Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46418 | −1.03533 | −0.517665 | − | 0.855584i | \(-0.673198\pi\) | ||||
−0.517665 | + | 0.855584i | \(0.673198\pi\) | |||||||
\(3\) | −1.88953 | −1.09092 | −0.545462 | − | 0.838136i | \(-0.683646\pi\) | ||||
−0.545462 | + | 0.838136i | \(0.683646\pi\) | |||||||
\(4\) | 0.143813 | 0.0719064 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.76661 | 1.12946 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.71779 | 0.960882 | ||||||||
\(9\) | 0.570340 | 0.190113 | ||||||||
\(10\) | 1.46418 | 0.463013 | ||||||||
\(11\) | −0.769647 | −0.232057 | −0.116029 | − | 0.993246i | \(-0.537016\pi\) | ||||
−0.116029 | + | 0.993246i | \(0.537016\pi\) | |||||||
\(12\) | −0.271739 | −0.0784443 | ||||||||
\(13\) | 1.91852 | 0.532102 | 0.266051 | − | 0.963959i | \(-0.414281\pi\) | ||||
0.266051 | + | 0.963959i | \(0.414281\pi\) | |||||||
\(14\) | 1.46418 | 0.391318 | ||||||||
\(15\) | 1.88953 | 0.487876 | ||||||||
\(16\) | −4.26694 | −1.06674 | ||||||||
\(17\) | 2.52935 | 0.613458 | 0.306729 | − | 0.951797i | \(-0.400766\pi\) | ||||
0.306729 | + | 0.951797i | \(0.400766\pi\) | |||||||
\(18\) | −0.835078 | −0.196830 | ||||||||
\(19\) | 3.94494 | 0.905032 | 0.452516 | − | 0.891756i | \(-0.350527\pi\) | ||||
0.452516 | + | 0.891756i | \(0.350527\pi\) | |||||||
\(20\) | −0.143813 | −0.0321575 | ||||||||
\(21\) | 1.88953 | 0.412330 | ||||||||
\(22\) | 1.12690 | 0.240256 | ||||||||
\(23\) | −6.34157 | −1.32231 | −0.661154 | − | 0.750250i | \(-0.729933\pi\) | ||||
−0.661154 | + | 0.750250i | \(0.729933\pi\) | |||||||
\(24\) | −5.13535 | −1.04825 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.80906 | −0.550901 | ||||||||
\(27\) | 4.59093 | 0.883524 | ||||||||
\(28\) | −0.143813 | −0.0271780 | ||||||||
\(29\) | 0.0132311 | 0.00245696 | 0.00122848 | − | 0.999999i | \(-0.499609\pi\) | ||||
0.00122848 | + | 0.999999i | \(0.499609\pi\) | |||||||
\(30\) | −2.76661 | −0.505112 | ||||||||
\(31\) | −1.12165 | −0.201454 | −0.100727 | − | 0.994914i | \(-0.532117\pi\) | ||||
−0.100727 | + | 0.994914i | \(0.532117\pi\) | |||||||
\(32\) | 0.811986 | 0.143540 | ||||||||
\(33\) | 1.45427 | 0.253157 | ||||||||
\(34\) | −3.70342 | −0.635130 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.0820221 | 0.0136704 | ||||||||
\(37\) | 0.322083 | 0.0529501 | 0.0264751 | − | 0.999649i | \(-0.491572\pi\) | ||||
0.0264751 | + | 0.999649i | \(0.491572\pi\) | |||||||
\(38\) | −5.77609 | −0.937006 | ||||||||
\(39\) | −3.62511 | −0.580483 | ||||||||
\(40\) | −2.71779 | −0.429720 | ||||||||
\(41\) | 1.44715 | 0.226007 | 0.113003 | − | 0.993595i | \(-0.463953\pi\) | ||||
0.113003 | + | 0.993595i | \(0.463953\pi\) | |||||||
\(42\) | −2.76661 | −0.426897 | ||||||||
\(43\) | 11.2694 | 1.71857 | 0.859286 | − | 0.511496i | \(-0.170908\pi\) | ||||
0.859286 | + | 0.511496i | \(0.170908\pi\) | |||||||
\(44\) | −0.110685 | −0.0166864 | ||||||||
\(45\) | −0.570340 | −0.0850212 | ||||||||
\(46\) | 9.28517 | 1.36902 | ||||||||
\(47\) | −10.0385 | −1.46427 | −0.732135 | − | 0.681159i | \(-0.761476\pi\) | ||||
−0.732135 | + | 0.681159i | \(0.761476\pi\) | |||||||
\(48\) | 8.06254 | 1.16373 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.46418 | −0.207066 | ||||||||
\(51\) | −4.77929 | −0.669235 | ||||||||
\(52\) | 0.275908 | 0.0382615 | ||||||||
\(53\) | 11.5769 | 1.59020 | 0.795101 | − | 0.606477i | \(-0.207418\pi\) | ||||
0.795101 | + | 0.606477i | \(0.207418\pi\) | |||||||
\(54\) | −6.72193 | −0.914738 | ||||||||
\(55\) | 0.769647 | 0.103779 | ||||||||
\(56\) | −2.71779 | −0.363179 | ||||||||
\(57\) | −7.45410 | −0.987320 | ||||||||
\(58\) | −0.0193727 | −0.00254376 | ||||||||
\(59\) | 8.40858 | 1.09470 | 0.547352 | − | 0.836902i | \(-0.315636\pi\) | ||||
0.547352 | + | 0.836902i | \(0.315636\pi\) | |||||||
\(60\) | 0.271739 | 0.0350814 | ||||||||
\(61\) | 10.5914 | 1.35609 | 0.678046 | − | 0.735019i | \(-0.262827\pi\) | ||||
0.678046 | + | 0.735019i | \(0.262827\pi\) | |||||||
\(62\) | 1.64229 | 0.208571 | ||||||||
\(63\) | −0.570340 | −0.0718561 | ||||||||
\(64\) | 7.34500 | 0.918124 | ||||||||
\(65\) | −1.91852 | −0.237963 | ||||||||
\(66\) | −2.12931 | −0.262101 | ||||||||
\(67\) | 9.82891 | 1.20079 | 0.600396 | − | 0.799703i | \(-0.295010\pi\) | ||||
0.600396 | + | 0.799703i | \(0.295010\pi\) | |||||||
\(68\) | 0.363753 | 0.0441115 | ||||||||
\(69\) | 11.9826 | 1.44254 | ||||||||
\(70\) | −1.46418 | −0.175003 | ||||||||
\(71\) | 11.9043 | 1.41278 | 0.706389 | − | 0.707823i | \(-0.250323\pi\) | ||||
0.706389 | + | 0.707823i | \(0.250323\pi\) | |||||||
\(72\) | 1.55006 | 0.182677 | ||||||||
\(73\) | −7.51649 | −0.879738 | −0.439869 | − | 0.898062i | \(-0.644975\pi\) | ||||
−0.439869 | + | 0.898062i | \(0.644975\pi\) | |||||||
\(74\) | −0.471586 | −0.0548208 | ||||||||
\(75\) | −1.88953 | −0.218185 | ||||||||
\(76\) | 0.567333 | 0.0650775 | ||||||||
\(77\) | 0.769647 | 0.0877094 | ||||||||
\(78\) | 5.30781 | 0.600991 | ||||||||
\(79\) | −13.3557 | −1.50263 | −0.751317 | − | 0.659941i | \(-0.770581\pi\) | ||||
−0.751317 | + | 0.659941i | \(0.770581\pi\) | |||||||
\(80\) | 4.26694 | 0.477059 | ||||||||
\(81\) | −10.3857 | −1.15397 | ||||||||
\(82\) | −2.11888 | −0.233991 | ||||||||
\(83\) | −4.86670 | −0.534190 | −0.267095 | − | 0.963670i | \(-0.586064\pi\) | ||||
−0.267095 | + | 0.963670i | \(0.586064\pi\) | |||||||
\(84\) | 0.271739 | 0.0296492 | ||||||||
\(85\) | −2.52935 | −0.274347 | ||||||||
\(86\) | −16.5004 | −1.77929 | ||||||||
\(87\) | −0.0250006 | −0.00268035 | ||||||||
\(88\) | −2.09174 | −0.222980 | ||||||||
\(89\) | 3.44228 | 0.364881 | 0.182440 | − | 0.983217i | \(-0.441600\pi\) | ||||
0.182440 | + | 0.983217i | \(0.441600\pi\) | |||||||
\(90\) | 0.835078 | 0.0880250 | ||||||||
\(91\) | −1.91852 | −0.201116 | ||||||||
\(92\) | −0.911998 | −0.0950823 | ||||||||
\(93\) | 2.11939 | 0.219770 | ||||||||
\(94\) | 14.6982 | 1.51600 | ||||||||
\(95\) | −3.94494 | −0.404742 | ||||||||
\(96\) | −1.53428 | −0.156591 | ||||||||
\(97\) | −11.6821 | −1.18614 | −0.593069 | − | 0.805152i | \(-0.702084\pi\) | ||||
−0.593069 | + | 0.805152i | \(0.702084\pi\) | |||||||
\(98\) | −1.46418 | −0.147904 | ||||||||
\(99\) | −0.438960 | −0.0441172 | ||||||||
\(100\) | 0.143813 | 0.0143813 | ||||||||
\(101\) | −2.74927 | −0.273562 | −0.136781 | − | 0.990601i | \(-0.543676\pi\) | ||||
−0.136781 | + | 0.990601i | \(0.543676\pi\) | |||||||
\(102\) | 6.99773 | 0.692879 | ||||||||
\(103\) | −0.582543 | −0.0573997 | −0.0286998 | − | 0.999588i | \(-0.509137\pi\) | ||||
−0.0286998 | + | 0.999588i | \(0.509137\pi\) | |||||||
\(104\) | 5.21413 | 0.511288 | ||||||||
\(105\) | −1.88953 | −0.184400 | ||||||||
\(106\) | −16.9506 | −1.64638 | ||||||||
\(107\) | 3.23972 | 0.313196 | 0.156598 | − | 0.987662i | \(-0.449947\pi\) | ||||
0.156598 | + | 0.987662i | \(0.449947\pi\) | |||||||
\(108\) | 0.660234 | 0.0635310 | ||||||||
\(109\) | 1.52795 | 0.146351 | 0.0731757 | − | 0.997319i | \(-0.476687\pi\) | ||||
0.0731757 | + | 0.997319i | \(0.476687\pi\) | |||||||
\(110\) | −1.12690 | −0.107446 | ||||||||
\(111\) | −0.608587 | −0.0577645 | ||||||||
\(112\) | 4.26694 | 0.403188 | ||||||||
\(113\) | −14.7035 | −1.38319 | −0.691595 | − | 0.722285i | \(-0.743092\pi\) | ||||
−0.691595 | + | 0.722285i | \(0.743092\pi\) | |||||||
\(114\) | 10.9141 | 1.02220 | ||||||||
\(115\) | 6.34157 | 0.591354 | ||||||||
\(116\) | 0.00190280 | 0.000176671 0 | ||||||||
\(117\) | 1.09421 | 0.101160 | ||||||||
\(118\) | −12.3117 | −1.13338 | ||||||||
\(119\) | −2.52935 | −0.231865 | ||||||||
\(120\) | 5.13535 | 0.468791 | ||||||||
\(121\) | −10.4076 | −0.946149 | ||||||||
\(122\) | −15.5077 | −1.40400 | ||||||||
\(123\) | −2.73444 | −0.246556 | ||||||||
\(124\) | −0.161307 | −0.0144858 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.835078 | 0.0743947 | ||||||||
\(127\) | 19.0927 | 1.69420 | 0.847102 | − | 0.531430i | \(-0.178345\pi\) | ||||
0.847102 | + | 0.531430i | \(0.178345\pi\) | |||||||
\(128\) | −12.3783 | −1.09410 | ||||||||
\(129\) | −21.2940 | −1.87483 | ||||||||
\(130\) | 2.80906 | 0.246370 | ||||||||
\(131\) | −20.0269 | −1.74976 | −0.874881 | − | 0.484337i | \(-0.839061\pi\) | ||||
−0.874881 | + | 0.484337i | \(0.839061\pi\) | |||||||
\(132\) | 0.209143 | 0.0182036 | ||||||||
\(133\) | −3.94494 | −0.342070 | ||||||||
\(134\) | −14.3913 | −1.24322 | ||||||||
\(135\) | −4.59093 | −0.395124 | ||||||||
\(136\) | 6.87423 | 0.589461 | ||||||||
\(137\) | 0.958552 | 0.0818947 | 0.0409473 | − | 0.999161i | \(-0.486962\pi\) | ||||
0.0409473 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(138\) | −17.5447 | −1.49350 | ||||||||
\(139\) | −6.50772 | −0.551978 | −0.275989 | − | 0.961161i | \(-0.589005\pi\) | ||||
−0.275989 | + | 0.961161i | \(0.589005\pi\) | |||||||
\(140\) | 0.143813 | 0.0121544 | ||||||||
\(141\) | 18.9682 | 1.59741 | ||||||||
\(142\) | −17.4300 | −1.46269 | ||||||||
\(143\) | −1.47659 | −0.123478 | ||||||||
\(144\) | −2.43361 | −0.202801 | ||||||||
\(145\) | −0.0132311 | −0.00109878 | ||||||||
\(146\) | 11.0055 | 0.910819 | ||||||||
\(147\) | −1.88953 | −0.155846 | ||||||||
\(148\) | 0.0463196 | 0.00380745 | ||||||||
\(149\) | −0.640380 | −0.0524620 | −0.0262310 | − | 0.999656i | \(-0.508351\pi\) | ||||
−0.0262310 | + | 0.999656i | \(0.508351\pi\) | |||||||
\(150\) | 2.76661 | 0.225893 | ||||||||
\(151\) | −7.01626 | −0.570975 | −0.285488 | − | 0.958382i | \(-0.592156\pi\) | ||||
−0.285488 | + | 0.958382i | \(0.592156\pi\) | |||||||
\(152\) | 10.7215 | 0.869629 | ||||||||
\(153\) | 1.44259 | 0.116626 | ||||||||
\(154\) | −1.12690 | −0.0908081 | ||||||||
\(155\) | 1.12165 | 0.0900928 | ||||||||
\(156\) | −0.521337 | −0.0417404 | ||||||||
\(157\) | 20.0864 | 1.60307 | 0.801535 | − | 0.597947i | \(-0.204017\pi\) | ||||
0.801535 | + | 0.597947i | \(0.204017\pi\) | |||||||
\(158\) | 19.5551 | 1.55572 | ||||||||
\(159\) | −21.8749 | −1.73479 | ||||||||
\(160\) | −0.811986 | −0.0641932 | ||||||||
\(161\) | 6.34157 | 0.499785 | ||||||||
\(162\) | 15.2065 | 1.19474 | ||||||||
\(163\) | 10.5575 | 0.826926 | 0.413463 | − | 0.910521i | \(-0.364319\pi\) | ||||
0.413463 | + | 0.910521i | \(0.364319\pi\) | |||||||
\(164\) | 0.208119 | 0.0162513 | ||||||||
\(165\) | −1.45427 | −0.113215 | ||||||||
\(166\) | 7.12571 | 0.553063 | ||||||||
\(167\) | −18.1655 | −1.40569 | −0.702845 | − | 0.711343i | \(-0.748087\pi\) | ||||
−0.702845 | + | 0.711343i | \(0.748087\pi\) | |||||||
\(168\) | 5.13535 | 0.396201 | ||||||||
\(169\) | −9.31927 | −0.716867 | ||||||||
\(170\) | 3.70342 | 0.284039 | ||||||||
\(171\) | 2.24996 | 0.172059 | ||||||||
\(172\) | 1.62069 | 0.123576 | ||||||||
\(173\) | 10.6660 | 0.810920 | 0.405460 | − | 0.914113i | \(-0.367111\pi\) | ||||
0.405460 | + | 0.914113i | \(0.367111\pi\) | |||||||
\(174\) | 0.0366054 | 0.00277504 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 3.28404 | 0.247544 | ||||||||
\(177\) | −15.8883 | −1.19424 | ||||||||
\(178\) | −5.04010 | −0.377772 | ||||||||
\(179\) | −13.4786 | −1.00744 | −0.503721 | − | 0.863867i | \(-0.668036\pi\) | ||||
−0.503721 | + | 0.863867i | \(0.668036\pi\) | |||||||
\(180\) | −0.0820221 | −0.00611357 | ||||||||
\(181\) | −4.65420 | −0.345944 | −0.172972 | − | 0.984927i | \(-0.555337\pi\) | ||||
−0.172972 | + | 0.984927i | \(0.555337\pi\) | |||||||
\(182\) | 2.80906 | 0.208221 | ||||||||
\(183\) | −20.0129 | −1.47939 | ||||||||
\(184\) | −17.2350 | −1.27058 | ||||||||
\(185\) | −0.322083 | −0.0236800 | ||||||||
\(186\) | −3.10316 | −0.227535 | ||||||||
\(187\) | −1.94671 | −0.142357 | ||||||||
\(188\) | −1.44367 | −0.105290 | ||||||||
\(189\) | −4.59093 | −0.333941 | ||||||||
\(190\) | 5.77609 | 0.419042 | ||||||||
\(191\) | −1.02369 | −0.0740715 | −0.0370357 | − | 0.999314i | \(-0.511792\pi\) | ||||
−0.0370357 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(192\) | −13.8786 | −1.00160 | ||||||||
\(193\) | 22.9306 | 1.65058 | 0.825289 | − | 0.564710i | \(-0.191012\pi\) | ||||
0.825289 | + | 0.564710i | \(0.191012\pi\) | |||||||
\(194\) | 17.1047 | 1.22804 | ||||||||
\(195\) | 3.62511 | 0.259600 | ||||||||
\(196\) | 0.143813 | 0.0102723 | ||||||||
\(197\) | 5.61528 | 0.400072 | 0.200036 | − | 0.979789i | \(-0.435894\pi\) | ||||
0.200036 | + | 0.979789i | \(0.435894\pi\) | |||||||
\(198\) | 0.642716 | 0.0456758 | ||||||||
\(199\) | 10.2793 | 0.728680 | 0.364340 | − | 0.931266i | \(-0.381295\pi\) | ||||
0.364340 | + | 0.931266i | \(0.381295\pi\) | |||||||
\(200\) | 2.71779 | 0.192176 | ||||||||
\(201\) | −18.5721 | −1.30997 | ||||||||
\(202\) | 4.02541 | 0.283227 | ||||||||
\(203\) | −0.0132311 | −0.000928642 0 | ||||||||
\(204\) | −0.687323 | −0.0481223 | ||||||||
\(205\) | −1.44715 | −0.101073 | ||||||||
\(206\) | 0.852946 | 0.0594275 | ||||||||
\(207\) | −3.61685 | −0.251388 | ||||||||
\(208\) | −8.18623 | −0.567613 | ||||||||
\(209\) | −3.03621 | −0.210019 | ||||||||
\(210\) | 2.76661 | 0.190914 | ||||||||
\(211\) | −19.5451 | −1.34554 | −0.672769 | − | 0.739853i | \(-0.734895\pi\) | ||||
−0.672769 | + | 0.739853i | \(0.734895\pi\) | |||||||
\(212\) | 1.66490 | 0.114346 | ||||||||
\(213\) | −22.4936 | −1.54123 | ||||||||
\(214\) | −4.74353 | −0.324261 | ||||||||
\(215\) | −11.2694 | −0.768568 | ||||||||
\(216\) | 12.4772 | 0.848963 | ||||||||
\(217\) | 1.12165 | 0.0761423 | ||||||||
\(218\) | −2.23719 | −0.151522 | ||||||||
\(219\) | 14.2027 | 0.959727 | ||||||||
\(220\) | 0.110685 | 0.00746238 | ||||||||
\(221\) | 4.85262 | 0.326422 | ||||||||
\(222\) | 0.891079 | 0.0598053 | ||||||||
\(223\) | 16.7732 | 1.12322 | 0.561610 | − | 0.827402i | \(-0.310182\pi\) | ||||
0.561610 | + | 0.827402i | \(0.310182\pi\) | |||||||
\(224\) | −0.811986 | −0.0542531 | ||||||||
\(225\) | 0.570340 | 0.0380227 | ||||||||
\(226\) | 21.5285 | 1.43206 | ||||||||
\(227\) | 6.28497 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(228\) | −1.07199 | −0.0709946 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −9.28517 | −0.612246 | ||||||||
\(231\) | −1.45427 | −0.0956843 | ||||||||
\(232\) | 0.0359593 | 0.00236085 | ||||||||
\(233\) | 24.2098 | 1.58604 | 0.793018 | − | 0.609198i | \(-0.208509\pi\) | ||||
0.793018 | + | 0.609198i | \(0.208509\pi\) | |||||||
\(234\) | −1.60212 | −0.104734 | ||||||||
\(235\) | 10.0385 | 0.654842 | ||||||||
\(236\) | 1.20926 | 0.0787162 | ||||||||
\(237\) | 25.2361 | 1.63926 | ||||||||
\(238\) | 3.70342 | 0.240057 | ||||||||
\(239\) | −21.2084 | −1.37186 | −0.685929 | − | 0.727669i | \(-0.740604\pi\) | ||||
−0.685929 | + | 0.727669i | \(0.740604\pi\) | |||||||
\(240\) | −8.06254 | −0.520434 | ||||||||
\(241\) | −23.0932 | −1.48756 | −0.743781 | − | 0.668423i | \(-0.766969\pi\) | ||||
−0.743781 | + | 0.668423i | \(0.766969\pi\) | |||||||
\(242\) | 15.2386 | 0.979576 | ||||||||
\(243\) | 5.85142 | 0.375369 | ||||||||
\(244\) | 1.52318 | 0.0975117 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 4.00370 | 0.255267 | ||||||||
\(247\) | 7.56846 | 0.481570 | ||||||||
\(248\) | −3.04839 | −0.193573 | ||||||||
\(249\) | 9.19581 | 0.582760 | ||||||||
\(250\) | 1.46418 | 0.0926027 | ||||||||
\(251\) | 12.4348 | 0.784878 | 0.392439 | − | 0.919778i | \(-0.371631\pi\) | ||||
0.392439 | + | 0.919778i | \(0.371631\pi\) | |||||||
\(252\) | −0.0820221 | −0.00516691 | ||||||||
\(253\) | 4.88077 | 0.306851 | ||||||||
\(254\) | −27.9551 | −1.75406 | ||||||||
\(255\) | 4.77929 | 0.299291 | ||||||||
\(256\) | 3.43409 | 0.214630 | ||||||||
\(257\) | −21.7890 | −1.35916 | −0.679582 | − | 0.733600i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733600i | \(0.737839\pi\) | |||||||
\(258\) | 31.1781 | 1.94107 | ||||||||
\(259\) | −0.322083 | −0.0200133 | ||||||||
\(260\) | −0.275908 | −0.0171111 | ||||||||
\(261\) | 0.00754623 | 0.000467100 0 | ||||||||
\(262\) | 29.3230 | 1.81158 | ||||||||
\(263\) | −17.4968 | −1.07890 | −0.539450 | − | 0.842018i | \(-0.681368\pi\) | ||||
−0.539450 | + | 0.842018i | \(0.681368\pi\) | |||||||
\(264\) | 3.95241 | 0.243254 | ||||||||
\(265\) | −11.5769 | −0.711160 | ||||||||
\(266\) | 5.77609 | 0.354155 | ||||||||
\(267\) | −6.50430 | −0.398057 | ||||||||
\(268\) | 1.41352 | 0.0863446 | ||||||||
\(269\) | 6.69885 | 0.408436 | 0.204218 | − | 0.978925i | \(-0.434535\pi\) | ||||
0.204218 | + | 0.978925i | \(0.434535\pi\) | |||||||
\(270\) | 6.72193 | 0.409083 | ||||||||
\(271\) | −29.1923 | −1.77330 | −0.886652 | − | 0.462438i | \(-0.846975\pi\) | ||||
−0.886652 | + | 0.462438i | \(0.846975\pi\) | |||||||
\(272\) | −10.7926 | −0.654397 | ||||||||
\(273\) | 3.62511 | 0.219402 | ||||||||
\(274\) | −1.40349 | −0.0847879 | ||||||||
\(275\) | −0.769647 | −0.0464115 | ||||||||
\(276\) | 1.72325 | 0.103728 | ||||||||
\(277\) | 7.87863 | 0.473381 | 0.236691 | − | 0.971585i | \(-0.423937\pi\) | ||||
0.236691 | + | 0.971585i | \(0.423937\pi\) | |||||||
\(278\) | 9.52845 | 0.571479 | ||||||||
\(279\) | −0.639720 | −0.0382990 | ||||||||
\(280\) | 2.71779 | 0.162419 | ||||||||
\(281\) | −12.6238 | −0.753075 | −0.376538 | − | 0.926401i | \(-0.622885\pi\) | ||||
−0.376538 | + | 0.926401i | \(0.622885\pi\) | |||||||
\(282\) | −27.7727 | −1.65384 | ||||||||
\(283\) | −15.9248 | −0.946632 | −0.473316 | − | 0.880893i | \(-0.656943\pi\) | ||||
−0.473316 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(284\) | 1.71199 | 0.101588 | ||||||||
\(285\) | 7.45410 | 0.441543 | ||||||||
\(286\) | 2.16198 | 0.127841 | ||||||||
\(287\) | −1.44715 | −0.0854226 | ||||||||
\(288\) | 0.463108 | 0.0272889 | ||||||||
\(289\) | −10.6024 | −0.623670 | ||||||||
\(290\) | 0.0193727 | 0.00113760 | ||||||||
\(291\) | 22.0737 | 1.29399 | ||||||||
\(292\) | −1.08097 | −0.0632588 | ||||||||
\(293\) | 11.0663 | 0.646499 | 0.323250 | − | 0.946314i | \(-0.395225\pi\) | ||||
0.323250 | + | 0.946314i | \(0.395225\pi\) | |||||||
\(294\) | 2.76661 | 0.161352 | ||||||||
\(295\) | −8.40858 | −0.489567 | ||||||||
\(296\) | 0.875353 | 0.0508788 | ||||||||
\(297\) | −3.53339 | −0.205028 | ||||||||
\(298\) | 0.937630 | 0.0543154 | ||||||||
\(299\) | −12.1664 | −0.703603 | ||||||||
\(300\) | −0.271739 | −0.0156889 | ||||||||
\(301\) | −11.2694 | −0.649559 | ||||||||
\(302\) | 10.2730 | 0.591148 | ||||||||
\(303\) | 5.19483 | 0.298435 | ||||||||
\(304\) | −16.8328 | −0.965430 | ||||||||
\(305\) | −10.5914 | −0.606463 | ||||||||
\(306\) | −2.11221 | −0.120747 | ||||||||
\(307\) | −32.9383 | −1.87989 | −0.939944 | − | 0.341329i | \(-0.889123\pi\) | ||||
−0.939944 | + | 0.341329i | \(0.889123\pi\) | |||||||
\(308\) | 0.110685 | 0.00630687 | ||||||||
\(309\) | 1.10074 | 0.0626186 | ||||||||
\(310\) | −1.64229 | −0.0932757 | ||||||||
\(311\) | −12.1127 | −0.686848 | −0.343424 | − | 0.939180i | \(-0.611587\pi\) | ||||
−0.343424 | + | 0.939180i | \(0.611587\pi\) | |||||||
\(312\) | −9.85228 | −0.557776 | ||||||||
\(313\) | 17.0096 | 0.961442 | 0.480721 | − | 0.876874i | \(-0.340375\pi\) | ||||
0.480721 | + | 0.876874i | \(0.340375\pi\) | |||||||
\(314\) | −29.4101 | −1.65971 | ||||||||
\(315\) | 0.570340 | 0.0321350 | ||||||||
\(316\) | −1.92072 | −0.108049 | ||||||||
\(317\) | 33.2939 | 1.86997 | 0.934985 | − | 0.354687i | \(-0.115412\pi\) | ||||
0.934985 | + | 0.354687i | \(0.115412\pi\) | |||||||
\(318\) | 32.0286 | 1.79608 | ||||||||
\(319\) | −0.0101833 | −0.000570155 0 | ||||||||
\(320\) | −7.34500 | −0.410598 | ||||||||
\(321\) | −6.12157 | −0.341673 | ||||||||
\(322\) | −9.28517 | −0.517442 | ||||||||
\(323\) | 9.97814 | 0.555199 | ||||||||
\(324\) | −1.49360 | −0.0829778 | ||||||||
\(325\) | 1.91852 | 0.106420 | ||||||||
\(326\) | −15.4580 | −0.856140 | ||||||||
\(327\) | −2.88712 | −0.159658 | ||||||||
\(328\) | 3.93304 | 0.217166 | ||||||||
\(329\) | 10.0385 | 0.553442 | ||||||||
\(330\) | 2.12931 | 0.117215 | ||||||||
\(331\) | 0.893604 | 0.0491169 | 0.0245584 | − | 0.999698i | \(-0.492182\pi\) | ||||
0.0245584 | + | 0.999698i | \(0.492182\pi\) | |||||||
\(332\) | −0.699894 | −0.0384117 | ||||||||
\(333\) | 0.183697 | 0.0100665 | ||||||||
\(334\) | 26.5975 | 1.45535 | ||||||||
\(335\) | −9.82891 | −0.537011 | ||||||||
\(336\) | −8.06254 | −0.439847 | ||||||||
\(337\) | 19.7816 | 1.07757 | 0.538786 | − | 0.842442i | \(-0.318883\pi\) | ||||
0.538786 | + | 0.842442i | \(0.318883\pi\) | |||||||
\(338\) | 13.6451 | 0.742193 | ||||||||
\(339\) | 27.7828 | 1.50895 | ||||||||
\(340\) | −0.363753 | −0.0197273 | ||||||||
\(341\) | 0.863272 | 0.0467488 | ||||||||
\(342\) | −3.29433 | −0.178137 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 30.6279 | 1.65134 | ||||||||
\(345\) | −11.9826 | −0.645122 | ||||||||
\(346\) | −15.6169 | −0.839569 | ||||||||
\(347\) | −3.00075 | −0.161089 | −0.0805444 | − | 0.996751i | \(-0.525666\pi\) | ||||
−0.0805444 | + | 0.996751i | \(0.525666\pi\) | |||||||
\(348\) | −0.00359541 | −0.000192734 0 | ||||||||
\(349\) | 1.20119 | 0.0642981 | 0.0321491 | − | 0.999483i | \(-0.489765\pi\) | ||||
0.0321491 | + | 0.999483i | \(0.489765\pi\) | |||||||
\(350\) | 1.46418 | 0.0782635 | ||||||||
\(351\) | 8.80780 | 0.470125 | ||||||||
\(352\) | −0.624943 | −0.0333096 | ||||||||
\(353\) | 19.6422 | 1.04545 | 0.522724 | − | 0.852502i | \(-0.324916\pi\) | ||||
0.522724 | + | 0.852502i | \(0.324916\pi\) | |||||||
\(354\) | 23.2633 | 1.23643 | ||||||||
\(355\) | −11.9043 | −0.631814 | ||||||||
\(356\) | 0.495043 | 0.0262372 | ||||||||
\(357\) | 4.77929 | 0.252947 | ||||||||
\(358\) | 19.7351 | 1.04303 | ||||||||
\(359\) | 11.6099 | 0.612749 | 0.306374 | − | 0.951911i | \(-0.400884\pi\) | ||||
0.306374 | + | 0.951911i | \(0.400884\pi\) | |||||||
\(360\) | −1.55006 | −0.0816954 | ||||||||
\(361\) | −3.43744 | −0.180918 | ||||||||
\(362\) | 6.81457 | 0.358166 | ||||||||
\(363\) | 19.6656 | 1.03218 | ||||||||
\(364\) | −0.275908 | −0.0144615 | ||||||||
\(365\) | 7.51649 | 0.393431 | ||||||||
\(366\) | 29.3023 | 1.53166 | ||||||||
\(367\) | −4.96078 | −0.258951 | −0.129475 | − | 0.991583i | \(-0.541329\pi\) | ||||
−0.129475 | + | 0.991583i | \(0.541329\pi\) | |||||||
\(368\) | 27.0591 | 1.41055 | ||||||||
\(369\) | 0.825367 | 0.0429669 | ||||||||
\(370\) | 0.471586 | 0.0245166 | ||||||||
\(371\) | −11.5769 | −0.601040 | ||||||||
\(372\) | 0.304795 | 0.0158029 | ||||||||
\(373\) | −15.7111 | −0.813489 | −0.406745 | − | 0.913542i | \(-0.633336\pi\) | ||||
−0.406745 | + | 0.913542i | \(0.633336\pi\) | |||||||
\(374\) | 2.85032 | 0.147387 | ||||||||
\(375\) | 1.88953 | 0.0975751 | ||||||||
\(376\) | −27.2826 | −1.40699 | ||||||||
\(377\) | 0.0253842 | 0.00130735 | ||||||||
\(378\) | 6.72193 | 0.345739 | ||||||||
\(379\) | 32.2233 | 1.65520 | 0.827601 | − | 0.561317i | \(-0.189705\pi\) | ||||
0.827601 | + | 0.561317i | \(0.189705\pi\) | |||||||
\(380\) | −0.567333 | −0.0291036 | ||||||||
\(381\) | −36.0763 | −1.84825 | ||||||||
\(382\) | 1.49886 | 0.0766883 | ||||||||
\(383\) | −9.02809 | −0.461314 | −0.230657 | − | 0.973035i | \(-0.574087\pi\) | ||||
−0.230657 | + | 0.973035i | \(0.574087\pi\) | |||||||
\(384\) | 23.3893 | 1.19358 | ||||||||
\(385\) | −0.769647 | −0.0392249 | ||||||||
\(386\) | −33.5744 | −1.70889 | ||||||||
\(387\) | 6.42740 | 0.326723 | ||||||||
\(388\) | −1.68004 | −0.0852909 | ||||||||
\(389\) | 24.8774 | 1.26134 | 0.630668 | − | 0.776053i | \(-0.282781\pi\) | ||||
0.630668 | + | 0.776053i | \(0.282781\pi\) | |||||||
\(390\) | −5.30781 | −0.268771 | ||||||||
\(391\) | −16.0400 | −0.811180 | ||||||||
\(392\) | 2.71779 | 0.137269 | ||||||||
\(393\) | 37.8416 | 1.90886 | ||||||||
\(394\) | −8.22177 | −0.414207 | ||||||||
\(395\) | 13.3557 | 0.671998 | ||||||||
\(396\) | −0.0631281 | −0.00317231 | ||||||||
\(397\) | 27.9280 | 1.40167 | 0.700833 | − | 0.713326i | \(-0.252812\pi\) | ||||
0.700833 | + | 0.713326i | \(0.252812\pi\) | |||||||
\(398\) | −15.0507 | −0.754424 | ||||||||
\(399\) | 7.45410 | 0.373172 | ||||||||
\(400\) | −4.26694 | −0.213347 | ||||||||
\(401\) | −25.6395 | −1.28037 | −0.640187 | − | 0.768219i | \(-0.721143\pi\) | ||||
−0.640187 | + | 0.768219i | \(0.721143\pi\) | |||||||
\(402\) | 27.1928 | 1.35625 | ||||||||
\(403\) | −2.15190 | −0.107194 | ||||||||
\(404\) | −0.395379 | −0.0196709 | ||||||||
\(405\) | 10.3857 | 0.516071 | ||||||||
\(406\) | 0.0193727 | 0.000961450 0 | ||||||||
\(407\) | −0.247890 | −0.0122875 | ||||||||
\(408\) | −12.9891 | −0.643056 | ||||||||
\(409\) | 23.9644 | 1.18497 | 0.592483 | − | 0.805583i | \(-0.298148\pi\) | ||||
0.592483 | + | 0.805583i | \(0.298148\pi\) | |||||||
\(410\) | 2.11888 | 0.104644 | ||||||||
\(411\) | −1.81122 | −0.0893408 | ||||||||
\(412\) | −0.0837771 | −0.00412740 | ||||||||
\(413\) | −8.40858 | −0.413759 | ||||||||
\(414\) | 5.29570 | 0.260270 | ||||||||
\(415\) | 4.86670 | 0.238897 | ||||||||
\(416\) | 1.55781 | 0.0763781 | ||||||||
\(417\) | 12.2966 | 0.602165 | ||||||||
\(418\) | 4.44555 | 0.217439 | ||||||||
\(419\) | −7.90795 | −0.386329 | −0.193164 | − | 0.981166i | \(-0.561875\pi\) | ||||
−0.193164 | + | 0.981166i | \(0.561875\pi\) | |||||||
\(420\) | −0.271739 | −0.0132595 | ||||||||
\(421\) | −27.1541 | −1.32341 | −0.661704 | − | 0.749765i | \(-0.730167\pi\) | ||||
−0.661704 | + | 0.749765i | \(0.730167\pi\) | |||||||
\(422\) | 28.6174 | 1.39307 | ||||||||
\(423\) | −5.72537 | −0.278377 | ||||||||
\(424\) | 31.4634 | 1.52800 | ||||||||
\(425\) | 2.52935 | 0.122692 | ||||||||
\(426\) | 32.9345 | 1.59568 | ||||||||
\(427\) | −10.5914 | −0.512555 | ||||||||
\(428\) | 0.465913 | 0.0225208 | ||||||||
\(429\) | 2.79006 | 0.134705 | ||||||||
\(430\) | 16.5004 | 0.795721 | ||||||||
\(431\) | −25.8805 | −1.24662 | −0.623311 | − | 0.781974i | \(-0.714213\pi\) | ||||
−0.623311 | + | 0.781974i | \(0.714213\pi\) | |||||||
\(432\) | −19.5892 | −0.942487 | ||||||||
\(433\) | 16.6908 | 0.802108 | 0.401054 | − | 0.916054i | \(-0.368644\pi\) | ||||
0.401054 | + | 0.916054i | \(0.368644\pi\) | |||||||
\(434\) | −1.64229 | −0.0788323 | ||||||||
\(435\) | 0.0250006 | 0.00119869 | ||||||||
\(436\) | 0.219739 | 0.0105236 | ||||||||
\(437\) | −25.0171 | −1.19673 | ||||||||
\(438\) | −20.7952 | −0.993633 | ||||||||
\(439\) | 26.8538 | 1.28166 | 0.640832 | − | 0.767681i | \(-0.278590\pi\) | ||||
0.640832 | + | 0.767681i | \(0.278590\pi\) | |||||||
\(440\) | 2.09174 | 0.0997196 | ||||||||
\(441\) | 0.570340 | 0.0271590 | ||||||||
\(442\) | −7.10509 | −0.337954 | ||||||||
\(443\) | −32.1592 | −1.52793 | −0.763965 | − | 0.645258i | \(-0.776750\pi\) | ||||
−0.763965 | + | 0.645258i | \(0.776750\pi\) | |||||||
\(444\) | −0.0875225 | −0.00415364 | ||||||||
\(445\) | −3.44228 | −0.163180 | ||||||||
\(446\) | −24.5590 | −1.16290 | ||||||||
\(447\) | 1.21002 | 0.0572320 | ||||||||
\(448\) | −7.34500 | −0.347018 | ||||||||
\(449\) | −3.72511 | −0.175799 | −0.0878994 | − | 0.996129i | \(-0.528015\pi\) | ||||
−0.0878994 | + | 0.996129i | \(0.528015\pi\) | |||||||
\(450\) | −0.835078 | −0.0393660 | ||||||||
\(451\) | −1.11379 | −0.0524466 | ||||||||
\(452\) | −2.11455 | −0.0994602 | ||||||||
\(453\) | 13.2575 | 0.622890 | ||||||||
\(454\) | −9.20231 | −0.431886 | ||||||||
\(455\) | 1.91852 | 0.0899417 | ||||||||
\(456\) | −20.2587 | −0.948698 | ||||||||
\(457\) | −22.5746 | −1.05599 | −0.527997 | − | 0.849246i | \(-0.677057\pi\) | ||||
−0.527997 | + | 0.849246i | \(0.677057\pi\) | |||||||
\(458\) | −1.46418 | −0.0684165 | ||||||||
\(459\) | 11.6121 | 0.542005 | ||||||||
\(460\) | 0.911998 | 0.0425221 | ||||||||
\(461\) | 27.0328 | 1.25904 | 0.629521 | − | 0.776983i | \(-0.283251\pi\) | ||||
0.629521 | + | 0.776983i | \(0.283251\pi\) | |||||||
\(462\) | 2.12931 | 0.0990647 | ||||||||
\(463\) | 4.32309 | 0.200911 | 0.100455 | − | 0.994942i | \(-0.467970\pi\) | ||||
0.100455 | + | 0.994942i | \(0.467970\pi\) | |||||||
\(464\) | −0.0564564 | −0.00262092 | ||||||||
\(465\) | −2.11939 | −0.0982843 | ||||||||
\(466\) | −35.4474 | −1.64207 | ||||||||
\(467\) | 4.23657 | 0.196045 | 0.0980224 | − | 0.995184i | \(-0.468748\pi\) | ||||
0.0980224 | + | 0.995184i | \(0.468748\pi\) | |||||||
\(468\) | 0.157361 | 0.00727403 | ||||||||
\(469\) | −9.82891 | −0.453857 | ||||||||
\(470\) | −14.6982 | −0.677977 | ||||||||
\(471\) | −37.9540 | −1.74883 | ||||||||
\(472\) | 22.8527 | 1.05188 | ||||||||
\(473\) | −8.67348 | −0.398807 | ||||||||
\(474\) | −36.9500 | −1.69717 | ||||||||
\(475\) | 3.94494 | 0.181006 | ||||||||
\(476\) | −0.363753 | −0.0166726 | ||||||||
\(477\) | 6.60274 | 0.302319 | ||||||||
\(478\) | 31.0528 | 1.42032 | ||||||||
\(479\) | 14.8047 | 0.676443 | 0.338222 | − | 0.941066i | \(-0.390175\pi\) | ||||
0.338222 | + | 0.941066i | \(0.390175\pi\) | |||||||
\(480\) | 1.53428 | 0.0700298 | ||||||||
\(481\) | 0.617924 | 0.0281749 | ||||||||
\(482\) | 33.8125 | 1.54012 | ||||||||
\(483\) | −11.9826 | −0.545228 | ||||||||
\(484\) | −1.49675 | −0.0680342 | ||||||||
\(485\) | 11.6821 | 0.530457 | ||||||||
\(486\) | −8.56751 | −0.388630 | ||||||||
\(487\) | 6.37497 | 0.288877 | 0.144439 | − | 0.989514i | \(-0.453862\pi\) | ||||
0.144439 | + | 0.989514i | \(0.453862\pi\) | |||||||
\(488\) | 28.7852 | 1.30305 | ||||||||
\(489\) | −19.9487 | −0.902112 | ||||||||
\(490\) | 1.46418 | 0.0661448 | ||||||||
\(491\) | 30.6198 | 1.38185 | 0.690925 | − | 0.722926i | \(-0.257203\pi\) | ||||
0.690925 | + | 0.722926i | \(0.257203\pi\) | |||||||
\(492\) | −0.393247 | −0.0177290 | ||||||||
\(493\) | 0.0334661 | 0.00150724 | ||||||||
\(494\) | −11.0816 | −0.498583 | ||||||||
\(495\) | 0.438960 | 0.0197298 | ||||||||
\(496\) | 4.78600 | 0.214898 | ||||||||
\(497\) | −11.9043 | −0.533980 | ||||||||
\(498\) | −13.4643 | −0.603349 | ||||||||
\(499\) | −43.0440 | −1.92691 | −0.963456 | − | 0.267866i | \(-0.913681\pi\) | ||||
−0.963456 | + | 0.267866i | \(0.913681\pi\) | |||||||
\(500\) | −0.143813 | −0.00643150 | ||||||||
\(501\) | 34.3244 | 1.53350 | ||||||||
\(502\) | −18.2068 | −0.812607 | ||||||||
\(503\) | 26.7587 | 1.19311 | 0.596556 | − | 0.802571i | \(-0.296535\pi\) | ||||
0.596556 | + | 0.802571i | \(0.296535\pi\) | |||||||
\(504\) | −1.55006 | −0.0690452 | ||||||||
\(505\) | 2.74927 | 0.122341 | ||||||||
\(506\) | −7.14631 | −0.317692 | ||||||||
\(507\) | 17.6091 | 0.782047 | ||||||||
\(508\) | 2.74577 | 0.121824 | ||||||||
\(509\) | 15.9496 | 0.706953 | 0.353477 | − | 0.935443i | \(-0.384999\pi\) | ||||
0.353477 | + | 0.935443i | \(0.384999\pi\) | |||||||
\(510\) | −6.99773 | −0.309865 | ||||||||
\(511\) | 7.51649 | 0.332510 | ||||||||
\(512\) | 19.7286 | 0.871888 | ||||||||
\(513\) | 18.1109 | 0.799617 | ||||||||
\(514\) | 31.9030 | 1.40718 | ||||||||
\(515\) | 0.582543 | 0.0256699 | ||||||||
\(516\) | −3.06234 | −0.134812 | ||||||||
\(517\) | 7.72613 | 0.339795 | ||||||||
\(518\) | 0.471586 | 0.0207203 | ||||||||
\(519\) | −20.1537 | −0.884651 | ||||||||
\(520\) | −5.21413 | −0.228655 | ||||||||
\(521\) | −2.30278 | −0.100887 | −0.0504433 | − | 0.998727i | \(-0.516063\pi\) | ||||
−0.0504433 | + | 0.998727i | \(0.516063\pi\) | |||||||
\(522\) | −0.0110490 | −0.000483602 0 | ||||||||
\(523\) | 15.1414 | 0.662088 | 0.331044 | − | 0.943615i | \(-0.392599\pi\) | ||||
0.331044 | + | 0.943615i | \(0.392599\pi\) | |||||||
\(524\) | −2.88013 | −0.125819 | ||||||||
\(525\) | 1.88953 | 0.0824660 | ||||||||
\(526\) | 25.6184 | 1.11702 | ||||||||
\(527\) | −2.83704 | −0.123583 | ||||||||
\(528\) | −6.20531 | −0.270051 | ||||||||
\(529\) | 17.2155 | 0.748498 | ||||||||
\(530\) | 16.9506 | 0.736285 | ||||||||
\(531\) | 4.79575 | 0.208118 | ||||||||
\(532\) | −0.567333 | −0.0245970 | ||||||||
\(533\) | 2.77639 | 0.120259 | ||||||||
\(534\) | 9.52344 | 0.412120 | ||||||||
\(535\) | −3.23972 | −0.140065 | ||||||||
\(536\) | 26.7129 | 1.15382 | ||||||||
\(537\) | 25.4684 | 1.09904 | ||||||||
\(538\) | −9.80830 | −0.422866 | ||||||||
\(539\) | −0.769647 | −0.0331511 | ||||||||
\(540\) | −0.660234 | −0.0284119 | ||||||||
\(541\) | −31.7684 | −1.36583 | −0.682916 | − | 0.730497i | \(-0.739288\pi\) | ||||
−0.682916 | + | 0.730497i | \(0.739288\pi\) | |||||||
\(542\) | 42.7426 | 1.83595 | ||||||||
\(543\) | 8.79427 | 0.377398 | ||||||||
\(544\) | 2.05380 | 0.0880559 | ||||||||
\(545\) | −1.52795 | −0.0654503 | ||||||||
\(546\) | −5.30781 | −0.227153 | ||||||||
\(547\) | 5.69976 | 0.243704 | 0.121852 | − | 0.992548i | \(-0.461117\pi\) | ||||
0.121852 | + | 0.992548i | \(0.461117\pi\) | |||||||
\(548\) | 0.137852 | 0.00588875 | ||||||||
\(549\) | 6.04071 | 0.257811 | ||||||||
\(550\) | 1.12690 | 0.0480511 | ||||||||
\(551\) | 0.0521960 | 0.00222362 | ||||||||
\(552\) | 32.5662 | 1.38611 | ||||||||
\(553\) | 13.3557 | 0.567942 | ||||||||
\(554\) | −11.5357 | −0.490105 | ||||||||
\(555\) | 0.608587 | 0.0258331 | ||||||||
\(556\) | −0.935893 | −0.0396907 | ||||||||
\(557\) | −32.6181 | −1.38207 | −0.691036 | − | 0.722821i | \(-0.742845\pi\) | ||||
−0.691036 | + | 0.722821i | \(0.742845\pi\) | |||||||
\(558\) | 0.936662 | 0.0396521 | ||||||||
\(559\) | 21.6206 | 0.914456 | ||||||||
\(560\) | −4.26694 | −0.180311 | ||||||||
\(561\) | 3.67837 | 0.155301 | ||||||||
\(562\) | 18.4835 | 0.779681 | ||||||||
\(563\) | −27.4771 | −1.15802 | −0.579011 | − | 0.815320i | \(-0.696561\pi\) | ||||
−0.579011 | + | 0.815320i | \(0.696561\pi\) | |||||||
\(564\) | 2.72786 | 0.114864 | ||||||||
\(565\) | 14.7035 | 0.618582 | ||||||||
\(566\) | 23.3167 | 0.980076 | ||||||||
\(567\) | 10.3857 | 0.436160 | ||||||||
\(568\) | 32.3533 | 1.35751 | ||||||||
\(569\) | 22.4018 | 0.939134 | 0.469567 | − | 0.882897i | \(-0.344410\pi\) | ||||
0.469567 | + | 0.882897i | \(0.344410\pi\) | |||||||
\(570\) | −10.9141 | −0.457142 | ||||||||
\(571\) | 40.6912 | 1.70287 | 0.851437 | − | 0.524457i | \(-0.175732\pi\) | ||||
0.851437 | + | 0.524457i | \(0.175732\pi\) | |||||||
\(572\) | −0.212352 | −0.00887887 | ||||||||
\(573\) | 1.93429 | 0.0808063 | ||||||||
\(574\) | 2.11888 | 0.0884405 | ||||||||
\(575\) | −6.34157 | −0.264462 | ||||||||
\(576\) | 4.18914 | 0.174548 | ||||||||
\(577\) | −17.9973 | −0.749237 | −0.374619 | − | 0.927179i | \(-0.622226\pi\) | ||||
−0.374619 | + | 0.927179i | \(0.622226\pi\) | |||||||
\(578\) | 15.5238 | 0.645703 | ||||||||
\(579\) | −43.3281 | −1.80065 | ||||||||
\(580\) | −0.00190280 | −7.90096e−5 0 | ||||||||
\(581\) | 4.86670 | 0.201905 | ||||||||
\(582\) | −32.3199 | −1.33970 | ||||||||
\(583\) | −8.91009 | −0.369018 | ||||||||
\(584\) | −20.4282 | −0.845325 | ||||||||
\(585\) | −1.09421 | −0.0452400 | ||||||||
\(586\) | −16.2030 | −0.669339 | ||||||||
\(587\) | 30.6407 | 1.26468 | 0.632338 | − | 0.774693i | \(-0.282095\pi\) | ||||
0.632338 | + | 0.774693i | \(0.282095\pi\) | |||||||
\(588\) | −0.271739 | −0.0112063 | ||||||||
\(589\) | −4.42483 | −0.182322 | ||||||||
\(590\) | 12.3117 | 0.506863 | ||||||||
\(591\) | −10.6103 | −0.436448 | ||||||||
\(592\) | −1.37431 | −0.0564838 | ||||||||
\(593\) | 34.1853 | 1.40382 | 0.701910 | − | 0.712265i | \(-0.252331\pi\) | ||||
0.701910 | + | 0.712265i | \(0.252331\pi\) | |||||||
\(594\) | 5.17351 | 0.212272 | ||||||||
\(595\) | 2.52935 | 0.103693 | ||||||||
\(596\) | −0.0920948 | −0.00377235 | ||||||||
\(597\) | −19.4231 | −0.794934 | ||||||||
\(598\) | 17.8138 | 0.728461 | ||||||||
\(599\) | 6.79367 | 0.277582 | 0.138791 | − | 0.990322i | \(-0.455678\pi\) | ||||
0.138791 | + | 0.990322i | \(0.455678\pi\) | |||||||
\(600\) | −5.13535 | −0.209650 | ||||||||
\(601\) | 6.73902 | 0.274891 | 0.137445 | − | 0.990509i | \(-0.456111\pi\) | ||||
0.137445 | + | 0.990509i | \(0.456111\pi\) | |||||||
\(602\) | 16.5004 | 0.672507 | ||||||||
\(603\) | 5.60582 | 0.228287 | ||||||||
\(604\) | −1.00903 | −0.0410568 | ||||||||
\(605\) | 10.4076 | 0.423131 | ||||||||
\(606\) | −7.60615 | −0.308979 | ||||||||
\(607\) | 7.00689 | 0.284401 | 0.142200 | − | 0.989838i | \(-0.454582\pi\) | ||||
0.142200 | + | 0.989838i | \(0.454582\pi\) | |||||||
\(608\) | 3.20324 | 0.129908 | ||||||||
\(609\) | 0.0250006 | 0.00101308 | ||||||||
\(610\) | 15.5077 | 0.627889 | ||||||||
\(611\) | −19.2592 | −0.779142 | ||||||||
\(612\) | 0.207463 | 0.00838618 | ||||||||
\(613\) | −47.6840 | −1.92594 | −0.962970 | − | 0.269610i | \(-0.913105\pi\) | ||||
−0.962970 | + | 0.269610i | \(0.913105\pi\) | |||||||
\(614\) | 48.2275 | 1.94630 | ||||||||
\(615\) | 2.73444 | 0.110263 | ||||||||
\(616\) | 2.09174 | 0.0842785 | ||||||||
\(617\) | 16.7927 | 0.676047 | 0.338024 | − | 0.941138i | \(-0.390242\pi\) | ||||
0.338024 | + | 0.941138i | \(0.390242\pi\) | |||||||
\(618\) | −1.61167 | −0.0648309 | ||||||||
\(619\) | 44.0610 | 1.77096 | 0.885481 | − | 0.464676i | \(-0.153829\pi\) | ||||
0.885481 | + | 0.464676i | \(0.153829\pi\) | |||||||
\(620\) | 0.161307 | 0.00647824 | ||||||||
\(621\) | −29.1137 | −1.16829 | ||||||||
\(622\) | 17.7351 | 0.711114 | ||||||||
\(623\) | −3.44228 | −0.137912 | ||||||||
\(624\) | 15.4682 | 0.619222 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.9051 | −0.995408 | ||||||||
\(627\) | 5.73703 | 0.229115 | ||||||||
\(628\) | 2.88868 | 0.115271 | ||||||||
\(629\) | 0.814661 | 0.0324827 | ||||||||
\(630\) | −0.835078 | −0.0332703 | ||||||||
\(631\) | 35.1985 | 1.40123 | 0.700615 | − | 0.713539i | \(-0.252909\pi\) | ||||
0.700615 | + | 0.713539i | \(0.252909\pi\) | |||||||
\(632\) | −36.2979 | −1.44385 | ||||||||
\(633\) | 36.9311 | 1.46788 | ||||||||
\(634\) | −48.7481 | −1.93603 | ||||||||
\(635\) | −19.0927 | −0.757671 | ||||||||
\(636\) | −3.14588 | −0.124742 | ||||||||
\(637\) | 1.91852 | 0.0760146 | ||||||||
\(638\) | 0.0149101 | 0.000590298 0 | ||||||||
\(639\) | 6.78949 | 0.268588 | ||||||||
\(640\) | 12.3783 | 0.489297 | ||||||||
\(641\) | −13.0336 | −0.514795 | −0.257398 | − | 0.966306i | \(-0.582865\pi\) | ||||
−0.257398 | + | 0.966306i | \(0.582865\pi\) | |||||||
\(642\) | 8.96306 | 0.353744 | ||||||||
\(643\) | 27.7186 | 1.09311 | 0.546557 | − | 0.837422i | \(-0.315938\pi\) | ||||
0.546557 | + | 0.837422i | \(0.315938\pi\) | |||||||
\(644\) | 0.911998 | 0.0359377 | ||||||||
\(645\) | 21.2940 | 0.838449 | ||||||||
\(646\) | −14.6098 | −0.574813 | ||||||||
\(647\) | 5.32167 | 0.209216 | 0.104608 | − | 0.994514i | \(-0.466641\pi\) | ||||
0.104608 | + | 0.994514i | \(0.466641\pi\) | |||||||
\(648\) | −28.2262 | −1.10883 | ||||||||
\(649\) | −6.47164 | −0.254034 | ||||||||
\(650\) | −2.80906 | −0.110180 | ||||||||
\(651\) | −2.11939 | −0.0830654 | ||||||||
\(652\) | 1.51830 | 0.0594612 | ||||||||
\(653\) | 12.4627 | 0.487702 | 0.243851 | − | 0.969813i | \(-0.421589\pi\) | ||||
0.243851 | + | 0.969813i | \(0.421589\pi\) | |||||||
\(654\) | 4.22725 | 0.165299 | ||||||||
\(655\) | 20.0269 | 0.782518 | ||||||||
\(656\) | −6.17491 | −0.241090 | ||||||||
\(657\) | −4.28695 | −0.167250 | ||||||||
\(658\) | −14.6982 | −0.572995 | ||||||||
\(659\) | 12.5914 | 0.490491 | 0.245245 | − | 0.969461i | \(-0.421131\pi\) | ||||
0.245245 | + | 0.969461i | \(0.421131\pi\) | |||||||
\(660\) | −0.209143 | −0.00814089 | ||||||||
\(661\) | 46.5201 | 1.80942 | 0.904712 | − | 0.426025i | \(-0.140086\pi\) | ||||
0.904712 | + | 0.426025i | \(0.140086\pi\) | |||||||
\(662\) | −1.30839 | −0.0508521 | ||||||||
\(663\) | −9.16918 | −0.356102 | ||||||||
\(664\) | −13.2267 | −0.513294 | ||||||||
\(665\) | 3.94494 | 0.152978 | ||||||||
\(666\) | −0.268965 | −0.0104222 | ||||||||
\(667\) | −0.0839060 | −0.00324885 | ||||||||
\(668\) | −2.61243 | −0.101078 | ||||||||
\(669\) | −31.6936 | −1.22535 | ||||||||
\(670\) | 14.3913 | 0.555983 | ||||||||
\(671\) | −8.15166 | −0.314691 | ||||||||
\(672\) | 1.53428 | 0.0591860 | ||||||||
\(673\) | 31.0920 | 1.19851 | 0.599255 | − | 0.800558i | \(-0.295464\pi\) | ||||
0.599255 | + | 0.800558i | \(0.295464\pi\) | |||||||
\(674\) | −28.9638 | −1.11564 | ||||||||
\(675\) | 4.59093 | 0.176705 | ||||||||
\(676\) | −1.34023 | −0.0515473 | ||||||||
\(677\) | 17.2356 | 0.662418 | 0.331209 | − | 0.943557i | \(-0.392544\pi\) | ||||
0.331209 | + | 0.943557i | \(0.392544\pi\) | |||||||
\(678\) | −40.6789 | −1.56226 | ||||||||
\(679\) | 11.6821 | 0.448318 | ||||||||
\(680\) | −6.87423 | −0.263615 | ||||||||
\(681\) | −11.8757 | −0.455077 | ||||||||
\(682\) | −1.26398 | −0.0484004 | ||||||||
\(683\) | 40.4199 | 1.54662 | 0.773312 | − | 0.634025i | \(-0.218598\pi\) | ||||
0.773312 | + | 0.634025i | \(0.218598\pi\) | |||||||
\(684\) | 0.323572 | 0.0123721 | ||||||||
\(685\) | −0.958552 | −0.0366244 | ||||||||
\(686\) | 1.46418 | 0.0559025 | ||||||||
\(687\) | −1.88953 | −0.0720902 | ||||||||
\(688\) | −48.0860 | −1.83326 | ||||||||
\(689\) | 22.2105 | 0.846151 | ||||||||
\(690\) | 17.5447 | 0.667913 | ||||||||
\(691\) | −7.98035 | −0.303587 | −0.151793 | − | 0.988412i | \(-0.548505\pi\) | ||||
−0.151793 | + | 0.988412i | \(0.548505\pi\) | |||||||
\(692\) | 1.53390 | 0.0583103 | ||||||||
\(693\) | 0.438960 | 0.0166747 | ||||||||
\(694\) | 4.39363 | 0.166780 | ||||||||
\(695\) | 6.50772 | 0.246852 | ||||||||
\(696\) | −0.0679464 | −0.00257550 | ||||||||
\(697\) | 3.66035 | 0.138646 | ||||||||
\(698\) | −1.75875 | −0.0665697 | ||||||||
\(699\) | −45.7452 | −1.73024 | ||||||||
\(700\) | −0.143813 | −0.00543561 | ||||||||
\(701\) | −5.54488 | −0.209427 | −0.104714 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104714 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(702\) | −12.8962 | −0.486734 | ||||||||
\(703\) | 1.27060 | 0.0479215 | ||||||||
\(704\) | −5.65305 | −0.213058 | ||||||||
\(705\) | −18.9682 | −0.714382 | ||||||||
\(706\) | −28.7596 | −1.08238 | ||||||||
\(707\) | 2.74927 | 0.103397 | ||||||||
\(708\) | −2.28494 | −0.0858733 | ||||||||
\(709\) | 4.91070 | 0.184425 | 0.0922125 | − | 0.995739i | \(-0.470606\pi\) | ||||
0.0922125 | + | 0.995739i | \(0.470606\pi\) | |||||||
\(710\) | 17.4300 | 0.654135 | ||||||||
\(711\) | −7.61729 | −0.285671 | ||||||||
\(712\) | 9.35537 | 0.350607 | ||||||||
\(713\) | 7.11299 | 0.266384 | ||||||||
\(714\) | −6.99773 | −0.261883 | ||||||||
\(715\) | 1.47659 | 0.0552212 | ||||||||
\(716\) | −1.93840 | −0.0724415 | ||||||||
\(717\) | 40.0740 | 1.49659 | ||||||||
\(718\) | −16.9990 | −0.634397 | ||||||||
\(719\) | 32.9807 | 1.22997 | 0.614987 | − | 0.788537i | \(-0.289161\pi\) | ||||
0.614987 | + | 0.788537i | \(0.289161\pi\) | |||||||
\(720\) | 2.43361 | 0.0906952 | ||||||||
\(721\) | 0.582543 | 0.0216950 | ||||||||
\(722\) | 5.03302 | 0.187309 | ||||||||
\(723\) | 43.6353 | 1.62282 | ||||||||
\(724\) | −0.669333 | −0.0248756 | ||||||||
\(725\) | 0.0132311 | 0.000491391 0 | ||||||||
\(726\) | −28.7939 | −1.06864 | ||||||||
\(727\) | 20.0670 | 0.744245 | 0.372122 | − | 0.928184i | \(-0.378630\pi\) | ||||
0.372122 | + | 0.928184i | \(0.378630\pi\) | |||||||
\(728\) | −5.21413 | −0.193249 | ||||||||
\(729\) | 20.1007 | 0.744472 | ||||||||
\(730\) | −11.0055 | −0.407330 | ||||||||
\(731\) | 28.5043 | 1.05427 | ||||||||
\(732\) | −2.87810 | −0.106378 | ||||||||
\(733\) | 33.3438 | 1.23158 | 0.615791 | − | 0.787909i | \(-0.288836\pi\) | ||||
0.615791 | + | 0.787909i | \(0.288836\pi\) | |||||||
\(734\) | 7.26346 | 0.268099 | ||||||||
\(735\) | 1.88953 | 0.0696965 | ||||||||
\(736\) | −5.14927 | −0.189804 | ||||||||
\(737\) | −7.56479 | −0.278653 | ||||||||
\(738\) | −1.20848 | −0.0444849 | ||||||||
\(739\) | 3.20237 | 0.117801 | 0.0589005 | − | 0.998264i | \(-0.481241\pi\) | ||||
0.0589005 | + | 0.998264i | \(0.481241\pi\) | |||||||
\(740\) | −0.0463196 | −0.00170274 | ||||||||
\(741\) | −14.3009 | −0.525355 | ||||||||
\(742\) | 16.9506 | 0.622274 | ||||||||
\(743\) | −43.5545 | −1.59786 | −0.798929 | − | 0.601425i | \(-0.794600\pi\) | ||||
−0.798929 | + | 0.601425i | \(0.794600\pi\) | |||||||
\(744\) | 5.76005 | 0.211174 | ||||||||
\(745\) | 0.640380 | 0.0234617 | ||||||||
\(746\) | 23.0038 | 0.842229 | ||||||||
\(747\) | −2.77568 | −0.101557 | ||||||||
\(748\) | −0.279961 | −0.0102364 | ||||||||
\(749\) | −3.23972 | −0.118377 | ||||||||
\(750\) | −2.76661 | −0.101022 | ||||||||
\(751\) | 5.49291 | 0.200439 | 0.100220 | − | 0.994965i | \(-0.468045\pi\) | ||||
0.100220 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(752\) | 42.8338 | 1.56199 | ||||||||
\(753\) | −23.4960 | −0.856242 | ||||||||
\(754\) | −0.0371669 | −0.00135354 | ||||||||
\(755\) | 7.01626 | 0.255348 | ||||||||
\(756\) | −0.660234 | −0.0240125 | ||||||||
\(757\) | −10.2688 | −0.373228 | −0.186614 | − | 0.982433i | \(-0.559751\pi\) | ||||
−0.186614 | + | 0.982433i | \(0.559751\pi\) | |||||||
\(758\) | −47.1807 | −1.71368 | ||||||||
\(759\) | −9.22238 | −0.334751 | ||||||||
\(760\) | −10.7215 | −0.388910 | ||||||||
\(761\) | 53.2524 | 1.93040 | 0.965200 | − | 0.261515i | \(-0.0842219\pi\) | ||||
0.965200 | + | 0.261515i | \(0.0842219\pi\) | |||||||
\(762\) | 52.8221 | 1.91354 | ||||||||
\(763\) | −1.52795 | −0.0553156 | ||||||||
\(764\) | −0.147219 | −0.00532621 | ||||||||
\(765\) | −1.44259 | −0.0521569 | ||||||||
\(766\) | 13.2187 | 0.477612 | ||||||||
\(767\) | 16.1321 | 0.582495 | ||||||||
\(768\) | −6.48882 | −0.234145 | ||||||||
\(769\) | 46.5471 | 1.67853 | 0.839266 | − | 0.543721i | \(-0.182985\pi\) | ||||
0.839266 | + | 0.543721i | \(0.182985\pi\) | |||||||
\(770\) | 1.12690 | 0.0406106 | ||||||||
\(771\) | 41.1711 | 1.48274 | ||||||||
\(772\) | 3.29771 | 0.118687 | ||||||||
\(773\) | −48.5510 | −1.74626 | −0.873129 | − | 0.487490i | \(-0.837913\pi\) | ||||
−0.873129 | + | 0.487490i | \(0.837913\pi\) | |||||||
\(774\) | −9.41085 | −0.338266 | ||||||||
\(775\) | −1.12165 | −0.0402907 | ||||||||
\(776\) | −31.7495 | −1.13974 | ||||||||
\(777\) | 0.608587 | 0.0218329 | ||||||||
\(778\) | −36.4249 | −1.30590 | ||||||||
\(779\) | 5.70892 | 0.204543 | ||||||||
\(780\) | 0.521337 | 0.0186669 | ||||||||
\(781\) | −9.16210 | −0.327846 | ||||||||
\(782\) | 23.4855 | 0.839838 | ||||||||
\(783\) | 0.0607431 | 0.00217078 | ||||||||
\(784\) | −4.26694 | −0.152391 | ||||||||
\(785\) | −20.0864 | −0.716915 | ||||||||
\(786\) | −55.4068 | −1.97629 | ||||||||
\(787\) | 36.6763 | 1.30737 | 0.653685 | − | 0.756767i | \(-0.273222\pi\) | ||||
0.653685 | + | 0.756767i | \(0.273222\pi\) | |||||||
\(788\) | 0.807549 | 0.0287677 | ||||||||
\(789\) | 33.0608 | 1.17700 | ||||||||
\(790\) | −19.5551 | −0.695739 | ||||||||
\(791\) | 14.7035 | 0.522797 | ||||||||
\(792\) | −1.19300 | −0.0423914 | ||||||||
\(793\) | 20.3199 | 0.721580 | ||||||||
\(794\) | −40.8915 | −1.45118 | ||||||||
\(795\) | 21.8749 | 0.775821 | ||||||||
\(796\) | 1.47829 | 0.0523967 | ||||||||
\(797\) | −41.0353 | −1.45355 | −0.726773 | − | 0.686878i | \(-0.758981\pi\) | ||||
−0.726773 | + | 0.686878i | \(0.758981\pi\) | |||||||
\(798\) | −10.9141 | −0.386356 | ||||||||
\(799\) | −25.3910 | −0.898268 | ||||||||
\(800\) | 0.811986 | 0.0287081 | ||||||||
\(801\) | 1.96327 | 0.0693687 | ||||||||
\(802\) | 37.5407 | 1.32561 | ||||||||
\(803\) | 5.78504 | 0.204150 | ||||||||
\(804\) | −2.67090 | −0.0941953 | ||||||||
\(805\) | −6.34157 | −0.223511 | ||||||||
\(806\) | 3.15077 | 0.110981 | ||||||||
\(807\) | −12.6577 | −0.445572 | ||||||||
\(808\) | −7.47191 | −0.262861 | ||||||||
\(809\) | −18.8459 | −0.662587 | −0.331294 | − | 0.943528i | \(-0.607485\pi\) | ||||
−0.331294 | + | 0.943528i | \(0.607485\pi\) | |||||||
\(810\) | −15.2065 | −0.534304 | ||||||||
\(811\) | −10.5096 | −0.369043 | −0.184521 | − | 0.982829i | \(-0.559073\pi\) | ||||
−0.184521 | + | 0.982829i | \(0.559073\pi\) | |||||||
\(812\) | −0.00190280 | −6.67753e−5 0 | ||||||||
\(813\) | 55.1598 | 1.93454 | ||||||||
\(814\) | 0.362955 | 0.0127216 | ||||||||
\(815\) | −10.5575 | −0.369812 | ||||||||
\(816\) | 20.3930 | 0.713897 | ||||||||
\(817\) | 44.4572 | 1.55536 | ||||||||
\(818\) | −35.0882 | −1.22683 | ||||||||
\(819\) | −1.09421 | −0.0382348 | ||||||||
\(820\) | −0.208119 | −0.00726782 | ||||||||
\(821\) | −34.8324 | −1.21566 | −0.607829 | − | 0.794068i | \(-0.707959\pi\) | ||||
−0.607829 | + | 0.794068i | \(0.707959\pi\) | |||||||
\(822\) | 2.65194 | 0.0924971 | ||||||||
\(823\) | −11.5837 | −0.403782 | −0.201891 | − | 0.979408i | \(-0.564709\pi\) | ||||
−0.201891 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(824\) | −1.58323 | −0.0551543 | ||||||||
\(825\) | 1.45427 | 0.0506313 | ||||||||
\(826\) | 12.3117 | 0.428377 | ||||||||
\(827\) | −44.0885 | −1.53311 | −0.766553 | − | 0.642181i | \(-0.778030\pi\) | ||||
−0.766553 | + | 0.642181i | \(0.778030\pi\) | |||||||
\(828\) | −0.520149 | −0.0180764 | ||||||||
\(829\) | 17.0857 | 0.593410 | 0.296705 | − | 0.954969i | \(-0.404112\pi\) | ||||
0.296705 | + | 0.954969i | \(0.404112\pi\) | |||||||
\(830\) | −7.12571 | −0.247337 | ||||||||
\(831\) | −14.8869 | −0.516422 | ||||||||
\(832\) | 14.0915 | 0.488536 | ||||||||
\(833\) | 2.52935 | 0.0876368 | ||||||||
\(834\) | −18.0043 | −0.623439 | ||||||||
\(835\) | 18.1655 | 0.628644 | ||||||||
\(836\) | −0.436646 | −0.0151017 | ||||||||
\(837\) | −5.14940 | −0.177989 | ||||||||
\(838\) | 11.5786 | 0.399977 | ||||||||
\(839\) | 2.86237 | 0.0988199 | 0.0494100 | − | 0.998779i | \(-0.484266\pi\) | ||||
0.0494100 | + | 0.998779i | \(0.484266\pi\) | |||||||
\(840\) | −5.13535 | −0.177186 | ||||||||
\(841\) | −28.9998 | −0.999994 | ||||||||
\(842\) | 39.7584 | 1.37016 | ||||||||
\(843\) | 23.8532 | 0.821547 | ||||||||
\(844\) | −2.81083 | −0.0967527 | ||||||||
\(845\) | 9.31927 | 0.320593 | ||||||||
\(846\) | 8.38296 | 0.288212 | ||||||||
\(847\) | 10.4076 | 0.357611 | ||||||||
\(848\) | −49.3978 | −1.69633 | ||||||||
\(849\) | 30.0905 | 1.03270 | ||||||||
\(850\) | −3.70342 | −0.127026 | ||||||||
\(851\) | −2.04251 | −0.0700164 | ||||||||
\(852\) | −3.23486 | −0.110824 | ||||||||
\(853\) | 37.8443 | 1.29576 | 0.647882 | − | 0.761741i | \(-0.275655\pi\) | ||||
0.647882 | + | 0.761741i | \(0.275655\pi\) | |||||||
\(854\) | 15.5077 | 0.530663 | ||||||||
\(855\) | −2.24996 | −0.0769469 | ||||||||
\(856\) | 8.80487 | 0.300944 | ||||||||
\(857\) | −30.0978 | −1.02812 | −0.514061 | − | 0.857754i | \(-0.671859\pi\) | ||||
−0.514061 | + | 0.857754i | \(0.671859\pi\) | |||||||
\(858\) | −4.08514 | −0.139464 | ||||||||
\(859\) | 6.33170 | 0.216035 | 0.108017 | − | 0.994149i | \(-0.465550\pi\) | ||||
0.108017 | + | 0.994149i | \(0.465550\pi\) | |||||||
\(860\) | −1.62069 | −0.0552650 | ||||||||
\(861\) | 2.73444 | 0.0931895 | ||||||||
\(862\) | 37.8937 | 1.29066 | ||||||||
\(863\) | −9.95428 | −0.338847 | −0.169424 | − | 0.985543i | \(-0.554191\pi\) | ||||
−0.169424 | + | 0.985543i | \(0.554191\pi\) | |||||||
\(864\) | 3.72777 | 0.126821 | ||||||||
\(865\) | −10.6660 | −0.362654 | ||||||||
\(866\) | −24.4382 | −0.830445 | ||||||||
\(867\) | 20.0336 | 0.680376 | ||||||||
\(868\) | 0.161307 | 0.00547512 | ||||||||
\(869\) | 10.2792 | 0.348697 | ||||||||
\(870\) | −0.0366054 | −0.00124104 | ||||||||
\(871\) | 18.8570 | 0.638945 | ||||||||
\(872\) | 4.15265 | 0.140626 | ||||||||
\(873\) | −6.66277 | −0.225501 | ||||||||
\(874\) | 36.6295 | 1.23901 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 2.04252 | 0.0690105 | ||||||||
\(877\) | 42.5212 | 1.43584 | 0.717920 | − | 0.696125i | \(-0.245094\pi\) | ||||
0.717920 | + | 0.696125i | \(0.245094\pi\) | |||||||
\(878\) | −39.3188 | −1.32694 | ||||||||
\(879\) | −20.9101 | −0.705281 | ||||||||
\(880\) | −3.28404 | −0.110705 | ||||||||
\(881\) | −14.6939 | −0.495051 | −0.247525 | − | 0.968881i | \(-0.579617\pi\) | ||||
−0.247525 | + | 0.968881i | \(0.579617\pi\) | |||||||
\(882\) | −0.835078 | −0.0281185 | ||||||||
\(883\) | 33.6629 | 1.13285 | 0.566424 | − | 0.824114i | \(-0.308327\pi\) | ||||
0.566424 | + | 0.824114i | \(0.308327\pi\) | |||||||
\(884\) | 0.697868 | 0.0234718 | ||||||||
\(885\) | 15.8883 | 0.534080 | ||||||||
\(886\) | 47.0867 | 1.58191 | ||||||||
\(887\) | −43.7898 | −1.47032 | −0.735159 | − | 0.677894i | \(-0.762893\pi\) | ||||
−0.735159 | + | 0.677894i | \(0.762893\pi\) | |||||||
\(888\) | −1.65401 | −0.0555049 | ||||||||
\(889\) | −19.0927 | −0.640349 | ||||||||
\(890\) | 5.04010 | 0.168945 | ||||||||
\(891\) | 7.99335 | 0.267787 | ||||||||
\(892\) | 2.41221 | 0.0807666 | ||||||||
\(893\) | −39.6014 | −1.32521 | ||||||||
\(894\) | −1.77168 | −0.0592540 | ||||||||
\(895\) | 13.4786 | 0.450542 | ||||||||
\(896\) | 12.3783 | 0.413531 | ||||||||
\(897\) | 22.9889 | 0.767577 | ||||||||
\(898\) | 5.45422 | 0.182010 | ||||||||
\(899\) | −0.0148406 | −0.000494963 0 | ||||||||
\(900\) | 0.0820221 | 0.00273407 | ||||||||
\(901\) | 29.2819 | 0.975522 | ||||||||
\(902\) | 1.63079 | 0.0542994 | ||||||||
\(903\) | 21.2940 | 0.708619 | ||||||||
\(904\) | −39.9610 | −1.32908 | ||||||||
\(905\) | 4.65420 | 0.154711 | ||||||||
\(906\) | −19.4113 | −0.644897 | ||||||||
\(907\) | 53.9213 | 1.79043 | 0.895213 | − | 0.445638i | \(-0.147023\pi\) | ||||
0.895213 | + | 0.445638i | \(0.147023\pi\) | |||||||
\(908\) | 0.903859 | 0.0299956 | ||||||||
\(909\) | −1.56802 | −0.0520078 | ||||||||
\(910\) | −2.80906 | −0.0931193 | ||||||||
\(911\) | −52.9483 | −1.75425 | −0.877127 | − | 0.480259i | \(-0.840543\pi\) | ||||
−0.877127 | + | 0.480259i | \(0.840543\pi\) | |||||||
\(912\) | 31.8062 | 1.05321 | ||||||||
\(913\) | 3.74565 | 0.123963 | ||||||||
\(914\) | 33.0532 | 1.09330 | ||||||||
\(915\) | 20.0129 | 0.661605 | ||||||||
\(916\) | 0.143813 | 0.00475171 | ||||||||
\(917\) | 20.0269 | 0.661348 | ||||||||
\(918\) | −17.0021 | −0.561153 | ||||||||
\(919\) | −4.10537 | −0.135424 | −0.0677119 | − | 0.997705i | \(-0.521570\pi\) | ||||
−0.0677119 | + | 0.997705i | \(0.521570\pi\) | |||||||
\(920\) | 17.2350 | 0.568222 | ||||||||
\(921\) | 62.2380 | 2.05081 | ||||||||
\(922\) | −39.5808 | −1.30352 | ||||||||
\(923\) | 22.8386 | 0.751743 | ||||||||
\(924\) | −0.209143 | −0.00688031 | ||||||||
\(925\) | 0.322083 | 0.0105900 | ||||||||
\(926\) | −6.32976 | −0.208009 | ||||||||
\(927\) | −0.332248 | −0.0109124 | ||||||||
\(928\) | 0.0107435 | 0.000352672 0 | ||||||||
\(929\) | −39.5635 | −1.29804 | −0.649018 | − | 0.760773i | \(-0.724820\pi\) | ||||
−0.649018 | + | 0.760773i | \(0.724820\pi\) | |||||||
\(930\) | 3.10316 | 0.101757 | ||||||||
\(931\) | 3.94494 | 0.129290 | ||||||||
\(932\) | 3.48168 | 0.114046 | ||||||||
\(933\) | 22.8874 | 0.749298 | ||||||||
\(934\) | −6.20308 | −0.202971 | ||||||||
\(935\) | 1.94671 | 0.0636641 | ||||||||
\(936\) | 2.97383 | 0.0972026 | ||||||||
\(937\) | 30.4221 | 0.993848 | 0.496924 | − | 0.867794i | \(-0.334463\pi\) | ||||
0.496924 | + | 0.867794i | \(0.334463\pi\) | |||||||
\(938\) | 14.3913 | 0.469891 | ||||||||
\(939\) | −32.1403 | −1.04886 | ||||||||
\(940\) | 1.44367 | 0.0470873 | ||||||||
\(941\) | −7.29449 | −0.237793 | −0.118897 | − | 0.992907i | \(-0.537936\pi\) | ||||
−0.118897 | + | 0.992907i | \(0.537936\pi\) | |||||||
\(942\) | 55.5713 | 1.81061 | ||||||||
\(943\) | −9.17720 | −0.298851 | ||||||||
\(944\) | −35.8789 | −1.16776 | ||||||||
\(945\) | 4.59093 | 0.149343 | ||||||||
\(946\) | 12.6995 | 0.412897 | ||||||||
\(947\) | 18.6095 | 0.604728 | 0.302364 | − | 0.953193i | \(-0.402224\pi\) | ||||
0.302364 | + | 0.953193i | \(0.402224\pi\) | |||||||
\(948\) | 3.62927 | 0.117873 | ||||||||
\(949\) | −14.4206 | −0.468111 | ||||||||
\(950\) | −5.77609 | −0.187401 | ||||||||
\(951\) | −62.9099 | −2.03999 | ||||||||
\(952\) | −6.87423 | −0.222795 | ||||||||
\(953\) | −48.0943 | −1.55793 | −0.778963 | − | 0.627070i | \(-0.784254\pi\) | ||||
−0.778963 | + | 0.627070i | \(0.784254\pi\) | |||||||
\(954\) | −9.66758 | −0.312999 | ||||||||
\(955\) | 1.02369 | 0.0331258 | ||||||||
\(956\) | −3.05004 | −0.0986453 | ||||||||
\(957\) | 0.0192417 | 0.000621995 0 | ||||||||
\(958\) | −21.6767 | −0.700342 | ||||||||
\(959\) | −0.958552 | −0.0309533 | ||||||||
\(960\) | 13.8786 | 0.447931 | ||||||||
\(961\) | −29.7419 | −0.959416 | ||||||||
\(962\) | −0.904749 | −0.0291703 | ||||||||
\(963\) | 1.84774 | 0.0595427 | ||||||||
\(964\) | −3.32109 | −0.106965 | ||||||||
\(965\) | −22.9306 | −0.738161 | ||||||||
\(966\) | 17.5447 | 0.564490 | ||||||||
\(967\) | 34.0401 | 1.09466 | 0.547328 | − | 0.836918i | \(-0.315645\pi\) | ||||
0.547328 | + | 0.836918i | \(0.315645\pi\) | |||||||
\(968\) | −28.2857 | −0.909138 | ||||||||
\(969\) | −18.8540 | −0.605679 | ||||||||
\(970\) | −17.1047 | −0.549198 | ||||||||
\(971\) | 24.5832 | 0.788912 | 0.394456 | − | 0.918915i | \(-0.370933\pi\) | ||||
0.394456 | + | 0.918915i | \(0.370933\pi\) | |||||||
\(972\) | 0.841508 | 0.0269914 | ||||||||
\(973\) | 6.50772 | 0.208628 | ||||||||
\(974\) | −9.33408 | −0.299083 | ||||||||
\(975\) | −3.62511 | −0.116097 | ||||||||
\(976\) | −45.1930 | −1.44659 | ||||||||
\(977\) | 48.4573 | 1.55029 | 0.775143 | − | 0.631785i | \(-0.217678\pi\) | ||||
0.775143 | + | 0.631785i | \(0.217678\pi\) | |||||||
\(978\) | 29.2084 | 0.933983 | ||||||||
\(979\) | −2.64934 | −0.0846732 | ||||||||
\(980\) | −0.143813 | −0.00459393 | ||||||||
\(981\) | 0.871453 | 0.0278233 | ||||||||
\(982\) | −44.8327 | −1.43067 | ||||||||
\(983\) | −18.1849 | −0.580007 | −0.290003 | − | 0.957026i | \(-0.593656\pi\) | ||||
−0.290003 | + | 0.957026i | \(0.593656\pi\) | |||||||
\(984\) | −7.43162 | −0.236911 | ||||||||
\(985\) | −5.61528 | −0.178918 | ||||||||
\(986\) | −0.0490003 | −0.00156049 | ||||||||
\(987\) | −18.9682 | −0.603763 | ||||||||
\(988\) | 1.08844 | 0.0346279 | ||||||||
\(989\) | −71.4658 | −2.27248 | ||||||||
\(990\) | −0.642716 | −0.0204268 | ||||||||
\(991\) | 23.4407 | 0.744619 | 0.372310 | − | 0.928109i | \(-0.378566\pi\) | ||||
0.372310 | + | 0.928109i | \(0.378566\pi\) | |||||||
\(992\) | −0.910762 | −0.0289167 | ||||||||
\(993\) | −1.68849 | −0.0535828 | ||||||||
\(994\) | 17.4300 | 0.552845 | ||||||||
\(995\) | −10.2793 | −0.325876 | ||||||||
\(996\) | 1.32247 | 0.0419042 | ||||||||
\(997\) | −21.4383 | −0.678959 | −0.339479 | − | 0.940613i | \(-0.610251\pi\) | ||||
−0.339479 | + | 0.940613i | \(0.610251\pi\) | |||||||
\(998\) | 63.0239 | 1.99499 | ||||||||
\(999\) | 1.47866 | 0.0467827 |
(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 | 8015.2.a.l.1.16 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.16 | ✓ | 62 | 1.1 | even | 1 | trivial |