Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.47977.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 60x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(8.58548\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.46549 | 0.511088 | 0.255544 | − | 0.966797i | \(-0.417745\pi\) | ||||
0.255544 | + | 0.966797i | \(0.417745\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 49.0474 | 1.34439 | 0.672197 | − | 0.740372i | \(-0.265351\pi\) | ||||
0.672197 | + | 0.740372i | \(0.265351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.4438 | 1.18287 | 0.591437 | − | 0.806351i | \(-0.298561\pi\) | ||||
0.591437 | + | 0.806351i | \(0.298561\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −27.9783 | −0.399162 | −0.199581 | − | 0.979881i | \(-0.563958\pi\) | ||||
−0.199581 | + | 0.979881i | \(0.563958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.3965 | 0.318724 | 0.159362 | − | 0.987220i | \(-0.449056\pi\) | ||||
0.159362 | + | 0.987220i | \(0.449056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.53451 | 0.0864384 | 0.0432192 | − | 0.999066i | \(-0.486239\pi\) | ||||
0.0432192 | + | 0.999066i | \(0.486239\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 218.379 | 1.39834 | 0.699171 | − | 0.714954i | \(-0.253552\pi\) | ||||
0.699171 | + | 0.714954i | \(0.253552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −158.961 | −0.920974 | −0.460487 | − | 0.887666i | \(-0.652325\pi\) | ||||
−0.460487 | + | 0.887666i | \(0.652325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 47.3274 | 0.228566 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 189.655 | 0.842678 | 0.421339 | − | 0.906903i | \(-0.361560\pi\) | ||||
0.421339 | + | 0.906903i | \(0.361560\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −246.146 | −0.937599 | −0.468800 | − | 0.883304i | \(-0.655313\pi\) | ||||
−0.468800 | + | 0.883304i | \(0.655313\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 40.2327 | 0.142684 | 0.0713422 | − | 0.997452i | \(-0.477272\pi\) | ||||
0.0713422 | + | 0.997452i | \(0.477272\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −213.965 | −0.664042 | −0.332021 | − | 0.943272i | \(-0.607730\pi\) | ||||
−0.332021 | + | 0.943272i | \(0.607730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −253.405 | −0.738789 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −283.310 | −0.734257 | −0.367128 | − | 0.930170i | \(-0.619659\pi\) | ||||
−0.367128 | + | 0.930170i | \(0.619659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 245.237 | 0.601232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −92.0000 | −0.203006 | −0.101503 | − | 0.994835i | \(-0.532365\pi\) | ||||
−0.101503 | + | 0.994835i | \(0.532365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 370.172 | 0.776978 | 0.388489 | − | 0.921453i | \(-0.372997\pi\) | ||||
0.388489 | + | 0.921453i | \(0.372997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 277.219 | 0.528997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1087.53 | 1.98302 | 0.991510 | − | 0.130029i | \(-0.0415071\pi\) | ||||
0.991510 | + | 0.130029i | \(0.0415071\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 333.681 | 0.557755 | 0.278877 | − | 0.960327i | \(-0.410038\pi\) | ||||
0.278877 | + | 0.960327i | \(0.410038\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −606.791 | −0.972871 | −0.486435 | − | 0.873717i | \(-0.661703\pi\) | ||||
−0.486435 | + | 0.873717i | \(0.661703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 464.257 | 0.687104 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −44.3751 | −0.0631973 | −0.0315986 | − | 0.999501i | \(-0.510060\pi\) | ||||
−0.0315986 | + | 0.999501i | \(0.510060\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −107.732 | −0.142471 | −0.0712355 | − | 0.997460i | \(-0.522694\pi\) | ||||
−0.0712355 | + | 0.997460i | \(0.522694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −139.892 | −0.178510 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 257.819 | 0.307065 | 0.153532 | − | 0.988144i | \(-0.450935\pi\) | ||||
0.153532 | + | 0.988144i | \(0.450935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 524.803 | 0.604553 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 131.982 | 0.142538 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1312.05 | 1.37339 | 0.686693 | − | 0.726947i | \(-0.259062\pi\) | ||||
0.686693 | + | 0.726947i | \(0.259062\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −63.3293 | −0.0623911 | −0.0311955 | − | 0.999513i | \(-0.509931\pi\) | ||||
−0.0311955 | + | 0.999513i | \(0.509931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1219.85 | 1.16695 | 0.583474 | − | 0.812132i | \(-0.301693\pi\) | ||||
0.583474 | + | 0.812132i | \(0.301693\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −42.3947 | −0.0383033 | −0.0191517 | − | 0.999817i | \(-0.506097\pi\) | ||||
−0.0191517 | + | 0.999817i | \(0.506097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 266.741 | 0.234396 | 0.117198 | − | 0.993109i | \(-0.462609\pi\) | ||||
0.117198 | + | 0.993109i | \(0.462609\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1871.60 | −1.55810 | −0.779049 | − | 0.626964i | \(-0.784297\pi\) | ||||
−0.779049 | + | 0.626964i | \(0.784297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 47.6726 | 0.0386564 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −264.829 | −0.204007 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1074.64 | 0.807397 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1232.11 | −0.860881 | −0.430441 | − | 0.902619i | \(-0.641642\pi\) | ||||
−0.430441 | + | 0.902619i | \(0.641642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1209.17 | 0.806458 | 0.403229 | − | 0.915099i | \(-0.367888\pi\) | ||||
0.403229 | + | 0.915099i | \(0.367888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 249.855 | 0.162896 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2629.66 | −1.63990 | −0.819952 | − | 0.572432i | \(-0.806000\pi\) | ||||
−0.819952 | + | 0.572432i | \(0.806000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2215.06 | 1.35165 | 0.675823 | − | 0.737064i | \(-0.263788\pi\) | ||||
0.675823 | + | 0.737064i | \(0.263788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2719.37 | 1.59025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1091.89 | 0.625358 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2446.94 | −1.34538 | −0.672689 | − | 0.739925i | \(-0.734861\pi\) | ||||
−0.672689 | + | 0.739925i | \(0.734861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 119.365 | 0.0643298 | 0.0321649 | − | 0.999483i | \(-0.489760\pi\) | ||||
0.0321649 | + | 0.999483i | \(0.489760\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −794.804 | −0.411872 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2212.86 | 1.12487 | 0.562437 | − | 0.826840i | \(-0.309864\pi\) | ||||
0.562437 | + | 0.826840i | \(0.309864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 90.2488 | 0.0441777 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3480.54 | 1.67250 | 0.836249 | − | 0.548349i | \(-0.184744\pi\) | ||||
0.836249 | + | 0.548349i | \(0.184744\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2477.15 | 1.14783 | 0.573916 | − | 0.818914i | \(-0.305424\pi\) | ||||
0.573916 | + | 0.818914i | \(0.305424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 877.018 | 0.399189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −26.7446 | −0.0117535 | −0.00587676 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587676 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 236.637 | 0.102218 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1400.75 | −0.584901 | −0.292451 | − | 0.956281i | \(-0.594471\pi\) | ||||
−0.292451 | + | 0.956281i | \(0.594471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3492.48 | 1.43422 | 0.717111 | − | 0.696959i | \(-0.245464\pi\) | ||||
0.717111 | + | 0.696959i | \(0.245464\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 948.275 | 0.376857 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1372.26 | −0.536631 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2728.16 | 1.03352 | 0.516762 | − | 0.856129i | \(-0.327137\pi\) | ||||
0.516762 | + | 0.856129i | \(0.327137\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2439.82 | 0.909959 | 0.454980 | − | 0.890502i | \(-0.349647\pi\) | ||||
0.454980 | + | 0.890502i | \(0.349647\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 765.906 | 0.276998 | 0.138499 | − | 0.990363i | \(-0.455772\pi\) | ||||
0.138499 | + | 0.990363i | \(0.455772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 754.031 | 0.268602 | 0.134301 | − | 0.990941i | \(-0.457121\pi\) | ||||
0.134301 | + | 0.990941i | \(0.457121\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2067.06 | 0.714676 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1230.73 | −0.419307 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1294.68 | 0.428491 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1024.68 | −0.334320 | −0.167160 | − | 0.985930i | \(-0.553460\pi\) | ||||
−0.167160 | + | 0.985930i | \(0.553460\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 201.163 | 0.0638104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1504.64 | −0.470699 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1551.23 | −0.472157 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1938.61 | −0.582147 | −0.291074 | − | 0.956701i | \(-0.594012\pi\) | ||||
−0.291074 | + | 0.956701i | \(0.594012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5876.07 | 1.71810 | 0.859050 | − | 0.511892i | \(-0.171055\pi\) | ||||
0.859050 | + | 0.511892i | \(0.171055\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5061.06 | 1.46046 | 0.730228 | − | 0.683204i | \(-0.239414\pi\) | ||||
0.730228 | + | 0.683204i | \(0.239414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1241.58 | −0.349093 | −0.174547 | − | 0.984649i | \(-0.555846\pi\) | ||||
−0.174547 | + | 0.984649i | \(0.555846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1069.82 | −0.296968 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3141.68 | −0.850286 | −0.425143 | − | 0.905126i | \(-0.639776\pi\) | ||||
−0.425143 | + | 0.905126i | \(0.639776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2682.15 | −0.716898 | −0.358449 | − | 0.933549i | \(-0.616694\pi\) | ||||
−0.358449 | + | 0.933549i | \(0.616694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1267.02 | −0.330396 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1463.52 | 0.377010 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4159.18 | −1.04592 | −0.522959 | − | 0.852358i | \(-0.675172\pi\) | ||||
−0.522959 | + | 0.852358i | \(0.675172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 467.643 | 0.116207 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2820.31 | 0.684537 | 0.342268 | − | 0.939602i | \(-0.388805\pi\) | ||||
0.342268 | + | 0.939602i | \(0.388805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1795.18 | 0.430683 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.1884 | −0.00637457 | −0.00318728 | − | 0.999995i | \(-0.501015\pi\) | ||||
−0.00318728 | + | 0.999995i | \(0.501015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1416.55 | −0.328370 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4955.54 | −1.12321 | −0.561607 | − | 0.827404i | \(-0.689817\pi\) | ||||
−0.561607 | + | 0.827404i | \(0.689817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6619.08 | 1.48369 | 0.741846 | − | 0.670570i | \(-0.233950\pi\) | ||||
0.741846 | + | 0.670570i | \(0.233950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1226.18 | 0.268879 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2999.18 | −0.650554 | −0.325277 | − | 0.945619i | \(-0.605457\pi\) | ||||
−0.325277 | + | 0.945619i | \(0.605457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3387.06 | −0.719058 | −0.359529 | − | 0.933134i | \(-0.617063\pi\) | ||||
−0.359529 | + | 0.933134i | \(0.617063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 79.4525 | 0.0166889 | 0.00834446 | − | 0.999965i | \(-0.497344\pi\) | ||||
0.00834446 | + | 0.999965i | \(0.497344\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2329.89 | −0.479196 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4130.21 | −0.840670 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6045.37 | −1.20537 | −0.602686 | − | 0.797978i | \(-0.705903\pi\) | ||||
−0.602686 | + | 0.797978i | \(0.705903\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −460.000 | −0.0907872 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 528.630 | 0.102246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 380.822 | 0.0729243 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1850.86 | 0.347475 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1529.87 | −0.284412 | −0.142206 | − | 0.989837i | \(-0.545420\pi\) | ||||
−0.142206 | + | 0.989837i | \(0.545420\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6583.78 | 1.20042 | 0.600212 | − | 0.799841i | \(-0.295083\pi\) | ||||
0.600212 | + | 0.799841i | \(0.295083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 110.352 | 0.0199281 | 0.00996403 | − | 0.999950i | \(-0.496828\pi\) | ||||
0.00996403 | + | 0.999950i | \(0.496828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4003.48 | −0.709331 | −0.354666 | − | 0.934993i | \(-0.615405\pi\) | ||||
−0.354666 | + | 0.934993i | \(0.615405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10710.9 | 1.87992 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −738.529 | −0.127222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1386.10 | 0.236575 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2025.28 | −0.339384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3066.52 | −0.509219 | −0.254609 | − | 0.967044i | \(-0.581947\pi\) | ||||
−0.254609 | + | 0.967044i | \(0.581947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5437.63 | 0.886834 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10714.9 | 1.73199 | 0.865993 | − | 0.500057i | \(-0.166687\pi\) | ||||
0.865993 | + | 0.500057i | \(0.166687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7796.61 | −1.23815 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5645.26 | −0.888674 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9008.73 | 1.39370 | 0.696850 | − | 0.717217i | \(-0.254584\pi\) | ||||
0.696850 | + | 0.717217i | \(0.254584\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9529.14 | −1.46156 | −0.730778 | − | 0.682615i | \(-0.760843\pi\) | ||||
−0.730778 | + | 0.682615i | \(0.760843\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −982.433 | −0.148129 | −0.0740646 | − | 0.997253i | \(-0.523597\pi\) | ||||
−0.0740646 | + | 0.997253i | \(0.523597\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1668.40 | 0.249436 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9887.90 | 1.45366 | 0.726829 | − | 0.686818i | \(-0.240993\pi\) | ||||
0.726829 | + | 0.686818i | \(0.240993\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6162.23 | −0.898415 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3033.96 | −0.435081 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3348.54 | −0.476274 | −0.238137 | − | 0.971232i | \(-0.576537\pi\) | ||||
−0.238137 | + | 0.971232i | \(0.576537\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2681.67 | −0.375270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9572.04 | 1.32874 | 0.664372 | − | 0.747402i | \(-0.268699\pi\) | ||||
0.664372 | + | 0.747402i | \(0.268699\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12107.8 | 1.65406 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9976.30 | −1.35211 | −0.676053 | − | 0.736853i | \(-0.736311\pi\) | ||||
−0.676053 | + | 0.736853i | \(0.736311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7619.84 | −1.01659 | −0.508297 | − | 0.861182i | \(-0.669725\pi\) | ||||
−0.508297 | + | 0.861182i | \(0.669725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2321.29 | 0.307282 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7802.78 | −1.01701 | −0.508504 | − | 0.861059i | \(-0.669801\pi\) | ||||
−0.508504 | + | 0.861059i | \(0.669801\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −266.760 | −0.0345029 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −221.875 | −0.0282627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8073.51 | −1.02065 | −0.510325 | − | 0.859982i | \(-0.670475\pi\) | ||||
−0.510325 | + | 0.859982i | \(0.670475\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6306.80 | −0.785403 | −0.392702 | − | 0.919666i | \(-0.628459\pi\) | ||||
−0.392702 | + | 0.919666i | \(0.628459\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8813.39 | −1.08940 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9302.08 | 1.13289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15362.3 | −1.85726 | −0.928629 | − | 0.371010i | \(-0.879012\pi\) | ||||
−0.928629 | + | 0.371010i | \(0.879012\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −870.825 | −0.103754 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −538.659 | −0.0637150 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13791.3 | 1.60799 | 0.803994 | − | 0.594637i | \(-0.202704\pi\) | ||||
0.803994 | + | 0.594637i | \(0.202704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9093.23 | −1.05268 | −0.526339 | − | 0.850275i | \(-0.676436\pi\) | ||||
−0.526339 | + | 0.850275i | \(0.676436\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −699.459 | −0.0798323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3503.86 | 0.397104 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 400.347 | 0.0447425 | 0.0223713 | − | 0.999750i | \(-0.492878\pi\) | ||||
0.0223713 | + | 0.999750i | \(0.492878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10063.9 | −1.11695 | −0.558474 | − | 0.829522i | \(-0.688613\pi\) | ||||
−0.558474 | + | 0.829522i | \(0.688613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 251.677 | 0.0275500 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11684.8 | −1.27035 | −0.635176 | − | 0.772368i | \(-0.719072\pi\) | ||||
−0.635176 | + | 0.772368i | \(0.719072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3698.68 | −0.396681 | −0.198341 | − | 0.980133i | \(-0.563555\pi\) | ||||
−0.198341 | + | 0.980133i | \(0.563555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1289.09 | 0.137323 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11318.1 | −1.18961 | −0.594804 | − | 0.803871i | \(-0.702770\pi\) | ||||
−0.594804 | + | 0.803871i | \(0.702770\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12072.8 | −1.26050 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2624.01 | 0.270364 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2436.98 | −0.249446 | −0.124723 | − | 0.992192i | \(-0.539804\pi\) | ||||
−0.124723 | + | 0.992192i | \(0.539804\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8575.54 | 0.866384 | 0.433192 | − | 0.901302i | \(-0.357387\pi\) | ||||
0.433192 | + | 0.901302i | \(0.357387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4711.30 | −0.472900 | −0.236450 | − | 0.971644i | \(-0.575984\pi\) | ||||
−0.236450 | + | 0.971644i | \(0.575984\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11075.4 | 1.09745 | 0.548726 | − | 0.836002i | \(-0.315113\pi\) | ||||
0.548726 | + | 0.836002i | \(0.315113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10294.0 | 1.01350 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1973.31 | 0.191824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 659.911 | 0.0637449 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17455.1 | −1.66502 | −0.832510 | − | 0.554010i | \(-0.813097\pi\) | ||||
−0.832510 | + | 0.554010i | \(0.813097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10515.2 | 0.996781 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6560.25 | 0.614197 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8285.77 | 0.770974 | 0.385487 | − | 0.922713i | \(-0.374034\pi\) | ||||
0.385487 | + | 0.922713i | \(0.374034\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7055.06 | −0.648453 | −0.324226 | − | 0.945980i | \(-0.605104\pi\) | ||||
−0.324226 | + | 0.945980i | \(0.605104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6109.88 | −0.558165 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3158.45 | 0.285062 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2778.49 | 0.249263 | 0.124632 | − | 0.992203i | \(-0.460225\pi\) | ||||
0.124632 | + | 0.992203i | \(0.460225\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5445.52 | −0.482711 | −0.241356 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241356 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −316.646 | −0.0279021 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16567.4 | −1.44270 | −0.721352 | − | 0.692569i | \(-0.756479\pi\) | ||||
−0.721352 | + | 0.692569i | \(0.756479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5743.58 | −0.497223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6099.26 | 0.521875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10494.4 | −0.892734 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3805.03 | 0.319964 | 0.159982 | − | 0.987120i | \(-0.448856\pi\) | ||||
0.159982 | + | 0.987120i | \(0.448856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7489.80 | −0.626207 | −0.313104 | − | 0.949719i | \(-0.601369\pi\) | ||||
−0.313104 | + | 0.949719i | \(0.601369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4447.46 | 0.367617 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12076.1 | −0.992528 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13647.3 | −1.10906 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −211.974 | −0.0171298 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12428.8 | −0.993224 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2063.73 | −0.164005 | −0.0820026 | − | 0.996632i | \(-0.526132\pi\) | ||||
−0.0820026 | + | 0.996632i | \(0.526132\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1333.71 | 0.104825 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12954.6 | −1.01261 | −0.506307 | − | 0.862353i | \(-0.668990\pi\) | ||||
−0.506307 | + | 0.862353i | \(0.668990\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5764.43 | 0.445686 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −420.032 | −0.0322994 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14340.8 | 1.09091 | 0.545457 | − | 0.838139i | \(-0.316356\pi\) | ||||
0.545457 | + | 0.838139i | \(0.316356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2230.65 | 0.168777 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12827.3 | 0.960222 | 0.480111 | − | 0.877208i | \(-0.340596\pi\) | ||||
0.480111 | + | 0.877208i | \(0.340596\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9357.98 | −0.696802 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15102.9 | −1.11274 | −0.556370 | − | 0.830935i | \(-0.687806\pi\) | ||||
−0.556370 | + | 0.830935i | \(0.687806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22553.6 | 1.65295 | 0.826477 | − | 0.562970i | \(-0.190342\pi\) | ||||
0.826477 | + | 0.562970i | \(0.190342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 238.363 | 0.0172877 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5007.38 | 0.361283 | 0.180641 | − | 0.983549i | \(-0.442183\pi\) | ||||
0.180641 | + | 0.983549i | \(0.442183\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1019.73 | −0.0728153 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13895.6 | −0.987131 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24975.4 | 1.75612 | 0.878062 | − | 0.478547i | \(-0.158837\pi\) | ||||
0.878062 | + | 0.478547i | \(0.158837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4196.00 | −0.293537 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19247.2 | 1.33287 | 0.666433 | − | 0.745565i | \(-0.267820\pi\) | ||||
0.666433 | + | 0.745565i | \(0.267820\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1324.14 | −0.0912346 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6000.84 | −0.409328 | −0.204664 | − | 0.978832i | \(-0.565610\pi\) | ||||
−0.204664 | + | 0.978832i | \(0.565610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8576.08 | −0.582073 | −0.291036 | − | 0.956712i | \(-0.594000\pi\) | ||||
−0.291036 | + | 0.956712i | \(0.594000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5373.22 | 0.361079 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2960.22 | −0.197943 | −0.0989715 | − | 0.995090i | \(-0.531555\pi\) | ||||
−0.0989715 | + | 0.995090i | \(0.531555\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11863.0 | −0.785477 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6483.88 | 0.427212 | 0.213606 | − | 0.976920i | \(-0.431479\pi\) | ||||
0.213606 | + | 0.976920i | \(0.431479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1169.84 | 0.0763304 | 0.0381652 | − | 0.999271i | \(-0.487849\pi\) | ||||
0.0381652 | + | 0.999271i | \(0.487849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2930.97 | 0.190316 | 0.0951580 | − | 0.995462i | \(-0.469664\pi\) | ||||
0.0951580 | + | 0.995462i | \(0.469664\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2440.38 | 0.156937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5306.23 | −0.336365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29359.9 | −1.85230 | −0.926150 | − | 0.377156i | \(-0.876902\pi\) | ||||
−0.926150 | + | 0.377156i | \(0.876902\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6160.54 | −0.384998 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14049.7 | −0.873894 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14661.8 | 0.903443 | 0.451721 | − | 0.892159i | \(-0.350810\pi\) | ||||
0.451721 | + | 0.892159i | \(0.350810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11141.3 | 0.683312 | 0.341656 | − | 0.939825i | \(-0.389012\pi\) | ||||
0.341656 | + | 0.939825i | \(0.389012\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17044.5 | −1.03569 | −0.517844 | − | 0.855475i | \(-0.673265\pi\) | ||||
−0.517844 | + | 0.855475i | \(0.673265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4512.36 | −0.272921 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19960.2 | −1.19618 | −0.598089 | − | 0.801430i | \(-0.704073\pi\) | ||||
−0.598089 | + | 0.801430i | \(0.704073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6045.87 | 0.360659 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13422.1 | −0.793399 | −0.396700 | − | 0.917948i | \(-0.629845\pi\) | ||||
−0.396700 | + | 0.917948i | \(0.629845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13349.5 | 0.785531 | 0.392765 | − | 0.919639i | \(-0.371518\pi\) | ||||
0.392765 | + | 0.919639i | \(0.371518\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1249.28 | 0.0728494 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2082.14 | 0.120871 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18156.0 | 1.04456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6927.58 | 0.396788 | 0.198394 | − | 0.980122i | \(-0.436427\pi\) | ||||
0.198394 | + | 0.980122i | \(0.436427\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6607.86 | 0.375126 | 0.187563 | − | 0.982253i | \(-0.439941\pi\) | ||||
0.187563 | + | 0.982253i | \(0.439941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12419.2 | 0.701922 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15422.7 | −0.864031 | −0.432015 | − | 0.901866i | \(-0.642197\pi\) | ||||
−0.432015 | + | 0.901866i | \(0.642197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13148.3 | −0.733388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15707.8 | −0.868533 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16254.6 | −0.894870 | −0.447435 | − | 0.894317i | \(-0.647662\pi\) | ||||
−0.447435 | + | 0.894317i | \(0.647662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11075.3 | 0.604475 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6886.76 | 0.374254 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10389.8 | −0.559796 | −0.279898 | − | 0.960030i | \(-0.590301\pi\) | ||||
−0.279898 | + | 0.960030i | \(0.590301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5006.22 | 0.268582 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −599.442 | −0.0318873 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7530.22 | 0.398877 | 0.199438 | − | 0.979910i | \(-0.436088\pi\) | ||||
0.199438 | + | 0.979910i | \(0.436088\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1515.61 | −0.0796075 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13596.9 | 0.711181 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33888.4 | −1.75775 | −0.878875 | − | 0.477051i | \(-0.841706\pi\) | ||||
−0.878875 | + | 0.477051i | \(0.841706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11546.5 | 0.596413 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5459.47 | 0.279669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13863.3 | −0.707239 | −0.353619 | − | 0.935389i | \(-0.615049\pi\) | ||||
−0.353619 | + | 0.935389i | \(0.615049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1125.64 | −0.0569541 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24497.7 | 1.23444 | 0.617219 | − | 0.786792i | \(-0.288259\pi\) | ||||
0.617219 | + | 0.786792i | \(0.288259\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53340.3 | 2.66596 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19029.1 | 0.947221 | 0.473611 | − | 0.880734i | \(-0.342950\pi\) | ||||
0.473611 | + | 0.880734i | \(0.342950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5639.67 | −0.278465 | −0.139233 | − | 0.990260i | \(-0.544464\pi\) | ||||
−0.139233 | + | 0.990260i | \(0.544464\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12234.7 | −0.601672 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −401.287 | −0.0195764 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14566.0 | −0.707753 | −0.353876 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353876 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 596.825 | 0.0287691 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2958.83 | −0.142061 | −0.0710307 | − | 0.997474i | \(-0.522629\pi\) | ||||
−0.0710307 | + | 0.997474i | \(0.522629\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −281.640 | −0.0134158 | −0.00670791 | − | 0.999978i | \(-0.502135\pi\) | ||||
−0.00670791 | + | 0.999978i | \(0.502135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2524.84 | 0.119797 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5100.83 | −0.240131 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29799.2 | 1.39738 | 0.698690 | − | 0.715425i | \(-0.253767\pi\) | ||||
0.698690 | + | 0.715425i | \(0.253767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8377.18 | −0.389788 | −0.194894 | − | 0.980824i | \(-0.562436\pi\) | ||||
−0.194894 | + | 0.980824i | \(0.562436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3974.02 | −0.184195 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6497.39 | −0.298836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16366.2 | 0.749843 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11064.3 | 0.503059 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17368.8 | −0.786697 | −0.393348 | − | 0.919389i | \(-0.628683\pi\) | ||||
−0.393348 | + | 0.919389i | \(0.628683\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17715.6 | −0.796325 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20523.7 | 0.919066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6003.86 | 0.266835 | 0.133418 | − | 0.991060i | \(-0.457405\pi\) | ||||
0.133418 | + | 0.991060i | \(0.457405\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5986.38 | 0.265060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29761.5 | −1.30792 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 451.244 | 0.0197568 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42392.2 | 1.84231 | 0.921157 | − | 0.389191i | \(-0.127246\pi\) | ||||
0.921157 | + | 0.389191i | \(0.127246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7148.82 | −0.309530 | −0.154765 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154765 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17402.7 | 0.747964 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1062.00 | 0.0454770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25700.4 | −1.09251 | −0.546254 | − | 0.837619i | \(-0.683947\pi\) | ||||
−0.546254 | + | 0.837619i | \(0.683947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19064.7 | −0.807476 | −0.403738 | − | 0.914875i | \(-0.632289\pi\) | ||||
−0.403738 | + | 0.914875i | \(0.632289\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41947.6 | 1.76380 | 0.881900 | − | 0.471437i | \(-0.156264\pi\) | ||||
0.881900 | + | 0.471437i | \(0.156264\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31403.8 | −1.31568 | −0.657841 | − | 0.753157i | \(-0.728530\pi\) | ||||
−0.657841 | + | 0.753157i | \(0.728530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7089.84 | 0.294896 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12385.8 | 0.513326 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25495.3 | −1.04910 | −0.524550 | − | 0.851380i | \(-0.675766\pi\) | ||||
−0.524550 | + | 0.851380i | \(0.675766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23300.3 | 0.955362 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4385.09 | 0.178523 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10172.0 | 0.412651 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1808.27 | 0.0728398 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13537.1 | −0.543377 | −0.271689 | − | 0.962385i | \(-0.587582\pi\) | ||||
−0.271689 | + | 0.962385i | \(0.587582\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15337.3 | 0.611332 | 0.305666 | − | 0.952139i | \(-0.401121\pi\) | ||||
0.305666 | + | 0.952139i | \(0.401121\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19720.1 | 0.783286 | 0.391643 | − | 0.920117i | \(-0.371907\pi\) | ||||
0.391643 | + | 0.920117i | \(0.371907\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21464.2 | −0.846641 | −0.423321 | − | 0.905980i | \(-0.639136\pi\) | ||||
−0.423321 | + | 0.905980i | \(0.639136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −133.723 | −0.00525633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2176.48 | −0.0849621 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60296.6 | 2.34566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1183.19 | 0.0457131 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3671.90 | 0.141381 | 0.0706905 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706905 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48518.9 | 1.85544 | 0.927720 | − | 0.373276i | \(-0.121766\pi\) | ||||
0.927720 | + | 0.373276i | \(0.121766\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13413.5 | 0.511210 | 0.255605 | − | 0.966781i | \(-0.417725\pi\) | ||||
0.255605 | + | 0.966781i | \(0.417725\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50035.0 | 1.89404 | 0.947018 | − | 0.321180i | \(-0.104079\pi\) | ||||
0.947018 | + | 0.321180i | \(0.104079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11662.5 | −0.439986 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5647.91 | −0.211646 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7003.77 | −0.261576 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34713.7 | −1.28784 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7926.54 | 0.293087 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17462.4 | 0.641403 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35905.1 | 1.31446 | 0.657228 | − | 0.753692i | \(-0.271729\pi\) | ||||
0.657228 | + | 0.753692i | \(0.271729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36938.6 | 1.34339 | 0.671697 | − | 0.740826i | \(-0.265566\pi\) | ||||
0.671697 | + | 0.740826i | \(0.265566\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5283.96 | −0.191537 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11445.4 | 0.412171 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35867.0 | 1.28742 | 0.643712 | − | 0.765268i | \(-0.277394\pi\) | ||||
0.643712 | + | 0.765268i | \(0.277394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18500.5 | 0.659753 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4741.37 | 0.168536 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11391.2 | 0.402297 | 0.201148 | − | 0.979561i | \(-0.435533\pi\) | ||||
0.201148 | + | 0.979561i | \(0.435533\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6688.98 | −0.235470 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6861.32 | −0.239988 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30928.7 | 1.07833 | 0.539166 | − | 0.842199i | \(-0.318740\pi\) | ||||
0.539166 | + | 0.842199i | \(0.318740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36684.3 | −1.27086 | −0.635428 | − | 0.772160i | \(-0.719176\pi\) | ||||
−0.635428 | + | 0.772160i | \(0.719176\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2346.88 | −0.0810446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39211.7 | −1.34552 | −0.672761 | − | 0.739860i | \(-0.734892\pi\) | ||||
−0.672761 | + | 0.739860i | \(0.734892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33642.8 | −1.15078 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30476.1 | −1.03591 | −0.517953 | − | 0.855409i | \(-0.673306\pi\) | ||||
−0.517953 | + | 0.855409i | \(0.673306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13640.8 | 0.462206 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24891.0 | −0.838136 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4522.48 | −0.151807 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12199.1 | 0.406946 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48866.8 | 1.62508 | 0.812538 | − | 0.582908i | \(-0.198085\pi\) | ||||
0.812538 | + | 0.582908i | \(0.198085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54060.7 | −1.78670 | −0.893352 | − | 0.449358i | \(-0.851653\pi\) | ||||
−0.893352 | + | 0.449358i | \(0.851653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20966.6 | 0.690811 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27233.7 | 0.891795 | 0.445898 | − | 0.895084i | \(-0.352885\pi\) | ||||
0.445898 | + | 0.895084i | \(0.352885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12645.3 | 0.412816 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −949.700 | −0.0308146 | −0.0154073 | − | 0.999881i | \(-0.504904\pi\) | ||||
−0.0154073 | + | 0.999881i | \(0.504904\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3829.53 | 0.123877 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 383.599 | 0.0123334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37146.4 | 1.19071 | 0.595356 | − | 0.803462i | \(-0.297011\pi\) | ||||
0.595356 | + | 0.803462i | \(0.297011\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3770.15 | 0.120123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45360.4 | 1.44090 | 0.720451 | − | 0.693506i | \(-0.243935\pi\) | ||||
0.720451 | + | 0.693506i | \(0.243935\pi\) | |||||||
\(998\) | 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 | 1080.4.a.n.1.2 | yes | 3 | |
3.2 | odd | 2 | 1080.4.a.h.1.2 | ✓ | 3 | ||
4.3 | odd | 2 | 2160.4.a.bn.1.2 | 3 | |||
12.11 | even | 2 | 2160.4.a.bf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.h.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
1080.4.a.n.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
2160.4.a.bf.1.2 | 3 | 12.11 | even | 2 | |||
2160.4.a.bn.1.2 | 3 | 4.3 | odd | 2 |