Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, 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("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4507648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 637) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.66745\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44785 | 1.73089 | 0.865444 | − | 0.501005i | \(-0.167036\pi\) | ||||
0.865444 | + | 0.501005i | \(0.167036\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.99195 | 1.99598 | ||||||||
\(5\) | −0.910286 | −0.407092 | −0.203546 | − | 0.979065i | \(-0.565247\pi\) | ||||
−0.203546 | + | 0.979065i | \(0.565247\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.87599 | 1.72392 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.22824 | −0.704632 | ||||||||
\(11\) | −3.67837 | −1.10907 | −0.554534 | − | 0.832161i | \(-0.687104\pi\) | ||||
−0.554534 | + | 0.832161i | \(0.687104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95177 | 0.987943 | ||||||||
\(17\) | −7.18531 | −1.74269 | −0.871347 | − | 0.490668i | \(-0.836753\pi\) | ||||
−0.871347 | + | 0.490668i | \(0.836753\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.97802 | −0.453789 | −0.226894 | − | 0.973919i | \(-0.572857\pi\) | ||||
−0.226894 | + | 0.973919i | \(0.572857\pi\) | |||||||
\(20\) | −3.63382 | −0.812547 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.00407 | −1.91967 | ||||||||
\(23\) | 0.596700 | 0.124421 | 0.0622103 | − | 0.998063i | \(-0.480185\pi\) | ||||
0.0622103 | + | 0.998063i | \(0.480185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.17138 | −0.834276 | ||||||||
\(26\) | 2.44785 | 0.480062 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.64900 | 0.677602 | 0.338801 | − | 0.940858i | \(-0.389979\pi\) | ||||
0.338801 | + | 0.940858i | \(0.389979\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.08833 | −1.27310 | −0.636551 | − | 0.771235i | \(-0.719639\pi\) | ||||
−0.636551 | + | 0.771235i | \(0.719639\pi\) | |||||||
\(32\) | −0.0786478 | −0.0139031 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17.5885 | −3.01641 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.710851 | 0.116863 | 0.0584316 | − | 0.998291i | \(-0.481390\pi\) | ||||
0.0584316 | + | 0.998291i | \(0.481390\pi\) | |||||||
\(38\) | −4.84189 | −0.785458 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.43855 | −0.701796 | ||||||||
\(41\) | −5.27529 | −0.823863 | −0.411931 | − | 0.911215i | \(-0.635146\pi\) | ||||
−0.411931 | + | 0.911215i | \(0.635146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0790 | 1.68954 | 0.844768 | − | 0.535132i | \(-0.179738\pi\) | ||||
0.844768 | + | 0.535132i | \(0.179738\pi\) | |||||||
\(44\) | −14.6839 | −2.21367 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.46063 | 0.215358 | ||||||||
\(47\) | −12.1135 | −1.76693 | −0.883467 | − | 0.468494i | \(-0.844797\pi\) | ||||
−0.883467 | + | 0.468494i | \(0.844797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.2109 | −1.44404 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.99195 | 0.553584 | ||||||||
\(53\) | 11.4484 | 1.57256 | 0.786282 | − | 0.617868i | \(-0.212003\pi\) | ||||
0.786282 | + | 0.617868i | \(0.212003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.34837 | 0.451494 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.93219 | 1.17285 | ||||||||
\(59\) | −9.58986 | −1.24849 | −0.624247 | − | 0.781227i | \(-0.714594\pi\) | ||||
−0.624247 | + | 0.781227i | \(0.714594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.98536 | 0.894384 | 0.447192 | − | 0.894438i | \(-0.352424\pi\) | ||||
0.447192 | + | 0.894438i | \(0.352424\pi\) | |||||||
\(62\) | −17.3511 | −2.20360 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.09606 | −1.01201 | ||||||||
\(65\) | −0.910286 | −0.112907 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.22839 | 0.150072 | 0.0750360 | − | 0.997181i | \(-0.476093\pi\) | ||||
0.0750360 | + | 0.997181i | \(0.476093\pi\) | |||||||
\(68\) | −28.6834 | −3.47837 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3635 | −1.34859 | −0.674297 | − | 0.738460i | \(-0.735553\pi\) | ||||
−0.674297 | + | 0.738460i | \(0.735553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.53419 | 0.764769 | 0.382384 | − | 0.924003i | \(-0.375103\pi\) | ||||
0.382384 | + | 0.924003i | \(0.375103\pi\) | |||||||
\(74\) | 1.74005 | 0.202277 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.89616 | −0.905752 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.5204 | −1.29615 | −0.648074 | − | 0.761577i | \(-0.724425\pi\) | ||||
−0.648074 | + | 0.761577i | \(0.724425\pi\) | |||||||
\(80\) | −3.59725 | −0.402184 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.9131 | −1.42601 | ||||||||
\(83\) | −7.16403 | −0.786355 | −0.393177 | − | 0.919463i | \(-0.628624\pi\) | ||||
−0.393177 | + | 0.919463i | \(0.628624\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.54069 | 0.709437 | ||||||||
\(86\) | 27.1198 | 2.92440 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −17.9357 | −1.91195 | ||||||||
\(89\) | −12.8490 | −1.36199 | −0.680997 | − | 0.732286i | \(-0.738453\pi\) | ||||
−0.680997 | + | 0.732286i | \(0.738453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.38200 | 0.248341 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −29.6520 | −3.05837 | ||||||||
\(95\) | 1.80056 | 0.184734 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.09062 | 0.923012 | 0.461506 | − | 0.887137i | \(-0.347309\pi\) | ||||
0.461506 | + | 0.887137i | \(0.347309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −16.6519 | −1.66519 | ||||||||
\(101\) | 5.80645 | 0.577763 | 0.288882 | − | 0.957365i | \(-0.406717\pi\) | ||||
0.288882 | + | 0.957365i | \(0.406717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8682 | 1.26794 | 0.633971 | − | 0.773357i | \(-0.281424\pi\) | ||||
0.633971 | + | 0.773357i | \(0.281424\pi\) | |||||||
\(104\) | 4.87599 | 0.478130 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 28.0240 | 2.72193 | ||||||||
\(107\) | −4.45747 | −0.430920 | −0.215460 | − | 0.976513i | \(-0.569125\pi\) | ||||
−0.215460 | + | 0.976513i | \(0.569125\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.878896 | 0.0841830 | 0.0420915 | − | 0.999114i | \(-0.486598\pi\) | ||||
0.0420915 | + | 0.999114i | \(0.486598\pi\) | |||||||
\(110\) | 8.19628 | 0.781485 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.36723 | 0.504906 | 0.252453 | − | 0.967609i | \(-0.418763\pi\) | ||||
0.252453 | + | 0.967609i | \(0.418763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.543168 | −0.0506507 | ||||||||
\(116\) | 14.5666 | 1.35248 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −23.4745 | −2.16100 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.53037 | 0.230034 | ||||||||
\(122\) | 17.0991 | 1.54808 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −28.2963 | −2.54108 | ||||||||
\(125\) | 8.34858 | 0.746720 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.61029 | 0.586568 | 0.293284 | − | 0.956025i | \(-0.405252\pi\) | ||||
0.293284 | + | 0.956025i | \(0.405252\pi\) | |||||||
\(128\) | −19.6606 | −1.73777 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.22824 | −0.195430 | ||||||||
\(131\) | 19.9665 | 1.74448 | 0.872240 | − | 0.489079i | \(-0.162667\pi\) | ||||
0.872240 | + | 0.489079i | \(0.162667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.00692 | 0.259758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −35.0355 | −3.00427 | ||||||||
\(137\) | −5.75451 | −0.491641 | −0.245821 | − | 0.969315i | \(-0.579057\pi\) | ||||
−0.245821 | + | 0.969315i | \(0.579057\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.55138 | −0.131586 | −0.0657931 | − | 0.997833i | \(-0.520958\pi\) | ||||
−0.0657931 | + | 0.997833i | \(0.520958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −27.8160 | −2.33427 | ||||||||
\(143\) | −3.67837 | −0.307600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.32163 | −0.275847 | ||||||||
\(146\) | 15.9947 | 1.32373 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.83768 | 0.233256 | ||||||||
\(149\) | −14.9337 | −1.22341 | −0.611707 | − | 0.791084i | \(-0.709517\pi\) | ||||
−0.611707 | + | 0.791084i | \(0.709517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.90102 | −0.642976 | −0.321488 | − | 0.946914i | \(-0.604183\pi\) | ||||
−0.321488 | + | 0.946914i | \(0.604183\pi\) | |||||||
\(152\) | −9.64481 | −0.782297 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.45241 | 0.518270 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4948 | 0.997194 | 0.498597 | − | 0.866834i | \(-0.333849\pi\) | ||||
0.498597 | + | 0.866834i | \(0.333849\pi\) | |||||||
\(158\) | −28.2002 | −2.24349 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.0715920 | 0.00565985 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.01427 | 0.549400 | 0.274700 | − | 0.961530i | \(-0.411421\pi\) | ||||
0.274700 | + | 0.961530i | \(0.411421\pi\) | |||||||
\(164\) | −21.0587 | −1.64441 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.5365 | −1.36109 | ||||||||
\(167\) | −4.82764 | −0.373574 | −0.186787 | − | 0.982400i | \(-0.559807\pi\) | ||||
−0.186787 | + | 0.982400i | \(0.559807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 16.0106 | 1.22796 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 44.2270 | 3.37227 | ||||||||
\(173\) | 22.2124 | 1.68878 | 0.844388 | − | 0.535732i | \(-0.179964\pi\) | ||||
0.844388 | + | 0.535732i | \(0.179964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.5361 | −1.09570 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −31.4524 | −2.35746 | ||||||||
\(179\) | −4.57505 | −0.341956 | −0.170978 | − | 0.985275i | \(-0.554693\pi\) | ||||
−0.170978 | + | 0.985275i | \(0.554693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.23332 | −0.537649 | −0.268824 | − | 0.963189i | \(-0.586635\pi\) | ||||
−0.268824 | + | 0.963189i | \(0.586635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.90951 | 0.214492 | ||||||||
\(185\) | −0.647078 | −0.0475741 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.4302 | 1.93277 | ||||||||
\(188\) | −48.3565 | −3.52676 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.40751 | 0.319754 | ||||||||
\(191\) | −1.97242 | −0.142719 | −0.0713596 | − | 0.997451i | \(-0.522734\pi\) | ||||
−0.0713596 | + | 0.997451i | \(0.522734\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.2073 | −1.81446 | −0.907230 | − | 0.420635i | \(-0.861807\pi\) | ||||
−0.907230 | + | 0.420635i | \(0.861807\pi\) | |||||||
\(194\) | 22.2524 | 1.59763 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.04497 | 0.216945 | 0.108473 | − | 0.994099i | \(-0.465404\pi\) | ||||
0.108473 | + | 0.994099i | \(0.465404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.05691 | 0.287587 | 0.143794 | − | 0.989608i | \(-0.454070\pi\) | ||||
0.143794 | + | 0.989608i | \(0.454070\pi\) | |||||||
\(200\) | −20.3396 | −1.43823 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.2133 | 1.00004 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.80203 | 0.335388 | ||||||||
\(206\) | 31.4994 | 2.19467 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.95177 | 0.274006 | ||||||||
\(209\) | 7.27588 | 0.503283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4116 | 1.12982 | 0.564910 | − | 0.825152i | \(-0.308911\pi\) | ||||
0.564910 | + | 0.825152i | \(0.308911\pi\) | |||||||
\(212\) | 45.7016 | 3.13880 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.9112 | −0.745875 | ||||||||
\(215\) | −10.0851 | −0.687797 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.15140 | 0.145711 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.3665 | 0.901170 | ||||||||
\(221\) | −7.18531 | −0.483336 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1205 | −1.07951 | −0.539755 | − | 0.841822i | \(-0.681483\pi\) | ||||
−0.539755 | + | 0.841822i | \(0.681483\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.1381 | 0.873936 | ||||||||
\(227\) | 8.67804 | 0.575982 | 0.287991 | − | 0.957633i | \(-0.407013\pi\) | ||||
0.287991 | + | 0.957633i | \(0.407013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7592 | −1.37180 | −0.685902 | − | 0.727694i | \(-0.740592\pi\) | ||||
−0.685902 | + | 0.727694i | \(0.740592\pi\) | |||||||
\(230\) | −1.32959 | −0.0876707 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.7925 | 1.16813 | ||||||||
\(233\) | 9.84468 | 0.644946 | 0.322473 | − | 0.946579i | \(-0.395486\pi\) | ||||
0.322473 | + | 0.946579i | \(0.395486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0267 | 0.719305 | ||||||||
\(236\) | −38.2823 | −2.49196 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.13539 | −0.0734424 | −0.0367212 | − | 0.999326i | \(-0.511691\pi\) | ||||
−0.0367212 | + | 0.999326i | \(0.511691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8208 | −1.40560 | −0.702802 | − | 0.711386i | \(-0.748068\pi\) | ||||
−0.702802 | + | 0.711386i | \(0.748068\pi\) | |||||||
\(242\) | 6.19396 | 0.398163 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 27.8852 | 1.78517 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.97802 | −0.125858 | ||||||||
\(248\) | −34.5626 | −2.19473 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 20.4360 | 1.29249 | ||||||||
\(251\) | −9.44377 | −0.596086 | −0.298043 | − | 0.954552i | \(-0.596334\pi\) | ||||
−0.298043 | + | 0.954552i | \(0.596334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.19488 | −0.137991 | ||||||||
\(254\) | 16.1810 | 1.01528 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.9341 | −1.99588 | ||||||||
\(257\) | 3.62752 | 0.226279 | 0.113139 | − | 0.993579i | \(-0.463909\pi\) | ||||
0.113139 | + | 0.993579i | \(0.463909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.63382 | −0.225360 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 48.8749 | 3.01950 | ||||||||
\(263\) | −6.59584 | −0.406717 | −0.203359 | − | 0.979104i | \(-0.565186\pi\) | ||||
−0.203359 | + | 0.979104i | \(0.565186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4214 | −0.640179 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.90369 | 0.299540 | ||||||||
\(269\) | −23.5313 | −1.43473 | −0.717365 | − | 0.696698i | \(-0.754652\pi\) | ||||
−0.717365 | + | 0.696698i | \(0.754652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.69767 | 0.163872 | 0.0819358 | − | 0.996638i | \(-0.473890\pi\) | ||||
0.0819358 | + | 0.996638i | \(0.473890\pi\) | |||||||
\(272\) | −28.3947 | −1.72168 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.0862 | −0.850976 | ||||||||
\(275\) | 15.3439 | 0.925269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.7549 | −1.48738 | −0.743690 | − | 0.668525i | \(-0.766926\pi\) | ||||
−0.743690 | + | 0.668525i | \(0.766926\pi\) | |||||||
\(278\) | −3.79754 | −0.227761 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.05377 | 0.241828 | 0.120914 | − | 0.992663i | \(-0.461418\pi\) | ||||
0.120914 | + | 0.992663i | \(0.461418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9237 | 0.768235 | 0.384118 | − | 0.923284i | \(-0.374506\pi\) | ||||
0.384118 | + | 0.923284i | \(0.374506\pi\) | |||||||
\(284\) | −45.3624 | −2.69176 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.00407 | −0.532422 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.6287 | 2.03698 | ||||||||
\(290\) | −8.13085 | −0.477460 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.0842 | 1.52646 | ||||||||
\(293\) | 23.5553 | 1.37611 | 0.688057 | − | 0.725656i | \(-0.258464\pi\) | ||||
0.688057 | + | 0.725656i | \(0.258464\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.72952 | 0.508252 | ||||||||
\(296\) | 3.46610 | 0.201463 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −36.5553 | −2.11759 | ||||||||
\(299\) | 0.596700 | 0.0345081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.3405 | −1.11292 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.81669 | −0.448318 | ||||||||
\(305\) | −6.35868 | −0.364097 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.9551 | 1.13890 | 0.569450 | − | 0.822026i | \(-0.307156\pi\) | ||||
0.569450 | + | 0.822026i | \(0.307156\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.7945 | 0.897068 | ||||||||
\(311\) | −6.48069 | −0.367486 | −0.183743 | − | 0.982974i | \(-0.558821\pi\) | ||||
−0.183743 | + | 0.982974i | \(0.558821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.1154 | 0.910897 | 0.455449 | − | 0.890262i | \(-0.349479\pi\) | ||||
0.455449 | + | 0.890262i | \(0.349479\pi\) | |||||||
\(314\) | 30.5854 | 1.72603 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −45.9889 | −2.58708 | ||||||||
\(317\) | −14.5303 | −0.816106 | −0.408053 | − | 0.912958i | \(-0.633792\pi\) | ||||
−0.408053 | + | 0.912958i | \(0.633792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.4224 | −0.751508 | ||||||||
\(320\) | 7.36974 | 0.411981 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.2127 | 0.790815 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.17138 | −0.231386 | ||||||||
\(326\) | 17.1699 | 0.950951 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −25.7223 | −1.42028 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.0945 | 1.15946 | 0.579730 | − | 0.814809i | \(-0.303158\pi\) | ||||
0.579730 | + | 0.814809i | \(0.303158\pi\) | |||||||
\(332\) | −28.5985 | −1.56955 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.8173 | −0.646615 | ||||||||
\(335\) | −1.11819 | −0.0610932 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.8693 | −1.79050 | −0.895251 | − | 0.445562i | \(-0.853004\pi\) | ||||
−0.895251 | + | 0.445562i | \(0.853004\pi\) | |||||||
\(338\) | 2.44785 | 0.133145 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26.1101 | 1.41602 | ||||||||
\(341\) | 26.0735 | 1.41196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 54.0213 | 2.91263 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 54.3725 | 2.92308 | ||||||||
\(347\) | −15.9160 | −0.854418 | −0.427209 | − | 0.904153i | \(-0.640503\pi\) | ||||
−0.427209 | + | 0.904153i | \(0.640503\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.6245 | −1.58576 | −0.792882 | − | 0.609375i | \(-0.791420\pi\) | ||||
−0.792882 | + | 0.609375i | \(0.791420\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.289295 | 0.0154195 | ||||||||
\(353\) | 28.7078 | 1.52796 | 0.763980 | − | 0.645240i | \(-0.223243\pi\) | ||||
0.763980 | + | 0.645240i | \(0.223243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3440 | 0.549002 | ||||||||
\(356\) | −51.2927 | −2.71851 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.1990 | −0.591887 | ||||||||
\(359\) | −27.2931 | −1.44048 | −0.720238 | − | 0.693727i | \(-0.755968\pi\) | ||||
−0.720238 | + | 0.693727i | \(0.755968\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0874 | −0.794076 | ||||||||
\(362\) | −17.7061 | −0.930610 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.94798 | −0.311332 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.98326 | −0.521122 | −0.260561 | − | 0.965457i | \(-0.583907\pi\) | ||||
−0.260561 | + | 0.965457i | \(0.583907\pi\) | |||||||
\(368\) | 2.35802 | 0.122921 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.58395 | −0.0823455 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.68608 | 0.242636 | 0.121318 | − | 0.992614i | \(-0.461288\pi\) | ||||
0.121318 | + | 0.992614i | \(0.461288\pi\) | |||||||
\(374\) | 64.6971 | 3.34541 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −59.0653 | −3.04606 | ||||||||
\(377\) | 3.64900 | 0.187933 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.45019 | −0.125858 | −0.0629288 | − | 0.998018i | \(-0.520044\pi\) | ||||
−0.0629288 | + | 0.998018i | \(0.520044\pi\) | |||||||
\(380\) | 7.18777 | 0.368725 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.82818 | −0.247031 | ||||||||
\(383\) | 10.7671 | 0.550175 | 0.275087 | − | 0.961419i | \(-0.411293\pi\) | ||||
0.275087 | + | 0.961419i | \(0.411293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −61.7035 | −3.14063 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 36.2893 | 1.84231 | ||||||||
\(389\) | −14.0372 | −0.711714 | −0.355857 | − | 0.934540i | \(-0.615811\pi\) | ||||
−0.355857 | + | 0.934540i | \(0.615811\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.28748 | −0.216827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.45363 | 0.375508 | ||||||||
\(395\) | 10.4869 | 0.527652 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.4605 | 1.32801 | 0.664007 | − | 0.747726i | \(-0.268854\pi\) | ||||
0.664007 | + | 0.747726i | \(0.268854\pi\) | |||||||
\(398\) | 9.93070 | 0.497781 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.4843 | −0.824217 | ||||||||
\(401\) | 19.0156 | 0.949593 | 0.474796 | − | 0.880096i | \(-0.342522\pi\) | ||||
0.474796 | + | 0.880096i | \(0.342522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.08833 | −0.353095 | ||||||||
\(404\) | 23.1791 | 1.15320 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.61477 | −0.129609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7759 | 0.631728 | 0.315864 | − | 0.948804i | \(-0.397706\pi\) | ||||
0.315864 | + | 0.948804i | \(0.397706\pi\) | |||||||
\(410\) | 11.7546 | 0.580520 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 51.3693 | 2.53078 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.52132 | 0.320119 | ||||||||
\(416\) | −0.0786478 | −0.00385603 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17.8102 | 0.871127 | ||||||||
\(419\) | −12.9811 | −0.634170 | −0.317085 | − | 0.948397i | \(-0.602704\pi\) | ||||
−0.317085 | + | 0.948397i | \(0.602704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.6737 | −0.568943 | −0.284472 | − | 0.958684i | \(-0.591818\pi\) | ||||
−0.284472 | + | 0.958684i | \(0.591818\pi\) | |||||||
\(422\) | 40.1731 | 1.95559 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 55.8225 | 2.71098 | ||||||||
\(425\) | 29.9726 | 1.45389 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17.7940 | −0.860107 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −24.6868 | −1.19050 | ||||||||
\(431\) | 0.467684 | 0.0225275 | 0.0112638 | − | 0.999937i | \(-0.496415\pi\) | ||||
0.0112638 | + | 0.999937i | \(0.496415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.27593 | −0.445773 | −0.222886 | − | 0.974844i | \(-0.571548\pi\) | ||||
−0.222886 | + | 0.974844i | \(0.571548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50851 | 0.168027 | ||||||||
\(437\) | −1.18029 | −0.0564607 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.7077 | −1.70424 | −0.852119 | − | 0.523348i | \(-0.824683\pi\) | ||||
−0.852119 | + | 0.523348i | \(0.824683\pi\) | |||||||
\(440\) | 16.3266 | 0.778340 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.5885 | −0.836601 | ||||||||
\(443\) | 36.3458 | 1.72684 | 0.863421 | − | 0.504484i | \(-0.168317\pi\) | ||||
0.863421 | + | 0.504484i | \(0.168317\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6963 | 0.554457 | ||||||||
\(446\) | −39.4605 | −1.86851 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.4910 | 1.91089 | 0.955444 | − | 0.295171i | \(-0.0953767\pi\) | ||||
0.955444 | + | 0.295171i | \(0.0953767\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4045 | 0.913720 | ||||||||
\(452\) | 21.4257 | 1.00778 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.2425 | 0.996960 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.01988 | 0.234820 | 0.117410 | − | 0.993084i | \(-0.462541\pi\) | ||||
0.117410 | + | 0.993084i | \(0.462541\pi\) | |||||||
\(458\) | −50.8153 | −2.37444 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.16830 | −0.101098 | ||||||||
\(461\) | 17.3627 | 0.808661 | 0.404331 | − | 0.914613i | \(-0.367505\pi\) | ||||
0.404331 | + | 0.914613i | \(0.367505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.4306 | 1.64660 | 0.823301 | − | 0.567606i | \(-0.192130\pi\) | ||||
0.823301 | + | 0.567606i | \(0.192130\pi\) | |||||||
\(464\) | 14.4200 | 0.669433 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.0983 | 1.11633 | ||||||||
\(467\) | −35.4958 | −1.64255 | −0.821275 | − | 0.570533i | \(-0.806737\pi\) | ||||
−0.821275 | + | 0.570533i | \(0.806737\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 26.9918 | 1.24504 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −46.7601 | −2.15231 | ||||||||
\(473\) | −40.7527 | −1.87381 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.25107 | 0.378585 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.77926 | −0.127121 | ||||||||
\(479\) | 24.0270 | 1.09782 | 0.548911 | − | 0.835881i | \(-0.315042\pi\) | ||||
0.548911 | + | 0.835881i | \(0.315042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.710851 | 0.0324120 | ||||||||
\(482\) | −53.4140 | −2.43294 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.1011 | 0.459142 | ||||||||
\(485\) | −8.27506 | −0.375751 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.8076 | 0.942880 | 0.471440 | − | 0.881898i | \(-0.343734\pi\) | ||||
0.471440 | + | 0.881898i | \(0.343734\pi\) | |||||||
\(488\) | 34.0606 | 1.54185 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.2195 | 1.63456 | 0.817281 | − | 0.576240i | \(-0.195481\pi\) | ||||
0.817281 | + | 0.576240i | \(0.195481\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.2192 | −1.18085 | ||||||||
\(494\) | −4.84189 | −0.217847 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.0115 | −1.25775 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.1828 | −1.79883 | −0.899416 | − | 0.437094i | \(-0.856008\pi\) | ||||
−0.899416 | + | 0.437094i | \(0.856008\pi\) | |||||||
\(500\) | 33.3271 | 1.49043 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.1169 | −1.03176 | ||||||||
\(503\) | −38.5636 | −1.71946 | −0.859732 | − | 0.510745i | \(-0.829370\pi\) | ||||
−0.859732 | + | 0.510745i | \(0.829370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.28553 | −0.235203 | ||||||||
\(506\) | −5.37273 | −0.238847 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.3879 | 1.17078 | ||||||||
\(509\) | −4.33977 | −0.192357 | −0.0961785 | − | 0.995364i | \(-0.530662\pi\) | ||||
−0.0961785 | + | 0.995364i | \(0.530662\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −38.8484 | −1.71687 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.87962 | 0.391663 | ||||||||
\(515\) | −11.7138 | −0.516170 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.5578 | 1.95965 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.43855 | −0.194643 | ||||||||
\(521\) | −13.7844 | −0.603905 | −0.301952 | − | 0.953323i | \(-0.597638\pi\) | ||||
−0.301952 | + | 0.953323i | \(0.597638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4834 | −1.28922 | −0.644609 | − | 0.764512i | \(-0.722980\pi\) | ||||
−0.644609 | + | 0.764512i | \(0.722980\pi\) | |||||||
\(524\) | 79.7052 | 3.48194 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.1456 | −0.703982 | ||||||||
\(527\) | 50.9318 | 2.21863 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6439 | −0.984520 | ||||||||
\(530\) | −25.5099 | −1.10808 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.27529 | −0.228498 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.05758 | 0.175424 | ||||||||
\(536\) | 5.98963 | 0.258713 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −57.6011 | −2.48336 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.2519 | 0.999679 | 0.499840 | − | 0.866118i | \(-0.333392\pi\) | ||||
0.499840 | + | 0.866118i | \(0.333392\pi\) | |||||||
\(542\) | 6.60348 | 0.283644 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.565109 | 0.0242288 | ||||||||
\(545\) | −0.800047 | −0.0342703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.18365 | 0.0506093 | 0.0253046 | − | 0.999680i | \(-0.491944\pi\) | ||||
0.0253046 | + | 0.999680i | \(0.491944\pi\) | |||||||
\(548\) | −22.9717 | −0.981304 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.5594 | 1.60154 | ||||||||
\(551\) | −7.21780 | −0.307488 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −60.5962 | −2.57449 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.19303 | −0.262643 | ||||||||
\(557\) | 6.42824 | 0.272373 | 0.136187 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136187 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0790 | 0.468593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.92300 | 0.418577 | ||||||||
\(563\) | −11.4563 | −0.482824 | −0.241412 | − | 0.970423i | \(-0.577610\pi\) | ||||
−0.241412 | + | 0.970423i | \(0.577610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.88571 | −0.205543 | ||||||||
\(566\) | 31.6353 | 1.32973 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −55.4081 | −2.32487 | ||||||||
\(569\) | −38.3335 | −1.60702 | −0.803512 | − | 0.595288i | \(-0.797038\pi\) | ||||
−0.803512 | + | 0.595288i | \(0.797038\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.25857 | 0.261913 | 0.130956 | − | 0.991388i | \(-0.458195\pi\) | ||||
0.130956 | + | 0.991388i | \(0.458195\pi\) | |||||||
\(572\) | −14.6839 | −0.613963 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.48906 | −0.103801 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.0451932 | 0.00188142 | 0.000940708 | − | 1.00000i | \(-0.499701\pi\) | ||||
0.000940708 | 1.00000i | \(0.499701\pi\) | ||||||||
\(578\) | 84.7657 | 3.52579 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.2598 | −0.550583 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42.1115 | −1.74408 | ||||||||
\(584\) | 31.8606 | 1.31840 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 57.6597 | 2.38190 | ||||||||
\(587\) | −2.71409 | −0.112023 | −0.0560113 | − | 0.998430i | \(-0.517838\pi\) | ||||
−0.0560113 | + | 0.998430i | \(0.517838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0209 | 0.577719 | ||||||||
\(590\) | 21.3685 | 0.879728 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.80912 | 0.115454 | ||||||||
\(593\) | −6.78615 | −0.278674 | −0.139337 | − | 0.990245i | \(-0.544497\pi\) | ||||
−0.139337 | + | 0.990245i | \(0.544497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −59.6145 | −2.44190 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.46063 | 0.0597296 | ||||||||
\(599\) | 26.8337 | 1.09640 | 0.548198 | − | 0.836348i | \(-0.315314\pi\) | ||||
0.548198 | + | 0.836348i | \(0.315314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3356 | 0.503178 | 0.251589 | − | 0.967834i | \(-0.419047\pi\) | ||||
0.251589 | + | 0.967834i | \(0.419047\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.5405 | −1.28336 | ||||||||
\(605\) | −2.30336 | −0.0936450 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.4596 | −0.708665 | −0.354332 | − | 0.935120i | \(-0.615292\pi\) | ||||
−0.354332 | + | 0.935120i | \(0.615292\pi\) | |||||||
\(608\) | 0.155567 | 0.00630907 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.5651 | −0.630211 | ||||||||
\(611\) | −12.1135 | −0.490059 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.05026 | 0.0424198 | 0.0212099 | − | 0.999775i | \(-0.493248\pi\) | ||||
0.0212099 | + | 0.999775i | \(0.493248\pi\) | |||||||
\(614\) | 48.8471 | 1.97131 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.5872 | −0.426223 | −0.213111 | − | 0.977028i | \(-0.568360\pi\) | ||||
−0.213111 | + | 0.977028i | \(0.568360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.23805 | 0.0497616 | 0.0248808 | − | 0.999690i | \(-0.492079\pi\) | ||||
0.0248808 | + | 0.999690i | \(0.492079\pi\) | |||||||
\(620\) | 25.7577 | 1.03445 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.8637 | −0.636078 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.2573 | 0.530292 | ||||||||
\(626\) | 39.4481 | 1.57666 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 49.8786 | 1.99037 | ||||||||
\(629\) | −5.10769 | −0.203657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.2658 | −0.846577 | −0.423289 | − | 0.905995i | \(-0.639124\pi\) | ||||
−0.423289 | + | 0.905995i | \(0.639124\pi\) | |||||||
\(632\) | −56.1735 | −2.23446 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35.5681 | −1.41259 | ||||||||
\(635\) | −6.01725 | −0.238787 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.8559 | −1.30078 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.8968 | 0.707433 | ||||||||
\(641\) | −11.0506 | −0.436474 | −0.218237 | − | 0.975896i | \(-0.570031\pi\) | ||||
−0.218237 | + | 0.975896i | \(0.570031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.50321 | 0.256461 | 0.128231 | − | 0.991744i | \(-0.459070\pi\) | ||||
0.128231 | + | 0.991744i | \(0.459070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.7905 | 1.36881 | ||||||||
\(647\) | 0.893941 | 0.0351444 | 0.0175722 | − | 0.999846i | \(-0.494406\pi\) | ||||
0.0175722 | + | 0.999846i | \(0.494406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.2750 | 1.38467 | ||||||||
\(650\) | −10.2109 | −0.400504 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28.0006 | 1.09659 | ||||||||
\(653\) | 38.5477 | 1.50849 | 0.754244 | − | 0.656594i | \(-0.228003\pi\) | ||||
0.754244 | + | 0.656594i | \(0.228003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.1752 | −0.710164 | ||||||||
\(656\) | −20.8468 | −0.813930 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8013 | 0.420759 | 0.210380 | − | 0.977620i | \(-0.432530\pi\) | ||||
0.210380 | + | 0.977620i | \(0.432530\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.6339 | 1.58047 | 0.790237 | − | 0.612801i | \(-0.209957\pi\) | ||||
0.790237 | + | 0.612801i | \(0.209957\pi\) | |||||||
\(662\) | 51.6361 | 2.00690 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34.9318 | −1.35562 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.17736 | 0.0843077 | ||||||||
\(668\) | −19.2717 | −0.745645 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.73716 | −0.105746 | ||||||||
\(671\) | −25.6947 | −0.991934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.3136 | 1.24560 | 0.622799 | − | 0.782382i | \(-0.285995\pi\) | ||||
0.622799 | + | 0.782382i | \(0.285995\pi\) | |||||||
\(674\) | −80.4589 | −3.09916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.99195 | 0.153537 | ||||||||
\(677\) | 25.2158 | 0.969123 | 0.484562 | − | 0.874757i | \(-0.338979\pi\) | ||||
0.484562 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.8923 | 1.22302 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 63.8238 | 2.44394 | ||||||||
\(683\) | 6.28731 | 0.240577 | 0.120289 | − | 0.992739i | \(-0.461618\pi\) | ||||
0.120289 | + | 0.992739i | \(0.461618\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.23826 | 0.200143 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 43.7818 | 1.66917 | ||||||||
\(689\) | 11.4484 | 0.436151 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.1531 | 0.652533 | 0.326267 | − | 0.945278i | \(-0.394209\pi\) | ||||
0.326267 | + | 0.945278i | \(0.394209\pi\) | |||||||
\(692\) | 88.6707 | 3.37076 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.9600 | −1.47890 | ||||||||
\(695\) | 1.41220 | 0.0535678 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.9046 | 1.43574 | ||||||||
\(698\) | −72.5162 | −2.74478 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.6620 | 0.893702 | 0.446851 | − | 0.894609i | \(-0.352545\pi\) | ||||
0.446851 | + | 0.894609i | \(0.352545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.40608 | −0.0530312 | ||||||||
\(704\) | 29.7803 | 1.12239 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 70.2722 | 2.64473 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5030 | −0.807563 | −0.403782 | − | 0.914855i | \(-0.632304\pi\) | ||||
−0.403782 | + | 0.914855i | \(0.632304\pi\) | |||||||
\(710\) | 25.3205 | 0.950262 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −62.6517 | −2.34797 | ||||||||
\(713\) | −4.22961 | −0.158400 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.34837 | 0.125222 | ||||||||
\(716\) | −18.2634 | −0.682535 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −66.8094 | −2.49330 | ||||||||
\(719\) | 12.8693 | 0.479943 | 0.239971 | − | 0.970780i | \(-0.422862\pi\) | ||||
0.239971 | + | 0.970780i | \(0.422862\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −36.9317 | −1.37446 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.8751 | −1.07313 | ||||||||
\(725\) | −15.2214 | −0.565307 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4329 | −0.609463 | −0.304732 | − | 0.952438i | \(-0.598567\pi\) | ||||
−0.304732 | + | 0.952438i | \(0.598567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.5597 | −0.538880 | ||||||||
\(731\) | −79.6063 | −2.94434 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.7222 | 0.802328 | 0.401164 | − | 0.916006i | \(-0.368606\pi\) | ||||
0.401164 | + | 0.916006i | \(0.368606\pi\) | |||||||
\(734\) | −24.4375 | −0.902004 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0469292 | −0.00172983 | ||||||||
\(737\) | −4.51848 | −0.166440 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.58001 | 0.0581218 | 0.0290609 | − | 0.999578i | \(-0.490748\pi\) | ||||
0.0290609 | + | 0.999578i | \(0.490748\pi\) | |||||||
\(740\) | −2.58310 | −0.0949568 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.9718 | −1.68654 | −0.843271 | − | 0.537489i | \(-0.819373\pi\) | ||||
−0.843271 | + | 0.537489i | \(0.819373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5939 | 0.498043 | ||||||||
\(746\) | 11.4708 | 0.419976 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 105.508 | 3.85776 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.42286 | −0.234373 | −0.117187 | − | 0.993110i | \(-0.537388\pi\) | ||||
−0.117187 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(752\) | −47.8698 | −1.74563 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.93219 | 0.325291 | ||||||||
\(755\) | 7.19219 | 0.261750 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.10016 | −0.221714 | −0.110857 | − | 0.993836i | \(-0.535360\pi\) | ||||
−0.110857 | + | 0.993836i | \(0.535360\pi\) | |||||||
\(758\) | −5.99768 | −0.217846 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.77954 | 0.318467 | ||||||||
\(761\) | −18.3948 | −0.666812 | −0.333406 | − | 0.942783i | \(-0.608198\pi\) | ||||
−0.333406 | + | 0.942783i | \(0.608198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.87380 | −0.284864 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.3563 | 0.952291 | ||||||||
\(767\) | −9.58986 | −0.346270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.1850 | −0.872133 | −0.436066 | − | 0.899914i | \(-0.643629\pi\) | ||||
−0.436066 | + | 0.899914i | \(0.643629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −100.626 | −3.62162 | ||||||||
\(773\) | 10.7601 | 0.387014 | 0.193507 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193507 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.5681 | 1.06212 | ||||||||
\(776\) | 44.3258 | 1.59120 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.3609 | −1.23190 | ||||||||
\(779\) | 10.4346 | 0.373860 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.7989 | 1.49568 | ||||||||
\(782\) | −10.4951 | −0.375303 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.3738 | −0.405950 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.7348 | −0.525238 | −0.262619 | − | 0.964900i | \(-0.584586\pi\) | ||||
−0.262619 | + | 0.964900i | \(0.584586\pi\) | |||||||
\(788\) | 12.1554 | 0.433018 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 25.6703 | 0.913307 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.98536 | 0.248058 | ||||||||
\(794\) | 64.7713 | 2.29865 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.1950 | 0.574017 | ||||||||
\(797\) | −32.5732 | −1.15380 | −0.576901 | − | 0.816814i | \(-0.695738\pi\) | ||||
−0.576901 | + | 0.816814i | \(0.695738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87.0392 | 3.07922 | ||||||||
\(800\) | 0.328070 | 0.0115990 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 46.5472 | 1.64364 | ||||||||
\(803\) | −24.0351 | −0.848181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.3511 | −0.611168 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.3122 | 0.996019 | ||||||||
\(809\) | 23.6926 | 0.832987 | 0.416493 | − | 0.909139i | \(-0.363259\pi\) | ||||
0.416493 | + | 0.909139i | \(0.363259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.8568 | 1.61025 | 0.805125 | − | 0.593105i | \(-0.202098\pi\) | ||||
0.805125 | + | 0.593105i | \(0.202098\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.40056 | −0.224339 | ||||||||
\(815\) | −6.38500 | −0.223657 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.9145 | −0.766693 | ||||||||
\(818\) | 31.2735 | 1.09345 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.1695 | 0.669427 | ||||||||
\(821\) | −13.2923 | −0.463905 | −0.231953 | − | 0.972727i | \(-0.574511\pi\) | ||||
−0.231953 | + | 0.972727i | \(0.574511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.13033 | −0.143974 | −0.0719871 | − | 0.997406i | \(-0.522934\pi\) | ||||
−0.0719871 | + | 0.997406i | \(0.522934\pi\) | |||||||
\(824\) | 62.7453 | 2.18584 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.67317 | 0.162502 | 0.0812510 | − | 0.996694i | \(-0.474108\pi\) | ||||
0.0812510 | + | 0.996694i | \(0.474108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.74971 | 0.0607700 | 0.0303850 | − | 0.999538i | \(-0.490327\pi\) | ||||
0.0303850 | + | 0.999538i | \(0.490327\pi\) | |||||||
\(830\) | 15.9632 | 0.554091 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.09606 | −0.280681 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.39454 | 0.152079 | ||||||||
\(836\) | 29.0450 | 1.00454 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.7758 | −1.09768 | ||||||||
\(839\) | 15.4495 | 0.533374 | 0.266687 | − | 0.963783i | \(-0.414071\pi\) | ||||
0.266687 | + | 0.963783i | \(0.414071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6848 | −0.540855 | ||||||||
\(842\) | −28.5755 | −0.984777 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 65.5143 | 2.25510 | ||||||||
\(845\) | −0.910286 | −0.0313148 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 45.2416 | 1.55360 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 73.3684 | 2.51652 | ||||||||
\(851\) | 0.424165 | 0.0145402 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.602575 | −0.0206318 | −0.0103159 | − | 0.999947i | \(-0.503284\pi\) | ||||
−0.0103159 | + | 0.999947i | \(0.503284\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.7346 | −0.742874 | ||||||||
\(857\) | 43.1639 | 1.47445 | 0.737226 | − | 0.675647i | \(-0.236135\pi\) | ||||
0.737226 | + | 0.675647i | \(0.236135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.9408 | 1.29452 | 0.647261 | − | 0.762269i | \(-0.275914\pi\) | ||||
0.647261 | + | 0.762269i | \(0.275914\pi\) | |||||||
\(860\) | −40.2592 | −1.37283 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.14482 | 0.0389927 | ||||||||
\(863\) | −33.9067 | −1.15420 | −0.577098 | − | 0.816675i | \(-0.695815\pi\) | ||||
−0.577098 | + | 0.816675i | \(0.695815\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.2196 | −0.687488 | ||||||||
\(866\) | −22.7061 | −0.771583 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.3763 | 1.43752 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22839 | 0.0416225 | ||||||||
\(872\) | 4.28549 | 0.145125 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.88916 | −0.0977272 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.51036 | 0.219839 | 0.109920 | − | 0.993940i | \(-0.464941\pi\) | ||||
0.109920 | + | 0.993940i | \(0.464941\pi\) | |||||||
\(878\) | −87.4071 | −2.94985 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.2320 | 0.446050 | ||||||||
\(881\) | 24.5160 | 0.825966 | 0.412983 | − | 0.910739i | \(-0.364487\pi\) | ||||
0.412983 | + | 0.910739i | \(0.364487\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.7175 | −0.966419 | −0.483210 | − | 0.875505i | \(-0.660529\pi\) | ||||
−0.483210 | + | 0.875505i | \(0.660529\pi\) | |||||||
\(884\) | −28.6834 | −0.964727 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 88.9690 | 2.98897 | ||||||||
\(887\) | −6.94442 | −0.233171 | −0.116585 | − | 0.993181i | \(-0.537195\pi\) | ||||
−0.116585 | + | 0.993181i | \(0.537195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28.6307 | 0.959704 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −64.3523 | −2.15467 | ||||||||
\(893\) | 23.9607 | 0.801815 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.16461 | 0.139208 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 99.1158 | 3.30754 | ||||||||
\(899\) | −25.8653 | −0.862656 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −82.2605 | −2.74050 | ||||||||
\(902\) | 47.4991 | 1.58155 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.1705 | 0.870419 | ||||||||
\(905\) | 6.58439 | 0.218873 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.229549 | 0.00762204 | 0.00381102 | − | 0.999993i | \(-0.498787\pi\) | ||||
0.00381102 | + | 0.999993i | \(0.498787\pi\) | |||||||
\(908\) | 34.6423 | 1.14965 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6727 | 0.883706 | 0.441853 | − | 0.897087i | \(-0.354321\pi\) | ||||
0.441853 | + | 0.897087i | \(0.354321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.3519 | 0.872122 | ||||||||
\(914\) | 12.2879 | 0.406447 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −82.8696 | −2.73809 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.2331 | −1.42613 | −0.713064 | − | 0.701099i | \(-0.752693\pi\) | ||||
−0.713064 | + | 0.701099i | \(0.752693\pi\) | |||||||
\(920\) | −2.64848 | −0.0873179 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 42.5012 | 1.39970 | ||||||||
\(923\) | −11.3635 | −0.374033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.96523 | −0.0974961 | ||||||||
\(926\) | 86.7287 | 2.85008 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.286986 | −0.00942077 | ||||||||
\(929\) | 23.8491 | 0.782465 | 0.391233 | − | 0.920292i | \(-0.372049\pi\) | ||||
0.391233 | + | 0.920292i | \(0.372049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39.2995 | 1.28730 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −86.8883 | −2.84307 | ||||||||
\(935\) | −24.0590 | −0.786815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.2033 | −0.888694 | −0.444347 | − | 0.895855i | \(-0.646564\pi\) | ||||
−0.444347 | + | 0.895855i | \(0.646564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 44.0182 | 1.43572 | ||||||||
\(941\) | −13.4515 | −0.438505 | −0.219253 | − | 0.975668i | \(-0.570362\pi\) | ||||
−0.219253 | + | 0.975668i | \(0.570362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.14777 | −0.102505 | ||||||||
\(944\) | −37.8970 | −1.23344 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −99.7564 | −3.24336 | ||||||||
\(947\) | −15.0341 | −0.488543 | −0.244271 | − | 0.969707i | \(-0.578549\pi\) | ||||
−0.244271 | + | 0.969707i | \(0.578549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.53419 | 0.212109 | ||||||||
\(950\) | 20.1974 | 0.655289 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.3775 | −0.919237 | −0.459618 | − | 0.888116i | \(-0.652014\pi\) | ||||
−0.459618 | + | 0.888116i | \(0.652014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.79546 | 0.0580999 | ||||||||
\(956\) | −4.53243 | −0.146589 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 58.8144 | 1.90021 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.2444 | 0.620787 | ||||||||
\(962\) | 1.74005 | 0.0561016 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −87.1077 | −2.80555 | ||||||||
\(965\) | 22.9458 | 0.738653 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.0994 | −1.67540 | −0.837701 | − | 0.546129i | \(-0.816101\pi\) | ||||
−0.837701 | + | 0.546129i | \(0.816101\pi\) | |||||||
\(968\) | 12.3381 | 0.396561 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.2561 | −0.650384 | ||||||||
\(971\) | 20.8418 | 0.668845 | 0.334423 | − | 0.942423i | \(-0.391459\pi\) | ||||
0.334423 | + | 0.942423i | \(0.391459\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 50.9337 | 1.63202 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27.6046 | 0.883601 | ||||||||
\(977\) | −34.6302 | −1.10792 | −0.553960 | − | 0.832544i | \(-0.686884\pi\) | ||||
−0.553960 | + | 0.832544i | \(0.686884\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.2634 | 1.51054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 88.6597 | 2.82924 | ||||||||
\(983\) | 58.8628 | 1.87743 | 0.938717 | − | 0.344690i | \(-0.112016\pi\) | ||||
0.938717 | + | 0.344690i | \(0.112016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.77180 | −0.0883168 | ||||||||
\(986\) | −64.1806 | −2.04393 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.89616 | −0.251210 | ||||||||
\(989\) | 6.61086 | 0.210213 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.3747 | −0.933118 | −0.466559 | − | 0.884490i | \(-0.654507\pi\) | ||||
−0.466559 | + | 0.884490i | \(0.654507\pi\) | |||||||
\(992\) | 0.557482 | 0.0177001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.69295 | −0.117075 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.50606 | −0.237719 | −0.118860 | − | 0.992911i | \(-0.537924\pi\) | ||||
−0.118860 | + | 0.992911i | \(0.537924\pi\) | |||||||
\(998\) | −98.3614 | −3.11358 | ||||||||
\(999\) | 0 | 0 |
(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 | 5733.2.a.br.1.6 | 6 | ||
3.2 | odd | 2 | 637.2.a.n.1.1 | yes | 6 | ||
7.6 | odd | 2 | 5733.2.a.bu.1.6 | 6 | |||
21.2 | odd | 6 | 637.2.e.n.508.6 | 12 | |||
21.5 | even | 6 | 637.2.e.o.508.6 | 12 | |||
21.11 | odd | 6 | 637.2.e.n.79.6 | 12 | |||
21.17 | even | 6 | 637.2.e.o.79.6 | 12 | |||
21.20 | even | 2 | 637.2.a.m.1.1 | ✓ | 6 | ||
39.38 | odd | 2 | 8281.2.a.cd.1.6 | 6 | |||
273.272 | even | 2 | 8281.2.a.cc.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.a.m.1.1 | ✓ | 6 | 21.20 | even | 2 | ||
637.2.a.n.1.1 | yes | 6 | 3.2 | odd | 2 | ||
637.2.e.n.79.6 | 12 | 21.11 | odd | 6 | |||
637.2.e.n.508.6 | 12 | 21.2 | odd | 6 | |||
637.2.e.o.79.6 | 12 | 21.17 | even | 6 | |||
637.2.e.o.508.6 | 12 | 21.5 | even | 6 | |||
5733.2.a.br.1.6 | 6 | 1.1 | even | 1 | trivial | ||
5733.2.a.bu.1.6 | 6 | 7.6 | odd | 2 | |||
8281.2.a.cc.1.6 | 6 | 273.272 | even | 2 | |||
8281.2.a.cd.1.6 | 6 | 39.38 | odd | 2 |