Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,4,Mod(1,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.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: | \(39.6492835239\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 672.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.00000 | 0.536656 | 0.268328 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268328 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −0.109640 | −0.0548202 | − | 0.998496i | \(-0.517459\pi\) | ||||
−0.0548202 | + | 0.998496i | \(0.517459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.0000 | −0.981393 | −0.490696 | − | 0.871331i | \(-0.663258\pi\) | ||||
−0.490696 | + | 0.871331i | \(0.663258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.0000 | −0.309839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −82.0000 | −1.16988 | −0.584939 | − | 0.811077i | \(-0.698882\pi\) | ||||
−0.584939 | + | 0.811077i | \(0.698882\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 84.0000 | 1.01426 | 0.507130 | − | 0.861870i | \(-0.330707\pi\) | ||||
0.507130 | + | 0.861870i | \(0.330707\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 44.0000 | 0.398897 | 0.199449 | − | 0.979908i | \(-0.436085\pi\) | ||||
0.199449 | + | 0.979908i | \(0.436085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 70.0000 | 0.448230 | 0.224115 | − | 0.974563i | \(-0.428051\pi\) | ||||
0.224115 | + | 0.974563i | \(0.428051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.000 | −0.880645 | −0.440323 | − | 0.897840i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897840i | \(0.645136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0000 | 0.0633010 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.0000 | 0.202837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −146.000 | −0.648710 | −0.324355 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324355 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 138.000 | 0.566607 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 94.0000 | 0.358057 | 0.179028 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179028 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 488.000 | 1.73068 | 0.865341 | − | 0.501184i | \(-0.167102\pi\) | ||||
0.865341 | + | 0.501184i | \(0.167102\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 54.0000 | 0.178885 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −32.0000 | −0.0993123 | −0.0496562 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496562 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 246.000 | 0.675429 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −562.000 | −1.45654 | −0.728270 | − | 0.685290i | \(-0.759675\pi\) | ||||
−0.728270 | + | 0.685290i | \(0.759675\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.0000 | −0.0588393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −252.000 | −0.585583 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −476.000 | −1.05034 | −0.525169 | − | 0.850998i | \(-0.675998\pi\) | ||||
−0.525169 | + | 0.850998i | \(0.675998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.0000 | 0.0713648 | 0.0356824 | − | 0.999363i | \(-0.488640\pi\) | ||||
0.0356824 | + | 0.999363i | \(0.488640\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −276.000 | −0.526671 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −520.000 | −0.948181 | −0.474090 | − | 0.880476i | \(-0.657223\pi\) | ||||
−0.474090 | + | 0.880476i | \(0.657223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −132.000 | −0.230303 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36.0000 | −0.0601748 | −0.0300874 | − | 0.999547i | \(-0.509579\pi\) | ||||
−0.0300874 | + | 0.999547i | \(0.509579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −654.000 | −1.04856 | −0.524280 | − | 0.851546i | \(-0.675666\pi\) | ||||
−0.524280 | + | 0.851546i | \(0.675666\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 267.000 | 0.411073 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −28.0000 | −0.0414402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −608.000 | −0.865890 | −0.432945 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432945 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 284.000 | 0.375579 | 0.187789 | − | 0.982209i | \(-0.439868\pi\) | ||||
0.187789 | + | 0.982209i | \(0.439868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −492.000 | −0.627822 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −210.000 | −0.258786 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −954.000 | −1.13622 | −0.568111 | − | 0.822952i | \(-0.692326\pi\) | ||||
−0.568111 | + | 0.822952i | \(0.692326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −322.000 | −0.370932 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 456.000 | 0.508441 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 504.000 | 0.544309 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1694.00 | −1.77319 | −0.886596 | − | 0.462544i | \(-0.846937\pi\) | ||||
−0.886596 | + | 0.462544i | \(0.846937\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −36.0000 | −0.0365468 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 318.000 | 0.313289 | 0.156644 | − | 0.987655i | \(-0.449932\pi\) | ||||
0.156644 | + | 0.987655i | \(0.449932\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −872.000 | −0.834182 | −0.417091 | − | 0.908865i | \(-0.636950\pi\) | ||||
−0.417091 | + | 0.908865i | \(0.636950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −126.000 | −0.117108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −364.000 | −0.328871 | −0.164436 | − | 0.986388i | \(-0.552580\pi\) | ||||
−0.164436 | + | 0.986388i | \(0.552580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 838.000 | 0.736384 | 0.368192 | − | 0.929750i | \(-0.379977\pi\) | ||||
0.368192 | + | 0.929750i | \(0.379977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 438.000 | 0.374533 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −366.000 | −0.304694 | −0.152347 | − | 0.988327i | \(-0.548683\pi\) | ||||
−0.152347 | + | 0.988327i | \(0.548683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 264.000 | 0.214071 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −414.000 | −0.327131 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −574.000 | −0.442172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1315.00 | −0.987979 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −282.000 | −0.206724 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1284.00 | −0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −536.000 | −0.374506 | −0.187253 | − | 0.982312i | \(-0.559958\pi\) | ||||
−0.187253 | + | 0.982312i | \(0.559958\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1464.00 | −0.999209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1980.00 | 1.32056 | 0.660280 | − | 0.751019i | \(-0.270438\pi\) | ||||
0.660280 | + | 0.751019i | \(0.270438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 588.000 | 0.383354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −162.000 | −0.103280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2878.00 | −1.79477 | −0.897387 | − | 0.441244i | \(-0.854537\pi\) | ||||
−0.897387 | + | 0.441244i | \(0.854537\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1436.00 | −0.876258 | −0.438129 | − | 0.898912i | \(-0.644359\pi\) | ||||
−0.438129 | + | 0.898912i | \(0.644359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 96.0000 | 0.0573380 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 184.000 | 0.107600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 420.000 | 0.240546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1374.00 | 0.755453 | 0.377726 | − | 0.925917i | \(-0.376706\pi\) | ||||
0.377726 | + | 0.925917i | \(0.376706\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 688.000 | 0.370786 | 0.185393 | − | 0.982664i | \(-0.440644\pi\) | ||||
0.185393 | + | 0.982664i | \(0.440644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −738.000 | −0.389959 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −912.000 | −0.472604 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.00305001 | −0.00152501 | − | 0.999999i | \(-0.500485\pi\) | ||||
−0.00152501 | + | 0.999999i | \(0.500485\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1686.00 | 0.840934 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 308.000 | 0.150769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −0.00768845 | −0.00384422 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384422 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 72.0000 | 0.0339709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1952.00 | 0.904493 | 0.452246 | − | 0.891893i | \(-0.350623\pi\) | ||||
0.452246 | + | 0.891893i | \(0.350623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −81.0000 | −0.0368685 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 756.000 | 0.338086 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −642.000 | −0.282141 | −0.141070 | − | 0.990000i | \(-0.545054\pi\) | ||||
−0.141070 | + | 0.990000i | \(0.545054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −623.000 | −0.269111 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1428.00 | 0.606413 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −468.000 | −0.195419 | −0.0977094 | − | 0.995215i | \(-0.531152\pi\) | ||||
−0.0977094 | + | 0.995215i | \(0.531152\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 138.000 | 0.0566710 | 0.0283355 | − | 0.999598i | \(-0.490979\pi\) | ||||
0.0283355 | + | 0.999598i | \(0.490979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −102.000 | −0.0412025 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −876.000 | −0.348134 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 328.000 | 0.128266 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1980.00 | 0.750093 | 0.375047 | − | 0.927006i | \(-0.377627\pi\) | ||||
0.375047 | + | 0.927006i | \(0.377627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1294.00 | −0.482612 | −0.241306 | − | 0.970449i | \(-0.577576\pi\) | ||||
−0.241306 | + | 0.970449i | \(0.577576\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 828.000 | 0.304073 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4542.00 | 1.64266 | 0.821330 | − | 0.570453i | \(-0.193232\pi\) | ||||
0.821330 | + | 0.570453i | \(0.193232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2992.00 | −1.06582 | −0.532908 | − | 0.846173i | \(-0.678901\pi\) | ||||
−0.532908 | + | 0.846173i | \(0.678901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1560.00 | 0.547432 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 490.000 | 0.169415 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 564.000 | 0.192154 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 396.000 | 0.132966 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −336.000 | −0.111204 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3344.00 | −1.09104 | −0.545522 | − | 0.838096i | \(-0.683669\pi\) | ||||
−0.545522 | + | 0.838096i | \(0.683669\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 108.000 | 0.0347420 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2928.00 | 0.928781 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1064.00 | −0.332853 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1962.00 | 0.605387 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3772.00 | 1.14811 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5640.00 | −1.69364 | −0.846821 | − | 0.531877i | \(-0.821487\pi\) | ||||
−0.846821 | + | 0.531877i | \(0.821487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −801.000 | −0.237333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2660.00 | 0.777755 | 0.388878 | − | 0.921289i | \(-0.372863\pi\) | ||||
0.388878 | + | 0.921289i | \(0.372863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5626.00 | 1.62348 | 0.811739 | − | 0.584020i | \(-0.198521\pi\) | ||||
0.811739 | + | 0.584020i | \(0.198521\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 84.0000 | 0.0239255 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −606.000 | −0.170388 | −0.0851939 | − | 0.996364i | \(-0.527151\pi\) | ||||
−0.0851939 | + | 0.996364i | \(0.527151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −192.000 | −0.0532966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1824.00 | 0.499922 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6300.00 | 1.70508 | 0.852538 | − | 0.522665i | \(-0.175062\pi\) | ||||
0.852538 | + | 0.522665i | \(0.175062\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2210.00 | 0.590700 | 0.295350 | − | 0.955389i | \(-0.404564\pi\) | ||||
0.295350 | + | 0.955389i | \(0.404564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 294.000 | 0.0766652 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3864.00 | −0.995386 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −852.000 | −0.216841 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5044.00 | −1.26842 | −0.634212 | − | 0.773159i | \(-0.718675\pi\) | ||||
−0.634212 | + | 0.773159i | \(0.718675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −176.000 | −0.0437353 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1476.00 | 0.362473 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −98.0000 | −0.0237863 | −0.0118931 | − | 0.999929i | \(-0.503786\pi\) | ||||
−0.0118931 | + | 0.999929i | \(0.503786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1022.00 | −0.245189 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 630.000 | 0.149410 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5732.00 | 1.34392 | 0.671959 | − | 0.740589i | \(-0.265453\pi\) | ||||
0.671959 | + | 0.740589i | \(0.265453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3372.00 | −0.781662 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2862.00 | 0.655998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 630.000 | 0.142795 | 0.0713974 | − | 0.997448i | \(-0.477254\pi\) | ||||
0.0713974 | + | 0.997448i | \(0.477254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2560.00 | 0.573834 | 0.286917 | − | 0.957955i | \(-0.407370\pi\) | ||||
0.286917 | + | 0.957955i | \(0.407370\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 966.000 | 0.214157 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 356.000 | 0.0780640 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2266.00 | −0.491519 | −0.245759 | − | 0.969331i | \(-0.579037\pi\) | ||||
−0.245759 | + | 0.969331i | \(0.579037\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1368.00 | −0.293548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4338.00 | 0.920937 | 0.460469 | − | 0.887676i | \(-0.347681\pi\) | ||||
0.460469 | + | 0.887676i | \(0.347681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6364.00 | −1.33675 | −0.668376 | − | 0.743824i | \(-0.733010\pi\) | ||||
−0.668376 | + | 0.743824i | \(0.733010\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1512.00 | −0.314257 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 658.000 | 0.135333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1811.00 | 0.368614 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5082.00 | 1.02375 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1778.00 | −0.354511 | −0.177256 | − | 0.984165i | \(-0.556722\pi\) | ||||
−0.177256 | + | 0.984165i | \(0.556722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2856.00 | −0.563670 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 108.000 | 0.0211003 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2024.00 | −0.391475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3416.00 | 0.654136 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −954.000 | −0.180877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 204.000 | 0.0382984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1364.00 | 0.253575 | 0.126788 | − | 0.991930i | \(-0.459533\pi\) | ||||
0.126788 | + | 0.991930i | \(0.459533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2616.00 | 0.481615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7512.00 | −1.36967 | −0.684834 | − | 0.728700i | \(-0.740125\pi\) | ||||
−0.684834 | + | 0.728700i | \(0.740125\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2914.00 | 0.526227 | 0.263113 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 378.000 | 0.0676123 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7846.00 | 1.39014 | 0.695071 | − | 0.718941i | \(-0.255373\pi\) | ||||
0.695071 | + | 0.718941i | \(0.255373\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −280.000 | −0.0491442 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1092.00 | 0.189874 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6888.00 | −1.18656 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4094.00 | 0.698752 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2514.00 | −0.425151 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −224.000 | −0.0375365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.0000 | 0.00398538 | 0.00199269 | − | 0.999998i | \(-0.499366\pi\) | ||||
0.00199269 | + | 0.999998i | \(0.499366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1314.00 | −0.216237 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3120.00 | −0.508847 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5970.00 | 0.965005 | 0.482502 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482502 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1098.00 | 0.175915 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 608.000 | 0.0965544 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −792.000 | −0.123594 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10212.0 | 1.57985 | 0.789926 | − | 0.613202i | \(-0.210119\pi\) | ||||
0.789926 | + | 0.613202i | \(0.210119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3914.00 | 0.600320 | 0.300160 | − | 0.953889i | \(-0.402960\pi\) | ||||
0.300160 | + | 0.953889i | \(0.402960\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1242.00 | 0.188869 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3222.00 | 0.485807 | 0.242903 | − | 0.970050i | \(-0.421900\pi\) | ||||
0.242903 | + | 0.970050i | \(0.421900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −216.000 | −0.0322932 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1722.00 | 0.255288 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3140.00 | 0.461624 | 0.230812 | − | 0.972998i | \(-0.425862\pi\) | ||||
0.230812 | + | 0.972998i | \(0.425862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 197.000 | 0.0287214 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3945.00 | 0.570410 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3924.00 | −0.562717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6680.00 | −0.950118 | −0.475059 | − | 0.879954i | \(-0.657573\pi\) | ||||
−0.475059 | + | 0.879954i | \(0.657573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 846.000 | 0.119352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3934.00 | −0.550520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7830.00 | 1.08692 | 0.543461 | − | 0.839434i | \(-0.317114\pi\) | ||||
0.543461 | + | 0.839434i | \(0.317114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3852.00 | 0.530444 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3220.00 | −0.439890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11368.0 | −1.54073 | −0.770363 | − | 0.637606i | \(-0.779925\pi\) | ||||
−0.770363 | + | 0.637606i | \(0.779925\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1608.00 | 0.216221 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −136.000 | −0.0181443 | −0.00907216 | − | 0.999959i | \(-0.502888\pi\) | ||||
−0.00907216 | + | 0.999959i | \(0.502888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −168.000 | −0.0222392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4392.00 | 0.576894 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13374.0 | 1.74316 | 0.871579 | − | 0.490255i | \(-0.163096\pi\) | ||||
0.871579 | + | 0.490255i | \(0.163096\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3608.00 | −0.466661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5940.00 | −0.762426 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3648.00 | −0.464686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6406.00 | −0.809844 | −0.404922 | − | 0.914351i | \(-0.632701\pi\) | ||||
−0.404922 | + | 0.914351i | \(0.632701\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1764.00 | −0.221329 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3958.00 | −0.492900 | −0.246450 | − | 0.969155i | \(-0.579264\pi\) | ||||
−0.246450 | + | 0.969155i | \(0.579264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6992.00 | 0.864259 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 486.000 | 0.0596285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 584.000 | 0.0711248 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12614.0 | −1.52499 | −0.762497 | − | 0.646992i | \(-0.776027\pi\) | ||||
−0.762497 | + | 0.646992i | \(0.776027\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8634.00 | 1.03621 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3332.00 | −0.396990 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1704.00 | 0.201557 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4308.00 | 0.505908 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1404.00 | 0.163699 | 0.0818495 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818495 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1482.00 | −0.171564 | −0.0857818 | − | 0.996314i | \(-0.527339\pi\) | ||||
−0.0857818 | + | 0.996314i | \(0.527339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −288.000 | −0.0331041 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7298.00 | 0.832953 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 238.000 | 0.0269734 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −552.000 | −0.0621231 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14228.0 | 1.59011 | 0.795056 | − | 0.606535i | \(-0.207441\pi\) | ||||
0.795056 | + | 0.606535i | \(0.207441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11674.0 | 1.29565 | 0.647825 | − | 0.761789i | \(-0.275679\pi\) | ||||
0.647825 | + | 0.761789i | \(0.275679\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1260.00 | −0.138879 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3696.00 | 0.404585 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14712.0 | −1.59947 | −0.799733 | − | 0.600356i | \(-0.795026\pi\) | ||||
−0.799733 | + | 0.600356i | \(0.795026\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2940.00 | 0.315313 | 0.157656 | − | 0.987494i | \(-0.449606\pi\) | ||||
0.157656 | + | 0.987494i | \(0.449606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5724.00 | −0.609761 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4122.00 | −0.436161 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4818.00 | 0.506404 | 0.253202 | − | 0.967413i | \(-0.418516\pi\) | ||||
0.253202 | + | 0.967413i | \(0.418516\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −376.000 | −0.0392575 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2064.00 | −0.214073 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1932.00 | −0.199063 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2122.00 | 0.217206 | 0.108603 | − | 0.994085i | \(-0.465362\pi\) | ||||
0.108603 | + | 0.994085i | \(0.465362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2214.00 | 0.225143 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15010.0 | −1.51645 | −0.758227 | − | 0.651991i | \(-0.773934\pi\) | ||||
−0.758227 | + | 0.651991i | \(0.773934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5712.00 | −0.573346 | −0.286673 | − | 0.958029i | \(-0.592549\pi\) | ||||
−0.286673 | + | 0.958029i | \(0.592549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2736.00 | 0.272858 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10356.0 | 1.02616 | 0.513082 | − | 0.858340i | \(-0.328504\pi\) | ||||
0.513082 | + | 0.858340i | \(0.328504\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3640.00 | −0.358379 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | 0.00176093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1952.00 | −0.189753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7476.00 | −0.722152 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5058.00 | −0.485513 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16992.0 | 1.62084 | 0.810422 | − | 0.585847i | \(-0.199238\pi\) | ||||
0.810422 | + | 0.585847i | \(0.199238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6716.00 | 0.636639 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −924.000 | −0.0870465 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10164.0 | −0.951595 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12000.0 | 1.11657 | 0.558287 | − | 0.829648i | \(-0.311459\pi\) | ||||
0.558287 | + | 0.829648i | \(0.311459\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.0000 | 0.00443893 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4804.00 | −0.441551 | −0.220775 | − | 0.975325i | \(-0.570859\pi\) | ||||
−0.220775 | + | 0.975325i | \(0.570859\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5740.00 | −0.524374 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −216.000 | −0.0196131 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −252.000 | −0.0227440 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11696.0 | 1.04927 | 0.524634 | − | 0.851328i | \(-0.324202\pi\) | ||||
0.524634 | + | 0.851328i | \(0.324202\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5856.00 | −0.522209 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3328.00 | −0.295006 | −0.147503 | − | 0.989062i | \(-0.547124\pi\) | ||||
−0.147503 | + | 0.989062i | \(0.547124\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1908.00 | 0.168128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 243.000 | 0.0212860 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15290.0 | −1.33147 | −0.665734 | − | 0.746189i | \(-0.731881\pi\) | ||||
−0.665734 | + | 0.746189i | \(0.731881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4578.00 | −0.396319 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2268.00 | −0.195194 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5232.00 | −0.447669 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 128.000 | 0.0108887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1926.00 | 0.162894 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1946.00 | −0.163639 | −0.0818194 | − | 0.996647i | \(-0.526073\pi\) | ||||
−0.0818194 | + | 0.996647i | \(0.526073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11468.0 | 0.958816 | 0.479408 | − | 0.877592i | \(-0.340851\pi\) | ||||
0.479408 | + | 0.877592i | \(0.340851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1869.00 | 0.155371 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12464.0 | 1.03025 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10231.0 | −0.840881 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4284.00 | −0.350113 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4324.00 | −0.351394 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2184.00 | −0.176491 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1404.00 | 0.112825 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −196.000 | −0.0156629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20178.0 | −1.60355 | −0.801774 | − | 0.597627i | \(-0.796110\pi\) | ||||
−0.801774 | + | 0.597627i | \(0.796110\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −414.000 | −0.0327190 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5028.00 | 0.395185 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4864.00 | −0.380200 | −0.190100 | − | 0.981765i | \(-0.560881\pi\) | ||||
−0.190100 | + | 0.981765i | \(0.560881\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 306.000 | 0.0237883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5880.00 | 0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4256.00 | −0.327276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2628.00 | 0.200995 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13722.0 | −1.04384 | −0.521921 | − | 0.852994i | \(-0.674784\pi\) | ||||
−0.521921 | + | 0.852994i | \(0.674784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22448.0 | −1.69848 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −984.000 | −0.0740544 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26468.0 | −1.98134 | −0.990669 | − | 0.136290i | \(-0.956482\pi\) | ||||
−0.990669 | + | 0.136290i | \(0.956482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2196.00 | −0.163516 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7518.00 | −0.553903 | −0.276952 | − | 0.960884i | \(-0.589324\pi\) | ||||
−0.276952 | + | 0.960884i | \(0.589324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16432.0 | 1.20430 | 0.602152 | − | 0.798381i | \(-0.294310\pi\) | ||||
0.602152 | + | 0.798381i | \(0.294310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5940.00 | −0.433066 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3916.00 | −0.284015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5822.00 | −0.420057 | −0.210029 | − | 0.977695i | \(-0.567356\pi\) | ||||
−0.210029 | + | 0.977695i | \(0.567356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3882.00 | 0.278636 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1988.00 | 0.141955 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2248.00 | 0.159696 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2484.00 | −0.175557 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21540.0 | −1.51457 | −0.757284 | − | 0.653086i | \(-0.773474\pi\) | ||||
−0.757284 | + | 0.653086i | \(0.773474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12768.0 | −0.893203 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13626.0 | −0.948390 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3066.00 | −0.212320 | −0.106160 | − | 0.994349i | \(-0.533856\pi\) | ||||
−0.106160 | + | 0.994349i | \(0.533856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3444.00 | −0.237295 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8976.00 | 0.615349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20652.0 | 1.40871 | 0.704355 | − | 0.709847i | \(-0.251236\pi\) | ||||
0.704355 | + | 0.709847i | \(0.251236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6074.00 | 0.412252 | 0.206126 | − | 0.978525i | \(-0.433914\pi\) | ||||
0.206126 | + | 0.978525i | \(0.433914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4680.00 | −0.316060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7890.00 | −0.530205 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8136.00 | 0.544036 | 0.272018 | − | 0.962292i | \(-0.412309\pi\) | ||||
0.272018 | + | 0.962292i | \(0.412309\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1470.00 | −0.0978118 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1472.00 | 0.0974644 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5102.00 | 0.336163 | 0.168081 | − | 0.985773i | \(-0.446243\pi\) | ||||
0.168081 | + | 0.985773i | \(0.446243\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1692.00 | −0.110940 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3074.00 | 0.200575 | 0.100287 | − | 0.994959i | \(-0.468024\pi\) | ||||
0.100287 | + | 0.994959i | \(0.468024\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5156.00 | −0.334793 | −0.167397 | − | 0.985890i | \(-0.553536\pi\) | ||||
−0.167397 | + | 0.985890i | \(0.553536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1188.00 | −0.0767678 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6678.00 | −0.429452 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1008.00 | 0.0642036 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11972.0 | 0.758911 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20320.0 | 1.28198 | 0.640988 | − | 0.767551i | \(-0.278525\pi\) | ||||
0.640988 | + | 0.767551i | \(0.278525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10032.0 | 0.629915 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3216.00 | −0.200981 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2254.00 | −0.140199 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −324.000 | −0.0200583 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14842.0 | 0.914546 | 0.457273 | − | 0.889326i | \(-0.348826\pi\) | ||||
0.457273 | + | 0.889326i | \(0.348826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14516.0 | −0.890288 | −0.445144 | − | 0.895459i | \(-0.646848\pi\) | ||||
−0.445144 | + | 0.895459i | \(0.646848\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8784.00 | −0.536232 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6096.00 | 0.370415 | 0.185207 | − | 0.982699i | \(-0.440704\pi\) | ||||
0.185207 | + | 0.982699i | \(0.440704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1904.00 | 0.115160 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3192.00 | 0.192173 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8650.00 | −0.518378 | −0.259189 | − | 0.965827i | \(-0.583455\pi\) | ||||
−0.259189 | + | 0.965827i | \(0.583455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11880.0 | 0.708687 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5886.00 | −0.349520 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22260.0 | −1.31582 | −0.657911 | − | 0.753096i | \(-0.728560\pi\) | ||||
−0.657911 | + | 0.753096i | \(0.728560\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14406.0 | −0.847698 | −0.423849 | − | 0.905733i | \(-0.639321\pi\) | ||||
−0.423849 | + | 0.905733i | \(0.639321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11316.0 | −0.662861 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3528.00 | 0.205729 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3080.00 | 0.178798 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16920.0 | 0.977825 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −136.000 | −0.00782447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8334.00 | −0.477343 | −0.238672 | − | 0.971100i | \(-0.576712\pi\) | ||||
−0.238672 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2403.00 | 0.137024 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22314.0 | −1.26676 | −0.633380 | − | 0.773841i | \(-0.718333\pi\) | ||||
−0.633380 | + | 0.773841i | \(0.718333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11858.0 | −0.670204 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7980.00 | −0.449037 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13692.0 | 0.767071 | 0.383536 | − | 0.923526i | \(-0.374706\pi\) | ||||
0.383536 | + | 0.923526i | \(0.374706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17268.0 | −0.963177 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16878.0 | −0.937316 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25852.0 | 1.42944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29020.0 | 1.59765 | 0.798823 | − | 0.601567i | \(-0.205457\pi\) | ||||
0.798823 | + | 0.601567i | \(0.205457\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −252.000 | −0.0138134 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8616.00 | −0.470250 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7708.00 | −0.418883 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1818.00 | 0.0983735 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16410.0 | −0.884161 | −0.442081 | − | 0.896975i | \(-0.645760\pi\) | ||||
−0.442081 | + | 0.896975i | \(0.645760\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12264.0 | −0.657959 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 576.000 | 0.0307708 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2226.00 | 0.118412 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11170.0 | −0.591676 | −0.295838 | − | 0.955238i | \(-0.595599\pi\) | ||||
−0.295838 | + | 0.955238i | \(0.595599\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5472.00 | −0.288630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6688.00 | −0.351287 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1104.00 | 0.0577444 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18900.0 | −0.984426 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22728.0 | 1.17888 | 0.589438 | − | 0.807814i | \(-0.299349\pi\) | ||||
0.589438 | + | 0.807814i | \(0.299349\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6104.00 | −0.315291 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6630.00 | −0.341041 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6230.00 | −0.319140 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1288.00 | −0.0657074 | −0.0328537 | − | 0.999460i | \(-0.510460\pi\) | ||||
−0.0328537 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40016.0 | −2.02469 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 266.000 | 0.0134037 | 0.00670187 | − | 0.999978i | \(-0.497867\pi\) | ||||
0.00670187 | + | 0.999978i | \(0.497867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −882.000 | −0.0442627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2080.00 | 0.103959 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25280.0 | 1.25838 | 0.629188 | − | 0.777253i | \(-0.283388\pi\) | ||||
0.629188 | + | 0.777253i | \(0.283388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11592.0 | 0.574687 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6964.00 | 0.343855 | 0.171928 | − | 0.985110i | \(-0.445000\pi\) | ||||
0.171928 | + | 0.985110i | \(0.445000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8244.00 | 0.405419 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2556.00 | 0.125193 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2548.00 | −0.124302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20208.0 | −0.981891 | −0.490946 | − | 0.871190i | \(-0.663349\pi\) | ||||
−0.490946 | + | 0.871190i | \(0.663349\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15132.0 | 0.732325 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4128.00 | 0.198985 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24766.0 | 1.18908 | 0.594541 | − | 0.804065i | \(-0.297334\pi\) | ||||
0.594541 | + | 0.804065i | \(0.297334\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 528.000 | 0.0252506 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34338.0 | −1.63568 | −0.817839 | − | 0.575447i | \(-0.804828\pi\) | ||||
−0.817839 | + | 0.575447i | \(0.804828\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5866.00 | 0.278327 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4428.00 | −0.209274 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21896.0 | 1.03079 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41178.0 | 1.93097 | 0.965485 | − | 0.260457i | \(-0.0838732\pi\) | ||||
0.965485 | + | 0.260457i | \(0.0838732\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 294.000 | 0.0137330 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21918.0 | 1.01984 | 0.509920 | − | 0.860222i | \(-0.329675\pi\) | ||||
0.509920 | + | 0.860222i | \(0.329675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13528.0 | 0.627019 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3066.00 | 0.141560 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7896.00 | 0.363162 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 144.000 | 0.00659760 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1890.00 | −0.0862619 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −0.00163681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17972.0 | −0.814019 | −0.407009 | − | 0.913424i | \(-0.633428\pi\) | ||||
−0.407009 | + | 0.913424i | \(0.633428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17196.0 | −0.775911 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2562.00 | −0.115163 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1564.00 | −0.0700369 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10116.0 | 0.451293 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27310.0 | 1.21376 | 0.606882 | − | 0.794792i | \(-0.292420\pi\) | ||||
0.606882 | + | 0.794792i | \(0.292420\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2624.00 | 0.116183 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8586.00 | −0.378741 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2616.00 | 0.114965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1848.00 | 0.0809111 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1890.00 | −0.0824426 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5734.00 | −0.249192 | −0.124596 | − | 0.992208i | \(-0.539764\pi\) | ||||
−0.124596 | + | 0.992208i | \(0.539764\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40556.0 | 1.75600 | 0.877999 | − | 0.478663i | \(-0.158878\pi\) | ||||
0.877999 | + | 0.478663i | \(0.158878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7680.00 | −0.331303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −96.0000 | −0.00412605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40992.0 | 1.75536 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2898.00 | −0.123644 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28046.0 | 1.19222 | 0.596110 | − | 0.802903i | \(-0.296712\pi\) | ||||
0.596110 | + | 0.802903i | \(0.296712\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31744.0 | 1.34450 | 0.672252 | − | 0.740323i | \(-0.265327\pi\) | ||||
0.672252 | + | 0.740323i | \(0.265327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1068.00 | −0.0450703 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41244.0 | −1.73421 | −0.867107 | − | 0.498123i | \(-0.834023\pi\) | ||||
−0.867107 | + | 0.498123i | \(0.834023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20298.0 | 0.850396 | 0.425198 | − | 0.905100i | \(-0.360204\pi\) | ||||
0.425198 | + | 0.905100i | \(0.360204\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6798.00 | 0.283779 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4018.00 | −0.167125 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11712.0 | 0.485402 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4104.00 | 0.169480 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40048.0 | −1.64793 | −0.823963 | − | 0.566643i | \(-0.808242\pi\) | ||||
−0.823963 | + | 0.566643i | \(0.808242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19489.0 | −0.799090 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13014.0 | −0.531703 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −486.000 | −0.0197857 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9205.00 | −0.373421 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19092.0 | 0.771774 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6424.00 | −0.258768 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7758.00 | −0.311405 | −0.155703 | − | 0.987804i | \(-0.549764\pi\) | ||||
−0.155703 | + | 0.987804i | \(0.549764\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4536.00 | 0.181436 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28434.0 | −1.13336 | −0.566678 | − | 0.823939i | \(-0.691772\pi\) | ||||
−0.566678 | + | 0.823939i | \(0.691772\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16028.0 | 0.636634 | 0.318317 | − | 0.947984i | \(-0.396882\pi\) | ||||
0.318317 | + | 0.947984i | \(0.396882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1974.00 | −0.0781344 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40188.0 | −1.58519 | −0.792593 | − | 0.609751i | \(-0.791269\pi\) | ||||
−0.792593 | + | 0.609751i | \(0.791269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3852.00 | −0.151413 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5433.00 | −0.212819 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2432.00 | 0.0949367 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23920.0 | 0.930538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15246.0 | −0.591064 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8988.00 | −0.347257 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32810.0 | −1.26330 | −0.631651 | − | 0.775253i | \(-0.717622\pi\) | ||||
−0.631651 | + | 0.775253i | \(0.717622\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5334.00 | 0.204677 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17414.0 | 0.665939 | 0.332970 | − | 0.942938i | \(-0.391949\pi\) | ||||
0.332970 | + | 0.942938i | \(0.391949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8656.00 | 0.329895 | 0.164948 | − | 0.986302i | \(-0.447254\pi\) | ||||
0.164948 | + | 0.986302i | \(0.447254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8568.00 | 0.325435 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3824.00 | −0.144755 | −0.0723773 | − | 0.997377i | \(-0.523059\pi\) | ||||
−0.0723773 | + | 0.997377i | \(0.523059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3752.00 | −0.141550 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −324.000 | −0.0121823 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2688.00 | −0.100728 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2808.00 | −0.104873 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6072.00 | 0.226018 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10640.0 | −0.394732 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46084.0 | 1.70397 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10248.0 | −0.377666 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 828.000 | 0.0304129 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41008.0 | 1.50127 | 0.750633 | − | 0.660719i | \(-0.229749\pi\) | ||||
0.750633 | + | 0.660719i | \(0.229749\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2862.00 | 0.104430 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51172.0 | 1.86104 | 0.930518 | − | 0.366246i | \(-0.119357\pi\) | ||||
0.930518 | + | 0.366246i | \(0.119357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1136.00 | −0.0411787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −612.000 | −0.0221116 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13860.0 | 0.499125 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31432.0 | 1.12823 | 0.564116 | − | 0.825695i | \(-0.309217\pi\) | ||||
0.564116 | + | 0.825695i | \(0.309217\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4092.00 | −0.146402 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1656.00 | 0.0590552 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12994.0 | 0.461881 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7848.00 | −0.278061 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38214.0 | 1.34958 | 0.674790 | − | 0.738009i | \(-0.264234\pi\) | ||||
0.674790 | + | 0.738009i | \(0.264234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4116.00 | 0.144894 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22536.0 | 0.790778 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1968.00 | 0.0688347 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41446.0 | −1.44502 | −0.722509 | − | 0.691362i | \(-0.757011\pi\) | ||||
−0.722509 | + | 0.691362i | \(0.757011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8742.00 | −0.303817 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2590.00 | 0.0897254 | 0.0448627 | − | 0.998993i | \(-0.485715\pi\) | ||||
0.0448627 | + | 0.998993i | \(0.485715\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4136.00 | 0.142828 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1134.00 | −0.0390360 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3980.00 | 0.136571 | 0.0682854 | − | 0.997666i | \(-0.478247\pi\) | ||||
0.0682854 | + | 0.997666i | \(0.478247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30084.0 | 1.02905 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23538.0 | −0.802599 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6778.00 | 0.230389 | 0.115195 | − | 0.993343i | \(-0.463251\pi\) | ||||
0.115195 | + | 0.993343i | \(0.463251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11880.0 | 0.402542 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 840.000 | 0.0283734 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20146.0 | −0.678361 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6687.00 | −0.224464 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3276.00 | −0.109624 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7764.00 | −0.258997 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 296.000 | 0.00984356 | 0.00492178 | − | 0.999988i | \(-0.498433\pi\) | ||||
0.00492178 | + | 0.999988i | \(0.498433\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20664.0 | 0.685060 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25356.0 | 0.838015 | 0.419008 | − | 0.907983i | \(-0.362378\pi\) | ||||
0.419008 | + | 0.907983i | \(0.362378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10052.0 | −0.331195 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12282.0 | −0.403424 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53290.0 | 1.74503 | 0.872517 | − | 0.488584i | \(-0.162486\pi\) | ||||
0.872517 | + | 0.488584i | \(0.162486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3816.00 | 0.124576 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7542.00 | 0.245461 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28584.0 | −0.927455 | −0.463727 | − | 0.885978i | \(-0.653488\pi\) | ||||
−0.463727 | + | 0.885978i | \(0.653488\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27252.0 | 0.881544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 672.000 | 0.0216717 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21472.0 | 0.690364 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3592.00 | 0.115140 | 0.0575699 | − | 0.998341i | \(-0.481665\pi\) | ||||
0.0575699 | + | 0.998341i | \(0.481665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −72.0000 | −0.00230096 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17952.0 | −0.571977 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9290.00 | 0.295103 | 0.147551 | − | 0.989054i | \(-0.452861\pi\) | ||||
0.147551 | + | 0.989054i | \(0.452861\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3942.00 | 0.124844 |
(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 | 672.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 2016.4.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 672.4.a.d.1.1 | yes | 1 | ||
8.3 | odd | 2 | 1344.4.a.c.1.1 | 1 | |||
8.5 | even | 2 | 1344.4.a.r.1.1 | 1 | |||
12.11 | even | 2 | 2016.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
672.4.a.d.1.1 | yes | 1 | 4.3 | odd | 2 | ||
1344.4.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
1344.4.a.r.1.1 | 1 | 8.5 | even | 2 | |||
2016.4.a.a.1.1 | 1 | 12.11 | even | 2 | |||
2016.4.a.b.1.1 | 1 | 3.2 | odd | 2 |