Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.5490444289\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.732051 | −0.203034 | −0.101517 | − | 0.994834i | \(-0.532370\pi\) | ||||
−0.101517 | + | 0.994834i | \(0.532370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.46410 | 0.319493 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.46410 | 0.643268 | 0.321634 | − | 0.946864i | \(-0.395768\pi\) | ||||
0.321634 | + | 0.946864i | \(0.395768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410 | 0.981382 | 0.490691 | − | 0.871334i | \(-0.336744\pi\) | ||||
0.490691 | + | 0.871334i | \(0.336744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.53590 | −0.441443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.26795 | −0.537248 | −0.268624 | − | 0.963245i | \(-0.586569\pi\) | ||||
−0.268624 | + | 0.963245i | \(0.586569\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.535898 | −0.0858124 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.92820 | −1.36154 | −0.680769 | − | 0.732498i | \(-0.738354\pi\) | ||||
−0.680769 | + | 0.732498i | \(0.738354\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.46410 | 0.367327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.928203 | −0.135392 | −0.0676962 | − | 0.997706i | \(-0.521565\pi\) | ||||
−0.0676962 | + | 0.997706i | \(0.521565\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53590 | 0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.26795 | 0.998330 | 0.499165 | − | 0.866507i | \(-0.333640\pi\) | ||||
0.499165 | + | 0.866507i | \(0.333640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46410 | 0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.732051 | −0.0969625 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.39230 | 1.07452 | 0.537262 | − | 0.843415i | \(-0.319459\pi\) | ||||
0.537262 | + | 0.843415i | \(0.319459\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.92820 | −0.620895 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.732051 | 0.0907997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.26795 | −0.399244 | −0.199622 | − | 0.979873i | \(-0.563971\pi\) | ||||
−0.199622 | + | 0.979873i | \(0.563971\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.53590 | 0.305286 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.46410 | −0.873607 | −0.436804 | − | 0.899557i | \(-0.643889\pi\) | ||||
−0.436804 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.92820 | −0.789542 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9282 | −1.22952 | −0.614759 | − | 0.788715i | \(-0.710747\pi\) | ||||
−0.614759 | + | 0.788715i | \(0.710747\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410 | 0.380235 | 0.190117 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190117 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | −0.375735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.53590 | 0.271877 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.53590 | −0.904803 | −0.452402 | − | 0.891814i | \(-0.649433\pi\) | ||||
−0.452402 | + | 0.891814i | \(0.649433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.46410 | −0.153480 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5885 | 1.48123 | 0.740617 | − | 0.671928i | \(-0.234533\pi\) | ||||
0.740617 | + | 0.671928i | \(0.234533\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.53590 | 0.857890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.39230 | −0.437051 | −0.218525 | − | 0.975831i | \(-0.570125\pi\) | ||||
−0.218525 | + | 0.975831i | \(0.570125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.66025 | −0.360656 | −0.180328 | − | 0.983607i | \(-0.557716\pi\) | ||||
−0.180328 | + | 0.983607i | \(0.557716\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.46410 | −0.142882 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6603 | −1.12724 | −0.563620 | − | 0.826034i | \(-0.690592\pi\) | ||||
−0.563620 | + | 0.826034i | \(0.690592\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.39230 | −0.612272 | −0.306136 | − | 0.951988i | \(-0.599036\pi\) | ||||
−0.306136 | + | 0.951988i | \(0.599036\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.39230 | −0.227068 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.5885 | −1.74865 | −0.874327 | − | 0.485336i | \(-0.838697\pi\) | ||||
−0.874327 | + | 0.485336i | \(0.838697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.46410 | −0.323029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.80385 | 0.166766 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.92820 | 0.635107 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.39230 | −0.396041 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5885 | −0.939574 | −0.469787 | − | 0.882780i | \(-0.655669\pi\) | ||||
−0.469787 | + | 0.882780i | \(0.655669\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.53590 | −0.575454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.07180 | 0.443125 | 0.221562 | − | 0.975146i | \(-0.428884\pi\) | ||||
0.221562 | + | 0.975146i | \(0.428884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | −0.173422 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.3205 | −1.47979 | −0.739895 | − | 0.672722i | \(-0.765125\pi\) | ||||
−0.739895 | + | 0.672722i | \(0.765125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.53590 | −0.384730 | −0.192365 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192365 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.679492 | −0.0572235 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.53590 | 0.212062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.46410 | −0.287678 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.19615 | −0.181136 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3923 | −1.34291 | −0.671455 | − | 0.741045i | \(-0.734330\pi\) | ||||
−0.671455 | + | 0.741045i | \(0.734330\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3923 | 1.00847 | 0.504236 | − | 0.863566i | \(-0.331774\pi\) | ||||
0.504236 | + | 0.863566i | \(0.331774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.53590 | −0.690086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.5359 | −1.31971 | −0.659854 | − | 0.751394i | \(-0.729382\pi\) | ||||
−0.659854 | + | 0.751394i | \(0.729382\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.32051 | 0.421944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.9282 | −1.63922 | −0.819612 | − | 0.572919i | \(-0.805811\pi\) | ||||
−0.819612 | + | 0.572919i | \(0.805811\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.53590 | 0.197419 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.26795 | −0.562411 | −0.281205 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4641 | −0.958777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.46410 | 0.188435 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1962 | −1.07931 | −0.539657 | − | 0.841885i | \(-0.681446\pi\) | ||||
−0.539657 | + | 0.841885i | \(0.681446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.07180 | 0.381220 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7846 | 1.55351 | 0.776757 | − | 0.629800i | \(-0.216863\pi\) | ||||
0.776757 | + | 0.629800i | \(0.216863\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.14359 | 0.454148 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.26795 | 0.240264 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | −0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.92820 | −0.501307 | −0.250654 | − | 0.968077i | \(-0.580646\pi\) | ||||
−0.250654 | + | 0.968077i | \(0.580646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1962 | −1.30979 | −0.654894 | − | 0.755721i | \(-0.727287\pi\) | ||||
−0.654894 | + | 0.755721i | \(0.727287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.535898 | 0.0383765 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9282 | 0.921096 | 0.460548 | − | 0.887635i | \(-0.347653\pi\) | ||||
0.460548 | + | 0.887635i | \(0.347653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0718 | 0.926635 | 0.463318 | − | 0.886192i | \(-0.346659\pi\) | ||||
0.463318 | + | 0.886192i | \(0.346659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.39230 | −0.168740 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820 | 0.486265 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.53590 | −0.593286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46410 | 0.239617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3205 | 1.05471 | 0.527354 | − | 0.849646i | \(-0.323184\pi\) | ||||
0.527354 | + | 0.849646i | \(0.323184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.92820 | −0.474713 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.92820 | 0.608898 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.9282 | 0.741855 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.46410 | −0.369230 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.53590 | −0.170583 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.66025 | 0.512969 | 0.256484 | − | 0.966548i | \(-0.417436\pi\) | ||||
0.256484 | + | 0.966548i | \(0.417436\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.19615 | 0.145764 | 0.0728819 | − | 0.997341i | \(-0.476780\pi\) | ||||
0.0728819 | + | 0.997341i | \(0.476780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5359 | −0.696232 | −0.348116 | − | 0.937452i | \(-0.613178\pi\) | ||||
−0.348116 | + | 0.937452i | \(0.613178\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.07180 | −0.333700 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9282 | 0.846955 | 0.423477 | − | 0.905907i | \(-0.360809\pi\) | ||||
0.423477 | + | 0.905907i | \(0.360809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.928203 | 0.0605493 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8564 | 0.896296 | 0.448148 | − | 0.893959i | \(-0.352084\pi\) | ||||
0.448148 | + | 0.893959i | \(0.352084\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8564 | 1.02140 | 0.510700 | − | 0.859759i | \(-0.329386\pi\) | ||||
0.510700 | + | 0.859759i | \(0.329386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.732051 | 0.0465793 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.53590 | 0.160706 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.53590 | −0.158804 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.12436 | 0.569162 | 0.284581 | − | 0.958652i | \(-0.408146\pi\) | ||||
0.284581 | + | 0.958652i | \(0.408146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.53590 | −0.406121 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.53590 | −0.528359 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4641 | 0.953557 | 0.476779 | − | 0.879023i | \(-0.341804\pi\) | ||||
0.476779 | + | 0.879023i | \(0.341804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.26795 | −0.446467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.24871 | −0.382415 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3923 | 0.633630 | 0.316815 | − | 0.948487i | \(-0.397387\pi\) | ||||
0.316815 | + | 0.948487i | \(0.397387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3923 | 1.11725 | 0.558626 | − | 0.829419i | \(-0.311329\pi\) | ||||
0.558626 | + | 0.829419i | \(0.311329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.07180 | −0.0648681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.46410 | −0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.39230 | 0.143740 | 0.0718698 | − | 0.997414i | \(-0.477103\pi\) | ||||
0.0718698 | + | 0.997414i | \(0.477103\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.4641 | −0.806075 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9282 | −0.771232 | −0.385616 | − | 0.922659i | \(-0.626011\pi\) | ||||
−0.385616 | + | 0.922659i | \(0.626011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.39230 | 0.142208 | 0.0711039 | − | 0.997469i | \(-0.477348\pi\) | ||||
0.0711039 | + | 0.997469i | \(0.477348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.732051 | 0.0433629 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.6795 | 0.626043 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.6603 | −0.681199 | −0.340600 | − | 0.940208i | \(-0.610630\pi\) | ||||
−0.340600 | + | 0.940208i | \(0.610630\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.92820 | −0.403376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564 | 0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.53590 | −0.146655 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.8564 | −1.02923 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.21539 | −0.184719 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.39230 | −0.480542 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1962 | 1.03851 | 0.519255 | − | 0.854620i | \(-0.326210\pi\) | ||||
0.519255 | + | 0.854620i | \(0.326210\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.67949 | −0.152431 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.3923 | −1.26975 | −0.634876 | − | 0.772614i | \(-0.718949\pi\) | ||||
−0.634876 | + | 0.772614i | \(0.718949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.7846 | −1.74005 | −0.870025 | − | 0.493008i | \(-0.835897\pi\) | ||||
−0.870025 | + | 0.493008i | \(0.835897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.92820 | 0.277673 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.1244 | 1.18646 | 0.593231 | − | 0.805032i | \(-0.297852\pi\) | ||||
0.593231 | + | 0.805032i | \(0.297852\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.53590 | −0.476427 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46410 | −0.192748 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.732051 | −0.0406069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.67949 | −0.258776 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.85641 | −0.102347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.2487 | −1.44276 | −0.721380 | − | 0.692540i | \(-0.756492\pi\) | ||||
−0.721380 | + | 0.692540i | \(0.756492\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.05256 | 0.441278 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.26795 | 0.178547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.7321 | −1.12935 | −0.564673 | − | 0.825314i | \(-0.690998\pi\) | ||||
−0.564673 | + | 0.825314i | \(0.690998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.6077 | −0.739069 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9282 | −1.02502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.53590 | −0.136528 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.1769 | 1.67366 | 0.836832 | − | 0.547459i | \(-0.184405\pi\) | ||||
0.836832 | + | 0.547459i | \(0.184405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.07180 | −0.378545 | −0.189272 | − | 0.981925i | \(-0.560613\pi\) | ||||
−0.189272 | + | 0.981925i | \(0.560613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.92820 | 0.156296 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3923 | 1.19182 | 0.595911 | − | 0.803050i | \(-0.296791\pi\) | ||||
0.595911 | + | 0.803050i | \(0.296791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.46410 | 0.502302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.07180 | 0.268428 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4641 | −0.816164 | −0.408082 | − | 0.912945i | \(-0.633802\pi\) | ||||
−0.408082 | + | 0.912945i | \(0.633802\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.732051 | 0.0384227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.46410 | 0.390689 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.8564 | −1.24529 | −0.622647 | − | 0.782503i | \(-0.713943\pi\) | ||||
−0.622647 | + | 0.782503i | \(0.713943\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.7846 | 0.769656 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.5359 | 0.754666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5885 | −0.755362 | −0.377681 | − | 0.925936i | \(-0.623278\pi\) | ||||
−0.377681 | + | 0.925936i | \(0.623278\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.732051 | −0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.53590 | −0.130605 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.07180 | −0.0550545 | −0.0275273 | − | 0.999621i | \(-0.508763\pi\) | ||||
−0.0275273 | + | 0.999621i | \(0.508763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.75129 | −0.397111 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6603 | 1.20898 | 0.604491 | − | 0.796612i | \(-0.293376\pi\) | ||||
0.604491 | + | 0.796612i | \(0.293376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.92820 | 0.353094 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.0000 | 1.11832 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.71281 | 0.187287 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9282 | 0.549858 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5359 | 0.629159 | 0.314579 | − | 0.949231i | \(-0.398137\pi\) | ||||
0.314579 | + | 0.949231i | \(0.398137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.46410 | −0.0732968 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.78461 | −0.139057 | −0.0695284 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695284 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.46410 | −0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3205 | 0.561137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.39230 | 0.316079 | 0.158040 | − | 0.987433i | \(-0.449483\pi\) | ||||
0.158040 | + | 0.987433i | \(0.449483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.6795 | −0.625433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.8564 | 0.681829 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.46410 | −0.170046 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.32051 | −0.162606 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.28719 | 0.111207 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.7846 | 0.812264 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.85641 | 0.0896281 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.5359 | −1.27819 | −0.639095 | − | 0.769128i | \(-0.720691\pi\) | ||||
−0.639095 | + | 0.769128i | \(0.720691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.6603 | −1.90595 | −0.952975 | − | 0.303049i | \(-0.901996\pi\) | ||||
−0.952975 | + | 0.303049i | \(0.901996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.53590 | −0.121587 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.46410 | −0.165710 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7128 | 1.13175 | 0.565875 | − | 0.824491i | \(-0.308538\pi\) | ||||
0.565875 | + | 0.824491i | \(0.308538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.39230 | 0.352015 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.3923 | −1.63403 | −0.817014 | − | 0.576618i | \(-0.804372\pi\) | ||||
−0.817014 | + | 0.576618i | \(0.804372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.53590 | 0.404640 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.46410 | 0.163481 | 0.0817405 | − | 0.996654i | \(-0.473952\pi\) | ||||
0.0817405 | + | 0.996654i | \(0.473952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.7846 | 0.978709 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.07180 | 0.426230 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.46410 | 0.0686381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.78461 | −0.317371 | −0.158685 | − | 0.987329i | \(-0.550726\pi\) | ||||
−0.158685 | + | 0.987329i | \(0.550726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.7128 | −1.57016 | −0.785081 | − | 0.619393i | \(-0.787379\pi\) | ||||
−0.785081 | + | 0.619393i | \(0.787379\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4641 | 0.532782 | 0.266391 | − | 0.963865i | \(-0.414169\pi\) | ||||
0.266391 | + | 0.963865i | \(0.414169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.32051 | −0.246204 | −0.123102 | − | 0.992394i | \(-0.539284\pi\) | ||||
−0.123102 | + | 0.992394i | \(0.539284\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.53590 | −0.301800 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1051 | −0.557774 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.9282 | 1.42208 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.9090 | −0.819995 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.60770 | −0.0734575 | −0.0367287 | − | 0.999325i | \(-0.511694\pi\) | ||||
−0.0367287 | + | 0.999325i | \(0.511694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.39230 | 0.109080 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.07180 | 0.230775 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.5885 | −0.662428 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.80385 | −0.0817401 | −0.0408701 | − | 0.999164i | \(-0.513013\pi\) | ||||
−0.0408701 | + | 0.999164i | \(0.513013\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.3205 | −0.692817 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.07180 | −0.228887 | −0.114443 | − | 0.993430i | \(-0.536508\pi\) | ||||
−0.114443 | + | 0.993430i | \(0.536508\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000 | 0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.53590 | −0.383660 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.9282 | −0.849046 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5359 | −0.740248 | −0.370124 | − | 0.928982i | \(-0.620685\pi\) | ||||
−0.370124 | + | 0.928982i | \(0.620685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.32051 | −0.237703 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.53590 | 0.380597 | 0.190298 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190298 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.39230 | 0.195455 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.12436 | −0.405227 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.3205 | −1.29961 | −0.649804 | − | 0.760102i | \(-0.725149\pi\) | ||||
−0.649804 | + | 0.760102i | \(0.725149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.9282 | −0.660385 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | 0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.66025 | 0.161290 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.21539 | 0.141413 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.3923 | −0.456172 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7846 | 1.17346 | 0.586728 | − | 0.809784i | \(-0.300416\pi\) | ||||
0.586728 | + | 0.809784i | \(0.300416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.3731 | −1.54676 | −0.773378 | − | 0.633945i | \(-0.781435\pi\) | ||||
−0.773378 | + | 0.633945i | \(0.781435\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.46410 | 0.0638986 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.9282 | 0.824525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.0718 | −0.740853 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.39230 | 0.190252 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.6603 | 0.504117 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.2154 | 0.656593 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3923 | 0.447628 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.1769 | −1.42639 | −0.713193 | − | 0.700967i | \(-0.752752\pi\) | ||||
−0.713193 | + | 0.700967i | \(0.752752\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.2487 | −0.439814 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.39230 | 0.273816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.26795 | −0.139727 | −0.0698637 | − | 0.997557i | \(-0.522256\pi\) | ||||
−0.0698637 | + | 0.997557i | \(0.522256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.6795 | −0.882579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46410 | −0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.8564 | −0.929429 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.39230 | 0.101548 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.3205 | 1.24235 | 0.621175 | − | 0.783672i | \(-0.286656\pi\) | ||||
0.621175 | + | 0.783672i | \(0.286656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.53590 | 0.276439 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.78461 | −0.370887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.8038 | −1.42466 | −0.712331 | − | 0.701844i | \(-0.752361\pi\) | ||||
−0.712331 | + | 0.701844i | \(0.752361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.5885 | 0.782022 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.92820 | 0.374949 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.32051 | 0.223047 | 0.111524 | − | 0.993762i | \(-0.464427\pi\) | ||||
0.111524 | + | 0.993762i | \(0.464427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.39230 | 0.100115 | 0.0500574 | − | 0.998746i | \(-0.484060\pi\) | ||||
0.0500574 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.07180 | −0.211877 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.46410 | 0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.7846 | 1.44810 | 0.724051 | − | 0.689746i | \(-0.242278\pi\) | ||||
0.724051 | + | 0.689746i | \(0.242278\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3205 | −0.553581 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.92820 | 0.287430 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.1769 | −1.04272 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.80385 | −0.0745799 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.1769 | 0.791516 | 0.395758 | − | 0.918355i | \(-0.370482\pi\) | ||||
0.395758 | + | 0.918355i | \(0.370482\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.46410 | −0.225144 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.46410 | 0.389301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.14359 | 0.170157 | 0.0850785 | − | 0.996374i | \(-0.472886\pi\) | ||||
0.0850785 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.92820 | −0.284029 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.56922 | 0.391642 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.7846 | 0.849236 | 0.424618 | − | 0.905373i | \(-0.360408\pi\) | ||||
0.424618 | + | 0.905373i | \(0.360408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.6410 | −1.82095 | −0.910473 | − | 0.413570i | \(-0.864282\pi\) | ||||
−0.910473 | + | 0.413570i | \(0.864282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.05256 | 0.327926 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9090 | 1.05161 | 0.525806 | − | 0.850604i | \(-0.323764\pi\) | ||||
0.525806 | + | 0.850604i | \(0.323764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.07180 | 0.205520 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.679492 | 0.0274893 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3923 | 0.581300 | 0.290650 | − | 0.956829i | \(-0.406129\pi\) | ||||
0.290650 | + | 0.956829i | \(0.406129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.39230 | 0.177115 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.3923 | 0.901480 | 0.450740 | − | 0.892655i | \(-0.351160\pi\) | ||||
0.450740 | + | 0.892655i | \(0.351160\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.3923 | −0.739249 | −0.369625 | − | 0.929181i | \(-0.620514\pi\) | ||||
−0.369625 | + | 0.929181i | \(0.620514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.8564 | −0.556038 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.0718 | −0.683967 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.53590 | 0.101274 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.3205 | −0.451378 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.53590 | 0.180571 | 0.0902856 | − | 0.995916i | \(-0.471222\pi\) | ||||
0.0902856 | + | 0.995916i | \(0.471222\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.2154 | 0.445772 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.5885 | 0.420190 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.19615 | 0.0870147 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.3205 | 0.922545 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0718 | −0.437310 | −0.218655 | − | 0.975802i | \(-0.570167\pi\) | ||||
−0.218655 | + | 0.975802i | \(0.570167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.39230 | −0.252088 | −0.126044 | − | 0.992025i | \(-0.540228\pi\) | ||||
−0.126044 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.53590 | 0.257351 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.53590 | 0.335581 | 0.167790 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167790 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | 0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.5359 | −0.803632 | −0.401816 | − | 0.915720i | \(-0.631621\pi\) | ||||
−0.401816 | + | 0.915720i | \(0.631621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.07180 | −0.198171 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.3923 | 0.717552 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.7846 | 1.27711 | 0.638554 | − | 0.769577i | \(-0.279533\pi\) | ||||
0.638554 | + | 0.769577i | \(0.279533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.7846 | −1.81971 | −0.909855 | − | 0.414926i | \(-0.863807\pi\) | ||||
−0.909855 | + | 0.414926i | \(0.863807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.85641 | −0.0720969 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.00000 | 0.0775567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | 0.464642 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.60770 | 0.216806 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.0718 | −1.12230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.2679 | −1.82205 | −0.911023 | − | 0.412356i | \(-0.864706\pi\) | ||||
−0.911023 | + | 0.412356i | \(0.864706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.9808 | 1.34442 | 0.672210 | − | 0.740361i | \(-0.265345\pi\) | ||||
0.672210 | + | 0.740361i | \(0.265345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.1769 | 1.11971 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.60770 | 0.0616070 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.339746 | 0.0130000 | 0.00650001 | − | 0.999979i | \(-0.497931\pi\) | ||||
0.00650001 | + | 0.999979i | \(0.497931\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3205 | 0.661783 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.71281 | −0.294262 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.32051 | −0.202695 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.1769 | 0.425190 | 0.212595 | − | 0.977140i | \(-0.431809\pi\) | ||||
0.212595 | + | 0.977140i | \(0.431809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.0718 | 0.648504 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.53590 | 0.172056 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.7846 | −0.787273 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.46410 | 0.357965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.4641 | 1.26392 | 0.631961 | − | 0.775000i | \(-0.282250\pi\) | ||||
0.631961 | + | 0.775000i | \(0.282250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.26795 | 0.123253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.679492 | 0.0255911 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.78461 | −0.330379 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7846 | −0.405025 | −0.202512 | − | 0.979280i | \(-0.564911\pi\) | ||||
−0.202512 | + | 0.979280i | \(0.564911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.9282 | 1.00989 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.9282 | 0.708867 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.53590 | −0.0948372 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.1436 | 0.378819 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.3205 | −0.645946 | −0.322973 | − | 0.946408i | \(-0.604682\pi\) | ||||
−0.322973 | + | 0.946408i | \(0.604682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.32051 | −0.272630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6077 | 0.431695 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.46410 | 0.128654 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.8564 | 1.03314 | 0.516568 | − | 0.856246i | \(-0.327209\pi\) | ||||
0.516568 | + | 0.856246i | \(0.327209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.9282 | −1.14392 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.7846 | 1.13706 | 0.568528 | − | 0.822664i | \(-0.307513\pi\) | ||||
0.568528 | + | 0.822664i | \(0.307513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.19615 | 0.0810063 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3205 | 0.416996 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.535898 | 0.0196867 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.1244 | 1.65545 | 0.827726 | − | 0.561132i | \(-0.189634\pi\) | ||||
0.827726 | + | 0.561132i | \(0.189634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3923 | 0.600568 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.53590 | −0.312312 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.3205 | −0.852113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5359 | −0.676385 | −0.338192 | − | 0.941077i | \(-0.609815\pi\) | ||||
−0.338192 | + | 0.941077i | \(0.609815\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.5692 | 0.640258 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.3923 | −0.451002 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.78461 | −0.318861 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3923 | 1.46422 | 0.732110 | − | 0.681186i | \(-0.238536\pi\) | ||||
0.732110 | + | 0.681186i | \(0.238536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.7846 | −0.462834 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.53590 | 0.308616 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.07180 | −0.183132 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.4641 | −1.35099 | −0.675495 | − | 0.737365i | \(-0.736070\pi\) | ||||
−0.675495 | + | 0.737365i | \(0.736070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.67949 | 0.240556 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.0526 | 0.577370 | 0.288685 | − | 0.957424i | \(-0.406782\pi\) | ||||
0.288685 | + | 0.957424i | \(0.406782\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.46410 | 0.196276 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.78461 | −0.171647 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.7846 | 1.17313 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.8564 | −0.495188 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.5359 | 0.590192 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.80385 | 0.0643002 | 0.0321501 | − | 0.999483i | \(-0.489765\pi\) | ||||
0.0321501 | + | 0.999483i | \(0.489765\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3205 | 0.403021 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.1769 | −1.32186 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.14359 | −0.218165 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.32051 | −0.188699 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.6603 | −0.413027 | −0.206514 | − | 0.978444i | \(-0.566212\pi\) | ||||
−0.206514 | + | 0.978444i | \(0.566212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.21539 | −0.113752 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0333 | 0.743176 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.8564 | 0.912453 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.92820 | −0.244187 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.60770 | 0.267804 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.7128 | −1.60718 | −0.803588 | − | 0.595185i | \(-0.797079\pi\) | ||||
−0.803588 | + | 0.595185i | \(0.797079\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.3923 | −1.27791 | −0.638953 | − | 0.769246i | \(-0.720632\pi\) | ||||
−0.638953 | + | 0.769246i | \(0.720632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.4641 | 0.472207 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.9282 | 0.733083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.92820 | 0.312358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.60770 | 0.126063 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.8564 | 1.53060 | 0.765300 | − | 0.643674i | \(-0.222591\pi\) | ||||
0.765300 | + | 0.643674i | \(0.222591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.5692 | 1.51873 | 0.759364 | − | 0.650666i | \(-0.225510\pi\) | ||||
0.759364 | + | 0.650666i | \(0.225510\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.53590 | −0.0882886 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.3397 | 0.429095 | 0.214548 | − | 0.976714i | \(-0.431172\pi\) | ||||
0.214548 | + | 0.976714i | \(0.431172\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.2487 | 1.39790 | 0.698948 | − | 0.715173i | \(-0.253652\pi\) | ||||
0.698948 | + | 0.715173i | \(0.253652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.75129 | 0.0607515 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.3923 | −0.360072 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.26795 | 0.251518 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.8564 | −0.755468 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.07180 | 0.175098 | 0.0875489 | − | 0.996160i | \(-0.472097\pi\) | ||||
0.0875489 | + | 0.996160i | \(0.472097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0000 | −0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.46410 | −0.325961 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4641 | 0.428778 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.00000 | 0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.75129 | 0.0601041 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.3205 | −0.388062 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.6410 | −0.843692 | −0.421846 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421846 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.46410 | −0.0842705 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.1962 | 0.484931 | 0.242466 | − | 0.970160i | \(-0.422044\pi\) | ||||
0.242466 | + | 0.970160i | \(0.422044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.71281 | 0.263158 | 0.131579 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131579 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.78461 | −0.299379 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.7321 | −1.38654 | −0.693268 | − | 0.720680i | \(-0.743830\pi\) | ||||
−0.693268 | + | 0.720680i | \(0.743830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.1962 | 0.482684 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.66025 | −0.124309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.8564 | 1.28419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.39230 | 0.0810602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.9474 | −1.21664 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.9808 | 1.72150 | 0.860749 | − | 0.509030i | \(-0.169996\pi\) | ||||
0.860749 | + | 0.509030i | \(0.169996\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.53590 | −0.287909 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.3205 | −1.18998 | −0.594989 | − | 0.803734i | \(-0.702844\pi\) | ||||
−0.594989 | + | 0.803734i | \(0.702844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.0000 | 0.740359 | 0.370179 | − | 0.928960i | \(-0.379296\pi\) | ||||
0.370179 | + | 0.928960i | \(0.379296\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.07180 | −0.170487 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.5885 | 1.83290 | 0.916451 | − | 0.400148i | \(-0.131041\pi\) | ||||
0.916451 | + | 0.400148i | \(0.131041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.1769 | −0.710251 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.4641 | −0.518067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.928203 | 0.0310611 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.7846 | −0.694753 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.85641 | −0.0619836 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.9282 | 0.631291 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1769 | 0.838765 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.0718 | −0.435002 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.5885 | −1.28131 | −0.640654 | − | 0.767829i | \(-0.721337\pi\) | ||||
−0.640654 | + | 0.767829i | \(0.721337\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.8231 | 0.358979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4641 | 0.711137 | 0.355569 | − | 0.934650i | \(-0.384287\pi\) | ||||
0.355569 | + | 0.934650i | \(0.384287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.14359 | −0.203101 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.1436 | 0.334971 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.4974 | −1.73173 | −0.865865 | − | 0.500278i | \(-0.833231\pi\) | ||||
−0.865865 | + | 0.500278i | \(0.833231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.3205 | 0.438926 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.92820 | 0.228045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.26795 | −0.107450 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.01924 | 0.296231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.5692 | 1.16699 | 0.583494 | − | 0.812117i | \(-0.301685\pi\) | ||||
0.583494 | + | 0.812117i | \(0.301685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.00000 | 0.0983210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.3923 | −0.536660 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.0000 | 0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1769 | −0.365134 | −0.182567 | − | 0.983193i | \(-0.558441\pi\) | ||||
−0.182567 | + | 0.983193i | \(0.558441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.5359 | −0.735431 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.6410 | 0.542482 | 0.271241 | − | 0.962512i | \(-0.412566\pi\) | ||||
0.271241 | + | 0.962512i | \(0.412566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7846 | −0.676840 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.3205 | −1.34274 | −0.671368 | − | 0.741124i | \(-0.734293\pi\) | ||||
−0.671368 | + | 0.741124i | \(0.734293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.46410 | 0.177372 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.4641 | 0.501458 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.4115 | 0.952733 | 0.476367 | − | 0.879247i | \(-0.341953\pi\) | ||||
0.476367 | + | 0.879247i | \(0.341953\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.92820 | 0.224191 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.78461 | −0.283966 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −34.6410 | −1.11862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.7321 | 0.925877 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.1962 | 0.585755 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.6795 | −0.343429 | −0.171715 | − | 0.985147i | \(-0.554931\pi\) | ||||
−0.171715 | + | 0.985147i | \(0.554931\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.53590 | −0.0814648 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.4641 | 0.688816 | 0.344408 | − | 0.938820i | \(-0.388080\pi\) | ||||
0.344408 | + | 0.938820i | \(0.388080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.07180 | −0.290828 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.535898 | −0.0171625 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.8038 | 0.697567 | 0.348783 | − | 0.937203i | \(-0.386595\pi\) | ||||
0.348783 | + | 0.937203i | \(0.386595\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.5692 | 0.945036 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.7513 | 0.502900 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.4449 | 1.80031 | 0.900156 | − | 0.435568i | \(-0.143452\pi\) | ||||
0.900156 | + | 0.435568i | \(0.143452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9282 | −0.411927 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.35898 | −0.0432569 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.9282 | −0.983460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.3923 | 0.393655 | 0.196827 | − | 0.980438i | \(-0.436936\pi\) | ||||
0.196827 | + | 0.980438i | \(0.436936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.2154 | −0.609782 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.0718 | −0.414404 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.60770 | −0.304279 | −0.152139 | − | 0.988359i | \(-0.548616\pi\) | ||||
−0.152139 | + | 0.988359i | \(0.548616\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.0718 | 0.413573 |
(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 | 6080.2.a.z.1.2 | 2 | ||
4.3 | odd | 2 | 6080.2.a.bj.1.1 | 2 | |||
8.3 | odd | 2 | 1520.2.a.l.1.2 | 2 | |||
8.5 | even | 2 | 380.2.a.d.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 3420.2.a.h.1.1 | 2 | |||
40.13 | odd | 4 | 1900.2.c.e.1749.2 | 4 | |||
40.19 | odd | 2 | 7600.2.a.bf.1.1 | 2 | |||
40.29 | even | 2 | 1900.2.a.d.1.2 | 2 | |||
40.37 | odd | 4 | 1900.2.c.e.1749.3 | 4 | |||
152.37 | odd | 2 | 7220.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.a.d.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
1520.2.a.l.1.2 | 2 | 8.3 | odd | 2 | |||
1900.2.a.d.1.2 | 2 | 40.29 | even | 2 | |||
1900.2.c.e.1749.2 | 4 | 40.13 | odd | 4 | |||
1900.2.c.e.1749.3 | 4 | 40.37 | odd | 4 | |||
3420.2.a.h.1.1 | 2 | 24.5 | odd | 2 | |||
6080.2.a.z.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6080.2.a.bj.1.1 | 2 | 4.3 | odd | 2 | |||
7220.2.a.h.1.2 | 2 | 152.37 | odd | 2 | |||
7600.2.a.bf.1.1 | 2 | 40.19 | odd | 2 |