Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.5955 | −1.87304 | −0.936522 | − | 0.350610i | \(-0.885974\pi\) | ||||
−0.936522 | + | 0.350610i | \(0.885974\pi\) | |||||||
\(3\) | 22.4642 | 1.44108 | 0.720540 | − | 0.693413i | \(-0.243894\pi\) | ||||
0.720540 | + | 0.693413i | \(0.243894\pi\) | |||||||
\(4\) | 80.2653 | 2.50829 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −238.020 | −2.69921 | ||||||||
\(7\) | 228.020 | 1.75884 | 0.879422 | − | 0.476043i | \(-0.157929\pi\) | ||||
0.879422 | + | 0.476043i | \(0.157929\pi\) | |||||||
\(8\) | −511.396 | −2.82509 | ||||||||
\(9\) | 261.641 | 1.07671 | ||||||||
\(10\) | 264.888 | 0.837650 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 1803.10 | 3.61465 | ||||||||
\(13\) | −327.465 | −0.537411 | −0.268705 | − | 0.963222i | \(-0.586596\pi\) | ||||
−0.268705 | + | 0.963222i | \(0.586596\pi\) | |||||||
\(14\) | −2415.99 | −3.29439 | ||||||||
\(15\) | −561.606 | −0.644471 | ||||||||
\(16\) | 2850.03 | 2.78323 | ||||||||
\(17\) | −132.516 | −0.111211 | −0.0556054 | − | 0.998453i | \(-0.517709\pi\) | ||||
−0.0556054 | + | 0.998453i | \(0.517709\pi\) | |||||||
\(18\) | −2772.23 | −2.01673 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −2006.63 | −1.12174 | ||||||||
\(21\) | 5122.29 | 2.53464 | ||||||||
\(22\) | 1282.06 | 0.564744 | ||||||||
\(23\) | −108.503 | −0.0427683 | −0.0213841 | − | 0.999771i | \(-0.506807\pi\) | ||||
−0.0213841 | + | 0.999771i | \(0.506807\pi\) | |||||||
\(24\) | −11488.1 | −4.07119 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 3469.66 | 1.00659 | ||||||||
\(27\) | 418.763 | 0.110550 | ||||||||
\(28\) | 18302.1 | 4.41169 | ||||||||
\(29\) | −2738.94 | −0.604766 | −0.302383 | − | 0.953187i | \(-0.597782\pi\) | ||||
−0.302383 | + | 0.953187i | \(0.597782\pi\) | |||||||
\(30\) | 5950.51 | 1.20712 | ||||||||
\(31\) | −1933.33 | −0.361328 | −0.180664 | − | 0.983545i | \(-0.557825\pi\) | ||||
−0.180664 | + | 0.983545i | \(0.557825\pi\) | |||||||
\(32\) | −13832.9 | −2.38802 | ||||||||
\(33\) | −2718.17 | −0.434502 | ||||||||
\(34\) | 1404.08 | 0.208303 | ||||||||
\(35\) | −5700.49 | −0.786579 | ||||||||
\(36\) | 21000.7 | 2.70071 | ||||||||
\(37\) | −9503.05 | −1.14119 | −0.570596 | − | 0.821231i | \(-0.693288\pi\) | ||||
−0.570596 | + | 0.821231i | \(0.693288\pi\) | |||||||
\(38\) | 3824.99 | 0.429706 | ||||||||
\(39\) | −7356.24 | −0.774452 | ||||||||
\(40\) | 12784.9 | 1.26342 | ||||||||
\(41\) | −7614.15 | −0.707395 | −0.353697 | − | 0.935360i | \(-0.615076\pi\) | ||||
−0.353697 | + | 0.935360i | \(0.615076\pi\) | |||||||
\(42\) | −54273.4 | −4.74748 | ||||||||
\(43\) | 9150.62 | 0.754709 | 0.377354 | − | 0.926069i | \(-0.376834\pi\) | ||||
0.377354 | + | 0.926069i | \(0.376834\pi\) | |||||||
\(44\) | −9712.10 | −0.756278 | ||||||||
\(45\) | −6541.03 | −0.481521 | ||||||||
\(46\) | 1149.65 | 0.0801068 | ||||||||
\(47\) | 12382.6 | 0.817648 | 0.408824 | − | 0.912613i | \(-0.365939\pi\) | ||||
0.408824 | + | 0.912613i | \(0.365939\pi\) | |||||||
\(48\) | 64023.6 | 4.01086 | ||||||||
\(49\) | 35186.0 | 2.09353 | ||||||||
\(50\) | −6622.21 | −0.374609 | ||||||||
\(51\) | −2976.88 | −0.160264 | ||||||||
\(52\) | −26284.1 | −1.34798 | ||||||||
\(53\) | −25658.9 | −1.25473 | −0.627363 | − | 0.778727i | \(-0.715866\pi\) | ||||
−0.627363 | + | 0.778727i | \(0.715866\pi\) | |||||||
\(54\) | −4437.02 | −0.207065 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | −116608. | −4.96890 | ||||||||
\(57\) | −8109.58 | −0.330607 | ||||||||
\(58\) | 29020.5 | 1.13275 | ||||||||
\(59\) | 43522.1 | 1.62772 | 0.813860 | − | 0.581062i | \(-0.197362\pi\) | ||||
0.813860 | + | 0.581062i | \(0.197362\pi\) | |||||||
\(60\) | −45077.4 | −1.61652 | ||||||||
\(61\) | 29686.3 | 1.02149 | 0.510743 | − | 0.859734i | \(-0.329371\pi\) | ||||
0.510743 | + | 0.859734i | \(0.329371\pi\) | |||||||
\(62\) | 20484.7 | 0.676783 | ||||||||
\(63\) | 59659.4 | 1.89377 | ||||||||
\(64\) | 55365.7 | 1.68963 | ||||||||
\(65\) | 8186.62 | 0.240337 | ||||||||
\(66\) | 28800.5 | 0.813841 | ||||||||
\(67\) | −48898.2 | −1.33078 | −0.665389 | − | 0.746496i | \(-0.731735\pi\) | ||||
−0.665389 | + | 0.746496i | \(0.731735\pi\) | |||||||
\(68\) | −10636.5 | −0.278949 | ||||||||
\(69\) | −2437.43 | −0.0616325 | ||||||||
\(70\) | 60399.8 | 1.47330 | ||||||||
\(71\) | −57364.6 | −1.35051 | −0.675256 | − | 0.737584i | \(-0.735967\pi\) | ||||
−0.675256 | + | 0.737584i | \(0.735967\pi\) | |||||||
\(72\) | −133802. | −3.04181 | ||||||||
\(73\) | 4278.32 | 0.0939649 | 0.0469825 | − | 0.998896i | \(-0.485040\pi\) | ||||
0.0469825 | + | 0.998896i | \(0.485040\pi\) | |||||||
\(74\) | 100690. | 2.13750 | ||||||||
\(75\) | 14040.1 | 0.288216 | ||||||||
\(76\) | −28975.8 | −0.575441 | ||||||||
\(77\) | −27590.4 | −0.530312 | ||||||||
\(78\) | 77943.3 | 1.45058 | ||||||||
\(79\) | −27638.7 | −0.498254 | −0.249127 | − | 0.968471i | \(-0.580144\pi\) | ||||
−0.249127 | + | 0.968471i | \(0.580144\pi\) | |||||||
\(80\) | −71250.7 | −1.24470 | ||||||||
\(81\) | −54171.7 | −0.917402 | ||||||||
\(82\) | 80676.0 | 1.32498 | ||||||||
\(83\) | −11849.0 | −0.188794 | −0.0943969 | − | 0.995535i | \(-0.530092\pi\) | ||||
−0.0943969 | + | 0.995535i | \(0.530092\pi\) | |||||||
\(84\) | 411142. | 6.35760 | ||||||||
\(85\) | 3312.91 | 0.0497350 | ||||||||
\(86\) | −96955.7 | −1.41360 | ||||||||
\(87\) | −61528.1 | −0.871516 | ||||||||
\(88\) | 61879.0 | 0.851797 | ||||||||
\(89\) | −64810.0 | −0.867296 | −0.433648 | − | 0.901082i | \(-0.642774\pi\) | ||||
−0.433648 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(90\) | 69305.7 | 0.901909 | ||||||||
\(91\) | −74668.5 | −0.945222 | ||||||||
\(92\) | −8709.01 | −0.107275 | ||||||||
\(93\) | −43430.7 | −0.520703 | ||||||||
\(94\) | −131200. | −1.53149 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | −310745. | −3.44132 | ||||||||
\(97\) | −55045.9 | −0.594013 | −0.297006 | − | 0.954876i | \(-0.595988\pi\) | ||||
−0.297006 | + | 0.954876i | \(0.595988\pi\) | |||||||
\(98\) | −372815. | −3.92128 | ||||||||
\(99\) | −31658.6 | −0.324641 | ||||||||
\(100\) | 50165.8 | 0.501658 | ||||||||
\(101\) | −170584. | −1.66393 | −0.831965 | − | 0.554828i | \(-0.812784\pi\) | ||||
−0.831965 | + | 0.554828i | \(0.812784\pi\) | |||||||
\(102\) | 31541.6 | 0.300181 | ||||||||
\(103\) | −57941.1 | −0.538138 | −0.269069 | − | 0.963121i | \(-0.586716\pi\) | ||||
−0.269069 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(104\) | 167464. | 1.51823 | ||||||||
\(105\) | −128057. | −1.13352 | ||||||||
\(106\) | 271870. | 2.35016 | ||||||||
\(107\) | −223745. | −1.88927 | −0.944633 | − | 0.328129i | \(-0.893582\pi\) | ||||
−0.944633 | + | 0.328129i | \(0.893582\pi\) | |||||||
\(108\) | 33612.2 | 0.277292 | ||||||||
\(109\) | 31502.0 | 0.253963 | 0.126982 | − | 0.991905i | \(-0.459471\pi\) | ||||
0.126982 | + | 0.991905i | \(0.459471\pi\) | |||||||
\(110\) | −32051.5 | −0.252561 | ||||||||
\(111\) | −213479. | −1.64455 | ||||||||
\(112\) | 649863. | 4.89527 | ||||||||
\(113\) | 7914.45 | 0.0583075 | 0.0291538 | − | 0.999575i | \(-0.490719\pi\) | ||||
0.0291538 | + | 0.999575i | \(0.490719\pi\) | |||||||
\(114\) | 85925.4 | 0.619240 | ||||||||
\(115\) | 2712.57 | 0.0191265 | ||||||||
\(116\) | −219842. | −1.51693 | ||||||||
\(117\) | −85678.3 | −0.578637 | ||||||||
\(118\) | −461139. | −3.04879 | ||||||||
\(119\) | −30216.3 | −0.195603 | ||||||||
\(120\) | 287203. | 1.82069 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −314543. | −1.91329 | ||||||||
\(123\) | −171046. | −1.01941 | ||||||||
\(124\) | −155179. | −0.906316 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −632123. | −3.54712 | ||||||||
\(127\) | 178662. | 0.982932 | 0.491466 | − | 0.870897i | \(-0.336461\pi\) | ||||
0.491466 | + | 0.870897i | \(0.336461\pi\) | |||||||
\(128\) | −143977. | −0.776729 | ||||||||
\(129\) | 205562. | 1.08760 | ||||||||
\(130\) | −86741.6 | −0.450162 | ||||||||
\(131\) | −67161.1 | −0.341932 | −0.170966 | − | 0.985277i | \(-0.554689\pi\) | ||||
−0.170966 | + | 0.985277i | \(0.554689\pi\) | |||||||
\(132\) | −218175. | −1.08986 | ||||||||
\(133\) | −82315.1 | −0.403507 | ||||||||
\(134\) | 518102. | 2.49261 | ||||||||
\(135\) | −10469.1 | −0.0494395 | ||||||||
\(136\) | 67768.4 | 0.314181 | ||||||||
\(137\) | −266220. | −1.21182 | −0.605912 | − | 0.795532i | \(-0.707192\pi\) | ||||
−0.605912 | + | 0.795532i | \(0.707192\pi\) | |||||||
\(138\) | 25825.9 | 0.115440 | ||||||||
\(139\) | 405369. | 1.77956 | 0.889781 | − | 0.456387i | \(-0.150857\pi\) | ||||
0.889781 | + | 0.456387i | \(0.150857\pi\) | |||||||
\(140\) | −457552. | −1.97297 | ||||||||
\(141\) | 278165. | 1.17830 | ||||||||
\(142\) | 607809. | 2.52957 | ||||||||
\(143\) | 39623.2 | 0.162035 | ||||||||
\(144\) | 745685. | 2.99674 | ||||||||
\(145\) | 68473.4 | 0.270459 | ||||||||
\(146\) | −45331.0 | −0.176000 | ||||||||
\(147\) | 790427. | 3.01695 | ||||||||
\(148\) | −762765. | −2.86244 | ||||||||
\(149\) | −198141. | −0.731152 | −0.365576 | − | 0.930781i | \(-0.619128\pi\) | ||||
−0.365576 | + | 0.930781i | \(0.619128\pi\) | |||||||
\(150\) | −148763. | −0.539841 | ||||||||
\(151\) | 124077. | 0.442843 | 0.221421 | − | 0.975178i | \(-0.428930\pi\) | ||||
0.221421 | + | 0.975178i | \(0.428930\pi\) | |||||||
\(152\) | 184614. | 0.648121 | ||||||||
\(153\) | −34671.7 | −0.119742 | ||||||||
\(154\) | 292335. | 0.993296 | ||||||||
\(155\) | 48333.2 | 0.161591 | ||||||||
\(156\) | −590451. | −1.94255 | ||||||||
\(157\) | −414135. | −1.34089 | −0.670445 | − | 0.741959i | \(-0.733897\pi\) | ||||
−0.670445 | + | 0.741959i | \(0.733897\pi\) | |||||||
\(158\) | 292847. | 0.933251 | ||||||||
\(159\) | −576408. | −1.80816 | ||||||||
\(160\) | 345822. | 1.06795 | ||||||||
\(161\) | −24740.8 | −0.0752227 | ||||||||
\(162\) | 573977. | 1.71833 | ||||||||
\(163\) | −48712.5 | −0.143606 | −0.0718028 | − | 0.997419i | \(-0.522875\pi\) | ||||
−0.0718028 | + | 0.997419i | \(0.522875\pi\) | |||||||
\(164\) | −611152. | −1.77435 | ||||||||
\(165\) | 67954.3 | 0.194315 | ||||||||
\(166\) | 125547. | 0.353619 | ||||||||
\(167\) | −305169. | −0.846740 | −0.423370 | − | 0.905957i | \(-0.639153\pi\) | ||||
−0.423370 | + | 0.905957i | \(0.639153\pi\) | |||||||
\(168\) | −2.61952e6 | −7.16058 | ||||||||
\(169\) | −264060. | −0.711190 | ||||||||
\(170\) | −35102.0 | −0.0931558 | ||||||||
\(171\) | −94452.5 | −0.247015 | ||||||||
\(172\) | 734477. | 1.89303 | ||||||||
\(173\) | 604626. | 1.53593 | 0.767965 | − | 0.640492i | \(-0.221270\pi\) | ||||
0.767965 | + | 0.640492i | \(0.221270\pi\) | |||||||
\(174\) | 651923. | 1.63239 | ||||||||
\(175\) | 142512. | 0.351769 | ||||||||
\(176\) | −344853. | −0.839175 | ||||||||
\(177\) | 977689. | 2.34567 | ||||||||
\(178\) | 686697. | 1.62448 | ||||||||
\(179\) | −449964. | −1.04965 | −0.524826 | − | 0.851210i | \(-0.675870\pi\) | ||||
−0.524826 | + | 0.851210i | \(0.675870\pi\) | |||||||
\(180\) | −525018. | −1.20779 | ||||||||
\(181\) | 671364. | 1.52322 | 0.761609 | − | 0.648037i | \(-0.224410\pi\) | ||||
0.761609 | + | 0.648037i | \(0.224410\pi\) | |||||||
\(182\) | 791152. | 1.77044 | ||||||||
\(183\) | 666880. | 1.47204 | ||||||||
\(184\) | 55488.0 | 0.120824 | ||||||||
\(185\) | 237576. | 0.510357 | ||||||||
\(186\) | 460172. | 0.975299 | ||||||||
\(187\) | 16034.5 | 0.0335313 | ||||||||
\(188\) | 993892. | 2.05090 | ||||||||
\(189\) | 95486.4 | 0.194441 | ||||||||
\(190\) | −95624.7 | −0.192170 | ||||||||
\(191\) | 706623. | 1.40154 | 0.700768 | − | 0.713389i | \(-0.252841\pi\) | ||||
0.700768 | + | 0.713389i | \(0.252841\pi\) | |||||||
\(192\) | 1.24375e6 | 2.43489 | ||||||||
\(193\) | 293006. | 0.566217 | 0.283109 | − | 0.959088i | \(-0.408634\pi\) | ||||
0.283109 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(194\) | 583241. | 1.11261 | ||||||||
\(195\) | 183906. | 0.346345 | ||||||||
\(196\) | 2.82422e6 | 5.25119 | ||||||||
\(197\) | 866535. | 1.59082 | 0.795409 | − | 0.606073i | \(-0.207256\pi\) | ||||
0.795409 | + | 0.606073i | \(0.207256\pi\) | |||||||
\(198\) | 335440. | 0.608067 | ||||||||
\(199\) | −610884. | −1.09352 | −0.546759 | − | 0.837290i | \(-0.684139\pi\) | ||||
−0.546759 | + | 0.837290i | \(0.684139\pi\) | |||||||
\(200\) | −319623. | −0.565019 | ||||||||
\(201\) | −1.09846e6 | −1.91776 | ||||||||
\(202\) | 1.80743e6 | 3.11661 | ||||||||
\(203\) | −624532. | −1.06369 | ||||||||
\(204\) | −238940. | −0.401988 | ||||||||
\(205\) | 190354. | 0.316357 | ||||||||
\(206\) | 613916. | 1.00796 | ||||||||
\(207\) | −28388.8 | −0.0460492 | ||||||||
\(208\) | −933284. | −1.49574 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | 1.35683e6 | 2.12314 | ||||||||
\(211\) | −750988. | −1.16125 | −0.580626 | − | 0.814170i | \(-0.697192\pi\) | ||||
−0.580626 | + | 0.814170i | \(0.697192\pi\) | |||||||
\(212\) | −2.05952e6 | −3.14722 | ||||||||
\(213\) | −1.28865e6 | −1.94620 | ||||||||
\(214\) | 2.37069e6 | 3.53868 | ||||||||
\(215\) | −228766. | −0.337516 | ||||||||
\(216\) | −214154. | −0.312314 | ||||||||
\(217\) | −440837. | −0.635520 | ||||||||
\(218\) | −333780. | −0.475684 | ||||||||
\(219\) | 96109.1 | 0.135411 | ||||||||
\(220\) | 242802. | 0.338218 | ||||||||
\(221\) | 43394.4 | 0.0597659 | ||||||||
\(222\) | 2.26192e6 | 3.08031 | ||||||||
\(223\) | 628265. | 0.846020 | 0.423010 | − | 0.906125i | \(-0.360974\pi\) | ||||
0.423010 | + | 0.906125i | \(0.360974\pi\) | |||||||
\(224\) | −3.15417e6 | −4.20015 | ||||||||
\(225\) | 163526. | 0.215343 | ||||||||
\(226\) | −83857.8 | −0.109212 | ||||||||
\(227\) | −756324. | −0.974189 | −0.487095 | − | 0.873349i | \(-0.661943\pi\) | ||||
−0.487095 | + | 0.873349i | \(0.661943\pi\) | |||||||
\(228\) | −650918. | −0.829257 | ||||||||
\(229\) | 1.23771e6 | 1.55966 | 0.779832 | − | 0.625989i | \(-0.215304\pi\) | ||||
0.779832 | + | 0.625989i | \(0.215304\pi\) | |||||||
\(230\) | −28741.1 | −0.0358248 | ||||||||
\(231\) | −619797. | −0.764222 | ||||||||
\(232\) | 1.40068e6 | 1.70852 | ||||||||
\(233\) | −866994. | −1.04623 | −0.523114 | − | 0.852263i | \(-0.675230\pi\) | ||||
−0.523114 | + | 0.852263i | \(0.675230\pi\) | |||||||
\(234\) | 907808. | 1.08381 | ||||||||
\(235\) | −309565. | −0.365664 | ||||||||
\(236\) | 3.49331e6 | 4.08279 | ||||||||
\(237\) | −620883. | −0.718024 | ||||||||
\(238\) | 320158. | 0.366372 | ||||||||
\(239\) | 193352. | 0.218955 | 0.109477 | − | 0.993989i | \(-0.465082\pi\) | ||||
0.109477 | + | 0.993989i | \(0.465082\pi\) | |||||||
\(240\) | −1.60059e6 | −1.79371 | ||||||||
\(241\) | 452316. | 0.501649 | 0.250824 | − | 0.968033i | \(-0.419298\pi\) | ||||
0.250824 | + | 0.968033i | \(0.419298\pi\) | |||||||
\(242\) | −155129. | −0.170277 | ||||||||
\(243\) | −1.31868e6 | −1.43260 | ||||||||
\(244\) | 2.38278e6 | 2.56218 | ||||||||
\(245\) | −879650. | −0.936257 | ||||||||
\(246\) | 1.81232e6 | 1.90940 | ||||||||
\(247\) | 118215. | 0.123290 | ||||||||
\(248\) | 988698. | 1.02079 | ||||||||
\(249\) | −266179. | −0.272067 | ||||||||
\(250\) | 165555. | 0.167530 | ||||||||
\(251\) | −232906. | −0.233344 | −0.116672 | − | 0.993171i | \(-0.537223\pi\) | ||||
−0.116672 | + | 0.993171i | \(0.537223\pi\) | |||||||
\(252\) | 4.78858e6 | 4.75013 | ||||||||
\(253\) | 13128.8 | 0.0128951 | ||||||||
\(254\) | −1.89302e6 | −1.84107 | ||||||||
\(255\) | 74421.9 | 0.0716721 | ||||||||
\(256\) | −246185. | −0.234781 | ||||||||
\(257\) | 639123. | 0.603603 | 0.301802 | − | 0.953371i | \(-0.402412\pi\) | ||||
0.301802 | + | 0.953371i | \(0.402412\pi\) | |||||||
\(258\) | −2.17803e6 | −2.03711 | ||||||||
\(259\) | −2.16688e6 | −2.00718 | ||||||||
\(260\) | 657101. | 0.602836 | ||||||||
\(261\) | −716619. | −0.651159 | ||||||||
\(262\) | 711607. | 0.640453 | ||||||||
\(263\) | −407575. | −0.363344 | −0.181672 | − | 0.983359i | \(-0.558151\pi\) | ||||
−0.181672 | + | 0.983359i | \(0.558151\pi\) | |||||||
\(264\) | 1.39006e6 | 1.22751 | ||||||||
\(265\) | 641473. | 0.561131 | ||||||||
\(266\) | 872173. | 0.755785 | ||||||||
\(267\) | −1.45591e6 | −1.24984 | ||||||||
\(268\) | −3.92483e6 | −3.33798 | ||||||||
\(269\) | −95555.2 | −0.0805144 | −0.0402572 | − | 0.999189i | \(-0.512818\pi\) | ||||
−0.0402572 | + | 0.999189i | \(0.512818\pi\) | |||||||
\(270\) | 110926. | 0.0926024 | ||||||||
\(271\) | −1.20863e6 | −0.999697 | −0.499848 | − | 0.866113i | \(-0.666611\pi\) | ||||
−0.499848 | + | 0.866113i | \(0.666611\pi\) | |||||||
\(272\) | −377675. | −0.309525 | ||||||||
\(273\) | −1.67737e6 | −1.36214 | ||||||||
\(274\) | 2.82074e6 | 2.26980 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | −195641. | −0.154592 | ||||||||
\(277\) | 909269. | 0.712021 | 0.356011 | − | 0.934482i | \(-0.384137\pi\) | ||||
0.356011 | + | 0.934482i | \(0.384137\pi\) | |||||||
\(278\) | −4.29510e6 | −3.33320 | ||||||||
\(279\) | −505839. | −0.389047 | ||||||||
\(280\) | 2.91521e6 | 2.22216 | ||||||||
\(281\) | 1.30972e6 | 0.989490 | 0.494745 | − | 0.869038i | \(-0.335261\pi\) | ||||
0.494745 | + | 0.869038i | \(0.335261\pi\) | |||||||
\(282\) | −2.94731e6 | −2.20700 | ||||||||
\(283\) | 1.41084e6 | 1.04716 | 0.523578 | − | 0.851978i | \(-0.324597\pi\) | ||||
0.523578 | + | 0.851978i | \(0.324597\pi\) | |||||||
\(284\) | −4.60439e6 | −3.38747 | ||||||||
\(285\) | 202740. | 0.147852 | ||||||||
\(286\) | −419829. | −0.303499 | ||||||||
\(287\) | −1.73618e6 | −1.24420 | ||||||||
\(288\) | −3.61925e6 | −2.57121 | ||||||||
\(289\) | −1.40230e6 | −0.987632 | ||||||||
\(290\) | −725513. | −0.506582 | ||||||||
\(291\) | −1.23656e6 | −0.856020 | ||||||||
\(292\) | 343400. | 0.235691 | ||||||||
\(293\) | −1.03848e6 | −0.706689 | −0.353344 | − | 0.935493i | \(-0.614956\pi\) | ||||
−0.353344 | + | 0.935493i | \(0.614956\pi\) | |||||||
\(294\) | −8.37499e6 | −5.65088 | ||||||||
\(295\) | −1.08805e6 | −0.727938 | ||||||||
\(296\) | 4.85983e6 | 3.22397 | ||||||||
\(297\) | −50670.4 | −0.0333321 | ||||||||
\(298\) | 2.09940e6 | 1.36948 | ||||||||
\(299\) | 35530.9 | 0.0229841 | ||||||||
\(300\) | 1.12694e6 | 0.722930 | ||||||||
\(301\) | 2.08652e6 | 1.32742 | ||||||||
\(302\) | −1.31466e6 | −0.829464 | ||||||||
\(303\) | −3.83204e6 | −2.39786 | ||||||||
\(304\) | −1.02886e6 | −0.638517 | ||||||||
\(305\) | −742158. | −0.456822 | ||||||||
\(306\) | 367366. | 0.224282 | ||||||||
\(307\) | 1.37627e6 | 0.833408 | 0.416704 | − | 0.909042i | \(-0.363185\pi\) | ||||
0.416704 | + | 0.909042i | \(0.363185\pi\) | |||||||
\(308\) | −2.21455e6 | −1.33018 | ||||||||
\(309\) | −1.30160e6 | −0.775500 | ||||||||
\(310\) | −512116. | −0.302667 | ||||||||
\(311\) | −616023. | −0.361157 | −0.180578 | − | 0.983561i | \(-0.557797\pi\) | ||||
−0.180578 | + | 0.983561i | \(0.557797\pi\) | |||||||
\(312\) | 3.76196e6 | 2.18790 | ||||||||
\(313\) | 631945. | 0.364602 | 0.182301 | − | 0.983243i | \(-0.441646\pi\) | ||||
0.182301 | + | 0.983243i | \(0.441646\pi\) | |||||||
\(314\) | 4.38798e6 | 2.51154 | ||||||||
\(315\) | −1.49149e6 | −0.846920 | ||||||||
\(316\) | −2.21843e6 | −1.24976 | ||||||||
\(317\) | −1.37672e6 | −0.769478 | −0.384739 | − | 0.923025i | \(-0.625709\pi\) | ||||
−0.384739 | + | 0.923025i | \(0.625709\pi\) | |||||||
\(318\) | 6.10735e6 | 3.38677 | ||||||||
\(319\) | 331411. | 0.182344 | ||||||||
\(320\) | −1.38414e6 | −0.755625 | ||||||||
\(321\) | −5.02625e6 | −2.72258 | ||||||||
\(322\) | 262142. | 0.140895 | ||||||||
\(323\) | 47838.4 | 0.0255135 | ||||||||
\(324\) | −4.34810e6 | −2.30111 | ||||||||
\(325\) | −204666. | −0.107482 | ||||||||
\(326\) | 516135. | 0.268980 | ||||||||
\(327\) | 707667. | 0.365982 | ||||||||
\(328\) | 3.89385e6 | 1.99846 | ||||||||
\(329\) | 2.82347e6 | 1.43812 | ||||||||
\(330\) | −720012. | −0.363961 | ||||||||
\(331\) | −1.82944e6 | −0.917799 | −0.458900 | − | 0.888488i | \(-0.651756\pi\) | ||||
−0.458900 | + | 0.888488i | \(0.651756\pi\) | |||||||
\(332\) | −951066. | −0.473550 | ||||||||
\(333\) | −2.48639e6 | −1.22874 | ||||||||
\(334\) | 3.23343e6 | 1.58598 | ||||||||
\(335\) | 1.22246e6 | 0.595142 | ||||||||
\(336\) | 1.45987e7 | 7.05448 | ||||||||
\(337\) | 2.19546e6 | 1.05306 | 0.526528 | − | 0.850158i | \(-0.323494\pi\) | ||||
0.526528 | + | 0.850158i | \(0.323494\pi\) | |||||||
\(338\) | 2.79785e6 | 1.33209 | ||||||||
\(339\) | 177792. | 0.0840258 | ||||||||
\(340\) | 265912. | 0.124750 | ||||||||
\(341\) | 233933. | 0.108944 | ||||||||
\(342\) | 1.00077e6 | 0.462670 | ||||||||
\(343\) | 4.19078e6 | 1.92335 | ||||||||
\(344\) | −4.67960e6 | −2.13212 | ||||||||
\(345\) | 60935.8 | 0.0275629 | ||||||||
\(346\) | −6.40633e6 | −2.87686 | ||||||||
\(347\) | 3.38911e6 | 1.51099 | 0.755496 | − | 0.655153i | \(-0.227396\pi\) | ||||
0.755496 | + | 0.655153i | \(0.227396\pi\) | |||||||
\(348\) | −4.93857e6 | −2.18602 | ||||||||
\(349\) | −2.36692e6 | −1.04021 | −0.520105 | − | 0.854103i | \(-0.674107\pi\) | ||||
−0.520105 | + | 0.854103i | \(0.674107\pi\) | |||||||
\(350\) | −1.50999e6 | −0.658878 | ||||||||
\(351\) | −137130. | −0.0594108 | ||||||||
\(352\) | 1.67378e6 | 0.720014 | ||||||||
\(353\) | 1.30486e6 | 0.557350 | 0.278675 | − | 0.960385i | \(-0.410105\pi\) | ||||
0.278675 | + | 0.960385i | \(0.410105\pi\) | |||||||
\(354\) | −1.03591e7 | −4.39355 | ||||||||
\(355\) | 1.43412e6 | 0.603967 | ||||||||
\(356\) | −5.20200e6 | −2.17543 | ||||||||
\(357\) | −678787. | −0.281879 | ||||||||
\(358\) | 4.76761e6 | 1.96604 | ||||||||
\(359\) | 1.15001e6 | 0.470942 | 0.235471 | − | 0.971881i | \(-0.424337\pi\) | ||||
0.235471 | + | 0.971881i | \(0.424337\pi\) | |||||||
\(360\) | 3.34506e6 | 1.36034 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −7.11346e6 | −2.85305 | ||||||||
\(363\) | 328899. | 0.131007 | ||||||||
\(364\) | −5.99328e6 | −2.37089 | ||||||||
\(365\) | −106958. | −0.0420224 | ||||||||
\(366\) | −7.06595e6 | −2.75720 | ||||||||
\(367\) | 2.61521e6 | 1.01354 | 0.506771 | − | 0.862081i | \(-0.330839\pi\) | ||||
0.506771 | + | 0.862081i | \(0.330839\pi\) | |||||||
\(368\) | −309236. | −0.119034 | ||||||||
\(369\) | −1.99218e6 | −0.761661 | ||||||||
\(370\) | −2.51725e6 | −0.955920 | ||||||||
\(371\) | −5.85075e6 | −2.20687 | ||||||||
\(372\) | −3.48598e6 | −1.30607 | ||||||||
\(373\) | −1.47523e6 | −0.549021 | −0.274511 | − | 0.961584i | \(-0.588516\pi\) | ||||
−0.274511 | + | 0.961584i | \(0.588516\pi\) | |||||||
\(374\) | −169894. | −0.0628056 | ||||||||
\(375\) | −351003. | −0.128894 | ||||||||
\(376\) | −6.33241e6 | −2.30993 | ||||||||
\(377\) | 896906. | 0.325008 | ||||||||
\(378\) | −1.01173e6 | −0.364195 | ||||||||
\(379\) | −916659. | −0.327801 | −0.163900 | − | 0.986477i | \(-0.552408\pi\) | ||||
−0.163900 | + | 0.986477i | \(0.552408\pi\) | |||||||
\(380\) | 724394. | 0.257345 | ||||||||
\(381\) | 4.01351e6 | 1.41648 | ||||||||
\(382\) | −7.48704e6 | −2.62514 | ||||||||
\(383\) | −1.78476e6 | −0.621704 | −0.310852 | − | 0.950458i | \(-0.600614\pi\) | ||||
−0.310852 | + | 0.950458i | \(0.600614\pi\) | |||||||
\(384\) | −3.23434e6 | −1.11933 | ||||||||
\(385\) | 689760. | 0.237163 | ||||||||
\(386\) | −3.10455e6 | −1.06055 | ||||||||
\(387\) | 2.39418e6 | 0.812605 | ||||||||
\(388\) | −4.41827e6 | −1.48996 | ||||||||
\(389\) | −4.74379e6 | −1.58947 | −0.794733 | − | 0.606959i | \(-0.792389\pi\) | ||||
−0.794733 | + | 0.606959i | \(0.792389\pi\) | |||||||
\(390\) | −1.94858e6 | −0.648720 | ||||||||
\(391\) | 14378.4 | 0.00475629 | ||||||||
\(392\) | −1.79940e7 | −5.91443 | ||||||||
\(393\) | −1.50872e6 | −0.492751 | ||||||||
\(394\) | −9.18140e6 | −2.97967 | ||||||||
\(395\) | 690969. | 0.222826 | ||||||||
\(396\) | −2.54109e6 | −0.814295 | ||||||||
\(397\) | −833631. | −0.265459 | −0.132730 | − | 0.991152i | \(-0.542374\pi\) | ||||
−0.132730 | + | 0.991152i | \(0.542374\pi\) | |||||||
\(398\) | 6.47264e6 | 2.04821 | ||||||||
\(399\) | −1.84915e6 | −0.581485 | ||||||||
\(400\) | 1.78127e6 | 0.556646 | ||||||||
\(401\) | −3.34621e6 | −1.03918 | −0.519592 | − | 0.854415i | \(-0.673916\pi\) | ||||
−0.519592 | + | 0.854415i | \(0.673916\pi\) | |||||||
\(402\) | 1.16388e7 | 3.59205 | ||||||||
\(403\) | 633097. | 0.194182 | ||||||||
\(404\) | −1.36920e7 | −4.17362 | ||||||||
\(405\) | 1.35429e6 | 0.410275 | ||||||||
\(406\) | 6.61725e6 | 1.99233 | ||||||||
\(407\) | 1.14987e6 | 0.344082 | ||||||||
\(408\) | 1.52236e6 | 0.452760 | ||||||||
\(409\) | 4.22939e6 | 1.25017 | 0.625086 | − | 0.780556i | \(-0.285064\pi\) | ||||
0.625086 | + | 0.780556i | \(0.285064\pi\) | |||||||
\(410\) | −2.01690e6 | −0.592550 | ||||||||
\(411\) | −5.98043e6 | −1.74634 | ||||||||
\(412\) | −4.65066e6 | −1.34981 | ||||||||
\(413\) | 9.92389e6 | 2.86290 | ||||||||
\(414\) | 300795. | 0.0862520 | ||||||||
\(415\) | 296226. | 0.0844312 | ||||||||
\(416\) | 4.52978e6 | 1.28335 | ||||||||
\(417\) | 9.10630e6 | 2.56449 | ||||||||
\(418\) | −462823. | −0.129561 | ||||||||
\(419\) | −5.89142e6 | −1.63940 | −0.819700 | − | 0.572793i | \(-0.805860\pi\) | ||||
−0.819700 | + | 0.572793i | \(0.805860\pi\) | |||||||
\(420\) | −1.02785e7 | −2.84321 | ||||||||
\(421\) | −3.94233e6 | −1.08405 | −0.542023 | − | 0.840363i | \(-0.682342\pi\) | ||||
−0.542023 | + | 0.840363i | \(0.682342\pi\) | |||||||
\(422\) | 7.95711e6 | 2.17508 | ||||||||
\(423\) | 3.23980e6 | 0.880373 | ||||||||
\(424\) | 1.31219e7 | 3.54472 | ||||||||
\(425\) | −82822.7 | −0.0222422 | ||||||||
\(426\) | 1.36539e7 | 3.64531 | ||||||||
\(427\) | 6.76907e6 | 1.79663 | ||||||||
\(428\) | −1.79589e7 | −4.73883 | ||||||||
\(429\) | 890105. | 0.233506 | ||||||||
\(430\) | 2.42389e6 | 0.632182 | ||||||||
\(431\) | −2.73361e6 | −0.708832 | −0.354416 | − | 0.935088i | \(-0.615320\pi\) | ||||
−0.354416 | + | 0.935088i | \(0.615320\pi\) | |||||||
\(432\) | 1.19349e6 | 0.307687 | ||||||||
\(433\) | −3.61717e6 | −0.927147 | −0.463574 | − | 0.886058i | \(-0.653433\pi\) | ||||
−0.463574 | + | 0.886058i | \(0.653433\pi\) | |||||||
\(434\) | 4.67091e6 | 1.19036 | ||||||||
\(435\) | 1.53820e6 | 0.389754 | ||||||||
\(436\) | 2.52851e6 | 0.637014 | ||||||||
\(437\) | 39169.5 | 0.00981171 | ||||||||
\(438\) | −1.01833e6 | −0.253631 | ||||||||
\(439\) | −684240. | −0.169452 | −0.0847260 | − | 0.996404i | \(-0.527002\pi\) | ||||
−0.0847260 | + | 0.996404i | \(0.527002\pi\) | |||||||
\(440\) | −1.54697e6 | −0.380935 | ||||||||
\(441\) | 9.20612e6 | 2.25414 | ||||||||
\(442\) | −459787. | −0.111944 | ||||||||
\(443\) | 540844. | 0.130937 | 0.0654685 | − | 0.997855i | \(-0.479146\pi\) | ||||
0.0654685 | + | 0.997855i | \(0.479146\pi\) | |||||||
\(444\) | −1.71349e7 | −4.12501 | ||||||||
\(445\) | 1.62025e6 | 0.387866 | ||||||||
\(446\) | −6.65680e6 | −1.58463 | ||||||||
\(447\) | −4.45107e6 | −1.05365 | ||||||||
\(448\) | 1.26245e7 | 2.97179 | ||||||||
\(449\) | −7.43199e6 | −1.73976 | −0.869880 | − | 0.493263i | \(-0.835804\pi\) | ||||
−0.869880 | + | 0.493263i | \(0.835804\pi\) | |||||||
\(450\) | −1.73264e6 | −0.403346 | ||||||||
\(451\) | 921312. | 0.213288 | ||||||||
\(452\) | 635255. | 0.146252 | ||||||||
\(453\) | 2.78730e6 | 0.638172 | ||||||||
\(454\) | 8.01366e6 | 1.82470 | ||||||||
\(455\) | 1.86671e6 | 0.422716 | ||||||||
\(456\) | 4.14721e6 | 0.933994 | ||||||||
\(457\) | −6.00823e6 | −1.34572 | −0.672862 | − | 0.739768i | \(-0.734935\pi\) | ||||
−0.672862 | + | 0.739768i | \(0.734935\pi\) | |||||||
\(458\) | −1.31142e7 | −2.92132 | ||||||||
\(459\) | −55493.0 | −0.0122944 | ||||||||
\(460\) | 217725. | 0.0479749 | ||||||||
\(461\) | −4.07554e6 | −0.893167 | −0.446583 | − | 0.894742i | \(-0.647359\pi\) | ||||
−0.446583 | + | 0.894742i | \(0.647359\pi\) | |||||||
\(462\) | 6.56708e6 | 1.43142 | ||||||||
\(463\) | −3.55382e6 | −0.770447 | −0.385223 | − | 0.922823i | \(-0.625876\pi\) | ||||
−0.385223 | + | 0.922823i | \(0.625876\pi\) | |||||||
\(464\) | −7.80605e6 | −1.68320 | ||||||||
\(465\) | 1.08577e6 | 0.232865 | ||||||||
\(466\) | 9.18626e6 | 1.95963 | ||||||||
\(467\) | 2.36666e6 | 0.502163 | 0.251081 | − | 0.967966i | \(-0.419214\pi\) | ||||
0.251081 | + | 0.967966i | \(0.419214\pi\) | |||||||
\(468\) | −6.87700e6 | −1.45139 | ||||||||
\(469\) | −1.11498e7 | −2.34063 | ||||||||
\(470\) | 3.28000e6 | 0.684903 | ||||||||
\(471\) | −9.30323e6 | −1.93233 | ||||||||
\(472\) | −2.22570e7 | −4.59846 | ||||||||
\(473\) | −1.10723e6 | −0.227553 | ||||||||
\(474\) | 6.57858e6 | 1.34489 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −2.42532e6 | −0.490628 | ||||||||
\(477\) | −6.71344e6 | −1.35098 | ||||||||
\(478\) | −2.04867e6 | −0.410111 | ||||||||
\(479\) | 4.78571e6 | 0.953032 | 0.476516 | − | 0.879166i | \(-0.341899\pi\) | ||||
0.476516 | + | 0.879166i | \(0.341899\pi\) | |||||||
\(480\) | 7.76862e6 | 1.53901 | ||||||||
\(481\) | 3.11192e6 | 0.613289 | ||||||||
\(482\) | −4.79253e6 | −0.939610 | ||||||||
\(483\) | −555783. | −0.108402 | ||||||||
\(484\) | 1.17516e6 | 0.228026 | ||||||||
\(485\) | 1.37615e6 | 0.265650 | ||||||||
\(486\) | 1.39722e7 | 2.68332 | ||||||||
\(487\) | 575099. | 0.109880 | 0.0549402 | − | 0.998490i | \(-0.482503\pi\) | ||||
0.0549402 | + | 0.998490i | \(0.482503\pi\) | |||||||
\(488\) | −1.51815e7 | −2.88579 | ||||||||
\(489\) | −1.09429e6 | −0.206947 | ||||||||
\(490\) | 9.32036e6 | 1.75365 | ||||||||
\(491\) | 2.42710e6 | 0.454344 | 0.227172 | − | 0.973855i | \(-0.427052\pi\) | ||||
0.227172 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(492\) | −1.37291e7 | −2.55698 | ||||||||
\(493\) | 362954. | 0.0672565 | ||||||||
\(494\) | −1.25255e6 | −0.230928 | ||||||||
\(495\) | 791465. | 0.145184 | ||||||||
\(496\) | −5.51004e6 | −1.00566 | ||||||||
\(497\) | −1.30803e7 | −2.37534 | ||||||||
\(498\) | 2.82031e6 | 0.509593 | ||||||||
\(499\) | −6.06164e6 | −1.08978 | −0.544890 | − | 0.838507i | \(-0.683429\pi\) | ||||
−0.544890 | + | 0.838507i | \(0.683429\pi\) | |||||||
\(500\) | −1.25415e6 | −0.224348 | ||||||||
\(501\) | −6.85540e6 | −1.22022 | ||||||||
\(502\) | 2.46776e6 | 0.437063 | ||||||||
\(503\) | 6.29223e6 | 1.10888 | 0.554440 | − | 0.832224i | \(-0.312932\pi\) | ||||
0.554440 | + | 0.832224i | \(0.312932\pi\) | |||||||
\(504\) | −3.05096e7 | −5.35008 | ||||||||
\(505\) | 4.26460e6 | 0.744132 | ||||||||
\(506\) | −139107. | −0.0241531 | ||||||||
\(507\) | −5.93190e6 | −1.02488 | ||||||||
\(508\) | 1.43404e7 | 2.46548 | ||||||||
\(509\) | 224729. | 0.0384471 | 0.0192236 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192236 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(510\) | −788540. | −0.134245 | ||||||||
\(511\) | 975541. | 0.165270 | ||||||||
\(512\) | 7.21574e6 | 1.21648 | ||||||||
\(513\) | −151174. | −0.0253619 | ||||||||
\(514\) | −6.77185e6 | −1.13058 | ||||||||
\(515\) | 1.44853e6 | 0.240663 | ||||||||
\(516\) | 1.64995e7 | 2.72801 | ||||||||
\(517\) | −1.49829e6 | −0.246530 | ||||||||
\(518\) | 2.29593e7 | 3.75953 | ||||||||
\(519\) | 1.35824e7 | 2.21340 | ||||||||
\(520\) | −4.18661e6 | −0.678975 | ||||||||
\(521\) | 5.15565e6 | 0.832126 | 0.416063 | − | 0.909336i | \(-0.363410\pi\) | ||||
0.416063 | + | 0.909336i | \(0.363410\pi\) | |||||||
\(522\) | 7.59296e6 | 1.21965 | ||||||||
\(523\) | −675240. | −0.107945 | −0.0539727 | − | 0.998542i | \(-0.517188\pi\) | ||||
−0.0539727 | + | 0.998542i | \(0.517188\pi\) | |||||||
\(524\) | −5.39070e6 | −0.857664 | ||||||||
\(525\) | 3.20143e6 | 0.506927 | ||||||||
\(526\) | 4.31847e6 | 0.680559 | ||||||||
\(527\) | 256198. | 0.0401836 | ||||||||
\(528\) | −7.74686e6 | −1.20932 | ||||||||
\(529\) | −6.42457e6 | −0.998171 | ||||||||
\(530\) | −6.79675e6 | −1.05102 | ||||||||
\(531\) | 1.13872e7 | 1.75259 | ||||||||
\(532\) | −6.60705e6 | −1.01211 | ||||||||
\(533\) | 2.49337e6 | 0.380162 | ||||||||
\(534\) | 1.54261e7 | 2.34101 | ||||||||
\(535\) | 5.59361e6 | 0.844905 | ||||||||
\(536\) | 2.50064e7 | 3.75957 | ||||||||
\(537\) | −1.01081e7 | −1.51263 | ||||||||
\(538\) | 1.01246e6 | 0.150807 | ||||||||
\(539\) | −4.25751e6 | −0.631224 | ||||||||
\(540\) | −840304. | −0.124009 | ||||||||
\(541\) | 1.86178e6 | 0.273486 | 0.136743 | − | 0.990607i | \(-0.456337\pi\) | ||||
0.136743 | + | 0.990607i | \(0.456337\pi\) | |||||||
\(542\) | 1.28060e7 | 1.87248 | ||||||||
\(543\) | 1.50817e7 | 2.19508 | ||||||||
\(544\) | 1.83308e6 | 0.265573 | ||||||||
\(545\) | −787549. | −0.113576 | ||||||||
\(546\) | 1.77726e7 | 2.55135 | ||||||||
\(547\) | 1.26308e7 | 1.80493 | 0.902467 | − | 0.430759i | \(-0.141754\pi\) | ||||
0.902467 | + | 0.430759i | \(0.141754\pi\) | |||||||
\(548\) | −2.13682e7 | −3.03961 | ||||||||
\(549\) | 7.76717e6 | 1.09985 | ||||||||
\(550\) | 801287. | 0.112949 | ||||||||
\(551\) | 988757. | 0.138743 | ||||||||
\(552\) | 1.24649e6 | 0.174118 | ||||||||
\(553\) | −6.30218e6 | −0.876351 | ||||||||
\(554\) | −9.63419e6 | −1.33365 | ||||||||
\(555\) | 5.33697e6 | 0.735465 | ||||||||
\(556\) | 3.25370e7 | 4.46366 | ||||||||
\(557\) | 3.37431e6 | 0.460837 | 0.230419 | − | 0.973092i | \(-0.425990\pi\) | ||||
0.230419 | + | 0.973092i | \(0.425990\pi\) | |||||||
\(558\) | 5.35963e6 | 0.728701 | ||||||||
\(559\) | −2.99651e6 | −0.405589 | ||||||||
\(560\) | −1.62466e7 | −2.18923 | ||||||||
\(561\) | 360202. | 0.0483213 | ||||||||
\(562\) | −1.38771e7 | −1.85336 | ||||||||
\(563\) | 9.41383e6 | 1.25169 | 0.625843 | − | 0.779949i | \(-0.284755\pi\) | ||||
0.625843 | + | 0.779949i | \(0.284755\pi\) | |||||||
\(564\) | 2.23270e7 | 2.95551 | ||||||||
\(565\) | −197861. | −0.0260759 | ||||||||
\(566\) | −1.49486e7 | −1.96137 | ||||||||
\(567\) | −1.23522e7 | −1.61357 | ||||||||
\(568\) | 2.93361e7 | 3.81532 | ||||||||
\(569\) | 1.22643e7 | 1.58804 | 0.794019 | − | 0.607892i | \(-0.207985\pi\) | ||||
0.794019 | + | 0.607892i | \(0.207985\pi\) | |||||||
\(570\) | −2.14813e6 | −0.276933 | ||||||||
\(571\) | −1.51714e7 | −1.94732 | −0.973658 | − | 0.228012i | \(-0.926778\pi\) | ||||
−0.973658 | + | 0.228012i | \(0.926778\pi\) | |||||||
\(572\) | 3.18037e6 | 0.406432 | ||||||||
\(573\) | 1.58737e7 | 2.01973 | ||||||||
\(574\) | 1.83957e7 | 2.33044 | ||||||||
\(575\) | −67814.3 | −0.00855365 | ||||||||
\(576\) | 1.44860e7 | 1.81924 | ||||||||
\(577\) | −5.28035e6 | −0.660273 | −0.330136 | − | 0.943933i | \(-0.607095\pi\) | ||||
−0.330136 | + | 0.943933i | \(0.607095\pi\) | |||||||
\(578\) | 1.48581e7 | 1.84988 | ||||||||
\(579\) | 6.58215e6 | 0.815965 | ||||||||
\(580\) | 5.49604e6 | 0.678391 | ||||||||
\(581\) | −2.70181e6 | −0.332059 | ||||||||
\(582\) | 1.31020e7 | 1.60336 | ||||||||
\(583\) | 3.10473e6 | 0.378314 | ||||||||
\(584\) | −2.18792e6 | −0.265460 | ||||||||
\(585\) | 2.14196e6 | 0.258774 | ||||||||
\(586\) | 1.10032e7 | 1.32366 | ||||||||
\(587\) | 6.33062e6 | 0.758317 | 0.379159 | − | 0.925332i | \(-0.376213\pi\) | ||||
0.379159 | + | 0.925332i | \(0.376213\pi\) | |||||||
\(588\) | 6.34438e7 | 7.56739 | ||||||||
\(589\) | 697932. | 0.0828943 | ||||||||
\(590\) | 1.15285e7 | 1.36346 | ||||||||
\(591\) | 1.94660e7 | 2.29250 | ||||||||
\(592\) | −2.70840e7 | −3.17620 | ||||||||
\(593\) | −1.15583e7 | −1.34977 | −0.674883 | − | 0.737925i | \(-0.735806\pi\) | ||||
−0.674883 | + | 0.737925i | \(0.735806\pi\) | |||||||
\(594\) | 536880. | 0.0624325 | ||||||||
\(595\) | 755409. | 0.0874761 | ||||||||
\(596\) | −1.59038e7 | −1.83394 | ||||||||
\(597\) | −1.37230e7 | −1.57585 | ||||||||
\(598\) | −376468. | −0.0430502 | ||||||||
\(599\) | 1.09319e7 | 1.24488 | 0.622442 | − | 0.782666i | \(-0.286141\pi\) | ||||
0.622442 | + | 0.782666i | \(0.286141\pi\) | |||||||
\(600\) | −7.18008e6 | −0.814237 | ||||||||
\(601\) | −127189. | −0.0143636 | −0.00718179 | − | 0.999974i | \(-0.502286\pi\) | ||||
−0.00718179 | + | 0.999974i | \(0.502286\pi\) | |||||||
\(602\) | −2.21078e7 | −2.48631 | ||||||||
\(603\) | −1.27938e7 | −1.43287 | ||||||||
\(604\) | 9.95909e6 | 1.11078 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 4.06025e7 | 4.49129 | ||||||||
\(607\) | −969525. | −0.106804 | −0.0534020 | − | 0.998573i | \(-0.517006\pi\) | ||||
−0.0534020 | + | 0.998573i | \(0.517006\pi\) | |||||||
\(608\) | 4.99367e6 | 0.547849 | ||||||||
\(609\) | −1.40296e7 | −1.53286 | ||||||||
\(610\) | 7.86356e6 | 0.855647 | ||||||||
\(611\) | −4.05486e6 | −0.439413 | ||||||||
\(612\) | −2.78294e6 | −0.300348 | ||||||||
\(613\) | −1.56423e7 | −1.68132 | −0.840658 | − | 0.541566i | \(-0.817832\pi\) | ||||
−0.840658 | + | 0.541566i | \(0.817832\pi\) | |||||||
\(614\) | −1.45823e7 | −1.56101 | ||||||||
\(615\) | 4.27615e6 | 0.455895 | ||||||||
\(616\) | 1.41096e7 | 1.49818 | ||||||||
\(617\) | −1.69700e6 | −0.179461 | −0.0897305 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897305 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(618\) | 1.37912e7 | 1.45254 | ||||||||
\(619\) | −1.13405e7 | −1.18961 | −0.594804 | − | 0.803871i | \(-0.702770\pi\) | ||||
−0.594804 | + | 0.803871i | \(0.702770\pi\) | |||||||
\(620\) | 3.87948e6 | 0.405317 | ||||||||
\(621\) | −45437.0 | −0.00472804 | ||||||||
\(622\) | 6.52709e6 | 0.676462 | ||||||||
\(623\) | −1.47780e7 | −1.52544 | ||||||||
\(624\) | −2.09655e7 | −2.15548 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −6.69580e6 | −0.682915 | ||||||||
\(627\) | 981260. | 0.0996816 | ||||||||
\(628\) | −3.32407e7 | −3.36334 | ||||||||
\(629\) | 1.25931e6 | 0.126913 | ||||||||
\(630\) | 1.58031e7 | 1.58632 | ||||||||
\(631\) | −1.51609e7 | −1.51583 | −0.757915 | − | 0.652353i | \(-0.773782\pi\) | ||||
−0.757915 | + | 0.652353i | \(0.773782\pi\) | |||||||
\(632\) | 1.41344e7 | 1.40761 | ||||||||
\(633\) | −1.68704e7 | −1.67346 | ||||||||
\(634\) | 1.45870e7 | 1.44127 | ||||||||
\(635\) | −4.46656e6 | −0.439581 | ||||||||
\(636\) | −4.62656e7 | −4.53539 | ||||||||
\(637\) | −1.15222e7 | −1.12509 | ||||||||
\(638\) | −3.51148e6 | −0.341538 | ||||||||
\(639\) | −1.50090e7 | −1.45411 | ||||||||
\(640\) | 3.59944e6 | 0.347364 | ||||||||
\(641\) | 9.53649e6 | 0.916734 | 0.458367 | − | 0.888763i | \(-0.348435\pi\) | ||||
0.458367 | + | 0.888763i | \(0.348435\pi\) | |||||||
\(642\) | 5.32558e7 | 5.09952 | ||||||||
\(643\) | 1.51603e7 | 1.44604 | 0.723019 | − | 0.690828i | \(-0.242754\pi\) | ||||
0.723019 | + | 0.690828i | \(0.242754\pi\) | |||||||
\(644\) | −1.98583e6 | −0.188680 | ||||||||
\(645\) | −5.13904e6 | −0.486388 | ||||||||
\(646\) | −506873. | −0.0477879 | ||||||||
\(647\) | −1.12088e7 | −1.05268 | −0.526341 | − | 0.850274i | \(-0.676436\pi\) | ||||
−0.526341 | + | 0.850274i | \(0.676436\pi\) | |||||||
\(648\) | 2.77032e7 | 2.59174 | ||||||||
\(649\) | −5.26617e6 | −0.490776 | ||||||||
\(650\) | 2.16854e6 | 0.201319 | ||||||||
\(651\) | −9.90307e6 | −0.915835 | ||||||||
\(652\) | −3.90992e6 | −0.360205 | ||||||||
\(653\) | 1.76291e7 | 1.61788 | 0.808941 | − | 0.587890i | \(-0.200041\pi\) | ||||
0.808941 | + | 0.587890i | \(0.200041\pi\) | |||||||
\(654\) | −7.49811e6 | −0.685500 | ||||||||
\(655\) | 1.67903e6 | 0.152916 | ||||||||
\(656\) | −2.17005e7 | −1.96884 | ||||||||
\(657\) | 1.11938e6 | 0.101173 | ||||||||
\(658\) | −2.99162e7 | −2.69365 | ||||||||
\(659\) | −5.51723e6 | −0.494889 | −0.247444 | − | 0.968902i | \(-0.579591\pi\) | ||||
−0.247444 | + | 0.968902i | \(0.579591\pi\) | |||||||
\(660\) | 5.45437e6 | 0.487399 | ||||||||
\(661\) | −8.91095e6 | −0.793268 | −0.396634 | − | 0.917977i | \(-0.629822\pi\) | ||||
−0.396634 | + | 0.917977i | \(0.629822\pi\) | |||||||
\(662\) | 1.93839e7 | 1.71908 | ||||||||
\(663\) | 974822. | 0.0861275 | ||||||||
\(664\) | 6.05955e6 | 0.533360 | ||||||||
\(665\) | 2.05788e6 | 0.180454 | ||||||||
\(666\) | 2.63446e7 | 2.30148 | ||||||||
\(667\) | 297183. | 0.0258648 | ||||||||
\(668\) | −2.44945e7 | −2.12387 | ||||||||
\(669\) | 1.41135e7 | 1.21918 | ||||||||
\(670\) | −1.29526e7 | −1.11473 | ||||||||
\(671\) | −3.59205e6 | −0.307989 | ||||||||
\(672\) | −7.08559e7 | −6.05275 | ||||||||
\(673\) | −2.03266e7 | −1.72993 | −0.864963 | − | 0.501836i | \(-0.832658\pi\) | ||||
−0.864963 | + | 0.501836i | \(0.832658\pi\) | |||||||
\(674\) | −2.32621e7 | −1.97242 | ||||||||
\(675\) | 261727. | 0.0221100 | ||||||||
\(676\) | −2.11948e7 | −1.78387 | ||||||||
\(677\) | −8.26460e6 | −0.693027 | −0.346514 | − | 0.938045i | \(-0.612635\pi\) | ||||
−0.346514 | + | 0.938045i | \(0.612635\pi\) | |||||||
\(678\) | −1.88380e6 | −0.157384 | ||||||||
\(679\) | −1.25516e7 | −1.04478 | ||||||||
\(680\) | −1.69421e6 | −0.140506 | ||||||||
\(681\) | −1.69902e7 | −1.40389 | ||||||||
\(682\) | −2.47864e6 | −0.204058 | ||||||||
\(683\) | 4.64558e6 | 0.381055 | 0.190528 | − | 0.981682i | \(-0.438980\pi\) | ||||
0.190528 | + | 0.981682i | \(0.438980\pi\) | |||||||
\(684\) | −7.58126e6 | −0.619585 | ||||||||
\(685\) | 6.65550e6 | 0.541944 | ||||||||
\(686\) | −4.44035e7 | −3.60253 | ||||||||
\(687\) | 2.78042e7 | 2.24760 | ||||||||
\(688\) | 2.60795e7 | 2.10053 | ||||||||
\(689\) | 8.40240e6 | 0.674303 | ||||||||
\(690\) | −645647. | −0.0516265 | ||||||||
\(691\) | 9.48487e6 | 0.755677 | 0.377838 | − | 0.925872i | \(-0.376667\pi\) | ||||
0.377838 | + | 0.925872i | \(0.376667\pi\) | |||||||
\(692\) | 4.85304e7 | 3.85256 | ||||||||
\(693\) | −7.21879e6 | −0.570994 | ||||||||
\(694\) | −3.59094e7 | −2.83015 | ||||||||
\(695\) | −1.01342e7 | −0.795845 | ||||||||
\(696\) | 3.14653e7 | 2.46211 | ||||||||
\(697\) | 1.00900e6 | 0.0786700 | ||||||||
\(698\) | 2.50788e7 | 1.94836 | ||||||||
\(699\) | −1.94763e7 | −1.50770 | ||||||||
\(700\) | 1.14388e7 | 0.882338 | ||||||||
\(701\) | 7.83639e6 | 0.602311 | 0.301155 | − | 0.953575i | \(-0.402628\pi\) | ||||
0.301155 | + | 0.953575i | \(0.402628\pi\) | |||||||
\(702\) | 1.45297e6 | 0.111279 | ||||||||
\(703\) | 3.43060e6 | 0.261807 | ||||||||
\(704\) | −6.69925e6 | −0.509442 | ||||||||
\(705\) | −6.95413e6 | −0.526951 | ||||||||
\(706\) | −1.38257e7 | −1.04394 | ||||||||
\(707\) | −3.88965e7 | −2.92659 | ||||||||
\(708\) | 7.84745e7 | 5.88363 | ||||||||
\(709\) | 2.05133e6 | 0.153257 | 0.0766284 | − | 0.997060i | \(-0.475584\pi\) | ||||
0.0766284 | + | 0.997060i | \(0.475584\pi\) | |||||||
\(710\) | −1.51952e7 | −1.13126 | ||||||||
\(711\) | −7.23144e6 | −0.536476 | ||||||||
\(712\) | 3.31436e7 | 2.45019 | ||||||||
\(713\) | 209772. | 0.0154534 | ||||||||
\(714\) | 7.19211e6 | 0.527972 | ||||||||
\(715\) | −990581. | −0.0724644 | ||||||||
\(716\) | −3.61165e7 | −2.63283 | ||||||||
\(717\) | 4.34350e6 | 0.315531 | ||||||||
\(718\) | −1.21850e7 | −0.882094 | ||||||||
\(719\) | −1.70751e7 | −1.23180 | −0.615901 | − | 0.787824i | \(-0.711208\pi\) | ||||
−0.615901 | + | 0.787824i | \(0.711208\pi\) | |||||||
\(720\) | −1.86421e7 | −1.34018 | ||||||||
\(721\) | −1.32117e7 | −0.946501 | ||||||||
\(722\) | −1.38082e6 | −0.0985812 | ||||||||
\(723\) | 1.01609e7 | 0.722916 | ||||||||
\(724\) | 5.38873e7 | 3.82067 | ||||||||
\(725\) | −1.71184e6 | −0.120953 | ||||||||
\(726\) | −3.48486e6 | −0.245382 | ||||||||
\(727\) | 2.28492e7 | 1.60337 | 0.801687 | − | 0.597745i | \(-0.203936\pi\) | ||||
0.801687 | + | 0.597745i | \(0.203936\pi\) | |||||||
\(728\) | 3.81852e7 | 2.67034 | ||||||||
\(729\) | −1.64595e7 | −1.14709 | ||||||||
\(730\) | 1.13328e6 | 0.0787098 | ||||||||
\(731\) | −1.21261e6 | −0.0839318 | ||||||||
\(732\) | 5.35274e7 | 3.69231 | ||||||||
\(733\) | −4.41789e6 | −0.303707 | −0.151854 | − | 0.988403i | \(-0.548524\pi\) | ||||
−0.151854 | + | 0.988403i | \(0.548524\pi\) | |||||||
\(734\) | −2.77096e7 | −1.89841 | ||||||||
\(735\) | −1.97607e7 | −1.34922 | ||||||||
\(736\) | 1.50091e6 | 0.102131 | ||||||||
\(737\) | 5.91668e6 | 0.401245 | ||||||||
\(738\) | 2.11082e7 | 1.42662 | ||||||||
\(739\) | −9.36075e6 | −0.630521 | −0.315261 | − | 0.949005i | \(-0.602092\pi\) | ||||
−0.315261 | + | 0.949005i | \(0.602092\pi\) | |||||||
\(740\) | 1.90691e7 | 1.28012 | ||||||||
\(741\) | 2.65560e6 | 0.177671 | ||||||||
\(742\) | 6.19918e7 | 4.13356 | ||||||||
\(743\) | 2.54119e6 | 0.168875 | 0.0844375 | − | 0.996429i | \(-0.473091\pi\) | ||||
0.0844375 | + | 0.996429i | \(0.473091\pi\) | |||||||
\(744\) | 2.22103e7 | 1.47103 | ||||||||
\(745\) | 4.95351e6 | 0.326981 | ||||||||
\(746\) | 1.56309e7 | 1.02834 | ||||||||
\(747\) | −3.10020e6 | −0.203277 | ||||||||
\(748\) | 1.28701e6 | 0.0841063 | ||||||||
\(749\) | −5.10182e7 | −3.32292 | ||||||||
\(750\) | 3.71907e6 | 0.241424 | ||||||||
\(751\) | 1.88882e7 | 1.22205 | 0.611027 | − | 0.791610i | \(-0.290757\pi\) | ||||
0.611027 | + | 0.791610i | \(0.290757\pi\) | |||||||
\(752\) | 3.52907e7 | 2.27570 | ||||||||
\(753\) | −5.23205e6 | −0.336267 | ||||||||
\(754\) | −9.50319e6 | −0.608753 | ||||||||
\(755\) | −3.10193e6 | −0.198045 | ||||||||
\(756\) | 7.66424e6 | 0.487713 | ||||||||
\(757\) | −7.78187e6 | −0.493565 | −0.246782 | − | 0.969071i | \(-0.579373\pi\) | ||||
−0.246782 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(758\) | 9.71249e6 | 0.613984 | ||||||||
\(759\) | 294929. | 0.0185829 | ||||||||
\(760\) | −4.61535e6 | −0.289848 | ||||||||
\(761\) | 2.24470e7 | 1.40506 | 0.702531 | − | 0.711653i | \(-0.252053\pi\) | ||||
0.702531 | + | 0.711653i | \(0.252053\pi\) | |||||||
\(762\) | −4.25253e7 | −2.65314 | ||||||||
\(763\) | 7.18307e6 | 0.446682 | ||||||||
\(764\) | 5.67173e7 | 3.51546 | ||||||||
\(765\) | 866794. | 0.0535503 | ||||||||
\(766\) | 1.89105e7 | 1.16448 | ||||||||
\(767\) | −1.42519e7 | −0.874754 | ||||||||
\(768\) | −5.53036e6 | −0.338338 | ||||||||
\(769\) | 1.04306e7 | 0.636054 | 0.318027 | − | 0.948082i | \(-0.396980\pi\) | ||||
0.318027 | + | 0.948082i | \(0.396980\pi\) | |||||||
\(770\) | −7.30837e6 | −0.444216 | ||||||||
\(771\) | 1.43574e7 | 0.869841 | ||||||||
\(772\) | 2.35182e7 | 1.42024 | ||||||||
\(773\) | −1.79072e7 | −1.07790 | −0.538950 | − | 0.842338i | \(-0.681179\pi\) | ||||
−0.538950 | + | 0.842338i | \(0.681179\pi\) | |||||||
\(774\) | −2.53676e7 | −1.52204 | ||||||||
\(775\) | −1.20833e6 | −0.0722656 | ||||||||
\(776\) | 2.81503e7 | 1.67814 | ||||||||
\(777\) | −4.86774e7 | −2.89251 | ||||||||
\(778\) | 5.02630e7 | 2.97714 | ||||||||
\(779\) | 2.74871e6 | 0.162288 | ||||||||
\(780\) | 1.47613e7 | 0.868735 | ||||||||
\(781\) | 6.94112e6 | 0.407194 | ||||||||
\(782\) | −152347. | −0.00890874 | ||||||||
\(783\) | −1.14697e6 | −0.0668570 | ||||||||
\(784\) | 1.00281e8 | 5.82678 | ||||||||
\(785\) | 1.03534e7 | 0.599664 | ||||||||
\(786\) | 1.59857e7 | 0.922944 | ||||||||
\(787\) | 2.42331e7 | 1.39467 | 0.697336 | − | 0.716744i | \(-0.254369\pi\) | ||||
0.697336 | + | 0.716744i | \(0.254369\pi\) | |||||||
\(788\) | 6.95527e7 | 3.99023 | ||||||||
\(789\) | −9.15585e6 | −0.523608 | ||||||||
\(790\) | −7.32118e6 | −0.417362 | ||||||||
\(791\) | 1.80465e6 | 0.102554 | ||||||||
\(792\) | 1.61901e7 | 0.917142 | ||||||||
\(793\) | −9.72123e6 | −0.548957 | ||||||||
\(794\) | 8.83276e6 | 0.497216 | ||||||||
\(795\) | 1.44102e7 | 0.808635 | ||||||||
\(796\) | −4.90328e7 | −2.74286 | ||||||||
\(797\) | 3.34923e7 | 1.86767 | 0.933833 | − | 0.357710i | \(-0.116442\pi\) | ||||
0.933833 | + | 0.357710i | \(0.116442\pi\) | |||||||
\(798\) | 1.95927e7 | 1.08915 | ||||||||
\(799\) | −1.64089e6 | −0.0909314 | ||||||||
\(800\) | −8.64554e6 | −0.477603 | ||||||||
\(801\) | −1.69570e7 | −0.933829 | ||||||||
\(802\) | 3.54549e7 | 1.94643 | ||||||||
\(803\) | −517676. | −0.0283315 | ||||||||
\(804\) | −8.81682e7 | −4.81030 | ||||||||
\(805\) | 618520. | 0.0336406 | ||||||||
\(806\) | −6.70800e6 | −0.363710 | ||||||||
\(807\) | −2.14657e6 | −0.116028 | ||||||||
\(808\) | 8.72361e7 | 4.70075 | ||||||||
\(809\) | −4.45649e6 | −0.239399 | −0.119699 | − | 0.992810i | \(-0.538193\pi\) | ||||
−0.119699 | + | 0.992810i | \(0.538193\pi\) | |||||||
\(810\) | −1.43494e7 | −0.768462 | ||||||||
\(811\) | −6.43065e6 | −0.343323 | −0.171662 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171662 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(812\) | −5.01282e7 | −2.66804 | ||||||||
\(813\) | −2.71508e7 | −1.44064 | ||||||||
\(814\) | −1.21835e7 | −0.644481 | ||||||||
\(815\) | 1.21781e6 | 0.0642224 | ||||||||
\(816\) | −8.48418e6 | −0.446051 | ||||||||
\(817\) | −3.30337e6 | −0.173142 | ||||||||
\(818\) | −4.48126e7 | −2.34162 | ||||||||
\(819\) | −1.95364e7 | −1.01773 | ||||||||
\(820\) | 1.52788e7 | 0.793514 | ||||||||
\(821\) | −1.20678e7 | −0.624843 | −0.312422 | − | 0.949944i | \(-0.601140\pi\) | ||||
−0.312422 | + | 0.949944i | \(0.601140\pi\) | |||||||
\(822\) | 6.33658e7 | 3.27096 | ||||||||
\(823\) | 7.87958e6 | 0.405512 | 0.202756 | − | 0.979229i | \(-0.435010\pi\) | ||||
0.202756 | + | 0.979229i | \(0.435010\pi\) | |||||||
\(824\) | 2.96309e7 | 1.52029 | ||||||||
\(825\) | −1.69886e6 | −0.0869004 | ||||||||
\(826\) | −1.05149e8 | −5.36234 | ||||||||
\(827\) | 1.40013e7 | 0.711877 | 0.355939 | − | 0.934509i | \(-0.384161\pi\) | ||||
0.355939 | + | 0.934509i | \(0.384161\pi\) | |||||||
\(828\) | −2.27864e6 | −0.115505 | ||||||||
\(829\) | −3.45248e7 | −1.74480 | −0.872400 | − | 0.488793i | \(-0.837437\pi\) | ||||
−0.872400 | + | 0.488793i | \(0.837437\pi\) | |||||||
\(830\) | −3.13867e6 | −0.158143 | ||||||||
\(831\) | 2.04260e7 | 1.02608 | ||||||||
\(832\) | −1.81303e7 | −0.908024 | ||||||||
\(833\) | −4.66272e6 | −0.232824 | ||||||||
\(834\) | −9.64860e7 | −4.80341 | ||||||||
\(835\) | 7.62924e6 | 0.378673 | ||||||||
\(836\) | 3.50607e6 | 0.173502 | ||||||||
\(837\) | −809608. | −0.0399449 | ||||||||
\(838\) | 6.24227e7 | 3.07067 | ||||||||
\(839\) | −1.35029e7 | −0.662249 | −0.331125 | − | 0.943587i | \(-0.607428\pi\) | ||||
−0.331125 | + | 0.943587i | \(0.607428\pi\) | |||||||
\(840\) | 6.54880e7 | 3.20231 | ||||||||
\(841\) | −1.30094e7 | −0.634258 | ||||||||
\(842\) | 4.17711e7 | 2.03047 | ||||||||
\(843\) | 2.94218e7 | 1.42593 | ||||||||
\(844\) | −6.02782e7 | −2.91276 | ||||||||
\(845\) | 6.60149e6 | 0.318054 | ||||||||
\(846\) | −3.43274e7 | −1.64898 | ||||||||
\(847\) | 3.33844e6 | 0.159895 | ||||||||
\(848\) | −7.31287e7 | −3.49219 | ||||||||
\(849\) | 3.16934e7 | 1.50904 | ||||||||
\(850\) | 877551. | 0.0416605 | ||||||||
\(851\) | 1.03111e6 | 0.0488068 | ||||||||
\(852\) | −1.03434e8 | −4.88162 | ||||||||
\(853\) | −3.14164e7 | −1.47837 | −0.739187 | − | 0.673500i | \(-0.764790\pi\) | ||||
−0.739187 | + | 0.673500i | \(0.764790\pi\) | |||||||
\(854\) | −7.17219e7 | −3.36517 | ||||||||
\(855\) | 2.36131e6 | 0.110468 | ||||||||
\(856\) | 1.14422e8 | 5.33735 | ||||||||
\(857\) | 3.05288e7 | 1.41990 | 0.709950 | − | 0.704252i | \(-0.248718\pi\) | ||||
0.709950 | + | 0.704252i | \(0.248718\pi\) | |||||||
\(858\) | −9.43114e6 | −0.437367 | ||||||||
\(859\) | 1.44745e7 | 0.669300 | 0.334650 | − | 0.942343i | \(-0.391382\pi\) | ||||
0.334650 | + | 0.942343i | \(0.391382\pi\) | |||||||
\(860\) | −1.83619e7 | −0.846588 | ||||||||
\(861\) | −3.90019e7 | −1.79299 | ||||||||
\(862\) | 2.89641e7 | 1.32767 | ||||||||
\(863\) | −1.89177e7 | −0.864650 | −0.432325 | − | 0.901718i | \(-0.642307\pi\) | ||||
−0.432325 | + | 0.901718i | \(0.642307\pi\) | |||||||
\(864\) | −5.79270e6 | −0.263996 | ||||||||
\(865\) | −1.51156e7 | −0.686888 | ||||||||
\(866\) | 3.83258e7 | 1.73659 | ||||||||
\(867\) | −3.15015e7 | −1.42326 | ||||||||
\(868\) | −3.53839e7 | −1.59407 | ||||||||
\(869\) | 3.34429e6 | 0.150229 | ||||||||
\(870\) | −1.62981e7 | −0.730026 | ||||||||
\(871\) | 1.60124e7 | 0.715175 | ||||||||
\(872\) | −1.61100e7 | −0.717470 | ||||||||
\(873\) | −1.44023e7 | −0.639581 | ||||||||
\(874\) | −415022. | −0.0183778 | ||||||||
\(875\) | −3.56281e6 | −0.157316 | ||||||||
\(876\) | 7.71422e6 | 0.339650 | ||||||||
\(877\) | −3.33427e7 | −1.46387 | −0.731933 | − | 0.681377i | \(-0.761382\pi\) | ||||
−0.731933 | + | 0.681377i | \(0.761382\pi\) | |||||||
\(878\) | 7.24988e6 | 0.317391 | ||||||||
\(879\) | −2.33286e7 | −1.01840 | ||||||||
\(880\) | 8.62133e6 | 0.375291 | ||||||||
\(881\) | −9.95791e6 | −0.432243 | −0.216122 | − | 0.976366i | \(-0.569341\pi\) | ||||
−0.216122 | + | 0.976366i | \(0.569341\pi\) | |||||||
\(882\) | −9.75437e7 | −4.22209 | ||||||||
\(883\) | 2.69760e7 | 1.16433 | 0.582164 | − | 0.813071i | \(-0.302206\pi\) | ||||
0.582164 | + | 0.813071i | \(0.302206\pi\) | |||||||
\(884\) | 3.48307e6 | 0.149910 | ||||||||
\(885\) | −2.44422e7 | −1.04902 | ||||||||
\(886\) | −5.73053e6 | −0.245251 | ||||||||
\(887\) | −945417. | −0.0403473 | −0.0201736 | − | 0.999796i | \(-0.506422\pi\) | ||||
−0.0201736 | + | 0.999796i | \(0.506422\pi\) | |||||||
\(888\) | 1.09172e8 | 4.64601 | ||||||||
\(889\) | 4.07385e7 | 1.72882 | ||||||||
\(890\) | −1.71674e7 | −0.726490 | ||||||||
\(891\) | 6.55477e6 | 0.276607 | ||||||||
\(892\) | 5.04279e7 | 2.12206 | ||||||||
\(893\) | −4.47011e6 | −0.187581 | ||||||||
\(894\) | 4.71615e7 | 1.97353 | ||||||||
\(895\) | 1.12491e7 | 0.469419 | ||||||||
\(896\) | −3.28297e7 | −1.36615 | ||||||||
\(897\) | 798173. | 0.0331220 | ||||||||
\(898\) | 7.87459e7 | 3.25865 | ||||||||
\(899\) | 5.29527e6 | 0.218519 | ||||||||
\(900\) | 1.31254e7 | 0.540142 | ||||||||
\(901\) | 3.40023e6 | 0.139539 | ||||||||
\(902\) | −9.76179e6 | −0.399497 | ||||||||
\(903\) | 4.68721e7 | 1.91291 | ||||||||
\(904\) | −4.04742e6 | −0.164724 | ||||||||
\(905\) | −1.67841e7 | −0.681204 | ||||||||
\(906\) | −2.95329e7 | −1.19532 | ||||||||
\(907\) | −1.00438e7 | −0.405396 | −0.202698 | − | 0.979241i | \(-0.564971\pi\) | ||||
−0.202698 | + | 0.979241i | \(0.564971\pi\) | |||||||
\(908\) | −6.07066e7 | −2.44355 | ||||||||
\(909\) | −4.46318e7 | −1.79158 | ||||||||
\(910\) | −1.97788e7 | −0.791765 | ||||||||
\(911\) | −4.24017e7 | −1.69273 | −0.846365 | − | 0.532604i | \(-0.821214\pi\) | ||||
−0.846365 | + | 0.532604i | \(0.821214\pi\) | |||||||
\(912\) | −2.31125e7 | −0.920154 | ||||||||
\(913\) | 1.43373e6 | 0.0569235 | ||||||||
\(914\) | 6.36604e7 | 2.52060 | ||||||||
\(915\) | −1.66720e7 | −0.658317 | ||||||||
\(916\) | 9.93453e7 | 3.91209 | ||||||||
\(917\) | −1.53141e7 | −0.601405 | ||||||||
\(918\) | 587978. | 0.0230279 | ||||||||
\(919\) | −2.97668e7 | −1.16263 | −0.581317 | − | 0.813677i | \(-0.697462\pi\) | ||||
−0.581317 | + | 0.813677i | \(0.697462\pi\) | |||||||
\(920\) | −1.38720e6 | −0.0540343 | ||||||||
\(921\) | 3.09168e7 | 1.20101 | ||||||||
\(922\) | 4.31825e7 | 1.67294 | ||||||||
\(923\) | 1.87849e7 | 0.725779 | ||||||||
\(924\) | −4.97482e7 | −1.91689 | ||||||||
\(925\) | −5.93941e6 | −0.228238 | ||||||||
\(926\) | 3.76546e7 | 1.44308 | ||||||||
\(927\) | −1.51598e7 | −0.579420 | ||||||||
\(928\) | 3.78874e7 | 1.44419 | ||||||||
\(929\) | 3.64559e7 | 1.38589 | 0.692944 | − | 0.720992i | \(-0.256313\pi\) | ||||
0.692944 | + | 0.720992i | \(0.256313\pi\) | |||||||
\(930\) | −1.15043e7 | −0.436167 | ||||||||
\(931\) | −1.27022e7 | −0.480289 | ||||||||
\(932\) | −6.95895e7 | −2.62424 | ||||||||
\(933\) | −1.38385e7 | −0.520456 | ||||||||
\(934\) | −2.50761e7 | −0.940572 | ||||||||
\(935\) | −400862. | −0.0149957 | ||||||||
\(936\) | 4.38156e7 | 1.63470 | ||||||||
\(937\) | −9.54170e6 | −0.355040 | −0.177520 | − | 0.984117i | \(-0.556807\pi\) | ||||
−0.177520 | + | 0.984117i | \(0.556807\pi\) | |||||||
\(938\) | 1.18138e8 | 4.38411 | ||||||||
\(939\) | 1.41962e7 | 0.525420 | ||||||||
\(940\) | −2.48473e7 | −0.917190 | ||||||||
\(941\) | 1.80646e7 | 0.665049 | 0.332525 | − | 0.943095i | \(-0.392100\pi\) | ||||
0.332525 | + | 0.943095i | \(0.392100\pi\) | |||||||
\(942\) | 9.85727e7 | 3.61934 | ||||||||
\(943\) | 826157. | 0.0302540 | ||||||||
\(944\) | 1.24039e8 | 4.53032 | ||||||||
\(945\) | −2.38716e6 | −0.0869565 | ||||||||
\(946\) | 1.17316e7 | 0.426217 | ||||||||
\(947\) | 2.57490e6 | 0.0933007 | 0.0466504 | − | 0.998911i | \(-0.485145\pi\) | ||||
0.0466504 | + | 0.998911i | \(0.485145\pi\) | |||||||
\(948\) | −4.98353e7 | −1.80101 | ||||||||
\(949\) | −1.40100e6 | −0.0504978 | ||||||||
\(950\) | 2.39062e6 | 0.0859411 | ||||||||
\(951\) | −3.09269e7 | −1.10888 | ||||||||
\(952\) | 1.54525e7 | 0.552595 | ||||||||
\(953\) | −4.35706e7 | −1.55404 | −0.777018 | − | 0.629478i | \(-0.783269\pi\) | ||||
−0.777018 | + | 0.629478i | \(0.783269\pi\) | |||||||
\(954\) | 7.11325e7 | 2.53044 | ||||||||
\(955\) | −1.76656e7 | −0.626786 | ||||||||
\(956\) | 1.55195e7 | 0.549202 | ||||||||
\(957\) | 7.44490e6 | 0.262772 | ||||||||
\(958\) | −5.07071e7 | −1.78507 | ||||||||
\(959\) | −6.07035e7 | −2.13141 | ||||||||
\(960\) | −3.10937e7 | −1.08892 | ||||||||
\(961\) | −2.48914e7 | −0.869442 | ||||||||
\(962\) | −3.29724e7 | −1.14872 | ||||||||
\(963\) | −5.85408e7 | −2.03420 | ||||||||
\(964\) | 3.63053e7 | 1.25828 | ||||||||
\(965\) | −7.32515e6 | −0.253220 | ||||||||
\(966\) | 5.88881e6 | 0.203042 | ||||||||
\(967\) | −1.31389e7 | −0.451850 | −0.225925 | − | 0.974145i | \(-0.572540\pi\) | ||||
−0.225925 | + | 0.974145i | \(0.572540\pi\) | |||||||
\(968\) | −7.48735e6 | −0.256827 | ||||||||
\(969\) | 1.07465e6 | 0.0367670 | ||||||||
\(970\) | −1.45810e7 | −0.497575 | ||||||||
\(971\) | 1.11231e7 | 0.378596 | 0.189298 | − | 0.981920i | \(-0.439379\pi\) | ||||
0.189298 | + | 0.981920i | \(0.439379\pi\) | |||||||
\(972\) | −1.05845e8 | −3.59338 | ||||||||
\(973\) | 9.24321e7 | 3.12997 | ||||||||
\(974\) | −6.09348e6 | −0.205811 | ||||||||
\(975\) | −4.59765e6 | −0.154890 | ||||||||
\(976\) | 8.46069e7 | 2.84303 | ||||||||
\(977\) | 1.39410e7 | 0.467259 | 0.233630 | − | 0.972326i | \(-0.424940\pi\) | ||||
0.233630 | + | 0.972326i | \(0.424940\pi\) | |||||||
\(978\) | 1.15946e7 | 0.387621 | ||||||||
\(979\) | 7.84201e6 | 0.261499 | ||||||||
\(980\) | −7.06054e7 | −2.34840 | ||||||||
\(981\) | 8.24221e6 | 0.273446 | ||||||||
\(982\) | −2.57165e7 | −0.851005 | ||||||||
\(983\) | 1.20959e7 | 0.399260 | 0.199630 | − | 0.979871i | \(-0.436026\pi\) | ||||
0.199630 | + | 0.979871i | \(0.436026\pi\) | |||||||
\(984\) | 8.74723e7 | 2.87994 | ||||||||
\(985\) | −2.16634e7 | −0.711435 | ||||||||
\(986\) | −3.84569e6 | −0.125974 | ||||||||
\(987\) | 6.34271e7 | 2.07244 | ||||||||
\(988\) | 9.48854e6 | 0.309248 | ||||||||
\(989\) | −992869. | −0.0322776 | ||||||||
\(990\) | −8.38599e6 | −0.271936 | ||||||||
\(991\) | −4.51300e7 | −1.45976 | −0.729880 | − | 0.683575i | \(-0.760424\pi\) | ||||
−0.729880 | + | 0.683575i | \(0.760424\pi\) | |||||||
\(992\) | 2.67435e7 | 0.862857 | ||||||||
\(993\) | −4.10969e7 | −1.32262 | ||||||||
\(994\) | 1.38592e8 | 4.44911 | ||||||||
\(995\) | 1.52721e7 | 0.489036 | ||||||||
\(996\) | −2.13650e7 | −0.682423 | ||||||||
\(997\) | −3.95987e7 | −1.26166 | −0.630831 | − | 0.775920i | \(-0.717286\pi\) | ||||
−0.630831 | + | 0.775920i | \(0.717286\pi\) | |||||||
\(998\) | 6.42263e7 | 2.04121 | ||||||||
\(999\) | −3.97953e6 | −0.126159 |
(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 | 1045.6.a.c.1.2 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.c.1.2 | ✓ | 37 | 1.1 | even | 1 | trivial |