Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.785811 | −0.453688 | −0.226844 | − | 0.973931i | \(-0.572841\pi\) | ||||
−0.226844 | + | 0.973931i | \(0.572841\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.42219 | −0.636023 | −0.318011 | − | 0.948087i | \(-0.603015\pi\) | ||||
−0.318011 | + | 0.948087i | \(0.603015\pi\) | |||||||
\(6\) | 0.785811 | 0.320806 | ||||||||
\(7\) | 3.87369 | 1.46412 | 0.732058 | − | 0.681242i | \(-0.238560\pi\) | ||||
0.732058 | + | 0.681242i | \(0.238560\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.38250 | −0.794167 | ||||||||
\(10\) | 1.42219 | 0.449736 | ||||||||
\(11\) | 4.24761 | 1.28070 | 0.640351 | − | 0.768082i | \(-0.278789\pi\) | ||||
0.640351 | + | 0.768082i | \(0.278789\pi\) | |||||||
\(12\) | −0.785811 | −0.226844 | ||||||||
\(13\) | 2.46631 | 0.684031 | 0.342016 | − | 0.939694i | \(-0.388890\pi\) | ||||
0.342016 | + | 0.939694i | \(0.388890\pi\) | |||||||
\(14\) | −3.87369 | −1.03529 | ||||||||
\(15\) | 1.11757 | 0.288556 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.55090 | 0.376149 | 0.188074 | − | 0.982155i | \(-0.439775\pi\) | ||||
0.188074 | + | 0.982155i | \(0.439775\pi\) | |||||||
\(18\) | 2.38250 | 0.561561 | ||||||||
\(19\) | −2.53414 | −0.581371 | −0.290686 | − | 0.956819i | \(-0.593883\pi\) | ||||
−0.290686 | + | 0.956819i | \(0.593883\pi\) | |||||||
\(20\) | −1.42219 | −0.318011 | ||||||||
\(21\) | −3.04399 | −0.664252 | ||||||||
\(22\) | −4.24761 | −0.905593 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.785811 | 0.160403 | ||||||||
\(25\) | −2.97737 | −0.595475 | ||||||||
\(26\) | −2.46631 | −0.483683 | ||||||||
\(27\) | 4.22963 | 0.813993 | ||||||||
\(28\) | 3.87369 | 0.732058 | ||||||||
\(29\) | 4.09137 | 0.759748 | 0.379874 | − | 0.925038i | \(-0.375967\pi\) | ||||
0.379874 | + | 0.925038i | \(0.375967\pi\) | |||||||
\(30\) | −1.11757 | −0.204040 | ||||||||
\(31\) | −7.27950 | −1.30744 | −0.653719 | − | 0.756738i | \(-0.726792\pi\) | ||||
−0.653719 | + | 0.756738i | \(0.726792\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.33782 | −0.581040 | ||||||||
\(34\) | −1.55090 | −0.265977 | ||||||||
\(35\) | −5.50912 | −0.931211 | ||||||||
\(36\) | −2.38250 | −0.397083 | ||||||||
\(37\) | −5.04022 | −0.828606 | −0.414303 | − | 0.910139i | \(-0.635975\pi\) | ||||
−0.414303 | + | 0.910139i | \(0.635975\pi\) | |||||||
\(38\) | 2.53414 | 0.411092 | ||||||||
\(39\) | −1.93805 | −0.310337 | ||||||||
\(40\) | 1.42219 | 0.224868 | ||||||||
\(41\) | −6.34949 | −0.991624 | −0.495812 | − | 0.868430i | \(-0.665129\pi\) | ||||
−0.495812 | + | 0.868430i | \(0.665129\pi\) | |||||||
\(42\) | 3.04399 | 0.469697 | ||||||||
\(43\) | −9.30138 | −1.41845 | −0.709223 | − | 0.704984i | \(-0.750954\pi\) | ||||
−0.709223 | + | 0.704984i | \(0.750954\pi\) | |||||||
\(44\) | 4.24761 | 0.640351 | ||||||||
\(45\) | 3.38837 | 0.505108 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −5.01571 | −0.731617 | −0.365808 | − | 0.930690i | \(-0.619207\pi\) | ||||
−0.365808 | + | 0.930690i | \(0.619207\pi\) | |||||||
\(48\) | −0.785811 | −0.113422 | ||||||||
\(49\) | 8.00545 | 1.14364 | ||||||||
\(50\) | 2.97737 | 0.421064 | ||||||||
\(51\) | −1.21871 | −0.170654 | ||||||||
\(52\) | 2.46631 | 0.342016 | ||||||||
\(53\) | −6.61052 | −0.908025 | −0.454013 | − | 0.890995i | \(-0.650008\pi\) | ||||
−0.454013 | + | 0.890995i | \(0.650008\pi\) | |||||||
\(54\) | −4.22963 | −0.575580 | ||||||||
\(55\) | −6.04091 | −0.814556 | ||||||||
\(56\) | −3.87369 | −0.517643 | ||||||||
\(57\) | 1.99135 | 0.263761 | ||||||||
\(58\) | −4.09137 | −0.537223 | ||||||||
\(59\) | −1.17415 | −0.152861 | −0.0764306 | − | 0.997075i | \(-0.524352\pi\) | ||||
−0.0764306 | + | 0.997075i | \(0.524352\pi\) | |||||||
\(60\) | 1.11757 | 0.144278 | ||||||||
\(61\) | 6.46185 | 0.827355 | 0.413677 | − | 0.910424i | \(-0.364244\pi\) | ||||
0.413677 | + | 0.910424i | \(0.364244\pi\) | |||||||
\(62\) | 7.27950 | 0.924498 | ||||||||
\(63\) | −9.22906 | −1.16275 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.50756 | −0.435060 | ||||||||
\(66\) | 3.33782 | 0.410857 | ||||||||
\(67\) | 9.88156 | 1.20723 | 0.603613 | − | 0.797278i | \(-0.293727\pi\) | ||||
0.603613 | + | 0.797278i | \(0.293727\pi\) | |||||||
\(68\) | 1.55090 | 0.188074 | ||||||||
\(69\) | 0.785811 | 0.0946006 | ||||||||
\(70\) | 5.50912 | 0.658466 | ||||||||
\(71\) | 6.27474 | 0.744674 | 0.372337 | − | 0.928098i | \(-0.378557\pi\) | ||||
0.372337 | + | 0.928098i | \(0.378557\pi\) | |||||||
\(72\) | 2.38250 | 0.280780 | ||||||||
\(73\) | −13.0599 | −1.52854 | −0.764271 | − | 0.644895i | \(-0.776901\pi\) | ||||
−0.764271 | + | 0.644895i | \(0.776901\pi\) | |||||||
\(74\) | 5.04022 | 0.585913 | ||||||||
\(75\) | 2.33965 | 0.270160 | ||||||||
\(76\) | −2.53414 | −0.290686 | ||||||||
\(77\) | 16.4539 | 1.87510 | ||||||||
\(78\) | 1.93805 | 0.219441 | ||||||||
\(79\) | −8.91977 | −1.00355 | −0.501776 | − | 0.864998i | \(-0.667320\pi\) | ||||
−0.501776 | + | 0.864998i | \(0.667320\pi\) | |||||||
\(80\) | −1.42219 | −0.159006 | ||||||||
\(81\) | 3.82381 | 0.424868 | ||||||||
\(82\) | 6.34949 | 0.701184 | ||||||||
\(83\) | 14.1085 | 1.54861 | 0.774307 | − | 0.632810i | \(-0.218099\pi\) | ||||
0.774307 | + | 0.632810i | \(0.218099\pi\) | |||||||
\(84\) | −3.04399 | −0.332126 | ||||||||
\(85\) | −2.20568 | −0.239239 | ||||||||
\(86\) | 9.30138 | 1.00299 | ||||||||
\(87\) | −3.21504 | −0.344689 | ||||||||
\(88\) | −4.24761 | −0.452797 | ||||||||
\(89\) | −11.5983 | −1.22941 | −0.614706 | − | 0.788756i | \(-0.710725\pi\) | ||||
−0.614706 | + | 0.788756i | \(0.710725\pi\) | |||||||
\(90\) | −3.38837 | −0.357166 | ||||||||
\(91\) | 9.55371 | 1.00150 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 5.72031 | 0.593169 | ||||||||
\(94\) | 5.01571 | 0.517331 | ||||||||
\(95\) | 3.60403 | 0.369765 | ||||||||
\(96\) | 0.785811 | 0.0802015 | ||||||||
\(97\) | −14.5136 | −1.47363 | −0.736817 | − | 0.676092i | \(-0.763672\pi\) | ||||
−0.736817 | + | 0.676092i | \(0.763672\pi\) | |||||||
\(98\) | −8.00545 | −0.808673 | ||||||||
\(99\) | −10.1199 | −1.01709 | ||||||||
\(100\) | −2.97737 | −0.297737 | ||||||||
\(101\) | −1.16747 | −0.116168 | −0.0580840 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580840 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(102\) | 1.21871 | 0.120671 | ||||||||
\(103\) | −3.01876 | −0.297447 | −0.148724 | − | 0.988879i | \(-0.547516\pi\) | ||||
−0.148724 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(104\) | −2.46631 | −0.241842 | ||||||||
\(105\) | 4.32913 | 0.422480 | ||||||||
\(106\) | 6.61052 | 0.642071 | ||||||||
\(107\) | −7.17272 | −0.693413 | −0.346706 | − | 0.937974i | \(-0.612700\pi\) | ||||
−0.346706 | + | 0.937974i | \(0.612700\pi\) | |||||||
\(108\) | 4.22963 | 0.406996 | ||||||||
\(109\) | −3.99600 | −0.382747 | −0.191373 | − | 0.981517i | \(-0.561294\pi\) | ||||
−0.191373 | + | 0.981517i | \(0.561294\pi\) | |||||||
\(110\) | 6.04091 | 0.575978 | ||||||||
\(111\) | 3.96066 | 0.375929 | ||||||||
\(112\) | 3.87369 | 0.366029 | ||||||||
\(113\) | 13.6826 | 1.28715 | 0.643574 | − | 0.765384i | \(-0.277451\pi\) | ||||
0.643574 | + | 0.765384i | \(0.277451\pi\) | |||||||
\(114\) | −1.99135 | −0.186507 | ||||||||
\(115\) | 1.42219 | 0.132620 | ||||||||
\(116\) | 4.09137 | 0.379874 | ||||||||
\(117\) | −5.87599 | −0.543235 | ||||||||
\(118\) | 1.17415 | 0.108089 | ||||||||
\(119\) | 6.00770 | 0.550725 | ||||||||
\(120\) | −1.11757 | −0.102020 | ||||||||
\(121\) | 7.04218 | 0.640199 | ||||||||
\(122\) | −6.46185 | −0.585028 | ||||||||
\(123\) | 4.98950 | 0.449888 | ||||||||
\(124\) | −7.27950 | −0.653719 | ||||||||
\(125\) | 11.3453 | 1.01476 | ||||||||
\(126\) | 9.22906 | 0.822190 | ||||||||
\(127\) | 14.2216 | 1.26197 | 0.630983 | − | 0.775797i | \(-0.282652\pi\) | ||||
0.630983 | + | 0.775797i | \(0.282652\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.30913 | 0.643533 | ||||||||
\(130\) | 3.50756 | 0.307634 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −3.33782 | −0.290520 | ||||||||
\(133\) | −9.81646 | −0.851195 | ||||||||
\(134\) | −9.88156 | −0.853637 | ||||||||
\(135\) | −6.01534 | −0.517718 | ||||||||
\(136\) | −1.55090 | −0.132989 | ||||||||
\(137\) | −16.5255 | −1.41187 | −0.705935 | − | 0.708277i | \(-0.749473\pi\) | ||||
−0.705935 | + | 0.708277i | \(0.749473\pi\) | |||||||
\(138\) | −0.785811 | −0.0668927 | ||||||||
\(139\) | 8.60490 | 0.729858 | 0.364929 | − | 0.931035i | \(-0.381093\pi\) | ||||
0.364929 | + | 0.931035i | \(0.381093\pi\) | |||||||
\(140\) | −5.50912 | −0.465606 | ||||||||
\(141\) | 3.94140 | 0.331926 | ||||||||
\(142\) | −6.27474 | −0.526564 | ||||||||
\(143\) | 10.4759 | 0.876041 | ||||||||
\(144\) | −2.38250 | −0.198542 | ||||||||
\(145\) | −5.81870 | −0.483217 | ||||||||
\(146\) | 13.0599 | 1.08084 | ||||||||
\(147\) | −6.29078 | −0.518854 | ||||||||
\(148\) | −5.04022 | −0.414303 | ||||||||
\(149\) | −15.3186 | −1.25495 | −0.627475 | − | 0.778637i | \(-0.715911\pi\) | ||||
−0.627475 | + | 0.778637i | \(0.715911\pi\) | |||||||
\(150\) | −2.33965 | −0.191032 | ||||||||
\(151\) | −13.1238 | −1.06800 | −0.534001 | − | 0.845484i | \(-0.679312\pi\) | ||||
−0.534001 | + | 0.845484i | \(0.679312\pi\) | |||||||
\(152\) | 2.53414 | 0.205546 | ||||||||
\(153\) | −3.69502 | −0.298725 | ||||||||
\(154\) | −16.4539 | −1.32589 | ||||||||
\(155\) | 10.3528 | 0.831560 | ||||||||
\(156\) | −1.93805 | −0.155169 | ||||||||
\(157\) | −0.761128 | −0.0607446 | −0.0303723 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303723 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(158\) | 8.91977 | 0.709618 | ||||||||
\(159\) | 5.19462 | 0.411960 | ||||||||
\(160\) | 1.42219 | 0.112434 | ||||||||
\(161\) | −3.87369 | −0.305289 | ||||||||
\(162\) | −3.82381 | −0.300427 | ||||||||
\(163\) | 19.8011 | 1.55094 | 0.775470 | − | 0.631384i | \(-0.217513\pi\) | ||||
0.775470 | + | 0.631384i | \(0.217513\pi\) | |||||||
\(164\) | −6.34949 | −0.495812 | ||||||||
\(165\) | 4.74701 | 0.369555 | ||||||||
\(166\) | −14.1085 | −1.09504 | ||||||||
\(167\) | 4.08020 | 0.315735 | 0.157868 | − | 0.987460i | \(-0.449538\pi\) | ||||
0.157868 | + | 0.987460i | \(0.449538\pi\) | |||||||
\(168\) | 3.04399 | 0.234849 | ||||||||
\(169\) | −6.91731 | −0.532101 | ||||||||
\(170\) | 2.20568 | 0.169168 | ||||||||
\(171\) | 6.03759 | 0.461706 | ||||||||
\(172\) | −9.30138 | −0.709223 | ||||||||
\(173\) | 2.46367 | 0.187309 | 0.0936545 | − | 0.995605i | \(-0.470145\pi\) | ||||
0.0936545 | + | 0.995605i | \(0.470145\pi\) | |||||||
\(174\) | 3.21504 | 0.243732 | ||||||||
\(175\) | −11.5334 | −0.871845 | ||||||||
\(176\) | 4.24761 | 0.320176 | ||||||||
\(177\) | 0.922660 | 0.0693513 | ||||||||
\(178\) | 11.5983 | 0.869326 | ||||||||
\(179\) | 10.7958 | 0.806916 | 0.403458 | − | 0.914998i | \(-0.367808\pi\) | ||||
0.403458 | + | 0.914998i | \(0.367808\pi\) | |||||||
\(180\) | 3.38837 | 0.252554 | ||||||||
\(181\) | 9.47637 | 0.704373 | 0.352187 | − | 0.935930i | \(-0.385438\pi\) | ||||
0.352187 | + | 0.935930i | \(0.385438\pi\) | |||||||
\(182\) | −9.55371 | −0.708168 | ||||||||
\(183\) | −5.07779 | −0.375361 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 7.16815 | 0.527013 | ||||||||
\(186\) | −5.72031 | −0.419434 | ||||||||
\(187\) | 6.58762 | 0.481734 | ||||||||
\(188\) | −5.01571 | −0.365808 | ||||||||
\(189\) | 16.3843 | 1.19178 | ||||||||
\(190\) | −3.60403 | −0.261464 | ||||||||
\(191\) | 6.80800 | 0.492610 | 0.246305 | − | 0.969192i | \(-0.420784\pi\) | ||||
0.246305 | + | 0.969192i | \(0.420784\pi\) | |||||||
\(192\) | −0.785811 | −0.0567110 | ||||||||
\(193\) | −14.7284 | −1.06018 | −0.530088 | − | 0.847943i | \(-0.677841\pi\) | ||||
−0.530088 | + | 0.847943i | \(0.677841\pi\) | |||||||
\(194\) | 14.5136 | 1.04202 | ||||||||
\(195\) | 2.75628 | 0.197381 | ||||||||
\(196\) | 8.00545 | 0.571818 | ||||||||
\(197\) | −13.0172 | −0.927438 | −0.463719 | − | 0.885982i | \(-0.653485\pi\) | ||||
−0.463719 | + | 0.885982i | \(0.653485\pi\) | |||||||
\(198\) | 10.1199 | 0.719192 | ||||||||
\(199\) | 16.5962 | 1.17647 | 0.588236 | − | 0.808690i | \(-0.299823\pi\) | ||||
0.588236 | + | 0.808690i | \(0.299823\pi\) | |||||||
\(200\) | 2.97737 | 0.210532 | ||||||||
\(201\) | −7.76504 | −0.547704 | ||||||||
\(202\) | 1.16747 | 0.0821432 | ||||||||
\(203\) | 15.8487 | 1.11236 | ||||||||
\(204\) | −1.21871 | −0.0853271 | ||||||||
\(205\) | 9.03018 | 0.630695 | ||||||||
\(206\) | 3.01876 | 0.210327 | ||||||||
\(207\) | 2.38250 | 0.165595 | ||||||||
\(208\) | 2.46631 | 0.171008 | ||||||||
\(209\) | −10.7640 | −0.744564 | ||||||||
\(210\) | −4.32913 | −0.298738 | ||||||||
\(211\) | −4.82200 | −0.331960 | −0.165980 | − | 0.986129i | \(-0.553079\pi\) | ||||
−0.165980 | + | 0.986129i | \(0.553079\pi\) | |||||||
\(212\) | −6.61052 | −0.454013 | ||||||||
\(213\) | −4.93076 | −0.337850 | ||||||||
\(214\) | 7.17272 | 0.490317 | ||||||||
\(215\) | 13.2283 | 0.902165 | ||||||||
\(216\) | −4.22963 | −0.287790 | ||||||||
\(217\) | −28.1985 | −1.91424 | ||||||||
\(218\) | 3.99600 | 0.270643 | ||||||||
\(219\) | 10.2626 | 0.693482 | ||||||||
\(220\) | −6.04091 | −0.407278 | ||||||||
\(221\) | 3.82500 | 0.257297 | ||||||||
\(222\) | −3.96066 | −0.265822 | ||||||||
\(223\) | −23.8010 | −1.59383 | −0.796915 | − | 0.604091i | \(-0.793536\pi\) | ||||
−0.796915 | + | 0.604091i | \(0.793536\pi\) | |||||||
\(224\) | −3.87369 | −0.258822 | ||||||||
\(225\) | 7.09360 | 0.472906 | ||||||||
\(226\) | −13.6826 | −0.910151 | ||||||||
\(227\) | −6.05338 | −0.401777 | −0.200889 | − | 0.979614i | \(-0.564383\pi\) | ||||
−0.200889 | + | 0.979614i | \(0.564383\pi\) | |||||||
\(228\) | 1.99135 | 0.131881 | ||||||||
\(229\) | −25.9038 | −1.71177 | −0.855885 | − | 0.517167i | \(-0.826987\pi\) | ||||
−0.855885 | + | 0.517167i | \(0.826987\pi\) | |||||||
\(230\) | −1.42219 | −0.0937765 | ||||||||
\(231\) | −12.9297 | −0.850710 | ||||||||
\(232\) | −4.09137 | −0.268611 | ||||||||
\(233\) | 10.7270 | 0.702746 | 0.351373 | − | 0.936236i | \(-0.385715\pi\) | ||||
0.351373 | + | 0.936236i | \(0.385715\pi\) | |||||||
\(234\) | 5.87599 | 0.384125 | ||||||||
\(235\) | 7.13330 | 0.465325 | ||||||||
\(236\) | −1.17415 | −0.0764306 | ||||||||
\(237\) | 7.00925 | 0.455300 | ||||||||
\(238\) | −6.00770 | −0.389422 | ||||||||
\(239\) | −24.0030 | −1.55263 | −0.776314 | − | 0.630347i | \(-0.782913\pi\) | ||||
−0.776314 | + | 0.630347i | \(0.782913\pi\) | |||||||
\(240\) | 1.11757 | 0.0721390 | ||||||||
\(241\) | 6.77771 | 0.436591 | 0.218295 | − | 0.975883i | \(-0.429950\pi\) | ||||
0.218295 | + | 0.975883i | \(0.429950\pi\) | |||||||
\(242\) | −7.04218 | −0.452689 | ||||||||
\(243\) | −15.6937 | −1.00675 | ||||||||
\(244\) | 6.46185 | 0.413677 | ||||||||
\(245\) | −11.3853 | −0.727379 | ||||||||
\(246\) | −4.98950 | −0.318119 | ||||||||
\(247\) | −6.24997 | −0.397676 | ||||||||
\(248\) | 7.27950 | 0.462249 | ||||||||
\(249\) | −11.0867 | −0.702588 | ||||||||
\(250\) | −11.3453 | −0.717543 | ||||||||
\(251\) | 11.3933 | 0.719136 | 0.359568 | − | 0.933119i | \(-0.382924\pi\) | ||||
0.359568 | + | 0.933119i | \(0.382924\pi\) | |||||||
\(252\) | −9.22906 | −0.581376 | ||||||||
\(253\) | −4.24761 | −0.267045 | ||||||||
\(254\) | −14.2216 | −0.892345 | ||||||||
\(255\) | 1.73324 | 0.108540 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.94455 | 0.620324 | 0.310162 | − | 0.950684i | \(-0.399617\pi\) | ||||
0.310162 | + | 0.950684i | \(0.399617\pi\) | |||||||
\(258\) | −7.30913 | −0.455046 | ||||||||
\(259\) | −19.5242 | −1.21318 | ||||||||
\(260\) | −3.50756 | −0.217530 | ||||||||
\(261\) | −9.74768 | −0.603366 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 9.89205 | 0.609970 | 0.304985 | − | 0.952357i | \(-0.401349\pi\) | ||||
0.304985 | + | 0.952357i | \(0.401349\pi\) | |||||||
\(264\) | 3.33782 | 0.205429 | ||||||||
\(265\) | 9.40142 | 0.577525 | ||||||||
\(266\) | 9.81646 | 0.601886 | ||||||||
\(267\) | 9.11404 | 0.557770 | ||||||||
\(268\) | 9.88156 | 0.603613 | ||||||||
\(269\) | 4.93260 | 0.300746 | 0.150373 | − | 0.988629i | \(-0.451953\pi\) | ||||
0.150373 | + | 0.988629i | \(0.451953\pi\) | |||||||
\(270\) | 6.01534 | 0.366082 | ||||||||
\(271\) | 28.7211 | 1.74468 | 0.872342 | − | 0.488895i | \(-0.162600\pi\) | ||||
0.872342 | + | 0.488895i | \(0.162600\pi\) | |||||||
\(272\) | 1.55090 | 0.0940371 | ||||||||
\(273\) | −7.50742 | −0.454370 | ||||||||
\(274\) | 16.5255 | 0.998343 | ||||||||
\(275\) | −12.6467 | −0.762626 | ||||||||
\(276\) | 0.785811 | 0.0473003 | ||||||||
\(277\) | −25.9935 | −1.56180 | −0.780898 | − | 0.624658i | \(-0.785238\pi\) | ||||
−0.780898 | + | 0.624658i | \(0.785238\pi\) | |||||||
\(278\) | −8.60490 | −0.516088 | ||||||||
\(279\) | 17.3434 | 1.03832 | ||||||||
\(280\) | 5.50912 | 0.329233 | ||||||||
\(281\) | 32.0766 | 1.91353 | 0.956763 | − | 0.290867i | \(-0.0939439\pi\) | ||||
0.956763 | + | 0.290867i | \(0.0939439\pi\) | |||||||
\(282\) | −3.94140 | −0.234707 | ||||||||
\(283\) | −30.7274 | −1.82655 | −0.913277 | − | 0.407340i | \(-0.866456\pi\) | ||||
−0.913277 | + | 0.407340i | \(0.866456\pi\) | |||||||
\(284\) | 6.27474 | 0.372337 | ||||||||
\(285\) | −2.83209 | −0.167758 | ||||||||
\(286\) | −10.4759 | −0.619454 | ||||||||
\(287\) | −24.5959 | −1.45185 | ||||||||
\(288\) | 2.38250 | 0.140390 | ||||||||
\(289\) | −14.5947 | −0.858512 | ||||||||
\(290\) | 5.81870 | 0.341686 | ||||||||
\(291\) | 11.4050 | 0.668570 | ||||||||
\(292\) | −13.0599 | −0.764271 | ||||||||
\(293\) | −13.4226 | −0.784156 | −0.392078 | − | 0.919932i | \(-0.628244\pi\) | ||||
−0.392078 | + | 0.919932i | \(0.628244\pi\) | |||||||
\(294\) | 6.29078 | 0.366885 | ||||||||
\(295\) | 1.66986 | 0.0972232 | ||||||||
\(296\) | 5.04022 | 0.292957 | ||||||||
\(297\) | 17.9658 | 1.04248 | ||||||||
\(298\) | 15.3186 | 0.887383 | ||||||||
\(299\) | −2.46631 | −0.142630 | ||||||||
\(300\) | 2.33965 | 0.135080 | ||||||||
\(301\) | −36.0306 | −2.07677 | ||||||||
\(302\) | 13.1238 | 0.755192 | ||||||||
\(303\) | 0.917415 | 0.0527041 | ||||||||
\(304\) | −2.53414 | −0.145343 | ||||||||
\(305\) | −9.18998 | −0.526217 | ||||||||
\(306\) | 3.69502 | 0.211230 | ||||||||
\(307\) | 13.7714 | 0.785976 | 0.392988 | − | 0.919544i | \(-0.371441\pi\) | ||||
0.392988 | + | 0.919544i | \(0.371441\pi\) | |||||||
\(308\) | 16.4539 | 0.937549 | ||||||||
\(309\) | 2.37218 | 0.134948 | ||||||||
\(310\) | −10.3528 | −0.588002 | ||||||||
\(311\) | 17.4388 | 0.988864 | 0.494432 | − | 0.869216i | \(-0.335376\pi\) | ||||
0.494432 | + | 0.869216i | \(0.335376\pi\) | |||||||
\(312\) | 1.93805 | 0.109721 | ||||||||
\(313\) | −14.0667 | −0.795099 | −0.397549 | − | 0.917581i | \(-0.630139\pi\) | ||||
−0.397549 | + | 0.917581i | \(0.630139\pi\) | |||||||
\(314\) | 0.761128 | 0.0429529 | ||||||||
\(315\) | 13.1255 | 0.739537 | ||||||||
\(316\) | −8.91977 | −0.501776 | ||||||||
\(317\) | 6.19260 | 0.347811 | 0.173905 | − | 0.984762i | \(-0.444361\pi\) | ||||
0.173905 | + | 0.984762i | \(0.444361\pi\) | |||||||
\(318\) | −5.19462 | −0.291300 | ||||||||
\(319\) | 17.3785 | 0.973011 | ||||||||
\(320\) | −1.42219 | −0.0795029 | ||||||||
\(321\) | 5.63640 | 0.314593 | ||||||||
\(322\) | 3.87369 | 0.215872 | ||||||||
\(323\) | −3.93020 | −0.218682 | ||||||||
\(324\) | 3.82381 | 0.212434 | ||||||||
\(325\) | −7.34313 | −0.407324 | ||||||||
\(326\) | −19.8011 | −1.09668 | ||||||||
\(327\) | 3.14010 | 0.173648 | ||||||||
\(328\) | 6.34949 | 0.350592 | ||||||||
\(329\) | −19.4293 | −1.07117 | ||||||||
\(330\) | −4.74701 | −0.261315 | ||||||||
\(331\) | −18.1773 | −0.999114 | −0.499557 | − | 0.866281i | \(-0.666504\pi\) | ||||
−0.499557 | + | 0.866281i | \(0.666504\pi\) | |||||||
\(332\) | 14.1085 | 0.774307 | ||||||||
\(333\) | 12.0083 | 0.658052 | ||||||||
\(334\) | −4.08020 | −0.223259 | ||||||||
\(335\) | −14.0535 | −0.767823 | ||||||||
\(336\) | −3.04399 | −0.166063 | ||||||||
\(337\) | 23.9544 | 1.30488 | 0.652440 | − | 0.757841i | \(-0.273745\pi\) | ||||
0.652440 | + | 0.757841i | \(0.273745\pi\) | |||||||
\(338\) | 6.91731 | 0.376252 | ||||||||
\(339\) | −10.7519 | −0.583964 | ||||||||
\(340\) | −2.20568 | −0.119620 | ||||||||
\(341\) | −30.9205 | −1.67444 | ||||||||
\(342\) | −6.03759 | −0.326475 | ||||||||
\(343\) | 3.89481 | 0.210300 | ||||||||
\(344\) | 9.30138 | 0.501497 | ||||||||
\(345\) | −1.11757 | −0.0601681 | ||||||||
\(346\) | −2.46367 | −0.132448 | ||||||||
\(347\) | −32.0717 | −1.72170 | −0.860849 | − | 0.508861i | \(-0.830067\pi\) | ||||
−0.860849 | + | 0.508861i | \(0.830067\pi\) | |||||||
\(348\) | −3.21504 | −0.172344 | ||||||||
\(349\) | 0.128543 | 0.00688074 | 0.00344037 | − | 0.999994i | \(-0.498905\pi\) | ||||
0.00344037 | + | 0.999994i | \(0.498905\pi\) | |||||||
\(350\) | 11.5334 | 0.616487 | ||||||||
\(351\) | 10.4316 | 0.556796 | ||||||||
\(352\) | −4.24761 | −0.226398 | ||||||||
\(353\) | 5.01443 | 0.266891 | 0.133446 | − | 0.991056i | \(-0.457396\pi\) | ||||
0.133446 | + | 0.991056i | \(0.457396\pi\) | |||||||
\(354\) | −0.922660 | −0.0490388 | ||||||||
\(355\) | −8.92387 | −0.473630 | ||||||||
\(356\) | −11.5983 | −0.614706 | ||||||||
\(357\) | −4.72092 | −0.249858 | ||||||||
\(358\) | −10.7958 | −0.570575 | ||||||||
\(359\) | −23.3707 | −1.23346 | −0.616730 | − | 0.787175i | \(-0.711543\pi\) | ||||
−0.616730 | + | 0.787175i | \(0.711543\pi\) | |||||||
\(360\) | −3.38837 | −0.178583 | ||||||||
\(361\) | −12.5781 | −0.662007 | ||||||||
\(362\) | −9.47637 | −0.498067 | ||||||||
\(363\) | −5.53383 | −0.290451 | ||||||||
\(364\) | 9.55371 | 0.500751 | ||||||||
\(365\) | 18.5736 | 0.972188 | ||||||||
\(366\) | 5.07779 | 0.265420 | ||||||||
\(367\) | 25.8392 | 1.34880 | 0.674398 | − | 0.738368i | \(-0.264403\pi\) | ||||
0.674398 | + | 0.738368i | \(0.264403\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 15.1277 | 0.787515 | ||||||||
\(370\) | −7.16815 | −0.372654 | ||||||||
\(371\) | −25.6071 | −1.32945 | ||||||||
\(372\) | 5.72031 | 0.296584 | ||||||||
\(373\) | −2.83438 | −0.146758 | −0.0733792 | − | 0.997304i | \(-0.523378\pi\) | ||||
−0.0733792 | + | 0.997304i | \(0.523378\pi\) | |||||||
\(374\) | −6.58762 | −0.340638 | ||||||||
\(375\) | −8.91530 | −0.460384 | ||||||||
\(376\) | 5.01571 | 0.258666 | ||||||||
\(377\) | 10.0906 | 0.519691 | ||||||||
\(378\) | −16.3843 | −0.842716 | ||||||||
\(379\) | −33.9194 | −1.74232 | −0.871160 | − | 0.490999i | \(-0.836632\pi\) | ||||
−0.871160 | + | 0.490999i | \(0.836632\pi\) | |||||||
\(380\) | 3.60403 | 0.184883 | ||||||||
\(381\) | −11.1755 | −0.572539 | ||||||||
\(382\) | −6.80800 | −0.348328 | ||||||||
\(383\) | 29.3851 | 1.50151 | 0.750753 | − | 0.660583i | \(-0.229691\pi\) | ||||
0.750753 | + | 0.660583i | \(0.229691\pi\) | |||||||
\(384\) | 0.785811 | 0.0401008 | ||||||||
\(385\) | −23.4006 | −1.19260 | ||||||||
\(386\) | 14.7284 | 0.749657 | ||||||||
\(387\) | 22.1605 | 1.12648 | ||||||||
\(388\) | −14.5136 | −0.736817 | ||||||||
\(389\) | 11.5197 | 0.584070 | 0.292035 | − | 0.956408i | \(-0.405668\pi\) | ||||
0.292035 | + | 0.956408i | \(0.405668\pi\) | |||||||
\(390\) | −2.75628 | −0.139570 | ||||||||
\(391\) | −1.55090 | −0.0784324 | ||||||||
\(392\) | −8.00545 | −0.404336 | ||||||||
\(393\) | 0.785811 | 0.0396389 | ||||||||
\(394\) | 13.0172 | 0.655798 | ||||||||
\(395\) | 12.6856 | 0.638282 | ||||||||
\(396\) | −10.1199 | −0.508546 | ||||||||
\(397\) | −30.2065 | −1.51602 | −0.758010 | − | 0.652243i | \(-0.773828\pi\) | ||||
−0.758010 | + | 0.652243i | \(0.773828\pi\) | |||||||
\(398\) | −16.5962 | −0.831891 | ||||||||
\(399\) | 7.71389 | 0.386177 | ||||||||
\(400\) | −2.97737 | −0.148869 | ||||||||
\(401\) | −3.54033 | −0.176796 | −0.0883978 | − | 0.996085i | \(-0.528175\pi\) | ||||
−0.0883978 | + | 0.996085i | \(0.528175\pi\) | |||||||
\(402\) | 7.76504 | 0.387285 | ||||||||
\(403\) | −17.9535 | −0.894328 | ||||||||
\(404\) | −1.16747 | −0.0580840 | ||||||||
\(405\) | −5.43819 | −0.270226 | ||||||||
\(406\) | −15.8487 | −0.786556 | ||||||||
\(407\) | −21.4089 | −1.06120 | ||||||||
\(408\) | 1.21871 | 0.0603354 | ||||||||
\(409\) | −24.7495 | −1.22378 | −0.611891 | − | 0.790942i | \(-0.709591\pi\) | ||||
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(410\) | −9.03018 | −0.445969 | ||||||||
\(411\) | 12.9859 | 0.640549 | ||||||||
\(412\) | −3.01876 | −0.148724 | ||||||||
\(413\) | −4.54829 | −0.223807 | ||||||||
\(414\) | −2.38250 | −0.117094 | ||||||||
\(415\) | −20.0650 | −0.984954 | ||||||||
\(416\) | −2.46631 | −0.120921 | ||||||||
\(417\) | −6.76183 | −0.331128 | ||||||||
\(418\) | 10.7640 | 0.526486 | ||||||||
\(419\) | 30.3852 | 1.48441 | 0.742206 | − | 0.670171i | \(-0.233779\pi\) | ||||
0.742206 | + | 0.670171i | \(0.233779\pi\) | |||||||
\(420\) | 4.32913 | 0.211240 | ||||||||
\(421\) | −23.4771 | −1.14420 | −0.572102 | − | 0.820183i | \(-0.693872\pi\) | ||||
−0.572102 | + | 0.820183i | \(0.693872\pi\) | |||||||
\(422\) | 4.82200 | 0.234731 | ||||||||
\(423\) | 11.9499 | 0.581026 | ||||||||
\(424\) | 6.61052 | 0.321035 | ||||||||
\(425\) | −4.61761 | −0.223987 | ||||||||
\(426\) | 4.93076 | 0.238896 | ||||||||
\(427\) | 25.0312 | 1.21134 | ||||||||
\(428\) | −7.17272 | −0.346706 | ||||||||
\(429\) | −8.23210 | −0.397449 | ||||||||
\(430\) | −13.2283 | −0.637927 | ||||||||
\(431\) | 16.7750 | 0.808025 | 0.404013 | − | 0.914753i | \(-0.367615\pi\) | ||||
0.404013 | + | 0.914753i | \(0.367615\pi\) | |||||||
\(432\) | 4.22963 | 0.203498 | ||||||||
\(433\) | 33.2177 | 1.59634 | 0.798170 | − | 0.602433i | \(-0.205802\pi\) | ||||
0.798170 | + | 0.602433i | \(0.205802\pi\) | |||||||
\(434\) | 28.1985 | 1.35357 | ||||||||
\(435\) | 4.57240 | 0.219230 | ||||||||
\(436\) | −3.99600 | −0.191373 | ||||||||
\(437\) | 2.53414 | 0.121224 | ||||||||
\(438\) | −10.2626 | −0.490366 | ||||||||
\(439\) | −4.02949 | −0.192317 | −0.0961585 | − | 0.995366i | \(-0.530656\pi\) | ||||
−0.0961585 | + | 0.995366i | \(0.530656\pi\) | |||||||
\(440\) | 6.04091 | 0.287989 | ||||||||
\(441\) | −19.0730 | −0.908238 | ||||||||
\(442\) | −3.82500 | −0.181937 | ||||||||
\(443\) | −23.2202 | −1.10323 | −0.551613 | − | 0.834100i | \(-0.685988\pi\) | ||||
−0.551613 | + | 0.834100i | \(0.685988\pi\) | |||||||
\(444\) | 3.96066 | 0.187965 | ||||||||
\(445\) | 16.4949 | 0.781934 | ||||||||
\(446\) | 23.8010 | 1.12701 | ||||||||
\(447\) | 12.0375 | 0.569356 | ||||||||
\(448\) | 3.87369 | 0.183015 | ||||||||
\(449\) | 15.7458 | 0.743092 | 0.371546 | − | 0.928415i | \(-0.378828\pi\) | ||||
0.371546 | + | 0.928415i | \(0.378828\pi\) | |||||||
\(450\) | −7.09360 | −0.334395 | ||||||||
\(451\) | −26.9702 | −1.26998 | ||||||||
\(452\) | 13.6826 | 0.643574 | ||||||||
\(453\) | 10.3129 | 0.484540 | ||||||||
\(454\) | 6.05338 | 0.284099 | ||||||||
\(455\) | −13.5872 | −0.636978 | ||||||||
\(456\) | −1.99135 | −0.0932537 | ||||||||
\(457\) | 22.8637 | 1.06952 | 0.534760 | − | 0.845004i | \(-0.320402\pi\) | ||||
0.534760 | + | 0.845004i | \(0.320402\pi\) | |||||||
\(458\) | 25.9038 | 1.21040 | ||||||||
\(459\) | 6.55973 | 0.306182 | ||||||||
\(460\) | 1.42219 | 0.0663100 | ||||||||
\(461\) | −1.40109 | −0.0652555 | −0.0326277 | − | 0.999468i | \(-0.510388\pi\) | ||||
−0.0326277 | + | 0.999468i | \(0.510388\pi\) | |||||||
\(462\) | 12.9297 | 0.601543 | ||||||||
\(463\) | −38.6071 | −1.79423 | −0.897113 | − | 0.441802i | \(-0.854339\pi\) | ||||
−0.897113 | + | 0.441802i | \(0.854339\pi\) | |||||||
\(464\) | 4.09137 | 0.189937 | ||||||||
\(465\) | −8.13537 | −0.377269 | ||||||||
\(466\) | −10.7270 | −0.496916 | ||||||||
\(467\) | −33.5864 | −1.55420 | −0.777098 | − | 0.629380i | \(-0.783309\pi\) | ||||
−0.777098 | + | 0.629380i | \(0.783309\pi\) | |||||||
\(468\) | −5.87599 | −0.271618 | ||||||||
\(469\) | 38.2781 | 1.76752 | ||||||||
\(470\) | −7.13330 | −0.329034 | ||||||||
\(471\) | 0.598103 | 0.0275591 | ||||||||
\(472\) | 1.17415 | 0.0540446 | ||||||||
\(473\) | −39.5086 | −1.81661 | ||||||||
\(474\) | −7.00925 | −0.321946 | ||||||||
\(475\) | 7.54508 | 0.346192 | ||||||||
\(476\) | 6.00770 | 0.275363 | ||||||||
\(477\) | 15.7496 | 0.721124 | ||||||||
\(478\) | 24.0030 | 1.09787 | ||||||||
\(479\) | 16.2242 | 0.741304 | 0.370652 | − | 0.928772i | \(-0.379134\pi\) | ||||
0.370652 | + | 0.928772i | \(0.379134\pi\) | |||||||
\(480\) | −1.11757 | −0.0510100 | ||||||||
\(481\) | −12.4307 | −0.566793 | ||||||||
\(482\) | −6.77771 | −0.308716 | ||||||||
\(483\) | 3.04399 | 0.138506 | ||||||||
\(484\) | 7.04218 | 0.320099 | ||||||||
\(485\) | 20.6411 | 0.937265 | ||||||||
\(486\) | 15.6937 | 0.711880 | ||||||||
\(487\) | −1.66642 | −0.0755125 | −0.0377562 | − | 0.999287i | \(-0.512021\pi\) | ||||
−0.0377562 | + | 0.999287i | \(0.512021\pi\) | |||||||
\(488\) | −6.46185 | −0.292514 | ||||||||
\(489\) | −15.5599 | −0.703644 | ||||||||
\(490\) | 11.3853 | 0.514334 | ||||||||
\(491\) | 5.78439 | 0.261046 | 0.130523 | − | 0.991445i | \(-0.458334\pi\) | ||||
0.130523 | + | 0.991445i | \(0.458334\pi\) | |||||||
\(492\) | 4.98950 | 0.224944 | ||||||||
\(493\) | 6.34530 | 0.285778 | ||||||||
\(494\) | 6.24997 | 0.281200 | ||||||||
\(495\) | 14.3925 | 0.646893 | ||||||||
\(496\) | −7.27950 | −0.326859 | ||||||||
\(497\) | 24.3064 | 1.09029 | ||||||||
\(498\) | 11.0867 | 0.496805 | ||||||||
\(499\) | −26.4914 | −1.18592 | −0.592959 | − | 0.805232i | \(-0.702041\pi\) | ||||
−0.592959 | + | 0.805232i | \(0.702041\pi\) | |||||||
\(500\) | 11.3453 | 0.507379 | ||||||||
\(501\) | −3.20627 | −0.143245 | ||||||||
\(502\) | −11.3933 | −0.508506 | ||||||||
\(503\) | −16.6310 | −0.741539 | −0.370769 | − | 0.928725i | \(-0.620906\pi\) | ||||
−0.370769 | + | 0.928725i | \(0.620906\pi\) | |||||||
\(504\) | 9.22906 | 0.411095 | ||||||||
\(505\) | 1.66037 | 0.0738855 | ||||||||
\(506\) | 4.24761 | 0.188829 | ||||||||
\(507\) | 5.43570 | 0.241408 | ||||||||
\(508\) | 14.2216 | 0.630983 | ||||||||
\(509\) | −12.7565 | −0.565422 | −0.282711 | − | 0.959205i | \(-0.591234\pi\) | ||||
−0.282711 | + | 0.959205i | \(0.591234\pi\) | |||||||
\(510\) | −1.73324 | −0.0767493 | ||||||||
\(511\) | −50.5899 | −2.23796 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.7185 | −0.473232 | ||||||||
\(514\) | −9.94455 | −0.438635 | ||||||||
\(515\) | 4.29325 | 0.189183 | ||||||||
\(516\) | 7.30913 | 0.321766 | ||||||||
\(517\) | −21.3048 | −0.936983 | ||||||||
\(518\) | 19.5242 | 0.857845 | ||||||||
\(519\) | −1.93598 | −0.0849799 | ||||||||
\(520\) | 3.50756 | 0.153817 | ||||||||
\(521\) | −12.7609 | −0.559063 | −0.279532 | − | 0.960137i | \(-0.590179\pi\) | ||||
−0.279532 | + | 0.960137i | \(0.590179\pi\) | |||||||
\(522\) | 9.74768 | 0.426644 | ||||||||
\(523\) | −6.25629 | −0.273569 | −0.136784 | − | 0.990601i | \(-0.543677\pi\) | ||||
−0.136784 | + | 0.990601i | \(0.543677\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 9.06309 | 0.395546 | ||||||||
\(526\) | −9.89205 | −0.431314 | ||||||||
\(527\) | −11.2898 | −0.491791 | ||||||||
\(528\) | −3.33782 | −0.145260 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −9.40142 | −0.408372 | ||||||||
\(531\) | 2.79741 | 0.121397 | ||||||||
\(532\) | −9.81646 | −0.425598 | ||||||||
\(533\) | −15.6598 | −0.678302 | ||||||||
\(534\) | −9.11404 | −0.394403 | ||||||||
\(535\) | 10.2010 | 0.441026 | ||||||||
\(536\) | −9.88156 | −0.426819 | ||||||||
\(537\) | −8.48346 | −0.366088 | ||||||||
\(538\) | −4.93260 | −0.212659 | ||||||||
\(539\) | 34.0040 | 1.46466 | ||||||||
\(540\) | −6.01534 | −0.258859 | ||||||||
\(541\) | −3.89662 | −0.167529 | −0.0837643 | − | 0.996486i | \(-0.526694\pi\) | ||||
−0.0837643 | + | 0.996486i | \(0.526694\pi\) | |||||||
\(542\) | −28.7211 | −1.23368 | ||||||||
\(543\) | −7.44664 | −0.319566 | ||||||||
\(544\) | −1.55090 | −0.0664943 | ||||||||
\(545\) | 5.68307 | 0.243436 | ||||||||
\(546\) | 7.50742 | 0.321288 | ||||||||
\(547\) | 4.45583 | 0.190517 | 0.0952587 | − | 0.995453i | \(-0.469632\pi\) | ||||
0.0952587 | + | 0.995453i | \(0.469632\pi\) | |||||||
\(548\) | −16.5255 | −0.705935 | ||||||||
\(549\) | −15.3954 | −0.657058 | ||||||||
\(550\) | 12.6467 | 0.539258 | ||||||||
\(551\) | −10.3681 | −0.441695 | ||||||||
\(552\) | −0.785811 | −0.0334463 | ||||||||
\(553\) | −34.5524 | −1.46932 | ||||||||
\(554\) | 25.9935 | 1.10436 | ||||||||
\(555\) | −5.63281 | −0.239099 | ||||||||
\(556\) | 8.60490 | 0.364929 | ||||||||
\(557\) | 43.4169 | 1.83963 | 0.919817 | − | 0.392348i | \(-0.128337\pi\) | ||||
0.919817 | + | 0.392348i | \(0.128337\pi\) | |||||||
\(558\) | −17.3434 | −0.734205 | ||||||||
\(559\) | −22.9401 | −0.970262 | ||||||||
\(560\) | −5.50912 | −0.232803 | ||||||||
\(561\) | −5.17662 | −0.218557 | ||||||||
\(562\) | −32.0766 | −1.35307 | ||||||||
\(563\) | −16.3347 | −0.688424 | −0.344212 | − | 0.938892i | \(-0.611854\pi\) | ||||
−0.344212 | + | 0.938892i | \(0.611854\pi\) | |||||||
\(564\) | 3.94140 | 0.165963 | ||||||||
\(565\) | −19.4592 | −0.818655 | ||||||||
\(566\) | 30.7274 | 1.29157 | ||||||||
\(567\) | 14.8123 | 0.622056 | ||||||||
\(568\) | −6.27474 | −0.263282 | ||||||||
\(569\) | 23.3598 | 0.979293 | 0.489647 | − | 0.871921i | \(-0.337126\pi\) | ||||
0.489647 | + | 0.871921i | \(0.337126\pi\) | |||||||
\(570\) | 2.83209 | 0.118623 | ||||||||
\(571\) | −4.00674 | −0.167677 | −0.0838384 | − | 0.996479i | \(-0.526718\pi\) | ||||
−0.0838384 | + | 0.996479i | \(0.526718\pi\) | |||||||
\(572\) | 10.4759 | 0.438020 | ||||||||
\(573\) | −5.34980 | −0.223491 | ||||||||
\(574\) | 24.5959 | 1.02661 | ||||||||
\(575\) | 2.97737 | 0.124165 | ||||||||
\(576\) | −2.38250 | −0.0992709 | ||||||||
\(577\) | −0.942727 | −0.0392463 | −0.0196231 | − | 0.999807i | \(-0.506247\pi\) | ||||
−0.0196231 | + | 0.999807i | \(0.506247\pi\) | |||||||
\(578\) | 14.5947 | 0.607060 | ||||||||
\(579\) | 11.5738 | 0.480989 | ||||||||
\(580\) | −5.81870 | −0.241608 | ||||||||
\(581\) | 54.6521 | 2.26735 | ||||||||
\(582\) | −11.4050 | −0.472751 | ||||||||
\(583\) | −28.0789 | −1.16291 | ||||||||
\(584\) | 13.0599 | 0.540421 | ||||||||
\(585\) | 8.35677 | 0.345510 | ||||||||
\(586\) | 13.4226 | 0.554482 | ||||||||
\(587\) | −1.48796 | −0.0614145 | −0.0307073 | − | 0.999528i | \(-0.509776\pi\) | ||||
−0.0307073 | + | 0.999528i | \(0.509776\pi\) | |||||||
\(588\) | −6.29078 | −0.259427 | ||||||||
\(589\) | 18.4473 | 0.760106 | ||||||||
\(590\) | −1.66986 | −0.0687472 | ||||||||
\(591\) | 10.2291 | 0.420768 | ||||||||
\(592\) | −5.04022 | −0.207152 | ||||||||
\(593\) | 1.86374 | 0.0765345 | 0.0382673 | − | 0.999268i | \(-0.487816\pi\) | ||||
0.0382673 | + | 0.999268i | \(0.487816\pi\) | |||||||
\(594\) | −17.9658 | −0.737146 | ||||||||
\(595\) | −8.54410 | −0.350274 | ||||||||
\(596\) | −15.3186 | −0.627475 | ||||||||
\(597\) | −13.0415 | −0.533751 | ||||||||
\(598\) | 2.46631 | 0.100855 | ||||||||
\(599\) | −11.8117 | −0.482614 | −0.241307 | − | 0.970449i | \(-0.577576\pi\) | ||||
−0.241307 | + | 0.970449i | \(0.577576\pi\) | |||||||
\(600\) | −2.33965 | −0.0955160 | ||||||||
\(601\) | 41.3786 | 1.68787 | 0.843934 | − | 0.536447i | \(-0.180234\pi\) | ||||
0.843934 | + | 0.536447i | \(0.180234\pi\) | |||||||
\(602\) | 36.0306 | 1.46850 | ||||||||
\(603\) | −23.5428 | −0.958738 | ||||||||
\(604\) | −13.1238 | −0.534001 | ||||||||
\(605\) | −10.0153 | −0.407181 | ||||||||
\(606\) | −0.917415 | −0.0372674 | ||||||||
\(607\) | −2.96436 | −0.120320 | −0.0601598 | − | 0.998189i | \(-0.519161\pi\) | ||||
−0.0601598 | + | 0.998189i | \(0.519161\pi\) | |||||||
\(608\) | 2.53414 | 0.102773 | ||||||||
\(609\) | −12.4541 | −0.504664 | ||||||||
\(610\) | 9.18998 | 0.372091 | ||||||||
\(611\) | −12.3703 | −0.500449 | ||||||||
\(612\) | −3.69502 | −0.149362 | ||||||||
\(613\) | −46.7489 | −1.88817 | −0.944086 | − | 0.329700i | \(-0.893052\pi\) | ||||
−0.944086 | + | 0.329700i | \(0.893052\pi\) | |||||||
\(614\) | −13.7714 | −0.555769 | ||||||||
\(615\) | −7.09602 | −0.286139 | ||||||||
\(616\) | −16.4539 | −0.662947 | ||||||||
\(617\) | −7.73953 | −0.311582 | −0.155791 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155791 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(618\) | −2.37218 | −0.0954229 | ||||||||
\(619\) | −1.07015 | −0.0430131 | −0.0215066 | − | 0.999769i | \(-0.506846\pi\) | ||||
−0.0215066 | + | 0.999769i | \(0.506846\pi\) | |||||||
\(620\) | 10.3528 | 0.415780 | ||||||||
\(621\) | −4.22963 | −0.169729 | ||||||||
\(622\) | −17.4388 | −0.699233 | ||||||||
\(623\) | −44.9280 | −1.80000 | ||||||||
\(624\) | −1.93805 | −0.0775843 | ||||||||
\(625\) | −1.24837 | −0.0499346 | ||||||||
\(626\) | 14.0667 | 0.562220 | ||||||||
\(627\) | 8.45850 | 0.337800 | ||||||||
\(628\) | −0.761128 | −0.0303723 | ||||||||
\(629\) | −7.81687 | −0.311679 | ||||||||
\(630\) | −13.1255 | −0.522932 | ||||||||
\(631\) | −8.86536 | −0.352924 | −0.176462 | − | 0.984307i | \(-0.556465\pi\) | ||||
−0.176462 | + | 0.984307i | \(0.556465\pi\) | |||||||
\(632\) | 8.91977 | 0.354809 | ||||||||
\(633\) | 3.78918 | 0.150607 | ||||||||
\(634\) | −6.19260 | −0.245939 | ||||||||
\(635\) | −20.2259 | −0.802639 | ||||||||
\(636\) | 5.19462 | 0.205980 | ||||||||
\(637\) | 19.7439 | 0.782283 | ||||||||
\(638\) | −17.3785 | −0.688022 | ||||||||
\(639\) | −14.9496 | −0.591395 | ||||||||
\(640\) | 1.42219 | 0.0562170 | ||||||||
\(641\) | −21.3470 | −0.843157 | −0.421578 | − | 0.906792i | \(-0.638524\pi\) | ||||
−0.421578 | + | 0.906792i | \(0.638524\pi\) | |||||||
\(642\) | −5.63640 | −0.222451 | ||||||||
\(643\) | −24.2440 | −0.956092 | −0.478046 | − | 0.878335i | \(-0.658655\pi\) | ||||
−0.478046 | + | 0.878335i | \(0.658655\pi\) | |||||||
\(644\) | −3.87369 | −0.152645 | ||||||||
\(645\) | −10.3950 | −0.409302 | ||||||||
\(646\) | 3.93020 | 0.154632 | ||||||||
\(647\) | −40.1279 | −1.57759 | −0.788796 | − | 0.614656i | \(-0.789295\pi\) | ||||
−0.788796 | + | 0.614656i | \(0.789295\pi\) | |||||||
\(648\) | −3.82381 | −0.150214 | ||||||||
\(649\) | −4.98733 | −0.195770 | ||||||||
\(650\) | 7.34313 | 0.288021 | ||||||||
\(651\) | 22.1587 | 0.868468 | ||||||||
\(652\) | 19.8011 | 0.775470 | ||||||||
\(653\) | 42.4364 | 1.66066 | 0.830331 | − | 0.557270i | \(-0.188151\pi\) | ||||
0.830331 | + | 0.557270i | \(0.188151\pi\) | |||||||
\(654\) | −3.14010 | −0.122788 | ||||||||
\(655\) | 1.42219 | 0.0555696 | ||||||||
\(656\) | −6.34949 | −0.247906 | ||||||||
\(657\) | 31.1152 | 1.21392 | ||||||||
\(658\) | 19.4293 | 0.757433 | ||||||||
\(659\) | 37.0603 | 1.44366 | 0.721832 | − | 0.692068i | \(-0.243300\pi\) | ||||
0.721832 | + | 0.692068i | \(0.243300\pi\) | |||||||
\(660\) | 4.74701 | 0.184777 | ||||||||
\(661\) | −47.4400 | −1.84520 | −0.922601 | − | 0.385755i | \(-0.873941\pi\) | ||||
−0.922601 | + | 0.385755i | \(0.873941\pi\) | |||||||
\(662\) | 18.1773 | 0.706480 | ||||||||
\(663\) | −3.00573 | −0.116733 | ||||||||
\(664\) | −14.1085 | −0.547518 | ||||||||
\(665\) | 13.9609 | 0.541380 | ||||||||
\(666\) | −12.0083 | −0.465313 | ||||||||
\(667\) | −4.09137 | −0.158418 | ||||||||
\(668\) | 4.08020 | 0.157868 | ||||||||
\(669\) | 18.7031 | 0.723102 | ||||||||
\(670\) | 14.0535 | 0.542933 | ||||||||
\(671\) | 27.4474 | 1.05960 | ||||||||
\(672\) | 3.04399 | 0.117424 | ||||||||
\(673\) | −10.1492 | −0.391223 | −0.195612 | − | 0.980681i | \(-0.562669\pi\) | ||||
−0.195612 | + | 0.980681i | \(0.562669\pi\) | |||||||
\(674\) | −23.9544 | −0.922689 | ||||||||
\(675\) | −12.5932 | −0.484712 | ||||||||
\(676\) | −6.91731 | −0.266051 | ||||||||
\(677\) | −6.88451 | −0.264593 | −0.132297 | − | 0.991210i | \(-0.542235\pi\) | ||||
−0.132297 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(678\) | 10.7519 | 0.412925 | ||||||||
\(679\) | −56.2212 | −2.15757 | ||||||||
\(680\) | 2.20568 | 0.0845838 | ||||||||
\(681\) | 4.75682 | 0.182282 | ||||||||
\(682\) | 30.9205 | 1.18401 | ||||||||
\(683\) | −43.2779 | −1.65598 | −0.827991 | − | 0.560741i | \(-0.810516\pi\) | ||||
−0.827991 | + | 0.560741i | \(0.810516\pi\) | |||||||
\(684\) | 6.03759 | 0.230853 | ||||||||
\(685\) | 23.5024 | 0.897981 | ||||||||
\(686\) | −3.89481 | −0.148705 | ||||||||
\(687\) | 20.3555 | 0.776610 | ||||||||
\(688\) | −9.30138 | −0.354612 | ||||||||
\(689\) | −16.3036 | −0.621118 | ||||||||
\(690\) | 1.11757 | 0.0425453 | ||||||||
\(691\) | −10.0098 | −0.380792 | −0.190396 | − | 0.981707i | \(-0.560977\pi\) | ||||
−0.190396 | + | 0.981707i | \(0.560977\pi\) | |||||||
\(692\) | 2.46367 | 0.0936545 | ||||||||
\(693\) | −39.2015 | −1.48914 | ||||||||
\(694\) | 32.0717 | 1.21742 | ||||||||
\(695\) | −12.2378 | −0.464206 | ||||||||
\(696\) | 3.21504 | 0.121866 | ||||||||
\(697\) | −9.84743 | −0.372998 | ||||||||
\(698\) | −0.128543 | −0.00486542 | ||||||||
\(699\) | −8.42936 | −0.318828 | ||||||||
\(700\) | −11.5334 | −0.435922 | ||||||||
\(701\) | −22.1761 | −0.837581 | −0.418790 | − | 0.908083i | \(-0.637546\pi\) | ||||
−0.418790 | + | 0.908083i | \(0.637546\pi\) | |||||||
\(702\) | −10.4316 | −0.393715 | ||||||||
\(703\) | 12.7726 | 0.481728 | ||||||||
\(704\) | 4.24761 | 0.160088 | ||||||||
\(705\) | −5.60543 | −0.211113 | ||||||||
\(706\) | −5.01443 | −0.188721 | ||||||||
\(707\) | −4.52243 | −0.170084 | ||||||||
\(708\) | 0.922660 | 0.0346757 | ||||||||
\(709\) | −49.8074 | −1.87056 | −0.935278 | − | 0.353915i | \(-0.884850\pi\) | ||||
−0.935278 | + | 0.353915i | \(0.884850\pi\) | |||||||
\(710\) | 8.92387 | 0.334907 | ||||||||
\(711\) | 21.2513 | 0.796988 | ||||||||
\(712\) | 11.5983 | 0.434663 | ||||||||
\(713\) | 7.27950 | 0.272619 | ||||||||
\(714\) | 4.72092 | 0.176676 | ||||||||
\(715\) | −14.8988 | −0.557182 | ||||||||
\(716\) | 10.7958 | 0.403458 | ||||||||
\(717\) | 18.8619 | 0.704409 | ||||||||
\(718\) | 23.3707 | 0.872187 | ||||||||
\(719\) | −7.28751 | −0.271778 | −0.135889 | − | 0.990724i | \(-0.543389\pi\) | ||||
−0.135889 | + | 0.990724i | \(0.543389\pi\) | |||||||
\(720\) | 3.38837 | 0.126277 | ||||||||
\(721\) | −11.6937 | −0.435498 | ||||||||
\(722\) | 12.5781 | 0.468110 | ||||||||
\(723\) | −5.32600 | −0.198076 | ||||||||
\(724\) | 9.47637 | 0.352187 | ||||||||
\(725\) | −12.1815 | −0.452411 | ||||||||
\(726\) | 5.53383 | 0.205380 | ||||||||
\(727\) | −0.170838 | −0.00633602 | −0.00316801 | − | 0.999995i | \(-0.501008\pi\) | ||||
−0.00316801 | + | 0.999995i | \(0.501008\pi\) | |||||||
\(728\) | −9.55371 | −0.354084 | ||||||||
\(729\) | 0.860836 | 0.0318828 | ||||||||
\(730\) | −18.5736 | −0.687441 | ||||||||
\(731\) | −14.4255 | −0.533547 | ||||||||
\(732\) | −5.07779 | −0.187681 | ||||||||
\(733\) | −43.1216 | −1.59273 | −0.796367 | − | 0.604814i | \(-0.793247\pi\) | ||||
−0.796367 | + | 0.604814i | \(0.793247\pi\) | |||||||
\(734\) | −25.8392 | −0.953743 | ||||||||
\(735\) | 8.94668 | 0.330003 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 41.9730 | 1.54610 | ||||||||
\(738\) | −15.1277 | −0.556857 | ||||||||
\(739\) | 9.57554 | 0.352242 | 0.176121 | − | 0.984369i | \(-0.443645\pi\) | ||||
0.176121 | + | 0.984369i | \(0.443645\pi\) | |||||||
\(740\) | 7.16815 | 0.263506 | ||||||||
\(741\) | 4.91130 | 0.180421 | ||||||||
\(742\) | 25.6071 | 0.940066 | ||||||||
\(743\) | 13.1943 | 0.484053 | 0.242027 | − | 0.970270i | \(-0.422188\pi\) | ||||
0.242027 | + | 0.970270i | \(0.422188\pi\) | |||||||
\(744\) | −5.72031 | −0.209717 | ||||||||
\(745\) | 21.7860 | 0.798176 | ||||||||
\(746\) | 2.83438 | 0.103774 | ||||||||
\(747\) | −33.6136 | −1.22986 | ||||||||
\(748\) | 6.58762 | 0.240867 | ||||||||
\(749\) | −27.7849 | −1.01524 | ||||||||
\(750\) | 8.91530 | 0.325541 | ||||||||
\(751\) | 10.1773 | 0.371374 | 0.185687 | − | 0.982609i | \(-0.440549\pi\) | ||||
0.185687 | + | 0.982609i | \(0.440549\pi\) | |||||||
\(752\) | −5.01571 | −0.182904 | ||||||||
\(753\) | −8.95295 | −0.326264 | ||||||||
\(754\) | −10.0906 | −0.367477 | ||||||||
\(755\) | 18.6646 | 0.679274 | ||||||||
\(756\) | 16.3843 | 0.595890 | ||||||||
\(757\) | 41.7124 | 1.51606 | 0.758031 | − | 0.652218i | \(-0.226161\pi\) | ||||
0.758031 | + | 0.652218i | \(0.226161\pi\) | |||||||
\(758\) | 33.9194 | 1.23201 | ||||||||
\(759\) | 3.33782 | 0.121155 | ||||||||
\(760\) | −3.60403 | −0.130732 | ||||||||
\(761\) | 25.8827 | 0.938246 | 0.469123 | − | 0.883133i | \(-0.344570\pi\) | ||||
0.469123 | + | 0.883133i | \(0.344570\pi\) | |||||||
\(762\) | 11.1755 | 0.404846 | ||||||||
\(763\) | −15.4792 | −0.560386 | ||||||||
\(764\) | 6.80800 | 0.246305 | ||||||||
\(765\) | 5.25502 | 0.189996 | ||||||||
\(766\) | −29.3851 | −1.06173 | ||||||||
\(767\) | −2.89582 | −0.104562 | ||||||||
\(768\) | −0.785811 | −0.0283555 | ||||||||
\(769\) | −11.2893 | −0.407101 | −0.203551 | − | 0.979064i | \(-0.565248\pi\) | ||||
−0.203551 | + | 0.979064i | \(0.565248\pi\) | |||||||
\(770\) | 23.4006 | 0.843299 | ||||||||
\(771\) | −7.81454 | −0.281434 | ||||||||
\(772\) | −14.7284 | −0.530088 | ||||||||
\(773\) | 15.5274 | 0.558483 | 0.279242 | − | 0.960221i | \(-0.409917\pi\) | ||||
0.279242 | + | 0.960221i | \(0.409917\pi\) | |||||||
\(774\) | −22.1605 | −0.796544 | ||||||||
\(775\) | 21.6738 | 0.778546 | ||||||||
\(776\) | 14.5136 | 0.521008 | ||||||||
\(777\) | 15.3424 | 0.550404 | ||||||||
\(778\) | −11.5197 | −0.413000 | ||||||||
\(779\) | 16.0905 | 0.576502 | ||||||||
\(780\) | 2.75628 | 0.0986907 | ||||||||
\(781\) | 26.6526 | 0.953706 | ||||||||
\(782\) | 1.55090 | 0.0554601 | ||||||||
\(783\) | 17.3050 | 0.618429 | ||||||||
\(784\) | 8.00545 | 0.285909 | ||||||||
\(785\) | 1.08247 | 0.0386350 | ||||||||
\(786\) | −0.785811 | −0.0280290 | ||||||||
\(787\) | 34.8319 | 1.24162 | 0.620811 | − | 0.783960i | \(-0.286803\pi\) | ||||
0.620811 | + | 0.783960i | \(0.286803\pi\) | |||||||
\(788\) | −13.0172 | −0.463719 | ||||||||
\(789\) | −7.77328 | −0.276736 | ||||||||
\(790\) | −12.6856 | −0.451334 | ||||||||
\(791\) | 53.0020 | 1.88453 | ||||||||
\(792\) | 10.1199 | 0.359596 | ||||||||
\(793\) | 15.9369 | 0.565937 | ||||||||
\(794\) | 30.2065 | 1.07199 | ||||||||
\(795\) | −7.38774 | −0.262016 | ||||||||
\(796\) | 16.5962 | 0.588236 | ||||||||
\(797\) | −3.51665 | −0.124566 | −0.0622830 | − | 0.998059i | \(-0.519838\pi\) | ||||
−0.0622830 | + | 0.998059i | \(0.519838\pi\) | |||||||
\(798\) | −7.71389 | −0.273069 | ||||||||
\(799\) | −7.77887 | −0.275197 | ||||||||
\(800\) | 2.97737 | 0.105266 | ||||||||
\(801\) | 27.6328 | 0.976359 | ||||||||
\(802\) | 3.54033 | 0.125013 | ||||||||
\(803\) | −55.4732 | −1.95761 | ||||||||
\(804\) | −7.76504 | −0.273852 | ||||||||
\(805\) | 5.50912 | 0.194171 | ||||||||
\(806\) | 17.9535 | 0.632385 | ||||||||
\(807\) | −3.87609 | −0.136445 | ||||||||
\(808\) | 1.16747 | 0.0410716 | ||||||||
\(809\) | −11.4465 | −0.402437 | −0.201218 | − | 0.979546i | \(-0.564490\pi\) | ||||
−0.201218 | + | 0.979546i | \(0.564490\pi\) | |||||||
\(810\) | 5.43819 | 0.191078 | ||||||||
\(811\) | 12.3087 | 0.432217 | 0.216109 | − | 0.976369i | \(-0.430663\pi\) | ||||
0.216109 | + | 0.976369i | \(0.430663\pi\) | |||||||
\(812\) | 15.8487 | 0.556179 | ||||||||
\(813\) | −22.5694 | −0.791543 | ||||||||
\(814\) | 21.4089 | 0.750380 | ||||||||
\(815\) | −28.1609 | −0.986434 | ||||||||
\(816\) | −1.21871 | −0.0426635 | ||||||||
\(817\) | 23.5710 | 0.824644 | ||||||||
\(818\) | 24.7495 | 0.865345 | ||||||||
\(819\) | −22.7617 | −0.795359 | ||||||||
\(820\) | 9.03018 | 0.315348 | ||||||||
\(821\) | 39.0355 | 1.36235 | 0.681174 | − | 0.732122i | \(-0.261470\pi\) | ||||
0.681174 | + | 0.732122i | \(0.261470\pi\) | |||||||
\(822\) | −12.9859 | −0.452936 | ||||||||
\(823\) | −3.40609 | −0.118729 | −0.0593644 | − | 0.998236i | \(-0.518907\pi\) | ||||
−0.0593644 | + | 0.998236i | \(0.518907\pi\) | |||||||
\(824\) | 3.01876 | 0.105164 | ||||||||
\(825\) | 9.93794 | 0.345995 | ||||||||
\(826\) | 4.54829 | 0.158255 | ||||||||
\(827\) | 40.6519 | 1.41361 | 0.706803 | − | 0.707411i | \(-0.250137\pi\) | ||||
0.706803 | + | 0.707411i | \(0.250137\pi\) | |||||||
\(828\) | 2.38250 | 0.0827976 | ||||||||
\(829\) | −30.8370 | −1.07101 | −0.535507 | − | 0.844530i | \(-0.679880\pi\) | ||||
−0.535507 | + | 0.844530i | \(0.679880\pi\) | |||||||
\(830\) | 20.0650 | 0.696468 | ||||||||
\(831\) | 20.4260 | 0.708569 | ||||||||
\(832\) | 2.46631 | 0.0855039 | ||||||||
\(833\) | 12.4157 | 0.430177 | ||||||||
\(834\) | 6.76183 | 0.234143 | ||||||||
\(835\) | −5.80282 | −0.200815 | ||||||||
\(836\) | −10.7640 | −0.372282 | ||||||||
\(837\) | −30.7896 | −1.06424 | ||||||||
\(838\) | −30.3852 | −1.04964 | ||||||||
\(839\) | 39.4504 | 1.36198 | 0.680989 | − | 0.732294i | \(-0.261550\pi\) | ||||
0.680989 | + | 0.732294i | \(0.261550\pi\) | |||||||
\(840\) | −4.32913 | −0.149369 | ||||||||
\(841\) | −12.2607 | −0.422784 | ||||||||
\(842\) | 23.4771 | 0.809074 | ||||||||
\(843\) | −25.2061 | −0.868145 | ||||||||
\(844\) | −4.82200 | −0.165980 | ||||||||
\(845\) | 9.83774 | 0.338428 | ||||||||
\(846\) | −11.9499 | −0.410847 | ||||||||
\(847\) | 27.2792 | 0.937325 | ||||||||
\(848\) | −6.61052 | −0.227006 | ||||||||
\(849\) | 24.1459 | 0.828686 | ||||||||
\(850\) | 4.61761 | 0.158383 | ||||||||
\(851\) | 5.04022 | 0.172776 | ||||||||
\(852\) | −4.93076 | −0.168925 | ||||||||
\(853\) | 24.7081 | 0.845988 | 0.422994 | − | 0.906132i | \(-0.360979\pi\) | ||||
0.422994 | + | 0.906132i | \(0.360979\pi\) | |||||||
\(854\) | −25.0312 | −0.856549 | ||||||||
\(855\) | −8.58660 | −0.293655 | ||||||||
\(856\) | 7.17272 | 0.245158 | ||||||||
\(857\) | 34.1846 | 1.16772 | 0.583861 | − | 0.811854i | \(-0.301541\pi\) | ||||
0.583861 | + | 0.811854i | \(0.301541\pi\) | |||||||
\(858\) | 8.23210 | 0.281039 | ||||||||
\(859\) | −27.2217 | −0.928793 | −0.464396 | − | 0.885628i | \(-0.653729\pi\) | ||||
−0.464396 | + | 0.885628i | \(0.653729\pi\) | |||||||
\(860\) | 13.2283 | 0.451082 | ||||||||
\(861\) | 19.3278 | 0.658689 | ||||||||
\(862\) | −16.7750 | −0.571360 | ||||||||
\(863\) | −21.5808 | −0.734618 | −0.367309 | − | 0.930099i | \(-0.619721\pi\) | ||||
−0.367309 | + | 0.930099i | \(0.619721\pi\) | |||||||
\(864\) | −4.22963 | −0.143895 | ||||||||
\(865\) | −3.50380 | −0.119133 | ||||||||
\(866\) | −33.2177 | −1.12878 | ||||||||
\(867\) | 11.4687 | 0.389497 | ||||||||
\(868\) | −28.1985 | −0.957120 | ||||||||
\(869\) | −37.8877 | −1.28525 | ||||||||
\(870\) | −4.57240 | −0.155019 | ||||||||
\(871\) | 24.3710 | 0.825780 | ||||||||
\(872\) | 3.99600 | 0.135321 | ||||||||
\(873\) | 34.5787 | 1.17031 | ||||||||
\(874\) | −2.53414 | −0.0857185 | ||||||||
\(875\) | 43.9483 | 1.48572 | ||||||||
\(876\) | 10.2626 | 0.346741 | ||||||||
\(877\) | −18.4620 | −0.623416 | −0.311708 | − | 0.950178i | \(-0.600901\pi\) | ||||
−0.311708 | + | 0.950178i | \(0.600901\pi\) | |||||||
\(878\) | 4.02949 | 0.135989 | ||||||||
\(879\) | 10.5476 | 0.355763 | ||||||||
\(880\) | −6.04091 | −0.203639 | ||||||||
\(881\) | −31.8132 | −1.07181 | −0.535907 | − | 0.844277i | \(-0.680030\pi\) | ||||
−0.535907 | + | 0.844277i | \(0.680030\pi\) | |||||||
\(882\) | 19.0730 | 0.642221 | ||||||||
\(883\) | 15.6302 | 0.526000 | 0.263000 | − | 0.964796i | \(-0.415288\pi\) | ||||
0.263000 | + | 0.964796i | \(0.415288\pi\) | |||||||
\(884\) | 3.82500 | 0.128649 | ||||||||
\(885\) | −1.31220 | −0.0441090 | ||||||||
\(886\) | 23.2202 | 0.780099 | ||||||||
\(887\) | 6.66364 | 0.223743 | 0.111872 | − | 0.993723i | \(-0.464315\pi\) | ||||
0.111872 | + | 0.993723i | \(0.464315\pi\) | |||||||
\(888\) | −3.96066 | −0.132911 | ||||||||
\(889\) | 55.0902 | 1.84767 | ||||||||
\(890\) | −16.4949 | −0.552911 | ||||||||
\(891\) | 16.2421 | 0.544129 | ||||||||
\(892\) | −23.8010 | −0.796915 | ||||||||
\(893\) | 12.7105 | 0.425341 | ||||||||
\(894\) | −12.0375 | −0.402595 | ||||||||
\(895\) | −15.3537 | −0.513217 | ||||||||
\(896\) | −3.87369 | −0.129411 | ||||||||
\(897\) | 1.93805 | 0.0647097 | ||||||||
\(898\) | −15.7458 | −0.525445 | ||||||||
\(899\) | −29.7831 | −0.993322 | ||||||||
\(900\) | 7.09360 | 0.236453 | ||||||||
\(901\) | −10.2523 | −0.341552 | ||||||||
\(902\) | 26.9702 | 0.898008 | ||||||||
\(903\) | 28.3133 | 0.942207 | ||||||||
\(904\) | −13.6826 | −0.455075 | ||||||||
\(905\) | −13.4772 | −0.447997 | ||||||||
\(906\) | −10.3129 | −0.342622 | ||||||||
\(907\) | 50.1996 | 1.66685 | 0.833425 | − | 0.552633i | \(-0.186377\pi\) | ||||
0.833425 | + | 0.552633i | \(0.186377\pi\) | |||||||
\(908\) | −6.05338 | −0.200889 | ||||||||
\(909\) | 2.78151 | 0.0922568 | ||||||||
\(910\) | 13.5872 | 0.450411 | ||||||||
\(911\) | −0.523949 | −0.0173592 | −0.00867960 | − | 0.999962i | \(-0.502763\pi\) | ||||
−0.00867960 | + | 0.999962i | \(0.502763\pi\) | |||||||
\(912\) | 1.99135 | 0.0659403 | ||||||||
\(913\) | 59.9276 | 1.98331 | ||||||||
\(914\) | −22.8637 | −0.756265 | ||||||||
\(915\) | 7.22159 | 0.238738 | ||||||||
\(916\) | −25.9038 | −0.855885 | ||||||||
\(917\) | −3.87369 | −0.127920 | ||||||||
\(918\) | −6.55973 | −0.216503 | ||||||||
\(919\) | 5.86338 | 0.193415 | 0.0967076 | − | 0.995313i | \(-0.469169\pi\) | ||||
0.0967076 | + | 0.995313i | \(0.469169\pi\) | |||||||
\(920\) | −1.42219 | −0.0468882 | ||||||||
\(921\) | −10.8217 | −0.356588 | ||||||||
\(922\) | 1.40109 | 0.0461426 | ||||||||
\(923\) | 15.4754 | 0.509380 | ||||||||
\(924\) | −12.9297 | −0.425355 | ||||||||
\(925\) | 15.0066 | 0.493414 | ||||||||
\(926\) | 38.6071 | 1.26871 | ||||||||
\(927\) | 7.19220 | 0.236223 | ||||||||
\(928\) | −4.09137 | −0.134306 | ||||||||
\(929\) | −31.0110 | −1.01744 | −0.508719 | − | 0.860933i | \(-0.669881\pi\) | ||||
−0.508719 | + | 0.860933i | \(0.669881\pi\) | |||||||
\(930\) | 8.13537 | 0.266769 | ||||||||
\(931\) | −20.2869 | −0.664877 | ||||||||
\(932\) | 10.7270 | 0.351373 | ||||||||
\(933\) | −13.7036 | −0.448636 | ||||||||
\(934\) | 33.5864 | 1.09898 | ||||||||
\(935\) | −9.36885 | −0.306394 | ||||||||
\(936\) | 5.87599 | 0.192063 | ||||||||
\(937\) | 39.6895 | 1.29660 | 0.648300 | − | 0.761385i | \(-0.275480\pi\) | ||||
0.648300 | + | 0.761385i | \(0.275480\pi\) | |||||||
\(938\) | −38.2781 | −1.24982 | ||||||||
\(939\) | 11.0538 | 0.360727 | ||||||||
\(940\) | 7.13330 | 0.232663 | ||||||||
\(941\) | −39.2170 | −1.27844 | −0.639219 | − | 0.769025i | \(-0.720742\pi\) | ||||
−0.639219 | + | 0.769025i | \(0.720742\pi\) | |||||||
\(942\) | −0.598103 | −0.0194872 | ||||||||
\(943\) | 6.34949 | 0.206768 | ||||||||
\(944\) | −1.17415 | −0.0382153 | ||||||||
\(945\) | −23.3015 | −0.757999 | ||||||||
\(946\) | 39.5086 | 1.28454 | ||||||||
\(947\) | 39.1458 | 1.27207 | 0.636033 | − | 0.771662i | \(-0.280574\pi\) | ||||
0.636033 | + | 0.771662i | \(0.280574\pi\) | |||||||
\(948\) | 7.00925 | 0.227650 | ||||||||
\(949\) | −32.2097 | −1.04557 | ||||||||
\(950\) | −7.54508 | −0.244795 | ||||||||
\(951\) | −4.86621 | −0.157798 | ||||||||
\(952\) | −6.00770 | −0.194711 | ||||||||
\(953\) | −16.8460 | −0.545694 | −0.272847 | − | 0.962057i | \(-0.587965\pi\) | ||||
−0.272847 | + | 0.962057i | \(0.587965\pi\) | |||||||
\(954\) | −15.7496 | −0.509911 | ||||||||
\(955\) | −9.68228 | −0.313311 | ||||||||
\(956\) | −24.0030 | −0.776314 | ||||||||
\(957\) | −13.6562 | −0.441444 | ||||||||
\(958\) | −16.2242 | −0.524181 | ||||||||
\(959\) | −64.0147 | −2.06714 | ||||||||
\(960\) | 1.11757 | 0.0360695 | ||||||||
\(961\) | 21.9911 | 0.709392 | ||||||||
\(962\) | 12.4307 | 0.400783 | ||||||||
\(963\) | 17.0890 | 0.550686 | ||||||||
\(964\) | 6.77771 | 0.218295 | ||||||||
\(965\) | 20.9466 | 0.674296 | ||||||||
\(966\) | −3.04399 | −0.0979387 | ||||||||
\(967\) | 10.1989 | 0.327973 | 0.163987 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163987 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(968\) | −7.04218 | −0.226344 | ||||||||
\(969\) | 3.08839 | 0.0992135 | ||||||||
\(970\) | −20.6411 | −0.662746 | ||||||||
\(971\) | 4.67632 | 0.150070 | 0.0750351 | − | 0.997181i | \(-0.476093\pi\) | ||||
0.0750351 | + | 0.997181i | \(0.476093\pi\) | |||||||
\(972\) | −15.6937 | −0.503375 | ||||||||
\(973\) | 33.3327 | 1.06860 | ||||||||
\(974\) | 1.66642 | 0.0533954 | ||||||||
\(975\) | 5.77031 | 0.184798 | ||||||||
\(976\) | 6.46185 | 0.206839 | ||||||||
\(977\) | −38.5977 | −1.23485 | −0.617425 | − | 0.786630i | \(-0.711824\pi\) | ||||
−0.617425 | + | 0.786630i | \(0.711824\pi\) | |||||||
\(978\) | 15.5599 | 0.497551 | ||||||||
\(979\) | −49.2649 | −1.57451 | ||||||||
\(980\) | −11.3853 | −0.363689 | ||||||||
\(981\) | 9.52046 | 0.303965 | ||||||||
\(982\) | −5.78439 | −0.184587 | ||||||||
\(983\) | −20.1571 | −0.642910 | −0.321455 | − | 0.946925i | \(-0.604172\pi\) | ||||
−0.321455 | + | 0.946925i | \(0.604172\pi\) | |||||||
\(984\) | −4.98950 | −0.159059 | ||||||||
\(985\) | 18.5130 | 0.589872 | ||||||||
\(986\) | −6.34530 | −0.202076 | ||||||||
\(987\) | 15.2678 | 0.485978 | ||||||||
\(988\) | −6.24997 | −0.198838 | ||||||||
\(989\) | 9.30138 | 0.295767 | ||||||||
\(990\) | −14.3925 | −0.457423 | ||||||||
\(991\) | 33.4154 | 1.06148 | 0.530738 | − | 0.847536i | \(-0.321915\pi\) | ||||
0.530738 | + | 0.847536i | \(0.321915\pi\) | |||||||
\(992\) | 7.27950 | 0.231124 | ||||||||
\(993\) | 14.2839 | 0.453286 | ||||||||
\(994\) | −24.3064 | −0.770951 | ||||||||
\(995\) | −23.6029 | −0.748263 | ||||||||
\(996\) | −11.0867 | −0.351294 | ||||||||
\(997\) | −17.8866 | −0.566474 | −0.283237 | − | 0.959050i | \(-0.591408\pi\) | ||||
−0.283237 | + | 0.959050i | \(0.591408\pi\) | |||||||
\(998\) | 26.4914 | 0.838571 | ||||||||
\(999\) | −21.3182 | −0.674479 |
(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 | 6026.2.a.h.1.10 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.10 | ✓ | 24 | 1.1 | even | 1 | trivial |