Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-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 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.60555 | −1.74073 | −0.870367 | − | 0.492403i | \(-0.836119\pi\) | ||||
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.60555 | 1.38863 | 0.694313 | − | 0.719673i | \(-0.255708\pi\) | ||||
0.694313 | + | 0.719673i | \(0.255708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.60555 | −1.35955 | −0.679773 | − | 0.733423i | \(-0.737922\pi\) | ||||
−0.679773 | + | 0.733423i | \(0.737922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.605551 | −0.138923 | −0.0694615 | − | 0.997585i | \(-0.522128\pi\) | ||||
−0.0694615 | + | 0.997585i | \(0.522128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.60555 | −1.00501 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.60555 | −0.960324 | −0.480162 | − | 0.877180i | \(-0.659422\pi\) | ||||
−0.480162 | + | 0.877180i | \(0.659422\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.21110 | 1.65436 | 0.827181 | − | 0.561935i | \(-0.189943\pi\) | ||||
0.827181 | + | 0.561935i | \(0.189943\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.60555 | 0.801724 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.60555 | −0.778480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.60555 | 1.57914 | 0.789571 | − | 0.613659i | \(-0.210303\pi\) | ||||
0.789571 | + | 0.613659i | \(0.210303\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.39445 | 0.686298 | 0.343149 | − | 0.939281i | \(-0.388506\pi\) | ||||
0.343149 | + | 0.939281i | \(0.388506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.60555 | 0.702340 | 0.351170 | − | 0.936312i | \(-0.385784\pi\) | ||||
0.351170 | + | 0.936312i | \(0.385784\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.60555 | 1.25525 | 0.627624 | − | 0.778516i | \(-0.284027\pi\) | ||||
0.627624 | + | 0.778516i | \(0.284027\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.2111 | 2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.60555 | −0.784934 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.60555 | 0.621012 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.605551 | −0.0802072 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.21110 | 0.678428 | 0.339214 | − | 0.940709i | \(-0.389839\pi\) | ||||
0.339214 | + | 0.940709i | \(0.389839\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.394449 | −0.0505040 | −0.0252520 | − | 0.999681i | \(-0.508039\pi\) | ||||
−0.0252520 | + | 0.999681i | \(0.508039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.60555 | −0.580245 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.39445 | 0.414698 | 0.207349 | − | 0.978267i | \(-0.433516\pi\) | ||||
0.207349 | + | 0.978267i | \(0.433516\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.60555 | −0.554443 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.6056 | 1.97072 | 0.985358 | − | 0.170497i | \(-0.0545373\pi\) | ||||
0.985358 | + | 0.170497i | \(0.0545373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.2111 | −2.41723 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.81665 | −1.07752 | −0.538759 | − | 0.842460i | \(-0.681107\pi\) | ||||
−0.538759 | + | 0.842460i | \(0.681107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.60555 | −0.608007 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4222 | −1.31675 | −0.658376 | − | 0.752690i | \(-0.728756\pi\) | ||||
−0.658376 | + | 0.752690i | \(0.728756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.21110 | 0.955147 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.605551 | −0.0621282 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.21110 | 0.326038 | 0.163019 | − | 0.986623i | \(-0.447877\pi\) | ||||
0.163019 | + | 0.986623i | \(0.447877\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.60555 | 0.462875 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2111 | −1.01604 | −0.508021 | − | 0.861344i | \(-0.669623\pi\) | ||||
−0.508021 | + | 0.861344i | \(0.669623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.81665 | 0.573132 | 0.286566 | − | 0.958061i | \(-0.407486\pi\) | ||||
0.286566 | + | 0.958061i | \(0.407486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.60555 | −0.449456 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.605551 | −0.0585409 | −0.0292704 | − | 0.999572i | \(-0.509318\pi\) | ||||
−0.0292704 | + | 0.999572i | \(0.509318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.60555 | 0.911719 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.39445 | −0.413395 | −0.206697 | − | 0.978405i | \(-0.566272\pi\) | ||||
−0.206697 | + | 0.978405i | \(0.566272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.60555 | −0.429470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.8167 | 2.36661 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2111 | 0.928282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.39445 | 0.396234 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.60555 | 0.405496 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.78890 | 0.241828 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.81665 | −0.411515 | −0.205757 | − | 0.978603i | \(-0.565966\pi\) | ||||
−0.205757 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.2111 | −1.45983 | −0.729913 | − | 0.683540i | \(-0.760440\pi\) | ||||
−0.729913 | + | 0.683540i | \(0.760440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.60555 | 0.724718 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | 0.249136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.2111 | 1.17211 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.21110 | −0.344987 | −0.172493 | − | 0.985011i | \(-0.555182\pi\) | ||||
−0.172493 | + | 0.985011i | \(0.555182\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.605551 | −0.0492791 | −0.0246395 | − | 0.999696i | \(-0.507844\pi\) | ||||
−0.0246395 | + | 0.999696i | \(0.507844\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.60555 | −0.453182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.21110 | 0.739854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6056 | 1.24546 | 0.622729 | − | 0.782437i | \(-0.286024\pi\) | ||||
0.622729 | + | 0.782437i | \(0.286024\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.2111 | 1.67167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.21110 | −0.721469 | −0.360735 | − | 0.932669i | \(-0.617474\pi\) | ||||
−0.360735 | + | 0.932669i | \(0.617474\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.60555 | 0.358542 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.78890 | −0.215811 | −0.107906 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107906 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.605551 | −0.0463077 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.6333 | 1.64475 | 0.822375 | − | 0.568946i | \(-0.192649\pi\) | ||||
0.822375 | + | 0.568946i | \(0.192649\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.4222 | 1.39259 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.21110 | 0.391690 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0278 | 1.42220 | 0.711101 | − | 0.703090i | \(-0.248197\pi\) | ||||
0.711101 | + | 0.703090i | \(0.248197\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.18335 | −0.236616 | −0.118308 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118308 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.394449 | −0.0291585 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.60555 | 0.706214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.8167 | −1.88790 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.60555 | −0.335005 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.6333 | 1.42062 | 0.710308 | − | 0.703891i | \(-0.248556\pi\) | ||||
0.710308 | + | 0.703891i | \(0.248556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.2111 | 1.59879 | 0.799395 | − | 0.600806i | \(-0.205153\pi\) | ||||
0.799395 | + | 0.600806i | \(0.205153\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.81665 | −0.128779 | −0.0643896 | − | 0.997925i | \(-0.520510\pi\) | ||||
−0.0643896 | + | 0.997925i | \(0.520510\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.39445 | 0.239426 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8167 | −0.969739 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.39445 | 0.306922 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.60555 | −0.320108 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.78890 | −0.192912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.6056 | 1.13779 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.60555 | 0.314096 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −42.4222 | −2.87981 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.00000 | −0.473016 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.3944 | 1.28725 | 0.643627 | − | 0.765339i | \(-0.277429\pi\) | ||||
0.643627 | + | 0.765339i | \(0.277429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.788897 | −0.0521318 | −0.0260659 | − | 0.999660i | \(-0.508298\pi\) | ||||
−0.0260659 | + | 0.999660i | \(0.508298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.2111 | −1.39559 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.60555 | 0.561364 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0000 | 0.779484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.0278 | 1.23080 | 0.615402 | − | 0.788214i | \(-0.288994\pi\) | ||||
0.615402 | + | 0.788214i | \(0.288994\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.6333 | 1.84443 | 0.922217 | − | 0.386673i | \(-0.126376\pi\) | ||||
0.922217 | + | 0.386673i | \(0.126376\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.2111 | 0.907914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.81665 | −0.622105 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.7889 | 0.933467 | 0.466733 | − | 0.884398i | \(-0.345431\pi\) | ||||
0.466733 | + | 0.884398i | \(0.345431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.2111 | −1.33353 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.60555 | −0.351033 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.3944 | −1.02266 | −0.511329 | − | 0.859385i | \(-0.670847\pi\) | ||||
−0.511329 | + | 0.859385i | \(0.670847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.2389 | −2.74887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.3944 | 0.702612 | 0.351306 | − | 0.936261i | \(-0.385738\pi\) | ||||
0.351306 | + | 0.936261i | \(0.385738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | 0.184289 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.4222 | −0.760227 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.6333 | −1.07512 | −0.537561 | − | 0.843225i | \(-0.680654\pi\) | ||||
−0.537561 | + | 0.843225i | \(0.680654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.2111 | −0.802517 | −0.401259 | − | 0.915965i | \(-0.631427\pi\) | ||||
−0.401259 | + | 0.915965i | \(0.631427\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.4222 | −1.11090 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.2389 | −1.27612 | −0.638060 | − | 0.769987i | \(-0.720263\pi\) | ||||
−0.638060 | + | 0.769987i | \(0.720263\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.21110 | 0.551454 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.60555 | −0.453709 | −0.226855 | − | 0.973929i | \(-0.572844\pi\) | ||||
−0.226855 | + | 0.973929i | \(0.572844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.39445 | 0.439554 | 0.219777 | − | 0.975550i | \(-0.429467\pi\) | ||||
0.219777 | + | 0.975550i | \(0.429467\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.605551 | −0.0358698 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2389 | −1.19466 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4222 | 0.848365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.21110 | 0.188238 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.2111 | 0.830221 | 0.415111 | − | 0.909771i | \(-0.363743\pi\) | ||||
0.415111 | + | 0.909771i | \(0.363743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.21110 | 0.303402 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.60555 | 0.267241 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.2111 | −1.22259 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.2111 | −0.586613 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.394449 | −0.0225861 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.6056 | −0.719437 | −0.359718 | − | 0.933061i | \(-0.617127\pi\) | ||||
−0.359718 | + | 0.933061i | \(0.617127\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.81665 | 0.330898 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.18335 | 0.350625 | 0.175313 | − | 0.984513i | \(-0.443906\pi\) | ||||
0.175313 | + | 0.984513i | \(0.443906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2111 | −0.633689 | −0.316844 | − | 0.948478i | \(-0.602623\pi\) | ||||
−0.316844 | + | 0.948478i | \(0.602623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.60555 | −0.259493 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2111 | −0.685844 | −0.342922 | − | 0.939364i | \(-0.611417\pi\) | ||||
−0.342922 | + | 0.939364i | \(0.611417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8167 | 0.773584 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.605551 | −0.0337986 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.39445 | 0.188872 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −39.6333 | −2.18505 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.6333 | −1.51886 | −0.759432 | − | 0.650587i | \(-0.774523\pi\) | ||||
−0.759432 | + | 0.650587i | \(0.774523\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.60555 | 0.526381 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.39445 | 0.185459 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.4222 | −1.71168 | −0.855838 | − | 0.517243i | \(-0.826958\pi\) | ||||
−0.855838 | + | 0.517243i | \(0.826958\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.39445 | −0.238674 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.4222 | 2.29729 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −33.2111 | −1.79323 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.60555 | −0.247955 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.0278 | −1.02146 | −0.510732 | − | 0.859740i | \(-0.670625\pi\) | ||||
−0.510732 | + | 0.859740i | \(0.670625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.57779 | 0.405630 | 0.202815 | − | 0.979217i | \(-0.434991\pi\) | ||||
0.202815 | + | 0.979217i | \(0.434991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.0278 | 1.06597 | 0.532985 | − | 0.846125i | \(-0.321070\pi\) | ||||
0.532985 | + | 0.846125i | \(0.321070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.6056 | 0.881331 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.8167 | 1.36636 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.8167 | 0.729215 | 0.364608 | − | 0.931161i | \(-0.381203\pi\) | ||||
0.364608 | + | 0.931161i | \(0.381203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6333 | −0.980700 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.2111 | 0.535944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | −0.366397 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.60555 | −0.449206 | −0.224603 | − | 0.974450i | \(-0.572109\pi\) | ||||
−0.224603 | + | 0.974450i | \(0.572109\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.39445 | 0.228766 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8167 | −0.717325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.02776 | 0.312105 | 0.156053 | − | 0.987749i | \(-0.450123\pi\) | ||||
0.156053 | + | 0.987749i | \(0.450123\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4222 | 1.15175 | 0.575876 | − | 0.817537i | \(-0.304661\pi\) | ||||
0.575876 | + | 0.817537i | \(0.304661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00000 | 0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.4222 | −0.532550 | −0.266275 | − | 0.963897i | \(-0.585793\pi\) | ||||
−0.266275 | + | 0.963897i | \(0.585793\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.2111 | −1.08102 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.60555 | 0.234113 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.63331 | 0.336322 | 0.168161 | − | 0.985760i | \(-0.446217\pi\) | ||||
0.168161 | + | 0.985760i | \(0.446217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8167 | 1.30560 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.78890 | 0.139620 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.4500 | 1.92010 | 0.960050 | − | 0.279829i | \(-0.0902779\pi\) | ||||
0.960050 | + | 0.279829i | \(0.0902779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.2389 | 2.19284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.4222 | −1.65262 | −0.826311 | − | 0.563214i | \(-0.809565\pi\) | ||||
−0.826311 | + | 0.563214i | \(0.809565\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.81665 | −0.237588 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | −1.18096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.81665 | −0.481881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.2111 | −0.842831 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4222 | 0.509158 | 0.254579 | − | 0.967052i | \(-0.418063\pi\) | ||||
0.254579 | + | 0.967052i | \(0.418063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6056 | −1.54036 | −0.770180 | − | 0.637826i | \(-0.779834\pi\) | ||||
−0.770180 | + | 0.637826i | \(0.779834\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.60555 | 0.418416 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.4222 | 1.08764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.81665 | 0.0879140 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.81665 | −0.280178 | −0.140089 | − | 0.990139i | \(-0.544739\pi\) | ||||
−0.140089 | + | 0.990139i | \(0.544739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.57779 | −0.316109 | −0.158054 | − | 0.987430i | \(-0.550522\pi\) | ||||
−0.158054 | + | 0.987430i | \(0.550522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.78890 | 0.133411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1833 | 0.676934 | 0.338467 | − | 0.940978i | \(-0.390092\pi\) | ||||
0.338467 | + | 0.940978i | \(0.390092\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.2111 | 0.676719 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.6333 | 1.31290 | 0.656449 | − | 0.754370i | \(-0.272058\pi\) | ||||
0.656449 | + | 0.754370i | \(0.272058\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.4222 | −0.588869 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.21110 | −0.199178 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.2389 | 0.953011 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.605551 | −0.0284513 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.63331 | 0.403849 | 0.201925 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201925 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.60555 | −0.261645 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.6333 | 1.14729 | 0.573644 | − | 0.819105i | \(-0.305529\pi\) | ||||
0.573644 | + | 0.819105i | \(0.305529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.8167 | 1.19980 | 0.599901 | − | 0.800074i | \(-0.295207\pi\) | ||||
0.599901 | + | 0.800074i | \(0.295207\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.21110 | 0.427155 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.8167 | 1.37975 | 0.689875 | − | 0.723928i | \(-0.257665\pi\) | ||||
0.689875 | + | 0.723928i | \(0.257665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6333 | −0.721879 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.6056 | 0.719066 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.2111 | 0.975288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.42221 | 0.111138 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.6333 | −1.81089 | −0.905446 | − | 0.424461i | \(-0.860463\pi\) | ||||
−0.905446 | + | 0.424461i | \(0.860463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.2111 | 0.965139 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.21110 | 0.145809 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.3944 | −1.06010 | −0.530052 | − | 0.847965i | \(-0.677828\pi\) | ||||
−0.530052 | + | 0.847965i | \(0.677828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.21110 | −0.416540 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.81665 | −0.0819844 | −0.0409922 | − | 0.999159i | \(-0.513052\pi\) | ||||
−0.0409922 | + | 0.999159i | \(0.513052\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.8167 | −0.757384 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.60555 | 0.207004 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −76.4777 | −3.43049 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7889 | −0.841107 | −0.420553 | − | 0.907268i | \(-0.638164\pi\) | ||||
−0.420553 | + | 0.907268i | \(0.638164\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.78890 | −0.124599 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.81665 | −0.259352 | −0.129676 | − | 0.991556i | \(-0.541394\pi\) | ||||
−0.129676 | + | 0.991556i | \(0.541394\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2111 | −0.454388 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.6333 | −1.71239 | −0.856196 | − | 0.516652i | \(-0.827178\pi\) | ||||
−0.856196 | + | 0.516652i | \(0.827178\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.2389 | 1.42616 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.605551 | −0.0267357 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.81665 | 0.256312 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.6333 | 1.74307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6333 | 0.949597 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.2389 | 1.19336 | 0.596678 | − | 0.802481i | \(-0.296487\pi\) | ||||
0.596678 | + | 0.802481i | \(0.296487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.0278 | −1.53166 | −0.765828 | − | 0.643045i | \(-0.777671\pi\) | ||||
−0.765828 | + | 0.643045i | \(0.777671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.4222 | 0.804011 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.6333 | −2.24918 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.78890 | −0.0777781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.21110 | 0.226143 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.605551 | −0.0261803 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.0278 | 0.821108 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 65.4500 | 2.81913 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.6056 | 0.756922 | 0.378461 | − | 0.925617i | \(-0.376453\pi\) | ||||
0.378461 | + | 0.925617i | \(0.376453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.18335 | −0.136610 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0278 | −0.813568 | −0.406784 | − | 0.913524i | \(-0.633350\pi\) | ||||
−0.406784 | + | 0.913524i | \(0.633350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.394449 | −0.0168347 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.81665 | −0.0773921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.2666 | −2.35018 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.60555 | 0.407733 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.8444 | −1.17981 | −0.589903 | − | 0.807474i | \(-0.700834\pi\) | ||||
−0.589903 | + | 0.807474i | \(0.700834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.8167 | −1.08998 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.6333 | −0.658865 | −0.329433 | − | 0.944179i | \(-0.606857\pi\) | ||||
−0.329433 | + | 0.944179i | \(0.606857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.39445 | −0.184876 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.60555 | −0.193415 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.78890 | −0.368450 | −0.184225 | − | 0.982884i | \(-0.558977\pi\) | ||||
−0.184225 | + | 0.982884i | \(0.558977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.4500 | 1.90202 | 0.951011 | − | 0.309158i | \(-0.100047\pi\) | ||||
0.951011 | + | 0.309158i | \(0.100047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.6333 | 0.820193 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.4222 | 0.768259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7889 | 0.490778 | 0.245389 | − | 0.969425i | \(-0.421084\pi\) | ||||
0.245389 | + | 0.969425i | \(0.421084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.2111 | 0.923062 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.2111 | 1.87567 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8167 | 0.572227 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5778 | −0.560416 | −0.280208 | − | 0.959939i | \(-0.590403\pi\) | ||||
−0.280208 | + | 0.959939i | \(0.590403\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.57779 | −0.229829 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.0278 | 0.822441 | 0.411221 | − | 0.911536i | \(-0.365103\pi\) | ||||
0.411221 | + | 0.911536i | \(0.365103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.8167 | 1.05838 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.81665 | −0.0743507 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.42221 | 0.0989686 | 0.0494843 | − | 0.998775i | \(-0.484242\pi\) | ||||
0.0494843 | + | 0.998775i | \(0.484242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.5778 | −0.431477 | −0.215739 | − | 0.976451i | \(-0.569216\pi\) | ||||
−0.215739 | + | 0.976451i | \(0.569216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.39445 | 0.138233 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.2111 | 0.415140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.0555 | −1.70698 | −0.853490 | − | 0.521109i | \(-0.825519\pi\) | ||||
−0.853490 | + | 0.521109i | \(0.825519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.8167 | −0.559879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.39445 | −0.258269 | −0.129135 | − | 0.991627i | \(-0.541220\pi\) | ||||
−0.129135 | + | 0.991627i | \(0.541220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.39445 | 0.177201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6056 | −0.789290 | −0.394645 | − | 0.918834i | \(-0.629132\pi\) | ||||
−0.394645 | + | 0.918834i | \(0.629132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.6333 | 0.949903 | 0.474951 | − | 0.880012i | \(-0.342466\pi\) | ||||
0.474951 | + | 0.880012i | \(0.342466\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.60555 | −0.184814 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 57.2111 | 2.29211 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.78890 | −0.111378 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −53.8444 | −2.14692 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.2111 | 1.64059 | 0.820294 | − | 0.571942i | \(-0.193810\pi\) | ||||
0.820294 | + | 0.571942i | \(0.193810\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.00000 | −0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.6056 | 0.656905 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.6056 | −1.32734 | −0.663670 | − | 0.748026i | \(-0.731002\pi\) | ||||
−0.663670 | + | 0.748026i | \(0.731002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.366692 | −0.0144609 | −0.00723047 | − | 0.999974i | \(-0.502302\pi\) | ||||
−0.00723047 | + | 0.999974i | \(0.502302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.60555 | 0.181343 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.4222 | −1.66266 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.6333 | 0.846577 | 0.423288 | − | 0.905995i | \(-0.360876\pi\) | ||||
0.423288 | + | 0.905995i | \(0.360876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.00000 | −0.273096 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.0000 | 1.55818 | 0.779089 | − | 0.626913i | \(-0.215682\pi\) | ||||
0.779089 | + | 0.626913i | \(0.215682\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.816654 | −0.0317642 | −0.0158821 | − | 0.999874i | \(-0.505056\pi\) | ||||
−0.0158821 | + | 0.999874i | \(0.505056\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.78890 | 0.108149 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8167 | −0.534983 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.81665 | −0.0701311 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | 0.578208 | 0.289104 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289104 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.0555 | −1.69319 | −0.846595 | − | 0.532237i | \(-0.821352\pi\) | ||||
−0.846595 | + | 0.532237i | \(0.821352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.7889 | −0.567546 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.3944 | 0.743197 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.4222 | 0.398795 | 0.199397 | − | 0.979919i | \(-0.436102\pi\) | ||||
0.199397 | + | 0.979919i | \(0.436102\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.81665 | −0.184035 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.788897 | −0.0300983 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.605551 | −0.0230363 | −0.0115181 | − | 0.999934i | \(-0.503666\pi\) | ||||
−0.0115181 | + | 0.999934i | \(0.503666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.2111 | −0.805743 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.2111 | −0.652854 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.6333 | −0.933053 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0000 | −0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.6333 | −1.87462 | −0.937312 | − | 0.348491i | \(-0.886694\pi\) | ||||
−0.937312 | + | 0.348491i | \(0.886694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.81665 | −0.219379 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.60555 | 0.324104 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.0278 | 1.76866 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.6056 | −1.48742 | −0.743709 | − | 0.668504i | \(-0.766935\pi\) | ||||
−0.743709 | + | 0.668504i | \(0.766935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42.4222 | −1.58872 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.0278 | 0.710605 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.2111 | −1.08939 | −0.544695 | − | 0.838634i | \(-0.683355\pi\) | ||||
−0.544695 | + | 0.838634i | \(0.683355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.7889 | −0.997671 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.6333 | 1.06488 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.0000 | −0.445669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.81665 | 0.215728 | 0.107864 | − | 0.994166i | \(-0.465599\pi\) | ||||
0.107864 | + | 0.994166i | \(0.465599\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8167 | −0.954863 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.2389 | 0.636732 | 0.318366 | − | 0.947968i | \(-0.396866\pi\) | ||||
0.318366 | + | 0.947968i | \(0.396866\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.2111 | 0.524184 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.6333 | 0.575860 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.2111 | −0.924906 | −0.462453 | − | 0.886644i | \(-0.653031\pi\) | ||||
−0.462453 | + | 0.886644i | \(0.653031\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.21110 | −0.154283 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.81665 | −0.359173 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.78890 | 0.101904 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.0278 | 0.986257 | 0.493128 | − | 0.869957i | \(-0.335853\pi\) | ||||
0.493128 | + | 0.869957i | \(0.335853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.7889 | 0.538937 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.605551 | −0.0220383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.422205 | 0.0153453 | 0.00767265 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767265 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21.2111 | −0.769914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.4222 | 1.46530 | 0.732652 | − | 0.680604i | \(-0.238282\pi\) | ||||
0.732652 | + | 0.680604i | \(0.238282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.21110 | −0.333464 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.60555 | −0.202669 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −49.6333 | −1.78982 | −0.894911 | − | 0.446244i | \(-0.852761\pi\) | ||||
−0.894911 | + | 0.446244i | \(0.852761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.3944 | −0.590432 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.6333 | −0.778096 | −0.389048 | − | 0.921217i | \(-0.627196\pi\) | ||||
−0.389048 | + | 0.921217i | \(0.627196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.8444 | −1.32349 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.2389 | −1.58706 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.66106 | −0.0953425 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 76.4777 | 2.73659 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6056 | 0.556986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.78890 | −0.241998 | −0.120999 | − | 0.992653i | \(-0.538610\pi\) | ||||
−0.120999 | + | 0.992653i | \(0.538610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3944 | 0.405653 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.2389 | 0.719611 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.00000 | 0.106399 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −54.8444 | −1.94269 | −0.971344 | − | 0.237677i | \(-0.923614\pi\) | ||||
−0.971344 | + | 0.237677i | \(0.923614\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.2389 | −1.70657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.4222 | −0.438917 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.2389 | −1.13768 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.2111 | 0.747593 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.6333 | −0.620722 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.3944 | −0.857663 | −0.428832 | − | 0.903384i | \(-0.641075\pi\) | ||||
−0.428832 | + | 0.903384i | \(0.641075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6333 | 0.689419 | 0.344709 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344709 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.2111 | −0.463334 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.21110 | −0.322651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.78890 | −0.0975712 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.21110 | 0.251669 | 0.125835 | − | 0.992051i | \(-0.459839\pi\) | ||||
0.125835 | + | 0.992051i | \(0.459839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.6333 | −0.823805 | −0.411903 | − | 0.911228i | \(-0.635136\pi\) | ||||
−0.411903 | + | 0.911228i | \(0.635136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.4222 | −0.641379 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.2111 | −0.459395 | −0.229698 | − | 0.973262i | \(-0.573774\pi\) | ||||
−0.229698 | + | 0.973262i | \(0.573774\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.1833 | 0.874654 | 0.437327 | − | 0.899303i | \(-0.355925\pi\) | ||||
0.437327 | + | 0.899303i | \(0.355925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.2389 | −0.736768 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −79.6611 | −2.76009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.78890 | −0.0965138 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.21110 | 0.318382 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.60555 | −0.261949 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.0278 | −1.61589 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.39445 | 0.253777 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.2389 | −1.51649 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.1833 | 0.519868 | 0.259934 | − | 0.965626i | \(-0.416299\pi\) | ||||
0.259934 | + | 0.965626i | \(0.416299\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.605551 | −0.0207094 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.6056 | 0.396438 | 0.198219 | − | 0.980158i | \(-0.436484\pi\) | ||||
0.198219 | + | 0.980158i | \(0.436484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.1833 | −0.893364 | −0.446682 | − | 0.894693i | \(-0.647395\pi\) | ||||
−0.446682 | + | 0.894693i | \(0.647395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.2389 | −0.689738 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.02776 | −0.103066 | −0.0515330 | − | 0.998671i | \(-0.516411\pi\) | ||||
−0.0515330 | + | 0.998671i | \(0.516411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.6333 | 0.735555 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.4222 | 0.489804 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.2666 | 1.87479 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.21110 | 0.108679 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.4500 | 1.40126 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.81665 | 0.0951116 | 0.0475558 | − | 0.998869i | \(-0.484857\pi\) | ||||
0.0475558 | + | 0.998869i | \(0.484857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.2111 | 0.479329 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.18335 | −0.242013 | −0.121007 | − | 0.992652i | \(-0.538612\pi\) | ||||
−0.121007 | + | 0.992652i | \(0.538612\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.21110 | −0.175368 | −0.0876838 | − | 0.996148i | \(-0.527947\pi\) | ||||
−0.0876838 | + | 0.996148i | \(0.527947\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.21110 | 0.175169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.6333 | −1.33076 | −0.665378 | − | 0.746507i | \(-0.731730\pi\) | ||||
−0.665378 | + | 0.746507i | \(0.731730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.4222 | −0.617861 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.60555 | 0.154292 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.21110 | −0.174383 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.0278 | 0.636028 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.6333 | 0.921622 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.8167 | −0.560244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.2111 | −0.705861 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.18335 | −0.105818 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.2111 | −0.837121 | −0.418560 | − | 0.908189i | \(-0.637465\pi\) | ||||
−0.418560 | + | 0.908189i | \(0.637465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.2111 | −0.338681 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.6333 | 0.783006 | 0.391503 | − | 0.920177i | \(-0.371955\pi\) | ||||
0.391503 | + | 0.920177i | \(0.371955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.2111 | −1.49627 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.394449 | −0.0130401 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.6333 | 1.30738 | 0.653691 | − | 0.756761i | \(-0.273220\pi\) | ||||
0.653691 | + | 0.756761i | \(0.273220\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.6056 | −0.415367 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.4222 | −1.26331 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.81665 | 0.191044 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.6056 | −0.905709 | −0.452854 | − | 0.891584i | \(-0.649594\pi\) | ||||
−0.452854 | + | 0.891584i | \(0.649594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.60555 | −0.282036 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.18335 | 0.202434 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.8167 | −0.844295 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.0555 | 1.47190 | 0.735950 | − | 0.677036i | \(-0.236736\pi\) | ||||
0.735950 | + | 0.677036i | \(0.236736\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.2111 | −0.365861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.7889 | −1.06889 | −0.534444 | − | 0.845204i | \(-0.679479\pi\) | ||||
−0.534444 | + | 0.845204i | \(0.679479\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.2389 | −0.659068 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.60555 | −0.149819 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.6333 | −1.28791 | −0.643955 | − | 0.765064i | \(-0.722707\pi\) | ||||
−0.643955 | + | 0.765064i | \(0.722707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.2111 | −0.395972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.2111 | 0.751881 | 0.375941 | − | 0.926644i | \(-0.377320\pi\) | ||||
0.375941 | + | 0.926644i | \(0.377320\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.6333 | 0.635319 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.8167 | 0.446629 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.1833 | 0.716338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.8444 | 1.73692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.605551 | −0.0195136 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.2111 | 0.715001 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.0278 | −1.25505 | −0.627524 | − | 0.778597i | \(-0.715932\pi\) | ||||
−0.627524 | + | 0.778597i | \(0.715932\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.39445 | 0.109045 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.2666 | 1.38849 | 0.694246 | − | 0.719738i | \(-0.255738\pi\) | ||||
0.694246 | + | 0.719738i | \(0.255738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 79.2666 | 2.54117 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.4500 | 0.462295 | 0.231148 | − | 0.972919i | \(-0.425752\pi\) | ||||
0.231148 | + | 0.972919i | \(0.425752\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.2111 | −1.82847 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7889 | 0.726853 | 0.363426 | − | 0.931623i | \(-0.381607\pi\) | ||||
0.363426 | + | 0.931623i | \(0.381607\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000 | 0.318626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.6333 | −1.26154 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.2111 | −0.674474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.6056 | −0.908685 | −0.454343 | − | 0.890827i | \(-0.650126\pi\) | ||||
−0.454343 | + | 0.890827i | \(0.650126\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.6333 | −0.876917 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.81665 | −0.0575918 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.44996 | −0.204272 | −0.102136 | − | 0.994770i | \(-0.532568\pi\) | ||||
−0.102136 | + | 0.994770i | \(0.532568\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.60555 | 0.303906 |
(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 | 4056.2.a.w.1.1 | 2 | ||
4.3 | odd | 2 | 8112.2.a.bn.1.2 | 2 | |||
13.4 | even | 6 | 312.2.q.d.289.1 | yes | 4 | ||
13.5 | odd | 4 | 4056.2.c.l.337.1 | 4 | |||
13.8 | odd | 4 | 4056.2.c.l.337.4 | 4 | |||
13.10 | even | 6 | 312.2.q.d.217.1 | ✓ | 4 | ||
13.12 | even | 2 | 4056.2.a.v.1.2 | 2 | |||
39.17 | odd | 6 | 936.2.t.e.289.1 | 4 | |||
39.23 | odd | 6 | 936.2.t.e.217.1 | 4 | |||
52.23 | odd | 6 | 624.2.q.i.529.2 | 4 | |||
52.43 | odd | 6 | 624.2.q.i.289.2 | 4 | |||
52.51 | odd | 2 | 8112.2.a.bl.1.1 | 2 | |||
156.23 | even | 6 | 1872.2.t.q.1153.2 | 4 | |||
156.95 | even | 6 | 1872.2.t.q.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.q.d.217.1 | ✓ | 4 | 13.10 | even | 6 | ||
312.2.q.d.289.1 | yes | 4 | 13.4 | even | 6 | ||
624.2.q.i.289.2 | 4 | 52.43 | odd | 6 | |||
624.2.q.i.529.2 | 4 | 52.23 | odd | 6 | |||
936.2.t.e.217.1 | 4 | 39.23 | odd | 6 | |||
936.2.t.e.289.1 | 4 | 39.17 | odd | 6 | |||
1872.2.t.q.289.2 | 4 | 156.95 | even | 6 | |||
1872.2.t.q.1153.2 | 4 | 156.23 | even | 6 | |||
4056.2.a.v.1.2 | 2 | 13.12 | even | 2 | |||
4056.2.a.w.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4056.2.c.l.337.1 | 4 | 13.5 | odd | 4 | |||
4056.2.c.l.337.4 | 4 | 13.8 | odd | 4 | |||
8112.2.a.bl.1.1 | 2 | 52.51 | odd | 2 | |||
8112.2.a.bn.1.2 | 2 | 4.3 | odd | 2 |