Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −1.49682 | −0.864191 | −0.432095 | − | 0.901828i | \(-0.642226\pi\) | ||||
−0.432095 | + | 0.901828i | \(0.642226\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.87951 | 0.840542 | 0.420271 | − | 0.907399i | \(-0.361935\pi\) | ||||
0.420271 | + | 0.907399i | \(0.361935\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.30247 | 0.870252 | 0.435126 | − | 0.900369i | \(-0.356704\pi\) | ||||
0.435126 | + | 0.900369i | \(0.356704\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.759523 | −0.253174 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.81852 | −0.548304 | −0.274152 | − | 0.961686i | \(-0.588397\pi\) | ||||
−0.274152 | + | 0.961686i | \(0.588397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.96322 | −1.37655 | −0.688275 | − | 0.725450i | \(-0.741632\pi\) | ||||
−0.688275 | + | 0.725450i | \(0.741632\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.81329 | −0.726388 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.03255 | 0.250430 | 0.125215 | − | 0.992130i | \(-0.460038\pi\) | ||||
0.125215 | + | 0.992130i | \(0.460038\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.211334 | 0.0484833 | 0.0242416 | − | 0.999706i | \(-0.492283\pi\) | ||||
0.0242416 | + | 0.999706i | \(0.492283\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.44639 | −0.752064 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.11965 | 0.441978 | 0.220989 | − | 0.975276i | \(-0.429071\pi\) | ||||
0.220989 | + | 0.975276i | \(0.429071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.46745 | −0.293490 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.62734 | 1.08298 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.54249 | 1.40060 | 0.700302 | − | 0.713846i | \(-0.253049\pi\) | ||||
0.700302 | + | 0.713846i | \(0.253049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.90121 | −0.700678 | −0.350339 | − | 0.936623i | \(-0.613934\pi\) | ||||
−0.350339 | + | 0.936623i | \(0.613934\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.72200 | 0.473839 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.32751 | 0.731483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5396 | 1.73269 | 0.866346 | − | 0.499444i | \(-0.166462\pi\) | ||||
0.866346 | + | 0.499444i | \(0.166462\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.42906 | 1.18960 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1358 | −1.73911 | −0.869557 | − | 0.493832i | \(-0.835596\pi\) | ||||
−0.869557 | + | 0.493832i | \(0.835596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.93637 | −0.752789 | −0.376395 | − | 0.926459i | \(-0.622836\pi\) | ||||
−0.376395 | + | 0.926459i | \(0.622836\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.42753 | −0.212803 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.06298 | 0.300916 | 0.150458 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150458 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.69862 | −0.242661 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.54555 | −0.216420 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.55722 | 0.625983 | 0.312991 | − | 0.949756i | \(-0.398669\pi\) | ||||
0.312991 | + | 0.949756i | \(0.398669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.41792 | −0.460872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.316329 | −0.0418988 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.41153 | −0.704521 | −0.352261 | − | 0.935902i | \(-0.614587\pi\) | ||||
−0.352261 | + | 0.935902i | \(0.614587\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.16675 | −0.917608 | −0.458804 | − | 0.888537i | \(-0.651722\pi\) | ||||
−0.458804 | + | 0.888537i | \(0.651722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.74878 | −0.220326 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.32841 | −1.15705 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.79698 | 0.952553 | 0.476276 | − | 0.879296i | \(-0.341986\pi\) | ||||
0.476276 | + | 0.879296i | \(0.341986\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.17275 | −0.381954 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2725 | −1.21913 | −0.609563 | − | 0.792738i | \(-0.708655\pi\) | ||||
−0.609563 | + | 0.792738i | \(0.708655\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.64668 | 0.309770 | 0.154885 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154885 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.19651 | 0.253631 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.18709 | −0.477163 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.66642 | 0.975049 | 0.487524 | − | 0.873109i | \(-0.337900\pi\) | ||||
0.487524 | + | 0.873109i | \(0.337900\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.14456 | −0.682729 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.364424 | 0.0400007 | 0.0200004 | − | 0.999800i | \(-0.493633\pi\) | ||||
0.0200004 | + | 0.999800i | \(0.493633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.94069 | 0.210497 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.2898 | −1.21039 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.80388 | 0.403211 | 0.201605 | − | 0.979467i | \(-0.435384\pi\) | ||||
0.201605 | + | 0.979467i | \(0.435384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4277 | −1.19795 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.83942 | 0.605520 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.397203 | 0.0407522 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0091 | −1.01627 | −0.508136 | − | 0.861277i | \(-0.669665\pi\) | ||||
−0.508136 | + | 0.861277i | \(0.669665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.38121 | 0.138816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9333 | −1.68492 | −0.842462 | − | 0.538755i | \(-0.818895\pi\) | ||||
−0.842462 | + | 0.538755i | \(0.818895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.03161 | 0.594313 | 0.297156 | − | 0.954829i | \(-0.403962\pi\) | ||||
0.297156 | + | 0.954829i | \(0.403962\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.47752 | −0.632141 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.91465 | −0.475117 | −0.237559 | − | 0.971373i | \(-0.576347\pi\) | ||||
−0.237559 | + | 0.971373i | \(0.576347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.8000 | −1.32180 | −0.660900 | − | 0.750474i | \(-0.729825\pi\) | ||||
−0.660900 | + | 0.750474i | \(0.729825\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.7758 | −1.49738 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.4824 | −1.17425 | −0.587125 | − | 0.809496i | \(-0.699740\pi\) | ||||
−0.587125 | + | 0.809496i | \(0.699740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.98391 | 0.371501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.76968 | 0.348507 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.37742 | 0.217938 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.69299 | −0.699363 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.6683 | 1.50293 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1556 | −1.08723 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6773 | 1.30240 | 0.651198 | − | 0.758908i | \(-0.274267\pi\) | ||||
0.651198 | + | 0.758908i | \(0.274267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.38887 | 0.650554 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.8734 | −1.73635 | −0.868175 | − | 0.496258i | \(-0.834707\pi\) | ||||
−0.868175 | + | 0.496258i | \(0.834707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.486590 | 0.0421927 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.5766 | 0.910291 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.30484 | 0.196916 | 0.0984581 | − | 0.995141i | \(-0.468609\pi\) | ||||
0.0984581 | + | 0.995141i | \(0.468609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.62987 | −0.392700 | −0.196350 | − | 0.980534i | \(-0.562909\pi\) | ||||
−0.196350 | + | 0.980534i | \(0.562909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.08791 | −0.260049 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.02571 | 0.754767 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1762 | 1.17727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.54254 | 0.209705 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.49152 | −0.695653 | −0.347826 | − | 0.937559i | \(-0.613080\pi\) | ||||
−0.347826 | + | 0.937559i | \(0.613080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2841 | 1.32518 | 0.662589 | − | 0.748983i | \(-0.269458\pi\) | ||||
0.662589 | + | 0.748983i | \(0.269458\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.784246 | −0.0634025 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.33236 | −0.588949 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.61317 | 0.128745 | 0.0643724 | − | 0.997926i | \(-0.479495\pi\) | ||||
0.0643724 | + | 0.997926i | \(0.479495\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.82136 | −0.540969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.88044 | 0.384633 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.62402 | −0.205529 | −0.102765 | − | 0.994706i | \(-0.532769\pi\) | ||||
−0.102765 | + | 0.994706i | \(0.532769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.11602 | 0.398281 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.84363 | 0.452194 | 0.226097 | − | 0.974105i | \(-0.427403\pi\) | ||||
0.226097 | + | 0.974105i | \(0.427403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6336 | 0.894890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.160513 | −0.0122747 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.89953 | −0.372504 | −0.186252 | − | 0.982502i | \(-0.559634\pi\) | ||||
−0.186252 | + | 0.982502i | \(0.559634\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37876 | −0.255410 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.10010 | 0.608841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.08895 | 0.679340 | 0.339670 | − | 0.940545i | \(-0.389685\pi\) | ||||
0.339670 | + | 0.940545i | \(0.389685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.30310 | −0.691494 | −0.345747 | − | 0.938328i | \(-0.612374\pi\) | ||||
−0.345747 | + | 0.938328i | \(0.612374\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7274 | 0.792989 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.8092 | 1.45640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.87771 | −0.137312 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.9568 | 0.942467 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2390 | 1.60916 | 0.804578 | − | 0.593847i | \(-0.202392\pi\) | ||||
0.804578 | + | 0.593847i | \(0.202392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.87845 | −0.279177 | −0.139589 | − | 0.990210i | \(-0.544578\pi\) | ||||
−0.139589 | + | 0.990210i | \(0.544578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.9630 | 0.999910 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.0630 | −1.71442 | −0.857208 | − | 0.514970i | \(-0.827803\pi\) | ||||
−0.857208 | + | 0.514970i | \(0.827803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.74164 | 0.690567 | 0.345283 | − | 0.938499i | \(-0.387783\pi\) | ||||
0.345283 | + | 0.938499i | \(0.387783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6707 | −0.823187 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.3664 | 1.21888 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.9298 | −1.46180 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.60993 | −0.111898 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.384314 | −0.0265836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.04372 | 0.416067 | 0.208033 | − | 0.978122i | \(-0.433294\pi\) | ||||
0.208033 | + | 0.978122i | \(0.433294\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.3762 | 1.05356 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.27795 | −0.632751 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.98243 | −0.609767 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.96161 | −0.267701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.12478 | −0.344730 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.91855 | −0.664195 | −0.332098 | − | 0.943245i | \(-0.607756\pi\) | ||||
−0.332098 | + | 0.943245i | \(0.607756\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.11456 | 0.0743041 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.628770 | −0.0417329 | −0.0208665 | − | 0.999782i | \(-0.506642\pi\) | ||||
−0.0208665 | + | 0.999782i | \(0.506642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.48054 | −0.362165 | −0.181082 | − | 0.983468i | \(-0.557960\pi\) | ||||
−0.181082 | + | 0.983468i | \(0.557960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.26732 | 0.412360 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.71906 | −0.571205 | −0.285602 | − | 0.958348i | \(-0.592194\pi\) | ||||
−0.285602 | + | 0.958348i | \(0.592194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.87738 | 0.252932 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.9721 | −0.842628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.4782 | 1.51868 | 0.759339 | − | 0.650696i | \(-0.225523\pi\) | ||||
0.759339 | + | 0.650696i | \(0.225523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.8821 | −1.73163 | −0.865814 | − | 0.500365i | \(-0.833199\pi\) | ||||
−0.865814 | + | 0.500365i | \(0.833199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.68470 | −0.492974 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.19258 | −0.203966 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.04890 | −0.0667397 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.545478 | −0.0345683 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0907 | −1.70995 | −0.854976 | − | 0.518668i | \(-0.826428\pi\) | ||||
−0.854976 | + | 0.518668i | \(0.826428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.85463 | −0.242338 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.90486 | −0.181910 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.43819 | 0.401603 | 0.200802 | − | 0.979632i | \(-0.435645\pi\) | ||||
0.200802 | + | 0.979632i | \(0.435645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.2670 | 1.50788 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.72869 | −0.354597 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.30854 | 0.389001 | 0.194501 | − | 0.980902i | \(-0.437691\pi\) | ||||
0.194501 | + | 0.980902i | \(0.437691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.56534 | 0.526165 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.69374 | −0.348451 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.3832 | 0.755016 | 0.377508 | − | 0.926006i | \(-0.376781\pi\) | ||||
0.377508 | + | 0.926006i | \(0.376781\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1618 | 0.921014 | 0.460507 | − | 0.887656i | \(-0.347668\pi\) | ||||
0.460507 | + | 0.887656i | \(0.347668\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.1052 | 1.03525 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.66858 | 0.160922 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4839 | 0.930336 | 0.465168 | − | 0.885222i | \(-0.345994\pi\) | ||||
0.465168 | + | 0.885222i | \(0.345994\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.96306 | 0.177394 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 33.3368 | 1.98871 | 0.994354 | − | 0.106113i | \(-0.0338405\pi\) | ||||
0.994354 | + | 0.106113i | \(0.0338405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.4421 | −0.917936 | −0.458968 | − | 0.888453i | \(-0.651781\pi\) | ||||
−0.458968 | + | 0.888453i | \(0.651781\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.594543 | −0.0352177 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.6398 | −1.51347 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9338 | −0.937285 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.9819 | 0.878253 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.03694 | −0.0605789 | −0.0302894 | − | 0.999541i | \(-0.509643\pi\) | ||||
−0.0302894 | + | 0.999541i | \(0.509643\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1710 | −0.592179 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.2334 | −0.593803 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5203 | −0.608405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3659 | −0.655117 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.3461 | 1.45610 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.4700 | −0.771288 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5339 | −0.886566 | −0.443283 | − | 0.896382i | \(-0.646186\pi\) | ||||
−0.443283 | + | 0.896382i | \(0.646186\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.02826 | −0.513599 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4895 | −1.21856 | −0.609278 | − | 0.792957i | \(-0.708541\pi\) | ||||
−0.609278 | + | 0.792957i | \(0.708541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.75177 | −0.438156 | −0.219078 | − | 0.975707i | \(-0.570305\pi\) | ||||
−0.219078 | + | 0.975707i | \(0.570305\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.28685 | −0.185193 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.2968 | −1.81397 | −0.906985 | − | 0.421162i | \(-0.861622\pi\) | ||||
−0.906985 | + | 0.421162i | \(0.861622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.7161 | −0.767957 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.35636 | 0.410592 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.218213 | 0.0121417 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.28328 | 0.404004 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.6561 | 1.14229 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.74995 | 0.261873 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.23607 | 0.232835 | 0.116418 | − | 0.993200i | \(-0.462859\pi\) | ||||
0.116418 | + | 0.993200i | \(0.462859\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00504 | −0.438673 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.6545 | 0.800660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.7445 | −0.857656 | −0.428828 | − | 0.903386i | \(-0.641073\pi\) | ||||
−0.428828 | + | 0.903386i | \(0.641073\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6840 | 1.01478 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.09442 | 0.384185 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0283 | −1.08143 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.96320 | −0.321048 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0116 | −0.805865 | −0.402933 | − | 0.915230i | \(-0.632009\pi\) | ||||
−0.402933 | + | 0.915230i | \(0.632009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.64527 | −0.195127 | −0.0975634 | − | 0.995229i | \(-0.531105\pi\) | ||||
−0.0975634 | + | 0.995229i | \(0.531105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.9297 | −1.49078 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.58183 | −0.137417 | −0.0687085 | − | 0.997637i | \(-0.521888\pi\) | ||||
−0.0687085 | + | 0.997637i | \(0.521888\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.3073 | −1.02473 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.55857 | −0.188340 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.76422 | 0.304224 | 0.152112 | − | 0.988363i | \(-0.451393\pi\) | ||||
0.152112 | + | 0.988363i | \(0.451393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9553 | −0.997649 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.5150 | 0.604383 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.97445 | 0.260375 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.6408 | 0.659842 | 0.329921 | − | 0.944009i | \(-0.392978\pi\) | ||||
0.329921 | + | 0.944009i | \(0.392978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.45787 | 0.440299 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.4929 | 0.544763 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.87581 | −0.407794 | −0.203897 | − | 0.978992i | \(-0.565361\pi\) | ||||
−0.203897 | + | 0.978992i | \(0.565361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.1948 | 0.939576 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.4350 | −1.92800 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.4837 | −1.66858 | −0.834288 | − | 0.551328i | \(-0.814121\pi\) | ||||
−0.834288 | + | 0.551328i | \(0.814121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.9693 | −1.12552 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.05717 | 0.156214 | 0.0781071 | − | 0.996945i | \(-0.475112\pi\) | ||||
0.0781071 | + | 0.996945i | \(0.475112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.86966 | −0.401075 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.74929 | 0.190587 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.07254 | 0.206486 | 0.103243 | − | 0.994656i | \(-0.467078\pi\) | ||||
0.103243 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.18865 | 0.110685 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.7470 | 1.50054 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.2886 | 0.819569 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.6198 | −0.532992 | −0.266496 | − | 0.963836i | \(-0.585866\pi\) | ||||
−0.266496 | + | 0.963836i | \(0.585866\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.728339 | −0.0364625 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1659 | 0.857223 | 0.428612 | − | 0.903489i | \(-0.359003\pi\) | ||||
0.428612 | + | 0.903489i | \(0.359003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.3626 | 0.964519 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.5487 | −0.573862 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.1664 | −0.950042 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.69622 | −0.331107 | −0.165553 | − | 0.986201i | \(-0.552941\pi\) | ||||
−0.165553 | + | 0.986201i | \(0.552941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.44994 | −0.170173 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.4599 | −0.613111 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.684938 | 0.0336223 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.93009 | 0.339368 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.0554 | −1.51716 | −0.758579 | − | 0.651581i | \(-0.774106\pi\) | ||||
−0.758579 | + | 0.651581i | \(0.774106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.45632 | 0.363399 | 0.181699 | − | 0.983354i | \(-0.441840\pi\) | ||||
0.181699 | + | 0.983354i | \(0.441840\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.56688 | −0.0761842 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.51522 | −0.0734988 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.5012 | −0.798551 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.5099 | −0.652263 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.40667 | 0.404935 | 0.202467 | − | 0.979289i | \(-0.435104\pi\) | ||||
0.202467 | + | 0.979289i | \(0.435104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.5111 | −1.85073 | −0.925363 | − | 0.379083i | \(-0.876240\pi\) | ||||
−0.925363 | + | 0.379083i | \(0.876240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.2192 | −1.01738 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.447954 | 0.0214286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.9382 | 1.85842 | 0.929209 | − | 0.369554i | \(-0.120489\pi\) | ||||
0.929209 | + | 0.369554i | \(0.120489\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.29014 | 0.0614354 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.65960 | −0.173873 | −0.0869363 | − | 0.996214i | \(-0.527708\pi\) | ||||
−0.0869363 | + | 0.996214i | \(0.527708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.14943 | 0.338915 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.7103 | 0.601177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.95150 | 0.139290 | 0.0696449 | − | 0.997572i | \(-0.477813\pi\) | ||||
0.0696449 | + | 0.997572i | \(0.477813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.2506 | 0.953563 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.3743 | −1.14521 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.4784 | −1.00692 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4664 | 0.817045 | 0.408522 | − | 0.912748i | \(-0.366044\pi\) | ||||
0.408522 | + | 0.912748i | \(0.366044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.81051 | 0.271212 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.89882 | 0.321310 | 0.160655 | − | 0.987011i | \(-0.448639\pi\) | ||||
0.160655 | + | 0.987011i | \(0.448639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.31179 | 0.200386 | 0.100193 | − | 0.994968i | \(-0.468054\pi\) | ||||
0.100193 | + | 0.994968i | \(0.468054\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.9752 | 0.508965 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.0933 | −1.16118 | −0.580589 | − | 0.814197i | \(-0.697178\pi\) | ||||
−0.580589 | + | 0.814197i | \(0.697178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.9523 | 0.828961 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.41463 | −0.111260 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.97687 | 0.412757 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.310122 | −0.0142294 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.46132 | −0.158483 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.19677 | 0.100373 | 0.0501865 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501865 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.3102 | −2.38514 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.30516 | −0.332396 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.8122 | −0.854219 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.9895 | −1.31364 | −0.656821 | − | 0.754047i | \(-0.728099\pi\) | ||||
−0.656821 | + | 0.754047i | \(0.728099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.92770 | 0.177617 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.3193 | −1.68420 | −0.842099 | − | 0.539324i | \(-0.818680\pi\) | ||||
−0.842099 | + | 0.539324i | \(0.818680\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.78800 | 0.350754 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.59599 | 0.116681 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.6522 | −1.06095 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.1580 | −1.93202 | −0.966008 | − | 0.258512i | \(-0.916768\pi\) | ||||
−0.966008 | + | 0.258512i | \(0.916768\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.74688 | −0.390782 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.3448 | 1.21924 | 0.609622 | − | 0.792692i | \(-0.291321\pi\) | ||||
0.609622 | + | 0.792692i | \(0.291321\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8262 | −1.41625 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.4134 | −0.773355 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.71800 | −0.297770 | −0.148885 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148885 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.09390 | 0.269578 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.18925 | 0.0525065 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.3365 | 0.499544 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.75156 | −0.164993 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.33373 | 0.321915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.6288 | 1.21044 | 0.605221 | − | 0.796058i | \(-0.293085\pi\) | ||||
0.605221 | + | 0.796058i | \(0.293085\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.1545 | −0.837567 | −0.418784 | − | 0.908086i | \(-0.637543\pi\) | ||||
−0.418784 | + | 0.908086i | \(0.637543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.05741 | 0.220723 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.02820 | −0.175471 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5071 | −0.804655 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.11018 | 0.178367 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 55.2693 | 2.39398 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.23713 | −0.399356 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.6045 | −0.587080 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.08898 | 0.133052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.8718 | −1.06932 | −0.534660 | − | 0.845067i | \(-0.679561\pi\) | ||||
−0.534660 | + | 0.845067i | \(0.679561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.9251 | 0.597583 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.9372 | −1.11103 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.8540 | 0.848898 | 0.424449 | − | 0.905452i | \(-0.360468\pi\) | ||||
0.424449 | + | 0.905452i | \(0.360468\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.44331 | 0.232315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.59398 | 0.0679059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.9542 | 0.848539 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −29.6508 | −1.25861 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.8384 | 1.39141 | 0.695704 | − | 0.718329i | \(-0.255093\pi\) | ||||
0.695704 | + | 0.718329i | \(0.255093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.5003 | 1.03625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.81060 | 0.118664 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.35298 | −0.183456 | −0.0917280 | − | 0.995784i | \(-0.529239\pi\) | ||||
−0.0917280 | + | 0.995784i | \(0.529239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.4609 | −0.987005 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.1477 | −0.594146 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.6528 | 0.446590 | 0.223295 | − | 0.974751i | \(-0.428319\pi\) | ||||
0.223295 | + | 0.974751i | \(0.428319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1385 | −0.717223 | −0.358612 | − | 0.933487i | \(-0.616750\pi\) | ||||
−0.358612 | + | 0.933487i | \(0.616750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.2878 | −1.39062 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.11049 | −0.129716 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.9957 | −1.66504 | −0.832522 | − | 0.553992i | \(-0.813104\pi\) | ||||
−0.832522 | + | 0.553992i | \(0.813104\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.80536 | 0.241262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.839076 | 0.0348107 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.28739 | −0.343229 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.08514 | 0.292935 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.68445 | −0.193348 | −0.0966739 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966739 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.824458 | −0.0339712 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.0180 | 1.48158 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.11715 | −0.128006 | −0.0640029 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640029 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.46838 | 0.183186 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.5815 | −0.596781 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.5081 | −1.32824 | −0.664122 | − | 0.747624i | \(-0.731195\pi\) | ||||
−0.664122 | + | 0.747624i | \(0.731195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.2343 | −1.19249 | −0.596247 | − | 0.802801i | \(-0.703342\pi\) | ||||
−0.596247 | + | 0.802801i | \(0.703342\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.92198 | −0.241162 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.4590 | −0.587844 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7184 | −0.922111 | −0.461056 | − | 0.887371i | \(-0.652529\pi\) | ||||
−0.461056 | + | 0.887371i | \(0.652529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −25.9944 | −1.05334 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.2390 | −0.414226 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.17862 | 0.0476042 | 0.0238021 | − | 0.999717i | \(-0.492423\pi\) | ||||
0.0238021 | + | 0.999717i | \(0.492423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.3281 | 1.26327 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.6531 | 1.59638 | 0.798188 | − | 0.602409i | \(-0.205792\pi\) | ||||
0.798188 | + | 0.602409i | \(0.205792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.15668 | −0.126878 | −0.0634388 | − | 0.997986i | \(-0.520207\pi\) | ||||
−0.0634388 | + | 0.997986i | \(0.520207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.9280 | 0.478654 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.75833 | 0.350895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5093 | −0.620374 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.575250 | 0.0229733 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.8826 | 0.433919 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.3471 | 1.44696 | 0.723478 | − | 0.690348i | \(-0.242542\pi\) | ||||
0.723478 | + | 0.690348i | \(0.242542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.04637 | −0.359561 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.5860 | 1.09472 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.43065 | 0.334034 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.80223 | 0.308651 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.3733 | 0.528215 | 0.264107 | − | 0.964493i | \(-0.414923\pi\) | ||||
0.264107 | + | 0.964493i | \(0.414923\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.4690 | 0.846654 | 0.423327 | − | 0.905977i | \(-0.360862\pi\) | ||||
0.423327 | + | 0.905977i | \(0.360862\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.8874 | 0.546817 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.8456 | 0.937466 | 0.468733 | − | 0.883340i | \(-0.344711\pi\) | ||||
0.468733 | + | 0.883340i | \(0.344711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.84096 | 0.386292 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.4451 | 0.526955 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.3555 | 1.26617 | 0.633085 | − | 0.774083i | \(-0.281788\pi\) | ||||
0.633085 | + | 0.774083i | \(0.281788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.3523 | −1.45947 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.01021 | −0.0784259 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.8321 | −1.39582 | −0.697911 | − | 0.716184i | \(-0.745887\pi\) | ||||
−0.697911 | + | 0.716184i | \(0.745887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.3011 | 0.672935 | 0.336468 | − | 0.941695i | \(-0.390768\pi\) | ||||
0.336468 | + | 0.941695i | \(0.390768\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.67088 | 0.297912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.914550 | 0.0354647 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9875 | 0.619037 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8463 | 0.573991 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0329 | 0.503128 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7605 | −1.22428 | −0.612139 | − | 0.790750i | \(-0.709691\pi\) | ||||
−0.612139 | + | 0.790750i | \(0.709691\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.25784 | −0.317844 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.6476 | 1.52378 | 0.761891 | − | 0.647706i | \(-0.224271\pi\) | ||||
0.761891 | + | 0.647706i | \(0.224271\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.0457 | −0.884413 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.941157 | 0.0360652 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.03826 | 0.307576 | 0.153788 | − | 0.988104i | \(-0.450853\pi\) | ||||
0.153788 | + | 0.988104i | \(0.450853\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.33197 | 0.165516 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.20340 | 0.312979 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6185 | −0.861697 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9017 | 0.757097 | 0.378549 | − | 0.925581i | \(-0.376423\pi\) | ||||
0.378549 | + | 0.925581i | \(0.376423\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.18019 | 0.120805 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.70187 | −0.330081 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.4982 | −0.435527 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0509 | 0.493630 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.7926 | 0.860866 | 0.430433 | − | 0.902623i | \(-0.358361\pi\) | ||||
0.430433 | + | 0.902623i | \(0.358361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.22736 | 0.0840066 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.80375 | −0.218582 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.9884 | −1.46631 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.48197 | −0.0932125 | −0.0466062 | − | 0.998913i | \(-0.514841\pi\) | ||||
−0.0466062 | + | 0.998913i | \(0.514841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.58235 | −0.246857 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.26922 | −0.309685 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.9639 | 0.634413 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35.1427 | −1.31243 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.1315 | −0.415137 | −0.207568 | − | 0.978221i | \(-0.566555\pi\) | ||||
−0.207568 | + | 0.978221i | \(0.566555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8876 | 0.517202 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.2377 | 1.49646 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.0682 | −0.411063 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4045 | 0.793848 | 0.396924 | − | 0.917851i | \(-0.370078\pi\) | ||||
0.396924 | + | 0.917851i | \(0.370078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9363 | 1.10875 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.09705 | −0.188521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.3401 | 1.85935 | 0.929677 | − | 0.368376i | \(-0.120086\pi\) | ||||
0.929677 | + | 0.368376i | \(0.120086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.77872 | 0.176266 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.1789 | −0.522288 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.0278 | 1.36209 | 0.681045 | − | 0.732241i | \(-0.261526\pi\) | ||||
0.681045 | + | 0.732241i | \(0.261526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.57001 | 0.0576758 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.6893 | −1.89630 | −0.948148 | − | 0.317830i | \(-0.897046\pi\) | ||||
−0.948148 | + | 0.317830i | \(0.897046\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9599 | −0.584725 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.276788 | −0.0101272 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.3158 | −0.413472 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 40.5500 | 1.47772 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.6060 | 1.11387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.4532 | 1.36126 | 0.680630 | − | 0.732627i | \(-0.261706\pi\) | ||||
0.680630 | + | 0.732627i | \(0.261706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.76969 | 0.209427 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.6323 | 0.892919 | 0.446459 | − | 0.894804i | \(-0.352685\pi\) | ||||
0.446459 | + | 0.894804i | \(0.352685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.7741 | −1.15030 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.47400 | −0.0532925 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.8586 | 0.969809 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9376 | 0.394419 | 0.197209 | − | 0.980361i | \(-0.436812\pi\) | ||||
0.197209 | + | 0.980361i | \(0.436812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.63682 | −0.347062 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.08473 | 0.146917 | 0.0734587 | − | 0.997298i | \(-0.476596\pi\) | ||||
0.0734587 | + | 0.997298i | \(0.476596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.72483 | 0.205642 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.3234 | −1.30310 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.35336 | −0.0843180 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.6808 | 0.668451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.4441 | 1.51683 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.03196 | 0.108215 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3460 | 0.689611 | 0.344805 | − | 0.938674i | \(-0.387945\pi\) | ||||
0.344805 | + | 0.938674i | \(0.387945\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.44276 | −0.336171 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.7405 | −1.02189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.5702 | 1.26313 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.8208 | −0.454707 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.4239 | 0.475498 | 0.237749 | − | 0.971327i | \(-0.423590\pi\) | ||||
0.237749 | + | 0.971327i | \(0.423590\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.13013 | 0.0753585 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.88914 | −0.102083 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.81303 | −0.169848 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.17283 | 0.323300 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5354 | −0.652478 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.9741 | 1.72184 | 0.860920 | − | 0.508741i | \(-0.169889\pi\) | ||||
0.860920 | + | 0.508741i | \(0.169889\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.3357 | −0.784313 | −0.392156 | − | 0.919899i | \(-0.628271\pi\) | ||||
−0.392156 | + | 0.919899i | \(0.628271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.6945 | −0.795932 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.93187 | −0.172756 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.04322 | −0.0364977 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.67958 | 0.303289 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.82106 | 0.342757 | 0.171379 | − | 0.985205i | \(-0.445178\pi\) | ||||
0.171379 | + | 0.985205i | \(0.445178\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.03553 | 0.210386 | 0.105193 | − | 0.994452i | \(-0.466454\pi\) | ||||
0.105193 | + | 0.994452i | \(0.466454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.99440 | −0.139067 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.57941 | 0.298335 | 0.149168 | − | 0.988812i | \(-0.452341\pi\) | ||||
0.149168 | + | 0.988812i | \(0.452341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.86624 | −0.273206 | −0.136603 | − | 0.990626i | \(-0.543618\pi\) | ||||
−0.136603 | + | 0.990626i | \(0.543618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.1766 | −0.803988 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.75392 | −0.0607696 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.9832 | 0.380088 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.9534 | −0.758822 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.4842 | 0.431004 | 0.215502 | − | 0.976503i | \(-0.430861\pi\) | ||||
0.215502 | + | 0.976503i | \(0.430861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.8891 | 0.961693 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −49.8993 | −1.71862 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.8654 | 0.752192 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.7129 | −0.608622 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.1140 | 0.793271 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.3402 | 0.765813 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.53692 | 0.0868625 | 0.0434312 | − | 0.999056i | \(-0.486171\pi\) | ||||
0.0434312 | + | 0.999056i | \(0.486171\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.301685 | −0.0103174 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.6249 | 1.62684 | 0.813419 | − | 0.581679i | \(-0.197604\pi\) | ||||
0.813419 | + | 0.581679i | \(0.197604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2554 | −1.10054 | −0.550270 | − | 0.834987i | \(-0.685475\pi\) | ||||
−0.550270 | + | 0.834987i | \(0.685475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38.3782 | 1.30793 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.0846 | −1.50066 | −0.750328 | − | 0.661065i | \(-0.770105\pi\) | ||||
−0.750328 | + | 0.661065i | \(0.770105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.20870 | −0.313105 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.8501 | 0.809993 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.7600 | −0.534623 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.6981 | −1.31124 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.60215 | 0.257294 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.9880 | −0.946166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.87223 | 0.0969883 | 0.0484942 | − | 0.998823i | \(-0.484558\pi\) | ||||
0.0484942 | + | 0.998823i | \(0.484558\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.55212 | 0.0523517 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.8617 | −0.904993 | −0.452497 | − | 0.891766i | \(-0.649467\pi\) | ||||
−0.452497 | + | 0.891766i | \(0.649467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.6776 | −1.73909 | −0.869545 | − | 0.493854i | \(-0.835588\pi\) | ||||
−0.869545 | + | 0.493854i | \(0.835588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.2242 | 0.511756 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0721 | −0.573225 | −0.286612 | − | 0.958047i | \(-0.592529\pi\) | ||||
−0.286612 | + | 0.958047i | \(0.592529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.7940 | 1.13341 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.1740 | 0.374343 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.435977 | 0.0145894 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.0828 | 0.571014 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.7470 | 0.525778 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.4248 | −0.981374 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.70557 | 0.156765 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.0127 | 0.566146 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.4853 | −0.581229 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.16270 | 0.0718114 | 0.0359057 | − | 0.999355i | \(-0.488568\pi\) | ||||
0.0359057 | + | 0.999355i | \(0.488568\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.8612 | 0.426580 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.36329 | 0.111431 | 0.0557154 | − | 0.998447i | \(-0.482256\pi\) | ||||
0.0557154 | + | 0.998447i | \(0.482256\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.662711 | −0.0219325 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.1621 | 0.666540 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −45.7580 | −1.51106 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.3416 | 1.72659 | 0.863295 | − | 0.504700i | \(-0.168397\pi\) | ||||
0.863295 | + | 0.504700i | \(0.168397\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.2515 | 0.766163 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.9849 | 1.67819 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.4663 | −0.508528 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.58115 | −0.150465 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.4929 | 0.344261 | 0.172130 | − | 0.985074i | \(-0.444935\pi\) | ||||
0.172130 | + | 0.985074i | \(0.444935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.358977 | −0.0117650 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.1659 | 1.05306 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.52918 | −0.115416 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.5560 | 0.834879 | 0.417440 | − | 0.908705i | \(-0.362928\pi\) | ||||
0.417440 | + | 0.908705i | \(0.362928\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.6030 | 0.378651 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0100 | −0.847901 | −0.423951 | − | 0.905685i | \(-0.639357\pi\) | ||||
−0.423951 | + | 0.905685i | \(0.639357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6040 | −0.768651 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.3524 | 0.792183 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.4385 | 1.54154 | 0.770772 | − | 0.637111i | \(-0.219871\pi\) | ||||
0.770772 | + | 0.637111i | \(0.219871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.1361 | −0.426414 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.3426 | 1.56762 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.4589 | −0.500763 | −0.250381 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250381 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.7983 | 1.35256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.5306 | 0.663661 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.30684 | 0.171367 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7805 | −0.509050 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.73279 | 0.120287 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.28958 | −0.234660 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.4940 | 0.498255 | 0.249127 | − | 0.968471i | \(-0.419856\pi\) | ||||
0.249127 | + | 0.968471i | \(0.419856\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.326626 | −0.0104927 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.9315 | 1.57029 | 0.785144 | − | 0.619314i | \(-0.212589\pi\) | ||||
0.785144 | + | 0.619314i | \(0.212589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.6601 | −0.341748 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.9018 | −0.349136 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.524054 | −0.0167660 | −0.00838298 | − | 0.999965i | \(-0.502668\pi\) | ||||
−0.00838298 | + | 0.999965i | \(0.502668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.91743 | −0.221082 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4814 | 0.334646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.30137 | 0.264773 | 0.132386 | − | 0.991198i | \(-0.457736\pi\) | ||||
0.132386 | + | 0.991198i | \(0.457736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.2266 | −1.44104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.10982 | −0.226308 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.4634 | −0.332717 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.33576 | −0.0741978 | −0.0370989 | − | 0.999312i | \(-0.511812\pi\) | ||||
−0.0370989 | + | 0.999312i | \(0.511812\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.34064 | −0.201214 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.3095 | 0.580450 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.22368 | 0.133765 | 0.0668827 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668827 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 59.3097 | 1.87647 |
(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 | 6008.2.a.c.1.14 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.c.1.14 | ✓ | 44 | 1.1 | even | 1 | trivial |