Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(1,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("189.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.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: | \(11.1513609911\) |
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 | \(\chi\) | \(=\) | 189.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | −12.0000 | −1.07331 | −0.536656 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536656 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −36.0000 | −1.13842 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.0000 | −1.30141 | −0.650706 | − | 0.759330i | \(-0.725527\pi\) | ||||
−0.650706 | + | 0.759330i | \(0.725527\pi\) | |||||||
\(14\) | 21.0000 | 0.400892 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | −117.000 | −1.66922 | −0.834608 | − | 0.550845i | \(-0.814306\pi\) | ||||
−0.834608 | + | 0.550845i | \(0.814306\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.0241490 | 0.0120745 | − | 0.999927i | \(-0.496156\pi\) | ||||
0.0120745 | + | 0.999927i | \(0.496156\pi\) | |||||||
\(20\) | −12.0000 | −0.134164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 36.0000 | 0.348874 | ||||||||
\(23\) | −75.0000 | −0.679938 | −0.339969 | − | 0.940437i | \(-0.610417\pi\) | ||||
−0.339969 | + | 0.940437i | \(0.610417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | −183.000 | −1.38036 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.00000 | 0.0472456 | ||||||||
\(29\) | 3.00000 | 0.0192099 | 0.00960493 | − | 0.999954i | \(-0.496943\pi\) | ||||
0.00960493 | + | 0.999954i | \(0.496943\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 263.000 | 1.52375 | 0.761874 | − | 0.647725i | \(-0.224279\pi\) | ||||
0.761874 | + | 0.647725i | \(0.224279\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −351.000 | −1.77047 | ||||||||
\(35\) | −84.0000 | −0.405674 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 218.000 | 0.968621 | 0.484311 | − | 0.874896i | \(-0.339070\pi\) | ||||
0.484311 | + | 0.874896i | \(0.339070\pi\) | |||||||
\(38\) | 6.00000 | 0.0256139 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 252.000 | 0.996117 | ||||||||
\(41\) | −246.000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 515.000 | 1.82644 | 0.913218 | − | 0.407471i | \(-0.133589\pi\) | ||||
0.913218 | + | 0.407471i | \(0.133589\pi\) | |||||||
\(44\) | 12.0000 | 0.0411152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −225.000 | −0.721183 | ||||||||
\(47\) | 318.000 | 0.986916 | 0.493458 | − | 0.869770i | \(-0.335733\pi\) | ||||
0.493458 | + | 0.869770i | \(0.335733\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 57.0000 | 0.161220 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −61.0000 | −0.162676 | ||||||||
\(53\) | −459.000 | −1.18959 | −0.594797 | − | 0.803876i | \(-0.702768\pi\) | ||||
−0.594797 | + | 0.803876i | \(0.702768\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −144.000 | −0.353036 | ||||||||
\(56\) | −147.000 | −0.350780 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.00000 | 0.0203751 | ||||||||
\(59\) | −255.000 | −0.562681 | −0.281340 | − | 0.959608i | \(-0.590779\pi\) | ||||
−0.281340 | + | 0.959608i | \(0.590779\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −862.000 | −1.80931 | −0.904654 | − | 0.426147i | \(-0.859871\pi\) | ||||
−0.904654 | + | 0.426147i | \(0.859871\pi\) | |||||||
\(62\) | 789.000 | 1.61618 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 732.000 | 1.39682 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 479.000 | 0.873420 | 0.436710 | − | 0.899602i | \(-0.356144\pi\) | ||||
0.436710 | + | 0.899602i | \(0.356144\pi\) | |||||||
\(68\) | −117.000 | −0.208652 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −252.000 | −0.430282 | ||||||||
\(71\) | −117.000 | −0.195568 | −0.0977841 | − | 0.995208i | \(-0.531175\pi\) | ||||
−0.0977841 | + | 0.995208i | \(0.531175\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −430.000 | −0.689420 | −0.344710 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344710 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(74\) | 654.000 | 1.02738 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.00301863 | ||||||||
\(77\) | 84.0000 | 0.124321 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −646.000 | −0.920009 | −0.460004 | − | 0.887917i | \(-0.652152\pi\) | ||||
−0.460004 | + | 0.887917i | \(0.652152\pi\) | |||||||
\(80\) | 852.000 | 1.19071 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −738.000 | −0.993884 | ||||||||
\(83\) | −348.000 | −0.460216 | −0.230108 | − | 0.973165i | \(-0.573908\pi\) | ||||
−0.230108 | + | 0.973165i | \(0.573908\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1404.00 | 1.79159 | ||||||||
\(86\) | 1545.00 | 1.93723 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −252.000 | −0.305265 | ||||||||
\(89\) | −585.000 | −0.696740 | −0.348370 | − | 0.937357i | \(-0.613265\pi\) | ||||
−0.348370 | + | 0.937357i | \(0.613265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −427.000 | −0.491888 | ||||||||
\(92\) | −75.0000 | −0.0849923 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 954.000 | 1.04678 | ||||||||
\(95\) | −24.0000 | −0.0259195 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −376.000 | −0.393577 | −0.196789 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196789 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(98\) | 147.000 | 0.151523 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19.0000 | 0.0190000 | ||||||||
\(101\) | −978.000 | −0.963511 | −0.481756 | − | 0.876306i | \(-0.660001\pi\) | ||||
−0.481756 | + | 0.876306i | \(0.660001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −655.000 | −0.626593 | −0.313296 | − | 0.949655i | \(-0.601433\pi\) | ||||
−0.313296 | + | 0.949655i | \(0.601433\pi\) | |||||||
\(104\) | 1281.00 | 1.20781 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1377.00 | −1.26176 | ||||||||
\(107\) | −108.000 | −0.0975771 | −0.0487886 | − | 0.998809i | \(-0.515536\pi\) | ||||
−0.0487886 | + | 0.998809i | \(0.515536\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 272.000 | 0.239017 | 0.119509 | − | 0.992833i | \(-0.461868\pi\) | ||||
0.119509 | + | 0.992833i | \(0.461868\pi\) | |||||||
\(110\) | −432.000 | −0.374451 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −497.000 | −0.419304 | ||||||||
\(113\) | 2256.00 | 1.87811 | 0.939056 | − | 0.343765i | \(-0.111702\pi\) | ||||
0.939056 | + | 0.343765i | \(0.111702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 900.000 | 0.729786 | ||||||||
\(116\) | 3.00000 | 0.00240123 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −765.000 | −0.596813 | ||||||||
\(119\) | −819.000 | −0.630904 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | −2586.00 | −1.91906 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 263.000 | 0.190469 | ||||||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1784.00 | 1.24649 | 0.623246 | − | 0.782026i | \(-0.285814\pi\) | ||||
0.623246 | + | 0.782026i | \(0.285814\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2196.00 | 1.48155 | ||||||||
\(131\) | −1749.00 | −1.16649 | −0.583247 | − | 0.812295i | \(-0.698218\pi\) | ||||
−0.583247 | + | 0.812295i | \(0.698218\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.0000 | 0.00912747 | ||||||||
\(134\) | 1437.00 | 0.926402 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2457.00 | 1.54916 | ||||||||
\(137\) | −1374.00 | −0.856852 | −0.428426 | − | 0.903577i | \(-0.640932\pi\) | ||||
−0.428426 | + | 0.903577i | \(0.640932\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2450.00 | 1.49501 | 0.747505 | − | 0.664257i | \(-0.231252\pi\) | ||||
0.747505 | + | 0.664257i | \(0.231252\pi\) | |||||||
\(140\) | −84.0000 | −0.0507093 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −351.000 | −0.207431 | ||||||||
\(143\) | −732.000 | −0.428062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.0000 | −0.0206182 | ||||||||
\(146\) | −1290.00 | −0.731241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 218.000 | 0.121078 | ||||||||
\(149\) | −921.000 | −0.506384 | −0.253192 | − | 0.967416i | \(-0.581480\pi\) | ||||
−0.253192 | + | 0.967416i | \(0.581480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 650.000 | 0.350306 | 0.175153 | − | 0.984541i | \(-0.443958\pi\) | ||||
0.175153 | + | 0.984541i | \(0.443958\pi\) | |||||||
\(152\) | −42.0000 | −0.0224122 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 252.000 | 0.131862 | ||||||||
\(155\) | −3156.00 | −1.63546 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −871.000 | −0.442760 | −0.221380 | − | 0.975188i | \(-0.571056\pi\) | ||||
−0.221380 | + | 0.975188i | \(0.571056\pi\) | |||||||
\(158\) | −1938.00 | −0.975816 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 540.000 | 0.266817 | ||||||||
\(161\) | −525.000 | −0.256993 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3697.00 | −1.77651 | −0.888256 | − | 0.459349i | \(-0.848083\pi\) | ||||
−0.888256 | + | 0.459349i | \(0.848083\pi\) | |||||||
\(164\) | −246.000 | −0.117130 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1044.00 | −0.488133 | ||||||||
\(167\) | 1824.00 | 0.845182 | 0.422591 | − | 0.906321i | \(-0.361121\pi\) | ||||
0.422591 | + | 0.906321i | \(0.361121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1524.00 | 0.693673 | ||||||||
\(170\) | 4212.00 | 1.90027 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 515.000 | 0.228305 | ||||||||
\(173\) | −744.000 | −0.326967 | −0.163483 | − | 0.986546i | \(-0.552273\pi\) | ||||
−0.163483 | + | 0.986546i | \(0.552273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 133.000 | 0.0574506 | ||||||||
\(176\) | −852.000 | −0.364897 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1755.00 | −0.739005 | ||||||||
\(179\) | −4572.00 | −1.90909 | −0.954546 | − | 0.298065i | \(-0.903659\pi\) | ||||
−0.954546 | + | 0.298065i | \(0.903659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3481.00 | −1.42951 | −0.714753 | − | 0.699377i | \(-0.753461\pi\) | ||||
−0.714753 | + | 0.699377i | \(0.753461\pi\) | |||||||
\(182\) | −1281.00 | −0.521725 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1575.00 | 0.631036 | ||||||||
\(185\) | −2616.00 | −1.03963 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1404.00 | −0.549041 | ||||||||
\(188\) | 318.000 | 0.123365 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −72.0000 | −0.0274917 | ||||||||
\(191\) | 3756.00 | 1.42290 | 0.711452 | − | 0.702735i | \(-0.248038\pi\) | ||||
0.711452 | + | 0.702735i | \(0.248038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4867.00 | −1.81520 | −0.907602 | − | 0.419832i | \(-0.862089\pi\) | ||||
−0.907602 | + | 0.419832i | \(0.862089\pi\) | |||||||
\(194\) | −1128.00 | −0.417452 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49.0000 | 0.0178571 | ||||||||
\(197\) | −18.0000 | −0.00650988 | −0.00325494 | − | 0.999995i | \(-0.501036\pi\) | ||||
−0.00325494 | + | 0.999995i | \(0.501036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1807.00 | −0.643693 | −0.321846 | − | 0.946792i | \(-0.604303\pi\) | ||||
−0.321846 | + | 0.946792i | \(0.604303\pi\) | |||||||
\(200\) | −399.000 | −0.141068 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2934.00 | −1.02196 | ||||||||
\(203\) | 21.0000 | 0.00726065 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2952.00 | 1.00574 | ||||||||
\(206\) | −1965.00 | −0.664602 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4331.00 | 1.44375 | ||||||||
\(209\) | 24.0000 | 0.00794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4273.00 | −1.39415 | −0.697075 | − | 0.716999i | \(-0.745515\pi\) | ||||
−0.697075 | + | 0.716999i | \(0.745515\pi\) | |||||||
\(212\) | −459.000 | −0.148699 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −324.000 | −0.103496 | ||||||||
\(215\) | −6180.00 | −1.96034 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1841.00 | 0.575923 | ||||||||
\(218\) | 816.000 | 0.253516 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −144.000 | −0.0441294 | ||||||||
\(221\) | 7137.00 | 2.17234 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2648.00 | 0.795171 | 0.397586 | − | 0.917565i | \(-0.369848\pi\) | ||||
0.397586 | + | 0.917565i | \(0.369848\pi\) | |||||||
\(224\) | −315.000 | −0.0939590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6768.00 | 1.99204 | ||||||||
\(227\) | 5493.00 | 1.60609 | 0.803047 | − | 0.595916i | \(-0.203211\pi\) | ||||
0.803047 | + | 0.595916i | \(0.203211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −790.000 | −0.227968 | −0.113984 | − | 0.993483i | \(-0.536361\pi\) | ||||
−0.113984 | + | 0.993483i | \(0.536361\pi\) | |||||||
\(230\) | 2700.00 | 0.774055 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −63.0000 | −0.0178282 | ||||||||
\(233\) | 6228.00 | 1.75112 | 0.875558 | − | 0.483114i | \(-0.160494\pi\) | ||||
0.875558 | + | 0.483114i | \(0.160494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3816.00 | −1.05927 | ||||||||
\(236\) | −255.000 | −0.0703351 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2457.00 | −0.669175 | ||||||||
\(239\) | 4812.00 | 1.30235 | 0.651177 | − | 0.758926i | \(-0.274276\pi\) | ||||
0.651177 | + | 0.758926i | \(0.274276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1622.00 | 0.433536 | 0.216768 | − | 0.976223i | \(-0.430448\pi\) | ||||
0.216768 | + | 0.976223i | \(0.430448\pi\) | |||||||
\(242\) | −3561.00 | −0.945908 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −862.000 | −0.226164 | ||||||||
\(245\) | −588.000 | −0.153330 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −122.000 | −0.0314278 | ||||||||
\(248\) | −5523.00 | −1.41416 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3816.00 | 0.965380 | ||||||||
\(251\) | −2880.00 | −0.724239 | −0.362119 | − | 0.932132i | \(-0.617947\pi\) | ||||
−0.362119 | + | 0.932132i | \(0.617947\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −900.000 | −0.223646 | ||||||||
\(254\) | 5352.00 | 1.32210 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −2190.00 | −0.531550 | −0.265775 | − | 0.964035i | \(-0.585628\pi\) | ||||
−0.265775 | + | 0.964035i | \(0.585628\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1526.00 | 0.366104 | ||||||||
\(260\) | 732.000 | 0.174603 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5247.00 | −1.23725 | ||||||||
\(263\) | −1869.00 | −0.438203 | −0.219102 | − | 0.975702i | \(-0.570313\pi\) | ||||
−0.219102 | + | 0.975702i | \(0.570313\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5508.00 | 1.27681 | ||||||||
\(266\) | 42.0000 | 0.00968115 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 479.000 | 0.109178 | ||||||||
\(269\) | −2268.00 | −0.514061 | −0.257030 | − | 0.966403i | \(-0.582744\pi\) | ||||
−0.257030 | + | 0.966403i | \(0.582744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2027.00 | 0.454360 | 0.227180 | − | 0.973853i | \(-0.427049\pi\) | ||||
0.227180 | + | 0.973853i | \(0.427049\pi\) | |||||||
\(272\) | 8307.00 | 1.85179 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4122.00 | −0.908829 | ||||||||
\(275\) | 228.000 | 0.0499961 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3944.00 | 0.855495 | 0.427747 | − | 0.903898i | \(-0.359307\pi\) | ||||
0.427747 | + | 0.903898i | \(0.359307\pi\) | |||||||
\(278\) | 7350.00 | 1.58570 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1764.00 | 0.376497 | ||||||||
\(281\) | 4602.00 | 0.976983 | 0.488492 | − | 0.872569i | \(-0.337547\pi\) | ||||
0.488492 | + | 0.872569i | \(0.337547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3220.00 | −0.676357 | −0.338179 | − | 0.941082i | \(-0.609811\pi\) | ||||
−0.338179 | + | 0.941082i | \(0.609811\pi\) | |||||||
\(284\) | −117.000 | −0.0244460 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2196.00 | −0.454029 | ||||||||
\(287\) | −1722.00 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8776.00 | 1.78628 | ||||||||
\(290\) | −108.000 | −0.0218689 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −430.000 | −0.0861776 | ||||||||
\(293\) | 6810.00 | 1.35783 | 0.678915 | − | 0.734216i | \(-0.262450\pi\) | ||||
0.678915 | + | 0.734216i | \(0.262450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3060.00 | 0.603933 | ||||||||
\(296\) | −4578.00 | −0.898956 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2763.00 | −0.537102 | ||||||||
\(299\) | 4575.00 | 0.884880 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3605.00 | 0.690328 | ||||||||
\(302\) | 1950.00 | 0.371556 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −142.000 | −0.0267903 | ||||||||
\(305\) | 10344.0 | 1.94195 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 758.000 | 0.140916 | 0.0704582 | − | 0.997515i | \(-0.477554\pi\) | ||||
0.0704582 | + | 0.997515i | \(0.477554\pi\) | |||||||
\(308\) | 84.0000 | 0.0155401 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9468.00 | −1.73467 | ||||||||
\(311\) | −9480.00 | −1.72849 | −0.864247 | − | 0.503068i | \(-0.832204\pi\) | ||||
−0.864247 | + | 0.503068i | \(0.832204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3350.00 | 0.604962 | 0.302481 | − | 0.953155i | \(-0.402185\pi\) | ||||
0.302481 | + | 0.953155i | \(0.402185\pi\) | |||||||
\(314\) | −2613.00 | −0.469618 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −646.000 | −0.115001 | ||||||||
\(317\) | 426.000 | 0.0754781 | 0.0377390 | − | 0.999288i | \(-0.487984\pi\) | ||||
0.0377390 | + | 0.999288i | \(0.487984\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000 | 0.00631854 | ||||||||
\(320\) | −5196.00 | −0.907704 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1575.00 | −0.272582 | ||||||||
\(323\) | −234.000 | −0.0403099 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1159.00 | −0.197815 | ||||||||
\(326\) | −11091.0 | −1.88428 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5166.00 | 0.869648 | ||||||||
\(329\) | 2226.00 | 0.373019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3103.00 | −0.515276 | −0.257638 | − | 0.966242i | \(-0.582944\pi\) | ||||
−0.257638 | + | 0.966242i | \(0.582944\pi\) | |||||||
\(332\) | −348.000 | −0.0575271 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5472.00 | 0.896451 | ||||||||
\(335\) | −5748.00 | −0.937453 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11725.0 | −1.89526 | −0.947628 | − | 0.319375i | \(-0.896527\pi\) | ||||
−0.947628 | + | 0.319375i | \(0.896527\pi\) | |||||||
\(338\) | 4572.00 | 0.735752 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1404.00 | 0.223949 | ||||||||
\(341\) | 3156.00 | 0.501193 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −10815.0 | −1.69507 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2232.00 | −0.346801 | ||||||||
\(347\) | −1506.00 | −0.232987 | −0.116493 | − | 0.993191i | \(-0.537165\pi\) | ||||
−0.116493 | + | 0.993191i | \(0.537165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10289.0 | 1.57810 | 0.789051 | − | 0.614328i | \(-0.210573\pi\) | ||||
0.789051 | + | 0.614328i | \(0.210573\pi\) | |||||||
\(350\) | 399.000 | 0.0609356 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −540.000 | −0.0817673 | ||||||||
\(353\) | 12693.0 | 1.91382 | 0.956912 | − | 0.290376i | \(-0.0937805\pi\) | ||||
0.956912 | + | 0.290376i | \(0.0937805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1404.00 | 0.209906 | ||||||||
\(356\) | −585.000 | −0.0870925 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13716.0 | −2.02490 | ||||||||
\(359\) | 5031.00 | 0.739627 | 0.369813 | − | 0.929106i | \(-0.379422\pi\) | ||||
0.369813 | + | 0.929106i | \(0.379422\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6855.00 | −0.999417 | ||||||||
\(362\) | −10443.0 | −1.51622 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −427.000 | −0.0614859 | ||||||||
\(365\) | 5160.00 | 0.739964 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9479.00 | 1.34823 | 0.674114 | − | 0.738627i | \(-0.264526\pi\) | ||||
0.674114 | + | 0.738627i | \(0.264526\pi\) | |||||||
\(368\) | 5325.00 | 0.754307 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7848.00 | −1.10270 | ||||||||
\(371\) | −3213.00 | −0.449624 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8566.00 | −1.18909 | −0.594545 | − | 0.804062i | \(-0.702668\pi\) | ||||
−0.594545 | + | 0.804062i | \(0.702668\pi\) | |||||||
\(374\) | −4212.00 | −0.582346 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6678.00 | −0.915935 | ||||||||
\(377\) | −183.000 | −0.0249999 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2320.00 | −0.314434 | −0.157217 | − | 0.987564i | \(-0.550252\pi\) | ||||
−0.157217 | + | 0.987564i | \(0.550252\pi\) | |||||||
\(380\) | −24.0000 | −0.00323993 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11268.0 | 1.50922 | ||||||||
\(383\) | −1092.00 | −0.145688 | −0.0728441 | − | 0.997343i | \(-0.523208\pi\) | ||||
−0.0728441 | + | 0.997343i | \(0.523208\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1008.00 | −0.133435 | ||||||||
\(386\) | −14601.0 | −1.92531 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −376.000 | −0.0491972 | ||||||||
\(389\) | −12570.0 | −1.63837 | −0.819183 | − | 0.573532i | \(-0.805573\pi\) | ||||
−0.819183 | + | 0.573532i | \(0.805573\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8775.00 | 1.13496 | ||||||||
\(392\) | −1029.00 | −0.132583 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −54.0000 | −0.00690477 | ||||||||
\(395\) | 7752.00 | 0.987457 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6802.00 | −0.859906 | −0.429953 | − | 0.902851i | \(-0.641470\pi\) | ||||
−0.429953 | + | 0.902851i | \(0.641470\pi\) | |||||||
\(398\) | −5421.00 | −0.682739 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1349.00 | −0.168625 | ||||||||
\(401\) | −8526.00 | −1.06177 | −0.530883 | − | 0.847445i | \(-0.678140\pi\) | ||||
−0.530883 | + | 0.847445i | \(0.678140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16043.0 | −1.98302 | ||||||||
\(404\) | −978.000 | −0.120439 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 63.0000 | 0.00770108 | ||||||||
\(407\) | 2616.00 | 0.318600 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13466.0 | 1.62800 | 0.813999 | − | 0.580867i | \(-0.197286\pi\) | ||||
0.813999 | + | 0.580867i | \(0.197286\pi\) | |||||||
\(410\) | 8856.00 | 1.06675 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −655.000 | −0.0783241 | ||||||||
\(413\) | −1785.00 | −0.212673 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4176.00 | 0.493956 | ||||||||
\(416\) | 2745.00 | 0.323521 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 72.0000 | 0.00842496 | ||||||||
\(419\) | −15339.0 | −1.78845 | −0.894223 | − | 0.447621i | \(-0.852271\pi\) | ||||
−0.894223 | + | 0.447621i | \(0.852271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4102.00 | −0.474868 | −0.237434 | − | 0.971404i | \(-0.576306\pi\) | ||||
−0.237434 | + | 0.971404i | \(0.576306\pi\) | |||||||
\(422\) | −12819.0 | −1.47872 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9639.00 | 1.10404 | ||||||||
\(425\) | −2223.00 | −0.253721 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6034.00 | −0.683854 | ||||||||
\(428\) | −108.000 | −0.0121971 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18540.0 | −2.07925 | ||||||||
\(431\) | −2592.00 | −0.289680 | −0.144840 | − | 0.989455i | \(-0.546267\pi\) | ||||
−0.144840 | + | 0.989455i | \(0.546267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9448.00 | −1.04860 | −0.524298 | − | 0.851535i | \(-0.675672\pi\) | ||||
−0.524298 | + | 0.851535i | \(0.675672\pi\) | |||||||
\(434\) | 5523.00 | 0.610858 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 272.000 | 0.0298772 | ||||||||
\(437\) | −150.000 | −0.0164198 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11369.0 | 1.23602 | 0.618010 | − | 0.786170i | \(-0.287939\pi\) | ||||
0.618010 | + | 0.786170i | \(0.287939\pi\) | |||||||
\(440\) | 3024.00 | 0.327644 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21411.0 | 2.30411 | ||||||||
\(443\) | −10842.0 | −1.16280 | −0.581398 | − | 0.813619i | \(-0.697494\pi\) | ||||
−0.581398 | + | 0.813619i | \(0.697494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7020.00 | 0.747820 | ||||||||
\(446\) | 7944.00 | 0.843407 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3031.00 | 0.319646 | ||||||||
\(449\) | 13140.0 | 1.38110 | 0.690551 | − | 0.723284i | \(-0.257368\pi\) | ||||
0.690551 | + | 0.723284i | \(0.257368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2952.00 | −0.308213 | ||||||||
\(452\) | 2256.00 | 0.234764 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16479.0 | 1.70352 | ||||||||
\(455\) | 5124.00 | 0.527949 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1379.00 | 0.141153 | 0.0705765 | − | 0.997506i | \(-0.477516\pi\) | ||||
0.0705765 | + | 0.997506i | \(0.477516\pi\) | |||||||
\(458\) | −2370.00 | −0.241797 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 900.000 | 0.0912233 | ||||||||
\(461\) | 678.000 | 0.0684981 | 0.0342490 | − | 0.999413i | \(-0.489096\pi\) | ||||
0.0342490 | + | 0.999413i | \(0.489096\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15734.0 | 1.57931 | 0.789655 | − | 0.613550i | \(-0.210259\pi\) | ||||
0.789655 | + | 0.613550i | \(0.210259\pi\) | |||||||
\(464\) | −213.000 | −0.0213109 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18684.0 | 1.85734 | ||||||||
\(467\) | −7416.00 | −0.734843 | −0.367421 | − | 0.930055i | \(-0.619759\pi\) | ||||
−0.367421 | + | 0.930055i | \(0.619759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3353.00 | 0.330122 | ||||||||
\(470\) | −11448.0 | −1.12353 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5355.00 | 0.522212 | ||||||||
\(473\) | 6180.00 | 0.600754 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.0000 | 0.00367065 | ||||||||
\(476\) | −819.000 | −0.0788630 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14436.0 | 1.38135 | ||||||||
\(479\) | −1248.00 | −0.119045 | −0.0595225 | − | 0.998227i | \(-0.518958\pi\) | ||||
−0.0595225 | + | 0.998227i | \(0.518958\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13298.0 | −1.26058 | ||||||||
\(482\) | 4866.00 | 0.459834 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1187.00 | −0.111476 | ||||||||
\(485\) | 4512.00 | 0.422432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20950.0 | −1.94935 | −0.974677 | − | 0.223619i | \(-0.928213\pi\) | ||||
−0.974677 | + | 0.223619i | \(0.928213\pi\) | |||||||
\(488\) | 18102.0 | 1.67918 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1764.00 | −0.162631 | ||||||||
\(491\) | −768.000 | −0.0705893 | −0.0352947 | − | 0.999377i | \(-0.511237\pi\) | ||||
−0.0352947 | + | 0.999377i | \(0.511237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −351.000 | −0.0320654 | ||||||||
\(494\) | −366.000 | −0.0333342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18673.0 | −1.69041 | ||||||||
\(497\) | −819.000 | −0.0739178 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4772.00 | 0.428104 | 0.214052 | − | 0.976822i | \(-0.431334\pi\) | ||||
0.214052 | + | 0.976822i | \(0.431334\pi\) | |||||||
\(500\) | 1272.00 | 0.113771 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8640.00 | −0.768171 | ||||||||
\(503\) | 11088.0 | 0.982882 | 0.491441 | − | 0.870911i | \(-0.336470\pi\) | ||||
0.491441 | + | 0.870911i | \(0.336470\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11736.0 | 1.03415 | ||||||||
\(506\) | −2700.00 | −0.237213 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1784.00 | 0.155811 | ||||||||
\(509\) | 16854.0 | 1.46766 | 0.733831 | − | 0.679332i | \(-0.237730\pi\) | ||||
0.733831 | + | 0.679332i | \(0.237730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3010.00 | −0.260576 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6570.00 | −0.563794 | ||||||||
\(515\) | 7860.00 | 0.672530 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3816.00 | 0.324618 | ||||||||
\(518\) | 4578.00 | 0.388312 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15372.0 | −1.29636 | ||||||||
\(521\) | 3195.00 | 0.268667 | 0.134333 | − | 0.990936i | \(-0.457111\pi\) | ||||
0.134333 | + | 0.990936i | \(0.457111\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 920.000 | 0.0769193 | 0.0384596 | − | 0.999260i | \(-0.487755\pi\) | ||||
0.0384596 | + | 0.999260i | \(0.487755\pi\) | |||||||
\(524\) | −1749.00 | −0.145812 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5607.00 | −0.464785 | ||||||||
\(527\) | −30771.0 | −2.54346 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6542.00 | −0.537684 | ||||||||
\(530\) | 16524.0 | 1.35426 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.0000 | 0.00114093 | ||||||||
\(533\) | 15006.0 | 1.21948 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1296.00 | 0.104731 | ||||||||
\(536\) | −10059.0 | −0.810602 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6804.00 | −0.545244 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7180.00 | −0.570596 | −0.285298 | − | 0.958439i | \(-0.592093\pi\) | ||||
−0.285298 | + | 0.958439i | \(0.592093\pi\) | |||||||
\(542\) | 6081.00 | 0.481921 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5265.00 | 0.414954 | ||||||||
\(545\) | −3264.00 | −0.256540 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11612.0 | 0.907666 | 0.453833 | − | 0.891087i | \(-0.350056\pi\) | ||||
0.453833 | + | 0.891087i | \(0.350056\pi\) | |||||||
\(548\) | −1374.00 | −0.107107 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 684.000 | 0.0530288 | ||||||||
\(551\) | 6.00000 | 0.000463899 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4522.00 | −0.347731 | ||||||||
\(554\) | 11832.0 | 0.907389 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2450.00 | 0.186876 | ||||||||
\(557\) | 9819.00 | 0.746938 | 0.373469 | − | 0.927643i | \(-0.378168\pi\) | ||||
0.373469 | + | 0.927643i | \(0.378168\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31415.0 | −2.37695 | ||||||||
\(560\) | 5964.00 | 0.450045 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13806.0 | 1.03625 | ||||||||
\(563\) | 15801.0 | 1.18283 | 0.591415 | − | 0.806368i | \(-0.298570\pi\) | ||||
0.591415 | + | 0.806368i | \(0.298570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27072.0 | −2.01580 | ||||||||
\(566\) | −9660.00 | −0.717385 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2457.00 | 0.181503 | ||||||||
\(569\) | −8340.00 | −0.614466 | −0.307233 | − | 0.951634i | \(-0.599403\pi\) | ||||
−0.307233 | + | 0.951634i | \(0.599403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1073.00 | 0.0786404 | 0.0393202 | − | 0.999227i | \(-0.487481\pi\) | ||||
0.0393202 | + | 0.999227i | \(0.487481\pi\) | |||||||
\(572\) | −732.000 | −0.0535078 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5166.00 | −0.375653 | ||||||||
\(575\) | −1425.00 | −0.103351 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22466.0 | 1.62092 | 0.810461 | − | 0.585793i | \(-0.199217\pi\) | ||||
0.810461 | + | 0.585793i | \(0.199217\pi\) | |||||||
\(578\) | 26328.0 | 1.89464 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −36.0000 | −0.00257727 | ||||||||
\(581\) | −2436.00 | −0.173945 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5508.00 | −0.391283 | ||||||||
\(584\) | 9030.00 | 0.639836 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20430.0 | 1.44020 | ||||||||
\(587\) | −3219.00 | −0.226341 | −0.113171 | − | 0.993576i | \(-0.536101\pi\) | ||||
−0.113171 | + | 0.993576i | \(0.536101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 526.000 | 0.0367970 | ||||||||
\(590\) | 9180.00 | 0.640567 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15478.0 | −1.07456 | ||||||||
\(593\) | −9342.00 | −0.646931 | −0.323465 | − | 0.946240i | \(-0.604848\pi\) | ||||
−0.323465 | + | 0.946240i | \(0.604848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9828.00 | 0.677158 | ||||||||
\(596\) | −921.000 | −0.0632980 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13725.0 | 0.938557 | ||||||||
\(599\) | 6927.00 | 0.472503 | 0.236252 | − | 0.971692i | \(-0.424081\pi\) | ||||
0.236252 | + | 0.971692i | \(0.424081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15172.0 | −1.02975 | −0.514874 | − | 0.857266i | \(-0.672161\pi\) | ||||
−0.514874 | + | 0.857266i | \(0.672161\pi\) | |||||||
\(602\) | 10815.0 | 0.732203 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 650.000 | 0.0437883 | ||||||||
\(605\) | 14244.0 | 0.957192 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4921.00 | −0.329056 | −0.164528 | − | 0.986372i | \(-0.552610\pi\) | ||||
−0.164528 | + | 0.986372i | \(0.552610\pi\) | |||||||
\(608\) | −90.0000 | −0.00600326 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 31032.0 | 2.05975 | ||||||||
\(611\) | −19398.0 | −1.28438 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 218.000 | 0.0143637 | 0.00718184 | − | 0.999974i | \(-0.497714\pi\) | ||||
0.00718184 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(614\) | 2274.00 | 0.149464 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1764.00 | −0.115379 | ||||||||
\(617\) | −22350.0 | −1.45831 | −0.729155 | − | 0.684349i | \(-0.760087\pi\) | ||||
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9290.00 | 0.603226 | 0.301613 | − | 0.953431i | \(-0.402475\pi\) | ||||
0.301613 | + | 0.953431i | \(0.402475\pi\) | |||||||
\(620\) | −3156.00 | −0.204432 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28440.0 | −1.83334 | ||||||||
\(623\) | −4095.00 | −0.263343 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 10050.0 | 0.641659 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −871.000 | −0.0553450 | ||||||||
\(629\) | −25506.0 | −1.61684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13988.0 | 0.882494 | 0.441247 | − | 0.897386i | \(-0.354536\pi\) | ||||
0.441247 | + | 0.897386i | \(0.354536\pi\) | |||||||
\(632\) | 13566.0 | 0.853839 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1278.00 | 0.0800566 | ||||||||
\(635\) | −21408.0 | −1.33787 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2989.00 | −0.185916 | ||||||||
\(638\) | 108.000 | 0.00670182 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19908.0 | −1.22958 | ||||||||
\(641\) | 11388.0 | 0.701714 | 0.350857 | − | 0.936429i | \(-0.385890\pi\) | ||||
0.350857 | + | 0.936429i | \(0.385890\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9956.00 | 0.610616 | 0.305308 | − | 0.952254i | \(-0.401241\pi\) | ||||
0.305308 | + | 0.952254i | \(0.401241\pi\) | |||||||
\(644\) | −525.000 | −0.0321241 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −702.000 | −0.0427551 | ||||||||
\(647\) | 7830.00 | 0.475779 | 0.237890 | − | 0.971292i | \(-0.423544\pi\) | ||||
0.237890 | + | 0.971292i | \(0.423544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3060.00 | −0.185078 | ||||||||
\(650\) | −3477.00 | −0.209814 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3697.00 | −0.222064 | ||||||||
\(653\) | 3633.00 | 0.217719 | 0.108859 | − | 0.994057i | \(-0.465280\pi\) | ||||
0.108859 | + | 0.994057i | \(0.465280\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20988.0 | 1.25201 | ||||||||
\(656\) | 17466.0 | 1.03953 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6678.00 | 0.395647 | ||||||||
\(659\) | −6036.00 | −0.356797 | −0.178398 | − | 0.983958i | \(-0.557092\pi\) | ||||
−0.178398 | + | 0.983958i | \(0.557092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5110.00 | −0.300690 | −0.150345 | − | 0.988634i | \(-0.548038\pi\) | ||||
−0.150345 | + | 0.988634i | \(0.548038\pi\) | |||||||
\(662\) | −9309.00 | −0.546533 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7308.00 | 0.427117 | ||||||||
\(665\) | −168.000 | −0.00979663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −225.000 | −0.0130615 | ||||||||
\(668\) | 1824.00 | 0.105648 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17244.0 | −0.994319 | ||||||||
\(671\) | −10344.0 | −0.595120 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12553.0 | −0.718993 | −0.359497 | − | 0.933146i | \(-0.617052\pi\) | ||||
−0.359497 | + | 0.933146i | \(0.617052\pi\) | |||||||
\(674\) | −35175.0 | −2.01022 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1524.00 | 0.0867091 | ||||||||
\(677\) | 22872.0 | 1.29844 | 0.649219 | − | 0.760602i | \(-0.275096\pi\) | ||||
0.649219 | + | 0.760602i | \(0.275096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2632.00 | −0.148758 | ||||||||
\(680\) | −29484.0 | −1.66273 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9468.00 | 0.531596 | ||||||||
\(683\) | −21672.0 | −1.21414 | −0.607069 | − | 0.794649i | \(-0.707655\pi\) | ||||
−0.607069 | + | 0.794649i | \(0.707655\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16488.0 | 0.919670 | ||||||||
\(686\) | 1029.00 | 0.0572703 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −36565.0 | −2.02620 | ||||||||
\(689\) | 27999.0 | 1.54815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17120.0 | 0.942512 | 0.471256 | − | 0.881997i | \(-0.343801\pi\) | ||||
0.471256 | + | 0.881997i | \(0.343801\pi\) | |||||||
\(692\) | −744.000 | −0.0408709 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4518.00 | −0.247120 | ||||||||
\(695\) | −29400.0 | −1.60461 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28782.0 | 1.56413 | ||||||||
\(698\) | 30867.0 | 1.67383 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 133.000 | 0.00718132 | ||||||||
\(701\) | 5562.00 | 0.299677 | 0.149839 | − | 0.988710i | \(-0.452125\pi\) | ||||
0.149839 | + | 0.988710i | \(0.452125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 436.000 | 0.0233913 | ||||||||
\(704\) | 5196.00 | 0.278170 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38079.0 | 2.02992 | ||||||||
\(707\) | −6846.00 | −0.364173 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16256.0 | 0.861082 | 0.430541 | − | 0.902571i | \(-0.358323\pi\) | ||||
0.430541 | + | 0.902571i | \(0.358323\pi\) | |||||||
\(710\) | 4212.00 | 0.222639 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12285.0 | 0.646629 | ||||||||
\(713\) | −19725.0 | −1.03605 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8784.00 | 0.459445 | ||||||||
\(716\) | −4572.00 | −0.238636 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15093.0 | 0.784493 | ||||||||
\(719\) | −20016.0 | −1.03821 | −0.519104 | − | 0.854711i | \(-0.673734\pi\) | ||||
−0.519104 | + | 0.854711i | \(0.673734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4585.00 | −0.236830 | ||||||||
\(722\) | −20565.0 | −1.06004 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3481.00 | −0.178688 | ||||||||
\(725\) | 57.0000 | 0.00291990 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3539.00 | 0.180542 | 0.0902711 | − | 0.995917i | \(-0.471227\pi\) | ||||
0.0902711 | + | 0.995917i | \(0.471227\pi\) | |||||||
\(728\) | 8967.00 | 0.456510 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15480.0 | 0.784850 | ||||||||
\(731\) | −60255.0 | −3.04872 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19663.0 | −0.990818 | −0.495409 | − | 0.868660i | \(-0.664982\pi\) | ||||
−0.495409 | + | 0.868660i | \(0.664982\pi\) | |||||||
\(734\) | 28437.0 | 1.43001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3375.00 | 0.169027 | ||||||||
\(737\) | 5748.00 | 0.287287 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17116.0 | −0.851992 | −0.425996 | − | 0.904725i | \(-0.640076\pi\) | ||||
−0.425996 | + | 0.904725i | \(0.640076\pi\) | |||||||
\(740\) | −2616.00 | −0.129954 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9639.00 | −0.476899 | ||||||||
\(743\) | 31641.0 | 1.56231 | 0.781155 | − | 0.624338i | \(-0.214631\pi\) | ||||
0.781155 | + | 0.624338i | \(0.214631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11052.0 | 0.543509 | ||||||||
\(746\) | −25698.0 | −1.26122 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1404.00 | −0.0686301 | ||||||||
\(749\) | −756.000 | −0.0368807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17314.0 | −0.841274 | −0.420637 | − | 0.907229i | \(-0.638193\pi\) | ||||
−0.420637 | + | 0.907229i | \(0.638193\pi\) | |||||||
\(752\) | −22578.0 | −1.09486 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −549.000 | −0.0265164 | ||||||||
\(755\) | −7800.00 | −0.375988 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12476.0 | 0.599007 | 0.299503 | − | 0.954095i | \(-0.403179\pi\) | ||||
0.299503 | + | 0.954095i | \(0.403179\pi\) | |||||||
\(758\) | −6960.00 | −0.333507 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 504.000 | 0.0240553 | ||||||||
\(761\) | −21855.0 | −1.04106 | −0.520528 | − | 0.853845i | \(-0.674265\pi\) | ||||
−0.520528 | + | 0.853845i | \(0.674265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1904.00 | 0.0903400 | ||||||||
\(764\) | 3756.00 | 0.177863 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3276.00 | −0.154526 | ||||||||
\(767\) | 15555.0 | 0.732280 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5812.00 | −0.272544 | −0.136272 | − | 0.990671i | \(-0.543512\pi\) | ||||
−0.136272 | + | 0.990671i | \(0.543512\pi\) | |||||||
\(770\) | −3024.00 | −0.141529 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4867.00 | −0.226900 | ||||||||
\(773\) | −252.000 | −0.0117255 | −0.00586275 | − | 0.999983i | \(-0.501866\pi\) | ||||
−0.00586275 | + | 0.999983i | \(0.501866\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4997.00 | 0.231610 | ||||||||
\(776\) | 7896.00 | 0.365270 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37710.0 | −1.73775 | ||||||||
\(779\) | −492.000 | −0.0226287 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1404.00 | −0.0643266 | ||||||||
\(782\) | 26325.0 | 1.20381 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3479.00 | −0.158482 | ||||||||
\(785\) | 10452.0 | 0.475220 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12886.0 | −0.583655 | −0.291827 | − | 0.956471i | \(-0.594263\pi\) | ||||
−0.291827 | + | 0.956471i | \(0.594263\pi\) | |||||||
\(788\) | −18.0000 | −0.000813735 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23256.0 | 1.04736 | ||||||||
\(791\) | 15792.0 | 0.709860 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52582.0 | 2.35466 | ||||||||
\(794\) | −20406.0 | −0.912068 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1807.00 | −0.0804616 | ||||||||
\(797\) | −39342.0 | −1.74851 | −0.874257 | − | 0.485464i | \(-0.838651\pi\) | ||||
−0.874257 | + | 0.485464i | \(0.838651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37206.0 | −1.64738 | ||||||||
\(800\) | −855.000 | −0.0377860 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25578.0 | −1.12617 | ||||||||
\(803\) | −5160.00 | −0.226765 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6300.00 | 0.275833 | ||||||||
\(806\) | −48129.0 | −2.10331 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 20538.0 | 0.894213 | ||||||||
\(809\) | 33264.0 | 1.44561 | 0.722806 | − | 0.691051i | \(-0.242852\pi\) | ||||
0.722806 | + | 0.691051i | \(0.242852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10258.0 | −0.444152 | −0.222076 | − | 0.975029i | \(-0.571283\pi\) | ||||
−0.222076 | + | 0.975029i | \(0.571283\pi\) | |||||||
\(812\) | 21.0000 | 0.000907581 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7848.00 | 0.337927 | ||||||||
\(815\) | 44364.0 | 1.90675 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1030.00 | 0.0441067 | ||||||||
\(818\) | 40398.0 | 1.72675 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2952.00 | 0.125717 | ||||||||
\(821\) | −33063.0 | −1.40549 | −0.702745 | − | 0.711442i | \(-0.748042\pi\) | ||||
−0.702745 | + | 0.711442i | \(0.748042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13102.0 | −0.554930 | −0.277465 | − | 0.960736i | \(-0.589494\pi\) | ||||
−0.277465 | + | 0.960736i | \(0.589494\pi\) | |||||||
\(824\) | 13755.0 | 0.581527 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5355.00 | −0.225574 | ||||||||
\(827\) | 25182.0 | 1.05884 | 0.529422 | − | 0.848359i | \(-0.322409\pi\) | ||||
0.529422 | + | 0.848359i | \(0.322409\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17170.0 | −0.719347 | −0.359674 | − | 0.933078i | \(-0.617112\pi\) | ||||
−0.359674 | + | 0.933078i | \(0.617112\pi\) | |||||||
\(830\) | 12528.0 | 0.523920 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26413.0 | −1.10061 | ||||||||
\(833\) | −5733.00 | −0.238459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21888.0 | −0.907144 | ||||||||
\(836\) | 24.0000 | 0.000992892 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −46017.0 | −1.89693 | ||||||||
\(839\) | 4458.00 | 0.183441 | 0.0917207 | − | 0.995785i | \(-0.470763\pi\) | ||||
0.0917207 | + | 0.995785i | \(0.470763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24380.0 | −0.999631 | ||||||||
\(842\) | −12306.0 | −0.503673 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4273.00 | −0.174269 | ||||||||
\(845\) | −18288.0 | −0.744528 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8309.00 | −0.337073 | ||||||||
\(848\) | 32589.0 | 1.31971 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6669.00 | −0.269112 | ||||||||
\(851\) | −16350.0 | −0.658603 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39773.0 | 1.59648 | 0.798242 | − | 0.602336i | \(-0.205763\pi\) | ||||
0.798242 | + | 0.602336i | \(0.205763\pi\) | |||||||
\(854\) | −18102.0 | −0.725337 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2268.00 | 0.0905592 | ||||||||
\(857\) | −4191.00 | −0.167050 | −0.0835250 | − | 0.996506i | \(-0.526618\pi\) | ||||
−0.0835250 | + | 0.996506i | \(0.526618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19946.0 | 0.792257 | 0.396128 | − | 0.918195i | \(-0.370353\pi\) | ||||
0.396128 | + | 0.918195i | \(0.370353\pi\) | |||||||
\(860\) | −6180.00 | −0.245042 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7776.00 | −0.307252 | ||||||||
\(863\) | 41067.0 | 1.61986 | 0.809929 | − | 0.586528i | \(-0.199506\pi\) | ||||
0.809929 | + | 0.586528i | \(0.199506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8928.00 | 0.350938 | ||||||||
\(866\) | −28344.0 | −1.11220 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1841.00 | 0.0719903 | ||||||||
\(869\) | −7752.00 | −0.302611 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29219.0 | −1.13668 | ||||||||
\(872\) | −5712.00 | −0.221827 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −450.000 | −0.0174159 | ||||||||
\(875\) | 8904.00 | 0.344012 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32056.0 | −1.23427 | −0.617135 | − | 0.786858i | \(-0.711707\pi\) | ||||
−0.617135 | + | 0.786858i | \(0.711707\pi\) | |||||||
\(878\) | 34107.0 | 1.31100 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10224.0 | 0.391649 | ||||||||
\(881\) | −1899.00 | −0.0726208 | −0.0363104 | − | 0.999341i | \(-0.511561\pi\) | ||||
−0.0363104 | + | 0.999341i | \(0.511561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8021.00 | 0.305694 | 0.152847 | − | 0.988250i | \(-0.451156\pi\) | ||||
0.152847 | + | 0.988250i | \(0.451156\pi\) | |||||||
\(884\) | 7137.00 | 0.271542 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32526.0 | −1.23333 | ||||||||
\(887\) | 6540.00 | 0.247567 | 0.123783 | − | 0.992309i | \(-0.460497\pi\) | ||||
0.123783 | + | 0.992309i | \(0.460497\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12488.0 | 0.471129 | ||||||||
\(890\) | 21060.0 | 0.793183 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2648.00 | 0.0993964 | ||||||||
\(893\) | 636.000 | 0.0238331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54864.0 | 2.04905 | ||||||||
\(896\) | 11613.0 | 0.432995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39420.0 | 1.46488 | ||||||||
\(899\) | 789.000 | 0.0292710 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53703.0 | 1.98569 | ||||||||
\(902\) | −8856.00 | −0.326910 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47376.0 | −1.74303 | ||||||||
\(905\) | 41772.0 | 1.53431 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5780.00 | 0.211601 | 0.105800 | − | 0.994387i | \(-0.466260\pi\) | ||||
0.105800 | + | 0.994387i | \(0.466260\pi\) | |||||||
\(908\) | 5493.00 | 0.200762 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15372.0 | 0.559975 | ||||||||
\(911\) | 27480.0 | 0.999400 | 0.499700 | − | 0.866199i | \(-0.333444\pi\) | ||||
0.499700 | + | 0.866199i | \(0.333444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4176.00 | −0.151375 | ||||||||
\(914\) | 4137.00 | 0.149715 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −790.000 | −0.0284960 | ||||||||
\(917\) | −12243.0 | −0.440894 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7450.00 | −0.267413 | −0.133707 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133707 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(920\) | −18900.0 | −0.677298 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2034.00 | 0.0726532 | ||||||||
\(923\) | 7137.00 | 0.254515 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4142.00 | 0.147230 | ||||||||
\(926\) | 47202.0 | 1.67511 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −135.000 | −0.00477542 | ||||||||
\(929\) | −7602.00 | −0.268475 | −0.134238 | − | 0.990949i | \(-0.542859\pi\) | ||||
−0.134238 | + | 0.990949i | \(0.542859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 98.0000 | 0.00344986 | ||||||||
\(932\) | 6228.00 | 0.218889 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22248.0 | −0.779418 | ||||||||
\(935\) | 16848.0 | 0.589293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6316.00 | −0.220208 | −0.110104 | − | 0.993920i | \(-0.535118\pi\) | ||||
−0.110104 | + | 0.993920i | \(0.535118\pi\) | |||||||
\(938\) | 10059.0 | 0.350147 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3816.00 | −0.132409 | ||||||||
\(941\) | 25170.0 | 0.871964 | 0.435982 | − | 0.899955i | \(-0.356401\pi\) | ||||
0.435982 | + | 0.899955i | \(0.356401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18450.0 | 0.637131 | ||||||||
\(944\) | 18105.0 | 0.624224 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18540.0 | 0.637196 | ||||||||
\(947\) | 20874.0 | 0.716277 | 0.358138 | − | 0.933669i | \(-0.383412\pi\) | ||||
0.358138 | + | 0.933669i | \(0.383412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26230.0 | 0.897220 | ||||||||
\(950\) | 114.000 | 0.00389331 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17199.0 | 0.585528 | ||||||||
\(953\) | −31824.0 | −1.08172 | −0.540861 | − | 0.841112i | \(-0.681901\pi\) | ||||
−0.540861 | + | 0.841112i | \(0.681901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45072.0 | −1.52722 | ||||||||
\(956\) | 4812.00 | 0.162794 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3744.00 | −0.126266 | ||||||||
\(959\) | −9618.00 | −0.323860 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 39378.0 | 1.32181 | ||||||||
\(962\) | −39894.0 | −1.33704 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1622.00 | 0.0541920 | ||||||||
\(965\) | 58404.0 | 1.94828 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7040.00 | 0.234117 | 0.117058 | − | 0.993125i | \(-0.462653\pi\) | ||||
0.117058 | + | 0.993125i | \(0.462653\pi\) | |||||||
\(968\) | 24927.0 | 0.827670 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13536.0 | 0.448056 | ||||||||
\(971\) | −27189.0 | −0.898596 | −0.449298 | − | 0.893382i | \(-0.648326\pi\) | ||||
−0.449298 | + | 0.893382i | \(0.648326\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17150.0 | 0.565060 | ||||||||
\(974\) | −62850.0 | −2.06760 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 61202.0 | 2.00720 | ||||||||
\(977\) | −33438.0 | −1.09496 | −0.547480 | − | 0.836819i | \(-0.684413\pi\) | ||||
−0.547480 | + | 0.836819i | \(0.684413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7020.00 | −0.229173 | ||||||||
\(980\) | −588.000 | −0.0191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2304.00 | −0.0748713 | ||||||||
\(983\) | 16212.0 | 0.526025 | 0.263012 | − | 0.964792i | \(-0.415284\pi\) | ||||
0.263012 | + | 0.964792i | \(0.415284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 216.000 | 0.00698714 | ||||||||
\(986\) | −1053.00 | −0.0340105 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −122.000 | −0.00392848 | ||||||||
\(989\) | −38625.0 | −1.24186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24194.0 | 0.775527 | 0.387764 | − | 0.921759i | \(-0.373248\pi\) | ||||
0.387764 | + | 0.921759i | \(0.373248\pi\) | |||||||
\(992\) | −11835.0 | −0.378792 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2457.00 | −0.0784017 | ||||||||
\(995\) | 21684.0 | 0.690883 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27565.0 | −0.875619 | −0.437810 | − | 0.899068i | \(-0.644246\pi\) | ||||
−0.437810 | + | 0.899068i | \(0.644246\pi\) | |||||||
\(998\) | 14316.0 | 0.454073 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 189.4.a.d.1.1 | yes | 1 | |
3.2 | odd | 2 | 189.4.a.a.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 1323.4.a.n.1.1 | 1 | |||
21.20 | even | 2 | 1323.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.4.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
189.4.a.d.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1323.4.a.a.1.1 | 1 | 21.20 | even | 2 | |||
1323.4.a.n.1.1 | 1 | 7.6 | odd | 2 |