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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2696x^{2} + 13833x + 894635 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-50.6958\) 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 | ||||||||
\(7\) | −198.741 | −1.53300 | −0.766502 | − | 0.642242i | \(-0.778004\pi\) | ||||
−0.766502 | + | 0.642242i | \(0.778004\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −301.688 | −0.751755 | −0.375877 | − | 0.926669i | \(-0.622659\pi\) | ||||
−0.375877 | + | 0.926669i | \(0.622659\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −414.182 | −0.679725 | −0.339862 | − | 0.940475i | \(-0.610380\pi\) | ||||
−0.339862 | + | 0.940475i | \(0.610380\pi\) | |||||||
\(14\) | 794.966 | 1.08400 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1804.45 | 1.51434 | 0.757168 | − | 0.653220i | \(-0.226582\pi\) | ||||
0.757168 | + | 0.653220i | \(0.226582\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | 1788.67 | 0.885080 | ||||||||
\(22\) | 1206.75 | 0.531571 | ||||||||
\(23\) | 2577.82 | 1.01609 | 0.508046 | − | 0.861330i | \(-0.330368\pi\) | ||||
0.508046 | + | 0.861330i | \(0.330368\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1656.73 | 0.480638 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3179.86 | −0.766502 | ||||||||
\(29\) | 2841.62 | 0.627439 | 0.313719 | − | 0.949516i | \(-0.398425\pi\) | ||||
0.313719 | + | 0.949516i | \(0.398425\pi\) | |||||||
\(30\) | −900.000 | −0.182574 | ||||||||
\(31\) | −510.669 | −0.0954411 | −0.0477206 | − | 0.998861i | \(-0.515196\pi\) | ||||
−0.0477206 | + | 0.998861i | \(0.515196\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 2715.19 | 0.434026 | ||||||||
\(34\) | −7217.80 | −1.07080 | ||||||||
\(35\) | 4968.53 | 0.685580 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 6458.05 | 0.775527 | 0.387764 | − | 0.921759i | \(-0.373248\pi\) | ||||
0.387764 | + | 0.921759i | \(0.373248\pi\) | |||||||
\(38\) | 1444.00 | 0.162221 | ||||||||
\(39\) | 3727.64 | 0.392439 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | −15588.5 | −1.44825 | −0.724125 | − | 0.689668i | \(-0.757756\pi\) | ||||
−0.724125 | + | 0.689668i | \(0.757756\pi\) | |||||||
\(42\) | −7154.69 | −0.625846 | ||||||||
\(43\) | 1117.24 | 0.0921455 | 0.0460727 | − | 0.998938i | \(-0.485329\pi\) | ||||
0.0460727 | + | 0.998938i | \(0.485329\pi\) | |||||||
\(44\) | −4827.01 | −0.375877 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −10311.3 | −0.718485 | ||||||||
\(47\) | 11966.1 | 0.790147 | 0.395074 | − | 0.918649i | \(-0.370719\pi\) | ||||
0.395074 | + | 0.918649i | \(0.370719\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 22691.1 | 1.35010 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −16240.0 | −0.874303 | ||||||||
\(52\) | −6626.91 | −0.339862 | ||||||||
\(53\) | 10801.4 | 0.528190 | 0.264095 | − | 0.964497i | \(-0.414927\pi\) | ||||
0.264095 | + | 0.964497i | \(0.414927\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 7542.20 | 0.336195 | ||||||||
\(56\) | 12719.4 | 0.541999 | ||||||||
\(57\) | 3249.00 | 0.132453 | ||||||||
\(58\) | −11366.5 | −0.443666 | ||||||||
\(59\) | −24206.6 | −0.905323 | −0.452662 | − | 0.891682i | \(-0.649525\pi\) | ||||
−0.452662 | + | 0.891682i | \(0.649525\pi\) | |||||||
\(60\) | 3600.00 | 0.129099 | ||||||||
\(61\) | 24297.8 | 0.836068 | 0.418034 | − | 0.908431i | \(-0.362719\pi\) | ||||
0.418034 | + | 0.908431i | \(0.362719\pi\) | |||||||
\(62\) | 2042.68 | 0.0674871 | ||||||||
\(63\) | −16098.1 | −0.511001 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 10354.6 | 0.303982 | ||||||||
\(66\) | −10860.8 | −0.306903 | ||||||||
\(67\) | 44459.2 | 1.20997 | 0.604985 | − | 0.796237i | \(-0.293179\pi\) | ||||
0.604985 | + | 0.796237i | \(0.293179\pi\) | |||||||
\(68\) | 28871.2 | 0.757168 | ||||||||
\(69\) | −23200.4 | −0.586641 | ||||||||
\(70\) | −19874.1 | −0.484778 | ||||||||
\(71\) | −17048.7 | −0.401371 | −0.200685 | − | 0.979656i | \(-0.564317\pi\) | ||||
−0.200685 | + | 0.979656i | \(0.564317\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 4995.94 | 0.109726 | 0.0548631 | − | 0.998494i | \(-0.482528\pi\) | ||||
0.0548631 | + | 0.998494i | \(0.482528\pi\) | |||||||
\(74\) | −25832.2 | −0.548380 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | −5776.00 | −0.114708 | ||||||||
\(77\) | 59957.9 | 1.15244 | ||||||||
\(78\) | −14910.6 | −0.277496 | ||||||||
\(79\) | −32826.8 | −0.591780 | −0.295890 | − | 0.955222i | \(-0.595616\pi\) | ||||
−0.295890 | + | 0.955222i | \(0.595616\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 62353.9 | 1.02407 | ||||||||
\(83\) | −4543.51 | −0.0723930 | −0.0361965 | − | 0.999345i | \(-0.511524\pi\) | ||||
−0.0361965 | + | 0.999345i | \(0.511524\pi\) | |||||||
\(84\) | 28618.8 | 0.442540 | ||||||||
\(85\) | −45111.2 | −0.677232 | ||||||||
\(86\) | −4468.95 | −0.0651567 | ||||||||
\(87\) | −25574.6 | −0.362252 | ||||||||
\(88\) | 19308.0 | 0.265785 | ||||||||
\(89\) | −20581.8 | −0.275428 | −0.137714 | − | 0.990472i | \(-0.543975\pi\) | ||||
−0.137714 | + | 0.990472i | \(0.543975\pi\) | |||||||
\(90\) | 8100.00 | 0.105409 | ||||||||
\(91\) | 82315.1 | 1.04202 | ||||||||
\(92\) | 41245.1 | 0.508046 | ||||||||
\(93\) | 4596.02 | 0.0551030 | ||||||||
\(94\) | −47864.4 | −0.558718 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 115889. | 1.25058 | 0.625290 | − | 0.780393i | \(-0.284981\pi\) | ||||
0.625290 | + | 0.780393i | \(0.284981\pi\) | |||||||
\(98\) | −90764.5 | −0.954665 | ||||||||
\(99\) | −24436.7 | −0.250585 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 69844.0 | 0.681280 | 0.340640 | − | 0.940194i | \(-0.389356\pi\) | ||||
0.340640 | + | 0.940194i | \(0.389356\pi\) | |||||||
\(102\) | 64960.2 | 0.618225 | ||||||||
\(103\) | −6073.57 | −0.0564093 | −0.0282047 | − | 0.999602i | \(-0.508979\pi\) | ||||
−0.0282047 | + | 0.999602i | \(0.508979\pi\) | |||||||
\(104\) | 26507.7 | 0.240319 | ||||||||
\(105\) | −44716.8 | −0.395820 | ||||||||
\(106\) | −43205.6 | −0.373487 | ||||||||
\(107\) | −176308. | −1.48872 | −0.744359 | − | 0.667780i | \(-0.767245\pi\) | ||||
−0.744359 | + | 0.667780i | \(0.767245\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 11317.0 | 0.0912360 | 0.0456180 | − | 0.998959i | \(-0.485474\pi\) | ||||
0.0456180 | + | 0.998959i | \(0.485474\pi\) | |||||||
\(110\) | −30168.8 | −0.237726 | ||||||||
\(111\) | −58122.4 | −0.447751 | ||||||||
\(112\) | −50877.8 | −0.383251 | ||||||||
\(113\) | 220212. | 1.62235 | 0.811177 | − | 0.584801i | \(-0.198827\pi\) | ||||
0.811177 | + | 0.584801i | \(0.198827\pi\) | |||||||
\(114\) | −12996.0 | −0.0936586 | ||||||||
\(115\) | −64445.5 | −0.454410 | ||||||||
\(116\) | 45466.0 | 0.313719 | ||||||||
\(117\) | −33548.8 | −0.226575 | ||||||||
\(118\) | 96826.4 | 0.640160 | ||||||||
\(119\) | −358619. | −2.32148 | ||||||||
\(120\) | −14400.0 | −0.0912871 | ||||||||
\(121\) | −70035.4 | −0.434865 | ||||||||
\(122\) | −97191.0 | −0.591189 | ||||||||
\(123\) | 140296. | 0.836148 | ||||||||
\(124\) | −8170.71 | −0.0477206 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 64392.2 | 0.361332 | ||||||||
\(127\) | 194607. | 1.07066 | 0.535328 | − | 0.844645i | \(-0.320188\pi\) | ||||
0.535328 | + | 0.844645i | \(0.320188\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −10055.1 | −0.0532002 | ||||||||
\(130\) | −41418.2 | −0.214948 | ||||||||
\(131\) | 81446.7 | 0.414663 | 0.207331 | − | 0.978271i | \(-0.433522\pi\) | ||||
0.207331 | + | 0.978271i | \(0.433522\pi\) | |||||||
\(132\) | 43443.0 | 0.217013 | ||||||||
\(133\) | 71745.6 | 0.351695 | ||||||||
\(134\) | −177837. | −0.855577 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | −115485. | −0.535399 | ||||||||
\(137\) | 150418. | 0.684697 | 0.342348 | − | 0.939573i | \(-0.388778\pi\) | ||||
0.342348 | + | 0.939573i | \(0.388778\pi\) | |||||||
\(138\) | 92801.4 | 0.414817 | ||||||||
\(139\) | 91266.1 | 0.400657 | 0.200328 | − | 0.979729i | \(-0.435799\pi\) | ||||
0.200328 | + | 0.979729i | \(0.435799\pi\) | |||||||
\(140\) | 79496.6 | 0.342790 | ||||||||
\(141\) | −107695. | −0.456192 | ||||||||
\(142\) | 68194.8 | 0.283812 | ||||||||
\(143\) | 124954. | 0.510986 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −71040.6 | −0.280599 | ||||||||
\(146\) | −19983.8 | −0.0775881 | ||||||||
\(147\) | −204220. | −0.779481 | ||||||||
\(148\) | 103329. | 0.387764 | ||||||||
\(149\) | −428133. | −1.57984 | −0.789920 | − | 0.613210i | \(-0.789878\pi\) | ||||
−0.789920 | + | 0.613210i | \(0.789878\pi\) | |||||||
\(150\) | 22500.0 | 0.0816497 | ||||||||
\(151\) | −317579. | −1.13347 | −0.566734 | − | 0.823901i | \(-0.691793\pi\) | ||||
−0.566734 | + | 0.823901i | \(0.691793\pi\) | |||||||
\(152\) | 23104.0 | 0.0811107 | ||||||||
\(153\) | 146160. | 0.504779 | ||||||||
\(154\) | −239831. | −0.814900 | ||||||||
\(155\) | 12766.7 | 0.0426826 | ||||||||
\(156\) | 59642.2 | 0.196220 | ||||||||
\(157\) | −532116. | −1.72289 | −0.861444 | − | 0.507853i | \(-0.830439\pi\) | ||||
−0.861444 | + | 0.507853i | \(0.830439\pi\) | |||||||
\(158\) | 131307. | 0.418452 | ||||||||
\(159\) | −97212.6 | −0.304951 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | −512319. | −1.55767 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −459461. | −1.35450 | −0.677251 | − | 0.735752i | \(-0.736829\pi\) | ||||
−0.677251 | + | 0.735752i | \(0.736829\pi\) | |||||||
\(164\) | −249415. | −0.724125 | ||||||||
\(165\) | −67879.8 | −0.194102 | ||||||||
\(166\) | 18174.1 | 0.0511896 | ||||||||
\(167\) | −159215. | −0.441767 | −0.220883 | − | 0.975300i | \(-0.570894\pi\) | ||||
−0.220883 | + | 0.975300i | \(0.570894\pi\) | |||||||
\(168\) | −114475. | −0.312923 | ||||||||
\(169\) | −199746. | −0.537975 | ||||||||
\(170\) | 180445. | 0.478875 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 17875.8 | 0.0460727 | ||||||||
\(173\) | −713321. | −1.81205 | −0.906025 | − | 0.423225i | \(-0.860898\pi\) | ||||
−0.906025 | + | 0.423225i | \(0.860898\pi\) | |||||||
\(174\) | 102298. | 0.256151 | ||||||||
\(175\) | −124213. | −0.306601 | ||||||||
\(176\) | −77232.1 | −0.187939 | ||||||||
\(177\) | 217859. | 0.522689 | ||||||||
\(178\) | 82327.1 | 0.194757 | ||||||||
\(179\) | −388360. | −0.905944 | −0.452972 | − | 0.891525i | \(-0.649636\pi\) | ||||
−0.452972 | + | 0.891525i | \(0.649636\pi\) | |||||||
\(180\) | −32400.0 | −0.0745356 | ||||||||
\(181\) | 467365. | 1.06038 | 0.530188 | − | 0.847880i | \(-0.322121\pi\) | ||||
0.530188 | + | 0.847880i | \(0.322121\pi\) | |||||||
\(182\) | −329260. | −0.736820 | ||||||||
\(183\) | −218680. | −0.482704 | ||||||||
\(184\) | −164980. | −0.359242 | ||||||||
\(185\) | −161451. | −0.346826 | ||||||||
\(186\) | −18384.1 | −0.0389637 | ||||||||
\(187\) | −544380. | −1.13841 | ||||||||
\(188\) | 191458. | 0.395074 | ||||||||
\(189\) | 144882. | 0.295027 | ||||||||
\(190\) | −36100.0 | −0.0725476 | ||||||||
\(191\) | −911864. | −1.80862 | −0.904308 | − | 0.426880i | \(-0.859613\pi\) | ||||
−0.904308 | + | 0.426880i | \(0.859613\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 451916. | 0.873303 | 0.436651 | − | 0.899631i | \(-0.356164\pi\) | ||||
0.436651 | + | 0.899631i | \(0.356164\pi\) | |||||||
\(194\) | −463554. | −0.884293 | ||||||||
\(195\) | −93191.0 | −0.175504 | ||||||||
\(196\) | 363058. | 0.675050 | ||||||||
\(197\) | −203508. | −0.373608 | −0.186804 | − | 0.982397i | \(-0.559813\pi\) | ||||
−0.186804 | + | 0.982397i | \(0.559813\pi\) | |||||||
\(198\) | 97746.9 | 0.177190 | ||||||||
\(199\) | 633693. | 1.13435 | 0.567174 | − | 0.823598i | \(-0.308037\pi\) | ||||
0.567174 | + | 0.823598i | \(0.308037\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −400132. | −0.698576 | ||||||||
\(202\) | −279376. | −0.481738 | ||||||||
\(203\) | −564748. | −0.961866 | ||||||||
\(204\) | −259841. | −0.437151 | ||||||||
\(205\) | 389712. | 0.647677 | ||||||||
\(206\) | 24294.3 | 0.0398874 | ||||||||
\(207\) | 208803. | 0.338697 | ||||||||
\(208\) | −106031. | −0.169931 | ||||||||
\(209\) | 108909. | 0.172464 | ||||||||
\(210\) | 178867. | 0.279887 | ||||||||
\(211\) | 238810. | 0.369271 | 0.184636 | − | 0.982807i | \(-0.440889\pi\) | ||||
0.184636 | + | 0.982807i | \(0.440889\pi\) | |||||||
\(212\) | 172822. | 0.264095 | ||||||||
\(213\) | 153438. | 0.231731 | ||||||||
\(214\) | 705232. | 1.05268 | ||||||||
\(215\) | −27930.9 | −0.0412087 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 101491. | 0.146312 | ||||||||
\(218\) | −45268.1 | −0.0645136 | ||||||||
\(219\) | −44963.5 | −0.0633504 | ||||||||
\(220\) | 120675. | 0.168097 | ||||||||
\(221\) | −747371. | −1.02933 | ||||||||
\(222\) | 232490. | 0.316608 | ||||||||
\(223\) | 112222. | 0.151117 | 0.0755587 | − | 0.997141i | \(-0.475926\pi\) | ||||
0.0755587 | + | 0.997141i | \(0.475926\pi\) | |||||||
\(224\) | 203511. | 0.270999 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −880849. | −1.14718 | ||||||||
\(227\) | 4499.63 | 0.00579578 | 0.00289789 | − | 0.999996i | \(-0.499078\pi\) | ||||
0.00289789 | + | 0.999996i | \(0.499078\pi\) | |||||||
\(228\) | 51984.0 | 0.0662266 | ||||||||
\(229\) | 1.36542e6 | 1.72059 | 0.860297 | − | 0.509793i | \(-0.170278\pi\) | ||||
0.860297 | + | 0.509793i | \(0.170278\pi\) | |||||||
\(230\) | 257782. | 0.321316 | ||||||||
\(231\) | −539621. | −0.665363 | ||||||||
\(232\) | −181864. | −0.221833 | ||||||||
\(233\) | 493115. | 0.595057 | 0.297528 | − | 0.954713i | \(-0.403838\pi\) | ||||
0.297528 | + | 0.954713i | \(0.403838\pi\) | |||||||
\(234\) | 134195. | 0.160213 | ||||||||
\(235\) | −299153. | −0.353365 | ||||||||
\(236\) | −387306. | −0.452662 | ||||||||
\(237\) | 295441. | 0.341664 | ||||||||
\(238\) | 1.43447e6 | 1.64154 | ||||||||
\(239\) | −1.08076e6 | −1.22386 | −0.611932 | − | 0.790910i | \(-0.709607\pi\) | ||||
−0.611932 | + | 0.790910i | \(0.709607\pi\) | |||||||
\(240\) | 57600.0 | 0.0645497 | ||||||||
\(241\) | −301534. | −0.334421 | −0.167210 | − | 0.985921i | \(-0.553476\pi\) | ||||
−0.167210 | + | 0.985921i | \(0.553476\pi\) | |||||||
\(242\) | 280142. | 0.307496 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 388764. | 0.418034 | ||||||||
\(245\) | −567278. | −0.603783 | ||||||||
\(246\) | −561185. | −0.591246 | ||||||||
\(247\) | 149520. | 0.155940 | ||||||||
\(248\) | 32682.8 | 0.0337435 | ||||||||
\(249\) | 40891.6 | 0.0417961 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | 1.53187e6 | 1.53475 | 0.767377 | − | 0.641196i | \(-0.221561\pi\) | ||||
0.767377 | + | 0.641196i | \(0.221561\pi\) | |||||||
\(252\) | −257569. | −0.255501 | ||||||||
\(253\) | −777696. | −0.763851 | ||||||||
\(254\) | −778429. | −0.757067 | ||||||||
\(255\) | 406001. | 0.391000 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 116577. | 0.110098 | 0.0550490 | − | 0.998484i | \(-0.482468\pi\) | ||||
0.0550490 | + | 0.998484i | \(0.482468\pi\) | |||||||
\(258\) | 40220.5 | 0.0376182 | ||||||||
\(259\) | −1.28348e6 | −1.18889 | ||||||||
\(260\) | 165673. | 0.151991 | ||||||||
\(261\) | 230171. | 0.209146 | ||||||||
\(262\) | −325787. | −0.293211 | ||||||||
\(263\) | −1.82569e6 | −1.62756 | −0.813780 | − | 0.581174i | \(-0.802594\pi\) | ||||
−0.813780 | + | 0.581174i | \(0.802594\pi\) | |||||||
\(264\) | −173772. | −0.153451 | ||||||||
\(265\) | −270035. | −0.236214 | ||||||||
\(266\) | −286983. | −0.248686 | ||||||||
\(267\) | 185236. | 0.159018 | ||||||||
\(268\) | 711347. | 0.604985 | ||||||||
\(269\) | −1.08156e6 | −0.911319 | −0.455659 | − | 0.890154i | \(-0.650597\pi\) | ||||
−0.455659 | + | 0.890154i | \(0.650597\pi\) | |||||||
\(270\) | −72900.0 | −0.0608581 | ||||||||
\(271\) | −321112. | −0.265603 | −0.132801 | − | 0.991143i | \(-0.542397\pi\) | ||||
−0.132801 | + | 0.991143i | \(0.542397\pi\) | |||||||
\(272\) | 461939. | 0.378584 | ||||||||
\(273\) | −740836. | −0.601611 | ||||||||
\(274\) | −601672. | −0.484154 | ||||||||
\(275\) | −188555. | −0.150351 | ||||||||
\(276\) | −371206. | −0.293320 | ||||||||
\(277\) | 546630. | 0.428049 | 0.214025 | − | 0.976828i | \(-0.431343\pi\) | ||||
0.214025 | + | 0.976828i | \(0.431343\pi\) | |||||||
\(278\) | −365064. | −0.283307 | ||||||||
\(279\) | −41364.2 | −0.0318137 | ||||||||
\(280\) | −317986. | −0.242389 | ||||||||
\(281\) | −423500. | −0.319954 | −0.159977 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159977 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(282\) | 430780. | 0.322576 | ||||||||
\(283\) | −2.14279e6 | −1.59043 | −0.795214 | − | 0.606329i | \(-0.792641\pi\) | ||||
−0.795214 | + | 0.606329i | \(0.792641\pi\) | |||||||
\(284\) | −272779. | −0.200685 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | −499815. | −0.361322 | ||||||||
\(287\) | 3.09807e6 | 2.22017 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 1.83618e6 | 1.29321 | ||||||||
\(290\) | 284162. | 0.198414 | ||||||||
\(291\) | −1.04300e6 | −0.722022 | ||||||||
\(292\) | 79935.1 | 0.0548631 | ||||||||
\(293\) | 263928. | 0.179604 | 0.0898020 | − | 0.995960i | \(-0.471377\pi\) | ||||
0.0898020 | + | 0.995960i | \(0.471377\pi\) | |||||||
\(294\) | 816881. | 0.551176 | ||||||||
\(295\) | 605165. | 0.404873 | ||||||||
\(296\) | −413315. | −0.274190 | ||||||||
\(297\) | 219930. | 0.144675 | ||||||||
\(298\) | 1.71253e6 | 1.11712 | ||||||||
\(299\) | −1.06769e6 | −0.690662 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | −222041. | −0.141259 | ||||||||
\(302\) | 1.27032e6 | 0.801484 | ||||||||
\(303\) | −628596. | −0.393337 | ||||||||
\(304\) | −92416.0 | −0.0573539 | ||||||||
\(305\) | −607444. | −0.373901 | ||||||||
\(306\) | −584642. | −0.356933 | ||||||||
\(307\) | 798387. | 0.483468 | 0.241734 | − | 0.970343i | \(-0.422284\pi\) | ||||
0.241734 | + | 0.970343i | \(0.422284\pi\) | |||||||
\(308\) | 959326. | 0.576221 | ||||||||
\(309\) | 54662.1 | 0.0325680 | ||||||||
\(310\) | −51066.9 | −0.0301811 | ||||||||
\(311\) | 2.02222e6 | 1.18557 | 0.592786 | − | 0.805360i | \(-0.298028\pi\) | ||||
0.592786 | + | 0.805360i | \(0.298028\pi\) | |||||||
\(312\) | −238569. | −0.138748 | ||||||||
\(313\) | −362645. | −0.209229 | −0.104614 | − | 0.994513i | \(-0.533361\pi\) | ||||
−0.104614 | + | 0.994513i | \(0.533361\pi\) | |||||||
\(314\) | 2.12846e6 | 1.21827 | ||||||||
\(315\) | 402451. | 0.228527 | ||||||||
\(316\) | −525228. | −0.295890 | ||||||||
\(317\) | −2.11373e6 | −1.18141 | −0.590705 | − | 0.806888i | \(-0.701150\pi\) | ||||
−0.590705 | + | 0.806888i | \(0.701150\pi\) | |||||||
\(318\) | 388850. | 0.215633 | ||||||||
\(319\) | −857283. | −0.471680 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | 1.58677e6 | 0.859512 | ||||||||
\(322\) | 2.04928e6 | 1.10144 | ||||||||
\(323\) | −651406. | −0.347413 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | −258864. | −0.135945 | ||||||||
\(326\) | 1.83784e6 | 0.957778 | ||||||||
\(327\) | −101853. | −0.0526751 | ||||||||
\(328\) | 997662. | 0.512034 | ||||||||
\(329\) | −2.37816e6 | −1.21130 | ||||||||
\(330\) | 271519. | 0.137251 | ||||||||
\(331\) | −1.32876e6 | −0.666619 | −0.333310 | − | 0.942817i | \(-0.608165\pi\) | ||||
−0.333310 | + | 0.942817i | \(0.608165\pi\) | |||||||
\(332\) | −72696.2 | −0.0361965 | ||||||||
\(333\) | 523102. | 0.258509 | ||||||||
\(334\) | 636860. | 0.312376 | ||||||||
\(335\) | −1.11148e6 | −0.541115 | ||||||||
\(336\) | 457900. | 0.221270 | ||||||||
\(337\) | −3.74811e6 | −1.79779 | −0.898893 | − | 0.438168i | \(-0.855628\pi\) | ||||
−0.898893 | + | 0.438168i | \(0.855628\pi\) | |||||||
\(338\) | 798985. | 0.380405 | ||||||||
\(339\) | −1.98191e6 | −0.936666 | ||||||||
\(340\) | −721780. | −0.338616 | ||||||||
\(341\) | 154063. | 0.0717483 | ||||||||
\(342\) | 116964. | 0.0540738 | ||||||||
\(343\) | −1.16942e6 | −0.536705 | ||||||||
\(344\) | −71503.2 | −0.0325784 | ||||||||
\(345\) | 580009. | 0.262354 | ||||||||
\(346\) | 2.85329e6 | 1.28131 | ||||||||
\(347\) | 1.31314e6 | 0.585448 | 0.292724 | − | 0.956197i | \(-0.405438\pi\) | ||||
0.292724 | + | 0.956197i | \(0.405438\pi\) | |||||||
\(348\) | −409194. | −0.181126 | ||||||||
\(349\) | 210346. | 0.0924421 | 0.0462211 | − | 0.998931i | \(-0.485282\pi\) | ||||
0.0462211 | + | 0.998931i | \(0.485282\pi\) | |||||||
\(350\) | 496853. | 0.216799 | ||||||||
\(351\) | 301939. | 0.130813 | ||||||||
\(352\) | 308928. | 0.132893 | ||||||||
\(353\) | 3.92766e6 | 1.67763 | 0.838816 | − | 0.544415i | \(-0.183248\pi\) | ||||
0.838816 | + | 0.544415i | \(0.183248\pi\) | |||||||
\(354\) | −871437. | −0.369597 | ||||||||
\(355\) | 426218. | 0.179498 | ||||||||
\(356\) | −329309. | −0.137714 | ||||||||
\(357\) | 3.22757e6 | 1.34031 | ||||||||
\(358\) | 1.55344e6 | 0.640599 | ||||||||
\(359\) | 4.41991e6 | 1.80999 | 0.904997 | − | 0.425418i | \(-0.139873\pi\) | ||||
0.904997 | + | 0.425418i | \(0.139873\pi\) | |||||||
\(360\) | 129600. | 0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −1.86946e6 | −0.749799 | ||||||||
\(363\) | 630319. | 0.251069 | ||||||||
\(364\) | 1.31704e6 | 0.521010 | ||||||||
\(365\) | −124899. | −0.0490710 | ||||||||
\(366\) | 874719. | 0.341323 | ||||||||
\(367\) | 1.56154e6 | 0.605184 | 0.302592 | − | 0.953120i | \(-0.402148\pi\) | ||||
0.302592 | + | 0.953120i | \(0.402148\pi\) | |||||||
\(368\) | 659921. | 0.254023 | ||||||||
\(369\) | −1.26267e6 | −0.482750 | ||||||||
\(370\) | 645805. | 0.245243 | ||||||||
\(371\) | −2.14669e6 | −0.809718 | ||||||||
\(372\) | 73536.4 | 0.0275515 | ||||||||
\(373\) | 2.44097e6 | 0.908429 | 0.454214 | − | 0.890892i | \(-0.349920\pi\) | ||||
0.454214 | + | 0.890892i | \(0.349920\pi\) | |||||||
\(374\) | 2.17752e6 | 0.804977 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | −765830. | −0.279359 | ||||||||
\(377\) | −1.17695e6 | −0.426486 | ||||||||
\(378\) | −579530. | −0.208615 | ||||||||
\(379\) | 807979. | 0.288936 | 0.144468 | − | 0.989509i | \(-0.453853\pi\) | ||||
0.144468 | + | 0.989509i | \(0.453853\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | −1.75146e6 | −0.618143 | ||||||||
\(382\) | 3.64745e6 | 1.27888 | ||||||||
\(383\) | −684813. | −0.238548 | −0.119274 | − | 0.992861i | \(-0.538057\pi\) | ||||
−0.119274 | + | 0.992861i | \(0.538057\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −1.49895e6 | −0.515388 | ||||||||
\(386\) | −1.80767e6 | −0.617518 | ||||||||
\(387\) | 90496.2 | 0.0307152 | ||||||||
\(388\) | 1.85422e6 | 0.625290 | ||||||||
\(389\) | 1.16065e6 | 0.388890 | 0.194445 | − | 0.980913i | \(-0.437709\pi\) | ||||
0.194445 | + | 0.980913i | \(0.437709\pi\) | |||||||
\(390\) | 372764. | 0.124100 | ||||||||
\(391\) | 4.65154e6 | 1.53870 | ||||||||
\(392\) | −1.45223e6 | −0.477333 | ||||||||
\(393\) | −733020. | −0.239406 | ||||||||
\(394\) | 814033. | 0.264181 | ||||||||
\(395\) | 820669. | 0.264652 | ||||||||
\(396\) | −390987. | −0.125292 | ||||||||
\(397\) | −3.70712e6 | −1.18049 | −0.590243 | − | 0.807226i | \(-0.700968\pi\) | ||||
−0.590243 | + | 0.807226i | \(0.700968\pi\) | |||||||
\(398\) | −2.53477e6 | −0.802105 | ||||||||
\(399\) | −645711. | −0.203051 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 4.29269e6 | 1.33312 | 0.666559 | − | 0.745452i | \(-0.267767\pi\) | ||||
0.666559 | + | 0.745452i | \(0.267767\pi\) | |||||||
\(402\) | 1.60053e6 | 0.493968 | ||||||||
\(403\) | 211510. | 0.0648737 | ||||||||
\(404\) | 1.11750e6 | 0.340640 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | 2.25899e6 | 0.680142 | ||||||||
\(407\) | −1.94831e6 | −0.583006 | ||||||||
\(408\) | 1.03936e6 | 0.309113 | ||||||||
\(409\) | 3.44742e6 | 1.01903 | 0.509514 | − | 0.860462i | \(-0.329825\pi\) | ||||
0.509514 | + | 0.860462i | \(0.329825\pi\) | |||||||
\(410\) | −1.55885e6 | −0.457977 | ||||||||
\(411\) | −1.35376e6 | −0.395310 | ||||||||
\(412\) | −97177.1 | −0.0282047 | ||||||||
\(413\) | 4.81085e6 | 1.38786 | ||||||||
\(414\) | −835213. | −0.239495 | ||||||||
\(415\) | 113588. | 0.0323751 | ||||||||
\(416\) | 424122. | 0.120159 | ||||||||
\(417\) | −821395. | −0.231319 | ||||||||
\(418\) | −435637. | −0.121951 | ||||||||
\(419\) | −4.12052e6 | −1.14661 | −0.573307 | − | 0.819341i | \(-0.694340\pi\) | ||||
−0.573307 | + | 0.819341i | \(0.694340\pi\) | |||||||
\(420\) | −715469. | −0.197910 | ||||||||
\(421\) | 954304. | 0.262411 | 0.131205 | − | 0.991355i | \(-0.458115\pi\) | ||||
0.131205 | + | 0.991355i | \(0.458115\pi\) | |||||||
\(422\) | −955238. | −0.261114 | ||||||||
\(423\) | 969254. | 0.263382 | ||||||||
\(424\) | −691290. | −0.186743 | ||||||||
\(425\) | 1.12778e6 | 0.302867 | ||||||||
\(426\) | −613754. | −0.163859 | ||||||||
\(427\) | −4.82897e6 | −1.28170 | ||||||||
\(428\) | −2.82093e6 | −0.744359 | ||||||||
\(429\) | −1.12458e6 | −0.295018 | ||||||||
\(430\) | 111724. | 0.0291390 | ||||||||
\(431\) | −7.40001e6 | −1.91884 | −0.959421 | − | 0.281979i | \(-0.909009\pi\) | ||||
−0.959421 | + | 0.281979i | \(0.909009\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 7.14705e6 | 1.83192 | 0.915962 | − | 0.401265i | \(-0.131429\pi\) | ||||
0.915962 | + | 0.401265i | \(0.131429\pi\) | |||||||
\(434\) | −405964. | −0.103458 | ||||||||
\(435\) | 639365. | 0.162004 | ||||||||
\(436\) | 181072. | 0.0456180 | ||||||||
\(437\) | −930592. | −0.233107 | ||||||||
\(438\) | 179854. | 0.0447955 | ||||||||
\(439\) | 4.71861e6 | 1.16857 | 0.584283 | − | 0.811550i | \(-0.301376\pi\) | ||||
0.584283 | + | 0.811550i | \(0.301376\pi\) | |||||||
\(440\) | −482701. | −0.118863 | ||||||||
\(441\) | 1.83798e6 | 0.450033 | ||||||||
\(442\) | 2.98948e6 | 0.727847 | ||||||||
\(443\) | −1.37982e6 | −0.334052 | −0.167026 | − | 0.985952i | \(-0.553416\pi\) | ||||
−0.167026 | + | 0.985952i | \(0.553416\pi\) | |||||||
\(444\) | −929959. | −0.223875 | ||||||||
\(445\) | 514545. | 0.123175 | ||||||||
\(446\) | −448886. | −0.106856 | ||||||||
\(447\) | 3.85320e6 | 0.912121 | ||||||||
\(448\) | −814045. | −0.191625 | ||||||||
\(449\) | −1.41603e6 | −0.331480 | −0.165740 | − | 0.986170i | \(-0.553001\pi\) | ||||
−0.165740 | + | 0.986170i | \(0.553001\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | 4.70285e6 | 1.08873 | ||||||||
\(452\) | 3.52340e6 | 0.811177 | ||||||||
\(453\) | 2.85821e6 | 0.654409 | ||||||||
\(454\) | −17998.5 | −0.00409823 | ||||||||
\(455\) | −2.05788e6 | −0.466006 | ||||||||
\(456\) | −207936. | −0.0468293 | ||||||||
\(457\) | −3.37617e6 | −0.756196 | −0.378098 | − | 0.925766i | \(-0.623422\pi\) | ||||
−0.378098 | + | 0.925766i | \(0.623422\pi\) | |||||||
\(458\) | −5.46169e6 | −1.21664 | ||||||||
\(459\) | −1.31544e6 | −0.291434 | ||||||||
\(460\) | −1.03113e6 | −0.227205 | ||||||||
\(461\) | −8.33350e6 | −1.82631 | −0.913156 | − | 0.407609i | \(-0.866362\pi\) | ||||
−0.913156 | + | 0.407609i | \(0.866362\pi\) | |||||||
\(462\) | 2.15848e6 | 0.470483 | ||||||||
\(463\) | 3.91094e6 | 0.847869 | 0.423935 | − | 0.905693i | \(-0.360649\pi\) | ||||
0.423935 | + | 0.905693i | \(0.360649\pi\) | |||||||
\(464\) | 727455. | 0.156860 | ||||||||
\(465\) | −114901. | −0.0246428 | ||||||||
\(466\) | −1.97246e6 | −0.420769 | ||||||||
\(467\) | −1.24245e6 | −0.263625 | −0.131813 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131813 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(468\) | −536780. | −0.113287 | ||||||||
\(469\) | −8.83588e6 | −1.85489 | ||||||||
\(470\) | 1.19661e6 | 0.249866 | ||||||||
\(471\) | 4.78904e6 | 0.994710 | ||||||||
\(472\) | 1.54922e6 | 0.320080 | ||||||||
\(473\) | −337057. | −0.0692708 | ||||||||
\(474\) | −1.18176e6 | −0.241593 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −5.73790e6 | −1.16074 | ||||||||
\(477\) | 874913. | 0.176063 | ||||||||
\(478\) | 4.32303e6 | 0.865403 | ||||||||
\(479\) | −124888. | −0.0248703 | −0.0124352 | − | 0.999923i | \(-0.503958\pi\) | ||||
−0.0124352 | + | 0.999923i | \(0.503958\pi\) | |||||||
\(480\) | −230400. | −0.0456435 | ||||||||
\(481\) | −2.67481e6 | −0.527145 | ||||||||
\(482\) | 1.20614e6 | 0.236471 | ||||||||
\(483\) | 4.61087e6 | 0.899322 | ||||||||
\(484\) | −1.12057e6 | −0.217433 | ||||||||
\(485\) | −2.89721e6 | −0.559276 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 3.21672e6 | 0.614599 | 0.307299 | − | 0.951613i | \(-0.400575\pi\) | ||||
0.307299 | + | 0.951613i | \(0.400575\pi\) | |||||||
\(488\) | −1.55506e6 | −0.295595 | ||||||||
\(489\) | 4.13515e6 | 0.782022 | ||||||||
\(490\) | 2.26911e6 | 0.426939 | ||||||||
\(491\) | −28485.2 | −0.00533231 | −0.00266616 | − | 0.999996i | \(-0.500849\pi\) | ||||
−0.00266616 | + | 0.999996i | \(0.500849\pi\) | |||||||
\(492\) | 2.24474e6 | 0.418074 | ||||||||
\(493\) | 5.12756e6 | 0.950154 | ||||||||
\(494\) | −598079. | −0.110266 | ||||||||
\(495\) | 610918. | 0.112065 | ||||||||
\(496\) | −130731. | −0.0238603 | ||||||||
\(497\) | 3.38828e6 | 0.615303 | ||||||||
\(498\) | −163566. | −0.0295543 | ||||||||
\(499\) | 3.58835e6 | 0.645124 | 0.322562 | − | 0.946548i | \(-0.395456\pi\) | ||||
0.322562 | + | 0.946548i | \(0.395456\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | 1.43294e6 | 0.255054 | ||||||||
\(502\) | −6.12750e6 | −1.08524 | ||||||||
\(503\) | 7.41843e6 | 1.30735 | 0.653676 | − | 0.756775i | \(-0.273226\pi\) | ||||
0.653676 | + | 0.756775i | \(0.273226\pi\) | |||||||
\(504\) | 1.03028e6 | 0.180666 | ||||||||
\(505\) | −1.74610e6 | −0.304678 | ||||||||
\(506\) | 3.11079e6 | 0.540124 | ||||||||
\(507\) | 1.79772e6 | 0.310600 | ||||||||
\(508\) | 3.11372e6 | 0.535328 | ||||||||
\(509\) | −6.14946e6 | −1.05207 | −0.526033 | − | 0.850464i | \(-0.676321\pi\) | ||||
−0.526033 | + | 0.850464i | \(0.676321\pi\) | |||||||
\(510\) | −1.62400e6 | −0.276479 | ||||||||
\(511\) | −992900. | −0.168211 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 263169. | 0.0441511 | ||||||||
\(514\) | −466308. | −0.0778511 | ||||||||
\(515\) | 151839. | 0.0252270 | ||||||||
\(516\) | −160882. | −0.0266001 | ||||||||
\(517\) | −3.61003e6 | −0.593997 | ||||||||
\(518\) | 5.13393e6 | 0.840669 | ||||||||
\(519\) | 6.41989e6 | 1.04619 | ||||||||
\(520\) | −662691. | −0.107474 | ||||||||
\(521\) | −1.23809e7 | −1.99829 | −0.999144 | − | 0.0413730i | \(-0.986827\pi\) | ||||
−0.999144 | + | 0.0413730i | \(0.986827\pi\) | |||||||
\(522\) | −920686. | −0.147889 | ||||||||
\(523\) | 5.11228e6 | 0.817261 | 0.408630 | − | 0.912700i | \(-0.366007\pi\) | ||||
0.408630 | + | 0.912700i | \(0.366007\pi\) | |||||||
\(524\) | 1.30315e6 | 0.207331 | ||||||||
\(525\) | 1.11792e6 | 0.177016 | ||||||||
\(526\) | 7.30275e6 | 1.15086 | ||||||||
\(527\) | −921477. | −0.144530 | ||||||||
\(528\) | 695089. | 0.108506 | ||||||||
\(529\) | 208803. | 0.0324412 | ||||||||
\(530\) | 1.08014e6 | 0.167028 | ||||||||
\(531\) | −1.96073e6 | −0.301774 | ||||||||
\(532\) | 1.14793e6 | 0.175848 | ||||||||
\(533\) | 6.45646e6 | 0.984412 | ||||||||
\(534\) | −740944. | −0.112443 | ||||||||
\(535\) | 4.40770e6 | 0.665775 | ||||||||
\(536\) | −2.84539e6 | −0.427789 | ||||||||
\(537\) | 3.49524e6 | 0.523047 | ||||||||
\(538\) | 4.32624e6 | 0.644400 | ||||||||
\(539\) | −6.84564e6 | −1.01494 | ||||||||
\(540\) | 291600. | 0.0430331 | ||||||||
\(541\) | 8.48019e6 | 1.24570 | 0.622848 | − | 0.782343i | \(-0.285975\pi\) | ||||
0.622848 | + | 0.782343i | \(0.285975\pi\) | |||||||
\(542\) | 1.28445e6 | 0.187810 | ||||||||
\(543\) | −4.20629e6 | −0.612209 | ||||||||
\(544\) | −1.84776e6 | −0.267699 | ||||||||
\(545\) | −282926. | −0.0408020 | ||||||||
\(546\) | 2.96334e6 | 0.425403 | ||||||||
\(547\) | −7.70141e6 | −1.10053 | −0.550265 | − | 0.834990i | \(-0.685473\pi\) | ||||
−0.550265 | + | 0.834990i | \(0.685473\pi\) | |||||||
\(548\) | 2.40669e6 | 0.342348 | ||||||||
\(549\) | 1.96812e6 | 0.278689 | ||||||||
\(550\) | 754220. | 0.106314 | ||||||||
\(551\) | −1.02583e6 | −0.143944 | ||||||||
\(552\) | 1.48482e6 | 0.207409 | ||||||||
\(553\) | 6.52403e6 | 0.907201 | ||||||||
\(554\) | −2.18652e6 | −0.302677 | ||||||||
\(555\) | 1.45306e6 | 0.200240 | ||||||||
\(556\) | 1.46026e6 | 0.200328 | ||||||||
\(557\) | 1.24208e6 | 0.169634 | 0.0848168 | − | 0.996397i | \(-0.472969\pi\) | ||||
0.0848168 | + | 0.996397i | \(0.472969\pi\) | |||||||
\(558\) | 165457. | 0.0224957 | ||||||||
\(559\) | −462739. | −0.0626336 | ||||||||
\(560\) | 1.27194e6 | 0.171395 | ||||||||
\(561\) | 4.89942e6 | 0.657261 | ||||||||
\(562\) | 1.69400e6 | 0.226242 | ||||||||
\(563\) | 3.60364e6 | 0.479149 | 0.239574 | − | 0.970878i | \(-0.422992\pi\) | ||||
0.239574 | + | 0.970878i | \(0.422992\pi\) | |||||||
\(564\) | −1.72312e6 | −0.228096 | ||||||||
\(565\) | −5.50531e6 | −0.725539 | ||||||||
\(566\) | 8.57117e6 | 1.12460 | ||||||||
\(567\) | −1.30394e6 | −0.170334 | ||||||||
\(568\) | 1.09112e6 | 0.141906 | ||||||||
\(569\) | −9.60760e6 | −1.24404 | −0.622020 | − | 0.783001i | \(-0.713688\pi\) | ||||
−0.622020 | + | 0.783001i | \(0.713688\pi\) | |||||||
\(570\) | 324900. | 0.0418854 | ||||||||
\(571\) | 1.86747e6 | 0.239698 | 0.119849 | − | 0.992792i | \(-0.461759\pi\) | ||||
0.119849 | + | 0.992792i | \(0.461759\pi\) | |||||||
\(572\) | 1.99926e6 | 0.255493 | ||||||||
\(573\) | 8.20677e6 | 1.04421 | ||||||||
\(574\) | −1.23923e7 | −1.56990 | ||||||||
\(575\) | 1.61114e6 | 0.203218 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −2.55886e6 | −0.319968 | −0.159984 | − | 0.987120i | \(-0.551144\pi\) | ||||
−0.159984 | + | 0.987120i | \(0.551144\pi\) | |||||||
\(578\) | −7.34472e6 | −0.914441 | ||||||||
\(579\) | −4.06725e6 | −0.504201 | ||||||||
\(580\) | −1.13665e6 | −0.140300 | ||||||||
\(581\) | 902984. | 0.110979 | ||||||||
\(582\) | 4.17199e6 | 0.510547 | ||||||||
\(583\) | −3.25865e6 | −0.397069 | ||||||||
\(584\) | −319740. | −0.0387941 | ||||||||
\(585\) | 838719. | 0.101327 | ||||||||
\(586\) | −1.05571e6 | −0.126999 | ||||||||
\(587\) | −1.35801e7 | −1.62671 | −0.813353 | − | 0.581771i | \(-0.802360\pi\) | ||||
−0.813353 | + | 0.581771i | \(0.802360\pi\) | |||||||
\(588\) | −3.26752e6 | −0.389740 | ||||||||
\(589\) | 184352. | 0.0218957 | ||||||||
\(590\) | −2.42066e6 | −0.286288 | ||||||||
\(591\) | 1.83157e6 | 0.215703 | ||||||||
\(592\) | 1.65326e6 | 0.193882 | ||||||||
\(593\) | 6.22471e6 | 0.726913 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(594\) | −879722. | −0.102301 | ||||||||
\(595\) | 8.96547e6 | 1.03820 | ||||||||
\(596\) | −6.85013e6 | −0.789920 | ||||||||
\(597\) | −5.70324e6 | −0.654916 | ||||||||
\(598\) | 4.27074e6 | 0.488372 | ||||||||
\(599\) | −4.47755e6 | −0.509887 | −0.254943 | − | 0.966956i | \(-0.582057\pi\) | ||||
−0.254943 | + | 0.966956i | \(0.582057\pi\) | |||||||
\(600\) | 360000. | 0.0408248 | ||||||||
\(601\) | −1.16870e7 | −1.31983 | −0.659913 | − | 0.751342i | \(-0.729407\pi\) | ||||
−0.659913 | + | 0.751342i | \(0.729407\pi\) | |||||||
\(602\) | 888165. | 0.0998855 | ||||||||
\(603\) | 3.60119e6 | 0.403323 | ||||||||
\(604\) | −5.08127e6 | −0.566734 | ||||||||
\(605\) | 1.75089e6 | 0.194478 | ||||||||
\(606\) | 2.51438e6 | 0.278131 | ||||||||
\(607\) | 4.20389e6 | 0.463105 | 0.231552 | − | 0.972822i | \(-0.425620\pi\) | ||||
0.231552 | + | 0.972822i | \(0.425620\pi\) | |||||||
\(608\) | 369664. | 0.0405554 | ||||||||
\(609\) | 5.08273e6 | 0.555334 | ||||||||
\(610\) | 2.42978e6 | 0.264388 | ||||||||
\(611\) | −4.95614e6 | −0.537082 | ||||||||
\(612\) | 2.33857e6 | 0.252389 | ||||||||
\(613\) | 1.57832e7 | 1.69646 | 0.848232 | − | 0.529625i | \(-0.177667\pi\) | ||||
0.848232 | + | 0.529625i | \(0.177667\pi\) | |||||||
\(614\) | −3.19355e6 | −0.341863 | ||||||||
\(615\) | −3.50740e6 | −0.373937 | ||||||||
\(616\) | −3.83730e6 | −0.407450 | ||||||||
\(617\) | −8.30305e6 | −0.878061 | −0.439031 | − | 0.898472i | \(-0.644678\pi\) | ||||
−0.439031 | + | 0.898472i | \(0.644678\pi\) | |||||||
\(618\) | −218649. | −0.0230290 | ||||||||
\(619\) | −8.94606e6 | −0.938437 | −0.469219 | − | 0.883082i | \(-0.655464\pi\) | ||||
−0.469219 | + | 0.883082i | \(0.655464\pi\) | |||||||
\(620\) | 204268. | 0.0213413 | ||||||||
\(621\) | −1.87923e6 | −0.195547 | ||||||||
\(622\) | −8.08889e6 | −0.838326 | ||||||||
\(623\) | 4.09045e6 | 0.422232 | ||||||||
\(624\) | 954276. | 0.0981098 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.45058e6 | 0.147947 | ||||||||
\(627\) | −980184. | −0.0995723 | ||||||||
\(628\) | −8.51385e6 | −0.861444 | ||||||||
\(629\) | 1.16532e7 | 1.17441 | ||||||||
\(630\) | −1.60981e6 | −0.161593 | ||||||||
\(631\) | −1.40262e7 | −1.40238 | −0.701189 | − | 0.712975i | \(-0.747347\pi\) | ||||
−0.701189 | + | 0.712975i | \(0.747347\pi\) | |||||||
\(632\) | 2.10091e6 | 0.209226 | ||||||||
\(633\) | −2.14929e6 | −0.213199 | ||||||||
\(634\) | 8.45490e6 | 0.835383 | ||||||||
\(635\) | −4.86518e6 | −0.478812 | ||||||||
\(636\) | −1.55540e6 | −0.152475 | ||||||||
\(637\) | −9.39826e6 | −0.917696 | ||||||||
\(638\) | 3.42913e6 | 0.333528 | ||||||||
\(639\) | −1.38095e6 | −0.133790 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | 1.24158e7 | 1.19352 | 0.596762 | − | 0.802419i | \(-0.296454\pi\) | ||||
0.596762 | + | 0.802419i | \(0.296454\pi\) | |||||||
\(642\) | −6.34709e6 | −0.607767 | ||||||||
\(643\) | −6.94150e6 | −0.662104 | −0.331052 | − | 0.943613i | \(-0.607404\pi\) | ||||
−0.331052 | + | 0.943613i | \(0.607404\pi\) | |||||||
\(644\) | −8.19711e6 | −0.778836 | ||||||||
\(645\) | 251378. | 0.0237919 | ||||||||
\(646\) | 2.60562e6 | 0.245658 | ||||||||
\(647\) | −1.17234e7 | −1.10101 | −0.550507 | − | 0.834831i | \(-0.685566\pi\) | ||||
−0.550507 | + | 0.834831i | \(0.685566\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 7.30284e6 | 0.680581 | ||||||||
\(650\) | 1.03546e6 | 0.0961276 | ||||||||
\(651\) | −913420. | −0.0844730 | ||||||||
\(652\) | −7.35138e6 | −0.677251 | ||||||||
\(653\) | 1.47343e7 | 1.35222 | 0.676108 | − | 0.736802i | \(-0.263665\pi\) | ||||
0.676108 | + | 0.736802i | \(0.263665\pi\) | |||||||
\(654\) | 407413. | 0.0372469 | ||||||||
\(655\) | −2.03617e6 | −0.185443 | ||||||||
\(656\) | −3.99065e6 | −0.362063 | ||||||||
\(657\) | 404671. | 0.0365754 | ||||||||
\(658\) | 9.51264e6 | 0.856517 | ||||||||
\(659\) | −8.13783e6 | −0.729953 | −0.364977 | − | 0.931017i | \(-0.618923\pi\) | ||||
−0.364977 | + | 0.931017i | \(0.618923\pi\) | |||||||
\(660\) | −1.08608e6 | −0.0970511 | ||||||||
\(661\) | −6.10515e6 | −0.543491 | −0.271746 | − | 0.962369i | \(-0.587601\pi\) | ||||
−0.271746 | + | 0.962369i | \(0.587601\pi\) | |||||||
\(662\) | 5.31505e6 | 0.471371 | ||||||||
\(663\) | 6.72634e6 | 0.594285 | ||||||||
\(664\) | 290785. | 0.0255948 | ||||||||
\(665\) | −1.79364e6 | −0.157283 | ||||||||
\(666\) | −2.09241e6 | −0.182793 | ||||||||
\(667\) | 7.32519e6 | 0.637535 | ||||||||
\(668\) | −2.54744e6 | −0.220883 | ||||||||
\(669\) | −1.00999e6 | −0.0872476 | ||||||||
\(670\) | 4.44592e6 | 0.382626 | ||||||||
\(671\) | −7.33034e6 | −0.628518 | ||||||||
\(672\) | −1.83160e6 | −0.156462 | ||||||||
\(673\) | −1.51100e7 | −1.28596 | −0.642978 | − | 0.765885i | \(-0.722301\pi\) | ||||
−0.642978 | + | 0.765885i | \(0.722301\pi\) | |||||||
\(674\) | 1.49925e7 | 1.27123 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | −3.19594e6 | −0.268987 | ||||||||
\(677\) | 1.53998e6 | 0.129135 | 0.0645673 | − | 0.997913i | \(-0.479433\pi\) | ||||
0.0645673 | + | 0.997913i | \(0.479433\pi\) | |||||||
\(678\) | 7.92764e6 | 0.662323 | ||||||||
\(679\) | −2.30319e7 | −1.91714 | ||||||||
\(680\) | 2.88712e6 | 0.239438 | ||||||||
\(681\) | −40496.6 | −0.00334619 | ||||||||
\(682\) | −616251. | −0.0507337 | ||||||||
\(683\) | −3.95959e6 | −0.324787 | −0.162394 | − | 0.986726i | \(-0.551921\pi\) | ||||
−0.162394 | + | 0.986726i | \(0.551921\pi\) | |||||||
\(684\) | −467856. | −0.0382360 | ||||||||
\(685\) | −3.76045e6 | −0.306206 | ||||||||
\(686\) | 4.67768e6 | 0.379508 | ||||||||
\(687\) | −1.22888e7 | −0.993386 | ||||||||
\(688\) | 286013. | 0.0230364 | ||||||||
\(689\) | −4.47375e6 | −0.359024 | ||||||||
\(690\) | −2.32004e6 | −0.185512 | ||||||||
\(691\) | −4.52472e6 | −0.360493 | −0.180247 | − | 0.983621i | \(-0.557690\pi\) | ||||
−0.180247 | + | 0.983621i | \(0.557690\pi\) | |||||||
\(692\) | −1.14131e7 | −0.906025 | ||||||||
\(693\) | 4.85659e6 | 0.384148 | ||||||||
\(694\) | −5.25257e6 | −0.413974 | ||||||||
\(695\) | −2.28165e6 | −0.179179 | ||||||||
\(696\) | 1.63677e6 | 0.128075 | ||||||||
\(697\) | −2.81286e7 | −2.19314 | ||||||||
\(698\) | −841383. | −0.0653665 | ||||||||
\(699\) | −4.43803e6 | −0.343556 | ||||||||
\(700\) | −1.98741e6 | −0.153300 | ||||||||
\(701\) | 1.15106e7 | 0.884716 | 0.442358 | − | 0.896839i | \(-0.354142\pi\) | ||||
0.442358 | + | 0.896839i | \(0.354142\pi\) | |||||||
\(702\) | −1.20776e6 | −0.0924988 | ||||||||
\(703\) | −2.33136e6 | −0.177918 | ||||||||
\(704\) | −1.23571e6 | −0.0939693 | ||||||||
\(705\) | 2.69237e6 | 0.204015 | ||||||||
\(706\) | −1.57106e7 | −1.18626 | ||||||||
\(707\) | −1.38809e7 | −1.04440 | ||||||||
\(708\) | 3.48575e6 | 0.261344 | ||||||||
\(709\) | −1.51111e6 | −0.112896 | −0.0564482 | − | 0.998406i | \(-0.517978\pi\) | ||||
−0.0564482 | + | 0.998406i | \(0.517978\pi\) | |||||||
\(710\) | −1.70487e6 | −0.126925 | ||||||||
\(711\) | −2.65897e6 | −0.197260 | ||||||||
\(712\) | 1.31723e6 | 0.0973785 | ||||||||
\(713\) | −1.31641e6 | −0.0969769 | ||||||||
\(714\) | −1.29103e7 | −0.947742 | ||||||||
\(715\) | −3.12384e6 | −0.228520 | ||||||||
\(716\) | −6.21376e6 | −0.452972 | ||||||||
\(717\) | 9.72681e6 | 0.706598 | ||||||||
\(718\) | −1.76796e7 | −1.27986 | ||||||||
\(719\) | −2.12663e7 | −1.53415 | −0.767077 | − | 0.641555i | \(-0.778289\pi\) | ||||
−0.767077 | + | 0.641555i | \(0.778289\pi\) | |||||||
\(720\) | −518400. | −0.0372678 | ||||||||
\(721\) | 1.20707e6 | 0.0864757 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | 2.71381e6 | 0.193078 | ||||||||
\(724\) | 7.47785e6 | 0.530188 | ||||||||
\(725\) | 1.77601e6 | 0.125488 | ||||||||
\(726\) | −2.52128e6 | −0.177533 | ||||||||
\(727\) | 1.16437e7 | 0.817064 | 0.408532 | − | 0.912744i | \(-0.366041\pi\) | ||||
0.408532 | + | 0.912744i | \(0.366041\pi\) | |||||||
\(728\) | −5.26817e6 | −0.368410 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 499594. | 0.0346985 | ||||||||
\(731\) | 2.01600e6 | 0.139539 | ||||||||
\(732\) | −3.49888e6 | −0.241352 | ||||||||
\(733\) | 1.12994e7 | 0.776777 | 0.388389 | − | 0.921496i | \(-0.373032\pi\) | ||||
0.388389 | + | 0.921496i | \(0.373032\pi\) | |||||||
\(734\) | −6.24616e6 | −0.427930 | ||||||||
\(735\) | 5.10551e6 | 0.348594 | ||||||||
\(736\) | −2.63969e6 | −0.179621 | ||||||||
\(737\) | −1.34128e7 | −0.909600 | ||||||||
\(738\) | 5.05066e6 | 0.341356 | ||||||||
\(739\) | −2.81064e6 | −0.189319 | −0.0946595 | − | 0.995510i | \(-0.530176\pi\) | ||||
−0.0946595 | + | 0.995510i | \(0.530176\pi\) | |||||||
\(740\) | −2.58322e6 | −0.173413 | ||||||||
\(741\) | −1.34568e6 | −0.0900317 | ||||||||
\(742\) | 8.58674e6 | 0.572557 | ||||||||
\(743\) | −1.42712e7 | −0.948395 | −0.474197 | − | 0.880419i | \(-0.657262\pi\) | ||||
−0.474197 | + | 0.880419i | \(0.657262\pi\) | |||||||
\(744\) | −294146. | −0.0194818 | ||||||||
\(745\) | 1.07033e7 | 0.706526 | ||||||||
\(746\) | −9.76389e6 | −0.642356 | ||||||||
\(747\) | −368025. | −0.0241310 | ||||||||
\(748\) | −8.71009e6 | −0.569205 | ||||||||
\(749\) | 3.50397e7 | 2.28221 | ||||||||
\(750\) | −562500. | −0.0365148 | ||||||||
\(751\) | −2.96243e6 | −0.191667 | −0.0958336 | − | 0.995397i | \(-0.530552\pi\) | ||||
−0.0958336 | + | 0.995397i | \(0.530552\pi\) | |||||||
\(752\) | 3.06332e6 | 0.197537 | ||||||||
\(753\) | −1.37869e7 | −0.886091 | ||||||||
\(754\) | 4.70780e6 | 0.301571 | ||||||||
\(755\) | 7.93948e6 | 0.506903 | ||||||||
\(756\) | 2.31812e6 | 0.147513 | ||||||||
\(757\) | 7.80798e6 | 0.495221 | 0.247610 | − | 0.968860i | \(-0.420355\pi\) | ||||
0.247610 | + | 0.968860i | \(0.420355\pi\) | |||||||
\(758\) | −3.23191e6 | −0.204309 | ||||||||
\(759\) | 6.99927e6 | 0.441010 | ||||||||
\(760\) | −577600. | −0.0362738 | ||||||||
\(761\) | −5.51776e6 | −0.345383 | −0.172691 | − | 0.984976i | \(-0.555246\pi\) | ||||
−0.172691 | + | 0.984976i | \(0.555246\pi\) | |||||||
\(762\) | 7.00586e6 | 0.437093 | ||||||||
\(763\) | −2.24916e6 | −0.139865 | ||||||||
\(764\) | −1.45898e7 | −0.904308 | ||||||||
\(765\) | −3.65401e6 | −0.225744 | ||||||||
\(766\) | 2.73925e6 | 0.168679 | ||||||||
\(767\) | 1.00259e7 | 0.615370 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 2.70117e6 | 0.164716 | 0.0823581 | − | 0.996603i | \(-0.473755\pi\) | ||||
0.0823581 | + | 0.996603i | \(0.473755\pi\) | |||||||
\(770\) | 5.99579e6 | 0.364434 | ||||||||
\(771\) | −1.04919e6 | −0.0635652 | ||||||||
\(772\) | 7.23066e6 | 0.436651 | ||||||||
\(773\) | 5.50350e6 | 0.331276 | 0.165638 | − | 0.986187i | \(-0.447032\pi\) | ||||
0.165638 | + | 0.986187i | \(0.447032\pi\) | |||||||
\(774\) | −361985. | −0.0217189 | ||||||||
\(775\) | −319168. | −0.0190882 | ||||||||
\(776\) | −7.41687e6 | −0.442147 | ||||||||
\(777\) | 1.15513e7 | 0.686404 | ||||||||
\(778\) | −4.64259e6 | −0.274987 | ||||||||
\(779\) | 5.62744e6 | 0.332252 | ||||||||
\(780\) | −1.49106e6 | −0.0877521 | ||||||||
\(781\) | 5.14339e6 | 0.301732 | ||||||||
\(782\) | −1.86062e7 | −1.08803 | ||||||||
\(783\) | −2.07154e6 | −0.120751 | ||||||||
\(784\) | 5.80893e6 | 0.337525 | ||||||||
\(785\) | 1.33029e7 | 0.770499 | ||||||||
\(786\) | 2.93208e6 | 0.169285 | ||||||||
\(787\) | −2.45039e7 | −1.41026 | −0.705129 | − | 0.709079i | \(-0.749111\pi\) | ||||
−0.705129 | + | 0.709079i | \(0.749111\pi\) | |||||||
\(788\) | −3.25613e6 | −0.186804 | ||||||||
\(789\) | 1.64312e7 | 0.939672 | ||||||||
\(790\) | −3.28268e6 | −0.187137 | ||||||||
\(791\) | −4.37653e7 | −2.48707 | ||||||||
\(792\) | 1.56395e6 | 0.0885951 | ||||||||
\(793\) | −1.00637e7 | −0.568296 | ||||||||
\(794\) | 1.48285e7 | 0.834730 | ||||||||
\(795\) | 2.43032e6 | 0.136378 | ||||||||
\(796\) | 1.01391e7 | 0.567174 | ||||||||
\(797\) | −631419. | −0.0352105 | −0.0176052 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176052 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(798\) | 2.58284e6 | 0.143579 | ||||||||
\(799\) | 2.15922e7 | 1.19655 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −1.66712e6 | −0.0918093 | ||||||||
\(802\) | −1.71708e7 | −0.942656 | ||||||||
\(803\) | −1.50722e6 | −0.0824872 | ||||||||
\(804\) | −6.40212e6 | −0.349288 | ||||||||
\(805\) | 1.28080e7 | 0.696612 | ||||||||
\(806\) | −846040. | −0.0458726 | ||||||||
\(807\) | 9.73405e6 | 0.526150 | ||||||||
\(808\) | −4.47002e6 | −0.240869 | ||||||||
\(809\) | 1.99246e7 | 1.07033 | 0.535165 | − | 0.844747i | \(-0.320249\pi\) | ||||
0.535165 | + | 0.844747i | \(0.320249\pi\) | |||||||
\(810\) | 656100. | 0.0351364 | ||||||||
\(811\) | 2.16776e7 | 1.15734 | 0.578668 | − | 0.815563i | \(-0.303573\pi\) | ||||
0.578668 | + | 0.815563i | \(0.303573\pi\) | |||||||
\(812\) | −9.03597e6 | −0.480933 | ||||||||
\(813\) | 2.89000e6 | 0.153346 | ||||||||
\(814\) | 7.79326e6 | 0.412248 | ||||||||
\(815\) | 1.14865e7 | 0.605752 | ||||||||
\(816\) | −4.15745e6 | −0.218576 | ||||||||
\(817\) | −403322. | −0.0211396 | ||||||||
\(818\) | −1.37897e7 | −0.720562 | ||||||||
\(819\) | 6.66752e6 | 0.347340 | ||||||||
\(820\) | 6.23539e6 | 0.323839 | ||||||||
\(821\) | 2.80653e7 | 1.45315 | 0.726577 | − | 0.687085i | \(-0.241110\pi\) | ||||
0.726577 | + | 0.687085i | \(0.241110\pi\) | |||||||
\(822\) | 5.41504e6 | 0.279526 | ||||||||
\(823\) | 2.38700e7 | 1.22844 | 0.614218 | − | 0.789137i | \(-0.289472\pi\) | ||||
0.614218 | + | 0.789137i | \(0.289472\pi\) | |||||||
\(824\) | 388709. | 0.0199437 | ||||||||
\(825\) | 1.69699e6 | 0.0868051 | ||||||||
\(826\) | −1.92434e7 | −0.981368 | ||||||||
\(827\) | 7.07804e6 | 0.359873 | 0.179937 | − | 0.983678i | \(-0.442411\pi\) | ||||
0.179937 | + | 0.983678i | \(0.442411\pi\) | |||||||
\(828\) | 3.34085e6 | 0.169349 | ||||||||
\(829\) | 7.00193e6 | 0.353860 | 0.176930 | − | 0.984223i | \(-0.443383\pi\) | ||||
0.176930 | + | 0.984223i | \(0.443383\pi\) | |||||||
\(830\) | −454351. | −0.0228927 | ||||||||
\(831\) | −4.91967e6 | −0.247134 | ||||||||
\(832\) | −1.69649e6 | −0.0849656 | ||||||||
\(833\) | 4.09450e7 | 2.04451 | ||||||||
\(834\) | 3.28558e6 | 0.163567 | ||||||||
\(835\) | 3.98038e6 | 0.197564 | ||||||||
\(836\) | 1.74255e6 | 0.0862322 | ||||||||
\(837\) | 372278. | 0.0183677 | ||||||||
\(838\) | 1.64821e7 | 0.810779 | ||||||||
\(839\) | 8.56136e6 | 0.419892 | 0.209946 | − | 0.977713i | \(-0.432671\pi\) | ||||
0.209946 | + | 0.977713i | \(0.432671\pi\) | |||||||
\(840\) | 2.86188e6 | 0.139943 | ||||||||
\(841\) | −1.24363e7 | −0.606320 | ||||||||
\(842\) | −3.81722e6 | −0.185552 | ||||||||
\(843\) | 3.81150e6 | 0.184726 | ||||||||
\(844\) | 3.82095e6 | 0.184636 | ||||||||
\(845\) | 4.99365e6 | 0.240590 | ||||||||
\(846\) | −3.87702e6 | −0.186239 | ||||||||
\(847\) | 1.39189e7 | 0.666650 | ||||||||
\(848\) | 2.76516e6 | 0.132048 | ||||||||
\(849\) | 1.92851e7 | 0.918234 | ||||||||
\(850\) | −4.51112e6 | −0.214160 | ||||||||
\(851\) | 1.66477e7 | 0.788006 | ||||||||
\(852\) | 2.45501e6 | 0.115866 | ||||||||
\(853\) | −3.54395e7 | −1.66769 | −0.833844 | − | 0.552001i | \(-0.813865\pi\) | ||||
−0.833844 | + | 0.552001i | \(0.813865\pi\) | |||||||
\(854\) | 1.93159e7 | 0.906295 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | 1.12837e7 | 0.526341 | ||||||||
\(857\) | −3.44320e7 | −1.60144 | −0.800719 | − | 0.599040i | \(-0.795549\pi\) | ||||
−0.800719 | + | 0.599040i | \(0.795549\pi\) | |||||||
\(858\) | 4.49833e6 | 0.208609 | ||||||||
\(859\) | −2.86492e7 | −1.32474 | −0.662368 | − | 0.749178i | \(-0.730449\pi\) | ||||
−0.662368 | + | 0.749178i | \(0.730449\pi\) | |||||||
\(860\) | −446895. | −0.0206044 | ||||||||
\(861\) | −2.78827e7 | −1.28182 | ||||||||
\(862\) | 2.96000e7 | 1.35683 | ||||||||
\(863\) | 9.18363e6 | 0.419747 | 0.209873 | − | 0.977729i | \(-0.432695\pi\) | ||||
0.209873 | + | 0.977729i | \(0.432695\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.78330e7 | 0.810373 | ||||||||
\(866\) | −2.85882e7 | −1.29537 | ||||||||
\(867\) | −1.65256e7 | −0.746638 | ||||||||
\(868\) | 1.62386e6 | 0.0731558 | ||||||||
\(869\) | 9.90343e6 | 0.444873 | ||||||||
\(870\) | −2.55746e6 | −0.114554 | ||||||||
\(871\) | −1.84142e7 | −0.822446 | ||||||||
\(872\) | −724290. | −0.0322568 | ||||||||
\(873\) | 9.38698e6 | 0.416860 | ||||||||
\(874\) | 3.72237e6 | 0.164832 | ||||||||
\(875\) | 3.10533e6 | 0.137116 | ||||||||
\(876\) | −719416. | −0.0316752 | ||||||||
\(877\) | −1.66240e7 | −0.729855 | −0.364927 | − | 0.931036i | \(-0.618906\pi\) | ||||
−0.364927 | + | 0.931036i | \(0.618906\pi\) | |||||||
\(878\) | −1.88745e7 | −0.826301 | ||||||||
\(879\) | −2.37535e6 | −0.103694 | ||||||||
\(880\) | 1.93080e6 | 0.0840487 | ||||||||
\(881\) | 4.29594e7 | 1.86474 | 0.932371 | − | 0.361503i | \(-0.117736\pi\) | ||||
0.932371 | + | 0.361503i | \(0.117736\pi\) | |||||||
\(882\) | −7.35193e6 | −0.318222 | ||||||||
\(883\) | −783434. | −0.0338143 | −0.0169072 | − | 0.999857i | \(-0.505382\pi\) | ||||
−0.0169072 | + | 0.999857i | \(0.505382\pi\) | |||||||
\(884\) | −1.19579e7 | −0.514666 | ||||||||
\(885\) | −5.44648e6 | −0.233753 | ||||||||
\(886\) | 5.51930e6 | 0.236211 | ||||||||
\(887\) | −3.06447e7 | −1.30781 | −0.653907 | − | 0.756575i | \(-0.726871\pi\) | ||||
−0.653907 | + | 0.756575i | \(0.726871\pi\) | |||||||
\(888\) | 3.71984e6 | 0.158304 | ||||||||
\(889\) | −3.86765e7 | −1.64132 | ||||||||
\(890\) | −2.05818e6 | −0.0870980 | ||||||||
\(891\) | −1.97937e6 | −0.0835283 | ||||||||
\(892\) | 1.79555e6 | 0.0755587 | ||||||||
\(893\) | −4.31976e6 | −0.181272 | ||||||||
\(894\) | −1.54128e7 | −0.644967 | ||||||||
\(895\) | 9.70899e6 | 0.405151 | ||||||||
\(896\) | 3.25618e6 | 0.135500 | ||||||||
\(897\) | 9.60917e6 | 0.398754 | ||||||||
\(898\) | 5.66413e6 | 0.234392 | ||||||||
\(899\) | −1.45113e6 | −0.0598835 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | 1.94906e7 | 0.799858 | ||||||||
\(902\) | −1.88114e7 | −0.769848 | ||||||||
\(903\) | 1.99837e6 | 0.0815561 | ||||||||
\(904\) | −1.40936e7 | −0.573589 | ||||||||
\(905\) | −1.16841e7 | −0.474215 | ||||||||
\(906\) | −1.14328e7 | −0.462737 | ||||||||
\(907\) | 1.13750e6 | 0.0459129 | 0.0229564 | − | 0.999736i | \(-0.492692\pi\) | ||||
0.0229564 | + | 0.999736i | \(0.492692\pi\) | |||||||
\(908\) | 71994.0 | 0.00289789 | ||||||||
\(909\) | 5.65736e6 | 0.227093 | ||||||||
\(910\) | 8.23151e6 | 0.329516 | ||||||||
\(911\) | 299756. | 0.0119666 | 0.00598331 | − | 0.999982i | \(-0.498095\pi\) | ||||
0.00598331 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(912\) | 831744. | 0.0331133 | ||||||||
\(913\) | 1.37072e6 | 0.0544218 | ||||||||
\(914\) | 1.35047e7 | 0.534711 | ||||||||
\(915\) | 5.46700e6 | 0.215872 | ||||||||
\(916\) | 2.18468e7 | 0.860297 | ||||||||
\(917\) | −1.61868e7 | −0.635680 | ||||||||
\(918\) | 5.26177e6 | 0.206075 | ||||||||
\(919\) | 2.91570e7 | 1.13882 | 0.569409 | − | 0.822055i | \(-0.307172\pi\) | ||||
0.569409 | + | 0.822055i | \(0.307172\pi\) | |||||||
\(920\) | 4.12451e6 | 0.160658 | ||||||||
\(921\) | −7.18549e6 | −0.279130 | ||||||||
\(922\) | 3.33340e7 | 1.29140 | ||||||||
\(923\) | 7.06127e6 | 0.272822 | ||||||||
\(924\) | −8.63393e6 | −0.332682 | ||||||||
\(925\) | 4.03628e6 | 0.155105 | ||||||||
\(926\) | −1.56438e7 | −0.599534 | ||||||||
\(927\) | −491959. | −0.0188031 | ||||||||
\(928\) | −2.90982e6 | −0.110917 | ||||||||
\(929\) | −1.17436e7 | −0.446439 | −0.223219 | − | 0.974768i | \(-0.571657\pi\) | ||||
−0.223219 | + | 0.974768i | \(0.571657\pi\) | |||||||
\(930\) | 459602. | 0.0174251 | ||||||||
\(931\) | −8.19150e6 | −0.309734 | ||||||||
\(932\) | 7.88984e6 | 0.297528 | ||||||||
\(933\) | −1.82000e7 | −0.684490 | ||||||||
\(934\) | 4.96980e6 | 0.186411 | ||||||||
\(935\) | 1.36095e7 | 0.509112 | ||||||||
\(936\) | 2.14712e6 | 0.0801063 | ||||||||
\(937\) | 1.29902e7 | 0.483355 | 0.241677 | − | 0.970357i | \(-0.422302\pi\) | ||||
0.241677 | + | 0.970357i | \(0.422302\pi\) | |||||||
\(938\) | 3.53435e7 | 1.31160 | ||||||||
\(939\) | 3.26381e6 | 0.120798 | ||||||||
\(940\) | −4.78644e6 | −0.176682 | ||||||||
\(941\) | −9.92638e6 | −0.365441 | −0.182720 | − | 0.983165i | \(-0.558490\pi\) | ||||
−0.182720 | + | 0.983165i | \(0.558490\pi\) | |||||||
\(942\) | −1.91562e7 | −0.703366 | ||||||||
\(943\) | −4.01842e7 | −1.47155 | ||||||||
\(944\) | −6.19689e6 | −0.226331 | ||||||||
\(945\) | −3.62206e6 | −0.131940 | ||||||||
\(946\) | 1.34823e6 | 0.0489819 | ||||||||
\(947\) | 9.18578e6 | 0.332844 | 0.166422 | − | 0.986055i | \(-0.446779\pi\) | ||||
0.166422 | + | 0.986055i | \(0.446779\pi\) | |||||||
\(948\) | 4.72705e6 | 0.170832 | ||||||||
\(949\) | −2.06923e6 | −0.0745836 | ||||||||
\(950\) | 902500. | 0.0324443 | ||||||||
\(951\) | 1.90235e7 | 0.682087 | ||||||||
\(952\) | 2.29516e7 | 0.820768 | ||||||||
\(953\) | 2.14198e7 | 0.763981 | 0.381991 | − | 0.924166i | \(-0.375239\pi\) | ||||
0.381991 | + | 0.924166i | \(0.375239\pi\) | |||||||
\(954\) | −3.49965e6 | −0.124496 | ||||||||
\(955\) | 2.27966e7 | 0.808838 | ||||||||
\(956\) | −1.72921e7 | −0.611932 | ||||||||
\(957\) | 7.71555e6 | 0.272325 | ||||||||
\(958\) | 499551. | 0.0175860 | ||||||||
\(959\) | −2.98943e7 | −1.04964 | ||||||||
\(960\) | 921600. | 0.0322749 | ||||||||
\(961\) | −2.83684e7 | −0.990891 | ||||||||
\(962\) | 1.06992e7 | 0.372748 | ||||||||
\(963\) | −1.42809e7 | −0.496239 | ||||||||
\(964\) | −4.82454e6 | −0.167210 | ||||||||
\(965\) | −1.12979e7 | −0.390553 | ||||||||
\(966\) | −1.84435e7 | −0.635917 | ||||||||
\(967\) | −7.43130e6 | −0.255563 | −0.127782 | − | 0.991802i | \(-0.540786\pi\) | ||||
−0.127782 | + | 0.991802i | \(0.540786\pi\) | |||||||
\(968\) | 4.48227e6 | 0.153748 | ||||||||
\(969\) | 5.86266e6 | 0.200579 | ||||||||
\(970\) | 1.15889e7 | 0.395468 | ||||||||
\(971\) | −1.82581e7 | −0.621451 | −0.310725 | − | 0.950500i | \(-0.600572\pi\) | ||||
−0.310725 | + | 0.950500i | \(0.600572\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −1.81384e7 | −0.614208 | ||||||||
\(974\) | −1.28669e7 | −0.434587 | ||||||||
\(975\) | 2.32977e6 | 0.0784878 | ||||||||
\(976\) | 6.22023e6 | 0.209017 | ||||||||
\(977\) | 1.40074e7 | 0.469483 | 0.234742 | − | 0.972058i | \(-0.424576\pi\) | ||||
0.234742 | + | 0.972058i | \(0.424576\pi\) | |||||||
\(978\) | −1.65406e7 | −0.552973 | ||||||||
\(979\) | 6.20927e6 | 0.207054 | ||||||||
\(980\) | −9.07645e6 | −0.301892 | ||||||||
\(981\) | 916679. | 0.0304120 | ||||||||
\(982\) | 113941. | 0.00377051 | ||||||||
\(983\) | 3.36595e7 | 1.11102 | 0.555512 | − | 0.831508i | \(-0.312522\pi\) | ||||
0.555512 | + | 0.831508i | \(0.312522\pi\) | |||||||
\(984\) | −8.97896e6 | −0.295623 | ||||||||
\(985\) | 5.08771e6 | 0.167083 | ||||||||
\(986\) | −2.05103e7 | −0.671860 | ||||||||
\(987\) | 2.14034e7 | 0.699344 | ||||||||
\(988\) | 2.39232e6 | 0.0779698 | ||||||||
\(989\) | 2.88003e6 | 0.0936282 | ||||||||
\(990\) | −2.44367e6 | −0.0792419 | ||||||||
\(991\) | 4.03291e6 | 0.130447 | 0.0652235 | − | 0.997871i | \(-0.479224\pi\) | ||||
0.0652235 | + | 0.997871i | \(0.479224\pi\) | |||||||
\(992\) | 522925. | 0.0168718 | ||||||||
\(993\) | 1.19589e7 | 0.384873 | ||||||||
\(994\) | −1.35531e7 | −0.435085 | ||||||||
\(995\) | −1.58423e7 | −0.507296 | ||||||||
\(996\) | 654266. | 0.0208981 | ||||||||
\(997\) | 1.78782e7 | 0.569622 | 0.284811 | − | 0.958584i | \(-0.408069\pi\) | ||||
0.284811 | + | 0.958584i | \(0.408069\pi\) | |||||||
\(998\) | −1.43534e7 | −0.456171 | ||||||||
\(999\) | −4.70792e6 | −0.149250 |
(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.i.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.i.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |