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: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.44622\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.44622 | 0.962765 | 0.481383 | − | 0.876511i | \(-0.340135\pi\) | ||||
0.481383 | + | 0.876511i | \(0.340135\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −2.33867 | −0.0730833 | ||||||||
\(5\) | −36.0000 | −0.643988 | −0.321994 | − | 0.946742i | \(-0.604353\pi\) | ||||
−0.321994 | + | 0.946742i | \(0.604353\pi\) | |||||||
\(6\) | 49.0160 | 0.555853 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −187.016 | −1.03313 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −196.064 | −0.620009 | ||||||||
\(11\) | 184.430 | 0.459569 | 0.229784 | − | 0.973242i | \(-0.426198\pi\) | ||||
0.229784 | + | 0.973242i | \(0.426198\pi\) | |||||||
\(12\) | −21.0480 | −0.0421947 | ||||||||
\(13\) | −147.872 | −0.242676 | −0.121338 | − | 0.992611i | \(-0.538719\pi\) | ||||
−0.121338 | + | 0.992611i | \(0.538719\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −324.000 | −0.371806 | ||||||||
\(16\) | −943.693 | −0.921576 | ||||||||
\(17\) | −1968.38 | −1.65191 | −0.825957 | − | 0.563733i | \(-0.809365\pi\) | ||||
−0.825957 | + | 0.563733i | \(0.809365\pi\) | |||||||
\(18\) | 441.144 | 0.320922 | ||||||||
\(19\) | −1892.51 | −1.20269 | −0.601346 | − | 0.798989i | \(-0.705369\pi\) | ||||
−0.601346 | + | 0.798989i | \(0.705369\pi\) | |||||||
\(20\) | 84.1920 | 0.0470647 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1004.45 | 0.442457 | ||||||||
\(23\) | 136.988 | 0.0539963 | 0.0269982 | − | 0.999635i | \(-0.491405\pi\) | ||||
0.0269982 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(24\) | −1683.14 | −0.596476 | ||||||||
\(25\) | −1829.00 | −0.585280 | ||||||||
\(26\) | −805.344 | −0.233640 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1259.58 | −0.278120 | −0.139060 | − | 0.990284i | \(-0.544408\pi\) | ||||
−0.139060 | + | 0.990284i | \(0.544408\pi\) | |||||||
\(30\) | −1764.58 | −0.357962 | ||||||||
\(31\) | −8969.02 | −1.67626 | −0.838129 | − | 0.545472i | \(-0.816350\pi\) | ||||
−0.838129 | + | 0.545472i | \(0.816350\pi\) | |||||||
\(32\) | 844.949 | 0.145866 | ||||||||
\(33\) | 1659.87 | 0.265332 | ||||||||
\(34\) | −10720.3 | −1.59041 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −189.432 | −0.0243611 | ||||||||
\(37\) | 12897.2 | 1.54879 | 0.774393 | − | 0.632705i | \(-0.218055\pi\) | ||||
0.774393 | + | 0.632705i | \(0.218055\pi\) | |||||||
\(38\) | −10307.0 | −1.15791 | ||||||||
\(39\) | −1330.85 | −0.140109 | ||||||||
\(40\) | 6732.58 | 0.665321 | ||||||||
\(41\) | −8975.62 | −0.833882 | −0.416941 | − | 0.908934i | \(-0.636898\pi\) | ||||
−0.416941 | + | 0.908934i | \(0.636898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13538.9 | 1.11664 | 0.558320 | − | 0.829626i | \(-0.311446\pi\) | ||||
0.558320 | + | 0.829626i | \(0.311446\pi\) | |||||||
\(44\) | −431.321 | −0.0335868 | ||||||||
\(45\) | −2916.00 | −0.214663 | ||||||||
\(46\) | 746.069 | 0.0519858 | ||||||||
\(47\) | 20046.1 | 1.32369 | 0.661845 | − | 0.749641i | \(-0.269774\pi\) | ||||
0.661845 | + | 0.749641i | \(0.269774\pi\) | |||||||
\(48\) | −8493.24 | −0.532072 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9961.14 | −0.563487 | ||||||||
\(51\) | −17715.5 | −0.953733 | ||||||||
\(52\) | 345.823 | 0.0177356 | ||||||||
\(53\) | 9334.33 | 0.456450 | 0.228225 | − | 0.973608i | \(-0.426708\pi\) | ||||
0.228225 | + | 0.973608i | \(0.426708\pi\) | |||||||
\(54\) | 3970.30 | 0.185284 | ||||||||
\(55\) | −6639.49 | −0.295956 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17032.6 | −0.694375 | ||||||||
\(58\) | −6859.96 | −0.267764 | ||||||||
\(59\) | −8866.46 | −0.331605 | −0.165802 | − | 0.986159i | \(-0.553021\pi\) | ||||
−0.165802 | + | 0.986159i | \(0.553021\pi\) | |||||||
\(60\) | 757.728 | 0.0271728 | ||||||||
\(61\) | 41148.3 | 1.41588 | 0.707942 | − | 0.706271i | \(-0.249624\pi\) | ||||
0.707942 | + | 0.706271i | \(0.249624\pi\) | |||||||
\(62\) | −48847.3 | −1.61384 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 34800.0 | 1.06201 | ||||||||
\(65\) | 5323.39 | 0.156281 | ||||||||
\(66\) | 9040.03 | 0.255452 | ||||||||
\(67\) | −55351.5 | −1.50641 | −0.753204 | − | 0.657787i | \(-0.771493\pi\) | ||||
−0.753204 | + | 0.657787i | \(0.771493\pi\) | |||||||
\(68\) | 4603.39 | 0.120727 | ||||||||
\(69\) | 1232.90 | 0.0311748 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63866.8 | −1.50359 | −0.751794 | − | 0.659398i | \(-0.770811\pi\) | ||||
−0.751794 | + | 0.659398i | \(0.770811\pi\) | |||||||
\(72\) | −15148.3 | −0.344376 | ||||||||
\(73\) | −41299.3 | −0.907060 | −0.453530 | − | 0.891241i | \(-0.649835\pi\) | ||||
−0.453530 | + | 0.891241i | \(0.649835\pi\) | |||||||
\(74\) | 70241.1 | 1.49112 | ||||||||
\(75\) | −16461.0 | −0.337912 | ||||||||
\(76\) | 4425.95 | 0.0878968 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7248.09 | −0.134892 | ||||||||
\(79\) | 16963.5 | 0.305808 | 0.152904 | − | 0.988241i | \(-0.451138\pi\) | ||||
0.152904 | + | 0.988241i | \(0.451138\pi\) | |||||||
\(80\) | 33973.0 | 0.593483 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −48883.2 | −0.802833 | ||||||||
\(83\) | 101693. | 1.62030 | 0.810150 | − | 0.586223i | \(-0.199386\pi\) | ||||
0.810150 | + | 0.586223i | \(0.199386\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 70861.8 | 1.06381 | ||||||||
\(86\) | 73736.0 | 1.07506 | ||||||||
\(87\) | −11336.2 | −0.160572 | ||||||||
\(88\) | −34491.4 | −0.474793 | ||||||||
\(89\) | −87102.5 | −1.16562 | −0.582808 | − | 0.812610i | \(-0.698046\pi\) | ||||
−0.582808 | + | 0.812610i | \(0.698046\pi\) | |||||||
\(90\) | −15881.2 | −0.206670 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −320.370 | −0.00394623 | ||||||||
\(93\) | −80721.2 | −0.967788 | ||||||||
\(94\) | 109176. | 1.27440 | ||||||||
\(95\) | 68130.4 | 0.774519 | ||||||||
\(96\) | 7604.54 | 0.0842160 | ||||||||
\(97\) | 118107. | 1.27452 | 0.637258 | − | 0.770650i | \(-0.280068\pi\) | ||||
0.637258 | + | 0.770650i | \(0.280068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14938.8 | 0.153190 | ||||||||
\(100\) | 4277.42 | 0.0427742 | ||||||||
\(101\) | −22232.7 | −0.216865 | −0.108432 | − | 0.994104i | \(-0.534583\pi\) | ||||
−0.108432 | + | 0.994104i | \(0.534583\pi\) | |||||||
\(102\) | −96482.3 | −0.918221 | ||||||||
\(103\) | −135931. | −1.26248 | −0.631239 | − | 0.775588i | \(-0.717453\pi\) | ||||
−0.631239 | + | 0.775588i | \(0.717453\pi\) | |||||||
\(104\) | 27654.4 | 0.250716 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 50836.8 | 0.439454 | ||||||||
\(107\) | 117626. | 0.993218 | 0.496609 | − | 0.867974i | \(-0.334578\pi\) | ||||
0.496609 | + | 0.867974i | \(0.334578\pi\) | |||||||
\(108\) | −1704.89 | −0.0140649 | ||||||||
\(109\) | −34664.2 | −0.279457 | −0.139729 | − | 0.990190i | \(-0.544623\pi\) | ||||
−0.139729 | + | 0.990190i | \(0.544623\pi\) | |||||||
\(110\) | −36160.1 | −0.284937 | ||||||||
\(111\) | 116075. | 0.894192 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −26584.5 | −0.195854 | −0.0979269 | − | 0.995194i | \(-0.531221\pi\) | ||||
−0.0979269 | + | 0.995194i | \(0.531221\pi\) | |||||||
\(114\) | −92763.4 | −0.668520 | ||||||||
\(115\) | −4931.58 | −0.0347730 | ||||||||
\(116\) | 2945.74 | 0.0203259 | ||||||||
\(117\) | −11977.6 | −0.0808921 | ||||||||
\(118\) | −48288.7 | −0.319257 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 60593.2 | 0.384123 | ||||||||
\(121\) | −127036. | −0.788797 | ||||||||
\(122\) | 224103. | 1.36316 | ||||||||
\(123\) | −80780.5 | −0.481442 | ||||||||
\(124\) | 20975.6 | 0.122507 | ||||||||
\(125\) | 178344. | 1.02090 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −137111. | −0.754334 | −0.377167 | − | 0.926145i | \(-0.623102\pi\) | ||||
−0.377167 | + | 0.926145i | \(0.623102\pi\) | |||||||
\(128\) | 162490. | 0.876600 | ||||||||
\(129\) | 121850. | 0.644693 | ||||||||
\(130\) | 28992.4 | 0.150462 | ||||||||
\(131\) | 54089.2 | 0.275380 | 0.137690 | − | 0.990475i | \(-0.456032\pi\) | ||||
0.137690 | + | 0.990475i | \(0.456032\pi\) | |||||||
\(132\) | −3881.89 | −0.0193913 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −301457. | −1.45032 | ||||||||
\(135\) | −26244.0 | −0.123935 | ||||||||
\(136\) | 368119. | 1.70664 | ||||||||
\(137\) | 422849. | 1.92479 | 0.962395 | − | 0.271653i | \(-0.0875703\pi\) | ||||
0.962395 | + | 0.271653i | \(0.0875703\pi\) | |||||||
\(138\) | 6714.62 | 0.0300140 | ||||||||
\(139\) | 9913.38 | 0.0435196 | 0.0217598 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217598 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180415. | 0.764233 | ||||||||
\(142\) | −347833. | −1.44760 | ||||||||
\(143\) | −27272.1 | −0.111526 | ||||||||
\(144\) | −76439.2 | −0.307192 | ||||||||
\(145\) | 45345.0 | 0.179106 | ||||||||
\(146\) | −224925. | −0.873285 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −30162.3 | −0.113190 | ||||||||
\(149\) | 505462. | 1.86519 | 0.932595 | − | 0.360925i | \(-0.117539\pi\) | ||||
0.932595 | + | 0.360925i | \(0.117539\pi\) | |||||||
\(150\) | −89650.3 | −0.325329 | ||||||||
\(151\) | −193103. | −0.689201 | −0.344601 | − | 0.938749i | \(-0.611986\pi\) | ||||
−0.344601 | + | 0.938749i | \(0.611986\pi\) | |||||||
\(152\) | 353930. | 1.24253 | ||||||||
\(153\) | −159439. | −0.550638 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 322885. | 1.07949 | ||||||||
\(156\) | 3112.41 | 0.0102397 | ||||||||
\(157\) | −264923. | −0.857770 | −0.428885 | − | 0.903359i | \(-0.641093\pi\) | ||||
−0.428885 | + | 0.903359i | \(0.641093\pi\) | |||||||
\(158\) | 92387.1 | 0.294421 | ||||||||
\(159\) | 84008.9 | 0.263532 | ||||||||
\(160\) | −30418.1 | −0.0939362 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 35732.7 | 0.106974 | ||||||||
\(163\) | −539093. | −1.58926 | −0.794629 | − | 0.607095i | \(-0.792335\pi\) | ||||
−0.794629 | + | 0.607095i | \(0.792335\pi\) | |||||||
\(164\) | 20991.0 | 0.0609429 | ||||||||
\(165\) | −59755.4 | −0.170871 | ||||||||
\(166\) | 553842. | 1.55997 | ||||||||
\(167\) | −218748. | −0.606949 | −0.303475 | − | 0.952840i | \(-0.598147\pi\) | ||||
−0.303475 | + | 0.952840i | \(0.598147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −349427. | −0.941108 | ||||||||
\(170\) | 385929. | 1.02420 | ||||||||
\(171\) | −153293. | −0.400898 | ||||||||
\(172\) | −31663.0 | −0.0816078 | ||||||||
\(173\) | −590201. | −1.49929 | −0.749644 | − | 0.661842i | \(-0.769775\pi\) | ||||
−0.749644 | + | 0.661842i | \(0.769775\pi\) | |||||||
\(174\) | −61739.7 | −0.154593 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −174046. | −0.423527 | ||||||||
\(177\) | −79798.2 | −0.191452 | ||||||||
\(178\) | −474380. | −1.12222 | ||||||||
\(179\) | −217352. | −0.507026 | −0.253513 | − | 0.967332i | \(-0.581586\pi\) | ||||
−0.253513 | + | 0.967332i | \(0.581586\pi\) | |||||||
\(180\) | 6819.55 | 0.0156882 | ||||||||
\(181\) | −188109. | −0.426790 | −0.213395 | − | 0.976966i | \(-0.568452\pi\) | ||||
−0.213395 | + | 0.976966i | \(0.568452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 370335. | 0.817461 | ||||||||
\(184\) | −25619.0 | −0.0557851 | ||||||||
\(185\) | −464300. | −0.997399 | ||||||||
\(186\) | −439626. | −0.931753 | ||||||||
\(187\) | −363029. | −0.759168 | ||||||||
\(188\) | −46881.2 | −0.0967396 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 371053. | 0.745680 | ||||||||
\(191\) | 173523. | 0.344170 | 0.172085 | − | 0.985082i | \(-0.444950\pi\) | ||||
0.172085 | + | 0.985082i | \(0.444950\pi\) | |||||||
\(192\) | 313200. | 0.613152 | ||||||||
\(193\) | 117781. | 0.227606 | 0.113803 | − | 0.993503i | \(-0.463697\pi\) | ||||
0.113803 | + | 0.993503i | \(0.463697\pi\) | |||||||
\(194\) | 643236. | 1.22706 | ||||||||
\(195\) | 47910.5 | 0.0902287 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 224734. | 0.412575 | 0.206288 | − | 0.978491i | \(-0.433862\pi\) | ||||
0.206288 | + | 0.978491i | \(0.433862\pi\) | |||||||
\(198\) | 81360.3 | 0.147486 | ||||||||
\(199\) | −740273. | −1.32513 | −0.662567 | − | 0.749003i | \(-0.730533\pi\) | ||||
−0.662567 | + | 0.749003i | \(0.730533\pi\) | |||||||
\(200\) | 342052. | 0.604669 | ||||||||
\(201\) | −498164. | −0.869725 | ||||||||
\(202\) | −121084. | −0.208790 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 41430.5 | 0.0697020 | ||||||||
\(205\) | 323122. | 0.537010 | ||||||||
\(206\) | −740308. | −1.21547 | ||||||||
\(207\) | 11096.1 | 0.0179988 | ||||||||
\(208\) | 139546. | 0.223645 | ||||||||
\(209\) | −349036. | −0.552720 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −705896. | −1.09153 | −0.545763 | − | 0.837939i | \(-0.683760\pi\) | ||||
−0.545763 | + | 0.837939i | \(0.683760\pi\) | |||||||
\(212\) | −21829.9 | −0.0333589 | ||||||||
\(213\) | −574801. | −0.868097 | ||||||||
\(214\) | 640618. | 0.956236 | ||||||||
\(215\) | −487402. | −0.719102 | ||||||||
\(216\) | −136335. | −0.198825 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −188789. | −0.269052 | ||||||||
\(219\) | −371694. | −0.523691 | ||||||||
\(220\) | 15527.5 | 0.0216295 | ||||||||
\(221\) | 291069. | 0.400881 | ||||||||
\(222\) | 632170. | 0.860897 | ||||||||
\(223\) | −42214.3 | −0.0568456 | −0.0284228 | − | 0.999596i | \(-0.509048\pi\) | ||||
−0.0284228 | + | 0.999596i | \(0.509048\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −148149. | −0.195093 | ||||||||
\(226\) | −144785. | −0.188561 | ||||||||
\(227\) | −742403. | −0.956258 | −0.478129 | − | 0.878290i | \(-0.658685\pi\) | ||||
−0.478129 | + | 0.878290i | \(0.658685\pi\) | |||||||
\(228\) | 39833.6 | 0.0507472 | ||||||||
\(229\) | −941236. | −1.18607 | −0.593034 | − | 0.805177i | \(-0.702070\pi\) | ||||
−0.593034 | + | 0.805177i | \(0.702070\pi\) | |||||||
\(230\) | −26858.5 | −0.0334782 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 235562. | 0.287333 | ||||||||
\(233\) | −512331. | −0.618246 | −0.309123 | − | 0.951022i | \(-0.600035\pi\) | ||||
−0.309123 | + | 0.951022i | \(0.600035\pi\) | |||||||
\(234\) | −65232.9 | −0.0778801 | ||||||||
\(235\) | −721661. | −0.852440 | ||||||||
\(236\) | 20735.7 | 0.0242348 | ||||||||
\(237\) | 152672. | 0.176558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −115323. | −0.130593 | −0.0652966 | − | 0.997866i | \(-0.520799\pi\) | ||||
−0.0652966 | + | 0.997866i | \(0.520799\pi\) | |||||||
\(240\) | 305757. | 0.342648 | ||||||||
\(241\) | 909864. | 1.00910 | 0.504549 | − | 0.863383i | \(-0.331659\pi\) | ||||
0.504549 | + | 0.863383i | \(0.331659\pi\) | |||||||
\(242\) | −691869. | −0.759426 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −96232.2 | −0.103477 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −439949. | −0.463516 | ||||||||
\(247\) | 279850. | 0.291865 | ||||||||
\(248\) | 1.67735e6 | 1.73179 | ||||||||
\(249\) | 915236. | 0.935481 | ||||||||
\(250\) | 971301. | 0.982888 | ||||||||
\(251\) | 321264. | 0.321868 | 0.160934 | − | 0.986965i | \(-0.448549\pi\) | ||||
0.160934 | + | 0.986965i | \(0.448549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25264.8 | 0.0248150 | ||||||||
\(254\) | −746738. | −0.726246 | ||||||||
\(255\) | 637756. | 0.614192 | ||||||||
\(256\) | −228642. | −0.218050 | ||||||||
\(257\) | 556492. | 0.525565 | 0.262782 | − | 0.964855i | \(-0.415360\pi\) | ||||
0.262782 | + | 0.964855i | \(0.415360\pi\) | |||||||
\(258\) | 663624. | 0.620688 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −12449.6 | −0.0114215 | ||||||||
\(261\) | −102026. | −0.0927065 | ||||||||
\(262\) | 294582. | 0.265126 | ||||||||
\(263\) | −233379. | −0.208052 | −0.104026 | − | 0.994575i | \(-0.533173\pi\) | ||||
−0.104026 | + | 0.994575i | \(0.533173\pi\) | |||||||
\(264\) | −310423. | −0.274122 | ||||||||
\(265\) | −336036. | −0.293948 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −783923. | −0.672969 | ||||||||
\(268\) | 129449. | 0.110093 | ||||||||
\(269\) | 1.47857e6 | 1.24584 | 0.622919 | − | 0.782286i | \(-0.285947\pi\) | ||||
0.622919 | + | 0.782286i | \(0.285947\pi\) | |||||||
\(270\) | −142931. | −0.119321 | ||||||||
\(271\) | −177762. | −0.147033 | −0.0735165 | − | 0.997294i | \(-0.523422\pi\) | ||||
−0.0735165 | + | 0.997294i | \(0.523422\pi\) | |||||||
\(272\) | 1.85755e6 | 1.52236 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.30293e6 | 1.85312 | ||||||||
\(275\) | −337323. | −0.268976 | ||||||||
\(276\) | −2883.33 | −0.00227836 | ||||||||
\(277\) | −1.22252e6 | −0.957318 | −0.478659 | − | 0.878001i | \(-0.658877\pi\) | ||||
−0.478659 | + | 0.878001i | \(0.658877\pi\) | |||||||
\(278\) | 53990.5 | 0.0418991 | ||||||||
\(279\) | −726491. | −0.558753 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 177799. | 0.134327 | 0.0671636 | − | 0.997742i | \(-0.478605\pi\) | ||||
0.0671636 | + | 0.997742i | \(0.478605\pi\) | |||||||
\(282\) | 982582. | 0.735776 | ||||||||
\(283\) | 1.09052e6 | 0.809406 | 0.404703 | − | 0.914448i | \(-0.367375\pi\) | ||||
0.404703 | + | 0.914448i | \(0.367375\pi\) | |||||||
\(284\) | 149363. | 0.109887 | ||||||||
\(285\) | 613174. | 0.447169 | ||||||||
\(286\) | −148530. | −0.107374 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 68440.8 | 0.0486221 | ||||||||
\(289\) | 2.45468e6 | 1.72882 | ||||||||
\(290\) | 246959. | 0.172437 | ||||||||
\(291\) | 1.06296e6 | 0.735843 | ||||||||
\(292\) | 96585.3 | 0.0662909 | ||||||||
\(293\) | −545742. | −0.371380 | −0.185690 | − | 0.982608i | \(-0.559452\pi\) | ||||
−0.185690 | + | 0.982608i | \(0.559452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 319193. | 0.213549 | ||||||||
\(296\) | −2.41198e6 | −1.60009 | ||||||||
\(297\) | 134450. | 0.0884440 | ||||||||
\(298\) | 2.75286e6 | 1.79574 | ||||||||
\(299\) | −20256.8 | −0.0131036 | ||||||||
\(300\) | 38496.8 | 0.0246957 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.05168e6 | −0.663539 | ||||||||
\(303\) | −200095. | −0.125207 | ||||||||
\(304\) | 1.78595e6 | 1.10837 | ||||||||
\(305\) | −1.48134e6 | −0.911811 | ||||||||
\(306\) | −868341. | −0.530135 | ||||||||
\(307\) | 3.29000e6 | 1.99228 | 0.996138 | − | 0.0878052i | \(-0.0279853\pi\) | ||||
0.996138 | + | 0.0878052i | \(0.0279853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.22338e6 | −0.728892 | ||||||||
\(310\) | 1.75850e6 | 1.03929 | ||||||||
\(311\) | 699712. | 0.410221 | 0.205111 | − | 0.978739i | \(-0.434245\pi\) | ||||
0.205111 | + | 0.978739i | \(0.434245\pi\) | |||||||
\(312\) | 248890. | 0.144751 | ||||||||
\(313\) | −623219. | −0.359567 | −0.179783 | − | 0.983706i | \(-0.557540\pi\) | ||||
−0.179783 | + | 0.983706i | \(0.557540\pi\) | |||||||
\(314\) | −1.44283e6 | −0.825831 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −39672.0 | −0.0223494 | ||||||||
\(317\) | −639244. | −0.357288 | −0.178644 | − | 0.983914i | \(-0.557171\pi\) | ||||
−0.178644 | + | 0.983914i | \(0.557171\pi\) | |||||||
\(318\) | 457531. | 0.253719 | ||||||||
\(319\) | −232305. | −0.127815 | ||||||||
\(320\) | −1.25280e6 | −0.683922 | ||||||||
\(321\) | 1.05864e6 | 0.573435 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.72519e6 | 1.98675 | ||||||||
\(324\) | −15344.0 | −0.00812037 | ||||||||
\(325\) | 270458. | 0.142034 | ||||||||
\(326\) | −2.93602e6 | −1.53008 | ||||||||
\(327\) | −311978. | −0.161345 | ||||||||
\(328\) | 1.67858e6 | 0.861506 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −325441. | −0.164508 | ||||||||
\(331\) | 1.40963e6 | 0.707190 | 0.353595 | − | 0.935399i | \(-0.384959\pi\) | ||||
0.353595 | + | 0.935399i | \(0.384959\pi\) | |||||||
\(332\) | −237826. | −0.118417 | ||||||||
\(333\) | 1.04467e6 | 0.516262 | ||||||||
\(334\) | −1.19135e6 | −0.584350 | ||||||||
\(335\) | 1.99265e6 | 0.970108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.55677e6 | −0.746704 | −0.373352 | − | 0.927690i | \(-0.621792\pi\) | ||||
−0.373352 | + | 0.927690i | \(0.621792\pi\) | |||||||
\(338\) | −1.90306e6 | −0.906066 | ||||||||
\(339\) | −239260. | −0.113076 | ||||||||
\(340\) | −165722. | −0.0777469 | ||||||||
\(341\) | −1.65416e6 | −0.770356 | ||||||||
\(342\) | −834870. | −0.385970 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.53200e6 | −1.15363 | ||||||||
\(345\) | −44384.3 | −0.0200762 | ||||||||
\(346\) | −3.21437e6 | −1.44346 | ||||||||
\(347\) | 248297. | 0.110700 | 0.0553500 | − | 0.998467i | \(-0.482373\pi\) | ||||
0.0553500 | + | 0.998467i | \(0.482373\pi\) | |||||||
\(348\) | 26511.7 | 0.0117352 | ||||||||
\(349\) | −1.86169e6 | −0.818171 | −0.409086 | − | 0.912496i | \(-0.634152\pi\) | ||||
−0.409086 | + | 0.912496i | \(0.634152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −107799. | −0.0467031 | ||||||||
\(352\) | 155834. | 0.0670356 | ||||||||
\(353\) | −1.77128e6 | −0.756574 | −0.378287 | − | 0.925688i | \(-0.623487\pi\) | ||||
−0.378287 | + | 0.925688i | \(0.623487\pi\) | |||||||
\(354\) | −434599. | −0.184323 | ||||||||
\(355\) | 2.29920e6 | 0.968292 | ||||||||
\(356\) | 203704. | 0.0851871 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.18375e6 | −0.488147 | ||||||||
\(359\) | −4.47560e6 | −1.83280 | −0.916401 | − | 0.400262i | \(-0.868919\pi\) | ||||
−0.916401 | + | 0.400262i | \(0.868919\pi\) | |||||||
\(360\) | 545339. | 0.221774 | ||||||||
\(361\) | 1.10550e6 | 0.446469 | ||||||||
\(362\) | −1.02449e6 | −0.410898 | ||||||||
\(363\) | −1.14333e6 | −0.455412 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.48678e6 | 0.584135 | ||||||||
\(366\) | 2.01693e6 | 0.787023 | ||||||||
\(367\) | −3.17097e6 | −1.22893 | −0.614465 | − | 0.788944i | \(-0.710628\pi\) | ||||
−0.614465 | + | 0.788944i | \(0.710628\pi\) | |||||||
\(368\) | −129275. | −0.0497617 | ||||||||
\(369\) | −727025. | −0.277961 | ||||||||
\(370\) | −2.52868e6 | −0.960261 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 188780. | 0.0707292 | ||||||||
\(373\) | −2.31179e6 | −0.860353 | −0.430177 | − | 0.902745i | \(-0.641549\pi\) | ||||
−0.430177 | + | 0.902745i | \(0.641549\pi\) | |||||||
\(374\) | −1.97714e6 | −0.730900 | ||||||||
\(375\) | 1.60510e6 | 0.589417 | ||||||||
\(376\) | −3.74895e6 | −1.36754 | ||||||||
\(377\) | 186257. | 0.0674931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −591840. | −0.211644 | −0.105822 | − | 0.994385i | \(-0.533747\pi\) | ||||
−0.105822 | + | 0.994385i | \(0.533747\pi\) | |||||||
\(380\) | −159334. | −0.0566044 | ||||||||
\(381\) | −1.23400e6 | −0.435515 | ||||||||
\(382\) | 945042. | 0.331354 | ||||||||
\(383\) | 3.59766e6 | 1.25321 | 0.626605 | − | 0.779337i | \(-0.284444\pi\) | ||||
0.626605 | + | 0.779337i | \(0.284444\pi\) | |||||||
\(384\) | 1.46241e6 | 0.506105 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 641464. | 0.219131 | ||||||||
\(387\) | 1.09665e6 | 0.372213 | ||||||||
\(388\) | −276212. | −0.0931459 | ||||||||
\(389\) | −2.24746e6 | −0.753040 | −0.376520 | − | 0.926409i | \(-0.622879\pi\) | ||||
−0.376520 | + | 0.926409i | \(0.622879\pi\) | |||||||
\(390\) | 260931. | 0.0868690 | ||||||||
\(391\) | −269646. | −0.0891973 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 486803. | 0.158991 | ||||||||
\(394\) | 1.22395e6 | 0.397213 | ||||||||
\(395\) | −610687. | −0.196936 | ||||||||
\(396\) | −34937.0 | −0.0111956 | ||||||||
\(397\) | 4.58670e6 | 1.46058 | 0.730288 | − | 0.683139i | \(-0.239386\pi\) | ||||
0.730288 | + | 0.683139i | \(0.239386\pi\) | |||||||
\(398\) | −4.03169e6 | −1.27579 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.72602e6 | 0.539380 | ||||||||
\(401\) | 6.00432e6 | 1.86468 | 0.932338 | − | 0.361589i | \(-0.117766\pi\) | ||||
0.932338 | + | 0.361589i | \(0.117766\pi\) | |||||||
\(402\) | −2.71311e6 | −0.837341 | ||||||||
\(403\) | 1.32627e6 | 0.406788 | ||||||||
\(404\) | 51994.9 | 0.0158492 | ||||||||
\(405\) | −236196. | −0.0715542 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.37864e6 | 0.711774 | ||||||||
\(408\) | 3.31307e6 | 0.985328 | ||||||||
\(409\) | 3.55340e6 | 1.05035 | 0.525177 | − | 0.850993i | \(-0.323999\pi\) | ||||
0.525177 | + | 0.850993i | \(0.323999\pi\) | |||||||
\(410\) | 1.75980e6 | 0.517014 | ||||||||
\(411\) | 3.80564e6 | 1.11128 | ||||||||
\(412\) | 317896. | 0.0922661 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 60431.6 | 0.0173286 | ||||||||
\(415\) | −3.66094e6 | −1.04345 | ||||||||
\(416\) | −124944. | −0.0353983 | ||||||||
\(417\) | 89220.4 | 0.0251260 | ||||||||
\(418\) | −1.90093e6 | −0.532139 | ||||||||
\(419\) | −2.01375e6 | −0.560365 | −0.280182 | − | 0.959947i | \(-0.590395\pi\) | ||||
−0.280182 | + | 0.959947i | \(0.590395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.89987e6 | −1.62232 | −0.811161 | − | 0.584823i | \(-0.801164\pi\) | ||||
−0.811161 | + | 0.584823i | \(0.801164\pi\) | |||||||
\(422\) | −3.84446e6 | −1.05088 | ||||||||
\(423\) | 1.62374e6 | 0.441230 | ||||||||
\(424\) | −1.74567e6 | −0.471571 | ||||||||
\(425\) | 3.60017e6 | 0.966832 | ||||||||
\(426\) | −3.13049e6 | −0.835774 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −275088. | −0.0725877 | ||||||||
\(429\) | −245449. | −0.0643898 | ||||||||
\(430\) | −2.65450e6 | −0.692327 | ||||||||
\(431\) | −3.81048e6 | −0.988066 | −0.494033 | − | 0.869443i | \(-0.664478\pi\) | ||||
−0.494033 | + | 0.869443i | \(0.664478\pi\) | |||||||
\(432\) | −687952. | −0.177357 | ||||||||
\(433\) | −6.59449e6 | −1.69029 | −0.845146 | − | 0.534536i | \(-0.820487\pi\) | ||||
−0.845146 | + | 0.534536i | \(0.820487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 408105. | 0.103407 | ||||||||
\(436\) | 81068.1 | 0.0204237 | ||||||||
\(437\) | −259252. | −0.0649410 | ||||||||
\(438\) | −2.02433e6 | −0.504192 | ||||||||
\(439\) | 4.55028e6 | 1.12688 | 0.563438 | − | 0.826158i | \(-0.309478\pi\) | ||||
0.563438 | + | 0.826158i | \(0.309478\pi\) | |||||||
\(440\) | 1.24169e6 | 0.305761 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.58523e6 | 0.385954 | ||||||||
\(443\) | 5.11537e6 | 1.23842 | 0.619210 | − | 0.785225i | \(-0.287453\pi\) | ||||
0.619210 | + | 0.785225i | \(0.287453\pi\) | |||||||
\(444\) | −271460. | −0.0653505 | ||||||||
\(445\) | 3.13569e6 | 0.750643 | ||||||||
\(446\) | −229908. | −0.0547290 | ||||||||
\(447\) | 4.54916e6 | 1.07687 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.95600e6 | 1.39424 | 0.697122 | − | 0.716953i | \(-0.254464\pi\) | ||||
0.697122 | + | 0.716953i | \(0.254464\pi\) | |||||||
\(450\) | −806852. | −0.187829 | ||||||||
\(451\) | −1.65537e6 | −0.383226 | ||||||||
\(452\) | 62172.2 | 0.0143136 | ||||||||
\(453\) | −1.73792e6 | −0.397911 | ||||||||
\(454\) | −4.04329e6 | −0.920652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.18537e6 | 0.717378 | ||||||||
\(457\) | −2.59834e6 | −0.581976 | −0.290988 | − | 0.956727i | \(-0.593984\pi\) | ||||
−0.290988 | + | 0.956727i | \(0.593984\pi\) | |||||||
\(458\) | −5.12618e6 | −1.14191 | ||||||||
\(459\) | −1.43495e6 | −0.317911 | ||||||||
\(460\) | 11533.3 | 0.00254132 | ||||||||
\(461\) | −4.51513e6 | −0.989505 | −0.494752 | − | 0.869034i | \(-0.664741\pi\) | ||||
−0.494752 | + | 0.869034i | \(0.664741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.55129e6 | −1.20349 | −0.601744 | − | 0.798689i | \(-0.705527\pi\) | ||||
−0.601744 | + | 0.798689i | \(0.705527\pi\) | |||||||
\(464\) | 1.18866e6 | 0.256308 | ||||||||
\(465\) | 2.90596e6 | 0.623244 | ||||||||
\(466\) | −2.79027e6 | −0.595225 | ||||||||
\(467\) | 7.95350e6 | 1.68759 | 0.843794 | − | 0.536668i | \(-0.180317\pi\) | ||||
0.843794 | + | 0.536668i | \(0.180317\pi\) | |||||||
\(468\) | 28011.7 | 0.00591187 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.93033e6 | −0.820699 | ||||||||
\(471\) | −2.38431e6 | −0.495233 | ||||||||
\(472\) | 1.65817e6 | 0.342590 | ||||||||
\(473\) | 2.49699e6 | 0.513173 | ||||||||
\(474\) | 831484. | 0.169984 | ||||||||
\(475\) | 3.46140e6 | 0.703912 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 756080. | 0.152150 | ||||||||
\(478\) | −628074. | −0.125731 | ||||||||
\(479\) | 6.56370e6 | 1.30710 | 0.653552 | − | 0.756882i | \(-0.273278\pi\) | ||||
0.653552 | + | 0.756882i | \(0.273278\pi\) | |||||||
\(480\) | −273763. | −0.0542341 | ||||||||
\(481\) | −1.90714e6 | −0.375854 | ||||||||
\(482\) | 4.95532e6 | 0.971525 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 297096. | 0.0576479 | ||||||||
\(485\) | −4.25185e6 | −0.820773 | ||||||||
\(486\) | 321594. | 0.0617614 | ||||||||
\(487\) | 4.66370e6 | 0.891062 | 0.445531 | − | 0.895266i | \(-0.353015\pi\) | ||||
0.445531 | + | 0.895266i | \(0.353015\pi\) | |||||||
\(488\) | −7.69539e6 | −1.46279 | ||||||||
\(489\) | −4.85183e6 | −0.917558 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −917227. | −0.171701 | −0.0858506 | − | 0.996308i | \(-0.527361\pi\) | ||||
−0.0858506 | + | 0.996308i | \(0.527361\pi\) | |||||||
\(492\) | 188919. | 0.0351854 | ||||||||
\(493\) | 2.47934e6 | 0.459430 | ||||||||
\(494\) | 1.52412e6 | 0.280998 | ||||||||
\(495\) | −537799. | −0.0986522 | ||||||||
\(496\) | 8.46401e6 | 1.54480 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.98458e6 | 0.900648 | ||||||||
\(499\) | 313436. | 0.0563504 | 0.0281752 | − | 0.999603i | \(-0.491030\pi\) | ||||
0.0281752 | + | 0.999603i | \(0.491030\pi\) | |||||||
\(500\) | −417087. | −0.0746108 | ||||||||
\(501\) | −1.96873e6 | −0.350422 | ||||||||
\(502\) | 1.74967e6 | 0.309883 | ||||||||
\(503\) | 3.74110e6 | 0.659294 | 0.329647 | − | 0.944104i | \(-0.393070\pi\) | ||||
0.329647 | + | 0.944104i | \(0.393070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 800378. | 0.139658 | ||||||||
\(506\) | 137598. | 0.0238910 | ||||||||
\(507\) | −3.14484e6 | −0.543349 | ||||||||
\(508\) | 320657. | 0.0551292 | ||||||||
\(509\) | −1.03017e7 | −1.76244 | −0.881220 | − | 0.472707i | \(-0.843277\pi\) | ||||
−0.881220 | + | 0.472707i | \(0.843277\pi\) | |||||||
\(510\) | 3.47336e6 | 0.591323 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.44492e6 | −1.08653 | ||||||||
\(513\) | −1.37964e6 | −0.231458 | ||||||||
\(514\) | 3.03078e6 | 0.505995 | ||||||||
\(515\) | 4.89350e6 | 0.813021 | ||||||||
\(516\) | −284967. | −0.0471163 | ||||||||
\(517\) | 3.69711e6 | 0.608326 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.31181e6 | −0.865614 | ||||||||
\(520\) | −995560. | −0.161458 | ||||||||
\(521\) | 6.57325e6 | 1.06093 | 0.530464 | − | 0.847707i | \(-0.322018\pi\) | ||||
0.530464 | + | 0.847707i | \(0.322018\pi\) | |||||||
\(522\) | −555657. | −0.0892546 | ||||||||
\(523\) | −8.36532e6 | −1.33730 | −0.668650 | − | 0.743578i | \(-0.733127\pi\) | ||||
−0.668650 | + | 0.743578i | \(0.733127\pi\) | |||||||
\(524\) | −126497. | −0.0201257 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.27103e6 | −0.200306 | ||||||||
\(527\) | 1.76545e7 | 2.76904 | ||||||||
\(528\) | −1.56641e6 | −0.244524 | ||||||||
\(529\) | −6.41758e6 | −0.997084 | ||||||||
\(530\) | −1.83013e6 | −0.283003 | ||||||||
\(531\) | −718184. | −0.110535 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32724e6 | 0.202364 | ||||||||
\(534\) | −4.26942e6 | −0.647911 | ||||||||
\(535\) | −4.23454e6 | −0.639620 | ||||||||
\(536\) | 1.03516e7 | 1.55631 | ||||||||
\(537\) | −1.95617e6 | −0.292732 | ||||||||
\(538\) | 8.05263e6 | 1.19945 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 61376.0 | 0.00905761 | ||||||||
\(541\) | −8.06623e6 | −1.18489 | −0.592444 | − | 0.805612i | \(-0.701837\pi\) | ||||
−0.592444 | + | 0.805612i | \(0.701837\pi\) | |||||||
\(542\) | −968129. | −0.141558 | ||||||||
\(543\) | −1.69298e6 | −0.246407 | ||||||||
\(544\) | −1.66318e6 | −0.240959 | ||||||||
\(545\) | 1.24791e6 | 0.179967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.90775e6 | 0.558416 | 0.279208 | − | 0.960231i | \(-0.409928\pi\) | ||||
0.279208 | + | 0.960231i | \(0.409928\pi\) | |||||||
\(548\) | −988902. | −0.140670 | ||||||||
\(549\) | 3.33301e6 | 0.471961 | ||||||||
\(550\) | −1.83714e6 | −0.258961 | ||||||||
\(551\) | 2.38377e6 | 0.334492 | ||||||||
\(552\) | −230571. | −0.0322075 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.65811e6 | −0.921672 | ||||||||
\(555\) | −4.17870e6 | −0.575849 | ||||||||
\(556\) | −23184.1 | −0.00318056 | ||||||||
\(557\) | −1.15862e7 | −1.58235 | −0.791177 | − | 0.611588i | \(-0.790531\pi\) | ||||
−0.791177 | + | 0.611588i | \(0.790531\pi\) | |||||||
\(558\) | −3.95663e6 | −0.537948 | ||||||||
\(559\) | −2.00203e6 | −0.270982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.26727e6 | −0.438306 | ||||||||
\(562\) | 968334. | 0.129326 | ||||||||
\(563\) | −1.91176e6 | −0.254192 | −0.127096 | − | 0.991890i | \(-0.540566\pi\) | ||||
−0.127096 | + | 0.991890i | \(0.540566\pi\) | |||||||
\(564\) | −421931. | −0.0558526 | ||||||||
\(565\) | 957041. | 0.126127 | ||||||||
\(566\) | 5.93920e6 | 0.779268 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.19441e7 | 1.55340 | ||||||||
\(569\) | 8.16817e6 | 1.05766 | 0.528828 | − | 0.848729i | \(-0.322632\pi\) | ||||
0.528828 | + | 0.848729i | \(0.322632\pi\) | |||||||
\(570\) | 3.33948e6 | 0.430519 | ||||||||
\(571\) | −7.46593e6 | −0.958283 | −0.479141 | − | 0.877738i | \(-0.659052\pi\) | ||||
−0.479141 | + | 0.877738i | \(0.659052\pi\) | |||||||
\(572\) | 63780.3 | 0.00815072 | ||||||||
\(573\) | 1.56170e6 | 0.198706 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −250552. | −0.0316030 | ||||||||
\(576\) | 2.81880e6 | 0.354004 | ||||||||
\(577\) | 6.88438e6 | 0.860845 | 0.430423 | − | 0.902627i | \(-0.358365\pi\) | ||||
0.430423 | + | 0.902627i | \(0.358365\pi\) | |||||||
\(578\) | 1.33687e7 | 1.66445 | ||||||||
\(579\) | 1.06003e6 | 0.131408 | ||||||||
\(580\) | −106047. | −0.0130896 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.78912e6 | 0.708444 | ||||||||
\(583\) | 1.72153e6 | 0.209770 | ||||||||
\(584\) | 7.72363e6 | 0.937108 | ||||||||
\(585\) | 431195. | 0.0520935 | ||||||||
\(586\) | −2.97223e6 | −0.357551 | ||||||||
\(587\) | 8.91086e6 | 1.06739 | 0.533696 | − | 0.845676i | \(-0.320803\pi\) | ||||
0.533696 | + | 0.845676i | \(0.320803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.69740e7 | 2.01602 | ||||||||
\(590\) | 1.73839e6 | 0.205598 | ||||||||
\(591\) | 2.02261e6 | 0.238200 | ||||||||
\(592\) | −1.21710e7 | −1.42732 | ||||||||
\(593\) | −1.23430e7 | −1.44140 | −0.720700 | − | 0.693247i | \(-0.756180\pi\) | ||||
−0.720700 | + | 0.693247i | \(0.756180\pi\) | |||||||
\(594\) | 732243. | 0.0851508 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.18211e6 | −0.136314 | ||||||||
\(597\) | −6.66246e6 | −0.765066 | ||||||||
\(598\) | −110323. | −0.0126157 | ||||||||
\(599\) | 9.05732e6 | 1.03141 | 0.515707 | − | 0.856765i | \(-0.327529\pi\) | ||||
0.515707 | + | 0.856765i | \(0.327529\pi\) | |||||||
\(600\) | 3.07847e6 | 0.349106 | ||||||||
\(601\) | −7.41700e6 | −0.837611 | −0.418805 | − | 0.908076i | \(-0.637551\pi\) | ||||
−0.418805 | + | 0.908076i | \(0.637551\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.48347e6 | −0.502136 | ||||||||
\(604\) | 451603. | 0.0503691 | ||||||||
\(605\) | 4.57331e6 | 0.507975 | ||||||||
\(606\) | −1.08976e6 | −0.120545 | ||||||||
\(607\) | 5.77813e6 | 0.636525 | 0.318263 | − | 0.948003i | \(-0.396901\pi\) | ||||
0.318263 | + | 0.948003i | \(0.396901\pi\) | |||||||
\(608\) | −1.59908e6 | −0.175432 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.06770e6 | −0.877860 | ||||||||
\(611\) | −2.96426e6 | −0.321228 | ||||||||
\(612\) | 372875. | 0.0402425 | ||||||||
\(613\) | 6.29264e6 | 0.676366 | 0.338183 | − | 0.941080i | \(-0.390188\pi\) | ||||
0.338183 | + | 0.941080i | \(0.390188\pi\) | |||||||
\(614\) | 1.79180e7 | 1.91809 | ||||||||
\(615\) | 2.90810e6 | 0.310043 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.79133e6 | −1.03545 | −0.517725 | − | 0.855547i | \(-0.673221\pi\) | ||||
−0.517725 | + | 0.855547i | \(0.673221\pi\) | |||||||
\(618\) | −6.66277e6 | −0.701752 | ||||||||
\(619\) | 1.32677e7 | 1.39178 | 0.695889 | − | 0.718150i | \(-0.255011\pi\) | ||||
0.695889 | + | 0.718150i | \(0.255011\pi\) | |||||||
\(620\) | −755120. | −0.0788927 | ||||||||
\(621\) | 99864.6 | 0.0103916 | ||||||||
\(622\) | 3.81079e6 | 0.394947 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.25591e6 | 0.129121 | ||||||||
\(625\) | −704759. | −0.0721673 | ||||||||
\(626\) | −3.39419e6 | −0.346178 | ||||||||
\(627\) | −3.14133e6 | −0.319113 | ||||||||
\(628\) | 619567. | 0.0626886 | ||||||||
\(629\) | −2.53867e7 | −2.55846 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.41233e6 | 0.441158 | 0.220579 | − | 0.975369i | \(-0.429205\pi\) | ||||
0.220579 | + | 0.975369i | \(0.429205\pi\) | |||||||
\(632\) | −3.17245e6 | −0.315938 | ||||||||
\(633\) | −6.35306e6 | −0.630193 | ||||||||
\(634\) | −3.48146e6 | −0.343984 | ||||||||
\(635\) | 4.93600e6 | 0.485782 | ||||||||
\(636\) | −196469. | −0.0192598 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.26518e6 | −0.123056 | ||||||||
\(639\) | −5.17321e6 | −0.501196 | ||||||||
\(640\) | −5.84964e6 | −0.564520 | ||||||||
\(641\) | 8.13035e6 | 0.781564 | 0.390782 | − | 0.920483i | \(-0.372205\pi\) | ||||
0.390782 | + | 0.920483i | \(0.372205\pi\) | |||||||
\(642\) | 5.76557e6 | 0.552083 | ||||||||
\(643\) | 3.12961e6 | 0.298513 | 0.149256 | − | 0.988799i | \(-0.452312\pi\) | ||||
0.149256 | + | 0.988799i | \(0.452312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.38661e6 | −0.415174 | ||||||||
\(646\) | 2.02882e7 | 1.91277 | ||||||||
\(647\) | −1.34660e7 | −1.26467 | −0.632336 | − | 0.774695i | \(-0.717904\pi\) | ||||
−0.632336 | + | 0.774695i | \(0.717904\pi\) | |||||||
\(648\) | −1.22701e6 | −0.114792 | ||||||||
\(649\) | −1.63524e6 | −0.152395 | ||||||||
\(650\) | 1.47297e6 | 0.136745 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.26076e6 | 0.116148 | ||||||||
\(653\) | 1.44772e7 | 1.32862 | 0.664312 | − | 0.747455i | \(-0.268725\pi\) | ||||
0.664312 | + | 0.747455i | \(0.268725\pi\) | |||||||
\(654\) | −1.69910e6 | −0.155337 | ||||||||
\(655\) | −1.94721e6 | −0.177341 | ||||||||
\(656\) | 8.47023e6 | 0.768485 | ||||||||
\(657\) | −3.34525e6 | −0.302353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 432708. | 0.0388134 | 0.0194067 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194067 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(660\) | 139748. | 0.0124878 | ||||||||
\(661\) | 29965.2 | 0.00266756 | 0.00133378 | − | 0.999999i | \(-0.499575\pi\) | ||||
0.00133378 | + | 0.999999i | \(0.499575\pi\) | |||||||
\(662\) | 7.67718e6 | 0.680858 | ||||||||
\(663\) | 2.61962e6 | 0.231449 | ||||||||
\(664\) | −1.90182e7 | −1.67398 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.68953e6 | 0.497039 | ||||||||
\(667\) | −172548. | −0.0150174 | ||||||||
\(668\) | 511578. | 0.0443579 | ||||||||
\(669\) | −379928. | −0.0328198 | ||||||||
\(670\) | 1.08524e7 | 0.933986 | ||||||||
\(671\) | 7.58899e6 | 0.650696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.71329e6 | −0.571344 | −0.285672 | − | 0.958327i | \(-0.592217\pi\) | ||||
−0.285672 | + | 0.958327i | \(0.592217\pi\) | |||||||
\(674\) | −8.47849e6 | −0.718901 | ||||||||
\(675\) | −1.33334e6 | −0.112637 | ||||||||
\(676\) | 817193. | 0.0687793 | ||||||||
\(677\) | 4.45929e6 | 0.373933 | 0.186967 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186967 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(678\) | −1.30306e6 | −0.108866 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.32523e7 | −1.09905 | ||||||||
\(681\) | −6.68163e6 | −0.552096 | ||||||||
\(682\) | −9.00892e6 | −0.741672 | ||||||||
\(683\) | −1.79839e7 | −1.47514 | −0.737569 | − | 0.675272i | \(-0.764026\pi\) | ||||
−0.737569 | + | 0.675272i | \(0.764026\pi\) | |||||||
\(684\) | 358502. | 0.0292989 | ||||||||
\(685\) | −1.52225e7 | −1.23954 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.47112e6 | −0.684777 | ||||||||
\(688\) | −1.27766e7 | −1.02907 | ||||||||
\(689\) | −1.38029e6 | −0.110770 | ||||||||
\(690\) | −241726. | −0.0193286 | ||||||||
\(691\) | −2.50935e6 | −0.199925 | −0.0999624 | − | 0.994991i | \(-0.531872\pi\) | ||||
−0.0999624 | + | 0.994991i | \(0.531872\pi\) | |||||||
\(692\) | 1.38028e6 | 0.109573 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.35228e6 | 0.106578 | ||||||||
\(695\) | −356882. | −0.0280261 | ||||||||
\(696\) | 2.12006e6 | 0.165892 | ||||||||
\(697\) | 1.76675e7 | 1.37750 | ||||||||
\(698\) | −1.01392e7 | −0.787707 | ||||||||
\(699\) | −4.61098e6 | −0.356944 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.68649e6 | 0.744512 | 0.372256 | − | 0.928130i | \(-0.378584\pi\) | ||||
0.372256 | + | 0.928130i | \(0.378584\pi\) | |||||||
\(702\) | −587096. | −0.0449641 | ||||||||
\(703\) | −2.44081e7 | −1.86271 | ||||||||
\(704\) | 6.41817e6 | 0.488067 | ||||||||
\(705\) | −6.49495e6 | −0.492156 | ||||||||
\(706\) | −9.64681e6 | −0.728403 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 186621. | 0.0139919 | ||||||||
\(709\) | −9.52720e6 | −0.711786 | −0.355893 | − | 0.934527i | \(-0.615823\pi\) | ||||
−0.355893 | + | 0.934527i | \(0.615823\pi\) | |||||||
\(710\) | 1.25220e7 | 0.932238 | ||||||||
\(711\) | 1.37405e6 | 0.101936 | ||||||||
\(712\) | 1.62896e7 | 1.20423 | ||||||||
\(713\) | −1.22865e6 | −0.0905118 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 981794. | 0.0718217 | ||||||||
\(716\) | 508313. | 0.0370552 | ||||||||
\(717\) | −1.03791e6 | −0.0753980 | ||||||||
\(718\) | −2.43751e7 | −1.76456 | ||||||||
\(719\) | −757176. | −0.0546229 | −0.0273114 | − | 0.999627i | \(-0.508695\pi\) | ||||
−0.0273114 | + | 0.999627i | \(0.508695\pi\) | |||||||
\(720\) | 2.75181e6 | 0.197828 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.02081e6 | 0.429845 | ||||||||
\(723\) | 8.18877e6 | 0.582603 | ||||||||
\(724\) | 439925. | 0.0311912 | ||||||||
\(725\) | 2.30378e6 | 0.162778 | ||||||||
\(726\) | −6.22682e6 | −0.438455 | ||||||||
\(727\) | 2.66570e7 | 1.87058 | 0.935288 | − | 0.353888i | \(-0.115141\pi\) | ||||
0.935288 | + | 0.353888i | \(0.115141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 8.09731e6 | 0.562385 | ||||||||
\(731\) | −2.66498e7 | −1.84459 | ||||||||
\(732\) | −866090. | −0.0597427 | ||||||||
\(733\) | −2.70857e7 | −1.86200 | −0.931001 | − | 0.365017i | \(-0.881063\pi\) | ||||
−0.931001 | + | 0.365017i | \(0.881063\pi\) | |||||||
\(734\) | −1.72698e7 | −1.18317 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 115748. | 0.00787625 | ||||||||
\(737\) | −1.02085e7 | −0.692298 | ||||||||
\(738\) | −3.95954e6 | −0.267611 | ||||||||
\(739\) | 2.19507e7 | 1.47855 | 0.739276 | − | 0.673402i | \(-0.235168\pi\) | ||||
0.739276 | + | 0.673402i | \(0.235168\pi\) | |||||||
\(740\) | 1.08584e6 | 0.0728932 | ||||||||
\(741\) | 2.51865e6 | 0.168508 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.77370e6 | 0.383691 | 0.191846 | − | 0.981425i | \(-0.438553\pi\) | ||||
0.191846 | + | 0.981425i | \(0.438553\pi\) | |||||||
\(744\) | 1.50962e7 | 0.999848 | ||||||||
\(745\) | −1.81966e7 | −1.20116 | ||||||||
\(746\) | −1.25905e7 | −0.828318 | ||||||||
\(747\) | 8.23712e6 | 0.540100 | ||||||||
\(748\) | 849005. | 0.0554825 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.74171e6 | 0.567470 | ||||||||
\(751\) | −8.37749e6 | −0.542018 | −0.271009 | − | 0.962577i | \(-0.587357\pi\) | ||||
−0.271009 | + | 0.962577i | \(0.587357\pi\) | |||||||
\(752\) | −1.89174e7 | −1.21988 | ||||||||
\(753\) | 2.89138e6 | 0.185831 | ||||||||
\(754\) | 1.01440e6 | 0.0649800 | ||||||||
\(755\) | 6.95170e6 | 0.443837 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.18828e7 | 0.753665 | 0.376833 | − | 0.926281i | \(-0.377013\pi\) | ||||
0.376833 | + | 0.926281i | \(0.377013\pi\) | |||||||
\(758\) | −3.22329e6 | −0.203764 | ||||||||
\(759\) | 227383. | 0.0143270 | ||||||||
\(760\) | −1.27415e7 | −0.800177 | ||||||||
\(761\) | −1.76940e7 | −1.10755 | −0.553777 | − | 0.832665i | \(-0.686814\pi\) | ||||
−0.553777 | + | 0.832665i | \(0.686814\pi\) | |||||||
\(762\) | −6.72064e6 | −0.419298 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −405811. | −0.0251531 | ||||||||
\(765\) | 5.73981e6 | 0.354604 | ||||||||
\(766\) | 1.95937e7 | 1.20655 | ||||||||
\(767\) | 1.31110e6 | 0.0804726 | ||||||||
\(768\) | −2.05778e6 | −0.125891 | ||||||||
\(769\) | 4.12006e6 | 0.251239 | 0.125620 | − | 0.992078i | \(-0.459908\pi\) | ||||
0.125620 | + | 0.992078i | \(0.459908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.00843e6 | 0.303435 | ||||||||
\(772\) | −275452. | −0.0166342 | ||||||||
\(773\) | −1.26864e7 | −0.763642 | −0.381821 | − | 0.924236i | \(-0.624703\pi\) | ||||
−0.381821 | + | 0.924236i | \(0.624703\pi\) | |||||||
\(774\) | 5.97262e6 | 0.358354 | ||||||||
\(775\) | 1.64043e7 | 0.981080 | ||||||||
\(776\) | −2.20879e7 | −1.31674 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.22402e7 | −0.725001 | ||||||||
\(779\) | 1.69865e7 | 1.00290 | ||||||||
\(780\) | −112047. | −0.00659421 | ||||||||
\(781\) | −1.17790e7 | −0.691002 | ||||||||
\(782\) | −1.46855e6 | −0.0858761 | ||||||||
\(783\) | −918235. | −0.0535241 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.53723e6 | 0.552393 | ||||||||
\(786\) | 2.65124e6 | 0.153071 | ||||||||
\(787\) | −9.14809e6 | −0.526494 | −0.263247 | − | 0.964728i | \(-0.584793\pi\) | ||||
−0.263247 | + | 0.964728i | \(0.584793\pi\) | |||||||
\(788\) | −525578. | −0.0301524 | ||||||||
\(789\) | −2.10041e6 | −0.120119 | ||||||||
\(790\) | −3.32594e6 | −0.189603 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.79380e6 | −0.158264 | ||||||||
\(793\) | −6.08468e6 | −0.343602 | ||||||||
\(794\) | 2.49802e7 | 1.40619 | ||||||||
\(795\) | −3.02432e6 | −0.169711 | ||||||||
\(796\) | 1.73125e6 | 0.0968451 | ||||||||
\(797\) | 1.10180e7 | 0.614408 | 0.307204 | − | 0.951644i | \(-0.400607\pi\) | ||||
0.307204 | + | 0.951644i | \(0.400607\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.94585e7 | −2.18662 | ||||||||
\(800\) | −1.54541e6 | −0.0853727 | ||||||||
\(801\) | −7.05530e6 | −0.388539 | ||||||||
\(802\) | 3.27009e7 | 1.79524 | ||||||||
\(803\) | −7.61684e6 | −0.416856 | ||||||||
\(804\) | 1.16504e6 | 0.0635624 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.22315e6 | 0.391642 | ||||||||
\(807\) | 1.33071e7 | 0.719285 | ||||||||
\(808\) | 4.15788e6 | 0.224049 | ||||||||
\(809\) | −3.10273e7 | −1.66676 | −0.833378 | − | 0.552703i | \(-0.813596\pi\) | ||||
−0.833378 | + | 0.552703i | \(0.813596\pi\) | |||||||
\(810\) | −1.28638e6 | −0.0688899 | ||||||||
\(811\) | 2.94456e7 | 1.57206 | 0.786028 | − | 0.618191i | \(-0.212134\pi\) | ||||
0.786028 | + | 0.618191i | \(0.212134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.59985e6 | −0.0848895 | ||||||||
\(814\) | 1.29546e7 | 0.685271 | ||||||||
\(815\) | 1.94073e7 | 1.02346 | ||||||||
\(816\) | 1.67180e7 | 0.878937 | ||||||||
\(817\) | −2.56226e7 | −1.34297 | ||||||||
\(818\) | 1.93526e7 | 1.01124 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −755675. | −0.0392464 | ||||||||
\(821\) | −5.23311e6 | −0.270958 | −0.135479 | − | 0.990780i | \(-0.543257\pi\) | ||||
−0.135479 | + | 0.990780i | \(0.543257\pi\) | |||||||
\(822\) | 2.07263e7 | 1.06990 | ||||||||
\(823\) | 1.41631e7 | 0.728884 | 0.364442 | − | 0.931226i | \(-0.381260\pi\) | ||||
0.364442 | + | 0.931226i | \(0.381260\pi\) | |||||||
\(824\) | 2.54212e7 | 1.30430 | ||||||||
\(825\) | −3.03591e6 | −0.155294 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.98006e7 | 1.51517 | 0.757585 | − | 0.652737i | \(-0.226379\pi\) | ||||
0.757585 | + | 0.652737i | \(0.226379\pi\) | |||||||
\(828\) | −25950.0 | −0.00131541 | ||||||||
\(829\) | 1.99304e7 | 1.00723 | 0.503617 | − | 0.863927i | \(-0.332002\pi\) | ||||
0.503617 | + | 0.863927i | \(0.332002\pi\) | |||||||
\(830\) | −1.99383e7 | −1.00460 | ||||||||
\(831\) | −1.10027e7 | −0.552708 | ||||||||
\(832\) | −5.14594e6 | −0.257725 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 485914. | 0.0241905 | ||||||||
\(835\) | 7.87492e6 | 0.390868 | ||||||||
\(836\) | 816280. | 0.0403946 | ||||||||
\(837\) | −6.53842e6 | −0.322596 | ||||||||
\(838\) | −1.09673e7 | −0.539500 | ||||||||
\(839\) | 1.88103e7 | 0.922552 | 0.461276 | − | 0.887257i | \(-0.347392\pi\) | ||||
0.461276 | + | 0.887257i | \(0.347392\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.89246e7 | −0.922650 | ||||||||
\(842\) | −3.21320e7 | −1.56191 | ||||||||
\(843\) | 1.60019e6 | 0.0775538 | ||||||||
\(844\) | 1.65085e6 | 0.0797724 | ||||||||
\(845\) | 1.25794e7 | 0.606062 | ||||||||
\(846\) | 8.84324e6 | 0.424801 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.80874e6 | −0.420653 | ||||||||
\(849\) | 9.81466e6 | 0.467311 | ||||||||
\(850\) | 1.96073e7 | 0.930833 | ||||||||
\(851\) | 1.76677e6 | 0.0836288 | ||||||||
\(852\) | 1.34427e6 | 0.0634434 | ||||||||
\(853\) | −2.05980e7 | −0.969285 | −0.484643 | − | 0.874712i | \(-0.661050\pi\) | ||||
−0.484643 | + | 0.874712i | \(0.661050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.51856e6 | 0.258173 | ||||||||
\(856\) | −2.19980e7 | −1.02612 | ||||||||
\(857\) | 2.47572e7 | 1.15146 | 0.575731 | − | 0.817639i | \(-0.304718\pi\) | ||||
0.575731 | + | 0.817639i | \(0.304718\pi\) | |||||||
\(858\) | −1.33677e6 | −0.0619923 | ||||||||
\(859\) | 3.91065e7 | 1.80828 | 0.904141 | − | 0.427234i | \(-0.140512\pi\) | ||||
0.904141 | + | 0.427234i | \(0.140512\pi\) | |||||||
\(860\) | 1.13987e6 | 0.0525544 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.07527e7 | −0.951275 | ||||||||
\(863\) | −3.93363e7 | −1.79790 | −0.898952 | − | 0.438048i | \(-0.855670\pi\) | ||||
−0.898952 | + | 0.438048i | \(0.855670\pi\) | |||||||
\(864\) | 615968. | 0.0280720 | ||||||||
\(865\) | 2.12472e7 | 0.965522 | ||||||||
\(866\) | −3.59151e7 | −1.62735 | ||||||||
\(867\) | 2.20921e7 | 0.998135 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.12859e6 | 0.140540 | ||||||||
\(870\) | 2.22263e6 | 0.0995563 | ||||||||
\(871\) | 8.18494e6 | 0.365570 | ||||||||
\(872\) | 6.48277e6 | 0.288715 | ||||||||
\(873\) | 9.56665e6 | 0.424839 | ||||||||
\(874\) | −1.41195e6 | −0.0625229 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 869268. | 0.0382731 | ||||||||
\(877\) | 8.09253e6 | 0.355292 | 0.177646 | − | 0.984094i | \(-0.443152\pi\) | ||||
0.177646 | + | 0.984094i | \(0.443152\pi\) | |||||||
\(878\) | 2.47818e7 | 1.08492 | ||||||||
\(879\) | −4.91168e6 | −0.214416 | ||||||||
\(880\) | 6.26564e6 | 0.272746 | ||||||||
\(881\) | 4.05755e6 | 0.176126 | 0.0880631 | − | 0.996115i | \(-0.471932\pi\) | ||||
0.0880631 | + | 0.996115i | \(0.471932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.79813e7 | 0.776102 | 0.388051 | − | 0.921638i | \(-0.373148\pi\) | ||||
0.388051 | + | 0.921638i | \(0.373148\pi\) | |||||||
\(884\) | −680713. | −0.0292977 | ||||||||
\(885\) | 2.87273e6 | 0.123293 | ||||||||
\(886\) | 2.78595e7 | 1.19231 | ||||||||
\(887\) | 1.53139e7 | 0.653547 | 0.326773 | − | 0.945103i | \(-0.394039\pi\) | ||||
0.326773 | + | 0.945103i | \(0.394039\pi\) | |||||||
\(888\) | −2.17079e7 | −0.923814 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.70777e7 | 0.722693 | ||||||||
\(891\) | 1.21005e6 | 0.0510632 | ||||||||
\(892\) | 98725.0 | 0.00415447 | ||||||||
\(893\) | −3.79376e7 | −1.59199 | ||||||||
\(894\) | 2.47757e7 | 1.03677 | ||||||||
\(895\) | 7.82466e6 | 0.326519 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −182311. | −0.00756539 | ||||||||
\(898\) | 3.24377e7 | 1.34233 | ||||||||
\(899\) | 1.12972e7 | 0.466200 | ||||||||
\(900\) | 346471. | 0.0142581 | ||||||||
\(901\) | −1.83735e7 | −0.754016 | ||||||||
\(902\) | −9.01554e6 | −0.368957 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.97172e6 | 0.202342 | ||||||||
\(905\) | 6.77194e6 | 0.274847 | ||||||||
\(906\) | −9.46512e6 | −0.383094 | ||||||||
\(907\) | −2.17757e7 | −0.878930 | −0.439465 | − | 0.898260i | \(-0.644832\pi\) | ||||
−0.439465 | + | 0.898260i | \(0.644832\pi\) | |||||||
\(908\) | 1.73623e6 | 0.0698865 | ||||||||
\(909\) | −1.80085e6 | −0.0722883 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.35112e6 | −0.213623 | −0.106812 | − | 0.994279i | \(-0.534064\pi\) | ||||
−0.106812 | + | 0.994279i | \(0.534064\pi\) | |||||||
\(912\) | 1.60736e7 | 0.639919 | ||||||||
\(913\) | 1.87552e7 | 0.744639 | ||||||||
\(914\) | −1.41511e7 | −0.560306 | ||||||||
\(915\) | −1.33321e7 | −0.526435 | ||||||||
\(916\) | 2.20124e6 | 0.0866818 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.81507e6 | −0.306074 | ||||||||
\(919\) | −2.67858e7 | −1.04620 | −0.523102 | − | 0.852270i | \(-0.675225\pi\) | ||||
−0.523102 | + | 0.852270i | \(0.675225\pi\) | |||||||
\(920\) | 922285. | 0.0359249 | ||||||||
\(921\) | 2.96100e7 | 1.15024 | ||||||||
\(922\) | −2.45904e7 | −0.952661 | ||||||||
\(923\) | 9.44411e6 | 0.364886 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.35890e7 | −0.906474 | ||||||||
\(926\) | −3.02336e7 | −1.15868 | ||||||||
\(927\) | −1.10104e7 | −0.420826 | ||||||||
\(928\) | −1.06428e6 | −0.0405683 | ||||||||
\(929\) | −739974. | −0.0281305 | −0.0140652 | − | 0.999901i | \(-0.504477\pi\) | ||||
−0.0140652 | + | 0.999901i | \(0.504477\pi\) | |||||||
\(930\) | 1.58265e7 | 0.600037 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.19817e6 | 0.0451834 | ||||||||
\(933\) | 6.29741e6 | 0.236841 | ||||||||
\(934\) | 4.33166e7 | 1.62475 | ||||||||
\(935\) | 1.30691e7 | 0.488895 | ||||||||
\(936\) | 2.24001e6 | 0.0835719 | ||||||||
\(937\) | 122654. | 0.00456385 | 0.00228193 | − | 0.999997i | \(-0.499274\pi\) | ||||
0.00228193 | + | 0.999997i | \(0.499274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.60897e6 | −0.207596 | ||||||||
\(940\) | 1.68772e6 | 0.0622991 | ||||||||
\(941\) | −1.22466e7 | −0.450861 | −0.225431 | − | 0.974259i | \(-0.572379\pi\) | ||||
−0.225431 | + | 0.974259i | \(0.572379\pi\) | |||||||
\(942\) | −1.29855e7 | −0.476794 | ||||||||
\(943\) | −1.22956e6 | −0.0450266 | ||||||||
\(944\) | 8.36722e6 | 0.305599 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.35992e7 | 0.494065 | ||||||||
\(947\) | −3.71174e6 | −0.134494 | −0.0672470 | − | 0.997736i | \(-0.521422\pi\) | ||||
−0.0672470 | + | 0.997736i | \(0.521422\pi\) | |||||||
\(948\) | −357048. | −0.0129034 | ||||||||
\(949\) | 6.10701e6 | 0.220122 | ||||||||
\(950\) | 1.88516e7 | 0.677702 | ||||||||
\(951\) | −5.75319e6 | −0.206280 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.32857e7 | −0.830533 | −0.415266 | − | 0.909700i | \(-0.636312\pi\) | ||||
−0.415266 | + | 0.909700i | \(0.636312\pi\) | |||||||
\(954\) | 4.11778e6 | 0.146485 | ||||||||
\(955\) | −6.24681e6 | −0.221641 | ||||||||
\(956\) | 269702. | 0.00954418 | ||||||||
\(957\) | −2.09075e6 | −0.0737940 | ||||||||
\(958\) | 3.57474e7 | 1.25843 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.12752e7 | −0.394862 | ||||||||
\(961\) | 5.18142e7 | 1.80984 | ||||||||
\(962\) | −1.03867e7 | −0.361859 | ||||||||
\(963\) | 9.52772e6 | 0.331073 | ||||||||
\(964\) | −2.12787e6 | −0.0737483 | ||||||||
\(965\) | −4.24013e6 | −0.146575 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.25257e7 | 0.774661 | 0.387330 | − | 0.921941i | \(-0.373397\pi\) | ||||
0.387330 | + | 0.921941i | \(0.373397\pi\) | |||||||
\(968\) | 2.37579e7 | 0.814927 | ||||||||
\(969\) | 3.35267e7 | 1.14705 | ||||||||
\(970\) | −2.31565e7 | −0.790212 | ||||||||
\(971\) | −1.99456e7 | −0.678890 | −0.339445 | − | 0.940626i | \(-0.610239\pi\) | ||||
−0.339445 | + | 0.940626i | \(0.610239\pi\) | |||||||
\(972\) | −138096. | −0.00468830 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.53995e7 | 0.857884 | ||||||||
\(975\) | 2.43412e6 | 0.0820032 | ||||||||
\(976\) | −3.88314e7 | −1.30484 | ||||||||
\(977\) | −959342. | −0.0321542 | −0.0160771 | − | 0.999871i | \(-0.505118\pi\) | ||||
−0.0160771 | + | 0.999871i | \(0.505118\pi\) | |||||||
\(978\) | −2.64242e7 | −0.883393 | ||||||||
\(979\) | −1.60643e7 | −0.535681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.80780e6 | −0.0931524 | ||||||||
\(982\) | −4.99542e6 | −0.165308 | ||||||||
\(983\) | −5.22097e7 | −1.72333 | −0.861663 | − | 0.507481i | \(-0.830577\pi\) | ||||
−0.861663 | + | 0.507481i | \(0.830577\pi\) | |||||||
\(984\) | 1.51073e7 | 0.497391 | ||||||||
\(985\) | −8.09042e6 | −0.265693 | ||||||||
\(986\) | 1.35030e7 | 0.442323 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −654475. | −0.0213305 | ||||||||
\(989\) | 1.85468e6 | 0.0602945 | ||||||||
\(990\) | −2.92897e6 | −0.0949789 | ||||||||
\(991\) | −1.76305e7 | −0.570269 | −0.285134 | − | 0.958488i | \(-0.592038\pi\) | ||||
−0.285134 | + | 0.958488i | \(0.592038\pi\) | |||||||
\(992\) | −7.57836e6 | −0.244510 | ||||||||
\(993\) | 1.26867e7 | 0.408296 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.66498e7 | 0.853369 | ||||||||
\(996\) | −2.14043e6 | −0.0683680 | ||||||||
\(997\) | −4.04875e7 | −1.28998 | −0.644990 | − | 0.764191i | \(-0.723138\pi\) | ||||
−0.644990 | + | 0.764191i | \(0.723138\pi\) | |||||||
\(998\) | 1.70704e6 | 0.0542522 | ||||||||
\(999\) | 9.40207e6 | 0.298064 |
(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.j.1.2 | yes | 2 | |
3.2 | odd | 2 | 441.6.a.r.1.1 | 2 | |||
7.2 | even | 3 | 147.6.e.m.67.1 | 4 | |||
7.3 | odd | 6 | 147.6.e.n.79.1 | 4 | |||
7.4 | even | 3 | 147.6.e.m.79.1 | 4 | |||
7.5 | odd | 6 | 147.6.e.n.67.1 | 4 | |||
7.6 | odd | 2 | 147.6.a.h.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 441.6.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.h.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
147.6.a.j.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
147.6.e.m.67.1 | 4 | 7.2 | even | 3 | |||
147.6.e.m.79.1 | 4 | 7.4 | even | 3 | |||
147.6.e.n.67.1 | 4 | 7.5 | odd | 6 | |||
147.6.e.n.79.1 | 4 | 7.3 | odd | 6 | |||
441.6.a.q.1.1 | 2 | 21.20 | even | 2 | |||
441.6.a.r.1.1 | 2 | 3.2 | odd | 2 |