Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(199,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.199");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.c (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: | \(72.1727189158\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.199 |
Dual form | 450.6.c.f.199.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 118.000i | − 0.910200i | −0.890440 | − | 0.455100i | \(-0.849603\pi\) | ||||
0.890440 | − | 0.455100i | \(-0.150397\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −192.000 | −0.478431 | −0.239216 | − | 0.970966i | \(-0.576890\pi\) | ||||
−0.239216 | + | 0.970966i | \(0.576890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1106.00i | − 1.81508i | −0.419961 | − | 0.907542i | \(-0.637956\pi\) | ||||
0.419961 | − | 0.907542i | \(-0.362044\pi\) | |||||||
\(14\) | −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 | \(-0.103597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2740.00 | 1.74127 | 0.870636 | − | 0.491928i | \(-0.163708\pi\) | ||||
0.870636 | + | 0.491928i | \(0.163708\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 768.000i | 0.338302i | ||||||||
\(23\) | 1566.00i | 0.617266i | 0.951181 | + | 0.308633i | \(0.0998714\pi\) | ||||
−0.951181 | + | 0.308633i | \(0.900129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4424.00 | −1.28346 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1888.00i | 0.455100i | ||||||||
\(29\) | 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 | \(0.721810\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3048.00 | −0.452187 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5518.00i | − 0.662640i | −0.943519 | − | 0.331320i | \(-0.892506\pi\) | ||||
0.943519 | − | 0.331320i | \(-0.107494\pi\) | |||||||
\(38\) | − 10960.0i | − 1.23127i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 378.000 | 0.0351182 | 0.0175591 | − | 0.999846i | \(-0.494410\pi\) | ||||
0.0175591 | + | 0.999846i | \(0.494410\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2434.00i | 0.200747i | 0.994950 | + | 0.100374i | \(0.0320038\pi\) | ||||
−0.994950 | + | 0.100374i | \(0.967996\pi\) | |||||||
\(44\) | 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 | \(-0.142629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2883.00 | 0.171536 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 17696.0i | 0.907542i | ||||||||
\(53\) | − 9174.00i | − 0.448610i | −0.974519 | − | 0.224305i | \(-0.927989\pi\) | ||||
0.974519 | − | 0.224305i | \(-0.0720112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7552.00 | 0.321804 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 23640.0i | − 0.922736i | ||||||||
\(59\) | −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 | \(0.554137\pi\) | |||||||
\(62\) | 27472.0i | 0.907635i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 33722.0i | 0.917754i | 0.888500 | + | 0.458877i | \(0.151748\pi\) | ||||
−0.888500 | + | 0.458877i | \(0.848252\pi\) | |||||||
\(68\) | 12192.0i | 0.319744i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −70212.0 | −1.65297 | −0.826486 | − | 0.562957i | \(-0.809664\pi\) | ||||
−0.826486 | + | 0.562957i | \(0.809664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 21986.0i | − 0.482880i | −0.970416 | − | 0.241440i | \(-0.922380\pi\) | ||||
0.970416 | − | 0.241440i | \(-0.0776197\pi\) | |||||||
\(74\) | −22072.0 | −0.468557 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43840.0 | −0.870636 | ||||||||
\(77\) | 22656.0i | 0.435468i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4520.00 | −0.0814837 | −0.0407418 | − | 0.999170i | \(-0.512972\pi\) | ||||
−0.0407418 | + | 0.999170i | \(0.512972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 1512.00i | − 0.0248323i | ||||||||
\(83\) | − 109074.i | − 1.73790i | −0.494896 | − | 0.868952i | \(-0.664794\pi\) | ||||
0.494896 | − | 0.868952i | \(-0.335206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9736.00 | 0.141950 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 12288.0i | − 0.169151i | ||||||||
\(89\) | 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 | ||||||||
\(92\) | − 25056.0i | − 0.308633i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −52488.0 | −0.612689 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1918.00i | − 0.0206976i | −0.999946 | − | 0.0103488i | \(-0.996706\pi\) | ||||
0.999946 | − | 0.0103488i | \(-0.00329418\pi\) | |||||||
\(98\) | − 11532.0i | − 0.121294i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −77622.0 | −0.757149 | −0.378575 | − | 0.925571i | \(-0.623586\pi\) | ||||
−0.378575 | + | 0.925571i | \(0.623586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 46714.0i | 0.433864i | 0.976187 | + | 0.216932i | \(0.0696051\pi\) | ||||
−0.976187 | + | 0.216932i | \(0.930395\pi\) | |||||||
\(104\) | 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 | \(0.998605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −206930. | −1.66823 | −0.834117 | − | 0.551587i | \(-0.814023\pi\) | ||||
−0.834117 | + | 0.551587i | \(0.814023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 30208.0i | − 0.227550i | ||||||||
\(113\) | 139386.i | 1.02689i | 0.858123 | + | 0.513444i | \(0.171631\pi\) | ||||
−0.858123 | + | 0.513444i | \(0.828369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −94560.0 | −0.652473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 139920.i | 0.925070i | ||||||||
\(119\) | −89916.0 | −0.582062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124187. | −0.771104 | ||||||||
\(122\) | 39352.0i | 0.239369i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 109888. | 0.641795 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 299882.i | 1.64984i | 0.565252 | + | 0.824919i | \(0.308779\pi\) | ||||
−0.565252 | + | 0.824919i | \(0.691221\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7872.00 | −0.0400781 | −0.0200390 | − | 0.999799i | \(-0.506379\pi\) | ||||
−0.0200390 | + | 0.999799i | \(0.506379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 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 | \(0.878054\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 282100. | 1.23841 | 0.619207 | − | 0.785228i | \(-0.287454\pi\) | ||||
0.619207 | + | 0.785228i | \(0.287454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 280848.i | 1.16883i | ||||||||
\(143\) | 212352.i | 0.868393i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −87944.0 | −0.341448 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 88288.0i | 0.331320i | ||||||||
\(149\) | −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.i | 0.615633i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 90624.0 | 0.307923 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3718.00i | − 0.0120382i | −0.999982 | − | 0.00601908i | \(-0.998084\pi\) | ||||
0.999982 | − | 0.00601908i | \(-0.00191594\pi\) | |||||||
\(158\) | 18080.0i | 0.0576177i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 184788. | 0.561835 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 43234.0i | 0.127455i | 0.997967 | + | 0.0637274i | \(0.0202988\pi\) | ||||
−0.997967 | + | 0.0637274i | \(0.979701\pi\) | |||||||
\(164\) | −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 | \(-0.0833162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −851943. | −2.29453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 38944.0i | − 0.100374i | ||||||||
\(173\) | − 374454.i | − 0.951225i | −0.879655 | − | 0.475612i | \(-0.842226\pi\) | ||||
0.879655 | − | 0.475612i | \(-0.157774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −49152.0 | −0.119608 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 153960.i | − 0.364215i | ||||||||
\(179\) | 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.i | 1.16820i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −100224. | −0.218236 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 146304.i | 0.305951i | ||||||||
\(188\) | 209952.i | 0.433237i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 356988. | 0.708060 | 0.354030 | − | 0.935234i | \(-0.384811\pi\) | ||||
0.354030 | + | 0.935234i | \(0.384811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 438694.i | 0.847751i | 0.905720 | + | 0.423876i | \(0.139331\pi\) | ||||
−0.905720 | + | 0.423876i | \(0.860669\pi\) | |||||||
\(194\) | −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 | \(0.954027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 162520. | 0.290920 | 0.145460 | − | 0.989364i | \(-0.453534\pi\) | ||||
0.145460 | + | 0.989364i | \(0.453534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 310488.i | 0.535385i | ||||||||
\(203\) | − 697380.i | − 1.18776i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 186856. | 0.306788 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4152.00 | 0.00619759 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 810424.i | 1.16832i | ||||||||
\(218\) | 827720.i | 1.17962i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −842772. | −1.16073 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 288274.i | 0.388189i | 0.980983 | + | 0.194095i | \(0.0621769\pi\) | ||||
−0.980983 | + | 0.194095i | \(0.937823\pi\) | |||||||
\(224\) | −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 | \(-0.258100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 415810. | 0.523970 | 0.261985 | − | 0.965072i | \(-0.415623\pi\) | ||||
0.261985 | + | 0.965072i | \(0.415623\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 378240.i | 0.461368i | ||||||||
\(233\) | 770586.i | 0.929889i | 0.885340 | + | 0.464945i | \(0.153926\pi\) | ||||
−0.885340 | + | 0.464945i | \(0.846074\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 559680. | 0.654124 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 359664.i | 0.411580i | ||||||||
\(239\) | −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.i | 0.545253i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 157408. | 0.169259 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 3.03044e6i | − 3.16055i | ||||||||
\(248\) | − 439552.i | − 0.453817i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −850752. | −0.852351 | −0.426176 | − | 0.904640i | \(-0.640139\pi\) | ||||
−0.426176 | + | 0.904640i | \(0.640139\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 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 | \(-0.127444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −651124. | −0.603135 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31488.0i | 0.0283395i | ||||||||
\(263\) | 1.36465e6i | 1.21655i | 0.793726 | + | 0.608276i | \(0.208139\pi\) | ||||
−0.793726 | + | 0.608276i | \(0.791861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.29328e6 | −1.12070 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 539552.i | − 0.458877i | ||||||||
\(269\) | −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.i | − 0.159872i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 656952. | 0.528637 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 438602.i | 0.343456i | 0.985144 | + | 0.171728i | \(0.0549350\pi\) | ||||
−0.985144 | + | 0.171728i | \(0.945065\pi\) | |||||||
\(278\) | − 1.12840e6i | − 0.875691i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.45670e6 | 1.10053 | 0.550267 | − | 0.834989i | \(-0.314526\pi\) | ||||
0.550267 | + | 0.834989i | \(0.314526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 120394.i | 0.0893591i | 0.999001 | + | 0.0446795i | \(0.0142267\pi\) | ||||
−0.999001 | + | 0.0446795i | \(0.985773\pi\) | |||||||
\(284\) | 1.12339e6 | 0.826486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 849408. | 0.614047 | ||||||||
\(287\) | − 44604.0i | − 0.0319646i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 839213. | 0.591055 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 351776.i | 0.241440i | ||||||||
\(293\) | − 2.64209e6i | − 1.79796i | −0.437993 | − | 0.898978i | \(-0.644311\pi\) | ||||
0.437993 | − | 0.898978i | \(-0.355689\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 353152. | 0.234278 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.55580e6i | 1.01488i | ||||||||
\(299\) | 1.73200e6 | 1.12039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 287212. | 0.182720 | ||||||||
\(302\) | 391792.i | 0.247194i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 701440. | 0.435318 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.44756e6i | − 0.876577i | −0.898834 | − | 0.438288i | \(-0.855585\pi\) | ||||
0.898834 | − | 0.438288i | \(-0.144415\pi\) | |||||||
\(308\) | − 362496.i | − 0.217734i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 928068. | 0.544100 | 0.272050 | − | 0.962283i | \(-0.412298\pi\) | ||||
0.272050 | + | 0.962283i | \(0.412298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 2.29563e6i | − 1.32446i | −0.749299 | − | 0.662232i | \(-0.769609\pi\) | ||||
0.749299 | − | 0.662232i | \(-0.230391\pi\) | |||||||
\(314\) | −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 | \(-0.277139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.13472e6 | −0.624327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 739152.i | − 0.397278i | ||||||||
\(323\) | − 2.08788e6i | − 1.11352i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 172936. | 0.0901242 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −746088. | −0.365952 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.21088e6i | − 1.06045i | −0.847857 | − | 0.530225i | \(-0.822108\pi\) | ||||
0.847857 | − | 0.530225i | \(-0.177892\pi\) | |||||||
\(338\) | 3.40777e6i | 1.62248i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.31866e6 | 0.614109 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 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 | \(0.826385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 311290. | 0.136805 | 0.0684024 | − | 0.997658i | \(-0.478210\pi\) | ||||
0.0684024 | + | 0.997658i | \(0.478210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 196608.i | 0.0845755i | ||||||||
\(353\) | − 3.08657e6i | − 1.31838i | −0.751977 | − | 0.659189i | \(-0.770900\pi\) | ||||
0.751977 | − | 0.659189i | \(-0.229100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −615840. | −0.257539 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 1.08840e6i | − 0.448829i | ||||||||
\(359\) | −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.i | 0.120994i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.08813e6 | 0.826045 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35762.0i | 0.0138598i | 0.999976 | + | 0.00692989i | \(0.00220587\pi\) | ||||
−0.999976 | + | 0.00692989i | \(0.997794\pi\) | |||||||
\(368\) | 400896.i | 0.154316i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.08253e6 | −0.408325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.71525e6i | 0.638346i | 0.947696 | + | 0.319173i | \(0.103405\pi\) | ||||
−0.947696 | + | 0.319173i | \(0.896595\pi\) | |||||||
\(374\) | 585216. | 0.216340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 839808. | 0.306345 | ||||||||
\(377\) | − 6.53646e6i | − 2.36859i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.10174e6 | 1.10919 | 0.554597 | − | 0.832119i | \(-0.312873\pi\) | ||||
0.554597 | + | 0.832119i | \(0.312873\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 1.42795e6i | − 0.500674i | ||||||||
\(383\) | 5.31949e6i | 1.85299i | 0.376309 | + | 0.926494i | \(0.377193\pi\) | ||||
−0.376309 | + | 0.926494i | \(0.622807\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.75478e6 | 0.599451 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30688.0i | 0.0103488i | ||||||||
\(389\) | 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.i | 0.0606470i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 627192. | 0.203545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 628562.i | 0.200157i | 0.994980 | + | 0.100079i | \(0.0319095\pi\) | ||||
−0.994980 | + | 0.100079i | \(0.968091\pi\) | |||||||
\(398\) | − 650080.i | − 0.205712i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.72432e6 | 0.846052 | 0.423026 | − | 0.906118i | \(-0.360968\pi\) | ||||
0.423026 | + | 0.906118i | \(0.360968\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.59601e6i | 2.32982i | ||||||||
\(404\) | 1.24195e6 | 0.378575 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.78952e6 | −0.839875 | ||||||||
\(407\) | 1.05946e6i | 0.317027i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.78019e6 | −0.526209 | −0.263104 | − | 0.964767i | \(-0.584746\pi\) | ||||
−0.263104 | + | 0.964767i | \(0.584746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 747424.i | − 0.216932i | ||||||||
\(413\) | 4.12764e6i | 1.19077i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.13254e6 | −0.320865 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.10432e6i | 0.589076i | ||||||||
\(419\) | 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.i | 0.198614i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 587136. | 0.158608 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.16088e6i | 0.308119i | ||||||||
\(428\) | − 16608.0i | − 0.00438236i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 548748. | 0.142292 | 0.0711459 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711459 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.49241e6i | 0.382534i | 0.981538 | + | 0.191267i | \(0.0612596\pi\) | ||||
−0.981538 | + | 0.191267i | \(0.938740\pi\) | |||||||
\(434\) | 3.24170e6 | 0.826129 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.31088e6 | 0.834117 | ||||||||
\(437\) | 4.29084e6i | 1.07483i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.86212e6 | −1.20411 | −0.602053 | − | 0.798456i | \(-0.705650\pi\) | ||||
−0.602053 | + | 0.798456i | \(0.705650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.37109e6i | 0.820757i | ||||||||
\(443\) | − 1.86155e6i | − 0.450678i | −0.974280 | − | 0.225339i | \(-0.927651\pi\) | ||||
0.974280 | − | 0.225339i | \(-0.0723490\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.15310e6 | 0.274491 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 483328.i | 0.113775i | ||||||||
\(449\) | 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 | ||||||||
\(452\) | − 2.23018e6i | − 0.513444i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.50209e6 | −1.02512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 6.48276e6i | − 1.45201i | −0.687690 | − | 0.726005i | \(-0.741375\pi\) | ||||
0.687690 | − | 0.726005i | \(-0.258625\pi\) | |||||||
\(458\) | − 1.66324e6i | − 0.370503i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.50910e6 | −0.330724 | −0.165362 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165362 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.68401e6i | − 1.88264i | −0.337513 | − | 0.941321i | \(-0.609586\pi\) | ||||
0.337513 | − | 0.941321i | \(-0.390414\pi\) | |||||||
\(464\) | 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 | \(-0.264621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.97920e6 | 0.835340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 2.23872e6i | − 0.462535i | ||||||||
\(473\) | − 467328.i | − 0.0960437i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.43866e6 | 0.291031 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.38128e6i | 0.476695i | ||||||||
\(479\) | −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 | ||||||||
\(482\) | − 1.09561e6i | − 0.214802i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.98699e6 | 0.385552 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.51808e6i | 1.05430i | 0.849771 | + | 0.527152i | \(0.176740\pi\) | ||||
−0.849771 | + | 0.527152i | \(0.823260\pi\) | |||||||
\(488\) | − 629632.i | − 0.119684i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51277e6 | 0.283184 | 0.141592 | − | 0.989925i | \(-0.454778\pi\) | ||||
0.141592 | + | 0.989925i | \(0.454778\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 4.50342e6i | − 0.834498i | ||||||||
\(494\) | −1.21218e7 | −2.23485 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.75821e6 | −0.320897 | ||||||||
\(497\) | 8.28502e6i | 1.50454i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.93042e6 | 0.347057 | 0.173528 | − | 0.984829i | \(-0.444483\pi\) | ||||
0.173528 | + | 0.984829i | \(0.444483\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.40301e6i | 0.602703i | ||||||||
\(503\) | 6.73105e6i | 1.18621i | 0.805124 | + | 0.593106i | \(0.202099\pi\) | ||||
−0.805124 | + | 0.593106i | \(0.797901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.20269e6 | −0.208822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 4.79811e6i | − 0.824919i | ||||||||
\(509\) | −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.i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.30161e6 | −0.551211 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.51942e6i | 0.414548i | ||||||||
\(518\) | 2.60450e6i | 0.426481i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.01110e7 | −1.63192 | −0.815962 | − | 0.578106i | \(-0.803792\pi\) | ||||
−0.815962 | + | 0.578106i | \(0.803792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03719e6i | 1.12498i | 0.826804 | + | 0.562491i | \(0.190157\pi\) | ||||
−0.826804 | + | 0.562491i | \(0.809843\pi\) | |||||||
\(524\) | 125952. | 0.0200390 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.45858e6 | 0.860232 | ||||||||
\(527\) | 5.23342e6i | 0.820840i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.98399e6 | 0.618983 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.17312e6i | 0.792453i | ||||||||
\(533\) | − 418068.i | − 0.0637425i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.15821e6 | −0.324475 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −780288. | −0.113047 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.44024e6i | 0.634510i | 0.948340 | + | 0.317255i | \(0.102761\pi\) | ||||
−0.948340 | + | 0.317255i | \(0.897239\pi\) | |||||||
\(548\) | − 2.62781e6i | − 0.373803i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61934e7 | 2.27227 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.788929\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.69200e6 | 0.364373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 5.82679e6i | − 0.778196i | ||||||||
\(563\) | − 9.81287e6i | − 1.30474i | −0.757899 | − | 0.652372i | \(-0.773774\pi\) | ||||
0.757899 | − | 0.652372i | \(-0.226226\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 481576. | 0.0631864 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 4.49357e6i | − 0.584414i | ||||||||
\(569\) | 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 | \(0.279292\pi\) | |||||||
\(572\) | − 3.39763e6i | − 0.434196i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −178416. | −0.0226024 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.50372e6i | 0.563160i | 0.959538 | + | 0.281580i | \(0.0908585\pi\) | ||||
−0.959538 | + | 0.281580i | \(0.909141\pi\) | |||||||
\(578\) | − 3.35685e6i | − 0.417939i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.28707e7 | −1.58184 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 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 | \(-0.0119341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.88183e7 | −2.23508 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 1.41261e6i | − 0.165660i | ||||||||
\(593\) | − 2.50385e6i | − 0.292397i | −0.989255 | − | 0.146198i | \(-0.953296\pi\) | ||||
0.989255 | − | 0.146198i | \(-0.0467038\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.22320e6 | 0.717626 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 6.92798e6i | − 0.792235i | ||||||||
\(599\) | −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 | \(0.786011\pi\) | |||||||
\(602\) | − 1.14885e6i | − 0.129203i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.56717e6 | 0.174793 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.13772e7i | 1.25333i | 0.779291 | + | 0.626663i | \(0.215580\pi\) | ||||
−0.779291 | + | 0.626663i | \(0.784420\pi\) | |||||||
\(608\) | − 2.80576e6i | − 0.307816i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.45129e7 | −1.57272 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.00161e6i | 0.752570i | 0.926504 | + | 0.376285i | \(0.122799\pi\) | ||||
−0.926504 | + | 0.376285i | \(0.877201\pi\) | |||||||
\(614\) | −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 | \(-0.137226\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.02362e6 | −0.422076 | −0.211038 | − | 0.977478i | \(-0.567684\pi\) | ||||
−0.211038 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 3.71227e6i | − 0.384737i | ||||||||
\(623\) | − 4.54182e6i | − 0.468824i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.18250e6 | −0.936538 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.09461e7 | −1.08152 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.18860e6i | − 0.311352i | ||||||||
\(638\) | 4.53888e6i | 0.441466i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.37390e6 | −0.612718 | −0.306359 | − | 0.951916i | \(-0.599111\pi\) | ||||
−0.306359 | + | 0.951916i | \(0.599111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.00457e6i | − 0.477352i | −0.971099 | − | 0.238676i | \(-0.923287\pi\) | ||||
0.971099 | − | 0.238676i | \(-0.0767134\pi\) | |||||||
\(644\) | −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 | \(0.865724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.71616e6 | 0.625906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 691744.i | − 0.0637274i | ||||||||
\(653\) | − 1.58477e6i | − 0.145440i | −0.997352 | − | 0.0727201i | \(-0.976832\pi\) | ||||
0.997352 | − | 0.0727201i | \(-0.0231680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 96768.0 | 0.00877955 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.19358e6i | 0.557670i | ||||||||
\(659\) | 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 | \(0.551452\pi\) | |||||||
\(662\) | − 1.52752e7i | − 1.35469i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.98074e6 | 0.614442 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.25506e6i | 0.805498i | ||||||||
\(668\) | 2.98435e6i | 0.258767i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.88890e6 | 0.161958 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 1.11313e7i | − 0.947349i | −0.880700 | − | 0.473675i | \(-0.842927\pi\) | ||||
0.880700 | − | 0.473675i | \(-0.157073\pi\) | |||||||
\(674\) | −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 | \(0.996857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −226324. | −0.0188389 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 5.27462e6i | − 0.434241i | ||||||||
\(683\) | 2.05830e7i | 1.68833i | 0.536084 | + | 0.844164i | \(0.319903\pi\) | ||||
−0.536084 | + | 0.844164i | \(0.680097\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.29368e6 | −0.754011 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.30895e6 | 0.733672 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 288036.i | − 0.0224577i | ||||||||
\(698\) | − 1.24516e6i | − 0.0967357i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.29304e6 | −0.0993843 | −0.0496921 | − | 0.998765i | \(-0.515824\pi\) | ||||
−0.0496921 | + | 0.998765i | \(0.515824\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.51193e7i | − 1.15384i | ||||||||
\(704\) | 786432. | 0.0598039 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.23463e7 | −0.932234 | ||||||||
\(707\) | 9.15940e6i | 0.689157i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.12720e7 | 1.58926 | 0.794628 | − | 0.607097i | \(-0.207666\pi\) | ||||
0.794628 | + | 0.607097i | \(0.207666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.46336e6i | 0.182108i | ||||||||
\(713\) | − 1.07553e7i | − 0.792316i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.35360e6 | −0.317370 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.41230e7i | 1.02239i | ||||||||
\(719\) | 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 | ||||||||
\(722\) | − 2.01260e7i | − 1.43686i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.20669e6 | 0.0855556 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 4.36740e6i | − 0.306469i | −0.988190 | − | 0.153235i | \(-0.951031\pi\) | ||||
0.988190 | − | 0.153235i | \(-0.0489690\pi\) | |||||||
\(728\) | − 8.35251e6i | − 0.584102i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.85471e6 | 0.128375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.05645e6i | 0.278860i | 0.990232 | + | 0.139430i | \(0.0445271\pi\) | ||||
−0.990232 | + | 0.139430i | \(0.955473\pi\) | |||||||
\(734\) | 143048. | 0.00980035 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.60358e6 | 0.109118 | ||||||||
\(737\) | − 6.47462e6i | − 0.439082i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −768260. | −0.0517484 | −0.0258742 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258742 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.33013e6i | 0.288729i | ||||||||
\(743\) | 6.18781e6i | 0.411211i | 0.978635 | + | 0.205605i | \(0.0659164\pi\) | ||||
−0.978635 | + | 0.205605i | \(0.934084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.86102e6 | 0.451379 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.61458e7 | −1.67484 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.93494e7i | 1.22724i | 0.789603 | + | 0.613618i | \(0.210286\pi\) | ||||
−0.789603 | + | 0.613618i | \(0.789714\pi\) | |||||||
\(758\) | − 1.24070e7i | − 0.784318i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.01992e7 | 1.89031 | 0.945155 | − | 0.326621i | \(-0.105910\pi\) | ||||
0.945155 | + | 0.326621i | \(0.105910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.44177e7i | 1.51843i | ||||||||
\(764\) | −5.71181e6 | −0.354030 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.12779e7 | 1.31026 | ||||||||
\(767\) | 3.86879e7i | 2.37458i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.15854e7 | −1.31627 | −0.658134 | − | 0.752901i | \(-0.728654\pi\) | ||||
−0.658134 | + | 0.752901i | \(0.728654\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 7.01910e6i | − 0.423876i | ||||||||
\(773\) | 3.90895e6i | 0.235294i | 0.993055 | + | 0.117647i | \(0.0375351\pi\) | ||||
−0.993055 | + | 0.117647i | \(0.962465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 122752. | 0.00731769 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 4.64580e6i | − 0.275177i | ||||||||
\(779\) | 1.03572e6 | 0.0611503 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.34807e7 | 0.790833 | ||||||||
\(782\) | − 4.77317e6i | − 0.279119i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 738048. | 0.0428839 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 2.65082e7i | − 1.52561i | −0.646628 | − | 0.762806i | \(-0.723821\pi\) | ||||
0.646628 | − | 0.762806i | \(-0.276179\pi\) | |||||||
\(788\) | − 2.50877e6i | − 0.143928i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.64475e7 | 0.934674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(-0.0973070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.99896e6 | −0.554100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1.08973e7i | − 0.598249i | ||||||||
\(803\) | 4.22131e6i | 0.231025i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.03840e7 | 1.64743 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 4.96781e6i | − 0.267693i | ||||||||
\(809\) | −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 | \(0.599200\pi\) | |||||||
\(812\) | 1.11581e7i | 0.593881i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.23782e6 | 0.224172 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.66916e6i | 0.349555i | ||||||||
\(818\) | 7.12076e6i | 0.372086i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.04347e7 | −1.57584 | −0.787918 | − | 0.615781i | \(-0.788841\pi\) | ||||
−0.787918 | + | 0.615781i | \(0.788841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 4.09773e6i | − 0.210884i | −0.994425 | − | 0.105442i | \(-0.966374\pi\) | ||||
0.994425 | − | 0.105442i | \(-0.0336257\pi\) | |||||||
\(824\) | −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 | \(0.857163\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.47617e7 | 1.25139 | 0.625697 | − | 0.780066i | \(-0.284815\pi\) | ||||
0.625697 | + | 0.780066i | \(0.284815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.53018e6i | 0.226886i | ||||||||
\(833\) | − 2.19685e6i | − 0.109695i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.41728e6 | 0.416539 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 2.60232e6i | − 0.128012i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 1.41624e7i | 0.688425i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.90637e6 | 0.140441 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.46541e7i | 0.701859i | ||||||||
\(848\) | − 2.34854e6i | − 0.112153i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.64119e6 | 0.409025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.82671e7i | − 1.33017i | −0.746765 | − | 0.665087i | \(-0.768394\pi\) | ||||
0.746765 | − | 0.665087i | \(-0.231606\pi\) | |||||||
\(854\) | 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 | \(-0.207489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.38111e7 | 1.56342 | 0.781710 | − | 0.623642i | \(-0.214348\pi\) | ||||
0.781710 | + | 0.623642i | \(0.214348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 2.19499e6i | − 0.100615i | ||||||||
\(863\) | 2.22817e7i | 1.01841i | 0.860646 | + | 0.509204i | \(0.170060\pi\) | ||||
−0.860646 | + | 0.509204i | \(0.829940\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.96966e6 | 0.270492 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1.29668e7i | − 0.584162i | ||||||||
\(869\) | 867840. | 0.0389843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.72965e7 | 1.66580 | ||||||||
\(872\) | − 1.32435e7i | − 0.589810i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.71634e7 | 0.760018 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.46748e7i | − 1.52235i | −0.648545 | − | 0.761177i | \(-0.724622\pi\) | ||||
0.648545 | − | 0.761177i | \(-0.275378\pi\) | |||||||
\(878\) | 1.94485e7i | 0.851431i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.42603e7 | −0.618998 | −0.309499 | − | 0.950900i | \(-0.600161\pi\) | ||||
−0.309499 | + | 0.950900i | \(0.600161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.75177e7i | 1.61933i | 0.586895 | + | 0.809663i | \(0.300350\pi\) | ||||
−0.586895 | + | 0.809663i | \(0.699650\pi\) | |||||||
\(884\) | 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 | \(-0.335800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.53861e7 | 1.50168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 4.61238e6i | − 0.194095i | ||||||||
\(893\) | − 3.59543e7i | − 1.50877i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.93331e6 | 0.0804511 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 1.49488e7i | − 0.618606i | ||||||||
\(899\) | −4.05899e7 | −1.67501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.99059e6 | −0.286881 | ||||||||
\(902\) | 290304.i | 0.0118806i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.92070e6 | −0.363060 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 3.57116e7i | − 1.44142i | −0.693235 | − | 0.720712i | \(-0.743815\pi\) | ||||
0.693235 | − | 0.720712i | \(-0.256185\pi\) | |||||||
\(908\) | 1.80084e7i | 0.724869i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.11389e7 | 0.843893 | 0.421947 | − | 0.906621i | \(-0.361347\pi\) | ||||
0.421947 | + | 0.906621i | \(0.361347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09422e7i | 0.831468i | ||||||||
\(914\) | −2.59310e7 | −1.02673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.65296e6 | −0.261985 | ||||||||
\(917\) | 928896.i | 0.0364791i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.85996e7 | −0.726465 | −0.363233 | − | 0.931698i | \(-0.618327\pi\) | ||||
−0.363233 | + | 0.931698i | \(0.618327\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.03641e6i | 0.233857i | ||||||||
\(923\) | 7.76545e7i | 3.00028i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.47360e7 | −1.33123 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 6.05184e6i | − 0.230684i | ||||||||
\(929\) | 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 | ||||||||
\(932\) | − 1.23294e7i | − 0.464945i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.78565e7 | −1.04486 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.19419e7i | − 0.816441i | −0.912883 | − | 0.408221i | \(-0.866149\pi\) | ||||
0.912883 | − | 0.408221i | \(-0.133851\pi\) | |||||||
\(938\) | − 1.59168e7i | − 0.590675i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.77722e6 | 0.286319 | 0.143160 | − | 0.989700i | \(-0.454274\pi\) | ||||
0.143160 | + | 0.989700i | \(0.454274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(-0.194874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.43165e7 | −0.876468 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 5.75462e6i | − 0.205790i | ||||||||
\(953\) | − 5.60285e6i | − 0.199838i | −0.994996 | − | 0.0999188i | \(-0.968142\pi\) | ||||
0.994996 | − | 0.0999188i | \(-0.0318583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.52512e6 | 0.337074 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.20421e7i | 0.775959i | ||||||||
\(959\) | 1.93801e7 | 0.680470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.85403e7 | 0.647601 | ||||||||
\(962\) | 2.44116e7i | 0.850470i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.38243e6 | −0.151888 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.03532e7i | − 0.699949i | −0.936759 | − | 0.349975i | \(-0.886190\pi\) | ||||
0.936759 | − | 0.349975i | \(-0.113810\pi\) | |||||||
\(968\) | − 7.94797e6i | − 0.272626i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.34306e7 | 0.797510 | 0.398755 | − | 0.917057i | \(-0.369442\pi\) | ||||
0.398755 | + | 0.917057i | \(0.369442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 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 | \(0.743543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.39008e6 | −0.246429 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 6.05107e6i | − 0.200241i | ||||||||
\(983\) | − 4.75003e7i | − 1.56788i | −0.620837 | − | 0.783940i | \(-0.713207\pi\) | ||||
0.620837 | − | 0.783940i | \(-0.286793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.80137e7 | −0.590079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.31401e7 | 1.06387 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.96332e7i | 0.944148i | 0.881559 | + | 0.472074i | \(0.156495\pi\) | ||||
−0.881559 | + | 0.472074i | \(0.843505\pi\) | |||||||
\(998\) | − 7.72168e6i | − 0.245406i | ||||||||
\(999\) | 0 | 0 |
(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 | 450.6.c.f.199.1 | 2 | ||
3.2 | odd | 2 | 50.6.b.b.49.2 | 2 | |||
5.2 | odd | 4 | 450.6.a.u.1.1 | 1 | |||
5.3 | odd | 4 | 90.6.a.b.1.1 | 1 | |||
5.4 | even | 2 | inner | 450.6.c.f.199.2 | 2 | ||
12.11 | even | 2 | 400.6.c.i.49.2 | 2 | |||
15.2 | even | 4 | 50.6.a.b.1.1 | 1 | |||
15.8 | even | 4 | 10.6.a.c.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 50.6.b.b.49.1 | 2 | |||
20.3 | even | 4 | 720.6.a.v.1.1 | 1 | |||
60.23 | odd | 4 | 80.6.a.c.1.1 | 1 | |||
60.47 | odd | 4 | 400.6.a.i.1.1 | 1 | |||
60.59 | even | 2 | 400.6.c.i.49.1 | 2 | |||
105.83 | odd | 4 | 490.6.a.k.1.1 | 1 | |||
120.53 | even | 4 | 320.6.a.f.1.1 | 1 | |||
120.83 | odd | 4 | 320.6.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.c.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
50.6.a.b.1.1 | 1 | 15.2 | even | 4 | |||
50.6.b.b.49.1 | 2 | 15.14 | odd | 2 | |||
50.6.b.b.49.2 | 2 | 3.2 | odd | 2 | |||
80.6.a.c.1.1 | 1 | 60.23 | odd | 4 | |||
90.6.a.b.1.1 | 1 | 5.3 | odd | 4 | |||
320.6.a.f.1.1 | 1 | 120.53 | even | 4 | |||
320.6.a.k.1.1 | 1 | 120.83 | odd | 4 | |||
400.6.a.i.1.1 | 1 | 60.47 | odd | 4 | |||
400.6.c.i.49.1 | 2 | 60.59 | even | 2 | |||
400.6.c.i.49.2 | 2 | 12.11 | even | 2 | |||
450.6.a.u.1.1 | 1 | 5.2 | odd | 4 | |||
450.6.c.f.199.1 | 2 | 1.1 | even | 1 | trivial | ||
450.6.c.f.199.2 | 2 | 5.4 | even | 2 | inner | ||
490.6.a.k.1.1 | 1 | 105.83 | odd | 4 | |||
720.6.a.v.1.1 | 1 | 20.3 | even | 4 |