Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,6,Mod(1,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.a (trivial) |
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: | yes |
Analytic conductor: | \(3.20767639626\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 20.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 22.0000 | 1.41130 | 0.705650 | − | 0.708560i | \(-0.250655\pi\) | ||||
0.705650 | + | 0.708560i | \(0.250655\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 218.000 | 1.68156 | 0.840778 | − | 0.541380i | \(-0.182098\pi\) | ||||
0.840778 | + | 0.541380i | \(0.182098\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −622.000 | −1.02078 | −0.510390 | − | 0.859943i | \(-0.670499\pi\) | ||||
−0.510390 | + | 0.859943i | \(0.670499\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −550.000 | −0.631153 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 186.000 | 0.156096 | 0.0780478 | − | 0.996950i | \(-0.475131\pi\) | ||||
0.0780478 | + | 0.996950i | \(0.475131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1204.00 | −0.765143 | −0.382571 | − | 0.923926i | \(-0.624961\pi\) | ||||
−0.382571 | + | 0.923926i | \(0.624961\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4796.00 | 2.37318 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3186.00 | −1.25582 | −0.627908 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627908 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −44.0000 | −0.0116156 | ||||||||
\(28\) | 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 | ||||||||
\(33\) | −10560.0 | −1.68803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5450.00 | −0.752015 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5618.00 | 0.674648 | 0.337324 | − | 0.941389i | \(-0.390478\pi\) | ||||
0.337324 | + | 0.941389i | \(0.390478\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −370.000 | −0.0305162 | −0.0152581 | − | 0.999884i | \(-0.504857\pi\) | ||||
−0.0152581 | + | 0.999884i | \(0.504857\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6025.00 | −0.443533 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16146.0 | 1.06615 | 0.533077 | − | 0.846066i | \(-0.321035\pi\) | ||||
0.533077 | + | 0.846066i | \(0.321035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30717.0 | 1.82763 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4092.00 | 0.220298 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4374.00 | −0.213889 | −0.106945 | − | 0.994265i | \(-0.534107\pi\) | ||||
−0.106945 | + | 0.994265i | \(0.534107\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12000.0 | 0.534902 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −26488.0 | −1.07985 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 52538.0 | 1.66772 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15550.0 | 0.456507 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11542.0 | −0.314119 | −0.157059 | − | 0.987589i | \(-0.550201\pi\) | ||||
−0.157059 | + | 0.987589i | \(0.550201\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 33698.0 | 0.740111 | 0.370056 | − | 0.929010i | \(-0.379339\pi\) | ||||
0.370056 | + | 0.929010i | \(0.379339\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13750.0 | 0.282260 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −104640. | −2.01127 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31208.0 | 0.562598 | 0.281299 | − | 0.959620i | \(-0.409235\pi\) | ||||
0.281299 | + | 0.959620i | \(0.409235\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59531.0 | −1.00816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −38466.0 | −0.612889 | −0.306444 | − | 0.951889i | \(-0.599139\pi\) | ||||
−0.306444 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4650.00 | −0.0698081 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 121572. | 1.72201 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 205832. | 2.46777 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30100.0 | 0.342182 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 94658.0 | 1.02148 | 0.510738 | − | 0.859737i | \(-0.329372\pi\) | ||||
0.510738 | + | 0.859737i | \(0.329372\pi\) | |||||||
\(98\) | 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. | −1.33217 | −0.666084 | − | 0.745877i | \(-0.732031\pi\) | ||||
−0.666084 | + | 0.745877i | \(0.732031\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −119900. | −1.06132 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −57054.0 | −0.481755 | −0.240878 | − | 0.970555i | \(-0.577435\pi\) | ||||
−0.240878 | + | 0.970555i | \(0.577435\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3118.00 | −0.0251368 | −0.0125684 | − | 0.999921i | \(-0.504001\pi\) | ||||
−0.0125684 | + | 0.999921i | \(0.504001\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 123596. | 0.952132 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −54534.0 | −0.401764 | −0.200882 | − | 0.979615i | \(-0.564381\pi\) | ||||
−0.200882 | + | 0.979615i | \(0.564381\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 79650.0 | 0.561618 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −149902. | −1.01238 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 40548.0 | 0.262484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 69349.0 | 0.430603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −316668. | −1.88730 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 24698.0 | 0.135879 | 0.0679395 | − | 0.997689i | \(-0.478358\pi\) | ||||
0.0679395 | + | 0.997689i | \(0.478358\pi\) | |||||||
\(128\) | 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. | −1.28663 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1100.00 | 0.00519467 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22158.0 | −0.100862 | −0.0504312 | − | 0.998728i | \(-0.516060\pi\) | ||||
−0.0504312 | + | 0.998728i | \(0.516060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −193204. | −0.848163 | −0.424081 | − | 0.905624i | \(-0.639403\pi\) | ||||
−0.424081 | + | 0.905624i | \(0.639403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 355212. | 1.50467 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 298560. | 1.22093 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −138150. | −0.545671 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 675774. | 2.57934 | ||||||||
\(148\) | 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 | ||||||||
\(153\) | 44826.0 | 0.154811 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −233900. | −0.781990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −335878. | −1.08751 | −0.543754 | − | 0.839245i | \(-0.682998\pi\) | ||||
−0.543754 | + | 0.839245i | \(0.682998\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −96228.0 | −0.301862 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −694548. | −2.11173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −101650. | −0.299667 | −0.149833 | − | 0.988711i | \(-0.547874\pi\) | ||||
−0.149833 | + | 0.988711i | \(0.547874\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 264000. | 0.754908 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 139242. | 0.386348 | 0.193174 | − | 0.981164i | \(-0.438122\pi\) | ||||
0.193174 | + | 0.981164i | \(0.438122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15591.0 | 0.0419911 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −290164. | −0.758845 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −265014. | −0.673215 | −0.336607 | − | 0.941645i | \(-0.609279\pi\) | ||||
−0.336607 | + | 0.941645i | \(0.609279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 136250. | 0.336311 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −258456. | −0.620088 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 290444. | 0.641113 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −140450. | −0.301712 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −89280.0 | −0.186703 | ||||||||
\(188\) | 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 | ||||||||
\(193\) | 1.00303e6 | 1.93831 | 0.969153 | − | 0.246459i | \(-0.0792672\pi\) | ||||
0.969153 | + | 0.246459i | \(0.0792672\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 342100. | 0.644268 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −823998. | −1.51273 | −0.756364 | − | 0.654151i | \(-0.773026\pi\) | ||||
−0.756364 | + | 0.654151i | \(0.773026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −906712. | −1.62307 | −0.811534 | − | 0.584305i | \(-0.801367\pi\) | ||||
−0.811534 | + | 0.584305i | \(0.801367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −253924. | −0.443316 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.20467e6 | 2.05176 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 359850. | 0.598049 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −767826. | −1.24548 | ||||||||
\(208\) | 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. | −0.981220 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9250.00 | 0.0136473 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.03961e6 | 2.94034 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 741356. | 1.04452 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −115692. | −0.159339 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −542050. | −0.729923 | −0.364962 | − | 0.931023i | \(-0.618918\pi\) | ||||
−0.364962 | + | 0.931023i | \(0.618918\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 150625. | 0.198354 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.44857e6 | −1.86585 | −0.932924 | − | 0.360075i | \(-0.882751\pi\) | ||||
−0.932924 | + | 0.360075i | \(0.882751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −478786. | −0.603327 | −0.301663 | − | 0.953414i | \(-0.597542\pi\) | ||||
−0.301663 | + | 0.953414i | \(0.597542\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.30208e6 | −2.83851 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 374106. | 0.451445 | 0.225723 | − | 0.974192i | \(-0.427526\pi\) | ||||
0.225723 | + | 0.974192i | \(0.427526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −403650. | −0.476799 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 686576. | 0.793995 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | −1.29899e6 | −1.41121 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −767925. | −0.817342 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 748888. | 0.781042 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | 1.52928e6 | 1.50205 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −102300. | −0.0985202 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.12877e6 | −1.06604 | −0.533021 | − | 0.846102i | \(-0.678943\pi\) | ||||
−0.533021 | + | 0.846102i | \(0.678943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.22472e6 | 1.13446 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.33177e6 | 1.21012 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −263082. | −0.234532 | −0.117266 | − | 0.993101i | \(-0.537413\pi\) | ||||
−0.117266 | + | 0.993101i | \(0.537413\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 109350. | 0.0956542 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.62931e6 | 2.25717 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | −2.98311e6 | −2.42250 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −300000. | −0.239216 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 743114. | 0.581910 | 0.290955 | − | 0.956737i | \(-0.406027\pi\) | ||||
0.290955 | + | 0.956737i | \(0.406027\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −1.63071e6 | −1.21035 | −0.605176 | − | 0.796092i | \(-0.706897\pi\) | ||||
−0.605176 | + | 0.796092i | \(0.706897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 662200. | 0.482922 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.13789e6 | −2.24871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.38526e6 | −0.975634 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.08248e6 | 1.44161 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 71250.0 | 0.0484859 | 0.0242430 | − | 0.999706i | \(-0.492282\pi\) | ||||
0.0242430 | + | 0.999706i | \(0.492282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 293700. | 0.196494 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21120.0 | 0.0138932 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.98169e6 | 1.28191 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −80660.0 | −0.0513147 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.22301e6 | 1.39103 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −330050. | −0.203156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.61762e6 | −0.979560 | −0.489780 | − | 0.871846i | \(-0.662923\pi\) | ||||
−0.489780 | + | 0.871846i | \(0.662923\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −2.70444e6 | −1.56033 | −0.780165 | − | 0.625574i | \(-0.784865\pi\) | ||||
−0.780165 | + | 0.625574i | \(0.784865\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.31345e6 | −0.745825 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.60347e6 | 1.45514 | 0.727568 | − | 0.686035i | \(-0.240650\pi\) | ||||
0.727568 | + | 0.686035i | \(0.240650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.65248e6 | −1.45940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.25519e6 | −0.679902 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −223944. | −0.119435 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −388750. | −0.204156 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −68596.0 | −0.0354756 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 1.35394e6 | 0.669096 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 288550. | 0.140478 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.71706e6 | 0.823588 | 0.411794 | − | 0.911277i | \(-0.364902\pi\) | ||||
0.411794 | + | 0.911277i | \(0.364902\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.19975e6 | −0.567010 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.49088e6 | −2.09144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.03238e6 | 1.39171 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.75230e6 | 0.792612 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 131370. | 0.0585696 | 0.0292848 | − | 0.999571i | \(-0.490677\pi\) | ||||
0.0292848 | + | 0.999571i | \(0.490677\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.50951e6 | 1.54235 | 0.771175 | − | 0.636623i | \(-0.219669\pi\) | ||||
0.771175 | + | 0.636623i | \(0.219669\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27368.0 | 0.0118570 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.21992e6 | 0.948202 | 0.474101 | − | 0.880470i | \(-0.342773\pi\) | ||||
0.474101 | + | 0.880470i | \(0.342773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 738300. | 0.310930 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 892056. | 0.370443 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 1.52568e6 | 0.607710 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −842450. | −0.330988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.29824e6 | −0.890697 | −0.445348 | − | 0.895357i | \(-0.646920\pi\) | ||||
−0.445348 | + | 0.895357i | \(0.646920\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.46895e6 | −1.32627 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −953532. | −0.359667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.73561e6 | −0.645920 | −0.322960 | − | 0.946413i | \(-0.604678\pi\) | ||||
−0.322960 | + | 0.946413i | \(0.604678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −343750. | −0.126231 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.43717e6 | −1.24551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.39115e6 | −1.92789 | −0.963947 | − | 0.266094i | \(-0.914267\pi\) | ||||
−0.963947 | + | 0.266094i | \(0.914267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 543356. | 0.191766 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.27281e6 | 1.14005 | 0.570026 | − | 0.821627i | \(-0.306933\pi\) | ||||
0.570026 | + | 0.821627i | \(0.306933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.61600e6 | 0.899468 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −89170.0 | −0.0302650 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 5.20608e6 | 1.70032 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −780200. | −0.251601 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −749422. | −0.238644 | −0.119322 | − | 0.992856i | \(-0.538072\pi\) | ||||
−0.119322 | + | 0.992856i | \(0.538072\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −5.81943e6 | −1.78492 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.48828e6 | 0.450864 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.69664e6 | −0.806932 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 999326. | 0.295392 | 0.147696 | − | 0.989033i | \(-0.452814\pi\) | ||||
0.147696 | + | 0.989033i | \(0.452814\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −487476. | −0.142347 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.56106e6 | −0.738831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 961650. | 0.274092 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.25049e6 | −1.19701 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 3.89119e6 | 1.05738 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 116250. | 0.0312191 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.87804e6 | 0.763882 | ||||||||
\(428\) | 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 | ||||||||
\(433\) | −2.01638e6 | −0.516836 | −0.258418 | − | 0.966033i | \(-0.583201\pi\) | ||||
−0.258418 | + | 0.966033i | \(0.583201\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.03930e6 | −0.770106 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.83594e6 | 0.960879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.58321e6 | 1.63033 | 0.815166 | − | 0.579227i | \(-0.196645\pi\) | ||||
0.815166 | + | 0.579227i | \(0.196645\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.40280e6 | 1.81259 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.81783e6 | −1.16638 | −0.583192 | − | 0.812334i | \(-0.698197\pi\) | ||||
−0.583192 | + | 0.812334i | \(0.698197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.98785e6 | −0.715251 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.86819e6 | 2.33598 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | −3.09892e6 | −0.709520 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.38990e6 | 0.767641 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.84383e6 | 0.636962 | 0.318481 | − | 0.947929i | \(-0.396827\pi\) | ||||
0.318481 | + | 0.947929i | \(0.396827\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 7.66857e6 | 1.66250 | 0.831250 | − | 0.555899i | \(-0.187626\pi\) | ||||
0.831250 | + | 0.555899i | \(0.187626\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.14580e6 | −1.10362 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.35903e6 | −0.288361 | −0.144181 | − | 0.989551i | \(-0.546055\pi\) | ||||
−0.144181 | + | 0.989551i | \(0.546055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51616e6 | −0.528209 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.38932e6 | −1.53480 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 177600. | 0.0364998 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −752500. | −0.153029 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.05413e6 | −0.212129 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | −1.52801e7 | −2.98028 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.36645e6 | −0.456818 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.46427e6 | 0.470833 | 0.235416 | − | 0.971895i | \(-0.424355\pi\) | ||||
0.235416 | + | 0.971895i | \(0.424355\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 1.02784e6 | 0.190461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.89200e6 | 0.530500 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.43798e6 | −1.16912 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.49416e6 | 1.16754 | 0.583769 | − | 0.811919i | \(-0.301577\pi\) | ||||
0.583769 | + | 0.811919i | \(0.301577\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.06332e6 | 0.545254 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.03565e7 | −1.82513 | −0.912565 | − | 0.408931i | \(-0.865902\pi\) | ||||
−0.912565 | + | 0.408931i | \(0.865902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.52615e6 | −0.440789 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 343002. | 0.0592621 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 52976.0 | 0.00888763 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.58585e6 | 0.595764 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.75008e6 | −1.27520 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 1.07361e6 | 0.171629 | 0.0858145 | − | 0.996311i | \(-0.472651\pi\) | ||||
0.0858145 | + | 0.996311i | \(0.472651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.99750e6 | 0.474636 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.74022e6 | 0.272946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.71425e6 | 0.577075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.83127e6 | −0.435757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.95307e6 | 1.36507 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.42635e6 | 0.215448 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.14186e6 | −0.470166 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 2.41274e6 | 0.351165 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 77950.0 | 0.0112415 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.69763e6 | 0.957091 | 0.478545 | − | 0.878063i | \(-0.341164\pi\) | ||||
0.478545 | + | 0.878063i | \(0.341164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.18168e6 | 0.450532 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65330e6 | −0.933595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.80334e6 | 0.946040 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.08990e6 | −0.425806 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.19008e7 | 1.62532 | 0.812662 | − | 0.582735i | \(-0.198018\pi\) | ||||
0.812662 | + | 0.582735i | \(0.198018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 230140. | 0.0311503 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.96416e6 | −0.263493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.75636e6 | 1.16427 | 0.582133 | − | 0.813093i | \(-0.302218\pi\) | ||||
0.582133 | + | 0.813093i | \(0.302218\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.36335e6 | 0.179674 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.29778e7 | −1.69528 | ||||||||
\(568\) | 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 | ||||||||
\(573\) | 6.48886e6 | 0.825623 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.99125e6 | −0.251163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.13404e6 | −0.391890 | −0.195945 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195945 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.20667e7 | 2.73553 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.38559e6 | −1.03061 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.09952e6 | 0.255828 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.74755e6 | 0.452749 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.13833e7 | 1.36355 | 0.681776 | − | 0.731561i | \(-0.261208\pi\) | ||||
0.681776 | + | 0.731561i | \(0.261208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.12646e7 | −1.33791 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.81280e7 | −2.13491 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.58655e7 | −1.85275 | −0.926376 | − | 0.376599i | \(-0.877094\pi\) | ||||
−0.926376 | + | 0.376599i | \(0.877094\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.01370e6 | −0.117386 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.99477e7 | −2.29064 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | −2.78162e6 | −0.311534 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.73372e6 | −0.192571 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −710398. | −0.0782582 | −0.0391291 | − | 0.999234i | \(-0.512458\pi\) | ||||
−0.0391291 | + | 0.999234i | \(0.512458\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.65027e7 | 2.89566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.00428e7 | −1.08831 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.96434e6 | 0.641078 | 0.320539 | − | 0.947235i | \(-0.396136\pi\) | ||||
0.320539 | + | 0.947235i | \(0.396136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.91670e6 | 0.844027 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.48432e7 | 1.56970 | 0.784848 | − | 0.619689i | \(-0.212741\pi\) | ||||
0.784848 | + | 0.619689i | \(0.212741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.82042e7 | −1.90961 | −0.954807 | − | 0.297227i | \(-0.903938\pi\) | ||||
−0.954807 | + | 0.297227i | \(0.903938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 140184. | 0.0145871 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.60541e7 | 2.68940 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.27142e7 | 1.29158 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 1.11404e7 | 1.10508 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −617450. | −0.0607670 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.91060e7 | −1.86561 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | −1.07915e7 | −1.02933 | −0.514665 | − | 0.857391i | \(-0.672084\pi\) | ||||
−0.514665 | + | 0.857391i | \(0.672084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 203500. | 0.0192604 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.62998e6 | −0.904409 | −0.452204 | − | 0.891914i | \(-0.649362\pi\) | ||||
−0.452204 | + | 0.891914i | \(0.649362\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.63904e6 | 0.525525 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.48714e7 | 4.14970 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.00019e7 | −0.917905 | −0.458953 | − | 0.888461i | \(-0.651775\pi\) | ||||
−0.458953 | + | 0.888461i | \(0.651775\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.91600e6 | −0.538797 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.12122e6 | 0.734020 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | −2.54522e6 | −0.224876 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.56180e6 | 0.575399 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.76058e7 | −1.53229 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.19251e7 | −1.03014 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.33696e6 | −0.543344 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.01231e6 | 0.171260 | 0.0856301 | − | 0.996327i | \(-0.472710\pi\) | ||||
0.0856301 | + | 0.996327i | \(0.472710\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −27500.0 | −0.00232313 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.62410e7 | 1.36188 | 0.680942 | − | 0.732337i | \(-0.261571\pi\) | ||||
0.680942 | + | 0.732337i | \(0.261571\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.06354e7 | 1.71767 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.18686e7 | −2.63327 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.62910e6 | 0.379704 | 0.189852 | − | 0.981813i | \(-0.439199\pi\) | ||||
0.189852 | + | 0.981813i | \(0.439199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 553950. | 0.0451070 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.05333e7 | −0.851476 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −2.52182e7 | −1.99472 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.83010e6 | 0.379310 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.67728e6 | −0.208743 | ||||||||
\(698\) | 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 | ||||||||
\(703\) | −6.76407e6 | −0.516202 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.88030e6 | −0.672907 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.20280e7 | 1.65740 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.88331e6 | −0.364837 | −0.182419 | − | 0.983221i | \(-0.558393\pi\) | ||||
−0.182419 | + | 0.983221i | \(0.558393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.52113e6 | 0.557968 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.98082e7 | −2.19590 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.46400e6 | −0.546017 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.72715e6 | 0.270757 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | −7.78241e6 | −0.553692 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.45375e6 | 0.244031 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.42411e6 | 0.450792 | 0.225396 | − | 0.974267i | \(-0.427632\pi\) | ||||
0.225396 | + | 0.974267i | \(0.427632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.41117e7 | −0.983472 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −68820.0 | −0.00476345 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.08556e6 | 0.624585 | 0.312293 | − | 0.949986i | \(-0.398903\pi\) | ||||
0.312293 | + | 0.949986i | \(0.398903\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.68944e7 | −1.15351 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.54016e6 | 0.375711 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.02457e7 | 1.36371 | 0.681854 | − | 0.731488i | \(-0.261174\pi\) | ||||
0.681854 | + | 0.731488i | \(0.261174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.64755e7 | 1.10229 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.44831e6 | −0.362067 | −0.181034 | − | 0.983477i | \(-0.557944\pi\) | ||||
−0.181034 | + | 0.983477i | \(0.557944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.12138e7 | −0.740226 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.27031e6 | −0.607845 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 2.76144e7 | 1.77479 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.52150e6 | 0.224833 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.90153e7 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(758\) | 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. | −0.0422689 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.12065e6 | −0.0692335 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.30726e6 | 0.448504 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.00704e7 | −0.614088 | −0.307044 | − | 0.951695i | \(-0.599340\pi\) | ||||
−0.307044 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.48330e7 | −1.50451 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.05963e6 | −0.244364 | −0.122182 | − | 0.992508i | \(-0.538989\pi\) | ||||
−0.122182 | + | 0.992508i | \(0.538989\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.84750e6 | 0.349716 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.69439e7 | 1.60106 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.73304e7 | 1.02321 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41754e7 | 0.831585 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −243144. | −0.0141729 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.39695e6 | 0.486348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.72256e7 | −0.991372 | −0.495686 | − | 0.868502i | \(-0.665083\pi\) | ||||
−0.495686 | + | 0.868502i | \(0.665083\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.78780e6 | −0.330995 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.18884e7 | −0.675589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.21164e6 | −0.463711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.40570e6 | 0.134997 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.10793e7 | −1.17547 | −0.587733 | − | 0.809055i | \(-0.699980\pi\) | ||||
−0.587733 | + | 0.809055i | \(0.699980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.00316e6 | 0.166422 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.88029e7 | 1.58619 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.61750e7 | −0.885231 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.73637e7 | 0.944393 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.61303e7 | −1.41241 | ||||||||
\(808\) | 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 | ||||||||
\(813\) | 9.48860e6 | 0.503473 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.54125e6 | 0.134015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 445480. | 0.0233493 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | −8.82786e6 | −0.454314 | −0.227157 | − | 0.973858i | \(-0.572943\pi\) | ||||
−0.227157 | + | 0.973858i | \(0.572943\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.60000e6 | −0.337605 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.06923e7 | −1.56051 | −0.780254 | − | 0.625463i | \(-0.784910\pi\) | ||||
−0.780254 | + | 0.625463i | \(0.784910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.28414e7 | 1.65972 | 0.829860 | − | 0.557972i | \(-0.188420\pi\) | ||||
0.829860 | + | 0.557972i | \(0.188420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.63485e7 | 0.821250 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.71336e6 | 0.285285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.48105e6 | −0.172780 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −411664. | −0.0203109 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 4.22824e7 | 2.04923 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −389775. | −0.0187790 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.51181e7 | 0.724083 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.58757e7 | −1.70817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.78989e7 | −0.847234 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.35126e7 | 1.10644 | 0.553221 | − | 0.833035i | \(-0.313399\pi\) | ||||
0.553221 | + | 0.833035i | \(0.313399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.25410e6 | 0.339366 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.13050e7 | −0.525799 | −0.262900 | − | 0.964823i | \(-0.584679\pi\) | ||||
−0.262900 | + | 0.964823i | \(0.584679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.00078e7 | 0.462758 | 0.231379 | − | 0.972864i | \(-0.425676\pi\) | ||||
0.231379 | + | 0.972864i | \(0.425676\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.90336e7 | −3.17360 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.61429e7 | 1.19489 | 0.597443 | − | 0.801911i | \(-0.296183\pi\) | ||||
0.597443 | + | 0.801911i | \(0.296183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.62535e6 | 0.301071 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.04757e7 | −1.37691 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.49798e7 | −0.672911 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.17912e6 | 0.320646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.28126e7 | 1.01307 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.40625e6 | −0.150403 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.92041e6 | −0.0843129 | −0.0421565 | − | 0.999111i | \(-0.513423\pi\) | ||||
−0.0421565 | + | 0.999111i | \(0.513423\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −2.05643e7 | −0.887590 | −0.443795 | − | 0.896128i | \(-0.646368\pi\) | ||||
−0.443795 | + | 0.896128i | \(0.646368\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.46140e6 | 0.277312 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.16868e7 | 1.35229 | 0.676143 | − | 0.736770i | \(-0.263650\pi\) | ||||
0.676143 | + | 0.736770i | \(0.263650\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.38416e6 | 0.228488 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.85749e7 | 1.20584 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.94398e7 | −0.815761 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.57030e6 | 0.148987 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.35972e7 | 1.80916 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.17013e7 | 2.13355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −813564. | −0.0333872 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.77452e6 | −0.0724205 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.74175e6 | −0.111277 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.96963e6 | 0.160225 | 0.0801127 | − | 0.996786i | \(-0.474472\pi\) | ||||
0.0801127 | + | 0.996786i | \(0.474472\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 1.84637e7 | 0.733063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.26110e6 | −0.286715 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.15875e7 | 2.02592 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.08126e6 | 0.315639 | 0.157819 | − | 0.987468i | \(-0.449554\pi\) | ||||
0.157819 | + | 0.987468i | \(0.449554\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.55877e7 | −1.38245 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.83689e7 | 0.709707 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.51125e6 | 0.134930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.45676e7 | −1.32120 | ||||||||
\(928\) | 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 | ||||||||
\(933\) | −1.50213e7 | −0.564943 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.23200e6 | 0.0834959 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.07620e7 | −0.772540 | −0.386270 | − | 0.922386i | \(-0.626237\pi\) | ||||
−0.386270 | + | 0.922386i | \(0.626237\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 4.58593e7 | 1.67938 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 239800. | 0.00873514 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.86700e6 | 0.0676503 | 0.0338252 | − | 0.999428i | \(-0.489231\pi\) | ||||
0.0338252 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.09602e7 | −0.755490 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.72763e7 | 2.05364 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.85501e7 | −1.37497 | −0.687484 | − | 0.726199i | \(-0.741285\pi\) | ||||
−0.687484 | + | 0.726199i | \(0.741285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.37370e6 | −0.261624 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.83546e7 | −2.05966 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.83044e6 | −0.169606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.89056e7 | 2.05754 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.37500e7 | −0.477790 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.50758e7 | −0.866837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.64875e7 | 0.567008 | 0.283504 | − | 0.958971i | \(-0.408503\pi\) | ||||
0.283504 | + | 0.958971i | \(0.408503\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | −4.21185e7 | −1.42623 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.55250e6 | −0.288125 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.77590e7 | −1.93590 | −0.967950 | − | 0.251143i | \(-0.919194\pi\) | ||||
−0.967950 | + | 0.251143i | \(0.919194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.73667e7 | −1.91295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −751438. | −0.0249299 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.10103e7 | −0.363425 | −0.181712 | − | 0.983352i | \(-0.558164\pi\) | ||||
−0.181712 | + | 0.983352i | \(0.558164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.06000e7 | 0.676512 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.74362e7 | 2.53018 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −1.45515e7 | −0.468311 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.26678e7 | 0.725858 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.52935e6 | 0.144311 | 0.0721553 | − | 0.997393i | \(-0.477012\pi\) | ||||
0.0721553 | + | 0.997393i | \(0.477012\pi\) | |||||||
\(998\) | 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 | 20.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 180.6.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 80.6.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 100.6.c.a.49.1 | 2 | |||
5.3 | odd | 4 | 100.6.c.a.49.2 | 2 | |||
5.4 | even | 2 | 100.6.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 980.6.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 320.6.a.n.1.1 | 1 | |||
8.5 | even | 2 | 320.6.a.c.1.1 | 1 | |||
12.11 | even | 2 | 720.6.a.l.1.1 | 1 | |||
15.2 | even | 4 | 900.6.d.h.649.2 | 2 | |||
15.8 | even | 4 | 900.6.d.h.649.1 | 2 | |||
15.14 | odd | 2 | 900.6.a.b.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.c.49.1 | 2 | |||
20.7 | even | 4 | 400.6.c.c.49.2 | 2 | |||
20.19 | odd | 2 | 400.6.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
80.6.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
100.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
100.6.c.a.49.1 | 2 | 5.2 | odd | 4 | |||
100.6.c.a.49.2 | 2 | 5.3 | odd | 4 | |||
180.6.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
320.6.a.c.1.1 | 1 | 8.5 | even | 2 | |||
320.6.a.n.1.1 | 1 | 8.3 | odd | 2 | |||
400.6.a.m.1.1 | 1 | 20.19 | odd | 2 | |||
400.6.c.c.49.1 | 2 | 20.3 | even | 4 | |||
400.6.c.c.49.2 | 2 | 20.7 | even | 4 | |||
720.6.a.l.1.1 | 1 | 12.11 | even | 2 | |||
900.6.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
900.6.d.h.649.1 | 2 | 15.8 | even | 4 | |||
900.6.d.h.649.2 | 2 | 15.2 | even | 4 | |||
980.6.a.b.1.1 | 1 | 7.6 | odd | 2 |