Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6016,2,Mod(1,6016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6016 = 2^{7} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6016.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: | \(48.0380018560\) |
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: | \( x^{13} - 4 x^{12} - 22 x^{11} + 96 x^{10} + 163 x^{9} - 840 x^{8} - 438 x^{7} + 3358 x^{6} + 5 x^{5} + \cdots - 832 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(2.61905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6016.1 |
$q$-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 | ||||||||
\(3\) | 2.61905 | 1.51211 | 0.756054 | − | 0.654510i | \(-0.227125\pi\) | ||||
0.756054 | + | 0.654510i | \(0.227125\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.63183 | −0.729777 | −0.364889 | − | 0.931051i | \(-0.618893\pi\) | ||||
−0.364889 | + | 0.931051i | \(0.618893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46539 | 1.30979 | 0.654897 | − | 0.755719i | \(-0.272712\pi\) | ||||
0.654897 | + | 0.755719i | \(0.272712\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.85941 | 1.28647 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.65260 | 0.498278 | 0.249139 | − | 0.968468i | \(-0.419852\pi\) | ||||
0.249139 | + | 0.968468i | \(0.419852\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82156 | −0.782561 | −0.391280 | − | 0.920271i | \(-0.627968\pi\) | ||||
−0.391280 | + | 0.920271i | \(0.627968\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.27384 | −1.10350 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.37109 | 1.54522 | 0.772608 | − | 0.634883i | \(-0.218952\pi\) | ||||
0.772608 | + | 0.634883i | \(0.218952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.98956 | 0.915267 | 0.457634 | − | 0.889141i | \(-0.348697\pi\) | ||||
0.457634 | + | 0.889141i | \(0.348697\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.07601 | 1.98055 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.04749 | −0.426931 | −0.213466 | − | 0.976951i | \(-0.568475\pi\) | ||||
−0.213466 | + | 0.976951i | \(0.568475\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.33713 | −0.467425 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.25082 | 0.433171 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0143200 | −0.00265916 | −0.00132958 | − | 0.999999i | \(-0.500423\pi\) | ||||
−0.00132958 | + | 0.999999i | \(0.500423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.31164 | 1.31321 | 0.656605 | − | 0.754235i | \(-0.271992\pi\) | ||||
0.656605 | + | 0.754235i | \(0.271992\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.32824 | 0.753450 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.65493 | −0.955857 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.31853 | −0.709962 | −0.354981 | − | 0.934874i | \(-0.615513\pi\) | ||||
−0.354981 | + | 0.934874i | \(0.615513\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.38981 | −1.18332 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1303 | 1.58208 | 0.791040 | − | 0.611764i | \(-0.209540\pi\) | ||||
0.791040 | + | 0.611764i | \(0.209540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.72811 | −0.263535 | −0.131767 | − | 0.991281i | \(-0.542065\pi\) | ||||
−0.131767 | + | 0.991281i | \(0.542065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.29790 | −0.938836 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00891 | 0.715558 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.6862 | 2.33653 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.63901 | 0.774577 | 0.387289 | − | 0.921959i | \(-0.373412\pi\) | ||||
0.387289 | + | 0.921959i | \(0.373412\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.69677 | −0.363632 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4488 | 1.38398 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.0598 | −1.70024 | −0.850118 | − | 0.526592i | \(-0.823469\pi\) | ||||
−0.850118 | + | 0.526592i | \(0.823469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.84494 | 0.236220 | 0.118110 | − | 0.993001i | \(-0.462316\pi\) | ||||
0.118110 | + | 0.993001i | \(0.462316\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.3743 | 1.68501 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.60432 | 0.571095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.19593 | 0.390445 | 0.195223 | − | 0.980759i | \(-0.437457\pi\) | ||||
0.195223 | + | 0.980759i | \(0.437457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.36247 | −0.645566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.78389 | −0.211708 | −0.105854 | − | 0.994382i | \(-0.533758\pi\) | ||||
−0.105854 | + | 0.994382i | \(0.533758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3324 | 1.56044 | 0.780221 | − | 0.625504i | \(-0.215107\pi\) | ||||
0.780221 | + | 0.625504i | \(0.215107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.12104 | −0.706797 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.72690 | 0.652641 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6560 | −1.42391 | −0.711954 | − | 0.702226i | \(-0.752189\pi\) | ||||
−0.711954 | + | 0.702226i | \(0.752189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.68320 | −0.631467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.77661 | 0.853594 | 0.426797 | − | 0.904348i | \(-0.359642\pi\) | ||||
0.426797 | + | 0.904348i | \(0.359642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.3965 | −1.12766 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0375047 | −0.00402093 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.300991 | −0.0319050 | −0.0159525 | − | 0.999873i | \(-0.505078\pi\) | ||||
−0.0159525 | + | 0.999873i | \(0.505078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.77781 | −1.02499 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.1495 | 1.98571 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.51029 | −0.667941 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.62682 | 0.368248 | 0.184124 | − | 0.982903i | \(-0.441055\pi\) | ||||
0.184124 | + | 0.982903i | \(0.441055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.37806 | 0.641019 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0396915 | 0.00394946 | 0.00197473 | − | 0.999998i | \(-0.499371\pi\) | ||||
0.00197473 | + | 0.999998i | \(0.499371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.87008 | 0.676930 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.8105 | −1.44536 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6779 | −1.22562 | −0.612810 | − | 0.790231i | \(-0.709961\pi\) | ||||
−0.612810 | + | 0.790231i | \(0.709961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.62362 | −0.251297 | −0.125649 | − | 0.992075i | \(-0.540101\pi\) | ||||
−0.125649 | + | 0.992075i | \(0.540101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3104 | −1.07354 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.67123 | 0.627577 | 0.313788 | − | 0.949493i | \(-0.398402\pi\) | ||||
0.313788 | + | 0.949493i | \(0.398402\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.34116 | 0.311565 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.8896 | −1.00674 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.0783 | 2.02391 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.26891 | −0.751719 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 26.5316 | 2.39227 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9730 | 1.07089 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.22819 | 0.286456 | 0.143228 | − | 0.989690i | \(-0.454252\pi\) | ||||
0.143228 | + | 0.989690i | \(0.454252\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.52601 | −0.398493 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.35330 | 0.118239 | 0.0591193 | − | 0.998251i | \(-0.481171\pi\) | ||||
0.0591193 | + | 0.998251i | \(0.481171\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8254 | 1.19881 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.67297 | −0.316119 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.40162 | 0.717799 | 0.358899 | − | 0.933376i | \(-0.383152\pi\) | ||||
0.358899 | + | 0.933376i | \(0.383152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.1511 | 1.45474 | 0.727369 | − | 0.686246i | \(-0.240743\pi\) | ||||
0.727369 | + | 0.686246i | \(0.240743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.61905 | −0.220564 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.66292 | −0.389933 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0233678 | 0.00194059 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.1186 | 1.08200 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.7241 | 1.94355 | 0.971777 | − | 0.235902i | \(-0.0758045\pi\) | ||||
0.971777 | + | 0.235902i | \(0.0758045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.68732 | −0.788343 | −0.394171 | − | 0.919037i | \(-0.628968\pi\) | ||||
−0.394171 | + | 0.919037i | \(0.628968\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.5886 | 1.98787 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.9314 | −0.958351 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.30532 | −0.742645 | −0.371323 | − | 0.928504i | \(-0.621096\pi\) | ||||
−0.371323 | + | 0.928504i | \(0.621096\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7688 | 1.17124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.09534 | −0.559192 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.783564 | 0.0613735 | 0.0306867 | − | 0.999529i | \(-0.490231\pi\) | ||||
0.0306867 | + | 0.999529i | \(0.490231\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.06296 | −0.549851 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.84752 | −0.297730 | −0.148865 | − | 0.988858i | \(-0.547562\pi\) | ||||
−0.148865 | + | 0.988858i | \(0.547562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.03878 | −0.387599 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.3973 | 1.17746 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.64476 | 0.201078 | 0.100539 | − | 0.994933i | \(-0.467943\pi\) | ||||
0.100539 | + | 0.994933i | \(0.467943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.09905 | −0.612230 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34.2041 | −2.57094 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.9594 | 1.64132 | 0.820660 | − | 0.571417i | \(-0.193606\pi\) | ||||
0.820660 | + | 0.571417i | \(0.193606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.3190 | −1.65896 | −0.829479 | − | 0.558538i | \(-0.811362\pi\) | ||||
−0.829479 | + | 0.558538i | \(0.811362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.83198 | 0.357190 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.04711 | 0.518114 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.5289 | 0.769947 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.79998 | 0.567365 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3650 | −1.25649 | −0.628244 | − | 0.778016i | \(-0.716226\pi\) | ||||
−0.628244 | + | 0.778016i | \(0.716226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.45220 | −0.176513 | −0.0882567 | − | 0.996098i | \(-0.528130\pi\) | ||||
−0.0882567 | + | 0.996098i | \(0.528130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0589 | 0.863557 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.2939 | −1.58838 | −0.794189 | − | 0.607671i | \(-0.792104\pi\) | ||||
−0.794189 | + | 0.607671i | \(0.792104\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3127 | 0.801936 | 0.400968 | − | 0.916092i | \(-0.368674\pi\) | ||||
0.400968 | + | 0.916092i | \(0.368674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.37029 | 0.590395 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0496243 | −0.00348294 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.5309 | −1.15457 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.90210 | −0.549234 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.59315 | 0.456058 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4994 | 0.998179 | 0.499089 | − | 0.866551i | \(-0.333668\pi\) | ||||
0.499089 | + | 0.866551i | \(0.333668\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.67208 | −0.320126 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.81999 | 0.192322 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.3377 | 1.72003 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.9182 | 2.35956 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.9764 | −1.20923 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.57749 | −0.440462 | −0.220231 | − | 0.975448i | \(-0.570681\pi\) | ||||
−0.220231 | + | 0.975448i | \(0.570681\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.01992 | −0.601328 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.60362 | −0.371925 | −0.185963 | − | 0.982557i | \(-0.559540\pi\) | ||||
−0.185963 | + | 0.982557i | \(0.559540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.74446 | 0.643932 | 0.321966 | − | 0.946751i | \(-0.395656\pi\) | ||||
0.321966 | + | 0.946751i | \(0.395656\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.9990 | 0.986863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7199 | −1.22638 | −0.613190 | − | 0.789935i | \(-0.710114\pi\) | ||||
−0.613190 | + | 0.789935i | \(0.710114\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.63183 | 0.106449 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.1466 | −2.15310 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.87605 | 0.509460 | 0.254730 | − | 0.967012i | \(-0.418013\pi\) | ||||
0.254730 | + | 0.967012i | \(0.418013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.54408 | 0.357125 | 0.178563 | − | 0.983929i | \(-0.442855\pi\) | ||||
0.178563 | + | 0.983929i | \(0.442855\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6370 | −1.38802 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.17369 | −0.522198 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.2568 | −0.716252 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.3673 | 1.29073 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.0982 | −1.39483 | −0.697414 | − | 0.716669i | \(-0.745666\pi\) | ||||
−0.697414 | + | 0.716669i | \(0.745666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.38368 | −0.212730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −27.2290 | −1.70515 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.2945 | 1.20356 | 0.601779 | − | 0.798663i | \(-0.294459\pi\) | ||||
0.601779 | + | 0.798663i | \(0.294459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.9654 | −0.929903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0552667 | −0.00342092 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.3983 | 1.25781 | 0.628907 | − | 0.777480i | \(-0.283502\pi\) | ||||
0.628907 | + | 0.777480i | \(0.283502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.20191 | −0.565269 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.788310 | −0.0482438 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.7330 | −1.62994 | −0.814969 | − | 0.579505i | \(-0.803246\pi\) | ||||
−0.814969 | + | 0.579505i | \(0.803246\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7183 | 0.833329 | 0.416665 | − | 0.909060i | \(-0.363199\pi\) | ||||
0.416665 | + | 0.909060i | \(0.363199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.6085 | −1.54990 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.86234 | −0.232908 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.58257 | −0.0950877 | −0.0475438 | − | 0.998869i | \(-0.515139\pi\) | ||||
−0.0475438 | + | 0.998869i | \(0.515139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.2186 | 1.68940 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.4464 | 0.623179 | 0.311590 | − | 0.950217i | \(-0.399139\pi\) | ||||
0.311590 | + | 0.950217i | \(0.399139\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.2512 | −1.26325 | −0.631626 | − | 0.775273i | \(-0.717612\pi\) | ||||
−0.631626 | + | 0.775273i | \(0.717612\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.0507 | −1.01000 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.1052 | 2.07220 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.5908 | 1.38769 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.49881 | 0.556830 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.2919 | 1.76967 | 0.884835 | − | 0.465905i | \(-0.154271\pi\) | ||||
0.884835 | + | 0.465905i | \(0.154271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.3113 | 1.24079 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.71971 | 0.215840 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.77712 | 0.334100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.98858 | −0.345176 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.103954 | 0.00597200 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.01063 | −0.172388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.59742 | −0.0911695 | −0.0455847 | − | 0.998960i | \(-0.514515\pi\) | ||||
−0.0455847 | + | 0.998960i | \(0.514515\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.9931 | 1.02359 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.6187 | 1.16918 | 0.584588 | − | 0.811330i | \(-0.301256\pi\) | ||||
0.584588 | + | 0.811330i | \(0.301256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8852 | 1.35007 | 0.675035 | − | 0.737786i | \(-0.264129\pi\) | ||||
0.675035 | + | 0.737786i | \(0.264129\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.8247 | −1.22968 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2961 | −0.915283 | −0.457641 | − | 0.889137i | \(-0.651306\pi\) | ||||
−0.457641 | + | 0.889137i | \(0.651306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0236652 | −0.00132500 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −33.2040 | −1.85327 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.4178 | 1.41429 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.59435 | 0.365789 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.87139 | −0.379989 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.46539 | −0.191053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.75022 | 0.151166 | 0.0755829 | − | 0.997140i | \(-0.475918\pi\) | ||||
0.0755829 | + | 0.997140i | \(0.475918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.6670 | −0.913344 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.21522 | −0.284938 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.7156 | −1.78213 | −0.891067 | − | 0.453871i | \(-0.850043\pi\) | ||||
−0.891067 | + | 0.453871i | \(0.850043\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.4723 | 0.948964 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0832 | 0.654344 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.89991 | −0.372560 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.75065 | 0.471119 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.03353 | −0.377580 | −0.188790 | − | 0.982018i | \(-0.560456\pi\) | ||||
−0.188790 | + | 0.982018i | \(0.560456\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2479 | 1.24443 | 0.622216 | − | 0.782846i | \(-0.286233\pi\) | ||||
0.622216 | + | 0.782846i | \(0.286233\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.35084 | −0.338983 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6215 | 0.831446 | 0.415723 | − | 0.909491i | \(-0.363529\pi\) | ||||
0.415723 | + | 0.909491i | \(0.363529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.91100 | 0.154500 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 57.8241 | 3.06037 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.7998 | 1.78388 | 0.891942 | − | 0.452150i | \(-0.149343\pi\) | ||||
0.891942 | + | 0.452150i | \(0.149343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.08343 | −0.162286 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.6567 | −1.13668 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.7563 | −1.13878 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.7411 | −1.23928 | −0.619638 | − | 0.784887i | \(-0.712721\pi\) | ||||
−0.619638 | + | 0.784887i | \(0.712721\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.0968 | 2.03530 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.5413 | 1.01454 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.15684 | −0.111677 | −0.0558385 | − | 0.998440i | \(-0.517783\pi\) | ||||
−0.0558385 | + | 0.998440i | \(0.517783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 31.3577 | 1.61931 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0404048 | 0.00208095 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.3159 | −0.632624 | −0.316312 | − | 0.948655i | \(-0.602445\pi\) | ||||
−0.316312 | + | 0.948655i | \(0.602445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.45478 | 0.433152 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.48160 | 0.177901 | 0.0889506 | − | 0.996036i | \(-0.471649\pi\) | ||||
0.0889506 | + | 0.996036i | \(0.471649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.34534 | −0.476283 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.66949 | −0.339029 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5890 | −0.587583 | −0.293792 | − | 0.955870i | \(-0.594917\pi\) | ||||
−0.293792 | + | 0.955870i | \(0.594917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.0447 | −0.659701 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.54436 | 0.178790 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.6524 | 1.03914 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.5181 | −1.07996 | −0.539982 | − | 0.841677i | \(-0.681569\pi\) | ||||
−0.539982 | + | 0.841677i | \(0.681569\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 36.2093 | 1.81273 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.8674 | −0.642565 | −0.321283 | − | 0.946983i | \(-0.604114\pi\) | ||||
−0.321283 | + | 0.946983i | \(0.604114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.6303 | −1.02767 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.27403 | 0.460830 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.13681 | −0.353758 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.3544 | −1.30314 | −0.651569 | − | 0.758589i | \(-0.725889\pi\) | ||||
−0.651569 | + | 0.758589i | \(0.725889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.0042 | 1.08539 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −45.2571 | −2.22696 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.6901 | −0.622933 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 44.9196 | 2.19972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.30358 | −0.259097 | −0.129549 | − | 0.991573i | \(-0.541353\pi\) | ||||
−0.129549 | + | 0.991573i | \(0.541353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6840 | −0.715652 | −0.357826 | − | 0.933788i | \(-0.616482\pi\) | ||||
−0.357826 | + | 0.933788i | \(0.616482\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.85941 | −0.187651 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.8900 | −0.722273 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.39343 | 0.309400 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.2124 | −0.589620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.9251 | 1.24877 | 0.624384 | − | 0.781118i | \(-0.285350\pi\) | ||||
0.624384 | + | 0.781118i | \(0.285350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.8031 | −1.72059 | −0.860293 | − | 0.509800i | \(-0.829719\pi\) | ||||
−0.860293 | + | 0.509800i | \(0.829719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0612014 | 0.00293438 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.16858 | −0.390756 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.2511 | 1.92108 | 0.960541 | − | 0.278140i | \(-0.0897178\pi\) | ||||
0.960541 | + | 0.278140i | \(0.0897178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3314 | 0.920543 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.1914 | −1.05435 | −0.527173 | − | 0.849758i | \(-0.676748\pi\) | ||||
−0.527173 | + | 0.849758i | \(0.676748\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.491167 | 0.0232835 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 62.1345 | 2.93886 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3870 | −0.490191 | −0.245095 | − | 0.969499i | \(-0.578819\pi\) | ||||
−0.245095 | + | 0.969499i | \(0.578819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7413 | 0.788316 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.3715 | −1.19206 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.9557 | 0.748016 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1022 | 0.893565 | 0.446783 | − | 0.894643i | \(-0.352570\pi\) | ||||
0.446783 | + | 0.894643i | \(0.352570\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.3402 | 0.669343 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.4515 | 1.41827 | 0.709135 | − | 0.705073i | \(-0.249086\pi\) | ||||
0.709135 | + | 0.705073i | \(0.249086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2642 | 0.477020 | 0.238510 | − | 0.971140i | \(-0.423341\pi\) | ||||
0.238510 | + | 0.971140i | \(0.423341\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.2488 | −1.44913 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5025 | −0.763647 | −0.381823 | − | 0.924235i | \(-0.624704\pi\) | ||||
−0.381823 | + | 0.924235i | \(0.624704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0751 | 0.511402 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.3711 | −1.12296 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.85588 | −0.131314 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.32410 | −0.427819 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.7632 | 0.996469 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.7101 | 0.672120 | 0.336060 | − | 0.941841i | \(-0.390905\pi\) | ||||
0.336060 | + | 0.941841i | \(0.390905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1850 | 0.555588 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.5830 | −0.845558 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.91836 | −0.268739 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.9025 | −1.35501 | −0.677506 | − | 0.735517i | \(-0.736939\pi\) | ||||
−0.677506 | + | 0.735517i | \(0.736939\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.05219 | 0.0928033 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.6866 | 0.753056 | 0.376528 | − | 0.926405i | \(-0.377118\pi\) | ||||
0.376528 | + | 0.926405i | \(0.377118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0912340 | −0.00410897 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.4079 | −0.467801 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.18185 | −0.277294 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.3924 | −1.09195 | −0.545976 | − | 0.837801i | \(-0.683841\pi\) | ||||
−0.545976 | + | 0.837801i | \(0.683841\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.0768 | −0.450200 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.84938 | 0.349987 | 0.174993 | − | 0.984570i | \(-0.444010\pi\) | ||||
0.174993 | + | 0.984570i | \(0.444010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0647699 | −0.00288222 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.1968 | −0.586091 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.2126 | −0.541314 | −0.270657 | − | 0.962676i | \(-0.587241\pi\) | ||||
−0.270657 | + | 0.962676i | \(0.587241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.2020 | 2.04386 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.97979 | 0.396468 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.2108 | −0.494008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.65260 | −0.0726813 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.92676 | 0.304051 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.64477 | 0.291112 | 0.145556 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145556 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.7936 | 1.52142 | 0.760710 | − | 0.649092i | \(-0.224851\pi\) | ||||
0.760710 | + | 0.649092i | \(0.224851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.2118 | −0.925758 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.5831 | 2.02919 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8078 | −0.817730 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −50.4029 | −2.18730 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.5832 | −1.23807 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.6882 | 0.894429 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 57.5126 | 2.48185 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.27772 | 0.356547 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.37482 | −0.360062 | −0.180031 | − | 0.983661i | \(-0.557620\pi\) | ||||
−0.180031 | + | 0.983661i | \(0.557620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −58.4545 | −2.50852 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.28131 | 0.183391 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.8403 | −1.14761 | −0.573804 | − | 0.818992i | \(-0.694533\pi\) | ||||
−0.573804 | + | 0.818992i | \(0.694533\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.12037 | 0.303890 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0571304 | −0.00243384 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.8578 | −1.86502 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.4567 | 0.783444 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.2642 | −0.646765 | −0.323383 | − | 0.946268i | \(-0.604820\pi\) | ||||
−0.323383 | + | 0.946268i | \(0.604820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.87598 | 0.206232 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.5756 | 1.16424 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.0665 | 1.30930 | 0.654649 | − | 0.755933i | \(-0.272817\pi\) | ||||
0.654649 | + | 0.755933i | \(0.272817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.8863 | −0.457991 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.6945 | −0.827091 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.5746 | −0.946378 | −0.473189 | − | 0.880961i | \(-0.656897\pi\) | ||||
−0.473189 | + | 0.880961i | \(0.656897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.84825 | −0.202893 | −0.101446 | − | 0.994841i | \(-0.532347\pi\) | ||||
−0.101446 | + | 0.994841i | \(0.532347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −45.4798 | −1.89995 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.78524 | 0.199558 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.6964 | −1.40280 | −0.701400 | − | 0.712768i | \(-0.747441\pi\) | ||||
−0.701400 | + | 0.712768i | \(0.747441\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.42243 | −0.266907 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.9490 | 1.11803 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.31903 | 0.385955 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.7699 | 0.734696 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.80827 | −0.404830 | −0.202415 | − | 0.979300i | \(-0.564879\pi\) | ||||
−0.202415 | + | 0.979300i | \(0.564879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.1702 | 1.20194 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −58.3889 | −2.40180 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.5006 | 1.29357 | 0.646787 | − | 0.762671i | \(-0.276112\pi\) | ||||
0.646787 | + | 0.762671i | \(0.276112\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0280 | −1.47701 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.6285 | 1.21261 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.1137 | −1.23041 | −0.615207 | − | 0.788366i | \(-0.710928\pi\) | ||||
−0.615207 | + | 0.788366i | \(0.710928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8979 | 0.607700 | 0.303850 | − | 0.952720i | \(-0.401728\pi\) | ||||
0.303850 | + | 0.952720i | \(0.401728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.3344 | 0.502295 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4935 | 0.548587 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1466 | −0.655370 | −0.327685 | − | 0.944787i | \(-0.606268\pi\) | ||||
−0.327685 | + | 0.944787i | \(0.606268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.129968 | −0.00526658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.82156 | 0.114148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.28385 | 0.0922436 | 0.0461218 | − | 0.998936i | \(-0.485314\pi\) | ||||
0.0461218 | + | 0.998936i | \(0.485314\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −43.2951 | −1.74583 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.7258 | −0.914907 | −0.457453 | − | 0.889234i | \(-0.651238\pi\) | ||||
−0.457453 | + | 0.889234i | \(0.651238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.8116 | −1.92171 | −0.960856 | − | 0.277049i | \(-0.910644\pi\) | ||||
−0.960856 | + | 0.277049i | \(0.910644\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.60854 | −0.184934 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.04305 | −0.0417889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.85221 | −0.314089 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.2678 | 0.689608 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.5137 | −1.09704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.71388 | −0.108038 | −0.0540190 | − | 0.998540i | \(-0.517203\pi\) | ||||
−0.0540190 | + | 0.998540i | \(0.517203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.9746 | 1.50935 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.26786 | −0.209049 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1329 | −0.559968 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.88474 | −0.272356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9355 | −0.510920 | −0.255460 | − | 0.966820i | \(-0.582227\pi\) | ||||
−0.255460 | + | 0.966820i | \(0.582227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.84592 | −0.348849 | −0.174424 | − | 0.984671i | \(-0.555806\pi\) | ||||
−0.174424 | + | 0.984671i | \(0.555806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.38568 | 0.290811 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.0899 | 1.53678 | 0.768391 | − | 0.639981i | \(-0.221058\pi\) | ||||
0.768391 | + | 0.639981i | \(0.221058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.5826 | −0.847190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 66.3606 | 2.60088 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.0186 | 1.29212 | 0.646058 | − | 0.763288i | \(-0.276416\pi\) | ||||
0.646058 | + | 0.763288i | \(0.276416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.20836 | −0.0862879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 51.4552 | 2.00746 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.1223 | −1.13444 | −0.567222 | − | 0.823565i | \(-0.691982\pi\) | ||||
−0.567222 | + | 0.823565i | \(0.691982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.5149 | −1.69253 | −0.846267 | − | 0.532759i | \(-0.821155\pi\) | ||||
−0.846267 | + | 0.532759i | \(0.821155\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −47.0811 | −1.82848 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.5607 | −0.874865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0293200 | 0.00113528 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.2268 | −0.666025 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.04895 | 0.117703 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.2537 | −1.28184 | −0.640918 | − | 0.767609i | \(-0.721446\pi\) | ||||
−0.640918 | + | 0.767609i | \(0.721446\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.26046 | −0.202475 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.4478 | 0.516840 | 0.258420 | − | 0.966033i | \(-0.416798\pi\) | ||||
0.258420 | + | 0.966033i | \(0.416798\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5683 | 0.482328 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6761 | −0.562391 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.3546 | −1.58239 | −0.791196 | − | 0.611563i | \(-0.790541\pi\) | ||||
−0.791196 | + | 0.611563i | \(0.790541\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.7100 | −0.523833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.5212 | 0.973694 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.9108 | −0.606154 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.0453 | −1.44731 | −0.723656 | − | 0.690161i | \(-0.757540\pi\) | ||||
−0.723656 | + | 0.690161i | \(0.757540\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.1024 | 0.839602 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.9877 | −1.06164 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.5408 | 2.44466 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −49.0283 | −1.85442 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.60173 | 0.324883 | 0.162441 | − | 0.986718i | \(-0.448063\pi\) | ||||
0.162441 | + | 0.986718i | \(0.448063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.2290 | −0.649805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.27384 | 0.160962 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.137547 | 0.00517297 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.55583 | −0.358877 | −0.179438 | − | 0.983769i | \(-0.557428\pi\) | ||||
−0.179438 | + | 0.983769i | \(0.557428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −48.8445 | −1.83181 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.9705 | −0.560650 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.60910 | 0.284564 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.6278 | 0.770358 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.2538 | 1.01639 | 0.508197 | − | 0.861241i | \(-0.330312\pi\) | ||||
0.508197 | + | 0.861241i | \(0.330312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8075 | 0.886638 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.5202 | 0.540012 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0334676 | 0.00124296 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.1115 | −1.19095 | −0.595475 | − | 0.803374i | \(-0.703036\pi\) | ||||
−0.595475 | + | 0.803374i | \(0.703036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.6188 | −1.46736 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0100 | −0.407218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.1534 | 0.965999 | 0.483000 | − | 0.875621i | \(-0.339547\pi\) | ||||
0.483000 | + | 0.875621i | \(0.339547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.4073 | −0.789619 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.28160 | 0.194550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.3389 | −0.968891 | −0.484445 | − | 0.874821i | \(-0.660979\pi\) | ||||
−0.484445 | + | 0.874821i | \(0.660979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.4821 | −1.08305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.7923 | −1.23972 | −0.619860 | − | 0.784713i | \(-0.712811\pi\) | ||||
−0.619860 | + | 0.784713i | \(0.712811\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.7137 | −1.41836 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.0131 | 1.09812 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.9338 | −1.60531 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.8704 | −1.67384 | −0.836918 | − | 0.547329i | \(-0.815645\pi\) | ||||
−0.836918 | + | 0.547329i | \(0.815645\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −57.8763 | −2.10913 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.8081 | 0.575315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.91756 | −0.287768 | −0.143884 | − | 0.989595i | \(-0.545959\pi\) | ||||
−0.143884 | + | 0.989595i | \(0.545959\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.86203 | −0.321671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.22789 | −0.225761 | −0.112881 | − | 0.993609i | \(-0.536008\pi\) | ||||
−0.112881 | + | 0.993609i | \(0.536008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.09186 | −0.329148 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −40.1245 | −1.45070 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.8489 | 1.33054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.267101 | 0.00963192 | 0.00481596 | − | 0.999988i | \(-0.498467\pi\) | ||||
0.00481596 | + | 0.999988i | \(0.498467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.5332 | 1.81991 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0193 | 0.540206 | 0.270103 | − | 0.962831i | \(-0.412942\pi\) | ||||
0.270103 | + | 0.962831i | \(0.412942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.0882 | −0.613827 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39.1950 | −1.40611 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.4152 | 1.44803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.94805 | −0.105490 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0322318 | −0.00115187 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.1847 | 0.541966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.17662 | −0.0775882 | −0.0387941 | − | 0.999247i | \(-0.512352\pi\) | ||||
−0.0387941 | + | 0.999247i | \(0.512352\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 53.4242 | 1.90195 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.1184 | 0.821996 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.20561 | −0.184857 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.1002 | −0.854747 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3168 | 0.613394 | 0.306697 | − | 0.951807i | \(-0.400776\pi\) | ||||
0.306697 | + | 0.951807i | \(0.400776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.37109 | −0.225393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.16165 | −0.0410448 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.0332 | 0.777534 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.5784 | 0.408085 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −70.0149 | −2.46464 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.9862 | −0.562046 | −0.281023 | − | 0.959701i | \(-0.590674\pi\) | ||||
−0.281023 | + | 0.959701i | \(0.590674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9350 | 1.12139 | 0.560695 | − | 0.828022i | \(-0.310534\pi\) | ||||
0.560695 | + | 0.828022i | \(0.310534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.9290 | 1.26008 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.27865 | −0.0447890 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.89441 | −0.241205 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −37.7365 | −1.31862 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0453 | −0.839186 | −0.419593 | − | 0.907712i | \(-0.637827\pi\) | ||||
−0.419593 | + | 0.907712i | \(0.637827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.2905 | 1.33472 | 0.667362 | − | 0.744734i | \(-0.267424\pi\) | ||||
0.667362 | + | 0.744734i | \(0.267424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.1156 | −0.352181 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.4132 | −1.47485 | −0.737425 | − | 0.675429i | \(-0.763959\pi\) | ||||
−0.737425 | + | 0.675429i | \(0.763959\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.0385 | −1.91157 | −0.955783 | − | 0.294072i | \(-0.904990\pi\) | ||||
−0.955783 | + | 0.294072i | \(0.904990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.14484 | −0.143783 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.9122 | 1.10569 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.27851 | 0.217277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.4572 | 0.568845 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.1435 | 0.419241 | 0.209621 | − | 0.977783i | \(-0.432777\pi\) | ||||
0.209621 | + | 0.977783i | \(0.432777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9998 | −0.999993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.3596 | 0.942314 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.22244 | 0.282861 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.6550 | −0.984596 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −55.6578 | −1.91017 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.84214 | 0.303105 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.8185 | 0.952487 | 0.476244 | − | 0.879313i | \(-0.341998\pi\) | ||||
0.476244 | + | 0.879313i | \(0.341998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.1258 | −0.859285 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0034 | 1.46897 | 0.734484 | − | 0.678626i | \(-0.237424\pi\) | ||||
0.734484 | + | 0.678626i | \(0.237424\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.8086 | 0.607620 | 0.303810 | − | 0.952733i | \(-0.401741\pi\) | ||||
0.303810 | + | 0.952733i | \(0.401741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 91.9423 | 3.13338 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.0611 | 0.682887 | 0.341444 | − | 0.939902i | \(-0.389084\pi\) | ||||
0.341444 | + | 0.939902i | \(0.389084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.31581 | −0.146742 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 61.7854 | 2.09834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.9153 | −0.709502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.01752 | −0.305547 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.9974 | 0.473739 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.4909 | 1.40265 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.3471 | 0.923446 | 0.461723 | − | 0.887024i | \(-0.347231\pi\) | ||||
0.461723 | + | 0.887024i | \(0.347231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 79.3358 | 2.67593 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.9501 | 1.21119 | 0.605595 | − | 0.795773i | \(-0.292935\pi\) | ||||
0.605595 | + | 0.795773i | \(0.292935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.9962 | 1.24502 | 0.622511 | − | 0.782611i | \(-0.286112\pi\) | ||||
0.622511 | + | 0.782611i | \(0.286112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 55.8154 | 1.87621 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.5813 | 1.06040 | 0.530198 | − | 0.847874i | \(-0.322118\pi\) | ||||
0.530198 | + | 0.847874i | \(0.322118\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.1869 | 0.375198 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.39207 | −0.314646 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.98956 | −0.133505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.8340 | −1.19780 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.1306 | 0.505195 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.104703 | −0.00349203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.9266 | 1.19689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.6844 | −0.521943 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.4208 | 1.21067 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.3465 | 0.509571 | 0.254786 | − | 0.966998i | \(-0.417995\pi\) | ||||
0.254786 | + | 0.966998i | \(0.417995\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.153186 | 0.00508085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.5434 | −1.31013 | −0.655066 | − | 0.755572i | \(-0.727359\pi\) | ||||
−0.655066 | + | 0.755572i | \(0.727359\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.8516 | 0.425327 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.88498 | −0.260669 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.68972 | 0.154868 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.4055 | 0.508179 | 0.254090 | − | 0.967181i | \(-0.418224\pi\) | ||||
0.254090 | + | 0.967181i | \(0.418224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.18371 | −0.137858 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.03335 | 0.165675 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0929 | 0.331854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.5144 | 0.870849 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.4517 | 0.342908 | 0.171454 | − | 0.985192i | \(-0.445154\pi\) | ||||
0.171454 | + | 0.985192i | \(0.445154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.9833 | 0.654927 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.0012 | 1.76792 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.1813 | −0.561890 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9830 | 0.424136 | 0.212068 | − | 0.977255i | \(-0.431980\pi\) | ||||
0.212068 | + | 0.977255i | \(0.431980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.5564 | 2.04145 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.4045 | −1.02376 | −0.511879 | − | 0.859058i | \(-0.671050\pi\) | ||||
−0.511879 | + | 0.859058i | \(0.671050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7416 | −0.675439 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.7282 | −0.414050 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.1004 | −1.40058 | −0.700288 | − | 0.713860i | \(-0.746945\pi\) | ||||
−0.700288 | + | 0.713860i | \(0.746945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.6183 | −1.22114 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.6804 | −1.38401 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.4745 | 0.695626 | 0.347813 | − | 0.937564i | \(-0.386924\pi\) | ||||
0.347813 | + | 0.937564i | \(0.386924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.3368 | 0.916957 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0619804 | −0.00200354 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.1149 | 0.940168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.4601 | 0.724521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −48.9292 | −1.57672 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.00158 | 0.128815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.8062 | 0.379662 | 0.189831 | − | 0.981817i | \(-0.439206\pi\) | ||||
0.189831 | + | 0.981817i | \(0.439206\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 66.5705 | 2.13855 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.32111 | −0.138671 | −0.0693354 | − | 0.997593i | \(-0.522088\pi\) | ||||
−0.0693354 | + | 0.997593i | \(0.522088\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 59.4353 | 1.90541 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 17.2709 | 0.553112 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.8679 | −1.81936 | −0.909682 | − | 0.415305i | \(-0.863675\pi\) | ||||
−0.909682 | + | 0.415305i | \(0.863675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.497418 | −0.0158976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1256 | −0.323286 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.6165 | −0.402404 | −0.201202 | − | 0.979550i | \(-0.564485\pi\) | ||||
−0.201202 | + | 0.979550i | \(0.564485\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.3800 | 1.15916 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.07601 | −0.288893 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.53829 | 0.112511 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.0364 | −0.541180 | −0.270590 | − | 0.962695i | \(-0.587219\pi\) | ||||
−0.270590 | + | 0.962695i | \(0.587219\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.20296 | 0.228579 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.4604 | −0.585235 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1632 | −0.416882 | −0.208441 | − | 0.978035i | \(-0.566839\pi\) | ||||
−0.208441 | + | 0.978035i | \(0.566839\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.72025 | −0.307535 |
(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 | 6016.2.a.o.1.11 | yes | 13 | |
4.3 | odd | 2 | 6016.2.a.m.1.3 | ✓ | 13 | ||
8.3 | odd | 2 | 6016.2.a.p.1.11 | yes | 13 | ||
8.5 | even | 2 | 6016.2.a.n.1.3 | yes | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6016.2.a.m.1.3 | ✓ | 13 | 4.3 | odd | 2 | ||
6016.2.a.n.1.3 | yes | 13 | 8.5 | even | 2 | ||
6016.2.a.o.1.11 | yes | 13 | 1.1 | even | 1 | trivial | |
6016.2.a.p.1.11 | yes | 13 | 8.3 | odd | 2 |