Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,6,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, 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("847.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(135.845095382\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.27492 | −1.46281 | −0.731406 | − | 0.681942i | \(-0.761136\pi\) | ||||
−0.731406 | + | 0.681942i | \(0.761136\pi\) | |||||||
\(3\) | −25.6495 | −1.64542 | −0.822708 | − | 0.568464i | \(-0.807538\pi\) | ||||
−0.822708 | + | 0.568464i | \(0.807538\pi\) | |||||||
\(4\) | 36.4743 | 1.13982 | ||||||||
\(5\) | 28.7492 | 0.514281 | 0.257140 | − | 0.966374i | \(-0.417220\pi\) | ||||
0.257140 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(6\) | 212.248 | 2.40694 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | −37.0241 | −0.204531 | ||||||||
\(9\) | 414.897 | 1.70740 | ||||||||
\(10\) | −237.897 | −0.752296 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −935.547 | −1.87548 | ||||||||
\(13\) | −300.640 | −0.493387 | −0.246694 | − | 0.969094i | \(-0.579344\pi\) | ||||
−0.246694 | + | 0.969094i | \(0.579344\pi\) | |||||||
\(14\) | 405.471 | 0.552891 | ||||||||
\(15\) | −737.402 | −0.846206 | ||||||||
\(16\) | −860.805 | −0.840630 | ||||||||
\(17\) | −613.106 | −0.514533 | −0.257267 | − | 0.966340i | \(-0.582822\pi\) | ||||
−0.257267 | + | 0.966340i | \(0.582822\pi\) | |||||||
\(18\) | −3433.24 | −2.49760 | ||||||||
\(19\) | 1700.95 | 1.08095 | 0.540477 | − | 0.841359i | \(-0.318244\pi\) | ||||
0.540477 | + | 0.841359i | \(0.318244\pi\) | |||||||
\(20\) | 1048.60 | 0.586188 | ||||||||
\(21\) | 1256.83 | 0.621909 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3188.15 | 1.25667 | 0.628333 | − | 0.777945i | \(-0.283738\pi\) | ||||
0.628333 | + | 0.777945i | \(0.283738\pi\) | |||||||
\(24\) | 949.650 | 0.336539 | ||||||||
\(25\) | −2298.49 | −0.735515 | ||||||||
\(26\) | 2487.77 | 0.721733 | ||||||||
\(27\) | −4409.07 | −1.16396 | ||||||||
\(28\) | −1787.24 | −0.430812 | ||||||||
\(29\) | −4299.28 | −0.949294 | −0.474647 | − | 0.880176i | \(-0.657424\pi\) | ||||
−0.474647 | + | 0.880176i | \(0.657424\pi\) | |||||||
\(30\) | 6101.94 | 1.23784 | ||||||||
\(31\) | 2028.46 | 0.379106 | 0.189553 | − | 0.981870i | \(-0.439296\pi\) | ||||
0.189553 | + | 0.981870i | \(0.439296\pi\) | |||||||
\(32\) | 8307.86 | 1.43421 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5073.40 | 0.752666 | ||||||||
\(35\) | −1408.71 | −0.194380 | ||||||||
\(36\) | 15133.1 | 1.94612 | ||||||||
\(37\) | 5154.46 | 0.618983 | 0.309491 | − | 0.950902i | \(-0.399841\pi\) | ||||
0.309491 | + | 0.950902i | \(0.399841\pi\) | |||||||
\(38\) | −14075.2 | −1.58123 | ||||||||
\(39\) | 7711.26 | 0.811827 | ||||||||
\(40\) | −1064.41 | −0.105186 | ||||||||
\(41\) | 7146.21 | 0.663921 | 0.331960 | − | 0.943293i | \(-0.392290\pi\) | ||||
0.331960 | + | 0.943293i | \(0.392290\pi\) | |||||||
\(42\) | −10400.1 | −0.909736 | ||||||||
\(43\) | 19584.3 | 1.61524 | 0.807620 | − | 0.589703i | \(-0.200755\pi\) | ||||
0.807620 | + | 0.589703i | \(0.200755\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11927.9 | 0.878081 | ||||||||
\(46\) | −26381.7 | −1.83827 | ||||||||
\(47\) | 19998.4 | 1.32054 | 0.660268 | − | 0.751030i | \(-0.270443\pi\) | ||||
0.660268 | + | 0.751030i | \(0.270443\pi\) | |||||||
\(48\) | 22079.2 | 1.38319 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 19019.8 | 1.07592 | ||||||||
\(51\) | 15725.9 | 0.846621 | ||||||||
\(52\) | −10965.6 | −0.562373 | ||||||||
\(53\) | 3948.82 | 0.193098 | 0.0965489 | − | 0.995328i | \(-0.469220\pi\) | ||||
0.0965489 | + | 0.995328i | \(0.469220\pi\) | |||||||
\(54\) | 36484.7 | 1.70265 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1814.18 | 0.0773055 | ||||||||
\(57\) | −43628.5 | −1.77862 | ||||||||
\(58\) | 35576.2 | 1.38864 | ||||||||
\(59\) | −29707.6 | −1.11106 | −0.555530 | − | 0.831497i | \(-0.687484\pi\) | ||||
−0.555530 | + | 0.831497i | \(0.687484\pi\) | |||||||
\(60\) | −26896.2 | −0.964523 | ||||||||
\(61\) | 50519.3 | 1.73833 | 0.869165 | − | 0.494522i | \(-0.164657\pi\) | ||||
0.869165 | + | 0.494522i | \(0.164657\pi\) | |||||||
\(62\) | −16785.3 | −0.554562 | ||||||||
\(63\) | −20330.0 | −0.645335 | ||||||||
\(64\) | −41201.1 | −1.25736 | ||||||||
\(65\) | −8643.14 | −0.253740 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5053.56 | 0.137534 | 0.0687671 | − | 0.997633i | \(-0.478093\pi\) | ||||
0.0687671 | + | 0.997633i | \(0.478093\pi\) | |||||||
\(68\) | −22362.6 | −0.586476 | ||||||||
\(69\) | −81774.5 | −2.06774 | ||||||||
\(70\) | 11657.0 | 0.284341 | ||||||||
\(71\) | 32853.3 | 0.773453 | 0.386726 | − | 0.922195i | \(-0.373606\pi\) | ||||
0.386726 | + | 0.922195i | \(0.373606\pi\) | |||||||
\(72\) | −15361.2 | −0.349215 | ||||||||
\(73\) | 11115.0 | 0.244119 | 0.122059 | − | 0.992523i | \(-0.461050\pi\) | ||||
0.122059 | + | 0.992523i | \(0.461050\pi\) | |||||||
\(74\) | −42652.7 | −0.905456 | ||||||||
\(75\) | 58955.0 | 1.21023 | ||||||||
\(76\) | 62040.8 | 1.23209 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −63810.0 | −1.18755 | ||||||||
\(79\) | −81889.4 | −1.47625 | −0.738125 | − | 0.674664i | \(-0.764288\pi\) | ||||
−0.738125 | + | 0.674664i | \(0.764288\pi\) | |||||||
\(80\) | −24747.4 | −0.432320 | ||||||||
\(81\) | 12270.6 | 0.207803 | ||||||||
\(82\) | −59134.3 | −0.971191 | ||||||||
\(83\) | −118234. | −1.88385 | −0.941926 | − | 0.335819i | \(-0.890987\pi\) | ||||
−0.941926 | + | 0.335819i | \(0.890987\pi\) | |||||||
\(84\) | 45841.8 | 0.708865 | ||||||||
\(85\) | −17626.3 | −0.264615 | ||||||||
\(86\) | −162058. | −2.36279 | ||||||||
\(87\) | 110274. | 1.56198 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −41695.4 | −0.557972 | −0.278986 | − | 0.960295i | \(-0.589998\pi\) | ||||
−0.278986 | + | 0.960295i | \(0.589998\pi\) | |||||||
\(90\) | −98702.8 | −1.28447 | ||||||||
\(91\) | 14731.3 | 0.186483 | ||||||||
\(92\) | 116286. | 1.43237 | ||||||||
\(93\) | −52028.9 | −0.623788 | ||||||||
\(94\) | −165485. | −1.93170 | ||||||||
\(95\) | 48900.9 | 0.555914 | ||||||||
\(96\) | −213092. | −2.35988 | ||||||||
\(97\) | 43682.8 | 0.471391 | 0.235695 | − | 0.971827i | \(-0.424263\pi\) | ||||
0.235695 | + | 0.971827i | \(0.424263\pi\) | |||||||
\(98\) | −19868.1 | −0.208973 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −83835.5 | −0.838355 | ||||||||
\(101\) | −25648.1 | −0.250179 | −0.125090 | − | 0.992145i | \(-0.539922\pi\) | ||||
−0.125090 | + | 0.992145i | \(0.539922\pi\) | |||||||
\(102\) | −130130. | −1.23845 | ||||||||
\(103\) | −14320.0 | −0.133000 | −0.0664999 | − | 0.997786i | \(-0.521183\pi\) | ||||
−0.0664999 | + | 0.997786i | \(0.521183\pi\) | |||||||
\(104\) | 11130.9 | 0.100913 | ||||||||
\(105\) | 36132.7 | 0.319836 | ||||||||
\(106\) | −32676.1 | −0.282466 | ||||||||
\(107\) | −17201.8 | −0.145249 | −0.0726247 | − | 0.997359i | \(-0.523138\pi\) | ||||
−0.0726247 | + | 0.997359i | \(0.523138\pi\) | |||||||
\(108\) | −160818. | −1.32670 | ||||||||
\(109\) | 86017.6 | 0.693459 | 0.346730 | − | 0.937965i | \(-0.387292\pi\) | ||||
0.346730 | + | 0.937965i | \(0.387292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −132209. | −1.01848 | ||||||||
\(112\) | 42179.4 | 0.317728 | ||||||||
\(113\) | 137568. | 1.01349 | 0.506745 | − | 0.862096i | \(-0.330848\pi\) | ||||
0.506745 | + | 0.862096i | \(0.330848\pi\) | |||||||
\(114\) | 361022. | 2.60179 | ||||||||
\(115\) | 91656.8 | 0.646279 | ||||||||
\(116\) | −156813. | −1.08202 | ||||||||
\(117\) | −124734. | −0.842407 | ||||||||
\(118\) | 245828. | 1.62527 | ||||||||
\(119\) | 30042.2 | 0.194475 | ||||||||
\(120\) | 27301.6 | 0.173075 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −418043. | −2.54285 | ||||||||
\(123\) | −183297. | −1.09243 | ||||||||
\(124\) | 73986.4 | 0.432113 | ||||||||
\(125\) | −155921. | −0.892542 | ||||||||
\(126\) | 168229. | 0.944004 | ||||||||
\(127\) | 70567.1 | 0.388233 | 0.194117 | − | 0.980978i | \(-0.437816\pi\) | ||||
0.194117 | + | 0.980978i | \(0.437816\pi\) | |||||||
\(128\) | 75084.2 | 0.405064 | ||||||||
\(129\) | −502328. | −2.65774 | ||||||||
\(130\) | 71521.3 | 0.371173 | ||||||||
\(131\) | 173712. | 0.884408 | 0.442204 | − | 0.896914i | \(-0.354197\pi\) | ||||
0.442204 | + | 0.896914i | \(0.354197\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −83346.5 | −0.408562 | ||||||||
\(134\) | −41817.8 | −0.201187 | ||||||||
\(135\) | −126757. | −0.598602 | ||||||||
\(136\) | 22699.7 | 0.105238 | ||||||||
\(137\) | −1989.94 | −0.00905813 | −0.00452907 | − | 0.999990i | \(-0.501442\pi\) | ||||
−0.00452907 | + | 0.999990i | \(0.501442\pi\) | |||||||
\(138\) | 676678. | 3.02471 | ||||||||
\(139\) | −366409. | −1.60853 | −0.804264 | − | 0.594272i | \(-0.797440\pi\) | ||||
−0.804264 | + | 0.594272i | \(0.797440\pi\) | |||||||
\(140\) | −51381.6 | −0.221558 | ||||||||
\(141\) | −512949. | −2.17283 | ||||||||
\(142\) | −271859. | −1.13142 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −357145. | −1.43529 | ||||||||
\(145\) | −123601. | −0.488204 | ||||||||
\(146\) | −91975.4 | −0.357100 | ||||||||
\(147\) | −61584.5 | −0.235059 | ||||||||
\(148\) | 188005. | 0.705529 | ||||||||
\(149\) | −140719. | −0.519261 | −0.259631 | − | 0.965708i | \(-0.583601\pi\) | ||||
−0.259631 | + | 0.965708i | \(0.583601\pi\) | |||||||
\(150\) | −487848. | −1.77034 | ||||||||
\(151\) | −50064.6 | −0.178685 | −0.0893425 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893425 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(152\) | −62976.1 | −0.221089 | ||||||||
\(153\) | −254376. | −0.878512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 58316.4 | 0.194967 | ||||||||
\(156\) | 281262. | 0.925337 | ||||||||
\(157\) | −89794.6 | −0.290738 | −0.145369 | − | 0.989378i | \(-0.546437\pi\) | ||||
−0.145369 | + | 0.989378i | \(0.546437\pi\) | |||||||
\(158\) | 677628. | 2.15948 | ||||||||
\(159\) | −101285. | −0.317726 | ||||||||
\(160\) | 238844. | 0.737589 | ||||||||
\(161\) | −156219. | −0.474975 | ||||||||
\(162\) | −101538. | −0.303977 | ||||||||
\(163\) | −481230. | −1.41868 | −0.709339 | − | 0.704867i | \(-0.751006\pi\) | ||||
−0.709339 | + | 0.704867i | \(0.751006\pi\) | |||||||
\(164\) | 260653. | 0.756750 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 978376. | 2.75572 | ||||||||
\(167\) | 86572.7 | 0.240209 | 0.120105 | − | 0.992761i | \(-0.461677\pi\) | ||||
0.120105 | + | 0.992761i | \(0.461677\pi\) | |||||||
\(168\) | −46532.8 | −0.127200 | ||||||||
\(169\) | −280909. | −0.756569 | ||||||||
\(170\) | 145856. | 0.387082 | ||||||||
\(171\) | 705718. | 1.84562 | ||||||||
\(172\) | 714323. | 1.84108 | ||||||||
\(173\) | 58137.4 | 0.147686 | 0.0738432 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738432 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(174\) | −912511. | −2.28489 | ||||||||
\(175\) | 112626. | 0.277999 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 761985. | 1.82816 | ||||||||
\(178\) | 345026. | 0.816209 | ||||||||
\(179\) | −209380. | −0.488431 | −0.244215 | − | 0.969721i | \(-0.578530\pi\) | ||||
−0.244215 | + | 0.969721i | \(0.578530\pi\) | |||||||
\(180\) | 435063. | 1.00085 | ||||||||
\(181\) | 278996. | 0.632996 | 0.316498 | − | 0.948593i | \(-0.397493\pi\) | ||||
0.316498 | + | 0.948593i | \(0.397493\pi\) | |||||||
\(182\) | −121901. | −0.272789 | ||||||||
\(183\) | −1.29579e6 | −2.86028 | ||||||||
\(184\) | −118038. | −0.257027 | ||||||||
\(185\) | 148186. | 0.318331 | ||||||||
\(186\) | 430535. | 0.912485 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 729426. | 1.50517 | ||||||||
\(189\) | 216045. | 0.439935 | ||||||||
\(190\) | −404651. | −0.813198 | ||||||||
\(191\) | −445132. | −0.882888 | −0.441444 | − | 0.897289i | \(-0.645534\pi\) | ||||
−0.441444 | + | 0.897289i | \(0.645534\pi\) | |||||||
\(192\) | 1.05679e6 | 2.06888 | ||||||||
\(193\) | 726811. | 1.40452 | 0.702260 | − | 0.711920i | \(-0.252174\pi\) | ||||
0.702260 | + | 0.711920i | \(0.252174\pi\) | |||||||
\(194\) | −361471. | −0.689556 | ||||||||
\(195\) | 221692. | 0.417507 | ||||||||
\(196\) | 87574.7 | 0.162831 | ||||||||
\(197\) | 364897. | 0.669892 | 0.334946 | − | 0.942237i | \(-0.391282\pi\) | ||||
0.334946 | + | 0.942237i | \(0.391282\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 289307. | 0.517877 | 0.258938 | − | 0.965894i | \(-0.416627\pi\) | ||||
0.258938 | + | 0.965894i | \(0.416627\pi\) | |||||||
\(200\) | 85099.3 | 0.150436 | ||||||||
\(201\) | −129621. | −0.226301 | ||||||||
\(202\) | 212236. | 0.365965 | ||||||||
\(203\) | 210665. | 0.358799 | ||||||||
\(204\) | 573589. | 0.964997 | ||||||||
\(205\) | 205448. | 0.341442 | ||||||||
\(206\) | 118497. | 0.194554 | ||||||||
\(207\) | 1.32276e6 | 2.14562 | ||||||||
\(208\) | 258792. | 0.414756 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −298995. | −0.467860 | ||||||||
\(211\) | −750147. | −1.15995 | −0.579976 | − | 0.814633i | \(-0.696938\pi\) | ||||
−0.579976 | + | 0.814633i | \(0.696938\pi\) | |||||||
\(212\) | 144030. | 0.220097 | ||||||||
\(213\) | −842672. | −1.27265 | ||||||||
\(214\) | 142343. | 0.212473 | ||||||||
\(215\) | 563033. | 0.830687 | ||||||||
\(216\) | 163242. | 0.238066 | ||||||||
\(217\) | −99394.3 | −0.143289 | ||||||||
\(218\) | −711788. | −1.01440 | ||||||||
\(219\) | −285093. | −0.401677 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 184324. | 0.253864 | ||||||||
\(222\) | 1.09402e6 | 1.48985 | ||||||||
\(223\) | 534398. | 0.719619 | 0.359810 | − | 0.933026i | \(-0.382842\pi\) | ||||
0.359810 | + | 0.933026i | \(0.382842\pi\) | |||||||
\(224\) | −407085. | −0.542082 | ||||||||
\(225\) | −953635. | −1.25582 | ||||||||
\(226\) | −1.13836e6 | −1.48255 | ||||||||
\(227\) | 410624. | 0.528907 | 0.264453 | − | 0.964398i | \(-0.414808\pi\) | ||||
0.264453 | + | 0.964398i | \(0.414808\pi\) | |||||||
\(228\) | −1.59132e6 | −2.02731 | ||||||||
\(229\) | 1.03036e6 | 1.29838 | 0.649189 | − | 0.760627i | \(-0.275108\pi\) | ||||
0.649189 | + | 0.760627i | \(0.275108\pi\) | |||||||
\(230\) | −758452. | −0.945385 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 159177. | 0.194160 | ||||||||
\(233\) | 119211. | 0.143856 | 0.0719278 | − | 0.997410i | \(-0.477085\pi\) | ||||
0.0719278 | + | 0.997410i | \(0.477085\pi\) | |||||||
\(234\) | 1.03217e6 | 1.23228 | ||||||||
\(235\) | 574937. | 0.679127 | ||||||||
\(236\) | −1.08356e6 | −1.26641 | ||||||||
\(237\) | 2.10042e6 | 2.42905 | ||||||||
\(238\) | −248597. | −0.284481 | ||||||||
\(239\) | 254090. | 0.287735 | 0.143868 | − | 0.989597i | \(-0.454046\pi\) | ||||
0.143868 | + | 0.989597i | \(0.454046\pi\) | |||||||
\(240\) | 634759. | 0.711346 | ||||||||
\(241\) | −1.41251e6 | −1.56656 | −0.783282 | − | 0.621667i | \(-0.786456\pi\) | ||||
−0.783282 | + | 0.621667i | \(0.786456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 756671. | 0.822037 | ||||||||
\(244\) | 1.84265e6 | 1.98138 | ||||||||
\(245\) | 69026.8 | 0.0734687 | ||||||||
\(246\) | 1.51677e6 | 1.59801 | ||||||||
\(247\) | −511372. | −0.533329 | ||||||||
\(248\) | −75101.7 | −0.0775391 | ||||||||
\(249\) | 3.03264e6 | 3.09972 | ||||||||
\(250\) | 1.29023e6 | 1.30562 | ||||||||
\(251\) | −1.67542e6 | −1.67857 | −0.839286 | − | 0.543690i | \(-0.817027\pi\) | ||||
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(252\) | −741520. | −0.735566 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −583937. | −0.567913 | ||||||||
\(255\) | 452106. | 0.435401 | ||||||||
\(256\) | 697120. | 0.664825 | ||||||||
\(257\) | 726996. | 0.686593 | 0.343296 | − | 0.939227i | \(-0.388456\pi\) | ||||
0.343296 | + | 0.939227i | \(0.388456\pi\) | |||||||
\(258\) | 4.15672e6 | 3.88778 | ||||||||
\(259\) | −252568. | −0.233953 | ||||||||
\(260\) | −315252. | −0.289217 | ||||||||
\(261\) | −1.78376e6 | −1.62082 | ||||||||
\(262\) | −1.43746e6 | −1.29372 | ||||||||
\(263\) | 225880. | 0.201367 | 0.100684 | − | 0.994918i | \(-0.467897\pi\) | ||||
0.100684 | + | 0.994918i | \(0.467897\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 113525. | 0.0993065 | ||||||||
\(266\) | 689685. | 0.597650 | ||||||||
\(267\) | 1.06947e6 | 0.918097 | ||||||||
\(268\) | 184325. | 0.156764 | ||||||||
\(269\) | 1.80527e6 | 1.52111 | 0.760557 | − | 0.649272i | \(-0.224926\pi\) | ||||
0.760557 | + | 0.649272i | \(0.224926\pi\) | |||||||
\(270\) | 1.04891e6 | 0.875643 | ||||||||
\(271\) | 1.71380e6 | 1.41754 | 0.708771 | − | 0.705439i | \(-0.249250\pi\) | ||||
0.708771 | + | 0.705439i | \(0.249250\pi\) | |||||||
\(272\) | 527765. | 0.432532 | ||||||||
\(273\) | −377852. | −0.306842 | ||||||||
\(274\) | 16466.6 | 0.0132504 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.98267e6 | −2.35685 | ||||||||
\(277\) | −2.23055e6 | −1.74668 | −0.873338 | − | 0.487115i | \(-0.838049\pi\) | ||||
−0.873338 | + | 0.487115i | \(0.838049\pi\) | |||||||
\(278\) | 3.03200e6 | 2.35298 | ||||||||
\(279\) | 841600. | 0.647285 | ||||||||
\(280\) | 52156.2 | 0.0397567 | ||||||||
\(281\) | −1.67140e6 | −1.26274 | −0.631371 | − | 0.775481i | \(-0.717507\pi\) | ||||
−0.631371 | + | 0.775481i | \(0.717507\pi\) | |||||||
\(282\) | 4.24461e6 | 3.17845 | ||||||||
\(283\) | 396152. | 0.294033 | 0.147016 | − | 0.989134i | \(-0.453033\pi\) | ||||
0.147016 | + | 0.989134i | \(0.453033\pi\) | |||||||
\(284\) | 1.19830e6 | 0.881597 | ||||||||
\(285\) | −1.25428e6 | −0.914710 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −350164. | −0.250938 | ||||||||
\(288\) | 3.44691e6 | 2.44877 | ||||||||
\(289\) | −1.04396e6 | −0.735256 | ||||||||
\(290\) | 1.02279e6 | 0.714150 | ||||||||
\(291\) | −1.12044e6 | −0.775634 | ||||||||
\(292\) | 405410. | 0.278251 | ||||||||
\(293\) | 929465. | 0.632505 | 0.316252 | − | 0.948675i | \(-0.397575\pi\) | ||||
0.316252 | + | 0.948675i | \(0.397575\pi\) | |||||||
\(294\) | 509606. | 0.343848 | ||||||||
\(295\) | −854068. | −0.571397 | ||||||||
\(296\) | −190839. | −0.126601 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.16443e6 | 0.759582 | ||||||||
\(299\) | −958485. | −0.620022 | ||||||||
\(300\) | 2.15034e6 | 1.37944 | ||||||||
\(301\) | −959631. | −0.610503 | ||||||||
\(302\) | 414280. | 0.261383 | ||||||||
\(303\) | 657860. | 0.411649 | ||||||||
\(304\) | −1.46418e6 | −0.908682 | ||||||||
\(305\) | 1.45239e6 | 0.893990 | ||||||||
\(306\) | 2.10494e6 | 1.28510 | ||||||||
\(307\) | −1.83295e6 | −1.10995 | −0.554976 | − | 0.831866i | \(-0.687273\pi\) | ||||
−0.554976 | + | 0.831866i | \(0.687273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 367302. | 0.218840 | ||||||||
\(310\) | −482563. | −0.285200 | ||||||||
\(311\) | −2.29685e6 | −1.34658 | −0.673289 | − | 0.739379i | \(-0.735119\pi\) | ||||
−0.673289 | + | 0.739379i | \(0.735119\pi\) | |||||||
\(312\) | −285502. | −0.166044 | ||||||||
\(313\) | −3.42470e6 | −1.97589 | −0.987943 | − | 0.154817i | \(-0.950521\pi\) | ||||
−0.987943 | + | 0.154817i | \(0.950521\pi\) | |||||||
\(314\) | 743043. | 0.425295 | ||||||||
\(315\) | −584469. | −0.331883 | ||||||||
\(316\) | −2.98685e6 | −1.68266 | ||||||||
\(317\) | 2.94305e6 | 1.64494 | 0.822470 | − | 0.568808i | \(-0.192595\pi\) | ||||
0.822470 | + | 0.568808i | \(0.192595\pi\) | |||||||
\(318\) | 838127. | 0.464774 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.18450e6 | −0.646635 | ||||||||
\(321\) | 441217. | 0.238996 | ||||||||
\(322\) | 1.29270e6 | 0.694799 | ||||||||
\(323\) | −1.04286e6 | −0.556187 | ||||||||
\(324\) | 447560. | 0.236858 | ||||||||
\(325\) | 691016. | 0.362894 | ||||||||
\(326\) | 3.98214e6 | 2.07526 | ||||||||
\(327\) | −2.20631e6 | −1.14103 | ||||||||
\(328\) | −264582. | −0.135792 | ||||||||
\(329\) | −979921. | −0.499116 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 966164. | 0.484709 | 0.242354 | − | 0.970188i | \(-0.422080\pi\) | ||||
0.242354 | + | 0.970188i | \(0.422080\pi\) | |||||||
\(332\) | −4.31250e6 | −2.14725 | ||||||||
\(333\) | 2.13857e6 | 1.05685 | ||||||||
\(334\) | −716382. | −0.351381 | ||||||||
\(335\) | 145286. | 0.0707312 | ||||||||
\(336\) | −1.08188e6 | −0.522795 | ||||||||
\(337\) | −136417. | −0.0654327 | −0.0327163 | − | 0.999465i | \(-0.510416\pi\) | ||||
−0.0327163 | + | 0.999465i | \(0.510416\pi\) | |||||||
\(338\) | 2.32450e6 | 1.10672 | ||||||||
\(339\) | −3.52854e6 | −1.66761 | ||||||||
\(340\) | −642906. | −0.301613 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.83976e6 | −2.69979 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | −725091. | −0.330367 | ||||||||
\(345\) | −2.35095e6 | −1.06340 | ||||||||
\(346\) | −481082. | −0.216038 | ||||||||
\(347\) | −355408. | −0.158454 | −0.0792270 | − | 0.996857i | \(-0.525245\pi\) | ||||
−0.0792270 | + | 0.996857i | \(0.525245\pi\) | |||||||
\(348\) | 4.02218e6 | 1.78038 | ||||||||
\(349\) | 140128. | 0.0615830 | 0.0307915 | − | 0.999526i | \(-0.490197\pi\) | ||||
0.0307915 | + | 0.999526i | \(0.490197\pi\) | |||||||
\(350\) | −931969. | −0.406660 | ||||||||
\(351\) | 1.32554e6 | 0.574283 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.48141e6 | 1.48703 | 0.743514 | − | 0.668721i | \(-0.233158\pi\) | ||||
0.743514 | + | 0.668721i | \(0.233158\pi\) | |||||||
\(354\) | −6.30536e6 | −2.67425 | ||||||||
\(355\) | 944507. | 0.397772 | ||||||||
\(356\) | −1.52081e6 | −0.635988 | ||||||||
\(357\) | −770568. | −0.319993 | ||||||||
\(358\) | 1.73260e6 | 0.714482 | ||||||||
\(359\) | −1.75285e6 | −0.717810 | −0.358905 | − | 0.933374i | \(-0.616850\pi\) | ||||
−0.358905 | + | 0.933374i | \(0.616850\pi\) | |||||||
\(360\) | −441621. | −0.179595 | ||||||||
\(361\) | 417127. | 0.168461 | ||||||||
\(362\) | −2.30867e6 | −0.925955 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 537315. | 0.212557 | ||||||||
\(365\) | 319546. | 0.125546 | ||||||||
\(366\) | 1.07226e7 | 4.18405 | ||||||||
\(367\) | −1.76939e6 | −0.685738 | −0.342869 | − | 0.939383i | \(-0.611399\pi\) | ||||
−0.342869 | + | 0.939383i | \(0.611399\pi\) | |||||||
\(368\) | −2.74438e6 | −1.05639 | ||||||||
\(369\) | 2.96494e6 | 1.13357 | ||||||||
\(370\) | −1.22623e6 | −0.465658 | ||||||||
\(371\) | −193492. | −0.0729841 | ||||||||
\(372\) | −1.89771e6 | −0.711006 | ||||||||
\(373\) | 4.16212e6 | 1.54897 | 0.774485 | − | 0.632592i | \(-0.218009\pi\) | ||||
0.774485 | + | 0.632592i | \(0.218009\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.99929e6 | 1.46860 | ||||||||
\(376\) | −740422. | −0.270091 | ||||||||
\(377\) | 1.29253e6 | 0.468369 | ||||||||
\(378\) | −1.78775e6 | −0.643543 | ||||||||
\(379\) | 618163. | 0.221057 | 0.110529 | − | 0.993873i | \(-0.464746\pi\) | ||||
0.110529 | + | 0.993873i | \(0.464746\pi\) | |||||||
\(380\) | 1.78362e6 | 0.633642 | ||||||||
\(381\) | −1.81001e6 | −0.638805 | ||||||||
\(382\) | 3.68343e6 | 1.29150 | ||||||||
\(383\) | −4.11163e6 | −1.43225 | −0.716123 | − | 0.697974i | \(-0.754085\pi\) | ||||
−0.716123 | + | 0.697974i | \(0.754085\pi\) | |||||||
\(384\) | −1.92587e6 | −0.666498 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.01430e6 | −2.05455 | ||||||||
\(387\) | 8.12547e6 | 2.75785 | ||||||||
\(388\) | 1.59330e6 | 0.537301 | ||||||||
\(389\) | 4.62076e6 | 1.54824 | 0.774122 | − | 0.633037i | \(-0.218192\pi\) | ||||
0.774122 | + | 0.633037i | \(0.218192\pi\) | |||||||
\(390\) | −1.83448e6 | −0.610735 | ||||||||
\(391\) | −1.95468e6 | −0.646596 | ||||||||
\(392\) | −88894.8 | −0.0292187 | ||||||||
\(393\) | −4.45564e6 | −1.45522 | ||||||||
\(394\) | −3.01949e6 | −0.979926 | ||||||||
\(395\) | −2.35425e6 | −0.759207 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.07349e6 | 1.61559 | 0.807794 | − | 0.589465i | \(-0.200661\pi\) | ||||
0.807794 | + | 0.589465i | \(0.200661\pi\) | |||||||
\(398\) | −2.39399e6 | −0.757557 | ||||||||
\(399\) | 2.13780e6 | 0.672255 | ||||||||
\(400\) | 1.97855e6 | 0.618296 | ||||||||
\(401\) | −1.48056e6 | −0.459795 | −0.229898 | − | 0.973215i | \(-0.573839\pi\) | ||||
−0.229898 | + | 0.973215i | \(0.573839\pi\) | |||||||
\(402\) | 1.07261e6 | 0.331036 | ||||||||
\(403\) | −609834. | −0.187046 | ||||||||
\(404\) | −935495. | −0.285160 | ||||||||
\(405\) | 352768. | 0.106869 | ||||||||
\(406\) | −1.74323e6 | −0.524856 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −582236. | −0.173160 | ||||||||
\(409\) | 4.53379e6 | 1.34015 | 0.670075 | − | 0.742294i | \(-0.266262\pi\) | ||||
0.670075 | + | 0.742294i | \(0.266262\pi\) | |||||||
\(410\) | −1.70006e6 | −0.499465 | ||||||||
\(411\) | 51041.0 | 0.0149044 | ||||||||
\(412\) | −522313. | −0.151596 | ||||||||
\(413\) | 1.45567e6 | 0.419941 | ||||||||
\(414\) | −1.09457e7 | −3.13865 | ||||||||
\(415\) | −3.39913e6 | −0.968829 | ||||||||
\(416\) | −2.49767e6 | −0.707623 | ||||||||
\(417\) | 9.39820e6 | 2.64670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 111026. | 0.0308952 | 0.0154476 | − | 0.999881i | \(-0.495083\pi\) | ||||
0.0154476 | + | 0.999881i | \(0.495083\pi\) | |||||||
\(420\) | 1.31791e6 | 0.364555 | ||||||||
\(421\) | −1.41151e6 | −0.388132 | −0.194066 | − | 0.980988i | \(-0.562168\pi\) | ||||
−0.194066 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(422\) | 6.20740e6 | 1.69679 | ||||||||
\(423\) | 8.29727e6 | 2.25468 | ||||||||
\(424\) | −146201. | −0.0394945 | ||||||||
\(425\) | 1.40922e6 | 0.378447 | ||||||||
\(426\) | 6.97304e6 | 1.86165 | ||||||||
\(427\) | −2.47544e6 | −0.657027 | ||||||||
\(428\) | −627422. | −0.165558 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.65905e6 | −1.21514 | ||||||||
\(431\) | −1.07640e6 | −0.279113 | −0.139557 | − | 0.990214i | \(-0.544568\pi\) | ||||
−0.139557 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(432\) | 3.79535e6 | 0.978459 | ||||||||
\(433\) | −310172. | −0.0795029 | −0.0397515 | − | 0.999210i | \(-0.512657\pi\) | ||||
−0.0397515 | + | 0.999210i | \(0.512657\pi\) | |||||||
\(434\) | 822480. | 0.209605 | ||||||||
\(435\) | 3.17030e6 | 0.803298 | ||||||||
\(436\) | 3.13743e6 | 0.790419 | ||||||||
\(437\) | 5.42288e6 | 1.35840 | ||||||||
\(438\) | 2.35912e6 | 0.587578 | ||||||||
\(439\) | −5.67650e6 | −1.40579 | −0.702893 | − | 0.711296i | \(-0.748109\pi\) | ||||
−0.702893 | + | 0.711296i | \(0.748109\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 996168. | 0.243914 | ||||||||
\(442\) | −1.52527e6 | −0.371356 | ||||||||
\(443\) | 4.05966e6 | 0.982834 | 0.491417 | − | 0.870924i | \(-0.336479\pi\) | ||||
0.491417 | + | 0.870924i | \(0.336479\pi\) | |||||||
\(444\) | −4.82223e6 | −1.16089 | ||||||||
\(445\) | −1.19871e6 | −0.286955 | ||||||||
\(446\) | −4.42210e6 | −1.05267 | ||||||||
\(447\) | 3.60936e6 | 0.854401 | ||||||||
\(448\) | 2.01885e6 | 0.475237 | ||||||||
\(449\) | −6.96544e6 | −1.63054 | −0.815272 | − | 0.579078i | \(-0.803413\pi\) | ||||
−0.815272 | + | 0.579078i | \(0.803413\pi\) | |||||||
\(450\) | 7.89125e6 | 1.83702 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.01767e6 | 1.15520 | ||||||||
\(453\) | 1.28413e6 | 0.294011 | ||||||||
\(454\) | −3.39788e6 | −0.773692 | ||||||||
\(455\) | 423514. | 0.0959045 | ||||||||
\(456\) | 1.61530e6 | 0.363783 | ||||||||
\(457\) | −1.79523e6 | −0.402096 | −0.201048 | − | 0.979581i | \(-0.564435\pi\) | ||||
−0.201048 | + | 0.979581i | \(0.564435\pi\) | |||||||
\(458\) | −8.52616e6 | −1.89928 | ||||||||
\(459\) | 2.70323e6 | 0.598896 | ||||||||
\(460\) | 3.34311e6 | 0.736642 | ||||||||
\(461\) | 2.11294e6 | 0.463058 | 0.231529 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231529 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.26223e6 | 0.273643 | 0.136822 | − | 0.990596i | \(-0.456311\pi\) | ||||
0.136822 | + | 0.990596i | \(0.456311\pi\) | |||||||
\(464\) | 3.70084e6 | 0.798005 | ||||||||
\(465\) | −1.49579e6 | −0.320802 | ||||||||
\(466\) | −986462. | −0.210434 | ||||||||
\(467\) | −3.58926e6 | −0.761576 | −0.380788 | − | 0.924662i | \(-0.624347\pi\) | ||||
−0.380788 | + | 0.924662i | \(0.624347\pi\) | |||||||
\(468\) | −4.54960e6 | −0.960192 | ||||||||
\(469\) | −247624. | −0.0519830 | ||||||||
\(470\) | −4.75756e6 | −0.993435 | ||||||||
\(471\) | 2.30319e6 | 0.478384 | ||||||||
\(472\) | 1.09990e6 | 0.227246 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.73808e7 | −3.55324 | ||||||||
\(475\) | −3.90960e6 | −0.795058 | ||||||||
\(476\) | 1.09577e6 | 0.221667 | ||||||||
\(477\) | 1.63835e6 | 0.329694 | ||||||||
\(478\) | −2.10257e6 | −0.420903 | ||||||||
\(479\) | 2.41693e6 | 0.481311 | 0.240655 | − | 0.970611i | \(-0.422638\pi\) | ||||
0.240655 | + | 0.970611i | \(0.422638\pi\) | |||||||
\(480\) | −6.12623e6 | −1.21364 | ||||||||
\(481\) | −1.54963e6 | −0.305398 | ||||||||
\(482\) | 1.16884e7 | 2.29159 | ||||||||
\(483\) | 4.00695e6 | 0.781531 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.25584e6 | 0.242427 | ||||||||
\(486\) | −6.26139e6 | −1.20249 | ||||||||
\(487\) | −5.19403e6 | −0.992388 | −0.496194 | − | 0.868212i | \(-0.665270\pi\) | ||||
−0.496194 | + | 0.868212i | \(0.665270\pi\) | |||||||
\(488\) | −1.87043e6 | −0.355543 | ||||||||
\(489\) | 1.23433e7 | 2.33432 | ||||||||
\(490\) | −571191. | −0.107471 | ||||||||
\(491\) | −5.38961e6 | −1.00891 | −0.504456 | − | 0.863437i | \(-0.668307\pi\) | ||||
−0.504456 | + | 0.863437i | \(0.668307\pi\) | |||||||
\(492\) | −6.68561e6 | −1.24517 | ||||||||
\(493\) | 2.63592e6 | 0.488443 | ||||||||
\(494\) | 4.23156e6 | 0.780160 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.74610e6 | −0.318688 | ||||||||
\(497\) | −1.60981e6 | −0.292338 | ||||||||
\(498\) | −2.50949e7 | −4.53431 | ||||||||
\(499\) | −3.29606e6 | −0.592576 | −0.296288 | − | 0.955099i | \(-0.595749\pi\) | ||||
−0.296288 | + | 0.955099i | \(0.595749\pi\) | |||||||
\(500\) | −5.68709e6 | −1.01734 | ||||||||
\(501\) | −2.22055e6 | −0.395244 | ||||||||
\(502\) | 1.38640e7 | 2.45544 | ||||||||
\(503\) | 1.06512e7 | 1.87706 | 0.938528 | − | 0.345204i | \(-0.112190\pi\) | ||||
0.938528 | + | 0.345204i | \(0.112190\pi\) | |||||||
\(504\) | 752698. | 0.131991 | ||||||||
\(505\) | −737361. | −0.128662 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.20517e6 | 1.24487 | ||||||||
\(508\) | 2.57388e6 | 0.442516 | ||||||||
\(509\) | −2.74268e6 | −0.469225 | −0.234612 | − | 0.972089i | \(-0.575382\pi\) | ||||
−0.234612 | + | 0.972089i | \(0.575382\pi\) | |||||||
\(510\) | −3.74114e6 | −0.636910 | ||||||||
\(511\) | −544633. | −0.0922682 | ||||||||
\(512\) | −8.17130e6 | −1.37758 | ||||||||
\(513\) | −7.49961e6 | −1.25819 | ||||||||
\(514\) | −6.01583e6 | −1.00436 | ||||||||
\(515\) | −411689. | −0.0683992 | ||||||||
\(516\) | −1.83220e7 | −3.02935 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.08998e6 | 0.342230 | ||||||||
\(519\) | −1.49120e6 | −0.243006 | ||||||||
\(520\) | 320004. | 0.0518976 | ||||||||
\(521\) | 4.97077e6 | 0.802286 | 0.401143 | − | 0.916015i | \(-0.368613\pi\) | ||||
0.401143 | + | 0.916015i | \(0.368613\pi\) | |||||||
\(522\) | 1.47605e7 | 2.37096 | ||||||||
\(523\) | −2.41579e6 | −0.386193 | −0.193096 | − | 0.981180i | \(-0.561853\pi\) | ||||
−0.193096 | + | 0.981180i | \(0.561853\pi\) | |||||||
\(524\) | 6.33603e6 | 1.00807 | ||||||||
\(525\) | −2.88880e6 | −0.457424 | ||||||||
\(526\) | −1.86914e6 | −0.294563 | ||||||||
\(527\) | −1.24366e6 | −0.195063 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.72798e6 | 0.579207 | ||||||||
\(530\) | −939412. | −0.145267 | ||||||||
\(531\) | −1.23256e7 | −1.89702 | ||||||||
\(532\) | −3.04000e6 | −0.465688 | ||||||||
\(533\) | −2.14843e6 | −0.327570 | ||||||||
\(534\) | −8.84974e6 | −1.34300 | ||||||||
\(535\) | −494537. | −0.0746989 | ||||||||
\(536\) | −187103. | −0.0281300 | ||||||||
\(537\) | 5.37050e6 | 0.803672 | ||||||||
\(538\) | −1.49385e7 | −2.22510 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.62337e6 | −0.682299 | ||||||||
\(541\) | −472165. | −0.0693587 | −0.0346794 | − | 0.999398i | \(-0.511041\pi\) | ||||
−0.0346794 | + | 0.999398i | \(0.511041\pi\) | |||||||
\(542\) | −1.41815e7 | −2.07360 | ||||||||
\(543\) | −7.15610e6 | −1.04154 | ||||||||
\(544\) | −5.09360e6 | −0.737951 | ||||||||
\(545\) | 2.47293e6 | 0.356633 | ||||||||
\(546\) | 3.12669e6 | 0.448852 | ||||||||
\(547\) | −7.63716e6 | −1.09135 | −0.545675 | − | 0.837997i | \(-0.683727\pi\) | ||||
−0.545675 | + | 0.837997i | \(0.683727\pi\) | |||||||
\(548\) | −72581.6 | −0.0103246 | ||||||||
\(549\) | 2.09603e7 | 2.96802 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.31285e6 | −1.02614 | ||||||||
\(552\) | 3.02763e6 | 0.422917 | ||||||||
\(553\) | 4.01258e6 | 0.557970 | ||||||||
\(554\) | 1.84576e7 | 2.55506 | ||||||||
\(555\) | −3.80091e6 | −0.523787 | ||||||||
\(556\) | −1.33645e7 | −1.83343 | ||||||||
\(557\) | 4.48807e6 | 0.612946 | 0.306473 | − | 0.951879i | \(-0.400851\pi\) | ||||
0.306473 | + | 0.951879i | \(0.400851\pi\) | |||||||
\(558\) | −6.96417e6 | −0.946856 | ||||||||
\(559\) | −5.88782e6 | −0.796938 | ||||||||
\(560\) | 1.21262e6 | 0.163402 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.38307e7 | 1.84715 | ||||||||
\(563\) | 2.16500e6 | 0.287864 | 0.143932 | − | 0.989588i | \(-0.454025\pi\) | ||||
0.143932 | + | 0.989588i | \(0.454025\pi\) | |||||||
\(564\) | −1.87094e7 | −2.47664 | ||||||||
\(565\) | 3.95495e6 | 0.521219 | ||||||||
\(566\) | −3.27812e6 | −0.430115 | ||||||||
\(567\) | −601258. | −0.0785422 | ||||||||
\(568\) | −1.21637e6 | −0.158195 | ||||||||
\(569\) | 1.13325e7 | 1.46739 | 0.733696 | − | 0.679478i | \(-0.237794\pi\) | ||||
0.733696 | + | 0.679478i | \(0.237794\pi\) | |||||||
\(570\) | 1.03791e7 | 1.33805 | ||||||||
\(571\) | 843773. | 0.108302 | 0.0541509 | − | 0.998533i | \(-0.482755\pi\) | ||||
0.0541509 | + | 0.998533i | \(0.482755\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.14174e7 | 1.45272 | ||||||||
\(574\) | 2.89758e6 | 0.367076 | ||||||||
\(575\) | −7.32792e6 | −0.924296 | ||||||||
\(576\) | −1.70942e7 | −2.14681 | ||||||||
\(577\) | −2.23784e6 | −0.279827 | −0.139914 | − | 0.990164i | \(-0.544682\pi\) | ||||
−0.139914 | + | 0.990164i | \(0.544682\pi\) | |||||||
\(578\) | 8.63866e6 | 1.07554 | ||||||||
\(579\) | −1.86423e7 | −2.31102 | ||||||||
\(580\) | −4.50824e6 | −0.556464 | ||||||||
\(581\) | 5.79346e6 | 0.712029 | ||||||||
\(582\) | 9.27156e6 | 1.13461 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −411521. | −0.0499299 | ||||||||
\(585\) | −3.58601e6 | −0.433234 | ||||||||
\(586\) | −7.69124e6 | −0.925236 | ||||||||
\(587\) | 1.21190e7 | 1.45168 | 0.725839 | − | 0.687864i | \(-0.241452\pi\) | ||||
0.725839 | + | 0.687864i | \(0.241452\pi\) | |||||||
\(588\) | −2.24625e6 | −0.267926 | ||||||||
\(589\) | 3.45030e6 | 0.409797 | ||||||||
\(590\) | 7.06734e6 | 0.835846 | ||||||||
\(591\) | −9.35942e6 | −1.10225 | ||||||||
\(592\) | −4.43698e6 | −0.520335 | ||||||||
\(593\) | −8.00167e6 | −0.934424 | −0.467212 | − | 0.884145i | \(-0.654742\pi\) | ||||
−0.467212 | + | 0.884145i | \(0.654742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 863689. | 0.100015 | ||||||||
\(596\) | −5.13261e6 | −0.591865 | ||||||||
\(597\) | −7.42058e6 | −0.852123 | ||||||||
\(598\) | 7.93138e6 | 0.906976 | ||||||||
\(599\) | 1.45899e7 | 1.66144 | 0.830719 | − | 0.556692i | \(-0.187930\pi\) | ||||
0.830719 | + | 0.556692i | \(0.187930\pi\) | |||||||
\(600\) | −2.18276e6 | −0.247529 | ||||||||
\(601\) | 8.67178e6 | 0.979314 | 0.489657 | − | 0.871915i | \(-0.337122\pi\) | ||||
0.489657 | + | 0.871915i | \(0.337122\pi\) | |||||||
\(602\) | 7.94087e6 | 0.893052 | ||||||||
\(603\) | 2.09671e6 | 0.234825 | ||||||||
\(604\) | −1.82607e6 | −0.203669 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.44374e6 | −0.602166 | ||||||||
\(607\) | 1.33059e7 | 1.46580 | 0.732898 | − | 0.680339i | \(-0.238167\pi\) | ||||
0.732898 | + | 0.680339i | \(0.238167\pi\) | |||||||
\(608\) | 1.41312e7 | 1.55032 | ||||||||
\(609\) | −5.40344e6 | −0.590374 | ||||||||
\(610\) | −1.20184e7 | −1.30774 | ||||||||
\(611\) | −6.01231e6 | −0.651536 | ||||||||
\(612\) | −9.27817e6 | −1.00135 | ||||||||
\(613\) | −2.35101e6 | −0.252699 | −0.126350 | − | 0.991986i | \(-0.540326\pi\) | ||||
−0.126350 | + | 0.991986i | \(0.540326\pi\) | |||||||
\(614\) | 1.51675e7 | 1.62365 | ||||||||
\(615\) | −5.26963e6 | −0.561814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.63523e6 | 1.01894 | 0.509470 | − | 0.860488i | \(-0.329841\pi\) | ||||
0.509470 | + | 0.860488i | \(0.329841\pi\) | |||||||
\(618\) | −3.03939e6 | −0.320122 | ||||||||
\(619\) | −4.86148e6 | −0.509967 | −0.254983 | − | 0.966945i | \(-0.582070\pi\) | ||||
−0.254983 | + | 0.966945i | \(0.582070\pi\) | |||||||
\(620\) | 2.12705e6 | 0.222228 | ||||||||
\(621\) | −1.40568e7 | −1.46271 | ||||||||
\(622\) | 1.90062e7 | 1.96979 | ||||||||
\(623\) | 2.04307e6 | 0.210894 | ||||||||
\(624\) | −6.63789e6 | −0.682446 | ||||||||
\(625\) | 2.70017e6 | 0.276498 | ||||||||
\(626\) | 2.83391e7 | 2.89035 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.27519e6 | −0.331389 | ||||||||
\(629\) | −3.16023e6 | −0.318487 | ||||||||
\(630\) | 4.83644e6 | 0.485483 | ||||||||
\(631\) | −6.59770e6 | −0.659659 | −0.329829 | − | 0.944041i | \(-0.606991\pi\) | ||||
−0.329829 | + | 0.944041i | \(0.606991\pi\) | |||||||
\(632\) | 3.03188e6 | 0.301939 | ||||||||
\(633\) | 1.92409e7 | 1.90860 | ||||||||
\(634\) | −2.43535e7 | −2.40624 | ||||||||
\(635\) | 2.02874e6 | 0.199661 | ||||||||
\(636\) | −3.69430e6 | −0.362151 | ||||||||
\(637\) | −721836. | −0.0704839 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.36308e7 | 1.32059 | ||||||||
\(640\) | 2.15861e6 | 0.208317 | ||||||||
\(641\) | 1.44525e7 | 1.38930 | 0.694651 | − | 0.719347i | \(-0.255559\pi\) | ||||
0.694651 | + | 0.719347i | \(0.255559\pi\) | |||||||
\(642\) | −3.65104e6 | −0.349606 | ||||||||
\(643\) | −1.54720e7 | −1.47577 | −0.737886 | − | 0.674926i | \(-0.764176\pi\) | ||||
−0.737886 | + | 0.674926i | \(0.764176\pi\) | |||||||
\(644\) | −5.69799e6 | −0.541386 | ||||||||
\(645\) | −1.44415e7 | −1.36683 | ||||||||
\(646\) | 8.62960e6 | 0.813597 | ||||||||
\(647\) | 1.66647e7 | 1.56508 | 0.782540 | − | 0.622601i | \(-0.213924\pi\) | ||||
0.782540 | + | 0.622601i | \(0.213924\pi\) | |||||||
\(648\) | −454306. | −0.0425022 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.71810e6 | −0.530845 | ||||||||
\(651\) | 2.54941e6 | 0.235770 | ||||||||
\(652\) | −1.75525e7 | −1.61704 | ||||||||
\(653\) | −1.33451e7 | −1.22472 | −0.612361 | − | 0.790578i | \(-0.709780\pi\) | ||||
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(654\) | 1.82570e7 | 1.66911 | ||||||||
\(655\) | 4.99409e6 | 0.454834 | ||||||||
\(656\) | −6.15149e6 | −0.558111 | ||||||||
\(657\) | 4.61157e6 | 0.416807 | ||||||||
\(658\) | 8.10877e6 | 0.730113 | ||||||||
\(659\) | 4.00667e6 | 0.359393 | 0.179697 | − | 0.983722i | \(-0.442488\pi\) | ||||
0.179697 | + | 0.983722i | \(0.442488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.08005e7 | 0.961478 | 0.480739 | − | 0.876864i | \(-0.340368\pi\) | ||||
0.480739 | + | 0.876864i | \(0.340368\pi\) | |||||||
\(662\) | −7.99493e6 | −0.709038 | ||||||||
\(663\) | −4.72782e6 | −0.417712 | ||||||||
\(664\) | 4.37750e6 | 0.385307 | ||||||||
\(665\) | −2.39614e6 | −0.210116 | ||||||||
\(666\) | −1.76965e7 | −1.54597 | ||||||||
\(667\) | −1.37068e7 | −1.19294 | ||||||||
\(668\) | 3.15767e6 | 0.273795 | ||||||||
\(669\) | −1.37070e7 | −1.18407 | ||||||||
\(670\) | −1.20223e6 | −0.103466 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.04415e7 | 0.891951 | ||||||||
\(673\) | −1.09119e7 | −0.928676 | −0.464338 | − | 0.885658i | \(-0.653708\pi\) | ||||
−0.464338 | + | 0.885658i | \(0.653708\pi\) | |||||||
\(674\) | 1.12884e6 | 0.0957158 | ||||||||
\(675\) | 1.01342e7 | 0.856110 | ||||||||
\(676\) | −1.02459e7 | −0.862353 | ||||||||
\(677\) | 1.35765e7 | 1.13846 | 0.569229 | − | 0.822179i | \(-0.307242\pi\) | ||||
0.569229 | + | 0.822179i | \(0.307242\pi\) | |||||||
\(678\) | 2.91984e7 | 2.43941 | ||||||||
\(679\) | −2.14046e6 | −0.178169 | ||||||||
\(680\) | 652598. | 0.0541219 | ||||||||
\(681\) | −1.05323e7 | −0.870272 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.26726e7 | −1.03948 | −0.519738 | − | 0.854326i | \(-0.673970\pi\) | ||||
−0.519738 | + | 0.854326i | \(0.673970\pi\) | |||||||
\(684\) | 2.57406e7 | 2.10367 | ||||||||
\(685\) | −57209.2 | −0.00465843 | ||||||||
\(686\) | 973536. | 0.0789845 | ||||||||
\(687\) | −2.64283e7 | −2.13637 | ||||||||
\(688\) | −1.68583e7 | −1.35782 | ||||||||
\(689\) | −1.18717e6 | −0.0952720 | ||||||||
\(690\) | 1.94539e7 | 1.55555 | ||||||||
\(691\) | 7.11964e6 | 0.567235 | 0.283617 | − | 0.958938i | \(-0.408465\pi\) | ||||
0.283617 | + | 0.958938i | \(0.408465\pi\) | |||||||
\(692\) | 2.12052e6 | 0.168336 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.94097e6 | 0.231789 | ||||||||
\(695\) | −1.05339e7 | −0.827235 | ||||||||
\(696\) | −4.08281e6 | −0.319474 | ||||||||
\(697\) | −4.38139e6 | −0.341609 | ||||||||
\(698\) | −1.15955e6 | −0.0900844 | ||||||||
\(699\) | −3.05770e6 | −0.236702 | ||||||||
\(700\) | 4.10794e6 | 0.316869 | ||||||||
\(701\) | 1.00155e7 | 0.769803 | 0.384902 | − | 0.922958i | \(-0.374235\pi\) | ||||
0.384902 | + | 0.922958i | \(0.374235\pi\) | |||||||
\(702\) | −1.09687e7 | −0.840068 | ||||||||
\(703\) | 8.76746e6 | 0.669092 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.47469e7 | −1.11745 | ||||||||
\(706\) | −2.88084e7 | −2.17524 | ||||||||
\(707\) | 1.25676e6 | 0.0945589 | ||||||||
\(708\) | 2.77928e7 | 2.08377 | ||||||||
\(709\) | −8.84454e6 | −0.660784 | −0.330392 | − | 0.943844i | \(-0.607181\pi\) | ||||
−0.330392 | + | 0.943844i | \(0.607181\pi\) | |||||||
\(710\) | −7.81571e6 | −0.581866 | ||||||||
\(711\) | −3.39757e7 | −2.52054 | ||||||||
\(712\) | 1.54373e6 | 0.114123 | ||||||||
\(713\) | 6.46703e6 | 0.476410 | ||||||||
\(714\) | 6.37638e6 | 0.468090 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.63698e6 | −0.556723 | ||||||||
\(717\) | −6.51728e6 | −0.473444 | ||||||||
\(718\) | 1.45047e7 | 1.05002 | ||||||||
\(719\) | 6.58086e6 | 0.474745 | 0.237373 | − | 0.971419i | \(-0.423714\pi\) | ||||
0.237373 | + | 0.971419i | \(0.423714\pi\) | |||||||
\(720\) | −1.02676e7 | −0.738141 | ||||||||
\(721\) | 701682. | 0.0502692 | ||||||||
\(722\) | −3.45169e6 | −0.246427 | ||||||||
\(723\) | 3.62301e7 | 2.57765 | ||||||||
\(724\) | 1.01762e7 | 0.721502 | ||||||||
\(725\) | 9.88183e6 | 0.698220 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.88401e7 | 1.32205 | 0.661023 | − | 0.750365i | \(-0.270122\pi\) | ||||
0.661023 | + | 0.750365i | \(0.270122\pi\) | |||||||
\(728\) | −545414. | −0.0381415 | ||||||||
\(729\) | −2.23900e7 | −1.56040 | ||||||||
\(730\) | −2.64422e6 | −0.183650 | ||||||||
\(731\) | −1.20073e7 | −0.831095 | ||||||||
\(732\) | −4.72631e7 | −3.26020 | ||||||||
\(733\) | 2.78330e6 | 0.191337 | 0.0956687 | − | 0.995413i | \(-0.469501\pi\) | ||||
0.0956687 | + | 0.995413i | \(0.469501\pi\) | |||||||
\(734\) | 1.46416e7 | 1.00311 | ||||||||
\(735\) | −1.77050e6 | −0.120887 | ||||||||
\(736\) | 2.64867e7 | 1.80233 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −2.45346e7 | −1.65821 | ||||||||
\(739\) | 2.48970e7 | 1.67701 | 0.838505 | − | 0.544894i | \(-0.183430\pi\) | ||||
0.838505 | + | 0.544894i | \(0.183430\pi\) | |||||||
\(740\) | 5.40499e6 | 0.362840 | ||||||||
\(741\) | 1.31164e7 | 0.877548 | ||||||||
\(742\) | 1.60113e6 | 0.106762 | ||||||||
\(743\) | 3.86085e6 | 0.256573 | 0.128286 | − | 0.991737i | \(-0.459052\pi\) | ||||
0.128286 | + | 0.991737i | \(0.459052\pi\) | |||||||
\(744\) | 1.92632e6 | 0.127584 | ||||||||
\(745\) | −4.04554e6 | −0.267046 | ||||||||
\(746\) | −3.44412e7 | −2.26585 | ||||||||
\(747\) | −4.90549e7 | −3.21648 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 842888. | 0.0548991 | ||||||||
\(750\) | −3.30938e7 | −2.14829 | ||||||||
\(751\) | 6.72737e6 | 0.435257 | 0.217628 | − | 0.976032i | \(-0.430168\pi\) | ||||
0.217628 | + | 0.976032i | \(0.430168\pi\) | |||||||
\(752\) | −1.72147e7 | −1.11008 | ||||||||
\(753\) | 4.29737e7 | 2.76195 | ||||||||
\(754\) | −1.06956e7 | −0.685136 | ||||||||
\(755\) | −1.43932e6 | −0.0918943 | ||||||||
\(756\) | 7.88007e6 | 0.501447 | ||||||||
\(757\) | 2.17782e7 | 1.38128 | 0.690642 | − | 0.723197i | \(-0.257328\pi\) | ||||
0.690642 | + | 0.723197i | \(0.257328\pi\) | |||||||
\(758\) | −5.11525e6 | −0.323366 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.81051e6 | −0.113702 | ||||||||
\(761\) | 2.57074e7 | 1.60915 | 0.804575 | − | 0.593851i | \(-0.202393\pi\) | ||||
0.804575 | + | 0.593851i | \(0.202393\pi\) | |||||||
\(762\) | 1.49777e7 | 0.934453 | ||||||||
\(763\) | −4.21486e6 | −0.262103 | ||||||||
\(764\) | −1.62359e7 | −1.00633 | ||||||||
\(765\) | −7.31310e6 | −0.451802 | ||||||||
\(766\) | 3.40234e7 | 2.09511 | ||||||||
\(767\) | 8.93127e6 | 0.548182 | ||||||||
\(768\) | −1.78808e7 | −1.09391 | ||||||||
\(769\) | 1.34375e7 | 0.819413 | 0.409706 | − | 0.912217i | \(-0.365631\pi\) | ||||
0.409706 | + | 0.912217i | \(0.365631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.86471e7 | −1.12973 | ||||||||
\(772\) | 2.65099e7 | 1.60090 | ||||||||
\(773\) | 3.05572e7 | 1.83935 | 0.919674 | − | 0.392682i | \(-0.128453\pi\) | ||||
0.919674 | + | 0.392682i | \(0.128453\pi\) | |||||||
\(774\) | −6.72376e7 | −4.03422 | ||||||||
\(775\) | −4.66237e6 | −0.278839 | ||||||||
\(776\) | −1.61731e6 | −0.0964140 | ||||||||
\(777\) | 6.47825e6 | 0.384951 | ||||||||
\(778\) | −3.82364e7 | −2.26479 | ||||||||
\(779\) | 1.21553e7 | 0.717667 | ||||||||
\(780\) | 8.08606e6 | 0.475883 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.61748e7 | 0.945849 | ||||||||
\(783\) | 1.89558e7 | 1.10494 | ||||||||
\(784\) | −2.06679e6 | −0.120090 | ||||||||
\(785\) | −2.58152e6 | −0.149521 | ||||||||
\(786\) | 3.68700e7 | 2.12871 | ||||||||
\(787\) | 2.07672e6 | 0.119520 | 0.0597602 | − | 0.998213i | \(-0.480966\pi\) | ||||
0.0597602 | + | 0.998213i | \(0.480966\pi\) | |||||||
\(788\) | 1.33093e7 | 0.763556 | ||||||||
\(789\) | −5.79372e6 | −0.331333 | ||||||||
\(790\) | 1.94812e7 | 1.11058 | ||||||||
\(791\) | −6.74081e6 | −0.383064 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.51881e7 | −0.857670 | ||||||||
\(794\) | −4.19827e7 | −2.36330 | ||||||||
\(795\) | −2.91187e6 | −0.163401 | ||||||||
\(796\) | 1.05523e7 | 0.590286 | ||||||||
\(797\) | −5.98563e6 | −0.333783 | −0.166892 | − | 0.985975i | \(-0.553373\pi\) | ||||
−0.166892 | + | 0.985975i | \(0.553373\pi\) | |||||||
\(798\) | −1.76901e7 | −0.983383 | ||||||||
\(799\) | −1.22611e7 | −0.679460 | ||||||||
\(800\) | −1.90955e7 | −1.05489 | ||||||||
\(801\) | −1.72993e7 | −0.952679 | ||||||||
\(802\) | 1.22515e7 | 0.672594 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.72784e6 | −0.257942 | ||||||||
\(805\) | −4.49118e6 | −0.244270 | ||||||||
\(806\) | 5.04633e6 | 0.273614 | ||||||||
\(807\) | −4.63043e7 | −2.50286 | ||||||||
\(808\) | 949597. | 0.0511695 | ||||||||
\(809\) | −1.96864e7 | −1.05754 | −0.528769 | − | 0.848766i | \(-0.677346\pi\) | ||||
−0.528769 | + | 0.848766i | \(0.677346\pi\) | |||||||
\(810\) | −2.91913e6 | −0.156329 | ||||||||
\(811\) | −8.50101e6 | −0.453856 | −0.226928 | − | 0.973912i | \(-0.572868\pi\) | ||||
−0.226928 | + | 0.973912i | \(0.572868\pi\) | |||||||
\(812\) | 7.68384e6 | 0.408967 | ||||||||
\(813\) | −4.39580e7 | −2.33245 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.38350e7 | −0.729599 | ||||||||
\(816\) | −1.35369e7 | −0.711695 | ||||||||
\(817\) | 3.33119e7 | 1.74600 | ||||||||
\(818\) | −3.75168e7 | −1.96039 | ||||||||
\(819\) | 6.11199e6 | 0.318400 | ||||||||
\(820\) | 7.49355e6 | 0.389182 | ||||||||
\(821\) | 1.36199e6 | 0.0705204 | 0.0352602 | − | 0.999378i | \(-0.488774\pi\) | ||||
0.0352602 | + | 0.999378i | \(0.488774\pi\) | |||||||
\(822\) | −422360. | −0.0218023 | ||||||||
\(823\) | −1.35934e6 | −0.0699566 | −0.0349783 | − | 0.999388i | \(-0.511136\pi\) | ||||
−0.0349783 | + | 0.999388i | \(0.511136\pi\) | |||||||
\(824\) | 530186. | 0.0272026 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.20456e7 | −0.614295 | ||||||||
\(827\) | −1.00727e7 | −0.512132 | −0.256066 | − | 0.966659i | \(-0.582426\pi\) | ||||
−0.256066 | + | 0.966659i | \(0.582426\pi\) | |||||||
\(828\) | 4.82465e7 | 2.44563 | ||||||||
\(829\) | −5.63984e6 | −0.285023 | −0.142512 | − | 0.989793i | \(-0.545518\pi\) | ||||
−0.142512 | + | 0.989793i | \(0.545518\pi\) | |||||||
\(830\) | 2.81275e7 | 1.41722 | ||||||||
\(831\) | 5.72125e7 | 2.87401 | ||||||||
\(832\) | 1.23867e7 | 0.620364 | ||||||||
\(833\) | −1.47207e6 | −0.0735048 | ||||||||
\(834\) | −7.77693e7 | −3.87163 | ||||||||
\(835\) | 2.48889e6 | 0.123535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.94361e6 | −0.441265 | ||||||||
\(838\) | −918733. | −0.0451938 | ||||||||
\(839\) | −1.16351e7 | −0.570642 | −0.285321 | − | 0.958432i | \(-0.592100\pi\) | ||||
−0.285321 | + | 0.958432i | \(0.592100\pi\) | |||||||
\(840\) | −1.33778e6 | −0.0654164 | ||||||||
\(841\) | −2.02735e6 | −0.0988413 | ||||||||
\(842\) | 1.16801e7 | 0.567764 | ||||||||
\(843\) | 4.28706e7 | 2.07774 | ||||||||
\(844\) | −2.73610e7 | −1.32214 | ||||||||
\(845\) | −8.07590e6 | −0.389089 | ||||||||
\(846\) | −6.86592e7 | −3.29817 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.39916e6 | −0.162324 | ||||||||
\(849\) | −1.01611e7 | −0.483806 | ||||||||
\(850\) | −1.16611e7 | −0.553597 | ||||||||
\(851\) | 1.64332e7 | 0.777854 | ||||||||
\(852\) | −3.07358e7 | −1.45059 | ||||||||
\(853\) | −2.85205e7 | −1.34210 | −0.671049 | − | 0.741413i | \(-0.734156\pi\) | ||||
−0.671049 | + | 0.741413i | \(0.734156\pi\) | |||||||
\(854\) | 2.04841e7 | 0.961108 | ||||||||
\(855\) | 2.02888e7 | 0.949165 | ||||||||
\(856\) | 636880. | 0.0297080 | ||||||||
\(857\) | 9.95725e6 | 0.463113 | 0.231557 | − | 0.972821i | \(-0.425618\pi\) | ||||
0.231557 | + | 0.972821i | \(0.425618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.49322e7 | −0.690463 | −0.345232 | − | 0.938517i | \(-0.612200\pi\) | ||||
−0.345232 | + | 0.938517i | \(0.612200\pi\) | |||||||
\(860\) | 2.05362e7 | 0.946834 | ||||||||
\(861\) | 8.98154e6 | 0.412898 | ||||||||
\(862\) | 8.90711e6 | 0.408290 | ||||||||
\(863\) | 3.84933e7 | 1.75937 | 0.879687 | − | 0.475553i | \(-0.157752\pi\) | ||||
0.879687 | + | 0.475553i | \(0.157752\pi\) | |||||||
\(864\) | −3.66300e7 | −1.66937 | ||||||||
\(865\) | 1.67140e6 | 0.0759523 | ||||||||
\(866\) | 2.56665e6 | 0.116298 | ||||||||
\(867\) | 2.67770e7 | 1.20980 | ||||||||
\(868\) | −3.62533e6 | −0.163323 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.62339e7 | −1.17507 | ||||||||
\(871\) | −1.51930e6 | −0.0678576 | ||||||||
\(872\) | −3.18472e6 | −0.141834 | ||||||||
\(873\) | 1.81239e7 | 0.804850 | ||||||||
\(874\) | −4.48739e7 | −1.98708 | ||||||||
\(875\) | 7.64011e6 | 0.337349 | ||||||||
\(876\) | −1.03986e7 | −0.457839 | ||||||||
\(877\) | −9.40311e6 | −0.412831 | −0.206416 | − | 0.978464i | \(-0.566180\pi\) | ||||
−0.206416 | + | 0.978464i | \(0.566180\pi\) | |||||||
\(878\) | 4.69726e7 | 2.05640 | ||||||||
\(879\) | −2.38403e7 | −1.04073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.10395e6 | 0.0479194 | 0.0239597 | − | 0.999713i | \(-0.492373\pi\) | ||||
0.0239597 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(882\) | −8.24321e6 | −0.356800 | ||||||||
\(883\) | 8.06579e6 | 0.348133 | 0.174067 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174067 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(884\) | 6.72308e6 | 0.289359 | ||||||||
\(885\) | 2.19064e7 | 0.940185 | ||||||||
\(886\) | −3.35933e7 | −1.43770 | ||||||||
\(887\) | 1.49902e7 | 0.639732 | 0.319866 | − | 0.947463i | \(-0.396362\pi\) | ||||
0.319866 | + | 0.947463i | \(0.396362\pi\) | |||||||
\(888\) | 4.89493e6 | 0.208312 | ||||||||
\(889\) | −3.45779e6 | −0.146738 | ||||||||
\(890\) | 9.91920e6 | 0.419761 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.94918e7 | 0.820237 | ||||||||
\(893\) | 3.40162e7 | 1.42744 | ||||||||
\(894\) | −2.98672e7 | −1.24983 | ||||||||
\(895\) | −6.01950e6 | −0.251190 | ||||||||
\(896\) | −3.67912e6 | −0.153100 | ||||||||
\(897\) | 2.45847e7 | 1.02019 | ||||||||
\(898\) | 5.76384e7 | 2.38518 | ||||||||
\(899\) | −8.72090e6 | −0.359883 | ||||||||
\(900\) | −3.47831e7 | −1.43140 | ||||||||
\(901\) | −2.42104e6 | −0.0993553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.46141e7 | 1.00453 | ||||||||
\(904\) | −5.09331e6 | −0.207290 | ||||||||
\(905\) | 8.02089e6 | 0.325538 | ||||||||
\(906\) | −1.06261e7 | −0.430083 | ||||||||
\(907\) | 4.12622e6 | 0.166546 | 0.0832730 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832730 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(908\) | 1.49772e7 | 0.602859 | ||||||||
\(909\) | −1.06413e7 | −0.427155 | ||||||||
\(910\) | −3.50454e6 | −0.140290 | ||||||||
\(911\) | 4.04272e7 | 1.61391 | 0.806953 | − | 0.590616i | \(-0.201115\pi\) | ||||
0.806953 | + | 0.590616i | \(0.201115\pi\) | |||||||
\(912\) | 3.75556e7 | 1.49516 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.48554e7 | 0.588191 | ||||||||
\(915\) | −3.72530e7 | −1.47099 | ||||||||
\(916\) | 3.75817e7 | 1.47992 | ||||||||
\(917\) | −8.51191e6 | −0.334275 | ||||||||
\(918\) | −2.23690e7 | −0.876072 | ||||||||
\(919\) | −2.18546e7 | −0.853600 | −0.426800 | − | 0.904346i | \(-0.640359\pi\) | ||||
−0.426800 | + | 0.904346i | \(0.640359\pi\) | |||||||
\(920\) | −3.39351e6 | −0.132184 | ||||||||
\(921\) | 4.70142e7 | 1.82633 | ||||||||
\(922\) | −1.74844e7 | −0.677366 | ||||||||
\(923\) | −9.87702e6 | −0.381612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.18474e7 | −0.455271 | ||||||||
\(926\) | −1.04448e7 | −0.400289 | ||||||||
\(927\) | −5.94134e6 | −0.227083 | ||||||||
\(928\) | −3.57178e7 | −1.36149 | ||||||||
\(929\) | 1.06843e7 | 0.406169 | 0.203085 | − | 0.979161i | \(-0.434903\pi\) | ||||
0.203085 | + | 0.979161i | \(0.434903\pi\) | |||||||
\(930\) | 1.23775e7 | 0.469274 | ||||||||
\(931\) | 4.08398e6 | 0.154422 | ||||||||
\(932\) | 4.34813e6 | 0.163970 | ||||||||
\(933\) | 5.89130e7 | 2.21568 | ||||||||
\(934\) | 2.97009e7 | 1.11404 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.61818e6 | 0.172298 | ||||||||
\(937\) | 3.99105e7 | 1.48504 | 0.742521 | − | 0.669823i | \(-0.233630\pi\) | ||||
0.742521 | + | 0.669823i | \(0.233630\pi\) | |||||||
\(938\) | 2.04907e6 | 0.0760414 | ||||||||
\(939\) | 8.78419e7 | 3.25116 | ||||||||
\(940\) | 2.09704e7 | 0.774082 | ||||||||
\(941\) | −1.32350e6 | −0.0487248 | −0.0243624 | − | 0.999703i | \(-0.507756\pi\) | ||||
−0.0243624 | + | 0.999703i | \(0.507756\pi\) | |||||||
\(942\) | −1.90587e7 | −0.699787 | ||||||||
\(943\) | 2.27832e7 | 0.834326 | ||||||||
\(944\) | 2.55724e7 | 0.933990 | ||||||||
\(945\) | 6.21110e6 | 0.226250 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.76322e7 | −1.00124 | −0.500622 | − | 0.865666i | \(-0.666895\pi\) | ||||
−0.500622 | + | 0.865666i | \(0.666895\pi\) | |||||||
\(948\) | 7.66113e7 | 2.76868 | ||||||||
\(949\) | −3.34160e6 | −0.120445 | ||||||||
\(950\) | 3.23517e7 | 1.16302 | ||||||||
\(951\) | −7.54879e7 | −2.70661 | ||||||||
\(952\) | −1.11229e6 | −0.0397763 | ||||||||
\(953\) | 3.07901e7 | 1.09819 | 0.549096 | − | 0.835759i | \(-0.314972\pi\) | ||||
0.549096 | + | 0.835759i | \(0.314972\pi\) | |||||||
\(954\) | −1.35572e7 | −0.482281 | ||||||||
\(955\) | −1.27972e7 | −0.454053 | ||||||||
\(956\) | 9.26775e6 | 0.327966 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.99999e7 | −0.704068 | ||||||||
\(959\) | 97507.1 | 0.00342365 | ||||||||
\(960\) | 3.03818e7 | 1.06398 | ||||||||
\(961\) | −2.45145e7 | −0.856278 | ||||||||
\(962\) | 1.28231e7 | 0.446740 | ||||||||
\(963\) | −7.13697e6 | −0.247998 | ||||||||
\(964\) | −5.15202e7 | −1.78560 | ||||||||
\(965\) | 2.08952e7 | 0.722318 | ||||||||
\(966\) | −3.31572e7 | −1.14323 | ||||||||
\(967\) | −2.92557e6 | −0.100611 | −0.0503055 | − | 0.998734i | \(-0.516019\pi\) | ||||
−0.0503055 | + | 0.998734i | \(0.516019\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.67489e7 | 0.915159 | ||||||||
\(970\) | −1.03920e7 | −0.354625 | ||||||||
\(971\) | 2.78109e6 | 0.0946601 | 0.0473301 | − | 0.998879i | \(-0.484929\pi\) | ||||
0.0473301 | + | 0.998879i | \(0.484929\pi\) | |||||||
\(972\) | 2.75990e7 | 0.936975 | ||||||||
\(973\) | 1.79540e7 | 0.607967 | ||||||||
\(974\) | 4.29801e7 | 1.45168 | ||||||||
\(975\) | −1.77242e7 | −0.597111 | ||||||||
\(976\) | −4.34872e7 | −1.46129 | ||||||||
\(977\) | 7.48673e6 | 0.250932 | 0.125466 | − | 0.992098i | \(-0.459957\pi\) | ||||
0.125466 | + | 0.992098i | \(0.459957\pi\) | |||||||
\(978\) | −1.02140e8 | −3.41467 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.51770e6 | 0.0837411 | ||||||||
\(981\) | 3.56884e7 | 1.18401 | ||||||||
\(982\) | 4.45985e7 | 1.47585 | ||||||||
\(983\) | 1.79815e7 | 0.593528 | 0.296764 | − | 0.954951i | \(-0.404093\pi\) | ||||
0.296764 | + | 0.954951i | \(0.404093\pi\) | |||||||
\(984\) | 6.78639e6 | 0.223435 | ||||||||
\(985\) | 1.04905e7 | 0.344512 | ||||||||
\(986\) | −2.18120e7 | −0.714501 | ||||||||
\(987\) | 2.51345e7 | 0.821253 | ||||||||
\(988\) | −1.86519e7 | −0.607899 | ||||||||
\(989\) | 6.24378e7 | 2.02982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.72778e7 | 1.20578 | 0.602888 | − | 0.797826i | \(-0.294017\pi\) | ||||
0.602888 | + | 0.797826i | \(0.294017\pi\) | |||||||
\(992\) | 1.68521e7 | 0.543720 | ||||||||
\(993\) | −2.47816e7 | −0.797548 | ||||||||
\(994\) | 1.33211e7 | 0.427635 | ||||||||
\(995\) | 8.31734e6 | 0.266334 | ||||||||
\(996\) | 1.10613e8 | 3.53313 | ||||||||
\(997\) | −4.87422e7 | −1.55298 | −0.776492 | − | 0.630128i | \(-0.783003\pi\) | ||||
−0.776492 | + | 0.630128i | \(0.783003\pi\) | |||||||
\(998\) | 2.72747e7 | 0.866828 | ||||||||
\(999\) | −2.27264e7 | −0.720471 |
(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 | 847.6.a.c.1.1 | 2 | ||
11.10 | odd | 2 | 7.6.a.b.1.2 | ✓ | 2 | ||
33.32 | even | 2 | 63.6.a.f.1.1 | 2 | |||
44.43 | even | 2 | 112.6.a.h.1.2 | 2 | |||
55.32 | even | 4 | 175.6.b.c.99.4 | 4 | |||
55.43 | even | 4 | 175.6.b.c.99.1 | 4 | |||
55.54 | odd | 2 | 175.6.a.c.1.1 | 2 | |||
77.10 | even | 6 | 49.6.c.d.30.1 | 4 | |||
77.32 | odd | 6 | 49.6.c.e.30.1 | 4 | |||
77.54 | even | 6 | 49.6.c.d.18.1 | 4 | |||
77.65 | odd | 6 | 49.6.c.e.18.1 | 4 | |||
77.76 | even | 2 | 49.6.a.f.1.2 | 2 | |||
88.21 | odd | 2 | 448.6.a.w.1.2 | 2 | |||
88.43 | even | 2 | 448.6.a.u.1.1 | 2 | |||
132.131 | odd | 2 | 1008.6.a.bq.1.1 | 2 | |||
231.230 | odd | 2 | 441.6.a.l.1.1 | 2 | |||
308.307 | odd | 2 | 784.6.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.b.1.2 | ✓ | 2 | 11.10 | odd | 2 | ||
49.6.a.f.1.2 | 2 | 77.76 | even | 2 | |||
49.6.c.d.18.1 | 4 | 77.54 | even | 6 | |||
49.6.c.d.30.1 | 4 | 77.10 | even | 6 | |||
49.6.c.e.18.1 | 4 | 77.65 | odd | 6 | |||
49.6.c.e.30.1 | 4 | 77.32 | odd | 6 | |||
63.6.a.f.1.1 | 2 | 33.32 | even | 2 | |||
112.6.a.h.1.2 | 2 | 44.43 | even | 2 | |||
175.6.a.c.1.1 | 2 | 55.54 | odd | 2 | |||
175.6.b.c.99.1 | 4 | 55.43 | even | 4 | |||
175.6.b.c.99.4 | 4 | 55.32 | even | 4 | |||
441.6.a.l.1.1 | 2 | 231.230 | odd | 2 | |||
448.6.a.u.1.1 | 2 | 88.43 | even | 2 | |||
448.6.a.w.1.2 | 2 | 88.21 | odd | 2 | |||
784.6.a.v.1.1 | 2 | 308.307 | odd | 2 | |||
847.6.a.c.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1008.6.a.bq.1.1 | 2 | 132.131 | odd | 2 |