Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 22 x^{10} + 67 x^{9} + 180 x^{8} - 383 x^{7} - 674 x^{6} + 875 x^{5} + 1077 x^{4} + \cdots + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1006) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.75875\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −2.73829 | −1.58095 | −0.790477 | − | 0.612491i | \(-0.790167\pi\) | ||||
−0.790477 | + | 0.612491i | \(0.790167\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48375 | −0.663552 | −0.331776 | − | 0.943358i | \(-0.607648\pi\) | ||||
−0.331776 | + | 0.943358i | \(0.607648\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.26909 | −0.857635 | −0.428818 | − | 0.903391i | \(-0.641070\pi\) | ||||
−0.428818 | + | 0.903391i | \(0.641070\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.49825 | 1.49942 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.54237 | −1.36958 | −0.684789 | − | 0.728742i | \(-0.740105\pi\) | ||||
−0.684789 | + | 0.728742i | \(0.740105\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.28908 | 0.357527 | 0.178764 | − | 0.983892i | \(-0.442790\pi\) | ||||
0.178764 | + | 0.983892i | \(0.442790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.06294 | 1.04905 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.35584 | 0.813910 | 0.406955 | − | 0.913448i | \(-0.366591\pi\) | ||||
0.406955 | + | 0.913448i | \(0.366591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.02589 | 1.38243 | 0.691217 | − | 0.722647i | \(-0.257075\pi\) | ||||
0.691217 | + | 0.722647i | \(0.257075\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.21343 | 1.35588 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.30148 | −0.896921 | −0.448460 | − | 0.893803i | \(-0.648028\pi\) | ||||
−0.448460 | + | 0.893803i | \(0.648028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.79849 | −0.559698 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.10265 | −0.789555 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.74625 | −1.06705 | −0.533526 | − | 0.845784i | \(-0.679133\pi\) | ||||
−0.533526 | + | 0.845784i | \(0.679133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2624 | 1.84318 | 0.921592 | − | 0.388161i | \(-0.126889\pi\) | ||||
0.921592 | + | 0.388161i | \(0.126889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.4384 | 2.16524 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.36676 | 0.569086 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.70900 | 0.774155 | 0.387077 | − | 0.922047i | \(-0.373485\pi\) | ||||
0.387077 | + | 0.922047i | \(0.373485\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.52989 | −0.565234 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.50770 | 1.01633 | 0.508166 | − | 0.861259i | \(-0.330324\pi\) | ||||
0.508166 | + | 0.861259i | \(0.330324\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.5570 | −1.91492 | −0.957460 | − | 0.288567i | \(-0.906821\pi\) | ||||
−0.957460 | + | 0.288567i | \(0.906821\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.67427 | −0.994942 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.97508 | −1.30915 | −0.654575 | − | 0.755997i | \(-0.727152\pi\) | ||||
−0.654575 | + | 0.755997i | \(0.727152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.85124 | −0.264462 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.18926 | −1.28675 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.39473 | −0.741023 | −0.370511 | − | 0.928828i | \(-0.620818\pi\) | ||||
−0.370511 | + | 0.928828i | \(0.620818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.73974 | 0.908786 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.5007 | −2.18557 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2282 | −1.59197 | −0.795986 | − | 0.605315i | \(-0.793047\pi\) | ||||
−0.795986 | + | 0.605315i | \(0.793047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71895 | −0.732236 | −0.366118 | − | 0.930568i | \(-0.619313\pi\) | ||||
−0.366118 | + | 0.930568i | \(0.619313\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.2069 | −1.28595 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.91267 | −0.237238 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.64755 | 1.05647 | 0.528233 | − | 0.849099i | \(-0.322855\pi\) | ||||
0.528233 | + | 0.849099i | \(0.322855\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.7787 | 1.41799 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7302 | −1.62947 | −0.814735 | − | 0.579833i | \(-0.803118\pi\) | ||||
−0.814735 | + | 0.579833i | \(0.803118\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.68126 | 0.430859 | 0.215430 | − | 0.976519i | \(-0.430885\pi\) | ||||
0.215430 | + | 0.976519i | \(0.430885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.66309 | 0.884857 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3070 | 1.17460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.72712 | 0.419334 | 0.209667 | − | 0.977773i | \(-0.432762\pi\) | ||||
0.209667 | + | 0.977773i | \(0.432762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.26049 | −0.251166 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.13641 | 0.344266 | 0.172133 | − | 0.985074i | \(-0.444934\pi\) | ||||
0.172133 | + | 0.985074i | \(0.444934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97922 | −0.540072 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.7349 | 1.68696 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6454 | −1.34041 | −0.670206 | − | 0.742176i | \(-0.733794\pi\) | ||||
−0.670206 | + | 0.742176i | \(0.733794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.92504 | −0.306628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.1015 | −2.91399 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.94091 | −0.917318 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6647 | 1.48897 | 0.744485 | − | 0.667639i | \(-0.232695\pi\) | ||||
0.744485 | + | 0.667639i | \(0.232695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.4327 | −2.05357 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8041 | −1.37356 | −0.686779 | − | 0.726867i | \(-0.740976\pi\) | ||||
−0.686779 | + | 0.726867i | \(0.740976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.19189 | 0.905704 | 0.452852 | − | 0.891586i | \(-0.350407\pi\) | ||||
0.452852 | + | 0.891586i | \(0.350407\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.21917 | −0.899699 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.1898 | −1.17843 | −0.589217 | − | 0.807975i | \(-0.700564\pi\) | ||||
−0.589217 | + | 0.807975i | \(0.700564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4565 | −1.38468 | −0.692341 | − | 0.721570i | \(-0.743421\pi\) | ||||
−0.692341 | + | 0.721570i | \(0.743421\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.8946 | −1.22390 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.33155 | −0.783766 | −0.391883 | − | 0.920015i | \(-0.628176\pi\) | ||||
−0.391883 | + | 0.920015i | \(0.628176\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.38232 | 0.595154 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.79862 | 0.536082 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.61469 | −0.698037 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.63315 | 0.875741 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.8200 | −1.60677 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5710 | 1.03494 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1126 | 1.16356 | 0.581779 | − | 0.813347i | \(-0.302357\pi\) | ||||
0.581779 | + | 0.813347i | \(0.302357\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 34.3847 | 3.02740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.60813 | 0.839467 | 0.419733 | − | 0.907647i | \(-0.362124\pi\) | ||||
0.419733 | + | 0.907647i | \(0.362124\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.6733 | −1.18562 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.08730 | 0.523911 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4046 | 0.888924 | 0.444462 | − | 0.895798i | \(-0.353395\pi\) | ||||
0.444462 | + | 0.895798i | \(0.353395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.09136 | −0.516663 | −0.258331 | − | 0.966056i | \(-0.583173\pi\) | ||||
−0.258331 | + | 0.966056i | \(0.583173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.5764 | 2.06971 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.85550 | −0.489661 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.52599 | 0.708045 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.06922 | 0.418103 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.59684 | 0.458511 | 0.229256 | − | 0.973366i | \(-0.426371\pi\) | ||||
0.229256 | + | 0.973366i | \(0.426371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.6914 | −1.60246 | −0.801230 | − | 0.598356i | \(-0.795821\pi\) | ||||
−0.801230 | + | 0.598356i | \(0.795821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.0954 | 1.22039 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2268 | −1.22305 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.2281 | −1.05572 | −0.527859 | − | 0.849332i | \(-0.677005\pi\) | ||||
−0.527859 | + | 0.849332i | \(0.677005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7723 | 1.17152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.76044 | 0.769231 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0382 | 0.786249 | 0.393125 | − | 0.919485i | \(-0.371394\pi\) | ||||
0.393125 | + | 0.919485i | \(0.371394\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.4554 | −1.43675 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.3143 | 1.33982 | 0.669911 | − | 0.742442i | \(-0.266332\pi\) | ||||
0.669911 | + | 0.742442i | \(0.266332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3383 | −0.872174 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.1060 | 2.07285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.01182 | −0.381042 | −0.190521 | − | 0.981683i | \(-0.561018\pi\) | ||||
−0.190521 | + | 0.981683i | \(0.561018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.35002 | 0.480017 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33.4843 | 2.51683 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.32616 | 0.398096 | 0.199048 | − | 0.979990i | \(-0.436215\pi\) | ||||
0.199048 | + | 0.979990i | \(0.436215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6765 | 0.793579 | 0.396789 | − | 0.917910i | \(-0.370124\pi\) | ||||
0.396789 | + | 0.917910i | \(0.370124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.6602 | 1.15763 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.98697 | −0.513692 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2435 | −1.11471 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.30928 | 0.677150 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.95164 | 0.720075 | 0.360038 | − | 0.932938i | \(-0.382764\pi\) | ||||
0.360038 | + | 0.932938i | \(0.382764\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8905 | −1.21580 | −0.607902 | − | 0.794012i | \(-0.707989\pi\) | ||||
−0.607902 | + | 0.794012i | \(0.707989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.23747 | 0.375063 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4888 | −1.17478 | −0.587388 | − | 0.809305i | \(-0.699844\pi\) | ||||
−0.587388 | + | 0.809305i | \(0.699844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.08774 | −0.147996 | −0.0739979 | − | 0.997258i | \(-0.523576\pi\) | ||||
−0.0739979 | + | 0.997258i | \(0.523576\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.6795 | −1.67022 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.0388 | 0.915141 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.65578 | −0.674389 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.3491 | −1.34486 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.3718 | −1.89335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2647 | −1.25739 | −0.628697 | − | 0.777651i | \(-0.716411\pi\) | ||||
−0.628697 | + | 0.777651i | \(0.716411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37.5972 | 2.57612 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.6314 | 1.27065 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.2863 | −1.58078 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0804 | −0.681168 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.32595 | 0.290995 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.67601 | 0.112234 | 0.0561169 | − | 0.998424i | \(-0.482128\pi\) | ||||
0.0561169 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.5883 | −0.839221 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.46448 | 0.429063 | 0.214531 | − | 0.976717i | \(-0.431178\pi\) | ||||
0.214531 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3663 | −1.08151 | −0.540757 | − | 0.841179i | \(-0.681862\pi\) | ||||
−0.540757 | + | 0.841179i | \(0.681862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.2237 | −1.85698 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7072 | −1.22555 | −0.612774 | − | 0.790258i | \(-0.709946\pi\) | ||||
−0.612774 | + | 0.790258i | \(0.709946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.3168 | 0.868690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.2060 | −0.662948 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.78654 | 0.633039 | 0.316519 | − | 0.948586i | \(-0.397486\pi\) | ||||
0.316519 | + | 0.948586i | \(0.397486\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.40661 | 0.348270 | 0.174135 | − | 0.984722i | \(-0.444287\pi\) | ||||
0.174135 | + | 0.984722i | \(0.444287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.4978 | 1.18664 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.74677 | 0.175485 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.76787 | 0.494258 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.58841 | −0.544269 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.6955 | 0.738213 | 0.369106 | − | 0.929387i | \(-0.379664\pi\) | ||||
0.369106 | + | 0.929387i | \(0.379664\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.5389 | 1.22840 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.6346 | 0.853829 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.81646 | 0.612334 | 0.306167 | − | 0.951978i | \(-0.400953\pi\) | ||||
0.306167 | + | 0.951978i | \(0.400953\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6851 | −0.663942 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.8481 | −1.59996 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5073 | −1.14121 | −0.570604 | − | 0.821225i | \(-0.693291\pi\) | ||||
−0.570604 | + | 0.821225i | \(0.693291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.00442 | 0.491707 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.6269 | 2.11913 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −32.5020 | −1.98168 | −0.990840 | − | 0.135043i | \(-0.956883\pi\) | ||||
−0.990840 | + | 0.135043i | \(0.956883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5799 | −0.885668 | −0.442834 | − | 0.896604i | \(-0.646027\pi\) | ||||
−0.442834 | + | 0.896604i | \(0.646027\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00963 | 0.484765 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.7118 | 0.766550 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.33979 | 0.441005 | 0.220503 | − | 0.975386i | \(-0.429230\pi\) | ||||
0.220503 | + | 0.975386i | \(0.429230\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46.1629 | 2.76370 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.5248 | 1.28406 | 0.642030 | − | 0.766680i | \(-0.278093\pi\) | ||||
0.642030 | + | 0.766680i | \(0.278093\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.57829 | −0.153264 | −0.0766318 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766318 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.4828 | 1.45024 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.7665 | −0.871641 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.73837 | −0.337551 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −40.1561 | −2.35399 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.15409 | 0.534787 | 0.267394 | − | 0.963587i | \(-0.413838\pi\) | ||||
0.267394 | + | 0.963587i | \(0.413838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.1435 | 1.05636 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.6358 | 1.08136 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.54497 | −0.320674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.4929 | 1.64230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 37.7996 | 2.17153 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.48548 | 0.485877 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.44659 | 0.139634 | 0.0698171 | − | 0.997560i | \(-0.477758\pi\) | ||||
0.0698171 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.1701 | −1.43188 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.6140 | 1.90608 | 0.953038 | − | 0.302850i | \(-0.0979382\pi\) | ||||
0.953038 | + | 0.302850i | \(0.0979382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.8099 | 0.837103 | 0.418552 | − | 0.908193i | \(-0.362538\pi\) | ||||
0.418552 | + | 0.908193i | \(0.362538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.1445 | 0.853297 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.52762 | −0.198131 | −0.0990653 | − | 0.995081i | \(-0.531585\pi\) | ||||
−0.0990653 | + | 0.995081i | \(0.531585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.1016 | 1.46141 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 33.3793 | 1.86305 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.2219 | 1.12518 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.60749 | −0.200107 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 39.5862 | 2.18912 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.3653 | 1.12277 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.4454 | 1.50854 | 0.754268 | − | 0.656566i | \(-0.227992\pi\) | ||||
0.754268 | + | 0.656566i | \(0.227992\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.1823 | 1.16078 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8308 | −0.701021 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.6271 | 1.34152 | 0.670761 | − | 0.741673i | \(-0.265967\pi\) | ||||
0.670761 | + | 0.741673i | \(0.265967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.8142 | 1.23910 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −46.6157 | −2.52438 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0842 | 1.08445 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.4767 | −0.940912 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.6383 | −1.75212 | −0.876058 | − | 0.482205i | \(-0.839836\pi\) | ||||
−0.876058 | + | 0.482205i | \(0.839836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9088 | 0.798048 | 0.399024 | − | 0.916940i | \(-0.369349\pi\) | ||||
0.399024 | + | 0.916940i | \(0.369349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.28866 | −0.282288 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.3756 | 1.56351 | 0.781753 | − | 0.623588i | \(-0.214326\pi\) | ||||
0.781753 | + | 0.623588i | \(0.214326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3721 | 1.08124 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.8513 | 1.10357 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.9128 | −1.10374 | −0.551868 | − | 0.833932i | \(-0.686085\pi\) | ||||
−0.551868 | + | 0.833932i | \(0.686085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3114 | 0.911124 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.3784 | −1.38451 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.46207 | −0.285898 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1787 | 0.740124 | 0.370062 | − | 0.929007i | \(-0.379336\pi\) | ||||
0.370062 | + | 0.929007i | \(0.379336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.2732 | 1.52390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2411 | 0.635527 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.24233 | 0.323215 | 0.161608 | − | 0.986855i | \(-0.448332\pi\) | ||||
0.161608 | + | 0.986855i | \(0.448332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.6848 | −1.63620 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.40739 | −0.381500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.864107 | −0.0443862 | −0.0221931 | − | 0.999754i | \(-0.507065\pi\) | ||||
−0.0221931 | + | 0.999754i | \(0.507065\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.9062 | −1.83953 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.99182 | −0.408363 | −0.204181 | − | 0.978933i | \(-0.565453\pi\) | ||||
−0.204181 | + | 0.978933i | \(0.565453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.2931 | −0.779407 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −56.4844 | −2.87126 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.0666 | −1.11882 | −0.559410 | − | 0.828891i | \(-0.688972\pi\) | ||||
−0.559410 | + | 0.828891i | \(0.688972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.4351 | −0.730013 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.3099 | −1.32716 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.53011 | −0.278250 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.9314 | −0.849765 | −0.424882 | − | 0.905249i | \(-0.639685\pi\) | ||||
−0.424882 | + | 0.905249i | \(0.639685\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 37.4415 | 1.87442 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.21200 | 0.460026 | 0.230013 | − | 0.973188i | \(-0.426123\pi\) | ||||
0.230013 | + | 0.973188i | \(0.426123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.2291 | 0.658988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.35400 | 0.166662 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.3900 | −1.06026 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.42103 | −0.119712 | −0.0598561 | − | 0.998207i | \(-0.519064\pi\) | ||||
−0.0598561 | + | 0.998207i | \(0.519064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.4908 | −1.40535 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.7468 | 1.36533 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.65364 | −0.228438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.6799 | 0.816820 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.8392 | 0.871500 | 0.435750 | − | 0.900068i | \(-0.356483\pi\) | ||||
0.435750 | + | 0.900068i | \(0.356483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.45330 | 0.411989 | 0.205994 | − | 0.978553i | \(-0.433957\pi\) | ||||
0.205994 | + | 0.978553i | \(0.433957\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −40.3722 | −1.96296 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.39127 | −0.455544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9768 | 0.627991 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.0341 | 0.774132 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.94384 | 0.0936314 | 0.0468157 | − | 0.998904i | \(-0.485093\pi\) | ||||
0.0468157 | + | 0.998904i | \(0.485093\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.76438 | −0.277018 | −0.138509 | − | 0.990361i | \(-0.544231\pi\) | ||||
−0.138509 | + | 0.990361i | \(0.544231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.3467 | −1.11939 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.9203 | −1.23993 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.55943 | 0.313064 | 0.156532 | − | 0.987673i | \(-0.449968\pi\) | ||||
0.156532 | + | 0.987673i | \(0.449968\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.32732 | −0.396539 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.19833 | −0.199469 | −0.0997344 | − | 0.995014i | \(-0.531799\pi\) | ||||
−0.0997344 | + | 0.995014i | \(0.531799\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7626 | 0.889433 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.3258 | −0.724885 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.3731 | 1.76374 | 0.881872 | − | 0.471489i | \(-0.156283\pi\) | ||||
0.881872 | + | 0.471489i | \(0.156283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.5604 | −1.39194 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.9207 | 2.53342 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.34003 | 0.203464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.8271 | −0.553246 | −0.276623 | − | 0.960978i | \(-0.589215\pi\) | ||||
−0.276623 | + | 0.960978i | \(0.589215\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.7678 | −0.642627 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1984 | 1.08046 | 0.540230 | − | 0.841518i | \(-0.318337\pi\) | ||||
0.540230 | + | 0.841518i | \(0.318337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0392 | 0.931299 | 0.465650 | − | 0.884969i | \(-0.345821\pi\) | ||||
0.465650 | + | 0.884969i | \(0.345821\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 41.6955 | 1.93358 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.81377 | −0.361578 | −0.180789 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180789 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.6221 | −0.906062 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.2224 | 1.66904 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 57.0384 | 2.62263 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.8634 | −0.773746 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.2668 | −1.11110 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.44168 | 0.248637 | 0.124318 | − | 0.992242i | \(-0.460326\pi\) | ||||
0.124318 | + | 0.992242i | \(0.460326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.07029 | 0.276781 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.7270 | −1.21612 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.7587 | −0.988010 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.0629078 | −0.00285062 | −0.00142531 | − | 0.999999i | \(-0.500454\pi\) | ||||
−0.00142531 | + | 0.999999i | \(0.500454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.4874 | −1.24302 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.2044 | −0.731296 | −0.365648 | − | 0.930753i | \(-0.619153\pi\) | ||||
−0.365648 | + | 0.930753i | \(0.619153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.2835 | −0.868484 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.3170 | 1.36265 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.1550 | 1.39749 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.19623 | 0.411680 | 0.205840 | − | 0.978586i | \(-0.434007\pi\) | ||||
0.205840 | + | 0.978586i | \(0.434007\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −47.4117 | −2.11820 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.4818 | 0.911427 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.0475 | 1.37887 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.7710 | −1.05363 | −0.526815 | − | 0.849980i | \(-0.676614\pi\) | ||||
−0.526815 | + | 0.849980i | \(0.676614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.35311 | −0.369520 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.7221 | −1.09151 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.6385 | −0.600982 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.7682 | 1.79298 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.7238 | 0.602410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.9106 | 0.609435 | 0.304717 | − | 0.952443i | \(-0.401438\pi\) | ||||
0.304717 | + | 0.952443i | \(0.401438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.8699 | 1.26239 | 0.631196 | − | 0.775623i | \(-0.282564\pi\) | ||||
0.631196 | + | 0.775623i | \(0.282564\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.3882 | −0.758885 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.4390 | 1.50018 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.49725 | −0.195533 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −55.0054 | −2.38703 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.38896 | 0.363366 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.0866 | 0.781953 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.5846 | −0.629372 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.40900 | 0.362201 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3229 | 0.486807 | 0.243404 | − | 0.969925i | \(-0.421736\pi\) | ||||
0.243404 | + | 0.969925i | \(0.421736\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.2354 | −1.25461 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.4498 | 0.918810 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2578 | −0.908917 | −0.454459 | − | 0.890768i | \(-0.650167\pi\) | ||||
−0.454459 | + | 0.890768i | \(0.650167\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.7253 | −1.09793 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.6263 | −1.47513 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.45717 | −0.359636 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.1324 | 0.812124 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.20090 | −0.177998 | −0.0889990 | − | 0.996032i | \(-0.528367\pi\) | ||||
−0.0889990 | + | 0.996032i | \(0.528367\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.1870 | −0.684636 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.7411 | 1.76231 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.1852 | 0.597836 | 0.298918 | − | 0.954279i | \(-0.403374\pi\) | ||||
0.298918 | + | 0.954279i | \(0.403374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.3619 | 0.520070 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.12926 | 0.215409 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.7571 | −1.75055 | −0.875274 | − | 0.483627i | \(-0.839319\pi\) | ||||
−0.875274 | + | 0.483627i | \(0.839319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.4943 | −0.648417 | −0.324209 | − | 0.945986i | \(-0.605098\pi\) | ||||
−0.324209 | + | 0.945986i | \(0.605098\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.2505 | −1.13841 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0377 | 0.502005 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.1385 | −1.42120 | −0.710601 | − | 0.703595i | \(-0.751577\pi\) | ||||
−0.710601 | + | 0.703595i | \(0.751577\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.2511 | 1.92213 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.11680 | −0.295254 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.5049 | 1.01489 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.60369 | −0.355719 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.6074 | 0.437812 | 0.218906 | − | 0.975746i | \(-0.429751\pi\) | ||||
0.218906 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 61.8402 | 2.54808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.1511 | 1.85727 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.82095 | 0.280103 | 0.140051 | − | 0.990144i | \(-0.455273\pi\) | ||||
0.140051 | + | 0.990144i | \(0.455273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.2983 | 0.463184 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.71684 | 0.233975 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.9243 | −1.18182 | −0.590908 | − | 0.806739i | \(-0.701231\pi\) | ||||
−0.590908 | + | 0.806739i | \(0.701231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.18366 | 0.333818 | 0.166909 | − | 0.985972i | \(-0.446621\pi\) | ||||
0.166909 | + | 0.985972i | \(0.446621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.8988 | 1.58408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.2932 | −0.581100 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.0315 | −1.09717 | −0.548587 | − | 0.836093i | \(-0.684834\pi\) | ||||
−0.548587 | + | 0.836093i | \(0.684834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −35.7039 | −1.44680 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.5696 | −0.468057 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.7511 | 1.16124 | 0.580622 | − | 0.814173i | \(-0.302809\pi\) | ||||
0.580622 | + | 0.814173i | \(0.302809\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.4404 | 1.06618 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.0195 | 1.77216 | 0.886079 | − | 0.463534i | \(-0.153419\pi\) | ||||
0.886079 | + | 0.463534i | \(0.153419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2639 | 0.613508 | 0.306754 | − | 0.951789i | \(-0.400757\pi\) | ||||
0.306754 | + | 0.951789i | \(0.400757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.6475 | 0.708169 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.6936 | 1.14958 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.17600 | −0.127040 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 74.9521 | 2.99330 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8026 | 0.630092 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.0998 | −1.43711 | −0.718555 | − | 0.695470i | \(-0.755196\pi\) | ||||
−0.718555 | + | 0.695470i | \(0.755196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 50.0141 | 1.98788 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.4558 | −0.772081 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.38640 | −0.0945524 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −61.7617 | −2.44326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.46253 | 0.255255 | 0.127627 | − | 0.991822i | \(-0.459264\pi\) | ||||
0.127627 | + | 0.991822i | \(0.459264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.1699 | −1.07148 | −0.535738 | − | 0.844384i | \(-0.679967\pi\) | ||||
−0.535738 | + | 0.844384i | \(0.679967\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −51.0182 | −2.00884 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.5369 | 1.16121 | 0.580607 | − | 0.814184i | \(-0.302815\pi\) | ||||
0.580607 | + | 0.814184i | \(0.302815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.5449 | 2.18033 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 63.7648 | 2.49914 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.1850 | 1.72909 | 0.864547 | − | 0.502552i | \(-0.167605\pi\) | ||||
0.864547 | + | 0.502552i | \(0.167605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2561 | −0.557030 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.5592 | 0.646037 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.6833 | −1.39002 | −0.695012 | − | 0.718999i | \(-0.744601\pi\) | ||||
−0.695012 | + | 0.718999i | \(0.744601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2086 | −0.630441 | −0.315221 | − | 0.949018i | \(-0.602078\pi\) | ||||
−0.315221 | + | 0.949018i | \(0.602078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.8457 | −0.460050 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.2877 | 0.786724 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.7174 | 0.957061 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.58940 | −0.177436 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.9776 | 1.00285 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.6223 | −0.949119 | −0.474560 | − | 0.880223i | \(-0.657393\pi\) | ||||
−0.474560 | + | 0.880223i | \(0.657393\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.4812 | 0.441913 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.20008 | 0.0845560 | 0.0422780 | − | 0.999106i | \(-0.486538\pi\) | ||||
0.0422780 | + | 0.999106i | \(0.486538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.2754 | −1.27699 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7016 | −0.678328 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4127 | 0.666280 | 0.333140 | − | 0.942877i | \(-0.391892\pi\) | ||||
0.333140 | + | 0.942877i | \(0.391892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4378 | −0.589848 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44.8157 | 1.70982 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.95425 | −0.264936 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.1005 | 0.764661 | 0.382330 | − | 0.924026i | \(-0.375122\pi\) | ||||
0.382330 | + | 0.924026i | \(0.375122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.3637 | 1.76121 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.03805 | 0.342833 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.8388 | 0.827202 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.2257 | 1.93753 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.92749 | 0.374956 | 0.187478 | − | 0.982269i | \(-0.439969\pi\) | ||||
0.187478 | + | 0.982269i | \(0.439969\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.3759 | 1.07022 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −36.4652 | −1.37336 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.3227 | 1.17801 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.7960 | 1.34435 | 0.672174 | − | 0.740393i | \(-0.265361\pi\) | ||||
0.672174 | + | 0.740393i | \(0.265361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.7655 | 0.628756 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −44.1436 | −1.65319 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.68808 | 0.324916 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.7984 | −1.00081 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.1524 | −0.938027 | −0.469014 | − | 0.883191i | \(-0.655390\pi\) | ||||
−0.469014 | + | 0.883191i | \(0.655390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.8572 | −0.776763 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.8049 | −0.550600 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.0808 | 0.597227 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.6890 | 0.989839 | 0.494919 | − | 0.868939i | \(-0.335198\pi\) | ||||
0.494919 | + | 0.868939i | \(0.335198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8710 | −1.62485 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.1391 | −1.55857 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.0102 | 1.84717 | 0.923584 | − | 0.383397i | \(-0.125246\pi\) | ||||
0.923584 | + | 0.383397i | \(0.125246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.52145 | −0.277433 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −39.2804 | −1.44691 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.7422 | −1.05730 | −0.528650 | − | 0.848840i | \(-0.677302\pi\) | ||||
−0.528650 | + | 0.848840i | \(0.677302\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.2707 | −0.781399 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.3309 | 1.55297 | 0.776485 | − | 0.630136i | \(-0.217001\pi\) | ||||
0.776485 | + | 0.630136i | \(0.217001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.30431 | −0.304246 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.1084 | 0.516198 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.6598 | 1.01067 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.1796 | 1.46617 | 0.733086 | − | 0.680135i | \(-0.238079\pi\) | ||||
0.733086 | + | 0.680135i | \(0.238079\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −32.0257 | −1.16708 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.2170 | 1.06332 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.2258 | −1.31665 | −0.658325 | − | 0.752734i | \(-0.728735\pi\) | ||||
−0.658325 | + | 0.752734i | \(0.728735\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −53.5033 | −1.94205 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2959 | 0.880726 | 0.440363 | − | 0.897820i | \(-0.354850\pi\) | ||||
0.440363 | + | 0.897820i | \(0.354850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.8031 | 1.18755 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.3978 | −0.809793 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.7631 | −0.569173 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.8393 | −1.03997 | −0.519985 | − | 0.854175i | \(-0.674062\pi\) | ||||
−0.519985 | + | 0.854175i | \(0.674062\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.8804 | −0.968072 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.7214 | 0.385621 | 0.192810 | − | 0.981236i | \(-0.438240\pi\) | ||||
0.192810 | + | 0.981236i | \(0.438240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.7193 | −1.03163 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29.2590 | 1.04966 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.2147 | 1.40501 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.3675 | 2.23169 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.5748 | 0.842496 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.6272 | 0.700524 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.1775 | 1.39653 | 0.698264 | − | 0.715841i | \(-0.253956\pi\) | ||||
0.698264 | + | 0.715841i | \(0.253956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.6784 | 1.80420 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.9050 | 0.672185 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.37220 | −0.261794 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21.9184 | −0.777367 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.9907 | −0.460153 | −0.230077 | − | 0.973172i | \(-0.573898\pi\) | ||||
−0.230077 | + | 0.973172i | \(0.573898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.1189 | −1.06553 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −56.8822 | −2.00984 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.7217 | −0.590095 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.4820 | −0.510425 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 88.9999 | 3.13294 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.8834 | 1.61317 | 0.806587 | − | 0.591115i | \(-0.201312\pi\) | ||||
0.806587 | + | 0.591115i | \(0.201312\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.78811 | −0.308592 | −0.154296 | − | 0.988025i | \(-0.549311\pi\) | ||||
−0.154296 | + | 0.988025i | \(0.549311\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.9241 | 1.40020 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8941 | −0.521718 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −75.6669 | −2.64725 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.1576 | −0.459763 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.7771 | 1.03923 | 0.519613 | − | 0.854402i | \(-0.326076\pi\) | ||||
0.519613 | + | 0.854402i | \(0.326076\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.40161 | −0.223146 | −0.111573 | − | 0.993756i | \(-0.535589\pi\) | ||||
−0.111573 | + | 0.993756i | \(0.535589\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.8086 | −1.21188 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.2358 | −0.529799 | −0.264900 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264900 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.979554 | −0.0340213 | −0.0170107 | − | 0.999855i | \(-0.505415\pi\) | ||||
−0.0170107 | + | 0.999855i | \(0.505415\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.0985 | −0.697209 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.21244 | −0.215248 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.6901 | −0.889042 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42.1031 | −1.45530 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.0218 | 0.553133 | 0.276566 | − | 0.960995i | \(-0.410803\pi\) | ||||
0.276566 | + | 0.960995i | \(0.410803\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.01938 | 0.138599 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −58.9411 | −2.03004 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.8231 | 0.578733 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.8585 | −0.751066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.06012 | 0.242303 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.2557 | −0.694355 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0533 | 0.412697 | 0.206349 | − | 0.978479i | \(-0.433842\pi\) | ||||
0.206349 | + | 0.978479i | \(0.433842\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −40.2184 | −1.37544 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2478 | 0.555014 | 0.277507 | − | 0.960724i | \(-0.410492\pi\) | ||||
0.277507 | + | 0.960724i | \(0.410492\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.6855 | −1.66113 | −0.830564 | − | 0.556923i | \(-0.811982\pi\) | ||||
−0.830564 | + | 0.556923i | \(0.811982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.4351 | 1.37803 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.0309 | 0.954183 | 0.477091 | − | 0.878854i | \(-0.341691\pi\) | ||||
0.477091 | + | 0.878854i | \(0.341691\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.43628 | 0.252841 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.7133 | 0.533653 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.9300 | −0.574310 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1474 | 0.377715 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 65.9653 | 2.23259 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.2556 | −0.887602 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.43157 | −0.149643 | −0.0748217 | − | 0.997197i | \(-0.523839\pi\) | ||||
−0.0748217 | + | 0.997197i | \(0.523839\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.0666 | −0.845474 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1050 | 0.407829 | 0.203914 | − | 0.978989i | \(-0.434634\pi\) | ||||
0.203914 | + | 0.978989i | \(0.434634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6896 | 0.999136 | 0.499568 | − | 0.866275i | \(-0.333492\pi\) | ||||
0.499568 | + | 0.866275i | \(0.333492\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.6823 | −1.67005 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.2081 | 1.38363 | 0.691816 | − | 0.722074i | \(-0.256811\pi\) | ||||
0.691816 | + | 0.722074i | \(0.256811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.7537 | −0.997907 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.2680 | 0.343991 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −54.0828 | −1.80981 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.90269 | −0.264158 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.1837 | 0.506971 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.9704 | −1.96677 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.1038 | −0.603125 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −78.0218 | −2.59640 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.8413 | −0.526581 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.7444 | 1.88417 | 0.942083 | − | 0.335380i | \(-0.108865\pi\) | ||||
0.942083 | + | 0.335380i | \(0.108865\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −62.0942 | −2.05953 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.5438 | −1.70772 | −0.853861 | − | 0.520501i | \(-0.825745\pi\) | ||||
−0.853861 | + | 0.520501i | \(0.825745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.2467 | −0.471499 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.2357 | −0.768150 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.8017 | −0.719956 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.67727 | −0.319224 | −0.159612 | − | 0.987180i | \(-0.551024\pi\) | ||||
−0.159612 | + | 0.987180i | \(0.551024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.69947 | −0.220755 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.6993 | −0.582580 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.1781 | −0.433293 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.3474 | 1.35803 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.3825 | −0.931201 | −0.465601 | − | 0.884995i | \(-0.654162\pi\) | ||||
−0.465601 | + | 0.884995i | \(0.654162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.1553 | −0.365602 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −92.0450 | −3.01342 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.6175 | 0.739670 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.0495 | 1.17769 | 0.588844 | − | 0.808247i | \(-0.299583\pi\) | ||||
0.588844 | + | 0.808247i | \(0.299583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40.5538 | −1.32342 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.76404 | −0.187902 | −0.0939512 | − | 0.995577i | \(-0.529950\pi\) | ||||
−0.0939512 | + | 0.995577i | \(0.529950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.9927 | −0.911569 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.8126 | −0.449325 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.33942 | 0.0435252 | 0.0217626 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217626 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.74545 | 0.154044 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.65965 | 0.313236 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.1859 | −0.686280 | −0.343140 | − | 0.939284i | \(-0.611491\pi\) | ||||
−0.343140 | + | 0.939284i | \(0.611491\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.7657 | −0.477808 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −71.4739 | −2.31042 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.6089 | −0.762372 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.3171 | 2.39732 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −54.8328 | −1.76696 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.0612 | 0.806749 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.9570 | −1.47788 | −0.738938 | − | 0.673773i | \(-0.764672\pi\) | ||||
−0.738938 | + | 0.673773i | \(0.764672\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −55.3735 | −1.77885 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7697 | 0.377707 | 0.188853 | − | 0.982005i | \(-0.439523\pi\) | ||||
0.188853 | + | 0.982005i | \(0.439523\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.8218 | 0.443108 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.87836 | 0.316361 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.5288 | 1.07268 | 0.536341 | − | 0.844001i | \(-0.319806\pi\) | ||||
0.536341 | + | 0.844001i | \(0.319806\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.4402 | 1.83580 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −65.0290 | −2.07622 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.8579 | −0.952320 | −0.476160 | − | 0.879359i | \(-0.657972\pi\) | ||||
−0.476160 | + | 0.879359i | \(0.657972\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.4652 | 0.779526 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −55.7660 | −1.77505 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.0136 | 1.71753 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.9384 | 1.20515 | 0.602577 | − | 0.798061i | \(-0.294141\pi\) | ||||
0.602577 | + | 0.798061i | \(0.294141\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −75.1536 | −2.38493 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.09768 | 0.0982030 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.1960 | 1.08300 | 0.541499 | − | 0.840701i | \(-0.317857\pi\) | ||||
0.541499 | + | 0.840701i | \(0.317857\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.3194 | −0.611238 |
(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 | 8048.2.a.r.1.2 | 12 | ||
4.3 | odd | 2 | 1006.2.a.i.1.11 | ✓ | 12 | ||
12.11 | even | 2 | 9054.2.a.bj.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1006.2.a.i.1.11 | ✓ | 12 | 4.3 | odd | 2 | ||
8048.2.a.r.1.2 | 12 | 1.1 | even | 1 | trivial | ||
9054.2.a.bj.1.9 | 12 | 12.11 | even | 2 |