Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,5,Mod(209,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.209");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.p (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(57.8871793270\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.1 | ||
Root | \(2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.209 |
Dual form | 560.5.p.e.209.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 5.00000 | 0.555556 | 0.277778 | − | 0.960645i | \(-0.410402\pi\) | ||||
0.277778 | + | 0.960645i | \(0.410402\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | − | 24.4949i | −0.200000 | − | 0.979796i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.0000 | + | 34.2929i | 0.714286 | + | 0.699854i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −56.0000 | −0.691358 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −89.0000 | −0.735537 | −0.367769 | − | 0.929917i | \(-0.619878\pi\) | ||||
−0.367769 | + | 0.929917i | \(0.619878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.00000 | 0.0295858 | 0.0147929 | − | 0.999891i | \(-0.495291\pi\) | ||||
0.0147929 | + | 0.999891i | \(0.495291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −25.0000 | − | 122.474i | −0.111111 | − | 0.544331i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 485.000 | 1.67820 | 0.839100 | − | 0.543977i | \(-0.183082\pi\) | ||||
0.839100 | + | 0.543977i | \(0.183082\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 220.454i | 0.610676i | 0.952244 | + | 0.305338i | \(0.0987695\pi\) | ||||
−0.952244 | + | 0.305338i | \(0.901231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 175.000 | + | 171.464i | 0.396825 | + | 0.388808i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 700.554i | − | 1.32430i | −0.749372 | − | 0.662149i | \(-0.769644\pi\) | ||
0.749372 | − | 0.662149i | \(-0.230356\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −575.000 | + | 244.949i | −0.920000 | + | 0.391918i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −685.000 | −0.939643 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 191.000 | 0.227111 | 0.113555 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113555 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1053.28i | − | 1.09603i | −0.836470 | − | 0.548013i | \(-0.815385\pi\) | ||
0.836470 | − | 0.548013i | \(-0.184615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −445.000 | −0.408632 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 665.000 | − | 1028.79i | 0.542857 | − | 0.839825i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1631.36i | − | 1.19164i | −0.803117 | − | 0.595822i | \(-0.796826\pi\) | ||
0.803117 | − | 0.595822i | \(-0.203174\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 25.0000 | 0.0164366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2914.89i | − | 1.73402i | −0.498288 | − | 0.867012i | \(-0.666038\pi\) | ||
0.498288 | − | 0.867012i | \(-0.333962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 377.221i | 0.204014i | 0.994784 | + | 0.102007i | \(0.0325264\pi\) | ||||
−0.994784 | + | 0.102007i | \(0.967474\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 280.000 | + | 1371.71i | 0.138272 | + | 0.677390i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2195.00 | −0.993662 | −0.496831 | − | 0.867847i | \(-0.665503\pi\) | ||||
−0.496831 | + | 0.867847i | \(0.665503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | + | 2400.50i | 0.0204082 | + | 0.999792i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2425.00 | 0.932334 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1587.27i | 0.565066i | 0.959258 | + | 0.282533i | \(0.0911746\pi\) | ||||
−0.959258 | + | 0.282533i | \(0.908825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 445.000 | + | 2180.05i | 0.147107 | + | 0.720676i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1102.27i | 0.339265i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 3625.24i | − | 1.04144i | −0.853728 | − | 0.520719i | \(-0.825664\pi\) | ||
0.853728 | − | 0.520719i | \(-0.174336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1935.10i | − | 0.520048i | −0.965602 | − | 0.260024i | \(-0.916270\pi\) | ||
0.965602 | − | 0.260024i | \(-0.0837304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1960.00 | − | 1920.40i | −0.493827 | − | 0.483850i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.0000 | − | 122.474i | −0.00591716 | − | 0.0289880i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2047.77i | 0.456176i | 0.973641 | + | 0.228088i | \(0.0732474\pi\) | ||||
−0.973641 | + | 0.228088i | \(0.926753\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3502.77i | − | 0.735722i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4454.00 | −0.883555 | −0.441777 | − | 0.897125i | \(-0.645652\pi\) | ||||
−0.441777 | + | 0.897125i | \(0.645652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8650.00 | −1.62319 | −0.811597 | − | 0.584218i | \(-0.801401\pi\) | ||||
−0.811597 | + | 0.584218i | \(0.801401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2875.00 | + | 1224.74i | −0.511111 | + | 0.217732i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3115.00 | − | 3052.06i | −0.525384 | − | 0.514769i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5561.00 | −0.891043 | −0.445522 | − | 0.895271i | \(-0.646982\pi\) | ||||
−0.445522 | + | 0.895271i | \(0.646982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1111.00 | 0.169334 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1990.00 | 0.288866 | 0.144433 | − | 0.989515i | \(-0.453864\pi\) | ||||
0.144433 | + | 0.989515i | \(0.453864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2425.00 | − | 11880.0i | −0.335640 | − | 1.64429i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 955.000 | 0.126173 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 808.332i | 0.102049i | 0.998697 | + | 0.0510246i | \(0.0162487\pi\) | ||||
−0.998697 | + | 0.0510246i | \(0.983751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 175.000 | + | 171.464i | 0.0211327 | + | 0.0207057i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5266.40i | − | 0.608903i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5400.00 | − | 1102.27i | 0.598338 | − | 0.122135i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9235.00 | −0.981507 | −0.490754 | − | 0.871298i | \(-0.663278\pi\) | ||||
−0.490754 | + | 0.871298i | \(0.663278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4984.00 | 0.508520 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4825.49i | 0.473041i | 0.971626 | + | 0.236521i | \(0.0760071\pi\) | ||||
−0.971626 | + | 0.236521i | \(0.923993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4715.00 | −0.444434 | −0.222217 | − | 0.974997i | \(-0.571329\pi\) | ||||
−0.222217 | + | 0.974997i | \(0.571329\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3325.00 | − | 5143.93i | 0.301587 | − | 0.466569i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12668.8i | − | 1.10654i | −0.833002 | − | 0.553269i | \(-0.813380\pi\) | ||
0.833002 | − | 0.553269i | \(-0.186620\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12311.0 | 1.03619 | 0.518096 | − | 0.855322i | \(-0.326641\pi\) | ||||
0.518096 | + | 0.855322i | \(0.326641\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 8156.80i | − | 0.662024i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3120.65i | − | 0.244393i | −0.992506 | − | 0.122196i | \(-0.961006\pi\) | ||
0.992506 | − | 0.122196i | \(-0.0389938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17160.0 | + | 3502.77i | −1.29754 | + | 0.264860i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −280.000 | −0.0204544 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16975.0 | + | 16632.0i | 1.19871 | + | 1.17450i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6720.00 | −0.458985 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 14574.5i | − | 0.963346i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8875.00 | + | 12859.8i | 0.568000 | + | 0.823029i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 23867.8i | − | 1.47981i | −0.672712 | − | 0.739904i | \(-0.734871\pi\) | ||
0.672712 | − | 0.739904i | \(-0.265129\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1886.11i | 0.113341i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6736.10i | 0.392524i | 0.980552 | + | 0.196262i | \(0.0628802\pi\) | ||||
−0.980552 | + | 0.196262i | \(0.937120\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7560.00 | + | 7715.89i | −0.427384 | + | 0.436197i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3425.00 | + | 16779.0i | 0.187929 | + | 0.920659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 23069.3i | − | 1.22912i | −0.788871 | − | 0.614558i | \(-0.789334\pi\) | ||
0.788871 | − | 0.614558i | \(-0.210666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 29491.9i | − | 1.52641i | −0.646154 | − | 0.763207i | \(-0.723624\pi\) | ||
0.646154 | − | 0.763207i | \(-0.276376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10975.0 | −0.552035 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −445.000 | −0.0217615 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −955.000 | − | 4678.53i | −0.0454221 | − | 0.222522i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 245.000 | + | 12002.5i | 0.0113379 | + | 0.555440i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 28346.0 | 1.27679 | 0.638395 | − | 0.769709i | \(-0.279599\pi\) | ||||
0.638395 | + | 0.769709i | \(0.279599\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17551.0 | 0.769747 | 0.384873 | − | 0.922969i | \(-0.374245\pi\) | ||||
0.384873 | + | 0.922969i | \(0.374245\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27160.0 | −1.16024 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25800.0 | + | 5266.40i | −1.07388 | + | 0.219205i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25790.0 | 1.04629 | 0.523145 | − | 0.852244i | \(-0.324759\pi\) | ||||
0.523145 | + | 0.852244i | \(0.324759\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7936.35i | 0.313925i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24024.0 | − | 24519.4i | 0.926816 | − | 0.945928i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 37153.9i | − | 1.39839i | −0.714930 | − | 0.699196i | \(-0.753542\pi\) | ||
0.714930 | − | 0.699196i | \(-0.246458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2225.00 | + | 10900.2i | 0.0817264 | + | 0.400376i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20795.0 | −0.745634 | −0.372817 | − | 0.927905i | \(-0.621608\pi\) | ||||
−0.372817 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28536.0 | −0.999125 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 12345.4i | − | 0.422196i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −115.000 | −0.00384243 | −0.00192121 | − | 0.999998i | \(-0.500612\pi\) | ||||
−0.00192121 | + | 0.999998i | \(0.500612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −28525.0 | − | 11145.2i | −0.931429 | − | 0.363924i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 18126.2i | − | 0.578577i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5318.00 | −0.165975 | −0.0829874 | − | 0.996551i | \(-0.526446\pi\) | ||||
−0.0829874 | + | 0.996551i | \(0.526446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12345.4i | 0.376833i | 0.982089 | + | 0.188417i | \(0.0603355\pi\) | ||||
−0.982089 | + | 0.188417i | \(0.939665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9675.48i | − | 0.288915i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −39960.0 | + | 8156.80i | −1.16757 | + | 0.238329i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −43165.0 | −1.23438 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23975.0 | − | 23490.6i | −0.671174 | − | 0.657613i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14263.0 | 0.390971 | 0.195485 | − | 0.980707i | \(-0.437372\pi\) | ||||
0.195485 | + | 0.980707i | \(0.437372\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 32005.0i | 0.859219i | 0.903015 | + | 0.429609i | \(0.141349\pi\) | ||||
−0.903015 | + | 0.429609i | \(0.858651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −125.000 | − | 612.372i | −0.00328731 | − | 0.0161045i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3394.99i | − | 0.0874795i | −0.999043 | − | 0.0437398i | \(-0.986073\pi\) | ||
0.999043 | − | 0.0437398i | \(-0.0139272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19400.0i | − | 0.489886i | −0.969538 | − | 0.244943i | \(-0.921231\pi\) | ||
0.969538 | − | 0.244943i | \(-0.0787692\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10238.9i | 0.253431i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6685.00 | + | 6549.94i | 0.162222 | + | 0.158944i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −71400.0 | + | 14574.5i | −1.69899 | + | 0.346805i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 39231.0i | 0.915565i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 19620.4i | − | 0.449175i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −52817.0 | −1.18634 | −0.593170 | − | 0.805078i | \(-0.702124\pi\) | ||||
−0.593170 | + | 0.805078i | \(0.702124\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22270.0 | −0.490864 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9240.00 | − | 1886.11i | 0.199892 | − | 0.0408027i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36120.0 | − | 36864.8i | 0.767058 | − | 0.782875i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43250.0 | −0.901774 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2425.00 | 0.0496509 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13645.0 | 0.274387 | 0.137194 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137194 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32200.0 | − | 13717.1i | 0.636049 | − | 0.270956i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 74485.0 | 1.44550 | 0.722748 | − | 0.691111i | \(-0.242879\pi\) | ||||
0.722748 | + | 0.691111i | \(0.242879\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 68463.2i | − | 1.30553i | −0.757561 | − | 0.652764i | \(-0.773609\pi\) | ||
0.757561 | − | 0.652764i | \(-0.226391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15575.0 | − | 15260.3i | −0.291880 | − | 0.285983i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 60169.3i | − | 1.10831i | −0.832412 | − | 0.554157i | \(-0.813041\pi\) | ||
0.832412 | − | 0.554157i | \(-0.186959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10975.0 | + | 53766.3i | 0.198732 | + | 0.973586i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27805.0 | −0.495024 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 75367.0 | 1.31943 | 0.659714 | − | 0.751517i | \(-0.270678\pi\) | ||||
0.659714 | + | 0.751517i | \(0.270678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 77869.3i | 1.34070i | 0.742044 | + | 0.670351i | \(0.233856\pi\) | ||||
−0.742044 | + | 0.670351i | \(0.766144\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 61040.0 | 1.03372 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 58555.0 | − | 13202.7i | 0.975510 | − | 0.219954i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1102.27i | 0.0180673i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9950.00 | 0.160481 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 50410.5i | 0.800154i | 0.916482 | + | 0.400077i | \(0.131017\pi\) | ||||
−0.916482 | + | 0.400077i | \(0.868983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 62349.3i | 0.974071i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12125.0 | − | 59400.1i | −0.186467 | − | 0.913497i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3370.00 | −0.0510227 | −0.0255114 | − | 0.999675i | \(-0.508121\pi\) | ||||
−0.0255114 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 55944.0 | − | 57097.6i | 0.833977 | − | 0.851174i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10696.0 | −0.157015 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 59385.4i | 0.858556i | 0.903173 | + | 0.429278i | \(0.141232\pi\) | ||||
−0.903173 | + | 0.429278i | \(0.858768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38880.0 | − | 7936.35i | 0.553649 | − | 0.113013i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4041.66i | 0.0566940i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 77012.0i | 1.06427i | 0.846658 | + | 0.532137i | \(0.178611\pi\) | ||||
−0.846658 | + | 0.532137i | \(0.821389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 143222.i | 1.95016i | 0.221855 | + | 0.975080i | \(0.428789\pi\) | ||||
−0.221855 | + | 0.975080i | \(0.571211\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 875.000 | + | 857.321i | 0.0117404 | + | 0.0115032i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 51175.0 | − | 21800.5i | 0.676694 | − | 0.288271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 101928.i | 1.32842i | 0.747547 | + | 0.664209i | \(0.231231\pi\) | ||||
−0.747547 | + | 0.664209i | \(0.768769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 58983.7i | 0.757746i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −47521.0 | −0.601829 | −0.300914 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300914 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −43115.0 | −0.538339 | −0.269169 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269169 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 27000.0 | − | 5511.35i | 0.332410 | − | 0.0678529i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 99960.0 | − | 102021.i | 1.21356 | − | 1.23859i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 151704. | 1.81636 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −46175.0 | −0.545282 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 162125. | 1.88849 | 0.944245 | − | 0.329243i | \(-0.106794\pi\) | ||||
0.944245 | + | 0.329243i | \(0.106794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −88800.0 | + | 18126.2i | −1.02040 | + | 0.208288i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 60965.0 | 0.691143 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3502.77i | − | 0.0391804i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12936.0 | + | 13202.7i | −0.142780 | + | 0.145724i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24127.5i | 0.262801i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −47400.0 | + | 9675.48i | −0.509540 | + | 0.104010i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33805.0 | 0.358678 | 0.179339 | − | 0.983787i | \(-0.442604\pi\) | ||||
0.179339 | + | 0.983787i | \(0.442604\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23575.0 | −0.246908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 50435.0i | − | 0.521448i | −0.965413 | − | 0.260724i | \(-0.916039\pi\) | ||
0.965413 | − | 0.260724i | \(-0.0839613\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −68155.0 | −0.695679 | −0.347840 | − | 0.937554i | \(-0.613085\pi\) | ||||
−0.347840 | + | 0.937554i | \(0.613085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −37240.0 | + | 57612.0i | −0.375309 | + | 0.580620i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 42435.0i | 0.422285i | 0.977455 | + | 0.211142i | \(0.0677184\pi\) | ||||
−0.977455 | + | 0.211142i | \(0.932282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16999.0 | −0.167048 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 63343.8i | − | 0.614744i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 106920.i | 1.02484i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2875.00 | + | 1224.74i | −0.0272189 | + | 0.0115952i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 61555.0 | 0.575662 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −76825.0 | − | 75272.8i | −0.709759 | − | 0.695419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 114706. | 1.04696 | 0.523480 | − | 0.852038i | \(-0.324633\pi\) | ||||
0.523480 | + | 0.852038i | \(0.324633\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 91356.2i | 0.823852i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 50160.0 | − | 10238.9i | 0.446959 | − | 0.0912352i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 117007.i | − | 1.03027i | −0.857108 | − | 0.515137i | \(-0.827741\pi\) | ||
0.857108 | − | 0.515137i | \(-0.172259\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 15603.2i | − | 0.135774i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 93742.0i | 0.806168i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −80605.0 | + | 85697.8i | −0.685131 | + | 0.728420i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −85800.0 | + | 17513.9i | −0.720857 | + | 0.147144i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 70481.6i | − | 0.585352i | −0.956212 | − | 0.292676i | \(-0.905454\pi\) | ||
0.956212 | − | 0.292676i | \(-0.0945457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 91390.5i | 0.750326i | 0.926959 | + | 0.375163i | \(0.122413\pi\) | ||||
−0.926959 | + | 0.375163i | \(0.877587\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3425.00 | −0.0278001 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11405.0 | 0.0915263 | 0.0457631 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457631 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22270.0 | + | 109100.i | 0.176711 | + | 0.865703i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 84875.0 | + | 83160.2i | 0.665953 | + | 0.652498i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −230366. | −1.78743 | −0.893716 | − | 0.448633i | \(-0.851911\pi\) | ||||
−0.893716 | + | 0.448633i | \(0.851911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 81721.0 | 0.627075 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −33600.0 | −0.254992 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43250.0 | + | 211881.i | 0.324639 | + | 1.59040i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 74485.0 | 0.553015 | 0.276507 | − | 0.961012i | \(-0.410823\pi\) | ||||
0.276507 | + | 0.961012i | \(0.410823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 163234.i | 1.19883i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −54432.0 | + | 55554.4i | −0.395464 | + | 0.403618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 102550.i | 0.737088i | 0.929610 | + | 0.368544i | \(0.120144\pi\) | ||||
−0.929610 | + | 0.368544i | \(0.879856\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 44375.0 | + | 64299.1i | 0.315556 | + | 0.457238i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 955.000 | 0.00671925 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 172954. | 1.20407 | 0.602036 | − | 0.798469i | \(-0.294357\pi\) | ||||
0.602036 | + | 0.798469i | \(0.294357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 119339.i | − | 0.822116i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −144050. | −0.982010 | −0.491005 | − | 0.871157i | \(-0.663370\pi\) | ||||
−0.491005 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −59185.0 | + | 91561.9i | −0.399292 | + | 0.617723i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 21124.4i | − | 0.141047i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −148969. | −0.984457 | −0.492228 | − | 0.870466i | \(-0.663818\pi\) | ||||
−0.492228 | + | 0.870466i | \(0.663818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 339769.i | − | 2.22244i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 33680.5i | 0.218069i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27805.0 | + | 136216.i | 0.178209 | + | 0.873040i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 256925. | 1.63014 | 0.815071 | − | 0.579361i | \(-0.196698\pi\) | ||||
0.815071 | + | 0.579361i | \(0.196698\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −37800.0 | + | 38579.5i | −0.237436 | + | 0.242332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35641.0 | −0.221647 | −0.110823 | − | 0.993840i | \(-0.535349\pi\) | ||||
−0.110823 | + | 0.993840i | \(0.535349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5266.40i | − | 0.0324268i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5555.00 | − | 27213.8i | −0.0338668 | − | 0.165913i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 145191.i | 0.876498i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 151721.i | − | 0.906985i | −0.891260 | − | 0.453493i | \(-0.850178\pi\) | ||
0.891260 | − | 0.453493i | \(-0.149822\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 115346.i | − | 0.682843i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 124320. | − | 126884.i | 0.728855 | − | 0.743884i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9950.00 | − | 48744.8i | −0.0577733 | − | 0.283030i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 147459.i | − | 0.848008i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 150889.i | − | 0.859465i | −0.902956 | − | 0.429733i | \(-0.858608\pi\) | ||
0.902956 | − | 0.429733i | \(-0.141392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4681.00 | −0.0264104 | −0.0132052 | − | 0.999913i | \(-0.504203\pi\) | ||||
−0.0132052 | + | 0.999913i | \(0.504203\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 122920. | 0.686976 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −278875. | + | 118800.i | −1.54394 | + | 0.657718i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 66360.0 | − | 67728.4i | 0.363957 | − | 0.371463i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2225.00 | −0.0120897 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 87103.0 | 0.468898 | 0.234449 | − | 0.972128i | \(-0.424671\pi\) | ||||
0.234449 | + | 0.972128i | \(0.424671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −231730. | −1.23597 | −0.617983 | − | 0.786192i | \(-0.712050\pi\) | ||||
−0.617983 | + | 0.786192i | \(0.712050\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4775.00 | − | 23392.6i | −0.0252345 | − | 0.123623i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 154440. | 0.808718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 246272.i | 1.27787i | 0.769262 | + | 0.638933i | \(0.220624\pi\) | ||||
−0.769262 | + | 0.638933i | \(0.779376\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2744.00 | − | 134428.i | −0.0141093 | − | 0.691214i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 349841.i | 1.78264i | 0.453376 | + | 0.891319i | \(0.350219\pi\) | ||||
−0.453376 | + | 0.891319i | \(0.649781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19800.0 | − | 4041.66i | 0.0999874 | − | 0.0204098i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 141730. | 0.709327 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 254711. | 1.26344 | 0.631721 | − | 0.775196i | \(-0.282349\pi\) | ||||
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 259425.i | 1.27544i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 87755.0 | 0.427637 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3325.00 | − | 5143.93i | 0.0160609 | − | 0.0248469i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 263629.i | − | 1.26229i | −0.775663 | − | 0.631147i | \(-0.782585\pi\) | ||
0.775663 | − | 0.631147i | \(-0.217415\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −332225. | −1.57691 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 128255.i | − | 0.603495i | −0.953388 | − | 0.301747i | \(-0.902430\pi\) | ||
0.953388 | − | 0.301747i | \(-0.0975699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 81857.0i | − | 0.381851i | −0.981605 | − | 0.190926i | \(-0.938851\pi\) | ||
0.981605 | − | 0.190926i | \(-0.0611489\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −129000. | + | 26332.0i | −0.596601 | + | 0.121781i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 204445. | 0.937438 | 0.468719 | − | 0.883347i | \(-0.344716\pi\) | ||||
0.468719 | + | 0.883347i | \(0.344716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −70224.0 | + | 71672.1i | −0.319257 | + | 0.325840i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 128950. | 0.581272 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 33572.7i | − | 0.150060i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −54000.0 | − | 126761.i | −0.239335 | − | 0.561822i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 88887.1i | − | 0.390663i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 79534.9i | 0.346647i | 0.984865 | + | 0.173323i | \(0.0554505\pi\) | ||||
−0.984865 | + | 0.173323i | \(0.944549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 8156.80i | − | 0.0352557i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 120120. | − | 122597.i | 0.514898 | − | 0.525515i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46175.0 | + | 226210.i | 0.196301 | + | 0.961677i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 164958.i | − | 0.695531i | −0.937582 | − | 0.347766i | \(-0.886941\pi\) | ||
0.937582 | − | 0.347766i | \(-0.113059\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 185769.i | − | 0.776884i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 74191.0 | 0.307743 | 0.153872 | − | 0.988091i | \(-0.450826\pi\) | ||||
0.153872 | + | 0.988091i | \(0.450826\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 92635.0 | 0.381137 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −24920.0 | − | 122083.i | −0.101704 | − | 0.498245i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −155890. | − | 152740.i | −0.631111 | − | 0.618360i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 278527. | 1.11858 | 0.559289 | − | 0.828973i | \(-0.311074\pi\) | ||||
0.559289 | + | 0.828973i | \(0.311074\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −103975. | −0.414241 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −60275.0 | −0.238233 | −0.119116 | − | 0.992880i | \(-0.538006\pi\) | ||||
−0.119116 | + | 0.992880i | \(0.538006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 118200. | − | 24127.5i | 0.463484 | − | 0.0946083i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −142680. | −0.555069 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 348709.i | 1.34595i | 0.739666 | + | 0.672974i | \(0.234983\pi\) | ||||
−0.739666 | + | 0.672974i | \(0.765017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −302750. | − | 296633.i | −1.15942 | − | 1.13600i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 151011.i | − | 0.573818i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23575.0 | + | 115493.i | 0.0888868 | + | 0.435455i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 195355. | 0.730876 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −575.000 | −0.00213468 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 84727.9i | 0.312141i | 0.987746 | + | 0.156070i | \(0.0498827\pi\) | ||||
−0.987746 | + | 0.156070i | \(0.950117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −235610. | −0.861371 | −0.430686 | − | 0.902502i | \(-0.641728\pi\) | ||||
−0.430686 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −142625. | − | 55725.9i | −0.517460 | − | 0.202180i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 510841.i | − | 1.83935i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −210935. | −0.753767 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 203014.i | 0.720006i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14574.5i | − | 0.0513025i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −310320. | + | 63343.8i | −1.08418 | + | 0.221308i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26590.0 | −0.0922082 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4361.00 | − | 213644.i | −0.0150110 | − | 0.735384i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 259199. | 0.885602 | 0.442801 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442801 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 61727.1i | 0.209352i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −61555.0 | − | 301557.i | −0.207238 | − | 1.01526i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 423894.i | − | 1.41672i | −0.705854 | − | 0.708358i | \(-0.749436\pi\) | ||
0.705854 | − | 0.708358i | \(-0.250564\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 108365.i | 0.359539i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42106.7i | 0.138691i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −194635. | − | 190703.i | −0.636459 | − | 0.623600i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −199800. | + | 40784.0i | −0.648649 | + | 0.132405i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 133389.i | − | 0.429943i | −0.976620 | − | 0.214972i | \(-0.931034\pi\) | ||
0.976620 | − | 0.214972i | \(-0.0689659\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1886.11i | 0.00603591i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −215825. | −0.685766 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −369770. | −1.16658 | −0.583290 | − | 0.812264i | \(-0.698235\pi\) | ||||
−0.583290 | + | 0.812264i | \(0.698235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −76440.0 | + | 15603.2i | −0.239455 | + | 0.0488785i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 38885.0 | + | 38099.4i | 0.120953 | + | 0.118509i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −326134. | −1.00733 | −0.503665 | − | 0.863899i | \(-0.668015\pi\) | ||||
−0.503665 | + | 0.863899i | \(0.668015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −306374. | −0.939679 | −0.469840 | − | 0.882752i | \(-0.655688\pi\) | ||||
−0.469840 | + | 0.882752i | \(0.655688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 71315.0 | 0.217206 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 171600. | + | 402819.i | 0.519017 | + | 1.21835i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −387595. | −1.16420 | −0.582099 | − | 0.813118i | \(-0.697768\pi\) | ||||
−0.582099 | + | 0.813118i | \(0.697768\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 160025.i | 0.477344i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 69650.0 | + | 68242.8i | 0.206333 | + | 0.202164i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 141267.i | − | 0.415627i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1400.00 | + | 6858.57i | 0.00409088 | + | 0.0200411i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 467350. | 1.35633 | 0.678166 | − | 0.734909i | \(-0.262775\pi\) | ||||
0.678166 | + | 0.734909i | \(0.262775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 232200. | 0.669317 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 16975.0i | − | 0.0485997i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −214315. | −0.609457 | −0.304729 | − | 0.952439i | \(-0.598566\pi\) | ||||
−0.304729 | + | 0.952439i | \(0.598566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 322525. | − | 498961.i | 0.911023 | − | 1.40939i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 96999.8i | − | 0.272159i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 283999. | 0.791522 | 0.395761 | − | 0.918353i | \(-0.370481\pi\) | ||||
0.395761 | + | 0.918353i | \(0.370481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 91219.0i | − | 0.252544i | −0.991996 | − | 0.126272i | \(-0.959699\pi\) | ||
0.991996 | − | 0.126272i | \(-0.0403011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 114675.i | − | 0.315381i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33600.0 | + | 164606.i | 0.0917970 | + | 0.449712i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −193715. | −0.525758 | −0.262879 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33425.0 | + | 32749.7i | 0.0901232 | + | 0.0883024i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10975.0 | −0.0293983 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 296231.i | 0.788334i | 0.919039 | + | 0.394167i | \(0.128967\pi\) | ||||
−0.919039 | + | 0.394167i | \(0.871033\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −357000. | + | 72872.3i | −0.943883 | + | 0.192669i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 424751.i | 1.11574i | 0.829927 | + | 0.557872i | \(0.188382\pi\) | ||||
−0.829927 | + | 0.557872i | \(0.811618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 375825.i | 0.980855i | 0.871482 | + | 0.490427i | \(0.163159\pi\) | ||||
−0.871482 | + | 0.490427i | \(0.836841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 479880.i | 1.24437i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27720.0 | + | 28291.6i | −0.0714196 | + | 0.0728923i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 270625. | − | 281691.i | 0.692800 | − | 0.721130i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 98102.1i | − | 0.249542i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 791210.i | − | 1.99982i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 471511. | 1.18422 | 0.592111 | − | 0.805856i | \(-0.298295\pi\) | ||||
0.592111 | + | 0.805856i | \(0.298295\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −264085. | −0.659077 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −584640. | + | 119339.i | −1.44991 | + | 0.295962i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 245.000 | + | 12002.5i | 0.000603792 | + | 0.0295796i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 249424. | 0.610853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 558794. | 1.35999 | 0.679995 | − | 0.733217i | \(-0.261982\pi\) | ||||
0.679995 | + | 0.733217i | \(0.261982\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −454235. | −1.09865 | −0.549324 | − | 0.835609i | \(-0.685115\pi\) | ||||
−0.549324 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 46200.0 | − | 9430.54i | 0.111051 | − | 0.0226682i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −129530. | −0.309430 | −0.154715 | − | 0.987959i | \(-0.549446\pi\) | ||||
−0.154715 | + | 0.987959i | \(0.549446\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 322647.i | 0.766016i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 180600. | − | 184324.i | 0.426143 | − | 0.434931i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 343903.i | 0.806511i | 0.915087 | + | 0.403255i | \(0.132121\pi\) | ||||
−0.915087 | + | 0.403255i | \(0.867879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 165000. | − | 33680.5i | 0.384593 | − | 0.0785047i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 484400. | 1.12221 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −526913. | −1.21330 | −0.606650 | − | 0.794969i | \(-0.707487\pi\) | ||||
−0.606650 | + | 0.794969i | \(0.707487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 191844.i | − | 0.439082i | −0.975603 | − | 0.219541i | \(-0.929544\pi\) | ||
0.975603 | − | 0.219541i | \(-0.0704559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12125.0 | 0.0275838 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 226800. | + | 146602.i | 0.512861 | + | 0.331510i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 133806.i | − | 0.300762i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68225.0 | 0.152437 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 172224.i | 0.382514i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 429792.i | − | 0.948918i | −0.880278 | − | 0.474459i | \(-0.842644\pi\) | ||
0.880278 | − | 0.474459i | \(-0.157356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 393875. | − | 167790.i | 0.864472 | − | 0.368263i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 79685.0 | 0.173860 | 0.0869299 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869299 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −323225. | − | 316695.i | −0.701076 | − | 0.686912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 372425. | 0.803054 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 719577.i | − | 1.54254i | −0.636510 | − | 0.771269i | \(-0.719622\pi\) | ||
0.636510 | − | 0.771269i | \(-0.280378\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −565080. | + | 115346.i | −1.20428 | + | 0.245823i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 342316.i | − | 0.725294i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7936.35i | 0.0167179i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 398532.i | 0.834655i | 0.908756 | + | 0.417328i | \(0.137033\pi\) | ||||
−0.908756 | + | 0.417328i | \(0.862967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 174440. | + | 170916.i | 0.363228 | + | 0.355890i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −722400. | + | 147459.i | −1.49557 | + | 0.305283i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.41372e6i | − | 2.91004i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 300846.i | − | 0.615730i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −658873. | −1.34081 | −0.670403 | − | 0.741998i | \(-0.733879\pi\) | ||||
−0.670403 | + | 0.741998i | \(0.733879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 359640. | 0.727708 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 54875.0 | + | 268831.i | 0.110407 | + | 0.540881i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −165480. | + | 168892.i | −0.331060 | + | 0.337887i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −593737. | −1.18114 | −0.590570 | − | 0.806986i | \(-0.701097\pi\) | ||||
−0.590570 | + | 0.806986i | \(0.701097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 311416. | 0.616030 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −737880. | −1.45147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2225.00 | + | 10900.2i | 0.00435229 | + | 0.0213218i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 376835. | 0.733015 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 75321.8i | 0.145701i | 0.997343 | + | 0.0728506i | \(0.0232096\pi\) | ||||
−0.997343 | + | 0.0728506i | \(0.976790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −165025. | − | 161691.i | −0.317453 | − | 0.311039i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 389346.i | 0.744834i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −109825. | + | 46785.3i | −0.208942 | + | 0.0890088i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 342190. | 0.647438 | 0.323719 | − | 0.946153i | \(-0.395067\pi\) | ||||
0.323719 | + | 0.946153i | \(0.395067\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 215209. | 0.404954 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 182952.i | 0.342376i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −958555. | −1.78406 | −0.892029 | − | 0.451978i | \(-0.850719\pi\) | ||||
−0.892029 | + | 0.451978i | \(0.850719\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 292775. | − | 66013.7i | 0.541950 | − | 0.122197i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 182252.i | − | 0.335534i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 229399. | 0.420052 | 0.210026 | − | 0.977696i | \(-0.432645\pi\) | ||||
0.210026 | + | 0.977696i | \(0.432645\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5511.35i | 0.0100374i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 97803.2i | − | 0.177164i | −0.996069 | − | 0.0885820i | \(-0.971766\pi\) | ||
0.996069 | − | 0.0885820i | \(-0.0282335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −141730. | − | 694332.i | −0.255358 | − | 1.25099i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −111440. | −0.199710 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 434448. | − | 443407.i | 0.774416 | − | 0.790385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −246977. | −0.437902 | −0.218951 | − | 0.975736i | \(-0.570263\pi\) | ||||
−0.218951 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 252052.i | 0.444530i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −87755.0 | − | 429910.i | −0.153949 | − | 0.754195i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.05636e6i | − | 1.84340i | −0.387906 | − | 0.921699i | \(-0.626802\pi\) | ||
0.387906 | − | 0.921699i | \(-0.373198\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 311747.i | 0.541151i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 406836.i | 0.702506i | 0.936281 | + | 0.351253i | \(0.114244\pi\) | ||||
−0.936281 | + | 0.351253i | \(0.885756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 430885. | + | 422179.i | 0.740137 | + | 0.725184i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 135800. | + | 665281.i | 0.232048 | + | 1.13680i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18126.2i | − | 0.0308118i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 592238.i | 1.00148i | 0.865597 | + | 0.500741i | \(0.166939\pi\) | ||||
−0.865597 | + | 0.500741i | \(0.833061\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16850.0 | −0.0283460 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 401165. | 0.671373 | 0.335687 | − | 0.941974i | \(-0.391032\pi\) | ||||
0.335687 | + | 0.941974i | \(0.391032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 258000. | + | 605636.i | 0.429553 | + | 1.00834i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 279720. | − | 285488.i | 0.463320 | − | 0.472874i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 642600. | 1.05893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 396406. | 0.649887 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −130835. | −0.213403 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −128950. | − | 631723.i | −0.209258 | − | 1.02515i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 357565. | 0.577305 | 0.288653 | − | 0.957434i | \(-0.406793\pi\) | ||||
0.288653 | + | 0.957434i | \(0.406793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 296927.i | 0.476975i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 107016. | − | 109223.i | 0.171039 | − | 0.174566i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9675.48i | − | 0.0153860i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 194400. | − | 39681.7i | 0.307583 | − | 0.0627851i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.18188e6 | 1.86062 | 0.930312 | − | 0.366769i | \(-0.119536\pi\) | ||||
0.930312 | + | 0.366769i | \(0.119536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.06458e6 | −1.66756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 45266.6i | − | 0.0705525i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 769850. | 1.19392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −720720. | − | 465868.i | −1.11218 | − | 0.718905i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 385060.i | 0.591264i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −272449. | −0.416283 | −0.208141 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208141 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.22117e6i | − | 1.85667i | −0.371749 | − | 0.928333i | \(-0.621242\pi\) | ||
0.371749 | − | 0.928333i | \(-0.378758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 716108.i | 1.08342i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −910080. | + | 185769.i | −1.37014 | + | 0.279678i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −83160.0 | −0.124586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9800.00 | − | 9602.00i | −0.0146103 | − | 0.0143151i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −621793. | −0.922485 | −0.461243 | − | 0.887274i | \(-0.652596\pi\) | ||||
−0.461243 | + | 0.887274i | \(0.652596\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 117394.i | − | 0.173319i | −0.996238 | − | 0.0866597i | \(-0.972381\pi\) | ||
0.996238 | − | 0.0866597i | \(-0.0276193\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 255875. | − | 109002.i | 0.375941 | − | 0.160150i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 199790.i | − | 0.292121i | −0.989276 | − | 0.146061i | \(-0.953341\pi\) | ||
0.989276 | − | 0.146061i | \(-0.0466595\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 197894.i | 0.287955i | 0.989581 | + | 0.143977i | \(0.0459892\pi\) | ||||
−0.989581 | + | 0.143977i | \(0.954011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 509641.i | 0.738010i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23765.0 | + | 1.16424e6i | 0.0342490 | + | 1.67785i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 103975. | + | 509371.i | 0.149127 | + | 0.730570i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 721497.i | 1.02987i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 826972.i | − | 1.17481i | −0.809294 | − | 0.587404i | \(-0.800150\pi\) | ||
0.809294 | − | 0.587404i | \(-0.199850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −670800. | −0.948421 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −237605. | −0.334349 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 142680. | + | 698986.i | 0.199825 | + | 0.978938i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −235200. | − | 230448.i | −0.327846 | − | 0.321223i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −215575. | −0.299077 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.14286e6 | −1.57809 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −385450. | −0.529749 | −0.264874 | − | 0.964283i | \(-0.585330\pi\) | ||||
−0.264874 | + | 0.964283i | \(0.585330\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −302400. | + | 61727.1i | −0.413666 | + | 0.0844392i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 356750. | 0.485738 | 0.242869 | − | 0.970059i | \(-0.421911\pi\) | ||||
0.242869 | + | 0.970059i | \(0.421911\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 578227.i | 0.783631i | 0.920044 | + | 0.391816i | \(0.128153\pi\) | ||||
−0.920044 | + | 0.391816i | \(0.871847\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 499800. | − | 510106.i | 0.674202 | − | 0.688104i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 151217.i | 0.203039i | 0.994834 | + | 0.101519i | \(0.0323704\pi\) | ||||
−0.994834 | + | 0.101519i | \(0.967630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 575.000 | + | 2816.91i | 0.000768485 | + | 0.00376479i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 758520. | 1.00909 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 494929. | 0.655395 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10238.9i | 0.0134963i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 517160. | 0.678573 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −130375. | + | 754443.i | −0.170286 | + | 0.985395i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 553981.i | 0.720271i | 0.932900 | + | 0.360136i | \(0.117270\pi\) | ||||
−0.932900 | + | 0.360136i | \(0.882730\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 810625. | 1.04916 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 531882.i | − | 0.685273i | −0.939468 | − | 0.342637i | \(-0.888680\pi\) | ||
0.939468 | − | 0.342637i | \(-0.111320\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 606675.i | 0.778099i | 0.921217 | + | 0.389049i | \(0.127196\pi\) | ||||
−0.921217 | + | 0.389049i | \(0.872804\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −444000. | + | 90631.1i | −0.566887 | + | 0.115715i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.35703e6 | 1.72481 | 0.862407 | − | 0.506216i | \(-0.168956\pi\) | ||||
0.862407 | + | 0.506216i | \(0.168956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 818496. | − | 835374.i | 1.03565 | − | 1.05701i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −98879.0 | −0.124551 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 483897.i | − | 0.606806i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26590.0 | + | 130264.i | 0.0331950 | + | 0.162621i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 17513.9i | − | 0.0217669i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 201177.i | − | 0.248919i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 769826.i | 0.948294i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −64680.0 | + | 66013.7i | −0.0793222 | + | 0.0809578i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 302400. | − | 61727.1i | 0.369219 | − | 0.0753666i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 452230.i | − | 0.549724i | −0.961484 | − | 0.274862i | \(-0.911368\pi\) | ||
0.961484 | − | 0.274862i | \(-0.0886321\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 270228.i | − | 0.327041i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 948106. | 1.14241 | 0.571203 | − | 0.820809i | \(-0.306477\pi\) | ||||
0.571203 | + | 0.820809i | \(0.306477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −177110. | −0.212472 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −237000. | + | 48377.4i | −0.283078 | + | 0.0577831i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −231000. | + | 235763.i | −0.274709 | + | 0.280374i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −394481. | −0.467084 | −0.233542 | − | 0.972347i | \(-0.575032\pi\) | ||||
−0.233542 | + | 0.972347i | \(0.575032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 169025. | 0.199265 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22270.0 | −0.0261407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 399600. | + | 938032.i | 0.467027 | + | 1.09631i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 264040. | 0.307263 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 139523.i | 0.161664i | 0.996728 | + | 0.0808322i | \(0.0257578\pi\) | ||||
−0.996728 | + | 0.0808322i | \(0.974242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −529200. | + | 10802.2i | −0.610549 | + | 0.0124628i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 252175.i | − | 0.289693i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 215825. | + | 1.05732e6i | 0.246876 | + | 1.20944i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 434285. | 0.494647 | 0.247324 | − | 0.968933i | \(-0.420449\pi\) | ||||
0.247324 | + | 0.968933i | \(0.420449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −340775. | −0.386488 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 539108.i | 0.608831i | 0.952539 | + | 0.304415i | \(0.0984611\pi\) | ||||
−0.952539 | + | 0.304415i | \(0.901539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.04204e6 | −2.29636 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −455525. | + | 704718.i | −0.510092 | + | 0.789136i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 167540.i | 0.186818i | 0.995628 | + | 0.0934091i | \(0.0297764\pi\) | ||||
−0.995628 | + | 0.0934091i | \(0.970224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43250.0 | −0.0480235 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 212175.i | 0.234603i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.31304e6i | 1.44575i | 0.690981 | + | 0.722873i | \(0.257179\pi\) | ||||
−0.690981 | + | 0.722873i | \(0.742821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −71315.0 | − | 349371.i | −0.0781941 | − | 0.383071i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −84995.0 | −0.0928046 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 791112. | − | 807425.i | 0.860203 | − | 0.877941i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −185879. | −0.201272 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 709451.i | 0.765014i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 783960. | − | 160025.i | 0.841859 | − | 0.171844i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 338745.i | − | 0.362259i | −0.983459 | − | 0.181130i | \(-0.942025\pi\) | ||
0.983459 | − | 0.181130i | \(-0.0579754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 534601.i | 0.569354i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.60718e6i | 1.70462i | 0.523039 | + | 0.852309i | \(0.324798\pi\) | ||||
−0.523039 | + | 0.852309i | \(0.675202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.01136e6 | − | 1.03221e6i | 1.06827 | − | 1.09030i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14375.0 | + | 6123.72i | −0.0151216 | + | 0.00644179i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.40070e6i | 1.46743i | 0.679459 | + | 0.733713i | \(0.262215\pi\) | ||||
−0.679459 | + | 0.733713i | \(0.737785\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 71941.5i | − | 0.0750610i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −689416. | −0.716380 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.73768e6 | 1.79831 | 0.899154 | − | 0.437633i | \(-0.144183\pi\) | ||||
0.899154 | + | 0.437633i | \(0.144183\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −83160.0 | + | 16975.0i | −0.0857121 | + | 0.0174959i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −384125. | − | 376364.i | −0.394310 | − | 0.386344i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 264264. | 0.270175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 423586. | 0.431315 | 0.215657 | − | 0.976469i | \(-0.430811\pi\) | ||||
0.215657 | + | 0.976469i | \(0.430811\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 573530. | 0.581645 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −475200. | + | 96999.8i | −0.479988 | + | 0.0979771i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −548035. | −0.551338 | −0.275669 | − | 0.961253i | \(-0.588899\pi\) | ||||
−0.275669 | + | 0.961253i | \(0.588899\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.11748e6i | 1.11972i |
(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 | 560.5.p.e.209.1 | 2 | ||
4.3 | odd | 2 | 35.5.c.c.34.1 | ✓ | 2 | ||
5.4 | even | 2 | 560.5.p.d.209.1 | 2 | |||
7.6 | odd | 2 | 560.5.p.d.209.2 | 2 | |||
12.11 | even | 2 | 315.5.e.d.244.2 | 2 | |||
20.3 | even | 4 | 175.5.d.e.76.1 | 4 | |||
20.7 | even | 4 | 175.5.d.e.76.4 | 4 | |||
20.19 | odd | 2 | 35.5.c.d.34.2 | yes | 2 | ||
28.27 | even | 2 | 35.5.c.d.34.1 | yes | 2 | ||
35.34 | odd | 2 | inner | 560.5.p.e.209.2 | 2 | ||
60.59 | even | 2 | 315.5.e.c.244.1 | 2 | |||
84.83 | odd | 2 | 315.5.e.c.244.2 | 2 | |||
140.27 | odd | 4 | 175.5.d.e.76.3 | 4 | |||
140.83 | odd | 4 | 175.5.d.e.76.2 | 4 | |||
140.139 | even | 2 | 35.5.c.c.34.2 | yes | 2 | ||
420.419 | odd | 2 | 315.5.e.d.244.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.5.c.c.34.1 | ✓ | 2 | 4.3 | odd | 2 | ||
35.5.c.c.34.2 | yes | 2 | 140.139 | even | 2 | ||
35.5.c.d.34.1 | yes | 2 | 28.27 | even | 2 | ||
35.5.c.d.34.2 | yes | 2 | 20.19 | odd | 2 | ||
175.5.d.e.76.1 | 4 | 20.3 | even | 4 | |||
175.5.d.e.76.2 | 4 | 140.83 | odd | 4 | |||
175.5.d.e.76.3 | 4 | 140.27 | odd | 4 | |||
175.5.d.e.76.4 | 4 | 20.7 | even | 4 | |||
315.5.e.c.244.1 | 2 | 60.59 | even | 2 | |||
315.5.e.c.244.2 | 2 | 84.83 | odd | 2 | |||
315.5.e.d.244.1 | 2 | 420.419 | odd | 2 | |||
315.5.e.d.244.2 | 2 | 12.11 | even | 2 | |||
560.5.p.d.209.1 | 2 | 5.4 | even | 2 | |||
560.5.p.d.209.2 | 2 | 7.6 | odd | 2 | |||
560.5.p.e.209.1 | 2 | 1.1 | even | 1 | trivial | ||
560.5.p.e.209.2 | 2 | 35.34 | odd | 2 | inner |