Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,6,Mod(49,50)]
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([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(8.01919099065\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.6.b.b.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | 6.00000i | 0.384900i | 0.981307 | + | 0.192450i | \(0.0616434\pi\) | ||||
−0.981307 | + | 0.192450i | \(0.938357\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 24.0000 | 0.272166 | ||||||||
\(7\) | 118.000i | 0.910200i | 0.890440 | + | 0.455100i | \(0.150397\pi\) | ||||
−0.890440 | + | 0.455100i | \(0.849603\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 207.000 | 0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 192.000 | 0.478431 | 0.239216 | − | 0.970966i | \(-0.423110\pi\) | ||||
0.239216 | + | 0.970966i | \(0.423110\pi\) | |||||||
\(12\) | − 96.0000i | − 0.192450i | ||||||||
\(13\) | 1106.00i | 1.81508i | 0.419961 | + | 0.907542i | \(0.362044\pi\) | ||||
−0.419961 | + | 0.907542i | \(0.637956\pi\) | |||||||
\(14\) | 472.000 | 0.643609 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − 762.000i | − 0.639488i | −0.947504 | − | 0.319744i | \(-0.896403\pi\) | ||||
0.947504 | − | 0.319744i | \(-0.103597\pi\) | |||||||
\(18\) | − 828.000i | − 0.602350i | ||||||||
\(19\) | 2740.00 | 1.74127 | 0.870636 | − | 0.491928i | \(-0.163708\pi\) | ||||
0.870636 | + | 0.491928i | \(0.163708\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −708.000 | −0.350336 | ||||||||
\(22\) | − 768.000i | − 0.338302i | ||||||||
\(23\) | 1566.00i | 0.617266i | 0.951181 | + | 0.308633i | \(0.0998714\pi\) | ||||
−0.951181 | + | 0.308633i | \(0.900129\pi\) | |||||||
\(24\) | −384.000 | −0.136083 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4424.00 | 1.28346 | ||||||||
\(27\) | 2700.00i | 0.712778i | ||||||||
\(28\) | − 1888.00i | − 0.455100i | ||||||||
\(29\) | −5910.00 | −1.30495 | −0.652473 | − | 0.757812i | \(-0.726268\pi\) | ||||
−0.652473 | + | 0.757812i | \(0.726268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6868.00 | −1.28359 | −0.641795 | − | 0.766877i | \(-0.721810\pi\) | ||||
−0.641795 | + | 0.766877i | \(0.721810\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | 1152.00i | 0.184148i | ||||||||
\(34\) | −3048.00 | −0.452187 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3312.00 | −0.425926 | ||||||||
\(37\) | 5518.00i | 0.662640i | 0.943519 | + | 0.331320i | \(0.107494\pi\) | ||||
−0.943519 | + | 0.331320i | \(0.892506\pi\) | |||||||
\(38\) | − 10960.0i | − 1.23127i | ||||||||
\(39\) | −6636.00 | −0.698626 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −378.000 | −0.0351182 | −0.0175591 | − | 0.999846i | \(-0.505590\pi\) | ||||
−0.0175591 | + | 0.999846i | \(0.505590\pi\) | |||||||
\(42\) | 2832.00i | 0.247725i | ||||||||
\(43\) | − 2434.00i | − 0.200747i | −0.994950 | − | 0.100374i | \(-0.967996\pi\) | ||||
0.994950 | − | 0.100374i | \(-0.0320038\pi\) | |||||||
\(44\) | −3072.00 | −0.239216 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6264.00 | 0.436473 | ||||||||
\(47\) | − 13122.0i | − 0.866474i | −0.901280 | − | 0.433237i | \(-0.857371\pi\) | ||||
0.901280 | − | 0.433237i | \(-0.142629\pi\) | |||||||
\(48\) | 1536.00i | 0.0962250i | ||||||||
\(49\) | 2883.00 | 0.171536 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4572.00 | 0.246139 | ||||||||
\(52\) | − 17696.0i | − 0.907542i | ||||||||
\(53\) | − 9174.00i | − 0.448610i | −0.974519 | − | 0.224305i | \(-0.927989\pi\) | ||||
0.974519 | − | 0.224305i | \(-0.0720112\pi\) | |||||||
\(54\) | 10800.0 | 0.504010 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7552.00 | −0.321804 | ||||||||
\(57\) | 16440.0i | 0.670216i | ||||||||
\(58\) | 23640.0i | 0.922736i | ||||||||
\(59\) | 34980.0 | 1.30825 | 0.654124 | − | 0.756388i | \(-0.273038\pi\) | ||||
0.654124 | + | 0.756388i | \(0.273038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9838.00 | −0.338518 | −0.169259 | − | 0.985572i | \(-0.554137\pi\) | ||||
−0.169259 | + | 0.985572i | \(0.554137\pi\) | |||||||
\(62\) | 27472.0i | 0.907635i | ||||||||
\(63\) | 24426.0i | 0.775356i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4608.00 | 0.130212 | ||||||||
\(67\) | − 33722.0i | − 0.917754i | −0.888500 | − | 0.458877i | \(-0.848252\pi\) | ||||
0.888500 | − | 0.458877i | \(-0.151748\pi\) | |||||||
\(68\) | 12192.0i | 0.319744i | ||||||||
\(69\) | −9396.00 | −0.237586 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 70212.0 | 1.65297 | 0.826486 | − | 0.562957i | \(-0.190336\pi\) | ||||
0.826486 | + | 0.562957i | \(0.190336\pi\) | |||||||
\(72\) | 13248.0i | 0.301175i | ||||||||
\(73\) | 21986.0i | 0.482880i | 0.970416 | + | 0.241440i | \(0.0776197\pi\) | ||||
−0.970416 | + | 0.241440i | \(0.922380\pi\) | |||||||
\(74\) | 22072.0 | 0.468557 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43840.0 | −0.870636 | ||||||||
\(77\) | 22656.0i | 0.435468i | ||||||||
\(78\) | 26544.0i | 0.494003i | ||||||||
\(79\) | −4520.00 | −0.0814837 | −0.0407418 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407418 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34101.0 | 0.577503 | ||||||||
\(82\) | 1512.00i | 0.0248323i | ||||||||
\(83\) | − 109074.i | − 1.73790i | −0.494896 | − | 0.868952i | \(-0.664794\pi\) | ||||
0.494896 | − | 0.868952i | \(-0.335206\pi\) | |||||||
\(84\) | 11328.0 | 0.175168 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9736.00 | −0.141950 | ||||||||
\(87\) | − 35460.0i | − 0.502274i | ||||||||
\(88\) | 12288.0i | 0.169151i | ||||||||
\(89\) | −38490.0 | −0.515078 | −0.257539 | − | 0.966268i | \(-0.582912\pi\) | ||||
−0.257539 | + | 0.966268i | \(0.582912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −130508. | −1.65209 | ||||||||
\(92\) | − 25056.0i | − 0.308633i | ||||||||
\(93\) | − 41208.0i | − 0.494054i | ||||||||
\(94\) | −52488.0 | −0.612689 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6144.00 | 0.0680414 | ||||||||
\(97\) | 1918.00i | 0.0206976i | 0.999946 | + | 0.0103488i | \(0.00329418\pi\) | ||||
−0.999946 | + | 0.0103488i | \(0.996706\pi\) | |||||||
\(98\) | − 11532.0i | − 0.121294i | ||||||||
\(99\) | 39744.0 | 0.407553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77622.0 | 0.757149 | 0.378575 | − | 0.925571i | \(-0.376414\pi\) | ||||
0.378575 | + | 0.925571i | \(0.376414\pi\) | |||||||
\(102\) | − 18288.0i | − 0.174047i | ||||||||
\(103\) | − 46714.0i | − 0.433864i | −0.976187 | − | 0.216932i | \(-0.930395\pi\) | ||||
0.976187 | − | 0.216932i | \(-0.0696051\pi\) | |||||||
\(104\) | −70784.0 | −0.641729 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −36696.0 | −0.317215 | ||||||||
\(107\) | 1038.00i | 0.00876472i | 0.999990 | + | 0.00438236i | \(0.00139495\pi\) | ||||
−0.999990 | + | 0.00438236i | \(0.998605\pi\) | |||||||
\(108\) | − 43200.0i | − 0.356389i | ||||||||
\(109\) | −206930. | −1.66823 | −0.834117 | − | 0.551587i | \(-0.814023\pi\) | ||||
−0.834117 | + | 0.551587i | \(0.814023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33108.0 | −0.255050 | ||||||||
\(112\) | 30208.0i | 0.227550i | ||||||||
\(113\) | 139386.i | 1.02689i | 0.858123 | + | 0.513444i | \(0.171631\pi\) | ||||
−0.858123 | + | 0.513444i | \(0.828369\pi\) | |||||||
\(114\) | 65760.0 | 0.473914 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 94560.0 | 0.652473 | ||||||||
\(117\) | 228942.i | 1.54618i | ||||||||
\(118\) | − 139920.i | − 0.925070i | ||||||||
\(119\) | 89916.0 | 0.582062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124187. | −0.771104 | ||||||||
\(122\) | 39352.0i | 0.239369i | ||||||||
\(123\) | − 2268.00i | − 0.0135170i | ||||||||
\(124\) | 109888. | 0.641795 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 97704.0 | 0.548259 | ||||||||
\(127\) | − 299882.i | − 1.64984i | −0.565252 | − | 0.824919i | \(-0.691221\pi\) | ||||
0.565252 | − | 0.824919i | \(-0.308779\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 14604.0 | 0.0772676 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7872.00 | 0.0400781 | 0.0200390 | − | 0.999799i | \(-0.493621\pi\) | ||||
0.0200390 | + | 0.999799i | \(0.493621\pi\) | |||||||
\(132\) | − 18432.0i | − 0.0920741i | ||||||||
\(133\) | 323320.i | 1.58491i | ||||||||
\(134\) | −134888. | −0.648950 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 48768.0 | 0.226093 | ||||||||
\(137\) | 164238.i | 0.747605i | 0.927508 | + | 0.373803i | \(0.121946\pi\) | ||||
−0.927508 | + | 0.373803i | \(0.878054\pi\) | |||||||
\(138\) | 37584.0i | 0.167998i | ||||||||
\(139\) | 282100. | 1.23841 | 0.619207 | − | 0.785228i | \(-0.287454\pi\) | ||||
0.619207 | + | 0.785228i | \(0.287454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 78732.0 | 0.333506 | ||||||||
\(142\) | − 280848.i | − 1.16883i | ||||||||
\(143\) | 212352.i | 0.868393i | ||||||||
\(144\) | 52992.0 | 0.212963 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 87944.0 | 0.341448 | ||||||||
\(147\) | 17298.0i | 0.0660241i | ||||||||
\(148\) | − 88288.0i | − 0.331320i | ||||||||
\(149\) | 388950. | 1.43525 | 0.717626 | − | 0.696429i | \(-0.245229\pi\) | ||||
0.717626 | + | 0.696429i | \(0.245229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −97948.0 | −0.349585 | −0.174793 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174793 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(152\) | 175360.i | 0.615633i | ||||||||
\(153\) | − 157734.i | − 0.544749i | ||||||||
\(154\) | 90624.0 | 0.307923 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 106176. | 0.349313 | ||||||||
\(157\) | 3718.00i | 0.0120382i | 0.999982 | + | 0.00601908i | \(0.00191594\pi\) | ||||
−0.999982 | + | 0.00601908i | \(0.998084\pi\) | |||||||
\(158\) | 18080.0i | 0.0576177i | ||||||||
\(159\) | 55044.0 | 0.172670 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −184788. | −0.561835 | ||||||||
\(162\) | − 136404.i | − 0.408357i | ||||||||
\(163\) | − 43234.0i | − 0.127455i | −0.997967 | − | 0.0637274i | \(-0.979701\pi\) | ||||
0.997967 | − | 0.0637274i | \(-0.0202988\pi\) | |||||||
\(164\) | 6048.00 | 0.0175591 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −436296. | −1.22888 | ||||||||
\(167\) | − 186522.i | − 0.517534i | −0.965940 | − | 0.258767i | \(-0.916684\pi\) | ||||
0.965940 | − | 0.258767i | \(-0.0833162\pi\) | |||||||
\(168\) | − 45312.0i | − 0.123863i | ||||||||
\(169\) | −851943. | −2.29453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 567180. | 1.48331 | ||||||||
\(172\) | 38944.0i | 0.100374i | ||||||||
\(173\) | − 374454.i | − 0.951225i | −0.879655 | − | 0.475612i | \(-0.842226\pi\) | ||||
0.879655 | − | 0.475612i | \(-0.157774\pi\) | |||||||
\(174\) | −141840. | −0.355161 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 49152.0 | 0.119608 | ||||||||
\(177\) | 209880.i | 0.503545i | ||||||||
\(178\) | 153960.i | 0.364215i | ||||||||
\(179\) | −272100. | −0.634740 | −0.317370 | − | 0.948302i | \(-0.602800\pi\) | ||||
−0.317370 | + | 0.948302i | \(0.602800\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −75418.0 | −0.171111 | −0.0855556 | − | 0.996333i | \(-0.527267\pi\) | ||||
−0.0855556 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(182\) | 522032.i | 1.16820i | ||||||||
\(183\) | − 59028.0i | − 0.130296i | ||||||||
\(184\) | −100224. | −0.218236 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −164832. | −0.349349 | ||||||||
\(187\) | − 146304.i | − 0.305951i | ||||||||
\(188\) | 209952.i | 0.433237i | ||||||||
\(189\) | −318600. | −0.648771 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −356988. | −0.708060 | −0.354030 | − | 0.935234i | \(-0.615189\pi\) | ||||
−0.354030 | + | 0.935234i | \(0.615189\pi\) | |||||||
\(192\) | − 24576.0i | − 0.0481125i | ||||||||
\(193\) | − 438694.i | − 0.847751i | −0.905720 | − | 0.423876i | \(-0.860669\pi\) | ||||
0.905720 | − | 0.423876i | \(-0.139331\pi\) | |||||||
\(194\) | 7672.00 | 0.0146354 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −46128.0 | −0.0857678 | ||||||||
\(197\) | 156798.i | 0.287856i | 0.989588 | + | 0.143928i | \(0.0459733\pi\) | ||||
−0.989588 | + | 0.143928i | \(0.954027\pi\) | |||||||
\(198\) | − 158976.i | − 0.288183i | ||||||||
\(199\) | 162520. | 0.290920 | 0.145460 | − | 0.989364i | \(-0.453534\pi\) | ||||
0.145460 | + | 0.989364i | \(0.453534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 202332. | 0.353244 | ||||||||
\(202\) | − 310488.i | − 0.535385i | ||||||||
\(203\) | − 697380.i | − 1.18776i | ||||||||
\(204\) | −73152.0 | −0.123070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −186856. | −0.306788 | ||||||||
\(207\) | 324162.i | 0.525819i | ||||||||
\(208\) | 283136.i | 0.453771i | ||||||||
\(209\) | 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.i | 0.224305i | ||||||||
\(213\) | 421272.i | 0.636229i | ||||||||
\(214\) | 4152.00 | 0.00619759 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −172800. | −0.252005 | ||||||||
\(217\) | − 810424.i | − 1.16832i | ||||||||
\(218\) | 827720.i | 1.17962i | ||||||||
\(219\) | −131916. | −0.185861 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 842772. | 1.16073 | ||||||||
\(222\) | 132432.i | 0.180348i | ||||||||
\(223\) | − 288274.i | − 0.388189i | −0.980983 | − | 0.194095i | \(-0.937823\pi\) | ||||
0.980983 | − | 0.194095i | \(-0.0621769\pi\) | |||||||
\(224\) | 120832. | 0.160902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 557544. | 0.726119 | ||||||||
\(227\) | − 1.12552e6i | − 1.44974i | −0.688887 | − | 0.724869i | \(-0.741900\pi\) | ||||
0.688887 | − | 0.724869i | \(-0.258100\pi\) | |||||||
\(228\) | − 263040.i | − 0.335108i | ||||||||
\(229\) | 415810. | 0.523970 | 0.261985 | − | 0.965072i | \(-0.415623\pi\) | ||||
0.261985 | + | 0.965072i | \(0.415623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −135936. | −0.167612 | ||||||||
\(232\) | − 378240.i | − 0.461368i | ||||||||
\(233\) | 770586.i | 0.929889i | 0.885340 | + | 0.464945i | \(0.153926\pi\) | ||||
−0.885340 | + | 0.464945i | \(0.846074\pi\) | |||||||
\(234\) | 915768. | 1.09332 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −559680. | −0.654124 | ||||||||
\(237\) | − 27120.0i | − 0.0313631i | ||||||||
\(238\) | − 359664.i | − 0.411580i | ||||||||
\(239\) | 595320. | 0.674149 | 0.337074 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337074 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 273902. | 0.303775 | 0.151888 | − | 0.988398i | \(-0.451465\pi\) | ||||
0.151888 | + | 0.988398i | \(0.451465\pi\) | |||||||
\(242\) | 496748.i | 0.545253i | ||||||||
\(243\) | 860706.i | 0.935059i | ||||||||
\(244\) | 157408. | 0.169259 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9072.00 | −0.00955796 | ||||||||
\(247\) | 3.03044e6i | 3.16055i | ||||||||
\(248\) | − 439552.i | − 0.453817i | ||||||||
\(249\) | 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.i | − 0.387678i | ||||||||
\(253\) | 300672.i | 0.295319i | ||||||||
\(254\) | −1.19953e6 | −1.16661 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − 825402.i | − 0.779530i | −0.920914 | − | 0.389765i | \(-0.872556\pi\) | ||||
0.920914 | − | 0.389765i | \(-0.127444\pi\) | |||||||
\(258\) | − 58416.0i | − 0.0546365i | ||||||||
\(259\) | −651124. | −0.603135 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.22337e6 | −1.11162 | ||||||||
\(262\) | − 31488.0i | − 0.0283395i | ||||||||
\(263\) | 1.36465e6i | 1.21655i | 0.793726 | + | 0.608276i | \(0.208139\pi\) | ||||
−0.793726 | + | 0.608276i | \(0.791861\pi\) | |||||||
\(264\) | −73728.0 | −0.0651062 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.29328e6 | 1.12070 | ||||||||
\(267\) | − 230940.i | − 0.198254i | ||||||||
\(268\) | 539552.i | 0.458877i | ||||||||
\(269\) | 113310. | 0.0954745 | 0.0477373 | − | 0.998860i | \(-0.484799\pi\) | ||||
0.0477373 | + | 0.998860i | \(0.484799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −849628. | −0.702758 | −0.351379 | − | 0.936233i | \(-0.614287\pi\) | ||||
−0.351379 | + | 0.936233i | \(0.614287\pi\) | |||||||
\(272\) | − 195072.i | − 0.159872i | ||||||||
\(273\) | − 783048.i | − 0.635890i | ||||||||
\(274\) | 656952. | 0.528637 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 150336. | 0.118793 | ||||||||
\(277\) | − 438602.i | − 0.343456i | −0.985144 | − | 0.171728i | \(-0.945065\pi\) | ||||
0.985144 | − | 0.171728i | \(-0.0549350\pi\) | |||||||
\(278\) | − 1.12840e6i | − 0.875691i | ||||||||
\(279\) | −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.i | − 0.235824i | ||||||||
\(283\) | − 120394.i | − 0.0893591i | −0.999001 | − | 0.0446795i | \(-0.985773\pi\) | ||||
0.999001 | − | 0.0446795i | \(-0.0142267\pi\) | |||||||
\(284\) | −1.12339e6 | −0.826486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 849408. | 0.614047 | ||||||||
\(287\) | − 44604.0i | − 0.0319646i | ||||||||
\(288\) | − 211968.i | − 0.150588i | ||||||||
\(289\) | 839213. | 0.591055 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11508.0 | −0.00796650 | ||||||||
\(292\) | − 351776.i | − 0.241440i | ||||||||
\(293\) | − 2.64209e6i | − 1.79796i | −0.437993 | − | 0.898978i | \(-0.644311\pi\) | ||||
0.437993 | − | 0.898978i | \(-0.355689\pi\) | |||||||
\(294\) | 69192.0 | 0.0466861 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −353152. | −0.234278 | ||||||||
\(297\) | 518400.i | 0.341015i | ||||||||
\(298\) | − 1.55580e6i | − 1.01488i | ||||||||
\(299\) | −1.73200e6 | −1.12039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 287212. | 0.182720 | ||||||||
\(302\) | 391792.i | 0.247194i | ||||||||
\(303\) | 465732.i | 0.291427i | ||||||||
\(304\) | 701440. | 0.435318 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −630936. | −0.385196 | ||||||||
\(307\) | 1.44756e6i | 0.876577i | 0.898834 | + | 0.438288i | \(0.144415\pi\) | ||||
−0.898834 | + | 0.438288i | \(0.855585\pi\) | |||||||
\(308\) | − 362496.i | − 0.217734i | ||||||||
\(309\) | 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.i | − 0.247002i | ||||||||
\(313\) | 2.29563e6i | 1.32446i | 0.749299 | + | 0.662232i | \(0.230391\pi\) | ||||
−0.749299 | + | 0.662232i | \(0.769609\pi\) | |||||||
\(314\) | 14872.0 | 0.00851227 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 72320.0 | 0.0407418 | ||||||||
\(317\) | − 2.73652e6i | − 1.52950i | −0.644324 | − | 0.764752i | \(-0.722861\pi\) | ||||
0.644324 | − | 0.764752i | \(-0.277139\pi\) | |||||||
\(318\) | − 220176.i | − 0.122096i | ||||||||
\(319\) | −1.13472e6 | −0.624327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6228.00 | −0.00337354 | ||||||||
\(322\) | 739152.i | 0.397278i | ||||||||
\(323\) | − 2.08788e6i | − 1.11352i | ||||||||
\(324\) | −545616. | −0.288752 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −172936. | −0.0901242 | ||||||||
\(327\) | − 1.24158e6i | − 0.642104i | ||||||||
\(328\) | − 24192.0i | − 0.0124162i | ||||||||
\(329\) | 1.54840e6 | 0.788665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.81879e6 | 1.91583 | 0.957913 | − | 0.287059i | \(-0.0926776\pi\) | ||||
0.957913 | + | 0.287059i | \(0.0926776\pi\) | |||||||
\(332\) | 1.74518e6i | 0.868952i | ||||||||
\(333\) | 1.14223e6i | 0.564471i | ||||||||
\(334\) | −746088. | −0.365952 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −181248. | −0.0875841 | ||||||||
\(337\) | 2.21088e6i | 1.06045i | 0.847857 | + | 0.530225i | \(0.177892\pi\) | ||||
−0.847857 | + | 0.530225i | \(0.822108\pi\) | |||||||
\(338\) | 3.40777e6i | 1.62248i | ||||||||
\(339\) | −836316. | −0.395249 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.31866e6 | −0.614109 | ||||||||
\(342\) | − 2.26872e6i | − 1.04886i | ||||||||
\(343\) | 2.32342e6i | 1.06633i | ||||||||
\(344\) | 155776. | 0.0709748 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.49782e6 | −0.672618 | ||||||||
\(347\) | 2.32724e6i | 1.03757i | 0.854905 | + | 0.518785i | \(0.173615\pi\) | ||||
−0.854905 | + | 0.518785i | \(0.826385\pi\) | |||||||
\(348\) | 567360.i | 0.251137i | ||||||||
\(349\) | 311290. | 0.136805 | 0.0684024 | − | 0.997658i | \(-0.478210\pi\) | ||||
0.0684024 | + | 0.997658i | \(0.478210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.98620e6 | −1.29375 | ||||||||
\(352\) | − 196608.i | − 0.0845755i | ||||||||
\(353\) | − 3.08657e6i | − 1.31838i | −0.751977 | − | 0.659189i | \(-0.770900\pi\) | ||||
0.751977 | − | 0.659189i | \(-0.229100\pi\) | |||||||
\(354\) | 839520. | 0.356060 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 615840. | 0.257539 | ||||||||
\(357\) | 539496.i | 0.224036i | ||||||||
\(358\) | 1.08840e6i | 0.448829i | ||||||||
\(359\) | 3.53076e6 | 1.44588 | 0.722940 | − | 0.690911i | \(-0.242790\pi\) | ||||
0.722940 | + | 0.690911i | \(0.242790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.03150e6 | 2.03203 | ||||||||
\(362\) | 301672.i | 0.120994i | ||||||||
\(363\) | − 745122.i | − 0.296798i | ||||||||
\(364\) | 2.08813e6 | 0.826045 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −236112. | −0.0921330 | ||||||||
\(367\) | − 35762.0i | − 0.0138598i | −0.999976 | − | 0.00692989i | \(-0.997794\pi\) | ||||
0.999976 | − | 0.00692989i | \(-0.00220587\pi\) | |||||||
\(368\) | 400896.i | 0.154316i | ||||||||
\(369\) | −78246.0 | −0.0299155 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.08253e6 | 0.408325 | ||||||||
\(372\) | 659328.i | 0.247027i | ||||||||
\(373\) | − 1.71525e6i | − 0.638346i | −0.947696 | − | 0.319173i | \(-0.896595\pi\) | ||||
0.947696 | − | 0.319173i | \(-0.103405\pi\) | |||||||
\(374\) | −585216. | −0.216340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 839808. | 0.306345 | ||||||||
\(377\) | − 6.53646e6i | − 2.36859i | ||||||||
\(378\) | 1.27440e6i | 0.458750i | ||||||||
\(379\) | 3.10174e6 | 1.10919 | 0.554597 | − | 0.832119i | \(-0.312873\pi\) | ||||
0.554597 | + | 0.832119i | \(0.312873\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.79929e6 | 0.635023 | ||||||||
\(382\) | 1.42795e6i | 0.500674i | ||||||||
\(383\) | 5.31949e6i | 1.85299i | 0.376309 | + | 0.926494i | \(0.377193\pi\) | ||||
−0.376309 | + | 0.926494i | \(0.622807\pi\) | |||||||
\(384\) | −98304.0 | −0.0340207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.75478e6 | −0.599451 | ||||||||
\(387\) | − 503838.i | − 0.171007i | ||||||||
\(388\) | − 30688.0i | − 0.0103488i | ||||||||
\(389\) | −1.16145e6 | −0.389158 | −0.194579 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194579 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.19329e6 | 0.394734 | ||||||||
\(392\) | 184512.i | 0.0606470i | ||||||||
\(393\) | 47232.0i | 0.0154261i | ||||||||
\(394\) | 627192. | 0.203545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −635904. | −0.203776 | ||||||||
\(397\) | − 628562.i | − 0.200157i | −0.994980 | − | 0.100079i | \(-0.968091\pi\) | ||||
0.994980 | − | 0.100079i | \(-0.0319095\pi\) | |||||||
\(398\) | − 650080.i | − 0.205712i | ||||||||
\(399\) | −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.i | − 0.249781i | ||||||||
\(403\) | − 7.59601e6i | − 2.32982i | ||||||||
\(404\) | −1.24195e6 | −0.378575 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.78952e6 | −0.839875 | ||||||||
\(407\) | 1.05946e6i | 0.317027i | ||||||||
\(408\) | 292608.i | 0.0870233i | ||||||||
\(409\) | −1.78019e6 | −0.526209 | −0.263104 | − | 0.964767i | \(-0.584746\pi\) | ||||
−0.263104 | + | 0.964767i | \(0.584746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −985428. | −0.287753 | ||||||||
\(412\) | 747424.i | 0.216932i | ||||||||
\(413\) | 4.12764e6i | 1.19077i | ||||||||
\(414\) | 1.29665e6 | 0.371810 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.13254e6 | 0.320865 | ||||||||
\(417\) | 1.69260e6i | 0.476666i | ||||||||
\(418\) | − 2.10432e6i | − 0.589076i | ||||||||
\(419\) | −650580. | −0.181036 | −0.0905181 | − | 0.995895i | \(-0.528852\pi\) | ||||
−0.0905181 | + | 0.995895i | \(0.528852\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.54060e6 | −0.973579 | −0.486790 | − | 0.873519i | \(-0.661832\pi\) | ||||
−0.486790 | + | 0.873519i | \(0.661832\pi\) | |||||||
\(422\) | 726592.i | 0.198614i | ||||||||
\(423\) | − 2.71625e6i | − 0.738107i | ||||||||
\(424\) | 587136. | 0.158608 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.68509e6 | 0.449882 | ||||||||
\(427\) | − 1.16088e6i | − 0.308119i | ||||||||
\(428\) | − 16608.0i | − 0.00438236i | ||||||||
\(429\) | −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.i | 0.178195i | ||||||||
\(433\) | − 1.49241e6i | − 0.382534i | −0.981538 | − | 0.191267i | \(-0.938740\pi\) | ||||
0.981538 | − | 0.191267i | \(-0.0612596\pi\) | |||||||
\(434\) | −3.24170e6 | −0.826129 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.31088e6 | 0.834117 | ||||||||
\(437\) | 4.29084e6i | 1.07483i | ||||||||
\(438\) | 527664.i | 0.131423i | ||||||||
\(439\) | −4.86212e6 | −1.20411 | −0.602053 | − | 0.798456i | \(-0.705650\pi\) | ||||
−0.602053 | + | 0.798456i | \(0.705650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 596781. | 0.146123 | ||||||||
\(442\) | − 3.37109e6i | − 0.820757i | ||||||||
\(443\) | − 1.86155e6i | − 0.450678i | −0.974280 | − | 0.225339i | \(-0.927651\pi\) | ||||
0.974280 | − | 0.225339i | \(-0.0723490\pi\) | |||||||
\(444\) | 529728. | 0.127525 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.15310e6 | −0.274491 | ||||||||
\(447\) | 2.33370e6i | 0.552429i | ||||||||
\(448\) | − 483328.i | − 0.113775i | ||||||||
\(449\) | −3.73719e6 | −0.874841 | −0.437421 | − | 0.899257i | \(-0.644108\pi\) | ||||
−0.437421 | + | 0.899257i | \(0.644108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −72576.0 | −0.0168016 | ||||||||
\(452\) | − 2.23018e6i | − 0.513444i | ||||||||
\(453\) | − 587688.i | − 0.134555i | ||||||||
\(454\) | −4.50209e6 | −1.02512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.05216e6 | −0.236957 | ||||||||
\(457\) | 6.48276e6i | 1.45201i | 0.687690 | + | 0.726005i | \(0.258625\pi\) | ||||
−0.687690 | + | 0.726005i | \(0.741375\pi\) | |||||||
\(458\) | − 1.66324e6i | − 0.370503i | ||||||||
\(459\) | 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.i | 0.118519i | ||||||||
\(463\) | 8.68401e6i | 1.88264i | 0.337513 | + | 0.941321i | \(0.390414\pi\) | ||||
−0.337513 | + | 0.941321i | \(0.609586\pi\) | |||||||
\(464\) | −1.51296e6 | −0.326236 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.08234e6 | 0.657531 | ||||||||
\(467\) | − 6.96412e6i | − 1.47766i | −0.673893 | − | 0.738829i | \(-0.735379\pi\) | ||||
0.673893 | − | 0.738829i | \(-0.264621\pi\) | |||||||
\(468\) | − 3.66307e6i | − 0.773091i | ||||||||
\(469\) | 3.97920e6 | 0.835340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22308.0 | −0.00463349 | ||||||||
\(472\) | 2.23872e6i | 0.462535i | ||||||||
\(473\) | − 467328.i | − 0.0960437i | ||||||||
\(474\) | −108480. | −0.0221771 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.43866e6 | −0.291031 | ||||||||
\(477\) | − 1.89902e6i | − 0.382149i | ||||||||
\(478\) | − 2.38128e6i | − 0.476695i | ||||||||
\(479\) | 5.51052e6 | 1.09737 | 0.548686 | − | 0.836029i | \(-0.315128\pi\) | ||||
0.548686 | + | 0.836029i | \(0.315128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.10291e6 | −1.20275 | ||||||||
\(482\) | − 1.09561e6i | − 0.214802i | ||||||||
\(483\) | − 1.10873e6i | − 0.216251i | ||||||||
\(484\) | 1.98699e6 | 0.385552 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.44282e6 | 0.661187 | ||||||||
\(487\) | − 5.51808e6i | − 1.05430i | −0.849771 | − | 0.527152i | \(-0.823260\pi\) | ||||
0.849771 | − | 0.527152i | \(-0.176740\pi\) | |||||||
\(488\) | − 629632.i | − 0.119684i | ||||||||
\(489\) | 259404. | 0.0490574 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.51277e6 | −0.283184 | −0.141592 | − | 0.989925i | \(-0.545222\pi\) | ||||
−0.141592 | + | 0.989925i | \(0.545222\pi\) | |||||||
\(492\) | 36288.0i | 0.00675850i | ||||||||
\(493\) | 4.50342e6i | 0.834498i | ||||||||
\(494\) | 1.21218e7 | 2.23485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.75821e6 | −0.320897 | ||||||||
\(497\) | 8.28502e6i | 1.50454i | ||||||||
\(498\) | − 2.61778e6i | − 0.472998i | ||||||||
\(499\) | 1.93042e6 | 0.347057 | 0.173528 | − | 0.984829i | \(-0.444483\pi\) | ||||
0.173528 | + | 0.984829i | \(0.444483\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.11913e6 | 0.199199 | ||||||||
\(502\) | − 3.40301e6i | − 0.602703i | ||||||||
\(503\) | 6.73105e6i | 1.18621i | 0.805124 | + | 0.593106i | \(0.202099\pi\) | ||||
−0.805124 | + | 0.593106i | \(0.797901\pi\) | |||||||
\(504\) | −1.56326e6 | −0.274130 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.20269e6 | 0.208822 | ||||||||
\(507\) | − 5.11166e6i | − 0.883165i | ||||||||
\(508\) | 4.79811e6i | 0.824919i | ||||||||
\(509\) | 556650. | 0.0952331 | 0.0476165 | − | 0.998866i | \(-0.484837\pi\) | ||||
0.0476165 | + | 0.998866i | \(0.484837\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.59435e6 | −0.439517 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 7.39800e6i | 1.24114i | ||||||||
\(514\) | −3.30161e6 | −0.551211 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −233664. | −0.0386338 | ||||||||
\(517\) | − 2.51942e6i | − 0.414548i | ||||||||
\(518\) | 2.60450e6i | 0.426481i | ||||||||
\(519\) | 2.24672e6 | 0.366127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.01110e7 | 1.63192 | 0.815962 | − | 0.578106i | \(-0.196208\pi\) | ||||
0.815962 | + | 0.578106i | \(0.196208\pi\) | |||||||
\(522\) | 4.89348e6i | 0.786034i | ||||||||
\(523\) | − 7.03719e6i | − 1.12498i | −0.826804 | − | 0.562491i | \(-0.809843\pi\) | ||||
0.826804 | − | 0.562491i | \(-0.190157\pi\) | |||||||
\(524\) | −125952. | −0.0200390 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.45858e6 | 0.860232 | ||||||||
\(527\) | 5.23342e6i | 0.820840i | ||||||||
\(528\) | 294912.i | 0.0460371i | ||||||||
\(529\) | 3.98399e6 | 0.618983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.24086e6 | 1.11443 | ||||||||
\(532\) | − 5.17312e6i | − 0.792453i | ||||||||
\(533\) | − 418068.i | − 0.0637425i | ||||||||
\(534\) | −923760. | −0.140186 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.15821e6 | 0.324475 | ||||||||
\(537\) | − 1.63260e6i | − 0.244312i | ||||||||
\(538\) | − 453240.i | − 0.0675107i | ||||||||
\(539\) | 553536. | 0.0820680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.23114e6 | −0.621533 | −0.310766 | − | 0.950486i | \(-0.600586\pi\) | ||||
−0.310766 | + | 0.950486i | \(0.600586\pi\) | |||||||
\(542\) | 3.39851e6i | 0.496925i | ||||||||
\(543\) | − 452508.i | − 0.0658608i | ||||||||
\(544\) | −780288. | −0.113047 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.13219e6 | −0.449642 | ||||||||
\(547\) | − 4.44024e6i | − 0.634510i | −0.948340 | − | 0.317255i | \(-0.897239\pi\) | ||||
0.948340 | − | 0.317255i | \(-0.102761\pi\) | |||||||
\(548\) | − 2.62781e6i | − 0.373803i | ||||||||
\(549\) | −2.03647e6 | −0.288367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.61934e7 | −2.27227 | ||||||||
\(552\) | − 601344.i | − 0.0839992i | ||||||||
\(553\) | − 533360.i | − 0.0741665i | ||||||||
\(554\) | −1.75441e6 | −0.242860 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.51360e6 | −0.619207 | ||||||||
\(557\) | 9.01448e6i | 1.23113i | 0.788088 | + | 0.615563i | \(0.211071\pi\) | ||||
−0.788088 | + | 0.615563i | \(0.788929\pi\) | |||||||
\(558\) | 5.68670e6i | 0.773170i | ||||||||
\(559\) | 2.69200e6 | 0.364373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 877824. | 0.117761 | ||||||||
\(562\) | 5.82679e6i | 0.778196i | ||||||||
\(563\) | − 9.81287e6i | − 1.30474i | −0.757899 | − | 0.652372i | \(-0.773774\pi\) | ||||
0.757899 | − | 0.652372i | \(-0.226226\pi\) | |||||||
\(564\) | −1.25971e6 | −0.166753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −481576. | −0.0631864 | ||||||||
\(567\) | 4.02392e6i | 0.525644i | ||||||||
\(568\) | 4.49357e6i | 0.584414i | ||||||||
\(569\) | −1.33152e7 | −1.72412 | −0.862061 | − | 0.506804i | \(-0.830827\pi\) | ||||
−0.862061 | + | 0.506804i | \(0.830827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.95895e6 | 1.27827 | 0.639136 | − | 0.769094i | \(-0.279292\pi\) | ||||
0.639136 | + | 0.769094i | \(0.279292\pi\) | |||||||
\(572\) | − 3.39763e6i | − 0.434196i | ||||||||
\(573\) | − 2.14193e6i | − 0.272533i | ||||||||
\(574\) | −178416. | −0.0226024 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −847872. | −0.106481 | ||||||||
\(577\) | − 4.50372e6i | − 0.563160i | −0.959538 | − | 0.281580i | \(-0.909141\pi\) | ||||
0.959538 | − | 0.281580i | \(-0.0908585\pi\) | |||||||
\(578\) | − 3.35685e6i | − 0.417939i | ||||||||
\(579\) | 2.63216e6 | 0.326300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.28707e7 | 1.58184 | ||||||||
\(582\) | 46032.0i | 0.00563316i | ||||||||
\(583\) | − 1.76141e6i | − 0.214629i | ||||||||
\(584\) | −1.40710e6 | −0.170724 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.05684e7 | −1.27135 | ||||||||
\(587\) | − 625842.i | − 0.0749669i | −0.999297 | − | 0.0374834i | \(-0.988066\pi\) | ||||
0.999297 | − | 0.0374834i | \(-0.0119341\pi\) | |||||||
\(588\) | − 276768.i | − 0.0330121i | ||||||||
\(589\) | −1.88183e7 | −2.23508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −940788. | −0.110796 | ||||||||
\(592\) | 1.41261e6i | 0.165660i | ||||||||
\(593\) | − 2.50385e6i | − 0.292397i | −0.989255 | − | 0.146198i | \(-0.953296\pi\) | ||||
0.989255 | − | 0.146198i | \(-0.0467038\pi\) | |||||||
\(594\) | 2.07360e6 | 0.241134 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.22320e6 | −0.717626 | ||||||||
\(597\) | 975120.i | 0.111975i | ||||||||
\(598\) | 6.92798e6i | 0.792235i | ||||||||
\(599\) | 756480. | 0.0861451 | 0.0430725 | − | 0.999072i | \(-0.486285\pi\) | ||||
0.0430725 | + | 0.999072i | \(0.486285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.38565e7 | −1.56483 | −0.782413 | − | 0.622760i | \(-0.786011\pi\) | ||||
−0.782413 | + | 0.622760i | \(0.786011\pi\) | |||||||
\(602\) | − 1.14885e6i | − 0.129203i | ||||||||
\(603\) | − 6.98045e6i | − 0.781791i | ||||||||
\(604\) | 1.56717e6 | 0.174793 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.86293e6 | 0.206070 | ||||||||
\(607\) | − 1.13772e7i | − 1.25333i | −0.779291 | − | 0.626663i | \(-0.784420\pi\) | ||||
0.779291 | − | 0.626663i | \(-0.215580\pi\) | |||||||
\(608\) | − 2.80576e6i | − 0.307816i | ||||||||
\(609\) | 4.18428e6 | 0.457170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.45129e7 | 1.57272 | ||||||||
\(612\) | 2.52374e6i | 0.272375i | ||||||||
\(613\) | − 7.00161e6i | − 0.752570i | −0.926504 | − | 0.376285i | \(-0.877201\pi\) | ||||
0.926504 | − | 0.376285i | \(-0.122799\pi\) | |||||||
\(614\) | 5.79023e6 | 0.619833 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44998e6 | −0.153961 | ||||||||
\(617\) | − 7.90300e6i | − 0.835755i | −0.908503 | − | 0.417878i | \(-0.862774\pi\) | ||||
0.908503 | − | 0.417878i | \(-0.137226\pi\) | |||||||
\(618\) | − 1.12114e6i | − 0.118083i | ||||||||
\(619\) | −4.02362e6 | −0.422076 | −0.211038 | − | 0.977478i | \(-0.567684\pi\) | ||||
−0.211038 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.22820e6 | −0.439974 | ||||||||
\(622\) | 3.71227e6i | 0.384737i | ||||||||
\(623\) | − 4.54182e6i | − 0.468824i | ||||||||
\(624\) | −1.69882e6 | −0.174657 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.18250e6 | 0.936538 | ||||||||
\(627\) | 3.15648e6i | 0.320652i | ||||||||
\(628\) | − 59488.0i | − 0.00601908i | ||||||||
\(629\) | 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.i | − 0.0288088i | ||||||||
\(633\) | − 1.08989e6i | − 0.108112i | ||||||||
\(634\) | −1.09461e7 | −1.08152 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −880704. | −0.0863351 | ||||||||
\(637\) | 3.18860e6i | 0.311352i | ||||||||
\(638\) | 4.53888e6i | 0.441466i | ||||||||
\(639\) | 1.45339e7 | 1.40809 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.37390e6 | 0.612718 | 0.306359 | − | 0.951916i | \(-0.400889\pi\) | ||||
0.306359 | + | 0.951916i | \(0.400889\pi\) | |||||||
\(642\) | 24912.0i | 0.00238545i | ||||||||
\(643\) | 5.00457e6i | 0.477352i | 0.971099 | + | 0.238676i | \(0.0767134\pi\) | ||||
−0.971099 | + | 0.238676i | \(0.923287\pi\) | |||||||
\(644\) | 2.95661e6 | 0.280918 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.35152e6 | −0.787380 | ||||||||
\(647\) | 8.71928e6i | 0.818879i | 0.912337 | + | 0.409440i | \(0.134276\pi\) | ||||
−0.912337 | + | 0.409440i | \(0.865724\pi\) | |||||||
\(648\) | 2.18246e6i | 0.204178i | ||||||||
\(649\) | 6.71616e6 | 0.625906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.86254e6 | 0.449688 | ||||||||
\(652\) | 691744.i | 0.0637274i | ||||||||
\(653\) | − 1.58477e6i | − 0.145440i | −0.997352 | − | 0.0727201i | \(-0.976832\pi\) | ||||
0.997352 | − | 0.0727201i | \(-0.0231680\pi\) | |||||||
\(654\) | −4.96632e6 | −0.454036 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −96768.0 | −0.00877955 | ||||||||
\(657\) | 4.55110e6i | 0.411342i | ||||||||
\(658\) | − 6.19358e6i | − 0.557670i | ||||||||
\(659\) | −1.26410e7 | −1.13388 | −0.566940 | − | 0.823759i | \(-0.691873\pi\) | ||||
−0.566940 | + | 0.823759i | \(0.691873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.61572e6 | −0.321878 | −0.160939 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160939 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(662\) | − 1.52752e7i | − 1.35469i | ||||||||
\(663\) | 5.05663e6i | 0.446763i | ||||||||
\(664\) | 6.98074e6 | 0.614442 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.56890e6 | 0.399141 | ||||||||
\(667\) | − 9.25506e6i | − 0.805498i | ||||||||
\(668\) | 2.98435e6i | 0.258767i | ||||||||
\(669\) | 1.72964e6 | 0.149414 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.88890e6 | −0.161958 | ||||||||
\(672\) | 724992.i | 0.0619313i | ||||||||
\(673\) | 1.11313e7i | 0.947349i | 0.880700 | + | 0.473675i | \(0.157073\pi\) | ||||
−0.880700 | + | 0.473675i | \(0.842927\pi\) | |||||||
\(674\) | 8.84351e6 | 0.749851 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.36311e7 | 1.14727 | ||||||||
\(677\) | 235518.i | 0.0197493i | 0.999951 | + | 0.00987467i | \(0.00314326\pi\) | ||||
−0.999951 | + | 0.00987467i | \(0.996857\pi\) | |||||||
\(678\) | 3.34526e6i | 0.279483i | ||||||||
\(679\) | −226324. | −0.0188389 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.75313e6 | 0.558004 | ||||||||
\(682\) | 5.27462e6i | 0.434241i | ||||||||
\(683\) | 2.05830e7i | 1.68833i | 0.536084 | + | 0.844164i | \(0.319903\pi\) | ||||
−0.536084 | + | 0.844164i | \(0.680097\pi\) | |||||||
\(684\) | −9.07488e6 | −0.741653 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.29368e6 | 0.754011 | ||||||||
\(687\) | 2.49486e6i | 0.201676i | ||||||||
\(688\) | − 623104.i | − 0.0501868i | ||||||||
\(689\) | 1.01464e7 | 0.814265 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.54825e6 | −0.760727 | −0.380363 | − | 0.924837i | \(-0.624201\pi\) | ||||
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(692\) | 5.99126e6i | 0.475612i | ||||||||
\(693\) | 4.68979e6i | 0.370954i | ||||||||
\(694\) | 9.30895e6 | 0.733672 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.26944e6 | 0.177581 | ||||||||
\(697\) | 288036.i | 0.0224577i | ||||||||
\(698\) | − 1.24516e6i | − 0.0967357i | ||||||||
\(699\) | −4.62352e6 | −0.357915 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.29304e6 | 0.0993843 | 0.0496921 | − | 0.998765i | \(-0.484176\pi\) | ||||
0.0496921 | + | 0.998765i | \(0.484176\pi\) | |||||||
\(702\) | 1.19448e7i | 0.914821i | ||||||||
\(703\) | 1.51193e7i | 1.15384i | ||||||||
\(704\) | −786432. | −0.0598039 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.23463e7 | −0.932234 | ||||||||
\(707\) | 9.15940e6i | 0.689157i | ||||||||
\(708\) | − 3.35808e6i | − 0.251772i | ||||||||
\(709\) | 2.12720e7 | 1.58926 | 0.794628 | − | 0.607097i | \(-0.207666\pi\) | ||||
0.794628 | + | 0.607097i | \(0.207666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −935640. | −0.0694120 | ||||||||
\(712\) | − 2.46336e6i | − 0.182108i | ||||||||
\(713\) | − 1.07553e7i | − 0.792316i | ||||||||
\(714\) | 2.15798e6 | 0.158417 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.35360e6 | 0.317370 | ||||||||
\(717\) | 3.57192e6i | 0.259480i | ||||||||
\(718\) | − 1.41230e7i | − 1.02239i | ||||||||
\(719\) | −8.31732e6 | −0.600014 | −0.300007 | − | 0.953937i | \(-0.596989\pi\) | ||||
−0.300007 | + | 0.953937i | \(0.596989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.51225e6 | 0.394903 | ||||||||
\(722\) | − 2.01260e7i | − 1.43686i | ||||||||
\(723\) | 1.64341e6i | 0.116923i | ||||||||
\(724\) | 1.20669e6 | 0.0855556 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.98049e6 | −0.209868 | ||||||||
\(727\) | 4.36740e6i | 0.306469i | 0.988190 | + | 0.153235i | \(0.0489690\pi\) | ||||
−0.988190 | + | 0.153235i | \(0.951031\pi\) | |||||||
\(728\) | − 8.35251e6i | − 0.584102i | ||||||||
\(729\) | 3.12231e6 | 0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.85471e6 | −0.128375 | ||||||||
\(732\) | 944448.i | 0.0651479i | ||||||||
\(733\) | − 4.05645e6i | − 0.278860i | −0.990232 | − | 0.139430i | \(-0.955473\pi\) | ||||
0.990232 | − | 0.139430i | \(-0.0445271\pi\) | |||||||
\(734\) | −143048. | −0.00980035 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.60358e6 | 0.109118 | ||||||||
\(737\) | − 6.47462e6i | − 0.439082i | ||||||||
\(738\) | 312984.i | 0.0211535i | ||||||||
\(739\) | −768260. | −0.0517484 | −0.0258742 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258742 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.81826e7 | −1.21650 | ||||||||
\(742\) | − 4.33013e6i | − 0.288729i | ||||||||
\(743\) | 6.18781e6i | 0.411211i | 0.978635 | + | 0.205605i | \(0.0659164\pi\) | ||||
−0.978635 | + | 0.205605i | \(0.934084\pi\) | |||||||
\(744\) | 2.63731e6 | 0.174674 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.86102e6 | −0.451379 | ||||||||
\(747\) | − 2.25783e7i | − 1.48044i | ||||||||
\(748\) | 2.34086e6i | 0.152976i | ||||||||
\(749\) | −122484. | −0.00797765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.81698e7 | 1.17557 | 0.587787 | − | 0.809016i | \(-0.299999\pi\) | ||||
0.587787 | + | 0.809016i | \(0.299999\pi\) | |||||||
\(752\) | − 3.35923e6i | − 0.216618i | ||||||||
\(753\) | 5.10451e6i | 0.328070i | ||||||||
\(754\) | −2.61458e7 | −1.67484 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.09760e6 | 0.324385 | ||||||||
\(757\) | − 1.93494e7i | − 1.22724i | −0.789603 | − | 0.613618i | \(-0.789714\pi\) | ||||
0.789603 | − | 0.613618i | \(-0.210286\pi\) | |||||||
\(758\) | − 1.24070e7i | − 0.784318i | ||||||||
\(759\) | −1.80403e6 | −0.113668 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.01992e7 | −1.89031 | −0.945155 | − | 0.326621i | \(-0.894090\pi\) | ||||
−0.945155 | + | 0.326621i | \(0.894090\pi\) | |||||||
\(762\) | − 7.19717e6i | − 0.449029i | ||||||||
\(763\) | − 2.44177e7i | − 1.51843i | ||||||||
\(764\) | 5.71181e6 | 0.354030 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.12779e7 | 1.31026 | ||||||||
\(767\) | 3.86879e7i | 2.37458i | ||||||||
\(768\) | 393216.i | 0.0240563i | ||||||||
\(769\) | −2.15854e7 | −1.31627 | −0.658134 | − | 0.752901i | \(-0.728654\pi\) | ||||
−0.658134 | + | 0.752901i | \(0.728654\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.95241e6 | 0.300041 | ||||||||
\(772\) | 7.01910e6i | 0.423876i | ||||||||
\(773\) | 3.90895e6i | 0.235294i | 0.993055 | + | 0.117647i | \(0.0375351\pi\) | ||||
−0.993055 | + | 0.117647i | \(0.962465\pi\) | |||||||
\(774\) | −2.01535e6 | −0.120920 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −122752. | −0.00731769 | ||||||||
\(777\) | − 3.90674e6i | − 0.232147i | ||||||||
\(778\) | 4.64580e6i | 0.275177i | ||||||||
\(779\) | −1.03572e6 | −0.0611503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34807e7 | 0.790833 | ||||||||
\(782\) | − 4.77317e6i | − 0.279119i | ||||||||
\(783\) | − 1.59570e7i | − 0.930137i | ||||||||
\(784\) | 738048. | 0.0428839 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 188928. | 0.0109079 | ||||||||
\(787\) | 2.65082e7i | 1.52561i | 0.646628 | + | 0.762806i | \(0.276179\pi\) | ||||
−0.646628 | + | 0.762806i | \(0.723821\pi\) | |||||||
\(788\) | − 2.50877e6i | − 0.143928i | ||||||||
\(789\) | −8.18788e6 | −0.468251 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.64475e7 | −0.934674 | ||||||||
\(792\) | 2.54362e6i | 0.144092i | ||||||||
\(793\) | − 1.08808e7i | − 0.614439i | ||||||||
\(794\) | −2.51425e6 | −0.141533 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.60032e6 | −0.145460 | ||||||||
\(797\) | − 1.07940e7i | − 0.601919i | −0.953637 | − | 0.300960i | \(-0.902693\pi\) | ||||
0.953637 | − | 0.300960i | \(-0.0973070\pi\) | |||||||
\(798\) | 7.75968e6i | 0.431357i | ||||||||
\(799\) | −9.99896e6 | −0.554100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.96743e6 | −0.438770 | ||||||||
\(802\) | 1.08973e7i | 0.598249i | ||||||||
\(803\) | 4.22131e6i | 0.231025i | ||||||||
\(804\) | −3.23731e6 | −0.176622 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.03840e7 | −1.64743 | ||||||||
\(807\) | 679860.i | 0.0367482i | ||||||||
\(808\) | 4.96781e6i | 0.267693i | ||||||||
\(809\) | 1.11446e7 | 0.598675 | 0.299338 | − | 0.954147i | \(-0.403234\pi\) | ||||
0.299338 | + | 0.954147i | \(0.403234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14866e7 | −0.613253 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(812\) | 1.11581e7i | 0.593881i | ||||||||
\(813\) | − 5.09777e6i | − 0.270492i | ||||||||
\(814\) | 4.23782e6 | 0.224172 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.17043e6 | 0.0615348 | ||||||||
\(817\) | − 6.66916e6i | − 0.349555i | ||||||||
\(818\) | 7.12076e6i | 0.372086i | ||||||||
\(819\) | −2.70152e7 | −1.40734 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.04347e7 | 1.57584 | 0.787918 | − | 0.615781i | \(-0.211159\pi\) | ||||
0.787918 | + | 0.615781i | \(0.211159\pi\) | |||||||
\(822\) | 3.94171e6i | 0.203472i | ||||||||
\(823\) | 4.09773e6i | 0.210884i | 0.994425 | + | 0.105442i | \(0.0336257\pi\) | ||||
−0.994425 | + | 0.105442i | \(0.966374\pi\) | |||||||
\(824\) | 2.98970e6 | 0.153394 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.65106e7 | 0.841999 | ||||||||
\(827\) | 1.70652e7i | 0.867654i | 0.900996 | + | 0.433827i | \(0.142837\pi\) | ||||
−0.900996 | + | 0.433827i | \(0.857163\pi\) | |||||||
\(828\) | − 5.18659e6i | − 0.262909i | ||||||||
\(829\) | 2.47617e7 | 1.25139 | 0.625697 | − | 0.780066i | \(-0.284815\pi\) | ||||
0.625697 | + | 0.780066i | \(0.284815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.63161e6 | 0.132196 | ||||||||
\(832\) | − 4.53018e6i | − 0.226886i | ||||||||
\(833\) | − 2.19685e6i | − 0.109695i | ||||||||
\(834\) | 6.77040e6 | 0.337054 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.41728e6 | −0.416539 | ||||||||
\(837\) | − 1.85436e7i | − 0.914914i | ||||||||
\(838\) | 2.60232e6i | 0.128012i | ||||||||
\(839\) | −3.16529e7 | −1.55242 | −0.776208 | − | 0.630476i | \(-0.782860\pi\) | ||||
−0.776208 | + | 0.630476i | \(0.782860\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.44170e7 | 0.702884 | ||||||||
\(842\) | 1.41624e7i | 0.688425i | ||||||||
\(843\) | − 8.74019e6i | − 0.423596i | ||||||||
\(844\) | 2.90637e6 | 0.140441 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.08650e7 | −0.521921 | ||||||||
\(847\) | − 1.46541e7i | − 0.701859i | ||||||||
\(848\) | − 2.34854e6i | − 0.112153i | ||||||||
\(849\) | 722364. | 0.0343943 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.64119e6 | −0.409025 | ||||||||
\(852\) | − 6.74035e6i | − 0.318115i | ||||||||
\(853\) | 2.82671e7i | 1.33017i | 0.746765 | + | 0.665087i | \(0.231606\pi\) | ||||
−0.746765 | + | 0.665087i | \(0.768394\pi\) | |||||||
\(854\) | −4.64354e6 | −0.217873 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −66432.0 | −0.00309880 | ||||||||
\(857\) | − 2.60870e7i | − 1.21331i | −0.794966 | − | 0.606655i | \(-0.792511\pi\) | ||||
0.794966 | − | 0.606655i | \(-0.207489\pi\) | |||||||
\(858\) | 5.09645e6i | 0.236347i | ||||||||
\(859\) | 3.38111e7 | 1.56342 | 0.781710 | − | 0.623642i | \(-0.214348\pi\) | ||||
0.781710 | + | 0.623642i | \(0.214348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 267624. | 0.0123032 | ||||||||
\(862\) | 2.19499e6i | 0.100615i | ||||||||
\(863\) | 2.22817e7i | 1.01841i | 0.860646 | + | 0.509204i | \(0.170060\pi\) | ||||
−0.860646 | + | 0.509204i | \(0.829940\pi\) | |||||||
\(864\) | 2.76480e6 | 0.126003 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.96966e6 | −0.270492 | ||||||||
\(867\) | 5.03528e6i | 0.227497i | ||||||||
\(868\) | 1.29668e7i | 0.584162i | ||||||||
\(869\) | −867840. | −0.0389843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72965e7 | 1.66580 | ||||||||
\(872\) | − 1.32435e7i | − 0.589810i | ||||||||
\(873\) | 397026.i | 0.0176313i | ||||||||
\(874\) | 1.71634e7 | 0.760018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.11066e6 | 0.0929303 | ||||||||
\(877\) | 3.46748e7i | 1.52235i | 0.648545 | + | 0.761177i | \(0.275378\pi\) | ||||
−0.648545 | + | 0.761177i | \(0.724622\pi\) | |||||||
\(878\) | 1.94485e7i | 0.851431i | ||||||||
\(879\) | 1.58526e7 | 0.692034 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.42603e7 | 0.618998 | 0.309499 | − | 0.950900i | \(-0.399839\pi\) | ||||
0.309499 | + | 0.950900i | \(0.399839\pi\) | |||||||
\(882\) | − 2.38712e6i | − 0.103325i | ||||||||
\(883\) | − 3.75177e7i | − 1.61933i | −0.586895 | − | 0.809663i | \(-0.699650\pi\) | ||||
0.586895 | − | 0.809663i | \(-0.300350\pi\) | |||||||
\(884\) | −1.34844e7 | −0.580363 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.44622e6 | −0.318677 | ||||||||
\(887\) | − 4.07657e7i | − 1.73975i | −0.493275 | − | 0.869873i | \(-0.664200\pi\) | ||||
0.493275 | − | 0.869873i | \(-0.335800\pi\) | |||||||
\(888\) | − 2.11891e6i | − 0.0901738i | ||||||||
\(889\) | 3.53861e7 | 1.50168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.54739e6 | 0.276296 | ||||||||
\(892\) | 4.61238e6i | 0.194095i | ||||||||
\(893\) | − 3.59543e7i | − 1.50877i | ||||||||
\(894\) | 9.33480e6 | 0.390626 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.93331e6 | −0.0804511 | ||||||||
\(897\) | − 1.03920e7i | − 0.431238i | ||||||||
\(898\) | 1.49488e7i | 0.618606i | ||||||||
\(899\) | 4.05899e7 | 1.67501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.99059e6 | −0.286881 | ||||||||
\(902\) | 290304.i | 0.0118806i | ||||||||
\(903\) | 1.72327e6i | 0.0703290i | ||||||||
\(904\) | −8.92070e6 | −0.363060 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.35075e6 | −0.0951451 | ||||||||
\(907\) | 3.57116e7i | 1.44142i | 0.693235 | + | 0.720712i | \(0.256185\pi\) | ||||
−0.693235 | + | 0.720712i | \(0.743815\pi\) | |||||||
\(908\) | 1.80084e7i | 0.724869i | ||||||||
\(909\) | 1.60678e7 | 0.644979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.11389e7 | −0.843893 | −0.421947 | − | 0.906621i | \(-0.638653\pi\) | ||||
−0.421947 | + | 0.906621i | \(0.638653\pi\) | |||||||
\(912\) | 4.20864e6i | 0.167554i | ||||||||
\(913\) | − 2.09422e7i | − 0.831468i | ||||||||
\(914\) | 2.59310e7 | 1.02673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.65296e6 | −0.261985 | ||||||||
\(917\) | 928896.i | 0.0364791i | ||||||||
\(918\) | − 8.22960e6i | − 0.322309i | ||||||||
\(919\) | −1.85996e7 | −0.726465 | −0.363233 | − | 0.931698i | \(-0.618327\pi\) | ||||
−0.363233 | + | 0.931698i | \(0.618327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.68535e6 | −0.337395 | ||||||||
\(922\) | − 6.03641e6i | − 0.233857i | ||||||||
\(923\) | 7.76545e7i | 3.00028i | ||||||||
\(924\) | 2.17498e6 | 0.0838059 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.47360e7 | 1.33123 | ||||||||
\(927\) | − 9.66980e6i | − 0.369588i | ||||||||
\(928\) | 6.05184e6i | 0.230684i | ||||||||
\(929\) | −4.45110e7 | −1.69211 | −0.846055 | − | 0.533096i | \(-0.821028\pi\) | ||||
−0.846055 | + | 0.533096i | \(0.821028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.89942e6 | 0.298690 | ||||||||
\(932\) | − 1.23294e7i | − 0.464945i | ||||||||
\(933\) | − 5.56841e6i | − 0.209424i | ||||||||
\(934\) | −2.78565e7 | −1.04486 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.46523e7 | −0.546658 | ||||||||
\(937\) | 2.19419e7i | 0.816441i | 0.912883 | + | 0.408221i | \(0.133851\pi\) | ||||
−0.912883 | + | 0.408221i | \(0.866149\pi\) | |||||||
\(938\) | − 1.59168e7i | − 0.590675i | ||||||||
\(939\) | −1.37738e7 | −0.509787 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.77722e6 | −0.286319 | −0.143160 | − | 0.989700i | \(-0.545726\pi\) | ||||
−0.143160 | + | 0.989700i | \(0.545726\pi\) | |||||||
\(942\) | 89232.0i | 0.00327637i | ||||||||
\(943\) | − 591948.i | − 0.0216773i | ||||||||
\(944\) | 8.95488e6 | 0.327062 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.86931e6 | −0.0679132 | ||||||||
\(947\) | − 3.17199e7i | − 1.14936i | −0.818378 | − | 0.574681i | \(-0.805126\pi\) | ||||
0.818378 | − | 0.574681i | \(-0.194874\pi\) | |||||||
\(948\) | 433920.i | 0.0156815i | ||||||||
\(949\) | −2.43165e7 | −0.876468 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.64191e7 | 0.588707 | ||||||||
\(952\) | 5.75462e6i | 0.205790i | ||||||||
\(953\) | − 5.60285e6i | − 0.199838i | −0.994996 | − | 0.0999188i | \(-0.968142\pi\) | ||||
0.994996 | − | 0.0999188i | \(-0.0318583\pi\) | |||||||
\(954\) | −7.59607e6 | −0.270220 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.52512e6 | −0.337074 | ||||||||
\(957\) | − 6.80832e6i | − 0.240304i | ||||||||
\(958\) | − 2.20421e7i | − 0.775959i | ||||||||
\(959\) | −1.93801e7 | −0.680470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.85403e7 | 0.647601 | ||||||||
\(962\) | 2.44116e7i | 0.850470i | ||||||||
\(963\) | 214866.i | 0.00746624i | ||||||||
\(964\) | −4.38243e6 | −0.151888 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.43491e6 | −0.152912 | ||||||||
\(967\) | 2.03532e7i | 0.699949i | 0.936759 | + | 0.349975i | \(0.113810\pi\) | ||||
−0.936759 | + | 0.349975i | \(0.886190\pi\) | |||||||
\(968\) | − 7.94797e6i | − 0.272626i | ||||||||
\(969\) | 1.25273e7 | 0.428595 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.34306e7 | −0.797510 | −0.398755 | − | 0.917057i | \(-0.630558\pi\) | ||||
−0.398755 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(972\) | − 1.37713e7i | − 0.467530i | ||||||||
\(973\) | 3.32878e7i | 1.12721i | ||||||||
\(974\) | −2.20723e7 | −0.745505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.51853e6 | −0.0846296 | ||||||||
\(977\) | 4.30412e7i | 1.44261i | 0.692619 | + | 0.721303i | \(0.256457\pi\) | ||||
−0.692619 | + | 0.721303i | \(0.743543\pi\) | |||||||
\(978\) | − 1.03762e6i | − 0.0346888i | ||||||||
\(979\) | −7.39008e6 | −0.246429 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.28345e7 | −1.42109 | ||||||||
\(982\) | 6.05107e6i | 0.200241i | ||||||||
\(983\) | − 4.75003e7i | − 1.56788i | −0.620837 | − | 0.783940i | \(-0.713207\pi\) | ||||
0.620837 | − | 0.783940i | \(-0.286793\pi\) | |||||||
\(984\) | 145152. | 0.00477898 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.80137e7 | 0.590079 | ||||||||
\(987\) | 9.29038e6i | 0.303557i | ||||||||
\(988\) | − 4.84870e7i | − 1.58028i | ||||||||
\(989\) | 3.81164e6 | 0.123914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.09231e7 | 0.676770 | 0.338385 | − | 0.941008i | \(-0.390119\pi\) | ||||
0.338385 | + | 0.941008i | \(0.390119\pi\) | |||||||
\(992\) | 7.03283e6i | 0.226909i | ||||||||
\(993\) | 2.29128e7i | 0.737402i | ||||||||
\(994\) | 3.31401e7 | 1.06387 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.04711e7 | −0.334460 | ||||||||
\(997\) | − 2.96332e7i | − 0.944148i | −0.881559 | − | 0.472074i | \(-0.843505\pi\) | ||||
0.881559 | − | 0.472074i | \(-0.156495\pi\) | |||||||
\(998\) | − 7.72168e6i | − 0.245406i | ||||||||
\(999\) | −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.b.b.49.1 | 2 | ||
3.2 | odd | 2 | 450.6.c.f.199.2 | 2 | |||
4.3 | odd | 2 | 400.6.c.i.49.1 | 2 | |||
5.2 | odd | 4 | 10.6.a.c.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 50.6.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 50.6.b.b.49.2 | 2 | ||
15.2 | even | 4 | 90.6.a.b.1.1 | 1 | |||
15.8 | even | 4 | 450.6.a.u.1.1 | 1 | |||
15.14 | odd | 2 | 450.6.c.f.199.1 | 2 | |||
20.3 | even | 4 | 400.6.a.i.1.1 | 1 | |||
20.7 | even | 4 | 80.6.a.c.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.i.49.2 | 2 | |||
35.27 | even | 4 | 490.6.a.k.1.1 | 1 | |||
40.27 | even | 4 | 320.6.a.k.1.1 | 1 | |||
40.37 | odd | 4 | 320.6.a.f.1.1 | 1 | |||
60.47 | odd | 4 | 720.6.a.v.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.c.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
50.6.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
50.6.b.b.49.1 | 2 | 1.1 | even | 1 | trivial | ||
50.6.b.b.49.2 | 2 | 5.4 | even | 2 | inner | ||
80.6.a.c.1.1 | 1 | 20.7 | even | 4 | |||
90.6.a.b.1.1 | 1 | 15.2 | even | 4 | |||
320.6.a.f.1.1 | 1 | 40.37 | odd | 4 | |||
320.6.a.k.1.1 | 1 | 40.27 | even | 4 | |||
400.6.a.i.1.1 | 1 | 20.3 | even | 4 | |||
400.6.c.i.49.1 | 2 | 4.3 | odd | 2 | |||
400.6.c.i.49.2 | 2 | 20.19 | odd | 2 | |||
450.6.a.u.1.1 | 1 | 15.8 | even | 4 | |||
450.6.c.f.199.1 | 2 | 15.14 | odd | 2 | |||
450.6.c.f.199.2 | 2 | 3.2 | odd | 2 | |||
490.6.a.k.1.1 | 1 | 35.27 | even | 4 | |||
720.6.a.v.1.1 | 1 | 60.47 | odd | 4 |