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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7081}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1770 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-41.5743\) of defining polynomial | ||
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 | ||||||||
\(5\) | 65.5743 | 1.17303 | 0.586515 | − | 0.809939i | \(-0.300500\pi\) | ||||
0.586515 | + | 0.809939i | \(0.300500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −245.574 | −0.611929 | −0.305965 | − | 0.952043i | \(-0.598979\pi\) | ||||
−0.305965 | + | 0.952043i | \(0.598979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 434.872 | 0.713679 | 0.356839 | − | 0.934166i | \(-0.383854\pi\) | ||||
0.356839 | + | 0.934166i | \(0.383854\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 590.169 | 0.677249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1102.30 | −0.925074 | −0.462537 | − | 0.886600i | \(-0.653061\pi\) | ||||
−0.462537 | + | 0.886600i | \(0.653061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2877.29 | −1.82852 | −0.914260 | − | 0.405127i | \(-0.867227\pi\) | ||||
−0.914260 | + | 0.405127i | \(0.867227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4229.43 | −1.66710 | −0.833552 | − | 0.552441i | \(-0.813696\pi\) | ||||
−0.833552 | + | 0.552441i | \(0.813696\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1174.99 | 0.375998 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4969.60 | 1.09730 | 0.548652 | − | 0.836051i | \(-0.315141\pi\) | ||||
0.548652 | + | 0.836051i | \(0.315141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8782.65 | −1.64143 | −0.820713 | − | 0.571341i | \(-0.806424\pi\) | ||||
−0.820713 | + | 0.571341i | \(0.806424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2210.17 | −0.353298 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2440.06 | −0.293019 | −0.146510 | − | 0.989209i | \(-0.546804\pi\) | ||||
−0.146510 | + | 0.989209i | \(0.546804\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3913.85 | 0.412043 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3668.55 | −0.340828 | −0.170414 | − | 0.985373i | \(-0.554511\pi\) | ||||
−0.170414 | + | 0.985373i | \(0.554511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7198.06 | −0.593669 | −0.296835 | − | 0.954929i | \(-0.595931\pi\) | ||||
−0.296835 | + | 0.954929i | \(0.595931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5311.52 | 0.391010 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3273.32 | 0.216145 | 0.108072 | − | 0.994143i | \(-0.465532\pi\) | ||||
0.108072 | + | 0.994143i | \(0.465532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9920.68 | −0.534092 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3021.67 | −0.147760 | −0.0738801 | − | 0.997267i | \(-0.523538\pi\) | ||||
−0.0738801 | + | 0.997267i | \(0.523538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16103.4 | −0.717811 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −25895.6 | −1.05570 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −51487.5 | −1.92562 | −0.962812 | − | 0.270171i | \(-0.912920\pi\) | ||||
−0.962812 | + | 0.270171i | \(0.912920\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13313.3 | −0.458101 | −0.229050 | − | 0.973415i | \(-0.573562\pi\) | ||||
−0.229050 | + | 0.973415i | \(0.573562\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28516.4 | 0.837166 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30895.7 | 0.840837 | 0.420418 | − | 0.907330i | \(-0.361883\pi\) | ||||
0.420418 | + | 0.907330i | \(0.361883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −38064.9 | −0.962503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −41882.8 | −0.986030 | −0.493015 | − | 0.870021i | \(-0.664105\pi\) | ||||
−0.493015 | + | 0.870021i | \(0.664105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34617.3 | 0.760302 | 0.380151 | − | 0.924924i | \(-0.375872\pi\) | ||||
0.380151 | + | 0.924924i | \(0.375872\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10574.9 | 0.217083 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 77543.5 | 1.39790 | 0.698952 | − | 0.715168i | \(-0.253650\pi\) | ||||
0.698952 | + | 0.715168i | \(0.253650\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 100908. | 1.60779 | 0.803897 | − | 0.594768i | \(-0.202756\pi\) | ||||
0.803897 | + | 0.594768i | \(0.202756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72282.4 | −1.08514 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 44726.4 | 0.633528 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 40783.7 | 0.545772 | 0.272886 | − | 0.962046i | \(-0.412022\pi\) | ||||
0.272886 | + | 0.962046i | \(0.412022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −79043.8 | −0.947678 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −188676. | −2.14491 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140147. | 1.51236 | 0.756178 | − | 0.654366i | \(-0.227064\pi\) | ||||
0.756178 | + | 0.654366i | \(0.227064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19891.5 | −0.203976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8576.45 | 0.0836574 | 0.0418287 | − | 0.999125i | \(-0.486682\pi\) | ||||
0.0418287 | + | 0.999125i | \(0.486682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35260.1 | −0.327485 | −0.163742 | − | 0.986503i | \(-0.552357\pi\) | ||||
−0.163742 | + | 0.986503i | \(0.552357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −192629. | −1.62653 | −0.813264 | − | 0.581895i | \(-0.802311\pi\) | ||||
−0.813264 | + | 0.581895i | \(0.802311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 123292. | 0.993961 | 0.496980 | − | 0.867762i | \(-0.334442\pi\) | ||||
0.496980 | + | 0.867762i | \(0.334442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21960.6 | −0.169175 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28400.9 | 0.209236 | 0.104618 | − | 0.994512i | \(-0.466638\pi\) | ||||
0.104618 | + | 0.994512i | \(0.466638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −277342. | −1.95556 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 35224.6 | 0.237893 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −100744. | −0.625542 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −33017.0 | −0.196777 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −127870. | −0.731973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −47198.8 | −0.259670 | −0.129835 | − | 0.991536i | \(-0.541445\pi\) | ||||
−0.129835 | + | 0.991536i | \(0.541445\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −64782.6 | −0.342755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 79809.3 | 0.406327 | 0.203163 | − | 0.979145i | \(-0.434878\pi\) | ||||
0.203163 | + | 0.979145i | \(0.434878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 47803.7 | 0.225750 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −86064.3 | −0.391761 | −0.195881 | − | 0.980628i | \(-0.562757\pi\) | ||||
−0.195881 | + | 0.980628i | \(0.562757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 270587. | 1.18787 | 0.593935 | − | 0.804513i | \(-0.297573\pi\) | ||||
0.593935 | + | 0.804513i | \(0.297573\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29459.9 | 0.124791 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −106793. | −0.436721 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 325878. | 1.28717 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −172548. | −0.636713 | −0.318356 | − | 0.947971i | \(-0.603131\pi\) | ||||
−0.318356 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17899.5 | −0.0638849 | −0.0319425 | − | 0.999490i | \(-0.510169\pi\) | ||||
−0.0319425 | + | 0.999490i | \(0.510169\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −89286.1 | −0.308358 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −575916. | −1.92544 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −179019. | −0.579628 | −0.289814 | − | 0.957083i | \(-0.593593\pi\) | ||||
−0.289814 | + | 0.957083i | \(0.593593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27195.1 | −0.0853094 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −237289. | −0.699534 | −0.349767 | − | 0.936837i | \(-0.613739\pi\) | ||||
−0.349767 | + | 0.936837i | \(0.613739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −144930. | −0.414428 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −94040.0 | −0.260928 | −0.130464 | − | 0.991453i | \(-0.541647\pi\) | ||||
−0.130464 | + | 0.991453i | \(0.541647\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −182180. | −0.490663 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −233061. | −0.609507 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 488713. | 1.24148 | 0.620739 | − | 0.784017i | \(-0.286833\pi\) | ||||
0.620739 | + | 0.784017i | \(0.286833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −463387. | −1.11176 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 812996. | 1.89651 | 0.948257 | − | 0.317505i | \(-0.102845\pi\) | ||||
0.948257 | + | 0.317505i | \(0.102845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −332961. | −0.755434 | −0.377717 | − | 0.925921i | \(-0.623291\pi\) | ||||
−0.377717 | + | 0.925921i | \(0.623291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −119820. | −0.264484 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −160005. | −0.343720 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 270696. | 0.566080 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −144288. | −0.286185 | −0.143092 | − | 0.989709i | \(-0.545705\pi\) | ||||
−0.143092 | + | 0.989709i | \(0.545705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −894619. | −1.72880 | −0.864400 | − | 0.502804i | \(-0.832302\pi\) | ||||
−0.864400 | + | 0.502804i | \(0.832302\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 256648. | 0.483338 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −599462. | −1.10052 | −0.550258 | − | 0.834995i | \(-0.685470\pi\) | ||||
−0.550258 | + | 0.834995i | \(0.685470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −778259. | −1.39313 | −0.696564 | − | 0.717494i | \(-0.745289\pi\) | ||||
−0.696564 | + | 0.717494i | \(0.745289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 278062. | 0.485457 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −240563. | −0.399801 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −342584. | −0.555701 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 706589. | 1.11893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −810532. | −1.25333 | −0.626663 | − | 0.779291i | \(-0.715580\pi\) | ||||
−0.626663 | + | 0.779291i | \(0.715580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −376945. | −0.569285 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −472008. | −0.696391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 311556. | 0.438961 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −479358. | −0.660206 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 220486. | 0.296905 | 0.148453 | − | 0.988920i | \(-0.452571\pi\) | ||||
0.148453 | + | 0.988920i | \(0.452571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 95174.5 | 0.125333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.34378e6 | 1.73087 | 0.865433 | − | 0.501025i | \(-0.167044\pi\) | ||||
0.865433 | + | 0.501025i | \(0.167044\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.04258e6 | −1.31378 | −0.656889 | − | 0.753987i | \(-0.728128\pi\) | ||||
−0.656889 | + | 0.753987i | \(0.728128\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 632511. | 0.763270 | 0.381635 | − | 0.924313i | \(-0.375361\pi\) | ||||
0.381635 | + | 0.924313i | \(0.375361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 214646. | 0.253544 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 697891. | 0.807081 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −684919. | −0.775612 | −0.387806 | − | 0.921741i | \(-0.626767\pi\) | ||||
−0.387806 | + | 0.921741i | \(0.626767\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7732.88 | −0.00857628 | −0.00428814 | − | 0.999991i | \(-0.501365\pi\) | ||||
−0.00428814 | + | 0.999991i | \(0.501365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.25125e6 | −1.30498 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 908172. | 0.928261 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.09614e6 | 1.09820 | 0.549098 | − | 0.835758i | \(-0.314971\pi\) | ||||
0.549098 | + | 0.835758i | \(0.314971\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03864e6 | 1.02015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −650542. | −0.626505 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 714920. | 0.675188 | 0.337594 | − | 0.941292i | \(-0.390387\pi\) | ||||
0.337594 | + | 0.941292i | \(0.390387\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 402538. | 0.365768 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −596513. | −0.531778 | −0.265889 | − | 0.964004i | \(-0.585665\pi\) | ||||
−0.265889 | + | 0.964004i | \(0.585665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −198144. | −0.173327 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 367053. | 0.315102 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.03308e6 | −1.71306 | −0.856531 | − | 0.516096i | \(-0.827385\pi\) | ||||
−0.856531 | + | 0.516096i | \(0.827385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79455e6 | 1.48434 | 0.742170 | − | 0.670212i | \(-0.233797\pi\) | ||||
0.742170 | + | 0.670212i | \(0.233797\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −288548. | −0.230084 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 423580. | 0.331693 | 0.165846 | − | 0.986152i | \(-0.446964\pi\) | ||||
0.165846 | + | 0.986152i | \(0.446964\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −711395. | −0.547142 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.63799e6 | −1.23750 | −0.618749 | − | 0.785589i | \(-0.712360\pi\) | ||||
−0.618749 | + | 0.785589i | \(0.712360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −294035. | −0.218240 | −0.109120 | − | 0.994029i | \(-0.534803\pi\) | ||||
−0.109120 | + | 0.994029i | \(0.534803\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.69809e6 | −1.23836 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −204798. | −0.144238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.26132e6 | 0.873159 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −356961. | −0.242913 | −0.121457 | − | 0.992597i | \(-0.538757\pi\) | ||||
−0.121457 | + | 0.992597i | \(0.538757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.37626e6 | −2.25881 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −179024. | −0.117766 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.83926e6 | −1.18978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 77188.1 | 0.0482996 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −873010. | −0.537365 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.04097e6 | −1.23592 | −0.617960 | − | 0.786210i | \(-0.712041\pi\) | ||||
−0.617960 | + | 0.786210i | \(0.712041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −317341. | −0.189073 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.04674e6 | 1.19994 | 0.599972 | − | 0.800021i | \(-0.295178\pi\) | ||||
0.599972 | + | 0.800021i | \(0.295178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 638545. | 0.368409 | 0.184205 | − | 0.982888i | \(-0.441029\pi\) | ||||
0.184205 | + | 0.982888i | \(0.441029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.49909e6 | 1.95572 | 0.977860 | − | 0.209260i | \(-0.0671056\pi\) | ||||
0.977860 | + | 0.209260i | \(0.0671056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.22041e6 | −0.671472 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.73366e6 | −0.939076 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.17163e6 | 1.69152 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 510972. | 0.268342 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.10963e6 | 0.573864 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.94179e6 | −1.47585 | −0.737923 | − | 0.674885i | \(-0.764193\pi\) | ||||
−0.737923 | + | 0.674885i | \(0.764193\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −197645. | −0.0976731 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.02597e6 | 0.986326 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.77854e6 | 1.33273 | 0.666364 | − | 0.745627i | \(-0.267850\pi\) | ||||
0.666364 | + | 0.745627i | \(0.267850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 255608. | 0.120802 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.15679e6 | 1.00444 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.49608e6 | −1.12904 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −172004. | −0.0766857 | −0.0383429 | − | 0.999265i | \(-0.512208\pi\) | ||||
−0.0383429 | + | 0.999265i | \(0.512208\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.88321e6 | −1.70658 | −0.853290 | − | 0.521436i | \(-0.825397\pi\) | ||||
−0.853290 | + | 0.521436i | \(0.825397\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 317021. | 0.137348 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −770935. | −0.329292 | −0.164646 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164646 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.74644e6 | −1.15664 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.14033e6 | 1.28600 | 0.642998 | − | 0.765868i | \(-0.277691\pi\) | ||||
0.642998 | + | 0.765868i | \(0.277691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.80271e6 | 2.34349 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −906698. | −0.361157 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.27001e6 | 0.891857 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −365684. | −0.141723 | −0.0708615 | − | 0.997486i | \(-0.522575\pi\) | ||||
−0.0708615 | + | 0.997486i | \(0.522575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −297153. | −0.113609 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −154260. | −0.0574091 | −0.0287045 | − | 0.999588i | \(-0.509138\pi\) | ||||
−0.0287045 | + | 0.999588i | \(0.509138\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.15083e6 | −0.422605 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.16114e6 | 0.783122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.06013e6 | 1.45192 | 0.725959 | − | 0.687738i | \(-0.241396\pi\) | ||||
0.725959 | + | 0.687738i | \(0.241396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −424789. | −0.149920 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.04303e6 | 0.711669 | 0.355834 | − | 0.934549i | \(-0.384197\pi\) | ||||
0.355834 | + | 0.934549i | \(0.384197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −583043. | −0.197890 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.12366e6 | −0.711560 | −0.355780 | − | 0.934570i | \(-0.615785\pi\) | ||||
−0.355780 | + | 0.934570i | \(0.615785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.66209e6 | 1.54219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 718284. | 0.234593 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.08486e6 | 1.63978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.66364e6 | −1.16664 | −0.583319 | − | 0.812243i | \(-0.698246\pi\) | ||||
−0.583319 | + | 0.812243i | \(0.698246\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −64089.7 | −0.0199034 | −0.00995170 | − | 0.999950i | \(-0.503168\pi\) | ||||
−0.00995170 | + | 0.999950i | \(0.503168\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.81933e6 | −1.17145 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 430233. | 0.130337 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 599216. | 0.179307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.02574e6 | 0.598790 | 0.299395 | − | 0.954129i | \(-0.403215\pi\) | ||||
0.299395 | + | 0.954129i | \(0.403215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −774579. | −0.226184 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.61698e6 | 1.88599 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.43528e6 | 0.685818 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.38986e6 | 0.665025 | 0.332513 | − | 0.943099i | \(-0.392104\pi\) | ||||
0.332513 | + | 0.943099i | \(0.392104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46875e6 | 0.953822 | 0.476911 | − | 0.878952i | \(-0.341756\pi\) | ||||
0.476911 | + | 0.878952i | \(0.341756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 265139. | 0.0720482 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.29519e6 | −0.347826 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −961140. | −0.252141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.60440e6 | −0.416025 | −0.208013 | − | 0.978126i | \(-0.566700\pi\) | ||||
−0.208013 | + | 0.978126i | \(0.566700\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 741661. | 0.190102 | 0.0950508 | − | 0.995472i | \(-0.469699\pi\) | ||||
0.0950508 | + | 0.995472i | \(0.469699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.93291e6 | 0.743147 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.21693e7 | 3.04833 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.86787e6 | 0.710230 | 0.355115 | − | 0.934823i | \(-0.384442\pi\) | ||||
0.355115 | + | 0.934823i | \(0.384442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −178298. | −0.0431655 | −0.0215827 | − | 0.999767i | \(-0.506871\pi\) | ||||
−0.0215827 | + | 0.999767i | \(0.506871\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.67436e6 | 0.640207 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.55293e6 | −0.367606 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.77890e6 | −0.650515 | −0.325258 | − | 0.945625i | \(-0.605451\pi\) | ||||
−0.325258 | + | 0.945625i | \(0.605451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 900903. | 0.208563 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −161095. | −0.0368840 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.41339e6 | 1.43647 | 0.718236 | − | 0.695800i | \(-0.244950\pi\) | ||||
0.718236 | + | 0.695800i | \(0.244950\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −803575. | −0.178031 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.88393e6 | −1.50864 | −0.754318 | − | 0.656510i | \(-0.772032\pi\) | ||||
−0.754318 | + | 0.656510i | \(0.772032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.70530e6 | 1.45367 | 0.726835 | − | 0.686812i | \(-0.240991\pi\) | ||||
0.726835 | + | 0.686812i | \(0.240991\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.18325e6 | −1.11165 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.25673e6 | −0.691017 | −0.345509 | − | 0.938416i | \(-0.612294\pi\) | ||||
−0.345509 | + | 0.938416i | \(0.612294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.61117e6 | −0.334648 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.76766e6 | 0.363283 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.38080e6 | −0.687520 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −244755. | −0.0492534 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.35832e6 | 1.86363 | 0.931814 | − | 0.362936i | \(-0.118226\pi\) | ||||
0.931814 | + | 0.362936i | \(0.118226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.06111e6 | −0.209122 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.19004e6 | 1.77404 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.62940e6 | −0.502382 | −0.251191 | − | 0.967938i | \(-0.580822\pi\) | ||||
−0.251191 | + | 0.967938i | \(0.580822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.13560e6 | −0.403876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.81856e6 | −0.902015 | −0.451008 | − | 0.892520i | \(-0.648935\pi\) | ||||
−0.451008 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.47798e6 | −1.01509 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.30437e6 | −0.239270 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.19098e6 | −0.753467 | −0.376733 | − | 0.926322i | \(-0.622953\pi\) | ||||
−0.376733 | + | 0.926322i | \(0.622953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −846360. | −0.150647 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.75338e6 | −0.308999 | −0.154500 | − | 0.987993i | \(-0.549377\pi\) | ||||
−0.154500 | + | 0.987993i | \(0.549377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 562395. | 0.0981326 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.63962e6 | −0.283284 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.61846e6 | 0.961221 | 0.480610 | − | 0.876934i | \(-0.340415\pi\) | ||||
0.480610 | + | 0.876934i | \(0.340415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.09755e6 | −0.351899 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.31216e6 | −0.384149 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −803844. | −0.132265 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.39842e6 | 0.716768 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.10718e7 | 1.78700 | 0.893498 | − | 0.449068i | \(-0.148244\pi\) | ||||
0.893498 | + | 0.449068i | \(0.148244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.59788e6 | −1.21461 | −0.607307 | − | 0.794467i | \(-0.707750\pi\) | ||||
−0.607307 | + | 0.794467i | \(0.707750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.68109e6 | 1.51844 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.14518e7 | 1.77924 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.17049e6 | −0.641875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.59535e6 | −0.243242 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.26315e7 | −1.90796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.31697e6 | 1.09495 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.35079e6 | −0.492214 | −0.246107 | − | 0.969243i | \(-0.579151\pi\) | ||||
−0.246107 | + | 0.969243i | \(0.579151\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.99665e6 | −0.436150 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.08480e6 | 1.16595 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00856e7 | −1.44123 | −0.720615 | − | 0.693335i | \(-0.756140\pi\) | ||||
−0.720615 | + | 0.693335i | \(0.756140\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.07838e6 | −0.152700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.42990e7 | −2.00644 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.44005e6 | −0.198447 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.35667e7 | 1.85284 | 0.926419 | − | 0.376495i | \(-0.122871\pi\) | ||||
0.926419 | + | 0.376495i | \(0.122871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.13023e6 | −0.423689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.43626e6 | 0.326826 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.96988e6 | −0.527845 | −0.263922 | − | 0.964544i | \(-0.585016\pi\) | ||||
−0.263922 | + | 0.964544i | \(0.585016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.86237e6 | 0.245440 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.17449e6 | −0.540534 | −0.270267 | − | 0.962785i | \(-0.587112\pi\) | ||||
−0.270267 | + | 0.962785i | \(0.587112\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.85666e6 | 0.495018 | 0.247509 | − | 0.968886i | \(-0.420388\pi\) | ||||
0.247509 | + | 0.968886i | \(0.420388\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.29859e6 | −0.165229 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.96956e6 | −0.626828 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.24575e6 | −0.280817 | −0.140408 | − | 0.990094i | \(-0.544842\pi\) | ||||
−0.140408 | + | 0.990094i | \(0.544842\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.05157e6 | −0.998123 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 742045. | 0.0904188 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.30983e6 | 0.279055 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.40082e6 | 0.766726 | 0.383363 | − | 0.923598i | \(-0.374766\pi\) | ||||
0.383363 | + | 0.923598i | \(0.374766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.52702e7 | 3.00138 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.39516e6 | −0.635383 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.11206e7 | 1.29865 | 0.649325 | − | 0.760511i | \(-0.275051\pi\) | ||||
0.649325 | + | 0.760511i | \(0.275051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.00433e6 | −0.804323 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.31341e7 | −1.49567 | −0.747833 | − | 0.663887i | \(-0.768905\pi\) | ||||
−0.747833 | + | 0.663887i | \(0.768905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.88546e6 | −0.890514 | −0.445257 | − | 0.895403i | \(-0.646888\pi\) | ||||
−0.445257 | + | 0.895403i | \(0.646888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.50255e6 | 0.280279 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.60624e6 | −0.733780 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.65934e6 | −0.843762 | −0.421881 | − | 0.906651i | \(-0.638630\pi\) | ||||
−0.421881 | + | 0.906651i | \(0.638630\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.42348e6 | 0.154258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.52413e7 | −1.63822 | −0.819108 | − | 0.573639i | \(-0.805531\pi\) | ||||
−0.819108 | + | 0.573639i | \(0.805531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.16507e6 | −0.230825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.35844e7 | 1.43657 | 0.718285 | − | 0.695749i | \(-0.244927\pi\) | ||||
0.718285 | + | 0.695749i | \(0.244927\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.37417e6 | 0.668647 | 0.334324 | − | 0.942458i | \(-0.391492\pi\) | ||||
0.334324 | + | 0.942458i | \(0.391492\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.08326e6 | −0.320834 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20569e7 | −1.23462 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.35930e6 | 0.646012 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.68967e6 | 0.271065 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.42736e7 | −1.42712 | −0.713561 | − | 0.700593i | \(-0.752919\pi\) | ||||
−0.713561 | + | 0.700593i | \(0.752919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.29479e6 | −0.723608 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.09503e6 | −0.304600 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.39251e6 | −0.328677 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.26960e6 | −0.891079 | −0.445539 | − | 0.895262i | \(-0.646988\pi\) | ||||
−0.445539 | + | 0.895262i | \(0.646988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17375e7 | 1.11956 | 0.559780 | − | 0.828641i | \(-0.310885\pi\) | ||||
0.559780 | + | 0.828641i | \(0.310885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.24807e6 | −0.402062 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.02545e7 | 0.963059 | 0.481529 | − | 0.876430i | \(-0.340082\pi\) | ||||
0.481529 | + | 0.876430i | \(0.340082\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26440e7 | 1.17835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.28977e6 | 0.760781 | 0.380391 | − | 0.924826i | \(-0.375790\pi\) | ||||
0.380391 | + | 0.924826i | \(0.375790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.23344e6 | 0.476633 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.80400e6 | 0.253434 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.06731e7 | −1.85435 | −0.927174 | − | 0.374631i | \(-0.877770\pi\) | ||||
−0.927174 | + | 0.374631i | \(0.877770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 194342. | 0.0173007 | 0.00865035 | − | 0.999963i | \(-0.497246\pi\) | ||||
0.00865035 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.31422e6 | −0.381170 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.10186e7 | −1.82932 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.98437e6 | 0.171418 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.26940e6 | 0.280325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.14437e7 | −0.973929 | −0.486965 | − | 0.873422i | \(-0.661896\pi\) | ||||
−0.486965 | + | 0.873422i | \(0.661896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 856571. | 0.0723609 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.03738e6 | 0.757828 | 0.378914 | − | 0.925432i | \(-0.376298\pi\) | ||||
0.378914 | + | 0.925432i | \(0.376298\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.20940e7 | 0.999316 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.11842e7 | −0.917392 | −0.458696 | − | 0.888593i | \(-0.651683\pi\) | ||||
−0.458696 | + | 0.888593i | \(0.651683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.64361e6 | −0.459548 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.38325e6 | −0.758510 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.31404e6 | −0.105453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.66930e6 | 0.451684 | 0.225842 | − | 0.974164i | \(-0.427487\pi\) | ||||
0.225842 | + | 0.974164i | \(0.427487\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.77435e7 | 1.39341 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.04384e6 | 0.315291 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.69260e6 | 0.440674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.31822e6 | −0.101320 | −0.0506599 | − | 0.998716i | \(-0.516132\pi\) | ||||
−0.0506599 | + | 0.998716i | \(0.516132\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.02077e6 | 0.535792 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.93181e6 | 0.146384 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.26035e6 | 0.617139 | 0.308570 | − | 0.951202i | \(-0.400150\pi\) | ||||
0.308570 | + | 0.951202i | \(0.400150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.28102e6 | 0.465968 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.71456e7 | 2.73643 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.00290e6 | −0.512287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.16427e6 | −0.447800 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.26743e7 | 1.63573 | 0.817865 | − | 0.575410i | \(-0.195157\pi\) | ||||
0.817865 | + | 0.575410i | \(0.195157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −69596.0 | −0.00495152 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.83925e6 | 0.412584 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.93477e7 | −1.35767 | −0.678833 | − | 0.734293i | \(-0.737514\pi\) | ||||
−0.678833 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.93440e6 | 0.549188 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.48584e7 | 1.02144 | 0.510720 | − | 0.859747i | \(-0.329379\pi\) | ||||
0.510720 | + | 0.859747i | \(0.329379\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.58720e6 | −0.514533 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.76818e7 | −1.19101 | −0.595504 | − | 0.803352i | \(-0.703048\pi\) | ||||
−0.595504 | + | 0.803352i | \(0.703048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.12613e7 | −0.753428 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.28756e6 | −0.550750 | −0.275375 | − | 0.961337i | \(-0.588802\pi\) | ||||
−0.275375 | + | 0.961337i | \(0.588802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.13147e7 | −0.746883 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.17355e6 | 0.535932 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.31365e7 | −1.49691 | −0.748457 | − | 0.663183i | \(-0.769205\pi\) | ||||
−0.748457 | + | 0.663183i | \(0.769205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.86523e6 | 0.634044 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.17375e6 | −0.0749389 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.95475e7 | −1.23980 | −0.619900 | − | 0.784681i | \(-0.712827\pi\) | ||||
−0.619900 | + | 0.784681i | \(0.712827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.34776e6 | 0.588984 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.82465e6 | 0.489783 | 0.244891 | − | 0.969551i | \(-0.421248\pi\) | ||||
0.244891 | + | 0.969551i | \(0.421248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.85488e6 | −0.361713 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.23905e7 | −1.37428 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.27325e6 | −0.504499 | −0.252250 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252250 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.43428e6 | 0.389820 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.88369e7 | −1.13386 | −0.566931 | − | 0.823765i | \(-0.691869\pi\) | ||||
−0.566931 | + | 0.823765i | \(0.691869\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.03196e7 | −0.617173 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.05555e7 | 0.623211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.02853e7 | 0.603381 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.62284e6 | 0.211176 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.17390e7 | −0.679920 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.83947e7 | −1.05866 | −0.529329 | − | 0.848417i | \(-0.677556\pi\) | ||||
−0.529329 | + | 0.848417i | \(0.677556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.36861e6 | −0.307022 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.78957e6 | −0.326937 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.78330e6 | −0.100070 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.70208e6 | 0.206443 | 0.103222 | − | 0.994658i | \(-0.467085\pi\) | ||||
0.103222 | + | 0.994658i | \(0.467085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.60818e6 | −0.199950 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.30348e6 | 0.181924 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.50113e6 | −0.465251 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.82977e7 | −0.989037 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.21913e7 | 0.654903 | 0.327451 | − | 0.944868i | \(-0.393810\pi\) | ||||
0.327451 | + | 0.944868i | \(0.393810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.52433e6 | −0.134770 | −0.0673851 | − | 0.997727i | \(-0.521466\pi\) | ||||
−0.0673851 | + | 0.997727i | \(0.521466\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.61510e7 | 0.856984 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.55601e7 | −0.820574 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.07109e7 | 1.08554 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.50051e6 | −0.491914 | −0.245957 | − | 0.969281i | \(-0.579102\pi\) | ||||
−0.245957 | + | 0.969281i | \(0.579102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.26336e7 | −1.16481 | −0.582403 | − | 0.812900i | \(-0.697887\pi\) | ||||
−0.582403 | + | 0.812900i | \(0.697887\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.59694e6 | −0.132839 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.09007e7 | 0.554230 | 0.277115 | − | 0.960837i | \(-0.410622\pi\) | ||||
0.277115 | + | 0.960837i | \(0.410622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.36120e7 | −1.19329 | −0.596647 | − | 0.802504i | \(-0.703501\pi\) | ||||
−0.596647 | + | 0.802504i | \(0.703501\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.81222e6 | 0.191503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.16661e6 | −0.306077 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.40255e6 | −0.315893 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.67438e7 | 1.31165 | 0.655826 | − | 0.754912i | \(-0.272321\pi\) | ||||
0.655826 | + | 0.754912i | \(0.272321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.18580e6 | 0.204075 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.47419e7 | −0.714469 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.19463e7 | −0.575562 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.64632e6 | −0.126001 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.03201e7 | 0.488494 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00667e6 | 0.235600 | 0.117800 | − | 0.993037i | \(-0.462416\pi\) | ||||
0.117800 | + | 0.993037i | \(0.462416\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.52828e7 | −0.714969 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.43624e7 | 1.13310 | 0.566549 | − | 0.824028i | \(-0.308278\pi\) | ||||
0.566549 | + | 0.824028i | \(0.308278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.99153e7 | −1.38328 | −0.691641 | − | 0.722241i | \(-0.743112\pi\) | ||||
−0.691641 | + | 0.722241i | \(0.743112\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.60103e7 | −1.18883 | −0.594414 | − | 0.804160i | \(-0.702616\pi\) | ||||
−0.594414 | + | 0.804160i | \(0.702616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.20471e7 | 1.45629 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.84318e6 | −0.0832759 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.90427e7 | −0.855419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.34357e7 | 0.600087 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.13519e7 | 0.504119 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.01375e7 | −0.884109 | −0.442055 | − | 0.896988i | \(-0.645750\pi\) | ||||
−0.442055 | + | 0.896988i | \(0.645750\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.21265e6 | −0.140246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.69393e7 | −1.60343 | −0.801713 | − | 0.597710i | \(-0.796078\pi\) | ||||
−0.801713 | + | 0.597710i | \(0.796078\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.27031e7 | 0.979904 | 0.489952 | − | 0.871749i | \(-0.337014\pi\) | ||||
0.489952 | + | 0.871749i | \(0.337014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.03863e7 | −1.30413 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.55979e7 | −0.665666 | −0.332833 | − | 0.942986i | \(-0.608005\pi\) | ||||
−0.332833 | + | 0.942986i | \(0.608005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61121e6 | −0.0679921 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.41831e6 | −0.395225 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.33117e7 | 2.22467 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.65533e7 | −0.686918 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.36463e7 | −1.80114 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.33078e6 | 0.136689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.18337e7 | −0.886146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.93485e7 | −0.780961 | −0.390480 | − | 0.920611i | \(-0.627691\pi\) | ||||
−0.390480 | + | 0.920611i | \(0.627691\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 694693. | 0.0278858 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.84661e7 | −1.53561 | −0.767807 | − | 0.640682i | \(-0.778652\pi\) | ||||
−0.767807 | + | 0.640682i | \(0.778652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.47804e7 | −0.983857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.85709e6 | −0.310248 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.95838e7 | 0.764905 | 0.382453 | − | 0.923975i | \(-0.375080\pi\) | ||||
0.382453 | + | 0.923975i | \(0.375080\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.83687e7 | −0.713558 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.82137e7 | −0.703709 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.86706e6 | −0.110175 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.85607e6 | −0.109162 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.28256e7 | −0.487572 | −0.243786 | − | 0.969829i | \(-0.578390\pi\) | ||||
−0.243786 | + | 0.969829i | \(0.578390\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.84206e7 | 0.692789 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.77507e7 | 0.664028 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.60430e6 | 0.208532 | 0.104266 | − | 0.994549i | \(-0.466751\pi\) | ||||
0.104266 | + | 0.994549i | \(0.466751\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.74690e6 | 0.212701 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.44348e7 | 1.26772 | 0.633861 | − | 0.773447i | \(-0.281469\pi\) | ||||
0.633861 | + | 0.773447i | \(0.281469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.55159e7 | 0.568196 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.10626e6 | −0.257493 | −0.128747 | − | 0.991678i | \(-0.541095\pi\) | ||||
−0.128747 | + | 0.991678i | \(0.541095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50541e7 | 0.542612 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.14918e7 | 1.12914 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.78058e7 | 1.34842 | 0.674212 | − | 0.738538i | \(-0.264483\pi\) | ||||
0.674212 | + | 0.738538i | \(0.264483\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.46158e6 | −0.335703 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.09837e7 | −0.387675 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.85058e7 | 1.69428 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.56029e7 | −0.542176 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.86641e7 | −2.02793 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.33643e7 | 0.459601 | 0.229800 | − | 0.973238i | \(-0.426193\pi\) | ||||
0.229800 | + | 0.973238i | \(0.426193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.85447e7 | 0.976598 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.68668e7 | 1.59521 | 0.797604 | − | 0.603181i | \(-0.206101\pi\) | ||||
0.797604 | + | 0.603181i | \(0.206101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.59874e6 | 0.154927 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.25939e7 | 1.42761 | 0.713807 | − | 0.700343i | \(-0.246969\pi\) | ||||
0.713807 | + | 0.700343i | \(0.246969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.00154e7 | −0.333974 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.98667e6 | 0.331320 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.20577e7 | 1.71831 | 0.859154 | − | 0.511718i | \(-0.170991\pi\) | ||||
0.859154 | + | 0.511718i | \(0.170991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.93093e7 | −1.29094 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.04437e7 | 0.989708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.91535e7 | 0.942989 | 0.471495 | − | 0.881869i | \(-0.343715\pi\) | ||||
0.471495 | + | 0.881869i | \(0.343715\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.64761e7 | −0.852080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.10338e7 | −1.63418 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.99304e6 | 0.286529 | 0.143264 | − | 0.989684i | \(-0.454240\pi\) | ||||
0.143264 | + | 0.989684i | \(0.454240\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.77880e6 | −0.0563916 |
(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.l.1.2 | 2 | ||
7.2 | even | 3 | 84.6.i.b.25.1 | ✓ | 4 | ||
7.3 | odd | 6 | 588.6.i.m.373.2 | 4 | |||
7.4 | even | 3 | 84.6.i.b.37.1 | yes | 4 | ||
7.5 | odd | 6 | 588.6.i.m.361.2 | 4 | |||
7.6 | odd | 2 | 588.6.a.h.1.1 | 2 | |||
21.2 | odd | 6 | 252.6.k.e.109.2 | 4 | |||
21.11 | odd | 6 | 252.6.k.e.37.2 | 4 | |||
28.11 | odd | 6 | 336.6.q.g.289.1 | 4 | |||
28.23 | odd | 6 | 336.6.q.g.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.i.b.25.1 | ✓ | 4 | 7.2 | even | 3 | ||
84.6.i.b.37.1 | yes | 4 | 7.4 | even | 3 | ||
252.6.k.e.37.2 | 4 | 21.11 | odd | 6 | |||
252.6.k.e.109.2 | 4 | 21.2 | odd | 6 | |||
336.6.q.g.193.1 | 4 | 28.23 | odd | 6 | |||
336.6.q.g.289.1 | 4 | 28.11 | odd | 6 | |||
588.6.a.h.1.1 | 2 | 7.6 | odd | 2 | |||
588.6.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
588.6.i.m.361.2 | 4 | 7.5 | odd | 6 | |||
588.6.i.m.373.2 | 4 | 7.3 | odd | 6 |