Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.551494 | 0.318405 | 0.159203 | − | 0.987246i | \(-0.449108\pi\) | ||||
0.159203 | + | 0.987246i | \(0.449108\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.33245 | −1.04311 | −0.521553 | − | 0.853219i | \(-0.674647\pi\) | ||||
−0.521553 | + | 0.853219i | \(0.674647\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.71388 | 0.647786 | 0.323893 | − | 0.946094i | \(-0.395008\pi\) | ||||
0.323893 | + | 0.946094i | \(0.395008\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.69585 | −0.898618 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.53671 | −1.06636 | −0.533179 | − | 0.846002i | \(-0.679003\pi\) | ||||
−0.533179 | + | 0.846002i | \(0.679003\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.69844 | 1.30311 | 0.651557 | − | 0.758600i | \(-0.274116\pi\) | ||||
0.651557 | + | 0.758600i | \(0.274116\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.28633 | −0.332130 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.32909 | 1.29250 | 0.646248 | − | 0.763128i | \(-0.276337\pi\) | ||||
0.646248 | + | 0.763128i | \(0.276337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.945194 | 0.206258 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.91953 | −0.817278 | −0.408639 | − | 0.912696i | \(-0.633997\pi\) | ||||
−0.408639 | + | 0.912696i | \(0.633997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.440343 | 0.0880686 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.14123 | −0.604530 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.324961 | −0.0603438 | −0.0301719 | − | 0.999545i | \(-0.509605\pi\) | ||||
−0.0301719 | + | 0.999545i | \(0.509605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84244 | 0.690123 | 0.345062 | − | 0.938580i | \(-0.387858\pi\) | ||||
0.345062 | + | 0.938580i | \(0.387858\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.95047 | −0.339534 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.99755 | −0.675709 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.10127 | −0.345447 | −0.172724 | − | 0.984970i | \(-0.555257\pi\) | ||||
−0.172724 | + | 0.984970i | \(0.555257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.59116 | 0.414918 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2921 | −1.76353 | −0.881764 | − | 0.471691i | \(-0.843644\pi\) | ||||
−0.881764 | + | 0.471691i | \(0.843644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.62033 | 0.704593 | 0.352297 | − | 0.935888i | \(-0.385401\pi\) | ||||
0.352297 | + | 0.935888i | \(0.385401\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.28796 | 0.937353 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.89204 | 0.421848 | 0.210924 | − | 0.977502i | \(-0.432353\pi\) | ||||
0.210924 | + | 0.977502i | \(0.432353\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.06262 | −0.580374 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.93896 | 0.411537 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.546107 | −0.0750136 | −0.0375068 | − | 0.999296i | \(-0.511942\pi\) | ||||
−0.0375068 | + | 0.999296i | \(0.511942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.24922 | 1.11232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.551494 | 0.0730471 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.300059 | 0.0390644 | 0.0195322 | − | 0.999809i | \(-0.493782\pi\) | ||||
0.0195322 | + | 0.999809i | \(0.493782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.09363 | 1.16432 | 0.582160 | − | 0.813074i | \(-0.302208\pi\) | ||||
0.582160 | + | 0.813074i | \(0.302208\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.62037 | −0.582112 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.9589 | −1.35928 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81788 | 0.344259 | 0.172130 | − | 0.985074i | \(-0.444935\pi\) | ||||
0.172130 | + | 0.985074i | \(0.444935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.16160 | −0.260226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.90768 | −0.345078 | −0.172539 | − | 0.985003i | \(-0.555197\pi\) | ||||
−0.172539 | + | 0.985003i | \(0.555197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.70923 | −0.551174 | −0.275587 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275587 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.242846 | 0.0280415 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.06150 | −0.690772 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.35520 | 0.706133 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.18505 | −0.788662 | −0.394331 | − | 0.918969i | \(-0.629024\pi\) | ||||
−0.394331 | + | 0.918969i | \(0.629024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.4299 | −1.34821 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.179214 | −0.0192138 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.382983 | −0.0405961 | −0.0202981 | − | 0.999794i | \(-0.506462\pi\) | ||||
−0.0202981 | + | 0.999794i | \(0.506462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.05256 | 0.844138 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.11908 | 0.219739 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.33245 | −0.239305 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.48403 | 0.962958 | 0.481479 | − | 0.876458i | \(-0.340100\pi\) | ||||
0.481479 | + | 0.876458i | \(0.340100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.53446 | 0.958249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5762 | −1.05237 | −0.526184 | − | 0.850371i | \(-0.676378\pi\) | ||||
−0.526184 | + | 0.850371i | \(0.676378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.86609 | 0.775069 | 0.387534 | − | 0.921855i | \(-0.373327\pi\) | ||||
0.387534 | + | 0.921855i | \(0.373327\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.20462 | −0.215149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.91970 | 0.185585 | 0.0927923 | − | 0.995685i | \(-0.470421\pi\) | ||||
0.0927923 | + | 0.995685i | \(0.470421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.90135 | −0.756812 | −0.378406 | − | 0.925640i | \(-0.623528\pi\) | ||||
−0.378406 | + | 0.925640i | \(0.623528\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.15884 | −0.109992 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1650 | 0.956244 | 0.478122 | − | 0.878294i | \(-0.341318\pi\) | ||||
0.478122 | + | 0.878294i | \(0.341318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.14212 | 0.852507 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.6663 | −1.17100 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.13342 | 0.837260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.50832 | 0.137120 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.22752 | −0.561516 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6352 | 0.951240 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.60435 | −0.231099 | −0.115549 | − | 0.993302i | \(-0.536863\pi\) | ||||
−0.115549 | + | 0.993302i | \(0.536863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.54808 | 0.224346 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.2620 | −1.68293 | −0.841466 | − | 0.540310i | \(-0.818307\pi\) | ||||
−0.841466 | + | 0.540310i | \(0.818307\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.71388 | 0.148612 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.32677 | 0.630588 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.62735 | −0.822520 | −0.411260 | − | 0.911518i | \(-0.634911\pi\) | ||||
−0.411260 | + | 0.911518i | \(0.634911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.73621 | −0.825815 | −0.412907 | − | 0.910773i | \(-0.635487\pi\) | ||||
−0.412907 | + | 0.910773i | \(0.635487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.59494 | 0.134318 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.6170 | −1.38959 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.757958 | 0.0629449 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.24051 | −0.184794 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.49126 | 0.613708 | 0.306854 | − | 0.951757i | \(-0.400724\pi\) | ||||
0.306854 | + | 0.951757i | \(0.400724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9995 | −1.30202 | −0.651009 | − | 0.759070i | \(-0.725654\pi\) | ||||
−0.651009 | + | 0.759070i | \(0.725654\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.3665 | −1.16146 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.96233 | −0.719871 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.30349 | −0.343456 | −0.171728 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171728 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.301175 | −0.0238847 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.71760 | −0.529421 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.6145 | −1.06637 | −0.533186 | − | 0.845998i | \(-0.679005\pi\) | ||||
−0.533186 | + | 0.845998i | \(0.679005\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.54939 | 0.354170 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.1152 | −0.937499 | −0.468749 | − | 0.883331i | \(-0.655295\pi\) | ||||
−0.468749 | + | 0.883331i | \(0.655295\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.07536 | 0.698105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.69585 | −0.206157 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.49273 | −0.721719 | −0.360860 | − | 0.932620i | \(-0.617517\pi\) | ||||
−0.360860 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.754695 | 0.0570495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.165481 | 0.0124383 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5105 | −0.860339 | −0.430169 | − | 0.902748i | \(-0.641546\pi\) | ||||
−0.430169 | + | 0.902748i | \(0.641546\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4754 | −1.07595 | −0.537974 | − | 0.842962i | \(-0.680810\pi\) | ||||
−0.537974 | + | 0.842962i | \(0.680810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.01508 | 0.370725 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.90112 | 0.360338 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.8475 | −1.37826 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.38369 | −0.391606 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2866 | 1.17846 | 0.589230 | − | 0.807966i | \(-0.299431\pi\) | ||||
0.589230 | + | 0.807966i | \(0.299431\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9798 | −1.36620 | −0.683098 | − | 0.730327i | \(-0.739368\pi\) | ||||
−0.683098 | + | 0.730327i | \(0.739368\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.04377 | −0.432803 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.9355 | −1.49159 | −0.745795 | − | 0.666176i | \(-0.767930\pi\) | ||||
−0.745795 | + | 0.666176i | \(0.767930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.29571 | −0.517179 | −0.258590 | − | 0.965987i | \(-0.583258\pi\) | ||||
−0.258590 | + | 0.965987i | \(0.583258\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.55404 | 0.109614 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.556945 | −0.0390899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.3383 | 1.83955 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.5665 | 0.734421 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.53671 | −0.244639 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1473 | −0.905095 | −0.452548 | − | 0.891740i | \(-0.649485\pi\) | ||||
−0.452548 | + | 0.891740i | \(0.649485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.60357 | −0.109874 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7767 | −0.734965 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.58549 | 0.447052 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.59711 | −0.175497 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.0384 | 1.68427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.6177 | 1.31370 | 0.656848 | − | 0.754023i | \(-0.271889\pi\) | ||||
0.656848 | + | 0.754023i | \(0.271889\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.18710 | −0.0791400 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.9438 | −1.58921 | −0.794604 | − | 0.607128i | \(-0.792321\pi\) | ||||
−0.794604 | + | 0.607128i | \(0.792321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6084 | 0.965348 | 0.482674 | − | 0.875800i | \(-0.339666\pi\) | ||||
0.482674 | + | 0.875800i | \(0.339666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.34288 | −0.219945 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1942 | −1.19194 | −0.595972 | − | 0.803005i | \(-0.703233\pi\) | ||||
−0.595972 | + | 0.803005i | \(0.703233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.74556 | −0.440032 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.551494 | −0.0358234 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.60613 | 0.362631 | 0.181315 | − | 0.983425i | \(-0.441965\pi\) | ||||
0.181315 | + | 0.983425i | \(0.441965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.7704 | −1.85327 | −0.926634 | − | 0.375965i | \(-0.877311\pi\) | ||||
−0.926634 | + | 0.375965i | \(0.877311\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.9285 | 0.829366 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.47587 | 0.605391 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.69844 | 0.298955 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.96251 | −0.251114 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7276 | 0.677123 | 0.338561 | − | 0.940944i | \(-0.390060\pi\) | ||||
0.338561 | + | 0.940944i | \(0.390060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8622 | 0.871511 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.85499 | −0.429276 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.13682 | −0.133291 | −0.0666456 | − | 0.997777i | \(-0.521230\pi\) | ||||
−0.0666456 | + | 0.997777i | \(0.521230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.60133 | −0.223776 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.876049 | 0.0542260 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.6137 | −1.39442 | −0.697211 | − | 0.716866i | \(-0.745576\pi\) | ||||
−0.697211 | + | 0.716866i | \(0.745576\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.27377 | 0.0782471 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.211213 | −0.0129260 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.7666 | 0.778394 | 0.389197 | − | 0.921154i | \(-0.372752\pi\) | ||||
0.389197 | + | 0.921154i | \(0.372752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.49307 | 0.212189 | 0.106095 | − | 0.994356i | \(-0.466165\pi\) | ||||
0.106095 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.44094 | 0.268778 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.55737 | −0.0939126 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.82775 | −0.290071 | −0.145036 | − | 0.989426i | \(-0.546330\pi\) | ||||
−0.145036 | + | 0.989426i | \(0.546330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.3587 | −0.620157 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4094 | 0.919246 | 0.459623 | − | 0.888114i | \(-0.347984\pi\) | ||||
0.459623 | + | 0.888114i | \(0.347984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4756 | 0.741596 | 0.370798 | − | 0.928714i | \(-0.379084\pi\) | ||||
0.370798 | + | 0.928714i | \(0.379084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.28633 | −0.0761959 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.3533 | −1.14239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.3992 | 0.670544 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.23039 | 0.306611 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.82125 | −0.340081 | −0.170040 | − | 0.985437i | \(-0.554390\pi\) | ||||
−0.170040 | + | 0.985437i | \(0.554390\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.699875 | −0.0407483 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1096 | 0.644645 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.4157 | −1.06501 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.91869 | 0.456425 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.83269 | −0.335079 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.2105 | −1.21451 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.3336 | −0.989282 | −0.494641 | − | 0.869097i | \(-0.664700\pi\) | ||||
−0.494641 | + | 0.869097i | \(0.664700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.33810 | 0.246786 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.0959 | −1.53647 | −0.768233 | − | 0.640170i | \(-0.778864\pi\) | ||||
−0.768233 | + | 0.640170i | \(0.778864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.12639 | −0.515854 | −0.257927 | − | 0.966164i | \(-0.583039\pi\) | ||||
−0.257927 | + | 0.966164i | \(0.583039\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.7768 | 0.607204 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.6116 | 1.04533 | 0.522667 | − | 0.852537i | \(-0.324937\pi\) | ||||
0.522667 | + | 0.852537i | \(0.324937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.14929 | 0.0643481 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.05870 | 0.0590911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.32909 | 0.296519 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.06893 | 0.114763 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.35755 | −0.240973 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.95661 | 0.273267 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.6394 | 1.40927 | 0.704635 | − | 0.709570i | \(-0.251111\pi\) | ||||
0.704635 | + | 0.709570i | \(0.251111\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.66473 | 0.310425 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.57258 | −0.359098 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0201 | 0.600301 | 0.300150 | − | 0.953892i | \(-0.402963\pi\) | ||||
0.300150 | + | 0.953892i | \(0.402963\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.60594 | 0.304473 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5896 | −0.735919 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.9600 | −1.02374 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.04182 | 0.271443 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.36718 | 0.234443 | 0.117221 | − | 0.993106i | \(-0.462601\pi\) | ||||
0.117221 | + | 0.993106i | \(0.462601\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.57504 | 0.191367 | 0.0956837 | − | 0.995412i | \(-0.469496\pi\) | ||||
0.0956837 | + | 0.995412i | \(0.469496\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.7589 | −0.787771 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2322 | −1.18330 | −0.591650 | − | 0.806195i | \(-0.701523\pi\) | ||||
−0.591650 | + | 0.806195i | \(0.701523\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.78202 | 0.359952 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.03703 | 0.266588 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.85641 | −0.256312 | −0.128156 | − | 0.991754i | \(-0.540906\pi\) | ||||
−0.128156 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.831830 | 0.0436597 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.9841 | 0.574932 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.91138 | −0.360771 | −0.180385 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180385 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.4418 | 1.58474 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.935962 | −0.0485927 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.0299 | 1.24422 | 0.622111 | − | 0.782929i | \(-0.286275\pi\) | ||||
0.622111 | + | 0.782929i | \(0.286275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.86524 | 0.302880 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.52681 | −0.0786348 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.4010 | −1.30476 | −0.652381 | − | 0.757891i | \(-0.726230\pi\) | ||||
−0.652381 | + | 0.757891i | \(0.726230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.43628 | −0.0735830 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.77378 | −0.0906361 | −0.0453181 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453181 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.1382 | 0.720547 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.4557 | −0.633161 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.9456 | −1.21409 | −0.607045 | − | 0.794668i | \(-0.707645\pi\) | ||||
−0.607045 | + | 0.794668i | \(0.707645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.8875 | −1.05633 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.6229 | −0.535854 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.33245 | 0.117359 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.9045 | −0.798224 | −0.399112 | − | 0.916902i | \(-0.630681\pi\) | ||||
−0.399112 | + | 0.916902i | \(0.630681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.945194 | 0.0473189 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.2798 | 1.66191 | 0.830956 | − | 0.556338i | \(-0.187794\pi\) | ||||
0.830956 | + | 0.556338i | \(0.187794\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0535 | 0.899309 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.8232 | −0.736571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.43160 | 0.368371 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.01715 | 0.346976 | 0.173488 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173488 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.30942 | −0.261895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.514266 | 0.0253054 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.7588 | 0.822657 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.36946 | −0.262944 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.4745 | 0.853684 | 0.426842 | − | 0.904326i | \(-0.359626\pi\) | ||||
0.426842 | + | 0.904326i | \(0.359626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.4501 | 0.606778 | 0.303389 | − | 0.952867i | \(-0.401882\pi\) | ||||
0.303389 | + | 0.952867i | \(0.401882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.79653 | −0.379080 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.34663 | 0.113828 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.5854 | 0.754230 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.16419 | −0.442451 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.27235 | 0.109455 | 0.0547277 | − | 0.998501i | \(-0.482571\pi\) | ||||
0.0547277 | + | 0.998501i | \(0.482571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.9362 | −0.910016 | −0.455008 | − | 0.890487i | \(-0.650364\pi\) | ||||
−0.455008 | + | 0.890487i | \(0.650364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.418009 | 0.0200420 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.91953 | −0.187496 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.3208 | 0.969858 | 0.484929 | − | 0.874553i | \(-0.338845\pi\) | ||||
0.484929 | + | 0.874553i | \(0.338845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.9522 | 0.521535 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.8608 | 0.516014 | 0.258007 | − | 0.966143i | \(-0.416934\pi\) | ||||
0.258007 | + | 0.966143i | \(0.416934\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.893291 | 0.0423460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.13138 | 0.195408 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.0385882 | −0.00182109 | −0.000910544 | − | 1.00000i | \(-0.500290\pi\) | ||||
−0.000910544 | 1.00000i | \(0.500290\pi\) | ||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.9369 | 1.88055 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.82360 | −0.414569 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.7822 | −0.880525 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.6041 | −1.15093 | −0.575465 | − | 0.817827i | \(-0.695179\pi\) | ||||
−0.575465 | + | 0.817827i | \(0.695179\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.7399 | −0.781352 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.44396 | −0.160401 | −0.0802006 | − | 0.996779i | \(-0.525556\pi\) | ||||
−0.0802006 | + | 0.996779i | \(0.525556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.63555 | −0.168958 | −0.0844792 | − | 0.996425i | \(-0.526923\pi\) | ||||
−0.0844792 | + | 0.996425i | \(0.526923\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.94267 | −0.229211 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.99303 | 0.323599 | 0.161799 | − | 0.986824i | \(-0.448270\pi\) | ||||
0.161799 | + | 0.986824i | \(0.448270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82951 | 0.223006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.37335 | −0.109358 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.3408 | −0.751349 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.440343 | 0.0202043 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.47223 | 0.0674086 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.4283 | −0.522173 | −0.261087 | − | 0.965315i | \(-0.584081\pi\) | ||||
−0.261087 | + | 0.965315i | \(0.584081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.87271 | −0.450157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.70471 | −0.168570 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.1211 | −1.00447 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.46872 | −0.429069 | −0.214534 | − | 0.976716i | \(-0.568823\pi\) | ||||
−0.214534 | + | 0.976716i | \(0.568823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.50833 | −0.339538 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.5301 | 1.24242 | 0.621208 | − | 0.783646i | \(-0.286642\pi\) | ||||
0.621208 | + | 0.783646i | \(0.286642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.73175 | −0.0779941 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.2387 | −0.999555 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.98341 | −0.223536 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.3914 | 1.04714 | 0.523571 | − | 0.851982i | \(-0.324600\pi\) | ||||
0.523571 | + | 0.851982i | \(0.324600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.68143 | −0.298504 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.3259 | −0.683349 | −0.341675 | − | 0.939818i | \(-0.610994\pi\) | ||||
−0.341675 | + | 0.939818i | \(0.610994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.6684 | 1.09773 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00500 | 0.222280 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.88553 | −0.216547 | −0.108274 | − | 0.994121i | \(-0.534532\pi\) | ||||
−0.108274 | + | 0.994121i | \(0.534532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.07105 | −0.357042 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.14123 | −0.138689 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.3473 | −0.808478 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2283 | −0.449841 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.23518 | −0.229799 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.1291 | −1.14474 | −0.572368 | − | 0.819997i | \(-0.693975\pi\) | ||||
−0.572368 | + | 0.819997i | \(0.693975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3655 | 1.59015 | 0.795076 | − | 0.606510i | \(-0.207431\pi\) | ||||
0.795076 | + | 0.606510i | \(0.207431\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.416209 | 0.0181649 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4767 | 0.891981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.63730 | −0.332056 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.808916 | −0.0351040 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −53.0552 | −2.29808 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.47762 | −0.193584 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.34800 | −0.273936 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.3683 | 0.618886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.96783 | −0.256577 | −0.128288 | − | 0.991737i | \(-0.540948\pi\) | ||||
−0.128288 | + | 0.991737i | \(0.540948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.98309 | −0.342587 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.4295 | 0.789435 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1536 | 0.690677 | 0.345338 | − | 0.938478i | \(-0.387764\pi\) | ||||
0.345338 | + | 0.938478i | \(0.387764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.5151 | −1.04628 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.324961 | −0.0138438 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.71388 | −0.0728816 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.70294 | 0.114733 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.78564 | 0.160403 | 0.0802014 | − | 0.996779i | \(-0.474444\pi\) | ||||
0.0802014 | + | 0.996779i | \(0.474444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.7083 | 0.918165 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.3943 | −0.438846 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.8237 | 1.50979 | 0.754894 | − | 0.655847i | \(-0.227688\pi\) | ||||
0.754894 | + | 0.655847i | \(0.227688\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.7094 | −0.997463 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.8920 | 0.457423 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.96194 | 0.166093 | 0.0830466 | − | 0.996546i | \(-0.473535\pi\) | ||||
0.0830466 | + | 0.996546i | \(0.473535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.11927 | 0.214235 | 0.107117 | − | 0.994246i | \(-0.465838\pi\) | ||||
0.107117 | + | 0.994246i | \(0.465838\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.98198 | 0.375227 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.72594 | −0.0719765 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.84993 | 0.285166 | 0.142583 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142583 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.4672 | −0.435004 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.3143 | −0.510884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93142 | 0.0799914 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.5436 | 1.22148 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.6010 | −1.71706 | −0.858529 | − | 0.512765i | \(-0.828621\pi\) | ||||
−0.858529 | + | 0.512765i | \(0.828621\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.84244 | 0.158325 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.5458 | −0.474930 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.4100 | −1.12560 | −0.562798 | − | 0.826595i | \(-0.690275\pi\) | ||||
−0.562798 | + | 0.826595i | \(0.690275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.3033 | −0.873350 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.02354 | −0.164673 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.4747 | 0.795715 | 0.397858 | − | 0.917447i | \(-0.369754\pi\) | ||||
0.397858 | + | 0.917447i | \(0.369754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.9379 | 0.772494 | 0.386247 | − | 0.922395i | \(-0.373771\pi\) | ||||
0.386247 | + | 0.922395i | \(0.373771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.59660 | −0.309357 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.51809 | −0.143031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.93694 | −0.281562 | −0.140781 | − | 0.990041i | \(-0.544961\pi\) | ||||
−0.140781 | + | 0.990041i | \(0.544961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.307152 | −0.0124464 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.5881 | 0.549715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.55651 | −0.143646 | −0.0718230 | − | 0.997417i | \(-0.522882\pi\) | ||||
−0.0718230 | + | 0.997417i | \(0.522882\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.5254 | 0.585721 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.5205 | 0.946898 | 0.473449 | − | 0.880821i | \(-0.343009\pi\) | ||||
0.473449 | + | 0.880821i | \(0.343009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.7111 | −1.39516 | −0.697579 | − | 0.716508i | \(-0.745739\pi\) | ||||
−0.697579 | + | 0.716508i | \(0.745739\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.3121 | 0.494069 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.656387 | −0.0262976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.0078 | −1.08031 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.95047 | −0.0778944 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.1979 | −0.446489 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.05530 | 0.121629 | 0.0608147 | − | 0.998149i | \(-0.480630\pi\) | ||||
0.0608147 | + | 0.998149i | \(0.480630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.25064 | −0.288187 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.07453 | 0.241060 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.0880 | −0.756293 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.83867 | 0.310093 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8983 | −0.943926 | −0.471963 | − | 0.881618i | \(-0.656454\pi\) | ||||
−0.471963 | + | 0.881618i | \(0.656454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.4725 | 0.886230 | 0.443115 | − | 0.896465i | \(-0.353873\pi\) | ||||
0.443115 | + | 0.896465i | \(0.353873\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.94329 | −0.234017 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.4452 | −0.685841 | −0.342921 | − | 0.939364i | \(-0.611416\pi\) | ||||
−0.342921 | + | 0.939364i | \(0.611416\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.06122 | −0.0416566 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.63185 | 0.142344 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.4384 | −1.34768 | −0.673838 | − | 0.738879i | \(-0.735356\pi\) | ||||
−0.673838 | + | 0.738879i | \(0.735356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.9278 | 1.75548 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.6954 | 0.495295 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.8064 | 0.927366 | 0.463683 | − | 0.886001i | \(-0.346528\pi\) | ||||
0.463683 | + | 0.886001i | \(0.346528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2148 | 0.513996 | 0.256998 | − | 0.966412i | \(-0.417267\pi\) | ||||
0.256998 | + | 0.966412i | \(0.417267\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.8085 | 0.536279 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.99755 | −0.155018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.27370 | 0.0493177 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8190 | 0.418287 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.1615 | −1.24158 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.09177 | −0.196273 | −0.0981367 | − | 0.995173i | \(-0.531288\pi\) | ||||
−0.0981367 | + | 0.995173i | \(0.531288\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.38322 | −0.0532401 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.8295 | 1.33861 | 0.669304 | − | 0.742989i | \(-0.266592\pi\) | ||||
0.669304 | + | 0.742989i | \(0.266592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.2545 | 0.623790 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.2049 | −0.506012 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.06932 | −0.0791805 | −0.0395903 | − | 0.999216i | \(-0.512605\pi\) | ||||
−0.0395903 | + | 0.999216i | \(0.512605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.4554 | 0.857975 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.05642 | 0.307372 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.56585 | −0.0977512 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3673 | 0.812849 | 0.406425 | − | 0.913684i | \(-0.366775\pi\) | ||||
0.406425 | + | 0.913684i | \(0.366775\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.3409 | 0.620740 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.7093 | 0.861412 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60.1766 | −2.27935 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0340 | −0.379521 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.5989 | 1.53340 | 0.766699 | − | 0.642007i | \(-0.221898\pi\) | ||||
0.766699 | + | 0.642007i | \(0.221898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.10127 | −0.0792510 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.72013 | −0.140108 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.1263 | −0.681709 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.2735 | 1.51250 | 0.756251 | − | 0.654282i | \(-0.227029\pi\) | ||||
0.756251 | + | 0.654282i | \(0.227029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.69585 | 0.101102 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.0606 | −0.564023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.7585 | 1.44948 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.09175 | 0.115463 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.23722 | −0.232609 | −0.116304 | − | 0.993214i | \(-0.537105\pi\) | ||||
−0.116304 | + | 0.993214i | \(0.537105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.4815 | 0.502078 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.8667 | −0.590090 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.143094 | −0.00531439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.57859 | −0.0585468 | −0.0292734 | − | 0.999571i | \(-0.509319\pi\) | ||||
−0.0292734 | + | 0.999571i | \(0.509319\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.9356 | −0.442058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.6222 | 0.910684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.6866 | −1.50279 | −0.751397 | − | 0.659850i | \(-0.770620\pi\) | ||||
−0.751397 | + | 0.659850i | \(0.770620\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.22588 | 0.192760 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.96603 | −0.367103 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5017 | 0.423097 | 0.211549 | − | 0.977367i | \(-0.432149\pi\) | ||||
0.211549 | + | 0.977367i | \(0.432149\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.59116 | 0.0951887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.8782 | 1.24287 | 0.621436 | − | 0.783465i | \(-0.286550\pi\) | ||||
0.621436 | + | 0.783465i | \(0.286550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.4730 | −0.640162 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.3699 | 0.708706 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.29014 | 0.120219 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8925 | −0.506946 | −0.253473 | − | 0.967342i | \(-0.581573\pi\) | ||||
−0.253473 | + | 0.967342i | \(0.581573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.91623 | 0.215599 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.3180 | 1.35814 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.65414 | 0.350886 | 0.175443 | − | 0.984490i | \(-0.443864\pi\) | ||||
0.175443 | + | 0.984490i | \(0.443864\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.64494 | 0.277494 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.5418 | 1.43339 | 0.716695 | − | 0.697387i | \(-0.245654\pi\) | ||||
0.716695 | + | 0.697387i | \(0.245654\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5420 | −0.490252 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33.5091 | 1.21152 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.40981 | 0.0509053 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.1385 | 0.437725 | 0.218863 | − | 0.975756i | \(-0.429765\pi\) | ||||
0.218863 | + | 0.975756i | \(0.429765\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.17844 | −0.0424406 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.9702 | −0.898116 | −0.449058 | − | 0.893503i | \(-0.648240\pi\) | ||||
−0.449058 | + | 0.893503i | \(0.648240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.69199 | 0.0607782 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.98611 | −0.0712513 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2921 | −0.404581 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.2836 | 0.367976 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.02078 | 0.0364796 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0377 | 0.358261 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8195 | 0.492611 | 0.246306 | − | 0.969192i | \(-0.420783\pi\) | ||||
0.246306 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4713 | −0.443991 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.4216 | 0.619441 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.7259 | 1.51724 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.702476 | 0.0249143 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.3248 | −1.53464 | −0.767322 | − | 0.641262i | \(-0.778411\pi\) | ||||
−0.767322 | + | 0.641262i | \(0.778411\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.4120 | 0.545236 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.03247 | 0.0364804 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.6552 | 0.587749 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.6685 | 0.552242 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.04071 | 0.247845 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.8498 | −1.22525 | −0.612626 | − | 0.790373i | \(-0.709887\pi\) | ||||
−0.612626 | + | 0.790373i | \(0.709887\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.98390 | 0.245238 | 0.122619 | − | 0.992454i | \(-0.460871\pi\) | ||||
0.122619 | + | 0.992454i | \(0.460871\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.92641 | 0.0675621 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.7553 | 1.11234 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.62033 | 0.161645 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.7085 | −0.758558 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.67463 | 0.163146 | 0.0815729 | − | 0.996667i | \(-0.474006\pi\) | ||||
0.0815729 | + | 0.996667i | \(0.474006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.1574 | −1.12094 | −0.560468 | − | 0.828176i | \(-0.689379\pi\) | ||||
−0.560468 | + | 0.828176i | \(0.689379\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.858877 | −0.0299023 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.0811 | 0.385326 | 0.192663 | − | 0.981265i | \(-0.438288\pi\) | ||||
0.192663 | + | 0.981265i | \(0.438288\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.8575 | 1.17592 | 0.587960 | − | 0.808890i | \(-0.299931\pi\) | ||||
0.587960 | + | 0.808890i | \(0.299931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.66247 | −0.0923602 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.6501 | −0.750130 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.2580 | 0.977910 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.0700 | −0.417200 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.4869 | 0.776335 | 0.388167 | − | 0.921589i | \(-0.373108\pi\) | ||||
0.388167 | + | 0.921589i | \(0.373108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8944 | −0.996359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.49817 | 0.292693 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.1679 | −0.728197 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.58508 | 0.0888244 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.88020 | 0.236128 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.23600 | 0.282326 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3748 | −0.526424 | −0.263212 | − | 0.964738i | \(-0.584782\pi\) | ||||
−0.263212 | + | 0.964738i | \(0.584782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.28796 | 0.215044 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.0666 | −0.685461 | −0.342731 | − | 0.939434i | \(-0.611352\pi\) | ||||
−0.342731 | + | 0.939434i | \(0.611352\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.6464 | 1.89863 | 0.949316 | − | 0.314324i | \(-0.101778\pi\) | ||||
0.949316 | + | 0.314324i | \(0.101778\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.6732 | −0.363742 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.38734 | 0.251468 | 0.125734 | − | 0.992064i | \(-0.459871\pi\) | ||||
0.125734 | + | 0.992064i | \(0.459871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1414 | 0.752829 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.28661 | 0.213504 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.53671 | 0.119975 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.2397 | 0.448609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.5676 | −0.865331 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.2274 | 0.616200 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.6251 | −1.13544 | −0.567719 | − | 0.823222i | \(-0.692174\pi\) | ||||
−0.567719 | + | 0.823222i | \(0.692174\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.21038 | −0.108283 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1146 | −0.509223 | −0.254611 | − | 0.967043i | \(-0.581948\pi\) | ||||
−0.254611 | + | 0.967043i | \(0.581948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.8924 | 1.74632 | 0.873159 | − | 0.487436i | \(-0.162068\pi\) | ||||
0.873159 | + | 0.487436i | \(0.162068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.385977 | −0.0129745 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.6676 | 1.19760 | 0.598801 | − | 0.800898i | \(-0.295644\pi\) | ||||
0.598801 | + | 0.800898i | \(0.295644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.46354 | −0.149702 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.4765 | −0.752991 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.89204 | 0.0967785 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.8478 | 0.897424 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.1561 | −0.339103 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.24865 | −0.0416447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.91026 | −0.0969547 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.36711 | 0.145328 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.7632 | 1.12233 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7811 | −0.391185 | −0.195592 | − | 0.980685i | \(-0.562663\pi\) | ||||
−0.195592 | + | 0.980685i | \(0.562663\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.5118 | 0.945677 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4484 | −0.346172 | −0.173086 | − | 0.984907i | \(-0.555374\pi\) | ||||
−0.173086 | + | 0.984907i | \(0.555374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.4114 | 0.840996 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.6974 | −0.386706 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.0128 | −1.09018 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.2675 | −0.437654 | −0.218827 | − | 0.975764i | \(-0.570223\pi\) | ||||
−0.218827 | + | 0.975764i | \(0.570223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.55938 | −0.314992 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.6615 | −0.449675 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.925281 | −0.0304230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.2058 | −0.696491 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.4918 | −0.705122 | −0.352561 | − | 0.935789i | \(-0.614689\pi\) | ||||
−0.352561 | + | 0.935789i | \(0.614689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.06262 | −0.133147 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.9432 | −0.489219 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.9608 | 1.43767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.4503 | −1.61547 | −0.807736 | − | 0.589544i | \(-0.799307\pi\) | ||||
−0.807736 | + | 0.589544i | \(0.799307\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.03315 | −0.164251 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0226 | −0.391926 | −0.195963 | − | 0.980611i | \(-0.562783\pi\) | ||||
−0.195963 | + | 0.980611i | \(0.562783\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.2597 | 1.44129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.5572 | 0.408486 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.52851 | −0.244644 | −0.122322 | − | 0.992490i | \(-0.539034\pi\) | ||||
−0.122322 | + | 0.992490i | \(0.539034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.1260 | −0.718242 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.2642 | 0.332839 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.3137 | 1.46786 | 0.733928 | − | 0.679227i | \(-0.237685\pi\) | ||||
0.733928 | + | 0.679227i | \(0.237685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.9878 | −1.22926 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.633829 | 0.0204888 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5001 | −0.532817 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.2356 | −0.523730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.17524 | −0.166770 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.2695 | 1.42509 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.5612 | −0.339626 | −0.169813 | − | 0.985476i | \(-0.554316\pi\) | ||||
−0.169813 | + | 0.985476i | \(0.554316\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.93896 | 0.0944131 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.9450 | −0.575882 | −0.287941 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287941 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.6867 | −0.534951 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.14100 | 0.0365412 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56.0463 | 1.79308 | 0.896541 | − | 0.442961i | \(-0.146072\pi\) | ||||
0.896541 | + | 0.442961i | \(0.146072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.35450 | 0.0432900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.3009 | 0.680085 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31.9561 | −1.01924 | −0.509621 | − | 0.860399i | \(-0.670215\pi\) | ||||
−0.509621 | + | 0.860399i | \(0.670215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.8310 | 1.55588 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.73354 | 0.0870096 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.1095 | −0.575849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.39318 | 0.298384 | 0.149192 | − | 0.988808i | \(-0.452333\pi\) | ||||
0.149192 | + | 0.988808i | \(0.452333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.1400 | 0.448719 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0169 | 0.539472 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.1148 | −1.14377 | −0.571884 | − | 0.820335i | \(-0.693787\pi\) | ||||
−0.571884 | + | 0.820335i | \(0.693787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.60058 | 0.208833 |
(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 | 6004.2.a.g.1.17 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.17 | ✓ | 27 | 1.1 | even | 1 | trivial |