Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + \cdots + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.83671\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.83671 | 1.71583 | 0.857915 | − | 0.513792i | \(-0.171760\pi\) | ||||
0.857915 | + | 0.513792i | \(0.171760\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.48179 | 1.69396 | 0.846979 | − | 0.531627i | \(-0.178419\pi\) | ||||
0.846979 | + | 0.531627i | \(0.178419\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10612 | 0.333509 | 0.166755 | − | 0.985998i | \(-0.446671\pi\) | ||||
0.166755 | + | 0.985998i | \(0.446671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.67402 | −1.57369 | −0.786845 | − | 0.617151i | \(-0.788287\pi\) | ||||
−0.786845 | + | 0.617151i | \(0.788287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.83671 | −0.990635 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.581232 | −0.140969 | −0.0704847 | − | 0.997513i | \(-0.522455\pi\) | ||||
−0.0704847 | + | 0.997513i | \(0.522455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.72213 | −1.08333 | −0.541665 | − | 0.840594i | \(-0.682206\pi\) | ||||
−0.541665 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.48179 | −0.978007 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.33676 | −0.695762 | −0.347881 | − | 0.937539i | \(-0.613099\pi\) | ||||
−0.347881 | + | 0.937539i | \(0.613099\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.72035 | 1.94407 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.38537 | 0.628648 | 0.314324 | − | 0.949316i | \(-0.398222\pi\) | ||||
0.314324 | + | 0.949316i | \(0.398222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.78132 | 0.499540 | 0.249770 | − | 0.968305i | \(-0.419645\pi\) | ||||
0.249770 | + | 0.968305i | \(0.419645\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.10612 | −0.192552 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 17.1953 | 2.90654 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.43128 | 0.728498 | 0.364249 | − | 0.931302i | \(-0.381326\pi\) | ||||
0.364249 | + | 0.931302i | \(0.381326\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.67402 | 0.908570 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.90332 | 0.921944 | 0.460972 | − | 0.887415i | \(-0.347501\pi\) | ||||
0.460972 | + | 0.887415i | \(0.347501\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0030 | 1.52544 | 0.762722 | − | 0.646727i | \(-0.223863\pi\) | ||||
0.762722 | + | 0.646727i | \(0.223863\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.83671 | 0.571943 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.4032 | −1.80920 | −0.904598 | − | 0.426266i | \(-0.859829\pi\) | ||||
−0.904598 | + | 0.426266i | \(0.859829\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0864 | 1.86949 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.581232 | 0.0813887 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.10414 | 0.701108 | 0.350554 | − | 0.936543i | \(-0.385993\pi\) | ||||
0.350554 | + | 0.936543i | \(0.385993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.24388 | 0.572245 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.72213 | 0.625461 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.77902 | −0.361798 | −0.180899 | − | 0.983502i | \(-0.557901\pi\) | ||||
−0.180899 | + | 0.983502i | \(0.557901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.42616 | 1.20690 | 0.603448 | − | 0.797402i | \(-0.293793\pi\) | ||||
0.603448 | + | 0.797402i | \(0.293793\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.48179 | 0.564652 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.7696 | −2.70018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.07361 | 1.10852 | 0.554259 | − | 0.832344i | \(-0.313002\pi\) | ||||
0.554259 | + | 0.832344i | \(0.313002\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.33676 | 0.401698 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8081 | 1.63872 | 0.819359 | − | 0.573281i | \(-0.194330\pi\) | ||||
0.819359 | + | 0.573281i | \(0.194330\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.14053 | 1.06982 | 0.534909 | − | 0.844910i | \(-0.320346\pi\) | ||||
0.534909 | + | 0.844910i | \(0.320346\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.72035 | −1.12241 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.95742 | 0.564950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.4215 | −1.96007 | −0.980034 | − | 0.198831i | \(-0.936286\pi\) | ||||
−0.980034 | + | 0.198831i | \(0.936286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.9891 | 1.86479 | 0.932397 | − | 0.361435i | \(-0.117713\pi\) | ||||
0.932397 | + | 0.361435i | \(0.117713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.23002 | −0.241879 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.38537 | −0.362950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50452 | −0.159478 | −0.0797391 | − | 0.996816i | \(-0.525409\pi\) | ||||
−0.0797391 | + | 0.996816i | \(0.525409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.4298 | −2.66576 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.78132 | −0.288410 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.1174 | −1.85881 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.761888 | 0.0773580 | 0.0386790 | − | 0.999252i | \(-0.487685\pi\) | ||||
0.0386790 | + | 0.999252i | \(0.487685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.10612 | 0.111170 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.37489 | −0.136807 | −0.0684034 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684034 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0629727 | −0.00620488 | −0.00310244 | − | 0.999995i | \(-0.500988\pi\) | ||||
−0.00310244 | + | 0.999995i | \(0.500988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.1953 | −1.67809 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.0437 | 0.970959 | 0.485480 | − | 0.874248i | \(-0.338645\pi\) | ||||
0.485480 | + | 0.874248i | \(0.338645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.87839 | 0.179917 | 0.0899584 | − | 0.995946i | \(-0.471327\pi\) | ||||
0.0899584 | + | 0.995946i | \(0.471327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.43128 | −0.420598 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.11228 | 0.386851 | 0.193425 | − | 0.981115i | \(-0.438040\pi\) | ||||
0.193425 | + | 0.981115i | \(0.438040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.8022 | −1.19381 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.67402 | −0.524563 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.60496 | −0.238796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.77649 | −0.888772 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.90332 | −0.532284 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.1106 | 1.61986 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.9118 | −1.76689 | −0.883445 | − | 0.468536i | \(-0.844782\pi\) | ||||
−0.883445 | + | 0.468536i | \(0.844782\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.0030 | −0.880715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.42577 | −0.561422 | −0.280711 | − | 0.959792i | \(-0.590570\pi\) | ||||
−0.280711 | + | 0.959792i | \(0.590570\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.1636 | −1.83512 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.83671 | −0.330212 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.42007 | −0.121325 | −0.0606625 | − | 0.998158i | \(-0.519321\pi\) | ||||
−0.0606625 | + | 0.998158i | \(0.519321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.43659 | 0.800401 | 0.400200 | − | 0.916428i | \(-0.368941\pi\) | ||||
0.400200 | + | 0.916428i | \(0.368941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4032 | 1.04454 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.27617 | −0.524840 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.9887 | 1.07865 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.0864 | −1.07935 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.81076 | 0.639882 | 0.319941 | − | 0.947437i | \(-0.396337\pi\) | ||||
0.319941 | + | 0.947437i | \(0.396337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.614618 | 0.0500169 | 0.0250085 | − | 0.999687i | \(-0.492039\pi\) | ||||
0.0250085 | + | 0.999687i | \(0.492039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.581232 | −0.0469898 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6711 | 0.857126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5892 | 1.48358 | 0.741792 | − | 0.670631i | \(-0.233976\pi\) | ||||
0.741792 | + | 0.670631i | \(0.233976\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.10414 | −0.404785 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.9547 | −1.17859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6487 | −1.38235 | −0.691175 | − | 0.722687i | \(-0.742907\pi\) | ||||
−0.691175 | + | 0.722687i | \(0.742907\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.24388 | −0.330386 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.1945 | 1.47650 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.72213 | −0.361110 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.79962 | 0.364909 | 0.182454 | − | 0.983214i | \(-0.441596\pi\) | ||||
0.182454 | + | 0.983214i | \(0.441596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43.5646 | 3.29317 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.77902 | 0.208884 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6389 | −1.54262 | −0.771310 | − | 0.636459i | \(-0.780398\pi\) | ||||
−0.771310 | + | 0.636459i | \(0.780398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9125 | 0.811123 | 0.405562 | − | 0.914068i | \(-0.367076\pi\) | ||||
0.405562 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.42616 | −0.696802 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.0015 | 1.24998 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.642915 | −0.0470146 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.48179 | −0.326002 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4748 | −0.757931 | −0.378965 | − | 0.925411i | \(-0.623720\pi\) | ||||
−0.378965 | + | 0.925411i | \(0.623720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.30352 | −0.597701 | −0.298850 | − | 0.954300i | \(-0.596603\pi\) | ||||
−0.298850 | + | 0.954300i | \(0.596603\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 21.7696 | 1.55895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7450 | 1.76301 | 0.881503 | − | 0.472179i | \(-0.156533\pi\) | ||||
0.881503 | + | 0.472179i | \(0.156533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9627 | −1.48601 | −0.743003 | − | 0.669288i | \(-0.766599\pi\) | ||||
−0.743003 | + | 0.669288i | \(0.766599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.07361 | −0.640003 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.1725 | 1.06490 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.6493 | 1.58190 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.33676 | −0.231921 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.22326 | −0.361301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3764 | −0.920866 | −0.460433 | − | 0.887694i | \(-0.652306\pi\) | ||||
−0.460433 | + | 0.887694i | \(0.652306\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.8081 | −0.946114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 38.3786 | 2.61740 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.4653 | 0.846200 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.14053 | −0.617660 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.29792 | 0.221842 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.31317 | −0.489726 | −0.244863 | − | 0.969558i | \(-0.578743\pi\) | ||||
−0.244863 | + | 0.969558i | \(0.578743\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.72035 | 0.648024 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.35302 | 0.156175 | 0.0780875 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780875 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.3540 | 1.08070 | 0.540350 | − | 0.841440i | \(-0.318292\pi\) | ||||
0.540350 | + | 0.841440i | \(0.318292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.95742 | −0.326174 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.5380 | −1.60753 | −0.803767 | − | 0.594944i | \(-0.797174\pi\) | ||||
−0.803767 | + | 0.594944i | \(0.797174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −47.5876 | −3.10427 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.4215 | 1.13165 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.5560 | −1.07092 | −0.535460 | − | 0.844561i | \(-0.679862\pi\) | ||||
−0.535460 | + | 0.844561i | \(0.679862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4248 | 0.864765 | 0.432383 | − | 0.901690i | \(-0.357673\pi\) | ||||
0.432383 | + | 0.901690i | \(0.357673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 50.2089 | 3.20773 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.7935 | 1.70483 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.9891 | −1.07664 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.08588 | 0.447257 | 0.223628 | − | 0.974674i | \(-0.428210\pi\) | ||||
0.223628 | + | 0.974674i | \(0.428210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.69087 | −0.232043 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.23002 | 0.139649 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.32571 | 0.581722 | 0.290861 | − | 0.956765i | \(-0.406058\pi\) | ||||
0.290861 | + | 0.956765i | \(0.406058\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.8601 | 1.23404 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.38537 | 0.209549 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.03494 | 0.0638170 | 0.0319085 | − | 0.999491i | \(-0.489841\pi\) | ||||
0.0319085 | + | 0.999491i | \(0.489841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.5831 | 1.20298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.50452 | 0.0920748 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2297 | −0.806630 | −0.403315 | − | 0.915061i | \(-0.632142\pi\) | ||||
−0.403315 | + | 0.915061i | \(0.632142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6279 | 0.949330 | 0.474665 | − | 0.880166i | \(-0.342569\pi\) | ||||
0.474665 | + | 0.880166i | \(0.342569\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.4298 | 1.53908 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.7519 | 0.648365 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.591123 | −0.0355171 | −0.0177586 | − | 0.999842i | \(-0.505653\pi\) | ||||
−0.0177586 | + | 0.999842i | \(0.505653\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.78132 | 0.166513 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.64950 | −0.277366 | −0.138683 | − | 0.990337i | \(-0.544287\pi\) | ||||
−0.138683 | + | 0.990337i | \(0.544287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.7408 | −1.41124 | −0.705621 | − | 0.708590i | \(-0.749332\pi\) | ||||
−0.705621 | + | 0.708590i | \(0.749332\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.1174 | 1.07319 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.4574 | 1.56173 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6622 | −0.980128 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.761888 | −0.0446627 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.7554 | −1.62149 | −0.810743 | − | 0.585402i | \(-0.800937\pi\) | ||||
−0.810743 | + | 0.585402i | \(0.800937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6623 | −0.620783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.10612 | −0.0641839 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.9328 | 1.09491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 44.8314 | 2.58404 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.37489 | 0.0789854 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.1654 | 2.07083 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.47952 | 0.0844405 | 0.0422202 | − | 0.999108i | \(-0.486557\pi\) | ||||
0.0422202 | + | 0.999108i | \(0.486557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0629727 | 0.00358239 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6599 | 1.11481 | 0.557404 | − | 0.830241i | \(-0.311797\pi\) | ||||
0.557404 | + | 0.830241i | \(0.311797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0409 | −0.737116 | −0.368558 | − | 0.929605i | \(-0.620148\pi\) | ||||
−0.368558 | + | 0.929605i | \(0.620148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.1953 | 0.968847 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.2143 | 0.742191 | 0.371096 | − | 0.928595i | \(-0.378982\pi\) | ||||
0.371096 | + | 0.928595i | \(0.378982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.74464 | 0.209660 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0437 | −0.560584 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.74465 | 0.152717 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −55.1535 | −3.05936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.87839 | −0.103875 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −55.5886 | −3.06470 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.4467 | −1.50860 | −0.754302 | − | 0.656527i | \(-0.772025\pi\) | ||||
−0.754302 | + | 0.656527i | \(0.772025\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.43128 | 0.242833 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.8128 | 1.90203 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.0032 | −1.52543 | −0.762716 | − | 0.646733i | \(-0.776135\pi\) | ||||
−0.762716 | + | 0.646733i | \(0.776135\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.11228 | −0.223348 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.07649 | 0.166601 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 27.2782 | 1.47288 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.8022 | 0.689246 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.7281 | 1.70325 | 0.851627 | − | 0.524148i | \(-0.175616\pi\) | ||||
0.851627 | + | 0.524148i | \(0.175616\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0742 | −1.18160 | −0.590802 | − | 0.806817i | \(-0.701189\pi\) | ||||
−0.590802 | + | 0.806817i | \(0.701189\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.67402 | 0.302857 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.7084 | 1.31509 | 0.657547 | − | 0.753413i | \(-0.271594\pi\) | ||||
0.657547 | + | 0.753413i | \(0.271594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 52.9776 | 2.81176 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.60496 | 0.137869 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.1424 | −1.37975 | −0.689873 | − | 0.723931i | \(-0.742334\pi\) | ||||
−0.689873 | + | 0.723931i | \(0.742334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.29851 | 0.173606 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.77649 | 0.513133 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.0696 | 1.83563 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7397 | 0.560607 | 0.280303 | − | 0.959911i | \(-0.409565\pi\) | ||||
0.280303 | + | 0.959911i | \(0.409565\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.90332 | 0.307315 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.8757 | 1.18765 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.2357 | −1.66910 | −0.834551 | − | 0.550930i | \(-0.814273\pi\) | ||||
−0.834551 | + | 0.550930i | \(0.814273\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.1106 | −0.935229 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.2087 | −0.989296 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1380 | −1.29125 | −0.645626 | − | 0.763654i | \(-0.723403\pi\) | ||||
−0.645626 | + | 0.763654i | \(0.723403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.9118 | 1.02011 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.2766 | 1.29157 | 0.645787 | − | 0.763518i | \(-0.276530\pi\) | ||||
0.645787 | + | 0.763518i | \(0.276530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.0202 | 0.969358 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0030 | 0.508481 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.01440 | −0.102134 | −0.0510670 | − | 0.998695i | \(-0.516262\pi\) | ||||
−0.0510670 | + | 0.998695i | \(0.516262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.93943 | 0.0980812 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.42577 | 0.324137 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −66.8411 | −3.36314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6705 | −1.48912 | −0.744561 | − | 0.667555i | \(-0.767341\pi\) | ||||
−0.744561 | + | 0.667555i | \(0.767341\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.1636 | 1.05950 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0918 | −0.553900 | −0.276950 | − | 0.960884i | \(-0.589324\pi\) | ||||
−0.276950 | + | 0.960884i | \(0.589324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.7813 | −0.786121 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.83671 | 0.190648 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.90155 | 0.242961 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.5517 | 1.06566 | 0.532831 | − | 0.846221i | \(-0.321128\pi\) | ||||
0.532831 | + | 0.846221i | \(0.321128\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.42007 | 0.0700470 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.4550 | −0.612870 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 65.1822 | 3.19967 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.43659 | −0.462112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.34797 | 0.114706 | 0.0573530 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573530 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1533 | −1.17716 | −0.588581 | − | 0.808439i | \(-0.700313\pi\) | ||||
−0.588581 | + | 0.808439i | \(0.700313\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.4032 | −0.603065 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.64978 | −0.274055 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.2461 | 2.04443 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.27617 | 0.303016 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.9384 | −0.719558 | −0.359779 | − | 0.933038i | \(-0.617148\pi\) | ||||
−0.359779 | + | 0.933038i | \(0.617148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2775 | −0.493907 | −0.246954 | − | 0.969027i | \(-0.579430\pi\) | ||||
−0.246954 | + | 0.969027i | \(0.579430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.9887 | −0.622760 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7566 | 0.753741 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.86030 | 0.136514 | 0.0682572 | − | 0.997668i | \(-0.478256\pi\) | ||||
0.0682572 | + | 0.997668i | \(0.478256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0864 | 0.623164 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.8556 | −1.22844 | −0.614219 | − | 0.789136i | \(-0.710529\pi\) | ||||
−0.614219 | + | 0.789136i | \(0.710529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.77239 | −0.273638 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.81076 | −0.369436 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.46562 | −0.352325 | −0.176162 | − | 0.984361i | \(-0.556368\pi\) | ||||
−0.176162 | + | 0.984361i | \(0.556368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.52981 | 0.307477 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.614618 | −0.0288773 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −97.5667 | −4.57400 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.6342 | 1.90079 | 0.950393 | − | 0.311052i | \(-0.100681\pi\) | ||||
0.950393 | + | 0.311052i | \(0.100681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.581232 | 0.0271296 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.791635 | 0.0368701 | 0.0184351 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184351 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.1065 | −1.63154 | −0.815769 | − | 0.578377i | \(-0.803686\pi\) | ||||
−0.815769 | + | 0.578377i | \(0.803686\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.6711 | −0.494862 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.1756 | −1.72028 | −0.860141 | − | 0.510056i | \(-0.829625\pi\) | ||||
−0.860141 | + | 0.510056i | \(0.829625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.6660 | 1.87778 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.5892 | −0.856547 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.0646 | 0.508749 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.9008 | −2.10607 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.10414 | 0.233703 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.1213 | 0.873675 | 0.436838 | − | 0.899540i | \(-0.356098\pi\) | ||||
0.436838 | + | 0.899540i | \(0.356098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.1432 | −1.14643 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.9547 | 0.680460 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.92315 | 0.132733 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.51757 | −0.431282 | −0.215641 | − | 0.976473i | \(-0.569184\pi\) | ||||
−0.215641 | + | 0.976473i | \(0.569184\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.6487 | 0.798100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.94043 | 0.132700 | 0.0663499 | − | 0.997796i | \(-0.478865\pi\) | ||||
0.0663499 | + | 0.997796i | \(0.478865\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.96769 | −0.0886201 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.24388 | 0.190748 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 61.8849 | 2.77592 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.1976 | 1.26230 | 0.631149 | − | 0.775662i | \(-0.282584\pi\) | ||||
0.631149 | + | 0.775662i | \(0.282584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.54162 | 0.202501 | 0.101250 | − | 0.994861i | \(-0.467716\pi\) | ||||
0.101250 | + | 0.994861i | \(0.467716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.27506 | −0.234737 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.1945 | −0.852457 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.0856 | 1.02325 | 0.511625 | − | 0.859209i | \(-0.329044\pi\) | ||||
0.511625 | + | 0.859209i | \(0.329044\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.9659 | 1.81223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.72213 | 0.208487 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.241608 | −0.0106465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7195 | −0.603383 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.79962 | −0.210680 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.64748 | 0.335042 | 0.167521 | − | 0.985868i | \(-0.446424\pi\) | ||||
0.167521 | + | 0.985868i | \(0.446424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1172 | 1.36066 | 0.680329 | − | 0.732906i | \(-0.261837\pi\) | ||||
0.680329 | + | 0.732906i | \(0.261837\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −43.5646 | −1.90131 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.61659 | −0.0704199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.8660 | −0.515915 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.77902 | −0.120599 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.4955 | −1.45085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.5347 | 1.66600 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.6389 | 0.890633 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.4752 | 0.623493 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3270 | −1.08889 | −0.544447 | − | 0.838795i | \(-0.683260\pi\) | ||||
−0.544447 | + | 0.838795i | \(0.683260\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.9125 | −0.468302 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.20683 | 0.308707 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8497 | −1.19077 | −0.595383 | − | 0.803442i | \(-0.703000\pi\) | ||||
−0.595383 | + | 0.803442i | \(0.703000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.42616 | 0.402299 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.9862 | −0.681034 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −78.0793 | −3.32027 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.0015 | −0.721675 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.21977 | 0.390654 | 0.195327 | − | 0.980738i | \(-0.437423\pi\) | ||||
0.195327 | + | 0.980738i | \(0.437423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.7572 | −2.40057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.642915 | 0.0271439 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.8905 | −0.711851 | −0.355926 | − | 0.934514i | \(-0.615834\pi\) | ||||
−0.355926 | + | 0.934514i | \(0.615834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.7776 | 0.663770 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.48179 | 0.188217 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.5370 | −1.61556 | −0.807778 | − | 0.589487i | \(-0.799330\pi\) | ||||
−0.807778 | + | 0.589487i | \(0.799330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6738 | 0.572232 | 0.286116 | − | 0.958195i | \(-0.407636\pi\) | ||||
0.286116 | + | 0.958195i | \(0.407636\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4748 | 0.437592 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.4345 | −1.35261 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.888543 | −0.0369905 | −0.0184953 | − | 0.999829i | \(-0.505888\pi\) | ||||
−0.0184953 | + | 0.999829i | \(0.505888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.30352 | 0.345083 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 76.1415 | 3.15888 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.64582 | 0.233826 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −21.7696 | −0.900061 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.2849 | 1.00234 | 0.501172 | − | 0.865348i | \(-0.332902\pi\) | ||||
0.501172 | + | 0.865348i | \(0.332902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.1338 | −0.541167 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.7450 | −1.01787 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.05351 | −0.248588 | −0.124294 | − | 0.992245i | \(-0.539667\pi\) | ||||
−0.124294 | + | 0.992245i | \(0.539667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.99448 | −0.409734 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.9627 | 0.857946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.9256 | 1.22273 | 0.611364 | − | 0.791349i | \(-0.290621\pi\) | ||||
0.611364 | + | 0.791349i | \(0.290621\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.2604 | −1.84621 | −0.923105 | − | 0.384548i | \(-0.874357\pi\) | ||||
−0.923105 | + | 0.384548i | \(0.874357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.07361 | 0.369506 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.5096 | −1.52498 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.72389 | 0.151148 | 0.0755740 | − | 0.997140i | \(-0.475921\pi\) | ||||
0.0755740 | + | 0.997140i | \(0.475921\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1725 | −0.614822 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 70.3761 | 2.84711 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.3721 | −1.42867 | −0.714333 | − | 0.699806i | \(-0.753270\pi\) | ||||
−0.714333 | + | 0.699806i | \(0.753270\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.6493 | −0.913309 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.32100 | −0.294732 | −0.147366 | − | 0.989082i | \(-0.547080\pi\) | ||||
−0.147366 | + | 0.989082i | \(0.547080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2901 | −0.614559 | −0.307280 | − | 0.951619i | \(-0.599419\pi\) | ||||
−0.307280 | + | 0.951619i | \(0.599419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.33676 | 0.133899 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.74292 | −0.270149 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8835 | 0.835341 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.22326 | 0.208597 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.57560 | −0.102696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2764 | −0.528524 | −0.264262 | − | 0.964451i | \(-0.585128\pi\) | ||||
−0.264262 | + | 0.964451i | \(0.585128\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.3764 | 0.531662 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −76.3959 | −3.03168 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −74.2527 | −2.94200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.8081 | 0.546239 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.17423 | 0.243867 | 0.121934 | − | 0.992538i | \(-0.461090\pi\) | ||||
0.121934 | + | 0.992538i | \(0.461090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.865911 | 0.0341482 | 0.0170741 | − | 0.999854i | \(-0.494565\pi\) | ||||
0.0170741 | + | 0.999854i | \(0.494565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −38.3786 | −1.51116 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.3420 | 1.35012 | 0.675062 | − | 0.737761i | \(-0.264117\pi\) | ||||
0.675062 | + | 0.737761i | \(0.264117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.07394 | −0.120663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.4653 | −0.488554 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.1698 | 0.671908 | 0.335954 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335954 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.6538 | −0.963305 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.14053 | 0.356606 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.8878 | 1.43695 | 0.718473 | − | 0.695555i | \(-0.244841\pi\) | ||||
0.718473 | + | 0.695555i | \(0.244841\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.5260 | 1.03174 | 0.515871 | − | 0.856666i | \(-0.327468\pi\) | ||||
0.515871 | + | 0.856666i | \(0.327468\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.29792 | −0.128081 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −81.1986 | −3.14875 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2962 | −0.437389 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.31317 | 0.282744 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4265 | 0.402511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.2730 | −1.05130 | −0.525648 | − | 0.850702i | \(-0.676177\pi\) | ||||
−0.525648 | + | 0.850702i | \(0.676177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.72035 | −0.374137 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4893 | 0.480004 | 0.240002 | − | 0.970772i | \(-0.422852\pi\) | ||||
0.240002 | + | 0.970772i | \(0.422852\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.41462 | 0.131041 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.35302 | −0.0901677 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6433 | −1.13427 | −0.567134 | − | 0.823626i | \(-0.691948\pi\) | ||||
−0.567134 | + | 0.823626i | \(0.691948\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.44841 | −0.208173 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3540 | −0.623943 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.9610 | −1.10333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.78092 | 0.0677493 | 0.0338747 | − | 0.999426i | \(-0.489215\pi\) | ||||
0.0338747 | + | 0.999426i | \(0.489215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.95742 | 0.188317 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.2055 | 1.37335 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.43120 | −0.129966 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.5380 | 0.928111 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8886 | 0.751182 | 0.375591 | − | 0.926785i | \(-0.377440\pi\) | ||||
0.375591 | + | 0.926785i | \(0.377440\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.9251 | −0.789204 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 47.5876 | 1.79225 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.16197 | −0.231745 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6852 | −1.56552 | −0.782760 | − | 0.622323i | \(-0.786189\pi\) | ||||
−0.782760 | + | 0.622323i | \(0.786189\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.4215 | −0.653356 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.28060 | −0.347561 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0799 | −0.900536 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.5560 | 0.618296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.0390 | 0.598153 | 0.299076 | − | 0.954229i | \(-0.403321\pi\) | ||||
0.299076 | + | 0.954229i | \(0.403321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.282230 | −0.0105108 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.4248 | −0.499272 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.9070 | 1.22214 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.28104 | 0.158775 | 0.0793874 | − | 0.996844i | \(-0.474704\pi\) | ||||
0.0793874 | + | 0.996844i | \(0.474704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.81406 | −0.215041 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.9604 | −0.552574 | −0.276287 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276287 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −50.2089 | −1.85198 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.0365 | 0.369701 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.78573 | 0.286403 | 0.143201 | − | 0.989694i | \(-0.454260\pi\) | ||||
0.143201 | + | 0.989694i | \(0.454260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.7935 | −0.984282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.23167 | −0.155245 | −0.0776224 | − | 0.996983i | \(-0.524733\pi\) | ||||
−0.0776224 | + | 0.996983i | \(0.524733\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.9676 | 1.09793 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.9891 | 0.621598 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.0137 | 1.64476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.4751 | −1.80537 | −0.902686 | − | 0.430301i | \(-0.858408\pi\) | ||||
−0.902686 | + | 0.430301i | \(0.858408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.08588 | −0.258224 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.35811 | 0.0858205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6590 | −0.496444 | −0.248222 | − | 0.968703i | \(-0.579846\pi\) | ||||
−0.248222 | + | 0.968703i | \(0.579846\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.69087 | 0.133970 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.48874 | 0.271467 | 0.135733 | − | 0.990745i | \(-0.456661\pi\) | ||||
0.135733 | + | 0.990745i | \(0.456661\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.41853 | 0.304771 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.23002 | −0.0806265 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.7682 | 0.569357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.7046 | 1.86452 | 0.932258 | − | 0.361795i | \(-0.117836\pi\) | ||||
0.932258 | + | 0.361795i | \(0.117836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.32571 | −0.335857 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.9350 | 0.645078 | 0.322539 | − | 0.946556i | \(-0.395464\pi\) | ||||
0.322539 | + | 0.946556i | \(0.395464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.0354 | 0.971142 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.8601 | −0.712476 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.8762 | −0.998770 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2735 | 0.546527 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.38537 | −0.120983 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 71.3216 | 2.54558 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.1192 | 0.360711 | 0.180356 | − | 0.983601i | \(-0.442275\pi\) | ||||
0.180356 | + | 0.983601i | \(0.442275\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.03494 | −0.0368448 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.4304 | 0.655309 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.4842 | −1.89928 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.5831 | −0.694542 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.51921 | 0.0892351 | 0.0446175 | − | 0.999004i | \(-0.485793\pi\) | ||||
0.0446175 | + | 0.999004i | \(0.485793\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.20915 | 0.255041 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50452 | −0.0531594 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.1106 | 0.356794 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −57.3767 | −2.02226 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.2297 | 0.465708 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.10619 | 0.109208 | 0.0546039 | − | 0.998508i | \(-0.482610\pi\) | ||||
0.0546039 | + | 0.998508i | \(0.482610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.4811 | −0.754303 | −0.377152 | − | 0.926152i | \(-0.623096\pi\) | ||||
−0.377152 | + | 0.926152i | \(0.623096\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.6279 | −0.548096 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −67.7128 | −2.37188 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.2355 | −1.65256 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.4298 | −0.888588 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.2130 | 0.530936 | 0.265468 | − | 0.964120i | \(-0.414473\pi\) | ||||
0.265468 | + | 0.964120i | \(0.414473\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.0861 | 0.386439 | 0.193219 | − | 0.981156i | \(-0.438107\pi\) | ||||
0.193219 | + | 0.981156i | \(0.438107\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.7519 | −0.374334 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.19279 | 0.0414773 | 0.0207387 | − | 0.999785i | \(-0.493398\pi\) | ||||
0.0207387 | + | 0.999785i | \(0.493398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.5477 | 1.23462 | 0.617311 | − | 0.786719i | \(-0.288222\pi\) | ||||
0.617311 | + | 0.786719i | \(0.288222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.591123 | 0.0205058 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.60626 | −0.263541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.83671 | 0.132775 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.78132 | −0.0961366 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.12432 | −0.211435 | −0.105718 | − | 0.994396i | \(-0.533714\pi\) | ||||
−0.105718 | + | 0.994396i | \(0.533714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5393 | −0.604802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.64950 | 0.160137 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 73.6437 | 2.53342 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.8162 | −1.50554 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.7408 | 0.814781 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7861 | −0.506861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7670 | −0.574091 | −0.287046 | − | 0.957917i | \(-0.592673\pi\) | ||||
−0.287046 | + | 0.957917i | \(0.592673\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.1174 | −0.619604 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0064 | −0.375972 | −0.187986 | − | 0.982172i | \(-0.560196\pi\) | ||||
−0.187986 | + | 0.982172i | \(0.560196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.9158 | 1.05483 | 0.527416 | − | 0.849607i | \(-0.323161\pi\) | ||||
0.527416 | + | 0.849607i | \(0.323161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.4574 | −0.901667 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.7791 | −0.639247 | −0.319624 | − | 0.947545i | \(-0.603556\pi\) | ||||
−0.319624 | + | 0.947545i | \(0.603556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.4148 | 0.626121 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6622 | 0.565877 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.2703 | −0.653700 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.4838 | −1.74446 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.761888 | 0.0257860 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 81.1681 | 2.74398 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.89364 | −0.300317 | −0.150158 | − | 0.988662i | \(-0.547978\pi\) | ||||
−0.150158 | + | 0.988662i | \(0.547978\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.7554 | 0.936166 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.0530 | 0.473457 | 0.236728 | − | 0.971576i | \(-0.423925\pi\) | ||||
0.236728 | + | 0.971576i | \(0.423925\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0318 | 1.04430 | 0.522151 | − | 0.852853i | \(-0.325130\pi\) | ||||
0.522151 | + | 0.852853i | \(0.325130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.6623 | 0.358409 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0309 | −0.571842 | −0.285921 | − | 0.958253i | \(-0.592300\pi\) | ||||
−0.285921 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −89.2406 | −2.99304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.10612 | 0.0370566 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 58.5696 | 1.95996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −79.1854 | −2.64687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.9328 | −0.632149 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.41581 | 0.314035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.96669 | −0.0988348 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −44.8314 | −1.49189 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.8683 | 1.39175 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.3207 | 1.87010 | 0.935049 | − | 0.354520i | \(-0.115356\pi\) | ||||
0.935049 | + | 0.354520i | \(0.115356\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.37489 | −0.0456023 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.9696 | −1.92062 | −0.960309 | − | 0.278937i | \(-0.910018\pi\) | ||||
−0.960309 | + | 0.278937i | \(0.910018\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.7920 | 0.621926 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36.1654 | −1.19559 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.7990 | −0.951026 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.93192 | −0.261650 | −0.130825 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130825 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.47952 | −0.0487517 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −78.3473 | −2.57883 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.0736 | 1.41625 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0629727 | −0.00206829 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1314 | 0.365209 | 0.182604 | − | 0.983186i | \(-0.441547\pi\) | ||||
0.182604 | + | 0.983186i | \(0.441547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −61.7959 | −2.02528 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.6599 | −0.643635 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.46668 | −0.0806690 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.29223 | 0.140221 | 0.0701105 | − | 0.997539i | \(-0.477665\pi\) | ||||
0.0701105 | + | 0.997539i | \(0.477665\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.0409 | 0.425574 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.4909 | −1.28737 | −0.643683 | − | 0.765292i | \(-0.722595\pi\) | ||||
−0.643683 | + | 0.765292i | \(0.722595\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.6979 | −0.641453 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.1953 | −0.559364 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.0910 | 1.27029 | 0.635144 | − | 0.772394i | \(-0.280941\pi\) | ||||
0.635144 | + | 0.772394i | \(0.280941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.8635 | −1.68356 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.2143 | −0.428504 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.7855 | 1.09442 | 0.547210 | − | 0.836995i | \(-0.315690\pi\) | ||||
0.547210 | + | 0.836995i | \(0.315690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.1888 | −1.30048 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.74464 | −0.121047 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.36447 | −0.205519 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.2642 | −0.750459 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.0437 | 0.323653 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.8582 | −1.02555 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.47656 | −0.176114 | −0.0880572 | − | 0.996115i | \(-0.528066\pi\) | ||||
−0.0880572 | + | 0.996115i | \(0.528066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.74465 | −0.0881709 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8330 | 0.764836 | 0.382418 | − | 0.923989i | \(-0.375091\pi\) | ||||
0.382418 | + | 0.923989i | \(0.375091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.2928 | 1.35584 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 55.1535 | 1.76632 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.9054 | −1.02075 | −0.510373 | − | 0.859953i | \(-0.670493\pi\) | ||||
−0.510373 | + | 0.859953i | \(0.670493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.66418 | −0.0531875 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.87839 | 0.0599723 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.5991 | 0.752696 | 0.376348 | − | 0.926478i | \(-0.377180\pi\) | ||||
0.376348 | + | 0.926478i | \(0.377180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 94.9393 | 3.02502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 55.5886 | 1.76941 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.3776 | −1.06135 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.7794 | −1.13657 | −0.568285 | − | 0.822832i | \(-0.692393\pi\) | ||||
−0.568285 | + | 0.822832i | \(0.692393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.4467 | 0.870993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −80.4278 | −2.54973 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.1383 | −1.11284 | −0.556420 | − | 0.830901i | \(-0.687825\pi\) | ||||
−0.556420 | + | 0.830901i | \(0.687825\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.43128 | −0.140199 |
(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 | 4008.2.a.k.1.10 | ✓ | 11 | |
4.3 | odd | 2 | 8016.2.a.be.1.10 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.10 | ✓ | 11 | 1.1 | even | 1 | trivial | |
8016.2.a.be.1.10 | 11 | 4.3 | odd | 2 |