Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | −1.59467 | −0.920682 | −0.460341 | − | 0.887742i | \(-0.652273\pi\) | ||||
−0.460341 | + | 0.887742i | \(0.652273\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.11777 | 0.947095 | 0.473548 | − | 0.880768i | \(-0.342973\pi\) | ||||
0.473548 | + | 0.880768i | \(0.342973\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.323115 | 0.122126 | 0.0610630 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610630 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.457036 | −0.152345 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.74648 | −0.828096 | −0.414048 | − | 0.910255i | \(-0.635885\pi\) | ||||
−0.414048 | + | 0.910255i | \(0.635885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.84536 | −1.34386 | −0.671931 | − | 0.740614i | \(-0.734535\pi\) | ||||
−0.671931 | + | 0.740614i | \(0.734535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.37714 | −0.871973 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.66010 | 1.13024 | 0.565120 | − | 0.825009i | \(-0.308830\pi\) | ||||
0.565120 | + | 0.825009i | \(0.308830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.515261 | −0.112439 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.81055 | 0.377526 | 0.188763 | − | 0.982023i | \(-0.439552\pi\) | ||||
0.188763 | + | 0.982023i | \(0.439552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.515054 | −0.103011 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.51282 | 1.06094 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.81219 | −0.707906 | −0.353953 | − | 0.935263i | \(-0.615163\pi\) | ||||
−0.353953 | + | 0.935263i | \(0.615163\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28850 | 0.590632 | 0.295316 | − | 0.955400i | \(-0.404575\pi\) | ||||
0.295316 | + | 0.955400i | \(0.404575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.37973 | 0.762413 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.684283 | 0.115665 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.27671 | 1.19628 | 0.598142 | − | 0.801390i | \(-0.295906\pi\) | ||||
0.598142 | + | 0.801390i | \(0.295906\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.72674 | 1.23727 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.37353 | 0.526856 | 0.263428 | − | 0.964679i | \(-0.415147\pi\) | ||||
0.263428 | + | 0.964679i | \(0.415147\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.47612 | −1.14010 | −0.570049 | − | 0.821611i | \(-0.693076\pi\) | ||||
−0.570049 | + | 0.821611i | \(0.693076\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.967896 | −0.144285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.2596 | 1.49652 | 0.748260 | − | 0.663406i | \(-0.230890\pi\) | ||||
0.748260 | + | 0.663406i | \(0.230890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.89560 | −0.985085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.43131 | −1.04059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.33093 | −0.182817 | −0.0914086 | − | 0.995813i | \(-0.529137\pi\) | ||||
−0.0914086 | + | 0.995813i | \(0.529137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.81642 | −0.784286 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.59467 | −0.211219 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.58694 | 0.727358 | 0.363679 | − | 0.931524i | \(-0.381521\pi\) | ||||
0.363679 | + | 0.931524i | \(0.381521\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.74082 | 0.350926 | 0.175463 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175463 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.147675 | −0.0186053 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.2614 | −1.27277 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.70222 | 0.696637 | 0.348318 | − | 0.937376i | \(-0.386753\pi\) | ||||
0.348318 | + | 0.937376i | \(0.386753\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.88723 | −0.347581 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.576483 | −0.0684159 | −0.0342080 | − | 0.999415i | \(-0.510891\pi\) | ||||
−0.0342080 | + | 0.999415i | \(0.510891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9394 | −1.51444 | −0.757218 | − | 0.653162i | \(-0.773442\pi\) | ||||
−0.757218 | + | 0.653162i | \(0.773442\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.821339 | 0.0948401 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.887431 | −0.101132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.42001 | −0.824446 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.16280 | −1.00575 | −0.502874 | − | 0.864360i | \(-0.667724\pi\) | ||||
−0.502874 | + | 0.864360i | \(0.667724\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.86901 | 1.07044 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.07918 | 0.651756 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.29079 | −0.560823 | −0.280412 | − | 0.959880i | \(-0.590471\pi\) | ||||
−0.280412 | + | 0.959880i | \(0.590471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.56561 | −0.164121 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.24407 | −0.543785 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.11777 | 0.217279 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8529 | −1.40655 | −0.703274 | − | 0.710919i | \(-0.748279\pi\) | ||||
−0.703274 | + | 0.710919i | \(0.748279\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.25524 | 0.126156 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.11741 | −0.608705 | −0.304353 | − | 0.952559i | \(-0.598440\pi\) | ||||
−0.304353 | + | 0.952559i | \(0.598440\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.31022 | −0.917363 | −0.458682 | − | 0.888601i | \(-0.651678\pi\) | ||||
−0.458682 | + | 0.888601i | \(0.651678\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.09120 | −0.106491 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.658953 | −0.0637034 | −0.0318517 | − | 0.999493i | \(-0.510140\pi\) | ||||
−0.0318517 | + | 0.999493i | \(0.510140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.90670 | 0.853107 | 0.426553 | − | 0.904462i | \(-0.359728\pi\) | ||||
0.426553 | + | 0.904462i | \(0.359728\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.6039 | −1.10140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.4760 | −1.36179 | −0.680895 | − | 0.732381i | \(-0.738409\pi\) | ||||
−0.680895 | + | 0.732381i | \(0.738409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.83433 | 0.357553 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.21450 | 0.204731 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50575 | 0.138032 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.45682 | −0.314257 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.37965 | −0.485067 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6796 | −1.04466 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2914 | −0.913218 | −0.456609 | − | 0.889668i | \(-0.650936\pi\) | ||||
−0.456609 | + | 0.889668i | \(0.650936\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.9219 | 1.04967 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.15233 | −0.100680 | −0.0503399 | − | 0.998732i | \(-0.516030\pi\) | ||||
−0.0503399 | + | 0.998732i | \(0.516030\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.323115 | 0.0280176 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.6749 | 1.00481 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.30339 | −0.282227 | −0.141114 | − | 0.989993i | \(-0.545068\pi\) | ||||
−0.141114 | + | 0.989993i | \(0.545068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.86153 | 0.836444 | 0.418222 | − | 0.908345i | \(-0.362653\pi\) | ||||
0.418222 | + | 0.908345i | \(0.362653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.3607 | −1.37782 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.3077 | 1.11285 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.07334 | −0.670455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.9962 | 0.906950 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.6577 | 1.52850 | 0.764251 | − | 0.644919i | \(-0.223109\pi\) | ||||
0.764251 | + | 0.644919i | \(0.223109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0737 | −1.71495 | −0.857477 | − | 0.514522i | \(-0.827969\pi\) | ||||
−0.857477 | + | 0.514522i | \(0.827969\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.12983 | −0.172187 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.96429 | 0.559385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4633 | −1.23410 | −0.617052 | − | 0.786922i | \(-0.711673\pi\) | ||||
−0.617052 | + | 0.786922i | \(0.711673\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.12239 | 0.168316 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.585017 | 0.0461058 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2557 | 1.19492 | 0.597458 | − | 0.801900i | \(-0.296177\pi\) | ||||
0.597458 | + | 0.801900i | \(0.296177\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.27526 | 0.722078 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.44396 | −0.343884 | −0.171942 | − | 0.985107i | \(-0.555004\pi\) | ||||
−0.171942 | + | 0.985107i | \(0.555004\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4775 | 0.805965 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.457036 | −0.0349504 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6175 | 0.959289 | 0.479645 | − | 0.877463i | \(-0.340766\pi\) | ||||
0.479645 | + | 0.877463i | \(0.340766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.166422 | −0.0125803 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.90932 | −0.669665 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.96773 | 0.221819 | 0.110909 | − | 0.993831i | \(-0.464624\pi\) | ||||
0.110909 | + | 0.993831i | \(0.464624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.3583 | −1.43889 | −0.719444 | − | 0.694550i | \(-0.755603\pi\) | ||||
−0.719444 | + | 0.694550i | \(0.755603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.37070 | −0.323091 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.4104 | 1.13299 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.7989 | −0.935947 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.78128 | 0.129569 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.02208 | 0.508100 | 0.254050 | − | 0.967191i | \(-0.418237\pi\) | ||||
0.254050 | + | 0.967191i | \(0.418237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4943 | −1.54719 | −0.773596 | − | 0.633679i | \(-0.781544\pi\) | ||||
−0.773596 | + | 0.633679i | \(0.781544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.3635 | 1.17181 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.72539 | 0.407917 | 0.203959 | − | 0.978980i | \(-0.434619\pi\) | ||||
0.203959 | + | 0.978980i | \(0.434619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6059 | 0.893608 | 0.446804 | − | 0.894632i | \(-0.352562\pi\) | ||||
0.446804 | + | 0.894632i | \(0.352562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.09314 | −0.641381 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.23178 | −0.0864538 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.14435 | 0.498983 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.827487 | −0.0575143 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.74648 | −0.189978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3083 | 0.847337 | 0.423669 | − | 0.905817i | \(-0.360742\pi\) | ||||
0.423669 | + | 0.905817i | \(0.360742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.919299 | 0.0629893 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.8327 | −1.07978 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.06257 | 0.0721316 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.6340 | 1.39431 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5799 | −1.51889 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.9471 | −0.733074 | −0.366537 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366537 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.235398 | 0.0156932 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5844 | −1.43261 | −0.716304 | − | 0.697789i | \(-0.754167\pi\) | ||||
−0.716304 | + | 0.697789i | \(0.754167\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.83177 | 0.451456 | 0.225728 | − | 0.974190i | \(-0.427524\pi\) | ||||
0.225728 | + | 0.974190i | \(0.427524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.41516 | 0.0931105 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.96517 | 0.521816 | 0.260908 | − | 0.965364i | \(-0.415978\pi\) | ||||
0.260908 | + | 0.965364i | \(0.415978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.7275 | 1.41735 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.59467 | 0.103585 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.5380 | −1.00507 | −0.502533 | − | 0.864558i | \(-0.667599\pi\) | ||||
−0.502533 | + | 0.864558i | \(0.667599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.188665 | 0.0121530 | 0.00607649 | − | 0.999982i | \(-0.498066\pi\) | ||||
0.00607649 | + | 0.999982i | \(0.498066\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.70601 | −0.301891 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.6033 | −0.932969 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.84536 | −0.308303 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.6116 | 0.925974 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9445 | 1.51136 | 0.755682 | − | 0.654939i | \(-0.227306\pi\) | ||||
0.755682 | + | 0.654939i | \(0.227306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.97265 | −0.312628 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −15.7378 | −0.985539 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.21562 | −0.325341 | −0.162671 | − | 0.986680i | \(-0.552011\pi\) | ||||
−0.162671 | + | 0.986680i | \(0.552011\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.35122 | 0.146097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.74231 | 0.107846 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.3965 | 1.56602 | 0.783008 | − | 0.622011i | \(-0.213684\pi\) | ||||
0.783008 | + | 0.622011i | \(0.213684\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.81860 | −0.173145 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.43706 | 0.516340 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5565 | −0.643641 | −0.321821 | − | 0.946801i | \(-0.604295\pi\) | ||||
−0.321821 | + | 0.946801i | \(0.604295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.38280 | −0.569964 | −0.284982 | − | 0.958533i | \(-0.591988\pi\) | ||||
−0.284982 | + | 0.958533i | \(0.591988\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.49663 | 0.151103 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41459 | 0.0853028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6843 | 0.702042 | 0.351021 | − | 0.936368i | \(-0.385835\pi\) | ||||
0.351021 | + | 0.936368i | \(0.385835\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50296 | −0.0899800 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.9348 | −1.36817 | −0.684087 | − | 0.729400i | \(-0.739799\pi\) | ||||
−0.684087 | + | 0.729400i | \(0.739799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.20607 | 0.0716936 | 0.0358468 | − | 0.999357i | \(-0.488587\pi\) | ||||
0.0358468 | + | 0.999357i | \(0.488587\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.37714 | −0.200044 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.09004 | 0.0643429 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.71650 | 0.277441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.0907 | 1.29498 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.3863 | −1.48308 | −0.741541 | − | 0.670908i | \(-0.765905\pi\) | ||||
−0.741541 | + | 0.670908i | \(0.765905\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.8319 | 0.688877 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.1409 | −0.878563 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.77278 | −0.507343 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.41565 | −0.139236 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.75523 | 0.560424 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.80443 | 0.332360 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.59655 | −0.0911202 | −0.0455601 | − | 0.998962i | \(-0.514507\pi\) | ||||
−0.0455601 | + | 0.998962i | \(0.514507\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.8467 | 0.844600 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.3100 | −1.32179 | −0.660893 | − | 0.750480i | \(-0.729822\pi\) | ||||
−0.660893 | + | 0.750480i | \(0.729822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3906 | −0.700356 | −0.350178 | − | 0.936683i | \(-0.613879\pi\) | ||||
−0.350178 | + | 0.936683i | \(0.613879\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.312742 | −0.0176210 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.44994 | 0.306099 | 0.153050 | − | 0.988219i | \(-0.451091\pi\) | ||||
0.153050 | + | 0.988219i | \(0.451091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4701 | 0.586214 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.05081 | 0.0586505 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.66010 | 0.259295 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.49562 | 0.138432 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.2032 | −0.785440 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31504 | 0.182764 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.97989 | 0.273720 | 0.136860 | − | 0.990590i | \(-0.456299\pi\) | ||||
0.136860 | + | 0.990590i | \(0.456299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.32572 | −0.182248 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0760 | 0.659781 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.12073 | 0.387891 | 0.193945 | − | 0.981012i | \(-0.437872\pi\) | ||||
0.193945 | + | 0.981012i | \(0.437872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.0844 | 1.25377 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.03182 | −0.489100 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.48988 | −0.242431 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.11448 | −0.329193 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.42469 | −0.237530 | −0.118765 | − | 0.992922i | \(-0.537893\pi\) | ||||
−0.118765 | + | 0.992922i | \(0.537893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.4416 | −1.41539 | −0.707694 | − | 0.706519i | \(-0.750264\pi\) | ||||
−0.707694 | + | 0.706519i | \(0.750264\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.7116 | −1.42576 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.8394 | −0.736599 | −0.368300 | − | 0.929707i | \(-0.620060\pi\) | ||||
−0.368300 | + | 0.929707i | \(0.620060\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.22086 | −0.0647964 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.40117 | −0.127083 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.3630 | 1.18027 | 0.590137 | − | 0.807303i | \(-0.299074\pi\) | ||||
0.590137 | + | 0.807303i | \(0.299074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.51249 | 0.289330 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.4026 | −1.43432 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.6459 | 1.07771 | 0.538854 | − | 0.842399i | \(-0.318858\pi\) | ||||
0.538854 | + | 0.842399i | \(0.318858\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.54182 | −0.0802640 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.430044 | −0.0223267 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.868107 | 0.0449489 | 0.0224745 | − | 0.999747i | \(-0.492846\pi\) | ||||
0.0224745 | + | 0.999747i | \(0.492846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.6251 | 0.961796 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.4715 | 0.951328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5120 | −1.31047 | −0.655233 | − | 0.755427i | \(-0.727429\pi\) | ||||
−0.655233 | + | 0.755427i | \(0.727429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.4114 | 0.840783 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.3575 | −1.19351 | −0.596756 | − | 0.802423i | \(-0.703544\pi\) | ||||
−0.596756 | + | 0.802423i | \(0.703544\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.87937 | −0.0957817 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.41685 | 0.173688 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.5571 | −0.890180 | −0.445090 | − | 0.895486i | \(-0.646828\pi\) | ||||
−0.445090 | + | 0.895486i | \(0.646828\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.43735 | 0.426695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.83759 | 0.0926941 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.11777 | −0.106557 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3117 | 1.42092 | 0.710462 | − | 0.703736i | \(-0.248486\pi\) | ||||
0.710462 | + | 0.703736i | \(0.248486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.515261 | −0.0257953 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9971 | 0.998607 | 0.499303 | − | 0.866427i | \(-0.333589\pi\) | ||||
0.499303 | + | 0.866427i | \(0.333589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.9340 | −0.793728 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.7139 | −0.780829 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.9854 | −0.990638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8900 | −0.835158 | −0.417579 | − | 0.908641i | \(-0.637121\pi\) | ||||
−0.417579 | + | 0.908641i | \(0.637121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.26780 | 0.259842 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.80523 | 0.0888294 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.4047 | −0.952539 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.7259 | −0.770099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.61500 | −0.420870 | −0.210435 | − | 0.977608i | \(-0.567488\pi\) | ||||
−0.210435 | + | 0.977608i | \(0.567488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.0975 | −1.17444 | −0.587221 | − | 0.809427i | \(-0.699778\pi\) | ||||
−0.587221 | + | 0.809427i | \(0.699778\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.68901 | −0.227988 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.40020 | −0.116427 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.885601 | 0.0428572 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.2214 | −1.02458 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.64339 | −0.0791594 | −0.0395797 | − | 0.999216i | \(-0.512602\pi\) | ||||
−0.0395797 | + | 0.999216i | \(0.512602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.6046 | −1.61493 | −0.807466 | − | 0.589914i | \(-0.799162\pi\) | ||||
−0.807466 | + | 0.589914i | \(0.799162\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8743 | 0.617275 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.81055 | 0.0866105 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.6851 | −0.987244 | −0.493622 | − | 0.869677i | \(-0.664327\pi\) | ||||
−0.493622 | + | 0.869677i | \(0.664327\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15153 | 0.150073 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.89239 | −0.422490 | −0.211245 | − | 0.977433i | \(-0.567752\pi\) | ||||
−0.211245 | + | 0.977433i | \(0.567752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.2047 | −0.531153 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.7529 | −1.40726 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.4988 | −1.15617 | −0.578086 | − | 0.815976i | \(-0.696200\pi\) | ||||
−0.578086 | + | 0.815976i | \(0.696200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.26534 | −0.436288 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.6056 | 1.57893 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.31560 | −0.155438 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.44191 | 0.0674497 | 0.0337249 | − | 0.999431i | \(-0.489263\pi\) | ||||
0.0337249 | + | 0.999431i | \(0.489263\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.6903 | 1.19912 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.91043 | 0.228702 | 0.114351 | − | 0.993440i | \(-0.463521\pi\) | ||||
0.114351 | + | 0.993440i | \(0.463521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5919 | 1.00346 | 0.501730 | − | 0.865024i | \(-0.332697\pi\) | ||||
0.501730 | + | 0.865024i | \(0.332697\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.1057 | −0.515016 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.06547 | −0.419500 | −0.209750 | − | 0.977755i | \(-0.567265\pi\) | ||||
−0.209750 | + | 0.977755i | \(0.567265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.84247 | 0.0850775 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.6588 | 1.13622 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.5330 | 0.944110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.515054 | −0.0236323 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.608282 | 0.0278513 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.3371 | −1.11199 | −0.555995 | − | 0.831186i | \(-0.687663\pi\) | ||||
−0.555995 | + | 0.831186i | \(0.687663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −35.2583 | −1.60764 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.932907 | −0.0424488 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.3372 | −1.33213 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.4169 | −1.87678 | −0.938389 | − | 0.345580i | \(-0.887682\pi\) | ||||
−0.938389 | + | 0.345580i | \(0.887682\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.3277 | −1.10014 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5948 | −0.748915 | −0.374457 | − | 0.927244i | \(-0.622171\pi\) | ||||
−0.374457 | + | 0.927244i | \(0.622171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.7652 | −0.800104 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.65831 | 0.119482 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.186270 | −0.00835537 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.9869 | −1.25287 | −0.626434 | − | 0.779475i | \(-0.715486\pi\) | ||||
−0.626434 | + | 0.779475i | \(0.715486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.08665 | 0.316608 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.84514 | 0.171447 | 0.0857233 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857233 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9553 | −0.576502 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.7082 | −0.742037 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.0894 | 0.801800 | 0.400900 | − | 0.916122i | \(-0.368697\pi\) | ||||
0.400900 | + | 0.916122i | \(0.368697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.18090 | −0.184952 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.51282 | 0.243397 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.7169 | −0.868830 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.1779 | −1.23926 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.1207 | −0.883200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.5432 | 1.16288 | 0.581439 | − | 0.813590i | \(-0.302490\pi\) | ||||
0.581439 | + | 0.813590i | \(0.302490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0736 | −0.527942 | −0.263971 | − | 0.964531i | \(-0.585032\pi\) | ||||
−0.263971 | + | 0.964531i | \(0.585032\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.265387 | 0.0115824 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.3247 | 0.667556 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7219 | −0.857474 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.55343 | −0.110809 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3460 | −0.708022 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.39551 | −0.0603332 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.73255 | −0.204225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.9386 | 0.815745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.21111 | 0.267036 | 0.133518 | − | 0.991046i | \(-0.457373\pi\) | ||||
0.133518 | + | 0.991046i | \(0.457373\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.8700 | 1.32476 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.8623 | 0.807974 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.17549 | 0.0930172 | 0.0465086 | − | 0.998918i | \(-0.485191\pi\) | ||||
0.0465086 | + | 0.998918i | \(0.485191\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.25265 | −0.0534619 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.81219 | −0.162405 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.323115 | −0.0137403 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.5745 | −1.04313 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3130 | 1.24203 | 0.621016 | − | 0.783798i | \(-0.286720\pi\) | ||||
0.621016 | + | 0.783798i | \(0.286720\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.2245 | 1.53213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.4100 | 0.861709 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.6181 | −1.45898 | −0.729490 | − | 0.683992i | \(-0.760242\pi\) | ||||
−0.729490 | + | 0.683992i | \(0.760242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.6569 | −1.28974 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.39752 | −0.100686 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.81835 | −0.243918 | −0.121959 | − | 0.992535i | \(-0.538918\pi\) | ||||
−0.121959 | + | 0.992535i | \(0.538918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.46730 | 0.354346 | 0.177173 | − | 0.984180i | \(-0.443305\pi\) | ||||
0.177173 | + | 0.984180i | \(0.443305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.1979 | −0.467798 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.932531 | −0.0388892 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.68430 | 0.278271 | 0.139135 | − | 0.990273i | \(-0.455568\pi\) | ||||
0.139135 | + | 0.990273i | \(0.455568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.2762 | 1.42447 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.96064 | −0.122828 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.65538 | 0.151390 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.68981 | 0.193900 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.0857 | 1.03540 | 0.517699 | − | 0.855563i | \(-0.326789\pi\) | ||||
0.517699 | + | 0.855563i | \(0.326789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.28850 | 0.135500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.13009 | −0.375562 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.566761 | −0.0232741 | −0.0116370 | − | 0.999932i | \(-0.503704\pi\) | ||||
−0.0116370 | + | 0.999932i | \(0.503704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.18883 | 0.130729 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.1022 | −0.822728 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5388 | −0.512320 | −0.256160 | − | 0.966634i | \(-0.582457\pi\) | ||||
−0.256160 | + | 0.966634i | \(0.582457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.16822 | 0.292398 | 0.146199 | − | 0.989255i | \(-0.453296\pi\) | ||||
0.146199 | + | 0.989255i | \(0.453296\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.60612 | −0.106129 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.32076 | −0.297631 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.4870 | 1.60273 | 0.801363 | − | 0.598178i | \(-0.204109\pi\) | ||||
0.801363 | + | 0.598178i | \(0.204109\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.96427 | 0.0795964 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.7116 | −2.01112 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.66030 | −0.228617 | −0.114309 | − | 0.993445i | \(-0.536465\pi\) | ||||
−0.114309 | + | 0.993445i | \(0.536465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.3929 | −0.459405 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.2467 | 1.53975 | 0.769876 | − | 0.638193i | \(-0.220318\pi\) | ||||
0.769876 | + | 0.638193i | \(0.220318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2732 | 0.855040 | 0.427520 | − | 0.904006i | \(-0.359387\pi\) | ||||
0.427520 | + | 0.904006i | \(0.359387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.98125 | 0.400534 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.70954 | −0.0684911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.1595 | −0.886378 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.37973 | 0.174910 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.9102 | 1.35209 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.4546 | 1.49104 | 0.745522 | − | 0.666481i | \(-0.232200\pi\) | ||||
0.745522 | + | 0.666481i | \(0.232200\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.6276 | −0.780128 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.7949 | −0.864904 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.4117 | 1.32382 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.263473 | 0.0104228 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.8514 | −0.665591 | −0.332795 | − | 0.942999i | \(-0.607992\pi\) | ||||
−0.332795 | + | 0.942999i | \(0.607992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.0714 | 1.22534 | 0.612668 | − | 0.790340i | \(-0.290096\pi\) | ||||
0.612668 | + | 0.790340i | \(0.290096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.2479 | 0.994134 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.7376 | 1.56224 | 0.781122 | − | 0.624378i | \(-0.214647\pi\) | ||||
0.781122 | + | 0.624378i | \(0.214647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.3444 | −0.602322 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.69444 | −0.0664103 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.6653 | −1.20002 | −0.600012 | − | 0.799991i | \(-0.704838\pi\) | ||||
−0.600012 | + | 0.799991i | \(0.704838\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.44038 | −0.0953534 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.91374 | 0.230717 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.5922 | −1.15275 | −0.576374 | − | 0.817186i | \(-0.695533\pi\) | ||||
−0.576374 | + | 0.817186i | \(0.695533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.6256 | −0.996719 | −0.498359 | − | 0.866971i | \(-0.666064\pi\) | ||||
−0.498359 | + | 0.866971i | \(0.666064\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.0074 | 1.39841 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.684283 | 0.0265354 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.90217 | −0.267253 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.4570 | 0.674928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.52762 | −0.290601 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.9893 | −1.96549 | −0.982746 | − | 0.184959i | \(-0.940785\pi\) | ||||
−0.982746 | + | 0.184959i | \(0.940785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.83940 | −0.109289 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.80318 | 0.261467 | 0.130734 | − | 0.991418i | \(-0.458267\pi\) | ||||
0.130734 | + | 0.991418i | \(0.458267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.47608 | −0.171776 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.4199 | 1.31898 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.1993 | 1.42339 | 0.711696 | − | 0.702488i | \(-0.247927\pi\) | ||||
0.711696 | + | 0.702488i | \(0.247927\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.99581 | −0.267296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.8944 | −0.415647 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.44884 | 0.245681 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2064 | 1.03498 | 0.517491 | − | 0.855689i | \(-0.326866\pi\) | ||||
0.517491 | + | 0.855689i | \(0.326866\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.405587 | 0.0154070 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.8844 | 0.792192 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7210 | 0.595474 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.7018 | −0.480426 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.6399 | −1.91264 | −0.956321 | − | 0.292320i | \(-0.905573\pi\) | ||||
−0.956321 | + | 0.292320i | \(0.905573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.27671 | 0.274446 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.6482 | −1.30493 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.97663 | −0.0743387 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.84863 | 0.294761 | 0.147381 | − | 0.989080i | \(-0.452916\pi\) | ||||
0.147381 | + | 0.989080i | \(0.452916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.457036 | 0.0171402 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.95401 | 0.222979 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.1827 | 1.05397 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.7779 | 0.925347 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2128 | −0.679222 | −0.339611 | − | 0.940566i | \(-0.610295\pi\) | ||||
−0.339611 | + | 0.940566i | \(0.610295\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00827 | −0.112034 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.300858 | −0.0111890 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.96348 | 0.0729219 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.3058 | −0.382221 | −0.191110 | − | 0.981569i | \(-0.561209\pi\) | ||||
−0.191110 | + | 0.981569i | \(0.561209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.7646 | 1.10239 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.8394 | −1.28858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.1499 | −0.965868 | −0.482934 | − | 0.875657i | \(-0.660429\pi\) | ||||
−0.482934 | + | 0.875657i | \(0.660429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.2874 | 0.858968 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.6611 | −0.576882 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.2626 | 1.03966 | 0.519829 | − | 0.854270i | \(-0.325996\pi\) | ||||
0.519829 | + | 0.854270i | \(0.325996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.72674 | 0.283849 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.8847 | 1.75672 | 0.878359 | − | 0.478001i | \(-0.158638\pi\) | ||||
0.878359 | + | 0.478001i | \(0.158638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.5128 | 1.44764 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.18773 | 0.153221 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.212918 | −0.00777984 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.6887 | 1.01037 | 0.505187 | − | 0.863010i | \(-0.331424\pi\) | ||||
0.505187 | + | 0.863010i | \(0.331424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −38.1835 | −1.39148 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.6293 | −1.62422 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.4259 | 1.43296 | 0.716479 | − | 0.697609i | \(-0.245753\pi\) | ||||
0.716479 | + | 0.697609i | \(0.245753\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.92973 | 0.287831 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3218 | −1.13541 | −0.567707 | − | 0.823231i | \(-0.692169\pi\) | ||||
−0.567707 | + | 0.823231i | \(0.692169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.87789 | 0.104187 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.51049 | −0.163077 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.0708 | −0.977469 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.33522 | 0.300576 | 0.150288 | − | 0.988642i | \(-0.451980\pi\) | ||||
0.150288 | + | 0.988642i | \(0.451980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.31718 | 0.299536 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.92025 | 0.356807 | 0.178403 | − | 0.983957i | \(-0.442907\pi\) | ||||
0.178403 | + | 0.983957i | \(0.442907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.69375 | −0.0608415 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.74941 | −0.134509 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.37353 | 0.120869 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.58330 | 0.0566550 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.0159 | −0.751048 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.7476 | −1.16881 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.203720 | 0.00726184 | 0.00363092 | − | 0.999993i | \(-0.498844\pi\) | ||||
0.00363092 | + | 0.999993i | \(0.498844\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40.4990 | −1.44180 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.67742 | −0.166310 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2803 | −0.471596 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.49473 | 0.159412 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.3088 | 0.400577 | 0.200288 | − | 0.979737i | \(-0.435812\pi\) | ||||
0.200288 | + | 0.979737i | \(0.435812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.8108 | 1.69143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.41808 | 0.0854387 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.5377 | 1.25410 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.23893 | 0.0436666 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.8341 | 0.592589 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.84585 | −0.100055 | −0.0500274 | − | 0.998748i | \(-0.515931\pi\) | ||||
−0.0500274 | + | 0.998748i | \(0.515931\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1837 | −0.743859 | −0.371930 | − | 0.928261i | \(-0.621304\pi\) | ||||
−0.371930 | + | 0.928261i | \(0.621304\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.9624 | 0.524756 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.3080 | 1.13170 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.47612 | −0.261556 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.715540 | 0.0250030 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.7164 | 1.17671 | 0.588355 | − | 0.808603i | \(-0.299776\pi\) | ||||
0.588355 | + | 0.808603i | \(0.299776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6129 | 0.823093 | 0.411547 | − | 0.911389i | \(-0.364989\pi\) | ||||
0.411547 | + | 0.911389i | \(0.364989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.25580 | −0.0785367 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.3631 | 0.569000 | 0.284500 | − | 0.958676i | \(-0.408172\pi\) | ||||
0.284500 | + | 0.958676i | \(0.408172\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.67950 | −0.127794 | −0.0638971 | − | 0.997956i | \(-0.520353\pi\) | ||||
−0.0638971 | + | 0.997956i | \(0.520353\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.6326 | −0.646358 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32.1341 | −1.11338 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.41129 | −0.325691 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.1289 | 0.626627 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.1408 | −1.90367 | −0.951835 | − | 0.306610i | \(-0.900805\pi\) | ||||
−0.951835 | + | 0.306610i | \(0.900805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4672 | −0.498869 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 36.5733 | 1.25965 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.1890 | 0.763325 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.11695 | −0.0383789 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.92329 | −0.0660070 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1749 | 0.451629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.6120 | 1.04813 | 0.524067 | − | 0.851677i | \(-0.324414\pi\) | ||||
0.524067 | + | 0.851677i | \(0.324414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.967896 | −0.0331013 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.3005 | 1.13752 | 0.568762 | − | 0.822502i | \(-0.307422\pi\) | ||||
0.568762 | + | 0.822502i | \(0.307422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.33281 | 0.181953 | 0.0909765 | − | 0.995853i | \(-0.471001\pi\) | ||||
0.0909765 | + | 0.995853i | \(0.471001\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.73825 | −0.0592393 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.8075 | 1.52527 | 0.762633 | − | 0.646831i | \(-0.223906\pi\) | ||||
0.762633 | + | 0.646831i | \(0.223906\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.7209 | 0.908538 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.52126 | −0.255435 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.74648 | 0.0931681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.6293 | −0.936184 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.33126 | 0.214281 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.77386 | −0.127580 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.94902 | 0.234652 | 0.117326 | − | 0.993093i | \(-0.462568\pi\) | ||||
0.117326 | + | 0.993093i | \(0.462568\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40.4826 | 1.36545 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5697 | 0.423484 | 0.211742 | − | 0.977326i | \(-0.432086\pi\) | ||||
0.211742 | + | 0.977326i | \(0.432086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.4749 | 0.487120 | 0.243560 | − | 0.969886i | \(-0.421685\pi\) | ||||
0.243560 | + | 0.969886i | \(0.421685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.8679 | −0.634237 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.66035 | 0.257209 | 0.128605 | − | 0.991696i | \(-0.458950\pi\) | ||||
0.128605 | + | 0.991696i | \(0.458950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.32532 | −0.111528 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20.3789 | 0.682720 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.2596 | 0.343325 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.28498 | 0.210084 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.9897 | 0.467101 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.5364 | −0.418112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.20226 | −0.206627 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.85215 | 0.128192 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.9963 | −1.36276 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.9321 | 0.661834 | 0.330917 | − | 0.943660i | \(-0.392642\pi\) | ||||
0.330917 | + | 0.943660i | \(0.392642\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.79587 | 0.0927333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.4198 | 0.775932 | 0.387966 | − | 0.921674i | \(-0.373178\pi\) | ||||
0.387966 | + | 0.921674i | \(0.373178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1655 | 0.832856 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.25613 | −0.305998 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.372336 | −0.0122956 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.6098 | −0.448945 | −0.224473 | − | 0.974480i | \(-0.572066\pi\) | ||||
−0.224473 | + | 0.974480i | \(0.572066\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.54597 | 0.0838927 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.79327 | 0.0919416 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.74790 | −0.123230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.25510 | 0.139756 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.8982 | 0.357557 | 0.178778 | − | 0.983889i | \(-0.442785\pi\) | ||||
0.178778 | + | 0.983889i | \(0.442785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.89560 | −0.225994 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.1716 | 1.21694 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.1051 | −0.886431 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.35143 | −0.305498 | −0.152749 | − | 0.988265i | \(-0.548813\pi\) | ||||
−0.152749 | + | 0.988265i | \(0.548813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.7588 | 0.644805 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1171 | 1.14478 | 0.572392 | − | 0.819980i | \(-0.306016\pi\) | ||||
0.572392 | + | 0.819980i | \(0.306016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.10795 | 0.198902 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.77233 | 0.122714 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −58.1433 | −1.88940 | −0.944702 | − | 0.327931i | \(-0.893649\pi\) | ||||
−0.944702 | + | 0.327931i | \(0.893649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.6958 | 2.03519 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.69084 | −0.281820 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.7717 | −1.15876 | −0.579380 | − | 0.815057i | \(-0.696705\pi\) | ||||
−0.579380 | + | 0.815057i | \(0.696705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.8711 | 0.481219 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.6964 | −0.539717 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.06737 | −0.0344673 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1858 | −0.651153 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.301165 | 0.00970490 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45.5199 | −1.46534 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.78169 | 0.0894530 | 0.0447265 | − | 0.998999i | \(-0.485758\pi\) | ||||
0.0447265 | + | 0.998999i | \(0.485758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.43131 | −0.238728 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.7553 | −1.46836 | −0.734179 | − | 0.678956i | \(-0.762432\pi\) | ||||
−0.734179 | + | 0.678956i | \(0.762432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.18641 | 0.102152 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.97969 | −0.127452 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.78690 | 0.0891607 | 0.0445804 | − | 0.999006i | \(-0.485805\pi\) | ||||
0.0445804 | + | 0.999006i | \(0.485805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.5311 | 0.464415 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.07068 | −0.129967 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5512 | 0.719272 | 0.359636 | − | 0.933093i | \(-0.382901\pi\) | ||||
0.359636 | + | 0.933093i | \(0.382901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1251 | 0.386336 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.28639 | −0.168268 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.5359 | −0.430417 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.8924 | −0.695437 | −0.347718 | − | 0.937599i | \(-0.613043\pi\) | ||||
−0.347718 | + | 0.937599i | \(0.613043\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.94127 | −0.252009 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.6964 | 0.846332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0148 | −1.04559 | −0.522795 | − | 0.852459i | \(-0.675111\pi\) | ||||
−0.522795 | + | 0.852459i | \(0.675111\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.1152 | 1.26919 |
(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 | 6004.2.a.g.1.9 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.9 | ✓ | 27 | 1.1 | even | 1 | trivial |