |
−0.412189 | + | 0.911099i | \(0.635236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23446.9 | −1.00774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1224.33 | −0.0524284 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | −0.824957 | − | 0.565196i | \(-0.808801\pi\) |
0.565196 | + | 0.824957i | \(0.308801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24349.7 | 1.01281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6518.30 | − | 6518.30i | 0.270150 | − | 0.270150i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2540.65 | + | 2540.65i | −0.103433 | + | 0.103433i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7371.03 | 0.299022 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | \(-0.911365\pi\) |
−0.274869 | − | 0.961482i | \(-0.588635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | 0.429719 | − | 0.902963i | \(-0.358612\pi\) |
−0.902963 | + | 0.429719i | \(0.858612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27636.7 | 1.09011 | 0.545054 | − | 0.838401i | \(-0.316509\pi\) | ||||
0.545054 | + | 0.838401i | \(0.316509\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12727.0 | −0.500266 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14615.1 | + | 14615.1i | 0.570520 | + | 0.570520i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9850.95i | 0.383223i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2520.12 | + | 2520.12i | 0.0973663 | + | 0.0973663i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11918.3 | + | 11918.3i | −0.458896 | + | 0.458896i | −0.898293 | − | 0.439397i | \(-0.855192\pi\) |
0.439397 | + | 0.898293i | \(0.355192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13330.0 | 0.509759 | 0.254880 | − | 0.966973i | \(-0.417964\pi\) | ||||
0.254880 | + | 0.966973i | \(0.417964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25172.1 | − | 25172.1i | 0.959353 | − | 0.959353i | −0.0398530 | − | 0.999206i | \(-0.512689\pi\) |
0.999206 | + | 0.0398530i | \(0.0126890\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9490.96 | − | 9490.96i | 0.355658 | − | 0.355658i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7009.27 | −0.261781 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43071.7i | 1.58205i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5320.20 | − | 5320.20i | −0.194768 | − | 0.194768i | 0.602985 | − | 0.797753i | \(-0.293978\pi\) |
−0.797753 | + | 0.602985i | \(0.793978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26016.0 | −0.946155 | −0.473077 | − | 0.881021i | \(-0.656857\pi\) | ||||
−0.473077 | + | 0.881021i | \(0.656857\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51000.2 | 1.84870 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9324.93 | −0.329323 | −0.164661 | − | 0.986350i | \(-0.552653\pi\) | ||||
−0.164661 | + | 0.986350i | \(0.552653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6530.06 | + | 6530.06i | −0.229875 | + | 0.229875i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1275.03 | 0.0429331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5809.78 | 0.195018 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17841.9 | −0.584249 | −0.292125 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292125 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39200.2 | − | 39200.2i | 1.27972 | − | 1.27972i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6145.84 | − | 6145.84i | 0.195815 | − | 0.195815i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25017.0 | − | 25017.0i | −0.794681 | − | 0.794681i | 0.187570 | − | 0.982251i | \(-0.439939\pi\) |
−0.982251 | + | 0.187570i | \(0.939939\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 576.4.k.a.433.2 | 10 | ||
3.2 | odd | 2 | 64.4.e.a.49.3 | 10 | |||
4.3 | odd | 2 | 144.4.k.a.37.3 | 10 | |||
12.11 | even | 2 | 16.4.e.a.5.3 | ✓ | 10 | ||
16.3 | odd | 4 | 144.4.k.a.109.3 | 10 | |||
16.13 | even | 4 | inner | 576.4.k.a.145.2 | 10 | ||
24.5 | odd | 2 | 128.4.e.a.97.3 | 10 | |||
24.11 | even | 2 | 128.4.e.b.97.3 | 10 | |||
48.5 | odd | 4 | 128.4.e.a.33.3 | 10 | |||
48.11 | even | 4 | 128.4.e.b.33.3 | 10 | |||
48.29 | odd | 4 | 64.4.e.a.17.3 | 10 | |||
48.35 | even | 4 | 16.4.e.a.13.3 | yes | 10 | ||
96.5 | odd | 8 | 1024.4.b.k.513.5 | 10 | |||
96.11 | even | 8 | 1024.4.b.j.513.5 | 10 | |||
96.29 | odd | 8 | 1024.4.a.m.1.5 | 10 | |||
96.35 | even | 8 | 1024.4.a.n.1.6 | 10 | |||
96.53 | odd | 8 | 1024.4.b.k.513.6 | 10 | |||
96.59 | even | 8 | 1024.4.b.j.513.6 | 10 | |||
96.77 | odd | 8 | 1024.4.a.m.1.6 | 10 | |||
96.83 | even | 8 | 1024.4.a.n.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.3 | ✓ | 10 | 12.11 | even | 2 | ||
16.4.e.a.13.3 | yes | 10 | 48.35 | even | 4 | ||
64.4.e.a.17.3 | 10 | 48.29 | odd | 4 | |||
64.4.e.a.49.3 | 10 | 3.2 | odd | 2 | |||
128.4.e.a.33.3 | 10 | 48.5 | odd | 4 | |||
128.4.e.a.97.3 | 10 | 24.5 | odd | 2 | |||
128.4.e.b.33.3 | 10 | 48.11 | even | 4 | |||
128.4.e.b.97.3 | 10 | 24.11 | even | 2 | |||
144.4.k.a.37.3 | 10 | 4.3 | odd | 2 | |||
144.4.k.a.109.3 | 10 | 16.3 | odd | 4 | |||
576.4.k.a.145.2 | 10 | 16.13 | even | 4 | inner | ||
576.4.k.a.433.2 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.a.m.1.5 | 10 | 96.29 | odd | 8 | |||
1024.4.a.m.1.6 | 10 | 96.77 | odd | 8 | |||
1024.4.a.n.1.5 | 10 | 96.83 | even | 8 | |||
1024.4.a.n.1.6 | 10 | 96.35 | even | 8 | |||
1024.4.b.j.513.5 | 10 | 96.11 | even | 8 | |||
1024.4.b.j.513.6 | 10 | 96.59 | even | 8 | |||
1024.4.b.k.513.5 | 10 | 96.5 | odd | 8 | |||
1024.4.b.k.513.6 | 10 | 96.53 | odd | 8 |