Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.77801 | −1.44062 | −0.720312 | − | 0.693650i | \(-0.756001\pi\) | ||||
−0.720312 | + | 0.693650i | \(0.756001\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.77801 | 0.770481 | 0.385240 | − | 0.922816i | \(-0.374119\pi\) | ||||
0.385240 | + | 0.922816i | \(0.374119\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.636672 | 0.154416 | 0.0772078 | − | 0.997015i | \(-0.475400\pi\) | ||||
0.0772078 | + | 0.997015i | \(0.475400\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50466 | −0.804025 | −0.402013 | − | 0.915634i | \(-0.631689\pi\) | ||||
−0.402013 | + | 0.915634i | \(0.631689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.36333 | −1.36734 | −0.683668 | − | 0.729793i | \(-0.739616\pi\) | ||||
−0.683668 | + | 0.729793i | \(0.739616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.15066 | −0.925087 | −0.462543 | − | 0.886597i | \(-0.653063\pi\) | ||||
−0.462543 | + | 0.886597i | \(0.653063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.19269 | 0.967135 | 0.483568 | − | 0.875307i | \(-0.339341\pi\) | ||||
0.483568 | + | 0.875307i | \(0.339341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.28267 | −1.26310 | −0.631548 | − | 0.775337i | \(-0.717580\pi\) | ||||
−0.631548 | + | 0.775337i | \(0.717580\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.50466 | −1.09467 | −0.547334 | − | 0.836914i | \(-0.684357\pi\) | ||||
−0.547334 | + | 0.836914i | \(0.684357\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.6974 | 2.38534 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.91934 | 0.675724 | 0.337862 | − | 0.941196i | \(-0.390296\pi\) | ||||
0.337862 | + | 0.941196i | \(0.390296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.77801 | 0.644266 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.65533 | 1.12683 | 0.563414 | − | 0.826175i | \(-0.309488\pi\) | ||||
0.563414 | + | 0.826175i | \(0.309488\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.0607 | −1.92832 | −0.964161 | − | 0.265317i | \(-0.914523\pi\) | ||||
−0.964161 | + | 0.265317i | \(0.914523\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0993 | 1.31725 | 0.658623 | − | 0.752473i | \(-0.271139\pi\) | ||||
0.658623 | + | 0.752473i | \(0.271139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2406 | −1.78378 | −0.891892 | − | 0.452249i | \(-0.850622\pi\) | ||||
−0.891892 | + | 0.452249i | \(0.850622\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.63667 | −0.728469 | −0.364235 | − | 0.931307i | \(-0.618669\pi\) | ||||
−0.364235 | + | 0.931307i | \(0.618669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.636672 | −0.0690567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.29200 | −0.984950 | −0.492475 | − | 0.870327i | \(-0.663908\pi\) | ||||
−0.492475 | + | 0.870327i | \(0.663908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.5233 | 1.41763 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.3820 | 1.72957 | 0.864786 | − | 0.502140i | \(-0.167454\pi\) | ||||
0.864786 | + | 0.502140i | \(0.167454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2920 | 1.50677 | 0.753383 | − | 0.657582i | \(-0.228421\pi\) | ||||
0.753383 | + | 0.657582i | \(0.228421\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.3820 | −1.48703 | −0.743516 | − | 0.668718i | \(-0.766843\pi\) | ||||
−0.743516 | + | 0.668718i | \(0.766843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2406 | −1.45979 | −0.729895 | − | 0.683560i | \(-0.760431\pi\) | ||||
−0.729895 | + | 0.683560i | \(0.760431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.19269 | −0.582559 | −0.291280 | − | 0.956638i | \(-0.594081\pi\) | ||||
−0.291280 | + | 0.956638i | \(0.594081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.09931 | 0.284114 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8294 | 1.07540 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.54669 | −0.571987 | −0.285993 | − | 0.958232i | \(-0.592324\pi\) | ||||
−0.285993 | + | 0.958232i | \(0.592324\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.0607 | −1.47935 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.7453 | 0.918034 | 0.459017 | − | 0.888427i | \(-0.348202\pi\) | ||||
0.459017 | + | 0.888427i | \(0.348202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4240 | 1.22343 | 0.611714 | − | 0.791079i | \(-0.290480\pi\) | ||||
0.611714 | + | 0.791079i | \(0.290480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.2733 | −1.10997 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.36333 | 0.611491 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.67531 | −0.546862 | −0.273431 | − | 0.961892i | \(-0.588159\pi\) | ||||
−0.273431 | + | 0.961892i | \(0.588159\pi\) | |||||||
\(150\) | 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 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.51399 | −0.504068 | −0.252034 | − | 0.967718i | \(-0.581099\pi\) | ||||
−0.252034 | + | 0.967718i | \(0.581099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.28267 | −0.406359 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.30133 | −0.631138 | −0.315569 | − | 0.948903i | \(-0.602195\pi\) | ||||
−0.315569 | + | 0.948903i | \(0.602195\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.86799 | 0.367986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.17064 | −0.386472 | −0.193236 | − | 0.981152i | \(-0.561898\pi\) | ||||
−0.193236 | + | 0.981152i | \(0.561898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8573 | 1.62464 | 0.812322 | − | 0.583209i | \(-0.198203\pi\) | ||||
0.812322 | + | 0.583209i | \(0.198203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.86799 | −0.210859 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.04202 | −0.222455 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.49534 | 0.614701 | 0.307350 | − | 0.951596i | \(-0.400558\pi\) | ||||
0.307350 | + | 0.951596i | \(0.400558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.83869 | 0.564241 | 0.282121 | − | 0.959379i | \(-0.408962\pi\) | ||||
0.282121 | + | 0.959379i | \(0.408962\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5747 | 1.25214 | 0.626072 | − | 0.779765i | \(-0.284662\pi\) | ||||
0.626072 | + | 0.779765i | \(0.284662\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.17997 | 0.296310 | 0.148155 | − | 0.988964i | \(-0.452667\pi\) | ||||
0.148155 | + | 0.988964i | \(0.452667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −35.8446 | −2.51580 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.19269 | −0.432516 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.28267 | 0.564874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.0734 | −1.70209 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.5653 | −1.63046 | −0.815230 | − | 0.579138i | \(-0.803389\pi\) | ||||
−0.815230 | + | 0.579138i | \(0.803389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.82003 | −0.384598 | −0.192299 | − | 0.981336i | \(-0.561594\pi\) | ||||
−0.192299 | + | 0.981336i | \(0.561594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.28267 | 0.149543 | 0.0747714 | − | 0.997201i | \(-0.476177\pi\) | ||||
0.0747714 | + | 0.997201i | \(0.476177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.50466 | 0.489550 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.53397 | −0.163909 | −0.0819544 | − | 0.996636i | \(-0.526116\pi\) | ||||
−0.0819544 | + | 0.996636i | \(0.526116\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.67531 | 0.172332 | 0.0861658 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861658 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.6974 | −1.06675 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.73599 | −0.619486 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.2827 | −0.775275 | −0.387638 | − | 0.921812i | \(-0.626709\pi\) | ||||
−0.387638 | + | 0.921812i | \(0.626709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.77801 | −0.300391 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.89004 | −0.616924 | −0.308462 | − | 0.951237i | \(-0.599814\pi\) | ||||
−0.308462 | + | 0.951237i | \(0.599814\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.9614 | 0.867517 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.26995 | 0.263297 | 0.131648 | − | 0.991296i | \(-0.457973\pi\) | ||||
0.131648 | + | 0.991296i | \(0.457973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.91934 | −0.302193 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.5526 | −1.86283 | −0.931413 | − | 0.363963i | \(-0.881423\pi\) | ||||
−0.931413 | + | 0.363963i | \(0.881423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.6974 | −1.43951 | −0.719756 | − | 0.694227i | \(-0.755746\pi\) | ||||
−0.719756 | + | 0.694227i | \(0.755746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.61670 | −0.514029 | −0.257014 | − | 0.966408i | \(-0.582739\pi\) | ||||
−0.257014 | + | 0.966408i | \(0.582739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.02930 | 0.417849 | 0.208924 | − | 0.977932i | \(-0.433004\pi\) | ||||
0.208924 | + | 0.977932i | \(0.433004\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 30.1460 | 1.77946 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5946 | −0.976156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.2793 | 1.24315 | 0.621574 | − | 0.783355i | \(-0.286493\pi\) | ||||
0.621574 | + | 0.783355i | \(0.286493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.65533 | −0.503933 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.77801 | 0.160656 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.3200 | −2.32401 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.45331 | −0.309229 | −0.154615 | − | 0.987975i | \(-0.549414\pi\) | ||||
−0.154615 | + | 0.987975i | \(0.549414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.60398 | 0.260232 | 0.130116 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130116 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.3527 | 1.70478 | 0.852388 | − | 0.522910i | \(-0.175153\pi\) | ||||
0.852388 | + | 0.522910i | \(0.175153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.1820 | 1.96982 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.23132 | −0.124154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.77801 | 0.154096 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.6099 | 1.33270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47.2066 | 2.54892 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.46264 | −0.454298 | −0.227149 | − | 0.973860i | \(-0.572941\pi\) | ||||
−0.227149 | + | 0.973860i | \(0.572941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.40535 | −0.342871 | −0.171435 | − | 0.985195i | \(-0.554840\pi\) | ||||
−0.171435 | + | 0.985195i | \(0.554840\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.7873 | 1.37252 | 0.686261 | − | 0.727356i | \(-0.259251\pi\) | ||||
0.686261 | + | 0.727356i | \(0.259251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.0993 | −0.589090 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.94865 | −0.313958 | −0.156979 | − | 0.987602i | \(-0.550175\pi\) | ||||
−0.156979 | + | 0.987602i | \(0.550175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.71733 | −0.353544 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.80731 | −0.398935 | −0.199468 | − | 0.979904i | \(-0.563921\pi\) | ||||
−0.199468 | + | 0.979904i | \(0.563921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.2593 | 1.18540 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5933 | −1.39904 | −0.699519 | − | 0.714614i | \(-0.746602\pi\) | ||||
−0.699519 | + | 0.714614i | \(0.746602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.636672 | 0.0321979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.55602 | 0.177579 | 0.0887895 | − | 0.996050i | \(-0.471700\pi\) | ||||
0.0887895 | + | 0.996050i | \(0.471700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.3086 | −0.712762 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 42.1341 | 2.07328 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.63667 | 0.325781 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.3527 | −1.38512 | −0.692560 | − | 0.721361i | \(-0.743517\pi\) | ||||
−0.692560 | + | 0.721361i | \(0.743517\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.32469 | 0.454458 | 0.227229 | − | 0.973841i | \(-0.427033\pi\) | ||||
0.227229 | + | 0.973841i | \(0.427033\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.636672 | 0.0308831 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −73.3153 | −3.54798 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.89730 | 0.187726 | 0.0938631 | − | 0.995585i | \(-0.470078\pi\) | ||||
0.0938631 | + | 0.995585i | \(0.470078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.4613 | −1.36776 | −0.683882 | − | 0.729593i | \(-0.739710\pi\) | ||||
−0.683882 | + | 0.729593i | \(0.739710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.47668 | −0.307716 | −0.153858 | − | 0.988093i | \(-0.549170\pi\) | ||||
−0.153858 | + | 0.988093i | \(0.549170\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.29200 | 0.440483 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.8166 | −0.793626 | −0.396813 | − | 0.917899i | \(-0.629884\pi\) | ||||
−0.396813 | + | 0.917899i | \(0.629884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.5887 | −1.39328 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.44398 | 0.393276 | 0.196638 | − | 0.980476i | \(-0.436998\pi\) | ||||
0.196638 | + | 0.980476i | \(0.436998\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.5140 | −1.41811 | −0.709053 | − | 0.705155i | \(-0.750877\pi\) | ||||
−0.709053 | + | 0.705155i | \(0.750877\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.2700 | −0.567786 | −0.283893 | − | 0.958856i | \(-0.591626\pi\) | ||||
−0.283893 | + | 0.958856i | \(0.591626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −65.3934 | −3.01959 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 39.5747 | 1.81965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50466 | −0.160805 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.06068 | 0.0484637 | 0.0242319 | − | 0.999706i | \(-0.492286\pi\) | ||||
0.0242319 | + | 0.999706i | \(0.492286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.96731 | 0.363278 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.81664 | −0.127113 | −0.0635566 | − | 0.997978i | \(-0.520244\pi\) | ||||
−0.0635566 | + | 0.997978i | \(0.520244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.68802 | −0.211138 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.2300 | 1.25871 | 0.629357 | − | 0.777116i | \(-0.283318\pi\) | ||||
0.629357 | + | 0.777116i | \(0.283318\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.3820 | −0.773488 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.70800 | −0.120030 | −0.0600150 | − | 0.998197i | \(-0.519115\pi\) | ||||
−0.0600150 | + | 0.998197i | \(0.519115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −74.1914 | −3.28203 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.2920 | −0.673846 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.8573 | 1.57700 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.4206 | −1.02608 | −0.513038 | − | 0.858366i | \(-0.671480\pi\) | ||||
−0.513038 | + | 0.858366i | \(0.671480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.01866 | 0.0882697 | 0.0441349 | − | 0.999026i | \(-0.485947\pi\) | ||||
0.0441349 | + | 0.999026i | \(0.485947\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.27928 | −0.142848 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.2033 | 0.745159 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.3820 | 0.665021 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.8060 | 1.09937 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.07472 | −0.300848 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.9193 | 1.56432 | 0.782161 | − | 0.623076i | \(-0.214117\pi\) | ||||
0.782161 | + | 0.623076i | \(0.214117\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.0093 | −0.973191 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.7860 | −1.59249 | −0.796245 | − | 0.604974i | \(-0.793184\pi\) | ||||
−0.796245 | + | 0.604974i | \(0.793184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.19269 | 0.260528 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9346 | 1.08724 | 0.543618 | − | 0.839333i | \(-0.317054\pi\) | ||||
0.543618 | + | 0.839333i | \(0.317054\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.69396 | 0.112739 | 0.0563694 | − | 0.998410i | \(-0.482048\pi\) | ||||
0.0563694 | + | 0.998410i | \(0.482048\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.3073 | −1.34033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5047 | −0.973464 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.2080 | −1.04044 | −0.520222 | − | 0.854031i | \(-0.674151\pi\) | ||||
−0.520222 | + | 0.854031i | \(0.674151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0514 | 0.743793 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.7313 | −1.83689 | −0.918447 | − | 0.395545i | \(-0.870556\pi\) | ||||
−0.918447 | + | 0.395545i | \(0.870556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.09931 | −0.127059 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.0093 | −0.940136 | −0.470068 | − | 0.882630i | \(-0.655771\pi\) | ||||
−0.470068 | + | 0.882630i | \(0.655771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.8867 | 1.66780 | 0.833901 | − | 0.551915i | \(-0.186103\pi\) | ||||
0.833901 | + | 0.551915i | \(0.186103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.0314 | 1.61160 | 0.805801 | − | 0.592186i | \(-0.201735\pi\) | ||||
0.805801 | + | 0.592186i | \(0.201735\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9066 | 0.920695 | 0.460348 | − | 0.887739i | \(-0.347725\pi\) | ||||
0.460348 | + | 0.887739i | \(0.347725\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −45.2334 | −1.81224 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.77801 | 0.189609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.3854 | 1.83786 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.7474 | 1.49093 | 0.745466 | − | 0.666544i | \(-0.232227\pi\) | ||||
0.745466 | + | 0.666544i | \(0.232227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8187 | 0.860446 | 0.430223 | − | 0.902723i | \(-0.358435\pi\) | ||||
0.430223 | + | 0.902723i | \(0.358435\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.4554 | −1.27595 | −0.637976 | − | 0.770056i | \(-0.720228\pi\) | ||||
−0.637976 | + | 0.770056i | \(0.720228\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.3552 | −1.62333 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.0607 | −0.589370 | −0.294685 | − | 0.955594i | \(-0.595215\pi\) | ||||
−0.294685 | + | 0.955594i | \(0.595215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.54669 | 0.255800 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.2500 | −1.25628 | −0.628140 | − | 0.778100i | \(-0.716184\pi\) | ||||
−0.628140 | + | 0.778100i | \(0.716184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0093 | −1.43950 | −0.719748 | − | 0.694235i | \(-0.755743\pi\) | ||||
−0.719748 | + | 0.694235i | \(0.755743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.0607 | 0.661585 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.36333 | −0.285109 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.98728 | 0.0763774 | 0.0381887 | − | 0.999271i | \(-0.487841\pi\) | ||||
0.0381887 | + | 0.999271i | \(0.487841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −71.7801 | −2.75467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.3179 | −0.662652 | −0.331326 | − | 0.943516i | \(-0.607496\pi\) | ||||
−0.331326 | + | 0.943516i | \(0.607496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.7453 | −0.410557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.4240 | −0.547134 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.94271 | 0.149341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.2127 | −1.29219 | −0.646097 | − | 0.763255i | \(-0.723600\pi\) | ||||
−0.646097 | + | 0.763255i | \(0.723600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0514 | −0.379094 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.15066 | −0.192894 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.2733 | 0.496395 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.5594 | −0.393799 | −0.196900 | − | 0.980424i | \(-0.563087\pi\) | ||||
−0.196900 | + | 0.980424i | \(0.563087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 74.4413 | 2.77234 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.47197 | −0.127374 | −0.0636871 | − | 0.997970i | \(-0.520286\pi\) | ||||
−0.0636871 | + | 0.997970i | \(0.520286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.67531 | 0.244564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8701 | −1.08279 | −0.541394 | − | 0.840769i | \(-0.682103\pi\) | ||||
−0.541394 | + | 0.840769i | \(0.682103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.1914 | −2.68591 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.5000 | 1.81636 | 0.908179 | − | 0.418583i | \(-0.137473\pi\) | ||||
0.908179 | + | 0.418583i | \(0.137473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.15066 | −0.185017 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.7033 | −0.777601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.0326 | −1.89766 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.1460 | −1.07187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.8387 | −1.48574 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.4847 | −0.902714 | −0.451357 | − | 0.892343i | \(-0.649060\pi\) | ||||
−0.451357 | + | 0.892343i | \(0.649060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.77801 | −0.169034 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 72.8199 | 2.56976 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.86799 | −0.171574 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.9380 | 1.08772 | 0.543861 | − | 0.839175i | \(-0.316962\pi\) | ||||
0.543861 | + | 0.839175i | \(0.316962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5946 | 1.10944 | 0.554719 | − | 0.832038i | \(-0.312826\pi\) | ||||
0.554719 | + | 0.832038i | \(0.312826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.282672 | 0.00990158 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.0280 | 1.01556 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 56.7640 | 1.98108 | 0.990538 | − | 0.137238i | \(-0.0438225\pi\) | ||||
0.990538 | + | 0.137238i | \(0.0438225\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.9066 | −0.380181 | −0.190091 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190091 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.75803 | −0.304547 | −0.152273 | − | 0.988338i | \(-0.548659\pi\) | ||||
−0.152273 | + | 0.988338i | \(0.548659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.2720 | 0.738808 | 0.369404 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369404 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.6307 | 0.368333 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.51399 | 0.225426 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.6240 | 0.504875 | 0.252437 | − | 0.967613i | \(-0.418768\pi\) | ||||
0.252437 | + | 0.967613i | \(0.418768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2186 | 0.869607 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.28267 | 0.181729 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.5852 | 1.97865 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.77075 | 0.231284 | 0.115642 | − | 0.993291i | \(-0.463107\pi\) | ||||
0.115642 | + | 0.993291i | \(0.463107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.9146 | −1.63483 | −0.817413 | − | 0.576052i | \(-0.804593\pi\) | ||||
−0.817413 | + | 0.576052i | \(0.804593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.8573 | 0.948275 | 0.474138 | − | 0.880451i | \(-0.342760\pi\) | ||||
0.474138 | + | 0.880451i | \(0.342760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.30133 | 0.282254 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.94394 | 0.235557 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.3179 | −1.26447 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.70329 | 0.259530 | 0.129765 | − | 0.991545i | \(-0.458578\pi\) | ||||
0.129765 | + | 0.991545i | \(0.458578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.9274 | −1.61288 | −0.806442 | − | 0.591313i | \(-0.798610\pi\) | ||||
−0.806442 | + | 0.591313i | \(0.798610\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.61462 | 0.255674 | 0.127837 | − | 0.991795i | \(-0.459197\pi\) | ||||
0.127837 | + | 0.991795i | \(0.459197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2593 | −0.780092 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.3013 | 0.880140 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.17064 | 0.172835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.9260 | 1.26490 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.13201 | 0.104342 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.5840 | −0.483190 | −0.241595 | − | 0.970377i | \(-0.577670\pi\) | ||||
−0.241595 | + | 0.970377i | \(0.577670\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.7101 | 1.04945 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.8340 | 1.01491 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.86799 | 0.0942990 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.3353 | −0.470327 | −0.235164 | − | 0.971956i | \(-0.575563\pi\) | ||||
−0.235164 | + | 0.971956i | \(0.575563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.5186 | −1.91787 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.77801 | −0.0905605 | −0.0452802 | − | 0.998974i | \(-0.514418\pi\) | ||||
−0.0452802 | + | 0.998974i | \(0.514418\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.19269 | 0.201662 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.6680 | 1.06157 | 0.530784 | − | 0.847507i | \(-0.321897\pi\) | ||||
0.530784 | + | 0.847507i | \(0.321897\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.3386 | −1.37437 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4347 | 0.823909 | 0.411955 | − | 0.911204i | \(-0.364846\pi\) | ||||
0.411955 | + | 0.911204i | \(0.364846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.49534 | −0.274903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 52.3081 | 1.68912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.47065 | −0.144215 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −59.6120 | −1.91304 | −0.956520 | − | 0.291667i | \(-0.905790\pi\) | ||||
−0.956520 | + | 0.291667i | \(0.905790\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.2160 | 2.25102 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.2207 | −0.358981 | −0.179491 | − | 0.983760i | \(-0.557445\pi\) | ||||
−0.179491 | + | 0.983760i | \(0.557445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.3973 | 1.41894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.29539 | −0.137002 | −0.0685008 | − | 0.997651i | \(-0.521822\pi\) | ||||
−0.0685008 | + | 0.997651i | \(0.521822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.5747 | −0.559976 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 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 | 8280.2.a.bi.1.3 | 3 | ||
3.2 | odd | 2 | 2760.2.a.u.1.3 | ✓ | 3 | ||
12.11 | even | 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 | 3.2 | odd | 2 | ||
5520.2.a.bz.1.1 | 3 | 12.11 | even | 2 | |||
8280.2.a.bi.1.3 | 3 | 1.1 | even | 1 | trivial |