Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,6,Mod(1,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.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: | \(3.04729257645\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 19.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.00000 | −1.06066 | −0.530330 | − | 0.847791i | \(-0.677932\pi\) | ||||
−0.530330 | + | 0.847791i | \(0.677932\pi\) | |||||||
\(3\) | 4.00000 | 0.256600 | 0.128300 | − | 0.991735i | \(-0.459048\pi\) | ||||
0.128300 | + | 0.991735i | \(0.459048\pi\) | |||||||
\(4\) | 4.00000 | 0.125000 | ||||||||
\(5\) | 54.0000 | 0.965981 | 0.482991 | − | 0.875625i | \(-0.339550\pi\) | ||||
0.482991 | + | 0.875625i | \(0.339550\pi\) | |||||||
\(6\) | −24.0000 | −0.272166 | ||||||||
\(7\) | 248.000 | 1.91296 | 0.956482 | − | 0.291793i | \(-0.0942518\pi\) | ||||
0.956482 | + | 0.291793i | \(0.0942518\pi\) | |||||||
\(8\) | 168.000 | 0.928078 | ||||||||
\(9\) | −227.000 | −0.934156 | ||||||||
\(10\) | −324.000 | −1.02458 | ||||||||
\(11\) | 204.000 | 0.508333 | 0.254167 | − | 0.967160i | \(-0.418199\pi\) | ||||
0.254167 | + | 0.967160i | \(0.418199\pi\) | |||||||
\(12\) | 16.0000 | 0.0320750 | ||||||||
\(13\) | −370.000 | −0.607216 | −0.303608 | − | 0.952797i | \(-0.598191\pi\) | ||||
−0.303608 | + | 0.952797i | \(0.598191\pi\) | |||||||
\(14\) | −1488.00 | −2.02900 | ||||||||
\(15\) | 216.000 | 0.247871 | ||||||||
\(16\) | −1136.00 | −1.10938 | ||||||||
\(17\) | 1554.00 | 1.30415 | 0.652077 | − | 0.758153i | \(-0.273898\pi\) | ||||
0.652077 | + | 0.758153i | \(0.273898\pi\) | |||||||
\(18\) | 1362.00 | 0.990822 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | 216.000 | 0.120748 | ||||||||
\(21\) | 992.000 | 0.490867 | ||||||||
\(22\) | −1224.00 | −0.539169 | ||||||||
\(23\) | −408.000 | −0.160820 | −0.0804101 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804101 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(24\) | 672.000 | 0.238145 | ||||||||
\(25\) | −209.000 | −0.0668800 | ||||||||
\(26\) | 2220.00 | 0.644050 | ||||||||
\(27\) | −1880.00 | −0.496305 | ||||||||
\(28\) | 992.000 | 0.239120 | ||||||||
\(29\) | 6174.00 | 1.36324 | 0.681619 | − | 0.731707i | \(-0.261276\pi\) | ||||
0.681619 | + | 0.731707i | \(0.261276\pi\) | |||||||
\(30\) | −1296.00 | −0.262907 | ||||||||
\(31\) | −7840.00 | −1.46525 | −0.732625 | − | 0.680632i | \(-0.761705\pi\) | ||||
−0.732625 | + | 0.680632i | \(0.761705\pi\) | |||||||
\(32\) | 1440.00 | 0.248592 | ||||||||
\(33\) | 816.000 | 0.130438 | ||||||||
\(34\) | −9324.00 | −1.38326 | ||||||||
\(35\) | 13392.0 | 1.84789 | ||||||||
\(36\) | −908.000 | −0.116770 | ||||||||
\(37\) | −5146.00 | −0.617967 | −0.308984 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308984 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(38\) | −2166.00 | −0.243332 | ||||||||
\(39\) | −1480.00 | −0.155812 | ||||||||
\(40\) | 9072.00 | 0.896506 | ||||||||
\(41\) | −7830.00 | −0.727448 | −0.363724 | − | 0.931507i | \(-0.618495\pi\) | ||||
−0.363724 | + | 0.931507i | \(0.618495\pi\) | |||||||
\(42\) | −5952.00 | −0.520643 | ||||||||
\(43\) | −12532.0 | −1.03359 | −0.516796 | − | 0.856108i | \(-0.672875\pi\) | ||||
−0.516796 | + | 0.856108i | \(0.672875\pi\) | |||||||
\(44\) | 816.000 | 0.0635416 | ||||||||
\(45\) | −12258.0 | −0.902378 | ||||||||
\(46\) | 2448.00 | 0.170576 | ||||||||
\(47\) | 2592.00 | 0.171155 | 0.0855777 | − | 0.996332i | \(-0.472726\pi\) | ||||
0.0855777 | + | 0.996332i | \(0.472726\pi\) | |||||||
\(48\) | −4544.00 | −0.284666 | ||||||||
\(49\) | 44697.0 | 2.65943 | ||||||||
\(50\) | 1254.00 | 0.0709370 | ||||||||
\(51\) | 6216.00 | 0.334646 | ||||||||
\(52\) | −1480.00 | −0.0759020 | ||||||||
\(53\) | −20778.0 | −1.01605 | −0.508024 | − | 0.861343i | \(-0.669624\pi\) | ||||
−0.508024 | + | 0.861343i | \(0.669624\pi\) | |||||||
\(54\) | 11280.0 | 0.526411 | ||||||||
\(55\) | 11016.0 | 0.491040 | ||||||||
\(56\) | 41664.0 | 1.77538 | ||||||||
\(57\) | 1444.00 | 0.0588681 | ||||||||
\(58\) | −37044.0 | −1.44593 | ||||||||
\(59\) | 18972.0 | 0.709550 | 0.354775 | − | 0.934952i | \(-0.384557\pi\) | ||||
0.354775 | + | 0.934952i | \(0.384557\pi\) | |||||||
\(60\) | 864.000 | 0.0309839 | ||||||||
\(61\) | −18418.0 | −0.633750 | −0.316875 | − | 0.948467i | \(-0.602634\pi\) | ||||
−0.316875 | + | 0.948467i | \(0.602634\pi\) | |||||||
\(62\) | 47040.0 | 1.55413 | ||||||||
\(63\) | −56296.0 | −1.78701 | ||||||||
\(64\) | 27712.0 | 0.845703 | ||||||||
\(65\) | −19980.0 | −0.586560 | ||||||||
\(66\) | −4896.00 | −0.138351 | ||||||||
\(67\) | −11548.0 | −0.314282 | −0.157141 | − | 0.987576i | \(-0.550228\pi\) | ||||
−0.157141 | + | 0.987576i | \(0.550228\pi\) | |||||||
\(68\) | 6216.00 | 0.163019 | ||||||||
\(69\) | −1632.00 | −0.0412665 | ||||||||
\(70\) | −80352.0 | −1.95998 | ||||||||
\(71\) | −72984.0 | −1.71823 | −0.859116 | − | 0.511781i | \(-0.828986\pi\) | ||||
−0.859116 | + | 0.511781i | \(0.828986\pi\) | |||||||
\(72\) | −38136.0 | −0.866970 | ||||||||
\(73\) | 59114.0 | 1.29832 | 0.649162 | − | 0.760650i | \(-0.275120\pi\) | ||||
0.649162 | + | 0.760650i | \(0.275120\pi\) | |||||||
\(74\) | 30876.0 | 0.655453 | ||||||||
\(75\) | −836.000 | −0.0171614 | ||||||||
\(76\) | 1444.00 | 0.0286770 | ||||||||
\(77\) | 50592.0 | 0.972423 | ||||||||
\(78\) | 8880.00 | 0.165263 | ||||||||
\(79\) | −44752.0 | −0.806761 | −0.403380 | − | 0.915032i | \(-0.632165\pi\) | ||||
−0.403380 | + | 0.915032i | \(0.632165\pi\) | |||||||
\(80\) | −61344.0 | −1.07164 | ||||||||
\(81\) | 47641.0 | 0.806805 | ||||||||
\(82\) | 46980.0 | 0.771575 | ||||||||
\(83\) | −27660.0 | −0.440714 | −0.220357 | − | 0.975419i | \(-0.570722\pi\) | ||||
−0.220357 | + | 0.975419i | \(0.570722\pi\) | |||||||
\(84\) | 3968.00 | 0.0613583 | ||||||||
\(85\) | 83916.0 | 1.25979 | ||||||||
\(86\) | 75192.0 | 1.09629 | ||||||||
\(87\) | 24696.0 | 0.349807 | ||||||||
\(88\) | 34272.0 | 0.471773 | ||||||||
\(89\) | 20730.0 | 0.277411 | 0.138706 | − | 0.990334i | \(-0.455706\pi\) | ||||
0.138706 | + | 0.990334i | \(0.455706\pi\) | |||||||
\(90\) | 73548.0 | 0.957116 | ||||||||
\(91\) | −91760.0 | −1.16158 | ||||||||
\(92\) | −1632.00 | −0.0201025 | ||||||||
\(93\) | −31360.0 | −0.375983 | ||||||||
\(94\) | −15552.0 | −0.181538 | ||||||||
\(95\) | 19494.0 | 0.221611 | ||||||||
\(96\) | 5760.00 | 0.0637888 | ||||||||
\(97\) | 14018.0 | 0.151271 | 0.0756357 | − | 0.997136i | \(-0.475901\pi\) | ||||
0.0756357 | + | 0.997136i | \(0.475901\pi\) | |||||||
\(98\) | −268182. | −2.82075 | ||||||||
\(99\) | −46308.0 | −0.474863 | ||||||||
\(100\) | −836.000 | −0.00836000 | ||||||||
\(101\) | 145782. | 1.42200 | 0.711001 | − | 0.703191i | \(-0.248242\pi\) | ||||
0.711001 | + | 0.703191i | \(0.248242\pi\) | |||||||
\(102\) | −37296.0 | −0.354946 | ||||||||
\(103\) | 90152.0 | 0.837302 | 0.418651 | − | 0.908147i | \(-0.362503\pi\) | ||||
0.418651 | + | 0.908147i | \(0.362503\pi\) | |||||||
\(104\) | −62160.0 | −0.563544 | ||||||||
\(105\) | 53568.0 | 0.474168 | ||||||||
\(106\) | 124668. | 1.07768 | ||||||||
\(107\) | 36108.0 | 0.304891 | 0.152445 | − | 0.988312i | \(-0.451285\pi\) | ||||
0.152445 | + | 0.988312i | \(0.451285\pi\) | |||||||
\(108\) | −7520.00 | −0.0620381 | ||||||||
\(109\) | 32654.0 | 0.263251 | 0.131626 | − | 0.991300i | \(-0.457980\pi\) | ||||
0.131626 | + | 0.991300i | \(0.457980\pi\) | |||||||
\(110\) | −66096.0 | −0.520827 | ||||||||
\(111\) | −20584.0 | −0.158570 | ||||||||
\(112\) | −281728. | −2.12219 | ||||||||
\(113\) | −145806. | −1.07419 | −0.537093 | − | 0.843523i | \(-0.680477\pi\) | ||||
−0.537093 | + | 0.843523i | \(0.680477\pi\) | |||||||
\(114\) | −8664.00 | −0.0624391 | ||||||||
\(115\) | −22032.0 | −0.155349 | ||||||||
\(116\) | 24696.0 | 0.170405 | ||||||||
\(117\) | 83990.0 | 0.567235 | ||||||||
\(118\) | −113832. | −0.752592 | ||||||||
\(119\) | 385392. | 2.49480 | ||||||||
\(120\) | 36288.0 | 0.230043 | ||||||||
\(121\) | −119435. | −0.741597 | ||||||||
\(122\) | 110508. | 0.672193 | ||||||||
\(123\) | −31320.0 | −0.186663 | ||||||||
\(124\) | −31360.0 | −0.183156 | ||||||||
\(125\) | −180036. | −1.03059 | ||||||||
\(126\) | 337776. | 1.89541 | ||||||||
\(127\) | −259936. | −1.43007 | −0.715035 | − | 0.699089i | \(-0.753589\pi\) | ||||
−0.715035 | + | 0.699089i | \(0.753589\pi\) | |||||||
\(128\) | −212352. | −1.14560 | ||||||||
\(129\) | −50128.0 | −0.265220 | ||||||||
\(130\) | 119880. | 0.622140 | ||||||||
\(131\) | −124092. | −0.631780 | −0.315890 | − | 0.948796i | \(-0.602303\pi\) | ||||
−0.315890 | + | 0.948796i | \(0.602303\pi\) | |||||||
\(132\) | 3264.00 | 0.0163048 | ||||||||
\(133\) | 89528.0 | 0.438864 | ||||||||
\(134\) | 69288.0 | 0.333347 | ||||||||
\(135\) | −101520. | −0.479421 | ||||||||
\(136\) | 261072. | 1.21036 | ||||||||
\(137\) | 84330.0 | 0.383867 | 0.191933 | − | 0.981408i | \(-0.438524\pi\) | ||||
0.191933 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(138\) | 9792.00 | 0.0437697 | ||||||||
\(139\) | −155476. | −0.682537 | −0.341269 | − | 0.939966i | \(-0.610857\pi\) | ||||
−0.341269 | + | 0.939966i | \(0.610857\pi\) | |||||||
\(140\) | 53568.0 | 0.230986 | ||||||||
\(141\) | 10368.0 | 0.0439185 | ||||||||
\(142\) | 437904. | 1.82246 | ||||||||
\(143\) | −75480.0 | −0.308668 | ||||||||
\(144\) | 257872. | 1.03633 | ||||||||
\(145\) | 333396. | 1.31686 | ||||||||
\(146\) | −354684. | −1.37708 | ||||||||
\(147\) | 178788. | 0.682409 | ||||||||
\(148\) | −20584.0 | −0.0772459 | ||||||||
\(149\) | −232794. | −0.859026 | −0.429513 | − | 0.903061i | \(-0.641315\pi\) | ||||
−0.429513 | + | 0.903061i | \(0.641315\pi\) | |||||||
\(150\) | 5016.00 | 0.0182024 | ||||||||
\(151\) | 496184. | 1.77093 | 0.885463 | − | 0.464710i | \(-0.153841\pi\) | ||||
0.885463 | + | 0.464710i | \(0.153841\pi\) | |||||||
\(152\) | 60648.0 | 0.212916 | ||||||||
\(153\) | −352758. | −1.21828 | ||||||||
\(154\) | −303552. | −1.03141 | ||||||||
\(155\) | −423360. | −1.41540 | ||||||||
\(156\) | −5920.00 | −0.0194765 | ||||||||
\(157\) | 128078. | 0.414692 | 0.207346 | − | 0.978268i | \(-0.433517\pi\) | ||||
0.207346 | + | 0.978268i | \(0.433517\pi\) | |||||||
\(158\) | 268512. | 0.855699 | ||||||||
\(159\) | −83112.0 | −0.260718 | ||||||||
\(160\) | 77760.0 | 0.240135 | ||||||||
\(161\) | −101184. | −0.307643 | ||||||||
\(162\) | −285846. | −0.855745 | ||||||||
\(163\) | −570652. | −1.68230 | −0.841148 | − | 0.540805i | \(-0.818120\pi\) | ||||
−0.841148 | + | 0.540805i | \(0.818120\pi\) | |||||||
\(164\) | −31320.0 | −0.0909310 | ||||||||
\(165\) | 44064.0 | 0.126001 | ||||||||
\(166\) | 165960. | 0.467448 | ||||||||
\(167\) | −39864.0 | −0.110609 | −0.0553044 | − | 0.998470i | \(-0.517613\pi\) | ||||
−0.0553044 | + | 0.998470i | \(0.517613\pi\) | |||||||
\(168\) | 166656. | 0.455562 | ||||||||
\(169\) | −234393. | −0.631288 | ||||||||
\(170\) | −503496. | −1.33621 | ||||||||
\(171\) | −81947.0 | −0.214310 | ||||||||
\(172\) | −50128.0 | −0.129199 | ||||||||
\(173\) | 223086. | 0.566705 | 0.283353 | − | 0.959016i | \(-0.408553\pi\) | ||||
0.283353 | + | 0.959016i | \(0.408553\pi\) | |||||||
\(174\) | −148176. | −0.371026 | ||||||||
\(175\) | −51832.0 | −0.127939 | ||||||||
\(176\) | −231744. | −0.563932 | ||||||||
\(177\) | 75888.0 | 0.182071 | ||||||||
\(178\) | −124380. | −0.294239 | ||||||||
\(179\) | 316980. | 0.739434 | 0.369717 | − | 0.929144i | \(-0.379455\pi\) | ||||
0.369717 | + | 0.929144i | \(0.379455\pi\) | |||||||
\(180\) | −49032.0 | −0.112797 | ||||||||
\(181\) | 857270. | 1.94501 | 0.972504 | − | 0.232888i | \(-0.0748176\pi\) | ||||
0.972504 | + | 0.232888i | \(0.0748176\pi\) | |||||||
\(182\) | 550560. | 1.23204 | ||||||||
\(183\) | −73672.0 | −0.162620 | ||||||||
\(184\) | −68544.0 | −0.149254 | ||||||||
\(185\) | −277884. | −0.596945 | ||||||||
\(186\) | 188160. | 0.398791 | ||||||||
\(187\) | 317016. | 0.662944 | ||||||||
\(188\) | 10368.0 | 0.0213944 | ||||||||
\(189\) | −466240. | −0.949413 | ||||||||
\(190\) | −116964. | −0.235054 | ||||||||
\(191\) | 783600. | 1.55421 | 0.777107 | − | 0.629368i | \(-0.216686\pi\) | ||||
0.777107 | + | 0.629368i | \(0.216686\pi\) | |||||||
\(192\) | 110848. | 0.217008 | ||||||||
\(193\) | 231074. | 0.446537 | 0.223269 | − | 0.974757i | \(-0.428327\pi\) | ||||
0.223269 | + | 0.974757i | \(0.428327\pi\) | |||||||
\(194\) | −84108.0 | −0.160448 | ||||||||
\(195\) | −79920.0 | −0.150511 | ||||||||
\(196\) | 178788. | 0.332428 | ||||||||
\(197\) | 438966. | 0.805871 | 0.402935 | − | 0.915228i | \(-0.367990\pi\) | ||||
0.402935 | + | 0.915228i | \(0.367990\pi\) | |||||||
\(198\) | 277848. | 0.503668 | ||||||||
\(199\) | −385000. | −0.689173 | −0.344586 | − | 0.938755i | \(-0.611981\pi\) | ||||
−0.344586 | + | 0.938755i | \(0.611981\pi\) | |||||||
\(200\) | −35112.0 | −0.0620698 | ||||||||
\(201\) | −46192.0 | −0.0806448 | ||||||||
\(202\) | −874692. | −1.50826 | ||||||||
\(203\) | 1.53115e6 | 2.60782 | ||||||||
\(204\) | 24864.0 | 0.0418307 | ||||||||
\(205\) | −422820. | −0.702701 | ||||||||
\(206\) | −540912. | −0.888093 | ||||||||
\(207\) | 92616.0 | 0.150231 | ||||||||
\(208\) | 420320. | 0.673630 | ||||||||
\(209\) | 73644.0 | 0.116620 | ||||||||
\(210\) | −321408. | −0.502931 | ||||||||
\(211\) | 438740. | 0.678424 | 0.339212 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339212 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(212\) | −83112.0 | −0.127006 | ||||||||
\(213\) | −291936. | −0.440899 | ||||||||
\(214\) | −216648. | −0.323385 | ||||||||
\(215\) | −676728. | −0.998431 | ||||||||
\(216\) | −315840. | −0.460609 | ||||||||
\(217\) | −1.94432e6 | −2.80297 | ||||||||
\(218\) | −195924. | −0.279220 | ||||||||
\(219\) | 236456. | 0.333150 | ||||||||
\(220\) | 44064.0 | 0.0613800 | ||||||||
\(221\) | −574980. | −0.791903 | ||||||||
\(222\) | 123504. | 0.168189 | ||||||||
\(223\) | −372352. | −0.501408 | −0.250704 | − | 0.968064i | \(-0.580662\pi\) | ||||
−0.250704 | + | 0.968064i | \(0.580662\pi\) | |||||||
\(224\) | 357120. | 0.475548 | ||||||||
\(225\) | 47443.0 | 0.0624764 | ||||||||
\(226\) | 874836. | 1.13935 | ||||||||
\(227\) | 1.01101e6 | 1.30224 | 0.651121 | − | 0.758974i | \(-0.274299\pi\) | ||||
0.651121 | + | 0.758974i | \(0.274299\pi\) | |||||||
\(228\) | 5776.00 | 0.00735851 | ||||||||
\(229\) | 571382. | 0.720009 | 0.360004 | − | 0.932951i | \(-0.382775\pi\) | ||||
0.360004 | + | 0.932951i | \(0.382775\pi\) | |||||||
\(230\) | 132192. | 0.164773 | ||||||||
\(231\) | 202368. | 0.249524 | ||||||||
\(232\) | 1.03723e6 | 1.26519 | ||||||||
\(233\) | −594678. | −0.717616 | −0.358808 | − | 0.933411i | \(-0.616817\pi\) | ||||
−0.358808 | + | 0.933411i | \(0.616817\pi\) | |||||||
\(234\) | −503940. | −0.601643 | ||||||||
\(235\) | 139968. | 0.165333 | ||||||||
\(236\) | 75888.0 | 0.0886938 | ||||||||
\(237\) | −179008. | −0.207015 | ||||||||
\(238\) | −2.31235e6 | −2.64613 | ||||||||
\(239\) | −380544. | −0.430933 | −0.215467 | − | 0.976511i | \(-0.569127\pi\) | ||||
−0.215467 | + | 0.976511i | \(0.569127\pi\) | |||||||
\(240\) | −245376. | −0.274982 | ||||||||
\(241\) | −1.07678e6 | −1.19422 | −0.597111 | − | 0.802159i | \(-0.703685\pi\) | ||||
−0.597111 | + | 0.802159i | \(0.703685\pi\) | |||||||
\(242\) | 716610. | 0.786583 | ||||||||
\(243\) | 647404. | 0.703331 | ||||||||
\(244\) | −73672.0 | −0.0792187 | ||||||||
\(245\) | 2.41364e6 | 2.56896 | ||||||||
\(246\) | 187920. | 0.197986 | ||||||||
\(247\) | −133570. | −0.139305 | ||||||||
\(248\) | −1.31712e6 | −1.35987 | ||||||||
\(249\) | −110640. | −0.113087 | ||||||||
\(250\) | 1.08022e6 | 1.09310 | ||||||||
\(251\) | −113316. | −0.113529 | −0.0567645 | − | 0.998388i | \(-0.518078\pi\) | ||||
−0.0567645 | + | 0.998388i | \(0.518078\pi\) | |||||||
\(252\) | −225184. | −0.223376 | ||||||||
\(253\) | −83232.0 | −0.0817502 | ||||||||
\(254\) | 1.55962e6 | 1.51682 | ||||||||
\(255\) | 335664. | 0.323262 | ||||||||
\(256\) | 387328. | 0.369385 | ||||||||
\(257\) | 553218. | 0.522473 | 0.261236 | − | 0.965275i | \(-0.415870\pi\) | ||||
0.261236 | + | 0.965275i | \(0.415870\pi\) | |||||||
\(258\) | 300768. | 0.281308 | ||||||||
\(259\) | −1.27621e6 | −1.18215 | ||||||||
\(260\) | −79920.0 | −0.0733199 | ||||||||
\(261\) | −1.40150e6 | −1.27348 | ||||||||
\(262\) | 744552. | 0.670103 | ||||||||
\(263\) | 824088. | 0.734656 | 0.367328 | − | 0.930091i | \(-0.380273\pi\) | ||||
0.367328 | + | 0.930091i | \(0.380273\pi\) | |||||||
\(264\) | 137088. | 0.121057 | ||||||||
\(265\) | −1.12201e6 | −0.981483 | ||||||||
\(266\) | −537168. | −0.465485 | ||||||||
\(267\) | 82920.0 | 0.0711838 | ||||||||
\(268\) | −46192.0 | −0.0392853 | ||||||||
\(269\) | 1.52158e6 | 1.28208 | 0.641039 | − | 0.767508i | \(-0.278504\pi\) | ||||
0.641039 | + | 0.767508i | \(0.278504\pi\) | |||||||
\(270\) | 609120. | 0.508503 | ||||||||
\(271\) | −1.08304e6 | −0.895821 | −0.447911 | − | 0.894078i | \(-0.647832\pi\) | ||||
−0.447911 | + | 0.894078i | \(0.647832\pi\) | |||||||
\(272\) | −1.76534e6 | −1.44680 | ||||||||
\(273\) | −367040. | −0.298062 | ||||||||
\(274\) | −505980. | −0.407152 | ||||||||
\(275\) | −42636.0 | −0.0339973 | ||||||||
\(276\) | −6528.00 | −0.00515831 | ||||||||
\(277\) | 658598. | 0.515728 | 0.257864 | − | 0.966181i | \(-0.416981\pi\) | ||||
0.257864 | + | 0.966181i | \(0.416981\pi\) | |||||||
\(278\) | 932856. | 0.723940 | ||||||||
\(279\) | 1.77968e6 | 1.36877 | ||||||||
\(280\) | 2.24986e6 | 1.71498 | ||||||||
\(281\) | 356346. | 0.269219 | 0.134610 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134610 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(282\) | −62208.0 | −0.0465826 | ||||||||
\(283\) | 405116. | 0.300686 | 0.150343 | − | 0.988634i | \(-0.451962\pi\) | ||||
0.150343 | + | 0.988634i | \(0.451962\pi\) | |||||||
\(284\) | −291936. | −0.214779 | ||||||||
\(285\) | 77976.0 | 0.0568655 | ||||||||
\(286\) | 452880. | 0.327392 | ||||||||
\(287\) | −1.94184e6 | −1.39158 | ||||||||
\(288\) | −326880. | −0.232224 | ||||||||
\(289\) | 995059. | 0.700816 | ||||||||
\(290\) | −2.00038e6 | −1.39674 | ||||||||
\(291\) | 56072.0 | 0.0388162 | ||||||||
\(292\) | 236456. | 0.162291 | ||||||||
\(293\) | −948570. | −0.645506 | −0.322753 | − | 0.946483i | \(-0.604608\pi\) | ||||
−0.322753 | + | 0.946483i | \(0.604608\pi\) | |||||||
\(294\) | −1.07273e6 | −0.723805 | ||||||||
\(295\) | 1.02449e6 | 0.685412 | ||||||||
\(296\) | −864528. | −0.573522 | ||||||||
\(297\) | −383520. | −0.252288 | ||||||||
\(298\) | 1.39676e6 | 0.911134 | ||||||||
\(299\) | 150960. | 0.0976526 | ||||||||
\(300\) | −3344.00 | −0.00214518 | ||||||||
\(301\) | −3.10794e6 | −1.97722 | ||||||||
\(302\) | −2.97710e6 | −1.87835 | ||||||||
\(303\) | 583128. | 0.364886 | ||||||||
\(304\) | −410096. | −0.254508 | ||||||||
\(305\) | −994572. | −0.612191 | ||||||||
\(306\) | 2.11655e6 | 1.29218 | ||||||||
\(307\) | −1.16235e6 | −0.703866 | −0.351933 | − | 0.936025i | \(-0.614476\pi\) | ||||
−0.351933 | + | 0.936025i | \(0.614476\pi\) | |||||||
\(308\) | 202368. | 0.121553 | ||||||||
\(309\) | 360608. | 0.214852 | ||||||||
\(310\) | 2.54016e6 | 1.50126 | ||||||||
\(311\) | −2.55718e6 | −1.49920 | −0.749600 | − | 0.661891i | \(-0.769754\pi\) | ||||
−0.749600 | + | 0.661891i | \(0.769754\pi\) | |||||||
\(312\) | −248640. | −0.144605 | ||||||||
\(313\) | −1.05943e6 | −0.611240 | −0.305620 | − | 0.952154i | \(-0.598864\pi\) | ||||
−0.305620 | + | 0.952154i | \(0.598864\pi\) | |||||||
\(314\) | −768468. | −0.439847 | ||||||||
\(315\) | −3.03998e6 | −1.72622 | ||||||||
\(316\) | −179008. | −0.100845 | ||||||||
\(317\) | 2.64425e6 | 1.47793 | 0.738967 | − | 0.673742i | \(-0.235314\pi\) | ||||
0.738967 | + | 0.673742i | \(0.235314\pi\) | |||||||
\(318\) | 498672. | 0.276533 | ||||||||
\(319\) | 1.25950e6 | 0.692979 | ||||||||
\(320\) | 1.49645e6 | 0.816933 | ||||||||
\(321\) | 144432. | 0.0782350 | ||||||||
\(322\) | 607104. | 0.326305 | ||||||||
\(323\) | 560994. | 0.299193 | ||||||||
\(324\) | 190564. | 0.100851 | ||||||||
\(325\) | 77330.0 | 0.0406106 | ||||||||
\(326\) | 3.42391e6 | 1.78434 | ||||||||
\(327\) | 130616. | 0.0675503 | ||||||||
\(328\) | −1.31544e6 | −0.675128 | ||||||||
\(329\) | 642816. | 0.327414 | ||||||||
\(330\) | −264384. | −0.133644 | ||||||||
\(331\) | 2.39083e6 | 1.19944 | 0.599720 | − | 0.800210i | \(-0.295279\pi\) | ||||
0.599720 | + | 0.800210i | \(0.295279\pi\) | |||||||
\(332\) | −110640. | −0.0550893 | ||||||||
\(333\) | 1.16814e6 | 0.577278 | ||||||||
\(334\) | 239184. | 0.117318 | ||||||||
\(335\) | −623592. | −0.303591 | ||||||||
\(336\) | −1.12691e6 | −0.544555 | ||||||||
\(337\) | −1.12382e6 | −0.539042 | −0.269521 | − | 0.962994i | \(-0.586865\pi\) | ||||
−0.269521 | + | 0.962994i | \(0.586865\pi\) | |||||||
\(338\) | 1.40636e6 | 0.669583 | ||||||||
\(339\) | −583224. | −0.275636 | ||||||||
\(340\) | 335664. | 0.157473 | ||||||||
\(341\) | −1.59936e6 | −0.744835 | ||||||||
\(342\) | 491682. | 0.227310 | ||||||||
\(343\) | 6.91672e6 | 3.17442 | ||||||||
\(344\) | −2.10538e6 | −0.959254 | ||||||||
\(345\) | −88128.0 | −0.0398627 | ||||||||
\(346\) | −1.33852e6 | −0.601081 | ||||||||
\(347\) | 2.00387e6 | 0.893399 | 0.446699 | − | 0.894684i | \(-0.352599\pi\) | ||||
0.446699 | + | 0.894684i | \(0.352599\pi\) | |||||||
\(348\) | 98784.0 | 0.0437259 | ||||||||
\(349\) | 3.60808e6 | 1.58567 | 0.792834 | − | 0.609437i | \(-0.208605\pi\) | ||||
0.792834 | + | 0.609437i | \(0.208605\pi\) | |||||||
\(350\) | 310992. | 0.135700 | ||||||||
\(351\) | 695600. | 0.301364 | ||||||||
\(352\) | 293760. | 0.126368 | ||||||||
\(353\) | −1.82825e6 | −0.780908 | −0.390454 | − | 0.920622i | \(-0.627682\pi\) | ||||
−0.390454 | + | 0.920622i | \(0.627682\pi\) | |||||||
\(354\) | −455328. | −0.193115 | ||||||||
\(355\) | −3.94114e6 | −1.65978 | ||||||||
\(356\) | 82920.0 | 0.0346764 | ||||||||
\(357\) | 1.54157e6 | 0.640165 | ||||||||
\(358\) | −1.90188e6 | −0.784288 | ||||||||
\(359\) | −2.61012e6 | −1.06887 | −0.534434 | − | 0.845210i | \(-0.679475\pi\) | ||||
−0.534434 | + | 0.845210i | \(0.679475\pi\) | |||||||
\(360\) | −2.05934e6 | −0.837477 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −5.14362e6 | −2.06299 | ||||||||
\(363\) | −477740. | −0.190294 | ||||||||
\(364\) | −367040. | −0.145198 | ||||||||
\(365\) | 3.19216e6 | 1.25416 | ||||||||
\(366\) | 442032. | 0.172485 | ||||||||
\(367\) | 391136. | 0.151587 | 0.0757936 | − | 0.997124i | \(-0.475851\pi\) | ||||
0.0757936 | + | 0.997124i | \(0.475851\pi\) | |||||||
\(368\) | 463488. | 0.178410 | ||||||||
\(369\) | 1.77741e6 | 0.679550 | ||||||||
\(370\) | 1.66730e6 | 0.633156 | ||||||||
\(371\) | −5.15294e6 | −1.94366 | ||||||||
\(372\) | −125440. | −0.0469979 | ||||||||
\(373\) | 262070. | 0.0975316 | 0.0487658 | − | 0.998810i | \(-0.484471\pi\) | ||||
0.0487658 | + | 0.998810i | \(0.484471\pi\) | |||||||
\(374\) | −1.90210e6 | −0.703159 | ||||||||
\(375\) | −720144. | −0.264449 | ||||||||
\(376\) | 435456. | 0.158845 | ||||||||
\(377\) | −2.28438e6 | −0.827780 | ||||||||
\(378\) | 2.79744e6 | 1.00700 | ||||||||
\(379\) | 824060. | 0.294687 | 0.147343 | − | 0.989085i | \(-0.452928\pi\) | ||||
0.147343 | + | 0.989085i | \(0.452928\pi\) | |||||||
\(380\) | 77976.0 | 0.0277014 | ||||||||
\(381\) | −1.03974e6 | −0.366956 | ||||||||
\(382\) | −4.70160e6 | −1.64849 | ||||||||
\(383\) | −3.89779e6 | −1.35776 | −0.678878 | − | 0.734251i | \(-0.737533\pi\) | ||||
−0.678878 | + | 0.734251i | \(0.737533\pi\) | |||||||
\(384\) | −849408. | −0.293960 | ||||||||
\(385\) | 2.73197e6 | 0.939342 | ||||||||
\(386\) | −1.38644e6 | −0.473624 | ||||||||
\(387\) | 2.84476e6 | 0.965537 | ||||||||
\(388\) | 56072.0 | 0.0189089 | ||||||||
\(389\) | 1.97401e6 | 0.661416 | 0.330708 | − | 0.943733i | \(-0.392713\pi\) | ||||
0.330708 | + | 0.943733i | \(0.392713\pi\) | |||||||
\(390\) | 479520. | 0.159641 | ||||||||
\(391\) | −634032. | −0.209734 | ||||||||
\(392\) | 7.50910e6 | 2.46816 | ||||||||
\(393\) | −496368. | −0.162115 | ||||||||
\(394\) | −2.63380e6 | −0.854755 | ||||||||
\(395\) | −2.41661e6 | −0.779316 | ||||||||
\(396\) | −185232. | −0.0593578 | ||||||||
\(397\) | −2.84403e6 | −0.905646 | −0.452823 | − | 0.891600i | \(-0.649583\pi\) | ||||
−0.452823 | + | 0.891600i | \(0.649583\pi\) | |||||||
\(398\) | 2.31000e6 | 0.730978 | ||||||||
\(399\) | 358112. | 0.112613 | ||||||||
\(400\) | 237424. | 0.0741950 | ||||||||
\(401\) | 5.80235e6 | 1.80195 | 0.900976 | − | 0.433869i | \(-0.142852\pi\) | ||||
0.900976 | + | 0.433869i | \(0.142852\pi\) | |||||||
\(402\) | 277152. | 0.0855368 | ||||||||
\(403\) | 2.90080e6 | 0.889724 | ||||||||
\(404\) | 583128. | 0.177750 | ||||||||
\(405\) | 2.57261e6 | 0.779358 | ||||||||
\(406\) | −9.18691e6 | −2.76601 | ||||||||
\(407\) | −1.04978e6 | −0.314133 | ||||||||
\(408\) | 1.04429e6 | 0.310577 | ||||||||
\(409\) | 5.35337e6 | 1.58241 | 0.791205 | − | 0.611551i | \(-0.209454\pi\) | ||||
0.791205 | + | 0.611551i | \(0.209454\pi\) | |||||||
\(410\) | 2.53692e6 | 0.745327 | ||||||||
\(411\) | 337320. | 0.0985003 | ||||||||
\(412\) | 360608. | 0.104663 | ||||||||
\(413\) | 4.70506e6 | 1.35734 | ||||||||
\(414\) | −555696. | −0.159344 | ||||||||
\(415\) | −1.49364e6 | −0.425722 | ||||||||
\(416\) | −532800. | −0.150949 | ||||||||
\(417\) | −621904. | −0.175139 | ||||||||
\(418\) | −441864. | −0.123694 | ||||||||
\(419\) | −1.14198e6 | −0.317778 | −0.158889 | − | 0.987296i | \(-0.550791\pi\) | ||||
−0.158889 | + | 0.987296i | \(0.550791\pi\) | |||||||
\(420\) | 214272. | 0.0592710 | ||||||||
\(421\) | −740794. | −0.203701 | −0.101850 | − | 0.994800i | \(-0.532476\pi\) | ||||
−0.101850 | + | 0.994800i | \(0.532476\pi\) | |||||||
\(422\) | −2.63244e6 | −0.719577 | ||||||||
\(423\) | −588384. | −0.159886 | ||||||||
\(424\) | −3.49070e6 | −0.942971 | ||||||||
\(425\) | −324786. | −0.0872218 | ||||||||
\(426\) | 1.75162e6 | 0.467644 | ||||||||
\(427\) | −4.56766e6 | −1.21234 | ||||||||
\(428\) | 144432. | 0.0381113 | ||||||||
\(429\) | −301920. | −0.0792043 | ||||||||
\(430\) | 4.06037e6 | 1.05900 | ||||||||
\(431\) | 1.30354e6 | 0.338010 | 0.169005 | − | 0.985615i | \(-0.445945\pi\) | ||||
0.169005 | + | 0.985615i | \(0.445945\pi\) | |||||||
\(432\) | 2.13568e6 | 0.550588 | ||||||||
\(433\) | −7.23557e6 | −1.85461 | −0.927305 | − | 0.374306i | \(-0.877881\pi\) | ||||
−0.927305 | + | 0.374306i | \(0.877881\pi\) | |||||||
\(434\) | 1.16659e7 | 2.97300 | ||||||||
\(435\) | 1.33358e6 | 0.337907 | ||||||||
\(436\) | 130616. | 0.0329064 | ||||||||
\(437\) | −147288. | −0.0368947 | ||||||||
\(438\) | −1.41874e6 | −0.353359 | ||||||||
\(439\) | −415336. | −0.102858 | −0.0514290 | − | 0.998677i | \(-0.516378\pi\) | ||||
−0.0514290 | + | 0.998677i | \(0.516378\pi\) | |||||||
\(440\) | 1.85069e6 | 0.455724 | ||||||||
\(441\) | −1.01462e7 | −2.48432 | ||||||||
\(442\) | 3.44988e6 | 0.839940 | ||||||||
\(443\) | 3.93203e6 | 0.951935 | 0.475967 | − | 0.879463i | \(-0.342098\pi\) | ||||
0.475967 | + | 0.879463i | \(0.342098\pi\) | |||||||
\(444\) | −82336.0 | −0.0198213 | ||||||||
\(445\) | 1.11942e6 | 0.267974 | ||||||||
\(446\) | 2.23411e6 | 0.531824 | ||||||||
\(447\) | −931176. | −0.220426 | ||||||||
\(448\) | 6.87258e6 | 1.61780 | ||||||||
\(449\) | −4.76624e6 | −1.11573 | −0.557866 | − | 0.829931i | \(-0.688380\pi\) | ||||
−0.557866 | + | 0.829931i | \(0.688380\pi\) | |||||||
\(450\) | −284658. | −0.0662662 | ||||||||
\(451\) | −1.59732e6 | −0.369786 | ||||||||
\(452\) | −583224. | −0.134273 | ||||||||
\(453\) | 1.98474e6 | 0.454420 | ||||||||
\(454\) | −6.06607e6 | −1.38124 | ||||||||
\(455\) | −4.95504e6 | −1.12207 | ||||||||
\(456\) | 242592. | 0.0546342 | ||||||||
\(457\) | 2.72215e6 | 0.609708 | 0.304854 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304854 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(458\) | −3.42829e6 | −0.763685 | ||||||||
\(459\) | −2.92152e6 | −0.647258 | ||||||||
\(460\) | −88128.0 | −0.0194187 | ||||||||
\(461\) | 2.46675e6 | 0.540596 | 0.270298 | − | 0.962777i | \(-0.412878\pi\) | ||||
0.270298 | + | 0.962777i | \(0.412878\pi\) | |||||||
\(462\) | −1.21421e6 | −0.264660 | ||||||||
\(463\) | −1.63734e6 | −0.354967 | −0.177483 | − | 0.984124i | \(-0.556796\pi\) | ||||
−0.177483 | + | 0.984124i | \(0.556796\pi\) | |||||||
\(464\) | −7.01366e6 | −1.51234 | ||||||||
\(465\) | −1.69344e6 | −0.363193 | ||||||||
\(466\) | 3.56807e6 | 0.761147 | ||||||||
\(467\) | 5.94565e6 | 1.26156 | 0.630779 | − | 0.775962i | \(-0.282735\pi\) | ||||
0.630779 | + | 0.775962i | \(0.282735\pi\) | |||||||
\(468\) | 335960. | 0.0709044 | ||||||||
\(469\) | −2.86390e6 | −0.601210 | ||||||||
\(470\) | −839808. | −0.175362 | ||||||||
\(471\) | 512312. | 0.106410 | ||||||||
\(472\) | 3.18730e6 | 0.658518 | ||||||||
\(473\) | −2.55653e6 | −0.525409 | ||||||||
\(474\) | 1.07405e6 | 0.219572 | ||||||||
\(475\) | −75449.0 | −0.0153433 | ||||||||
\(476\) | 1.54157e6 | 0.311850 | ||||||||
\(477\) | 4.71661e6 | 0.949147 | ||||||||
\(478\) | 2.28326e6 | 0.457074 | ||||||||
\(479\) | −3.85531e6 | −0.767752 | −0.383876 | − | 0.923385i | \(-0.625411\pi\) | ||||
−0.383876 | + | 0.923385i | \(0.625411\pi\) | |||||||
\(480\) | 311040. | 0.0616188 | ||||||||
\(481\) | 1.90402e6 | 0.375240 | ||||||||
\(482\) | 6.46069e6 | 1.26666 | ||||||||
\(483\) | −404736. | −0.0789413 | ||||||||
\(484\) | −477740. | −0.0926997 | ||||||||
\(485\) | 756972. | 0.146125 | ||||||||
\(486\) | −3.88442e6 | −0.745995 | ||||||||
\(487\) | −4.54847e6 | −0.869047 | −0.434523 | − | 0.900661i | \(-0.643083\pi\) | ||||
−0.434523 | + | 0.900661i | \(0.643083\pi\) | |||||||
\(488\) | −3.09422e6 | −0.588169 | ||||||||
\(489\) | −2.28261e6 | −0.431677 | ||||||||
\(490\) | −1.44818e7 | −2.72479 | ||||||||
\(491\) | 1.66820e6 | 0.312281 | 0.156140 | − | 0.987735i | \(-0.450095\pi\) | ||||
0.156140 | + | 0.987735i | \(0.450095\pi\) | |||||||
\(492\) | −125280. | −0.0233329 | ||||||||
\(493\) | 9.59440e6 | 1.77787 | ||||||||
\(494\) | 801420. | 0.147755 | ||||||||
\(495\) | −2.50063e6 | −0.458708 | ||||||||
\(496\) | 8.90624e6 | 1.62551 | ||||||||
\(497\) | −1.81000e7 | −3.28691 | ||||||||
\(498\) | 663840. | 0.119947 | ||||||||
\(499\) | −956044. | −0.171880 | −0.0859402 | − | 0.996300i | \(-0.527389\pi\) | ||||
−0.0859402 | + | 0.996300i | \(0.527389\pi\) | |||||||
\(500\) | −720144. | −0.128823 | ||||||||
\(501\) | −159456. | −0.0283822 | ||||||||
\(502\) | 679896. | 0.120416 | ||||||||
\(503\) | 5.70410e6 | 1.00523 | 0.502617 | − | 0.864509i | \(-0.332370\pi\) | ||||
0.502617 | + | 0.864509i | \(0.332370\pi\) | |||||||
\(504\) | −9.45773e6 | −1.65848 | ||||||||
\(505\) | 7.87223e6 | 1.37363 | ||||||||
\(506\) | 499392. | 0.0867092 | ||||||||
\(507\) | −937572. | −0.161989 | ||||||||
\(508\) | −1.03974e6 | −0.178759 | ||||||||
\(509\) | 6.66109e6 | 1.13960 | 0.569798 | − | 0.821785i | \(-0.307022\pi\) | ||||
0.569798 | + | 0.821785i | \(0.307022\pi\) | |||||||
\(510\) | −2.01398e6 | −0.342871 | ||||||||
\(511\) | 1.46603e7 | 2.48365 | ||||||||
\(512\) | 4.47130e6 | 0.753804 | ||||||||
\(513\) | −678680. | −0.113860 | ||||||||
\(514\) | −3.31931e6 | −0.554166 | ||||||||
\(515\) | 4.86821e6 | 0.808818 | ||||||||
\(516\) | −200512. | −0.0331525 | ||||||||
\(517\) | 528768. | 0.0870039 | ||||||||
\(518\) | 7.65725e6 | 1.25386 | ||||||||
\(519\) | 892344. | 0.145417 | ||||||||
\(520\) | −3.35664e6 | −0.544373 | ||||||||
\(521\) | 5.91547e6 | 0.954761 | 0.477380 | − | 0.878697i | \(-0.341586\pi\) | ||||
0.477380 | + | 0.878697i | \(0.341586\pi\) | |||||||
\(522\) | 8.40899e6 | 1.35073 | ||||||||
\(523\) | 5.56872e6 | 0.890227 | 0.445114 | − | 0.895474i | \(-0.353163\pi\) | ||||
0.445114 | + | 0.895474i | \(0.353163\pi\) | |||||||
\(524\) | −496368. | −0.0789724 | ||||||||
\(525\) | −207328. | −0.0328292 | ||||||||
\(526\) | −4.94453e6 | −0.779221 | ||||||||
\(527\) | −1.21834e7 | −1.91091 | ||||||||
\(528\) | −926976. | −0.144705 | ||||||||
\(529\) | −6.26988e6 | −0.974137 | ||||||||
\(530\) | 6.73207e6 | 1.04102 | ||||||||
\(531\) | −4.30664e6 | −0.662831 | ||||||||
\(532\) | 358112. | 0.0548580 | ||||||||
\(533\) | 2.89710e6 | 0.441718 | ||||||||
\(534\) | −497520. | −0.0755018 | ||||||||
\(535\) | 1.94983e6 | 0.294519 | ||||||||
\(536\) | −1.94006e6 | −0.291678 | ||||||||
\(537\) | 1.26792e6 | 0.189739 | ||||||||
\(538\) | −9.12949e6 | −1.35985 | ||||||||
\(539\) | 9.11819e6 | 1.35188 | ||||||||
\(540\) | −406080. | −0.0599276 | ||||||||
\(541\) | 744878. | 0.109419 | 0.0547094 | − | 0.998502i | \(-0.482577\pi\) | ||||
0.0547094 | + | 0.998502i | \(0.482577\pi\) | |||||||
\(542\) | 6.49824e6 | 0.950162 | ||||||||
\(543\) | 3.42908e6 | 0.499089 | ||||||||
\(544\) | 2.23776e6 | 0.324202 | ||||||||
\(545\) | 1.76332e6 | 0.254296 | ||||||||
\(546\) | 2.20224e6 | 0.316143 | ||||||||
\(547\) | −6.02403e6 | −0.860833 | −0.430416 | − | 0.902631i | \(-0.641633\pi\) | ||||
−0.430416 | + | 0.902631i | \(0.641633\pi\) | |||||||
\(548\) | 337320. | 0.0479834 | ||||||||
\(549\) | 4.18089e6 | 0.592021 | ||||||||
\(550\) | 255816. | 0.0360596 | ||||||||
\(551\) | 2.22881e6 | 0.312748 | ||||||||
\(552\) | −274176. | −0.0382985 | ||||||||
\(553\) | −1.10985e7 | −1.54330 | ||||||||
\(554\) | −3.95159e6 | −0.547012 | ||||||||
\(555\) | −1.11154e6 | −0.153176 | ||||||||
\(556\) | −621904. | −0.0853172 | ||||||||
\(557\) | −5.29744e6 | −0.723483 | −0.361741 | − | 0.932278i | \(-0.617818\pi\) | ||||
−0.361741 | + | 0.932278i | \(0.617818\pi\) | |||||||
\(558\) | −1.06781e7 | −1.45180 | ||||||||
\(559\) | 4.63684e6 | 0.627614 | ||||||||
\(560\) | −1.52133e7 | −2.05000 | ||||||||
\(561\) | 1.26806e6 | 0.170112 | ||||||||
\(562\) | −2.13808e6 | −0.285550 | ||||||||
\(563\) | −6.33332e6 | −0.842094 | −0.421047 | − | 0.907039i | \(-0.638337\pi\) | ||||
−0.421047 | + | 0.907039i | \(0.638337\pi\) | |||||||
\(564\) | 41472.0 | 0.00548981 | ||||||||
\(565\) | −7.87352e6 | −1.03764 | ||||||||
\(566\) | −2.43070e6 | −0.318926 | ||||||||
\(567\) | 1.18150e7 | 1.54339 | ||||||||
\(568\) | −1.22613e7 | −1.59465 | ||||||||
\(569\) | −3.07508e6 | −0.398176 | −0.199088 | − | 0.979982i | \(-0.563798\pi\) | ||||
−0.199088 | + | 0.979982i | \(0.563798\pi\) | |||||||
\(570\) | −467856. | −0.0603150 | ||||||||
\(571\) | 359036. | 0.0460837 | 0.0230419 | − | 0.999735i | \(-0.492665\pi\) | ||||
0.0230419 | + | 0.999735i | \(0.492665\pi\) | |||||||
\(572\) | −301920. | −0.0385835 | ||||||||
\(573\) | 3.13440e6 | 0.398812 | ||||||||
\(574\) | 1.16510e7 | 1.47600 | ||||||||
\(575\) | 85272.0 | 0.0107557 | ||||||||
\(576\) | −6.29062e6 | −0.790019 | ||||||||
\(577\) | 6.43104e6 | 0.804159 | 0.402079 | − | 0.915605i | \(-0.368288\pi\) | ||||
0.402079 | + | 0.915605i | \(0.368288\pi\) | |||||||
\(578\) | −5.97035e6 | −0.743328 | ||||||||
\(579\) | 924296. | 0.114582 | ||||||||
\(580\) | 1.33358e6 | 0.164608 | ||||||||
\(581\) | −6.85968e6 | −0.843070 | ||||||||
\(582\) | −336432. | −0.0411709 | ||||||||
\(583\) | −4.23871e6 | −0.516491 | ||||||||
\(584\) | 9.93115e6 | 1.20495 | ||||||||
\(585\) | 4.53546e6 | 0.547938 | ||||||||
\(586\) | 5.69142e6 | 0.684663 | ||||||||
\(587\) | −7.47330e6 | −0.895194 | −0.447597 | − | 0.894235i | \(-0.647720\pi\) | ||||
−0.447597 | + | 0.894235i | \(0.647720\pi\) | |||||||
\(588\) | 715152. | 0.0853012 | ||||||||
\(589\) | −2.83024e6 | −0.336151 | ||||||||
\(590\) | −6.14693e6 | −0.726989 | ||||||||
\(591\) | 1.75586e6 | 0.206786 | ||||||||
\(592\) | 5.84586e6 | 0.685557 | ||||||||
\(593\) | −9.41451e6 | −1.09941 | −0.549707 | − | 0.835358i | \(-0.685261\pi\) | ||||
−0.549707 | + | 0.835358i | \(0.685261\pi\) | |||||||
\(594\) | 2.30112e6 | 0.267592 | ||||||||
\(595\) | 2.08112e7 | 2.40993 | ||||||||
\(596\) | −931176. | −0.107378 | ||||||||
\(597\) | −1.54000e6 | −0.176842 | ||||||||
\(598\) | −905760. | −0.103576 | ||||||||
\(599\) | −1.22340e6 | −0.139316 | −0.0696581 | − | 0.997571i | \(-0.522191\pi\) | ||||
−0.0696581 | + | 0.997571i | \(0.522191\pi\) | |||||||
\(600\) | −140448. | −0.0159271 | ||||||||
\(601\) | 4.64268e6 | 0.524304 | 0.262152 | − | 0.965027i | \(-0.415568\pi\) | ||||
0.262152 | + | 0.965027i | \(0.415568\pi\) | |||||||
\(602\) | 1.86476e7 | 2.09716 | ||||||||
\(603\) | 2.62140e6 | 0.293589 | ||||||||
\(604\) | 1.98474e6 | 0.221366 | ||||||||
\(605\) | −6.44949e6 | −0.716369 | ||||||||
\(606\) | −3.49877e6 | −0.387020 | ||||||||
\(607\) | −2.06646e6 | −0.227644 | −0.113822 | − | 0.993501i | \(-0.536309\pi\) | ||||
−0.113822 | + | 0.993501i | \(0.536309\pi\) | |||||||
\(608\) | 519840. | 0.0570310 | ||||||||
\(609\) | 6.12461e6 | 0.669168 | ||||||||
\(610\) | 5.96743e6 | 0.649326 | ||||||||
\(611\) | −959040. | −0.103928 | ||||||||
\(612\) | −1.41103e6 | −0.152285 | ||||||||
\(613\) | −1.60408e7 | −1.72415 | −0.862077 | − | 0.506778i | \(-0.830837\pi\) | ||||
−0.862077 | + | 0.506778i | \(0.830837\pi\) | |||||||
\(614\) | 6.97409e6 | 0.746563 | ||||||||
\(615\) | −1.69128e6 | −0.180313 | ||||||||
\(616\) | 8.49946e6 | 0.902484 | ||||||||
\(617\) | 8.10983e6 | 0.857628 | 0.428814 | − | 0.903393i | \(-0.358932\pi\) | ||||
0.428814 | + | 0.903393i | \(0.358932\pi\) | |||||||
\(618\) | −2.16365e6 | −0.227885 | ||||||||
\(619\) | 6.43147e6 | 0.674658 | 0.337329 | − | 0.941387i | \(-0.390477\pi\) | ||||
0.337329 | + | 0.941387i | \(0.390477\pi\) | |||||||
\(620\) | −1.69344e6 | −0.176926 | ||||||||
\(621\) | 767040. | 0.0798158 | ||||||||
\(622\) | 1.53431e7 | 1.59014 | ||||||||
\(623\) | 5.14104e6 | 0.530678 | ||||||||
\(624\) | 1.68128e6 | 0.172854 | ||||||||
\(625\) | −9.06882e6 | −0.928647 | ||||||||
\(626\) | 6.35658e6 | 0.648317 | ||||||||
\(627\) | 294576. | 0.0299246 | ||||||||
\(628\) | 512312. | 0.0518365 | ||||||||
\(629\) | −7.99688e6 | −0.805924 | ||||||||
\(630\) | 1.82399e7 | 1.83093 | ||||||||
\(631\) | 5.74292e6 | 0.574195 | 0.287097 | − | 0.957901i | \(-0.407310\pi\) | ||||
0.287097 | + | 0.957901i | \(0.407310\pi\) | |||||||
\(632\) | −7.51834e6 | −0.748737 | ||||||||
\(633\) | 1.75496e6 | 0.174084 | ||||||||
\(634\) | −1.58655e7 | −1.56759 | ||||||||
\(635\) | −1.40365e7 | −1.38142 | ||||||||
\(636\) | −332448. | −0.0325897 | ||||||||
\(637\) | −1.65379e7 | −1.61485 | ||||||||
\(638\) | −7.55698e6 | −0.735015 | ||||||||
\(639\) | 1.65674e7 | 1.60510 | ||||||||
\(640\) | −1.14670e7 | −1.10662 | ||||||||
\(641\) | 6.62781e6 | 0.637125 | 0.318563 | − | 0.947902i | \(-0.396800\pi\) | ||||
0.318563 | + | 0.947902i | \(0.396800\pi\) | |||||||
\(642\) | −866592. | −0.0829807 | ||||||||
\(643\) | −1.67112e7 | −1.59397 | −0.796986 | − | 0.603997i | \(-0.793574\pi\) | ||||
−0.796986 | + | 0.603997i | \(0.793574\pi\) | |||||||
\(644\) | −404736. | −0.0384554 | ||||||||
\(645\) | −2.70691e6 | −0.256197 | ||||||||
\(646\) | −3.36596e6 | −0.317342 | ||||||||
\(647\) | −599400. | −0.0562932 | −0.0281466 | − | 0.999604i | \(-0.508961\pi\) | ||||
−0.0281466 | + | 0.999604i | \(0.508961\pi\) | |||||||
\(648\) | 8.00369e6 | 0.748777 | ||||||||
\(649\) | 3.87029e6 | 0.360688 | ||||||||
\(650\) | −463980. | −0.0430741 | ||||||||
\(651\) | −7.77728e6 | −0.719242 | ||||||||
\(652\) | −2.28261e6 | −0.210287 | ||||||||
\(653\) | 1.12433e7 | 1.03183 | 0.515916 | − | 0.856639i | \(-0.327451\pi\) | ||||
0.515916 | + | 0.856639i | \(0.327451\pi\) | |||||||
\(654\) | −783696. | −0.0716479 | ||||||||
\(655\) | −6.70097e6 | −0.610287 | ||||||||
\(656\) | 8.89488e6 | 0.807013 | ||||||||
\(657\) | −1.34189e7 | −1.21284 | ||||||||
\(658\) | −3.85690e6 | −0.347275 | ||||||||
\(659\) | 1.00891e7 | 0.904981 | 0.452490 | − | 0.891769i | \(-0.350536\pi\) | ||||
0.452490 | + | 0.891769i | \(0.350536\pi\) | |||||||
\(660\) | 176256. | 0.0157501 | ||||||||
\(661\) | 2.21936e7 | 1.97571 | 0.987855 | − | 0.155377i | \(-0.0496593\pi\) | ||||
0.987855 | + | 0.155377i | \(0.0496593\pi\) | |||||||
\(662\) | −1.43450e7 | −1.27220 | ||||||||
\(663\) | −2.29992e6 | −0.203202 | ||||||||
\(664\) | −4.64688e6 | −0.409017 | ||||||||
\(665\) | 4.83451e6 | 0.423934 | ||||||||
\(666\) | −7.00885e6 | −0.612296 | ||||||||
\(667\) | −2.51899e6 | −0.219236 | ||||||||
\(668\) | −159456. | −0.0138261 | ||||||||
\(669\) | −1.48941e6 | −0.128661 | ||||||||
\(670\) | 3.74155e6 | 0.322007 | ||||||||
\(671\) | −3.75727e6 | −0.322156 | ||||||||
\(672\) | 1.42848e6 | 0.122026 | ||||||||
\(673\) | 1.00785e7 | 0.857742 | 0.428871 | − | 0.903366i | \(-0.358911\pi\) | ||||
0.428871 | + | 0.903366i | \(0.358911\pi\) | |||||||
\(674\) | 6.74293e6 | 0.571741 | ||||||||
\(675\) | 392920. | 0.0331929 | ||||||||
\(676\) | −937572. | −0.0789111 | ||||||||
\(677\) | −6.39388e6 | −0.536158 | −0.268079 | − | 0.963397i | \(-0.586389\pi\) | ||||
−0.268079 | + | 0.963397i | \(0.586389\pi\) | |||||||
\(678\) | 3.49934e6 | 0.292356 | ||||||||
\(679\) | 3.47646e6 | 0.289377 | ||||||||
\(680\) | 1.40979e7 | 1.16918 | ||||||||
\(681\) | 4.04405e6 | 0.334155 | ||||||||
\(682\) | 9.59616e6 | 0.790017 | ||||||||
\(683\) | −2.25396e7 | −1.84882 | −0.924411 | − | 0.381398i | \(-0.875443\pi\) | ||||
−0.924411 | + | 0.381398i | \(0.875443\pi\) | |||||||
\(684\) | −327788. | −0.0267888 | ||||||||
\(685\) | 4.55382e6 | 0.370808 | ||||||||
\(686\) | −4.15003e7 | −3.36698 | ||||||||
\(687\) | 2.28553e6 | 0.184754 | ||||||||
\(688\) | 1.42364e7 | 1.14664 | ||||||||
\(689\) | 7.68786e6 | 0.616961 | ||||||||
\(690\) | 528768. | 0.0422807 | ||||||||
\(691\) | −2.24043e6 | −0.178499 | −0.0892495 | − | 0.996009i | \(-0.528447\pi\) | ||||
−0.0892495 | + | 0.996009i | \(0.528447\pi\) | |||||||
\(692\) | 892344. | 0.0708381 | ||||||||
\(693\) | −1.14844e7 | −0.908395 | ||||||||
\(694\) | −1.20232e7 | −0.947593 | ||||||||
\(695\) | −8.39570e6 | −0.659318 | ||||||||
\(696\) | 4.14893e6 | 0.324648 | ||||||||
\(697\) | −1.21678e7 | −0.948704 | ||||||||
\(698\) | −2.16485e7 | −1.68186 | ||||||||
\(699\) | −2.37871e6 | −0.184140 | ||||||||
\(700\) | −207328. | −0.0159924 | ||||||||
\(701\) | 7.24184e6 | 0.556614 | 0.278307 | − | 0.960492i | \(-0.410227\pi\) | ||||
0.278307 | + | 0.960492i | \(0.410227\pi\) | |||||||
\(702\) | −4.17360e6 | −0.319645 | ||||||||
\(703\) | −1.85771e6 | −0.141771 | ||||||||
\(704\) | 5.65325e6 | 0.429899 | ||||||||
\(705\) | 559872. | 0.0424244 | ||||||||
\(706\) | 1.09695e7 | 0.828278 | ||||||||
\(707\) | 3.61539e7 | 2.72024 | ||||||||
\(708\) | 303552. | 0.0227588 | ||||||||
\(709\) | −1.10476e7 | −0.825377 | −0.412688 | − | 0.910872i | \(-0.635410\pi\) | ||||
−0.412688 | + | 0.910872i | \(0.635410\pi\) | |||||||
\(710\) | 2.36468e7 | 1.76046 | ||||||||
\(711\) | 1.01587e7 | 0.753641 | ||||||||
\(712\) | 3.48264e6 | 0.257459 | ||||||||
\(713\) | 3.19872e6 | 0.235642 | ||||||||
\(714\) | −9.24941e6 | −0.678998 | ||||||||
\(715\) | −4.07592e6 | −0.298168 | ||||||||
\(716\) | 1.26792e6 | 0.0924292 | ||||||||
\(717\) | −1.52218e6 | −0.110578 | ||||||||
\(718\) | 1.56607e7 | 1.13371 | ||||||||
\(719\) | −1.76408e7 | −1.27261 | −0.636305 | − | 0.771438i | \(-0.719538\pi\) | ||||
−0.636305 | + | 0.771438i | \(0.719538\pi\) | |||||||
\(720\) | 1.39251e7 | 1.00108 | ||||||||
\(721\) | 2.23577e7 | 1.60173 | ||||||||
\(722\) | −781926. | −0.0558242 | ||||||||
\(723\) | −4.30713e6 | −0.306438 | ||||||||
\(724\) | 3.42908e6 | 0.243126 | ||||||||
\(725\) | −1.29037e6 | −0.0911733 | ||||||||
\(726\) | 2.86644e6 | 0.201837 | ||||||||
\(727\) | 1.02224e7 | 0.717325 | 0.358662 | − | 0.933467i | \(-0.383233\pi\) | ||||
0.358662 | + | 0.933467i | \(0.383233\pi\) | |||||||
\(728\) | −1.54157e7 | −1.07804 | ||||||||
\(729\) | −8.98715e6 | −0.626330 | ||||||||
\(730\) | −1.91529e7 | −1.33023 | ||||||||
\(731\) | −1.94747e7 | −1.34796 | ||||||||
\(732\) | −294688. | −0.0203275 | ||||||||
\(733\) | −2.27060e7 | −1.56092 | −0.780460 | − | 0.625206i | \(-0.785015\pi\) | ||||
−0.780460 | + | 0.625206i | \(0.785015\pi\) | |||||||
\(734\) | −2.34682e6 | −0.160783 | ||||||||
\(735\) | 9.65455e6 | 0.659195 | ||||||||
\(736\) | −587520. | −0.0399786 | ||||||||
\(737\) | −2.35579e6 | −0.159760 | ||||||||
\(738\) | −1.06645e7 | −0.720772 | ||||||||
\(739\) | 1.39817e7 | 0.941779 | 0.470889 | − | 0.882192i | \(-0.343933\pi\) | ||||
0.470889 | + | 0.882192i | \(0.343933\pi\) | |||||||
\(740\) | −1.11154e6 | −0.0746181 | ||||||||
\(741\) | −534280. | −0.0357457 | ||||||||
\(742\) | 3.09177e7 | 2.06156 | ||||||||
\(743\) | 2.12383e7 | 1.41140 | 0.705698 | − | 0.708513i | \(-0.250634\pi\) | ||||
0.705698 | + | 0.708513i | \(0.250634\pi\) | |||||||
\(744\) | −5.26848e6 | −0.348942 | ||||||||
\(745\) | −1.25709e7 | −0.829803 | ||||||||
\(746\) | −1.57242e6 | −0.103448 | ||||||||
\(747\) | 6.27882e6 | 0.411696 | ||||||||
\(748\) | 1.26806e6 | 0.0828681 | ||||||||
\(749\) | 8.95478e6 | 0.583244 | ||||||||
\(750\) | 4.32086e6 | 0.280490 | ||||||||
\(751\) | 1.08008e6 | 0.0698805 | 0.0349403 | − | 0.999389i | \(-0.488876\pi\) | ||||
0.0349403 | + | 0.999389i | \(0.488876\pi\) | |||||||
\(752\) | −2.94451e6 | −0.189875 | ||||||||
\(753\) | −453264. | −0.0291316 | ||||||||
\(754\) | 1.37063e7 | 0.877993 | ||||||||
\(755\) | 2.67939e7 | 1.71068 | ||||||||
\(756\) | −1.86496e6 | −0.118677 | ||||||||
\(757\) | −6.16086e6 | −0.390752 | −0.195376 | − | 0.980728i | \(-0.562593\pi\) | ||||
−0.195376 | + | 0.980728i | \(0.562593\pi\) | |||||||
\(758\) | −4.94436e6 | −0.312563 | ||||||||
\(759\) | −332928. | −0.0209771 | ||||||||
\(760\) | 3.27499e6 | 0.205673 | ||||||||
\(761\) | −6.96471e6 | −0.435955 | −0.217977 | − | 0.975954i | \(-0.569946\pi\) | ||||
−0.217977 | + | 0.975954i | \(0.569946\pi\) | |||||||
\(762\) | 6.23846e6 | 0.389216 | ||||||||
\(763\) | 8.09819e6 | 0.503590 | ||||||||
\(764\) | 3.13440e6 | 0.194277 | ||||||||
\(765\) | −1.90489e7 | −1.17684 | ||||||||
\(766\) | 2.33868e7 | 1.44012 | ||||||||
\(767\) | −7.01964e6 | −0.430850 | ||||||||
\(768\) | 1.54931e6 | 0.0947842 | ||||||||
\(769\) | 1.08349e7 | 0.660710 | 0.330355 | − | 0.943857i | \(-0.392832\pi\) | ||||
0.330355 | + | 0.943857i | \(0.392832\pi\) | |||||||
\(770\) | −1.63918e7 | −0.996323 | ||||||||
\(771\) | 2.21287e6 | 0.134067 | ||||||||
\(772\) | 924296. | 0.0558172 | ||||||||
\(773\) | 2.62798e7 | 1.58188 | 0.790940 | − | 0.611894i | \(-0.209592\pi\) | ||||
0.790940 | + | 0.611894i | \(0.209592\pi\) | |||||||
\(774\) | −1.70686e7 | −1.02411 | ||||||||
\(775\) | 1.63856e6 | 0.0979959 | ||||||||
\(776\) | 2.35502e6 | 0.140392 | ||||||||
\(777\) | −5.10483e6 | −0.303339 | ||||||||
\(778\) | −1.18440e7 | −0.701537 | ||||||||
\(779\) | −2.82663e6 | −0.166888 | ||||||||
\(780\) | −319680. | −0.0188139 | ||||||||
\(781\) | −1.48887e7 | −0.873434 | ||||||||
\(782\) | 3.80419e6 | 0.222457 | ||||||||
\(783\) | −1.16071e7 | −0.676581 | ||||||||
\(784\) | −5.07758e7 | −2.95030 | ||||||||
\(785\) | 6.91621e6 | 0.400585 | ||||||||
\(786\) | 2.97821e6 | 0.171949 | ||||||||
\(787\) | −1.54390e7 | −0.888550 | −0.444275 | − | 0.895890i | \(-0.646539\pi\) | ||||
−0.444275 | + | 0.895890i | \(0.646539\pi\) | |||||||
\(788\) | 1.75586e6 | 0.100734 | ||||||||
\(789\) | 3.29635e6 | 0.188513 | ||||||||
\(790\) | 1.44996e7 | 0.826589 | ||||||||
\(791\) | −3.61599e7 | −2.05488 | ||||||||
\(792\) | −7.77974e6 | −0.440709 | ||||||||
\(793\) | 6.81466e6 | 0.384823 | ||||||||
\(794\) | 1.70642e7 | 0.960583 | ||||||||
\(795\) | −4.48805e6 | −0.251849 | ||||||||
\(796\) | −1.54000e6 | −0.0861466 | ||||||||
\(797\) | 1.19255e7 | 0.665016 | 0.332508 | − | 0.943100i | \(-0.392105\pi\) | ||||
0.332508 | + | 0.943100i | \(0.392105\pi\) | |||||||
\(798\) | −2.14867e6 | −0.119444 | ||||||||
\(799\) | 4.02797e6 | 0.223213 | ||||||||
\(800\) | −300960. | −0.0166258 | ||||||||
\(801\) | −4.70571e6 | −0.259146 | ||||||||
\(802\) | −3.48141e7 | −1.91126 | ||||||||
\(803\) | 1.20593e7 | 0.659981 | ||||||||
\(804\) | −184768. | −0.0100806 | ||||||||
\(805\) | −5.46394e6 | −0.297177 | ||||||||
\(806\) | −1.74048e7 | −0.943695 | ||||||||
\(807\) | 6.08633e6 | 0.328982 | ||||||||
\(808\) | 2.44914e7 | 1.31973 | ||||||||
\(809\) | 3.49378e7 | 1.87683 | 0.938414 | − | 0.345514i | \(-0.112295\pi\) | ||||
0.938414 | + | 0.345514i | \(0.112295\pi\) | |||||||
\(810\) | −1.54357e7 | −0.826634 | ||||||||
\(811\) | −5.93602e6 | −0.316915 | −0.158458 | − | 0.987366i | \(-0.550652\pi\) | ||||
−0.158458 | + | 0.987366i | \(0.550652\pi\) | |||||||
\(812\) | 6.12461e6 | 0.325978 | ||||||||
\(813\) | −4.33216e6 | −0.229868 | ||||||||
\(814\) | 6.29870e6 | 0.333189 | ||||||||
\(815\) | −3.08152e7 | −1.62507 | ||||||||
\(816\) | −7.06138e6 | −0.371248 | ||||||||
\(817\) | −4.52405e6 | −0.237122 | ||||||||
\(818\) | −3.21202e7 | −1.67840 | ||||||||
\(819\) | 2.08295e7 | 1.08510 | ||||||||
\(820\) | −1.69128e6 | −0.0878377 | ||||||||
\(821\) | 2.08358e7 | 1.07883 | 0.539415 | − | 0.842040i | \(-0.318645\pi\) | ||||
0.539415 | + | 0.842040i | \(0.318645\pi\) | |||||||
\(822\) | −2.02392e6 | −0.104475 | ||||||||
\(823\) | −2.37266e7 | −1.22106 | −0.610528 | − | 0.791995i | \(-0.709043\pi\) | ||||
−0.610528 | + | 0.791995i | \(0.709043\pi\) | |||||||
\(824\) | 1.51455e7 | 0.777082 | ||||||||
\(825\) | −170544. | −0.00872372 | ||||||||
\(826\) | −2.82303e7 | −1.43968 | ||||||||
\(827\) | −1.11613e7 | −0.567480 | −0.283740 | − | 0.958901i | \(-0.591575\pi\) | ||||
−0.283740 | + | 0.958901i | \(0.591575\pi\) | |||||||
\(828\) | 370464. | 0.0187789 | ||||||||
\(829\) | −8.58071e6 | −0.433647 | −0.216824 | − | 0.976211i | \(-0.569570\pi\) | ||||
−0.216824 | + | 0.976211i | \(0.569570\pi\) | |||||||
\(830\) | 8.96184e6 | 0.451546 | ||||||||
\(831\) | 2.63439e6 | 0.132336 | ||||||||
\(832\) | −1.02534e7 | −0.513525 | ||||||||
\(833\) | 6.94591e7 | 3.46830 | ||||||||
\(834\) | 3.73142e6 | 0.185763 | ||||||||
\(835\) | −2.15266e6 | −0.106846 | ||||||||
\(836\) | 294576. | 0.0145775 | ||||||||
\(837\) | 1.47392e7 | 0.727211 | ||||||||
\(838\) | 6.85188e6 | 0.337054 | ||||||||
\(839\) | 1.09293e7 | 0.536027 | 0.268014 | − | 0.963415i | \(-0.413633\pi\) | ||||
0.268014 | + | 0.963415i | \(0.413633\pi\) | |||||||
\(840\) | 8.99942e6 | 0.440065 | ||||||||
\(841\) | 1.76071e7 | 0.858417 | ||||||||
\(842\) | 4.44476e6 | 0.216057 | ||||||||
\(843\) | 1.42538e6 | 0.0690817 | ||||||||
\(844\) | 1.75496e6 | 0.0848030 | ||||||||
\(845\) | −1.26572e7 | −0.609813 | ||||||||
\(846\) | 3.53030e6 | 0.169585 | ||||||||
\(847\) | −2.96199e7 | −1.41865 | ||||||||
\(848\) | 2.36038e7 | 1.12718 | ||||||||
\(849\) | 1.62046e6 | 0.0771561 | ||||||||
\(850\) | 1.94872e6 | 0.0925127 | ||||||||
\(851\) | 2.09957e6 | 0.0993816 | ||||||||
\(852\) | −1.16774e6 | −0.0551123 | ||||||||
\(853\) | 3.84963e7 | 1.81153 | 0.905767 | − | 0.423775i | \(-0.139295\pi\) | ||||
0.905767 | + | 0.423775i | \(0.139295\pi\) | |||||||
\(854\) | 2.74060e7 | 1.28588 | ||||||||
\(855\) | −4.42514e6 | −0.207020 | ||||||||
\(856\) | 6.06614e6 | 0.282962 | ||||||||
\(857\) | −6.86045e6 | −0.319081 | −0.159540 | − | 0.987191i | \(-0.551001\pi\) | ||||
−0.159540 | + | 0.987191i | \(0.551001\pi\) | |||||||
\(858\) | 1.81152e6 | 0.0840088 | ||||||||
\(859\) | −6.58868e6 | −0.304660 | −0.152330 | − | 0.988330i | \(-0.548678\pi\) | ||||
−0.152330 | + | 0.988330i | \(0.548678\pi\) | |||||||
\(860\) | −2.70691e6 | −0.124804 | ||||||||
\(861\) | −7.76736e6 | −0.357080 | ||||||||
\(862\) | −7.82122e6 | −0.358514 | ||||||||
\(863\) | −1.66861e7 | −0.762657 | −0.381328 | − | 0.924440i | \(-0.624533\pi\) | ||||
−0.381328 | + | 0.924440i | \(0.624533\pi\) | |||||||
\(864\) | −2.70720e6 | −0.123378 | ||||||||
\(865\) | 1.20466e7 | 0.547426 | ||||||||
\(866\) | 4.34134e7 | 1.96711 | ||||||||
\(867\) | 3.98024e6 | 0.179830 | ||||||||
\(868\) | −7.77728e6 | −0.350371 | ||||||||
\(869\) | −9.12941e6 | −0.410103 | ||||||||
\(870\) | −8.00150e6 | −0.358405 | ||||||||
\(871\) | 4.27276e6 | 0.190837 | ||||||||
\(872\) | 5.48587e6 | 0.244317 | ||||||||
\(873\) | −3.18209e6 | −0.141311 | ||||||||
\(874\) | 883728. | 0.0391327 | ||||||||
\(875\) | −4.46489e7 | −1.97147 | ||||||||
\(876\) | 945824. | 0.0416438 | ||||||||
\(877\) | 3.34255e7 | 1.46750 | 0.733751 | − | 0.679418i | \(-0.237768\pi\) | ||||
0.733751 | + | 0.679418i | \(0.237768\pi\) | |||||||
\(878\) | 2.49202e6 | 0.109097 | ||||||||
\(879\) | −3.79428e6 | −0.165637 | ||||||||
\(880\) | −1.25142e7 | −0.544748 | ||||||||
\(881\) | −2.04334e6 | −0.0886954 | −0.0443477 | − | 0.999016i | \(-0.514121\pi\) | ||||
−0.0443477 | + | 0.999016i | \(0.514121\pi\) | |||||||
\(882\) | 6.08773e7 | 2.63502 | ||||||||
\(883\) | 4.25705e7 | 1.83741 | 0.918706 | − | 0.394942i | \(-0.129235\pi\) | ||||
0.918706 | + | 0.394942i | \(0.129235\pi\) | |||||||
\(884\) | −2.29992e6 | −0.0989879 | ||||||||
\(885\) | 4.09795e6 | 0.175877 | ||||||||
\(886\) | −2.35922e7 | −1.00968 | ||||||||
\(887\) | −1.47058e7 | −0.627597 | −0.313798 | − | 0.949490i | \(-0.601602\pi\) | ||||
−0.313798 | + | 0.949490i | \(0.601602\pi\) | |||||||
\(888\) | −3.45811e6 | −0.147166 | ||||||||
\(889\) | −6.44641e7 | −2.73567 | ||||||||
\(890\) | −6.71652e6 | −0.284230 | ||||||||
\(891\) | 9.71876e6 | 0.410126 | ||||||||
\(892\) | −1.48941e6 | −0.0626760 | ||||||||
\(893\) | 935712. | 0.0392657 | ||||||||
\(894\) | 5.58706e6 | 0.233797 | ||||||||
\(895\) | 1.71169e7 | 0.714279 | ||||||||
\(896\) | −5.26633e7 | −2.19148 | ||||||||
\(897\) | 603840. | 0.0250577 | ||||||||
\(898\) | 2.85974e7 | 1.18341 | ||||||||
\(899\) | −4.84042e7 | −1.99748 | ||||||||
\(900\) | 189772. | 0.00780955 | ||||||||
\(901\) | −3.22890e7 | −1.32508 | ||||||||
\(902\) | 9.58392e6 | 0.392217 | ||||||||
\(903\) | −1.24317e7 | −0.507356 | ||||||||
\(904\) | −2.44954e7 | −0.996928 | ||||||||
\(905\) | 4.62926e7 | 1.87884 | ||||||||
\(906\) | −1.19084e7 | −0.481985 | ||||||||
\(907\) | −3.89732e7 | −1.57307 | −0.786534 | − | 0.617547i | \(-0.788127\pi\) | ||||
−0.786534 | + | 0.617547i | \(0.788127\pi\) | |||||||
\(908\) | 4.04405e6 | 0.162780 | ||||||||
\(909\) | −3.30925e7 | −1.32837 | ||||||||
\(910\) | 2.97302e7 | 1.19013 | ||||||||
\(911\) | 3.47532e7 | 1.38739 | 0.693695 | − | 0.720268i | \(-0.255981\pi\) | ||||
0.693695 | + | 0.720268i | \(0.255981\pi\) | |||||||
\(912\) | −1.64038e6 | −0.0653068 | ||||||||
\(913\) | −5.64264e6 | −0.224030 | ||||||||
\(914\) | −1.63329e7 | −0.646693 | ||||||||
\(915\) | −3.97829e6 | −0.157088 | ||||||||
\(916\) | 2.28553e6 | 0.0900011 | ||||||||
\(917\) | −3.07748e7 | −1.20857 | ||||||||
\(918\) | 1.75291e7 | 0.686520 | ||||||||
\(919\) | −1.81251e7 | −0.707931 | −0.353966 | − | 0.935258i | \(-0.615167\pi\) | ||||
−0.353966 | + | 0.935258i | \(0.615167\pi\) | |||||||
\(920\) | −3.70138e6 | −0.144176 | ||||||||
\(921\) | −4.64939e6 | −0.180612 | ||||||||
\(922\) | −1.48005e7 | −0.573389 | ||||||||
\(923\) | 2.70041e7 | 1.04334 | ||||||||
\(924\) | 809472. | 0.0311905 | ||||||||
\(925\) | 1.07551e6 | 0.0413297 | ||||||||
\(926\) | 9.82406e6 | 0.376499 | ||||||||
\(927\) | −2.04645e7 | −0.782171 | ||||||||
\(928\) | 8.89056e6 | 0.338890 | ||||||||
\(929\) | −4.55062e6 | −0.172994 | −0.0864971 | − | 0.996252i | \(-0.527567\pi\) | ||||
−0.0864971 | + | 0.996252i | \(0.527567\pi\) | |||||||
\(930\) | 1.01606e7 | 0.385224 | ||||||||
\(931\) | 1.61356e7 | 0.610115 | ||||||||
\(932\) | −2.37871e6 | −0.0897020 | ||||||||
\(933\) | −1.02287e7 | −0.384695 | ||||||||
\(934\) | −3.56739e7 | −1.33808 | ||||||||
\(935\) | 1.71189e7 | 0.640392 | ||||||||
\(936\) | 1.41103e7 | 0.526438 | ||||||||
\(937\) | 5.07809e6 | 0.188952 | 0.0944760 | − | 0.995527i | \(-0.469882\pi\) | ||||
0.0944760 | + | 0.995527i | \(0.469882\pi\) | |||||||
\(938\) | 1.71834e7 | 0.637680 | ||||||||
\(939\) | −4.23772e6 | −0.156844 | ||||||||
\(940\) | 559872. | 0.0206666 | ||||||||
\(941\) | 1.40795e7 | 0.518339 | 0.259170 | − | 0.965832i | \(-0.416551\pi\) | ||||
0.259170 | + | 0.965832i | \(0.416551\pi\) | |||||||
\(942\) | −3.07387e6 | −0.112865 | ||||||||
\(943\) | 3.19464e6 | 0.116988 | ||||||||
\(944\) | −2.15522e7 | −0.787157 | ||||||||
\(945\) | −2.51770e7 | −0.917115 | ||||||||
\(946\) | 1.53392e7 | 0.557281 | ||||||||
\(947\) | 2.09673e7 | 0.759746 | 0.379873 | − | 0.925039i | \(-0.375968\pi\) | ||||
0.379873 | + | 0.925039i | \(0.375968\pi\) | |||||||
\(948\) | −716032. | −0.0258769 | ||||||||
\(949\) | −2.18722e7 | −0.788364 | ||||||||
\(950\) | 452694. | 0.0162741 | ||||||||
\(951\) | 1.05770e7 | 0.379238 | ||||||||
\(952\) | 6.47459e7 | 2.31537 | ||||||||
\(953\) | −1.79751e6 | −0.0641120 | −0.0320560 | − | 0.999486i | \(-0.510205\pi\) | ||||
−0.0320560 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(954\) | −2.82996e7 | −1.00672 | ||||||||
\(955\) | 4.23144e7 | 1.50134 | ||||||||
\(956\) | −1.52218e6 | −0.0538667 | ||||||||
\(957\) | 5.03798e6 | 0.177818 | ||||||||
\(958\) | 2.31319e7 | 0.814324 | ||||||||
\(959\) | 2.09138e7 | 0.734323 | ||||||||
\(960\) | 5.98579e6 | 0.209625 | ||||||||
\(961\) | 3.28364e7 | 1.14696 | ||||||||
\(962\) | −1.14241e7 | −0.398002 | ||||||||
\(963\) | −8.19652e6 | −0.284815 | ||||||||
\(964\) | −4.30713e6 | −0.149278 | ||||||||
\(965\) | 1.24780e7 | 0.431347 | ||||||||
\(966\) | 2.42842e6 | 0.0837298 | ||||||||
\(967\) | −2.30807e7 | −0.793750 | −0.396875 | − | 0.917873i | \(-0.629905\pi\) | ||||
−0.396875 | + | 0.917873i | \(0.629905\pi\) | |||||||
\(968\) | −2.00651e7 | −0.688260 | ||||||||
\(969\) | 2.24398e6 | 0.0767730 | ||||||||
\(970\) | −4.54183e6 | −0.154989 | ||||||||
\(971\) | −5.52696e7 | −1.88121 | −0.940607 | − | 0.339498i | \(-0.889743\pi\) | ||||
−0.940607 | + | 0.339498i | \(0.889743\pi\) | |||||||
\(972\) | 2.58962e6 | 0.0879164 | ||||||||
\(973\) | −3.85580e7 | −1.30567 | ||||||||
\(974\) | 2.72908e7 | 0.921763 | ||||||||
\(975\) | 309320. | 0.0104207 | ||||||||
\(976\) | 2.09228e7 | 0.703066 | ||||||||
\(977\) | −3.06110e7 | −1.02599 | −0.512993 | − | 0.858393i | \(-0.671463\pi\) | ||||
−0.512993 | + | 0.858393i | \(0.671463\pi\) | |||||||
\(978\) | 1.36956e7 | 0.457863 | ||||||||
\(979\) | 4.22892e6 | 0.141017 | ||||||||
\(980\) | 9.65455e6 | 0.321120 | ||||||||
\(981\) | −7.41246e6 | −0.245918 | ||||||||
\(982\) | −1.00092e7 | −0.331224 | ||||||||
\(983\) | 1.55466e7 | 0.513160 | 0.256580 | − | 0.966523i | \(-0.417404\pi\) | ||||
0.256580 | + | 0.966523i | \(0.417404\pi\) | |||||||
\(984\) | −5.26176e6 | −0.173238 | ||||||||
\(985\) | 2.37042e7 | 0.778456 | ||||||||
\(986\) | −5.75664e7 | −1.88572 | ||||||||
\(987\) | 2.57126e6 | 0.0840144 | ||||||||
\(988\) | −534280. | −0.0174131 | ||||||||
\(989\) | 5.11306e6 | 0.166223 | ||||||||
\(990\) | 1.50038e7 | 0.486534 | ||||||||
\(991\) | −7.44554e6 | −0.240831 | −0.120415 | − | 0.992724i | \(-0.538423\pi\) | ||||
−0.120415 | + | 0.992724i | \(0.538423\pi\) | |||||||
\(992\) | −1.12896e7 | −0.364250 | ||||||||
\(993\) | 9.56331e6 | 0.307776 | ||||||||
\(994\) | 1.08600e8 | 3.48630 | ||||||||
\(995\) | −2.07900e7 | −0.665728 | ||||||||
\(996\) | −442560. | −0.0141359 | ||||||||
\(997\) | −2.71926e7 | −0.866388 | −0.433194 | − | 0.901301i | \(-0.642614\pi\) | ||||
−0.433194 | + | 0.901301i | \(0.642614\pi\) | |||||||
\(998\) | 5.73626e6 | 0.182307 | ||||||||
\(999\) | 9.67448e6 | 0.306700 |
(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 | 19.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 171.6.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 304.6.a.a.1.1 | 1 | |||
5.4 | even | 2 | 475.6.a.b.1.1 | 1 | |||
7.6 | odd | 2 | 931.6.a.a.1.1 | 1 | |||
19.18 | odd | 2 | 361.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
171.6.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
304.6.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
361.6.a.c.1.1 | 1 | 19.18 | odd | 2 | |||
475.6.a.b.1.1 | 1 | 5.4 | even | 2 | |||
931.6.a.a.1.1 | 1 | 7.6 | odd | 2 |