Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 6052x^{3} - 41130x^{2} + 7064712x + 22607640 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(72.1421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 46.3009 | 0.357145 | 0.178572 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178572 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −592.198 | −1.47566 | −0.737828 | − | 0.674989i | \(-0.764148\pi\) | ||||
−0.737828 | + | 0.674989i | \(0.764148\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 661.340 | 1.08534 | 0.542670 | − | 0.839946i | \(-0.317413\pi\) | ||||
0.542670 | + | 0.839946i | \(0.317413\pi\) | |||||||
\(14\) | 185.204 | 0.252539 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1404.99 | −1.17910 | −0.589552 | − | 0.807730i | \(-0.700696\pi\) | ||||
−0.589552 | + | 0.807730i | \(0.700696\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −416.708 | −0.206198 | ||||||||
\(22\) | −2368.79 | −1.04345 | ||||||||
\(23\) | 4775.78 | 1.88246 | 0.941229 | − | 0.337770i | \(-0.109673\pi\) | ||||
0.941229 | + | 0.337770i | \(0.109673\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2645.36 | 0.767452 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 740.814 | 0.178572 | ||||||||
\(29\) | −178.254 | −0.0393590 | −0.0196795 | − | 0.999806i | \(-0.506265\pi\) | ||||
−0.0196795 | + | 0.999806i | \(0.506265\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | 5053.62 | 0.944492 | 0.472246 | − | 0.881467i | \(-0.343443\pi\) | ||||
0.472246 | + | 0.881467i | \(0.343443\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 5329.78 | 0.851970 | ||||||||
\(34\) | −5619.98 | −0.833753 | ||||||||
\(35\) | 1157.52 | 0.159720 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −3602.75 | −0.432643 | −0.216322 | − | 0.976322i | \(-0.569406\pi\) | ||||
−0.216322 | + | 0.976322i | \(0.569406\pi\) | |||||||
\(38\) | 1444.00 | 0.162221 | ||||||||
\(39\) | −5952.06 | −0.626622 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 15148.4 | 1.40736 | 0.703682 | − | 0.710515i | \(-0.251538\pi\) | ||||
0.703682 | + | 0.710515i | \(0.251538\pi\) | |||||||
\(42\) | −1666.83 | −0.145804 | ||||||||
\(43\) | −22204.5 | −1.83135 | −0.915673 | − | 0.401925i | \(-0.868341\pi\) | ||||
−0.915673 | + | 0.401925i | \(0.868341\pi\) | |||||||
\(44\) | −9475.16 | −0.737828 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | 19103.1 | 1.33110 | ||||||||
\(47\) | 12230.4 | 0.807596 | 0.403798 | − | 0.914848i | \(-0.367690\pi\) | ||||
0.403798 | + | 0.914848i | \(0.367690\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −14663.2 | −0.872448 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | 12645.0 | 0.680757 | ||||||||
\(52\) | 10581.4 | 0.542670 | ||||||||
\(53\) | 9600.78 | 0.469480 | 0.234740 | − | 0.972058i | \(-0.424576\pi\) | ||||
0.234740 | + | 0.972058i | \(0.424576\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | −14804.9 | −0.659933 | ||||||||
\(56\) | 2963.26 | 0.126270 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | −713.016 | −0.0278310 | ||||||||
\(59\) | 2191.79 | 0.0819726 | 0.0409863 | − | 0.999160i | \(-0.486950\pi\) | ||||
0.0409863 | + | 0.999160i | \(0.486950\pi\) | |||||||
\(60\) | −3600.00 | −0.129099 | ||||||||
\(61\) | 926.400 | 0.0318768 | 0.0159384 | − | 0.999873i | \(-0.494926\pi\) | ||||
0.0159384 | + | 0.999873i | \(0.494926\pi\) | |||||||
\(62\) | 20214.5 | 0.667856 | ||||||||
\(63\) | 3750.37 | 0.119048 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 16533.5 | 0.485379 | ||||||||
\(66\) | 21319.1 | 0.602434 | ||||||||
\(67\) | −17934.5 | −0.488094 | −0.244047 | − | 0.969763i | \(-0.578475\pi\) | ||||
−0.244047 | + | 0.969763i | \(0.578475\pi\) | |||||||
\(68\) | −22479.9 | −0.589552 | ||||||||
\(69\) | −42982.1 | −1.08684 | ||||||||
\(70\) | 4630.09 | 0.112939 | ||||||||
\(71\) | 43250.3 | 1.01822 | 0.509112 | − | 0.860700i | \(-0.329974\pi\) | ||||
0.509112 | + | 0.860700i | \(0.329974\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | −13130.3 | −0.288381 | −0.144190 | − | 0.989550i | \(-0.546058\pi\) | ||||
−0.144190 | + | 0.989550i | \(0.546058\pi\) | |||||||
\(74\) | −14411.0 | −0.305925 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 5776.00 | 0.114708 | ||||||||
\(77\) | −27419.3 | −0.527022 | ||||||||
\(78\) | −23808.2 | −0.443089 | ||||||||
\(79\) | 109029. | 1.96551 | 0.982755 | − | 0.184913i | \(-0.0592002\pi\) | ||||
0.982755 | + | 0.184913i | \(0.0592002\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 60593.5 | 0.995157 | ||||||||
\(83\) | 5873.28 | 0.0935806 | 0.0467903 | − | 0.998905i | \(-0.485101\pi\) | ||||
0.0467903 | + | 0.998905i | \(0.485101\pi\) | |||||||
\(84\) | −6667.33 | −0.103099 | ||||||||
\(85\) | −35124.9 | −0.527312 | ||||||||
\(86\) | −88818.1 | −1.29496 | ||||||||
\(87\) | 1604.29 | 0.0227239 | ||||||||
\(88\) | −37900.6 | −0.521723 | ||||||||
\(89\) | 66508.0 | 0.890018 | 0.445009 | − | 0.895526i | \(-0.353200\pi\) | ||||
0.445009 | + | 0.895526i | \(0.353200\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | 30620.6 | 0.387624 | ||||||||
\(92\) | 76412.6 | 0.941229 | ||||||||
\(93\) | −45482.6 | −0.545302 | ||||||||
\(94\) | 48921.4 | 0.571057 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 145294. | 1.56790 | 0.783949 | − | 0.620825i | \(-0.213202\pi\) | ||||
0.783949 | + | 0.620825i | \(0.213202\pi\) | |||||||
\(98\) | −58652.9 | −0.616914 | ||||||||
\(99\) | −47968.0 | −0.491885 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 2653.33 | 0.0258814 | 0.0129407 | − | 0.999916i | \(-0.495881\pi\) | ||||
0.0129407 | + | 0.999916i | \(0.495881\pi\) | |||||||
\(102\) | 50579.8 | 0.481368 | ||||||||
\(103\) | 32721.2 | 0.303904 | 0.151952 | − | 0.988388i | \(-0.451444\pi\) | ||||
0.151952 | + | 0.988388i | \(0.451444\pi\) | |||||||
\(104\) | 42325.7 | 0.383726 | ||||||||
\(105\) | −10417.7 | −0.0922144 | ||||||||
\(106\) | 38403.1 | 0.331972 | ||||||||
\(107\) | −119594. | −1.00983 | −0.504916 | − | 0.863169i | \(-0.668476\pi\) | ||||
−0.504916 | + | 0.863169i | \(0.668476\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 107852. | 0.869485 | 0.434742 | − | 0.900555i | \(-0.356839\pi\) | ||||
0.434742 | + | 0.900555i | \(0.356839\pi\) | |||||||
\(110\) | −59219.8 | −0.466643 | ||||||||
\(111\) | 32424.8 | 0.249787 | ||||||||
\(112\) | 11853.0 | 0.0892862 | ||||||||
\(113\) | 259806. | 1.91405 | 0.957026 | − | 0.290002i | \(-0.0936558\pi\) | ||||
0.957026 | + | 0.290002i | \(0.0936558\pi\) | |||||||
\(114\) | −12996.0 | −0.0936586 | ||||||||
\(115\) | 119395. | 0.841861 | ||||||||
\(116\) | −2852.06 | −0.0196795 | ||||||||
\(117\) | 53568.5 | 0.361780 | ||||||||
\(118\) | 8767.15 | 0.0579634 | ||||||||
\(119\) | −65052.5 | −0.421111 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | 189647. | 1.17756 | ||||||||
\(122\) | 3705.60 | 0.0225403 | ||||||||
\(123\) | −136335. | −0.812542 | ||||||||
\(124\) | 80857.9 | 0.472246 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 15001.5 | 0.0841798 | ||||||||
\(127\) | −162333. | −0.893095 | −0.446548 | − | 0.894760i | \(-0.647347\pi\) | ||||
−0.446548 | + | 0.894760i | \(0.647347\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 199841. | 1.05733 | ||||||||
\(130\) | 66134.0 | 0.343215 | ||||||||
\(131\) | 260155. | 1.32450 | 0.662252 | − | 0.749281i | \(-0.269601\pi\) | ||||
0.662252 | + | 0.749281i | \(0.269601\pi\) | |||||||
\(132\) | 85276.4 | 0.425985 | ||||||||
\(133\) | 16714.6 | 0.0819346 | ||||||||
\(134\) | −71738.2 | −0.345135 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | −89919.7 | −0.416877 | ||||||||
\(137\) | 75669.6 | 0.344445 | 0.172223 | − | 0.985058i | \(-0.444905\pi\) | ||||
0.172223 | + | 0.985058i | \(0.444905\pi\) | |||||||
\(138\) | −171928. | −0.768510 | ||||||||
\(139\) | −79493.2 | −0.348974 | −0.174487 | − | 0.984659i | \(-0.555827\pi\) | ||||
−0.174487 | + | 0.984659i | \(0.555827\pi\) | |||||||
\(140\) | 18520.4 | 0.0798600 | ||||||||
\(141\) | −110073. | −0.466266 | ||||||||
\(142\) | 173001. | 0.719993 | ||||||||
\(143\) | −391644. | −1.60159 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −4456.35 | −0.0176019 | ||||||||
\(146\) | −52521.0 | −0.203916 | ||||||||
\(147\) | 131969. | 0.503708 | ||||||||
\(148\) | −57644.0 | −0.216322 | ||||||||
\(149\) | 490284. | 1.80918 | 0.904590 | − | 0.426283i | \(-0.140177\pi\) | ||||
0.904590 | + | 0.426283i | \(0.140177\pi\) | |||||||
\(150\) | −22500.0 | −0.0816497 | ||||||||
\(151\) | −210024. | −0.749595 | −0.374797 | − | 0.927107i | \(-0.622288\pi\) | ||||
−0.374797 | + | 0.927107i | \(0.622288\pi\) | |||||||
\(152\) | 23104.0 | 0.0811107 | ||||||||
\(153\) | −113805. | −0.393035 | ||||||||
\(154\) | −109677. | −0.372661 | ||||||||
\(155\) | 126340. | 0.422389 | ||||||||
\(156\) | −95232.9 | −0.313311 | ||||||||
\(157\) | 13799.4 | 0.0446797 | 0.0223399 | − | 0.999750i | \(-0.492888\pi\) | ||||
0.0223399 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(158\) | 436117. | 1.38983 | ||||||||
\(159\) | −86407.0 | −0.271054 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 221123. | 0.672310 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | 7959.84 | 0.0234658 | 0.0117329 | − | 0.999931i | \(-0.496265\pi\) | ||||
0.0117329 | + | 0.999931i | \(0.496265\pi\) | |||||||
\(164\) | 242374. | 0.703682 | ||||||||
\(165\) | 133244. | 0.381013 | ||||||||
\(166\) | 23493.1 | 0.0661715 | ||||||||
\(167\) | 408123. | 1.13240 | 0.566200 | − | 0.824268i | \(-0.308413\pi\) | ||||
0.566200 | + | 0.824268i | \(0.308413\pi\) | |||||||
\(168\) | −26669.3 | −0.0729018 | ||||||||
\(169\) | 66077.0 | 0.177965 | ||||||||
\(170\) | −140499. | −0.372866 | ||||||||
\(171\) | 29241.0 | 0.0764719 | ||||||||
\(172\) | −355272. | −0.915673 | ||||||||
\(173\) | 563088. | 1.43041 | 0.715206 | − | 0.698914i | \(-0.246333\pi\) | ||||
0.715206 | + | 0.698914i | \(0.246333\pi\) | |||||||
\(174\) | 6417.14 | 0.0160683 | ||||||||
\(175\) | 28938.1 | 0.0714289 | ||||||||
\(176\) | −151603. | −0.368914 | ||||||||
\(177\) | −19726.1 | −0.0473269 | ||||||||
\(178\) | 266032. | 0.629338 | ||||||||
\(179\) | −705880. | −1.64664 | −0.823319 | − | 0.567579i | \(-0.807880\pi\) | ||||
−0.823319 | + | 0.567579i | \(0.807880\pi\) | |||||||
\(180\) | 32400.0 | 0.0745356 | ||||||||
\(181\) | 28650.5 | 0.0650034 | 0.0325017 | − | 0.999472i | \(-0.489653\pi\) | ||||
0.0325017 | + | 0.999472i | \(0.489653\pi\) | |||||||
\(182\) | 122482. | 0.274091 | ||||||||
\(183\) | −8337.60 | −0.0184041 | ||||||||
\(184\) | 305650. | 0.665549 | ||||||||
\(185\) | −90068.8 | −0.193484 | ||||||||
\(186\) | −181930. | −0.385587 | ||||||||
\(187\) | 832035. | 1.73995 | ||||||||
\(188\) | 195686. | 0.403798 | ||||||||
\(189\) | −33753.3 | −0.0687325 | ||||||||
\(190\) | 36100.0 | 0.0725476 | ||||||||
\(191\) | 137123. | 0.271974 | 0.135987 | − | 0.990711i | \(-0.456579\pi\) | ||||
0.135987 | + | 0.990711i | \(0.456579\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 930902. | 1.79892 | 0.899458 | − | 0.437008i | \(-0.143962\pi\) | ||||
0.899458 | + | 0.437008i | \(0.143962\pi\) | |||||||
\(194\) | 581175. | 1.10867 | ||||||||
\(195\) | −148801. | −0.280234 | ||||||||
\(196\) | −234612. | −0.436224 | ||||||||
\(197\) | −1812.91 | −0.00332820 | −0.00166410 | − | 0.999999i | \(-0.500530\pi\) | ||||
−0.00166410 | + | 0.999999i | \(0.500530\pi\) | |||||||
\(198\) | −191872. | −0.347815 | ||||||||
\(199\) | 605207. | 1.08336 | 0.541678 | − | 0.840586i | \(-0.317789\pi\) | ||||
0.541678 | + | 0.840586i | \(0.317789\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | 161411. | 0.281801 | ||||||||
\(202\) | 10613.3 | 0.0183009 | ||||||||
\(203\) | −8253.32 | −0.0140569 | ||||||||
\(204\) | 202319. | 0.340378 | ||||||||
\(205\) | 378709. | 0.629392 | ||||||||
\(206\) | 130885. | 0.214892 | ||||||||
\(207\) | 386839. | 0.627486 | ||||||||
\(208\) | 169303. | 0.271335 | ||||||||
\(209\) | −213783. | −0.338539 | ||||||||
\(210\) | −41670.8 | −0.0652054 | ||||||||
\(211\) | −1.06405e6 | −1.64534 | −0.822669 | − | 0.568520i | \(-0.807516\pi\) | ||||
−0.822669 | + | 0.568520i | \(0.807516\pi\) | |||||||
\(212\) | 153613. | 0.234740 | ||||||||
\(213\) | −389253. | −0.587872 | ||||||||
\(214\) | −478375. | −0.714058 | ||||||||
\(215\) | −555113. | −0.819002 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 233987. | 0.337320 | ||||||||
\(218\) | 431408. | 0.614819 | ||||||||
\(219\) | 118172. | 0.166497 | ||||||||
\(220\) | −236879. | −0.329967 | ||||||||
\(221\) | −929179. | −1.27973 | ||||||||
\(222\) | 129699. | 0.176626 | ||||||||
\(223\) | −339331. | −0.456942 | −0.228471 | − | 0.973551i | \(-0.573373\pi\) | ||||
−0.228471 | + | 0.973551i | \(0.573373\pi\) | |||||||
\(224\) | 47412.1 | 0.0631349 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 1.03923e6 | 1.35344 | ||||||||
\(227\) | −563086. | −0.725287 | −0.362643 | − | 0.931928i | \(-0.618126\pi\) | ||||
−0.362643 | + | 0.931928i | \(0.618126\pi\) | |||||||
\(228\) | −51984.0 | −0.0662266 | ||||||||
\(229\) | −143103. | −0.180327 | −0.0901633 | − | 0.995927i | \(-0.528739\pi\) | ||||
−0.0901633 | + | 0.995927i | \(0.528739\pi\) | |||||||
\(230\) | 477578. | 0.595285 | ||||||||
\(231\) | 246773. | 0.304277 | ||||||||
\(232\) | −11408.3 | −0.0139155 | ||||||||
\(233\) | −149712. | −0.180663 | −0.0903313 | − | 0.995912i | \(-0.528793\pi\) | ||||
−0.0903313 | + | 0.995912i | \(0.528793\pi\) | |||||||
\(234\) | 214274. | 0.255817 | ||||||||
\(235\) | 305759. | 0.361168 | ||||||||
\(236\) | 35068.6 | 0.0409863 | ||||||||
\(237\) | −981263. | −1.13479 | ||||||||
\(238\) | −260210. | −0.297770 | ||||||||
\(239\) | −881537. | −0.998265 | −0.499133 | − | 0.866526i | \(-0.666348\pi\) | ||||
−0.499133 | + | 0.866526i | \(0.666348\pi\) | |||||||
\(240\) | −57600.0 | −0.0645497 | ||||||||
\(241\) | −889167. | −0.986145 | −0.493072 | − | 0.869988i | \(-0.664126\pi\) | ||||
−0.493072 | + | 0.869988i | \(0.664126\pi\) | |||||||
\(242\) | 758588. | 0.832659 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 14822.4 | 0.0159384 | ||||||||
\(245\) | −366581. | −0.390170 | ||||||||
\(246\) | −545341. | −0.574554 | ||||||||
\(247\) | 238744. | 0.248994 | ||||||||
\(248\) | 323431. | 0.333928 | ||||||||
\(249\) | −52859.5 | −0.0540288 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | 119596. | 0.119820 | 0.0599102 | − | 0.998204i | \(-0.480919\pi\) | ||||
0.0599102 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(252\) | 60005.9 | 0.0595241 | ||||||||
\(253\) | −2.82821e6 | −2.77786 | ||||||||
\(254\) | −649332. | −0.631514 | ||||||||
\(255\) | 316124. | 0.304444 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −339118. | −0.320272 | −0.160136 | − | 0.987095i | \(-0.551193\pi\) | ||||
−0.160136 | + | 0.987095i | \(0.551193\pi\) | |||||||
\(258\) | 799363. | 0.747644 | ||||||||
\(259\) | −166811. | −0.154516 | ||||||||
\(260\) | 264536. | 0.242690 | ||||||||
\(261\) | −14438.6 | −0.0131197 | ||||||||
\(262\) | 1.04062e6 | 0.936566 | ||||||||
\(263\) | 65039.2 | 0.0579810 | 0.0289905 | − | 0.999580i | \(-0.490771\pi\) | ||||
0.0289905 | + | 0.999580i | \(0.490771\pi\) | |||||||
\(264\) | 341106. | 0.301217 | ||||||||
\(265\) | 240020. | 0.209958 | ||||||||
\(266\) | 66858.5 | 0.0579365 | ||||||||
\(267\) | −598572. | −0.513852 | ||||||||
\(268\) | −286953. | −0.244047 | ||||||||
\(269\) | −1.33562e6 | −1.12539 | −0.562695 | − | 0.826665i | \(-0.690235\pi\) | ||||
−0.562695 | + | 0.826665i | \(0.690235\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | −1.43923e6 | −1.19044 | −0.595218 | − | 0.803564i | \(-0.702934\pi\) | ||||
−0.595218 | + | 0.803564i | \(0.702934\pi\) | |||||||
\(272\) | −359679. | −0.294776 | ||||||||
\(273\) | −275585. | −0.223795 | ||||||||
\(274\) | 302678. | 0.243559 | ||||||||
\(275\) | −370123. | −0.295131 | ||||||||
\(276\) | −687713. | −0.543419 | ||||||||
\(277\) | −1.13151e6 | −0.886054 | −0.443027 | − | 0.896508i | \(-0.646095\pi\) | ||||
−0.443027 | + | 0.896508i | \(0.646095\pi\) | |||||||
\(278\) | −317973. | −0.246762 | ||||||||
\(279\) | 409343. | 0.314831 | ||||||||
\(280\) | 74081.4 | 0.0564695 | ||||||||
\(281\) | 1.28968e6 | 0.974349 | 0.487175 | − | 0.873305i | \(-0.338028\pi\) | ||||
0.487175 | + | 0.873305i | \(0.338028\pi\) | |||||||
\(282\) | −440293. | −0.329700 | ||||||||
\(283\) | 1.20910e6 | 0.897418 | 0.448709 | − | 0.893678i | \(-0.351884\pi\) | ||||
0.448709 | + | 0.893678i | \(0.351884\pi\) | |||||||
\(284\) | 692004. | 0.509112 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | −1.56657e6 | −1.13249 | ||||||||
\(287\) | 701383. | 0.502632 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | 554154. | 0.390288 | ||||||||
\(290\) | −17825.4 | −0.0124464 | ||||||||
\(291\) | −1.30764e6 | −0.905226 | ||||||||
\(292\) | −210084. | −0.144190 | ||||||||
\(293\) | 399283. | 0.271714 | 0.135857 | − | 0.990728i | \(-0.456621\pi\) | ||||
0.135857 | + | 0.990728i | \(0.456621\pi\) | |||||||
\(294\) | 527876. | 0.356175 | ||||||||
\(295\) | 54794.7 | 0.0366592 | ||||||||
\(296\) | −230576. | −0.152963 | ||||||||
\(297\) | 431712. | 0.283990 | ||||||||
\(298\) | 1.96113e6 | 1.27928 | ||||||||
\(299\) | 3.15842e6 | 2.04311 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | −1.02809e6 | −0.654055 | ||||||||
\(302\) | −840096. | −0.530043 | ||||||||
\(303\) | −23879.9 | −0.0149426 | ||||||||
\(304\) | 92416.0 | 0.0573539 | ||||||||
\(305\) | 23160.0 | 0.0142557 | ||||||||
\(306\) | −455218. | −0.277918 | ||||||||
\(307\) | 1.59355e6 | 0.964982 | 0.482491 | − | 0.875901i | \(-0.339732\pi\) | ||||
0.482491 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(308\) | −438708. | −0.263511 | ||||||||
\(309\) | −294491. | −0.175459 | ||||||||
\(310\) | 505362. | 0.298674 | ||||||||
\(311\) | −895028. | −0.524730 | −0.262365 | − | 0.964969i | \(-0.584502\pi\) | ||||
−0.262365 | + | 0.964969i | \(0.584502\pi\) | |||||||
\(312\) | −380932. | −0.221544 | ||||||||
\(313\) | 593284. | 0.342296 | 0.171148 | − | 0.985245i | \(-0.445252\pi\) | ||||
0.171148 | + | 0.985245i | \(0.445252\pi\) | |||||||
\(314\) | 55197.5 | 0.0315933 | ||||||||
\(315\) | 93759.3 | 0.0532400 | ||||||||
\(316\) | 1.74447e6 | 0.982755 | ||||||||
\(317\) | 3.44435e6 | 1.92513 | 0.962564 | − | 0.271054i | \(-0.0873723\pi\) | ||||
0.962564 | + | 0.271054i | \(0.0873723\pi\) | |||||||
\(318\) | −345628. | −0.191664 | ||||||||
\(319\) | 105562. | 0.0580803 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 1.07634e6 | 0.583026 | ||||||||
\(322\) | 884492. | 0.475395 | ||||||||
\(323\) | −507203. | −0.270505 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 413337. | 0.217068 | ||||||||
\(326\) | 31839.4 | 0.0165928 | ||||||||
\(327\) | −970668. | −0.501997 | ||||||||
\(328\) | 969496. | 0.497578 | ||||||||
\(329\) | 566276. | 0.288429 | ||||||||
\(330\) | 532978. | 0.269417 | ||||||||
\(331\) | 2.39189e6 | 1.19997 | 0.599986 | − | 0.800011i | \(-0.295173\pi\) | ||||
0.599986 | + | 0.800011i | \(0.295173\pi\) | |||||||
\(332\) | 93972.5 | 0.0467903 | ||||||||
\(333\) | −291823. | −0.144214 | ||||||||
\(334\) | 1.63249e6 | 0.800728 | ||||||||
\(335\) | −448364. | −0.218282 | ||||||||
\(336\) | −106677. | −0.0515494 | ||||||||
\(337\) | −1.00905e6 | −0.483992 | −0.241996 | − | 0.970277i | \(-0.577802\pi\) | ||||
−0.241996 | + | 0.970277i | \(0.577802\pi\) | |||||||
\(338\) | 264308. | 0.125840 | ||||||||
\(339\) | −2.33826e6 | −1.10508 | ||||||||
\(340\) | −561998. | −0.263656 | ||||||||
\(341\) | −2.99274e6 | −1.39374 | ||||||||
\(342\) | 116964. | 0.0540738 | ||||||||
\(343\) | −1.45710e6 | −0.668735 | ||||||||
\(344\) | −1.42109e6 | −0.647478 | ||||||||
\(345\) | −1.07455e6 | −0.486048 | ||||||||
\(346\) | 2.25235e6 | 1.01145 | ||||||||
\(347\) | 558349. | 0.248933 | 0.124466 | − | 0.992224i | \(-0.460278\pi\) | ||||
0.124466 | + | 0.992224i | \(0.460278\pi\) | |||||||
\(348\) | 25668.6 | 0.0113620 | ||||||||
\(349\) | 1.60518e6 | 0.705441 | 0.352721 | − | 0.935729i | \(-0.385257\pi\) | ||||
0.352721 | + | 0.935729i | \(0.385257\pi\) | |||||||
\(350\) | 115752. | 0.0505079 | ||||||||
\(351\) | −482117. | −0.208874 | ||||||||
\(352\) | −606410. | −0.260861 | ||||||||
\(353\) | −2.25469e6 | −0.963053 | −0.481527 | − | 0.876432i | \(-0.659918\pi\) | ||||
−0.481527 | + | 0.876432i | \(0.659918\pi\) | |||||||
\(354\) | −78904.4 | −0.0334652 | ||||||||
\(355\) | 1.08126e6 | 0.455363 | ||||||||
\(356\) | 1.06413e6 | 0.445009 | ||||||||
\(357\) | 585473. | 0.243129 | ||||||||
\(358\) | −2.82352e6 | −1.16435 | ||||||||
\(359\) | −3.72457e6 | −1.52525 | −0.762623 | − | 0.646843i | \(-0.776089\pi\) | ||||
−0.762623 | + | 0.646843i | \(0.776089\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 114602. | 0.0459643 | ||||||||
\(363\) | −1.70682e6 | −0.679864 | ||||||||
\(364\) | 489930. | 0.193812 | ||||||||
\(365\) | −328256. | −0.128968 | ||||||||
\(366\) | −33350.4 | −0.0130136 | ||||||||
\(367\) | −608999. | −0.236021 | −0.118011 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118011 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(368\) | 1.22260e6 | 0.470614 | ||||||||
\(369\) | 1.22702e6 | 0.469121 | ||||||||
\(370\) | −360275. | −0.136814 | ||||||||
\(371\) | 444525. | 0.167672 | ||||||||
\(372\) | −727721. | −0.272651 | ||||||||
\(373\) | −1.14524e6 | −0.426212 | −0.213106 | − | 0.977029i | \(-0.568358\pi\) | ||||
−0.213106 | + | 0.977029i | \(0.568358\pi\) | |||||||
\(374\) | 3.32814e6 | 1.23033 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | 782743. | 0.285528 | ||||||||
\(377\) | −117886. | −0.0427180 | ||||||||
\(378\) | −135013. | −0.0486012 | ||||||||
\(379\) | −3.85601e6 | −1.37892 | −0.689461 | − | 0.724323i | \(-0.742153\pi\) | ||||
−0.689461 | + | 0.724323i | \(0.742153\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | 1.46100e6 | 0.515629 | ||||||||
\(382\) | 548492. | 0.192315 | ||||||||
\(383\) | 366401. | 0.127632 | 0.0638160 | − | 0.997962i | \(-0.479673\pi\) | ||||
0.0638160 | + | 0.997962i | \(0.479673\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −685482. | −0.235692 | ||||||||
\(386\) | 3.72361e6 | 1.27203 | ||||||||
\(387\) | −1.79857e6 | −0.610448 | ||||||||
\(388\) | 2.32470e6 | 0.783949 | ||||||||
\(389\) | −1.72920e6 | −0.579389 | −0.289695 | − | 0.957119i | \(-0.593554\pi\) | ||||
−0.289695 | + | 0.957119i | \(0.593554\pi\) | |||||||
\(390\) | −595206. | −0.198155 | ||||||||
\(391\) | −6.70995e6 | −2.21961 | ||||||||
\(392\) | −938447. | −0.308457 | ||||||||
\(393\) | −2.34139e6 | −0.764703 | ||||||||
\(394\) | −7251.63 | −0.00235340 | ||||||||
\(395\) | 2.72573e6 | 0.879003 | ||||||||
\(396\) | −767488. | −0.245943 | ||||||||
\(397\) | −495411. | −0.157757 | −0.0788787 | − | 0.996884i | \(-0.525134\pi\) | ||||
−0.0788787 | + | 0.996884i | \(0.525134\pi\) | |||||||
\(398\) | 2.42083e6 | 0.766049 | ||||||||
\(399\) | −150432. | −0.0473050 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −616557. | −0.191475 | −0.0957376 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957376 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(402\) | 645644. | 0.199263 | ||||||||
\(403\) | 3.34216e6 | 1.02510 | ||||||||
\(404\) | 42453.2 | 0.0129407 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | −33013.3 | −0.00993971 | ||||||||
\(407\) | 2.13354e6 | 0.638432 | ||||||||
\(408\) | 809277. | 0.240684 | ||||||||
\(409\) | 4.43760e6 | 1.31172 | 0.655859 | − | 0.754884i | \(-0.272307\pi\) | ||||
0.655859 | + | 0.754884i | \(0.272307\pi\) | |||||||
\(410\) | 1.51484e6 | 0.445048 | ||||||||
\(411\) | −681026. | −0.198865 | ||||||||
\(412\) | 523539. | 0.151952 | ||||||||
\(413\) | 101482. | 0.0292761 | ||||||||
\(414\) | 1.54735e6 | 0.443699 | ||||||||
\(415\) | 146832. | 0.0418505 | ||||||||
\(416\) | 677212. | 0.191863 | ||||||||
\(417\) | 715439. | 0.201480 | ||||||||
\(418\) | −855133. | −0.239383 | ||||||||
\(419\) | 5.99895e6 | 1.66932 | 0.834662 | − | 0.550763i | \(-0.185663\pi\) | ||||
0.834662 | + | 0.550763i | \(0.185663\pi\) | |||||||
\(420\) | −166683. | −0.0461072 | ||||||||
\(421\) | −2.34020e6 | −0.643500 | −0.321750 | − | 0.946825i | \(-0.604271\pi\) | ||||
−0.321750 | + | 0.946825i | \(0.604271\pi\) | |||||||
\(422\) | −4.25619e6 | −1.16343 | ||||||||
\(423\) | 990659. | 0.269199 | ||||||||
\(424\) | 614450. | 0.165986 | ||||||||
\(425\) | −878122. | −0.235821 | ||||||||
\(426\) | −1.55701e6 | −0.415688 | ||||||||
\(427\) | 42893.2 | 0.0113846 | ||||||||
\(428\) | −1.91350e6 | −0.504916 | ||||||||
\(429\) | 3.52479e6 | 0.924678 | ||||||||
\(430\) | −2.22045e6 | −0.579122 | ||||||||
\(431\) | −3.18571e6 | −0.826064 | −0.413032 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413032 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −3.76503e6 | −0.965048 | −0.482524 | − | 0.875883i | \(-0.660280\pi\) | ||||
−0.482524 | + | 0.875883i | \(0.660280\pi\) | |||||||
\(434\) | 935948. | 0.238521 | ||||||||
\(435\) | 40107.2 | 0.0101625 | ||||||||
\(436\) | 1.72563e6 | 0.434742 | ||||||||
\(437\) | 1.72406e6 | 0.431865 | ||||||||
\(438\) | 472689. | 0.117731 | ||||||||
\(439\) | −3.73627e6 | −0.925287 | −0.462644 | − | 0.886544i | \(-0.653099\pi\) | ||||
−0.462644 | + | 0.886544i | \(0.653099\pi\) | |||||||
\(440\) | −947516. | −0.233322 | ||||||||
\(441\) | −1.18772e6 | −0.290816 | ||||||||
\(442\) | −3.71672e6 | −0.904906 | ||||||||
\(443\) | 1.62775e6 | 0.394075 | 0.197037 | − | 0.980396i | \(-0.436868\pi\) | ||||
0.197037 | + | 0.980396i | \(0.436868\pi\) | |||||||
\(444\) | 518796. | 0.124893 | ||||||||
\(445\) | 1.66270e6 | 0.398028 | ||||||||
\(446\) | −1.35732e6 | −0.323107 | ||||||||
\(447\) | −4.41255e6 | −1.04453 | ||||||||
\(448\) | 189648. | 0.0446431 | ||||||||
\(449\) | 737503. | 0.172643 | 0.0863213 | − | 0.996267i | \(-0.472489\pi\) | ||||
0.0863213 | + | 0.996267i | \(0.472489\pi\) | |||||||
\(450\) | 202500. | 0.0471405 | ||||||||
\(451\) | −8.97083e6 | −2.07678 | ||||||||
\(452\) | 4.15690e6 | 0.957026 | ||||||||
\(453\) | 1.89022e6 | 0.432779 | ||||||||
\(454\) | −2.25234e6 | −0.512855 | ||||||||
\(455\) | 765515. | 0.173351 | ||||||||
\(456\) | −207936. | −0.0468293 | ||||||||
\(457\) | −893631. | −0.200156 | −0.100078 | − | 0.994980i | \(-0.531909\pi\) | ||||
−0.100078 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(458\) | −572412. | −0.127510 | ||||||||
\(459\) | 1.02424e6 | 0.226919 | ||||||||
\(460\) | 1.91031e6 | 0.420930 | ||||||||
\(461\) | −5.46587e6 | −1.19786 | −0.598931 | − | 0.800801i | \(-0.704408\pi\) | ||||
−0.598931 | + | 0.800801i | \(0.704408\pi\) | |||||||
\(462\) | 987094. | 0.215156 | ||||||||
\(463\) | −4.05984e6 | −0.880149 | −0.440074 | − | 0.897961i | \(-0.645048\pi\) | ||||
−0.440074 | + | 0.897961i | \(0.645048\pi\) | |||||||
\(464\) | −45633.0 | −0.00983976 | ||||||||
\(465\) | −1.13706e6 | −0.243867 | ||||||||
\(466\) | −598850. | −0.127748 | ||||||||
\(467\) | 5.53201e6 | 1.17379 | 0.586895 | − | 0.809663i | \(-0.300350\pi\) | ||||
0.586895 | + | 0.809663i | \(0.300350\pi\) | |||||||
\(468\) | 857096. | 0.180890 | ||||||||
\(469\) | −830385. | −0.174320 | ||||||||
\(470\) | 1.22304e6 | 0.255384 | ||||||||
\(471\) | −124194. | −0.0257958 | ||||||||
\(472\) | 140274. | 0.0289817 | ||||||||
\(473\) | 1.31495e7 | 2.70243 | ||||||||
\(474\) | −3.92505e6 | −0.802416 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −1.04084e6 | −0.210556 | ||||||||
\(477\) | 777663. | 0.156493 | ||||||||
\(478\) | −3.52615e6 | −0.705880 | ||||||||
\(479\) | 1.07783e6 | 0.214640 | 0.107320 | − | 0.994225i | \(-0.465773\pi\) | ||||
0.107320 | + | 0.994225i | \(0.465773\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | −2.38264e6 | −0.469566 | ||||||||
\(482\) | −3.55667e6 | −0.697310 | ||||||||
\(483\) | −1.99011e6 | −0.388158 | ||||||||
\(484\) | 3.03435e6 | 0.588779 | ||||||||
\(485\) | 3.63235e6 | 0.701185 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −5.51455e6 | −1.05363 | −0.526814 | − | 0.849980i | \(-0.676614\pi\) | ||||
−0.526814 | + | 0.849980i | \(0.676614\pi\) | |||||||
\(488\) | 59289.6 | 0.0112701 | ||||||||
\(489\) | −71638.6 | −0.0135480 | ||||||||
\(490\) | −1.46632e6 | −0.275892 | ||||||||
\(491\) | −9.17738e6 | −1.71797 | −0.858984 | − | 0.512003i | \(-0.828904\pi\) | ||||
−0.858984 | + | 0.512003i | \(0.828904\pi\) | |||||||
\(492\) | −2.18137e6 | −0.406271 | ||||||||
\(493\) | 250446. | 0.0464084 | ||||||||
\(494\) | 954974. | 0.176066 | ||||||||
\(495\) | −1.19920e6 | −0.219978 | ||||||||
\(496\) | 1.29373e6 | 0.236123 | ||||||||
\(497\) | 2.00253e6 | 0.363653 | ||||||||
\(498\) | −211438. | −0.0382041 | ||||||||
\(499\) | −8.41157e6 | −1.51226 | −0.756129 | − | 0.654423i | \(-0.772912\pi\) | ||||
−0.756129 | + | 0.654423i | \(0.772912\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | −3.67311e6 | −0.653792 | ||||||||
\(502\) | 478383. | 0.0847259 | ||||||||
\(503\) | −2.49352e6 | −0.439433 | −0.219717 | − | 0.975564i | \(-0.570513\pi\) | ||||
−0.219717 | + | 0.975564i | \(0.570513\pi\) | |||||||
\(504\) | 240024. | 0.0420899 | ||||||||
\(505\) | 66333.1 | 0.0115745 | ||||||||
\(506\) | −1.13128e7 | −1.96424 | ||||||||
\(507\) | −594693. | −0.102748 | ||||||||
\(508\) | −2.59733e6 | −0.446548 | ||||||||
\(509\) | −5.47906e6 | −0.937370 | −0.468685 | − | 0.883365i | \(-0.655272\pi\) | ||||
−0.468685 | + | 0.883365i | \(0.655272\pi\) | |||||||
\(510\) | 1.26450e6 | 0.215274 | ||||||||
\(511\) | −607942. | −0.102994 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | −1.35647e6 | −0.226466 | ||||||||
\(515\) | 818030. | 0.135910 | ||||||||
\(516\) | 3.19745e6 | 0.528664 | ||||||||
\(517\) | −7.24279e6 | −1.19173 | ||||||||
\(518\) | −667242. | −0.109260 | ||||||||
\(519\) | −5.06779e6 | −0.825848 | ||||||||
\(520\) | 1.05814e6 | 0.171607 | ||||||||
\(521\) | −9.26335e6 | −1.49511 | −0.747556 | − | 0.664199i | \(-0.768773\pi\) | ||||
−0.747556 | + | 0.664199i | \(0.768773\pi\) | |||||||
\(522\) | −57754.3 | −0.00927701 | ||||||||
\(523\) | −1.81815e6 | −0.290654 | −0.145327 | − | 0.989384i | \(-0.546423\pi\) | ||||
−0.145327 | + | 0.989384i | \(0.546423\pi\) | |||||||
\(524\) | 4.16248e6 | 0.662252 | ||||||||
\(525\) | −260442. | −0.0412395 | ||||||||
\(526\) | 260157. | 0.0409988 | ||||||||
\(527\) | −7.10031e6 | −1.11365 | ||||||||
\(528\) | 1.36442e6 | 0.212992 | ||||||||
\(529\) | 1.63718e7 | 2.54365 | ||||||||
\(530\) | 960078. | 0.148463 | ||||||||
\(531\) | 177535. | 0.0273242 | ||||||||
\(532\) | 267434. | 0.0409673 | ||||||||
\(533\) | 1.00182e7 | 1.52747 | ||||||||
\(534\) | −2.39429e6 | −0.363348 | ||||||||
\(535\) | −2.98984e6 | −0.451610 | ||||||||
\(536\) | −1.14781e6 | −0.172567 | ||||||||
\(537\) | 6.35292e6 | 0.950687 | ||||||||
\(538\) | −5.34249e6 | −0.795770 | ||||||||
\(539\) | 8.68353e6 | 1.28743 | ||||||||
\(540\) | −291600. | −0.0430331 | ||||||||
\(541\) | 1.05448e7 | 1.54898 | 0.774491 | − | 0.632585i | \(-0.218006\pi\) | ||||
0.774491 | + | 0.632585i | \(0.218006\pi\) | |||||||
\(542\) | −5.75690e6 | −0.841765 | ||||||||
\(543\) | −257855. | −0.0375297 | ||||||||
\(544\) | −1.43871e6 | −0.208438 | ||||||||
\(545\) | 2.69630e6 | 0.388845 | ||||||||
\(546\) | −1.10234e6 | −0.158247 | ||||||||
\(547\) | −1.27881e7 | −1.82742 | −0.913711 | − | 0.406365i | \(-0.866796\pi\) | ||||
−0.913711 | + | 0.406365i | \(0.866796\pi\) | |||||||
\(548\) | 1.21071e6 | 0.172223 | ||||||||
\(549\) | 75038.4 | 0.0106256 | ||||||||
\(550\) | −1.48049e6 | −0.208689 | ||||||||
\(551\) | −64349.7 | −0.00902958 | ||||||||
\(552\) | −2.75085e6 | −0.384255 | ||||||||
\(553\) | 5.04815e6 | 0.701971 | ||||||||
\(554\) | −4.52605e6 | −0.626534 | ||||||||
\(555\) | 810619. | 0.111708 | ||||||||
\(556\) | −1.27189e6 | −0.174487 | ||||||||
\(557\) | −2.52948e6 | −0.345457 | −0.172728 | − | 0.984970i | \(-0.555258\pi\) | ||||
−0.172728 | + | 0.984970i | \(0.555258\pi\) | |||||||
\(558\) | 1.63737e6 | 0.222619 | ||||||||
\(559\) | −1.46847e7 | −1.98763 | ||||||||
\(560\) | 296326. | 0.0399300 | ||||||||
\(561\) | −7.48831e6 | −1.00456 | ||||||||
\(562\) | 5.15870e6 | 0.688969 | ||||||||
\(563\) | 549145. | 0.0730156 | 0.0365078 | − | 0.999333i | \(-0.488377\pi\) | ||||
0.0365078 | + | 0.999333i | \(0.488377\pi\) | |||||||
\(564\) | −1.76117e6 | −0.233133 | ||||||||
\(565\) | 6.49516e6 | 0.855990 | ||||||||
\(566\) | 4.83638e6 | 0.634570 | ||||||||
\(567\) | 303780. | 0.0396827 | ||||||||
\(568\) | 2.76802e6 | 0.359996 | ||||||||
\(569\) | 1.17774e7 | 1.52499 | 0.762496 | − | 0.646992i | \(-0.223973\pi\) | ||||
0.762496 | + | 0.646992i | \(0.223973\pi\) | |||||||
\(570\) | −324900. | −0.0418854 | ||||||||
\(571\) | 1.46636e7 | 1.88213 | 0.941065 | − | 0.338226i | \(-0.109827\pi\) | ||||
0.941065 | + | 0.338226i | \(0.109827\pi\) | |||||||
\(572\) | −6.26630e6 | −0.800794 | ||||||||
\(573\) | −1.23411e6 | −0.157024 | ||||||||
\(574\) | 2.80553e6 | 0.355415 | ||||||||
\(575\) | 2.98487e6 | 0.376491 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.56628e7 | −1.95853 | −0.979264 | − | 0.202590i | \(-0.935064\pi\) | ||||
−0.979264 | + | 0.202590i | \(0.935064\pi\) | |||||||
\(578\) | 2.21661e6 | 0.275976 | ||||||||
\(579\) | −8.37812e6 | −1.03860 | ||||||||
\(580\) | −71301.6 | −0.00880095 | ||||||||
\(581\) | 271938. | 0.0334218 | ||||||||
\(582\) | −5.23058e6 | −0.640092 | ||||||||
\(583\) | −5.68556e6 | −0.692790 | ||||||||
\(584\) | −840336. | −0.101958 | ||||||||
\(585\) | 1.33921e6 | 0.161793 | ||||||||
\(586\) | 1.59713e6 | 0.192131 | ||||||||
\(587\) | 909404. | 0.108934 | 0.0544668 | − | 0.998516i | \(-0.482654\pi\) | ||||
0.0544668 | + | 0.998516i | \(0.482654\pi\) | |||||||
\(588\) | 2.11150e6 | 0.251854 | ||||||||
\(589\) | 1.82436e6 | 0.216681 | ||||||||
\(590\) | 219179. | 0.0259220 | ||||||||
\(591\) | 16316.2 | 0.00192154 | ||||||||
\(592\) | −922305. | −0.108161 | ||||||||
\(593\) | −1.47954e7 | −1.72779 | −0.863896 | − | 0.503670i | \(-0.831983\pi\) | ||||
−0.863896 | + | 0.503670i | \(0.831983\pi\) | |||||||
\(594\) | 1.72685e6 | 0.200811 | ||||||||
\(595\) | −1.62631e6 | −0.188327 | ||||||||
\(596\) | 7.84454e6 | 0.904590 | ||||||||
\(597\) | −5.44686e6 | −0.625476 | ||||||||
\(598\) | 1.26337e7 | 1.44470 | ||||||||
\(599\) | 1.42416e7 | 1.62178 | 0.810888 | − | 0.585202i | \(-0.198985\pi\) | ||||
0.810888 | + | 0.585202i | \(0.198985\pi\) | |||||||
\(600\) | −360000. | −0.0408248 | ||||||||
\(601\) | 1.40092e6 | 0.158208 | 0.0791040 | − | 0.996866i | \(-0.474794\pi\) | ||||
0.0791040 | + | 0.996866i | \(0.474794\pi\) | |||||||
\(602\) | −4.11236e6 | −0.462487 | ||||||||
\(603\) | −1.45270e6 | −0.162698 | ||||||||
\(604\) | −3.36038e6 | −0.374797 | ||||||||
\(605\) | 4.74117e6 | 0.526620 | ||||||||
\(606\) | −95519.7 | −0.0105660 | ||||||||
\(607\) | 1.00463e7 | 1.10671 | 0.553356 | − | 0.832945i | \(-0.313347\pi\) | ||||
0.553356 | + | 0.832945i | \(0.313347\pi\) | |||||||
\(608\) | 369664. | 0.0405554 | ||||||||
\(609\) | 74279.9 | 0.00811574 | ||||||||
\(610\) | 92640.0 | 0.0100803 | ||||||||
\(611\) | 8.08842e6 | 0.876517 | ||||||||
\(612\) | −1.82087e6 | −0.196517 | ||||||||
\(613\) | −4.38057e6 | −0.470847 | −0.235424 | − | 0.971893i | \(-0.575648\pi\) | ||||
−0.235424 | + | 0.971893i | \(0.575648\pi\) | |||||||
\(614\) | 6.37419e6 | 0.682345 | ||||||||
\(615\) | −3.40838e6 | −0.363380 | ||||||||
\(616\) | −1.75483e6 | −0.186331 | ||||||||
\(617\) | −3.77700e6 | −0.399424 | −0.199712 | − | 0.979855i | \(-0.564001\pi\) | ||||
−0.199712 | + | 0.979855i | \(0.564001\pi\) | |||||||
\(618\) | −1.17796e6 | −0.124068 | ||||||||
\(619\) | −1.55698e7 | −1.63327 | −0.816633 | − | 0.577157i | \(-0.804162\pi\) | ||||
−0.816633 | + | 0.577157i | \(0.804162\pi\) | |||||||
\(620\) | 2.02145e6 | 0.211195 | ||||||||
\(621\) | −3.48155e6 | −0.362279 | ||||||||
\(622\) | −3.58011e6 | −0.371040 | ||||||||
\(623\) | 3.07938e6 | 0.317865 | ||||||||
\(624\) | −1.52373e6 | −0.156655 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.37314e6 | 0.242040 | ||||||||
\(627\) | 1.92405e6 | 0.195455 | ||||||||
\(628\) | 220790. | 0.0223399 | ||||||||
\(629\) | 5.06185e6 | 0.510132 | ||||||||
\(630\) | 375037. | 0.0376464 | ||||||||
\(631\) | −1.44580e6 | −0.144556 | −0.0722778 | − | 0.997385i | \(-0.523027\pi\) | ||||
−0.0722778 | + | 0.997385i | \(0.523027\pi\) | |||||||
\(632\) | 6.97787e6 | 0.694913 | ||||||||
\(633\) | 9.57643e6 | 0.949936 | ||||||||
\(634\) | 1.37774e7 | 1.36127 | ||||||||
\(635\) | −4.05833e6 | −0.399404 | ||||||||
\(636\) | −1.38251e6 | −0.135527 | ||||||||
\(637\) | −9.69737e6 | −0.946903 | ||||||||
\(638\) | 422246. | 0.0410690 | ||||||||
\(639\) | 3.50327e6 | 0.339408 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | 1.41495e7 | 1.36018 | 0.680092 | − | 0.733127i | \(-0.261940\pi\) | ||||
0.680092 | + | 0.733127i | \(0.261940\pi\) | |||||||
\(642\) | 4.30537e6 | 0.412262 | ||||||||
\(643\) | −3.07758e6 | −0.293550 | −0.146775 | − | 0.989170i | \(-0.546889\pi\) | ||||
−0.146775 | + | 0.989170i | \(0.546889\pi\) | |||||||
\(644\) | 3.53797e6 | 0.336155 | ||||||||
\(645\) | 4.99602e6 | 0.472851 | ||||||||
\(646\) | −2.02881e6 | −0.191276 | ||||||||
\(647\) | 1.66462e7 | 1.56335 | 0.781673 | − | 0.623688i | \(-0.214367\pi\) | ||||
0.781673 | + | 0.623688i | \(0.214367\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | −1.29797e6 | −0.120963 | ||||||||
\(650\) | 1.65335e6 | 0.153490 | ||||||||
\(651\) | −2.10588e6 | −0.194752 | ||||||||
\(652\) | 127357. | 0.0117329 | ||||||||
\(653\) | −1.12480e7 | −1.03227 | −0.516133 | − | 0.856509i | \(-0.672629\pi\) | ||||
−0.516133 | + | 0.856509i | \(0.672629\pi\) | |||||||
\(654\) | −3.88267e6 | −0.354966 | ||||||||
\(655\) | 6.50387e6 | 0.592337 | ||||||||
\(656\) | 3.87798e6 | 0.351841 | ||||||||
\(657\) | −1.06355e6 | −0.0961269 | ||||||||
\(658\) | 2.26510e6 | 0.203950 | ||||||||
\(659\) | 4.63676e6 | 0.415912 | 0.207956 | − | 0.978138i | \(-0.433319\pi\) | ||||
0.207956 | + | 0.978138i | \(0.433319\pi\) | |||||||
\(660\) | 2.13191e6 | 0.190506 | ||||||||
\(661\) | −1.86324e7 | −1.65869 | −0.829346 | − | 0.558736i | \(-0.811287\pi\) | ||||
−0.829346 | + | 0.558736i | \(0.811287\pi\) | |||||||
\(662\) | 9.56756e6 | 0.848508 | ||||||||
\(663\) | 8.36261e6 | 0.738853 | ||||||||
\(664\) | 375890. | 0.0330857 | ||||||||
\(665\) | 417865. | 0.0366423 | ||||||||
\(666\) | −1.16729e6 | −0.101975 | ||||||||
\(667\) | −851303. | −0.0740917 | ||||||||
\(668\) | 6.52997e6 | 0.566200 | ||||||||
\(669\) | 3.05398e6 | 0.263816 | ||||||||
\(670\) | −1.79345e6 | −0.154349 | ||||||||
\(671\) | −548612. | −0.0470391 | ||||||||
\(672\) | −426709. | −0.0364509 | ||||||||
\(673\) | 8.43418e6 | 0.717803 | 0.358901 | − | 0.933376i | \(-0.383151\pi\) | ||||
0.358901 | + | 0.933376i | \(0.383151\pi\) | |||||||
\(674\) | −4.03620e6 | −0.342234 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 1.05723e6 | 0.0889823 | ||||||||
\(677\) | −1.49945e6 | −0.125736 | −0.0628679 | − | 0.998022i | \(-0.520025\pi\) | ||||
−0.0628679 | + | 0.998022i | \(0.520025\pi\) | |||||||
\(678\) | −9.35303e6 | −0.781409 | ||||||||
\(679\) | 6.72723e6 | 0.559966 | ||||||||
\(680\) | −2.24799e6 | −0.186433 | ||||||||
\(681\) | 5.06777e6 | 0.418745 | ||||||||
\(682\) | −1.19710e7 | −0.985526 | ||||||||
\(683\) | −1.78268e6 | −0.146225 | −0.0731124 | − | 0.997324i | \(-0.523293\pi\) | ||||
−0.0731124 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(684\) | 467856. | 0.0382360 | ||||||||
\(685\) | 1.89174e6 | 0.154041 | ||||||||
\(686\) | −5.82840e6 | −0.472867 | ||||||||
\(687\) | 1.28793e6 | 0.104112 | ||||||||
\(688\) | −5.68436e6 | −0.457836 | ||||||||
\(689\) | 6.34938e6 | 0.509546 | ||||||||
\(690\) | −4.29821e6 | −0.343688 | ||||||||
\(691\) | −4.90602e6 | −0.390872 | −0.195436 | − | 0.980716i | \(-0.562612\pi\) | ||||
−0.195436 | + | 0.980716i | \(0.562612\pi\) | |||||||
\(692\) | 9.00941e6 | 0.715206 | ||||||||
\(693\) | −2.22096e6 | −0.175674 | ||||||||
\(694\) | 2.23340e6 | 0.176022 | ||||||||
\(695\) | −1.98733e6 | −0.156066 | ||||||||
\(696\) | 102674. | 0.00803413 | ||||||||
\(697\) | −2.12834e7 | −1.65943 | ||||||||
\(698\) | 6.42073e6 | 0.498822 | ||||||||
\(699\) | 1.34741e6 | 0.104306 | ||||||||
\(700\) | 463009. | 0.0357145 | ||||||||
\(701\) | 1.07045e7 | 0.822756 | 0.411378 | − | 0.911465i | \(-0.365048\pi\) | ||||
0.411378 | + | 0.911465i | \(0.365048\pi\) | |||||||
\(702\) | −1.92847e6 | −0.147696 | ||||||||
\(703\) | −1.30059e6 | −0.0992552 | ||||||||
\(704\) | −2.42564e6 | −0.184457 | ||||||||
\(705\) | −2.75183e6 | −0.208521 | ||||||||
\(706\) | −9.01876e6 | −0.680981 | ||||||||
\(707\) | 122851. | 0.00924339 | ||||||||
\(708\) | −315617. | −0.0236634 | ||||||||
\(709\) | −1.25861e7 | −0.940319 | −0.470159 | − | 0.882581i | \(-0.655804\pi\) | ||||
−0.470159 | + | 0.882581i | \(0.655804\pi\) | |||||||
\(710\) | 4.32503e6 | 0.321990 | ||||||||
\(711\) | 8.83137e6 | 0.655170 | ||||||||
\(712\) | 4.25651e6 | 0.314669 | ||||||||
\(713\) | 2.41350e7 | 1.77797 | ||||||||
\(714\) | 2.34189e6 | 0.171918 | ||||||||
\(715\) | −9.79109e6 | −0.716252 | ||||||||
\(716\) | −1.12941e7 | −0.823319 | ||||||||
\(717\) | 7.93384e6 | 0.576349 | ||||||||
\(718\) | −1.48983e7 | −1.07851 | ||||||||
\(719\) | −1.28196e7 | −0.924810 | −0.462405 | − | 0.886669i | \(-0.653013\pi\) | ||||
−0.462405 | + | 0.886669i | \(0.653013\pi\) | |||||||
\(720\) | 518400. | 0.0372678 | ||||||||
\(721\) | 1.51502e6 | 0.108538 | ||||||||
\(722\) | 521284. | 0.0372161 | ||||||||
\(723\) | 8.00250e6 | 0.569351 | ||||||||
\(724\) | 458408. | 0.0325017 | ||||||||
\(725\) | −111409. | −0.00787181 | ||||||||
\(726\) | −6.82729e6 | −0.480736 | ||||||||
\(727\) | 2.14041e7 | 1.50197 | 0.750985 | − | 0.660320i | \(-0.229579\pi\) | ||||
0.750985 | + | 0.660320i | \(0.229579\pi\) | |||||||
\(728\) | 1.95972e6 | 0.137046 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.31303e6 | −0.0911940 | ||||||||
\(731\) | 3.11972e7 | 2.15935 | ||||||||
\(732\) | −133402. | −0.00920203 | ||||||||
\(733\) | 2.20700e7 | 1.51720 | 0.758599 | − | 0.651558i | \(-0.225884\pi\) | ||||
0.758599 | + | 0.651558i | \(0.225884\pi\) | |||||||
\(734\) | −2.43600e6 | −0.166892 | ||||||||
\(735\) | 3.29923e6 | 0.225265 | ||||||||
\(736\) | 4.89040e6 | 0.332775 | ||||||||
\(737\) | 1.06208e7 | 0.720258 | ||||||||
\(738\) | 4.90807e6 | 0.331719 | ||||||||
\(739\) | −1.34951e7 | −0.909004 | −0.454502 | − | 0.890746i | \(-0.650183\pi\) | ||||
−0.454502 | + | 0.890746i | \(0.650183\pi\) | |||||||
\(740\) | −1.44110e6 | −0.0967420 | ||||||||
\(741\) | −2.14869e6 | −0.143757 | ||||||||
\(742\) | 1.77810e6 | 0.118562 | ||||||||
\(743\) | 2.01371e7 | 1.33821 | 0.669107 | − | 0.743166i | \(-0.266677\pi\) | ||||
0.669107 | + | 0.743166i | \(0.266677\pi\) | |||||||
\(744\) | −2.91088e6 | −0.192794 | ||||||||
\(745\) | 1.22571e7 | 0.809090 | ||||||||
\(746\) | −4.58097e6 | −0.301377 | ||||||||
\(747\) | 475736. | 0.0311935 | ||||||||
\(748\) | 1.33126e7 | 0.869976 | ||||||||
\(749\) | −5.53729e6 | −0.360656 | ||||||||
\(750\) | −562500. | −0.0365148 | ||||||||
\(751\) | −1.94257e7 | −1.25683 | −0.628414 | − | 0.777879i | \(-0.716296\pi\) | ||||
−0.628414 | + | 0.777879i | \(0.716296\pi\) | |||||||
\(752\) | 3.13097e6 | 0.201899 | ||||||||
\(753\) | −1.07636e6 | −0.0691784 | ||||||||
\(754\) | −471546. | −0.0302062 | ||||||||
\(755\) | −5.25060e6 | −0.335229 | ||||||||
\(756\) | −540053. | −0.0343663 | ||||||||
\(757\) | 6.77650e6 | 0.429799 | 0.214900 | − | 0.976636i | \(-0.431058\pi\) | ||||
0.214900 | + | 0.976636i | \(0.431058\pi\) | |||||||
\(758\) | −1.54240e7 | −0.975045 | ||||||||
\(759\) | 2.54539e7 | 1.60380 | ||||||||
\(760\) | 577600. | 0.0362738 | ||||||||
\(761\) | −3.45254e6 | −0.216111 | −0.108056 | − | 0.994145i | \(-0.534462\pi\) | ||||
−0.108056 | + | 0.994145i | \(0.534462\pi\) | |||||||
\(762\) | 5.84399e6 | 0.364605 | ||||||||
\(763\) | 4.99364e6 | 0.310532 | ||||||||
\(764\) | 2.19397e6 | 0.135987 | ||||||||
\(765\) | −2.84511e6 | −0.175771 | ||||||||
\(766\) | 1.46560e6 | 0.0902494 | ||||||||
\(767\) | 1.44952e6 | 0.0889682 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 3.09539e7 | 1.88756 | 0.943779 | − | 0.330578i | \(-0.107244\pi\) | ||||
0.943779 | + | 0.330578i | \(0.107244\pi\) | |||||||
\(770\) | −2.74193e6 | −0.166659 | ||||||||
\(771\) | 3.05206e6 | 0.184909 | ||||||||
\(772\) | 1.48944e7 | 0.899458 | ||||||||
\(773\) | 5.07221e6 | 0.305315 | 0.152658 | − | 0.988279i | \(-0.451217\pi\) | ||||
0.152658 | + | 0.988279i | \(0.451217\pi\) | |||||||
\(774\) | −7.19426e6 | −0.431652 | ||||||||
\(775\) | 3.15851e6 | 0.188898 | ||||||||
\(776\) | 9.29880e6 | 0.554336 | ||||||||
\(777\) | 1.50130e6 | 0.0892100 | ||||||||
\(778\) | −6.91679e6 | −0.409690 | ||||||||
\(779\) | 5.46856e6 | 0.322871 | ||||||||
\(780\) | −2.38082e6 | −0.140117 | ||||||||
\(781\) | −2.56127e7 | −1.50255 | ||||||||
\(782\) | −2.68398e7 | −1.56950 | ||||||||
\(783\) | 129947. | 0.00757465 | ||||||||
\(784\) | −3.75379e6 | −0.218112 | ||||||||
\(785\) | 344984. | 0.0199814 | ||||||||
\(786\) | −9.36557e6 | −0.540727 | ||||||||
\(787\) | −1.04173e7 | −0.599542 | −0.299771 | − | 0.954011i | \(-0.596910\pi\) | ||||
−0.299771 | + | 0.954011i | \(0.596910\pi\) | |||||||
\(788\) | −29006.5 | −0.00166410 | ||||||||
\(789\) | −585353. | −0.0334753 | ||||||||
\(790\) | 1.09029e7 | 0.621549 | ||||||||
\(791\) | 1.20293e7 | 0.683594 | ||||||||
\(792\) | −3.06995e6 | −0.173908 | ||||||||
\(793\) | 612665. | 0.0345971 | ||||||||
\(794\) | −1.98164e6 | −0.111551 | ||||||||
\(795\) | −2.16018e6 | −0.121219 | ||||||||
\(796\) | 9.68332e6 | 0.541678 | ||||||||
\(797\) | 2.74038e7 | 1.52815 | 0.764074 | − | 0.645129i | \(-0.223196\pi\) | ||||
0.764074 | + | 0.645129i | \(0.223196\pi\) | |||||||
\(798\) | −601726. | −0.0334497 | ||||||||
\(799\) | −1.71836e7 | −0.952241 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | 5.38715e6 | 0.296673 | ||||||||
\(802\) | −2.46623e6 | −0.135393 | ||||||||
\(803\) | 7.77571e6 | 0.425550 | ||||||||
\(804\) | 2.58257e6 | 0.140901 | ||||||||
\(805\) | 5.52808e6 | 0.300666 | ||||||||
\(806\) | 1.33686e7 | 0.724852 | ||||||||
\(807\) | 1.20206e7 | 0.649744 | ||||||||
\(808\) | 169813. | 0.00915044 | ||||||||
\(809\) | 3.67103e7 | 1.97205 | 0.986023 | − | 0.166607i | \(-0.0532811\pi\) | ||||
0.986023 | + | 0.166607i | \(0.0532811\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | 2.46123e7 | 1.31401 | 0.657006 | − | 0.753885i | \(-0.271823\pi\) | ||||
0.657006 | + | 0.753885i | \(0.271823\pi\) | |||||||
\(812\) | −132053. | −0.00702843 | ||||||||
\(813\) | 1.29530e7 | 0.687298 | ||||||||
\(814\) | 8.53416e6 | 0.451440 | ||||||||
\(815\) | 198996. | 0.0104942 | ||||||||
\(816\) | 3.23711e6 | 0.170189 | ||||||||
\(817\) | −8.01583e6 | −0.420139 | ||||||||
\(818\) | 1.77504e7 | 0.927524 | ||||||||
\(819\) | 2.48027e6 | 0.129208 | ||||||||
\(820\) | 6.05935e6 | 0.314696 | ||||||||
\(821\) | 1.19995e7 | 0.621305 | 0.310653 | − | 0.950523i | \(-0.399452\pi\) | ||||
0.310653 | + | 0.950523i | \(0.399452\pi\) | |||||||
\(822\) | −2.72411e6 | −0.140619 | ||||||||
\(823\) | 2.80911e7 | 1.44567 | 0.722834 | − | 0.691022i | \(-0.242839\pi\) | ||||
0.722834 | + | 0.691022i | \(0.242839\pi\) | |||||||
\(824\) | 2.09416e6 | 0.107446 | ||||||||
\(825\) | 3.33111e6 | 0.170394 | ||||||||
\(826\) | 405927. | 0.0207013 | ||||||||
\(827\) | 1.74273e7 | 0.886066 | 0.443033 | − | 0.896505i | \(-0.353902\pi\) | ||||
0.443033 | + | 0.896505i | \(0.353902\pi\) | |||||||
\(828\) | 6.18942e6 | 0.313743 | ||||||||
\(829\) | 1.76895e7 | 0.893981 | 0.446990 | − | 0.894539i | \(-0.352496\pi\) | ||||
0.446990 | + | 0.894539i | \(0.352496\pi\) | |||||||
\(830\) | 587328. | 0.0295928 | ||||||||
\(831\) | 1.01836e7 | 0.511563 | ||||||||
\(832\) | 2.70885e6 | 0.135668 | ||||||||
\(833\) | 2.06018e7 | 1.02871 | ||||||||
\(834\) | 2.86175e6 | 0.142468 | ||||||||
\(835\) | 1.02031e7 | 0.506425 | ||||||||
\(836\) | −3.42053e6 | −0.169269 | ||||||||
\(837\) | −3.68409e6 | −0.181767 | ||||||||
\(838\) | 2.39958e7 | 1.18039 | ||||||||
\(839\) | −3.44796e7 | −1.69106 | −0.845528 | − | 0.533931i | \(-0.820714\pi\) | ||||
−0.845528 | + | 0.533931i | \(0.820714\pi\) | |||||||
\(840\) | −666733. | −0.0326027 | ||||||||
\(841\) | −2.04794e7 | −0.998451 | ||||||||
\(842\) | −9.36082e6 | −0.455023 | ||||||||
\(843\) | −1.16071e7 | −0.562541 | ||||||||
\(844\) | −1.70248e7 | −0.822669 | ||||||||
\(845\) | 1.65193e6 | 0.0795882 | ||||||||
\(846\) | 3.96263e6 | 0.190352 | ||||||||
\(847\) | 8.78082e6 | 0.420559 | ||||||||
\(848\) | 2.45780e6 | 0.117370 | ||||||||
\(849\) | −1.08819e7 | −0.518124 | ||||||||
\(850\) | −3.51249e6 | −0.166751 | ||||||||
\(851\) | −1.72060e7 | −0.814433 | ||||||||
\(852\) | −6.22804e6 | −0.293936 | ||||||||
\(853\) | 2.17229e7 | 1.02222 | 0.511110 | − | 0.859515i | \(-0.329234\pi\) | ||||
0.511110 | + | 0.859515i | \(0.329234\pi\) | |||||||
\(854\) | 171573. | 0.00805014 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | −7.65399e6 | −0.357029 | ||||||||
\(857\) | 1.25946e7 | 0.585778 | 0.292889 | − | 0.956147i | \(-0.405383\pi\) | ||||
0.292889 | + | 0.956147i | \(0.405383\pi\) | |||||||
\(858\) | 1.40992e7 | 0.653846 | ||||||||
\(859\) | −2.38444e7 | −1.10256 | −0.551281 | − | 0.834320i | \(-0.685861\pi\) | ||||
−0.551281 | + | 0.834320i | \(0.685861\pi\) | |||||||
\(860\) | −8.88181e6 | −0.409501 | ||||||||
\(861\) | −6.31245e6 | −0.290195 | ||||||||
\(862\) | −1.27429e7 | −0.584115 | ||||||||
\(863\) | −3.48578e7 | −1.59321 | −0.796604 | − | 0.604501i | \(-0.793373\pi\) | ||||
−0.796604 | + | 0.604501i | \(0.793373\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 1.40772e7 | 0.639699 | ||||||||
\(866\) | −1.50601e7 | −0.682392 | ||||||||
\(867\) | −4.98738e6 | −0.225333 | ||||||||
\(868\) | 3.74379e6 | 0.168660 | ||||||||
\(869\) | −6.45668e7 | −2.90041 | ||||||||
\(870\) | 160429. | 0.00718594 | ||||||||
\(871\) | −1.18608e7 | −0.529748 | ||||||||
\(872\) | 6.90253e6 | 0.307409 | ||||||||
\(873\) | 1.17688e7 | 0.522633 | ||||||||
\(874\) | 6.89623e6 | 0.305375 | ||||||||
\(875\) | 723451. | 0.0319440 | ||||||||
\(876\) | 1.89076e6 | 0.0832483 | ||||||||
\(877\) | −1.07520e7 | −0.472052 | −0.236026 | − | 0.971747i | \(-0.575845\pi\) | ||||
−0.236026 | + | 0.971747i | \(0.575845\pi\) | |||||||
\(878\) | −1.49451e7 | −0.654277 | ||||||||
\(879\) | −3.59355e6 | −0.156874 | ||||||||
\(880\) | −3.79006e6 | −0.164983 | ||||||||
\(881\) | −2.91868e7 | −1.26691 | −0.633457 | − | 0.773778i | \(-0.718365\pi\) | ||||
−0.633457 | + | 0.773778i | \(0.718365\pi\) | |||||||
\(882\) | −4.75089e6 | −0.205638 | ||||||||
\(883\) | 1.27529e6 | 0.0550436 | 0.0275218 | − | 0.999621i | \(-0.491238\pi\) | ||||
0.0275218 | + | 0.999621i | \(0.491238\pi\) | |||||||
\(884\) | −1.48669e7 | −0.639865 | ||||||||
\(885\) | −493152. | −0.0211652 | ||||||||
\(886\) | 6.51100e6 | 0.278653 | ||||||||
\(887\) | 2.02105e6 | 0.0862517 | 0.0431258 | − | 0.999070i | \(-0.486268\pi\) | ||||
0.0431258 | + | 0.999070i | \(0.486268\pi\) | |||||||
\(888\) | 2.07519e6 | 0.0883130 | ||||||||
\(889\) | −7.51616e6 | −0.318964 | ||||||||
\(890\) | 6.65080e6 | 0.281448 | ||||||||
\(891\) | −3.88541e6 | −0.163962 | ||||||||
\(892\) | −5.42929e6 | −0.228471 | ||||||||
\(893\) | 4.41516e6 | 0.185275 | ||||||||
\(894\) | −1.76502e7 | −0.738595 | ||||||||
\(895\) | −1.76470e7 | −0.736399 | ||||||||
\(896\) | 758594. | 0.0315674 | ||||||||
\(897\) | −2.84257e7 | −1.17959 | ||||||||
\(898\) | 2.95001e6 | 0.122077 | ||||||||
\(899\) | −900828. | −0.0371743 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | −1.34890e7 | −0.553566 | ||||||||
\(902\) | −3.58833e7 | −1.46851 | ||||||||
\(903\) | 9.25280e6 | 0.377619 | ||||||||
\(904\) | 1.66276e7 | 0.676720 | ||||||||
\(905\) | 716263. | 0.0290704 | ||||||||
\(906\) | 7.56086e6 | 0.306021 | ||||||||
\(907\) | 1.65529e6 | 0.0668122 | 0.0334061 | − | 0.999442i | \(-0.489365\pi\) | ||||
0.0334061 | + | 0.999442i | \(0.489365\pi\) | |||||||
\(908\) | −9.00937e6 | −0.362643 | ||||||||
\(909\) | 214919. | 0.00862712 | ||||||||
\(910\) | 3.06206e6 | 0.122577 | ||||||||
\(911\) | −3.22406e7 | −1.28708 | −0.643542 | − | 0.765411i | \(-0.722536\pi\) | ||||
−0.643542 | + | 0.765411i | \(0.722536\pi\) | |||||||
\(912\) | −831744. | −0.0331133 | ||||||||
\(913\) | −3.47814e6 | −0.138093 | ||||||||
\(914\) | −3.57452e6 | −0.141531 | ||||||||
\(915\) | −208440. | −0.00823054 | ||||||||
\(916\) | −2.28965e6 | −0.0901633 | ||||||||
\(917\) | 1.20454e7 | 0.473040 | ||||||||
\(918\) | 4.09697e6 | 0.160456 | ||||||||
\(919\) | 4.54273e7 | 1.77431 | 0.887153 | − | 0.461475i | \(-0.152680\pi\) | ||||
0.887153 | + | 0.461475i | \(0.152680\pi\) | |||||||
\(920\) | 7.64126e6 | 0.297643 | ||||||||
\(921\) | −1.43419e7 | −0.557133 | ||||||||
\(922\) | −2.18635e7 | −0.847017 | ||||||||
\(923\) | 2.86031e7 | 1.10512 | ||||||||
\(924\) | 3.94837e6 | 0.152138 | ||||||||
\(925\) | −2.25172e6 | −0.0865287 | ||||||||
\(926\) | −1.62393e7 | −0.622359 | ||||||||
\(927\) | 2.65042e6 | 0.101301 | ||||||||
\(928\) | −182532. | −0.00695776 | ||||||||
\(929\) | −1.91920e7 | −0.729593 | −0.364796 | − | 0.931087i | \(-0.618861\pi\) | ||||
−0.364796 | + | 0.931087i | \(0.618861\pi\) | |||||||
\(930\) | −4.54826e6 | −0.172440 | ||||||||
\(931\) | −5.29343e6 | −0.200153 | ||||||||
\(932\) | −2.39540e6 | −0.0903313 | ||||||||
\(933\) | 8.05525e6 | 0.302953 | ||||||||
\(934\) | 2.21280e7 | 0.829995 | ||||||||
\(935\) | 2.08009e7 | 0.778130 | ||||||||
\(936\) | 3.42838e6 | 0.127909 | ||||||||
\(937\) | −1.24587e7 | −0.463578 | −0.231789 | − | 0.972766i | \(-0.574458\pi\) | ||||
−0.231789 | + | 0.972766i | \(0.574458\pi\) | |||||||
\(938\) | −3.32154e6 | −0.123263 | ||||||||
\(939\) | −5.33956e6 | −0.197625 | ||||||||
\(940\) | 4.89214e6 | 0.180584 | ||||||||
\(941\) | 1.53659e7 | 0.565699 | 0.282849 | − | 0.959164i | \(-0.408720\pi\) | ||||
0.282849 | + | 0.959164i | \(0.408720\pi\) | |||||||
\(942\) | −496777. | −0.0182404 | ||||||||
\(943\) | 7.23454e7 | 2.64930 | ||||||||
\(944\) | 561098. | 0.0204931 | ||||||||
\(945\) | −843834. | −0.0307381 | ||||||||
\(946\) | 5.25978e7 | 1.91091 | ||||||||
\(947\) | 1.55748e7 | 0.564349 | 0.282175 | − | 0.959363i | \(-0.408944\pi\) | ||||
0.282175 | + | 0.959363i | \(0.408944\pi\) | |||||||
\(948\) | −1.57002e7 | −0.567394 | ||||||||
\(949\) | −8.68356e6 | −0.312991 | ||||||||
\(950\) | 902500. | 0.0324443 | ||||||||
\(951\) | −3.09992e7 | −1.11147 | ||||||||
\(952\) | −4.16336e6 | −0.148885 | ||||||||
\(953\) | 3.55359e7 | 1.26746 | 0.633731 | − | 0.773554i | \(-0.281523\pi\) | ||||
0.633731 | + | 0.773554i | \(0.281523\pi\) | |||||||
\(954\) | 3.11065e6 | 0.110657 | ||||||||
\(955\) | 3.42808e6 | 0.121630 | ||||||||
\(956\) | −1.41046e7 | −0.499133 | ||||||||
\(957\) | −950054. | −0.0335327 | ||||||||
\(958\) | 4.31131e6 | 0.151773 | ||||||||
\(959\) | 3.50357e6 | 0.123017 | ||||||||
\(960\) | −921600. | −0.0322749 | ||||||||
\(961\) | −3.09011e6 | −0.107936 | ||||||||
\(962\) | −9.53057e6 | −0.332033 | ||||||||
\(963\) | −9.68709e6 | −0.336610 | ||||||||
\(964\) | −1.42267e7 | −0.493072 | ||||||||
\(965\) | 2.32726e7 | 0.804499 | ||||||||
\(966\) | −7.96043e6 | −0.274469 | ||||||||
\(967\) | −2.87843e7 | −0.989895 | −0.494948 | − | 0.868923i | \(-0.664813\pi\) | ||||
−0.494948 | + | 0.868923i | \(0.664813\pi\) | |||||||
\(968\) | 1.21374e7 | 0.416330 | ||||||||
\(969\) | 4.56483e6 | 0.156176 | ||||||||
\(970\) | 1.45294e7 | 0.495813 | ||||||||
\(971\) | −2.81369e6 | −0.0957697 | −0.0478849 | − | 0.998853i | \(-0.515248\pi\) | ||||
−0.0478849 | + | 0.998853i | \(0.515248\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −3.68060e6 | −0.124634 | ||||||||
\(974\) | −2.20582e7 | −0.745028 | ||||||||
\(975\) | −3.72004e6 | −0.125324 | ||||||||
\(976\) | 237159. | 0.00796919 | ||||||||
\(977\) | 3.57564e7 | 1.19844 | 0.599222 | − | 0.800583i | \(-0.295477\pi\) | ||||
0.599222 | + | 0.800583i | \(0.295477\pi\) | |||||||
\(978\) | −286554. | −0.00957987 | ||||||||
\(979\) | −3.93859e7 | −1.31336 | ||||||||
\(980\) | −5.86529e6 | −0.195085 | ||||||||
\(981\) | 8.73601e6 | 0.289828 | ||||||||
\(982\) | −3.67095e7 | −1.21479 | ||||||||
\(983\) | −2.56559e7 | −0.846845 | −0.423422 | − | 0.905932i | \(-0.639171\pi\) | ||||
−0.423422 | + | 0.905932i | \(0.639171\pi\) | |||||||
\(984\) | −8.72546e6 | −0.287277 | ||||||||
\(985\) | −45322.7 | −0.00148842 | ||||||||
\(986\) | 1.00178e6 | 0.0328157 | ||||||||
\(987\) | −5.09649e6 | −0.166524 | ||||||||
\(988\) | 3.81990e6 | 0.124497 | ||||||||
\(989\) | −1.06044e8 | −3.44743 | ||||||||
\(990\) | −4.79680e6 | −0.155548 | ||||||||
\(991\) | −1.79995e7 | −0.582205 | −0.291103 | − | 0.956692i | \(-0.594022\pi\) | ||||
−0.291103 | + | 0.956692i | \(0.594022\pi\) | |||||||
\(992\) | 5.17490e6 | 0.166964 | ||||||||
\(993\) | −2.15270e7 | −0.692804 | ||||||||
\(994\) | 8.01010e6 | 0.257142 | ||||||||
\(995\) | 1.51302e7 | 0.484492 | ||||||||
\(996\) | −845753. | −0.0270144 | ||||||||
\(997\) | 5.65443e7 | 1.80157 | 0.900785 | − | 0.434266i | \(-0.142992\pi\) | ||||
0.900785 | + | 0.434266i | \(0.142992\pi\) | |||||||
\(998\) | −3.36463e7 | −1.06933 | ||||||||
\(999\) | 2.62641e6 | 0.0832623 |
(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 | 570.6.a.o.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.o.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial |