Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.257");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 32 x^{14} + 356 x^{13} + 1348 x^{12} - 8992 x^{11} + 22064 x^{10} + \cdots + 21479188203 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{54}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.6 | ||
Root | \(6.34189 + 3.61720i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.5.e.b.257.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −4.08506 | + | 8.01949i | −0.453895 | + | 0.891055i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 47.0883i | − | 1.88353i | −0.336270 | − | 0.941766i | \(-0.609165\pi\) | ||
0.336270 | − | 0.941766i | \(-0.390835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.4570 | −0.274633 | −0.137316 | − | 0.990527i | \(-0.543848\pi\) | ||||
−0.137316 | + | 0.990527i | \(0.543848\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −47.6246 | − | 65.5202i | −0.587958 | − | 0.808892i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 135.410i | − | 1.11909i | −0.828799 | − | 0.559546i | \(-0.810975\pi\) | ||
0.828799 | − | 0.559546i | \(-0.189025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −80.8573 | −0.478445 | −0.239223 | − | 0.970965i | \(-0.576893\pi\) | ||||
−0.239223 | + | 0.970965i | \(0.576893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 377.624 | + | 192.358i | 1.67833 | + | 0.854926i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 430.724i | − | 1.49039i | −0.666845 | − | 0.745197i | \(-0.732356\pi\) | ||
0.666845 | − | 0.745197i | \(-0.267644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 43.5828 | 0.120728 | 0.0603640 | − | 0.998176i | \(-0.480774\pi\) | ||||
0.0603640 | + | 0.998176i | \(0.480774\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 54.9727 | − | 107.918i | 0.124655 | − | 0.244713i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 873.291i | 1.65083i | 0.564524 | + | 0.825416i | \(0.309060\pi\) | ||||
−0.564524 | + | 0.825416i | \(0.690940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1592.31 | −2.54769 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 719.988 | − | 114.271i | 0.987638 | − | 0.156751i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 707.044i | 0.840718i | 0.907358 | + | 0.420359i | \(0.138096\pi\) | ||||
−0.907358 | + | 0.420359i | \(0.861904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −677.729 | −0.705233 | −0.352616 | − | 0.935768i | \(-0.614708\pi\) | ||||
−0.352616 | + | 0.935768i | \(0.614708\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1085.92 | + | 553.159i | 0.997173 | + | 0.507951i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 633.668i | 0.517280i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1630.90 | 1.19130 | 0.595652 | − | 0.803242i | \(-0.296894\pi\) | ||||
0.595652 | + | 0.803242i | \(0.296894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 330.307 | − | 648.435i | 0.217164 | − | 0.426321i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1227.00i | 0.729922i | 0.931023 | + | 0.364961i | \(0.118918\pi\) | ||||
−0.931023 | + | 0.364961i | \(0.881082\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1431.45 | 0.774175 | 0.387088 | − | 0.922043i | \(-0.373481\pi\) | ||||
0.387088 | + | 0.922043i | \(0.373481\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3085.23 | + | 2242.56i | −1.52357 | + | 1.10744i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2066.09i | − | 0.935307i | −0.883912 | − | 0.467653i | \(-0.845100\pi\) | ||
0.883912 | − | 0.467653i | \(-0.154900\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2219.91 | −0.924577 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3454.19 | + | 1759.53i | 1.32802 | + | 0.676483i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1465.79i | 0.521818i | 0.965363 | + | 0.260909i | \(0.0840222\pi\) | ||||
−0.965363 | + | 0.260909i | \(0.915978\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6376.24 | −2.10785 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −178.038 | + | 349.512i | −0.0547979 | + | 0.107575i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 470.434i | − | 0.135143i | −0.997714 | − | 0.0675716i | \(-0.978475\pi\) | ||
0.997714 | − | 0.0675716i | \(-0.0215251\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −39.9022 | −0.0107235 | −0.00536176 | − | 0.999986i | \(-0.501707\pi\) | ||||
−0.00536176 | + | 0.999986i | \(0.501707\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 640.885 | + | 881.706i | 0.161473 | + | 0.222148i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3807.43i | 0.901167i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4525.04 | −1.00803 | −0.504014 | − | 0.863695i | \(-0.668144\pi\) | ||||
−0.504014 | + | 0.863695i | \(0.668144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7003.35 | − | 3567.44i | −1.47098 | − | 0.749306i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9851.74i | 1.95432i | 0.212498 | + | 0.977161i | \(0.431840\pi\) | ||||
−0.212498 | + | 0.977161i | \(0.568160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3277.79 | −0.615086 | −0.307543 | − | 0.951534i | \(-0.599507\pi\) | ||||
−0.307543 | + | 0.951534i | \(0.599507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6504.67 | − | 12769.5i | 1.15639 | − | 2.27013i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1822.22i | 0.307340i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6933.92 | −1.11103 | −0.555514 | − | 0.831507i | \(-0.687478\pi\) | ||||
−0.555514 | + | 0.831507i | \(0.687478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2024.80 | + | 6240.75i | −0.308611 | + | 0.951188i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12738.8i | − | 1.84915i | −0.380998 | − | 0.924576i | \(-0.624420\pi\) | ||
0.380998 | − | 0.924576i | \(-0.375580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20282.0 | −2.80720 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5670.14 | − | 2888.32i | −0.749126 | − | 0.381598i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9780.60i | − | 1.23477i | −0.786662 | − | 0.617384i | \(-0.788192\pi\) | ||
0.786662 | − | 0.617384i | \(-0.211808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1088.10 | 0.131397 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2768.56 | − | 5435.04i | 0.320102 | − | 0.628401i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2052.24i | − | 0.227395i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9324.85 | −0.991056 | −0.495528 | − | 0.868592i | \(-0.665025\pi\) | ||||
−0.495528 | + | 0.868592i | \(0.665025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8872.11 | + | 6448.86i | −0.905225 | + | 0.657979i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4534.01i | − | 0.444467i | −0.974993 | − | 0.222233i | \(-0.928665\pi\) | ||
0.974993 | − | 0.222233i | \(-0.0713347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −256.703 | −0.0241967 | −0.0120984 | − | 0.999927i | \(-0.503851\pi\) | ||||
−0.0120984 | + | 0.999927i | \(0.503851\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5081.69 | − | 2588.57i | −0.460925 | − | 0.234791i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14130.8i | 1.23424i | 0.786871 | + | 0.617118i | \(0.211700\pi\) | ||||
−0.786871 | + | 0.617118i | \(0.788300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3260.70 | 0.274447 | 0.137223 | − | 0.990540i | \(-0.456182\pi\) | ||||
0.137223 | + | 0.990540i | \(0.456182\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6662.31 | + | 13079.0i | −0.540728 | + | 1.06152i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17389.3i | 1.36184i | 0.732358 | + | 0.680920i | \(0.238420\pi\) | ||||
−0.732358 | + | 0.680920i | \(0.761580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 41121.8 | 3.10940 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3850.79 | + | 5297.79i | 0.281306 | + | 0.387010i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5796.25i | 0.409311i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3694.93 | −0.252369 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9839.91 | − | 5012.36i | −0.650401 | − | 0.331308i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 45548.8i | 2.91512i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −240.146 | −0.0148891 | −0.00744454 | − | 0.999972i | \(-0.502370\pi\) | ||||
−0.00744454 | + | 0.999972i | \(0.502370\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5847.56 | + | 11479.5i | −0.351395 | + | 0.689833i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10373.7i | 0.604493i | 0.953230 | + | 0.302247i | \(0.0977366\pi\) | ||||
−0.953230 | + | 0.302247i | \(0.902263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −586.494 | −0.0331559 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5380.83 | − | 33903.0i | −0.295245 | − | 1.86025i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17099.0i | − | 0.911025i | −0.890230 | − | 0.455512i | \(-0.849456\pi\) | ||
0.890230 | − | 0.455512i | \(-0.150544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20249.2 | 1.04804 | 0.524021 | − | 0.851705i | \(-0.324431\pi\) | ||||
0.524021 | + | 0.851705i | \(0.324431\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16569.0 | + | 8440.11i | 0.833410 | + | 0.424531i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10948.9i | 0.535425i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33293.5 | 1.58352 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9068.46 | − | 17802.5i | 0.419661 | − | 0.823849i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 5185.03i | − | 0.233550i | −0.993158 | − | 0.116775i | \(-0.962744\pi\) | ||
0.993158 | − | 0.116775i | \(-0.0372556\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30009.7 | 1.31616 | 0.658078 | − | 0.752950i | \(-0.271370\pi\) | ||||
0.658078 | + | 0.752950i | \(0.271370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28221.1 | + | 20513.0i | −1.20557 | + | 0.876288i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31913.1i | 1.32833i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21627.7 | −0.877429 | −0.438714 | − | 0.898627i | \(-0.644566\pi\) | ||||
−0.438714 | + | 0.898627i | \(0.644566\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11754.9 | − | 5987.82i | −0.464968 | − | 0.236851i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11751.9i | − | 0.453373i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −33476.0 | −1.25996 | −0.629982 | − | 0.776610i | \(-0.716938\pi\) | ||||
−0.629982 | + | 0.776610i | \(0.716938\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 26047.3 | − | 51134.2i | 0.956742 | − | 1.87821i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 32548.8i | 1.16708i | 0.812083 | + | 0.583542i | \(0.198334\pi\) | ||||
−0.812083 | + | 0.583542i | \(0.801666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22023.1 | −0.771090 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2075.61 | − | 2855.55i | −0.0709829 | − | 0.0976558i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4318.22i | 0.144282i | 0.997394 | + | 0.0721410i | \(0.0229832\pi\) | ||||
−0.997394 | + | 0.0721410i | \(0.977017\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21427.7 | 0.699680 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3772.64 | + | 1921.75i | 0.120420 | + | 0.0613409i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 10769.0i | − | 0.336101i | −0.985778 | − | 0.168051i | \(-0.946253\pi\) | ||
0.985778 | − | 0.168051i | \(-0.0537472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17404.6 | 0.531260 | 0.265630 | − | 0.964075i | \(-0.414420\pi\) | ||||
0.265630 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 163.003 | − | 319.996i | 0.00486736 | − | 0.00955525i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 76796.1i | − | 2.24386i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −58324.4 | −1.66789 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9688.89 | + | 1537.75i | −0.271238 | + | 0.0430489i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21212.1i | 0.581457i | 0.956806 | + | 0.290729i | \(0.0938977\pi\) | ||||
−0.956806 | + | 0.290729i | \(0.906102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 62278.9 | 1.67196 | 0.835980 | − | 0.548759i | \(-0.184900\pi\) | ||||
0.835980 | + | 0.548759i | \(0.184900\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −30533.7 | − | 15553.6i | −0.802989 | − | 0.409036i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 62929.2i | − | 1.62151i | −0.585384 | − | 0.810756i | \(-0.699056\pi\) | ||
0.585384 | − | 0.810756i | \(-0.300944\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28784.6 | 0.726867 | 0.363433 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363433 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18485.1 | − | 36288.5i | 0.457540 | − | 0.898209i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9514.70i | − | 0.230889i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57777.3 | 1.37483 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 57218.2 | − | 41590.1i | 1.33534 | − | 0.970620i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5901.55i | − | 0.135106i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1138.03 | 0.0255616 | 0.0127808 | − | 0.999918i | \(-0.495932\pi\) | ||||
0.0127808 | + | 0.999918i | \(0.495932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −79006.0 | − | 40244.9i | −1.74141 | − | 0.887058i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 67404.5i | − | 1.45818i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9120.20 | 0.193680 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13390.0 | − | 26286.2i | 0.279185 | − | 0.548075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34827.1i | 0.713072i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −67526.2 | −1.35788 | −0.678942 | − | 0.734192i | \(-0.737561\pi\) | ||||
−0.678942 | + | 0.734192i | \(0.737561\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 75832.9 | + | 104328.i | 1.49793 | + | 2.06081i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 69701.4i | 1.35266i | 0.736597 | + | 0.676332i | \(0.236431\pi\) | ||||
−0.736597 | + | 0.676332i | \(0.763569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4886.85 | 0.0931877 | 0.0465938 | − | 0.998914i | \(-0.485163\pi\) | ||||
0.0465938 | + | 0.998914i | \(0.485163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14613.3 | − | 7443.87i | −0.273857 | − | 0.139500i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18388.2i | 0.338710i | 0.985555 | + | 0.169355i | \(0.0541684\pi\) | ||||
−0.985555 | + | 0.169355i | \(0.945832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −97288.7 | −1.76168 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28325.5 | − | 55606.5i | 0.504290 | − | 0.989986i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 44332.4i | 0.776114i | 0.921635 | + | 0.388057i | \(0.126854\pi\) | ||||
−0.921635 | + | 0.388057i | \(0.873146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −37613.5 | −0.647604 | −0.323802 | − | 0.946125i | \(-0.604961\pi\) | ||||
−0.323802 | + | 0.946125i | \(0.604961\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −41776.2 | − | 41731.7i | −0.707484 | − | 0.706730i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 104532.i | 1.74147i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3523.99 | −0.0577617 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 102159. | + | 52038.8i | 1.64770 | + | 0.839321i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 35403.3i | 0.561948i | 0.959715 | + | 0.280974i | \(0.0906575\pi\) | ||||
−0.959715 | + | 0.280974i | \(0.909343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 118252. | 1.84744 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 82853.3 | − | 162652.i | 1.27418 | − | 2.50137i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 26838.2i | − | 0.406338i | −0.979144 | − | 0.203169i | \(-0.934876\pi\) | ||
0.979144 | − | 0.203169i | \(-0.0651241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21947.0 | −0.327171 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 46325.7 | − | 33672.7i | 0.680050 | − | 0.494307i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6793.65i | 0.0982182i | 0.998793 | + | 0.0491091i | \(0.0156382\pi\) | ||||
−0.998793 | + | 0.0491091i | \(0.984362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 69021.3 | 0.982860 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 78435.5 | + | 39954.3i | 1.10025 | + | 0.560456i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 39971.6i | 0.552392i | 0.961101 | + | 0.276196i | \(0.0890738\pi\) | ||||
−0.961101 | + | 0.276196i | \(0.910926\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10277.6 | 0.139944 | 0.0699720 | − | 0.997549i | \(-0.477709\pi\) | ||||
0.0699720 | + | 0.997549i | \(0.477709\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4444.94 | + | 8725.99i | −0.0596404 | + | 0.117082i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 215615.i | 2.85110i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20101.1 | −0.261975 | −0.130988 | − | 0.991384i | \(-0.541815\pi\) | ||||
−0.130988 | + | 0.991384i | \(0.541815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32276.5 | + | 44404.9i | 0.414647 | + | 0.570457i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 131139.i | − | 1.66081i | −0.557159 | − | 0.830406i | \(-0.688109\pi\) | ||
0.557159 | − | 0.830406i | \(-0.311891\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 71448.1 | 0.892109 | 0.446054 | − | 0.895006i | \(-0.352829\pi\) | ||||
0.446054 | + | 0.895006i | \(0.352829\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16457.9 | + | 8383.51i | 0.202621 | + | 0.103213i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 16511.7i | − | 0.200461i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −102002. | −1.22127 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38092.6 | − | 74780.6i | 0.449836 | − | 0.883085i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 21604.4i | − | 0.251656i | −0.992052 | − | 0.125828i | \(-0.959841\pi\) | ||
0.992052 | − | 0.125828i | \(-0.0401587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22151.9 | −0.254547 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15473.5 | − | 97493.8i | −0.175418 | − | 1.10526i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 70611.9i | − | 0.789834i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19263.0 | −0.212614 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36360.4 | + | 18521.7i | 0.396044 | + | 0.201742i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1878.93i | 0.0201981i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −109205. | −1.15869 | −0.579343 | − | 0.815084i | \(-0.696691\pi\) | ||||
−0.579343 | + | 0.815084i | \(0.696691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1048.65 | − | 2058.63i | 0.0109828 | − | 0.0215606i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 87204.3i | 0.901606i | 0.892623 | + | 0.450803i | \(0.148862\pi\) | ||||
−0.892623 | + | 0.450803i | \(0.851138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −45320.5 | −0.462601 | −0.231300 | − | 0.972882i | \(-0.574298\pi\) | ||||
−0.231300 | + | 0.972882i | \(0.574298\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 41518.0 | − | 30178.2i | 0.418423 | − | 0.304139i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 56611.4i | − | 0.563360i | −0.959508 | − | 0.281680i | \(-0.909108\pi\) | ||
0.959508 | − | 0.281680i | \(-0.0908916\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 95741.0 | 0.940842 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −113322. | − | 57725.0i | −1.09977 | − | 0.560214i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18772.1i | − | 0.179932i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 128750. | 1.21893 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13320.1 | + | 26149.2i | −0.124570 | + | 0.244547i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27803.4i | 0.256866i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −80681.1 | −0.736404 | −0.368202 | − | 0.929746i | \(-0.620026\pi\) | ||||
−0.368202 | + | 0.929746i | \(0.620026\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −77670.7 | − | 106857.i | −0.700437 | − | 0.963636i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 213076.i | 1.89865i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 96509.7 | 0.849790 | 0.424895 | − | 0.905243i | \(-0.360311\pi\) | ||||
0.424895 | + | 0.905243i | \(0.360311\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −139454. | − | 71036.5i | −1.21347 | − | 0.618133i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 91771.4i | 0.789221i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 62183.6 | 0.528552 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −167985. | + | 329776.i | −1.41134 | + | 2.77064i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 111073.i | − | 0.922466i | −0.887279 | − | 0.461233i | \(-0.847407\pi\) | ||
0.887279 | − | 0.461233i | \(-0.152593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −162219. | −1.33184 | −0.665919 | − | 0.746024i | \(-0.731960\pi\) | ||||
−0.665919 | + | 0.746024i | \(0.731960\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −58216.3 | + | 9239.66i | −0.472531 | + | 0.0749966i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 181489.i | − | 1.45647i | −0.685327 | − | 0.728236i | \(-0.740341\pi\) | ||
0.685327 | − | 0.728236i | \(-0.259659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 463902. | 3.68103 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −46483.0 | − | 23678.0i | −0.364719 | − | 0.185784i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 143379.i | 1.11249i | 0.831017 | + | 0.556247i | \(0.187759\pi\) | ||||
−0.831017 | + | 0.556247i | \(0.812241\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −128422. | −0.985425 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15094.0 | − | 29631.5i | 0.114549 | − | 0.224874i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 154346.i | 1.15853i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −106490. | −0.790635 | −0.395318 | − | 0.918544i | \(-0.629366\pi\) | ||||
−0.395318 | + | 0.918544i | \(0.629366\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 80393.2 | − | 58435.3i | 0.590428 | − | 0.429163i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 19725.1i | − | 0.143308i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −173884. | −1.24981 | −0.624903 | − | 0.780702i | \(-0.714862\pi\) | ||||
−0.624903 | + | 0.780702i | \(0.714862\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −365278. | − | 186070.i | −2.59754 | − | 1.32316i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 57169.7i | − | 0.402238i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16828.6 | 0.117158 | 0.0585788 | − | 0.998283i | \(-0.481343\pi\) | ||||
0.0585788 | + | 0.998283i | \(0.481343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 981.011 | − | 1925.85i | 0.00675809 | − | 0.0132670i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 149500.i | − | 1.01916i | −0.860422 | − | 0.509582i | \(-0.829800\pi\) | ||
0.860422 | − | 0.509582i | \(-0.170200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 85805.1 | 0.578884 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −68172.2 | − | 93788.9i | −0.455183 | − | 0.626224i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 70496.4i | 0.465873i | 0.972492 | + | 0.232937i | \(0.0748334\pi\) | ||||
−0.972492 | + | 0.232937i | \(0.925167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 376147. | 2.46039 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −83191.9 | − | 42377.2i | −0.538637 | − | 0.274377i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 326506.i | 2.09265i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −155197. | −0.984698 | −0.492349 | − | 0.870398i | \(-0.663862\pi\) | ||||
−0.492349 | + | 0.870398i | \(0.663862\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2395.86 | − | 4703.39i | 0.0150493 | − | 0.0295437i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 59448.0i | 0.369699i | 0.982767 | + | 0.184850i | \(0.0591798\pi\) | ||||
−0.982767 | + | 0.184850i | \(0.940820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 54799.3 | 0.337415 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 293866. | + | 95344.2i | 1.79159 | + | 0.581279i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 220840.i | − | 1.33318i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 166697. | 0.996507 | 0.498254 | − | 0.867031i | \(-0.333975\pi\) | ||||
0.498254 | + | 0.867031i | \(0.333975\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 137125. | + | 69850.5i | 0.811773 | + | 0.413510i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6330.63i | 0.0371148i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −599848. | −3.48293 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −82719.3 | + | 162389.i | −0.475701 | + | 0.933863i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 229117.i | − | 1.30506i | −0.757765 | − | 0.652528i | \(-0.773709\pi\) | ||
0.757765 | − | 0.652528i | \(-0.226291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −56063.1 | −0.316310 | −0.158155 | − | 0.987414i | \(-0.550555\pi\) | ||||
−0.158155 | + | 0.987414i | \(0.550555\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −135371. | + | 98396.8i | −0.756562 | + | 0.549921i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 685844.i | 3.79706i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 536.965 | 0.00294503 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −87804.7 | − | 44726.9i | −0.477093 | − | 0.243027i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 161763.i | 0.870813i | 0.900234 | + | 0.435406i | \(0.143395\pi\) | ||||
−0.900234 | + | 0.435406i | \(0.856605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −248951. | −1.32782 | −0.663909 | − | 0.747814i | \(-0.731104\pi\) | ||||
−0.663909 | + | 0.747814i | \(0.731104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −136006. | + | 266997.i | −0.718752 | + | 1.41100i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38060.4i | 0.199302i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −267787. | −1.38950 | −0.694752 | − | 0.719249i | \(-0.744486\pi\) | ||||
−0.694752 | + | 0.719249i | \(0.744486\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 105722. | + | 145449.i | 0.543612 | + | 0.747882i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 73935.0i | − | 0.376741i | −0.982098 | − | 0.188370i | \(-0.939679\pi\) | ||
0.982098 | − | 0.188370i | \(-0.0603205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −460552. | −2.32573 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41581.4 | + | 21181.2i | 0.208106 | + | 0.106007i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 81901.6i | − | 0.406256i | −0.979152 | − | 0.203128i | \(-0.934889\pi\) | ||
0.979152 | − | 0.203128i | \(-0.0651108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 166148. | 0.816850 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −122591. | + | 240662.i | −0.597397 | + | 1.17277i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 51236.6i | − | 0.247490i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 174674. | 0.836365 | 0.418183 | − | 0.908363i | \(-0.362667\pi\) | ||||
0.418183 | + | 0.908363i | \(0.362667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −49219.3 | − | 310116.i | −0.233620 | − | 1.47197i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 365747.i | − | 1.72099i | −0.509458 | − | 0.860495i | \(-0.670154\pi\) | ||
0.509458 | − | 0.860495i | \(-0.329846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 99999.2 | 0.466482 | 0.233241 | − | 0.972419i | \(-0.425067\pi\) | ||||
0.233241 | + | 0.972419i | \(0.425067\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −255927. | − | 130367.i | −1.18361 | − | 0.602922i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 341556.i | − | 1.56613i | −0.621938 | − | 0.783067i | \(-0.713654\pi\) | ||
0.621938 | − | 0.783067i | \(-0.286346\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 60893.5 | 0.276838 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 88350.6 | − | 173444.i | 0.398261 | − | 0.781837i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 193833.i | − | 0.866374i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −69397.1 | −0.307577 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 96038.6 | − | 69807.4i | 0.422094 | − | 0.306807i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 168022.i | − | 0.732309i | −0.930554 | − | 0.366155i | \(-0.880674\pi\) | ||
0.930554 | − | 0.366155i | \(-0.119326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −131870. | −0.569974 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 94244.2 | + | 48007.1i | 0.403980 | + | 0.205784i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 439091.i | 1.86669i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −173451. | −0.731339 | −0.365669 | − | 0.930745i | \(-0.619160\pi\) | ||||
−0.365669 | + | 0.930745i | \(0.619160\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 136751. | − | 268460.i | 0.571892 | − | 1.12270i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 46403.4i | 0.192481i | 0.995358 | + | 0.0962403i | \(0.0306817\pi\) | ||||
−0.995358 | + | 0.0962403i | \(0.969318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 304541. | 1.25300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 303666. | + | 417772.i | 1.23932 | + | 1.70502i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 132575.i | − | 0.536721i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 269136. | 1.08086 | 0.540432 | − | 0.841388i | \(-0.318261\pi\) | ||||
0.540432 | + | 0.841388i | \(0.318261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −261025. | − | 132964.i | −1.03994 | − | 0.529734i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 494532.i | 1.95460i | 0.211854 | + | 0.977301i | \(0.432050\pi\) | ||||
−0.211854 | + | 0.977301i | \(0.567950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −213499. | −0.837167 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 89965.7 | − | 176614.i | 0.349994 | − | 0.687084i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 291389.i | − | 1.12470i | −0.826899 | − | 0.562350i | \(-0.809897\pi\) | ||
0.826899 | − | 0.562350i | \(-0.190103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44109.3 | 0.168923 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31379.1 | − | 4980.25i | 0.119236 | − | 0.0189242i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12087.7i | 0.0455753i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −279770. | −1.04669 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34629.9 | − | 17640.2i | −0.128563 | − | 0.0654890i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 47916.2i | − | 0.176525i | −0.996097 | − | 0.0882626i | \(-0.971869\pi\) | ||
0.996097 | − | 0.0882626i | \(-0.0281315\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −256372. | −0.937275 | −0.468638 | − | 0.883390i | \(-0.655255\pi\) | ||||
−0.468638 | + | 0.883390i | \(0.655255\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −87533.4 | + | 171839.i | −0.317581 | + | 0.623453i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 291914.i | 1.05107i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −482796. | −1.72525 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30822.9 | + | 22404.2i | −0.109316 | + | 0.0794585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 99211.8i | − | 0.349228i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 665393. | 2.32472 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 86362.1 | + | 43992.1i | 0.299485 | + | 0.152555i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 300598.i | 1.03469i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 555503. | 1.89798 | 0.948991 | − | 0.315303i | \(-0.102106\pi\) | ||||
0.948991 | + | 0.315303i | \(0.102106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −71098.8 | + | 139576.i | −0.241136 | + | 0.473382i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 153541.i | − | 0.516929i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −441029. | −1.47398 | −0.736992 | − | 0.675902i | \(-0.763754\pi\) | ||||
−0.736992 | + | 0.675902i | \(0.763754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1900.33 | + | 2614.40i | 0.00630498 | + | 0.00867417i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30815.0i | 0.101498i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 93309.9 | 0.305125 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 615866. | + | 313717.i | 1.99940 | + | 1.01848i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 284934.i | − | 0.918403i | −0.888332 | − | 0.459201i | \(-0.848136\pi\) | ||
0.888332 | − | 0.459201i | \(-0.151864\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −115743. | −0.370401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 238259. | − | 467732.i | 0.757047 | − | 1.48618i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 47991.2i | − | 0.151407i | −0.997130 | − | 0.0757033i | \(-0.975880\pi\) | ||
0.997130 | − | 0.0757033i | \(-0.0241202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 818834. | 2.56507 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27247.7 | − | 83981.8i | 0.0847548 | − | 0.261228i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 115826.i | 0.357752i | 0.983872 | + | 0.178876i | \(0.0572461\pi\) | ||||
−0.983872 | + | 0.178876i | \(0.942754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −364260. | −1.11722 | −0.558611 | − | 0.829430i | \(-0.688666\pi\) | ||||
−0.558611 | + | 0.829430i | \(0.688666\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −170111. | − | 86652.8i | −0.518110 | − | 0.263921i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1.39055e6i | − | 4.20581i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24454.8 | −0.0734536 | −0.0367268 | − | 0.999325i | \(-0.511693\pi\) | ||||
−0.0367268 | + | 0.999325i | \(0.511693\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −254413. | + | 499445.i | −0.758895 | + | 1.48981i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 171426.i | 0.507838i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 198482. | 0.583962 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 249464. | − | 181327.i | 0.728946 | − | 0.529848i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 469246.i | − | 1.36183i | −0.732361 | − | 0.680917i | \(-0.761582\pi\) | ||
0.732361 | − | 0.680917i | \(-0.238418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29537.3 | −0.0851413 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 504661. | + | 257070.i | 1.44486 | + | 0.735997i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 420993.i | 1.19720i | 0.801049 | + | 0.598599i | \(0.204276\pi\) | ||||
−0.801049 | + | 0.598599i | \(0.795724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 272936. | 0.770950 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −117587. | + | 230838.i | −0.329921 | + | 0.647678i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 451331.i | − | 1.25789i | −0.777452 | − | 0.628943i | \(-0.783488\pi\) | ||
0.777452 | − | 0.628943i | \(-0.216512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −52086.7 | −0.144204 | −0.0721021 | − | 0.997397i | \(-0.522971\pi\) | ||||
−0.0721021 | + | 0.997397i | \(0.522971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 215503. | + | 296482.i | 0.592678 | + | 0.815386i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 173988.i | 0.475344i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −433006. | −1.17521 | −0.587606 | − | 0.809147i | \(-0.699929\pi\) | ||||
−0.587606 | + | 0.809147i | \(0.699929\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 76303.1 | + | 38868.1i | 0.205735 | + | 0.104799i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 167059.i | 0.447493i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 136805. | 0.364067 | 0.182033 | − | 0.983292i | \(-0.441732\pi\) | ||||
0.182033 | + | 0.983292i | \(0.441732\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −236024. | + | 463344.i | −0.624029 | + | 1.22505i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 473739.i | 1.24443i | 0.782848 | + | 0.622213i | \(0.213766\pi\) | ||||
−0.782848 | + | 0.622213i | \(0.786234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −148551. | −0.387700 | −0.193850 | − | 0.981031i | \(-0.562097\pi\) | ||||
−0.193850 | + | 0.981031i | \(0.562097\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 99791.9 | + | 628759.i | 0.258769 | + | 1.63043i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 131618.i | 0.339108i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.14962e6 | 2.94304 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 47327.5 | + | 24108.2i | 0.120387 | + | 0.0613239i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 702465.i | − | 1.77551i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −376817. | −0.946393 | −0.473197 | − | 0.880957i | \(-0.656900\pi\) | ||||
−0.473197 | + | 0.880957i | \(0.656900\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4648.91 | + | 9126.40i | −0.0116023 | + | 0.0227768i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11308.1i | 0.0280441i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 179496. | 0.442360 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 645488. | − | 469185.i | 1.58084 | − | 1.14906i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 53679.4i | − | 0.130645i | −0.997864 | − | 0.0653223i | \(-0.979192\pi\) | ||
0.997864 | − | 0.0653223i | \(-0.0208076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −298361. | −0.721640 | −0.360820 | − | 0.932636i | \(-0.617503\pi\) | ||||
−0.360820 | + | 0.932636i | \(0.617503\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 540550. | + | 275352.i | 1.29932 | + | 0.661863i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 239784.i | 0.572811i | 0.958109 | + | 0.286405i | \(0.0924604\pi\) | ||||
−0.958109 | + | 0.286405i | \(0.907540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −63701.5 | −0.151238 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37256.6 | + | 73139.4i | −0.0879105 | + | 0.172580i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 334473.i | 0.784394i | 0.919881 | + | 0.392197i | \(0.128285\pi\) | ||||
−0.919881 | + | 0.392197i | \(0.871715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 488480. | 1.13858 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 156103. | + | 214762.i | 0.361644 | + | 0.497538i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 403774.i | 0.929753i | 0.885375 | + | 0.464877i | \(0.153901\pi\) | ||||
−0.885375 | + | 0.464877i | \(0.846099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 434314. | 0.994033 | 0.497016 | − | 0.867741i | \(-0.334429\pi\) | ||||
0.497016 | + | 0.867741i | \(0.334429\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −279296. | − | 142271.i | −0.635386 | − | 0.323660i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 27617.0i | 0.0624501i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −617455. | −1.38789 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 275848. | − | 541526.i | 0.616337 | − | 1.20995i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5403.17i | 0.0120006i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 202502. | 0.447095 | 0.223547 | − | 0.974693i | \(-0.428236\pi\) | ||||
0.223547 | + | 0.974693i | \(0.428236\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.14644e6 | + | 181955.i | −2.51620 | + | 0.399352i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 572509.i | − | 1.24912i | −0.780976 | − | 0.624561i | \(-0.785278\pi\) | ||
0.780976 | − | 0.624561i | \(-0.214722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 125485. | 0.272177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −558970. | − | 284734.i | −1.20530 | − | 0.613968i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 500197.i | − | 1.07226i | −0.844136 | − | 0.536130i | \(-0.819886\pi\) | ||
0.844136 | − | 0.536130i | \(-0.180114\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −805163. | −1.71594 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19963.1 | + | 39190.1i | −0.0422975 | + | 0.0830353i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 118519.i | − | 0.249661i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 199477. | 0.417769 | 0.208885 | − | 0.977940i | \(-0.433017\pi\) | ||||
0.208885 | + | 0.977940i | \(0.433017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 119392. | − | 86782.3i | 0.248605 | − | 0.180703i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 953501.i | − | 1.97402i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 528497. | 1.08787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −147464. | − | 75116.9i | −0.301809 | − | 0.153739i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 465306.i | − | 0.946896i | −0.880822 | − | 0.473448i | \(-0.843009\pi\) | ||
0.880822 | − | 0.473448i | \(-0.156991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 71079.0 | 0.143824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 397430. | − | 780207.i | 0.799618 | − | 1.56975i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 61014.2i | 0.122065i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −609830. | −1.21316 | −0.606578 | − | 0.795024i | \(-0.707458\pi\) | ||||
−0.606578 | + | 0.795024i | \(0.707458\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 330225. | + | 454312.i | 0.653237 | + | 0.898700i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 591854.i | − | 1.16422i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 515565. | 1.00849 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −355524. | − | 181101.i | −0.691561 | − | 0.352275i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 149703.i | 0.289583i | 0.989462 | + | 0.144792i | \(0.0462512\pi\) | ||||
−0.989462 | + | 0.144792i | \(0.953749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3454.46 | 0.00664522 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 153653. | − | 301641.i | 0.293945 | − | 0.577051i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.12583e6i | − | 2.14189i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 583781. | 1.10454 | 0.552270 | − | 0.833666i | \(-0.313762\pi\) | ||||
0.552270 | + | 0.833666i | \(0.313762\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 505325. | − | 164548.i | 0.950859 | − | 0.309626i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 616560.i | − | 1.15383i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −362613. | −0.674894 | −0.337447 | − | 0.941344i | \(-0.609563\pi\) | ||||
−0.337447 | + | 0.941344i | \(0.609563\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −838291. | − | 427018.i | −1.55174 | − | 0.790445i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 612737.i | 1.12808i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −507748. | −0.929736 | −0.464868 | − | 0.885380i | \(-0.653898\pi\) | ||||
−0.464868 | + | 0.885380i | \(0.653898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14395.7 | − | 28260.6i | 0.0262178 | − | 0.0514689i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 332553.i | − | 0.602398i | −0.953561 | − | 0.301199i | \(-0.902613\pi\) | ||
0.953561 | − | 0.301199i | \(-0.0973868\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −244154. | −0.439898 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −834649. | + | 606680.i | −1.49576 | + | 1.08722i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 190158.i | − | 0.338962i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 504118. | 0.893824 | 0.446912 | − | 0.894578i | \(-0.352524\pi\) | ||||
0.446912 | + | 0.894578i | \(0.352524\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −283916. | − | 144624.i | −0.500726 | − | 0.255066i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.41310e6i | − | 2.47902i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −456478. | −0.796578 | −0.398289 | − | 0.917260i | \(-0.630396\pi\) | ||||
−0.398289 | + | 0.917260i | \(0.630396\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −483068. | + | 948325.i | −0.838542 | + | 1.64617i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 297610.i | − | 0.513899i | −0.966425 | − | 0.256950i | \(-0.917283\pi\) | ||
0.966425 | − | 0.256950i | \(-0.0827174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43879.3 | −0.0753721 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 965924. | + | 1.32888e6i | 1.65052 | + | 2.27072i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38038.0i | 0.0646587i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 58486.7 | 0.0989018 | 0.0494509 | − | 0.998777i | \(-0.484253\pi\) | ||||
0.0494509 | + | 0.998777i | \(0.484253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 215229. | + | 109636.i | 0.362070 | + | 0.184435i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 328151.i | − | 0.549180i | −0.961561 | − | 0.274590i | \(-0.911458\pi\) | ||
0.961561 | − | 0.274590i | \(-0.0885422\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.07915e6 | 1.79671 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 89654.7 | − | 176004.i | 0.148502 | − | 0.291528i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 53476.0i | 0.0881220i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.33403e6 | 2.18707 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 80794.8 | + | 509064.i | 0.131783 | + | 0.830326i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.01841e6i | 1.65266i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 668331. | 1.07905 | 0.539526 | − | 0.841969i | \(-0.318603\pi\) | ||||
0.539526 | + | 0.841969i | \(0.318603\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54481.7 | − | 27752.5i | −0.0875178 | − | 0.0445808i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 234009.i | − | 0.374006i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3226.39 | 0.00513062 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −281956. | + | 553516.i | −0.446116 | + | 0.875782i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 247744.i | 0.390020i | 0.980801 | + | 0.195010i | \(0.0624739\pi\) | ||||
−0.980801 | + | 0.195010i | \(0.937526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −889915. | −1.39397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −640827. | + | 465797.i | −0.998794 | + | 0.725992i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 443847.i | 0.688338i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −553376. | −0.853942 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −320552. | − | 163286.i | −0.492211 | − | 0.250728i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 402635.i | − | 0.615197i | −0.951516 | − | 0.307599i | \(-0.900475\pi\) | ||
0.951516 | − | 0.307599i | \(-0.0995254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 257418. | 0.391378 | 0.195689 | − | 0.980666i | \(-0.437306\pi\) | ||||
0.195689 | + | 0.980666i | \(0.437306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41984.7 | + | 82421.3i | −0.0635199 | + | 0.124698i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.57633e6i | 2.37318i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62386.6 | 0.0934646 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −51820.2 | − | 71292.4i | −0.0772558 | − | 0.106286i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 924513.i | 1.37160i | 0.727791 | + | 0.685799i | \(0.240547\pi\) | ||||
−0.727791 | + | 0.685799i | \(0.759453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −607274. | −0.896572 | −0.448286 | − | 0.893890i | \(-0.647965\pi\) | ||||
−0.448286 | + | 0.893890i | \(0.647965\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.72912e6 | − | 880798.i | −2.54049 | − | 1.29410i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 588258.i | 0.860116i | 0.902801 | + | 0.430058i | \(0.141507\pi\) | ||||
−0.902801 | + | 0.430058i | \(0.858493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 517960. | 0.753680 | 0.376840 | − | 0.926278i | \(-0.377011\pi\) | ||||
0.376840 | + | 0.926278i | \(0.377011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 82114.2 | − | 161201.i | 0.118909 | − | 0.233434i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 956167.i | 1.37798i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53267e6 | 2.19824 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −487957. | + | 77444.8i | −0.696515 | + | 0.110546i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 610245.i | − | 0.866923i | −0.901172 | − | 0.433462i | \(-0.857292\pi\) | ||
0.901172 | − | 0.433462i | \(-0.142708\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 207369. | 0.293193 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.05167e6 | + | 535712.i | 1.47987 | + | 0.753835i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.03703e6i | 1.45237i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49722.7 | 0.0693087 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −291870. | + | 572978.i | −0.404924 | + | 0.794918i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.42425e6i | 1.96664i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.21432e6 | −1.66891 | −0.834456 | − | 0.551074i | \(-0.814218\pi\) | ||||
−0.834456 | + | 0.551074i | \(0.814218\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −134463. | + | 97737.0i | −0.183938 | + | 0.133699i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 471294.i | 0.641697i | 0.947131 | + | 0.320848i | \(0.103968\pi\) | ||||
−0.947131 | + | 0.320848i | \(0.896032\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 83030.5 | 0.112526 | 0.0562628 | − | 0.998416i | \(-0.482082\pi\) | ||||
0.0562628 | + | 0.998416i | \(0.482082\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 132416. | + | 67451.4i | 0.178621 | + | 0.0909882i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.01156e6i | − | 1.35822i | −0.734038 | − | 0.679108i | \(-0.762367\pi\) | ||
0.734038 | − | 0.679108i | \(-0.237633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 203337. | 0.271760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 416684. | − | 818003.i | 0.554330 | − | 1.08822i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 938924.i | 1.24334i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 365883. | 0.482287 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 444092. | + | 610966.i | 0.582699 | + | 0.801657i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 612951.i | − | 0.800589i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.31317e6 | 1.70734 | 0.853670 | − | 0.520814i | \(-0.174371\pi\) | ||||
0.853670 | + | 0.520814i | \(0.174371\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 173256. | + | 88255.3i | 0.224239 | + | 0.114225i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.01689e6i | − | 1.31015i | −0.755563 | − | 0.655076i | \(-0.772637\pi\) | ||
0.755563 | − | 0.655076i | \(-0.227363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −78120.5 | −0.100194 | −0.0500972 | − | 0.998744i | \(-0.515953\pi\) | ||||
−0.0500972 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 90491.9 | − | 177647.i | 0.115538 | − | 0.226815i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.12684e6i | − | 1.43224i | −0.697978 | − | 0.716119i | \(-0.745917\pi\) | ||
0.697978 | − | 0.716119i | \(-0.254083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3231.65 | 0.00408903 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 845061. | + | 274178.i | 1.06447 | + | 0.345364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 90046.0i | − | 0.112918i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −507095. | −0.633058 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 566272. | + | 288454.i | 0.703785 | + | 0.358502i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 479184.i | − | 0.592902i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 631348. | 0.777713 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 78690.7 | − | 154480.i | 0.0965046 | − | 0.189451i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 819553.i | − | 1.00064i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −684108. | −0.831592 | −0.415796 | − | 0.909458i | \(-0.636497\pi\) | ||||
−0.415796 | + | 0.909458i | \(0.636497\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −297069. | + | 215930.i | −0.359526 | + | 0.261328i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 217276.i | 0.261804i | 0.991395 | + | 0.130902i | \(0.0417873\pi\) | ||||
−0.991395 | + | 0.130902i | \(0.958213\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.72496e6 | −2.06937 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15068.0 | − | 7675.53i | −0.0179976 | − | 0.00916782i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 139599.i | − | 0.166014i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −953956. | −1.12953 | −0.564764 | − | 0.825252i | \(-0.691033\pi\) | ||||
−0.564764 | + | 0.825252i | \(0.691033\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 446109. | − | 875770.i | 0.525923 | − | 1.03245i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 796585.i | − | 0.935037i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.59689e6 | −3.03508 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12225.4 | + | 16819.3i | 0.0142267 | + | 0.0195725i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.35448e6i | 1.56942i | 0.619860 | + | 0.784712i | \(0.287189\pi\) | ||||
−0.619860 | + | 0.784712i | \(0.712811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −96749.8 | −0.111622 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −699334. | − | 356235.i | −0.803381 | − | 0.409235i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.74640e6i | 3.14152i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −915233. | −1.04244 | −0.521222 | − | 0.853421i | \(-0.674524\pi\) | ||||
−0.521222 | + | 0.853421i | \(0.674524\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 185137. | − | 363448.i | 0.209972 | − | 0.412203i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 85021.4i | − | 0.0960172i | −0.998847 | − | 0.0480086i | \(-0.984713\pi\) | ||
0.998847 | − | 0.0480086i | \(-0.0152875\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.07153e6 | −1.20498 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 72409.9 | + | 456233.i | 0.0810839 | + | 0.510885i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 647558.i | − | 0.722069i | −0.932552 | − | 0.361034i | \(-0.882424\pi\) | ||
0.932552 | − | 0.361034i | \(-0.117576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 265033. | 0.294285 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 453995. | + | 231261.i | 0.501984 | + | 0.255706i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.08402e6i | 1.19358i | 0.802396 | + | 0.596792i | \(0.203558\pi\) | ||||
−0.802396 | + | 0.596792i | \(0.796442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 998843. | 1.09519 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −391108. | + | 767795.i | −0.427044 | + | 0.838342i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 230102.i | 0.250197i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −464205. | −0.502647 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 925850. | − | 672972.i | 0.998362 | − | 0.725678i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.93261e6i | − | 3.14919i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.36907e6 | −1.46410 | −0.732052 | − | 0.681249i | \(-0.761437\pi\) | ||||
−0.732052 | + | 0.681249i | \(0.761437\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 150543. | + | 76685.3i | 0.160329 | + | 0.0816703i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.36937e6i | 1.45239i | 0.687490 | + | 0.726194i | \(0.258713\pi\) | ||||
−0.687490 | + | 0.726194i | \(0.741287\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −272494. | −0.287827 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −525950. | + | 1.03251e6i | −0.553267 | + | 1.08613i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 410297.i | − | 0.429842i | −0.976631 | − | 0.214921i | \(-0.931051\pi\) | ||
0.976631 | − | 0.214921i | \(-0.0689494\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.32439e6 | −1.38182 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −155289. | − | 213642.i | −0.161363 | − | 0.221997i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 196933.i | − | 0.203804i | −0.994794 | − | 0.101902i | \(-0.967507\pi\) | ||
0.994794 | − | 0.101902i | \(-0.0324928\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.96323e6 | −3.05417 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −222969. | − | 113579.i | −0.228882 | − | 0.116590i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.25007e6i | 1.27803i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 948066. | 0.965365 | 0.482682 | − | 0.875795i | \(-0.339663\pi\) | ||||
0.482682 | + | 0.875795i | \(0.339663\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 329587. | − | 647022.i | 0.334250 | − | 0.656176i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.35542e6i | − | 1.36908i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 300322. | 0.302132 | 0.151066 | − | 0.988524i | \(-0.451729\pi\) | ||||
0.151066 | + | 0.988524i | \(0.451729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.17423e6 | − | 186364.i | 1.17658 | − | 0.186738i |
(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 | 384.5.e.b.257.6 | yes | 16 | |
3.2 | odd | 2 | inner | 384.5.e.b.257.5 | yes | 16 | |
4.3 | odd | 2 | 384.5.e.c.257.11 | yes | 16 | ||
8.3 | odd | 2 | 384.5.e.a.257.6 | yes | 16 | ||
8.5 | even | 2 | 384.5.e.d.257.11 | yes | 16 | ||
12.11 | even | 2 | 384.5.e.c.257.12 | yes | 16 | ||
24.5 | odd | 2 | 384.5.e.d.257.12 | yes | 16 | ||
24.11 | even | 2 | 384.5.e.a.257.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.e.a.257.5 | ✓ | 16 | 24.11 | even | 2 | ||
384.5.e.a.257.6 | yes | 16 | 8.3 | odd | 2 | ||
384.5.e.b.257.5 | yes | 16 | 3.2 | odd | 2 | inner | |
384.5.e.b.257.6 | yes | 16 | 1.1 | even | 1 | trivial | |
384.5.e.c.257.11 | yes | 16 | 4.3 | odd | 2 | ||
384.5.e.c.257.12 | yes | 16 | 12.11 | even | 2 | ||
384.5.e.d.257.11 | yes | 16 | 8.5 | even | 2 | ||
384.5.e.d.257.12 | yes | 16 | 24.5 | odd | 2 |