Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("147.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 97x^{2} + 7x + 294 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.79080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.790805 | −0.139796 | −0.0698979 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698979 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −31.3746 | −0.980457 | ||||||||
\(5\) | 104.192 | 1.86384 | 0.931919 | − | 0.362667i | \(-0.118134\pi\) | ||||
0.931919 | + | 0.362667i | \(0.118134\pi\) | |||||||
\(6\) | 7.11724 | 0.0807112 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 50.1170 | 0.276860 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −82.3953 | −0.260557 | ||||||||
\(11\) | −497.660 | −1.24008 | −0.620041 | − | 0.784569i | \(-0.712884\pi\) | ||||
−0.620041 | + | 0.784569i | \(0.712884\pi\) | |||||||
\(12\) | 282.372 | 0.566067 | ||||||||
\(13\) | 206.551 | 0.338977 | 0.169488 | − | 0.985532i | \(-0.445789\pi\) | ||||
0.169488 | + | 0.985532i | \(0.445789\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −937.725 | −1.07609 | ||||||||
\(16\) | 964.355 | 0.941753 | ||||||||
\(17\) | −63.1586 | −0.0530042 | −0.0265021 | − | 0.999649i | \(-0.508437\pi\) | ||||
−0.0265021 | + | 0.999649i | \(0.508437\pi\) | |||||||
\(18\) | −64.0552 | −0.0465986 | ||||||||
\(19\) | −1323.95 | −0.841374 | −0.420687 | − | 0.907206i | \(-0.638211\pi\) | ||||
−0.420687 | + | 0.907206i | \(0.638211\pi\) | |||||||
\(20\) | −3268.98 | −1.82741 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 393.552 | 0.173358 | ||||||||
\(23\) | −194.437 | −0.0766408 | −0.0383204 | − | 0.999266i | \(-0.512201\pi\) | ||||
−0.0383204 | + | 0.999266i | \(0.512201\pi\) | |||||||
\(24\) | −451.053 | −0.159845 | ||||||||
\(25\) | 7730.91 | 2.47389 | ||||||||
\(26\) | −163.342 | −0.0473875 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4323.14 | 0.954562 | 0.477281 | − | 0.878751i | \(-0.341622\pi\) | ||||
0.477281 | + | 0.878751i | \(0.341622\pi\) | |||||||
\(30\) | 741.558 | 0.150433 | ||||||||
\(31\) | 7525.31 | 1.40644 | 0.703219 | − | 0.710974i | \(-0.251745\pi\) | ||||
0.703219 | + | 0.710974i | \(0.251745\pi\) | |||||||
\(32\) | −2366.36 | −0.408513 | ||||||||
\(33\) | 4478.94 | 0.715962 | ||||||||
\(34\) | 49.9461 | 0.00740977 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2541.34 | −0.326819 | ||||||||
\(37\) | 10355.6 | 1.24358 | 0.621789 | − | 0.783185i | \(-0.286406\pi\) | ||||
0.621789 | + | 0.783185i | \(0.286406\pi\) | |||||||
\(38\) | 1046.99 | 0.117621 | ||||||||
\(39\) | −1858.96 | −0.195708 | ||||||||
\(40\) | 5221.77 | 0.516022 | ||||||||
\(41\) | 4180.92 | 0.388429 | 0.194215 | − | 0.980959i | \(-0.437784\pi\) | ||||
0.194215 | + | 0.980959i | \(0.437784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5960.87 | 0.491630 | 0.245815 | − | 0.969317i | \(-0.420944\pi\) | ||||
0.245815 | + | 0.969317i | \(0.420944\pi\) | |||||||
\(44\) | 15613.9 | 1.21585 | ||||||||
\(45\) | 8439.53 | 0.621279 | ||||||||
\(46\) | 153.762 | 0.0107141 | ||||||||
\(47\) | 4389.74 | 0.289864 | 0.144932 | − | 0.989442i | \(-0.453704\pi\) | ||||
0.144932 | + | 0.989442i | \(0.453704\pi\) | |||||||
\(48\) | −8679.20 | −0.543721 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6113.64 | −0.345840 | ||||||||
\(51\) | 568.427 | 0.0306020 | ||||||||
\(52\) | −6480.47 | −0.332352 | ||||||||
\(53\) | 17784.8 | 0.869679 | 0.434839 | − | 0.900508i | \(-0.356805\pi\) | ||||
0.434839 | + | 0.900508i | \(0.356805\pi\) | |||||||
\(54\) | 576.497 | 0.0269037 | ||||||||
\(55\) | −51852.0 | −2.31131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11915.6 | 0.485768 | ||||||||
\(58\) | −3418.76 | −0.133444 | ||||||||
\(59\) | −3500.47 | −0.130917 | −0.0654585 | − | 0.997855i | \(-0.520851\pi\) | ||||
−0.0654585 | + | 0.997855i | \(0.520851\pi\) | |||||||
\(60\) | 29420.8 | 1.05506 | ||||||||
\(61\) | 10632.5 | 0.365855 | 0.182928 | − | 0.983126i | \(-0.441443\pi\) | ||||
0.182928 | + | 0.983126i | \(0.441443\pi\) | |||||||
\(62\) | −5951.06 | −0.196614 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −28988.0 | −0.884645 | ||||||||
\(65\) | 21520.9 | 0.631797 | ||||||||
\(66\) | −3541.97 | −0.100089 | ||||||||
\(67\) | −13274.7 | −0.361276 | −0.180638 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180638 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(68\) | 1981.58 | 0.0519683 | ||||||||
\(69\) | 1749.94 | 0.0442486 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38811.1 | 0.913713 | 0.456857 | − | 0.889540i | \(-0.348975\pi\) | ||||
0.456857 | + | 0.889540i | \(0.348975\pi\) | |||||||
\(72\) | 4059.47 | 0.0922866 | ||||||||
\(73\) | −31375.6 | −0.689105 | −0.344552 | − | 0.938767i | \(-0.611969\pi\) | ||||
−0.344552 | + | 0.938767i | \(0.611969\pi\) | |||||||
\(74\) | −8189.30 | −0.173847 | ||||||||
\(75\) | −69578.2 | −1.42830 | ||||||||
\(76\) | 41538.6 | 0.824931 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1470.08 | 0.0273592 | ||||||||
\(79\) | 39491.5 | 0.711927 | 0.355964 | − | 0.934500i | \(-0.384153\pi\) | ||||
0.355964 | + | 0.934500i | \(0.384153\pi\) | |||||||
\(80\) | 100478. | 1.75528 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −3306.29 | −0.0543008 | ||||||||
\(83\) | 102372. | 1.63112 | 0.815559 | − | 0.578675i | \(-0.196430\pi\) | ||||
0.815559 | + | 0.578675i | \(0.196430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6580.60 | −0.0987912 | ||||||||
\(86\) | −4713.88 | −0.0687279 | ||||||||
\(87\) | −38908.2 | −0.551117 | ||||||||
\(88\) | −24941.2 | −0.343329 | ||||||||
\(89\) | 112821. | 1.50978 | 0.754892 | − | 0.655849i | \(-0.227689\pi\) | ||||
0.754892 | + | 0.655849i | \(0.227689\pi\) | |||||||
\(90\) | −6674.02 | −0.0868523 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6100.40 | 0.0751430 | ||||||||
\(93\) | −67727.8 | −0.812007 | ||||||||
\(94\) | −3471.43 | −0.0405218 | ||||||||
\(95\) | −137945. | −1.56818 | ||||||||
\(96\) | 21297.2 | 0.235855 | ||||||||
\(97\) | −30334.3 | −0.327345 | −0.163672 | − | 0.986515i | \(-0.552334\pi\) | ||||
−0.163672 | + | 0.986515i | \(0.552334\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −40310.4 | −0.413361 | ||||||||
\(100\) | −242554. | −2.42554 | ||||||||
\(101\) | −106796. | −1.04172 | −0.520862 | − | 0.853641i | \(-0.674390\pi\) | ||||
−0.520862 | + | 0.853641i | \(0.674390\pi\) | |||||||
\(102\) | −449.515 | −0.00427803 | ||||||||
\(103\) | −157536. | −1.46314 | −0.731570 | − | 0.681767i | \(-0.761212\pi\) | ||||
−0.731570 | + | 0.681767i | \(0.761212\pi\) | |||||||
\(104\) | 10351.7 | 0.0938490 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14064.3 | −0.121578 | ||||||||
\(107\) | −89324.3 | −0.754241 | −0.377121 | − | 0.926164i | \(-0.623086\pi\) | ||||
−0.377121 | + | 0.926164i | \(0.623086\pi\) | |||||||
\(108\) | 22872.1 | 0.188689 | ||||||||
\(109\) | 167605. | 1.35120 | 0.675600 | − | 0.737268i | \(-0.263885\pi\) | ||||
0.675600 | + | 0.737268i | \(0.263885\pi\) | |||||||
\(110\) | 41004.8 | 0.323112 | ||||||||
\(111\) | −93200.8 | −0.717980 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −115794. | −0.853079 | −0.426539 | − | 0.904469i | \(-0.640267\pi\) | ||||
−0.426539 | + | 0.904469i | \(0.640267\pi\) | |||||||
\(114\) | −9422.91 | −0.0679083 | ||||||||
\(115\) | −20258.8 | −0.142846 | ||||||||
\(116\) | −135637. | −0.935907 | ||||||||
\(117\) | 16730.7 | 0.112992 | ||||||||
\(118\) | 2768.19 | 0.0183017 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −46995.9 | −0.297925 | ||||||||
\(121\) | 86614.1 | 0.537805 | ||||||||
\(122\) | −8408.20 | −0.0511451 | ||||||||
\(123\) | −37628.2 | −0.224260 | ||||||||
\(124\) | −236104. | −1.37895 | ||||||||
\(125\) | 479898. | 2.74709 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 201513. | 1.10865 | 0.554325 | − | 0.832300i | \(-0.312977\pi\) | ||||
0.554325 | + | 0.832300i | \(0.312977\pi\) | |||||||
\(128\) | 98647.4 | 0.532183 | ||||||||
\(129\) | −53647.8 | −0.283843 | ||||||||
\(130\) | −17018.9 | −0.0883227 | ||||||||
\(131\) | −38469.6 | −0.195857 | −0.0979285 | − | 0.995193i | \(-0.531222\pi\) | ||||
−0.0979285 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(132\) | −140525. | −0.701970 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10497.7 | 0.0505049 | ||||||||
\(135\) | −75955.7 | −0.358696 | ||||||||
\(136\) | −3165.32 | −0.0146747 | ||||||||
\(137\) | −241722. | −1.10031 | −0.550155 | − | 0.835063i | \(-0.685431\pi\) | ||||
−0.550155 | + | 0.835063i | \(0.685431\pi\) | |||||||
\(138\) | −1383.86 | −0.00618577 | ||||||||
\(139\) | 53112.2 | 0.233162 | 0.116581 | − | 0.993181i | \(-0.462807\pi\) | ||||
0.116581 | + | 0.993181i | \(0.462807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −39507.6 | −0.167353 | ||||||||
\(142\) | −30692.0 | −0.127733 | ||||||||
\(143\) | −102792. | −0.420359 | ||||||||
\(144\) | 78112.8 | 0.313918 | ||||||||
\(145\) | 450435. | 1.77915 | ||||||||
\(146\) | 24812.0 | 0.0963340 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −324905. | −1.21927 | ||||||||
\(149\) | 129062. | 0.476248 | 0.238124 | − | 0.971235i | \(-0.423468\pi\) | ||||
0.238124 | + | 0.971235i | \(0.423468\pi\) | |||||||
\(150\) | 55022.8 | 0.199671 | ||||||||
\(151\) | 153206. | 0.546808 | 0.273404 | − | 0.961899i | \(-0.411850\pi\) | ||||
0.273404 | + | 0.961899i | \(0.411850\pi\) | |||||||
\(152\) | −66352.6 | −0.232943 | ||||||||
\(153\) | −5115.85 | −0.0176681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 784075. | 2.62137 | ||||||||
\(156\) | 58324.2 | 0.191884 | ||||||||
\(157\) | 151188. | 0.489517 | 0.244758 | − | 0.969584i | \(-0.421291\pi\) | ||||
0.244758 | + | 0.969584i | \(0.421291\pi\) | |||||||
\(158\) | −31230.0 | −0.0995245 | ||||||||
\(159\) | −160063. | −0.502109 | ||||||||
\(160\) | −246555. | −0.761402 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5188.47 | −0.0155329 | ||||||||
\(163\) | −32916.7 | −0.0970392 | −0.0485196 | − | 0.998822i | \(-0.515450\pi\) | ||||
−0.0485196 | + | 0.998822i | \(0.515450\pi\) | |||||||
\(164\) | −131175. | −0.380838 | ||||||||
\(165\) | 466668. | 1.33444 | ||||||||
\(166\) | −80956.1 | −0.228023 | ||||||||
\(167\) | −217586. | −0.603725 | −0.301862 | − | 0.953352i | \(-0.597608\pi\) | ||||
−0.301862 | + | 0.953352i | \(0.597608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328630. | −0.885095 | ||||||||
\(170\) | 5203.97 | 0.0138106 | ||||||||
\(171\) | −107240. | −0.280458 | ||||||||
\(172\) | −187020. | −0.482022 | ||||||||
\(173\) | 421242. | 1.07008 | 0.535041 | − | 0.844826i | \(-0.320296\pi\) | ||||
0.535041 | + | 0.844826i | \(0.320296\pi\) | |||||||
\(174\) | 30768.8 | 0.0770438 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −479921. | −1.16785 | ||||||||
\(177\) | 31504.2 | 0.0755849 | ||||||||
\(178\) | −89219.4 | −0.211062 | ||||||||
\(179\) | 3494.06 | 0.00815075 | 0.00407538 | − | 0.999992i | \(-0.498703\pi\) | ||||
0.00407538 | + | 0.999992i | \(0.498703\pi\) | |||||||
\(180\) | −264787. | −0.609138 | ||||||||
\(181\) | −594611. | −1.34908 | −0.674538 | − | 0.738240i | \(-0.735657\pi\) | ||||
−0.674538 | + | 0.738240i | \(0.735657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −95692.2 | −0.211227 | ||||||||
\(184\) | −9744.61 | −0.0212188 | ||||||||
\(185\) | 1.07897e6 | 2.31783 | ||||||||
\(186\) | 53559.5 | 0.113515 | ||||||||
\(187\) | 31431.5 | 0.0657296 | ||||||||
\(188\) | −137726. | −0.284199 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 109088. | 0.219226 | ||||||||
\(191\) | 828644. | 1.64356 | 0.821778 | − | 0.569807i | \(-0.192982\pi\) | ||||
0.821778 | + | 0.569807i | \(0.192982\pi\) | |||||||
\(192\) | 260892. | 0.510750 | ||||||||
\(193\) | 219739. | 0.424633 | 0.212316 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212316 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(194\) | 23988.5 | 0.0457614 | ||||||||
\(195\) | −193688. | −0.364768 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 475612. | 0.873146 | 0.436573 | − | 0.899669i | \(-0.356192\pi\) | ||||
0.436573 | + | 0.899669i | \(0.356192\pi\) | |||||||
\(198\) | 31877.7 | 0.0577862 | ||||||||
\(199\) | −627555. | −1.12336 | −0.561681 | − | 0.827354i | \(-0.689845\pi\) | ||||
−0.561681 | + | 0.827354i | \(0.689845\pi\) | |||||||
\(200\) | 387450. | 0.684921 | ||||||||
\(201\) | 119473. | 0.208583 | ||||||||
\(202\) | 84455.1 | 0.145629 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −17834.2 | −0.0300039 | ||||||||
\(205\) | 435617. | 0.723969 | ||||||||
\(206\) | 124580. | 0.204541 | ||||||||
\(207\) | −15749.4 | −0.0255469 | ||||||||
\(208\) | 199189. | 0.319232 | ||||||||
\(209\) | 658879. | 1.04337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 570989. | 0.882920 | 0.441460 | − | 0.897281i | \(-0.354461\pi\) | ||||
0.441460 | + | 0.897281i | \(0.354461\pi\) | |||||||
\(212\) | −557991. | −0.852683 | ||||||||
\(213\) | −349300. | −0.527533 | ||||||||
\(214\) | 70638.1 | 0.105440 | ||||||||
\(215\) | 621073. | 0.916319 | ||||||||
\(216\) | −36535.3 | −0.0532817 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −132543. | −0.188892 | ||||||||
\(219\) | 282381. | 0.397855 | ||||||||
\(220\) | 1.62684e6 | 2.26614 | ||||||||
\(221\) | −13045.5 | −0.0179672 | ||||||||
\(222\) | 73703.7 | 0.100371 | ||||||||
\(223\) | −4233.11 | −0.00570029 | −0.00285015 | − | 0.999996i | \(-0.500907\pi\) | ||||
−0.00285015 | + | 0.999996i | \(0.500907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 626204. | 0.824630 | ||||||||
\(226\) | 91570.3 | 0.119257 | ||||||||
\(227\) | −1.12986e6 | −1.45533 | −0.727664 | − | 0.685934i | \(-0.759394\pi\) | ||||
−0.727664 | + | 0.685934i | \(0.759394\pi\) | |||||||
\(228\) | −373847. | −0.476274 | ||||||||
\(229\) | −804643. | −1.01395 | −0.506973 | − | 0.861962i | \(-0.669236\pi\) | ||||
−0.506973 | + | 0.861962i | \(0.669236\pi\) | |||||||
\(230\) | 16020.7 | 0.0199693 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 216663. | 0.264280 | ||||||||
\(233\) | 1.16927e6 | 1.41100 | 0.705498 | − | 0.708712i | \(-0.250723\pi\) | ||||
0.705498 | + | 0.708712i | \(0.250723\pi\) | |||||||
\(234\) | −13230.7 | −0.0157958 | ||||||||
\(235\) | 457374. | 0.540259 | ||||||||
\(236\) | 109826. | 0.128358 | ||||||||
\(237\) | −355423. | −0.411031 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.70554e6 | −1.93138 | −0.965689 | − | 0.259700i | \(-0.916376\pi\) | ||||
−0.965689 | + | 0.259700i | \(0.916376\pi\) | |||||||
\(240\) | −904300. | −1.01341 | ||||||||
\(241\) | −951196. | −1.05494 | −0.527470 | − | 0.849574i | \(-0.676859\pi\) | ||||
−0.527470 | + | 0.849574i | \(0.676859\pi\) | |||||||
\(242\) | −68494.9 | −0.0751830 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −333590. | −0.358705 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 29756.6 | 0.0313506 | ||||||||
\(247\) | −273465. | −0.285206 | ||||||||
\(248\) | 377146. | 0.389386 | ||||||||
\(249\) | −921346. | −0.941726 | ||||||||
\(250\) | −379505. | −0.384032 | ||||||||
\(251\) | −1.14498e6 | −1.14713 | −0.573566 | − | 0.819159i | \(-0.694440\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 96763.6 | 0.0950409 | ||||||||
\(254\) | −159358. | −0.154985 | ||||||||
\(255\) | 59225.4 | 0.0570371 | ||||||||
\(256\) | 849606. | 0.810248 | ||||||||
\(257\) | −1.18374e6 | −1.11795 | −0.558976 | − | 0.829184i | \(-0.688806\pi\) | ||||
−0.558976 | + | 0.829184i | \(0.688806\pi\) | |||||||
\(258\) | 42425.0 | 0.0396800 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −675211. | −0.619450 | ||||||||
\(261\) | 350174. | 0.318187 | ||||||||
\(262\) | 30421.9 | 0.0273800 | ||||||||
\(263\) | 448316. | 0.399664 | 0.199832 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199832 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(264\) | 224471. | 0.198221 | ||||||||
\(265\) | 1.85303e6 | 1.62094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.01539e6 | −0.871674 | ||||||||
\(268\) | 416490. | 0.354216 | ||||||||
\(269\) | −747474. | −0.629819 | −0.314909 | − | 0.949122i | \(-0.601974\pi\) | ||||
−0.314909 | + | 0.949122i | \(0.601974\pi\) | |||||||
\(270\) | 60066.2 | 0.0501442 | ||||||||
\(271\) | 232637. | 0.192423 | 0.0962114 | − | 0.995361i | \(-0.469328\pi\) | ||||
0.0962114 | + | 0.995361i | \(0.469328\pi\) | |||||||
\(272\) | −60907.3 | −0.0499169 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 191155. | 0.153819 | ||||||||
\(275\) | −3.84736e6 | −3.06783 | ||||||||
\(276\) | −54903.6 | −0.0433838 | ||||||||
\(277\) | −2.42924e6 | −1.90227 | −0.951134 | − | 0.308778i | \(-0.900080\pi\) | ||||
−0.951134 | + | 0.308778i | \(0.900080\pi\) | |||||||
\(278\) | −42001.4 | −0.0325951 | ||||||||
\(279\) | 609550. | 0.468812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.51704e6 | 1.90163 | 0.950813 | − | 0.309766i | \(-0.100251\pi\) | ||||
0.950813 | + | 0.309766i | \(0.100251\pi\) | |||||||
\(282\) | 31242.8 | 0.0233953 | ||||||||
\(283\) | −260994. | −0.193716 | −0.0968579 | − | 0.995298i | \(-0.530879\pi\) | ||||
−0.0968579 | + | 0.995298i | \(0.530879\pi\) | |||||||
\(284\) | −1.21768e6 | −0.895857 | ||||||||
\(285\) | 1.24151e6 | 0.905392 | ||||||||
\(286\) | 81288.6 | 0.0587645 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −191675. | −0.136171 | ||||||||
\(289\) | −1.41587e6 | −0.997191 | ||||||||
\(290\) | −356206. | −0.248718 | ||||||||
\(291\) | 273009. | 0.188993 | ||||||||
\(292\) | 984399. | 0.675638 | ||||||||
\(293\) | −65011.7 | −0.0442408 | −0.0221204 | − | 0.999755i | \(-0.507042\pi\) | ||||
−0.0221204 | + | 0.999755i | \(0.507042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −364720. | −0.244008 | ||||||||
\(296\) | 518994. | 0.344297 | ||||||||
\(297\) | 362794. | 0.238654 | ||||||||
\(298\) | −102063. | −0.0665775 | ||||||||
\(299\) | −40161.3 | −0.0259794 | ||||||||
\(300\) | 2.18299e6 | 1.40039 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −121156. | −0.0764414 | ||||||||
\(303\) | 961167. | 0.601440 | ||||||||
\(304\) | −1.27676e6 | −0.792367 | ||||||||
\(305\) | 1.10781e6 | 0.681895 | ||||||||
\(306\) | 4045.64 | 0.00246992 | ||||||||
\(307\) | 2.35599e6 | 1.42668 | 0.713342 | − | 0.700816i | \(-0.247181\pi\) | ||||
0.713342 | + | 0.700816i | \(0.247181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.41782e6 | 0.844744 | ||||||||
\(310\) | −620051. | −0.366457 | ||||||||
\(311\) | 2.11805e6 | 1.24176 | 0.620878 | − | 0.783907i | \(-0.286776\pi\) | ||||
0.620878 | + | 0.783907i | \(0.286776\pi\) | |||||||
\(312\) | −93165.6 | −0.0541837 | ||||||||
\(313\) | 187514. | 0.108186 | 0.0540931 | − | 0.998536i | \(-0.482773\pi\) | ||||
0.0540931 | + | 0.998536i | \(0.482773\pi\) | |||||||
\(314\) | −119560. | −0.0684324 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.23903e6 | −0.698014 | ||||||||
\(317\) | −1.00541e6 | −0.561947 | −0.280974 | − | 0.959716i | \(-0.590657\pi\) | ||||
−0.280974 | + | 0.959716i | \(0.590657\pi\) | |||||||
\(318\) | 126579. | 0.0701928 | ||||||||
\(319\) | −2.15145e6 | −1.18374 | ||||||||
\(320\) | −3.02031e6 | −1.64883 | ||||||||
\(321\) | 803919. | 0.435461 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 83619.1 | 0.0445964 | ||||||||
\(324\) | −205849. | −0.108940 | ||||||||
\(325\) | 1.59683e6 | 0.838591 | ||||||||
\(326\) | 26030.7 | 0.0135657 | ||||||||
\(327\) | −1.50844e6 | −0.780116 | ||||||||
\(328\) | 209535. | 0.107540 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −369043. | −0.186549 | ||||||||
\(331\) | 1.67984e6 | 0.842748 | 0.421374 | − | 0.906887i | \(-0.361548\pi\) | ||||
0.421374 | + | 0.906887i | \(0.361548\pi\) | |||||||
\(332\) | −3.21188e6 | −1.59924 | ||||||||
\(333\) | 838807. | 0.414526 | ||||||||
\(334\) | 172068. | 0.0843982 | ||||||||
\(335\) | −1.38312e6 | −0.673360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −995036. | −0.477270 | −0.238635 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238635 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(338\) | 259882. | 0.123733 | ||||||||
\(339\) | 1.04214e6 | 0.492525 | ||||||||
\(340\) | 206464. | 0.0968605 | ||||||||
\(341\) | −3.74505e6 | −1.74410 | ||||||||
\(342\) | 84806.2 | 0.0392069 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 298741. | 0.136113 | ||||||||
\(345\) | 182329. | 0.0824722 | ||||||||
\(346\) | −333121. | −0.149593 | ||||||||
\(347\) | 4.05665e6 | 1.80861 | 0.904304 | − | 0.426890i | \(-0.140391\pi\) | ||||
0.904304 | + | 0.426890i | \(0.140391\pi\) | |||||||
\(348\) | 1.22073e6 | 0.540346 | ||||||||
\(349\) | −2.86202e6 | −1.25779 | −0.628897 | − | 0.777488i | \(-0.716493\pi\) | ||||
−0.628897 | + | 0.777488i | \(0.716493\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −150576. | −0.0652361 | ||||||||
\(352\) | 1.17764e6 | 0.506590 | ||||||||
\(353\) | −832685. | −0.355667 | −0.177834 | − | 0.984061i | \(-0.556909\pi\) | ||||
−0.177834 | + | 0.984061i | \(0.556909\pi\) | |||||||
\(354\) | −24913.7 | −0.0105665 | ||||||||
\(355\) | 4.04379e6 | 1.70301 | ||||||||
\(356\) | −3.53972e6 | −1.48028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2763.12 | −0.00113944 | ||||||||
\(359\) | −2.69751e6 | −1.10465 | −0.552327 | − | 0.833627i | \(-0.686260\pi\) | ||||
−0.552327 | + | 0.833627i | \(0.686260\pi\) | |||||||
\(360\) | 422964. | 0.172007 | ||||||||
\(361\) | −723243. | −0.292090 | ||||||||
\(362\) | 470221. | 0.188595 | ||||||||
\(363\) | −779527. | −0.310502 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.26908e6 | −1.28438 | ||||||||
\(366\) | 75673.8 | 0.0295286 | ||||||||
\(367\) | −1.45482e6 | −0.563826 | −0.281913 | − | 0.959440i | \(-0.590969\pi\) | ||||
−0.281913 | + | 0.959440i | \(0.590969\pi\) | |||||||
\(368\) | −187507. | −0.0721767 | ||||||||
\(369\) | 338654. | 0.129476 | ||||||||
\(370\) | −853257. | −0.324023 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.12494e6 | 0.796138 | ||||||||
\(373\) | −2.04689e6 | −0.761766 | −0.380883 | − | 0.924623i | \(-0.624380\pi\) | ||||
−0.380883 | + | 0.924623i | \(0.624380\pi\) | |||||||
\(374\) | −24856.2 | −0.00918872 | ||||||||
\(375\) | −4.31908e6 | −1.58604 | ||||||||
\(376\) | 220000. | 0.0802516 | ||||||||
\(377\) | 892950. | 0.323574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −416898. | −0.149084 | −0.0745421 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745421 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(380\) | 4.32798e6 | 1.53754 | ||||||||
\(381\) | −1.81362e6 | −0.640079 | ||||||||
\(382\) | −655296. | −0.229762 | ||||||||
\(383\) | 3.87626e6 | 1.35025 | 0.675127 | − | 0.737701i | \(-0.264089\pi\) | ||||
0.675127 | + | 0.737701i | \(0.264089\pi\) | |||||||
\(384\) | −887827. | −0.307256 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −173771. | −0.0593619 | ||||||||
\(387\) | 482830. | 0.163877 | ||||||||
\(388\) | 951729. | 0.320947 | ||||||||
\(389\) | 2.83802e6 | 0.950915 | 0.475458 | − | 0.879739i | \(-0.342283\pi\) | ||||
0.475458 | + | 0.879739i | \(0.342283\pi\) | |||||||
\(390\) | 153170. | 0.0509931 | ||||||||
\(391\) | 12280.4 | 0.00406228 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 346226. | 0.113078 | ||||||||
\(394\) | −376116. | −0.122062 | ||||||||
\(395\) | 4.11468e6 | 1.32692 | ||||||||
\(396\) | 1.26472e6 | 0.405283 | ||||||||
\(397\) | −4.34266e6 | −1.38286 | −0.691432 | − | 0.722442i | \(-0.743020\pi\) | ||||
−0.691432 | + | 0.722442i | \(0.743020\pi\) | |||||||
\(398\) | 496274. | 0.157041 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.45534e6 | 2.32979 | ||||||||
\(401\) | 3.40304e6 | 1.05683 | 0.528417 | − | 0.848985i | \(-0.322786\pi\) | ||||
0.528417 | + | 0.848985i | \(0.322786\pi\) | |||||||
\(402\) | −94479.6 | −0.0291590 | ||||||||
\(403\) | 1.55436e6 | 0.476749 | ||||||||
\(404\) | 3.35070e6 | 1.02137 | ||||||||
\(405\) | 683602. | 0.207093 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.15359e6 | −1.54214 | ||||||||
\(408\) | 28487.9 | 0.00847246 | ||||||||
\(409\) | 5.29431e6 | 1.56495 | 0.782477 | − | 0.622680i | \(-0.213956\pi\) | ||||
0.782477 | + | 0.622680i | \(0.213956\pi\) | |||||||
\(410\) | −344488. | −0.101208 | ||||||||
\(411\) | 2.17550e6 | 0.635264 | ||||||||
\(412\) | 4.94262e6 | 1.43455 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12454.7 | 0.00357136 | ||||||||
\(415\) | 1.06663e7 | 3.04014 | ||||||||
\(416\) | −488775. | −0.138476 | ||||||||
\(417\) | −478010. | −0.134616 | ||||||||
\(418\) | −521045. | −0.145859 | ||||||||
\(419\) | −2.87267e6 | −0.799376 | −0.399688 | − | 0.916651i | \(-0.630881\pi\) | ||||
−0.399688 | + | 0.916651i | \(0.630881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.08688e6 | 0.573843 | 0.286921 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286921 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(422\) | −451541. | −0.123429 | ||||||||
\(423\) | 355569. | 0.0966213 | ||||||||
\(424\) | 891319. | 0.240779 | ||||||||
\(425\) | −488273. | −0.131127 | ||||||||
\(426\) | 276228. | 0.0737469 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.80252e6 | 0.739501 | ||||||||
\(429\) | 925130. | 0.242694 | ||||||||
\(430\) | −491148. | −0.128098 | ||||||||
\(431\) | −2.42863e6 | −0.629751 | −0.314876 | − | 0.949133i | \(-0.601963\pi\) | ||||
−0.314876 | + | 0.949133i | \(0.601963\pi\) | |||||||
\(432\) | −703015. | −0.181240 | ||||||||
\(433\) | −956219. | −0.245097 | −0.122548 | − | 0.992463i | \(-0.539107\pi\) | ||||
−0.122548 | + | 0.992463i | \(0.539107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.05392e6 | −1.02719 | ||||||||
\(436\) | −5.25853e6 | −1.32479 | ||||||||
\(437\) | 257426. | 0.0644836 | ||||||||
\(438\) | −223308. | −0.0556185 | ||||||||
\(439\) | −2.64205e6 | −0.654304 | −0.327152 | − | 0.944972i | \(-0.606089\pi\) | ||||
−0.327152 | + | 0.944972i | \(0.606089\pi\) | |||||||
\(440\) | −2.59867e6 | −0.639910 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10316.4 | 0.00251174 | ||||||||
\(443\) | −3.43966e6 | −0.832733 | −0.416366 | − | 0.909197i | \(-0.636697\pi\) | ||||
−0.416366 | + | 0.909197i | \(0.636697\pi\) | |||||||
\(444\) | 2.92414e6 | 0.703949 | ||||||||
\(445\) | 1.17550e7 | 2.81399 | ||||||||
\(446\) | 3347.56 | 0.000796878 0 | ||||||||
\(447\) | −1.16156e6 | −0.274962 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.39903e6 | 1.02977 | 0.514886 | − | 0.857259i | \(-0.327834\pi\) | ||||
0.514886 | + | 0.857259i | \(0.327834\pi\) | |||||||
\(450\) | −495205. | −0.115280 | ||||||||
\(451\) | −2.08067e6 | −0.481684 | ||||||||
\(452\) | 3.63299e6 | 0.836407 | ||||||||
\(453\) | −1.37886e6 | −0.315699 | ||||||||
\(454\) | 893501. | 0.203449 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 597173. | 0.134490 | ||||||||
\(457\) | −2.25110e6 | −0.504202 | −0.252101 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252101 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(458\) | 636316. | 0.141745 | ||||||||
\(459\) | 46042.6 | 0.0102007 | ||||||||
\(460\) | 635611. | 0.140054 | ||||||||
\(461\) | −1.85307e6 | −0.406107 | −0.203053 | − | 0.979168i | \(-0.565087\pi\) | ||||
−0.203053 | + | 0.979168i | \(0.565087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.01089e6 | −0.652744 | −0.326372 | − | 0.945241i | \(-0.605826\pi\) | ||||
−0.326372 | + | 0.945241i | \(0.605826\pi\) | |||||||
\(464\) | 4.16904e6 | 0.898962 | ||||||||
\(465\) | −7.05668e6 | −1.51345 | ||||||||
\(466\) | −924667. | −0.197252 | ||||||||
\(467\) | 1.06725e6 | 0.226452 | 0.113226 | − | 0.993569i | \(-0.463882\pi\) | ||||
0.113226 | + | 0.993569i | \(0.463882\pi\) | |||||||
\(468\) | −524918. | −0.110784 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −361694. | −0.0755260 | ||||||||
\(471\) | −1.36069e6 | −0.282623 | ||||||||
\(472\) | −175433. | −0.0362456 | ||||||||
\(473\) | −2.96648e6 | −0.609662 | ||||||||
\(474\) | 281070. | 0.0574605 | ||||||||
\(475\) | −1.02354e7 | −2.08147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.44057e6 | 0.289893 | ||||||||
\(478\) | 1.34875e6 | 0.269999 | ||||||||
\(479\) | 5.68788e6 | 1.13269 | 0.566346 | − | 0.824168i | \(-0.308357\pi\) | ||||
0.566346 | + | 0.824168i | \(0.308357\pi\) | |||||||
\(480\) | 2.21900e6 | 0.439596 | ||||||||
\(481\) | 2.13897e6 | 0.421544 | ||||||||
\(482\) | 752211. | 0.147476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.71749e6 | −0.527295 | ||||||||
\(485\) | −3.16059e6 | −0.610117 | ||||||||
\(486\) | 46696.2 | 0.00896791 | ||||||||
\(487\) | −6.84477e6 | −1.30779 | −0.653893 | − | 0.756587i | \(-0.726865\pi\) | ||||
−0.653893 | + | 0.756587i | \(0.726865\pi\) | |||||||
\(488\) | 532867. | 0.101291 | ||||||||
\(489\) | 296250. | 0.0560256 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.60132e6 | 1.04854 | 0.524272 | − | 0.851551i | \(-0.324338\pi\) | ||||
0.524272 | + | 0.851551i | \(0.324338\pi\) | |||||||
\(492\) | 1.18057e6 | 0.219877 | ||||||||
\(493\) | −273043. | −0.0505958 | ||||||||
\(494\) | 216257. | 0.0398706 | ||||||||
\(495\) | −4.20001e6 | −0.770438 | ||||||||
\(496\) | 7.25708e6 | 1.32452 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 728605. | 0.131649 | ||||||||
\(499\) | −2.33529e6 | −0.419845 | −0.209923 | − | 0.977718i | \(-0.567321\pi\) | ||||
−0.209923 | + | 0.977718i | \(0.567321\pi\) | |||||||
\(500\) | −1.50566e7 | −2.69341 | ||||||||
\(501\) | 1.95827e6 | 0.348561 | ||||||||
\(502\) | 905455. | 0.160364 | ||||||||
\(503\) | 1.08278e7 | 1.90819 | 0.954093 | − | 0.299510i | \(-0.0968233\pi\) | ||||
0.954093 | + | 0.299510i | \(0.0968233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11273e7 | −1.94161 | ||||||||
\(506\) | −76521.1 | −0.0132863 | ||||||||
\(507\) | 2.95767e6 | 0.511010 | ||||||||
\(508\) | −6.32240e6 | −1.08698 | ||||||||
\(509\) | −3.17847e6 | −0.543781 | −0.271890 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271890 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(510\) | −46835.7 | −0.00797356 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.82859e6 | −0.645452 | ||||||||
\(513\) | 965163. | 0.161923 | ||||||||
\(514\) | 936107. | 0.156285 | ||||||||
\(515\) | −1.64139e7 | −2.72705 | ||||||||
\(516\) | 1.68318e6 | 0.278296 | ||||||||
\(517\) | −2.18460e6 | −0.359455 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.79118e6 | −0.617812 | ||||||||
\(520\) | 1.07856e6 | 0.174919 | ||||||||
\(521\) | 6.35837e6 | 1.02625 | 0.513123 | − | 0.858315i | \(-0.328489\pi\) | ||||
0.513123 | + | 0.858315i | \(0.328489\pi\) | |||||||
\(522\) | −276919. | −0.0444813 | ||||||||
\(523\) | 7.22187e6 | 1.15450 | 0.577252 | − | 0.816566i | \(-0.304125\pi\) | ||||
0.577252 | + | 0.816566i | \(0.304125\pi\) | |||||||
\(524\) | 1.20697e6 | 0.192029 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −354531. | −0.0558714 | ||||||||
\(527\) | −475288. | −0.0745471 | ||||||||
\(528\) | 4.31929e6 | 0.674260 | ||||||||
\(529\) | −6.39854e6 | −0.994126 | ||||||||
\(530\) | −1.46538e6 | −0.226601 | ||||||||
\(531\) | −283538. | −0.0436390 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 863574. | 0.131668 | ||||||||
\(534\) | 802974. | 0.121856 | ||||||||
\(535\) | −9.30685e6 | −1.40578 | ||||||||
\(536\) | −665290. | −0.100023 | ||||||||
\(537\) | −31446.5 | −0.00470584 | ||||||||
\(538\) | 591106. | 0.0880461 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.38308e6 | 0.351686 | ||||||||
\(541\) | −9.43165e6 | −1.38546 | −0.692731 | − | 0.721196i | \(-0.743593\pi\) | ||||
−0.692731 | + | 0.721196i | \(0.743593\pi\) | |||||||
\(542\) | −183971. | −0.0268999 | ||||||||
\(543\) | 5.35150e6 | 0.778889 | ||||||||
\(544\) | 149456. | 0.0216529 | ||||||||
\(545\) | 1.74630e7 | 2.51842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.91568e6 | 1.41695 | 0.708474 | − | 0.705737i | \(-0.249384\pi\) | ||||
0.708474 | + | 0.705737i | \(0.249384\pi\) | |||||||
\(548\) | 7.58394e6 | 1.07881 | ||||||||
\(549\) | 861230. | 0.121952 | ||||||||
\(550\) | 3.04251e6 | 0.428870 | ||||||||
\(551\) | −5.72364e6 | −0.803144 | ||||||||
\(552\) | 87701.5 | 0.0122507 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.92106e6 | 0.265929 | ||||||||
\(555\) | −9.71075e6 | −1.33820 | ||||||||
\(556\) | −1.66638e6 | −0.228605 | ||||||||
\(557\) | 9.64613e6 | 1.31739 | 0.658696 | − | 0.752409i | \(-0.271108\pi\) | ||||
0.658696 | + | 0.752409i | \(0.271108\pi\) | |||||||
\(558\) | −482036. | −0.0655381 | ||||||||
\(559\) | 1.23123e6 | 0.166651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −282883. | −0.0379490 | ||||||||
\(562\) | −1.99049e6 | −0.265839 | ||||||||
\(563\) | −3.09504e6 | −0.411524 | −0.205762 | − | 0.978602i | \(-0.565967\pi\) | ||||
−0.205762 | + | 0.978602i | \(0.565967\pi\) | |||||||
\(564\) | 1.23954e6 | 0.164082 | ||||||||
\(565\) | −1.20648e7 | −1.59000 | ||||||||
\(566\) | 206396. | 0.0270807 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.94509e6 | 0.252970 | ||||||||
\(569\) | −1.23185e7 | −1.59507 | −0.797533 | − | 0.603275i | \(-0.793862\pi\) | ||||
−0.797533 | + | 0.603275i | \(0.793862\pi\) | |||||||
\(570\) | −981789. | −0.126570 | ||||||||
\(571\) | −3.23510e6 | −0.415238 | −0.207619 | − | 0.978210i | \(-0.566571\pi\) | ||||
−0.207619 | + | 0.978210i | \(0.566571\pi\) | |||||||
\(572\) | 3.22507e6 | 0.412144 | ||||||||
\(573\) | −7.45780e6 | −0.948908 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.50318e6 | −0.189601 | ||||||||
\(576\) | −2.34803e6 | −0.294882 | ||||||||
\(577\) | 9.05049e6 | 1.13170 | 0.565852 | − | 0.824507i | \(-0.308547\pi\) | ||||
0.565852 | + | 0.824507i | \(0.308547\pi\) | |||||||
\(578\) | 1.11968e6 | 0.139403 | ||||||||
\(579\) | −1.97765e6 | −0.245162 | ||||||||
\(580\) | −1.41322e7 | −1.74438 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −215897. | −0.0264204 | ||||||||
\(583\) | −8.85077e6 | −1.07847 | ||||||||
\(584\) | −1.57245e6 | −0.190785 | ||||||||
\(585\) | 1.74320e6 | 0.210599 | ||||||||
\(586\) | 51411.6 | 0.00618468 | ||||||||
\(587\) | 2.13170e6 | 0.255347 | 0.127673 | − | 0.991816i | \(-0.459249\pi\) | ||||
0.127673 | + | 0.991816i | \(0.459249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.96318e6 | −1.18334 | ||||||||
\(590\) | 288422. | 0.0341113 | ||||||||
\(591\) | −4.28051e6 | −0.504111 | ||||||||
\(592\) | 9.98652e6 | 1.17114 | ||||||||
\(593\) | 7.26933e6 | 0.848903 | 0.424451 | − | 0.905451i | \(-0.360467\pi\) | ||||
0.424451 | + | 0.905451i | \(0.360467\pi\) | |||||||
\(594\) | −286899. | −0.0333629 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.04927e6 | −0.466941 | ||||||||
\(597\) | 5.64800e6 | 0.648573 | ||||||||
\(598\) | 31759.8 | 0.00363182 | ||||||||
\(599\) | −2.20565e6 | −0.251171 | −0.125585 | − | 0.992083i | \(-0.540081\pi\) | ||||
−0.125585 | + | 0.992083i | \(0.540081\pi\) | |||||||
\(600\) | −3.48705e6 | −0.395439 | ||||||||
\(601\) | 1.00121e7 | 1.13067 | 0.565336 | − | 0.824860i | \(-0.308746\pi\) | ||||
0.565336 | + | 0.824860i | \(0.308746\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.07525e6 | −0.120425 | ||||||||
\(604\) | −4.80679e6 | −0.536121 | ||||||||
\(605\) | 9.02447e6 | 1.00238 | ||||||||
\(606\) | −760096. | −0.0840789 | ||||||||
\(607\) | −6.32139e6 | −0.696371 | −0.348185 | − | 0.937426i | \(-0.613202\pi\) | ||||
−0.348185 | + | 0.937426i | \(0.613202\pi\) | |||||||
\(608\) | 3.13295e6 | 0.343712 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −876065. | −0.0953261 | ||||||||
\(611\) | 906706. | 0.0982570 | ||||||||
\(612\) | 160508. | 0.0173228 | ||||||||
\(613\) | 1.43078e7 | 1.53788 | 0.768941 | − | 0.639319i | \(-0.220784\pi\) | ||||
0.768941 | + | 0.639319i | \(0.220784\pi\) | |||||||
\(614\) | −1.86313e6 | −0.199445 | ||||||||
\(615\) | −3.92055e6 | −0.417984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.73991e7 | 1.83999 | 0.919993 | − | 0.391936i | \(-0.128194\pi\) | ||||
0.919993 | + | 0.391936i | \(0.128194\pi\) | |||||||
\(618\) | −1.12122e6 | −0.118092 | ||||||||
\(619\) | −8.26736e6 | −0.867242 | −0.433621 | − | 0.901095i | \(-0.642764\pi\) | ||||
−0.433621 | + | 0.901095i | \(0.642764\pi\) | |||||||
\(620\) | −2.46001e7 | −2.57014 | ||||||||
\(621\) | 141745. | 0.0147495 | ||||||||
\(622\) | −1.67497e6 | −0.173592 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.79270e6 | −0.184309 | ||||||||
\(625\) | 2.58422e7 | 2.64625 | ||||||||
\(626\) | −148287. | −0.0151240 | ||||||||
\(627\) | −5.92991e6 | −0.602392 | ||||||||
\(628\) | −4.74346e6 | −0.479950 | ||||||||
\(629\) | −654048. | −0.0659148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.83238e6 | 0.283190 | 0.141595 | − | 0.989925i | \(-0.454777\pi\) | ||||
0.141595 | + | 0.989925i | \(0.454777\pi\) | |||||||
\(632\) | 1.97919e6 | 0.197104 | ||||||||
\(633\) | −5.13890e6 | −0.509754 | ||||||||
\(634\) | 795084. | 0.0785579 | ||||||||
\(635\) | 2.09960e7 | 2.06634 | ||||||||
\(636\) | 5.02192e6 | 0.492297 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.70138e6 | 0.165481 | ||||||||
\(639\) | 3.14370e6 | 0.304571 | ||||||||
\(640\) | 1.02782e7 | 0.991902 | ||||||||
\(641\) | −3.57176e6 | −0.343350 | −0.171675 | − | 0.985154i | \(-0.554918\pi\) | ||||
−0.171675 | + | 0.985154i | \(0.554918\pi\) | |||||||
\(642\) | −635743. | −0.0608757 | ||||||||
\(643\) | 5.96911e6 | 0.569354 | 0.284677 | − | 0.958624i | \(-0.408114\pi\) | ||||
0.284677 | + | 0.958624i | \(0.408114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.58966e6 | −0.529037 | ||||||||
\(646\) | −66126.4 | −0.00623439 | ||||||||
\(647\) | 1.68276e6 | 0.158038 | 0.0790189 | − | 0.996873i | \(-0.474821\pi\) | ||||
0.0790189 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(648\) | 328817. | 0.0307622 | ||||||||
\(649\) | 1.74204e6 | 0.162348 | ||||||||
\(650\) | −1.26278e6 | −0.117232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.03275e6 | 0.0951427 | ||||||||
\(653\) | 1.70305e7 | 1.56295 | 0.781475 | − | 0.623937i | \(-0.214468\pi\) | ||||
0.781475 | + | 0.623937i | \(0.214468\pi\) | |||||||
\(654\) | 1.19288e6 | 0.109057 | ||||||||
\(655\) | −4.00821e6 | −0.365046 | ||||||||
\(656\) | 4.03189e6 | 0.365804 | ||||||||
\(657\) | −2.54143e6 | −0.229702 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.99303e7 | −1.78772 | −0.893862 | − | 0.448342i | \(-0.852015\pi\) | ||||
−0.893862 | + | 0.448342i | \(0.852015\pi\) | |||||||
\(660\) | −1.46415e7 | −1.30836 | ||||||||
\(661\) | −9.55735e6 | −0.850812 | −0.425406 | − | 0.905003i | \(-0.639869\pi\) | ||||
−0.425406 | + | 0.905003i | \(0.639869\pi\) | |||||||
\(662\) | −1.32843e6 | −0.117813 | ||||||||
\(663\) | 117409. | 0.0103734 | ||||||||
\(664\) | 5.13056e6 | 0.451591 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −663333. | −0.0579490 | ||||||||
\(667\) | −840579. | −0.0731584 | ||||||||
\(668\) | 6.82666e6 | 0.591926 | ||||||||
\(669\) | 38098.0 | 0.00329107 | ||||||||
\(670\) | 1.09378e6 | 0.0941330 | ||||||||
\(671\) | −5.29135e6 | −0.453691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80397e7 | 1.53530 | 0.767648 | − | 0.640872i | \(-0.221427\pi\) | ||||
0.767648 | + | 0.640872i | \(0.221427\pi\) | |||||||
\(674\) | 786879. | 0.0667204 | ||||||||
\(675\) | −5.63583e6 | −0.476101 | ||||||||
\(676\) | 1.03106e7 | 0.867798 | ||||||||
\(677\) | 1.44741e7 | 1.21372 | 0.606861 | − | 0.794808i | \(-0.292429\pi\) | ||||
0.606861 | + | 0.794808i | \(0.292429\pi\) | |||||||
\(678\) | −824133. | −0.0688530 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −329800. | −0.0273513 | ||||||||
\(681\) | 1.01688e7 | 0.840234 | ||||||||
\(682\) | 2.96160e6 | 0.243818 | ||||||||
\(683\) | 2.68785e6 | 0.220472 | 0.110236 | − | 0.993905i | \(-0.464839\pi\) | ||||
0.110236 | + | 0.993905i | \(0.464839\pi\) | |||||||
\(684\) | 3.36463e6 | 0.274977 | ||||||||
\(685\) | −2.51854e7 | −2.05080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.24179e6 | 0.585402 | ||||||||
\(688\) | 5.74839e6 | 0.462994 | ||||||||
\(689\) | 3.67347e6 | 0.294801 | ||||||||
\(690\) | −144187. | −0.0115293 | ||||||||
\(691\) | −4.67627e6 | −0.372567 | −0.186284 | − | 0.982496i | \(-0.559644\pi\) | ||||
−0.186284 | + | 0.982496i | \(0.559644\pi\) | |||||||
\(692\) | −1.32163e7 | −1.04917 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.20802e6 | −0.252836 | ||||||||
\(695\) | 5.53385e6 | 0.434576 | ||||||||
\(696\) | −1.94996e6 | −0.152582 | ||||||||
\(697\) | −264061. | −0.0205884 | ||||||||
\(698\) | 2.26330e6 | 0.175834 | ||||||||
\(699\) | −1.05235e7 | −0.814639 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.34801e6 | 0.487913 | 0.243957 | − | 0.969786i | \(-0.421555\pi\) | ||||
0.243957 | + | 0.969786i | \(0.421555\pi\) | |||||||
\(702\) | 119076. | 0.00911973 | ||||||||
\(703\) | −1.37104e7 | −1.04631 | ||||||||
\(704\) | 1.44262e7 | 1.09703 | ||||||||
\(705\) | −4.11637e6 | −0.311919 | ||||||||
\(706\) | 658492. | 0.0497208 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −988433. | −0.0741078 | ||||||||
\(709\) | −6.41052e6 | −0.478936 | −0.239468 | − | 0.970904i | \(-0.576973\pi\) | ||||
−0.239468 | + | 0.970904i | \(0.576973\pi\) | |||||||
\(710\) | −3.19785e6 | −0.238074 | ||||||||
\(711\) | 3.19881e6 | 0.237309 | ||||||||
\(712\) | 5.65425e6 | 0.417998 | ||||||||
\(713\) | −1.46320e6 | −0.107790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07101e7 | −0.783481 | ||||||||
\(716\) | −109625. | −0.00799146 | ||||||||
\(717\) | 1.53499e7 | 1.11508 | ||||||||
\(718\) | 2.13320e6 | 0.154426 | ||||||||
\(719\) | −7.34505e6 | −0.529874 | −0.264937 | − | 0.964266i | \(-0.585351\pi\) | ||||
−0.264937 | + | 0.964266i | \(0.585351\pi\) | |||||||
\(720\) | 8.13870e6 | 0.585092 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 571944. | 0.0408329 | ||||||||
\(723\) | 8.56077e6 | 0.609070 | ||||||||
\(724\) | 1.86557e7 | 1.32271 | ||||||||
\(725\) | 3.34218e7 | 2.36148 | ||||||||
\(726\) | 616454. | 0.0434069 | ||||||||
\(727\) | −1.57839e7 | −1.10759 | −0.553793 | − | 0.832655i | \(-0.686820\pi\) | ||||
−0.553793 | + | 0.832655i | \(0.686820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.58520e6 | 0.179551 | ||||||||
\(731\) | −376480. | −0.0260584 | ||||||||
\(732\) | 3.00231e6 | 0.207099 | ||||||||
\(733\) | −1.35367e7 | −0.930579 | −0.465289 | − | 0.885159i | \(-0.654050\pi\) | ||||
−0.465289 | + | 0.885159i | \(0.654050\pi\) | |||||||
\(734\) | 1.15048e6 | 0.0788205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 460109. | 0.0313088 | ||||||||
\(737\) | 6.60631e6 | 0.448012 | ||||||||
\(738\) | −267809. | −0.0181003 | ||||||||
\(739\) | −7.33702e6 | −0.494207 | −0.247103 | − | 0.968989i | \(-0.579479\pi\) | ||||
−0.247103 | + | 0.968989i | \(0.579479\pi\) | |||||||
\(740\) | −3.38524e7 | −2.27253 | ||||||||
\(741\) | 2.46118e6 | 0.164664 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.20844e7 | 0.803068 | 0.401534 | − | 0.915844i | \(-0.368477\pi\) | ||||
0.401534 | + | 0.915844i | \(0.368477\pi\) | |||||||
\(744\) | −3.39431e6 | −0.224812 | ||||||||
\(745\) | 1.34472e7 | 0.887649 | ||||||||
\(746\) | 1.61869e6 | 0.106492 | ||||||||
\(747\) | 8.29212e6 | 0.543706 | ||||||||
\(748\) | −986151. | −0.0644450 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.41555e6 | 0.221721 | ||||||||
\(751\) | 8.78176e6 | 0.568175 | 0.284087 | − | 0.958798i | \(-0.408309\pi\) | ||||
0.284087 | + | 0.958798i | \(0.408309\pi\) | |||||||
\(752\) | 4.23327e6 | 0.272980 | ||||||||
\(753\) | 1.03048e7 | 0.662297 | ||||||||
\(754\) | −706149. | −0.0452343 | ||||||||
\(755\) | 1.59628e7 | 1.01916 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 465874. | 0.0295480 | 0.0147740 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147740 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(758\) | 329685. | 0.0208414 | ||||||||
\(759\) | −870872. | −0.0548719 | ||||||||
\(760\) | −6.91339e6 | −0.434167 | ||||||||
\(761\) | −1.49978e7 | −0.938786 | −0.469393 | − | 0.882989i | \(-0.655527\pi\) | ||||
−0.469393 | + | 0.882989i | \(0.655527\pi\) | |||||||
\(762\) | 1.43422e6 | 0.0894804 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.59984e7 | −1.61144 | ||||||||
\(765\) | −533029. | −0.0329304 | ||||||||
\(766\) | −3.06536e6 | −0.188760 | ||||||||
\(767\) | −723026. | −0.0443778 | ||||||||
\(768\) | −7.64646e6 | −0.467797 | ||||||||
\(769\) | 1.85606e7 | 1.13181 | 0.565907 | − | 0.824469i | \(-0.308526\pi\) | ||||
0.565907 | + | 0.824469i | \(0.308526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.06537e7 | 0.645450 | ||||||||
\(772\) | −6.89422e6 | −0.416334 | ||||||||
\(773\) | −1.22760e7 | −0.738941 | −0.369470 | − | 0.929243i | \(-0.620461\pi\) | ||||
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(774\) | −381825. | −0.0229093 | ||||||||
\(775\) | 5.81775e7 | 3.47937 | ||||||||
\(776\) | −1.52027e6 | −0.0906286 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.24432e6 | −0.132934 | ||||||||
\(779\) | −5.53534e6 | −0.326814 | ||||||||
\(780\) | 6.07690e6 | 0.357640 | ||||||||
\(781\) | −1.93147e7 | −1.13308 | ||||||||
\(782\) | −9711.39 | −0.000567890 0 | ||||||||
\(783\) | −3.15157e6 | −0.183706 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.57525e7 | 0.912380 | ||||||||
\(786\) | −273797. | −0.0158079 | ||||||||
\(787\) | −5.26991e6 | −0.303296 | −0.151648 | − | 0.988435i | \(-0.548458\pi\) | ||||
−0.151648 | + | 0.988435i | \(0.548458\pi\) | |||||||
\(788\) | −1.49221e7 | −0.856082 | ||||||||
\(789\) | −4.03484e6 | −0.230746 | ||||||||
\(790\) | −3.25391e6 | −0.185497 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.02024e6 | −0.114443 | ||||||||
\(793\) | 2.19615e6 | 0.124016 | ||||||||
\(794\) | 3.43420e6 | 0.193319 | ||||||||
\(795\) | −1.66772e7 | −0.935850 | ||||||||
\(796\) | 1.96893e7 | 1.10141 | ||||||||
\(797\) | −1.11889e7 | −0.623940 | −0.311970 | − | 0.950092i | \(-0.600989\pi\) | ||||
−0.311970 | + | 0.950092i | \(0.600989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −277250. | −0.0153640 | ||||||||
\(800\) | −1.82941e7 | −1.01062 | ||||||||
\(801\) | 9.13850e6 | 0.503261 | ||||||||
\(802\) | −2.69114e6 | −0.147741 | ||||||||
\(803\) | 1.56144e7 | 0.854547 | ||||||||
\(804\) | −3.74841e6 | −0.204507 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.22920e6 | −0.0666476 | ||||||||
\(807\) | 6.72727e6 | 0.363626 | ||||||||
\(808\) | −5.35231e6 | −0.288412 | ||||||||
\(809\) | 7.05051e6 | 0.378747 | 0.189374 | − | 0.981905i | \(-0.439354\pi\) | ||||
0.189374 | + | 0.981905i | \(0.439354\pi\) | |||||||
\(810\) | −540596. | −0.0289508 | ||||||||
\(811\) | 2.54873e7 | 1.36073 | 0.680364 | − | 0.732875i | \(-0.261822\pi\) | ||||
0.680364 | + | 0.732875i | \(0.261822\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.09374e6 | −0.111095 | ||||||||
\(814\) | 4.07548e6 | 0.215585 | ||||||||
\(815\) | −3.42964e6 | −0.180865 | ||||||||
\(816\) | 548166. | 0.0288195 | ||||||||
\(817\) | −7.89192e6 | −0.413645 | ||||||||
\(818\) | −4.18677e6 | −0.218774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.36673e7 | −0.709820 | ||||||||
\(821\) | −2.34879e7 | −1.21615 | −0.608073 | − | 0.793881i | \(-0.708057\pi\) | ||||
−0.608073 | + | 0.793881i | \(0.708057\pi\) | |||||||
\(822\) | −1.72040e6 | −0.0888073 | ||||||||
\(823\) | −1.20903e7 | −0.622213 | −0.311107 | − | 0.950375i | \(-0.600700\pi\) | ||||
−0.311107 | + | 0.950375i | \(0.600700\pi\) | |||||||
\(824\) | −7.89521e6 | −0.405084 | ||||||||
\(825\) | 3.46263e7 | 1.77121 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.33335e6 | 0.169480 | 0.0847398 | − | 0.996403i | \(-0.472994\pi\) | ||||
0.0847398 | + | 0.996403i | \(0.472994\pi\) | |||||||
\(828\) | 494132. | 0.0250477 | ||||||||
\(829\) | 7.70534e6 | 0.389408 | 0.194704 | − | 0.980862i | \(-0.437625\pi\) | ||||
0.194704 | + | 0.980862i | \(0.437625\pi\) | |||||||
\(830\) | −8.43496e6 | −0.424999 | ||||||||
\(831\) | 2.18632e7 | 1.09828 | ||||||||
\(832\) | −5.98752e6 | −0.299874 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 378013. | 0.0188188 | ||||||||
\(835\) | −2.26706e7 | −1.12524 | ||||||||
\(836\) | −2.06721e7 | −1.02298 | ||||||||
\(837\) | −5.48595e6 | −0.270669 | ||||||||
\(838\) | 2.27172e6 | 0.111749 | ||||||||
\(839\) | −2.40843e7 | −1.18121 | −0.590607 | − | 0.806959i | \(-0.701112\pi\) | ||||
−0.590607 | + | 0.806959i | \(0.701112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.82163e6 | −0.0888116 | ||||||||
\(842\) | −1.65032e6 | −0.0802208 | ||||||||
\(843\) | −2.26534e7 | −1.09790 | ||||||||
\(844\) | −1.79146e7 | −0.865665 | ||||||||
\(845\) | −3.42405e7 | −1.64967 | ||||||||
\(846\) | −281186. | −0.0135073 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.71509e7 | 0.819023 | ||||||||
\(849\) | 2.34895e6 | 0.111842 | ||||||||
\(850\) | 386129. | 0.0183310 | ||||||||
\(851\) | −2.01352e6 | −0.0953088 | ||||||||
\(852\) | 1.09592e7 | 0.517223 | ||||||||
\(853\) | 2.82938e7 | 1.33143 | 0.665716 | − | 0.746206i | \(-0.268126\pi\) | ||||
0.665716 | + | 0.746206i | \(0.268126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.11736e7 | −0.522728 | ||||||||
\(856\) | −4.47666e6 | −0.208819 | ||||||||
\(857\) | −2.16176e7 | −1.00544 | −0.502719 | − | 0.864450i | \(-0.667667\pi\) | ||||
−0.502719 | + | 0.864450i | \(0.667667\pi\) | |||||||
\(858\) | −731598. | −0.0339277 | ||||||||
\(859\) | −3.25382e7 | −1.50456 | −0.752282 | − | 0.658841i | \(-0.771047\pi\) | ||||
−0.752282 | + | 0.658841i | \(0.771047\pi\) | |||||||
\(860\) | −1.94859e7 | −0.898411 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.92058e6 | 0.0880366 | ||||||||
\(863\) | 8.06384e6 | 0.368566 | 0.184283 | − | 0.982873i | \(-0.441004\pi\) | ||||
0.184283 | + | 0.982873i | \(0.441004\pi\) | |||||||
\(864\) | 1.72508e6 | 0.0786184 | ||||||||
\(865\) | 4.38900e7 | 1.99446 | ||||||||
\(866\) | 756183. | 0.0342635 | ||||||||
\(867\) | 1.27428e7 | 0.575728 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.96533e7 | −0.882849 | ||||||||
\(870\) | 3.20586e6 | 0.143597 | ||||||||
\(871\) | −2.74192e6 | −0.122464 | ||||||||
\(872\) | 8.39983e6 | 0.374093 | ||||||||
\(873\) | −2.45708e6 | −0.109115 | ||||||||
\(874\) | −203574. | −0.00901454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.85959e6 | −0.390080 | ||||||||
\(877\) | 1.70312e7 | 0.747732 | 0.373866 | − | 0.927483i | \(-0.378032\pi\) | ||||
0.373866 | + | 0.927483i | \(0.378032\pi\) | |||||||
\(878\) | 2.08934e6 | 0.0914690 | ||||||||
\(879\) | 585106. | 0.0255424 | ||||||||
\(880\) | −5.00038e7 | −2.17669 | ||||||||
\(881\) | −1.24740e7 | −0.541459 | −0.270729 | − | 0.962655i | \(-0.587265\pi\) | ||||
−0.270729 | + | 0.962655i | \(0.587265\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.28955e6 | 0.314629 | 0.157315 | − | 0.987549i | \(-0.449716\pi\) | ||||
0.157315 | + | 0.987549i | \(0.449716\pi\) | |||||||
\(884\) | 409298. | 0.0176160 | ||||||||
\(885\) | 3.28248e6 | 0.140878 | ||||||||
\(886\) | 2.72010e6 | 0.116413 | ||||||||
\(887\) | −1.87675e7 | −0.800937 | −0.400469 | − | 0.916310i | \(-0.631153\pi\) | ||||
−0.400469 | + | 0.916310i | \(0.631153\pi\) | |||||||
\(888\) | −4.67094e6 | −0.198780 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.29592e6 | −0.393385 | ||||||||
\(891\) | −3.26514e6 | −0.137787 | ||||||||
\(892\) | 132812. | 0.00558889 | ||||||||
\(893\) | −5.81181e6 | −0.243884 | ||||||||
\(894\) | 918566. | 0.0384385 | ||||||||
\(895\) | 364052. | 0.0151917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 361452. | 0.0149992 | ||||||||
\(898\) | −3.47878e6 | −0.143958 | ||||||||
\(899\) | 3.25330e7 | 1.34253 | ||||||||
\(900\) | −1.96469e7 | −0.808515 | ||||||||
\(901\) | −1.12326e6 | −0.0460966 | ||||||||
\(902\) | 1.64541e6 | 0.0673375 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.80323e6 | −0.236183 | ||||||||
\(905\) | −6.19535e7 | −2.51446 | ||||||||
\(906\) | 1.09041e6 | 0.0441335 | ||||||||
\(907\) | 1.26367e6 | 0.0510052 | 0.0255026 | − | 0.999675i | \(-0.491881\pi\) | ||||
0.0255026 | + | 0.999675i | \(0.491881\pi\) | |||||||
\(908\) | 3.54490e7 | 1.42689 | ||||||||
\(909\) | −8.65051e6 | −0.347242 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.47718e7 | −0.988921 | −0.494461 | − | 0.869200i | \(-0.664634\pi\) | ||||
−0.494461 | + | 0.869200i | \(0.664634\pi\) | |||||||
\(912\) | 1.14909e7 | 0.457473 | ||||||||
\(913\) | −5.09463e7 | −2.02272 | ||||||||
\(914\) | 1.78018e6 | 0.0704854 | ||||||||
\(915\) | −9.97033e6 | −0.393692 | ||||||||
\(916\) | 2.52454e7 | 0.994130 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −36410.7 | −0.00142601 | ||||||||
\(919\) | −9.36676e6 | −0.365848 | −0.182924 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182924 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(920\) | −1.01531e6 | −0.0395483 | ||||||||
\(921\) | −2.12039e7 | −0.823696 | ||||||||
\(922\) | 1.46542e6 | 0.0567721 | ||||||||
\(923\) | 8.01648e6 | 0.309727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00586e7 | 3.07648 | ||||||||
\(926\) | 2.38103e6 | 0.0912509 | ||||||||
\(927\) | −1.27604e7 | −0.487713 | ||||||||
\(928\) | −1.02301e7 | −0.389951 | ||||||||
\(929\) | 6.87350e6 | 0.261300 | 0.130650 | − | 0.991429i | \(-0.458294\pi\) | ||||
0.130650 | + | 0.991429i | \(0.458294\pi\) | |||||||
\(930\) | 5.58046e6 | 0.211574 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.66855e7 | −1.38342 | ||||||||
\(933\) | −1.90625e7 | −0.716928 | ||||||||
\(934\) | −843990. | −0.0316570 | ||||||||
\(935\) | 3.27490e6 | 0.122509 | ||||||||
\(936\) | 838490. | 0.0312830 | ||||||||
\(937\) | 4.26197e7 | 1.58585 | 0.792923 | − | 0.609322i | \(-0.208558\pi\) | ||||
0.792923 | + | 0.609322i | \(0.208558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.68762e6 | −0.0624614 | ||||||||
\(940\) | −1.43499e7 | −0.529701 | ||||||||
\(941\) | −4.50226e6 | −0.165751 | −0.0828755 | − | 0.996560i | \(-0.526410\pi\) | ||||
−0.0828755 | + | 0.996560i | \(0.526410\pi\) | |||||||
\(942\) | 1.07604e6 | 0.0395095 | ||||||||
\(943\) | −812926. | −0.0297695 | ||||||||
\(944\) | −3.37569e6 | −0.123291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.34591e6 | 0.0852282 | ||||||||
\(947\) | 3.37725e7 | 1.22374 | 0.611870 | − | 0.790959i | \(-0.290418\pi\) | ||||
0.611870 | + | 0.790959i | \(0.290418\pi\) | |||||||
\(948\) | 1.11513e7 | 0.402999 | ||||||||
\(949\) | −6.48068e6 | −0.233590 | ||||||||
\(950\) | 8.09419e6 | 0.290981 | ||||||||
\(951\) | 9.04870e6 | 0.324440 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.81813e7 | 1.71849 | 0.859244 | − | 0.511566i | \(-0.170934\pi\) | ||||
0.859244 | + | 0.511566i | \(0.170934\pi\) | |||||||
\(954\) | −1.13921e6 | −0.0405258 | ||||||||
\(955\) | 8.63379e7 | 3.06332 | ||||||||
\(956\) | 5.35107e7 | 1.89363 | ||||||||
\(957\) | 1.93631e7 | 0.683430 | ||||||||
\(958\) | −4.49800e6 | −0.158346 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.71828e7 | 0.951955 | ||||||||
\(961\) | 2.80012e7 | 0.978066 | ||||||||
\(962\) | −1.69151e6 | −0.0589301 | ||||||||
\(963\) | −7.23527e6 | −0.251414 | ||||||||
\(964\) | 2.98434e7 | 1.03432 | ||||||||
\(965\) | 2.28950e7 | 0.791446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.54640e7 | −1.21961 | −0.609805 | − | 0.792551i | \(-0.708752\pi\) | ||||
−0.609805 | + | 0.792551i | \(0.708752\pi\) | |||||||
\(968\) | 4.34084e6 | 0.148897 | ||||||||
\(969\) | −752572. | −0.0257477 | ||||||||
\(970\) | 2.49941e6 | 0.0852919 | ||||||||
\(971\) | 7.84296e6 | 0.266951 | 0.133476 | − | 0.991052i | \(-0.457386\pi\) | ||||
0.133476 | + | 0.991052i | \(0.457386\pi\) | |||||||
\(972\) | 1.85264e6 | 0.0628964 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.41288e6 | 0.182823 | ||||||||
\(975\) | −1.43715e7 | −0.484161 | ||||||||
\(976\) | 1.02535e7 | 0.344545 | ||||||||
\(977\) | −2.47534e7 | −0.829658 | −0.414829 | − | 0.909899i | \(-0.636159\pi\) | ||||
−0.414829 | + | 0.909899i | \(0.636159\pi\) | |||||||
\(978\) | −234276. | −0.00783215 | ||||||||
\(979\) | −5.61464e7 | −1.87226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.35760e7 | 0.450400 | ||||||||
\(982\) | −4.42955e6 | −0.146582 | ||||||||
\(983\) | −4.53129e7 | −1.49568 | −0.747838 | − | 0.663881i | \(-0.768908\pi\) | ||||
−0.747838 | + | 0.663881i | \(0.768908\pi\) | |||||||
\(984\) | −1.88581e6 | −0.0620885 | ||||||||
\(985\) | 4.95548e7 | 1.62740 | ||||||||
\(986\) | 215924. | 0.00707308 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.57985e6 | 0.279632 | ||||||||
\(989\) | −1.15902e6 | −0.0376789 | ||||||||
\(990\) | 3.32139e6 | 0.107704 | ||||||||
\(991\) | −3.74143e7 | −1.21019 | −0.605095 | − | 0.796154i | \(-0.706865\pi\) | ||||
−0.605095 | + | 0.796154i | \(0.706865\pi\) | |||||||
\(992\) | −1.78076e7 | −0.574548 | ||||||||
\(993\) | −1.51186e7 | −0.486561 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.53861e7 | −2.09376 | ||||||||
\(996\) | 2.89069e7 | 0.923322 | ||||||||
\(997\) | −4.65278e7 | −1.48243 | −0.741216 | − | 0.671267i | \(-0.765751\pi\) | ||||
−0.741216 | + | 0.671267i | \(0.765751\pi\) | |||||||
\(998\) | 1.84676e6 | 0.0586926 | ||||||||
\(999\) | −7.54927e6 | −0.239327 |
(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 | 147.6.a.l.1.2 | 4 | ||
3.2 | odd | 2 | 441.6.a.v.1.3 | 4 | |||
7.2 | even | 3 | 147.6.e.o.67.3 | 8 | |||
7.3 | odd | 6 | 21.6.e.c.16.3 | yes | 8 | ||
7.4 | even | 3 | 147.6.e.o.79.3 | 8 | |||
7.5 | odd | 6 | 21.6.e.c.4.3 | ✓ | 8 | ||
7.6 | odd | 2 | 147.6.a.m.1.2 | 4 | |||
21.5 | even | 6 | 63.6.e.e.46.2 | 8 | |||
21.17 | even | 6 | 63.6.e.e.37.2 | 8 | |||
21.20 | even | 2 | 441.6.a.w.1.3 | 4 | |||
28.3 | even | 6 | 336.6.q.j.289.4 | 8 | |||
28.19 | even | 6 | 336.6.q.j.193.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.c.4.3 | ✓ | 8 | 7.5 | odd | 6 | ||
21.6.e.c.16.3 | yes | 8 | 7.3 | odd | 6 | ||
63.6.e.e.37.2 | 8 | 21.17 | even | 6 | |||
63.6.e.e.46.2 | 8 | 21.5 | even | 6 | |||
147.6.a.l.1.2 | 4 | 1.1 | even | 1 | trivial | ||
147.6.a.m.1.2 | 4 | 7.6 | odd | 2 | |||
147.6.e.o.67.3 | 8 | 7.2 | even | 3 | |||
147.6.e.o.79.3 | 8 | 7.4 | even | 3 | |||
336.6.q.j.193.4 | 8 | 28.19 | even | 6 | |||
336.6.q.j.289.4 | 8 | 28.3 | even | 6 | |||
441.6.a.v.1.3 | 4 | 3.2 | odd | 2 | |||
441.6.a.w.1.3 | 4 | 21.20 | even | 2 |