Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(11.5305\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.5305 | −1.86154 | −0.930769 | − | 0.365607i | \(-0.880862\pi\) | ||||
−0.930769 | + | 0.365607i | \(0.880862\pi\) | |||||||
\(3\) | 27.4953 | 1.76382 | 0.881911 | − | 0.471417i | \(-0.156257\pi\) | ||||
0.881911 | + | 0.471417i | \(0.156257\pi\) | |||||||
\(4\) | 78.8905 | 2.46533 | ||||||||
\(5\) | 86.8464 | 1.55356 | 0.776778 | − | 0.629775i | \(-0.216853\pi\) | ||||
0.776778 | + | 0.629775i | \(0.216853\pi\) | |||||||
\(6\) | −289.538 | −3.28342 | ||||||||
\(7\) | −19.8137 | −0.152834 | −0.0764171 | − | 0.997076i | \(-0.524348\pi\) | ||||
−0.0764171 | + | 0.997076i | \(0.524348\pi\) | |||||||
\(8\) | −493.778 | −2.72776 | ||||||||
\(9\) | 512.989 | 2.11107 | ||||||||
\(10\) | −914.532 | −2.89200 | ||||||||
\(11\) | −85.3712 | −0.212730 | −0.106365 | − | 0.994327i | \(-0.533921\pi\) | ||||
−0.106365 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(12\) | 2169.11 | 4.34840 | ||||||||
\(13\) | −229.081 | −0.375951 | −0.187975 | − | 0.982174i | \(-0.560193\pi\) | ||||
−0.187975 | + | 0.982174i | \(0.560193\pi\) | |||||||
\(14\) | 208.647 | 0.284507 | ||||||||
\(15\) | 2387.86 | 2.74019 | ||||||||
\(16\) | 2675.21 | 2.61251 | ||||||||
\(17\) | 1356.51 | 1.13841 | 0.569207 | − | 0.822194i | \(-0.307250\pi\) | ||||
0.569207 | + | 0.822194i | \(0.307250\pi\) | |||||||
\(18\) | −5402.01 | −3.92983 | ||||||||
\(19\) | −2795.35 | −1.77645 | −0.888223 | − | 0.459413i | \(-0.848060\pi\) | ||||
−0.888223 | + | 0.459413i | \(0.848060\pi\) | |||||||
\(20\) | 6851.35 | 3.83002 | ||||||||
\(21\) | −544.783 | −0.269572 | ||||||||
\(22\) | 898.997 | 0.396006 | ||||||||
\(23\) | −1856.11 | −0.731618 | −0.365809 | − | 0.930690i | \(-0.619208\pi\) | ||||
−0.365809 | + | 0.930690i | \(0.619208\pi\) | |||||||
\(24\) | −13576.6 | −4.81129 | ||||||||
\(25\) | 4417.29 | 1.41353 | ||||||||
\(26\) | 2412.33 | 0.699847 | ||||||||
\(27\) | 7423.41 | 1.95972 | ||||||||
\(28\) | −1563.11 | −0.376786 | ||||||||
\(29\) | 7312.96 | 1.61472 | 0.807362 | − | 0.590057i | \(-0.200895\pi\) | ||||
0.807362 | + | 0.590057i | \(0.200895\pi\) | |||||||
\(30\) | −25145.3 | −5.10098 | ||||||||
\(31\) | −2937.36 | −0.548975 | −0.274488 | − | 0.961591i | \(-0.588508\pi\) | ||||
−0.274488 | + | 0.961591i | \(0.588508\pi\) | |||||||
\(32\) | −12370.3 | −2.13553 | ||||||||
\(33\) | −2347.30 | −0.375218 | ||||||||
\(34\) | −14284.7 | −2.11920 | ||||||||
\(35\) | −1720.75 | −0.237436 | ||||||||
\(36\) | 40469.9 | 5.20447 | ||||||||
\(37\) | 2577.36 | 0.309507 | 0.154754 | − | 0.987953i | \(-0.450542\pi\) | ||||
0.154754 | + | 0.987953i | \(0.450542\pi\) | |||||||
\(38\) | 29436.3 | 3.30692 | ||||||||
\(39\) | −6298.65 | −0.663110 | ||||||||
\(40\) | −42882.8 | −4.23773 | ||||||||
\(41\) | −3532.54 | −0.328192 | −0.164096 | − | 0.986444i | \(-0.552471\pi\) | ||||
−0.164096 | + | 0.986444i | \(0.552471\pi\) | |||||||
\(42\) | 5736.81 | 0.501819 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | −6734.97 | −0.524450 | ||||||||
\(45\) | 44551.2 | 3.27966 | ||||||||
\(46\) | 19545.7 | 1.36194 | ||||||||
\(47\) | −7065.73 | −0.466566 | −0.233283 | − | 0.972409i | \(-0.574947\pi\) | ||||
−0.233283 | + | 0.972409i | \(0.574947\pi\) | |||||||
\(48\) | 73555.6 | 4.60800 | ||||||||
\(49\) | −16414.4 | −0.976642 | ||||||||
\(50\) | −46516.1 | −2.63135 | ||||||||
\(51\) | 37297.6 | 2.00796 | ||||||||
\(52\) | −18072.3 | −0.926842 | ||||||||
\(53\) | −3852.63 | −0.188394 | −0.0941972 | − | 0.995554i | \(-0.530028\pi\) | ||||
−0.0941972 | + | 0.995554i | \(0.530028\pi\) | |||||||
\(54\) | −78171.9 | −3.64810 | ||||||||
\(55\) | −7414.18 | −0.330488 | ||||||||
\(56\) | 9783.57 | 0.416896 | ||||||||
\(57\) | −76858.8 | −3.13333 | ||||||||
\(58\) | −77008.8 | −3.00587 | ||||||||
\(59\) | 27996.1 | 1.04705 | 0.523524 | − | 0.852011i | \(-0.324617\pi\) | ||||
0.523524 | + | 0.852011i | \(0.324617\pi\) | |||||||
\(60\) | 188380. | 6.75547 | ||||||||
\(61\) | −39244.4 | −1.35037 | −0.675186 | − | 0.737648i | \(-0.735937\pi\) | ||||
−0.675186 | + | 0.737648i | \(0.735937\pi\) | |||||||
\(62\) | 30931.7 | 1.02194 | ||||||||
\(63\) | −10164.2 | −0.322643 | ||||||||
\(64\) | 44658.1 | 1.36286 | ||||||||
\(65\) | −19894.9 | −0.584060 | ||||||||
\(66\) | 24718.2 | 0.698484 | ||||||||
\(67\) | −14809.1 | −0.403034 | −0.201517 | − | 0.979485i | \(-0.564587\pi\) | ||||
−0.201517 | + | 0.979485i | \(0.564587\pi\) | |||||||
\(68\) | 107016. | 2.80656 | ||||||||
\(69\) | −51034.2 | −1.29044 | ||||||||
\(70\) | 18120.3 | 0.441997 | ||||||||
\(71\) | 8956.13 | 0.210850 | 0.105425 | − | 0.994427i | \(-0.466380\pi\) | ||||
0.105425 | + | 0.994427i | \(0.466380\pi\) | |||||||
\(72\) | −253303. | −5.75849 | ||||||||
\(73\) | 35168.6 | 0.772411 | 0.386205 | − | 0.922413i | \(-0.373786\pi\) | ||||
0.386205 | + | 0.922413i | \(0.373786\pi\) | |||||||
\(74\) | −27140.8 | −0.576160 | ||||||||
\(75\) | 121455. | 2.49322 | ||||||||
\(76\) | −220526. | −4.37952 | ||||||||
\(77\) | 1691.52 | 0.0325125 | ||||||||
\(78\) | 66327.6 | 1.23441 | ||||||||
\(79\) | −13263.6 | −0.239108 | −0.119554 | − | 0.992828i | \(-0.538146\pi\) | ||||
−0.119554 | + | 0.992828i | \(0.538146\pi\) | |||||||
\(80\) | 232332. | 4.05868 | ||||||||
\(81\) | 79452.3 | 1.34553 | ||||||||
\(82\) | 37199.3 | 0.610942 | ||||||||
\(83\) | −9812.47 | −0.156345 | −0.0781724 | − | 0.996940i | \(-0.524908\pi\) | ||||
−0.0781724 | + | 0.996940i | \(0.524908\pi\) | |||||||
\(84\) | −42978.2 | −0.664584 | ||||||||
\(85\) | 117808. | 1.76859 | ||||||||
\(86\) | −19470.8 | −0.283882 | ||||||||
\(87\) | 201072. | 2.84808 | ||||||||
\(88\) | 42154.4 | 0.580278 | ||||||||
\(89\) | −87124.9 | −1.16592 | −0.582958 | − | 0.812502i | \(-0.698105\pi\) | ||||
−0.582958 | + | 0.812502i | \(0.698105\pi\) | |||||||
\(90\) | −469145. | −6.10521 | ||||||||
\(91\) | 4538.95 | 0.0574581 | ||||||||
\(92\) | −146429. | −1.80368 | ||||||||
\(93\) | −80763.5 | −0.968295 | ||||||||
\(94\) | 74405.4 | 0.868530 | ||||||||
\(95\) | −242766. | −2.75981 | ||||||||
\(96\) | −340124. | −3.76669 | ||||||||
\(97\) | 83982.4 | 0.906272 | 0.453136 | − | 0.891441i | \(-0.350305\pi\) | ||||
0.453136 | + | 0.891441i | \(0.350305\pi\) | |||||||
\(98\) | 172851. | 1.81806 | ||||||||
\(99\) | −43794.5 | −0.449088 | ||||||||
\(100\) | 348482. | 3.48482 | ||||||||
\(101\) | 74775.4 | 0.729382 | 0.364691 | − | 0.931129i | \(-0.381175\pi\) | ||||
0.364691 | + | 0.931129i | \(0.381175\pi\) | |||||||
\(102\) | −392760. | −3.73789 | ||||||||
\(103\) | 29400.7 | 0.273064 | 0.136532 | − | 0.990636i | \(-0.456404\pi\) | ||||
0.136532 | + | 0.990636i | \(0.456404\pi\) | |||||||
\(104\) | 113115. | 1.02551 | ||||||||
\(105\) | −47312.4 | −0.418795 | ||||||||
\(106\) | 40570.0 | 0.350704 | ||||||||
\(107\) | −199822. | −1.68727 | −0.843635 | − | 0.536917i | \(-0.819589\pi\) | ||||
−0.843635 | + | 0.536917i | \(0.819589\pi\) | |||||||
\(108\) | 585637. | 4.83135 | ||||||||
\(109\) | −39465.7 | −0.318166 | −0.159083 | − | 0.987265i | \(-0.550854\pi\) | ||||
−0.159083 | + | 0.987265i | \(0.550854\pi\) | |||||||
\(110\) | 78074.7 | 0.615217 | ||||||||
\(111\) | 70865.2 | 0.545915 | ||||||||
\(112\) | −53005.8 | −0.399281 | ||||||||
\(113\) | 41487.8 | 0.305650 | 0.152825 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152825 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(114\) | 809358. | 5.83282 | ||||||||
\(115\) | −161196. | −1.13661 | ||||||||
\(116\) | 576923. | 3.98082 | ||||||||
\(117\) | −117516. | −0.793657 | ||||||||
\(118\) | −294811. | −1.94912 | ||||||||
\(119\) | −26877.5 | −0.173989 | ||||||||
\(120\) | −1.17907e6 | −7.47460 | ||||||||
\(121\) | −153763. | −0.954746 | ||||||||
\(122\) | 413262. | 2.51377 | ||||||||
\(123\) | −97128.1 | −0.578871 | ||||||||
\(124\) | −231730. | −1.35340 | ||||||||
\(125\) | 112231. | 0.642448 | ||||||||
\(126\) | 107034. | 0.600612 | ||||||||
\(127\) | 357769. | 1.96831 | 0.984156 | − | 0.177305i | \(-0.0567379\pi\) | ||||
0.984156 | + | 0.177305i | \(0.0567379\pi\) | |||||||
\(128\) | −74420.5 | −0.401483 | ||||||||
\(129\) | 50838.7 | 0.268980 | ||||||||
\(130\) | 209502. | 1.08725 | ||||||||
\(131\) | −61207.9 | −0.311623 | −0.155811 | − | 0.987787i | \(-0.549799\pi\) | ||||
−0.155811 | + | 0.987787i | \(0.549799\pi\) | |||||||
\(132\) | −185180. | −0.925036 | ||||||||
\(133\) | 55386.2 | 0.271502 | ||||||||
\(134\) | 155946. | 0.750263 | ||||||||
\(135\) | 644697. | 3.04453 | ||||||||
\(136\) | −669814. | −3.10533 | ||||||||
\(137\) | −309777. | −1.41009 | −0.705047 | − | 0.709161i | \(-0.749074\pi\) | ||||
−0.705047 | + | 0.709161i | \(0.749074\pi\) | |||||||
\(138\) | 537414. | 2.40221 | ||||||||
\(139\) | −193740. | −0.850517 | −0.425259 | − | 0.905072i | \(-0.639817\pi\) | ||||
−0.425259 | + | 0.905072i | \(0.639817\pi\) | |||||||
\(140\) | −135751. | −0.585358 | ||||||||
\(141\) | −194274. | −0.822938 | ||||||||
\(142\) | −94312.1 | −0.392506 | ||||||||
\(143\) | 19556.9 | 0.0799762 | ||||||||
\(144\) | 1.37235e6 | 5.51518 | ||||||||
\(145\) | 635104. | 2.50856 | ||||||||
\(146\) | −370342. | −1.43787 | ||||||||
\(147\) | −451319. | −1.72262 | ||||||||
\(148\) | 203329. | 0.763037 | ||||||||
\(149\) | −455017. | −1.67904 | −0.839521 | − | 0.543327i | \(-0.817164\pi\) | ||||
−0.839521 | + | 0.543327i | \(0.817164\pi\) | |||||||
\(150\) | −1.27897e6 | −4.64123 | ||||||||
\(151\) | −505868. | −1.80549 | −0.902744 | − | 0.430179i | \(-0.858451\pi\) | ||||
−0.902744 | + | 0.430179i | \(0.858451\pi\) | |||||||
\(152\) | 1.38028e6 | 4.84572 | ||||||||
\(153\) | 695874. | 2.40327 | ||||||||
\(154\) | −17812.5 | −0.0605232 | ||||||||
\(155\) | −255099. | −0.852864 | ||||||||
\(156\) | −496903. | −1.63478 | ||||||||
\(157\) | 348495. | 1.12836 | 0.564179 | − | 0.825652i | \(-0.309193\pi\) | ||||
0.564179 | + | 0.825652i | \(0.309193\pi\) | |||||||
\(158\) | 139672. | 0.445108 | ||||||||
\(159\) | −105929. | −0.332294 | ||||||||
\(160\) | −1.07432e6 | −3.31766 | ||||||||
\(161\) | 36776.4 | 0.111816 | ||||||||
\(162\) | −836669. | −2.50476 | ||||||||
\(163\) | 104915. | 0.309291 | 0.154645 | − | 0.987970i | \(-0.450576\pi\) | ||||
0.154645 | + | 0.987970i | \(0.450576\pi\) | |||||||
\(164\) | −278684. | −0.809100 | ||||||||
\(165\) | −203855. | −0.582923 | ||||||||
\(166\) | 103330. | 0.291042 | ||||||||
\(167\) | 186982. | 0.518809 | 0.259405 | − | 0.965769i | \(-0.416474\pi\) | ||||
0.259405 | + | 0.965769i | \(0.416474\pi\) | |||||||
\(168\) | 269002. | 0.735329 | ||||||||
\(169\) | −318815. | −0.858661 | ||||||||
\(170\) | −1.24057e6 | −3.29230 | ||||||||
\(171\) | −1.43398e6 | −3.75019 | ||||||||
\(172\) | 145868. | 0.375959 | ||||||||
\(173\) | 491718. | 1.24911 | 0.624555 | − | 0.780981i | \(-0.285280\pi\) | ||||
0.624555 | + | 0.780981i | \(0.285280\pi\) | |||||||
\(174\) | −2.11738e6 | −5.30182 | ||||||||
\(175\) | −87522.9 | −0.216036 | ||||||||
\(176\) | −228386. | −0.555761 | ||||||||
\(177\) | 769758. | 1.84681 | ||||||||
\(178\) | 917464. | 2.17040 | ||||||||
\(179\) | 374509. | 0.873634 | 0.436817 | − | 0.899550i | \(-0.356106\pi\) | ||||
0.436817 | + | 0.899550i | \(0.356106\pi\) | |||||||
\(180\) | 3.51467e6 | 8.08543 | ||||||||
\(181\) | 460794. | 1.04547 | 0.522733 | − | 0.852496i | \(-0.324912\pi\) | ||||
0.522733 | + | 0.852496i | \(0.324912\pi\) | |||||||
\(182\) | −47797.2 | −0.106961 | ||||||||
\(183\) | −1.07904e6 | −2.38181 | ||||||||
\(184\) | 916507. | 1.99568 | ||||||||
\(185\) | 223834. | 0.480837 | ||||||||
\(186\) | 850476. | 1.80252 | ||||||||
\(187\) | −115807. | −0.242175 | ||||||||
\(188\) | −557419. | −1.15024 | ||||||||
\(189\) | −147085. | −0.299512 | ||||||||
\(190\) | 2.55643e6 | 5.13749 | ||||||||
\(191\) | −22464.4 | −0.0445565 | −0.0222783 | − | 0.999752i | \(-0.507092\pi\) | ||||
−0.0222783 | + | 0.999752i | \(0.507092\pi\) | |||||||
\(192\) | 1.22789e6 | 2.40384 | ||||||||
\(193\) | 830124. | 1.60417 | 0.802083 | − | 0.597212i | \(-0.203725\pi\) | ||||
0.802083 | + | 0.597212i | \(0.203725\pi\) | |||||||
\(194\) | −884372. | −1.68706 | ||||||||
\(195\) | −547015. | −1.03018 | ||||||||
\(196\) | −1.29494e6 | −2.40774 | ||||||||
\(197\) | 802058. | 1.47245 | 0.736224 | − | 0.676738i | \(-0.236607\pi\) | ||||
0.736224 | + | 0.676738i | \(0.236607\pi\) | |||||||
\(198\) | 461176. | 0.835995 | ||||||||
\(199\) | −187945. | −0.336432 | −0.168216 | − | 0.985750i | \(-0.553801\pi\) | ||||
−0.168216 | + | 0.985750i | \(0.553801\pi\) | |||||||
\(200\) | −2.18116e6 | −3.85579 | ||||||||
\(201\) | −407180. | −0.710879 | ||||||||
\(202\) | −787419. | −1.35777 | ||||||||
\(203\) | −144897. | −0.246785 | ||||||||
\(204\) | 2.94242e6 | 4.95028 | ||||||||
\(205\) | −306788. | −0.509864 | ||||||||
\(206\) | −309602. | −0.508319 | ||||||||
\(207\) | −952164. | −1.54449 | ||||||||
\(208\) | −612841. | −0.982176 | ||||||||
\(209\) | 238642. | 0.377904 | ||||||||
\(210\) | 498221. | 0.779604 | ||||||||
\(211\) | 327613. | 0.506589 | 0.253294 | − | 0.967389i | \(-0.418486\pi\) | ||||
0.253294 | + | 0.967389i | \(0.418486\pi\) | |||||||
\(212\) | −303936. | −0.464454 | ||||||||
\(213\) | 246251. | 0.371902 | ||||||||
\(214\) | 2.10422e6 | 3.14092 | ||||||||
\(215\) | 160579. | 0.236915 | ||||||||
\(216\) | −3.66552e6 | −5.34566 | ||||||||
\(217\) | 58200.0 | 0.0839022 | ||||||||
\(218\) | 415592. | 0.592278 | ||||||||
\(219\) | 966970. | 1.36239 | ||||||||
\(220\) | −584908. | −0.814762 | ||||||||
\(221\) | −310751. | −0.427988 | ||||||||
\(222\) | −746243. | −1.01624 | ||||||||
\(223\) | −166692. | −0.224467 | −0.112234 | − | 0.993682i | \(-0.535801\pi\) | ||||
−0.112234 | + | 0.993682i | \(0.535801\pi\) | |||||||
\(224\) | 245101. | 0.326382 | ||||||||
\(225\) | 2.26602e6 | 2.98406 | ||||||||
\(226\) | −436886. | −0.568980 | ||||||||
\(227\) | −155259. | −0.199982 | −0.0999912 | − | 0.994988i | \(-0.531881\pi\) | ||||
−0.0999912 | + | 0.994988i | \(0.531881\pi\) | |||||||
\(228\) | −6.06343e6 | −7.72469 | ||||||||
\(229\) | −1.01590e6 | −1.28016 | −0.640079 | − | 0.768309i | \(-0.721098\pi\) | ||||
−0.640079 | + | 0.768309i | \(0.721098\pi\) | |||||||
\(230\) | 1.69747e6 | 2.11584 | ||||||||
\(231\) | 46508.7 | 0.0573462 | ||||||||
\(232\) | −3.61098e6 | −4.40458 | ||||||||
\(233\) | 23299.8 | 0.0281166 | 0.0140583 | − | 0.999901i | \(-0.495525\pi\) | ||||
0.0140583 | + | 0.999901i | \(0.495525\pi\) | |||||||
\(234\) | 1.23750e6 | 1.47742 | ||||||||
\(235\) | −613633. | −0.724835 | ||||||||
\(236\) | 2.20862e6 | 2.58132 | ||||||||
\(237\) | −364686. | −0.421743 | ||||||||
\(238\) | 283032. | 0.323887 | ||||||||
\(239\) | 4871.64 | 0.00551671 | 0.00275836 | − | 0.999996i | \(-0.499122\pi\) | ||||
0.00275836 | + | 0.999996i | \(0.499122\pi\) | |||||||
\(240\) | 6.38804e6 | 7.15879 | ||||||||
\(241\) | 918873. | 1.01909 | 0.509545 | − | 0.860444i | \(-0.329814\pi\) | ||||
0.509545 | + | 0.860444i | \(0.329814\pi\) | |||||||
\(242\) | 1.61919e6 | 1.77730 | ||||||||
\(243\) | 380672. | 0.413557 | ||||||||
\(244\) | −3.09601e6 | −3.32911 | ||||||||
\(245\) | −1.42553e6 | −1.51727 | ||||||||
\(246\) | 1.02280e6 | 1.07759 | ||||||||
\(247\) | 640362. | 0.667856 | ||||||||
\(248\) | 1.45040e6 | 1.49748 | ||||||||
\(249\) | −269796. | −0.275764 | ||||||||
\(250\) | −1.18184e6 | −1.19594 | ||||||||
\(251\) | 1.47118e6 | 1.47395 | 0.736973 | − | 0.675922i | \(-0.236254\pi\) | ||||
0.736973 | + | 0.675922i | \(0.236254\pi\) | |||||||
\(252\) | −801859. | −0.795421 | ||||||||
\(253\) | 158458. | 0.155637 | ||||||||
\(254\) | −3.76747e6 | −3.66409 | ||||||||
\(255\) | 3.23916e6 | 3.11948 | ||||||||
\(256\) | −645377. | −0.615480 | ||||||||
\(257\) | −813506. | −0.768295 | −0.384147 | − | 0.923272i | \(-0.625505\pi\) | ||||
−0.384147 | + | 0.923272i | \(0.625505\pi\) | |||||||
\(258\) | −535355. | −0.500717 | ||||||||
\(259\) | −51067.0 | −0.0473033 | ||||||||
\(260\) | −1.56952e6 | −1.43990 | ||||||||
\(261\) | 3.75147e6 | 3.40879 | ||||||||
\(262\) | 644546. | 0.580098 | ||||||||
\(263\) | 691865. | 0.616782 | 0.308391 | − | 0.951260i | \(-0.400209\pi\) | ||||
0.308391 | + | 0.951260i | \(0.400209\pi\) | |||||||
\(264\) | 1.15905e6 | 1.02351 | ||||||||
\(265\) | −334587. | −0.292681 | ||||||||
\(266\) | −583242. | −0.505411 | ||||||||
\(267\) | −2.39552e6 | −2.05647 | ||||||||
\(268\) | −1.16830e6 | −0.993610 | ||||||||
\(269\) | −759828. | −0.640228 | −0.320114 | − | 0.947379i | \(-0.603721\pi\) | ||||
−0.320114 | + | 0.947379i | \(0.603721\pi\) | |||||||
\(270\) | −6.78895e6 | −5.66752 | ||||||||
\(271\) | 954020. | 0.789104 | 0.394552 | − | 0.918874i | \(-0.370900\pi\) | ||||
0.394552 | + | 0.918874i | \(0.370900\pi\) | |||||||
\(272\) | 3.62895e6 | 2.97412 | ||||||||
\(273\) | 124799. | 0.101346 | ||||||||
\(274\) | 3.26209e6 | 2.62494 | ||||||||
\(275\) | −377110. | −0.300702 | ||||||||
\(276\) | −4.02611e6 | −3.18136 | ||||||||
\(277\) | 1.03398e6 | 0.809680 | 0.404840 | − | 0.914387i | \(-0.367327\pi\) | ||||
0.404840 | + | 0.914387i | \(0.367327\pi\) | |||||||
\(278\) | 2.04017e6 | 1.58327 | ||||||||
\(279\) | −1.50683e6 | −1.15892 | ||||||||
\(280\) | 849668. | 0.647670 | ||||||||
\(281\) | 2.05117e6 | 1.54966 | 0.774829 | − | 0.632171i | \(-0.217836\pi\) | ||||
0.774829 | + | 0.632171i | \(0.217836\pi\) | |||||||
\(282\) | 2.04580e6 | 1.53193 | ||||||||
\(283\) | −2.37044e6 | −1.75940 | −0.879698 | − | 0.475533i | \(-0.842255\pi\) | ||||
−0.879698 | + | 0.475533i | \(0.842255\pi\) | |||||||
\(284\) | 706553. | 0.519815 | ||||||||
\(285\) | −6.67491e6 | −4.86780 | ||||||||
\(286\) | −205943. | −0.148879 | ||||||||
\(287\) | 69992.7 | 0.0501589 | ||||||||
\(288\) | −6.34583e6 | −4.50824 | ||||||||
\(289\) | 420259. | 0.295987 | ||||||||
\(290\) | −6.68793e6 | −4.66979 | ||||||||
\(291\) | 2.30912e6 | 1.59850 | ||||||||
\(292\) | 2.77447e6 | 1.90425 | ||||||||
\(293\) | 1.48623e6 | 1.01138 | 0.505692 | − | 0.862714i | \(-0.331237\pi\) | ||||
0.505692 | + | 0.862714i | \(0.331237\pi\) | |||||||
\(294\) | 4.75259e6 | 3.20673 | ||||||||
\(295\) | 2.43136e6 | 1.62665 | ||||||||
\(296\) | −1.27264e6 | −0.844263 | ||||||||
\(297\) | −633746. | −0.416892 | ||||||||
\(298\) | 4.79153e6 | 3.12560 | ||||||||
\(299\) | 425200. | 0.275052 | ||||||||
\(300\) | 9.58161e6 | 6.14661 | ||||||||
\(301\) | −36635.5 | −0.0233070 | ||||||||
\(302\) | 5.32702e6 | 3.36099 | ||||||||
\(303\) | 2.05597e6 | 1.28650 | ||||||||
\(304\) | −7.47815e6 | −4.64098 | ||||||||
\(305\) | −3.40824e6 | −2.09788 | ||||||||
\(306\) | −7.32787e6 | −4.47378 | ||||||||
\(307\) | −1.62571e6 | −0.984456 | −0.492228 | − | 0.870466i | \(-0.663817\pi\) | ||||
−0.492228 | + | 0.870466i | \(0.663817\pi\) | |||||||
\(308\) | 133445. | 0.0801539 | ||||||||
\(309\) | 808378. | 0.481636 | ||||||||
\(310\) | 2.68631e6 | 1.58764 | ||||||||
\(311\) | 2.07269e6 | 1.21516 | 0.607581 | − | 0.794258i | \(-0.292140\pi\) | ||||
0.607581 | + | 0.794258i | \(0.292140\pi\) | |||||||
\(312\) | 3.11013e6 | 1.80881 | ||||||||
\(313\) | −345918. | −0.199578 | −0.0997889 | − | 0.995009i | \(-0.531817\pi\) | ||||
−0.0997889 | + | 0.995009i | \(0.531817\pi\) | |||||||
\(314\) | −3.66981e6 | −2.10048 | ||||||||
\(315\) | −882725. | −0.501244 | ||||||||
\(316\) | −1.04637e6 | −0.589479 | ||||||||
\(317\) | 574435. | 0.321065 | 0.160532 | − | 0.987031i | \(-0.448679\pi\) | ||||
0.160532 | + | 0.987031i | \(0.448679\pi\) | |||||||
\(318\) | 1.11548e6 | 0.618579 | ||||||||
\(319\) | −624316. | −0.343501 | ||||||||
\(320\) | 3.87839e6 | 2.11727 | ||||||||
\(321\) | −5.49417e6 | −2.97604 | ||||||||
\(322\) | −387272. | −0.208150 | ||||||||
\(323\) | −3.79191e6 | −2.02233 | ||||||||
\(324\) | 6.26803e6 | 3.31718 | ||||||||
\(325\) | −1.01192e6 | −0.531419 | ||||||||
\(326\) | −1.10480e6 | −0.575757 | ||||||||
\(327\) | −1.08512e6 | −0.561187 | ||||||||
\(328\) | 1.74429e6 | 0.895229 | ||||||||
\(329\) | 139998. | 0.0713072 | ||||||||
\(330\) | 2.14668e6 | 1.08513 | ||||||||
\(331\) | −1.12898e6 | −0.566393 | −0.283196 | − | 0.959062i | \(-0.591395\pi\) | ||||
−0.283196 | + | 0.959062i | \(0.591395\pi\) | |||||||
\(332\) | −774111. | −0.385441 | ||||||||
\(333\) | 1.32216e6 | 0.653390 | ||||||||
\(334\) | −1.96900e6 | −0.965784 | ||||||||
\(335\) | −1.28612e6 | −0.626135 | ||||||||
\(336\) | −1.45741e6 | −0.704260 | ||||||||
\(337\) | −370207. | −0.177570 | −0.0887850 | − | 0.996051i | \(-0.528298\pi\) | ||||
−0.0887850 | + | 0.996051i | \(0.528298\pi\) | |||||||
\(338\) | 3.35726e6 | 1.59843 | ||||||||
\(339\) | 1.14072e6 | 0.539112 | ||||||||
\(340\) | 9.29392e6 | 4.36015 | ||||||||
\(341\) | 250766. | 0.116784 | ||||||||
\(342\) | 1.51005e7 | 6.98113 | ||||||||
\(343\) | 658239. | 0.302098 | ||||||||
\(344\) | −912996. | −0.415980 | ||||||||
\(345\) | −4.43214e6 | −2.00477 | ||||||||
\(346\) | −5.17801e6 | −2.32527 | ||||||||
\(347\) | 372676. | 0.166153 | 0.0830764 | − | 0.996543i | \(-0.473525\pi\) | ||||
0.0830764 | + | 0.996543i | \(0.473525\pi\) | |||||||
\(348\) | 1.58626e7 | 7.02146 | ||||||||
\(349\) | −2.14587e6 | −0.943060 | −0.471530 | − | 0.881850i | \(-0.656298\pi\) | ||||
−0.471530 | + | 0.881850i | \(0.656298\pi\) | |||||||
\(350\) | 921656. | 0.402160 | ||||||||
\(351\) | −1.70056e6 | −0.736759 | ||||||||
\(352\) | 1.05607e6 | 0.454292 | ||||||||
\(353\) | −2.87740e6 | −1.22903 | −0.614517 | − | 0.788904i | \(-0.710649\pi\) | ||||
−0.614517 | + | 0.788904i | \(0.710649\pi\) | |||||||
\(354\) | −8.10591e6 | −3.43790 | ||||||||
\(355\) | 777807. | 0.327568 | ||||||||
\(356\) | −6.87332e6 | −2.87436 | ||||||||
\(357\) | −739003. | −0.306885 | ||||||||
\(358\) | −3.94375e6 | −1.62630 | ||||||||
\(359\) | 647359. | 0.265100 | 0.132550 | − | 0.991176i | \(-0.457684\pi\) | ||||
0.132550 | + | 0.991176i | \(0.457684\pi\) | |||||||
\(360\) | −2.19984e7 | −8.94613 | ||||||||
\(361\) | 5.33787e6 | 2.15576 | ||||||||
\(362\) | −4.85237e6 | −1.94618 | ||||||||
\(363\) | −4.22775e6 | −1.68400 | ||||||||
\(364\) | 358080. | 0.141653 | ||||||||
\(365\) | 3.05427e6 | 1.19998 | ||||||||
\(366\) | 1.13627e7 | 4.43384 | ||||||||
\(367\) | 3.06021e6 | 1.18600 | 0.593001 | − | 0.805202i | \(-0.297943\pi\) | ||||
0.593001 | + | 0.805202i | \(0.297943\pi\) | |||||||
\(368\) | −4.96549e6 | −1.91136 | ||||||||
\(369\) | −1.81215e6 | −0.692834 | ||||||||
\(370\) | −2.35708e6 | −0.895096 | ||||||||
\(371\) | 76335.0 | 0.0287931 | ||||||||
\(372\) | −6.37147e6 | −2.38716 | ||||||||
\(373\) | 3.54156e6 | 1.31802 | 0.659010 | − | 0.752134i | \(-0.270975\pi\) | ||||
0.659010 | + | 0.752134i | \(0.270975\pi\) | |||||||
\(374\) | 1.21950e6 | 0.450819 | ||||||||
\(375\) | 3.08582e6 | 1.13316 | ||||||||
\(376\) | 3.48890e6 | 1.27268 | ||||||||
\(377\) | −1.67526e6 | −0.607057 | ||||||||
\(378\) | 1.54888e6 | 0.557554 | ||||||||
\(379\) | −3.92757e6 | −1.40451 | −0.702257 | − | 0.711923i | \(-0.747824\pi\) | ||||
−0.702257 | + | 0.711923i | \(0.747824\pi\) | |||||||
\(380\) | −1.91519e7 | −6.80383 | ||||||||
\(381\) | 9.83696e6 | 3.47175 | ||||||||
\(382\) | 236560. | 0.0829437 | ||||||||
\(383\) | −1.29688e6 | −0.451754 | −0.225877 | − | 0.974156i | \(-0.572525\pi\) | ||||
−0.225877 | + | 0.974156i | \(0.572525\pi\) | |||||||
\(384\) | −2.04621e6 | −0.708145 | ||||||||
\(385\) | 146902. | 0.0505099 | ||||||||
\(386\) | −8.74158e6 | −2.98622 | ||||||||
\(387\) | 948517. | 0.321934 | ||||||||
\(388\) | 6.62541e6 | 2.23426 | ||||||||
\(389\) | −100541. | −0.0336874 | −0.0168437 | − | 0.999858i | \(-0.505362\pi\) | ||||
−0.0168437 | + | 0.999858i | \(0.505362\pi\) | |||||||
\(390\) | 5.76031e6 | 1.91772 | ||||||||
\(391\) | −2.51783e6 | −0.832884 | ||||||||
\(392\) | 8.10508e6 | 2.66405 | ||||||||
\(393\) | −1.68293e6 | −0.549647 | ||||||||
\(394\) | −8.44603e6 | −2.74102 | ||||||||
\(395\) | −1.15190e6 | −0.371467 | ||||||||
\(396\) | −3.45497e6 | −1.10715 | ||||||||
\(397\) | 3.36979e6 | 1.07307 | 0.536533 | − | 0.843879i | \(-0.319734\pi\) | ||||
0.536533 | + | 0.843879i | \(0.319734\pi\) | |||||||
\(398\) | 1.97914e6 | 0.626281 | ||||||||
\(399\) | 1.52286e6 | 0.478880 | ||||||||
\(400\) | 1.18172e7 | 3.69287 | ||||||||
\(401\) | 4.73407e6 | 1.47019 | 0.735095 | − | 0.677964i | \(-0.237138\pi\) | ||||
0.735095 | + | 0.677964i | \(0.237138\pi\) | |||||||
\(402\) | 4.28779e6 | 1.32333 | ||||||||
\(403\) | 672894. | 0.206388 | ||||||||
\(404\) | 5.89906e6 | 1.79817 | ||||||||
\(405\) | 6.90015e6 | 2.09036 | ||||||||
\(406\) | 1.52583e6 | 0.459400 | ||||||||
\(407\) | −220032. | −0.0658416 | ||||||||
\(408\) | −1.84167e7 | −5.47724 | ||||||||
\(409\) | −84169.8 | −0.0248799 | −0.0124399 | − | 0.999923i | \(-0.503960\pi\) | ||||
−0.0124399 | + | 0.999923i | \(0.503960\pi\) | |||||||
\(410\) | 3.23062e6 | 0.949131 | ||||||||
\(411\) | −8.51740e6 | −2.48715 | ||||||||
\(412\) | 2.31943e6 | 0.673191 | ||||||||
\(413\) | −554705. | −0.160025 | ||||||||
\(414\) | 1.00267e7 | 2.87513 | ||||||||
\(415\) | −852178. | −0.242890 | ||||||||
\(416\) | 2.83380e6 | 0.802854 | ||||||||
\(417\) | −5.32694e6 | −1.50016 | ||||||||
\(418\) | −2.51301e6 | −0.703483 | ||||||||
\(419\) | −1.45191e6 | −0.404022 | −0.202011 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202011 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(420\) | −3.73250e6 | −1.03247 | ||||||||
\(421\) | 4.69910e6 | 1.29214 | 0.646070 | − | 0.763278i | \(-0.276411\pi\) | ||||
0.646070 | + | 0.763278i | \(0.276411\pi\) | |||||||
\(422\) | −3.44992e6 | −0.943034 | ||||||||
\(423\) | −3.62464e6 | −0.984950 | ||||||||
\(424\) | 1.90235e6 | 0.513896 | ||||||||
\(425\) | 5.99210e6 | 1.60919 | ||||||||
\(426\) | −2.59314e6 | −0.692311 | ||||||||
\(427\) | 777577. | 0.206383 | ||||||||
\(428\) | −1.57641e7 | −4.15967 | ||||||||
\(429\) | 537723. | 0.141064 | ||||||||
\(430\) | −1.69097e6 | −0.441026 | ||||||||
\(431\) | 3.34282e6 | 0.866803 | 0.433401 | − | 0.901201i | \(-0.357313\pi\) | ||||
0.433401 | + | 0.901201i | \(0.357313\pi\) | |||||||
\(432\) | 1.98592e7 | 5.11979 | ||||||||
\(433\) | 629642. | 0.161389 | 0.0806945 | − | 0.996739i | \(-0.474286\pi\) | ||||
0.0806945 | + | 0.996739i | \(0.474286\pi\) | |||||||
\(434\) | −612872. | −0.156187 | ||||||||
\(435\) | 1.74623e7 | 4.42465 | ||||||||
\(436\) | −3.11347e6 | −0.784383 | ||||||||
\(437\) | 5.18847e6 | 1.29968 | ||||||||
\(438\) | −1.01826e7 | −2.53615 | ||||||||
\(439\) | 6.24963e6 | 1.54772 | 0.773861 | − | 0.633355i | \(-0.218323\pi\) | ||||
0.773861 | + | 0.633355i | \(0.218323\pi\) | |||||||
\(440\) | 3.66096e6 | 0.901494 | ||||||||
\(441\) | −8.42041e6 | −2.06175 | ||||||||
\(442\) | 3.27235e6 | 0.796716 | ||||||||
\(443\) | 6.58305e6 | 1.59374 | 0.796871 | − | 0.604149i | \(-0.206487\pi\) | ||||
0.796871 | + | 0.604149i | \(0.206487\pi\) | |||||||
\(444\) | 5.59059e6 | 1.34586 | ||||||||
\(445\) | −7.56648e6 | −1.81131 | ||||||||
\(446\) | 1.75534e6 | 0.417855 | ||||||||
\(447\) | −1.25108e7 | −2.96153 | ||||||||
\(448\) | −884842. | −0.208291 | ||||||||
\(449\) | 1.62106e6 | 0.379476 | 0.189738 | − | 0.981835i | \(-0.439236\pi\) | ||||
0.189738 | + | 0.981835i | \(0.439236\pi\) | |||||||
\(450\) | −2.38622e7 | −5.55495 | ||||||||
\(451\) | 301577. | 0.0698163 | ||||||||
\(452\) | 3.27300e6 | 0.753528 | ||||||||
\(453\) | −1.39090e7 | −3.18456 | ||||||||
\(454\) | 1.63495e6 | 0.372275 | ||||||||
\(455\) | 394191. | 0.0892644 | ||||||||
\(456\) | 3.79512e7 | 8.54699 | ||||||||
\(457\) | −6.01194e6 | −1.34656 | −0.673278 | − | 0.739390i | \(-0.735114\pi\) | ||||
−0.673278 | + | 0.739390i | \(0.735114\pi\) | |||||||
\(458\) | 1.06979e7 | 2.38306 | ||||||||
\(459\) | 1.00699e7 | 2.23097 | ||||||||
\(460\) | −1.27169e7 | −2.80211 | ||||||||
\(461\) | −1.97072e6 | −0.431889 | −0.215945 | − | 0.976406i | \(-0.569283\pi\) | ||||
−0.215945 | + | 0.976406i | \(0.569283\pi\) | |||||||
\(462\) | −489758. | −0.106752 | ||||||||
\(463\) | −925538. | −0.200651 | −0.100326 | − | 0.994955i | \(-0.531988\pi\) | ||||
−0.100326 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(464\) | 1.95637e7 | 4.21848 | ||||||||
\(465\) | −7.01401e6 | −1.50430 | ||||||||
\(466\) | −245357. | −0.0523401 | ||||||||
\(467\) | 1.87994e6 | 0.398890 | 0.199445 | − | 0.979909i | \(-0.436086\pi\) | ||||
0.199445 | + | 0.979909i | \(0.436086\pi\) | |||||||
\(468\) | −9.27090e6 | −1.95662 | ||||||||
\(469\) | 293423. | 0.0615973 | ||||||||
\(470\) | 6.46184e6 | 1.34931 | ||||||||
\(471\) | 9.58195e6 | 1.99022 | ||||||||
\(472\) | −1.38238e7 | −2.85610 | ||||||||
\(473\) | −157851. | −0.0324411 | ||||||||
\(474\) | 3.84031e6 | 0.785091 | ||||||||
\(475\) | −1.23479e7 | −2.51107 | ||||||||
\(476\) | −2.12038e6 | −0.428939 | ||||||||
\(477\) | −1.97636e6 | −0.397713 | ||||||||
\(478\) | −51300.6 | −0.0102696 | ||||||||
\(479\) | 8.18229e6 | 1.62943 | 0.814716 | − | 0.579860i | \(-0.196893\pi\) | ||||
0.814716 | + | 0.579860i | \(0.196893\pi\) | |||||||
\(480\) | −2.95386e7 | −5.85176 | ||||||||
\(481\) | −590425. | −0.116360 | ||||||||
\(482\) | −9.67615e6 | −1.89708 | ||||||||
\(483\) | 1.01118e6 | 0.197224 | ||||||||
\(484\) | −1.21304e7 | −2.35376 | ||||||||
\(485\) | 7.29356e6 | 1.40794 | ||||||||
\(486\) | −4.00865e6 | −0.769853 | ||||||||
\(487\) | −1.84424e6 | −0.352367 | −0.176184 | − | 0.984357i | \(-0.556375\pi\) | ||||
−0.176184 | + | 0.984357i | \(0.556375\pi\) | |||||||
\(488\) | 1.93780e7 | 3.68350 | ||||||||
\(489\) | 2.88465e6 | 0.545534 | ||||||||
\(490\) | 1.50115e7 | 2.82445 | ||||||||
\(491\) | −4.29014e6 | −0.803096 | −0.401548 | − | 0.915838i | \(-0.631528\pi\) | ||||
−0.401548 | + | 0.915838i | \(0.631528\pi\) | |||||||
\(492\) | −7.66248e6 | −1.42711 | ||||||||
\(493\) | 9.92009e6 | 1.83822 | ||||||||
\(494\) | −6.74330e6 | −1.24324 | ||||||||
\(495\) | −3.80339e6 | −0.697683 | ||||||||
\(496\) | −7.85806e6 | −1.43420 | ||||||||
\(497\) | −177454. | −0.0322252 | ||||||||
\(498\) | 2.84108e6 | 0.513346 | ||||||||
\(499\) | −7.80338e6 | −1.40291 | −0.701457 | − | 0.712711i | \(-0.747467\pi\) | ||||
−0.701457 | + | 0.712711i | \(0.747467\pi\) | |||||||
\(500\) | 8.85396e6 | 1.58384 | ||||||||
\(501\) | 5.14111e6 | 0.915087 | ||||||||
\(502\) | −1.54922e7 | −2.74381 | ||||||||
\(503\) | 673490. | 0.118689 | 0.0593446 | − | 0.998238i | \(-0.481099\pi\) | ||||
0.0593446 | + | 0.998238i | \(0.481099\pi\) | |||||||
\(504\) | 5.01886e6 | 0.880094 | ||||||||
\(505\) | 6.49397e6 | 1.13314 | ||||||||
\(506\) | −1.66864e6 | −0.289725 | ||||||||
\(507\) | −8.76589e6 | −1.51452 | ||||||||
\(508\) | 2.82246e7 | 4.85253 | ||||||||
\(509\) | 9.44081e6 | 1.61516 | 0.807579 | − | 0.589760i | \(-0.200778\pi\) | ||||
0.807579 | + | 0.589760i | \(0.200778\pi\) | |||||||
\(510\) | −3.41098e7 | −5.80703 | ||||||||
\(511\) | −696821. | −0.118051 | ||||||||
\(512\) | 9.17757e6 | 1.54722 | ||||||||
\(513\) | −2.07510e7 | −3.48134 | ||||||||
\(514\) | 8.56659e6 | 1.43021 | ||||||||
\(515\) | 2.55334e6 | 0.424220 | ||||||||
\(516\) | 4.01069e6 | 0.663124 | ||||||||
\(517\) | 603210. | 0.0992527 | ||||||||
\(518\) | 537759. | 0.0880569 | ||||||||
\(519\) | 1.35199e7 | 2.20321 | ||||||||
\(520\) | 9.82365e6 | 1.59318 | ||||||||
\(521\) | −1.01037e7 | −1.63074 | −0.815369 | − | 0.578941i | \(-0.803466\pi\) | ||||
−0.815369 | + | 0.578941i | \(0.803466\pi\) | |||||||
\(522\) | −3.95046e7 | −6.34559 | ||||||||
\(523\) | 1.22441e6 | 0.195737 | 0.0978687 | − | 0.995199i | \(-0.468797\pi\) | ||||
0.0978687 | + | 0.995199i | \(0.468797\pi\) | |||||||
\(524\) | −4.82872e6 | −0.768252 | ||||||||
\(525\) | −2.40647e6 | −0.381049 | ||||||||
\(526\) | −7.28565e6 | −1.14816 | ||||||||
\(527\) | −3.98455e6 | −0.624961 | ||||||||
\(528\) | −6.27953e6 | −0.980262 | ||||||||
\(529\) | −2.99120e6 | −0.464735 | ||||||||
\(530\) | 3.52336e6 | 0.544838 | ||||||||
\(531\) | 1.43617e7 | 2.21039 | ||||||||
\(532\) | 4.36944e6 | 0.669340 | ||||||||
\(533\) | 809239. | 0.123384 | ||||||||
\(534\) | 2.52259e7 | 3.82819 | ||||||||
\(535\) | −1.73539e7 | −2.62127 | ||||||||
\(536\) | 7.31240e6 | 1.09938 | ||||||||
\(537\) | 1.02972e7 | 1.54093 | ||||||||
\(538\) | 8.00133e6 | 1.19181 | ||||||||
\(539\) | 1.40132e6 | 0.207761 | ||||||||
\(540\) | 5.08604e7 | 7.50577 | ||||||||
\(541\) | −2.66077e6 | −0.390853 | −0.195426 | − | 0.980718i | \(-0.562609\pi\) | ||||
−0.195426 | + | 0.980718i | \(0.562609\pi\) | |||||||
\(542\) | −1.00463e7 | −1.46895 | ||||||||
\(543\) | 1.26696e7 | 1.84402 | ||||||||
\(544\) | −1.67804e7 | −2.43112 | ||||||||
\(545\) | −3.42745e6 | −0.494288 | ||||||||
\(546\) | −1.31420e6 | −0.188659 | ||||||||
\(547\) | 7.44368e6 | 1.06370 | 0.531850 | − | 0.846839i | \(-0.321497\pi\) | ||||
0.531850 | + | 0.846839i | \(0.321497\pi\) | |||||||
\(548\) | −2.44385e7 | −3.47634 | ||||||||
\(549\) | −2.01320e7 | −2.85072 | ||||||||
\(550\) | 3.97114e6 | 0.559768 | ||||||||
\(551\) | −2.04423e7 | −2.86847 | ||||||||
\(552\) | 2.51996e7 | 3.52002 | ||||||||
\(553\) | 262801. | 0.0365438 | ||||||||
\(554\) | −1.08883e7 | −1.50725 | ||||||||
\(555\) | 6.15438e6 | 0.848110 | ||||||||
\(556\) | −1.52843e7 | −2.09680 | ||||||||
\(557\) | 5.55246e6 | 0.758311 | 0.379155 | − | 0.925333i | \(-0.376215\pi\) | ||||
0.379155 | + | 0.925333i | \(0.376215\pi\) | |||||||
\(558\) | 1.58676e7 | 2.15738 | ||||||||
\(559\) | −423571. | −0.0573320 | ||||||||
\(560\) | −4.60337e6 | −0.620305 | ||||||||
\(561\) | −3.18414e6 | −0.427154 | ||||||||
\(562\) | −2.15998e7 | −2.88475 | ||||||||
\(563\) | −2.05400e6 | −0.273105 | −0.136552 | − | 0.990633i | \(-0.543602\pi\) | ||||
−0.136552 | + | 0.990633i | \(0.543602\pi\) | |||||||
\(564\) | −1.53264e7 | −2.02881 | ||||||||
\(565\) | 3.60307e6 | 0.474845 | ||||||||
\(566\) | 2.49618e7 | 3.27518 | ||||||||
\(567\) | −1.57424e6 | −0.205643 | ||||||||
\(568\) | −4.42234e6 | −0.575150 | ||||||||
\(569\) | 5.13151e6 | 0.664453 | 0.332227 | − | 0.943200i | \(-0.392200\pi\) | ||||
0.332227 | + | 0.943200i | \(0.392200\pi\) | |||||||
\(570\) | 7.02898e7 | 9.06161 | ||||||||
\(571\) | −1.13394e7 | −1.45546 | −0.727730 | − | 0.685863i | \(-0.759425\pi\) | ||||
−0.727730 | + | 0.685863i | \(0.759425\pi\) | |||||||
\(572\) | 1.54286e6 | 0.197167 | ||||||||
\(573\) | −617664. | −0.0785898 | ||||||||
\(574\) | −737055. | −0.0933728 | ||||||||
\(575\) | −8.19899e6 | −1.03417 | ||||||||
\(576\) | 2.29091e7 | 2.87708 | ||||||||
\(577\) | −9.19195e6 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(578\) | −4.42552e6 | −0.550992 | ||||||||
\(579\) | 2.28245e7 | 2.82946 | ||||||||
\(580\) | 5.01037e7 | 6.18443 | ||||||||
\(581\) | 194421. | 0.0238948 | ||||||||
\(582\) | −2.43160e7 | −2.97567 | ||||||||
\(583\) | 328904. | 0.0400772 | ||||||||
\(584\) | −1.73655e7 | −2.10695 | ||||||||
\(585\) | −1.02058e7 | −1.23299 | ||||||||
\(586\) | −1.56506e7 | −1.88273 | ||||||||
\(587\) | 7.32138e6 | 0.876997 | 0.438498 | − | 0.898732i | \(-0.355510\pi\) | ||||
0.438498 | + | 0.898732i | \(0.355510\pi\) | |||||||
\(588\) | −3.56047e7 | −4.24683 | ||||||||
\(589\) | 8.21094e6 | 0.975225 | ||||||||
\(590\) | −2.56033e7 | −3.02807 | ||||||||
\(591\) | 2.20528e7 | 2.59714 | ||||||||
\(592\) | 6.89498e6 | 0.808591 | ||||||||
\(593\) | 8.89330e6 | 1.03855 | 0.519274 | − | 0.854608i | \(-0.326203\pi\) | ||||
0.519274 | + | 0.854608i | \(0.326203\pi\) | |||||||
\(594\) | 6.67363e6 | 0.776061 | ||||||||
\(595\) | −2.33421e6 | −0.270301 | ||||||||
\(596\) | −3.58965e7 | −4.13939 | ||||||||
\(597\) | −5.16758e6 | −0.593406 | ||||||||
\(598\) | −4.47755e6 | −0.512021 | ||||||||
\(599\) | 7.52622e6 | 0.857057 | 0.428529 | − | 0.903528i | \(-0.359032\pi\) | ||||
0.428529 | + | 0.903528i | \(0.359032\pi\) | |||||||
\(600\) | −5.99716e7 | −6.80092 | ||||||||
\(601\) | 1.53849e7 | 1.73743 | 0.868716 | − | 0.495311i | \(-0.164946\pi\) | ||||
0.868716 | + | 0.495311i | \(0.164946\pi\) | |||||||
\(602\) | 385789. | 0.0433869 | ||||||||
\(603\) | −7.59690e6 | −0.850830 | ||||||||
\(604\) | −3.99081e7 | −4.45112 | ||||||||
\(605\) | −1.33537e7 | −1.48325 | ||||||||
\(606\) | −2.16503e7 | −2.39487 | ||||||||
\(607\) | −1.10155e7 | −1.21348 | −0.606740 | − | 0.794900i | \(-0.707523\pi\) | ||||
−0.606740 | + | 0.794900i | \(0.707523\pi\) | |||||||
\(608\) | 3.45793e7 | 3.79365 | ||||||||
\(609\) | −3.98397e6 | −0.435285 | ||||||||
\(610\) | 3.58903e7 | 3.90528 | ||||||||
\(611\) | 1.61863e6 | 0.175406 | ||||||||
\(612\) | 5.48978e7 | 5.92484 | ||||||||
\(613\) | −8.89814e6 | −0.956419 | −0.478209 | − | 0.878246i | \(-0.658714\pi\) | ||||
−0.478209 | + | 0.878246i | \(0.658714\pi\) | |||||||
\(614\) | 1.71194e7 | 1.83260 | ||||||||
\(615\) | −8.43522e6 | −0.899309 | ||||||||
\(616\) | −835235. | −0.0886864 | ||||||||
\(617\) | 7.40581e6 | 0.783177 | 0.391588 | − | 0.920140i | \(-0.371926\pi\) | ||||
0.391588 | + | 0.920140i | \(0.371926\pi\) | |||||||
\(618\) | −8.51259e6 | −0.896583 | ||||||||
\(619\) | 1.41475e7 | 1.48406 | 0.742032 | − | 0.670364i | \(-0.233862\pi\) | ||||
0.742032 | + | 0.670364i | \(0.233862\pi\) | |||||||
\(620\) | −2.01249e7 | −2.10259 | ||||||||
\(621\) | −1.37787e7 | −1.43377 | ||||||||
\(622\) | −2.18264e7 | −2.26207 | ||||||||
\(623\) | 1.72627e6 | 0.178192 | ||||||||
\(624\) | −1.68502e7 | −1.73238 | ||||||||
\(625\) | −4.05719e6 | −0.415456 | ||||||||
\(626\) | 3.64267e6 | 0.371522 | ||||||||
\(627\) | 6.56153e6 | 0.666555 | ||||||||
\(628\) | 2.74929e7 | 2.78177 | ||||||||
\(629\) | 3.49621e6 | 0.352347 | ||||||||
\(630\) | 9.29549e6 | 0.933085 | ||||||||
\(631\) | 9.57148e6 | 0.956986 | 0.478493 | − | 0.878091i | \(-0.341183\pi\) | ||||
0.478493 | + | 0.878091i | \(0.341183\pi\) | |||||||
\(632\) | 6.54927e6 | 0.652229 | ||||||||
\(633\) | 9.00781e6 | 0.893532 | ||||||||
\(634\) | −6.04906e6 | −0.597675 | ||||||||
\(635\) | 3.10710e7 | 3.05788 | ||||||||
\(636\) | −8.35680e6 | −0.819214 | ||||||||
\(637\) | 3.76023e6 | 0.367169 | ||||||||
\(638\) | 6.57433e6 | 0.639440 | ||||||||
\(639\) | 4.59440e6 | 0.445119 | ||||||||
\(640\) | −6.46315e6 | −0.623727 | ||||||||
\(641\) | −637566. | −0.0612887 | −0.0306443 | − | 0.999530i | \(-0.509756\pi\) | ||||
−0.0306443 | + | 0.999530i | \(0.509756\pi\) | |||||||
\(642\) | 5.78561e7 | 5.54002 | ||||||||
\(643\) | −1.89702e7 | −1.80944 | −0.904718 | − | 0.426010i | \(-0.859919\pi\) | ||||
−0.904718 | + | 0.426010i | \(0.859919\pi\) | |||||||
\(644\) | 2.90131e6 | 0.275664 | ||||||||
\(645\) | 4.41516e6 | 0.417876 | ||||||||
\(646\) | 3.99306e7 | 3.76465 | ||||||||
\(647\) | 2.02807e7 | 1.90468 | 0.952338 | − | 0.305044i | \(-0.0986713\pi\) | ||||
0.952338 | + | 0.305044i | \(0.0986713\pi\) | |||||||
\(648\) | −3.92318e7 | −3.67029 | ||||||||
\(649\) | −2.39006e6 | −0.222739 | ||||||||
\(650\) | 1.06560e7 | 0.989258 | ||||||||
\(651\) | 1.60022e6 | 0.147989 | ||||||||
\(652\) | 8.27676e6 | 0.762503 | ||||||||
\(653\) | −3.76628e6 | −0.345645 | −0.172822 | − | 0.984953i | \(-0.555289\pi\) | ||||
−0.172822 | + | 0.984953i | \(0.555289\pi\) | |||||||
\(654\) | 1.14268e7 | 1.04467 | ||||||||
\(655\) | −5.31568e6 | −0.484123 | ||||||||
\(656\) | −9.45029e6 | −0.857404 | ||||||||
\(657\) | 1.80411e7 | 1.63061 | ||||||||
\(658\) | −1.47425e6 | −0.132741 | ||||||||
\(659\) | −1.70994e7 | −1.53379 | −0.766897 | − | 0.641770i | \(-0.778200\pi\) | ||||
−0.766897 | + | 0.641770i | \(0.778200\pi\) | |||||||
\(660\) | −1.60822e7 | −1.43709 | ||||||||
\(661\) | 875240. | 0.0779154 | 0.0389577 | − | 0.999241i | \(-0.487596\pi\) | ||||
0.0389577 | + | 0.999241i | \(0.487596\pi\) | |||||||
\(662\) | 1.18887e7 | 1.05436 | ||||||||
\(663\) | −8.54417e6 | −0.754894 | ||||||||
\(664\) | 4.84518e6 | 0.426472 | ||||||||
\(665\) | 4.81009e6 | 0.421793 | ||||||||
\(666\) | −1.39229e7 | −1.21631 | ||||||||
\(667\) | −1.35737e7 | −1.18136 | ||||||||
\(668\) | 1.47511e7 | 1.27904 | ||||||||
\(669\) | −4.58324e6 | −0.395920 | ||||||||
\(670\) | 1.35434e7 | 1.16557 | ||||||||
\(671\) | 3.35034e6 | 0.287265 | ||||||||
\(672\) | 6.73913e6 | 0.575679 | ||||||||
\(673\) | −1.59835e7 | −1.36030 | −0.680149 | − | 0.733074i | \(-0.738085\pi\) | ||||
−0.680149 | + | 0.733074i | \(0.738085\pi\) | |||||||
\(674\) | 3.89844e6 | 0.330553 | ||||||||
\(675\) | 3.27914e7 | 2.77013 | ||||||||
\(676\) | −2.51515e7 | −2.11688 | ||||||||
\(677\) | −2.27744e7 | −1.90974 | −0.954871 | − | 0.297020i | \(-0.904007\pi\) | ||||
−0.954871 | + | 0.297020i | \(0.904007\pi\) | |||||||
\(678\) | −1.20123e7 | −1.00358 | ||||||||
\(679\) | −1.66400e6 | −0.138509 | ||||||||
\(680\) | −5.81709e7 | −4.82429 | ||||||||
\(681\) | −4.26888e6 | −0.352733 | ||||||||
\(682\) | −2.64068e6 | −0.217398 | ||||||||
\(683\) | −1.16349e7 | −0.954354 | −0.477177 | − | 0.878807i | \(-0.658340\pi\) | ||||
−0.477177 | + | 0.878807i | \(0.658340\pi\) | |||||||
\(684\) | −1.13128e8 | −9.24545 | ||||||||
\(685\) | −2.69030e7 | −2.19066 | ||||||||
\(686\) | −6.93156e6 | −0.562368 | ||||||||
\(687\) | −2.79325e7 | −2.25797 | ||||||||
\(688\) | 4.94647e6 | 0.398404 | ||||||||
\(689\) | 882566. | 0.0708271 | ||||||||
\(690\) | 4.66724e7 | 3.73197 | ||||||||
\(691\) | −5.50626e6 | −0.438694 | −0.219347 | − | 0.975647i | \(-0.570393\pi\) | ||||
−0.219347 | + | 0.975647i | \(0.570393\pi\) | |||||||
\(692\) | 3.87918e7 | 3.07946 | ||||||||
\(693\) | 867731. | 0.0686360 | ||||||||
\(694\) | −3.92444e6 | −0.309300 | ||||||||
\(695\) | −1.68257e7 | −1.32133 | ||||||||
\(696\) | −9.92848e7 | −7.76890 | ||||||||
\(697\) | −4.79192e6 | −0.373618 | ||||||||
\(698\) | 2.25970e7 | 1.75554 | ||||||||
\(699\) | 640633. | 0.0495926 | ||||||||
\(700\) | −6.90473e6 | −0.532600 | ||||||||
\(701\) | −1.26842e7 | −0.974916 | −0.487458 | − | 0.873146i | \(-0.662076\pi\) | ||||
−0.487458 | + | 0.873146i | \(0.662076\pi\) | |||||||
\(702\) | 1.79077e7 | 1.37151 | ||||||||
\(703\) | −7.20462e6 | −0.549823 | ||||||||
\(704\) | −3.81251e6 | −0.289921 | ||||||||
\(705\) | −1.68720e7 | −1.27848 | ||||||||
\(706\) | 3.03004e7 | 2.28789 | ||||||||
\(707\) | −1.48158e6 | −0.111475 | ||||||||
\(708\) | 6.07266e7 | 4.55298 | ||||||||
\(709\) | 919145. | 0.0686702 | 0.0343351 | − | 0.999410i | \(-0.489069\pi\) | ||||
0.0343351 | + | 0.999410i | \(0.489069\pi\) | |||||||
\(710\) | −8.19067e6 | −0.609780 | ||||||||
\(711\) | −6.80408e6 | −0.504772 | ||||||||
\(712\) | 4.30203e7 | 3.18034 | ||||||||
\(713\) | 5.45207e6 | 0.401640 | ||||||||
\(714\) | 7.78203e6 | 0.571278 | ||||||||
\(715\) | 1.69845e6 | 0.124247 | ||||||||
\(716\) | 2.95452e7 | 2.15379 | ||||||||
\(717\) | 133947. | 0.00973049 | ||||||||
\(718\) | −6.81699e6 | −0.493493 | ||||||||
\(719\) | 7.21135e6 | 0.520228 | 0.260114 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260114 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(720\) | 1.19184e8 | 8.56814 | ||||||||
\(721\) | −582536. | −0.0417335 | ||||||||
\(722\) | −5.62102e7 | −4.01303 | ||||||||
\(723\) | 2.52646e7 | 1.79749 | ||||||||
\(724\) | 3.63522e7 | 2.57742 | ||||||||
\(725\) | 3.23035e7 | 2.28247 | ||||||||
\(726\) | 4.45201e7 | 3.13483 | ||||||||
\(727\) | −4.15671e6 | −0.291685 | −0.145842 | − | 0.989308i | \(-0.546589\pi\) | ||||
−0.145842 | + | 0.989308i | \(0.546589\pi\) | |||||||
\(728\) | −2.24123e6 | −0.156732 | ||||||||
\(729\) | −8.84023e6 | −0.616091 | ||||||||
\(730\) | −3.21628e7 | −2.23381 | ||||||||
\(731\) | 2.50818e6 | 0.173607 | ||||||||
\(732\) | −8.51256e7 | −5.87195 | ||||||||
\(733\) | 4.05351e6 | 0.278658 | 0.139329 | − | 0.990246i | \(-0.455505\pi\) | ||||
0.139329 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(734\) | −3.22254e7 | −2.20779 | ||||||||
\(735\) | −3.91954e7 | −2.67619 | ||||||||
\(736\) | 2.29606e7 | 1.56239 | ||||||||
\(737\) | 1.26427e6 | 0.0857375 | ||||||||
\(738\) | 1.90828e7 | 1.28974 | ||||||||
\(739\) | 1.27176e7 | 0.856629 | 0.428315 | − | 0.903630i | \(-0.359108\pi\) | ||||
0.428315 | + | 0.903630i | \(0.359108\pi\) | |||||||
\(740\) | 1.76584e7 | 1.18542 | ||||||||
\(741\) | 1.76069e7 | 1.17798 | ||||||||
\(742\) | −803842. | −0.0535995 | ||||||||
\(743\) | −1.86660e6 | −0.124045 | −0.0620224 | − | 0.998075i | \(-0.519755\pi\) | ||||
−0.0620224 | + | 0.998075i | \(0.519755\pi\) | |||||||
\(744\) | 3.98792e7 | 2.64128 | ||||||||
\(745\) | −3.95165e7 | −2.60848 | ||||||||
\(746\) | −3.72942e7 | −2.45355 | ||||||||
\(747\) | −5.03369e6 | −0.330054 | ||||||||
\(748\) | −9.13605e6 | −0.597041 | ||||||||
\(749\) | 3.95922e6 | 0.257873 | ||||||||
\(750\) | −3.24951e7 | −2.10943 | ||||||||
\(751\) | 2.61334e7 | 1.69081 | 0.845407 | − | 0.534122i | \(-0.179358\pi\) | ||||
0.845407 | + | 0.534122i | \(0.179358\pi\) | |||||||
\(752\) | −1.89023e7 | −1.21891 | ||||||||
\(753\) | 4.04505e7 | 2.59978 | ||||||||
\(754\) | 1.76413e7 | 1.13006 | ||||||||
\(755\) | −4.39328e7 | −2.80492 | ||||||||
\(756\) | −1.16036e7 | −0.738396 | ||||||||
\(757\) | 1.20591e6 | 0.0764846 | 0.0382423 | − | 0.999268i | \(-0.487824\pi\) | ||||
0.0382423 | + | 0.999268i | \(0.487824\pi\) | |||||||
\(758\) | 4.13591e7 | 2.61456 | ||||||||
\(759\) | 4.35685e6 | 0.274516 | ||||||||
\(760\) | 1.19872e8 | 7.52810 | ||||||||
\(761\) | −1.63050e6 | −0.102061 | −0.0510303 | − | 0.998697i | \(-0.516251\pi\) | ||||
−0.0510303 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(762\) | −1.03588e8 | −6.46280 | ||||||||
\(763\) | 781961. | 0.0486266 | ||||||||
\(764\) | −1.77223e6 | −0.109846 | ||||||||
\(765\) | 6.04341e7 | 3.73361 | ||||||||
\(766\) | 1.36567e7 | 0.840958 | ||||||||
\(767\) | −6.41337e6 | −0.393639 | ||||||||
\(768\) | −1.77448e7 | −1.08560 | ||||||||
\(769\) | −3.03077e6 | −0.184815 | −0.0924074 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924074 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(770\) | −1.54695e6 | −0.0940262 | ||||||||
\(771\) | −2.23676e7 | −1.35513 | ||||||||
\(772\) | 6.54888e7 | 3.95480 | ||||||||
\(773\) | 1.56440e7 | 0.941669 | 0.470834 | − | 0.882222i | \(-0.343953\pi\) | ||||
0.470834 | + | 0.882222i | \(0.343953\pi\) | |||||||
\(774\) | −9.98831e6 | −0.599294 | ||||||||
\(775\) | −1.29752e7 | −0.775995 | ||||||||
\(776\) | −4.14686e7 | −2.47210 | ||||||||
\(777\) | −1.40410e6 | −0.0834346 | ||||||||
\(778\) | 1.05874e6 | 0.0627104 | ||||||||
\(779\) | 9.87468e6 | 0.583015 | ||||||||
\(780\) | −4.31542e7 | −2.53973 | ||||||||
\(781\) | −764595. | −0.0448543 | ||||||||
\(782\) | 2.65139e7 | 1.55045 | ||||||||
\(783\) | 5.42871e7 | 3.16441 | ||||||||
\(784\) | −4.39120e7 | −2.55149 | ||||||||
\(785\) | 3.02655e7 | 1.75297 | ||||||||
\(786\) | 1.77220e7 | 1.02319 | ||||||||
\(787\) | 2.77750e7 | 1.59852 | 0.799260 | − | 0.600986i | \(-0.205225\pi\) | ||||
0.799260 | + | 0.600986i | \(0.205225\pi\) | |||||||
\(788\) | 6.32747e7 | 3.63007 | ||||||||
\(789\) | 1.90230e7 | 1.08789 | ||||||||
\(790\) | 1.21300e7 | 0.691500 | ||||||||
\(791\) | −822028. | −0.0467138 | ||||||||
\(792\) | 2.16247e7 | 1.22501 | ||||||||
\(793\) | 8.99016e6 | 0.507673 | ||||||||
\(794\) | −3.54854e7 | −1.99756 | ||||||||
\(795\) | −9.19957e6 | −0.516237 | ||||||||
\(796\) | −1.48270e7 | −0.829414 | ||||||||
\(797\) | −646020. | −0.0360247 | −0.0180123 | − | 0.999838i | \(-0.505734\pi\) | ||||
−0.0180123 | + | 0.999838i | \(0.505734\pi\) | |||||||
\(798\) | −1.60364e7 | −0.891454 | ||||||||
\(799\) | −9.58473e6 | −0.531145 | ||||||||
\(800\) | −5.46432e7 | −3.01864 | ||||||||
\(801\) | −4.46941e7 | −2.46132 | ||||||||
\(802\) | −4.98519e7 | −2.73682 | ||||||||
\(803\) | −3.00239e6 | −0.164315 | ||||||||
\(804\) | −3.21226e7 | −1.75255 | ||||||||
\(805\) | 3.19390e6 | 0.173713 | ||||||||
\(806\) | −7.08588e6 | −0.384199 | ||||||||
\(807\) | −2.08917e7 | −1.12925 | ||||||||
\(808\) | −3.69224e7 | −1.98958 | ||||||||
\(809\) | −1.67691e6 | −0.0900823 | −0.0450412 | − | 0.998985i | \(-0.514342\pi\) | ||||
−0.0450412 | + | 0.998985i | \(0.514342\pi\) | |||||||
\(810\) | −7.26617e7 | −3.89128 | ||||||||
\(811\) | 1.09231e7 | 0.583169 | 0.291585 | − | 0.956545i | \(-0.405817\pi\) | ||||
0.291585 | + | 0.956545i | \(0.405817\pi\) | |||||||
\(812\) | −1.14310e7 | −0.608406 | ||||||||
\(813\) | 2.62310e7 | 1.39184 | ||||||||
\(814\) | 2.31704e6 | 0.122567 | ||||||||
\(815\) | 9.11145e6 | 0.480500 | ||||||||
\(816\) | 9.97789e7 | 5.24582 | ||||||||
\(817\) | −5.16860e6 | −0.270905 | ||||||||
\(818\) | 886346. | 0.0463148 | ||||||||
\(819\) | 2.32843e6 | 0.121298 | ||||||||
\(820\) | −2.42027e7 | −1.25698 | ||||||||
\(821\) | 1.94364e7 | 1.00637 | 0.503186 | − | 0.864178i | \(-0.332161\pi\) | ||||
0.503186 | + | 0.864178i | \(0.332161\pi\) | |||||||
\(822\) | 8.96921e7 | 4.62993 | ||||||||
\(823\) | −3.08462e7 | −1.58746 | −0.793730 | − | 0.608271i | \(-0.791864\pi\) | ||||
−0.793730 | + | 0.608271i | \(0.791864\pi\) | |||||||
\(824\) | −1.45174e7 | −0.744853 | ||||||||
\(825\) | −1.03687e7 | −0.530384 | ||||||||
\(826\) | 5.84130e6 | 0.297892 | ||||||||
\(827\) | −1.97925e7 | −1.00632 | −0.503161 | − | 0.864193i | \(-0.667830\pi\) | ||||
−0.503161 | + | 0.864193i | \(0.667830\pi\) | |||||||
\(828\) | −7.51167e7 | −3.80768 | ||||||||
\(829\) | −1.75755e7 | −0.888223 | −0.444111 | − | 0.895972i | \(-0.646481\pi\) | ||||
−0.444111 | + | 0.895972i | \(0.646481\pi\) | |||||||
\(830\) | 8.97382e6 | 0.452150 | ||||||||
\(831\) | 2.84296e7 | 1.42813 | ||||||||
\(832\) | −1.02303e7 | −0.512367 | ||||||||
\(833\) | −2.22663e7 | −1.11182 | ||||||||
\(834\) | 5.60951e7 | 2.79261 | ||||||||
\(835\) | 1.62387e7 | 0.805999 | ||||||||
\(836\) | 1.88266e7 | 0.931657 | ||||||||
\(837\) | −2.18052e7 | −1.07584 | ||||||||
\(838\) | 1.52893e7 | 0.752103 | ||||||||
\(839\) | −1.50238e7 | −0.736842 | −0.368421 | − | 0.929659i | \(-0.620101\pi\) | ||||
−0.368421 | + | 0.929659i | \(0.620101\pi\) | |||||||
\(840\) | 2.33618e7 | 1.14237 | ||||||||
\(841\) | 3.29682e7 | 1.60733 | ||||||||
\(842\) | −4.94837e7 | −2.40537 | ||||||||
\(843\) | 5.63974e7 | 2.73332 | ||||||||
\(844\) | 2.58456e7 | 1.24891 | ||||||||
\(845\) | −2.76879e7 | −1.33398 | ||||||||
\(846\) | 3.81691e7 | 1.83352 | ||||||||
\(847\) | 3.04661e6 | 0.145918 | ||||||||
\(848\) | −1.03066e7 | −0.492183 | ||||||||
\(849\) | −6.51759e7 | −3.10326 | ||||||||
\(850\) | −6.30995e7 | −2.99556 | ||||||||
\(851\) | −4.78387e6 | −0.226441 | ||||||||
\(852\) | 1.94269e7 | 0.916861 | ||||||||
\(853\) | 3.88390e7 | 1.82766 | 0.913829 | − | 0.406099i | \(-0.133111\pi\) | ||||
0.913829 | + | 0.406099i | \(0.133111\pi\) | |||||||
\(854\) | −8.18824e6 | −0.384190 | ||||||||
\(855\) | −1.24536e8 | −5.82613 | ||||||||
\(856\) | 9.86679e7 | 4.60248 | ||||||||
\(857\) | −3.57330e6 | −0.166195 | −0.0830975 | − | 0.996541i | \(-0.526481\pi\) | ||||
−0.0830975 | + | 0.996541i | \(0.526481\pi\) | |||||||
\(858\) | −5.66247e6 | −0.262596 | ||||||||
\(859\) | 3.27850e6 | 0.151598 | 0.0757988 | − | 0.997123i | \(-0.475849\pi\) | ||||
0.0757988 | + | 0.997123i | \(0.475849\pi\) | |||||||
\(860\) | 1.26681e7 | 0.584073 | ||||||||
\(861\) | 1.92447e6 | 0.0884713 | ||||||||
\(862\) | −3.52014e7 | −1.61359 | ||||||||
\(863\) | 1.93441e7 | 0.884139 | 0.442070 | − | 0.896981i | \(-0.354244\pi\) | ||||
0.442070 | + | 0.896981i | \(0.354244\pi\) | |||||||
\(864\) | −9.18298e7 | −4.18504 | ||||||||
\(865\) | 4.27039e7 | 1.94056 | ||||||||
\(866\) | −6.63042e6 | −0.300432 | ||||||||
\(867\) | 1.15551e7 | 0.522068 | ||||||||
\(868\) | 4.59142e6 | 0.206846 | ||||||||
\(869\) | 1.13233e6 | 0.0508655 | ||||||||
\(870\) | −1.83886e8 | −8.23667 | ||||||||
\(871\) | 3.39248e6 | 0.151521 | ||||||||
\(872\) | 1.94873e7 | 0.867881 | ||||||||
\(873\) | 4.30820e7 | 1.91320 | ||||||||
\(874\) | −5.46370e7 | −2.41940 | ||||||||
\(875\) | −2.22371e6 | −0.0981880 | ||||||||
\(876\) | 7.62847e7 | 3.35875 | ||||||||
\(877\) | −2.57531e7 | −1.13066 | −0.565329 | − | 0.824866i | \(-0.691251\pi\) | ||||
−0.565329 | + | 0.824866i | \(0.691251\pi\) | |||||||
\(878\) | −6.58114e7 | −2.88115 | ||||||||
\(879\) | 4.08642e7 | 1.78390 | ||||||||
\(880\) | −1.98345e7 | −0.863405 | ||||||||
\(881\) | 4.39384e6 | 0.190724 | 0.0953618 | − | 0.995443i | \(-0.469599\pi\) | ||||
0.0953618 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(882\) | 8.86708e7 | 3.83804 | ||||||||
\(883\) | 2.21529e7 | 0.956156 | 0.478078 | − | 0.878317i | \(-0.341334\pi\) | ||||
0.478078 | + | 0.878317i | \(0.341334\pi\) | |||||||
\(884\) | −2.45153e7 | −1.05513 | ||||||||
\(885\) | 6.68507e7 | 2.86912 | ||||||||
\(886\) | −6.93226e7 | −2.96681 | ||||||||
\(887\) | −4.36187e7 | −1.86150 | −0.930750 | − | 0.365655i | \(-0.880845\pi\) | ||||
−0.930750 | + | 0.365655i | \(0.880845\pi\) | |||||||
\(888\) | −3.49917e7 | −1.48913 | ||||||||
\(889\) | −7.08874e6 | −0.300825 | ||||||||
\(890\) | 7.96785e7 | 3.37183 | ||||||||
\(891\) | −6.78294e6 | −0.286236 | ||||||||
\(892\) | −1.31504e7 | −0.553385 | ||||||||
\(893\) | 1.97512e7 | 0.828828 | ||||||||
\(894\) | 1.31744e8 | 5.51300 | ||||||||
\(895\) | 3.25247e7 | 1.35724 | ||||||||
\(896\) | 1.47455e6 | 0.0613604 | ||||||||
\(897\) | 1.16910e7 | 0.485143 | ||||||||
\(898\) | −1.70705e7 | −0.706409 | ||||||||
\(899\) | −2.14808e7 | −0.886443 | ||||||||
\(900\) | 1.78768e8 | 7.35669 | ||||||||
\(901\) | −5.22613e6 | −0.214471 | ||||||||
\(902\) | −3.17574e6 | −0.129966 | ||||||||
\(903\) | −1.00730e6 | −0.0411094 | ||||||||
\(904\) | −2.04858e7 | −0.833742 | ||||||||
\(905\) | 4.00183e7 | 1.62419 | ||||||||
\(906\) | 1.46468e8 | 5.92818 | ||||||||
\(907\) | 1.38621e7 | 0.559515 | 0.279758 | − | 0.960071i | \(-0.409746\pi\) | ||||
0.279758 | + | 0.960071i | \(0.409746\pi\) | |||||||
\(908\) | −1.22484e7 | −0.493022 | ||||||||
\(909\) | 3.83589e7 | 1.53977 | ||||||||
\(910\) | −4.15101e6 | −0.166169 | ||||||||
\(911\) | −2.31037e7 | −0.922329 | −0.461164 | − | 0.887315i | \(-0.652568\pi\) | ||||
−0.461164 | + | 0.887315i | \(0.652568\pi\) | |||||||
\(912\) | −2.05614e8 | −8.18587 | ||||||||
\(913\) | 837702. | 0.0332593 | ||||||||
\(914\) | 6.33085e7 | 2.50666 | ||||||||
\(915\) | −9.37103e7 | −3.70028 | ||||||||
\(916\) | −8.01451e7 | −3.15601 | ||||||||
\(917\) | 1.21275e6 | 0.0476266 | ||||||||
\(918\) | −1.06041e8 | −4.15305 | ||||||||
\(919\) | −2.27313e7 | −0.887842 | −0.443921 | − | 0.896066i | \(-0.646413\pi\) | ||||
−0.443921 | + | 0.896066i | \(0.646413\pi\) | |||||||
\(920\) | 7.95953e7 | 3.10040 | ||||||||
\(921\) | −4.46992e7 | −1.73640 | ||||||||
\(922\) | 2.07526e7 | 0.803978 | ||||||||
\(923\) | −2.05168e6 | −0.0792694 | ||||||||
\(924\) | 3.66910e6 | 0.141377 | ||||||||
\(925\) | 1.13850e7 | 0.437499 | ||||||||
\(926\) | 9.74634e6 | 0.373520 | ||||||||
\(927\) | 1.50822e7 | 0.576455 | ||||||||
\(928\) | −9.04635e7 | −3.44829 | ||||||||
\(929\) | −3.32467e7 | −1.26389 | −0.631945 | − | 0.775013i | \(-0.717743\pi\) | ||||
−0.631945 | + | 0.775013i | \(0.717743\pi\) | |||||||
\(930\) | 7.38607e7 | 2.80031 | ||||||||
\(931\) | 4.58840e7 | 1.73495 | ||||||||
\(932\) | 1.83813e6 | 0.0693165 | ||||||||
\(933\) | 5.69892e7 | 2.14333 | ||||||||
\(934\) | −1.97967e7 | −0.742548 | ||||||||
\(935\) | −1.00574e7 | −0.376233 | ||||||||
\(936\) | 5.80269e7 | 2.16491 | ||||||||
\(937\) | 1.72533e7 | 0.641981 | 0.320991 | − | 0.947082i | \(-0.395984\pi\) | ||||
0.320991 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(938\) | −3.08988e6 | −0.114666 | ||||||||
\(939\) | −9.51110e6 | −0.352019 | ||||||||
\(940\) | −4.84098e7 | −1.78696 | ||||||||
\(941\) | 1.12167e6 | 0.0412945 | 0.0206473 | − | 0.999787i | \(-0.493427\pi\) | ||||
0.0206473 | + | 0.999787i | \(0.493427\pi\) | |||||||
\(942\) | −1.00902e8 | −3.70488 | ||||||||
\(943\) | 6.55679e6 | 0.240111 | ||||||||
\(944\) | 7.48954e7 | 2.73543 | ||||||||
\(945\) | −1.27738e7 | −0.465309 | ||||||||
\(946\) | 1.66225e6 | 0.0603903 | ||||||||
\(947\) | 3.89113e7 | 1.40994 | 0.704970 | − | 0.709237i | \(-0.250960\pi\) | ||||
0.704970 | + | 0.709237i | \(0.250960\pi\) | |||||||
\(948\) | −2.87702e7 | −1.03973 | ||||||||
\(949\) | −8.05647e6 | −0.290388 | ||||||||
\(950\) | 1.30029e8 | 4.67445 | ||||||||
\(951\) | 1.57942e7 | 0.566301 | ||||||||
\(952\) | 1.32715e7 | 0.474600 | ||||||||
\(953\) | −1.79943e7 | −0.641803 | −0.320902 | − | 0.947113i | \(-0.603986\pi\) | ||||
−0.320902 | + | 0.947113i | \(0.603986\pi\) | |||||||
\(954\) | 2.08120e7 | 0.740358 | ||||||||
\(955\) | −1.95095e6 | −0.0692210 | ||||||||
\(956\) | 384326. | 0.0136005 | ||||||||
\(957\) | −1.71657e7 | −0.605874 | ||||||||
\(958\) | −8.61632e7 | −3.03325 | ||||||||
\(959\) | 6.13783e6 | 0.215510 | ||||||||
\(960\) | 1.06637e8 | 3.73449 | ||||||||
\(961\) | −2.00011e7 | −0.698626 | ||||||||
\(962\) | 6.21744e6 | 0.216608 | ||||||||
\(963\) | −1.02507e8 | −3.56194 | ||||||||
\(964\) | 7.24903e7 | 2.51239 | ||||||||
\(965\) | 7.20932e7 | 2.49216 | ||||||||
\(966\) | −1.06482e7 | −0.367140 | ||||||||
\(967\) | 2.31110e7 | 0.794791 | 0.397395 | − | 0.917648i | \(-0.369914\pi\) | ||||
0.397395 | + | 0.917648i | \(0.369914\pi\) | |||||||
\(968\) | 7.59247e7 | 2.60432 | ||||||||
\(969\) | −1.04260e8 | −3.56703 | ||||||||
\(970\) | −7.68045e7 | −2.62094 | ||||||||
\(971\) | −3.50927e7 | −1.19445 | −0.597226 | − | 0.802073i | \(-0.703730\pi\) | ||||
−0.597226 | + | 0.802073i | \(0.703730\pi\) | |||||||
\(972\) | 3.00314e7 | 1.01955 | ||||||||
\(973\) | 3.83871e6 | 0.129988 | ||||||||
\(974\) | 1.94207e7 | 0.655945 | ||||||||
\(975\) | −2.78230e7 | −0.937329 | ||||||||
\(976\) | −1.04987e8 | −3.52786 | ||||||||
\(977\) | 7.20029e6 | 0.241331 | 0.120666 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120666 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(978\) | −3.03767e7 | −1.01553 | ||||||||
\(979\) | 7.43795e6 | 0.248026 | ||||||||
\(980\) | −1.12461e8 | −3.74056 | ||||||||
\(981\) | −2.02455e7 | −0.671669 | ||||||||
\(982\) | 4.51771e7 | 1.49499 | ||||||||
\(983\) | −3.28324e7 | −1.08373 | −0.541863 | − | 0.840467i | \(-0.682281\pi\) | ||||
−0.541863 | + | 0.840467i | \(0.682281\pi\) | |||||||
\(984\) | 4.79597e7 | 1.57902 | ||||||||
\(985\) | 6.96558e7 | 2.28753 | ||||||||
\(986\) | −1.04463e8 | −3.42193 | ||||||||
\(987\) | 3.84929e6 | 0.125773 | ||||||||
\(988\) | 5.05184e7 | 1.64648 | ||||||||
\(989\) | −3.43195e6 | −0.111571 | ||||||||
\(990\) | 4.00514e7 | 1.29876 | ||||||||
\(991\) | 5.19670e7 | 1.68090 | 0.840452 | − | 0.541885i | \(-0.182289\pi\) | ||||
0.840452 | + | 0.541885i | \(0.182289\pi\) | |||||||
\(992\) | 3.63360e7 | 1.17235 | ||||||||
\(993\) | −3.10417e7 | −0.999015 | ||||||||
\(994\) | 1.86867e6 | 0.0599884 | ||||||||
\(995\) | −1.63223e7 | −0.522665 | ||||||||
\(996\) | −2.12844e7 | −0.679849 | ||||||||
\(997\) | −5.30582e6 | −0.169050 | −0.0845249 | − | 0.996421i | \(-0.526937\pi\) | ||||
−0.0845249 | + | 0.996421i | \(0.526937\pi\) | |||||||
\(998\) | 8.21731e7 | 2.61158 | ||||||||
\(999\) | 1.91328e7 | 0.606548 |
(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 | 43.6.a.b.1.1 | ✓ | 10 | |
3.2 | odd | 2 | 387.6.a.e.1.10 | 10 | |||
4.3 | odd | 2 | 688.6.a.h.1.1 | 10 | |||
5.4 | even | 2 | 1075.6.a.b.1.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.b.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
387.6.a.e.1.10 | 10 | 3.2 | odd | 2 | |||
688.6.a.h.1.1 | 10 | 4.3 | odd | 2 | |||
1075.6.a.b.1.10 | 10 | 5.4 | even | 2 |