Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.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: | \(76.4664753674\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 81) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.1244 | 1.08444 | 0.542218 | − | 0.840238i | \(-0.317585\pi\) | ||||
0.542218 | + | 0.840238i | \(0.317585\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000 | 1.18789 | 0.593944 | − | 0.804506i | \(-0.297570\pi\) | ||||
0.593944 | + | 0.804506i | \(0.297570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 58.8897 | 1.61417 | 0.807087 | − | 0.590432i | \(-0.201043\pi\) | ||||
0.807087 | + | 0.590432i | \(0.201043\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −49.0000 | −1.04540 | −0.522698 | − | 0.852518i | \(-0.675075\pi\) | ||||
−0.522698 | + | 0.852518i | \(0.675075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36.3731 | −0.518927 | −0.259464 | − | 0.965753i | \(-0.583546\pi\) | ||||
−0.259464 | + | 0.965753i | \(0.583546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70.0000 | 0.845216 | 0.422608 | − | 0.906313i | \(-0.361115\pi\) | ||||
0.422608 | + | 0.906313i | \(0.361115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.2487 | 0.219835 | 0.109918 | − | 0.993941i | \(-0.464941\pi\) | ||||
0.109918 | + | 0.993941i | \(0.464941\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.0000 | 0.176000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 278.860 | 1.78562 | 0.892811 | − | 0.450432i | \(-0.148730\pi\) | ||||
0.892811 | + | 0.450432i | \(0.148730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 112.000 | 0.648897 | 0.324448 | − | 0.945903i | \(-0.394821\pi\) | ||||
0.324448 | + | 0.945903i | \(0.394821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 266.736 | 1.28819 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 281.000 | 1.24854 | 0.624272 | − | 0.781207i | \(-0.285396\pi\) | ||||
0.624272 | + | 0.781207i | \(0.285396\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.4974 | 0.184732 | 0.0923662 | − | 0.995725i | \(-0.470557\pi\) | ||||
0.0923662 | + | 0.995725i | \(0.470557\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −50.0000 | −0.177324 | −0.0886620 | − | 0.996062i | \(-0.528259\pi\) | ||||
−0.0886620 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −242.487 | −0.752561 | −0.376281 | − | 0.926506i | \(-0.622797\pi\) | ||||
−0.376281 | + | 0.926506i | \(0.622797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 141.000 | 0.411079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −374.123 | −0.969618 | −0.484809 | − | 0.874620i | \(-0.661111\pi\) | ||||
−0.484809 | + | 0.874620i | \(0.661111\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 714.000 | 1.75047 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 96.9948 | 0.214028 | 0.107014 | − | 0.994258i | \(-0.465871\pi\) | ||||
0.107014 | + | 0.994258i | \(0.465871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −679.000 | −1.42520 | −0.712599 | − | 0.701572i | \(-0.752482\pi\) | ||||
−0.712599 | + | 0.701572i | \(0.752482\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −594.093 | −1.13366 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 274.000 | 0.499618 | 0.249809 | − | 0.968295i | \(-0.419632\pi\) | ||||
0.249809 | + | 0.968295i | \(0.419632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −446.869 | −0.746952 | −0.373476 | − | 0.927640i | \(-0.621834\pi\) | ||||
−0.373476 | + | 0.927640i | \(0.621834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −511.000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1295.57 | 1.91746 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 526.000 | 0.749109 | 0.374555 | − | 0.927205i | \(-0.377796\pi\) | ||||
0.374555 | + | 0.927205i | \(0.377796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −387.979 | −0.513088 | −0.256544 | − | 0.966533i | \(-0.582584\pi\) | ||||
−0.256544 | + | 0.966533i | \(0.582584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −441.000 | −0.562743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 36.3731 | 0.0433206 | 0.0216603 | − | 0.999765i | \(-0.493105\pi\) | ||||
0.0216603 | + | 0.999765i | \(0.493105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1078.00 | −1.24181 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 848.705 | 0.916582 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1778.00 | 1.86112 | 0.930560 | − | 0.366141i | \(-0.119321\pi\) | ||||
0.930560 | + | 0.366141i | \(0.119321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 242.487 | 0.238895 | 0.119447 | − | 0.992841i | \(-0.461888\pi\) | ||||
0.119447 | + | 0.992841i | \(0.461888\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −896.000 | −0.857141 | −0.428570 | − | 0.903508i | \(-0.640983\pi\) | ||||
−0.428570 | + | 0.903508i | \(0.640983\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −374.123 | −0.338017 | −0.169009 | − | 0.985615i | \(-0.554057\pi\) | ||||
−0.169009 | + | 0.985615i | \(0.554057\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −205.000 | −0.180142 | −0.0900708 | − | 0.995935i | \(-0.528709\pi\) | ||||
−0.0900708 | + | 0.995935i | \(0.528709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −361.999 | −0.301363 | −0.150681 | − | 0.988582i | \(-0.548147\pi\) | ||||
−0.150681 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 294.000 | 0.238397 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −800.207 | −0.616428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2137.00 | 1.60556 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1248.81 | −0.893575 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −146.000 | −0.102011 | −0.0510055 | − | 0.998698i | \(-0.516243\pi\) | ||||
−0.0510055 | + | 0.998698i | \(0.516243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2643.11 | 1.76282 | 0.881411 | − | 0.472351i | \(-0.156595\pi\) | ||||
0.881411 | + | 0.472351i | \(0.156595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1540.00 | 1.00402 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1965.88 | −1.22596 | −0.612979 | − | 0.790099i | \(-0.710029\pi\) | ||||
−0.612979 | + | 0.790099i | \(0.710029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3136.00 | 1.91361 | 0.956806 | − | 0.290727i | \(-0.0938973\pi\) | ||||
0.956806 | + | 0.290727i | \(0.0938973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2885.60 | −1.68745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3381.00 | 1.93639 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 313.501 | 0.172369 | 0.0861846 | − | 0.996279i | \(-0.472533\pi\) | ||||
0.0861846 | + | 0.996279i | \(0.472533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2092.00 | 1.12745 | 0.563724 | − | 0.825963i | \(-0.309368\pi\) | ||||
0.563724 | + | 0.825963i | \(0.309368\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1357.93 | 0.703686 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1337.00 | 0.679645 | 0.339822 | − | 0.940490i | \(-0.389633\pi\) | ||||
0.339822 | + | 0.940490i | \(0.389633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 533.472 | 0.261139 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1744.00 | 0.838041 | 0.419020 | − | 0.907977i | \(-0.362374\pi\) | ||||
0.419020 | + | 0.907977i | \(0.362374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2740.10 | −1.26967 | −0.634837 | − | 0.772646i | \(-0.718933\pi\) | ||||
−0.634837 | + | 0.772646i | \(0.718933\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 204.000 | 0.0928539 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2194.51 | −0.964424 | −0.482212 | − | 0.876055i | \(-0.660167\pi\) | ||||
−0.482212 | + | 0.876055i | \(0.660167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 484.000 | 0.209068 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2473.37 | −1.03278 | −0.516392 | − | 0.856352i | \(-0.672725\pi\) | ||||
−0.516392 | + | 0.856352i | \(0.672725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −70.0000 | −0.0287462 | −0.0143731 | − | 0.999897i | \(-0.504575\pi\) | ||||
−0.0143731 | + | 0.999897i | \(0.504575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3406.94 | 1.35396 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2142.00 | −0.837639 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2075.00 | 0.786081 | 0.393041 | − | 0.919521i | \(-0.371423\pi\) | ||||
0.393041 | + | 0.919521i | \(0.371423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −121.000 | −0.0451283 | −0.0225642 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225642 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2956.61 | −1.06929 | −0.534644 | − | 0.845077i | \(-0.679554\pi\) | ||||
−0.534644 | + | 0.845077i | \(0.679554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4228.00 | 1.50611 | 0.753053 | − | 0.657960i | \(-0.228581\pi\) | ||||
0.753053 | + | 0.657960i | \(0.228581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6134.92 | 2.12112 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 588.000 | 0.200330 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4122.28 | 1.36433 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 202.000 | 0.0659064 | 0.0329532 | − | 0.999457i | \(-0.489509\pi\) | ||||
0.0329532 | + | 0.999457i | \(0.489509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −606.218 | −0.192296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2464.00 | 0.770817 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1782.28 | 0.542485 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 238.000 | 0.0714693 | 0.0357347 | − | 0.999361i | \(-0.488623\pi\) | ||||
0.0357347 | + | 0.999361i | \(0.488623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5552.95 | −1.62362 | −0.811812 | − | 0.583919i | \(-0.801518\pi\) | ||||
−0.811812 | + | 0.583919i | \(0.801518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2975.00 | 0.858487 | 0.429244 | − | 0.903189i | \(-0.358780\pi\) | ||||
0.429244 | + | 0.903189i | \(0.358780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 181.865 | 0.0511347 | 0.0255674 | − | 0.999673i | \(-0.491861\pi\) | ||||
0.0255674 | + | 0.999673i | \(0.491861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2940.00 | −0.816104 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5417.85 | 1.46633 | 0.733163 | − | 0.680053i | \(-0.238043\pi\) | ||||
0.733163 | + | 0.680053i | \(0.238043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2443.00 | −0.652977 | −0.326489 | − | 0.945201i | \(-0.605865\pi\) | ||||
−0.326489 | + | 0.945201i | \(0.605865\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1709.53 | 0.445788 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3430.00 | −0.883586 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5310.47 | 1.33543 | 0.667717 | − | 0.744416i | \(-0.267272\pi\) | ||||
0.667717 | + | 0.744416i | \(0.267272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1428.00 | 0.354852 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7795.96 | 1.89221 | 0.946106 | − | 0.323856i | \(-0.104979\pi\) | ||||
0.946106 | + | 0.323856i | \(0.104979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6182.00 | 1.48313 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2487.22 | −0.583152 | −0.291576 | − | 0.956548i | \(-0.594180\pi\) | ||||
−0.291576 | + | 0.956548i | \(0.594180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4536.00 | −1.05149 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 109.119 | 0.0247328 | 0.0123664 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123664 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5614.00 | 1.25840 | 0.629200 | − | 0.777244i | \(-0.283383\pi\) | ||||
0.629200 | + | 0.777244i | \(0.283383\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1295.57 | 0.284095 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6026.00 | 1.30710 | 0.653551 | − | 0.756882i | \(-0.273279\pi\) | ||||
0.653551 | + | 0.756882i | \(0.273279\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4657.48 | −0.988762 | −0.494381 | − | 0.869245i | \(-0.664605\pi\) | ||||
−0.494381 | + | 0.869245i | \(0.664605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −140.000 | −0.0294068 | −0.0147034 | − | 0.999892i | \(-0.504680\pi\) | ||||
−0.0147034 | + | 0.999892i | \(0.504680\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1066.94 | 0.219441 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3590.00 | −0.730714 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2485.49 | 0.495577 | 0.247788 | − | 0.968814i | \(-0.420296\pi\) | ||||
0.247788 | + | 0.968814i | \(0.420296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1176.00 | 0.232100 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1188.19 | −0.229815 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1100.00 | −0.210641 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8232.44 | −1.54553 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2968.00 | 0.551768 | 0.275884 | − | 0.961191i | \(-0.411029\pi\) | ||||
0.275884 | + | 0.961191i | \(0.411029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5286.22 | −0.963839 | −0.481920 | − | 0.876215i | \(-0.660060\pi\) | ||||
−0.481920 | + | 0.876215i | \(0.660060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5593.00 | −1.01002 | −0.505008 | − | 0.863115i | \(-0.668510\pi\) | ||||
−0.505008 | + | 0.863115i | \(0.668510\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7504.98 | −1.32972 | −0.664860 | − | 0.746968i | \(-0.731509\pi\) | ||||
−0.664860 | + | 0.746968i | \(0.731509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16422.0 | 2.88231 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2546.11 | −0.438606 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1078.00 | −0.183990 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5334.72 | −0.893959 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7754.00 | −1.28761 | −0.643804 | − | 0.765190i | \(-0.722645\pi\) | ||||
−0.643804 | + | 0.765190i | \(0.722645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3322.07 | 0.541804 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2570.00 | 0.415421 | 0.207710 | − | 0.978190i | \(-0.433399\pi\) | ||||
0.207710 | + | 0.978190i | \(0.433399\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6595.65 | 1.04743 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4444.00 | −0.699573 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5587.60 | −0.864432 | −0.432216 | − | 0.901770i | \(-0.642268\pi\) | ||||
−0.432216 | + | 0.901770i | \(0.642268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6790.00 | −1.04143 | −0.520717 | − | 0.853729i | \(-0.674335\pi\) | ||||
−0.520717 | + | 0.853729i | \(0.674335\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8244.56 | 1.24310 | 0.621549 | − | 0.783375i | \(-0.286504\pi\) | ||||
0.621549 | + | 0.783375i | \(0.286504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5418.00 | −0.810021 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7409.71 | −1.08933 | −0.544665 | − | 0.838653i | \(-0.683343\pi\) | ||||
−0.544665 | + | 0.838653i | \(0.683343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1959.00 | −0.285610 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6195.55 | −0.888465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9436.00 | 1.34211 | 0.671056 | − | 0.741407i | \(-0.265841\pi\) | ||||
0.671056 | + | 0.741407i | \(0.265841\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8230.71 | −1.15180 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1742.00 | 0.241816 | 0.120908 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120908 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13664.1 | −1.86668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8408.00 | −1.13955 | −0.569776 | − | 0.821800i | \(-0.692970\pi\) | ||||
−0.569776 | + | 0.821800i | \(0.692970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2497.62 | 0.333217 | 0.166609 | − | 0.986023i | \(-0.446718\pi\) | ||||
0.166609 | + | 0.986023i | \(0.446718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15708.0 | 2.07936 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5334.72 | 0.695324 | 0.347662 | − | 0.937620i | \(-0.386976\pi\) | ||||
0.347662 | + | 0.937620i | \(0.386976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −882.000 | −0.114078 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6377.41 | 0.812360 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8813.00 | 1.11414 | 0.557068 | − | 0.830467i | \(-0.311926\pi\) | ||||
0.557068 | + | 0.830467i | \(0.311926\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8145.83 | −1.01442 | −0.507211 | − | 0.861822i | \(-0.669324\pi\) | ||||
−0.507211 | + | 0.861822i | \(0.669324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5488.00 | −0.678354 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16548.0 | 2.01537 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6125.00 | 0.740493 | 0.370247 | − | 0.928933i | \(-0.379273\pi\) | ||||
0.370247 | + | 0.928933i | \(0.379273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2133.89 | 0.254241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4704.00 | −0.556410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5189.22 | 0.605036 | 0.302518 | − | 0.953144i | \(-0.402173\pi\) | ||||
0.302518 | + | 0.953144i | \(0.402173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3695.00 | 0.427751 | 0.213876 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213876 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −800.207 | −0.0913312 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14938.0 | −1.69298 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2618.86 | −0.292682 | −0.146341 | − | 0.989234i | \(-0.546750\pi\) | ||||
−0.146341 | + | 0.989234i | \(0.546750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15757.0 | −1.74881 | −0.874403 | − | 0.485200i | \(-0.838747\pi\) | ||||
−0.874403 | + | 0.485200i | \(0.838747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1697.41 | 0.185808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 868.000 | 0.0943676 | 0.0471838 | − | 0.998886i | \(-0.484975\pi\) | ||||
0.0471838 | + | 0.998886i | \(0.484975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5771.19 | −0.618956 | −0.309478 | − | 0.950907i | \(-0.600154\pi\) | ||||
−0.309478 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 441.000 | 0.0469784 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18560.7 | 1.95085 | 0.975425 | − | 0.220332i | \(-0.0707142\pi\) | ||||
0.975425 | + | 0.220332i | \(0.0707142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2856.00 | 0.298190 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13070.1 | −1.34667 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2659.00 | −0.272172 | −0.136086 | − | 0.990697i | \(-0.543452\pi\) | ||||
−0.136086 | + | 0.990697i | \(0.543452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 387.979 | 0.0391974 | 0.0195987 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0195987 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8968.00 | 0.900169 | 0.450085 | − | 0.892986i | \(-0.351394\pi\) | ||||
0.450085 | + | 0.892986i | \(0.351394\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10620.9 | −1.05242 | −0.526208 | − | 0.850356i | \(-0.676387\pi\) | ||||
−0.526208 | + | 0.850356i | \(0.676387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6028.00 | 0.593491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2944.49 | −0.286232 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1540.00 | 0.148758 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15252.4 | 1.45491 | 0.727455 | − | 0.686156i | \(-0.240703\pi\) | ||||
0.727455 | + | 0.686156i | \(0.240703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13769.0 | −1.30522 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21557.1 | 2.01826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3688.00 | 0.343161 | 0.171580 | − | 0.985170i | \(-0.445113\pi\) | ||||
0.171580 | + | 0.985170i | \(0.445113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10596.7 | −0.973975 | −0.486988 | − | 0.873409i | \(-0.661904\pi\) | ||||
−0.486988 | + | 0.873409i | \(0.661904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10143.0 | −0.926608 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9831.12 | −0.887296 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18086.0 | −1.62253 | −0.811263 | − | 0.584681i | \(-0.801220\pi\) | ||||
−0.811263 | + | 0.584681i | \(0.801220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21096.4 | 1.87006 | 0.935031 | − | 0.354566i | \(-0.115371\pi\) | ||||
0.935031 | + | 0.354566i | \(0.115371\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2940.00 | 0.259066 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2424.87 | −0.211160 | −0.105580 | − | 0.994411i | \(-0.533670\pi\) | ||||
−0.105580 | + | 0.994411i | \(0.533670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11242.0 | −0.973223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10863.4 | −0.929514 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14280.0 | −1.21477 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15858.7 | 1.33355 | 0.666776 | − | 0.745258i | \(-0.267674\pi\) | ||||
0.666776 | + | 0.745258i | \(0.267674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7238.00 | −0.605154 | −0.302577 | − | 0.953125i | \(-0.597847\pi\) | ||||
−0.302577 | + | 0.953125i | \(0.597847\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4073.78 | −0.336730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11579.0 | −0.951673 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2376.37 | −0.193119 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4536.00 | −0.366558 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8303.45 | 0.663553 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15541.0 | −1.23505 | −0.617523 | − | 0.786553i | \(-0.711864\pi\) | ||||
−0.617523 | + | 0.786553i | \(0.711864\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2485.49 | −0.195352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12956.0 | −1.01272 | −0.506361 | − | 0.862322i | \(-0.669010\pi\) | ||||
−0.506361 | + | 0.862322i | \(0.669010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19520.2 | 1.50924 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11572.0 | 0.889858 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18960.8 | −1.44236 | −0.721179 | − | 0.692749i | \(-0.756399\pi\) | ||||
−0.721179 | + | 0.692749i | \(0.756399\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2450.00 | 0.185374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18574.5 | 1.39045 | 0.695224 | − | 0.718793i | \(-0.255305\pi\) | ||||
0.695224 | + | 0.718793i | \(0.255305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4389.00 | −0.326808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2305.36 | 0.169852 | 0.0849259 | − | 0.996387i | \(-0.472935\pi\) | ||||
0.0849259 | + | 0.996387i | \(0.472935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −968.000 | −0.0709449 | −0.0354725 | − | 0.999371i | \(-0.511294\pi\) | ||||
−0.0354725 | + | 0.999371i | \(0.511294\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 533.472 | 0.0386910 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18011.0 | 1.29949 | 0.649747 | − | 0.760151i | \(-0.274875\pi\) | ||||
0.649747 | + | 0.760151i | \(0.274875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8535.55 | −0.609491 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22032.0 | −1.56513 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23594.0 | −1.65899 | −0.829496 | − | 0.558512i | \(-0.811372\pi\) | ||||
−0.829496 | + | 0.558512i | \(0.811372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7840.00 | 0.548458 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2727.98 | −0.188912 | −0.0944559 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944559 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9702.00 | −0.668476 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15990.3 | −1.09073 | −0.545364 | − | 0.838200i | \(-0.683608\pi\) | ||||
−0.545364 | + | 0.838200i | \(0.683608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21217.0 | −1.44003 | −0.720016 | − | 0.693957i | \(-0.755866\pi\) | ||||
−0.720016 | + | 0.693957i | \(0.755866\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25909.7 | 1.74113 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2786.00 | −0.186294 | −0.0931468 | − | 0.995652i | \(-0.529693\pi\) | ||||
−0.0931468 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11881.9 | 0.786725 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9178.00 | −0.604724 | −0.302362 | − | 0.953193i | \(-0.597775\pi\) | ||||
−0.302362 | + | 0.953193i | \(0.597775\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15628.3 | −1.01973 | −0.509863 | − | 0.860255i | \(-0.670304\pi\) | ||||
−0.509863 | + | 0.860255i | \(0.670304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13748.0 | −0.892696 | −0.446348 | − | 0.894859i | \(-0.647276\pi\) | ||||
−0.446348 | + | 0.894859i | \(0.647276\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 800.207 | 0.0514601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17891.0 | −1.14502 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10220.8 | −0.647903 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8948.00 | −0.564523 | −0.282262 | − | 0.959337i | \(-0.591085\pi\) | ||||
−0.282262 | + | 0.959337i | \(0.591085\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1770.16 | −0.110624 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6909.00 | −0.429740 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5745.21 | 0.354013 | 0.177006 | − | 0.984210i | \(-0.443359\pi\) | ||||
0.177006 | + | 0.984210i | \(0.443359\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3920.00 | −0.240419 | −0.120210 | − | 0.992749i | \(-0.538357\pi\) | ||||
−0.120210 | + | 0.992749i | \(0.538357\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2837.10 | −0.172392 | −0.0861962 | − | 0.996278i | \(-0.527471\pi\) | ||||
−0.0861962 | + | 0.996278i | \(0.527471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5712.00 | 0.345479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20673.8 | −1.23894 | −0.619469 | − | 0.785021i | \(-0.712652\pi\) | ||||
−0.619469 | + | 0.785021i | \(0.712652\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32046.0 | 1.91167 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3308.22 | −0.195554 | −0.0977768 | − | 0.995208i | \(-0.531173\pi\) | ||||
−0.0977768 | + | 0.995208i | \(0.531173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32431.0 | −1.90835 | −0.954175 | − | 0.299248i | \(-0.903264\pi\) | ||||
−0.954175 | + | 0.299248i | \(0.903264\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18671.5 | 1.08880 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6762.00 | 0.392542 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39986.1 | −2.30052 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20399.0 | 1.16839 | 0.584193 | − | 0.811615i | \(-0.301411\pi\) | ||||
0.584193 | + | 0.811615i | \(0.301411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 387.979 | 0.0220255 | 0.0110127 | − | 0.999939i | \(-0.496494\pi\) | ||||
0.0110127 | + | 0.999939i | \(0.496494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39116.0 | 2.21080 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25669.0 | 1.43806 | 0.719031 | − | 0.694978i | \(-0.244586\pi\) | ||||
0.719031 | + | 0.694978i | \(0.244586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23835.0 | −1.32947 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18332.0 | 1.01364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5782.00 | 0.318318 | 0.159159 | − | 0.987253i | \(-0.449122\pi\) | ||||
0.159159 | + | 0.987253i | \(0.449122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 38022.0 | 2.07519 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1764.00 | −0.0958626 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13047.5 | −0.702994 | −0.351497 | − | 0.936189i | \(-0.614327\pi\) | ||||
−0.351497 | + | 0.936189i | \(0.614327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19670.0 | 1.05529 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5334.72 | 0.283780 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17879.0 | 0.947052 | 0.473526 | − | 0.880780i | \(-0.342981\pi\) | ||||
0.473526 | + | 0.880780i | \(0.342981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2715.86 | 0.142650 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34986.0 | −1.82993 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10548.2 | −0.547123 | −0.273561 | − | 0.961855i | \(-0.588202\pi\) | ||||
−0.273561 | + | 0.961855i | \(0.588202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19712.0 | −1.01819 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6134.92 | 0.314269 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32746.0 | 1.67054 | 0.835270 | − | 0.549841i | \(-0.185312\pi\) | ||||
0.835270 | + | 0.549841i | \(0.185312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1818.65 | 0.0920182 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27482.0 | 1.38482 | 0.692408 | − | 0.721506i | \(-0.256550\pi\) | ||||
0.692408 | + | 0.721506i | \(0.256550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16135.8 | 0.806471 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24716.0 | −1.23030 | −0.615151 | − | 0.788410i | \(-0.710905\pi\) | ||||
−0.615151 | + | 0.788410i | \(0.710905\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31849.0 | −1.57258 | −0.786288 | − | 0.617860i | \(-0.788000\pi\) | ||||
−0.786288 | + | 0.617860i | \(0.788000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3801.00 | 0.186923 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8230.71 | −0.401527 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7358.00 | −0.357520 | −0.178760 | − | 0.983893i | \(-0.557209\pi\) | ||||
−0.178760 | + | 0.983893i | \(0.557209\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25364.2 | 1.22264 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30886.0 | −1.48292 | −0.741460 | − | 0.670997i | \(-0.765866\pi\) | ||||
−0.741460 | + | 0.670997i | \(0.765866\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23775.9 | −1.13255 | −0.566277 | − | 0.824215i | \(-0.691617\pi\) | ||||
−0.566277 | + | 0.824215i | \(0.691617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4510.00 | −0.213988 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4752.75 | −0.223744 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7609.00 | −0.356811 | −0.178405 | − | 0.983957i | \(-0.557094\pi\) | ||||
−0.178405 | + | 0.983957i | \(0.557094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10293.6 | −0.478958 | −0.239479 | − | 0.970902i | \(-0.576977\pi\) | ||||
−0.239479 | + | 0.970902i | \(0.576977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2464.00 | 0.114206 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3394.82 | 0.156139 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26316.0 | −1.20571 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16210.3 | 0.737031 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40054.0 | 1.81419 | 0.907097 | − | 0.420921i | \(-0.138293\pi\) | ||||
0.907097 | + | 0.420921i | \(0.138293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7963.97 | −0.357985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33271.0 | 1.48990 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10099.6 | −0.448865 | −0.224433 | − | 0.974490i | \(-0.572053\pi\) | ||||
−0.224433 | + | 0.974490i | \(0.572053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8820.00 | 0.390525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30092.7 | −1.32247 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6468.00 | 0.283189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9773.96 | −0.424764 | −0.212382 | − | 0.977187i | \(-0.568122\pi\) | ||||
−0.212382 | + | 0.977187i | \(0.568122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35840.0 | −1.55180 | −0.775902 | − | 0.630854i | \(-0.782705\pi\) | ||||
−0.775902 | + | 0.630854i | \(0.782705\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21144.9 | 0.908801 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3500.00 | −0.149877 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8024.59 | −0.341121 | −0.170560 | − | 0.985347i | \(-0.554558\pi\) | ||||
−0.170560 | + | 0.985347i | \(0.554558\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14828.0 | −0.628034 | −0.314017 | − | 0.949417i | \(-0.601675\pi\) | ||||
−0.314017 | + | 0.949417i | \(0.601675\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38981.5 | −1.63908 | −0.819541 | − | 0.573021i | \(-0.805772\pi\) | ||||
−0.819541 | + | 0.573021i | \(0.805772\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27146.0 | 1.13730 | 0.568649 | − | 0.822580i | \(-0.307466\pi\) | ||||
0.568649 | + | 0.822580i | \(0.307466\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5128.60 | −0.213320 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33222.0 | −1.37688 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24176.0 | −0.994812 | −0.497406 | − | 0.867518i | \(-0.665714\pi\) | ||||
−0.497406 | + | 0.867518i | \(0.665714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53374.0 | 2.18845 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2473.37 | 0.100694 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47014.0 | 1.90723 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6813.89 | 0.274474 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19670.0 | 0.789552 | 0.394776 | − | 0.918777i | \(-0.370822\pi\) | ||||
0.394776 | + | 0.918777i | \(0.370822\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 133.368 | 0.00531594 | 0.00265797 | − | 0.999996i | \(-0.499154\pi\) | ||||
0.00265797 | + | 0.999996i | \(0.499154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14756.0 | −0.586110 | −0.293055 | − | 0.956096i | \(-0.594672\pi\) | ||||
−0.293055 | + | 0.956096i | \(0.594672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28215.1 | −1.11292 | −0.556462 | − | 0.830873i | \(-0.687842\pi\) | ||||
−0.556462 | + | 0.830873i | \(0.687842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26607.0 | −1.04586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30976.0 | 1.20919 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13426.0 | −0.522299 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27473.8 | −1.06147 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31963.0 | −1.23069 | −0.615344 | − | 0.788258i | \(-0.710983\pi\) | ||||
−0.615344 | + | 0.788258i | \(0.710983\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31571.8 | −1.20736 | −0.603679 | − | 0.797228i | \(-0.706299\pi\) | ||||
−0.603679 | + | 0.797228i | \(0.706299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34112.0 | −1.30007 | −0.650034 | − | 0.759905i | \(-0.725245\pi\) | ||||
−0.650034 | + | 0.759905i | \(0.725245\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36688.3 | 1.38881 | 0.694404 | − | 0.719585i | \(-0.255668\pi\) | ||||
0.694404 | + | 0.719585i | \(0.255668\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3212.00 | −0.121178 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16974.1 | −0.636077 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29988.0 | −1.11999 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31232.3 | 1.15868 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13608.0 | 0.503161 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −848.705 | −0.0311734 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36716.0 | −1.34414 | −0.672070 | − | 0.740488i | \(-0.734595\pi\) | ||||
−0.672070 | + | 0.740488i | \(0.734595\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54535.4 | 1.98336 | 0.991678 | − | 0.128745i | \(-0.0410949\pi\) | ||||
0.991678 | + | 0.128745i | \(0.0410949\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22848.0 | −0.828213 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 58148.4 | 2.09403 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4318.00 | 0.154992 | 0.0774960 | − | 0.996993i | \(-0.475307\pi\) | ||||
0.0774960 | + | 0.996993i | \(0.475307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21896.6 | 0.780861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6182.00 | 0.219744 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33402.6 | −1.17966 | −0.589830 | − | 0.807528i | \(-0.700805\pi\) | ||||
−0.589830 | + | 0.807528i | \(0.700805\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9870.00 | 0.347450 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25970.4 | −0.908366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13489.0 | −0.470295 | −0.235148 | − | 0.971960i | \(-0.575557\pi\) | ||||
−0.235148 | + | 0.971960i | \(0.575557\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20599.3 | 0.713621 | 0.356810 | − | 0.934177i | \(-0.383864\pi\) | ||||
0.356810 | + | 0.934177i | \(0.383864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1176.00 | 0.0406106 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15543.4 | 0.533362 | 0.266681 | − | 0.963785i | \(-0.414073\pi\) | ||||
0.266681 | + | 0.963785i | \(0.414073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25039.0 | 0.856481 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2582.49 | −0.0877807 | −0.0438903 | − | 0.999036i | \(-0.513975\pi\) | ||||
−0.0438903 | + | 0.999036i | \(0.513975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25158.0 | 0.852454 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −43249.3 | −1.45630 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17247.0 | −0.578933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1467.05 | −0.0489388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41494.0 | 1.37989 | 0.689947 | − | 0.723860i | \(-0.257634\pi\) | ||||
0.689947 | + | 0.723860i | \(0.257634\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2837.10 | 0.0937661 | 0.0468830 | − | 0.998900i | \(-0.485071\pi\) | ||||
0.0468830 | + | 0.998900i | \(0.485071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68992.0 | 2.27316 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47479.0 | 1.55475 | 0.777373 | − | 0.629040i | \(-0.216552\pi\) | ||||
0.777373 | + | 0.629040i | \(0.216552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2142.00 | 0.0699271 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17798.6 | 0.577503 | 0.288752 | − | 0.957404i | \(-0.406760\pi\) | ||||
0.288752 | + | 0.957404i | \(0.406760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35847.0 | −1.15957 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1212.44 | −0.0389820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21706.0 | 0.695776 | 0.347888 | − | 0.937536i | \(-0.386899\pi\) | ||||
0.347888 | + | 0.937536i | \(0.386899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51261.8 | 1.63327 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25375.0 | −0.806052 | −0.403026 | − | 0.915188i | \(-0.632042\pi\) | ||||
−0.403026 | + | 0.915188i | \(0.632042\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1296.4.a.o.1.2 | 2 | ||
3.2 | odd | 2 | inner | 1296.4.a.o.1.1 | 2 | ||
4.3 | odd | 2 | 81.4.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 81.4.a.c.1.2 | yes | 2 | ||
20.19 | odd | 2 | 2025.4.a.k.1.2 | 2 | |||
36.7 | odd | 6 | 81.4.c.f.28.2 | 4 | |||
36.11 | even | 6 | 81.4.c.f.28.1 | 4 | |||
36.23 | even | 6 | 81.4.c.f.55.1 | 4 | |||
36.31 | odd | 6 | 81.4.c.f.55.2 | 4 | |||
60.59 | even | 2 | 2025.4.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
81.4.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
81.4.a.c.1.2 | yes | 2 | 12.11 | even | 2 | ||
81.4.c.f.28.1 | 4 | 36.11 | even | 6 | |||
81.4.c.f.28.2 | 4 | 36.7 | odd | 6 | |||
81.4.c.f.55.1 | 4 | 36.23 | even | 6 | |||
81.4.c.f.55.2 | 4 | 36.31 | odd | 6 | |||
1296.4.a.o.1.1 | 2 | 3.2 | odd | 2 | inner | ||
1296.4.a.o.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2025.4.a.k.1.1 | 2 | 60.59 | even | 2 | |||
2025.4.a.k.1.2 | 2 | 20.19 | odd | 2 |