Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,6,Mod(1,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, 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("84.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.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: | \(13.4722408643\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 84.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −34.0000 | −0.608210 | −0.304105 | − | 0.952638i | \(-0.598357\pi\) | ||||
−0.304105 | + | 0.952638i | \(0.598357\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −332.000 | −0.827287 | −0.413644 | − | 0.910439i | \(-0.635744\pi\) | ||||
−0.413644 | + | 0.910439i | \(0.635744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1026.00 | −1.68379 | −0.841897 | − | 0.539638i | \(-0.818561\pi\) | ||||
−0.841897 | + | 0.539638i | \(0.818561\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −306.000 | −0.351150 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 922.000 | 0.773764 | 0.386882 | − | 0.922129i | \(-0.373552\pi\) | ||||
0.386882 | + | 0.922129i | \(0.373552\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 452.000 | 0.287246 | 0.143623 | − | 0.989632i | \(-0.454125\pi\) | ||||
0.143623 | + | 0.989632i | \(0.454125\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3776.00 | −1.48838 | −0.744188 | − | 0.667971i | \(-0.767163\pi\) | ||||
−0.744188 | + | 0.667971i | \(0.767163\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1969.00 | −0.630080 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1166.00 | 0.257456 | 0.128728 | − | 0.991680i | \(-0.458911\pi\) | ||||
0.128728 | + | 0.991680i | \(0.458911\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9792.00 | −1.83007 | −0.915034 | − | 0.403377i | \(-0.867836\pi\) | ||||
−0.915034 | + | 0.403377i | \(0.867836\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2988.00 | −0.477635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1666.00 | 0.229882 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2390.00 | 0.287008 | 0.143504 | − | 0.989650i | \(-0.454163\pi\) | ||||
0.143504 | + | 0.989650i | \(0.454163\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9234.00 | −0.972139 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7230.00 | −0.671705 | −0.335853 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335853 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4652.00 | 0.383679 | 0.191840 | − | 0.981426i | \(-0.438555\pi\) | ||||
0.191840 | + | 0.981426i | \(0.438555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2754.00 | −0.202737 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24672.0 | 1.62914 | 0.814572 | − | 0.580062i | \(-0.196972\pi\) | ||||
0.814572 | + | 0.580062i | \(0.196972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8298.00 | 0.446733 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1110.00 | 0.0542792 | 0.0271396 | − | 0.999632i | \(-0.491360\pi\) | ||||
0.0271396 | + | 0.999632i | \(0.491360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11288.0 | 0.503165 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4068.00 | 0.165842 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 46892.0 | 1.75375 | 0.876877 | − | 0.480715i | \(-0.159623\pi\) | ||||
0.876877 | + | 0.480715i | \(0.159623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9762.00 | −0.335903 | −0.167952 | − | 0.985795i | \(-0.553715\pi\) | ||||
−0.167952 | + | 0.985795i | \(0.553715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 34884.0 | 1.02410 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −26252.0 | −0.714456 | −0.357228 | − | 0.934017i | \(-0.616278\pi\) | ||||
−0.357228 | + | 0.934017i | \(0.616278\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −33984.0 | −0.859314 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 65440.0 | 1.54063 | 0.770313 | − | 0.637666i | \(-0.220100\pi\) | ||||
0.770313 | + | 0.637666i | \(0.220100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5606.00 | −0.123125 | −0.0615625 | − | 0.998103i | \(-0.519608\pi\) | ||||
−0.0615625 | + | 0.998103i | \(0.519608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17721.0 | −0.363777 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16268.0 | 0.312685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9840.00 | −0.177389 | −0.0886946 | − | 0.996059i | \(-0.528270\pi\) | ||||
−0.0886946 | + | 0.996059i | \(0.528270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 61108.0 | 0.973650 | 0.486825 | − | 0.873500i | \(-0.338155\pi\) | ||||
0.486825 | + | 0.873500i | \(0.338155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −31348.0 | −0.470611 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10494.0 | 0.148642 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −62958.0 | −0.842512 | −0.421256 | − | 0.906942i | \(-0.638411\pi\) | ||||
−0.421256 | + | 0.906942i | \(0.638411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50274.0 | 0.636414 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −88128.0 | −1.05659 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15368.0 | −0.174706 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −37838.0 | −0.408318 | −0.204159 | − | 0.978938i | \(-0.565446\pi\) | ||||
−0.204159 | + | 0.978938i | \(0.565446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26892.0 | −0.275762 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −56146.0 | −0.547666 | −0.273833 | − | 0.961777i | \(-0.588291\pi\) | ||||
−0.273833 | + | 0.961777i | \(0.588291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −26392.0 | −0.245120 | −0.122560 | − | 0.992461i | \(-0.539110\pi\) | ||||
−0.122560 | + | 0.992461i | \(0.539110\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14994.0 | 0.132722 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 47124.0 | 0.397908 | 0.198954 | − | 0.980009i | \(-0.436246\pi\) | ||||
0.198954 | + | 0.980009i | \(0.436246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −221474. | −1.78549 | −0.892743 | − | 0.450566i | \(-0.851222\pi\) | ||||
−0.892743 | + | 0.450566i | \(0.851222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21510.0 | 0.165704 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 54194.0 | 0.399259 | 0.199630 | − | 0.979871i | \(-0.436026\pi\) | ||||
0.199630 | + | 0.979871i | \(0.436026\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 128384. | 0.905245 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −83106.0 | −0.561265 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −45178.0 | −0.292455 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50827.0 | −0.315596 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −65070.0 | −0.387809 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 173196. | 0.991432 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −245760. | −1.35208 | −0.676039 | − | 0.736866i | \(-0.736305\pi\) | ||||
−0.676039 | + | 0.736866i | \(0.736305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 41868.0 | 0.221517 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −150268. | −0.765047 | −0.382524 | − | 0.923946i | \(-0.624945\pi\) | ||||
−0.382524 | + | 0.923946i | \(0.624945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22148.0 | −0.108569 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24786.0 | −0.117050 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −401638. | −1.82824 | −0.914120 | − | 0.405443i | \(-0.867117\pi\) | ||||
−0.914120 | + | 0.405443i | \(0.867117\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 374092. | 1.64226 | 0.821129 | − | 0.570743i | \(-0.193345\pi\) | ||||
0.821129 | + | 0.570743i | \(0.193345\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 222048. | 0.940587 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 340632. | 1.39298 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −39644.0 | −0.156588 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −456042. | −1.68283 | −0.841413 | − | 0.540393i | \(-0.818276\pi\) | ||||
−0.841413 | + | 0.540393i | \(0.818276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8024.00 | −0.0286384 | −0.0143192 | − | 0.999897i | \(-0.504558\pi\) | ||||
−0.0143192 | + | 0.999897i | \(0.504558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 74682.0 | 0.257921 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 332928. | 1.11307 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 110078. | 0.356411 | 0.178206 | − | 0.983993i | \(-0.442971\pi\) | ||||
0.178206 | + | 0.983993i | \(0.442971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9990.00 | 0.0313381 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 185024. | 0.562553 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3628.00 | −0.0106954 | −0.00534772 | − | 0.999986i | \(-0.501702\pi\) | ||||
−0.00534772 | + | 0.999986i | \(0.501702\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 101592. | 0.290502 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 192824. | 0.535020 | 0.267510 | − | 0.963555i | \(-0.413799\pi\) | ||||
0.267510 | + | 0.963555i | \(0.413799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 681383. | 1.83516 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36612.0 | 0.0957488 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 157142. | 0.399188 | 0.199594 | − | 0.979879i | \(-0.436038\pi\) | ||||
0.199594 | + | 0.979879i | \(0.436038\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 96481.0 | 0.238148 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 422028. | 1.01253 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −446868. | −1.04243 | −0.521215 | − | 0.853426i | \(-0.674521\pi\) | ||||
−0.521215 | + | 0.853426i | \(0.674521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 805638. | 1.82786 | 0.913931 | − | 0.405869i | \(-0.133031\pi\) | ||||
0.913931 | + | 0.405869i | \(0.133031\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −87858.0 | −0.193934 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −81260.0 | −0.174561 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −306104. | −0.640125 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −747912. | −1.48343 | −0.741715 | − | 0.670715i | \(-0.765987\pi\) | ||||
−0.741715 | + | 0.670715i | \(0.765987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −577534. | −1.11605 | −0.558026 | − | 0.829824i | \(-0.688441\pi\) | ||||
−0.558026 | + | 0.829824i | \(0.688441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 313956. | 0.591265 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −771098. | −1.41561 | −0.707806 | − | 0.706407i | \(-0.750315\pi\) | ||||
−0.707806 | + | 0.706407i | \(0.750315\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 557240. | 0.997492 | 0.498746 | − | 0.866748i | \(-0.333794\pi\) | ||||
0.498746 | + | 0.866748i | \(0.333794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −236268. | −0.412491 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −57134.0 | −0.0973093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 245820. | 0.408538 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −305856. | −0.496125 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −150064. | −0.237635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19660.0 | −0.0304003 | −0.0152001 | − | 0.999884i | \(-0.504839\pi\) | ||||
−0.0152001 | + | 0.999884i | \(0.504839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 588960. | 0.889481 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −158168. | −0.233358 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 479808. | 0.691701 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −50454.0 | −0.0710862 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −945972. | −1.30286 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −896848. | −1.20769 | −0.603847 | − | 0.797100i | \(-0.706366\pi\) | ||||
−0.603847 | + | 0.797100i | \(0.706366\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −159489. | −0.210027 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 234228. | 0.301699 | 0.150850 | − | 0.988557i | \(-0.451799\pi\) | ||||
0.150850 | + | 0.988557i | \(0.451799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.03563e6 | −1.30501 | −0.652506 | − | 0.757784i | \(-0.726282\pi\) | ||||
−0.652506 | + | 0.757784i | \(0.726282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 146412. | 0.180529 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 457114. | 0.551613 | 0.275807 | − | 0.961213i | \(-0.411055\pi\) | ||||
0.275807 | + | 0.961213i | \(0.411055\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −838848. | −0.990863 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −88560.0 | −0.102416 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 676344. | 0.765901 | 0.382951 | − | 0.923769i | \(-0.374908\pi\) | ||||
0.382951 | + | 0.923769i | \(0.374908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −96670.0 | −0.107213 | −0.0536067 | − | 0.998562i | \(-0.517072\pi\) | ||||
−0.0536067 | + | 0.998562i | \(0.517072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −81634.0 | −0.0868872 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −463752. | −0.483664 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 549972. | 0.562137 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 288876. | 0.289419 | 0.144710 | − | 0.989474i | \(-0.453775\pi\) | ||||
0.144710 | + | 0.989474i | \(0.453775\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.25363e6 | 1.23131 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −282132. | −0.271708 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −711846. | −0.672285 | −0.336142 | − | 0.941811i | \(-0.609122\pi\) | ||||
−0.336142 | + | 0.941811i | \(0.609122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −117110. | −0.108479 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 94446.0 | 0.0858188 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.87368e6 | −1.67034 | −0.835172 | − | 0.549988i | \(-0.814632\pi\) | ||||
−0.835172 | + | 0.549988i | \(0.814632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37740.0 | −0.0330132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −566622. | −0.486424 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.37660e6 | −1.15992 | −0.579960 | − | 0.814645i | \(-0.696932\pi\) | ||||
−0.579960 | + | 0.814645i | \(0.696932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −781776. | −0.646635 | −0.323317 | − | 0.946291i | \(-0.604798\pi\) | ||||
−0.323317 | + | 0.946291i | \(0.604798\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 452466. | 0.367434 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 653708. | 0.521257 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.06932e6 | 1.62042 | 0.810210 | − | 0.586139i | \(-0.199353\pi\) | ||||
0.810210 | + | 0.586139i | \(0.199353\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −793152. | −0.610023 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.87911e6 | 1.41967 | 0.709835 | − | 0.704368i | \(-0.248770\pi\) | ||||
0.709835 | + | 0.704368i | \(0.248770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 670156. | 0.497405 | 0.248702 | − | 0.968580i | \(-0.419996\pi\) | ||||
0.248702 | + | 0.968580i | \(0.419996\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −138312. | −0.100867 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 354270. | 0.253881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −569773. | −0.401289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −340542. | −0.235743 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.69611e6 | 1.15421 | 0.577105 | − | 0.816670i | \(-0.304182\pi\) | ||||
0.577105 | + | 0.816670i | \(0.304182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.59433e6 | −1.06665 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −242028. | −0.159212 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.87418e6 | 2.50612 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −227948. | −0.145017 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −505314. | −0.316195 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 331908. | 0.204300 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.09459e6 | −0.662834 | −0.331417 | − | 0.943484i | \(-0.607527\pi\) | ||||
−0.331417 | + | 0.943484i | \(0.607527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −237528. | −0.141520 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.21249e6 | 0.710848 | 0.355424 | − | 0.934705i | \(-0.384337\pi\) | ||||
0.355424 | + | 0.934705i | \(0.384337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.69436e6 | 0.977564 | 0.488782 | − | 0.872406i | \(-0.337441\pi\) | ||||
0.488782 | + | 0.872406i | \(0.337441\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 134946. | 0.0766273 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 333342. | 0.186312 | 0.0931562 | − | 0.995652i | \(-0.470304\pi\) | ||||
0.0931562 | + | 0.995652i | \(0.470304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −387112. | −0.212990 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 424116. | 0.229732 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 416744. | 0.222261 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.02019e6 | 1.06092 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.99327e6 | −1.03085 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.20893e6 | −0.615759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.83614e6 | 0.921162 | 0.460581 | − | 0.887618i | \(-0.347641\pi\) | ||||
0.460581 | + | 0.887618i | \(0.347641\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 193590. | 0.0956692 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 892568. | 0.434540 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −973518. | −0.466949 | −0.233474 | − | 0.972363i | \(-0.575009\pi\) | ||||
−0.233474 | + | 0.972363i | \(0.575009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 487746. | 0.230512 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.25094e6 | 1.51399 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.15546e6 | 0.522644 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.39810e6 | 1.51500 | 0.757500 | − | 0.652835i | \(-0.226421\pi\) | ||||
0.757500 | + | 0.652835i | \(0.226421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34370.0 | −0.0151048 | −0.00755242 | − | 0.999971i | \(-0.502404\pi\) | ||||
−0.00755242 | + | 0.999971i | \(0.502404\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −747954. | −0.324046 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.50239e6 | −1.06885 | −0.534427 | − | 0.845215i | \(-0.679472\pi\) | ||||
−0.534427 | + | 0.845215i | \(0.679472\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.22496e6 | −0.937025 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −406602. | −0.168849 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.02800e6 | −1.23999 | −0.619997 | − | 0.784604i | \(-0.712866\pi\) | ||||
−0.619997 | + | 0.784604i | \(0.712866\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.27180e6 | −0.917490 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −457443. | −0.182209 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 190604. | 0.0748859 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.20944e6 | −1.24384 | −0.621919 | − | 0.783081i | \(-0.713647\pi\) | ||||
−0.621919 | + | 0.783081i | \(0.713647\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −585630. | −0.223902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54390.0 | −0.0205156 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.51505e6 | 0.563837 | 0.281919 | − | 0.959438i | \(-0.409029\pi\) | ||||
0.281919 | + | 0.959438i | \(0.409029\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.55876e6 | 0.572403 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.19632e6 | −0.433503 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 643516. | 0.230124 | 0.115062 | − | 0.993358i | \(-0.463293\pi\) | ||||
0.115062 | + | 0.993358i | \(0.463293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.21184e6 | −0.780623 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.75082e6 | 1.65490 | 0.827449 | − | 0.561541i | \(-0.189791\pi\) | ||||
0.827449 | + | 0.561541i | \(0.189791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −553112. | −0.190178 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 376812. | 0.127893 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 379574. | 0.127181 | 0.0635905 | − | 0.997976i | \(-0.479745\pi\) | ||||
0.0635905 | + | 0.997976i | \(0.479745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.48147e6 | −1.15165 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.35241e6 | −0.441700 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 334560. | 0.107890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.42133e6 | −1.72635 | −0.863176 | − | 0.504902i | \(-0.831528\pi\) | ||||
−0.863176 | + | 0.504902i | \(0.831528\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −199332. | −0.0626823 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.20643e6 | −1.92744 | −0.963720 | − | 0.266915i | \(-0.913996\pi\) | ||||
−0.963720 | + | 0.266915i | \(0.913996\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00466e7 | 3.08146 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −223074. | −0.0675789 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −793480. | −0.237438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.25397e6 | −1.25744 | −0.628719 | − | 0.777633i | \(-0.716420\pi\) | ||||
−0.628719 | + | 0.777633i | \(0.716420\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.61474e6 | −1.05554 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.29771e6 | −0.662857 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07767e6 | −0.592184 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.36683e6 | 0.948158 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −725484. | −0.201880 | −0.100940 | − | 0.994893i | \(-0.532185\pi\) | ||||
−0.100940 | + | 0.994893i | \(0.532185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.49867e6 | −1.78698 | −0.893489 | − | 0.449086i | \(-0.851750\pi\) | ||||
−0.893489 | + | 0.449086i | \(0.851750\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.99843e6 | 0.543048 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.81542e6 | −0.487533 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 478338. | 0.126959 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.06569e6 | 0.804238 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.96524e6 | −0.509592 | −0.254796 | − | 0.966995i | \(-0.582008\pi\) | ||||
−0.254796 | + | 0.966995i | \(0.582008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.33531e6 | 1.11122 | 0.555611 | − | 0.831442i | \(-0.312484\pi\) | ||||
0.555611 | + | 0.831442i | \(0.312484\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −356796. | −0.0904059 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.70675e6 | −0.427530 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.47748e6 | 1.60415 | 0.802075 | − | 0.597224i | \(-0.203730\pi\) | ||||
0.802075 | + | 0.597224i | \(0.203730\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.32696e6 | 1.04755 | 0.523774 | − | 0.851857i | \(-0.324524\pi\) | ||||
0.523774 | + | 0.851857i | \(0.324524\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.14057e6 | 0.512424 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.10438e6 | −0.971580 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 482210. | 0.112881 | 0.0564404 | − | 0.998406i | \(-0.482025\pi\) | ||||
0.0564404 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.40036e6 | 0.555693 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −72216.0 | −0.0165344 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.70932e6 | −0.387074 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.52164e6 | 1.90868 | 0.954339 | − | 0.298725i | \(-0.0965613\pi\) | ||||
0.954339 | + | 0.298725i | \(0.0965613\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 672138. | 0.148911 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.99857e6 | −1.31461 | −0.657303 | − | 0.753627i | \(-0.728303\pi\) | ||||
−0.657303 | + | 0.753627i | \(0.728303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.59483e6 | −0.996133 | −0.498066 | − | 0.867139i | \(-0.665956\pi\) | ||||
−0.498066 | + | 0.867139i | \(0.665956\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.99635e6 | 0.642629 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.84330e6 | 1.87639 | 0.938193 | − | 0.346113i | \(-0.112499\pi\) | ||||
0.938193 | + | 0.346113i | \(0.112499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28635e6 | 0.270039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 990702. | 0.205774 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.54446e6 | −0.317413 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −889988. | −0.180988 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 89910.0 | 0.0180931 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.56062e6 | −1.30649 | −0.653245 | − | 0.757146i | \(-0.726593\pi\) | ||||
−0.653245 | + | 0.757146i | \(0.726593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.45214e6 | −0.483262 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.66522e6 | 0.324790 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.28649e6 | 0.248343 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.87772e6 | 1.50514 | 0.752572 | − | 0.658510i | \(-0.228813\pi\) | ||||
0.752572 | + | 0.658510i | \(0.228813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32652.0 | −0.00617501 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 637860. | 0.119405 | 0.0597024 | − | 0.998216i | \(-0.480985\pi\) | ||||
0.0597024 | + | 0.998216i | \(0.480985\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.07505e6 | 0.199210 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 914328. | 0.167722 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.20656e6 | −0.582302 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.93646e6 | −0.887492 | −0.443746 | − | 0.896153i | \(-0.646351\pi\) | ||||
−0.443746 | + | 0.896153i | \(0.646351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.73542e6 | 0.308894 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 226872. | 0.0399817 | 0.0199908 | − | 0.999800i | \(-0.493636\pi\) | ||||
0.0199908 | + | 0.999800i | \(0.493636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.90896e6 | 0.333096 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.13245e6 | 1.05953 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.37404e6 | 0.919404 | 0.459702 | − | 0.888073i | \(-0.347956\pi\) | ||||
0.459702 | + | 0.888073i | \(0.347956\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 274694. | 0.0465368 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 329508. | 0.0552806 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 897328. | 0.149085 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.19110e6 | −1.34777 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.41428e6 | 0.230471 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.61419e6 | −1.55174 | −0.775869 | − | 0.630894i | \(-0.782688\pi\) | ||||
−0.775869 | + | 0.630894i | \(0.782688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.96430e6 | 0.793604 | 0.396802 | − | 0.917904i | \(-0.370120\pi\) | ||||
0.396802 | + | 0.917904i | \(0.370120\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 868329. | 0.137495 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.02822e6 | −1.41604 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.82183e6 | 1.21526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.79825e6 | 0.584585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.41798e6 | 1.13101 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.60222e6 | −0.242012 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.02181e6 | −0.601847 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −797132. | −0.118184 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.20449e7 | 1.76934 | 0.884668 | − | 0.466221i | \(-0.154385\pi\) | ||||
0.884668 | + | 0.466221i | \(0.154385\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.25074e6 | 1.05532 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.53012e6 | 1.08595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.23695e6 | 0.605459 | 0.302730 | − | 0.953077i | \(-0.402102\pi\) | ||||
0.302730 | + | 0.953077i | \(0.402102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −790722. | −0.111968 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 527032. | 0.0739534 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 482160. | 0.0670468 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −731340. | −0.100783 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.02575e7 | −1.40089 | −0.700444 | − | 0.713708i | \(-0.747014\pi\) | ||||
−0.700444 | + | 0.713708i | \(0.747014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.77295e6 | −0.646037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.75494e6 | −0.369577 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.40777e6 | −0.719031 | −0.359515 | − | 0.933139i | \(-0.617058\pi\) | ||||
−0.359515 | + | 0.933139i | \(0.617058\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84260e6 | −0.242834 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.38967e6 | 0.697882 | 0.348941 | − | 0.937145i | \(-0.386541\pi\) | ||||
0.348941 | + | 0.937145i | \(0.386541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.24552e6 | −1.05835 | −0.529173 | − | 0.848514i | \(-0.677498\pi\) | ||||
−0.529173 | + | 0.848514i | \(0.677498\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.73121e6 | −0.856459 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.43494e6 | 0.937795 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.15408e6 | −0.144310 | −0.0721549 | − | 0.997393i | \(-0.522988\pi\) | ||||
−0.0721549 | + | 0.997393i | \(0.522988\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.19781e6 | −0.644353 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.99429e6 | −0.368005 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −368520. | −0.0449045 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.82560e6 | 0.341367 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.16464e6 | −0.858221 | −0.429111 | − | 0.903252i | \(-0.641173\pi\) | ||||
−0.429111 | + | 0.903252i | \(0.641173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.42598e6 | −0.525680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.93988e6 | −0.817304 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.45534e7 | 1.69953 | 0.849763 | − | 0.527165i | \(-0.176745\pi\) | ||||
0.849763 | + | 0.527165i | \(0.176745\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.53605e6 | 0.177874 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.01516e6 | 0.575903 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.04320e7 | −1.18795 | −0.593977 | − | 0.804482i | \(-0.702443\pi\) | ||||
−0.593977 | + | 0.804482i | \(0.702443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 416858. | 0.0470763 | 0.0235381 | − | 0.999723i | \(-0.492507\pi\) | ||||
0.0235381 | + | 0.999723i | \(0.492507\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.12641e6 | −0.238152 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.72812e6 | 0.191949 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.90834e6 | −0.871191 | −0.435596 | − | 0.900143i | \(-0.643462\pi\) | ||||
−0.435596 | + | 0.900143i | \(0.643462\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −514206. | −0.0561816 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.53135e7 | −2.74314 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.13761e7 | −1.22277 | −0.611383 | − | 0.791335i | \(-0.709387\pi\) | ||||
−0.611383 | + | 0.791335i | \(0.709387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.21238e6 | 0.235870 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.77271e6 | −0.927728 | −0.463864 | − | 0.885906i | \(-0.653537\pi\) | ||||
−0.463864 | + | 0.885906i | \(0.653537\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44110e7 | 1.51171 | 0.755854 | − | 0.654740i | \(-0.227222\pi\) | ||||
0.755854 | + | 0.654740i | \(0.227222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.75270e6 | −0.286438 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.08494e6 | 0.318439 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 264461. | 0.0270808 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.35058e6 | −0.137199 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.20358e6 | 0.222076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.29466e7 | −1.29444 | −0.647221 | − | 0.762303i | \(-0.724069\pi\) | ||||
−0.647221 | + | 0.762303i | \(0.724069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −176940. | −0.0175516 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.35584e6 | 0.822348 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.46343e6 | −0.240542 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.30064e6 | 0.513542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.89035e6 | −0.470105 | −0.235052 | − | 0.971983i | \(-0.575526\pi\) | ||||
−0.235052 | + | 0.971983i | \(0.575526\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.22604e6 | 0.116943 | 0.0584717 | − | 0.998289i | \(-0.481377\pi\) | ||||
0.0584717 | + | 0.998289i | \(0.481377\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.42351e6 | −0.134729 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.21098e7 | 1.13731 | 0.568654 | − | 0.822577i | \(-0.307464\pi\) | ||||
0.568654 | + | 0.822577i | \(0.307464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.55681e7 | −1.45086 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.31827e6 | 0.399354 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.28697e6 | 0.852298 | 0.426149 | − | 0.904653i | \(-0.359870\pi\) | ||||
0.426149 | + | 0.904653i | \(0.359870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.10911e6 | 0.465310 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −454086. | −0.0410416 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 451612. | 0.0405090 | 0.0202545 | − | 0.999795i | \(-0.493552\pi\) | ||||
0.0202545 | + | 0.999795i | \(0.493552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.85508e6 | −0.165143 | −0.0825714 | − | 0.996585i | \(-0.526313\pi\) | ||||
−0.0825714 | + | 0.996585i | \(0.526313\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.51375e6 | −0.752206 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 753032. | 0.0660327 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.40282e6 | −0.383192 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.07163e6 | −0.697262 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.24098e6 | 0.277889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.14534e7 | 1.82582 | 0.912911 | − | 0.408158i | \(-0.133829\pi\) | ||||
0.912911 | + | 0.408158i | \(0.133829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.43540e6 | −0.121259 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.56987e7 | 1.31641 | 0.658205 | − | 0.752839i | \(-0.271316\pi\) | ||||
0.658205 | + | 0.752839i | \(0.271316\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.85406e6 | 0.154330 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.10805e6 | 0.174186 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.40250e7 | 1.15040 | 0.575201 | − | 0.818012i | \(-0.304924\pi\) | ||||
0.575201 | + | 0.818012i | \(0.304924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.36557e7 | 1.11196 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.32063e6 | −0.753449 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.13886e6 | −0.0913950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.89819e7 | −1.51232 | −0.756160 | − | 0.654387i | \(-0.772927\pi\) | ||||
−0.756160 | + | 0.654387i | \(0.772927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.31771e6 | 0.104228 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.27191e7 | −0.998839 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.66606e6 | −0.519741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.11403e6 | 0.318474 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.22806e7 | 1.71250 | 0.856251 | − | 0.516560i | \(-0.172788\pi\) | ||||
0.856251 | + | 0.516560i | \(0.172788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.08028e6 | 0.0824419 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.54963e6 | −0.572075 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.75115e6 | 0.206998 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −476266. | −0.0355823 | −0.0177911 | − | 0.999842i | \(-0.505663\pi\) | ||||
−0.0177911 | + | 0.999842i | \(0.505663\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −797040. | −0.0591298 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.69746e7 | 2.72383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.15815e7 | −0.847226 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.08710e6 | 0.442193 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −263568. | −0.0190139 | −0.00950693 | − | 0.999955i | \(-0.503026\pi\) | ||||
−0.00950693 | + | 0.999955i | \(0.503026\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.29321e6 | 0.0926468 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −870030. | −0.0618997 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.29585e6 | −0.162218 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.28319e6 | 0.651420 | 0.325710 | − | 0.945470i | \(-0.394397\pi\) | ||||
0.325710 | + | 0.945470i | \(0.394397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.28914e6 | 0.296877 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.89547e7 | −1.30304 | −0.651520 | − | 0.758631i | \(-0.725868\pi\) | ||||
−0.651520 | + | 0.758631i | \(0.725868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −734706. | −0.0501644 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.71566e6 | 0.591060 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.95454e7 | 1.31654 | 0.658269 | − | 0.752783i | \(-0.271289\pi\) | ||||
0.658269 | + | 0.752783i | \(0.271289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.17377e6 | −0.279243 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.54683e7 | 1.02795 | 0.513973 | − | 0.857806i | \(-0.328173\pi\) | ||||
0.513973 | + | 0.857806i | \(0.328173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.55054e7 | 1.02351 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.94975e6 | 0.324550 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.30908e6 | −0.150395 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.45188e7 | −0.939354 | −0.469677 | − | 0.882838i | \(-0.655630\pi\) | ||||
−0.469677 | + | 0.882838i | \(0.655630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.59988e6 | 0.167096 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 272816. | 0.0174182 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.54477e6 | 0.541952 | 0.270976 | − | 0.962586i | \(-0.412654\pi\) | ||||
0.270976 | + | 0.962586i | \(0.412654\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.12827e7 | 0.710899 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.50398e6 | −0.532305 | −0.266153 | − | 0.963931i | \(-0.585753\pi\) | ||||
−0.266153 | + | 0.963931i | \(0.585753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.08522e7 | 0.674850 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.53919e6 | −0.156870 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.81112e7 | −2.95296 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.66581e7 | −1.01580 | −0.507901 | − | 0.861415i | \(-0.669578\pi\) | ||||
−0.507901 | + | 0.861415i | \(0.669578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.40661e6 | −0.388144 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.17326e7 | 1.30817 | 0.654083 | − | 0.756423i | \(-0.273055\pi\) | ||||
0.654083 | + | 0.756423i | \(0.273055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.92804e7 | 1.15309 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.05399e6 | −0.0626302 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.26796e6 | −0.192945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.17261e7 | −1.27454 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 850014. | 0.0495475 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.74265e6 | −0.216773 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.05602e6 | 0.118329 | 0.0591644 | − | 0.998248i | \(-0.481156\pi\) | ||||
0.0591644 | + | 0.998248i | \(0.481156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.68631e7 | −0.964374 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.65551e6 | −0.150906 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00158e7 | 0.565592 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −339660. | −0.0190602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.17641e7 | 1.77129 | 0.885647 | − | 0.464359i | \(-0.153715\pi\) | ||||
0.885647 | + | 0.464359i | \(0.153715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.27476e7 | 1.26057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.09960e6 | −0.280837 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.86119e6 | 0.101860 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.29082e6 | −0.342151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.23894e7 | −0.669680 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.14050e7 | −1.14986 | −0.574930 | − | 0.818203i | \(-0.694971\pi\) | ||||
−0.574930 | + | 0.818203i | \(0.694971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.61432e6 | −0.353129 | −0.176564 | − | 0.984289i | \(-0.556498\pi\) | ||||
−0.176564 | + | 0.984289i | \(0.556498\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.03598e6 | −0.373335 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 123352. | 0.00650507 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.10270e6 | 0.110211 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.07219e6 | 0.212138 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.78006e7 | 0.921674 | 0.460837 | − | 0.887485i | \(-0.347549\pi\) | ||||
0.460837 | + | 0.887485i | \(0.347549\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.23818e7 | −0.637212 | −0.318606 | − | 0.947887i | \(-0.603215\pi\) | ||||
−0.318606 | + | 0.947887i | \(0.603215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.88337e6 | 0.300948 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.17279e7 | −1.10473 | −0.552363 | − | 0.833604i | \(-0.686274\pi\) | ||||
−0.552363 | + | 0.833604i | \(0.686274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.35893e7 | −0.686771 | −0.343385 | − | 0.939195i | \(-0.611574\pi\) | ||||
−0.343385 | + | 0.939195i | \(0.611574\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.86239e7 | 0.935550 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.21372e6 | 0.110538 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.55602e6 | −0.325405 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.13837e6 | −0.352197 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −171272. | −0.00840004 | −0.00420002 | − | 0.999991i | \(-0.501337\pi\) | ||||
−0.00420002 | + | 0.999991i | \(0.501337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.91516e7 | −0.933716 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.69120e7 | 0.819647 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.31670e7 | −1.11617 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.49052e6 | 0.119284 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.03140e6 | 0.287177 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.02464e6 | −0.427175 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.90172e7 | 1.36547 | 0.682737 | − | 0.730664i | \(-0.260789\pi\) | ||||
0.682737 | + | 0.730664i | \(0.260789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.24481e6 | −0.0582354 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.84967e7 | −1.79049 | −0.895243 | − | 0.445578i | \(-0.852998\pi\) | ||||
−0.895243 | + | 0.445578i | \(0.852998\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.98458e7 | −0.917670 | −0.458835 | − | 0.888521i | \(-0.651733\pi\) | ||||
−0.458835 | + | 0.888521i | \(0.651733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.18843e6 | 0.146578 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.70833e7 | −0.780808 | −0.390404 | − | 0.920644i | \(-0.627665\pi\) | ||||
−0.390404 | + | 0.920644i | \(0.627665\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.34283e6 | −0.242790 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.12796e6 | −0.231684 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.26688e6 | 0.146752 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.69346e7 | 1.20300 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.06488e6 | −0.136106 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.48660e6 | −0.374726 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.53810e7 | −1.11432 | −0.557159 | − | 0.830406i | \(-0.688109\pi\) | ||||
−0.557159 | + | 0.830406i | \(0.688109\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.52650e7 | 0.666384 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.59580e7 | −1.12676 | −0.563381 | − | 0.826198i | \(-0.690499\pi\) | ||||
−0.563381 | + | 0.826198i | \(0.690499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.37666e6 | 0.188904 | 0.0944520 | − | 0.995529i | \(-0.469890\pi\) | ||||
0.0944520 | + | 0.995529i | \(0.469890\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.43490e7 | −0.615832 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.23310e7 | 1.37978 | 0.689889 | − | 0.723915i | \(-0.257659\pi\) | ||||
0.689889 | + | 0.723915i | \(0.257659\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.20422e7 | 0.511038 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.17825e6 | −0.0919208 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.11517e7 | 0.467966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.51935e7 | 0.634017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.48676e7 | 1.44691 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.14175e7 | −0.471163 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.02342e6 | 0.0419993 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.05153e6 | −0.0837257 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.73917e7 | −1.11173 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.67108e7 | −1.48175 | −0.740876 | − | 0.671642i | \(-0.765589\pi\) | ||||
−0.740876 | + | 0.671642i | \(0.765589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.54783e6 | −0.182555 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.52261e7 | 1.40627 | 0.703135 | − | 0.711056i | \(-0.251783\pi\) | ||||
0.703135 | + | 0.711056i | \(0.251783\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.02879e7 | −0.805488 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.98717e6 | 0.117953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.36313e6 | 0.289161 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.16978e6 | −0.123806 | −0.0619029 | − | 0.998082i | \(-0.519717\pi\) | ||||
−0.0619029 | + | 0.998082i | \(0.519717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.85129e6 | −0.382687 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.71414e7 | −2.59410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.70591e6 | −0.180838 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.13775e6 | −0.0817068 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.98030e7 | −1.13298 | −0.566488 | − | 0.824070i | \(-0.691698\pi\) | ||||
−0.566488 | + | 0.824070i | \(0.691698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.08525e6 | 0.0410352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.09124e7 | 0.410408 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.04075e7 | 0.389331 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.62312e7 | −0.603952 | −0.301976 | − | 0.953316i | \(-0.597646\pi\) | ||||
−0.301976 | + | 0.953316i | \(0.597646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.52493e7 | 0.564397 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.09759e7 | 0.404079 | 0.202040 | − | 0.979377i | \(-0.435243\pi\) | ||||
0.202040 | + | 0.979377i | \(0.435243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.73005e7 | 0.999749 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.21451e6 | 0.0442408 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.50304e6 | 0.126932 | 0.0634658 | − | 0.997984i | \(-0.479785\pi\) | ||||
0.0634658 | + | 0.997984i | \(0.479785\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.75176e6 | 0.207317 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.00008e6 | 0.107568 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.00120e7 | −0.357098 | −0.178549 | − | 0.983931i | \(-0.557140\pi\) | ||||
−0.178549 | + | 0.983931i | \(0.557140\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.54290e7 | 0.902238 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.48401e6 | −0.122970 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.96803e7 | 0.691010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.72541e7 | 2.34915 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.81704e6 | 0.132636 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.96362e7 | 0.678794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −652984. | −0.0224562 | −0.0112281 | − | 0.999937i | \(-0.503574\pi\) | ||||
−0.0112281 | + | 0.999937i | \(0.503574\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.75070e6 | 0.128322 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.24897e7 | −0.425112 | −0.212556 | − | 0.977149i | \(-0.568179\pi\) | ||||
−0.212556 | + | 0.977149i | \(0.568179\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.83305e7 | −0.620715 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.81817e7 | 0.612525 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.43408e6 | −0.249167 | −0.124584 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124584 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.09021e7 | 0.696999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.79394e7 | −0.595162 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.44904e7 | 0.808373 | 0.404187 | − | 0.914677i | \(-0.367555\pi\) | ||||
0.404187 | + | 0.914677i | \(0.367555\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.62173e7 | 0.860990 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.08804e7 | −0.355509 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.75660e7 | −0.571059 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.87464e7 | 1.57673 | 0.788367 | − | 0.615206i | \(-0.210927\pi\) | ||||
0.788367 | + | 0.615206i | \(0.210927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.65253e7 | 0.531833 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.89462e7 | −0.606685 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.35242e6 | 0.0749510 | 0.0374755 | − | 0.999298i | \(-0.488068\pi\) | ||||
0.0374755 | + | 0.999298i | \(0.488068\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.74231e6 | 0.0552347 |
(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 | 84.6.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 252.6.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 336.6.a.e.1.1 | 1 | |||
7.2 | even | 3 | 588.6.i.c.361.1 | 2 | |||
7.3 | odd | 6 | 588.6.i.e.373.1 | 2 | |||
7.4 | even | 3 | 588.6.i.c.373.1 | 2 | |||
7.5 | odd | 6 | 588.6.i.e.361.1 | 2 | |||
7.6 | odd | 2 | 588.6.a.b.1.1 | 1 | |||
12.11 | even | 2 | 1008.6.a.u.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
252.6.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
336.6.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
588.6.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
588.6.i.c.361.1 | 2 | 7.2 | even | 3 | |||
588.6.i.c.373.1 | 2 | 7.4 | even | 3 | |||
588.6.i.e.361.1 | 2 | 7.5 | odd | 6 | |||
588.6.i.e.373.1 | 2 | 7.3 | odd | 6 | |||
1008.6.a.u.1.1 | 1 | 12.11 | even | 2 |