Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,6,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(87.7299494377\) |
Analytic rank: | \(0\) |
Dimension: | \(117\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.59008 | −1.69530 | −0.847652 | − | 0.530553i | \(-0.821984\pi\) | ||||
−0.847652 | + | 0.530553i | \(0.821984\pi\) | |||||||
\(3\) | 16.3551 | 1.04918 | 0.524589 | − | 0.851356i | \(-0.324219\pi\) | ||||
0.524589 | + | 0.851356i | \(0.324219\pi\) | |||||||
\(4\) | 59.9697 | 1.87405 | ||||||||
\(5\) | 7.17600 | 0.128368 | 0.0641841 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641841 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(6\) | −156.846 | −1.77867 | ||||||||
\(7\) | 253.293 | 1.95379 | 0.976895 | − | 0.213721i | \(-0.0685584\pi\) | ||||
0.976895 | + | 0.213721i | \(0.0685584\pi\) | |||||||
\(8\) | −268.232 | −1.48178 | ||||||||
\(9\) | 24.4881 | 0.100774 | ||||||||
\(10\) | −68.8184 | −0.217623 | ||||||||
\(11\) | 232.324 | 0.578913 | 0.289456 | − | 0.957191i | \(-0.406526\pi\) | ||||
0.289456 | + | 0.957191i | \(0.406526\pi\) | |||||||
\(12\) | 980.808 | 1.96621 | ||||||||
\(13\) | −147.492 | −0.242052 | −0.121026 | − | 0.992649i | \(-0.538619\pi\) | ||||
−0.121026 | + | 0.992649i | \(0.538619\pi\) | |||||||
\(14\) | −2429.10 | −3.31227 | ||||||||
\(15\) | 117.364 | 0.134681 | ||||||||
\(16\) | 653.334 | 0.638021 | ||||||||
\(17\) | 32.0243 | 0.0268756 | 0.0134378 | − | 0.999910i | \(-0.495722\pi\) | ||||
0.0134378 | + | 0.999910i | \(0.495722\pi\) | |||||||
\(18\) | −234.843 | −0.170843 | ||||||||
\(19\) | 356.352 | 0.226462 | 0.113231 | − | 0.993569i | \(-0.463880\pi\) | ||||
0.113231 | + | 0.993569i | \(0.463880\pi\) | |||||||
\(20\) | 430.342 | 0.240569 | ||||||||
\(21\) | 4142.62 | 2.04987 | ||||||||
\(22\) | −2228.01 | −0.981432 | ||||||||
\(23\) | 2571.17 | 1.01347 | 0.506735 | − | 0.862102i | \(-0.330852\pi\) | ||||
0.506735 | + | 0.862102i | \(0.330852\pi\) | |||||||
\(24\) | −4386.95 | −1.55466 | ||||||||
\(25\) | −3073.51 | −0.983522 | ||||||||
\(26\) | 1414.46 | 0.410352 | ||||||||
\(27\) | −3573.78 | −0.943448 | ||||||||
\(28\) | 15189.9 | 3.66150 | ||||||||
\(29\) | 3131.09 | 0.691353 | 0.345677 | − | 0.938354i | \(-0.387649\pi\) | ||||
0.345677 | + | 0.938354i | \(0.387649\pi\) | |||||||
\(30\) | −1125.53 | −0.228325 | ||||||||
\(31\) | −4885.47 | −0.913065 | −0.456533 | − | 0.889707i | \(-0.650909\pi\) | ||||
−0.456533 | + | 0.889707i | \(0.650909\pi\) | |||||||
\(32\) | 2317.89 | 0.400145 | ||||||||
\(33\) | 3799.68 | 0.607382 | ||||||||
\(34\) | −307.116 | −0.0455623 | ||||||||
\(35\) | 1817.63 | 0.250804 | ||||||||
\(36\) | 1468.55 | 0.188856 | ||||||||
\(37\) | 8933.18 | 1.07276 | 0.536379 | − | 0.843977i | \(-0.319792\pi\) | ||||
0.536379 | + | 0.843977i | \(0.319792\pi\) | |||||||
\(38\) | −3417.45 | −0.383922 | ||||||||
\(39\) | −2412.24 | −0.253956 | ||||||||
\(40\) | −1924.83 | −0.190214 | ||||||||
\(41\) | −235.516 | −0.0218807 | −0.0109404 | − | 0.999940i | \(-0.503482\pi\) | ||||
−0.0109404 | + | 0.999940i | \(0.503482\pi\) | |||||||
\(42\) | −39728.1 | −3.47516 | ||||||||
\(43\) | 5683.28 | 0.468735 | 0.234368 | − | 0.972148i | \(-0.424698\pi\) | ||||
0.234368 | + | 0.972148i | \(0.424698\pi\) | |||||||
\(44\) | 13932.4 | 1.08491 | ||||||||
\(45\) | 175.727 | 0.0129362 | ||||||||
\(46\) | −24657.7 | −1.71814 | ||||||||
\(47\) | 29165.7 | 1.92587 | 0.962935 | − | 0.269732i | \(-0.0869351\pi\) | ||||
0.962935 | + | 0.269732i | \(0.0869351\pi\) | |||||||
\(48\) | 10685.3 | 0.669398 | ||||||||
\(49\) | 47350.2 | 2.81729 | ||||||||
\(50\) | 29475.2 | 1.66737 | ||||||||
\(51\) | 523.760 | 0.0281973 | ||||||||
\(52\) | −8845.04 | −0.453619 | ||||||||
\(53\) | −23417.4 | −1.14511 | −0.572557 | − | 0.819865i | \(-0.694048\pi\) | ||||
−0.572557 | + | 0.819865i | \(0.694048\pi\) | |||||||
\(54\) | 34272.8 | 1.59943 | ||||||||
\(55\) | 1667.16 | 0.0743139 | ||||||||
\(56\) | −67941.2 | −2.89510 | ||||||||
\(57\) | 5828.17 | 0.237599 | ||||||||
\(58\) | −30027.4 | −1.17205 | ||||||||
\(59\) | 7454.46 | 0.278796 | 0.139398 | − | 0.990236i | \(-0.455483\pi\) | ||||
0.139398 | + | 0.990236i | \(0.455483\pi\) | |||||||
\(60\) | 7038.28 | 0.252399 | ||||||||
\(61\) | 30262.1 | 1.04130 | 0.520648 | − | 0.853772i | \(-0.325691\pi\) | ||||
0.520648 | + | 0.853772i | \(0.325691\pi\) | |||||||
\(62\) | 46852.0 | 1.54792 | ||||||||
\(63\) | 6202.67 | 0.196892 | ||||||||
\(64\) | −43135.4 | −1.31639 | ||||||||
\(65\) | −1058.40 | −0.0310718 | ||||||||
\(66\) | −36439.2 | −1.02970 | ||||||||
\(67\) | −31380.7 | −0.854035 | −0.427017 | − | 0.904243i | \(-0.640436\pi\) | ||||
−0.427017 | + | 0.904243i | \(0.640436\pi\) | |||||||
\(68\) | 1920.49 | 0.0503663 | ||||||||
\(69\) | 42051.6 | 1.06331 | ||||||||
\(70\) | −17431.2 | −0.425189 | ||||||||
\(71\) | 73810.7 | 1.73769 | 0.868847 | − | 0.495081i | \(-0.164862\pi\) | ||||
0.868847 | + | 0.495081i | \(0.164862\pi\) | |||||||
\(72\) | −6568.49 | −0.149326 | ||||||||
\(73\) | 72207.8 | 1.58590 | 0.792952 | − | 0.609285i | \(-0.208543\pi\) | ||||
0.792952 | + | 0.609285i | \(0.208543\pi\) | |||||||
\(74\) | −85669.9 | −1.81865 | ||||||||
\(75\) | −50267.4 | −1.03189 | ||||||||
\(76\) | 21370.3 | 0.424402 | ||||||||
\(77\) | 58846.1 | 1.13107 | ||||||||
\(78\) | 23133.6 | 0.430533 | ||||||||
\(79\) | −41830.8 | −0.754100 | −0.377050 | − | 0.926193i | \(-0.623061\pi\) | ||||
−0.377050 | + | 0.926193i | \(0.623061\pi\) | |||||||
\(80\) | 4688.32 | 0.0819016 | ||||||||
\(81\) | −64399.9 | −1.09062 | ||||||||
\(82\) | 2258.62 | 0.0370944 | ||||||||
\(83\) | −27176.2 | −0.433006 | −0.216503 | − | 0.976282i | \(-0.569465\pi\) | ||||
−0.216503 | + | 0.976282i | \(0.569465\pi\) | |||||||
\(84\) | 248432. | 3.84157 | ||||||||
\(85\) | 229.807 | 0.00344997 | ||||||||
\(86\) | −54503.1 | −0.794648 | ||||||||
\(87\) | 51209.1 | 0.725353 | ||||||||
\(88\) | −62316.8 | −0.857824 | ||||||||
\(89\) | 28556.0 | 0.382139 | 0.191070 | − | 0.981576i | \(-0.438804\pi\) | ||||
0.191070 | + | 0.981576i | \(0.438804\pi\) | |||||||
\(90\) | −1685.23 | −0.0219308 | ||||||||
\(91\) | −37358.6 | −0.472920 | ||||||||
\(92\) | 154192. | 1.89930 | ||||||||
\(93\) | −79902.1 | −0.957968 | ||||||||
\(94\) | −279701. | −3.26494 | ||||||||
\(95\) | 2557.18 | 0.0290705 | ||||||||
\(96\) | 37909.2 | 0.419823 | ||||||||
\(97\) | −168665. | −1.82010 | −0.910050 | − | 0.414499i | \(-0.863957\pi\) | ||||
−0.910050 | + | 0.414499i | \(0.863957\pi\) | |||||||
\(98\) | −454093. | −4.77617 | ||||||||
\(99\) | 5689.19 | 0.0583395 | ||||||||
\(100\) | −184317. | −1.84317 | ||||||||
\(101\) | −66683.6 | −0.650452 | −0.325226 | − | 0.945636i | \(-0.605440\pi\) | ||||
−0.325226 | + | 0.945636i | \(0.605440\pi\) | |||||||
\(102\) | −5022.90 | −0.0478029 | ||||||||
\(103\) | −190069. | −1.76530 | −0.882651 | − | 0.470029i | \(-0.844243\pi\) | ||||
−0.882651 | + | 0.470029i | \(0.844243\pi\) | |||||||
\(104\) | 39562.0 | 0.358670 | ||||||||
\(105\) | 29727.4 | 0.263138 | ||||||||
\(106\) | 224575. | 1.94131 | ||||||||
\(107\) | 66433.1 | 0.560951 | 0.280476 | − | 0.959861i | \(-0.409508\pi\) | ||||
0.280476 | + | 0.959861i | \(0.409508\pi\) | |||||||
\(108\) | −214318. | −1.76807 | ||||||||
\(109\) | −81034.9 | −0.653290 | −0.326645 | − | 0.945147i | \(-0.605918\pi\) | ||||
−0.326645 | + | 0.945147i | \(0.605918\pi\) | |||||||
\(110\) | −15988.2 | −0.125985 | ||||||||
\(111\) | 146103. | 1.12551 | ||||||||
\(112\) | 165485. | 1.24656 | ||||||||
\(113\) | 49830.3 | 0.367111 | 0.183555 | − | 0.983009i | \(-0.441239\pi\) | ||||
0.183555 | + | 0.983009i | \(0.441239\pi\) | |||||||
\(114\) | −55892.6 | −0.402802 | ||||||||
\(115\) | 18450.7 | 0.130097 | ||||||||
\(116\) | 187770. | 1.29563 | ||||||||
\(117\) | −3611.80 | −0.0243926 | ||||||||
\(118\) | −71488.9 | −0.472643 | ||||||||
\(119\) | 8111.54 | 0.0525092 | ||||||||
\(120\) | −31480.7 | −0.199568 | ||||||||
\(121\) | −107076. | −0.664860 | ||||||||
\(122\) | −290216. | −1.76531 | ||||||||
\(123\) | −3851.88 | −0.0229567 | ||||||||
\(124\) | −292980. | −1.71113 | ||||||||
\(125\) | −44480.4 | −0.254621 | ||||||||
\(126\) | −59484.1 | −0.333791 | ||||||||
\(127\) | −195474. | −1.07543 | −0.537713 | − | 0.843128i | \(-0.680711\pi\) | ||||
−0.537713 | + | 0.843128i | \(0.680711\pi\) | |||||||
\(128\) | 339500. | 1.83153 | ||||||||
\(129\) | 92950.3 | 0.491787 | ||||||||
\(130\) | 10150.1 | 0.0526762 | ||||||||
\(131\) | 195818. | 0.996950 | 0.498475 | − | 0.866904i | \(-0.333894\pi\) | ||||
0.498475 | + | 0.866904i | \(0.333894\pi\) | |||||||
\(132\) | 227866. | 1.13827 | ||||||||
\(133\) | 90261.5 | 0.442459 | ||||||||
\(134\) | 300943. | 1.44785 | ||||||||
\(135\) | −25645.4 | −0.121109 | ||||||||
\(136\) | −8589.94 | −0.0398238 | ||||||||
\(137\) | 212839. | 0.968836 | 0.484418 | − | 0.874837i | \(-0.339031\pi\) | ||||
0.484418 | + | 0.874837i | \(0.339031\pi\) | |||||||
\(138\) | −403279. | −1.80263 | ||||||||
\(139\) | 281393. | 1.23531 | 0.617656 | − | 0.786448i | \(-0.288082\pi\) | ||||
0.617656 | + | 0.786448i | \(0.288082\pi\) | |||||||
\(140\) | 109003. | 0.470020 | ||||||||
\(141\) | 477006. | 2.02058 | ||||||||
\(142\) | −707850. | −2.94592 | ||||||||
\(143\) | −34265.9 | −0.140127 | ||||||||
\(144\) | 15998.9 | 0.0642961 | ||||||||
\(145\) | 22468.7 | 0.0887477 | ||||||||
\(146\) | −692478. | −2.68859 | ||||||||
\(147\) | 774416. | 2.95584 | ||||||||
\(148\) | 535720. | 2.01040 | ||||||||
\(149\) | 468800. | 1.72990 | 0.864952 | − | 0.501855i | \(-0.167349\pi\) | ||||
0.864952 | + | 0.501855i | \(0.167349\pi\) | |||||||
\(150\) | 482068. | 1.74936 | ||||||||
\(151\) | 80770.8 | 0.288278 | 0.144139 | − | 0.989557i | \(-0.453959\pi\) | ||||
0.144139 | + | 0.989557i | \(0.453959\pi\) | |||||||
\(152\) | −95585.0 | −0.335568 | ||||||||
\(153\) | 784.216 | 0.00270837 | ||||||||
\(154\) | −564339. | −1.91751 | ||||||||
\(155\) | −35058.1 | −0.117208 | ||||||||
\(156\) | −144661. | −0.475927 | ||||||||
\(157\) | −184657. | −0.597885 | −0.298942 | − | 0.954271i | \(-0.596634\pi\) | ||||
−0.298942 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(158\) | 401161. | 1.27843 | ||||||||
\(159\) | −382993. | −1.20143 | ||||||||
\(160\) | 16633.1 | 0.0513658 | ||||||||
\(161\) | 651258. | 1.98011 | ||||||||
\(162\) | 617601. | 1.84893 | ||||||||
\(163\) | 488799. | 1.44099 | 0.720495 | − | 0.693460i | \(-0.243915\pi\) | ||||
0.720495 | + | 0.693460i | \(0.243915\pi\) | |||||||
\(164\) | −14123.8 | −0.0410056 | ||||||||
\(165\) | 27266.5 | 0.0779685 | ||||||||
\(166\) | 260622. | 0.734076 | ||||||||
\(167\) | 287397. | 0.797427 | 0.398714 | − | 0.917075i | \(-0.369457\pi\) | ||||
0.398714 | + | 0.917075i | \(0.369457\pi\) | |||||||
\(168\) | −1.11118e6 | −3.03747 | ||||||||
\(169\) | −349539. | −0.941411 | ||||||||
\(170\) | −2203.86 | −0.00584874 | ||||||||
\(171\) | 8726.40 | 0.0228215 | ||||||||
\(172\) | 340824. | 0.878435 | ||||||||
\(173\) | −214167. | −0.544048 | −0.272024 | − | 0.962291i | \(-0.587693\pi\) | ||||
−0.272024 | + | 0.962291i | \(0.587693\pi\) | |||||||
\(174\) | −491100. | −1.22969 | ||||||||
\(175\) | −778497. | −1.92159 | ||||||||
\(176\) | 151785. | 0.369359 | ||||||||
\(177\) | 121918. | 0.292506 | ||||||||
\(178\) | −273854. | −0.647842 | ||||||||
\(179\) | −535369. | −1.24888 | −0.624440 | − | 0.781072i | \(-0.714673\pi\) | ||||
−0.624440 | + | 0.781072i | \(0.714673\pi\) | |||||||
\(180\) | 10538.3 | 0.0242431 | ||||||||
\(181\) | 294854. | 0.668977 | 0.334488 | − | 0.942400i | \(-0.391437\pi\) | ||||
0.334488 | + | 0.942400i | \(0.391437\pi\) | |||||||
\(182\) | 358272. | 0.801742 | ||||||||
\(183\) | 494938. | 1.09250 | ||||||||
\(184\) | −689669. | −1.50174 | ||||||||
\(185\) | 64104.4 | 0.137708 | ||||||||
\(186\) | 766268. | 1.62405 | ||||||||
\(187\) | 7440.03 | 0.0155586 | ||||||||
\(188\) | 1.74906e6 | 3.60918 | ||||||||
\(189\) | −905212. | −1.84330 | ||||||||
\(190\) | −24523.6 | −0.0492833 | ||||||||
\(191\) | 256898. | 0.509540 | 0.254770 | − | 0.967002i | \(-0.418000\pi\) | ||||
0.254770 | + | 0.967002i | \(0.418000\pi\) | |||||||
\(192\) | −705482. | −1.38113 | ||||||||
\(193\) | 265223. | 0.512528 | 0.256264 | − | 0.966607i | \(-0.417508\pi\) | ||||
0.256264 | + | 0.966607i | \(0.417508\pi\) | |||||||
\(194\) | 1.61751e6 | 3.08562 | ||||||||
\(195\) | −17310.2 | −0.0325999 | ||||||||
\(196\) | 2.83958e6 | 5.27976 | ||||||||
\(197\) | −119175. | −0.218786 | −0.109393 | − | 0.993999i | \(-0.534891\pi\) | ||||
−0.109393 | + | 0.993999i | \(0.534891\pi\) | |||||||
\(198\) | −54559.8 | −0.0989031 | ||||||||
\(199\) | 346776. | 0.620750 | 0.310375 | − | 0.950614i | \(-0.399545\pi\) | ||||
0.310375 | + | 0.950614i | \(0.399545\pi\) | |||||||
\(200\) | 824411. | 1.45737 | ||||||||
\(201\) | −513233. | −0.896034 | ||||||||
\(202\) | 639501. | 1.10271 | ||||||||
\(203\) | 793082. | 1.35076 | ||||||||
\(204\) | 31409.7 | 0.0528432 | ||||||||
\(205\) | −1690.06 | −0.00280878 | ||||||||
\(206\) | 1.82278e6 | 2.99272 | ||||||||
\(207\) | 62963.1 | 0.102132 | ||||||||
\(208\) | −96361.4 | −0.154435 | ||||||||
\(209\) | 82789.3 | 0.131102 | ||||||||
\(210\) | −285088. | −0.446099 | ||||||||
\(211\) | 1.08726e6 | 1.68123 | 0.840617 | − | 0.541630i | \(-0.182193\pi\) | ||||
0.840617 | + | 0.541630i | \(0.182193\pi\) | |||||||
\(212\) | −1.40433e6 | −2.14600 | ||||||||
\(213\) | 1.20718e6 | 1.82315 | ||||||||
\(214\) | −637099. | −0.950982 | ||||||||
\(215\) | 40783.2 | 0.0601707 | ||||||||
\(216\) | 958600. | 1.39799 | ||||||||
\(217\) | −1.23745e6 | −1.78394 | ||||||||
\(218\) | 777132. | 1.10752 | ||||||||
\(219\) | 1.18096e6 | 1.66389 | ||||||||
\(220\) | 99979.0 | 0.139268 | ||||||||
\(221\) | −4723.33 | −0.00650530 | ||||||||
\(222\) | −1.40114e6 | −1.90809 | ||||||||
\(223\) | 189487. | 0.255162 | 0.127581 | − | 0.991828i | \(-0.459279\pi\) | ||||
0.127581 | + | 0.991828i | \(0.459279\pi\) | |||||||
\(224\) | 587104. | 0.781799 | ||||||||
\(225\) | −75264.4 | −0.0991136 | ||||||||
\(226\) | −477876. | −0.622364 | ||||||||
\(227\) | −118108. | −0.152130 | −0.0760650 | − | 0.997103i | \(-0.524236\pi\) | ||||
−0.0760650 | + | 0.997103i | \(0.524236\pi\) | |||||||
\(228\) | 349513. | 0.445273 | ||||||||
\(229\) | −1.08976e6 | −1.37323 | −0.686615 | − | 0.727021i | \(-0.740904\pi\) | ||||
−0.686615 | + | 0.727021i | \(0.740904\pi\) | |||||||
\(230\) | −176944. | −0.220554 | ||||||||
\(231\) | 962432. | 1.18670 | ||||||||
\(232\) | −839857. | −1.02444 | ||||||||
\(233\) | −12191.7 | −0.0147121 | −0.00735606 | − | 0.999973i | \(-0.502342\pi\) | ||||
−0.00735606 | + | 0.999973i | \(0.502342\pi\) | |||||||
\(234\) | 34637.5 | 0.0413529 | ||||||||
\(235\) | 209293. | 0.247220 | ||||||||
\(236\) | 447041. | 0.522478 | ||||||||
\(237\) | −684146. | −0.791185 | ||||||||
\(238\) | −77790.3 | −0.0890191 | ||||||||
\(239\) | 249853. | 0.282937 | 0.141468 | − | 0.989943i | \(-0.454818\pi\) | ||||
0.141468 | + | 0.989943i | \(0.454818\pi\) | |||||||
\(240\) | 76677.8 | 0.0859294 | ||||||||
\(241\) | 1.40842e6 | 1.56203 | 0.781017 | − | 0.624510i | \(-0.214701\pi\) | ||||
0.781017 | + | 0.624510i | \(0.214701\pi\) | |||||||
\(242\) | 1.02687e6 | 1.12714 | ||||||||
\(243\) | −184838. | −0.200805 | ||||||||
\(244\) | 1.81481e6 | 1.95144 | ||||||||
\(245\) | 339785. | 0.361651 | ||||||||
\(246\) | 36939.9 | 0.0389186 | ||||||||
\(247\) | −52559.0 | −0.0548157 | ||||||||
\(248\) | 1.31044e6 | 1.35297 | ||||||||
\(249\) | −444469. | −0.454300 | ||||||||
\(250\) | 426571. | 0.431660 | ||||||||
\(251\) | −532829. | −0.533831 | −0.266915 | − | 0.963720i | \(-0.586004\pi\) | ||||
−0.266915 | + | 0.963720i | \(0.586004\pi\) | |||||||
\(252\) | 371972. | 0.368985 | ||||||||
\(253\) | 597345. | 0.586711 | ||||||||
\(254\) | 1.87461e6 | 1.82317 | ||||||||
\(255\) | 3758.50 | 0.00361963 | ||||||||
\(256\) | −1.87550e6 | −1.78861 | ||||||||
\(257\) | −9092.38 | −0.00858707 | −0.00429353 | − | 0.999991i | \(-0.501367\pi\) | ||||
−0.00429353 | + | 0.999991i | \(0.501367\pi\) | |||||||
\(258\) | −891402. | −0.833728 | ||||||||
\(259\) | 2.26271e6 | 2.09594 | ||||||||
\(260\) | −63472.0 | −0.0582302 | ||||||||
\(261\) | 76674.5 | 0.0696706 | ||||||||
\(262\) | −1.87791e6 | −1.69013 | ||||||||
\(263\) | −560522. | −0.499693 | −0.249847 | − | 0.968285i | \(-0.580380\pi\) | ||||
−0.249847 | + | 0.968285i | \(0.580380\pi\) | |||||||
\(264\) | −1.01919e6 | −0.900010 | ||||||||
\(265\) | −168043. | −0.146996 | ||||||||
\(266\) | −865615. | −0.750103 | ||||||||
\(267\) | 467035. | 0.400932 | ||||||||
\(268\) | −1.88189e6 | −1.60051 | ||||||||
\(269\) | −2.09358e6 | −1.76404 | −0.882019 | − | 0.471214i | \(-0.843816\pi\) | ||||
−0.882019 | + | 0.471214i | \(0.843816\pi\) | |||||||
\(270\) | 245942. | 0.205316 | ||||||||
\(271\) | 457713. | 0.378591 | 0.189295 | − | 0.981920i | \(-0.439380\pi\) | ||||
0.189295 | + | 0.981920i | \(0.439380\pi\) | |||||||
\(272\) | 20922.6 | 0.0171472 | ||||||||
\(273\) | −611003. | −0.496177 | ||||||||
\(274\) | −2.04115e6 | −1.64247 | ||||||||
\(275\) | −714050. | −0.569373 | ||||||||
\(276\) | 2.52182e6 | 1.99270 | ||||||||
\(277\) | 416800. | 0.326383 | 0.163192 | − | 0.986594i | \(-0.447821\pi\) | ||||
0.163192 | + | 0.986594i | \(0.447821\pi\) | |||||||
\(278\) | −2.69859e6 | −2.09423 | ||||||||
\(279\) | −119636. | −0.0920134 | ||||||||
\(280\) | −487545. | −0.371638 | ||||||||
\(281\) | −1.02702e6 | −0.775910 | −0.387955 | − | 0.921678i | \(-0.626818\pi\) | ||||
−0.387955 | + | 0.921678i | \(0.626818\pi\) | |||||||
\(282\) | −4.57453e6 | −3.42550 | ||||||||
\(283\) | 1.68071e6 | 1.24746 | 0.623729 | − | 0.781640i | \(-0.285617\pi\) | ||||
0.623729 | + | 0.781640i | \(0.285617\pi\) | |||||||
\(284\) | 4.42640e6 | 3.25653 | ||||||||
\(285\) | 41822.9 | 0.0305001 | ||||||||
\(286\) | 328613. | 0.237558 | ||||||||
\(287\) | −59654.6 | −0.0427503 | ||||||||
\(288\) | 56760.7 | 0.0403243 | ||||||||
\(289\) | −1.41883e6 | −0.999278 | ||||||||
\(290\) | −215476. | −0.150454 | ||||||||
\(291\) | −2.75852e6 | −1.90961 | ||||||||
\(292\) | 4.33028e6 | 2.97207 | ||||||||
\(293\) | −478521. | −0.325636 | −0.162818 | − | 0.986656i | \(-0.552058\pi\) | ||||
−0.162818 | + | 0.986656i | \(0.552058\pi\) | |||||||
\(294\) | −7.42672e6 | −5.01105 | ||||||||
\(295\) | 53493.2 | 0.0357885 | ||||||||
\(296\) | −2.39616e6 | −1.58960 | ||||||||
\(297\) | −830275. | −0.546174 | ||||||||
\(298\) | −4.49583e6 | −2.93271 | ||||||||
\(299\) | −379226. | −0.245313 | ||||||||
\(300\) | −3.01452e6 | −1.93381 | ||||||||
\(301\) | 1.43953e6 | 0.915810 | ||||||||
\(302\) | −774598. | −0.488719 | ||||||||
\(303\) | −1.09061e6 | −0.682440 | ||||||||
\(304\) | 232817. | 0.144488 | ||||||||
\(305\) | 217160. | 0.133669 | ||||||||
\(306\) | −7520.70 | −0.00459150 | ||||||||
\(307\) | 343199. | 0.207826 | 0.103913 | − | 0.994586i | \(-0.466864\pi\) | ||||
0.103913 | + | 0.994586i | \(0.466864\pi\) | |||||||
\(308\) | 3.52898e6 | 2.11969 | ||||||||
\(309\) | −3.10860e6 | −1.85212 | ||||||||
\(310\) | 336210. | 0.198704 | ||||||||
\(311\) | 1.55766e6 | 0.913213 | 0.456607 | − | 0.889669i | \(-0.349065\pi\) | ||||
0.456607 | + | 0.889669i | \(0.349065\pi\) | |||||||
\(312\) | 647039. | 0.376308 | ||||||||
\(313\) | −1.29291e6 | −0.745945 | −0.372973 | − | 0.927842i | \(-0.621662\pi\) | ||||
−0.372973 | + | 0.927842i | \(0.621662\pi\) | |||||||
\(314\) | 1.77088e6 | 1.01360 | ||||||||
\(315\) | 44510.3 | 0.0252746 | ||||||||
\(316\) | −2.50858e6 | −1.41322 | ||||||||
\(317\) | 592011. | 0.330888 | 0.165444 | − | 0.986219i | \(-0.447094\pi\) | ||||
0.165444 | + | 0.986219i | \(0.447094\pi\) | |||||||
\(318\) | 3.67293e6 | 2.03678 | ||||||||
\(319\) | 727428. | 0.400233 | ||||||||
\(320\) | −309540. | −0.168982 | ||||||||
\(321\) | 1.08652e6 | 0.588538 | ||||||||
\(322\) | −6.24562e6 | −3.35688 | ||||||||
\(323\) | 11411.9 | 0.00608630 | ||||||||
\(324\) | −3.86205e6 | −2.04388 | ||||||||
\(325\) | 453317. | 0.238064 | ||||||||
\(326\) | −4.68762e6 | −2.44292 | ||||||||
\(327\) | −1.32533e6 | −0.685417 | ||||||||
\(328\) | 63172.9 | 0.0324225 | ||||||||
\(329\) | 7.38745e6 | 3.76275 | ||||||||
\(330\) | −261488. | −0.132180 | ||||||||
\(331\) | 1.56073e6 | 0.782991 | 0.391496 | − | 0.920180i | \(-0.371958\pi\) | ||||
0.391496 | + | 0.920180i | \(0.371958\pi\) | |||||||
\(332\) | −1.62975e6 | −0.811476 | ||||||||
\(333\) | 218757. | 0.108106 | ||||||||
\(334\) | −2.75616e6 | −1.35188 | ||||||||
\(335\) | −225188. | −0.109631 | ||||||||
\(336\) | 2.70651e6 | 1.30786 | ||||||||
\(337\) | −94315.9 | −0.0452387 | −0.0226193 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226193 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(338\) | 3.35211e6 | 1.59598 | ||||||||
\(339\) | 814977. | 0.385164 | ||||||||
\(340\) | 13781.4 | 0.00646542 | ||||||||
\(341\) | −1.13501e6 | −0.528585 | ||||||||
\(342\) | −83686.9 | −0.0386894 | ||||||||
\(343\) | 7.73638e6 | 3.55061 | ||||||||
\(344\) | −1.52443e6 | −0.694565 | ||||||||
\(345\) | 301762. | 0.136495 | ||||||||
\(346\) | 2.05388e6 | 0.922326 | ||||||||
\(347\) | −3.82991e6 | −1.70752 | −0.853758 | − | 0.520671i | \(-0.825682\pi\) | ||||
−0.853758 | + | 0.520671i | \(0.825682\pi\) | |||||||
\(348\) | 3.07100e6 | 1.35935 | ||||||||
\(349\) | 3.56667e6 | 1.56747 | 0.783735 | − | 0.621095i | \(-0.213312\pi\) | ||||
0.783735 | + | 0.621095i | \(0.213312\pi\) | |||||||
\(350\) | 7.46585e6 | 3.25768 | ||||||||
\(351\) | 527103. | 0.228364 | ||||||||
\(352\) | 538502. | 0.231649 | ||||||||
\(353\) | 1.80004e6 | 0.768855 | 0.384428 | − | 0.923155i | \(-0.374399\pi\) | ||||
0.384428 | + | 0.923155i | \(0.374399\pi\) | |||||||
\(354\) | −1.16920e6 | −0.495887 | ||||||||
\(355\) | 529665. | 0.223064 | ||||||||
\(356\) | 1.71249e6 | 0.716149 | ||||||||
\(357\) | 132665. | 0.0550915 | ||||||||
\(358\) | 5.13424e6 | 2.11723 | ||||||||
\(359\) | 3.58201e6 | 1.46687 | 0.733434 | − | 0.679761i | \(-0.237916\pi\) | ||||
0.733434 | + | 0.679761i | \(0.237916\pi\) | |||||||
\(360\) | −47135.5 | −0.0191687 | ||||||||
\(361\) | −2.34911e6 | −0.948715 | ||||||||
\(362\) | −2.82768e6 | −1.13412 | ||||||||
\(363\) | −1.75124e6 | −0.697557 | ||||||||
\(364\) | −2.24038e6 | −0.886276 | ||||||||
\(365\) | 518163. | 0.203579 | ||||||||
\(366\) | −4.74650e6 | −1.85213 | ||||||||
\(367\) | −2.16977e6 | −0.840909 | −0.420454 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420454 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(368\) | 1.67983e6 | 0.646616 | ||||||||
\(369\) | −5767.35 | −0.00220501 | ||||||||
\(370\) | −614767. | −0.233457 | ||||||||
\(371\) | −5.93145e6 | −2.23731 | ||||||||
\(372\) | −4.79170e6 | −1.79528 | ||||||||
\(373\) | −4.38410e6 | −1.63158 | −0.815790 | − | 0.578348i | \(-0.803697\pi\) | ||||
−0.815790 | + | 0.578348i | \(0.803697\pi\) | |||||||
\(374\) | −71350.5 | −0.0263766 | ||||||||
\(375\) | −727481. | −0.267143 | ||||||||
\(376\) | −7.82315e6 | −2.85373 | ||||||||
\(377\) | −461810. | −0.167344 | ||||||||
\(378\) | 8.68106e6 | 3.12495 | ||||||||
\(379\) | 2.70002e6 | 0.965536 | 0.482768 | − | 0.875748i | \(-0.339631\pi\) | ||||
0.482768 | + | 0.875748i | \(0.339631\pi\) | |||||||
\(380\) | 153353. | 0.0544797 | ||||||||
\(381\) | −3.19699e6 | −1.12831 | ||||||||
\(382\) | −2.46368e6 | −0.863824 | ||||||||
\(383\) | 1.88809e6 | 0.657696 | 0.328848 | − | 0.944383i | \(-0.393340\pi\) | ||||
0.328848 | + | 0.944383i | \(0.393340\pi\) | |||||||
\(384\) | 5.55254e6 | 1.92160 | ||||||||
\(385\) | 422279. | 0.145194 | ||||||||
\(386\) | −2.54351e6 | −0.868891 | ||||||||
\(387\) | 139173. | 0.0472364 | ||||||||
\(388\) | −1.01148e7 | −3.41096 | ||||||||
\(389\) | 3.15103e6 | 1.05579 | 0.527896 | − | 0.849309i | \(-0.322981\pi\) | ||||
0.527896 | + | 0.849309i | \(0.322981\pi\) | |||||||
\(390\) | 166006. | 0.0552667 | ||||||||
\(391\) | 82340.0 | 0.0272376 | ||||||||
\(392\) | −1.27008e7 | −4.17462 | ||||||||
\(393\) | 3.20261e6 | 1.04598 | ||||||||
\(394\) | 1.14290e6 | 0.370909 | ||||||||
\(395\) | −300178. | −0.0968024 | ||||||||
\(396\) | 341179. | 0.109331 | ||||||||
\(397\) | −1.21894e6 | −0.388157 | −0.194079 | − | 0.980986i | \(-0.562172\pi\) | ||||
−0.194079 | + | 0.980986i | \(0.562172\pi\) | |||||||
\(398\) | −3.32561e6 | −1.05236 | ||||||||
\(399\) | 1.47623e6 | 0.464219 | ||||||||
\(400\) | −2.00803e6 | −0.627508 | ||||||||
\(401\) | 2.31902e6 | 0.720185 | 0.360093 | − | 0.932917i | \(-0.382745\pi\) | ||||
0.360093 | + | 0.932917i | \(0.382745\pi\) | |||||||
\(402\) | 4.92195e6 | 1.51905 | ||||||||
\(403\) | 720566. | 0.221010 | ||||||||
\(404\) | −3.99899e6 | −1.21898 | ||||||||
\(405\) | −462134. | −0.140001 | ||||||||
\(406\) | −7.60572e6 | −2.28995 | ||||||||
\(407\) | 2.07539e6 | 0.621033 | ||||||||
\(408\) | −140489. | −0.0417823 | ||||||||
\(409\) | −2.34601e6 | −0.693461 | −0.346731 | − | 0.937965i | \(-0.612708\pi\) | ||||
−0.346731 | + | 0.937965i | \(0.612708\pi\) | |||||||
\(410\) | 16207.9 | 0.00476174 | ||||||||
\(411\) | 3.48100e6 | 1.01648 | ||||||||
\(412\) | −1.13984e7 | −3.30827 | ||||||||
\(413\) | 1.88816e6 | 0.544708 | ||||||||
\(414\) | −603822. | −0.173144 | ||||||||
\(415\) | −195016. | −0.0555841 | ||||||||
\(416\) | −341869. | −0.0968561 | ||||||||
\(417\) | 4.60221e6 | 1.29606 | ||||||||
\(418\) | −793956. | −0.222257 | ||||||||
\(419\) | 404570. | 0.112579 | 0.0562897 | − | 0.998414i | \(-0.482073\pi\) | ||||
0.0562897 | + | 0.998414i | \(0.482073\pi\) | |||||||
\(420\) | 1.78274e6 | 0.493135 | ||||||||
\(421\) | −6.03339e6 | −1.65904 | −0.829518 | − | 0.558480i | \(-0.811385\pi\) | ||||
−0.829518 | + | 0.558480i | \(0.811385\pi\) | |||||||
\(422\) | −1.04269e7 | −2.85020 | ||||||||
\(423\) | 714213. | 0.194078 | ||||||||
\(424\) | 6.28128e6 | 1.69681 | ||||||||
\(425\) | −98427.0 | −0.0264327 | ||||||||
\(426\) | −1.15769e7 | −3.09079 | ||||||||
\(427\) | 7.66516e6 | 2.03447 | ||||||||
\(428\) | 3.98397e6 | 1.05125 | ||||||||
\(429\) | −560422. | −0.147018 | ||||||||
\(430\) | −391114. | −0.102008 | ||||||||
\(431\) | 4.40463e6 | 1.14213 | 0.571066 | − | 0.820904i | \(-0.306530\pi\) | ||||
0.571066 | + | 0.820904i | \(0.306530\pi\) | |||||||
\(432\) | −2.33487e6 | −0.601940 | ||||||||
\(433\) | −5.79371e6 | −1.48504 | −0.742518 | − | 0.669826i | \(-0.766369\pi\) | ||||
−0.742518 | + | 0.669826i | \(0.766369\pi\) | |||||||
\(434\) | 1.18673e7 | 3.02431 | ||||||||
\(435\) | 367476. | 0.0931122 | ||||||||
\(436\) | −4.85964e6 | −1.22430 | ||||||||
\(437\) | 916242. | 0.229513 | ||||||||
\(438\) | −1.13255e7 | −2.82081 | ||||||||
\(439\) | −5.74057e6 | −1.42165 | −0.710827 | − | 0.703367i | \(-0.751679\pi\) | ||||
−0.710827 | + | 0.703367i | \(0.751679\pi\) | |||||||
\(440\) | −447185. | −0.110117 | ||||||||
\(441\) | 1.15952e6 | 0.283911 | ||||||||
\(442\) | 45297.1 | 0.0110285 | ||||||||
\(443\) | 5.56239e6 | 1.34664 | 0.673321 | − | 0.739350i | \(-0.264867\pi\) | ||||
0.673321 | + | 0.739350i | \(0.264867\pi\) | |||||||
\(444\) | 8.76173e6 | 2.10927 | ||||||||
\(445\) | 204917. | 0.0490545 | ||||||||
\(446\) | −1.81719e6 | −0.432577 | ||||||||
\(447\) | 7.66725e6 | 1.81498 | ||||||||
\(448\) | −1.09259e7 | −2.57195 | ||||||||
\(449\) | 999227. | 0.233910 | 0.116955 | − | 0.993137i | \(-0.462687\pi\) | ||||
0.116955 | + | 0.993137i | \(0.462687\pi\) | |||||||
\(450\) | 721792. | 0.168028 | ||||||||
\(451\) | −54716.2 | −0.0126670 | ||||||||
\(452\) | 2.98831e6 | 0.687985 | ||||||||
\(453\) | 1.32101e6 | 0.302455 | ||||||||
\(454\) | 1.13267e6 | 0.257906 | ||||||||
\(455\) | −268085. | −0.0607078 | ||||||||
\(456\) | −1.56330e6 | −0.352071 | ||||||||
\(457\) | 3.18082e6 | 0.712441 | 0.356220 | − | 0.934402i | \(-0.384065\pi\) | ||||
0.356220 | + | 0.934402i | \(0.384065\pi\) | |||||||
\(458\) | 1.04509e7 | 2.32804 | ||||||||
\(459\) | −114448. | −0.0253557 | ||||||||
\(460\) | 1.10648e6 | 0.243809 | ||||||||
\(461\) | 2.73926e6 | 0.600317 | 0.300159 | − | 0.953889i | \(-0.402960\pi\) | ||||
0.300159 | + | 0.953889i | \(0.402960\pi\) | |||||||
\(462\) | −9.22980e6 | −2.01181 | ||||||||
\(463\) | 1.54179e6 | 0.334252 | 0.167126 | − | 0.985936i | \(-0.446551\pi\) | ||||
0.167126 | + | 0.985936i | \(0.446551\pi\) | |||||||
\(464\) | 2.04565e6 | 0.441098 | ||||||||
\(465\) | −573377. | −0.122973 | ||||||||
\(466\) | 116920. | 0.0249415 | ||||||||
\(467\) | 6.14108e6 | 1.30302 | 0.651512 | − | 0.758638i | \(-0.274135\pi\) | ||||
0.651512 | + | 0.758638i | \(0.274135\pi\) | |||||||
\(468\) | −216598. | −0.0457131 | ||||||||
\(469\) | −7.94850e6 | −1.66860 | ||||||||
\(470\) | −2.00713e6 | −0.419114 | ||||||||
\(471\) | −3.02008e6 | −0.627288 | ||||||||
\(472\) | −1.99952e6 | −0.413115 | ||||||||
\(473\) | 1.32036e6 | 0.271357 | ||||||||
\(474\) | 6.56102e6 | 1.34130 | ||||||||
\(475\) | −1.09525e6 | −0.222730 | ||||||||
\(476\) | 486446. | 0.0984051 | ||||||||
\(477\) | −573448. | −0.115398 | ||||||||
\(478\) | −2.39611e6 | −0.479663 | ||||||||
\(479\) | 1.31361e6 | 0.261594 | 0.130797 | − | 0.991409i | \(-0.458246\pi\) | ||||
0.130797 | + | 0.991409i | \(0.458246\pi\) | |||||||
\(480\) | 272036. | 0.0538919 | ||||||||
\(481\) | −1.31757e6 | −0.259664 | ||||||||
\(482\) | −1.35069e7 | −2.64812 | ||||||||
\(483\) | 1.06514e7 | 2.07748 | ||||||||
\(484\) | −6.42134e6 | −1.24598 | ||||||||
\(485\) | −1.21034e6 | −0.233643 | ||||||||
\(486\) | 1.77261e6 | 0.340426 | ||||||||
\(487\) | −6.71405e6 | −1.28281 | −0.641405 | − | 0.767203i | \(-0.721648\pi\) | ||||
−0.641405 | + | 0.767203i | \(0.721648\pi\) | |||||||
\(488\) | −8.11724e6 | −1.54298 | ||||||||
\(489\) | 7.99433e6 | 1.51186 | ||||||||
\(490\) | −3.25857e6 | −0.613107 | ||||||||
\(491\) | −5.21717e6 | −0.976632 | −0.488316 | − | 0.872667i | \(-0.662389\pi\) | ||||
−0.488316 | + | 0.872667i | \(0.662389\pi\) | |||||||
\(492\) | −230996. | −0.0430222 | ||||||||
\(493\) | 100271. | 0.0185805 | ||||||||
\(494\) | 504046. | 0.0929293 | ||||||||
\(495\) | 40825.6 | 0.00748893 | ||||||||
\(496\) | −3.19184e6 | −0.582555 | ||||||||
\(497\) | 1.86957e7 | 3.39509 | ||||||||
\(498\) | 4.26249e6 | 0.770177 | ||||||||
\(499\) | 9.90693e6 | 1.78110 | 0.890549 | − | 0.454887i | \(-0.150320\pi\) | ||||
0.890549 | + | 0.454887i | \(0.150320\pi\) | |||||||
\(500\) | −2.66748e6 | −0.477173 | ||||||||
\(501\) | 4.70040e6 | 0.836643 | ||||||||
\(502\) | 5.10987e6 | 0.905005 | ||||||||
\(503\) | −9.57206e6 | −1.68689 | −0.843443 | − | 0.537219i | \(-0.819475\pi\) | ||||
−0.843443 | + | 0.537219i | \(0.819475\pi\) | |||||||
\(504\) | −1.66375e6 | −0.291751 | ||||||||
\(505\) | −478521. | −0.0834974 | ||||||||
\(506\) | −5.72859e6 | −0.994652 | ||||||||
\(507\) | −5.71674e6 | −0.987707 | ||||||||
\(508\) | −1.17225e7 | −2.01540 | ||||||||
\(509\) | −6.64078e6 | −1.13612 | −0.568060 | − | 0.822987i | \(-0.692306\pi\) | ||||
−0.568060 | + | 0.822987i | \(0.692306\pi\) | |||||||
\(510\) | −36044.3 | −0.00613637 | ||||||||
\(511\) | 1.82897e7 | 3.09852 | ||||||||
\(512\) | 7.12219e6 | 1.20071 | ||||||||
\(513\) | −1.27352e6 | −0.213655 | ||||||||
\(514\) | 87196.7 | 0.0145577 | ||||||||
\(515\) | −1.36394e6 | −0.226608 | ||||||||
\(516\) | 5.57420e6 | 0.921634 | ||||||||
\(517\) | 6.77589e6 | 1.11491 | ||||||||
\(518\) | −2.16996e7 | −3.55326 | ||||||||
\(519\) | −3.50271e6 | −0.570803 | ||||||||
\(520\) | 283897. | 0.0460417 | ||||||||
\(521\) | 512688. | 0.0827483 | 0.0413741 | − | 0.999144i | \(-0.486826\pi\) | ||||
0.0413741 | + | 0.999144i | \(0.486826\pi\) | |||||||
\(522\) | −735314. | −0.118113 | ||||||||
\(523\) | −2.33631e6 | −0.373487 | −0.186743 | − | 0.982409i | \(-0.559793\pi\) | ||||
−0.186743 | + | 0.982409i | \(0.559793\pi\) | |||||||
\(524\) | 1.17431e7 | 1.86834 | ||||||||
\(525\) | −1.27324e7 | −2.01609 | ||||||||
\(526\) | 5.37546e6 | 0.847132 | ||||||||
\(527\) | −156454. | −0.0245392 | ||||||||
\(528\) | 2.48246e6 | 0.387523 | ||||||||
\(529\) | 174563. | 0.0271215 | ||||||||
\(530\) | 1.61155e6 | 0.249203 | ||||||||
\(531\) | 182546. | 0.0280954 | ||||||||
\(532\) | 5.41295e6 | 0.829192 | ||||||||
\(533\) | 34736.7 | 0.00529628 | ||||||||
\(534\) | −4.47890e6 | −0.679702 | ||||||||
\(535\) | 476724. | 0.0720082 | ||||||||
\(536\) | 8.41730e6 | 1.26550 | ||||||||
\(537\) | −8.75600e6 | −1.31030 | ||||||||
\(538\) | 2.00776e7 | 2.99058 | ||||||||
\(539\) | 1.10006e7 | 1.63097 | ||||||||
\(540\) | −1.53795e6 | −0.226964 | ||||||||
\(541\) | −7.19645e6 | −1.05712 | −0.528561 | − | 0.848895i | \(-0.677268\pi\) | ||||
−0.528561 | + | 0.848895i | \(0.677268\pi\) | |||||||
\(542\) | −4.38951e6 | −0.641826 | ||||||||
\(543\) | 4.82236e6 | 0.701875 | ||||||||
\(544\) | 74228.8 | 0.0107541 | ||||||||
\(545\) | −581506. | −0.0838616 | ||||||||
\(546\) | 5.85956e6 | 0.841170 | ||||||||
\(547\) | 299209. | 0.0427569 | ||||||||
\(548\) | 1.27639e7 | 1.81565 | ||||||||
\(549\) | 741061. | 0.104936 | ||||||||
\(550\) | 6.84780e6 | 0.965260 | ||||||||
\(551\) | 1.11577e6 | 0.156565 | ||||||||
\(552\) | −1.12796e7 | −1.57560 | ||||||||
\(553\) | −1.05955e7 | −1.47335 | ||||||||
\(554\) | −3.99714e6 | −0.553319 | ||||||||
\(555\) | 1.04843e6 | 0.144480 | ||||||||
\(556\) | 1.68751e7 | 2.31504 | ||||||||
\(557\) | 2.09970e6 | 0.286760 | 0.143380 | − | 0.989668i | \(-0.454203\pi\) | ||||
0.143380 | + | 0.989668i | \(0.454203\pi\) | |||||||
\(558\) | 1.14732e6 | 0.155991 | ||||||||
\(559\) | −838237. | −0.113459 | ||||||||
\(560\) | 1.18752e6 | 0.160019 | ||||||||
\(561\) | 121682. | 0.0163238 | ||||||||
\(562\) | 9.84917e6 | 1.31540 | ||||||||
\(563\) | −7.60608e6 | −1.01132 | −0.505662 | − | 0.862732i | \(-0.668752\pi\) | ||||
−0.505662 | + | 0.862732i | \(0.668752\pi\) | |||||||
\(564\) | 2.86059e7 | 3.78668 | ||||||||
\(565\) | 357582. | 0.0471253 | ||||||||
\(566\) | −1.61181e7 | −2.11482 | ||||||||
\(567\) | −1.63120e7 | −2.13084 | ||||||||
\(568\) | −1.97984e7 | −2.57489 | ||||||||
\(569\) | 7.62657e6 | 0.987526 | 0.493763 | − | 0.869597i | \(-0.335621\pi\) | ||||
0.493763 | + | 0.869597i | \(0.335621\pi\) | |||||||
\(570\) | −401085. | −0.0517070 | ||||||||
\(571\) | 4.09627e6 | 0.525773 | 0.262887 | − | 0.964827i | \(-0.415325\pi\) | ||||
0.262887 | + | 0.964827i | \(0.415325\pi\) | |||||||
\(572\) | −2.05492e6 | −0.262606 | ||||||||
\(573\) | 4.20159e6 | 0.534598 | ||||||||
\(574\) | 572092. | 0.0724747 | ||||||||
\(575\) | −7.90250e6 | −0.996770 | ||||||||
\(576\) | −1.05631e6 | −0.132658 | ||||||||
\(577\) | −7.49194e6 | −0.936817 | −0.468409 | − | 0.883512i | \(-0.655172\pi\) | ||||
−0.468409 | + | 0.883512i | \(0.655172\pi\) | |||||||
\(578\) | 1.36067e7 | 1.69408 | ||||||||
\(579\) | 4.33774e6 | 0.537733 | ||||||||
\(580\) | 1.34744e6 | 0.166318 | ||||||||
\(581\) | −6.88354e6 | −0.846002 | ||||||||
\(582\) | 2.64545e7 | 3.23736 | ||||||||
\(583\) | −5.44043e6 | −0.662921 | ||||||||
\(584\) | −1.93684e7 | −2.34997 | ||||||||
\(585\) | −25918.3 | −0.00313124 | ||||||||
\(586\) | 4.58906e6 | 0.552051 | ||||||||
\(587\) | 1.33786e6 | 0.160257 | 0.0801283 | − | 0.996785i | \(-0.474467\pi\) | ||||
0.0801283 | + | 0.996785i | \(0.474467\pi\) | |||||||
\(588\) | 4.64415e7 | 5.53940 | ||||||||
\(589\) | −1.74095e6 | −0.206775 | ||||||||
\(590\) | −513004. | −0.0606723 | ||||||||
\(591\) | −1.94911e6 | −0.229545 | ||||||||
\(592\) | 5.83635e6 | 0.684442 | ||||||||
\(593\) | −8.52167e6 | −0.995149 | −0.497574 | − | 0.867421i | \(-0.665776\pi\) | ||||
−0.497574 | + | 0.867421i | \(0.665776\pi\) | |||||||
\(594\) | 7.96241e6 | 0.925930 | ||||||||
\(595\) | 58208.3 | 0.00674051 | ||||||||
\(596\) | 2.81138e7 | 3.24193 | ||||||||
\(597\) | 5.67155e6 | 0.651277 | ||||||||
\(598\) | 3.63681e6 | 0.415880 | ||||||||
\(599\) | 5.82269e6 | 0.663066 | 0.331533 | − | 0.943444i | \(-0.392434\pi\) | ||||
0.331533 | + | 0.943444i | \(0.392434\pi\) | |||||||
\(600\) | 1.34833e7 | 1.52904 | ||||||||
\(601\) | 1.57854e7 | 1.78266 | 0.891332 | − | 0.453351i | \(-0.149772\pi\) | ||||
0.891332 | + | 0.453351i | \(0.149772\pi\) | |||||||
\(602\) | −1.38052e7 | −1.55258 | ||||||||
\(603\) | −768455. | −0.0860647 | ||||||||
\(604\) | 4.84380e6 | 0.540249 | ||||||||
\(605\) | −768380. | −0.0853469 | ||||||||
\(606\) | 1.04591e7 | 1.15694 | ||||||||
\(607\) | −5.66946e6 | −0.624554 | −0.312277 | − | 0.949991i | \(-0.601092\pi\) | ||||
−0.312277 | + | 0.949991i | \(0.601092\pi\) | |||||||
\(608\) | 825984. | 0.0906177 | ||||||||
\(609\) | 1.29709e7 | 1.41719 | ||||||||
\(610\) | −2.08259e6 | −0.226610 | ||||||||
\(611\) | −4.30170e6 | −0.466162 | ||||||||
\(612\) | 47029.2 | 0.00507562 | ||||||||
\(613\) | −1.48861e7 | −1.60004 | −0.800020 | − | 0.599974i | \(-0.795178\pi\) | ||||
−0.800020 | + | 0.599974i | \(0.795178\pi\) | |||||||
\(614\) | −3.29130e6 | −0.352328 | ||||||||
\(615\) | −27641.1 | −0.00294691 | ||||||||
\(616\) | −1.57844e7 | −1.67601 | ||||||||
\(617\) | −4.64218e6 | −0.490918 | −0.245459 | − | 0.969407i | \(-0.578939\pi\) | ||||
−0.245459 | + | 0.969407i | \(0.578939\pi\) | |||||||
\(618\) | 2.98117e7 | 3.13990 | ||||||||
\(619\) | 1.12810e7 | 1.18337 | 0.591687 | − | 0.806168i | \(-0.298462\pi\) | ||||
0.591687 | + | 0.806168i | \(0.298462\pi\) | |||||||
\(620\) | −2.10242e6 | −0.219655 | ||||||||
\(621\) | −9.18878e6 | −0.956156 | ||||||||
\(622\) | −1.49381e7 | −1.54817 | ||||||||
\(623\) | 7.23302e6 | 0.746620 | ||||||||
\(624\) | −1.57600e6 | −0.162029 | ||||||||
\(625\) | 9.28551e6 | 0.950836 | ||||||||
\(626\) | 1.23991e7 | 1.26460 | ||||||||
\(627\) | 1.35402e6 | 0.137549 | ||||||||
\(628\) | −1.10738e7 | −1.12047 | ||||||||
\(629\) | 286079. | 0.0288310 | ||||||||
\(630\) | −426858. | −0.0428481 | ||||||||
\(631\) | 8.32225e6 | 0.832084 | 0.416042 | − | 0.909345i | \(-0.363417\pi\) | ||||
0.416042 | + | 0.909345i | \(0.363417\pi\) | |||||||
\(632\) | 1.12204e7 | 1.11741 | ||||||||
\(633\) | 1.77822e7 | 1.76391 | ||||||||
\(634\) | −5.67743e6 | −0.560956 | ||||||||
\(635\) | −1.40272e6 | −0.138050 | ||||||||
\(636\) | −2.29680e7 | −2.25154 | ||||||||
\(637\) | −6.98377e6 | −0.681933 | ||||||||
\(638\) | −6.97609e6 | −0.678517 | ||||||||
\(639\) | 1.80749e6 | 0.175115 | ||||||||
\(640\) | 2.43625e6 | 0.235110 | ||||||||
\(641\) | −8.11956e6 | −0.780526 | −0.390263 | − | 0.920703i | \(-0.627616\pi\) | ||||
−0.390263 | + | 0.920703i | \(0.627616\pi\) | |||||||
\(642\) | −1.04198e7 | −0.997750 | ||||||||
\(643\) | −1.17963e7 | −1.12517 | −0.562587 | − | 0.826738i | \(-0.690194\pi\) | ||||
−0.562587 | + | 0.826738i | \(0.690194\pi\) | |||||||
\(644\) | 3.90558e7 | 3.71083 | ||||||||
\(645\) | 667011. | 0.0631297 | ||||||||
\(646\) | −109442. | −0.0103181 | ||||||||
\(647\) | 1.92066e7 | 1.80381 | 0.901903 | − | 0.431938i | \(-0.142170\pi\) | ||||
0.901903 | + | 0.431938i | \(0.142170\pi\) | |||||||
\(648\) | 1.72741e7 | 1.61606 | ||||||||
\(649\) | 1.73185e6 | 0.161398 | ||||||||
\(650\) | −4.34735e6 | −0.403590 | ||||||||
\(651\) | −2.02386e7 | −1.87167 | ||||||||
\(652\) | 2.93131e7 | 2.70049 | ||||||||
\(653\) | −1.46736e7 | −1.34664 | −0.673321 | − | 0.739350i | \(-0.735133\pi\) | ||||
−0.673321 | + | 0.739350i | \(0.735133\pi\) | |||||||
\(654\) | 1.27100e7 | 1.16199 | ||||||||
\(655\) | 1.40519e6 | 0.127977 | ||||||||
\(656\) | −153871. | −0.0139604 | ||||||||
\(657\) | 1.76823e6 | 0.159818 | ||||||||
\(658\) | −7.08463e7 | −6.37900 | ||||||||
\(659\) | −1.80634e7 | −1.62027 | −0.810133 | − | 0.586247i | \(-0.800605\pi\) | ||||
−0.810133 | + | 0.586247i | \(0.800605\pi\) | |||||||
\(660\) | 1.63516e6 | 0.146117 | ||||||||
\(661\) | −1.94465e6 | −0.173116 | −0.0865580 | − | 0.996247i | \(-0.527587\pi\) | ||||
−0.0865580 | + | 0.996247i | \(0.527587\pi\) | |||||||
\(662\) | −1.49675e7 | −1.32741 | ||||||||
\(663\) | −77250.3 | −0.00682522 | ||||||||
\(664\) | 7.28952e6 | 0.641621 | ||||||||
\(665\) | 647716. | 0.0567977 | ||||||||
\(666\) | −2.09790e6 | −0.183273 | ||||||||
\(667\) | 8.05055e6 | 0.700666 | ||||||||
\(668\) | 1.72351e7 | 1.49442 | ||||||||
\(669\) | 3.09907e6 | 0.267711 | ||||||||
\(670\) | 2.15957e6 | 0.185857 | ||||||||
\(671\) | 7.03061e6 | 0.602819 | ||||||||
\(672\) | 9.60212e6 | 0.820246 | ||||||||
\(673\) | 9.47231e6 | 0.806154 | 0.403077 | − | 0.915166i | \(-0.367941\pi\) | ||||
0.403077 | + | 0.915166i | \(0.367941\pi\) | |||||||
\(674\) | 904497. | 0.0766933 | ||||||||
\(675\) | 1.09840e7 | 0.927901 | ||||||||
\(676\) | −2.09618e7 | −1.76425 | ||||||||
\(677\) | 4.21500e6 | 0.353449 | 0.176724 | − | 0.984260i | \(-0.443450\pi\) | ||||
0.176724 | + | 0.984260i | \(0.443450\pi\) | |||||||
\(678\) | −7.81570e6 | −0.652971 | ||||||||
\(679\) | −4.27216e7 | −3.55609 | ||||||||
\(680\) | −61641.4 | −0.00511211 | ||||||||
\(681\) | −1.93166e6 | −0.159611 | ||||||||
\(682\) | 1.08849e7 | 0.896112 | ||||||||
\(683\) | 1.20346e7 | 0.987147 | 0.493573 | − | 0.869704i | \(-0.335690\pi\) | ||||
0.493573 | + | 0.869704i | \(0.335690\pi\) | |||||||
\(684\) | 523320. | 0.0427688 | ||||||||
\(685\) | 1.52733e6 | 0.124368 | ||||||||
\(686\) | −7.41926e7 | −6.01936 | ||||||||
\(687\) | −1.78231e7 | −1.44076 | ||||||||
\(688\) | 3.71308e6 | 0.299063 | ||||||||
\(689\) | 3.45387e6 | 0.277178 | ||||||||
\(690\) | −2.89393e6 | −0.231401 | ||||||||
\(691\) | 1.48943e7 | 1.18665 | 0.593327 | − | 0.804962i | \(-0.297814\pi\) | ||||
0.593327 | + | 0.804962i | \(0.297814\pi\) | |||||||
\(692\) | −1.28435e7 | −1.01957 | ||||||||
\(693\) | 1.44103e6 | 0.113983 | ||||||||
\(694\) | 3.67291e7 | 2.89476 | ||||||||
\(695\) | 2.01928e6 | 0.158575 | ||||||||
\(696\) | −1.37359e7 | −1.07482 | ||||||||
\(697\) | −7542.25 | −0.000588057 0 | ||||||||
\(698\) | −3.42047e7 | −2.65734 | ||||||||
\(699\) | −199396. | −0.0154356 | ||||||||
\(700\) | −4.66862e7 | −3.60117 | ||||||||
\(701\) | −2.58343e6 | −0.198564 | −0.0992822 | − | 0.995059i | \(-0.531655\pi\) | ||||
−0.0992822 | + | 0.995059i | \(0.531655\pi\) | |||||||
\(702\) | −5.05496e6 | −0.387146 | ||||||||
\(703\) | 3.18336e6 | 0.242939 | ||||||||
\(704\) | −1.00214e7 | −0.762074 | ||||||||
\(705\) | 3.42300e6 | 0.259378 | ||||||||
\(706\) | −1.72625e7 | −1.30344 | ||||||||
\(707\) | −1.68905e7 | −1.27085 | ||||||||
\(708\) | 7.31139e6 | 0.548172 | ||||||||
\(709\) | −8.76096e6 | −0.654540 | −0.327270 | − | 0.944931i | \(-0.606129\pi\) | ||||
−0.327270 | + | 0.944931i | \(0.606129\pi\) | |||||||
\(710\) | −5.07953e6 | −0.378162 | ||||||||
\(711\) | −1.02436e6 | −0.0759938 | ||||||||
\(712\) | −7.65961e6 | −0.566248 | ||||||||
\(713\) | −1.25614e7 | −0.925364 | ||||||||
\(714\) | −1.27227e6 | −0.0933968 | ||||||||
\(715\) | −245892. | −0.0179879 | ||||||||
\(716\) | −3.21059e7 | −2.34047 | ||||||||
\(717\) | 4.08636e6 | 0.296851 | ||||||||
\(718\) | −3.43518e7 | −2.48679 | ||||||||
\(719\) | −2.55779e7 | −1.84520 | −0.922599 | − | 0.385761i | \(-0.873939\pi\) | ||||
−0.922599 | + | 0.385761i | \(0.873939\pi\) | |||||||
\(720\) | 114808. | 0.00825357 | ||||||||
\(721\) | −4.81432e7 | −3.44903 | ||||||||
\(722\) | 2.25282e7 | 1.60836 | ||||||||
\(723\) | 2.30348e7 | 1.63885 | ||||||||
\(724\) | 1.76823e7 | 1.25370 | ||||||||
\(725\) | −9.62341e6 | −0.679961 | ||||||||
\(726\) | 1.67946e7 | 1.18257 | ||||||||
\(727\) | 6.23788e6 | 0.437725 | 0.218862 | − | 0.975756i | \(-0.429765\pi\) | ||||
0.218862 | + | 0.975756i | \(0.429765\pi\) | |||||||
\(728\) | 1.00208e7 | 0.700765 | ||||||||
\(729\) | 1.26262e7 | 0.879938 | ||||||||
\(730\) | −4.96922e6 | −0.345129 | ||||||||
\(731\) | 182003. | 0.0125975 | ||||||||
\(732\) | 2.96813e7 | 2.04741 | ||||||||
\(733\) | 1.16371e7 | 0.799992 | 0.399996 | − | 0.916517i | \(-0.369012\pi\) | ||||
0.399996 | + | 0.916517i | \(0.369012\pi\) | |||||||
\(734\) | 2.08083e7 | 1.42559 | ||||||||
\(735\) | 5.55721e6 | 0.379436 | ||||||||
\(736\) | 5.95968e6 | 0.405535 | ||||||||
\(737\) | −7.29050e6 | −0.494411 | ||||||||
\(738\) | 55309.4 | 0.00373816 | ||||||||
\(739\) | 3.60083e6 | 0.242545 | 0.121272 | − | 0.992619i | \(-0.461303\pi\) | ||||
0.121272 | + | 0.992619i | \(0.461303\pi\) | |||||||
\(740\) | 3.84432e6 | 0.258072 | ||||||||
\(741\) | −859607. | −0.0575114 | ||||||||
\(742\) | 5.68831e7 | 3.79292 | ||||||||
\(743\) | 2.66981e6 | 0.177422 | 0.0887111 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887111 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(744\) | 2.14323e7 | 1.41950 | ||||||||
\(745\) | 3.36411e6 | 0.222064 | ||||||||
\(746\) | 4.20439e7 | 2.76602 | ||||||||
\(747\) | −665495. | −0.0436358 | ||||||||
\(748\) | 446177. | 0.0291577 | ||||||||
\(749\) | 1.68270e7 | 1.09598 | ||||||||
\(750\) | 6.97660e6 | 0.452888 | ||||||||
\(751\) | −4.71505e6 | −0.305061 | −0.152530 | − | 0.988299i | \(-0.548742\pi\) | ||||
−0.152530 | + | 0.988299i | \(0.548742\pi\) | |||||||
\(752\) | 1.90549e7 | 1.22875 | ||||||||
\(753\) | −8.71445e6 | −0.560083 | ||||||||
\(754\) | 4.42879e6 | 0.283698 | ||||||||
\(755\) | 579611. | 0.0370057 | ||||||||
\(756\) | −5.42853e7 | −3.45444 | ||||||||
\(757\) | −931738. | −0.0590954 | −0.0295477 | − | 0.999563i | \(-0.509407\pi\) | ||||
−0.0295477 | + | 0.999563i | \(0.509407\pi\) | |||||||
\(758\) | −2.58934e7 | −1.63688 | ||||||||
\(759\) | 9.76962e6 | 0.615564 | ||||||||
\(760\) | −685917. | −0.0430762 | ||||||||
\(761\) | −6.36554e6 | −0.398450 | −0.199225 | − | 0.979954i | \(-0.563842\pi\) | ||||
−0.199225 | + | 0.979954i | \(0.563842\pi\) | |||||||
\(762\) | 3.06594e7 | 1.91283 | ||||||||
\(763\) | −2.05256e7 | −1.27639 | ||||||||
\(764\) | 1.54061e7 | 0.954904 | ||||||||
\(765\) | 5627.53 | 0.000347668 0 | ||||||||
\(766\) | −1.81069e7 | −1.11499 | ||||||||
\(767\) | −1.09947e6 | −0.0674832 | ||||||||
\(768\) | −3.06739e7 | −1.87657 | ||||||||
\(769\) | 1.83708e6 | 0.112024 | 0.0560121 | − | 0.998430i | \(-0.482161\pi\) | ||||
0.0560121 | + | 0.998430i | \(0.482161\pi\) | |||||||
\(770\) | −4.04969e6 | −0.246147 | ||||||||
\(771\) | −148706. | −0.00900936 | ||||||||
\(772\) | 1.59053e7 | 0.960505 | ||||||||
\(773\) | 2.34910e7 | 1.41401 | 0.707007 | − | 0.707207i | \(-0.250045\pi\) | ||||
0.707007 | + | 0.707207i | \(0.250045\pi\) | |||||||
\(774\) | −1.33468e6 | −0.0800801 | ||||||||
\(775\) | 1.50155e7 | 0.898019 | ||||||||
\(776\) | 4.52412e7 | 2.69700 | ||||||||
\(777\) | 3.70068e7 | 2.19902 | ||||||||
\(778\) | −3.02186e7 | −1.78989 | ||||||||
\(779\) | −83926.8 | −0.00495515 | ||||||||
\(780\) | −1.03809e6 | −0.0610939 | ||||||||
\(781\) | 1.71480e7 | 1.00597 | ||||||||
\(782\) | −789647. | −0.0461760 | ||||||||
\(783\) | −1.11898e7 | −0.652256 | ||||||||
\(784\) | 3.09355e7 | 1.79749 | ||||||||
\(785\) | −1.32510e6 | −0.0767494 | ||||||||
\(786\) | −3.07133e7 | −1.77325 | ||||||||
\(787\) | 2.63184e6 | 0.151469 | 0.0757343 | − | 0.997128i | \(-0.475870\pi\) | ||||
0.0757343 | + | 0.997128i | \(0.475870\pi\) | |||||||
\(788\) | −7.14689e6 | −0.410017 | ||||||||
\(789\) | −9.16738e6 | −0.524267 | ||||||||
\(790\) | 2.87873e6 | 0.164109 | ||||||||
\(791\) | 1.26216e7 | 0.717257 | ||||||||
\(792\) | −1.52602e6 | −0.0864465 | ||||||||
\(793\) | −4.46341e6 | −0.252048 | ||||||||
\(794\) | 1.16898e7 | 0.658044 | ||||||||
\(795\) | −2.74835e6 | −0.154225 | ||||||||
\(796\) | 2.07961e7 | 1.16332 | ||||||||
\(797\) | −7.57868e6 | −0.422618 | −0.211309 | − | 0.977419i | \(-0.567773\pi\) | ||||
−0.211309 | + | 0.977419i | \(0.567773\pi\) | |||||||
\(798\) | −1.41572e7 | −0.786991 | ||||||||
\(799\) | 934011. | 0.0517589 | ||||||||
\(800\) | −7.12404e6 | −0.393551 | ||||||||
\(801\) | 699282. | 0.0385098 | ||||||||
\(802\) | −2.22396e7 | −1.22093 | ||||||||
\(803\) | 1.67756e7 | 0.918099 | ||||||||
\(804\) | −3.07784e7 | −1.67922 | ||||||||
\(805\) | 4.67343e6 | 0.254183 | ||||||||
\(806\) | −6.91029e6 | −0.374678 | ||||||||
\(807\) | −3.42406e7 | −1.85079 | ||||||||
\(808\) | 1.78867e7 | 0.963830 | ||||||||
\(809\) | −2.29499e6 | −0.123285 | −0.0616423 | − | 0.998098i | \(-0.519634\pi\) | ||||
−0.0616423 | + | 0.998098i | \(0.519634\pi\) | |||||||
\(810\) | 4.43190e6 | 0.237344 | ||||||||
\(811\) | −1.81498e7 | −0.968993 | −0.484496 | − | 0.874793i | \(-0.660997\pi\) | ||||
−0.484496 | + | 0.874793i | \(0.660997\pi\) | |||||||
\(812\) | 4.75609e7 | 2.53139 | ||||||||
\(813\) | 7.48593e6 | 0.397209 | ||||||||
\(814\) | −1.99032e7 | −1.05284 | ||||||||
\(815\) | 3.50762e6 | 0.184977 | ||||||||
\(816\) | 342190. | 0.0179905 | ||||||||
\(817\) | 2.02525e6 | 0.106151 | ||||||||
\(818\) | 2.24985e7 | 1.17563 | ||||||||
\(819\) | −914843. | −0.0476581 | ||||||||
\(820\) | −101353. | −0.00526381 | ||||||||
\(821\) | −2.15947e7 | −1.11812 | −0.559060 | − | 0.829127i | \(-0.688838\pi\) | ||||
−0.559060 | + | 0.829127i | \(0.688838\pi\) | |||||||
\(822\) | −3.33831e7 | −1.72324 | ||||||||
\(823\) | 2.14246e7 | 1.10259 | 0.551293 | − | 0.834311i | \(-0.314135\pi\) | ||||
0.551293 | + | 0.834311i | \(0.314135\pi\) | |||||||
\(824\) | 5.09826e7 | 2.61580 | ||||||||
\(825\) | −1.16783e7 | −0.597374 | ||||||||
\(826\) | −1.81076e7 | −0.923445 | ||||||||
\(827\) | 2.04251e7 | 1.03849 | 0.519244 | − | 0.854626i | \(-0.326214\pi\) | ||||
0.519244 | + | 0.854626i | \(0.326214\pi\) | |||||||
\(828\) | 3.77588e6 | 0.191400 | ||||||||
\(829\) | 1.19639e7 | 0.604624 | 0.302312 | − | 0.953209i | \(-0.402242\pi\) | ||||
0.302312 | + | 0.953209i | \(0.402242\pi\) | |||||||
\(830\) | 1.87022e6 | 0.0942320 | ||||||||
\(831\) | 6.81679e6 | 0.342434 | ||||||||
\(832\) | 6.36212e6 | 0.318635 | ||||||||
\(833\) | 1.51636e6 | 0.0757164 | ||||||||
\(834\) | −4.41356e7 | −2.19722 | ||||||||
\(835\) | 2.06236e6 | 0.102364 | ||||||||
\(836\) | 4.96485e6 | 0.245692 | ||||||||
\(837\) | 1.74596e7 | 0.861429 | ||||||||
\(838\) | −3.87986e6 | −0.190856 | ||||||||
\(839\) | 1.76289e7 | 0.864612 | 0.432306 | − | 0.901727i | \(-0.357700\pi\) | ||||
0.432306 | + | 0.901727i | \(0.357700\pi\) | |||||||
\(840\) | −7.97384e6 | −0.389914 | ||||||||
\(841\) | −1.07074e7 | −0.522031 | ||||||||
\(842\) | 5.78607e7 | 2.81257 | ||||||||
\(843\) | −1.67969e7 | −0.814068 | ||||||||
\(844\) | 6.52028e7 | 3.15072 | ||||||||
\(845\) | −2.50829e6 | −0.120847 | ||||||||
\(846\) | −6.84936e6 | −0.329021 | ||||||||
\(847\) | −2.71217e7 | −1.29900 | ||||||||
\(848\) | −1.52994e7 | −0.730607 | ||||||||
\(849\) | 2.74881e7 | 1.30881 | ||||||||
\(850\) | 943923. | 0.0448115 | ||||||||
\(851\) | 2.29687e7 | 1.08721 | ||||||||
\(852\) | 7.23941e7 | 3.41668 | ||||||||
\(853\) | −1.36691e7 | −0.643233 | −0.321616 | − | 0.946870i | \(-0.604226\pi\) | ||||
−0.321616 | + | 0.946870i | \(0.604226\pi\) | |||||||
\(854\) | −7.35095e7 | −3.44905 | ||||||||
\(855\) | 62620.6 | 0.00292956 | ||||||||
\(856\) | −1.78195e7 | −0.831209 | ||||||||
\(857\) | 1.76341e7 | 0.820164 | 0.410082 | − | 0.912049i | \(-0.365500\pi\) | ||||
0.410082 | + | 0.912049i | \(0.365500\pi\) | |||||||
\(858\) | 5.37449e6 | 0.249241 | ||||||||
\(859\) | −1.52978e7 | −0.707367 | −0.353684 | − | 0.935365i | \(-0.615071\pi\) | ||||
−0.353684 | + | 0.935365i | \(0.615071\pi\) | |||||||
\(860\) | 2.44575e6 | 0.112763 | ||||||||
\(861\) | −975654. | −0.0448527 | ||||||||
\(862\) | −4.22407e7 | −1.93626 | ||||||||
\(863\) | −3.39009e7 | −1.54947 | −0.774736 | − | 0.632285i | \(-0.782117\pi\) | ||||
−0.774736 | + | 0.632285i | \(0.782117\pi\) | |||||||
\(864\) | −8.28361e6 | −0.377516 | ||||||||
\(865\) | −1.53686e6 | −0.0698384 | ||||||||
\(866\) | 5.55622e7 | 2.51759 | ||||||||
\(867\) | −2.32051e7 | −1.04842 | ||||||||
\(868\) | −7.42097e7 | −3.34319 | ||||||||
\(869\) | −9.71832e6 | −0.436558 | ||||||||
\(870\) | −3.52413e6 | −0.157853 | ||||||||
\(871\) | 4.62839e6 | 0.206721 | ||||||||
\(872\) | 2.17361e7 | 0.968035 | ||||||||
\(873\) | −4.13029e6 | −0.183419 | ||||||||
\(874\) | −8.78683e6 | −0.389093 | ||||||||
\(875\) | −1.12666e7 | −0.497476 | ||||||||
\(876\) | 7.08220e7 | 3.11823 | ||||||||
\(877\) | 1.05119e7 | 0.461513 | 0.230756 | − | 0.973012i | \(-0.425880\pi\) | ||||
0.230756 | + | 0.973012i | \(0.425880\pi\) | |||||||
\(878\) | 5.50525e7 | 2.41013 | ||||||||
\(879\) | −7.82624e6 | −0.341650 | ||||||||
\(880\) | 1.08921e6 | 0.0474139 | ||||||||
\(881\) | −3.89606e7 | −1.69116 | −0.845581 | − | 0.533847i | \(-0.820746\pi\) | ||||
−0.845581 | + | 0.533847i | \(0.820746\pi\) | |||||||
\(882\) | −1.11199e7 | −0.481314 | ||||||||
\(883\) | 1.11872e7 | 0.482857 | 0.241428 | − | 0.970419i | \(-0.422384\pi\) | ||||
0.241428 | + | 0.970419i | \(0.422384\pi\) | |||||||
\(884\) | −283257. | −0.0121913 | ||||||||
\(885\) | 874884. | 0.0375485 | ||||||||
\(886\) | −5.33438e7 | −2.28297 | ||||||||
\(887\) | 2.48580e7 | 1.06086 | 0.530428 | − | 0.847730i | \(-0.322031\pi\) | ||||
0.530428 | + | 0.847730i | \(0.322031\pi\) | |||||||
\(888\) | −3.91894e7 | −1.66777 | ||||||||
\(889\) | −4.95122e7 | −2.10115 | ||||||||
\(890\) | −1.96518e6 | −0.0831623 | ||||||||
\(891\) | −1.49617e7 | −0.631373 | ||||||||
\(892\) | 1.13635e7 | 0.478187 | ||||||||
\(893\) | 1.03933e7 | 0.436137 | ||||||||
\(894\) | −7.35296e7 | −3.07694 | ||||||||
\(895\) | −3.84181e6 | −0.160316 | ||||||||
\(896\) | 8.59929e7 | 3.57843 | ||||||||
\(897\) | −6.20227e6 | −0.257377 | ||||||||
\(898\) | −9.58267e6 | −0.396548 | ||||||||
\(899\) | −1.52968e7 | −0.631251 | ||||||||
\(900\) | −4.51358e6 | −0.185744 | ||||||||
\(901\) | −749926. | −0.0307756 | ||||||||
\(902\) | 524733. | 0.0214744 | ||||||||
\(903\) | 2.35437e7 | 0.960848 | ||||||||
\(904\) | −1.33661e7 | −0.543979 | ||||||||
\(905\) | 2.11587e6 | 0.0858753 | ||||||||
\(906\) | −1.26686e7 | −0.512753 | ||||||||
\(907\) | 2.60929e7 | 1.05318 | 0.526592 | − | 0.850118i | \(-0.323470\pi\) | ||||
0.526592 | + | 0.850118i | \(0.323470\pi\) | |||||||
\(908\) | −7.08290e6 | −0.285100 | ||||||||
\(909\) | −1.63296e6 | −0.0655488 | ||||||||
\(910\) | 2.57096e6 | 0.102918 | ||||||||
\(911\) | −2.70240e7 | −1.07883 | −0.539415 | − | 0.842040i | \(-0.681355\pi\) | ||||
−0.539415 | + | 0.842040i | \(0.681355\pi\) | |||||||
\(912\) | 3.80774e6 | 0.151593 | ||||||||
\(913\) | −6.31370e6 | −0.250673 | ||||||||
\(914\) | −3.05043e7 | −1.20780 | ||||||||
\(915\) | 3.55167e6 | 0.140243 | ||||||||
\(916\) | −6.53527e7 | −2.57350 | ||||||||
\(917\) | 4.95992e7 | 1.94783 | ||||||||
\(918\) | 1.09756e6 | 0.0429856 | ||||||||
\(919\) | −5.01531e7 | −1.95888 | −0.979442 | − | 0.201727i | \(-0.935345\pi\) | ||||
−0.979442 | + | 0.201727i | \(0.935345\pi\) | |||||||
\(920\) | −4.94906e6 | −0.192776 | ||||||||
\(921\) | 5.61303e6 | 0.218046 | ||||||||
\(922\) | −2.62697e7 | −1.01772 | ||||||||
\(923\) | −1.08865e7 | −0.420613 | ||||||||
\(924\) | 5.77167e7 | 2.22393 | ||||||||
\(925\) | −2.74562e7 | −1.05508 | ||||||||
\(926\) | −1.47859e7 | −0.566658 | ||||||||
\(927\) | −4.65444e6 | −0.177897 | ||||||||
\(928\) | 7.25750e6 | 0.276642 | ||||||||
\(929\) | −1.17678e7 | −0.447360 | −0.223680 | − | 0.974663i | \(-0.571807\pi\) | ||||
−0.223680 | + | 0.974663i | \(0.571807\pi\) | |||||||
\(930\) | 5.49873e6 | 0.208476 | ||||||||
\(931\) | 1.68734e7 | 0.638010 | ||||||||
\(932\) | −731134. | −0.0275713 | ||||||||
\(933\) | 2.54757e7 | 0.958123 | ||||||||
\(934\) | −5.88934e7 | −2.20902 | ||||||||
\(935\) | 53389.7 | 0.00199723 | ||||||||
\(936\) | 968799. | 0.0361447 | ||||||||
\(937\) | −4.04239e7 | −1.50414 | −0.752072 | − | 0.659081i | \(-0.770945\pi\) | ||||
−0.752072 | + | 0.659081i | \(0.770945\pi\) | |||||||
\(938\) | 7.62268e7 | 2.82879 | ||||||||
\(939\) | −2.11456e7 | −0.782630 | ||||||||
\(940\) | 1.25512e7 | 0.463304 | ||||||||
\(941\) | 8.74255e6 | 0.321858 | 0.160929 | − | 0.986966i | \(-0.448551\pi\) | ||||
0.160929 | + | 0.986966i | \(0.448551\pi\) | |||||||
\(942\) | 2.89629e7 | 1.06344 | ||||||||
\(943\) | −605552. | −0.0221754 | ||||||||
\(944\) | 4.87025e6 | 0.177878 | ||||||||
\(945\) | −6.49580e6 | −0.236621 | ||||||||
\(946\) | −1.26624e7 | −0.460032 | ||||||||
\(947\) | 1.28481e7 | 0.465546 | 0.232773 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232773 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(948\) | −4.10280e7 | −1.48272 | ||||||||
\(949\) | −1.06501e7 | −0.383872 | ||||||||
\(950\) | 1.05035e7 | 0.377596 | ||||||||
\(951\) | 9.68237e6 | 0.347161 | ||||||||
\(952\) | −2.17577e6 | −0.0778074 | ||||||||
\(953\) | −4.17412e7 | −1.48879 | −0.744393 | − | 0.667742i | \(-0.767261\pi\) | ||||
−0.744393 | + | 0.667742i | \(0.767261\pi\) | |||||||
\(954\) | 5.49941e6 | 0.195634 | ||||||||
\(955\) | 1.84350e6 | 0.0654087 | ||||||||
\(956\) | 1.49836e7 | 0.530238 | ||||||||
\(957\) | 1.18971e7 | 0.419916 | ||||||||
\(958\) | −1.25976e7 | −0.443481 | ||||||||
\(959\) | 5.39107e7 | 1.89290 | ||||||||
\(960\) | −5.06254e6 | −0.177292 | ||||||||
\(961\) | −4.76138e6 | −0.166312 | ||||||||
\(962\) | 1.26356e7 | 0.440209 | ||||||||
\(963\) | 1.62682e6 | 0.0565294 | ||||||||
\(964\) | 8.44627e7 | 2.92733 | ||||||||
\(965\) | 1.90324e6 | 0.0657923 | ||||||||
\(966\) | −1.02148e8 | −3.52197 | ||||||||
\(967\) | 1.12651e7 | 0.387407 | 0.193703 | − | 0.981060i | \(-0.437950\pi\) | ||||
0.193703 | + | 0.981060i | \(0.437950\pi\) | |||||||
\(968\) | 2.87213e7 | 0.985180 | ||||||||
\(969\) | 186643. | 0.00638561 | ||||||||
\(970\) | 1.16072e7 | 0.396095 | ||||||||
\(971\) | 1.76257e7 | 0.599926 | 0.299963 | − | 0.953951i | \(-0.403026\pi\) | ||||
0.299963 | + | 0.953951i | \(0.403026\pi\) | |||||||
\(972\) | −1.10847e7 | −0.376320 | ||||||||
\(973\) | 7.12749e7 | 2.41354 | ||||||||
\(974\) | 6.43883e7 | 2.17475 | ||||||||
\(975\) | 7.41403e6 | 0.249771 | ||||||||
\(976\) | 1.97712e7 | 0.664369 | ||||||||
\(977\) | −1.23278e6 | −0.0413189 | −0.0206594 | − | 0.999787i | \(-0.506577\pi\) | ||||
−0.0206594 | + | 0.999787i | \(0.506577\pi\) | |||||||
\(978\) | −7.66663e7 | −2.56305 | ||||||||
\(979\) | 6.63425e6 | 0.221225 | ||||||||
\(980\) | 2.03768e7 | 0.677752 | ||||||||
\(981\) | −1.98439e6 | −0.0658348 | ||||||||
\(982\) | 5.00331e7 | 1.65569 | ||||||||
\(983\) | 4.04820e7 | 1.33622 | 0.668110 | − | 0.744063i | \(-0.267104\pi\) | ||||
0.668110 | + | 0.744063i | \(0.267104\pi\) | |||||||
\(984\) | 1.03320e6 | 0.0340170 | ||||||||
\(985\) | −855199. | −0.0280852 | ||||||||
\(986\) | −961607. | −0.0314996 | ||||||||
\(987\) | 1.20822e8 | 3.94779 | ||||||||
\(988\) | −3.15195e6 | −0.102728 | ||||||||
\(989\) | 1.46127e7 | 0.475049 | ||||||||
\(990\) | −391521. | −0.0126960 | ||||||||
\(991\) | −3.85983e7 | −1.24849 | −0.624243 | − | 0.781230i | \(-0.714592\pi\) | ||||
−0.624243 | + | 0.781230i | \(0.714592\pi\) | |||||||
\(992\) | −1.13240e7 | −0.365358 | ||||||||
\(993\) | 2.55258e7 | 0.821497 | ||||||||
\(994\) | −1.79293e8 | −5.75570 | ||||||||
\(995\) | 2.48847e6 | 0.0796845 | ||||||||
\(996\) | −2.66547e7 | −0.851383 | ||||||||
\(997\) | 3.04171e7 | 0.969125 | 0.484562 | − | 0.874757i | \(-0.338979\pi\) | ||||
0.484562 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(998\) | −9.50083e7 | −3.01950 | ||||||||
\(999\) | −3.19252e7 | −1.01209 |
(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 | 547.6.a.b.1.11 | ✓ | 117 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.6.a.b.1.11 | ✓ | 117 | 1.1 | even | 1 | trivial |