Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.86799 | 1.83993 | 0.919964 | − | 0.392003i | \(-0.128218\pi\) | ||||
0.919964 | + | 0.392003i | \(0.128218\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.77801 | 1.44062 | 0.720312 | − | 0.693650i | \(-0.243999\pi\) | ||||
0.720312 | + | 0.693650i | \(0.243999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.77801 | 0.770481 | 0.385240 | − | 0.922816i | \(-0.374119\pi\) | ||||
0.385240 | + | 0.922816i | \(0.374119\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.636672 | −0.154416 | −0.0772078 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772078 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50466 | −0.804025 | −0.402013 | − | 0.915634i | \(-0.631689\pi\) | ||||
−0.402013 | + | 0.915634i | \(0.631689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.86799 | 1.06228 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.36333 | 1.36734 | 0.683668 | − | 0.729793i | \(-0.260384\pi\) | ||||
0.683668 | + | 0.729793i | \(0.260384\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.15066 | −0.925087 | −0.462543 | − | 0.886597i | \(-0.653063\pi\) | ||||
−0.462543 | + | 0.886597i | \(0.653063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.77801 | 0.831744 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.86799 | 0.822841 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.86799 | 0.471495 | 0.235748 | − | 0.971814i | \(-0.424246\pi\) | ||||
0.235748 | + | 0.971814i | \(0.424246\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.77801 | 0.444837 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.19269 | −0.967135 | −0.483568 | − | 0.875307i | \(-0.660659\pi\) | ||||
−0.483568 | + | 0.875307i | \(0.660659\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.28267 | −1.26310 | −0.631548 | − | 0.775337i | \(-0.717580\pi\) | ||||
−0.631548 | + | 0.775337i | \(0.717580\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.50466 | 1.09467 | 0.547334 | − | 0.836914i | \(-0.315643\pi\) | ||||
0.547334 | + | 0.836914i | \(0.315643\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.6974 | 2.38534 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.636672 | −0.0891519 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.91934 | −0.675724 | −0.337862 | − | 0.941196i | \(-0.609704\pi\) | ||||
−0.337862 | + | 0.941196i | \(0.609704\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.77801 | 0.644266 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.50466 | −0.464204 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.65533 | −1.12683 | −0.563414 | − | 0.826175i | \(-0.690512\pi\) | ||||
−0.563414 | + | 0.826175i | \(0.690512\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.0607 | −1.92832 | −0.964161 | − | 0.265317i | \(-0.914523\pi\) | ||||
−0.964161 | + | 0.265317i | \(0.914523\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.86799 | 0.613309 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.77801 | 0.344569 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.4333 | −1.64114 | −0.820572 | − | 0.571544i | \(-0.806345\pi\) | ||||
−0.820572 | + | 0.571544i | \(0.806345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.0993 | −1.31725 | −0.658623 | − | 0.752473i | \(-0.728861\pi\) | ||||
−0.658623 | + | 0.752473i | \(0.728861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2406 | −1.78378 | −0.891892 | − | 0.452249i | \(-0.850622\pi\) | ||||
−0.891892 | + | 0.452249i | \(0.850622\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.2593 | 2.65064 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.45331 | −0.163510 | −0.0817552 | − | 0.996652i | \(-0.526053\pi\) | ||||
−0.0817552 | + | 0.996652i | \(0.526053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.63667 | 0.728469 | 0.364235 | − | 0.931307i | \(-0.381331\pi\) | ||||
0.364235 | + | 0.931307i | \(0.381331\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.636672 | −0.0690567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.36333 | 0.789432 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.29200 | 0.984950 | 0.492475 | − | 0.870327i | \(-0.336092\pi\) | ||||
0.492475 | + | 0.870327i | \(0.336092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5233 | 1.41763 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.15066 | −0.534099 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50466 | −0.359571 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7453 | −1.49716 | −0.748580 | − | 0.663045i | \(-0.769264\pi\) | ||||
−0.748580 | + | 0.663045i | \(0.769264\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.77801 | 0.480208 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3820 | −1.72957 | −0.864786 | − | 0.502140i | \(-0.832546\pi\) | ||||
−0.864786 | + | 0.502140i | \(0.832546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2920 | 1.50677 | 0.753383 | − | 0.657582i | \(-0.228421\pi\) | ||||
0.753383 | + | 0.657582i | \(0.228421\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.86799 | 0.475067 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3820 | 1.48703 | 0.743516 | − | 0.668718i | \(-0.233157\pi\) | ||||
0.743516 | + | 0.668718i | \(0.233157\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2406 | −1.45979 | −0.729895 | − | 0.683560i | \(-0.760431\pi\) | ||||
−0.729895 | + | 0.683560i | \(0.760431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.86799 | 0.272218 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.19269 | 0.582559 | 0.291280 | − | 0.956638i | \(-0.405919\pi\) | ||||
0.291280 | + | 0.956638i | \(0.405919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.77801 | 0.256827 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.09931 | −0.284114 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8294 | 1.07540 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.19269 | −0.558376 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.77801 | −0.423980 | −0.211990 | − | 0.977272i | \(-0.567994\pi\) | ||||
−0.211990 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.28267 | −0.729249 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.54669 | 0.571987 | 0.285993 | − | 0.958232i | \(-0.407676\pi\) | ||||
0.285993 | + | 0.958232i | \(0.407676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.0607 | −1.47935 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.7453 | −0.918034 | −0.459017 | − | 0.888427i | \(-0.651798\pi\) | ||||
−0.459017 | + | 0.888427i | \(0.651798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4240 | 1.22343 | 0.611714 | − | 0.791079i | \(-0.290480\pi\) | ||||
0.611714 | + | 0.791079i | \(0.290480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.50466 | 0.632007 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.2733 | 1.10997 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.36333 | 0.611491 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.6974 | 1.37717 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.67531 | 0.546862 | 0.273431 | − | 0.961892i | \(-0.411841\pi\) | ||||
0.273431 | + | 0.961892i | \(0.411841\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3013 | 1.48934 | 0.744671 | − | 0.667432i | \(-0.232607\pi\) | ||||
0.744671 | + | 0.667432i | \(0.232607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.636672 | −0.0514719 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.15066 | −0.413711 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4427 | 1.47188 | 0.735942 | − | 0.677044i | \(-0.236739\pi\) | ||||
0.735942 | + | 0.677044i | \(0.236739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.91934 | −0.390129 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.86799 | −0.383652 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.282672 | −0.0221406 | −0.0110703 | − | 0.999939i | \(-0.503524\pi\) | ||||
−0.0110703 | + | 0.999939i | \(0.503524\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.77801 | 0.371967 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.51399 | 0.504068 | 0.252034 | − | 0.967718i | \(-0.418901\pi\) | ||||
0.252034 | + | 0.967718i | \(0.418901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.28267 | −0.406359 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50466 | −0.268008 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.30133 | 0.631138 | 0.315569 | − | 0.948903i | \(-0.397805\pi\) | ||||
0.315569 | + | 0.948903i | \(0.397805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.86799 | 0.367986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.65533 | −0.650574 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.17064 | 0.386472 | 0.193236 | − | 0.981152i | \(-0.438102\pi\) | ||||
0.193236 | + | 0.981152i | \(0.438102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8573 | 1.62464 | 0.812322 | − | 0.583209i | \(-0.198203\pi\) | ||||
0.812322 | + | 0.583209i | \(0.198203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.0607 | −1.11332 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.86799 | 0.210859 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.04202 | −0.222455 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.86799 | 0.354094 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.49534 | −0.614701 | −0.307350 | − | 0.951596i | \(-0.599442\pi\) | ||||
−0.307350 | + | 0.951596i | \(0.599442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.83869 | 0.564241 | 0.282121 | − | 0.959379i | \(-0.408962\pi\) | ||||
0.282121 | + | 0.959379i | \(0.408962\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.77801 | 0.198937 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5747 | −1.25214 | −0.626072 | − | 0.779765i | \(-0.715338\pi\) | ||||
−0.626072 | + | 0.779765i | \(0.715338\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.17997 | 0.296310 | 0.148155 | − | 0.988964i | \(-0.452667\pi\) | ||||
0.148155 | + | 0.988964i | \(0.452667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4333 | −0.947515 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 35.8446 | 2.51580 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.19269 | −0.432516 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.7453 | −1.15830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4240 | −1.54373 | −0.771866 | − | 0.635785i | \(-0.780676\pi\) | ||||
−0.771866 | + | 0.635785i | \(0.780676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.0993 | −0.760512 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.28267 | −0.564874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.0734 | −1.70209 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2406 | −1.02987 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.76868 | −0.118974 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.2827 | −0.822509 | −0.411254 | − | 0.911521i | \(-0.634909\pi\) | ||||
−0.411254 | + | 0.911521i | \(0.634909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.5653 | 1.63046 | 0.815230 | − | 0.579138i | \(-0.196611\pi\) | ||||
0.815230 | + | 0.579138i | \(0.196611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.82003 | −0.384598 | −0.192299 | − | 0.981336i | \(-0.561594\pi\) | ||||
−0.192299 | + | 0.981336i | \(0.561594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.2593 | 1.53035 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.28267 | −0.149543 | −0.0747714 | − | 0.997201i | \(-0.523823\pi\) | ||||
−0.0747714 | + | 0.997201i | \(0.523823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.50466 | 0.489550 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.45331 | −0.0944028 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.53397 | 0.163909 | 0.0819544 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819544 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.67531 | 0.172332 | 0.0861658 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861658 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.6974 | 1.06675 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.73599 | −0.619486 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.63667 | 0.420582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2827 | 0.775275 | 0.387638 | − | 0.921812i | \(-0.373291\pi\) | ||||
0.387638 | + | 0.921812i | \(0.373291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.77801 | −0.300391 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.636672 | −0.0398699 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.89004 | 0.616924 | 0.308462 | − | 0.951237i | \(-0.400186\pi\) | ||||
0.308462 | + | 0.951237i | \(0.400186\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.9614 | 0.867517 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.36333 | 0.455779 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.26995 | −0.263297 | −0.131648 | − | 0.991296i | \(-0.542027\pi\) | ||||
−0.131648 | + | 0.991296i | \(0.542027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.91934 | −0.302193 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.29200 | 0.568661 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.5526 | 1.86283 | 0.931413 | − | 0.363963i | \(-0.118577\pi\) | ||||
0.931413 | + | 0.363963i | \(0.118577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.6974 | −1.43951 | −0.719756 | − | 0.694227i | \(-0.755746\pi\) | ||||
−0.719756 | + | 0.694227i | \(0.755746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.5233 | 0.818469 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.77801 | 0.288125 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.5840 | 1.23677 | 0.618386 | − | 0.785874i | \(-0.287787\pi\) | ||||
0.618386 | + | 0.785874i | \(0.287787\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.15066 | −0.308362 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.61670 | 0.514029 | 0.257014 | − | 0.966408i | \(-0.417261\pi\) | ||||
0.257014 | + | 0.966408i | \(0.417261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.02930 | 0.417849 | 0.208924 | − | 0.977932i | \(-0.433004\pi\) | ||||
0.208924 | + | 0.977932i | \(0.433004\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.50466 | −0.207598 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.1460 | −1.77946 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5946 | −0.976156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.7453 | −0.864386 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.2793 | −1.24315 | −0.621574 | − | 0.783355i | \(-0.713507\pi\) | ||||
−0.621574 | + | 0.783355i | \(0.713507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.65533 | −0.503933 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.77801 | 0.277248 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.77801 | −0.160656 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.3200 | −2.32401 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.3820 | −0.998569 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.0607 | −0.862372 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.0607 | 0.745412 | 0.372706 | − | 0.927949i | \(-0.378430\pi\) | ||||
0.372706 | + | 0.927949i | \(0.378430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.2920 | 0.869932 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.45331 | 0.309229 | 0.154615 | − | 0.987975i | \(-0.450586\pi\) | ||||
0.154615 | + | 0.987975i | \(0.450586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.60398 | 0.260232 | 0.130116 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130116 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.86799 | 0.274280 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.3527 | −1.70478 | −0.852388 | − | 0.522910i | \(-0.824847\pi\) | ||||
−0.852388 | + | 0.522910i | \(0.824847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.1820 | 1.96982 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.3820 | 0.858539 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.23132 | 0.124154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.77801 | 0.154096 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.2406 | −0.842810 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.5327 | 2.01411 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.42401 | 0.353095 | 0.176548 | − | 0.984292i | \(-0.443507\pi\) | ||||
0.176548 | + | 0.984292i | \(0.443507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.86799 | 0.157165 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.4333 | −0.733942 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.1120 | −1.36794 | −0.683970 | − | 0.729510i | \(-0.739748\pi\) | ||||
−0.683970 | + | 0.729510i | \(0.739748\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.19269 | 0.336341 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.6099 | −1.33270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47.2066 | 2.54892 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.46264 | 0.454298 | 0.227149 | − | 0.973860i | \(-0.427059\pi\) | ||||
0.227149 | + | 0.973860i | \(0.427059\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.40535 | −0.342871 | −0.171435 | − | 0.985195i | \(-0.554840\pi\) | ||||
−0.171435 | + | 0.985195i | \(0.554840\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.77801 | 0.148279 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.7873 | −1.37252 | −0.686261 | − | 0.727356i | \(-0.740749\pi\) | ||||
−0.686261 | + | 0.727356i | \(0.740749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.0993 | −0.589090 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.09931 | −0.164033 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.94865 | 0.313958 | 0.156979 | − | 0.987602i | \(-0.449825\pi\) | ||||
0.156979 | + | 0.987602i | \(0.449825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.71733 | −0.353544 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.8294 | 0.620880 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2406 | −0.797732 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.5013 | −0.548162 | −0.274081 | − | 0.961707i | \(-0.588374\pi\) | ||||
−0.274081 | + | 0.961707i | \(0.588374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.19269 | −0.322378 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.9473 | −1.24328 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.17064 | −0.371282 | −0.185641 | − | 0.982618i | \(-0.559436\pi\) | ||||
−0.185641 | + | 0.982618i | \(0.559436\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.4554 | 1.05351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.11203 | −0.365321 | −0.182660 | − | 0.983176i | \(-0.558471\pi\) | ||||
−0.182660 | + | 0.983176i | \(0.558471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.77801 | −0.244785 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.80731 | 0.398935 | 0.199468 | − | 0.979904i | \(-0.436079\pi\) | ||||
0.199468 | + | 0.979904i | \(0.436079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.2593 | 1.18540 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.28267 | −0.421032 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.5933 | 1.39904 | 0.699519 | − | 0.714614i | \(-0.253398\pi\) | ||||
0.699519 | + | 0.714614i | \(0.253398\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.636672 | 0.0321979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.54669 | 0.330237 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.45331 | −0.0731241 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6426 | −0.734892 | −0.367446 | − | 0.930045i | \(-0.619768\pi\) | ||||
−0.367446 | + | 0.930045i | \(0.619768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.0607 | −0.854102 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.55602 | −0.177579 | −0.0887895 | − | 0.996050i | \(-0.528300\pi\) | ||||
−0.0887895 | + | 0.996050i | \(0.528300\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3086 | −0.712762 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.7033 | 0.679247 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.9894 | 1.43343 | 0.716716 | − | 0.697366i | \(-0.245645\pi\) | ||||
0.716716 | + | 0.697366i | \(0.245645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7453 | −0.530027 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −42.1341 | −2.07328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.63667 | 0.325781 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.4240 | 0.706347 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.3527 | 1.38512 | 0.692560 | − | 0.721361i | \(-0.256483\pi\) | ||||
0.692560 | + | 0.721361i | \(0.256483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.32469 | 0.454458 | 0.227229 | − | 0.973841i | \(-0.427033\pi\) | ||||
0.227229 | + | 0.973841i | \(0.427033\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.50466 | 0.364889 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.636672 | −0.0308831 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −73.3153 | −3.54798 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.2733 | 0.640843 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.89730 | −0.187726 | −0.0938631 | − | 0.995585i | \(-0.529922\pi\) | ||||
−0.0938631 | + | 0.995585i | \(0.529922\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.4613 | −1.36776 | −0.683882 | − | 0.729593i | \(-0.739710\pi\) | ||||
−0.683882 | + | 0.729593i | \(0.739710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.36333 | 0.353045 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.50466 | 0.167651 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.0866 | 0.910953 | 0.455477 | − | 0.890248i | \(-0.349469\pi\) | ||||
0.455477 | + | 0.890248i | \(0.349469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.6974 | 0.795112 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.47668 | 0.307716 | 0.153858 | − | 0.988093i | \(-0.450830\pi\) | ||||
0.153858 | + | 0.988093i | \(0.450830\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.29200 | 0.440483 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.67531 | 0.315731 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.8166 | 0.793626 | 0.396813 | − | 0.917899i | \(-0.370116\pi\) | ||||
0.396813 | + | 0.917899i | \(0.370116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.5887 | −1.39328 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.3013 | 0.859871 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.5233 | 0.633983 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.52671 | −0.211751 | −0.105875 | − | 0.994379i | \(-0.533764\pi\) | ||||
−0.105875 | + | 0.994379i | \(0.533764\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.636672 | −0.0297173 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.44398 | −0.393276 | −0.196638 | − | 0.980476i | \(-0.563002\pi\) | ||||
−0.196638 | + | 0.980476i | \(0.563002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5140 | −1.41811 | −0.709053 | − | 0.705155i | \(-0.750877\pi\) | ||||
−0.709053 | + | 0.705155i | \(0.750877\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.15066 | −0.238856 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2700 | 0.567786 | 0.283893 | − | 0.958856i | \(-0.408374\pi\) | ||||
0.283893 | + | 0.958856i | \(0.408374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −65.3934 | −3.01959 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.4427 | 0.849793 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.5747 | −1.81965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50466 | −0.160805 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.91934 | −0.225241 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.06068 | −0.0484637 | −0.0242319 | − | 0.999706i | \(-0.507714\pi\) | ||||
−0.0242319 | + | 0.999706i | \(0.507714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.96731 | 0.363278 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.86799 | −0.221501 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.7453 | −0.669550 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.13795 | −0.232823 | −0.116411 | − | 0.993201i | \(-0.537139\pi\) | ||||
−0.116411 | + | 0.993201i | \(0.537139\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.282672 | −0.0127829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.81664 | 0.127113 | 0.0635566 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635566 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.68802 | −0.211138 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.77801 | 0.214755 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −54.0314 | −2.42364 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.2534 | 0.593302 | 0.296651 | − | 0.954986i | \(-0.404130\pi\) | ||||
0.296651 | + | 0.954986i | \(0.404130\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.51399 | 0.291024 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.2300 | −1.25871 | −0.629357 | − | 0.777116i | \(-0.716682\pi\) | ||||
−0.629357 | + | 0.777116i | \(0.716682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3820 | −0.773488 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.28267 | −0.234612 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.70800 | 0.120030 | 0.0600150 | − | 0.998197i | \(-0.480885\pi\) | ||||
0.0600150 | + | 0.998197i | \(0.480885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −74.1914 | −3.28203 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.50466 | −0.154735 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.2920 | 0.673846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.8573 | 1.57700 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.30133 | 0.364388 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4206 | 1.02608 | 0.513038 | − | 0.858366i | \(-0.328520\pi\) | ||||
0.513038 | + | 0.858366i | \(0.328520\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.01866 | 0.0882697 | 0.0441349 | − | 0.999026i | \(-0.485947\pi\) | ||||
0.0441349 | + | 0.999026i | \(0.485947\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.86799 | 0.212457 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.27928 | 0.142848 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.65533 | −0.375609 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.2033 | −0.745159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.3820 | 0.665021 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.17064 | 0.223130 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 79.7801 | 3.43637 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8387 | 0.508985 | 0.254492 | − | 0.967075i | \(-0.418092\pi\) | ||||
0.254492 | + | 0.967075i | \(0.418092\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.8573 | 0.937988 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.2406 | −0.652838 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.0607 | −0.642774 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.8060 | −1.09937 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.07472 | −0.300848 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.86799 | 0.121740 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.9193 | −1.56432 | −0.782161 | − | 0.623076i | \(-0.785883\pi\) | ||||
−0.782161 | + | 0.623076i | \(0.785883\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.0093 | −0.973191 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.04202 | −0.128434 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.7860 | 1.59249 | 0.796245 | − | 0.604974i | \(-0.206816\pi\) | ||||
0.796245 | + | 0.604974i | \(0.206816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.19269 | 0.260528 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.86799 | 0.204436 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.9346 | −1.08724 | −0.543618 | − | 0.839333i | \(-0.682946\pi\) | ||||
−0.543618 | + | 0.839333i | \(0.682946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.69396 | 0.112739 | 0.0563694 | − | 0.998410i | \(-0.482048\pi\) | ||||
0.0563694 | + | 0.998410i | \(0.482048\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.49534 | −0.354898 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3947 | 0.724151 | 0.362075 | − | 0.932149i | \(-0.382068\pi\) | ||||
0.362075 | + | 0.932149i | \(0.382068\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.83869 | 0.325765 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.3073 | 1.34033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5047 | −0.973464 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.77801 | 0.114856 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.2080 | 1.04044 | 0.520222 | − | 0.854031i | \(-0.325849\pi\) | ||||
0.520222 | + | 0.854031i | \(0.325849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0514 | 0.743793 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5747 | −0.722925 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.7313 | 1.83689 | 0.918447 | − | 0.395545i | \(-0.129444\pi\) | ||||
0.918447 | + | 0.395545i | \(0.129444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.09931 | −0.127059 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.17997 | 0.171075 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.0093 | 0.940136 | 0.470068 | − | 0.882630i | \(-0.344229\pi\) | ||||
0.470068 | + | 0.882630i | \(0.344229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.8867 | 1.66780 | 0.833901 | − | 0.551915i | \(-0.186103\pi\) | ||||
0.833901 | + | 0.551915i | \(0.186103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.4333 | −0.547048 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.8294 | 0.480932 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.65665 | −0.107830 | −0.0539150 | − | 0.998546i | \(-0.517170\pi\) | ||||
−0.0539150 | + | 0.998546i | \(0.517170\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.8446 | 1.45250 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.8480 | 0.843420 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.0000 | −1.53481 | −0.767403 | − | 0.641165i | \(-0.778451\pi\) | ||||
−0.767403 | + | 0.641165i | \(0.778451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.19269 | −0.249713 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.0314 | −1.61160 | −0.805801 | − | 0.592186i | \(-0.798265\pi\) | ||||
−0.805801 | + | 0.592186i | \(0.798265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9066 | 0.920695 | 0.460348 | − | 0.887739i | \(-0.347725\pi\) | ||||
0.460348 | + | 0.887739i | \(0.347725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.2334 | 1.81224 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.7453 | −0.668743 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.82597 | −0.0728062 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1566 | −1.24032 | −0.620162 | − | 0.784473i | \(-0.712933\pi\) | ||||
−0.620162 | + | 0.784473i | \(0.712933\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.4240 | −0.891274 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.77801 | −0.189609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.3854 | 1.83786 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.0993 | −0.439082 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.7474 | −1.49093 | −0.745466 | − | 0.666544i | \(-0.767773\pi\) | ||||
−0.745466 | + | 0.666544i | \(0.767773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8187 | 0.860446 | 0.430223 | − | 0.902723i | \(-0.358435\pi\) | ||||
0.430223 | + | 0.902723i | \(0.358435\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.28267 | −0.326130 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.4554 | 1.27595 | 0.637976 | − | 0.770056i | \(-0.279772\pi\) | ||||
0.637976 | + | 0.770056i | \(0.279772\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.3552 | −1.62333 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.0734 | −0.982704 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0607 | 0.589370 | 0.294685 | − | 0.955594i | \(-0.404785\pi\) | ||||
0.294685 | + | 0.955594i | \(0.404785\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.54669 | 0.255800 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.2406 | −0.594594 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.2500 | 1.25628 | 0.628140 | − | 0.778100i | \(-0.283816\pi\) | ||||
0.628140 | + | 0.778100i | \(0.283816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0093 | −1.43950 | −0.719748 | − | 0.694235i | \(-0.755743\pi\) | ||||
−0.719748 | + | 0.694235i | \(0.755743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.76868 | −0.0686898 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.0607 | −0.661585 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.36333 | −0.285109 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.2827 | −0.474876 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −71.9600 | −2.77799 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.411290 | −0.0158541 | −0.00792704 | − | 0.999969i | \(-0.502523\pi\) | ||||
−0.00792704 | + | 0.999969i | \(0.502523\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.98728 | −0.0763774 | −0.0381887 | − | 0.999271i | \(-0.512159\pi\) | ||||
−0.0381887 | + | 0.999271i | \(0.512159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −71.7801 | −2.75467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.5653 | 0.941346 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.3179 | 0.662652 | 0.331326 | − | 0.943516i | \(-0.392504\pi\) | ||||
0.331326 | + | 0.943516i | \(0.392504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.7453 | −0.410557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.82003 | −0.222048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.6660 | −0.520632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.94139 | −0.226021 | −0.113011 | − | 0.993594i | \(-0.536049\pi\) | ||||
−0.113011 | + | 0.993594i | \(0.536049\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.2593 | 0.883548 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.4240 | 0.547134 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.94271 | 0.149341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.28267 | −0.0863386 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.2127 | 1.29219 | 0.646097 | − | 0.763255i | \(-0.276400\pi\) | ||||
0.646097 | + | 0.763255i | \(0.276400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0514 | −0.379094 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.50466 | 0.282642 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −84.6154 | −3.18229 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.6354 | 0.699865 | 0.349933 | − | 0.936775i | \(-0.386204\pi\) | ||||
0.349933 | + | 0.936775i | \(0.386204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.45331 | −0.0545035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.15066 | 0.192894 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.2733 | 0.496395 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.53397 | 0.0946328 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5594 | 0.393799 | 0.196900 | − | 0.980424i | \(-0.436913\pi\) | ||||
0.196900 | + | 0.980424i | \(0.436913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 74.4413 | 2.77234 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.67531 | 0.0994957 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.36333 | 0.273467 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.3493 | −1.75609 | −0.878044 | − | 0.478580i | \(-0.841152\pi\) | ||||
−0.878044 | + | 0.478580i | \(0.841152\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.27334 | 0.195042 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.1600 | −1.55721 | −0.778607 | − | 0.627511i | \(-0.784074\pi\) | ||||
−0.778607 | + | 0.627511i | \(0.784074\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.6974 | 0.615891 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −64.1846 | −2.36427 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.2933 | 0.489003 | 0.244501 | − | 0.969649i | \(-0.421376\pi\) | ||||
0.244501 | + | 0.969649i | \(0.421376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.73599 | −0.357660 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.47197 | 0.127374 | 0.0636871 | − | 0.997970i | \(-0.479714\pi\) | ||||
0.0636871 | + | 0.997970i | \(0.479714\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.67531 | 0.244564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.63667 | 0.242823 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 74.8794 | 2.73603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5513 | 0.822909 | 0.411454 | − | 0.911430i | \(-0.365021\pi\) | ||||
0.411454 | + | 0.911430i | \(0.365021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.2827 | 0.447605 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.3013 | 0.666054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9028 | −0.505304 | −0.252652 | − | 0.967557i | \(-0.581303\pi\) | ||||
−0.252652 | + | 0.967557i | \(0.581303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.77801 | −0.173431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.8701 | 1.08279 | 0.541394 | − | 0.840769i | \(-0.317897\pi\) | ||||
0.541394 | + | 0.840769i | \(0.317897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.1914 | −2.68591 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.636672 | −0.0230189 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.0446 | −0.868199 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.4299 | 0.376114 | 0.188057 | − | 0.982158i | \(-0.439781\pi\) | ||||
0.188057 | + | 0.982158i | \(0.439781\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.89004 | 0.356181 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.5000 | −1.81636 | −0.908179 | − | 0.418583i | \(-0.862527\pi\) | ||||
−0.908179 | + | 0.418583i | \(0.862527\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.15066 | −0.185017 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.9614 | 0.500861 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.7033 | 0.777601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.0326 | −1.89766 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.36333 | 0.263144 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.4427 | 0.658247 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.2907 | 1.47185 | 0.735927 | − | 0.677061i | \(-0.236747\pi\) | ||||
0.735927 | + | 0.677061i | \(0.236747\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.26995 | −0.152014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.1460 | 1.07187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.8387 | −1.48574 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.91934 | −0.174471 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4847 | 0.902714 | 0.451357 | − | 0.892343i | \(-0.350940\pi\) | ||||
0.451357 | + | 0.892343i | \(0.350940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.77801 | −0.169034 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.29200 | 0.328317 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −72.8199 | −2.56976 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.86799 | −0.171574 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.5526 | 1.07550 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.9380 | −1.08772 | −0.543861 | − | 0.839175i | \(-0.683038\pi\) | ||||
−0.543861 | + | 0.839175i | \(0.683038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5946 | 1.10944 | 0.554719 | − | 0.832038i | \(-0.312826\pi\) | ||||
0.554719 | + | 0.832038i | \(0.312826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6974 | −0.831102 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.282672 | −0.00990158 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.0280 | 1.01556 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.5233 | 0.472543 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −56.7640 | −1.98108 | −0.990538 | − | 0.137238i | \(-0.956178\pi\) | ||||
−0.990538 | + | 0.137238i | \(0.956178\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.9066 | −0.380181 | −0.190091 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190091 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.77801 | 0.166349 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.75803 | 0.304547 | 0.152273 | − | 0.988338i | \(-0.451341\pi\) | ||||
0.152273 | + | 0.988338i | \(0.451341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.2720 | 0.738808 | 0.369404 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369404 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.5840 | 0.714051 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.6307 | −0.368333 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.51399 | 0.225426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.15066 | −0.178033 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.6240 | −0.504875 | −0.252437 | − | 0.967613i | \(-0.581232\pi\) | ||||
−0.252437 | + | 0.967613i | \(0.581232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2186 | 0.869607 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.61670 | 0.296775 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.28267 | −0.181729 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.5852 | 1.97865 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.02930 | 0.241245 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.86799 | −0.0983135 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.6867 | −1.80396 | −0.901979 | − | 0.431779i | \(-0.857886\pi\) | ||||
−0.901979 | + | 0.431779i | \(0.857886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.50466 | −0.119857 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.77075 | −0.231284 | −0.115642 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.9146 | −1.63483 | −0.817413 | − | 0.576052i | \(-0.804593\pi\) | ||||
−0.817413 | + | 0.576052i | \(0.804593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.1460 | −1.02737 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.8573 | −0.948275 | −0.474138 | − | 0.880451i | \(-0.657240\pi\) | ||||
−0.474138 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.30133 | 0.282254 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.5946 | −0.563584 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.94394 | −0.235557 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.3179 | −1.26447 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.7453 | −0.499053 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.86799 | 0.164568 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.4440 | 0.420203 | 0.210102 | − | 0.977680i | \(-0.432620\pi\) | ||||
0.210102 | + | 0.977680i | \(0.432620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.2793 | −0.717732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.70329 | −0.259530 | −0.129765 | − | 0.991545i | \(-0.541422\pi\) | ||||
−0.129765 | + | 0.991545i | \(0.541422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.9274 | −1.61288 | −0.806442 | − | 0.591313i | \(-0.798610\pi\) | ||||
−0.806442 | + | 0.591313i | \(0.798610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.65533 | −0.290946 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.61462 | −0.255674 | −0.127837 | − | 0.991795i | \(-0.540803\pi\) | ||||
−0.127837 | + | 0.991795i | \(0.540803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2593 | −0.780092 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.77801 | 0.160069 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.3013 | −0.880140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.17064 | 0.172835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.77801 | −0.0927550 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −37.9260 | −1.26490 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.13201 | 0.104342 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.3200 | −1.34177 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.8573 | 0.726563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.0759 | 1.66274 | 0.831372 | − | 0.555716i | \(-0.187556\pi\) | ||||
0.831372 | + | 0.555716i | \(0.187556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.3820 | −0.576524 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5840 | 0.483190 | 0.241595 | − | 0.970377i | \(-0.422330\pi\) | ||||
0.241595 | + | 0.970377i | \(0.422330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.7101 | 1.04945 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.0607 | −0.497891 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.8692 | 1.05241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.03731 | 0.265127 | 0.132563 | − | 0.991175i | \(-0.457679\pi\) | ||||
0.132563 | + | 0.991175i | \(0.457679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0607 | 0.430364 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.8340 | −1.01491 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.86799 | 0.0942990 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.2920 | 0.502255 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.3353 | 0.470327 | 0.235164 | − | 0.971956i | \(-0.424437\pi\) | ||||
0.235164 | + | 0.971956i | \(0.424437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.5186 | −1.91787 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.45331 | 0.178533 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.04202 | −0.0994848 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.7080 | 0.480489 | 0.240245 | − | 0.970712i | \(-0.422772\pi\) | ||||
0.240245 | + | 0.970712i | \(0.422772\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.60398 | 0.150245 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.77801 | 0.0905605 | 0.0452802 | − | 0.998974i | \(-0.485582\pi\) | ||||
0.0452802 | + | 0.998974i | \(0.485582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.19269 | 0.201662 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.86799 | 0.158356 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.6680 | −1.06157 | −0.530784 | − | 0.847507i | \(-0.678103\pi\) | ||||
−0.530784 | + | 0.847507i | \(0.678103\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.3386 | −1.37437 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.3527 | −0.984253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.4347 | −0.823909 | −0.411955 | − | 0.911204i | \(-0.635154\pi\) | ||||
−0.411955 | + | 0.911204i | \(0.635154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.49534 | −0.274903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.1820 | 1.13727 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −52.3081 | −1.68912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.47065 | −0.144215 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.3820 | 0.495678 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.83869 | 0.252336 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.4740 | −1.49450 | −0.747252 | − | 0.664541i | \(-0.768627\pi\) | ||||
−0.747252 | + | 0.664541i | \(0.768627\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.23132 | 0.0716804 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.6120 | 1.91304 | 0.956520 | − | 0.291667i | \(-0.0942100\pi\) | ||||
0.956520 | + | 0.291667i | \(0.0942100\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.2160 | 2.25102 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.77801 | 0.0889675 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.2207 | 0.358981 | 0.179491 | − | 0.983760i | \(-0.442555\pi\) | ||||
0.179491 | + | 0.983760i | \(0.442555\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.3973 | 1.41894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.2406 | −0.486596 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.29539 | 0.137002 | 0.0685008 | − | 0.997651i | \(-0.478178\pi\) | ||||
0.0685008 | + | 0.997651i | \(0.478178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.5747 | −0.559976 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 36.5327 | 1.16285 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.28267 | 0.263374 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.3841 | 0.838117 | 0.419059 | − | 0.907959i | \(-0.362360\pi\) | ||||
0.419059 | + | 0.907959i | \(0.362360\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.42401 | 0.203860 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.17997 | 0.132514 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.2547 | 0.419780 | 0.209890 | − | 0.977725i | \(-0.432689\pi\) | ||||
0.209890 | + | 0.977725i | \(0.432689\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.86799 | 0.0907393 |
(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 | 2760.2.a.u.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bi.1.3 | 3 | |||
4.3 | odd | 2 | 5520.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.u.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5520.2.a.bz.1.1 | 3 | 4.3 | odd | 2 | |||
8280.2.a.bi.1.3 | 3 | 3.2 | odd | 2 |