Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,4,Mod(1,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, 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("112.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.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: | \(6.60821392064\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 112.1 |
$q$-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 | ||||||||
\(3\) | 10.0000 | 1.92450 | 0.962250 | − | 0.272166i | \(-0.0877398\pi\) | ||||
0.962250 | + | 0.272166i | \(0.0877398\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.00000 | −0.715542 | −0.357771 | − | 0.933809i | \(-0.616463\pi\) | ||||
−0.357771 | + | 0.933809i | \(0.616463\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 73.0000 | 2.70370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 40.0000 | 1.09640 | 0.548202 | − | 0.836346i | \(-0.315312\pi\) | ||||
0.548202 | + | 0.836346i | \(0.315312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0000 | −0.256015 | −0.128008 | − | 0.991773i | \(-0.540858\pi\) | ||||
−0.128008 | + | 0.991773i | \(0.540858\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −80.0000 | −1.37706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −58.0000 | −0.827474 | −0.413737 | − | 0.910396i | \(-0.635777\pi\) | ||||
−0.413737 | + | 0.910396i | \(0.635777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.0000 | −0.313937 | −0.156969 | − | 0.987604i | \(-0.550172\pi\) | ||||
−0.156969 | + | 0.987604i | \(0.550172\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 70.0000 | 0.727393 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 64.0000 | 0.580214 | 0.290107 | − | 0.956994i | \(-0.406309\pi\) | ||||
0.290107 | + | 0.956994i | \(0.406309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.0000 | −0.488000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 460.000 | 3.27878 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −62.0000 | −0.397004 | −0.198502 | − | 0.980101i | \(-0.563608\pi\) | ||||
−0.198502 | + | 0.980101i | \(0.563608\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −252.000 | −1.46002 | −0.730009 | − | 0.683438i | \(-0.760484\pi\) | ||||
−0.730009 | + | 0.683438i | \(0.760484\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 400.000 | 2.11003 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −56.0000 | −0.270449 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 26.0000 | 0.115524 | 0.0577618 | − | 0.998330i | \(-0.481604\pi\) | ||||
0.0577618 | + | 0.998330i | \(0.481604\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −120.000 | −0.492702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.0228547 | 0.0114273 | − | 0.999935i | \(-0.496362\pi\) | ||||
0.0114273 | + | 0.999935i | \(0.496362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −416.000 | −1.47534 | −0.737668 | − | 0.675164i | \(-0.764073\pi\) | ||||
−0.737668 | + | 0.675164i | \(0.764073\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −584.000 | −1.93461 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 396.000 | 1.22899 | 0.614495 | − | 0.788921i | \(-0.289360\pi\) | ||||
0.614495 | + | 0.788921i | \(0.289360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −580.000 | −1.59248 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −450.000 | −1.16627 | −0.583134 | − | 0.812376i | \(-0.698174\pi\) | ||||
−0.583134 | + | 0.812376i | \(0.698174\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −320.000 | −0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −260.000 | −0.604173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −274.000 | −0.604606 | −0.302303 | − | 0.953212i | \(-0.597755\pi\) | ||||
−0.302303 | + | 0.953212i | \(0.597755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −576.000 | −1.20900 | −0.604502 | − | 0.796604i | \(-0.706628\pi\) | ||||
−0.604502 | + | 0.796604i | \(0.706628\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 511.000 | 1.02190 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 96.0000 | 0.183190 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 476.000 | 0.867950 | 0.433975 | − | 0.900925i | \(-0.357111\pi\) | ||||
0.433975 | + | 0.900925i | \(0.357111\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 640.000 | 1.11662 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 448.000 | 0.748843 | 0.374421 | − | 0.927259i | \(-0.377841\pi\) | ||||
0.374421 | + | 0.927259i | \(0.377841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −158.000 | −0.253322 | −0.126661 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126661 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −610.000 | −0.939156 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 280.000 | 0.414402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 936.000 | 1.33302 | 0.666508 | − | 0.745498i | \(-0.267788\pi\) | ||||
0.666508 | + | 0.745498i | \(0.267788\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2629.00 | 3.60631 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −530.000 | −0.700904 | −0.350452 | − | 0.936581i | \(-0.613972\pi\) | ||||
−0.350452 | + | 0.936581i | \(0.613972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 464.000 | 0.592093 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −620.000 | −0.764034 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −390.000 | −0.464493 | −0.232247 | − | 0.972657i | \(-0.574608\pi\) | ||||
−0.232247 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −84.0000 | −0.0967648 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2520.00 | −2.80980 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 208.000 | 0.224635 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 214.000 | 0.224004 | 0.112002 | − | 0.993708i | \(-0.464274\pi\) | ||||
0.112002 | + | 0.993708i | \(0.464274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2920.00 | 2.96435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1432.00 | 1.41079 | 0.705393 | − | 0.708817i | \(-0.250771\pi\) | ||||
0.705393 | + | 0.708817i | \(0.250771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −764.000 | −0.730866 | −0.365433 | − | 0.930838i | \(-0.619079\pi\) | ||||
−0.365433 | + | 0.930838i | \(0.619079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −560.000 | −0.520480 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −324.000 | −0.292731 | −0.146366 | − | 0.989231i | \(-0.546758\pi\) | ||||
−0.146366 | + | 0.989231i | \(0.546758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1334.00 | −1.17224 | −0.586119 | − | 0.810225i | \(-0.699345\pi\) | ||||
−0.586119 | + | 0.810225i | \(0.699345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 260.000 | 0.222325 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1798.00 | 1.49683 | 0.748414 | − | 0.663232i | \(-0.230816\pi\) | ||||
0.748414 | + | 0.663232i | \(0.230816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −512.000 | −0.415167 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −876.000 | −0.692190 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −406.000 | −0.312756 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269.000 | 0.202104 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 60.0000 | 0.0439839 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1488.00 | 1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 384.000 | 0.268303 | 0.134152 | − | 0.990961i | \(-0.457169\pi\) | ||||
0.134152 | + | 0.990961i | \(0.457169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4160.00 | −2.83928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1814.00 | 1.20985 | 0.604923 | − | 0.796284i | \(-0.293204\pi\) | ||||
0.604923 | + | 0.796284i | \(0.293204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −182.000 | −0.118657 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3680.00 | −2.34610 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1666.00 | 1.03895 | 0.519474 | − | 0.854486i | \(-0.326128\pi\) | ||||
0.519474 | + | 0.854486i | \(0.326128\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1126.00 | −0.687094 | −0.343547 | − | 0.939135i | \(-0.611628\pi\) | ||||
−0.343547 | + | 0.939135i | \(0.611628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3960.00 | 2.36519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −480.000 | −0.280697 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 496.000 | 0.284073 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 490.000 | 0.274929 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2694.00 | 1.48122 | 0.740608 | − | 0.671938i | \(-0.234538\pi\) | ||||
0.740608 | + | 0.671938i | \(0.234538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2648.00 | 1.42709 | 0.713547 | − | 0.700607i | \(-0.247088\pi\) | ||||
0.713547 | + | 0.700607i | \(0.247088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4234.00 | −2.23725 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2016.00 | 1.04470 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −556.000 | −0.282635 | −0.141317 | − | 0.989964i | \(-0.545134\pi\) | ||||
−0.141317 | + | 0.989964i | \(0.545134\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4500.00 | −2.24449 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 448.000 | 0.219300 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 328.000 | 0.157613 | 0.0788066 | − | 0.996890i | \(-0.474889\pi\) | ||||
0.0788066 | + | 0.996890i | \(0.474889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3200.00 | −1.50982 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4268.00 | 1.97765 | 0.988826 | − | 0.149077i | \(-0.0476302\pi\) | ||||
0.988826 | + | 0.149077i | \(0.0476302\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2053.00 | −0.934456 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1898.00 | −0.848793 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3476.00 | −1.52760 | −0.763802 | − | 0.645451i | \(-0.776669\pi\) | ||||
−0.763802 | + | 0.645451i | \(0.776669\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −427.000 | −0.184447 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2740.00 | −1.16357 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2268.00 | −0.947029 | −0.473515 | − | 0.880786i | \(-0.657015\pi\) | ||||
−0.473515 | + | 0.880786i | \(0.657015\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −276.000 | −0.113342 | −0.0566710 | − | 0.998393i | \(-0.518049\pi\) | ||||
−0.0566710 | + | 0.998393i | \(0.518049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5760.00 | −2.32673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −208.000 | −0.0826620 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2320.00 | −0.907247 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3220.00 | 1.23926 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3000.00 | 1.13650 | 0.568252 | − | 0.822854i | \(-0.307620\pi\) | ||||
0.568252 | + | 0.822854i | \(0.307620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3278.00 | 1.22257 | 0.611284 | − | 0.791411i | \(-0.290653\pi\) | ||||
0.611284 | + | 0.791411i | \(0.290653\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 960.000 | 0.352549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2362.00 | −0.854241 | −0.427121 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427121 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1036.00 | 0.369046 | 0.184523 | − | 0.982828i | \(-0.440926\pi\) | ||||
0.184523 | + | 0.982828i | \(0.440926\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4760.00 | 1.67037 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −434.000 | −0.150053 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −48.0000 | −0.0163535 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4672.00 | 1.56873 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1040.00 | −0.344202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3524.00 | −1.14977 | −0.574887 | − | 0.818233i | \(-0.694954\pi\) | ||||
−0.574887 | + | 0.818233i | \(0.694954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4480.00 | 1.44115 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3328.00 | 1.05566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1764.00 | −0.551835 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1580.00 | −0.487518 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 696.000 | 0.211846 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1336.00 | 0.401189 | 0.200595 | − | 0.979674i | \(-0.435713\pi\) | ||||
0.200595 | + | 0.979674i | \(0.435713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4453.00 | −1.31941 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1290.00 | −0.377182 | −0.188591 | − | 0.982056i | \(-0.560392\pi\) | ||||
−0.188591 | + | 0.982056i | \(0.560392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5524.00 | 1.59404 | 0.797022 | − | 0.603950i | \(-0.206407\pi\) | ||||
0.797022 | + | 0.603950i | \(0.206407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2800.00 | 0.797517 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6314.00 | 1.77530 | 0.887648 | − | 0.460523i | \(-0.152338\pi\) | ||||
0.887648 | + | 0.460523i | \(0.152338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3168.00 | −0.879394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9360.00 | 2.56539 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3960.00 | 1.07176 | 0.535881 | − | 0.844294i | \(-0.319980\pi\) | ||||
0.535881 | + | 0.844294i | \(0.319980\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7018.00 | −1.87581 | −0.937903 | − | 0.346898i | \(-0.887235\pi\) | ||||
−0.937903 | + | 0.346898i | \(0.887235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13870.0 | 3.66157 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −392.000 | −0.102220 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 312.000 | 0.0803728 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5300.00 | −1.34889 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2394.00 | 0.602024 | 0.301012 | − | 0.953620i | \(-0.402676\pi\) | ||||
0.301012 | + | 0.953620i | \(0.402676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2560.00 | 0.636149 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4640.00 | 1.13948 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2766.00 | −0.671355 | −0.335678 | − | 0.941977i | \(-0.608965\pi\) | ||||
−0.335678 | + | 0.941977i | \(0.608965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 182.000 | 0.0436638 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4526.00 | −1.07338 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7968.00 | −1.86817 | −0.934084 | − | 0.357055i | \(-0.883781\pi\) | ||||
−0.934084 | + | 0.357055i | \(0.883781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3600.00 | 0.834514 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3900.00 | −0.893918 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2900.00 | −0.657309 | −0.328654 | − | 0.944450i | \(-0.606595\pi\) | ||||
−0.328654 | + | 0.944450i | \(0.606595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2640.00 | −0.591766 | −0.295883 | − | 0.955224i | \(-0.595614\pi\) | ||||
−0.295883 | + | 0.955224i | \(0.595614\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −840.000 | −0.186224 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2440.00 | −0.535046 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1522.00 | −0.330138 | −0.165069 | − | 0.986282i | \(-0.552785\pi\) | ||||
−0.165069 | + | 0.986282i | \(0.552785\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18396.0 | −3.94745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4534.00 | −0.962547 | −0.481274 | − | 0.876570i | \(-0.659826\pi\) | ||||
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4834.00 | −1.01538 | −0.507688 | − | 0.861541i | \(-0.669500\pi\) | ||||
−0.507688 | + | 0.861541i | \(0.669500\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2080.00 | 0.432311 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.0000 | 0.00863826 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1549.00 | −0.315286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2140.00 | 0.431096 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4656.00 | −0.928350 | −0.464175 | − | 0.885744i | \(-0.653649\pi\) | ||||
−0.464175 | + | 0.885744i | \(0.653649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2192.00 | 0.432621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18400.0 | 3.59487 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −768.000 | −0.148544 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2912.00 | −0.557624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14320.0 | 2.71506 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4608.00 | 0.865093 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7238.00 | 1.34558 | 0.672792 | − | 0.739831i | \(-0.265095\pi\) | ||||
0.672792 | + | 0.739831i | \(0.265095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7640.00 | −1.40655 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1096.00 | −0.199834 | −0.0999171 | − | 0.994996i | \(-0.531858\pi\) | ||||
−0.0999171 | + | 0.994996i | \(0.531858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3818.00 | −0.689476 | −0.344738 | − | 0.938699i | \(-0.612032\pi\) | ||||
−0.344738 | + | 0.938699i | \(0.612032\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4088.00 | −0.731215 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1998.00 | 0.354003 | 0.177001 | − | 0.984211i | \(-0.443360\pi\) | ||||
0.177001 | + | 0.984211i | \(0.443360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2480.00 | −0.435277 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3240.00 | −0.563362 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1508.00 | 0.259775 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 732.000 | 0.124936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13340.0 | −2.25597 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2772.00 | 0.464515 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7936.00 | 1.31783 | 0.658915 | − | 0.752217i | \(-0.271016\pi\) | ||||
0.658915 | + | 0.752217i | \(0.271016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1898.00 | 0.312342 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3808.00 | −0.621055 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2766.00 | 0.447103 | 0.223551 | − | 0.974692i | \(-0.428235\pi\) | ||||
0.223551 | + | 0.974692i | \(0.428235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17980.0 | 2.88065 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10080.0 | −1.60077 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5120.00 | −0.798990 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8352.00 | −1.29210 | −0.646050 | − | 0.763295i | \(-0.723580\pi\) | ||||
−0.646050 | + | 0.763295i | \(0.723580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5924.00 | −0.908609 | −0.454304 | − | 0.890847i | \(-0.650112\pi\) | ||||
−0.454304 | + | 0.890847i | \(0.650112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5520.00 | −0.839418 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2226.00 | 0.335632 | 0.167816 | − | 0.985818i | \(-0.446329\pi\) | ||||
0.167816 | + | 0.985818i | \(0.446329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3584.00 | −0.535828 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4060.00 | −0.601899 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3880.00 | −0.570414 | −0.285207 | − | 0.958466i | \(-0.592062\pi\) | ||||
−0.285207 | + | 0.958466i | \(0.592062\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6183.00 | −0.901443 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2690.00 | 0.388949 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1264.00 | 0.181262 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2584.00 | 0.367531 | 0.183765 | − | 0.982970i | \(-0.441171\pi\) | ||||
0.183765 | + | 0.982970i | \(0.441171\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 438.000 | 0.0617923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3150.00 | −0.440808 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10534.0 | 1.46228 | 0.731139 | − | 0.682228i | \(-0.238989\pi\) | ||||
0.731139 | + | 0.682228i | \(0.238989\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14880.0 | 2.04907 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 744.000 | 0.101639 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4472.00 | 0.606098 | 0.303049 | − | 0.952975i | \(-0.401995\pi\) | ||||
0.303049 | + | 0.952975i | \(0.401995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3840.00 | 0.516350 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2468.00 | −0.329266 | −0.164633 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164633 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2240.00 | −0.296522 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30368.0 | −3.98887 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1046.00 | −0.136335 | −0.0681675 | − | 0.997674i | \(-0.521715\pi\) | ||||
−0.0681675 | + | 0.997674i | \(0.521715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3712.00 | −0.480112 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18140.0 | 2.32835 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7488.00 | −0.953828 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2124.00 | 0.268515 | 0.134258 | − | 0.990946i | \(-0.457135\pi\) | ||||
0.134258 | + | 0.990946i | \(0.457135\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1820.00 | −0.228356 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11598.0 | 1.44433 | 0.722165 | − | 0.691721i | \(-0.243147\pi\) | ||||
0.722165 | + | 0.691721i | \(0.243147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3024.00 | 0.373787 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21032.0 | −2.58047 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1040.00 | 0.126661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2770.00 | −0.334884 | −0.167442 | − | 0.985882i | \(-0.553551\pi\) | ||||
−0.167442 | + | 0.985882i | \(0.553551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16660.0 | 1.99946 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1918.00 | −0.228520 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4240.00 | 0.501526 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11260.0 | −1.32231 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9438.00 | −1.10042 | −0.550211 | − | 0.835026i | \(-0.685453\pi\) | ||||
−0.550211 | + | 0.835026i | \(0.685453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5550.00 | 0.642495 | 0.321248 | − | 0.946995i | \(-0.395898\pi\) | ||||
0.321248 | + | 0.946995i | \(0.395898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28908.0 | 3.32283 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3538.00 | 0.403808 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4032.00 | −0.456961 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4800.00 | −0.540201 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3000.00 | 0.335278 | 0.167639 | − | 0.985848i | \(-0.446386\pi\) | ||||
0.167639 | + | 0.985848i | \(0.446386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12926.0 | 1.43460 | 0.717302 | − | 0.696762i | \(-0.245377\pi\) | ||||
0.717302 | + | 0.696762i | \(0.245377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4960.00 | 0.546698 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1664.00 | −0.182151 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 408.000 | 0.0443571 | 0.0221786 | − | 0.999754i | \(-0.492940\pi\) | ||||
0.0221786 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3577.00 | 0.386243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14452.0 | 1.54997 | 0.774983 | − | 0.631982i | \(-0.217758\pi\) | ||||
0.774983 | + | 0.631982i | \(0.217758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3120.00 | 0.332364 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26940.0 | 2.85060 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10258.0 | 1.07818 | 0.539092 | − | 0.842247i | \(-0.318767\pi\) | ||||
0.539092 | + | 0.842247i | \(0.318767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 240.000 | 0.0250580 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26480.0 | 2.74644 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 672.000 | 0.0692392 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5498.00 | −0.562769 | −0.281385 | − | 0.959595i | \(-0.590794\pi\) | ||||
−0.281385 | + | 0.959595i | \(0.590794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26680.0 | −2.71311 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16316.0 | −1.64840 | −0.824199 | − | 0.566300i | \(-0.808375\pi\) | ||||
−0.824199 | + | 0.566300i | \(0.808375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8944.00 | −0.897760 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20160.0 | 2.01053 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9422.00 | 0.933615 | 0.466807 | − | 0.884359i | \(-0.345404\pi\) | ||||
0.466807 | + | 0.884359i | \(0.345404\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3332.00 | 0.328054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5560.00 | −0.543931 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16640.0 | −1.61756 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1586.00 | 0.153201 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32850.0 | −3.15325 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13820.0 | −1.31827 | −0.659136 | − | 0.752024i | \(-0.729078\pi\) | ||||
−0.659136 | + | 0.752024i | \(0.729078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −312.000 | −0.0295758 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4480.00 | 0.422044 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1712.00 | −0.160284 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13264.0 | 1.23419 | 0.617094 | − | 0.786890i | \(-0.288310\pi\) | ||||
0.617094 | + | 0.786890i | \(0.288310\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3280.00 | 0.303327 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5940.00 | 0.545964 | 0.272982 | − | 0.962019i | \(-0.411990\pi\) | ||||
0.272982 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3596.00 | 0.328511 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23360.0 | −2.12112 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3136.00 | 0.283036 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8252.00 | 0.740301 | 0.370151 | − | 0.928972i | \(-0.379306\pi\) | ||||
0.370151 | + | 0.928972i | \(0.379306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42680.0 | 3.80599 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4704.00 | −0.416980 | −0.208490 | − | 0.978024i | \(-0.566855\pi\) | ||||
−0.208490 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11456.0 | −1.00948 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20530.0 | −1.79836 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10788.0 | −0.939430 | −0.469715 | − | 0.882818i | \(-0.655643\pi\) | ||||
−0.469715 | + | 0.882818i | \(0.655643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1106.00 | −0.0957467 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11960.0 | −1.02933 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6112.00 | 0.522965 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15840.0 | 1.34747 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −34760.0 | −2.93987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14586.0 | −1.22653 | −0.613267 | − | 0.789876i | \(-0.710145\pi\) | ||||
−0.613267 | + | 0.789876i | \(0.710145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.0000 | −0.00217381 | −0.00108690 | − | 0.999999i | \(-0.500346\pi\) | ||||
−0.00108690 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4270.00 | −0.354968 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14616.0 | 1.20813 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8071.00 | −0.663352 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20002.0 | −1.63468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −72.0000 | −0.00585116 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2592.00 | 0.209462 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22680.0 | −1.82256 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1960.00 | 0.156629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11214.0 | 0.891178 | 0.445589 | − | 0.895238i | \(-0.352994\pi\) | ||||
0.445589 | + | 0.895238i | \(0.352994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2760.00 | −0.218127 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10672.0 | 0.838786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5424.00 | 0.423973 | 0.211987 | − | 0.977273i | \(-0.432007\pi\) | ||||
0.211987 | + | 0.977273i | \(0.432007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −42048.0 | −3.26879 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1612.00 | 0.124634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6552.00 | 0.503833 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2080.00 | −0.159083 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17618.0 | −1.34021 | −0.670106 | − | 0.742265i | \(-0.733752\pi\) | ||||
−0.670106 | + | 0.742265i | \(0.733752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4992.00 | 0.377709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23200.0 | −1.74600 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3562.00 | 0.266644 | 0.133322 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133322 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14384.0 | −1.07104 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18403.0 | 1.36306 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2838.00 | 0.209095 | 0.104548 | − | 0.994520i | \(-0.466661\pi\) | ||||
0.104548 | + | 0.994520i | \(0.466661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 360.000 | 0.0263845 | 0.0131922 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131922 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30000.0 | 2.18720 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3904.00 | −0.283144 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22018.0 | 1.58860 | 0.794299 | − | 0.607527i | \(-0.207838\pi\) | ||||
0.794299 | + | 0.607527i | \(0.207838\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 32780.0 | 2.35283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3710.00 | −0.264917 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18000.0 | −1.27870 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7008.00 | 0.495291 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1454.00 | −0.102237 | −0.0511184 | − | 0.998693i | \(-0.516279\pi\) | ||||
−0.0511184 | + | 0.998693i | \(0.516279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6552.00 | 0.458354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23620.0 | −1.64399 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13818.0 | 0.956892 | 0.478446 | − | 0.878117i | \(-0.341200\pi\) | ||||
0.478446 | + | 0.878117i | \(0.341200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3248.00 | 0.223790 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10360.0 | 0.710229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6696.00 | −0.456746 | −0.228373 | − | 0.973574i | \(-0.573341\pi\) | ||||
−0.228373 | + | 0.973574i | \(0.573341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10010.0 | 0.679395 | 0.339698 | − | 0.940535i | \(-0.389675\pi\) | ||||
0.339698 | + | 0.940535i | \(0.389675\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34748.0 | 2.34668 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2152.00 | −0.144614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2880.00 | −0.192579 | −0.0962896 | − | 0.995353i | \(-0.530697\pi\) | ||||
−0.0962896 | + | 0.995353i | \(0.530697\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4340.00 | −0.288778 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4752.00 | −0.314640 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6522.00 | 0.429724 | 0.214862 | − | 0.976644i | \(-0.431070\pi\) | ||||
0.214862 | + | 0.976644i | \(0.431070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −480.000 | −0.0314723 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6614.00 | 0.431555 | 0.215778 | − | 0.976443i | \(-0.430771\pi\) | ||||
0.215778 | + | 0.976443i | \(0.430771\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5266.00 | −0.341936 | −0.170968 | − | 0.985277i | \(-0.554689\pi\) | ||||
−0.170968 | + | 0.985277i | \(0.554689\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29440.0 | 1.90239 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2730.00 | −0.175562 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4279.00 | −0.273856 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10400.0 | −0.662418 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1508.00 | −0.0955928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3344.00 | −0.210971 | −0.105485 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105485 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35240.0 | −2.21274 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3072.00 | −0.191982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −588.000 | −0.0365736 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32704.0 | 2.02465 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4882.00 | −0.300823 | −0.150411 | − | 0.988623i | \(-0.548060\pi\) | ||||
−0.150411 | + | 0.988623i | \(0.548060\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15898.0 | 0.975048 | 0.487524 | − | 0.873110i | \(-0.337900\pi\) | ||||
0.487524 | + | 0.873110i | \(0.337900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33280.0 | 2.03163 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6132.00 | −0.372602 | −0.186301 | − | 0.982493i | \(-0.559650\pi\) | ||||
−0.186301 | + | 0.982493i | \(0.559650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10960.0 | −0.662893 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17640.0 | −1.06201 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24198.0 | −1.45014 | −0.725070 | − | 0.688676i | \(-0.758192\pi\) | ||||
−0.725070 | + | 0.688676i | \(0.758192\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14512.0 | −0.865696 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11534.0 | −0.684907 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17456.0 | −1.03185 | −0.515925 | − | 0.856634i | \(-0.672552\pi\) | ||||
−0.515925 | + | 0.856634i | \(0.672552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −656.000 | −0.0386013 | −0.0193006 | − | 0.999814i | \(-0.506144\pi\) | ||||
−0.0193006 | + | 0.999814i | \(0.506144\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6960.00 | 0.407698 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1456.00 | 0.0849041 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3968.00 | −0.230347 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13360.0 | 0.772089 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23040.0 | −1.32556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18214.0 | −1.04324 | −0.521618 | − | 0.853179i | \(-0.674671\pi\) | ||||
−0.521618 | + | 0.853179i | \(0.674671\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −28060.0 | −1.60004 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30252.0 | 1.71740 | 0.858699 | − | 0.512480i | \(-0.171273\pi\) | ||||
0.858699 | + | 0.512480i | \(0.171273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1498.00 | 0.0846656 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12900.0 | −0.725887 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10836.0 | 0.607069 | 0.303534 | − | 0.952820i | \(-0.401833\pi\) | ||||
0.303534 | + | 0.952820i | \(0.401833\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13328.0 | −0.743411 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 55240.0 | 3.06774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5400.00 | 0.298583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9578.00 | −0.527300 | −0.263650 | − | 0.964618i | \(-0.584926\pi\) | ||||
−0.263650 | + | 0.964618i | \(0.584926\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20440.0 | 1.12042 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9008.00 | 0.491644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −348.000 | −0.0189117 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 63140.0 | 3.41656 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12442.0 | 0.670368 | 0.335184 | − | 0.942153i | \(-0.391202\pi\) | ||||
0.335184 | + | 0.942153i | \(0.391202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −676.000 | −0.0362672 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31680.0 | −1.69239 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10024.0 | 0.533227 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25174.0 | −1.33347 | −0.666734 | − | 0.745295i | \(-0.732308\pi\) | ||||
−0.666734 | + | 0.745295i | \(0.732308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 68328.0 | 3.60408 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16128.0 | −0.847123 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3840.00 | 0.200850 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39600.0 | 2.06261 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34188.0 | −1.77329 | −0.886646 | − | 0.462448i | \(-0.846971\pi\) | ||||
−0.886646 | + | 0.462448i | \(0.846971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5348.00 | −0.276241 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −70180.0 | −3.60999 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3782.00 | 0.193738 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5204.00 | 0.265482 | 0.132741 | − | 0.991151i | \(-0.457622\pi\) | ||||
0.132741 | + | 0.991151i | \(0.457622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 67717.0 | 3.44038 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24128.0 | 1.22080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32880.0 | −1.65682 | −0.828411 | − | 0.560121i | \(-0.810755\pi\) | ||||
−0.828411 | + | 0.560121i | \(0.810755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3920.00 | −0.196723 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19040.0 | 0.951625 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3912.00 | 0.194730 | 0.0973648 | − | 0.995249i | \(-0.468959\pi\) | ||||
0.0973648 | + | 0.995249i | \(0.468959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3120.00 | 0.154678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16008.0 | 0.790413 | 0.395206 | − | 0.918592i | \(-0.370673\pi\) | ||||
0.395206 | + | 0.918592i | \(0.370673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21552.0 | −1.05987 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −38690.0 | −1.89504 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2268.00 | −0.110642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9960.00 | −0.483949 | −0.241974 | − | 0.970283i | \(-0.577795\pi\) | ||||
−0.241974 | + | 0.970283i | \(0.577795\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23940.0 | 1.15860 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21184.0 | −1.02115 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12378.0 | 0.594301 | 0.297151 | − | 0.954831i | \(-0.403964\pi\) | ||||
0.297151 | + | 0.954831i | \(0.403964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25600.0 | 1.22427 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34670.0 | 1.65149 | 0.825747 | − | 0.564041i | \(-0.190754\pi\) | ||||
0.825747 | + | 0.564041i | \(0.190754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9338.00 | −0.443065 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33872.0 | 1.60084 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3288.00 | 0.154789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10898.0 | −0.511043 | −0.255521 | − | 0.966803i | \(-0.582247\pi\) | ||||
−0.255521 | + | 0.966803i | \(0.582247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27660.0 | −1.29202 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25808.0 | −1.20084 | −0.600420 | − | 0.799685i | \(-0.705000\pi\) | ||||
−0.600420 | + | 0.799685i | \(0.705000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15372.0 | 0.712488 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1820.00 | 0.0840311 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −156.000 | −0.00717494 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17920.0 | 0.821035 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28520.0 | −1.30169 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4448.00 | 0.202237 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21054.0 | 0.953614 | 0.476807 | − | 0.879008i | \(-0.341794\pi\) | ||||
0.476807 | + | 0.879008i | \(0.341794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −79680.0 | −3.59529 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12586.0 | 0.565748 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6912.00 | 0.309524 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36000.0 | 1.60602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24276.0 | −1.07892 | −0.539461 | − | 0.842011i | \(-0.681372\pi\) | ||||
−0.539461 | + | 0.842011i | \(0.681372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22968.0 | −1.01696 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28470.0 | −1.25585 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6320.00 | −0.277743 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3584.00 | −0.156919 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29000.0 | −1.26499 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21526.0 | 0.935493 | 0.467747 | − | 0.883863i | \(-0.345066\pi\) | ||||
0.467747 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12806.0 | 0.554475 | 0.277238 | − | 0.960801i | \(-0.410581\pi\) | ||||
0.277238 | + | 0.960801i | \(0.410581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26400.0 | −1.13885 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2624.00 | −0.112779 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10816.0 | 0.463163 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6132.00 | −0.261623 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13214.0 | 0.561720 | 0.280860 | − | 0.959749i | \(-0.409380\pi\) | ||||
0.280860 | + | 0.959749i | \(0.409380\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32248.0 | −1.36585 | −0.682925 | − | 0.730488i | \(-0.739292\pi\) | ||||
−0.682925 | + | 0.730488i | \(0.739292\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24400.0 | −1.02970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14316.0 | 0.601954 | 0.300977 | − | 0.953631i | \(-0.402687\pi\) | ||||
0.300977 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25168.0 | 1.05443 | 0.527214 | − | 0.849733i | \(-0.323237\pi\) | ||||
0.527214 | + | 0.849733i | \(0.323237\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15220.0 | −0.635350 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2842.00 | −0.118211 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34144.0 | −1.41509 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −115920. | −4.78707 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9356.00 | −0.384988 | −0.192494 | − | 0.981298i | \(-0.561658\pi\) | ||||
−0.192494 | + | 0.981298i | \(0.561658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20545.0 | −0.842388 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −45340.0 | −1.85242 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16424.0 | 0.668642 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1883.00 | 0.0763880 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48340.0 | −1.95409 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1664.00 | 0.0670284 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2372.00 | 0.0952119 | 0.0476059 | − | 0.998866i | \(-0.484841\pi\) | ||||
0.0476059 | + | 0.998866i | \(0.484841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15184.0 | 0.607347 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11694.0 | 0.466114 | 0.233057 | − | 0.972463i | \(-0.425127\pi\) | ||||
0.233057 | + | 0.972463i | \(0.425127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20506.0 | 0.814500 | 0.407250 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407250 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 420.000 | 0.0166243 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28136.0 | 1.10980 | 0.554902 | − | 0.831916i | \(-0.312756\pi\) | ||||
0.554902 | + | 0.831916i | \(0.312756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27808.0 | 1.09306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15490.0 | −0.606768 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37440.0 | 1.46152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5712.00 | −0.222209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15622.0 | 0.605641 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10416.0 | 0.402429 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37070.0 | −1.42733 | −0.713663 | − | 0.700489i | \(-0.752965\pi\) | ||||
−0.713663 | + | 0.700489i | \(0.752965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −46560.0 | −1.78661 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6198.00 | −0.237021 | −0.118511 | − | 0.992953i | \(-0.537812\pi\) | ||||
−0.118511 | + | 0.992953i | \(0.537812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31876.0 | 1.21485 | 0.607425 | − | 0.794377i | \(-0.292202\pi\) | ||||
0.607425 | + | 0.794377i | \(0.292202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21920.0 | 0.832579 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 132.000 | 0.00499676 | 0.00249838 | − | 0.999997i | \(-0.499205\pi\) | ||||
0.00249838 | + | 0.999997i | \(0.499205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2688.00 | 0.101409 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 105160. | 3.95398 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10296.0 | −0.385826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18144.0 | 0.677639 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7680.00 | −0.285873 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15624.0 | 0.579632 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26100.0 | 0.965058 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29120.0 | −1.07315 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2208.00 | 0.0811010 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38244.0 | −1.40008 | −0.700039 | − | 0.714104i | \(-0.746834\pi\) | ||||
−0.700039 | + | 0.714104i | \(0.746834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 104536. | 3.81435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7008.00 | 0.254869 | 0.127434 | − | 0.991847i | \(-0.459326\pi\) | ||||
0.127434 | + | 0.991847i | \(0.459326\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21200.0 | −0.768475 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 46080.0 | 1.66487 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12698.0 | 0.457279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36664.0 | −1.31603 | −0.658016 | − | 0.753004i | \(-0.728604\pi\) | ||||
−0.658016 | + | 0.753004i | \(0.728604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 72380.0 | 2.58958 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5376.00 | −0.191715 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1586.00 | −0.0563755 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −55772.0 | −1.97604 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45510.0 | 1.60725 | 0.803625 | − | 0.595136i | \(-0.202902\pi\) | ||||
0.803625 | + | 0.595136i | \(0.202902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1274.00 | −0.0448482 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10960.0 | −0.384581 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18560.0 | 0.649173 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3838.00 | −0.133812 | −0.0669061 | − | 0.997759i | \(-0.521313\pi\) | ||||
−0.0669061 | + | 0.997759i | \(0.521313\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38180.0 | −1.32690 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16832.0 | −0.583111 | −0.291556 | − | 0.956554i | \(-0.594173\pi\) | ||||
−0.291556 | + | 0.956554i | \(0.594173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 384.000 | 0.0132606 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25760.0 | −0.886744 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40928.0 | 1.40442 | 0.702208 | − | 0.711972i | \(-0.252198\pi\) | ||||
0.702208 | + | 0.711972i | \(0.252198\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1896.00 | 0.0648543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19980.0 | 0.681279 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24070.0 | −0.818157 | −0.409079 | − | 0.912499i | \(-0.634150\pi\) | ||||
−0.409079 | + | 0.912499i | \(0.634150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24000.0 | −0.813217 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24800.0 | −0.837691 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11662.0 | 0.392686 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33713.0 | 1.13165 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23652.0 | −0.791459 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26224.0 | −0.874798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17152.0 | 0.570394 | 0.285197 | − | 0.958469i | \(-0.407941\pi\) | ||||
0.285197 | + | 0.958469i | \(0.407941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15080.0 | 0.499937 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32910.0 | 1.08767 | 0.543837 | − | 0.839191i | \(-0.316971\pi\) | ||||
0.543837 | + | 0.839191i | \(0.316971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7882.00 | −0.259697 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7320.00 | 0.240439 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6822.00 | −0.223393 | −0.111697 | − | 0.993742i | \(-0.535628\pi\) | ||||
−0.111697 | + | 0.993742i | \(0.535628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15600.0 | −0.509273 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −97382.0 | −3.16939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48420.0 | 1.57107 | 0.785533 | − | 0.618820i | \(-0.212389\pi\) | ||||
0.785533 | + | 0.618820i | \(0.212389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18896.0 | 0.611245 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27720.0 | 0.893959 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −26624.0 | −0.856010 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49216.0 | 1.57760 | 0.788798 | − | 0.614652i | \(-0.210704\pi\) | ||||
0.788798 | + | 0.614652i | \(0.210704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 79360.0 | 2.53617 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8288.00 | −0.264068 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35264.0 | 1.12018 | 0.560091 | − | 0.828431i | \(-0.310766\pi\) | ||||
0.560091 | + | 0.828431i | \(0.310766\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11960.0 | 0.378776 |
(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 | 112.4.a.g.1.1 | 1 | ||
3.2 | odd | 2 | 1008.4.a.o.1.1 | 1 | |||
4.3 | odd | 2 | 28.4.a.a.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 784.4.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 448.4.a.p.1.1 | 1 | |||
8.5 | even | 2 | 448.4.a.a.1.1 | 1 | |||
12.11 | even | 2 | 252.4.a.d.1.1 | 1 | |||
20.3 | even | 4 | 700.4.e.a.449.1 | 2 | |||
20.7 | even | 4 | 700.4.e.a.449.2 | 2 | |||
20.19 | odd | 2 | 700.4.a.n.1.1 | 1 | |||
28.3 | even | 6 | 196.4.e.a.177.1 | 2 | |||
28.11 | odd | 6 | 196.4.e.f.177.1 | 2 | |||
28.19 | even | 6 | 196.4.e.a.165.1 | 2 | |||
28.23 | odd | 6 | 196.4.e.f.165.1 | 2 | |||
28.27 | even | 2 | 196.4.a.d.1.1 | 1 | |||
84.11 | even | 6 | 1764.4.k.d.1549.1 | 2 | |||
84.23 | even | 6 | 1764.4.k.d.361.1 | 2 | |||
84.47 | odd | 6 | 1764.4.k.m.361.1 | 2 | |||
84.59 | odd | 6 | 1764.4.k.m.1549.1 | 2 | |||
84.83 | odd | 2 | 1764.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
112.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
196.4.a.d.1.1 | 1 | 28.27 | even | 2 | |||
196.4.e.a.165.1 | 2 | 28.19 | even | 6 | |||
196.4.e.a.177.1 | 2 | 28.3 | even | 6 | |||
196.4.e.f.165.1 | 2 | 28.23 | odd | 6 | |||
196.4.e.f.177.1 | 2 | 28.11 | odd | 6 | |||
252.4.a.d.1.1 | 1 | 12.11 | even | 2 | |||
448.4.a.a.1.1 | 1 | 8.5 | even | 2 | |||
448.4.a.p.1.1 | 1 | 8.3 | odd | 2 | |||
700.4.a.n.1.1 | 1 | 20.19 | odd | 2 | |||
700.4.e.a.449.1 | 2 | 20.3 | even | 4 | |||
700.4.e.a.449.2 | 2 | 20.7 | even | 4 | |||
784.4.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
1008.4.a.o.1.1 | 1 | 3.2 | odd | 2 | |||
1764.4.a.c.1.1 | 1 | 84.83 | odd | 2 | |||
1764.4.k.d.361.1 | 2 | 84.23 | even | 6 | |||
1764.4.k.d.1549.1 | 2 | 84.11 | even | 6 | |||
1764.4.k.m.361.1 | 2 | 84.47 | odd | 6 | |||
1764.4.k.m.1549.1 | 2 | 84.59 | odd | 6 |