Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [100,6,Mod(49,100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("100.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.c (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: | \(16.0383819813\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 100.49 |
Dual form | 100.6.c.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(77\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 22.0000i | 1.41130i | 0.708560 | + | 0.705650i | \(0.249345\pi\) | ||||
−0.708560 | + | 0.705650i | \(0.750655\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 218.000i | − 1.68156i | −0.541380 | − | 0.840778i | \(-0.682098\pi\) | ||||
0.541380 | − | 0.840778i | \(-0.317902\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −241.000 | −0.991770 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −480.000 | −1.19608 | −0.598039 | − | 0.801467i | \(-0.704053\pi\) | ||||
−0.598039 | + | 0.801467i | \(0.704053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 622.000i | − 1.02078i | −0.859943 | − | 0.510390i | \(-0.829501\pi\) | ||||
0.859943 | − | 0.510390i | \(-0.170499\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | 4796.00 | 2.37318 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 44.0000i | 0.0116156i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5526.00 | −1.22016 | −0.610079 | − | 0.792341i | \(-0.708862\pi\) | ||||
−0.610079 | + | 0.792341i | \(0.708862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9356.00 | 1.74858 | 0.874291 | − | 0.485402i | \(-0.161327\pi\) | ||||
0.874291 | + | 0.485402i | \(0.161327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 10560.0i | − 1.68803i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5618.00i | − 0.674648i | −0.941389 | − | 0.337324i | \(-0.890478\pi\) | ||||
0.941389 | − | 0.337324i | \(-0.109522\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13684.0 | 1.44063 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14394.0 | −1.33728 | −0.668639 | − | 0.743587i | \(-0.733123\pi\) | ||||
−0.668639 | + | 0.743587i | \(0.733123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 370.000i | − 0.0305162i | −0.999884 | − | 0.0152581i | \(-0.995143\pi\) | ||||
0.999884 | − | 0.0152581i | \(-0.00485699\pi\) | |||||||
\(44\) | 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 | ||||||||
\(51\) | 4092.00 | 0.220298 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 26488.0i | 1.07985i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11748.0 | 0.439374 | 0.219687 | − | 0.975570i | \(-0.429496\pi\) | ||||
0.219687 | + | 0.975570i | \(0.429496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13202.0 | 0.454271 | 0.227136 | − | 0.973863i | \(-0.427064\pi\) | ||||
0.227136 | + | 0.973863i | \(0.427064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 52538.0i | 1.66772i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11542.0i | 0.314119i | 0.987589 | + | 0.157059i | \(0.0502014\pi\) | ||||
−0.987589 | + | 0.157059i | \(0.949799\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 70092.0 | 1.77233 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −29532.0 | −0.695260 | −0.347630 | − | 0.937632i | \(-0.613013\pi\) | ||||
−0.347630 | + | 0.937632i | \(0.613013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33698.0i | 0.740111i | 0.929010 | + | 0.370056i | \(0.120661\pi\) | ||||
−0.929010 | + | 0.370056i | \(0.879339\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | −59531.0 | −1.00816 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | − 121572.i | − 1.72201i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −119514. | −1.59935 | −0.799675 | − | 0.600432i | \(-0.794995\pi\) | ||||
−0.799675 | + | 0.600432i | \(0.794995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −135596. | −1.71650 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 205832.i | 2.46777i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 94658.0i | − 1.02148i | −0.859737 | − | 0.510738i | \(-0.829372\pi\) | ||||
0.859737 | − | 0.510738i | \(-0.170628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 115680. | 1.18623 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 101046. | 0.985634 | 0.492817 | − | 0.870133i | \(-0.335967\pi\) | ||||
0.492817 | + | 0.870133i | \(0.335967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 143434.i | − 1.33217i | −0.745877 | − | 0.666084i | \(-0.767969\pi\) | ||||
0.745877 | − | 0.666084i | \(-0.232031\pi\) | |||||||
\(104\) | 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 | ||||||||
\(111\) | 123596. | 0.952132 | ||||||||
\(112\) | 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 | ||||||||
\(117\) | 149902.i | 1.01238i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −40548.0 | −0.262484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69349.0 | 0.430603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 316668.i | − 1.88730i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 24698.0i | − 0.135879i | −0.997689 | − | 0.0679395i | \(-0.978358\pi\) | ||||
0.997689 | − | 0.0679395i | \(-0.0216425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8140.00 | 0.0430675 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 236640. | 1.20479 | 0.602393 | − | 0.798200i | \(-0.294214\pi\) | ||||
0.602393 | + | 0.798200i | \(0.294214\pi\) | |||||||
\(132\) | 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 | ||||||||
\(141\) | 355212. | 1.50467 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 298560.i | 1.22093i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 675774.i | − 2.57934i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −448554. | −1.65519 | −0.827597 | − | 0.561322i | \(-0.810293\pi\) | ||||
−0.827597 | + | 0.561322i | \(0.810293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −140860. | −0.502742 | −0.251371 | − | 0.967891i | \(-0.580881\pi\) | ||||
−0.251371 | + | 0.967891i | \(0.580881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 44826.0i | 0.154811i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 335878.i | 1.08751i | 0.839245 | + | 0.543754i | \(0.182998\pi\) | ||||
−0.839245 | + | 0.543754i | \(0.817002\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 96228.0 | 0.301862 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −694548. | −2.11173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 101650.i | − 0.299667i | −0.988711 | − | 0.149833i | \(-0.952126\pi\) | ||||
0.988711 | − | 0.149833i | \(-0.0478737\pi\) | |||||||
\(164\) | 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 | ||||||||
\(171\) | −290164. | −0.758845 | ||||||||
\(172\) | 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 | ||||||||
\(177\) | 258456.i | 0.620088i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 142812. | 0.333144 | 0.166572 | − | 0.986029i | \(-0.446730\pi\) | ||||
0.166572 | + | 0.986029i | \(0.446730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 109670. | 0.248824 | 0.124412 | − | 0.992231i | \(-0.460296\pi\) | ||||
0.124412 | + | 0.992231i | \(0.460296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 290444.i | 0.641113i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 89280.0i | 0.186703i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9592.00 | 0.0195324 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 294948. | 0.585008 | 0.292504 | − | 0.956264i | \(-0.405511\pi\) | ||||
0.292504 | + | 0.956264i | \(0.405511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00303e6i | 1.93831i | 0.246459 | + | 0.969153i | \(0.420733\pi\) | ||||
−0.246459 | + | 0.969153i | \(0.579267\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | −253924. | −0.443316 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.20467e6i | 2.05176i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 767826.i | 1.24548i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | − 649704.i | − 0.981220i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 2.03961e6i | − 2.94034i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −741356. | −1.04452 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −115692. | −0.159339 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 542050.i | − 0.729923i | −0.931023 | − | 0.364962i | \(-0.881082\pi\) | ||||
0.931023 | − | 0.364962i | \(-0.118918\pi\) | |||||||
\(224\) | 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 | ||||||||
\(231\) | −2.30208e6 | −2.83851 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | − 686576.i | − 0.793995i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −169416. | −0.191849 | −0.0959245 | − | 0.995389i | \(-0.530581\pi\) | ||||
−0.0959245 | + | 0.995389i | \(0.530581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −353746. | −0.392328 | −0.196164 | − | 0.980571i | \(-0.562848\pi\) | ||||
−0.196164 | + | 0.980571i | \(0.562848\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.29899e6i | − 1.41121i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 748888.i | − 0.781042i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 846252. | 0.864971 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.25520e6 | 1.25756 | 0.628780 | − | 0.777583i | \(-0.283555\pi\) | ||||
0.628780 | + | 0.777583i | \(0.283555\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | 1.33177e6 | 1.21012 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | − 2.62931e6i | − 2.25717i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.18774e6 | 1.00079 | 0.500393 | − | 0.865798i | \(-0.333189\pi\) | ||||
0.500393 | + | 0.865798i | \(0.333189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 431300. | 0.356744 | 0.178372 | − | 0.983963i | \(-0.442917\pi\) | ||||
0.178372 | + | 0.983963i | \(0.442917\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 2.98311e6i | − 2.42250i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 743114.i | − 0.581910i | −0.956737 | − | 0.290955i | \(-0.906027\pi\) | ||||
0.956737 | − | 0.290955i | \(-0.0939730\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.25480e6 | −1.73419 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.92193e6 | 1.45201 | 0.726007 | − | 0.687687i | \(-0.241374\pi\) | ||||
0.726007 | + | 0.687687i | \(0.241374\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.63071e6i | − 1.21035i | −0.796092 | − | 0.605176i | \(-0.793103\pi\) | ||||
0.796092 | − | 0.605176i | \(-0.206897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.13789e6i | 2.24871i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.38526e6 | 0.975634 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.08248e6 | 1.44161 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | − 21120.0i | − 0.0138932i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.98169e6 | −1.28191 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −80660.0 | −0.0513147 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.22301e6i | 1.39103i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.61762e6i | 0.979560i | 0.871846 | + | 0.489780i | \(0.162923\pi\) | ||||
−0.871846 | + | 0.489780i | \(0.837077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.15555e6 | 1.88009 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −682788. | −0.400299 | −0.200150 | − | 0.979765i | \(-0.564143\pi\) | ||||
−0.200150 | + | 0.979765i | \(0.564143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 2.70444e6i | − 1.56033i | −0.625574 | − | 0.780165i | \(-0.715135\pi\) | ||||
0.625574 | − | 0.780165i | \(-0.284865\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | −1.25519e6 | −0.679902 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 223944.i | − 0.119435i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 68596.0i | 0.0354756i | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 1.35394e6i | 0.669096i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1.71706e6i | − 0.823588i | −0.911277 | − | 0.411794i | \(-0.864902\pi\) | ||||
0.911277 | − | 0.411794i | \(-0.135098\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.19975e6 | 0.567010 | ||||||||
\(340\) | 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 | ||||||||
\(351\) | 27368.0 | 0.0118570 | ||||||||
\(352\) | 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 | ||||||||
\(357\) | − 892056.i | − 0.370443i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.39730e6 | −1.80074 | −0.900369 | − | 0.435128i | \(-0.856703\pi\) | ||||
−0.900369 | + | 0.435128i | \(0.856703\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.02648e6 | −0.414557 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.52568e6i | 0.607710i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29824e6i | 0.890697i | 0.895357 | + | 0.445348i | \(0.146920\pi\) | ||||
−0.895357 | + | 0.445348i | \(0.853080\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.46895e6 | 1.32627 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −953532. | −0.359667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.73561e6i | − 0.645920i | −0.946413 | − | 0.322960i | \(-0.895322\pi\) | ||||
0.946413 | − | 0.322960i | \(-0.104678\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | 543356. | 0.191766 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 89170.0i | 0.0302650i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −603114. | −0.202081 | −0.101040 | − | 0.994882i | \(-0.532217\pi\) | ||||
−0.101040 | + | 0.994882i | \(0.532217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −592596. | −0.196027 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.20608e6i | 1.70032i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 749422.i | 0.238644i | 0.992856 | + | 0.119322i | \(0.0380721\pi\) | ||||
−0.992856 | + | 0.119322i | \(0.961928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.77438e6 | 1.81582 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31357e6 | 1.65016 | 0.825079 | − | 0.565018i | \(-0.191131\pi\) | ||||
0.825079 | + | 0.565018i | \(0.191131\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | −487476. | −0.142347 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.56106e6i | − 0.738831i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.25049e6i | 1.19701i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.03740e6 | −0.566944 | −0.283472 | − | 0.958980i | \(-0.591486\pi\) | ||||
−0.283472 | + | 0.958980i | \(0.591486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.11461e6 | −1.40640 | −0.703198 | − | 0.710994i | \(-0.748245\pi\) | ||||
−0.703198 | + | 0.710994i | \(0.748245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.89119e6i | 1.05738i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.87804e6i | − 0.763882i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.56832e6 | −1.72310 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.30404e6 | −0.856747 | −0.428374 | − | 0.903602i | \(-0.640913\pi\) | ||||
−0.428374 | + | 0.903602i | \(0.640913\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 2.01638e6i | − 0.516836i | −0.966033 | − | 0.258418i | \(-0.916799\pi\) | ||||
0.966033 | − | 0.258418i | \(-0.0832012\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | 7.40280e6 | 1.81259 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | − 9.86819e6i | − 2.33598i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.20399e6 | 1.45230 | 0.726149 | − | 0.687538i | \(-0.241308\pi\) | ||||
0.726149 | + | 0.687538i | \(0.241308\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.90912e6 | 1.59949 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.09892e6i | − 0.709520i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 2.84383e6i | − 0.636962i | −0.947929 | − | 0.318481i | \(-0.896827\pi\) | ||||
0.947929 | − | 0.318481i | \(-0.103173\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8184.00 | 0.00181315 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.75605e6 | −0.384844 | −0.192422 | − | 0.981312i | \(-0.561634\pi\) | ||||
−0.192422 | + | 0.981312i | \(0.561634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.66857e6i | 1.66250i | 0.555899 | + | 0.831250i | \(0.312374\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(464\) | 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 | ||||||||
\(471\) | −7.38932e6 | −1.53480 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 177600.i | 0.0364998i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.05413e6i | 0.212129i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.02706e6 | 0.403672 | 0.201836 | − | 0.979419i | \(-0.435309\pi\) | ||||
0.201836 | + | 0.979419i | \(0.435309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.49440e6 | −0.688667 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.52801e7i | − 2.98028i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.46427e6i | − 0.470833i | −0.971895 | − | 0.235416i | \(-0.924355\pi\) | ||||
0.971895 | − | 0.235416i | \(-0.0756454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.23630e6 | 0.422920 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.03848e7 | 1.94399 | 0.971996 | − | 0.234998i | \(-0.0755084\pi\) | ||||
0.971996 | + | 0.234998i | \(0.0755084\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | 3.06332e6 | 0.545254 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − 343002.i | − 0.0592621i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.87305e6 | −1.00478 | −0.502388 | − | 0.864643i | \(-0.667545\pi\) | ||||
−0.502388 | + | 0.864643i | \(0.667545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.34616e6 | 1.24454 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 52976.0i | 0.00888763i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.75008e6i | 1.27520i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.83031e6 | 0.950108 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.17295e6 | 0.350717 | 0.175358 | − | 0.984505i | \(-0.443892\pi\) | ||||
0.175358 | + | 0.984505i | \(0.443892\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.07361e6i | 0.171629i | 0.996311 | + | 0.0858145i | \(0.0273492\pi\) | ||||
−0.996311 | + | 0.0858145i | \(0.972651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.74022e6i | − 0.272946i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.71425e6 | −0.577075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.83127e6 | −0.435757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.95307e6i | 1.36507i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.14186e6i | 0.470166i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 2.41274e6i | 0.351165i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6.69763e6i | − 0.957091i | −0.878063 | − | 0.478545i | \(-0.841164\pi\) | ||||
0.878063 | − | 0.478545i | \(-0.158836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.18168e6 | −0.450532 | ||||||||
\(550\) | 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 | ||||||||
\(561\) | −1.96416e6 | −0.263493 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 1.29778e7i | 1.69528i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.15677e6 | 0.149784 | 0.0748922 | − | 0.997192i | \(-0.476139\pi\) | ||||
0.0748922 | + | 0.997192i | \(0.476139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.07807e6 | −0.908500 | −0.454250 | − | 0.890874i | \(-0.650093\pi\) | ||||
−0.454250 | + | 0.890874i | \(0.650093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.48886e6i | 0.825623i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.13404e6i | 0.391890i | 0.980615 | + | 0.195945i | \(0.0627775\pi\) | ||||
−0.980615 | + | 0.195945i | \(0.937223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.20667e7 | −2.73553 | ||||||||
\(580\) | 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 | ||||||||
\(591\) | −1.81280e7 | −2.13491 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 1.99477e7i | 2.29064i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50998e7 | 1.71951 | 0.859756 | − | 0.510705i | \(-0.170615\pi\) | ||||
0.859756 | + | 0.510705i | \(0.170615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.08705e6 | −0.913280 | −0.456640 | − | 0.889652i | \(-0.650947\pi\) | ||||
−0.456640 | + | 0.889652i | \(0.650947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.78162e6i | − 0.311534i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 710398.i | 0.0782582i | 0.999234 | + | 0.0391291i | \(0.0124584\pi\) | ||||
−0.999234 | + | 0.0391291i | \(0.987542\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.65027e7 | −2.89566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00428e7 | −1.08831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.96434e6i | 0.641078i | 0.947235 | + | 0.320539i | \(0.103864\pi\) | ||||
−0.947235 | + | 0.320539i | \(0.896136\pi\) | |||||||
\(614\) | 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 | ||||||||
\(621\) | 140184. | 0.0145871 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.60541e7i | 2.68940i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.27142e7i | − 1.29158i | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 1.11404e7i | 1.10508i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.91060e7i | 1.86561i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.11721e6 | 0.689537 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.44046e6 | 0.715245 | 0.357622 | − | 0.933866i | \(-0.383587\pi\) | ||||
0.357622 | + | 0.933866i | \(0.383587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.07915e7i | − 1.02933i | −0.857391 | − | 0.514665i | \(-0.827916\pi\) | ||||
0.857391 | − | 0.514665i | \(-0.172084\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 4.48714e7 | 4.14970 | ||||||||
\(652\) | 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 | ||||||||
\(657\) | − 8.12122e6i | − 0.734020i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.01060e6 | 0.359746 | 0.179873 | − | 0.983690i | \(-0.442431\pi\) | ||||
0.179873 | + | 0.983690i | \(0.442431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20338e7 | 1.07127 | 0.535636 | − | 0.844449i | \(-0.320072\pi\) | ||||
0.535636 | + | 0.844449i | \(0.320072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.54522e6i | − 0.224876i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.76058e7i | 1.53229i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.19251e7 | 1.03014 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.33696e6 | −0.543344 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.01231e6i | 0.171260i | 0.996327 | + | 0.0856301i | \(0.0272903\pi\) | ||||
−0.996327 | + | 0.0856301i | \(0.972710\pi\) | |||||||
\(674\) | 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 | ||||||||
\(681\) | −3.18686e7 | −2.63327 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 1.05333e7i | 0.851476i | ||||||||
\(688\) | 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 | ||||||||
\(693\) | − 2.52182e7i | − 1.99472i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.67728e6i | 0.208743i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.23033e6 | −0.637125 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.99543e7 | 1.53370 | 0.766851 | − | 0.641825i | \(-0.221822\pi\) | ||||
0.766851 | + | 0.641825i | \(0.221822\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | 7.52113e6 | 0.557968 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.98082e7i | − 2.19590i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.72715e6i | − 0.270757i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.35778e7 | 0.979505 | 0.489753 | − | 0.871861i | \(-0.337087\pi\) | ||||
0.489753 | + | 0.871861i | \(0.337087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.12686e7 | −2.24012 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 7.78241e6i | − 0.553692i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6.42411e6i | − 0.450792i | −0.974267 | − | 0.225396i | \(-0.927632\pi\) | ||||
0.974267 | − | 0.225396i | \(-0.0723677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.41117e7 | 0.983472 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −68820.0 | −0.00476345 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.08556e6i | 0.624585i | 0.949986 | + | 0.312293i | \(0.101097\pi\) | ||||
−0.949986 | + | 0.312293i | \(0.898903\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 1.64755e7 | 1.10229 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 9.27031e6i | 0.607845i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 2.76144e7i | 1.77479i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.90153e7i | − 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.36442e7 | −2.11985 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.23551e7 | 1.39931 | 0.699656 | − | 0.714480i | \(-0.253337\pi\) | ||||
0.699656 | + | 0.714480i | \(0.253337\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | −2.48330e7 | −1.50451 | ||||||||
\(772\) | 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 | ||||||||
\(777\) | − 2.69439e7i | − 1.60106i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.73304e7 | −1.02321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41754e7 | 0.831585 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 243144.i | − 0.0141729i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.72256e7i | 0.991372i | 0.868502 | + | 0.495686i | \(0.165083\pi\) | ||||
−0.868502 | + | 0.495686i | \(0.834917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.78780e6 | 0.330995 | ||||||||
\(790\) | 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 | ||||||||
\(801\) | 2.88029e7 | 1.58619 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.61750e7i | − 0.885231i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.61303e7i | 1.41241i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.87877e7 | 1.00926 | 0.504629 | − | 0.863336i | \(-0.331629\pi\) | ||||
0.504629 | + | 0.863336i | \(0.331629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.32456e7 | −0.707164 | −0.353582 | − | 0.935404i | \(-0.615036\pi\) | ||||
−0.353582 | + | 0.935404i | \(0.615036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.48860e6i | 0.503473i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 445480.i | − 0.0233493i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.26786e7 | 1.70237 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.66925e6 | −0.397096 | −0.198548 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198548 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.82786e6i | − 0.454314i | −0.973858 | − | 0.227157i | \(-0.927057\pi\) | ||||
0.973858 | − | 0.227157i | \(-0.0729430\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | 1.63485e7 | 0.821250 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.71336e6i | 0.285285i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 411664.i | 0.0203109i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.42117e6 | 0.413017 | 0.206508 | − | 0.978445i | \(-0.433790\pi\) | ||||
0.206508 | + | 0.978445i | \(0.433790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00255e7 | 0.488784 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.22824e7i | 2.04923i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.51181e7i | − 0.724083i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.58757e7 | 1.70817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.78989e7 | −0.847234 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.35126e7i | 1.10644i | 0.833035 | + | 0.553221i | \(0.186601\pi\) | ||||
−0.833035 | + | 0.553221i | \(0.813399\pi\) | |||||||
\(854\) | 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 | ||||||||
\(861\) | −6.90336e7 | −3.17360 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 3.04757e7i | 1.37691i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.49798e7 | 0.672911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.17912e6 | 0.320646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.28126e7i | 1.01307i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.92041e6i | 0.0843129i | 0.999111 | + | 0.0421565i | \(0.0134228\pi\) | ||||
−0.999111 | + | 0.0421565i | \(0.986577\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.56750e6 | −0.0684282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.56594e7 | −1.11380 | −0.556899 | − | 0.830580i | \(-0.688009\pi\) | ||||
−0.556899 | + | 0.830580i | \(0.688009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.05643e7i | − 0.887590i | −0.896128 | − | 0.443795i | \(-0.853632\pi\) | ||||
0.896128 | − | 0.443795i | \(-0.146368\pi\) | |||||||
\(884\) | 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 | ||||||||
\(891\) | 2.85749e7 | 1.20584 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.94398e7i | − 0.815761i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 4.35972e7i | − 1.80916i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.17013e7 | −2.13355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −813564. | −0.0333872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.77452e6i | − 0.0724205i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.96963e6i | − 0.160225i | −0.996786 | − | 0.0801127i | \(-0.974472\pi\) | ||||
0.996786 | − | 0.0801127i | \(-0.0255280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.43521e7 | −0.977522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.37945e7 | −0.550692 | −0.275346 | − | 0.961345i | \(-0.588792\pi\) | ||||
−0.275346 | + | 0.961345i | \(0.588792\pi\) | |||||||
\(912\) | 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 | ||||||||
\(921\) | −3.55877e7 | −1.38245 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.83689e7i | 0.709707i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.45676e7i | 1.32120i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.99956e7 | −1.14030 | −0.570150 | − | 0.821541i | \(-0.693115\pi\) | ||||
−0.570150 | + | 0.821541i | \(0.693115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.69833e7 | −1.39840 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.50213e7i | − 0.564943i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.07620e7i | 0.772540i | 0.922386 | + | 0.386270i | \(0.126237\pi\) | ||||
−0.922386 | + | 0.386270i | \(0.873763\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.94976e7 | 2.20209 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.47642e6 | −0.127985 | −0.0639923 | − | 0.997950i | \(-0.520383\pi\) | ||||
−0.0639923 | + | 0.997950i | \(0.520383\pi\) | |||||||
\(942\) | 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 | ||||||||
\(951\) | 5.72763e7 | 2.05364 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 5.83546e7i | 2.05966i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.83044e6 | 0.169606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.89056e7 | 2.05754 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.37500e7i | − 0.477790i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.64875e7i | − 0.567008i | −0.958971 | − | 0.283504i | \(-0.908503\pi\) | ||||
0.958971 | − | 0.283504i | \(-0.0914969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.92677e6 | 0.168559 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.36976e7 | −0.806597 | −0.403299 | − | 0.915068i | \(-0.632136\pi\) | ||||
−0.403299 | + | 0.915068i | \(0.632136\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −751438. | −0.0249299 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | − 7.74362e7i | − 2.53018i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | − 1.45515e7i | − 0.468311i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.52935e6i | − 0.144311i | −0.997393 | − | 0.0721553i | \(-0.977012\pi\) | ||||
0.997393 | − | 0.0721553i | \(-0.0229877\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 247192. | 0.00783647 |
(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 | 100.6.c.a.49.2 | 2 | ||
3.2 | odd | 2 | 900.6.d.h.649.1 | 2 | |||
4.3 | odd | 2 | 400.6.c.c.49.1 | 2 | |||
5.2 | odd | 4 | 20.6.a.a.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 100.6.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 100.6.c.a.49.1 | 2 | ||
15.2 | even | 4 | 180.6.a.e.1.1 | 1 | |||
15.8 | even | 4 | 900.6.a.b.1.1 | 1 | |||
15.14 | odd | 2 | 900.6.d.h.649.2 | 2 | |||
20.3 | even | 4 | 400.6.a.m.1.1 | 1 | |||
20.7 | even | 4 | 80.6.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.c.49.2 | 2 | |||
35.27 | even | 4 | 980.6.a.b.1.1 | 1 | |||
40.27 | even | 4 | 320.6.a.n.1.1 | 1 | |||
40.37 | odd | 4 | 320.6.a.c.1.1 | 1 | |||
60.47 | odd | 4 | 720.6.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.6.a.a.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
80.6.a.b.1.1 | 1 | 20.7 | even | 4 | |||
100.6.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
100.6.c.a.49.1 | 2 | 5.4 | even | 2 | inner | ||
100.6.c.a.49.2 | 2 | 1.1 | even | 1 | trivial | ||
180.6.a.e.1.1 | 1 | 15.2 | even | 4 | |||
320.6.a.c.1.1 | 1 | 40.37 | odd | 4 | |||
320.6.a.n.1.1 | 1 | 40.27 | even | 4 | |||
400.6.a.m.1.1 | 1 | 20.3 | even | 4 | |||
400.6.c.c.49.1 | 2 | 4.3 | odd | 2 | |||
400.6.c.c.49.2 | 2 | 20.19 | odd | 2 | |||
720.6.a.l.1.1 | 1 | 60.47 | odd | 4 | |||
900.6.a.b.1.1 | 1 | 15.8 | even | 4 | |||
900.6.d.h.649.1 | 2 | 3.2 | odd | 2 | |||
900.6.d.h.649.2 | 2 | 15.14 | odd | 2 | |||
980.6.a.b.1.1 | 1 | 35.27 | even | 4 |