Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.112481\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.112481 | 0.0795362 | 0.0397681 | − | 0.999209i | \(-0.487338\pi\) | ||||
0.0397681 | + | 0.999209i | \(0.487338\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.98735 | −0.993674 | ||||||||
\(5\) | 1.06131 | 0.474634 | 0.237317 | − | 0.971432i | \(-0.423732\pi\) | ||||
0.237317 | + | 0.971432i | \(0.423732\pi\) | |||||||
\(6\) | 0.112481 | 0.0459202 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.448501 | −0.158569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.119378 | 0.0377506 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.98735 | −0.573698 | ||||||||
\(13\) | 5.84183 | 1.62023 | 0.810117 | − | 0.586269i | \(-0.199404\pi\) | ||||
0.810117 | + | 0.586269i | \(0.199404\pi\) | |||||||
\(14\) | 0.112481 | 0.0300618 | ||||||||
\(15\) | 1.06131 | 0.274030 | ||||||||
\(16\) | 3.92425 | 0.981062 | ||||||||
\(17\) | −2.80535 | −0.680397 | −0.340199 | − | 0.940354i | \(-0.610494\pi\) | ||||
−0.340199 | + | 0.940354i | \(0.610494\pi\) | |||||||
\(18\) | 0.112481 | 0.0265121 | ||||||||
\(19\) | 3.56160 | 0.817088 | 0.408544 | − | 0.912739i | \(-0.366037\pi\) | ||||
0.408544 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(20\) | −2.10920 | −0.471631 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.72213 | 0.984631 | 0.492316 | − | 0.870417i | \(-0.336151\pi\) | ||||
0.492316 | + | 0.870417i | \(0.336151\pi\) | |||||||
\(24\) | −0.448501 | −0.0915499 | ||||||||
\(25\) | −3.87361 | −0.774723 | ||||||||
\(26\) | 0.657096 | 0.128867 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.98735 | −0.375573 | ||||||||
\(29\) | −8.59581 | −1.59620 | −0.798100 | − | 0.602524i | \(-0.794162\pi\) | ||||
−0.798100 | + | 0.602524i | \(0.794162\pi\) | |||||||
\(30\) | 0.119378 | 0.0217953 | ||||||||
\(31\) | 1.74159 | 0.312798 | 0.156399 | − | 0.987694i | \(-0.450011\pi\) | ||||
0.156399 | + | 0.987694i | \(0.450011\pi\) | |||||||
\(32\) | 1.33841 | 0.236599 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.315549 | −0.0541162 | ||||||||
\(35\) | 1.06131 | 0.179395 | ||||||||
\(36\) | −1.98735 | −0.331225 | ||||||||
\(37\) | 4.74526 | 0.780116 | 0.390058 | − | 0.920790i | \(-0.372455\pi\) | ||||
0.390058 | + | 0.920790i | \(0.372455\pi\) | |||||||
\(38\) | 0.400613 | 0.0649880 | ||||||||
\(39\) | 5.84183 | 0.935442 | ||||||||
\(40\) | −0.476001 | −0.0752623 | ||||||||
\(41\) | −6.13922 | −0.958784 | −0.479392 | − | 0.877601i | \(-0.659143\pi\) | ||||
−0.479392 | + | 0.877601i | \(0.659143\pi\) | |||||||
\(42\) | 0.112481 | 0.0173562 | ||||||||
\(43\) | −5.25083 | −0.800744 | −0.400372 | − | 0.916353i | \(-0.631119\pi\) | ||||
−0.400372 | + | 0.916353i | \(0.631119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.06131 | 0.158211 | ||||||||
\(46\) | 0.531150 | 0.0783138 | ||||||||
\(47\) | −8.19149 | −1.19485 | −0.597426 | − | 0.801924i | \(-0.703810\pi\) | ||||
−0.597426 | + | 0.801924i | \(0.703810\pi\) | |||||||
\(48\) | 3.92425 | 0.566416 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.435708 | −0.0616185 | ||||||||
\(51\) | −2.80535 | −0.392828 | ||||||||
\(52\) | −11.6098 | −1.60998 | ||||||||
\(53\) | 14.3391 | 1.96963 | 0.984815 | − | 0.173609i | \(-0.0555427\pi\) | ||||
0.984815 | + | 0.173609i | \(0.0555427\pi\) | |||||||
\(54\) | 0.112481 | 0.0153067 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.448501 | −0.0599335 | ||||||||
\(57\) | 3.56160 | 0.471746 | ||||||||
\(58\) | −0.966866 | −0.126956 | ||||||||
\(59\) | 3.90570 | 0.508479 | 0.254239 | − | 0.967141i | \(-0.418175\pi\) | ||||
0.254239 | + | 0.967141i | \(0.418175\pi\) | |||||||
\(60\) | −2.10920 | −0.272297 | ||||||||
\(61\) | 14.7518 | 1.88878 | 0.944390 | − | 0.328827i | \(-0.106653\pi\) | ||||
0.944390 | + | 0.328827i | \(0.106653\pi\) | |||||||
\(62\) | 0.195896 | 0.0248788 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −7.69795 | −0.962244 | ||||||||
\(65\) | 6.20002 | 0.769018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.29079 | 1.01288 | 0.506441 | − | 0.862275i | \(-0.330961\pi\) | ||||
0.506441 | + | 0.862275i | \(0.330961\pi\) | |||||||
\(68\) | 5.57521 | 0.676093 | ||||||||
\(69\) | 4.72213 | 0.568477 | ||||||||
\(70\) | 0.119378 | 0.0142684 | ||||||||
\(71\) | 11.6370 | 1.38106 | 0.690531 | − | 0.723303i | \(-0.257377\pi\) | ||||
0.690531 | + | 0.723303i | \(0.257377\pi\) | |||||||
\(72\) | −0.448501 | −0.0528564 | ||||||||
\(73\) | 4.20049 | 0.491630 | 0.245815 | − | 0.969317i | \(-0.420944\pi\) | ||||
0.245815 | + | 0.969317i | \(0.420944\pi\) | |||||||
\(74\) | 0.533752 | 0.0620474 | ||||||||
\(75\) | −3.87361 | −0.447286 | ||||||||
\(76\) | −7.07815 | −0.811919 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.657096 | 0.0744015 | ||||||||
\(79\) | −6.80421 | −0.765533 | −0.382767 | − | 0.923845i | \(-0.625029\pi\) | ||||
−0.382767 | + | 0.923845i | \(0.625029\pi\) | |||||||
\(80\) | 4.16486 | 0.465645 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.690546 | −0.0762580 | ||||||||
\(83\) | −1.16511 | −0.127887 | −0.0639437 | − | 0.997954i | \(-0.520368\pi\) | ||||
−0.0639437 | + | 0.997954i | \(0.520368\pi\) | |||||||
\(84\) | −1.98735 | −0.216837 | ||||||||
\(85\) | −2.97736 | −0.322940 | ||||||||
\(86\) | −0.590619 | −0.0636881 | ||||||||
\(87\) | −8.59581 | −0.921567 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.90784 | 0.308230 | 0.154115 | − | 0.988053i | \(-0.450747\pi\) | ||||
0.154115 | + | 0.988053i | \(0.450747\pi\) | |||||||
\(90\) | 0.119378 | 0.0125835 | ||||||||
\(91\) | 5.84183 | 0.612391 | ||||||||
\(92\) | −9.38451 | −0.978402 | ||||||||
\(93\) | 1.74159 | 0.180594 | ||||||||
\(94\) | −0.921388 | −0.0950340 | ||||||||
\(95\) | 3.77998 | 0.387818 | ||||||||
\(96\) | 1.33841 | 0.136601 | ||||||||
\(97\) | −4.85294 | −0.492741 | −0.246371 | − | 0.969176i | \(-0.579238\pi\) | ||||
−0.246371 | + | 0.969176i | \(0.579238\pi\) | |||||||
\(98\) | 0.112481 | 0.0113623 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.69822 | 0.769822 | ||||||||
\(101\) | 9.29858 | 0.925243 | 0.462622 | − | 0.886556i | \(-0.346909\pi\) | ||||
0.462622 | + | 0.886556i | \(0.346909\pi\) | |||||||
\(102\) | −0.315549 | −0.0312440 | ||||||||
\(103\) | 12.9880 | 1.27974 | 0.639871 | − | 0.768482i | \(-0.278988\pi\) | ||||
0.639871 | + | 0.768482i | \(0.278988\pi\) | |||||||
\(104\) | −2.62007 | −0.256919 | ||||||||
\(105\) | 1.06131 | 0.103574 | ||||||||
\(106\) | 1.61288 | 0.156657 | ||||||||
\(107\) | 1.85275 | 0.179112 | 0.0895558 | − | 0.995982i | \(-0.471455\pi\) | ||||
0.0895558 | + | 0.995982i | \(0.471455\pi\) | |||||||
\(108\) | −1.98735 | −0.191233 | ||||||||
\(109\) | 4.65704 | 0.446063 | 0.223032 | − | 0.974811i | \(-0.428405\pi\) | ||||
0.223032 | + | 0.974811i | \(0.428405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.74526 | 0.450400 | ||||||||
\(112\) | 3.92425 | 0.370807 | ||||||||
\(113\) | 10.8478 | 1.02048 | 0.510238 | − | 0.860033i | \(-0.329557\pi\) | ||||
0.510238 | + | 0.860033i | \(0.329557\pi\) | |||||||
\(114\) | 0.400613 | 0.0375209 | ||||||||
\(115\) | 5.01166 | 0.467339 | ||||||||
\(116\) | 17.0829 | 1.58610 | ||||||||
\(117\) | 5.84183 | 0.540078 | ||||||||
\(118\) | 0.439317 | 0.0404425 | ||||||||
\(119\) | −2.80535 | −0.257166 | ||||||||
\(120\) | −0.476001 | −0.0434527 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.65930 | 0.150226 | ||||||||
\(123\) | −6.13922 | −0.553554 | ||||||||
\(124\) | −3.46114 | −0.310820 | ||||||||
\(125\) | −9.41769 | −0.842344 | ||||||||
\(126\) | 0.112481 | 0.0100206 | ||||||||
\(127\) | 7.62096 | 0.676251 | 0.338125 | − | 0.941101i | \(-0.390207\pi\) | ||||
0.338125 | + | 0.941101i | \(0.390207\pi\) | |||||||
\(128\) | −3.54269 | −0.313132 | ||||||||
\(129\) | −5.25083 | −0.462310 | ||||||||
\(130\) | 0.697385 | 0.0611647 | ||||||||
\(131\) | −5.66648 | −0.495083 | −0.247541 | − | 0.968877i | \(-0.579623\pi\) | ||||
−0.247541 | + | 0.968877i | \(0.579623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.56160 | 0.308830 | ||||||||
\(134\) | 0.932557 | 0.0805607 | ||||||||
\(135\) | 1.06131 | 0.0913434 | ||||||||
\(136\) | 1.25820 | 0.107890 | ||||||||
\(137\) | 16.4003 | 1.40117 | 0.700585 | − | 0.713569i | \(-0.252922\pi\) | ||||
0.700585 | + | 0.713569i | \(0.252922\pi\) | |||||||
\(138\) | 0.531150 | 0.0452145 | ||||||||
\(139\) | −18.9801 | −1.60987 | −0.804934 | − | 0.593364i | \(-0.797799\pi\) | ||||
−0.804934 | + | 0.593364i | \(0.797799\pi\) | |||||||
\(140\) | −2.10920 | −0.178260 | ||||||||
\(141\) | −8.19149 | −0.689848 | ||||||||
\(142\) | 1.30895 | 0.109844 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.92425 | 0.327021 | ||||||||
\(145\) | −9.12285 | −0.757611 | ||||||||
\(146\) | 0.472475 | 0.0391023 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −9.43048 | −0.775181 | ||||||||
\(149\) | −10.7491 | −0.880601 | −0.440301 | − | 0.897850i | \(-0.645128\pi\) | ||||
−0.440301 | + | 0.897850i | \(0.645128\pi\) | |||||||
\(150\) | −0.435708 | −0.0355754 | ||||||||
\(151\) | −7.18148 | −0.584420 | −0.292210 | − | 0.956354i | \(-0.594391\pi\) | ||||
−0.292210 | + | 0.956354i | \(0.594391\pi\) | |||||||
\(152\) | −1.59738 | −0.129565 | ||||||||
\(153\) | −2.80535 | −0.226799 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.84837 | 0.148465 | ||||||||
\(156\) | −11.6098 | −0.929524 | ||||||||
\(157\) | 2.24993 | 0.179564 | 0.0897821 | − | 0.995961i | \(-0.471383\pi\) | ||||
0.0897821 | + | 0.995961i | \(0.471383\pi\) | |||||||
\(158\) | −0.765345 | −0.0608876 | ||||||||
\(159\) | 14.3391 | 1.13717 | ||||||||
\(160\) | 1.42047 | 0.112298 | ||||||||
\(161\) | 4.72213 | 0.372156 | ||||||||
\(162\) | 0.112481 | 0.00883735 | ||||||||
\(163\) | −15.9040 | −1.24570 | −0.622850 | − | 0.782341i | \(-0.714025\pi\) | ||||
−0.622850 | + | 0.782341i | \(0.714025\pi\) | |||||||
\(164\) | 12.2008 | 0.952719 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.131053 | −0.0101717 | ||||||||
\(167\) | 6.98786 | 0.540737 | 0.270368 | − | 0.962757i | \(-0.412854\pi\) | ||||
0.270368 | + | 0.962757i | \(0.412854\pi\) | |||||||
\(168\) | −0.448501 | −0.0346026 | ||||||||
\(169\) | 21.1270 | 1.62516 | ||||||||
\(170\) | −0.334896 | −0.0256854 | ||||||||
\(171\) | 3.56160 | 0.272363 | ||||||||
\(172\) | 10.4352 | 0.795679 | ||||||||
\(173\) | −20.8297 | −1.58365 | −0.791826 | − | 0.610747i | \(-0.790869\pi\) | ||||
−0.791826 | + | 0.610747i | \(0.790869\pi\) | |||||||
\(174\) | −0.966866 | −0.0732979 | ||||||||
\(175\) | −3.87361 | −0.292818 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.90570 | 0.293570 | ||||||||
\(178\) | 0.327077 | 0.0245154 | ||||||||
\(179\) | −13.4636 | −1.00631 | −0.503157 | − | 0.864195i | \(-0.667828\pi\) | ||||
−0.503157 | + | 0.864195i | \(0.667828\pi\) | |||||||
\(180\) | −2.10920 | −0.157210 | ||||||||
\(181\) | −0.103986 | −0.00772924 | −0.00386462 | − | 0.999993i | \(-0.501230\pi\) | ||||
−0.00386462 | + | 0.999993i | \(0.501230\pi\) | |||||||
\(182\) | 0.657096 | 0.0487072 | ||||||||
\(183\) | 14.7518 | 1.09049 | ||||||||
\(184\) | −2.11788 | −0.156132 | ||||||||
\(185\) | 5.03621 | 0.370269 | ||||||||
\(186\) | 0.195896 | 0.0143638 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 16.2794 | 1.18729 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0.425176 | 0.0308455 | ||||||||
\(191\) | 13.7323 | 0.993633 | 0.496817 | − | 0.867856i | \(-0.334502\pi\) | ||||
0.496817 | + | 0.867856i | \(0.334502\pi\) | |||||||
\(192\) | −7.69795 | −0.555552 | ||||||||
\(193\) | 12.5508 | 0.903424 | 0.451712 | − | 0.892164i | \(-0.350813\pi\) | ||||
0.451712 | + | 0.892164i | \(0.350813\pi\) | |||||||
\(194\) | −0.545864 | −0.0391908 | ||||||||
\(195\) | 6.20002 | 0.443993 | ||||||||
\(196\) | −1.98735 | −0.141953 | ||||||||
\(197\) | −2.10513 | −0.149984 | −0.0749920 | − | 0.997184i | \(-0.523893\pi\) | ||||
−0.0749920 | + | 0.997184i | \(0.523893\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.57256 | −0.465916 | −0.232958 | − | 0.972487i | \(-0.574840\pi\) | ||||
−0.232958 | + | 0.972487i | \(0.574840\pi\) | |||||||
\(200\) | 1.73732 | 0.122847 | ||||||||
\(201\) | 8.29079 | 0.584787 | ||||||||
\(202\) | 1.04591 | 0.0735903 | ||||||||
\(203\) | −8.59581 | −0.603307 | ||||||||
\(204\) | 5.57521 | 0.390343 | ||||||||
\(205\) | −6.51564 | −0.455072 | ||||||||
\(206\) | 1.46090 | 0.101786 | ||||||||
\(207\) | 4.72213 | 0.328210 | ||||||||
\(208\) | 22.9248 | 1.58955 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.119378 | 0.00823785 | ||||||||
\(211\) | −6.99883 | −0.481819 | −0.240910 | − | 0.970548i | \(-0.577446\pi\) | ||||
−0.240910 | + | 0.970548i | \(0.577446\pi\) | |||||||
\(212\) | −28.4968 | −1.95717 | ||||||||
\(213\) | 11.6370 | 0.797357 | ||||||||
\(214\) | 0.208399 | 0.0142459 | ||||||||
\(215\) | −5.57278 | −0.380060 | ||||||||
\(216\) | −0.448501 | −0.0305166 | ||||||||
\(217\) | 1.74159 | 0.118227 | ||||||||
\(218\) | 0.523829 | 0.0354782 | ||||||||
\(219\) | 4.20049 | 0.283843 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3884 | −1.10240 | ||||||||
\(222\) | 0.533752 | 0.0358231 | ||||||||
\(223\) | 18.5592 | 1.24281 | 0.621406 | − | 0.783488i | \(-0.286562\pi\) | ||||
0.621406 | + | 0.783488i | \(0.286562\pi\) | |||||||
\(224\) | 1.33841 | 0.0894260 | ||||||||
\(225\) | −3.87361 | −0.258241 | ||||||||
\(226\) | 1.22017 | 0.0811647 | ||||||||
\(227\) | −9.07063 | −0.602039 | −0.301019 | − | 0.953618i | \(-0.597327\pi\) | ||||
−0.301019 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(228\) | −7.07815 | −0.468762 | ||||||||
\(229\) | 27.1538 | 1.79437 | 0.897186 | − | 0.441653i | \(-0.145608\pi\) | ||||
0.897186 | + | 0.441653i | \(0.145608\pi\) | |||||||
\(230\) | 0.563717 | 0.0371704 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.85523 | 0.253108 | ||||||||
\(233\) | 1.57052 | 0.102888 | 0.0514439 | − | 0.998676i | \(-0.483618\pi\) | ||||
0.0514439 | + | 0.998676i | \(0.483618\pi\) | |||||||
\(234\) | 0.657096 | 0.0429557 | ||||||||
\(235\) | −8.69375 | −0.567118 | ||||||||
\(236\) | −7.76199 | −0.505262 | ||||||||
\(237\) | −6.80421 | −0.441981 | ||||||||
\(238\) | −0.315549 | −0.0204540 | ||||||||
\(239\) | 15.3004 | 0.989702 | 0.494851 | − | 0.868978i | \(-0.335223\pi\) | ||||
0.494851 | + | 0.868978i | \(0.335223\pi\) | |||||||
\(240\) | 4.16486 | 0.268841 | ||||||||
\(241\) | −21.1065 | −1.35959 | −0.679796 | − | 0.733401i | \(-0.737932\pi\) | ||||
−0.679796 | + | 0.733401i | \(0.737932\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −29.3171 | −1.87683 | ||||||||
\(245\) | 1.06131 | 0.0678049 | ||||||||
\(246\) | −0.690546 | −0.0440276 | ||||||||
\(247\) | 20.8063 | 1.32387 | ||||||||
\(248\) | −0.781104 | −0.0496002 | ||||||||
\(249\) | −1.16511 | −0.0738358 | ||||||||
\(250\) | −1.05931 | −0.0669968 | ||||||||
\(251\) | 2.70154 | 0.170519 | 0.0852597 | − | 0.996359i | \(-0.472828\pi\) | ||||
0.0852597 | + | 0.996359i | \(0.472828\pi\) | |||||||
\(252\) | −1.98735 | −0.125191 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.857214 | 0.0537864 | ||||||||
\(255\) | −2.97736 | −0.186449 | ||||||||
\(256\) | 14.9974 | 0.937339 | ||||||||
\(257\) | −28.4992 | −1.77773 | −0.888865 | − | 0.458169i | \(-0.848505\pi\) | ||||
−0.888865 | + | 0.458169i | \(0.848505\pi\) | |||||||
\(258\) | −0.590619 | −0.0367703 | ||||||||
\(259\) | 4.74526 | 0.294856 | ||||||||
\(260\) | −12.3216 | −0.764153 | ||||||||
\(261\) | −8.59581 | −0.532067 | ||||||||
\(262\) | −0.637372 | −0.0393770 | ||||||||
\(263\) | 15.9889 | 0.985917 | 0.492959 | − | 0.870053i | \(-0.335915\pi\) | ||||
0.492959 | + | 0.870053i | \(0.335915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.2183 | 0.934853 | ||||||||
\(266\) | 0.400613 | 0.0245632 | ||||||||
\(267\) | 2.90784 | 0.177957 | ||||||||
\(268\) | −16.4767 | −1.00647 | ||||||||
\(269\) | −13.9351 | −0.849638 | −0.424819 | − | 0.905278i | \(-0.639662\pi\) | ||||
−0.424819 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(270\) | 0.119378 | 0.00726510 | ||||||||
\(271\) | 17.0917 | 1.03825 | 0.519125 | − | 0.854698i | \(-0.326258\pi\) | ||||
0.519125 | + | 0.854698i | \(0.326258\pi\) | |||||||
\(272\) | −11.0089 | −0.667512 | ||||||||
\(273\) | 5.84183 | 0.353564 | ||||||||
\(274\) | 1.84472 | 0.111444 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.38451 | −0.564881 | ||||||||
\(277\) | 29.1940 | 1.75410 | 0.877048 | − | 0.480402i | \(-0.159509\pi\) | ||||
0.877048 | + | 0.480402i | \(0.159509\pi\) | |||||||
\(278\) | −2.13490 | −0.128043 | ||||||||
\(279\) | 1.74159 | 0.104266 | ||||||||
\(280\) | −0.476001 | −0.0284465 | ||||||||
\(281\) | −14.4070 | −0.859449 | −0.429724 | − | 0.902960i | \(-0.641389\pi\) | ||||
−0.429724 | + | 0.902960i | \(0.641389\pi\) | |||||||
\(282\) | −0.921388 | −0.0548679 | ||||||||
\(283\) | −0.457299 | −0.0271836 | −0.0135918 | − | 0.999908i | \(-0.504327\pi\) | ||||
−0.0135918 | + | 0.999908i | \(0.504327\pi\) | |||||||
\(284\) | −23.1268 | −1.37233 | ||||||||
\(285\) | 3.77998 | 0.223907 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.13922 | −0.362386 | ||||||||
\(288\) | 1.33841 | 0.0788664 | ||||||||
\(289\) | −9.13001 | −0.537060 | ||||||||
\(290\) | −1.02615 | −0.0602575 | ||||||||
\(291\) | −4.85294 | −0.284484 | ||||||||
\(292\) | −8.34783 | −0.488520 | ||||||||
\(293\) | −23.4778 | −1.37159 | −0.685793 | − | 0.727797i | \(-0.740544\pi\) | ||||
−0.685793 | + | 0.727797i | \(0.740544\pi\) | |||||||
\(294\) | 0.112481 | 0.00656003 | ||||||||
\(295\) | 4.14517 | 0.241341 | ||||||||
\(296\) | −2.12825 | −0.123702 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.20907 | −0.0700396 | ||||||||
\(299\) | 27.5859 | 1.59533 | ||||||||
\(300\) | 7.69822 | 0.444457 | ||||||||
\(301\) | −5.25083 | −0.302653 | ||||||||
\(302\) | −0.807781 | −0.0464825 | ||||||||
\(303\) | 9.29858 | 0.534190 | ||||||||
\(304\) | 13.9766 | 0.801614 | ||||||||
\(305\) | 15.6563 | 0.896479 | ||||||||
\(306\) | −0.315549 | −0.0180387 | ||||||||
\(307\) | −6.02778 | −0.344023 | −0.172012 | − | 0.985095i | \(-0.555027\pi\) | ||||
−0.172012 | + | 0.985095i | \(0.555027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9880 | 0.738859 | ||||||||
\(310\) | 0.207907 | 0.0118083 | ||||||||
\(311\) | −27.0571 | −1.53427 | −0.767134 | − | 0.641487i | \(-0.778318\pi\) | ||||
−0.767134 | + | 0.641487i | \(0.778318\pi\) | |||||||
\(312\) | −2.62007 | −0.148332 | ||||||||
\(313\) | −3.09281 | −0.174816 | −0.0874080 | − | 0.996173i | \(-0.527858\pi\) | ||||
−0.0874080 | + | 0.996173i | \(0.527858\pi\) | |||||||
\(314\) | 0.253075 | 0.0142818 | ||||||||
\(315\) | 1.06131 | 0.0597983 | ||||||||
\(316\) | 13.5223 | 0.760690 | ||||||||
\(317\) | −26.3521 | −1.48008 | −0.740042 | − | 0.672561i | \(-0.765194\pi\) | ||||
−0.740042 | + | 0.672561i | \(0.765194\pi\) | |||||||
\(318\) | 1.61288 | 0.0904458 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.16994 | −0.456714 | ||||||||
\(321\) | 1.85275 | 0.103410 | ||||||||
\(322\) | 0.531150 | 0.0295998 | ||||||||
\(323\) | −9.99154 | −0.555944 | ||||||||
\(324\) | −1.98735 | −0.110408 | ||||||||
\(325\) | −22.6290 | −1.25523 | ||||||||
\(326\) | −1.78890 | −0.0990782 | ||||||||
\(327\) | 4.65704 | 0.257535 | ||||||||
\(328\) | 2.75345 | 0.152034 | ||||||||
\(329\) | −8.19149 | −0.451612 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1728 | 0.559150 | 0.279575 | − | 0.960124i | \(-0.409806\pi\) | ||||
0.279575 | + | 0.960124i | \(0.409806\pi\) | |||||||
\(332\) | 2.31548 | 0.127078 | ||||||||
\(333\) | 4.74526 | 0.260039 | ||||||||
\(334\) | 0.786002 | 0.0430081 | ||||||||
\(335\) | 8.79913 | 0.480748 | ||||||||
\(336\) | 3.92425 | 0.214085 | ||||||||
\(337\) | 0.483631 | 0.0263451 | 0.0131725 | − | 0.999913i | \(-0.495807\pi\) | ||||
0.0131725 | + | 0.999913i | \(0.495807\pi\) | |||||||
\(338\) | 2.37639 | 0.129259 | ||||||||
\(339\) | 10.8478 | 0.589172 | ||||||||
\(340\) | 5.91704 | 0.320897 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.400613 | 0.0216627 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.35500 | 0.126973 | ||||||||
\(345\) | 5.01166 | 0.269819 | ||||||||
\(346\) | −2.34295 | −0.125958 | ||||||||
\(347\) | −2.19027 | −0.117580 | −0.0587900 | − | 0.998270i | \(-0.518724\pi\) | ||||
−0.0587900 | + | 0.998270i | \(0.518724\pi\) | |||||||
\(348\) | 17.0829 | 0.915737 | ||||||||
\(349\) | 4.11130 | 0.220073 | 0.110036 | − | 0.993928i | \(-0.464903\pi\) | ||||
0.110036 | + | 0.993928i | \(0.464903\pi\) | |||||||
\(350\) | −0.435708 | −0.0232896 | ||||||||
\(351\) | 5.84183 | 0.311814 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.0161 | −1.91694 | −0.958471 | − | 0.285191i | \(-0.907943\pi\) | ||||
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(354\) | 0.439317 | 0.0233495 | ||||||||
\(355\) | 12.3506 | 0.655499 | ||||||||
\(356\) | −5.77888 | −0.306280 | ||||||||
\(357\) | −2.80535 | −0.148475 | ||||||||
\(358\) | −1.51440 | −0.0800383 | ||||||||
\(359\) | −28.3376 | −1.49560 | −0.747801 | − | 0.663923i | \(-0.768890\pi\) | ||||
−0.747801 | + | 0.663923i | \(0.768890\pi\) | |||||||
\(360\) | −0.476001 | −0.0250874 | ||||||||
\(361\) | −6.31498 | −0.332367 | ||||||||
\(362\) | −0.0116965 | −0.000614754 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.6098 | −0.608517 | ||||||||
\(365\) | 4.45804 | 0.233344 | ||||||||
\(366\) | 1.65930 | 0.0867332 | ||||||||
\(367\) | 5.71592 | 0.298369 | 0.149184 | − | 0.988809i | \(-0.452335\pi\) | ||||
0.149184 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(368\) | 18.5308 | 0.965984 | ||||||||
\(369\) | −6.13922 | −0.319595 | ||||||||
\(370\) | 0.566478 | 0.0294498 | ||||||||
\(371\) | 14.3391 | 0.744450 | ||||||||
\(372\) | −3.46114 | −0.179452 | ||||||||
\(373\) | 0.428982 | 0.0222119 | 0.0111059 | − | 0.999938i | \(-0.496465\pi\) | ||||
0.0111059 | + | 0.999938i | \(0.496465\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.41769 | −0.486327 | ||||||||
\(376\) | 3.67390 | 0.189467 | ||||||||
\(377\) | −50.2153 | −2.58622 | ||||||||
\(378\) | 0.112481 | 0.00578540 | ||||||||
\(379\) | 6.21110 | 0.319043 | 0.159521 | − | 0.987194i | \(-0.449005\pi\) | ||||
0.159521 | + | 0.987194i | \(0.449005\pi\) | |||||||
\(380\) | −7.51213 | −0.385364 | ||||||||
\(381\) | 7.62096 | 0.390433 | ||||||||
\(382\) | 1.54462 | 0.0790298 | ||||||||
\(383\) | 36.9787 | 1.88952 | 0.944762 | − | 0.327759i | \(-0.106293\pi\) | ||||
0.944762 | + | 0.327759i | \(0.106293\pi\) | |||||||
\(384\) | −3.54269 | −0.180787 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.41172 | 0.0718549 | ||||||||
\(387\) | −5.25083 | −0.266915 | ||||||||
\(388\) | 9.64448 | 0.489624 | ||||||||
\(389\) | −14.4235 | −0.731301 | −0.365650 | − | 0.930752i | \(-0.619153\pi\) | ||||
−0.365650 | + | 0.930752i | \(0.619153\pi\) | |||||||
\(390\) | 0.697385 | 0.0353135 | ||||||||
\(391\) | −13.2472 | −0.669940 | ||||||||
\(392\) | −0.448501 | −0.0226527 | ||||||||
\(393\) | −5.66648 | −0.285836 | ||||||||
\(394\) | −0.236787 | −0.0119292 | ||||||||
\(395\) | −7.22140 | −0.363348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.6802 | −0.837156 | −0.418578 | − | 0.908181i | \(-0.637471\pi\) | ||||
−0.418578 | + | 0.908181i | \(0.637471\pi\) | |||||||
\(398\) | −0.739288 | −0.0370572 | ||||||||
\(399\) | 3.56160 | 0.178303 | ||||||||
\(400\) | −15.2010 | −0.760051 | ||||||||
\(401\) | 0.429298 | 0.0214381 | 0.0107191 | − | 0.999943i | \(-0.496588\pi\) | ||||
0.0107191 | + | 0.999943i | \(0.496588\pi\) | |||||||
\(402\) | 0.932557 | 0.0465117 | ||||||||
\(403\) | 10.1741 | 0.506806 | ||||||||
\(404\) | −18.4795 | −0.919390 | ||||||||
\(405\) | 1.06131 | 0.0527371 | ||||||||
\(406\) | −0.966866 | −0.0479847 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.25820 | 0.0622903 | ||||||||
\(409\) | −2.53087 | −0.125144 | −0.0625718 | − | 0.998040i | \(-0.519930\pi\) | ||||
−0.0625718 | + | 0.998040i | \(0.519930\pi\) | |||||||
\(410\) | −0.732886 | −0.0361947 | ||||||||
\(411\) | 16.4003 | 0.808966 | ||||||||
\(412\) | −25.8116 | −1.27165 | ||||||||
\(413\) | 3.90570 | 0.192187 | ||||||||
\(414\) | 0.531150 | 0.0261046 | ||||||||
\(415\) | −1.23655 | −0.0606997 | ||||||||
\(416\) | 7.81875 | 0.383346 | ||||||||
\(417\) | −18.9801 | −0.929458 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.2313 | −0.939508 | −0.469754 | − | 0.882797i | \(-0.655657\pi\) | ||||
−0.469754 | + | 0.882797i | \(0.655657\pi\) | |||||||
\(420\) | −2.10920 | −0.102918 | ||||||||
\(421\) | −16.8316 | −0.820322 | −0.410161 | − | 0.912013i | \(-0.634527\pi\) | ||||
−0.410161 | + | 0.912013i | \(0.634527\pi\) | |||||||
\(422\) | −0.787236 | −0.0383221 | ||||||||
\(423\) | −8.19149 | −0.398284 | ||||||||
\(424\) | −6.43111 | −0.312322 | ||||||||
\(425\) | 10.8668 | 0.527119 | ||||||||
\(426\) | 1.30895 | 0.0634187 | ||||||||
\(427\) | 14.7518 | 0.713892 | ||||||||
\(428\) | −3.68205 | −0.177979 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.626832 | −0.0302285 | ||||||||
\(431\) | 13.1978 | 0.635713 | 0.317857 | − | 0.948139i | \(-0.397037\pi\) | ||||
0.317857 | + | 0.948139i | \(0.397037\pi\) | |||||||
\(432\) | 3.92425 | 0.188805 | ||||||||
\(433\) | 12.4390 | 0.597779 | 0.298890 | − | 0.954288i | \(-0.403384\pi\) | ||||
0.298890 | + | 0.954288i | \(0.403384\pi\) | |||||||
\(434\) | 0.195896 | 0.00940330 | ||||||||
\(435\) | −9.12285 | −0.437407 | ||||||||
\(436\) | −9.25516 | −0.443242 | ||||||||
\(437\) | 16.8183 | 0.804530 | ||||||||
\(438\) | 0.472475 | 0.0225757 | ||||||||
\(439\) | −2.80796 | −0.134017 | −0.0670084 | − | 0.997752i | \(-0.521345\pi\) | ||||
−0.0670084 | + | 0.997752i | \(0.521345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −1.84338 | −0.0876808 | ||||||||
\(443\) | 12.2025 | 0.579758 | 0.289879 | − | 0.957063i | \(-0.406385\pi\) | ||||
0.289879 | + | 0.957063i | \(0.406385\pi\) | |||||||
\(444\) | −9.43048 | −0.447551 | ||||||||
\(445\) | 3.08613 | 0.146297 | ||||||||
\(446\) | 2.08755 | 0.0988485 | ||||||||
\(447\) | −10.7491 | −0.508415 | ||||||||
\(448\) | −7.69795 | −0.363694 | ||||||||
\(449\) | −4.53613 | −0.214073 | −0.107037 | − | 0.994255i | \(-0.534136\pi\) | ||||
−0.107037 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(450\) | −0.435708 | −0.0205395 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −21.5584 | −1.01402 | ||||||||
\(453\) | −7.18148 | −0.337415 | ||||||||
\(454\) | −1.02027 | −0.0478839 | ||||||||
\(455\) | 6.20002 | 0.290661 | ||||||||
\(456\) | −1.59738 | −0.0748044 | ||||||||
\(457\) | −35.9900 | −1.68354 | −0.841772 | − | 0.539834i | \(-0.818487\pi\) | ||||
−0.841772 | + | 0.539834i | \(0.818487\pi\) | |||||||
\(458\) | 3.05429 | 0.142717 | ||||||||
\(459\) | −2.80535 | −0.130943 | ||||||||
\(460\) | −9.95991 | −0.464383 | ||||||||
\(461\) | 3.38164 | 0.157499 | 0.0787493 | − | 0.996894i | \(-0.474907\pi\) | ||||
0.0787493 | + | 0.996894i | \(0.474907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.189385 | 0.00880145 | 0.00440073 | − | 0.999990i | \(-0.498599\pi\) | ||||
0.00440073 | + | 0.999990i | \(0.498599\pi\) | |||||||
\(464\) | −33.7321 | −1.56597 | ||||||||
\(465\) | 1.84837 | 0.0857162 | ||||||||
\(466\) | 0.176653 | 0.00818331 | ||||||||
\(467\) | −9.82028 | −0.454428 | −0.227214 | − | 0.973845i | \(-0.572962\pi\) | ||||
−0.227214 | + | 0.973845i | \(0.572962\pi\) | |||||||
\(468\) | −11.6098 | −0.536661 | ||||||||
\(469\) | 8.29079 | 0.382833 | ||||||||
\(470\) | −0.977882 | −0.0451063 | ||||||||
\(471\) | 2.24993 | 0.103671 | ||||||||
\(472\) | −1.75171 | −0.0806291 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.765345 | −0.0351535 | ||||||||
\(475\) | −13.7963 | −0.633016 | ||||||||
\(476\) | 5.57521 | 0.255539 | ||||||||
\(477\) | 14.3391 | 0.656543 | ||||||||
\(478\) | 1.72101 | 0.0787171 | ||||||||
\(479\) | 6.10821 | 0.279091 | 0.139546 | − | 0.990216i | \(-0.455436\pi\) | ||||
0.139546 | + | 0.990216i | \(0.455436\pi\) | |||||||
\(480\) | 1.42047 | 0.0648353 | ||||||||
\(481\) | 27.7210 | 1.26397 | ||||||||
\(482\) | −2.37409 | −0.108137 | ||||||||
\(483\) | 4.72213 | 0.214864 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.15049 | −0.233872 | ||||||||
\(486\) | 0.112481 | 0.00510225 | ||||||||
\(487\) | 3.41377 | 0.154693 | 0.0773464 | − | 0.997004i | \(-0.475355\pi\) | ||||
0.0773464 | + | 0.997004i | \(0.475355\pi\) | |||||||
\(488\) | −6.61622 | −0.299502 | ||||||||
\(489\) | −15.9040 | −0.719205 | ||||||||
\(490\) | 0.119378 | 0.00539294 | ||||||||
\(491\) | −31.9564 | −1.44217 | −0.721087 | − | 0.692845i | \(-0.756357\pi\) | ||||
−0.721087 | + | 0.692845i | \(0.756357\pi\) | |||||||
\(492\) | 12.2008 | 0.550053 | ||||||||
\(493\) | 24.1142 | 1.08605 | ||||||||
\(494\) | 2.34032 | 0.105296 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.83442 | 0.306875 | ||||||||
\(497\) | 11.6370 | 0.521992 | ||||||||
\(498\) | −0.131053 | −0.00587262 | ||||||||
\(499\) | 21.9134 | 0.980979 | 0.490489 | − | 0.871447i | \(-0.336818\pi\) | ||||
0.490489 | + | 0.871447i | \(0.336818\pi\) | |||||||
\(500\) | 18.7162 | 0.837015 | ||||||||
\(501\) | 6.98786 | 0.312195 | ||||||||
\(502\) | 0.303872 | 0.0135625 | ||||||||
\(503\) | 32.9708 | 1.47010 | 0.735049 | − | 0.678014i | \(-0.237159\pi\) | ||||
0.735049 | + | 0.678014i | \(0.237159\pi\) | |||||||
\(504\) | −0.448501 | −0.0199778 | ||||||||
\(505\) | 9.86871 | 0.439152 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.1270 | 0.938284 | ||||||||
\(508\) | −15.1455 | −0.671973 | ||||||||
\(509\) | 26.7351 | 1.18501 | 0.592506 | − | 0.805566i | \(-0.298139\pi\) | ||||
0.592506 | + | 0.805566i | \(0.298139\pi\) | |||||||
\(510\) | −0.334896 | −0.0148295 | ||||||||
\(511\) | 4.20049 | 0.185819 | ||||||||
\(512\) | 8.77230 | 0.387685 | ||||||||
\(513\) | 3.56160 | 0.157249 | ||||||||
\(514\) | −3.20562 | −0.141394 | ||||||||
\(515\) | 13.7843 | 0.607409 | ||||||||
\(516\) | 10.4352 | 0.459385 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.533752 | 0.0234517 | ||||||||
\(519\) | −20.8297 | −0.914322 | ||||||||
\(520\) | −2.78072 | −0.121943 | ||||||||
\(521\) | 11.4012 | 0.499496 | 0.249748 | − | 0.968311i | \(-0.419652\pi\) | ||||
0.249748 | + | 0.968311i | \(0.419652\pi\) | |||||||
\(522\) | −0.966866 | −0.0423186 | ||||||||
\(523\) | 15.0700 | 0.658966 | 0.329483 | − | 0.944161i | \(-0.393125\pi\) | ||||
0.329483 | + | 0.944161i | \(0.393125\pi\) | |||||||
\(524\) | 11.2613 | 0.491951 | ||||||||
\(525\) | −3.87361 | −0.169058 | ||||||||
\(526\) | 1.79845 | 0.0784161 | ||||||||
\(527\) | −4.88576 | −0.212827 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.701531 | −0.0305014 | ||||||||
\(530\) | 1.71177 | 0.0743546 | ||||||||
\(531\) | 3.90570 | 0.169493 | ||||||||
\(532\) | −7.07815 | −0.306877 | ||||||||
\(533\) | −35.8643 | −1.55345 | ||||||||
\(534\) | 0.327077 | 0.0141540 | ||||||||
\(535\) | 1.96634 | 0.0850125 | ||||||||
\(536\) | −3.71843 | −0.160612 | ||||||||
\(537\) | −13.4636 | −0.580995 | ||||||||
\(538\) | −1.56744 | −0.0675769 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.10920 | −0.0907655 | ||||||||
\(541\) | −26.8970 | −1.15639 | −0.578196 | − | 0.815898i | \(-0.696243\pi\) | ||||
−0.578196 | + | 0.815898i | \(0.696243\pi\) | |||||||
\(542\) | 1.92250 | 0.0825784 | ||||||||
\(543\) | −0.103986 | −0.00446248 | ||||||||
\(544\) | −3.75470 | −0.160981 | ||||||||
\(545\) | 4.94258 | 0.211717 | ||||||||
\(546\) | 0.657096 | 0.0281211 | ||||||||
\(547\) | 10.0770 | 0.430860 | 0.215430 | − | 0.976519i | \(-0.430885\pi\) | ||||
0.215430 | + | 0.976519i | \(0.430885\pi\) | |||||||
\(548\) | −32.5931 | −1.39231 | ||||||||
\(549\) | 14.7518 | 0.629594 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.6148 | −1.30424 | ||||||||
\(552\) | −2.11788 | −0.0901429 | ||||||||
\(553\) | −6.80421 | −0.289344 | ||||||||
\(554\) | 3.28377 | 0.139514 | ||||||||
\(555\) | 5.03621 | 0.213775 | ||||||||
\(556\) | 37.7200 | 1.59968 | ||||||||
\(557\) | 30.8543 | 1.30734 | 0.653669 | − | 0.756781i | \(-0.273229\pi\) | ||||
0.653669 | + | 0.756781i | \(0.273229\pi\) | |||||||
\(558\) | 0.195896 | 0.00829293 | ||||||||
\(559\) | −30.6745 | −1.29739 | ||||||||
\(560\) | 4.16486 | 0.175997 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.62051 | −0.0683572 | ||||||||
\(563\) | 14.0259 | 0.591122 | 0.295561 | − | 0.955324i | \(-0.404493\pi\) | ||||
0.295561 | + | 0.955324i | \(0.404493\pi\) | |||||||
\(564\) | 16.2794 | 0.685484 | ||||||||
\(565\) | 11.5129 | 0.484353 | ||||||||
\(566\) | −0.0514375 | −0.00216208 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −5.21923 | −0.218994 | ||||||||
\(569\) | 28.5547 | 1.19708 | 0.598538 | − | 0.801094i | \(-0.295749\pi\) | ||||
0.598538 | + | 0.801094i | \(0.295749\pi\) | |||||||
\(570\) | 0.425176 | 0.0178087 | ||||||||
\(571\) | −18.0629 | −0.755907 | −0.377953 | − | 0.925825i | \(-0.623372\pi\) | ||||
−0.377953 | + | 0.925825i | \(0.623372\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.7323 | 0.573675 | ||||||||
\(574\) | −0.690546 | −0.0288228 | ||||||||
\(575\) | −18.2917 | −0.762816 | ||||||||
\(576\) | −7.69795 | −0.320748 | ||||||||
\(577\) | −35.7797 | −1.48953 | −0.744764 | − | 0.667328i | \(-0.767438\pi\) | ||||
−0.744764 | + | 0.667328i | \(0.767438\pi\) | |||||||
\(578\) | −1.02695 | −0.0427157 | ||||||||
\(579\) | 12.5508 | 0.521592 | ||||||||
\(580\) | 18.1303 | 0.752819 | ||||||||
\(581\) | −1.16511 | −0.0483369 | ||||||||
\(582\) | −0.545864 | −0.0226268 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.88392 | −0.0779573 | ||||||||
\(585\) | 6.20002 | 0.256339 | ||||||||
\(586\) | −2.64080 | −0.109091 | ||||||||
\(587\) | −16.8458 | −0.695301 | −0.347651 | − | 0.937624i | \(-0.613020\pi\) | ||||
−0.347651 | + | 0.937624i | \(0.613020\pi\) | |||||||
\(588\) | −1.98735 | −0.0819569 | ||||||||
\(589\) | 6.20285 | 0.255584 | ||||||||
\(590\) | 0.466254 | 0.0191954 | ||||||||
\(591\) | −2.10513 | −0.0865934 | ||||||||
\(592\) | 18.6216 | 0.765342 | ||||||||
\(593\) | −36.1560 | −1.48475 | −0.742375 | − | 0.669985i | \(-0.766301\pi\) | ||||
−0.742375 | + | 0.669985i | \(0.766301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.97736 | −0.122060 | ||||||||
\(596\) | 21.3622 | 0.875030 | ||||||||
\(597\) | −6.57256 | −0.268997 | ||||||||
\(598\) | 3.10289 | 0.126887 | ||||||||
\(599\) | −34.5880 | −1.41323 | −0.706614 | − | 0.707599i | \(-0.749778\pi\) | ||||
−0.706614 | + | 0.707599i | \(0.749778\pi\) | |||||||
\(600\) | 1.73732 | 0.0709258 | ||||||||
\(601\) | 38.8660 | 1.58538 | 0.792688 | − | 0.609627i | \(-0.208681\pi\) | ||||
0.792688 | + | 0.609627i | \(0.208681\pi\) | |||||||
\(602\) | −0.590619 | −0.0240718 | ||||||||
\(603\) | 8.29079 | 0.337627 | ||||||||
\(604\) | 14.2721 | 0.580723 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.04591 | 0.0424874 | ||||||||
\(607\) | 21.3067 | 0.864813 | 0.432406 | − | 0.901679i | \(-0.357665\pi\) | ||||
0.432406 | + | 0.901679i | \(0.357665\pi\) | |||||||
\(608\) | 4.76687 | 0.193322 | ||||||||
\(609\) | −8.59581 | −0.348320 | ||||||||
\(610\) | 1.76104 | 0.0713025 | ||||||||
\(611\) | −47.8534 | −1.93594 | ||||||||
\(612\) | 5.57521 | 0.225364 | ||||||||
\(613\) | 0.456270 | 0.0184286 | 0.00921429 | − | 0.999958i | \(-0.497067\pi\) | ||||
0.00921429 | + | 0.999958i | \(0.497067\pi\) | |||||||
\(614\) | −0.678011 | −0.0273623 | ||||||||
\(615\) | −6.51564 | −0.262736 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.2733 | −0.735656 | −0.367828 | − | 0.929894i | \(-0.619899\pi\) | ||||
−0.367828 | + | 0.929894i | \(0.619899\pi\) | |||||||
\(618\) | 1.46090 | 0.0587660 | ||||||||
\(619\) | 31.0436 | 1.24775 | 0.623875 | − | 0.781525i | \(-0.285558\pi\) | ||||
0.623875 | + | 0.781525i | \(0.285558\pi\) | |||||||
\(620\) | −3.67336 | −0.147526 | ||||||||
\(621\) | 4.72213 | 0.189492 | ||||||||
\(622\) | −3.04341 | −0.122030 | ||||||||
\(623\) | 2.90784 | 0.116500 | ||||||||
\(624\) | 22.9248 | 0.917727 | ||||||||
\(625\) | 9.37294 | 0.374918 | ||||||||
\(626\) | −0.347883 | −0.0139042 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.47140 | −0.178428 | ||||||||
\(629\) | −13.3121 | −0.530788 | ||||||||
\(630\) | 0.119378 | 0.00475612 | ||||||||
\(631\) | −29.8472 | −1.18820 | −0.594098 | − | 0.804393i | \(-0.702491\pi\) | ||||
−0.594098 | + | 0.804393i | \(0.702491\pi\) | |||||||
\(632\) | 3.05170 | 0.121390 | ||||||||
\(633\) | −6.99883 | −0.278179 | ||||||||
\(634\) | −2.96412 | −0.117720 | ||||||||
\(635\) | 8.08823 | 0.320972 | ||||||||
\(636\) | −28.4968 | −1.12997 | ||||||||
\(637\) | 5.84183 | 0.231462 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.6370 | 0.460354 | ||||||||
\(640\) | −3.75990 | −0.148623 | ||||||||
\(641\) | −3.64805 | −0.144089 | −0.0720447 | − | 0.997401i | \(-0.522952\pi\) | ||||
−0.0720447 | + | 0.997401i | \(0.522952\pi\) | |||||||
\(642\) | 0.208399 | 0.00822485 | ||||||||
\(643\) | 34.5924 | 1.36419 | 0.682095 | − | 0.731263i | \(-0.261069\pi\) | ||||
0.682095 | + | 0.731263i | \(0.261069\pi\) | |||||||
\(644\) | −9.38451 | −0.369801 | ||||||||
\(645\) | −5.57278 | −0.219428 | ||||||||
\(646\) | −1.12386 | −0.0442177 | ||||||||
\(647\) | 14.3914 | 0.565784 | 0.282892 | − | 0.959152i | \(-0.408706\pi\) | ||||
0.282892 | + | 0.959152i | \(0.408706\pi\) | |||||||
\(648\) | −0.448501 | −0.0176188 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.54534 | −0.0998363 | ||||||||
\(651\) | 1.74159 | 0.0682582 | ||||||||
\(652\) | 31.6068 | 1.23782 | ||||||||
\(653\) | −23.4343 | −0.917056 | −0.458528 | − | 0.888680i | \(-0.651623\pi\) | ||||
−0.458528 | + | 0.888680i | \(0.651623\pi\) | |||||||
\(654\) | 0.523829 | 0.0204833 | ||||||||
\(655\) | −6.01392 | −0.234983 | ||||||||
\(656\) | −24.0918 | −0.940627 | ||||||||
\(657\) | 4.20049 | 0.163877 | ||||||||
\(658\) | −0.921388 | −0.0359195 | ||||||||
\(659\) | −38.6951 | −1.50735 | −0.753674 | − | 0.657248i | \(-0.771720\pi\) | ||||
−0.753674 | + | 0.657248i | \(0.771720\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.3882 | −1.18196 | −0.590982 | − | 0.806684i | \(-0.701260\pi\) | ||||
−0.590982 | + | 0.806684i | \(0.701260\pi\) | |||||||
\(662\) | 1.14425 | 0.0444726 | ||||||||
\(663\) | −16.3884 | −0.636472 | ||||||||
\(664\) | 0.522553 | 0.0202790 | ||||||||
\(665\) | 3.77998 | 0.146581 | ||||||||
\(666\) | 0.533752 | 0.0206825 | ||||||||
\(667\) | −40.5905 | −1.57167 | ||||||||
\(668\) | −13.8873 | −0.537316 | ||||||||
\(669\) | 18.5592 | 0.717538 | ||||||||
\(670\) | 0.989736 | 0.0382368 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.33841 | 0.0516301 | ||||||||
\(673\) | −18.1911 | −0.701217 | −0.350609 | − | 0.936522i | \(-0.614025\pi\) | ||||
−0.350609 | + | 0.936522i | \(0.614025\pi\) | |||||||
\(674\) | 0.0543994 | 0.00209539 | ||||||||
\(675\) | −3.87361 | −0.149095 | ||||||||
\(676\) | −41.9867 | −1.61487 | ||||||||
\(677\) | 5.83832 | 0.224385 | 0.112192 | − | 0.993687i | \(-0.464213\pi\) | ||||
0.112192 | + | 0.993687i | \(0.464213\pi\) | |||||||
\(678\) | 1.22017 | 0.0468605 | ||||||||
\(679\) | −4.85294 | −0.186239 | ||||||||
\(680\) | 1.33535 | 0.0512083 | ||||||||
\(681\) | −9.07063 | −0.347587 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.17118 | 0.121342 | 0.0606710 | − | 0.998158i | \(-0.480676\pi\) | ||||
0.0606710 | + | 0.998158i | \(0.480676\pi\) | |||||||
\(684\) | −7.07815 | −0.270640 | ||||||||
\(685\) | 17.4058 | 0.665043 | ||||||||
\(686\) | 0.112481 | 0.00429455 | ||||||||
\(687\) | 27.1538 | 1.03598 | ||||||||
\(688\) | −20.6056 | −0.785580 | ||||||||
\(689\) | 83.7668 | 3.19126 | ||||||||
\(690\) | 0.563717 | 0.0214603 | ||||||||
\(691\) | −23.9093 | −0.909554 | −0.454777 | − | 0.890605i | \(-0.650281\pi\) | ||||
−0.454777 | + | 0.890605i | \(0.650281\pi\) | |||||||
\(692\) | 41.3958 | 1.57363 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.246364 | −0.00935186 | ||||||||
\(695\) | −20.1438 | −0.764098 | ||||||||
\(696\) | 3.85523 | 0.146132 | ||||||||
\(697\) | 17.2226 | 0.652354 | ||||||||
\(698\) | 0.462443 | 0.0175037 | ||||||||
\(699\) | 1.57052 | 0.0594023 | ||||||||
\(700\) | 7.69822 | 0.290965 | ||||||||
\(701\) | −41.3167 | −1.56051 | −0.780254 | − | 0.625462i | \(-0.784910\pi\) | ||||
−0.780254 | + | 0.625462i | \(0.784910\pi\) | |||||||
\(702\) | 0.657096 | 0.0248005 | ||||||||
\(703\) | 16.9007 | 0.637423 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.69375 | −0.327425 | ||||||||
\(706\) | −4.05113 | −0.152466 | ||||||||
\(707\) | 9.29858 | 0.349709 | ||||||||
\(708\) | −7.76199 | −0.291713 | ||||||||
\(709\) | −49.4717 | −1.85795 | −0.928975 | − | 0.370143i | \(-0.879309\pi\) | ||||
−0.928975 | + | 0.370143i | \(0.879309\pi\) | |||||||
\(710\) | 1.38920 | 0.0521359 | ||||||||
\(711\) | −6.80421 | −0.255178 | ||||||||
\(712\) | −1.30417 | −0.0488758 | ||||||||
\(713\) | 8.22400 | 0.307991 | ||||||||
\(714\) | −0.315549 | −0.0118091 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.7568 | 0.999948 | ||||||||
\(717\) | 15.3004 | 0.571405 | ||||||||
\(718\) | −3.18745 | −0.118954 | ||||||||
\(719\) | −18.6951 | −0.697209 | −0.348605 | − | 0.937270i | \(-0.613344\pi\) | ||||
−0.348605 | + | 0.937270i | \(0.613344\pi\) | |||||||
\(720\) | 4.16486 | 0.155215 | ||||||||
\(721\) | 12.9880 | 0.483697 | ||||||||
\(722\) | −0.710316 | −0.0264352 | ||||||||
\(723\) | −21.1065 | −0.784961 | ||||||||
\(724\) | 0.206657 | 0.00768034 | ||||||||
\(725\) | 33.2968 | 1.23661 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.9216 | −0.998468 | −0.499234 | − | 0.866467i | \(-0.666385\pi\) | ||||
−0.499234 | + | 0.866467i | \(0.666385\pi\) | |||||||
\(728\) | −2.62007 | −0.0971063 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.501445 | 0.0185593 | ||||||||
\(731\) | 14.7304 | 0.544824 | ||||||||
\(732\) | −29.3171 | −1.08359 | ||||||||
\(733\) | 30.5427 | 1.12812 | 0.564061 | − | 0.825733i | \(-0.309238\pi\) | ||||
0.564061 | + | 0.825733i | \(0.309238\pi\) | |||||||
\(734\) | 0.642933 | 0.0237311 | ||||||||
\(735\) | 1.06131 | 0.0391472 | ||||||||
\(736\) | 6.32012 | 0.232963 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.690546 | −0.0254193 | ||||||||
\(739\) | 12.7624 | 0.469472 | 0.234736 | − | 0.972059i | \(-0.424577\pi\) | ||||
0.234736 | + | 0.972059i | \(0.424577\pi\) | |||||||
\(740\) | −10.0087 | −0.367927 | ||||||||
\(741\) | 20.8063 | 0.764338 | ||||||||
\(742\) | 1.61288 | 0.0592107 | ||||||||
\(743\) | −31.0657 | −1.13969 | −0.569844 | − | 0.821753i | \(-0.692996\pi\) | ||||
−0.569844 | + | 0.821753i | \(0.692996\pi\) | |||||||
\(744\) | −0.781104 | −0.0286367 | ||||||||
\(745\) | −11.4082 | −0.417963 | ||||||||
\(746\) | 0.0482524 | 0.00176665 | ||||||||
\(747\) | −1.16511 | −0.0426291 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.85275 | 0.0676978 | ||||||||
\(750\) | −1.05931 | −0.0386806 | ||||||||
\(751\) | −12.6379 | −0.461164 | −0.230582 | − | 0.973053i | \(-0.574063\pi\) | ||||
−0.230582 | + | 0.973053i | \(0.574063\pi\) | |||||||
\(752\) | −32.1455 | −1.17222 | ||||||||
\(753\) | 2.70154 | 0.0984495 | ||||||||
\(754\) | −5.64827 | −0.205698 | ||||||||
\(755\) | −7.62180 | −0.277386 | ||||||||
\(756\) | −1.98735 | −0.0722791 | ||||||||
\(757\) | −13.6857 | −0.497415 | −0.248708 | − | 0.968579i | \(-0.580006\pi\) | ||||
−0.248708 | + | 0.968579i | \(0.580006\pi\) | |||||||
\(758\) | 0.698631 | 0.0253754 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.69533 | −0.0614959 | ||||||||
\(761\) | −24.1444 | −0.875233 | −0.437617 | − | 0.899162i | \(-0.644177\pi\) | ||||
−0.437617 | + | 0.899162i | \(0.644177\pi\) | |||||||
\(762\) | 0.857214 | 0.0310536 | ||||||||
\(763\) | 4.65704 | 0.168596 | ||||||||
\(764\) | −27.2908 | −0.987348 | ||||||||
\(765\) | −2.97736 | −0.107647 | ||||||||
\(766\) | 4.15940 | 0.150285 | ||||||||
\(767\) | 22.8165 | 0.823854 | ||||||||
\(768\) | 14.9974 | 0.541173 | ||||||||
\(769\) | −3.51499 | −0.126754 | −0.0633770 | − | 0.997990i | \(-0.520187\pi\) | ||||
−0.0633770 | + | 0.997990i | \(0.520187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.4992 | −1.02637 | ||||||||
\(772\) | −24.9428 | −0.897709 | ||||||||
\(773\) | 8.07699 | 0.290509 | 0.145255 | − | 0.989394i | \(-0.453600\pi\) | ||||
0.145255 | + | 0.989394i | \(0.453600\pi\) | |||||||
\(774\) | −0.590619 | −0.0212294 | ||||||||
\(775\) | −6.74624 | −0.242332 | ||||||||
\(776\) | 2.17655 | 0.0781336 | ||||||||
\(777\) | 4.74526 | 0.170235 | ||||||||
\(778\) | −1.62237 | −0.0581648 | ||||||||
\(779\) | −21.8655 | −0.783411 | ||||||||
\(780\) | −12.3216 | −0.441184 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.49006 | −0.0532845 | ||||||||
\(783\) | −8.59581 | −0.307189 | ||||||||
\(784\) | 3.92425 | 0.140152 | ||||||||
\(785\) | 2.38788 | 0.0852273 | ||||||||
\(786\) | −0.637372 | −0.0227343 | ||||||||
\(787\) | 5.32791 | 0.189920 | 0.0949598 | − | 0.995481i | \(-0.469728\pi\) | ||||
0.0949598 | + | 0.995481i | \(0.469728\pi\) | |||||||
\(788\) | 4.18362 | 0.149035 | ||||||||
\(789\) | 15.9889 | 0.569220 | ||||||||
\(790\) | −0.812271 | −0.0288993 | ||||||||
\(791\) | 10.8478 | 0.385704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 86.1778 | 3.06026 | ||||||||
\(794\) | −1.87621 | −0.0665842 | ||||||||
\(795\) | 15.2183 | 0.539738 | ||||||||
\(796\) | 13.0620 | 0.462969 | ||||||||
\(797\) | 44.3138 | 1.56968 | 0.784838 | − | 0.619701i | \(-0.212746\pi\) | ||||
0.784838 | + | 0.619701i | \(0.212746\pi\) | |||||||
\(798\) | 0.400613 | 0.0141815 | ||||||||
\(799\) | 22.9800 | 0.812974 | ||||||||
\(800\) | −5.18447 | −0.183299 | ||||||||
\(801\) | 2.90784 | 0.102743 | ||||||||
\(802\) | 0.0482880 | 0.00170511 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −16.4767 | −0.581088 | ||||||||
\(805\) | 5.01166 | 0.176638 | ||||||||
\(806\) | 1.14439 | 0.0403094 | ||||||||
\(807\) | −13.9351 | −0.490539 | ||||||||
\(808\) | −4.17043 | −0.146715 | ||||||||
\(809\) | −10.8499 | −0.381462 | −0.190731 | − | 0.981642i | \(-0.561086\pi\) | ||||
−0.190731 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(810\) | 0.119378 | 0.00419451 | ||||||||
\(811\) | −36.0883 | −1.26723 | −0.633615 | − | 0.773648i | \(-0.718430\pi\) | ||||
−0.633615 | + | 0.773648i | \(0.718430\pi\) | |||||||
\(812\) | 17.0829 | 0.599491 | ||||||||
\(813\) | 17.0917 | 0.599434 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.8792 | −0.591252 | ||||||||
\(816\) | −11.0089 | −0.385388 | ||||||||
\(817\) | −18.7014 | −0.654278 | ||||||||
\(818\) | −0.284675 | −0.00995343 | ||||||||
\(819\) | 5.84183 | 0.204130 | ||||||||
\(820\) | 12.9488 | 0.452193 | ||||||||
\(821\) | −52.1407 | −1.81972 | −0.909861 | − | 0.414913i | \(-0.863812\pi\) | ||||
−0.909861 | + | 0.414913i | \(0.863812\pi\) | |||||||
\(822\) | 1.84472 | 0.0643420 | ||||||||
\(823\) | 26.1122 | 0.910213 | 0.455106 | − | 0.890437i | \(-0.349601\pi\) | ||||
0.455106 | + | 0.890437i | \(0.349601\pi\) | |||||||
\(824\) | −5.82512 | −0.202928 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.439317 | 0.0152858 | ||||||||
\(827\) | −7.68971 | −0.267397 | −0.133699 | − | 0.991022i | \(-0.542685\pi\) | ||||
−0.133699 | + | 0.991022i | \(0.542685\pi\) | |||||||
\(828\) | −9.38451 | −0.326134 | ||||||||
\(829\) | −25.3084 | −0.878997 | −0.439498 | − | 0.898243i | \(-0.644844\pi\) | ||||
−0.439498 | + | 0.898243i | \(0.644844\pi\) | |||||||
\(830\) | −0.139088 | −0.00482782 | ||||||||
\(831\) | 29.1940 | 1.01273 | ||||||||
\(832\) | −44.9701 | −1.55906 | ||||||||
\(833\) | −2.80535 | −0.0971996 | ||||||||
\(834\) | −2.13490 | −0.0739255 | ||||||||
\(835\) | 7.41632 | 0.256652 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.74159 | 0.0601981 | ||||||||
\(838\) | −2.16315 | −0.0747249 | ||||||||
\(839\) | −7.10737 | −0.245374 | −0.122687 | − | 0.992445i | \(-0.539151\pi\) | ||||
−0.122687 | + | 0.992445i | \(0.539151\pi\) | |||||||
\(840\) | −0.476001 | −0.0164236 | ||||||||
\(841\) | 44.8879 | 1.54786 | ||||||||
\(842\) | −1.89324 | −0.0652452 | ||||||||
\(843\) | −14.4070 | −0.496203 | ||||||||
\(844\) | 13.9091 | 0.478771 | ||||||||
\(845\) | 22.4224 | 0.771354 | ||||||||
\(846\) | −0.921388 | −0.0316780 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 56.2703 | 1.93233 | ||||||||
\(849\) | −0.457299 | −0.0156945 | ||||||||
\(850\) | 1.22231 | 0.0419250 | ||||||||
\(851\) | 22.4077 | 0.768126 | ||||||||
\(852\) | −23.1268 | −0.792313 | ||||||||
\(853\) | −29.8933 | −1.02353 | −0.511764 | − | 0.859126i | \(-0.671008\pi\) | ||||
−0.511764 | + | 0.859126i | \(0.671008\pi\) | |||||||
\(854\) | 1.65930 | 0.0567802 | ||||||||
\(855\) | 3.77998 | 0.129273 | ||||||||
\(856\) | −0.830959 | −0.0284016 | ||||||||
\(857\) | 31.9946 | 1.09291 | 0.546457 | − | 0.837487i | \(-0.315976\pi\) | ||||
0.546457 | + | 0.837487i | \(0.315976\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8113 | −0.641835 | −0.320917 | − | 0.947107i | \(-0.603991\pi\) | ||||
−0.320917 | + | 0.947107i | \(0.603991\pi\) | |||||||
\(860\) | 11.0751 | 0.377656 | ||||||||
\(861\) | −6.13922 | −0.209224 | ||||||||
\(862\) | 1.48450 | 0.0505622 | ||||||||
\(863\) | 19.1665 | 0.652435 | 0.326217 | − | 0.945295i | \(-0.394226\pi\) | ||||
0.326217 | + | 0.945295i | \(0.394226\pi\) | |||||||
\(864\) | 1.33841 | 0.0455335 | ||||||||
\(865\) | −22.1068 | −0.751655 | ||||||||
\(866\) | 1.39915 | 0.0475451 | ||||||||
\(867\) | −9.13001 | −0.310071 | ||||||||
\(868\) | −3.46114 | −0.117479 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.02615 | −0.0347897 | ||||||||
\(871\) | 48.4334 | 1.64110 | ||||||||
\(872\) | −2.08869 | −0.0707319 | ||||||||
\(873\) | −4.85294 | −0.164247 | ||||||||
\(874\) | 1.89175 | 0.0639892 | ||||||||
\(875\) | −9.41769 | −0.318376 | ||||||||
\(876\) | −8.34783 | −0.282047 | ||||||||
\(877\) | 20.4286 | 0.689825 | 0.344912 | − | 0.938635i | \(-0.387909\pi\) | ||||
0.344912 | + | 0.938635i | \(0.387909\pi\) | |||||||
\(878\) | −0.315843 | −0.0106592 | ||||||||
\(879\) | −23.4778 | −0.791885 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.2279 | 0.984712 | 0.492356 | − | 0.870394i | \(-0.336136\pi\) | ||||
0.492356 | + | 0.870394i | \(0.336136\pi\) | |||||||
\(882\) | 0.112481 | 0.00378744 | ||||||||
\(883\) | −29.5803 | −0.995456 | −0.497728 | − | 0.867333i | \(-0.665832\pi\) | ||||
−0.497728 | + | 0.867333i | \(0.665832\pi\) | |||||||
\(884\) | 32.5694 | 1.09543 | ||||||||
\(885\) | 4.14517 | 0.139339 | ||||||||
\(886\) | 1.37255 | 0.0461117 | ||||||||
\(887\) | −56.1787 | −1.88630 | −0.943148 | − | 0.332373i | \(-0.892151\pi\) | ||||
−0.943148 | + | 0.332373i | \(0.892151\pi\) | |||||||
\(888\) | −2.12825 | −0.0714195 | ||||||||
\(889\) | 7.62096 | 0.255599 | ||||||||
\(890\) | 0.347131 | 0.0116359 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36.8835 | −1.23495 | ||||||||
\(893\) | −29.1749 | −0.976299 | ||||||||
\(894\) | −1.20907 | −0.0404374 | ||||||||
\(895\) | −14.2891 | −0.477631 | ||||||||
\(896\) | −3.54269 | −0.118353 | ||||||||
\(897\) | 27.5859 | 0.921065 | ||||||||
\(898\) | −0.510229 | −0.0170265 | ||||||||
\(899\) | −14.9704 | −0.499289 | ||||||||
\(900\) | 7.69822 | 0.256607 | ||||||||
\(901\) | −40.2262 | −1.34013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.25083 | −0.174737 | ||||||||
\(904\) | −4.86526 | −0.161816 | ||||||||
\(905\) | −0.110362 | −0.00366856 | ||||||||
\(906\) | −0.807781 | −0.0268367 | ||||||||
\(907\) | −37.3467 | −1.24008 | −0.620038 | − | 0.784572i | \(-0.712883\pi\) | ||||
−0.620038 | + | 0.784572i | \(0.712883\pi\) | |||||||
\(908\) | 18.0265 | 0.598230 | ||||||||
\(909\) | 9.29858 | 0.308414 | ||||||||
\(910\) | 0.697385 | 0.0231181 | ||||||||
\(911\) | −17.4355 | −0.577664 | −0.288832 | − | 0.957380i | \(-0.593267\pi\) | ||||
−0.288832 | + | 0.957380i | \(0.593267\pi\) | |||||||
\(912\) | 13.9766 | 0.462812 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −4.04820 | −0.133903 | ||||||||
\(915\) | 15.6563 | 0.517583 | ||||||||
\(916\) | −53.9640 | −1.78302 | ||||||||
\(917\) | −5.66648 | −0.187124 | ||||||||
\(918\) | −0.315549 | −0.0104147 | ||||||||
\(919\) | 50.9223 | 1.67977 | 0.839885 | − | 0.542764i | \(-0.182622\pi\) | ||||
0.839885 | + | 0.542764i | \(0.182622\pi\) | |||||||
\(920\) | −2.24774 | −0.0741056 | ||||||||
\(921\) | −6.02778 | −0.198622 | ||||||||
\(922\) | 0.380371 | 0.0125268 | ||||||||
\(923\) | 67.9816 | 2.23764 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3813 | −0.604373 | ||||||||
\(926\) | 0.0213022 | 0.000700034 0 | ||||||||
\(927\) | 12.9880 | 0.426581 | ||||||||
\(928\) | −11.5047 | −0.377660 | ||||||||
\(929\) | −57.2057 | −1.87686 | −0.938428 | − | 0.345474i | \(-0.887718\pi\) | ||||
−0.938428 | + | 0.345474i | \(0.887718\pi\) | |||||||
\(930\) | 0.207907 | 0.00681754 | ||||||||
\(931\) | 3.56160 | 0.116727 | ||||||||
\(932\) | −3.12116 | −0.102237 | ||||||||
\(933\) | −27.0571 | −0.885810 | ||||||||
\(934\) | −1.10460 | −0.0361435 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.62007 | −0.0856397 | ||||||||
\(937\) | 27.1139 | 0.885773 | 0.442887 | − | 0.896578i | \(-0.353954\pi\) | ||||
0.442887 | + | 0.896578i | \(0.353954\pi\) | |||||||
\(938\) | 0.932557 | 0.0304491 | ||||||||
\(939\) | −3.09281 | −0.100930 | ||||||||
\(940\) | 17.2775 | 0.563530 | ||||||||
\(941\) | 4.91368 | 0.160181 | 0.0800907 | − | 0.996788i | \(-0.474479\pi\) | ||||
0.0800907 | + | 0.996788i | \(0.474479\pi\) | |||||||
\(942\) | 0.253075 | 0.00824563 | ||||||||
\(943\) | −28.9901 | −0.944049 | ||||||||
\(944\) | 15.3269 | 0.498849 | ||||||||
\(945\) | 1.06131 | 0.0345245 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.1937 | 0.851181 | 0.425591 | − | 0.904916i | \(-0.360066\pi\) | ||||
0.425591 | + | 0.904916i | \(0.360066\pi\) | |||||||
\(948\) | 13.5223 | 0.439185 | ||||||||
\(949\) | 24.5385 | 0.796555 | ||||||||
\(950\) | −1.55182 | −0.0503477 | ||||||||
\(951\) | −26.3521 | −0.854527 | ||||||||
\(952\) | 1.25820 | 0.0407786 | ||||||||
\(953\) | 10.0177 | 0.324505 | 0.162252 | − | 0.986749i | \(-0.448124\pi\) | ||||
0.162252 | + | 0.986749i | \(0.448124\pi\) | |||||||
\(954\) | 1.61288 | 0.0522189 | ||||||||
\(955\) | 14.5743 | 0.471612 | ||||||||
\(956\) | −30.4073 | −0.983441 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.687058 | 0.0221978 | ||||||||
\(959\) | 16.4003 | 0.529593 | ||||||||
\(960\) | −8.16994 | −0.263684 | ||||||||
\(961\) | −27.9669 | −0.902157 | ||||||||
\(962\) | 3.11809 | 0.100531 | ||||||||
\(963\) | 1.85275 | 0.0597039 | ||||||||
\(964\) | 41.9461 | 1.35099 | ||||||||
\(965\) | 13.3203 | 0.428796 | ||||||||
\(966\) | 0.531150 | 0.0170895 | ||||||||
\(967\) | 6.98983 | 0.224778 | 0.112389 | − | 0.993664i | \(-0.464150\pi\) | ||||
0.112389 | + | 0.993664i | \(0.464150\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.99154 | −0.320975 | ||||||||
\(970\) | −0.579333 | −0.0186013 | ||||||||
\(971\) | 58.1274 | 1.86540 | 0.932699 | − | 0.360656i | \(-0.117447\pi\) | ||||
0.932699 | + | 0.360656i | \(0.117447\pi\) | |||||||
\(972\) | −1.98735 | −0.0637442 | ||||||||
\(973\) | −18.9801 | −0.608473 | ||||||||
\(974\) | 0.383985 | 0.0123037 | ||||||||
\(975\) | −22.6290 | −0.724708 | ||||||||
\(976\) | 57.8899 | 1.85301 | ||||||||
\(977\) | −3.78047 | −0.120948 | −0.0604739 | − | 0.998170i | \(-0.519261\pi\) | ||||
−0.0604739 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(978\) | −1.78890 | −0.0572028 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −2.10920 | −0.0673759 | ||||||||
\(981\) | 4.65704 | 0.148688 | ||||||||
\(982\) | −3.59449 | −0.114705 | ||||||||
\(983\) | 10.2712 | 0.327602 | 0.163801 | − | 0.986493i | \(-0.447625\pi\) | ||||
0.163801 | + | 0.986493i | \(0.447625\pi\) | |||||||
\(984\) | 2.75345 | 0.0877767 | ||||||||
\(985\) | −2.23420 | −0.0711875 | ||||||||
\(986\) | 2.71240 | 0.0863803 | ||||||||
\(987\) | −8.19149 | −0.260738 | ||||||||
\(988\) | −41.3493 | −1.31550 | ||||||||
\(989\) | −24.7951 | −0.788438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.5225 | −0.651919 | −0.325960 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325960 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(992\) | 2.33095 | 0.0740078 | ||||||||
\(993\) | 10.1728 | 0.322825 | ||||||||
\(994\) | 1.30895 | 0.0415173 | ||||||||
\(995\) | −6.97555 | −0.221140 | ||||||||
\(996\) | 2.31548 | 0.0733687 | ||||||||
\(997\) | −7.37003 | −0.233411 | −0.116706 | − | 0.993167i | \(-0.537233\pi\) | ||||
−0.116706 | + | 0.993167i | \(0.537233\pi\) | |||||||
\(998\) | 2.46484 | 0.0780233 | ||||||||
\(999\) | 4.74526 | 0.150133 |
(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 | 2541.2.a.br.1.6 | 10 | ||
3.2 | odd | 2 | 7623.2.a.cy.1.5 | 10 | |||
11.7 | odd | 10 | 231.2.j.g.148.3 | yes | 20 | ||
11.8 | odd | 10 | 231.2.j.g.64.3 | ✓ | 20 | ||
11.10 | odd | 2 | 2541.2.a.bq.1.5 | 10 | |||
33.8 | even | 10 | 693.2.m.j.64.3 | 20 | |||
33.29 | even | 10 | 693.2.m.j.379.3 | 20 | |||
33.32 | even | 2 | 7623.2.a.cx.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.64.3 | ✓ | 20 | 11.8 | odd | 10 | ||
231.2.j.g.148.3 | yes | 20 | 11.7 | odd | 10 | ||
693.2.m.j.64.3 | 20 | 33.8 | even | 10 | |||
693.2.m.j.379.3 | 20 | 33.29 | even | 10 | |||
2541.2.a.bq.1.5 | 10 | 11.10 | odd | 2 | |||
2541.2.a.br.1.6 | 10 | 1.1 | even | 1 | trivial | ||
7623.2.a.cx.1.6 | 10 | 33.32 | even | 2 | |||
7623.2.a.cy.1.5 | 10 | 3.2 | odd | 2 |