Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.94547 | −1.12322 | −0.561608 | − | 0.827404i | \(-0.689817\pi\) | ||||
−0.561608 | + | 0.827404i | \(0.689817\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.68966 | −0.755639 | −0.377820 | − | 0.925879i | \(-0.623326\pi\) | ||||
−0.377820 | + | 0.925879i | \(0.623326\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.54452 | −0.583773 | −0.291886 | − | 0.956453i | \(-0.594283\pi\) | ||||
−0.291886 | + | 0.956453i | \(0.594283\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.784840 | 0.261613 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.23286 | −0.673232 | −0.336616 | − | 0.941642i | \(-0.609282\pi\) | ||||
−0.336616 | + | 0.941642i | \(0.609282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.94704 | −0.540012 | −0.270006 | − | 0.962859i | \(-0.587026\pi\) | ||||
−0.270006 | + | 0.962859i | \(0.587026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.28718 | 0.848746 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.28556 | −0.554331 | −0.277165 | − | 0.960822i | \(-0.589395\pi\) | ||||
−0.277165 | + | 0.960822i | \(0.589395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00481 | 0.655702 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.628320 | 0.131014 | 0.0655069 | − | 0.997852i | \(-0.479134\pi\) | ||||
0.0655069 | + | 0.997852i | \(0.479134\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.14505 | −0.429009 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.30952 | 0.829367 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.85349 | 1.82975 | 0.914874 | − | 0.403740i | \(-0.132290\pi\) | ||||
0.914874 | + | 0.403740i | \(0.132290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.81551 | 1.58331 | 0.791656 | − | 0.610967i | \(-0.209219\pi\) | ||||
0.791656 | + | 0.610967i | \(0.209219\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.34395 | 0.756185 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.60971 | 0.441122 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.52622 | −0.415309 | −0.207654 | − | 0.978202i | \(-0.566583\pi\) | ||||
−0.207654 | + | 0.978202i | \(0.566583\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.78791 | 0.606550 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82145 | 1.37768 | 0.688840 | − | 0.724914i | \(-0.258120\pi\) | ||||
0.688840 | + | 0.724914i | \(0.258120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.39479 | −0.365203 | −0.182601 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182601 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32611 | −0.197685 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22440 | −0.178597 | −0.0892986 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0892986 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.61447 | −0.659210 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.44649 | 0.622633 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.98586 | 0.822221 | 0.411111 | − | 0.911585i | \(-0.365141\pi\) | ||||
0.411111 | + | 0.911585i | \(0.365141\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.77277 | 0.508721 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.94547 | −0.257683 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.90536 | −1.15938 | −0.579690 | − | 0.814837i | \(-0.696826\pi\) | ||||
−0.579690 | + | 0.814837i | \(0.696826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.227978 | −0.0291896 | −0.0145948 | − | 0.999893i | \(-0.504646\pi\) | ||||
−0.0145948 | + | 0.999893i | \(0.504646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.21220 | −0.152723 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.28984 | 0.408055 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6449 | 1.30048 | 0.650239 | − | 0.759729i | \(-0.274669\pi\) | ||||
0.650239 | + | 0.759729i | \(0.274669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.22238 | −0.147157 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5083 | −1.36579 | −0.682894 | − | 0.730517i | \(-0.739279\pi\) | ||||
−0.682894 | + | 0.730517i | \(0.739279\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5499 | 1.23477 | 0.617384 | − | 0.786662i | \(-0.288192\pi\) | ||||
0.617384 | + | 0.786662i | \(0.288192\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.17311 | 0.481870 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.44869 | 0.393014 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7385 | −1.19317 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.1289 | 1.22155 | 0.610777 | − | 0.791802i | \(-0.290857\pi\) | ||||
0.610777 | + | 0.791802i | \(0.290857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.86183 | 0.418874 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.1696 | −2.05520 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.0896524 | 0.00950313 | 0.00475157 | − | 0.999989i | \(-0.498488\pi\) | ||||
0.00475157 | + | 0.999989i | \(0.498488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00724 | 0.315244 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.1503 | −1.77840 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.68966 | −0.173356 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.86913 | −0.697455 | −0.348727 | − | 0.937224i | \(-0.613386\pi\) | ||||
−0.348727 | + | 0.937224i | \(0.613386\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75244 | −0.176127 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.5738 | −1.94767 | −0.973834 | − | 0.227261i | \(-0.927023\pi\) | ||||
−0.973834 | + | 0.227261i | \(0.927023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.97112 | −0.292753 | −0.146377 | − | 0.989229i | \(-0.546761\pi\) | ||||
−0.146377 | + | 0.989229i | \(0.546761\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.07710 | −0.495475 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.77671 | 0.461782 | 0.230891 | − | 0.972980i | \(-0.425836\pi\) | ||||
0.230891 | + | 0.972980i | \(0.425836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.04370 | 0.866230 | 0.433115 | − | 0.901339i | \(-0.357414\pi\) | ||||
0.433115 | + | 0.901339i | \(0.357414\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.91469 | 0.466481 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.42838 | 0.886947 | 0.443474 | − | 0.896287i | \(-0.353746\pi\) | ||||
0.443474 | + | 0.896287i | \(0.353746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.06165 | −0.0989992 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.52812 | −0.141274 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.53009 | 0.323603 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.01434 | −0.546759 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.1618 | −1.54743 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0727 | 1.07982 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2289 | 0.907667 | 0.453834 | − | 0.891086i | \(-0.350056\pi\) | ||||
0.453834 | + | 0.891086i | \(0.350056\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.65899 | 0.410201 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.42246 | −0.124281 | −0.0621406 | − | 0.998067i | \(-0.519793\pi\) | ||||
−0.0621406 | + | 0.998067i | \(0.519793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.54452 | −0.133927 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.28163 | −0.626703 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.43714 | −0.549962 | −0.274981 | − | 0.961450i | \(-0.588672\pi\) | ||||
−0.274981 | + | 0.961450i | \(0.588672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9811 | −1.60996 | −0.804978 | − | 0.593304i | \(-0.797823\pi\) | ||||
−0.804978 | + | 0.593304i | \(0.797823\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.38203 | 0.200603 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.34747 | 0.363554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.6491 | −1.38263 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.97729 | 0.740435 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.7653 | −1.53731 | −0.768657 | − | 0.639661i | \(-0.779075\pi\) | ||||
−0.768657 | + | 0.639661i | \(0.779075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.69858 | 0.138228 | 0.0691141 | − | 0.997609i | \(-0.477983\pi\) | ||||
0.0691141 | + | 0.997609i | \(0.477983\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.79380 | −0.145020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.8952 | −1.19641 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.35957 | −0.108506 | −0.0542529 | − | 0.998527i | \(-0.517278\pi\) | ||||
−0.0542529 | + | 0.998527i | \(0.517278\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6453 | −0.923532 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.970451 | −0.0764823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2339 | 0.801583 | 0.400791 | − | 0.916169i | \(-0.368735\pi\) | ||||
0.400791 | + | 0.916169i | \(0.368735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.33981 | −0.571403 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.7932 | 1.84117 | 0.920587 | − | 0.390538i | \(-0.127711\pi\) | ||||
0.920587 | + | 0.390538i | \(0.127711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.20903 | −0.708387 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.784840 | 0.0600182 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.59167 | 0.349098 | 0.174549 | − | 0.984648i | \(-0.444153\pi\) | ||||
0.174549 | + | 0.984648i | \(0.444153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.31306 | 0.250444 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.3251 | 1.30223 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.5661 | 1.38770 | 0.693849 | − | 0.720120i | \(-0.255913\pi\) | ||||
0.693849 | + | 0.720120i | \(0.255913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.19440 | −0.386096 | −0.193048 | − | 0.981189i | \(-0.561837\pi\) | ||||
−0.193048 | + | 0.981189i | \(0.561837\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.443524 | 0.0327863 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.26846 | 0.313824 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.10334 | 0.373193 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.65613 | −0.484162 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9035 | 1.22309 | 0.611546 | − | 0.791209i | \(-0.290548\pi\) | ||||
0.611546 | + | 0.791209i | \(0.290548\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.36408 | 0.674041 | 0.337021 | − | 0.941497i | \(-0.390581\pi\) | ||||
0.337021 | + | 0.941497i | \(0.390581\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.40028 | −0.458333 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.78091 | 0.411873 | 0.205936 | − | 0.978565i | \(-0.433976\pi\) | ||||
0.205936 | + | 0.978565i | \(0.433976\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.99799 | 0.637851 | 0.318925 | − | 0.947780i | \(-0.396678\pi\) | ||||
0.318925 | + | 0.947780i | \(0.396678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.7093 | −1.46072 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2189 | −1.06816 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.9053 | −1.04103 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.493131 | 0.0342750 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.23286 | −0.154450 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7868 | 0.880281 | 0.440141 | − | 0.897929i | \(-0.354929\pi\) | ||||
0.440141 | + | 0.897929i | \(0.354929\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.3891 | 1.53408 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.04639 | 0.275961 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.6157 | −0.924294 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.5244 | −1.38691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.45009 | 0.299345 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.2912 | 1.09094 | 0.545469 | − | 0.838131i | \(-0.316352\pi\) | ||||
0.545469 | + | 0.838131i | \(0.316352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.68352 | −0.112235 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.2508 | −1.01223 | −0.506116 | − | 0.862465i | \(-0.668919\pi\) | ||||
−0.506116 | + | 0.862465i | \(0.668919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.04728 | 0.399616 | 0.199808 | − | 0.979835i | \(-0.435968\pi\) | ||||
0.199808 | + | 0.979835i | \(0.435968\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.70931 | −0.441440 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.5034 | −1.67078 | −0.835390 | − | 0.549657i | \(-0.814758\pi\) | ||||
−0.835390 | + | 0.549657i | \(0.814758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.06882 | 0.134955 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.94547 | 0.126372 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.0987 | −1.75287 | −0.876435 | − | 0.481520i | \(-0.840085\pi\) | ||||
−0.876435 | + | 0.481520i | \(0.840085\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.2881 | −1.30687 | −0.653437 | − | 0.756981i | \(-0.726673\pi\) | ||||
−0.653437 | + | 0.756981i | \(0.726673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.96293 | 0.510822 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.79689 | 0.498125 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.94704 | −0.123887 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.6509 | −1.37207 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.6565 | −1.05135 | −0.525674 | − | 0.850686i | \(-0.676187\pi\) | ||||
−0.525674 | + | 0.850686i | \(0.676187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.40295 | −0.0882027 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.51306 | −0.470486 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5528 | −0.658264 | −0.329132 | − | 0.944284i | \(-0.606756\pi\) | ||||
−0.329132 | + | 0.944284i | \(0.606756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.90180 | 0.242446 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.73342 | 0.478687 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.7219 | −0.969453 | −0.484727 | − | 0.874666i | \(-0.661081\pi\) | ||||
−0.484727 | + | 0.874666i | \(0.661081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.1141 | −0.621303 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.174416 | −0.0106741 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.8377 | −0.965644 | −0.482822 | − | 0.875719i | \(-0.660388\pi\) | ||||
−0.482822 | + | 0.875719i | \(0.660388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.3871 | −1.17768 | −0.588841 | − | 0.808249i | \(-0.700416\pi\) | ||||
−0.588841 | + | 0.808249i | \(0.700416\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.85048 | −0.354087 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.78958 | 0.288823 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.1338 | −0.849219 | −0.424610 | − | 0.905377i | \(-0.639589\pi\) | ||||
−0.424610 | + | 0.905377i | \(0.639589\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.91877 | 0.414216 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.7341 | −1.89310 | −0.946549 | − | 0.322559i | \(-0.895457\pi\) | ||||
−0.946549 | + | 0.322559i | \(0.895457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.2319 | 1.26210 | 0.631052 | − | 0.775740i | \(-0.282623\pi\) | ||||
0.631052 | + | 0.775740i | \(0.282623\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.28718 | 0.194716 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.6249 | −0.804252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7762 | −0.692718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.3637 | 0.783392 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2583 | 0.657715 | 0.328857 | − | 0.944380i | \(-0.393336\pi\) | ||||
0.328857 | + | 0.944380i | \(0.393336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0470 | 0.876073 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.62255 | −0.558357 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.22337 | −0.0707491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.69880 | 0.213195 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.0802 | 2.18765 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.385206 | 0.0220568 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.3753 | 0.820442 | 0.410221 | − | 0.911986i | \(-0.365452\pi\) | ||||
0.410221 | + | 0.911986i | \(0.365452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.78021 | 0.328825 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5755 | 1.11002 | 0.555011 | − | 0.831843i | \(-0.312714\pi\) | ||||
0.555011 | + | 0.831843i | \(0.312714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0882 | −0.965883 | −0.482942 | − | 0.875652i | \(-0.660432\pi\) | ||||
−0.482942 | + | 0.875652i | \(0.660432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.04821 | 0.115403 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.37892 | −0.302110 | −0.151055 | − | 0.988525i | \(-0.548267\pi\) | ||||
−0.151055 | + | 0.988525i | \(0.548267\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.0015 | −1.23184 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.29293 | −0.518681 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.28556 | −0.127172 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.17649 | 0.231670 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.5942 | −0.972963 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.89111 | 0.104260 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.89404 | −0.378931 | −0.189465 | − | 0.981887i | \(-0.560675\pi\) | ||||
−0.189465 | + | 0.981887i | \(0.560675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.98268 | −0.108650 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.9862 | −0.982693 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8477 | 0.917751 | 0.458876 | − | 0.888500i | \(-0.348252\pi\) | ||||
0.458876 | + | 0.888500i | \(0.348252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.3426 | −0.996233 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.6838 | −1.06594 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9387 | 0.968601 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.06540 | 0.111197 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.878020 | −0.0471346 | −0.0235673 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235673 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5273 | 0.884685 | 0.442342 | − | 0.896846i | \(-0.354148\pi\) | ||||
0.442342 | + | 0.896846i | \(0.354148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.39082 | −0.447869 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.6844 | −0.888020 | −0.444010 | − | 0.896022i | \(-0.646444\pi\) | ||||
−0.444010 | + | 0.896022i | \(0.646444\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4452 | 1.03204 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.86768 | −0.363476 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3069 | −1.17732 | −0.588658 | − | 0.808382i | \(-0.700343\pi\) | ||||
−0.588658 | + | 0.808382i | \(0.700343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.7007 | 0.614128 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.8257 | −0.933040 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.87588 | −0.150120 | −0.0750598 | − | 0.997179i | \(-0.523915\pi\) | ||||
−0.0750598 | + | 0.997179i | \(0.523915\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.92343 | 0.360420 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.24526 | −0.479990 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.25843 | −0.375827 | −0.187914 | − | 0.982186i | \(-0.560172\pi\) | ||||
−0.187914 | + | 0.982186i | \(0.560172\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.4870 | −1.21287 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.1852 | −0.988086 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9269 | 0.664011 | 0.332005 | − | 0.943278i | \(-0.392275\pi\) | ||||
0.332005 | + | 0.943278i | \(0.392275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.9000 | −1.01951 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.3525 | −1.44874 | −0.724372 | − | 0.689409i | \(-0.757870\pi\) | ||||
−0.724372 | + | 0.689409i | \(0.757870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.82711 | −0.296977 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.87953 | −0.0955419 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.0792 | 1.22086 | 0.610431 | − | 0.792069i | \(-0.290996\pi\) | ||||
0.610431 | + | 0.792069i | \(0.290996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.43607 | −0.0726250 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.76735 | 0.139595 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.68966 | 0.0850161 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.21626 | −0.412362 | −0.206181 | − | 0.978514i | \(-0.566104\pi\) | ||||
−0.206181 | + | 0.978514i | \(0.566104\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.00481 | 0.150428 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.3379 | −0.666065 | −0.333032 | − | 0.942915i | \(-0.608072\pi\) | ||||
−0.333032 | + | 0.942915i | \(0.608072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1642 | −0.855008 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.1445 | 0.901608 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.64070 | 0.279599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.1978 | 1.09761 | 0.548805 | − | 0.835950i | \(-0.315083\pi\) | ||||
0.548805 | + | 0.835950i | \(0.315083\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.5232 | 0.617726 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.7545 | 0.676814 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.8041 | −0.923055 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.9271 | 1.80833 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.89237 | −0.190155 | −0.0950774 | − | 0.995470i | \(-0.530310\pi\) | ||||
−0.0950774 | + | 0.995470i | \(0.530310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.31264 | 0.0639741 | 0.0319870 | − | 0.999488i | \(-0.489816\pi\) | ||||
0.0319870 | + | 0.999488i | \(0.489816\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.960959 | −0.0467234 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.90264 | 0.237813 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.352116 | 0.0170401 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.45786 | −0.408349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.429092 | −0.0206686 | −0.0103343 | − | 0.999947i | \(-0.503290\pi\) | ||||
−0.0103343 | + | 0.999947i | \(0.503290\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.4872 | −1.03261 | −0.516303 | − | 0.856406i | \(-0.672692\pi\) | ||||
−0.516303 | + | 0.856406i | \(0.672692\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 32.3902 | 1.55299 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.628320 | 0.0300566 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.2766 | 1.25411 | 0.627057 | − | 0.778973i | \(-0.284259\pi\) | ||||
0.627057 | + | 0.778973i | \(0.284259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.62162 | −0.172458 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.58447 | 0.217815 | 0.108907 | − | 0.994052i | \(-0.465265\pi\) | ||||
0.108907 | + | 0.994052i | \(0.465265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.151482 | −0.00718094 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.5073 | 1.72673 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.8035 | −1.87844 | −0.939222 | − | 0.343310i | \(-0.888452\pi\) | ||||
−0.939222 | + | 0.343310i | \(0.888452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.6971 | −0.927498 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.30452 | −0.155260 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.08122 | −0.238211 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.2471 | −0.760006 | −0.380003 | − | 0.924985i | \(-0.624077\pi\) | ||||
−0.380003 | + | 0.924985i | \(0.624077\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.84968 | −0.459744 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.66095 | 0.263657 | 0.131828 | − | 0.991273i | \(-0.457915\pi\) | ||||
0.131828 | + | 0.991273i | \(0.457915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.9993 | −0.743550 | −0.371775 | − | 0.928323i | \(-0.621251\pi\) | ||||
−0.371775 | + | 0.928323i | \(0.621251\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.9782 | 1.34383 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.9373 | −1.80180 | −0.900902 | − | 0.434022i | \(-0.857094\pi\) | ||||
−0.900902 | + | 0.434022i | \(0.857094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4412 | −0.759184 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.64501 | 0.121875 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.34724 | 0.245866 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.14505 | −0.0984214 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.69795 | 0.215104 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.3865 | 0.977175 | 0.488588 | − | 0.872515i | \(-0.337512\pi\) | ||||
0.488588 | + | 0.872515i | \(0.337512\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.91867 | 0.224272 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.88798 | 0.0859061 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.6065 | 0.527024 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0325 | 0.681185 | 0.340593 | − | 0.940211i | \(-0.389372\pi\) | ||||
0.340593 | + | 0.940211i | \(0.389372\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.9098 | −0.900351 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.71053 | −0.212583 | −0.106292 | − | 0.994335i | \(-0.533898\pi\) | ||||
−0.106292 | + | 0.994335i | \(0.533898\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.5208 | −1.01429 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.96102 | 0.133088 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7748 | 0.797310 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.0601 | 1.74857 | 0.874286 | − | 0.485411i | \(-0.161330\pi\) | ||||
0.874286 | + | 0.485411i | \(0.161330\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −46.2889 | −2.06804 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.2588 | −0.769533 | −0.384766 | − | 0.923014i | \(-0.625718\pi\) | ||||
−0.384766 | + | 0.923014i | \(0.625718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.0731 | 1.47173 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.9159 | 0.795671 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.59053 | −0.114823 | −0.0574116 | − | 0.998351i | \(-0.518285\pi\) | ||||
−0.0574116 | + | 0.998351i | \(0.518285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.2945 | −0.720824 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.30952 | 0.190270 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.02018 | 0.221216 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.73391 | 0.120237 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.93293 | −0.392112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.33931 | 0.190109 | 0.0950543 | − | 0.995472i | \(-0.469698\pi\) | ||||
0.0950543 | + | 0.995472i | \(0.469698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.4972 | 1.94573 | 0.972863 | − | 0.231382i | \(-0.0743247\pi\) | ||||
0.972863 | + | 0.231382i | \(0.0743247\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.44545 | −0.281302 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.1484 | −0.877679 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6052 | −0.982835 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.98929 | −0.303309 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.1757 | −0.743964 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.07102 | −0.348941 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.1198 | −1.55868 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3035 | 0.443801 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.8530 | −1.58443 | −0.792217 | − | 0.610239i | \(-0.791073\pi\) | ||||
−0.792217 | + | 0.610239i | \(0.791073\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.1055 | 0.433670 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.2808 | −0.654557 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0232 | 0.813371 | 0.406686 | − | 0.913568i | \(-0.366684\pi\) | ||||
0.406686 | + | 0.913568i | \(0.366684\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.178927 | −0.00763640 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.85349 | 0.419773 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54452 | 0.0656795 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.30415 | −0.352492 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.76386 | 0.244223 | 0.122111 | − | 0.992516i | \(-0.461033\pi\) | ||||
0.122111 | + | 0.992516i | \(0.461033\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.66276 | 0.197214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.92838 | −0.419176 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.1413 | 0.469551 | 0.234776 | − | 0.972050i | \(-0.424564\pi\) | ||||
0.234776 | + | 0.972050i | \(0.424564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.9308 | −0.670212 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.5859 | 0.696541 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.34362 | −0.391705 | −0.195852 | − | 0.980633i | \(-0.562747\pi\) | ||||
−0.195852 | + | 0.980633i | \(0.562747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4434 | −1.02292 | −0.511462 | − | 0.859306i | \(-0.670896\pi\) | ||||
−0.511462 | + | 0.859306i | \(0.670896\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.8851 | −1.37380 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.34778 | −0.0562061 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.9054 | 1.32824 | 0.664119 | − | 0.747627i | \(-0.268807\pi\) | ||||
0.664119 | + | 0.747627i | \(0.268807\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.2175 | −0.757094 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.1888 | −0.713110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3656 | −0.553546 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.58200 | 0.106753 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.8863 | 0.696974 | 0.348487 | − | 0.937314i | \(-0.386696\pi\) | ||||
0.348487 | + | 0.937314i | \(0.386696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.81551 | 0.363237 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.2466 | −0.462622 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.6755 | 1.13650 | 0.568248 | − | 0.822857i | \(-0.307621\pi\) | ||||
0.568248 | + | 0.822857i | \(0.307621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.96466 | −0.244527 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.5053 | −0.716444 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.44481 | −0.181610 | −0.0908050 | − | 0.995869i | \(-0.528944\pi\) | ||||
−0.0908050 | + | 0.995869i | \(0.528944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4815 | −0.917039 | −0.458519 | − | 0.888684i | \(-0.651620\pi\) | ||||
−0.458519 | + | 0.888684i | \(0.651620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.35453 | 0.340223 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.1622 | 0.413152 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.9989 | −1.50174 | −0.750869 | − | 0.660451i | \(-0.770365\pi\) | ||||
−0.750869 | + | 0.660451i | \(0.770365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.6078 | 1.19977 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.38396 | 0.0964447 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.5150 | 1.67677 | 0.838387 | − | 0.545075i | \(-0.183499\pi\) | ||||
0.838387 | + | 0.545075i | \(0.183499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.9977 | 1.16930 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.1286 | 1.53500 | 0.767499 | − | 0.641050i | \(-0.221501\pi\) | ||||
0.767499 | + | 0.641050i | \(0.221501\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.5820 | −1.75171 | −0.875854 | − | 0.482575i | \(-0.839701\pi\) | ||||
−0.875854 | + | 0.482575i | \(0.839701\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.70776 | 0.108659 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.138470 | −0.00554767 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.67355 | −0.386942 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.34395 | 0.173481 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.77385 | 0.230218 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4660 | 0.655503 | 0.327751 | − | 0.944764i | \(-0.393709\pi\) | ||||
0.327751 | + | 0.944764i | \(0.393709\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.8763 | −0.988746 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.2834 | −0.685869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.98456 | 0.355981 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.03221 | −0.357309 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.2420 | −1.03650 | −0.518249 | − | 0.855230i | \(-0.673416\pi\) | ||||
−0.518249 | + | 0.855230i | \(0.673416\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.0795 | −0.910169 | −0.455084 | − | 0.890448i | \(-0.650391\pi\) | ||||
−0.455084 | + | 0.890448i | \(0.650391\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.87212 | −0.309964 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.9237 | 1.53025 | 0.765124 | − | 0.643883i | \(-0.222677\pi\) | ||||
0.765124 | + | 0.643883i | \(0.222677\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.8844 | 0.780531 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.4889 | 1.03818 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.3366 | −1.06976 | −0.534882 | − | 0.844927i | \(-0.679644\pi\) | ||||
−0.534882 | + | 0.844927i | \(0.679644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.40348 | 0.0939118 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.27996 | 0.323032 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0685 | −0.548031 | −0.274015 | − | 0.961725i | \(-0.588352\pi\) | ||||
−0.274015 | + | 0.961725i | \(0.588352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.0153979 | 0.000598911 0 | 0.000299455 | − | 1.00000i | \(-0.499905\pi\) | ||||
0.000299455 | 1.00000i | \(0.499905\pi\) | ||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.65750 | −0.336229 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.60971 | 0.101200 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.19115 | 0.239722 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31.6939 | −1.22536 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.509043 | 0.0196514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6003 | 0.485705 | 0.242853 | − | 0.970063i | \(-0.421917\pi\) | ||||
0.242853 | + | 0.970063i | \(0.421917\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.24412 | −0.355806 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.5166 | 1.78778 | 0.893890 | − | 0.448287i | \(-0.147966\pi\) | ||||
0.893890 | + | 0.448287i | \(0.147966\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.6095 | 0.407155 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.6699 | 1.13695 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.26070 | 0.0865034 | 0.0432517 | − | 0.999064i | \(-0.486228\pi\) | ||||
0.0432517 | + | 0.999064i | \(0.486228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8766 | 0.415573 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.7648 | −0.448855 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.6547 | −0.444010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.6231 | 1.81167 | 0.905834 | − | 0.423634i | \(-0.139246\pi\) | ||||
0.905834 | + | 0.423634i | \(0.139246\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.70667 | 0.102818 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.0716 | 1.21655 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.1620 | −0.763690 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 49.6159 | 1.87665 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.00884 | −0.113642 | −0.0568212 | − | 0.998384i | \(-0.518096\pi\) | ||||
−0.0568212 | + | 0.998384i | \(0.518096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.52622 | −0.0952784 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.02483 | −0.151584 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.2321 | 1.13700 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.3215 | 1.66453 | 0.832264 | − | 0.554380i | \(-0.187044\pi\) | ||||
0.832264 | + | 0.554380i | \(0.187044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.784840 | −0.0294338 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.53896 | 0.207436 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.34575 | −0.274715 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 52.7197 | 1.96885 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.7352 | −1.29541 | −0.647703 | − | 0.761893i | \(-0.724270\pi\) | ||||
−0.647703 | + | 0.761893i | \(0.724270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.58894 | 0.170901 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 39.4699 | 1.46790 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.1362 | −0.784978 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.8591 | −1.62665 | −0.813323 | − | 0.581813i | \(-0.802344\pi\) | ||||
−0.813323 | + | 0.581813i | \(0.802344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.7240 | 0.619409 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.47345 | 0.202443 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.9794 | −0.774890 | −0.387445 | − | 0.921893i | \(-0.626642\pi\) | ||||
−0.387445 | + | 0.921893i | \(0.626642\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.1686 | −0.559502 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.7685 | −0.875524 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.0946 | −0.408121 | −0.204060 | − | 0.978958i | \(-0.565414\pi\) | ||||
−0.204060 | + | 0.978958i | \(0.565414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.78791 | 0.139152 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.3365 | −1.77329 | −0.886646 | − | 0.462448i | \(-0.846971\pi\) | ||||
−0.886646 | + | 0.462448i | \(0.846971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.7070 | 1.16165 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.73440 | 0.319575 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.37771 | −0.269576 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.57879 | 0.203573 | 0.101786 | − | 0.994806i | \(-0.467544\pi\) | ||||
0.101786 | + | 0.994806i | \(0.467544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.4047 | 1.18089 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.87002 | −0.104451 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.6358 | −1.07713 | −0.538565 | − | 0.842584i | \(-0.681034\pi\) | ||||
−0.538565 | + | 0.842584i | \(0.681034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.72939 | 0.0990707 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.3976 | 0.884412 | 0.442206 | − | 0.896913i | \(-0.354196\pi\) | ||||
0.442206 | + | 0.896913i | \(0.354196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.9682 | −0.505681 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.03092 | 0.109583 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.3391 | 0.626079 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.1113 | −1.04978 | −0.524891 | − | 0.851170i | \(-0.675894\pi\) | ||||
−0.524891 | + | 0.851170i | \(0.675894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.5301 | 0.739372 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.6129 | −0.885266 | −0.442633 | − | 0.896703i | \(-0.645955\pi\) | ||||
−0.442633 | + | 0.896703i | \(0.645955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.9097 | −0.679256 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.59082 | −0.272319 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.82145 | 0.316061 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.6965 | 0.919493 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.4638 | 1.51753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.29722 | 0.0819913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.2216 | 0.827760 | 0.413880 | − | 0.910331i | \(-0.364173\pi\) | ||||
0.413880 | + | 0.910331i | \(0.364173\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.5864 | 1.08891 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.5623 | −0.517775 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.443883 | 0.0157628 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.6766 | 0.697857 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.1051 | −0.995535 | −0.497768 | − | 0.867310i | \(-0.665847\pi\) | ||||
−0.497768 | + | 0.867310i | \(0.665847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.79845 | 0.0990019 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.0703628 | 0.00248615 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.5564 | −0.831286 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.63973 | 0.0577930 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.8118 | 1.08463 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.22258 | −0.0781419 | −0.0390709 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390709 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.34496 | −0.187687 | −0.0938435 | − | 0.995587i | \(-0.529915\pi\) | ||||
−0.0938435 | + | 0.995587i | \(0.529915\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.7169 | 1.32279 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.2919 | −0.605708 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.39479 | −0.0837832 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.36020 | 0.0824722 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.49136 | −0.296351 | −0.148175 | − | 0.988961i | \(-0.547340\pi\) | ||||
−0.148175 | + | 0.988961i | \(0.547340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.2158 | −1.71555 | −0.857777 | − | 0.514022i | \(-0.828155\pi\) | ||||
−0.857777 | + | 0.514022i | \(0.828155\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.31797 | −0.324410 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5404 | 1.13154 | 0.565770 | − | 0.824563i | \(-0.308579\pi\) | ||||
0.565770 | + | 0.824563i | \(0.308579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.2391 | −0.390349 | −0.195175 | − | 0.980769i | \(-0.562527\pi\) | ||||
−0.195175 | + | 0.980769i | \(0.562527\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.4969 | 0.953856 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5467 | 0.365420 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.2025 | −1.39126 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.9906 | 1.31315 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.38218 | 0.220337 | 0.110169 | − | 0.993913i | \(-0.464861\pi\) | ||||
0.110169 | + | 0.993913i | \(0.464861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 68.0913 | 2.34798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 61.7377 | 2.12636 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.5601 | 0.535285 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.28926 | 0.319183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.3059 | −1.41762 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.58728 | −0.0544112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.2401 | 1.48051 | 0.740257 | − | 0.672324i | \(-0.234704\pi\) | ||||
0.740257 | + | 0.672324i | \(0.234704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.32611 | −0.0453521 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.2471 | 0.828264 | 0.414132 | − | 0.910217i | \(-0.364085\pi\) | ||||
0.414132 | + | 0.910217i | \(0.364085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.6247 | 1.24962 | 0.624809 | − | 0.780778i | \(-0.285177\pi\) | ||||
0.624809 | + | 0.780778i | \(0.285177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.5068 | 0.903348 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.93754 | −0.0999951 | −0.0499976 | − | 0.998749i | \(-0.515921\pi\) | ||||
−0.0499976 | + | 0.998749i | \(0.515921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.75836 | −0.263792 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.9102 | 0.778071 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.23286 | 0.0757445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.7260 | −0.702274 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.39117 | −0.182464 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.6465 | −0.630367 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.4490 | −1.80485 | −0.902423 | − | 0.430852i | \(-0.858213\pi\) | ||||
−0.902423 | + | 0.430852i | \(0.858213\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.9026 | −0.738755 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.6903 | −0.697074 | −0.348537 | − | 0.937295i | \(-0.613321\pi\) | ||||
−0.348537 | + | 0.937295i | \(0.613321\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.44494 | −0.317848 | −0.158924 | − | 0.987291i | \(-0.550802\pi\) | ||||
−0.158924 | + | 0.987291i | \(0.550802\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.2735 | −0.984018 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.7502 | −0.595993 | −0.297997 | − | 0.954567i | \(-0.596318\pi\) | ||||
−0.297997 | + | 0.954567i | \(0.596318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.7987 | −0.529871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.9777 | 0.803282 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.22440 | −0.0409730 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3705 | −1.04860 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.38002 | 0.0794665 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 86.8636 | 2.89706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.6811 | −0.455782 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.19589 | −0.239464 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.77677 | 0.291750 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.7606 | −1.25382 | −0.626911 | − | 0.779091i | \(-0.715681\pi\) | ||||
−0.626911 | + | 0.779091i | \(0.715681\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.3623 | −0.509536 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.5142 | 1.37543 | 0.687714 | − | 0.725982i | \(-0.258614\pi\) | ||||
0.687714 | + | 0.725982i | \(0.258614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.8492 | −0.822390 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.749406 | −0.0247746 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.19702 | 0.0725519 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3875 | 0.474598 | 0.237299 | − | 0.971437i | \(-0.423738\pi\) | ||||
0.237299 | + | 0.971437i | \(0.423738\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.9667 | −0.921533 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.4072 | 0.737543 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.41887 | 0.178171 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.33185 | −0.0765881 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.6503 | −1.85864 | −0.929319 | − | 0.369279i | \(-0.879605\pi\) | ||||
−0.929319 | + | 0.369279i | \(0.879605\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.61447 | −0.151233 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.0834 | −1.24679 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.62292 | −0.281999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.7060 | 1.59116 | 0.795578 | − | 0.605851i | \(-0.207167\pi\) | ||||
0.795578 | + | 0.605851i | \(0.207167\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.2446 | 1.08490 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.3910 | 0.762525 | 0.381263 | − | 0.924467i | \(-0.375489\pi\) | ||||
0.381263 | + | 0.924467i | \(0.375489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.54270 | 0.180495 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.2466 | 0.365852 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.9401 | 0.907932 | 0.453966 | − | 0.891019i | \(-0.350009\pi\) | ||||
0.453966 | + | 0.891019i | \(0.350009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.5410 | −0.666790 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.4645 | 0.339335 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.6415 | −1.28412 | −0.642058 | − | 0.766656i | \(-0.721919\pi\) | ||||
−0.642058 | + | 0.766656i | \(0.721919\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.5611 | −0.924216 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 42.8031 | 1.38363 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.94228 | 0.321053 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.7132 | 1.50688 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.74895 | 0.120808 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.8221 | −0.509332 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5629 | −0.436155 | −0.218077 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218077 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.44649 | 0.142842 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6345 | 0.405461 | 0.202730 | − | 0.979235i | \(-0.435019\pi\) | ||||
0.202730 | + | 0.979235i | \(0.435019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.3166 | 0.939848 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.12523 | −0.260216 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.4667 | −0.942725 | −0.471362 | − | 0.881940i | \(-0.656238\pi\) | ||||
−0.471362 | + | 0.881940i | \(0.656238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.200181 | −0.00639782 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.09786 | 0.226617 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.8277 | 0.536721 | 0.268360 | − | 0.963319i | \(-0.413518\pi\) | ||||
0.268360 | + | 0.963319i | \(0.413518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.76778 | −0.311227 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.67909 | −0.117107 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.50470 | −0.0478466 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7334 | −0.880979 | −0.440490 | − | 0.897758i | \(-0.645195\pi\) | ||||
−0.440490 | + | 0.897758i | \(0.645195\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.4121 | 0.425621 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.2036 | −0.481985 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.5922 | 1.44392 | 0.721960 | − | 0.691935i | \(-0.243241\pi\) | ||||
0.721960 | + | 0.691935i | \(0.243241\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8868 | −0.344444 |
(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 | 6004.2.a.g.1.7 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.7 | ✓ | 27 | 1.1 | even | 1 | trivial |