Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, 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("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(1\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.13628 | −1.51058 | −0.755290 | − | 0.655391i | \(-0.772504\pi\) | ||||
−0.755290 | + | 0.655391i | \(0.772504\pi\) | |||||||
\(3\) | −0.861354 | −0.497303 | −0.248652 | − | 0.968593i | \(-0.579987\pi\) | ||||
−0.248652 | + | 0.968593i | \(0.579987\pi\) | |||||||
\(4\) | 2.56370 | 1.28185 | ||||||||
\(5\) | 1.50403 | 0.672622 | 0.336311 | − | 0.941751i | \(-0.390821\pi\) | ||||
0.336311 | + | 0.941751i | \(0.390821\pi\) | |||||||
\(6\) | 1.84010 | 0.751216 | ||||||||
\(7\) | −3.07386 | −1.16181 | −0.580905 | − | 0.813971i | \(-0.697301\pi\) | ||||
−0.580905 | + | 0.813971i | \(0.697301\pi\) | |||||||
\(8\) | −1.20423 | −0.425759 | ||||||||
\(9\) | −2.25807 | −0.752689 | ||||||||
\(10\) | −3.21303 | −1.01605 | ||||||||
\(11\) | −1.80814 | −0.545176 | −0.272588 | − | 0.962131i | \(-0.587880\pi\) | ||||
−0.272588 | + | 0.962131i | \(0.587880\pi\) | |||||||
\(12\) | −2.20826 | −0.637469 | ||||||||
\(13\) | 1.56008 | 0.432689 | 0.216344 | − | 0.976317i | \(-0.430587\pi\) | ||||
0.216344 | + | 0.976317i | \(0.430587\pi\) | |||||||
\(14\) | 6.56664 | 1.75501 | ||||||||
\(15\) | −1.29550 | −0.334497 | ||||||||
\(16\) | −2.55483 | −0.638708 | ||||||||
\(17\) | −5.85280 | −1.41951 | −0.709756 | − | 0.704447i | \(-0.751195\pi\) | ||||
−0.709756 | + | 0.704447i | \(0.751195\pi\) | |||||||
\(18\) | 4.82387 | 1.13700 | ||||||||
\(19\) | −4.73888 | −1.08717 | −0.543586 | − | 0.839353i | \(-0.682934\pi\) | ||||
−0.543586 | + | 0.839353i | \(0.682934\pi\) | |||||||
\(20\) | 3.85588 | 0.862201 | ||||||||
\(21\) | 2.64768 | 0.577772 | ||||||||
\(22\) | 3.86271 | 0.823532 | ||||||||
\(23\) | 4.68229 | 0.976324 | 0.488162 | − | 0.872753i | \(-0.337668\pi\) | ||||
0.488162 | + | 0.872753i | \(0.337668\pi\) | |||||||
\(24\) | 1.03727 | 0.211731 | ||||||||
\(25\) | −2.73790 | −0.547580 | ||||||||
\(26\) | −3.33278 | −0.653611 | ||||||||
\(27\) | 4.52906 | 0.871618 | ||||||||
\(28\) | −7.88047 | −1.48927 | ||||||||
\(29\) | 3.88648 | 0.721702 | 0.360851 | − | 0.932624i | \(-0.382486\pi\) | ||||
0.360851 | + | 0.932624i | \(0.382486\pi\) | |||||||
\(30\) | 2.76756 | 0.505285 | ||||||||
\(31\) | 6.05166 | 1.08691 | 0.543455 | − | 0.839438i | \(-0.317116\pi\) | ||||
0.543455 | + | 0.839438i | \(0.317116\pi\) | |||||||
\(32\) | 7.86630 | 1.39058 | ||||||||
\(33\) | 1.55745 | 0.271118 | ||||||||
\(34\) | 12.5032 | 2.14429 | ||||||||
\(35\) | −4.62317 | −0.781459 | ||||||||
\(36\) | −5.78902 | −0.964836 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 10.1236 | 1.64226 | ||||||||
\(39\) | −1.34378 | −0.215178 | ||||||||
\(40\) | −1.81119 | −0.286375 | ||||||||
\(41\) | 5.01348 | 0.782975 | 0.391487 | − | 0.920183i | \(-0.371961\pi\) | ||||
0.391487 | + | 0.920183i | \(0.371961\pi\) | |||||||
\(42\) | −5.65620 | −0.872771 | ||||||||
\(43\) | −1.88723 | −0.287800 | −0.143900 | − | 0.989592i | \(-0.545964\pi\) | ||||
−0.143900 | + | 0.989592i | \(0.545964\pi\) | |||||||
\(44\) | −4.63554 | −0.698834 | ||||||||
\(45\) | −3.39620 | −0.506276 | ||||||||
\(46\) | −10.0027 | −1.47482 | ||||||||
\(47\) | 6.96769 | 1.01634 | 0.508171 | − | 0.861256i | \(-0.330322\pi\) | ||||
0.508171 | + | 0.861256i | \(0.330322\pi\) | |||||||
\(48\) | 2.20062 | 0.317632 | ||||||||
\(49\) | 2.44862 | 0.349803 | ||||||||
\(50\) | 5.84892 | 0.827163 | ||||||||
\(51\) | 5.04134 | 0.705928 | ||||||||
\(52\) | 3.99959 | 0.554643 | ||||||||
\(53\) | 4.59970 | 0.631817 | 0.315908 | − | 0.948790i | \(-0.397691\pi\) | ||||
0.315908 | + | 0.948790i | \(0.397691\pi\) | |||||||
\(54\) | −9.67535 | −1.31665 | ||||||||
\(55\) | −2.71950 | −0.366697 | ||||||||
\(56\) | 3.70163 | 0.494651 | ||||||||
\(57\) | 4.08185 | 0.540655 | ||||||||
\(58\) | −8.30262 | −1.09019 | ||||||||
\(59\) | 7.15569 | 0.931592 | 0.465796 | − | 0.884892i | \(-0.345768\pi\) | ||||
0.465796 | + | 0.884892i | \(0.345768\pi\) | |||||||
\(60\) | −3.32128 | −0.428776 | ||||||||
\(61\) | 13.7289 | 1.75781 | 0.878904 | − | 0.476998i | \(-0.158275\pi\) | ||||
0.878904 | + | 0.476998i | \(0.158275\pi\) | |||||||
\(62\) | −12.9281 | −1.64187 | ||||||||
\(63\) | 6.94099 | 0.874482 | ||||||||
\(64\) | −11.6950 | −1.46187 | ||||||||
\(65\) | 2.34641 | 0.291036 | ||||||||
\(66\) | −3.32716 | −0.409545 | ||||||||
\(67\) | −8.22758 | −1.00516 | −0.502579 | − | 0.864531i | \(-0.667616\pi\) | ||||
−0.502579 | + | 0.864531i | \(0.667616\pi\) | |||||||
\(68\) | −15.0048 | −1.81960 | ||||||||
\(69\) | −4.03311 | −0.485529 | ||||||||
\(70\) | 9.87641 | 1.18046 | ||||||||
\(71\) | −4.95883 | −0.588505 | −0.294253 | − | 0.955728i | \(-0.595071\pi\) | ||||
−0.294253 | + | 0.955728i | \(0.595071\pi\) | |||||||
\(72\) | 2.71923 | 0.320464 | ||||||||
\(73\) | 16.1812 | 1.89386 | 0.946931 | − | 0.321436i | \(-0.104166\pi\) | ||||
0.946931 | + | 0.321436i | \(0.104166\pi\) | |||||||
\(74\) | 2.13628 | 0.248338 | ||||||||
\(75\) | 2.35830 | 0.272313 | ||||||||
\(76\) | −12.1491 | −1.39359 | ||||||||
\(77\) | 5.55798 | 0.633391 | ||||||||
\(78\) | 2.87070 | 0.325043 | ||||||||
\(79\) | 9.56083 | 1.07568 | 0.537839 | − | 0.843048i | \(-0.319241\pi\) | ||||
0.537839 | + | 0.843048i | \(0.319241\pi\) | |||||||
\(80\) | −3.84254 | −0.429609 | ||||||||
\(81\) | 2.87308 | 0.319231 | ||||||||
\(82\) | −10.7102 | −1.18275 | ||||||||
\(83\) | 5.83991 | 0.641013 | 0.320507 | − | 0.947246i | \(-0.396147\pi\) | ||||
0.320507 | + | 0.947246i | \(0.396147\pi\) | |||||||
\(84\) | 6.78787 | 0.740618 | ||||||||
\(85\) | −8.80278 | −0.954796 | ||||||||
\(86\) | 4.03166 | 0.434745 | ||||||||
\(87\) | −3.34764 | −0.358905 | ||||||||
\(88\) | 2.17742 | 0.232114 | ||||||||
\(89\) | 4.75958 | 0.504514 | 0.252257 | − | 0.967660i | \(-0.418827\pi\) | ||||
0.252257 | + | 0.967660i | \(0.418827\pi\) | |||||||
\(90\) | 7.25524 | 0.764770 | ||||||||
\(91\) | −4.79547 | −0.502702 | ||||||||
\(92\) | 12.0040 | 1.25150 | ||||||||
\(93\) | −5.21263 | −0.540524 | ||||||||
\(94\) | −14.8850 | −1.53527 | ||||||||
\(95\) | −7.12741 | −0.731256 | ||||||||
\(96\) | −6.77568 | −0.691539 | ||||||||
\(97\) | −10.2835 | −1.04413 | −0.522066 | − | 0.852905i | \(-0.674839\pi\) | ||||
−0.522066 | + | 0.852905i | \(0.674839\pi\) | |||||||
\(98\) | −5.23095 | −0.528405 | ||||||||
\(99\) | 4.08291 | 0.410348 | ||||||||
\(100\) | −7.01916 | −0.701916 | ||||||||
\(101\) | −17.2754 | −1.71897 | −0.859483 | − | 0.511164i | \(-0.829215\pi\) | ||||
−0.859483 | + | 0.511164i | \(0.829215\pi\) | |||||||
\(102\) | −10.7697 | −1.06636 | ||||||||
\(103\) | −0.330529 | −0.0325680 | −0.0162840 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162840 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(104\) | −1.87869 | −0.184221 | ||||||||
\(105\) | 3.98219 | 0.388622 | ||||||||
\(106\) | −9.82625 | −0.954410 | ||||||||
\(107\) | 0.979488 | 0.0946906 | 0.0473453 | − | 0.998879i | \(-0.484924\pi\) | ||||
0.0473453 | + | 0.998879i | \(0.484924\pi\) | |||||||
\(108\) | 11.6112 | 1.11728 | ||||||||
\(109\) | −0.177182 | −0.0169709 | −0.00848546 | − | 0.999964i | \(-0.502701\pi\) | ||||
−0.00848546 | + | 0.999964i | \(0.502701\pi\) | |||||||
\(110\) | 5.80962 | 0.553925 | ||||||||
\(111\) | 0.861354 | 0.0817562 | ||||||||
\(112\) | 7.85320 | 0.742058 | ||||||||
\(113\) | −16.5884 | −1.56051 | −0.780254 | − | 0.625462i | \(-0.784910\pi\) | ||||
−0.780254 | + | 0.625462i | \(0.784910\pi\) | |||||||
\(114\) | −8.71999 | −0.816702 | ||||||||
\(115\) | 7.04229 | 0.656697 | ||||||||
\(116\) | 9.96378 | 0.925114 | ||||||||
\(117\) | −3.52277 | −0.325680 | ||||||||
\(118\) | −15.2866 | −1.40724 | ||||||||
\(119\) | 17.9907 | 1.64920 | ||||||||
\(120\) | 1.56008 | 0.142415 | ||||||||
\(121\) | −7.73062 | −0.702783 | ||||||||
\(122\) | −29.3289 | −2.65531 | ||||||||
\(123\) | −4.31839 | −0.389376 | ||||||||
\(124\) | 15.5147 | 1.39326 | ||||||||
\(125\) | −11.6380 | −1.04094 | ||||||||
\(126\) | −14.8279 | −1.32098 | ||||||||
\(127\) | −0.646451 | −0.0573632 | −0.0286816 | − | 0.999589i | \(-0.509131\pi\) | ||||
−0.0286816 | + | 0.999589i | \(0.509131\pi\) | |||||||
\(128\) | 9.25117 | 0.817696 | ||||||||
\(129\) | 1.62557 | 0.143124 | ||||||||
\(130\) | −5.01259 | −0.439633 | ||||||||
\(131\) | 9.53249 | 0.832857 | 0.416429 | − | 0.909168i | \(-0.363282\pi\) | ||||
0.416429 | + | 0.909168i | \(0.363282\pi\) | |||||||
\(132\) | 3.99285 | 0.347533 | ||||||||
\(133\) | 14.5666 | 1.26309 | ||||||||
\(134\) | 17.5764 | 1.51837 | ||||||||
\(135\) | 6.81184 | 0.586270 | ||||||||
\(136\) | 7.04811 | 0.604370 | ||||||||
\(137\) | −7.89736 | −0.674717 | −0.337359 | − | 0.941376i | \(-0.609534\pi\) | ||||
−0.337359 | + | 0.941376i | \(0.609534\pi\) | |||||||
\(138\) | 8.61586 | 0.733430 | ||||||||
\(139\) | −12.8766 | −1.09218 | −0.546088 | − | 0.837728i | \(-0.683884\pi\) | ||||
−0.546088 | + | 0.837728i | \(0.683884\pi\) | |||||||
\(140\) | −11.8524 | −1.00171 | ||||||||
\(141\) | −6.00165 | −0.505430 | ||||||||
\(142\) | 10.5935 | 0.888984 | ||||||||
\(143\) | −2.82085 | −0.235891 | ||||||||
\(144\) | 5.76899 | 0.480749 | ||||||||
\(145\) | 5.84538 | 0.485432 | ||||||||
\(146\) | −34.5675 | −2.86083 | ||||||||
\(147\) | −2.10913 | −0.173958 | ||||||||
\(148\) | −2.56370 | −0.210735 | ||||||||
\(149\) | −14.8877 | −1.21965 | −0.609824 | − | 0.792537i | \(-0.708760\pi\) | ||||
−0.609824 | + | 0.792537i | \(0.708760\pi\) | |||||||
\(150\) | −5.03800 | −0.411351 | ||||||||
\(151\) | −4.57817 | −0.372566 | −0.186283 | − | 0.982496i | \(-0.559644\pi\) | ||||
−0.186283 | + | 0.982496i | \(0.559644\pi\) | |||||||
\(152\) | 5.70669 | 0.462874 | ||||||||
\(153\) | 13.2160 | 1.06845 | ||||||||
\(154\) | −11.8734 | −0.956787 | ||||||||
\(155\) | 9.10187 | 0.731080 | ||||||||
\(156\) | −3.44506 | −0.275826 | ||||||||
\(157\) | 14.9052 | 1.18956 | 0.594782 | − | 0.803887i | \(-0.297238\pi\) | ||||
0.594782 | + | 0.803887i | \(0.297238\pi\) | |||||||
\(158\) | −20.4246 | −1.62490 | ||||||||
\(159\) | −3.96197 | −0.314205 | ||||||||
\(160\) | 11.8311 | 0.935334 | ||||||||
\(161\) | −14.3927 | −1.13430 | ||||||||
\(162\) | −6.13771 | −0.482224 | ||||||||
\(163\) | −1.00000 | −0.0783260 | ||||||||
\(164\) | 12.8531 | 1.00366 | ||||||||
\(165\) | 2.34245 | 0.182360 | ||||||||
\(166\) | −12.4757 | −0.968301 | ||||||||
\(167\) | 20.1670 | 1.56057 | 0.780284 | − | 0.625426i | \(-0.215075\pi\) | ||||
0.780284 | + | 0.625426i | \(0.215075\pi\) | |||||||
\(168\) | −3.18842 | −0.245992 | ||||||||
\(169\) | −10.5661 | −0.812780 | ||||||||
\(170\) | 18.8052 | 1.44229 | ||||||||
\(171\) | 10.7007 | 0.818304 | ||||||||
\(172\) | −4.83830 | −0.368917 | ||||||||
\(173\) | 2.77070 | 0.210653 | 0.105326 | − | 0.994438i | \(-0.466411\pi\) | ||||
0.105326 | + | 0.994438i | \(0.466411\pi\) | |||||||
\(174\) | 7.15150 | 0.542154 | ||||||||
\(175\) | 8.41592 | 0.636184 | ||||||||
\(176\) | 4.61951 | 0.348208 | ||||||||
\(177\) | −6.16359 | −0.463284 | ||||||||
\(178\) | −10.1678 | −0.762109 | ||||||||
\(179\) | 23.4233 | 1.75074 | 0.875372 | − | 0.483451i | \(-0.160617\pi\) | ||||
0.875372 | + | 0.483451i | \(0.160617\pi\) | |||||||
\(180\) | −8.70685 | −0.648970 | ||||||||
\(181\) | 6.06222 | 0.450601 | 0.225301 | − | 0.974289i | \(-0.427664\pi\) | ||||
0.225301 | + | 0.974289i | \(0.427664\pi\) | |||||||
\(182\) | 10.2445 | 0.759372 | ||||||||
\(183\) | −11.8255 | −0.874164 | ||||||||
\(184\) | −5.63854 | −0.415679 | ||||||||
\(185\) | −1.50403 | −0.110578 | ||||||||
\(186\) | 11.1356 | 0.816505 | ||||||||
\(187\) | 10.5827 | 0.773884 | ||||||||
\(188\) | 17.8631 | 1.30280 | ||||||||
\(189\) | −13.9217 | −1.01265 | ||||||||
\(190\) | 15.2262 | 1.10462 | ||||||||
\(191\) | −13.6800 | −0.989853 | −0.494926 | − | 0.868935i | \(-0.664805\pi\) | ||||
−0.494926 | + | 0.868935i | \(0.664805\pi\) | |||||||
\(192\) | 10.0735 | 0.726994 | ||||||||
\(193\) | −4.72926 | −0.340420 | −0.170210 | − | 0.985408i | \(-0.554445\pi\) | ||||
−0.170210 | + | 0.985408i | \(0.554445\pi\) | |||||||
\(194\) | 21.9685 | 1.57724 | ||||||||
\(195\) | −2.02109 | −0.144733 | ||||||||
\(196\) | 6.27754 | 0.448395 | ||||||||
\(197\) | −21.5882 | −1.53809 | −0.769047 | − | 0.639192i | \(-0.779269\pi\) | ||||
−0.769047 | + | 0.639192i | \(0.779269\pi\) | |||||||
\(198\) | −8.72225 | −0.619864 | ||||||||
\(199\) | −21.5374 | −1.52675 | −0.763375 | − | 0.645956i | \(-0.776459\pi\) | ||||
−0.763375 | + | 0.645956i | \(0.776459\pi\) | |||||||
\(200\) | 3.29705 | 0.233137 | ||||||||
\(201\) | 7.08686 | 0.499869 | ||||||||
\(202\) | 36.9051 | 2.59664 | ||||||||
\(203\) | −11.9465 | −0.838480 | ||||||||
\(204\) | 12.9245 | 0.904895 | ||||||||
\(205\) | 7.54042 | 0.526646 | ||||||||
\(206\) | 0.706103 | 0.0491965 | ||||||||
\(207\) | −10.5729 | −0.734869 | ||||||||
\(208\) | −3.98575 | −0.276362 | ||||||||
\(209\) | 8.56857 | 0.592700 | ||||||||
\(210\) | −8.50709 | −0.587045 | ||||||||
\(211\) | −6.16563 | −0.424459 | −0.212230 | − | 0.977220i | \(-0.568073\pi\) | ||||
−0.212230 | + | 0.977220i | \(0.568073\pi\) | |||||||
\(212\) | 11.7923 | 0.809895 | ||||||||
\(213\) | 4.27131 | 0.292666 | ||||||||
\(214\) | −2.09246 | −0.143038 | ||||||||
\(215\) | −2.83845 | −0.193581 | ||||||||
\(216\) | −5.45402 | −0.371099 | ||||||||
\(217\) | −18.6020 | −1.26278 | ||||||||
\(218\) | 0.378510 | 0.0256359 | ||||||||
\(219\) | −13.9377 | −0.941824 | ||||||||
\(220\) | −6.97199 | −0.470051 | ||||||||
\(221\) | −9.13085 | −0.614207 | ||||||||
\(222\) | −1.84010 | −0.123499 | ||||||||
\(223\) | 1.89843 | 0.127128 | 0.0635641 | − | 0.997978i | \(-0.479753\pi\) | ||||
0.0635641 | + | 0.997978i | \(0.479753\pi\) | |||||||
\(224\) | −24.1799 | −1.61559 | ||||||||
\(225\) | 6.18236 | 0.412157 | ||||||||
\(226\) | 35.4376 | 2.35727 | ||||||||
\(227\) | 12.8688 | 0.854133 | 0.427067 | − | 0.904220i | \(-0.359547\pi\) | ||||
0.427067 | + | 0.904220i | \(0.359547\pi\) | |||||||
\(228\) | 10.4647 | 0.693039 | ||||||||
\(229\) | 8.54671 | 0.564782 | 0.282391 | − | 0.959299i | \(-0.408872\pi\) | ||||
0.282391 | + | 0.959299i | \(0.408872\pi\) | |||||||
\(230\) | −15.0443 | −0.991993 | ||||||||
\(231\) | −4.78739 | −0.314987 | ||||||||
\(232\) | −4.68021 | −0.307271 | ||||||||
\(233\) | −22.5414 | −1.47674 | −0.738370 | − | 0.674396i | \(-0.764404\pi\) | ||||
−0.738370 | + | 0.674396i | \(0.764404\pi\) | |||||||
\(234\) | 7.52563 | 0.491966 | ||||||||
\(235\) | 10.4796 | 0.683614 | ||||||||
\(236\) | 18.3451 | 1.19416 | ||||||||
\(237\) | −8.23527 | −0.534938 | ||||||||
\(238\) | −38.4332 | −2.49126 | ||||||||
\(239\) | −7.60840 | −0.492146 | −0.246073 | − | 0.969251i | \(-0.579140\pi\) | ||||
−0.246073 | + | 0.969251i | \(0.579140\pi\) | |||||||
\(240\) | 3.30979 | 0.213646 | ||||||||
\(241\) | −4.94063 | −0.318254 | −0.159127 | − | 0.987258i | \(-0.550868\pi\) | ||||
−0.159127 | + | 0.987258i | \(0.550868\pi\) | |||||||
\(242\) | 16.5148 | 1.06161 | ||||||||
\(243\) | −16.0619 | −1.03037 | ||||||||
\(244\) | 35.1969 | 2.25325 | ||||||||
\(245\) | 3.68280 | 0.235285 | ||||||||
\(246\) | 9.22530 | 0.588183 | ||||||||
\(247\) | −7.39304 | −0.470408 | ||||||||
\(248\) | −7.28759 | −0.462762 | ||||||||
\(249\) | −5.03023 | −0.318778 | ||||||||
\(250\) | 24.8621 | 1.57242 | ||||||||
\(251\) | 5.05769 | 0.319239 | 0.159619 | − | 0.987179i | \(-0.448973\pi\) | ||||
0.159619 | + | 0.987179i | \(0.448973\pi\) | |||||||
\(252\) | 17.7946 | 1.12096 | ||||||||
\(253\) | −8.46624 | −0.532268 | ||||||||
\(254\) | 1.38100 | 0.0866518 | ||||||||
\(255\) | 7.58231 | 0.474823 | ||||||||
\(256\) | 3.62684 | 0.226678 | ||||||||
\(257\) | 18.9308 | 1.18087 | 0.590435 | − | 0.807085i | \(-0.298956\pi\) | ||||
0.590435 | + | 0.807085i | \(0.298956\pi\) | |||||||
\(258\) | −3.47269 | −0.216200 | ||||||||
\(259\) | 3.07386 | 0.191000 | ||||||||
\(260\) | 6.01549 | 0.373065 | ||||||||
\(261\) | −8.77594 | −0.543217 | ||||||||
\(262\) | −20.3641 | −1.25810 | ||||||||
\(263\) | 5.58788 | 0.344563 | 0.172282 | − | 0.985048i | \(-0.444886\pi\) | ||||
0.172282 | + | 0.985048i | \(0.444886\pi\) | |||||||
\(264\) | −1.87553 | −0.115431 | ||||||||
\(265\) | 6.91807 | 0.424974 | ||||||||
\(266\) | −31.1185 | −1.90800 | ||||||||
\(267\) | −4.09968 | −0.250896 | ||||||||
\(268\) | −21.0931 | −1.28846 | ||||||||
\(269\) | −6.82385 | −0.416058 | −0.208029 | − | 0.978123i | \(-0.566705\pi\) | ||||
−0.208029 | + | 0.978123i | \(0.566705\pi\) | |||||||
\(270\) | −14.5520 | −0.885607 | ||||||||
\(271\) | −14.5790 | −0.885613 | −0.442807 | − | 0.896617i | \(-0.646017\pi\) | ||||
−0.442807 | + | 0.896617i | \(0.646017\pi\) | |||||||
\(272\) | 14.9529 | 0.906655 | ||||||||
\(273\) | 4.13060 | 0.249995 | ||||||||
\(274\) | 16.8710 | 1.01921 | ||||||||
\(275\) | 4.95051 | 0.298527 | ||||||||
\(276\) | −10.3397 | −0.622376 | ||||||||
\(277\) | 25.4534 | 1.52934 | 0.764672 | − | 0.644420i | \(-0.222901\pi\) | ||||
0.764672 | + | 0.644420i | \(0.222901\pi\) | |||||||
\(278\) | 27.5080 | 1.64982 | ||||||||
\(279\) | −13.6651 | −0.818106 | ||||||||
\(280\) | 5.56736 | 0.332713 | ||||||||
\(281\) | −18.7019 | −1.11566 | −0.557831 | − | 0.829954i | \(-0.688366\pi\) | ||||
−0.557831 | + | 0.829954i | \(0.688366\pi\) | |||||||
\(282\) | 12.8212 | 0.763493 | ||||||||
\(283\) | 14.4768 | 0.860554 | 0.430277 | − | 0.902697i | \(-0.358416\pi\) | ||||
0.430277 | + | 0.902697i | \(0.358416\pi\) | |||||||
\(284\) | −12.7130 | −0.754376 | ||||||||
\(285\) | 6.13922 | 0.363656 | ||||||||
\(286\) | 6.02614 | 0.356333 | ||||||||
\(287\) | −15.4108 | −0.909668 | ||||||||
\(288\) | −17.7627 | −1.04667 | ||||||||
\(289\) | 17.2553 | 1.01502 | ||||||||
\(290\) | −12.4874 | −0.733284 | ||||||||
\(291\) | 8.85774 | 0.519250 | ||||||||
\(292\) | 41.4837 | 2.42765 | ||||||||
\(293\) | −3.40397 | −0.198862 | −0.0994310 | − | 0.995044i | \(-0.531702\pi\) | ||||
−0.0994310 | + | 0.995044i | \(0.531702\pi\) | |||||||
\(294\) | 4.50570 | 0.262778 | ||||||||
\(295\) | 10.7624 | 0.626609 | ||||||||
\(296\) | 1.20423 | 0.0699944 | ||||||||
\(297\) | −8.18919 | −0.475185 | ||||||||
\(298\) | 31.8043 | 1.84237 | ||||||||
\(299\) | 7.30475 | 0.422444 | ||||||||
\(300\) | 6.04598 | 0.349065 | ||||||||
\(301\) | 5.80108 | 0.334369 | ||||||||
\(302\) | 9.78026 | 0.562790 | ||||||||
\(303\) | 14.8802 | 0.854848 | ||||||||
\(304\) | 12.1070 | 0.694386 | ||||||||
\(305\) | 20.6487 | 1.18234 | ||||||||
\(306\) | −28.2332 | −1.61398 | ||||||||
\(307\) | −31.3361 | −1.78844 | −0.894221 | − | 0.447625i | \(-0.852270\pi\) | ||||
−0.894221 | + | 0.447625i | \(0.852270\pi\) | |||||||
\(308\) | 14.2490 | 0.811913 | ||||||||
\(309\) | 0.284702 | 0.0161962 | ||||||||
\(310\) | −19.4442 | −1.10435 | ||||||||
\(311\) | 1.14417 | 0.0648799 | 0.0324399 | − | 0.999474i | \(-0.489672\pi\) | ||||
0.0324399 | + | 0.999474i | \(0.489672\pi\) | |||||||
\(312\) | 1.61822 | 0.0916138 | ||||||||
\(313\) | 32.5807 | 1.84157 | 0.920784 | − | 0.390073i | \(-0.127550\pi\) | ||||
0.920784 | + | 0.390073i | \(0.127550\pi\) | |||||||
\(314\) | −31.8417 | −1.79693 | ||||||||
\(315\) | 10.4394 | 0.588196 | ||||||||
\(316\) | 24.5111 | 1.37886 | ||||||||
\(317\) | −20.3265 | −1.14165 | −0.570825 | − | 0.821071i | \(-0.693377\pi\) | ||||
−0.570825 | + | 0.821071i | \(0.693377\pi\) | |||||||
\(318\) | 8.46389 | 0.474631 | ||||||||
\(319\) | −7.02732 | −0.393454 | ||||||||
\(320\) | −17.5896 | −0.983287 | ||||||||
\(321\) | −0.843686 | −0.0470900 | ||||||||
\(322\) | 30.7469 | 1.71346 | ||||||||
\(323\) | 27.7357 | 1.54326 | ||||||||
\(324\) | 7.36572 | 0.409207 | ||||||||
\(325\) | −4.27134 | −0.236932 | ||||||||
\(326\) | 2.13628 | 0.118318 | ||||||||
\(327\) | 0.152616 | 0.00843969 | ||||||||
\(328\) | −6.03738 | −0.333359 | ||||||||
\(329\) | −21.4177 | −1.18080 | ||||||||
\(330\) | −5.00414 | −0.275469 | ||||||||
\(331\) | 18.1496 | 0.997592 | 0.498796 | − | 0.866719i | \(-0.333776\pi\) | ||||
0.498796 | + | 0.866719i | \(0.333776\pi\) | |||||||
\(332\) | 14.9718 | 0.821684 | ||||||||
\(333\) | 2.25807 | 0.123741 | ||||||||
\(334\) | −43.0824 | −2.35736 | ||||||||
\(335\) | −12.3745 | −0.676092 | ||||||||
\(336\) | −6.76439 | −0.369028 | ||||||||
\(337\) | −35.9417 | −1.95787 | −0.978934 | − | 0.204178i | \(-0.934548\pi\) | ||||
−0.978934 | + | 0.204178i | \(0.934548\pi\) | |||||||
\(338\) | 22.5723 | 1.22777 | ||||||||
\(339\) | 14.2885 | 0.776046 | ||||||||
\(340\) | −22.5677 | −1.22391 | ||||||||
\(341\) | −10.9423 | −0.592558 | ||||||||
\(342\) | −22.8597 | −1.23611 | ||||||||
\(343\) | 13.9903 | 0.755406 | ||||||||
\(344\) | 2.27266 | 0.122533 | ||||||||
\(345\) | −6.06591 | −0.326578 | ||||||||
\(346\) | −5.91900 | −0.318208 | ||||||||
\(347\) | −22.9431 | −1.23165 | −0.615824 | − | 0.787883i | \(-0.711177\pi\) | ||||
−0.615824 | + | 0.787883i | \(0.711177\pi\) | |||||||
\(348\) | −8.58235 | −0.460062 | ||||||||
\(349\) | −11.5807 | −0.619901 | −0.309950 | − | 0.950753i | \(-0.600312\pi\) | ||||
−0.309950 | + | 0.950753i | \(0.600312\pi\) | |||||||
\(350\) | −17.9788 | −0.961006 | ||||||||
\(351\) | 7.06571 | 0.377139 | ||||||||
\(352\) | −14.2234 | −0.758110 | ||||||||
\(353\) | 17.4702 | 0.929847 | 0.464924 | − | 0.885351i | \(-0.346082\pi\) | ||||
0.464924 | + | 0.885351i | \(0.346082\pi\) | |||||||
\(354\) | 13.1672 | 0.699827 | ||||||||
\(355\) | −7.45823 | −0.395842 | ||||||||
\(356\) | 12.2021 | 0.646712 | ||||||||
\(357\) | −15.4964 | −0.820155 | ||||||||
\(358\) | −50.0389 | −2.64464 | ||||||||
\(359\) | 17.2379 | 0.909781 | 0.454890 | − | 0.890547i | \(-0.349678\pi\) | ||||
0.454890 | + | 0.890547i | \(0.349678\pi\) | |||||||
\(360\) | 4.08980 | 0.215551 | ||||||||
\(361\) | 3.45696 | 0.181945 | ||||||||
\(362\) | −12.9506 | −0.680669 | ||||||||
\(363\) | 6.65880 | 0.349496 | ||||||||
\(364\) | −12.2942 | −0.644390 | ||||||||
\(365\) | 24.3369 | 1.27385 | ||||||||
\(366\) | 25.2625 | 1.32049 | ||||||||
\(367\) | 10.1832 | 0.531561 | 0.265781 | − | 0.964034i | \(-0.414370\pi\) | ||||
0.265781 | + | 0.964034i | \(0.414370\pi\) | |||||||
\(368\) | −11.9625 | −0.623586 | ||||||||
\(369\) | −11.3208 | −0.589337 | ||||||||
\(370\) | 3.21303 | 0.167037 | ||||||||
\(371\) | −14.1388 | −0.734051 | ||||||||
\(372\) | −13.3636 | −0.692872 | ||||||||
\(373\) | 25.2556 | 1.30768 | 0.653842 | − | 0.756631i | \(-0.273156\pi\) | ||||
0.653842 | + | 0.756631i | \(0.273156\pi\) | |||||||
\(374\) | −22.6076 | −1.16901 | ||||||||
\(375\) | 10.0245 | 0.517661 | ||||||||
\(376\) | −8.39069 | −0.432717 | ||||||||
\(377\) | 6.06323 | 0.312272 | ||||||||
\(378\) | 29.7407 | 1.52970 | ||||||||
\(379\) | −22.8613 | −1.17431 | −0.587154 | − | 0.809475i | \(-0.699752\pi\) | ||||
−0.587154 | + | 0.809475i | \(0.699752\pi\) | |||||||
\(380\) | −18.2726 | −0.937362 | ||||||||
\(381\) | 0.556823 | 0.0285269 | ||||||||
\(382\) | 29.2244 | 1.49525 | ||||||||
\(383\) | 5.13943 | 0.262613 | 0.131306 | − | 0.991342i | \(-0.458083\pi\) | ||||
0.131306 | + | 0.991342i | \(0.458083\pi\) | |||||||
\(384\) | −7.96854 | −0.406643 | ||||||||
\(385\) | 8.35936 | 0.426033 | ||||||||
\(386\) | 10.1030 | 0.514231 | ||||||||
\(387\) | 4.26150 | 0.216624 | ||||||||
\(388\) | −26.3639 | −1.33842 | ||||||||
\(389\) | 35.2080 | 1.78512 | 0.892559 | − | 0.450931i | \(-0.148908\pi\) | ||||
0.892559 | + | 0.450931i | \(0.148908\pi\) | |||||||
\(390\) | 4.31762 | 0.218631 | ||||||||
\(391\) | −27.4045 | −1.38590 | ||||||||
\(392\) | −2.94870 | −0.148932 | ||||||||
\(393\) | −8.21085 | −0.414183 | ||||||||
\(394\) | 46.1184 | 2.32341 | ||||||||
\(395\) | 14.3798 | 0.723525 | ||||||||
\(396\) | 10.4674 | 0.526005 | ||||||||
\(397\) | 27.4755 | 1.37895 | 0.689477 | − | 0.724308i | \(-0.257840\pi\) | ||||
0.689477 | + | 0.724308i | \(0.257840\pi\) | |||||||
\(398\) | 46.0101 | 2.30628 | ||||||||
\(399\) | −12.5470 | −0.628138 | ||||||||
\(400\) | 6.99487 | 0.349744 | ||||||||
\(401\) | −17.1495 | −0.856407 | −0.428203 | − | 0.903682i | \(-0.640853\pi\) | ||||
−0.428203 | + | 0.903682i | \(0.640853\pi\) | |||||||
\(402\) | −15.1395 | −0.755091 | ||||||||
\(403\) | 9.44109 | 0.470294 | ||||||||
\(404\) | −44.2890 | −2.20346 | ||||||||
\(405\) | 4.32119 | 0.214722 | ||||||||
\(406\) | 25.5211 | 1.26659 | ||||||||
\(407\) | 1.80814 | 0.0896264 | ||||||||
\(408\) | −6.07092 | −0.300555 | ||||||||
\(409\) | 23.5970 | 1.16679 | 0.583397 | − | 0.812187i | \(-0.301723\pi\) | ||||
0.583397 | + | 0.812187i | \(0.301723\pi\) | |||||||
\(410\) | −16.1085 | −0.795541 | ||||||||
\(411\) | 6.80243 | 0.335539 | ||||||||
\(412\) | −0.847378 | −0.0417473 | ||||||||
\(413\) | −21.9956 | −1.08233 | ||||||||
\(414\) | 22.5867 | 1.11008 | ||||||||
\(415\) | 8.78339 | 0.431160 | ||||||||
\(416\) | 12.2721 | 0.601688 | ||||||||
\(417\) | 11.0913 | 0.543143 | ||||||||
\(418\) | −18.3049 | −0.895321 | ||||||||
\(419\) | −13.1801 | −0.643888 | −0.321944 | − | 0.946759i | \(-0.604336\pi\) | ||||
−0.321944 | + | 0.946759i | \(0.604336\pi\) | |||||||
\(420\) | 10.2092 | 0.498156 | ||||||||
\(421\) | −19.8361 | −0.966753 | −0.483377 | − | 0.875413i | \(-0.660590\pi\) | ||||
−0.483377 | + | 0.875413i | \(0.660590\pi\) | |||||||
\(422\) | 13.1715 | 0.641180 | ||||||||
\(423\) | −15.7335 | −0.764990 | ||||||||
\(424\) | −5.53909 | −0.269002 | ||||||||
\(425\) | 16.0244 | 0.777296 | ||||||||
\(426\) | −9.12473 | −0.442095 | ||||||||
\(427\) | −42.2008 | −2.04224 | ||||||||
\(428\) | 2.51112 | 0.121379 | ||||||||
\(429\) | 2.42975 | 0.117310 | ||||||||
\(430\) | 6.06373 | 0.292419 | ||||||||
\(431\) | 17.3934 | 0.837810 | 0.418905 | − | 0.908030i | \(-0.362414\pi\) | ||||
0.418905 | + | 0.908030i | \(0.362414\pi\) | |||||||
\(432\) | −11.5710 | −0.556710 | ||||||||
\(433\) | −12.5269 | −0.602002 | −0.301001 | − | 0.953624i | \(-0.597321\pi\) | ||||
−0.301001 | + | 0.953624i | \(0.597321\pi\) | |||||||
\(434\) | 39.7391 | 1.90754 | ||||||||
\(435\) | −5.03494 | −0.241407 | ||||||||
\(436\) | −0.454241 | −0.0217542 | ||||||||
\(437\) | −22.1888 | −1.06143 | ||||||||
\(438\) | 29.7749 | 1.42270 | ||||||||
\(439\) | −4.43921 | −0.211872 | −0.105936 | − | 0.994373i | \(-0.533784\pi\) | ||||
−0.105936 | + | 0.994373i | \(0.533784\pi\) | |||||||
\(440\) | 3.27490 | 0.156125 | ||||||||
\(441\) | −5.52915 | −0.263293 | ||||||||
\(442\) | 19.5061 | 0.927809 | ||||||||
\(443\) | 1.11323 | 0.0528911 | 0.0264456 | − | 0.999650i | \(-0.491581\pi\) | ||||
0.0264456 | + | 0.999650i | \(0.491581\pi\) | |||||||
\(444\) | 2.20826 | 0.104799 | ||||||||
\(445\) | 7.15854 | 0.339347 | ||||||||
\(446\) | −4.05558 | −0.192037 | ||||||||
\(447\) | 12.8236 | 0.606535 | ||||||||
\(448\) | 35.9487 | 1.69842 | ||||||||
\(449\) | −18.1387 | −0.856017 | −0.428009 | − | 0.903775i | \(-0.640785\pi\) | ||||
−0.428009 | + | 0.903775i | \(0.640785\pi\) | |||||||
\(450\) | −13.2073 | −0.622597 | ||||||||
\(451\) | −9.06510 | −0.426859 | ||||||||
\(452\) | −42.5278 | −2.00034 | ||||||||
\(453\) | 3.94342 | 0.185278 | ||||||||
\(454\) | −27.4914 | −1.29024 | ||||||||
\(455\) | −7.21253 | −0.338129 | ||||||||
\(456\) | −4.91548 | −0.230189 | ||||||||
\(457\) | 39.7129 | 1.85769 | 0.928845 | − | 0.370469i | \(-0.120803\pi\) | ||||
0.928845 | + | 0.370469i | \(0.120803\pi\) | |||||||
\(458\) | −18.2582 | −0.853149 | ||||||||
\(459\) | −26.5077 | −1.23727 | ||||||||
\(460\) | 18.0543 | 0.841788 | ||||||||
\(461\) | −38.7701 | −1.80570 | −0.902852 | − | 0.429952i | \(-0.858531\pi\) | ||||
−0.902852 | + | 0.429952i | \(0.858531\pi\) | |||||||
\(462\) | 10.2272 | 0.475813 | ||||||||
\(463\) | −25.8031 | −1.19917 | −0.599586 | − | 0.800311i | \(-0.704668\pi\) | ||||
−0.599586 | + | 0.800311i | \(0.704668\pi\) | |||||||
\(464\) | −9.92931 | −0.460957 | ||||||||
\(465\) | −7.83994 | −0.363569 | ||||||||
\(466\) | 48.1549 | 2.23073 | ||||||||
\(467\) | 20.8600 | 0.965286 | 0.482643 | − | 0.875817i | \(-0.339677\pi\) | ||||
0.482643 | + | 0.875817i | \(0.339677\pi\) | |||||||
\(468\) | −9.03134 | −0.417474 | ||||||||
\(469\) | 25.2904 | 1.16780 | ||||||||
\(470\) | −22.3874 | −1.03265 | ||||||||
\(471\) | −12.8387 | −0.591574 | ||||||||
\(472\) | −8.61709 | −0.396634 | ||||||||
\(473\) | 3.41238 | 0.156902 | ||||||||
\(474\) | 17.5929 | 0.808067 | ||||||||
\(475\) | 12.9746 | 0.595314 | ||||||||
\(476\) | 46.1228 | 2.11404 | ||||||||
\(477\) | −10.3864 | −0.475562 | ||||||||
\(478\) | 16.2537 | 0.743426 | ||||||||
\(479\) | −4.39948 | −0.201017 | −0.100509 | − | 0.994936i | \(-0.532047\pi\) | ||||
−0.100509 | + | 0.994936i | \(0.532047\pi\) | |||||||
\(480\) | −10.1908 | −0.465145 | ||||||||
\(481\) | −1.56008 | −0.0711336 | ||||||||
\(482\) | 10.5546 | 0.480748 | ||||||||
\(483\) | 12.3972 | 0.564093 | ||||||||
\(484\) | −19.8190 | −0.900864 | ||||||||
\(485\) | −15.4667 | −0.702306 | ||||||||
\(486\) | 34.3128 | 1.55646 | ||||||||
\(487\) | 3.14012 | 0.142292 | 0.0711461 | − | 0.997466i | \(-0.477334\pi\) | ||||
0.0711461 | + | 0.997466i | \(0.477334\pi\) | |||||||
\(488\) | −16.5328 | −0.748403 | ||||||||
\(489\) | 0.861354 | 0.0389518 | ||||||||
\(490\) | −7.86749 | −0.355417 | ||||||||
\(491\) | −39.1019 | −1.76464 | −0.882322 | − | 0.470646i | \(-0.844021\pi\) | ||||
−0.882322 | + | 0.470646i | \(0.844021\pi\) | |||||||
\(492\) | −11.0711 | −0.499122 | ||||||||
\(493\) | −22.7468 | −1.02446 | ||||||||
\(494\) | 15.7936 | 0.710588 | ||||||||
\(495\) | 6.14082 | 0.276009 | ||||||||
\(496\) | −15.4610 | −0.694219 | ||||||||
\(497\) | 15.2428 | 0.683731 | ||||||||
\(498\) | 10.7460 | 0.481539 | ||||||||
\(499\) | 12.5714 | 0.562772 | 0.281386 | − | 0.959595i | \(-0.409206\pi\) | ||||
0.281386 | + | 0.959595i | \(0.409206\pi\) | |||||||
\(500\) | −29.8364 | −1.33433 | ||||||||
\(501\) | −17.3709 | −0.776075 | ||||||||
\(502\) | −10.8047 | −0.482235 | ||||||||
\(503\) | 22.1614 | 0.988127 | 0.494063 | − | 0.869426i | \(-0.335511\pi\) | ||||
0.494063 | + | 0.869426i | \(0.335511\pi\) | |||||||
\(504\) | −8.35854 | −0.372319 | ||||||||
\(505\) | −25.9827 | −1.15621 | ||||||||
\(506\) | 18.0863 | 0.804034 | ||||||||
\(507\) | 9.10120 | 0.404198 | ||||||||
\(508\) | −1.65731 | −0.0735312 | ||||||||
\(509\) | 1.68174 | 0.0745420 | 0.0372710 | − | 0.999305i | \(-0.488134\pi\) | ||||
0.0372710 | + | 0.999305i | \(0.488134\pi\) | |||||||
\(510\) | −16.1980 | −0.717258 | ||||||||
\(511\) | −49.7387 | −2.20031 | ||||||||
\(512\) | −26.2503 | −1.16011 | ||||||||
\(513\) | −21.4627 | −0.947600 | ||||||||
\(514\) | −40.4415 | −1.78380 | ||||||||
\(515\) | −0.497125 | −0.0219059 | ||||||||
\(516\) | 4.16749 | 0.183464 | ||||||||
\(517\) | −12.5986 | −0.554085 | ||||||||
\(518\) | −6.56664 | −0.288521 | ||||||||
\(519\) | −2.38656 | −0.104758 | ||||||||
\(520\) | −2.82561 | −0.123911 | ||||||||
\(521\) | −23.4398 | −1.02692 | −0.513459 | − | 0.858114i | \(-0.671636\pi\) | ||||
−0.513459 | + | 0.858114i | \(0.671636\pi\) | |||||||
\(522\) | 18.7479 | 0.820573 | ||||||||
\(523\) | 10.4211 | 0.455684 | 0.227842 | − | 0.973698i | \(-0.426833\pi\) | ||||
0.227842 | + | 0.973698i | \(0.426833\pi\) | |||||||
\(524\) | 24.4385 | 1.06760 | ||||||||
\(525\) | −7.24909 | −0.316376 | ||||||||
\(526\) | −11.9373 | −0.520490 | ||||||||
\(527\) | −35.4192 | −1.54288 | ||||||||
\(528\) | −3.97903 | −0.173165 | ||||||||
\(529\) | −1.07620 | −0.0467915 | ||||||||
\(530\) | −14.7790 | −0.641957 | ||||||||
\(531\) | −16.1580 | −0.701199 | ||||||||
\(532\) | 37.3446 | 1.61909 | ||||||||
\(533\) | 7.82145 | 0.338784 | ||||||||
\(534\) | 8.75808 | 0.378999 | ||||||||
\(535\) | 1.47318 | 0.0636910 | ||||||||
\(536\) | 9.90788 | 0.427955 | ||||||||
\(537\) | −20.1758 | −0.870650 | ||||||||
\(538\) | 14.5777 | 0.628488 | ||||||||
\(539\) | −4.42746 | −0.190704 | ||||||||
\(540\) | 17.4635 | 0.751510 | ||||||||
\(541\) | −22.7892 | −0.979785 | −0.489893 | − | 0.871783i | \(-0.662964\pi\) | ||||
−0.489893 | + | 0.871783i | \(0.662964\pi\) | |||||||
\(542\) | 31.1449 | 1.33779 | ||||||||
\(543\) | −5.22172 | −0.224085 | ||||||||
\(544\) | −46.0399 | −1.97394 | ||||||||
\(545\) | −0.266486 | −0.0114150 | ||||||||
\(546\) | −8.82414 | −0.377638 | ||||||||
\(547\) | 30.2551 | 1.29362 | 0.646808 | − | 0.762653i | \(-0.276103\pi\) | ||||
0.646808 | + | 0.762653i | \(0.276103\pi\) | |||||||
\(548\) | −20.2465 | −0.864887 | ||||||||
\(549\) | −31.0009 | −1.32308 | ||||||||
\(550\) | −10.5757 | −0.450949 | ||||||||
\(551\) | −18.4176 | −0.784614 | ||||||||
\(552\) | 4.85678 | 0.206718 | ||||||||
\(553\) | −29.3887 | −1.24973 | ||||||||
\(554\) | −54.3756 | −2.31020 | ||||||||
\(555\) | 1.29550 | 0.0549910 | ||||||||
\(556\) | −33.0117 | −1.40001 | ||||||||
\(557\) | −38.9178 | −1.64900 | −0.824500 | − | 0.565862i | \(-0.808543\pi\) | ||||
−0.824500 | + | 0.565862i | \(0.808543\pi\) | |||||||
\(558\) | 29.1924 | 1.23581 | ||||||||
\(559\) | −2.94423 | −0.124528 | ||||||||
\(560\) | 11.8114 | 0.499124 | ||||||||
\(561\) | −9.11546 | −0.384855 | ||||||||
\(562\) | 39.9526 | 1.68530 | ||||||||
\(563\) | −20.0995 | −0.847093 | −0.423547 | − | 0.905874i | \(-0.639215\pi\) | ||||
−0.423547 | + | 0.905874i | \(0.639215\pi\) | |||||||
\(564\) | −15.3864 | −0.647886 | ||||||||
\(565\) | −24.9495 | −1.04963 | ||||||||
\(566\) | −30.9264 | −1.29994 | ||||||||
\(567\) | −8.83144 | −0.370886 | ||||||||
\(568\) | 5.97157 | 0.250561 | ||||||||
\(569\) | 8.88209 | 0.372357 | 0.186178 | − | 0.982516i | \(-0.440390\pi\) | ||||
0.186178 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(570\) | −13.1151 | −0.549332 | ||||||||
\(571\) | −3.08809 | −0.129233 | −0.0646163 | − | 0.997910i | \(-0.520582\pi\) | ||||
−0.0646163 | + | 0.997910i | \(0.520582\pi\) | |||||||
\(572\) | −7.23183 | −0.302378 | ||||||||
\(573\) | 11.7834 | 0.492257 | ||||||||
\(574\) | 32.9217 | 1.37413 | ||||||||
\(575\) | −12.8196 | −0.534615 | ||||||||
\(576\) | 26.4081 | 1.10034 | ||||||||
\(577\) | 9.49723 | 0.395375 | 0.197687 | − | 0.980265i | \(-0.436657\pi\) | ||||
0.197687 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(578\) | −36.8622 | −1.53326 | ||||||||
\(579\) | 4.07357 | 0.169292 | ||||||||
\(580\) | 14.9858 | 0.622252 | ||||||||
\(581\) | −17.9511 | −0.744736 | ||||||||
\(582\) | −18.9226 | −0.784369 | ||||||||
\(583\) | −8.31691 | −0.344451 | ||||||||
\(584\) | −19.4858 | −0.806329 | ||||||||
\(585\) | −5.29835 | −0.219060 | ||||||||
\(586\) | 7.27184 | 0.300397 | ||||||||
\(587\) | −14.5936 | −0.602343 | −0.301171 | − | 0.953570i | \(-0.597378\pi\) | ||||
−0.301171 | + | 0.953570i | \(0.597378\pi\) | |||||||
\(588\) | −5.40718 | −0.222989 | ||||||||
\(589\) | −28.6781 | −1.18166 | ||||||||
\(590\) | −22.9915 | −0.946543 | ||||||||
\(591\) | 18.5951 | 0.764899 | ||||||||
\(592\) | 2.55483 | 0.105003 | ||||||||
\(593\) | 9.70102 | 0.398373 | 0.199187 | − | 0.979962i | \(-0.436170\pi\) | ||||
0.199187 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(594\) | 17.4944 | 0.717805 | ||||||||
\(595\) | 27.0585 | 1.10929 | ||||||||
\(596\) | −38.1676 | −1.56341 | ||||||||
\(597\) | 18.5514 | 0.759257 | ||||||||
\(598\) | −15.6050 | −0.638136 | ||||||||
\(599\) | −44.2925 | −1.80974 | −0.904871 | − | 0.425686i | \(-0.860033\pi\) | ||||
−0.904871 | + | 0.425686i | \(0.860033\pi\) | |||||||
\(600\) | −2.83993 | −0.115940 | ||||||||
\(601\) | 19.5791 | 0.798647 | 0.399324 | − | 0.916810i | \(-0.369245\pi\) | ||||
0.399324 | + | 0.916810i | \(0.369245\pi\) | |||||||
\(602\) | −12.3928 | −0.505091 | ||||||||
\(603\) | 18.5784 | 0.756572 | ||||||||
\(604\) | −11.7371 | −0.477574 | ||||||||
\(605\) | −11.6271 | −0.472708 | ||||||||
\(606\) | −31.7884 | −1.29132 | ||||||||
\(607\) | −18.9130 | −0.767656 | −0.383828 | − | 0.923405i | \(-0.625395\pi\) | ||||
−0.383828 | + | 0.923405i | \(0.625395\pi\) | |||||||
\(608\) | −37.2774 | −1.51180 | ||||||||
\(609\) | 10.2902 | 0.416979 | ||||||||
\(610\) | −44.1114 | −1.78602 | ||||||||
\(611\) | 10.8702 | 0.439760 | ||||||||
\(612\) | 33.8820 | 1.36960 | ||||||||
\(613\) | −3.93350 | −0.158873 | −0.0794364 | − | 0.996840i | \(-0.525312\pi\) | ||||
−0.0794364 | + | 0.996840i | \(0.525312\pi\) | |||||||
\(614\) | 66.9427 | 2.70159 | ||||||||
\(615\) | −6.49498 | −0.261903 | ||||||||
\(616\) | −6.69308 | −0.269672 | ||||||||
\(617\) | −13.5226 | −0.544399 | −0.272200 | − | 0.962241i | \(-0.587751\pi\) | ||||
−0.272200 | + | 0.962241i | \(0.587751\pi\) | |||||||
\(618\) | −0.608205 | −0.0244656 | ||||||||
\(619\) | 43.6578 | 1.75475 | 0.877377 | − | 0.479801i | \(-0.159291\pi\) | ||||
0.877377 | + | 0.479801i | \(0.159291\pi\) | |||||||
\(620\) | 23.3345 | 0.937136 | ||||||||
\(621\) | 21.2064 | 0.850982 | ||||||||
\(622\) | −2.44427 | −0.0980063 | ||||||||
\(623\) | −14.6303 | −0.586150 | ||||||||
\(624\) | 3.43314 | 0.137436 | ||||||||
\(625\) | −3.81442 | −0.152577 | ||||||||
\(626\) | −69.6015 | −2.78183 | ||||||||
\(627\) | −7.38058 | −0.294752 | ||||||||
\(628\) | 38.2125 | 1.52484 | ||||||||
\(629\) | 5.85280 | 0.233366 | ||||||||
\(630\) | −22.3016 | −0.888517 | ||||||||
\(631\) | −11.4879 | −0.457327 | −0.228664 | − | 0.973505i | \(-0.573436\pi\) | ||||
−0.228664 | + | 0.973505i | \(0.573436\pi\) | |||||||
\(632\) | −11.5134 | −0.457980 | ||||||||
\(633\) | 5.31079 | 0.211085 | ||||||||
\(634\) | 43.4232 | 1.72455 | ||||||||
\(635\) | −0.972281 | −0.0385838 | ||||||||
\(636\) | −10.1573 | −0.402764 | ||||||||
\(637\) | 3.82005 | 0.151356 | ||||||||
\(638\) | 15.0123 | 0.594344 | ||||||||
\(639\) | 11.1974 | 0.442962 | ||||||||
\(640\) | 13.9140 | 0.550000 | ||||||||
\(641\) | −29.1193 | −1.15014 | −0.575071 | − | 0.818104i | \(-0.695025\pi\) | ||||
−0.575071 | + | 0.818104i | \(0.695025\pi\) | |||||||
\(642\) | 1.80235 | 0.0711331 | ||||||||
\(643\) | 48.1988 | 1.90078 | 0.950388 | − | 0.311067i | \(-0.100686\pi\) | ||||
0.950388 | + | 0.311067i | \(0.100686\pi\) | |||||||
\(644\) | −36.8986 | −1.45401 | ||||||||
\(645\) | 2.44491 | 0.0962683 | ||||||||
\(646\) | −59.2513 | −2.33121 | ||||||||
\(647\) | 11.7233 | 0.460891 | 0.230445 | − | 0.973085i | \(-0.425982\pi\) | ||||
0.230445 | + | 0.973085i | \(0.425982\pi\) | |||||||
\(648\) | −3.45984 | −0.135915 | ||||||||
\(649\) | −12.9385 | −0.507881 | ||||||||
\(650\) | 9.12480 | 0.357904 | ||||||||
\(651\) | 16.0229 | 0.627987 | ||||||||
\(652\) | −2.56370 | −0.100402 | ||||||||
\(653\) | −36.7252 | −1.43717 | −0.718584 | − | 0.695440i | \(-0.755209\pi\) | ||||
−0.718584 | + | 0.695440i | \(0.755209\pi\) | |||||||
\(654\) | −0.326031 | −0.0127488 | ||||||||
\(655\) | 14.3371 | 0.560198 | ||||||||
\(656\) | −12.8086 | −0.500092 | ||||||||
\(657\) | −36.5382 | −1.42549 | ||||||||
\(658\) | 45.7543 | 1.78369 | ||||||||
\(659\) | −17.2769 | −0.673014 | −0.336507 | − | 0.941681i | \(-0.609246\pi\) | ||||
−0.336507 | + | 0.941681i | \(0.609246\pi\) | |||||||
\(660\) | 6.00535 | 0.233758 | ||||||||
\(661\) | −35.1251 | −1.36621 | −0.683103 | − | 0.730322i | \(-0.739370\pi\) | ||||
−0.683103 | + | 0.730322i | \(0.739370\pi\) | |||||||
\(662\) | −38.7727 | −1.50694 | ||||||||
\(663\) | 7.86490 | 0.305447 | ||||||||
\(664\) | −7.03258 | −0.272917 | ||||||||
\(665\) | 21.9087 | 0.849581 | ||||||||
\(666\) | −4.82387 | −0.186921 | ||||||||
\(667\) | 18.1976 | 0.704615 | ||||||||
\(668\) | 51.7021 | 2.00042 | ||||||||
\(669\) | −1.63522 | −0.0632212 | ||||||||
\(670\) | 26.4355 | 1.02129 | ||||||||
\(671\) | −24.8239 | −0.958315 | ||||||||
\(672\) | 20.8275 | 0.803438 | ||||||||
\(673\) | −41.2185 | −1.58886 | −0.794428 | − | 0.607359i | \(-0.792229\pi\) | ||||
−0.794428 | + | 0.607359i | \(0.792229\pi\) | |||||||
\(674\) | 76.7816 | 2.95752 | ||||||||
\(675\) | −12.4001 | −0.477280 | ||||||||
\(676\) | −27.0885 | −1.04186 | ||||||||
\(677\) | −44.6147 | −1.71468 | −0.857341 | − | 0.514749i | \(-0.827885\pi\) | ||||
−0.857341 | + | 0.514749i | \(0.827885\pi\) | |||||||
\(678\) | −30.5243 | −1.17228 | ||||||||
\(679\) | 31.6101 | 1.21308 | ||||||||
\(680\) | 10.6006 | 0.406513 | ||||||||
\(681\) | −11.0846 | −0.424763 | ||||||||
\(682\) | 23.3758 | 0.895105 | ||||||||
\(683\) | −6.56790 | −0.251314 | −0.125657 | − | 0.992074i | \(-0.540104\pi\) | ||||
−0.125657 | + | 0.992074i | \(0.540104\pi\) | |||||||
\(684\) | 27.4334 | 1.04894 | ||||||||
\(685\) | −11.8779 | −0.453830 | ||||||||
\(686\) | −29.8872 | −1.14110 | ||||||||
\(687\) | −7.36175 | −0.280868 | ||||||||
\(688\) | 4.82156 | 0.183820 | ||||||||
\(689\) | 7.17590 | 0.273380 | ||||||||
\(690\) | 12.9585 | 0.493321 | ||||||||
\(691\) | 12.4604 | 0.474016 | 0.237008 | − | 0.971508i | \(-0.423833\pi\) | ||||
0.237008 | + | 0.971508i | \(0.423833\pi\) | |||||||
\(692\) | 7.10326 | 0.270025 | ||||||||
\(693\) | −12.5503 | −0.476747 | ||||||||
\(694\) | 49.0129 | 1.86050 | ||||||||
\(695\) | −19.3667 | −0.734622 | ||||||||
\(696\) | 4.03132 | 0.152807 | ||||||||
\(697\) | −29.3429 | −1.11144 | ||||||||
\(698\) | 24.7396 | 0.936410 | ||||||||
\(699\) | 19.4162 | 0.734387 | ||||||||
\(700\) | 21.5759 | 0.815493 | ||||||||
\(701\) | −30.9476 | −1.16888 | −0.584438 | − | 0.811439i | \(-0.698685\pi\) | ||||
−0.584438 | + | 0.811439i | \(0.698685\pi\) | |||||||
\(702\) | −15.0943 | −0.569699 | ||||||||
\(703\) | 4.73888 | 0.178730 | ||||||||
\(704\) | 21.1462 | 0.796977 | ||||||||
\(705\) | −9.02665 | −0.339963 | ||||||||
\(706\) | −37.3214 | −1.40461 | ||||||||
\(707\) | 53.1022 | 1.99711 | ||||||||
\(708\) | −15.8016 | −0.593861 | ||||||||
\(709\) | −3.15529 | −0.118499 | −0.0592497 | − | 0.998243i | \(-0.518871\pi\) | ||||
−0.0592497 | + | 0.998243i | \(0.518871\pi\) | |||||||
\(710\) | 15.9329 | 0.597950 | ||||||||
\(711\) | −21.5890 | −0.809651 | ||||||||
\(712\) | −5.73162 | −0.214801 | ||||||||
\(713\) | 28.3356 | 1.06118 | ||||||||
\(714\) | 33.1046 | 1.23891 | ||||||||
\(715\) | −4.24264 | −0.158666 | ||||||||
\(716\) | 60.0505 | 2.24419 | ||||||||
\(717\) | 6.55353 | 0.244746 | ||||||||
\(718\) | −36.8250 | −1.37430 | ||||||||
\(719\) | 34.4768 | 1.28577 | 0.642883 | − | 0.765964i | \(-0.277738\pi\) | ||||
0.642883 | + | 0.765964i | \(0.277738\pi\) | |||||||
\(720\) | 8.67672 | 0.323362 | ||||||||
\(721\) | 1.01600 | 0.0378378 | ||||||||
\(722\) | −7.38504 | −0.274843 | ||||||||
\(723\) | 4.25564 | 0.158269 | ||||||||
\(724\) | 15.5417 | 0.577604 | ||||||||
\(725\) | −10.6408 | −0.395189 | ||||||||
\(726\) | −14.2251 | −0.527942 | ||||||||
\(727\) | 5.44394 | 0.201905 | 0.100952 | − | 0.994891i | \(-0.467811\pi\) | ||||
0.100952 | + | 0.994891i | \(0.467811\pi\) | |||||||
\(728\) | 5.77485 | 0.214030 | ||||||||
\(729\) | 5.21577 | 0.193177 | ||||||||
\(730\) | −51.9906 | −1.92426 | ||||||||
\(731\) | 11.0456 | 0.408536 | ||||||||
\(732\) | −30.3170 | −1.12055 | ||||||||
\(733\) | −42.7675 | −1.57965 | −0.789827 | − | 0.613329i | \(-0.789830\pi\) | ||||
−0.789827 | + | 0.613329i | \(0.789830\pi\) | |||||||
\(734\) | −21.7543 | −0.802965 | ||||||||
\(735\) | −3.17219 | −0.117008 | ||||||||
\(736\) | 36.8323 | 1.35766 | ||||||||
\(737\) | 14.8766 | 0.547988 | ||||||||
\(738\) | 24.1844 | 0.890240 | ||||||||
\(739\) | −27.8389 | −1.02407 | −0.512036 | − | 0.858964i | \(-0.671108\pi\) | ||||
−0.512036 | + | 0.858964i | \(0.671108\pi\) | |||||||
\(740\) | −3.85588 | −0.141745 | ||||||||
\(741\) | 6.36802 | 0.233935 | ||||||||
\(742\) | 30.2045 | 1.10884 | ||||||||
\(743\) | −44.0846 | −1.61731 | −0.808653 | − | 0.588286i | \(-0.799803\pi\) | ||||
−0.808653 | + | 0.588286i | \(0.799803\pi\) | |||||||
\(744\) | 6.27719 | 0.230133 | ||||||||
\(745\) | −22.3915 | −0.820362 | ||||||||
\(746\) | −53.9530 | −1.97536 | ||||||||
\(747\) | −13.1869 | −0.482484 | ||||||||
\(748\) | 27.1309 | 0.992004 | ||||||||
\(749\) | −3.01081 | −0.110013 | ||||||||
\(750\) | −21.4151 | −0.781968 | ||||||||
\(751\) | 34.0298 | 1.24176 | 0.620882 | − | 0.783904i | \(-0.286774\pi\) | ||||
0.620882 | + | 0.783904i | \(0.286774\pi\) | |||||||
\(752\) | −17.8013 | −0.649146 | ||||||||
\(753\) | −4.35646 | −0.158758 | ||||||||
\(754\) | −12.9528 | −0.471712 | ||||||||
\(755\) | −6.88569 | −0.250596 | ||||||||
\(756\) | −35.6911 | −1.29807 | ||||||||
\(757\) | −18.1340 | −0.659092 | −0.329546 | − | 0.944139i | \(-0.606896\pi\) | ||||
−0.329546 | + | 0.944139i | \(0.606896\pi\) | |||||||
\(758\) | 48.8383 | 1.77389 | ||||||||
\(759\) | 7.29244 | 0.264699 | ||||||||
\(760\) | 8.58303 | 0.311339 | ||||||||
\(761\) | −9.13881 | −0.331282 | −0.165641 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165641 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(762\) | −1.18953 | −0.0430922 | ||||||||
\(763\) | 0.544631 | 0.0197170 | ||||||||
\(764\) | −35.0715 | −1.26884 | ||||||||
\(765\) | 19.8773 | 0.718665 | ||||||||
\(766\) | −10.9793 | −0.396698 | ||||||||
\(767\) | 11.1635 | 0.403089 | ||||||||
\(768\) | −3.12400 | −0.112728 | ||||||||
\(769\) | 41.0704 | 1.48104 | 0.740518 | − | 0.672037i | \(-0.234580\pi\) | ||||
0.740518 | + | 0.672037i | \(0.234580\pi\) | |||||||
\(770\) | −17.8580 | −0.643556 | ||||||||
\(771\) | −16.3061 | −0.587250 | ||||||||
\(772\) | −12.1244 | −0.436368 | ||||||||
\(773\) | −0.718435 | −0.0258403 | −0.0129201 | − | 0.999917i | \(-0.504113\pi\) | ||||
−0.0129201 | + | 0.999917i | \(0.504113\pi\) | |||||||
\(774\) | −9.10376 | −0.327228 | ||||||||
\(775\) | −16.5688 | −0.595170 | ||||||||
\(776\) | 12.3837 | 0.444549 | ||||||||
\(777\) | −2.64768 | −0.0949851 | ||||||||
\(778\) | −75.2143 | −2.69656 | ||||||||
\(779\) | −23.7583 | −0.851229 | ||||||||
\(780\) | −5.18147 | −0.185526 | ||||||||
\(781\) | 8.96628 | 0.320839 | ||||||||
\(782\) | 58.5437 | 2.09352 | ||||||||
\(783\) | 17.6021 | 0.629048 | ||||||||
\(784\) | −6.25582 | −0.223422 | ||||||||
\(785\) | 22.4178 | 0.800127 | ||||||||
\(786\) | 17.5407 | 0.625656 | ||||||||
\(787\) | −1.94168 | −0.0692135 | −0.0346067 | − | 0.999401i | \(-0.511018\pi\) | ||||
−0.0346067 | + | 0.999401i | \(0.511018\pi\) | |||||||
\(788\) | −55.3457 | −1.97161 | ||||||||
\(789\) | −4.81314 | −0.171352 | ||||||||
\(790\) | −30.7192 | −1.09294 | ||||||||
\(791\) | 50.9905 | 1.81302 | ||||||||
\(792\) | −4.91676 | −0.174709 | ||||||||
\(793\) | 21.4182 | 0.760584 | ||||||||
\(794\) | −58.6954 | −2.08302 | ||||||||
\(795\) | −5.95891 | −0.211341 | ||||||||
\(796\) | −55.2156 | −1.95707 | ||||||||
\(797\) | 42.9732 | 1.52219 | 0.761094 | − | 0.648641i | \(-0.224662\pi\) | ||||
0.761094 | + | 0.648641i | \(0.224662\pi\) | |||||||
\(798\) | 26.8040 | 0.948853 | ||||||||
\(799\) | −40.7805 | −1.44271 | ||||||||
\(800\) | −21.5371 | −0.761453 | ||||||||
\(801\) | −10.7474 | −0.379742 | ||||||||
\(802\) | 36.6362 | 1.29367 | ||||||||
\(803\) | −29.2579 | −1.03249 | ||||||||
\(804\) | 18.1686 | 0.640757 | ||||||||
\(805\) | −21.6470 | −0.762957 | ||||||||
\(806\) | −20.1688 | −0.710417 | ||||||||
\(807\) | 5.87776 | 0.206907 | ||||||||
\(808\) | 20.8035 | 0.731866 | ||||||||
\(809\) | −42.1542 | −1.48206 | −0.741031 | − | 0.671471i | \(-0.765663\pi\) | ||||
−0.741031 | + | 0.671471i | \(0.765663\pi\) | |||||||
\(810\) | −9.23129 | −0.324354 | ||||||||
\(811\) | −39.0880 | −1.37257 | −0.686283 | − | 0.727335i | \(-0.740759\pi\) | ||||
−0.686283 | + | 0.727335i | \(0.740759\pi\) | |||||||
\(812\) | −30.6273 | −1.07481 | ||||||||
\(813\) | 12.5577 | 0.440418 | ||||||||
\(814\) | −3.86271 | −0.135388 | ||||||||
\(815\) | −1.50403 | −0.0526838 | ||||||||
\(816\) | −12.8798 | −0.450882 | ||||||||
\(817\) | 8.94335 | 0.312888 | ||||||||
\(818\) | −50.4098 | −1.76254 | ||||||||
\(819\) | 10.8285 | 0.378379 | ||||||||
\(820\) | 19.3314 | 0.675082 | ||||||||
\(821\) | −17.3874 | −0.606826 | −0.303413 | − | 0.952859i | \(-0.598126\pi\) | ||||
−0.303413 | + | 0.952859i | \(0.598126\pi\) | |||||||
\(822\) | −14.5319 | −0.506859 | ||||||||
\(823\) | 36.6943 | 1.27908 | 0.639541 | − | 0.768757i | \(-0.279125\pi\) | ||||
0.639541 | + | 0.768757i | \(0.279125\pi\) | |||||||
\(824\) | 0.398032 | 0.0138661 | ||||||||
\(825\) | −4.26415 | −0.148459 | ||||||||
\(826\) | 46.9888 | 1.63495 | ||||||||
\(827\) | −4.52228 | −0.157255 | −0.0786276 | − | 0.996904i | \(-0.525054\pi\) | ||||
−0.0786276 | + | 0.996904i | \(0.525054\pi\) | |||||||
\(828\) | −27.1058 | −0.941993 | ||||||||
\(829\) | −49.2312 | −1.70987 | −0.854935 | − | 0.518736i | \(-0.826403\pi\) | ||||
−0.854935 | + | 0.518736i | \(0.826403\pi\) | |||||||
\(830\) | −18.7638 | −0.651301 | ||||||||
\(831\) | −21.9244 | −0.760548 | ||||||||
\(832\) | −18.2451 | −0.632536 | ||||||||
\(833\) | −14.3313 | −0.496550 | ||||||||
\(834\) | −23.6941 | −0.820461 | ||||||||
\(835\) | 30.3317 | 1.04967 | ||||||||
\(836\) | 21.9673 | 0.759754 | ||||||||
\(837\) | 27.4084 | 0.947371 | ||||||||
\(838\) | 28.1563 | 0.972644 | ||||||||
\(839\) | −10.0115 | −0.345635 | −0.172818 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172818 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(840\) | −4.79547 | −0.165459 | ||||||||
\(841\) | −13.8953 | −0.479147 | ||||||||
\(842\) | 42.3755 | 1.46036 | ||||||||
\(843\) | 16.1090 | 0.554822 | ||||||||
\(844\) | −15.8068 | −0.544094 | ||||||||
\(845\) | −15.8918 | −0.546694 | ||||||||
\(846\) | 33.6112 | 1.15558 | ||||||||
\(847\) | 23.7628 | 0.816501 | ||||||||
\(848\) | −11.7515 | −0.403547 | ||||||||
\(849\) | −12.4696 | −0.427956 | ||||||||
\(850\) | −34.2326 | −1.17417 | ||||||||
\(851\) | −4.68229 | −0.160507 | ||||||||
\(852\) | 10.9504 | 0.375154 | ||||||||
\(853\) | −11.2609 | −0.385566 | −0.192783 | − | 0.981241i | \(-0.561751\pi\) | ||||
−0.192783 | + | 0.981241i | \(0.561751\pi\) | |||||||
\(854\) | 90.1528 | 3.08497 | ||||||||
\(855\) | 16.0942 | 0.550409 | ||||||||
\(856\) | −1.17953 | −0.0403154 | ||||||||
\(857\) | 23.6931 | 0.809339 | 0.404670 | − | 0.914463i | \(-0.367387\pi\) | ||||
0.404670 | + | 0.914463i | \(0.367387\pi\) | |||||||
\(858\) | −5.19064 | −0.177206 | ||||||||
\(859\) | −46.4974 | −1.58647 | −0.793235 | − | 0.608916i | \(-0.791605\pi\) | ||||
−0.793235 | + | 0.608916i | \(0.791605\pi\) | |||||||
\(860\) | −7.27694 | −0.248142 | ||||||||
\(861\) | 13.2741 | 0.452381 | ||||||||
\(862\) | −37.1572 | −1.26558 | ||||||||
\(863\) | 53.9120 | 1.83518 | 0.917592 | − | 0.397523i | \(-0.130130\pi\) | ||||
0.917592 | + | 0.397523i | \(0.130130\pi\) | |||||||
\(864\) | 35.6270 | 1.21205 | ||||||||
\(865\) | 4.16722 | 0.141690 | ||||||||
\(866\) | 26.7609 | 0.909373 | ||||||||
\(867\) | −14.8629 | −0.504771 | ||||||||
\(868\) | −47.6899 | −1.61870 | ||||||||
\(869\) | −17.2874 | −0.586434 | ||||||||
\(870\) | 10.7561 | 0.364665 | ||||||||
\(871\) | −12.8357 | −0.434921 | ||||||||
\(872\) | 0.213367 | 0.00722552 | ||||||||
\(873\) | 23.2209 | 0.785907 | ||||||||
\(874\) | 47.4015 | 1.60338 | ||||||||
\(875\) | 35.7737 | 1.20937 | ||||||||
\(876\) | −35.7322 | −1.20728 | ||||||||
\(877\) | −27.4341 | −0.926385 | −0.463192 | − | 0.886258i | \(-0.653296\pi\) | ||||
−0.463192 | + | 0.886258i | \(0.653296\pi\) | |||||||
\(878\) | 9.48340 | 0.320049 | ||||||||
\(879\) | 2.93202 | 0.0988947 | ||||||||
\(880\) | 6.94787 | 0.234213 | ||||||||
\(881\) | 21.8568 | 0.736374 | 0.368187 | − | 0.929752i | \(-0.379979\pi\) | ||||
0.368187 | + | 0.929752i | \(0.379979\pi\) | |||||||
\(882\) | 11.8118 | 0.397725 | ||||||||
\(883\) | 51.9615 | 1.74864 | 0.874321 | − | 0.485348i | \(-0.161307\pi\) | ||||
0.874321 | + | 0.485348i | \(0.161307\pi\) | |||||||
\(884\) | −23.4088 | −0.787323 | ||||||||
\(885\) | −9.27021 | −0.311615 | ||||||||
\(886\) | −2.37817 | −0.0798962 | ||||||||
\(887\) | −23.5921 | −0.792147 | −0.396073 | − | 0.918219i | \(-0.629627\pi\) | ||||
−0.396073 | + | 0.918219i | \(0.629627\pi\) | |||||||
\(888\) | −1.03727 | −0.0348084 | ||||||||
\(889\) | 1.98710 | 0.0666452 | ||||||||
\(890\) | −15.2927 | −0.512611 | ||||||||
\(891\) | −5.19494 | −0.174037 | ||||||||
\(892\) | 4.86700 | 0.162959 | ||||||||
\(893\) | −33.0190 | −1.10494 | ||||||||
\(894\) | −27.3948 | −0.916219 | ||||||||
\(895\) | 35.2294 | 1.17759 | ||||||||
\(896\) | −28.4368 | −0.950007 | ||||||||
\(897\) | −6.29198 | −0.210083 | ||||||||
\(898\) | 38.7494 | 1.29308 | ||||||||
\(899\) | 23.5197 | 0.784425 | ||||||||
\(900\) | 15.8497 | 0.528325 | ||||||||
\(901\) | −26.9211 | −0.896872 | ||||||||
\(902\) | 19.3656 | 0.644804 | ||||||||
\(903\) | −4.99679 | −0.166283 | ||||||||
\(904\) | 19.9763 | 0.664401 | ||||||||
\(905\) | 9.11775 | 0.303084 | ||||||||
\(906\) | −8.42427 | −0.279878 | ||||||||
\(907\) | 5.28546 | 0.175501 | 0.0877505 | − | 0.996142i | \(-0.472032\pi\) | ||||
0.0877505 | + | 0.996142i | \(0.472032\pi\) | |||||||
\(908\) | 32.9918 | 1.09487 | ||||||||
\(909\) | 39.0090 | 1.29385 | ||||||||
\(910\) | 15.4080 | 0.510770 | ||||||||
\(911\) | 11.3593 | 0.376351 | 0.188175 | − | 0.982135i | \(-0.439743\pi\) | ||||
0.188175 | + | 0.982135i | \(0.439743\pi\) | |||||||
\(912\) | −10.4285 | −0.345321 | ||||||||
\(913\) | −10.5594 | −0.349465 | ||||||||
\(914\) | −84.8379 | −2.80619 | ||||||||
\(915\) | −17.7858 | −0.587982 | ||||||||
\(916\) | 21.9112 | 0.723967 | ||||||||
\(917\) | −29.3015 | −0.967622 | ||||||||
\(918\) | 56.6279 | 1.86900 | ||||||||
\(919\) | 54.3921 | 1.79423 | 0.897115 | − | 0.441797i | \(-0.145659\pi\) | ||||
0.897115 | + | 0.441797i | \(0.145659\pi\) | |||||||
\(920\) | −8.48053 | −0.279595 | ||||||||
\(921\) | 26.9914 | 0.889399 | ||||||||
\(922\) | 82.8239 | 2.72766 | ||||||||
\(923\) | −7.73619 | −0.254640 | ||||||||
\(924\) | −12.2735 | −0.403767 | ||||||||
\(925\) | 2.73790 | 0.0900215 | ||||||||
\(926\) | 55.1227 | 1.81144 | ||||||||
\(927\) | 0.746357 | 0.0245136 | ||||||||
\(928\) | 30.5722 | 1.00358 | ||||||||
\(929\) | −6.36264 | −0.208751 | −0.104376 | − | 0.994538i | \(-0.533284\pi\) | ||||
−0.104376 | + | 0.994538i | \(0.533284\pi\) | |||||||
\(930\) | 16.7483 | 0.549199 | ||||||||
\(931\) | −11.6037 | −0.380296 | ||||||||
\(932\) | −57.7896 | −1.89296 | ||||||||
\(933\) | −0.985535 | −0.0322650 | ||||||||
\(934\) | −44.5629 | −1.45814 | ||||||||
\(935\) | 15.9167 | 0.520531 | ||||||||
\(936\) | 4.24222 | 0.138661 | ||||||||
\(937\) | 16.8228 | 0.549577 | 0.274788 | − | 0.961505i | \(-0.411392\pi\) | ||||
0.274788 | + | 0.961505i | \(0.411392\pi\) | |||||||
\(938\) | −54.0275 | −1.76406 | ||||||||
\(939\) | −28.0635 | −0.915818 | ||||||||
\(940\) | 26.8666 | 0.876292 | ||||||||
\(941\) | −36.5857 | −1.19266 | −0.596330 | − | 0.802739i | \(-0.703375\pi\) | ||||
−0.596330 | + | 0.802739i | \(0.703375\pi\) | |||||||
\(942\) | 27.4270 | 0.893620 | ||||||||
\(943\) | 23.4746 | 0.764437 | ||||||||
\(944\) | −18.2816 | −0.595015 | ||||||||
\(945\) | −20.9386 | −0.681134 | ||||||||
\(946\) | −7.28982 | −0.237012 | ||||||||
\(947\) | −22.7184 | −0.738247 | −0.369124 | − | 0.929380i | \(-0.620342\pi\) | ||||
−0.369124 | + | 0.929380i | \(0.620342\pi\) | |||||||
\(948\) | −21.1128 | −0.685711 | ||||||||
\(949\) | 25.2439 | 0.819453 | ||||||||
\(950\) | −27.7173 | −0.899269 | ||||||||
\(951\) | 17.5083 | 0.567747 | ||||||||
\(952\) | −21.6649 | −0.702164 | ||||||||
\(953\) | 20.9042 | 0.677154 | 0.338577 | − | 0.940939i | \(-0.390054\pi\) | ||||
0.338577 | + | 0.940939i | \(0.390054\pi\) | |||||||
\(954\) | 22.1883 | 0.718374 | ||||||||
\(955\) | −20.5752 | −0.665797 | ||||||||
\(956\) | −19.5057 | −0.630859 | ||||||||
\(957\) | 6.05301 | 0.195666 | ||||||||
\(958\) | 9.39854 | 0.303653 | ||||||||
\(959\) | 24.2754 | 0.783894 | ||||||||
\(960\) | 15.1509 | 0.488992 | ||||||||
\(961\) | 5.62263 | 0.181375 | ||||||||
\(962\) | 3.33278 | 0.107453 | ||||||||
\(963\) | −2.21175 | −0.0712726 | ||||||||
\(964\) | −12.6663 | −0.407955 | ||||||||
\(965\) | −7.11295 | −0.228974 | ||||||||
\(966\) | −26.4839 | −0.852107 | ||||||||
\(967\) | 43.3065 | 1.39264 | 0.696321 | − | 0.717730i | \(-0.254819\pi\) | ||||
0.696321 | + | 0.717730i | \(0.254819\pi\) | |||||||
\(968\) | 9.30943 | 0.299216 | ||||||||
\(969\) | −23.8903 | −0.767466 | ||||||||
\(970\) | 33.0412 | 1.06089 | ||||||||
\(971\) | −21.8133 | −0.700023 | −0.350011 | − | 0.936745i | \(-0.613822\pi\) | ||||
−0.350011 | + | 0.936745i | \(0.613822\pi\) | |||||||
\(972\) | −41.1780 | −1.32078 | ||||||||
\(973\) | 39.5808 | 1.26890 | ||||||||
\(974\) | −6.70817 | −0.214944 | ||||||||
\(975\) | 3.67914 | 0.117827 | ||||||||
\(976\) | −35.0751 | −1.12273 | ||||||||
\(977\) | 3.15259 | 0.100860 | 0.0504302 | − | 0.998728i | \(-0.483941\pi\) | ||||
0.0504302 | + | 0.998728i | \(0.483941\pi\) | |||||||
\(978\) | −1.84010 | −0.0588398 | ||||||||
\(979\) | −8.60600 | −0.275049 | ||||||||
\(980\) | 9.44159 | 0.301601 | ||||||||
\(981\) | 0.400088 | 0.0127738 | ||||||||
\(982\) | 83.5327 | 2.66564 | ||||||||
\(983\) | 9.92042 | 0.316412 | 0.158206 | − | 0.987406i | \(-0.449429\pi\) | ||||
0.158206 | + | 0.987406i | \(0.449429\pi\) | |||||||
\(984\) | 5.20032 | 0.165780 | ||||||||
\(985\) | −32.4692 | −1.03456 | ||||||||
\(986\) | 48.5936 | 1.54754 | ||||||||
\(987\) | 18.4482 | 0.587214 | ||||||||
\(988\) | −18.9535 | −0.602993 | ||||||||
\(989\) | −8.83655 | −0.280986 | ||||||||
\(990\) | −13.1185 | −0.416934 | ||||||||
\(991\) | 56.8811 | 1.80689 | 0.903444 | − | 0.428705i | \(-0.141030\pi\) | ||||
0.903444 | + | 0.428705i | \(0.141030\pi\) | |||||||
\(992\) | 47.6042 | 1.51144 | ||||||||
\(993\) | −15.6332 | −0.496106 | ||||||||
\(994\) | −32.5629 | −1.03283 | ||||||||
\(995\) | −32.3929 | −1.02692 | ||||||||
\(996\) | −12.8960 | −0.408626 | ||||||||
\(997\) | 57.4344 | 1.81897 | 0.909484 | − | 0.415740i | \(-0.136477\pi\) | ||||
0.909484 | + | 0.415740i | \(0.136477\pi\) | |||||||
\(998\) | −26.8560 | −0.850112 | ||||||||
\(999\) | −4.52906 | −0.143293 |
(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 | 6031.2.a.c.1.17 | ✓ | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.c.1.17 | ✓ | 110 | 1.1 | even | 1 | trivial |