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: | \(0\) |
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 | 1.5 | ||
Root | \(0.473713\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.473713 | −0.334966 | −0.167483 | − | 0.985875i | \(-0.553564\pi\) | ||||
−0.167483 | + | 0.985875i | \(0.553564\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77560 | −0.887798 | ||||||||
\(5\) | −3.75881 | −1.68099 | −0.840496 | − | 0.541818i | \(-0.817736\pi\) | ||||
−0.840496 | + | 0.541818i | \(0.817736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.78855 | 0.632348 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.78060 | 0.563075 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.70774 | 0.750993 | 0.375496 | − | 0.926824i | \(-0.377472\pi\) | ||||
0.375496 | + | 0.926824i | \(0.377472\pi\) | |||||||
\(14\) | 0.473713 | 0.126605 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.70393 | 0.675983 | ||||||||
\(17\) | −2.48283 | −0.602174 | −0.301087 | − | 0.953597i | \(-0.597349\pi\) | ||||
−0.301087 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.74466 | −0.400253 | −0.200126 | − | 0.979770i | \(-0.564135\pi\) | ||||
−0.200126 | + | 0.979770i | \(0.564135\pi\) | |||||||
\(20\) | 6.67413 | 1.49238 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.79843 | −0.792028 | −0.396014 | − | 0.918244i | \(-0.629607\pi\) | ||||
−0.396014 | + | 0.918244i | \(0.629607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.12868 | 1.82574 | ||||||||
\(26\) | −1.28269 | −0.251557 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.77560 | 0.335556 | ||||||||
\(29\) | 5.80060 | 1.07714 | 0.538572 | − | 0.842580i | \(-0.318964\pi\) | ||||
0.538572 | + | 0.842580i | \(0.318964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.24763 | 0.403686 | 0.201843 | − | 0.979418i | \(-0.435307\pi\) | ||||
0.201843 | + | 0.979418i | \(0.435307\pi\) | |||||||
\(32\) | −4.85799 | −0.858779 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.17615 | 0.201707 | ||||||||
\(35\) | 3.75881 | 0.635355 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.65311 | −1.25816 | −0.629082 | − | 0.777339i | \(-0.716569\pi\) | ||||
−0.629082 | + | 0.777339i | \(0.716569\pi\) | |||||||
\(38\) | 0.826469 | 0.134071 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.72282 | −1.06297 | ||||||||
\(41\) | 4.18500 | 0.653587 | 0.326793 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326793 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.75162 | 1.18211 | 0.591056 | − | 0.806631i | \(-0.298711\pi\) | ||||
0.591056 | + | 0.806631i | \(0.298711\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.79937 | 0.265302 | ||||||||
\(47\) | −12.4071 | −1.80976 | −0.904878 | − | 0.425670i | \(-0.860038\pi\) | ||||
−0.904878 | + | 0.425670i | \(0.860038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.32437 | −0.611559 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.80786 | −0.666730 | ||||||||
\(53\) | −8.83956 | −1.21421 | −0.607103 | − | 0.794623i | \(-0.707669\pi\) | ||||
−0.607103 | + | 0.794623i | \(0.707669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.78855 | −0.239005 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.74782 | −0.360806 | ||||||||
\(59\) | −4.54166 | −0.591274 | −0.295637 | − | 0.955300i | \(-0.595532\pi\) | ||||
−0.295637 | + | 0.955300i | \(0.595532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4825 | −1.47019 | −0.735093 | − | 0.677967i | \(-0.762861\pi\) | ||||
−0.735093 | + | 0.677967i | \(0.762861\pi\) | |||||||
\(62\) | −1.06473 | −0.135221 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.10658 | −0.388322 | ||||||||
\(65\) | −10.1779 | −1.26241 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2041 | −1.49096 | −0.745481 | − | 0.666527i | \(-0.767780\pi\) | ||||
−0.745481 | + | 0.666527i | \(0.767780\pi\) | |||||||
\(68\) | 4.40849 | 0.534609 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.78060 | −0.212822 | ||||||||
\(71\) | −7.75988 | −0.920928 | −0.460464 | − | 0.887678i | \(-0.652317\pi\) | ||||
−0.460464 | + | 0.887678i | \(0.652317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6796 | 1.83516 | 0.917580 | − | 0.397552i | \(-0.130140\pi\) | ||||
0.917580 | + | 0.397552i | \(0.130140\pi\) | |||||||
\(74\) | 3.62538 | 0.421441 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.09781 | 0.355344 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.05380 | −0.793615 | −0.396807 | − | 0.917902i | \(-0.629882\pi\) | ||||
−0.396807 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(80\) | −10.1636 | −1.13632 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.98249 | −0.218929 | ||||||||
\(83\) | −11.9004 | −1.30624 | −0.653122 | − | 0.757253i | \(-0.726541\pi\) | ||||
−0.653122 | + | 0.757253i | \(0.726541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.33248 | 1.01225 | ||||||||
\(86\) | −3.67204 | −0.395967 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.69179 | 0.179329 | 0.0896647 | − | 0.995972i | \(-0.471420\pi\) | ||||
0.0896647 | + | 0.995972i | \(0.471420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70774 | −0.283848 | ||||||||
\(92\) | 6.74448 | 0.703161 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.87739 | 0.606206 | ||||||||
\(95\) | 6.55786 | 0.672822 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.99638 | 0.710375 | 0.355188 | − | 0.934795i | \(-0.384417\pi\) | ||||
0.355188 | + | 0.934795i | \(0.384417\pi\) | |||||||
\(98\) | −0.473713 | −0.0478522 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.2088 | −1.62088 | ||||||||
\(101\) | −2.71683 | −0.270335 | −0.135167 | − | 0.990823i | \(-0.543157\pi\) | ||||
−0.135167 | + | 0.990823i | \(0.543157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.255788 | −0.0252036 | −0.0126018 | − | 0.999921i | \(-0.504011\pi\) | ||||
−0.0126018 | + | 0.999921i | \(0.504011\pi\) | |||||||
\(104\) | 4.84293 | 0.474888 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.18741 | 0.406717 | ||||||||
\(107\) | −11.8608 | −1.14662 | −0.573311 | − | 0.819338i | \(-0.694341\pi\) | ||||
−0.573311 | + | 0.819338i | \(0.694341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.8720 | −1.52026 | −0.760129 | − | 0.649772i | \(-0.774864\pi\) | ||||
−0.760129 | + | 0.649772i | \(0.774864\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.70393 | −0.255498 | ||||||||
\(113\) | 5.11650 | 0.481320 | 0.240660 | − | 0.970609i | \(-0.422636\pi\) | ||||
0.240660 | + | 0.970609i | \(0.422636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.2776 | 1.33139 | ||||||||
\(116\) | −10.2995 | −0.956286 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.15144 | 0.198056 | ||||||||
\(119\) | 2.48283 | 0.227600 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.43942 | 0.492462 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.99088 | −0.358392 | ||||||||
\(125\) | −15.5189 | −1.38805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.203338 | 0.0180433 | 0.00902166 | − | 0.999959i | \(-0.497128\pi\) | ||||
0.00902166 | + | 0.999959i | \(0.497128\pi\) | |||||||
\(128\) | 11.1876 | 0.988853 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.82140 | 0.422865 | ||||||||
\(131\) | 10.2788 | 0.898067 | 0.449034 | − | 0.893515i | \(-0.351768\pi\) | ||||
0.449034 | + | 0.893515i | \(0.351768\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.74466 | 0.151281 | ||||||||
\(134\) | 5.78122 | 0.499421 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.44065 | −0.380783 | ||||||||
\(137\) | 17.1096 | 1.46177 | 0.730887 | − | 0.682499i | \(-0.239107\pi\) | ||||
0.730887 | + | 0.682499i | \(0.239107\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.5009 | 1.65405 | 0.827023 | − | 0.562168i | \(-0.190032\pi\) | ||||
0.827023 | + | 0.562168i | \(0.190032\pi\) | |||||||
\(140\) | −6.67413 | −0.564067 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.67596 | 0.308479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.8034 | −1.81067 | ||||||||
\(146\) | −7.42763 | −0.614715 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.5888 | 1.11699 | ||||||||
\(149\) | 9.89037 | 0.810251 | 0.405125 | − | 0.914261i | \(-0.367228\pi\) | ||||
0.405125 | + | 0.914261i | \(0.367228\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5014 | −1.26148 | −0.630741 | − | 0.775993i | \(-0.717249\pi\) | ||||
−0.630741 | + | 0.775993i | \(0.717249\pi\) | |||||||
\(152\) | −3.12041 | −0.253099 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.44843 | −0.678594 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9536 | 1.35305 | 0.676523 | − | 0.736422i | \(-0.263486\pi\) | ||||
0.676523 | + | 0.736422i | \(0.263486\pi\) | |||||||
\(158\) | 3.34148 | 0.265834 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.2603 | 1.44360 | ||||||||
\(161\) | 3.79843 | 0.299359 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.9739 | 1.56447 | 0.782237 | − | 0.622981i | \(-0.214079\pi\) | ||||
0.782237 | + | 0.622981i | \(0.214079\pi\) | |||||||
\(164\) | −7.43086 | −0.580253 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.63739 | 0.437547 | ||||||||
\(167\) | −17.4516 | −1.35044 | −0.675222 | − | 0.737615i | \(-0.735952\pi\) | ||||
−0.675222 | + | 0.737615i | \(0.735952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.66813 | −0.436010 | ||||||||
\(170\) | −4.42092 | −0.339069 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.7637 | −1.04948 | ||||||||
\(173\) | 9.35944 | 0.711585 | 0.355793 | − | 0.934565i | \(-0.384211\pi\) | ||||
0.355793 | + | 0.934565i | \(0.384211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.12868 | −0.690063 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.801423 | −0.0600692 | ||||||||
\(179\) | −5.49347 | −0.410602 | −0.205301 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205301 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1844 | −0.831332 | −0.415666 | − | 0.909517i | \(-0.636451\pi\) | ||||
−0.415666 | + | 0.909517i | \(0.636451\pi\) | |||||||
\(182\) | 1.28269 | 0.0950795 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.79369 | −0.500837 | ||||||||
\(185\) | 28.7666 | 2.11496 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 22.0299 | 1.60670 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.10654 | −0.225372 | ||||||||
\(191\) | 5.75822 | 0.416650 | 0.208325 | − | 0.978060i | \(-0.433199\pi\) | ||||
0.208325 | + | 0.978060i | \(0.433199\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.8846 | −1.07142 | −0.535708 | − | 0.844404i | \(-0.679955\pi\) | ||||
−0.535708 | + | 0.844404i | \(0.679955\pi\) | |||||||
\(194\) | −3.31428 | −0.237951 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.77560 | −0.126828 | ||||||||
\(197\) | −12.5476 | −0.893978 | −0.446989 | − | 0.894540i | \(-0.647504\pi\) | ||||
−0.446989 | + | 0.894540i | \(0.647504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.834418 | 0.0591503 | 0.0295752 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295752 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(200\) | 16.3271 | 1.15450 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.28700 | 0.0905528 | ||||||||
\(203\) | −5.80060 | −0.407122 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.7306 | −1.09867 | ||||||||
\(206\) | 0.121170 | 0.00844233 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.32155 | 0.507658 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.8703 | −1.84983 | −0.924914 | − | 0.380176i | \(-0.875863\pi\) | ||||
−0.924914 | + | 0.380176i | \(0.875863\pi\) | |||||||
\(212\) | 15.6955 | 1.07797 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.61859 | 0.384079 | ||||||||
\(215\) | −29.1369 | −1.98712 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.24763 | −0.152579 | ||||||||
\(218\) | 7.51876 | 0.509234 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.72285 | −0.452228 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.01918 | 0.269144 | 0.134572 | − | 0.990904i | \(-0.457034\pi\) | ||||
0.134572 | + | 0.990904i | \(0.457034\pi\) | |||||||
\(224\) | 4.85799 | 0.324588 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.42375 | −0.161226 | ||||||||
\(227\) | 11.7020 | 0.776690 | 0.388345 | − | 0.921514i | \(-0.373047\pi\) | ||||
0.388345 | + | 0.921514i | \(0.373047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.54504 | −0.432508 | −0.216254 | − | 0.976337i | \(-0.569384\pi\) | ||||
−0.216254 | + | 0.976337i | \(0.569384\pi\) | |||||||
\(230\) | −6.76349 | −0.445971 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.3746 | 0.681129 | ||||||||
\(233\) | −0.172567 | −0.0113052 | −0.00565262 | − | 0.999984i | \(-0.501799\pi\) | ||||
−0.00565262 | + | 0.999984i | \(0.501799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 46.6358 | 3.04219 | ||||||||
\(236\) | 8.06415 | 0.524932 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.17615 | −0.0762383 | ||||||||
\(239\) | 10.4504 | 0.675982 | 0.337991 | − | 0.941149i | \(-0.390253\pi\) | ||||
0.337991 | + | 0.941149i | \(0.390253\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.41821 | −0.220186 | −0.110093 | − | 0.993921i | \(-0.535115\pi\) | ||||
−0.110093 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.3883 | 1.30523 | ||||||||
\(245\) | −3.75881 | −0.240142 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.72409 | −0.300587 | ||||||||
\(248\) | 4.02000 | 0.255270 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.35151 | 0.464951 | ||||||||
\(251\) | −12.6751 | −0.800047 | −0.400024 | − | 0.916505i | \(-0.630998\pi\) | ||||
−0.400024 | + | 0.916505i | \(0.630998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.0963238 | −0.00604389 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.913441 | 0.0570901 | ||||||||
\(257\) | 18.1852 | 1.13436 | 0.567182 | − | 0.823593i | \(-0.308034\pi\) | ||||
0.567182 | + | 0.823593i | \(0.308034\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.65311 | 0.475541 | ||||||||
\(260\) | 18.0718 | 1.12077 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.86922 | −0.300822 | ||||||||
\(263\) | −15.7837 | −0.973264 | −0.486632 | − | 0.873607i | \(-0.661775\pi\) | ||||
−0.486632 | + | 0.873607i | \(0.661775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.2262 | 2.04107 | ||||||||
\(266\) | −0.826469 | −0.0506741 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.6695 | 1.32367 | ||||||||
\(269\) | −22.9896 | −1.40170 | −0.700851 | − | 0.713308i | \(-0.747196\pi\) | ||||
−0.700851 | + | 0.713308i | \(0.747196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.34021 | 0.567377 | 0.283689 | − | 0.958916i | \(-0.408442\pi\) | ||||
0.283689 | + | 0.958916i | \(0.408442\pi\) | |||||||
\(272\) | −6.71339 | −0.407059 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.10505 | −0.489644 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.4367 | 1.16784 | 0.583918 | − | 0.811813i | \(-0.301519\pi\) | ||||
0.583918 | + | 0.811813i | \(0.301519\pi\) | |||||||
\(278\) | −9.23784 | −0.554049 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.72282 | 0.401765 | ||||||||
\(281\) | 4.44358 | 0.265082 | 0.132541 | − | 0.991178i | \(-0.457686\pi\) | ||||
0.132541 | + | 0.991178i | \(0.457686\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8486 | 0.823216 | 0.411608 | − | 0.911361i | \(-0.364967\pi\) | ||||
0.411608 | + | 0.911361i | \(0.364967\pi\) | |||||||
\(284\) | 13.7784 | 0.817598 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.18500 | −0.247033 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8356 | −0.637387 | ||||||||
\(290\) | 10.3285 | 0.606512 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −27.8406 | −1.62925 | ||||||||
\(293\) | 19.2359 | 1.12377 | 0.561887 | − | 0.827214i | \(-0.310076\pi\) | ||||
0.561887 | + | 0.827214i | \(0.310076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.0713 | 0.993927 | ||||||||
\(296\) | −13.6880 | −0.795596 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.68520 | −0.271406 | ||||||||
\(299\) | −10.2852 | −0.594807 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.75162 | −0.446796 | ||||||||
\(302\) | 7.34319 | 0.422553 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.71745 | −0.270564 | ||||||||
\(305\) | 43.1606 | 2.47137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.24474 | 0.128114 | 0.0640571 | − | 0.997946i | \(-0.479596\pi\) | ||||
0.0640571 | + | 0.997946i | \(0.479596\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00213 | 0.227306 | ||||||||
\(311\) | −12.6291 | −0.716129 | −0.358065 | − | 0.933697i | \(-0.616563\pi\) | ||||
−0.358065 | + | 0.933697i | \(0.616563\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.06646 | 0.0602797 | 0.0301398 | − | 0.999546i | \(-0.490405\pi\) | ||||
0.0301398 | + | 0.999546i | \(0.490405\pi\) | |||||||
\(314\) | −8.03115 | −0.453224 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.5247 | 0.704569 | ||||||||
\(317\) | 25.1710 | 1.41374 | 0.706872 | − | 0.707342i | \(-0.250106\pi\) | ||||
0.706872 | + | 0.707342i | \(0.250106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 11.6770 | 0.652766 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.79937 | −0.100275 | ||||||||
\(323\) | 4.33169 | 0.241022 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.7181 | 1.37111 | ||||||||
\(326\) | −9.46188 | −0.524045 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.48507 | 0.413294 | ||||||||
\(329\) | 12.4071 | 0.684024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.53640 | −0.469203 | −0.234601 | − | 0.972092i | \(-0.575378\pi\) | ||||
−0.234601 | + | 0.972092i | \(0.575378\pi\) | |||||||
\(332\) | 21.1304 | 1.15968 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.26704 | 0.452352 | ||||||||
\(335\) | 45.8728 | 2.50630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2565 | −0.940020 | −0.470010 | − | 0.882661i | \(-0.655750\pi\) | ||||
−0.470010 | + | 0.882661i | \(0.655750\pi\) | |||||||
\(338\) | 2.68507 | 0.146048 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.5707 | −0.898673 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 13.8642 | 0.747505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.43369 | −0.238357 | ||||||||
\(347\) | −4.15698 | −0.223159 | −0.111579 | − | 0.993756i | \(-0.535591\pi\) | ||||
−0.111579 | + | 0.993756i | \(0.535591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.70785 | 0.412592 | 0.206296 | − | 0.978490i | \(-0.433859\pi\) | ||||
0.206296 | + | 0.978490i | \(0.433859\pi\) | |||||||
\(350\) | 4.32437 | 0.231147 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.84242 | 0.257736 | 0.128868 | − | 0.991662i | \(-0.458866\pi\) | ||||
0.128868 | + | 0.991662i | \(0.458866\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.1679 | 1.54807 | ||||||||
\(356\) | −3.00393 | −0.159208 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.60233 | 0.137537 | ||||||||
\(359\) | −4.41834 | −0.233191 | −0.116596 | − | 0.993179i | \(-0.537198\pi\) | ||||
−0.116596 | + | 0.993179i | \(0.537198\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9562 | −0.839798 | ||||||||
\(362\) | 5.29821 | 0.278468 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.80786 | 0.252000 | ||||||||
\(365\) | −58.9367 | −3.08489 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.5315 | −1.54153 | −0.770766 | − | 0.637118i | \(-0.780126\pi\) | ||||
−0.770766 | + | 0.637118i | \(0.780126\pi\) | |||||||
\(368\) | −10.2707 | −0.535398 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.6271 | −0.708440 | ||||||||
\(371\) | 8.83956 | 0.458927 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.64965 | 0.396084 | 0.198042 | − | 0.980194i | \(-0.436542\pi\) | ||||
0.198042 | + | 0.980194i | \(0.436542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.1906 | −1.14440 | ||||||||
\(377\) | 15.7065 | 0.808927 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2094 | −0.575788 | −0.287894 | − | 0.957662i | \(-0.592955\pi\) | ||||
−0.287894 | + | 0.957662i | \(0.592955\pi\) | |||||||
\(380\) | −11.6441 | −0.597330 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.72774 | −0.139563 | ||||||||
\(383\) | 24.7447 | 1.26440 | 0.632199 | − | 0.774806i | \(-0.282153\pi\) | ||||
0.632199 | + | 0.774806i | \(0.282153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.05102 | 0.358887 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.4228 | −0.630670 | ||||||||
\(389\) | 29.0347 | 1.47212 | 0.736060 | − | 0.676917i | \(-0.236684\pi\) | ||||
0.736060 | + | 0.676917i | \(0.236684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.43085 | 0.476939 | ||||||||
\(392\) | 1.78855 | 0.0903354 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.94395 | 0.299452 | ||||||||
\(395\) | 26.5139 | 1.33406 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.27461 | −0.415291 | −0.207645 | − | 0.978204i | \(-0.566580\pi\) | ||||
−0.207645 | + | 0.978204i | \(0.566580\pi\) | |||||||
\(398\) | −0.395275 | −0.0198133 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.6833 | 1.23417 | ||||||||
\(401\) | 26.7390 | 1.33528 | 0.667642 | − | 0.744483i | \(-0.267304\pi\) | ||||
0.667642 | + | 0.744483i | \(0.267304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.08601 | 0.303166 | ||||||||
\(404\) | 4.82399 | 0.240003 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.74782 | 0.136372 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.6829 | 1.71496 | 0.857479 | − | 0.514519i | \(-0.172030\pi\) | ||||
0.857479 | + | 0.514519i | \(0.172030\pi\) | |||||||
\(410\) | 7.45180 | 0.368018 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.454177 | 0.0223757 | ||||||||
\(413\) | 4.54166 | 0.223480 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.7315 | 2.19578 | ||||||||
\(416\) | −13.1542 | −0.644936 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.34546 | 0.212290 | 0.106145 | − | 0.994351i | \(-0.466149\pi\) | ||||
0.106145 | + | 0.994351i | \(0.466149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.73841 | −0.230936 | −0.115468 | − | 0.993311i | \(-0.536837\pi\) | ||||
−0.115468 | + | 0.993311i | \(0.536837\pi\) | |||||||
\(422\) | 12.7288 | 0.619629 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.8100 | −0.767800 | ||||||||
\(425\) | −22.6649 | −1.09941 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.4825 | 0.555678 | ||||||||
\(428\) | 21.0599 | 1.01797 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.8025 | 0.665617 | ||||||||
\(431\) | 29.8622 | 1.43841 | 0.719206 | − | 0.694797i | \(-0.244506\pi\) | ||||
0.719206 | + | 0.694797i | \(0.244506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7239 | −1.04399 | −0.521993 | − | 0.852950i | \(-0.674811\pi\) | ||||
−0.521993 | + | 0.852950i | \(0.674811\pi\) | |||||||
\(434\) | 1.06473 | 0.0511088 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.1822 | 1.34968 | ||||||||
\(437\) | 6.62698 | 0.317012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.3447 | −1.92555 | −0.962773 | − | 0.270313i | \(-0.912873\pi\) | ||||
−0.962773 | + | 0.270313i | \(0.912873\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.18470 | 0.151481 | ||||||||
\(443\) | 13.8789 | 0.659408 | 0.329704 | − | 0.944084i | \(-0.393051\pi\) | ||||
0.329704 | + | 0.944084i | \(0.393051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.35912 | −0.301451 | ||||||||
\(446\) | −1.90394 | −0.0901540 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.10658 | 0.146772 | ||||||||
\(449\) | 14.3023 | 0.674966 | 0.337483 | − | 0.941332i | \(-0.390425\pi\) | ||||
0.337483 | + | 0.941332i | \(0.390425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.08484 | −0.427315 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.54340 | −0.260164 | ||||||||
\(455\) | 10.1779 | 0.477147 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.1278 | −0.660869 | −0.330435 | − | 0.943829i | \(-0.607195\pi\) | ||||
−0.330435 | + | 0.943829i | \(0.607195\pi\) | |||||||
\(458\) | 3.10047 | 0.144875 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −25.3513 | −1.18201 | ||||||||
\(461\) | 0.966736 | 0.0450254 | 0.0225127 | − | 0.999747i | \(-0.492833\pi\) | ||||
0.0225127 | + | 0.999747i | \(0.492833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.8119 | 1.47842 | 0.739212 | − | 0.673473i | \(-0.235198\pi\) | ||||
0.739212 | + | 0.673473i | \(0.235198\pi\) | |||||||
\(464\) | 15.6844 | 0.728131 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0817473 | 0.00378687 | ||||||||
\(467\) | 29.6133 | 1.37034 | 0.685169 | − | 0.728384i | \(-0.259728\pi\) | ||||
0.685169 | + | 0.728384i | \(0.259728\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.2041 | 0.563531 | ||||||||
\(470\) | −22.0920 | −1.01903 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.12298 | −0.373891 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.9264 | −0.730756 | ||||||||
\(476\) | −4.40849 | −0.202063 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.95051 | −0.226431 | ||||||||
\(479\) | 26.5853 | 1.21471 | 0.607356 | − | 0.794430i | \(-0.292230\pi\) | ||||
0.607356 | + | 0.794430i | \(0.292230\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7226 | −0.944871 | ||||||||
\(482\) | 1.61925 | 0.0737548 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.2981 | −1.19414 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.1343 | 0.640486 | 0.320243 | − | 0.947335i | \(-0.396235\pi\) | ||||
0.320243 | + | 0.947335i | \(0.396235\pi\) | |||||||
\(488\) | −20.5370 | −0.929668 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.78060 | 0.0804392 | ||||||||
\(491\) | −15.4186 | −0.695831 | −0.347916 | − | 0.937526i | \(-0.613110\pi\) | ||||
−0.347916 | + | 0.937526i | \(0.613110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.4019 | −0.648627 | ||||||||
\(494\) | 2.23786 | 0.100686 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.07744 | 0.272885 | ||||||||
\(497\) | 7.75988 | 0.348078 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.7024 | 1.37443 | 0.687214 | − | 0.726455i | \(-0.258833\pi\) | ||||
0.687214 | + | 0.726455i | \(0.258833\pi\) | |||||||
\(500\) | 27.5553 | 1.23231 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00438 | 0.267988 | ||||||||
\(503\) | 18.1890 | 0.811005 | 0.405503 | − | 0.914094i | \(-0.367096\pi\) | ||||
0.405503 | + | 0.914094i | \(0.367096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2121 | 0.454431 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.361046 | −0.0160188 | ||||||||
\(509\) | 32.1744 | 1.42611 | 0.713054 | − | 0.701110i | \(-0.247312\pi\) | ||||
0.713054 | + | 0.701110i | \(0.247312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.6796 | −0.693625 | ||||||||
\(512\) | −22.8079 | −1.00798 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.61458 | −0.379973 | ||||||||
\(515\) | 0.961461 | 0.0423670 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.62538 | −0.159290 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.2037 | −0.798284 | ||||||||
\(521\) | 27.8238 | 1.21898 | 0.609490 | − | 0.792793i | \(-0.291374\pi\) | ||||
0.609490 | + | 0.792793i | \(0.291374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.1282 | −0.836419 | −0.418209 | − | 0.908351i | \(-0.637342\pi\) | ||||
−0.418209 | + | 0.908351i | \(0.637342\pi\) | |||||||
\(524\) | −18.2511 | −0.797302 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.47694 | 0.326010 | ||||||||
\(527\) | −5.58048 | −0.243089 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.57190 | −0.372691 | ||||||||
\(530\) | −15.7397 | −0.683689 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.09781 | −0.134307 | ||||||||
\(533\) | 11.3319 | 0.490839 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 44.5824 | 1.92746 | ||||||||
\(536\) | −21.8275 | −0.942806 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.8905 | 0.469522 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.6820 | 1.83504 | 0.917521 | − | 0.397688i | \(-0.130187\pi\) | ||||
0.917521 | + | 0.397688i | \(0.130187\pi\) | |||||||
\(542\) | −4.42458 | −0.190052 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.0615 | 0.517134 | ||||||||
\(545\) | 59.6597 | 2.55554 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.1162 | −1.07389 | −0.536946 | − | 0.843617i | \(-0.680422\pi\) | ||||
−0.536946 | + | 0.843617i | \(0.680422\pi\) | |||||||
\(548\) | −30.3798 | −1.29776 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.1201 | −0.431130 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.05380 | 0.299958 | ||||||||
\(554\) | −9.20740 | −0.391185 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −34.6258 | −1.46846 | ||||||||
\(557\) | 4.25720 | 0.180383 | 0.0901917 | − | 0.995924i | \(-0.471252\pi\) | ||||
0.0901917 | + | 0.995924i | \(0.471252\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.9894 | 0.887757 | ||||||||
\(560\) | 10.1636 | 0.429490 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.10498 | −0.0887933 | ||||||||
\(563\) | 7.43714 | 0.313438 | 0.156719 | − | 0.987643i | \(-0.449908\pi\) | ||||
0.156719 | + | 0.987643i | \(0.449908\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.2320 | −0.809096 | ||||||||
\(566\) | −6.56028 | −0.275749 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.8789 | −0.582347 | ||||||||
\(569\) | −43.6293 | −1.82904 | −0.914518 | − | 0.404546i | \(-0.867430\pi\) | ||||
−0.914518 | + | 0.404546i | \(0.867430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1074 | −1.42735 | −0.713676 | − | 0.700476i | \(-0.752971\pi\) | ||||
−0.713676 | + | 0.700476i | \(0.752971\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.98249 | 0.0827474 | ||||||||
\(575\) | −34.6747 | −1.44603 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.0804 | 1.16900 | 0.584501 | − | 0.811393i | \(-0.301290\pi\) | ||||
0.584501 | + | 0.811393i | \(0.301290\pi\) | |||||||
\(578\) | 5.13295 | 0.213503 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 38.7140 | 1.60751 | ||||||||
\(581\) | 11.9004 | 0.493713 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 28.0437 | 1.16046 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.11230 | −0.376426 | ||||||||
\(587\) | 6.72735 | 0.277668 | 0.138834 | − | 0.990316i | \(-0.455665\pi\) | ||||
0.138834 | + | 0.990316i | \(0.455665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.92136 | −0.161577 | ||||||||
\(590\) | −8.08687 | −0.332931 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.6935 | −0.850497 | ||||||||
\(593\) | −20.8442 | −0.855969 | −0.427984 | − | 0.903786i | \(-0.640776\pi\) | ||||
−0.427984 | + | 0.903786i | \(0.640776\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.33248 | −0.382594 | ||||||||
\(596\) | −17.5613 | −0.719339 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.87222 | 0.199240 | ||||||||
\(599\) | −0.180675 | −0.00738218 | −0.00369109 | − | 0.999993i | \(-0.501175\pi\) | ||||
−0.00369109 | + | 0.999993i | \(0.501175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.6043 | 1.12600 | 0.563001 | − | 0.826456i | \(-0.309647\pi\) | ||||
0.563001 | + | 0.826456i | \(0.309647\pi\) | |||||||
\(602\) | 3.67204 | 0.149661 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.5241 | 1.11994 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.3280 | 0.946854 | 0.473427 | − | 0.880833i | \(-0.343017\pi\) | ||||
0.473427 | + | 0.880833i | \(0.343017\pi\) | |||||||
\(608\) | 8.47554 | 0.343729 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.4457 | −0.827824 | ||||||||
\(611\) | −33.5951 | −1.35911 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.5003 | −0.787608 | −0.393804 | − | 0.919194i | \(-0.628841\pi\) | ||||
−0.393804 | + | 0.919194i | \(0.628841\pi\) | |||||||
\(614\) | −1.06336 | −0.0429139 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2566 | 0.936276 | 0.468138 | − | 0.883655i | \(-0.344925\pi\) | ||||
0.468138 | + | 0.883655i | \(0.344925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5491 | −1.14749 | −0.573743 | − | 0.819035i | \(-0.694509\pi\) | ||||
−0.573743 | + | 0.819035i | \(0.694509\pi\) | |||||||
\(620\) | 15.0010 | 0.602454 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.98256 | 0.239879 | ||||||||
\(623\) | −1.69179 | −0.0677801 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.6893 | 0.507574 | ||||||||
\(626\) | −0.505194 | −0.0201916 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.1028 | −1.20123 | ||||||||
\(629\) | 19.0013 | 0.757633 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.30112 | 0.211034 | 0.105517 | − | 0.994417i | \(-0.466350\pi\) | ||||
0.105517 | + | 0.994417i | \(0.466350\pi\) | |||||||
\(632\) | −12.6161 | −0.501840 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.9238 | −0.473556 | ||||||||
\(635\) | −0.764309 | −0.0303307 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.70774 | 0.107285 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −42.0521 | −1.66225 | ||||||||
\(641\) | 29.8881 | 1.18051 | 0.590255 | − | 0.807217i | \(-0.299027\pi\) | ||||
0.590255 | + | 0.807217i | \(0.299027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4403 | 1.51594 | 0.757969 | − | 0.652291i | \(-0.226192\pi\) | ||||
0.757969 | + | 0.652291i | \(0.226192\pi\) | |||||||
\(644\) | −6.74448 | −0.265770 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.05198 | −0.0807340 | ||||||||
\(647\) | 32.3602 | 1.27221 | 0.636105 | − | 0.771603i | \(-0.280545\pi\) | ||||
0.636105 | + | 0.771603i | \(0.280545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −11.7093 | −0.459276 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −35.4655 | −1.38894 | ||||||||
\(653\) | −23.9046 | −0.935459 | −0.467729 | − | 0.883872i | \(-0.654928\pi\) | ||||
−0.467729 | + | 0.883872i | \(0.654928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.6363 | −1.50964 | ||||||||
\(656\) | 11.3160 | 0.441814 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.87739 | −0.229124 | ||||||||
\(659\) | −34.5124 | −1.34441 | −0.672205 | − | 0.740365i | \(-0.734653\pi\) | ||||
−0.672205 | + | 0.740365i | \(0.734653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.56237 | −0.0996647 | −0.0498324 | − | 0.998758i | \(-0.515869\pi\) | ||||
−0.0498324 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(662\) | 4.04380 | 0.157167 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.2845 | −0.826000 | ||||||||
\(665\) | −6.55786 | −0.254303 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0332 | −0.853128 | ||||||||
\(668\) | 30.9869 | 1.19892 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.7305 | −0.839523 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6670 | 1.41341 | 0.706704 | − | 0.707509i | \(-0.250181\pi\) | ||||
0.706704 | + | 0.707509i | \(0.250181\pi\) | |||||||
\(674\) | 8.17462 | 0.314874 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.0643 | 0.387089 | ||||||||
\(677\) | −31.9812 | −1.22914 | −0.614568 | − | 0.788864i | \(-0.710670\pi\) | ||||
−0.614568 | + | 0.788864i | \(0.710670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.99638 | −0.268497 | ||||||||
\(680\) | 16.6916 | 0.640093 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.96871 | −0.266650 | −0.133325 | − | 0.991072i | \(-0.542565\pi\) | ||||
−0.133325 | + | 0.991072i | \(0.542565\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −64.3119 | −2.45723 | ||||||||
\(686\) | 0.473713 | 0.0180864 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.9599 | 0.799087 | ||||||||
\(689\) | −23.9352 | −0.911860 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.07203 | −0.192949 | −0.0964746 | − | 0.995335i | \(-0.530757\pi\) | ||||
−0.0964746 | + | 0.995335i | \(0.530757\pi\) | |||||||
\(692\) | −16.6186 | −0.631744 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.96922 | 0.0747505 | ||||||||
\(695\) | −73.3003 | −2.78044 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.3906 | −0.393573 | ||||||||
\(698\) | −3.65131 | −0.138204 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.2088 | 0.612637 | ||||||||
\(701\) | −0.418223 | −0.0157961 | −0.00789803 | − | 0.999969i | \(-0.502514\pi\) | ||||
−0.00789803 | + | 0.999969i | \(0.502514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3521 | 0.503583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.29392 | −0.0863328 | ||||||||
\(707\) | 2.71683 | 0.102177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.60664 | −0.135450 | −0.0677251 | − | 0.997704i | \(-0.521574\pi\) | ||||
−0.0677251 | + | 0.997704i | \(0.521574\pi\) | |||||||
\(710\) | −13.8172 | −0.518551 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.02585 | 0.113398 | ||||||||
\(713\) | −8.53748 | −0.319731 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.75419 | 0.364531 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.09303 | 0.0781110 | ||||||||
\(719\) | 17.9697 | 0.670155 | 0.335078 | − | 0.942190i | \(-0.391237\pi\) | ||||
0.335078 | + | 0.942190i | \(0.391237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.255788 | 0.00952606 | ||||||||
\(722\) | 7.55864 | 0.281303 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.8590 | 0.738055 | ||||||||
\(725\) | 52.9518 | 1.96658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0774 | 0.373752 | 0.186876 | − | 0.982384i | \(-0.440164\pi\) | ||||
0.186876 | + | 0.982384i | \(0.440164\pi\) | |||||||
\(728\) | −4.84293 | −0.179491 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 27.9191 | 1.03333 | ||||||||
\(731\) | −19.2459 | −0.711836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.2275 | −0.451631 | −0.225816 | − | 0.974170i | \(-0.572505\pi\) | ||||
−0.225816 | + | 0.974170i | \(0.572505\pi\) | |||||||
\(734\) | 13.9895 | 0.516360 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.4527 | 0.680177 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.49821 | 0.128684 | 0.0643419 | − | 0.997928i | \(-0.479505\pi\) | ||||
0.0643419 | + | 0.997928i | \(0.479505\pi\) | |||||||
\(740\) | −51.0779 | −1.87766 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.18741 | −0.153725 | ||||||||
\(743\) | −2.73642 | −0.100389 | −0.0501947 | − | 0.998739i | \(-0.515984\pi\) | ||||
−0.0501947 | + | 0.998739i | \(0.515984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.1761 | −1.36203 | ||||||||
\(746\) | −3.62374 | −0.132674 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.8608 | 0.433382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0480 | −0.366655 | −0.183327 | − | 0.983052i | \(-0.558687\pi\) | ||||
−0.183327 | + | 0.983052i | \(0.558687\pi\) | |||||||
\(752\) | −33.5479 | −1.22337 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.44038 | −0.270963 | ||||||||
\(755\) | 58.2667 | 2.12054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1490 | 0.550600 | 0.275300 | − | 0.961358i | \(-0.411223\pi\) | ||||
0.275300 | + | 0.961358i | \(0.411223\pi\) | |||||||
\(758\) | 5.31004 | 0.192869 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.7290 | 0.425457 | ||||||||
\(761\) | −35.4413 | −1.28475 | −0.642373 | − | 0.766392i | \(-0.722050\pi\) | ||||
−0.642373 | + | 0.766392i | \(0.722050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.8720 | 0.574604 | ||||||||
\(764\) | −10.2243 | −0.369901 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.7219 | −0.423530 | ||||||||
\(767\) | −12.2976 | −0.444042 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.7592 | 1.39769 | 0.698845 | − | 0.715273i | \(-0.253698\pi\) | ||||
0.698845 | + | 0.715273i | \(0.253698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26.4290 | 0.951200 | ||||||||
\(773\) | −26.5419 | −0.954646 | −0.477323 | − | 0.878728i | \(-0.658393\pi\) | ||||
−0.477323 | + | 0.878728i | \(0.658393\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.5179 | 0.737025 | ||||||||
\(776\) | 12.5134 | 0.449204 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.7541 | −0.493109 | ||||||||
\(779\) | −7.30140 | −0.261600 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.46752 | −0.159758 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.70393 | 0.0965690 | ||||||||
\(785\) | −63.7255 | −2.27446 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.6802 | 0.701524 | 0.350762 | − | 0.936465i | \(-0.385923\pi\) | ||||
0.350762 | + | 0.936465i | \(0.385923\pi\) | |||||||
\(788\) | 22.2794 | 0.793672 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.5600 | −0.446864 | ||||||||
\(791\) | −5.11650 | −0.181922 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.0917 | −1.10410 | ||||||||
\(794\) | 3.91979 | 0.139108 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.48159 | −0.0525135 | ||||||||
\(797\) | 25.2797 | 0.895451 | 0.447726 | − | 0.894171i | \(-0.352234\pi\) | ||||
0.447726 | + | 0.894171i | \(0.352234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.8046 | 1.08979 | ||||||||
\(800\) | −44.3470 | −1.56790 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.6666 | −0.447274 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.2776 | −0.503219 | ||||||||
\(806\) | −2.88302 | −0.101550 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.85918 | −0.170945 | ||||||||
\(809\) | 35.7891 | 1.25828 | 0.629138 | − | 0.777293i | \(-0.283408\pi\) | ||||
0.629138 | + | 0.777293i | \(0.283408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9415 | 0.735355 | 0.367677 | − | 0.929953i | \(-0.380153\pi\) | ||||
0.367677 | + | 0.929953i | \(0.380153\pi\) | |||||||
\(812\) | 10.2995 | 0.361442 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −75.0780 | −2.62987 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.5240 | −0.473143 | ||||||||
\(818\) | −16.4297 | −0.574452 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.9312 | 0.975401 | ||||||||
\(821\) | 8.06663 | 0.281527 | 0.140764 | − | 0.990043i | \(-0.455044\pi\) | ||||
0.140764 | + | 0.990043i | \(0.455044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.1359 | −0.701895 | −0.350948 | − | 0.936395i | \(-0.614140\pi\) | ||||
−0.350948 | + | 0.936395i | \(0.614140\pi\) | |||||||
\(824\) | −0.457490 | −0.0159374 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.15144 | −0.0748583 | ||||||||
\(827\) | 21.4181 | 0.744780 | 0.372390 | − | 0.928076i | \(-0.378538\pi\) | ||||
0.372390 | + | 0.928076i | \(0.378538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.3960 | −0.951504 | −0.475752 | − | 0.879580i | \(-0.657824\pi\) | ||||
−0.475752 | + | 0.879580i | \(0.657824\pi\) | |||||||
\(830\) | −21.1899 | −0.735512 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.41181 | −0.291627 | ||||||||
\(833\) | −2.48283 | −0.0860248 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 65.5972 | 2.27008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.05850 | −0.0711097 | ||||||||
\(839\) | 20.3757 | 0.703446 | 0.351723 | − | 0.936104i | \(-0.385596\pi\) | ||||
0.351723 | + | 0.936104i | \(0.385596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.64691 | 0.160238 | ||||||||
\(842\) | 2.24465 | 0.0773556 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.7108 | 1.64227 | ||||||||
\(845\) | 21.3055 | 0.732930 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −23.9016 | −0.820783 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.7367 | 0.368264 | ||||||||
\(851\) | 29.0698 | 0.996501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.28686 | −0.283737 | −0.141868 | − | 0.989886i | \(-0.545311\pi\) | ||||
−0.141868 | + | 0.989886i | \(0.545311\pi\) | |||||||
\(854\) | −5.43942 | −0.186133 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.2135 | −0.725064 | ||||||||
\(857\) | 31.0459 | 1.06051 | 0.530254 | − | 0.847839i | \(-0.322097\pi\) | ||||
0.530254 | + | 0.847839i | \(0.322097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.63124 | −0.0556573 | −0.0278287 | − | 0.999613i | \(-0.508859\pi\) | ||||
−0.0278287 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(860\) | 51.7354 | 1.76416 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.1461 | −0.481819 | ||||||||
\(863\) | −5.32862 | −0.181388 | −0.0906942 | − | 0.995879i | \(-0.528909\pi\) | ||||
−0.0906942 | + | 0.995879i | \(0.528909\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −35.1804 | −1.19617 | ||||||||
\(866\) | 10.2909 | 0.349699 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.99088 | 0.135459 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.0454 | −1.11970 | ||||||||
\(872\) | −28.3878 | −0.961332 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.13929 | −0.106188 | ||||||||
\(875\) | 15.5189 | 0.524635 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1267 | −0.544561 | −0.272281 | − | 0.962218i | \(-0.587778\pi\) | ||||
−0.272281 | + | 0.962218i | \(0.587778\pi\) | |||||||
\(878\) | 19.1118 | 0.644992 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.1173 | 1.18313 | 0.591565 | − | 0.806257i | \(-0.298510\pi\) | ||||
0.591565 | + | 0.806257i | \(0.298510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.480232 | 0.0161611 | 0.00808054 | − | 0.999967i | \(-0.497428\pi\) | ||||
0.00808054 | + | 0.999967i | \(0.497428\pi\) | |||||||
\(884\) | 11.9371 | 0.401487 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.57463 | −0.220879 | ||||||||
\(887\) | −36.7238 | −1.23306 | −0.616532 | − | 0.787330i | \(-0.711463\pi\) | ||||
−0.616532 | + | 0.787330i | \(0.711463\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.203338 | −0.00681973 | ||||||||
\(890\) | 3.01240 | 0.100976 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.13644 | −0.238946 | ||||||||
\(893\) | 21.6461 | 0.724360 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.6489 | 0.690218 | ||||||||
\(896\) | −11.1876 | −0.373751 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.77517 | −0.226090 | ||||||||
\(899\) | 13.0376 | 0.434828 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.9471 | 0.731163 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.15112 | 0.304362 | ||||||||
\(905\) | 42.0402 | 1.39746 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1917 | 0.404818 | 0.202409 | − | 0.979301i | \(-0.435123\pi\) | ||||
0.202409 | + | 0.979301i | \(0.435123\pi\) | |||||||
\(908\) | −20.7781 | −0.689544 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.82140 | −0.159828 | ||||||||
\(911\) | 8.11848 | 0.268977 | 0.134489 | − | 0.990915i | \(-0.457061\pi\) | ||||
0.134489 | + | 0.990915i | \(0.457061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.69251 | 0.221369 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.6213 | 0.383980 | ||||||||
\(917\) | −10.2788 | −0.339438 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.6539 | −1.63793 | −0.818965 | − | 0.573843i | \(-0.805452\pi\) | ||||
−0.818965 | + | 0.573843i | \(0.805452\pi\) | |||||||
\(920\) | 25.5362 | 0.841903 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.457955 | −0.0150820 | ||||||||
\(923\) | −21.0118 | −0.691610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −69.8627 | −2.29707 | ||||||||
\(926\) | −15.0697 | −0.495221 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.1792 | −0.925028 | ||||||||
\(929\) | 0.373776 | 0.0122632 | 0.00613160 | − | 0.999981i | \(-0.498048\pi\) | ||||
0.00613160 | + | 0.999981i | \(0.498048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.74466 | −0.0571790 | ||||||||
\(932\) | 0.306409 | 0.0100368 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.0282 | −0.459016 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.0667 | −1.50493 | −0.752467 | − | 0.658630i | \(-0.771136\pi\) | ||||
−0.752467 | + | 0.658630i | \(0.771136\pi\) | |||||||
\(938\) | −5.78122 | −0.188763 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −82.8064 | −2.70085 | ||||||||
\(941\) | 19.3374 | 0.630380 | 0.315190 | − | 0.949029i | \(-0.397932\pi\) | ||||
0.315190 | + | 0.949029i | \(0.397932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.8964 | −0.517659 | ||||||||
\(944\) | −12.2803 | −0.399691 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.06969 | 0.262230 | 0.131115 | − | 0.991367i | \(-0.458144\pi\) | ||||
0.131115 | + | 0.991367i | \(0.458144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.4563 | 1.37819 | ||||||||
\(950\) | 7.54457 | 0.244778 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.44065 | 0.143922 | ||||||||
\(953\) | −34.6358 | −1.12196 | −0.560982 | − | 0.827828i | \(-0.689576\pi\) | ||||
−0.560982 | + | 0.827828i | \(0.689576\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.6441 | −0.700385 | ||||||||
\(956\) | −18.5557 | −0.600136 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.5938 | −0.406887 | ||||||||
\(959\) | −17.1096 | −0.552498 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9482 | −0.837037 | ||||||||
\(962\) | 9.81659 | 0.316499 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.06935 | 0.195481 | ||||||||
\(965\) | 55.9483 | 1.80104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.15074 | 0.262110 | 0.131055 | − | 0.991375i | \(-0.458164\pi\) | ||||
0.131055 | + | 0.991375i | \(0.458164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.4578 | 0.399994 | ||||||||
\(971\) | −33.4330 | −1.07292 | −0.536458 | − | 0.843927i | \(-0.680238\pi\) | ||||
−0.536458 | + | 0.843927i | \(0.680238\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.5009 | −0.625171 | ||||||||
\(974\) | −6.69560 | −0.214541 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.0480 | −0.993821 | ||||||||
\(977\) | 5.48798 | 0.175576 | 0.0877880 | − | 0.996139i | \(-0.472020\pi\) | ||||
0.0877880 | + | 0.996139i | \(0.472020\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.67413 | 0.213197 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.30398 | 0.233080 | ||||||||
\(983\) | −14.5404 | −0.463767 | −0.231884 | − | 0.972744i | \(-0.574489\pi\) | ||||
−0.231884 | + | 0.972744i | \(0.574489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 47.1640 | 1.50277 | ||||||||
\(986\) | 6.82235 | 0.217268 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.38808 | 0.266860 | ||||||||
\(989\) | −29.4440 | −0.936266 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.68326 | −0.307599 | −0.153799 | − | 0.988102i | \(-0.549151\pi\) | ||||
−0.153799 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(992\) | −10.9190 | −0.346677 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.67596 | −0.116594 | ||||||||
\(995\) | −3.13642 | −0.0994312 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.2216 | −0.798775 | −0.399388 | − | 0.916782i | \(-0.630777\pi\) | ||||
−0.399388 | + | 0.916782i | \(0.630777\pi\) | |||||||
\(998\) | −14.5441 | −0.460387 | ||||||||
\(999\) | 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.cx.1.5 | 10 | ||
3.2 | odd | 2 | 2541.2.a.bq.1.6 | 10 | |||
11.5 | even | 5 | 693.2.m.j.190.3 | 20 | |||
11.9 | even | 5 | 693.2.m.j.631.3 | 20 | |||
11.10 | odd | 2 | 7623.2.a.cy.1.6 | 10 | |||
33.5 | odd | 10 | 231.2.j.g.190.3 | yes | 20 | ||
33.20 | odd | 10 | 231.2.j.g.169.3 | ✓ | 20 | ||
33.32 | even | 2 | 2541.2.a.br.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.169.3 | ✓ | 20 | 33.20 | odd | 10 | ||
231.2.j.g.190.3 | yes | 20 | 33.5 | odd | 10 | ||
693.2.m.j.190.3 | 20 | 11.5 | even | 5 | |||
693.2.m.j.631.3 | 20 | 11.9 | even | 5 | |||
2541.2.a.bq.1.6 | 10 | 3.2 | odd | 2 | |||
2541.2.a.br.1.5 | 10 | 33.32 | even | 2 | |||
7623.2.a.cx.1.5 | 10 | 1.1 | even | 1 | trivial | ||
7623.2.a.cy.1.6 | 10 | 11.10 | odd | 2 |