Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 605) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.210756\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.74483 | 1.94089 | 0.970443 | − | 0.241332i | \(-0.0775843\pi\) | ||||
0.970443 | + | 0.241332i | \(0.0775843\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.53407 | 2.76704 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.32331 | −0.878130 | −0.439065 | − | 0.898455i | \(-0.644690\pi\) | ||||
−0.439065 | + | 0.898455i | \(0.644690\pi\) | |||||||
\(8\) | 9.70041 | 3.42961 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.74483 | 0.867990 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.534070 | −0.148124 | −0.0740622 | − | 0.997254i | \(-0.523596\pi\) | ||||
−0.0740622 | + | 0.997254i | \(0.523596\pi\) | |||||||
\(14\) | −6.37709 | −1.70435 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.5578 | 3.88945 | ||||||||
\(17\) | −2.42151 | −0.587303 | −0.293651 | − | 0.955913i | \(-0.594870\pi\) | ||||
−0.293651 | + | 0.955913i | \(0.594870\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.95558 | 1.13689 | 0.568444 | − | 0.822722i | \(-0.307546\pi\) | ||||
0.568444 | + | 0.822722i | \(0.307546\pi\) | |||||||
\(20\) | 5.53407 | 1.23746 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.53407 | 0.945419 | 0.472709 | − | 0.881218i | \(-0.343276\pi\) | ||||
0.472709 | + | 0.881218i | \(0.343276\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.46593 | −0.287492 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.8574 | −2.42982 | ||||||||
\(29\) | 5.48965 | 1.01940 | 0.509701 | − | 0.860351i | \(-0.329756\pi\) | ||||
0.509701 | + | 0.860351i | \(0.329756\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.04442 | 0.187583 | 0.0937915 | − | 0.995592i | \(-0.470101\pi\) | ||||
0.0937915 | + | 0.995592i | \(0.470101\pi\) | |||||||
\(32\) | 23.3026 | 4.11936 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.64663 | −1.13989 | ||||||||
\(35\) | −2.32331 | −0.392712 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.48965 | 1.23129 | 0.615646 | − | 0.788023i | \(-0.288895\pi\) | ||||
0.615646 | + | 0.788023i | \(0.288895\pi\) | |||||||
\(38\) | 13.6022 | 2.20657 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.70041 | 1.53377 | ||||||||
\(41\) | −10.6022 | −1.65579 | −0.827894 | − | 0.560885i | \(-0.810461\pi\) | ||||
−0.827894 | + | 0.560885i | \(0.810461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.32331 | 0.659299 | 0.329650 | − | 0.944103i | \(-0.393069\pi\) | ||||
0.329650 | + | 0.944103i | \(0.393069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.4452 | 1.83495 | ||||||||
\(47\) | −6.76855 | −0.987294 | −0.493647 | − | 0.869662i | \(-0.664337\pi\) | ||||
−0.493647 | + | 0.869662i | \(0.664337\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.60221 | −0.228887 | ||||||||
\(50\) | 2.74483 | 0.388177 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.95558 | −0.409865 | ||||||||
\(53\) | 4.53407 | 0.622802 | 0.311401 | − | 0.950279i | \(-0.399202\pi\) | ||||
0.311401 | + | 0.950279i | \(0.399202\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −22.5371 | −3.01165 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.0681 | 1.97854 | ||||||||
\(59\) | 6.44523 | 0.839098 | 0.419549 | − | 0.907733i | \(-0.362188\pi\) | ||||
0.419549 | + | 0.907733i | \(0.362188\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.79861 | 0.870472 | 0.435236 | − | 0.900316i | \(-0.356665\pi\) | ||||
0.435236 | + | 0.900316i | \(0.356665\pi\) | |||||||
\(62\) | 2.86675 | 0.364077 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32.8461 | 4.10576 | ||||||||
\(65\) | −0.534070 | −0.0662433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.721104 | 0.0880968 | 0.0440484 | − | 0.999029i | \(-0.485974\pi\) | ||||
0.0440484 | + | 0.999029i | \(0.485974\pi\) | |||||||
\(68\) | −13.4008 | −1.62509 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.37709 | −0.762208 | ||||||||
\(71\) | −4.53407 | −0.538095 | −0.269048 | − | 0.963127i | \(-0.586709\pi\) | ||||
−0.269048 | + | 0.963127i | \(0.586709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.06814 | 0.125016 | 0.0625082 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625082 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(74\) | 20.5578 | 2.38979 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 27.4245 | 3.14581 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.64663 | 0.522787 | 0.261393 | − | 0.965232i | \(-0.415818\pi\) | ||||
0.261393 | + | 0.965232i | \(0.415818\pi\) | |||||||
\(80\) | 15.5578 | 1.73941 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −29.1012 | −3.21369 | ||||||||
\(83\) | −13.6022 | −1.49304 | −0.746518 | − | 0.665365i | \(-0.768276\pi\) | ||||
−0.746518 | + | 0.665365i | \(0.768276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.42151 | −0.262650 | ||||||||
\(86\) | 11.8667 | 1.27962 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7148 | −1.34776 | −0.673881 | − | 0.738840i | \(-0.735374\pi\) | ||||
−0.673881 | + | 0.738840i | \(0.735374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.24081 | 0.130073 | ||||||||
\(92\) | 25.0919 | 2.61601 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.5785 | −1.91622 | ||||||||
\(95\) | 4.95558 | 0.508432 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.75919 | 0.483222 | 0.241611 | − | 0.970373i | \(-0.422324\pi\) | ||||
0.241611 | + | 0.970373i | \(0.422324\pi\) | |||||||
\(98\) | −4.39779 | −0.444244 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.53407 | 0.553407 | ||||||||
\(101\) | 6.57849 | 0.654584 | 0.327292 | − | 0.944923i | \(-0.393864\pi\) | ||||
0.327292 | + | 0.944923i | \(0.393864\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.3564 | 1.61164 | 0.805822 | − | 0.592158i | \(-0.201724\pi\) | ||||
0.805822 | + | 0.592158i | \(0.201724\pi\) | |||||||
\(104\) | −5.18070 | −0.508009 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.4452 | 1.20879 | ||||||||
\(107\) | −10.2108 | −0.987111 | −0.493556 | − | 0.869714i | \(-0.664303\pi\) | ||||
−0.493556 | + | 0.869714i | \(0.664303\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0919 | −1.15819 | −0.579095 | − | 0.815260i | \(-0.696594\pi\) | ||||
−0.579095 | + | 0.815260i | \(0.696594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −36.1456 | −3.41544 | ||||||||
\(113\) | 10.8430 | 1.02003 | 0.510013 | − | 0.860167i | \(-0.329641\pi\) | ||||
0.510013 | + | 0.860167i | \(0.329641\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.53407 | 0.422804 | ||||||||
\(116\) | 30.3801 | 2.82072 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.6910 | 1.62859 | ||||||||
\(119\) | 5.62593 | 0.515728 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 18.6610 | 1.68949 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.77988 | 0.519049 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.12192 | −0.720704 | −0.360352 | − | 0.932816i | \(-0.617343\pi\) | ||||
−0.360352 | + | 0.932816i | \(0.617343\pi\) | |||||||
\(128\) | 43.5515 | 3.84944 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.46593 | −0.128571 | ||||||||
\(131\) | −5.79861 | −0.506627 | −0.253313 | − | 0.967384i | \(-0.581520\pi\) | ||||
−0.253313 | + | 0.967384i | \(0.581520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.5134 | −0.998336 | ||||||||
\(134\) | 1.97930 | 0.170986 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.4897 | −2.01422 | ||||||||
\(137\) | −8.86675 | −0.757537 | −0.378769 | − | 0.925491i | \(-0.623652\pi\) | ||||
−0.378769 | + | 0.925491i | \(0.623652\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8667 | −1.43062 | −0.715309 | − | 0.698808i | \(-0.753714\pi\) | ||||
−0.715309 | + | 0.698808i | \(0.753714\pi\) | |||||||
\(140\) | −12.8574 | −1.08665 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.4452 | −1.04438 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.48965 | 0.455891 | ||||||||
\(146\) | 2.93186 | 0.242642 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 41.4483 | 3.40703 | ||||||||
\(149\) | −4.46593 | −0.365863 | −0.182932 | − | 0.983126i | \(-0.558559\pi\) | ||||
−0.182932 | + | 0.983126i | \(0.558559\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5134 | −0.936945 | −0.468473 | − | 0.883478i | \(-0.655196\pi\) | ||||
−0.468473 | + | 0.883478i | \(0.655196\pi\) | |||||||
\(152\) | 48.0712 | 3.89909 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.04442 | 0.0838897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.91116 | −0.471762 | −0.235881 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235881 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(158\) | 12.7542 | 1.01467 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 23.3026 | 1.84223 | ||||||||
\(161\) | −10.5341 | −0.830201 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.4990 | 1.84058 | 0.920292 | − | 0.391231i | \(-0.127951\pi\) | ||||
0.920292 | + | 0.391231i | \(0.127951\pi\) | |||||||
\(164\) | −58.6734 | −4.58162 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −37.3357 | −2.89781 | ||||||||
\(167\) | −14.2345 | −1.10150 | −0.550748 | − | 0.834671i | \(-0.685658\pi\) | ||||
−0.550748 | + | 0.834671i | \(0.685658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7148 | −0.978059 | ||||||||
\(170\) | −6.64663 | −0.509773 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.9255 | 1.82430 | ||||||||
\(173\) | 6.44523 | 0.490022 | 0.245011 | − | 0.969520i | \(-0.421208\pi\) | ||||
0.245011 | + | 0.969520i | \(0.421208\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.32331 | −0.175626 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −34.8998 | −2.61585 | ||||||||
\(179\) | −16.9793 | −1.26909 | −0.634546 | − | 0.772885i | \(-0.718813\pi\) | ||||
−0.634546 | + | 0.772885i | \(0.718813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.48965 | 0.333713 | 0.166857 | − | 0.985981i | \(-0.446638\pi\) | ||||
0.166857 | + | 0.985981i | \(0.446638\pi\) | |||||||
\(182\) | 3.40582 | 0.252456 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 43.9823 | 3.24242 | ||||||||
\(185\) | 7.48965 | 0.550650 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −37.4576 | −2.73188 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.6022 | 0.986808 | ||||||||
\(191\) | 2.75919 | 0.199648 | 0.0998239 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998239 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8036 | 0.849642 | 0.424821 | − | 0.905277i | \(-0.360337\pi\) | ||||
0.424821 | + | 0.905277i | \(0.360337\pi\) | |||||||
\(194\) | 13.0631 | 0.937879 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.86675 | −0.633339 | ||||||||
\(197\) | 6.51035 | 0.463843 | 0.231922 | − | 0.972734i | \(-0.425499\pi\) | ||||
0.231922 | + | 0.972734i | \(0.425499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9586 | 1.69838 | 0.849190 | − | 0.528087i | \(-0.177090\pi\) | ||||
0.849190 | + | 0.528087i | \(0.177090\pi\) | |||||||
\(200\) | 9.70041 | 0.685922 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.0568 | 1.27047 | ||||||||
\(203\) | −12.7542 | −0.895168 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.6022 | −0.740491 | ||||||||
\(206\) | 44.8955 | 3.12802 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.30895 | −0.576122 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8667 | −1.16115 | −0.580577 | − | 0.814205i | \(-0.697173\pi\) | ||||
−0.580577 | + | 0.814205i | \(0.697173\pi\) | |||||||
\(212\) | 25.0919 | 1.72332 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −28.0267 | −1.91587 | ||||||||
\(215\) | 4.32331 | 0.294848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.42651 | −0.164722 | ||||||||
\(218\) | −33.1901 | −2.24791 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.29326 | 0.0869939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.0174 | −1.67529 | −0.837644 | − | 0.546216i | \(-0.816068\pi\) | ||||
−0.837644 | + | 0.546216i | \(0.816068\pi\) | |||||||
\(224\) | −54.1393 | −3.61733 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 29.7622 | 1.97975 | ||||||||
\(227\) | −4.00936 | −0.266111 | −0.133055 | − | 0.991109i | \(-0.542479\pi\) | ||||
−0.133055 | + | 0.991109i | \(0.542479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.3327 | −1.14538 | −0.572688 | − | 0.819774i | \(-0.694099\pi\) | ||||
−0.572688 | + | 0.819774i | \(0.694099\pi\) | |||||||
\(230\) | 12.4452 | 0.820614 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 53.2519 | 3.49616 | ||||||||
\(233\) | −2.11256 | −0.138398 | −0.0691992 | − | 0.997603i | \(-0.522044\pi\) | ||||
−0.0691992 | + | 0.997603i | \(0.522044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.76855 | −0.441531 | ||||||||
\(236\) | 35.6684 | 2.32181 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.4422 | 1.00097 | ||||||||
\(239\) | 23.9349 | 1.54822 | 0.774110 | − | 0.633052i | \(-0.218198\pi\) | ||||
0.774110 | + | 0.633052i | \(0.218198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5134 | −0.934889 | −0.467444 | − | 0.884023i | \(-0.654825\pi\) | ||||
−0.467444 | + | 0.884023i | \(0.654825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 37.6240 | 2.40863 | ||||||||
\(245\) | −1.60221 | −0.102361 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.64663 | −0.168401 | ||||||||
\(248\) | 10.1313 | 0.643337 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.74483 | 0.173598 | ||||||||
\(251\) | −28.8066 | −1.81826 | −0.909129 | − | 0.416514i | \(-0.863252\pi\) | ||||
−0.909129 | + | 0.416514i | \(0.863252\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −22.2933 | −1.39880 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 53.8491 | 3.36557 | ||||||||
\(257\) | 27.6497 | 1.72474 | 0.862369 | − | 0.506280i | \(-0.168980\pi\) | ||||
0.862369 | + | 0.506280i | \(0.168980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.4008 | −1.08123 | ||||||||
\(260\) | −2.95558 | −0.183297 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.9162 | −0.983304 | ||||||||
\(263\) | −3.13325 | −0.193205 | −0.0966024 | − | 0.995323i | \(-0.530798\pi\) | ||||
−0.0966024 | + | 0.995323i | \(0.530798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.53407 | 0.278526 | ||||||||
\(266\) | −31.6022 | −1.93766 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.99064 | 0.243767 | ||||||||
\(269\) | −18.0030 | −1.09766 | −0.548832 | − | 0.835933i | \(-0.684927\pi\) | ||||
−0.548832 | + | 0.835933i | \(0.684927\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.3327 | 1.23512 | 0.617561 | − | 0.786523i | \(-0.288121\pi\) | ||||
0.617561 | + | 0.786523i | \(0.288121\pi\) | |||||||
\(272\) | −37.6734 | −2.28428 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.3377 | −1.47029 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.4897 | −1.53152 | −0.765762 | − | 0.643124i | \(-0.777638\pi\) | ||||
−0.765762 | + | 0.643124i | \(0.777638\pi\) | |||||||
\(278\) | −46.2963 | −2.77667 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −22.5371 | −1.34685 | ||||||||
\(281\) | −18.2726 | −1.09005 | −0.545025 | − | 0.838420i | \(-0.683480\pi\) | ||||
−0.545025 | + | 0.838420i | \(0.683480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0538 | −0.657079 | −0.328539 | − | 0.944490i | \(-0.606556\pi\) | ||||
−0.328539 | + | 0.944490i | \(0.606556\pi\) | |||||||
\(284\) | −25.0919 | −1.48893 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.6323 | 1.45400 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1363 | −0.655075 | ||||||||
\(290\) | 15.0681 | 0.884832 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.91116 | 0.345925 | ||||||||
\(293\) | −27.1393 | −1.58550 | −0.792748 | − | 0.609550i | \(-0.791350\pi\) | ||||
−0.792748 | + | 0.609550i | \(0.791350\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.44523 | 0.375256 | ||||||||
\(296\) | 72.6527 | 4.22285 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.2582 | −0.710098 | ||||||||
\(299\) | −2.42151 | −0.140040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0444 | −0.578951 | ||||||||
\(302\) | −31.6022 | −1.81850 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 77.0979 | 4.42187 | ||||||||
\(305\) | 6.79861 | 0.389287 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7385 | 0.669951 | 0.334976 | − | 0.942227i | \(-0.391272\pi\) | ||||
0.334976 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.86675 | 0.162820 | ||||||||
\(311\) | −10.6416 | −0.603431 | −0.301716 | − | 0.953398i | \(-0.597559\pi\) | ||||
−0.301716 | + | 0.953398i | \(0.597559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.1807 | −1.53634 | −0.768172 | − | 0.640244i | \(-0.778833\pi\) | ||||
−0.768172 | + | 0.640244i | \(0.778833\pi\) | |||||||
\(314\) | −16.2251 | −0.915636 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.7148 | 1.44657 | ||||||||
\(317\) | −4.97930 | −0.279666 | −0.139833 | − | 0.990175i | \(-0.544657\pi\) | ||||
−0.139833 | + | 0.990175i | \(0.544657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 32.8461 | 1.83615 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −28.9142 | −1.61132 | ||||||||
\(323\) | −12.0000 | −0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.534070 | −0.0296249 | ||||||||
\(326\) | 64.5007 | 3.57236 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −102.846 | −5.67871 | ||||||||
\(329\) | 15.7255 | 0.866973 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.55477 | 0.415247 | 0.207624 | − | 0.978209i | \(-0.433427\pi\) | ||||
0.207624 | + | 0.978209i | \(0.433427\pi\) | |||||||
\(332\) | −75.2756 | −4.13128 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −39.0712 | −2.13788 | ||||||||
\(335\) | 0.721104 | 0.0393981 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.69105 | 0.201064 | 0.100532 | − | 0.994934i | \(-0.467946\pi\) | ||||
0.100532 | + | 0.994934i | \(0.467946\pi\) | |||||||
\(338\) | −34.8998 | −1.89830 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.4008 | −0.726761 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9856 | 1.07912 | ||||||||
\(344\) | 41.9379 | 2.26114 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.6910 | 0.951077 | ||||||||
\(347\) | 15.7655 | 0.846338 | 0.423169 | − | 0.906051i | \(-0.360918\pi\) | ||||
0.423169 | + | 0.906051i | \(0.360918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5578 | −0.565146 | −0.282573 | − | 0.959246i | \(-0.591188\pi\) | ||||
−0.282573 | + | 0.959246i | \(0.591188\pi\) | |||||||
\(350\) | −6.37709 | −0.340870 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.5528 | 1.30681 | 0.653407 | − | 0.757007i | \(-0.273339\pi\) | ||||
0.653407 | + | 0.757007i | \(0.273339\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.53407 | −0.240643 | ||||||||
\(356\) | −70.3644 | −3.72931 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −46.6052 | −2.46316 | ||||||||
\(359\) | 16.6704 | 0.879827 | 0.439914 | − | 0.898040i | \(-0.355009\pi\) | ||||
0.439914 | + | 0.898040i | \(0.355009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.55779 | 0.292515 | ||||||||
\(362\) | 12.3233 | 0.647699 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.86675 | 0.359915 | ||||||||
\(365\) | 1.06814 | 0.0559090 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2789 | 0.797552 | 0.398776 | − | 0.917048i | \(-0.369435\pi\) | ||||
0.398776 | + | 0.917048i | \(0.369435\pi\) | |||||||
\(368\) | 70.5401 | 3.67716 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.5578 | 1.06875 | ||||||||
\(371\) | −10.5341 | −0.546902 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8461 | 0.924033 | 0.462017 | − | 0.886871i | \(-0.347126\pi\) | ||||
0.462017 | + | 0.886871i | \(0.347126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −65.6577 | −3.38604 | ||||||||
\(377\) | −2.93186 | −0.150998 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.89244 | 0.0972082 | 0.0486041 | − | 0.998818i | \(-0.484523\pi\) | ||||
0.0486041 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(380\) | 27.4245 | 1.40685 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.57349 | 0.387493 | ||||||||
\(383\) | −5.31698 | −0.271685 | −0.135842 | − | 0.990730i | \(-0.543374\pi\) | ||||
−0.135842 | + | 0.990730i | \(0.543374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.3988 | 1.64906 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 26.3377 | 1.33709 | ||||||||
\(389\) | 26.8273 | 1.36020 | 0.680100 | − | 0.733120i | \(-0.261936\pi\) | ||||
0.680100 | + | 0.733120i | \(0.261936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.9793 | −0.555247 | ||||||||
\(392\) | −15.5421 | −0.784994 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.8698 | 0.900266 | ||||||||
\(395\) | 4.64663 | 0.233797 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.5972 | 1.58582 | 0.792909 | − | 0.609340i | \(-0.208565\pi\) | ||||
0.792909 | + | 0.609340i | \(0.208565\pi\) | |||||||
\(398\) | 65.7622 | 3.29636 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.5578 | 0.777890 | ||||||||
\(401\) | 3.13628 | 0.156618 | 0.0783092 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783092 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.557793 | −0.0277856 | ||||||||
\(404\) | 36.4058 | 1.81126 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −35.0080 | −1.73742 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.424538 | 0.0209921 | 0.0104960 | − | 0.999945i | \(-0.496659\pi\) | ||||
0.0104960 | + | 0.999945i | \(0.496659\pi\) | |||||||
\(410\) | −29.1012 | −1.43721 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 90.5175 | 4.45947 | ||||||||
\(413\) | −14.9743 | −0.736837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.6022 | −0.667706 | ||||||||
\(416\) | −12.4452 | −0.610178 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.71174 | −0.327890 | −0.163945 | − | 0.986469i | \(-0.552422\pi\) | ||||
−0.163945 | + | 0.986469i | \(0.552422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.77988 | 0.135483 | 0.0677416 | − | 0.997703i | \(-0.478421\pi\) | ||||
0.0677416 | + | 0.997703i | \(0.478421\pi\) | |||||||
\(422\) | −46.2963 | −2.25367 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 43.9823 | 2.13597 | ||||||||
\(425\) | −2.42151 | −0.117461 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.7953 | −0.764388 | ||||||||
\(428\) | −56.5070 | −2.73137 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.8667 | 0.572265 | ||||||||
\(431\) | −16.1964 | −0.780153 | −0.390076 | − | 0.920782i | \(-0.627551\pi\) | ||||
−0.390076 | + | 0.920782i | \(0.627551\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.82733 | 0.376157 | 0.188079 | − | 0.982154i | \(-0.439774\pi\) | ||||
0.188079 | + | 0.982154i | \(0.439774\pi\) | |||||||
\(434\) | −6.66035 | −0.319707 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −66.9172 | −3.20475 | ||||||||
\(437\) | 22.4690 | 1.07484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.7355 | 0.989650 | 0.494825 | − | 0.868993i | \(-0.335232\pi\) | ||||
0.494825 | + | 0.868993i | \(0.335232\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.54977 | 0.168845 | ||||||||
\(443\) | −5.30262 | −0.251935 | −0.125968 | − | 0.992034i | \(-0.540204\pi\) | ||||
−0.125968 | + | 0.992034i | \(0.540204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.7148 | −0.602738 | ||||||||
\(446\) | −68.6684 | −3.25154 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −76.3117 | −3.60539 | ||||||||
\(449\) | 30.0030 | 1.41593 | 0.707965 | − | 0.706247i | \(-0.249613\pi\) | ||||
0.707965 | + | 0.706247i | \(0.249613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 60.0061 | 2.82245 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.0050 | −0.516490 | ||||||||
\(455\) | 1.24081 | 0.0581702 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.5134 | 1.75480 | 0.877401 | − | 0.479758i | \(-0.159276\pi\) | ||||
0.877401 | + | 0.479758i | \(0.159276\pi\) | |||||||
\(458\) | −47.5752 | −2.22304 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 25.0919 | 1.16991 | ||||||||
\(461\) | −15.7829 | −0.735083 | −0.367542 | − | 0.930007i | \(-0.619800\pi\) | ||||
−0.367542 | + | 0.930007i | \(0.619800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5672 | −0.769941 | −0.384970 | − | 0.922929i | \(-0.625788\pi\) | ||||
−0.384970 | + | 0.922929i | \(0.625788\pi\) | |||||||
\(464\) | 85.4069 | 3.96491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.79861 | −0.268615 | ||||||||
\(467\) | −3.70041 | −0.171234 | −0.0856172 | − | 0.996328i | \(-0.527286\pi\) | ||||
−0.0856172 | + | 0.996328i | \(0.527286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.67535 | −0.0773605 | ||||||||
\(470\) | −18.5785 | −0.856962 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 62.5214 | 2.87778 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.95558 | 0.227378 | ||||||||
\(476\) | 31.1343 | 1.42704 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 65.6971 | 3.00492 | ||||||||
\(479\) | −1.26454 | −0.0577781 | −0.0288890 | − | 0.999583i | \(-0.509197\pi\) | ||||
−0.0288890 | + | 0.999583i | \(0.509197\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | −39.8367 | −1.81451 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.75919 | 0.216104 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.6022 | 0.978890 | 0.489445 | − | 0.872034i | \(-0.337199\pi\) | ||||
0.489445 | + | 0.872034i | \(0.337199\pi\) | |||||||
\(488\) | 65.9492 | 2.98538 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.39779 | −0.198672 | ||||||||
\(491\) | −25.5371 | −1.15247 | −0.576237 | − | 0.817283i | \(-0.695479\pi\) | ||||
−0.576237 | + | 0.817283i | \(0.695479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.2933 | −0.598698 | ||||||||
\(494\) | −7.26454 | −0.326847 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.2488 | 0.729594 | ||||||||
\(497\) | 10.5341 | 0.472518 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.3614 | 1.09057 | 0.545283 | − | 0.838252i | \(-0.316422\pi\) | ||||
0.545283 | + | 0.838252i | \(0.316422\pi\) | |||||||
\(500\) | 5.53407 | 0.247491 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −79.0692 | −3.52903 | ||||||||
\(503\) | 12.4960 | 0.557169 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.57849 | 0.292739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −44.9473 | −1.99421 | ||||||||
\(509\) | −24.4483 | −1.08365 | −0.541825 | − | 0.840491i | \(-0.682266\pi\) | ||||
−0.541825 | + | 0.840491i | \(0.682266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.48163 | −0.109781 | ||||||||
\(512\) | 60.7034 | 2.68274 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 75.8935 | 3.34752 | ||||||||
\(515\) | 16.3564 | 0.720749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −47.7622 | −2.09855 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.18070 | −0.227189 | ||||||||
\(521\) | 0.0394184 | 0.00172695 | 0.000863476 | − | 1.00000i | \(-0.499725\pi\) | ||||
0.000863476 | 1.00000i | \(0.499725\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.0919 | −0.922283 | −0.461141 | − | 0.887327i | \(-0.652560\pi\) | ||||
−0.461141 | + | 0.887327i | \(0.652560\pi\) | |||||||
\(524\) | −32.0899 | −1.40185 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.60024 | −0.374988 | ||||||||
\(527\) | −2.52907 | −0.110168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.44221 | −0.106183 | ||||||||
\(530\) | 12.4452 | 0.540586 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −63.7158 | −2.76243 | ||||||||
\(533\) | 5.66232 | 0.245263 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2108 | −0.441449 | ||||||||
\(536\) | 6.99500 | 0.302138 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −49.4152 | −2.13044 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.4402 | −1.43771 | −0.718854 | − | 0.695161i | \(-0.755333\pi\) | ||||
−0.718854 | + | 0.695161i | \(0.755333\pi\) | |||||||
\(542\) | 55.8097 | 2.39723 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −56.4276 | −2.41931 | ||||||||
\(545\) | −12.0919 | −0.517958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8066 | 1.40271 | 0.701355 | − | 0.712812i | \(-0.252579\pi\) | ||||
0.701355 | + | 0.712812i | \(0.252579\pi\) | |||||||
\(548\) | −49.0692 | −2.09613 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.2044 | 1.15895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.7956 | −0.459075 | ||||||||
\(554\) | −69.9647 | −2.97251 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −93.3418 | −3.95857 | ||||||||
\(557\) | −28.3327 | −1.20049 | −0.600247 | − | 0.799815i | \(-0.704931\pi\) | ||||
−0.600247 | + | 0.799815i | \(0.704931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.30895 | −0.0976583 | ||||||||
\(560\) | −36.1456 | −1.52743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.1550 | −2.11566 | ||||||||
\(563\) | −29.0361 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8430 | 0.456169 | ||||||||
\(566\) | −30.3407 | −1.27531 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.9823 | −1.84546 | ||||||||
\(569\) | −28.7098 | −1.20358 | −0.601788 | − | 0.798656i | \(-0.705545\pi\) | ||||
−0.601788 | + | 0.798656i | \(0.705545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.824301 | 0.0344959 | 0.0172480 | − | 0.999851i | \(-0.494510\pi\) | ||||
0.0172480 | + | 0.999851i | \(0.494510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 67.6113 | 2.82204 | ||||||||
\(575\) | 4.53407 | 0.189084 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.5421 | −1.31311 | −0.656557 | − | 0.754276i | \(-0.727988\pi\) | ||||
−0.656557 | + | 0.754276i | \(0.727988\pi\) | |||||||
\(578\) | −30.5672 | −1.27143 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 30.3801 | 1.26147 | ||||||||
\(581\) | 31.6022 | 1.31108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.3614 | 0.428758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −74.4927 | −3.07726 | ||||||||
\(587\) | 26.7735 | 1.10506 | 0.552531 | − | 0.833492i | \(-0.313662\pi\) | ||||
0.552531 | + | 0.833492i | \(0.313662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.17570 | 0.213261 | ||||||||
\(590\) | 17.6910 | 0.728329 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 116.522 | 4.78904 | ||||||||
\(593\) | 11.0731 | 0.454719 | 0.227360 | − | 0.973811i | \(-0.426991\pi\) | ||||
0.227360 | + | 0.973811i | \(0.426991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.62593 | 0.230641 | ||||||||
\(596\) | −24.7148 | −1.01236 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.64663 | −0.271801 | ||||||||
\(599\) | 11.9349 | 0.487646 | 0.243823 | − | 0.969820i | \(-0.421598\pi\) | ||||
0.243823 | + | 0.969820i | \(0.421598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.26454 | 0.214745 | 0.107372 | − | 0.994219i | \(-0.465756\pi\) | ||||
0.107372 | + | 0.994219i | \(0.465756\pi\) | |||||||
\(602\) | −27.5702 | −1.12368 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −63.7158 | −2.59256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.8461 | 1.45495 | 0.727473 | − | 0.686136i | \(-0.240695\pi\) | ||||
0.727473 | + | 0.686136i | \(0.240695\pi\) | |||||||
\(608\) | 115.478 | 4.68325 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.6610 | 0.755561 | ||||||||
\(611\) | 3.61488 | 0.146242 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.55779 | 0.264867 | 0.132433 | − | 0.991192i | \(-0.457721\pi\) | ||||
0.132433 | + | 0.991192i | \(0.457721\pi\) | |||||||
\(614\) | 32.2201 | 1.30030 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.7986 | −0.716545 | −0.358272 | − | 0.933617i | \(-0.616634\pi\) | ||||
−0.358272 | + | 0.933617i | \(0.616634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.8905 | 1.80430 | 0.902150 | − | 0.431422i | \(-0.141988\pi\) | ||||
0.902150 | + | 0.431422i | \(0.141988\pi\) | |||||||
\(620\) | 5.77988 | 0.232126 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29.2094 | −1.17119 | ||||||||
\(623\) | 29.5404 | 1.18351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −74.6063 | −2.98187 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.7128 | −1.30538 | ||||||||
\(629\) | −18.1363 | −0.723141 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9112 | 0.872270 | 0.436135 | − | 0.899881i | \(-0.356347\pi\) | ||||
0.436135 | + | 0.899881i | \(0.356347\pi\) | |||||||
\(632\) | 45.0742 | 1.79296 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.6673 | −0.542799 | ||||||||
\(635\) | −8.12192 | −0.322309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.855693 | 0.0339038 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.5515 | 1.72152 | ||||||||
\(641\) | −35.7335 | −1.41139 | −0.705694 | − | 0.708517i | \(-0.749365\pi\) | ||||
−0.705694 | + | 0.708517i | \(0.749365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.412150 | 0.0162536 | 0.00812681 | − | 0.999967i | \(-0.497413\pi\) | ||||
0.00812681 | + | 0.999967i | \(0.497413\pi\) | |||||||
\(644\) | −58.2963 | −2.29720 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.9379 | −1.29592 | ||||||||
\(647\) | 16.5484 | 0.650586 | 0.325293 | − | 0.945613i | \(-0.394537\pi\) | ||||
0.325293 | + | 0.945613i | \(0.394537\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.46593 | −0.0574985 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 130.045 | 5.09296 | ||||||||
\(653\) | −11.0080 | −0.430777 | −0.215389 | − | 0.976528i | \(-0.569102\pi\) | ||||
−0.215389 | + | 0.976528i | \(0.569102\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.79861 | −0.226570 | ||||||||
\(656\) | −164.947 | −6.44010 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43.1637 | 1.68269 | ||||||||
\(659\) | −42.9980 | −1.67497 | −0.837483 | − | 0.546464i | \(-0.815974\pi\) | ||||
−0.837483 | + | 0.546464i | \(0.815974\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4927 | 0.758177 | 0.379089 | − | 0.925360i | \(-0.376238\pi\) | ||||
0.379089 | + | 0.925360i | \(0.376238\pi\) | |||||||
\(662\) | 20.7365 | 0.805948 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −131.947 | −5.12054 | ||||||||
\(665\) | −11.5134 | −0.446470 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.8905 | 0.963763 | ||||||||
\(668\) | −78.7746 | −3.04788 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.97930 | 0.0764672 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.80663 | −0.262376 | −0.131188 | − | 0.991357i | \(-0.541879\pi\) | ||||
−0.131188 | + | 0.991357i | \(0.541879\pi\) | |||||||
\(674\) | 10.1313 | 0.390242 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −70.3644 | −2.70632 | ||||||||
\(677\) | 1.02070 | 0.0392285 | 0.0196143 | − | 0.999808i | \(-0.493756\pi\) | ||||
0.0196143 | + | 0.999808i | \(0.493756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.0571 | −0.424332 | ||||||||
\(680\) | −23.4897 | −0.900787 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.09820 | −0.0802853 | −0.0401426 | − | 0.999194i | \(-0.512781\pi\) | ||||
−0.0401426 | + | 0.999194i | \(0.512781\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.86675 | −0.338781 | ||||||||
\(686\) | 54.8571 | 2.09445 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 67.2612 | 2.56431 | ||||||||
\(689\) | −2.42151 | −0.0922523 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.9950 | 0.456311 | 0.228156 | − | 0.973625i | \(-0.426730\pi\) | ||||
0.228156 | + | 0.973625i | \(0.426730\pi\) | |||||||
\(692\) | 35.6684 | 1.35591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.2736 | 1.64264 | ||||||||
\(695\) | −16.8667 | −0.639792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.6734 | 0.972449 | ||||||||
\(698\) | −28.9793 | −1.09688 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.8574 | −0.485963 | ||||||||
\(701\) | −29.3594 | −1.10889 | −0.554445 | − | 0.832220i | \(-0.687069\pi\) | ||||
−0.554445 | + | 0.832220i | \(0.687069\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.1156 | 1.39984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 67.3931 | 2.53637 | ||||||||
\(707\) | −15.2839 | −0.574810 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.5451 | −1.41004 | −0.705018 | − | 0.709189i | \(-0.749061\pi\) | ||||
−0.705018 | + | 0.709189i | \(0.749061\pi\) | |||||||
\(710\) | −12.4452 | −0.467061 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −123.338 | −4.62230 | ||||||||
\(713\) | 4.73546 | 0.177345 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −93.9647 | −3.51162 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 45.7572 | 1.70764 | ||||||||
\(719\) | 3.99500 | 0.148988 | 0.0744942 | − | 0.997221i | \(-0.476266\pi\) | ||||
0.0744942 | + | 0.997221i | \(0.476266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.0011 | −1.41523 | ||||||||
\(722\) | 15.2552 | 0.567739 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.8461 | 0.923396 | ||||||||
\(725\) | 5.48965 | 0.203881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4990 | −0.945706 | −0.472853 | − | 0.881141i | \(-0.656776\pi\) | ||||
−0.472853 | + | 0.881141i | \(0.656776\pi\) | |||||||
\(728\) | 12.0364 | 0.446098 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.93186 | 0.108513 | ||||||||
\(731\) | −10.4690 | −0.387208 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.2024 | −1.33717 | −0.668584 | − | 0.743637i | \(-0.733099\pi\) | ||||
−0.668584 | + | 0.743637i | \(0.733099\pi\) | |||||||
\(734\) | 41.9379 | 1.54796 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 105.656 | 3.89452 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.06011 | −0.222925 | −0.111462 | − | 0.993769i | \(-0.535553\pi\) | ||||
−0.111462 | + | 0.993769i | \(0.535553\pi\) | |||||||
\(740\) | 41.4483 | 1.52367 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.9142 | −1.06147 | ||||||||
\(743\) | −36.2869 | −1.33124 | −0.665619 | − | 0.746292i | \(-0.731832\pi\) | ||||
−0.665619 | + | 0.746292i | \(0.731832\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.46593 | −0.163619 | ||||||||
\(746\) | 48.9843 | 1.79344 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.7228 | 0.866812 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.7335 | −0.574123 | −0.287062 | − | 0.957912i | \(-0.592678\pi\) | ||||
−0.287062 | + | 0.957912i | \(0.592678\pi\) | |||||||
\(752\) | −105.304 | −3.84003 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.04744 | −0.293071 | ||||||||
\(755\) | −11.5134 | −0.419015 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1393 | −0.913704 | −0.456852 | − | 0.889543i | \(-0.651023\pi\) | ||||
−0.456852 | + | 0.889543i | \(0.651023\pi\) | |||||||
\(758\) | 5.19442 | 0.188670 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.0712 | 1.74372 | ||||||||
\(761\) | 15.4709 | 0.560821 | 0.280410 | − | 0.959880i | \(-0.409529\pi\) | ||||
0.280410 | + | 0.959880i | \(0.409529\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0932 | 1.01704 | ||||||||
\(764\) | 15.2695 | 0.552432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.5942 | −0.527309 | ||||||||
\(767\) | −3.44221 | −0.124291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.3220 | 0.624647 | 0.312323 | − | 0.949976i | \(-0.398893\pi\) | ||||
0.312323 | + | 0.949976i | \(0.398893\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 65.3220 | 2.35099 | ||||||||
\(773\) | 22.6991 | 0.816429 | 0.408214 | − | 0.912886i | \(-0.366152\pi\) | ||||
0.408214 | + | 0.912886i | \(0.366152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.04442 | 0.0375166 | ||||||||
\(776\) | 46.1661 | 1.65726 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 73.6363 | 2.63999 | ||||||||
\(779\) | −52.5401 | −1.88245 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −30.1363 | −1.07767 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.9269 | −0.890245 | ||||||||
\(785\) | −5.91116 | −0.210978 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.10122 | 0.110547 | 0.0552734 | − | 0.998471i | \(-0.482397\pi\) | ||||
0.0552734 | + | 0.998471i | \(0.482397\pi\) | |||||||
\(788\) | 36.0287 | 1.28347 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.7542 | 0.453774 | ||||||||
\(791\) | −25.1918 | −0.895716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.63093 | −0.128938 | ||||||||
\(794\) | 86.7288 | 3.07789 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 132.589 | 4.69948 | ||||||||
\(797\) | 19.0919 | 0.676268 | 0.338134 | − | 0.941098i | \(-0.390204\pi\) | ||||
0.338134 | + | 0.941098i | \(0.390204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3901 | 0.579841 | ||||||||
\(800\) | 23.3026 | 0.823872 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.60855 | 0.303978 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.5341 | −0.371277 | ||||||||
\(806\) | −1.53104 | −0.0539287 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 63.8140 | 2.24497 | ||||||||
\(809\) | −4.46896 | −0.157120 | −0.0785601 | − | 0.996909i | \(-0.525032\pi\) | ||||
−0.0785601 | + | 0.996909i | \(0.525032\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.86675 | −0.170895 | −0.0854473 | − | 0.996343i | \(-0.527232\pi\) | ||||
−0.0854473 | + | 0.996343i | \(0.527232\pi\) | |||||||
\(812\) | −70.5826 | −2.47696 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.4990 | 0.823135 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.4245 | 0.749550 | ||||||||
\(818\) | 1.16528 | 0.0407432 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.6734 | −2.04896 | ||||||||
\(821\) | −17.0050 | −0.593479 | −0.296739 | − | 0.954959i | \(-0.595899\pi\) | ||||
−0.296739 | + | 0.954959i | \(0.595899\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.7479 | −0.758082 | −0.379041 | − | 0.925380i | \(-0.623746\pi\) | ||||
−0.379041 | + | 0.925380i | \(0.623746\pi\) | |||||||
\(824\) | 158.664 | 5.52731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −41.1019 | −1.43012 | ||||||||
\(827\) | 20.7084 | 0.720103 | 0.360051 | − | 0.932932i | \(-0.382759\pi\) | ||||
0.360051 | + | 0.932932i | \(0.382759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3090 | 0.392776 | 0.196388 | − | 0.980526i | \(-0.437079\pi\) | ||||
0.196388 | + | 0.980526i | \(0.437079\pi\) | |||||||
\(830\) | −37.3357 | −1.29594 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.5421 | −0.608163 | ||||||||
\(833\) | 3.87977 | 0.134426 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.2345 | −0.492604 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.4226 | −0.636397 | ||||||||
\(839\) | 43.5084 | 1.50208 | 0.751038 | − | 0.660259i | \(-0.229554\pi\) | ||||
0.751038 | + | 0.660259i | \(0.229554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.13628 | 0.0391821 | ||||||||
\(842\) | 7.63029 | 0.262957 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −93.3418 | −3.21296 | ||||||||
\(845\) | −12.7148 | −0.437401 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 70.5401 | 2.42236 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.64663 | −0.227977 | ||||||||
\(851\) | 33.9586 | 1.16409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.11559 | −0.0381969 | −0.0190985 | − | 0.999818i | \(-0.506080\pi\) | ||||
−0.0190985 | + | 0.999818i | \(0.506080\pi\) | |||||||
\(854\) | −43.3553 | −1.48359 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −99.0485 | −3.38541 | ||||||||
\(857\) | −7.80361 | −0.266566 | −0.133283 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133283 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5341 | 1.04181 | 0.520905 | − | 0.853615i | \(-0.325595\pi\) | ||||
0.520905 | + | 0.853615i | \(0.325595\pi\) | |||||||
\(860\) | 23.9255 | 0.815854 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −44.4563 | −1.51419 | ||||||||
\(863\) | 4.28959 | 0.146019 | 0.0730097 | − | 0.997331i | \(-0.476740\pi\) | ||||
0.0730097 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.44523 | 0.219145 | ||||||||
\(866\) | 21.4847 | 0.730078 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.4285 | −0.455792 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.385120 | −0.0130493 | ||||||||
\(872\) | −117.296 | −3.97214 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 61.6734 | 2.08613 | ||||||||
\(875\) | −2.32331 | −0.0785424 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3644 | 0.383749 | 0.191875 | − | 0.981419i | \(-0.438543\pi\) | ||||
0.191875 | + | 0.981419i | \(0.438543\pi\) | |||||||
\(878\) | 56.9152 | 1.92080 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.3277 | 0.381639 | 0.190820 | − | 0.981625i | \(-0.438885\pi\) | ||||
0.190820 | + | 0.981625i | \(0.438885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.2883 | 1.05293 | 0.526467 | − | 0.850196i | \(-0.323516\pi\) | ||||
0.526467 | + | 0.850196i | \(0.323516\pi\) | |||||||
\(884\) | 7.15698 | 0.240715 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.5548 | −0.488977 | ||||||||
\(887\) | 28.2819 | 0.949614 | 0.474807 | − | 0.880090i | \(-0.342518\pi\) | ||||
0.474807 | + | 0.880090i | \(0.342518\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.8698 | 0.632872 | ||||||||
\(890\) | −34.8998 | −1.16984 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −138.448 | −4.63558 | ||||||||
\(893\) | −33.5421 | −1.12244 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9793 | −0.567556 | ||||||||
\(896\) | −101.184 | −3.38031 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 82.3531 | 2.74816 | ||||||||
\(899\) | 5.73349 | 0.191223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9793 | −0.365774 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 105.182 | 3.49829 | ||||||||
\(905\) | 4.48965 | 0.149241 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.6166 | 1.11622 | 0.558110 | − | 0.829767i | \(-0.311527\pi\) | ||||
0.558110 | + | 0.829767i | \(0.311527\pi\) | |||||||
\(908\) | −22.1881 | −0.736338 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.40582 | 0.112902 | ||||||||
\(911\) | −7.53104 | −0.249515 | −0.124757 | − | 0.992187i | \(-0.539815\pi\) | ||||
−0.124757 | + | 0.992187i | \(0.539815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 102.968 | 3.40587 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −95.9202 | −3.16929 | ||||||||
\(917\) | 13.4720 | 0.444884 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0424 | 1.32088 | 0.660439 | − | 0.750880i | \(-0.270370\pi\) | ||||
0.660439 | + | 0.750880i | \(0.270370\pi\) | |||||||
\(920\) | 43.9823 | 1.45005 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −43.3213 | −1.42671 | ||||||||
\(923\) | 2.42151 | 0.0797050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.48965 | 0.246258 | ||||||||
\(926\) | −45.4740 | −1.49437 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 127.923 | 4.19929 | ||||||||
\(929\) | −51.3407 | −1.68443 | −0.842217 | − | 0.539139i | \(-0.818750\pi\) | ||||
−0.842217 | + | 0.539139i | \(0.818750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.93989 | −0.260219 | ||||||||
\(932\) | −11.6910 | −0.382953 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.1570 | −0.332346 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.8510 | −1.17120 | −0.585601 | − | 0.810599i | \(-0.699142\pi\) | ||||
−0.585601 | + | 0.810599i | \(0.699142\pi\) | |||||||
\(938\) | −4.59855 | −0.150148 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −37.4576 | −1.22173 | ||||||||
\(941\) | 0.607210 | 0.0197945 | 0.00989724 | − | 0.999951i | \(-0.496850\pi\) | ||||
0.00989724 | + | 0.999951i | \(0.496850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −48.0712 | −1.56541 | ||||||||
\(944\) | 100.274 | 3.26363 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.3851 | 0.857401 | 0.428701 | − | 0.903447i | \(-0.358972\pi\) | ||||
0.428701 | + | 0.903447i | \(0.358972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.570462 | −0.0185180 | ||||||||
\(950\) | 13.6022 | 0.441314 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 54.5738 | 1.76875 | ||||||||
\(953\) | 35.3594 | 1.14540 | 0.572702 | − | 0.819764i | \(-0.305895\pi\) | ||||
0.572702 | + | 0.819764i | \(0.305895\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.75919 | 0.0892852 | ||||||||
\(956\) | 132.457 | 4.28398 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.47093 | −0.112141 | ||||||||
\(959\) | 20.6002 | 0.665216 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9092 | −0.964813 | ||||||||
\(962\) | −10.9793 | −0.353987 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −80.3180 | −2.58687 | ||||||||
\(965\) | 11.8036 | 0.379971 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.86872 | −0.124410 | −0.0622048 | − | 0.998063i | \(-0.519813\pi\) | ||||
−0.0622048 | + | 0.998063i | \(0.519813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.0631 | 0.419432 | ||||||||
\(971\) | −24.1076 | −0.773648 | −0.386824 | − | 0.922153i | \(-0.626428\pi\) | ||||
−0.386824 | + | 0.922153i | \(0.626428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.1868 | 1.25627 | ||||||||
\(974\) | 59.2943 | 1.89991 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 105.771 | 3.38566 | ||||||||
\(977\) | −10.8143 | −0.345980 | −0.172990 | − | 0.984924i | \(-0.555343\pi\) | ||||
−0.172990 | + | 0.984924i | \(0.555343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.86675 | −0.283238 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −70.0949 | −2.23682 | ||||||||
\(983\) | 38.7084 | 1.23461 | 0.617304 | − | 0.786725i | \(-0.288225\pi\) | ||||
0.617304 | + | 0.786725i | \(0.288225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.51035 | 0.207437 | ||||||||
\(986\) | −36.4877 | −1.16200 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.6466 | −0.465971 | ||||||||
\(989\) | 19.6022 | 0.623314 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.4533 | 1.95213 | 0.976064 | − | 0.217485i | \(-0.0697854\pi\) | ||||
0.976064 | + | 0.217485i | \(0.0697854\pi\) | |||||||
\(992\) | 24.3377 | 0.772722 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 28.9142 | 0.917102 | ||||||||
\(995\) | 23.9586 | 0.759539 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.3377 | −1.21417 | −0.607083 | − | 0.794638i | \(-0.707661\pi\) | ||||
−0.607083 | + | 0.794638i | \(0.707661\pi\) | |||||||
\(998\) | 66.8678 | 2.11666 | ||||||||
\(999\) | 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 | 5445.2.a.bb.1.3 | 3 | ||
3.2 | odd | 2 | 605.2.a.h.1.1 | yes | 3 | ||
11.10 | odd | 2 | 5445.2.a.bd.1.1 | 3 | |||
12.11 | even | 2 | 9680.2.a.cb.1.2 | 3 | |||
15.14 | odd | 2 | 3025.2.a.p.1.3 | 3 | |||
33.2 | even | 10 | 605.2.g.p.81.1 | 12 | |||
33.5 | odd | 10 | 605.2.g.o.366.3 | 12 | |||
33.8 | even | 10 | 605.2.g.p.251.3 | 12 | |||
33.14 | odd | 10 | 605.2.g.o.251.1 | 12 | |||
33.17 | even | 10 | 605.2.g.p.366.1 | 12 | |||
33.20 | odd | 10 | 605.2.g.o.81.3 | 12 | |||
33.26 | odd | 10 | 605.2.g.o.511.1 | 12 | |||
33.29 | even | 10 | 605.2.g.p.511.3 | 12 | |||
33.32 | even | 2 | 605.2.a.g.1.3 | ✓ | 3 | ||
132.131 | odd | 2 | 9680.2.a.bz.1.2 | 3 | |||
165.164 | even | 2 | 3025.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.g.1.3 | ✓ | 3 | 33.32 | even | 2 | ||
605.2.a.h.1.1 | yes | 3 | 3.2 | odd | 2 | ||
605.2.g.o.81.3 | 12 | 33.20 | odd | 10 | |||
605.2.g.o.251.1 | 12 | 33.14 | odd | 10 | |||
605.2.g.o.366.3 | 12 | 33.5 | odd | 10 | |||
605.2.g.o.511.1 | 12 | 33.26 | odd | 10 | |||
605.2.g.p.81.1 | 12 | 33.2 | even | 10 | |||
605.2.g.p.251.3 | 12 | 33.8 | even | 10 | |||
605.2.g.p.366.1 | 12 | 33.17 | even | 10 | |||
605.2.g.p.511.3 | 12 | 33.29 | even | 10 | |||
3025.2.a.p.1.3 | 3 | 15.14 | odd | 2 | |||
3025.2.a.u.1.1 | 3 | 165.164 | even | 2 | |||
5445.2.a.bb.1.3 | 3 | 1.1 | even | 1 | trivial | ||
5445.2.a.bd.1.1 | 3 | 11.10 | odd | 2 | |||
9680.2.a.bz.1.2 | 3 | 132.131 | odd | 2 | |||
9680.2.a.cb.1.2 | 3 | 12.11 | even | 2 |