Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6988960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 22x^{4} - 11x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 693) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.342036\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.342036 | 0.241856 | 0.120928 | − | 0.992661i | \(-0.461413\pi\) | ||||
0.120928 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.88301 | −0.941506 | ||||||||
\(5\) | −2.14896 | −0.961045 | −0.480522 | − | 0.876982i | \(-0.659553\pi\) | ||||
−0.480522 | + | 0.876982i | \(0.659553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.32813 | −0.469565 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.735023 | −0.232435 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.42874 | −0.396262 | −0.198131 | − | 0.980176i | \(-0.563487\pi\) | ||||
−0.198131 | + | 0.980176i | \(0.563487\pi\) | |||||||
\(14\) | 0.342036 | 0.0914131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.31175 | 0.827938 | ||||||||
\(17\) | −1.38414 | −0.335704 | −0.167852 | − | 0.985812i | \(-0.553683\pi\) | ||||
−0.167852 | + | 0.985812i | \(0.553683\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.59251 | 0.594762 | 0.297381 | − | 0.954759i | \(-0.403887\pi\) | ||||
0.297381 | + | 0.954759i | \(0.403887\pi\) | |||||||
\(20\) | 4.04652 | 0.904829 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0906318 | −0.0188980 | −0.00944902 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944902 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.381966 | −0.0763932 | ||||||||
\(26\) | −0.488682 | −0.0958384 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.88301 | −0.355856 | ||||||||
\(29\) | 7.74489 | 1.43819 | 0.719095 | − | 0.694912i | \(-0.244557\pi\) | ||||
0.719095 | + | 0.694912i | \(0.244557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.82857 | −0.867238 | −0.433619 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433619 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(32\) | 3.78900 | 0.669807 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.473428 | −0.0811922 | ||||||||
\(35\) | −2.14896 | −0.363241 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0702129 | −0.0115429 | −0.00577146 | − | 0.999983i | \(-0.501837\pi\) | ||||
−0.00577146 | + | 0.999983i | \(0.501837\pi\) | |||||||
\(38\) | 0.886732 | 0.143847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.85410 | 0.451273 | ||||||||
\(41\) | −6.70278 | −1.04680 | −0.523399 | − | 0.852088i | \(-0.675336\pi\) | ||||
−0.523399 | + | 0.852088i | \(0.675336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.28623 | −0.958640 | −0.479320 | − | 0.877640i | \(-0.659117\pi\) | ||||
−0.479320 | + | 0.877640i | \(0.659117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0309994 | −0.00457061 | ||||||||
\(47\) | 9.19116 | 1.34067 | 0.670334 | − | 0.742059i | \(-0.266151\pi\) | ||||
0.670334 | + | 0.742059i | \(0.266151\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.130646 | −0.0184762 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.69034 | 0.373083 | ||||||||
\(53\) | 3.73461 | 0.512988 | 0.256494 | − | 0.966546i | \(-0.417433\pi\) | ||||
0.256494 | + | 0.966546i | \(0.417433\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.32813 | −0.177479 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.64903 | 0.347835 | ||||||||
\(59\) | 9.65657 | 1.25718 | 0.628589 | − | 0.777737i | \(-0.283633\pi\) | ||||
0.628589 | + | 0.777737i | \(0.283633\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33728 | −0.811406 | −0.405703 | − | 0.914005i | \(-0.632973\pi\) | ||||
−0.405703 | + | 0.914005i | \(0.632973\pi\) | |||||||
\(62\) | −1.65155 | −0.209747 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.32753 | −0.665941 | ||||||||
\(65\) | 3.07031 | 0.380825 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.09564 | 0.866871 | 0.433435 | − | 0.901185i | \(-0.357301\pi\) | ||||
0.433435 | + | 0.901185i | \(0.357301\pi\) | |||||||
\(68\) | 2.60636 | 0.316068 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.735023 | −0.0878520 | ||||||||
\(71\) | −8.96377 | −1.06380 | −0.531902 | − | 0.846806i | \(-0.678522\pi\) | ||||
−0.531902 | + | 0.846806i | \(0.678522\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9787 | 1.40200 | 0.700998 | − | 0.713164i | \(-0.252738\pi\) | ||||
0.700998 | + | 0.713164i | \(0.252738\pi\) | |||||||
\(74\) | −0.0240154 | −0.00279173 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.88172 | −0.559972 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.63043 | −0.183438 | −0.0917188 | − | 0.995785i | \(-0.529236\pi\) | ||||
−0.0917188 | + | 0.995785i | \(0.529236\pi\) | |||||||
\(80\) | −7.11683 | −0.795686 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.29259 | −0.253175 | ||||||||
\(83\) | 9.90374 | 1.08708 | 0.543538 | − | 0.839384i | \(-0.317084\pi\) | ||||
0.543538 | + | 0.839384i | \(0.317084\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.97447 | 0.322627 | ||||||||
\(86\) | −2.15012 | −0.231853 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.2098 | 1.18823 | 0.594116 | − | 0.804379i | \(-0.297502\pi\) | ||||
0.594116 | + | 0.804379i | \(0.297502\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.42874 | −0.149773 | ||||||||
\(92\) | 0.170661 | 0.0177926 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.14371 | 0.324249 | ||||||||
\(95\) | −5.57120 | −0.571593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.60490 | −0.569092 | −0.284546 | − | 0.958662i | \(-0.591843\pi\) | ||||
−0.284546 | + | 0.958662i | \(0.591843\pi\) | |||||||
\(98\) | 0.342036 | 0.0345509 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.719246 | 0.0719246 | ||||||||
\(101\) | 0.901574 | 0.0897100 | 0.0448550 | − | 0.998994i | \(-0.485717\pi\) | ||||
0.0448550 | + | 0.998994i | \(0.485717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.35087 | 0.724303 | 0.362151 | − | 0.932119i | \(-0.382042\pi\) | ||||
0.362151 | + | 0.932119i | \(0.382042\pi\) | |||||||
\(104\) | 1.89756 | 0.186071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.27737 | 0.124069 | ||||||||
\(107\) | 5.44055 | 0.525958 | 0.262979 | − | 0.964802i | \(-0.415295\pi\) | ||||
0.262979 | + | 0.964802i | \(0.415295\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.08042 | −0.582399 | −0.291199 | − | 0.956662i | \(-0.594054\pi\) | ||||
−0.291199 | + | 0.956662i | \(0.594054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.31175 | 0.312931 | ||||||||
\(113\) | 2.59385 | 0.244009 | 0.122005 | − | 0.992530i | \(-0.461068\pi\) | ||||
0.122005 | + | 0.992530i | \(0.461068\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.194764 | 0.0181619 | ||||||||
\(116\) | −14.5837 | −1.35406 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.30290 | 0.304056 | ||||||||
\(119\) | −1.38414 | −0.126884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.16758 | −0.196244 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.09226 | 0.816509 | ||||||||
\(125\) | 11.5656 | 1.03446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1692 | −1.34605 | −0.673026 | − | 0.739619i | \(-0.735006\pi\) | ||||
−0.673026 | + | 0.739619i | \(0.735006\pi\) | |||||||
\(128\) | −9.40021 | −0.830869 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.05016 | 0.0921050 | ||||||||
\(131\) | −20.0775 | −1.75418 | −0.877090 | − | 0.480327i | \(-0.840518\pi\) | ||||
−0.877090 | + | 0.480327i | \(0.840518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.59251 | 0.224799 | ||||||||
\(134\) | 2.42697 | 0.209658 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.83833 | 0.157635 | ||||||||
\(137\) | 8.44658 | 0.721640 | 0.360820 | − | 0.932635i | \(-0.382497\pi\) | ||||
0.360820 | + | 0.932635i | \(0.382497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.71368 | 0.654265 | 0.327133 | − | 0.944978i | \(-0.393918\pi\) | ||||
0.327133 | + | 0.944978i | \(0.393918\pi\) | |||||||
\(140\) | 4.04652 | 0.341993 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.06593 | −0.257288 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.6435 | −1.38216 | ||||||||
\(146\) | 4.09714 | 0.339081 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.132212 | 0.0108677 | ||||||||
\(149\) | −15.6852 | −1.28498 | −0.642489 | − | 0.766295i | \(-0.722098\pi\) | ||||
−0.642489 | + | 0.766295i | \(0.722098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1212 | 1.06779 | 0.533893 | − | 0.845552i | \(-0.320729\pi\) | ||||
0.533893 | + | 0.845552i | \(0.320729\pi\) | |||||||
\(152\) | −3.44319 | −0.279279 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3764 | 0.833454 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.43775 | 0.114745 | 0.0573727 | − | 0.998353i | \(-0.481728\pi\) | ||||
0.0573727 | + | 0.998353i | \(0.481728\pi\) | |||||||
\(158\) | −0.557666 | −0.0443655 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.14242 | −0.643715 | ||||||||
\(161\) | −0.0906318 | −0.00714279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.5018 | −1.76248 | −0.881240 | − | 0.472669i | \(-0.843291\pi\) | ||||
−0.881240 | + | 0.472669i | \(0.843291\pi\) | |||||||
\(164\) | 12.6214 | 0.985566 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.38744 | 0.262916 | ||||||||
\(167\) | 4.91085 | 0.380013 | 0.190007 | − | 0.981783i | \(-0.439149\pi\) | ||||
0.190007 | + | 0.981783i | \(0.439149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9587 | −0.842977 | ||||||||
\(170\) | 1.01738 | 0.0780293 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.8370 | 0.902565 | ||||||||
\(173\) | −18.3873 | −1.39796 | −0.698979 | − | 0.715142i | \(-0.746362\pi\) | ||||
−0.698979 | + | 0.715142i | \(0.746362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.381966 | −0.0288739 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.83414 | 0.287381 | ||||||||
\(179\) | −26.4300 | −1.97547 | −0.987734 | − | 0.156143i | \(-0.950094\pi\) | ||||
−0.987734 | + | 0.156143i | \(0.950094\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8451 | −1.54941 | −0.774704 | − | 0.632324i | \(-0.782101\pi\) | ||||
−0.774704 | + | 0.632324i | \(0.782101\pi\) | |||||||
\(182\) | −0.488682 | −0.0362235 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.120371 | 0.00887386 | ||||||||
\(185\) | 0.150885 | 0.0110933 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.3071 | −1.26225 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.90555 | −0.138243 | ||||||||
\(191\) | −0.938968 | −0.0679414 | −0.0339707 | − | 0.999423i | \(-0.510815\pi\) | ||||
−0.0339707 | + | 0.999423i | \(0.510815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.21482 | −0.159426 | −0.0797131 | − | 0.996818i | \(-0.525400\pi\) | ||||
−0.0797131 | + | 0.996818i | \(0.525400\pi\) | |||||||
\(194\) | −1.91708 | −0.137638 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.88301 | −0.134501 | ||||||||
\(197\) | −1.24390 | −0.0886239 | −0.0443120 | − | 0.999018i | \(-0.514110\pi\) | ||||
−0.0443120 | + | 0.999018i | \(0.514110\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.3929 | −0.949398 | −0.474699 | − | 0.880148i | \(-0.657443\pi\) | ||||
−0.474699 | + | 0.880148i | \(0.657443\pi\) | |||||||
\(200\) | 0.507301 | 0.0358716 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.308371 | 0.0216969 | ||||||||
\(203\) | 7.74489 | 0.543585 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.4040 | 1.00602 | ||||||||
\(206\) | 2.51426 | 0.175177 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.73164 | −0.328080 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.1727 | −1.31990 | −0.659951 | − | 0.751309i | \(-0.729423\pi\) | ||||
−0.659951 | + | 0.751309i | \(0.729423\pi\) | |||||||
\(212\) | −7.03231 | −0.482981 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.86087 | 0.127206 | ||||||||
\(215\) | 13.5089 | 0.921296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.82857 | −0.327785 | ||||||||
\(218\) | −2.07972 | −0.140857 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.97759 | 0.133027 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.91656 | 0.530132 | 0.265066 | − | 0.964230i | \(-0.414606\pi\) | ||||
0.265066 | + | 0.964230i | \(0.414606\pi\) | |||||||
\(224\) | 3.78900 | 0.253163 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.887192 | 0.0590151 | ||||||||
\(227\) | 16.6032 | 1.10199 | 0.550997 | − | 0.834507i | \(-0.314248\pi\) | ||||
0.550997 | + | 0.834507i | \(0.314248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4568 | −1.61615 | −0.808076 | − | 0.589078i | \(-0.799491\pi\) | ||||
−0.808076 | + | 0.589078i | \(0.799491\pi\) | |||||||
\(230\) | 0.0666165 | 0.00439256 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.2862 | −0.675324 | ||||||||
\(233\) | −13.3219 | −0.872750 | −0.436375 | − | 0.899765i | \(-0.643738\pi\) | ||||
−0.436375 | + | 0.899765i | \(0.643738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.7514 | −1.28844 | ||||||||
\(236\) | −18.1834 | −1.18364 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.473428 | −0.0306878 | ||||||||
\(239\) | 8.18018 | 0.529132 | 0.264566 | − | 0.964368i | \(-0.414771\pi\) | ||||
0.264566 | + | 0.964368i | \(0.414771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.51553 | −0.0976239 | −0.0488119 | − | 0.998808i | \(-0.515543\pi\) | ||||
−0.0488119 | + | 0.998808i | \(0.515543\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.9332 | 0.763943 | ||||||||
\(245\) | −2.14896 | −0.137292 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.70402 | −0.235681 | ||||||||
\(248\) | 6.41298 | 0.407225 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.95587 | 0.250191 | ||||||||
\(251\) | −28.2044 | −1.78025 | −0.890124 | − | 0.455718i | \(-0.849382\pi\) | ||||
−0.890124 | + | 0.455718i | \(0.849382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.18843 | −0.325551 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.43984 | 0.464990 | ||||||||
\(257\) | −18.4980 | −1.15387 | −0.576936 | − | 0.816790i | \(-0.695752\pi\) | ||||
−0.576936 | + | 0.816790i | \(0.695752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0702129 | −0.00436282 | ||||||||
\(260\) | −5.78143 | −0.358549 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.86723 | −0.424259 | ||||||||
\(263\) | −21.4858 | −1.32487 | −0.662437 | − | 0.749118i | \(-0.730478\pi\) | ||||
−0.662437 | + | 0.749118i | \(0.730478\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.02553 | −0.493004 | ||||||||
\(266\) | 0.886732 | 0.0543690 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.3612 | −0.816164 | ||||||||
\(269\) | 12.6544 | 0.771553 | 0.385776 | − | 0.922592i | \(-0.373934\pi\) | ||||
0.385776 | + | 0.922592i | \(0.373934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.91475 | −0.359295 | −0.179648 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179648 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(272\) | −4.58395 | −0.277942 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.88904 | 0.174533 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.0735 | 1.08593 | 0.542966 | − | 0.839755i | \(-0.317301\pi\) | ||||
0.542966 | + | 0.839755i | \(0.317301\pi\) | |||||||
\(278\) | 2.63836 | 0.158238 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.85410 | 0.170565 | ||||||||
\(281\) | 27.2162 | 1.62358 | 0.811791 | − | 0.583948i | \(-0.198493\pi\) | ||||
0.811791 | + | 0.583948i | \(0.198493\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1420 | 0.602877 | 0.301439 | − | 0.953486i | \(-0.402533\pi\) | ||||
0.301439 | + | 0.953486i | \(0.402533\pi\) | |||||||
\(284\) | 16.8789 | 1.00158 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.70278 | −0.395653 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0841 | −0.887303 | ||||||||
\(290\) | −5.69267 | −0.334285 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.5559 | −1.31999 | ||||||||
\(293\) | 15.6060 | 0.911715 | 0.455857 | − | 0.890053i | \(-0.349333\pi\) | ||||
0.455857 | + | 0.890053i | \(0.349333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.7516 | −1.20820 | ||||||||
\(296\) | 0.0932519 | 0.00542016 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.36490 | −0.310780 | ||||||||
\(299\) | 0.129489 | 0.00748857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.28623 | −0.362332 | ||||||||
\(302\) | 4.48792 | 0.258251 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.58574 | 0.492426 | ||||||||
\(305\) | 13.6186 | 0.779797 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.30071 | −0.302528 | −0.151264 | − | 0.988493i | \(-0.548334\pi\) | ||||
−0.151264 | + | 0.988493i | \(0.548334\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.54911 | 0.201576 | ||||||||
\(311\) | 17.3542 | 0.984064 | 0.492032 | − | 0.870577i | \(-0.336254\pi\) | ||||
0.492032 | + | 0.870577i | \(0.336254\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.0377 | −1.81088 | −0.905438 | − | 0.424479i | \(-0.860457\pi\) | ||||
−0.905438 | + | 0.424479i | \(0.860457\pi\) | |||||||
\(314\) | 0.491764 | 0.0277519 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.07012 | 0.172707 | ||||||||
\(317\) | 30.7237 | 1.72561 | 0.862806 | − | 0.505535i | \(-0.168705\pi\) | ||||
0.862806 | + | 0.505535i | \(0.168705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 11.4487 | 0.639999 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0309994 | −0.00172753 | ||||||||
\(323\) | −3.58840 | −0.199664 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.545731 | 0.0302717 | ||||||||
\(326\) | −7.69645 | −0.426267 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.90217 | 0.491540 | ||||||||
\(329\) | 9.19116 | 0.506725 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6112 | 0.803103 | 0.401551 | − | 0.915837i | \(-0.368471\pi\) | ||||
0.401551 | + | 0.915837i | \(0.368471\pi\) | |||||||
\(332\) | −18.6488 | −1.02349 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.67969 | 0.0919086 | ||||||||
\(335\) | −15.2483 | −0.833101 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.43376 | −0.241522 | −0.120761 | − | 0.992682i | \(-0.538533\pi\) | ||||
−0.120761 | + | 0.992682i | \(0.538533\pi\) | |||||||
\(338\) | −3.74827 | −0.203879 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.60097 | −0.303755 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.34893 | 0.450144 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.28911 | −0.338105 | ||||||||
\(347\) | −35.9285 | −1.92875 | −0.964373 | − | 0.264547i | \(-0.914778\pi\) | ||||
−0.964373 | + | 0.264547i | \(0.914778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.4747 | 1.68480 | 0.842401 | − | 0.538852i | \(-0.181142\pi\) | ||||
0.842401 | + | 0.538852i | \(0.181142\pi\) | |||||||
\(350\) | −0.130646 | −0.00698334 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.3003 | −0.867575 | −0.433788 | − | 0.901015i | \(-0.642823\pi\) | ||||
−0.433788 | + | 0.901015i | \(0.642823\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.2628 | 1.02236 | ||||||||
\(356\) | −21.1081 | −1.11873 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.04001 | −0.477779 | ||||||||
\(359\) | 1.02233 | 0.0539566 | 0.0269783 | − | 0.999636i | \(-0.491411\pi\) | ||||
0.0269783 | + | 0.999636i | \(0.491411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2789 | −0.646258 | ||||||||
\(362\) | −7.12980 | −0.374734 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.69034 | 0.141012 | ||||||||
\(365\) | −25.7417 | −1.34738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.2692 | −1.31904 | −0.659520 | − | 0.751687i | \(-0.729240\pi\) | ||||
−0.659520 | + | 0.751687i | \(0.729240\pi\) | |||||||
\(368\) | −0.300150 | −0.0156464 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.0516081 | 0.00268298 | ||||||||
\(371\) | 3.73461 | 0.193891 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.3019 | 1.31008 | 0.655041 | − | 0.755593i | \(-0.272651\pi\) | ||||
0.655041 | + | 0.755593i | \(0.272651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.2071 | −0.629531 | ||||||||
\(377\) | −11.0654 | −0.569900 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.6718 | −1.42141 | −0.710703 | − | 0.703492i | \(-0.751623\pi\) | ||||
−0.710703 | + | 0.703492i | \(0.751623\pi\) | |||||||
\(380\) | 10.4906 | 0.538158 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.321161 | −0.0164320 | ||||||||
\(383\) | 13.9689 | 0.713776 | 0.356888 | − | 0.934147i | \(-0.383838\pi\) | ||||
0.356888 | + | 0.934147i | \(0.383838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.757549 | −0.0385582 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.5541 | 0.535803 | ||||||||
\(389\) | −31.2813 | −1.58603 | −0.793013 | − | 0.609205i | \(-0.791489\pi\) | ||||
−0.793013 | + | 0.609205i | \(0.791489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.125448 | 0.00634415 | ||||||||
\(392\) | −1.32813 | −0.0670807 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.425458 | −0.0214343 | ||||||||
\(395\) | 3.50373 | 0.176292 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.7080 | −1.24006 | −0.620031 | − | 0.784578i | \(-0.712880\pi\) | ||||
−0.620031 | + | 0.784578i | \(0.712880\pi\) | |||||||
\(398\) | −4.58086 | −0.229618 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.26498 | −0.0632489 | ||||||||
\(401\) | 17.0929 | 0.853577 | 0.426788 | − | 0.904351i | \(-0.359645\pi\) | ||||
0.426788 | + | 0.904351i | \(0.359645\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.89879 | 0.343653 | ||||||||
\(404\) | −1.69767 | −0.0844624 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.64903 | 0.131469 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.5499 | 0.719447 | 0.359723 | − | 0.933059i | \(-0.382871\pi\) | ||||
0.359723 | + | 0.933059i | \(0.382871\pi\) | |||||||
\(410\) | 4.92670 | 0.243312 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.8418 | −0.681935 | ||||||||
\(413\) | 9.65657 | 0.475169 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.2827 | −1.04473 | ||||||||
\(416\) | −5.41351 | −0.265419 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.2910 | −0.502750 | −0.251375 | − | 0.967890i | \(-0.580883\pi\) | ||||
−0.251375 | + | 0.967890i | \(0.580883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.19049 | 0.155495 | 0.0777474 | − | 0.996973i | \(-0.475227\pi\) | ||||
0.0777474 | + | 0.996973i | \(0.475227\pi\) | |||||||
\(422\) | −6.55775 | −0.319226 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.96005 | −0.240881 | ||||||||
\(425\) | 0.528696 | 0.0256455 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.33728 | −0.306682 | ||||||||
\(428\) | −10.2446 | −0.495192 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.62052 | 0.222821 | ||||||||
\(431\) | 9.16247 | 0.441341 | 0.220670 | − | 0.975348i | \(-0.429175\pi\) | ||||
0.220670 | + | 0.975348i | \(0.429175\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3185 | 0.640045 | 0.320023 | − | 0.947410i | \(-0.396309\pi\) | ||||
0.320023 | + | 0.947410i | \(0.396309\pi\) | |||||||
\(434\) | −1.65155 | −0.0792769 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.4495 | 0.548331 | ||||||||
\(437\) | −0.234964 | −0.0112398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.75126 | 0.131310 | 0.0656551 | − | 0.997842i | \(-0.479086\pi\) | ||||
0.0656551 | + | 0.997842i | \(0.479086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.676406 | 0.0321734 | ||||||||
\(443\) | 0.431953 | 0.0205227 | 0.0102614 | − | 0.999947i | \(-0.496734\pi\) | ||||
0.0102614 | + | 0.999947i | \(0.496734\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0893 | −1.14194 | ||||||||
\(446\) | 2.70775 | 0.128216 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.32753 | −0.251702 | ||||||||
\(449\) | 1.71629 | 0.0809969 | 0.0404984 | − | 0.999180i | \(-0.487105\pi\) | ||||
0.0404984 | + | 0.999180i | \(0.487105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.88425 | −0.229736 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.67890 | 0.266524 | ||||||||
\(455\) | 3.07031 | 0.143938 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2291 | −0.665611 | −0.332806 | − | 0.942995i | \(-0.607995\pi\) | ||||
−0.332806 | + | 0.942995i | \(0.607995\pi\) | |||||||
\(458\) | −8.36512 | −0.390876 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.366743 | −0.0170995 | ||||||||
\(461\) | −11.3215 | −0.527295 | −0.263647 | − | 0.964619i | \(-0.584926\pi\) | ||||
−0.263647 | + | 0.964619i | \(0.584926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7695 | 1.01171 | 0.505856 | − | 0.862618i | \(-0.331177\pi\) | ||||
0.505856 | + | 0.862618i | \(0.331177\pi\) | |||||||
\(464\) | 25.6492 | 1.19073 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.55659 | −0.211080 | ||||||||
\(467\) | −1.42300 | −0.0658487 | −0.0329243 | − | 0.999458i | \(-0.510482\pi\) | ||||
−0.0329243 | + | 0.999458i | \(0.510482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.09564 | 0.327646 | ||||||||
\(470\) | −6.75571 | −0.311618 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.8252 | −0.590327 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.990250 | −0.0454358 | ||||||||
\(476\) | 2.60636 | 0.119462 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.79792 | 0.127974 | ||||||||
\(479\) | −2.30945 | −0.105521 | −0.0527607 | − | 0.998607i | \(-0.516802\pi\) | ||||
−0.0527607 | + | 0.998607i | \(0.516802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.100316 | 0.00457402 | ||||||||
\(482\) | −0.518366 | −0.0236109 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0447 | 0.546922 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.4197 | −0.970621 | −0.485310 | − | 0.874342i | \(-0.661293\pi\) | ||||
−0.485310 | + | 0.874342i | \(0.661293\pi\) | |||||||
\(488\) | 8.41674 | 0.381008 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.735023 | −0.0332049 | ||||||||
\(491\) | −4.12202 | −0.186024 | −0.0930121 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930121 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.7200 | −0.482807 | ||||||||
\(494\) | −1.26691 | −0.0570010 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.9910 | −0.718019 | ||||||||
\(497\) | −8.96377 | −0.402080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.6026 | −1.54903 | −0.774513 | − | 0.632558i | \(-0.782005\pi\) | ||||
−0.774513 | + | 0.632558i | \(0.782005\pi\) | |||||||
\(500\) | −21.7782 | −0.973952 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.64694 | −0.430564 | ||||||||
\(503\) | 20.2258 | 0.901823 | 0.450912 | − | 0.892569i | \(-0.351099\pi\) | ||||
0.450912 | + | 0.892569i | \(0.351099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.93745 | −0.0862153 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 28.5638 | 1.26732 | ||||||||
\(509\) | −15.2989 | −0.678111 | −0.339055 | − | 0.940766i | \(-0.610107\pi\) | ||||
−0.339055 | + | 0.940766i | \(0.610107\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9787 | 0.529904 | ||||||||
\(512\) | 21.3451 | 0.943330 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.32698 | −0.279071 | ||||||||
\(515\) | −15.7967 | −0.696087 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.0240154 | −0.00105517 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.07778 | −0.178822 | ||||||||
\(521\) | 33.0833 | 1.44941 | 0.724703 | − | 0.689061i | \(-0.241977\pi\) | ||||
0.724703 | + | 0.689061i | \(0.241977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.8339 | −1.65436 | −0.827182 | − | 0.561935i | \(-0.810057\pi\) | ||||
−0.827182 | + | 0.561935i | \(0.810057\pi\) | |||||||
\(524\) | 37.8062 | 1.65157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.34894 | −0.320429 | ||||||||
\(527\) | 6.68345 | 0.291135 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9918 | −0.999643 | ||||||||
\(530\) | −2.74502 | −0.119236 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.88172 | −0.211649 | ||||||||
\(533\) | 9.57654 | 0.414806 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6915 | −0.505469 | ||||||||
\(536\) | −9.42394 | −0.407052 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.32827 | 0.186605 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.62898 | 0.242009 | 0.121004 | − | 0.992652i | \(-0.461389\pi\) | ||||
0.121004 | + | 0.992652i | \(0.461389\pi\) | |||||||
\(542\) | −2.02306 | −0.0868978 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.24453 | −0.224857 | ||||||||
\(545\) | 13.0666 | 0.559711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.5885 | −0.666515 | −0.333257 | − | 0.942836i | \(-0.608148\pi\) | ||||
−0.333257 | + | 0.942836i | \(0.608148\pi\) | |||||||
\(548\) | −15.9050 | −0.679428 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0787 | 0.855380 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.63043 | −0.0693329 | ||||||||
\(554\) | 6.18179 | 0.262639 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.5249 | −0.615995 | ||||||||
\(557\) | −21.7599 | −0.921996 | −0.460998 | − | 0.887401i | \(-0.652508\pi\) | ||||
−0.460998 | + | 0.887401i | \(0.652508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.98140 | 0.379873 | ||||||||
\(560\) | −7.11683 | −0.300741 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.30892 | 0.392673 | ||||||||
\(563\) | 34.0550 | 1.43525 | 0.717624 | − | 0.696431i | \(-0.245230\pi\) | ||||
0.717624 | + | 0.696431i | \(0.245230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.57409 | −0.234504 | ||||||||
\(566\) | 3.46892 | 0.145810 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.9051 | 0.499525 | ||||||||
\(569\) | 13.9128 | 0.583257 | 0.291628 | − | 0.956532i | \(-0.405803\pi\) | ||||
0.291628 | + | 0.956532i | \(0.405803\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.06966 | 0.128461 | 0.0642306 | − | 0.997935i | \(-0.479541\pi\) | ||||
0.0642306 | + | 0.997935i | \(0.479541\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.29259 | −0.0956910 | ||||||||
\(575\) | 0.0346183 | 0.00144368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.00483 | −0.333246 | −0.166623 | − | 0.986021i | \(-0.553286\pi\) | ||||
−0.166623 | + | 0.986021i | \(0.553286\pi\) | |||||||
\(578\) | −5.15933 | −0.214600 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 31.3398 | 1.30132 | ||||||||
\(581\) | 9.90374 | 0.410876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.9092 | −0.658328 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.33783 | 0.220504 | ||||||||
\(587\) | 37.9360 | 1.56579 | 0.782894 | − | 0.622155i | \(-0.213743\pi\) | ||||
0.782894 | + | 0.622155i | \(0.213743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5181 | −0.515800 | ||||||||
\(590\) | −7.09780 | −0.292212 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.232528 | −0.00955683 | ||||||||
\(593\) | 34.8764 | 1.43220 | 0.716101 | − | 0.697997i | \(-0.245925\pi\) | ||||
0.716101 | + | 0.697997i | \(0.245925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.97447 | 0.121941 | ||||||||
\(596\) | 29.5353 | 1.20981 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0442901 | 0.00181116 | ||||||||
\(599\) | −4.02161 | −0.164319 | −0.0821593 | − | 0.996619i | \(-0.526182\pi\) | ||||
−0.0821593 | + | 0.996619i | \(0.526182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.89949 | −0.159063 | −0.0795317 | − | 0.996832i | \(-0.525342\pi\) | ||||
−0.0795317 | + | 0.996832i | \(0.525342\pi\) | |||||||
\(602\) | −2.15012 | −0.0876323 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.7073 | −1.00533 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.4175 | −1.76226 | −0.881131 | − | 0.472872i | \(-0.843217\pi\) | ||||
−0.881131 | + | 0.472872i | \(0.843217\pi\) | |||||||
\(608\) | 9.82301 | 0.398376 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.65805 | 0.188599 | ||||||||
\(611\) | −13.1318 | −0.531255 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.27638 | −0.0919420 | −0.0459710 | − | 0.998943i | \(-0.514638\pi\) | ||||
−0.0459710 | + | 0.998943i | \(0.514638\pi\) | |||||||
\(614\) | −1.81304 | −0.0731682 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −48.3316 | −1.94575 | −0.972877 | − | 0.231321i | \(-0.925695\pi\) | ||||
−0.972877 | + | 0.231321i | \(0.925695\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5642 | −0.906933 | −0.453467 | − | 0.891273i | \(-0.649813\pi\) | ||||
−0.453467 | + | 0.891273i | \(0.649813\pi\) | |||||||
\(620\) | −19.5389 | −0.784702 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.93575 | 0.238002 | ||||||||
\(623\) | 11.2098 | 0.449109 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.9443 | −0.917771 | ||||||||
\(626\) | −10.9580 | −0.437972 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.70731 | −0.108033 | ||||||||
\(629\) | 0.0971848 | 0.00387501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.18412 | 0.325805 | 0.162902 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162902 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(632\) | 2.16542 | 0.0861359 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.5086 | 0.417350 | ||||||||
\(635\) | 32.5981 | 1.29362 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.42874 | −0.0566088 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.2007 | 0.798502 | ||||||||
\(641\) | 2.53026 | 0.0999394 | 0.0499697 | − | 0.998751i | \(-0.484088\pi\) | ||||
0.0499697 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.2359 | −1.82337 | −0.911684 | − | 0.410893i | \(-0.865217\pi\) | ||||
−0.911684 | + | 0.410893i | \(0.865217\pi\) | |||||||
\(644\) | 0.170661 | 0.00672497 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.22736 | −0.0482900 | ||||||||
\(647\) | −20.5421 | −0.807593 | −0.403796 | − | 0.914849i | \(-0.632310\pi\) | ||||
−0.403796 | + | 0.914849i | \(0.632310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.186660 | 0.00732140 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.3712 | 1.65939 | ||||||||
\(653\) | 20.0643 | 0.785177 | 0.392588 | − | 0.919714i | \(-0.371580\pi\) | ||||
0.392588 | + | 0.919714i | \(0.371580\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.1458 | 1.68584 | ||||||||
\(656\) | −22.1980 | −0.866684 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.14371 | 0.122555 | ||||||||
\(659\) | 12.5993 | 0.490800 | 0.245400 | − | 0.969422i | \(-0.421081\pi\) | ||||
0.245400 | + | 0.969422i | \(0.421081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.5153 | 1.22580 | 0.612902 | − | 0.790159i | \(-0.290002\pi\) | ||||
0.612902 | + | 0.790159i | \(0.290002\pi\) | |||||||
\(662\) | 4.99755 | 0.194235 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1535 | −0.510453 | ||||||||
\(665\) | −5.57120 | −0.216042 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.701933 | −0.0271790 | ||||||||
\(668\) | −9.24719 | −0.357785 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.21546 | −0.201491 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.7136 | −1.60794 | −0.803970 | − | 0.594670i | \(-0.797283\pi\) | ||||
−0.803970 | + | 0.594670i | \(0.797283\pi\) | |||||||
\(674\) | −1.51651 | −0.0584136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 20.6353 | 0.793667 | ||||||||
\(677\) | −50.6961 | −1.94841 | −0.974205 | − | 0.225665i | \(-0.927544\pi\) | ||||
−0.974205 | + | 0.225665i | \(0.927544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.60490 | −0.215096 | ||||||||
\(680\) | −3.95049 | −0.151494 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.6596 | 1.24969 | 0.624843 | − | 0.780751i | \(-0.285163\pi\) | ||||
0.624843 | + | 0.780751i | \(0.285163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.1514 | −0.693528 | ||||||||
\(686\) | 0.342036 | 0.0130590 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.8184 | −0.793695 | ||||||||
\(689\) | −5.33579 | −0.203277 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4348 | −0.777378 | −0.388689 | − | 0.921369i | \(-0.627072\pi\) | ||||
−0.388689 | + | 0.921369i | \(0.627072\pi\) | |||||||
\(692\) | 34.6234 | 1.31619 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.2889 | −0.466479 | ||||||||
\(695\) | −16.5764 | −0.628778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.27762 | 0.351415 | ||||||||
\(698\) | 10.7655 | 0.407480 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.719246 | 0.0271850 | ||||||||
\(701\) | −13.9425 | −0.526602 | −0.263301 | − | 0.964714i | \(-0.584811\pi\) | ||||
−0.263301 | + | 0.964714i | \(0.584811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.182027 | −0.00686529 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.57528 | −0.209828 | ||||||||
\(707\) | 0.901574 | 0.0339072 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.6094 | 1.22467 | 0.612337 | − | 0.790597i | \(-0.290230\pi\) | ||||
0.612337 | + | 0.790597i | \(0.290230\pi\) | |||||||
\(710\) | 6.58857 | 0.247265 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.8880 | −0.557952 | ||||||||
\(713\) | 0.437623 | 0.0163891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 49.7679 | 1.85991 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.349675 | 0.0130497 | ||||||||
\(719\) | −3.83226 | −0.142919 | −0.0714595 | − | 0.997444i | \(-0.522766\pi\) | ||||
−0.0714595 | + | 0.997444i | \(0.522766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.35087 | 0.273761 | ||||||||
\(722\) | −4.19983 | −0.156302 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 39.2516 | 1.45878 | ||||||||
\(725\) | −2.95828 | −0.109868 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.9072 | −0.775407 | −0.387703 | − | 0.921784i | \(-0.626732\pi\) | ||||
−0.387703 | + | 0.921784i | \(0.626732\pi\) | |||||||
\(728\) | 1.89756 | 0.0703281 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.80458 | −0.325872 | ||||||||
\(731\) | 8.70105 | 0.321820 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8357 | −0.400225 | −0.200113 | − | 0.979773i | \(-0.564131\pi\) | ||||
−0.200113 | + | 0.979773i | \(0.564131\pi\) | |||||||
\(734\) | −8.64297 | −0.319018 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.343404 | −0.0126580 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.6110 | 0.647832 | 0.323916 | − | 0.946086i | \(-0.395001\pi\) | ||||
0.323916 | + | 0.946086i | \(0.395001\pi\) | |||||||
\(740\) | −0.284118 | −0.0104444 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.27737 | 0.0468938 | ||||||||
\(743\) | −40.1071 | −1.47139 | −0.735694 | − | 0.677314i | \(-0.763144\pi\) | ||||
−0.735694 | + | 0.677314i | \(0.763144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.7068 | 1.23492 | ||||||||
\(746\) | 8.65417 | 0.316852 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.44055 | 0.198793 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4784 | 0.382364 | 0.191182 | − | 0.981555i | \(-0.438768\pi\) | ||||
0.191182 | + | 0.981555i | \(0.438768\pi\) | |||||||
\(752\) | 30.4388 | 1.10999 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.78479 | −0.137834 | ||||||||
\(755\) | −28.1969 | −1.02619 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.8147 | −1.15633 | −0.578163 | − | 0.815921i | \(-0.696230\pi\) | ||||
−0.578163 | + | 0.815921i | \(0.696230\pi\) | |||||||
\(758\) | −9.46477 | −0.343776 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.39928 | 0.268400 | ||||||||
\(761\) | 27.1687 | 0.984866 | 0.492433 | − | 0.870350i | \(-0.336108\pi\) | ||||
0.492433 | + | 0.870350i | \(0.336108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.08042 | −0.220126 | ||||||||
\(764\) | 1.76809 | 0.0639672 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.77786 | 0.172631 | ||||||||
\(767\) | −13.7967 | −0.498172 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.9373 | −0.827141 | −0.413570 | − | 0.910472i | \(-0.635718\pi\) | ||||
−0.413570 | + | 0.910472i | \(0.635718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.17053 | 0.150101 | ||||||||
\(773\) | −5.12745 | −0.184422 | −0.0922108 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922108 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.84435 | 0.0662511 | ||||||||
\(776\) | 7.44404 | 0.267226 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.6993 | −0.383590 | ||||||||
\(779\) | −17.3770 | −0.622596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.0429076 | 0.00153437 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.31175 | 0.118277 | ||||||||
\(785\) | −3.08968 | −0.110275 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.17069 | 0.184315 | 0.0921575 | − | 0.995744i | \(-0.470624\pi\) | ||||
0.0921575 | + | 0.995744i | \(0.470624\pi\) | |||||||
\(788\) | 2.34227 | 0.0834399 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.19840 | 0.0426372 | ||||||||
\(791\) | 2.59385 | 0.0922267 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.05434 | 0.321529 | ||||||||
\(794\) | −8.45105 | −0.299917 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.2190 | 0.893864 | ||||||||
\(797\) | 16.1138 | 0.570779 | 0.285390 | − | 0.958412i | \(-0.407877\pi\) | ||||
0.285390 | + | 0.958412i | \(0.407877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.7219 | −0.450068 | ||||||||
\(800\) | −1.44727 | −0.0511687 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.84638 | 0.206443 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.194764 | 0.00686454 | ||||||||
\(806\) | 2.35964 | 0.0831146 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.19741 | −0.0421247 | ||||||||
\(809\) | 22.0178 | 0.774106 | 0.387053 | − | 0.922057i | \(-0.373493\pi\) | ||||
0.387053 | + | 0.922057i | \(0.373493\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.3784 | 1.90948 | 0.954742 | − | 0.297436i | \(-0.0961315\pi\) | ||||
0.954742 | + | 0.297436i | \(0.0961315\pi\) | |||||||
\(812\) | −14.5837 | −0.511788 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48.3556 | 1.69382 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.2971 | −0.570163 | ||||||||
\(818\) | 4.97660 | 0.174003 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.1229 | −0.947173 | ||||||||
\(821\) | 5.20805 | 0.181762 | 0.0908811 | − | 0.995862i | \(-0.471032\pi\) | ||||
0.0908811 | + | 0.995862i | \(0.471032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6472 | 0.928863 | 0.464431 | − | 0.885609i | \(-0.346259\pi\) | ||||
0.464431 | + | 0.885609i | \(0.346259\pi\) | |||||||
\(824\) | −9.76292 | −0.340107 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.30290 | 0.114923 | ||||||||
\(827\) | −23.7490 | −0.825834 | −0.412917 | − | 0.910769i | \(-0.635490\pi\) | ||||
−0.412917 | + | 0.910769i | \(0.635490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.4053 | −0.430854 | −0.215427 | − | 0.976520i | \(-0.569114\pi\) | ||||
−0.215427 | + | 0.976520i | \(0.569114\pi\) | |||||||
\(830\) | −7.27947 | −0.252674 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.61167 | 0.263887 | ||||||||
\(833\) | −1.38414 | −0.0479578 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5532 | −0.365210 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.51991 | −0.121593 | ||||||||
\(839\) | 5.24545 | 0.181093 | 0.0905464 | − | 0.995892i | \(-0.471139\pi\) | ||||
0.0905464 | + | 0.995892i | \(0.471139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.9833 | 1.06839 | ||||||||
\(842\) | 1.09126 | 0.0376074 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 36.1024 | 1.24269 | ||||||||
\(845\) | 23.5498 | 0.810138 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.3681 | 0.424722 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.180833 | 0.00620253 | ||||||||
\(851\) | 0.00636352 | 0.000218139 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.2236 | 1.65114 | 0.825572 | − | 0.564297i | \(-0.190853\pi\) | ||||
0.825572 | + | 0.564297i | \(0.190853\pi\) | |||||||
\(854\) | −2.16758 | −0.0741731 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.22576 | −0.246972 | ||||||||
\(857\) | 46.9168 | 1.60265 | 0.801323 | − | 0.598232i | \(-0.204130\pi\) | ||||
0.801323 | + | 0.598232i | \(0.204130\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.1096 | 0.924967 | 0.462483 | − | 0.886628i | \(-0.346959\pi\) | ||||
0.462483 | + | 0.886628i | \(0.346959\pi\) | |||||||
\(860\) | −25.4373 | −0.867406 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.13390 | 0.106741 | ||||||||
\(863\) | −53.4934 | −1.82094 | −0.910468 | − | 0.413579i | \(-0.864279\pi\) | ||||
−0.910468 | + | 0.413579i | \(0.864279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.5135 | 1.34350 | ||||||||
\(866\) | 4.55540 | 0.154799 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.09226 | 0.308611 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.1378 | −0.343508 | ||||||||
\(872\) | 8.07559 | 0.273474 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.0803661 | −0.00271842 | ||||||||
\(875\) | 11.5656 | 0.390990 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.7852 | −1.51229 | −0.756144 | − | 0.654405i | \(-0.772919\pi\) | ||||
−0.756144 | + | 0.654405i | \(0.772919\pi\) | |||||||
\(878\) | 0.941029 | 0.0317582 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.08926 | 0.272534 | 0.136267 | − | 0.990672i | \(-0.456489\pi\) | ||||
0.136267 | + | 0.990672i | \(0.456489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.9784 | −0.537715 | −0.268858 | − | 0.963180i | \(-0.586646\pi\) | ||||
−0.268858 | + | 0.963180i | \(0.586646\pi\) | |||||||
\(884\) | −3.72382 | −0.125245 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.147744 | 0.00496355 | ||||||||
\(887\) | 11.9660 | 0.401780 | 0.200890 | − | 0.979614i | \(-0.435617\pi\) | ||||
0.200890 | + | 0.979614i | \(0.435617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.1692 | −0.508760 | ||||||||
\(890\) | −8.23943 | −0.276186 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.9070 | −0.499122 | ||||||||
\(893\) | 23.8281 | 0.797378 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.7970 | 1.89851 | ||||||||
\(896\) | −9.40021 | −0.314039 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.587035 | 0.0195896 | ||||||||
\(899\) | −37.3968 | −1.24725 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.16924 | −0.172212 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.44497 | −0.114578 | ||||||||
\(905\) | 44.7954 | 1.48905 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.50652 | 0.0500231 | 0.0250115 | − | 0.999687i | \(-0.492038\pi\) | ||||
0.0250115 | + | 0.999687i | \(0.492038\pi\) | |||||||
\(908\) | −31.2640 | −1.03753 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.05016 | 0.0348124 | ||||||||
\(911\) | −28.6169 | −0.948120 | −0.474060 | − | 0.880492i | \(-0.657212\pi\) | ||||
−0.474060 | + | 0.880492i | \(0.657212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −4.86689 | −0.160982 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.0525 | 1.52162 | ||||||||
\(917\) | −20.0775 | −0.663017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.5014 | 0.643292 | 0.321646 | − | 0.946860i | \(-0.395764\pi\) | ||||
0.321646 | + | 0.946860i | \(0.395764\pi\) | |||||||
\(920\) | −0.258672 | −0.00852818 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.87236 | −0.127530 | ||||||||
\(923\) | 12.8069 | 0.421545 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0268189 | 0.000881801 0 | ||||||||
\(926\) | 7.44595 | 0.244689 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29.3454 | 0.963310 | ||||||||
\(929\) | 32.1276 | 1.05407 | 0.527036 | − | 0.849843i | \(-0.323303\pi\) | ||||
0.527036 | + | 0.849843i | \(0.323303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.59251 | 0.0849660 | ||||||||
\(932\) | 25.0854 | 0.821699 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.486719 | −0.0159259 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.1102 | 1.24501 | 0.622503 | − | 0.782618i | \(-0.286116\pi\) | ||||
0.622503 | + | 0.782618i | \(0.286116\pi\) | |||||||
\(938\) | 2.42697 | 0.0792433 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 37.1922 | 1.21308 | ||||||||
\(941\) | 38.5091 | 1.25536 | 0.627681 | − | 0.778471i | \(-0.284004\pi\) | ||||
0.627681 | + | 0.778471i | \(0.284004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.607485 | 0.0197824 | ||||||||
\(944\) | 31.9802 | 1.04087 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.6307 | −0.995363 | −0.497681 | − | 0.867360i | \(-0.665815\pi\) | ||||
−0.497681 | + | 0.867360i | \(0.665815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.1144 | −0.555557 | ||||||||
\(950\) | −0.338701 | −0.0109889 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.83833 | 0.0595805 | ||||||||
\(953\) | 22.6934 | 0.735113 | 0.367556 | − | 0.930001i | \(-0.380195\pi\) | ||||
0.367556 | + | 0.930001i | \(0.380195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.01781 | 0.0652947 | ||||||||
\(956\) | −15.4034 | −0.498180 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.789915 | −0.0255210 | ||||||||
\(959\) | 8.44658 | 0.272754 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.68486 | −0.247899 | ||||||||
\(962\) | 0.0343118 | 0.00110626 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.85376 | 0.0919134 | ||||||||
\(965\) | 4.75956 | 0.153216 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.2333 | 1.51892 | 0.759460 | − | 0.650554i | \(-0.225463\pi\) | ||||
0.759460 | + | 0.650554i | \(0.225463\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.11973 | 0.132277 | ||||||||
\(971\) | −9.17271 | −0.294366 | −0.147183 | − | 0.989109i | \(-0.547021\pi\) | ||||
−0.147183 | + | 0.989109i | \(0.547021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.71368 | 0.247289 | ||||||||
\(974\) | −7.32633 | −0.234751 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.9875 | −0.671794 | ||||||||
\(977\) | 30.4667 | 0.974715 | 0.487358 | − | 0.873202i | \(-0.337961\pi\) | ||||
0.487358 | + | 0.873202i | \(0.337961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.04652 | 0.129261 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.40988 | −0.0449911 | ||||||||
\(983\) | −40.1688 | −1.28119 | −0.640593 | − | 0.767881i | \(-0.721311\pi\) | ||||
−0.640593 | + | 0.767881i | \(0.721311\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.67308 | 0.0851716 | ||||||||
\(986\) | −3.66665 | −0.116770 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.97472 | 0.221895 | ||||||||
\(989\) | 0.569732 | 0.0181164 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.77851 | 0.0882624 | 0.0441312 | − | 0.999026i | \(-0.485948\pi\) | ||||
0.0441312 | + | 0.999026i | \(0.485948\pi\) | |||||||
\(992\) | −18.2955 | −0.580882 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.06593 | −0.0972455 | ||||||||
\(995\) | 28.7808 | 0.912414 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.0755 | 0.509117 | 0.254559 | − | 0.967057i | \(-0.418070\pi\) | ||||
0.254559 | + | 0.967057i | \(0.418070\pi\) | |||||||
\(998\) | −11.8354 | −0.374642 | ||||||||
\(999\) | 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 | 7623.2.a.cv.1.5 | 8 | ||
3.2 | odd | 2 | inner | 7623.2.a.cv.1.4 | 8 | ||
11.2 | odd | 10 | 693.2.m.h.631.3 | yes | 16 | ||
11.6 | odd | 10 | 693.2.m.h.190.3 | yes | 16 | ||
11.10 | odd | 2 | 7623.2.a.cu.1.4 | 8 | |||
33.2 | even | 10 | 693.2.m.h.631.2 | yes | 16 | ||
33.17 | even | 10 | 693.2.m.h.190.2 | ✓ | 16 | ||
33.32 | even | 2 | 7623.2.a.cu.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.2.m.h.190.2 | ✓ | 16 | 33.17 | even | 10 | ||
693.2.m.h.190.3 | yes | 16 | 11.6 | odd | 10 | ||
693.2.m.h.631.2 | yes | 16 | 33.2 | even | 10 | ||
693.2.m.h.631.3 | yes | 16 | 11.2 | odd | 10 | ||
7623.2.a.cu.1.4 | 8 | 11.10 | odd | 2 | |||
7623.2.a.cu.1.5 | 8 | 33.32 | even | 2 | |||
7623.2.a.cv.1.4 | 8 | 3.2 | odd | 2 | inner | ||
7623.2.a.cv.1.5 | 8 | 1.1 | even | 1 | trivial |