Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,6,Mod(649,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.649");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(144.345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.649 |
Dual form | 900.6.d.h.649.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 218.000i | 1.68156i | 0.541380 | + | 0.840778i | \(0.317902\pi\) | ||||
−0.541380 | + | 0.840778i | \(0.682098\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 480.000 | 1.19608 | 0.598039 | − | 0.801467i | \(-0.295947\pi\) | ||||
0.598039 | + | 0.801467i | \(0.295947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 622.000i | 1.02078i | 0.859943 | + | 0.510390i | \(0.170499\pi\) | ||||
−0.859943 | + | 0.510390i | \(0.829501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 186.000i | − 0.156096i | −0.996950 | − | 0.0780478i | \(-0.975131\pi\) | ||||
0.996950 | − | 0.0780478i | \(-0.0248687\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1204.00 | 0.765143 | 0.382571 | − | 0.923926i | \(-0.375039\pi\) | ||||
0.382571 | + | 0.923926i | \(0.375039\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3186.00i | − 1.25582i | −0.778287 | − | 0.627908i | \(-0.783911\pi\) | ||||
0.778287 | − | 0.627908i | \(-0.216089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5526.00 | 1.22016 | 0.610079 | − | 0.792341i | \(-0.291138\pi\) | ||||
0.610079 | + | 0.792341i | \(0.291138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9356.00 | 1.74858 | 0.874291 | − | 0.485402i | \(-0.161327\pi\) | ||||
0.874291 | + | 0.485402i | \(0.161327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5618.00i | 0.674648i | 0.941389 | + | 0.337324i | \(0.109522\pi\) | ||||
−0.941389 | + | 0.337324i | \(0.890478\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14394.0 | 1.33728 | 0.668639 | − | 0.743587i | \(-0.266877\pi\) | ||||
0.668639 | + | 0.743587i | \(0.266877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 370.000i | 0.0305162i | 0.999884 | + | 0.0152581i | \(0.00485699\pi\) | ||||
−0.999884 | + | 0.0152581i | \(0.995143\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 16146.0i | − 1.06615i | −0.846066 | − | 0.533077i | \(-0.821035\pi\) | ||||
0.846066 | − | 0.533077i | \(-0.178965\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −30717.0 | −1.82763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4374.00i | − 0.213889i | −0.994265 | − | 0.106945i | \(-0.965893\pi\) | ||||
0.994265 | − | 0.106945i | \(-0.0341068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11748.0 | −0.439374 | −0.219687 | − | 0.975570i | \(-0.570504\pi\) | ||||
−0.219687 | + | 0.975570i | \(0.570504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13202.0 | 0.454271 | 0.227136 | − | 0.973863i | \(-0.427064\pi\) | ||||
0.227136 | + | 0.973863i | \(0.427064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11542.0i | − 0.314119i | −0.987589 | − | 0.157059i | \(-0.949799\pi\) | ||||
0.987589 | − | 0.157059i | \(-0.0502014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29532.0 | 0.695260 | 0.347630 | − | 0.937632i | \(-0.386987\pi\) | ||||
0.347630 | + | 0.937632i | \(0.386987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 33698.0i | − 0.740111i | −0.929010 | − | 0.370056i | \(-0.879339\pi\) | ||||
0.929010 | − | 0.370056i | \(-0.120661\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 104640.i | 2.01127i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31208.0 | −0.562598 | −0.281299 | − | 0.959620i | \(-0.590765\pi\) | ||||
−0.281299 | + | 0.959620i | \(0.590765\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 38466.0i | − 0.612889i | −0.951889 | − | 0.306444i | \(-0.900861\pi\) | ||||
0.951889 | − | 0.306444i | \(-0.0991394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 119514. | 1.59935 | 0.799675 | − | 0.600432i | \(-0.205005\pi\) | ||||
0.799675 | + | 0.600432i | \(0.205005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −135596. | −1.71650 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 94658.0i | 1.02148i | 0.859737 | + | 0.510738i | \(0.170628\pi\) | ||||
−0.859737 | + | 0.510738i | \(0.829372\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −101046. | −0.985634 | −0.492817 | − | 0.870133i | \(-0.664033\pi\) | ||||
−0.492817 | + | 0.870133i | \(0.664033\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 143434.i | 1.33217i | 0.745877 | + | 0.666084i | \(0.232031\pi\) | ||||
−0.745877 | + | 0.666084i | \(0.767969\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 57054.0i | 0.481755i | 0.970555 | + | 0.240878i | \(0.0774353\pi\) | ||||
−0.970555 | + | 0.240878i | \(0.922565\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3118.00 | 0.0251368 | 0.0125684 | − | 0.999921i | \(-0.495999\pi\) | ||||
0.0125684 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 54534.0i | − 0.401764i | −0.979615 | − | 0.200882i | \(-0.935619\pi\) | ||||
0.979615 | − | 0.200882i | \(-0.0643808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 40548.0 | 0.262484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69349.0 | 0.430603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 24698.0i | 0.135879i | 0.997689 | + | 0.0679395i | \(0.0216425\pi\) | ||||
−0.997689 | + | 0.0679395i | \(0.978358\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −236640. | −1.20479 | −0.602393 | − | 0.798200i | \(-0.705786\pi\) | ||||
−0.602393 | + | 0.798200i | \(0.705786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 262472.i | 1.28663i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22158.0i | 0.100862i | 0.998728 | + | 0.0504312i | \(0.0160596\pi\) | ||||
−0.998728 | + | 0.0504312i | \(0.983940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 193204. | 0.848163 | 0.424081 | − | 0.905624i | \(-0.360597\pi\) | ||||
0.424081 | + | 0.905624i | \(0.360597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 298560.i | 1.22093i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 448554. | 1.65519 | 0.827597 | − | 0.561322i | \(-0.189707\pi\) | ||||
0.827597 | + | 0.561322i | \(0.189707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −140860. | −0.502742 | −0.251371 | − | 0.967891i | \(-0.580881\pi\) | ||||
−0.251371 | + | 0.967891i | \(0.580881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 335878.i | − 1.08751i | −0.839245 | − | 0.543754i | \(-0.817002\pi\) | ||||
0.839245 | − | 0.543754i | \(-0.182998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 694548. | 2.11173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 101650.i | 0.299667i | 0.988711 | + | 0.149833i | \(0.0478737\pi\) | ||||
−0.988711 | + | 0.149833i | \(0.952126\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 139242.i | − 0.386348i | −0.981164 | − | 0.193174i | \(-0.938122\pi\) | ||||
0.981164 | − | 0.193174i | \(-0.0618782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15591.0 | −0.0419911 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 265014.i | − 0.673215i | −0.941645 | − | 0.336607i | \(-0.890721\pi\) | ||||
0.941645 | − | 0.336607i | \(-0.109279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −142812. | −0.333144 | −0.166572 | − | 0.986029i | \(-0.553270\pi\) | ||||
−0.166572 | + | 0.986029i | \(0.553270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 109670. | 0.248824 | 0.124412 | − | 0.992231i | \(-0.460296\pi\) | ||||
0.124412 | + | 0.992231i | \(0.460296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 89280.0i | − 0.186703i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −294948. | −0.585008 | −0.292504 | − | 0.956264i | \(-0.594489\pi\) | ||||
−0.292504 | + | 0.956264i | \(0.594489\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1.00303e6i | − 1.93831i | −0.246459 | − | 0.969153i | \(-0.579267\pi\) | ||||
0.246459 | − | 0.969153i | \(-0.420733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 823998.i | 1.51273i | 0.654151 | + | 0.756364i | \(0.273026\pi\) | ||||
−0.654151 | + | 0.756364i | \(0.726974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 906712. | 1.62307 | 0.811534 | − | 0.584305i | \(-0.198633\pi\) | ||||
0.811534 | + | 0.584305i | \(0.198633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.20467e6i | 2.05176i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 577920. | 0.915170 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 506384. | 0.783022 | 0.391511 | − | 0.920173i | \(-0.371953\pi\) | ||||
0.391511 | + | 0.920173i | \(0.371953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.03961e6i | 2.94034i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 115692. | 0.159339 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 542050.i | 0.729923i | 0.931023 | + | 0.364962i | \(0.118918\pi\) | ||||
−0.931023 | + | 0.364962i | \(0.881082\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.44857e6i | 1.86585i | 0.360075 | + | 0.932924i | \(0.382751\pi\) | ||||
−0.360075 | + | 0.932924i | \(0.617249\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 478786. | 0.603327 | 0.301663 | − | 0.953414i | \(-0.402458\pi\) | ||||
0.301663 | + | 0.953414i | \(0.402458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 374106.i | 0.451445i | 0.974192 | + | 0.225723i | \(0.0724743\pi\) | ||||
−0.974192 | + | 0.225723i | \(0.927526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 169416. | 0.191849 | 0.0959245 | − | 0.995389i | \(-0.469419\pi\) | ||||
0.0959245 | + | 0.995389i | \(0.469419\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −353746. | −0.392328 | −0.196164 | − | 0.980571i | \(-0.562848\pi\) | ||||
−0.196164 | + | 0.980571i | \(0.562848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 748888.i | 0.781042i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.25520e6 | −1.25756 | −0.628780 | − | 0.777583i | \(-0.716445\pi\) | ||||
−0.628780 | + | 0.777583i | \(0.716445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.52928e6i | − 1.50205i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.12877e6i | 1.06604i | 0.846102 | + | 0.533021i | \(0.178943\pi\) | ||||
−0.846102 | + | 0.533021i | \(0.821057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.22472e6 | −1.13446 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 263082.i | − 0.234532i | −0.993101 | − | 0.117266i | \(-0.962587\pi\) | ||||
0.993101 | − | 0.117266i | \(-0.0374130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.18774e6 | −1.00079 | −0.500393 | − | 0.865798i | \(-0.666811\pi\) | ||||
−0.500393 | + | 0.865798i | \(0.666811\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 431300. | 0.356744 | 0.178372 | − | 0.983963i | \(-0.442917\pi\) | ||||
0.178372 | + | 0.983963i | \(0.442917\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 743114.i | 0.581910i | 0.956737 | + | 0.290955i | \(0.0939730\pi\) | ||||
−0.956737 | + | 0.290955i | \(0.906027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92193e6 | −1.45201 | −0.726007 | − | 0.687687i | \(-0.758626\pi\) | ||||
−0.726007 | + | 0.687687i | \(0.758626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.63071e6i | 1.21035i | 0.796092 | + | 0.605176i | \(0.206897\pi\) | ||||
−0.796092 | + | 0.605176i | \(0.793103\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.13789e6i | 2.24871i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.38526e6 | 0.975634 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 71250.0i | 0.0484859i | 0.999706 | + | 0.0242430i | \(0.00771753\pi\) | ||||
−0.999706 | + | 0.0242430i | \(0.992282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.98169e6 | 1.28191 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −80660.0 | −0.0513147 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.61762e6i | − 0.979560i | −0.871846 | − | 0.489780i | \(-0.837077\pi\) | ||||
0.871846 | − | 0.489780i | \(-0.162923\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 682788. | 0.400299 | 0.200150 | − | 0.979765i | \(-0.435857\pi\) | ||||
0.200150 | + | 0.979765i | \(0.435857\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70444e6i | 1.56033i | 0.625574 | + | 0.780165i | \(0.284865\pi\) | ||||
−0.625574 | + | 0.780165i | \(0.715135\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.60347e6i | − 1.45514i | −0.686035 | − | 0.727568i | \(-0.740650\pi\) | ||||
0.686035 | − | 0.727568i | \(-0.259350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.65248e6 | 1.45940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 223944.i | − 0.119435i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.51983e6 | 1.79280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −661432. | −0.331830 | −0.165915 | − | 0.986140i | \(-0.553058\pi\) | ||||
−0.165915 | + | 0.986140i | \(0.553058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.71706e6i | 0.823588i | 0.911277 | + | 0.411794i | \(0.135098\pi\) | ||||
−0.911277 | + | 0.411794i | \(0.864902\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.49088e6 | 2.09144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.03238e6i | − 1.39171i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 131370.i | − 0.0585696i | −0.999571 | − | 0.0292848i | \(-0.990677\pi\) | ||||
0.999571 | − | 0.0292848i | \(-0.00932298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.50951e6 | −1.54235 | −0.771175 | − | 0.636623i | \(-0.780331\pi\) | ||||
−0.771175 | + | 0.636623i | \(0.780331\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.21992e6i | 0.948202i | 0.880470 | + | 0.474101i | \(0.157227\pi\) | ||||
−0.880470 | + | 0.474101i | \(0.842773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.39730e6 | 1.80074 | 0.900369 | − | 0.435128i | \(-0.143297\pi\) | ||||
0.900369 | + | 0.435128i | \(0.143297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.02648e6 | −0.414557 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.29824e6i | − 0.890697i | −0.895357 | − | 0.445348i | \(-0.853080\pi\) | ||||
0.895357 | − | 0.445348i | \(-0.146920\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 953532. | 0.359667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.73561e6i | 0.645920i | 0.946413 | + | 0.322960i | \(0.104678\pi\) | ||||
−0.946413 | + | 0.322960i | \(0.895322\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.43717e6i | 1.24551i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.39115e6 | 1.92789 | 0.963947 | − | 0.266094i | \(-0.0857331\pi\) | ||||
0.963947 | + | 0.266094i | \(0.0857331\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.27281e6i | 1.14005i | 0.821627 | + | 0.570026i | \(0.193067\pi\) | ||||
−0.821627 | + | 0.570026i | \(0.806933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 603114. | 0.202081 | 0.101040 | − | 0.994882i | \(-0.467783\pi\) | ||||
0.101040 | + | 0.994882i | \(0.467783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −592596. | −0.196027 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 749422.i | − 0.238644i | −0.992856 | − | 0.119322i | \(-0.961928\pi\) | ||||
0.992856 | − | 0.119322i | \(-0.0380721\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.31357e6 | −1.65016 | −0.825079 | − | 0.565018i | \(-0.808869\pi\) | ||||
−0.825079 | + | 0.565018i | \(0.808869\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.81943e6i | 1.78492i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.69664e6i | 0.806932i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −999326. | −0.295392 | −0.147696 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147696 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.56106e6i | − 0.738831i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.03740e6 | 0.566944 | 0.283472 | − | 0.958980i | \(-0.408514\pi\) | ||||
0.283472 | + | 0.958980i | \(0.408514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.11461e6 | −1.40640 | −0.703198 | − | 0.710994i | \(-0.748245\pi\) | ||||
−0.703198 | + | 0.710994i | \(0.748245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.87804e6i | 0.763882i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.30404e6 | 0.856747 | 0.428374 | − | 0.903602i | \(-0.359087\pi\) | ||||
0.428374 | + | 0.903602i | \(0.359087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.01638e6i | 0.516836i | 0.966033 | + | 0.258418i | \(0.0832012\pi\) | ||||
−0.966033 | + | 0.258418i | \(0.916799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.83594e6i | − 0.960879i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.58321e6 | −1.63033 | −0.815166 | − | 0.579227i | \(-0.803355\pi\) | ||||
−0.815166 | + | 0.579227i | \(0.803355\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.81783e6i | − 1.16638i | −0.812334 | − | 0.583192i | \(-0.801803\pi\) | ||||
0.812334 | − | 0.583192i | \(-0.198197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.20399e6 | −1.45230 | −0.726149 | − | 0.687538i | \(-0.758692\pi\) | ||||
−0.726149 | + | 0.687538i | \(0.758692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.90912e6 | 1.59949 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.84383e6i | 0.636962i | 0.947929 | + | 0.318481i | \(0.103173\pi\) | ||||
−0.947929 | + | 0.318481i | \(0.896827\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.75605e6 | 0.384844 | 0.192422 | − | 0.981312i | \(-0.438366\pi\) | ||||
0.192422 | + | 0.981312i | \(0.438366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.66857e6i | − 1.66250i | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
0.555899 | − | 0.831250i | \(-0.312374\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.35903e6i | 0.288361i | 0.989551 | + | 0.144181i | \(0.0460546\pi\) | ||||
−0.989551 | + | 0.144181i | \(0.953945\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.51616e6 | 0.528209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 177600.i | 0.0364998i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.02706e6 | −0.403672 | −0.201836 | − | 0.979419i | \(-0.564691\pi\) | ||||
−0.201836 | + | 0.979419i | \(0.564691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.49440e6 | −0.688667 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.46427e6i | 0.470833i | 0.971895 | + | 0.235416i | \(0.0756454\pi\) | ||||
−0.971895 | + | 0.235416i | \(0.924355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.03848e7 | −1.94399 | −0.971996 | − | 0.234998i | \(-0.924492\pi\) | ||||
−0.971996 | + | 0.234998i | \(0.924492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.02784e6i | − 0.190461i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.43798e6i | 1.16912i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.49416e6 | −1.16754 | −0.583769 | − | 0.811919i | \(-0.698423\pi\) | ||||
−0.583769 | + | 0.811919i | \(0.698423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.03565e7i | − 1.82513i | −0.408931 | − | 0.912565i | \(-0.634098\pi\) | ||||
0.408931 | − | 0.912565i | \(-0.365902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.87305e6 | 1.00478 | 0.502388 | − | 0.864643i | \(-0.332455\pi\) | ||||
0.502388 | + | 0.864643i | \(0.332455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.34616e6 | 1.24454 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7.75008e6i | − 1.27520i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.17295e6 | −0.350717 | −0.175358 | − | 0.984505i | \(-0.556108\pi\) | ||||
−0.175358 | + | 0.984505i | \(0.556108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.07361e6i | − 0.171629i | −0.996311 | − | 0.0858145i | \(-0.972651\pi\) | ||||
0.996311 | − | 0.0858145i | \(-0.0273492\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.74022e6i | − 0.272946i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.71425e6 | −0.577075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.95307e6i | 1.36507i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.47442e7 | −2.18599 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.09033e6 | 1.04153 | 0.520767 | − | 0.853699i | \(-0.325646\pi\) | ||||
0.520767 | + | 0.853699i | \(0.325646\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.69763e6i | 0.957091i | 0.878063 | + | 0.478545i | \(0.158836\pi\) | ||||
−0.878063 | + | 0.478545i | \(0.841164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.65330e6 | 0.933595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 6.80334e6i | − 0.946040i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.19008e7i | − 1.62532i | −0.582735 | − | 0.812662i | \(-0.698018\pi\) | ||||
0.582735 | − | 0.812662i | \(-0.301982\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −230140. | −0.0311503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.75636e6i | 1.16427i | 0.813093 | + | 0.582133i | \(0.197782\pi\) | ||||
−0.813093 | + | 0.582133i | \(0.802218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.15677e6 | −0.149784 | −0.0748922 | − | 0.997192i | \(-0.523861\pi\) | ||||
−0.0748922 | + | 0.997192i | \(0.523861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.07807e6 | −0.908500 | −0.454250 | − | 0.890874i | \(-0.650093\pi\) | ||||
−0.454250 | + | 0.890874i | \(0.650093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 3.13404e6i | − 0.391890i | −0.980615 | − | 0.195945i | \(-0.937223\pi\) | ||||
0.980615 | − | 0.195945i | \(-0.0627775\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.38559e6 | 1.03061 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.09952e6i | − 0.255828i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.13833e7i | − 1.36355i | −0.731561 | − | 0.681776i | \(-0.761208\pi\) | ||||
0.731561 | − | 0.681776i | \(-0.238792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.12646e7 | 1.33791 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.58655e7i | − 1.85275i | −0.376599 | − | 0.926376i | \(-0.622906\pi\) | ||||
0.376599 | − | 0.926376i | \(-0.377094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.50998e7 | −1.71951 | −0.859756 | − | 0.510705i | \(-0.829385\pi\) | ||||
−0.859756 | + | 0.510705i | \(0.829385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.08705e6 | −0.913280 | −0.456640 | − | 0.889652i | \(-0.650947\pi\) | ||||
−0.456640 | + | 0.889652i | \(0.650947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 710398.i | − 0.0782582i | −0.999234 | − | 0.0391291i | \(-0.987542\pi\) | ||||
0.999234 | − | 0.0391291i | \(-0.0124584\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00428e7 | 1.08831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5.96434e6i | − 0.641078i | −0.947235 | − | 0.320539i | \(-0.896136\pi\) | ||||
0.947235 | − | 0.320539i | \(-0.103864\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1.48432e7i | − 1.56970i | −0.619689 | − | 0.784848i | \(-0.712741\pi\) | ||||
0.619689 | − | 0.784848i | \(-0.287259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.82042e7 | 1.90961 | 0.954807 | − | 0.297227i | \(-0.0960620\pi\) | ||||
0.954807 | + | 0.297227i | \(0.0960620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.60541e7i | 2.68940i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.04495e6 | 0.105310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.09461e6 | 0.109443 | 0.0547214 | − | 0.998502i | \(-0.482573\pi\) | ||||
0.0547214 | + | 0.998502i | \(0.482573\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.91060e7i | − 1.86561i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.44046e6 | −0.715245 | −0.357622 | − | 0.933866i | \(-0.616413\pi\) | ||||
−0.357622 | + | 0.933866i | \(0.616413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.07915e7i | 1.02933i | 0.857391 | + | 0.514665i | \(0.172084\pi\) | ||||
−0.857391 | + | 0.514665i | \(0.827916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.62998e6i | 0.904409i | 0.891914 | + | 0.452204i | \(0.149362\pi\) | ||||
−0.891914 | + | 0.452204i | \(0.850638\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.63904e6 | −0.525525 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.00019e7i | − 0.917905i | −0.888461 | − | 0.458953i | \(-0.848225\pi\) | ||||
0.888461 | − | 0.458953i | \(-0.151775\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.01060e6 | −0.359746 | −0.179873 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179873 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20338e7 | 1.07127 | 0.535636 | − | 0.844449i | \(-0.320072\pi\) | ||||
0.535636 | + | 0.844449i | \(0.320072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.76058e7i | − 1.53229i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.33696e6 | 0.543344 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 2.01231e6i | − 0.171260i | −0.996327 | − | 0.0856301i | \(-0.972710\pi\) | ||||
0.996327 | − | 0.0856301i | \(-0.0272903\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.62410e7i | − 1.36188i | −0.732337 | − | 0.680942i | \(-0.761571\pi\) | ||||
0.732337 | − | 0.680942i | \(-0.238429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.06354e7 | −1.71767 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.62910e6i | 0.379704i | 0.981813 | + | 0.189852i | \(0.0608008\pi\) | ||||
−0.981813 | + | 0.189852i | \(0.939199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.72063e6 | 0.218334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.16794e7 | 0.930517 | 0.465258 | − | 0.885175i | \(-0.345961\pi\) | ||||
0.465258 | + | 0.885175i | \(0.345961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 2.67728e6i | − 0.208743i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.99543e7 | −1.53370 | −0.766851 | − | 0.641825i | \(-0.778178\pi\) | ||||
−0.766851 | + | 0.641825i | \(0.778178\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.76407e6i | 0.516202i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.20280e7i | − 1.65740i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.88331e6 | 0.364837 | 0.182419 | − | 0.983221i | \(-0.441607\pi\) | ||||
0.182419 | + | 0.983221i | \(0.441607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.98082e7i | − 2.19590i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.35778e7 | −0.979505 | −0.489753 | − | 0.871861i | \(-0.662913\pi\) | ||||
−0.489753 | + | 0.871861i | \(0.662913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.12686e7 | −2.24012 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.42411e6i | 0.450792i | 0.974267 | + | 0.225396i | \(0.0723677\pi\) | ||||
−0.974267 | + | 0.225396i | \(0.927632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68820.0 | 0.00476345 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9.08556e6i | − 0.624585i | −0.949986 | − | 0.312293i | \(-0.898903\pi\) | ||||
0.949986 | − | 0.312293i | \(-0.101097\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 5.54016e6i | − 0.375711i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.02457e7 | −1.36371 | −0.681854 | − | 0.731488i | \(-0.738826\pi\) | ||||
−0.681854 | + | 0.731488i | \(0.738826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 5.44831e6i | − 0.362067i | −0.983477 | − | 0.181034i | \(-0.942056\pi\) | ||||
0.983477 | − | 0.181034i | \(-0.0579443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.24378e7 | −0.810099 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.14072e6 | −0.0738041 | −0.0369021 | − | 0.999319i | \(-0.511749\pi\) | ||||
−0.0369021 | + | 0.999319i | \(0.511749\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.90153e7i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.23551e7 | −1.39931 | −0.699656 | − | 0.714480i | \(-0.746663\pi\) | ||||
−0.699656 | + | 0.714480i | \(0.746663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 679724.i | 0.0422689i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 7.30726e6i | − 0.448504i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00704e7 | 0.614088 | 0.307044 | − | 0.951695i | \(-0.400660\pi\) | ||||
0.307044 | + | 0.951695i | \(0.400660\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 4.05963e6i | − 0.244364i | −0.992508 | − | 0.122182i | \(-0.961011\pi\) | ||||
0.992508 | − | 0.122182i | \(-0.0389892\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.73304e7 | 1.02321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41754e7 | 0.831585 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.72256e7i | − 0.991372i | −0.868502 | − | 0.495686i | \(-0.834917\pi\) | ||||
0.868502 | − | 0.495686i | \(-0.165083\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.18884e7 | 0.675589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.21164e6i | 0.463711i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.10793e7i | 1.17547i | 0.809055 | + | 0.587733i | \(0.199980\pi\) | ||||
−0.809055 | + | 0.587733i | \(0.800020\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00316e6 | −0.166422 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.61750e7i | − 0.885231i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.87877e7 | −1.00926 | −0.504629 | − | 0.863336i | \(-0.668371\pi\) | ||||
−0.504629 | + | 0.863336i | \(0.668371\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.32456e7 | −0.707164 | −0.353582 | − | 0.935404i | \(-0.615036\pi\) | ||||
−0.353582 | + | 0.935404i | \(0.615036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 445480.i | 0.0233493i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.66925e6 | 0.397096 | 0.198548 | − | 0.980091i | \(-0.436377\pi\) | ||||
0.198548 | + | 0.980091i | \(0.436377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.82786e6i | 0.454314i | 0.973858 | + | 0.227157i | \(0.0729430\pi\) | ||||
−0.973858 | + | 0.227157i | \(0.927057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.06923e7i | 1.56051i | 0.625463 | + | 0.780254i | \(0.284910\pi\) | ||||
−0.625463 | + | 0.780254i | \(0.715090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.28414e7 | −1.65972 | −0.829860 | − | 0.557972i | \(-0.811580\pi\) | ||||
−0.829860 | + | 0.557972i | \(0.811580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.71336e6i | 0.285285i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.42117e6 | −0.413017 | −0.206508 | − | 0.978445i | \(-0.566210\pi\) | ||||
−0.206508 | + | 0.978445i | \(0.566210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00255e7 | 0.488784 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.51181e7i | 0.724083i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.78989e7 | 0.847234 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.35126e7i | − 1.10644i | −0.833035 | − | 0.553221i | \(-0.813399\pi\) | ||||
0.833035 | − | 0.553221i | \(-0.186601\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.13050e7i | 0.525799i | 0.964823 | + | 0.262900i | \(0.0846788\pi\) | ||||
−0.964823 | + | 0.262900i | \(0.915321\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.00078e7 | −0.462758 | −0.231379 | − | 0.972864i | \(-0.574324\pi\) | ||||
−0.231379 | + | 0.972864i | \(0.574324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.61429e7i | 1.19489i | 0.801911 | + | 0.597443i | \(0.203817\pi\) | ||||
−0.801911 | + | 0.597443i | \(0.796183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.49798e7 | −0.672911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.17912e6 | 0.320646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.92041e6i | − 0.0843129i | −0.999111 | − | 0.0421565i | \(-0.986577\pi\) | ||||
0.999111 | − | 0.0421565i | \(-0.0134228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.56594e7 | 1.11380 | 0.556899 | − | 0.830580i | \(-0.311991\pi\) | ||||
0.556899 | + | 0.830580i | \(0.311991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.05643e7i | 0.887590i | 0.896128 | + | 0.443795i | \(0.146368\pi\) | ||||
−0.896128 | + | 0.443795i | \(0.853632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 3.16868e7i | − 1.35229i | −0.736770 | − | 0.676143i | \(-0.763650\pi\) | ||||
0.736770 | − | 0.676143i | \(-0.236350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.38416e6 | −0.228488 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.94398e7i | − 0.815761i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.17013e7 | 2.13355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −813564. | −0.0333872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.96963e6i | 0.160225i | 0.996786 | + | 0.0801127i | \(0.0255280\pi\) | ||||
−0.996786 | + | 0.0801127i | \(0.974472\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.37945e7 | 0.550692 | 0.275346 | − | 0.961345i | \(-0.411208\pi\) | ||||
0.275346 | + | 0.961345i | \(0.411208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.84637e7i | − 0.733063i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5.15875e7i | − 2.02592i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.08126e6 | −0.315639 | −0.157819 | − | 0.987468i | \(-0.550446\pi\) | ||||
−0.157819 | + | 0.987468i | \(0.550446\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.83689e7i | 0.709707i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.99956e7 | 1.14030 | 0.570150 | − | 0.821541i | \(-0.306885\pi\) | ||||
0.570150 | + | 0.821541i | \(0.306885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.69833e7 | −1.39840 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.07620e7i | − 0.772540i | −0.922386 | − | 0.386270i | \(-0.873763\pi\) | ||||
0.922386 | − | 0.386270i | \(-0.126237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.47642e6 | 0.127985 | 0.0639923 | − | 0.997950i | \(-0.479617\pi\) | ||||
0.0639923 | + | 0.997950i | \(0.479617\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.58593e7i | − 1.67938i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.86700e6i | − 0.0676503i | −0.999428 | − | 0.0338252i | \(-0.989231\pi\) | ||||
0.999428 | − | 0.0338252i | \(-0.0107689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.09602e7 | 0.755490 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.85501e7i | − 1.37497i | −0.726199 | − | 0.687484i | \(-0.758715\pi\) | ||||
0.726199 | − | 0.687484i | \(-0.241285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.83044e6 | −0.169606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.89056e7 | 2.05754 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.64875e7i | 0.567008i | 0.958971 | + | 0.283504i | \(0.0914969\pi\) | ||||
−0.958971 | + | 0.283504i | \(0.908503\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.36976e7 | 0.806597 | 0.403299 | − | 0.915068i | \(-0.367864\pi\) | ||||
0.403299 | + | 0.915068i | \(0.367864\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.21185e7i | 1.42623i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.77590e7i | 1.93590i | 0.251143 | + | 0.967950i | \(0.419194\pi\) | ||||
−0.251143 | + | 0.967950i | \(0.580806\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.73667e7 | 1.91295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.10103e7i | − 0.363425i | −0.983352 | − | 0.181712i | \(-0.941836\pi\) | ||||
0.983352 | − | 0.181712i | \(-0.0581640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.17882e6 | 0.0383228 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.70807e7 | 1.19940 | 0.599700 | − | 0.800225i | \(-0.295287\pi\) | ||||
0.599700 | + | 0.800225i | \(0.295287\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.52935e6i | 0.144311i | 0.997393 | + | 0.0721553i | \(0.0229877\pi\) | ||||
−0.997393 | + | 0.0721553i | \(0.977012\pi\) | |||||||
\(998\) | 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 | 900.6.d.h.649.2 | 2 | ||
3.2 | odd | 2 | 100.6.c.a.49.1 | 2 | |||
5.2 | odd | 4 | 900.6.a.b.1.1 | 1 | |||
5.3 | odd | 4 | 180.6.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 900.6.d.h.649.1 | 2 | ||
12.11 | even | 2 | 400.6.c.c.49.2 | 2 | |||
15.2 | even | 4 | 100.6.a.a.1.1 | 1 | |||
15.8 | even | 4 | 20.6.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 100.6.c.a.49.2 | 2 | |||
20.3 | even | 4 | 720.6.a.l.1.1 | 1 | |||
60.23 | odd | 4 | 80.6.a.b.1.1 | 1 | |||
60.47 | odd | 4 | 400.6.a.m.1.1 | 1 | |||
60.59 | even | 2 | 400.6.c.c.49.1 | 2 | |||
105.83 | odd | 4 | 980.6.a.b.1.1 | 1 | |||
120.53 | even | 4 | 320.6.a.c.1.1 | 1 | |||
120.83 | odd | 4 | 320.6.a.n.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.6.a.a.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
80.6.a.b.1.1 | 1 | 60.23 | odd | 4 | |||
100.6.a.a.1.1 | 1 | 15.2 | even | 4 | |||
100.6.c.a.49.1 | 2 | 3.2 | odd | 2 | |||
100.6.c.a.49.2 | 2 | 15.14 | odd | 2 | |||
180.6.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
320.6.a.c.1.1 | 1 | 120.53 | even | 4 | |||
320.6.a.n.1.1 | 1 | 120.83 | odd | 4 | |||
400.6.a.m.1.1 | 1 | 60.47 | odd | 4 | |||
400.6.c.c.49.1 | 2 | 60.59 | even | 2 | |||
400.6.c.c.49.2 | 2 | 12.11 | even | 2 | |||
720.6.a.l.1.1 | 1 | 20.3 | even | 4 | |||
900.6.a.b.1.1 | 1 | 5.2 | odd | 4 | |||
900.6.d.h.649.1 | 2 | 5.4 | even | 2 | inner | ||
900.6.d.h.649.2 | 2 | 1.1 | even | 1 | trivial | ||
980.6.a.b.1.1 | 1 | 105.83 | odd | 4 |