Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6050,2,Mod(1,6050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6050.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6050 = 2 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6050.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: | \(48.3094932229\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1210) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6050.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.732051 | −0.422650 | −0.211325 | − | 0.977416i | \(-0.567778\pi\) | ||||
−0.211325 | + | 0.977416i | \(0.567778\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.732051 | 0.298858 | ||||||||
\(7\) | −1.26795 | −0.479240 | −0.239620 | − | 0.970867i | \(-0.577023\pi\) | ||||
−0.239620 | + | 0.970867i | \(0.577023\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | 2.46410 | 0.683419 | 0.341709 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341709 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(14\) | 1.26795 | 0.338874 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 2.46410 | 0.580794 | ||||||||
\(19\) | −4.19615 | −0.962663 | −0.481332 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481332 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.928203 | 0.202551 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.73205 | −0.569672 | −0.284836 | − | 0.958576i | \(-0.591939\pi\) | ||||
−0.284836 | + | 0.958576i | \(0.591939\pi\) | |||||||
\(24\) | 0.732051 | 0.149429 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.46410 | −0.483250 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | −1.26795 | −0.239620 | ||||||||
\(29\) | 3.73205 | 0.693024 | 0.346512 | − | 0.938045i | \(-0.387366\pi\) | ||||
0.346512 | + | 0.938045i | \(0.387366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.73205 | 1.56832 | 0.784161 | − | 0.620557i | \(-0.213093\pi\) | ||||
0.784161 | + | 0.620557i | \(0.213093\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.73205 | 0.297044 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46410 | −0.410684 | ||||||||
\(37\) | 7.92820 | 1.30339 | 0.651694 | − | 0.758482i | \(-0.274059\pi\) | ||||
0.651694 | + | 0.758482i | \(0.274059\pi\) | |||||||
\(38\) | 4.19615 | 0.680706 | ||||||||
\(39\) | −1.80385 | −0.288847 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4641 | 1.63422 | 0.817109 | − | 0.576483i | \(-0.195575\pi\) | ||||
0.817109 | + | 0.576483i | \(0.195575\pi\) | |||||||
\(42\) | −0.928203 | −0.143225 | ||||||||
\(43\) | −9.46410 | −1.44326 | −0.721631 | − | 0.692278i | \(-0.756607\pi\) | ||||
−0.721631 | + | 0.692278i | \(0.756607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.73205 | 0.402819 | ||||||||
\(47\) | −6.73205 | −0.981971 | −0.490985 | − | 0.871168i | \(-0.663363\pi\) | ||||
−0.490985 | + | 0.871168i | \(0.663363\pi\) | |||||||
\(48\) | −0.732051 | −0.105662 | ||||||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.26795 | 0.177548 | ||||||||
\(52\) | 2.46410 | 0.341709 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | −4.00000 | −0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.26795 | 0.169437 | ||||||||
\(57\) | 3.07180 | 0.406869 | ||||||||
\(58\) | −3.73205 | −0.490042 | ||||||||
\(59\) | 13.8564 | 1.80395 | 0.901975 | − | 0.431788i | \(-0.142117\pi\) | ||||
0.901975 | + | 0.431788i | \(0.142117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | −8.73205 | −1.10897 | ||||||||
\(63\) | 3.12436 | 0.393632 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.26795 | −0.887921 | −0.443961 | − | 0.896046i | \(-0.646427\pi\) | ||||
−0.443961 | + | 0.896046i | \(0.646427\pi\) | |||||||
\(68\) | −1.73205 | −0.210042 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 2.46410 | 0.290397 | ||||||||
\(73\) | −12.9282 | −1.51313 | −0.756566 | − | 0.653917i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653917i | \(0.773124\pi\) | |||||||
\(74\) | −7.92820 | −0.921635 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.19615 | −0.481332 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.80385 | 0.204246 | ||||||||
\(79\) | −7.26795 | −0.817708 | −0.408854 | − | 0.912600i | \(-0.634072\pi\) | ||||
−0.408854 | + | 0.912600i | \(0.634072\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | −10.4641 | −1.15557 | ||||||||
\(83\) | 3.26795 | 0.358704 | 0.179352 | − | 0.983785i | \(-0.442600\pi\) | ||||
0.179352 | + | 0.983785i | \(0.442600\pi\) | |||||||
\(84\) | 0.928203 | 0.101275 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.46410 | 1.02054 | ||||||||
\(87\) | −2.73205 | −0.292907 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.464102 | 0.0491947 | 0.0245973 | − | 0.999697i | \(-0.492170\pi\) | ||||
0.0245973 | + | 0.999697i | \(0.492170\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.12436 | −0.327521 | ||||||||
\(92\) | −2.73205 | −0.284836 | ||||||||
\(93\) | −6.39230 | −0.662851 | ||||||||
\(94\) | 6.73205 | 0.694358 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.732051 | 0.0747146 | ||||||||
\(97\) | 17.1962 | 1.74600 | 0.873002 | − | 0.487716i | \(-0.162170\pi\) | ||||
0.873002 | + | 0.487716i | \(0.162170\pi\) | |||||||
\(98\) | 5.39230 | 0.544705 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | −1.26795 | −0.125546 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | −2.46410 | −0.241625 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | −11.6603 | −1.12724 | −0.563620 | − | 0.826034i | \(-0.690592\pi\) | ||||
−0.563620 | + | 0.826034i | \(0.690592\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −8.26795 | −0.791926 | −0.395963 | − | 0.918266i | \(-0.629589\pi\) | ||||
−0.395963 | + | 0.918266i | \(0.629589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.80385 | −0.550877 | ||||||||
\(112\) | −1.26795 | −0.119810 | ||||||||
\(113\) | −6.80385 | −0.640052 | −0.320026 | − | 0.947409i | \(-0.603692\pi\) | ||||
−0.320026 | + | 0.947409i | \(0.603692\pi\) | |||||||
\(114\) | −3.07180 | −0.287700 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.73205 | 0.346512 | ||||||||
\(117\) | −6.07180 | −0.561338 | ||||||||
\(118\) | −13.8564 | −1.27559 | ||||||||
\(119\) | 2.19615 | 0.201321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.92820 | −0.808322 | ||||||||
\(123\) | −7.66025 | −0.690702 | ||||||||
\(124\) | 8.73205 | 0.784161 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.12436 | −0.278340 | ||||||||
\(127\) | −21.8564 | −1.93944 | −0.969721 | − | 0.244215i | \(-0.921470\pi\) | ||||
−0.969721 | + | 0.244215i | \(0.921470\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.92820 | 0.609994 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.46410 | −0.477401 | −0.238700 | − | 0.971093i | \(-0.576721\pi\) | ||||
−0.238700 | + | 0.971093i | \(0.576721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.32051 | 0.461347 | ||||||||
\(134\) | 7.26795 | 0.627855 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.73205 | 0.148522 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | −2.00000 | −0.170251 | ||||||||
\(139\) | 9.26795 | 0.786097 | 0.393049 | − | 0.919518i | \(-0.371420\pi\) | ||||
0.393049 | + | 0.919518i | \(0.371420\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.92820 | 0.415030 | ||||||||
\(142\) | −6.92820 | −0.581402 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.9282 | 1.06995 | ||||||||
\(147\) | 3.94744 | 0.325579 | ||||||||
\(148\) | 7.92820 | 0.651694 | ||||||||
\(149\) | 13.5885 | 1.11321 | 0.556605 | − | 0.830777i | \(-0.312104\pi\) | ||||
0.556605 | + | 0.830777i | \(0.312104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.9282 | −0.889325 | −0.444662 | − | 0.895698i | \(-0.646676\pi\) | ||||
−0.444662 | + | 0.895698i | \(0.646676\pi\) | |||||||
\(152\) | 4.19615 | 0.340353 | ||||||||
\(153\) | 4.26795 | 0.345043 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.80385 | −0.144423 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 7.26795 | 0.578207 | ||||||||
\(159\) | 2.19615 | 0.174166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.46410 | 0.273009 | ||||||||
\(162\) | −4.46410 | −0.350733 | ||||||||
\(163\) | 9.12436 | 0.714675 | 0.357337 | − | 0.933975i | \(-0.383685\pi\) | ||||
0.357337 | + | 0.933975i | \(0.383685\pi\) | |||||||
\(164\) | 10.4641 | 0.817109 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.26795 | −0.253642 | ||||||||
\(167\) | 15.3205 | 1.18554 | 0.592768 | − | 0.805373i | \(-0.298035\pi\) | ||||
0.592768 | + | 0.805373i | \(0.298035\pi\) | |||||||
\(168\) | −0.928203 | −0.0716124 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3397 | 0.790700 | ||||||||
\(172\) | −9.46410 | −0.721631 | ||||||||
\(173\) | 6.53590 | 0.496915 | 0.248458 | − | 0.968643i | \(-0.420076\pi\) | ||||
0.248458 | + | 0.968643i | \(0.420076\pi\) | |||||||
\(174\) | 2.73205 | 0.207116 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1436 | −0.762439 | ||||||||
\(178\) | −0.464102 | −0.0347859 | ||||||||
\(179\) | −21.8564 | −1.63362 | −0.816812 | − | 0.576904i | \(-0.804261\pi\) | ||||
−0.816812 | + | 0.576904i | \(0.804261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.66025 | −0.643712 | −0.321856 | − | 0.946789i | \(-0.604307\pi\) | ||||
−0.321856 | + | 0.946789i | \(0.604307\pi\) | |||||||
\(182\) | 3.12436 | 0.231593 | ||||||||
\(183\) | −6.53590 | −0.483148 | ||||||||
\(184\) | 2.73205 | 0.201409 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.39230 | 0.468707 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.73205 | −0.490985 | ||||||||
\(189\) | −5.07180 | −0.368919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.46410 | 0.105939 | 0.0529693 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529693 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(192\) | −0.732051 | −0.0528312 | ||||||||
\(193\) | −13.1962 | −0.949880 | −0.474940 | − | 0.880018i | \(-0.657530\pi\) | ||||
−0.474940 | + | 0.880018i | \(0.657530\pi\) | |||||||
\(194\) | −17.1962 | −1.23461 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.39230 | −0.385165 | ||||||||
\(197\) | −10.0718 | −0.717586 | −0.358793 | − | 0.933417i | \(-0.616812\pi\) | ||||
−0.358793 | + | 0.933417i | \(0.616812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0718 | −0.926635 | −0.463318 | − | 0.886192i | \(-0.653341\pi\) | ||||
−0.463318 | + | 0.886192i | \(0.653341\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.32051 | 0.375280 | ||||||||
\(202\) | 10.0000 | 0.703598 | ||||||||
\(203\) | −4.73205 | −0.332125 | ||||||||
\(204\) | 1.26795 | 0.0887742 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 6.73205 | 0.467910 | ||||||||
\(208\) | 2.46410 | 0.170855 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.07180 | −0.624528 | −0.312264 | − | 0.949995i | \(-0.601087\pi\) | ||||
−0.312264 | + | 0.949995i | \(0.601087\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | −5.07180 | −0.347514 | ||||||||
\(214\) | 11.6603 | 0.797079 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −11.0718 | −0.751603 | ||||||||
\(218\) | 8.26795 | 0.559976 | ||||||||
\(219\) | 9.46410 | 0.639525 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.26795 | −0.287093 | ||||||||
\(222\) | 5.80385 | 0.389529 | ||||||||
\(223\) | 20.3923 | 1.36557 | 0.682785 | − | 0.730619i | \(-0.260769\pi\) | ||||
0.682785 | + | 0.730619i | \(0.260769\pi\) | |||||||
\(224\) | 1.26795 | 0.0847184 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.80385 | 0.452585 | ||||||||
\(227\) | −28.3923 | −1.88446 | −0.942232 | − | 0.334962i | \(-0.891277\pi\) | ||||
−0.942232 | + | 0.334962i | \(0.891277\pi\) | |||||||
\(228\) | 3.07180 | 0.203435 | ||||||||
\(229\) | 9.33975 | 0.617188 | 0.308594 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308594 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.73205 | −0.245021 | ||||||||
\(233\) | 13.1962 | 0.864509 | 0.432254 | − | 0.901752i | \(-0.357718\pi\) | ||||
0.432254 | + | 0.901752i | \(0.357718\pi\) | |||||||
\(234\) | 6.07180 | 0.396926 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.8564 | 0.901975 | ||||||||
\(237\) | 5.32051 | 0.345604 | ||||||||
\(238\) | −2.19615 | −0.142355 | ||||||||
\(239\) | 16.7321 | 1.08231 | 0.541153 | − | 0.840924i | \(-0.317988\pi\) | ||||
0.541153 | + | 0.840924i | \(0.317988\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.3205 | −1.24454 | −0.622272 | − | 0.782801i | \(-0.713790\pi\) | ||||
−0.622272 | + | 0.782801i | \(0.713790\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2679 | −0.979439 | ||||||||
\(244\) | 8.92820 | 0.571570 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.66025 | 0.488400 | ||||||||
\(247\) | −10.3397 | −0.657902 | ||||||||
\(248\) | −8.73205 | −0.554486 | ||||||||
\(249\) | −2.39230 | −0.151606 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.5885 | −1.04705 | −0.523527 | − | 0.852009i | \(-0.675384\pi\) | ||||
−0.523527 | + | 0.852009i | \(0.675384\pi\) | |||||||
\(252\) | 3.12436 | 0.196816 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.8564 | 1.37139 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.9808 | 1.74539 | 0.872696 | − | 0.488264i | \(-0.162370\pi\) | ||||
0.872696 | + | 0.488264i | \(0.162370\pi\) | |||||||
\(258\) | −6.92820 | −0.431331 | ||||||||
\(259\) | −10.0526 | −0.624636 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.19615 | −0.569228 | ||||||||
\(262\) | 5.46410 | 0.337573 | ||||||||
\(263\) | −10.0526 | −0.619867 | −0.309934 | − | 0.950758i | \(-0.600307\pi\) | ||||
−0.309934 | + | 0.950758i | \(0.600307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.32051 | −0.326221 | ||||||||
\(267\) | −0.339746 | −0.0207921 | ||||||||
\(268\) | −7.26795 | −0.443961 | ||||||||
\(269\) | −5.19615 | −0.316815 | −0.158408 | − | 0.987374i | \(-0.550636\pi\) | ||||
−0.158408 | + | 0.987374i | \(0.550636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8564 | 1.08470 | 0.542350 | − | 0.840153i | \(-0.317535\pi\) | ||||
0.542350 | + | 0.840153i | \(0.317535\pi\) | |||||||
\(272\) | −1.73205 | −0.105021 | ||||||||
\(273\) | 2.28719 | 0.138427 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | −13.9282 | −0.836865 | −0.418432 | − | 0.908248i | \(-0.637420\pi\) | ||||
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(278\) | −9.26795 | −0.555855 | ||||||||
\(279\) | −21.5167 | −1.28817 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.3923 | −1.69374 | −0.846871 | − | 0.531798i | \(-0.821517\pi\) | ||||
−0.846871 | + | 0.531798i | \(0.821517\pi\) | |||||||
\(282\) | −4.92820 | −0.293470 | ||||||||
\(283\) | −10.5359 | −0.626294 | −0.313147 | − | 0.949705i | \(-0.601383\pi\) | ||||
−0.313147 | + | 0.949705i | \(0.601383\pi\) | |||||||
\(284\) | 6.92820 | 0.411113 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.2679 | −0.783182 | ||||||||
\(288\) | 2.46410 | 0.145199 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5885 | −0.737948 | ||||||||
\(292\) | −12.9282 | −0.756566 | ||||||||
\(293\) | −1.53590 | −0.0897281 | −0.0448641 | − | 0.998993i | \(-0.514285\pi\) | ||||
−0.0448641 | + | 0.998993i | \(0.514285\pi\) | |||||||
\(294\) | −3.94744 | −0.230219 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.92820 | −0.460817 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.5885 | −0.787158 | ||||||||
\(299\) | −6.73205 | −0.389325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | 10.9282 | 0.628847 | ||||||||
\(303\) | 7.32051 | 0.420552 | ||||||||
\(304\) | −4.19615 | −0.240666 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.26795 | −0.243982 | ||||||||
\(307\) | 8.73205 | 0.498364 | 0.249182 | − | 0.968457i | \(-0.419838\pi\) | ||||
0.249182 | + | 0.968457i | \(0.419838\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.85641 | −0.333159 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3923 | 0.702703 | 0.351352 | − | 0.936244i | \(-0.385722\pi\) | ||||
0.351352 | + | 0.936244i | \(0.385722\pi\) | |||||||
\(312\) | 1.80385 | 0.102123 | ||||||||
\(313\) | −6.26795 | −0.354285 | −0.177143 | − | 0.984185i | \(-0.556685\pi\) | ||||
−0.177143 | + | 0.984185i | \(0.556685\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.26795 | −0.408854 | ||||||||
\(317\) | 25.4641 | 1.43021 | 0.715103 | − | 0.699019i | \(-0.246380\pi\) | ||||
0.715103 | + | 0.699019i | \(0.246380\pi\) | |||||||
\(318\) | −2.19615 | −0.123154 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.53590 | 0.476427 | ||||||||
\(322\) | −3.46410 | −0.193047 | ||||||||
\(323\) | 7.26795 | 0.404400 | ||||||||
\(324\) | 4.46410 | 0.248006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.12436 | −0.505351 | ||||||||
\(327\) | 6.05256 | 0.334707 | ||||||||
\(328\) | −10.4641 | −0.577783 | ||||||||
\(329\) | 8.53590 | 0.470599 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.46410 | −0.520194 | −0.260097 | − | 0.965582i | \(-0.583755\pi\) | ||||
−0.260097 | + | 0.965582i | \(0.583755\pi\) | |||||||
\(332\) | 3.26795 | 0.179352 | ||||||||
\(333\) | −19.5359 | −1.07056 | ||||||||
\(334\) | −15.3205 | −0.838301 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.928203 | 0.0506376 | ||||||||
\(337\) | −22.6603 | −1.23438 | −0.617191 | − | 0.786813i | \(-0.711730\pi\) | ||||
−0.617191 | + | 0.786813i | \(0.711730\pi\) | |||||||
\(338\) | 6.92820 | 0.376845 | ||||||||
\(339\) | 4.98076 | 0.270518 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.3397 | −0.559109 | ||||||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | 9.46410 | 0.510270 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.53590 | −0.351372 | ||||||||
\(347\) | −21.4641 | −1.15225 | −0.576127 | − | 0.817360i | \(-0.695437\pi\) | ||||
−0.576127 | + | 0.817360i | \(0.695437\pi\) | |||||||
\(348\) | −2.73205 | −0.146453 | ||||||||
\(349\) | 26.1244 | 1.39840 | 0.699202 | − | 0.714924i | \(-0.253539\pi\) | ||||
0.699202 | + | 0.714924i | \(0.253539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.85641 | 0.526096 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.12436 | −0.432416 | −0.216208 | − | 0.976347i | \(-0.569369\pi\) | ||||
−0.216208 | + | 0.976347i | \(0.569369\pi\) | |||||||
\(354\) | 10.1436 | 0.539126 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.464102 | 0.0245973 | ||||||||
\(357\) | −1.60770 | −0.0850883 | ||||||||
\(358\) | 21.8564 | 1.15515 | ||||||||
\(359\) | 13.5167 | 0.713382 | 0.356691 | − | 0.934222i | \(-0.383905\pi\) | ||||
0.356691 | + | 0.934222i | \(0.383905\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.39230 | −0.0732792 | ||||||||
\(362\) | 8.66025 | 0.455173 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.12436 | −0.163761 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.53590 | 0.341637 | ||||||||
\(367\) | 3.41154 | 0.178081 | 0.0890405 | − | 0.996028i | \(-0.471620\pi\) | ||||
0.0890405 | + | 0.996028i | \(0.471620\pi\) | |||||||
\(368\) | −2.73205 | −0.142418 | ||||||||
\(369\) | −25.7846 | −1.34229 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.80385 | 0.197486 | ||||||||
\(372\) | −6.39230 | −0.331426 | ||||||||
\(373\) | 12.3923 | 0.641649 | 0.320825 | − | 0.947139i | \(-0.396040\pi\) | ||||
0.320825 | + | 0.947139i | \(0.396040\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.73205 | 0.347179 | ||||||||
\(377\) | 9.19615 | 0.473626 | ||||||||
\(378\) | 5.07180 | 0.260865 | ||||||||
\(379\) | 14.2487 | 0.731907 | 0.365954 | − | 0.930633i | \(-0.380743\pi\) | ||||
0.365954 | + | 0.930633i | \(0.380743\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.0000 | 0.819705 | ||||||||
\(382\) | −1.46410 | −0.0749100 | ||||||||
\(383\) | 23.3205 | 1.19162 | 0.595811 | − | 0.803125i | \(-0.296831\pi\) | ||||
0.595811 | + | 0.803125i | \(0.296831\pi\) | |||||||
\(384\) | 0.732051 | 0.0373573 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.1962 | 0.671666 | ||||||||
\(387\) | 23.3205 | 1.18545 | ||||||||
\(388\) | 17.1962 | 0.873002 | ||||||||
\(389\) | 28.2679 | 1.43324 | 0.716621 | − | 0.697463i | \(-0.245688\pi\) | ||||
0.716621 | + | 0.697463i | \(0.245688\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.73205 | 0.239310 | ||||||||
\(392\) | 5.39230 | 0.272353 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 10.0718 | 0.507410 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7128 | −1.34068 | −0.670339 | − | 0.742055i | \(-0.733851\pi\) | ||||
−0.670339 | + | 0.742055i | \(0.733851\pi\) | |||||||
\(398\) | 13.0718 | 0.655230 | ||||||||
\(399\) | −3.89488 | −0.194988 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.32051 | 0.115881 | 0.0579403 | − | 0.998320i | \(-0.481547\pi\) | ||||
0.0579403 | + | 0.998320i | \(0.481547\pi\) | |||||||
\(402\) | −5.32051 | −0.265363 | ||||||||
\(403\) | 21.5167 | 1.07182 | ||||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.73205 | 0.234848 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.26795 | −0.0627728 | ||||||||
\(409\) | −17.3923 | −0.859994 | −0.429997 | − | 0.902830i | \(-0.641485\pi\) | ||||
−0.429997 | + | 0.902830i | \(0.641485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.39230 | −0.216656 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | −17.5692 | −0.864525 | ||||||||
\(414\) | −6.73205 | −0.330862 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.46410 | −0.120813 | ||||||||
\(417\) | −6.78461 | −0.332244 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.41154 | 0.166665 | 0.0833324 | − | 0.996522i | \(-0.473444\pi\) | ||||
0.0833324 | + | 0.996522i | \(0.473444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0526 | −0.831091 | −0.415545 | − | 0.909572i | \(-0.636409\pi\) | ||||
−0.415545 | + | 0.909572i | \(0.636409\pi\) | |||||||
\(422\) | 9.07180 | 0.441608 | ||||||||
\(423\) | 16.5885 | 0.806558 | ||||||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.07180 | 0.245729 | ||||||||
\(427\) | −11.3205 | −0.547838 | ||||||||
\(428\) | −11.6603 | −0.563620 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.8564 | −0.860113 | −0.430056 | − | 0.902802i | \(-0.641506\pi\) | ||||
−0.430056 | + | 0.902802i | \(0.641506\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 19.5885 | 0.941361 | 0.470681 | − | 0.882304i | \(-0.344008\pi\) | ||||
0.470681 | + | 0.882304i | \(0.344008\pi\) | |||||||
\(434\) | 11.0718 | 0.531463 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.26795 | −0.395963 | ||||||||
\(437\) | 11.4641 | 0.548402 | ||||||||
\(438\) | −9.46410 | −0.452212 | ||||||||
\(439\) | −17.1244 | −0.817301 | −0.408650 | − | 0.912691i | \(-0.634000\pi\) | ||||
−0.408650 | + | 0.912691i | \(0.634000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.2872 | 0.632723 | ||||||||
\(442\) | 4.26795 | 0.203006 | ||||||||
\(443\) | −12.7846 | −0.607415 | −0.303708 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303708 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(444\) | −5.80385 | −0.275438 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −20.3923 | −0.965604 | ||||||||
\(447\) | −9.94744 | −0.470498 | ||||||||
\(448\) | −1.26795 | −0.0599050 | ||||||||
\(449\) | −21.9282 | −1.03486 | −0.517428 | − | 0.855727i | \(-0.673110\pi\) | ||||
−0.517428 | + | 0.855727i | \(0.673110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.80385 | −0.320026 | ||||||||
\(453\) | 8.00000 | 0.375873 | ||||||||
\(454\) | 28.3923 | 1.33252 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.07180 | −0.143850 | ||||||||
\(457\) | 15.5885 | 0.729197 | 0.364599 | − | 0.931165i | \(-0.381206\pi\) | ||||
0.364599 | + | 0.931165i | \(0.381206\pi\) | |||||||
\(458\) | −9.33975 | −0.436418 | ||||||||
\(459\) | −6.92820 | −0.323381 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.51666 | −0.396660 | −0.198330 | − | 0.980135i | \(-0.563552\pi\) | ||||
−0.198330 | + | 0.980135i | \(0.563552\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 3.73205 | 0.173256 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.1962 | −0.611300 | ||||||||
\(467\) | −25.1769 | −1.16505 | −0.582524 | − | 0.812813i | \(-0.697935\pi\) | ||||
−0.582524 | + | 0.812813i | \(0.697935\pi\) | |||||||
\(468\) | −6.07180 | −0.280669 | ||||||||
\(469\) | 9.21539 | 0.425527 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.32051 | 0.337311 | ||||||||
\(472\) | −13.8564 | −0.637793 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.32051 | −0.244379 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.19615 | 0.100660 | ||||||||
\(477\) | 7.39230 | 0.338470 | ||||||||
\(478\) | −16.7321 | −0.765306 | ||||||||
\(479\) | −2.14359 | −0.0979433 | −0.0489716 | − | 0.998800i | \(-0.515594\pi\) | ||||
−0.0489716 | + | 0.998800i | \(0.515594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.5359 | 0.890760 | ||||||||
\(482\) | 19.3205 | 0.880025 | ||||||||
\(483\) | −2.53590 | −0.115387 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.2679 | 0.692568 | ||||||||
\(487\) | −38.8372 | −1.75988 | −0.879940 | − | 0.475085i | \(-0.842417\pi\) | ||||
−0.879940 | + | 0.475085i | \(0.842417\pi\) | |||||||
\(488\) | −8.92820 | −0.404161 | ||||||||
\(489\) | −6.67949 | −0.302057 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.9090 | −1.62055 | −0.810274 | − | 0.586051i | \(-0.800682\pi\) | ||||
−0.810274 | + | 0.586051i | \(0.800682\pi\) | |||||||
\(492\) | −7.66025 | −0.345351 | ||||||||
\(493\) | −6.46410 | −0.291128 | ||||||||
\(494\) | 10.3397 | 0.465207 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.73205 | 0.392081 | ||||||||
\(497\) | −8.78461 | −0.394044 | ||||||||
\(498\) | 2.39230 | 0.107202 | ||||||||
\(499\) | −10.9282 | −0.489214 | −0.244607 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244607 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.2154 | −0.501067 | ||||||||
\(502\) | 16.5885 | 0.740379 | ||||||||
\(503\) | −15.1244 | −0.674362 | −0.337181 | − | 0.941440i | \(-0.609473\pi\) | ||||
−0.337181 | + | 0.941440i | \(0.609473\pi\) | |||||||
\(504\) | −3.12436 | −0.139170 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.07180 | 0.225246 | ||||||||
\(508\) | −21.8564 | −0.969721 | ||||||||
\(509\) | −8.92820 | −0.395736 | −0.197868 | − | 0.980229i | \(-0.563402\pi\) | ||||
−0.197868 | + | 0.980229i | \(0.563402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3923 | 0.725153 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −16.7846 | −0.741059 | ||||||||
\(514\) | −27.9808 | −1.23418 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.92820 | 0.304997 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 10.0526 | 0.441684 | ||||||||
\(519\) | −4.78461 | −0.210021 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.1769 | −0.927777 | −0.463889 | − | 0.885893i | \(-0.653546\pi\) | ||||
−0.463889 | + | 0.885893i | \(0.653546\pi\) | |||||||
\(522\) | 9.19615 | 0.402505 | ||||||||
\(523\) | −26.9282 | −1.17749 | −0.588744 | − | 0.808320i | \(-0.700377\pi\) | ||||
−0.588744 | + | 0.808320i | \(0.700377\pi\) | |||||||
\(524\) | −5.46410 | −0.238700 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0526 | 0.438312 | ||||||||
\(527\) | −15.1244 | −0.658827 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.5359 | −0.675474 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.1436 | −1.48171 | ||||||||
\(532\) | 5.32051 | 0.230673 | ||||||||
\(533\) | 25.7846 | 1.11686 | ||||||||
\(534\) | 0.339746 | 0.0147022 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.26795 | 0.313928 | ||||||||
\(537\) | 16.0000 | 0.690451 | ||||||||
\(538\) | 5.19615 | 0.224022 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.0718 | 1.07792 | 0.538960 | − | 0.842331i | \(-0.318817\pi\) | ||||
0.538960 | + | 0.842331i | \(0.318817\pi\) | |||||||
\(542\) | −17.8564 | −0.766998 | ||||||||
\(543\) | 6.33975 | 0.272065 | ||||||||
\(544\) | 1.73205 | 0.0742611 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.28719 | −0.0978826 | ||||||||
\(547\) | −31.3205 | −1.33917 | −0.669584 | − | 0.742736i | \(-0.733528\pi\) | ||||
−0.669584 | + | 0.742736i | \(0.733528\pi\) | |||||||
\(548\) | 6.00000 | 0.256307 | ||||||||
\(549\) | −22.0000 | −0.938937 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.6603 | −0.667149 | ||||||||
\(552\) | −2.00000 | −0.0851257 | ||||||||
\(553\) | 9.21539 | 0.391878 | ||||||||
\(554\) | 13.9282 | 0.591753 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.26795 | 0.393049 | ||||||||
\(557\) | −1.46410 | −0.0620360 | −0.0310180 | − | 0.999519i | \(-0.509875\pi\) | ||||
−0.0310180 | + | 0.999519i | \(0.509875\pi\) | |||||||
\(558\) | 21.5167 | 0.910873 | ||||||||
\(559\) | −23.3205 | −0.986352 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.3923 | 1.19766 | ||||||||
\(563\) | −43.3731 | −1.82796 | −0.913978 | − | 0.405763i | \(-0.867006\pi\) | ||||
−0.913978 | + | 0.405763i | \(0.867006\pi\) | |||||||
\(564\) | 4.92820 | 0.207515 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.5359 | 0.442857 | ||||||||
\(567\) | −5.66025 | −0.237708 | ||||||||
\(568\) | −6.92820 | −0.290701 | ||||||||
\(569\) | −3.32051 | −0.139203 | −0.0696015 | − | 0.997575i | \(-0.522173\pi\) | ||||
−0.0696015 | + | 0.997575i | \(0.522173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.4449 | 1.60887 | 0.804434 | − | 0.594042i | \(-0.202469\pi\) | ||||
0.804434 | + | 0.594042i | \(0.202469\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.07180 | −0.0447750 | ||||||||
\(574\) | 13.2679 | 0.553793 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.46410 | −0.102671 | ||||||||
\(577\) | −12.2679 | −0.510721 | −0.255361 | − | 0.966846i | \(-0.582194\pi\) | ||||
−0.255361 | + | 0.966846i | \(0.582194\pi\) | |||||||
\(578\) | 14.0000 | 0.582323 | ||||||||
\(579\) | 9.66025 | 0.401466 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.14359 | −0.171905 | ||||||||
\(582\) | 12.5885 | 0.521808 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.9282 | 0.534973 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.53590 | 0.0634474 | ||||||||
\(587\) | −24.7321 | −1.02080 | −0.510400 | − | 0.859937i | \(-0.670503\pi\) | ||||
−0.510400 | + | 0.859937i | \(0.670503\pi\) | |||||||
\(588\) | 3.94744 | 0.162790 | ||||||||
\(589\) | −36.6410 | −1.50977 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.37307 | 0.303287 | ||||||||
\(592\) | 7.92820 | 0.325847 | ||||||||
\(593\) | 38.9090 | 1.59780 | 0.798900 | − | 0.601464i | \(-0.205416\pi\) | ||||
0.798900 | + | 0.601464i | \(0.205416\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.5885 | 0.556605 | ||||||||
\(597\) | 9.56922 | 0.391642 | ||||||||
\(598\) | 6.73205 | 0.275294 | ||||||||
\(599\) | −36.7321 | −1.50083 | −0.750415 | − | 0.660966i | \(-0.770147\pi\) | ||||
−0.750415 | + | 0.660966i | \(0.770147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.7846 | −0.643868 | −0.321934 | − | 0.946762i | \(-0.604333\pi\) | ||||
−0.321934 | + | 0.946762i | \(0.604333\pi\) | |||||||
\(602\) | −12.0000 | −0.489083 | ||||||||
\(603\) | 17.9090 | 0.729309 | ||||||||
\(604\) | −10.9282 | −0.444662 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.32051 | −0.297375 | ||||||||
\(607\) | −13.6603 | −0.554453 | −0.277226 | − | 0.960805i | \(-0.589415\pi\) | ||||
−0.277226 | + | 0.960805i | \(0.589415\pi\) | |||||||
\(608\) | 4.19615 | 0.170176 | ||||||||
\(609\) | 3.46410 | 0.140372 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.5885 | −0.671097 | ||||||||
\(612\) | 4.26795 | 0.172522 | ||||||||
\(613\) | −27.0000 | −1.09052 | −0.545260 | − | 0.838267i | \(-0.683569\pi\) | ||||
−0.545260 | + | 0.838267i | \(0.683569\pi\) | |||||||
\(614\) | −8.73205 | −0.352397 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.33975 | −0.376004 | −0.188002 | − | 0.982169i | \(-0.560201\pi\) | ||||
−0.188002 | + | 0.982169i | \(0.560201\pi\) | |||||||
\(618\) | 5.85641 | 0.235579 | ||||||||
\(619\) | 2.33975 | 0.0940423 | 0.0470212 | − | 0.998894i | \(-0.485027\pi\) | ||||
0.0470212 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.9282 | −0.438534 | ||||||||
\(622\) | −12.3923 | −0.496886 | ||||||||
\(623\) | −0.588457 | −0.0235760 | ||||||||
\(624\) | −1.80385 | −0.0722117 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.26795 | 0.250518 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.0000 | −0.399043 | ||||||||
\(629\) | −13.7321 | −0.547533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.2679 | −0.448570 | −0.224285 | − | 0.974524i | \(-0.572005\pi\) | ||||
−0.224285 | + | 0.974524i | \(0.572005\pi\) | |||||||
\(632\) | 7.26795 | 0.289103 | ||||||||
\(633\) | 6.64102 | 0.263957 | ||||||||
\(634\) | −25.4641 | −1.01131 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.19615 | 0.0870831 | ||||||||
\(637\) | −13.2872 | −0.526458 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.0718 | −0.675350 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.32051 | −0.0916546 | −0.0458273 | − | 0.998949i | \(-0.514592\pi\) | ||||
−0.0458273 | + | 0.998949i | \(0.514592\pi\) | |||||||
\(642\) | −8.53590 | −0.336885 | ||||||||
\(643\) | −26.5885 | −1.04855 | −0.524273 | − | 0.851550i | \(-0.675663\pi\) | ||||
−0.524273 | + | 0.851550i | \(0.675663\pi\) | |||||||
\(644\) | 3.46410 | 0.136505 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.26795 | −0.285954 | ||||||||
\(647\) | −25.8564 | −1.01652 | −0.508260 | − | 0.861204i | \(-0.669711\pi\) | ||||
−0.508260 | + | 0.861204i | \(0.669711\pi\) | |||||||
\(648\) | −4.46410 | −0.175366 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.10512 | 0.317665 | ||||||||
\(652\) | 9.12436 | 0.357337 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | −6.05256 | −0.236674 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.4641 | 0.408555 | ||||||||
\(657\) | 31.8564 | 1.24284 | ||||||||
\(658\) | −8.53590 | −0.332764 | ||||||||
\(659\) | 26.7321 | 1.04133 | 0.520666 | − | 0.853760i | \(-0.325684\pi\) | ||||
0.520666 | + | 0.853760i | \(0.325684\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3731 | 1.64812 | 0.824061 | − | 0.566502i | \(-0.191703\pi\) | ||||
0.824061 | + | 0.566502i | \(0.191703\pi\) | |||||||
\(662\) | 9.46410 | 0.367833 | ||||||||
\(663\) | 3.12436 | 0.121340 | ||||||||
\(664\) | −3.26795 | −0.126821 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.5359 | 0.757001 | ||||||||
\(667\) | −10.1962 | −0.394797 | ||||||||
\(668\) | 15.3205 | 0.592768 | ||||||||
\(669\) | −14.9282 | −0.577158 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.928203 | −0.0358062 | ||||||||
\(673\) | −10.7846 | −0.415716 | −0.207858 | − | 0.978159i | \(-0.566649\pi\) | ||||
−0.207858 | + | 0.978159i | \(0.566649\pi\) | |||||||
\(674\) | 22.6603 | 0.872840 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.92820 | −0.266469 | ||||||||
\(677\) | 5.14359 | 0.197684 | 0.0988422 | − | 0.995103i | \(-0.468486\pi\) | ||||
0.0988422 | + | 0.995103i | \(0.468486\pi\) | |||||||
\(678\) | −4.98076 | −0.191285 | ||||||||
\(679\) | −21.8038 | −0.836755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.7846 | 0.796468 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.33975 | 0.319112 | 0.159556 | − | 0.987189i | \(-0.448994\pi\) | ||||
0.159556 | + | 0.987189i | \(0.448994\pi\) | |||||||
\(684\) | 10.3397 | 0.395350 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.7128 | −0.599918 | ||||||||
\(687\) | −6.83717 | −0.260854 | ||||||||
\(688\) | −9.46410 | −0.360815 | ||||||||
\(689\) | −7.39230 | −0.281624 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.3205 | −1.19149 | −0.595744 | − | 0.803174i | \(-0.703143\pi\) | ||||
−0.595744 | + | 0.803174i | \(0.703143\pi\) | |||||||
\(692\) | 6.53590 | 0.248458 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.4641 | 0.814766 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.73205 | 0.103558 | ||||||||
\(697\) | −18.1244 | −0.686509 | ||||||||
\(698\) | −26.1244 | −0.988821 | ||||||||
\(699\) | −9.66025 | −0.365384 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.4449 | 1.79197 | 0.895984 | − | 0.444087i | \(-0.146472\pi\) | ||||
0.895984 | + | 0.444087i | \(0.146472\pi\) | |||||||
\(702\) | −9.85641 | −0.372006 | ||||||||
\(703\) | −33.2679 | −1.25472 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.12436 | 0.305764 | ||||||||
\(707\) | 12.6795 | 0.476861 | ||||||||
\(708\) | −10.1436 | −0.381220 | ||||||||
\(709\) | −14.0000 | −0.525781 | −0.262891 | − | 0.964826i | \(-0.584676\pi\) | ||||
−0.262891 | + | 0.964826i | \(0.584676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.9090 | 0.671639 | ||||||||
\(712\) | −0.464102 | −0.0173929 | ||||||||
\(713\) | −23.8564 | −0.893429 | ||||||||
\(714\) | 1.60770 | 0.0601665 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.8564 | −0.816812 | ||||||||
\(717\) | −12.2487 | −0.457437 | ||||||||
\(718\) | −13.5167 | −0.504437 | ||||||||
\(719\) | 32.4449 | 1.20999 | 0.604995 | − | 0.796230i | \(-0.293175\pi\) | ||||
0.604995 | + | 0.796230i | \(0.293175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.1436 | −0.377767 | ||||||||
\(722\) | 1.39230 | 0.0518162 | ||||||||
\(723\) | 14.1436 | 0.526006 | ||||||||
\(724\) | −8.66025 | −0.321856 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.12436 | −0.115876 | −0.0579380 | − | 0.998320i | \(-0.518453\pi\) | ||||
−0.0579380 | + | 0.998320i | \(0.518453\pi\) | |||||||
\(728\) | 3.12436 | 0.115796 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3923 | 0.606291 | ||||||||
\(732\) | −6.53590 | −0.241574 | ||||||||
\(733\) | −2.21539 | −0.0818273 | −0.0409137 | − | 0.999163i | \(-0.513027\pi\) | ||||
−0.0409137 | + | 0.999163i | \(0.513027\pi\) | |||||||
\(734\) | −3.41154 | −0.125922 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.73205 | 0.100705 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 25.7846 | 0.949145 | ||||||||
\(739\) | −23.8038 | −0.875639 | −0.437819 | − | 0.899063i | \(-0.644249\pi\) | ||||
−0.437819 | + | 0.899063i | \(0.644249\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.56922 | 0.278062 | ||||||||
\(742\) | −3.80385 | −0.139644 | ||||||||
\(743\) | 44.9808 | 1.65018 | 0.825092 | − | 0.564998i | \(-0.191123\pi\) | ||||
0.825092 | + | 0.564998i | \(0.191123\pi\) | |||||||
\(744\) | 6.39230 | 0.234353 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.3923 | −0.453715 | ||||||||
\(747\) | −8.05256 | −0.294628 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.7846 | 0.540218 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.3923 | −1.47394 | −0.736968 | − | 0.675928i | \(-0.763743\pi\) | ||||
−0.736968 | + | 0.675928i | \(0.763743\pi\) | |||||||
\(752\) | −6.73205 | −0.245493 | ||||||||
\(753\) | 12.1436 | 0.442537 | ||||||||
\(754\) | −9.19615 | −0.334904 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.07180 | −0.184459 | ||||||||
\(757\) | −18.4641 | −0.671089 | −0.335545 | − | 0.942024i | \(-0.608920\pi\) | ||||
−0.335545 | + | 0.942024i | \(0.608920\pi\) | |||||||
\(758\) | −14.2487 | −0.517537 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.24871 | −0.117766 | −0.0588828 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588828 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(762\) | −16.0000 | −0.579619 | ||||||||
\(763\) | 10.4833 | 0.379522 | ||||||||
\(764\) | 1.46410 | 0.0529693 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.3205 | −0.842604 | ||||||||
\(767\) | 34.1436 | 1.23285 | ||||||||
\(768\) | −0.732051 | −0.0264156 | ||||||||
\(769\) | −9.00000 | −0.324548 | −0.162274 | − | 0.986746i | \(-0.551883\pi\) | ||||
−0.162274 | + | 0.986746i | \(0.551883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.4833 | −0.737689 | ||||||||
\(772\) | −13.1962 | −0.474940 | ||||||||
\(773\) | −13.4641 | −0.484270 | −0.242135 | − | 0.970243i | \(-0.577848\pi\) | ||||
−0.242135 | + | 0.970243i | \(0.577848\pi\) | |||||||
\(774\) | −23.3205 | −0.838238 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.1962 | −0.617306 | ||||||||
\(777\) | 7.35898 | 0.264002 | ||||||||
\(778\) | −28.2679 | −1.01346 | ||||||||
\(779\) | −43.9090 | −1.57320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.73205 | −0.169218 | ||||||||
\(783\) | 14.9282 | 0.533490 | ||||||||
\(784\) | −5.39230 | −0.192582 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.00000 | −0.142675 | ||||||||
\(787\) | 32.3923 | 1.15466 | 0.577330 | − | 0.816511i | \(-0.304094\pi\) | ||||
0.577330 | + | 0.816511i | \(0.304094\pi\) | |||||||
\(788\) | −10.0718 | −0.358793 | ||||||||
\(789\) | 7.35898 | 0.261987 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.62693 | 0.306738 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.0000 | 0.781243 | ||||||||
\(794\) | 26.7128 | 0.948002 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.0718 | −0.463318 | ||||||||
\(797\) | 42.2487 | 1.49653 | 0.748263 | − | 0.663402i | \(-0.230888\pi\) | ||||
0.748263 | + | 0.663402i | \(0.230888\pi\) | |||||||
\(798\) | 3.89488 | 0.137877 | ||||||||
\(799\) | 11.6603 | 0.412510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.14359 | −0.0404069 | ||||||||
\(802\) | −2.32051 | −0.0819400 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.32051 | 0.187640 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −21.5167 | −0.757892 | ||||||||
\(807\) | 3.80385 | 0.133902 | ||||||||
\(808\) | 10.0000 | 0.351799 | ||||||||
\(809\) | 20.3923 | 0.716955 | 0.358478 | − | 0.933538i | \(-0.383296\pi\) | ||||
0.358478 | + | 0.933538i | \(0.383296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | −4.73205 | −0.166062 | ||||||||
\(813\) | −13.0718 | −0.458448 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.26795 | 0.0443871 | ||||||||
\(817\) | 39.7128 | 1.38938 | ||||||||
\(818\) | 17.3923 | 0.608108 | ||||||||
\(819\) | 7.69873 | 0.269015 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.0718 | −1.08441 | −0.542207 | − | 0.840245i | \(-0.682411\pi\) | ||||
−0.542207 | + | 0.840245i | \(0.682411\pi\) | |||||||
\(822\) | 4.39230 | 0.153199 | ||||||||
\(823\) | −13.4641 | −0.469329 | −0.234665 | − | 0.972076i | \(-0.575399\pi\) | ||||
−0.234665 | + | 0.972076i | \(0.575399\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.5692 | 0.611311 | ||||||||
\(827\) | 31.3731 | 1.09095 | 0.545474 | − | 0.838128i | \(-0.316350\pi\) | ||||
0.545474 | + | 0.838128i | \(0.316350\pi\) | |||||||
\(828\) | 6.73205 | 0.233955 | ||||||||
\(829\) | −1.87564 | −0.0651438 | −0.0325719 | − | 0.999469i | \(-0.510370\pi\) | ||||
−0.0325719 | + | 0.999469i | \(0.510370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.1962 | 0.353701 | ||||||||
\(832\) | 2.46410 | 0.0854274 | ||||||||
\(833\) | 9.33975 | 0.323603 | ||||||||
\(834\) | 6.78461 | 0.234932 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.9282 | 1.20730 | ||||||||
\(838\) | −3.41154 | −0.117850 | ||||||||
\(839\) | −23.6603 | −0.816843 | −0.408421 | − | 0.912794i | \(-0.633921\pi\) | ||||
−0.408421 | + | 0.912794i | \(0.633921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0718 | −0.519717 | ||||||||
\(842\) | 17.0526 | 0.587670 | ||||||||
\(843\) | 20.7846 | 0.715860 | ||||||||
\(844\) | −9.07180 | −0.312264 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16.5885 | −0.570323 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 7.71281 | 0.264703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.6603 | −0.742504 | ||||||||
\(852\) | −5.07180 | −0.173757 | ||||||||
\(853\) | −21.3923 | −0.732459 | −0.366229 | − | 0.930525i | \(-0.619351\pi\) | ||||
−0.366229 | + | 0.930525i | \(0.619351\pi\) | |||||||
\(854\) | 11.3205 | 0.387380 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.6603 | 0.398539 | ||||||||
\(857\) | 32.0000 | 1.09310 | 0.546550 | − | 0.837427i | \(-0.315941\pi\) | ||||
0.546550 | + | 0.837427i | \(0.315941\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4641 | −0.459389 | −0.229695 | − | 0.973263i | \(-0.573773\pi\) | ||||
−0.229695 | + | 0.973263i | \(0.573773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.71281 | 0.331012 | ||||||||
\(862\) | 17.8564 | 0.608192 | ||||||||
\(863\) | 38.4449 | 1.30868 | 0.654339 | − | 0.756201i | \(-0.272947\pi\) | ||||
0.654339 | + | 0.756201i | \(0.272947\pi\) | |||||||
\(864\) | −4.00000 | −0.136083 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.5885 | −0.665643 | ||||||||
\(867\) | 10.2487 | 0.348064 | ||||||||
\(868\) | −11.0718 | −0.375801 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.9090 | −0.606822 | ||||||||
\(872\) | 8.26795 | 0.279988 | ||||||||
\(873\) | −42.3731 | −1.43411 | ||||||||
\(874\) | −11.4641 | −0.387779 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.46410 | 0.319762 | ||||||||
\(877\) | −33.7846 | −1.14083 | −0.570413 | − | 0.821358i | \(-0.693217\pi\) | ||||
−0.570413 | + | 0.821358i | \(0.693217\pi\) | |||||||
\(878\) | 17.1244 | 0.577919 | ||||||||
\(879\) | 1.12436 | 0.0379236 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.39230 | 0.249053 | 0.124527 | − | 0.992216i | \(-0.460259\pi\) | ||||
0.124527 | + | 0.992216i | \(0.460259\pi\) | |||||||
\(882\) | −13.2872 | −0.447403 | ||||||||
\(883\) | −17.0718 | −0.574512 | −0.287256 | − | 0.957854i | \(-0.592743\pi\) | ||||
−0.287256 | + | 0.957854i | \(0.592743\pi\) | |||||||
\(884\) | −4.26795 | −0.143547 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7846 | 0.429507 | ||||||||
\(887\) | 48.9808 | 1.64461 | 0.822307 | − | 0.569045i | \(-0.192687\pi\) | ||||
0.822307 | + | 0.569045i | \(0.192687\pi\) | |||||||
\(888\) | 5.80385 | 0.194764 | ||||||||
\(889\) | 27.7128 | 0.929458 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.3923 | 0.682785 | ||||||||
\(893\) | 28.2487 | 0.945307 | ||||||||
\(894\) | 9.94744 | 0.332692 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.26795 | 0.0423592 | ||||||||
\(897\) | 4.92820 | 0.164548 | ||||||||
\(898\) | 21.9282 | 0.731754 | ||||||||
\(899\) | 32.5885 | 1.08689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19615 | 0.173109 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.78461 | −0.292334 | ||||||||
\(904\) | 6.80385 | 0.226293 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | 8.39230 | 0.278662 | 0.139331 | − | 0.990246i | \(-0.455505\pi\) | ||||
0.139331 | + | 0.990246i | \(0.455505\pi\) | |||||||
\(908\) | −28.3923 | −0.942232 | ||||||||
\(909\) | 24.6410 | 0.817291 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.4641 | −0.578612 | −0.289306 | − | 0.957237i | \(-0.593424\pi\) | ||||
−0.289306 | + | 0.957237i | \(0.593424\pi\) | |||||||
\(912\) | 3.07180 | 0.101717 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −15.5885 | −0.515620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.33975 | 0.308594 | ||||||||
\(917\) | 6.92820 | 0.228789 | ||||||||
\(918\) | 6.92820 | 0.228665 | ||||||||
\(919\) | 28.1051 | 0.927102 | 0.463551 | − | 0.886070i | \(-0.346575\pi\) | ||||
0.463551 | + | 0.886070i | \(0.346575\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.39230 | −0.210634 | ||||||||
\(922\) | 8.51666 | 0.280481 | ||||||||
\(923\) | 17.0718 | 0.561925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.00000 | −0.131448 | ||||||||
\(927\) | −19.7128 | −0.647454 | ||||||||
\(928\) | −3.73205 | −0.122511 | ||||||||
\(929\) | 14.0718 | 0.461681 | 0.230840 | − | 0.972992i | \(-0.425852\pi\) | ||||
0.230840 | + | 0.972992i | \(0.425852\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.6269 | 0.741568 | ||||||||
\(932\) | 13.1962 | 0.432254 | ||||||||
\(933\) | −9.07180 | −0.296997 | ||||||||
\(934\) | 25.1769 | 0.823814 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.07180 | 0.198463 | ||||||||
\(937\) | −16.2679 | −0.531451 | −0.265725 | − | 0.964049i | \(-0.585611\pi\) | ||||
−0.265725 | + | 0.964049i | \(0.585611\pi\) | |||||||
\(938\) | −9.21539 | −0.300893 | ||||||||
\(939\) | 4.58846 | 0.149739 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.51666 | −0.0820408 | −0.0410204 | − | 0.999158i | \(-0.513061\pi\) | ||||
−0.0410204 | + | 0.999158i | \(0.513061\pi\) | |||||||
\(942\) | −7.32051 | −0.238515 | ||||||||
\(943\) | −28.5885 | −0.930968 | ||||||||
\(944\) | 13.8564 | 0.450988 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.9090 | 1.49184 | 0.745920 | − | 0.666035i | \(-0.232010\pi\) | ||||
0.745920 | + | 0.666035i | \(0.232010\pi\) | |||||||
\(948\) | 5.32051 | 0.172802 | ||||||||
\(949\) | −31.8564 | −1.03410 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.6410 | −0.604476 | ||||||||
\(952\) | −2.19615 | −0.0711777 | ||||||||
\(953\) | 19.3397 | 0.626476 | 0.313238 | − | 0.949675i | \(-0.398586\pi\) | ||||
0.313238 | + | 0.949675i | \(0.398586\pi\) | |||||||
\(954\) | −7.39230 | −0.239335 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.7321 | 0.541153 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.14359 | 0.0692564 | ||||||||
\(959\) | −7.60770 | −0.245665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.2487 | 1.45964 | ||||||||
\(962\) | −19.5359 | −0.629863 | ||||||||
\(963\) | 28.7321 | 0.925877 | ||||||||
\(964\) | −19.3205 | −0.622272 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.53590 | 0.0815912 | ||||||||
\(967\) | 53.3731 | 1.71636 | 0.858181 | − | 0.513347i | \(-0.171595\pi\) | ||||
0.858181 | + | 0.513347i | \(0.171595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.32051 | −0.170919 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.7321 | 0.601140 | 0.300570 | − | 0.953760i | \(-0.402823\pi\) | ||||
0.300570 | + | 0.953760i | \(0.402823\pi\) | |||||||
\(972\) | −15.2679 | −0.489720 | ||||||||
\(973\) | −11.7513 | −0.376729 | ||||||||
\(974\) | 38.8372 | 1.24442 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.92820 | 0.285785 | ||||||||
\(977\) | −41.0526 | −1.31339 | −0.656694 | − | 0.754157i | \(-0.728046\pi\) | ||||
−0.656694 | + | 0.754157i | \(0.728046\pi\) | |||||||
\(978\) | 6.67949 | 0.213587 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.3731 | 0.650462 | ||||||||
\(982\) | 35.9090 | 1.14590 | ||||||||
\(983\) | −44.0000 | −1.40338 | −0.701691 | − | 0.712481i | \(-0.747571\pi\) | ||||
−0.701691 | + | 0.712481i | \(0.747571\pi\) | |||||||
\(984\) | 7.66025 | 0.244200 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.46410 | 0.205859 | ||||||||
\(987\) | −6.24871 | −0.198899 | ||||||||
\(988\) | −10.3397 | −0.328951 | ||||||||
\(989\) | 25.8564 | 0.822186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.2487 | −1.21501 | −0.607505 | − | 0.794316i | \(-0.707830\pi\) | ||||
−0.607505 | + | 0.794316i | \(0.707830\pi\) | |||||||
\(992\) | −8.73205 | −0.277243 | ||||||||
\(993\) | 6.92820 | 0.219860 | ||||||||
\(994\) | 8.78461 | 0.278631 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.39230 | −0.0758031 | ||||||||
\(997\) | 21.1436 | 0.669624 | 0.334812 | − | 0.942285i | \(-0.391327\pi\) | ||||
0.334812 | + | 0.942285i | \(0.391327\pi\) | |||||||
\(998\) | 10.9282 | 0.345926 | ||||||||
\(999\) | 31.7128 | 1.00335 |
(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 | 6050.2.a.cd.1.1 | 2 | ||
5.2 | odd | 4 | 1210.2.b.i.969.2 | ✓ | 4 | ||
5.3 | odd | 4 | 1210.2.b.i.969.3 | yes | 4 | ||
5.4 | even | 2 | 6050.2.a.cn.1.2 | 2 | |||
11.10 | odd | 2 | 6050.2.a.cu.1.1 | 2 | |||
55.32 | even | 4 | 1210.2.b.j.969.4 | yes | 4 | ||
55.43 | even | 4 | 1210.2.b.j.969.1 | yes | 4 | ||
55.54 | odd | 2 | 6050.2.a.bt.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1210.2.b.i.969.2 | ✓ | 4 | 5.2 | odd | 4 | ||
1210.2.b.i.969.3 | yes | 4 | 5.3 | odd | 4 | ||
1210.2.b.j.969.1 | yes | 4 | 55.43 | even | 4 | ||
1210.2.b.j.969.4 | yes | 4 | 55.32 | even | 4 | ||
6050.2.a.bt.1.2 | 2 | 55.54 | odd | 2 | |||
6050.2.a.cd.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6050.2.a.cn.1.2 | 2 | 5.4 | even | 2 | |||
6050.2.a.cu.1.1 | 2 | 11.10 | odd | 2 |