Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,6,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(4.00959549532\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2]\) |
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 | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.63325 | −1.17260 | −0.586302 | − | 0.810093i | \(-0.699417\pi\) | ||||
−0.586302 | + | 0.810093i | \(0.699417\pi\) | |||||||
\(3\) | −19.8997 | −1.27657 | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||||
−0.638285 | + | 0.769800i | \(0.720356\pi\) | |||||||
\(4\) | 12.0000 | 0.375000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 132.000 | 1.49691 | ||||||||
\(7\) | 59.6992 | 0.460494 | 0.230247 | − | 0.973132i | \(-0.426047\pi\) | ||||
0.230247 | + | 0.973132i | \(0.426047\pi\) | |||||||
\(8\) | 132.665 | 0.732877 | ||||||||
\(9\) | 153.000 | 0.629630 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 252.000 | 0.627941 | 0.313970 | − | 0.949433i | \(-0.398341\pi\) | ||||
0.313970 | + | 0.949433i | \(0.398341\pi\) | |||||||
\(12\) | −238.797 | −0.478714 | ||||||||
\(13\) | −119.398 | −0.195948 | −0.0979739 | − | 0.995189i | \(-0.531236\pi\) | ||||
−0.0979739 | + | 0.995189i | \(0.531236\pi\) | |||||||
\(14\) | −396.000 | −0.539977 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1264.00 | −1.23438 | ||||||||
\(17\) | 689.858 | 0.578945 | 0.289473 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289473 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(18\) | −1014.89 | −0.738306 | ||||||||
\(19\) | 220.000 | 0.139810 | 0.0699051 | − | 0.997554i | \(-0.477730\pi\) | ||||
0.0699051 | + | 0.997554i | \(0.477730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1188.00 | −0.587852 | ||||||||
\(22\) | −1671.58 | −0.736326 | ||||||||
\(23\) | 2434.40 | 0.959561 | 0.479781 | − | 0.877388i | \(-0.340716\pi\) | ||||
0.479781 | + | 0.877388i | \(0.340716\pi\) | |||||||
\(24\) | −2640.00 | −0.935569 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 792.000 | 0.229769 | ||||||||
\(27\) | 1790.98 | 0.472804 | ||||||||
\(28\) | 716.391 | 0.172685 | ||||||||
\(29\) | 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 | \(-0.282663\pi\) | ||||
0.630955 | + | 0.775820i | \(0.282663\pi\) | |||||||
\(32\) | 4139.15 | 0.714556 | ||||||||
\(33\) | −5014.74 | −0.801610 | ||||||||
\(34\) | −4576.00 | −0.678873 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1836.00 | 0.236111 | ||||||||
\(37\) | −13969.6 | −1.67757 | −0.838785 | − | 0.544464i | \(-0.816733\pi\) | ||||
−0.838785 | + | 0.544464i | \(0.816733\pi\) | |||||||
\(38\) | −1459.31 | −0.163942 | ||||||||
\(39\) | 2376.00 | 0.250141 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −198.000 | −0.0183952 | −0.00919762 | − | 0.999958i | \(-0.502928\pi\) | ||||
−0.00919762 | + | 0.999958i | \(0.502928\pi\) | |||||||
\(42\) | 7880.30 | 0.689318 | ||||||||
\(43\) | −417.895 | −0.0344664 | −0.0172332 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172332 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(44\) | 3024.00 | 0.235478 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −16148.0 | −1.12519 | ||||||||
\(47\) | 10540.2 | 0.695994 | 0.347997 | − | 0.937496i | \(-0.386862\pi\) | ||||
0.347997 | + | 0.937496i | \(0.386862\pi\) | |||||||
\(48\) | 25153.3 | 1.57577 | ||||||||
\(49\) | −13243.0 | −0.787945 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13728.0 | −0.739064 | ||||||||
\(52\) | −1432.78 | −0.0734804 | ||||||||
\(53\) | −5823.99 | −0.284794 | −0.142397 | − | 0.989810i | \(-0.545481\pi\) | ||||
−0.142397 | + | 0.989810i | \(0.545481\pi\) | |||||||
\(54\) | −11880.0 | −0.554411 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7920.00 | 0.337485 | ||||||||
\(57\) | −4377.94 | −0.178477 | ||||||||
\(58\) | −45968.4 | −1.79428 | ||||||||
\(59\) | 24660.0 | 0.922281 | 0.461140 | − | 0.887327i | \(-0.347440\pi\) | ||||
0.461140 | + | 0.887327i | \(0.347440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5698.00 | −0.196064 | −0.0980320 | − | 0.995183i | \(-0.531255\pi\) | ||||
−0.0980320 | + | 0.995183i | \(0.531255\pi\) | |||||||
\(62\) | −44787.7 | −1.47972 | ||||||||
\(63\) | 9133.98 | 0.289941 | ||||||||
\(64\) | 12992.0 | 0.396484 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 33264.0 | 0.939971 | ||||||||
\(67\) | 43640.1 | 1.18768 | 0.593840 | − | 0.804583i | \(-0.297611\pi\) | ||||
0.593840 | + | 0.804583i | \(0.297611\pi\) | |||||||
\(68\) | 8278.30 | 0.217104 | ||||||||
\(69\) | −48444.0 | −1.22495 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53352.0 | 1.25604 | 0.628022 | − | 0.778196i | \(-0.283865\pi\) | ||||
0.628022 | + | 0.778196i | \(0.283865\pi\) | |||||||
\(72\) | 20297.7 | 0.461441 | ||||||||
\(73\) | 70922.7 | 1.55768 | 0.778840 | − | 0.627223i | \(-0.215808\pi\) | ||||
0.778840 | + | 0.627223i | \(0.215808\pi\) | |||||||
\(74\) | 92664.0 | 1.96712 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2640.00 | 0.0524288 | ||||||||
\(77\) | 15044.2 | 0.289163 | ||||||||
\(78\) | −15760.6 | −0.293316 | ||||||||
\(79\) | −51920.0 | −0.935981 | −0.467990 | − | 0.883734i | \(-0.655022\pi\) | ||||
−0.467990 | + | 0.883734i | \(0.655022\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72819.0 | −1.23320 | ||||||||
\(82\) | 1313.38 | 0.0215703 | ||||||||
\(83\) | −61841.8 | −0.985342 | −0.492671 | − | 0.870216i | \(-0.663979\pi\) | ||||
−0.492671 | + | 0.870216i | \(0.663979\pi\) | |||||||
\(84\) | −14256.0 | −0.220445 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2772.00 | 0.0404154 | ||||||||
\(87\) | −137905. | −1.95336 | ||||||||
\(88\) | 33431.6 | 0.460204 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 29212.8 | 0.359836 | ||||||||
\(93\) | −134363. | −1.61092 | ||||||||
\(94\) | −69916.0 | −0.816125 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −82368.0 | −0.912180 | ||||||||
\(97\) | 101250. | 1.09261 | 0.546305 | − | 0.837586i | \(-0.316034\pi\) | ||||
0.546305 | + | 0.837586i | \(0.316034\pi\) | |||||||
\(98\) | 87844.1 | 0.923948 | ||||||||
\(99\) | 38556.0 | 0.395370 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −109098. | −1.06418 | −0.532088 | − | 0.846689i | \(-0.678592\pi\) | ||||
−0.532088 | + | 0.846689i | \(0.678592\pi\) | |||||||
\(102\) | 91061.3 | 0.866629 | ||||||||
\(103\) | 70624.2 | 0.655935 | 0.327967 | − | 0.944689i | \(-0.393636\pi\) | ||||
0.327967 | + | 0.944689i | \(0.393636\pi\) | |||||||
\(104\) | −15840.0 | −0.143606 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 38632.0 | 0.333951 | ||||||||
\(107\) | −97117.4 | −0.820045 | −0.410022 | − | 0.912075i | \(-0.634479\pi\) | ||||
−0.410022 | + | 0.912075i | \(0.634479\pi\) | |||||||
\(108\) | 21491.7 | 0.177301 | ||||||||
\(109\) | 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 | ||||||||
\(112\) | −75459.8 | −0.568422 | ||||||||
\(113\) | 105018. | 0.773688 | 0.386844 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386844 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(114\) | 29040.0 | 0.209283 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 83160.0 | 0.573812 | ||||||||
\(117\) | −18268.0 | −0.123375 | ||||||||
\(118\) | −163576. | −1.08147 | ||||||||
\(119\) | 41184.0 | 0.266601 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −97547.0 | −0.605690 | ||||||||
\(122\) | 37796.3 | 0.229905 | ||||||||
\(123\) | 3940.15 | 0.0234828 | ||||||||
\(124\) | 81024.0 | 0.473216 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −60588.0 | −0.339985 | ||||||||
\(127\) | 87220.6 | 0.479855 | 0.239927 | − | 0.970791i | \(-0.422876\pi\) | ||||
0.239927 | + | 0.970791i | \(0.422876\pi\) | |||||||
\(128\) | −218632. | −1.17947 | ||||||||
\(129\) | 8316.00 | 0.0439987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 192852. | 0.981852 | 0.490926 | − | 0.871201i | \(-0.336659\pi\) | ||||
0.490926 | + | 0.871201i | \(0.336659\pi\) | |||||||
\(132\) | −60176.8 | −0.300604 | ||||||||
\(133\) | 13133.8 | 0.0643817 | ||||||||
\(134\) | −289476. | −1.39268 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 91520.0 | 0.424296 | ||||||||
\(137\) | 143570. | 0.653525 | 0.326763 | − | 0.945106i | \(-0.394042\pi\) | ||||
0.326763 | + | 0.945106i | \(0.394042\pi\) | |||||||
\(138\) | 321341. | 1.43638 | ||||||||
\(139\) | 318340. | 1.39751 | 0.698754 | − | 0.715362i | \(-0.253738\pi\) | ||||
0.698754 | + | 0.715362i | \(0.253738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −209748. | −0.888485 | ||||||||
\(142\) | −353897. | −1.47284 | ||||||||
\(143\) | −30088.4 | −0.123044 | ||||||||
\(144\) | −193392. | −0.777199 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −470448. | −1.82654 | ||||||||
\(147\) | 263532. | 1.00587 | ||||||||
\(148\) | −167635. | −0.629088 | ||||||||
\(149\) | −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 | \(-0.589711\pi\) | ||||
−0.278118 | + | 0.960547i | \(0.589711\pi\) | |||||||
\(152\) | 29186.3 | 0.102464 | ||||||||
\(153\) | 105548. | 0.364521 | ||||||||
\(154\) | −99792.0 | −0.339074 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 28512.0 | 0.0938029 | ||||||||
\(157\) | −356643. | −1.15474 | −0.577371 | − | 0.816482i | \(-0.695921\pi\) | ||||
−0.577371 | + | 0.816482i | \(0.695921\pi\) | |||||||
\(158\) | 344398. | 1.09753 | ||||||||
\(159\) | 115896. | 0.363560 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 145332. | 0.441872 | ||||||||
\(162\) | 483027. | 1.44605 | ||||||||
\(163\) | −144890. | −0.427139 | −0.213570 | − | 0.976928i | \(-0.568509\pi\) | ||||
−0.213570 | + | 0.976928i | \(0.568509\pi\) | |||||||
\(164\) | −2376.00 | −0.00689822 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 410212. | 1.15542 | ||||||||
\(167\) | 18102.1 | 0.0502272 | 0.0251136 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251136 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(168\) | −157606. | −0.430824 | ||||||||
\(169\) | −357037. | −0.961604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 33660.0 | 0.0880286 | ||||||||
\(172\) | −5014.74 | −0.0129249 | ||||||||
\(173\) | −492572. | −1.25128 | −0.625640 | − | 0.780112i | \(-0.715162\pi\) | ||||
−0.625640 | + | 0.780112i | \(0.715162\pi\) | |||||||
\(174\) | 914760. | 2.29052 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −318528. | −0.775115 | ||||||||
\(177\) | −490728. | −1.17736 | ||||||||
\(178\) | −66266.2 | −0.156762 | ||||||||
\(179\) | −444420. | −1.03672 | −0.518359 | − | 0.855163i | \(-0.673457\pi\) | ||||
−0.518359 | + | 0.855163i | \(0.673457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 156902. | 0.355985 | 0.177993 | − | 0.984032i | \(-0.443040\pi\) | ||||
0.177993 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(182\) | 47281.8 | 0.105807 | ||||||||
\(183\) | 113389. | 0.250289 | ||||||||
\(184\) | 322960. | 0.703241 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 891264. | 1.88897 | ||||||||
\(187\) | 173844. | 0.363543 | ||||||||
\(188\) | 126483. | 0.260998 | ||||||||
\(189\) | 106920. | 0.217723 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 332352. | 0.659196 | 0.329598 | − | 0.944121i | \(-0.393087\pi\) | ||||
0.329598 | + | 0.944121i | \(0.393087\pi\) | |||||||
\(192\) | −258538. | −0.506140 | ||||||||
\(193\) | 786120. | 1.51913 | 0.759566 | − | 0.650430i | \(-0.225411\pi\) | ||||
0.759566 | + | 0.650430i | \(0.225411\pi\) | |||||||
\(194\) | −671616. | −1.28120 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −158916. | −0.295480 | ||||||||
\(197\) | −59606.4 | −0.109428 | −0.0547138 | − | 0.998502i | \(-0.517425\pi\) | ||||
−0.0547138 | + | 0.998502i | \(0.517425\pi\) | |||||||
\(198\) | −255752. | −0.463613 | ||||||||
\(199\) | 395800. | 0.708505 | 0.354253 | − | 0.935150i | \(-0.384735\pi\) | ||||
0.354253 | + | 0.935150i | \(0.384735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −868428. | −1.51616 | ||||||||
\(202\) | 723674. | 1.24786 | ||||||||
\(203\) | 413716. | 0.704631 | ||||||||
\(204\) | −164736. | −0.277149 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −468468. | −0.769151 | ||||||||
\(207\) | 372464. | 0.604168 | ||||||||
\(208\) | 150920. | 0.241873 | ||||||||
\(209\) | 55440.0 | 0.0877925 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −251548. | −0.388969 | −0.194484 | − | 0.980906i | \(-0.562303\pi\) | ||||
−0.194484 | + | 0.980906i | \(0.562303\pi\) | |||||||
\(212\) | −69887.9 | −0.106798 | ||||||||
\(213\) | −1.06169e6 | −1.60343 | ||||||||
\(214\) | 644204. | 0.961588 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 237600. | 0.346507 | ||||||||
\(217\) | 403089. | 0.581101 | ||||||||
\(218\) | −139365. | −0.198615 | ||||||||
\(219\) | −1.41134e6 | −1.98849 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82368.0 | −0.113443 | ||||||||
\(222\) | −1.84399e6 | −2.51117 | ||||||||
\(223\) | −288765. | −0.388851 | −0.194425 | − | 0.980917i | \(-0.562284\pi\) | ||||
−0.194425 | + | 0.980917i | \(0.562284\pi\) | |||||||
\(224\) | 247104. | 0.329048 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −696608. | −0.907230 | ||||||||
\(227\) | −1.16414e6 | −1.49948 | −0.749741 | − | 0.661731i | \(-0.769822\pi\) | ||||
−0.749741 | + | 0.661731i | \(0.769822\pi\) | |||||||
\(228\) | −52535.3 | −0.0669290 | ||||||||
\(229\) | −547670. | −0.690129 | −0.345064 | − | 0.938579i | \(-0.612143\pi\) | ||||
−0.345064 | + | 0.938579i | \(0.612143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −299376. | −0.369137 | ||||||||
\(232\) | 919368. | 1.12142 | ||||||||
\(233\) | 48104.3 | 0.0580489 | 0.0290245 | − | 0.999579i | \(-0.490760\pi\) | ||||
0.0290245 | + | 0.999579i | \(0.490760\pi\) | |||||||
\(234\) | 121176. | 0.144669 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 295920. | 0.345855 | ||||||||
\(237\) | 1.03319e6 | 1.19484 | ||||||||
\(238\) | −273184. | −0.312617 | ||||||||
\(239\) | 1.00584e6 | 1.13903 | 0.569514 | − | 0.821982i | \(-0.307132\pi\) | ||||
0.569514 | + | 0.821982i | \(0.307132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 895202. | 0.992838 | 0.496419 | − | 0.868083i | \(-0.334648\pi\) | ||||
0.496419 | + | 0.868083i | \(0.334648\pi\) | |||||||
\(242\) | 647054. | 0.710235 | ||||||||
\(243\) | 1.01387e6 | 1.10146 | ||||||||
\(244\) | −68376.0 | −0.0735240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −26136.0 | −0.0275360 | ||||||||
\(247\) | −26267.7 | −0.0273955 | ||||||||
\(248\) | 895754. | 0.924825 | ||||||||
\(249\) | 1.23064e6 | 1.25786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 558252. | 0.559301 | 0.279651 | − | 0.960102i | \(-0.409781\pi\) | ||||
0.279651 | + | 0.960102i | \(0.409781\pi\) | |||||||
\(252\) | 109608. | 0.108728 | ||||||||
\(253\) | 613469. | 0.602548 | ||||||||
\(254\) | −578556. | −0.562680 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.03450e6 | 0.986572 | ||||||||
\(257\) | 787924. | 0.744135 | 0.372067 | − | 0.928206i | \(-0.378649\pi\) | ||||
0.372067 | + | 0.928206i | \(0.378649\pi\) | |||||||
\(258\) | −55162.1 | −0.0515931 | ||||||||
\(259\) | −833976. | −0.772510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.06029e6 | 0.963437 | ||||||||
\(262\) | −1.27924e6 | −1.15132 | ||||||||
\(263\) | −1.63173e6 | −1.45465 | −0.727327 | − | 0.686291i | \(-0.759238\pi\) | ||||
−0.727327 | + | 0.686291i | \(0.759238\pi\) | |||||||
\(264\) | −665280. | −0.587482 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −87120.0 | −0.0754942 | ||||||||
\(267\) | −198798. | −0.170661 | ||||||||
\(268\) | 523682. | 0.445380 | ||||||||
\(269\) | 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 | \(-0.751919\pi\) | ||||
−0.711357 | + | 0.702831i | \(0.751919\pi\) | |||||||
\(272\) | −871980. | −0.714635 | ||||||||
\(273\) | 141845. | 0.115188 | ||||||||
\(274\) | −952336. | −0.766326 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −581328. | −0.459355 | ||||||||
\(277\) | −1.27243e6 | −0.996402 | −0.498201 | − | 0.867062i | \(-0.666006\pi\) | ||||
−0.498201 | + | 0.867062i | \(0.666006\pi\) | |||||||
\(278\) | −2.11163e6 | −1.63872 | ||||||||
\(279\) | 1.03306e6 | 0.794536 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.46500e6 | 1.10681 | 0.553404 | − | 0.832913i | \(-0.313329\pi\) | ||||
0.553404 | + | 0.832913i | \(0.313329\pi\) | |||||||
\(282\) | 1.39131e6 | 1.04184 | ||||||||
\(283\) | −1.65051e6 | −1.22504 | −0.612521 | − | 0.790455i | \(-0.709844\pi\) | ||||
−0.612521 | + | 0.790455i | \(0.709844\pi\) | |||||||
\(284\) | 640224. | 0.471016 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 199584. | 0.144281 | ||||||||
\(287\) | −11820.5 | −0.00847089 | ||||||||
\(288\) | 633290. | 0.449905 | ||||||||
\(289\) | −943953. | −0.664823 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.01485e6 | −1.39479 | ||||||||
\(292\) | 851072. | 0.584130 | ||||||||
\(293\) | 2.38772e6 | 1.62485 | 0.812426 | − | 0.583064i | \(-0.198146\pi\) | ||||
0.812426 | + | 0.583064i | \(0.198146\pi\) | |||||||
\(294\) | −1.74808e6 | −1.17948 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.85328e6 | −1.22945 | ||||||||
\(297\) | 451326. | 0.296893 | ||||||||
\(298\) | 558188. | 0.364116 | ||||||||
\(299\) | −290664. | −0.188024 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24948.0 | −0.0158716 | ||||||||
\(302\) | 1.03378e6 | 0.652244 | ||||||||
\(303\) | 2.17102e6 | 1.35849 | ||||||||
\(304\) | −278080. | −0.172578 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −700128. | −0.427439 | ||||||||
\(307\) | −928264. | −0.562115 | −0.281058 | − | 0.959691i | \(-0.590685\pi\) | ||||
−0.281058 | + | 0.959691i | \(0.590685\pi\) | |||||||
\(308\) | 180531. | 0.108436 | ||||||||
\(309\) | −1.40540e6 | −0.837346 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 568152. | 0.333092 | 0.166546 | − | 0.986034i | \(-0.446739\pi\) | ||||
0.166546 | + | 0.986034i | \(0.446739\pi\) | |||||||
\(312\) | 315212. | 0.183323 | ||||||||
\(313\) | −1.72244e6 | −0.993766 | −0.496883 | − | 0.867818i | \(-0.665522\pi\) | ||||
−0.496883 | + | 0.867818i | \(0.665522\pi\) | |||||||
\(314\) | 2.36570e6 | 1.35405 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −623040. | −0.350993 | ||||||||
\(317\) | −131643. | −0.0735785 | −0.0367893 | − | 0.999323i | \(-0.511713\pi\) | ||||
−0.0367893 | + | 0.999323i | \(0.511713\pi\) | |||||||
\(318\) | −768767. | −0.426311 | ||||||||
\(319\) | 1.74636e6 | 0.960853 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.93261e6 | 1.04684 | ||||||||
\(322\) | −964023. | −0.518141 | ||||||||
\(323\) | 151769. | 0.0809424 | ||||||||
\(324\) | −873828. | −0.462449 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 961092. | 0.500865 | ||||||||
\(327\) | −418094. | −0.216224 | ||||||||
\(328\) | −26267.7 | −0.0134815 | ||||||||
\(329\) | 629244. | 0.320501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.58055e6 | −0.792935 | −0.396468 | − | 0.918049i | \(-0.629764\pi\) | ||||
−0.396468 | + | 0.918049i | \(0.629764\pi\) | |||||||
\(332\) | −742101. | −0.369503 | ||||||||
\(333\) | −2.13735e6 | −1.05625 | ||||||||
\(334\) | −120076. | −0.0588966 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.50163e6 | 0.725630 | ||||||||
\(337\) | −1.22885e6 | −0.589419 | −0.294709 | − | 0.955587i | \(-0.595223\pi\) | ||||
−0.294709 | + | 0.955587i | \(0.595223\pi\) | |||||||
\(338\) | 2.36832e6 | 1.12758 | ||||||||
\(339\) | −2.08982e6 | −0.987667 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70150e6 | 0.792405 | ||||||||
\(342\) | −223275. | −0.103223 | ||||||||
\(343\) | −1.79396e6 | −0.823338 | ||||||||
\(344\) | −55440.0 | −0.0252596 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.26735e6 | 1.46726 | ||||||||
\(347\) | 3.84224e6 | 1.71301 | 0.856506 | − | 0.516137i | \(-0.172630\pi\) | ||||
0.856506 | + | 0.516137i | \(0.172630\pi\) | |||||||
\(348\) | −1.65486e6 | −0.732511 | ||||||||
\(349\) | 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 | ||||||||
\(352\) | 1.04307e6 | 0.448699 | ||||||||
\(353\) | −295365. | −0.126160 | −0.0630802 | − | 0.998008i | \(-0.520092\pi\) | ||||
−0.0630802 | + | 0.998008i | \(0.520092\pi\) | |||||||
\(354\) | 3.25512e6 | 1.38057 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 119880. | 0.0501328 | ||||||||
\(357\) | −819551. | −0.340334 | ||||||||
\(358\) | 2.94795e6 | 1.21566 | ||||||||
\(359\) | −1.10484e6 | −0.452442 | −0.226221 | − | 0.974076i | \(-0.572637\pi\) | ||||
−0.226221 | + | 0.974076i | \(0.572637\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.42770e6 | −0.980453 | ||||||||
\(362\) | −1.04077e6 | −0.417430 | ||||||||
\(363\) | 1.94116e6 | 0.773206 | ||||||||
\(364\) | −85536.0 | −0.0338373 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −752136. | −0.293490 | ||||||||
\(367\) | 1.83760e6 | 0.712174 | 0.356087 | − | 0.934453i | \(-0.384111\pi\) | ||||
0.356087 | + | 0.934453i | \(0.384111\pi\) | |||||||
\(368\) | −3.07708e6 | −1.18446 | ||||||||
\(369\) | −30294.0 | −0.0115822 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −347688. | −0.131146 | ||||||||
\(372\) | −1.61236e6 | −0.604093 | ||||||||
\(373\) | 2.93350e6 | 1.09173 | 0.545864 | − | 0.837874i | \(-0.316202\pi\) | ||||
0.545864 | + | 0.837874i | \(0.316202\pi\) | |||||||
\(374\) | −1.15315e6 | −0.426292 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.39832e6 | 0.510078 | ||||||||
\(377\) | −827432. | −0.299832 | ||||||||
\(378\) | −709227. | −0.255303 | ||||||||
\(379\) | −5.09342e6 | −1.82143 | −0.910713 | − | 0.413040i | \(-0.864467\pi\) | ||||
−0.910713 | + | 0.413040i | \(0.864467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.73567e6 | −0.612568 | ||||||||
\(382\) | −2.20457e6 | −0.772976 | ||||||||
\(383\) | 3.17485e6 | 1.10593 | 0.552964 | − | 0.833205i | \(-0.313497\pi\) | ||||
0.552964 | + | 0.833205i | \(0.313497\pi\) | |||||||
\(384\) | 4.35072e6 | 1.50568 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.21453e6 | −1.78134 | ||||||||
\(387\) | −63937.9 | −0.0217011 | ||||||||
\(388\) | 1.21500e6 | 0.409729 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | −1.75688e6 | −0.577467 | ||||||||
\(393\) | −3.83771e6 | −1.25340 | ||||||||
\(394\) | 395384. | 0.128315 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 462672. | 0.148264 | ||||||||
\(397\) | 4.90405e6 | 1.56163 | 0.780817 | − | 0.624760i | \(-0.214803\pi\) | ||||
0.780817 | + | 0.624760i | \(0.214803\pi\) | |||||||
\(398\) | −2.62544e6 | −0.830796 | ||||||||
\(399\) | −261360. | −0.0821877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −642798. | −0.199624 | −0.0998122 | − | 0.995006i | \(-0.531824\pi\) | ||||
−0.0998122 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(402\) | 5.76050e6 | 1.77785 | ||||||||
\(403\) | −806179. | −0.247268 | ||||||||
\(404\) | −1.30918e6 | −0.399066 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.74428e6 | −0.826254 | ||||||||
\(407\) | −3.52035e6 | −1.05341 | ||||||||
\(408\) | −1.82123e6 | −0.541643 | ||||||||
\(409\) | 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 | ||||||||
\(412\) | 847490. | 0.245975 | ||||||||
\(413\) | 1.47218e6 | 0.424704 | ||||||||
\(414\) | −2.47064e6 | −0.708450 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −494208. | −0.140016 | ||||||||
\(417\) | −6.33489e6 | −1.78402 | ||||||||
\(418\) | −367747. | −0.102946 | ||||||||
\(419\) | 2.93742e6 | 0.817393 | 0.408697 | − | 0.912670i | \(-0.365983\pi\) | ||||
0.408697 | + | 0.912670i | \(0.365983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.71770e6 | 0.747303 | 0.373651 | − | 0.927569i | \(-0.378106\pi\) | ||||
0.373651 | + | 0.927569i | \(0.378106\pi\) | |||||||
\(422\) | 1.66858e6 | 0.456106 | ||||||||
\(423\) | 1.61266e6 | 0.438219 | ||||||||
\(424\) | −772640. | −0.208719 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.04246e6 | 1.88019 | ||||||||
\(427\) | −340166. | −0.0902862 | ||||||||
\(428\) | −1.16541e6 | −0.307517 | ||||||||
\(429\) | 598752. | 0.157074 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.99435e6 | 1.29505 | 0.647524 | − | 0.762045i | \(-0.275804\pi\) | ||||
0.647524 | + | 0.762045i | \(0.275804\pi\) | |||||||
\(432\) | −2.26380e6 | −0.583617 | ||||||||
\(433\) | −2.08183e6 | −0.533612 | −0.266806 | − | 0.963750i | \(-0.585968\pi\) | ||||
−0.266806 | + | 0.963750i | \(0.585968\pi\) | |||||||
\(434\) | −2.67379e6 | −0.681402 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 252120. | 0.0635172 | ||||||||
\(437\) | 535569. | 0.134156 | ||||||||
\(438\) | 9.36180e6 | 2.33171 | ||||||||
\(439\) | 4.70404e6 | 1.16496 | 0.582478 | − | 0.812846i | \(-0.302083\pi\) | ||||
0.582478 | + | 0.812846i | \(0.302083\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.02618e6 | −0.496114 | ||||||||
\(442\) | 546368. | 0.133024 | ||||||||
\(443\) | −5.70103e6 | −1.38021 | −0.690103 | − | 0.723711i | \(-0.742435\pi\) | ||||
−0.690103 | + | 0.723711i | \(0.742435\pi\) | |||||||
\(444\) | 3.33590e6 | 0.803075 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.91545e6 | 0.455968 | ||||||||
\(447\) | 1.67456e6 | 0.396399 | ||||||||
\(448\) | 775613. | 0.182579 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 1.26021e6 | 0.290133 | ||||||||
\(453\) | 3.10134e6 | 0.710074 | ||||||||
\(454\) | 7.72204e6 | 1.75830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −580800. | −0.130802 | ||||||||
\(457\) | 2.15371e6 | 0.482388 | 0.241194 | − | 0.970477i | \(-0.422461\pi\) | ||||
0.241194 | + | 0.970477i | \(0.422461\pi\) | |||||||
\(458\) | 3.63283e6 | 0.809248 | ||||||||
\(459\) | 1.23552e6 | 0.273727 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.85130e6 | −0.844024 | −0.422012 | − | 0.906590i | \(-0.638676\pi\) | ||||
−0.422012 | + | 0.906590i | \(0.638676\pi\) | |||||||
\(462\) | 1.98584e6 | 0.432851 | ||||||||
\(463\) | −2.08213e6 | −0.451394 | −0.225697 | − | 0.974198i | \(-0.572466\pi\) | ||||
−0.225697 | + | 0.974198i | \(0.572466\pi\) | |||||||
\(464\) | −8.75952e6 | −1.88880 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −319088. | −0.0680684 | ||||||||
\(467\) | −1.30822e6 | −0.277579 | −0.138790 | − | 0.990322i | \(-0.544321\pi\) | ||||
−0.138790 | + | 0.990322i | \(0.544321\pi\) | |||||||
\(468\) | −219216. | −0.0462655 | ||||||||
\(469\) | 2.60528e6 | 0.546919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.09711e6 | 1.47411 | ||||||||
\(472\) | 3.27152e6 | 0.675919 | ||||||||
\(473\) | −105309. | −0.0216429 | ||||||||
\(474\) | −6.85344e6 | −1.40108 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 494208. | 0.0999752 | ||||||||
\(477\) | −891071. | −0.179315 | ||||||||
\(478\) | −6.67199e6 | −1.33563 | ||||||||
\(479\) | 6.76368e6 | 1.34693 | 0.673464 | − | 0.739220i | \(-0.264806\pi\) | ||||
0.673464 | + | 0.739220i | \(0.264806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.66795e6 | 0.328716 | ||||||||
\(482\) | −5.93810e6 | −1.16421 | ||||||||
\(483\) | −2.89207e6 | −0.564080 | ||||||||
\(484\) | −1.17056e6 | −0.227134 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.72527e6 | −1.29157 | ||||||||
\(487\) | −6.67193e6 | −1.27476 | −0.637381 | − | 0.770549i | \(-0.719982\pi\) | ||||
−0.637381 | + | 0.770549i | \(0.719982\pi\) | |||||||
\(488\) | −755925. | −0.143691 | ||||||||
\(489\) | 2.88328e6 | 0.545273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.87575e6 | −1.28711 | −0.643556 | − | 0.765399i | \(-0.722542\pi\) | ||||
−0.643556 | + | 0.765399i | \(0.722542\pi\) | |||||||
\(492\) | 47281.8 | 0.00880605 | ||||||||
\(493\) | 4.78072e6 | 0.885881 | ||||||||
\(494\) | 174240. | 0.0321241 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.53453e6 | −1.55767 | ||||||||
\(497\) | 3.18507e6 | 0.578400 | ||||||||
\(498\) | −8.16312e6 | −1.47497 | ||||||||
\(499\) | −6.94010e6 | −1.24771 | −0.623856 | − | 0.781539i | \(-0.714435\pi\) | ||||
−0.623856 | + | 0.781539i | \(0.714435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −360228. | −0.0641185 | ||||||||
\(502\) | −3.70302e6 | −0.655839 | ||||||||
\(503\) | 921007. | 0.162309 | 0.0811546 | − | 0.996702i | \(-0.474139\pi\) | ||||
0.0811546 | + | 0.996702i | \(0.474139\pi\) | |||||||
\(504\) | 1.21176e6 | 0.212491 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.06930e6 | −0.706550 | ||||||||
\(507\) | 7.10495e6 | 1.22755 | ||||||||
\(508\) | 1.04665e6 | 0.179946 | ||||||||
\(509\) | −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 | ||||||||
\(512\) | 134151. | 0.0226161 | ||||||||
\(513\) | 394015. | 0.0661027 | ||||||||
\(514\) | −5.22650e6 | −0.872575 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 99792.0 | 0.0164995 | ||||||||
\(517\) | 2.65614e6 | 0.437043 | ||||||||
\(518\) | 5.53197e6 | 0.905848 | ||||||||
\(519\) | 9.80206e6 | 1.59735 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −147798. | −0.0238547 | −0.0119274 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119274 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(522\) | −7.03317e6 | −1.12973 | ||||||||
\(523\) | 1.23884e7 | 1.98043 | 0.990216 | − | 0.139543i | \(-0.0445634\pi\) | ||||
0.990216 | + | 0.139543i | \(0.0445634\pi\) | |||||||
\(524\) | 2.31422e6 | 0.368194 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.08237e7 | 1.70573 | ||||||||
\(527\) | 4.65792e6 | 0.730576 | ||||||||
\(528\) | 6.33863e6 | 0.989488 | ||||||||
\(529\) | −510027. | −0.0792417 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.77298e6 | 0.580695 | ||||||||
\(532\) | 157606. | 0.0241431 | ||||||||
\(533\) | 23640.9 | 0.00360451 | ||||||||
\(534\) | 1.31868e6 | 0.200118 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.78952e6 | 0.870423 | ||||||||
\(537\) | 8.84385e6 | 1.32344 | ||||||||
\(538\) | −1.15178e7 | −1.71559 | ||||||||
\(539\) | −3.33724e6 | −0.494783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.99810e6 | −1.46867 | −0.734335 | − | 0.678787i | \(-0.762506\pi\) | ||||
−0.734335 | + | 0.678787i | \(0.762506\pi\) | |||||||
\(542\) | 1.14095e7 | 1.66828 | ||||||||
\(543\) | −3.12231e6 | −0.454440 | ||||||||
\(544\) | 2.85542e6 | 0.413688 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −940896. | −0.135070 | ||||||||
\(547\) | −1.18580e7 | −1.69451 | −0.847253 | − | 0.531189i | \(-0.821745\pi\) | ||||
−0.847253 | + | 0.531189i | \(0.821745\pi\) | |||||||
\(548\) | 1.72284e6 | 0.245072 | ||||||||
\(549\) | −871794. | −0.123448 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.52460e6 | 0.213933 | ||||||||
\(552\) | −6.42682e6 | −0.897736 | ||||||||
\(553\) | −3.09958e6 | −0.431013 | ||||||||
\(554\) | 8.44034e6 | 1.16838 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.82008e6 | 0.524065 | ||||||||
\(557\) | −904550. | −0.123536 | −0.0617681 | − | 0.998091i | \(-0.519674\pi\) | ||||
−0.0617681 | + | 0.998091i | \(0.519674\pi\) | |||||||
\(558\) | −6.85252e6 | −0.931676 | ||||||||
\(559\) | 49896.0 | 0.00675361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.45946e6 | −0.464088 | ||||||||
\(562\) | −9.71772e6 | −1.29785 | ||||||||
\(563\) | −8.68719e6 | −1.15507 | −0.577535 | − | 0.816366i | \(-0.695985\pi\) | ||||
−0.577535 | + | 0.816366i | \(0.695985\pi\) | |||||||
\(564\) | −2.51698e6 | −0.333182 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.09482e7 | 1.43649 | ||||||||
\(567\) | −4.34724e6 | −0.567879 | ||||||||
\(568\) | 7.07794e6 | 0.920526 | ||||||||
\(569\) | 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 | \(-0.125806\pi\) | ||||
0.922908 | + | 0.385021i | \(0.125806\pi\) | |||||||
\(572\) | −361061. | −0.0461414 | ||||||||
\(573\) | −6.61372e6 | −0.841510 | ||||||||
\(574\) | 78408.0 | 0.00993300 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.98778e6 | 0.249638 | ||||||||
\(577\) | −5.63943e6 | −0.705173 | −0.352586 | − | 0.935779i | \(-0.614698\pi\) | ||||
−0.352586 | + | 0.935779i | \(0.614698\pi\) | |||||||
\(578\) | 6.26148e6 | 0.779574 | ||||||||
\(579\) | −1.56436e7 | −1.93928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.69191e6 | −0.453744 | ||||||||
\(582\) | 1.33650e7 | 1.63554 | ||||||||
\(583\) | −1.46765e6 | −0.178834 | ||||||||
\(584\) | 9.40896e6 | 1.14159 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.58383e7 | −1.90531 | ||||||||
\(587\) | −1.28473e6 | −0.153893 | −0.0769464 | − | 0.997035i | \(-0.524517\pi\) | ||||
−0.0769464 | + | 0.997035i | \(0.524517\pi\) | |||||||
\(588\) | 3.16239e6 | 0.377200 | ||||||||
\(589\) | 1.48544e6 | 0.176428 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.18615e6 | 0.139692 | ||||||||
\(592\) | 1.76576e7 | 2.07075 | ||||||||
\(593\) | 7.00943e6 | 0.818552 | 0.409276 | − | 0.912411i | \(-0.365781\pi\) | ||||
0.409276 | + | 0.912411i | \(0.365781\pi\) | |||||||
\(594\) | −2.99376e6 | −0.348138 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.00980e6 | −0.116445 | ||||||||
\(597\) | −7.87632e6 | −0.904456 | ||||||||
\(598\) | 1.92805e6 | 0.220478 | ||||||||
\(599\) | 8.80020e6 | 1.00213 | 0.501067 | − | 0.865409i | \(-0.332941\pi\) | ||||
0.501067 | + | 0.865409i | \(0.332941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.07670e7 | −1.21593 | −0.607965 | − | 0.793964i | \(-0.708014\pi\) | ||||
−0.607965 | + | 0.793964i | \(0.708014\pi\) | |||||||
\(602\) | 165486. | 0.0186110 | ||||||||
\(603\) | 6.67694e6 | 0.747798 | ||||||||
\(604\) | −1.87018e6 | −0.208588 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.44009e7 | −1.59298 | ||||||||
\(607\) | 1.51219e7 | 1.66584 | 0.832921 | − | 0.553391i | \(-0.186667\pi\) | ||||
0.832921 | + | 0.553391i | \(0.186667\pi\) | |||||||
\(608\) | 910613. | 0.0999021 | ||||||||
\(609\) | −8.23284e6 | −0.899511 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.25849e6 | −0.136379 | ||||||||
\(612\) | 1.26658e6 | 0.136695 | ||||||||
\(613\) | −8.31622e6 | −0.893871 | −0.446936 | − | 0.894566i | \(-0.647485\pi\) | ||||
−0.446936 | + | 0.894566i | \(0.647485\pi\) | |||||||
\(614\) | 6.15740e6 | 0.659139 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.99584e6 | 0.211921 | ||||||||
\(617\) | −1.21083e7 | −1.28047 | −0.640237 | − | 0.768178i | \(-0.721164\pi\) | ||||
−0.640237 | + | 0.768178i | \(0.721164\pi\) | |||||||
\(618\) | 9.32240e6 | 0.981875 | ||||||||
\(619\) | −9.73238e6 | −1.02092 | −0.510461 | − | 0.859901i | \(-0.670525\pi\) | ||||
−0.510461 | + | 0.859901i | \(0.670525\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.35996e6 | 0.453684 | ||||||||
\(622\) | −3.76869e6 | −0.390584 | ||||||||
\(623\) | 596395. | 0.0615622 | ||||||||
\(624\) | −3.00326e6 | −0.308768 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.14254e7 | 1.16529 | ||||||||
\(627\) | −1.10324e6 | −0.112073 | ||||||||
\(628\) | −4.27972e6 | −0.433028 | ||||||||
\(629\) | −9.63706e6 | −0.971220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.60145e6 | −0.859999 | −0.430000 | − | 0.902829i | \(-0.641486\pi\) | ||||
−0.430000 | + | 0.902829i | \(0.641486\pi\) | |||||||
\(632\) | −6.88797e6 | −0.685959 | ||||||||
\(633\) | 5.00574e6 | 0.496546 | ||||||||
\(634\) | 873224. | 0.0862785 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.39075e6 | 0.136335 | ||||||||
\(637\) | 1.58119e6 | 0.154396 | ||||||||
\(638\) | −1.15840e7 | −1.12670 | ||||||||
\(639\) | 8.16286e6 | 0.790842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.42440e6 | −0.617572 | −0.308786 | − | 0.951132i | \(-0.599923\pi\) | ||||
−0.308786 | + | 0.951132i | \(0.599923\pi\) | |||||||
\(642\) | −1.28195e7 | −1.22753 | ||||||||
\(643\) | 3.64721e6 | 0.347883 | 0.173941 | − | 0.984756i | \(-0.444350\pi\) | ||||
0.173941 | + | 0.984756i | \(0.444350\pi\) | |||||||
\(644\) | 1.74398e6 | 0.165702 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.00672e6 | −0.0949134 | ||||||||
\(647\) | −3.78036e6 | −0.355036 | −0.177518 | − | 0.984118i | \(-0.556807\pi\) | ||||
−0.177518 | + | 0.984118i | \(0.556807\pi\) | |||||||
\(648\) | −9.66053e6 | −0.903782 | ||||||||
\(649\) | 6.21432e6 | 0.579138 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.02138e6 | −0.741816 | ||||||||
\(652\) | −1.73868e6 | −0.160177 | ||||||||
\(653\) | −1.66957e7 | −1.53223 | −0.766113 | − | 0.642706i | \(-0.777812\pi\) | ||||
−0.766113 | + | 0.642706i | \(0.777812\pi\) | |||||||
\(654\) | 2.77332e6 | 0.253545 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 250272. | 0.0227066 | ||||||||
\(657\) | 1.08512e7 | 0.980761 | ||||||||
\(658\) | −4.17393e6 | −0.375821 | ||||||||
\(659\) | 1.22166e6 | 0.109581 | 0.0547907 | − | 0.998498i | \(-0.482551\pi\) | ||||
0.0547907 | + | 0.998498i | \(0.482551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.62789e7 | 1.44918 | 0.724589 | − | 0.689182i | \(-0.242030\pi\) | ||||
0.724589 | + | 0.689182i | \(0.242030\pi\) | |||||||
\(662\) | 1.04842e7 | 0.929799 | ||||||||
\(663\) | 1.63910e6 | 0.144818 | ||||||||
\(664\) | −8.20424e6 | −0.722135 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.41776e7 | 1.23856 | ||||||||
\(667\) | 1.68704e7 | 1.46829 | ||||||||
\(668\) | 217226. | 0.0188352 | ||||||||
\(669\) | 5.74636e6 | 0.496395 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.43590e6 | −0.123117 | ||||||||
\(672\) | −4.91731e6 | −0.420053 | ||||||||
\(673\) | 1.43928e7 | 1.22492 | 0.612459 | − | 0.790503i | \(-0.290181\pi\) | ||||
0.612459 | + | 0.790503i | \(0.290181\pi\) | |||||||
\(674\) | 8.15126e6 | 0.691155 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.28444e6 | −0.360602 | ||||||||
\(677\) | −2.62429e6 | −0.220059 | −0.110030 | − | 0.993928i | \(-0.535095\pi\) | ||||
−0.110030 | + | 0.993928i | \(0.535095\pi\) | |||||||
\(678\) | 1.38623e7 | 1.15814 | ||||||||
\(679\) | 6.04454e6 | 0.503140 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.31661e7 | 1.91419 | ||||||||
\(682\) | −1.12865e7 | −0.929177 | ||||||||
\(683\) | 1.03039e7 | 0.845184 | 0.422592 | − | 0.906320i | \(-0.361120\pi\) | ||||
0.422592 | + | 0.906320i | \(0.361120\pi\) | |||||||
\(684\) | 403920. | 0.0330107 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.18998e7 | 0.965449 | ||||||||
\(687\) | 1.08985e7 | 0.880998 | ||||||||
\(688\) | 528219. | 0.0425444 | ||||||||
\(689\) | 695376. | 0.0558048 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.50285e6 | 0.358751 | 0.179375 | − | 0.983781i | \(-0.442592\pi\) | ||||
0.179375 | + | 0.983781i | \(0.442592\pi\) | |||||||
\(692\) | −5.91086e6 | −0.469230 | ||||||||
\(693\) | 2.30176e6 | 0.182066 | ||||||||
\(694\) | −2.54865e7 | −2.00868 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.82952e7 | −1.43157 | ||||||||
\(697\) | −136592. | −0.0106498 | ||||||||
\(698\) | −1.05764e7 | −0.821672 | ||||||||
\(699\) | −957264. | −0.0741035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.88090e6 | −0.375150 | −0.187575 | − | 0.982250i | \(-0.560063\pi\) | ||||
−0.187575 | + | 0.982250i | \(0.560063\pi\) | |||||||
\(702\) | 1.41845e6 | 0.108636 | ||||||||
\(703\) | −3.07332e6 | −0.234541 | ||||||||
\(704\) | 3.27398e6 | 0.248969 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.95923e6 | 0.147936 | ||||||||
\(707\) | −6.51307e6 | −0.490046 | ||||||||
\(708\) | −5.88873e6 | −0.441508 | ||||||||
\(709\) | 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 | ||||||||
\(712\) | 1.32532e6 | 0.0979765 | ||||||||
\(713\) | 1.64371e7 | 1.21088 | ||||||||
\(714\) | 5.43629e6 | 0.399077 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.33304e6 | −0.388770 | ||||||||
\(717\) | −2.00160e7 | −1.45405 | ||||||||
\(718\) | 7.32868e6 | 0.530536 | ||||||||
\(719\) | 1.19167e7 | 0.859675 | 0.429838 | − | 0.902906i | \(-0.358571\pi\) | ||||
0.429838 | + | 0.902906i | \(0.358571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.21621e6 | 0.302054 | ||||||||
\(722\) | 1.61035e7 | 1.14968 | ||||||||
\(723\) | −1.78143e7 | −1.26743 | ||||||||
\(724\) | 1.88282e6 | 0.133494 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.28762e7 | −0.906664 | ||||||||
\(727\) | 1.38269e6 | 0.0970264 | 0.0485132 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485132 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(728\) | −945636. | −0.0661296 | ||||||||
\(729\) | −2.48079e6 | −0.172890 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −288288. | −0.0199541 | ||||||||
\(732\) | 1.36067e6 | 0.0938585 | ||||||||
\(733\) | −6.09661e6 | −0.419110 | −0.209555 | − | 0.977797i | \(-0.567202\pi\) | ||||
−0.209555 | + | 0.977797i | \(0.567202\pi\) | |||||||
\(734\) | −1.21893e7 | −0.835099 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00764e7 | 0.685660 | ||||||||
\(737\) | 1.09973e7 | 0.745793 | ||||||||
\(738\) | 200948. | 0.0135813 | ||||||||
\(739\) | −6.16946e6 | −0.415562 | −0.207781 | − | 0.978175i | \(-0.566624\pi\) | ||||
−0.207781 | + | 0.978175i | \(0.566624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 522720. | 0.0349723 | ||||||||
\(742\) | 2.30630e6 | 0.153782 | ||||||||
\(743\) | −1.57574e7 | −1.04716 | −0.523578 | − | 0.851978i | \(-0.675403\pi\) | ||||
−0.523578 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(744\) | −1.78253e7 | −1.18060 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.94586e7 | −1.28016 | ||||||||
\(747\) | −9.46179e6 | −0.620400 | ||||||||
\(748\) | 2.08613e6 | 0.136329 | ||||||||
\(749\) | −5.79784e6 | −0.377626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51816e7 | −0.982243 | −0.491122 | − | 0.871091i | \(-0.663413\pi\) | ||||
−0.491122 | + | 0.871091i | \(0.663413\pi\) | |||||||
\(752\) | −1.33229e7 | −0.859118 | ||||||||
\(753\) | −1.11091e7 | −0.713987 | ||||||||
\(754\) | 5.48856e6 | 0.351585 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.28304e6 | 0.0816461 | ||||||||
\(757\) | 652274. | 0.0413705 | 0.0206852 | − | 0.999786i | \(-0.493415\pi\) | ||||
0.0206852 | + | 0.999786i | \(0.493415\pi\) | |||||||
\(758\) | 3.37859e7 | 2.13581 | ||||||||
\(759\) | −1.22079e7 | −0.769194 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.51420e6 | 0.282566 | 0.141283 | − | 0.989969i | \(-0.454877\pi\) | ||||
0.141283 | + | 0.989969i | \(0.454877\pi\) | |||||||
\(762\) | 1.15131e7 | 0.718300 | ||||||||
\(763\) | 1.25428e6 | 0.0779980 | ||||||||
\(764\) | 3.98822e6 | 0.247199 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.10596e7 | −1.29681 | ||||||||
\(767\) | −2.94437e6 | −0.180719 | ||||||||
\(768\) | −2.05862e7 | −1.25943 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 9.43344e6 | 0.569674 | ||||||||
\(773\) | −1.04245e7 | −0.627492 | −0.313746 | − | 0.949507i | \(-0.601584\pi\) | ||||
−0.313746 | + | 0.949507i | \(0.601584\pi\) | |||||||
\(774\) | 424116. | 0.0254467 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.34323e7 | 0.800750 | ||||||||
\(777\) | 1.65959e7 | 0.986163 | ||||||||
\(778\) | 1.19393e7 | 0.707177 | ||||||||
\(779\) | −43560.0 | −0.00257184 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34447e7 | 0.788721 | ||||||||
\(782\) | −1.11398e7 | −0.651421 | ||||||||
\(783\) | 1.24115e7 | 0.723467 | ||||||||
\(784\) | 1.67392e7 | 0.972620 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.54565e7 | 1.46974 | ||||||||
\(787\) | −3.45366e7 | −1.98766 | −0.993830 | − | 0.110913i | \(-0.964622\pi\) | ||||
−0.993830 | + | 0.110913i | \(0.964622\pi\) | |||||||
\(788\) | −715277. | −0.0410354 | ||||||||
\(789\) | 3.24711e7 | 1.85697 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.26947e6 | 0.356279 | ||||||||
\(792\) | 5.11503e6 | 0.289758 | ||||||||
\(793\) | 680333. | 0.0384183 | ||||||||
\(794\) | −3.25298e7 | −1.83118 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.74960e6 | 0.265689 | ||||||||
\(797\) | 2.09287e7 | 1.16707 | 0.583533 | − | 0.812089i | \(-0.301670\pi\) | ||||
0.583533 | + | 0.812089i | \(0.301670\pi\) | |||||||
\(798\) | 1.73367e6 | 0.0963736 | ||||||||
\(799\) | 7.27126e6 | 0.402942 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.52847e6 | 0.0841735 | ||||||||
\(802\) | 4.26384e6 | 0.234080 | ||||||||
\(803\) | 1.78725e7 | 0.978131 | ||||||||
\(804\) | −1.04211e7 | −0.568558 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.34758e6 | 0.289948 | ||||||||
\(807\) | −3.45533e7 | −1.86770 | ||||||||
\(808\) | −1.44735e7 | −0.779910 | ||||||||
\(809\) | −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 | \(-0.533661\pi\) | ||||
−0.105553 | + | 0.994414i | \(0.533661\pi\) | |||||||
\(812\) | 4.96459e6 | 0.264237 | ||||||||
\(813\) | 3.42285e7 | 1.81619 | ||||||||
\(814\) | 2.33513e7 | 1.23524 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.73522e7 | 0.912282 | ||||||||
\(817\) | −91936.8 | −0.00481875 | ||||||||
\(818\) | −1.36453e7 | −0.713018 | ||||||||
\(819\) | −1.09058e6 | −0.0568132 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.43550e6 | −0.177882 | −0.0889410 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889410 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(822\) | 1.89512e7 | 0.978269 | ||||||||
\(823\) | −3.94833e6 | −0.203195 | −0.101598 | − | 0.994826i | \(-0.532395\pi\) | ||||
−0.101598 | + | 0.994826i | \(0.532395\pi\) | |||||||
\(824\) | 9.36936e6 | 0.480720 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.76536e6 | −0.498010 | ||||||||
\(827\) | 3.38176e7 | 1.71941 | 0.859705 | − | 0.510791i | \(-0.170647\pi\) | ||||
0.859705 | + | 0.510791i | \(0.170647\pi\) | |||||||
\(828\) | 4.46956e6 | 0.226563 | ||||||||
\(829\) | −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 | ||||||||
\(832\) | −1.55123e6 | −0.0776903 | ||||||||
\(833\) | −9.13579e6 | −0.456177 | ||||||||
\(834\) | 4.20209e7 | 2.09194 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 665280. | 0.0329222 | ||||||||
\(837\) | 1.20927e7 | 0.596635 | ||||||||
\(838\) | −1.94846e7 | −0.958478 | ||||||||
\(839\) | −2.89012e7 | −1.41746 | −0.708729 | − | 0.705481i | \(-0.750731\pi\) | ||||
−0.708729 | + | 0.705481i | \(0.750731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.75138e7 | 1.34140 | ||||||||
\(842\) | −1.80272e7 | −0.876290 | ||||||||
\(843\) | −2.91532e7 | −1.41292 | ||||||||
\(844\) | −3.01858e6 | −0.145863 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.06971e7 | −0.513857 | ||||||||
\(847\) | −5.82348e6 | −0.278917 | ||||||||
\(848\) | 7.36153e6 | 0.351543 | ||||||||
\(849\) | 3.28446e7 | 1.56385 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.40077e7 | −1.60973 | ||||||||
\(852\) | −1.27403e7 | −0.601285 | ||||||||
\(853\) | −2.02107e7 | −0.951062 | −0.475531 | − | 0.879699i | \(-0.657744\pi\) | ||||
−0.475531 | + | 0.879699i | \(0.657744\pi\) | |||||||
\(854\) | 2.25641e6 | 0.105870 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.28841e7 | −0.600992 | ||||||||
\(857\) | −1.70522e7 | −0.793101 | −0.396550 | − | 0.918013i | \(-0.629793\pi\) | ||||
−0.396550 | + | 0.918013i | \(0.629793\pi\) | |||||||
\(858\) | −3.97167e6 | −0.184185 | ||||||||
\(859\) | −1.95505e7 | −0.904015 | −0.452008 | − | 0.892014i | \(-0.649292\pi\) | ||||
−0.452008 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 235224. | 0.0108137 | ||||||||
\(862\) | −3.31288e7 | −1.51858 | ||||||||
\(863\) | 2.70896e7 | 1.23816 | 0.619078 | − | 0.785330i | \(-0.287507\pi\) | ||||
0.619078 | + | 0.785330i | \(0.287507\pi\) | |||||||
\(864\) | 7.41312e6 | 0.337844 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.38093e7 | 0.625716 | ||||||||
\(867\) | 1.87844e7 | 0.848692 | ||||||||
\(868\) | 4.83707e6 | 0.217913 | ||||||||
\(869\) | −1.30838e7 | −0.587741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.21057e6 | −0.232723 | ||||||||
\(872\) | 2.78729e6 | 0.124134 | ||||||||
\(873\) | 1.54912e7 | 0.687940 | ||||||||
\(874\) | −3.55256e6 | −0.157312 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.69361e7 | −0.745682 | ||||||||
\(877\) | −1.98285e6 | −0.0870545 | −0.0435272 | − | 0.999052i | \(-0.513860\pi\) | ||||
−0.0435272 | + | 0.999052i | \(0.513860\pi\) | |||||||
\(878\) | −3.12031e7 | −1.36603 | ||||||||
\(879\) | −4.75150e7 | −2.07424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.22840e7 | −1.83542 | −0.917712 | − | 0.397247i | \(-0.869966\pi\) | ||||
−0.917712 | + | 0.397247i | \(0.869966\pi\) | |||||||
\(882\) | 1.34402e7 | 0.581745 | ||||||||
\(883\) | 134502. | 0.00580535 | 0.00290267 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290267 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(884\) | −988416. | −0.0425411 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.78164e7 | 1.61844 | ||||||||
\(887\) | −3.87668e6 | −0.165444 | −0.0827219 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827219 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(888\) | 3.68798e7 | 1.56948 | ||||||||
\(889\) | 5.20700e6 | 0.220970 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.83504e7 | −0.774374 | ||||||||
\(892\) | −3.46518e6 | −0.145819 | ||||||||
\(893\) | 2.31885e6 | 0.0973070 | ||||||||
\(894\) | −1.11078e7 | −0.464819 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.30522e7 | −0.543141 | ||||||||
\(897\) | 5.78414e6 | 0.240026 | ||||||||
\(898\) | 4.11477e7 | 1.70277 | ||||||||
\(899\) | 4.67914e7 | 1.93093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.01773e6 | −0.164880 | ||||||||
\(902\) | 330973. | 0.0135449 | ||||||||
\(903\) | 496459. | 0.0202611 | ||||||||
\(904\) | 1.39322e7 | 0.567019 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.05719e7 | −0.832635 | ||||||||
\(907\) | 2.87363e7 | 1.15988 | 0.579939 | − | 0.814660i | \(-0.303076\pi\) | ||||
0.579939 | + | 0.814660i | \(0.303076\pi\) | |||||||
\(908\) | −1.39697e7 | −0.562306 | ||||||||
\(909\) | −1.66920e7 | −0.670037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.87675e6 | 0.0749223 | 0.0374611 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374611 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(912\) | 5.53372e6 | 0.220308 | ||||||||
\(913\) | −1.55841e7 | −0.618736 | ||||||||
\(914\) | −1.42861e7 | −0.565650 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.57204e6 | −0.258798 | ||||||||
\(917\) | 1.15131e7 | 0.452137 | ||||||||
\(918\) | −8.19551e6 | −0.320974 | ||||||||
\(919\) | 6.76852e6 | 0.264366 | 0.132183 | − | 0.991225i | \(-0.457801\pi\) | ||||
0.132183 | + | 0.991225i | \(0.457801\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.84722e7 | 0.717579 | ||||||||
\(922\) | 2.55466e7 | 0.989706 | ||||||||
\(923\) | −6.37015e6 | −0.246119 | ||||||||
\(924\) | −3.59251e6 | −0.138426 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.38113e7 | 0.529306 | ||||||||
\(927\) | 1.08055e7 | 0.412996 | ||||||||
\(928\) | 2.86843e7 | 1.09339 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 577252. | 0.0217684 | ||||||||
\(933\) | −1.13061e7 | −0.425214 | ||||||||
\(934\) | 8.67772e6 | 0.325491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.42352e6 | −0.0904184 | ||||||||
\(937\) | −3.92632e7 | −1.46096 | −0.730478 | − | 0.682936i | \(-0.760703\pi\) | ||||
−0.730478 | + | 0.682936i | \(0.760703\pi\) | |||||||
\(938\) | −1.72815e7 | −0.641319 | ||||||||
\(939\) | 3.42762e7 | 1.26861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.94919e7 | 1.08575 | 0.542874 | − | 0.839814i | \(-0.317336\pi\) | ||||
0.542874 | + | 0.839814i | \(0.317336\pi\) | |||||||
\(942\) | −4.70769e7 | −1.72855 | ||||||||
\(943\) | −482012. | −0.0176514 | ||||||||
\(944\) | −3.11702e7 | −1.13844 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 698544. | 0.0253785 | ||||||||
\(947\) | −2.09628e7 | −0.759581 | −0.379791 | − | 0.925072i | \(-0.624004\pi\) | ||||
−0.379791 | + | 0.925072i | \(0.624004\pi\) | |||||||
\(948\) | 1.23983e7 | 0.448067 | ||||||||
\(949\) | −8.46806e6 | −0.305224 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.61967e6 | 0.0939281 | ||||||||
\(952\) | 5.46368e6 | 0.195386 | ||||||||
\(953\) | −1.64122e7 | −0.585375 | −0.292687 | − | 0.956208i | \(-0.594549\pi\) | ||||
−0.292687 | + | 0.956208i | \(0.594549\pi\) | |||||||
\(954\) | 5.91070e6 | 0.210265 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.20701e7 | 0.427135 | ||||||||
\(957\) | −3.47521e7 | −1.22660 | ||||||||
\(958\) | −4.48652e7 | −1.57941 | ||||||||
\(959\) | 8.57102e6 | 0.300944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.69604e7 | 0.592416 | ||||||||
\(962\) | −1.10639e7 | −0.385454 | ||||||||
\(963\) | −1.48590e7 | −0.516325 | ||||||||
\(964\) | 1.07424e7 | 0.372314 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.91838e7 | 0.661443 | ||||||||
\(967\) | 4.71911e7 | 1.62291 | 0.811454 | − | 0.584416i | \(-0.198676\pi\) | ||||
0.811454 | + | 0.584416i | \(0.198676\pi\) | |||||||
\(968\) | −1.29411e7 | −0.443897 | ||||||||
\(969\) | −3.02016e6 | −0.103329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.84771e7 | 1.30965 | 0.654823 | − | 0.755783i | \(-0.272743\pi\) | ||||
0.654823 | + | 0.755783i | \(0.272743\pi\) | |||||||
\(972\) | 1.21665e7 | 0.413046 | ||||||||
\(973\) | 1.90047e7 | 0.643544 | ||||||||
\(974\) | 4.42566e7 | 1.49479 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.20227e6 | 0.242016 | ||||||||
\(977\) | −2.70184e7 | −0.905572 | −0.452786 | − | 0.891619i | \(-0.649570\pi\) | ||||
−0.452786 | + | 0.891619i | \(0.649570\pi\) | |||||||
\(978\) | −1.91255e7 | −0.639389 | ||||||||
\(979\) | 2.51748e6 | 0.0839478 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21453e6 | 0.106646 | ||||||||
\(982\) | 4.56086e7 | 1.50927 | ||||||||
\(983\) | 2.88475e7 | 0.952192 | 0.476096 | − | 0.879393i | \(-0.342051\pi\) | ||||
0.476096 | + | 0.879393i | \(0.342051\pi\) | |||||||
\(984\) | 522720. | 0.0172100 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.17117e7 | −1.03879 | ||||||||
\(987\) | −1.25218e7 | −0.409142 | ||||||||
\(988\) | −315212. | −0.0102733 | ||||||||
\(989\) | −1.01732e6 | −0.0330726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.21596e7 | −1.68714 | −0.843569 | − | 0.537021i | \(-0.819550\pi\) | ||||
−0.843569 | + | 0.537021i | \(0.819550\pi\) | |||||||
\(992\) | 2.79475e7 | 0.901704 | ||||||||
\(993\) | 3.14525e7 | 1.01224 | ||||||||
\(994\) | −2.11274e7 | −0.678235 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.47676e7 | 0.471696 | ||||||||
\(997\) | 9.78148e6 | 0.311650 | 0.155825 | − | 0.987785i | \(-0.450196\pi\) | ||||
0.155825 | + | 0.987785i | \(0.450196\pi\) | |||||||
\(998\) | 4.60354e7 | 1.46307 | ||||||||
\(999\) | −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 | 25.6.a.c.1.1 | 2 | ||
3.2 | odd | 2 | 225.6.a.n.1.2 | 2 | |||
4.3 | odd | 2 | 400.6.a.t.1.2 | 2 | |||
5.2 | odd | 4 | 5.6.b.a.4.1 | ✓ | 2 | ||
5.3 | odd | 4 | 5.6.b.a.4.2 | yes | 2 | ||
5.4 | even | 2 | inner | 25.6.a.c.1.2 | 2 | ||
15.2 | even | 4 | 45.6.b.b.19.2 | 2 | |||
15.8 | even | 4 | 45.6.b.b.19.1 | 2 | |||
15.14 | odd | 2 | 225.6.a.n.1.1 | 2 | |||
20.3 | even | 4 | 80.6.c.a.49.2 | 2 | |||
20.7 | even | 4 | 80.6.c.a.49.1 | 2 | |||
20.19 | odd | 2 | 400.6.a.t.1.1 | 2 | |||
35.13 | even | 4 | 245.6.b.a.99.2 | 2 | |||
35.27 | even | 4 | 245.6.b.a.99.1 | 2 | |||
40.3 | even | 4 | 320.6.c.g.129.1 | 2 | |||
40.13 | odd | 4 | 320.6.c.f.129.2 | 2 | |||
40.27 | even | 4 | 320.6.c.g.129.2 | 2 | |||
40.37 | odd | 4 | 320.6.c.f.129.1 | 2 | |||
60.23 | odd | 4 | 720.6.f.f.289.1 | 2 | |||
60.47 | odd | 4 | 720.6.f.f.289.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.b.a.4.1 | ✓ | 2 | 5.2 | odd | 4 | ||
5.6.b.a.4.2 | yes | 2 | 5.3 | odd | 4 | ||
25.6.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
25.6.a.c.1.2 | 2 | 5.4 | even | 2 | inner | ||
45.6.b.b.19.1 | 2 | 15.8 | even | 4 | |||
45.6.b.b.19.2 | 2 | 15.2 | even | 4 | |||
80.6.c.a.49.1 | 2 | 20.7 | even | 4 | |||
80.6.c.a.49.2 | 2 | 20.3 | even | 4 | |||
225.6.a.n.1.1 | 2 | 15.14 | odd | 2 | |||
225.6.a.n.1.2 | 2 | 3.2 | odd | 2 | |||
245.6.b.a.99.1 | 2 | 35.27 | even | 4 | |||
245.6.b.a.99.2 | 2 | 35.13 | even | 4 | |||
320.6.c.f.129.1 | 2 | 40.37 | odd | 4 | |||
320.6.c.f.129.2 | 2 | 40.13 | odd | 4 | |||
320.6.c.g.129.1 | 2 | 40.3 | even | 4 | |||
320.6.c.g.129.2 | 2 | 40.27 | even | 4 | |||
400.6.a.t.1.1 | 2 | 20.19 | odd | 2 | |||
400.6.a.t.1.2 | 2 | 4.3 | odd | 2 | |||
720.6.f.f.289.1 | 2 | 60.23 | odd | 4 | |||
720.6.f.f.289.2 | 2 | 60.47 | odd | 4 |