Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + \cdots + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.68837\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68837 | 0.755064 | 0.377532 | − | 0.925997i | \(-0.376773\pi\) | ||||
0.377532 | + | 0.925997i | \(0.376773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.722089 | −0.272924 | −0.136462 | − | 0.990645i | \(-0.543573\pi\) | ||||
−0.136462 | + | 0.990645i | \(0.543573\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.92380 | −1.48458 | −0.742291 | − | 0.670077i | \(-0.766261\pi\) | ||||
−0.742291 | + | 0.670077i | \(0.766261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.15606 | −1.43003 | −0.715017 | − | 0.699108i | \(-0.753581\pi\) | ||||
−0.715017 | + | 0.699108i | \(0.753581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.68837 | −0.435936 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.50170 | 1.09182 | 0.545911 | − | 0.837843i | \(-0.316184\pi\) | ||||
0.545911 | + | 0.837843i | \(0.316184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.23024 | −0.741069 | −0.370535 | − | 0.928819i | \(-0.620825\pi\) | ||||
−0.370535 | + | 0.928819i | \(0.620825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.722089 | 0.157573 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.11854 | −1.90135 | −0.950673 | − | 0.310194i | \(-0.899606\pi\) | ||||
−0.950673 | + | 0.310194i | \(0.899606\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.14939 | −0.429878 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.58248 | 0.293859 | 0.146930 | − | 0.989147i | \(-0.453061\pi\) | ||||
0.146930 | + | 0.989147i | \(0.453061\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.13513 | 0.383480 | 0.191740 | − | 0.981446i | \(-0.438587\pi\) | ||||
0.191740 | + | 0.981446i | \(0.438587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.92380 | 0.857124 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.21916 | −0.206075 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.13571 | −1.33750 | −0.668751 | − | 0.743486i | \(-0.733171\pi\) | ||||
−0.668751 | + | 0.743486i | \(0.733171\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.15606 | 0.825630 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.37711 | 0.839763 | 0.419882 | − | 0.907579i | \(-0.362072\pi\) | ||||
0.419882 | + | 0.907579i | \(0.362072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.74675 | 0.723872 | 0.361936 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361936 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.68837 | 0.251688 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.74876 | 0.546812 | 0.273406 | − | 0.961899i | \(-0.411850\pi\) | ||||
0.273406 | + | 0.961899i | \(0.411850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47859 | −0.925513 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50170 | −0.630364 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47444 | 0.202530 | 0.101265 | − | 0.994859i | \(-0.467711\pi\) | ||||
0.101265 | + | 0.994859i | \(0.467711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.31323 | −1.12096 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.23024 | 0.427856 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.12417 | −0.406733 | −0.203366 | − | 0.979103i | \(-0.565188\pi\) | ||||
−0.203366 | + | 0.979103i | \(0.565188\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.12058 | 1.16777 | 0.583886 | − | 0.811836i | \(-0.301532\pi\) | ||||
0.583886 | + | 0.811836i | \(0.301532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.722089 | −0.0909747 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.70535 | −1.07977 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6505 | −1.42333 | −0.711667 | − | 0.702517i | \(-0.752059\pi\) | ||||
−0.711667 | + | 0.702517i | \(0.752059\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.11854 | 1.09774 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6974 | 1.62559 | 0.812793 | − | 0.582552i | \(-0.197946\pi\) | ||||
0.812793 | + | 0.582552i | \(0.197946\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.51026 | −0.293804 | −0.146902 | − | 0.989151i | \(-0.546930\pi\) | ||||
−0.146902 | + | 0.989151i | \(0.546930\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.14939 | 0.248190 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.55542 | 0.405178 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4674 | 1.40269 | 0.701344 | − | 0.712823i | \(-0.252584\pi\) | ||||
0.701344 | + | 0.712823i | \(0.252584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.96218 | 0.325141 | 0.162571 | − | 0.986697i | \(-0.448021\pi\) | ||||
0.162571 | + | 0.986697i | \(0.448021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.60056 | 0.824396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.58248 | −0.169660 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.54127 | 0.799373 | 0.399687 | − | 0.916652i | \(-0.369119\pi\) | ||||
0.399687 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.72313 | 0.390290 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.13513 | −0.221402 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.45386 | −0.559555 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.3021 | 1.55369 | 0.776847 | − | 0.629689i | \(-0.216818\pi\) | ||||
0.776847 | + | 0.629689i | \(0.216818\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.92380 | −0.494861 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.99072 | −0.297588 | −0.148794 | − | 0.988868i | \(-0.547539\pi\) | ||||
−0.148794 | + | 0.988868i | \(0.547539\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.09205 | −0.600268 | −0.300134 | − | 0.953897i | \(-0.597031\pi\) | ||||
−0.300134 | + | 0.953897i | \(0.597031\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.21916 | 0.118977 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2446 | −1.18373 | −0.591865 | − | 0.806037i | \(-0.701608\pi\) | ||||
−0.591865 | + | 0.806037i | \(0.701608\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7801 | 1.70303 | 0.851514 | − | 0.524332i | \(-0.175685\pi\) | ||||
0.851514 | + | 0.524332i | \(0.175685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.13571 | 0.772207 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4321 | 1.35766 | 0.678829 | − | 0.734296i | \(-0.262488\pi\) | ||||
0.678829 | + | 0.734296i | \(0.262488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.3955 | −1.43564 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.15606 | −0.476678 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.25063 | −0.297985 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.2439 | 1.20399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.37711 | −0.484838 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0709 | −1.07965 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.6883 | 1.12591 | 0.562954 | − | 0.826488i | \(-0.309665\pi\) | ||||
0.562954 | + | 0.826488i | \(0.309665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.74675 | −0.417928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7297 | 1.19957 | 0.599786 | − | 0.800160i | \(-0.295252\pi\) | ||||
0.599786 | + | 0.800160i | \(0.295252\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.33252 | 0.202256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.68837 | −0.145312 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.1614 | −1.29533 | −0.647664 | − | 0.761926i | \(-0.724254\pi\) | ||||
−0.647664 | + | 0.761926i | \(0.724254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.47213 | 0.803415 | 0.401708 | − | 0.915768i | \(-0.368417\pi\) | ||||
0.401708 | + | 0.915768i | \(0.368417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.74876 | −0.315702 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.3874 | 2.12300 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.67182 | 0.221883 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.47859 | 0.534345 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.3592 | 1.25828 | 0.629139 | − | 0.777293i | \(-0.283408\pi\) | ||||
0.629139 | + | 0.777293i | \(0.283408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8576 | 1.04634 | 0.523170 | − | 0.852228i | \(-0.324749\pi\) | ||||
0.523170 | + | 0.852228i | \(0.324749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50170 | 0.363941 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.60489 | 0.289552 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.41216 | −0.352129 | −0.176064 | − | 0.984379i | \(-0.556337\pi\) | ||||
−0.176064 | + | 0.984379i | \(0.556337\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.47444 | −0.116931 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.58439 | 0.518923 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.45760 | 0.662450 | 0.331225 | − | 0.943552i | \(-0.392538\pi\) | ||||
0.331225 | + | 0.943552i | \(0.392538\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.31323 | 0.647184 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.5849 | 1.04499 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.23024 | −0.247023 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.24683 | −0.322880 | −0.161440 | − | 0.986882i | \(-0.551614\pi\) | ||||
−0.161440 | + | 0.986882i | \(0.551614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.55205 | 0.117324 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.12417 | 0.234827 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.599313 | −0.0447948 | −0.0223974 | − | 0.999749i | \(-0.507130\pi\) | ||||
−0.0223974 | + | 0.999749i | \(0.507130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.3349 | −1.80880 | −0.904400 | − | 0.426686i | \(-0.859681\pi\) | ||||
−0.904400 | + | 0.426686i | \(0.859681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.12058 | −0.674213 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.7361 | −1.00990 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.1655 | −1.62090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.722089 | 0.0525242 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.3821 | −0.968294 | −0.484147 | − | 0.874987i | \(-0.660870\pi\) | ||||
−0.484147 | + | 0.874987i | \(0.660870\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8898 | −0.855847 | −0.427924 | − | 0.903815i | \(-0.640755\pi\) | ||||
−0.427924 | + | 0.903815i | \(0.640755\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.70535 | 0.623403 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9713 | 1.35165 | 0.675823 | − | 0.737064i | \(-0.263788\pi\) | ||||
0.675823 | + | 0.737064i | \(0.263788\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.3938 | −1.44568 | −0.722838 | − | 0.691017i | \(-0.757163\pi\) | ||||
−0.722838 | + | 0.691017i | \(0.757163\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6505 | 0.821762 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.14269 | −0.0802013 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.07857 | 0.634075 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.11854 | −0.633782 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.9051 | 1.10018 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.39036 | −0.164559 | −0.0822797 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822797 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.6974 | −0.938533 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.01429 | 0.546570 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.54175 | −0.104661 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.51026 | 0.169628 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2110 | −1.56134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.4864 | −1.10401 | −0.552006 | − | 0.833840i | \(-0.686137\pi\) | ||||
−0.552006 | + | 0.833840i | \(0.686137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.14939 | −0.143293 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.37540 | −0.356778 | −0.178389 | − | 0.983960i | \(-0.557089\pi\) | ||||
−0.178389 | + | 0.983960i | \(0.557089\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.85562 | −0.519114 | −0.259557 | − | 0.965728i | \(-0.583577\pi\) | ||||
−0.259557 | + | 0.965728i | \(0.583577\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.55542 | −0.233930 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.08638 | 0.333220 | 0.166610 | − | 0.986023i | \(-0.446718\pi\) | ||||
0.166610 | + | 0.986023i | \(0.446718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.32930 | 0.412878 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.4674 | −0.809842 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8450 | 0.830877 | 0.415438 | − | 0.909621i | \(-0.363628\pi\) | ||||
0.415438 | + | 0.909621i | \(0.363628\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.56580 | 0.358524 | 0.179262 | − | 0.983801i | \(-0.442629\pi\) | ||||
0.179262 | + | 0.983801i | \(0.442629\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.9383 | −0.698821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.6553 | 1.05975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.96218 | −0.187720 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.4878 | 0.851343 | 0.425671 | − | 0.904878i | \(-0.360038\pi\) | ||||
0.425671 | + | 0.904878i | \(0.360038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.8979 | 2.82271 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.60056 | −0.475965 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0902 | 0.941299 | 0.470650 | − | 0.882320i | \(-0.344020\pi\) | ||||
0.470650 | + | 0.882320i | \(0.344020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.87470 | 0.365036 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.58248 | 0.0979531 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8686 | −0.731847 | −0.365924 | − | 0.930645i | \(-0.619247\pi\) | ||||
−0.365924 | + | 0.930645i | \(0.619247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.48941 | 0.152923 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.54127 | −0.461518 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.857197 | 0.0522642 | 0.0261321 | − | 0.999658i | \(-0.491681\pi\) | ||||
0.0261321 | + | 0.999658i | \(0.491681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.9528 | −1.02981 | −0.514905 | − | 0.857247i | \(-0.672173\pi\) | ||||
−0.514905 | + | 0.857247i | \(0.672173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.72313 | −0.225334 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5832 | 0.638190 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.3840 | 1.88568 | 0.942840 | − | 0.333247i | \(-0.108144\pi\) | ||||
0.942840 | + | 0.333247i | \(0.108144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.13513 | 0.127827 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.26822 | −0.493241 | −0.246620 | − | 0.969112i | \(-0.579320\pi\) | ||||
−0.246620 | + | 0.969112i | \(0.579320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.24839 | 0.371428 | 0.185714 | − | 0.982604i | \(-0.440540\pi\) | ||||
0.185714 | + | 0.982604i | \(0.440540\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.45386 | 0.323059 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.88275 | −0.229192 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.26531 | 0.192077 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.3021 | −0.897026 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.7074 | −1.32658 | −0.663289 | − | 0.748363i | \(-0.730840\pi\) | ||||
−0.663289 | + | 0.748363i | \(0.730840\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.27478 | −0.307109 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.92380 | 0.285708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 47.0157 | 2.71899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.42757 | −0.197562 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.99072 | 0.171813 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.3990 | 0.881742 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.71355 | 0.554381 | 0.277191 | − | 0.960815i | \(-0.410597\pi\) | ||||
0.277191 | + | 0.960815i | \(0.410597\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.09205 | 0.346565 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6568 | 1.73839 | 0.869193 | − | 0.494474i | \(-0.164639\pi\) | ||||
0.869193 | + | 0.494474i | \(0.164639\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.88725 | 0.219720 | 0.109860 | − | 0.993947i | \(-0.464960\pi\) | ||||
0.109860 | + | 0.993947i | \(0.464960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.21916 | −0.0686917 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.2051 | −1.02250 | −0.511250 | − | 0.859432i | \(-0.670817\pi\) | ||||
−0.511250 | + | 0.859432i | \(0.670817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.79183 | −0.436259 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2446 | 0.683427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5416 | −0.809116 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.0824 | 0.614740 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.7801 | −0.983243 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.70694 | −0.149238 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8334 | −1.36497 | −0.682483 | − | 0.730902i | \(-0.739100\pi\) | ||||
−0.682483 | + | 0.730902i | \(0.739100\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.13571 | −0.445834 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.6704 | −1.07471 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.67704 | −0.0913543 | −0.0456771 | − | 0.998956i | \(-0.514545\pi\) | ||||
−0.0456771 | + | 0.998956i | \(0.514545\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.4321 | −0.783845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.5129 | −0.569308 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.73274 | 0.525519 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.3955 | 0.828866 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.4895 | −0.724152 | −0.362076 | − | 0.932149i | \(-0.617932\pi\) | ||||
−0.362076 | + | 0.932149i | \(0.617932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.01732 | 0.322099 | 0.161050 | − | 0.986946i | \(-0.448512\pi\) | ||||
0.161050 | + | 0.986946i | \(0.448512\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.15606 | 0.275210 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.0017 | 1.17103 | 0.585515 | − | 0.810661i | \(-0.300892\pi\) | ||||
0.585515 | + | 0.810661i | \(0.300892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.1264 | 1.22742 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.25063 | 0.172041 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.7777 | −1.09661 | −0.548303 | − | 0.836280i | \(-0.684726\pi\) | ||||
−0.548303 | + | 0.836280i | \(0.684726\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.56552 | −0.450817 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.2439 | −0.695122 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.23826 | −0.221841 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.9260 | 1.61432 | 0.807162 | − | 0.590330i | \(-0.201002\pi\) | ||||
0.807162 | + | 0.590330i | \(0.201002\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.37711 | 0.279921 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.06468 | −0.0552753 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.24001 | −0.0642053 | −0.0321027 | − | 0.999485i | \(-0.510220\pi\) | ||||
−0.0321027 | + | 0.999485i | \(0.510220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0709 | 0.623336 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.15936 | −0.420229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.1456 | 1.85667 | 0.928337 | − | 0.371739i | \(-0.121238\pi\) | ||||
0.928337 | + | 0.371739i | \(0.121238\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6883 | −0.650044 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.4479 | −0.738253 | −0.369127 | − | 0.929379i | \(-0.620343\pi\) | ||||
−0.369127 | + | 0.929379i | \(0.620343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00289 | 0.305936 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.74675 | 0.241291 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.58955 | −0.435508 | −0.217754 | − | 0.976004i | \(-0.569873\pi\) | ||||
−0.217754 | + | 0.976004i | \(0.569873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −41.0489 | −2.07593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.7297 | −0.692573 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.0496 | 1.05912 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3990 | 1.37512 | 0.687558 | − | 0.726129i | \(-0.258683\pi\) | ||||
0.687558 | + | 0.726129i | \(0.258683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.33252 | −0.116772 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.71562 | 0.185549 | 0.0927747 | − | 0.995687i | \(-0.470426\pi\) | ||||
0.0927747 | + | 0.995687i | \(0.470426\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0088 | −0.548389 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.68837 | 0.0838960 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.0586 | 1.98563 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4154 | −1.55339 | −0.776695 | − | 0.629877i | \(-0.783105\pi\) | ||||
−0.776695 | + | 0.629877i | \(0.783105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.1614 | 0.747858 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.25593 | 0.111007 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.00126 | 0.245502 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.47213 | −0.463852 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.3030 | −1.48040 | −0.740200 | − | 0.672387i | \(-0.765269\pi\) | ||||
−0.740200 | + | 0.672387i | \(0.765269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.7995 | −1.54981 | −0.774907 | − | 0.632075i | \(-0.782203\pi\) | ||||
−0.774907 | + | 0.632075i | \(0.782203\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.74876 | 0.182271 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.67592 | −0.469351 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.58587 | −0.318713 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.3874 | −1.22572 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.1018 | 0.920101 | 0.460051 | − | 0.887893i | \(-0.347831\pi\) | ||||
0.460051 | + | 0.887893i | \(0.347831\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.19475 | −0.105473 | −0.0527365 | − | 0.998608i | \(-0.516794\pi\) | ||||
−0.0527365 | + | 0.998608i | \(0.516794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.67182 | −0.128104 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.4551 | 1.40903 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.8050 | 1.13615 | 0.568074 | − | 0.822977i | \(-0.307689\pi\) | ||||
0.568074 | + | 0.822977i | \(0.307689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.47859 | −0.308504 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.1042 | −1.14522 | −0.572612 | − | 0.819826i | \(-0.694070\pi\) | ||||
−0.572612 | + | 0.819826i | \(0.694070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7325 | 0.603578 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.3592 | −0.726467 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.66111 | −0.267164 | −0.133582 | − | 0.991038i | \(-0.542648\pi\) | ||||
−0.133582 | + | 0.991038i | \(0.542648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.4758 | −1.24670 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.8576 | −0.604105 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.28604 | 0.294694 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1307 | 0.707786 | 0.353893 | − | 0.935286i | \(-0.384858\pi\) | ||||
0.353893 | + | 0.935286i | \(0.384858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.50170 | −0.210121 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.92069 | −0.182605 | −0.0913023 | − | 0.995823i | \(-0.529103\pi\) | ||||
−0.0913023 | + | 0.995823i | \(0.529103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.3205 | 1.50206 | 0.751030 | − | 0.660268i | \(-0.229557\pi\) | ||||
0.751030 | + | 0.660268i | \(0.229557\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.60489 | −0.167173 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8059 | −1.28670 | −0.643352 | − | 0.765570i | \(-0.722457\pi\) | ||||
−0.643352 | + | 0.765570i | \(0.722457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.41269 | 0.388462 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.41216 | 0.203302 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.3721 | −1.07465 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.94306 | 0.318570 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.47444 | 0.0675100 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.80360 | 0.0824086 | 0.0412043 | − | 0.999151i | \(-0.486881\pi\) | ||||
0.0412043 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.9482 | 1.91267 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.58439 | −0.299600 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.8357 | 1.17314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.5627 | 1.70213 | 0.851064 | − | 0.525062i | \(-0.175958\pi\) | ||||
0.851064 | + | 0.525062i | \(0.175958\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.45760 | −0.382466 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.5565 | 0.882570 | 0.441285 | − | 0.897367i | \(-0.354523\pi\) | ||||
0.441285 | + | 0.897367i | \(0.354523\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.12386 | 0.320842 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.31323 | −0.373652 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.89077 | −0.443661 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.2225 | 0.457623 | 0.228812 | − | 0.973471i | \(-0.426516\pi\) | ||||
0.228812 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.2594 | −0.502034 | −0.251017 | − | 0.967983i | \(-0.580765\pi\) | ||||
−0.251017 | + | 0.967983i | \(0.580765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.04946 | −0.224698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.5849 | −0.603328 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.84518 | −0.347731 | −0.173866 | − | 0.984769i | \(-0.555626\pi\) | ||||
−0.173866 | + | 0.984769i | \(0.555626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.81263 | 0.0801861 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.23024 | 0.142619 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.2857 | −0.453241 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.4581 | −0.811788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.24683 | 0.186415 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.2656 | −1.23834 | −0.619168 | − | 0.785258i | \(-0.712530\pi\) | ||||
−0.619168 | + | 0.785258i | \(0.712530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.43781 | −0.150325 | −0.0751624 | − | 0.997171i | \(-0.523948\pi\) | ||||
−0.0751624 | + | 0.997171i | \(0.523948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.55205 | −0.0677371 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.61170 | 0.418692 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.1477 | 2.61512 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.12417 | −0.135578 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.7247 | −1.20089 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.6735 | −0.893792 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.599313 | 0.0258623 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.8993 | 1.37400 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.8036 | 1.02340 | 0.511699 | − | 0.859165i | \(-0.329016\pi\) | ||||
0.511699 | + | 0.859165i | \(0.329016\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.3349 | 1.04431 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.0195 | 1.28589 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.5205 | 0.535337 | 0.267669 | − | 0.963511i | \(-0.413747\pi\) | ||||
0.267669 | + | 0.963511i | \(0.413747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.12058 | 0.389257 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.11180 | −0.217770 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.00255 | −0.382827 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.7361 | 0.583066 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.1939 | 1.23699 | 0.618493 | − | 0.785790i | \(-0.287743\pi\) | ||||
0.618493 | + | 0.785790i | \(0.287743\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.4745 | −1.03516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.1655 | 0.935828 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.1606 | 1.60828 | 0.804139 | − | 0.594441i | \(-0.202627\pi\) | ||||
0.804139 | + | 0.594441i | \(0.202627\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.3668 | 1.02512 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.722089 | −0.0303249 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6265 | 0.864709 | 0.432354 | − | 0.901704i | \(-0.357683\pi\) | ||||
0.432354 | + | 0.901704i | \(0.357683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.5539 | 1.02755 | 0.513774 | − | 0.857925i | \(-0.328247\pi\) | ||||
0.513774 | + | 0.857925i | \(0.328247\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.3821 | 0.559045 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.5993 | 0.817348 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.6540 | −1.52593 | −0.762963 | − | 0.646443i | \(-0.776256\pi\) | ||||
−0.762963 | + | 0.646443i | \(0.776256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.8898 | 0.494124 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.13896 | −0.0887388 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.25986 | −0.300673 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.70535 | −0.359922 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0092 | 0.495671 | 0.247836 | − | 0.968802i | \(-0.420281\pi\) | ||||
0.247836 | + | 0.968802i | \(0.420281\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.89698 | −0.284185 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.9713 | −0.780374 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.6797 | −0.808150 | −0.404075 | − | 0.914726i | \(-0.632407\pi\) | ||||
−0.404075 | + | 0.914726i | \(0.632407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.48828 | −0.224997 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.3938 | 0.834662 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.13982 | 0.250866 | 0.125433 | − | 0.992102i | \(-0.459968\pi\) | ||||
0.125433 | + | 0.992102i | \(0.459968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.1181 | −1.14696 | −0.573482 | − | 0.819218i | \(-0.694408\pi\) | ||||
−0.573482 | + | 0.819218i | \(0.694408\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.6505 | −0.474445 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.3606 | 0.909087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.8152 | −0.560743 | −0.280372 | − | 0.959892i | \(-0.590458\pi\) | ||||
−0.280372 | + | 0.959892i | \(0.590458\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.14269 | 0.0463042 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.3288 | −0.781960 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.5891 | 0.710416 | 0.355208 | − | 0.934787i | \(-0.384410\pi\) | ||||
0.355208 | + | 0.934787i | \(0.384410\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.07857 | −0.366083 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.71765 | −0.310701 | −0.155351 | − | 0.987859i | \(-0.549651\pi\) | ||||
−0.155351 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.1563 | −1.01112 | −0.505559 | − | 0.862792i | \(-0.668714\pi\) | ||||
−0.505559 | + | 0.862792i | \(0.668714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.11854 | 0.365914 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.44547 | −0.218168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.63315 | −0.385326 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.9051 | −0.635188 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.6245 | −1.46032 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0287 | 1.27504 | 0.637521 | − | 0.770433i | \(-0.279960\pi\) | ||||
0.637521 | + | 0.770433i | \(0.279960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.39036 | 0.0950084 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.4227 | 0.850133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.4040 | 1.32351 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.6974 | 0.541862 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.3785 | 1.39737 | 0.698683 | − | 0.715431i | \(-0.253770\pi\) | ||||
0.698683 | + | 0.715431i | \(0.253770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.42726 | 0.332339 | 0.166169 | − | 0.986097i | \(-0.446860\pi\) | ||||
0.166169 | + | 0.986097i | \(0.446860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.01429 | −0.315562 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.0291 | −1.77028 | −0.885138 | − | 0.465328i | \(-0.845936\pi\) | ||||
−0.885138 | + | 0.465328i | \(0.845936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.3828 | 0.603829 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.54175 | 0.0604260 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.0405 | −1.72344 | −0.861719 | − | 0.507386i | \(-0.830612\pi\) | ||||
−0.861719 | + | 0.507386i | \(0.830612\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.1809 | 0.905754 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.51026 | −0.0979346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.6642 | 1.93464 | 0.967321 | − | 0.253555i | \(-0.0815999\pi\) | ||||
0.967321 | + | 0.253555i | \(0.0815999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.2095 | 0.474893 | 0.237446 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237446 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2110 | 0.901442 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.93817 | 0.152716 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.4299 | −0.558728 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.4864 | 0.637401 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.9080 | −1.73365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.6693 | 1.18221 | 0.591107 | − | 0.806593i | \(-0.298691\pi\) | ||||
0.591107 | + | 0.806593i | \(0.298691\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.14939 | 0.0827301 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8194 | 0.607988 | 0.303994 | − | 0.952674i | \(-0.401680\pi\) | ||||
0.303994 | + | 0.952674i | \(0.401680\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.0495 | −0.424041 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.37540 | 0.205986 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.58263 | 0.328405 | 0.164203 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.5982 | −0.978055 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.85562 | 0.299711 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.60230 | −0.289625 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.22154 | 0.236679 | 0.118339 | − | 0.992973i | \(-0.462243\pi\) | ||||
0.118339 | + | 0.992973i | \(0.462243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.55542 | 0.135059 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.9925 | 0.606630 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.2061 | 0.916873 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.08638 | −0.192385 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.5201 | −0.661724 | −0.330862 | − | 0.943679i | \(-0.607339\pi\) | ||||
−0.330862 | + | 0.943679i | \(0.607339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.2803 | 0.991181 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.32930 | −0.238375 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.15957 | 0.0812190 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.8631 | 1.45953 | 0.729766 | − | 0.683697i | \(-0.239629\pi\) | ||||
0.729766 | + | 0.683697i | \(0.239629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4674 | 0.467563 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.4692 | −0.729129 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.8635 | 1.60300 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.8450 | −0.479707 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.3606 | 0.386383 | 0.193192 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193192 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.39901 | 0.163828 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.56580 | −0.206994 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.40137 | −0.126324 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.7807 | 1.92044 | 0.960220 | − | 0.279244i | \(-0.0900840\pi\) | ||||
0.960220 | + | 0.279244i | \(0.0900840\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.3684 | 0.790340 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.7091 | 0.395550 | 0.197775 | − | 0.980247i | \(-0.436628\pi\) | ||||
0.197775 | + | 0.980247i | \(0.436628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.9383 | 0.403465 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 57.3647 | 2.11306 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.3746 | 1.48520 | 0.742602 | − | 0.669734i | \(-0.233592\pi\) | ||||
0.742602 | + | 0.669734i | \(0.233592\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.6553 | −0.611849 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.6651 | 0.611383 | 0.305692 | − | 0.952131i | \(-0.401112\pi\) | ||||
0.305692 | + | 0.952131i | \(0.401112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.9321 | 0.950080 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.96218 | 0.108380 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.84169 | 0.323068 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7654 | −0.940191 | −0.470096 | − | 0.882615i | \(-0.655781\pi\) | ||||
−0.470096 | + | 0.882615i | \(0.655781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.4878 | −0.491523 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7085 | 0.790054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.58635 | −0.130348 | −0.0651740 | − | 0.997874i | \(-0.520760\pi\) | ||||
−0.0651740 | + | 0.997874i | \(0.520760\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −44.8979 | −1.62969 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.56070 | 0.0928255 | 0.0464127 | − | 0.998922i | \(-0.485221\pi\) | ||||
0.0464127 | + | 0.998922i | \(0.485221\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.8388 | −0.464797 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.60056 | 0.274799 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.1084 | 0.581641 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5797 | −0.525756 | −0.262878 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262878 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0902 | −0.543459 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.4680 | −0.772151 | −0.386076 | − | 0.922467i | \(-0.626170\pi\) | ||||
−0.386076 | + | 0.922467i | \(0.626170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.58923 | −0.164850 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.87470 | −0.210754 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.3694 | −0.622323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −67.4435 | −2.41332 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.58248 | −0.0565533 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.44938 | −0.265880 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.87234 | 0.102388 | 0.0511939 | − | 0.998689i | \(-0.483697\pi\) | ||||
0.0511939 | + | 0.998689i | \(0.483697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.8686 | 0.422532 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.4213 | −0.370538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.0263 | −1.66995 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.48941 | −0.0882902 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.8716 | 1.41232 | 0.706162 | − | 0.708050i | \(-0.250425\pi\) | ||||
0.706162 | + | 0.708050i | \(0.250425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8758 | 0.597022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.54127 | 0.266458 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.3600 | 0.436176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.1169 | 0.391820 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.857197 | −0.0301748 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.6315 | −1.46369 | −0.731843 | − | 0.681473i | \(-0.761339\pi\) | ||||
−0.731843 | + | 0.681473i | \(0.761339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.3043 | −1.48551 | −0.742753 | − | 0.669565i | \(-0.766480\pi\) | ||||
−0.742753 | + | 0.669565i | \(0.766480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.9528 | 0.594561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.2796 | 0.500192 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.3332 | −0.536439 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.72313 | 0.130097 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.9001 | −1.56702 | −0.783512 | − | 0.621377i | \(-0.786574\pi\) | ||||
−0.783512 | + | 0.621377i | \(0.786574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.8823 | 0.762769 | 0.381385 | − | 0.924416i | \(-0.375447\pi\) | ||||
0.381385 | + | 0.924416i | \(0.375447\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.5832 | −0.368459 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5690 | 0.610934 | 0.305467 | − | 0.952203i | \(-0.401187\pi\) | ||||
0.305467 | + | 0.952203i | \(0.401187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.8075 | 0.375361 | 0.187680 | − | 0.982230i | \(-0.439903\pi\) | ||||
0.187680 | + | 0.982230i | \(0.439903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.3840 | −1.08870 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.1647 | −1.01050 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68837 | 0.0584286 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.13513 | −0.0738008 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.0750 | 1.00378 | 0.501891 | − | 0.864931i | \(-0.332638\pi\) | ||||
0.501891 | + | 0.864931i | \(0.332638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4958 | −0.913647 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.26822 | 0.284773 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.9364 | 0.789038 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.56324 | −0.328597 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.24839 | −0.214444 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 74.1858 | 2.54305 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.6140 | 1.66451 | 0.832256 | − | 0.554392i | \(-0.187049\pi\) | ||||
0.832256 | + | 0.554392i | \(0.187049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.45386 | −0.186518 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.4623 | 1.24553 | 0.622763 | − | 0.782410i | \(-0.286010\pi\) | ||||
0.622763 | + | 0.782410i | \(0.286010\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.60352 | 0.293548 | 0.146774 | − | 0.989170i | \(-0.453111\pi\) | ||||
0.146774 | + | 0.989170i | \(0.453111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.88275 | 0.132324 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.4936 | 0.901852 | 0.450926 | − | 0.892561i | \(-0.351094\pi\) | ||||
0.450926 | + | 0.892561i | \(0.351094\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.17024 | −0.243795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.26531 | −0.110896 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −61.3869 | −2.08241 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.0706 | 2.03541 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.3021 | 0.517898 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.71623 | 0.294662 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8702 | 0.603432 | 0.301716 | − | 0.953398i | \(-0.402441\pi\) | ||||
0.301716 | + | 0.953398i | \(0.402441\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.7074 | 0.765900 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.2404 | 0.782990 | 0.391495 | − | 0.920180i | \(-0.371958\pi\) | ||||
0.391495 | + | 0.920180i | \(0.371958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.2781 | −1.11990 | −0.559948 | − | 0.828528i | \(-0.689179\pi\) | ||||
−0.559948 | + | 0.828528i | \(0.689179\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.27478 | 0.177310 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.3015 | −0.513775 | −0.256887 | − | 0.966441i | \(-0.582697\pi\) | ||||
−0.256887 | + | 0.966441i | \(0.582697\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.16212 | −0.307288 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.92380 | −0.164954 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.1094 | −0.405226 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.01187 | −0.0338229 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −47.0157 | −1.56981 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.37880 | 0.112689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.63749 | 0.221127 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.42757 | 0.114063 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.0864 | −1.36576 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.7007 | −0.886583 | −0.443292 | − | 0.896377i | \(-0.646189\pi\) | ||||
−0.443292 | + | 0.896377i | \(0.646189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.99072 | −0.0991961 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.6323 | 0.517920 | 0.258960 | − | 0.965888i | \(-0.416620\pi\) | ||||
0.258960 | + | 0.965888i | \(0.416620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.5852 | −0.482699 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.3990 | −0.509074 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.91409 | −0.327392 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.3950 | 0.606795 | 0.303398 | − | 0.952864i | \(-0.401879\pi\) | ||||
0.303398 | + | 0.952864i | \(0.401879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.71355 | −0.320072 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −70.6248 | −2.32464 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.4868 | 0.574963 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.09205 | −0.200089 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.2625 | 0.599174 | 0.299587 | − | 0.954069i | \(-0.403151\pi\) | ||||
0.299587 | + | 0.954069i | \(0.403151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.9274 | 0.685869 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.6568 | −1.00366 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −37.4236 | −1.22388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.89282 | 0.127173 | 0.0635864 | − | 0.997976i | \(-0.479746\pi\) | ||||
0.0635864 | + | 0.997976i | \(0.479746\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.88725 | −0.126856 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.3525 | −1.51105 | −0.755524 | − | 0.655121i | \(-0.772618\pi\) | ||||
−0.755524 | + | 0.655121i | \(0.772618\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.0314 | −1.59668 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.21916 | 0.0396592 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.6858 | 0.347243 | 0.173622 | − | 0.984812i | \(-0.444453\pi\) | ||||
0.173622 | + | 0.984812i | \(0.444453\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9431 | 0.420149 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.2051 | 0.590340 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.70387 | −0.314339 | −0.157170 | − | 0.987572i | \(-0.550237\pi\) | ||||
−0.157170 | + | 0.987572i | \(0.550237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5940 | −0.731124 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.79183 | 0.251874 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.9479 | 0.353526 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4412 | −0.852943 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.2446 | −0.394577 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.0744 | −0.646219 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.89854 | −0.0932107 | −0.0466054 | − | 0.998913i | \(-0.514840\pi\) | ||||
−0.0466054 | + | 0.998913i | \(0.514840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5416 | 0.467143 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.8901 | 0.862944 | 0.431472 | − | 0.902126i | \(-0.357994\pi\) | ||||
0.431472 | + | 0.902126i | \(0.357994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.83972 | −0.219271 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.0824 | −0.354921 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.0951 | −0.866849 | −0.433425 | − | 0.901190i | \(-0.642695\pi\) | ||||
−0.433425 | + | 0.901190i | \(0.642695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.1317 | −1.18674 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.7801 | 0.567676 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.8416 | 1.20696 | 0.603481 | − | 0.797378i | \(-0.293780\pi\) | ||||
0.603481 | + | 0.797378i | \(0.293780\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.0306 | 1.02058 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.70694 | 0.0861627 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.2834 | −1.37633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.3760 | 1.15552 | 0.577761 | − | 0.816206i | \(-0.303927\pi\) | ||||
0.577761 | + | 0.816206i | \(0.303927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.8334 | 0.788063 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.4323 | −1.09158 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.9879 | −1.89984 | −0.949918 | − | 0.312501i | \(-0.898833\pi\) | ||||
−0.949918 | + | 0.312501i | \(0.898833\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.13571 | 0.257402 |
(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 | 8016.2.a.bg.1.9 | 13 | ||
4.3 | odd | 2 | 4008.2.a.m.1.9 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.9 | ✓ | 13 | 4.3 | odd | 2 | ||
8016.2.a.bg.1.9 | 13 | 1.1 | even | 1 | trivial |