Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,6,Mod(1,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, 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("471.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.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: | \(75.5407791319\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 471.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.49004 | −1.14729 | −0.573644 | − | 0.819105i | \(-0.694471\pi\) | ||||
−0.573644 | + | 0.819105i | \(0.694471\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 10.1206 | 0.316268 | ||||||||
\(5\) | 53.7142 | 0.960869 | 0.480434 | − | 0.877031i | \(-0.340479\pi\) | ||||
0.480434 | + | 0.877031i | \(0.340479\pi\) | |||||||
\(6\) | 58.4103 | 0.662386 | ||||||||
\(7\) | −12.0983 | −0.0933212 | −0.0466606 | − | 0.998911i | \(-0.514858\pi\) | ||||
−0.0466606 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(8\) | 141.998 | 0.784437 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −348.607 | −1.10239 | ||||||||
\(11\) | 408.862 | 1.01882 | 0.509408 | − | 0.860525i | \(-0.329865\pi\) | ||||
0.509408 | + | 0.860525i | \(0.329865\pi\) | |||||||
\(12\) | −91.0850 | −0.182597 | ||||||||
\(13\) | 189.549 | 0.311073 | 0.155537 | − | 0.987830i | \(-0.450289\pi\) | ||||
0.155537 | + | 0.987830i | \(0.450289\pi\) | |||||||
\(14\) | 78.5186 | 0.107066 | ||||||||
\(15\) | −483.428 | −0.554758 | ||||||||
\(16\) | −1245.43 | −1.21624 | ||||||||
\(17\) | −1386.60 | −1.16367 | −0.581833 | − | 0.813308i | \(-0.697664\pi\) | ||||
−0.581833 | + | 0.813308i | \(0.697664\pi\) | |||||||
\(18\) | −525.693 | −0.382429 | ||||||||
\(19\) | −1113.04 | −0.707339 | −0.353669 | − | 0.935370i | \(-0.615066\pi\) | ||||
−0.353669 | + | 0.935370i | \(0.615066\pi\) | |||||||
\(20\) | 543.618 | 0.303892 | ||||||||
\(21\) | 108.885 | 0.0538790 | ||||||||
\(22\) | −2653.53 | −1.16887 | ||||||||
\(23\) | 514.374 | 0.202749 | 0.101375 | − | 0.994848i | \(-0.467676\pi\) | ||||
0.101375 | + | 0.994848i | \(0.467676\pi\) | |||||||
\(24\) | −1277.99 | −0.452895 | ||||||||
\(25\) | −239.786 | −0.0767316 | ||||||||
\(26\) | −1230.18 | −0.356890 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −122.442 | −0.0295145 | ||||||||
\(29\) | 8455.59 | 1.86702 | 0.933510 | − | 0.358551i | \(-0.116729\pi\) | ||||
0.933510 | + | 0.358551i | \(0.116729\pi\) | |||||||
\(30\) | 3137.46 | 0.636466 | ||||||||
\(31\) | −9630.57 | −1.79990 | −0.899949 | − | 0.435995i | \(-0.856396\pi\) | ||||
−0.899949 | + | 0.435995i | \(0.856396\pi\) | |||||||
\(32\) | 3538.95 | 0.610942 | ||||||||
\(33\) | −3679.76 | −0.588213 | ||||||||
\(34\) | 8999.08 | 1.33506 | ||||||||
\(35\) | −649.852 | −0.0896694 | ||||||||
\(36\) | 819.765 | 0.105423 | ||||||||
\(37\) | −2498.37 | −0.300022 | −0.150011 | − | 0.988684i | \(-0.547931\pi\) | ||||
−0.150011 | + | 0.988684i | \(0.547931\pi\) | |||||||
\(38\) | 7223.68 | 0.811521 | ||||||||
\(39\) | −1705.94 | −0.179598 | ||||||||
\(40\) | 7627.32 | 0.753741 | ||||||||
\(41\) | −8737.69 | −0.811777 | −0.405889 | − | 0.913923i | \(-0.633038\pi\) | ||||
−0.405889 | + | 0.913923i | \(0.633038\pi\) | |||||||
\(42\) | −706.667 | −0.0618147 | ||||||||
\(43\) | 11668.7 | 0.962392 | 0.481196 | − | 0.876613i | \(-0.340203\pi\) | ||||
0.481196 | + | 0.876613i | \(0.340203\pi\) | |||||||
\(44\) | 4137.92 | 0.322218 | ||||||||
\(45\) | 4350.85 | 0.320290 | ||||||||
\(46\) | −3338.31 | −0.232612 | ||||||||
\(47\) | −10604.0 | −0.700205 | −0.350103 | − | 0.936711i | \(-0.613853\pi\) | ||||
−0.350103 | + | 0.936711i | \(0.613853\pi\) | |||||||
\(48\) | 11208.9 | 0.702198 | ||||||||
\(49\) | −16660.6 | −0.991291 | ||||||||
\(50\) | 1556.22 | 0.0880332 | ||||||||
\(51\) | 12479.4 | 0.671843 | ||||||||
\(52\) | 1918.34 | 0.0983824 | ||||||||
\(53\) | 7888.65 | 0.385756 | 0.192878 | − | 0.981223i | \(-0.438218\pi\) | ||||
0.192878 | + | 0.981223i | \(0.438218\pi\) | |||||||
\(54\) | 4731.24 | 0.220795 | ||||||||
\(55\) | 21961.7 | 0.978948 | ||||||||
\(56\) | −1717.94 | −0.0732046 | ||||||||
\(57\) | 10017.4 | 0.408382 | ||||||||
\(58\) | −54877.1 | −2.14201 | ||||||||
\(59\) | 18115.2 | 0.677507 | 0.338753 | − | 0.940875i | \(-0.389995\pi\) | ||||
0.338753 | + | 0.940875i | \(0.389995\pi\) | |||||||
\(60\) | −4892.56 | −0.175452 | ||||||||
\(61\) | 3430.96 | 0.118057 | 0.0590285 | − | 0.998256i | \(-0.481200\pi\) | ||||
0.0590285 | + | 0.998256i | \(0.481200\pi\) | |||||||
\(62\) | 62502.8 | 2.06500 | ||||||||
\(63\) | −979.965 | −0.0311071 | ||||||||
\(64\) | 16885.9 | 0.515317 | ||||||||
\(65\) | 10181.5 | 0.298900 | ||||||||
\(66\) | 23881.8 | 0.674850 | ||||||||
\(67\) | −49952.6 | −1.35947 | −0.679737 | − | 0.733456i | \(-0.737906\pi\) | ||||
−0.679737 | + | 0.733456i | \(0.737906\pi\) | |||||||
\(68\) | −14033.2 | −0.368030 | ||||||||
\(69\) | −4629.37 | −0.117057 | ||||||||
\(70\) | 4217.56 | 0.102877 | ||||||||
\(71\) | 51047.2 | 1.20178 | 0.600892 | − | 0.799330i | \(-0.294812\pi\) | ||||
0.600892 | + | 0.799330i | \(0.294812\pi\) | |||||||
\(72\) | 11501.9 | 0.261479 | ||||||||
\(73\) | 37546.7 | 0.824640 | 0.412320 | − | 0.911039i | \(-0.364719\pi\) | ||||
0.412320 | + | 0.911039i | \(0.364719\pi\) | |||||||
\(74\) | 16214.5 | 0.344211 | ||||||||
\(75\) | 2158.08 | 0.0443010 | ||||||||
\(76\) | −11264.6 | −0.223708 | ||||||||
\(77\) | −4946.55 | −0.0950771 | ||||||||
\(78\) | 11071.6 | 0.206051 | ||||||||
\(79\) | 74312.4 | 1.33966 | 0.669828 | − | 0.742516i | \(-0.266368\pi\) | ||||
0.669828 | + | 0.742516i | \(0.266368\pi\) | |||||||
\(80\) | −66897.4 | −1.16865 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 56707.9 | 0.931342 | ||||||||
\(83\) | 91279.3 | 1.45438 | 0.727189 | − | 0.686438i | \(-0.240827\pi\) | ||||
0.727189 | + | 0.686438i | \(0.240827\pi\) | |||||||
\(84\) | 1101.98 | 0.0170402 | ||||||||
\(85\) | −74480.0 | −1.11813 | ||||||||
\(86\) | −75730.4 | −1.10414 | ||||||||
\(87\) | −76100.3 | −1.07792 | ||||||||
\(88\) | 58057.8 | 0.799197 | ||||||||
\(89\) | −71017.1 | −0.950360 | −0.475180 | − | 0.879889i | \(-0.657617\pi\) | ||||
−0.475180 | + | 0.879889i | \(0.657617\pi\) | |||||||
\(90\) | −28237.2 | −0.367464 | ||||||||
\(91\) | −2293.22 | −0.0290297 | ||||||||
\(92\) | 5205.76 | 0.0641231 | ||||||||
\(93\) | 86675.1 | 1.03917 | ||||||||
\(94\) | 68820.4 | 0.803337 | ||||||||
\(95\) | −59786.1 | −0.679660 | ||||||||
\(96\) | −31850.6 | −0.352727 | ||||||||
\(97\) | 7163.89 | 0.0773071 | 0.0386535 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386535 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(98\) | 108128. | 1.13730 | ||||||||
\(99\) | 33117.9 | 0.339605 | ||||||||
\(100\) | −2426.77 | −0.0242677 | ||||||||
\(101\) | −148793. | −1.45138 | −0.725688 | − | 0.688024i | \(-0.758478\pi\) | ||||
−0.725688 | + | 0.688024i | \(0.758478\pi\) | |||||||
\(102\) | −80991.7 | −0.770797 | ||||||||
\(103\) | −40507.6 | −0.376221 | −0.188111 | − | 0.982148i | \(-0.560236\pi\) | ||||
−0.188111 | + | 0.982148i | \(0.560236\pi\) | |||||||
\(104\) | 26915.6 | 0.244017 | ||||||||
\(105\) | 5848.67 | 0.0517707 | ||||||||
\(106\) | −51197.6 | −0.442573 | ||||||||
\(107\) | −222721. | −1.88062 | −0.940312 | − | 0.340313i | \(-0.889467\pi\) | ||||
−0.940312 | + | 0.340313i | \(0.889467\pi\) | |||||||
\(108\) | −7377.89 | −0.0608657 | ||||||||
\(109\) | −108927. | −0.878150 | −0.439075 | − | 0.898450i | \(-0.644694\pi\) | ||||
−0.439075 | + | 0.898450i | \(0.644694\pi\) | |||||||
\(110\) | −142532. | −1.12313 | ||||||||
\(111\) | 22485.4 | 0.173218 | ||||||||
\(112\) | 15067.6 | 0.113501 | ||||||||
\(113\) | −24340.1 | −0.179319 | −0.0896594 | − | 0.995972i | \(-0.528578\pi\) | ||||
−0.0896594 | + | 0.995972i | \(0.528578\pi\) | |||||||
\(114\) | −65013.1 | −0.468532 | ||||||||
\(115\) | 27629.2 | 0.194816 | ||||||||
\(116\) | 85575.3 | 0.590478 | ||||||||
\(117\) | 15353.5 | 0.103691 | ||||||||
\(118\) | −117568. | −0.777295 | ||||||||
\(119\) | 16775.5 | 0.108595 | ||||||||
\(120\) | −68645.9 | −0.435173 | ||||||||
\(121\) | 6117.48 | 0.0379847 | ||||||||
\(122\) | −22267.1 | −0.135445 | ||||||||
\(123\) | 78639.2 | 0.468680 | ||||||||
\(124\) | −97466.8 | −0.569249 | ||||||||
\(125\) | −180737. | −1.03460 | ||||||||
\(126\) | 6360.01 | 0.0356887 | ||||||||
\(127\) | 258492. | 1.42213 | 0.711063 | − | 0.703128i | \(-0.248214\pi\) | ||||
0.711063 | + | 0.703128i | \(0.248214\pi\) | |||||||
\(128\) | −222837. | −1.20216 | ||||||||
\(129\) | −105018. | −0.555637 | ||||||||
\(130\) | −66078.0 | −0.342925 | ||||||||
\(131\) | −230011. | −1.17104 | −0.585518 | − | 0.810660i | \(-0.699109\pi\) | ||||
−0.585518 | + | 0.810660i | \(0.699109\pi\) | |||||||
\(132\) | −37241.3 | −0.186033 | ||||||||
\(133\) | 13465.9 | 0.0660097 | ||||||||
\(134\) | 324194. | 1.55971 | ||||||||
\(135\) | −39157.6 | −0.184919 | ||||||||
\(136\) | −196895. | −0.912824 | ||||||||
\(137\) | −164567. | −0.749104 | −0.374552 | − | 0.927206i | \(-0.622204\pi\) | ||||
−0.374552 | + | 0.927206i | \(0.622204\pi\) | |||||||
\(138\) | 30044.8 | 0.134298 | ||||||||
\(139\) | 300503. | 1.31920 | 0.659601 | − | 0.751616i | \(-0.270725\pi\) | ||||
0.659601 | + | 0.751616i | \(0.270725\pi\) | |||||||
\(140\) | −6576.87 | −0.0283595 | ||||||||
\(141\) | 95436.1 | 0.404264 | ||||||||
\(142\) | −331298. | −1.37879 | ||||||||
\(143\) | 77499.4 | 0.316926 | ||||||||
\(144\) | −100880. | −0.405414 | ||||||||
\(145\) | 454185. | 1.79396 | ||||||||
\(146\) | −243679. | −0.946098 | ||||||||
\(147\) | 149946. | 0.572322 | ||||||||
\(148\) | −25284.9 | −0.0948872 | ||||||||
\(149\) | 258903. | 0.955371 | 0.477685 | − | 0.878531i | \(-0.341476\pi\) | ||||
0.477685 | + | 0.878531i | \(0.341476\pi\) | |||||||
\(150\) | −14006.0 | −0.0508260 | ||||||||
\(151\) | −278910. | −0.995455 | −0.497727 | − | 0.867334i | \(-0.665832\pi\) | ||||
−0.497727 | + | 0.867334i | \(0.665832\pi\) | |||||||
\(152\) | −158050. | −0.554863 | ||||||||
\(153\) | −112315. | −0.387889 | ||||||||
\(154\) | 32103.3 | 0.109081 | ||||||||
\(155\) | −517298. | −1.72947 | ||||||||
\(156\) | −17265.1 | −0.0568011 | ||||||||
\(157\) | −24649.0 | −0.0798087 | ||||||||
\(158\) | −482290. | −1.53697 | ||||||||
\(159\) | −70997.8 | −0.222716 | ||||||||
\(160\) | 190092. | 0.587035 | ||||||||
\(161\) | −6223.07 | −0.0189208 | ||||||||
\(162\) | −42581.1 | −0.127476 | ||||||||
\(163\) | −95574.8 | −0.281757 | −0.140878 | − | 0.990027i | \(-0.544993\pi\) | ||||
−0.140878 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(164\) | −88430.3 | −0.256739 | ||||||||
\(165\) | −197655. | −0.565196 | ||||||||
\(166\) | −592406. | −1.66859 | ||||||||
\(167\) | −261265. | −0.724920 | −0.362460 | − | 0.931999i | \(-0.618063\pi\) | ||||
−0.362460 | + | 0.931999i | \(0.618063\pi\) | |||||||
\(168\) | 15461.5 | 0.0422647 | ||||||||
\(169\) | −335364. | −0.903233 | ||||||||
\(170\) | 483378. | 1.28282 | ||||||||
\(171\) | −90156.4 | −0.235780 | ||||||||
\(172\) | 118094. | 0.304373 | ||||||||
\(173\) | −549175. | −1.39507 | −0.697534 | − | 0.716552i | \(-0.745719\pi\) | ||||
−0.697534 | + | 0.716552i | \(0.745719\pi\) | |||||||
\(174\) | 493894. | 1.23669 | ||||||||
\(175\) | 2901.01 | 0.00716069 | ||||||||
\(176\) | −509210. | −1.23913 | ||||||||
\(177\) | −163037. | −0.391159 | ||||||||
\(178\) | 460904. | 1.09034 | ||||||||
\(179\) | −58805.3 | −0.137178 | −0.0685890 | − | 0.997645i | \(-0.521850\pi\) | ||||
−0.0685890 | + | 0.997645i | \(0.521850\pi\) | |||||||
\(180\) | 44033.0 | 0.101297 | ||||||||
\(181\) | 51739.5 | 0.117389 | 0.0586943 | − | 0.998276i | \(-0.481306\pi\) | ||||
0.0586943 | + | 0.998276i | \(0.481306\pi\) | |||||||
\(182\) | 14883.1 | 0.0333054 | ||||||||
\(183\) | −30878.7 | −0.0681602 | ||||||||
\(184\) | 73040.3 | 0.159044 | ||||||||
\(185\) | −134198. | −0.288282 | ||||||||
\(186\) | −562525. | −1.19223 | ||||||||
\(187\) | −566928. | −1.18556 | ||||||||
\(188\) | −107319. | −0.221452 | ||||||||
\(189\) | 8819.68 | 0.0179597 | ||||||||
\(190\) | 388014. | 0.779765 | ||||||||
\(191\) | −30685.3 | −0.0608621 | −0.0304311 | − | 0.999537i | \(-0.509688\pi\) | ||||
−0.0304311 | + | 0.999537i | \(0.509688\pi\) | |||||||
\(192\) | −151973. | −0.297518 | ||||||||
\(193\) | 759969. | 1.46860 | 0.734299 | − | 0.678826i | \(-0.237511\pi\) | ||||
0.734299 | + | 0.678826i | \(0.237511\pi\) | |||||||
\(194\) | −46493.9 | −0.0886934 | ||||||||
\(195\) | −91633.1 | −0.172570 | ||||||||
\(196\) | −168615. | −0.313513 | ||||||||
\(197\) | 494617. | 0.908037 | 0.454019 | − | 0.890992i | \(-0.349990\pi\) | ||||
0.454019 | + | 0.890992i | \(0.349990\pi\) | |||||||
\(198\) | −214936. | −0.389625 | ||||||||
\(199\) | −545815. | −0.977042 | −0.488521 | − | 0.872552i | \(-0.662463\pi\) | ||||
−0.488521 | + | 0.872552i | \(0.662463\pi\) | |||||||
\(200\) | −34049.3 | −0.0601912 | ||||||||
\(201\) | 449573. | 0.784893 | ||||||||
\(202\) | 965674. | 1.66515 | ||||||||
\(203\) | −102299. | −0.174233 | ||||||||
\(204\) | 126298. | 0.212482 | ||||||||
\(205\) | −469338. | −0.780011 | ||||||||
\(206\) | 262896. | 0.431634 | ||||||||
\(207\) | 41664.3 | 0.0675831 | ||||||||
\(208\) | −236070. | −0.378340 | ||||||||
\(209\) | −455081. | −0.720648 | ||||||||
\(210\) | −37958.1 | −0.0593958 | ||||||||
\(211\) | 65101.0 | 0.100666 | 0.0503328 | − | 0.998733i | \(-0.483972\pi\) | ||||
0.0503328 | + | 0.998733i | \(0.483972\pi\) | |||||||
\(212\) | 79837.6 | 0.122002 | ||||||||
\(213\) | −459425. | −0.693850 | ||||||||
\(214\) | 1.44547e6 | 2.15762 | ||||||||
\(215\) | 626776. | 0.924732 | ||||||||
\(216\) | −103517. | −0.150965 | ||||||||
\(217\) | 116514. | 0.167969 | ||||||||
\(218\) | 706939. | 1.00749 | ||||||||
\(219\) | −337920. | −0.476106 | ||||||||
\(220\) | 222265. | 0.309609 | ||||||||
\(221\) | −262828. | −0.361986 | ||||||||
\(222\) | −145931. | −0.198730 | ||||||||
\(223\) | −205645. | −0.276922 | −0.138461 | − | 0.990368i | \(-0.544216\pi\) | ||||
−0.138461 | + | 0.990368i | \(0.544216\pi\) | |||||||
\(224\) | −42815.4 | −0.0570138 | ||||||||
\(225\) | −19422.7 | −0.0255772 | ||||||||
\(226\) | 157968. | 0.205730 | ||||||||
\(227\) | −643697. | −0.829119 | −0.414559 | − | 0.910022i | \(-0.636064\pi\) | ||||
−0.414559 | + | 0.910022i | \(0.636064\pi\) | |||||||
\(228\) | 101381. | 0.129158 | ||||||||
\(229\) | −1.26241e6 | −1.59078 | −0.795391 | − | 0.606097i | \(-0.792734\pi\) | ||||
−0.795391 | + | 0.606097i | \(0.792734\pi\) | |||||||
\(230\) | −179314. | −0.223509 | ||||||||
\(231\) | 44519.0 | 0.0548928 | ||||||||
\(232\) | 1.20068e6 | 1.46456 | ||||||||
\(233\) | 400693. | 0.483528 | 0.241764 | − | 0.970335i | \(-0.422274\pi\) | ||||
0.241764 | + | 0.970335i | \(0.422274\pi\) | |||||||
\(234\) | −99644.4 | −0.118963 | ||||||||
\(235\) | −569586. | −0.672805 | ||||||||
\(236\) | 183336. | 0.214273 | ||||||||
\(237\) | −668811. | −0.773451 | ||||||||
\(238\) | −108874. | −0.124589 | ||||||||
\(239\) | 44637.9 | 0.0505486 | 0.0252743 | − | 0.999681i | \(-0.491954\pi\) | ||||
0.0252743 | + | 0.999681i | \(0.491954\pi\) | |||||||
\(240\) | 602076. | 0.674720 | ||||||||
\(241\) | 1.05576e6 | 1.17091 | 0.585455 | − | 0.810705i | \(-0.300916\pi\) | ||||
0.585455 | + | 0.810705i | \(0.300916\pi\) | |||||||
\(242\) | −39702.6 | −0.0435794 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 34723.3 | 0.0373376 | ||||||||
\(245\) | −894912. | −0.952500 | ||||||||
\(246\) | −510371. | −0.537710 | ||||||||
\(247\) | −210976. | −0.220034 | ||||||||
\(248\) | −1.36753e6 | −1.41191 | ||||||||
\(249\) | −821514. | −0.839685 | ||||||||
\(250\) | 1.17299e6 | 1.18698 | ||||||||
\(251\) | −1.86845e6 | −1.87196 | −0.935981 | − | 0.352050i | \(-0.885485\pi\) | ||||
−0.935981 | + | 0.352050i | \(0.885485\pi\) | |||||||
\(252\) | −9917.79 | −0.00983815 | ||||||||
\(253\) | 210308. | 0.206564 | ||||||||
\(254\) | −1.67762e6 | −1.63159 | ||||||||
\(255\) | 670320. | 0.645553 | ||||||||
\(256\) | 905868. | 0.863903 | ||||||||
\(257\) | 1.77957e6 | 1.68067 | 0.840336 | − | 0.542066i | \(-0.182358\pi\) | ||||
0.840336 | + | 0.542066i | \(0.182358\pi\) | |||||||
\(258\) | 681573. | 0.637475 | ||||||||
\(259\) | 30226.1 | 0.0279984 | ||||||||
\(260\) | 103042. | 0.0945325 | ||||||||
\(261\) | 684903. | 0.622340 | ||||||||
\(262\) | 1.49278e6 | 1.34351 | ||||||||
\(263\) | 648289. | 0.577935 | 0.288968 | − | 0.957339i | \(-0.406688\pi\) | ||||
0.288968 | + | 0.957339i | \(0.406688\pi\) | |||||||
\(264\) | −522520. | −0.461417 | ||||||||
\(265\) | 423732. | 0.370661 | ||||||||
\(266\) | −87394.5 | −0.0757321 | ||||||||
\(267\) | 639154. | 0.548690 | ||||||||
\(268\) | −505548. | −0.429958 | ||||||||
\(269\) | −1.72426e6 | −1.45285 | −0.726427 | − | 0.687243i | \(-0.758821\pi\) | ||||
−0.726427 | + | 0.687243i | \(0.758821\pi\) | |||||||
\(270\) | 254134. | 0.212155 | ||||||||
\(271\) | −457774. | −0.378641 | −0.189320 | − | 0.981915i | \(-0.560628\pi\) | ||||
−0.189320 | + | 0.981915i | \(0.560628\pi\) | |||||||
\(272\) | 1.72692e6 | 1.41530 | ||||||||
\(273\) | 20639.0 | 0.0167603 | ||||||||
\(274\) | 1.06805e6 | 0.859437 | ||||||||
\(275\) | −98039.6 | −0.0781754 | ||||||||
\(276\) | −46851.8 | −0.0370215 | ||||||||
\(277\) | −314535. | −0.246303 | −0.123152 | − | 0.992388i | \(-0.539300\pi\) | ||||
−0.123152 | + | 0.992388i | \(0.539300\pi\) | |||||||
\(278\) | −1.95027e6 | −1.51350 | ||||||||
\(279\) | −780076. | −0.599966 | ||||||||
\(280\) | −92277.9 | −0.0703400 | ||||||||
\(281\) | 1.83840e6 | 1.38891 | 0.694454 | − | 0.719537i | \(-0.255646\pi\) | ||||
0.694454 | + | 0.719537i | \(0.255646\pi\) | |||||||
\(282\) | −619384. | −0.463807 | ||||||||
\(283\) | 2.41935e6 | 1.79569 | 0.897846 | − | 0.440310i | \(-0.145132\pi\) | ||||
0.897846 | + | 0.440310i | \(0.145132\pi\) | |||||||
\(284\) | 516627. | 0.380085 | ||||||||
\(285\) | 538075. | 0.392402 | ||||||||
\(286\) | −502974. | −0.363605 | ||||||||
\(287\) | 105711. | 0.0757560 | ||||||||
\(288\) | 286655. | 0.203647 | ||||||||
\(289\) | 502800. | 0.354120 | ||||||||
\(290\) | −2.94768e6 | −2.05819 | ||||||||
\(291\) | −64475.0 | −0.0446333 | ||||||||
\(292\) | 379993. | 0.260807 | ||||||||
\(293\) | −2.83548e6 | −1.92956 | −0.964779 | − | 0.263063i | \(-0.915267\pi\) | ||||
−0.964779 | + | 0.263063i | \(0.915267\pi\) | |||||||
\(294\) | −973153. | −0.656618 | ||||||||
\(295\) | 973045. | 0.650995 | ||||||||
\(296\) | −354765. | −0.235348 | ||||||||
\(297\) | −298061. | −0.196071 | ||||||||
\(298\) | −1.68029e6 | −1.09608 | ||||||||
\(299\) | 97499.0 | 0.0630699 | ||||||||
\(300\) | 21841.0 | 0.0140110 | ||||||||
\(301\) | −141172. | −0.0898115 | ||||||||
\(302\) | 1.81014e6 | 1.14207 | ||||||||
\(303\) | 1.33914e6 | 0.837952 | ||||||||
\(304\) | 1.38622e6 | 0.860296 | ||||||||
\(305\) | 184291. | 0.113437 | ||||||||
\(306\) | 728925. | 0.445020 | ||||||||
\(307\) | 111078. | 0.0672640 | 0.0336320 | − | 0.999434i | \(-0.489293\pi\) | ||||
0.0336320 | + | 0.999434i | \(0.489293\pi\) | |||||||
\(308\) | −50061.9 | −0.0300698 | ||||||||
\(309\) | 364568. | 0.217211 | ||||||||
\(310\) | 3.35728e6 | 1.98419 | ||||||||
\(311\) | 1.53921e6 | 0.902393 | 0.451197 | − | 0.892425i | \(-0.350997\pi\) | ||||
0.451197 | + | 0.892425i | \(0.350997\pi\) | |||||||
\(312\) | −242240. | −0.140884 | ||||||||
\(313\) | −3.30981e6 | −1.90960 | −0.954799 | − | 0.297252i | \(-0.903930\pi\) | ||||
−0.954799 | + | 0.297252i | \(0.903930\pi\) | |||||||
\(314\) | 159973. | 0.0915635 | ||||||||
\(315\) | −52638.0 | −0.0298898 | ||||||||
\(316\) | 752083. | 0.423690 | ||||||||
\(317\) | 2.37916e6 | 1.32977 | 0.664883 | − | 0.746947i | \(-0.268481\pi\) | ||||
0.664883 | + | 0.746947i | \(0.268481\pi\) | |||||||
\(318\) | 460778. | 0.255520 | ||||||||
\(319\) | 3.45717e6 | 1.90215 | ||||||||
\(320\) | 907013. | 0.495152 | ||||||||
\(321\) | 2.00449e6 | 1.08578 | ||||||||
\(322\) | 40387.9 | 0.0217076 | ||||||||
\(323\) | 1.54334e6 | 0.823107 | ||||||||
\(324\) | 66401.0 | 0.0351408 | ||||||||
\(325\) | −45451.2 | −0.0238692 | ||||||||
\(326\) | 620284. | 0.323256 | ||||||||
\(327\) | 980342. | 0.507000 | ||||||||
\(328\) | −1.24074e6 | −0.636789 | ||||||||
\(329\) | 128291. | 0.0653440 | ||||||||
\(330\) | 1.28279e6 | 0.648442 | ||||||||
\(331\) | −1.77311e6 | −0.889540 | −0.444770 | − | 0.895645i | \(-0.646715\pi\) | ||||
−0.444770 | + | 0.895645i | \(0.646715\pi\) | |||||||
\(332\) | 923798. | 0.459972 | ||||||||
\(333\) | −202368. | −0.100007 | ||||||||
\(334\) | 1.69562e6 | 0.831692 | ||||||||
\(335\) | −2.68316e6 | −1.30628 | ||||||||
\(336\) | −135609. | −0.0655299 | ||||||||
\(337\) | −3.00944e6 | −1.44348 | −0.721741 | − | 0.692163i | \(-0.756658\pi\) | ||||
−0.721741 | + | 0.692163i | \(0.756658\pi\) | |||||||
\(338\) | 2.17653e6 | 1.03627 | ||||||||
\(339\) | 219061. | 0.103530 | ||||||||
\(340\) | −753780. | −0.353628 | ||||||||
\(341\) | −3.93758e6 | −1.83376 | ||||||||
\(342\) | 585118. | 0.270507 | ||||||||
\(343\) | 404902. | 0.185830 | ||||||||
\(344\) | 1.65694e6 | 0.754936 | ||||||||
\(345\) | −248663. | −0.112477 | ||||||||
\(346\) | 3.56416e6 | 1.60054 | ||||||||
\(347\) | −1.87604e6 | −0.836408 | −0.418204 | − | 0.908353i | \(-0.637340\pi\) | ||||
−0.418204 | + | 0.908353i | \(0.637340\pi\) | |||||||
\(348\) | −770178. | −0.340913 | ||||||||
\(349\) | −1.01235e6 | −0.444904 | −0.222452 | − | 0.974944i | \(-0.571406\pi\) | ||||
−0.222452 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(350\) | −18827.7 | −0.00821536 | ||||||||
\(351\) | −138181. | −0.0598661 | ||||||||
\(352\) | 1.44694e6 | 0.622437 | ||||||||
\(353\) | 660022. | 0.281917 | 0.140959 | − | 0.990015i | \(-0.454982\pi\) | ||||
0.140959 | + | 0.990015i | \(0.454982\pi\) | |||||||
\(354\) | 1.05812e6 | 0.448771 | ||||||||
\(355\) | 2.74196e6 | 1.15476 | ||||||||
\(356\) | −718733. | −0.300568 | ||||||||
\(357\) | −150980. | −0.0626972 | ||||||||
\(358\) | 381649. | 0.157382 | ||||||||
\(359\) | 3.20094e6 | 1.31081 | 0.655407 | − | 0.755276i | \(-0.272497\pi\) | ||||
0.655407 | + | 0.755276i | \(0.272497\pi\) | |||||||
\(360\) | 617813. | 0.251247 | ||||||||
\(361\) | −1.23724e6 | −0.499672 | ||||||||
\(362\) | −335791. | −0.134678 | ||||||||
\(363\) | −55057.3 | −0.0219305 | ||||||||
\(364\) | −23208.7 | −0.00918116 | ||||||||
\(365\) | 2.01679e6 | 0.792370 | ||||||||
\(366\) | 200404. | 0.0781993 | ||||||||
\(367\) | 3.83047e6 | 1.48452 | 0.742261 | − | 0.670111i | \(-0.233754\pi\) | ||||
0.742261 | + | 0.670111i | \(0.233754\pi\) | |||||||
\(368\) | −640618. | −0.246592 | ||||||||
\(369\) | −707753. | −0.270592 | ||||||||
\(370\) | 870950. | 0.330742 | ||||||||
\(371\) | −95439.5 | −0.0359992 | ||||||||
\(372\) | 877201. | 0.328656 | ||||||||
\(373\) | −2.81066e6 | −1.04601 | −0.523006 | − | 0.852329i | \(-0.675190\pi\) | ||||
−0.523006 | + | 0.852329i | \(0.675190\pi\) | |||||||
\(374\) | 3.67938e6 | 1.36018 | ||||||||
\(375\) | 1.62663e6 | 0.597325 | ||||||||
\(376\) | −1.50575e6 | −0.549267 | ||||||||
\(377\) | 1.60275e6 | 0.580780 | ||||||||
\(378\) | −57240.0 | −0.0206049 | ||||||||
\(379\) | 3.39956e6 | 1.21570 | 0.607848 | − | 0.794054i | \(-0.292033\pi\) | ||||
0.607848 | + | 0.794054i | \(0.292033\pi\) | |||||||
\(380\) | −605069. | −0.214954 | ||||||||
\(381\) | −2.32643e6 | −0.821065 | ||||||||
\(382\) | 199149. | 0.0698263 | ||||||||
\(383\) | −2.65736e6 | −0.925664 | −0.462832 | − | 0.886446i | \(-0.653167\pi\) | ||||
−0.462832 | + | 0.886446i | \(0.653167\pi\) | |||||||
\(384\) | 2.00553e6 | 0.694066 | ||||||||
\(385\) | −265700. | −0.0913566 | ||||||||
\(386\) | −4.93223e6 | −1.68490 | ||||||||
\(387\) | 945166. | 0.320797 | ||||||||
\(388\) | 72502.5 | 0.0244497 | ||||||||
\(389\) | −919912. | −0.308228 | −0.154114 | − | 0.988053i | \(-0.549252\pi\) | ||||
−0.154114 | + | 0.988053i | \(0.549252\pi\) | |||||||
\(390\) | 594702. | 0.197988 | ||||||||
\(391\) | −713231. | −0.235933 | ||||||||
\(392\) | −2.36578e6 | −0.777606 | ||||||||
\(393\) | 2.07010e6 | 0.676098 | ||||||||
\(394\) | −3.21008e6 | −1.04178 | ||||||||
\(395\) | 3.99163e6 | 1.28723 | ||||||||
\(396\) | 335171. | 0.107406 | ||||||||
\(397\) | −1.57113e6 | −0.500306 | −0.250153 | − | 0.968206i | \(-0.580481\pi\) | ||||
−0.250153 | + | 0.968206i | \(0.580481\pi\) | |||||||
\(398\) | 3.54236e6 | 1.12095 | ||||||||
\(399\) | −121194. | −0.0381107 | ||||||||
\(400\) | 298638. | 0.0933243 | ||||||||
\(401\) | −839693. | −0.260771 | −0.130386 | − | 0.991463i | \(-0.541622\pi\) | ||||
−0.130386 | + | 0.991463i | \(0.541622\pi\) | |||||||
\(402\) | −2.91775e6 | −0.900497 | ||||||||
\(403\) | −1.82546e6 | −0.559900 | ||||||||
\(404\) | −1.50587e6 | −0.459023 | ||||||||
\(405\) | 352419. | 0.106763 | ||||||||
\(406\) | 663921. | 0.199895 | ||||||||
\(407\) | −1.02149e6 | −0.305667 | ||||||||
\(408\) | 1.77205e6 | 0.527019 | ||||||||
\(409\) | 2.75499e6 | 0.814351 | 0.407175 | − | 0.913350i | \(-0.366514\pi\) | ||||
0.407175 | + | 0.913350i | \(0.366514\pi\) | |||||||
\(410\) | 3.04602e6 | 0.894897 | ||||||||
\(411\) | 1.48111e6 | 0.432495 | ||||||||
\(412\) | −409960. | −0.118987 | ||||||||
\(413\) | −219164. | −0.0632258 | ||||||||
\(414\) | −270403. | −0.0775373 | ||||||||
\(415\) | 4.90299e6 | 1.39747 | ||||||||
\(416\) | 670804. | 0.190048 | ||||||||
\(417\) | −2.70452e6 | −0.761642 | ||||||||
\(418\) | 2.95349e6 | 0.826790 | ||||||||
\(419\) | −5.30682e6 | −1.47672 | −0.738361 | − | 0.674405i | \(-0.764400\pi\) | ||||
−0.738361 | + | 0.674405i | \(0.764400\pi\) | |||||||
\(420\) | 59191.8 | 0.0163734 | ||||||||
\(421\) | 2.65251e6 | 0.729376 | 0.364688 | − | 0.931130i | \(-0.381176\pi\) | ||||
0.364688 | + | 0.931130i | \(0.381176\pi\) | |||||||
\(422\) | −422508. | −0.115492 | ||||||||
\(423\) | −858925. | −0.233402 | ||||||||
\(424\) | 1.12018e6 | 0.302602 | ||||||||
\(425\) | 332488. | 0.0892901 | ||||||||
\(426\) | 2.98169e6 | 0.796045 | ||||||||
\(427\) | −41508.9 | −0.0110172 | ||||||||
\(428\) | −2.25406e6 | −0.594780 | ||||||||
\(429\) | −697494. | −0.182977 | ||||||||
\(430\) | −4.06780e6 | −1.06093 | ||||||||
\(431\) | −5.36270e6 | −1.39056 | −0.695281 | − | 0.718738i | \(-0.744720\pi\) | ||||
−0.695281 | + | 0.718738i | \(0.744720\pi\) | |||||||
\(432\) | 907920. | 0.234066 | ||||||||
\(433\) | −4.30075e6 | −1.10236 | −0.551181 | − | 0.834386i | \(-0.685823\pi\) | ||||
−0.551181 | + | 0.834386i | \(0.685823\pi\) | |||||||
\(434\) | −756179. | −0.192708 | ||||||||
\(435\) | −4.08767e6 | −1.03574 | ||||||||
\(436\) | −1.10240e6 | −0.277730 | ||||||||
\(437\) | −572520. | −0.143413 | ||||||||
\(438\) | 2.19311e6 | 0.546230 | ||||||||
\(439\) | −6.67144e6 | −1.65218 | −0.826092 | − | 0.563535i | \(-0.809441\pi\) | ||||
−0.826092 | + | 0.563535i | \(0.809441\pi\) | |||||||
\(440\) | 3.11853e6 | 0.767923 | ||||||||
\(441\) | −1.34951e6 | −0.330430 | ||||||||
\(442\) | 1.70576e6 | 0.415301 | ||||||||
\(443\) | −4.85639e6 | −1.17572 | −0.587860 | − | 0.808962i | \(-0.700030\pi\) | ||||
−0.587860 | + | 0.808962i | \(0.700030\pi\) | |||||||
\(444\) | 227564. | 0.0547831 | ||||||||
\(445\) | −3.81463e6 | −0.913171 | ||||||||
\(446\) | 1.33465e6 | 0.317709 | ||||||||
\(447\) | −2.33013e6 | −0.551583 | ||||||||
\(448\) | −204291. | −0.0480900 | ||||||||
\(449\) | −813545. | −0.190443 | −0.0952217 | − | 0.995456i | \(-0.530356\pi\) | ||||
−0.0952217 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(450\) | 126054. | 0.0293444 | ||||||||
\(451\) | −3.57251e6 | −0.827051 | ||||||||
\(452\) | −246335. | −0.0567127 | ||||||||
\(453\) | 2.51019e6 | 0.574726 | ||||||||
\(454\) | 4.17762e6 | 0.951237 | ||||||||
\(455\) | −123179. | −0.0278937 | ||||||||
\(456\) | 1.42245e6 | 0.320350 | ||||||||
\(457\) | −526564. | −0.117940 | −0.0589699 | − | 0.998260i | \(-0.518782\pi\) | ||||
−0.0589699 | + | 0.998260i | \(0.518782\pi\) | |||||||
\(458\) | 8.19306e6 | 1.82508 | ||||||||
\(459\) | 1.01083e6 | 0.223948 | ||||||||
\(460\) | 279623. | 0.0616138 | ||||||||
\(461\) | −2.05668e6 | −0.450729 | −0.225364 | − | 0.974275i | \(-0.572357\pi\) | ||||
−0.225364 | + | 0.974275i | \(0.572357\pi\) | |||||||
\(462\) | −288930. | −0.0629778 | ||||||||
\(463\) | −119244. | −0.0258514 | −0.0129257 | − | 0.999916i | \(-0.504114\pi\) | ||||
−0.0129257 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(464\) | −1.05309e7 | −2.27075 | ||||||||
\(465\) | 4.65568e6 | 0.998507 | ||||||||
\(466\) | −2.60051e6 | −0.554746 | ||||||||
\(467\) | −1.79160e6 | −0.380145 | −0.190073 | − | 0.981770i | \(-0.560872\pi\) | ||||
−0.190073 | + | 0.981770i | \(0.560872\pi\) | |||||||
\(468\) | 155386. | 0.0327941 | ||||||||
\(469\) | 604343. | 0.126868 | ||||||||
\(470\) | 3.69663e6 | 0.771901 | ||||||||
\(471\) | 221841. | 0.0460776 | ||||||||
\(472\) | 2.57233e6 | 0.531462 | ||||||||
\(473\) | 4.77090e6 | 0.980500 | ||||||||
\(474\) | 4.34061e6 | 0.887370 | ||||||||
\(475\) | 266892. | 0.0542753 | ||||||||
\(476\) | 169778. | 0.0343450 | ||||||||
\(477\) | 638981. | 0.128585 | ||||||||
\(478\) | −289701. | −0.0579937 | ||||||||
\(479\) | 2.09969e6 | 0.418134 | 0.209067 | − | 0.977901i | \(-0.432957\pi\) | ||||
0.209067 | + | 0.977901i | \(0.432957\pi\) | |||||||
\(480\) | −1.71083e6 | −0.338925 | ||||||||
\(481\) | −473563. | −0.0933288 | ||||||||
\(482\) | −6.85193e6 | −1.34337 | ||||||||
\(483\) | 56007.6 | 0.0109239 | ||||||||
\(484\) | 61912.3 | 0.0120133 | ||||||||
\(485\) | 384802. | 0.0742820 | ||||||||
\(486\) | 383230. | 0.0735985 | ||||||||
\(487\) | −1.41491e6 | −0.270338 | −0.135169 | − | 0.990823i | \(-0.543158\pi\) | ||||
−0.135169 | + | 0.990823i | \(0.543158\pi\) | |||||||
\(488\) | 487191. | 0.0926083 | ||||||||
\(489\) | 860173. | 0.162672 | ||||||||
\(490\) | 5.80801e6 | 1.09279 | ||||||||
\(491\) | 5.27735e6 | 0.987899 | 0.493950 | − | 0.869491i | \(-0.335553\pi\) | ||||
0.493950 | + | 0.869491i | \(0.335553\pi\) | |||||||
\(492\) | 795873. | 0.148228 | ||||||||
\(493\) | −1.17245e7 | −2.17259 | ||||||||
\(494\) | 1.36924e6 | 0.252442 | ||||||||
\(495\) | 1.77890e6 | 0.326316 | ||||||||
\(496\) | 1.19942e7 | 2.18911 | ||||||||
\(497\) | −617586. | −0.112152 | ||||||||
\(498\) | 5.33165e6 | 0.963360 | ||||||||
\(499\) | −8.77519e6 | −1.57763 | −0.788815 | − | 0.614631i | \(-0.789305\pi\) | ||||
−0.788815 | + | 0.614631i | \(0.789305\pi\) | |||||||
\(500\) | −1.82916e6 | −0.327210 | ||||||||
\(501\) | 2.35139e6 | 0.418533 | ||||||||
\(502\) | 1.21263e7 | 2.14768 | ||||||||
\(503\) | −2.53969e6 | −0.447569 | −0.223785 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223785 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(504\) | −139153. | −0.0244015 | ||||||||
\(505\) | −7.99231e6 | −1.39458 | ||||||||
\(506\) | −1.36491e6 | −0.236988 | ||||||||
\(507\) | 3.01828e6 | 0.521482 | ||||||||
\(508\) | 2.61609e6 | 0.449772 | ||||||||
\(509\) | −5.11284e6 | −0.874717 | −0.437359 | − | 0.899287i | \(-0.644086\pi\) | ||||
−0.437359 | + | 0.899287i | \(0.644086\pi\) | |||||||
\(510\) | −4.35040e6 | −0.740635 | ||||||||
\(511\) | −454252. | −0.0769563 | ||||||||
\(512\) | 1.25165e6 | 0.211013 | ||||||||
\(513\) | 811408. | 0.136127 | ||||||||
\(514\) | −1.15495e7 | −1.92821 | ||||||||
\(515\) | −2.17583e6 | −0.361499 | ||||||||
\(516\) | −1.06285e6 | −0.175730 | ||||||||
\(517\) | −4.33558e6 | −0.713380 | ||||||||
\(518\) | −196169. | −0.0321222 | ||||||||
\(519\) | 4.94257e6 | 0.805443 | ||||||||
\(520\) | 1.44575e6 | 0.234469 | ||||||||
\(521\) | −5.15371e6 | −0.831813 | −0.415906 | − | 0.909407i | \(-0.636536\pi\) | ||||
−0.415906 | + | 0.909407i | \(0.636536\pi\) | |||||||
\(522\) | −4.44505e6 | −0.714003 | ||||||||
\(523\) | 1.21604e7 | 1.94399 | 0.971995 | − | 0.235004i | \(-0.0755102\pi\) | ||||
0.971995 | + | 0.235004i | \(0.0755102\pi\) | |||||||
\(524\) | −2.32784e6 | −0.370361 | ||||||||
\(525\) | −26109.1 | −0.00413423 | ||||||||
\(526\) | −4.20742e6 | −0.663058 | ||||||||
\(527\) | 1.33537e7 | 2.09448 | ||||||||
\(528\) | 4.58289e6 | 0.715410 | ||||||||
\(529\) | −6.17176e6 | −0.958893 | ||||||||
\(530\) | −2.75004e6 | −0.425255 | ||||||||
\(531\) | 1.46733e6 | 0.225836 | ||||||||
\(532\) | 136283. | 0.0208767 | ||||||||
\(533\) | −1.65622e6 | −0.252522 | ||||||||
\(534\) | −4.14813e6 | −0.629505 | ||||||||
\(535\) | −1.19633e7 | −1.80703 | ||||||||
\(536\) | −7.09319e6 | −1.06642 | ||||||||
\(537\) | 529248. | 0.0791997 | ||||||||
\(538\) | 1.11905e7 | 1.66684 | ||||||||
\(539\) | −6.81191e6 | −1.00994 | ||||||||
\(540\) | −396297. | −0.0584839 | ||||||||
\(541\) | −366606. | −0.0538526 | −0.0269263 | − | 0.999637i | \(-0.508572\pi\) | ||||
−0.0269263 | + | 0.999637i | \(0.508572\pi\) | |||||||
\(542\) | 2.97097e6 | 0.434410 | ||||||||
\(543\) | −465656. | −0.0677744 | ||||||||
\(544\) | −4.90711e6 | −0.710933 | ||||||||
\(545\) | −5.85092e6 | −0.843787 | ||||||||
\(546\) | −133948. | −0.0192289 | ||||||||
\(547\) | −376659. | −0.0538245 | −0.0269122 | − | 0.999638i | \(-0.508567\pi\) | ||||
−0.0269122 | + | 0.999638i | \(0.508567\pi\) | |||||||
\(548\) | −1.66551e6 | −0.236917 | ||||||||
\(549\) | 277908. | 0.0393523 | ||||||||
\(550\) | 636281. | 0.0896896 | ||||||||
\(551\) | −9.41143e6 | −1.32062 | ||||||||
\(552\) | −657363. | −0.0918242 | ||||||||
\(553\) | −899056. | −0.125018 | ||||||||
\(554\) | 2.04134e6 | 0.282580 | ||||||||
\(555\) | 1.20778e6 | 0.166439 | ||||||||
\(556\) | 3.04126e6 | 0.417221 | ||||||||
\(557\) | −9.44657e6 | −1.29014 | −0.645069 | − | 0.764124i | \(-0.723171\pi\) | ||||
−0.645069 | + | 0.764124i | \(0.723171\pi\) | |||||||
\(558\) | 5.06272e6 | 0.688333 | ||||||||
\(559\) | 2.21179e6 | 0.299374 | ||||||||
\(560\) | 809346. | 0.109060 | ||||||||
\(561\) | 5.10235e6 | 0.684484 | ||||||||
\(562\) | −1.19313e7 | −1.59348 | ||||||||
\(563\) | −761921. | −0.101307 | −0.0506534 | − | 0.998716i | \(-0.516130\pi\) | ||||
−0.0506534 | + | 0.998716i | \(0.516130\pi\) | |||||||
\(564\) | 965867. | 0.127856 | ||||||||
\(565\) | −1.30741e6 | −0.172302 | ||||||||
\(566\) | −1.57016e7 | −2.06017 | ||||||||
\(567\) | −79377.1 | −0.0103690 | ||||||||
\(568\) | 7.24862e6 | 0.942724 | ||||||||
\(569\) | −176674. | −0.0228766 | −0.0114383 | − | 0.999935i | \(-0.503641\pi\) | ||||
−0.0114383 | + | 0.999935i | \(0.503641\pi\) | |||||||
\(570\) | −3.49213e6 | −0.450197 | ||||||||
\(571\) | 2.95597e6 | 0.379410 | 0.189705 | − | 0.981841i | \(-0.439247\pi\) | ||||
0.189705 | + | 0.981841i | \(0.439247\pi\) | |||||||
\(572\) | 784337. | 0.100233 | ||||||||
\(573\) | 276168. | 0.0351388 | ||||||||
\(574\) | −686071. | −0.0869139 | ||||||||
\(575\) | −123340. | −0.0155573 | ||||||||
\(576\) | 1.36776e6 | 0.171772 | ||||||||
\(577\) | −7.92331e6 | −0.990757 | −0.495378 | − | 0.868677i | \(-0.664971\pi\) | ||||
−0.495378 | + | 0.868677i | \(0.664971\pi\) | |||||||
\(578\) | −3.26319e6 | −0.406278 | ||||||||
\(579\) | −6.83973e6 | −0.847895 | ||||||||
\(580\) | 4.59661e6 | 0.567372 | ||||||||
\(581\) | −1.10433e6 | −0.135724 | ||||||||
\(582\) | 418445. | 0.0512072 | ||||||||
\(583\) | 3.22537e6 | 0.393014 | ||||||||
\(584\) | 5.33156e6 | 0.646878 | ||||||||
\(585\) | 824698. | 0.0996335 | ||||||||
\(586\) | 1.84024e7 | 2.21376 | ||||||||
\(587\) | −909665. | −0.108965 | −0.0544824 | − | 0.998515i | \(-0.517351\pi\) | ||||
−0.0544824 | + | 0.998515i | \(0.517351\pi\) | |||||||
\(588\) | 1.51753e6 | 0.181007 | ||||||||
\(589\) | 1.07192e7 | 1.27314 | ||||||||
\(590\) | −6.31509e6 | −0.746878 | ||||||||
\(591\) | −4.45155e6 | −0.524255 | ||||||||
\(592\) | 3.11155e6 | 0.364899 | ||||||||
\(593\) | −1.31675e7 | −1.53768 | −0.768841 | − | 0.639440i | \(-0.779166\pi\) | ||||
−0.768841 | + | 0.639440i | \(0.779166\pi\) | |||||||
\(594\) | 1.93442e6 | 0.224950 | ||||||||
\(595\) | 901084. | 0.104345 | ||||||||
\(596\) | 2.62025e6 | 0.302153 | ||||||||
\(597\) | 4.91234e6 | 0.564095 | ||||||||
\(598\) | −632772. | −0.0723593 | ||||||||
\(599\) | −8.03738e6 | −0.915267 | −0.457633 | − | 0.889141i | \(-0.651303\pi\) | ||||
−0.457633 | + | 0.889141i | \(0.651303\pi\) | |||||||
\(600\) | 306443. | 0.0347514 | ||||||||
\(601\) | −3.43853e6 | −0.388317 | −0.194158 | − | 0.980970i | \(-0.562198\pi\) | ||||
−0.194158 | + | 0.980970i | \(0.562198\pi\) | |||||||
\(602\) | 916211. | 0.103040 | ||||||||
\(603\) | −4.04616e6 | −0.453158 | ||||||||
\(604\) | −2.82272e6 | −0.314830 | ||||||||
\(605\) | 328595. | 0.0364983 | ||||||||
\(606\) | −8.69107e6 | −0.961372 | ||||||||
\(607\) | −9.28237e6 | −1.02256 | −0.511278 | − | 0.859415i | \(-0.670828\pi\) | ||||
−0.511278 | + | 0.859415i | \(0.670828\pi\) | |||||||
\(608\) | −3.93900e6 | −0.432143 | ||||||||
\(609\) | 920687. | 0.100593 | ||||||||
\(610\) | −1.19606e6 | −0.130145 | ||||||||
\(611\) | −2.00998e6 | −0.217815 | ||||||||
\(612\) | −1.13669e6 | −0.122677 | ||||||||
\(613\) | −6.71656e6 | −0.721931 | −0.360966 | − | 0.932579i | \(-0.617553\pi\) | ||||
−0.360966 | + | 0.932579i | \(0.617553\pi\) | |||||||
\(614\) | −720901. | −0.0771711 | ||||||||
\(615\) | 4.22404e6 | 0.450340 | ||||||||
\(616\) | −702402. | −0.0745820 | ||||||||
\(617\) | 1.04403e7 | 1.10408 | 0.552040 | − | 0.833817i | \(-0.313849\pi\) | ||||
0.552040 | + | 0.833817i | \(0.313849\pi\) | |||||||
\(618\) | −2.36606e6 | −0.249204 | ||||||||
\(619\) | 6.24861e6 | 0.655476 | 0.327738 | − | 0.944769i | \(-0.393714\pi\) | ||||
0.327738 | + | 0.944769i | \(0.393714\pi\) | |||||||
\(620\) | −5.23535e6 | −0.546974 | ||||||||
\(621\) | −374979. | −0.0390191 | ||||||||
\(622\) | −9.98950e6 | −1.03530 | ||||||||
\(623\) | 859188. | 0.0886887 | ||||||||
\(624\) | 2.12463e6 | 0.218435 | ||||||||
\(625\) | −8.95880e6 | −0.917381 | ||||||||
\(626\) | 2.14808e7 | 2.19086 | ||||||||
\(627\) | 4.09573e6 | 0.416066 | ||||||||
\(628\) | −249462. | −0.0252409 | ||||||||
\(629\) | 3.46424e6 | 0.349125 | ||||||||
\(630\) | 341622. | 0.0342922 | ||||||||
\(631\) | −1.67341e7 | −1.67312 | −0.836562 | − | 0.547872i | \(-0.815438\pi\) | ||||
−0.836562 | + | 0.547872i | \(0.815438\pi\) | |||||||
\(632\) | 1.05522e7 | 1.05088 | ||||||||
\(633\) | −585909. | −0.0581193 | ||||||||
\(634\) | −1.54408e7 | −1.52562 | ||||||||
\(635\) | 1.38847e7 | 1.36648 | ||||||||
\(636\) | −718538. | −0.0704380 | ||||||||
\(637\) | −3.15800e6 | −0.308364 | ||||||||
\(638\) | −2.24372e7 | −2.18231 | ||||||||
\(639\) | 4.13483e6 | 0.400595 | ||||||||
\(640\) | −1.19695e7 | −1.15512 | ||||||||
\(641\) | −2.33047e6 | −0.224026 | −0.112013 | − | 0.993707i | \(-0.535730\pi\) | ||||
−0.112013 | + | 0.993707i | \(0.535730\pi\) | |||||||
\(642\) | −1.30092e7 | −1.24570 | ||||||||
\(643\) | 1.05557e7 | 1.00684 | 0.503418 | − | 0.864043i | \(-0.332076\pi\) | ||||
0.503418 | + | 0.864043i | \(0.332076\pi\) | |||||||
\(644\) | −62980.9 | −0.00598404 | ||||||||
\(645\) | −5.64098e6 | −0.533894 | ||||||||
\(646\) | −1.00164e7 | −0.944340 | ||||||||
\(647\) | 1.82707e7 | 1.71591 | 0.857955 | − | 0.513725i | \(-0.171735\pi\) | ||||
0.857955 | + | 0.513725i | \(0.171735\pi\) | |||||||
\(648\) | 931651. | 0.0871597 | ||||||||
\(649\) | 7.40664e6 | 0.690254 | ||||||||
\(650\) | 294980. | 0.0273848 | ||||||||
\(651\) | −1.04862e6 | −0.0969767 | ||||||||
\(652\) | −967270. | −0.0891105 | ||||||||
\(653\) | 1.46761e7 | 1.34688 | 0.673439 | − | 0.739243i | \(-0.264816\pi\) | ||||
0.673439 | + | 0.739243i | \(0.264816\pi\) | |||||||
\(654\) | −6.36245e6 | −0.581675 | ||||||||
\(655\) | −1.23548e7 | −1.12521 | ||||||||
\(656\) | 1.08822e7 | 0.987318 | ||||||||
\(657\) | 3.04128e6 | 0.274880 | ||||||||
\(658\) | −832612. | −0.0749683 | ||||||||
\(659\) | 6.25839e6 | 0.561370 | 0.280685 | − | 0.959800i | \(-0.409438\pi\) | ||||
0.280685 | + | 0.959800i | \(0.409438\pi\) | |||||||
\(660\) | −2.00038e6 | −0.178753 | ||||||||
\(661\) | 1.03393e7 | 0.920425 | 0.460213 | − | 0.887809i | \(-0.347773\pi\) | ||||
0.460213 | + | 0.887809i | \(0.347773\pi\) | |||||||
\(662\) | 1.15075e7 | 1.02056 | ||||||||
\(663\) | 2.36545e6 | 0.208992 | ||||||||
\(664\) | 1.29615e7 | 1.14087 | ||||||||
\(665\) | 723312. | 0.0634267 | ||||||||
\(666\) | 1.31338e6 | 0.114737 | ||||||||
\(667\) | 4.34934e6 | 0.378537 | ||||||||
\(668\) | −2.64415e6 | −0.229269 | ||||||||
\(669\) | 1.85081e6 | 0.159881 | ||||||||
\(670\) | 1.74138e7 | 1.49867 | ||||||||
\(671\) | 1.40279e6 | 0.120278 | ||||||||
\(672\) | 385339. | 0.0329169 | ||||||||
\(673\) | −4.39568e6 | −0.374101 | −0.187050 | − | 0.982350i | \(-0.559893\pi\) | ||||
−0.187050 | + | 0.982350i | \(0.559893\pi\) | |||||||
\(674\) | 1.95314e7 | 1.65609 | ||||||||
\(675\) | 174804. | 0.0147670 | ||||||||
\(676\) | −3.39407e6 | −0.285663 | ||||||||
\(677\) | −1.43024e7 | −1.19933 | −0.599664 | − | 0.800252i | \(-0.704699\pi\) | ||||
−0.599664 | + | 0.800252i | \(0.704699\pi\) | |||||||
\(678\) | −1.42171e6 | −0.118778 | ||||||||
\(679\) | −86671.1 | −0.00721439 | ||||||||
\(680\) | −1.05760e7 | −0.877104 | ||||||||
\(681\) | 5.79327e6 | 0.478692 | ||||||||
\(682\) | 2.55550e7 | 2.10385 | ||||||||
\(683\) | 2.04865e7 | 1.68041 | 0.840207 | − | 0.542266i | \(-0.182433\pi\) | ||||
0.840207 | + | 0.542266i | \(0.182433\pi\) | |||||||
\(684\) | −912433. | −0.0745694 | ||||||||
\(685\) | −8.83960e6 | −0.719791 | ||||||||
\(686\) | −2.62783e6 | −0.213200 | ||||||||
\(687\) | 1.13617e7 | 0.918438 | ||||||||
\(688\) | −1.45326e7 | −1.17050 | ||||||||
\(689\) | 1.49528e6 | 0.119998 | ||||||||
\(690\) | 1.61383e6 | 0.129043 | ||||||||
\(691\) | 1.39854e7 | 1.11424 | 0.557120 | − | 0.830432i | \(-0.311906\pi\) | ||||
0.557120 | + | 0.830432i | \(0.311906\pi\) | |||||||
\(692\) | −5.55796e6 | −0.441215 | ||||||||
\(693\) | −400671. | −0.0316924 | ||||||||
\(694\) | 1.21756e7 | 0.959600 | ||||||||
\(695\) | 1.61413e7 | 1.26758 | ||||||||
\(696\) | −1.08061e7 | −0.845565 | ||||||||
\(697\) | 1.21157e7 | 0.944638 | ||||||||
\(698\) | 6.57017e6 | 0.510433 | ||||||||
\(699\) | −3.60624e6 | −0.279165 | ||||||||
\(700\) | 29359.9 | 0.00226469 | ||||||||
\(701\) | −9.57044e6 | −0.735592 | −0.367796 | − | 0.929907i | \(-0.619887\pi\) | ||||
−0.367796 | + | 0.929907i | \(0.619887\pi\) | |||||||
\(702\) | 896800. | 0.0686836 | ||||||||
\(703\) | 2.78079e6 | 0.212217 | ||||||||
\(704\) | 6.90401e6 | 0.525013 | ||||||||
\(705\) | 5.12627e6 | 0.388444 | ||||||||
\(706\) | −4.28357e6 | −0.323440 | ||||||||
\(707\) | 1.80015e6 | 0.135444 | ||||||||
\(708\) | −1.65003e6 | −0.123711 | ||||||||
\(709\) | −6.16711e6 | −0.460751 | −0.230375 | − | 0.973102i | \(-0.573995\pi\) | ||||
−0.230375 | + | 0.973102i | \(0.573995\pi\) | |||||||
\(710\) | −1.77954e7 | −1.32484 | ||||||||
\(711\) | 6.01930e6 | 0.446552 | ||||||||
\(712\) | −1.00843e7 | −0.745498 | ||||||||
\(713\) | −4.95372e6 | −0.364928 | ||||||||
\(714\) | 979864. | 0.0719317 | ||||||||
\(715\) | 4.16282e6 | 0.304524 | ||||||||
\(716\) | −595143. | −0.0433849 | ||||||||
\(717\) | −401741. | −0.0291842 | ||||||||
\(718\) | −2.07742e7 | −1.50388 | ||||||||
\(719\) | −1.64122e7 | −1.18398 | −0.591989 | − | 0.805946i | \(-0.701657\pi\) | ||||
−0.591989 | + | 0.805946i | \(0.701657\pi\) | |||||||
\(720\) | −5.41869e6 | −0.389550 | ||||||||
\(721\) | 490074. | 0.0351094 | ||||||||
\(722\) | 8.02971e6 | 0.573267 | ||||||||
\(723\) | −9.50186e6 | −0.676025 | ||||||||
\(724\) | 523633. | 0.0371262 | ||||||||
\(725\) | −2.02754e6 | −0.143260 | ||||||||
\(726\) | 357324. | 0.0251606 | ||||||||
\(727\) | 9.51476e6 | 0.667670 | 0.333835 | − | 0.942632i | \(-0.391657\pi\) | ||||
0.333835 | + | 0.942632i | \(0.391657\pi\) | |||||||
\(728\) | −325634. | −0.0227720 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.30890e7 | −0.909076 | ||||||||
\(731\) | −1.61798e7 | −1.11990 | ||||||||
\(732\) | −312510. | −0.0215569 | ||||||||
\(733\) | −2.36547e7 | −1.62614 | −0.813070 | − | 0.582165i | \(-0.802206\pi\) | ||||
−0.813070 | + | 0.582165i | \(0.802206\pi\) | |||||||
\(734\) | −2.48599e7 | −1.70317 | ||||||||
\(735\) | 8.05421e6 | 0.549926 | ||||||||
\(736\) | 1.82035e6 | 0.123868 | ||||||||
\(737\) | −2.04237e7 | −1.38505 | ||||||||
\(738\) | 4.59334e6 | 0.310447 | ||||||||
\(739\) | 1.19644e7 | 0.805895 | 0.402948 | − | 0.915223i | \(-0.367986\pi\) | ||||
0.402948 | + | 0.915223i | \(0.367986\pi\) | |||||||
\(740\) | −1.35816e6 | −0.0911741 | ||||||||
\(741\) | 1.89878e6 | 0.127037 | ||||||||
\(742\) | 619406. | 0.0413015 | ||||||||
\(743\) | 575787. | 0.0382640 | 0.0191320 | − | 0.999817i | \(-0.493910\pi\) | ||||
0.0191320 | + | 0.999817i | \(0.493910\pi\) | |||||||
\(744\) | 1.23077e7 | 0.815165 | ||||||||
\(745\) | 1.39068e7 | 0.917985 | ||||||||
\(746\) | 1.82413e7 | 1.20008 | ||||||||
\(747\) | 7.39362e6 | 0.484792 | ||||||||
\(748\) | −5.73763e6 | −0.374955 | ||||||||
\(749\) | 2.69455e6 | 0.175502 | ||||||||
\(750\) | −1.05569e7 | −0.685303 | ||||||||
\(751\) | 2.87169e6 | 0.185797 | 0.0928984 | − | 0.995676i | \(-0.470387\pi\) | ||||
0.0928984 | + | 0.995676i | \(0.470387\pi\) | |||||||
\(752\) | 1.32066e7 | 0.851620 | ||||||||
\(753\) | 1.68161e7 | 1.08078 | ||||||||
\(754\) | −1.04019e7 | −0.666321 | ||||||||
\(755\) | −1.49814e7 | −0.956501 | ||||||||
\(756\) | 89260.1 | 0.00568006 | ||||||||
\(757\) | 2.43408e7 | 1.54381 | 0.771907 | − | 0.635736i | \(-0.219303\pi\) | ||||
0.771907 | + | 0.635736i | \(0.219303\pi\) | |||||||
\(758\) | −2.20633e7 | −1.39475 | ||||||||
\(759\) | −1.89277e6 | −0.119260 | ||||||||
\(760\) | −8.48953e6 | −0.533150 | ||||||||
\(761\) | −1.27985e7 | −0.801119 | −0.400560 | − | 0.916271i | \(-0.631184\pi\) | ||||
−0.400560 | + | 0.916271i | \(0.631184\pi\) | |||||||
\(762\) | 1.50986e7 | 0.941997 | ||||||||
\(763\) | 1.31783e6 | 0.0819500 | ||||||||
\(764\) | −310552. | −0.0192487 | ||||||||
\(765\) | −6.03288e6 | −0.372710 | ||||||||
\(766\) | 1.72464e7 | 1.06200 | ||||||||
\(767\) | 3.43372e6 | 0.210754 | ||||||||
\(768\) | −8.15282e6 | −0.498775 | ||||||||
\(769\) | −3.09108e7 | −1.88493 | −0.942464 | − | 0.334308i | \(-0.891498\pi\) | ||||
−0.942464 | + | 0.334308i | \(0.891498\pi\) | |||||||
\(770\) | 1.72440e6 | 0.104812 | ||||||||
\(771\) | −1.60162e7 | −0.970336 | ||||||||
\(772\) | 7.69132e6 | 0.464470 | ||||||||
\(773\) | 8.01637e6 | 0.482535 | 0.241268 | − | 0.970459i | \(-0.422437\pi\) | ||||
0.241268 | + | 0.970459i | \(0.422437\pi\) | |||||||
\(774\) | −6.13416e6 | −0.368047 | ||||||||
\(775\) | 2.30928e6 | 0.138109 | ||||||||
\(776\) | 1.01726e6 | 0.0606426 | ||||||||
\(777\) | −272035. | −0.0161649 | ||||||||
\(778\) | 5.97026e6 | 0.353626 | ||||||||
\(779\) | 9.72541e6 | 0.574202 | ||||||||
\(780\) | −927379. | −0.0545784 | ||||||||
\(781\) | 2.08713e7 | 1.22440 | ||||||||
\(782\) | 4.62889e6 | 0.270683 | ||||||||
\(783\) | −6.16413e6 | −0.359308 | ||||||||
\(784\) | 2.07497e7 | 1.20565 | ||||||||
\(785\) | −1.32400e6 | −0.0766857 | ||||||||
\(786\) | −1.34350e7 | −0.775678 | ||||||||
\(787\) | 5.16502e6 | 0.297259 | 0.148630 | − | 0.988893i | \(-0.452514\pi\) | ||||
0.148630 | + | 0.988893i | \(0.452514\pi\) | |||||||
\(788\) | 5.00580e6 | 0.287183 | ||||||||
\(789\) | −5.83460e6 | −0.333671 | ||||||||
\(790\) | −2.59058e7 | −1.47683 | ||||||||
\(791\) | 294474. | 0.0167342 | ||||||||
\(792\) | 4.70268e6 | 0.266399 | ||||||||
\(793\) | 650335. | 0.0367244 | ||||||||
\(794\) | 1.01967e7 | 0.573994 | ||||||||
\(795\) | −3.81359e6 | −0.214001 | ||||||||
\(796\) | −5.52396e6 | −0.309007 | ||||||||
\(797\) | 2.83505e7 | 1.58094 | 0.790469 | − | 0.612503i | \(-0.209837\pi\) | ||||
0.790469 | + | 0.612503i | \(0.209837\pi\) | |||||||
\(798\) | 786550. | 0.0437239 | ||||||||
\(799\) | 1.47035e7 | 0.814806 | ||||||||
\(800\) | −848593. | −0.0468786 | ||||||||
\(801\) | −5.75239e6 | −0.316787 | ||||||||
\(802\) | 5.44963e6 | 0.299179 | ||||||||
\(803\) | 1.53514e7 | 0.840155 | ||||||||
\(804\) | 4.54993e6 | 0.248236 | ||||||||
\(805\) | −334267. | −0.0181804 | ||||||||
\(806\) | 1.18473e7 | 0.642366 | ||||||||
\(807\) | 1.55183e7 | 0.838806 | ||||||||
\(808\) | −2.11284e7 | −1.13851 | ||||||||
\(809\) | 1.80146e7 | 0.967730 | 0.483865 | − | 0.875143i | \(-0.339233\pi\) | ||||
0.483865 | + | 0.875143i | \(0.339233\pi\) | |||||||
\(810\) | −2.28721e6 | −0.122488 | ||||||||
\(811\) | −2.46156e7 | −1.31419 | −0.657094 | − | 0.753809i | \(-0.728215\pi\) | ||||
−0.657094 | + | 0.753809i | \(0.728215\pi\) | |||||||
\(812\) | −1.03532e6 | −0.0551041 | ||||||||
\(813\) | 4.11996e6 | 0.218608 | ||||||||
\(814\) | 6.62951e6 | 0.350688 | ||||||||
\(815\) | −5.13372e6 | −0.270731 | ||||||||
\(816\) | −1.55422e7 | −0.817124 | ||||||||
\(817\) | −1.29878e7 | −0.680737 | ||||||||
\(818\) | −1.78800e7 | −0.934294 | ||||||||
\(819\) | −185751. | −0.00967657 | ||||||||
\(820\) | −4.74996e6 | −0.246692 | ||||||||
\(821\) | −1.36498e7 | −0.706753 | −0.353376 | − | 0.935481i | \(-0.614966\pi\) | ||||
−0.353376 | + | 0.935481i | \(0.614966\pi\) | |||||||
\(822\) | −9.61243e6 | −0.496196 | ||||||||
\(823\) | 2.89241e7 | 1.48854 | 0.744270 | − | 0.667879i | \(-0.232797\pi\) | ||||
0.744270 | + | 0.667879i | \(0.232797\pi\) | |||||||
\(824\) | −5.75201e6 | −0.295122 | ||||||||
\(825\) | 882357. | 0.0451346 | ||||||||
\(826\) | 1.42238e6 | 0.0725381 | ||||||||
\(827\) | 1.19903e7 | 0.609632 | 0.304816 | − | 0.952411i | \(-0.401405\pi\) | ||||
0.304816 | + | 0.952411i | \(0.401405\pi\) | |||||||
\(828\) | 421666. | 0.0213744 | ||||||||
\(829\) | −3.09969e7 | −1.56651 | −0.783253 | − | 0.621703i | \(-0.786441\pi\) | ||||
−0.783253 | + | 0.621703i | \(0.786441\pi\) | |||||||
\(830\) | −3.18206e7 | −1.60329 | ||||||||
\(831\) | 2.83082e6 | 0.142203 | ||||||||
\(832\) | 3.20070e6 | 0.160301 | ||||||||
\(833\) | 2.31016e7 | 1.15353 | ||||||||
\(834\) | 1.75525e7 | 0.873822 | ||||||||
\(835\) | −1.40336e7 | −0.696553 | ||||||||
\(836\) | −4.60568e6 | −0.227917 | ||||||||
\(837\) | 7.02069e6 | 0.346390 | ||||||||
\(838\) | 3.44414e7 | 1.69423 | ||||||||
\(839\) | 2.03934e7 | 1.00019 | 0.500097 | − | 0.865969i | \(-0.333298\pi\) | ||||
0.500097 | + | 0.865969i | \(0.333298\pi\) | |||||||
\(840\) | 830501. | 0.0406108 | ||||||||
\(841\) | 5.09859e7 | 2.48577 | ||||||||
\(842\) | −1.72149e7 | −0.836804 | ||||||||
\(843\) | −1.65456e7 | −0.801887 | ||||||||
\(844\) | 658858. | 0.0318373 | ||||||||
\(845\) | −1.80138e7 | −0.867889 | ||||||||
\(846\) | 5.57445e6 | 0.267779 | ||||||||
\(847\) | −74011.3 | −0.00354478 | ||||||||
\(848\) | −9.82478e6 | −0.469173 | ||||||||
\(849\) | −2.17741e7 | −1.03674 | ||||||||
\(850\) | −2.15786e6 | −0.102441 | ||||||||
\(851\) | −1.28510e6 | −0.0608293 | ||||||||
\(852\) | −4.64964e6 | −0.219442 | ||||||||
\(853\) | 359222. | 0.0169040 | 0.00845202 | − | 0.999964i | \(-0.497310\pi\) | ||||
0.00845202 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(854\) | 269394. | 0.0126399 | ||||||||
\(855\) | −4.84268e6 | −0.226553 | ||||||||
\(856\) | −3.16260e7 | −1.47523 | ||||||||
\(857\) | −2.39434e7 | −1.11361 | −0.556805 | − | 0.830643i | \(-0.687973\pi\) | ||||
−0.556805 | + | 0.830643i | \(0.687973\pi\) | |||||||
\(858\) | 4.52676e6 | 0.209928 | ||||||||
\(859\) | 1.66368e7 | 0.769283 | 0.384642 | − | 0.923066i | \(-0.374325\pi\) | ||||
0.384642 | + | 0.923066i | \(0.374325\pi\) | |||||||
\(860\) | 6.34332e6 | 0.292463 | ||||||||
\(861\) | −951403. | −0.0437378 | ||||||||
\(862\) | 3.48041e7 | 1.59537 | ||||||||
\(863\) | 1.76303e7 | 0.805808 | 0.402904 | − | 0.915242i | \(-0.368001\pi\) | ||||
0.402904 | + | 0.915242i | \(0.368001\pi\) | |||||||
\(864\) | −2.57990e6 | −0.117576 | ||||||||
\(865\) | −2.94985e7 | −1.34048 | ||||||||
\(866\) | 2.79120e7 | 1.26473 | ||||||||
\(867\) | −4.52520e6 | −0.204451 | ||||||||
\(868\) | 1.17919e6 | 0.0531230 | ||||||||
\(869\) | 3.03835e7 | 1.36486 | ||||||||
\(870\) | 2.65291e7 | 1.18830 | ||||||||
\(871\) | −9.46845e6 | −0.422896 | ||||||||
\(872\) | −1.54674e7 | −0.688854 | ||||||||
\(873\) | 580275. | 0.0257690 | ||||||||
\(874\) | 3.71568e6 | 0.164535 | ||||||||
\(875\) | 2.18661e6 | 0.0965499 | ||||||||
\(876\) | −3.41994e6 | −0.150577 | ||||||||
\(877\) | −3.11672e7 | −1.36835 | −0.684177 | − | 0.729316i | \(-0.739839\pi\) | ||||
−0.684177 | + | 0.729316i | \(0.739839\pi\) | |||||||
\(878\) | 4.32979e7 | 1.89553 | ||||||||
\(879\) | 2.55193e7 | 1.11403 | ||||||||
\(880\) | −2.73518e7 | −1.19064 | ||||||||
\(881\) | −1.53039e7 | −0.664296 | −0.332148 | − | 0.943227i | \(-0.607773\pi\) | ||||
−0.332148 | + | 0.943227i | \(0.607773\pi\) | |||||||
\(882\) | 8.75837e6 | 0.379098 | ||||||||
\(883\) | −2.03128e7 | −0.876736 | −0.438368 | − | 0.898796i | \(-0.644443\pi\) | ||||
−0.438368 | + | 0.898796i | \(0.644443\pi\) | |||||||
\(884\) | −2.65997e6 | −0.114484 | ||||||||
\(885\) | −8.75740e6 | −0.375852 | ||||||||
\(886\) | 3.15181e7 | 1.34889 | ||||||||
\(887\) | 1.54297e7 | 0.658490 | 0.329245 | − | 0.944244i | \(-0.393206\pi\) | ||||
0.329245 | + | 0.944244i | \(0.393206\pi\) | |||||||
\(888\) | 3.19288e6 | 0.135878 | ||||||||
\(889\) | −3.12732e6 | −0.132714 | ||||||||
\(890\) | 2.47571e7 | 1.04767 | ||||||||
\(891\) | 2.68255e6 | 0.113202 | ||||||||
\(892\) | −2.08125e6 | −0.0875813 | ||||||||
\(893\) | 1.18027e7 | 0.495283 | ||||||||
\(894\) | 1.51226e7 | 0.632825 | ||||||||
\(895\) | −3.15868e6 | −0.131810 | ||||||||
\(896\) | 2.69595e6 | 0.112187 | ||||||||
\(897\) | −877491. | −0.0364134 | ||||||||
\(898\) | 5.27994e6 | 0.218493 | ||||||||
\(899\) | −8.14322e7 | −3.36045 | ||||||||
\(900\) | −196569. | −0.00808924 | ||||||||
\(901\) | −1.09384e7 | −0.448892 | ||||||||
\(902\) | 2.31857e7 | 0.948865 | ||||||||
\(903\) | 1.27055e6 | 0.0518527 | ||||||||
\(904\) | −3.45625e6 | −0.140664 | ||||||||
\(905\) | 2.77915e6 | 0.112795 | ||||||||
\(906\) | −1.62912e7 | −0.659376 | ||||||||
\(907\) | −3.01591e7 | −1.21731 | −0.608653 | − | 0.793437i | \(-0.708290\pi\) | ||||
−0.608653 | + | 0.793437i | \(0.708290\pi\) | |||||||
\(908\) | −6.51457e6 | −0.262223 | ||||||||
\(909\) | −1.20523e7 | −0.483792 | ||||||||
\(910\) | 799434. | 0.0320021 | ||||||||
\(911\) | −4.20094e7 | −1.67707 | −0.838533 | − | 0.544850i | \(-0.816586\pi\) | ||||
−0.838533 | + | 0.544850i | \(0.816586\pi\) | |||||||
\(912\) | −1.24760e7 | −0.496692 | ||||||||
\(913\) | 3.73207e7 | 1.48174 | ||||||||
\(914\) | 3.41742e6 | 0.135311 | ||||||||
\(915\) | −1.65862e6 | −0.0654930 | ||||||||
\(916\) | −1.27763e7 | −0.503113 | ||||||||
\(917\) | 2.78275e6 | 0.109282 | ||||||||
\(918\) | −6.56033e6 | −0.256932 | ||||||||
\(919\) | 7.01610e6 | 0.274036 | 0.137018 | − | 0.990569i | \(-0.456248\pi\) | ||||
0.137018 | + | 0.990569i | \(0.456248\pi\) | |||||||
\(920\) | 3.92330e6 | 0.152821 | ||||||||
\(921\) | −999703. | −0.0388349 | ||||||||
\(922\) | 1.33480e7 | 0.517115 | ||||||||
\(923\) | 9.67594e6 | 0.373843 | ||||||||
\(924\) | 450557. | 0.0173608 | ||||||||
\(925\) | 599076. | 0.0230212 | ||||||||
\(926\) | 773897. | 0.0296590 | ||||||||
\(927\) | −3.28112e6 | −0.125407 | ||||||||
\(928\) | 2.99239e7 | 1.14064 | ||||||||
\(929\) | −2.32591e7 | −0.884205 | −0.442102 | − | 0.896965i | \(-0.645767\pi\) | ||||
−0.442102 | + | 0.896965i | \(0.645767\pi\) | |||||||
\(930\) | −3.02156e7 | −1.14557 | ||||||||
\(931\) | 1.85440e7 | 0.701179 | ||||||||
\(932\) | 4.05524e6 | 0.152924 | ||||||||
\(933\) | −1.38529e7 | −0.520997 | ||||||||
\(934\) | 1.16276e7 | 0.436135 | ||||||||
\(935\) | −3.04521e7 | −1.13917 | ||||||||
\(936\) | 2.18016e6 | 0.0813392 | ||||||||
\(937\) | 2.67172e7 | 0.994127 | 0.497063 | − | 0.867714i | \(-0.334412\pi\) | ||||
0.497063 | + | 0.867714i | \(0.334412\pi\) | |||||||
\(938\) | −3.92221e6 | −0.145554 | ||||||||
\(939\) | 2.97883e7 | 1.10251 | ||||||||
\(940\) | −5.76453e6 | −0.212786 | ||||||||
\(941\) | 1.98434e7 | 0.730536 | 0.365268 | − | 0.930902i | \(-0.380977\pi\) | ||||
0.365268 | + | 0.930902i | \(0.380977\pi\) | |||||||
\(942\) | −1.43976e6 | −0.0528642 | ||||||||
\(943\) | −4.49444e6 | −0.164587 | ||||||||
\(944\) | −2.25613e7 | −0.824013 | ||||||||
\(945\) | 473742. | 0.0172569 | ||||||||
\(946\) | −3.09633e7 | −1.12491 | ||||||||
\(947\) | 1.69820e7 | 0.615338 | 0.307669 | − | 0.951493i | \(-0.400451\pi\) | ||||
0.307669 | + | 0.951493i | \(0.400451\pi\) | |||||||
\(948\) | −6.76875e6 | −0.244617 | ||||||||
\(949\) | 7.11692e6 | 0.256523 | ||||||||
\(950\) | −1.73214e6 | −0.0622693 | ||||||||
\(951\) | −2.14124e7 | −0.767741 | ||||||||
\(952\) | 2.38210e6 | 0.0851858 | ||||||||
\(953\) | 3.45013e7 | 1.23056 | 0.615281 | − | 0.788308i | \(-0.289042\pi\) | ||||
0.615281 | + | 0.788308i | \(0.289042\pi\) | |||||||
\(954\) | −4.14701e6 | −0.147524 | ||||||||
\(955\) | −1.64824e6 | −0.0584805 | ||||||||
\(956\) | 451760. | 0.0159869 | ||||||||
\(957\) | −3.11146e7 | −1.09821 | ||||||||
\(958\) | −1.36270e7 | −0.479720 | ||||||||
\(959\) | 1.99099e6 | 0.0699073 | ||||||||
\(960\) | −8.16311e6 | −0.285876 | ||||||||
\(961\) | 6.41188e7 | 2.23963 | ||||||||
\(962\) | 3.07344e6 | 0.107075 | ||||||||
\(963\) | −1.80404e7 | −0.626875 | ||||||||
\(964\) | 1.06849e7 | 0.370321 | ||||||||
\(965\) | 4.08211e7 | 1.41113 | ||||||||
\(966\) | −363491. | −0.0125329 | ||||||||
\(967\) | −4.89993e7 | −1.68509 | −0.842546 | − | 0.538625i | \(-0.818944\pi\) | ||||
−0.842546 | + | 0.538625i | \(0.818944\pi\) | |||||||
\(968\) | 868672. | 0.0297966 | ||||||||
\(969\) | −1.38901e7 | −0.475221 | ||||||||
\(970\) | −2.49738e6 | −0.0852227 | ||||||||
\(971\) | −4.29193e7 | −1.46085 | −0.730424 | − | 0.682994i | \(-0.760677\pi\) | ||||
−0.730424 | + | 0.682994i | \(0.760677\pi\) | |||||||
\(972\) | −597609. | −0.0202886 | ||||||||
\(973\) | −3.63558e6 | −0.123109 | ||||||||
\(974\) | 9.18282e6 | 0.310155 | ||||||||
\(975\) | 409061. | 0.0137809 | ||||||||
\(976\) | −4.27303e6 | −0.143586 | ||||||||
\(977\) | −3.80735e7 | −1.27611 | −0.638053 | − | 0.769993i | \(-0.720260\pi\) | ||||
−0.638053 | + | 0.769993i | \(0.720260\pi\) | |||||||
\(978\) | −5.58255e6 | −0.186632 | ||||||||
\(979\) | −2.90362e7 | −0.968241 | ||||||||
\(980\) | −9.05701e6 | −0.301245 | ||||||||
\(981\) | −8.82308e6 | −0.292717 | ||||||||
\(982\) | −3.42502e7 | −1.13340 | ||||||||
\(983\) | 5.41317e7 | 1.78677 | 0.893384 | − | 0.449294i | \(-0.148325\pi\) | ||||
0.893384 | + | 0.449294i | \(0.148325\pi\) | |||||||
\(984\) | 1.11666e7 | 0.367650 | ||||||||
\(985\) | 2.65680e7 | 0.872504 | ||||||||
\(986\) | 7.60925e7 | 2.49258 | ||||||||
\(987\) | −1.15462e6 | −0.0377264 | ||||||||
\(988\) | −2.13519e6 | −0.0695897 | ||||||||
\(989\) | 6.00209e6 | 0.195124 | ||||||||
\(990\) | −1.15451e7 | −0.374378 | ||||||||
\(991\) | 3.79447e7 | 1.22735 | 0.613674 | − | 0.789560i | \(-0.289691\pi\) | ||||
0.613674 | + | 0.789560i | \(0.289691\pi\) | |||||||
\(992\) | −3.40821e7 | −1.09963 | ||||||||
\(993\) | 1.59580e7 | 0.513576 | ||||||||
\(994\) | 4.00816e6 | 0.128670 | ||||||||
\(995\) | −2.93180e7 | −0.938809 | ||||||||
\(996\) | −8.31418e6 | −0.265565 | ||||||||
\(997\) | 3.60970e7 | 1.15009 | 0.575047 | − | 0.818120i | \(-0.304984\pi\) | ||||
0.575047 | + | 0.818120i | \(0.304984\pi\) | |||||||
\(998\) | 5.69513e7 | 1.80999 | ||||||||
\(999\) | 1.82131e6 | 0.0577392 |
(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 | 471.6.a.b.1.9 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.6.a.b.1.9 | ✓ | 30 | 1.1 | even | 1 | trivial |