Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 251) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.35567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 2.19353 | 1.26643 | 0.633217 | − | 0.773975i | \(-0.281734\pi\) | ||||
0.633217 | + | 0.773975i | \(0.281734\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.455887 | 0.203879 | 0.101939 | − | 0.994791i | \(-0.467495\pi\) | ||||
0.101939 | + | 0.994791i | \(0.467495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54920 | −0.963508 | −0.481754 | − | 0.876307i | \(-0.660000\pi\) | ||||
−0.481754 | + | 0.876307i | \(0.660000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.81156 | 0.603854 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.262360 | 0.0791044 | 0.0395522 | − | 0.999218i | \(-0.487407\pi\) | ||||
0.0395522 | + | 0.999218i | \(0.487407\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.81156 | −1.61184 | −0.805919 | − | 0.592026i | \(-0.798328\pi\) | ||||
−0.805919 | + | 0.592026i | \(0.798328\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.25546 | 0.547030 | 0.273515 | − | 0.961868i | \(-0.411814\pi\) | ||||
0.273515 | + | 0.961868i | \(0.411814\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.64252 | 1.75331 | 0.876657 | − | 0.481116i | \(-0.159769\pi\) | ||||
0.876657 | + | 0.481116i | \(0.159769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.59174 | −1.22022 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.29374 | −0.478278 | −0.239139 | − | 0.970985i | \(-0.576865\pi\) | ||||
−0.239139 | + | 0.970985i | \(0.576865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79217 | −0.958433 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.60687 | −0.501693 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.68079 | −1.42629 | −0.713144 | − | 0.701018i | \(-0.752729\pi\) | ||||
−0.713144 | + | 0.701018i | \(0.752729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.67390 | −1.19867 | −0.599334 | − | 0.800499i | \(-0.704568\pi\) | ||||
−0.599334 | + | 0.800499i | \(0.704568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.575493 | 0.100180 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.16215 | −0.196439 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.67997 | −0.769382 | −0.384691 | − | 0.923045i | \(-0.625692\pi\) | ||||
−0.384691 | + | 0.923045i | \(0.625692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.7478 | −2.04128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.97880 | −1.08990 | −0.544952 | − | 0.838467i | \(-0.683452\pi\) | ||||
−0.544952 | + | 0.838467i | \(0.683452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.67816 | 1.47591 | 0.737953 | − | 0.674852i | \(-0.235793\pi\) | ||||
0.737953 | + | 0.674852i | \(0.235793\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.825867 | 0.123113 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.331192 | −0.0483094 | −0.0241547 | − | 0.999708i | \(-0.507689\pi\) | ||||
−0.0241547 | + | 0.999708i | \(0.507689\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.501572 | −0.0716532 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.94742 | 0.692777 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.11646 | 0.565439 | 0.282720 | − | 0.959203i | \(-0.408763\pi\) | ||||
0.282720 | + | 0.959203i | \(0.408763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.119606 | 0.0161277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.7641 | 2.22045 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.70312 | −0.482105 | −0.241052 | − | 0.970512i | \(-0.577493\pi\) | ||||
−0.241052 | + | 0.970512i | \(0.577493\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.97371 | −1.02093 | −0.510464 | − | 0.859899i | \(-0.670526\pi\) | ||||
−0.510464 | + | 0.859899i | \(0.670526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.61803 | −0.581818 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.64941 | −0.328619 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.81074 | −0.465556 | −0.232778 | − | 0.972530i | \(-0.574781\pi\) | ||||
−0.232778 | + | 0.972530i | \(0.574781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.03138 | −0.605707 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4735 | 1.24297 | 0.621486 | − | 0.783425i | \(-0.286529\pi\) | ||||
0.621486 | + | 0.783425i | \(0.286529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.70131 | 1.01841 | 0.509205 | − | 0.860645i | \(-0.329939\pi\) | ||||
0.509205 | + | 0.860645i | \(0.329939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.5117 | −1.21379 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.668808 | −0.0762177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.03513 | 0.904023 | 0.452012 | − | 0.892012i | \(-0.350707\pi\) | ||||
0.452012 | + | 0.892012i | \(0.350707\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1529 | −1.23921 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.34188 | −0.696112 | −0.348056 | − | 0.937474i | \(-0.613158\pi\) | ||||
−0.348056 | + | 0.937474i | \(0.613158\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.02824 | 0.111528 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.8480 | −1.80630 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.06388 | −0.748770 | −0.374385 | − | 0.927273i | \(-0.622146\pi\) | ||||
−0.374385 | + | 0.927273i | \(0.622146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.8148 | 1.55302 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.6394 | −1.51803 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.48412 | 0.357463 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.60980 | 0.163451 | 0.0817253 | − | 0.996655i | \(-0.473957\pi\) | ||||
0.0817253 | + | 0.996655i | \(0.473957\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.475281 | 0.0477675 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.2290 | 1.71435 | 0.857175 | − | 0.515025i | \(-0.172217\pi\) | ||||
0.857175 | + | 0.515025i | \(0.172217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.70019 | −0.364590 | −0.182295 | − | 0.983244i | \(-0.558353\pi\) | ||||
−0.182295 | + | 0.983244i | \(0.558353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.54920 | −0.248777 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.57054 | −0.828545 | −0.414273 | − | 0.910153i | \(-0.635964\pi\) | ||||
−0.414273 | + | 0.910153i | \(0.635964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4835 | −1.29149 | −0.645743 | − | 0.763555i | \(-0.723452\pi\) | ||||
−0.645743 | + | 0.763555i | \(0.723452\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.2656 | −0.974371 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.21111 | −0.772436 | −0.386218 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386218 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.04569 | −0.0975107 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.5280 | −0.973314 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.74963 | −0.527067 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9312 | −0.993742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.3082 | −1.38029 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.46412 | −0.399283 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5249 | −1.02267 | −0.511333 | − | 0.859383i | \(-0.670848\pi\) | ||||
−0.511333 | + | 0.859383i | \(0.670848\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 21.2293 | 1.86914 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.43407 | −0.736889 | −0.368444 | − | 0.929650i | \(-0.620109\pi\) | ||||
−0.368444 | + | 0.929650i | \(0.620109\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.4823 | −1.68933 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.18844 | −0.102285 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1227 | −1.12115 | −0.560573 | − | 0.828105i | \(-0.689419\pi\) | ||||
−0.560573 | + | 0.828105i | \(0.689419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.24430 | 0.275178 | 0.137589 | − | 0.990489i | \(-0.456065\pi\) | ||||
0.137589 | + | 0.990489i | \(0.456065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.726479 | −0.0611806 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.52472 | −0.127503 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.50157 | −0.290790 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.10021 | −0.0907440 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.6846 | 1.61262 | 0.806312 | − | 0.591491i | \(-0.201460\pi\) | ||||
0.806312 | + | 0.591491i | \(0.201460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.55985 | 0.452454 | 0.226227 | − | 0.974075i | \(-0.427361\pi\) | ||||
0.226227 | + | 0.974075i | \(0.427361\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.08591 | 0.330326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.04254 | −0.244383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1782 | 1.61040 | 0.805199 | − | 0.593004i | \(-0.202058\pi\) | ||||
0.805199 | + | 0.593004i | \(0.202058\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.02957 | 0.716091 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.84720 | 0.460824 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7329 | 0.840666 | 0.420333 | − | 0.907370i | \(-0.361913\pi\) | ||||
0.420333 | + | 0.907370i | \(0.361913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.262360 | 0.0204247 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.902422 | −0.0698315 | −0.0349158 | − | 0.999390i | \(-0.511116\pi\) | ||||
−0.0349158 | + | 0.999390i | \(0.511116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.7742 | 1.59802 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.8449 | 1.05874 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.8342 | −1.43194 | −0.715970 | − | 0.698131i | \(-0.754015\pi\) | ||||
−0.715970 | + | 0.698131i | \(0.754015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2162 | 0.923458 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.12288 | −0.610553 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.62493 | −0.270940 | −0.135470 | − | 0.990781i | \(-0.543254\pi\) | ||||
−0.135470 | + | 0.990781i | \(0.543254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9275 | 0.960897 | 0.480449 | − | 0.877023i | \(-0.340474\pi\) | ||||
0.480449 | + | 0.877023i | \(0.340474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.4905 | −1.29294 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.13354 | −0.156861 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.591742 | 0.0432725 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.64544 | 0.483385 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.1631 | −1.31424 | −0.657118 | − | 0.753788i | \(-0.728225\pi\) | ||||
−0.657118 | + | 0.753788i | \(0.728225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.01737 | −0.433140 | −0.216570 | − | 0.976267i | \(-0.569487\pi\) | ||||
−0.216570 | + | 0.976267i | \(0.569487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.81156 | −0.416175 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.69571 | −0.334555 | −0.167278 | − | 0.985910i | \(-0.553498\pi\) | ||||
−0.167278 | + | 0.985910i | \(0.553498\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.3162 | −1.44018 | −0.720088 | − | 0.693882i | \(-0.755899\pi\) | ||||
−0.720088 | + | 0.693882i | \(0.755899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.35895 | −0.589595 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.5799 | 1.37424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.18154 | −0.222208 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.15525 | −0.288810 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00509 | 0.138695 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.99017 | 0.481223 | 0.240612 | − | 0.970621i | \(-0.422652\pi\) | ||||
0.240612 | + | 0.970621i | \(0.422652\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.9738 | 1.57414 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.41214 | 0.300906 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.0131 | 1.15492 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.0866 | 1.28975 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.1078 | −0.881723 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.89566 | 0.193908 | 0.0969538 | − | 0.995289i | \(-0.469090\pi\) | ||||
0.0969538 | + | 0.995289i | \(0.469090\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.68130 | −0.578754 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.83372 | 0.453570 | 0.226785 | − | 0.973945i | \(-0.427179\pi\) | ||||
0.226785 | + | 0.973945i | \(0.427179\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2121 | 1.40173 | 0.700867 | − | 0.713292i | \(-0.252797\pi\) | ||||
0.700867 | + | 0.713292i | \(0.252797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.46705 | −0.0965247 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.0079 | 1.96588 | 0.982941 | − | 0.183920i | \(-0.0588788\pi\) | ||||
0.982941 | + | 0.183920i | \(0.0588788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.150986 | −0.00984925 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.6253 | 1.14489 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.6721 | −0.690320 | −0.345160 | − | 0.938544i | \(-0.612175\pi\) | ||||
−0.345160 | + | 0.938544i | \(0.612175\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7527 | −0.757057 | −0.378529 | − | 0.925590i | \(-0.623570\pi\) | ||||
−0.378529 | + | 0.925590i | \(0.623570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.6436 | −1.06769 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.228660 | −0.0146086 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −44.4149 | −2.82606 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.9111 | −0.881579 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.601785 | −0.0378339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.25546 | 0.141242 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.9181 | −1.11770 | −0.558851 | − | 0.829268i | \(-0.688757\pi\) | ||||
−0.558851 | + | 0.829268i | \(0.688757\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9302 | 0.741305 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.9142 | −0.861269 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.8907 | 0.918200 | 0.459100 | − | 0.888385i | \(-0.348172\pi\) | ||||
0.459100 | + | 0.888385i | \(0.348172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.87664 | 0.115281 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.4948 | −0.948267 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.40922 | 0.0859214 | 0.0429607 | − | 0.999077i | \(-0.486321\pi\) | ||||
0.0429607 | + | 0.999077i | \(0.486321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.918888 | −0.0558185 | −0.0279092 | − | 0.999610i | \(-0.508885\pi\) | ||||
−0.0279092 | + | 0.999610i | \(0.508885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 32.4968 | 1.96679 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.25727 | −0.0758163 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4782 | 1.35058 | 0.675292 | − | 0.737551i | \(-0.264018\pi\) | ||||
0.675292 | + | 0.737551i | \(0.264018\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.0902 | −0.723820 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.3905 | −1.09709 | −0.548544 | − | 0.836122i | \(-0.684818\pi\) | ||||
−0.548544 | + | 0.836122i | \(0.684818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1472 | 0.781517 | 0.390758 | − | 0.920493i | \(-0.372213\pi\) | ||||
0.390758 | + | 0.920493i | \(0.372213\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.64252 | 0.452704 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.7904 | 1.05013 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9129 | −0.700758 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.53114 | 0.206999 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.5099 | −1.25662 | −0.628312 | − | 0.777961i | \(-0.716254\pi\) | ||||
−0.628312 | + | 0.777961i | \(0.716254\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.68820 | −0.0982909 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.683938 | −0.0396861 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.3302 | 0.770906 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.6716 | −1.42205 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.7923 | 2.17111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.63511 | −0.208146 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.66639 | −0.323398 | −0.161699 | − | 0.986840i | \(-0.551697\pi\) | ||||
−0.161699 | + | 0.986840i | \(0.551697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.11646 | −0.461729 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.3965 | 1.49681 | 0.748405 | − | 0.663242i | \(-0.230820\pi\) | ||||
0.748405 | + | 0.663242i | \(0.230820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.4172 | −0.871434 | −0.435717 | − | 0.900084i | \(-0.643505\pi\) | ||||
−0.435717 | + | 0.900084i | \(0.643505\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.10530 | −0.118620 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.2318 | −1.08017 | −0.540084 | − | 0.841611i | \(-0.681607\pi\) | ||||
−0.540084 | + | 0.841611i | \(0.681607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.01513 | −0.112826 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7997 | −1.04930 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.2374 | 0.959115 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.8500 | 1.54484 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.5765 | −1.63558 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.844276 | 0.0465464 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.61743 | 0.418692 | 0.209346 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209346 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.47805 | −0.464594 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.73726 | −0.0949169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.32541 | 0.126673 | 0.0633367 | − | 0.997992i | \(-0.479826\pi\) | ||||
0.0633367 | + | 0.997992i | \(0.479826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0113 | −0.978239 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.75096 | −0.0948199 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1230 | 1.03255 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.29374 | −0.123491 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.7701 | −0.846585 | −0.423293 | − | 0.905993i | \(-0.639126\pi\) | ||||
−0.423293 | + | 0.905993i | \(0.639126\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.5020 | −1.68626 | −0.843132 | − | 0.537706i | \(-0.819291\pi\) | ||||
−0.843132 | + | 0.537706i | \(0.819291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.1500 | 0.808647 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 37.4767 | 1.99468 | 0.997341 | − | 0.0728782i | \(-0.0232184\pi\) | ||||
0.997341 | + | 0.0728782i | \(0.0232184\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.77472 | 0.253416 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.6120 | −0.667496 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.9690 | 1.21226 | 0.606128 | − | 0.795367i | \(-0.292722\pi\) | ||||
0.606128 | + | 0.795367i | \(0.292722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.4081 | 2.07411 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.9778 | −1.25851 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.96681 | 0.207632 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.9369 | 0.988499 | 0.494250 | − | 0.869320i | \(-0.335443\pi\) | ||||
0.494250 | + | 0.869320i | \(0.335443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6425 | −0.658143 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4937 | −0.544805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.83341 | 0.302042 | 0.151021 | − | 0.988531i | \(-0.451744\pi\) | ||||
0.151021 | + | 0.988531i | \(0.451744\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.79217 | −0.505665 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44.6374 | 2.29894 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.7528 | −1.57967 | −0.789833 | − | 0.613322i | \(-0.789833\pi\) | ||||
−0.789833 | + | 0.613322i | \(0.789833\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.2801 | −1.29514 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.9560 | −0.559824 | −0.279912 | − | 0.960026i | \(-0.590305\pi\) | ||||
−0.279912 | + | 0.960026i | \(0.590305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.304901 | −0.0155392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.5326 | 0.891231 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.331033 | 0.0167840 | 0.00839201 | − | 0.999965i | \(-0.497329\pi\) | ||||
0.00839201 | + | 0.999965i | \(0.497329\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.17344 | −0.261632 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.5004 | −0.933220 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.66311 | 0.184311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3473 | 0.870635 | 0.435318 | − | 0.900277i | \(-0.356636\pi\) | ||||
0.435318 | + | 0.900277i | \(0.356636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −42.7350 | −2.13942 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.14177 | −0.106955 | −0.0534774 | − | 0.998569i | \(-0.517031\pi\) | ||||
−0.0534774 | + | 0.998569i | \(0.517031\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.7858 | 1.93206 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.08447 | −0.252650 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.22784 | −0.0608615 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.4823 | −1.06223 | −0.531117 | − | 0.847299i | \(-0.678227\pi\) | ||||
−0.531117 | + | 0.847299i | \(0.678227\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.7849 | −1.41986 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.43999 | 0.464511 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.89118 | −0.141922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.11646 | 0.348495 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.5083 | 0.562217 | 0.281108 | − | 0.959676i | \(-0.409298\pi\) | ||||
0.281108 | + | 0.959676i | \(0.409298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1653 | −0.739111 | −0.369556 | − | 0.929209i | \(-0.620490\pi\) | ||||
−0.369556 | + | 0.929209i | \(0.620490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.599975 | −0.0291718 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8086 | −0.524292 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.3266 | 0.983673 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.34451 | −0.161475 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.0776 | −1.49696 | −0.748478 | − | 0.663159i | \(-0.769215\pi\) | ||||
−0.748478 | + | 0.663159i | \(0.769215\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.4376 | 1.79914 | 0.899568 | − | 0.436781i | \(-0.143882\pi\) | ||||
0.899568 | + | 0.436781i | \(0.143882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.68079 | −0.368266 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.5299 | −0.838571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.32227 | 0.206291 | 0.103145 | − | 0.994666i | \(-0.467109\pi\) | ||||
0.103145 | + | 0.994666i | \(0.467109\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.908629 | −0.0432680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.6334 | 1.78802 | 0.894008 | − | 0.448050i | \(-0.147881\pi\) | ||||
0.894008 | + | 0.448050i | \(0.147881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.22033 | −0.152658 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 43.1787 | 2.04228 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.7504 | 1.45120 | 0.725600 | − | 0.688117i | \(-0.241562\pi\) | ||||
0.725600 | + | 0.688117i | \(0.241562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.83095 | −0.0862163 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.1957 | 0.573003 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.75389 | 0.316627 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.13474 | 0.286971 | 0.143485 | − | 0.989652i | \(-0.454169\pi\) | ||||
0.143485 | + | 0.989652i | \(0.454169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.87970 | −0.274441 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.48434 | −0.441730 | −0.220865 | − | 0.975304i | \(-0.570888\pi\) | ||||
−0.220865 | + | 0.975304i | \(0.570888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.49963 | −0.0696937 | −0.0348468 | − | 0.999393i | \(-0.511094\pi\) | ||||
−0.0348468 | + | 0.999393i | \(0.511094\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.67390 | −0.309495 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.6702 | 1.00278 | 0.501389 | − | 0.865222i | \(-0.332823\pi\) | ||||
0.501389 | + | 0.865222i | \(0.332823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.71433 | 0.448566 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.2615 | 2.03946 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.53916 | 0.116751 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.6242 | −1.68043 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.45722 | 0.341443 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.96540 | −0.226875 | −0.113437 | − | 0.993545i | \(-0.536186\pi\) | ||||
−0.113437 | + | 0.993545i | \(0.536186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.1979 | 1.24012 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.8260 | 0.583603 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.733887 | 0.0333241 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.1715 | 1.50314 | 0.751571 | − | 0.659652i | \(-0.229296\pi\) | ||||
0.751571 | + | 0.659652i | \(0.229296\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.5429 | 1.06465 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.8677 | −1.30278 | −0.651390 | − | 0.758743i | \(-0.725814\pi\) | ||||
−0.651390 | + | 0.758743i | \(0.725814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.3237 | −0.780222 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.216674 | 0.00973878 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.6990 | −1.19761 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.8314 | 1.91740 | 0.958699 | − | 0.284422i | \(-0.0918016\pi\) | ||||
0.958699 | + | 0.284422i | \(0.0918016\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.97949 | −0.0884370 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.6267 | −0.785935 | −0.392968 | − | 0.919552i | \(-0.628552\pi\) | ||||
−0.392968 | + | 0.919552i | \(0.628552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.85448 | 0.349520 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 45.5689 | 2.02378 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.4363 | 1.30474 | 0.652371 | − | 0.757900i | \(-0.273775\pi\) | ||||
0.652371 | + | 0.757900i | \(0.273775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.1814 | −0.981247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.9231 | −0.879625 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.68687 | −0.0743322 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0868915 | −0.00382148 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −41.3134 | −1.81346 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.8139 | 1.78809 | 0.894045 | − | 0.447976i | \(-0.147855\pi\) | ||||
0.894045 | + | 0.447976i | \(0.147855\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.92026 | −0.127694 | −0.0638471 | − | 0.997960i | \(-0.520337\pi\) | ||||
−0.0638471 | + | 0.997960i | \(0.520337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.7966 | 1.16950 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0527 | −0.655707 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7388 | −0.771250 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.70842 | −0.291121 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.5577 | 1.75675 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.90720 | −0.168923 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.95139 | −0.343128 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.131592 | −0.00566808 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4385 | −1.22267 | −0.611333 | − | 0.791373i | \(-0.709366\pi\) | ||||
−0.611333 | + | 0.791373i | \(0.709366\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.3569 | 1.21691 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.14696 | −0.263307 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.23749 | −0.0529111 | −0.0264555 | − | 0.999650i | \(-0.508422\pi\) | ||||
−0.0264555 | + | 0.999650i | \(0.508422\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.4449 | −0.616492 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −58.7006 | −2.50073 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.4832 | −0.871033 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.67997 | −0.198654 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.1991 | 1.23721 | 0.618603 | − | 0.785704i | \(-0.287699\pi\) | ||||
0.618603 | + | 0.785704i | \(0.287699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.2452 | −2.37892 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29800 | 0.0548017 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.13098 | 0.0898103 | 0.0449051 | − | 0.998991i | \(-0.485701\pi\) | ||||
0.0449051 | + | 0.998991i | \(0.485701\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.74334 | −0.157483 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.4311 | 1.19399 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.35256 | −0.392080 | −0.196040 | − | 0.980596i | \(-0.562808\pi\) | ||||
−0.196040 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.3673 | −1.14529 | −0.572644 | − | 0.819804i | \(-0.694082\pi\) | ||||
−0.572644 | + | 0.819804i | \(0.694082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.8413 | −1.66439 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.9920 | 0.458397 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.00690 | −0.208440 | −0.104220 | − | 0.994554i | \(-0.533235\pi\) | ||||
−0.104220 | + | 0.994554i | \(0.533235\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.1993 | −0.548542 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.1667 | 0.670709 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.07999 | 0.0447288 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.79958 | −0.198438 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.7558 | −1.51707 | −0.758537 | − | 0.651630i | \(-0.774086\pi\) | ||||
−0.758537 | + | 0.651630i | \(0.774086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.0054 | −2.10164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.3002 | −0.423692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5502 | 0.433244 | 0.216622 | − | 0.976256i | \(-0.430496\pi\) | ||||
0.216622 | + | 0.976256i | \(0.430496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.62118 | −0.107458 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −44.5641 | −1.82389 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.6049 | 1.78165 | 0.890823 | − | 0.454350i | \(-0.150129\pi\) | ||||
0.890823 | + | 0.454350i | \(0.150129\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.1345 | −1.35158 | −0.675792 | − | 0.737093i | \(-0.736198\pi\) | ||||
−0.675792 | + | 0.737093i | \(0.736198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.90338 | −0.281127 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.98337 | −0.202603 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.1597 | −1.06179 | −0.530896 | − | 0.847437i | \(-0.678144\pi\) | ||||
−0.530896 | + | 0.847437i | \(0.678144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 42.9490 | 1.74038 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.92474 | 0.0778668 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.7113 | −0.432624 | −0.216312 | − | 0.976324i | \(-0.569403\pi\) | ||||
−0.216312 | + | 0.976324i | \(0.569403\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.97880 | −0.281412 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.2739 | 1.17852 | 0.589261 | − | 0.807943i | \(-0.299419\pi\) | ||||
0.589261 | + | 0.807943i | \(0.299419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3879 | −0.819457 | −0.409729 | − | 0.912207i | \(-0.634377\pi\) | ||||
−0.409729 | + | 0.912207i | \(0.634377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.97949 | 0.239949 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.0072 | 0.721445 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9257 | 0.877028 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.39822 | 0.175648 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.5555 | −0.420875 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.9356 | 0.913050 | 0.456525 | − | 0.889710i | \(-0.349094\pi\) | ||||
0.456525 | + | 0.889710i | \(0.349094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.3331 | 0.609437 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.25403 | −0.208500 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.91492 | 0.115493 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.9733 | 0.750573 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.48994 | −0.256337 | −0.128169 | − | 0.991752i | \(-0.540910\pi\) | ||||
−0.128169 | + | 0.991752i | \(0.540910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.9651 | −1.61550 | −0.807752 | − | 0.589522i | \(-0.799316\pi\) | ||||
−0.807752 | + | 0.589522i | \(0.799316\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.67816 | 0.381077 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5401 | 0.768202 | 0.384101 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384101 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.971548 | −0.0381366 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 37.3187 | 1.46264 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.6102 | −1.00220 | −0.501102 | − | 0.865388i | \(-0.667072\pi\) | ||||
−0.501102 | + | 0.865388i | \(0.667072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.84498 | −0.150236 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7629 | 0.614971 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.8852 | −0.930436 | −0.465218 | − | 0.885196i | \(-0.654024\pi\) | ||||
−0.465218 | + | 0.885196i | \(0.654024\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.9682 | −0.659987 | −0.329993 | − | 0.943983i | \(-0.607047\pi\) | ||||
−0.329993 | + | 0.943983i | \(0.607047\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.7522 | −1.11664 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.88173 | −0.344419 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.6177 | 0.682162 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.35170 | 0.245571 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.09198 | −0.0807600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.7852 | −1.14813 | −0.574067 | − | 0.818808i | \(-0.694635\pi\) | ||||
−0.574067 | + | 0.818808i | \(0.694635\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.4926 | 0.480839 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.3504 | −1.20489 | −0.602447 | − | 0.798159i | \(-0.705808\pi\) | ||||
−0.602447 | + | 0.798159i | \(0.705808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.10371 | −0.157486 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.9900 | 0.574416 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.52663 | 0.173207 | 0.0866033 | − | 0.996243i | \(-0.472399\pi\) | ||||
0.0866033 | + | 0.996243i | \(0.472399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.98245 | −0.228578 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.5293 | 1.77520 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.9231 | −0.911396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.9329 | −1.21478 | −0.607392 | − | 0.794402i | \(-0.707784\pi\) | ||||
−0.607392 | + | 0.794402i | \(0.707784\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.21159 | −0.0460243 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.47903 | 0.0561030 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7404 | −0.596210 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 65.8231 | 2.48966 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9368 | −0.941849 | −0.470924 | − | 0.882174i | \(-0.656080\pi\) | ||||
−0.470924 | + | 0.882174i | \(0.656080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.7667 | −1.34897 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.331192 | −0.0124734 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.9202 | −1.65179 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.35240 | −0.276125 | −0.138063 | − | 0.990424i | \(-0.544087\pi\) | ||||
−0.138063 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.5561 | 0.545898 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.3082 | 0.573296 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.695099 | −0.0259952 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.4095 | −0.874244 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.4992 | 1.65954 | 0.829771 | − | 0.558105i | \(-0.188471\pi\) | ||||
0.829771 | + | 0.558105i | \(0.188471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.43252 | 0.351286 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.7798 | −0.958763 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 36.8076 | 1.36700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.68657 | 0.210903 | 0.105452 | − | 0.994424i | \(-0.466371\pi\) | ||||
0.105452 | + | 0.994424i | \(0.466371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.04947 | −0.112943 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8287 | 0.807364 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2952 | −1.26672 | −0.633361 | − | 0.773856i | \(-0.718325\pi\) | ||||
−0.633361 | + | 0.773856i | \(0.718325\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.501572 | −0.0185008 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.999784 | −0.0368275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56934 | 0.204871 | 0.102436 | − | 0.994740i | \(-0.467336\pi\) | ||||
0.102436 | + | 0.994740i | \(0.467336\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −97.4254 | −3.57901 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.0644 | 0.699407 | 0.349703 | − | 0.936860i | \(-0.386282\pi\) | ||||
0.349703 | + | 0.936860i | \(0.386282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.97394 | 0.328780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.4887 | −0.420350 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.8480 | 0.798310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.6818 | 1.52099 | 0.760496 | − | 0.649343i | \(-0.224956\pi\) | ||||
0.760496 | + | 0.649343i | \(0.224956\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.19353 | 0.0799366 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.53466 | 0.0922458 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −54.3880 | −1.97677 | −0.988383 | − | 0.151984i | \(-0.951434\pi\) | ||||
−0.988383 | + | 0.151984i | \(0.951434\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.32003 | −0.0479141 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.55028 | 0.128698 | 0.0643489 | − | 0.997927i | \(-0.479503\pi\) | ||||
0.0643489 | + | 0.997927i | \(0.479503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.3722 | 1.24436 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.86271 | 0.0673465 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.5209 | 0.777074 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.3633 | −1.16705 | −0.583526 | − | 0.812094i | \(-0.698327\pi\) | ||||
−0.583526 | + | 0.812094i | \(0.698327\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.3039 | −1.41549 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.4219 | 0.770492 | 0.385246 | − | 0.922814i | \(-0.374117\pi\) | ||||
0.385246 | + | 0.922814i | \(0.374117\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.9824 | 1.14884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.1692 | 0.938814 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.3356 | −1.91094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.74782 | 0.0983246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.0229 | 0.715558 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.19899 | 0.328326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0246158 | −0.000877457 0 | −0.000438729 | − | 1.00000i | \(-0.500140\pi\) | ||||
−0.000438729 | 1.00000i | \(0.500140\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.6632 | 1.16284 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.9318 | 0.744248 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.3397 | 1.64557 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.11646 | 0.145996 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.27168 | −0.0450451 | −0.0225225 | − | 0.999746i | \(-0.507170\pi\) | ||||
−0.0225225 | + | 0.999746i | \(0.507170\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.746992 | −0.0264267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7966 | −0.452147 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.28287 | 0.0805608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.66566 | 0.0939523 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.09115 | 0.108814 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.4312 | −0.542533 | −0.271266 | − | 0.962504i | \(-0.587442\pi\) | ||||
−0.271266 | + | 0.962504i | \(0.587442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.0794 | 1.33715 | 0.668575 | − | 0.743645i | \(-0.266905\pi\) | ||||
0.668575 | + | 0.743645i | \(0.266905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.01561 | −0.0706904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.89299 | 0.171394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 73.9655 | 2.58772 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 26.8380 | 0.937795 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9233 | 1.07923 | 0.539615 | − | 0.841912i | \(-0.318570\pi\) | ||||
0.539615 | + | 0.841912i | \(0.318570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.9040 | −1.32125 | −0.660626 | − | 0.750716i | \(-0.729709\pi\) | ||||
−0.660626 | + | 0.750716i | \(0.729709\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.75786 | −0.0960163 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.6417 | 1.72621 | 0.863106 | − | 0.505022i | \(-0.168516\pi\) | ||||
0.863106 | + | 0.505022i | \(0.168516\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.8020 | −1.34765 | −0.673825 | − | 0.738891i | \(-0.735350\pi\) | ||||
−0.673825 | + | 0.738891i | \(0.735350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49.3065 | 1.71042 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.13128 | −0.0391964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.411402 | −0.0142372 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.3980 | 0.601363 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.6653 | −1.43845 | −0.719223 | − | 0.694780i | \(-0.755502\pi\) | ||||
−0.719223 | + | 0.694780i | \(0.755502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.9946 | 1.03430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.3402 | −1.38939 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.47070 | 0.325802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.8657 | 0.957478 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.8386 | 0.989739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.7346 | 0.367978 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6962 | 0.982540 | 0.491270 | − | 0.871007i | \(-0.336533\pi\) | ||||
0.491270 | + | 0.871007i | \(0.336533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.31170 | 0.215856 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.3022 | 0.693510 | 0.346755 | − | 0.937956i | \(-0.387284\pi\) | ||||
0.346755 | + | 0.937956i | \(0.387284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7410 | 0.434717 | 0.217359 | − | 0.976092i | \(-0.430256\pi\) | ||||
0.217359 | + | 0.976092i | \(0.430256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.0236 | 1.32992 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.4251 | −1.34204 | −0.671022 | − | 0.741437i | \(-0.734145\pi\) | ||||
−0.671022 | + | 0.741437i | \(0.734145\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.58628 | −0.291942 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.1313 | −0.887464 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.10810 | 0.0715122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.1463 | 0.750400 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.91625 | 0.0987002 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3799 | 0.384712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3896 | 0.620974 | 0.310487 | − | 0.950578i | \(-0.399508\pi\) | ||||
0.310487 | + | 0.950578i | \(0.399508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −47.1826 | −1.59143 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.24414 | −0.277752 | −0.138876 | − | 0.990310i | \(-0.544349\pi\) | ||||
−0.138876 | + | 0.990310i | \(0.544349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.3808 | −0.652217 | −0.326109 | − | 0.945332i | \(-0.605738\pi\) | ||||
−0.326109 | + | 0.945332i | \(0.605738\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.70312 | −0.124479 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.71734 | 0.326276 | 0.163138 | − | 0.986603i | \(-0.447838\pi\) | ||||
0.163138 | + | 0.986603i | \(0.447838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.3792 | 0.985346 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.92608 | −0.0980273 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.53114 | −0.0847015 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.65256 | −0.0552389 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.2402 | 0.976301 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.2608 | 1.70964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.28452 | 0.309312 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −54.1178 | −1.80093 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.89350 | 0.195907 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1518 | 0.403492 | 0.201746 | − | 0.979438i | \(-0.435338\pi\) | ||||
0.201746 | + | 0.979438i | \(0.435338\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.2114 | 1.03522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.0279 | 0.862343 | 0.431172 | − | 0.902270i | \(-0.358100\pi\) | ||||
0.431172 | + | 0.902270i | \(0.358100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.66385 | −0.0550655 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.97371 | −0.263603 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.5002 | 0.709998 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.54348 | 0.248836 | 0.124418 | − | 0.992230i | \(-0.460294\pi\) | ||||
0.124418 | + | 0.992230i | \(0.460294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.4294 | −0.409562 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.8672 | −2.00347 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4272 | 0.737402 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.70312 | −0.220159 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.9637 | 1.93454 | 0.967268 | − | 0.253758i | \(-0.0816667\pi\) | ||||
0.967268 | + | 0.253758i | \(0.0816667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.83327 | −0.125630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 57.9015 | 1.89561 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.269767 | 0.00882234 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.7067 | −0.349774 | −0.174887 | − | 0.984589i | \(-0.555956\pi\) | ||||
−0.174887 | + | 0.984589i | \(0.555956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33.8181 | −1.10361 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.4127 | 0.502439 | 0.251220 | − | 0.967930i | \(-0.419168\pi\) | ||||
0.251220 | + | 0.967930i | \(0.419168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0075 | 0.521277 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.02957 | 0.0985519 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.5351 | 0.797285 | 0.398643 | − | 0.917106i | \(-0.369481\pi\) | ||||
0.398643 | + | 0.917106i | \(0.369481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.5682 | −1.64151 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −42.1856 | −1.36796 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.3819 | −0.789807 | −0.394903 | − | 0.918723i | \(-0.629222\pi\) | ||||
−0.394903 | + | 0.918723i | \(0.629222\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.28032 | −0.267945 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.42024 | −0.142886 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.4523 | 1.08023 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5409 | 0.436803 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5261 | −0.500320 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.74324 | −0.0883080 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.8858 | 1.21832 | 0.609162 | − | 0.793046i | \(-0.291506\pi\) | ||||
0.609162 | + | 0.793046i | \(0.291506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.8107 | 1.21466 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.04262 | −0.290192 | −0.145096 | − | 0.989418i | \(-0.546349\pi\) | ||||
−0.145096 | + | 0.989418i | \(0.546349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.27038 | −0.265136 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 61.0897 | 1.95644 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.3756 | 0.523902 | 0.261951 | − | 0.965081i | \(-0.415634\pi\) | ||||
0.261951 | + | 0.965081i | \(0.415634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.85328 | −0.0592310 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.4262 | −0.779869 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.6092 | 0.753018 | 0.376509 | − | 0.926413i | \(-0.377124\pi\) | ||||
0.376509 | + | 0.926413i | \(0.377124\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.14071 | −0.0682087 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.85194 | 0.0589480 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.1992 | −0.705893 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.1253 | −1.62405 | −0.812024 | − | 0.583625i | \(-0.801634\pi\) | ||||
−0.812024 | + | 0.583625i | \(0.801634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.7090 | 0.530245 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.26188 | −0.293621 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0524 | −0.951768 | −0.475884 | − | 0.879508i | \(-0.657872\pi\) | ||||
−0.475884 | + | 0.879508i | \(0.657872\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.2001 | 0.385994 |
(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 | 4016.2.a.c.1.4 | 4 | ||
4.3 | odd | 2 | 251.2.a.a.1.1 | ✓ | 4 | ||
12.11 | even | 2 | 2259.2.a.f.1.3 | 4 | |||
20.19 | odd | 2 | 6275.2.a.c.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
251.2.a.a.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
2259.2.a.f.1.3 | 4 | 12.11 | even | 2 | |||
4016.2.a.c.1.4 | 4 | 1.1 | even | 1 | trivial | ||
6275.2.a.c.1.4 | 4 | 20.19 | odd | 2 |