Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,6,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, 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("50.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(8.01919099065\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 | ||||||||
\(3\) | −6.00000 | −0.384900 | −0.192450 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192450 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 24.0000 | 0.272166 | ||||||||
\(7\) | 118.000 | 0.910200 | 0.455100 | − | 0.890440i | \(-0.349603\pi\) | ||||
0.455100 | + | 0.890440i | \(0.349603\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | −207.000 | −0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 192.000 | 0.478431 | 0.239216 | − | 0.970966i | \(-0.423110\pi\) | ||||
0.239216 | + | 0.970966i | \(0.423110\pi\) | |||||||
\(12\) | −96.0000 | −0.192450 | ||||||||
\(13\) | −1106.00 | −1.81508 | −0.907542 | − | 0.419961i | \(-0.862044\pi\) | ||||
−0.907542 | + | 0.419961i | \(0.862044\pi\) | |||||||
\(14\) | −472.000 | −0.643609 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −762.000 | −0.639488 | −0.319744 | − | 0.947504i | \(-0.603597\pi\) | ||||
−0.319744 | + | 0.947504i | \(0.603597\pi\) | |||||||
\(18\) | 828.000 | 0.602350 | ||||||||
\(19\) | −2740.00 | −1.74127 | −0.870636 | − | 0.491928i | \(-0.836292\pi\) | ||||
−0.870636 | + | 0.491928i | \(0.836292\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −708.000 | −0.350336 | ||||||||
\(22\) | −768.000 | −0.338302 | ||||||||
\(23\) | −1566.00 | −0.617266 | −0.308633 | − | 0.951181i | \(-0.599871\pi\) | ||||
−0.308633 | + | 0.951181i | \(0.599871\pi\) | |||||||
\(24\) | 384.000 | 0.136083 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4424.00 | 1.28346 | ||||||||
\(27\) | 2700.00 | 0.712778 | ||||||||
\(28\) | 1888.00 | 0.455100 | ||||||||
\(29\) | 5910.00 | 1.30495 | 0.652473 | − | 0.757812i | \(-0.273732\pi\) | ||||
0.652473 | + | 0.757812i | \(0.273732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6868.00 | −1.28359 | −0.641795 | − | 0.766877i | \(-0.721810\pi\) | ||||
−0.641795 | + | 0.766877i | \(0.721810\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −1152.00 | −0.184148 | ||||||||
\(34\) | 3048.00 | 0.452187 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3312.00 | −0.425926 | ||||||||
\(37\) | 5518.00 | 0.662640 | 0.331320 | − | 0.943519i | \(-0.392506\pi\) | ||||
0.331320 | + | 0.943519i | \(0.392506\pi\) | |||||||
\(38\) | 10960.0 | 1.23127 | ||||||||
\(39\) | 6636.00 | 0.698626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.000 | −0.0351182 | −0.0175591 | − | 0.999846i | \(-0.505590\pi\) | ||||
−0.0175591 | + | 0.999846i | \(0.505590\pi\) | |||||||
\(42\) | 2832.00 | 0.247725 | ||||||||
\(43\) | 2434.00 | 0.200747 | 0.100374 | − | 0.994950i | \(-0.467996\pi\) | ||||
0.100374 | + | 0.994950i | \(0.467996\pi\) | |||||||
\(44\) | 3072.00 | 0.239216 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6264.00 | 0.436473 | ||||||||
\(47\) | −13122.0 | −0.866474 | −0.433237 | − | 0.901280i | \(-0.642629\pi\) | ||||
−0.433237 | + | 0.901280i | \(0.642629\pi\) | |||||||
\(48\) | −1536.00 | −0.0962250 | ||||||||
\(49\) | −2883.00 | −0.171536 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4572.00 | 0.246139 | ||||||||
\(52\) | −17696.0 | −0.907542 | ||||||||
\(53\) | 9174.00 | 0.448610 | 0.224305 | − | 0.974519i | \(-0.427989\pi\) | ||||
0.224305 | + | 0.974519i | \(0.427989\pi\) | |||||||
\(54\) | −10800.0 | −0.504010 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7552.00 | −0.321804 | ||||||||
\(57\) | 16440.0 | 0.670216 | ||||||||
\(58\) | −23640.0 | −0.922736 | ||||||||
\(59\) | −34980.0 | −1.30825 | −0.654124 | − | 0.756388i | \(-0.726962\pi\) | ||||
−0.654124 | + | 0.756388i | \(0.726962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9838.00 | −0.338518 | −0.169259 | − | 0.985572i | \(-0.554137\pi\) | ||||
−0.169259 | + | 0.985572i | \(0.554137\pi\) | |||||||
\(62\) | 27472.0 | 0.907635 | ||||||||
\(63\) | −24426.0 | −0.775356 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4608.00 | 0.130212 | ||||||||
\(67\) | −33722.0 | −0.917754 | −0.458877 | − | 0.888500i | \(-0.651748\pi\) | ||||
−0.458877 | + | 0.888500i | \(0.651748\pi\) | |||||||
\(68\) | −12192.0 | −0.319744 | ||||||||
\(69\) | 9396.00 | 0.237586 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70212.0 | 1.65297 | 0.826486 | − | 0.562957i | \(-0.190336\pi\) | ||||
0.826486 | + | 0.562957i | \(0.190336\pi\) | |||||||
\(72\) | 13248.0 | 0.301175 | ||||||||
\(73\) | −21986.0 | −0.482880 | −0.241440 | − | 0.970416i | \(-0.577620\pi\) | ||||
−0.241440 | + | 0.970416i | \(0.577620\pi\) | |||||||
\(74\) | −22072.0 | −0.468557 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43840.0 | −0.870636 | ||||||||
\(77\) | 22656.0 | 0.435468 | ||||||||
\(78\) | −26544.0 | −0.494003 | ||||||||
\(79\) | 4520.00 | 0.0814837 | 0.0407418 | − | 0.999170i | \(-0.487028\pi\) | ||||
0.0407418 | + | 0.999170i | \(0.487028\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34101.0 | 0.577503 | ||||||||
\(82\) | 1512.00 | 0.0248323 | ||||||||
\(83\) | 109074. | 1.73790 | 0.868952 | − | 0.494896i | \(-0.164794\pi\) | ||||
0.868952 | + | 0.494896i | \(0.164794\pi\) | |||||||
\(84\) | −11328.0 | −0.175168 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9736.00 | −0.141950 | ||||||||
\(87\) | −35460.0 | −0.502274 | ||||||||
\(88\) | −12288.0 | −0.169151 | ||||||||
\(89\) | 38490.0 | 0.515078 | 0.257539 | − | 0.966268i | \(-0.417088\pi\) | ||||
0.257539 | + | 0.966268i | \(0.417088\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −130508. | −1.65209 | ||||||||
\(92\) | −25056.0 | −0.308633 | ||||||||
\(93\) | 41208.0 | 0.494054 | ||||||||
\(94\) | 52488.0 | 0.612689 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6144.00 | 0.0680414 | ||||||||
\(97\) | 1918.00 | 0.0206976 | 0.0103488 | − | 0.999946i | \(-0.496706\pi\) | ||||
0.0103488 | + | 0.999946i | \(0.496706\pi\) | |||||||
\(98\) | 11532.0 | 0.121294 | ||||||||
\(99\) | −39744.0 | −0.407553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77622.0 | 0.757149 | 0.378575 | − | 0.925571i | \(-0.376414\pi\) | ||||
0.378575 | + | 0.925571i | \(0.376414\pi\) | |||||||
\(102\) | −18288.0 | −0.174047 | ||||||||
\(103\) | 46714.0 | 0.433864 | 0.216932 | − | 0.976187i | \(-0.430395\pi\) | ||||
0.216932 | + | 0.976187i | \(0.430395\pi\) | |||||||
\(104\) | 70784.0 | 0.641729 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −36696.0 | −0.317215 | ||||||||
\(107\) | 1038.00 | 0.00876472 | 0.00438236 | − | 0.999990i | \(-0.498605\pi\) | ||||
0.00438236 | + | 0.999990i | \(0.498605\pi\) | |||||||
\(108\) | 43200.0 | 0.356389 | ||||||||
\(109\) | 206930. | 1.66823 | 0.834117 | − | 0.551587i | \(-0.185977\pi\) | ||||
0.834117 | + | 0.551587i | \(0.185977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33108.0 | −0.255050 | ||||||||
\(112\) | 30208.0 | 0.227550 | ||||||||
\(113\) | −139386. | −1.02689 | −0.513444 | − | 0.858123i | \(-0.671631\pi\) | ||||
−0.513444 | + | 0.858123i | \(0.671631\pi\) | |||||||
\(114\) | −65760.0 | −0.473914 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 94560.0 | 0.652473 | ||||||||
\(117\) | 228942. | 1.54618 | ||||||||
\(118\) | 139920. | 0.925070 | ||||||||
\(119\) | −89916.0 | −0.582062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124187. | −0.771104 | ||||||||
\(122\) | 39352.0 | 0.239369 | ||||||||
\(123\) | 2268.00 | 0.0135170 | ||||||||
\(124\) | −109888. | −0.641795 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 97704.0 | 0.548259 | ||||||||
\(127\) | −299882. | −1.64984 | −0.824919 | − | 0.565252i | \(-0.808779\pi\) | ||||
−0.824919 | + | 0.565252i | \(0.808779\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −14604.0 | −0.0772676 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7872.00 | 0.0400781 | 0.0200390 | − | 0.999799i | \(-0.493621\pi\) | ||||
0.0200390 | + | 0.999799i | \(0.493621\pi\) | |||||||
\(132\) | −18432.0 | −0.0920741 | ||||||||
\(133\) | −323320. | −1.58491 | ||||||||
\(134\) | 134888. | 0.648950 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 48768.0 | 0.226093 | ||||||||
\(137\) | 164238. | 0.747605 | 0.373803 | − | 0.927508i | \(-0.378054\pi\) | ||||
0.373803 | + | 0.927508i | \(0.378054\pi\) | |||||||
\(138\) | −37584.0 | −0.167998 | ||||||||
\(139\) | −282100. | −1.23841 | −0.619207 | − | 0.785228i | \(-0.712546\pi\) | ||||
−0.619207 | + | 0.785228i | \(0.712546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 78732.0 | 0.333506 | ||||||||
\(142\) | −280848. | −1.16883 | ||||||||
\(143\) | −212352. | −0.868393 | ||||||||
\(144\) | −52992.0 | −0.212963 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 87944.0 | 0.341448 | ||||||||
\(147\) | 17298.0 | 0.0660241 | ||||||||
\(148\) | 88288.0 | 0.331320 | ||||||||
\(149\) | −388950. | −1.43525 | −0.717626 | − | 0.696429i | \(-0.754771\pi\) | ||||
−0.717626 | + | 0.696429i | \(0.754771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −97948.0 | −0.349585 | −0.174793 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174793 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(152\) | 175360. | 0.615633 | ||||||||
\(153\) | 157734. | 0.544749 | ||||||||
\(154\) | −90624.0 | −0.307923 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 106176. | 0.349313 | ||||||||
\(157\) | 3718.00 | 0.0120382 | 0.00601908 | − | 0.999982i | \(-0.498084\pi\) | ||||
0.00601908 | + | 0.999982i | \(0.498084\pi\) | |||||||
\(158\) | −18080.0 | −0.0576177 | ||||||||
\(159\) | −55044.0 | −0.172670 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −184788. | −0.561835 | ||||||||
\(162\) | −136404. | −0.408357 | ||||||||
\(163\) | 43234.0 | 0.127455 | 0.0637274 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637274 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(164\) | −6048.00 | −0.0175591 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −436296. | −1.22888 | ||||||||
\(167\) | −186522. | −0.517534 | −0.258767 | − | 0.965940i | \(-0.583316\pi\) | ||||
−0.258767 | + | 0.965940i | \(0.583316\pi\) | |||||||
\(168\) | 45312.0 | 0.123863 | ||||||||
\(169\) | 851943. | 2.29453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 567180. | 1.48331 | ||||||||
\(172\) | 38944.0 | 0.100374 | ||||||||
\(173\) | 374454. | 0.951225 | 0.475612 | − | 0.879655i | \(-0.342226\pi\) | ||||
0.475612 | + | 0.879655i | \(0.342226\pi\) | |||||||
\(174\) | 141840. | 0.355161 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 49152.0 | 0.119608 | ||||||||
\(177\) | 209880. | 0.503545 | ||||||||
\(178\) | −153960. | −0.364215 | ||||||||
\(179\) | 272100. | 0.634740 | 0.317370 | − | 0.948302i | \(-0.397200\pi\) | ||||
0.317370 | + | 0.948302i | \(0.397200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −75418.0 | −0.171111 | −0.0855556 | − | 0.996333i | \(-0.527267\pi\) | ||||
−0.0855556 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(182\) | 522032. | 1.16820 | ||||||||
\(183\) | 59028.0 | 0.130296 | ||||||||
\(184\) | 100224. | 0.218236 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −164832. | −0.349349 | ||||||||
\(187\) | −146304. | −0.305951 | ||||||||
\(188\) | −209952. | −0.433237 | ||||||||
\(189\) | 318600. | 0.648771 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −356988. | −0.708060 | −0.354030 | − | 0.935234i | \(-0.615189\pi\) | ||||
−0.354030 | + | 0.935234i | \(0.615189\pi\) | |||||||
\(192\) | −24576.0 | −0.0481125 | ||||||||
\(193\) | 438694. | 0.847751 | 0.423876 | − | 0.905720i | \(-0.360669\pi\) | ||||
0.423876 | + | 0.905720i | \(0.360669\pi\) | |||||||
\(194\) | −7672.00 | −0.0146354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −46128.0 | −0.0857678 | ||||||||
\(197\) | 156798. | 0.287856 | 0.143928 | − | 0.989588i | \(-0.454027\pi\) | ||||
0.143928 | + | 0.989588i | \(0.454027\pi\) | |||||||
\(198\) | 158976. | 0.288183 | ||||||||
\(199\) | −162520. | −0.290920 | −0.145460 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145460 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 202332. | 0.353244 | ||||||||
\(202\) | −310488. | −0.535385 | ||||||||
\(203\) | 697380. | 1.18776 | ||||||||
\(204\) | 73152.0 | 0.123070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −186856. | −0.306788 | ||||||||
\(207\) | 324162. | 0.525819 | ||||||||
\(208\) | −283136. | −0.453771 | ||||||||
\(209\) | −526080. | −0.833079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −181648. | −0.280882 | −0.140441 | − | 0.990089i | \(-0.544852\pi\) | ||||
−0.140441 | + | 0.990089i | \(0.544852\pi\) | |||||||
\(212\) | 146784. | 0.224305 | ||||||||
\(213\) | −421272. | −0.636229 | ||||||||
\(214\) | −4152.00 | −0.00619759 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −172800. | −0.252005 | ||||||||
\(217\) | −810424. | −1.16832 | ||||||||
\(218\) | −827720. | −1.17962 | ||||||||
\(219\) | 131916. | 0.185861 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 842772. | 1.16073 | ||||||||
\(222\) | 132432. | 0.180348 | ||||||||
\(223\) | 288274. | 0.388189 | 0.194095 | − | 0.980983i | \(-0.437823\pi\) | ||||
0.194095 | + | 0.980983i | \(0.437823\pi\) | |||||||
\(224\) | −120832. | −0.160902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 557544. | 0.726119 | ||||||||
\(227\) | −1.12552e6 | −1.44974 | −0.724869 | − | 0.688887i | \(-0.758100\pi\) | ||||
−0.724869 | + | 0.688887i | \(0.758100\pi\) | |||||||
\(228\) | 263040. | 0.335108 | ||||||||
\(229\) | −415810. | −0.523970 | −0.261985 | − | 0.965072i | \(-0.584377\pi\) | ||||
−0.261985 | + | 0.965072i | \(0.584377\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −135936. | −0.167612 | ||||||||
\(232\) | −378240. | −0.461368 | ||||||||
\(233\) | −770586. | −0.929889 | −0.464945 | − | 0.885340i | \(-0.653926\pi\) | ||||
−0.464945 | + | 0.885340i | \(0.653926\pi\) | |||||||
\(234\) | −915768. | −1.09332 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −559680. | −0.654124 | ||||||||
\(237\) | −27120.0 | −0.0313631 | ||||||||
\(238\) | 359664. | 0.411580 | ||||||||
\(239\) | −595320. | −0.674149 | −0.337074 | − | 0.941478i | \(-0.609437\pi\) | ||||
−0.337074 | + | 0.941478i | \(0.609437\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 273902. | 0.303775 | 0.151888 | − | 0.988398i | \(-0.451465\pi\) | ||||
0.151888 | + | 0.988398i | \(0.451465\pi\) | |||||||
\(242\) | 496748. | 0.545253 | ||||||||
\(243\) | −860706. | −0.935059 | ||||||||
\(244\) | −157408. | −0.169259 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9072.00 | −0.00955796 | ||||||||
\(247\) | 3.03044e6 | 3.16055 | ||||||||
\(248\) | 439552. | 0.453817 | ||||||||
\(249\) | −654444. | −0.668920 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 850752. | 0.852351 | 0.426176 | − | 0.904640i | \(-0.359861\pi\) | ||||
0.426176 | + | 0.904640i | \(0.359861\pi\) | |||||||
\(252\) | −390816. | −0.387678 | ||||||||
\(253\) | −300672. | −0.295319 | ||||||||
\(254\) | 1.19953e6 | 1.16661 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −825402. | −0.779530 | −0.389765 | − | 0.920914i | \(-0.627444\pi\) | ||||
−0.389765 | + | 0.920914i | \(0.627444\pi\) | |||||||
\(258\) | 58416.0 | 0.0546365 | ||||||||
\(259\) | 651124. | 0.603135 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.22337e6 | −1.11162 | ||||||||
\(262\) | −31488.0 | −0.0283395 | ||||||||
\(263\) | −1.36465e6 | −1.21655 | −0.608276 | − | 0.793726i | \(-0.708139\pi\) | ||||
−0.608276 | + | 0.793726i | \(0.708139\pi\) | |||||||
\(264\) | 73728.0 | 0.0651062 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.29328e6 | 1.12070 | ||||||||
\(267\) | −230940. | −0.198254 | ||||||||
\(268\) | −539552. | −0.458877 | ||||||||
\(269\) | −113310. | −0.0954745 | −0.0477373 | − | 0.998860i | \(-0.515201\pi\) | ||||
−0.0477373 | + | 0.998860i | \(0.515201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −849628. | −0.702758 | −0.351379 | − | 0.936233i | \(-0.614287\pi\) | ||||
−0.351379 | + | 0.936233i | \(0.614287\pi\) | |||||||
\(272\) | −195072. | −0.159872 | ||||||||
\(273\) | 783048. | 0.635890 | ||||||||
\(274\) | −656952. | −0.528637 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 150336. | 0.118793 | ||||||||
\(277\) | −438602. | −0.343456 | −0.171728 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171728 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(278\) | 1.12840e6 | 0.875691 | ||||||||
\(279\) | 1.42168e6 | 1.09343 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.45670e6 | −1.10053 | −0.550267 | − | 0.834989i | \(-0.685474\pi\) | ||||
−0.550267 | + | 0.834989i | \(0.685474\pi\) | |||||||
\(282\) | −314928. | −0.235824 | ||||||||
\(283\) | 120394. | 0.0893591 | 0.0446795 | − | 0.999001i | \(-0.485773\pi\) | ||||
0.0446795 | + | 0.999001i | \(0.485773\pi\) | |||||||
\(284\) | 1.12339e6 | 0.826486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 849408. | 0.614047 | ||||||||
\(287\) | −44604.0 | −0.0319646 | ||||||||
\(288\) | 211968. | 0.150588 | ||||||||
\(289\) | −839213. | −0.591055 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11508.0 | −0.00796650 | ||||||||
\(292\) | −351776. | −0.241440 | ||||||||
\(293\) | 2.64209e6 | 1.79796 | 0.898978 | − | 0.437993i | \(-0.144311\pi\) | ||||
0.898978 | + | 0.437993i | \(0.144311\pi\) | |||||||
\(294\) | −69192.0 | −0.0466861 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −353152. | −0.234278 | ||||||||
\(297\) | 518400. | 0.341015 | ||||||||
\(298\) | 1.55580e6 | 1.01488 | ||||||||
\(299\) | 1.73200e6 | 1.12039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 287212. | 0.182720 | ||||||||
\(302\) | 391792. | 0.247194 | ||||||||
\(303\) | −465732. | −0.291427 | ||||||||
\(304\) | −701440. | −0.435318 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −630936. | −0.385196 | ||||||||
\(307\) | 1.44756e6 | 0.876577 | 0.438288 | − | 0.898834i | \(-0.355585\pi\) | ||||
0.438288 | + | 0.898834i | \(0.355585\pi\) | |||||||
\(308\) | 362496. | 0.217734 | ||||||||
\(309\) | −280284. | −0.166994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −928068. | −0.544100 | −0.272050 | − | 0.962283i | \(-0.587702\pi\) | ||||
−0.272050 | + | 0.962283i | \(0.587702\pi\) | |||||||
\(312\) | −424704. | −0.247002 | ||||||||
\(313\) | −2.29563e6 | −1.32446 | −0.662232 | − | 0.749299i | \(-0.730391\pi\) | ||||
−0.662232 | + | 0.749299i | \(0.730391\pi\) | |||||||
\(314\) | −14872.0 | −0.00851227 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 72320.0 | 0.0407418 | ||||||||
\(317\) | −2.73652e6 | −1.52950 | −0.764752 | − | 0.644324i | \(-0.777139\pi\) | ||||
−0.764752 | + | 0.644324i | \(0.777139\pi\) | |||||||
\(318\) | 220176. | 0.122096 | ||||||||
\(319\) | 1.13472e6 | 0.624327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6228.00 | −0.00337354 | ||||||||
\(322\) | 739152. | 0.397278 | ||||||||
\(323\) | 2.08788e6 | 1.11352 | ||||||||
\(324\) | 545616. | 0.288752 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −172936. | −0.0901242 | ||||||||
\(327\) | −1.24158e6 | −0.642104 | ||||||||
\(328\) | 24192.0 | 0.0124162 | ||||||||
\(329\) | −1.54840e6 | −0.788665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.81879e6 | 1.91583 | 0.957913 | − | 0.287059i | \(-0.0926776\pi\) | ||||
0.957913 | + | 0.287059i | \(0.0926776\pi\) | |||||||
\(332\) | 1.74518e6 | 0.868952 | ||||||||
\(333\) | −1.14223e6 | −0.564471 | ||||||||
\(334\) | 746088. | 0.365952 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −181248. | −0.0875841 | ||||||||
\(337\) | 2.21088e6 | 1.06045 | 0.530225 | − | 0.847857i | \(-0.322108\pi\) | ||||
0.530225 | + | 0.847857i | \(0.322108\pi\) | |||||||
\(338\) | −3.40777e6 | −1.62248 | ||||||||
\(339\) | 836316. | 0.395249 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.31866e6 | −0.614109 | ||||||||
\(342\) | −2.26872e6 | −1.04886 | ||||||||
\(343\) | −2.32342e6 | −1.06633 | ||||||||
\(344\) | −155776. | −0.0709748 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.49782e6 | −0.672618 | ||||||||
\(347\) | 2.32724e6 | 1.03757 | 0.518785 | − | 0.854905i | \(-0.326385\pi\) | ||||
0.518785 | + | 0.854905i | \(0.326385\pi\) | |||||||
\(348\) | −567360. | −0.251137 | ||||||||
\(349\) | −311290. | −0.136805 | −0.0684024 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684024 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.98620e6 | −1.29375 | ||||||||
\(352\) | −196608. | −0.0845755 | ||||||||
\(353\) | 3.08657e6 | 1.31838 | 0.659189 | − | 0.751977i | \(-0.270900\pi\) | ||||
0.659189 | + | 0.751977i | \(0.270900\pi\) | |||||||
\(354\) | −839520. | −0.356060 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 615840. | 0.257539 | ||||||||
\(357\) | 539496. | 0.224036 | ||||||||
\(358\) | −1.08840e6 | −0.448829 | ||||||||
\(359\) | −3.53076e6 | −1.44588 | −0.722940 | − | 0.690911i | \(-0.757210\pi\) | ||||
−0.722940 | + | 0.690911i | \(0.757210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.03150e6 | 2.03203 | ||||||||
\(362\) | 301672. | 0.120994 | ||||||||
\(363\) | 745122. | 0.296798 | ||||||||
\(364\) | −2.08813e6 | −0.826045 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −236112. | −0.0921330 | ||||||||
\(367\) | −35762.0 | −0.0138598 | −0.00692989 | − | 0.999976i | \(-0.502206\pi\) | ||||
−0.00692989 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(368\) | −400896. | −0.154316 | ||||||||
\(369\) | 78246.0 | 0.0299155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.08253e6 | 0.408325 | ||||||||
\(372\) | 659328. | 0.247027 | ||||||||
\(373\) | 1.71525e6 | 0.638346 | 0.319173 | − | 0.947696i | \(-0.396595\pi\) | ||||
0.319173 | + | 0.947696i | \(0.396595\pi\) | |||||||
\(374\) | 585216. | 0.216340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 839808. | 0.306345 | ||||||||
\(377\) | −6.53646e6 | −2.36859 | ||||||||
\(378\) | −1.27440e6 | −0.458750 | ||||||||
\(379\) | −3.10174e6 | −1.10919 | −0.554597 | − | 0.832119i | \(-0.687127\pi\) | ||||
−0.554597 | + | 0.832119i | \(0.687127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.79929e6 | 0.635023 | ||||||||
\(382\) | 1.42795e6 | 0.500674 | ||||||||
\(383\) | −5.31949e6 | −1.85299 | −0.926494 | − | 0.376309i | \(-0.877193\pi\) | ||||
−0.926494 | + | 0.376309i | \(0.877193\pi\) | |||||||
\(384\) | 98304.0 | 0.0340207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.75478e6 | −0.599451 | ||||||||
\(387\) | −503838. | −0.171007 | ||||||||
\(388\) | 30688.0 | 0.0103488 | ||||||||
\(389\) | 1.16145e6 | 0.389158 | 0.194579 | − | 0.980887i | \(-0.437666\pi\) | ||||
0.194579 | + | 0.980887i | \(0.437666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19329e6 | 0.394734 | ||||||||
\(392\) | 184512. | 0.0606470 | ||||||||
\(393\) | −47232.0 | −0.0154261 | ||||||||
\(394\) | −627192. | −0.203545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −635904. | −0.203776 | ||||||||
\(397\) | −628562. | −0.200157 | −0.100079 | − | 0.994980i | \(-0.531909\pi\) | ||||
−0.100079 | + | 0.994980i | \(0.531909\pi\) | |||||||
\(398\) | 650080. | 0.205712 | ||||||||
\(399\) | 1.93992e6 | 0.610031 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.72432e6 | −0.846052 | −0.423026 | − | 0.906118i | \(-0.639032\pi\) | ||||
−0.423026 | + | 0.906118i | \(0.639032\pi\) | |||||||
\(402\) | −809328. | −0.249781 | ||||||||
\(403\) | 7.59601e6 | 2.32982 | ||||||||
\(404\) | 1.24195e6 | 0.378575 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.78952e6 | −0.839875 | ||||||||
\(407\) | 1.05946e6 | 0.317027 | ||||||||
\(408\) | −292608. | −0.0870233 | ||||||||
\(409\) | 1.78019e6 | 0.526209 | 0.263104 | − | 0.964767i | \(-0.415254\pi\) | ||||
0.263104 | + | 0.964767i | \(0.415254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −985428. | −0.287753 | ||||||||
\(412\) | 747424. | 0.216932 | ||||||||
\(413\) | −4.12764e6 | −1.19077 | ||||||||
\(414\) | −1.29665e6 | −0.371810 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.13254e6 | 0.320865 | ||||||||
\(417\) | 1.69260e6 | 0.476666 | ||||||||
\(418\) | 2.10432e6 | 0.589076 | ||||||||
\(419\) | 650580. | 0.181036 | 0.0905181 | − | 0.995895i | \(-0.471148\pi\) | ||||
0.0905181 | + | 0.995895i | \(0.471148\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.54060e6 | −0.973579 | −0.486790 | − | 0.873519i | \(-0.661832\pi\) | ||||
−0.486790 | + | 0.873519i | \(0.661832\pi\) | |||||||
\(422\) | 726592. | 0.198614 | ||||||||
\(423\) | 2.71625e6 | 0.738107 | ||||||||
\(424\) | −587136. | −0.158608 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.68509e6 | 0.449882 | ||||||||
\(427\) | −1.16088e6 | −0.308119 | ||||||||
\(428\) | 16608.0 | 0.00438236 | ||||||||
\(429\) | 1.27411e6 | 0.334245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −548748. | −0.142292 | −0.0711459 | − | 0.997466i | \(-0.522666\pi\) | ||||
−0.0711459 | + | 0.997466i | \(0.522666\pi\) | |||||||
\(432\) | 691200. | 0.178195 | ||||||||
\(433\) | 1.49241e6 | 0.382534 | 0.191267 | − | 0.981538i | \(-0.438740\pi\) | ||||
0.191267 | + | 0.981538i | \(0.438740\pi\) | |||||||
\(434\) | 3.24170e6 | 0.826129 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.31088e6 | 0.834117 | ||||||||
\(437\) | 4.29084e6 | 1.07483 | ||||||||
\(438\) | −527664. | −0.131423 | ||||||||
\(439\) | 4.86212e6 | 1.20411 | 0.602053 | − | 0.798456i | \(-0.294350\pi\) | ||||
0.602053 | + | 0.798456i | \(0.294350\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 596781. | 0.146123 | ||||||||
\(442\) | −3.37109e6 | −0.820757 | ||||||||
\(443\) | 1.86155e6 | 0.450678 | 0.225339 | − | 0.974280i | \(-0.427651\pi\) | ||||
0.225339 | + | 0.974280i | \(0.427651\pi\) | |||||||
\(444\) | −529728. | −0.127525 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.15310e6 | −0.274491 | ||||||||
\(447\) | 2.33370e6 | 0.552429 | ||||||||
\(448\) | 483328. | 0.113775 | ||||||||
\(449\) | 3.73719e6 | 0.874841 | 0.437421 | − | 0.899257i | \(-0.355892\pi\) | ||||
0.437421 | + | 0.899257i | \(0.355892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −72576.0 | −0.0168016 | ||||||||
\(452\) | −2.23018e6 | −0.513444 | ||||||||
\(453\) | 587688. | 0.134555 | ||||||||
\(454\) | 4.50209e6 | 1.02512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.05216e6 | −0.236957 | ||||||||
\(457\) | 6.48276e6 | 1.45201 | 0.726005 | − | 0.687690i | \(-0.241375\pi\) | ||||
0.726005 | + | 0.687690i | \(0.241375\pi\) | |||||||
\(458\) | 1.66324e6 | 0.370503 | ||||||||
\(459\) | −2.05740e6 | −0.455813 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.50910e6 | 0.330724 | 0.165362 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165362 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(462\) | 543744. | 0.118519 | ||||||||
\(463\) | −8.68401e6 | −1.88264 | −0.941321 | − | 0.337513i | \(-0.890414\pi\) | ||||
−0.941321 | + | 0.337513i | \(0.890414\pi\) | |||||||
\(464\) | 1.51296e6 | 0.326236 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.08234e6 | 0.657531 | ||||||||
\(467\) | −6.96412e6 | −1.47766 | −0.738829 | − | 0.673893i | \(-0.764621\pi\) | ||||
−0.738829 | + | 0.673893i | \(0.764621\pi\) | |||||||
\(468\) | 3.66307e6 | 0.773091 | ||||||||
\(469\) | −3.97920e6 | −0.835340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22308.0 | −0.00463349 | ||||||||
\(472\) | 2.23872e6 | 0.462535 | ||||||||
\(473\) | 467328. | 0.0960437 | ||||||||
\(474\) | 108480. | 0.0221771 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.43866e6 | −0.291031 | ||||||||
\(477\) | −1.89902e6 | −0.382149 | ||||||||
\(478\) | 2.38128e6 | 0.476695 | ||||||||
\(479\) | −5.51052e6 | −1.09737 | −0.548686 | − | 0.836029i | \(-0.684872\pi\) | ||||
−0.548686 | + | 0.836029i | \(0.684872\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.10291e6 | −1.20275 | ||||||||
\(482\) | −1.09561e6 | −0.214802 | ||||||||
\(483\) | 1.10873e6 | 0.216251 | ||||||||
\(484\) | −1.98699e6 | −0.385552 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.44282e6 | 0.661187 | ||||||||
\(487\) | −5.51808e6 | −1.05430 | −0.527152 | − | 0.849771i | \(-0.676740\pi\) | ||||
−0.527152 | + | 0.849771i | \(0.676740\pi\) | |||||||
\(488\) | 629632. | 0.119684 | ||||||||
\(489\) | −259404. | −0.0490574 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.51277e6 | −0.283184 | −0.141592 | − | 0.989925i | \(-0.545222\pi\) | ||||
−0.141592 | + | 0.989925i | \(0.545222\pi\) | |||||||
\(492\) | 36288.0 | 0.00675850 | ||||||||
\(493\) | −4.50342e6 | −0.834498 | ||||||||
\(494\) | −1.21218e7 | −2.23485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.75821e6 | −0.320897 | ||||||||
\(497\) | 8.28502e6 | 1.50454 | ||||||||
\(498\) | 2.61778e6 | 0.472998 | ||||||||
\(499\) | −1.93042e6 | −0.347057 | −0.173528 | − | 0.984829i | \(-0.555517\pi\) | ||||
−0.173528 | + | 0.984829i | \(0.555517\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.11913e6 | 0.199199 | ||||||||
\(502\) | −3.40301e6 | −0.602703 | ||||||||
\(503\) | −6.73105e6 | −1.18621 | −0.593106 | − | 0.805124i | \(-0.702099\pi\) | ||||
−0.593106 | + | 0.805124i | \(0.702099\pi\) | |||||||
\(504\) | 1.56326e6 | 0.274130 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.20269e6 | 0.208822 | ||||||||
\(507\) | −5.11166e6 | −0.883165 | ||||||||
\(508\) | −4.79811e6 | −0.824919 | ||||||||
\(509\) | −556650. | −0.0952331 | −0.0476165 | − | 0.998866i | \(-0.515163\pi\) | ||||
−0.0476165 | + | 0.998866i | \(0.515163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.59435e6 | −0.439517 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −7.39800e6 | −1.24114 | ||||||||
\(514\) | 3.30161e6 | 0.551211 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −233664. | −0.0386338 | ||||||||
\(517\) | −2.51942e6 | −0.414548 | ||||||||
\(518\) | −2.60450e6 | −0.426481 | ||||||||
\(519\) | −2.24672e6 | −0.366127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.01110e7 | 1.63192 | 0.815962 | − | 0.578106i | \(-0.196208\pi\) | ||||
0.815962 | + | 0.578106i | \(0.196208\pi\) | |||||||
\(522\) | 4.89348e6 | 0.786034 | ||||||||
\(523\) | 7.03719e6 | 1.12498 | 0.562491 | − | 0.826804i | \(-0.309843\pi\) | ||||
0.562491 | + | 0.826804i | \(0.309843\pi\) | |||||||
\(524\) | 125952. | 0.0200390 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.45858e6 | 0.860232 | ||||||||
\(527\) | 5.23342e6 | 0.820840 | ||||||||
\(528\) | −294912. | −0.0460371 | ||||||||
\(529\) | −3.98399e6 | −0.618983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.24086e6 | 1.11443 | ||||||||
\(532\) | −5.17312e6 | −0.792453 | ||||||||
\(533\) | 418068. | 0.0637425 | ||||||||
\(534\) | 923760. | 0.140186 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.15821e6 | 0.324475 | ||||||||
\(537\) | −1.63260e6 | −0.244312 | ||||||||
\(538\) | 453240. | 0.0675107 | ||||||||
\(539\) | −553536. | −0.0820680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.23114e6 | −0.621533 | −0.310766 | − | 0.950486i | \(-0.600586\pi\) | ||||
−0.310766 | + | 0.950486i | \(0.600586\pi\) | |||||||
\(542\) | 3.39851e6 | 0.496925 | ||||||||
\(543\) | 452508. | 0.0658608 | ||||||||
\(544\) | 780288. | 0.113047 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.13219e6 | −0.449642 | ||||||||
\(547\) | −4.44024e6 | −0.634510 | −0.317255 | − | 0.948340i | \(-0.602761\pi\) | ||||
−0.317255 | + | 0.948340i | \(0.602761\pi\) | |||||||
\(548\) | 2.62781e6 | 0.373803 | ||||||||
\(549\) | 2.03647e6 | 0.288367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.61934e7 | −2.27227 | ||||||||
\(552\) | −601344. | −0.0839992 | ||||||||
\(553\) | 533360. | 0.0741665 | ||||||||
\(554\) | 1.75441e6 | 0.242860 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.51360e6 | −0.619207 | ||||||||
\(557\) | 9.01448e6 | 1.23113 | 0.615563 | − | 0.788088i | \(-0.288929\pi\) | ||||
0.615563 | + | 0.788088i | \(0.288929\pi\) | |||||||
\(558\) | −5.68670e6 | −0.773170 | ||||||||
\(559\) | −2.69200e6 | −0.364373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 877824. | 0.117761 | ||||||||
\(562\) | 5.82679e6 | 0.778196 | ||||||||
\(563\) | 9.81287e6 | 1.30474 | 0.652372 | − | 0.757899i | \(-0.273774\pi\) | ||||
0.652372 | + | 0.757899i | \(0.273774\pi\) | |||||||
\(564\) | 1.25971e6 | 0.166753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −481576. | −0.0631864 | ||||||||
\(567\) | 4.02392e6 | 0.525644 | ||||||||
\(568\) | −4.49357e6 | −0.584414 | ||||||||
\(569\) | 1.33152e7 | 1.72412 | 0.862061 | − | 0.506804i | \(-0.169173\pi\) | ||||
0.862061 | + | 0.506804i | \(0.169173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.95895e6 | 1.27827 | 0.639136 | − | 0.769094i | \(-0.279292\pi\) | ||||
0.639136 | + | 0.769094i | \(0.279292\pi\) | |||||||
\(572\) | −3.39763e6 | −0.434196 | ||||||||
\(573\) | 2.14193e6 | 0.272533 | ||||||||
\(574\) | 178416. | 0.0226024 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −847872. | −0.106481 | ||||||||
\(577\) | −4.50372e6 | −0.563160 | −0.281580 | − | 0.959538i | \(-0.590859\pi\) | ||||
−0.281580 | + | 0.959538i | \(0.590859\pi\) | |||||||
\(578\) | 3.35685e6 | 0.417939 | ||||||||
\(579\) | −2.63216e6 | −0.326300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.28707e7 | 1.58184 | ||||||||
\(582\) | 46032.0 | 0.00563316 | ||||||||
\(583\) | 1.76141e6 | 0.214629 | ||||||||
\(584\) | 1.40710e6 | 0.170724 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.05684e7 | −1.27135 | ||||||||
\(587\) | −625842. | −0.0749669 | −0.0374834 | − | 0.999297i | \(-0.511934\pi\) | ||||
−0.0374834 | + | 0.999297i | \(0.511934\pi\) | |||||||
\(588\) | 276768. | 0.0330121 | ||||||||
\(589\) | 1.88183e7 | 2.23508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −940788. | −0.110796 | ||||||||
\(592\) | 1.41261e6 | 0.165660 | ||||||||
\(593\) | 2.50385e6 | 0.292397 | 0.146198 | − | 0.989255i | \(-0.453296\pi\) | ||||
0.146198 | + | 0.989255i | \(0.453296\pi\) | |||||||
\(594\) | −2.07360e6 | −0.241134 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.22320e6 | −0.717626 | ||||||||
\(597\) | 975120. | 0.111975 | ||||||||
\(598\) | −6.92798e6 | −0.792235 | ||||||||
\(599\) | −756480. | −0.0861451 | −0.0430725 | − | 0.999072i | \(-0.513715\pi\) | ||||
−0.0430725 | + | 0.999072i | \(0.513715\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.38565e7 | −1.56483 | −0.782413 | − | 0.622760i | \(-0.786011\pi\) | ||||
−0.782413 | + | 0.622760i | \(0.786011\pi\) | |||||||
\(602\) | −1.14885e6 | −0.129203 | ||||||||
\(603\) | 6.98045e6 | 0.781791 | ||||||||
\(604\) | −1.56717e6 | −0.174793 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.86293e6 | 0.206070 | ||||||||
\(607\) | −1.13772e7 | −1.25333 | −0.626663 | − | 0.779291i | \(-0.715580\pi\) | ||||
−0.626663 | + | 0.779291i | \(0.715580\pi\) | |||||||
\(608\) | 2.80576e6 | 0.307816 | ||||||||
\(609\) | −4.18428e6 | −0.457170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.45129e7 | 1.57272 | ||||||||
\(612\) | 2.52374e6 | 0.272375 | ||||||||
\(613\) | 7.00161e6 | 0.752570 | 0.376285 | − | 0.926504i | \(-0.377201\pi\) | ||||
0.376285 | + | 0.926504i | \(0.377201\pi\) | |||||||
\(614\) | −5.79023e6 | −0.619833 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44998e6 | −0.153961 | ||||||||
\(617\) | −7.90300e6 | −0.835755 | −0.417878 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417878 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(618\) | 1.12114e6 | 0.118083 | ||||||||
\(619\) | 4.02362e6 | 0.422076 | 0.211038 | − | 0.977478i | \(-0.432316\pi\) | ||||
0.211038 | + | 0.977478i | \(0.432316\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.22820e6 | −0.439974 | ||||||||
\(622\) | 3.71227e6 | 0.384737 | ||||||||
\(623\) | 4.54182e6 | 0.468824 | ||||||||
\(624\) | 1.69882e6 | 0.174657 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.18250e6 | 0.936538 | ||||||||
\(627\) | 3.15648e6 | 0.320652 | ||||||||
\(628\) | 59488.0 | 0.00601908 | ||||||||
\(629\) | −4.20472e6 | −0.423750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00227e7 | −1.00210 | −0.501049 | − | 0.865419i | \(-0.667052\pi\) | ||||
−0.501049 | + | 0.865419i | \(0.667052\pi\) | |||||||
\(632\) | −289280. | −0.0288088 | ||||||||
\(633\) | 1.08989e6 | 0.108112 | ||||||||
\(634\) | 1.09461e7 | 1.08152 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −880704. | −0.0863351 | ||||||||
\(637\) | 3.18860e6 | 0.311352 | ||||||||
\(638\) | −4.53888e6 | −0.441466 | ||||||||
\(639\) | −1.45339e7 | −1.40809 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.37390e6 | 0.612718 | 0.306359 | − | 0.951916i | \(-0.400889\pi\) | ||||
0.306359 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(642\) | 24912.0 | 0.00238545 | ||||||||
\(643\) | −5.00457e6 | −0.477352 | −0.238676 | − | 0.971099i | \(-0.576713\pi\) | ||||
−0.238676 | + | 0.971099i | \(0.576713\pi\) | |||||||
\(644\) | −2.95661e6 | −0.280918 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.35152e6 | −0.787380 | ||||||||
\(647\) | 8.71928e6 | 0.818879 | 0.409440 | − | 0.912337i | \(-0.365724\pi\) | ||||
0.409440 | + | 0.912337i | \(0.365724\pi\) | |||||||
\(648\) | −2.18246e6 | −0.204178 | ||||||||
\(649\) | −6.71616e6 | −0.625906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.86254e6 | 0.449688 | ||||||||
\(652\) | 691744. | 0.0637274 | ||||||||
\(653\) | 1.58477e6 | 0.145440 | 0.0727201 | − | 0.997352i | \(-0.476832\pi\) | ||||
0.0727201 | + | 0.997352i | \(0.476832\pi\) | |||||||
\(654\) | 4.96632e6 | 0.454036 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −96768.0 | −0.00877955 | ||||||||
\(657\) | 4.55110e6 | 0.411342 | ||||||||
\(658\) | 6.19358e6 | 0.557670 | ||||||||
\(659\) | 1.26410e7 | 1.13388 | 0.566940 | − | 0.823759i | \(-0.308127\pi\) | ||||
0.566940 | + | 0.823759i | \(0.308127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.61572e6 | −0.321878 | −0.160939 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160939 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(662\) | −1.52752e7 | −1.35469 | ||||||||
\(663\) | −5.05663e6 | −0.446763 | ||||||||
\(664\) | −6.98074e6 | −0.614442 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.56890e6 | 0.399141 | ||||||||
\(667\) | −9.25506e6 | −0.805498 | ||||||||
\(668\) | −2.98435e6 | −0.258767 | ||||||||
\(669\) | −1.72964e6 | −0.149414 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.88890e6 | −0.161958 | ||||||||
\(672\) | 724992. | 0.0619313 | ||||||||
\(673\) | −1.11313e7 | −0.947349 | −0.473675 | − | 0.880700i | \(-0.657073\pi\) | ||||
−0.473675 | + | 0.880700i | \(0.657073\pi\) | |||||||
\(674\) | −8.84351e6 | −0.749851 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.36311e7 | 1.14727 | ||||||||
\(677\) | 235518. | 0.0197493 | 0.00987467 | − | 0.999951i | \(-0.496857\pi\) | ||||
0.00987467 | + | 0.999951i | \(0.496857\pi\) | |||||||
\(678\) | −3.34526e6 | −0.279483 | ||||||||
\(679\) | 226324. | 0.0188389 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.75313e6 | 0.558004 | ||||||||
\(682\) | 5.27462e6 | 0.434241 | ||||||||
\(683\) | −2.05830e7 | −1.68833 | −0.844164 | − | 0.536084i | \(-0.819903\pi\) | ||||
−0.844164 | + | 0.536084i | \(0.819903\pi\) | |||||||
\(684\) | 9.07488e6 | 0.741653 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.29368e6 | 0.754011 | ||||||||
\(687\) | 2.49486e6 | 0.201676 | ||||||||
\(688\) | 623104. | 0.0501868 | ||||||||
\(689\) | −1.01464e7 | −0.814265 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.54825e6 | −0.760727 | −0.380363 | − | 0.924837i | \(-0.624201\pi\) | ||||
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(692\) | 5.99126e6 | 0.475612 | ||||||||
\(693\) | −4.68979e6 | −0.370954 | ||||||||
\(694\) | −9.30895e6 | −0.733672 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.26944e6 | 0.177581 | ||||||||
\(697\) | 288036. | 0.0224577 | ||||||||
\(698\) | 1.24516e6 | 0.0967357 | ||||||||
\(699\) | 4.62352e6 | 0.357915 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.29304e6 | 0.0993843 | 0.0496921 | − | 0.998765i | \(-0.484176\pi\) | ||||
0.0496921 | + | 0.998765i | \(0.484176\pi\) | |||||||
\(702\) | 1.19448e7 | 0.914821 | ||||||||
\(703\) | −1.51193e7 | −1.15384 | ||||||||
\(704\) | 786432. | 0.0598039 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.23463e7 | −0.932234 | ||||||||
\(707\) | 9.15940e6 | 0.689157 | ||||||||
\(708\) | 3.35808e6 | 0.251772 | ||||||||
\(709\) | −2.12720e7 | −1.58926 | −0.794628 | − | 0.607097i | \(-0.792334\pi\) | ||||
−0.794628 | + | 0.607097i | \(0.792334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −935640. | −0.0694120 | ||||||||
\(712\) | −2.46336e6 | −0.182108 | ||||||||
\(713\) | 1.07553e7 | 0.792316 | ||||||||
\(714\) | −2.15798e6 | −0.158417 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.35360e6 | 0.317370 | ||||||||
\(717\) | 3.57192e6 | 0.259480 | ||||||||
\(718\) | 1.41230e7 | 1.02239 | ||||||||
\(719\) | 8.31732e6 | 0.600014 | 0.300007 | − | 0.953937i | \(-0.403011\pi\) | ||||
0.300007 | + | 0.953937i | \(0.403011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.51225e6 | 0.394903 | ||||||||
\(722\) | −2.01260e7 | −1.43686 | ||||||||
\(723\) | −1.64341e6 | −0.116923 | ||||||||
\(724\) | −1.20669e6 | −0.0855556 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.98049e6 | −0.209868 | ||||||||
\(727\) | 4.36740e6 | 0.306469 | 0.153235 | − | 0.988190i | \(-0.451031\pi\) | ||||
0.153235 | + | 0.988190i | \(0.451031\pi\) | |||||||
\(728\) | 8.35251e6 | 0.584102 | ||||||||
\(729\) | −3.12231e6 | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.85471e6 | −0.128375 | ||||||||
\(732\) | 944448. | 0.0651479 | ||||||||
\(733\) | 4.05645e6 | 0.278860 | 0.139430 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139430 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(734\) | 143048. | 0.00980035 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.60358e6 | 0.109118 | ||||||||
\(737\) | −6.47462e6 | −0.439082 | ||||||||
\(738\) | −312984. | −0.0211535 | ||||||||
\(739\) | 768260. | 0.0517484 | 0.0258742 | − | 0.999665i | \(-0.491763\pi\) | ||||
0.0258742 | + | 0.999665i | \(0.491763\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.81826e7 | −1.21650 | ||||||||
\(742\) | −4.33013e6 | −0.288729 | ||||||||
\(743\) | −6.18781e6 | −0.411211 | −0.205605 | − | 0.978635i | \(-0.565916\pi\) | ||||
−0.205605 | + | 0.978635i | \(0.565916\pi\) | |||||||
\(744\) | −2.63731e6 | −0.174674 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.86102e6 | −0.451379 | ||||||||
\(747\) | −2.25783e7 | −1.48044 | ||||||||
\(748\) | −2.34086e6 | −0.152976 | ||||||||
\(749\) | 122484. | 0.00797765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.81698e7 | 1.17557 | 0.587787 | − | 0.809016i | \(-0.299999\pi\) | ||||
0.587787 | + | 0.809016i | \(0.299999\pi\) | |||||||
\(752\) | −3.35923e6 | −0.216618 | ||||||||
\(753\) | −5.10451e6 | −0.328070 | ||||||||
\(754\) | 2.61458e7 | 1.67484 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.09760e6 | 0.324385 | ||||||||
\(757\) | −1.93494e7 | −1.22724 | −0.613618 | − | 0.789603i | \(-0.710286\pi\) | ||||
−0.613618 | + | 0.789603i | \(0.710286\pi\) | |||||||
\(758\) | 1.24070e7 | 0.784318 | ||||||||
\(759\) | 1.80403e6 | 0.113668 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.01992e7 | −1.89031 | −0.945155 | − | 0.326621i | \(-0.894090\pi\) | ||||
−0.945155 | + | 0.326621i | \(0.894090\pi\) | |||||||
\(762\) | −7.19717e6 | −0.449029 | ||||||||
\(763\) | 2.44177e7 | 1.51843 | ||||||||
\(764\) | −5.71181e6 | −0.354030 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.12779e7 | 1.31026 | ||||||||
\(767\) | 3.86879e7 | 2.37458 | ||||||||
\(768\) | −393216. | −0.0240563 | ||||||||
\(769\) | 2.15854e7 | 1.31627 | 0.658134 | − | 0.752901i | \(-0.271346\pi\) | ||||
0.658134 | + | 0.752901i | \(0.271346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.95241e6 | 0.300041 | ||||||||
\(772\) | 7.01910e6 | 0.423876 | ||||||||
\(773\) | −3.90895e6 | −0.235294 | −0.117647 | − | 0.993055i | \(-0.537535\pi\) | ||||
−0.117647 | + | 0.993055i | \(0.537535\pi\) | |||||||
\(774\) | 2.01535e6 | 0.120920 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −122752. | −0.00731769 | ||||||||
\(777\) | −3.90674e6 | −0.232147 | ||||||||
\(778\) | −4.64580e6 | −0.275177 | ||||||||
\(779\) | 1.03572e6 | 0.0611503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34807e7 | 0.790833 | ||||||||
\(782\) | −4.77317e6 | −0.279119 | ||||||||
\(783\) | 1.59570e7 | 0.930137 | ||||||||
\(784\) | −738048. | −0.0428839 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 188928. | 0.0109079 | ||||||||
\(787\) | 2.65082e7 | 1.52561 | 0.762806 | − | 0.646628i | \(-0.223821\pi\) | ||||
0.762806 | + | 0.646628i | \(0.223821\pi\) | |||||||
\(788\) | 2.50877e6 | 0.143928 | ||||||||
\(789\) | 8.18788e6 | 0.468251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.64475e7 | −0.934674 | ||||||||
\(792\) | 2.54362e6 | 0.144092 | ||||||||
\(793\) | 1.08808e7 | 0.614439 | ||||||||
\(794\) | 2.51425e6 | 0.141533 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.60032e6 | −0.145460 | ||||||||
\(797\) | −1.07940e7 | −0.601919 | −0.300960 | − | 0.953637i | \(-0.597307\pi\) | ||||
−0.300960 | + | 0.953637i | \(0.597307\pi\) | |||||||
\(798\) | −7.75968e6 | −0.431357 | ||||||||
\(799\) | 9.99896e6 | 0.554100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.96743e6 | −0.438770 | ||||||||
\(802\) | 1.08973e7 | 0.598249 | ||||||||
\(803\) | −4.22131e6 | −0.231025 | ||||||||
\(804\) | 3.23731e6 | 0.176622 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.03840e7 | −1.64743 | ||||||||
\(807\) | 679860. | 0.0367482 | ||||||||
\(808\) | −4.96781e6 | −0.267693 | ||||||||
\(809\) | −1.11446e7 | −0.598675 | −0.299338 | − | 0.954147i | \(-0.596766\pi\) | ||||
−0.299338 | + | 0.954147i | \(0.596766\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14866e7 | −0.613253 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(812\) | 1.11581e7 | 0.593881 | ||||||||
\(813\) | 5.09777e6 | 0.270492 | ||||||||
\(814\) | −4.23782e6 | −0.224172 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.17043e6 | 0.0615348 | ||||||||
\(817\) | −6.66916e6 | −0.349555 | ||||||||
\(818\) | −7.12076e6 | −0.372086 | ||||||||
\(819\) | 2.70152e7 | 1.40734 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.04347e7 | 1.57584 | 0.787918 | − | 0.615781i | \(-0.211159\pi\) | ||||
0.787918 | + | 0.615781i | \(0.211159\pi\) | |||||||
\(822\) | 3.94171e6 | 0.203472 | ||||||||
\(823\) | −4.09773e6 | −0.210884 | −0.105442 | − | 0.994425i | \(-0.533626\pi\) | ||||
−0.105442 | + | 0.994425i | \(0.533626\pi\) | |||||||
\(824\) | −2.98970e6 | −0.153394 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.65106e7 | 0.841999 | ||||||||
\(827\) | 1.70652e7 | 0.867654 | 0.433827 | − | 0.900996i | \(-0.357163\pi\) | ||||
0.433827 | + | 0.900996i | \(0.357163\pi\) | |||||||
\(828\) | 5.18659e6 | 0.262909 | ||||||||
\(829\) | −2.47617e7 | −1.25139 | −0.625697 | − | 0.780066i | \(-0.715185\pi\) | ||||
−0.625697 | + | 0.780066i | \(0.715185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.63161e6 | 0.132196 | ||||||||
\(832\) | −4.53018e6 | −0.226886 | ||||||||
\(833\) | 2.19685e6 | 0.109695 | ||||||||
\(834\) | −6.77040e6 | −0.337054 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.41728e6 | −0.416539 | ||||||||
\(837\) | −1.85436e7 | −0.914914 | ||||||||
\(838\) | −2.60232e6 | −0.128012 | ||||||||
\(839\) | 3.16529e7 | 1.55242 | 0.776208 | − | 0.630476i | \(-0.217140\pi\) | ||||
0.776208 | + | 0.630476i | \(0.217140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.44170e7 | 0.702884 | ||||||||
\(842\) | 1.41624e7 | 0.688425 | ||||||||
\(843\) | 8.74019e6 | 0.423596 | ||||||||
\(844\) | −2.90637e6 | −0.140441 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.08650e7 | −0.521921 | ||||||||
\(847\) | −1.46541e7 | −0.701859 | ||||||||
\(848\) | 2.34854e6 | 0.112153 | ||||||||
\(849\) | −722364. | −0.0343943 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.64119e6 | −0.409025 | ||||||||
\(852\) | −6.74035e6 | −0.318115 | ||||||||
\(853\) | −2.82671e7 | −1.33017 | −0.665087 | − | 0.746765i | \(-0.731606\pi\) | ||||
−0.665087 | + | 0.746765i | \(0.731606\pi\) | |||||||
\(854\) | 4.64354e6 | 0.217873 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −66432.0 | −0.00309880 | ||||||||
\(857\) | −2.60870e7 | −1.21331 | −0.606655 | − | 0.794966i | \(-0.707489\pi\) | ||||
−0.606655 | + | 0.794966i | \(0.707489\pi\) | |||||||
\(858\) | −5.09645e6 | −0.236347 | ||||||||
\(859\) | −3.38111e7 | −1.56342 | −0.781710 | − | 0.623642i | \(-0.785652\pi\) | ||||
−0.781710 | + | 0.623642i | \(0.785652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 267624. | 0.0123032 | ||||||||
\(862\) | 2.19499e6 | 0.100615 | ||||||||
\(863\) | −2.22817e7 | −1.01841 | −0.509204 | − | 0.860646i | \(-0.670060\pi\) | ||||
−0.509204 | + | 0.860646i | \(0.670060\pi\) | |||||||
\(864\) | −2.76480e6 | −0.126003 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.96966e6 | −0.270492 | ||||||||
\(867\) | 5.03528e6 | 0.227497 | ||||||||
\(868\) | −1.29668e7 | −0.584162 | ||||||||
\(869\) | 867840. | 0.0389843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72965e7 | 1.66580 | ||||||||
\(872\) | −1.32435e7 | −0.589810 | ||||||||
\(873\) | −397026. | −0.0176313 | ||||||||
\(874\) | −1.71634e7 | −0.760018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.11066e6 | 0.0929303 | ||||||||
\(877\) | 3.46748e7 | 1.52235 | 0.761177 | − | 0.648545i | \(-0.224622\pi\) | ||||
0.761177 | + | 0.648545i | \(0.224622\pi\) | |||||||
\(878\) | −1.94485e7 | −0.851431 | ||||||||
\(879\) | −1.58526e7 | −0.692034 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.42603e7 | 0.618998 | 0.309499 | − | 0.950900i | \(-0.399839\pi\) | ||||
0.309499 | + | 0.950900i | \(0.399839\pi\) | |||||||
\(882\) | −2.38712e6 | −0.103325 | ||||||||
\(883\) | 3.75177e7 | 1.61933 | 0.809663 | − | 0.586895i | \(-0.199650\pi\) | ||||
0.809663 | + | 0.586895i | \(0.199650\pi\) | |||||||
\(884\) | 1.34844e7 | 0.580363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.44622e6 | −0.318677 | ||||||||
\(887\) | −4.07657e7 | −1.73975 | −0.869873 | − | 0.493275i | \(-0.835800\pi\) | ||||
−0.869873 | + | 0.493275i | \(0.835800\pi\) | |||||||
\(888\) | 2.11891e6 | 0.0901738 | ||||||||
\(889\) | −3.53861e7 | −1.50168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.54739e6 | 0.276296 | ||||||||
\(892\) | 4.61238e6 | 0.194095 | ||||||||
\(893\) | 3.59543e7 | 1.50877 | ||||||||
\(894\) | −9.33480e6 | −0.390626 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.93331e6 | −0.0804511 | ||||||||
\(897\) | −1.03920e7 | −0.431238 | ||||||||
\(898\) | −1.49488e7 | −0.618606 | ||||||||
\(899\) | −4.05899e7 | −1.67501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.99059e6 | −0.286881 | ||||||||
\(902\) | 290304. | 0.0118806 | ||||||||
\(903\) | −1.72327e6 | −0.0703290 | ||||||||
\(904\) | 8.92070e6 | 0.363060 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.35075e6 | −0.0951451 | ||||||||
\(907\) | 3.57116e7 | 1.44142 | 0.720712 | − | 0.693235i | \(-0.243815\pi\) | ||||
0.720712 | + | 0.693235i | \(0.243815\pi\) | |||||||
\(908\) | −1.80084e7 | −0.724869 | ||||||||
\(909\) | −1.60678e7 | −0.644979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.11389e7 | −0.843893 | −0.421947 | − | 0.906621i | \(-0.638653\pi\) | ||||
−0.421947 | + | 0.906621i | \(0.638653\pi\) | |||||||
\(912\) | 4.20864e6 | 0.167554 | ||||||||
\(913\) | 2.09422e7 | 0.831468 | ||||||||
\(914\) | −2.59310e7 | −1.02673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.65296e6 | −0.261985 | ||||||||
\(917\) | 928896. | 0.0364791 | ||||||||
\(918\) | 8.22960e6 | 0.322309 | ||||||||
\(919\) | 1.85996e7 | 0.726465 | 0.363233 | − | 0.931698i | \(-0.381673\pi\) | ||||
0.363233 | + | 0.931698i | \(0.381673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.68535e6 | −0.337395 | ||||||||
\(922\) | −6.03641e6 | −0.233857 | ||||||||
\(923\) | −7.76545e7 | −3.00028 | ||||||||
\(924\) | −2.17498e6 | −0.0838059 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.47360e7 | 1.33123 | ||||||||
\(927\) | −9.66980e6 | −0.369588 | ||||||||
\(928\) | −6.05184e6 | −0.230684 | ||||||||
\(929\) | 4.45110e7 | 1.69211 | 0.846055 | − | 0.533096i | \(-0.178972\pi\) | ||||
0.846055 | + | 0.533096i | \(0.178972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.89942e6 | 0.298690 | ||||||||
\(932\) | −1.23294e7 | −0.464945 | ||||||||
\(933\) | 5.56841e6 | 0.209424 | ||||||||
\(934\) | 2.78565e7 | 1.04486 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.46523e7 | −0.546658 | ||||||||
\(937\) | 2.19419e7 | 0.816441 | 0.408221 | − | 0.912883i | \(-0.366149\pi\) | ||||
0.408221 | + | 0.912883i | \(0.366149\pi\) | |||||||
\(938\) | 1.59168e7 | 0.590675 | ||||||||
\(939\) | 1.37738e7 | 0.509787 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.77722e6 | −0.286319 | −0.143160 | − | 0.989700i | \(-0.545726\pi\) | ||||
−0.143160 | + | 0.989700i | \(0.545726\pi\) | |||||||
\(942\) | 89232.0 | 0.00327637 | ||||||||
\(943\) | 591948. | 0.0216773 | ||||||||
\(944\) | −8.95488e6 | −0.327062 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.86931e6 | −0.0679132 | ||||||||
\(947\) | −3.17199e7 | −1.14936 | −0.574681 | − | 0.818378i | \(-0.694874\pi\) | ||||
−0.574681 | + | 0.818378i | \(0.694874\pi\) | |||||||
\(948\) | −433920. | −0.0156815 | ||||||||
\(949\) | 2.43165e7 | 0.876468 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.64191e7 | 0.588707 | ||||||||
\(952\) | 5.75462e6 | 0.205790 | ||||||||
\(953\) | 5.60285e6 | 0.199838 | 0.0999188 | − | 0.994996i | \(-0.468142\pi\) | ||||
0.0999188 | + | 0.994996i | \(0.468142\pi\) | |||||||
\(954\) | 7.59607e6 | 0.270220 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.52512e6 | −0.337074 | ||||||||
\(957\) | −6.80832e6 | −0.240304 | ||||||||
\(958\) | 2.20421e7 | 0.775959 | ||||||||
\(959\) | 1.93801e7 | 0.680470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.85403e7 | 0.647601 | ||||||||
\(962\) | 2.44116e7 | 0.850470 | ||||||||
\(963\) | −214866. | −0.00746624 | ||||||||
\(964\) | 4.38243e6 | 0.151888 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.43491e6 | −0.152912 | ||||||||
\(967\) | 2.03532e7 | 0.699949 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(968\) | 7.94797e6 | 0.272626 | ||||||||
\(969\) | −1.25273e7 | −0.428595 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.34306e7 | −0.797510 | −0.398755 | − | 0.917057i | \(-0.630558\pi\) | ||||
−0.398755 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(972\) | −1.37713e7 | −0.467530 | ||||||||
\(973\) | −3.32878e7 | −1.12721 | ||||||||
\(974\) | 2.20723e7 | 0.745505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.51853e6 | −0.0846296 | ||||||||
\(977\) | 4.30412e7 | 1.44261 | 0.721303 | − | 0.692619i | \(-0.243543\pi\) | ||||
0.721303 | + | 0.692619i | \(0.243543\pi\) | |||||||
\(978\) | 1.03762e6 | 0.0346888 | ||||||||
\(979\) | 7.39008e6 | 0.246429 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.28345e7 | −1.42109 | ||||||||
\(982\) | 6.05107e6 | 0.200241 | ||||||||
\(983\) | 4.75003e7 | 1.56788 | 0.783940 | − | 0.620837i | \(-0.213207\pi\) | ||||
0.783940 | + | 0.620837i | \(0.213207\pi\) | |||||||
\(984\) | −145152. | −0.00477898 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.80137e7 | 0.590079 | ||||||||
\(987\) | 9.29038e6 | 0.303557 | ||||||||
\(988\) | 4.84870e7 | 1.58028 | ||||||||
\(989\) | −3.81164e6 | −0.123914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.09231e7 | 0.676770 | 0.338385 | − | 0.941008i | \(-0.390119\pi\) | ||||
0.338385 | + | 0.941008i | \(0.390119\pi\) | |||||||
\(992\) | 7.03283e6 | 0.226909 | ||||||||
\(993\) | −2.29128e7 | −0.737402 | ||||||||
\(994\) | −3.31401e7 | −1.06387 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.04711e7 | −0.334460 | ||||||||
\(997\) | −2.96332e7 | −0.944148 | −0.472074 | − | 0.881559i | \(-0.656495\pi\) | ||||
−0.472074 | + | 0.881559i | \(0.656495\pi\) | |||||||
\(998\) | 7.72168e6 | 0.245406 | ||||||||
\(999\) | 1.48986e7 | 0.472315 |
(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 | 50.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 450.6.a.u.1.1 | 1 | |||
4.3 | odd | 2 | 400.6.a.i.1.1 | 1 | |||
5.2 | odd | 4 | 50.6.b.b.49.1 | 2 | |||
5.3 | odd | 4 | 50.6.b.b.49.2 | 2 | |||
5.4 | even | 2 | 10.6.a.c.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 450.6.c.f.199.2 | 2 | |||
15.8 | even | 4 | 450.6.c.f.199.1 | 2 | |||
15.14 | odd | 2 | 90.6.a.b.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.i.49.2 | 2 | |||
20.7 | even | 4 | 400.6.c.i.49.1 | 2 | |||
20.19 | odd | 2 | 80.6.a.c.1.1 | 1 | |||
35.34 | odd | 2 | 490.6.a.k.1.1 | 1 | |||
40.19 | odd | 2 | 320.6.a.k.1.1 | 1 | |||
40.29 | even | 2 | 320.6.a.f.1.1 | 1 | |||
60.59 | even | 2 | 720.6.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
50.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
50.6.b.b.49.1 | 2 | 5.2 | odd | 4 | |||
50.6.b.b.49.2 | 2 | 5.3 | odd | 4 | |||
80.6.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
90.6.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
320.6.a.f.1.1 | 1 | 40.29 | even | 2 | |||
320.6.a.k.1.1 | 1 | 40.19 | odd | 2 | |||
400.6.a.i.1.1 | 1 | 4.3 | odd | 2 | |||
400.6.c.i.49.1 | 2 | 20.7 | even | 4 | |||
400.6.c.i.49.2 | 2 | 20.3 | even | 4 | |||
450.6.a.u.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.c.f.199.1 | 2 | 15.8 | even | 4 | |||
450.6.c.f.199.2 | 2 | 15.2 | even | 4 | |||
490.6.a.k.1.1 | 1 | 35.34 | odd | 2 | |||
720.6.a.v.1.1 | 1 | 60.59 | even | 2 |