Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [660,2,Mod(1,660)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(660, 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("660.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 660.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: | \(5.27012653340\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 660.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60555 | −0.984806 | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60555 | 0.722650 | 0.361325 | − | 0.932440i | \(-0.382325\pi\) | ||||
0.361325 | + | 0.932440i | \(0.382325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.605551 | −0.146868 | −0.0734339 | − | 0.997300i | \(-0.523396\pi\) | ||||
−0.0734339 | + | 0.997300i | \(0.523396\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.21110 | 1.65434 | 0.827170 | − | 0.561951i | \(-0.189949\pi\) | ||||
0.827170 | + | 0.561951i | \(0.189949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.60555 | 0.568578 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.21110 | −0.935942 | −0.467971 | − | 0.883744i | \(-0.655015\pi\) | ||||
−0.467971 | + | 0.883744i | \(0.655015\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.60555 | −0.440419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2111 | 1.84309 | 0.921547 | − | 0.388267i | \(-0.126926\pi\) | ||||
0.921547 | + | 0.388267i | \(0.126926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.60555 | −0.417222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.00000 | 1.24939 | 0.624695 | − | 0.780869i | \(-0.285223\pi\) | ||||
0.624695 | + | 0.780869i | \(0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6056 | −1.61733 | −0.808666 | − | 0.588268i | \(-0.799810\pi\) | ||||
−0.808666 | + | 0.588268i | \(0.799810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.21110 | 1.34358 | 0.671789 | − | 0.740743i | \(-0.265526\pi\) | ||||
0.671789 | + | 0.740743i | \(0.265526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.605551 | 0.0847941 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.21110 | −0.955134 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.21110 | −0.923287 | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||||
−0.461644 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.60555 | −0.328269 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.60555 | 0.323179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4222 | 1.71160 | 0.855800 | − | 0.517306i | \(-0.173065\pi\) | ||||
0.855800 | + | 0.517306i | \(0.173065\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.60555 | −0.773121 | −0.386561 | − | 0.922264i | \(-0.626337\pi\) | ||||
−0.386561 | + | 0.922264i | \(0.626337\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.60555 | −0.296930 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.21110 | 0.361277 | 0.180639 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180639 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.39445 | −0.372589 | −0.186295 | − | 0.982494i | \(-0.559648\pi\) | ||||
−0.186295 | + | 0.982494i | \(0.559648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.605551 | −0.0656813 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.00000 | −0.857690 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.78890 | −0.711670 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.21110 | 0.540366 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.21110 | 0.739844 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4222 | 1.66742 | 0.833711 | − | 0.552201i | \(-0.186212\pi\) | ||||
0.833711 | + | 0.552201i | \(0.186212\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.21110 | −0.916539 | −0.458269 | − | 0.888813i | \(-0.651531\pi\) | ||||
−0.458269 | + | 0.888813i | \(0.651531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2111 | −1.30173 | −0.650864 | − | 0.759194i | \(-0.725593\pi\) | ||||
−0.650864 | + | 0.759194i | \(0.725593\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.60555 | 0.254276 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.81665 | −0.562317 | −0.281159 | − | 0.959661i | \(-0.590719\pi\) | ||||
−0.281159 | + | 0.959661i | \(0.590719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.2111 | −1.06411 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.2111 | −1.43094 | −0.715470 | − | 0.698643i | \(-0.753787\pi\) | ||||
−0.715470 | + | 0.698643i | \(0.753787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.60555 | 0.240883 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.57779 | 0.144636 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.00000 | −0.721336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.39445 | −0.123737 | −0.0618687 | − | 0.998084i | \(-0.519706\pi\) | ||||
−0.0618687 | + | 0.998084i | \(0.519706\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.6056 | 0.933767 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.2111 | −1.85322 | −0.926611 | − | 0.376021i | \(-0.877292\pi\) | ||||
−0.926611 | + | 0.376021i | \(0.877292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.7889 | −1.62920 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4222 | −1.05364 | −0.526819 | − | 0.849978i | \(-0.676615\pi\) | ||||
−0.526819 | + | 0.849978i | \(0.676615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.21110 | −0.775715 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.60555 | 0.217887 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.211103 | 0.0174114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.21110 | 0.426910 | 0.213455 | − | 0.976953i | \(-0.431528\pi\) | ||||
0.213455 | + | 0.976953i | \(0.431528\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.78890 | −0.389715 | −0.194857 | − | 0.980832i | \(-0.562424\pi\) | ||||
−0.194857 | + | 0.980832i | \(0.562424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.605551 | −0.0489559 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.21110 | −0.418566 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2111 | −0.894743 | −0.447372 | − | 0.894348i | \(-0.647640\pi\) | ||||
−0.447372 | + | 0.894348i | \(0.647640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.21110 | 0.721469 | 0.360735 | − | 0.932669i | \(-0.382526\pi\) | ||||
0.360735 | + | 0.932669i | \(0.382526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.81665 | 0.140577 | 0.0702884 | − | 0.997527i | \(-0.477608\pi\) | ||||
0.0702884 | + | 0.997527i | \(0.477608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.21110 | −0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.21110 | 0.551447 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.8167 | 1.65869 | 0.829345 | − | 0.558737i | \(-0.188714\pi\) | ||||
0.829345 | + | 0.558737i | \(0.188714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.60555 | −0.196961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.78890 | 0.653274 | 0.326637 | − | 0.945150i | \(-0.394085\pi\) | ||||
0.326637 | + | 0.945150i | \(0.394085\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.21110 | 0.533060 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.2111 | 0.824257 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.605551 | −0.0442823 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.60555 | 0.189526 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4222 | −0.754124 | −0.377062 | − | 0.926188i | \(-0.623066\pi\) | ||||
−0.377062 | + | 0.926188i | \(0.623066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.183346 | −0.0131975 | −0.00659877 | − | 0.999978i | \(-0.502100\pi\) | ||||
−0.00659877 | + | 0.999978i | \(0.502100\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.60555 | −0.186587 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.6056 | −1.46808 | −0.734042 | − | 0.679104i | \(-0.762369\pi\) | ||||
−0.734042 | + | 0.679104i | \(0.762369\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.4222 | 1.30592 | 0.652958 | − | 0.757394i | \(-0.273528\pi\) | ||||
0.652958 | + | 0.757394i | \(0.273528\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.8444 | −1.46299 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | 0.558744 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.21110 | 0.498802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.78890 | −0.605053 | −0.302526 | − | 0.953141i | \(-0.597830\pi\) | ||||
−0.302526 | + | 0.953141i | \(0.597830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.4222 | −0.988193 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.6056 | −0.723293 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5778 | 0.921721 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.60555 | 0.446362 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.57779 | −0.106134 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.21110 | −0.348961 | −0.174481 | − | 0.984661i | \(-0.555825\pi\) | ||||
−0.174481 | + | 0.984661i | \(0.555825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.81665 | 0.386065 | 0.193032 | − | 0.981192i | \(-0.438168\pi\) | ||||
0.193032 | + | 0.981192i | \(0.438168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.4222 | 1.34954 | 0.674769 | − | 0.738029i | \(-0.264243\pi\) | ||||
0.674769 | + | 0.738029i | \(0.264243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.60555 | 0.171433 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.39445 | −0.222378 | −0.111189 | − | 0.993799i | \(-0.535466\pi\) | ||||
−0.111189 | + | 0.993799i | \(0.535466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.21110 | 0.600866 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.21110 | −0.208584 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.2111 | 1.37203 | 0.686016 | − | 0.727586i | \(-0.259358\pi\) | ||||
0.686016 | + | 0.727586i | \(0.259358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.788897 | −0.0508174 | −0.0254087 | − | 0.999677i | \(-0.508089\pi\) | ||||
−0.0254087 | + | 0.999677i | \(0.508089\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.211103 | −0.0134868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.7889 | 1.19551 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.39445 | 0.215114 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.4222 | 1.16280 | 0.581400 | − | 0.813618i | \(-0.302505\pi\) | ||||
0.581400 | + | 0.813618i | \(0.302505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.605551 | 0.0379211 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.78890 | −0.548236 | −0.274118 | − | 0.961696i | \(-0.588386\pi\) | ||||
−0.274118 | + | 0.961696i | \(0.588386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.2111 | −1.81509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | 0.495188 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.0278 | 1.17330 | 0.586651 | − | 0.809840i | \(-0.300446\pi\) | ||||
0.586651 | + | 0.809840i | \(0.300446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.42221 | 0.513511 | 0.256755 | − | 0.966476i | \(-0.417347\pi\) | ||||
0.256755 | + | 0.966476i | \(0.417347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.2111 | −1.16699 | −0.583496 | − | 0.812116i | \(-0.698315\pi\) | ||||
−0.583496 | + | 0.812116i | \(0.698315\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.78890 | 0.410883 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2389 | −1.09587 | −0.547933 | − | 0.836522i | \(-0.684585\pi\) | ||||
−0.547933 | + | 0.836522i | \(0.684585\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.21110 | −0.311981 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.60555 | −0.154884 | −0.0774420 | − | 0.996997i | \(-0.524675\pi\) | ||||
−0.0774420 | + | 0.996997i | \(0.524675\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.21110 | −0.427149 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.8444 | −1.23041 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6333 | −0.978430 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4222 | −0.962687 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.81665 | −0.106130 | −0.0530650 | − | 0.998591i | \(-0.516899\pi\) | ||||
−0.0530650 | + | 0.998591i | \(0.516899\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.6333 | 1.59276 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.21110 | 0.529164 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.21110 | −0.412907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.39445 | 0.0795854 | 0.0397927 | − | 0.999208i | \(-0.487330\pi\) | ||||
0.0397927 | + | 0.999208i | \(0.487330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.2111 | 0.751553 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.57779 | 0.0894685 | 0.0447343 | − | 0.998999i | \(-0.485756\pi\) | ||||
0.0447343 | + | 0.998999i | \(0.485756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2111 | 1.31197 | 0.655985 | − | 0.754774i | \(-0.272254\pi\) | ||||
0.655985 | + | 0.754774i | \(0.272254\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.60555 | −0.146806 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.21110 | −0.180353 | −0.0901767 | − | 0.995926i | \(-0.528743\pi\) | ||||
−0.0901767 | + | 0.995926i | \(0.528743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.81665 | 0.324654 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.36669 | −0.242969 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.60555 | 0.144530 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.2111 | −1.16587 | −0.582934 | − | 0.812520i | \(-0.698095\pi\) | ||||
−0.582934 | + | 0.812520i | \(0.698095\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.2111 | 0.614365 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2389 | 1.21143 | 0.605714 | − | 0.795683i | \(-0.292888\pi\) | ||||
0.605714 | + | 0.795683i | \(0.292888\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.2111 | 0.826154 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.21110 | −0.282197 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.7889 | 1.01451 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.02776 | 0.377270 | 0.188635 | − | 0.982047i | \(-0.439594\pi\) | ||||
0.188635 | + | 0.982047i | \(0.439594\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.2111 | −1.24246 | −0.621231 | − | 0.783628i | \(-0.713367\pi\) | ||||
−0.621231 | + | 0.783628i | \(0.713367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.60555 | −0.139074 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.0000 | −1.38384 | −0.691920 | − | 0.721974i | \(-0.743235\pi\) | ||||
−0.691920 | + | 0.721974i | \(0.743235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.4222 | 0.765451 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.57779 | −0.0835058 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.2111 | 1.75281 | 0.876407 | − | 0.481570i | \(-0.159933\pi\) | ||||
0.876407 | + | 0.481570i | \(0.159933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.0000 | 1.73684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.60555 | −0.345750 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2111 | 1.10721 | 0.553605 | − | 0.832779i | \(-0.313252\pi\) | ||||
0.553605 | + | 0.832779i | \(0.313252\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.00000 | 0.416463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.21110 | −0.270547 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.60555 | −0.134910 | −0.0674552 | − | 0.997722i | \(-0.521488\pi\) | ||||
−0.0674552 | + | 0.997722i | \(0.521488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.8444 | 1.07354 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4222 | 0.535353 | 0.267676 | − | 0.963509i | \(-0.413744\pi\) | ||||
0.267676 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.39445 | 0.0714398 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.2111 | 1.69701 | 0.848504 | − | 0.529189i | \(-0.177504\pi\) | ||||
0.848504 | + | 0.529189i | \(0.177504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.60555 | −0.132791 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.6056 | −0.539110 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.8444 | −1.36107 | −0.680533 | − | 0.732718i | \(-0.738252\pi\) | ||||
−0.680533 | + | 0.732718i | \(0.738252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.2111 | 1.06996 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.21110 | 0.161568 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.422205 | −0.0211899 | −0.0105949 | − | 0.999944i | \(-0.503373\pi\) | ||||
−0.0105949 | + | 0.999944i | \(0.503373\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.7889 | 0.940621 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.42221 | −0.420585 | −0.210292 | − | 0.977639i | \(-0.567442\pi\) | ||||
−0.210292 | + | 0.977639i | \(0.567442\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.5778 | −0.676358 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2111 | 0.555714 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | −0.0988936 | −0.0494468 | − | 0.998777i | \(-0.515746\pi\) | ||||
−0.0494468 | + | 0.998777i | \(0.515746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.8444 | −1.02569 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.39445 | −0.166627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4222 | 0.608318 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.78890 | −0.233397 | −0.116698 | − | 0.993167i | \(-0.537231\pi\) | ||||
−0.116698 | + | 0.993167i | \(0.537231\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.21110 | 0.447859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.605551 | −0.0293736 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.7889 | 0.909258 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.60555 | −0.125797 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.4222 | −1.46539 | −0.732693 | − | 0.680559i | \(-0.761737\pi\) | ||||
−0.732693 | + | 0.680559i | \(0.761737\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.4222 | −0.981429 | −0.490714 | − | 0.871321i | \(-0.663264\pi\) | ||||
−0.490714 | + | 0.871321i | \(0.663264\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0000 | −0.477274 | −0.238637 | − | 0.971109i | \(-0.576701\pi\) | ||||
−0.238637 | + | 0.971109i | \(0.576701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.211103 | −0.0100525 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7889 | 0.512596 | 0.256298 | − | 0.966598i | \(-0.417497\pi\) | ||||
0.256298 | + | 0.966598i | \(0.417497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | 0.284427 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.21110 | −0.246477 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.8444 | −1.83318 | −0.916591 | − | 0.399827i | \(-0.869070\pi\) | ||||
−0.916591 | + | 0.399827i | \(0.869070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.78890 | 0.225002 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.78890 | −0.318268 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.60555 | 0.121883 | 0.0609413 | − | 0.998141i | \(-0.480590\pi\) | ||||
0.0609413 | + | 0.998141i | \(0.480590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.605551 | 0.0282647 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.21110 | 0.242705 | 0.121353 | − | 0.992609i | \(-0.461277\pi\) | ||||
0.121353 | + | 0.992609i | \(0.461277\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2111 | −0.613972 | −0.306986 | − | 0.951714i | \(-0.599320\pi\) | ||||
−0.306986 | + | 0.951714i | \(0.599320\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.21110 | 0.241659 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.00000 | −0.185098 | −0.0925490 | − | 0.995708i | \(-0.529501\pi\) | ||||
−0.0925490 | + | 0.995708i | \(0.529501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4222 | 0.481253 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.2111 | 0.516580 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.6056 | −0.487644 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.21110 | 0.330868 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | 0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.2111 | −1.33469 | −0.667345 | − | 0.744749i | \(-0.732569\pi\) | ||||
−0.667345 | + | 0.744749i | \(0.732569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.2111 | 1.33191 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.4222 | 0.745694 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.4222 | 1.55982 | 0.779910 | − | 0.625892i | \(-0.215265\pi\) | ||||
0.779910 | + | 0.625892i | \(0.215265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.21110 | −0.416540 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4222 | −1.55345 | −0.776726 | − | 0.629838i | \(-0.783121\pi\) | ||||
−0.776726 | + | 0.629838i | \(0.783121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.84441 | −0.218181 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.5778 | −1.68559 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.81665 | −0.0811621 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.8167 | 1.15111 | 0.575554 | − | 0.817764i | \(-0.304787\pi\) | ||||
0.575554 | + | 0.817764i | \(0.304787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.21110 | −0.409889 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.21110 | 0.275845 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.422205 | 0.0187139 | 0.00935696 | − | 0.999956i | \(-0.497022\pi\) | ||||
0.00935696 | + | 0.999956i | \(0.497022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2111 | 0.761374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.21110 | −0.318378 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2111 | −0.582151 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.21110 | 0.405104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.8167 | −0.957645 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.4222 | 0.894713 | 0.447357 | − | 0.894356i | \(-0.352366\pi\) | ||||
0.447357 | + | 0.894356i | \(0.352366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2389 | −0.972437 | −0.486219 | − | 0.873837i | \(-0.661624\pi\) | ||||
−0.486219 | + | 0.873837i | \(0.661624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.60555 | 0.113716 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.15559 | 0.137460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.00000 | 0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.8444 | 0.902872 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.81665 | −0.251476 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.211103 | −0.00909283 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.4222 | 1.39394 | 0.696970 | − | 0.717101i | \(-0.254531\pi\) | ||||
0.696970 | + | 0.717101i | \(0.254531\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.78890 | −0.377168 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.8167 | −1.53141 | −0.765705 | − | 0.643192i | \(-0.777610\pi\) | ||||
−0.765705 | + | 0.643192i | \(0.777610\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.21110 | −0.307762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 57.6888 | 2.45763 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.36669 | −0.355788 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.2111 | −0.475885 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.0278 | −1.82314 | −0.911572 | − | 0.411140i | \(-0.865131\pi\) | ||||
−0.911572 | + | 0.411140i | \(0.865131\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.6333 | −1.16876 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.605551 | 0.0255664 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.81665 | 0.0765628 | 0.0382814 | − | 0.999267i | \(-0.487812\pi\) | ||||
0.0382814 | + | 0.999267i | \(0.487812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.2111 | −0.639936 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.60555 | −0.109423 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.6333 | 0.655382 | 0.327691 | − | 0.944785i | \(-0.393729\pi\) | ||||
0.327691 | + | 0.944785i | \(0.393729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.4222 | −0.687248 | −0.343624 | − | 0.939107i | \(-0.611655\pi\) | ||||
−0.343624 | + | 0.939107i | \(0.611655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4222 | 0.435394 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.2111 | 1.79890 | 0.899451 | − | 0.437022i | \(-0.143967\pi\) | ||||
0.899451 | + | 0.437022i | \(0.143967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.183346 | 0.00761961 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.84441 | 0.366928 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | 0.0828315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.60555 | 0.107726 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.4222 | −0.925463 | −0.462732 | − | 0.886498i | \(-0.653131\pi\) | ||||
−0.462732 | + | 0.886498i | \(0.653131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.5778 | −1.54837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.6056 | 0.847599 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.0278 | −0.945637 | −0.472818 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472818 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.57779 | 0.0646833 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.4222 | −0.753971 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.2111 | −0.946801 | −0.473400 | − | 0.880847i | \(-0.656974\pi\) | ||||
−0.473400 | + | 0.880847i | \(0.656974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.0278 | 1.66527 | 0.832633 | − | 0.553826i | \(-0.186833\pi\) | ||||
0.832633 | + | 0.553826i | \(0.186833\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.8444 | 0.844658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.183346 | −0.00740528 | −0.00370264 | − | 0.999993i | \(-0.501179\pi\) | ||||
−0.00370264 | + | 0.999993i | \(0.501179\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | −0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.2111 | −1.57858 | −0.789290 | − | 0.614021i | \(-0.789551\pi\) | ||||
−0.789290 | + | 0.614021i | \(0.789551\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.6333 | 0.949903 | 0.474951 | − | 0.880012i | \(-0.342466\pi\) | ||||
0.474951 | + | 0.880012i | \(0.342466\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.6333 | −0.626335 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.21110 | −0.287984 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.78890 | −0.270691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.8444 | −0.829803 | −0.414901 | − | 0.909866i | \(-0.636184\pi\) | ||||
−0.414901 | + | 0.909866i | \(0.636184\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.78890 | 0.349327 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.39445 | −0.0553370 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.550039 | −0.0217933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.4222 | 0.570534 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.8444 | −1.53426 | −0.767131 | − | 0.641490i | \(-0.778316\pi\) | ||||
−0.767131 | + | 0.641490i | \(0.778316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.6333 | 1.72073 | 0.860365 | − | 0.509679i | \(-0.170236\pi\) | ||||
0.860365 | + | 0.509679i | \(0.170236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.6056 | 0.417593 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.7889 | 1.21044 | 0.605218 | − | 0.796060i | \(-0.293086\pi\) | ||||
0.605218 | + | 0.796060i | \(0.293086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.5778 | −0.532156 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.2111 | 0.751789 | 0.375894 | − | 0.926663i | \(-0.377336\pi\) | ||||
0.375894 | + | 0.926663i | \(0.377336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.2111 | −0.828786 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.60555 | −0.257707 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.2666 | −1.60509 | −0.802543 | − | 0.596595i | \(-0.796520\pi\) | ||||
−0.802543 | + | 0.596595i | \(0.796520\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.57779 | 0.0612765 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.7889 | −0.728602 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.21110 | 0.201473 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.21110 | −0.278382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6056 | −0.717191 | −0.358596 | − | 0.933493i | \(-0.616744\pi\) | ||||
−0.358596 | + | 0.933493i | \(0.616744\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.6056 | 0.484471 | 0.242235 | − | 0.970218i | \(-0.422119\pi\) | ||||
0.242235 | + | 0.970218i | \(0.422119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.7889 | −1.64209 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.81665 | −0.222895 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.2111 | −1.72995 | −0.864977 | − | 0.501811i | \(-0.832667\pi\) | ||||
−0.864977 | + | 0.501811i | \(0.832667\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.4222 | −0.779156 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.21110 | 0.198527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.4222 | −1.61382 | −0.806908 | − | 0.590677i | \(-0.798861\pi\) | ||||
−0.806908 | + | 0.590677i | \(0.798861\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.60555 | −0.0989767 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.4222 | −0.471201 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.84441 | −0.183495 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.39445 | 0.128390 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5778 | 0.663904 | 0.331952 | − | 0.943296i | \(-0.392293\pi\) | ||||
0.331952 | + | 0.943296i | \(0.392293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 80.8444 | 3.04910 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.21110 | −0.346910 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.0000 | 0.902613 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.6333 | −1.41335 | −0.706674 | − | 0.707539i | \(-0.749805\pi\) | ||||
−0.706674 | + | 0.707539i | \(0.749805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.21110 | 0.120426 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.60555 | 0.0974421 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.2111 | −0.792143 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.42221 | 0.0903330 | 0.0451665 | − | 0.998979i | \(-0.485618\pi\) | ||||
0.0451665 | + | 0.998979i | \(0.485618\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.4222 | 1.28195 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.788897 | 0.0293394 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.00000 | 0.297113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.8444 | 1.06978 | 0.534890 | − | 0.844922i | \(-0.320353\pi\) | ||||
0.534890 | + | 0.844922i | \(0.320353\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.42221 | 0.237534 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6056 | −0.539468 | −0.269734 | − | 0.962935i | \(-0.586936\pi\) | ||||
−0.269734 | + | 0.962935i | \(0.586936\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.211103 | 0.00778663 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.2666 | −1.66516 | −0.832580 | − | 0.553905i | \(-0.813137\pi\) | ||||
−0.832580 | + | 0.553905i | \(0.813137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.7889 | −0.690227 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.6056 | 1.63642 | 0.818209 | − | 0.574920i | \(-0.194967\pi\) | ||||
0.818209 | + | 0.574920i | \(0.194967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.21110 | 0.190920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.39445 | −0.124196 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1556 | 0.553773 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | 0.291924 | 0.145962 | − | 0.989290i | \(-0.453372\pi\) | ||||
0.145962 | + | 0.989290i | \(0.453372\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.4222 | −0.671342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.78890 | −0.174286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2111 | −0.989004 | −0.494502 | − | 0.869176i | \(-0.664650\pi\) | ||||
−0.494502 | + | 0.869176i | \(0.664650\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6333 | −0.566707 | −0.283353 | − | 0.959016i | \(-0.591447\pi\) | ||||
−0.283353 | + | 0.959016i | \(0.591447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.0555 | 0.943273 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.605551 | −0.0218938 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.8444 | 0.752648 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7889 | −1.03815 | −0.519077 | − | 0.854727i | \(-0.673724\pi\) | ||||
−0.519077 | + | 0.854727i | \(0.673724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.78890 | 0.316524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0555 | 0.865217 | 0.432608 | − | 0.901582i | \(-0.357593\pi\) | ||||
0.432608 | + | 0.901582i | \(0.357593\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.21110 | −0.187188 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.2111 | 1.04794 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 57.6888 | 2.06692 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4222 | 0.516067 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.00000 | −0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2111 | −0.400141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.97224 | 0.105949 | 0.0529745 | − | 0.998596i | \(-0.483130\pi\) | ||||
0.0529745 | + | 0.998596i | \(0.483130\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.0278 | −0.677406 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.6333 | 1.40920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.7889 | −0.667213 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00000 | −0.0709327 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.0555 | −1.13546 | −0.567732 | − | 0.823213i | \(-0.692179\pi\) | ||||
−0.567732 | + | 0.823213i | \(0.692179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.57779 | −0.197328 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.60555 | −0.233105 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.42221 | −0.296476 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.0000 | −0.421898 | −0.210949 | − | 0.977497i | \(-0.567655\pi\) | ||||
−0.210949 | + | 0.977497i | \(0.567655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.4222 | −1.27896 | −0.639478 | − | 0.768809i | \(-0.720850\pi\) | ||||
−0.639478 | + | 0.768809i | \(0.720850\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.2111 | 0.673763 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.21110 | 0.322651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −76.4777 | −2.67562 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.78890 | −0.237223 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.8444 | 1.56508 | 0.782540 | − | 0.622600i | \(-0.213924\pi\) | ||||
0.782540 | + | 0.622600i | \(0.213924\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.7889 | 0.933802 | 0.466901 | − | 0.884310i | \(-0.345370\pi\) | ||||
0.466901 | + | 0.884310i | \(0.345370\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.60555 | 0.160151 | 0.0800754 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800754 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.6333 | 1.72384 | 0.861918 | − | 0.507048i | \(-0.169263\pi\) | ||||
0.861918 | + | 0.507048i | \(0.169263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2389 | 0.632699 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.127833 | 0.00442917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.81665 | 0.0628679 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.21110 | 0.180122 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.57779 | 0.0544715 | 0.0272358 | − | 0.999629i | \(-0.491330\pi\) | ||||
0.0272358 | + | 0.999629i | \(0.491330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.21110 | −0.213668 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.60555 | −0.0895278 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.60555 | 0.0894223 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.2389 | 0.350572 | 0.175286 | − | 0.984518i | \(-0.443915\pi\) | ||||
0.175286 | + | 0.984518i | \(0.443915\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.21110 | 0.246615 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0278 | −0.376701 | −0.188350 | − | 0.982102i | \(-0.560314\pi\) | ||||
−0.188350 | + | 0.982102i | \(0.560314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.7889 | 1.45994 | 0.729969 | − | 0.683480i | \(-0.239534\pi\) | ||||
0.729969 | + | 0.683480i | \(0.239534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.8444 | 0.710376 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.63331 | −0.123679 | −0.0618396 | − | 0.998086i | \(-0.519697\pi\) | ||||
−0.0618396 | + | 0.998086i | \(0.519697\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.8167 | 0.741788 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6333 | 0.564897 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.21110 | 0.108929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4222 | −0.353143 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.4222 | 0.555807 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.60555 | −0.0880837 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.2389 | 0.886023 | 0.443012 | − | 0.896516i | \(-0.353910\pi\) | ||||
0.443012 | + | 0.896516i | \(0.353910\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.81665 | 0.0612742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.8444 | −1.03917 | −0.519587 | − | 0.854417i | \(-0.673914\pi\) | ||||
−0.519587 | + | 0.854417i | \(0.673914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4222 | −0.754567 | −0.377284 | − | 0.926098i | \(-0.623142\pi\) | ||||
−0.377284 | + | 0.926098i | \(0.623142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.0278 | −0.773196 | −0.386598 | − | 0.922248i | \(-0.626350\pi\) | ||||
−0.386598 | + | 0.922248i | \(0.626350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.63331 | 0.121857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 66.4222 | 2.22273 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0000 | 0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.6888 | −1.39040 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21110 | −0.0403477 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.6333 | −0.919579 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.78890 | 0.292153 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.0555 | 1.26361 | 0.631806 | − | 0.775126i | \(-0.282314\pi\) | ||||
0.631806 | + | 0.775126i | \(0.282314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.21110 | −0.305513 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4222 | −0.345303 | −0.172652 | − | 0.984983i | \(-0.555233\pi\) | ||||
−0.172652 | + | 0.984983i | \(0.555233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.39445 | −0.112340 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.21110 | 0.238392 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 55.2666 | 1.82506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.39445 | −0.0459486 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.5778 | 1.23689 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.2111 | 0.368619 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.2111 | −0.433910 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.8444 | −1.01197 | −0.505986 | − | 0.862542i | \(-0.668871\pi\) | ||||
−0.505986 | + | 0.862542i | \(0.668871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.52228 | −0.0498908 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.57779 | −0.0516547 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.605551 | −0.0198036 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.0278 | 1.86302 | 0.931508 | − | 0.363721i | \(-0.118494\pi\) | ||||
0.931508 | + | 0.363721i | \(0.118494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.2111 | −0.757466 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.7889 | 1.26448 | 0.632241 | − | 0.774772i | \(-0.282135\pi\) | ||||
0.632241 | + | 0.774772i | \(0.282135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.60555 | 0.0847586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6333 | 1.28791 | 0.643955 | − | 0.765064i | \(-0.277293\pi\) | ||||
0.643955 | + | 0.765064i | \(0.277293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.2111 | −0.558696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.21110 | 0.104127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.4500 | 0.953978 | 0.476989 | − | 0.878909i | \(-0.341728\pi\) | ||||
0.476989 | + | 0.878909i | \(0.341728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.4222 | −0.337255 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.00000 | −0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.6333 | 0.504826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.84441 | −0.124013 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.81665 | −0.187439 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.183346 | −0.00590212 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.18335 | 0.134527 | 0.0672637 | − | 0.997735i | \(-0.478573\pi\) | ||||
0.0672637 | + | 0.997735i | \(0.478573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.36669 | 0.140278 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.3667 | 1.03763 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.60555 | −0.0834444 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.4777 | −1.54620 | −0.773100 | − | 0.634285i | \(-0.781295\pi\) | ||||
−0.773100 | + | 0.634285i | \(0.781295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.6056 | −0.656547 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.0000 | 0.763928 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.63331 | 0.242480 | 0.121240 | − | 0.992623i | \(-0.461313\pi\) | ||||
0.121240 | + | 0.992623i | \(0.461313\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.2111 | 0.673114 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.4222 | 0.584023 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.0278 | −0.665956 | −0.332978 | − | 0.942935i | \(-0.608053\pi\) | ||||
−0.332978 | + | 0.942935i | \(0.608053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.2111 | −0.354704 |
(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 | 660.2.a.e.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1980.2.a.h.1.1 | 2 | |||
4.3 | odd | 2 | 2640.2.a.bc.1.2 | 2 | |||
5.2 | odd | 4 | 3300.2.c.l.1849.3 | 4 | |||
5.3 | odd | 4 | 3300.2.c.l.1849.2 | 4 | |||
5.4 | even | 2 | 3300.2.a.w.1.2 | 2 | |||
11.10 | odd | 2 | 7260.2.a.w.1.2 | 2 | |||
12.11 | even | 2 | 7920.2.a.bo.1.2 | 2 | |||
15.2 | even | 4 | 9900.2.c.q.5149.2 | 4 | |||
15.8 | even | 4 | 9900.2.c.q.5149.3 | 4 | |||
15.14 | odd | 2 | 9900.2.a.bl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
660.2.a.e.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1980.2.a.h.1.1 | 2 | 3.2 | odd | 2 | |||
2640.2.a.bc.1.2 | 2 | 4.3 | odd | 2 | |||
3300.2.a.w.1.2 | 2 | 5.4 | even | 2 | |||
3300.2.c.l.1849.2 | 4 | 5.3 | odd | 4 | |||
3300.2.c.l.1849.3 | 4 | 5.2 | odd | 4 | |||
7260.2.a.w.1.2 | 2 | 11.10 | odd | 2 | |||
7920.2.a.bo.1.2 | 2 | 12.11 | even | 2 | |||
9900.2.a.bl.1.2 | 2 | 15.14 | odd | 2 | |||
9900.2.c.q.5149.2 | 4 | 15.2 | even | 4 | |||
9900.2.c.q.5149.3 | 4 | 15.8 | even | 4 |