Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(127,128)]
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, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.127");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.c (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: | \(8\) |
Coefficient field: | 8.0.205520896.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 12x^{6} - 12x^{5} - 8x^{4} + 12x^{3} + 12x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{39} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.8 | ||
Root | \(1.55050 + 0.642239i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.127 |
Dual form | 128.5.c.a.127.1 |
$q$-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 | ||||||||
\(3\) | 16.7135i | 1.85705i | 0.371264 | + | 0.928527i | \(0.378925\pi\) | ||||
−0.371264 | + | 0.928527i | \(0.621075\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.1891 | −0.407562 | −0.203781 | − | 0.979016i | \(-0.565323\pi\) | ||||
−0.203781 | + | 0.979016i | \(0.565323\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 80.4325i | − 1.64148i | −0.571302 | − | 0.820740i | \(-0.693561\pi\) | ||||
0.571302 | − | 0.820740i | \(-0.306439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −198.341 | −2.44865 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 21.6419i | 0.178859i | 0.995993 | + | 0.0894293i | \(0.0285043\pi\) | ||||
−0.995993 | + | 0.0894293i | \(0.971496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −179.095 | −1.05974 | −0.529868 | − | 0.848080i | \(-0.677758\pi\) | ||||
−0.529868 | + | 0.848080i | \(0.677758\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 170.295i | − 0.756866i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 148.472 | 0.513743 | 0.256871 | − | 0.966446i | \(-0.417308\pi\) | ||||
0.256871 | + | 0.966446i | \(0.417308\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 322.535i | − 0.893447i | −0.894672 | − | 0.446724i | \(-0.852591\pi\) | ||||
0.894672 | − | 0.446724i | \(-0.147409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1344.31 | 3.04832 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 327.187i | − 0.618502i | −0.950980 | − | 0.309251i | \(-0.899922\pi\) | ||||
0.950980 | − | 0.309251i | \(-0.100078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −521.183 | −0.833893 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1961.18i | − 2.69023i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 699.401 | 0.831630 | 0.415815 | − | 0.909449i | \(-0.363496\pi\) | ||||
0.415815 | + | 0.909449i | \(0.363496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1042.58i | 1.08489i | 0.840090 | + | 0.542447i | \(0.182502\pi\) | ||||
−0.840090 | + | 0.542447i | \(0.817498\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −361.712 | −0.332150 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 819.532i | 0.669005i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1145.75 | −0.836921 | −0.418461 | − | 0.908235i | \(-0.637430\pi\) | ||||
−0.418461 | + | 0.908235i | \(0.637430\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 2993.31i | − 1.96799i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −792.708 | −0.471569 | −0.235785 | − | 0.971805i | \(-0.575766\pi\) | ||||
−0.235785 | + | 0.971805i | \(0.575766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 231.755i | 0.125341i | 0.998034 | + | 0.0626704i | \(0.0199617\pi\) | ||||
−0.998034 | + | 0.0626704i | \(0.980038\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2020.91 | 0.997979 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2963.98i | − 1.34177i | −0.741560 | − | 0.670887i | \(-0.765914\pi\) | ||||
0.741560 | − | 0.670887i | \(-0.234086\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4068.39 | −1.69446 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2481.48i | 0.954048i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4672.55 | −1.66342 | −0.831711 | − | 0.555209i | \(-0.812638\pi\) | ||||
−0.831711 | + | 0.555209i | \(0.812638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 220.510i | − 0.0728960i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5390.68 | 1.65918 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1055.65i | − 0.303262i | −0.988437 | − | 0.151631i | \(-0.951547\pi\) | ||||
0.988437 | − | 0.151631i | \(-0.0484525\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2911.64 | −0.782488 | −0.391244 | − | 0.920287i | \(-0.627955\pi\) | ||||
−0.391244 | + | 0.920287i | \(0.627955\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15953.1i | 4.01942i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1824.81 | 0.431908 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4623.44i | 1.02995i | 0.857206 | + | 0.514974i | \(0.172198\pi\) | ||||
−0.857206 | + | 0.514974i | \(0.827802\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5468.45 | 1.14859 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 2548.28i | − 0.505511i | −0.967530 | − | 0.252756i | \(-0.918663\pi\) | ||||
0.967530 | − | 0.252756i | \(-0.0813368\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4928.49 | 0.924843 | 0.462421 | − | 0.886660i | \(-0.346981\pi\) | ||||
0.462421 | + | 0.886660i | \(0.346981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 8710.79i | − 1.54859i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1740.71 | 0.293593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 4356.41i | − 0.698031i | −0.937117 | − | 0.349015i | \(-0.886516\pi\) | ||||
0.937117 | − | 0.349015i | \(-0.113484\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16712.5 | 2.54725 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5655.05i | 0.820881i | 0.911887 | + | 0.410441i | \(0.134625\pi\) | ||||
−0.911887 | + | 0.410441i | \(0.865375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1512.79 | −0.209382 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11689.4i | 1.54438i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12202.4 | −1.54051 | −0.770254 | − | 0.637737i | \(-0.779871\pi\) | ||||
−0.770254 | + | 0.637737i | \(0.779871\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14405.1i | 1.73953i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17425.2 | −2.01471 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3286.32i | 0.364136i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1193.17 | 0.126811 | 0.0634057 | − | 0.997988i | \(-0.479804\pi\) | ||||
0.0634057 | + | 0.997988i | \(0.479804\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 4292.47i | − 0.437963i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10516.4 | −1.03092 | −0.515461 | − | 0.856913i | \(-0.672379\pi\) | ||||
−0.515461 | + | 0.856913i | \(0.672379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9535.67i | − 0.898828i | −0.893324 | − | 0.449414i | \(-0.851633\pi\) | ||||
0.893324 | − | 0.449414i | \(-0.148367\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13697.2 | −1.24238 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4262.42i | 0.372296i | 0.982522 | + | 0.186148i | \(0.0596004\pi\) | ||||
−0.982522 | + | 0.186148i | \(0.940400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1271.33 | −0.107005 | −0.0535025 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535025 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 19149.4i | − 1.55421i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20599.9 | −1.61327 | −0.806637 | − | 0.591047i | \(-0.798715\pi\) | ||||
−0.806637 | + | 0.591047i | \(0.798715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3333.73i | 0.252078i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 35521.9 | 2.59492 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 11941.9i | − 0.843298i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14172.6 | 0.968010 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 13248.9i | − 0.875730i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11678.5 | 0.747426 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3740.54i | 0.231914i | 0.993254 | + | 0.115957i | \(0.0369935\pi\) | ||||
−0.993254 | + | 0.115957i | \(0.963007\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3873.44 | −0.232765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 19766.1i | − 1.15180i | −0.817519 | − | 0.575901i | \(-0.804651\pi\) | ||||
0.817519 | − | 0.575901i | \(-0.195349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25942.3 | −1.46658 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19982.5i | 1.09644i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 25580.0 | 1.36288 | 0.681442 | − | 0.731872i | \(-0.261353\pi\) | ||||
0.681442 | + | 0.731872i | \(0.261353\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6090.33i | 0.315218i | 0.987502 | + | 0.157609i | \(0.0503786\pi\) | ||||
−0.987502 | + | 0.157609i | \(0.949621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 49538.4 | 2.49175 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3875.96i | − 0.189543i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7126.23 | −0.338941 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 67997.0i | − 3.14670i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1392.16 | 0.0627070 | 0.0313535 | − | 0.999508i | \(-0.490018\pi\) | ||||
0.0313535 | + | 0.999508i | \(0.490018\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 27582.1i | 1.20969i | 0.796343 | + | 0.604845i | \(0.206765\pi\) | ||||
−0.796343 | + | 0.604845i | \(0.793235\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29448.0 | −1.25798 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 10622.9i | − 0.442162i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3752.20 | 0.152225 | 0.0761126 | − | 0.997099i | \(-0.475749\pi\) | ||||
0.0761126 | + | 0.997099i | \(0.475749\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 78094.7i | − 3.08907i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26316.5 | −1.01526 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6009.11i | 0.226170i | 0.993585 | + | 0.113085i | \(0.0360732\pi\) | ||||
−0.993585 | + | 0.113085i | \(0.963927\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3685.50 | 0.135372 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5470.03i | 0.196136i | 0.995180 | + | 0.0980679i | \(0.0312662\pi\) | ||||
−0.995180 | + | 0.0980679i | \(0.968734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3514.13 | 0.123039 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 63971.8i | 2.18774i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 33724.9 | 1.12683 | 0.563415 | − | 0.826174i | \(-0.309487\pi\) | ||||
0.563415 | + | 0.826174i | \(0.309487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 41920.1i | 1.36882i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17643.7 | 0.563174 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 53202.0i | 1.66043i | 0.557441 | + | 0.830217i | \(0.311783\pi\) | ||||
−0.557441 | + | 0.830217i | \(0.688217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −41714.5 | −1.27330 | −0.636648 | − | 0.771154i | \(-0.719680\pi\) | ||||
−0.636648 | + | 0.771154i | \(0.719680\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 48663.7i | − 1.45312i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11674.1 | 0.341098 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3213.20i | 0.0918872i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −157742. | −4.41596 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 31457.1i | − 0.862287i | −0.902283 | − | 0.431143i | \(-0.858110\pi\) | ||||
0.902283 | − | 0.431143i | \(-0.141890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18486.9 | 0.496307 | 0.248153 | − | 0.968721i | \(-0.420176\pi\) | ||||
0.248153 | + | 0.968721i | \(0.420176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 30499.0i | 0.802077i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 49310.2 | 1.27059 | 0.635293 | − | 0.772271i | \(-0.280879\pi\) | ||||
0.635293 | + | 0.772271i | \(0.280879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 59391.0i | 1.49973i | 0.661589 | + | 0.749867i | \(0.269883\pi\) | ||||
−0.661589 | + | 0.749867i | \(0.730117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −77273.8 | −1.91267 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 56254.6i | − 1.36510i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8076.94 | 0.192194 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64894.7i | 1.51450i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6980.25 | 0.159801 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 33767.5i | − 0.758463i | −0.925302 | − | 0.379231i | \(-0.876188\pi\) | ||||
0.925302 | − | 0.379231i | \(-0.123812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 42590.7 | 0.938762 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 2361.37i | − 0.0510842i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 83857.6 | 1.78083 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 82372.2i | 1.71748i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26590.6 | −0.544431 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9229.31i | 0.185592i | 0.995685 | + | 0.0927961i | \(0.0295805\pi\) | ||||
−0.995685 | + | 0.0927961i | \(0.970420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 103372. | 2.04191 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 67230.4i | − 1.30471i | −0.757914 | − | 0.652355i | \(-0.773781\pi\) | ||||
0.757914 | − | 0.652355i | \(-0.226219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −50287.7 | −0.958939 | −0.479469 | − | 0.877559i | \(-0.659171\pi\) | ||||
−0.479469 | + | 0.877559i | \(0.659171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 29093.4i | 0.545218i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 52737.2 | 0.971416 | 0.485708 | − | 0.874121i | \(-0.338562\pi\) | ||||
0.485708 | + | 0.874121i | \(0.338562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30200.1i | 0.546856i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 72810.8 | 1.29628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 97480.3i | 1.70656i | 0.521455 | + | 0.853279i | \(0.325389\pi\) | ||||
−0.521455 | + | 0.853279i | \(0.674611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 97612.5 | 1.68063 | 0.840313 | − | 0.542101i | \(-0.182371\pi\) | ||||
0.840313 | + | 0.542101i | \(0.182371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 120469.i | 2.04015i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 41453.1 | 0.690597 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 57764.4i | 0.946818i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −94515.7 | −1.52442 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 92490.6i | − 1.46808i | −0.679106 | − | 0.734041i | \(-0.737632\pi\) | ||||
0.679106 | − | 0.734041i | \(-0.262368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7080.95 | 0.110624 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 25283.9i | − 0.388834i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −84387.6 | −1.27765 | −0.638826 | − | 0.769351i | \(-0.720580\pi\) | ||||
−0.638826 | + | 0.769351i | \(0.720580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 92155.2i | 1.37379i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −138720. | −2.03637 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 136592.i | − 1.97476i | −0.158373 | − | 0.987379i | \(-0.550625\pi\) | ||||
0.158373 | − | 0.987379i | \(-0.449375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 47608.9 | 0.677948 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 203944.i | − 2.86081i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 54275.8 | 0.750070 | 0.375035 | − | 0.927011i | \(-0.377631\pi\) | ||||
0.375035 | + | 0.927011i | \(0.377631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14987.4i | 0.204074i | 0.994781 | + | 0.102037i | \(0.0325359\pi\) | ||||
−0.994781 | + | 0.102037i | \(0.967464\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −240759. | −3.23041 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 11279.4i | − 0.149149i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26442.7 | 0.344625 | 0.172312 | − | 0.985042i | \(-0.444876\pi\) | ||||
0.172312 | + | 0.985042i | \(0.444876\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 206787.i | − 2.65653i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17733.6 | 0.224587 | 0.112293 | − | 0.993675i | \(-0.464180\pi\) | ||||
0.112293 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 106916.i | 1.33497i | 0.744624 | + | 0.667484i | \(0.232629\pi\) | ||||
−0.744624 | + | 0.667484i | \(0.767371\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −54925.9 | −0.676220 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 63759.5i | 0.774071i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −61477.2 | −0.736069 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19942.0i | 0.235496i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −99532.1 | −1.15939 | −0.579693 | − | 0.814835i | \(-0.696827\pi\) | ||||
−0.579693 | + | 0.814835i | \(0.696827\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10756.1i | 0.123598i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 42443.6 | 0.481170 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 58597.7i | 0.655448i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18640.6 | 0.205744 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 175766.i | − 1.91448i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29666.9 | 0.318913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 46693.1i | 0.495422i | 0.968834 | + | 0.247711i | \(0.0796784\pi\) | ||||
−0.968834 | + | 0.247711i | \(0.920322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 159374. | 1.66917 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21716.8i | 0.224530i | 0.993678 | + | 0.112265i | \(0.0358106\pi\) | ||||
−0.993678 | + | 0.112265i | \(0.964189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 55851.2 | 0.570091 | 0.285045 | − | 0.958514i | \(-0.407991\pi\) | ||||
0.285045 | + | 0.958514i | \(0.407991\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 162547.i | − 1.63816i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 105442. | 1.04929 | 0.524643 | − | 0.851322i | \(-0.324199\pi\) | ||||
0.524643 | + | 0.851322i | \(0.324199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15136.3i | 0.148744i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −71239.9 | −0.691374 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 47887.2i | − 0.459002i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 93341.4 | 0.883706 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 21248.3i | − 0.198714i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −238400. | −2.20249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 22761.2i | − 0.207749i | −0.994590 | − | 0.103874i | \(-0.966876\pi\) | ||||
0.994590 | − | 0.103874i | \(-0.0331240\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 227248. | 2.04933 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 47108.5i | − 0.419768i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 134406. | 1.18348 | 0.591739 | − | 0.806130i | \(-0.298442\pi\) | ||||
0.591739 | + | 0.806130i | \(0.298442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 344296.i | − 2.99594i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22563.5 | −0.194043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 134112.i | 1.13994i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −55718.3 | −0.468123 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 211717.i | − 1.75832i | −0.476527 | − | 0.879160i | \(-0.658105\pi\) | ||||
0.476527 | − | 0.879160i | \(-0.341895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −241146. | −1.97984 | −0.989918 | − | 0.141638i | \(-0.954763\pi\) | ||||
−0.989918 | + | 0.141638i | \(0.954763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351238.i | 2.85093i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 172104. | 1.38115 | 0.690577 | − | 0.723259i | \(-0.257357\pi\) | ||||
0.690577 | + | 0.723259i | \(0.257357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25964.6i | 0.206027i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 199592. | 1.56605 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 210237.i | − 1.63125i | −0.578584 | − | 0.815623i | \(-0.696394\pi\) | ||||
0.578584 | − | 0.815623i | \(-0.303606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26292.5 | 0.201752 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 236874.i | 1.79765i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −50216.6 | −0.376931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 111614.i | − 0.828681i | −0.910122 | − | 0.414341i | \(-0.864012\pi\) | ||||
0.910122 | − | 0.414341i | \(-0.135988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 157226. | 1.15471 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 375825.i | 2.73047i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −173970. | −1.25042 | −0.625211 | − | 0.780455i | \(-0.714987\pi\) | ||||
−0.625211 | + | 0.780455i | \(0.714987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 195189.i | 1.38801i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −125259. | −0.881308 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28736.9i | 0.200060i | 0.994984 | + | 0.100030i | \(0.0318939\pi\) | ||||
−0.994984 | + | 0.100030i | \(0.968106\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −62517.5 | −0.430677 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 470.577i | − 0.00320799i | −0.999999 | − | 0.00160399i | \(-0.999489\pi\) | ||||
0.999999 | − | 0.00160399i | \(-0.000510568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17736.2 | −0.119657 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 45966.5i | − 0.306916i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 185468. | 1.22566 | 0.612831 | − | 0.790214i | \(-0.290031\pi\) | ||||
0.612831 | + | 0.790214i | \(0.290031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 48578.0i | − 0.317751i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 330360. | 2.13896 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 44387.7i | 0.284491i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −292155. | −1.85367 | −0.926835 | − | 0.375469i | \(-0.877482\pi\) | ||||
−0.926835 | + | 0.375469i | \(0.877482\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 433586.i | − 2.72351i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −113040. | −0.702982 | −0.351491 | − | 0.936191i | \(-0.614325\pi\) | ||||
−0.351491 | + | 0.936191i | \(0.614325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 186722.i | − 1.14970i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −170285. | −1.03816 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 24796.1i | − 0.149691i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −318260. | −1.90255 | −0.951273 | − | 0.308350i | \(-0.900223\pi\) | ||||
−0.951273 | + | 0.308350i | \(0.900223\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 427531.i | 2.53095i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −84909.0 | −0.497798 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 57619.7i | − 0.334560i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −101791. | −0.585377 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 86121.4i | 0.490549i | 0.969454 | + | 0.245275i | \(0.0788782\pi\) | ||||
−0.969454 | + | 0.245275i | \(0.921122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −151053. | −0.852244 | −0.426122 | − | 0.904666i | \(-0.640121\pi\) | ||||
−0.426122 | + | 0.904666i | \(0.640121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 587878.i | 3.28554i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −77380.9 | −0.428406 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 234191.i | 1.28444i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 64780.8 | 0.351991 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 122934.i | 0.661785i | 0.943668 | + | 0.330893i | \(0.107350\pi\) | ||||
−0.943668 | + | 0.330893i | \(0.892650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −204083. | −1.08851 | −0.544255 | − | 0.838920i | \(-0.683187\pi\) | ||||
−0.544255 | + | 0.838920i | \(0.683187\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 119104.i | − 0.629432i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −105529. | −0.552599 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 219346.i | 1.13815i | 0.822284 | + | 0.569077i | \(0.192699\pi\) | ||||
−0.822284 | + | 0.569077i | \(0.807301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 806928. | 4.14914 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39511.3i | 0.201332i | 0.994920 | + | 0.100666i | \(0.0320974\pi\) | ||||
−0.994920 | + | 0.100666i | \(0.967903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 124331. | 0.627853 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23267.8i | 0.116450i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 204669. | 1.01522 | 0.507608 | − | 0.861588i | \(-0.330530\pi\) | ||||
0.507608 | + | 0.861588i | \(0.330530\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 17155.7i | − 0.0843442i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −460994. | −2.24646 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 146774.i | − 0.708969i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −62590.3 | −0.299691 | −0.149846 | − | 0.988709i | \(-0.547878\pi\) | ||||
−0.149846 | + | 0.988709i | \(0.547878\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 291179.i | − 1.38208i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −73091.9 | −0.343928 | −0.171964 | − | 0.985103i | \(-0.555011\pi\) | ||||
−0.171964 | + | 0.985103i | \(0.555011\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 143210.i | 0.668055i | 0.942563 | + | 0.334028i | \(0.108408\pi\) | ||||
−0.942563 | + | 0.334028i | \(0.891592\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 177547. | 0.821119 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 149694.i | 0.686389i | 0.939264 | + | 0.343194i | \(0.111509\pi\) | ||||
−0.939264 | + | 0.343194i | \(0.888491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 371875. | 1.69064 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62712.4i | 0.282691i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5015.62 | −0.0224183 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 168100.i | 0.745040i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 926758. | 4.07314 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 79876.1i | 0.348133i | 0.984734 | + | 0.174067i | \(0.0556908\pi\) | ||||
−0.984734 | + | 0.174067i | \(0.944309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 205198. | 0.886915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 439841.i | − 1.88539i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12157.3 | −0.0516835 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 345681.i | − 1.45753i | −0.684763 | − | 0.728766i | \(-0.740094\pi\) | ||||
0.684763 | − | 0.728766i | \(-0.259906\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −100433. | −0.420010 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 319173.i | − 1.32392i | −0.749538 | − | 0.661961i | \(-0.769724\pi\) | ||||
0.749538 | − | 0.661961i | \(-0.230276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 103841. | 0.427244 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 43736.2i | 0.178497i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −204965. | −0.829786 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 186219.i | − 0.747866i | −0.927456 | − | 0.373933i | \(-0.878009\pi\) | ||||
0.927456 | − | 0.373933i | \(-0.121991\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −91423.3 | −0.364235 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 109815.i | − 0.434038i | −0.976167 | − | 0.217019i | \(-0.930367\pi\) | ||||
0.976167 | − | 0.217019i | \(-0.0696333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 107153. | 0.420165 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 58733.4i | 0.228491i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −248990. | −0.961052 | −0.480526 | − | 0.876981i | \(-0.659554\pi\) | ||||
−0.480526 | + | 0.876981i | \(0.659554\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 396411.i | − 1.51811i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −632547. | −2.40358 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 97159.5i | 0.366328i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 64146.0 | 0.239988 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 563661.i | 2.09258i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 163712. | 0.603123 | 0.301562 | − | 0.953447i | \(-0.402492\pi\) | ||||
0.301562 | + | 0.953447i | \(0.402492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 106787.i | 0.390406i | 0.980763 | + | 0.195203i | \(0.0625366\pi\) | ||||
−0.980763 | + | 0.195203i | \(0.937463\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −700631. | −2.54197 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 154794.i | 0.557356i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 172789. | 0.617456 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 209380.i | 0.742583i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 141970. | 0.499739 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 43430.0i | − 0.151734i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −889191. | −3.08352 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 88047.6i | − 0.303068i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23108.9 | −0.0789558 | −0.0394779 | − | 0.999220i | \(-0.512569\pi\) | ||||
−0.0394779 | + | 0.999220i | \(0.512569\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 697194.i | − 2.36458i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12953.6 | 0.0436112 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 99858.8i | − 0.333743i | −0.985979 | − | 0.166871i | \(-0.946634\pi\) | ||||
0.985979 | − | 0.166871i | \(-0.0533664\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 577497. | 1.91604 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 225581.i | − 0.743018i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −350397. | −1.14580 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 195114.i | 0.633437i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −404414. | −1.30352 | −0.651758 | − | 0.758427i | \(-0.725968\pi\) | ||||
−0.651758 | + | 0.758427i | \(0.725968\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 41506.2i | − 0.132828i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −53703.9 | −0.170640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 69169.2i | − 0.218221i | −0.994030 | − | 0.109110i | \(-0.965200\pi\) | ||||
0.994030 | − | 0.109110i | \(-0.0348002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 209893. | 0.657510 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.34423e6i | − 4.18126i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 123521. | 0.381519 | 0.190759 | − | 0.981637i | \(-0.438905\pi\) | ||||
0.190759 | + | 0.981637i | \(0.438905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 192876.i | − 0.591571i | −0.955254 | − | 0.295785i | \(-0.904419\pi\) | ||||
0.955254 | − | 0.295785i | \(-0.0955814\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 525758. | 1.60131 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 170525.i | 0.515764i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −94086.0 | −0.282601 | −0.141300 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141300 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 308981.i | 0.921669i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 454850. | 1.34746 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 101123.i | − 0.297517i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −361935. | −1.05759 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 304527.i | − 0.883792i | −0.897066 | − | 0.441896i | \(-0.854306\pi\) | ||||
0.897066 | − | 0.441896i | \(-0.145694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 336269. | 0.969296 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 824146.i | 2.35955i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 122010. | 0.346966 | 0.173483 | − | 0.984837i | \(-0.444498\pi\) | ||||
0.173483 | + | 0.984837i | \(0.444498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 121677.i | 0.343697i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −992631. | −2.78509 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 329463.i | 0.918232i | 0.888376 | + | 0.459116i | \(0.151834\pi\) | ||||
−0.888376 | + | 0.459116i | \(0.848166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −102795. | −0.284593 | −0.142297 | − | 0.989824i | \(-0.545449\pi\) | ||||
−0.142297 | + | 0.989824i | \(0.545449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 917017.i | − 2.52199i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −144406. | −0.394524 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 560628.i | − 1.52159i | −0.648993 | − | 0.760794i | \(-0.724810\pi\) | ||||
0.648993 | − | 0.760794i | \(-0.275190\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 940210. | 2.53507 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 530834.i | 1.42192i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 454035. | 1.20828 | 0.604140 | − | 0.796878i | \(-0.293517\pi\) | ||||
0.604140 | + | 0.796878i | \(0.293517\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 134994.i | 0.356914i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 245819. | 0.645721 | 0.322860 | − | 0.946447i | \(-0.395356\pi\) | ||||
0.322860 | + | 0.946447i | \(0.395356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 577432.i | − 1.50702i | −0.657435 | − | 0.753511i | \(-0.728359\pi\) | ||||
0.657435 | − | 0.753511i | \(-0.271641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −641672. | −1.66391 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 981467.i | 2.52871i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 206746. | 0.529270 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 116664.i | 0.296759i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −170111. | −0.429962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 588831.i | 1.47888i | 0.673224 | + | 0.739438i | \(0.264909\pi\) | ||||
−0.673224 | + | 0.739438i | \(0.735091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 564373. | 1.40851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 38112.6i | − 0.0945193i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 728630. | 1.79568 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 505428.i | 1.23782i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −86370.6 | −0.210208 | −0.105104 | − | 0.994461i | \(-0.533518\pi\) | ||||
−0.105104 | + | 0.994461i | \(0.533518\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 671327.i | − 1.62372i | −0.583849 | − | 0.811862i | \(-0.698454\pi\) | ||||
0.583849 | − | 0.811862i | \(-0.301546\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 39466.7 | 0.0948661 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 208533.i | − 0.498158i | −0.968483 | − | 0.249079i | \(-0.919872\pi\) | ||||
0.968483 | − | 0.249079i | \(-0.0801278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22846.4 | 0.0542410 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.40155e6i | 3.30710i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 556984. | 1.30622 | 0.653110 | − | 0.757263i | \(-0.273464\pi\) | ||||
0.653110 | + | 0.757263i | \(0.273464\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 201398.i | 0.469431i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −977521. | −2.26462 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 295904.i | − 0.681364i | −0.940179 | − | 0.340682i | \(-0.889342\pi\) | ||||
0.940179 | − | 0.340682i | \(-0.110658\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −280826. | −0.642739 | −0.321370 | − | 0.946954i | \(-0.604143\pi\) | ||||
−0.321370 | + | 0.946954i | \(0.604143\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 444421.i | − 1.01104i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 264327. | 0.597721 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 228835.i | − 0.514365i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −154254. | −0.344655 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 63013.4i | − 0.139955i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −395861. | −0.874003 | −0.437001 | − | 0.899461i | \(-0.643960\pi\) | ||||
−0.437001 | + | 0.899461i | \(0.643960\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.02213e6i | 2.24336i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −296569. | −0.647065 | −0.323532 | − | 0.946217i | \(-0.604870\pi\) | ||||
−0.323532 | + | 0.946217i | \(0.604870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 95969.5i | − 0.208158i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.12365e6 | 2.42292 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 144692.i | − 0.310172i | −0.987901 | − | 0.155086i | \(-0.950435\pi\) | ||||
0.987901 | − | 0.155086i | \(-0.0495654\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −260636. | −0.555461 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 840483.i | − 1.78080i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 836832. | 1.76279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 359909.i | − 0.753766i | −0.926261 | − | 0.376883i | \(-0.876996\pi\) | ||||
0.926261 | − | 0.376883i | \(-0.123004\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −345254. | −0.718907 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 62054.7i | − 0.128471i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −117695. | −0.242265 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 881423.i | 1.80397i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 75448.9 | 0.153538 | 0.0767692 | − | 0.997049i | \(-0.475540\pi\) | ||||
0.0767692 | + | 0.997049i | \(0.475540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 369542.i | 0.747745i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −504750. | −1.01554 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 845863.i | 1.69224i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −484369. | −0.963571 | −0.481785 | − | 0.876289i | \(-0.660012\pi\) | ||||
−0.481785 | + | 0.876289i | \(0.660012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 864054.i | 1.70923i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 341120. | 0.671009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39492.4i | 0.0772505i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.62924e6 | −3.16917 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47114.4i | 0.0911373i | 0.998961 | + | 0.0455687i | \(0.0145100\pi\) | ||||
−0.998961 | + | 0.0455687i | \(0.985490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −766978. | −1.47541 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.63145e6i | 3.12102i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −364516. | −0.693490 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 134342.i | − 0.254180i | −0.991891 | − | 0.127090i | \(-0.959436\pi\) | ||||
0.991891 | − | 0.127090i | \(-0.0405637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −659746. | −1.24143 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34409.0i | 0.0643929i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 429578. | 0.799529 | 0.399764 | − | 0.916618i | \(-0.369092\pi\) | ||||
0.399764 | + | 0.916618i | \(0.369092\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 692826.i | 1.28248i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −100060. | −0.184215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 975871.i | − 1.78691i | −0.449148 | − | 0.893457i | \(-0.648273\pi\) | ||||
0.449148 | − | 0.893457i | \(-0.351727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −965445. | −1.75829 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 671044.i | − 1.21555i | −0.794109 | − | 0.607776i | \(-0.792062\pi\) | ||||
0.794109 | − | 0.607776i | \(-0.207938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14184.8 | −0.0255570 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.12163e6i | − 2.01005i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 342837. | 0.611116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 272637.i | − 0.483399i | −0.970351 | − | 0.241699i | \(-0.922295\pi\) | ||||
0.970351 | − | 0.241699i | \(-0.0777048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.54584e6 | 2.72631 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 281036.i | − 0.493024i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 850551. | 1.48426 | 0.742128 | − | 0.670259i | \(-0.233817\pi\) | ||||
0.742128 | + | 0.670259i | \(0.233817\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 118347.i | 0.205435i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 65767.8 | 0.113565 | 0.0567824 | − | 0.998387i | \(-0.481916\pi\) | ||||
0.0567824 | + | 0.998387i | \(0.481916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 102256.i | 0.175647i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 300047. | 0.512704 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 189063.i | 0.321378i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −542462. | −0.917310 | −0.458655 | − | 0.888614i | \(-0.651669\pi\) | ||||
−0.458655 | + | 0.888614i | \(0.651669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.41041e6i | − 2.37267i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 91838.1 | 0.153697 | 0.0768483 | − | 0.997043i | \(-0.475514\pi\) | ||||
0.0768483 | + | 0.997043i | \(0.475514\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 543377.i | − 0.904686i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.54024e6 | −2.55120 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 255676.i | 0.421322i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 55149.6 | 0.0904150 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 1.37165e6i | − 2.23727i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38231.4 | −0.0620412 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 546617.i | 0.882539i | 0.897375 | + | 0.441270i | \(0.145472\pi\) | ||||
−0.897375 | + | 0.441270i | \(0.854528\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.28293e6 | 3.66724 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.65690e6i | 2.64816i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 521461. | 0.829231 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 795711.i | 1.25899i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 822216. | 1.29440 | 0.647201 | − | 0.762320i | \(-0.275940\pi\) | ||||
0.647201 | + | 0.762320i | \(0.275940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 440066.i | − 0.689326i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.42023e6 | 3.77217 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 106662.i | 0.165416i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 268140. | 0.413781 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 907138.i | 1.39292i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −216481. | −0.330767 | −0.165384 | − | 0.986229i | \(-0.552886\pi\) | ||||
−0.165384 | + | 0.986229i | \(0.552886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 64418.9i | − 0.0979427i | −0.998800 | − | 0.0489713i | \(-0.984406\pi\) | ||||
0.998800 | − | 0.0489713i | \(-0.0155943\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −250491. | −0.378976 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 61227.2i | − 0.0921784i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 74749.0 | 0.111985 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.85712e6i | − 4.25952i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.13414e6 | −1.68260 | −0.841300 | − | 0.540569i | \(-0.818209\pi\) | ||||
−0.841300 | + | 0.540569i | \(0.818209\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 686626.i | 1.01373i | 0.862026 | + | 0.506863i | \(0.169195\pi\) | ||||
−0.862026 | + | 0.506863i | \(0.830805\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 188518. | 0.276978 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 453622.i | 0.663259i | 0.943410 | + | 0.331630i | \(0.107598\pi\) | ||||
−0.943410 | + | 0.331630i | \(0.892402\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −649128. | −0.944542 | −0.472271 | − | 0.881453i | \(-0.656566\pi\) | ||||
−0.472271 | + | 0.881453i | \(0.656566\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 441950.i | 0.639987i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −604040. | −0.870515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 55734.5i | − 0.0799376i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.04469e6 | 2.91861 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 564460.i | − 0.801879i | −0.916104 | − | 0.400940i | \(-0.868684\pi\) | ||||
0.916104 | − | 0.400940i | \(-0.131316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −218120. | −0.308392 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 296390.i | 0.417070i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35805.7 | −0.0501462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.13994e6i | − 1.58897i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.78694e6 | −2.47911 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 374873.i | 0.517637i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6797.28 | 0.00934194 | 0.00467097 | − | 0.999989i | \(-0.498513\pi\) | ||||
0.00467097 | + | 0.999989i | \(0.498513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 651812.i | − 0.891642i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −936730. | −1.27542 | −0.637709 | − | 0.770277i | \(-0.720118\pi\) | ||||
−0.637709 | + | 0.770277i | \(0.720118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 850774.i | − 1.15300i | −0.817099 | − | 0.576498i | \(-0.804419\pi\) | ||||
0.817099 | − | 0.576498i | \(-0.195581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.06564e6 | −1.43749 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 657197.i | 0.882417i | 0.897405 | + | 0.441209i | \(0.145450\pi\) | ||||
−0.897405 | + | 0.441209i | \(0.854550\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −343625. | −0.459253 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.02750e6i | − 1.36692i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 94280.9 | 0.124849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 828036.i | − 1.09147i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −236654. | −0.310517 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 939333.i | − 1.22688i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 751857. | 0.977544 | 0.488772 | − | 0.872412i | \(-0.337445\pi\) | ||||
0.488772 | + | 0.872412i | \(0.337445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1.66353e6i | − 2.15304i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −277963. | −0.358125 | −0.179062 | − | 0.983838i | \(-0.557306\pi\) | ||||
−0.179062 | + | 0.983838i | \(0.557306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 481184.i | 0.617149i | 0.951200 | + | 0.308574i | \(0.0998519\pi\) | ||||
−0.951200 | + | 0.308574i | \(0.900148\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −179773. | −0.229529 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 772804.i | − 0.982250i | −0.871089 | − | 0.491125i | \(-0.836586\pi\) | ||||
0.871089 | − | 0.491125i | \(-0.163414\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 300861. | 0.380682 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 361690.i | 0.455597i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −955985. | −1.19880 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 542078.i | − 0.676730i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −979373. | −1.21720 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 729184.i | 0.902231i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −693741. | −0.854571 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 311550.i | 0.382079i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 425031. | 0.518948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.03068e6i | 1.25288i | 0.779469 | + | 0.626440i | \(0.215489\pi\) | ||||
−0.779469 | + | 0.626440i | \(0.784511\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.08584e6 | 2.52437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 716922.i | − 0.863843i | −0.901911 | − | 0.431922i | \(-0.857836\pi\) | ||||
0.901911 | − | 0.431922i | \(-0.142164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −122386. | −0.146822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 495837.i | 0.592239i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.58984e6 | −1.89066 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 223092.i | − 0.264152i | −0.991240 | − | 0.132076i | \(-0.957836\pi\) | ||||
0.991240 | − | 0.132076i | \(-0.0421642\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −780404. | −0.920027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 456385.i | 0.535708i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 597143. | 0.697903 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.89131e6i | 2.20092i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28837.6 | −0.0334140 | −0.0167070 | − | 0.999860i | \(-0.505318\pi\) | ||||
−0.0167070 | + | 0.999860i | \(0.505318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.31220e6i | 1.51391i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −362963. | −0.416965 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 32739.5i | − 0.0374498i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 887467. | 1.01082 | 0.505409 | − | 0.862880i | \(-0.331342\pi\) | ||||
0.505409 | + | 0.862880i | \(0.331342\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 933469.i | 1.05869i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 186343. | 0.210442 | 0.105221 | − | 0.994449i | \(-0.466445\pi\) | ||||
0.105221 | + | 0.994449i | \(0.466445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 259364.i | 0.291666i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.60725e6 | 1.79978 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.50276e6i | − 1.67567i | −0.545920 | − | 0.837837i | \(-0.683820\pi\) | ||||
0.545920 | − | 0.837837i | \(-0.316180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −882669. | −0.980089 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.76230e6i | 1.94858i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 740506. | 0.815347 | 0.407674 | − | 0.913128i | \(-0.366340\pi\) | ||||
0.407674 | + | 0.913128i | \(0.366340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 320518.i | 0.351436i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −252981. | −0.276226 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.05746e6i | − 2.23715i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −163459. | −0.176996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 845411.i | − 0.911624i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −188364. | −0.202276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 401772.i | − 0.429662i | −0.976651 | − | 0.214831i | \(-0.931080\pi\) | ||||
0.976651 | − | 0.214831i | \(-0.0689201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 800363. | 0.852392 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.06855e6i | 1.13333i | 0.823947 | + | 0.566667i | \(0.191768\pi\) | ||||
−0.823947 | + | 0.566667i | \(0.808232\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 489860. | 0.517424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.56006e6i | 1.64109i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −674685. | −0.706825 | −0.353412 | − | 0.935468i | \(-0.614979\pi\) | ||||
−0.353412 | + | 0.935468i | \(0.614979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 264082.i | − 0.275533i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 252156. | 0.262018 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 751517.i | 0.777735i | 0.921294 | + | 0.388868i | \(0.127134\pi\) | ||||
−0.921294 | + | 0.388868i | \(0.872866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −502424. | −0.517843 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.98450e6i | − 4.09015i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 75827.3 | 0.0775235 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 328889.i | 0.334890i | 0.985881 | + | 0.167445i | \(0.0535516\pi\) | ||||
−0.985881 | + | 0.167445i | \(0.946448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 380418. | 0.385801 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 605138.i | − 0.611235i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −105510. | −0.106146 | −0.0530729 | − | 0.998591i | \(-0.516902\pi\) | ||||
−0.0530729 | + | 0.998591i | \(0.516902\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.24701e6i | 2.25151i |
(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.c.a.127.8 | yes | 8 | |
3.2 | odd | 2 | 1152.5.g.b.127.5 | 8 | |||
4.3 | odd | 2 | inner | 128.5.c.a.127.1 | ✓ | 8 | |
8.3 | odd | 2 | 128.5.c.b.127.8 | yes | 8 | ||
8.5 | even | 2 | 128.5.c.b.127.1 | yes | 8 | ||
12.11 | even | 2 | 1152.5.g.b.127.6 | 8 | |||
16.3 | odd | 4 | 256.5.d.h.127.8 | 8 | |||
16.5 | even | 4 | 256.5.d.h.127.7 | 8 | |||
16.11 | odd | 4 | 256.5.d.g.127.1 | 8 | |||
16.13 | even | 4 | 256.5.d.g.127.2 | 8 | |||
24.5 | odd | 2 | 1152.5.g.a.127.3 | 8 | |||
24.11 | even | 2 | 1152.5.g.a.127.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.5.c.a.127.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
128.5.c.a.127.8 | yes | 8 | 1.1 | even | 1 | trivial | |
128.5.c.b.127.1 | yes | 8 | 8.5 | even | 2 | ||
128.5.c.b.127.8 | yes | 8 | 8.3 | odd | 2 | ||
256.5.d.g.127.1 | 8 | 16.11 | odd | 4 | |||
256.5.d.g.127.2 | 8 | 16.13 | even | 4 | |||
256.5.d.h.127.7 | 8 | 16.5 | even | 4 | |||
256.5.d.h.127.8 | 8 | 16.3 | odd | 4 | |||
1152.5.g.a.127.3 | 8 | 24.5 | odd | 2 | |||
1152.5.g.a.127.4 | 8 | 24.11 | even | 2 | |||
1152.5.g.b.127.5 | 8 | 3.2 | odd | 2 | |||
1152.5.g.b.127.6 | 8 | 12.11 | even | 2 |