Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(289,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.t (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.5 | ||
Character | \(\chi\) | \(=\) | 3024.1873 |
Dual form | 3024.2.t.k.289.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.526004 | −0.235236 | −0.117618 | − | 0.993059i | \(-0.537526\pi\) | ||||
−0.117618 | + | 0.993059i | \(0.537526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.43963 | − | 1.02383i | −0.922092 | − | 0.386971i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.61052 | 1.39012 | 0.695062 | − | 0.718950i | \(-0.255377\pi\) | ||||
0.695062 | + | 0.718950i | \(0.255377\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.244554 | − | 0.423580i | 0.0678270 | − | 0.117480i | −0.830118 | − | 0.557588i | \(-0.811727\pi\) |
0.897945 | + | 0.440109i | \(0.145060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.75579 | + | 4.77318i | −0.668378 | + | 1.15767i | 0.309979 | + | 0.950743i | \(0.399678\pi\) |
−0.978357 | + | 0.206922i | \(0.933655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83782 | − | 3.18319i | −0.421624 | − | 0.730274i | 0.574475 | − | 0.818522i | \(-0.305206\pi\) |
−0.996099 | + | 0.0882484i | \(0.971873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0539537 | −0.0112501 | −0.00562506 | − | 0.999984i | \(-0.501791\pi\) | ||||
−0.00562506 | + | 0.999984i | \(0.501791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72332 | −0.944664 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.28471 | + | 5.68929i | 0.609956 | + | 1.05647i | 0.991247 | + | 0.132019i | \(0.0421461\pi\) |
−0.381292 | + | 0.924455i | \(0.624521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.03820 | + | 5.26231i | 0.545676 | + | 0.945139i | 0.998564 | + | 0.0535717i | \(0.0170606\pi\) |
−0.452888 | + | 0.891568i | \(0.649606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.28325 | + | 0.538539i | 0.216909 | + | 0.0910297i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.223731 | + | 0.387513i | 0.0367811 | + | 0.0637068i | 0.883830 | − | 0.467808i | \(-0.154956\pi\) |
−0.847049 | + | 0.531515i | \(0.821623\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.52284 | + | 4.36968i | −0.394001 | + | 0.682430i | −0.992973 | − | 0.118340i | \(-0.962243\pi\) |
0.598972 | + | 0.800770i | \(0.295576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.84893 | − | 4.93449i | −0.434458 | − | 0.752503i | 0.562794 | − | 0.826598i | \(-0.309727\pi\) |
−0.997251 | + | 0.0740947i | \(0.976393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.59810 | − | 7.96415i | 0.670702 | − | 1.16169i | −0.307003 | − | 0.951709i | \(-0.599326\pi\) |
0.977705 | − | 0.209982i | \(-0.0673406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.90354 | + | 4.99552i | 0.700506 | + | 0.713646i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37138 | − | 7.57145i | 0.600455 | − | 1.04002i | −0.392297 | − | 0.919839i | \(-0.628320\pi\) |
0.992752 | − | 0.120180i | \(-0.0383471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.42515 | −0.327008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.31538 | + | 5.74241i | 0.431626 | + | 0.747598i | 0.997014 | − | 0.0772273i | \(-0.0246067\pi\) |
−0.565388 | + | 0.824825i | \(0.691273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.232812 | − | 0.403243i | 0.0298086 | − | 0.0516299i | −0.850736 | − | 0.525593i | \(-0.823844\pi\) |
0.880545 | + | 0.473963i | \(0.157177\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.128636 | + | 0.222805i | −0.0159554 | + | 0.0276355i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.59679 | + | 4.49777i | 0.317248 | + | 0.549490i | 0.979913 | − | 0.199426i | \(-0.0639079\pi\) |
−0.662665 | + | 0.748916i | \(0.730575\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.76328 | 0.209263 | 0.104632 | − | 0.994511i | \(-0.466634\pi\) | ||||
0.104632 | + | 0.994511i | \(0.466634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.23776 | + | 9.07207i | −0.613034 | + | 1.06181i | 0.377692 | + | 0.925931i | \(0.376718\pi\) |
−0.990726 | + | 0.135875i | \(0.956616\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.2479 | − | 4.72039i | −1.28182 | − | 0.537938i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.18509 | − | 14.1770i | 0.920895 | − | 1.59504i | 0.122860 | − | 0.992424i | \(-0.460793\pi\) |
0.798034 | − | 0.602612i | \(-0.205873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.49251 | + | 7.78126i | 0.493117 | + | 0.854104i | 0.999969 | − | 0.00792925i | \(-0.00252399\pi\) |
−0.506851 | + | 0.862034i | \(0.669191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44956 | − | 2.51071i | 0.157227 | − | 0.272325i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.05145 | + | 12.2135i | 0.747452 | + | 1.29463i | 0.949040 | + | 0.315155i | \(0.102056\pi\) |
−0.201588 | + | 0.979470i | \(0.564610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03029 | + | 0.782994i | −0.108004 | + | 0.0820801i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.966699 | + | 1.67437i | 0.0991813 | + | 0.171787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.22413 | + | 9.04847i | 0.530430 | + | 0.918732i | 0.999370 | + | 0.0355020i | \(0.0113030\pi\) |
−0.468939 | + | 0.883230i | \(0.655364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.96508 | 0.991562 | 0.495781 | − | 0.868448i | \(-0.334882\pi\) | ||||
0.495781 | + | 0.868448i | \(0.334882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.6511 | −1.14801 | −0.574006 | − | 0.818851i | \(-0.694611\pi\) | ||||
−0.574006 | + | 0.818851i | \(0.694611\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.45556 | + | 4.25316i | 0.237388 | + | 0.411168i | 0.959964 | − | 0.280123i | \(-0.0903754\pi\) |
−0.722576 | + | 0.691292i | \(0.757042\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.76353 | + | 16.9109i | −0.935177 | + | 1.61977i | −0.160858 | + | 0.986978i | \(0.551426\pi\) |
−0.774319 | + | 0.632796i | \(0.781907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.48658 | + | 9.50304i | −0.516134 | + | 0.893971i | 0.483690 | + | 0.875239i | \(0.339296\pi\) |
−0.999825 | + | 0.0187317i | \(0.994037\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0283799 | 0.00264644 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.6100 | − | 8.82330i | 1.06429 | − | 0.808830i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2569 | 0.932444 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.11451 | 0.457456 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6107 | 1.47396 | 0.736979 | − | 0.675915i | \(-0.236252\pi\) | ||||
0.736979 | + | 0.675915i | \(0.236252\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.81696 | 0.508230 | 0.254115 | − | 0.967174i | \(-0.418216\pi\) | ||||
0.254115 | + | 0.967174i | \(0.418216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.22454 | + | 9.64740i | 0.106181 | + | 0.836536i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.22626 | 0.788253 | 0.394126 | − | 0.919056i | \(-0.371047\pi\) | ||||
0.394126 | + | 0.919056i | \(0.371047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.88477 | + | 11.9248i | −0.583959 | + | 1.01145i | 0.411046 | + | 0.911615i | \(0.365164\pi\) |
−0.995004 | + | 0.0998314i | \(0.968170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.12752 | − | 1.95292i | 0.0942880 | − | 0.163312i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72777 | − | 2.99259i | −0.143484 | − | 0.248521i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.30086 | 0.680033 | 0.340016 | − | 0.940420i | \(-0.389567\pi\) | ||||
0.340016 | + | 0.940420i | \(0.389567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4979 | 1.17982 | 0.589911 | − | 0.807468i | \(-0.299163\pi\) | ||||
0.589911 | + | 0.807468i | \(0.299163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.59811 | − | 2.76800i | −0.128363 | − | 0.222331i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.24434 | + | 10.8155i | 0.498352 | + | 0.863172i | 0.999998 | − | 0.00190155i | \(-0.000605282\pi\) |
−0.501646 | + | 0.865073i | \(0.667272\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.131627 | + | 0.0552394i | 0.0103736 | + | 0.00435348i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.48448 | + | 4.30325i | 0.194600 | + | 0.337057i | 0.946769 | − | 0.321913i | \(-0.104326\pi\) |
−0.752169 | + | 0.658970i | \(0.770993\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0088 | + | 17.3357i | −0.774504 | + | 1.34148i | 0.160569 | + | 0.987025i | \(0.448667\pi\) |
−0.935073 | + | 0.354456i | \(0.884666\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38039 | + | 11.0512i | 0.490799 | + | 0.850089i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.52742 | − | 7.84173i | 0.344214 | − | 0.596196i | −0.640997 | − | 0.767543i | \(-0.721479\pi\) |
0.985211 | + | 0.171348i | \(0.0548122\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5231 | + | 4.83588i | 0.871067 | + | 0.365558i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.69175 | + | 13.3225i | −0.574908 | + | 0.995770i | 0.421143 | + | 0.906994i | \(0.361629\pi\) |
−0.996052 | + | 0.0887763i | \(0.971704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.54973 | −0.709826 | −0.354913 | − | 0.934899i | \(-0.615489\pi\) | ||||
−0.354913 | + | 0.934899i | \(0.615489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.117683 | − | 0.203834i | −0.00865225 | − | 0.0149861i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.7056 | + | 22.0068i | −0.929129 | + | 1.60930i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.52163 | − | 9.56375i | 0.399531 | − | 0.692009i | −0.594137 | − | 0.804364i | \(-0.702506\pi\) |
0.993668 | + | 0.112355i | \(0.0358395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3496 | − | 23.1221i | −0.960923 | − | 1.66437i | −0.720192 | − | 0.693775i | \(-0.755946\pi\) |
−0.240731 | − | 0.970592i | \(-0.577387\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8386 | −0.914715 | −0.457357 | − | 0.889283i | \(-0.651204\pi\) | ||||
−0.457357 | + | 0.889283i | \(0.651204\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1408 | + | 17.5644i | −0.718864 | + | 1.24511i | 0.242586 | + | 0.970130i | \(0.422004\pi\) |
−0.961450 | + | 0.274979i | \(0.911329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.18860 | − | 17.2427i | −0.153610 | − | 1.21020i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.32702 | − | 2.29847i | 0.0926833 | − | 0.160532i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.47329 | − | 14.6762i | −0.586109 | − | 1.01517i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.77903 | + | 8.27752i | −0.329002 | + | 0.569848i | −0.982314 | − | 0.187241i | \(-0.940046\pi\) |
0.653312 | + | 0.757088i | \(0.273379\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.49855 | + | 2.59556i | 0.102200 | + | 0.177016i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.02435 | − | 15.9487i | −0.137422 | − | 1.08267i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.34788 | + | 2.33460i | 0.0906683 | + | 0.157042i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.9155 | − | 20.6383i | −0.797921 | − | 1.38204i | −0.920968 | − | 0.389639i | \(-0.872600\pi\) |
0.123046 | − | 0.992401i | \(-0.460734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.67134 | −0.177303 | −0.0886514 | − | 0.996063i | \(-0.528256\pi\) | ||||
−0.0886514 | + | 0.996063i | \(0.528256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.32516 | 0.417978 | 0.208989 | − | 0.977918i | \(-0.432983\pi\) | ||||
0.208989 | + | 0.977918i | \(0.432983\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.63381 | − | 8.02600i | −0.303571 | − | 0.525801i | 0.673371 | − | 0.739305i | \(-0.264846\pi\) |
−0.976942 | + | 0.213504i | \(0.931512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.41862 | + | 4.18918i | −0.157774 | + | 0.273272i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.69219 | − | 2.93096i | 0.109459 | − | 0.189588i | −0.806092 | − | 0.591790i | \(-0.798422\pi\) |
0.915551 | + | 0.402202i | \(0.131755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1596 | 0.847687 | 0.423844 | − | 0.905735i | \(-0.360681\pi\) | ||||
0.423844 | + | 0.905735i | \(0.360681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.57929 | − | 2.62767i | −0.164784 | − | 0.167876i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.79778 | −0.114390 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.30235 | −0.145323 | −0.0726614 | − | 0.997357i | \(-0.523149\pi\) | ||||
−0.0726614 | + | 0.997357i | \(0.523149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.248755 | −0.0156391 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.1323 | 1.81722 | 0.908610 | − | 0.417646i | \(-0.137145\pi\) | ||||
0.908610 | + | 0.417646i | \(0.137145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.149072 | − | 1.17445i | −0.00926286 | − | 0.0729767i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.71837 | −0.167622 | −0.0838110 | − | 0.996482i | \(-0.526709\pi\) | ||||
−0.0838110 | + | 0.996482i | \(0.526709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.29936 | + | 3.98261i | −0.141249 | + | 0.244650i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.80840 | + | 4.86428i | −0.171231 | + | 0.296581i | −0.938850 | − | 0.344325i | \(-0.888108\pi\) |
0.767620 | + | 0.640906i | \(0.221441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.25164 | + | 12.5602i | 0.440506 | + | 0.762978i | 0.997727 | − | 0.0673860i | \(-0.0214659\pi\) |
−0.557221 | + | 0.830364i | \(0.688133\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.7770 | −1.31320 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.74791 | −0.105022 | −0.0525108 | − | 0.998620i | \(-0.516722\pi\) | ||||
−0.0525108 | + | 0.998620i | \(0.516722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.35657 | − | 9.27786i | −0.319546 | − | 0.553471i | 0.660847 | − | 0.750521i | \(-0.270197\pi\) |
−0.980393 | + | 0.197050i | \(0.936864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.29833 | − | 10.9090i | −0.374397 | − | 0.648474i | 0.615840 | − | 0.787871i | \(-0.288817\pi\) |
−0.990237 | + | 0.139397i | \(0.955483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6286 | − | 8.07743i | 0.627386 | − | 0.476796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.68881 | − | 11.5854i | −0.393459 | − | 0.681491i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.57575 | − | 2.72928i | 0.0920562 | − | 0.159446i | −0.816320 | − | 0.577600i | \(-0.803989\pi\) |
0.908376 | + | 0.418154i | \(0.137323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.74391 | − | 3.02053i | −0.101534 | − | 0.175862i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0131946 | + | 0.0228537i | −0.000763063 | + | 0.00132166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.89824 | + | 14.9551i | 0.109413 | + | 0.861999i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.122460 | + | 0.212107i | −0.00701206 | + | 0.0121452i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.3884 | 1.16363 | 0.581813 | − | 0.813322i | \(-0.302343\pi\) | ||||
0.581813 | + | 0.813322i | \(0.302343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3507 | − | 19.6600i | −0.643640 | − | 1.11482i | −0.984614 | − | 0.174744i | \(-0.944090\pi\) |
0.340974 | − | 0.940073i | \(-0.389243\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.35389 | − | 14.4694i | 0.472190 | − | 0.817857i | −0.527304 | − | 0.849677i | \(-0.676797\pi\) |
0.999494 | + | 0.0318201i | \(0.0101304\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.16401 | − | 8.94433i | 0.290040 | − | 0.502364i | −0.683779 | − | 0.729689i | \(-0.739665\pi\) |
0.973819 | + | 0.227325i | \(0.0729981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.1442 | + | 26.2306i | 0.847914 | + | 1.46863i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.2586 | 1.12722 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.15511 | + | 2.00070i | −0.0640738 | + | 0.110979i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.3716 | + | 14.7219i | −1.06799 | + | 0.811643i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3158 | + | 19.5995i | −0.621970 | + | 1.07728i | 0.367148 | + | 0.930162i | \(0.380334\pi\) |
−0.989118 | + | 0.147122i | \(0.952999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.36592 | − | 2.36585i | −0.0746283 | − | 0.129260i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.78253 | − | 11.7477i | 0.369468 | − | 0.639938i | −0.620014 | − | 0.784590i | \(-0.712873\pi\) |
0.989482 | + | 0.144653i | \(0.0462066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.0077 | + | 24.2620i | 0.758558 | + | 1.31386i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.84824 | − | 17.2076i | −0.369770 | − | 0.929123i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.5131 | + | 28.6015i | 0.886470 | + | 1.53541i | 0.844019 | + | 0.536313i | \(0.180183\pi\) |
0.0424511 | + | 0.999099i | \(0.486483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1773 | − | 17.6276i | −0.544778 | − | 0.943584i | −0.998621 | − | 0.0525019i | \(-0.983280\pi\) |
0.453842 | − | 0.891082i | \(-0.350053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.50763 | 0.293141 | 0.146571 | − | 0.989200i | \(-0.453176\pi\) | ||||
0.146571 | + | 0.989200i | \(0.453176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.927495 | −0.0492263 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4656 | − | 18.1270i | −0.552354 | − | 0.956704i | −0.998104 | − | 0.0615472i | \(-0.980397\pi\) |
0.445751 | − | 0.895157i | \(-0.352937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.74486 | − | 4.75424i | 0.144467 | − | 0.250223i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.75509 | − | 4.77195i | 0.144208 | − | 0.249775i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.28637 | −0.223747 | −0.111873 | − | 0.993722i | \(-0.535685\pi\) | ||||
−0.111873 | + | 0.993722i | \(0.535685\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.4164 | + | 13.9959i | −0.956132 | + | 0.726633i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.2892 | −0.584534 | −0.292267 | − | 0.956337i | \(-0.594410\pi\) | ||||
−0.292267 | + | 0.956337i | \(0.594410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.21316 | 0.165486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.5828 | 1.05727 | 0.528634 | − | 0.848850i | \(-0.322705\pi\) | ||||
0.528634 | + | 0.848850i | \(0.322705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6215 | −1.10481 | −0.552405 | − | 0.833576i | \(-0.686290\pi\) | ||||
−0.552405 | + | 0.833576i | \(0.686290\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.91646 | + | 2.48295i | 0.301531 | + | 0.126543i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6848 | 0.744550 | 0.372275 | − | 0.928123i | \(-0.378578\pi\) | ||||
0.372275 | + | 0.928123i | \(0.378578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.148685 | − | 0.257531i | 0.00751934 | − | 0.0130239i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.30539 | + | 7.45716i | −0.216628 | + | 0.375210i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.13424 | − | 5.42866i | −0.157303 | − | 0.272457i | 0.776592 | − | 0.630003i | \(-0.216947\pi\) |
−0.933895 | + | 0.357547i | \(0.883613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3901 | −1.46767 | −0.733836 | − | 0.679327i | \(-0.762272\pi\) | ||||
−0.733836 | + | 0.679327i | \(0.762272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.97201 | 0.148046 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.03152 | + | 1.78664i | 0.0511303 | + | 0.0885603i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.816425 | + | 1.41409i | 0.0403696 | + | 0.0699222i | 0.885504 | − | 0.464631i | \(-0.153813\pi\) |
−0.845135 | + | 0.534554i | \(0.820480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.20904 | − | 17.4037i | −0.108700 | − | 0.856381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.36308 | − | 4.09298i | −0.115999 | − | 0.200916i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.01823 | + | 15.6200i | −0.440569 | + | 0.763088i | −0.997732 | − | 0.0673151i | \(-0.978557\pi\) |
0.557162 | + | 0.830404i | \(0.311890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8278 | + | 29.1465i | 0.820135 | + | 1.42052i | 0.905581 | + | 0.424172i | \(0.139435\pi\) |
−0.0854466 | + | 0.996343i | \(0.527232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.0165 | − | 22.5452i | 0.631393 | − | 1.09360i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.980827 | + | 0.745401i | −0.0474655 | + | 0.0360725i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1545 | + | 19.3202i | −0.537295 | + | 0.930622i | 0.461754 | + | 0.887008i | \(0.347220\pi\) |
−0.999048 | + | 0.0436135i | \(0.986113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.32414 | 0.351976 | 0.175988 | − | 0.984392i | \(-0.443688\pi\) | ||||
0.175988 | + | 0.984392i | \(0.443688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0991570 | + | 0.171745i | 0.00474332 | + | 0.00821567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3364 | + | 21.3673i | −0.588785 | + | 1.01981i | 0.405607 | + | 0.914048i | \(0.367060\pi\) |
−0.994392 | + | 0.105758i | \(0.966273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.2682 | + | 26.4452i | −0.725412 | + | 1.25645i | 0.233393 | + | 0.972383i | \(0.425017\pi\) |
−0.958804 | + | 0.284067i | \(0.908316\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.70909 | − | 6.42434i | −0.175828 | − | 0.304543i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.4782 | 1.95748 | 0.978738 | − | 0.205116i | \(-0.0657572\pi\) | ||||
0.978738 | + | 0.205116i | \(0.0657572\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.6316 | + | 20.1465i | −0.547710 | + | 0.948662i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.541939 | − | 0.411858i | 0.0254065 | − | 0.0193082i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.81446 | − | 10.0709i | 0.271989 | − | 0.471099i | −0.697382 | − | 0.716700i | \(-0.745652\pi\) |
0.969371 | + | 0.245601i | \(0.0789852\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.60886 | + | 9.71483i | 0.261231 | + | 0.452465i | 0.966569 | − | 0.256406i | \(-0.0825383\pi\) |
−0.705339 | + | 0.708871i | \(0.749205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9362 | − | 34.5305i | 0.926514 | − | 1.60477i | 0.137405 | − | 0.990515i | \(-0.456124\pi\) |
0.789108 | − | 0.614254i | \(-0.210543\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.7818 | + | 20.4067i | 0.545198 | + | 0.944311i | 0.998594 | + | 0.0530016i | \(0.0168788\pi\) |
−0.453397 | + | 0.891309i | \(0.649788\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.73024 | − | 13.6315i | −0.0798950 | − | 0.629446i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1350 | − | 22.7506i | −0.603950 | − | 1.04607i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.68059 | + | 15.0352i | 0.398293 | + | 0.689864i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.2297 | 0.650172 | 0.325086 | − | 0.945685i | \(-0.394607\pi\) | ||||
0.325086 | + | 0.945685i | \(0.394607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.218857 | 0.00997902 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.74792 | − | 4.75953i | −0.124776 | − | 0.216119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9818 | − | 24.2171i | 0.633574 | − | 1.09738i | −0.353242 | − | 0.935532i | \(-0.614921\pi\) |
0.986815 | − | 0.161850i | \(-0.0517460\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2543 | − | 29.8853i | 0.778676 | − | 1.34871i | −0.154030 | − | 0.988066i | \(-0.549225\pi\) |
0.932705 | − | 0.360639i | \(-0.117442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.2080 | −1.63072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.30175 | − | 1.80530i | −0.192960 | − | 0.0809789i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.2873 | −1.17678 | −0.588390 | − | 0.808577i | \(-0.700238\pi\) | ||||
−0.588390 | + | 0.808577i | \(0.700238\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.09068 | 0.271570 | 0.135785 | − | 0.990738i | \(-0.456644\pi\) | ||||
0.135785 | + | 0.990738i | \(0.456644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.24167 | −0.233251 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.17231 | 0.362231 | 0.181116 | − | 0.983462i | \(-0.442029\pi\) | ||||
0.181116 | + | 0.983462i | \(0.442029\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.0664 | − | 16.7699i | 0.976162 | − | 0.741856i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.12850 | 0.270054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1996 | − | 36.7189i | 0.932360 | − | 1.61489i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0485 | + | 22.6007i | −0.571666 | + | 0.990155i | 0.424729 | + | 0.905321i | \(0.360370\pi\) |
−0.996395 | + | 0.0848346i | \(0.972964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6655 | − | 23.6694i | −0.597553 | − | 1.03499i | −0.993181 | − | 0.116581i | \(-0.962807\pi\) |
0.395628 | − | 0.918411i | \(-0.370527\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.4906 | −1.45887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9971 | −0.999873 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.23394 | + | 2.13725i | 0.0534478 | + | 0.0925744i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.29164 | − | 2.23718i | −0.0558423 | − | 0.0967217i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.6079 | + | 23.0320i | 0.973790 | + | 0.992057i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.79086 | − | 10.0301i | −0.248969 | − | 0.431226i | 0.714271 | − | 0.699869i | \(-0.246758\pi\) |
−0.963240 | + | 0.268643i | \(0.913425\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.13566 | − | 8.89522i | 0.219987 | − | 0.381029i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3651 | − | 35.2734i | −0.870750 | − | 1.50818i | −0.861222 | − | 0.508228i | \(-0.830301\pi\) |
−0.00952755 | − | 0.999955i | \(-0.503033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0734 | − | 20.9117i | 0.514344 | − | 0.890869i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.4834 | + | 26.2064i | −1.46638 | + | 1.11441i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0085 | + | 17.3353i | −0.424075 | + | 0.734520i | −0.996334 | − | 0.0855533i | \(-0.972734\pi\) |
0.572258 | + | 0.820074i | \(0.306068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.78687 | −0.117872 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.4664 | − | 21.5924i | −0.525396 | − | 0.910013i | −0.999562 | − | 0.0295776i | \(-0.990584\pi\) |
0.474166 | − | 0.880435i | \(-0.342750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.88597 | − | 4.99864i | 0.121414 | − | 0.210294i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.90013 | + | 8.48727i | −0.205424 | + | 0.355805i | −0.950268 | − | 0.311434i | \(-0.899191\pi\) |
0.744844 | + | 0.667239i | \(0.232524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3948 | − | 35.3247i | −0.853494 | − | 1.47829i | −0.878035 | − | 0.478596i | \(-0.841146\pi\) |
0.0245416 | − | 0.999699i | \(-0.492187\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.254841 | 0.0106276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2505 | + | 17.7544i | −0.426734 | + | 0.739125i | −0.996581 | − | 0.0826259i | \(-0.973669\pi\) |
0.569846 | + | 0.821751i | \(0.307003\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.99336 | − | 23.5829i | −0.124185 | − | 0.978385i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.1543 | − | 34.9083i | 0.834707 | − | 1.44575i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.2916 | − | 33.4141i | −0.796251 | − | 1.37915i | −0.922042 | − | 0.387090i | \(-0.873480\pi\) |
0.125791 | − | 0.992057i | \(-0.459853\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1673 | − | 19.3423i | 0.460141 | − | 0.796987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.26539 | + | 2.19172i | 0.0519634 | + | 0.0900032i | 0.890837 | − | 0.454323i | \(-0.150119\pi\) |
−0.838874 | + | 0.544326i | \(0.816785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.10693 | + | 4.64109i | −0.250360 | + | 0.190266i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.01092 | + | 13.8753i | 0.327317 | + | 0.566930i | 0.981979 | − | 0.188992i | \(-0.0605221\pi\) |
−0.654661 | + | 0.755922i | \(0.727189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1601 | − | 38.3824i | −0.903929 | − | 1.56565i | −0.822349 | − | 0.568983i | \(-0.807337\pi\) |
−0.0815796 | − | 0.996667i | \(-0.525996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.39517 | −0.219345 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.59214 | 0.389333 | 0.194666 | − | 0.980870i | \(-0.437638\pi\) | ||||
0.194666 | + | 0.980870i | \(0.437638\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.24897 | − | 3.89533i | −0.0909835 | − | 0.157588i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2371 | − | 19.4632i | 0.453861 | − | 0.786110i | −0.544761 | − | 0.838591i | \(-0.683380\pi\) |
0.998622 | + | 0.0524815i | \(0.0167131\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.7056 | + | 20.2746i | −0.471248 | + | 0.816226i | −0.999459 | − | 0.0328875i | \(-0.989530\pi\) |
0.528211 | + | 0.849113i | \(0.322863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.9769 | −0.642164 | −0.321082 | − | 0.947051i | \(-0.604047\pi\) | ||||
−0.321082 | + | 0.947051i | \(0.604047\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.69838 | − | 37.0158i | −0.188236 | − | 1.48301i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.9263 | 0.837054 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.46622 | −0.0983348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.882517 | 0.0351324 | 0.0175662 | − | 0.999846i | \(-0.494408\pi\) | ||||
0.0175662 | + | 0.999846i | \(0.494408\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.73728 | −0.346729 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.31518 | − | 0.855367i | 0.131352 | − | 0.0338909i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.4282 | −1.59682 | −0.798408 | − | 0.602116i | \(-0.794324\pi\) | ||||
−0.798408 | + | 0.602116i | \(0.794324\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.99047 | + | 5.17964i | −0.117932 | + | 0.204265i | −0.918948 | − | 0.394378i | \(-0.870960\pi\) |
0.801016 | + | 0.598643i | \(0.204293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.4743 | + | 28.5343i | −0.647672 | + | 1.12180i | 0.336005 | + | 0.941860i | \(0.390924\pi\) |
−0.983677 | + | 0.179941i | \(0.942409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2856 | + | 26.4755i | 0.600014 | + | 1.03925i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.0333 | −1.01876 | −0.509380 | − | 0.860542i | \(-0.670125\pi\) | ||||
−0.509380 | + | 0.860542i | \(0.670125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.05974 | −0.119554 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.91651 | + | 8.51565i | 0.191520 | + | 0.331722i | 0.945754 | − | 0.324883i | \(-0.105325\pi\) |
−0.754234 | + | 0.656606i | \(0.771992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.75760 | + | 4.77630i | 0.107258 | + | 0.185777i | 0.914659 | − | 0.404227i | \(-0.132460\pi\) |
−0.807400 | + | 0.590004i | \(0.799126\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.644111 | − | 5.07458i | −0.0249776 | − | 0.196784i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.177222 | − | 0.306958i | −0.00686208 | − | 0.0118855i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.07339 | − | 1.85916i | 0.0414376 | − | 0.0717720i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6176 | + | 33.9788i | 0.756205 | + | 1.30978i | 0.944773 | + | 0.327725i | \(0.106282\pi\) |
−0.188569 | + | 0.982060i | \(0.560385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5816 | + | 32.1843i | −0.714149 | + | 1.23694i | 0.249138 | + | 0.968468i | \(0.419853\pi\) |
−0.963287 | + | 0.268474i | \(0.913481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.48084 | − | 27.4235i | −0.133582 | − | 1.05242i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.10586 | + | 8.84360i | −0.195370 | + | 0.338391i | −0.947022 | − | 0.321169i | \(-0.895924\pi\) |
0.751652 | + | 0.659560i | \(0.229257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85305 | −0.185426 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.13807 | − | 3.70325i | −0.0814542 | − | 0.141083i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5381 | + | 30.3768i | −0.667179 | + | 1.15559i | 0.311510 | + | 0.950243i | \(0.399165\pi\) |
−0.978690 | + | 0.205346i | \(0.934168\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.62142 | − | 6.27248i | 0.137368 | − | 0.237929i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.9048 | − | 24.0839i | −0.526683 | − | 0.912242i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2500 | −0.651522 | −0.325761 | − | 0.945452i | \(-0.605621\pi\) | ||||
−0.325761 | + | 0.945452i | \(0.605621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.822352 | − | 1.42436i | 0.0310156 | − | 0.0537206i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.3111 | − | 10.2025i | −0.914311 | − | 0.383706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.25734 | − | 12.5701i | 0.272555 | − | 0.472079i | −0.696960 | − | 0.717110i | \(-0.745465\pi\) |
0.969515 | + | 0.245030i | \(0.0787980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.163922 | − | 0.283921i | −0.00613893 | − | 0.0106329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.593081 | + | 1.02725i | −0.0221800 | + | 0.0384168i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.4295 | − | 38.8491i | −0.836480 | − | 1.44883i | −0.892820 | − | 0.450414i | \(-0.851277\pi\) |
0.0563403 | − | 0.998412i | \(-0.482057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.4242 | + | 11.9287i | 1.05857 | + | 0.444248i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.5147 | − | 26.8723i | −0.576203 | − | 0.998013i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.22039 | + | 3.84582i | 0.0823496 | + | 0.142634i | 0.904259 | − | 0.426985i | \(-0.140424\pi\) |
−0.821909 | + | 0.569619i | \(0.807091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.4043 | 1.16153 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.2720 | −1.41361 | −0.706803 | − | 0.707410i | \(-0.749863\pi\) | ||||
−0.706803 | + | 0.707410i | \(0.749863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9725 | + | 20.7370i | 0.441014 | + | 0.763859i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.59381 | − | 4.49261i | 0.0954148 | − | 0.165263i | −0.814367 | − | 0.580350i | \(-0.802916\pi\) |
0.909782 | + | 0.415087i | \(0.136249\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.3351 | − | 28.2932i | 0.599276 | − | 1.03798i | −0.393653 | − | 0.919259i | \(-0.628789\pi\) |
0.992928 | − | 0.118716i | \(-0.0378779\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.36629 | −0.159968 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.63614 | − | 12.8902i | −0.0597832 | − | 0.470997i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1221 | 0.588304 | 0.294152 | − | 0.955759i | \(-0.404963\pi\) | ||||
0.294152 | + | 0.955759i | \(0.404963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.62595 | −0.277537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.6421 | 1.65889 | 0.829444 | − | 0.558589i | \(-0.188657\pi\) | ||||
0.829444 | + | 0.558589i | \(0.188657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2300 | −0.443338 | −0.221669 | − | 0.975122i | \(-0.571150\pi\) | ||||
−0.221669 | + | 0.975122i | \(0.571150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.1333 | − | 31.2601i | 1.48912 | − | 1.13169i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.24316 | 0.117104 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.17344 | − | 5.49656i | 0.114437 | − | 0.198211i | −0.803117 | − | 0.595821i | \(-0.796827\pi\) |
0.917555 | + | 0.397610i | \(0.130160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4515 | + | 42.3512i | −0.879459 | + | 1.52327i | −0.0275225 | + | 0.999621i | \(0.508762\pi\) |
−0.851936 | + | 0.523646i | \(0.824572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.3504 | − | 24.8556i | −0.515481 | − | 0.892839i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.5460 | 0.664481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.12965 | 0.290902 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.28455 | − | 5.68900i | −0.117231 | − | 0.203049i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5749 | − | 20.0483i | −0.412600 | − | 0.714645i | 0.582573 | − | 0.812778i | \(-0.302046\pi\) |
−0.995173 | + | 0.0981337i | \(0.968713\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.1147 | − | 17.5665i | 0.821864 | − | 0.624594i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.113870 | − | 0.197229i | −0.00404365 | − | 0.00700381i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.2284 | + | 41.9648i | −0.858214 | + | 1.48647i | 0.0154170 | + | 0.999881i | \(0.495092\pi\) |
−0.873631 | + | 0.486589i | \(0.838241\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.3429 | + | 43.8951i | 0.896566 | + | 1.55290i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.1488 | + | 41.8270i | −0.852193 | + | 1.47604i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0692363 | − | 0.0290562i | −0.00244026 | − | 0.00102410i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.2647 | − | 17.7791i | 0.360889 | − | 0.625078i | −0.627218 | − | 0.778844i | \(-0.715807\pi\) |
0.988107 | + | 0.153765i | \(0.0491399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7882 | −0.975776 | −0.487888 | − | 0.872906i | \(-0.662233\pi\) | ||||
−0.487888 | + | 0.872906i | \(0.662233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.30685 | − | 2.26353i | −0.0457769 | − | 0.0792880i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4716 | + | 18.1374i | −0.366356 | + | 0.634546i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.27932 | + | 14.3402i | −0.288950 | + | 0.500477i | −0.973559 | − | 0.228434i | \(-0.926640\pi\) |
0.684609 | + | 0.728910i | \(0.259973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.7352 | + | 22.0580i | 0.443922 | + | 0.768895i | 0.997976 | − | 0.0635853i | \(-0.0202535\pi\) |
−0.554055 | + | 0.832480i | \(0.686920\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0798 | 1.25462 | 0.627309 | − | 0.778771i | \(-0.284156\pi\) | ||||
0.627309 | + | 0.778771i | \(0.284156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.3539 | − | 38.7180i | 0.776381 | − | 1.34473i | −0.157633 | − | 0.987498i | \(-0.550386\pi\) |
0.934015 | − | 0.357234i | \(-0.116280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.3577 | + | 9.63884i | −1.29437 | + | 0.333966i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.26467 | − | 9.11868i | 0.182191 | − | 0.315565i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.86805 | − | 13.6279i | −0.271635 | − | 0.470486i | 0.697645 | − | 0.716443i | \(-0.254231\pi\) |
−0.969281 | + | 0.245957i | \(0.920898\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.07866 | + | 12.2606i | −0.244092 | + | 0.422779i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.35611 | − | 5.81296i | −0.115454 | − | 0.199972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.0230 | − | 10.5013i | −0.859799 | − | 0.360829i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0120711 | − | 0.0209078i | −0.000413792 | − | 0.000716709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2010 | + | 24.5968i | 0.486231 | + | 0.842177i | 0.999875 | − | 0.0158264i | \(-0.00503792\pi\) |
−0.513643 | + | 0.858004i | \(0.671705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.97734 | 0.306660 | 0.153330 | − | 0.988175i | \(-0.451000\pi\) | ||||
0.153330 | + | 0.988175i | \(0.451000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.942900 | 0.0321713 | 0.0160857 | − | 0.999871i | \(-0.494880\pi\) | ||||
0.0160857 | + | 0.999871i | \(0.494880\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.0488 | − | 22.6011i | −0.444185 | − | 0.769351i | 0.553810 | − | 0.832643i | \(-0.313173\pi\) |
−0.997995 | + | 0.0632920i | \(0.979840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.38145 | + | 4.12478i | −0.0809716 | + | 0.140247i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.7375 | − | 65.3633i | 1.28016 | − | 2.21730i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.54022 | 0.0860720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.4775 | − | 5.23639i | −0.421816 | − | 0.177022i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.3589 | −0.890077 | −0.445038 | − | 0.895512i | \(-0.646810\pi\) | ||||
−0.445038 | + | 0.895512i | \(0.646810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.6077 | 1.53656 | 0.768281 | − | 0.640113i | \(-0.221112\pi\) | ||||
0.768281 | + | 0.640113i | \(0.221112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.1575 | 0.880271 | 0.440136 | − | 0.897931i | \(-0.354930\pi\) | ||||
0.440136 | + | 0.897931i | \(0.354930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.1925 | 1.24880 | 0.624401 | − | 0.781104i | \(-0.285343\pi\) | ||||
0.624401 | + | 0.781104i | \(0.285343\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.5238 | − | 17.0065i | −1.35912 | − | 0.570380i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.8019 | −1.13114 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.04589 | − | 7.00769i | 0.135239 | − | 0.234241i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.9592 | + | 34.5704i | −0.665677 | + | 1.15299i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0932 | + | 41.7307i | 0.802662 | + | 1.39025i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.02320 | 0.166977 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.8461 | −0.858206 | −0.429103 | − | 0.903255i | \(-0.641170\pi\) | ||||
−0.429103 | + | 0.903255i | \(0.641170\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.41211 | − | 4.17790i | −0.0799169 | − | 0.138420i | 0.823297 | − | 0.567611i | \(-0.192132\pi\) |
−0.903214 | + | 0.429191i | \(0.858799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7128 | + | 35.8756i | 0.685494 | + | 1.18731i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.1912 | − | 5.95558i | −0.468635 | − | 0.196670i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.58183 | − | 16.5962i | −0.316075 | − | 0.547459i | 0.663590 | − | 0.748096i | \(-0.269032\pi\) |
−0.979666 | + | 0.200638i | \(0.935699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.431218 | − | 0.746891i | 0.0141937 | − | 0.0245842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05675 | − | 1.83035i | −0.0347458 | − | 0.0601815i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.0457 | − | 46.8445i | 0.887340 | − | 1.53692i | 0.0443327 | − | 0.999017i | \(-0.485884\pi\) |
0.843008 | − | 0.537902i | \(-0.180783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.88990 | − | 24.7898i | 0.225807 | − | 0.812452i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.68322 | − | 11.5757i | 0.218565 | − | 0.378565i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.6345 | −0.543426 | −0.271713 | − | 0.962378i | \(-0.587590\pi\) | ||||
−0.271713 | + | 0.962378i | \(0.587590\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.44956 | − | 2.51071i | −0.0472543 | − | 0.0818468i | 0.841431 | − | 0.540365i | \(-0.181714\pi\) |
−0.888685 | + | 0.458518i | \(0.848380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.136116 | − | 0.235760i | 0.00443256 | − | 0.00767742i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.8655 | − | 49.9966i | 0.938004 | − | 1.62467i | 0.168816 | − | 0.985648i | \(-0.446006\pi\) |
0.769188 | − | 0.639023i | \(-0.220661\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.56183 | + | 4.43722i | 0.0831605 | + | 0.144038i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.4070 | −0.661046 | −0.330523 | − | 0.943798i | \(-0.607225\pi\) | ||||
−0.330523 | + | 0.943798i | \(0.607225\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.90440 | + | 5.03057i | −0.0939843 | + | 0.162786i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.5086 | − | 9.44612i | −0.726841 | − | 0.305031i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.96129 | + | 5.12911i | −0.0955256 | + | 0.165455i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.02193 | + | 12.1623i | 0.226044 | + | 0.391519i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.26365 | + | 7.38486i | −0.137110 | + | 0.237481i | −0.926401 | − | 0.376537i | \(-0.877115\pi\) |
0.789292 | + | 0.614019i | \(0.210448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.42651 | + | 16.3272i | 0.302511 | + | 0.523965i | 0.976704 | − | 0.214590i | \(-0.0688417\pi\) |
−0.674193 | + | 0.738555i | \(0.735508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.0052 | − | 22.0431i | 0.929864 | − | 0.706671i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.305649 | + | 0.529400i | 0.00977859 | + | 0.0169370i | 0.870873 | − | 0.491508i | \(-0.163554\pi\) |
−0.861095 | + | 0.508445i | \(0.830221\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.5108 | + | 56.3104i | 1.03905 | + | 1.79969i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.25167 | −0.231292 | −0.115646 | − | 0.993290i | \(-0.536894\pi\) | ||||
−0.115646 | + | 0.993290i | \(0.536894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.75318 | 0.215174 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.153710 | + | 0.266234i | 0.00488770 | + | 0.00846575i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.49266 | − | 4.31741i | 0.0791819 | − | 0.137147i | −0.823715 | − | 0.567004i | \(-0.808103\pi\) |
0.902897 | + | 0.429857i | \(0.141436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.33412 | − | 9.23896i | 0.169103 | − | 0.292895i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.18344 | −0.100821 | −0.0504104 | − | 0.998729i | \(-0.516053\pi\) | ||||
−0.0504104 | + | 0.998729i | \(0.516053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3024.2.t.k.1873.5 | 22 | ||
3.2 | odd | 2 | 1008.2.t.l.193.6 | 22 | |||
4.3 | odd | 2 | 1512.2.t.c.361.5 | 22 | |||
7.2 | even | 3 | 3024.2.q.l.2305.7 | 22 | |||
9.2 | odd | 6 | 1008.2.q.l.529.2 | 22 | |||
9.7 | even | 3 | 3024.2.q.l.2881.7 | 22 | |||
12.11 | even | 2 | 504.2.t.c.193.6 | yes | 22 | ||
21.2 | odd | 6 | 1008.2.q.l.625.2 | 22 | |||
28.23 | odd | 6 | 1512.2.q.d.793.7 | 22 | |||
36.7 | odd | 6 | 1512.2.q.d.1369.7 | 22 | |||
36.11 | even | 6 | 504.2.q.c.25.10 | ✓ | 22 | ||
63.2 | odd | 6 | 1008.2.t.l.961.6 | 22 | |||
63.16 | even | 3 | inner | 3024.2.t.k.289.5 | 22 | ||
84.23 | even | 6 | 504.2.q.c.121.10 | yes | 22 | ||
252.79 | odd | 6 | 1512.2.t.c.289.5 | 22 | |||
252.191 | even | 6 | 504.2.t.c.457.6 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.10 | ✓ | 22 | 36.11 | even | 6 | ||
504.2.q.c.121.10 | yes | 22 | 84.23 | even | 6 | ||
504.2.t.c.193.6 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.457.6 | yes | 22 | 252.191 | even | 6 | ||
1008.2.q.l.529.2 | 22 | 9.2 | odd | 6 | |||
1008.2.q.l.625.2 | 22 | 21.2 | odd | 6 | |||
1008.2.t.l.193.6 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.961.6 | 22 | 63.2 | odd | 6 | |||
1512.2.q.d.793.7 | 22 | 28.23 | odd | 6 | |||
1512.2.q.d.1369.7 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.289.5 | 22 | 252.79 | odd | 6 | |||
1512.2.t.c.361.5 | 22 | 4.3 | odd | 2 | |||
3024.2.q.l.2305.7 | 22 | 7.2 | even | 3 | |||
3024.2.q.l.2881.7 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.289.5 | 22 | 63.16 | even | 3 | inner | ||
3024.2.t.k.1873.5 | 22 | 1.1 | even | 1 | trivial |