Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [297,2,Mod(1,297)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(297, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("297.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.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: | \(2.37155694003\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 297.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | −1.93185 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.46410 | 2.73205 | ||||||||
\(5\) | 0.732051 | 0.327383 | 0.163692 | − | 0.986512i | \(-0.447660\pi\) | ||||
0.163692 | + | 0.986512i | \(0.447660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.73205 | −1.41058 | −0.705291 | − | 0.708918i | \(-0.749184\pi\) | ||||
−0.705291 | + | 0.708918i | \(0.749184\pi\) | |||||||
\(8\) | −9.46410 | −3.34607 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | −0.632456 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.267949 | −0.0743157 | −0.0371579 | − | 0.999309i | \(-0.511830\pi\) | ||||
−0.0371579 | + | 0.999309i | \(0.511830\pi\) | |||||||
\(14\) | 10.1962 | 2.72504 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.9282 | 3.73205 | ||||||||
\(17\) | 4.19615 | 1.01772 | 0.508858 | − | 0.860850i | \(-0.330068\pi\) | ||||
0.508858 | + | 0.860850i | \(0.330068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.19615 | −1.19208 | −0.596040 | − | 0.802955i | \(-0.703260\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 4.00000 | 0.894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.73205 | 0.582475 | ||||||||
\(23\) | −8.00000 | −1.66812 | −0.834058 | − | 0.551677i | \(-0.813988\pi\) | ||||
−0.834058 | + | 0.551677i | \(0.813988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 0.732051 | 0.143567 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −20.3923 | −3.85378 | ||||||||
\(29\) | 1.26795 | 0.235452 | 0.117726 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.535898 | 0.0962502 | 0.0481251 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481251 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(32\) | −21.8564 | −3.86370 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.4641 | −1.96608 | ||||||||
\(35\) | −2.73205 | −0.461801 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.46410 | −1.06269 | −0.531346 | − | 0.847155i | \(-0.678314\pi\) | ||||
−0.531346 | + | 0.847155i | \(0.678314\pi\) | |||||||
\(38\) | 14.1962 | 2.30292 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.92820 | −1.09545 | ||||||||
\(41\) | −1.46410 | −0.228654 | −0.114327 | − | 0.993443i | \(-0.536471\pi\) | ||||
−0.114327 | + | 0.993443i | \(0.536471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | −5.46410 | −0.823744 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.8564 | 3.22255 | ||||||||
\(47\) | −10.1962 | −1.48726 | −0.743631 | − | 0.668590i | \(-0.766898\pi\) | ||||
−0.743631 | + | 0.668590i | \(0.766898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | 12.1962 | 1.72480 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.46410 | −0.203034 | ||||||||
\(53\) | −4.73205 | −0.649997 | −0.324999 | − | 0.945715i | \(-0.605364\pi\) | ||||
−0.324999 | + | 0.945715i | \(0.605364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.732051 | −0.0987097 | ||||||||
\(56\) | 35.3205 | 4.71990 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.46410 | −0.454859 | ||||||||
\(59\) | −10.1962 | −1.32743 | −0.663713 | − | 0.747987i | \(-0.731020\pi\) | ||||
−0.663713 | + | 0.747987i | \(0.731020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.26795 | −0.546455 | −0.273227 | − | 0.961949i | \(-0.588091\pi\) | ||||
−0.273227 | + | 0.961949i | \(0.588091\pi\) | |||||||
\(62\) | −1.46410 | −0.185941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | −0.196152 | −0.0243297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.92820 | 0.724245 | 0.362123 | − | 0.932130i | \(-0.382052\pi\) | ||||
0.362123 | + | 0.932130i | \(0.382052\pi\) | |||||||
\(68\) | 22.9282 | 2.78045 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.46410 | 0.892131 | ||||||||
\(71\) | 13.8564 | 1.64445 | 0.822226 | − | 0.569160i | \(-0.192732\pi\) | ||||
0.822226 | + | 0.569160i | \(0.192732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.19615 | 0.374081 | 0.187041 | − | 0.982352i | \(-0.440110\pi\) | ||||
0.187041 | + | 0.982352i | \(0.440110\pi\) | |||||||
\(74\) | 17.6603 | 2.05296 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −28.3923 | −3.25682 | ||||||||
\(77\) | 3.73205 | 0.425307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.73205 | −0.644906 | −0.322453 | − | 0.946585i | \(-0.604507\pi\) | ||||
−0.322453 | + | 0.946585i | \(0.604507\pi\) | |||||||
\(80\) | 10.9282 | 1.22181 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.00000 | 0.441726 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.07180 | 0.333183 | ||||||||
\(86\) | −9.46410 | −1.02054 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.46410 | 1.00888 | ||||||||
\(89\) | 0.339746 | 0.0360130 | 0.0180065 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180065 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | −43.7128 | −4.55738 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 27.8564 | 2.87317 | ||||||||
\(95\) | −3.80385 | −0.390267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.39230 | −0.547506 | −0.273753 | − | 0.961800i | \(-0.588265\pi\) | ||||
−0.273753 | + | 0.961800i | \(0.588265\pi\) | |||||||
\(98\) | −18.9282 | −1.91204 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −24.3923 | −2.43923 | ||||||||
\(101\) | 0.196152 | 0.0195179 | 0.00975895 | − | 0.999952i | \(-0.496894\pi\) | ||||
0.00975895 | + | 0.999952i | \(0.496894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8564 | 1.26678 | 0.633390 | − | 0.773833i | \(-0.281663\pi\) | ||||
0.633390 | + | 0.773833i | \(0.281663\pi\) | |||||||
\(104\) | 2.53590 | 0.248665 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.9282 | 1.25570 | ||||||||
\(107\) | −5.66025 | −0.547197 | −0.273599 | − | 0.961844i | \(-0.588214\pi\) | ||||
−0.273599 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8564 | 1.13564 | 0.567819 | − | 0.823154i | \(-0.307787\pi\) | ||||
0.567819 | + | 0.823154i | \(0.307787\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −55.7128 | −5.26437 | ||||||||
\(113\) | 11.6603 | 1.09690 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.85641 | −0.546113 | ||||||||
\(116\) | 6.92820 | 0.643268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.8564 | 2.56439 | ||||||||
\(119\) | −15.6603 | −1.43557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.6603 | 1.05567 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.92820 | 0.262960 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.46410 | 0.484861 | 0.242430 | − | 0.970169i | \(-0.422055\pi\) | ||||
0.242430 | + | 0.970169i | \(0.422055\pi\) | |||||||
\(128\) | −37.8564 | −3.34607 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.535898 | 0.0470014 | ||||||||
\(131\) | 15.1244 | 1.32142 | 0.660711 | − | 0.750641i | \(-0.270255\pi\) | ||||
0.660711 | + | 0.750641i | \(0.270255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3923 | 1.68153 | ||||||||
\(134\) | −16.1962 | −1.39913 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −39.7128 | −3.40535 | ||||||||
\(137\) | 8.39230 | 0.717003 | 0.358501 | − | 0.933529i | \(-0.383288\pi\) | ||||
0.358501 | + | 0.933529i | \(0.383288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.19615 | −0.610370 | −0.305185 | − | 0.952293i | \(-0.598718\pi\) | ||||
−0.305185 | + | 0.952293i | \(0.598718\pi\) | |||||||
\(140\) | −14.9282 | −1.26166 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −37.8564 | −3.17684 | ||||||||
\(143\) | 0.267949 | 0.0224070 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.928203 | 0.0770831 | ||||||||
\(146\) | −8.73205 | −0.722670 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −35.3205 | −2.90333 | ||||||||
\(149\) | −9.85641 | −0.807468 | −0.403734 | − | 0.914876i | \(-0.632288\pi\) | ||||
−0.403734 | + | 0.914876i | \(0.632288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.80385 | −0.390932 | −0.195466 | − | 0.980711i | \(-0.562622\pi\) | ||||
−0.195466 | + | 0.980711i | \(0.562622\pi\) | |||||||
\(152\) | 49.1769 | 3.98877 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.1962 | −0.821629 | ||||||||
\(155\) | 0.392305 | 0.0315107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5359 | 0.840856 | 0.420428 | − | 0.907326i | \(-0.361880\pi\) | ||||
0.420428 | + | 0.907326i | \(0.361880\pi\) | |||||||
\(158\) | 15.6603 | 1.24586 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.0000 | −1.26491 | ||||||||
\(161\) | 29.8564 | 2.35301 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.0000 | 1.48819 | 0.744097 | − | 0.668071i | \(-0.232880\pi\) | ||||
0.744097 | + | 0.668071i | \(0.232880\pi\) | |||||||
\(164\) | −8.00000 | −0.624695 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.7321 | −1.75906 | −0.879529 | − | 0.475844i | \(-0.842143\pi\) | ||||
−0.879529 | + | 0.475844i | \(0.842143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9282 | −0.994477 | ||||||||
\(170\) | −8.39230 | −0.643660 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.9282 | 1.44326 | ||||||||
\(173\) | 4.39230 | 0.333941 | 0.166970 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166970 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.6603 | 1.25940 | ||||||||
\(176\) | −14.9282 | −1.12526 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.928203 | −0.0695718 | ||||||||
\(179\) | 14.1962 | 1.06107 | 0.530535 | − | 0.847663i | \(-0.321991\pi\) | ||||
0.530535 | + | 0.847663i | \(0.321991\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3205 | −1.21309 | −0.606547 | − | 0.795048i | \(-0.707446\pi\) | ||||
−0.606547 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(182\) | −2.73205 | −0.202513 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 75.7128 | 5.58162 | ||||||||
\(185\) | −4.73205 | −0.347907 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.19615 | −0.306853 | ||||||||
\(188\) | −55.7128 | −4.06327 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.3923 | 0.753937 | ||||||||
\(191\) | 4.00000 | 0.289430 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.80385 | −0.201825 | −0.100913 | − | 0.994895i | \(-0.532176\pi\) | ||||
−0.100913 | + | 0.994895i | \(0.532176\pi\) | |||||||
\(194\) | 14.7321 | 1.05770 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 37.8564 | 2.70403 | ||||||||
\(197\) | −9.66025 | −0.688265 | −0.344132 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344132 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0000 | −1.06332 | −0.531661 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531661 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(200\) | 42.2487 | 2.98744 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.535898 | −0.0377057 | ||||||||
\(203\) | −4.73205 | −0.332125 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.07180 | −0.0748575 | ||||||||
\(206\) | −35.1244 | −2.44723 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 5.19615 | 0.359425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.33975 | −0.642975 | −0.321487 | − | 0.946914i | \(-0.604183\pi\) | ||||
−0.321487 | + | 0.946914i | \(0.604183\pi\) | |||||||
\(212\) | −25.8564 | −1.77583 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.4641 | 1.05710 | ||||||||
\(215\) | 2.53590 | 0.172947 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | −32.3923 | −2.19388 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | −1.12436 | −0.0756323 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8564 | 1.19575 | 0.597877 | − | 0.801588i | \(-0.296011\pi\) | ||||
0.597877 | + | 0.801588i | \(0.296011\pi\) | |||||||
\(224\) | 81.5692 | 5.45007 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.8564 | −2.11906 | ||||||||
\(227\) | 29.6603 | 1.96862 | 0.984310 | − | 0.176447i | \(-0.0564605\pi\) | ||||
0.984310 | + | 0.176447i | \(0.0564605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3923 | −1.08323 | −0.541617 | − | 0.840625i | \(-0.682188\pi\) | ||||
−0.541617 | + | 0.840625i | \(0.682188\pi\) | |||||||
\(230\) | 16.0000 | 1.05501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | −0.787839 | ||||||||
\(233\) | 6.33975 | 0.415331 | 0.207665 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207665 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.46410 | −0.486904 | ||||||||
\(236\) | −55.7128 | −3.62660 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 42.7846 | 2.77331 | ||||||||
\(239\) | −16.3923 | −1.06033 | −0.530165 | − | 0.847894i | \(-0.677870\pi\) | ||||
−0.530165 | + | 0.847894i | \(0.677870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.1962 | 0.978870 | 0.489435 | − | 0.872040i | \(-0.337203\pi\) | ||||
0.489435 | + | 0.872040i | \(0.337203\pi\) | |||||||
\(242\) | −2.73205 | −0.175623 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −23.3205 | −1.49294 | ||||||||
\(245\) | 5.07180 | 0.324025 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.39230 | 0.0885902 | ||||||||
\(248\) | −5.07180 | −0.322059 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.9282 | 1.19712 | ||||||||
\(251\) | −10.5885 | −0.668337 | −0.334169 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334169 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | −14.9282 | −0.936679 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 43.7128 | 2.73205 | ||||||||
\(257\) | 12.7321 | 0.794204 | 0.397102 | − | 0.917775i | \(-0.370016\pi\) | ||||
0.397102 | + | 0.917775i | \(0.370016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.1244 | 1.49901 | ||||||||
\(260\) | −1.07180 | −0.0664700 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −41.3205 | −2.55279 | ||||||||
\(263\) | −4.87564 | −0.300645 | −0.150323 | − | 0.988637i | \(-0.548031\pi\) | ||||
−0.150323 | + | 0.988637i | \(0.548031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.46410 | −0.212798 | ||||||||
\(266\) | −52.9808 | −3.24846 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 32.3923 | 1.97867 | ||||||||
\(269\) | 26.9282 | 1.64184 | 0.820921 | − | 0.571042i | \(-0.193461\pi\) | ||||
0.820921 | + | 0.571042i | \(0.193461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.26795 | −0.137768 | −0.0688841 | − | 0.997625i | \(-0.521944\pi\) | ||||
−0.0688841 | + | 0.997625i | \(0.521944\pi\) | |||||||
\(272\) | 62.6410 | 3.79817 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.9282 | −1.38514 | ||||||||
\(275\) | 4.46410 | 0.269195 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.85641 | −0.592214 | −0.296107 | − | 0.955155i | \(-0.595689\pi\) | ||||
−0.296107 | + | 0.955155i | \(0.595689\pi\) | |||||||
\(278\) | 19.6603 | 1.17914 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.8564 | 1.54522 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.2487 | −1.56032 | −0.780162 | − | 0.625578i | \(-0.784863\pi\) | ||||
−0.780162 | + | 0.625578i | \(0.784863\pi\) | |||||||
\(284\) | 75.7128 | 4.49273 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.732051 | −0.0432871 | ||||||||
\(287\) | 5.46410 | 0.322536 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.607695 | 0.0357468 | ||||||||
\(290\) | −2.53590 | −0.148913 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.4641 | 1.02201 | ||||||||
\(293\) | 27.1244 | 1.58462 | 0.792311 | − | 0.610118i | \(-0.208878\pi\) | ||||
0.792311 | + | 0.610118i | \(0.208878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.46410 | −0.434577 | ||||||||
\(296\) | 61.1769 | 3.55584 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.9282 | 1.55991 | ||||||||
\(299\) | 2.14359 | 0.123967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9282 | −0.745169 | ||||||||
\(302\) | 13.1244 | 0.755222 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −77.5692 | −4.44890 | ||||||||
\(305\) | −3.12436 | −0.178900 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.3205 | −1.55926 | −0.779632 | − | 0.626238i | \(-0.784594\pi\) | ||||
−0.779632 | + | 0.626238i | \(0.784594\pi\) | |||||||
\(308\) | 20.3923 | 1.16196 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.07180 | −0.0608740 | ||||||||
\(311\) | −30.5885 | −1.73451 | −0.867256 | − | 0.497862i | \(-0.834119\pi\) | ||||
−0.867256 | + | 0.497862i | \(0.834119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.92820 | −0.108988 | −0.0544942 | − | 0.998514i | \(-0.517355\pi\) | ||||
−0.0544942 | + | 0.998514i | \(0.517355\pi\) | |||||||
\(314\) | −28.7846 | −1.62441 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −31.3205 | −1.76192 | ||||||||
\(317\) | −10.5885 | −0.594707 | −0.297354 | − | 0.954767i | \(-0.596104\pi\) | ||||
−0.297354 | + | 0.954767i | \(0.596104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.26795 | −0.0709915 | ||||||||
\(320\) | 21.8564 | 1.22181 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −81.5692 | −4.54567 | ||||||||
\(323\) | −21.8038 | −1.21320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.19615 | 0.0663506 | ||||||||
\(326\) | −51.9090 | −2.87497 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.8564 | 0.765092 | ||||||||
\(329\) | 38.0526 | 2.09791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.3923 | −1.50562 | −0.752809 | − | 0.658239i | \(-0.771301\pi\) | ||||
−0.752809 | + | 0.658239i | \(0.771301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 62.1051 | 3.39824 | ||||||||
\(335\) | 4.33975 | 0.237106 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9808 | −1.63316 | −0.816578 | − | 0.577235i | \(-0.804132\pi\) | ||||
−0.816578 | + | 0.577235i | \(0.804132\pi\) | |||||||
\(338\) | 35.3205 | 1.92118 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.7846 | 0.910273 | ||||||||
\(341\) | −0.535898 | −0.0290205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.267949 | 0.0144679 | ||||||||
\(344\) | −32.7846 | −1.76763 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | −0.645124 | ||||||||
\(347\) | −10.3397 | −0.555067 | −0.277533 | − | 0.960716i | \(-0.589517\pi\) | ||||
−0.277533 | + | 0.960716i | \(0.589517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.87564 | −0.314516 | −0.157258 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157258 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(350\) | −45.5167 | −2.43297 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.8564 | 1.16495 | ||||||||
\(353\) | −21.1244 | −1.12434 | −0.562168 | − | 0.827023i | \(-0.690033\pi\) | ||||
−0.562168 | + | 0.827023i | \(0.690033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.1436 | 0.538366 | ||||||||
\(356\) | 1.85641 | 0.0983893 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.7846 | −2.04983 | ||||||||
\(359\) | −6.53590 | −0.344952 | −0.172476 | − | 0.985014i | \(-0.555177\pi\) | ||||
−0.172476 | + | 0.985014i | \(0.555177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.00000 | 0.421053 | ||||||||
\(362\) | 44.5885 | 2.34352 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.46410 | 0.286397 | ||||||||
\(365\) | 2.33975 | 0.122468 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.9282 | 0.727046 | 0.363523 | − | 0.931585i | \(-0.381574\pi\) | ||||
0.363523 | + | 0.931585i | \(0.381574\pi\) | |||||||
\(368\) | −119.426 | −6.22549 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.9282 | 0.672105 | ||||||||
\(371\) | 17.6603 | 0.916875 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.1244 | −1.04200 | −0.521000 | − | 0.853557i | \(-0.674441\pi\) | ||||
−0.521000 | + | 0.853557i | \(0.674441\pi\) | |||||||
\(374\) | 11.4641 | 0.592795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 96.4974 | 4.97647 | ||||||||
\(377\) | −0.339746 | −0.0174978 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.8564 | 0.763122 | 0.381561 | − | 0.924344i | \(-0.375387\pi\) | ||||
0.381561 | + | 0.924344i | \(0.375387\pi\) | |||||||
\(380\) | −20.7846 | −1.06623 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.9282 | −0.559136 | ||||||||
\(383\) | −24.7321 | −1.26375 | −0.631874 | − | 0.775071i | \(-0.717714\pi\) | ||||
−0.631874 | + | 0.775071i | \(0.717714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.73205 | 0.139238 | ||||||||
\(386\) | 7.66025 | 0.389897 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −29.4641 | −1.49581 | ||||||||
\(389\) | −21.4641 | −1.08827 | −0.544137 | − | 0.838997i | \(-0.683143\pi\) | ||||
−0.544137 | + | 0.838997i | \(0.683143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.5692 | −1.69767 | ||||||||
\(392\) | −65.5692 | −3.31175 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.3923 | 1.32963 | ||||||||
\(395\) | −4.19615 | −0.211131 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3923 | 1.02346 | 0.511730 | − | 0.859146i | \(-0.329005\pi\) | ||||
0.511730 | + | 0.859146i | \(0.329005\pi\) | |||||||
\(398\) | 40.9808 | 2.05418 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −66.6410 | −3.33205 | ||||||||
\(401\) | 6.53590 | 0.326387 | 0.163194 | − | 0.986594i | \(-0.447820\pi\) | ||||
0.163194 | + | 0.986594i | \(0.447820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.143594 | −0.00715290 | ||||||||
\(404\) | 1.07180 | 0.0533239 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.9282 | 0.641616 | ||||||||
\(407\) | 6.46410 | 0.320414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9090 | 1.62724 | 0.813622 | − | 0.581394i | \(-0.197493\pi\) | ||||
0.813622 | + | 0.581394i | \(0.197493\pi\) | |||||||
\(410\) | 2.92820 | 0.144614 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 70.2487 | 3.46091 | ||||||||
\(413\) | 38.0526 | 1.87244 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.85641 | 0.287134 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.1962 | −0.694357 | ||||||||
\(419\) | −23.7128 | −1.15845 | −0.579223 | − | 0.815169i | \(-0.696644\pi\) | ||||
−0.579223 | + | 0.815169i | \(0.696644\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8564 | 1.01648 | 0.508240 | − | 0.861216i | \(-0.330296\pi\) | ||||
0.508240 | + | 0.861216i | \(0.330296\pi\) | |||||||
\(422\) | 25.5167 | 1.24213 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 44.7846 | 2.17493 | ||||||||
\(425\) | −18.7321 | −0.908638 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.9282 | 0.770820 | ||||||||
\(428\) | −30.9282 | −1.49497 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.92820 | −0.334108 | ||||||||
\(431\) | −14.5359 | −0.700170 | −0.350085 | − | 0.936718i | \(-0.613847\pi\) | ||||
−0.350085 | + | 0.936718i | \(0.613847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.60770 | −0.173375 | −0.0866874 | − | 0.996236i | \(-0.527628\pi\) | ||||
−0.0866874 | + | 0.996236i | \(0.527628\pi\) | |||||||
\(434\) | 5.46410 | 0.262285 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 64.7846 | 3.10262 | ||||||||
\(437\) | 41.5692 | 1.98853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.5359 | 1.45740 | 0.728699 | − | 0.684834i | \(-0.240125\pi\) | ||||
0.728699 | + | 0.684834i | \(0.240125\pi\) | |||||||
\(440\) | 6.92820 | 0.330289 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.07180 | 0.146110 | ||||||||
\(443\) | 3.26795 | 0.155265 | 0.0776325 | − | 0.996982i | \(-0.475264\pi\) | ||||
0.0776325 | + | 0.996982i | \(0.475264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.248711 | 0.0117900 | ||||||||
\(446\) | −48.7846 | −2.31002 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −111.426 | −5.26437 | ||||||||
\(449\) | 10.2487 | 0.483667 | 0.241833 | − | 0.970318i | \(-0.422251\pi\) | ||||
0.241833 | + | 0.970318i | \(0.422251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.46410 | 0.0689419 | ||||||||
\(452\) | 63.7128 | 2.99680 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −81.0333 | −3.80308 | ||||||||
\(455\) | 0.732051 | 0.0343191 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0718 | −0.517917 | −0.258958 | − | 0.965888i | \(-0.583379\pi\) | ||||
−0.258958 | + | 0.965888i | \(0.583379\pi\) | |||||||
\(458\) | 44.7846 | 2.09265 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −32.0000 | −1.49201 | ||||||||
\(461\) | 29.6603 | 1.38142 | 0.690708 | − | 0.723134i | \(-0.257299\pi\) | ||||
0.690708 | + | 0.723134i | \(0.257299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.7846 | −1.19831 | −0.599156 | − | 0.800632i | \(-0.704497\pi\) | ||||
−0.599156 | + | 0.800632i | \(0.704497\pi\) | |||||||
\(464\) | 18.9282 | 0.878720 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.3205 | −0.802357 | ||||||||
\(467\) | 18.9282 | 0.875893 | 0.437946 | − | 0.899001i | \(-0.355706\pi\) | ||||
0.437946 | + | 0.899001i | \(0.355706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.1244 | −1.02161 | ||||||||
\(470\) | 20.3923 | 0.940627 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 96.4974 | 4.44165 | ||||||||
\(473\) | −3.46410 | −0.159280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.1962 | 1.06431 | ||||||||
\(476\) | −85.5692 | −3.92206 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 44.7846 | 2.04840 | ||||||||
\(479\) | 11.5167 | 0.526210 | 0.263105 | − | 0.964767i | \(-0.415253\pi\) | ||||
0.263105 | + | 0.964767i | \(0.415253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73205 | 0.0789747 | ||||||||
\(482\) | −41.5167 | −1.89103 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.46410 | 0.248368 | ||||||||
\(485\) | −3.94744 | −0.179244 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8564 | 0.854465 | 0.427233 | − | 0.904142i | \(-0.359489\pi\) | ||||
0.427233 | + | 0.904142i | \(0.359489\pi\) | |||||||
\(488\) | 40.3923 | 1.82847 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.8564 | −0.625969 | ||||||||
\(491\) | 30.0526 | 1.35625 | 0.678126 | − | 0.734945i | \(-0.262792\pi\) | ||||
0.678126 | + | 0.734945i | \(0.262792\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.32051 | 0.239624 | ||||||||
\(494\) | −3.80385 | −0.171143 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −51.7128 | −2.31964 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.4641 | −0.871333 | −0.435666 | − | 0.900108i | \(-0.643487\pi\) | ||||
−0.435666 | + | 0.900108i | \(0.643487\pi\) | |||||||
\(500\) | −37.8564 | −1.69299 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.9282 | 1.29113 | ||||||||
\(503\) | −22.9282 | −1.02232 | −0.511159 | − | 0.859486i | \(-0.670784\pi\) | ||||
−0.511159 | + | 0.859486i | \(0.670784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.143594 | 0.00638983 | ||||||||
\(506\) | −21.8564 | −0.971636 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29.8564 | 1.32466 | ||||||||
\(509\) | −16.0526 | −0.711517 | −0.355759 | − | 0.934578i | \(-0.615777\pi\) | ||||
−0.355759 | + | 0.934578i | \(0.615777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9282 | −0.527673 | ||||||||
\(512\) | −43.7128 | −1.93185 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −34.7846 | −1.53428 | ||||||||
\(515\) | 9.41154 | 0.414722 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1962 | 0.448426 | ||||||||
\(518\) | −65.9090 | −2.89587 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.85641 | 0.0814088 | ||||||||
\(521\) | −20.7846 | −0.910590 | −0.455295 | − | 0.890341i | \(-0.650466\pi\) | ||||
−0.455295 | + | 0.890341i | \(0.650466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.9808 | 1.74824 | 0.874118 | − | 0.485713i | \(-0.161440\pi\) | ||||
0.874118 | + | 0.485713i | \(0.161440\pi\) | |||||||
\(524\) | 82.6410 | 3.61019 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.3205 | 0.580802 | ||||||||
\(527\) | 2.24871 | 0.0979554 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 9.46410 | 0.411094 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 105.962 | 4.59401 | ||||||||
\(533\) | 0.392305 | 0.0169926 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.14359 | −0.179143 | ||||||||
\(536\) | −56.1051 | −2.42337 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −73.5692 | −3.17179 | ||||||||
\(539\) | −6.92820 | −0.298419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.5885 | −1.01415 | −0.507073 | − | 0.861903i | \(-0.669273\pi\) | ||||
−0.507073 | + | 0.861903i | \(0.669273\pi\) | |||||||
\(542\) | 6.19615 | 0.266148 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −91.7128 | −3.93215 | ||||||||
\(545\) | 8.67949 | 0.371789 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.8038 | −0.718481 | −0.359240 | − | 0.933245i | \(-0.616964\pi\) | ||||
−0.359240 | + | 0.933245i | \(0.616964\pi\) | |||||||
\(548\) | 45.8564 | 1.95889 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.1962 | −0.520046 | ||||||||
\(551\) | −6.58846 | −0.280678 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.3923 | 0.909693 | ||||||||
\(554\) | 26.9282 | 1.14407 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −39.3205 | −1.66756 | ||||||||
\(557\) | −29.2679 | −1.24012 | −0.620061 | − | 0.784553i | \(-0.712892\pi\) | ||||
−0.620061 | + | 0.784553i | \(0.712892\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.928203 | −0.0392588 | ||||||||
\(560\) | −40.7846 | −1.72346 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.7128 | 1.50512 | 0.752558 | − | 0.658526i | \(-0.228820\pi\) | ||||
0.752558 | + | 0.658526i | \(0.228820\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.53590 | 0.359108 | ||||||||
\(566\) | 71.7128 | 3.01431 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −131.138 | −5.50245 | ||||||||
\(569\) | −35.3205 | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1244 | 1.34436 | 0.672181 | − | 0.740387i | \(-0.265358\pi\) | ||||
0.672181 | + | 0.740387i | \(0.265358\pi\) | |||||||
\(572\) | 1.46410 | 0.0612172 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.9282 | −0.623091 | ||||||||
\(575\) | 35.7128 | 1.48933 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | −0.124892 | −0.0624458 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624458 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(578\) | −1.66025 | −0.0690575 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.07180 | 0.210595 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.73205 | 0.195982 | ||||||||
\(584\) | −30.2487 | −1.25170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −74.1051 | −3.06125 | ||||||||
\(587\) | 1.41154 | 0.0582606 | 0.0291303 | − | 0.999576i | \(-0.490726\pi\) | ||||
0.0291303 | + | 0.999576i | \(0.490726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.78461 | −0.114738 | ||||||||
\(590\) | 20.3923 | 0.839538 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −96.4974 | −3.96602 | ||||||||
\(593\) | −47.7128 | −1.95933 | −0.979665 | − | 0.200639i | \(-0.935698\pi\) | ||||
−0.979665 | + | 0.200639i | \(0.935698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4641 | −0.469982 | ||||||||
\(596\) | −53.8564 | −2.20604 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.85641 | −0.239486 | ||||||||
\(599\) | −46.2487 | −1.88967 | −0.944836 | − | 0.327545i | \(-0.893779\pi\) | ||||
−0.944836 | + | 0.327545i | \(0.893779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.85641 | 0.157306 | 0.0786531 | − | 0.996902i | \(-0.474938\pi\) | ||||
0.0786531 | + | 0.996902i | \(0.474938\pi\) | |||||||
\(602\) | 35.3205 | 1.43956 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.2487 | −1.06804 | ||||||||
\(605\) | 0.732051 | 0.0297621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.5885 | −1.52567 | −0.762834 | − | 0.646594i | \(-0.776193\pi\) | ||||
−0.762834 | + | 0.646594i | \(0.776193\pi\) | |||||||
\(608\) | 113.569 | 4.60584 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.53590 | 0.345608 | ||||||||
\(611\) | 2.73205 | 0.110527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9090 | 0.925284 | 0.462642 | − | 0.886545i | \(-0.346901\pi\) | ||||
0.462642 | + | 0.886545i | \(0.346901\pi\) | |||||||
\(614\) | 74.6410 | 3.01227 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.3205 | −1.42310 | ||||||||
\(617\) | −37.8564 | −1.52404 | −0.762021 | − | 0.647553i | \(-0.775793\pi\) | ||||
−0.762021 | + | 0.647553i | \(0.775793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4641 | 0.822522 | 0.411261 | − | 0.911518i | \(-0.365089\pi\) | ||||
0.411261 | + | 0.911518i | \(0.365089\pi\) | |||||||
\(620\) | 2.14359 | 0.0860888 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 83.5692 | 3.35082 | ||||||||
\(623\) | −1.26795 | −0.0507993 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 5.26795 | 0.210550 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 57.5692 | 2.29726 | ||||||||
\(629\) | −27.1244 | −1.08152 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.39230 | −0.135046 | −0.0675228 | − | 0.997718i | \(-0.521510\pi\) | ||||
−0.0675228 | + | 0.997718i | \(0.521510\pi\) | |||||||
\(632\) | 54.2487 | 2.15790 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.9282 | 1.14889 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85641 | −0.0735535 | ||||||||
\(638\) | 3.46410 | 0.137145 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.7128 | −1.09545 | ||||||||
\(641\) | −2.87564 | −0.113581 | −0.0567906 | − | 0.998386i | \(-0.518087\pi\) | ||||
−0.0567906 | + | 0.998386i | \(0.518087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.3923 | 1.19856 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(644\) | 163.138 | 6.42856 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 59.5692 | 2.34372 | ||||||||
\(647\) | −26.2487 | −1.03194 | −0.515972 | − | 0.856606i | \(-0.672569\pi\) | ||||
−0.515972 | + | 0.856606i | \(0.672569\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1962 | 0.400234 | ||||||||
\(650\) | −3.26795 | −0.128180 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 103.818 | 4.06582 | ||||||||
\(653\) | 29.4641 | 1.15302 | 0.576510 | − | 0.817090i | \(-0.304414\pi\) | ||||
0.576510 | + | 0.817090i | \(0.304414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.0718 | 0.432611 | ||||||||
\(656\) | −21.8564 | −0.853349 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −103.962 | −4.05284 | ||||||||
\(659\) | 37.6603 | 1.46704 | 0.733518 | − | 0.679670i | \(-0.237877\pi\) | ||||
0.733518 | + | 0.679670i | \(0.237877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.60770 | 0.101428 | 0.0507138 | − | 0.998713i | \(-0.483850\pi\) | ||||
0.0507138 | + | 0.998713i | \(0.483850\pi\) | |||||||
\(662\) | 74.8372 | 2.90863 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.1962 | 0.550503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.1436 | −0.392762 | ||||||||
\(668\) | −124.210 | −4.80584 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.8564 | −0.458053 | ||||||||
\(671\) | 4.26795 | 0.164762 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.44486 | −0.364073 | −0.182036 | − | 0.983292i | \(-0.558269\pi\) | ||||
−0.182036 | + | 0.983292i | \(0.558269\pi\) | |||||||
\(674\) | 81.9090 | 3.15502 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −70.6410 | −2.71696 | ||||||||
\(677\) | −30.2487 | −1.16255 | −0.581276 | − | 0.813706i | \(-0.697446\pi\) | ||||
−0.581276 | + | 0.813706i | \(0.697446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.1244 | 0.772302 | ||||||||
\(680\) | −29.0718 | −1.11485 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.46410 | 0.0560633 | ||||||||
\(683\) | 22.5885 | 0.864323 | 0.432162 | − | 0.901796i | \(-0.357751\pi\) | ||||
0.432162 | + | 0.901796i | \(0.357751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.14359 | 0.234735 | ||||||||
\(686\) | −0.732051 | −0.0279498 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 51.7128 | 1.97153 | ||||||||
\(689\) | 1.26795 | 0.0483050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.21539 | −0.274486 | −0.137243 | − | 0.990537i | \(-0.543824\pi\) | ||||
−0.137243 | + | 0.990537i | \(0.543824\pi\) | |||||||
\(692\) | 24.0000 | 0.912343 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.2487 | 1.07231 | ||||||||
\(695\) | −5.26795 | −0.199825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14359 | −0.232705 | ||||||||
\(698\) | 16.0526 | 0.607598 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 91.0333 | 3.44074 | ||||||||
\(701\) | −9.94744 | −0.375710 | −0.187855 | − | 0.982197i | \(-0.560153\pi\) | ||||
−0.187855 | + | 0.982197i | \(0.560153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.5885 | 1.26681 | ||||||||
\(704\) | −29.8564 | −1.12526 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 57.7128 | 2.17205 | ||||||||
\(707\) | −0.732051 | −0.0275316 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.3923 | −1.32919 | −0.664593 | − | 0.747206i | \(-0.731395\pi\) | ||||
−0.664593 | + | 0.747206i | \(0.731395\pi\) | |||||||
\(710\) | −27.7128 | −1.04004 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.21539 | −0.120502 | ||||||||
\(713\) | −4.28719 | −0.160556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.196152 | 0.00733568 | ||||||||
\(716\) | 77.5692 | 2.89890 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.8564 | 0.666395 | ||||||||
\(719\) | −22.9808 | −0.857038 | −0.428519 | − | 0.903533i | \(-0.640964\pi\) | ||||
−0.428519 | + | 0.903533i | \(0.640964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.9808 | −1.78690 | ||||||||
\(722\) | −21.8564 | −0.813411 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −89.1769 | −3.31423 | ||||||||
\(725\) | −5.66025 | −0.210217 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.3205 | −1.08744 | −0.543719 | − | 0.839268i | \(-0.682984\pi\) | ||||
−0.543719 | + | 0.839268i | \(0.682984\pi\) | |||||||
\(728\) | −9.46410 | −0.350763 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.39230 | −0.236590 | ||||||||
\(731\) | 14.5359 | 0.537630 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.9282 | 0.920744 | 0.460372 | − | 0.887726i | \(-0.347716\pi\) | ||||
0.460372 | + | 0.887726i | \(0.347716\pi\) | |||||||
\(734\) | −38.0526 | −1.40455 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 174.851 | 6.44510 | ||||||||
\(737\) | −5.92820 | −0.218368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.2487 | −1.25986 | −0.629930 | − | 0.776652i | \(-0.716916\pi\) | ||||
−0.629930 | + | 0.776652i | \(0.716916\pi\) | |||||||
\(740\) | −25.8564 | −0.950500 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −48.2487 | −1.77127 | ||||||||
\(743\) | −28.5885 | −1.04881 | −0.524404 | − | 0.851469i | \(-0.675712\pi\) | ||||
−0.524404 | + | 0.851469i | \(0.675712\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.21539 | −0.264351 | ||||||||
\(746\) | 54.9808 | 2.01299 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.9282 | −0.838338 | ||||||||
\(749\) | 21.1244 | 0.771867 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.3205 | −0.814487 | −0.407243 | − | 0.913320i | \(-0.633510\pi\) | ||||
−0.407243 | + | 0.913320i | \(0.633510\pi\) | |||||||
\(752\) | −152.210 | −5.55054 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.928203 | 0.0338032 | ||||||||
\(755\) | −3.51666 | −0.127984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3205 | 1.02933 | 0.514663 | − | 0.857392i | \(-0.327917\pi\) | ||||
0.514663 | + | 0.857392i | \(0.327917\pi\) | |||||||
\(758\) | −40.5885 | −1.47424 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 36.0000 | 1.30586 | ||||||||
\(761\) | 0.679492 | 0.0246316 | 0.0123158 | − | 0.999924i | \(-0.496080\pi\) | ||||
0.0123158 | + | 0.999924i | \(0.496080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −44.2487 | −1.60191 | ||||||||
\(764\) | 21.8564 | 0.790737 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 67.5692 | 2.44138 | ||||||||
\(767\) | 2.73205 | 0.0986486 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.5885 | −0.922743 | −0.461372 | − | 0.887207i | \(-0.652643\pi\) | ||||
−0.461372 | + | 0.887207i | \(0.652643\pi\) | |||||||
\(770\) | −7.46410 | −0.268988 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.3205 | −0.551397 | ||||||||
\(773\) | −21.1244 | −0.759790 | −0.379895 | − | 0.925030i | \(-0.624040\pi\) | ||||
−0.379895 | + | 0.925030i | \(0.624040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.39230 | −0.0859341 | ||||||||
\(776\) | 51.0333 | 1.83199 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 58.6410 | 2.10238 | ||||||||
\(779\) | 7.60770 | 0.272574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8564 | −0.495821 | ||||||||
\(782\) | 91.7128 | 3.27964 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 103.426 | 3.69377 | ||||||||
\(785\) | 7.71281 | 0.275282 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0526 | 0.821735 | 0.410867 | − | 0.911695i | \(-0.365226\pi\) | ||||
0.410867 | + | 0.911695i | \(0.365226\pi\) | |||||||
\(788\) | −52.7846 | −1.88037 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.4641 | 0.407874 | ||||||||
\(791\) | −43.5167 | −1.54727 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14359 | 0.0406102 | ||||||||
\(794\) | −55.7128 | −1.97717 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −81.9615 | −2.90505 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.7846 | −1.51361 | ||||||||
\(800\) | 97.5692 | 3.44959 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.8564 | −0.630532 | ||||||||
\(803\) | −3.19615 | −0.112790 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.8564 | 0.770337 | ||||||||
\(806\) | 0.392305 | 0.0138183 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.85641 | −0.0653082 | ||||||||
\(809\) | −23.4115 | −0.823106 | −0.411553 | − | 0.911386i | \(-0.635013\pi\) | ||||
−0.411553 | + | 0.911386i | \(0.635013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.3923 | 0.716071 | 0.358035 | − | 0.933708i | \(-0.383447\pi\) | ||||
0.358035 | + | 0.933708i | \(0.383447\pi\) | |||||||
\(812\) | −25.8564 | −0.907382 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.6603 | −0.618992 | ||||||||
\(815\) | 13.9090 | 0.487210 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0000 | −0.629740 | ||||||||
\(818\) | −89.9090 | −3.14359 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.85641 | −0.204515 | ||||||||
\(821\) | 12.3923 | 0.432494 | 0.216247 | − | 0.976339i | \(-0.430618\pi\) | ||||
0.216247 | + | 0.976339i | \(0.430618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.7128 | 1.69802 | 0.849011 | − | 0.528375i | \(-0.177199\pi\) | ||||
0.849011 | + | 0.528375i | \(0.177199\pi\) | |||||||
\(824\) | −121.674 | −4.23873 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −103.962 | −3.61728 | ||||||||
\(827\) | 44.9808 | 1.56413 | 0.782067 | − | 0.623194i | \(-0.214165\pi\) | ||||
0.782067 | + | 0.623194i | \(0.214165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.607695 | −0.0211061 | −0.0105531 | − | 0.999944i | \(-0.503359\pi\) | ||||
−0.0105531 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.00000 | −0.277350 | ||||||||
\(833\) | 29.0718 | 1.00728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.6410 | −0.575886 | ||||||||
\(836\) | 28.3923 | 0.981968 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 64.7846 | 2.23795 | ||||||||
\(839\) | 35.0333 | 1.20948 | 0.604742 | − | 0.796421i | \(-0.293276\pi\) | ||||
0.604742 | + | 0.796421i | \(0.293276\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | −56.9808 | −1.96369 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −51.0333 | −1.75664 | ||||||||
\(845\) | −9.46410 | −0.325575 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.73205 | −0.128235 | ||||||||
\(848\) | −70.6410 | −2.42582 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 51.1769 | 1.75535 | ||||||||
\(851\) | 51.7128 | 1.77269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2679 | 0.420047 | 0.210023 | − | 0.977696i | \(-0.432646\pi\) | ||||
0.210023 | + | 0.977696i | \(0.432646\pi\) | |||||||
\(854\) | −43.5167 | −1.48911 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 53.5692 | 1.83096 | ||||||||
\(857\) | −23.8038 | −0.813124 | −0.406562 | − | 0.913623i | \(-0.633272\pi\) | ||||
−0.406562 | + | 0.913623i | \(0.633272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.8564 | 0.984568 | 0.492284 | − | 0.870435i | \(-0.336162\pi\) | ||||
0.492284 | + | 0.870435i | \(0.336162\pi\) | |||||||
\(860\) | 13.8564 | 0.472500 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.7128 | 1.35262 | ||||||||
\(863\) | 17.9090 | 0.609628 | 0.304814 | − | 0.952412i | \(-0.401406\pi\) | ||||
0.304814 | + | 0.952412i | \(0.401406\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.21539 | 0.109327 | ||||||||
\(866\) | 9.85641 | 0.334934 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.9282 | −0.370927 | ||||||||
\(869\) | 5.73205 | 0.194447 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.58846 | −0.0538228 | ||||||||
\(872\) | −112.210 | −3.79992 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −113.569 | −3.84154 | ||||||||
\(875\) | 25.8564 | 0.874106 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1962 | −0.378067 | −0.189034 | − | 0.981971i | \(-0.560536\pi\) | ||||
−0.189034 | + | 0.981971i | \(0.560536\pi\) | |||||||
\(878\) | −83.4256 | −2.81548 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.9282 | −0.368390 | ||||||||
\(881\) | 51.3205 | 1.72903 | 0.864516 | − | 0.502605i | \(-0.167625\pi\) | ||||
0.864516 | + | 0.502605i | \(0.167625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.67949 | −0.191130 | −0.0955651 | − | 0.995423i | \(-0.530466\pi\) | ||||
−0.0955651 | + | 0.995423i | \(0.530466\pi\) | |||||||
\(884\) | −6.14359 | −0.206631 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.92820 | −0.299949 | ||||||||
\(887\) | −6.73205 | −0.226040 | −0.113020 | − | 0.993593i | \(-0.536052\pi\) | ||||
−0.113020 | + | 0.993593i | \(0.536052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.3923 | −0.683936 | ||||||||
\(890\) | −0.679492 | −0.0227766 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 97.5692 | 3.26686 | ||||||||
\(893\) | 52.9808 | 1.77293 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.3923 | 0.347376 | ||||||||
\(896\) | 141.282 | 4.71990 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.0000 | −0.934372 | ||||||||
\(899\) | 0.679492 | 0.0226623 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8564 | −0.661513 | ||||||||
\(902\) | −4.00000 | −0.133185 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −110.354 | −3.67031 | ||||||||
\(905\) | −11.9474 | −0.397146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.4641 | 0.413864 | 0.206932 | − | 0.978355i | \(-0.433652\pi\) | ||||
0.206932 | + | 0.978355i | \(0.433652\pi\) | |||||||
\(908\) | 162.067 | 5.37837 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.00000 | −0.0662994 | ||||||||
\(911\) | 9.46410 | 0.313560 | 0.156780 | − | 0.987634i | \(-0.449889\pi\) | ||||
0.156780 | + | 0.987634i | \(0.449889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 30.2487 | 1.00054 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −89.5692 | −2.95945 | ||||||||
\(917\) | −56.4449 | −1.86397 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.3205 | −1.42901 | −0.714506 | − | 0.699629i | \(-0.753348\pi\) | ||||
−0.714506 | + | 0.699629i | \(0.753348\pi\) | |||||||
\(920\) | 55.4256 | 1.82733 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −81.0333 | −2.66869 | ||||||||
\(923\) | −3.71281 | −0.122209 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8564 | 0.948793 | ||||||||
\(926\) | 70.4449 | 2.31496 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −27.7128 | −0.909718 | ||||||||
\(929\) | −43.2679 | −1.41958 | −0.709788 | − | 0.704416i | \(-0.751209\pi\) | ||||
−0.709788 | + | 0.704416i | \(0.751209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.0000 | −1.17985 | ||||||||
\(932\) | 34.6410 | 1.13470 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −51.7128 | −1.69209 | ||||||||
\(935\) | −3.07180 | −0.100458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.1962 | −1.47649 | −0.738247 | − | 0.674531i | \(-0.764346\pi\) | ||||
−0.738247 | + | 0.674531i | \(0.764346\pi\) | |||||||
\(938\) | 60.4449 | 1.97359 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −40.7846 | −1.33025 | ||||||||
\(941\) | −26.5359 | −0.865046 | −0.432523 | − | 0.901623i | \(-0.642376\pi\) | ||||
−0.432523 | + | 0.901623i | \(0.642376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.7128 | 0.381422 | ||||||||
\(944\) | −152.210 | −4.95402 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.46410 | 0.307704 | ||||||||
\(947\) | 23.6603 | 0.768855 | 0.384427 | − | 0.923155i | \(-0.374399\pi\) | ||||
0.384427 | + | 0.923155i | \(0.374399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.856406 | −0.0278001 | ||||||||
\(950\) | −63.3731 | −2.05609 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 148.210 | 4.80352 | ||||||||
\(953\) | 6.14359 | 0.199011 | 0.0995053 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995053 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.92820 | 0.0947544 | ||||||||
\(956\) | −89.5692 | −2.89688 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.4641 | −1.01656 | ||||||||
\(959\) | −31.3205 | −1.01139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7128 | −0.990736 | ||||||||
\(962\) | −4.73205 | −0.152567 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 83.0333 | 2.67432 | ||||||||
\(965\) | −2.05256 | −0.0660742 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.4115 | 0.977969 | 0.488985 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488985 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(968\) | −9.46410 | −0.304188 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.7846 | 0.346273 | ||||||||
\(971\) | −2.58846 | −0.0830675 | −0.0415338 | − | 0.999137i | \(-0.513224\pi\) | ||||
−0.0415338 | + | 0.999137i | \(0.513224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.8564 | 0.860977 | ||||||||
\(974\) | −51.5167 | −1.65070 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −63.7128 | −2.03940 | ||||||||
\(977\) | 35.6603 | 1.14087 | 0.570436 | − | 0.821342i | \(-0.306774\pi\) | ||||
0.570436 | + | 0.821342i | \(0.306774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.339746 | −0.0108583 | ||||||||
\(980\) | 27.7128 | 0.885253 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −82.1051 | −2.62008 | ||||||||
\(983\) | 16.0526 | 0.511997 | 0.255999 | − | 0.966677i | \(-0.417596\pi\) | ||||
0.255999 | + | 0.966677i | \(0.417596\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.07180 | −0.225326 | ||||||||
\(986\) | −14.5359 | −0.462917 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.60770 | 0.242033 | ||||||||
\(989\) | −27.7128 | −0.881216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.4641 | −0.840660 | −0.420330 | − | 0.907371i | \(-0.638086\pi\) | ||||
−0.420330 | + | 0.907371i | \(0.638086\pi\) | |||||||
\(992\) | −11.7128 | −0.371882 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 141.282 | 4.48119 | ||||||||
\(995\) | −10.9808 | −0.348114 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.143594 | 0.00454765 | 0.00227383 | − | 0.999997i | \(-0.499276\pi\) | ||||
0.00227383 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(998\) | 53.1769 | 1.68329 | ||||||||
\(999\) | 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 | 297.2.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 297.2.a.f.1.2 | yes | 2 | ||
4.3 | odd | 2 | 4752.2.a.w.1.2 | 2 | |||
5.4 | even | 2 | 7425.2.a.bl.1.2 | 2 | |||
9.2 | odd | 6 | 891.2.e.m.595.1 | 4 | |||
9.4 | even | 3 | 891.2.e.p.298.2 | 4 | |||
9.5 | odd | 6 | 891.2.e.m.298.1 | 4 | |||
9.7 | even | 3 | 891.2.e.p.595.2 | 4 | |||
11.10 | odd | 2 | 3267.2.a.q.1.2 | 2 | |||
12.11 | even | 2 | 4752.2.a.bf.1.1 | 2 | |||
15.14 | odd | 2 | 7425.2.a.z.1.1 | 2 | |||
33.32 | even | 2 | 3267.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
297.2.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
297.2.a.f.1.2 | yes | 2 | 3.2 | odd | 2 | ||
891.2.e.m.298.1 | 4 | 9.5 | odd | 6 | |||
891.2.e.m.595.1 | 4 | 9.2 | odd | 6 | |||
891.2.e.p.298.2 | 4 | 9.4 | even | 3 | |||
891.2.e.p.595.2 | 4 | 9.7 | even | 3 | |||
3267.2.a.l.1.1 | 2 | 33.32 | even | 2 | |||
3267.2.a.q.1.2 | 2 | 11.10 | odd | 2 | |||
4752.2.a.w.1.2 | 2 | 4.3 | odd | 2 | |||
4752.2.a.bf.1.1 | 2 | 12.11 | even | 2 | |||
7425.2.a.z.1.1 | 2 | 15.14 | odd | 2 | |||
7425.2.a.bl.1.2 | 2 | 5.4 | even | 2 |