Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 16 x^{10} + 13 x^{9} + 93 x^{8} - 59 x^{7} - 238 x^{6} + 108 x^{5} + 257 x^{4} - 71 x^{3} - 93 x^{2} + 13 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.72434\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.72434 | 1.21929 | 0.609647 | − | 0.792673i | \(-0.291311\pi\) | ||||
0.609647 | + | 0.792673i | \(0.291311\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.973355 | 0.486677 | ||||||||
\(5\) | 0.0158764 | 0.00710016 | 0.00355008 | − | 0.999994i | \(-0.498870\pi\) | ||||
0.00355008 | + | 0.999994i | \(0.498870\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.08835 | 1.16729 | 0.583643 | − | 0.812011i | \(-0.301627\pi\) | ||||
0.583643 | + | 0.812011i | \(0.301627\pi\) | |||||||
\(8\) | −1.77029 | −0.625891 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0273764 | 0.00865718 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.101547 | 0.0281640 | 0.0140820 | − | 0.999901i | \(-0.495517\pi\) | ||||
0.0140820 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(14\) | 5.32537 | 1.42326 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99929 | −1.24982 | ||||||||
\(17\) | 0.754411 | 0.182971 | 0.0914857 | − | 0.995806i | \(-0.470838\pi\) | ||||
0.0914857 | + | 0.995806i | \(0.470838\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.01153 | −1.37914 | −0.689569 | − | 0.724220i | \(-0.742200\pi\) | ||||
−0.689569 | + | 0.724220i | \(0.742200\pi\) | |||||||
\(20\) | 0.0154534 | 0.00345549 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.72434 | 0.367631 | ||||||||
\(23\) | −7.29458 | −1.52103 | −0.760513 | − | 0.649323i | \(-0.775052\pi\) | ||||
−0.760513 | + | 0.649323i | \(0.775052\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99975 | −0.999950 | ||||||||
\(26\) | 0.175101 | 0.0343402 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.00606 | 0.568091 | ||||||||
\(29\) | −2.30385 | −0.427814 | −0.213907 | − | 0.976854i | \(-0.568619\pi\) | ||||
−0.213907 | + | 0.976854i | \(0.568619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2560 | −1.84203 | −0.921016 | − | 0.389524i | \(-0.872640\pi\) | ||||
−0.921016 | + | 0.389524i | \(0.872640\pi\) | |||||||
\(32\) | −5.07991 | −0.898010 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.30086 | 0.223096 | ||||||||
\(35\) | 0.0490319 | 0.00828791 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.17730 | −0.193547 | −0.0967737 | − | 0.995306i | \(-0.530852\pi\) | ||||
−0.0967737 | + | 0.995306i | \(0.530852\pi\) | |||||||
\(38\) | −10.3659 | −1.68158 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0281059 | −0.00444393 | ||||||||
\(41\) | 6.03943 | 0.943200 | 0.471600 | − | 0.881813i | \(-0.343677\pi\) | ||||
0.471600 | + | 0.881813i | \(0.343677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.46377 | −0.528219 | −0.264110 | − | 0.964493i | \(-0.585078\pi\) | ||||
−0.264110 | + | 0.964493i | \(0.585078\pi\) | |||||||
\(44\) | 0.973355 | 0.146739 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.5783 | −1.85458 | ||||||||
\(47\) | −4.51719 | −0.658900 | −0.329450 | − | 0.944173i | \(-0.606863\pi\) | ||||
−0.329450 | + | 0.944173i | \(0.606863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.53789 | 0.362555 | ||||||||
\(50\) | −8.62127 | −1.21923 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0988411 | 0.0137068 | ||||||||
\(53\) | −5.67332 | −0.779290 | −0.389645 | − | 0.920965i | \(-0.627402\pi\) | ||||
−0.389645 | + | 0.920965i | \(0.627402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0158764 | 0.00214078 | ||||||||
\(56\) | −5.46726 | −0.730593 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.97263 | −0.521631 | ||||||||
\(59\) | −1.22945 | −0.160061 | −0.0800307 | − | 0.996792i | \(-0.525502\pi\) | ||||
−0.0800307 | + | 0.996792i | \(0.525502\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −17.6849 | −2.24598 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.23908 | 0.154885 | ||||||||
\(65\) | 0.00161220 | 0.000199969 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.40484 | 1.14898 | 0.574492 | − | 0.818510i | \(-0.305200\pi\) | ||||
0.574492 | + | 0.818510i | \(0.305200\pi\) | |||||||
\(68\) | 0.734309 | 0.0890481 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0845478 | 0.0101054 | ||||||||
\(71\) | 9.66939 | 1.14755 | 0.573773 | − | 0.819014i | \(-0.305479\pi\) | ||||
0.573773 | + | 0.819014i | \(0.305479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.87787 | 0.687953 | 0.343977 | − | 0.938978i | \(-0.388226\pi\) | ||||
0.343977 | + | 0.938978i | \(0.388226\pi\) | |||||||
\(74\) | −2.03007 | −0.235991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.85135 | −0.671196 | ||||||||
\(77\) | 3.08835 | 0.351950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7844 | 1.21333 | 0.606667 | − | 0.794956i | \(-0.292506\pi\) | ||||
0.606667 | + | 0.794956i | \(0.292506\pi\) | |||||||
\(80\) | −0.0793709 | −0.00887394 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.4140 | 1.15004 | ||||||||
\(83\) | 14.4808 | 1.58948 | 0.794738 | − | 0.606953i | \(-0.207608\pi\) | ||||
0.794738 | + | 0.606953i | \(0.207608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0119774 | 0.00129913 | ||||||||
\(86\) | −5.97272 | −0.644055 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.77029 | −0.188713 | ||||||||
\(89\) | −5.44295 | −0.576952 | −0.288476 | − | 0.957487i | \(-0.593149\pi\) | ||||
−0.288476 | + | 0.957487i | \(0.593149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.313612 | 0.0328754 | ||||||||
\(92\) | −7.10021 | −0.740249 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.78918 | −0.803392 | ||||||||
\(95\) | −0.0954416 | −0.00979210 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.37384 | −0.647165 | −0.323583 | − | 0.946200i | \(-0.604887\pi\) | ||||
−0.323583 | + | 0.946200i | \(0.604887\pi\) | |||||||
\(98\) | 4.37618 | 0.442061 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.86653 | −0.486653 | ||||||||
\(101\) | 8.76993 | 0.872640 | 0.436320 | − | 0.899791i | \(-0.356282\pi\) | ||||
0.436320 | + | 0.899791i | \(0.356282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.7090 | −1.15372 | −0.576860 | − | 0.816843i | \(-0.695722\pi\) | ||||
−0.576860 | + | 0.816843i | \(0.695722\pi\) | |||||||
\(104\) | −0.179767 | −0.0176276 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.78274 | −0.950184 | ||||||||
\(107\) | 2.21519 | 0.214150 | 0.107075 | − | 0.994251i | \(-0.465851\pi\) | ||||
0.107075 | + | 0.994251i | \(0.465851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6496 | −1.78630 | −0.893152 | − | 0.449755i | \(-0.851511\pi\) | ||||
−0.893152 | + | 0.449755i | \(0.851511\pi\) | |||||||
\(110\) | 0.0273764 | 0.00261024 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −15.4395 | −1.45890 | ||||||||
\(113\) | −7.43324 | −0.699261 | −0.349630 | − | 0.936888i | \(-0.613693\pi\) | ||||
−0.349630 | + | 0.936888i | \(0.613693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.115812 | −0.0107995 | ||||||||
\(116\) | −2.24246 | −0.208208 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.12000 | −0.195162 | ||||||||
\(119\) | 2.32988 | 0.213580 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.72434 | −0.156115 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.98273 | −0.896476 | ||||||||
\(125\) | −0.158760 | −0.0142000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.148396 | −0.0131680 | −0.00658402 | − | 0.999978i | \(-0.502096\pi\) | ||||
−0.00658402 | + | 0.999978i | \(0.502096\pi\) | |||||||
\(128\) | 12.2964 | 1.08686 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.00277999 | 0.000243821 0 | ||||||||
\(131\) | −8.37503 | −0.731730 | −0.365865 | − | 0.930668i | \(-0.619227\pi\) | ||||
−0.365865 | + | 0.930668i | \(0.619227\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.5657 | −1.60985 | ||||||||
\(134\) | 16.2172 | 1.40095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.33552 | −0.114520 | ||||||||
\(137\) | 5.01664 | 0.428600 | 0.214300 | − | 0.976768i | \(-0.431253\pi\) | ||||
0.214300 | + | 0.976768i | \(0.431253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4343 | −1.05466 | −0.527331 | − | 0.849660i | \(-0.676807\pi\) | ||||
−0.527331 | + | 0.849660i | \(0.676807\pi\) | |||||||
\(140\) | 0.0477255 | 0.00403354 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 16.6733 | 1.39920 | ||||||||
\(143\) | 0.101547 | 0.00849177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0365769 | −0.00303755 | ||||||||
\(146\) | 10.1355 | 0.838817 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.14593 | −0.0941952 | ||||||||
\(149\) | −14.1975 | −1.16310 | −0.581552 | − | 0.813509i | \(-0.697554\pi\) | ||||
−0.581552 | + | 0.813509i | \(0.697554\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.9461 | 1.46043 | 0.730215 | − | 0.683218i | \(-0.239420\pi\) | ||||
0.730215 | + | 0.683218i | \(0.239420\pi\) | |||||||
\(152\) | 10.6421 | 0.863191 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.32537 | 0.429130 | ||||||||
\(155\) | −0.162829 | −0.0130787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8815 | −0.948249 | −0.474124 | − | 0.880458i | \(-0.657235\pi\) | ||||
−0.474124 | + | 0.880458i | \(0.657235\pi\) | |||||||
\(158\) | 18.5959 | 1.47941 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.0806509 | −0.00637601 | ||||||||
\(161\) | −22.5282 | −1.77547 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.0288 | −1.88208 | −0.941040 | − | 0.338294i | \(-0.890150\pi\) | ||||
−0.941040 | + | 0.338294i | \(0.890150\pi\) | |||||||
\(164\) | 5.87851 | 0.459034 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.9699 | 1.93804 | ||||||||
\(167\) | 24.8668 | 1.92425 | 0.962126 | − | 0.272605i | \(-0.0878852\pi\) | ||||
0.962126 | + | 0.272605i | \(0.0878852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9897 | −0.999207 | ||||||||
\(170\) | 0.0206531 | 0.00158402 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.37147 | −0.257072 | ||||||||
\(173\) | −0.865461 | −0.0657998 | −0.0328999 | − | 0.999459i | \(-0.510474\pi\) | ||||
−0.0328999 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.4410 | −1.16723 | ||||||||
\(176\) | −4.99929 | −0.376836 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.38551 | −0.703474 | ||||||||
\(179\) | 9.95118 | 0.743786 | 0.371893 | − | 0.928276i | \(-0.378709\pi\) | ||||
0.371893 | + | 0.928276i | \(0.378709\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7754 | 1.02391 | 0.511957 | − | 0.859011i | \(-0.328921\pi\) | ||||
0.511957 | + | 0.859011i | \(0.328921\pi\) | |||||||
\(182\) | 0.540774 | 0.0400848 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.9135 | 0.951996 | ||||||||
\(185\) | −0.0186914 | −0.00137422 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.754411 | 0.0551680 | ||||||||
\(188\) | −4.39683 | −0.320672 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.164574 | −0.0119395 | ||||||||
\(191\) | −22.0940 | −1.59866 | −0.799332 | − | 0.600889i | \(-0.794813\pi\) | ||||
−0.799332 | + | 0.600889i | \(0.794813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.04001 | −0.290806 | −0.145403 | − | 0.989372i | \(-0.546448\pi\) | ||||
−0.145403 | + | 0.989372i | \(0.546448\pi\) | |||||||
\(194\) | −10.9907 | −0.789085 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.47026 | 0.176447 | ||||||||
\(197\) | 24.3663 | 1.73603 | 0.868013 | − | 0.496541i | \(-0.165397\pi\) | ||||
0.868013 | + | 0.496541i | \(0.165397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.80517 | −0.127965 | −0.0639824 | − | 0.997951i | \(-0.520380\pi\) | ||||
−0.0639824 | + | 0.997951i | \(0.520380\pi\) | |||||||
\(200\) | 8.85099 | 0.625859 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.1224 | 1.06400 | ||||||||
\(203\) | −7.11509 | −0.499381 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0958846 | 0.00669687 | ||||||||
\(206\) | −20.1903 | −1.40672 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.507662 | −0.0352000 | ||||||||
\(209\) | −6.01153 | −0.415826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0724 | 0.899940 | 0.449970 | − | 0.893044i | \(-0.351435\pi\) | ||||
0.449970 | + | 0.893044i | \(0.351435\pi\) | |||||||
\(212\) | −5.52215 | −0.379263 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.81974 | 0.261112 | ||||||||
\(215\) | −0.0549923 | −0.00375044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.6741 | −2.15018 | ||||||||
\(218\) | −32.1582 | −2.17803 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0154534 | 0.00104187 | ||||||||
\(221\) | 0.0766080 | 0.00515321 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.8988 | −1.60038 | −0.800190 | − | 0.599747i | \(-0.795268\pi\) | ||||
−0.800190 | + | 0.599747i | \(0.795268\pi\) | |||||||
\(224\) | −15.6885 | −1.04823 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.8175 | −0.852604 | ||||||||
\(227\) | −14.8395 | −0.984930 | −0.492465 | − | 0.870332i | \(-0.663904\pi\) | ||||
−0.492465 | + | 0.870332i | \(0.663904\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7034 | −1.36812 | −0.684060 | − | 0.729426i | \(-0.739787\pi\) | ||||
−0.684060 | + | 0.729426i | \(0.739787\pi\) | |||||||
\(230\) | −0.199699 | −0.0131678 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.07848 | 0.267765 | ||||||||
\(233\) | −16.2119 | −1.06208 | −0.531039 | − | 0.847347i | \(-0.678198\pi\) | ||||
−0.531039 | + | 0.847347i | \(0.678198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0717169 | −0.00467829 | ||||||||
\(236\) | −1.19670 | −0.0778983 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.01751 | 0.260417 | ||||||||
\(239\) | 15.1898 | 0.982547 | 0.491273 | − | 0.871005i | \(-0.336532\pi\) | ||||
0.491273 | + | 0.871005i | \(0.336532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.58027 | −0.359457 | −0.179729 | − | 0.983716i | \(-0.557522\pi\) | ||||
−0.179729 | + | 0.983716i | \(0.557522\pi\) | |||||||
\(242\) | 1.72434 | 0.110845 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.973355 | −0.0623127 | ||||||||
\(245\) | 0.0402926 | 0.00257420 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.610451 | −0.0388421 | ||||||||
\(248\) | 18.1561 | 1.15291 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.273757 | −0.0173139 | ||||||||
\(251\) | 8.68870 | 0.548426 | 0.274213 | − | 0.961669i | \(-0.411583\pi\) | ||||
0.274213 | + | 0.961669i | \(0.411583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.29458 | −0.458606 | ||||||||
\(254\) | −0.255886 | −0.0160557 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.7251 | 1.17032 | ||||||||
\(257\) | −19.3953 | −1.20985 | −0.604923 | − | 0.796284i | \(-0.706796\pi\) | ||||
−0.604923 | + | 0.796284i | \(0.706796\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.63592 | −0.225925 | ||||||||
\(260\) | 0.00156924 | 9.73204e−5 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.4414 | −0.892194 | ||||||||
\(263\) | 10.4687 | 0.645526 | 0.322763 | − | 0.946480i | \(-0.395388\pi\) | ||||
0.322763 | + | 0.946480i | \(0.395388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0900721 | −0.00553308 | ||||||||
\(266\) | −32.0136 | −1.96288 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.15425 | 0.559185 | ||||||||
\(269\) | 12.2219 | 0.745182 | 0.372591 | − | 0.927996i | \(-0.378469\pi\) | ||||
0.372591 | + | 0.927996i | \(0.378469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.4349 | −1.11984 | −0.559922 | − | 0.828546i | \(-0.689169\pi\) | ||||
−0.559922 | + | 0.828546i | \(0.689169\pi\) | |||||||
\(272\) | −3.77152 | −0.228682 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.65040 | 0.522590 | ||||||||
\(275\) | −4.99975 | −0.301496 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1637 | 1.51194 | 0.755971 | − | 0.654605i | \(-0.227165\pi\) | ||||
0.755971 | + | 0.654605i | \(0.227165\pi\) | |||||||
\(278\) | −21.4409 | −1.28594 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0868006 | −0.00518733 | ||||||||
\(281\) | 7.27100 | 0.433752 | 0.216876 | − | 0.976199i | \(-0.430413\pi\) | ||||
0.216876 | + | 0.976199i | \(0.430413\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.06532 | 0.241658 | 0.120829 | − | 0.992673i | \(-0.461445\pi\) | ||||
0.120829 | + | 0.992673i | \(0.461445\pi\) | |||||||
\(284\) | 9.41175 | 0.558485 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.175101 | 0.0103540 | ||||||||
\(287\) | 18.6518 | 1.10098 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4309 | −0.966521 | ||||||||
\(290\) | −0.0630711 | −0.00370366 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.72126 | 0.334811 | ||||||||
\(293\) | −6.32001 | −0.369219 | −0.184609 | − | 0.982812i | \(-0.559102\pi\) | ||||
−0.184609 | + | 0.982812i | \(0.559102\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0195194 | −0.00113646 | ||||||||
\(296\) | 2.08417 | 0.121140 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.4813 | −1.41816 | ||||||||
\(299\) | −0.740741 | −0.0428382 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6973 | −0.616583 | ||||||||
\(302\) | 30.9451 | 1.78069 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 30.0534 | 1.72368 | ||||||||
\(305\) | −0.0158764 | −0.000909082 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.6825 | 0.780900 | 0.390450 | − | 0.920624i | \(-0.372319\pi\) | ||||
0.390450 | + | 0.920624i | \(0.372319\pi\) | |||||||
\(308\) | 3.00606 | 0.171286 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.280773 | −0.0159468 | ||||||||
\(311\) | 26.7956 | 1.51944 | 0.759718 | − | 0.650252i | \(-0.225337\pi\) | ||||
0.759718 | + | 0.650252i | \(0.225337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7559 | 1.00362 | 0.501810 | − | 0.864978i | \(-0.332668\pi\) | ||||
0.501810 | + | 0.864978i | \(0.332668\pi\) | |||||||
\(314\) | −20.4878 | −1.15619 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4970 | 0.590503 | ||||||||
\(317\) | 5.56189 | 0.312387 | 0.156193 | − | 0.987726i | \(-0.450078\pi\) | ||||
0.156193 | + | 0.987726i | \(0.450078\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.30385 | −0.128991 | ||||||||
\(320\) | 0.0196721 | 0.00109971 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −38.8463 | −2.16482 | ||||||||
\(323\) | −4.53516 | −0.252343 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.507708 | −0.0281626 | ||||||||
\(326\) | −41.4339 | −2.29481 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6915 | −0.590341 | ||||||||
\(329\) | −13.9506 | −0.769124 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9891 | −0.658979 | −0.329490 | − | 0.944159i | \(-0.606877\pi\) | ||||
−0.329490 | + | 0.944159i | \(0.606877\pi\) | |||||||
\(332\) | 14.0950 | 0.773562 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 42.8789 | 2.34623 | ||||||||
\(335\) | 0.149315 | 0.00815797 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.0217 | 1.14513 | 0.572563 | − | 0.819861i | \(-0.305949\pi\) | ||||
0.572563 | + | 0.819861i | \(0.305949\pi\) | |||||||
\(338\) | −22.3987 | −1.21833 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0116582 | 0.000632256 0 | ||||||||
\(341\) | −10.2560 | −0.555394 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7806 | −0.744080 | ||||||||
\(344\) | 6.13186 | 0.330608 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.49235 | −0.0802293 | ||||||||
\(347\) | 1.01042 | 0.0542421 | 0.0271211 | − | 0.999632i | \(-0.491366\pi\) | ||||
0.0271211 | + | 0.999632i | \(0.491366\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.58868 | −0.406213 | −0.203106 | − | 0.979157i | \(-0.565104\pi\) | ||||
−0.203106 | + | 0.979157i | \(0.565104\pi\) | |||||||
\(350\) | −26.6255 | −1.42319 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.07991 | −0.270760 | ||||||||
\(353\) | 8.01525 | 0.426609 | 0.213304 | − | 0.976986i | \(-0.431577\pi\) | ||||
0.213304 | + | 0.976986i | \(0.431577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.153516 | 0.00814776 | ||||||||
\(356\) | −5.29793 | −0.280789 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.1592 | 0.906894 | ||||||||
\(359\) | −8.17890 | −0.431666 | −0.215833 | − | 0.976430i | \(-0.569247\pi\) | ||||
−0.215833 | + | 0.976430i | \(0.569247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.1385 | 0.902024 | ||||||||
\(362\) | 23.7534 | 1.24845 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.305255 | 0.0159997 | ||||||||
\(365\) | 0.0933197 | 0.00488458 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.9078 | 1.03918 | 0.519589 | − | 0.854416i | \(-0.326085\pi\) | ||||
0.519589 | + | 0.854416i | \(0.326085\pi\) | |||||||
\(368\) | 36.4677 | 1.90101 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0322303 | −0.00167558 | ||||||||
\(371\) | −17.5212 | −0.909654 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0859 | 0.677562 | 0.338781 | − | 0.940865i | \(-0.389985\pi\) | ||||
0.338781 | + | 0.940865i | \(0.389985\pi\) | |||||||
\(374\) | 1.30086 | 0.0672660 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.99672 | 0.412399 | ||||||||
\(377\) | −0.233949 | −0.0120490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3665 | −1.40572 | −0.702861 | − | 0.711327i | \(-0.748095\pi\) | ||||
−0.702861 | + | 0.711327i | \(0.748095\pi\) | |||||||
\(380\) | −0.0928986 | −0.00476560 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −38.0976 | −1.94924 | ||||||||
\(383\) | −4.11063 | −0.210043 | −0.105022 | − | 0.994470i | \(-0.533491\pi\) | ||||
−0.105022 | + | 0.994470i | \(0.533491\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0490319 | 0.00249890 | ||||||||
\(386\) | −6.96636 | −0.354579 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.20401 | −0.314961 | ||||||||
\(389\) | 22.1925 | 1.12520 | 0.562602 | − | 0.826728i | \(-0.309800\pi\) | ||||
0.562602 | + | 0.826728i | \(0.309800\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.50311 | −0.278304 | ||||||||
\(392\) | −4.49279 | −0.226920 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 42.0158 | 2.11673 | ||||||||
\(395\) | 0.171217 | 0.00861487 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.9958 | −1.80658 | −0.903288 | − | 0.429035i | \(-0.858854\pi\) | ||||
−0.903288 | + | 0.429035i | \(0.858854\pi\) | |||||||
\(398\) | −3.11272 | −0.156027 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.9952 | 1.24976 | ||||||||
\(401\) | −17.0516 | −0.851517 | −0.425759 | − | 0.904837i | \(-0.639993\pi\) | ||||
−0.425759 | + | 0.904837i | \(0.639993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.04146 | −0.0518790 | ||||||||
\(404\) | 8.53625 | 0.424694 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.2688 | −0.608893 | ||||||||
\(407\) | −1.17730 | −0.0583568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8530 | 1.27835 | 0.639175 | − | 0.769061i | \(-0.279276\pi\) | ||||
0.639175 | + | 0.769061i | \(0.279276\pi\) | |||||||
\(410\) | 0.165338 | 0.00816545 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.3970 | −0.561490 | ||||||||
\(413\) | −3.79698 | −0.186837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.229904 | 0.0112855 | ||||||||
\(416\) | −0.515849 | −0.0252916 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.3659 | −0.507014 | ||||||||
\(419\) | 7.87860 | 0.384895 | 0.192447 | − | 0.981307i | \(-0.438358\pi\) | ||||
0.192447 | + | 0.981307i | \(0.438358\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.42205 | 0.118044 | 0.0590218 | − | 0.998257i | \(-0.481202\pi\) | ||||
0.0590218 | + | 0.998257i | \(0.481202\pi\) | |||||||
\(422\) | 22.5413 | 1.09729 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.0434 | 0.487751 | ||||||||
\(425\) | −3.77186 | −0.182962 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.08835 | −0.149456 | ||||||||
\(428\) | 2.15617 | 0.104222 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0948255 | −0.00457289 | ||||||||
\(431\) | −7.22840 | −0.348180 | −0.174090 | − | 0.984730i | \(-0.555698\pi\) | ||||
−0.174090 | + | 0.984730i | \(0.555698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2577 | −0.685181 | −0.342591 | − | 0.939485i | \(-0.611304\pi\) | ||||
−0.342591 | + | 0.939485i | \(0.611304\pi\) | |||||||
\(434\) | −54.6170 | −2.62170 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.1526 | −0.869354 | ||||||||
\(437\) | 43.8516 | 2.09770 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.01932 | 0.382741 | 0.191371 | − | 0.981518i | \(-0.438707\pi\) | ||||
0.191371 | + | 0.981518i | \(0.438707\pi\) | |||||||
\(440\) | −0.0281059 | −0.00133989 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.132098 | 0.00628328 | ||||||||
\(443\) | 20.7827 | 0.987418 | 0.493709 | − | 0.869627i | \(-0.335641\pi\) | ||||
0.493709 | + | 0.869627i | \(0.335641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.0864147 | −0.00409645 | ||||||||
\(446\) | −41.2096 | −1.95133 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.82670 | 0.180795 | ||||||||
\(449\) | −12.9208 | −0.609772 | −0.304886 | − | 0.952389i | \(-0.598618\pi\) | ||||
−0.304886 | + | 0.952389i | \(0.598618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.03943 | 0.284386 | ||||||||
\(452\) | −7.23518 | −0.340314 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.5883 | −1.20092 | ||||||||
\(455\) | 0.00497904 | 0.000233421 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.8263 | 1.44200 | 0.720998 | − | 0.692938i | \(-0.243684\pi\) | ||||
0.720998 | + | 0.692938i | \(0.243684\pi\) | |||||||
\(458\) | −35.6998 | −1.66814 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.112726 | −0.00525588 | ||||||||
\(461\) | 20.0826 | 0.935340 | 0.467670 | − | 0.883903i | \(-0.345094\pi\) | ||||
0.467670 | + | 0.883903i | \(0.345094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.14479 | 0.378520 | 0.189260 | − | 0.981927i | \(-0.439391\pi\) | ||||
0.189260 | + | 0.981927i | \(0.439391\pi\) | |||||||
\(464\) | 11.5176 | 0.534692 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.9549 | −1.29499 | ||||||||
\(467\) | 25.6676 | 1.18776 | 0.593878 | − | 0.804555i | \(-0.297596\pi\) | ||||
0.593878 | + | 0.804555i | \(0.297596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.0454 | 1.34119 | ||||||||
\(470\) | −0.123664 | −0.00570421 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.17649 | 0.100181 | ||||||||
\(473\) | −3.46377 | −0.159264 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.0561 | 1.37907 | ||||||||
\(476\) | 2.26780 | 0.103945 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.1924 | 1.19801 | ||||||||
\(479\) | 10.8572 | 0.496079 | 0.248039 | − | 0.968750i | \(-0.420214\pi\) | ||||
0.248039 | + | 0.968750i | \(0.420214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.119551 | −0.00545107 | ||||||||
\(482\) | −9.62230 | −0.438284 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.973355 | 0.0442434 | ||||||||
\(485\) | −0.101194 | −0.00459498 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.88276 | −0.130630 | −0.0653151 | − | 0.997865i | \(-0.520805\pi\) | ||||
−0.0653151 | + | 0.997865i | \(0.520805\pi\) | |||||||
\(488\) | 1.77029 | 0.0801371 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0694782 | 0.00313870 | ||||||||
\(491\) | −7.83502 | −0.353589 | −0.176795 | − | 0.984248i | \(-0.556573\pi\) | ||||
−0.176795 | + | 0.984248i | \(0.556573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.73805 | −0.0782778 | ||||||||
\(494\) | −1.05263 | −0.0473599 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 51.2727 | 2.30221 | ||||||||
\(497\) | 29.8624 | 1.33951 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.4204 | 0.779842 | 0.389921 | − | 0.920848i | \(-0.372502\pi\) | ||||
0.389921 | + | 0.920848i | \(0.372502\pi\) | |||||||
\(500\) | −0.154530 | −0.00691080 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.9823 | 0.668693 | ||||||||
\(503\) | −1.37826 | −0.0614537 | −0.0307268 | − | 0.999528i | \(-0.509782\pi\) | ||||
−0.0307268 | + | 0.999528i | \(0.509782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.139235 | 0.00619588 | ||||||||
\(506\) | −12.5783 | −0.559176 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.144442 | −0.00640859 | ||||||||
\(509\) | 32.1408 | 1.42462 | 0.712308 | − | 0.701867i | \(-0.247650\pi\) | ||||
0.712308 | + | 0.701867i | \(0.247650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.1529 | 0.803038 | ||||||||
\(512\) | 7.69559 | 0.340100 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −33.4441 | −1.47516 | ||||||||
\(515\) | −0.185897 | −0.00819160 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.51719 | −0.198666 | ||||||||
\(518\) | −6.26957 | −0.275469 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.00285406 | −0.000125159 0 | ||||||||
\(521\) | −24.1606 | −1.05849 | −0.529247 | − | 0.848468i | \(-0.677526\pi\) | ||||
−0.529247 | + | 0.848468i | \(0.677526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.9398 | −1.13427 | −0.567134 | − | 0.823625i | \(-0.691948\pi\) | ||||
−0.567134 | + | 0.823625i | \(0.691948\pi\) | |||||||
\(524\) | −8.15188 | −0.356116 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0516 | 0.787086 | ||||||||
\(527\) | −7.73724 | −0.337039 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.2109 | 1.31352 | ||||||||
\(530\) | −0.155315 | −0.00674645 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.0710 | −0.783477 | ||||||||
\(533\) | 0.613285 | 0.0265643 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0351693 | 0.00152050 | ||||||||
\(536\) | −16.6493 | −0.719139 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.0747 | 0.908596 | ||||||||
\(539\) | 2.53789 | 0.109314 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.42991 | 0.147463 | 0.0737317 | − | 0.997278i | \(-0.476509\pi\) | ||||
0.0737317 | + | 0.997278i | \(0.476509\pi\) | |||||||
\(542\) | −31.7882 | −1.36542 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.83234 | −0.164310 | ||||||||
\(545\) | −0.296089 | −0.0126830 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.1231 | −1.88657 | −0.943284 | − | 0.331986i | \(-0.892281\pi\) | ||||
−0.943284 | + | 0.331986i | \(0.892281\pi\) | |||||||
\(548\) | 4.88297 | 0.208590 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.62127 | −0.367612 | ||||||||
\(551\) | 13.8497 | 0.590015 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.3058 | 1.41631 | ||||||||
\(554\) | 43.3909 | 1.84350 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.1030 | −0.513280 | ||||||||
\(557\) | −34.2569 | −1.45151 | −0.725756 | − | 0.687952i | \(-0.758510\pi\) | ||||
−0.725756 | + | 0.687952i | \(0.758510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.351734 | −0.0148768 | ||||||||
\(560\) | −0.245125 | −0.0103584 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.5377 | 0.528871 | ||||||||
\(563\) | −46.3008 | −1.95134 | −0.975672 | − | 0.219234i | \(-0.929644\pi\) | ||||
−0.975672 | + | 0.219234i | \(0.929644\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.118013 | −0.00496486 | ||||||||
\(566\) | 7.01000 | 0.294652 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.1176 | −0.718239 | ||||||||
\(569\) | −7.09897 | −0.297604 | −0.148802 | − | 0.988867i | \(-0.547542\pi\) | ||||
−0.148802 | + | 0.988867i | \(0.547542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.2690 | −1.68521 | −0.842603 | − | 0.538535i | \(-0.818978\pi\) | ||||
−0.842603 | + | 0.538535i | \(0.818978\pi\) | |||||||
\(572\) | 0.0988411 | 0.00413275 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 32.1622 | 1.34242 | ||||||||
\(575\) | 36.4711 | 1.52095 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.5093 | −1.22849 | −0.614245 | − | 0.789116i | \(-0.710539\pi\) | ||||
−0.614245 | + | 0.789116i | \(0.710539\pi\) | |||||||
\(578\) | −28.3324 | −1.17847 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.0356023 | −0.00147831 | ||||||||
\(581\) | 44.7218 | 1.85537 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.67332 | −0.234965 | ||||||||
\(584\) | −10.4055 | −0.430584 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.8979 | −0.450186 | ||||||||
\(587\) | 28.2736 | 1.16698 | 0.583488 | − | 0.812122i | \(-0.301687\pi\) | ||||
0.583488 | + | 0.812122i | \(0.301687\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 61.6542 | 2.54042 | ||||||||
\(590\) | −0.0336580 | −0.00138568 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.88568 | 0.241900 | ||||||||
\(593\) | −19.3146 | −0.793155 | −0.396578 | − | 0.918001i | \(-0.629802\pi\) | ||||
−0.396578 | + | 0.918001i | \(0.629802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0369902 | 0.00151645 | ||||||||
\(596\) | −13.8192 | −0.566056 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.27729 | −0.0522323 | ||||||||
\(599\) | 0.248575 | 0.0101565 | 0.00507825 | − | 0.999987i | \(-0.498384\pi\) | ||||
0.00507825 | + | 0.999987i | \(0.498384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.9655 | 0.855202 | 0.427601 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427601 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(602\) | −18.4458 | −0.751796 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.4679 | 0.710758 | ||||||||
\(605\) | 0.0158764 | 0.000645469 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.54313 | 0.184400 | 0.0921999 | − | 0.995741i | \(-0.470610\pi\) | ||||
0.0921999 | + | 0.995741i | \(0.470610\pi\) | |||||||
\(608\) | 30.5380 | 1.23848 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.0273764 | −0.00110844 | ||||||||
\(611\) | −0.458706 | −0.0185573 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.9967 | 1.00961 | 0.504803 | − | 0.863234i | \(-0.331565\pi\) | ||||
0.504803 | + | 0.863234i | \(0.331565\pi\) | |||||||
\(614\) | 23.5933 | 0.952146 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.46726 | −0.220282 | ||||||||
\(617\) | −30.7047 | −1.23612 | −0.618062 | − | 0.786130i | \(-0.712082\pi\) | ||||
−0.618062 | + | 0.786130i | \(0.712082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.34685 | −0.0541345 | −0.0270673 | − | 0.999634i | \(-0.508617\pi\) | ||||
−0.0270673 | + | 0.999634i | \(0.508617\pi\) | |||||||
\(620\) | −0.158490 | −0.00636512 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 46.2047 | 1.85264 | ||||||||
\(623\) | −16.8097 | −0.673468 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9962 | 0.999849 | ||||||||
\(626\) | 30.6172 | 1.22371 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.5649 | −0.461491 | ||||||||
\(629\) | −0.888170 | −0.0354137 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.15674 | −0.0858584 | −0.0429292 | − | 0.999078i | \(-0.513669\pi\) | ||||
−0.0429292 | + | 0.999078i | \(0.513669\pi\) | |||||||
\(632\) | −19.0914 | −0.759415 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.59060 | 0.380891 | ||||||||
\(635\) | −0.00235600 | −9.34951e−5 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.257714 | 0.0102110 | ||||||||
\(638\) | −3.97263 | −0.157278 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.195223 | 0.00771688 | ||||||||
\(641\) | 1.74552 | 0.0689437 | 0.0344719 | − | 0.999406i | \(-0.489025\pi\) | ||||
0.0344719 | + | 0.999406i | \(0.489025\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.6804 | −1.32823 | −0.664113 | − | 0.747632i | \(-0.731191\pi\) | ||||
−0.664113 | + | 0.747632i | \(0.731191\pi\) | |||||||
\(644\) | −21.9279 | −0.864081 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.82017 | −0.307680 | ||||||||
\(647\) | −43.0126 | −1.69100 | −0.845500 | − | 0.533975i | \(-0.820698\pi\) | ||||
−0.845500 | + | 0.533975i | \(0.820698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.22945 | −0.0482603 | ||||||||
\(650\) | −0.875463 | −0.0343385 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.3885 | −0.915966 | ||||||||
\(653\) | −8.68472 | −0.339859 | −0.169930 | − | 0.985456i | \(-0.554354\pi\) | ||||
−0.169930 | + | 0.985456i | \(0.554354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.132966 | −0.00519540 | ||||||||
\(656\) | −30.1929 | −1.17883 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.0557 | −0.937788 | ||||||||
\(659\) | −18.6856 | −0.727887 | −0.363944 | − | 0.931421i | \(-0.618570\pi\) | ||||
−0.363944 | + | 0.931421i | \(0.618570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.0230 | 1.44003 | 0.720013 | − | 0.693960i | \(-0.244136\pi\) | ||||
0.720013 | + | 0.693960i | \(0.244136\pi\) | |||||||
\(662\) | −20.6733 | −0.803489 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25.6352 | −0.994838 | ||||||||
\(665\) | −0.294757 | −0.0114302 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.8056 | 0.650716 | ||||||||
\(668\) | 24.2042 | 0.936490 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.257471 | 0.00994696 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9352 | −0.729900 | −0.364950 | − | 0.931027i | \(-0.618914\pi\) | ||||
−0.364950 | + | 0.931027i | \(0.618914\pi\) | |||||||
\(674\) | 36.2486 | 1.39624 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6436 | −0.486291 | ||||||||
\(677\) | 16.3128 | 0.626951 | 0.313476 | − | 0.949596i | \(-0.398507\pi\) | ||||
0.313476 | + | 0.949596i | \(0.398507\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.6846 | −0.755427 | ||||||||
\(680\) | −0.0212034 | −0.000813112 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.6849 | −0.677188 | ||||||||
\(683\) | 42.7001 | 1.63387 | 0.816937 | − | 0.576726i | \(-0.195670\pi\) | ||||
0.816937 | + | 0.576726i | \(0.195670\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0796463 | 0.00304313 | ||||||||
\(686\) | −23.7624 | −0.907252 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.3164 | 0.660181 | ||||||||
\(689\) | −0.576107 | −0.0219479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7488 | 0.789323 | 0.394661 | − | 0.918827i | \(-0.370862\pi\) | ||||
0.394661 | + | 0.918827i | \(0.370862\pi\) | |||||||
\(692\) | −0.842401 | −0.0320233 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.74231 | 0.0661371 | ||||||||
\(695\) | −0.197412 | −0.00748826 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.55621 | 0.172579 | ||||||||
\(698\) | −13.0855 | −0.495293 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.0295 | −0.568063 | ||||||||
\(701\) | −13.8266 | −0.522222 | −0.261111 | − | 0.965309i | \(-0.584089\pi\) | ||||
−0.261111 | + | 0.965309i | \(0.584089\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.07739 | 0.266929 | ||||||||
\(704\) | 1.23908 | 0.0466995 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8210 | 0.520161 | ||||||||
\(707\) | 27.0846 | 1.01862 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.7009 | −1.45344 | −0.726721 | − | 0.686933i | \(-0.758957\pi\) | ||||
−0.726721 | + | 0.686933i | \(0.758957\pi\) | |||||||
\(710\) | 0.264713 | 0.00993451 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.63559 | 0.361109 | ||||||||
\(713\) | 74.8132 | 2.80178 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.00161220 | 6.02929e−5 0 | ||||||||
\(716\) | 9.68603 | 0.361984 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.1032 | −0.526328 | ||||||||
\(719\) | −3.99446 | −0.148968 | −0.0744841 | − | 0.997222i | \(-0.523731\pi\) | ||||
−0.0744841 | + | 0.997222i | \(0.523731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.1614 | −1.34672 | ||||||||
\(722\) | 29.5525 | 1.09983 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.4083 | 0.498316 | ||||||||
\(725\) | 11.5187 | 0.427793 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.349160 | 0.0129496 | 0.00647481 | − | 0.999979i | \(-0.497939\pi\) | ||||
0.00647481 | + | 0.999979i | \(0.497939\pi\) | |||||||
\(728\) | −0.555183 | −0.0205764 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.160915 | 0.00595573 | ||||||||
\(731\) | −2.61310 | −0.0966491 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.4730 | −1.27329 | −0.636644 | − | 0.771158i | \(-0.719678\pi\) | ||||
−0.636644 | + | 0.771158i | \(0.719678\pi\) | |||||||
\(734\) | 34.3278 | 1.26706 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.0558 | 1.36590 | ||||||||
\(737\) | 9.40484 | 0.346432 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.6069 | 0.390181 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(740\) | −0.0181933 | −0.000668801 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.2125 | −1.10914 | ||||||||
\(743\) | 24.4783 | 0.898021 | 0.449010 | − | 0.893527i | \(-0.351777\pi\) | ||||
0.449010 | + | 0.893527i | \(0.351777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.225405 | −0.00825822 | ||||||||
\(746\) | 22.5645 | 0.826147 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.734309 | 0.0268490 | ||||||||
\(749\) | 6.84127 | 0.249975 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.8215 | −0.650315 | −0.325157 | − | 0.945660i | \(-0.605417\pi\) | ||||
−0.325157 | + | 0.945660i | \(0.605417\pi\) | |||||||
\(752\) | 22.5827 | 0.823508 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.403407 | −0.0146912 | ||||||||
\(755\) | 0.284919 | 0.0103693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.8569 | −0.867092 | −0.433546 | − | 0.901131i | \(-0.642738\pi\) | ||||
−0.433546 | + | 0.901131i | \(0.642738\pi\) | |||||||
\(758\) | −47.1892 | −1.71399 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.168959 | 0.00612879 | ||||||||
\(761\) | −25.1121 | −0.910314 | −0.455157 | − | 0.890411i | \(-0.650417\pi\) | ||||
−0.455157 | + | 0.890411i | \(0.650417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −57.5963 | −2.08513 | ||||||||
\(764\) | −21.5053 | −0.778034 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.08813 | −0.256105 | ||||||||
\(767\) | −0.124847 | −0.00450797 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.7996 | 1.32703 | 0.663514 | − | 0.748164i | \(-0.269064\pi\) | ||||
0.663514 | + | 0.748164i | \(0.269064\pi\) | |||||||
\(770\) | 0.0845478 | 0.00304689 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.93237 | −0.141529 | ||||||||
\(773\) | 26.2515 | 0.944201 | 0.472101 | − | 0.881545i | \(-0.343496\pi\) | ||||
0.472101 | + | 0.881545i | \(0.343496\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.2774 | 1.84194 | ||||||||
\(776\) | 11.2835 | 0.405055 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.2675 | 1.37195 | ||||||||
\(779\) | −36.3062 | −1.30080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.66939 | 0.345998 | ||||||||
\(782\) | −9.48924 | −0.339335 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.6876 | −0.453130 | ||||||||
\(785\) | −0.188636 | −0.00673272 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.7502 | 1.48823 | 0.744116 | − | 0.668050i | \(-0.232871\pi\) | ||||
0.744116 | + | 0.668050i | \(0.232871\pi\) | |||||||
\(788\) | 23.7171 | 0.844885 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.295237 | 0.0105041 | ||||||||
\(791\) | −22.9564 | −0.816237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.101547 | −0.00360603 | ||||||||
\(794\) | −62.0690 | −2.20275 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.75707 | −0.0622776 | ||||||||
\(797\) | −4.53552 | −0.160656 | −0.0803282 | − | 0.996768i | \(-0.525597\pi\) | ||||
−0.0803282 | + | 0.996768i | \(0.525597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.40782 | −0.120560 | ||||||||
\(800\) | 25.3983 | 0.897965 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29.4028 | −1.03825 | ||||||||
\(803\) | 5.87787 | 0.207426 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.357667 | −0.0126061 | ||||||||
\(806\) | −1.79584 | −0.0632558 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.5253 | −0.546178 | ||||||||
\(809\) | 50.1441 | 1.76297 | 0.881486 | − | 0.472210i | \(-0.156544\pi\) | ||||
0.881486 | + | 0.472210i | \(0.156544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4087 | 0.646418 | 0.323209 | − | 0.946328i | \(-0.395238\pi\) | ||||
0.323209 | + | 0.946328i | \(0.395238\pi\) | |||||||
\(812\) | −6.92551 | −0.243038 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.03007 | −0.0711540 | ||||||||
\(815\) | −0.381492 | −0.0133631 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.8225 | 0.728488 | ||||||||
\(818\) | 44.5795 | 1.55869 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0933297 | 0.00325922 | ||||||||
\(821\) | −23.9297 | −0.835154 | −0.417577 | − | 0.908642i | \(-0.637121\pi\) | ||||
−0.417577 | + | 0.908642i | \(0.637121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.32320 | −0.115839 | −0.0579197 | − | 0.998321i | \(-0.518447\pi\) | ||||
−0.0579197 | + | 0.998321i | \(0.518447\pi\) | |||||||
\(824\) | 20.7283 | 0.722103 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.54730 | −0.227810 | ||||||||
\(827\) | 47.6416 | 1.65666 | 0.828331 | − | 0.560239i | \(-0.189291\pi\) | ||||
0.828331 | + | 0.560239i | \(0.189291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −53.2947 | −1.85100 | −0.925501 | − | 0.378744i | \(-0.876356\pi\) | ||||
−0.925501 | + | 0.378744i | \(0.876356\pi\) | |||||||
\(830\) | 0.396432 | 0.0137604 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.125824 | 0.00436217 | ||||||||
\(833\) | 1.91461 | 0.0663373 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.394796 | 0.0136625 | ||||||||
\(836\) | −5.85135 | −0.202373 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.5854 | 0.469300 | ||||||||
\(839\) | −52.8010 | −1.82289 | −0.911447 | − | 0.411417i | \(-0.865034\pi\) | ||||
−0.911447 | + | 0.411417i | \(0.865034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6923 | −0.816975 | ||||||||
\(842\) | 4.17645 | 0.143930 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.7241 | 0.437981 | ||||||||
\(845\) | −0.206230 | −0.00709453 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.08835 | 0.106117 | ||||||||
\(848\) | 28.3626 | 0.973974 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.50398 | −0.223085 | ||||||||
\(851\) | 8.58793 | 0.294391 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.34877 | 0.320096 | 0.160048 | − | 0.987109i | \(-0.448835\pi\) | ||||
0.160048 | + | 0.987109i | \(0.448835\pi\) | |||||||
\(854\) | −5.32537 | −0.182230 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.92152 | −0.134035 | ||||||||
\(857\) | −10.5206 | −0.359376 | −0.179688 | − | 0.983724i | \(-0.557509\pi\) | ||||
−0.179688 | + | 0.983724i | \(0.557509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2276 | −0.587799 | −0.293899 | − | 0.955836i | \(-0.594953\pi\) | ||||
−0.293899 | + | 0.955836i | \(0.594953\pi\) | |||||||
\(860\) | −0.0535270 | −0.00182526 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.4642 | −0.424533 | ||||||||
\(863\) | 50.3781 | 1.71489 | 0.857446 | − | 0.514574i | \(-0.172050\pi\) | ||||
0.857446 | + | 0.514574i | \(0.172050\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0137404 | −0.000467189 0 | ||||||||
\(866\) | −24.5851 | −0.835437 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −30.8301 | −1.04644 | ||||||||
\(869\) | 10.7844 | 0.365834 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.955032 | 0.0323600 | ||||||||
\(872\) | 33.0151 | 1.11803 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 75.6151 | 2.55772 | ||||||||
\(875\) | −0.490307 | −0.0165754 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.22641 | −0.0751806 | −0.0375903 | − | 0.999293i | \(-0.511968\pi\) | ||||
−0.0375903 | + | 0.999293i | \(0.511968\pi\) | |||||||
\(878\) | 13.8280 | 0.466674 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0793709 | −0.00267559 | ||||||||
\(881\) | 22.8872 | 0.771088 | 0.385544 | − | 0.922689i | \(-0.374014\pi\) | ||||
0.385544 | + | 0.922689i | \(0.374014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.5534 | −1.60030 | −0.800150 | − | 0.599800i | \(-0.795247\pi\) | ||||
−0.800150 | + | 0.599800i | \(0.795247\pi\) | |||||||
\(884\) | 0.0745668 | 0.00250795 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.8365 | 1.20395 | ||||||||
\(887\) | 40.1853 | 1.34929 | 0.674646 | − | 0.738142i | \(-0.264296\pi\) | ||||
0.674646 | + | 0.738142i | \(0.264296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.458299 | −0.0153709 | ||||||||
\(890\) | −0.149009 | −0.00499478 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.2620 | −0.778869 | ||||||||
\(893\) | 27.1552 | 0.908714 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.157989 | 0.00528100 | ||||||||
\(896\) | 37.9756 | 1.26868 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.2799 | −0.743491 | ||||||||
\(899\) | 23.6283 | 0.788048 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.28001 | −0.142588 | ||||||||
\(902\) | 10.4140 | 0.346750 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.1590 | 0.437661 | ||||||||
\(905\) | 0.218704 | 0.00726996 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.9220 | −1.82365 | −0.911827 | − | 0.410574i | \(-0.865328\pi\) | ||||
−0.911827 | + | 0.410574i | \(0.865328\pi\) | |||||||
\(908\) | −14.4441 | −0.479343 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.00858556 | 0.000284609 0 | ||||||||
\(911\) | 16.0542 | 0.531900 | 0.265950 | − | 0.963987i | \(-0.414314\pi\) | ||||
0.265950 | + | 0.963987i | \(0.414314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4808 | 0.479245 | ||||||||
\(914\) | 53.1551 | 1.75822 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.1518 | −0.665833 | ||||||||
\(917\) | −25.8650 | −0.854138 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.1366 | 0.631257 | 0.315628 | − | 0.948883i | \(-0.397785\pi\) | ||||
0.315628 | + | 0.948883i | \(0.397785\pi\) | |||||||
\(920\) | 0.205020 | 0.00675932 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.6293 | 1.14045 | ||||||||
\(923\) | 0.981896 | 0.0323195 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.88622 | 0.193538 | ||||||||
\(926\) | 14.0444 | 0.461528 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.7034 | 0.384181 | ||||||||
\(929\) | −17.7836 | −0.583461 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.2566 | −0.500014 | ||||||||
\(932\) | −15.7800 | −0.516890 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44.2598 | 1.44822 | ||||||||
\(935\) | 0.0119774 | 0.000391701 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6353 | 0.837468 | 0.418734 | − | 0.908109i | \(-0.362474\pi\) | ||||
0.418734 | + | 0.908109i | \(0.362474\pi\) | |||||||
\(938\) | 50.0842 | 1.63531 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0698060 | −0.00227682 | ||||||||
\(941\) | 0.103553 | 0.00337572 | 0.00168786 | − | 0.999999i | \(-0.499463\pi\) | ||||
0.00168786 | + | 0.999999i | \(0.499463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.0551 | −1.43463 | ||||||||
\(944\) | 6.14640 | 0.200048 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.97272 | −0.194190 | ||||||||
\(947\) | −30.1840 | −0.980847 | −0.490424 | − | 0.871484i | \(-0.663158\pi\) | ||||
−0.490424 | + | 0.871484i | \(0.663158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.596879 | 0.0193755 | ||||||||
\(950\) | 51.8270 | 1.68149 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.12456 | −0.133678 | ||||||||
\(953\) | −43.1394 | −1.39742 | −0.698712 | − | 0.715403i | \(-0.746243\pi\) | ||||
−0.698712 | + | 0.715403i | \(0.746243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.350774 | −0.0113508 | ||||||||
\(956\) | 14.7851 | 0.478183 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.7216 | 0.604866 | ||||||||
\(959\) | 15.4931 | 0.500299 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.1856 | 2.39309 | ||||||||
\(962\) | −0.206147 | −0.00664646 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.43159 | −0.174940 | ||||||||
\(965\) | −0.0641410 | −0.00206477 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.7195 | −0.762768 | −0.381384 | − | 0.924417i | \(-0.624553\pi\) | ||||
−0.381384 | + | 0.924417i | \(0.624553\pi\) | |||||||
\(968\) | −1.77029 | −0.0568992 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.174493 | −0.00560263 | ||||||||
\(971\) | 24.5335 | 0.787319 | 0.393659 | − | 0.919256i | \(-0.371209\pi\) | ||||
0.393659 | + | 0.919256i | \(0.371209\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.4013 | −1.23109 | ||||||||
\(974\) | −4.97086 | −0.159277 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.99929 | 0.160023 | ||||||||
\(977\) | −28.8837 | −0.924071 | −0.462035 | − | 0.886861i | \(-0.652881\pi\) | ||||
−0.462035 | + | 0.886861i | \(0.652881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.44295 | −0.173958 | ||||||||
\(980\) | 0.0392190 | 0.00125280 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.5103 | −0.431129 | ||||||||
\(983\) | −42.5661 | −1.35765 | −0.678823 | − | 0.734302i | \(-0.737510\pi\) | ||||
−0.678823 | + | 0.734302i | \(0.737510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.386850 | 0.0123261 | ||||||||
\(986\) | −2.99699 | −0.0954436 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.594186 | −0.0189036 | ||||||||
\(989\) | 25.2667 | 0.803435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.11669 | −0.0990050 | −0.0495025 | − | 0.998774i | \(-0.515764\pi\) | ||||
−0.0495025 | + | 0.998774i | \(0.515764\pi\) | |||||||
\(992\) | 52.0996 | 1.65416 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 51.4931 | 1.63326 | ||||||||
\(995\) | −0.0286596 | −0.000908571 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.2915 | −0.452618 | −0.226309 | − | 0.974056i | \(-0.572666\pi\) | ||||
−0.226309 | + | 0.974056i | \(0.572666\pi\) | |||||||
\(998\) | 30.0386 | 0.950857 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6039.2.a.e.1.10 | 12 | ||
3.2 | odd | 2 | 2013.2.a.d.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.d.1.3 | ✓ | 12 | 3.2 | odd | 2 | ||
6039.2.a.e.1.10 | 12 | 1.1 | even | 1 | trivial |