Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,5,Mod(7,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.c (of order \(4\), degree \(2\), 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: | \(2.58424907710\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.7 |
Dual form | 25.5.c.a.18.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.250000 | + | 0.250000i | 0.820971 | − | 0.570971i | \(-0.193433\pi\) |
−0.570971 | + | 0.820971i | \(0.693433\pi\) | |||||||
\(3\) | 6.00000 | − | 6.00000i | 0.666667 | − | 0.666667i | −0.290276 | − | 0.956943i | \(-0.593747\pi\) |
0.956943 | + | 0.290276i | \(0.0937472\pi\) | |||||||
\(4\) | − | 14.0000i | − | 0.875000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 12.0000 | 0.333333 | ||||||||
\(7\) | 26.0000 | + | 26.0000i | 0.530612 | + | 0.530612i | 0.920755 | − | 0.390142i | \(-0.127574\pi\) |
−0.390142 | + | 0.920755i | \(0.627574\pi\) | |||||||
\(8\) | 30.0000 | − | 30.0000i | 0.468750 | − | 0.468750i | ||||
\(9\) | 9.00000i | 0.111111i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.00000 | −0.0661157 | −0.0330579 | − | 0.999453i | \(-0.510525\pi\) | ||||
−0.0330579 | + | 0.999453i | \(0.510525\pi\) | |||||||
\(12\) | −84.0000 | − | 84.0000i | −0.583333 | − | 0.583333i | ||||
\(13\) | −139.000 | + | 139.000i | −0.822485 | + | 0.822485i | −0.986464 | − | 0.163979i | \(-0.947567\pi\) |
0.163979 | + | 0.986464i | \(0.447567\pi\) | |||||||
\(14\) | 52.0000i | 0.265306i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −164.000 | −0.640625 | ||||||||
\(17\) | 1.00000 | + | 1.00000i | 0.00346021 | + | 0.00346021i | 0.708835 | − | 0.705375i | \(-0.249221\pi\) |
−0.705375 | + | 0.708835i | \(0.749221\pi\) | |||||||
\(18\) | −9.00000 | + | 9.00000i | −0.0277778 | + | 0.0277778i | ||||
\(19\) | 180.000i | 0.498615i | 0.968424 | + | 0.249307i | \(0.0802030\pi\) | ||||
−0.968424 | + | 0.249307i | \(0.919797\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 312.000 | 0.707483 | ||||||||
\(22\) | −8.00000 | − | 8.00000i | −0.0165289 | − | 0.0165289i | ||||
\(23\) | 166.000 | − | 166.000i | 0.313800 | − | 0.313800i | −0.532580 | − | 0.846380i | \(-0.678777\pi\) |
0.846380 | + | 0.532580i | \(0.178777\pi\) | |||||||
\(24\) | − | 360.000i | − | 0.625000i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −278.000 | −0.411243 | ||||||||
\(27\) | 540.000 | + | 540.000i | 0.740741 | + | 0.740741i | ||||
\(28\) | 364.000 | − | 364.000i | 0.464286 | − | 0.464286i | ||||
\(29\) | − | 480.000i | − | 0.570749i | −0.958416 | − | 0.285375i | \(-0.907882\pi\) | ||
0.958416 | − | 0.285375i | \(-0.0921180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 572.000 | 0.595213 | 0.297607 | − | 0.954689i | \(-0.403812\pi\) | ||||
0.297607 | + | 0.954689i | \(0.403812\pi\) | |||||||
\(32\) | −644.000 | − | 644.000i | −0.628906 | − | 0.628906i | ||||
\(33\) | −48.0000 | + | 48.0000i | −0.0440771 | + | 0.0440771i | ||||
\(34\) | 2.00000i | 0.00173010i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 126.000 | 0.0972222 | ||||||||
\(37\) | 251.000 | + | 251.000i | 0.183346 | + | 0.183346i | 0.792812 | − | 0.609466i | \(-0.208616\pi\) |
−0.609466 | + | 0.792812i | \(0.708616\pi\) | |||||||
\(38\) | −180.000 | + | 180.000i | −0.124654 | + | 0.124654i | ||||
\(39\) | 1668.00i | 1.09665i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1688.00 | −1.00416 | −0.502082 | − | 0.864820i | \(-0.667432\pi\) | ||||
−0.502082 | + | 0.864820i | \(0.667432\pi\) | |||||||
\(42\) | 312.000 | + | 312.000i | 0.176871 | + | 0.176871i | ||||
\(43\) | −1474.00 | + | 1474.00i | −0.797188 | + | 0.797188i | −0.982651 | − | 0.185463i | \(-0.940621\pi\) |
0.185463 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(44\) | 112.000i | 0.0578512i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 332.000 | 0.156900 | ||||||||
\(47\) | −2474.00 | − | 2474.00i | −1.11996 | − | 1.11996i | −0.991746 | − | 0.128218i | \(-0.959074\pi\) |
−0.128218 | − | 0.991746i | \(-0.540926\pi\) | |||||||
\(48\) | −984.000 | + | 984.000i | −0.427083 | + | 0.427083i | ||||
\(49\) | − | 1049.00i | − | 0.436901i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000 | 0.00461361 | ||||||||
\(52\) | 1946.00 | + | 1946.00i | 0.719675 | + | 0.719675i | ||||
\(53\) | 3331.00 | − | 3331.00i | 1.18583 | − | 1.18583i | 0.207622 | − | 0.978209i | \(-0.433428\pi\) |
0.978209 | − | 0.207622i | \(-0.0665724\pi\) | |||||||
\(54\) | 1080.00i | 0.370370i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1560.00 | 0.497449 | ||||||||
\(57\) | 1080.00 | + | 1080.00i | 0.332410 | + | 0.332410i | ||||
\(58\) | 480.000 | − | 480.000i | 0.142687 | − | 0.142687i | ||||
\(59\) | − | 3660.00i | − | 1.05142i | −0.850663 | − | 0.525711i | \(-0.823799\pi\) | ||
0.850663 | − | 0.525711i | \(-0.176201\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1592.00 | 0.427842 | 0.213921 | − | 0.976851i | \(-0.431376\pi\) | ||||
0.213921 | + | 0.976851i | \(0.431376\pi\) | |||||||
\(62\) | 572.000 | + | 572.000i | 0.148803 | + | 0.148803i | ||||
\(63\) | −234.000 | + | 234.000i | −0.0589569 | + | 0.0589569i | ||||
\(64\) | 1336.00i | 0.326172i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −96.0000 | −0.0220386 | ||||||||
\(67\) | −874.000 | − | 874.000i | −0.194698 | − | 0.194698i | 0.603025 | − | 0.797723i | \(-0.293962\pi\) |
−0.797723 | + | 0.603025i | \(0.793962\pi\) | |||||||
\(68\) | 14.0000 | − | 14.0000i | 0.00302768 | − | 0.00302768i | ||||
\(69\) | − | 1992.00i | − | 0.418399i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6068.00 | −1.20373 | −0.601865 | − | 0.798598i | \(-0.705575\pi\) | ||||
−0.601865 | + | 0.798598i | \(0.705575\pi\) | |||||||
\(72\) | 270.000 | + | 270.000i | 0.0520833 | + | 0.0520833i | ||||
\(73\) | 791.000 | − | 791.000i | 0.148433 | − | 0.148433i | −0.628985 | − | 0.777418i | \(-0.716529\pi\) |
0.777418 | + | 0.628985i | \(0.216529\pi\) | |||||||
\(74\) | 502.000i | 0.0916728i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2520.00 | 0.436288 | ||||||||
\(77\) | −208.000 | − | 208.000i | −0.0350818 | − | 0.0350818i | ||||
\(78\) | −1668.00 | + | 1668.00i | −0.274162 | + | 0.274162i | ||||
\(79\) | 9120.00i | 1.46130i | 0.682750 | + | 0.730652i | \(0.260784\pi\) | ||||
−0.682750 | + | 0.730652i | \(0.739216\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5751.00 | 0.876543 | ||||||||
\(82\) | −1688.00 | − | 1688.00i | −0.251041 | − | 0.251041i | ||||
\(83\) | −5654.00 | + | 5654.00i | −0.820729 | + | 0.820729i | −0.986213 | − | 0.165484i | \(-0.947081\pi\) |
0.165484 | + | 0.986213i | \(0.447081\pi\) | |||||||
\(84\) | − | 4368.00i | − | 0.619048i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2948.00 | −0.398594 | ||||||||
\(87\) | −2880.00 | − | 2880.00i | −0.380499 | − | 0.380499i | ||||
\(88\) | −240.000 | + | 240.000i | −0.0309917 | + | 0.0309917i | ||||
\(89\) | 2160.00i | 0.272693i | 0.990661 | + | 0.136346i | \(0.0435360\pi\) | ||||
−0.990661 | + | 0.136346i | \(0.956464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7228.00 | −0.872841 | ||||||||
\(92\) | −2324.00 | − | 2324.00i | −0.274575 | − | 0.274575i | ||||
\(93\) | 3432.00 | − | 3432.00i | 0.396809 | − | 0.396809i | ||||
\(94\) | − | 4948.00i | − | 0.559982i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7728.00 | −0.838542 | ||||||||
\(97\) | 6551.00 | + | 6551.00i | 0.696248 | + | 0.696248i | 0.963599 | − | 0.267351i | \(-0.0861483\pi\) |
−0.267351 | + | 0.963599i | \(0.586148\pi\) | |||||||
\(98\) | 1049.00 | − | 1049.00i | 0.109225 | − | 0.109225i | ||||
\(99\) | − | 72.0000i | − | 0.00734619i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16102.0 | 1.57847 | 0.789236 | − | 0.614090i | \(-0.210477\pi\) | ||||
0.789236 | + | 0.614090i | \(0.210477\pi\) | |||||||
\(102\) | 12.0000 | + | 12.0000i | 0.00115340 | + | 0.00115340i | ||||
\(103\) | −994.000 | + | 994.000i | −0.0936940 | + | 0.0936940i | −0.752400 | − | 0.658706i | \(-0.771104\pi\) |
0.658706 | + | 0.752400i | \(0.271104\pi\) | |||||||
\(104\) | 8340.00i | 0.771080i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6662.00 | 0.592916 | ||||||||
\(107\) | 8326.00 | + | 8326.00i | 0.727225 | + | 0.727225i | 0.970066 | − | 0.242841i | \(-0.0780793\pi\) |
−0.242841 | + | 0.970066i | \(0.578079\pi\) | |||||||
\(108\) | 7560.00 | − | 7560.00i | 0.648148 | − | 0.648148i | ||||
\(109\) | − | 17010.0i | − | 1.43170i | −0.698255 | − | 0.715849i | \(-0.746040\pi\) | ||
0.698255 | − | 0.715849i | \(-0.253960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3012.00 | 0.244461 | ||||||||
\(112\) | −4264.00 | − | 4264.00i | −0.339923 | − | 0.339923i | ||||
\(113\) | 5161.00 | − | 5161.00i | 0.404182 | − | 0.404182i | −0.475522 | − | 0.879704i | \(-0.657741\pi\) |
0.879704 | + | 0.475522i | \(0.157741\pi\) | |||||||
\(114\) | 2160.00i | 0.166205i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6720.00 | −0.499405 | ||||||||
\(117\) | −1251.00 | − | 1251.00i | −0.0913872 | − | 0.0913872i | ||||
\(118\) | 3660.00 | − | 3660.00i | 0.262856 | − | 0.262856i | ||||
\(119\) | 52.0000i | 0.00367206i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14577.0 | −0.995629 | ||||||||
\(122\) | 1592.00 | + | 1592.00i | 0.106960 | + | 0.106960i | ||||
\(123\) | −10128.0 | + | 10128.0i | −0.669443 | + | 0.669443i | ||||
\(124\) | − | 8008.00i | − | 0.520812i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −468.000 | −0.0294785 | ||||||||
\(127\) | −12574.0 | − | 12574.0i | −0.779590 | − | 0.779590i | 0.200171 | − | 0.979761i | \(-0.435850\pi\) |
−0.979761 | + | 0.200171i | \(0.935850\pi\) | |||||||
\(128\) | −11640.0 | + | 11640.0i | −0.710449 | + | 0.710449i | ||||
\(129\) | 17688.0i | 1.06292i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20272.0 | 1.18128 | 0.590642 | − | 0.806934i | \(-0.298875\pi\) | ||||
0.590642 | + | 0.806934i | \(0.298875\pi\) | |||||||
\(132\) | 672.000 | + | 672.000i | 0.0385675 | + | 0.0385675i | ||||
\(133\) | −4680.00 | + | 4680.00i | −0.264571 | + | 0.264571i | ||||
\(134\) | − | 1748.00i | − | 0.0973491i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 60.0000 | 0.00324394 | ||||||||
\(137\) | 10351.0 | + | 10351.0i | 0.551494 | + | 0.551494i | 0.926872 | − | 0.375378i | \(-0.122487\pi\) |
−0.375378 | + | 0.926872i | \(0.622487\pi\) | |||||||
\(138\) | 1992.00 | − | 1992.00i | 0.104600 | − | 0.104600i | ||||
\(139\) | 27060.0i | 1.40055i | 0.713874 | + | 0.700274i | \(0.246939\pi\) | ||||
−0.713874 | + | 0.700274i | \(0.753061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29688.0 | −1.49329 | ||||||||
\(142\) | −6068.00 | − | 6068.00i | −0.300932 | − | 0.300932i | ||||
\(143\) | 1112.00 | − | 1112.00i | 0.0543792 | − | 0.0543792i | ||||
\(144\) | − | 1476.00i | − | 0.0711806i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1582.00 | 0.0742166 | ||||||||
\(147\) | −6294.00 | − | 6294.00i | −0.291268 | − | 0.291268i | ||||
\(148\) | 3514.00 | − | 3514.00i | 0.160427 | − | 0.160427i | ||||
\(149\) | − | 16350.0i | − | 0.736453i | −0.929736 | − | 0.368227i | \(-0.879965\pi\) | ||
0.929736 | − | 0.368227i | \(-0.120035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1052.00 | 0.0461383 | 0.0230692 | − | 0.999734i | \(-0.492656\pi\) | ||||
0.0230692 | + | 0.999734i | \(0.492656\pi\) | |||||||
\(152\) | 5400.00 | + | 5400.00i | 0.233726 | + | 0.233726i | ||||
\(153\) | −9.00000 | + | 9.00000i | −0.000384468 | + | 0.000384468i | ||||
\(154\) | − | 416.000i | − | 0.0175409i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 23352.0 | 0.959566 | ||||||||
\(157\) | −6499.00 | − | 6499.00i | −0.263662 | − | 0.263662i | 0.562878 | − | 0.826540i | \(-0.309694\pi\) |
−0.826540 | + | 0.562878i | \(0.809694\pi\) | |||||||
\(158\) | −9120.00 | + | 9120.00i | −0.365326 | + | 0.365326i | ||||
\(159\) | − | 39972.0i | − | 1.58111i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8632.00 | 0.333012 | ||||||||
\(162\) | 5751.00 | + | 5751.00i | 0.219136 | + | 0.219136i | ||||
\(163\) | 19286.0 | − | 19286.0i | 0.725884 | − | 0.725884i | −0.243913 | − | 0.969797i | \(-0.578431\pi\) |
0.969797 | + | 0.243913i | \(0.0784313\pi\) | |||||||
\(164\) | 23632.0i | 0.878644i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11308.0 | −0.410364 | ||||||||
\(167\) | 15526.0 | + | 15526.0i | 0.556707 | + | 0.556707i | 0.928368 | − | 0.371661i | \(-0.121212\pi\) |
−0.371661 | + | 0.928368i | \(0.621212\pi\) | |||||||
\(168\) | 9360.00 | − | 9360.00i | 0.331633 | − | 0.331633i | ||||
\(169\) | − | 10081.0i | − | 0.352964i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1620.00 | −0.0554017 | ||||||||
\(172\) | 20636.0 | + | 20636.0i | 0.697539 | + | 0.697539i | ||||
\(173\) | 16891.0 | − | 16891.0i | 0.564369 | − | 0.564369i | −0.366176 | − | 0.930545i | \(-0.619333\pi\) |
0.930545 | + | 0.366176i | \(0.119333\pi\) | |||||||
\(174\) | − | 5760.00i | − | 0.190250i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1312.00 | 0.0423554 | ||||||||
\(177\) | −21960.0 | − | 21960.0i | −0.700948 | − | 0.700948i | ||||
\(178\) | −2160.00 | + | 2160.00i | −0.0681732 | + | 0.0681732i | ||||
\(179\) | 10620.0i | 0.331450i | 0.986172 | + | 0.165725i | \(0.0529965\pi\) | ||||
−0.986172 | + | 0.165725i | \(0.947004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24122.0 | 0.736302 | 0.368151 | − | 0.929766i | \(-0.379991\pi\) | ||||
0.368151 | + | 0.929766i | \(0.379991\pi\) | |||||||
\(182\) | −7228.00 | − | 7228.00i | −0.218210 | − | 0.218210i | ||||
\(183\) | 9552.00 | − | 9552.00i | 0.285228 | − | 0.285228i | ||||
\(184\) | − | 9960.00i | − | 0.294187i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6864.00 | 0.198404 | ||||||||
\(187\) | −8.00000 | − | 8.00000i | −0.000228774 | − | 0.000228774i | ||||
\(188\) | −34636.0 | + | 34636.0i | −0.979968 | + | 0.979968i | ||||
\(189\) | 28080.0i | 0.786092i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −45188.0 | −1.23867 | −0.619336 | − | 0.785126i | \(-0.712598\pi\) | ||||
−0.619336 | + | 0.785126i | \(0.712598\pi\) | |||||||
\(192\) | 8016.00 | + | 8016.00i | 0.217448 | + | 0.217448i | ||||
\(193\) | −39199.0 | + | 39199.0i | −1.05235 | + | 1.05235i | −0.0537986 | + | 0.998552i | \(0.517133\pi\) |
−0.998552 | + | 0.0537986i | \(0.982867\pi\) | |||||||
\(194\) | 13102.0i | 0.348124i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14686.0 | −0.382289 | ||||||||
\(197\) | −28349.0 | − | 28349.0i | −0.730475 | − | 0.730475i | 0.240239 | − | 0.970714i | \(-0.422774\pi\) |
−0.970714 | + | 0.240239i | \(0.922774\pi\) | |||||||
\(198\) | 72.0000 | − | 72.0000i | 0.00183655 | − | 0.00183655i | ||||
\(199\) | − | 1800.00i | − | 0.0454534i | −0.999742 | − | 0.0227267i | \(-0.992765\pi\) | ||
0.999742 | − | 0.0227267i | \(-0.00723476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10488.0 | −0.259598 | ||||||||
\(202\) | 16102.0 | + | 16102.0i | 0.394618 | + | 0.394618i | ||||
\(203\) | 12480.0 | − | 12480.0i | 0.302846 | − | 0.302846i | ||||
\(204\) | − | 168.000i | − | 0.00403691i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1988.00 | −0.0468470 | ||||||||
\(207\) | 1494.00 | + | 1494.00i | 0.0348666 | + | 0.0348666i | ||||
\(208\) | 22796.0 | − | 22796.0i | 0.526905 | − | 0.526905i | ||||
\(209\) | − | 1440.00i | − | 0.0329663i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18392.0 | 0.413108 | 0.206554 | − | 0.978435i | \(-0.433775\pi\) | ||||
0.206554 | + | 0.978435i | \(0.433775\pi\) | |||||||
\(212\) | −46634.0 | − | 46634.0i | −1.03760 | − | 1.03760i | ||||
\(213\) | −36408.0 | + | 36408.0i | −0.802486 | + | 0.802486i | ||||
\(214\) | 16652.0i | 0.363613i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 32400.0 | 0.694444 | ||||||||
\(217\) | 14872.0 | + | 14872.0i | 0.315827 | + | 0.315827i | ||||
\(218\) | 17010.0 | − | 17010.0i | 0.357924 | − | 0.357924i | ||||
\(219\) | − | 9492.00i | − | 0.197911i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −278.000 | −0.00569194 | ||||||||
\(222\) | 3012.00 | + | 3012.00i | 0.0611152 | + | 0.0611152i | ||||
\(223\) | 866.000 | − | 866.000i | 0.0174144 | − | 0.0174144i | −0.698346 | − | 0.715760i | \(-0.746080\pi\) |
0.715760 | + | 0.698346i | \(0.246080\pi\) | |||||||
\(224\) | − | 33488.0i | − | 0.667411i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10322.0 | 0.202091 | ||||||||
\(227\) | 45226.0 | + | 45226.0i | 0.877681 | + | 0.877681i | 0.993294 | − | 0.115614i | \(-0.0368835\pi\) |
−0.115614 | + | 0.993294i | \(0.536883\pi\) | |||||||
\(228\) | 15120.0 | − | 15120.0i | 0.290859 | − | 0.290859i | ||||
\(229\) | 39120.0i | 0.745981i | 0.927835 | + | 0.372991i | \(0.121668\pi\) | ||||
−0.927835 | + | 0.372991i | \(0.878332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2496.00 | −0.0467757 | ||||||||
\(232\) | −14400.0 | − | 14400.0i | −0.267539 | − | 0.267539i | ||||
\(233\) | 33121.0 | − | 33121.0i | 0.610087 | − | 0.610087i | −0.332882 | − | 0.942969i | \(-0.608021\pi\) |
0.942969 | + | 0.332882i | \(0.108021\pi\) | |||||||
\(234\) | − | 2502.00i | − | 0.0456936i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −51240.0 | −0.919994 | ||||||||
\(237\) | 54720.0 | + | 54720.0i | 0.974203 | + | 0.974203i | ||||
\(238\) | −52.0000 | + | 52.0000i | −0.000918014 | + | 0.000918014i | ||||
\(239\) | − | 88440.0i | − | 1.54829i | −0.633007 | − | 0.774146i | \(-0.718180\pi\) | ||
0.633007 | − | 0.774146i | \(-0.281820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20312.0 | 0.349718 | 0.174859 | − | 0.984593i | \(-0.444053\pi\) | ||||
0.174859 | + | 0.984593i | \(0.444053\pi\) | |||||||
\(242\) | −14577.0 | − | 14577.0i | −0.248907 | − | 0.248907i | ||||
\(243\) | −9234.00 | + | 9234.00i | −0.156379 | + | 0.156379i | ||||
\(244\) | − | 22288.0i | − | 0.374362i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20256.0 | −0.334721 | ||||||||
\(247\) | −25020.0 | − | 25020.0i | −0.410103 | − | 0.410103i | ||||
\(248\) | 17160.0 | − | 17160.0i | 0.279006 | − | 0.279006i | ||||
\(249\) | 67848.0i | 1.09430i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 74752.0 | 1.18652 | 0.593260 | − | 0.805011i | \(-0.297840\pi\) | ||||
0.593260 | + | 0.805011i | \(0.297840\pi\) | |||||||
\(252\) | 3276.00 | + | 3276.00i | 0.0515873 | + | 0.0515873i | ||||
\(253\) | −1328.00 | + | 1328.00i | −0.0207471 | + | 0.0207471i | ||||
\(254\) | − | 25148.0i | − | 0.389795i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1904.00 | −0.0290527 | ||||||||
\(257\) | −37799.0 | − | 37799.0i | −0.572287 | − | 0.572287i | 0.360480 | − | 0.932767i | \(-0.382613\pi\) |
−0.932767 | + | 0.360480i | \(0.882613\pi\) | |||||||
\(258\) | −17688.0 | + | 17688.0i | −0.265729 | + | 0.265729i | ||||
\(259\) | 13052.0i | 0.194571i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4320.00 | 0.0634166 | ||||||||
\(262\) | 20272.0 | + | 20272.0i | 0.295321 | + | 0.295321i | ||||
\(263\) | 33586.0 | − | 33586.0i | 0.485564 | − | 0.485564i | −0.421339 | − | 0.906903i | \(-0.638440\pi\) |
0.906903 | + | 0.421339i | \(0.138440\pi\) | |||||||
\(264\) | 2880.00i | 0.0413223i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9360.00 | −0.132286 | ||||||||
\(267\) | 12960.0 | + | 12960.0i | 0.181795 | + | 0.181795i | ||||
\(268\) | −12236.0 | + | 12236.0i | −0.170361 | + | 0.170361i | ||||
\(269\) | 28530.0i | 0.394273i | 0.980376 | + | 0.197137i | \(0.0631642\pi\) | ||||
−0.980376 | + | 0.197137i | \(0.936836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7468.00 | −0.101687 | −0.0508435 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508435 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(272\) | −164.000 | − | 164.000i | −0.00221670 | − | 0.00221670i | ||||
\(273\) | −43368.0 | + | 43368.0i | −0.581894 | + | 0.581894i | ||||
\(274\) | 20702.0i | 0.275747i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −27888.0 | −0.366100 | ||||||||
\(277\) | −6499.00 | − | 6499.00i | −0.0847007 | − | 0.0847007i | 0.663487 | − | 0.748188i | \(-0.269076\pi\) |
−0.748188 | + | 0.663487i | \(0.769076\pi\) | |||||||
\(278\) | −27060.0 | + | 27060.0i | −0.350137 | + | 0.350137i | ||||
\(279\) | 5148.00i | 0.0661348i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −97928.0 | −1.24021 | −0.620104 | − | 0.784520i | \(-0.712909\pi\) | ||||
−0.620104 | + | 0.784520i | \(0.712909\pi\) | |||||||
\(282\) | −29688.0 | − | 29688.0i | −0.373321 | − | 0.373321i | ||||
\(283\) | −59854.0 | + | 59854.0i | −0.747344 | + | 0.747344i | −0.973980 | − | 0.226636i | \(-0.927227\pi\) |
0.226636 | + | 0.973980i | \(0.427227\pi\) | |||||||
\(284\) | 84952.0i | 1.05326i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2224.00 | 0.0271896 | ||||||||
\(287\) | −43888.0 | − | 43888.0i | −0.532822 | − | 0.532822i | ||||
\(288\) | 5796.00 | − | 5796.00i | 0.0698785 | − | 0.0698785i | ||||
\(289\) | − | 83519.0i | − | 0.999976i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 78612.0 | 0.928331 | ||||||||
\(292\) | −11074.0 | − | 11074.0i | −0.129879 | − | 0.129879i | ||||
\(293\) | −28499.0 | + | 28499.0i | −0.331967 | + | 0.331967i | −0.853333 | − | 0.521366i | \(-0.825423\pi\) |
0.521366 | + | 0.853333i | \(0.325423\pi\) | |||||||
\(294\) | − | 12588.0i | − | 0.145634i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15060.0 | 0.171886 | ||||||||
\(297\) | −4320.00 | − | 4320.00i | −0.0489746 | − | 0.0489746i | ||||
\(298\) | 16350.0 | − | 16350.0i | 0.184113 | − | 0.184113i | ||||
\(299\) | 46148.0i | 0.516191i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −76648.0 | −0.845995 | ||||||||
\(302\) | 1052.00 | + | 1052.00i | 0.0115346 | + | 0.0115346i | ||||
\(303\) | 96612.0 | − | 96612.0i | 1.05232 | − | 1.05232i | ||||
\(304\) | − | 29520.0i | − | 0.319425i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −18.0000 | −0.000192234 | ||||||||
\(307\) | 117926. | + | 117926.i | 1.25122 | + | 1.25122i | 0.955175 | + | 0.296043i | \(0.0956671\pi\) |
0.296043 | + | 0.955175i | \(0.404333\pi\) | |||||||
\(308\) | −2912.00 | + | 2912.00i | −0.0306966 | + | 0.0306966i | ||||
\(309\) | 11928.0i | 0.124925i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3892.00 | 0.0402395 | 0.0201197 | − | 0.999798i | \(-0.493595\pi\) | ||||
0.0201197 | + | 0.999798i | \(0.493595\pi\) | |||||||
\(312\) | 50040.0 | + | 50040.0i | 0.514053 | + | 0.514053i | ||||
\(313\) | 49961.0 | − | 49961.0i | 0.509967 | − | 0.509967i | −0.404549 | − | 0.914516i | \(-0.632571\pi\) |
0.914516 | + | 0.404549i | \(0.132571\pi\) | |||||||
\(314\) | − | 12998.0i | − | 0.131831i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 127680. | 1.27864 | ||||||||
\(317\) | −17099.0 | − | 17099.0i | −0.170158 | − | 0.170158i | 0.616891 | − | 0.787049i | \(-0.288392\pi\) |
−0.787049 | + | 0.616891i | \(0.788392\pi\) | |||||||
\(318\) | 39972.0 | − | 39972.0i | 0.395277 | − | 0.395277i | ||||
\(319\) | 3840.00i | 0.0377355i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 99912.0 | 0.969633 | ||||||||
\(322\) | 8632.00 | + | 8632.00i | 0.0832530 | + | 0.0832530i | ||||
\(323\) | −180.000 | + | 180.000i | −0.00172531 | + | 0.00172531i | ||||
\(324\) | − | 80514.0i | − | 0.766975i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 38572.0 | 0.362942 | ||||||||
\(327\) | −102060. | − | 102060.i | −0.954465 | − | 0.954465i | ||||
\(328\) | −50640.0 | + | 50640.0i | −0.470702 | + | 0.470702i | ||||
\(329\) | − | 128648.i | − | 1.18853i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −143128. | −1.30638 | −0.653189 | − | 0.757195i | \(-0.726569\pi\) | ||||
−0.653189 | + | 0.757195i | \(0.726569\pi\) | |||||||
\(332\) | 79156.0 | + | 79156.0i | 0.718138 | + | 0.718138i | ||||
\(333\) | −2259.00 | + | 2259.00i | −0.0203717 | + | 0.0203717i | ||||
\(334\) | 31052.0i | 0.278353i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −51168.0 | −0.453231 | ||||||||
\(337\) | −103249. | − | 103249.i | −0.909130 | − | 0.909130i | 0.0870719 | − | 0.996202i | \(-0.472249\pi\) |
−0.996202 | + | 0.0870719i | \(0.972249\pi\) | |||||||
\(338\) | 10081.0 | − | 10081.0i | 0.0882410 | − | 0.0882410i | ||||
\(339\) | − | 61932.0i | − | 0.538909i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4576.00 | −0.0393529 | ||||||||
\(342\) | −1620.00 | − | 1620.00i | −0.0138504 | − | 0.0138504i | ||||
\(343\) | 89700.0 | − | 89700.0i | 0.762437 | − | 0.762437i | ||||
\(344\) | 88440.0i | 0.747363i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33782.0 | 0.282185 | ||||||||
\(347\) | 104626. | + | 104626.i | 0.868922 | + | 0.868922i | 0.992353 | − | 0.123431i | \(-0.0393899\pi\) |
−0.123431 | + | 0.992353i | \(0.539390\pi\) | |||||||
\(348\) | −40320.0 | + | 40320.0i | −0.332937 | + | 0.332937i | ||||
\(349\) | 94800.0i | 0.778319i | 0.921170 | + | 0.389159i | \(0.127234\pi\) | ||||
−0.921170 | + | 0.389159i | \(0.872766\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −150120. | −1.21850 | ||||||||
\(352\) | 5152.00 | + | 5152.00i | 0.0415806 | + | 0.0415806i | ||||
\(353\) | −63569.0 | + | 63569.0i | −0.510148 | + | 0.510148i | −0.914572 | − | 0.404424i | \(-0.867472\pi\) |
0.404424 | + | 0.914572i | \(0.367472\pi\) | |||||||
\(354\) | − | 43920.0i | − | 0.350474i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 30240.0 | 0.238606 | ||||||||
\(357\) | 312.000 | + | 312.000i | 0.00244804 | + | 0.00244804i | ||||
\(358\) | −10620.0 | + | 10620.0i | −0.0828626 | + | 0.0828626i | ||||
\(359\) | 141840.i | 1.10055i | 0.834983 | + | 0.550275i | \(0.185477\pi\) | ||||
−0.834983 | + | 0.550275i | \(0.814523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 97921.0 | 0.751383 | ||||||||
\(362\) | 24122.0 | + | 24122.0i | 0.184076 | + | 0.184076i | ||||
\(363\) | −87462.0 | + | 87462.0i | −0.663752 | + | 0.663752i | ||||
\(364\) | 101192.i | 0.763736i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 19104.0 | 0.142614 | ||||||||
\(367\) | −142174. | − | 142174.i | −1.05557 | − | 1.05557i | −0.998362 | − | 0.0572103i | \(-0.981779\pi\) |
−0.0572103 | − | 0.998362i | \(-0.518221\pi\) | |||||||
\(368\) | −27224.0 | + | 27224.0i | −0.201028 | + | 0.201028i | ||||
\(369\) | − | 15192.0i | − | 0.111574i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 173212. | 1.25843 | ||||||||
\(372\) | −48048.0 | − | 48048.0i | −0.347208 | − | 0.347208i | ||||
\(373\) | −10309.0 | + | 10309.0i | −0.0740967 | + | 0.0740967i | −0.743184 | − | 0.669087i | \(-0.766685\pi\) |
0.669087 | + | 0.743184i | \(0.266685\pi\) | |||||||
\(374\) | − | 16.0000i | − | 0.000114387i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −148440. | −1.04997 | ||||||||
\(377\) | 66720.0 | + | 66720.0i | 0.469433 | + | 0.469433i | ||||
\(378\) | −28080.0 | + | 28080.0i | −0.196523 | + | 0.196523i | ||||
\(379\) | − | 115380.i | − | 0.803253i | −0.915804 | − | 0.401626i | \(-0.868445\pi\) | ||
0.915804 | − | 0.401626i | \(-0.131555\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −150888. | −1.03945 | ||||||||
\(382\) | −45188.0 | − | 45188.0i | −0.309668 | − | 0.309668i | ||||
\(383\) | −62654.0 | + | 62654.0i | −0.427121 | + | 0.427121i | −0.887647 | − | 0.460525i | \(-0.847661\pi\) |
0.460525 | + | 0.887647i | \(0.347661\pi\) | |||||||
\(384\) | 139680.i | 0.947266i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −78398.0 | −0.526175 | ||||||||
\(387\) | −13266.0 | − | 13266.0i | −0.0885764 | − | 0.0885764i | ||||
\(388\) | 91714.0 | − | 91714.0i | 0.609217 | − | 0.609217i | ||||
\(389\) | − | 132690.i | − | 0.876878i | −0.898761 | − | 0.438439i | \(-0.855532\pi\) | ||
0.898761 | − | 0.438439i | \(-0.144468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 332.000 | 0.00217162 | ||||||||
\(392\) | −31470.0 | − | 31470.0i | −0.204797 | − | 0.204797i | ||||
\(393\) | 121632. | − | 121632.i | 0.787522 | − | 0.787522i | ||||
\(394\) | − | 56698.0i | − | 0.365237i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1008.00 | −0.00642792 | ||||||||
\(397\) | 88451.0 | + | 88451.0i | 0.561205 | + | 0.561205i | 0.929650 | − | 0.368444i | \(-0.120110\pi\) |
−0.368444 | + | 0.929650i | \(0.620110\pi\) | |||||||
\(398\) | 1800.00 | − | 1800.00i | 0.0113633 | − | 0.0113633i | ||||
\(399\) | 56160.0i | 0.352762i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 63202.0 | 0.393045 | 0.196522 | − | 0.980499i | \(-0.437035\pi\) | ||||
0.196522 | + | 0.980499i | \(0.437035\pi\) | |||||||
\(402\) | −10488.0 | − | 10488.0i | −0.0648994 | − | 0.0648994i | ||||
\(403\) | −79508.0 | + | 79508.0i | −0.489554 | + | 0.489554i | ||||
\(404\) | − | 225428.i | − | 1.38116i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24960.0 | 0.151423 | ||||||||
\(407\) | −2008.00 | − | 2008.00i | −0.0121220 | − | 0.0121220i | ||||
\(408\) | 360.000 | − | 360.000i | 0.00216263 | − | 0.00216263i | ||||
\(409\) | 52890.0i | 0.316175i | 0.987425 | + | 0.158087i | \(0.0505327\pi\) | ||||
−0.987425 | + | 0.158087i | \(0.949467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 124212. | 0.735326 | ||||||||
\(412\) | 13916.0 | + | 13916.0i | 0.0819823 | + | 0.0819823i | ||||
\(413\) | 95160.0 | − | 95160.0i | 0.557897 | − | 0.557897i | ||||
\(414\) | 2988.00i | 0.0174333i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 179032. | 1.03453 | ||||||||
\(417\) | 162360. | + | 162360.i | 0.933699 | + | 0.933699i | ||||
\(418\) | 1440.00 | − | 1440.00i | 0.00824157 | − | 0.00824157i | ||||
\(419\) | 256980.i | 1.46376i | 0.681431 | + | 0.731882i | \(0.261358\pi\) | ||||
−0.681431 | + | 0.731882i | \(0.738642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 186632. | 1.05298 | 0.526492 | − | 0.850180i | \(-0.323507\pi\) | ||||
0.526492 | + | 0.850180i | \(0.323507\pi\) | |||||||
\(422\) | 18392.0 | + | 18392.0i | 0.103277 | + | 0.103277i | ||||
\(423\) | 22266.0 | − | 22266.0i | 0.124440 | − | 0.124440i | ||||
\(424\) | − | 199860.i | − | 1.11172i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −72816.0 | −0.401243 | ||||||||
\(427\) | 41392.0 | + | 41392.0i | 0.227018 | + | 0.227018i | ||||
\(428\) | 116564. | − | 116564.i | 0.636322 | − | 0.636322i | ||||
\(429\) | − | 13344.0i | − | 0.0725056i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −208028. | −1.11987 | −0.559935 | − | 0.828537i | \(-0.689174\pi\) | ||||
−0.559935 | + | 0.828537i | \(0.689174\pi\) | |||||||
\(432\) | −88560.0 | − | 88560.0i | −0.474537 | − | 0.474537i | ||||
\(433\) | 151271. | − | 151271.i | 0.806826 | − | 0.806826i | −0.177326 | − | 0.984152i | \(-0.556745\pi\) |
0.984152 | + | 0.177326i | \(0.0567447\pi\) | |||||||
\(434\) | 29744.0i | 0.157914i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −238140. | −1.25274 | ||||||||
\(437\) | 29880.0 | + | 29880.0i | 0.156465 | + | 0.156465i | ||||
\(438\) | 9492.00 | − | 9492.00i | 0.0494777 | − | 0.0494777i | ||||
\(439\) | − | 158640.i | − | 0.823159i | −0.911374 | − | 0.411579i | \(-0.864977\pi\) | ||
0.911374 | − | 0.411579i | \(-0.135023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9441.00 | 0.0485446 | ||||||||
\(442\) | −278.000 | − | 278.000i | −0.00142298 | − | 0.00142298i | ||||
\(443\) | −252974. | + | 252974.i | −1.28905 | + | 1.28905i | −0.353679 | + | 0.935367i | \(0.615070\pi\) |
−0.935367 | + | 0.353679i | \(0.884930\pi\) | |||||||
\(444\) | − | 42168.0i | − | 0.213903i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1732.00 | 0.00870719 | ||||||||
\(447\) | −98100.0 | − | 98100.0i | −0.490969 | − | 0.490969i | ||||
\(448\) | −34736.0 | + | 34736.0i | −0.173071 | + | 0.173071i | ||||
\(449\) | 123750.i | 0.613836i | 0.951736 | + | 0.306918i | \(0.0992978\pi\) | ||||
−0.951736 | + | 0.306918i | \(0.900702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13504.0 | 0.0663910 | ||||||||
\(452\) | −72254.0 | − | 72254.0i | −0.353659 | − | 0.353659i | ||||
\(453\) | 6312.00 | − | 6312.00i | 0.0307589 | − | 0.0307589i | ||||
\(454\) | 90452.0i | 0.438840i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 64800.0 | 0.311634 | ||||||||
\(457\) | 32201.0 | + | 32201.0i | 0.154183 | + | 0.154183i | 0.779983 | − | 0.625800i | \(-0.215227\pi\) |
−0.625800 | + | 0.779983i | \(0.715227\pi\) | |||||||
\(458\) | −39120.0 | + | 39120.0i | −0.186495 | + | 0.186495i | ||||
\(459\) | 1080.00i | 0.00512623i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 75142.0 | 0.353574 | 0.176787 | − | 0.984249i | \(-0.443430\pi\) | ||||
0.176787 | + | 0.984249i | \(0.443430\pi\) | |||||||
\(462\) | −2496.00 | − | 2496.00i | −0.0116939 | − | 0.0116939i | ||||
\(463\) | −235714. | + | 235714.i | −1.09957 | + | 1.09957i | −0.105111 | + | 0.994461i | \(0.533520\pi\) |
−0.994461 | + | 0.105111i | \(0.966480\pi\) | |||||||
\(464\) | 78720.0i | 0.365636i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 66242.0 | 0.305043 | ||||||||
\(467\) | −28574.0 | − | 28574.0i | −0.131020 | − | 0.131020i | 0.638556 | − | 0.769576i | \(-0.279532\pi\) |
−0.769576 | + | 0.638556i | \(0.779532\pi\) | |||||||
\(468\) | −17514.0 | + | 17514.0i | −0.0799638 | + | 0.0799638i | ||||
\(469\) | − | 45448.0i | − | 0.206618i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −77988.0 | −0.351549 | ||||||||
\(472\) | −109800. | − | 109800.i | −0.492854 | − | 0.492854i | ||||
\(473\) | 11792.0 | − | 11792.0i | 0.0527066 | − | 0.0527066i | ||||
\(474\) | 109440.i | 0.487101i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 728.000 | 0.00321305 | ||||||||
\(477\) | 29979.0 | + | 29979.0i | 0.131759 | + | 0.131759i | ||||
\(478\) | 88440.0 | − | 88440.0i | 0.387073 | − | 0.387073i | ||||
\(479\) | 26520.0i | 0.115585i | 0.998329 | + | 0.0577926i | \(0.0184062\pi\) | ||||
−0.998329 | + | 0.0577926i | \(0.981594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −69778.0 | −0.301598 | ||||||||
\(482\) | 20312.0 | + | 20312.0i | 0.0874296 | + | 0.0874296i | ||||
\(483\) | 51792.0 | − | 51792.0i | 0.222008 | − | 0.222008i | ||||
\(484\) | 204078.i | 0.871175i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −18468.0 | −0.0781893 | ||||||||
\(487\) | −41374.0 | − | 41374.0i | −0.174449 | − | 0.174449i | 0.614482 | − | 0.788931i | \(-0.289365\pi\) |
−0.788931 | + | 0.614482i | \(0.789365\pi\) | |||||||
\(488\) | 47760.0 | − | 47760.0i | 0.200551 | − | 0.200551i | ||||
\(489\) | − | 231432.i | − | 0.967845i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −149288. | −0.619244 | −0.309622 | − | 0.950860i | \(-0.600203\pi\) | ||||
−0.309622 | + | 0.950860i | \(0.600203\pi\) | |||||||
\(492\) | 141792. | + | 141792.i | 0.585762 | + | 0.585762i | ||||
\(493\) | 480.000 | − | 480.000i | 0.00197491 | − | 0.00197491i | ||||
\(494\) | − | 50040.0i | − | 0.205052i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −93808.0 | −0.381309 | ||||||||
\(497\) | −157768. | − | 157768.i | −0.638714 | − | 0.638714i | ||||
\(498\) | −67848.0 | + | 67848.0i | −0.273576 | + | 0.273576i | ||||
\(499\) | 284100.i | 1.14096i | 0.821312 | + | 0.570480i | \(0.193243\pi\) | ||||
−0.821312 | + | 0.570480i | \(0.806757\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 186312. | 0.742276 | ||||||||
\(502\) | 74752.0 | + | 74752.0i | 0.296630 | + | 0.296630i | ||||
\(503\) | 117406. | − | 117406.i | 0.464039 | − | 0.464039i | −0.435938 | − | 0.899977i | \(-0.643583\pi\) |
0.899977 | + | 0.435938i | \(0.143583\pi\) | |||||||
\(504\) | 14040.0i | 0.0552721i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2656.00 | −0.0103735 | ||||||||
\(507\) | −60486.0 | − | 60486.0i | −0.235309 | − | 0.235309i | ||||
\(508\) | −176036. | + | 176036.i | −0.682141 | + | 0.682141i | ||||
\(509\) | − | 234960.i | − | 0.906898i | −0.891282 | − | 0.453449i | \(-0.850193\pi\) | ||
0.891282 | − | 0.453449i | \(-0.149807\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41132.0 | 0.157521 | ||||||||
\(512\) | 184336. | + | 184336.i | 0.703186 | + | 0.703186i | ||||
\(513\) | −97200.0 | + | 97200.0i | −0.369344 | + | 0.369344i | ||||
\(514\) | − | 75598.0i | − | 0.286144i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 247632. | 0.930052 | ||||||||
\(517\) | 19792.0 | + | 19792.0i | 0.0740472 | + | 0.0740472i | ||||
\(518\) | −13052.0 | + | 13052.0i | −0.0486427 | + | 0.0486427i | ||||
\(519\) | − | 202692.i | − | 0.752492i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −171218. | −0.630774 | −0.315387 | − | 0.948963i | \(-0.602134\pi\) | ||||
−0.315387 | + | 0.948963i | \(0.602134\pi\) | |||||||
\(522\) | 4320.00 | + | 4320.00i | 0.0158541 | + | 0.0158541i | ||||
\(523\) | 332666. | − | 332666.i | 1.21620 | − | 1.21620i | 0.247248 | − | 0.968952i | \(-0.420474\pi\) |
0.968952 | − | 0.247248i | \(-0.0795262\pi\) | |||||||
\(524\) | − | 283808.i | − | 1.03362i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 67172.0 | 0.242782 | ||||||||
\(527\) | 572.000 | + | 572.000i | 0.00205956 | + | 0.00205956i | ||||
\(528\) | 7872.00 | − | 7872.00i | 0.0282369 | − | 0.0282369i | ||||
\(529\) | 224729.i | 0.803060i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32940.0 | 0.116825 | ||||||||
\(532\) | 65520.0 | + | 65520.0i | 0.231500 | + | 0.231500i | ||||
\(533\) | 234632. | − | 234632.i | 0.825910 | − | 0.825910i | ||||
\(534\) | 25920.0i | 0.0908976i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −52440.0 | −0.182530 | ||||||||
\(537\) | 63720.0 | + | 63720.0i | 0.220967 | + | 0.220967i | ||||
\(538\) | −28530.0 | + | 28530.0i | −0.0985683 | + | 0.0985683i | ||||
\(539\) | 8392.00i | 0.0288860i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13862.0 | 0.0473621 | 0.0236811 | − | 0.999720i | \(-0.492461\pi\) | ||||
0.0236811 | + | 0.999720i | \(0.492461\pi\) | |||||||
\(542\) | −7468.00 | − | 7468.00i | −0.0254218 | − | 0.0254218i | ||||
\(543\) | 144732. | − | 144732.i | 0.490868 | − | 0.490868i | ||||
\(544\) | − | 1288.00i | − | 0.00435229i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −86736.0 | −0.290947 | ||||||||
\(547\) | 180026. | + | 180026.i | 0.601673 | + | 0.601673i | 0.940756 | − | 0.339083i | \(-0.110117\pi\) |
−0.339083 | + | 0.940756i | \(0.610117\pi\) | |||||||
\(548\) | 144914. | − | 144914.i | 0.482558 | − | 0.482558i | ||||
\(549\) | 14328.0i | 0.0475380i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 86400.0 | 0.284584 | ||||||||
\(552\) | −59760.0 | − | 59760.0i | −0.196125 | − | 0.196125i | ||||
\(553\) | −237120. | + | 237120.i | −0.775386 | + | 0.775386i | ||||
\(554\) | − | 12998.0i | − | 0.0423503i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 378840. | 1.22548 | ||||||||
\(557\) | −422549. | − | 422549.i | −1.36197 | − | 1.36197i | −0.871408 | − | 0.490560i | \(-0.836792\pi\) |
−0.490560 | − | 0.871408i | \(-0.663208\pi\) | |||||||
\(558\) | −5148.00 | + | 5148.00i | −0.0165337 | + | 0.0165337i | ||||
\(559\) | − | 409772.i | − | 1.31135i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −96.0000 | −0.000305032 | ||||||||
\(562\) | −97928.0 | − | 97928.0i | −0.310052 | − | 0.310052i | ||||
\(563\) | −105314. | + | 105314.i | −0.332253 | + | 0.332253i | −0.853442 | − | 0.521188i | \(-0.825489\pi\) |
0.521188 | + | 0.853442i | \(0.325489\pi\) | |||||||
\(564\) | 415632.i | 1.30662i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −119708. | −0.373672 | ||||||||
\(567\) | 149526. | + | 149526.i | 0.465105 | + | 0.465105i | ||||
\(568\) | −182040. | + | 182040.i | −0.564248 | + | 0.564248i | ||||
\(569\) | 85830.0i | 0.265103i | 0.991176 | + | 0.132551i | \(0.0423170\pi\) | ||||
−0.991176 | + | 0.132551i | \(0.957683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −142168. | −0.436043 | −0.218022 | − | 0.975944i | \(-0.569960\pi\) | ||||
−0.218022 | + | 0.975944i | \(0.569960\pi\) | |||||||
\(572\) | −15568.0 | − | 15568.0i | −0.0475818 | − | 0.0475818i | ||||
\(573\) | −271128. | + | 271128.i | −0.825781 | + | 0.825781i | ||||
\(574\) | − | 87776.0i | − | 0.266411i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12024.0 | −0.0362413 | ||||||||
\(577\) | 154601. | + | 154601.i | 0.464366 | + | 0.464366i | 0.900084 | − | 0.435717i | \(-0.143505\pi\) |
−0.435717 | + | 0.900084i | \(0.643505\pi\) | |||||||
\(578\) | 83519.0 | − | 83519.0i | 0.249994 | − | 0.249994i | ||||
\(579\) | 470388.i | 1.40313i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −294008. | −0.870977 | ||||||||
\(582\) | 78612.0 | + | 78612.0i | 0.232083 | + | 0.232083i | ||||
\(583\) | −26648.0 | + | 26648.0i | −0.0784021 | + | 0.0784021i | ||||
\(584\) | − | 47460.0i | − | 0.139156i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −56998.0 | −0.165983 | ||||||||
\(587\) | −222974. | − | 222974.i | −0.647110 | − | 0.647110i | 0.305184 | − | 0.952294i | \(-0.401282\pi\) |
−0.952294 | + | 0.305184i | \(0.901282\pi\) | |||||||
\(588\) | −88116.0 | + | 88116.0i | −0.254859 | + | 0.254859i | ||||
\(589\) | 102960.i | 0.296782i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −340188. | −0.973967 | ||||||||
\(592\) | −41164.0 | − | 41164.0i | −0.117456 | − | 0.117456i | ||||
\(593\) | −148049. | + | 148049.i | −0.421014 | + | 0.421014i | −0.885553 | − | 0.464539i | \(-0.846220\pi\) |
0.464539 | + | 0.885553i | \(0.346220\pi\) | |||||||
\(594\) | − | 8640.00i | − | 0.0244873i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −228900. | −0.644397 | ||||||||
\(597\) | −10800.0 | − | 10800.0i | −0.0303023 | − | 0.0303023i | ||||
\(598\) | −46148.0 | + | 46148.0i | −0.129048 | + | 0.129048i | ||||
\(599\) | 31800.0i | 0.0886285i | 0.999018 | + | 0.0443143i | \(0.0141103\pi\) | ||||
−0.999018 | + | 0.0443143i | \(0.985890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −71848.0 | −0.198914 | −0.0994571 | − | 0.995042i | \(-0.531711\pi\) | ||||
−0.0994571 | + | 0.995042i | \(0.531711\pi\) | |||||||
\(602\) | −76648.0 | − | 76648.0i | −0.211499 | − | 0.211499i | ||||
\(603\) | 7866.00 | − | 7866.00i | 0.0216331 | − | 0.0216331i | ||||
\(604\) | − | 14728.0i | − | 0.0403710i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 193224. | 0.526158 | ||||||||
\(607\) | 13526.0 | + | 13526.0i | 0.0367106 | + | 0.0367106i | 0.725224 | − | 0.688513i | \(-0.241736\pi\) |
−0.688513 | + | 0.725224i | \(0.741736\pi\) | |||||||
\(608\) | 115920. | − | 115920.i | 0.313582 | − | 0.313582i | ||||
\(609\) | − | 149760.i | − | 0.403795i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 687772. | 1.84231 | ||||||||
\(612\) | 126.000 | + | 126.000i | 0.000336409 | + | 0.000336409i | ||||
\(613\) | 303461. | − | 303461.i | 0.807573 | − | 0.807573i | −0.176693 | − | 0.984266i | \(-0.556540\pi\) |
0.984266 | + | 0.176693i | \(0.0565399\pi\) | |||||||
\(614\) | 235852.i | 0.625609i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12480.0 | −0.0328892 | ||||||||
\(617\) | −122399. | − | 122399.i | −0.321520 | − | 0.321520i | 0.527830 | − | 0.849350i | \(-0.323006\pi\) |
−0.849350 | + | 0.527830i | \(0.823006\pi\) | |||||||
\(618\) | −11928.0 | + | 11928.0i | −0.0312313 | + | 0.0312313i | ||||
\(619\) | − | 110220.i | − | 0.287660i | −0.989602 | − | 0.143830i | \(-0.954058\pi\) | ||
0.989602 | − | 0.143830i | \(-0.0459418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 179280. | 0.464888 | ||||||||
\(622\) | 3892.00 | + | 3892.00i | 0.0100599 | + | 0.0100599i | ||||
\(623\) | −56160.0 | + | 56160.0i | −0.144694 | + | 0.144694i | ||||
\(624\) | − | 273552.i | − | 0.702539i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 99922.0 | 0.254984 | ||||||||
\(627\) | −8640.00 | − | 8640.00i | −0.0219775 | − | 0.0219775i | ||||
\(628\) | −90986.0 | + | 90986.0i | −0.230704 | + | 0.230704i | ||||
\(629\) | 502.000i | 0.00126883i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 620372. | 1.55809 | 0.779047 | − | 0.626966i | \(-0.215703\pi\) | ||||
0.779047 | + | 0.626966i | \(0.215703\pi\) | |||||||
\(632\) | 273600. | + | 273600.i | 0.684986 | + | 0.684986i | ||||
\(633\) | 110352. | − | 110352.i | 0.275406 | − | 0.275406i | ||||
\(634\) | − | 34198.0i | − | 0.0850790i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −559608. | −1.38347 | ||||||||
\(637\) | 145811. | + | 145811.i | 0.359345 | + | 0.359345i | ||||
\(638\) | −3840.00 | + | 3840.00i | −0.00943387 | + | 0.00943387i | ||||
\(639\) | − | 54612.0i | − | 0.133748i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −722888. | −1.75936 | −0.879680 | − | 0.475565i | \(-0.842244\pi\) | ||||
−0.879680 | + | 0.475565i | \(0.842244\pi\) | |||||||
\(642\) | 99912.0 | + | 99912.0i | 0.242408 | + | 0.242408i | ||||
\(643\) | 393026. | − | 393026.i | 0.950603 | − | 0.950603i | −0.0482328 | − | 0.998836i | \(-0.515359\pi\) |
0.998836 | + | 0.0482328i | \(0.0153589\pi\) | |||||||
\(644\) | − | 120848.i | − | 0.291385i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −360.000 | −0.000862656 | ||||||||
\(647\) | 338626. | + | 338626.i | 0.808931 | + | 0.808931i | 0.984472 | − | 0.175541i | \(-0.0561674\pi\) |
−0.175541 | + | 0.984472i | \(0.556167\pi\) | |||||||
\(648\) | 172530. | − | 172530.i | 0.410880 | − | 0.410880i | ||||
\(649\) | 29280.0i | 0.0695155i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 178464. | 0.421103 | ||||||||
\(652\) | −270004. | − | 270004.i | −0.635148 | − | 0.635148i | ||||
\(653\) | −254669. | + | 254669.i | −0.597241 | + | 0.597241i | −0.939577 | − | 0.342336i | \(-0.888782\pi\) |
0.342336 | + | 0.939577i | \(0.388782\pi\) | |||||||
\(654\) | − | 204120.i | − | 0.477233i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 276832. | 0.643293 | ||||||||
\(657\) | 7119.00 | + | 7119.00i | 0.0164926 | + | 0.0164926i | ||||
\(658\) | 128648. | − | 128648.i | 0.297133 | − | 0.297133i | ||||
\(659\) | − | 603660.i | − | 1.39002i | −0.718999 | − | 0.695011i | \(-0.755400\pi\) | ||
0.718999 | − | 0.695011i | \(-0.244600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14792.0 | 0.0338551 | 0.0169275 | − | 0.999857i | \(-0.494612\pi\) | ||||
0.0169275 | + | 0.999857i | \(0.494612\pi\) | |||||||
\(662\) | −143128. | − | 143128.i | −0.326594 | − | 0.326594i | ||||
\(663\) | −1668.00 | + | 1668.00i | −0.00379463 | + | 0.00379463i | ||||
\(664\) | 339240.i | 0.769433i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4518.00 | −0.0101859 | ||||||||
\(667\) | −79680.0 | − | 79680.0i | −0.179101 | − | 0.179101i | ||||
\(668\) | 217364. | − | 217364.i | 0.487119 | − | 0.487119i | ||||
\(669\) | − | 10392.0i | − | 0.0232192i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12736.0 | −0.0282871 | ||||||||
\(672\) | −200928. | − | 200928.i | −0.444940 | − | 0.444940i | ||||
\(673\) | −300409. | + | 300409.i | −0.663258 | + | 0.663258i | −0.956147 | − | 0.292888i | \(-0.905384\pi\) |
0.292888 | + | 0.956147i | \(0.405384\pi\) | |||||||
\(674\) | − | 206498.i | − | 0.454565i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −141134. | −0.308843 | ||||||||
\(677\) | 256051. | + | 256051.i | 0.558662 | + | 0.558662i | 0.928926 | − | 0.370264i | \(-0.120733\pi\) |
−0.370264 | + | 0.928926i | \(0.620733\pi\) | |||||||
\(678\) | 61932.0 | − | 61932.0i | 0.134727 | − | 0.134727i | ||||
\(679\) | 340652.i | 0.738876i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 542712. | 1.17024 | ||||||||
\(682\) | −4576.00 | − | 4576.00i | −0.00983824 | − | 0.00983824i | ||||
\(683\) | −341954. | + | 341954.i | −0.733038 | + | 0.733038i | −0.971220 | − | 0.238183i | \(-0.923448\pi\) |
0.238183 | + | 0.971220i | \(0.423448\pi\) | |||||||
\(684\) | 22680.0i | 0.0484765i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 179400. | 0.381219 | ||||||||
\(687\) | 234720. | + | 234720.i | 0.497321 | + | 0.497321i | ||||
\(688\) | 241736. | − | 241736.i | 0.510698 | − | 0.510698i | ||||
\(689\) | 926018.i | 1.95066i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −717688. | −1.50307 | −0.751536 | − | 0.659692i | \(-0.770687\pi\) | ||||
−0.751536 | + | 0.659692i | \(0.770687\pi\) | |||||||
\(692\) | −236474. | − | 236474.i | −0.493823 | − | 0.493823i | ||||
\(693\) | 1872.00 | − | 1872.00i | 0.00389798 | − | 0.00389798i | ||||
\(694\) | 209252.i | 0.434461i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −172800. | −0.356718 | ||||||||
\(697\) | −1688.00 | − | 1688.00i | −0.00347462 | − | 0.00347462i | ||||
\(698\) | −94800.0 | + | 94800.0i | −0.194580 | + | 0.194580i | ||||
\(699\) | − | 397452.i | − | 0.813449i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 267352. | 0.544061 | 0.272030 | − | 0.962289i | \(-0.412305\pi\) | ||||
0.272030 | + | 0.962289i | \(0.412305\pi\) | |||||||
\(702\) | −150120. | − | 150120.i | −0.304624 | − | 0.304624i | ||||
\(703\) | −45180.0 | + | 45180.0i | −0.0914188 | + | 0.0914188i | ||||
\(704\) | − | 10688.0i | − | 0.0215651i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −127138. | −0.255074 | ||||||||
\(707\) | 418652. | + | 418652.i | 0.837557 | + | 0.837557i | ||||
\(708\) | −307440. | + | 307440.i | −0.613330 | + | 0.613330i | ||||
\(709\) | − | 159360.i | − | 0.317020i | −0.987357 | − | 0.158510i | \(-0.949331\pi\) | ||
0.987357 | − | 0.158510i | \(-0.0506690\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −82080.0 | −0.162367 | ||||||||
\(712\) | 64800.0 | + | 64800.0i | 0.127825 | + | 0.127825i | ||||
\(713\) | 94952.0 | − | 94952.0i | 0.186778 | − | 0.186778i | ||||
\(714\) | 624.000i | 0.00122402i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 148680. | 0.290019 | ||||||||
\(717\) | −530640. | − | 530640.i | −1.03219 | − | 1.03219i | ||||
\(718\) | −141840. | + | 141840.i | −0.275138 | + | 0.275138i | ||||
\(719\) | 364680.i | 0.705430i | 0.935731 | + | 0.352715i | \(0.114742\pi\) | ||||
−0.935731 | + | 0.352715i | \(0.885258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51688.0 | −0.0994304 | ||||||||
\(722\) | 97921.0 | + | 97921.0i | 0.187846 | + | 0.187846i | ||||
\(723\) | 121872. | − | 121872.i | 0.233146 | − | 0.233146i | ||||
\(724\) | − | 337708.i | − | 0.644265i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −174924. | −0.331876 | ||||||||
\(727\) | −716374. | − | 716374.i | −1.35541 | − | 1.35541i | −0.879486 | − | 0.475925i | \(-0.842113\pi\) |
−0.475925 | − | 0.879486i | \(-0.657887\pi\) | |||||||
\(728\) | −216840. | + | 216840.i | −0.409144 | + | 0.409144i | ||||
\(729\) | 576639.i | 1.08505i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2948.00 | −0.00551687 | ||||||||
\(732\) | −133728. | − | 133728.i | −0.249574 | − | 0.249574i | ||||
\(733\) | −641029. | + | 641029.i | −1.19308 | + | 1.19308i | −0.216883 | + | 0.976198i | \(0.569589\pi\) |
−0.976198 | + | 0.216883i | \(0.930411\pi\) | |||||||
\(734\) | − | 284348.i | − | 0.527786i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −213808. | −0.394701 | ||||||||
\(737\) | 6992.00 | + | 6992.00i | 0.0128726 | + | 0.0128726i | ||||
\(738\) | 15192.0 | − | 15192.0i | 0.0278934 | − | 0.0278934i | ||||
\(739\) | − | 607140.i | − | 1.11173i | −0.831272 | − | 0.555866i | \(-0.812387\pi\) | ||
0.831272 | − | 0.555866i | \(-0.187613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −300240. | −0.546805 | ||||||||
\(742\) | 173212. | + | 173212.i | 0.314608 | + | 0.314608i | ||||
\(743\) | 248026. | − | 248026.i | 0.449283 | − | 0.449283i | −0.445833 | − | 0.895116i | \(-0.647093\pi\) |
0.895116 | + | 0.445833i | \(0.147093\pi\) | |||||||
\(744\) | − | 205920.i | − | 0.372008i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20618.0 | −0.0370484 | ||||||||
\(747\) | −50886.0 | − | 50886.0i | −0.0911921 | − | 0.0911921i | ||||
\(748\) | −112.000 | + | 112.000i | −0.000200177 | + | 0.000200177i | ||||
\(749\) | 432952.i | 0.771749i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 169052. | 0.299737 | 0.149869 | − | 0.988706i | \(-0.452115\pi\) | ||||
0.149869 | + | 0.988706i | \(0.452115\pi\) | |||||||
\(752\) | 405736. | + | 405736.i | 0.717477 | + | 0.717477i | ||||
\(753\) | 448512. | − | 448512.i | 0.791014 | − | 0.791014i | ||||
\(754\) | 133440.i | 0.234716i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 393120. | 0.687831 | ||||||||
\(757\) | 166301. | + | 166301.i | 0.290204 | + | 0.290204i | 0.837161 | − | 0.546957i | \(-0.184214\pi\) |
−0.546957 | + | 0.837161i | \(0.684214\pi\) | |||||||
\(758\) | 115380. | − | 115380.i | 0.200813 | − | 0.200813i | ||||
\(759\) | 15936.0i | 0.0276628i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 557842. | 0.963256 | 0.481628 | − | 0.876376i | \(-0.340046\pi\) | ||||
0.481628 | + | 0.876376i | \(0.340046\pi\) | |||||||
\(762\) | −150888. | − | 150888.i | −0.259863 | − | 0.259863i | ||||
\(763\) | 442260. | − | 442260.i | 0.759676 | − | 0.759676i | ||||
\(764\) | 632632.i | 1.08384i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −125308. | −0.213561 | ||||||||
\(767\) | 508740. | + | 508740.i | 0.864779 | + | 0.864779i | ||||
\(768\) | −11424.0 | + | 11424.0i | −0.0193685 | + | 0.0193685i | ||||
\(769\) | − | 678720.i | − | 1.14773i | −0.818952 | − | 0.573863i | \(-0.805444\pi\) | ||
0.818952 | − | 0.573863i | \(-0.194556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −453588. | −0.763050 | ||||||||
\(772\) | 548786. | + | 548786.i | 0.920807 | + | 0.920807i | ||||
\(773\) | 164341. | − | 164341.i | 0.275034 | − | 0.275034i | −0.556089 | − | 0.831123i | \(-0.687699\pi\) |
0.831123 | + | 0.556089i | \(0.187699\pi\) | |||||||
\(774\) | − | 26532.0i | − | 0.0442882i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 393060. | 0.652733 | ||||||||
\(777\) | 78312.0 | + | 78312.0i | 0.129714 | + | 0.129714i | ||||
\(778\) | 132690. | − | 132690.i | 0.219219 | − | 0.219219i | ||||
\(779\) | − | 303840.i | − | 0.500691i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48544.0 | 0.0795854 | ||||||||
\(782\) | 332.000 | + | 332.000i | 0.000542906 | + | 0.000542906i | ||||
\(783\) | 259200. | − | 259200.i | 0.422777 | − | 0.422777i | ||||
\(784\) | 172036.i | 0.279890i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 243264. | 0.393761 | ||||||||
\(787\) | −323074. | − | 323074.i | −0.521618 | − | 0.521618i | 0.396442 | − | 0.918060i | \(-0.370245\pi\) |
−0.918060 | + | 0.396442i | \(0.870245\pi\) | |||||||
\(788\) | −396886. | + | 396886.i | −0.639166 | + | 0.639166i | ||||
\(789\) | − | 403032.i | − | 0.647419i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 268372. | 0.428928 | ||||||||
\(792\) | −2160.00 | − | 2160.00i | −0.00344353 | − | 0.00344353i | ||||
\(793\) | −221288. | + | 221288.i | −0.351894 | + | 0.351894i | ||||
\(794\) | 176902.i | 0.280603i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25200.0 | −0.0397717 | ||||||||
\(797\) | −510299. | − | 510299.i | −0.803356 | − | 0.803356i | 0.180262 | − | 0.983619i | \(-0.442305\pi\) |
−0.983619 | + | 0.180262i | \(0.942305\pi\) | |||||||
\(798\) | −56160.0 | + | 56160.0i | −0.0881904 | + | 0.0881904i | ||||
\(799\) | − | 4948.00i | − | 0.00775061i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19440.0 | −0.0302992 | ||||||||
\(802\) | 63202.0 | + | 63202.0i | 0.0982612 | + | 0.0982612i | ||||
\(803\) | −6328.00 | + | 6328.00i | −0.00981376 | + | 0.00981376i | ||||
\(804\) | 146832.i | 0.227148i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −159016. | −0.244777 | ||||||||
\(807\) | 171180. | + | 171180.i | 0.262849 | + | 0.262849i | ||||
\(808\) | 483060. | − | 483060.i | 0.739909 | − | 0.739909i | ||||
\(809\) | − | 1.18656e6i | − | 1.81298i | −0.422229 | − | 0.906489i | \(-0.638752\pi\) | ||
0.422229 | − | 0.906489i | \(-0.361248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −431008. | −0.655305 | −0.327653 | − | 0.944798i | \(-0.606258\pi\) | ||||
−0.327653 | + | 0.944798i | \(0.606258\pi\) | |||||||
\(812\) | −174720. | − | 174720.i | −0.264991 | − | 0.264991i | ||||
\(813\) | −44808.0 | + | 44808.0i | −0.0677914 | + | 0.0677914i | ||||
\(814\) | − | 4016.00i | − | 0.00606101i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1968.00 | −0.00295559 | ||||||||
\(817\) | −265320. | − | 265320.i | −0.397490 | − | 0.397490i | ||||
\(818\) | −52890.0 | + | 52890.0i | −0.0790436 | + | 0.0790436i | ||||
\(819\) | − | 65052.0i | − | 0.0969824i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −639368. | −0.948560 | −0.474280 | − | 0.880374i | \(-0.657291\pi\) | ||||
−0.474280 | + | 0.880374i | \(0.657291\pi\) | |||||||
\(822\) | 124212. | + | 124212.i | 0.183831 | + | 0.183831i | ||||
\(823\) | 74966.0 | − | 74966.0i | 0.110679 | − | 0.110679i | −0.649599 | − | 0.760277i | \(-0.725063\pi\) |
0.760277 | + | 0.649599i | \(0.225063\pi\) | |||||||
\(824\) | 59640.0i | 0.0878382i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 190320. | 0.278949 | ||||||||
\(827\) | 144226. | + | 144226.i | 0.210879 | + | 0.210879i | 0.804641 | − | 0.593762i | \(-0.202358\pi\) |
−0.593762 | + | 0.804641i | \(0.702358\pi\) | |||||||
\(828\) | 20916.0 | − | 20916.0i | 0.0305083 | − | 0.0305083i | ||||
\(829\) | 685170.i | 0.996987i | 0.866894 | + | 0.498493i | \(0.166113\pi\) | ||||
−0.866894 | + | 0.498493i | \(0.833887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −77988.0 | −0.112934 | ||||||||
\(832\) | −185704. | − | 185704.i | −0.268272 | − | 0.268272i | ||||
\(833\) | 1049.00 | − | 1049.00i | 0.00151177 | − | 0.00151177i | ||||
\(834\) | 324720.i | 0.466850i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20160.0 | −0.0288455 | ||||||||
\(837\) | 308880. | + | 308880.i | 0.440899 | + | 0.440899i | ||||
\(838\) | −256980. | + | 256980.i | −0.365941 | + | 0.365941i | ||||
\(839\) | 445560.i | 0.632969i | 0.948598 | + | 0.316484i | \(0.102502\pi\) | ||||
−0.948598 | + | 0.316484i | \(0.897498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 476881. | 0.674245 | ||||||||
\(842\) | 186632. | + | 186632.i | 0.263246 | + | 0.263246i | ||||
\(843\) | −587568. | + | 587568.i | −0.826805 | + | 0.826805i | ||||
\(844\) | − | 257488.i | − | 0.361470i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 44532.0 | 0.0622202 | ||||||||
\(847\) | −379002. | − | 379002.i | −0.528293 | − | 0.528293i | ||||
\(848\) | −546284. | + | 546284.i | −0.759673 | + | 0.759673i | ||||
\(849\) | 718248.i | 0.996458i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 83332.0 | 0.115068 | ||||||||
\(852\) | 509712. | + | 509712.i | 0.702175 | + | 0.702175i | ||||
\(853\) | 319781. | − | 319781.i | 0.439496 | − | 0.439496i | −0.452347 | − | 0.891842i | \(-0.649413\pi\) |
0.891842 | + | 0.452347i | \(0.149413\pi\) | |||||||
\(854\) | 82784.0i | 0.113509i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 499560. | 0.681774 | ||||||||
\(857\) | −576449. | − | 576449.i | −0.784873 | − | 0.784873i | 0.195776 | − | 0.980649i | \(-0.437277\pi\) |
−0.980649 | + | 0.195776i | \(0.937277\pi\) | |||||||
\(858\) | 13344.0 | − | 13344.0i | 0.0181264 | − | 0.0181264i | ||||
\(859\) | 807540.i | 1.09440i | 0.837001 | + | 0.547202i | \(0.184307\pi\) | ||||
−0.837001 | + | 0.547202i | \(0.815693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −526656. | −0.710429 | ||||||||
\(862\) | −208028. | − | 208028.i | −0.279967 | − | 0.279967i | ||||
\(863\) | −507914. | + | 507914.i | −0.681975 | + | 0.681975i | −0.960445 | − | 0.278470i | \(-0.910173\pi\) |
0.278470 | + | 0.960445i | \(0.410173\pi\) | |||||||
\(864\) | − | 695520.i | − | 0.931713i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 302542. | 0.403413 | ||||||||
\(867\) | −501114. | − | 501114.i | −0.666651 | − | 0.666651i | ||||
\(868\) | 208208. | − | 208208.i | 0.276349 | − | 0.276349i | ||||
\(869\) | − | 72960.0i | − | 0.0966152i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 242972. | 0.320273 | ||||||||
\(872\) | −510300. | − | 510300.i | −0.671108 | − | 0.671108i | ||||
\(873\) | −58959.0 | + | 58959.0i | −0.0773609 | + | 0.0773609i | ||||
\(874\) | 59760.0i | 0.0782326i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −132888. | −0.173172 | ||||||||
\(877\) | 673901. | + | 673901.i | 0.876187 | + | 0.876187i | 0.993138 | − | 0.116951i | \(-0.0373119\pi\) |
−0.116951 | + | 0.993138i | \(0.537312\pi\) | |||||||
\(878\) | 158640. | − | 158640.i | 0.205790 | − | 0.205790i | ||||
\(879\) | 341988.i | 0.442622i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.33753e6 | −1.72326 | −0.861631 | − | 0.507536i | \(-0.830556\pi\) | ||||
−0.861631 | + | 0.507536i | \(0.830556\pi\) | |||||||
\(882\) | 9441.00 | + | 9441.00i | 0.0121361 | + | 0.0121361i | ||||
\(883\) | −131554. | + | 131554.i | −0.168726 | + | 0.168726i | −0.786419 | − | 0.617693i | \(-0.788067\pi\) |
0.617693 | + | 0.786419i | \(0.288067\pi\) | |||||||
\(884\) | 3892.00i | 0.00498045i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −505948. | −0.644523 | ||||||||
\(887\) | 327826. | + | 327826.i | 0.416674 | + | 0.416674i | 0.884056 | − | 0.467382i | \(-0.154803\pi\) |
−0.467382 | + | 0.884056i | \(0.654803\pi\) | |||||||
\(888\) | 90360.0 | − | 90360.0i | 0.114591 | − | 0.114591i | ||||
\(889\) | − | 653848.i | − | 0.827320i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −46008.0 | −0.0579533 | ||||||||
\(892\) | −12124.0 | − | 12124.0i | −0.0152376 | − | 0.0152376i | ||||
\(893\) | 445320. | − | 445320.i | 0.558431 | − | 0.558431i | ||||
\(894\) | − | 196200.i | − | 0.245484i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −605280. | −0.753946 | ||||||||
\(897\) | 276888. | + | 276888.i | 0.344127 | + | 0.344127i | ||||
\(898\) | −123750. | + | 123750.i | −0.153459 | + | 0.153459i | ||||
\(899\) | − | 274560.i | − | 0.339717i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6662.00 | 0.00820644 | ||||||||
\(902\) | 13504.0 | + | 13504.0i | 0.0165978 | + | 0.0165978i | ||||
\(903\) | −459888. | + | 459888.i | −0.563997 | + | 0.563997i | ||||
\(904\) | − | 309660.i | − | 0.378921i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12624.0 | 0.0153794 | ||||||||
\(907\) | −105274. | − | 105274.i | −0.127970 | − | 0.127970i | 0.640221 | − | 0.768191i | \(-0.278843\pi\) |
−0.768191 | + | 0.640221i | \(0.778843\pi\) | |||||||
\(908\) | 633164. | − | 633164.i | 0.767970 | − | 0.767970i | ||||
\(909\) | 144918.i | 0.175386i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.59209e6 | 1.91837 | 0.959183 | − | 0.282787i | \(-0.0912588\pi\) | ||||
0.959183 | + | 0.282787i | \(0.0912588\pi\) | |||||||
\(912\) | −177120. | − | 177120.i | −0.212950 | − | 0.212950i | ||||
\(913\) | 45232.0 | − | 45232.0i | 0.0542631 | − | 0.0542631i | ||||
\(914\) | 64402.0i | 0.0770916i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 547680. | 0.652734 | ||||||||
\(917\) | 527072. | + | 527072.i | 0.626803 | + | 0.626803i | ||||
\(918\) | −1080.00 | + | 1080.00i | −0.00128156 | + | 0.00128156i | ||||
\(919\) | 515880.i | 0.610826i | 0.952220 | + | 0.305413i | \(0.0987946\pi\) | ||||
−0.952220 | + | 0.305413i | \(0.901205\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.41511e6 | 1.66829 | ||||||||
\(922\) | 75142.0 | + | 75142.0i | 0.0883936 | + | 0.0883936i | ||||
\(923\) | 843452. | − | 843452.i | 0.990050 | − | 0.990050i | ||||
\(924\) | 34944.0i | 0.0409288i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −471428. | −0.549786 | ||||||||
\(927\) | −8946.00 | − | 8946.00i | −0.0104104 | − | 0.0104104i | ||||
\(928\) | −309120. | + | 309120.i | −0.358948 | + | 0.358948i | ||||
\(929\) | − | 1.60023e6i | − | 1.85418i | −0.374844 | − | 0.927088i | \(-0.622304\pi\) | ||
0.374844 | − | 0.927088i | \(-0.377696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 188820. | 0.217846 | ||||||||
\(932\) | −463694. | − | 463694.i | −0.533826 | − | 0.533826i | ||||
\(933\) | 23352.0 | − | 23352.0i | 0.0268263 | − | 0.0268263i | ||||
\(934\) | − | 57148.0i | − | 0.0655100i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −75060.0 | −0.0856755 | ||||||||
\(937\) | 908801. | + | 908801.i | 1.03512 | + | 1.03512i | 0.999361 | + | 0.0357569i | \(0.0113842\pi\) |
0.0357569 | + | 0.999361i | \(0.488616\pi\) | |||||||
\(938\) | 45448.0 | − | 45448.0i | 0.0516546 | − | 0.0516546i | ||||
\(939\) | − | 599532.i | − | 0.679957i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 455962. | 0.514931 | 0.257466 | − | 0.966287i | \(-0.417113\pi\) | ||||
0.257466 | + | 0.966287i | \(0.417113\pi\) | |||||||
\(942\) | −77988.0 | − | 77988.0i | −0.0878873 | − | 0.0878873i | ||||
\(943\) | −280208. | + | 280208.i | −0.315106 | + | 0.315106i | ||||
\(944\) | 600240.i | 0.673567i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23584.0 | 0.0263533 | ||||||||
\(947\) | −463274. | − | 463274.i | −0.516580 | − | 0.516580i | 0.399955 | − | 0.916535i | \(-0.369026\pi\) |
−0.916535 | + | 0.399955i | \(0.869026\pi\) | |||||||
\(948\) | 766080. | − | 766080.i | 0.852427 | − | 0.852427i | ||||
\(949\) | 219898.i | 0.244168i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −205188. | −0.226877 | ||||||||
\(952\) | 1560.00 | + | 1560.00i | 0.00172128 | + | 0.00172128i | ||||
\(953\) | 1.03428e6 | − | 1.03428e6i | 1.13881 | − | 1.13881i | 0.150151 | − | 0.988663i | \(-0.452024\pi\) |
0.988663 | − | 0.150151i | \(-0.0479759\pi\) | |||||||
\(954\) | 59958.0i | 0.0658795i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.23816e6 | −1.35476 | ||||||||
\(957\) | 23040.0 | + | 23040.0i | 0.0251570 | + | 0.0251570i | ||||
\(958\) | −26520.0 | + | 26520.0i | −0.0288963 | + | 0.0288963i | ||||
\(959\) | 538252.i | 0.585259i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −596337. | −0.645721 | ||||||||
\(962\) | −69778.0 | − | 69778.0i | −0.0753995 | − | 0.0753995i | ||||
\(963\) | −74934.0 | + | 74934.0i | −0.0808028 | + | 0.0808028i | ||||
\(964\) | − | 284368.i | − | 0.306004i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 103584. | 0.111004 | ||||||||
\(967\) | 1.10253e6 | + | 1.10253e6i | 1.17906 | + | 1.17906i | 0.979984 | + | 0.199076i | \(0.0637940\pi\) |
0.199076 | + | 0.979984i | \(0.436206\pi\) | |||||||
\(968\) | −437310. | + | 437310.i | −0.466701 | + | 0.466701i | ||||
\(969\) | 2160.00i | 0.00230042i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −264368. | −0.280395 | −0.140198 | − | 0.990124i | \(-0.544774\pi\) | ||||
−0.140198 | + | 0.990124i | \(0.544774\pi\) | |||||||
\(972\) | 129276. | + | 129276.i | 0.136831 | + | 0.136831i | ||||
\(973\) | −703560. | + | 703560.i | −0.743148 | + | 0.743148i | ||||
\(974\) | − | 82748.0i | − | 0.0872247i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −261088. | −0.274086 | ||||||||
\(977\) | −866249. | − | 866249.i | −0.907515 | − | 0.907515i | 0.0885566 | − | 0.996071i | \(-0.471775\pi\) |
−0.996071 | + | 0.0885566i | \(0.971775\pi\) | |||||||
\(978\) | 231432. | − | 231432.i | 0.241961 | − | 0.241961i | ||||
\(979\) | − | 17280.0i | − | 0.0180293i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 153090. | 0.159078 | ||||||||
\(982\) | −149288. | − | 149288.i | −0.154811 | − | 0.154811i | ||||
\(983\) | −1.08205e6 | + | 1.08205e6i | −1.11980 | + | 1.11980i | −0.128034 | + | 0.991770i | \(0.540867\pi\) |
−0.991770 | + | 0.128034i | \(0.959133\pi\) | |||||||
\(984\) | 607680.i | 0.627603i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 960.000 | 0.000987455 | ||||||||
\(987\) | −771888. | − | 771888.i | −0.792355 | − | 0.792355i | ||||
\(988\) | −350280. | + | 350280.i | −0.358840 | + | 0.358840i | ||||
\(989\) | 489368.i | 0.500314i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54988.0 | −0.0559913 | −0.0279957 | − | 0.999608i | \(-0.508912\pi\) | ||||
−0.0279957 | + | 0.999608i | \(0.508912\pi\) | |||||||
\(992\) | −368368. | − | 368368.i | −0.374333 | − | 0.374333i | ||||
\(993\) | −858768. | + | 858768.i | −0.870918 | + | 0.870918i | ||||
\(994\) | − | 315536.i | − | 0.319357i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 949872. | 0.957517 | ||||||||
\(997\) | −73099.0 | − | 73099.0i | −0.0735396 | − | 0.0735396i | 0.669380 | − | 0.742920i | \(-0.266560\pi\) |
−0.742920 | + | 0.669380i | \(0.766560\pi\) | |||||||
\(998\) | −284100. | + | 284100.i | −0.285240 | + | 0.285240i | ||||
\(999\) | 271080.i | 0.271623i |
(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 | 25.5.c.a.7.1 | 2 | ||
3.2 | odd | 2 | 225.5.g.b.82.1 | 2 | |||
4.3 | odd | 2 | 400.5.p.a.257.1 | 2 | |||
5.2 | odd | 4 | 5.5.c.a.3.1 | yes | 2 | ||
5.3 | odd | 4 | inner | 25.5.c.a.18.1 | 2 | ||
5.4 | even | 2 | 5.5.c.a.2.1 | ✓ | 2 | ||
15.2 | even | 4 | 45.5.g.b.28.1 | 2 | |||
15.8 | even | 4 | 225.5.g.b.118.1 | 2 | |||
15.14 | odd | 2 | 45.5.g.b.37.1 | 2 | |||
20.3 | even | 4 | 400.5.p.a.193.1 | 2 | |||
20.7 | even | 4 | 80.5.p.d.33.1 | 2 | |||
20.19 | odd | 2 | 80.5.p.d.17.1 | 2 | |||
40.19 | odd | 2 | 320.5.p.c.257.1 | 2 | |||
40.27 | even | 4 | 320.5.p.c.193.1 | 2 | |||
40.29 | even | 2 | 320.5.p.h.257.1 | 2 | |||
40.37 | odd | 4 | 320.5.p.h.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.5.c.a.2.1 | ✓ | 2 | 5.4 | even | 2 | ||
5.5.c.a.3.1 | yes | 2 | 5.2 | odd | 4 | ||
25.5.c.a.7.1 | 2 | 1.1 | even | 1 | trivial | ||
25.5.c.a.18.1 | 2 | 5.3 | odd | 4 | inner | ||
45.5.g.b.28.1 | 2 | 15.2 | even | 4 | |||
45.5.g.b.37.1 | 2 | 15.14 | odd | 2 | |||
80.5.p.d.17.1 | 2 | 20.19 | odd | 2 | |||
80.5.p.d.33.1 | 2 | 20.7 | even | 4 | |||
225.5.g.b.82.1 | 2 | 3.2 | odd | 2 | |||
225.5.g.b.118.1 | 2 | 15.8 | even | 4 | |||
320.5.p.c.193.1 | 2 | 40.27 | even | 4 | |||
320.5.p.c.257.1 | 2 | 40.19 | odd | 2 | |||
320.5.p.h.193.1 | 2 | 40.37 | odd | 4 | |||
320.5.p.h.257.1 | 2 | 40.29 | even | 2 | |||
400.5.p.a.193.1 | 2 | 20.3 | even | 4 | |||
400.5.p.a.257.1 | 2 | 4.3 | odd | 2 |