Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,6,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, 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("588.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.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: | \(94.3056860500\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-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 | ||||||||
\(5\) | 68.0000 | 1.21642 | 0.608210 | − | 0.793776i | \(-0.291888\pi\) | ||||
0.608210 | + | 0.793776i | \(0.291888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −388.000 | −0.966830 | −0.483415 | − | 0.875391i | \(-0.660604\pi\) | ||||
−0.483415 | + | 0.875391i | \(0.660604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −316.000 | −0.518595 | −0.259298 | − | 0.965797i | \(-0.583491\pi\) | ||||
−0.259298 | + | 0.965797i | \(0.583491\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 612.000 | 0.702301 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1056.00 | −0.886220 | −0.443110 | − | 0.896467i | \(-0.646125\pi\) | ||||
−0.443110 | + | 0.896467i | \(0.646125\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1052.00 | 0.668547 | 0.334273 | − | 0.942476i | \(-0.391509\pi\) | ||||
0.334273 | + | 0.942476i | \(0.391509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 624.000 | 0.245960 | 0.122980 | − | 0.992409i | \(-0.460755\pi\) | ||||
0.122980 | + | 0.992409i | \(0.460755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1499.00 | 0.479680 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7250.00 | 1.60082 | 0.800411 | − | 0.599452i | \(-0.204615\pi\) | ||||
0.800411 | + | 0.599452i | \(0.204615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2296.00 | 0.429109 | 0.214555 | − | 0.976712i | \(-0.431170\pi\) | ||||
0.214555 | + | 0.976712i | \(0.431170\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3492.00 | −0.558199 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12426.0 | 1.49220 | 0.746100 | − | 0.665834i | \(-0.231924\pi\) | ||||
0.746100 | + | 0.665834i | \(0.231924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2844.00 | −0.299411 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5376.00 | 0.499459 | 0.249729 | − | 0.968316i | \(-0.419658\pi\) | ||||
0.249729 | + | 0.968316i | \(0.419658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 14164.0 | 1.16819 | 0.584097 | − | 0.811684i | \(-0.301449\pi\) | ||||
0.584097 | + | 0.811684i | \(0.301449\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5508.00 | 0.405474 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4712.00 | 0.311143 | 0.155572 | − | 0.987825i | \(-0.450278\pi\) | ||||
0.155572 | + | 0.987825i | \(0.450278\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9504.00 | −0.511659 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3782.00 | 0.184940 | 0.0924702 | − | 0.995715i | \(-0.470524\pi\) | ||||
0.0924702 | + | 0.995715i | \(0.470524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −26384.0 | −1.17607 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9468.00 | 0.385986 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 25244.0 | 0.944122 | 0.472061 | − | 0.881566i | \(-0.343510\pi\) | ||||
0.472061 | + | 0.881566i | \(0.343510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 20668.0 | 0.711171 | 0.355585 | − | 0.934644i | \(-0.384282\pi\) | ||||
0.355585 | + | 0.934644i | \(0.384282\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21488.0 | −0.630830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49012.0 | 1.33388 | 0.666938 | − | 0.745113i | \(-0.267605\pi\) | ||||
0.666938 | + | 0.745113i | \(0.267605\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5616.00 | 0.142005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4760.00 | 0.112063 | 0.0560313 | − | 0.998429i | \(-0.482155\pi\) | ||||
0.0560313 | + | 0.998429i | \(0.482155\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65264.0 | −1.43340 | −0.716699 | − | 0.697383i | \(-0.754348\pi\) | ||||
−0.716699 | + | 0.697383i | \(0.754348\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13491.0 | 0.276943 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −49736.0 | −0.896609 | −0.448305 | − | 0.893881i | \(-0.647972\pi\) | ||||
−0.448305 | + | 0.893881i | \(0.647972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7788.00 | 0.124088 | 0.0620441 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620441 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −71808.0 | −1.07802 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 65250.0 | 0.924235 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 36904.0 | 0.493854 | 0.246927 | − | 0.969034i | \(-0.420579\pi\) | ||||
0.246927 | + | 0.969034i | \(0.420579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20664.0 | 0.247746 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 71536.0 | 0.813234 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −98264.0 | −1.06039 | −0.530194 | − | 0.847876i | \(-0.677881\pi\) | ||||
−0.530194 | + | 0.847876i | \(0.677881\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −31428.0 | −0.322277 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 197060. | 1.92218 | 0.961092 | − | 0.276228i | \(-0.0890844\pi\) | ||||
0.961092 | + | 0.276228i | \(0.0890844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 183464. | 1.70395 | 0.851977 | − | 0.523579i | \(-0.175404\pi\) | ||||
0.851977 | + | 0.523579i | \(0.175404\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −55004.0 | −0.464446 | −0.232223 | − | 0.972663i | \(-0.574600\pi\) | ||||
−0.232223 | + | 0.972663i | \(0.574600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −118430. | −0.954763 | −0.477381 | − | 0.878696i | \(-0.658414\pi\) | ||||
−0.477381 | + | 0.878696i | \(0.658414\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 111834. | 0.861522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −151694. | −1.11756 | −0.558782 | − | 0.829315i | \(-0.688731\pi\) | ||||
−0.558782 | + | 0.829315i | \(0.688731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42432.0 | 0.299191 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −25596.0 | −0.172865 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10507.0 | −0.0652402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 48384.0 | 0.288363 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −110568. | −0.632928 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 239216. | 1.31608 | 0.658038 | − | 0.752985i | \(-0.271387\pi\) | ||||
0.658038 | + | 0.752985i | \(0.271387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 127476. | 0.674457 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 164652. | 0.838279 | 0.419140 | − | 0.907922i | \(-0.362332\pi\) | ||||
0.419140 | + | 0.907922i | \(0.362332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 49572.0 | 0.234100 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −179050. | −0.815029 | −0.407514 | − | 0.913199i | \(-0.633604\pi\) | ||||
−0.407514 | + | 0.913199i | \(0.633604\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −392172. | −1.72163 | −0.860815 | − | 0.508919i | \(-0.830045\pi\) | ||||
−0.860815 | + | 0.508919i | \(0.830045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 42408.0 | 0.179639 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 122608. | 0.501394 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 493000. | 1.94727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 429062. | 1.58327 | 0.791634 | − | 0.610996i | \(-0.209231\pi\) | ||||
0.791634 | + | 0.610996i | \(0.209231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −263048. | −0.938842 | −0.469421 | − | 0.882974i | \(-0.655537\pi\) | ||||
−0.469421 | + | 0.882974i | \(0.655537\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −85536.0 | −0.295407 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 156128. | 0.521977 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 145796. | 0.472059 | 0.236030 | − | 0.971746i | \(-0.424154\pi\) | ||||
0.236030 | + | 0.971746i | \(0.424154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 34038.0 | 0.106775 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 248604. | 0.732891 | 0.366445 | − | 0.930440i | \(-0.380575\pi\) | ||||
0.366445 | + | 0.930440i | \(0.380575\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −237456. | −0.679005 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 75064.0 | 0.208277 | 0.104138 | − | 0.994563i | \(-0.466792\pi\) | ||||
0.104138 | + | 0.994563i | \(0.466792\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −271437. | −0.731059 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 85212.0 | 0.222849 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 608572. | 1.54595 | 0.772977 | − | 0.634434i | \(-0.218767\pi\) | ||||
0.772977 | + | 0.634434i | \(0.218767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 227196. | 0.545089 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5676.00 | 0.0132407 | 0.00662033 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00662033 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −111980. | −0.254065 | −0.127032 | − | 0.991899i | \(-0.540545\pi\) | ||||
−0.127032 | + | 0.991899i | \(0.540545\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 186012. | 0.410595 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 844968. | 1.81514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 409728. | 0.856824 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −871824. | −1.72920 | −0.864600 | − | 0.502460i | \(-0.832428\pi\) | ||||
−0.864600 | + | 0.502460i | \(0.832428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 384770. | 0.743546 | 0.371773 | − | 0.928324i | \(-0.378750\pi\) | ||||
0.371773 | + | 0.928324i | \(0.378750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −193392. | −0.364210 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −365226. | −0.670496 | −0.335248 | − | 0.942130i | \(-0.608820\pi\) | ||||
−0.335248 | + | 0.942130i | \(0.608820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 819928. | 1.46772 | 0.733860 | − | 0.679301i | \(-0.237717\pi\) | ||||
0.733860 | + | 0.679301i | \(0.237717\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 441108. | 0.770114 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 365568. | 0.607552 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 50544.0 | 0.0819868 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −408176. | −0.646371 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 348596. | 0.539034 | 0.269517 | − | 0.962996i | \(-0.413136\pi\) | ||||
0.269517 | + | 0.962996i | \(0.413136\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 42840.0 | 0.0646994 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 963152. | 1.42102 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −587376. | −0.827572 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 333696. | 0.459590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 421168. | 0.567144 | 0.283572 | − | 0.958951i | \(-0.408481\pi\) | ||||
0.283572 | + | 0.958951i | \(0.408481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 121419. | 0.159893 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −133364. | −0.171781 | −0.0858903 | − | 0.996305i | \(-0.527373\pi\) | ||||
−0.0858903 | + | 0.996305i | \(0.527373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −442300. | −0.557350 | −0.278675 | − | 0.960385i | \(-0.589895\pi\) | ||||
−0.278675 | + | 0.960385i | \(0.589895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −798826. | −0.963967 | −0.481984 | − | 0.876180i | \(-0.660084\pi\) | ||||
−0.481984 | + | 0.876180i | \(0.660084\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 320416. | 0.378481 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −447624. | −0.517657 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.22695e6 | −1.38942 | −0.694709 | − | 0.719291i | \(-0.744467\pi\) | ||||
−0.694709 | + | 0.719291i | \(0.744467\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 960232. | 1.06496 | 0.532480 | − | 0.846442i | \(-0.321260\pi\) | ||||
0.532480 | + | 0.846442i | \(0.321260\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −332432. | −0.346705 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 70092.0 | 0.0716424 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.46177e6 | −1.46452 | −0.732260 | − | 0.681025i | \(-0.761534\pi\) | ||||
−0.732260 | + | 0.681025i | \(0.761534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −242112. | −0.237802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −646272. | −0.622393 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 124360. | 0.117449 | 0.0587243 | − | 0.998274i | \(-0.481297\pi\) | ||||
0.0587243 | + | 0.998274i | \(0.481297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 587250. | 0.533607 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.19718e6 | 1.06726 | 0.533628 | − | 0.845719i | \(-0.320828\pi\) | ||||
0.533628 | + | 0.845719i | \(0.320828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 257176. | 0.224965 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 332136. | 0.285127 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −797092. | −0.671626 | −0.335813 | − | 0.941929i | \(-0.609011\pi\) | ||||
−0.335813 | + | 0.941929i | \(0.609011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.96102e6 | 1.62203 | 0.811016 | − | 0.585023i | \(-0.198915\pi\) | ||||
0.811016 | + | 0.585023i | \(0.198915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −581612. | −0.463769 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 421510. | 0.330072 | 0.165036 | − | 0.986288i | \(-0.447226\pi\) | ||||
0.165036 | + | 0.986288i | \(0.447226\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 185976. | 0.143036 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 223206. | 0.168632 | 0.0843160 | − | 0.996439i | \(-0.473129\pi\) | ||||
0.0843160 | + | 0.996439i | \(0.473129\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.13804e6 | 1.58690 | 0.793452 | − | 0.608633i | \(-0.208282\pi\) | ||||
0.793452 | + | 0.608633i | \(0.208282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 643824. | 0.469521 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −304721. | −0.214614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −884376. | −0.612216 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −418572. | −0.284840 | −0.142420 | − | 0.989806i | \(-0.545488\pi\) | ||||
−0.142420 | + | 0.989806i | \(0.545488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.71659e6 | 1.14845 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −282852. | −0.186066 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −197184. | −0.127554 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.77354e6 | 1.10977 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.40542e6 | 0.865083 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.65972e6 | 1.00506 | 0.502528 | − | 0.864561i | \(-0.332404\pi\) | ||||
0.502528 | + | 0.864561i | \(0.332404\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.65118e6 | 0.983778 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −95936.0 | −0.0562446 | −0.0281223 | − | 0.999604i | \(-0.508953\pi\) | ||||
−0.0281223 | + | 0.999604i | \(0.508953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.03434e6 | −1.75067 | −0.875334 | − | 0.483518i | \(-0.839359\pi\) | ||||
−0.875334 | + | 0.483518i | \(0.839359\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27918.0 | 0.0156040 | 0.00780200 | − | 0.999970i | \(-0.497517\pi\) | ||||
0.00780200 | + | 0.999970i | \(0.497517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81300e6 | −1.54772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −495036. | −0.268148 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.11091e6 | −0.592480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −473684. | −0.248760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.06587e6 | −0.551233 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.39236e6 | 0.698522 | 0.349261 | − | 0.937025i | \(-0.386433\pi\) | ||||
0.349261 | + | 0.937025i | \(0.386433\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.00651e6 | 0.497400 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.33282e6 | 1.62255 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.41473e6 | 1.63788 | 0.818940 | − | 0.573879i | \(-0.194562\pi\) | ||||
0.818940 | + | 0.573879i | \(0.194562\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.36525e6 | −0.645226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −890848. | −0.414875 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 381888. | 0.172738 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.43055e6 | −1.52947 | −0.764733 | − | 0.644347i | \(-0.777129\pi\) | ||||
−0.764733 | + | 0.644347i | \(0.777129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −388620. | −0.170790 | −0.0853948 | − | 0.996347i | \(-0.527215\pi\) | ||||
−0.0853948 | + | 0.996347i | \(0.527215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −230364. | −0.0998037 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −293016. | −0.125157 | −0.0625784 | − | 0.998040i | \(-0.519932\pi\) | ||||
−0.0625784 | + | 0.998040i | \(0.519932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 323680. | 0.136315 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −976928. | −0.400061 | −0.200031 | − | 0.979790i | \(-0.564104\pi\) | ||||
−0.200031 | + | 0.979790i | \(0.564104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.36940e6 | −0.553045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −94563.0 | −0.0376664 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.43795e6 | −1.74361 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.16514e6 | −1.61422 | −0.807112 | − | 0.590398i | \(-0.798971\pi\) | ||||
−0.807112 | + | 0.590398i | \(0.798971\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 435456. | 0.166486 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.10989e6 | 1.15737 | 0.578687 | − | 0.815550i | \(-0.303565\pi\) | ||||
0.578687 | + | 0.815550i | \(0.303565\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −995112. | −0.365421 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.29100e6 | −0.830179 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23592e6 | −0.441968 | −0.220984 | − | 0.975277i | \(-0.570927\pi\) | ||||
−0.220984 | + | 0.975277i | \(0.570927\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.15294e6 | 0.759837 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.71116e6 | −0.944405 | −0.472202 | − | 0.881490i | \(-0.656541\pi\) | ||||
−0.472202 | + | 0.881490i | \(0.656541\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.14728e6 | 0.389398 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.14276e6 | 1.72315 | 0.861574 | − | 0.507633i | \(-0.169479\pi\) | ||||
0.861574 | + | 0.507633i | \(0.169479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −658944. | −0.217975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.48187e6 | 0.483981 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.38205e6 | −1.09065 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.72825e6 | −1.82409 | −0.912044 | − | 0.410092i | \(-0.865497\pi\) | ||||
−0.912044 | + | 0.410092i | \(0.865497\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.06229e6 | −1.57212 | −0.786061 | − | 0.618149i | \(-0.787883\pi\) | ||||
−0.786061 | + | 0.618149i | \(0.787883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −725536. | −0.222534 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 446148. | 0.135158 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.82129e6 | −1.44270 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.60335e6 | −1.65630 | −0.828151 | − | 0.560505i | \(-0.810607\pi\) | ||||
−0.828151 | + | 0.560505i | \(0.810607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.61145e6 | −0.470557 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 529584. | 0.150944 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.52955e6 | −0.993983 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.55808e6 | 1.54664 | 0.773321 | − | 0.634014i | \(-0.218594\pi\) | ||||
0.773321 | + | 0.634014i | \(0.218594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −689226. | −0.189521 | −0.0947603 | − | 0.995500i | \(-0.530208\pi\) | ||||
−0.0947603 | + | 0.995500i | \(0.530208\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 381672. | 0.103714 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.58294e6 | −0.425102 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.10347e6 | 0.289480 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.37897e6 | 0.616873 | 0.308436 | − | 0.951245i | \(-0.400194\pi\) | ||||
0.308436 | + | 0.951245i | \(0.400194\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −790312. | −0.202572 | −0.101286 | − | 0.994857i | \(-0.532296\pi\) | ||||
−0.101286 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.43700e6 | 1.12426 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 656448. | 0.164436 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 899904. | 0.222861 | 0.111431 | − | 0.993772i | \(-0.464457\pi\) | ||||
0.111431 | + | 0.993772i | \(0.464457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.17691e6 | −1.25332 | −0.626659 | − | 0.779294i | \(-0.715578\pi\) | ||||
−0.626659 | + | 0.779294i | \(0.715578\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.50947e6 | 0.600734 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.86156e6 | 0.914100 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.34717e6 | −1.48581 | −0.742906 | − | 0.669395i | \(-0.766553\pi\) | ||||
−0.742906 | + | 0.669395i | \(0.766553\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.08589e6 | −0.482892 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.36743e6 | −0.542041 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −219382. | −0.0491372 | −0.0245686 | − | 0.999698i | \(-0.507821\pi\) | ||||
−0.0245686 | + | 0.999698i | \(0.507821\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −769824. | −0.170553 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.60859e6 | 0.352527 | 0.176264 | − | 0.984343i | \(-0.443599\pi\) | ||||
0.176264 | + | 0.984343i | \(0.443599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.95250e6 | −0.856880 | −0.428440 | − | 0.903570i | \(-0.640937\pi\) | ||||
−0.428440 | + | 0.903570i | \(0.640937\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.40515e6 | 0.301364 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.13170e6 | −1.72540 | −0.862699 | − | 0.505718i | \(-0.831228\pi\) | ||||
−0.862699 | + | 0.505718i | \(0.831228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.31216e6 | 0.272544 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.49563e6 | −1.12944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.57695e6 | 0.320688 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 306342. | 0.0616468 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.43060e6 | −1.08146 | −0.540728 | − | 0.841197i | \(-0.681851\pi\) | ||||
−0.540728 | + | 0.841197i | \(0.681851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.92662e6 | −0.773848 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.68195e6 | −1.28988 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.26982e6 | 0.433679 | 0.216839 | − | 0.976207i | \(-0.430425\pi\) | ||||
0.216839 | + | 0.976207i | \(0.430425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.23744e6 | 0.423135 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.00020e6 | −1.12321 | −0.561607 | − | 0.827404i | \(-0.689817\pi\) | ||||
−0.561607 | + | 0.827404i | \(0.689817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.65600e6 | −1.41868 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.13710e6 | −0.392024 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.90784e6 | 0.882347 | 0.441173 | − | 0.897422i | \(-0.354562\pi\) | ||||
0.441173 | + | 0.897422i | \(0.354562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 675576. | 0.120249 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.70974e6 | 0.653768 | 0.326884 | − | 0.945064i | \(-0.394001\pi\) | ||||
0.326884 | + | 0.945064i | \(0.394001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.34001e7 | 2.33819 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.44293e6 | −0.422077 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.77594e6 | −1.15924 | −0.579622 | − | 0.814885i | \(-0.696800\pi\) | ||||
−0.579622 | + | 0.814885i | \(0.696800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 766908. | 0.128662 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.24756e7 | 2.07273 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.82826e6 | −0.300823 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.47715e6 | 0.892557 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.92925e6 | 1.11839 | 0.559193 | − | 0.829037i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829037i | \(0.311111\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.08732e6 | 1.29286 | 0.646429 | − | 0.762974i | \(-0.276262\pi\) | ||||
0.646429 | + | 0.762974i | \(0.276262\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.42458e6 | −0.380285 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.04697e6 | −0.939504 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.04476e6 | 0.314707 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.69882e6 | −0.259017 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.74027e6 | −0.564961 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 51084.0 | 0.00764450 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.11361e6 | 1.33874 | 0.669372 | − | 0.742927i | \(-0.266563\pi\) | ||||
0.669372 | + | 0.742927i | \(0.266563\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.00782e6 | −0.146684 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.05324e6 | −1.16139 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.27702e7 | 1.82486 | 0.912432 | − | 0.409228i | \(-0.134202\pi\) | ||||
0.912432 | + | 0.409228i | \(0.134202\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.67411e6 | 0.237057 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.62700e6 | 1.07022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.60471e6 | 1.04797 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.10633e6 | 0.560811 | 0.280405 | − | 0.959882i | \(-0.409531\pi\) | ||||
0.280405 | + | 0.959882i | \(0.409531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.47582e6 | −0.605820 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.68755e6 | 0.494688 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.71036e6 | −0.759264 | −0.379632 | − | 0.925138i | \(-0.623949\pi\) | ||||
−0.379632 | + | 0.925138i | \(0.623949\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.03152e7 | −1.35943 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.47279e6 | −0.838129 | −0.419065 | − | 0.907956i | \(-0.637642\pi\) | ||||
−0.419065 | + | 0.907956i | \(0.637642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.82942e6 | −0.363168 | −0.181584 | − | 0.983375i | \(-0.558122\pi\) | ||||
−0.181584 | + | 0.983375i | \(0.558122\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.84642e6 | −0.998354 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 935376. | 0.117982 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.01253e6 | 0.126610 | 0.0633049 | − | 0.997994i | \(-0.479836\pi\) | ||||
0.0633049 | + | 0.997994i | \(0.479836\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.46293e6 | 0.429287 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.46742e6 | −0.178806 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.74053e6 | −0.210277 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.36384e7 | 1.63368 | 0.816842 | − | 0.576861i | \(-0.195723\pi\) | ||||
0.816842 | + | 0.576861i | \(0.195723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.41539e6 | 0.286879 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.28703e6 | −0.387111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.26710e6 | −1.08220 | −0.541099 | − | 0.840959i | \(-0.681992\pi\) | ||||
−0.541099 | + | 0.840959i | \(0.681992\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.37935e6 | 0.847388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.55012e6 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.10675e6 | 0.237918 | 0.118959 | − | 0.992899i | \(-0.462044\pi\) | ||||
0.118959 | + | 0.992899i | \(0.462044\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.96997e6 | 0.444625 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −714476. | −0.0793596 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.71018e6 | 0.298556 | 0.149278 | − | 0.988795i | \(-0.452305\pi\) | ||||
0.149278 | + | 0.988795i | \(0.452305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.48899e6 | −0.161358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00044e7 | −1.07532 | −0.537661 | − | 0.843161i | \(-0.680692\pi\) | ||||
−0.537661 | + | 0.843161i | \(0.680692\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.29011e6 | 0.350770 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.67826e7 | −1.77479 | −0.887394 | − | 0.461012i | \(-0.847486\pi\) | ||||
−0.887394 | + | 0.461012i | \(0.847486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.93800e6 | 1.04249 | 0.521245 | − | 0.853407i | \(-0.325468\pi\) | ||||
0.521245 | + | 0.853407i | \(0.325468\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 454896. | 0.0473351 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.22030e7 | −1.24959 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.67358e6 | −0.373182 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.31219e7 | −1.32242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.58563e6 | 0.158536 | 0.0792682 | − | 0.996853i | \(-0.474742\pi\) | ||||
0.0792682 | + | 0.996853i | \(0.474742\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.13736e6 | 0.311211 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.62667e7 | 1.60090 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 385560. | 0.0373542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.27623e6 | −0.699457 | −0.349729 | − | 0.936851i | \(-0.613726\pi\) | ||||
−0.349729 | + | 0.936851i | \(0.613726\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.98124e7 | 1.88977 | 0.944887 | − | 0.327395i | \(-0.106171\pi\) | ||||
0.944887 | + | 0.327395i | \(0.106171\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.66837e6 | 0.820423 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.96553e6 | 0.748090 | 0.374045 | − | 0.927411i | \(-0.377971\pi\) | ||||
0.374045 | + | 0.927411i | \(0.377971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.79467e6 | −0.912805 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.51767e6 | 0.139281 | 0.0696407 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696407 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11963e7 | 1.01970 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.28638e6 | −0.477799 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.00208e7 | −0.898850 | −0.449425 | − | 0.893318i | \(-0.648371\pi\) | ||||
−0.449425 | + | 0.893318i | \(0.648371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.52180e7 | 1.35473 | 0.677367 | − | 0.735645i | \(-0.263121\pi\) | ||||
0.677367 | + | 0.735645i | \(0.263121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00326e6 | 0.265344 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.52400e6 | 0.393739 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.79051e6 | 0.327441 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.01918e6 | −0.687581 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.83024e6 | −0.581297 | −0.290649 | − | 0.956830i | \(-0.593871\pi\) | ||||
−0.290649 | + | 0.956830i | \(0.593871\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.09277e6 | 0.0923145 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.03576e7 | 1.70708 | 0.853541 | − | 0.521025i | \(-0.174450\pi\) | ||||
0.853541 | + | 0.521025i | \(0.174450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.20028e6 | −0.0991775 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.71637e6 | 0.468888 | 0.234444 | − | 0.972130i | \(-0.424673\pi\) | ||||
0.234444 | + | 0.972130i | \(0.424673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21754e7 | −0.991418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.98070e6 | −0.321786 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.19511e6 | −0.0959093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.83950e7 | 1.46557 | 0.732783 | − | 0.680463i | \(-0.238221\pi\) | ||||
0.732783 | + | 0.680463i | \(0.238221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.66677e7 | −2.09423 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.67706e6 | −0.442630 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.18943e6 | −0.556547 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.34726e7 | −1.80412 | −0.902061 | − | 0.431608i | \(-0.857946\pi\) | ||||
−0.902061 | + | 0.431608i | \(0.857946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.30722e7 | 0.997605 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.88374e6 | 0.218516 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.69921e7 | 1.26950 | 0.634748 | − | 0.772719i | \(-0.281104\pi\) | ||||
0.634748 | + | 0.772719i | \(0.281104\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.02862e6 | −0.298870 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.43270e6 | 0.105544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.33734e6 | 0.609906 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.10426e7 | −0.802181 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.41663e6 | 0.607178 | 0.303589 | − | 0.952803i | \(-0.401815\pi\) | ||||
0.303589 | + | 0.952803i | \(0.401815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.64209e6 | 0.614855 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.08677e7 | 0.767882 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.81598e6 | 0.408119 | 0.204059 | − | 0.978959i | \(-0.434586\pi\) | ||||
0.204059 | + | 0.978959i | \(0.434586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.49572e7 | −1.03528 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.56330e7 | 1.07468 | 0.537342 | − | 0.843364i | \(-0.319428\pi\) | ||||
0.537342 | + | 0.843364i | \(0.319428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.90167e7 | −1.28963 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.66970e6 | −0.314541 | −0.157271 | − | 0.987556i | \(-0.550270\pi\) | ||||
−0.157271 | + | 0.987556i | \(0.550270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.99189e6 | −0.200170 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.57172e7 | −1.04449 | −0.522243 | − | 0.852797i | \(-0.674904\pi\) | ||||
−0.522243 | + | 0.852797i | \(0.674904\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.91762e7 | 1.92592 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 630828. | 0.0413628 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.70359e7 | 1.10221 | 0.551105 | − | 0.834436i | \(-0.314206\pi\) | ||||
0.551105 | + | 0.834436i | \(0.314206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.31559e7 | −0.845541 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.78873e7 | −1.14203 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.41750e7 | −0.899050 | −0.449525 | − | 0.893268i | \(-0.648407\pi\) | ||||
−0.449525 | + | 0.893268i | \(0.648407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.17901e6 | −0.137295 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.51493e6 | −0.532990 | −0.266495 | − | 0.963836i | \(-0.585866\pi\) | ||||
−0.266495 | + | 0.963836i | \(0.585866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.81645e6 | −0.359339 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.97710e6 | −0.489617 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.11392e7 | −1.28906 | −0.644529 | − | 0.764580i | \(-0.722947\pi\) | ||||
−0.644529 | + | 0.764580i | \(0.722947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.11924e6 | 0.0678090 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.75355e7 | 1.65747 | 0.828733 | − | 0.559644i | \(-0.189062\pi\) | ||||
0.828733 | + | 0.559644i | \(0.189062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.44170e6 | 0.205835 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.65555e6 | 0.333911 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.84688e6 | −0.108346 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.28525e6 | 0.308078 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.91413e6 | 0.574223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 165196. | 0.00950742 | 0.00475371 | − | 0.999989i | \(-0.498487\pi\) | ||||
0.00475371 | + | 0.999989i | \(0.498487\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.07746e7 | 0.616181 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.53109e6 | −0.368810 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.31458e6 | 0.129884 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.05169e7 | −1.14411 | −0.572053 | − | 0.820217i | \(-0.693853\pi\) | ||||
−0.572053 | + | 0.820217i | \(0.693853\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.97587e6 | −0.275742 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.98922e6 | 0.164618 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.53224e7 | 1.38585 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.17383e6 | −0.387764 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.67666e7 | −0.900689 | −0.450345 | − | 0.892855i | \(-0.648699\pi\) | ||||
−0.450345 | + | 0.892855i | \(0.648699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.49085e7 | 1.32983 | 0.664914 | − | 0.746920i | \(-0.268468\pi\) | ||||
0.664914 | + | 0.746920i | \(0.268468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.76492e7 | 0.936481 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.69051e7 | 0.891503 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.49005e7 | 0.780992 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.90271e7 | 0.985180 | 0.492590 | − | 0.870261i | \(-0.336050\pi\) | ||||
0.492590 | + | 0.870261i | \(0.336050\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.67886e6 | −0.446646 | −0.223323 | − | 0.974745i | \(-0.571690\pi\) | ||||
−0.223323 | + | 0.974745i | \(0.571690\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.23451e6 | −0.267757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.49462e7 | 0.759917 | 0.379959 | − | 0.925003i | \(-0.375938\pi\) | ||||
0.379959 | + | 0.925003i | \(0.375938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.09614e7 | 0.553959 | 0.276980 | − | 0.960876i | \(-0.410667\pi\) | ||||
0.276980 | + | 0.960876i | \(0.410667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.79359e6 | 0.190567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.10435e6 | 0.253352 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.67378e6 | 0.0825821 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.94433e7 | 1.93450 | 0.967249 | − | 0.253829i | \(-0.0816899\pi\) | ||||
0.967249 | + | 0.253829i | \(0.0816899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.20514e7 | 1.56263 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.00885e6 | 0.0973597 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.84577e7 | −0.889275 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.92424e7 | 0.916199 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.75382e6 | 0.367022 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.50962e7 | −1.18096 | −0.590480 | − | 0.807052i | \(-0.701062\pi\) | ||||
−0.590480 | + | 0.807052i | \(0.701062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.79442e6 | 0.271078 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.18078e7 | 0.549183 | 0.274592 | − | 0.961561i | \(-0.411457\pi\) | ||||
0.274592 | + | 0.961561i | \(0.411457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.36552e7 | 0.631414 | 0.315707 | − | 0.948857i | \(-0.397758\pi\) | ||||
0.315707 | + | 0.948857i | \(0.397758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.55181e6 | 0.436575 | 0.218287 | − | 0.975885i | \(-0.429953\pi\) | ||||
0.218287 | + | 0.975885i | \(0.429953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.13829e7 | 1.88053 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.74249e6 | −0.123907 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.92976e7 | 0.866868 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.54878e7 | −0.691742 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.95938e6 | −0.353463 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.04774e6 | −0.133807 | −0.0669036 | − | 0.997759i | \(-0.521312\pi\) | ||||
−0.0669036 | + | 0.997759i | \(0.521312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.76715e6 | −0.164453 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.83230e7 | −1.22942 | −0.614709 | − | 0.788754i | \(-0.710727\pi\) | ||||
−0.614709 | + | 0.788754i | \(0.710727\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.31394e6 | 0.229359 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.54493e7 | 0.663058 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.17727e7 | 1.35595 | 0.677977 | − | 0.735083i | \(-0.262857\pi\) | ||||
0.677977 | + | 0.735083i | \(0.262857\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.54567e6 | −0.107426 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.95702e6 | 0.208014 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 385968. | 0.0161062 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.77466e6 | −0.0736433 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.66460e7 | 0.686927 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.99379e6 | −0.163898 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.61464e6 | −0.309049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.84483e7 | −1.95551 | −0.977755 | − | 0.209748i | \(-0.932736\pi\) | ||||
−0.977755 | + | 0.209748i | \(0.932736\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.59619e7 | 0.640728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.96512e7 | −0.784499 | −0.392249 | − | 0.919859i | \(-0.628303\pi\) | ||||
−0.392249 | + | 0.919859i | \(0.628303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.02174e6 | −0.119972 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.26488e7 | 0.499456 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.08466e6 | −0.0423646 | −0.0211823 | − | 0.999776i | \(-0.506743\pi\) | ||||
−0.0211823 | + | 0.999776i | \(0.506743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.49375e7 | 0.580269 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.50416e6 | −0.0581152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.86266e7 | 0.715779 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.48606e7 | 0.567985 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.21130e7 | 0.840636 | 0.420318 | − | 0.907377i | \(-0.361919\pi\) | ||||
0.420318 | + | 0.907377i | \(0.361919\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −863424. | −0.0324728 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.78615e7 | 1.04226 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.55016e7 | −0.576803 | −0.288402 | − | 0.957510i | \(-0.593124\pi\) | ||||
−0.288402 | + | 0.957510i | \(0.593124\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.73091e7 | −1.01075 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.85343e7 | −0.682344 | −0.341172 | − | 0.940001i | \(-0.610824\pi\) | ||||
−0.341172 | + | 0.940001i | \(0.610824\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.35462e6 | 0.122847 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.06016e6 | −0.147119 | −0.0735593 | − | 0.997291i | \(-0.523436\pi\) | ||||
−0.0735593 | + | 0.997291i | \(0.523436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.06234e7 | 0.743353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 251262. | 0.00900898 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.72676e6 | −0.168590 | −0.0842949 | − | 0.996441i | \(-0.526864\pi\) | ||||
−0.0842949 | + | 0.996441i | \(0.526864\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.92840e7 | −2.10344 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.53170e7 | −0.893578 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.33575e7 | −0.815865 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.45532e6 | −0.154815 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.61644e7 | 0.904465 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.50253e7 | −0.516721 | −0.258360 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258360 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.99821e6 | −0.342068 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.47511e7 | −1.18283 | −0.591413 | − | 0.806369i | \(-0.701430\pi\) | ||||
−0.591413 | + | 0.806369i | \(0.701430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.26316e6 | −0.143622 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.15367e7 | 0.386675 | 0.193337 | − | 0.981132i | \(-0.438069\pi\) | ||||
0.193337 | + | 0.981132i | \(0.438069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.43188e7 | −0.477473 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.59283e6 | −0.318254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.66786e7 | −0.880601 | −0.440300 | − | 0.897851i | \(-0.645128\pi\) | ||||
−0.440300 | + | 0.897851i | \(0.645128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.48354e7 | −0.815605 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.83834e6 | 0.287329 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.59159e7 | −0.514811 | −0.257406 | − | 0.966303i | \(-0.582868\pi\) | ||||
−0.257406 | + | 0.966303i | \(0.582868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.25312e7 | 0.403292 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.57551e7 | 1.78536 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.18775e6 | −0.165288 | −0.0826439 | − | 0.996579i | \(-0.526336\pi\) | ||||
−0.0826439 | + | 0.996579i | \(0.526336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.05855e6 | 0.287174 |
(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 | 588.6.a.f.1.1 | yes | 1 | |
7.2 | even | 3 | 588.6.i.a.361.1 | 2 | |||
7.3 | odd | 6 | 588.6.i.g.373.1 | 2 | |||
7.4 | even | 3 | 588.6.i.a.373.1 | 2 | |||
7.5 | odd | 6 | 588.6.i.g.361.1 | 2 | |||
7.6 | odd | 2 | 588.6.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.6.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
588.6.a.f.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
588.6.i.a.361.1 | 2 | 7.2 | even | 3 | |||
588.6.i.a.373.1 | 2 | 7.4 | even | 3 | |||
588.6.i.g.361.1 | 2 | 7.5 | odd | 6 | |||
588.6.i.g.373.1 | 2 | 7.3 | odd | 6 |