Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [480,4,Mod(1,480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("480.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.a (trivial) |
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: | yes |
Analytic conductor: | \(28.3209168028\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 480.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.0000 | −0.647939 | −0.323970 | − | 0.946068i | \(-0.605018\pi\) | ||||
−0.323970 | + | 0.946068i | \(0.605018\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −24.0000 | −0.657843 | −0.328921 | − | 0.944357i | \(-0.606685\pi\) | ||||
−0.328921 | + | 0.944357i | \(0.606685\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.0000 | 0.810716 | 0.405358 | − | 0.914158i | \(-0.367147\pi\) | ||||
0.405358 | + | 0.914158i | \(0.367147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.00000 | −0.0856008 | −0.0428004 | − | 0.999084i | \(-0.513628\pi\) | ||||
−0.0428004 | + | 0.999084i | \(0.513628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.000 | 1.25575 | 0.627875 | − | 0.778314i | \(-0.283925\pi\) | ||||
0.627875 | + | 0.778314i | \(0.283925\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −36.0000 | −0.374088 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 100.000 | 0.906584 | 0.453292 | − | 0.891362i | \(-0.350249\pi\) | ||||
0.453292 | + | 0.891362i | \(0.350249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 230.000 | 1.47276 | 0.736378 | − | 0.676570i | \(-0.236535\pi\) | ||||
0.736378 | + | 0.676570i | \(0.236535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −56.0000 | −0.324448 | −0.162224 | − | 0.986754i | \(-0.551867\pi\) | ||||
−0.162224 | + | 0.986754i | \(0.551867\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −72.0000 | −0.379806 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −60.0000 | −0.289767 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 190.000 | 0.844211 | 0.422106 | − | 0.906547i | \(-0.361291\pi\) | ||||
0.422106 | + | 0.906547i | \(0.361291\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 114.000 | 0.468067 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 202.000 | 0.769441 | 0.384721 | − | 0.923033i | \(-0.374298\pi\) | ||||
0.384721 | + | 0.923033i | \(0.374298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −148.000 | −0.524879 | −0.262439 | − | 0.964948i | \(-0.584527\pi\) | ||||
−0.262439 | + | 0.964948i | \(0.584527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 124.000 | 0.384835 | 0.192418 | − | 0.981313i | \(-0.438367\pi\) | ||||
0.192418 | + | 0.981313i | \(0.438367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −199.000 | −0.580175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.0000 | −0.0494217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 206.000 | 0.533892 | 0.266946 | − | 0.963711i | \(-0.413985\pi\) | ||||
0.266946 | + | 0.963711i | \(0.413985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −120.000 | −0.294196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 312.000 | 0.725007 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −128.000 | −0.282444 | −0.141222 | − | 0.989978i | \(-0.545103\pi\) | ||||
−0.141222 | + | 0.989978i | \(0.545103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 190.000 | 0.398803 | 0.199402 | − | 0.979918i | \(-0.436100\pi\) | ||||
0.199402 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −108.000 | −0.215980 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 190.000 | 0.362563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −204.000 | −0.371979 | −0.185989 | − | 0.982552i | \(-0.559549\pi\) | ||||
−0.185989 | + | 0.982552i | \(0.559549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 300.000 | 0.523417 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −440.000 | −0.735470 | −0.367735 | − | 0.929931i | \(-0.619867\pi\) | ||||
−0.367735 | + | 0.929931i | \(0.619867\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1210.00 | 1.94000 | 0.969999 | − | 0.243111i | \(-0.0781678\pi\) | ||||
0.969999 | + | 0.243111i | \(0.0781678\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 288.000 | 0.426242 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 816.000 | 1.16212 | 0.581058 | − | 0.813862i | \(-0.302639\pi\) | ||||
0.581058 | + | 0.813862i | \(0.302639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1412.00 | −1.86731 | −0.933657 | − | 0.358167i | \(-0.883402\pi\) | ||||
−0.933657 | + | 0.358167i | \(0.883402\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30.0000 | −0.0382818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 690.000 | 0.850296 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −214.000 | −0.254876 | −0.127438 | − | 0.991847i | \(-0.540675\pi\) | ||||
−0.127438 | + | 0.991847i | \(0.540675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −456.000 | −0.525294 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −168.000 | −0.187320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 520.000 | 0.561588 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1202.00 | 1.25819 | 0.629096 | − | 0.777328i | \(-0.283425\pi\) | ||||
0.629096 | + | 0.777328i | \(0.283425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −216.000 | −0.219281 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1342.00 | 1.32212 | 0.661059 | − | 0.750334i | \(-0.270107\pi\) | ||||
0.661059 | + | 0.750334i | \(0.270107\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 908.000 | 0.868620 | 0.434310 | − | 0.900763i | \(-0.356992\pi\) | ||||
0.434310 | + | 0.900763i | \(0.356992\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −180.000 | −0.167297 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −876.000 | −0.791459 | −0.395730 | − | 0.918367i | \(-0.629508\pi\) | ||||
−0.395730 | + | 0.918367i | \(0.629508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 302.000 | 0.265379 | 0.132690 | − | 0.991158i | \(-0.457639\pi\) | ||||
0.132690 | + | 0.991158i | \(0.457639\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 570.000 | 0.487405 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −998.000 | −0.830831 | −0.415416 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415416 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 500.000 | 0.405437 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 342.000 | 0.270239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 72.0000 | 0.0554641 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −755.000 | −0.567243 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 606.000 | 0.444237 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 836.000 | 0.584118 | 0.292059 | − | 0.956400i | \(-0.405660\pi\) | ||||
0.292059 | + | 0.956400i | \(0.405660\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −444.000 | −0.303039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1480.00 | −0.987085 | −0.493543 | − | 0.869722i | \(-0.664298\pi\) | ||||
−0.493543 | + | 0.869722i | \(0.664298\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1248.00 | −0.813649 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1346.00 | 0.839391 | 0.419695 | − | 0.907665i | \(-0.362137\pi\) | ||||
0.419695 | + | 0.907665i | \(0.362137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 824.000 | 0.502811 | 0.251406 | − | 0.967882i | \(-0.419107\pi\) | ||||
0.251406 | + | 0.967882i | \(0.419107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 372.000 | 0.222185 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −912.000 | −0.533324 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1150.00 | 0.658637 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −597.000 | −0.334964 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2450.00 | −1.34706 | −0.673530 | − | 0.739160i | \(-0.735223\pi\) | ||||
−0.673530 | + | 0.739160i | \(0.735223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2696.00 | 1.45296 | 0.726481 | − | 0.687186i | \(-0.241154\pi\) | ||||
0.726481 | + | 0.687186i | \(0.241154\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −54.0000 | −0.0285336 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −280.000 | −0.145098 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −554.000 | −0.281618 | −0.140809 | − | 0.990037i | \(-0.544970\pi\) | ||||
−0.140809 | + | 0.990037i | \(0.544970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 618.000 | 0.308243 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1200.00 | −0.587411 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1364.00 | −0.655440 | −0.327720 | − | 0.944775i | \(-0.606280\pi\) | ||||
−0.327720 | + | 0.944775i | \(0.606280\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −360.000 | −0.169854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2004.00 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.000 | −0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 936.000 | 0.418583 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1546.00 | −0.679423 | −0.339712 | − | 0.940530i | \(-0.610329\pi\) | ||||
−0.339712 | + | 0.940530i | \(0.610329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −300.000 | −0.129588 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −384.000 | −0.163069 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1072.00 | −0.447626 | −0.223813 | − | 0.974632i | \(-0.571850\pi\) | ||||
−0.223813 | + | 0.974632i | \(0.571850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3754.00 | −1.54162 | −0.770808 | − | 0.637067i | \(-0.780147\pi\) | ||||
−0.770808 | + | 0.637067i | \(0.780147\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 570.000 | 0.230249 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 950.000 | 0.377543 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 144.000 | 0.0563119 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −324.000 | −0.124696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1224.00 | 0.463694 | 0.231847 | − | 0.972752i | \(-0.425523\pi\) | ||||
0.231847 | + | 0.972752i | \(0.425523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1694.00 | −0.631797 | −0.315898 | − | 0.948793i | \(-0.602306\pi\) | ||||
−0.315898 | + | 0.948793i | \(0.602306\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 570.000 | 0.209326 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3134.00 | 1.13344 | 0.566721 | − | 0.823909i | \(-0.308212\pi\) | ||||
0.566721 | + | 0.823909i | \(0.308212\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2560.00 | 0.911928 | 0.455964 | − | 0.889998i | \(-0.349295\pi\) | ||||
0.455964 | + | 0.889998i | \(0.349295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −612.000 | −0.214762 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2760.00 | −0.954256 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1010.00 | 0.344105 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 900.000 | 0.302195 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2496.00 | −0.826086 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1856.00 | −0.605556 | −0.302778 | − | 0.953061i | \(-0.597914\pi\) | ||||
−0.302778 | + | 0.953061i | \(0.597914\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1320.00 | −0.424624 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −740.000 | −0.234733 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 672.000 | 0.210223 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3630.00 | 1.12006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −228.000 | −0.0693979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1596.00 | 0.479265 | 0.239632 | − | 0.970864i | \(-0.422973\pi\) | ||||
0.239632 | + | 0.970864i | \(0.422973\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3996.00 | −1.16839 | −0.584193 | − | 0.811614i | \(-0.698589\pi\) | ||||
−0.584193 | + | 0.811614i | \(0.698589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6090.00 | −1.75737 | −0.878687 | − | 0.477399i | \(-0.841580\pi\) | ||||
−0.878687 | + | 0.477399i | \(0.841580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 864.000 | 0.246091 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −894.000 | −0.251364 | −0.125682 | − | 0.992071i | \(-0.540112\pi\) | ||||
−0.125682 | + | 0.992071i | \(0.540112\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 620.000 | 0.172104 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2448.00 | 0.670948 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6336.00 | −1.71482 | −0.857410 | − | 0.514635i | \(-0.827928\pi\) | ||||
−0.857410 | + | 0.514635i | \(0.827928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 338.000 | 0.0903423 | 0.0451711 | − | 0.998979i | \(-0.485617\pi\) | ||||
0.0451711 | + | 0.998979i | \(0.485617\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −995.000 | −0.259462 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3952.00 | 1.01806 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4236.00 | −1.07809 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4872.00 | −1.22517 | −0.612585 | − | 0.790404i | \(-0.709870\pi\) | ||||
−0.612585 | + | 0.790404i | \(0.709870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2400.00 | −0.596390 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −90.0000 | −0.0221020 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1878.00 | −0.455823 | −0.227911 | − | 0.973682i | \(-0.573190\pi\) | ||||
−0.227911 | + | 0.973682i | \(0.573190\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2280.00 | −0.546997 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2070.00 | 0.490919 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2244.00 | 0.526125 | 0.263063 | − | 0.964779i | \(-0.415267\pi\) | ||||
0.263063 | + | 0.964779i | \(0.415267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1030.00 | 0.238764 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −642.000 | −0.147153 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4314.00 | −0.977804 | −0.488902 | − | 0.872339i | \(-0.662602\pi\) | ||||
−0.488902 | + | 0.872339i | \(0.662602\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6392.00 | −1.43279 | −0.716395 | − | 0.697694i | \(-0.754209\pi\) | ||||
−0.716395 | + | 0.697694i | \(0.754209\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1368.00 | −0.303279 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −600.000 | −0.131569 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4398.00 | 0.953972 | 0.476986 | − | 0.878911i | \(-0.341729\pi\) | ||||
0.476986 | + | 0.878911i | \(0.341729\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −504.000 | −0.108149 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7622.00 | −1.61812 | −0.809058 | − | 0.587729i | \(-0.800022\pi\) | ||||
−0.809058 | + | 0.587729i | \(0.800022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1020.00 | 0.214250 | 0.107125 | − | 0.994246i | \(-0.465836\pi\) | ||||
0.107125 | + | 0.994246i | \(0.465836\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1560.00 | 0.324233 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2424.00 | −0.498551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4877.00 | −0.992673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3606.00 | 0.726417 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3746.00 | −0.746907 | −0.373453 | − | 0.927649i | \(-0.621826\pi\) | ||||
−0.373453 | + | 0.927649i | \(0.621826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −640.000 | −0.126313 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −648.000 | −0.126602 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3800.00 | 0.734982 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1776.00 | 0.340089 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4026.00 | 0.763326 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 950.000 | 0.178350 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9700.00 | 1.80328 | 0.901642 | − | 0.432483i | \(-0.142362\pi\) | ||||
0.901642 | + | 0.432483i | \(0.142362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2724.00 | 0.501498 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4152.00 | 0.757036 | 0.378518 | − | 0.925594i | \(-0.376434\pi\) | ||||
0.378518 | + | 0.925594i | \(0.376434\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6362.00 | 1.14889 | 0.574443 | − | 0.818544i | \(-0.305219\pi\) | ||||
0.574443 | + | 0.818544i | \(0.305219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −540.000 | −0.0965891 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10886.0 | 1.92877 | 0.964383 | − | 0.264511i | \(-0.0852104\pi\) | ||||
0.964383 | + | 0.264511i | \(0.0852104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5520.00 | −0.968842 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2628.00 | −0.456949 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −624.000 | −0.107493 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 950.000 | 0.162143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 906.000 | 0.153217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1488.00 | −0.249350 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4128.00 | 0.685485 | 0.342742 | − | 0.939429i | \(-0.388644\pi\) | ||||
0.342742 | + | 0.939429i | \(0.388644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1710.00 | 0.281404 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1020.00 | −0.166354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12002.0 | 1.94003 | 0.970016 | − | 0.243042i | \(-0.0781453\pi\) | ||||
0.970016 | + | 0.243042i | \(0.0781453\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2994.00 | −0.479681 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1344.00 | 0.213436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6504.00 | 1.02386 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1500.00 | 0.234079 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6276.00 | 0.970932 | 0.485466 | − | 0.874256i | \(-0.338650\pi\) | ||||
0.485466 | + | 0.874256i | \(0.338650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9362.00 | −1.43592 | −0.717960 | − | 0.696084i | \(-0.754924\pi\) | ||||
−0.717960 | + | 0.696084i | \(0.754924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1026.00 | 0.156022 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −838.000 | −0.126352 | −0.0631760 | − | 0.998002i | \(-0.520123\pi\) | ||||
−0.0631760 | + | 0.998002i | \(0.520123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2200.00 | −0.328912 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 216.000 | 0.0320222 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6896.00 | −1.01381 | −0.506904 | − | 0.862003i | \(-0.669210\pi\) | ||||
−0.506904 | + | 0.862003i | \(0.669210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3957.00 | 0.576906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2265.00 | −0.327498 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6050.00 | 0.867593 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1132.00 | −0.161008 | −0.0805040 | − | 0.996754i | \(-0.525653\pi\) | ||||
−0.0805040 | + | 0.996754i | \(0.525653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1818.00 | 0.256480 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2472.00 | −0.345930 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12578.0 | −1.74602 | −0.873008 | − | 0.487705i | \(-0.837834\pi\) | ||||
−0.873008 | + | 0.487705i | \(0.837834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8740.00 | 1.19399 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11752.0 | 1.59277 | 0.796385 | − | 0.604790i | \(-0.206743\pi\) | ||||
0.796385 | + | 0.604790i | \(0.206743\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2508.00 | 0.337241 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7372.00 | −0.983529 | −0.491764 | − | 0.870728i | \(-0.663648\pi\) | ||||
−0.491764 | + | 0.870728i | \(0.663648\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1440.00 | 0.190621 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1332.00 | −0.174960 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6654.00 | 0.867278 | 0.433639 | − | 0.901087i | \(-0.357229\pi\) | ||||
0.433639 | + | 0.901087i | \(0.357229\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −600.000 | −0.0776044 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4440.00 | −0.569894 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4080.00 | 0.519714 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4278.00 | 0.540823 | 0.270411 | − | 0.962745i | \(-0.412840\pi\) | ||||
0.270411 | + | 0.962745i | \(0.412840\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3744.00 | −0.469761 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9074.00 | 1.13001 | 0.565005 | − | 0.825088i | \(-0.308874\pi\) | ||||
0.565005 | + | 0.825088i | \(0.308874\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2128.00 | −0.263035 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4560.00 | −0.555358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6682.00 | 0.807833 | 0.403916 | − | 0.914796i | \(-0.367649\pi\) | ||||
0.403916 | + | 0.914796i | \(0.367649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4038.00 | 0.484623 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1536.00 | 0.183006 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7060.00 | −0.835089 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2472.00 | 0.290298 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4832.00 | 0.563386 | 0.281693 | − | 0.959505i | \(-0.409104\pi\) | ||||
0.281693 | + | 0.959505i | \(0.409104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3974.00 | 0.460050 | 0.230025 | − | 0.973185i | \(-0.426119\pi\) | ||||
0.230025 | + | 0.973185i | \(0.426119\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1116.00 | 0.128278 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −150.000 | −0.0171202 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2280.00 | −0.258400 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2736.00 | −0.307915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1112.00 | 0.124276 | 0.0621382 | − | 0.998068i | \(-0.480208\pi\) | ||||
0.0621382 | + | 0.998068i | \(0.480208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1106.00 | 0.122751 | 0.0613753 | − | 0.998115i | \(-0.480451\pi\) | ||||
0.0613753 | + | 0.998115i | \(0.480451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3450.00 | 0.380264 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10400.0 | 1.13844 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9280.00 | −1.00891 | −0.504454 | − | 0.863439i | \(-0.668306\pi\) | ||||
−0.504454 | + | 0.863439i | \(0.668306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1791.00 | −0.193392 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7004.00 | 0.751174 | 0.375587 | − | 0.926787i | \(-0.377441\pi\) | ||||
0.375587 | + | 0.926787i | \(0.377441\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1070.00 | −0.113984 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7350.00 | −0.777725 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11502.0 | −1.20894 | −0.604469 | − | 0.796629i | \(-0.706615\pi\) | ||||
−0.604469 | + | 0.796629i | \(0.706615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4848.00 | −0.506172 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8088.00 | 0.838868 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2280.00 | −0.234919 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11578.0 | 1.18511 | 0.592556 | − | 0.805529i | \(-0.298119\pi\) | ||||
0.592556 | + | 0.805529i | \(0.298119\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −162.000 | −0.0164739 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6362.00 | −0.642750 | −0.321375 | − | 0.946952i | \(-0.604145\pi\) | ||||
−0.321375 | + | 0.946952i | \(0.604145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2892.00 | 0.290286 | 0.145143 | − | 0.989411i | \(-0.453636\pi\) | ||||
0.145143 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −840.000 | −0.0837722 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11036.0 | −1.09354 | −0.546772 | − | 0.837281i | \(-0.684144\pi\) | ||||
−0.546772 | + | 0.837281i | \(0.684144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2448.00 | 0.241019 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1662.00 | −0.162592 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3552.00 | 0.345288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2600.00 | 0.251150 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1854.00 | 0.177964 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13664.0 | −1.30339 | −0.651695 | − | 0.758481i | \(-0.725942\pi\) | ||||
−0.651695 | + | 0.758481i | \(0.725942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7220.00 | 0.684415 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3600.00 | −0.339142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6010.00 | 0.562680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4820.00 | 0.448491 | 0.224245 | − | 0.974533i | \(-0.428008\pi\) | ||||
0.224245 | + | 0.974533i | \(0.428008\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4092.00 | −0.378418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17464.0 | 1.60517 | 0.802586 | − | 0.596537i | \(-0.203457\pi\) | ||||
0.802586 | + | 0.596537i | \(0.203457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1380.00 | −0.126069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1080.00 | −0.0980654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5280.00 | 0.476540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13960.0 | 1.25238 | 0.626188 | − | 0.779672i | \(-0.284614\pi\) | ||||
0.626188 | + | 0.779672i | \(0.284614\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6012.00 | −0.536120 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20388.0 | 1.80727 | 0.903634 | − | 0.428305i | \(-0.140889\pi\) | ||||
0.903634 | + | 0.428305i | \(0.140889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6710.00 | 0.591269 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2259.00 | −0.197881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12954.0 | −1.12805 | −0.564024 | − | 0.825759i | \(-0.690747\pi\) | ||||
−0.564024 | + | 0.825759i | \(0.690747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14520.0 | −1.25700 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2808.00 | 0.241669 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4540.00 | 0.388459 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2976.00 | −0.253161 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4638.00 | −0.392265 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3542.00 | −0.297846 | −0.148923 | − | 0.988849i | \(-0.547581\pi\) | ||||
−0.148923 | + | 0.988849i | \(0.547581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1532.00 | 0.128087 | 0.0640437 | − | 0.997947i | \(-0.479600\pi\) | ||||
0.0640437 | + | 0.997947i | \(0.479600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −900.000 | −0.0748176 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 336.000 | 0.0277730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2167.00 | −0.178105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1152.00 | −0.0941479 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7676.00 | 0.623798 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4380.00 | −0.353951 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3216.00 | −0.258437 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4776.00 | 0.381664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11826.0 | −0.939814 | −0.469907 | − | 0.882716i | \(-0.655713\pi\) | ||||
−0.469907 | + | 0.882716i | \(0.655713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11262.0 | −0.890053 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1510.00 | 0.118681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11260.0 | −0.880151 | −0.440076 | − | 0.897961i | \(-0.645048\pi\) | ||||
−0.440076 | + | 0.897961i | \(0.645048\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1710.00 | 0.132934 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23920.0 | 1.84941 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9792.00 | −0.752980 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2850.00 | 0.217974 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4374.00 | 0.332733 | 0.166367 | − | 0.986064i | \(-0.446797\pi\) | ||||
0.166367 | + | 0.986064i | \(0.446797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5624.00 | −0.425527 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 432.000 | 0.0325117 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11604.0 | −0.868651 | −0.434325 | − | 0.900756i | \(-0.643013\pi\) | ||||
−0.434325 | + | 0.900756i | \(0.643013\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4990.00 | −0.371559 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −972.000 | −0.0719932 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7990.00 | −0.588679 | −0.294339 | − | 0.955701i | \(-0.595100\pi\) | ||||
−0.294339 | + | 0.955701i | \(0.595100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26080.0 | −1.91141 | −0.955704 | − | 0.294329i | \(-0.904904\pi\) | ||||
−0.955704 | + | 0.294329i | \(0.904904\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3672.00 | 0.267714 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2500.00 | 0.181317 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13922.0 | 1.00447 | 0.502236 | − | 0.864731i | \(-0.332511\pi\) | ||||
0.502236 | + | 0.864731i | \(0.332511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5082.00 | −0.364768 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16944.0 | 1.20991 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4944.00 | −0.351217 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1710.00 | 0.120854 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26340.0 | 1.85208 | 0.926038 | − | 0.377431i | \(-0.123193\pi\) | ||||
0.926038 | + | 0.377431i | \(0.123193\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5824.00 | −0.407426 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9402.00 | 0.654394 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9478.00 | −0.656349 | −0.328174 | − | 0.944617i | \(-0.606433\pi\) | ||||
−0.328174 | + | 0.944617i | \(0.606433\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 360.000 | 0.0248043 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7680.00 | 0.526502 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6528.00 | 0.445287 | 0.222643 | − | 0.974900i | \(-0.428531\pi\) | ||||
0.222643 | + | 0.974900i | \(0.428531\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2090.00 | 0.141852 | 0.0709259 | − | 0.997482i | \(-0.477405\pi\) | ||||
0.0709259 | + | 0.997482i | \(0.477405\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1836.00 | −0.123993 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3775.00 | −0.253679 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8788.00 | 0.587634 | 0.293817 | − | 0.955862i | \(-0.405074\pi\) | ||||
0.293817 | + | 0.955862i | \(0.405074\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8280.00 | −0.550940 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4712.00 | 0.311992 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2626.00 | −0.173023 | −0.0865115 | − | 0.996251i | \(-0.527572\pi\) | ||||
−0.0865115 | + | 0.996251i | \(0.527572\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3030.00 | 0.198669 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29214.0 | −1.90618 | −0.953089 | − | 0.302691i | \(-0.902115\pi\) | ||||
−0.953089 | + | 0.302691i | \(0.902115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22984.0 | 1.49242 | 0.746208 | − | 0.665713i | \(-0.231873\pi\) | ||||
0.746208 | + | 0.665713i | \(0.231873\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2700.00 | 0.174472 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2568.00 | 0.165144 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7488.00 | −0.476941 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1140.00 | −0.0722651 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4472.00 | 0.282136 | 0.141068 | − | 0.990000i | \(-0.454946\pi\) | ||||
0.141068 | + | 0.990000i | \(0.454946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5568.00 | −0.349618 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4180.00 | 0.261226 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7562.00 | −0.470357 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3960.00 | −0.245157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8798.00 | −0.542122 | −0.271061 | − | 0.962562i | \(-0.587374\pi\) | ||||
−0.271061 | + | 0.962562i | \(0.587374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29428.0 | −1.80486 | −0.902432 | − | 0.430833i | \(-0.858220\pi\) | ||||
−0.902432 | + | 0.430833i | \(0.858220\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2220.00 | −0.135523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4860.00 | 0.295311 | 0.147656 | − | 0.989039i | \(-0.452827\pi\) | ||||
0.147656 | + | 0.989039i | \(0.452827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3072.00 | 0.185804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2016.00 | 0.121372 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6570.00 | −0.393727 | −0.196864 | − | 0.980431i | \(-0.563076\pi\) | ||||
−0.196864 | + | 0.980431i | \(0.563076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7400.00 | −0.441438 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10890.0 | 0.646666 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26496.0 | 1.56622 | 0.783109 | − | 0.621885i | \(-0.213633\pi\) | ||||
0.783109 | + | 0.621885i | \(0.213633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19642.0 | −1.15580 | −0.577901 | − | 0.816107i | \(-0.696128\pi\) | ||||
−0.577901 | + | 0.816107i | \(0.696128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −684.000 | −0.0400669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6240.00 | −0.363875 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23000.0 | 1.33518 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4788.00 | 0.276704 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4560.00 | −0.262350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19582.0 | −1.12159 | −0.560795 | − | 0.827954i | \(-0.689505\pi\) | ||||
−0.560795 | + | 0.827954i | \(0.689505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22914.0 | −1.30082 | −0.650411 | − | 0.759582i | \(-0.725403\pi\) | ||||
−0.650411 | + | 0.759582i | \(0.725403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14424.0 | −0.815232 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11988.0 | −0.674569 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13764.0 | −0.771105 | −0.385553 | − | 0.922686i | \(-0.625989\pi\) | ||||
−0.385553 | + | 0.922686i | \(0.625989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6730.00 | 0.375387 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18270.0 | −1.01462 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7828.00 | 0.432835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34688.0 | −1.90969 | −0.954843 | − | 0.297109i | \(-0.903977\pi\) | ||||
−0.954843 | + | 0.297109i | \(0.903977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2592.00 | 0.142081 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4120.00 | 0.224864 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1212.00 | −0.0658648 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2682.00 | −0.145125 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17226.0 | −0.928127 | −0.464064 | − | 0.885802i | \(-0.653609\pi\) | ||||
−0.464064 | + | 0.885802i | \(0.653609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19760.0 | 1.06012 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1860.00 | 0.0993640 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16104.0 | −0.856652 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12970.0 | −0.687022 | −0.343511 | − | 0.939149i | \(-0.611616\pi\) | ||||
−0.343511 | + | 0.939149i | \(0.611616\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7344.00 | 0.387372 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5600.00 | −0.294140 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4560.00 | −0.238510 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19008.0 | −0.990051 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10832.0 | 0.561843 | 0.280922 | − | 0.959731i | \(-0.409360\pi\) | ||||
0.280922 | + | 0.959731i | \(0.409360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10896.0 | −0.562813 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1014.00 | 0.0521592 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5750.00 | 0.294551 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35588.0 | 1.81552 | 0.907762 | − | 0.419486i | \(-0.137790\pi\) | ||||
0.907762 | + | 0.419486i | \(0.137790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 888.000 | 0.0449300 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19238.0 | 0.969402 | 0.484701 | − | 0.874680i | \(-0.338928\pi\) | ||||
0.484701 | + | 0.874680i | \(0.338928\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2985.00 | −0.149801 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4896.00 | 0.244703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4072.00 | −0.202694 | −0.101347 | − | 0.994851i | \(-0.532315\pi\) | ||||
−0.101347 | + | 0.994851i | \(0.532315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11856.0 | 0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31268.0 | 1.54389 | 0.771946 | − | 0.635688i | \(-0.219284\pi\) | ||||
0.771946 | + | 0.635688i | \(0.219284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12250.0 | −0.602423 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12708.0 | −0.622438 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10512.0 | 0.512817 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28216.0 | −1.37099 | −0.685497 | − | 0.728075i | \(-0.740415\pi\) | ||||
−0.685497 | + | 0.728075i | \(0.740415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14616.0 | −0.707353 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13480.0 | 0.649785 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33874.0 | −1.62638 | −0.813191 | − | 0.581997i | \(-0.802272\pi\) | ||||
−0.813191 | + | 0.581997i | \(0.802272\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7200.00 | −0.344326 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5466.00 | 0.260371 | 0.130186 | − | 0.991490i | \(-0.458443\pi\) | ||||
0.130186 | + | 0.991490i | \(0.458443\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3624.00 | −0.171950 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −270.000 | −0.0127606 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4864.00 | −0.228982 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8878.00 | −0.416318 | −0.208159 | − | 0.978095i | \(-0.566747\pi\) | ||||
−0.208159 | + | 0.978095i | \(0.566747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5634.00 | −0.263169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9538.00 | −0.443801 | −0.221900 | − | 0.975069i | \(-0.571226\pi\) | ||||
−0.221900 | + | 0.975069i | \(0.571226\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1400.00 | −0.0648897 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6840.00 | −0.315809 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21008.0 | 0.966226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10560.0 | 0.483824 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6210.00 | 0.283432 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2770.00 | −0.125943 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5404.00 | −0.244767 | −0.122384 | − | 0.992483i | \(-0.539054\pi\) | ||||
−0.122384 | + | 0.992483i | \(0.539054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6732.00 | 0.303759 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11976.0 | 0.538328 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7220.00 | 0.323316 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3090.00 | 0.137850 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16326.0 | 0.725592 | 0.362796 | − | 0.931869i | \(-0.381822\pi\) | ||||
0.362796 | + | 0.931869i | \(0.381822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −744.000 | −0.0329422 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1926.00 | −0.0849586 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29040.0 | −1.27621 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6000.00 | −0.262698 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12942.0 | −0.564535 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26202.0 | 1.13871 | 0.569353 | − | 0.822093i | \(-0.307194\pi\) | ||||
0.569353 | + | 0.822093i | \(0.307194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26208.0 | −1.13476 | −0.567378 | − | 0.823457i | \(-0.692042\pi\) | ||||
−0.567378 | + | 0.823457i | \(0.692042\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19176.0 | −0.827222 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6820.00 | −0.293122 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15392.0 | −0.659116 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4104.00 | −0.175098 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1986.00 | −0.0844237 | −0.0422119 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422119 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5236.00 | −0.221769 | −0.110884 | − | 0.993833i | \(-0.535368\pi\) | ||||
−0.110884 | + | 0.993833i | \(0.535368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1800.00 | −0.0759612 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26044.0 | −1.09509 | −0.547545 | − | 0.836777i | \(-0.684437\pi\) | ||||
−0.547545 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21246.0 | 0.890113 | 0.445057 | − | 0.895502i | \(-0.353184\pi\) | ||||
0.445057 | + | 0.895502i | \(0.353184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13194.0 | 0.550776 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1194.00 | 0.0496634 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10020.0 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1512.00 | −0.0624401 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17440.0 | −0.717635 | −0.358817 | − | 0.933408i | \(-0.616820\pi\) | ||||
−0.358817 | + | 0.933408i | \(0.616820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28511.0 | 1.16901 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22866.0 | −0.934219 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3765.00 | −0.153278 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9060.00 | 0.367539 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3060.00 | 0.123697 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19000.0 | 0.765349 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33582.0 | 1.34798 | 0.673989 | − | 0.738741i | \(-0.264579\pi\) | ||||
0.673989 | + | 0.738741i | \(0.264579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4680.00 | 0.187196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18942.0 | −0.755013 | −0.377507 | − | 0.926007i | \(-0.623218\pi\) | ||||
−0.377507 | + | 0.926007i | \(0.623218\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25720.0 | 1.02160 | 0.510800 | − | 0.859699i | \(-0.329349\pi\) | ||||
0.510800 | + | 0.859699i | \(0.329349\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7272.00 | −0.287839 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32436.0 | 1.27941 | 0.639707 | − | 0.768619i | \(-0.279056\pi\) | ||||
0.639707 | + | 0.768619i | \(0.279056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7730.00 | −0.303847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14631.0 | −0.573120 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19584.0 | −0.764490 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7752.00 | −0.301569 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10818.0 | 0.419397 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1500.00 | −0.0579534 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8646.00 | 0.332902 | 0.166451 | − | 0.986050i | \(-0.446769\pi\) | ||||
0.166451 | + | 0.986050i | \(0.446769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11238.0 | −0.431227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27442.0 | 1.04943 | 0.524713 | − | 0.851279i | \(-0.324173\pi\) | ||||
0.524713 | + | 0.851279i | \(0.324173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14116.0 | −0.537986 | −0.268993 | − | 0.963142i | \(-0.586691\pi\) | ||||
−0.268993 | + | 0.963142i | \(0.586691\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1920.00 | −0.0729267 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4124.00 | 0.156111 | 0.0780554 | − | 0.996949i | \(-0.475129\pi\) | ||||
0.0780554 | + | 0.996949i | \(0.475129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10032.0 | −0.378473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1944.00 | −0.0730937 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12896.0 | 0.483257 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5360.00 | −0.200184 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11400.0 | 0.424342 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12880.0 | −0.477833 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1236.00 | −0.0457016 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5328.00 | 0.196351 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18770.0 | −0.689432 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42100.0 | 1.54124 | 0.770622 | − | 0.637293i | \(-0.219946\pi\) | ||||
0.770622 | + | 0.637293i | \(0.219946\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12078.0 | 0.440706 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34152.0 | 1.24205 | 0.621024 | − | 0.783791i | \(-0.286717\pi\) | ||||
0.621024 | + | 0.783791i | \(0.286717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33888.0 | 1.22840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2850.00 | 0.102971 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17760.0 | 0.639571 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41984.0 | 1.50699 | 0.753495 | − | 0.657453i | \(-0.228366\pi\) | ||||
0.753495 | + | 0.657453i | \(0.228366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29100.0 | 1.04113 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16720.0 | −0.596257 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4750.00 | 0.168842 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8172.00 | 0.289540 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48434.0 | 1.71051 | 0.855257 | − | 0.518204i | \(-0.173399\pi\) | ||||
0.855257 | + | 0.518204i | \(0.173399\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20696.0 | −0.728554 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12456.0 | 0.437075 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 720.000 | 0.0251834 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25590.0 | −0.892197 | −0.446099 | − | 0.894984i | \(-0.647187\pi\) | ||||
−0.446099 | + | 0.894984i | \(0.647187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19086.0 | 0.663310 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18906.0 | −0.654961 | −0.327480 | − | 0.944858i | \(-0.606200\pi\) | ||||
−0.327480 | + | 0.944858i | \(0.606200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20200.0 | 0.697564 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1620.00 | −0.0557657 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36316.0 | −1.24616 | −0.623079 | − | 0.782159i | \(-0.714118\pi\) | ||||
−0.623079 | + | 0.782159i | \(0.714118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45980.0 | 1.57279 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32658.0 | 1.11357 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15890.0 | 0.540113 | 0.270056 | − | 0.962844i | \(-0.412958\pi\) | ||||
0.270056 | + | 0.962844i | \(0.412958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6120.00 | 0.207370 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16560.0 | −0.559361 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16152.0 | −0.543874 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26655.0 | −0.894733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7884.00 | −0.263820 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8470.00 | −0.282548 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 116.000 | 0.00385761 | 0.00192880 | − | 0.999998i | \(-0.499386\pi\) | ||||
0.00192880 | + | 0.999998i | \(0.499386\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1872.00 | −0.0620612 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4744.00 | 0.156789 | 0.0783945 | − | 0.996922i | \(-0.475021\pi\) | ||||
0.0783945 | + | 0.996922i | \(0.475021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9888.00 | −0.325791 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2850.00 | 0.0936134 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18374.0 | −0.601675 | −0.300837 | − | 0.953675i | \(-0.597266\pi\) | ||||
−0.300837 | + | 0.953675i | \(0.597266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5136.00 | 0.167668 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2718.00 | 0.0884598 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13036.0 | −0.422974 | −0.211487 | − | 0.977381i | \(-0.567831\pi\) | ||||
−0.211487 | + | 0.977381i | \(0.567831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15670.0 | 0.506891 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4464.00 | −0.143962 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14800.0 | −0.475847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15224.0 | 0.487998 | 0.243999 | − | 0.969775i | \(-0.421541\pi\) | ||||
0.243999 | + | 0.969775i | \(0.421541\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12384.0 | 0.395765 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12800.0 | 0.407826 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43794.0 | −1.39114 | −0.695572 | − | 0.718457i | \(-0.744849\pi\) | ||||
−0.695572 | + | 0.718457i | \(0.744849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5130.00 | 0.162468 |
(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 | 480.4.a.j.1.1 | yes | 1 | |
3.2 | odd | 2 | 1440.4.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 480.4.a.e.1.1 | ✓ | 1 | ||
5.4 | even | 2 | 2400.4.a.g.1.1 | 1 | |||
8.3 | odd | 2 | 960.4.a.y.1.1 | 1 | |||
8.5 | even | 2 | 960.4.a.d.1.1 | 1 | |||
12.11 | even | 2 | 1440.4.a.g.1.1 | 1 | |||
20.19 | odd | 2 | 2400.4.a.p.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.4.a.e.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
480.4.a.j.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
960.4.a.d.1.1 | 1 | 8.5 | even | 2 | |||
960.4.a.y.1.1 | 1 | 8.3 | odd | 2 | |||
1440.4.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
1440.4.a.g.1.1 | 1 | 12.11 | even | 2 | |||
2400.4.a.g.1.1 | 1 | 5.4 | even | 2 | |||
2400.4.a.p.1.1 | 1 | 20.19 | odd | 2 |