Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(63,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.63");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.d (of order \(2\), degree \(1\), 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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 63.1 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.63 |
Dual form | 128.5.d.c.63.2 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.79796 | −1.08866 | −0.544331 | − | 0.838870i | \(-0.683216\pi\) | ||||
−0.544331 | + | 0.838870i | \(0.683216\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 8.00000i | − 0.320000i | −0.987117 | − | 0.160000i | \(-0.948851\pi\) | ||||
0.987117 | − | 0.160000i | \(-0.0511494\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 78.3837i | 1.59967i | 0.600222 | + | 0.799833i | \(0.295079\pi\) | ||||
−0.600222 | + | 0.799833i | \(0.704921\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.0000 | 0.185185 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 107.778 | 0.890724 | 0.445362 | − | 0.895351i | \(-0.353075\pi\) | ||||
0.445362 | + | 0.895351i | \(0.353075\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 216.000i | − 1.27811i | −0.769162 | − | 0.639053i | \(-0.779326\pi\) | ||||
0.769162 | − | 0.639053i | \(-0.220674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 78.3837i | 0.348372i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −162.000 | −0.560554 | −0.280277 | − | 0.959919i | \(-0.590426\pi\) | ||||
−0.280277 | + | 0.959919i | \(0.590426\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −440.908 | −1.22135 | −0.610676 | − | 0.791880i | \(-0.709102\pi\) | ||||
−0.610676 | + | 0.791880i | \(0.709102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 768.000i | − 1.74150i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 705.453i | − 1.33356i | −0.745255 | − | 0.666780i | \(-0.767672\pi\) | ||||
0.745255 | − | 0.666780i | \(-0.232328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 561.000 | 0.897600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 646.665 | 0.887058 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1304.00i | − 1.55054i | −0.631633 | − | 0.775268i | \(-0.717615\pi\) | ||||
0.631633 | − | 0.775268i | \(-0.282385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 627.069i | − 0.652518i | −0.945280 | − | 0.326259i | \(-0.894212\pi\) | ||||
0.945280 | − | 0.326259i | \(-0.105788\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1056.00 | −0.969697 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 627.069 | 0.511893 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1512.00i | − 1.10446i | −0.833693 | − | 0.552228i | \(-0.813778\pi\) | ||||
0.833693 | − | 0.552228i | \(-0.186222\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2116.36i | 1.39143i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1890.00 | 1.12433 | 0.562165 | − | 0.827025i | \(-0.309968\pi\) | ||||
0.562165 | + | 0.827025i | \(0.309968\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2909.99 | −1.57382 | −0.786910 | − | 0.617068i | \(-0.788321\pi\) | ||||
−0.786910 | + | 0.617068i | \(0.788321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 120.000i | − 0.0592593i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1410.91i | 0.638708i | 0.947635 | + | 0.319354i | \(0.103466\pi\) | ||||
−0.947635 | + | 0.319354i | \(0.896534\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3743.00 | −1.55893 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1587.27 | 0.610253 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1976.00i | 0.703453i | 0.936103 | + | 0.351727i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351727i | \(0.885595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 862.220i | − 0.285032i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4320.00 | 1.32964 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2263.33 | 0.650195 | 0.325097 | − | 0.945681i | \(-0.394603\pi\) | ||||
0.325097 | + | 0.945681i | \(0.394603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2376.00i | 0.638538i | 0.947664 | + | 0.319269i | \(0.103437\pi\) | ||||
−0.947664 | + | 0.319269i | \(0.896563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1175.76i | 0.296235i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1728.00 | −0.408994 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1675.45 | 0.373235 | 0.186617 | − | 0.982433i | \(-0.440248\pi\) | ||||
0.186617 | + | 0.982433i | \(0.440248\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6912.00i | 1.45180i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 7759.98i | − 1.53937i | −0.638422 | − | 0.769687i | \(-0.720412\pi\) | ||||
0.638422 | − | 0.769687i | \(-0.279588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2750.00 | 0.516044 | 0.258022 | − | 0.966139i | \(-0.416929\pi\) | ||||
0.258022 | + | 0.966139i | \(0.416929\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5496.65 | −0.977183 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8448.00i | 1.42486i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 7995.13i | − 1.28107i | −0.767931 | − | 0.640533i | \(-0.778713\pi\) | ||||
0.767931 | − | 0.640533i | \(-0.221287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7551.00 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9337.45 | −1.35542 | −0.677708 | − | 0.735332i | \(-0.737026\pi\) | ||||
−0.677708 | + | 0.735332i | \(0.737026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1296.00i | 0.179377i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12776.5i | 1.68801i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2430.00 | 0.306779 | 0.153390 | − | 0.988166i | \(-0.450981\pi\) | ||||
0.153390 | + | 0.988166i | \(0.450981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16930.9 | 2.04454 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6144.00i | 0.710371i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3527.27i | 0.390833i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7454.00 | 0.792220 | 0.396110 | − | 0.918203i | \(-0.370360\pi\) | ||||
0.396110 | + | 0.918203i | \(0.370360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1616.66 | 0.164949 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1496.00i | 0.146652i | 0.997308 | + | 0.0733261i | \(0.0233614\pi\) | ||||
−0.997308 | + | 0.0733261i | \(0.976639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2586.66i | 0.243818i | 0.992541 | + | 0.121909i | \(0.0389015\pi\) | ||||
−0.992541 | + | 0.121909i | \(0.961098\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6144.00 | −0.557279 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1067.98 | −0.0932813 | −0.0466406 | − | 0.998912i | \(-0.514852\pi\) | ||||
−0.0466406 | + | 0.998912i | \(0.514852\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 14904.0i | − 1.25444i | −0.778842 | − | 0.627220i | \(-0.784193\pi\) | ||||
0.778842 | − | 0.627220i | \(-0.215807\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14814.5i | 1.20238i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −702.000 | −0.0549769 | −0.0274884 | − | 0.999622i | \(-0.508751\pi\) | ||||
−0.0274884 | + | 0.999622i | \(0.508751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5643.62 | −0.426739 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 3240.00i | − 0.236686i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 12698.2i | − 0.896699i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3025.00 | −0.206612 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18518.1 | −1.22402 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9488.00i | − 0.607232i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3448.88i | − 0.213831i | −0.994268 | − | 0.106916i | \(-0.965903\pi\) | ||||
0.994268 | − | 0.106916i | \(-0.0340974\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28512.0 | 1.71336 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9592.20 | 0.558954 | 0.279477 | − | 0.960152i | \(-0.409839\pi\) | ||||
0.279477 | + | 0.960152i | \(0.409839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 34560.0i | − 1.95376i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5173.32i | − 0.283859i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −32670.0 | −1.74064 | −0.870318 | − | 0.492490i | \(-0.836087\pi\) | ||||
−0.870318 | + | 0.492490i | \(0.836087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1322.72 | 0.0684605 | 0.0342302 | − | 0.999414i | \(-0.489102\pi\) | ||||
0.0342302 | + | 0.999414i | \(0.489102\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 13824.0i | − 0.695337i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 23280.0i | − 1.13844i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10432.0 | −0.496171 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36673.8 | 1.69715 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 872.000i | − 0.0392775i | −0.999807 | − | 0.0196388i | \(-0.993748\pi\) | ||||
0.999807 | − | 0.0196388i | \(-0.00625161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 9484.42i | − 0.415965i | −0.978133 | − | 0.207983i | \(-0.933310\pi\) | ||||
0.978133 | − | 0.207983i | \(-0.0666898\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2430.00 | −0.103806 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5016.55 | −0.208806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 28728.0i | − 1.16548i | −0.812657 | − | 0.582742i | \(-0.801980\pi\) | ||||
0.812657 | − | 0.582742i | \(-0.198020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 19360.8i | − 0.765823i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 55296.0 | 2.13325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −31128.1 | −1.17160 | −0.585798 | − | 0.810457i | \(-0.699219\pi\) | ||||
−0.585798 | + | 0.810457i | \(0.699219\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8448.00i | 0.310303i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 54319.9i | 1.94772i | 0.227155 | + | 0.973859i | \(0.427058\pi\) | ||||
−0.227155 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18095.0 | −0.633556 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6613.62 | −0.226176 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25256.0i | 0.843864i | 0.906628 | + | 0.421932i | \(0.138648\pi\) | ||||
−0.906628 | + | 0.421932i | \(0.861352\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43973.2i | 1.43586i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22176.0 | −0.707843 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8945.54 | −0.279190 | −0.139595 | − | 0.990209i | \(-0.544580\pi\) | ||||
−0.139595 | + | 0.990209i | \(0.544580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 36072.0i | − 1.10107i | −0.834814 | − | 0.550533i | \(-0.814425\pi\) | ||||
0.834814 | − | 0.550533i | \(-0.185575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 23280.0i | − 0.695152i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12096.0 | −0.353426 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17460.0 | −0.499298 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 50688.0i | 1.41900i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 31039.9i | 0.850852i | 0.904993 | + | 0.425426i | \(0.139876\pi\) | ||||
−0.904993 | + | 0.425426i | \(0.860124\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 41374.0 | 1.11074 | 0.555371 | − | 0.831603i | \(-0.312576\pi\) | ||||
0.555371 | + | 0.831603i | \(0.312576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16930.9 | 0.445256 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 67640.0i | 1.74289i | 0.490489 | + | 0.871447i | \(0.336818\pi\) | ||||
−0.490489 | + | 0.871447i | \(0.663182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 25004.4i | − 0.631408i | −0.948858 | − | 0.315704i | \(-0.897759\pi\) | ||||
0.948858 | − | 0.315704i | \(-0.102241\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16416.0 | −0.406327 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 102212. | 2.48034 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 15120.0i | − 0.359786i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 10581.8i | − 0.246955i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −47520.0 | −1.08789 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26189.9 | −0.588260 | −0.294130 | − | 0.955765i | \(-0.595030\pi\) | ||||
−0.294130 | + | 0.955765i | \(0.595030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 76032.0i | 1.67586i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23280.0i | 0.503623i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 49152.0 | 1.04381 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26944.4 | −0.561798 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34992.0i | 0.716447i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20693.3i | − 0.416121i | −0.978116 | − | 0.208061i | \(-0.933285\pi\) | ||||
0.978116 | − | 0.208061i | \(-0.0667151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8415.00 | 0.166222 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −77923.2 | −1.51222 | −0.756110 | − | 0.654445i | \(-0.772902\pi\) | ||||
−0.756110 | + | 0.654445i | \(0.772902\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 14472.0i | − 0.275967i | −0.990435 | − | 0.137984i | \(-0.955938\pi\) | ||||
0.990435 | − | 0.137984i | \(-0.0440621\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 82773.2i | − 1.55119i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2754.00 | −0.0507285 | −0.0253643 | − | 0.999678i | \(-0.508075\pi\) | ||||
−0.0253643 | + | 0.999678i | \(0.508075\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11287.2 | 0.204387 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 78336.0i | 1.39465i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 91708.9i | − 1.60552i | −0.596302 | − | 0.802760i | \(-0.703364\pi\) | ||||
0.596302 | − | 0.802760i | \(-0.296636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −97570.0 | −1.67990 | −0.839948 | − | 0.542667i | \(-0.817414\pi\) | ||||
−0.839948 | + | 0.542667i | \(0.817414\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21604.5 | 0.365874 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29944.0i | 0.498859i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 95236.2i | 1.56102i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 91488.0 | 1.47559 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −67811.7 | −1.07636 | −0.538179 | − | 0.842830i | \(-0.680888\pi\) | ||||
−0.538179 | + | 0.842830i | \(0.680888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 76032.0i | − 1.18783i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 12698.2i | − 0.195281i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 80514.0 | 1.21900 | 0.609502 | − | 0.792785i | \(-0.291369\pi\) | ||||
0.609502 | + | 0.792785i | \(0.291369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 118516. | 1.76676 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 19560.0i | − 0.287136i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14814.5i | 0.214179i | 0.994249 | + | 0.107089i | \(0.0341531\pi\) | ||||
−0.994249 | + | 0.107089i | \(0.965847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15808.0 | 0.225105 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23809.0 | −0.333979 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 44872.0i | 0.620113i | 0.950718 | + | 0.310057i | \(0.100348\pi\) | ||||
−0.950718 | + | 0.310057i | \(0.899652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 91395.4i | 1.24447i | 0.782829 | + | 0.622237i | \(0.213776\pi\) | ||||
−0.782829 | + | 0.622237i | \(0.786224\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −165888. | −2.22582 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60463.2 | 0.799513 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 90504.0i | − 1.17953i | −0.807576 | − | 0.589764i | \(-0.799221\pi\) | ||||
0.807576 | − | 0.589764i | \(-0.200779\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 9406.04i | − 0.120837i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23166.0 | 0.293385 | 0.146693 | − | 0.989182i | \(-0.453137\pi\) | ||||
0.146693 | + | 0.989182i | \(0.453137\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 70809.8 | 0.884140 | 0.442070 | − | 0.896981i | \(-0.354244\pi\) | ||||
0.442070 | + | 0.896981i | \(0.354244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 34560.0i | − 0.425485i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 148145.i | 1.79855i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −57277.0 | −0.685780 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −73034.0 | −0.862460 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 37768.0i | − 0.439935i | −0.975507 | − | 0.219968i | \(-0.929405\pi\) | ||||
0.975507 | − | 0.219968i | \(-0.0705952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 18106.6i | − 0.208062i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 69696.0 | 0.790123 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −152378. | −1.70443 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 228096.i | − 2.51759i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 14657.7i | − 0.159655i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19008.0 | 0.204332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −38535.4 | −0.408868 | −0.204434 | − | 0.978880i | \(-0.565535\pi\) | ||||
−0.204434 | + | 0.978880i | \(0.565535\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 25344.0i | − 0.265435i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 85359.8i | − 0.882537i | −0.897375 | − | 0.441268i | \(-0.854529\pi\) | ||||
0.897375 | − | 0.441268i | \(-0.145471\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 93602.0 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9406.04 | 0.0947951 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 49192.0i | 0.489526i | 0.969583 | + | 0.244763i | \(0.0787102\pi\) | ||||
−0.969583 | + | 0.244763i | \(0.921290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 140542.i | − 1.38110i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10464.0 | 0.101552 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 71427.1 | 0.684633 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 121176.i | − 1.14723i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 146029.i | 1.36566i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −110592. | −1.02172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16490.0 | 0.150509 | 0.0752547 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752547 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 22680.0i | − 0.204529i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 13403.6i | − 0.119435i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −93758.0 | −0.825560 | −0.412780 | − | 0.910831i | \(-0.635442\pi\) | ||||
−0.412780 | + | 0.910831i | \(0.635442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6878.17 | 0.0598513 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 67584.0i | − 0.581213i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 105191.i | − 0.894108i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 55296.0 | 0.464575 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 220405. | 1.83047 | 0.915235 | − | 0.402920i | \(-0.132005\pi\) | ||||
0.915235 | + | 0.402920i | \(0.132005\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 48600.0i | − 0.399012i | −0.979897 | − | 0.199506i | \(-0.936066\pi\) | ||||
0.979897 | − | 0.199506i | \(-0.0639337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 139680.i | − 1.13375i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 108162. | 0.868011 | 0.434006 | − | 0.900910i | \(-0.357100\pi\) | ||||
0.434006 | + | 0.900910i | \(0.357100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −62079.9 | −0.492600 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 124416.i | 0.976202i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 50087.2i | − 0.388631i | −0.980939 | − | 0.194316i | \(-0.937751\pi\) | ||||
0.980939 | − | 0.194316i | \(-0.0622486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 64079.0 | 0.491701 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29638.8 | 0.224930 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 22000.0i | − 0.165134i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 61296.0i | − 0.455093i | −0.973767 | − | 0.227547i | \(-0.926930\pi\) | ||||
0.973767 | − | 0.227547i | \(-0.0730704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28350.0 | 0.208209 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −154886. | −1.12529 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 54648.0i | 0.392787i | 0.980525 | + | 0.196393i | \(0.0629229\pi\) | ||||
−0.980525 | + | 0.196393i | \(0.937077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 92963.0i | 0.661070i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −281664. | −1.98175 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −103790. | −0.722564 | −0.361282 | − | 0.932457i | \(-0.617661\pi\) | ||||
−0.361282 | + | 0.932457i | \(0.617661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 33792.0i | 0.232790i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 124160.i | 0.846415i | 0.906033 | + | 0.423207i | \(0.139096\pi\) | ||||
−0.906033 | + | 0.423207i | \(0.860904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 67584.0 | 0.455955 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −43649.9 | −0.291448 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 129112.i | 0.853233i | 0.904433 | + | 0.426616i | \(0.140295\pi\) | ||||
−0.904433 | + | 0.426616i | \(0.859705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 114283.i | 0.747532i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −93984.0 | −0.608512 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −63961.1 | −0.409941 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 232200.i | 1.47327i | 0.676293 | + | 0.736633i | \(0.263585\pi\) | ||||
−0.676293 | + | 0.736633i | \(0.736415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 338617.i | 2.12698i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 151902. | 0.944658 | 0.472329 | − | 0.881422i | \(-0.343413\pi\) | ||||
0.472329 | + | 0.881422i | \(0.343413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −135447. | −0.833987 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 60408.0i | 0.368285i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 162960.i | − 0.983765i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28450.0 | 0.170073 | 0.0850366 | − | 0.996378i | \(-0.472899\pi\) | ||||
0.0850366 | + | 0.996378i | \(0.472899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 320099. | 1.89496 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 177408.i | 1.04010i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 74699.6i | 0.433733i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12960.0 | −0.0745303 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 291382. | 1.65972 | 0.829858 | − | 0.557974i | \(-0.188421\pi\) | ||||
0.829858 | + | 0.557974i | \(0.188421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 119880.i | − 0.676367i | −0.941080 | − | 0.338184i | \(-0.890188\pi\) | ||||
0.941080 | − | 0.338184i | \(-0.109812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21163.6i | 0.118279i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −90882.0 | −0.503153 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −186240. | −1.02145 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 228096.i | 1.23938i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 170720.i | − 0.919028i | −0.888170 | − | 0.459514i | \(-0.848024\pi\) | ||||
0.888170 | − | 0.459514i | \(-0.151976\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 215518. | 1.14950 | 0.574748 | − | 0.818330i | \(-0.305100\pi\) | ||||
0.574748 | + | 0.818330i | \(0.305100\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 102212. | 0.540163 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 311040.i | 1.62875i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 75169.9i | 0.390045i | 0.980799 | + | 0.195023i | \(0.0624781\pi\) | ||||
−0.980799 | + | 0.195023i | \(0.937522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −56145.0 | −0.288691 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −185270. | −0.944054 | −0.472027 | − | 0.881584i | \(-0.656477\pi\) | ||||
−0.472027 | + | 0.881584i | \(0.656477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 19440.0i | − 0.0981694i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8543.82i | 0.0427599i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 177822. | 0.882049 | 0.441025 | − | 0.897495i | \(-0.354615\pi\) | ||||
0.441025 | + | 0.897495i | \(0.354615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 203700. | 1.00147 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 92928.0i | 0.452846i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 135447.i | − 0.654254i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −203294. | −0.973402 | −0.486701 | − | 0.873569i | \(-0.661800\pi\) | ||||
−0.486701 | + | 0.873569i | \(0.661800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −104760. | −0.497244 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 286648.i | − 1.34880i | −0.738367 | − | 0.674399i | \(-0.764403\pi\) | ||||
0.738367 | − | 0.674399i | \(-0.235597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 332817.i | − 1.55254i | −0.630399 | − | 0.776271i | \(-0.717109\pi\) | ||||
0.630399 | − | 0.776271i | \(-0.282891\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 49152.0 | 0.227319 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 58738.8 | 0.269334 | 0.134667 | − | 0.990891i | \(-0.457004\pi\) | ||||
0.134667 | + | 0.990891i | \(0.457004\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 131328.i | 0.597051i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 281476.i | 1.26882i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −313632. | −1.40184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −247349. | −1.09629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29640.0i | 0.130269i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 186240.i | − 0.811710i | −0.913937 | − | 0.405855i | \(-0.866974\pi\) | ||||
0.913937 | − | 0.405855i | \(-0.133026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −326592. | −1.41161 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −541788. | −2.32239 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 59632.0i | − 0.253510i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 363308.i | − 1.53185i | −0.642927 | − | 0.765927i | \(-0.722280\pi\) | ||||
0.642927 | − | 0.765927i | \(-0.277720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 304992. | 1.27547 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 107533. | 0.446043 | 0.223022 | − | 0.974813i | \(-0.428408\pi\) | ||||
0.223022 | + | 0.974813i | \(0.428408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 211248.i | 0.869158i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 12933.3i | − 0.0527836i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 608256. | 2.46249 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 385089. | 1.54654 | 0.773268 | − | 0.634079i | \(-0.218621\pi\) | ||||
0.773268 | + | 0.634079i | \(0.218621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 532224.i | − 2.12041i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 210930.i | 0.833688i | 0.908978 | + | 0.416844i | \(0.136864\pi\) | ||||
−0.908978 | + | 0.416844i | \(0.863136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11968.0 | 0.0469287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 177294. | 0.689729 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 171512.i | − 0.662001i | −0.943630 | − | 0.331001i | \(-0.892614\pi\) | ||||
0.943630 | − | 0.331001i | \(-0.107386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 215555.i | 0.825499i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −285120. | −1.08341 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20693.3 | 0.0780216 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 152064.i | 0.568912i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 247457.i | − 0.918683i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −184734. | −0.680568 | −0.340284 | − | 0.940323i | \(-0.610523\pi\) | ||||
−0.340284 | + | 0.940323i | \(0.610523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 420009. | 1.53552 | 0.767760 | − | 0.640738i | \(-0.221371\pi\) | ||||
0.767760 | + | 0.640738i | \(0.221371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 430848.i | − 1.56317i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 101585.i | 0.365771i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −217823. | −0.778381 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 33949.9 | 0.120406 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 408240.i | − 1.43701i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8543.82i | 0.0298500i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 87648.0 | 0.303944 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −403411. | −1.38858 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 230904.i | − 0.788927i | −0.918912 | − | 0.394464i | \(-0.870930\pi\) | ||||
0.918912 | − | 0.394464i | \(-0.129070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 353432.i | 1.19869i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −119232. | −0.401421 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39769.9 | 0.132917 | 0.0664584 | − | 0.997789i | \(-0.478830\pi\) | ||||
0.0664584 | + | 0.997789i | \(0.478830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35640.0i | 0.118248i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 574944.i | 1.89375i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 626688. | 2.04928 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 118516. | 0.384761 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23144.0i | 0.0745981i | 0.999304 | + | 0.0372991i | \(0.0118754\pi\) | ||||
−0.999304 | + | 0.0372991i | \(0.988125\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 628559.i | 2.01151i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 171072. | 0.543567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −491123. | −1.54943 | −0.774717 | − | 0.632308i | \(-0.782108\pi\) | ||||
−0.774717 | + | 0.632308i | \(0.782108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5616.00i | 0.0175926i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 591875.i | − 1.84104i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −127710. | −0.394458 | −0.197229 | − | 0.980357i | \(-0.563194\pi\) | ||||
−0.197229 | + | 0.980357i | \(0.563194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39064.5 | 0.119815 | 0.0599073 | − | 0.998204i | \(-0.480919\pi\) | ||||
0.0599073 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 304128.i | − 0.926290i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 395759.i | − 1.19700i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −270718. | −0.813140 | −0.406570 | − | 0.913620i | \(-0.633275\pi\) | ||||
−0.406570 | + | 0.913620i | \(0.633275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −405381. | −1.20922 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 731904.i | − 2.16821i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 212968.i | 0.626582i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25920.0 | −0.0757396 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 273353. | 0.793319 | 0.396660 | − | 0.917966i | \(-0.370169\pi\) | ||||
0.396660 | + | 0.917966i | \(0.370169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 276480.i | 0.796954i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 662734.i | − 1.89742i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −62910.0 | −0.178900 | −0.0894500 | − | 0.995991i | \(-0.528511\pi\) | ||||
−0.0894500 | + | 0.995991i | \(0.528511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −101585. | −0.286944 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 244992.i | 0.687390i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 261723.i | 0.729438i | 0.931118 | + | 0.364719i | \(0.118835\pi\) | ||||
−0.931118 | + | 0.364719i | \(0.881165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 203902. | 0.564511 | 0.282256 | − | 0.959339i | \(-0.408917\pi\) | ||||
0.282256 | + | 0.959339i | \(0.408917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25131.8 | 0.0691176 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24200.0i | 0.0661157i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 369657.i | − 1.00328i | −0.865077 | − | 0.501640i | \(-0.832730\pi\) | ||||
0.865077 | − | 0.501640i | \(-0.167270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.00147e6 | −2.70025 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 304756. | 0.816337 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 222264.i | 0.591491i | 0.955267 | + | 0.295746i | \(0.0955680\pi\) | ||||
−0.955267 | + | 0.295746i | \(0.904432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 148145.i | 0.391685i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 363582. | 0.955063 | 0.477532 | − | 0.878615i | \(-0.341532\pi\) | ||||
0.477532 | + | 0.878615i | \(0.341532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 317718. | 0.829203 | 0.414602 | − | 0.910003i | \(-0.363921\pi\) | ||||
0.414602 | + | 0.910003i | \(0.363921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 456192.i | − 1.18294i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 190472.i | 0.490745i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 274721. | 0.703286 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 465599. | 1.18434 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 244944.i | 0.619107i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 348415.i | − 0.875062i | −0.899203 | − | 0.437531i | \(-0.855853\pi\) | ||||
0.899203 | − | 0.437531i | \(-0.144147\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 256608. | 0.640417 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27591.1 | −0.0684259 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 808488.i | 1.99248i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 116400.i | − 0.285069i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 67230.0 | 0.163624 | 0.0818120 | − | 0.996648i | \(-0.473929\pi\) | ||||
0.0818120 | + | 0.996648i | \(0.473929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −74513.5 | −0.180224 | −0.0901121 | − | 0.995932i | \(-0.528723\pi\) | ||||
−0.0901121 | + | 0.995932i | \(0.528723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 228096.i | − 0.548275i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 380239.i | − 0.908340i | −0.890915 | − | 0.454170i | \(-0.849936\pi\) | ||||
0.890915 | − | 0.454170i | \(-0.150064\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 243936. | 0.579144 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −481589. | −1.13636 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 89288.0i | 0.209395i | 0.994504 | + | 0.104698i | \(0.0333875\pi\) | ||||
−0.994504 | + | 0.104698i | \(0.966613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 76737.6i | − 0.178865i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41250.0 | 0.0955638 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 223149. | 0.513834 | 0.256917 | − | 0.966433i | \(-0.417293\pi\) | ||||
0.256917 | + | 0.966433i | \(0.417293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 560088.i | 1.28190i | 0.767584 | + | 0.640949i | \(0.221459\pi\) | ||||
−0.767584 | + | 0.640949i | \(0.778541\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 342850.i | − 0.779969i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −276480. | −0.625202 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −919911. | −2.06773 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 202752.i | 0.453015i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 256079.i | 0.568761i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −810722. | −1.78995 | −0.894977 | − | 0.446112i | \(-0.852808\pi\) | ||||
−0.894977 | + | 0.446112i | \(0.852808\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 362779. | 0.796223 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 655768.i | 1.43078i | 0.698725 | + | 0.715390i | \(0.253751\pi\) | ||||
−0.698725 | + | 0.715390i | \(0.746249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 584272.i | 1.26729i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 763488. | 1.64630 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 189208. | 0.405601 | 0.202800 | − | 0.979220i | \(-0.434996\pi\) | ||||
0.202800 | + | 0.979220i | \(0.434996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 261360.i | 0.557004i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 141796.i | 0.300435i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 426816. | 0.899088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −569389. | −1.19248 | −0.596242 | − | 0.802804i | \(-0.703340\pi\) | ||||
−0.596242 | + | 0.802804i | \(0.703340\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 126720.i | 0.263863i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 10581.8i | − 0.0219073i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −306180. | −0.630248 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26983.6 | 0.0552262 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 519224.i | − 1.05662i | −0.849052 | − | 0.528310i | \(-0.822826\pi\) | ||||
0.849052 | − | 0.528310i | \(-0.177174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 666653.i | 1.34893i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −110592. | −0.222508 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −117262. | −0.234595 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 919512.i | 1.82922i | 0.404342 | + | 0.914608i | \(0.367501\pi\) | ||||
−0.404342 | + | 0.914608i | \(0.632499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 119927.i | − 0.237234i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −442368. | −0.870171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −186240. | −0.364301 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 898560.i | 1.74787i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 656071.i | 1.26909i | 0.772885 | + | 0.634546i | \(0.218813\pi\) | ||||
−0.772885 | + | 0.634546i | \(0.781187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −202752. | −0.390027 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 955987. | 1.82884 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 731544.i | − 1.39176i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 488722.i | 0.924684i | 0.886702 | + | 0.462342i | \(0.152991\pi\) | ||||
−0.886702 | + | 0.462342i | \(0.847009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 399951. | 0.752578 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 471419. | 0.882211 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 706536.i | 1.31500i | 0.753454 | + | 0.657501i | \(0.228386\pi\) | ||||
−0.753454 | + | 0.657501i | \(0.771614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 293390.i | − 0.543089i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 180576. | 0.332449 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 172748. | 0.316318 | 0.158159 | − | 0.987414i | \(-0.449444\pi\) | ||||
0.158159 | + | 0.987414i | \(0.449444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 933120.i | − 1.69942i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 250436.i | − 0.453648i | −0.973936 | − | 0.226824i | \(-0.927166\pi\) | ||||
0.973936 | − | 0.226824i | \(-0.0728342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6976.00 | −0.0125688 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −140062. | −0.251003 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 83712.0i | − 0.149219i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 536301.i | − 0.950887i | −0.879746 | − | 0.475443i | \(-0.842288\pi\) | ||||
0.879746 | − | 0.475443i | \(-0.157712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 664416. | 1.17179 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −75875.4 | −0.133109 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 470232.i | 0.820579i | 0.911955 | + | 0.410290i | \(0.134572\pi\) | ||||
−0.911955 | + | 0.410290i | \(0.865428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 744958.i | 1.29315i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −691038. | −1.19325 | −0.596627 | − | 0.802519i | \(-0.703493\pi\) | ||||
−0.596627 | + | 0.802519i | \(0.703493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16823e6 | 2.00669 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19440.0i | 0.0332180i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 488879.i | − 0.831018i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 304030. | 0.514119 | 0.257060 | − | 0.966396i | \(-0.417246\pi\) | ||||
0.257060 | + | 0.966396i | \(0.417246\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −788873. | −1.32708 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 533720.i | 0.893212i | 0.894731 | + | 0.446606i | \(0.147367\pi\) | ||||
−0.894731 | + | 0.446606i | \(0.852633\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 351786.i | − 0.585700i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.16122e6 | −1.92341 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −833316. | −1.37320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 836352.i | − 1.37116i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 843252.i | − 1.37541i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −229824. | −0.372955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.17467e6 | −1.89656 | −0.948278 | − | 0.317442i | \(-0.897176\pi\) | ||||
−0.948278 | + | 0.317442i | \(0.897176\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 145152.i | − 0.233168i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 55025.3i | − 0.0879447i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 513216. | 0.816120 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −154886. | −0.245063 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 552376.i | − 0.869597i | −0.900528 | − | 0.434799i | \(-0.856820\pi\) | ||||
0.900528 | − | 0.434799i | \(-0.143180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 228567.i | − 0.358030i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36450.0 | 0.0568110 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 296388. | 0.459653 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 442368.i | − 0.682640i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 439654.i | − 0.675094i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 803682. | 1.22797 | 0.613984 | − | 0.789318i | \(-0.289566\pi\) | ||||
0.613984 | + | 0.789318i | \(0.289566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −68869.9 | −0.104710 | −0.0523549 | − | 0.998629i | \(-0.516673\pi\) | ||||
−0.0523549 | + | 0.998629i | \(0.516673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 895488.i | − 1.35481i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 249025.i | 0.374910i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.28304e6 | 1.92219 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 253963. | 0.378619 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 867592.i | − 1.28715i | −0.765383 | − | 0.643575i | \(-0.777450\pi\) | ||||
0.765383 | − | 0.643575i | \(-0.222550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 30177.7i | − 0.0445540i | −0.999752 | − | 0.0222770i | \(-0.992908\pi\) | ||||
0.999752 | − | 0.0222770i | \(-0.00709158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −592416. | −0.870400 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 864680. | 1.26428 | 0.632141 | − | 0.774853i | \(-0.282176\pi\) | ||||
0.632141 | + | 0.774853i | \(0.282176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 449928.i | 0.654687i | 0.944905 | + | 0.327344i | \(0.106153\pi\) | ||||
−0.944905 | + | 0.327344i | \(0.893847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 886754.i | 1.28411i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 606366. | 0.873866 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 434559. | 0.623269 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 405504.i | − 0.578821i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 800689.i | − 1.13747i | −0.822521 | − | 0.568735i | \(-0.807433\pi\) | ||||
0.822521 | − | 0.568735i | \(-0.192567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −993135. | −1.40416 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −226980. | −0.319398 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 144760.i | 0.202738i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 237111.i | − 0.330510i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −693792. | −0.962529 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.06665e6 | −1.47286 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 121608.i | − 0.167134i | −0.996502 | − | 0.0835669i | \(-0.973369\pi\) | ||||
0.996502 | − | 0.0835669i | \(-0.0266312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 52909.0i | 0.0723764i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.26473e6 | −1.72202 | −0.861009 | − | 0.508590i | \(-0.830167\pi\) | ||||
−0.861009 | + | 0.508590i | \(0.830167\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 967088. | 1.31063 | 0.655314 | − | 0.755356i | \(-0.272536\pi\) | ||||
0.655314 | + | 0.755356i | \(0.272536\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.45152e6i | − 1.95802i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 428915.i | 0.575904i | 0.957645 | + | 0.287952i | \(0.0929744\pi\) | ||||
−0.957645 | + | 0.287952i | \(0.907026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 202048. | 0.270036 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 561198. | 0.746582 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 861696.i | − 1.14108i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 361897.i | − 0.477034i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 111810. | 0.146707 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 743704. | 0.971369 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 519048.i | 0.674852i | 0.941352 | + | 0.337426i | \(0.109556\pi\) | ||||
−0.941352 | + | 0.337426i | \(0.890444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 370049.i | 0.478941i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 434754. | 0.560134 | 0.280067 | − | 0.959980i | \(-0.409643\pi\) | ||||
0.280067 | + | 0.959980i | \(0.409643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 474329. | 0.608357 | 0.304178 | − | 0.952615i | \(-0.401618\pi\) | ||||
0.304178 | + | 0.952615i | \(0.401618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 177408.i | 0.226510i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 298407.i | 0.379281i | 0.981854 | + | 0.189641i | \(0.0607323\pi\) | ||||
−0.981854 | + | 0.189641i | \(0.939268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 270336. | 0.342058 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −813828. | −1.02513 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 622080.i | − 0.780088i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71564.3i | 0.0893409i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.49299e6 | 1.85555 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −817698. | −1.01175 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 320112.i | − 0.394323i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.23488e6i | 2.74080i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −288576. | −0.352341 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −693549. | −0.843067 | −0.421534 | − | 0.906813i | \(-0.638508\pi\) | ||||
−0.421534 | + | 0.906813i | \(0.638508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22440.0i | 0.0271578i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.13296e6i | 1.36514i | 0.730821 | + | 0.682570i | \(0.239138\pi\) | ||||
−0.730821 | + | 0.682570i | \(0.760862\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00637e6 | −1.20730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −186240. | −0.222449 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 751872.i | 0.894139i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 526817.i | − 0.623776i | −0.950119 | − | 0.311888i | \(-0.899039\pi\) | ||||
0.950119 | − | 0.311888i | \(-0.100961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 377568. | 0.445119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.67616e6 | −1.96748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 848232.i | − 0.991360i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 38799.9i | 0.0451514i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −371682. | −0.430666 | −0.215333 | − | 0.976541i | \(-0.569084\pi\) | ||||
−0.215333 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65032e6 | 1.90401 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 836352.i | 0.960784i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 139680.i | 0.159775i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −532418. | −0.606420 | −0.303210 | − | 0.952924i | \(-0.598058\pi\) | ||||
−0.303210 | + | 0.952924i | \(0.598058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −917109. | −1.04013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 614600.i | 0.694086i | 0.937849 | + | 0.347043i | \(0.112814\pi\) | ||||
−0.937849 | + | 0.347043i | \(0.887186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.33331e6i | − 1.49936i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 405504. | 0.454079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 583988. | 0.651184 | 0.325592 | − | 0.945510i | \(-0.394436\pi\) | ||||
0.325592 | + | 0.945510i | \(0.394436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 594000.i | − 0.659560i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 481981.i | − 0.532929i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 604962. | 0.666104 | 0.333052 | − | 0.942908i | \(-0.391921\pi\) | ||||
0.333052 | + | 0.942908i | \(0.391921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 248319. | 0.272273 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.37702e6i | 1.50355i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.56079e6i | − 2.78444i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 530305. | 0.574221 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16019.7 | −0.0172743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 330992.i | − 0.355437i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.39405e6i | 1.49082i | 0.666604 | + | 0.745412i | \(0.267747\pi\) | ||||
−0.666604 | + | 0.745412i | \(0.732253\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −699840. | −0.745334 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 662175. | 0.702319 | 0.351160 | − | 0.936316i | \(-0.385787\pi\) | ||||
0.351160 | + | 0.936316i | \(0.385787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 103680.i | 0.109514i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.18728e6i | 1.24894i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −815778. | −0.854639 | −0.427320 | − | 0.904101i | \(-0.640542\pi\) | ||||
−0.427320 | + | 0.904101i | \(0.640542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 261899. | 0.273256 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 223560.i | − 0.232304i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.23384e6i | − 1.27688i | −0.769671 | − | 0.638441i | \(-0.779580\pi\) | ||||
0.769671 | − | 0.638441i | \(-0.220420\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 541120. | 0.557726 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.08358e6 | 1.11231 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.05286e6i | 2.09878i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 417315.i | 0.424929i | 0.977169 | + | 0.212464i | \(0.0681490\pi\) | ||||
−0.977169 | + | 0.212464i | \(0.931851\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −161568. | −0.163854 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −200035. | −0.202051 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.80252e6i | 1.81338i | 0.421793 | + | 0.906692i | \(0.361401\pi\) | ||||
−0.421793 | + | 0.906692i | \(0.638599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 977758.i | − 0.979716i |
(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 | 128.5.d.c.63.1 | ✓ | 4 | |
3.2 | odd | 2 | 1152.5.b.i.703.4 | 4 | |||
4.3 | odd | 2 | inner | 128.5.d.c.63.3 | yes | 4 | |
8.3 | odd | 2 | inner | 128.5.d.c.63.2 | yes | 4 | |
8.5 | even | 2 | inner | 128.5.d.c.63.4 | yes | 4 | |
12.11 | even | 2 | 1152.5.b.i.703.3 | 4 | |||
16.3 | odd | 4 | 256.5.c.c.255.2 | 2 | |||
16.5 | even | 4 | 256.5.c.f.255.2 | 2 | |||
16.11 | odd | 4 | 256.5.c.f.255.1 | 2 | |||
16.13 | even | 4 | 256.5.c.c.255.1 | 2 | |||
24.5 | odd | 2 | 1152.5.b.i.703.2 | 4 | |||
24.11 | even | 2 | 1152.5.b.i.703.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.5.d.c.63.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
128.5.d.c.63.2 | yes | 4 | 8.3 | odd | 2 | inner | |
128.5.d.c.63.3 | yes | 4 | 4.3 | odd | 2 | inner | |
128.5.d.c.63.4 | yes | 4 | 8.5 | even | 2 | inner | |
256.5.c.c.255.1 | 2 | 16.13 | even | 4 | |||
256.5.c.c.255.2 | 2 | 16.3 | odd | 4 | |||
256.5.c.f.255.1 | 2 | 16.11 | odd | 4 | |||
256.5.c.f.255.2 | 2 | 16.5 | even | 4 | |||
1152.5.b.i.703.1 | 4 | 24.11 | even | 2 | |||
1152.5.b.i.703.2 | 4 | 24.5 | odd | 2 | |||
1152.5.b.i.703.3 | 4 | 12.11 | even | 2 | |||
1152.5.b.i.703.4 | 4 | 3.2 | odd | 2 |