Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,4,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("495.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(29.2059454528\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.107990 | 0.0539949 | − | 0.998541i | \(-0.482805\pi\) | ||||
0.0539949 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.0000 | −0.469362 | −0.234681 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234681 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | −72.0000 | −1.02721 | −0.513605 | − | 0.858027i | \(-0.671690\pi\) | ||||
−0.513605 | + | 0.858027i | \(0.671690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 122.000 | 1.47309 | 0.736545 | − | 0.676388i | \(-0.236456\pi\) | ||||
0.736545 | + | 0.676388i | \(0.236456\pi\) | |||||||
\(20\) | −40.0000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.0000 | −0.107990 | ||||||||
\(29\) | −96.0000 | −0.614716 | −0.307358 | − | 0.951594i | \(-0.599445\pi\) | ||||
−0.307358 | + | 0.951594i | \(0.599445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −112.000 | −0.648897 | −0.324448 | − | 0.945903i | \(-0.605179\pi\) | ||||
−0.324448 | + | 0.945903i | \(0.605179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.0000 | 0.0482945 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 266.000 | 1.18190 | 0.590948 | − | 0.806710i | \(-0.298754\pi\) | ||||
0.590948 | + | 0.806710i | \(0.298754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 96.0000 | 0.365675 | 0.182838 | − | 0.983143i | \(-0.441472\pi\) | ||||
0.182838 | + | 0.983143i | \(0.441472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −382.000 | −1.35475 | −0.677377 | − | 0.735636i | \(-0.736884\pi\) | ||||
−0.677377 | + | 0.735636i | \(0.736884\pi\) | |||||||
\(44\) | −88.0000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −360.000 | −1.11726 | −0.558632 | − | 0.829416i | \(-0.688674\pi\) | ||||
−0.558632 | + | 0.829416i | \(0.688674\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −339.000 | −0.988338 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 176.000 | 0.469362 | ||||||||
\(53\) | −318.000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −660.000 | −1.45635 | −0.728175 | − | 0.685391i | \(-0.759631\pi\) | ||||
−0.728175 | + | 0.685391i | \(0.759631\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −430.000 | −0.902555 | −0.451278 | − | 0.892384i | \(-0.649032\pi\) | ||||
−0.451278 | + | 0.892384i | \(0.649032\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | −110.000 | −0.209905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 380.000 | 0.692901 | 0.346451 | − | 0.938068i | \(-0.387387\pi\) | ||||
0.346451 | + | 0.938068i | \(0.387387\pi\) | |||||||
\(68\) | 576.000 | 1.02721 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −168.000 | −0.280816 | −0.140408 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140408 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 218.000 | 0.349520 | 0.174760 | − | 0.984611i | \(-0.444085\pi\) | ||||
0.174760 | + | 0.984611i | \(0.444085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −976.000 | −1.47309 | ||||||||
\(77\) | 22.0000 | 0.0325602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −706.000 | −1.00546 | −0.502729 | − | 0.864444i | \(-0.667671\pi\) | ||||
−0.502729 | + | 0.864444i | \(0.667671\pi\) | |||||||
\(80\) | 320.000 | 0.447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1068.00 | −1.41239 | −0.706194 | − | 0.708018i | \(-0.749589\pi\) | ||||
−0.706194 | + | 0.708018i | \(0.749589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −360.000 | −0.459382 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.00714605 | 0.00357303 | − | 0.999994i | \(-0.498863\pi\) | ||||
0.00357303 | + | 0.999994i | \(0.498863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −44.0000 | −0.0506863 | ||||||||
\(92\) | 576.000 | 0.652741 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 610.000 | 0.658786 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 686.000 | 0.718070 | 0.359035 | − | 0.933324i | \(-0.383106\pi\) | ||||
0.359035 | + | 0.933324i | \(0.383106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −200.000 | −0.200000 | ||||||||
\(101\) | 960.000 | 0.945778 | 0.472889 | − | 0.881122i | \(-0.343211\pi\) | ||||
0.472889 | + | 0.881122i | \(0.343211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −844.000 | −0.807396 | −0.403698 | − | 0.914892i | \(-0.632275\pi\) | ||||
−0.403698 | + | 0.914892i | \(0.632275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2172.00 | −1.96238 | −0.981192 | − | 0.193033i | \(-0.938168\pi\) | ||||
−0.981192 | + | 0.193033i | \(0.938168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 614.000 | 0.539546 | 0.269773 | − | 0.962924i | \(-0.413051\pi\) | ||||
0.269773 | + | 0.962924i | \(0.413051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 128.000 | 0.107990 | ||||||||
\(113\) | −1254.00 | −1.04395 | −0.521975 | − | 0.852961i | \(-0.674805\pi\) | ||||
−0.521975 | + | 0.852961i | \(0.674805\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −360.000 | −0.291915 | ||||||||
\(116\) | 768.000 | 0.614716 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −144.000 | −0.110928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 896.000 | 0.648897 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1394.00 | 0.973996 | 0.486998 | − | 0.873403i | \(-0.338092\pi\) | ||||
0.486998 | + | 0.873403i | \(0.338092\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 252.000 | 0.168071 | 0.0840357 | − | 0.996463i | \(-0.473219\pi\) | ||||
0.0840357 | + | 0.996463i | \(0.473219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 244.000 | 0.159079 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1050.00 | 0.654800 | 0.327400 | − | 0.944886i | \(-0.393828\pi\) | ||||
0.327400 | + | 0.944886i | \(0.393828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1874.00 | 1.14353 | 0.571765 | − | 0.820418i | \(-0.306259\pi\) | ||||
0.571765 | + | 0.820418i | \(0.306259\pi\) | |||||||
\(140\) | −80.0000 | −0.0482945 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −242.000 | −0.141518 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −480.000 | −0.274909 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2128.00 | −1.18190 | ||||||||
\(149\) | −1476.00 | −0.811534 | −0.405767 | − | 0.913976i | \(-0.632996\pi\) | ||||
−0.405767 | + | 0.913976i | \(0.632996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1478.00 | 0.796543 | 0.398271 | − | 0.917268i | \(-0.369610\pi\) | ||||
0.398271 | + | 0.917268i | \(0.369610\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −560.000 | −0.290195 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 854.000 | 0.434119 | 0.217059 | − | 0.976158i | \(-0.430354\pi\) | ||||
0.217059 | + | 0.976158i | \(0.430354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −144.000 | −0.0704894 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1544.00 | 0.741935 | 0.370968 | − | 0.928646i | \(-0.379026\pi\) | ||||
0.370968 | + | 0.928646i | \(0.379026\pi\) | |||||||
\(164\) | −768.000 | −0.365675 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −240.000 | −0.111208 | −0.0556041 | − | 0.998453i | \(-0.517708\pi\) | ||||
−0.0556041 | + | 0.998453i | \(0.517708\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1713.00 | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3056.00 | 1.35475 | ||||||||
\(173\) | −2532.00 | −1.11274 | −0.556371 | − | 0.830934i | \(-0.687807\pi\) | ||||
−0.556371 | + | 0.830934i | \(0.687807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.0000 | 0.0215980 | ||||||||
\(176\) | 704.000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1092.00 | −0.455977 | −0.227989 | − | 0.973664i | \(-0.573215\pi\) | ||||
−0.227989 | + | 0.973664i | \(0.573215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2290.00 | −0.940411 | −0.470205 | − | 0.882557i | \(-0.655820\pi\) | ||||
−0.470205 | + | 0.882557i | \(0.655820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1330.00 | 0.528560 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −792.000 | −0.309715 | ||||||||
\(188\) | 2880.00 | 1.11726 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4392.00 | 1.66384 | 0.831921 | − | 0.554894i | \(-0.187241\pi\) | ||||
0.831921 | + | 0.554894i | \(0.187241\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5074.00 | −1.89241 | −0.946203 | − | 0.323572i | \(-0.895116\pi\) | ||||
−0.946203 | + | 0.323572i | \(0.895116\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2712.00 | 0.988338 | ||||||||
\(197\) | −1692.00 | −0.611929 | −0.305964 | − | 0.952043i | \(-0.598979\pi\) | ||||
−0.305964 | + | 0.952043i | \(0.598979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4664.00 | 1.66142 | 0.830709 | − | 0.556707i | \(-0.187935\pi\) | ||||
0.830709 | + | 0.556707i | \(0.187935\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −192.000 | −0.0663830 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 480.000 | 0.163535 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1408.00 | −0.469362 | ||||||||
\(209\) | 1342.00 | 0.444153 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1870.00 | −0.610124 | −0.305062 | − | 0.952333i | \(-0.598677\pi\) | ||||
−0.305062 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(212\) | 2544.00 | 0.824163 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1910.00 | −0.605865 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −224.000 | −0.0700742 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −440.000 | −0.134840 | ||||||||
\(221\) | 1584.00 | 0.482133 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2300.00 | 0.690670 | 0.345335 | − | 0.938479i | \(-0.387765\pi\) | ||||
0.345335 | + | 0.938479i | \(0.387765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1332.00 | 0.389462 | 0.194731 | − | 0.980857i | \(-0.437617\pi\) | ||||
0.194731 | + | 0.980857i | \(0.437617\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6022.00 | −1.73775 | −0.868875 | − | 0.495031i | \(-0.835157\pi\) | ||||
−0.868875 | + | 0.495031i | \(0.835157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4716.00 | 1.32599 | 0.662994 | − | 0.748624i | \(-0.269285\pi\) | ||||
0.662994 | + | 0.748624i | \(0.269285\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1800.00 | −0.499656 | ||||||||
\(236\) | 5280.00 | 1.45635 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6420.00 | 1.73755 | 0.868777 | − | 0.495204i | \(-0.164907\pi\) | ||||
0.868777 | + | 0.495204i | \(0.164907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3302.00 | 0.882575 | 0.441287 | − | 0.897366i | \(-0.354522\pi\) | ||||
0.441287 | + | 0.897366i | \(0.354522\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3440.00 | 0.902555 | ||||||||
\(245\) | −1695.00 | −0.441998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2684.00 | −0.691412 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −732.000 | −0.184077 | −0.0920387 | − | 0.995755i | \(-0.529338\pi\) | ||||
−0.0920387 | + | 0.995755i | \(0.529338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −792.000 | −0.196809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 3438.00 | 0.834461 | 0.417231 | − | 0.908801i | \(-0.363001\pi\) | ||||
0.417231 | + | 0.908801i | \(0.363001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 532.000 | 0.127633 | ||||||||
\(260\) | 880.000 | 0.209905 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 696.000 | 0.163183 | 0.0815916 | − | 0.996666i | \(-0.474000\pi\) | ||||
0.0815916 | + | 0.996666i | \(0.474000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1590.00 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3040.00 | −0.692901 | ||||||||
\(269\) | 7338.00 | 1.66322 | 0.831609 | − | 0.555361i | \(-0.187420\pi\) | ||||
0.831609 | + | 0.555361i | \(0.187420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5114.00 | 1.14632 | 0.573161 | − | 0.819443i | \(-0.305717\pi\) | ||||
0.573161 | + | 0.819443i | \(0.305717\pi\) | |||||||
\(272\) | −4608.00 | −1.02721 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 275.000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 986.000 | 0.213874 | 0.106937 | − | 0.994266i | \(-0.465896\pi\) | ||||
0.106937 | + | 0.994266i | \(0.465896\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3312.00 | −0.703122 | −0.351561 | − | 0.936165i | \(-0.614349\pi\) | ||||
−0.351561 | + | 0.936165i | \(0.614349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4298.00 | 0.902790 | 0.451395 | − | 0.892324i | \(-0.350927\pi\) | ||||
0.451395 | + | 0.892324i | \(0.350927\pi\) | |||||||
\(284\) | 1344.00 | 0.280816 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 192.000 | 0.0394892 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 271.000 | 0.0551598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1744.00 | −0.349520 | ||||||||
\(293\) | −2736.00 | −0.545525 | −0.272763 | − | 0.962081i | \(-0.587937\pi\) | ||||
−0.272763 | + | 0.962081i | \(0.587937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3300.00 | −0.651300 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1584.00 | 0.306372 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −764.000 | −0.146300 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7808.00 | 1.47309 | ||||||||
\(305\) | −2150.00 | −0.403635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −250.000 | −0.0464764 | −0.0232382 | − | 0.999730i | \(-0.507398\pi\) | ||||
−0.0232382 | + | 0.999730i | \(0.507398\pi\) | |||||||
\(308\) | −176.000 | −0.0325602 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7248.00 | −1.32153 | −0.660766 | − | 0.750592i | \(-0.729768\pi\) | ||||
−0.660766 | + | 0.750592i | \(0.729768\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7786.00 | −1.40604 | −0.703020 | − | 0.711170i | \(-0.748166\pi\) | ||||
−0.703020 | + | 0.711170i | \(0.748166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5648.00 | 1.00546 | ||||||||
\(317\) | 4230.00 | 0.749465 | 0.374733 | − | 0.927133i | \(-0.377735\pi\) | ||||
0.374733 | + | 0.927133i | \(0.377735\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1056.00 | −0.185344 | ||||||||
\(320\) | −2560.00 | −0.447214 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8784.00 | −1.51317 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −550.000 | −0.0938723 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −720.000 | −0.120653 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7736.00 | 1.28462 | 0.642310 | − | 0.766445i | \(-0.277976\pi\) | ||||
0.642310 | + | 0.766445i | \(0.277976\pi\) | |||||||
\(332\) | 8544.00 | 1.41239 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1900.00 | 0.309875 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2014.00 | −0.325548 | −0.162774 | − | 0.986663i | \(-0.552044\pi\) | ||||
−0.162774 | + | 0.986663i | \(0.552044\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2880.00 | 0.459382 | ||||||||
\(341\) | −1232.00 | −0.195650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1364.00 | −0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7692.00 | −1.18999 | −0.594997 | − | 0.803728i | \(-0.702847\pi\) | ||||
−0.594997 | + | 0.803728i | \(0.702847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1750.00 | −0.268411 | −0.134205 | − | 0.990954i | \(-0.542848\pi\) | ||||
−0.134205 | + | 0.990954i | \(0.542848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8034.00 | −1.21135 | −0.605675 | − | 0.795712i | \(-0.707097\pi\) | ||||
−0.605675 | + | 0.795712i | \(0.707097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −840.000 | −0.125585 | ||||||||
\(356\) | −48.0000 | −0.00714605 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2304.00 | −0.338720 | −0.169360 | − | 0.985554i | \(-0.554170\pi\) | ||||
−0.169360 | + | 0.985554i | \(0.554170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8025.00 | 1.17000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 352.000 | 0.0506863 | ||||||||
\(365\) | 1090.00 | 0.156310 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2356.00 | −0.335101 | −0.167551 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167551 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(368\) | −4608.00 | −0.652741 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −636.000 | −0.0890013 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8602.00 | −1.19409 | −0.597044 | − | 0.802209i | \(-0.703658\pi\) | ||||
−0.597044 | + | 0.802209i | \(0.703658\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2112.00 | 0.288524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12016.0 | −1.62855 | −0.814275 | − | 0.580479i | \(-0.802865\pi\) | ||||
−0.814275 | + | 0.580479i | \(0.802865\pi\) | |||||||
\(380\) | −4880.00 | −0.658786 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1728.00 | −0.230540 | −0.115270 | − | 0.993334i | \(-0.536773\pi\) | ||||
−0.115270 | + | 0.993334i | \(0.536773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 110.000 | 0.0145613 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5488.00 | −0.718070 | ||||||||
\(389\) | −8010.00 | −1.04402 | −0.522009 | − | 0.852940i | \(-0.674817\pi\) | ||||
−0.522009 | + | 0.852940i | \(0.674817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5184.00 | 0.670502 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3530.00 | −0.449655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10150.0 | −1.28316 | −0.641579 | − | 0.767057i | \(-0.721720\pi\) | ||||
−0.641579 | + | 0.767057i | \(0.721720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | −11862.0 | −1.47721 | −0.738604 | − | 0.674140i | \(-0.764514\pi\) | ||||
−0.738604 | + | 0.674140i | \(0.764514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2464.00 | 0.304567 | ||||||||
\(404\) | −7680.00 | −0.945778 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2926.00 | 0.356355 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −682.000 | −0.0824517 | −0.0412258 | − | 0.999150i | \(-0.513126\pi\) | ||||
−0.0412258 | + | 0.999150i | \(0.513126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6752.00 | 0.807396 | ||||||||
\(413\) | −1320.00 | −0.157271 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5340.00 | −0.631639 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10836.0 | −1.26342 | −0.631710 | − | 0.775205i | \(-0.717647\pi\) | ||||
−0.631710 | + | 0.775205i | \(0.717647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12350.0 | 1.42970 | 0.714848 | − | 0.699280i | \(-0.246496\pi\) | ||||
0.714848 | + | 0.699280i | \(0.246496\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1800.00 | −0.205442 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −860.000 | −0.0974668 | ||||||||
\(428\) | 17376.0 | 1.96238 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5940.00 | 0.663851 | 0.331925 | − | 0.943306i | \(-0.392302\pi\) | ||||
0.331925 | + | 0.943306i | \(0.392302\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12898.0 | −1.43150 | −0.715749 | − | 0.698358i | \(-0.753914\pi\) | ||||
−0.715749 | + | 0.698358i | \(0.753914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4912.00 | −0.539546 | ||||||||
\(437\) | −8784.00 | −0.961546 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11450.0 | 1.24483 | 0.622413 | − | 0.782689i | \(-0.286152\pi\) | ||||
0.622413 | + | 0.782689i | \(0.286152\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2100.00 | −0.225224 | −0.112612 | − | 0.993639i | \(-0.535922\pi\) | ||||
−0.112612 | + | 0.993639i | \(0.535922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.0000 | 0.00319581 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1024.00 | −0.107990 | ||||||||
\(449\) | 11934.0 | 1.25434 | 0.627172 | − | 0.778881i | \(-0.284212\pi\) | ||||
0.627172 | + | 0.778881i | \(0.284212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1056.00 | 0.110255 | ||||||||
\(452\) | 10032.0 | 1.04395 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −220.000 | −0.0226676 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 578.000 | 0.0591635 | 0.0295817 | − | 0.999562i | \(-0.490582\pi\) | ||||
0.0295817 | + | 0.999562i | \(0.490582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2880.00 | 0.291915 | ||||||||
\(461\) | 324.000 | 0.0327336 | 0.0163668 | − | 0.999866i | \(-0.494790\pi\) | ||||
0.0163668 | + | 0.999866i | \(0.494790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11788.0 | −1.18323 | −0.591614 | − | 0.806221i | \(-0.701509\pi\) | ||||
−0.591614 | + | 0.806221i | \(0.701509\pi\) | |||||||
\(464\) | −6144.00 | −0.614716 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14484.0 | 1.43520 | 0.717601 | − | 0.696454i | \(-0.245240\pi\) | ||||
0.717601 | + | 0.696454i | \(0.245240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 760.000 | 0.0748263 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4202.00 | −0.408474 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3050.00 | 0.294618 | ||||||||
\(476\) | 1152.00 | 0.110928 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3084.00 | 0.294179 | 0.147089 | − | 0.989123i | \(-0.453010\pi\) | ||||
0.147089 | + | 0.989123i | \(0.453010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5852.00 | −0.554736 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −968.000 | −0.0909091 | ||||||||
\(485\) | 3430.00 | 0.321130 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5584.00 | −0.519579 | −0.259790 | − | 0.965665i | \(-0.583653\pi\) | ||||
−0.259790 | + | 0.965665i | \(0.583653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10752.0 | 0.988250 | 0.494125 | − | 0.869391i | \(-0.335488\pi\) | ||||
0.494125 | + | 0.869391i | \(0.335488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6912.00 | 0.631442 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7168.00 | −0.648897 | ||||||||
\(497\) | −336.000 | −0.0303253 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13372.0 | −1.19963 | −0.599813 | − | 0.800141i | \(-0.704758\pi\) | ||||
−0.599813 | + | 0.800141i | \(0.704758\pi\) | |||||||
\(500\) | −1000.00 | −0.0894427 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9072.00 | −0.804176 | −0.402088 | − | 0.915601i | \(-0.631715\pi\) | ||||
−0.402088 | + | 0.915601i | \(0.631715\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4800.00 | 0.422965 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11152.0 | −0.973996 | ||||||||
\(509\) | 14586.0 | 1.27016 | 0.635082 | − | 0.772445i | \(-0.280966\pi\) | ||||
0.635082 | + | 0.772445i | \(0.280966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 436.000 | 0.0377446 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4220.00 | −0.361078 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3960.00 | −0.336868 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2718.00 | −0.228556 | −0.114278 | − | 0.993449i | \(-0.536455\pi\) | ||||
−0.114278 | + | 0.993449i | \(0.536455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2086.00 | −0.174406 | −0.0872031 | − | 0.996191i | \(-0.527793\pi\) | ||||
−0.0872031 | + | 0.996191i | \(0.527793\pi\) | |||||||
\(524\) | −2016.00 | −0.168071 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8064.00 | 0.666553 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1952.00 | −0.159079 | ||||||||
\(533\) | −2112.00 | −0.171634 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10860.0 | −0.877605 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3729.00 | −0.297995 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13838.0 | 1.09971 | 0.549854 | − | 0.835261i | \(-0.314683\pi\) | ||||
0.549854 | + | 0.835261i | \(0.314683\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3070.00 | 0.241292 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23546.0 | 1.84050 | 0.920251 | − | 0.391329i | \(-0.127985\pi\) | ||||
0.920251 | + | 0.391329i | \(0.127985\pi\) | |||||||
\(548\) | −8400.00 | −0.654800 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11712.0 | −0.905532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1412.00 | −0.108579 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14992.0 | −1.14353 | ||||||||
\(557\) | −15624.0 | −1.18853 | −0.594264 | − | 0.804270i | \(-0.702557\pi\) | ||||
−0.594264 | + | 0.804270i | \(0.702557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8404.00 | 0.635870 | ||||||||
\(560\) | 640.000 | 0.0482945 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2400.00 | −0.179659 | −0.0898294 | − | 0.995957i | \(-0.528632\pi\) | ||||
−0.0898294 | + | 0.995957i | \(0.528632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6270.00 | −0.466869 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18300.0 | 1.34829 | 0.674144 | − | 0.738600i | \(-0.264513\pi\) | ||||
0.674144 | + | 0.738600i | \(0.264513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25454.0 | 1.86553 | 0.932764 | − | 0.360487i | \(-0.117389\pi\) | ||||
0.932764 | + | 0.360487i | \(0.117389\pi\) | |||||||
\(572\) | 1936.00 | 0.141518 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1800.00 | −0.130548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19802.0 | 1.42871 | 0.714357 | − | 0.699781i | \(-0.246719\pi\) | ||||
0.714357 | + | 0.699781i | \(0.246719\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3840.00 | 0.274909 | ||||||||
\(581\) | −2136.00 | −0.152524 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3498.00 | −0.248495 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18396.0 | −1.29350 | −0.646750 | − | 0.762702i | \(-0.723872\pi\) | ||||
−0.646750 | + | 0.762702i | \(0.723872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13664.0 | −0.955883 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17024.0 | 1.18190 | ||||||||
\(593\) | −15012.0 | −1.03958 | −0.519788 | − | 0.854295i | \(-0.673989\pi\) | ||||
−0.519788 | + | 0.854295i | \(0.673989\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −720.000 | −0.0496086 | ||||||||
\(596\) | 11808.0 | 0.811534 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15408.0 | −1.05101 | −0.525504 | − | 0.850791i | \(-0.676123\pi\) | ||||
−0.525504 | + | 0.850791i | \(0.676123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1558.00 | −0.105744 | −0.0528720 | − | 0.998601i | \(-0.516838\pi\) | ||||
−0.0528720 | + | 0.998601i | \(0.516838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11824.0 | −0.796543 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22970.0 | 1.53595 | 0.767977 | − | 0.640478i | \(-0.221264\pi\) | ||||
0.767977 | + | 0.640478i | \(0.221264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7920.00 | 0.524401 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11482.0 | −0.756531 | −0.378266 | − | 0.925697i | \(-0.623479\pi\) | ||||
−0.378266 | + | 0.925697i | \(0.623479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −246.000 | −0.0160512 | −0.00802560 | − | 0.999968i | \(-0.502555\pi\) | ||||
−0.00802560 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11648.0 | 0.756337 | 0.378169 | − | 0.925737i | \(-0.376554\pi\) | ||||
0.378169 | + | 0.925737i | \(0.376554\pi\) | |||||||
\(620\) | 4480.00 | 0.290195 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0000 | 0.000771701 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6832.00 | −0.434119 | ||||||||
\(629\) | −19152.0 | −1.21405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22024.0 | −1.38948 | −0.694740 | − | 0.719261i | \(-0.744480\pi\) | ||||
−0.694740 | + | 0.719261i | \(0.744480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6970.00 | 0.435584 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7458.00 | 0.463888 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2322.00 | −0.143079 | −0.0715394 | − | 0.997438i | \(-0.522791\pi\) | ||||
−0.0715394 | + | 0.997438i | \(0.522791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14024.0 | 0.860113 | 0.430056 | − | 0.902802i | \(-0.358494\pi\) | ||||
0.430056 | + | 0.902802i | \(0.358494\pi\) | |||||||
\(644\) | 1152.00 | 0.0704894 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7152.00 | 0.434581 | 0.217291 | − | 0.976107i | \(-0.430278\pi\) | ||||
0.217291 | + | 0.976107i | \(0.430278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7260.00 | −0.439106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12352.0 | −0.741935 | ||||||||
\(653\) | 3138.00 | 0.188054 | 0.0940271 | − | 0.995570i | \(-0.470026\pi\) | ||||
0.0940271 | + | 0.995570i | \(0.470026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1260.00 | 0.0751638 | ||||||||
\(656\) | 6144.00 | 0.365675 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15876.0 | 0.938454 | 0.469227 | − | 0.883078i | \(-0.344533\pi\) | ||||
0.469227 | + | 0.883078i | \(0.344533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20554.0 | −1.20947 | −0.604734 | − | 0.796428i | \(-0.706720\pi\) | ||||
−0.604734 | + | 0.796428i | \(0.706720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1220.00 | 0.0711422 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6912.00 | 0.401250 | ||||||||
\(668\) | 1920.00 | 0.111208 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4730.00 | −0.272131 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27806.0 | 1.59263 | 0.796317 | − | 0.604880i | \(-0.206779\pi\) | ||||
0.796317 | + | 0.604880i | \(0.206779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13704.0 | 0.779700 | ||||||||
\(677\) | −20820.0 | −1.18195 | −0.590973 | − | 0.806691i | \(-0.701256\pi\) | ||||
−0.590973 | + | 0.806691i | \(0.701256\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1372.00 | 0.0775442 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7020.00 | 0.393284 | 0.196642 | − | 0.980475i | \(-0.436996\pi\) | ||||
0.196642 | + | 0.980475i | \(0.436996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5250.00 | 0.292835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24448.0 | −1.35475 | ||||||||
\(689\) | 6996.00 | 0.386831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12536.0 | 0.690147 | 0.345074 | − | 0.938576i | \(-0.387854\pi\) | ||||
0.345074 | + | 0.938576i | \(0.387854\pi\) | |||||||
\(692\) | 20256.0 | 1.11274 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9370.00 | 0.511402 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6912.00 | −0.375625 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −400.000 | −0.0215980 | ||||||||
\(701\) | 33276.0 | 1.79289 | 0.896446 | − | 0.443153i | \(-0.146140\pi\) | ||||
0.896446 | + | 0.443153i | \(0.146140\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32452.0 | 1.74104 | ||||||||
\(704\) | −5632.00 | −0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1920.00 | 0.102134 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9818.00 | 0.520060 | 0.260030 | − | 0.965601i | \(-0.416267\pi\) | ||||
0.260030 | + | 0.965601i | \(0.416267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8064.00 | 0.423561 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1210.00 | −0.0632887 | ||||||||
\(716\) | 8736.00 | 0.455977 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3216.00 | −0.166810 | −0.0834051 | − | 0.996516i | \(-0.526580\pi\) | ||||
−0.0834051 | + | 0.996516i | \(0.526580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1688.00 | −0.0871906 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18320.0 | 0.940411 | ||||||||
\(725\) | −2400.00 | −0.122943 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10960.0 | −0.559125 | −0.279563 | − | 0.960127i | \(-0.590189\pi\) | ||||
−0.279563 | + | 0.960127i | \(0.590189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27504.0 | 1.39162 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14618.0 | 0.736600 | 0.368300 | − | 0.929707i | \(-0.379940\pi\) | ||||
0.368300 | + | 0.929707i | \(0.379940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4180.00 | 0.208918 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36518.0 | 1.81778 | 0.908888 | − | 0.417040i | \(-0.136933\pi\) | ||||
0.908888 | + | 0.417040i | \(0.136933\pi\) | |||||||
\(740\) | −10640.0 | −0.528560 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37452.0 | 1.84923 | 0.924617 | − | 0.380899i | \(-0.124385\pi\) | ||||
0.924617 | + | 0.380899i | \(0.124385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7380.00 | −0.362929 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6336.00 | 0.309715 | ||||||||
\(749\) | −4344.00 | −0.211918 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10648.0 | −0.517378 | −0.258689 | − | 0.965961i | \(-0.583291\pi\) | ||||
−0.258689 | + | 0.965961i | \(0.583291\pi\) | |||||||
\(752\) | −23040.0 | −1.11726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7390.00 | 0.356225 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1258.00 | −0.0604000 | −0.0302000 | − | 0.999544i | \(-0.509614\pi\) | ||||
−0.0302000 | + | 0.999544i | \(0.509614\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1740.00 | −0.0828843 | −0.0414421 | − | 0.999141i | \(-0.513195\pi\) | ||||
−0.0414421 | + | 0.999141i | \(0.513195\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1228.00 | 0.0582655 | ||||||||
\(764\) | −35136.0 | −1.66384 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14520.0 | 0.683555 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10774.0 | −0.505228 | −0.252614 | − | 0.967567i | \(-0.581290\pi\) | ||||
−0.252614 | + | 0.967567i | \(0.581290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 40592.0 | 1.89241 | ||||||||
\(773\) | 19146.0 | 0.890859 | 0.445429 | − | 0.895317i | \(-0.353051\pi\) | ||||
0.445429 | + | 0.895317i | \(0.353051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2800.00 | −0.129779 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11712.0 | 0.538673 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1848.00 | −0.0846692 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21696.0 | −0.988338 | ||||||||
\(785\) | 4270.00 | 0.194144 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30670.0 | −1.38916 | −0.694579 | − | 0.719416i | \(-0.744409\pi\) | ||||
−0.694579 | + | 0.719416i | \(0.744409\pi\) | |||||||
\(788\) | 13536.0 | 0.611929 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2508.00 | −0.112736 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9460.00 | 0.423625 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −37312.0 | −1.66142 | ||||||||
\(797\) | −11970.0 | −0.531994 | −0.265997 | − | 0.963974i | \(-0.585701\pi\) | ||||
−0.265997 | + | 0.963974i | \(0.585701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25920.0 | 1.14766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2398.00 | 0.105384 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −720.000 | −0.0315238 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19932.0 | 0.866220 | 0.433110 | − | 0.901341i | \(-0.357416\pi\) | ||||
0.433110 | + | 0.901341i | \(0.357416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31462.0 | −1.36224 | −0.681122 | − | 0.732170i | \(-0.738508\pi\) | ||||
−0.681122 | + | 0.732170i | \(0.738508\pi\) | |||||||
\(812\) | 1536.00 | 0.0663830 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7720.00 | 0.331803 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46604.0 | −1.99568 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3840.00 | −0.163535 | ||||||||
\(821\) | 39720.0 | 1.68847 | 0.844237 | − | 0.535970i | \(-0.180054\pi\) | ||||
0.844237 | + | 0.535970i | \(0.180054\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28492.0 | −1.20677 | −0.603383 | − | 0.797451i | \(-0.706181\pi\) | ||||
−0.603383 | + | 0.797451i | \(0.706181\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18324.0 | 0.770481 | 0.385241 | − | 0.922816i | \(-0.374118\pi\) | ||||
0.385241 | + | 0.922816i | \(0.374118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21626.0 | 0.906034 | 0.453017 | − | 0.891502i | \(-0.350348\pi\) | ||||
0.453017 | + | 0.891502i | \(0.350348\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11264.0 | 0.469362 | ||||||||
\(833\) | 24408.0 | 1.01523 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1200.00 | −0.0497338 | ||||||||
\(836\) | −10736.0 | −0.444153 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36960.0 | 1.52086 | 0.760430 | − | 0.649420i | \(-0.224988\pi\) | ||||
0.760430 | + | 0.649420i | \(0.224988\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15173.0 | −0.622125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14960.0 | 0.610124 | ||||||||
\(845\) | −8565.00 | −0.348692 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 242.000 | 0.00981726 | ||||||||
\(848\) | −20352.0 | −0.824163 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19152.0 | −0.771471 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31502.0 | 1.26449 | 0.632244 | − | 0.774769i | \(-0.282134\pi\) | ||||
0.632244 | + | 0.774769i | \(0.282134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5640.00 | −0.224806 | −0.112403 | − | 0.993663i | \(-0.535855\pi\) | ||||
−0.112403 | + | 0.993663i | \(0.535855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2056.00 | −0.0816645 | −0.0408323 | − | 0.999166i | \(-0.513001\pi\) | ||||
−0.0408323 | + | 0.999166i | \(0.513001\pi\) | |||||||
\(860\) | 15280.0 | 0.605865 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18336.0 | −0.723250 | −0.361625 | − | 0.932324i | \(-0.617778\pi\) | ||||
−0.361625 | + | 0.932324i | \(0.617778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12660.0 | −0.497633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1792.00 | 0.0700742 | ||||||||
\(869\) | −7766.00 | −0.303157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8360.00 | −0.325221 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 250.000 | 0.00965891 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51346.0 | −1.97700 | −0.988501 | − | 0.151213i | \(-0.951682\pi\) | ||||
−0.988501 | + | 0.151213i | \(0.951682\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3520.00 | 0.134840 | ||||||||
\(881\) | −32910.0 | −1.25853 | −0.629266 | − | 0.777190i | \(-0.716644\pi\) | ||||
−0.629266 | + | 0.777190i | \(0.716644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15356.0 | 0.585244 | 0.292622 | − | 0.956228i | \(-0.405472\pi\) | ||||
0.292622 | + | 0.956228i | \(0.405472\pi\) | |||||||
\(884\) | −12672.0 | −0.482133 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18372.0 | −0.695458 | −0.347729 | − | 0.937595i | \(-0.613047\pi\) | ||||
−0.347729 | + | 0.937595i | \(0.613047\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2788.00 | 0.105182 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18400.0 | −0.690670 | ||||||||
\(893\) | −43920.0 | −1.64583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5460.00 | −0.203919 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10752.0 | 0.398887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22896.0 | 0.846589 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11450.0 | −0.420565 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7640.00 | 0.279694 | 0.139847 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139847 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(908\) | −10656.0 | −0.389462 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53040.0 | 1.92897 | 0.964486 | − | 0.264134i | \(-0.0850860\pi\) | ||||
0.964486 | + | 0.264134i | \(0.0850860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11748.0 | −0.425851 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 48176.0 | 1.73775 | ||||||||
\(917\) | 504.000 | 0.0181500 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11302.0 | −0.405679 | −0.202839 | − | 0.979212i | \(-0.565017\pi\) | ||||
−0.202839 | + | 0.979212i | \(0.565017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3696.00 | 0.131804 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6650.00 | 0.236379 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19254.0 | −0.679982 | −0.339991 | − | 0.940429i | \(-0.610424\pi\) | ||||
−0.339991 | + | 0.940429i | \(0.610424\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41358.0 | −1.45591 | ||||||||
\(932\) | −37728.0 | −1.32599 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3960.00 | −0.138509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22214.0 | 0.774493 | 0.387246 | − | 0.921976i | \(-0.373426\pi\) | ||||
0.387246 | + | 0.921976i | \(0.373426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14400.0 | 0.499656 | ||||||||
\(941\) | −41736.0 | −1.44586 | −0.722930 | − | 0.690921i | \(-0.757205\pi\) | ||||
−0.722930 | + | 0.690921i | \(0.757205\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6912.00 | −0.238691 | ||||||||
\(944\) | −42240.0 | −1.45635 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42732.0 | −1.46632 | −0.733159 | − | 0.680057i | \(-0.761955\pi\) | ||||
−0.733159 | + | 0.680057i | \(0.761955\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4796.00 | −0.164051 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25056.0 | 0.851672 | 0.425836 | − | 0.904800i | \(-0.359980\pi\) | ||||
0.425836 | + | 0.904800i | \(0.359980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21960.0 | 0.744093 | ||||||||
\(956\) | −51360.0 | −1.73755 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2100.00 | 0.0707117 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17247.0 | −0.578933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26416.0 | −0.882575 | ||||||||
\(965\) | −25370.0 | −0.846310 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14326.0 | −0.476415 | −0.238207 | − | 0.971214i | \(-0.576560\pi\) | ||||
−0.238207 | + | 0.971214i | \(0.576560\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45924.0 | −1.51779 | −0.758894 | − | 0.651215i | \(-0.774260\pi\) | ||||
−0.758894 | + | 0.651215i | \(0.774260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3748.00 | 0.123490 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27520.0 | −0.902555 | ||||||||
\(977\) | 38946.0 | 1.27533 | 0.637663 | − | 0.770316i | \(-0.279901\pi\) | ||||
0.637663 | + | 0.770316i | \(0.279901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.0000 | 0.00215462 | ||||||||
\(980\) | 13560.0 | 0.441998 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21000.0 | −0.681379 | −0.340690 | − | 0.940176i | \(-0.610661\pi\) | ||||
−0.340690 | + | 0.940176i | \(0.610661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8460.00 | −0.273663 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21472.0 | 0.691412 | ||||||||
\(989\) | 27504.0 | 0.884304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7760.00 | 0.248743 | 0.124372 | − | 0.992236i | \(-0.460309\pi\) | ||||
0.124372 | + | 0.992236i | \(0.460309\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23320.0 | 0.743009 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21350.0 | 0.678196 | 0.339098 | − | 0.940751i | \(-0.389878\pi\) | ||||
0.339098 | + | 0.940751i | \(0.389878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 495.4.a.c.1.1 | 1 | ||
3.2 | odd | 2 | 165.4.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | 2475.4.a.f.1.1 | 1 | |||
15.2 | even | 4 | 825.4.c.g.199.2 | 2 | |||
15.8 | even | 4 | 825.4.c.g.199.1 | 2 | |||
15.14 | odd | 2 | 825.4.a.e.1.1 | 1 | |||
33.32 | even | 2 | 1815.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
495.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
825.4.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
825.4.c.g.199.1 | 2 | 15.8 | even | 4 | |||
825.4.c.g.199.2 | 2 | 15.2 | even | 4 | |||
1815.4.a.f.1.1 | 1 | 33.32 | even | 2 | |||
2475.4.a.f.1.1 | 1 | 5.4 | even | 2 |