Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(64.1535279252\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.31662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-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 | ||||||||
\(3\) | −19.8997 | −1.27657 | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||||
−0.638285 | + | 0.769800i | \(0.720356\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 59.6992 | 0.460494 | 0.230247 | − | 0.973132i | \(-0.426047\pi\) | ||||
0.230247 | + | 0.973132i | \(0.426047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 153.000 | 0.629630 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −252.000 | −0.627941 | −0.313970 | − | 0.949433i | \(-0.601659\pi\) | ||||
−0.313970 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 119.398 | 0.195948 | 0.0979739 | − | 0.995189i | \(-0.468764\pi\) | ||||
0.0979739 | + | 0.995189i | \(0.468764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −689.858 | −0.578945 | −0.289473 | − | 0.957186i | \(-0.593480\pi\) | ||||
−0.289473 | + | 0.957186i | \(0.593480\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −220.000 | −0.139810 | −0.0699051 | − | 0.997554i | \(-0.522270\pi\) | ||||
−0.0699051 | + | 0.997554i | \(0.522270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1188.00 | −0.587852 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2434.40 | 0.959561 | 0.479781 | − | 0.877388i | \(-0.340716\pi\) | ||||
0.479781 | + | 0.877388i | \(0.340716\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1790.98 | 0.472804 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6930.00 | 1.53016 | 0.765082 | − | 0.643932i | \(-0.222698\pi\) | ||||
0.765082 | + | 0.643932i | \(0.222698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6752.00 | −1.26191 | −0.630955 | − | 0.775820i | \(-0.717337\pi\) | ||||
−0.630955 | + | 0.775820i | \(0.717337\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5014.74 | 0.801610 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13969.6 | 1.67757 | 0.838785 | − | 0.544464i | \(-0.183267\pi\) | ||||
0.838785 | + | 0.544464i | \(0.183267\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2376.00 | −0.250141 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.000 | −0.0183952 | −0.00919762 | − | 0.999958i | \(-0.502928\pi\) | ||||
−0.00919762 | + | 0.999958i | \(0.502928\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −417.895 | −0.0344664 | −0.0172332 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172332 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10540.2 | 0.695994 | 0.347997 | − | 0.937496i | \(-0.386862\pi\) | ||||
0.347997 | + | 0.937496i | \(0.386862\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13243.0 | −0.787945 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13728.0 | 0.739064 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5823.99 | 0.284794 | 0.142397 | − | 0.989810i | \(-0.454519\pi\) | ||||
0.142397 | + | 0.989810i | \(0.454519\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4377.94 | 0.178477 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −24660.0 | −0.922281 | −0.461140 | − | 0.887327i | \(-0.652560\pi\) | ||||
−0.461140 | + | 0.887327i | \(0.652560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5698.00 | −0.196064 | −0.0980320 | − | 0.995183i | \(-0.531255\pi\) | ||||
−0.0980320 | + | 0.995183i | \(0.531255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9133.98 | 0.289941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 43640.1 | 1.18768 | 0.593840 | − | 0.804583i | \(-0.297611\pi\) | ||||
0.593840 | + | 0.804583i | \(0.297611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −48444.0 | −1.22495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −53352.0 | −1.25604 | −0.628022 | − | 0.778196i | \(-0.716135\pi\) | ||||
−0.628022 | + | 0.778196i | \(0.716135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −70922.7 | −1.55768 | −0.778840 | − | 0.627223i | \(-0.784192\pi\) | ||||
−0.778840 | + | 0.627223i | \(0.784192\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15044.2 | −0.289163 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 51920.0 | 0.935981 | 0.467990 | − | 0.883734i | \(-0.344978\pi\) | ||||
0.467990 | + | 0.883734i | \(0.344978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72819.0 | −1.23320 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −61841.8 | −0.985342 | −0.492671 | − | 0.870216i | \(-0.663979\pi\) | ||||
−0.492671 | + | 0.870216i | \(0.663979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −137905. | −1.95336 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9990.00 | 0.133687 | 0.0668437 | − | 0.997763i | \(-0.478707\pi\) | ||||
0.0668437 | + | 0.997763i | \(0.478707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7128.00 | 0.0902328 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 134363. | 1.61092 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −101250. | −1.09261 | −0.546305 | − | 0.837586i | \(-0.683966\pi\) | ||||
−0.546305 | + | 0.837586i | \(0.683966\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −38556.0 | −0.395370 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −109098. | −1.06418 | −0.532088 | − | 0.846689i | \(-0.678592\pi\) | ||||
−0.532088 | + | 0.846689i | \(0.678592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 70624.2 | 0.655935 | 0.327967 | − | 0.944689i | \(-0.393636\pi\) | ||||
0.327967 | + | 0.944689i | \(0.393636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −97117.4 | −0.820045 | −0.410022 | − | 0.912075i | \(-0.634479\pi\) | ||||
−0.410022 | + | 0.912075i | \(0.634479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 21010.0 | 0.169379 | 0.0846895 | − | 0.996407i | \(-0.473010\pi\) | ||||
0.0846895 | + | 0.996407i | \(0.473010\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −277992. | −2.14153 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −105018. | −0.773688 | −0.386844 | − | 0.922145i | \(-0.626435\pi\) | ||||
−0.386844 | + | 0.922145i | \(0.626435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18268.0 | 0.123375 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −41184.0 | −0.266601 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −97547.0 | −0.605690 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3940.15 | 0.0234828 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 87220.6 | 0.479855 | 0.239927 | − | 0.970791i | \(-0.422876\pi\) | ||||
0.239927 | + | 0.970791i | \(0.422876\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8316.00 | 0.0439987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −192852. | −0.981852 | −0.490926 | − | 0.871201i | \(-0.663341\pi\) | ||||
−0.490926 | + | 0.871201i | \(0.663341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13133.8 | −0.0643817 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −143570. | −0.653525 | −0.326763 | − | 0.945106i | \(-0.605958\pi\) | ||||
−0.326763 | + | 0.945106i | \(0.605958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −318340. | −1.39751 | −0.698754 | − | 0.715362i | \(-0.746262\pi\) | ||||
−0.698754 | + | 0.715362i | \(0.746262\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −209748. | −0.888485 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30088.4 | −0.123044 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 263532. | 1.00587 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −84150.0 | −0.310519 | −0.155260 | − | 0.987874i | \(-0.549621\pi\) | ||||
−0.155260 | + | 0.987874i | \(0.549621\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155848. | 0.556236 | 0.278118 | − | 0.960547i | \(-0.410289\pi\) | ||||
0.278118 | + | 0.960547i | \(0.410289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −105548. | −0.364521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 356643. | 1.15474 | 0.577371 | − | 0.816482i | \(-0.304079\pi\) | ||||
0.577371 | + | 0.816482i | \(0.304079\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −115896. | −0.363560 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 145332. | 0.441872 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −144890. | −0.427139 | −0.213570 | − | 0.976928i | \(-0.568509\pi\) | ||||
−0.213570 | + | 0.976928i | \(0.568509\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18102.1 | 0.0502272 | 0.0251136 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251136 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −357037. | −0.961604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33660.0 | −0.0880286 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 492572. | 1.25128 | 0.625640 | − | 0.780112i | \(-0.284838\pi\) | ||||
0.625640 | + | 0.780112i | \(0.284838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 490728. | 1.17736 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 444420. | 1.03672 | 0.518359 | − | 0.855163i | \(-0.326543\pi\) | ||||
0.518359 | + | 0.855163i | \(0.326543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 156902. | 0.355985 | 0.177993 | − | 0.984032i | \(-0.443040\pi\) | ||||
0.177993 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 113389. | 0.250289 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 173844. | 0.363543 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 106920. | 0.217723 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −332352. | −0.659196 | −0.329598 | − | 0.944121i | \(-0.606913\pi\) | ||||
−0.329598 | + | 0.944121i | \(0.606913\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −786120. | −1.51913 | −0.759566 | − | 0.650430i | \(-0.774589\pi\) | ||||
−0.759566 | + | 0.650430i | \(0.774589\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 59606.4 | 0.109428 | 0.0547138 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547138 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −395800. | −0.708505 | −0.354253 | − | 0.935150i | \(-0.615265\pi\) | ||||
−0.354253 | + | 0.935150i | \(0.615265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −868428. | −1.51616 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 413716. | 0.704631 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 372464. | 0.604168 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 55440.0 | 0.0877925 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 251548. | 0.388969 | 0.194484 | − | 0.980906i | \(-0.437697\pi\) | ||||
0.194484 | + | 0.980906i | \(0.437697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.06169e6 | 1.60343 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −403089. | −0.581101 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.41134e6 | 1.98849 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82368.0 | −0.113443 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −288765. | −0.388851 | −0.194425 | − | 0.980917i | \(-0.562284\pi\) | ||||
−0.194425 | + | 0.980917i | \(0.562284\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.16414e6 | −1.49948 | −0.749741 | − | 0.661731i | \(-0.769822\pi\) | ||||
−0.749741 | + | 0.661731i | \(0.769822\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −547670. | −0.690129 | −0.345064 | − | 0.938579i | \(-0.612143\pi\) | ||||
−0.345064 | + | 0.938579i | \(0.612143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 299376. | 0.369137 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −48104.3 | −0.0580489 | −0.0290245 | − | 0.999579i | \(-0.509240\pi\) | ||||
−0.0290245 | + | 0.999579i | \(0.509240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.03319e6 | −1.19484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.00584e6 | −1.13903 | −0.569514 | − | 0.821982i | \(-0.692868\pi\) | ||||
−0.569514 | + | 0.821982i | \(0.692868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 895202. | 0.992838 | 0.496419 | − | 0.868083i | \(-0.334648\pi\) | ||||
0.496419 | + | 0.868083i | \(0.334648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.01387e6 | 1.10146 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26267.7 | −0.0273955 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.23064e6 | 1.25786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −558252. | −0.559301 | −0.279651 | − | 0.960102i | \(-0.590219\pi\) | ||||
−0.279651 | + | 0.960102i | \(0.590219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −613469. | −0.602548 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −787924. | −0.744135 | −0.372067 | − | 0.928206i | \(-0.621351\pi\) | ||||
−0.372067 | + | 0.928206i | \(0.621351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 833976. | 0.772510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.06029e6 | 0.963437 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.63173e6 | −1.45465 | −0.727327 | − | 0.686291i | \(-0.759238\pi\) | ||||
−0.727327 | + | 0.686291i | \(0.759238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −198798. | −0.170661 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.73637e6 | 1.46306 | 0.731529 | − | 0.681810i | \(-0.238807\pi\) | ||||
0.731529 | + | 0.681810i | \(0.238807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.72005e6 | 1.42271 | 0.711357 | − | 0.702831i | \(-0.248081\pi\) | ||||
0.711357 | + | 0.702831i | \(0.248081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −141845. | −0.115188 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27243e6 | 0.996402 | 0.498201 | − | 0.867062i | \(-0.333994\pi\) | ||||
0.498201 | + | 0.867062i | \(0.333994\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.03306e6 | −0.794536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.46500e6 | 1.10681 | 0.553404 | − | 0.832913i | \(-0.313329\pi\) | ||||
0.553404 | + | 0.832913i | \(0.313329\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.65051e6 | −1.22504 | −0.612521 | − | 0.790455i | \(-0.709844\pi\) | ||||
−0.612521 | + | 0.790455i | \(0.709844\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11820.5 | −0.00847089 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −943953. | −0.664823 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.01485e6 | 1.39479 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.38772e6 | −1.62485 | −0.812426 | − | 0.583064i | \(-0.801854\pi\) | ||||
−0.812426 | + | 0.583064i | \(0.801854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −451326. | −0.296893 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 290664. | 0.188024 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24948.0 | −0.0158716 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.17102e6 | 1.35849 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −928264. | −0.562115 | −0.281058 | − | 0.959691i | \(-0.590685\pi\) | ||||
−0.281058 | + | 0.959691i | \(0.590685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.40540e6 | −0.837346 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −568152. | −0.333092 | −0.166546 | − | 0.986034i | \(-0.553261\pi\) | ||||
−0.166546 | + | 0.986034i | \(0.553261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.72244e6 | 0.993766 | 0.496883 | − | 0.867818i | \(-0.334478\pi\) | ||||
0.496883 | + | 0.867818i | \(0.334478\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 131643. | 0.0735785 | 0.0367893 | − | 0.999323i | \(-0.488287\pi\) | ||||
0.0367893 | + | 0.999323i | \(0.488287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.74636e6 | −0.960853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.93261e6 | 1.04684 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 151769. | 0.0809424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −418094. | −0.216224 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 629244. | 0.320501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.58055e6 | 0.792935 | 0.396468 | − | 0.918049i | \(-0.370236\pi\) | ||||
0.396468 | + | 0.918049i | \(0.370236\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.13735e6 | 1.05625 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.22885e6 | 0.589419 | 0.294709 | − | 0.955587i | \(-0.404777\pi\) | ||||
0.294709 | + | 0.955587i | \(0.404777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.08982e6 | 0.987667 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70150e6 | 0.792405 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.79396e6 | −0.823338 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.84224e6 | 1.71301 | 0.856506 | − | 0.516137i | \(-0.172630\pi\) | ||||
0.856506 | + | 0.516137i | \(0.172630\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.59445e6 | 0.700725 | 0.350362 | − | 0.936614i | \(-0.386058\pi\) | ||||
0.350362 | + | 0.936614i | \(0.386058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 213840. | 0.0926448 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 295365. | 0.126160 | 0.0630802 | − | 0.998008i | \(-0.479908\pi\) | ||||
0.0630802 | + | 0.998008i | \(0.479908\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 819551. | 0.340334 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.10484e6 | 0.452442 | 0.226221 | − | 0.974076i | \(-0.427363\pi\) | ||||
0.226221 | + | 0.974076i | \(0.427363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.42770e6 | −0.980453 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94116e6 | 0.773206 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.83760e6 | 0.712174 | 0.356087 | − | 0.934453i | \(-0.384111\pi\) | ||||
0.356087 | + | 0.934453i | \(0.384111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −30294.0 | −0.0115822 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 347688. | 0.131146 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.93350e6 | −1.09173 | −0.545864 | − | 0.837874i | \(-0.683798\pi\) | ||||
−0.545864 | + | 0.837874i | \(0.683798\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 827432. | 0.299832 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.09342e6 | 1.82143 | 0.910713 | − | 0.413040i | \(-0.135533\pi\) | ||||
0.910713 | + | 0.413040i | \(0.135533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.73567e6 | −0.612568 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.17485e6 | 1.10593 | 0.552964 | − | 0.833205i | \(-0.313497\pi\) | ||||
0.552964 | + | 0.833205i | \(0.313497\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −63937.9 | −0.0217011 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.79991e6 | −0.603083 | −0.301541 | − | 0.953453i | \(-0.597501\pi\) | ||||
−0.301541 | + | 0.953453i | \(0.597501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.67939e6 | −0.555533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.83771e6 | 1.25340 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.90405e6 | −1.56163 | −0.780817 | − | 0.624760i | \(-0.785197\pi\) | ||||
−0.780817 | + | 0.624760i | \(0.785197\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 261360. | 0.0821877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −642798. | −0.199624 | −0.0998122 | − | 0.995006i | \(-0.531824\pi\) | ||||
−0.0998122 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −806179. | −0.247268 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.52035e6 | −1.05341 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.05711e6 | 0.608064 | 0.304032 | − | 0.952662i | \(-0.401667\pi\) | ||||
0.304032 | + | 0.952662i | \(0.401667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.85701e6 | 0.834271 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.47218e6 | −0.424704 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.33489e6 | 1.78402 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.93742e6 | −0.817393 | −0.408697 | − | 0.912670i | \(-0.634017\pi\) | ||||
−0.408697 | + | 0.912670i | \(0.634017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.71770e6 | 0.747303 | 0.373651 | − | 0.927569i | \(-0.378106\pi\) | ||||
0.373651 | + | 0.927569i | \(0.378106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.61266e6 | 0.438219 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −340166. | −0.0902862 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 598752. | 0.157074 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.99435e6 | −1.29505 | −0.647524 | − | 0.762045i | \(-0.724196\pi\) | ||||
−0.647524 | + | 0.762045i | \(0.724196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.08183e6 | 0.533612 | 0.266806 | − | 0.963750i | \(-0.414032\pi\) | ||||
0.266806 | + | 0.963750i | \(0.414032\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −535569. | −0.134156 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.70404e6 | −1.16496 | −0.582478 | − | 0.812846i | \(-0.697917\pi\) | ||||
−0.582478 | + | 0.812846i | \(0.697917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.02618e6 | −0.496114 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.70103e6 | −1.38021 | −0.690103 | − | 0.723711i | \(-0.742435\pi\) | ||||
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.67456e6 | 0.396399 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.20325e6 | −1.45212 | −0.726062 | − | 0.687630i | \(-0.758651\pi\) | ||||
−0.726062 | + | 0.687630i | \(0.758651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 49896.0 | 0.0115511 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.10134e6 | −0.710074 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.15371e6 | −0.482388 | −0.241194 | − | 0.970477i | \(-0.577539\pi\) | ||||
−0.241194 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23552e6 | −0.273727 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.85130e6 | −0.844024 | −0.422012 | − | 0.906590i | \(-0.638676\pi\) | ||||
−0.422012 | + | 0.906590i | \(0.638676\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.08213e6 | −0.451394 | −0.225697 | − | 0.974198i | \(-0.572466\pi\) | ||||
−0.225697 | + | 0.974198i | \(0.572466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.30822e6 | −0.277579 | −0.138790 | − | 0.990322i | \(-0.544321\pi\) | ||||
−0.138790 | + | 0.990322i | \(0.544321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.60528e6 | 0.546919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.09711e6 | −1.47411 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 105309. | 0.0216429 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 891071. | 0.179315 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.76368e6 | −1.34693 | −0.673464 | − | 0.739220i | \(-0.735194\pi\) | ||||
−0.673464 | + | 0.739220i | \(0.735194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.66795e6 | 0.328716 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.89207e6 | −0.564080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.67193e6 | −1.27476 | −0.637381 | − | 0.770549i | \(-0.719982\pi\) | ||||
−0.637381 | + | 0.770549i | \(0.719982\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.88328e6 | 0.545273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.87575e6 | 1.28711 | 0.643556 | − | 0.765399i | \(-0.277458\pi\) | ||||
0.643556 | + | 0.765399i | \(0.277458\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.78072e6 | −0.885881 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.18507e6 | −0.578400 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.94010e6 | 1.24771 | 0.623856 | − | 0.781539i | \(-0.285565\pi\) | ||||
0.623856 | + | 0.781539i | \(0.285565\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −360228. | −0.0641185 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 921007. | 0.162309 | 0.0811546 | − | 0.996702i | \(-0.474139\pi\) | ||||
0.0811546 | + | 0.996702i | \(0.474139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.10495e6 | 1.22755 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.97979e6 | −0.851955 | −0.425977 | − | 0.904734i | \(-0.640070\pi\) | ||||
−0.425977 | + | 0.904734i | \(0.640070\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.23403e6 | −0.717302 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −394015. | −0.0661027 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.65614e6 | −0.437043 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.80206e6 | −1.59735 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −147798. | −0.0238547 | −0.0119274 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119274 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.23884e7 | 1.98043 | 0.990216 | − | 0.139543i | \(-0.0445634\pi\) | ||||
0.990216 | + | 0.139543i | \(0.0445634\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.65792e6 | 0.730576 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −510027. | −0.0792417 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.77298e6 | −0.580695 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23640.9 | −0.00360451 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.84385e6 | −1.32344 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.33724e6 | 0.494783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.99810e6 | −1.46867 | −0.734335 | − | 0.678787i | \(-0.762506\pi\) | ||||
−0.734335 | + | 0.678787i | \(0.762506\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.12231e6 | −0.454440 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.18580e7 | −1.69451 | −0.847253 | − | 0.531189i | \(-0.821745\pi\) | ||||
−0.847253 | + | 0.531189i | \(0.821745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −871794. | −0.123448 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.52460e6 | −0.213933 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.09958e6 | 0.431013 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 904550. | 0.123536 | 0.0617681 | − | 0.998091i | \(-0.480326\pi\) | ||||
0.0617681 | + | 0.998091i | \(0.480326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −49896.0 | −0.00675361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.45946e6 | −0.464088 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.68719e6 | −1.15507 | −0.577535 | − | 0.816366i | \(-0.695985\pi\) | ||||
−0.577535 | + | 0.816366i | \(0.695985\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.34724e6 | −0.567879 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.27007e6 | 0.293940 | 0.146970 | − | 0.989141i | \(-0.453048\pi\) | ||||
0.146970 | + | 0.989141i | \(0.453048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.43807e7 | −1.84582 | −0.922908 | − | 0.385021i | \(-0.874194\pi\) | ||||
−0.922908 | + | 0.385021i | \(0.874194\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.61372e6 | 0.841510 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63943e6 | 0.705173 | 0.352586 | − | 0.935779i | \(-0.385302\pi\) | ||||
0.352586 | + | 0.935779i | \(0.385302\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.56436e7 | 1.93928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.69191e6 | −0.453744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.46765e6 | −0.178834 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.28473e6 | −0.153893 | −0.0769464 | − | 0.997035i | \(-0.524517\pi\) | ||||
−0.0769464 | + | 0.997035i | \(0.524517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.48544e6 | 0.176428 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.18615e6 | −0.139692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.00943e6 | −0.818552 | −0.409276 | − | 0.912411i | \(-0.634219\pi\) | ||||
−0.409276 | + | 0.912411i | \(0.634219\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.87632e6 | 0.904456 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.80020e6 | −1.00213 | −0.501067 | − | 0.865409i | \(-0.667059\pi\) | ||||
−0.501067 | + | 0.865409i | \(0.667059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.07670e7 | −1.21593 | −0.607965 | − | 0.793964i | \(-0.708014\pi\) | ||||
−0.607965 | + | 0.793964i | \(0.708014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.67694e6 | 0.747798 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.51219e7 | 1.66584 | 0.832921 | − | 0.553391i | \(-0.186667\pi\) | ||||
0.832921 | + | 0.553391i | \(0.186667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.23284e6 | −0.899511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.25849e6 | 0.136379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.31622e6 | 0.893871 | 0.446936 | − | 0.894566i | \(-0.352515\pi\) | ||||
0.446936 | + | 0.894566i | \(0.352515\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.21083e7 | 1.28047 | 0.640237 | − | 0.768178i | \(-0.278836\pi\) | ||||
0.640237 | + | 0.768178i | \(0.278836\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.73238e6 | 1.02092 | 0.510461 | − | 0.859901i | \(-0.329475\pi\) | ||||
0.510461 | + | 0.859901i | \(0.329475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.35996e6 | 0.453684 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 596395. | 0.0615622 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.10324e6 | −0.112073 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.63706e6 | −0.971220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.60145e6 | 0.859999 | 0.430000 | − | 0.902829i | \(-0.358514\pi\) | ||||
0.430000 | + | 0.902829i | \(0.358514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.00574e6 | −0.496546 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.58119e6 | −0.154396 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.16286e6 | −0.790842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.42440e6 | −0.617572 | −0.308786 | − | 0.951132i | \(-0.599923\pi\) | ||||
−0.308786 | + | 0.951132i | \(0.599923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.64721e6 | 0.347883 | 0.173941 | − | 0.984756i | \(-0.444350\pi\) | ||||
0.173941 | + | 0.984756i | \(0.444350\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.78036e6 | −0.355036 | −0.177518 | − | 0.984118i | \(-0.556807\pi\) | ||||
−0.177518 | + | 0.984118i | \(0.556807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.21432e6 | 0.579138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.02138e6 | 0.741816 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.66957e7 | 1.53223 | 0.766113 | − | 0.642706i | \(-0.222188\pi\) | ||||
0.766113 | + | 0.642706i | \(0.222188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.08512e7 | −0.980761 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.22166e6 | −0.109581 | −0.0547907 | − | 0.998498i | \(-0.517449\pi\) | ||||
−0.0547907 | + | 0.998498i | \(0.517449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.62789e7 | 1.44918 | 0.724589 | − | 0.689182i | \(-0.242030\pi\) | ||||
0.724589 | + | 0.689182i | \(0.242030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.63910e6 | 0.144818 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.68704e7 | 1.46829 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.74636e6 | 0.496395 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.43590e6 | 0.123117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.43928e7 | −1.22492 | −0.612459 | − | 0.790503i | \(-0.709819\pi\) | ||||
−0.612459 | + | 0.790503i | \(0.709819\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.62429e6 | 0.220059 | 0.110030 | − | 0.993928i | \(-0.464905\pi\) | ||||
0.110030 | + | 0.993928i | \(0.464905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.04454e6 | −0.503140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.31661e7 | 1.91419 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.03039e7 | 0.845184 | 0.422592 | − | 0.906320i | \(-0.361120\pi\) | ||||
0.422592 | + | 0.906320i | \(0.361120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08985e7 | 0.880998 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 695376. | 0.0558048 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.50285e6 | −0.358751 | −0.179375 | − | 0.983781i | \(-0.557408\pi\) | ||||
−0.179375 | + | 0.983781i | \(0.557408\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.30176e6 | −0.182066 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 136592. | 0.0106498 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 957264. | 0.0741035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88090e6 | −0.375150 | −0.187575 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187575 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.07332e6 | −0.234541 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.51307e6 | −0.490046 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.96961e6 | 0.744839 | 0.372420 | − | 0.928064i | \(-0.378528\pi\) | ||||
0.372420 | + | 0.928064i | \(0.378528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.94376e6 | 0.589321 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.64371e7 | −1.21088 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.00160e7 | 1.45405 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.19167e7 | −0.859675 | −0.429838 | − | 0.902906i | \(-0.641429\pi\) | ||||
−0.429838 | + | 0.902906i | \(0.641429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.21621e6 | 0.302054 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.78143e7 | −1.26743 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.38269e6 | 0.0970264 | 0.0485132 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485132 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.48079e6 | −0.172890 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 288288. | 0.0199541 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.09661e6 | 0.419110 | 0.209555 | − | 0.977797i | \(-0.432798\pi\) | ||||
0.209555 | + | 0.977797i | \(0.432798\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.09973e7 | −0.745793 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.16946e6 | 0.415562 | 0.207781 | − | 0.978175i | \(-0.433376\pi\) | ||||
0.207781 | + | 0.978175i | \(0.433376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 522720. | 0.0349723 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.57574e7 | −1.04716 | −0.523578 | − | 0.851978i | \(-0.675403\pi\) | ||||
−0.523578 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.46179e6 | −0.620400 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.79784e6 | −0.377626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.51816e7 | 0.982243 | 0.491122 | − | 0.871091i | \(-0.336587\pi\) | ||||
0.491122 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.11091e7 | 0.713987 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −652274. | −0.0413705 | −0.0206852 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206852 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.22079e7 | 0.769194 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.51420e6 | 0.282566 | 0.141283 | − | 0.989969i | \(-0.454877\pi\) | ||||
0.141283 | + | 0.989969i | \(0.454877\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.25428e6 | 0.0779980 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.94437e6 | −0.180719 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.20799e7 | 0.736625 | 0.368312 | − | 0.929702i | \(-0.379936\pi\) | ||||
0.368312 | + | 0.929702i | \(0.379936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.56795e7 | 0.949939 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.04245e7 | 0.627492 | 0.313746 | − | 0.949507i | \(-0.398416\pi\) | ||||
0.313746 | + | 0.949507i | \(0.398416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.65959e7 | −0.986163 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43560.0 | 0.00257184 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34447e7 | 0.788721 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.24115e7 | 0.723467 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.45366e7 | −1.98766 | −0.993830 | − | 0.110913i | \(-0.964622\pi\) | ||||
−0.993830 | + | 0.110913i | \(0.964622\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.24711e7 | 1.85697 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.26947e6 | −0.356279 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −680333. | −0.0384183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.09287e7 | −1.16707 | −0.583533 | − | 0.812089i | \(-0.698330\pi\) | ||||
−0.583533 | + | 0.812089i | \(0.698330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.27126e6 | −0.402942 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.52847e6 | 0.0841735 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.78725e7 | 0.978131 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.45533e7 | −1.86770 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.48797e7 | −1.33651 | −0.668257 | − | 0.743930i | \(-0.732959\pi\) | ||||
−0.668257 | + | 0.743930i | \(0.732959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.95415e6 | 0.211106 | 0.105553 | − | 0.994414i | \(-0.466339\pi\) | ||||
0.105553 | + | 0.994414i | \(0.466339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.42285e7 | −1.81619 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 91936.8 | 0.00481875 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.09058e6 | 0.0568132 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.43550e6 | −0.177882 | −0.0889410 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889410 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.94833e6 | −0.203195 | −0.101598 | − | 0.994826i | \(-0.532395\pi\) | ||||
−0.101598 | + | 0.994826i | \(0.532395\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.38176e7 | 1.71941 | 0.859705 | − | 0.510791i | \(-0.170647\pi\) | ||||
0.859705 | + | 0.510791i | \(0.170647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.52015e7 | −0.768244 | −0.384122 | − | 0.923282i | \(-0.625496\pi\) | ||||
−0.384122 | + | 0.923282i | \(0.625496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.53210e7 | −1.27198 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.13579e6 | 0.456177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.20927e7 | −0.596635 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.89012e7 | 1.41746 | 0.708729 | − | 0.705481i | \(-0.249269\pi\) | ||||
0.708729 | + | 0.705481i | \(0.249269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75138e7 | 1.34140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.91532e7 | −1.41292 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.82348e6 | −0.278917 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.28446e7 | 1.56385 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.40077e7 | 1.60973 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.02107e7 | 0.951062 | 0.475531 | − | 0.879699i | \(-0.342256\pi\) | ||||
0.475531 | + | 0.879699i | \(0.342256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.70522e7 | 0.793101 | 0.396550 | − | 0.918013i | \(-0.370207\pi\) | ||||
0.396550 | + | 0.918013i | \(0.370207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.95505e7 | 0.904015 | 0.452008 | − | 0.892014i | \(-0.350708\pi\) | ||||
0.452008 | + | 0.892014i | \(0.350708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 235224. | 0.0108137 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.70896e7 | 1.23816 | 0.619078 | − | 0.785330i | \(-0.287507\pi\) | ||||
0.619078 | + | 0.785330i | \(0.287507\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.87844e7 | 0.848692 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.30838e7 | −0.587741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.21057e6 | 0.232723 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.54912e7 | −0.687940 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.98285e6 | 0.0870545 | 0.0435272 | − | 0.999052i | \(-0.486140\pi\) | ||||
0.0435272 | + | 0.999052i | \(0.486140\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.75150e7 | 2.07424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.22840e7 | −1.83542 | −0.917712 | − | 0.397247i | \(-0.869966\pi\) | ||||
−0.917712 | + | 0.397247i | \(0.869966\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 134502. | 0.00580535 | 0.00290267 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290267 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.87668e6 | −0.165444 | −0.0827219 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827219 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.20700e6 | 0.220970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.83504e7 | 0.774374 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.31885e6 | −0.0973070 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.78414e6 | −0.240026 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.67914e7 | −1.93093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.01773e6 | −0.164880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 496459. | 0.0202611 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.87363e7 | 1.15988 | 0.579939 | − | 0.814660i | \(-0.303076\pi\) | ||||
0.579939 | + | 0.814660i | \(0.303076\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.66920e7 | −0.670037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.87675e6 | −0.0749223 | −0.0374611 | − | 0.999298i | \(-0.511927\pi\) | ||||
−0.0374611 | + | 0.999298i | \(0.511927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.55841e7 | 0.618736 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.15131e7 | −0.452137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.76852e6 | −0.264366 | −0.132183 | − | 0.991225i | \(-0.542199\pi\) | ||||
−0.132183 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.84722e7 | 0.717579 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.37015e6 | −0.246119 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.08055e7 | 0.412996 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.15356e7 | −0.438530 | −0.219265 | − | 0.975665i | \(-0.570366\pi\) | ||||
−0.219265 | + | 0.975665i | \(0.570366\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.91346e6 | 0.110163 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.13061e7 | 0.425214 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.92632e7 | 1.46096 | 0.730478 | − | 0.682936i | \(-0.239297\pi\) | ||||
0.730478 | + | 0.682936i | \(0.239297\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.42762e7 | −1.26861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.94919e7 | 1.08575 | 0.542874 | − | 0.839814i | \(-0.317336\pi\) | ||||
0.542874 | + | 0.839814i | \(0.317336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −482012. | −0.0176514 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.09628e7 | −0.759581 | −0.379791 | − | 0.925072i | \(-0.624004\pi\) | ||||
−0.379791 | + | 0.925072i | \(0.624004\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.46806e6 | −0.305224 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.61967e6 | −0.0939281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.64122e7 | 0.585375 | 0.292687 | − | 0.956208i | \(-0.405451\pi\) | ||||
0.292687 | + | 0.956208i | \(0.405451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.47521e7 | 1.22660 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.57102e6 | −0.300944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.69604e7 | 0.592416 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.48590e7 | −0.516325 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.71911e7 | 1.62291 | 0.811454 | − | 0.584416i | \(-0.198676\pi\) | ||||
0.811454 | + | 0.584416i | \(0.198676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.02016e6 | −0.103329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.84771e7 | −1.30965 | −0.654823 | − | 0.755783i | \(-0.727257\pi\) | ||||
−0.654823 | + | 0.755783i | \(0.727257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.90047e7 | −0.643544 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.70184e7 | 0.905572 | 0.452786 | − | 0.891619i | \(-0.350430\pi\) | ||||
0.452786 | + | 0.891619i | \(0.350430\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.51748e6 | −0.0839478 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21453e6 | 0.106646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.88475e7 | 0.952192 | 0.476096 | − | 0.879393i | \(-0.342051\pi\) | ||||
0.476096 | + | 0.879393i | \(0.342051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.25218e7 | −0.409142 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.01732e6 | −0.0330726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.21596e7 | 1.68714 | 0.843569 | − | 0.537021i | \(-0.180450\pi\) | ||||
0.843569 | + | 0.537021i | \(0.180450\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.14525e7 | −1.01224 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.78148e6 | −0.311650 | −0.155825 | − | 0.987785i | \(-0.549804\pi\) | ||||
−0.155825 | + | 0.987785i | \(0.549804\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.50193e7 | 0.793161 |
(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 | 400.6.a.t.1.1 | 2 | ||
4.3 | odd | 2 | 25.6.a.c.1.2 | 2 | |||
5.2 | odd | 4 | 80.6.c.a.49.2 | 2 | |||
5.3 | odd | 4 | 80.6.c.a.49.1 | 2 | |||
5.4 | even | 2 | inner | 400.6.a.t.1.2 | 2 | ||
12.11 | even | 2 | 225.6.a.n.1.1 | 2 | |||
15.2 | even | 4 | 720.6.f.f.289.1 | 2 | |||
15.8 | even | 4 | 720.6.f.f.289.2 | 2 | |||
20.3 | even | 4 | 5.6.b.a.4.1 | ✓ | 2 | ||
20.7 | even | 4 | 5.6.b.a.4.2 | yes | 2 | ||
20.19 | odd | 2 | 25.6.a.c.1.1 | 2 | |||
40.3 | even | 4 | 320.6.c.f.129.1 | 2 | |||
40.13 | odd | 4 | 320.6.c.g.129.2 | 2 | |||
40.27 | even | 4 | 320.6.c.f.129.2 | 2 | |||
40.37 | odd | 4 | 320.6.c.g.129.1 | 2 | |||
60.23 | odd | 4 | 45.6.b.b.19.2 | 2 | |||
60.47 | odd | 4 | 45.6.b.b.19.1 | 2 | |||
60.59 | even | 2 | 225.6.a.n.1.2 | 2 | |||
140.27 | odd | 4 | 245.6.b.a.99.2 | 2 | |||
140.83 | odd | 4 | 245.6.b.a.99.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.b.a.4.1 | ✓ | 2 | 20.3 | even | 4 | ||
5.6.b.a.4.2 | yes | 2 | 20.7 | even | 4 | ||
25.6.a.c.1.1 | 2 | 20.19 | odd | 2 | |||
25.6.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
45.6.b.b.19.1 | 2 | 60.47 | odd | 4 | |||
45.6.b.b.19.2 | 2 | 60.23 | odd | 4 | |||
80.6.c.a.49.1 | 2 | 5.3 | odd | 4 | |||
80.6.c.a.49.2 | 2 | 5.2 | odd | 4 | |||
225.6.a.n.1.1 | 2 | 12.11 | even | 2 | |||
225.6.a.n.1.2 | 2 | 60.59 | even | 2 | |||
245.6.b.a.99.1 | 2 | 140.83 | odd | 4 | |||
245.6.b.a.99.2 | 2 | 140.27 | odd | 4 | |||
320.6.c.f.129.1 | 2 | 40.3 | even | 4 | |||
320.6.c.f.129.2 | 2 | 40.27 | even | 4 | |||
320.6.c.g.129.1 | 2 | 40.37 | odd | 4 | |||
320.6.c.g.129.2 | 2 | 40.13 | odd | 4 | |||
400.6.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
400.6.a.t.1.2 | 2 | 5.4 | even | 2 | inner | ||
720.6.f.f.289.1 | 2 | 15.2 | even | 4 | |||
720.6.f.f.289.2 | 2 | 15.8 | even | 4 |