Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.396413 | 0.228869 | 0.114435 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114435 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.85319 | −0.828771 | −0.414386 | − | 0.910101i | \(-0.636004\pi\) | ||||
−0.414386 | + | 0.910101i | \(0.636004\pi\) | |||||||
\(6\) | −0.396413 | −0.161835 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.84286 | −0.947619 | ||||||||
\(10\) | 1.85319 | 0.586030 | ||||||||
\(11\) | 4.50165 | 1.35730 | 0.678650 | − | 0.734462i | \(-0.262565\pi\) | ||||
0.678650 | + | 0.734462i | \(0.262565\pi\) | |||||||
\(12\) | 0.396413 | 0.114435 | ||||||||
\(13\) | −5.91310 | −1.64000 | −0.819999 | − | 0.572365i | \(-0.806026\pi\) | ||||
−0.819999 | + | 0.572365i | \(0.806026\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.734628 | −0.189680 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.27375 | −1.76414 | −0.882071 | − | 0.471116i | \(-0.843851\pi\) | ||||
−0.882071 | + | 0.471116i | \(0.843851\pi\) | |||||||
\(18\) | 2.84286 | 0.670068 | ||||||||
\(19\) | 8.32838 | 1.91066 | 0.955330 | − | 0.295540i | \(-0.0954997\pi\) | ||||
0.955330 | + | 0.295540i | \(0.0954997\pi\) | |||||||
\(20\) | −1.85319 | −0.414386 | ||||||||
\(21\) | 0.396413 | 0.0865044 | ||||||||
\(22\) | −4.50165 | −0.959756 | ||||||||
\(23\) | 4.63014 | 0.965451 | 0.482726 | − | 0.875772i | \(-0.339647\pi\) | ||||
0.482726 | + | 0.875772i | \(0.339647\pi\) | |||||||
\(24\) | −0.396413 | −0.0809175 | ||||||||
\(25\) | −1.56569 | −0.313138 | ||||||||
\(26\) | 5.91310 | 1.15965 | ||||||||
\(27\) | −2.31618 | −0.445750 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.78767 | 0.889048 | 0.444524 | − | 0.895767i | \(-0.353373\pi\) | ||||
0.444524 | + | 0.895767i | \(0.353373\pi\) | |||||||
\(30\) | 0.734628 | 0.134124 | ||||||||
\(31\) | −2.20360 | −0.395779 | −0.197890 | − | 0.980224i | \(-0.563409\pi\) | ||||
−0.197890 | + | 0.980224i | \(0.563409\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.78451 | 0.310644 | ||||||||
\(34\) | 7.27375 | 1.24744 | ||||||||
\(35\) | −1.85319 | −0.313246 | ||||||||
\(36\) | −2.84286 | −0.473809 | ||||||||
\(37\) | 4.81524 | 0.791620 | 0.395810 | − | 0.918332i | \(-0.370464\pi\) | ||||
0.395810 | + | 0.918332i | \(0.370464\pi\) | |||||||
\(38\) | −8.32838 | −1.35104 | ||||||||
\(39\) | −2.34403 | −0.375345 | ||||||||
\(40\) | 1.85319 | 0.293015 | ||||||||
\(41\) | 0.513367 | 0.0801745 | 0.0400872 | − | 0.999196i | \(-0.487236\pi\) | ||||
0.0400872 | + | 0.999196i | \(0.487236\pi\) | |||||||
\(42\) | −0.396413 | −0.0611678 | ||||||||
\(43\) | −9.72662 | −1.48330 | −0.741648 | − | 0.670789i | \(-0.765956\pi\) | ||||
−0.741648 | + | 0.670789i | \(0.765956\pi\) | |||||||
\(44\) | 4.50165 | 0.678650 | ||||||||
\(45\) | 5.26835 | 0.785359 | ||||||||
\(46\) | −4.63014 | −0.682677 | ||||||||
\(47\) | −2.59821 | −0.378987 | −0.189494 | − | 0.981882i | \(-0.560685\pi\) | ||||
−0.189494 | + | 0.981882i | \(0.560685\pi\) | |||||||
\(48\) | 0.396413 | 0.0572173 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.56569 | 0.221422 | ||||||||
\(51\) | −2.88341 | −0.403758 | ||||||||
\(52\) | −5.91310 | −0.819999 | ||||||||
\(53\) | 0.359603 | 0.0493953 | 0.0246977 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246977 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(54\) | 2.31618 | 0.315193 | ||||||||
\(55\) | −8.34241 | −1.12489 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 3.30148 | 0.437291 | ||||||||
\(58\) | −4.78767 | −0.628652 | ||||||||
\(59\) | −13.9736 | −1.81921 | −0.909604 | − | 0.415477i | \(-0.863615\pi\) | ||||
−0.909604 | + | 0.415477i | \(0.863615\pi\) | |||||||
\(60\) | −0.734628 | −0.0948401 | ||||||||
\(61\) | −6.74430 | −0.863519 | −0.431759 | − | 0.901989i | \(-0.642107\pi\) | ||||
−0.431759 | + | 0.901989i | \(0.642107\pi\) | |||||||
\(62\) | 2.20360 | 0.279858 | ||||||||
\(63\) | −2.84286 | −0.358166 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.9581 | 1.35918 | ||||||||
\(66\) | −1.78451 | −0.219658 | ||||||||
\(67\) | 13.8107 | 1.68725 | 0.843624 | − | 0.536935i | \(-0.180418\pi\) | ||||
0.843624 | + | 0.536935i | \(0.180418\pi\) | |||||||
\(68\) | −7.27375 | −0.882071 | ||||||||
\(69\) | 1.83545 | 0.220962 | ||||||||
\(70\) | 1.85319 | 0.221498 | ||||||||
\(71\) | 2.79743 | 0.331994 | 0.165997 | − | 0.986126i | \(-0.446916\pi\) | ||||
0.165997 | + | 0.986126i | \(0.446916\pi\) | |||||||
\(72\) | 2.84286 | 0.335034 | ||||||||
\(73\) | −7.79200 | −0.911984 | −0.455992 | − | 0.889984i | \(-0.650715\pi\) | ||||
−0.455992 | + | 0.889984i | \(0.650715\pi\) | |||||||
\(74\) | −4.81524 | −0.559760 | ||||||||
\(75\) | −0.620660 | −0.0716677 | ||||||||
\(76\) | 8.32838 | 0.955330 | ||||||||
\(77\) | 4.50165 | 0.513011 | ||||||||
\(78\) | 2.34403 | 0.265409 | ||||||||
\(79\) | −5.54692 | −0.624077 | −0.312039 | − | 0.950069i | \(-0.601012\pi\) | ||||
−0.312039 | + | 0.950069i | \(0.601012\pi\) | |||||||
\(80\) | −1.85319 | −0.207193 | ||||||||
\(81\) | 7.61040 | 0.845601 | ||||||||
\(82\) | −0.513367 | −0.0566919 | ||||||||
\(83\) | 16.1813 | 1.77613 | 0.888065 | − | 0.459718i | \(-0.152050\pi\) | ||||
0.888065 | + | 0.459718i | \(0.152050\pi\) | |||||||
\(84\) | 0.396413 | 0.0432522 | ||||||||
\(85\) | 13.4796 | 1.46207 | ||||||||
\(86\) | 9.72662 | 1.04885 | ||||||||
\(87\) | 1.89789 | 0.203476 | ||||||||
\(88\) | −4.50165 | −0.479878 | ||||||||
\(89\) | −3.71243 | −0.393517 | −0.196758 | − | 0.980452i | \(-0.563041\pi\) | ||||
−0.196758 | + | 0.980452i | \(0.563041\pi\) | |||||||
\(90\) | −5.26835 | −0.555333 | ||||||||
\(91\) | −5.91310 | −0.619861 | ||||||||
\(92\) | 4.63014 | 0.482726 | ||||||||
\(93\) | −0.873537 | −0.0905816 | ||||||||
\(94\) | 2.59821 | 0.267985 | ||||||||
\(95\) | −15.4341 | −1.58350 | ||||||||
\(96\) | −0.396413 | −0.0404587 | ||||||||
\(97\) | −13.5994 | −1.38081 | −0.690406 | − | 0.723422i | \(-0.742568\pi\) | ||||
−0.690406 | + | 0.723422i | \(0.742568\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −12.7976 | −1.28620 | ||||||||
\(100\) | −1.56569 | −0.156569 | ||||||||
\(101\) | 9.17375 | 0.912822 | 0.456411 | − | 0.889769i | \(-0.349135\pi\) | ||||
0.456411 | + | 0.889769i | \(0.349135\pi\) | |||||||
\(102\) | 2.88341 | 0.285500 | ||||||||
\(103\) | 4.11643 | 0.405604 | 0.202802 | − | 0.979220i | \(-0.434995\pi\) | ||||
0.202802 | + | 0.979220i | \(0.434995\pi\) | |||||||
\(104\) | 5.91310 | 0.579827 | ||||||||
\(105\) | −0.734628 | −0.0716924 | ||||||||
\(106\) | −0.359603 | −0.0349278 | ||||||||
\(107\) | 0.279089 | 0.0269806 | 0.0134903 | − | 0.999909i | \(-0.495706\pi\) | ||||
0.0134903 | + | 0.999909i | \(0.495706\pi\) | |||||||
\(108\) | −2.31618 | −0.222875 | ||||||||
\(109\) | 18.3186 | 1.75460 | 0.877300 | − | 0.479943i | \(-0.159343\pi\) | ||||
0.877300 | + | 0.479943i | \(0.159343\pi\) | |||||||
\(110\) | 8.34241 | 0.795418 | ||||||||
\(111\) | 1.90882 | 0.181177 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 0.364997 | 0.0343360 | 0.0171680 | − | 0.999853i | \(-0.494535\pi\) | ||||
0.0171680 | + | 0.999853i | \(0.494535\pi\) | |||||||
\(114\) | −3.30148 | −0.309212 | ||||||||
\(115\) | −8.58053 | −0.800138 | ||||||||
\(116\) | 4.78767 | 0.444524 | ||||||||
\(117\) | 16.8101 | 1.55409 | ||||||||
\(118\) | 13.9736 | 1.28637 | ||||||||
\(119\) | −7.27375 | −0.666783 | ||||||||
\(120\) | 0.734628 | 0.0670621 | ||||||||
\(121\) | 9.26489 | 0.842262 | ||||||||
\(122\) | 6.74430 | 0.610600 | ||||||||
\(123\) | 0.203505 | 0.0183495 | ||||||||
\(124\) | −2.20360 | −0.197890 | ||||||||
\(125\) | 12.1675 | 1.08829 | ||||||||
\(126\) | 2.84286 | 0.253262 | ||||||||
\(127\) | −6.00997 | −0.533299 | −0.266649 | − | 0.963794i | \(-0.585917\pi\) | ||||
−0.266649 | + | 0.963794i | \(0.585917\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.85576 | −0.339481 | ||||||||
\(130\) | −10.9581 | −0.961088 | ||||||||
\(131\) | 20.2084 | 1.76562 | 0.882808 | − | 0.469735i | \(-0.155650\pi\) | ||||
0.882808 | + | 0.469735i | \(0.155650\pi\) | |||||||
\(132\) | 1.78451 | 0.155322 | ||||||||
\(133\) | 8.32838 | 0.722162 | ||||||||
\(134\) | −13.8107 | −1.19306 | ||||||||
\(135\) | 4.29233 | 0.369425 | ||||||||
\(136\) | 7.27375 | 0.623719 | ||||||||
\(137\) | 12.4323 | 1.06216 | 0.531082 | − | 0.847320i | \(-0.321786\pi\) | ||||
0.531082 | + | 0.847320i | \(0.321786\pi\) | |||||||
\(138\) | −1.83545 | −0.156244 | ||||||||
\(139\) | 2.95241 | 0.250420 | 0.125210 | − | 0.992130i | \(-0.460040\pi\) | ||||
0.125210 | + | 0.992130i | \(0.460040\pi\) | |||||||
\(140\) | −1.85319 | −0.156623 | ||||||||
\(141\) | −1.02996 | −0.0867385 | ||||||||
\(142\) | −2.79743 | −0.234755 | ||||||||
\(143\) | −26.6187 | −2.22597 | ||||||||
\(144\) | −2.84286 | −0.236905 | ||||||||
\(145\) | −8.87245 | −0.736817 | ||||||||
\(146\) | 7.79200 | 0.644870 | ||||||||
\(147\) | 0.396413 | 0.0326956 | ||||||||
\(148\) | 4.81524 | 0.395810 | ||||||||
\(149\) | 2.62018 | 0.214653 | 0.107327 | − | 0.994224i | \(-0.465771\pi\) | ||||
0.107327 | + | 0.994224i | \(0.465771\pi\) | |||||||
\(150\) | 0.620660 | 0.0506767 | ||||||||
\(151\) | −8.04927 | −0.655041 | −0.327520 | − | 0.944844i | \(-0.606213\pi\) | ||||
−0.327520 | + | 0.944844i | \(0.606213\pi\) | |||||||
\(152\) | −8.32838 | −0.675521 | ||||||||
\(153\) | 20.6782 | 1.67173 | ||||||||
\(154\) | −4.50165 | −0.362754 | ||||||||
\(155\) | 4.08369 | 0.328010 | ||||||||
\(156\) | −2.34403 | −0.187672 | ||||||||
\(157\) | 12.2632 | 0.978707 | 0.489354 | − | 0.872085i | \(-0.337233\pi\) | ||||
0.489354 | + | 0.872085i | \(0.337233\pi\) | |||||||
\(158\) | 5.54692 | 0.441289 | ||||||||
\(159\) | 0.142551 | 0.0113051 | ||||||||
\(160\) | 1.85319 | 0.146507 | ||||||||
\(161\) | 4.63014 | 0.364906 | ||||||||
\(162\) | −7.61040 | −0.597930 | ||||||||
\(163\) | 13.3927 | 1.04899 | 0.524497 | − | 0.851413i | \(-0.324254\pi\) | ||||
0.524497 | + | 0.851413i | \(0.324254\pi\) | |||||||
\(164\) | 0.513367 | 0.0400872 | ||||||||
\(165\) | −3.30704 | −0.257453 | ||||||||
\(166\) | −16.1813 | −1.25591 | ||||||||
\(167\) | −11.5887 | −0.896761 | −0.448380 | − | 0.893843i | \(-0.647999\pi\) | ||||
−0.448380 | + | 0.893843i | \(0.647999\pi\) | |||||||
\(168\) | −0.396413 | −0.0305839 | ||||||||
\(169\) | 21.9647 | 1.68959 | ||||||||
\(170\) | −13.4796 | −1.03384 | ||||||||
\(171\) | −23.6764 | −1.81058 | ||||||||
\(172\) | −9.72662 | −0.741648 | ||||||||
\(173\) | −9.41841 | −0.716068 | −0.358034 | − | 0.933709i | \(-0.616553\pi\) | ||||
−0.358034 | + | 0.933709i | \(0.616553\pi\) | |||||||
\(174\) | −1.89789 | −0.143879 | ||||||||
\(175\) | −1.56569 | −0.118355 | ||||||||
\(176\) | 4.50165 | 0.339325 | ||||||||
\(177\) | −5.53931 | −0.416360 | ||||||||
\(178\) | 3.71243 | 0.278258 | ||||||||
\(179\) | 7.68557 | 0.574447 | 0.287223 | − | 0.957864i | \(-0.407268\pi\) | ||||
0.287223 | + | 0.957864i | \(0.407268\pi\) | |||||||
\(180\) | 5.26835 | 0.392680 | ||||||||
\(181\) | 10.6450 | 0.791235 | 0.395618 | − | 0.918415i | \(-0.370531\pi\) | ||||
0.395618 | + | 0.918415i | \(0.370531\pi\) | |||||||
\(182\) | 5.91310 | 0.438308 | ||||||||
\(183\) | −2.67353 | −0.197633 | ||||||||
\(184\) | −4.63014 | −0.341339 | ||||||||
\(185\) | −8.92354 | −0.656072 | ||||||||
\(186\) | 0.873537 | 0.0640509 | ||||||||
\(187\) | −32.7439 | −2.39447 | ||||||||
\(188\) | −2.59821 | −0.189494 | ||||||||
\(189\) | −2.31618 | −0.168478 | ||||||||
\(190\) | 15.4341 | 1.11970 | ||||||||
\(191\) | −13.7742 | −0.996664 | −0.498332 | − | 0.866986i | \(-0.666054\pi\) | ||||
−0.498332 | + | 0.866986i | \(0.666054\pi\) | |||||||
\(192\) | 0.396413 | 0.0286086 | ||||||||
\(193\) | −24.8018 | −1.78527 | −0.892637 | − | 0.450776i | \(-0.851147\pi\) | ||||
−0.892637 | + | 0.450776i | \(0.851147\pi\) | |||||||
\(194\) | 13.5994 | 0.976381 | ||||||||
\(195\) | 4.34393 | 0.311075 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −14.4839 | −1.03194 | −0.515969 | − | 0.856607i | \(-0.672568\pi\) | ||||
−0.515969 | + | 0.856607i | \(0.672568\pi\) | |||||||
\(198\) | 12.7976 | 0.909483 | ||||||||
\(199\) | 2.67035 | 0.189296 | 0.0946482 | − | 0.995511i | \(-0.469827\pi\) | ||||
0.0946482 | + | 0.995511i | \(0.469827\pi\) | |||||||
\(200\) | 1.56569 | 0.110711 | ||||||||
\(201\) | 5.47475 | 0.386159 | ||||||||
\(202\) | −9.17375 | −0.645462 | ||||||||
\(203\) | 4.78767 | 0.336028 | ||||||||
\(204\) | −2.88341 | −0.201879 | ||||||||
\(205\) | −0.951366 | −0.0664463 | ||||||||
\(206\) | −4.11643 | −0.286805 | ||||||||
\(207\) | −13.1628 | −0.914880 | ||||||||
\(208\) | −5.91310 | −0.410000 | ||||||||
\(209\) | 37.4915 | 2.59334 | ||||||||
\(210\) | 0.734628 | 0.0506942 | ||||||||
\(211\) | 8.51835 | 0.586427 | 0.293214 | − | 0.956047i | \(-0.405275\pi\) | ||||
0.293214 | + | 0.956047i | \(0.405275\pi\) | |||||||
\(212\) | 0.359603 | 0.0246977 | ||||||||
\(213\) | 1.10894 | 0.0759833 | ||||||||
\(214\) | −0.279089 | −0.0190781 | ||||||||
\(215\) | 18.0253 | 1.22931 | ||||||||
\(216\) | 2.31618 | 0.157596 | ||||||||
\(217\) | −2.20360 | −0.149590 | ||||||||
\(218\) | −18.3186 | −1.24069 | ||||||||
\(219\) | −3.08885 | −0.208725 | ||||||||
\(220\) | −8.34241 | −0.562445 | ||||||||
\(221\) | 43.0104 | 2.89319 | ||||||||
\(222\) | −1.90882 | −0.128112 | ||||||||
\(223\) | −3.39491 | −0.227340 | −0.113670 | − | 0.993519i | \(-0.536261\pi\) | ||||
−0.113670 | + | 0.993519i | \(0.536261\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.45104 | 0.296736 | ||||||||
\(226\) | −0.364997 | −0.0242792 | ||||||||
\(227\) | 17.3804 | 1.15358 | 0.576789 | − | 0.816893i | \(-0.304306\pi\) | ||||
0.576789 | + | 0.816893i | \(0.304306\pi\) | |||||||
\(228\) | 3.30148 | 0.218646 | ||||||||
\(229\) | −18.7849 | −1.24134 | −0.620670 | − | 0.784072i | \(-0.713139\pi\) | ||||
−0.620670 | + | 0.784072i | \(0.713139\pi\) | |||||||
\(230\) | 8.58053 | 0.565783 | ||||||||
\(231\) | 1.78451 | 0.117412 | ||||||||
\(232\) | −4.78767 | −0.314326 | ||||||||
\(233\) | 15.2182 | 0.996976 | 0.498488 | − | 0.866897i | \(-0.333889\pi\) | ||||
0.498488 | + | 0.866897i | \(0.333889\pi\) | |||||||
\(234\) | −16.8101 | −1.09891 | ||||||||
\(235\) | 4.81497 | 0.314094 | ||||||||
\(236\) | −13.9736 | −0.909604 | ||||||||
\(237\) | −2.19887 | −0.142832 | ||||||||
\(238\) | 7.27375 | 0.471487 | ||||||||
\(239\) | 24.4542 | 1.58181 | 0.790906 | − | 0.611937i | \(-0.209610\pi\) | ||||
0.790906 | + | 0.611937i | \(0.209610\pi\) | |||||||
\(240\) | −0.734628 | −0.0474200 | ||||||||
\(241\) | 26.0041 | 1.67507 | 0.837536 | − | 0.546382i | \(-0.183995\pi\) | ||||
0.837536 | + | 0.546382i | \(0.183995\pi\) | |||||||
\(242\) | −9.26489 | −0.595570 | ||||||||
\(243\) | 9.96542 | 0.639282 | ||||||||
\(244\) | −6.74430 | −0.431759 | ||||||||
\(245\) | −1.85319 | −0.118396 | ||||||||
\(246\) | −0.203505 | −0.0129750 | ||||||||
\(247\) | −49.2465 | −3.13348 | ||||||||
\(248\) | 2.20360 | 0.139929 | ||||||||
\(249\) | 6.41448 | 0.406501 | ||||||||
\(250\) | −12.1675 | −0.769538 | ||||||||
\(251\) | 13.0731 | 0.825168 | 0.412584 | − | 0.910920i | \(-0.364626\pi\) | ||||
0.412584 | + | 0.910920i | \(0.364626\pi\) | |||||||
\(252\) | −2.84286 | −0.179083 | ||||||||
\(253\) | 20.8433 | 1.31041 | ||||||||
\(254\) | 6.00997 | 0.377099 | ||||||||
\(255\) | 5.34350 | 0.334623 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.55008 | 0.221448 | 0.110724 | − | 0.993851i | \(-0.464683\pi\) | ||||
0.110724 | + | 0.993851i | \(0.464683\pi\) | |||||||
\(258\) | 3.85576 | 0.240049 | ||||||||
\(259\) | 4.81524 | 0.299204 | ||||||||
\(260\) | 10.9581 | 0.679592 | ||||||||
\(261\) | −13.6107 | −0.842478 | ||||||||
\(262\) | −20.2084 | −1.24848 | ||||||||
\(263\) | 21.7902 | 1.34364 | 0.671820 | − | 0.740714i | \(-0.265513\pi\) | ||||
0.671820 | + | 0.740714i | \(0.265513\pi\) | |||||||
\(264\) | −1.78451 | −0.109829 | ||||||||
\(265\) | −0.666413 | −0.0409374 | ||||||||
\(266\) | −8.32838 | −0.510646 | ||||||||
\(267\) | −1.47165 | −0.0900638 | ||||||||
\(268\) | 13.8107 | 0.843624 | ||||||||
\(269\) | 25.2657 | 1.54048 | 0.770238 | − | 0.637756i | \(-0.220137\pi\) | ||||
0.770238 | + | 0.637756i | \(0.220137\pi\) | |||||||
\(270\) | −4.29233 | −0.261223 | ||||||||
\(271\) | −25.3538 | −1.54013 | −0.770067 | − | 0.637963i | \(-0.779777\pi\) | ||||
−0.770067 | + | 0.637963i | \(0.779777\pi\) | |||||||
\(272\) | −7.27375 | −0.441036 | ||||||||
\(273\) | −2.34403 | −0.141867 | ||||||||
\(274\) | −12.4323 | −0.751063 | ||||||||
\(275\) | −7.04820 | −0.425023 | ||||||||
\(276\) | 1.83545 | 0.110481 | ||||||||
\(277\) | 18.4191 | 1.10670 | 0.553348 | − | 0.832950i | \(-0.313350\pi\) | ||||
0.553348 | + | 0.832950i | \(0.313350\pi\) | |||||||
\(278\) | −2.95241 | −0.177074 | ||||||||
\(279\) | 6.26453 | 0.375048 | ||||||||
\(280\) | 1.85319 | 0.110749 | ||||||||
\(281\) | 18.5363 | 1.10578 | 0.552892 | − | 0.833253i | \(-0.313524\pi\) | ||||
0.552892 | + | 0.833253i | \(0.313524\pi\) | |||||||
\(282\) | 1.02996 | 0.0613334 | ||||||||
\(283\) | −25.6547 | −1.52502 | −0.762508 | − | 0.646979i | \(-0.776032\pi\) | ||||
−0.762508 | + | 0.646979i | \(0.776032\pi\) | |||||||
\(284\) | 2.79743 | 0.165997 | ||||||||
\(285\) | −6.11826 | −0.362414 | ||||||||
\(286\) | 26.6187 | 1.57400 | ||||||||
\(287\) | 0.513367 | 0.0303031 | ||||||||
\(288\) | 2.84286 | 0.167517 | ||||||||
\(289\) | 35.9074 | 2.11220 | ||||||||
\(290\) | 8.87245 | 0.521008 | ||||||||
\(291\) | −5.39099 | −0.316025 | ||||||||
\(292\) | −7.79200 | −0.455992 | ||||||||
\(293\) | −14.1525 | −0.826795 | −0.413398 | − | 0.910551i | \(-0.635658\pi\) | ||||
−0.413398 | + | 0.910551i | \(0.635658\pi\) | |||||||
\(294\) | −0.396413 | −0.0231193 | ||||||||
\(295\) | 25.8957 | 1.50771 | ||||||||
\(296\) | −4.81524 | −0.279880 | ||||||||
\(297\) | −10.4267 | −0.605016 | ||||||||
\(298\) | −2.62018 | −0.151783 | ||||||||
\(299\) | −27.3785 | −1.58334 | ||||||||
\(300\) | −0.620660 | −0.0358339 | ||||||||
\(301\) | −9.72662 | −0.560633 | ||||||||
\(302\) | 8.04927 | 0.463184 | ||||||||
\(303\) | 3.63659 | 0.208917 | ||||||||
\(304\) | 8.32838 | 0.477665 | ||||||||
\(305\) | 12.4985 | 0.715660 | ||||||||
\(306\) | −20.6782 | −1.18209 | ||||||||
\(307\) | 19.9849 | 1.14060 | 0.570299 | − | 0.821437i | \(-0.306827\pi\) | ||||
0.570299 | + | 0.821437i | \(0.306827\pi\) | |||||||
\(308\) | 4.50165 | 0.256506 | ||||||||
\(309\) | 1.63181 | 0.0928302 | ||||||||
\(310\) | −4.08369 | −0.231938 | ||||||||
\(311\) | 6.95173 | 0.394197 | 0.197098 | − | 0.980384i | \(-0.436848\pi\) | ||||
0.197098 | + | 0.980384i | \(0.436848\pi\) | |||||||
\(312\) | 2.34403 | 0.132704 | ||||||||
\(313\) | −34.7474 | −1.96404 | −0.982021 | − | 0.188773i | \(-0.939549\pi\) | ||||
−0.982021 | + | 0.188773i | \(0.939549\pi\) | |||||||
\(314\) | −12.2632 | −0.692050 | ||||||||
\(315\) | 5.26835 | 0.296838 | ||||||||
\(316\) | −5.54692 | −0.312039 | ||||||||
\(317\) | 12.2511 | 0.688089 | 0.344045 | − | 0.938953i | \(-0.388203\pi\) | ||||
0.344045 | + | 0.938953i | \(0.388203\pi\) | |||||||
\(318\) | −0.142551 | −0.00799389 | ||||||||
\(319\) | 21.5524 | 1.20670 | ||||||||
\(320\) | −1.85319 | −0.103596 | ||||||||
\(321\) | 0.110635 | 0.00617502 | ||||||||
\(322\) | −4.63014 | −0.258028 | ||||||||
\(323\) | −60.5785 | −3.37068 | ||||||||
\(324\) | 7.61040 | 0.422800 | ||||||||
\(325\) | 9.25809 | 0.513546 | ||||||||
\(326\) | −13.3927 | −0.741750 | ||||||||
\(327\) | 7.26171 | 0.401574 | ||||||||
\(328\) | −0.513367 | −0.0283460 | ||||||||
\(329\) | −2.59821 | −0.143244 | ||||||||
\(330\) | 3.30704 | 0.182047 | ||||||||
\(331\) | −29.8082 | −1.63841 | −0.819203 | − | 0.573504i | \(-0.805584\pi\) | ||||
−0.819203 | + | 0.573504i | \(0.805584\pi\) | |||||||
\(332\) | 16.1813 | 0.888065 | ||||||||
\(333\) | −13.6890 | −0.750154 | ||||||||
\(334\) | 11.5887 | 0.634106 | ||||||||
\(335\) | −25.5939 | −1.39834 | ||||||||
\(336\) | 0.396413 | 0.0216261 | ||||||||
\(337\) | 19.7025 | 1.07326 | 0.536632 | − | 0.843817i | \(-0.319697\pi\) | ||||
0.536632 | + | 0.843817i | \(0.319697\pi\) | |||||||
\(338\) | −21.9647 | −1.19472 | ||||||||
\(339\) | 0.144690 | 0.00785846 | ||||||||
\(340\) | 13.4796 | 0.731035 | ||||||||
\(341\) | −9.91986 | −0.537191 | ||||||||
\(342\) | 23.6764 | 1.28027 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 9.72662 | 0.524424 | ||||||||
\(345\) | −3.40143 | −0.183127 | ||||||||
\(346\) | 9.41841 | 0.506337 | ||||||||
\(347\) | −22.8987 | −1.22927 | −0.614634 | − | 0.788812i | \(-0.710696\pi\) | ||||
−0.614634 | + | 0.788812i | \(0.710696\pi\) | |||||||
\(348\) | 1.89789 | 0.101738 | ||||||||
\(349\) | 18.5304 | 0.991907 | 0.495954 | − | 0.868349i | \(-0.334819\pi\) | ||||
0.495954 | + | 0.868349i | \(0.334819\pi\) | |||||||
\(350\) | 1.56569 | 0.0836897 | ||||||||
\(351\) | 13.6958 | 0.731029 | ||||||||
\(352\) | −4.50165 | −0.239939 | ||||||||
\(353\) | 4.38016 | 0.233132 | 0.116566 | − | 0.993183i | \(-0.462811\pi\) | ||||
0.116566 | + | 0.993183i | \(0.462811\pi\) | |||||||
\(354\) | 5.53931 | 0.294411 | ||||||||
\(355\) | −5.18417 | −0.275147 | ||||||||
\(356\) | −3.71243 | −0.196758 | ||||||||
\(357\) | −2.88341 | −0.152606 | ||||||||
\(358\) | −7.68557 | −0.406195 | ||||||||
\(359\) | 7.23830 | 0.382023 | 0.191011 | − | 0.981588i | \(-0.438823\pi\) | ||||
0.191011 | + | 0.981588i | \(0.438823\pi\) | |||||||
\(360\) | −5.26835 | −0.277666 | ||||||||
\(361\) | 50.3619 | 2.65062 | ||||||||
\(362\) | −10.6450 | −0.559488 | ||||||||
\(363\) | 3.67272 | 0.192768 | ||||||||
\(364\) | −5.91310 | −0.309931 | ||||||||
\(365\) | 14.4400 | 0.755826 | ||||||||
\(366\) | 2.67353 | 0.139748 | ||||||||
\(367\) | 30.9515 | 1.61566 | 0.807828 | − | 0.589418i | \(-0.200643\pi\) | ||||
0.807828 | + | 0.589418i | \(0.200643\pi\) | |||||||
\(368\) | 4.63014 | 0.241363 | ||||||||
\(369\) | −1.45943 | −0.0759749 | ||||||||
\(370\) | 8.92354 | 0.463913 | ||||||||
\(371\) | 0.359603 | 0.0186697 | ||||||||
\(372\) | −0.873537 | −0.0452908 | ||||||||
\(373\) | −6.41367 | −0.332087 | −0.166043 | − | 0.986118i | \(-0.553099\pi\) | ||||
−0.166043 | + | 0.986118i | \(0.553099\pi\) | |||||||
\(374\) | 32.7439 | 1.69315 | ||||||||
\(375\) | 4.82334 | 0.249076 | ||||||||
\(376\) | 2.59821 | 0.133992 | ||||||||
\(377\) | −28.3099 | −1.45804 | ||||||||
\(378\) | 2.31618 | 0.119132 | ||||||||
\(379\) | 33.8537 | 1.73895 | 0.869474 | − | 0.493979i | \(-0.164458\pi\) | ||||
0.869474 | + | 0.493979i | \(0.164458\pi\) | |||||||
\(380\) | −15.4341 | −0.791750 | ||||||||
\(381\) | −2.38243 | −0.122056 | ||||||||
\(382\) | 13.7742 | 0.704748 | ||||||||
\(383\) | 31.4277 | 1.60588 | 0.802941 | − | 0.596059i | \(-0.203268\pi\) | ||||
0.802941 | + | 0.596059i | \(0.203268\pi\) | |||||||
\(384\) | −0.396413 | −0.0202294 | ||||||||
\(385\) | −8.34241 | −0.425169 | ||||||||
\(386\) | 24.8018 | 1.26238 | ||||||||
\(387\) | 27.6514 | 1.40560 | ||||||||
\(388\) | −13.5994 | −0.690406 | ||||||||
\(389\) | 16.4239 | 0.832723 | 0.416362 | − | 0.909199i | \(-0.363305\pi\) | ||||
0.416362 | + | 0.909199i | \(0.363305\pi\) | |||||||
\(390\) | −4.34393 | −0.219963 | ||||||||
\(391\) | −33.6785 | −1.70319 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 8.01087 | 0.404095 | ||||||||
\(394\) | 14.4839 | 0.729691 | ||||||||
\(395\) | 10.2795 | 0.517217 | ||||||||
\(396\) | −12.7976 | −0.643101 | ||||||||
\(397\) | −13.5998 | −0.682553 | −0.341277 | − | 0.939963i | \(-0.610859\pi\) | ||||
−0.341277 | + | 0.939963i | \(0.610859\pi\) | |||||||
\(398\) | −2.67035 | −0.133853 | ||||||||
\(399\) | 3.30148 | 0.165281 | ||||||||
\(400\) | −1.56569 | −0.0782846 | ||||||||
\(401\) | 10.9174 | 0.545188 | 0.272594 | − | 0.962129i | \(-0.412118\pi\) | ||||
0.272594 | + | 0.962129i | \(0.412118\pi\) | |||||||
\(402\) | −5.47475 | −0.273056 | ||||||||
\(403\) | 13.0301 | 0.649077 | ||||||||
\(404\) | 9.17375 | 0.456411 | ||||||||
\(405\) | −14.1035 | −0.700809 | ||||||||
\(406\) | −4.78767 | −0.237608 | ||||||||
\(407\) | 21.6765 | 1.07447 | ||||||||
\(408\) | 2.88341 | 0.142750 | ||||||||
\(409\) | 3.69620 | 0.182765 | 0.0913827 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913827 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(410\) | 0.951366 | 0.0469846 | ||||||||
\(411\) | 4.92833 | 0.243097 | ||||||||
\(412\) | 4.11643 | 0.202802 | ||||||||
\(413\) | −13.9736 | −0.687596 | ||||||||
\(414\) | 13.1628 | 0.646918 | ||||||||
\(415\) | −29.9870 | −1.47200 | ||||||||
\(416\) | 5.91310 | 0.289913 | ||||||||
\(417\) | 1.17037 | 0.0573134 | ||||||||
\(418\) | −37.4915 | −1.83377 | ||||||||
\(419\) | 15.6733 | 0.765692 | 0.382846 | − | 0.923812i | \(-0.374944\pi\) | ||||
0.382846 | + | 0.923812i | \(0.374944\pi\) | |||||||
\(420\) | −0.734628 | −0.0358462 | ||||||||
\(421\) | −8.12216 | −0.395850 | −0.197925 | − | 0.980217i | \(-0.563420\pi\) | ||||
−0.197925 | + | 0.980217i | \(0.563420\pi\) | |||||||
\(422\) | −8.51835 | −0.414667 | ||||||||
\(423\) | 7.38633 | 0.359136 | ||||||||
\(424\) | −0.359603 | −0.0174639 | ||||||||
\(425\) | 11.3884 | 0.552421 | ||||||||
\(426\) | −1.10894 | −0.0537283 | ||||||||
\(427\) | −6.74430 | −0.326379 | ||||||||
\(428\) | 0.279089 | 0.0134903 | ||||||||
\(429\) | −10.5520 | −0.509456 | ||||||||
\(430\) | −18.0253 | −0.869256 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −2.31618 | −0.111437 | ||||||||
\(433\) | 22.6687 | 1.08939 | 0.544693 | − | 0.838635i | \(-0.316646\pi\) | ||||
0.544693 | + | 0.838635i | \(0.316646\pi\) | |||||||
\(434\) | 2.20360 | 0.105776 | ||||||||
\(435\) | −3.51716 | −0.168635 | ||||||||
\(436\) | 18.3186 | 0.877300 | ||||||||
\(437\) | 38.5616 | 1.84465 | ||||||||
\(438\) | 3.08885 | 0.147591 | ||||||||
\(439\) | −9.28641 | −0.443216 | −0.221608 | − | 0.975136i | \(-0.571131\pi\) | ||||
−0.221608 | + | 0.975136i | \(0.571131\pi\) | |||||||
\(440\) | 8.34241 | 0.397709 | ||||||||
\(441\) | −2.84286 | −0.135374 | ||||||||
\(442\) | −43.0104 | −2.04579 | ||||||||
\(443\) | −34.2337 | −1.62649 | −0.813245 | − | 0.581922i | \(-0.802301\pi\) | ||||
−0.813245 | + | 0.581922i | \(0.802301\pi\) | |||||||
\(444\) | 1.90882 | 0.0905887 | ||||||||
\(445\) | 6.87983 | 0.326135 | ||||||||
\(446\) | 3.39491 | 0.160754 | ||||||||
\(447\) | 1.03867 | 0.0491275 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −16.4904 | −0.778231 | −0.389116 | − | 0.921189i | \(-0.627219\pi\) | ||||
−0.389116 | + | 0.921189i | \(0.627219\pi\) | |||||||
\(450\) | −4.45104 | −0.209824 | ||||||||
\(451\) | 2.31100 | 0.108821 | ||||||||
\(452\) | 0.364997 | 0.0171680 | ||||||||
\(453\) | −3.19084 | −0.149919 | ||||||||
\(454\) | −17.3804 | −0.815702 | ||||||||
\(455\) | 10.9581 | 0.513723 | ||||||||
\(456\) | −3.30148 | −0.154606 | ||||||||
\(457\) | −28.1687 | −1.31768 | −0.658838 | − | 0.752284i | \(-0.728952\pi\) | ||||
−0.658838 | + | 0.752284i | \(0.728952\pi\) | |||||||
\(458\) | 18.7849 | 0.877760 | ||||||||
\(459\) | 16.8473 | 0.786366 | ||||||||
\(460\) | −8.58053 | −0.400069 | ||||||||
\(461\) | −16.2469 | −0.756692 | −0.378346 | − | 0.925664i | \(-0.623507\pi\) | ||||
−0.378346 | + | 0.925664i | \(0.623507\pi\) | |||||||
\(462\) | −1.78451 | −0.0830231 | ||||||||
\(463\) | 28.9035 | 1.34326 | 0.671629 | − | 0.740888i | \(-0.265595\pi\) | ||||
0.671629 | + | 0.740888i | \(0.265595\pi\) | |||||||
\(464\) | 4.78767 | 0.222262 | ||||||||
\(465\) | 1.61883 | 0.0750714 | ||||||||
\(466\) | −15.2182 | −0.704969 | ||||||||
\(467\) | −6.68344 | −0.309273 | −0.154636 | − | 0.987971i | \(-0.549421\pi\) | ||||
−0.154636 | + | 0.987971i | \(0.549421\pi\) | |||||||
\(468\) | 16.8101 | 0.777047 | ||||||||
\(469\) | 13.8107 | 0.637720 | ||||||||
\(470\) | −4.81497 | −0.222098 | ||||||||
\(471\) | 4.86128 | 0.223996 | ||||||||
\(472\) | 13.9736 | 0.643187 | ||||||||
\(473\) | −43.7859 | −2.01328 | ||||||||
\(474\) | 2.19887 | 0.100998 | ||||||||
\(475\) | −13.0397 | −0.598301 | ||||||||
\(476\) | −7.27375 | −0.333392 | ||||||||
\(477\) | −1.02230 | −0.0468079 | ||||||||
\(478\) | −24.4542 | −1.11851 | ||||||||
\(479\) | −27.5978 | −1.26098 | −0.630488 | − | 0.776199i | \(-0.717145\pi\) | ||||
−0.630488 | + | 0.776199i | \(0.717145\pi\) | |||||||
\(480\) | 0.734628 | 0.0335310 | ||||||||
\(481\) | −28.4730 | −1.29826 | ||||||||
\(482\) | −26.0041 | −1.18445 | ||||||||
\(483\) | 1.83545 | 0.0835158 | ||||||||
\(484\) | 9.26489 | 0.421131 | ||||||||
\(485\) | 25.2023 | 1.14438 | ||||||||
\(486\) | −9.96542 | −0.452040 | ||||||||
\(487\) | −20.2647 | −0.918281 | −0.459140 | − | 0.888364i | \(-0.651843\pi\) | ||||
−0.459140 | + | 0.888364i | \(0.651843\pi\) | |||||||
\(488\) | 6.74430 | 0.305300 | ||||||||
\(489\) | 5.30902 | 0.240082 | ||||||||
\(490\) | 1.85319 | 0.0837185 | ||||||||
\(491\) | 28.2429 | 1.27458 | 0.637291 | − | 0.770623i | \(-0.280055\pi\) | ||||
0.637291 | + | 0.770623i | \(0.280055\pi\) | |||||||
\(492\) | 0.203505 | 0.00917473 | ||||||||
\(493\) | −34.8243 | −1.56841 | ||||||||
\(494\) | 49.2465 | 2.21570 | ||||||||
\(495\) | 23.7163 | 1.06597 | ||||||||
\(496\) | −2.20360 | −0.0989448 | ||||||||
\(497\) | 2.79743 | 0.125482 | ||||||||
\(498\) | −6.41448 | −0.287440 | ||||||||
\(499\) | 20.0006 | 0.895351 | 0.447675 | − | 0.894196i | \(-0.352252\pi\) | ||||
0.447675 | + | 0.894196i | \(0.352252\pi\) | |||||||
\(500\) | 12.1675 | 0.544146 | ||||||||
\(501\) | −4.59391 | −0.205241 | ||||||||
\(502\) | −13.0731 | −0.583482 | ||||||||
\(503\) | 33.7244 | 1.50370 | 0.751848 | − | 0.659337i | \(-0.229163\pi\) | ||||
0.751848 | + | 0.659337i | \(0.229163\pi\) | |||||||
\(504\) | 2.84286 | 0.126631 | ||||||||
\(505\) | −17.0007 | −0.756520 | ||||||||
\(506\) | −20.8433 | −0.926597 | ||||||||
\(507\) | 8.70710 | 0.386696 | ||||||||
\(508\) | −6.00997 | −0.266649 | ||||||||
\(509\) | 22.5708 | 1.00043 | 0.500217 | − | 0.865900i | \(-0.333253\pi\) | ||||
0.500217 | + | 0.865900i | \(0.333253\pi\) | |||||||
\(510\) | −5.34350 | −0.236614 | ||||||||
\(511\) | −7.79200 | −0.344698 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −19.2901 | −0.851677 | ||||||||
\(514\) | −3.55008 | −0.156587 | ||||||||
\(515\) | −7.62852 | −0.336153 | ||||||||
\(516\) | −3.85576 | −0.169740 | ||||||||
\(517\) | −11.6962 | −0.514399 | ||||||||
\(518\) | −4.81524 | −0.211569 | ||||||||
\(519\) | −3.73358 | −0.163886 | ||||||||
\(520\) | −10.9581 | −0.480544 | ||||||||
\(521\) | −9.29541 | −0.407239 | −0.203620 | − | 0.979050i | \(-0.565271\pi\) | ||||
−0.203620 | + | 0.979050i | \(0.565271\pi\) | |||||||
\(522\) | 13.6107 | 0.595722 | ||||||||
\(523\) | −2.04093 | −0.0892437 | −0.0446219 | − | 0.999004i | \(-0.514208\pi\) | ||||
−0.0446219 | + | 0.999004i | \(0.514208\pi\) | |||||||
\(524\) | 20.2084 | 0.882808 | ||||||||
\(525\) | −0.620660 | −0.0270878 | ||||||||
\(526\) | −21.7902 | −0.950097 | ||||||||
\(527\) | 16.0285 | 0.698211 | ||||||||
\(528\) | 1.78451 | 0.0776610 | ||||||||
\(529\) | −1.56179 | −0.0679040 | ||||||||
\(530\) | 0.666413 | 0.0289471 | ||||||||
\(531\) | 39.7249 | 1.72392 | ||||||||
\(532\) | 8.32838 | 0.361081 | ||||||||
\(533\) | −3.03559 | −0.131486 | ||||||||
\(534\) | 1.47165 | 0.0636847 | ||||||||
\(535\) | −0.517205 | −0.0223607 | ||||||||
\(536\) | −13.8107 | −0.596532 | ||||||||
\(537\) | 3.04666 | 0.131473 | ||||||||
\(538\) | −25.2657 | −1.08928 | ||||||||
\(539\) | 4.50165 | 0.193900 | ||||||||
\(540\) | 4.29233 | 0.184712 | ||||||||
\(541\) | 9.48686 | 0.407872 | 0.203936 | − | 0.978984i | \(-0.434627\pi\) | ||||
0.203936 | + | 0.978984i | \(0.434627\pi\) | |||||||
\(542\) | 25.3538 | 1.08904 | ||||||||
\(543\) | 4.21981 | 0.181089 | ||||||||
\(544\) | 7.27375 | 0.311859 | ||||||||
\(545\) | −33.9477 | −1.45416 | ||||||||
\(546\) | 2.34403 | 0.100315 | ||||||||
\(547\) | 14.6635 | 0.626964 | 0.313482 | − | 0.949594i | \(-0.398504\pi\) | ||||
0.313482 | + | 0.949594i | \(0.398504\pi\) | |||||||
\(548\) | 12.4323 | 0.531082 | ||||||||
\(549\) | 19.1731 | 0.818287 | ||||||||
\(550\) | 7.04820 | 0.300536 | ||||||||
\(551\) | 39.8735 | 1.69867 | ||||||||
\(552\) | −1.83545 | −0.0781219 | ||||||||
\(553\) | −5.54692 | −0.235879 | ||||||||
\(554\) | −18.4191 | −0.782553 | ||||||||
\(555\) | −3.53741 | −0.150155 | ||||||||
\(556\) | 2.95241 | 0.125210 | ||||||||
\(557\) | −15.3489 | −0.650353 | −0.325176 | − | 0.945653i | \(-0.605424\pi\) | ||||
−0.325176 | + | 0.945653i | \(0.605424\pi\) | |||||||
\(558\) | −6.26453 | −0.265199 | ||||||||
\(559\) | 57.5145 | 2.43260 | ||||||||
\(560\) | −1.85319 | −0.0783115 | ||||||||
\(561\) | −12.9801 | −0.548020 | ||||||||
\(562\) | −18.5363 | −0.781907 | ||||||||
\(563\) | 34.7976 | 1.46654 | 0.733271 | − | 0.679936i | \(-0.237993\pi\) | ||||
0.733271 | + | 0.679936i | \(0.237993\pi\) | |||||||
\(564\) | −1.02996 | −0.0433693 | ||||||||
\(565\) | −0.676408 | −0.0284567 | ||||||||
\(566\) | 25.6547 | 1.07835 | ||||||||
\(567\) | 7.61040 | 0.319607 | ||||||||
\(568\) | −2.79743 | −0.117378 | ||||||||
\(569\) | −22.8252 | −0.956881 | −0.478441 | − | 0.878120i | \(-0.658798\pi\) | ||||
−0.478441 | + | 0.878120i | \(0.658798\pi\) | |||||||
\(570\) | 6.11826 | 0.256266 | ||||||||
\(571\) | −18.6595 | −0.780875 | −0.390437 | − | 0.920630i | \(-0.627676\pi\) | ||||
−0.390437 | + | 0.920630i | \(0.627676\pi\) | |||||||
\(572\) | −26.6187 | −1.11298 | ||||||||
\(573\) | −5.46026 | −0.228106 | ||||||||
\(574\) | −0.513367 | −0.0214275 | ||||||||
\(575\) | −7.24937 | −0.302320 | ||||||||
\(576\) | −2.84286 | −0.118452 | ||||||||
\(577\) | −24.7924 | −1.03212 | −0.516061 | − | 0.856552i | \(-0.672602\pi\) | ||||
−0.516061 | + | 0.856552i | \(0.672602\pi\) | |||||||
\(578\) | −35.9074 | −1.49355 | ||||||||
\(579\) | −9.83176 | −0.408594 | ||||||||
\(580\) | −8.87245 | −0.368409 | ||||||||
\(581\) | 16.1813 | 0.671314 | ||||||||
\(582\) | 5.39099 | 0.223464 | ||||||||
\(583\) | 1.61881 | 0.0670442 | ||||||||
\(584\) | 7.79200 | 0.322435 | ||||||||
\(585\) | −31.1523 | −1.28799 | ||||||||
\(586\) | 14.1525 | 0.584633 | ||||||||
\(587\) | 31.6830 | 1.30770 | 0.653849 | − | 0.756625i | \(-0.273153\pi\) | ||||
0.653849 | + | 0.756625i | \(0.273153\pi\) | |||||||
\(588\) | 0.396413 | 0.0163478 | ||||||||
\(589\) | −18.3524 | −0.756199 | ||||||||
\(590\) | −25.8957 | −1.06611 | ||||||||
\(591\) | −5.74163 | −0.236179 | ||||||||
\(592\) | 4.81524 | 0.197905 | ||||||||
\(593\) | 11.0718 | 0.454665 | 0.227332 | − | 0.973817i | \(-0.427000\pi\) | ||||
0.227332 | + | 0.973817i | \(0.427000\pi\) | |||||||
\(594\) | 10.4267 | 0.427811 | ||||||||
\(595\) | 13.4796 | 0.552611 | ||||||||
\(596\) | 2.62018 | 0.107327 | ||||||||
\(597\) | 1.05856 | 0.0433241 | ||||||||
\(598\) | 27.3785 | 1.11959 | ||||||||
\(599\) | 7.47933 | 0.305597 | 0.152799 | − | 0.988257i | \(-0.451171\pi\) | ||||
0.152799 | + | 0.988257i | \(0.451171\pi\) | |||||||
\(600\) | 0.620660 | 0.0253384 | ||||||||
\(601\) | 4.47727 | 0.182632 | 0.0913158 | − | 0.995822i | \(-0.470893\pi\) | ||||
0.0913158 | + | 0.995822i | \(0.470893\pi\) | |||||||
\(602\) | 9.72662 | 0.396428 | ||||||||
\(603\) | −39.2619 | −1.59887 | ||||||||
\(604\) | −8.04927 | −0.327520 | ||||||||
\(605\) | −17.1696 | −0.698043 | ||||||||
\(606\) | −3.63659 | −0.147726 | ||||||||
\(607\) | 21.2494 | 0.862488 | 0.431244 | − | 0.902235i | \(-0.358075\pi\) | ||||
0.431244 | + | 0.902235i | \(0.358075\pi\) | |||||||
\(608\) | −8.32838 | −0.337760 | ||||||||
\(609\) | 1.89789 | 0.0769065 | ||||||||
\(610\) | −12.4985 | −0.506048 | ||||||||
\(611\) | 15.3634 | 0.621539 | ||||||||
\(612\) | 20.6782 | 0.835867 | ||||||||
\(613\) | 18.3626 | 0.741657 | 0.370828 | − | 0.928701i | \(-0.379074\pi\) | ||||
0.370828 | + | 0.928701i | \(0.379074\pi\) | |||||||
\(614\) | −19.9849 | −0.806525 | ||||||||
\(615\) | −0.377134 | −0.0152075 | ||||||||
\(616\) | −4.50165 | −0.181377 | ||||||||
\(617\) | 13.3137 | 0.535988 | 0.267994 | − | 0.963421i | \(-0.413639\pi\) | ||||
0.267994 | + | 0.963421i | \(0.413639\pi\) | |||||||
\(618\) | −1.63181 | −0.0656409 | ||||||||
\(619\) | −30.6216 | −1.23078 | −0.615392 | − | 0.788221i | \(-0.711002\pi\) | ||||
−0.615392 | + | 0.788221i | \(0.711002\pi\) | |||||||
\(620\) | 4.08369 | 0.164005 | ||||||||
\(621\) | −10.7243 | −0.430350 | ||||||||
\(622\) | −6.95173 | −0.278739 | ||||||||
\(623\) | −3.71243 | −0.148735 | ||||||||
\(624\) | −2.34403 | −0.0938362 | ||||||||
\(625\) | −14.7202 | −0.588806 | ||||||||
\(626\) | 34.7474 | 1.38879 | ||||||||
\(627\) | 14.8621 | 0.593535 | ||||||||
\(628\) | 12.2632 | 0.489354 | ||||||||
\(629\) | −35.0248 | −1.39653 | ||||||||
\(630\) | −5.26835 | −0.209896 | ||||||||
\(631\) | −15.3971 | −0.612948 | −0.306474 | − | 0.951879i | \(-0.599149\pi\) | ||||
−0.306474 | + | 0.951879i | \(0.599149\pi\) | |||||||
\(632\) | 5.54692 | 0.220645 | ||||||||
\(633\) | 3.37678 | 0.134215 | ||||||||
\(634\) | −12.2511 | −0.486552 | ||||||||
\(635\) | 11.1376 | 0.441983 | ||||||||
\(636\) | 0.142551 | 0.00565253 | ||||||||
\(637\) | −5.91310 | −0.234285 | ||||||||
\(638\) | −21.5524 | −0.853269 | ||||||||
\(639\) | −7.95270 | −0.314604 | ||||||||
\(640\) | 1.85319 | 0.0732537 | ||||||||
\(641\) | −22.8879 | −0.904016 | −0.452008 | − | 0.892014i | \(-0.649292\pi\) | ||||
−0.452008 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(642\) | −0.110635 | −0.00436640 | ||||||||
\(643\) | −1.91750 | −0.0756189 | −0.0378095 | − | 0.999285i | \(-0.512038\pi\) | ||||
−0.0378095 | + | 0.999285i | \(0.512038\pi\) | |||||||
\(644\) | 4.63014 | 0.182453 | ||||||||
\(645\) | 7.14545 | 0.281352 | ||||||||
\(646\) | 60.5785 | 2.38343 | ||||||||
\(647\) | −2.59839 | −0.102153 | −0.0510767 | − | 0.998695i | \(-0.516265\pi\) | ||||
−0.0510767 | + | 0.998695i | \(0.516265\pi\) | |||||||
\(648\) | −7.61040 | −0.298965 | ||||||||
\(649\) | −62.9043 | −2.46921 | ||||||||
\(650\) | −9.25809 | −0.363132 | ||||||||
\(651\) | −0.873537 | −0.0342366 | ||||||||
\(652\) | 13.3927 | 0.524497 | ||||||||
\(653\) | 5.61564 | 0.219757 | 0.109878 | − | 0.993945i | \(-0.464954\pi\) | ||||
0.109878 | + | 0.993945i | \(0.464954\pi\) | |||||||
\(654\) | −7.26171 | −0.283955 | ||||||||
\(655\) | −37.4500 | −1.46329 | ||||||||
\(656\) | 0.513367 | 0.0200436 | ||||||||
\(657\) | 22.1515 | 0.864214 | ||||||||
\(658\) | 2.59821 | 0.101289 | ||||||||
\(659\) | 12.4802 | 0.486160 | 0.243080 | − | 0.970006i | \(-0.421842\pi\) | ||||
0.243080 | + | 0.970006i | \(0.421842\pi\) | |||||||
\(660\) | −3.30704 | −0.128726 | ||||||||
\(661\) | 49.7759 | 1.93606 | 0.968028 | − | 0.250842i | \(-0.0807074\pi\) | ||||
0.968028 | + | 0.250842i | \(0.0807074\pi\) | |||||||
\(662\) | 29.8082 | 1.15853 | ||||||||
\(663\) | 17.0499 | 0.662162 | ||||||||
\(664\) | −16.1813 | −0.627957 | ||||||||
\(665\) | −15.4341 | −0.598507 | ||||||||
\(666\) | 13.6890 | 0.530439 | ||||||||
\(667\) | 22.1676 | 0.858332 | ||||||||
\(668\) | −11.5887 | −0.448380 | ||||||||
\(669\) | −1.34579 | −0.0520311 | ||||||||
\(670\) | 25.5939 | 0.988777 | ||||||||
\(671\) | −30.3605 | −1.17205 | ||||||||
\(672\) | −0.396413 | −0.0152920 | ||||||||
\(673\) | 11.8038 | 0.455002 | 0.227501 | − | 0.973778i | \(-0.426945\pi\) | ||||
0.227501 | + | 0.973778i | \(0.426945\pi\) | |||||||
\(674\) | −19.7025 | −0.758912 | ||||||||
\(675\) | 3.62643 | 0.139581 | ||||||||
\(676\) | 21.9647 | 0.844797 | ||||||||
\(677\) | 30.0895 | 1.15643 | 0.578217 | − | 0.815883i | \(-0.303749\pi\) | ||||
0.578217 | + | 0.815883i | \(0.303749\pi\) | |||||||
\(678\) | −0.144690 | −0.00555677 | ||||||||
\(679\) | −13.5994 | −0.521898 | ||||||||
\(680\) | −13.4796 | −0.516920 | ||||||||
\(681\) | 6.88981 | 0.264018 | ||||||||
\(682\) | 9.91986 | 0.379851 | ||||||||
\(683\) | −11.1270 | −0.425763 | −0.212881 | − | 0.977078i | \(-0.568285\pi\) | ||||
−0.212881 | + | 0.977078i | \(0.568285\pi\) | |||||||
\(684\) | −23.6764 | −0.905289 | ||||||||
\(685\) | −23.0394 | −0.880291 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −7.44658 | −0.284105 | ||||||||
\(688\) | −9.72662 | −0.370824 | ||||||||
\(689\) | −2.12637 | −0.0810082 | ||||||||
\(690\) | 3.40143 | 0.129490 | ||||||||
\(691\) | −16.2487 | −0.618128 | −0.309064 | − | 0.951041i | \(-0.600016\pi\) | ||||
−0.309064 | + | 0.951041i | \(0.600016\pi\) | |||||||
\(692\) | −9.41841 | −0.358034 | ||||||||
\(693\) | −12.7976 | −0.486139 | ||||||||
\(694\) | 22.8987 | 0.869224 | ||||||||
\(695\) | −5.47137 | −0.207541 | ||||||||
\(696\) | −1.89789 | −0.0719395 | ||||||||
\(697\) | −3.73410 | −0.141439 | ||||||||
\(698\) | −18.5304 | −0.701384 | ||||||||
\(699\) | 6.03268 | 0.228177 | ||||||||
\(700\) | −1.56569 | −0.0591776 | ||||||||
\(701\) | −4.16286 | −0.157229 | −0.0786146 | − | 0.996905i | \(-0.525050\pi\) | ||||
−0.0786146 | + | 0.996905i | \(0.525050\pi\) | |||||||
\(702\) | −13.6958 | −0.516916 | ||||||||
\(703\) | 40.1031 | 1.51252 | ||||||||
\(704\) | 4.50165 | 0.169662 | ||||||||
\(705\) | 1.90872 | 0.0718864 | ||||||||
\(706\) | −4.38016 | −0.164849 | ||||||||
\(707\) | 9.17375 | 0.345014 | ||||||||
\(708\) | −5.53931 | −0.208180 | ||||||||
\(709\) | −18.9149 | −0.710365 | −0.355183 | − | 0.934797i | \(-0.615581\pi\) | ||||
−0.355183 | + | 0.934797i | \(0.615581\pi\) | |||||||
\(710\) | 5.18417 | 0.194559 | ||||||||
\(711\) | 15.7691 | 0.591388 | ||||||||
\(712\) | 3.71243 | 0.139129 | ||||||||
\(713\) | −10.2030 | −0.382105 | ||||||||
\(714\) | 2.88341 | 0.107909 | ||||||||
\(715\) | 49.3295 | 1.84482 | ||||||||
\(716\) | 7.68557 | 0.287223 | ||||||||
\(717\) | 9.69397 | 0.362028 | ||||||||
\(718\) | −7.23830 | −0.270131 | ||||||||
\(719\) | −21.3952 | −0.797906 | −0.398953 | − | 0.916971i | \(-0.630626\pi\) | ||||
−0.398953 | + | 0.916971i | \(0.630626\pi\) | |||||||
\(720\) | 5.26835 | 0.196340 | ||||||||
\(721\) | 4.11643 | 0.153304 | ||||||||
\(722\) | −50.3619 | −1.87427 | ||||||||
\(723\) | 10.3084 | 0.383372 | ||||||||
\(724\) | 10.6450 | 0.395618 | ||||||||
\(725\) | −7.49601 | −0.278395 | ||||||||
\(726\) | −3.67272 | −0.136307 | ||||||||
\(727\) | 22.7888 | 0.845190 | 0.422595 | − | 0.906319i | \(-0.361119\pi\) | ||||
0.422595 | + | 0.906319i | \(0.361119\pi\) | |||||||
\(728\) | 5.91310 | 0.219154 | ||||||||
\(729\) | −18.8808 | −0.699289 | ||||||||
\(730\) | −14.4400 | −0.534450 | ||||||||
\(731\) | 70.7490 | 2.61675 | ||||||||
\(732\) | −2.67353 | −0.0988164 | ||||||||
\(733\) | 7.70908 | 0.284741 | 0.142371 | − | 0.989813i | \(-0.454527\pi\) | ||||
0.142371 | + | 0.989813i | \(0.454527\pi\) | |||||||
\(734\) | −30.9515 | −1.14244 | ||||||||
\(735\) | −0.734628 | −0.0270972 | ||||||||
\(736\) | −4.63014 | −0.170669 | ||||||||
\(737\) | 62.1711 | 2.29010 | ||||||||
\(738\) | 1.45943 | 0.0537223 | ||||||||
\(739\) | 15.0538 | 0.553762 | 0.276881 | − | 0.960904i | \(-0.410699\pi\) | ||||
0.276881 | + | 0.960904i | \(0.410699\pi\) | |||||||
\(740\) | −8.92354 | −0.328036 | ||||||||
\(741\) | −19.5220 | −0.717157 | ||||||||
\(742\) | −0.359603 | −0.0132015 | ||||||||
\(743\) | 26.2891 | 0.964454 | 0.482227 | − | 0.876046i | \(-0.339828\pi\) | ||||
0.482227 | + | 0.876046i | \(0.339828\pi\) | |||||||
\(744\) | 0.873537 | 0.0320254 | ||||||||
\(745\) | −4.85568 | −0.177898 | ||||||||
\(746\) | 6.41367 | 0.234821 | ||||||||
\(747\) | −46.0011 | −1.68309 | ||||||||
\(748\) | −32.7439 | −1.19723 | ||||||||
\(749\) | 0.279089 | 0.0101977 | ||||||||
\(750\) | −4.82334 | −0.176124 | ||||||||
\(751\) | 38.5238 | 1.40575 | 0.702877 | − | 0.711311i | \(-0.251898\pi\) | ||||
0.702877 | + | 0.711311i | \(0.251898\pi\) | |||||||
\(752\) | −2.59821 | −0.0947468 | ||||||||
\(753\) | 5.18235 | 0.188855 | ||||||||
\(754\) | 28.3099 | 1.03099 | ||||||||
\(755\) | 14.9168 | 0.542879 | ||||||||
\(756\) | −2.31618 | −0.0842388 | ||||||||
\(757\) | −13.8897 | −0.504828 | −0.252414 | − | 0.967619i | \(-0.581225\pi\) | ||||
−0.252414 | + | 0.967619i | \(0.581225\pi\) | |||||||
\(758\) | −33.8537 | −1.22962 | ||||||||
\(759\) | 8.26255 | 0.299912 | ||||||||
\(760\) | 15.4341 | 0.559852 | ||||||||
\(761\) | −33.8042 | −1.22540 | −0.612701 | − | 0.790315i | \(-0.709917\pi\) | ||||
−0.612701 | + | 0.790315i | \(0.709917\pi\) | |||||||
\(762\) | 2.38243 | 0.0863063 | ||||||||
\(763\) | 18.3186 | 0.663176 | ||||||||
\(764\) | −13.7742 | −0.498332 | ||||||||
\(765\) | −38.3206 | −1.38549 | ||||||||
\(766\) | −31.4277 | −1.13553 | ||||||||
\(767\) | 82.6272 | 2.98350 | ||||||||
\(768\) | 0.396413 | 0.0143043 | ||||||||
\(769\) | −42.6134 | −1.53668 | −0.768340 | − | 0.640042i | \(-0.778917\pi\) | ||||
−0.768340 | + | 0.640042i | \(0.778917\pi\) | |||||||
\(770\) | 8.34241 | 0.300640 | ||||||||
\(771\) | 1.40730 | 0.0506826 | ||||||||
\(772\) | −24.8018 | −0.892637 | ||||||||
\(773\) | 33.6637 | 1.21080 | 0.605399 | − | 0.795922i | \(-0.293013\pi\) | ||||
0.605399 | + | 0.795922i | \(0.293013\pi\) | |||||||
\(774\) | −27.6514 | −0.993909 | ||||||||
\(775\) | 3.45017 | 0.123934 | ||||||||
\(776\) | 13.5994 | 0.488191 | ||||||||
\(777\) | 1.90882 | 0.0684786 | ||||||||
\(778\) | −16.4239 | −0.588824 | ||||||||
\(779\) | 4.27552 | 0.153186 | ||||||||
\(780\) | 4.34393 | 0.155538 | ||||||||
\(781\) | 12.5931 | 0.450616 | ||||||||
\(782\) | 33.6785 | 1.20434 | ||||||||
\(783\) | −11.0891 | −0.396293 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −22.7260 | −0.811124 | ||||||||
\(786\) | −8.01087 | −0.285738 | ||||||||
\(787\) | 8.08015 | 0.288026 | 0.144013 | − | 0.989576i | \(-0.453999\pi\) | ||||
0.144013 | + | 0.989576i | \(0.453999\pi\) | |||||||
\(788\) | −14.4839 | −0.515969 | ||||||||
\(789\) | 8.63791 | 0.307518 | ||||||||
\(790\) | −10.2795 | −0.365728 | ||||||||
\(791\) | 0.364997 | 0.0129778 | ||||||||
\(792\) | 12.7976 | 0.454741 | ||||||||
\(793\) | 39.8797 | 1.41617 | ||||||||
\(794\) | 13.5998 | 0.482638 | ||||||||
\(795\) | −0.264175 | −0.00936931 | ||||||||
\(796\) | 2.67035 | 0.0946482 | ||||||||
\(797\) | 46.4614 | 1.64575 | 0.822873 | − | 0.568225i | \(-0.192370\pi\) | ||||
0.822873 | + | 0.568225i | \(0.192370\pi\) | |||||||
\(798\) | −3.30148 | −0.116871 | ||||||||
\(799\) | 18.8987 | 0.668588 | ||||||||
\(800\) | 1.56569 | 0.0553556 | ||||||||
\(801\) | 10.5539 | 0.372904 | ||||||||
\(802\) | −10.9174 | −0.385506 | ||||||||
\(803\) | −35.0769 | −1.23784 | ||||||||
\(804\) | 5.47475 | 0.193079 | ||||||||
\(805\) | −8.58053 | −0.302424 | ||||||||
\(806\) | −13.0301 | −0.458967 | ||||||||
\(807\) | 10.0157 | 0.352568 | ||||||||
\(808\) | −9.17375 | −0.322731 | ||||||||
\(809\) | 36.1851 | 1.27220 | 0.636100 | − | 0.771607i | \(-0.280547\pi\) | ||||
0.636100 | + | 0.771607i | \(0.280547\pi\) | |||||||
\(810\) | 14.1035 | 0.495547 | ||||||||
\(811\) | −42.5480 | −1.49406 | −0.747031 | − | 0.664790i | \(-0.768521\pi\) | ||||
−0.747031 | + | 0.664790i | \(0.768521\pi\) | |||||||
\(812\) | 4.78767 | 0.168014 | ||||||||
\(813\) | −10.0506 | −0.352489 | ||||||||
\(814\) | −21.6765 | −0.759762 | ||||||||
\(815\) | −24.8191 | −0.869375 | ||||||||
\(816\) | −2.88341 | −0.100939 | ||||||||
\(817\) | −81.0070 | −2.83408 | ||||||||
\(818\) | −3.69620 | −0.129235 | ||||||||
\(819\) | 16.8101 | 0.587392 | ||||||||
\(820\) | −0.951366 | −0.0332232 | ||||||||
\(821\) | 43.5049 | 1.51833 | 0.759166 | − | 0.650897i | \(-0.225607\pi\) | ||||
0.759166 | + | 0.650897i | \(0.225607\pi\) | |||||||
\(822\) | −4.92833 | −0.171895 | ||||||||
\(823\) | −32.9144 | −1.14732 | −0.573661 | − | 0.819093i | \(-0.694477\pi\) | ||||
−0.573661 | + | 0.819093i | \(0.694477\pi\) | |||||||
\(824\) | −4.11643 | −0.143403 | ||||||||
\(825\) | −2.79400 | −0.0972745 | ||||||||
\(826\) | 13.9736 | 0.486204 | ||||||||
\(827\) | −3.23098 | −0.112352 | −0.0561761 | − | 0.998421i | \(-0.517891\pi\) | ||||
−0.0561761 | + | 0.998421i | \(0.517891\pi\) | |||||||
\(828\) | −13.1628 | −0.457440 | ||||||||
\(829\) | −6.72134 | −0.233442 | −0.116721 | − | 0.993165i | \(-0.537238\pi\) | ||||
−0.116721 | + | 0.993165i | \(0.537238\pi\) | |||||||
\(830\) | 29.9870 | 1.04086 | ||||||||
\(831\) | 7.30157 | 0.253289 | ||||||||
\(832\) | −5.91310 | −0.205000 | ||||||||
\(833\) | −7.27375 | −0.252020 | ||||||||
\(834\) | −1.17037 | −0.0405267 | ||||||||
\(835\) | 21.4761 | 0.743210 | ||||||||
\(836\) | 37.4915 | 1.29667 | ||||||||
\(837\) | 5.10395 | 0.176418 | ||||||||
\(838\) | −15.6733 | −0.541426 | ||||||||
\(839\) | 38.7657 | 1.33834 | 0.669170 | − | 0.743110i | \(-0.266650\pi\) | ||||
0.669170 | + | 0.743110i | \(0.266650\pi\) | |||||||
\(840\) | 0.734628 | 0.0253471 | ||||||||
\(841\) | −6.07823 | −0.209594 | ||||||||
\(842\) | 8.12216 | 0.279908 | ||||||||
\(843\) | 7.34803 | 0.253080 | ||||||||
\(844\) | 8.51835 | 0.293214 | ||||||||
\(845\) | −40.7048 | −1.40029 | ||||||||
\(846\) | −7.38633 | −0.253947 | ||||||||
\(847\) | 9.26489 | 0.318345 | ||||||||
\(848\) | 0.359603 | 0.0123488 | ||||||||
\(849\) | −10.1699 | −0.349029 | ||||||||
\(850\) | −11.3884 | −0.390620 | ||||||||
\(851\) | 22.2952 | 0.764270 | ||||||||
\(852\) | 1.10894 | 0.0379916 | ||||||||
\(853\) | −10.3735 | −0.355182 | −0.177591 | − | 0.984104i | \(-0.556830\pi\) | ||||
−0.177591 | + | 0.984104i | \(0.556830\pi\) | |||||||
\(854\) | 6.74430 | 0.230785 | ||||||||
\(855\) | 43.8768 | 1.50055 | ||||||||
\(856\) | −0.279089 | −0.00953907 | ||||||||
\(857\) | −31.0956 | −1.06221 | −0.531103 | − | 0.847307i | \(-0.678222\pi\) | ||||
−0.531103 | + | 0.847307i | \(0.678222\pi\) | |||||||
\(858\) | 10.5520 | 0.360240 | ||||||||
\(859\) | 13.8503 | 0.472567 | 0.236284 | − | 0.971684i | \(-0.424071\pi\) | ||||
0.236284 | + | 0.971684i | \(0.424071\pi\) | |||||||
\(860\) | 18.0253 | 0.614657 | ||||||||
\(861\) | 0.203505 | 0.00693545 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −43.7122 | −1.48798 | −0.743990 | − | 0.668191i | \(-0.767069\pi\) | ||||
−0.743990 | + | 0.668191i | \(0.767069\pi\) | |||||||
\(864\) | 2.31618 | 0.0787982 | ||||||||
\(865\) | 17.4541 | 0.593457 | ||||||||
\(866\) | −22.6687 | −0.770312 | ||||||||
\(867\) | 14.2341 | 0.483417 | ||||||||
\(868\) | −2.20360 | −0.0747952 | ||||||||
\(869\) | −24.9703 | −0.847060 | ||||||||
\(870\) | 3.51716 | 0.119243 | ||||||||
\(871\) | −81.6641 | −2.76708 | ||||||||
\(872\) | −18.3186 | −0.620345 | ||||||||
\(873\) | 38.6612 | 1.30848 | ||||||||
\(874\) | −38.5616 | −1.30436 | ||||||||
\(875\) | 12.1675 | 0.411335 | ||||||||
\(876\) | −3.08885 | −0.104363 | ||||||||
\(877\) | 37.6783 | 1.27231 | 0.636153 | − | 0.771563i | \(-0.280525\pi\) | ||||
0.636153 | + | 0.771563i | \(0.280525\pi\) | |||||||
\(878\) | 9.28641 | 0.313401 | ||||||||
\(879\) | −5.61022 | −0.189228 | ||||||||
\(880\) | −8.34241 | −0.281223 | ||||||||
\(881\) | 34.8598 | 1.17446 | 0.587228 | − | 0.809421i | \(-0.300219\pi\) | ||||
0.587228 | + | 0.809421i | \(0.300219\pi\) | |||||||
\(882\) | 2.84286 | 0.0957240 | ||||||||
\(883\) | −27.9868 | −0.941830 | −0.470915 | − | 0.882178i | \(-0.656076\pi\) | ||||
−0.470915 | + | 0.882178i | \(0.656076\pi\) | |||||||
\(884\) | 43.0104 | 1.44660 | ||||||||
\(885\) | 10.2654 | 0.345067 | ||||||||
\(886\) | 34.2337 | 1.15010 | ||||||||
\(887\) | 37.6784 | 1.26512 | 0.632558 | − | 0.774513i | \(-0.282005\pi\) | ||||
0.632558 | + | 0.774513i | \(0.282005\pi\) | |||||||
\(888\) | −1.90882 | −0.0640559 | ||||||||
\(889\) | −6.00997 | −0.201568 | ||||||||
\(890\) | −6.87983 | −0.230612 | ||||||||
\(891\) | 34.2594 | 1.14773 | ||||||||
\(892\) | −3.39491 | −0.113670 | ||||||||
\(893\) | −21.6388 | −0.724116 | ||||||||
\(894\) | −1.03867 | −0.0347384 | ||||||||
\(895\) | −14.2428 | −0.476085 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −10.8532 | −0.362377 | ||||||||
\(898\) | 16.4904 | 0.550293 | ||||||||
\(899\) | −10.5501 | −0.351866 | ||||||||
\(900\) | 4.45104 | 0.148368 | ||||||||
\(901\) | −2.61566 | −0.0871404 | ||||||||
\(902\) | −2.31100 | −0.0769479 | ||||||||
\(903\) | −3.85576 | −0.128312 | ||||||||
\(904\) | −0.364997 | −0.0121396 | ||||||||
\(905\) | −19.7272 | −0.655753 | ||||||||
\(906\) | 3.19084 | 0.106008 | ||||||||
\(907\) | −16.3508 | −0.542920 | −0.271460 | − | 0.962450i | \(-0.587506\pi\) | ||||
−0.271460 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(908\) | 17.3804 | 0.576789 | ||||||||
\(909\) | −26.0796 | −0.865007 | ||||||||
\(910\) | −10.9581 | −0.363257 | ||||||||
\(911\) | −30.0717 | −0.996320 | −0.498160 | − | 0.867085i | \(-0.665991\pi\) | ||||
−0.498160 | + | 0.867085i | \(0.665991\pi\) | |||||||
\(912\) | 3.30148 | 0.109323 | ||||||||
\(913\) | 72.8427 | 2.41074 | ||||||||
\(914\) | 28.1687 | 0.931738 | ||||||||
\(915\) | 4.95455 | 0.163792 | ||||||||
\(916\) | −18.7849 | −0.620670 | ||||||||
\(917\) | 20.2084 | 0.667340 | ||||||||
\(918\) | −16.8473 | −0.556045 | ||||||||
\(919\) | −0.935366 | −0.0308549 | −0.0154274 | − | 0.999881i | \(-0.504911\pi\) | ||||
−0.0154274 | + | 0.999881i | \(0.504911\pi\) | |||||||
\(920\) | 8.58053 | 0.282892 | ||||||||
\(921\) | 7.92227 | 0.261048 | ||||||||
\(922\) | 16.2469 | 0.535062 | ||||||||
\(923\) | −16.5415 | −0.544470 | ||||||||
\(924\) | 1.78451 | 0.0587062 | ||||||||
\(925\) | −7.53918 | −0.247887 | ||||||||
\(926\) | −28.9035 | −0.949827 | ||||||||
\(927\) | −11.7024 | −0.384358 | ||||||||
\(928\) | −4.78767 | −0.157163 | ||||||||
\(929\) | 45.6012 | 1.49613 | 0.748063 | − | 0.663628i | \(-0.230984\pi\) | ||||
0.748063 | + | 0.663628i | \(0.230984\pi\) | |||||||
\(930\) | −1.61883 | −0.0530835 | ||||||||
\(931\) | 8.32838 | 0.272952 | ||||||||
\(932\) | 15.2182 | 0.498488 | ||||||||
\(933\) | 2.75576 | 0.0902194 | ||||||||
\(934\) | 6.68344 | 0.218689 | ||||||||
\(935\) | 60.6806 | 1.98447 | ||||||||
\(936\) | −16.8101 | −0.549455 | ||||||||
\(937\) | 4.53867 | 0.148272 | 0.0741359 | − | 0.997248i | \(-0.476380\pi\) | ||||
0.0741359 | + | 0.997248i | \(0.476380\pi\) | |||||||
\(938\) | −13.8107 | −0.450936 | ||||||||
\(939\) | −13.7743 | −0.449509 | ||||||||
\(940\) | 4.81497 | 0.157047 | ||||||||
\(941\) | −8.02901 | −0.261738 | −0.130869 | − | 0.991400i | \(-0.541777\pi\) | ||||
−0.130869 | + | 0.991400i | \(0.541777\pi\) | |||||||
\(942\) | −4.86128 | −0.158389 | ||||||||
\(943\) | 2.37696 | 0.0774046 | ||||||||
\(944\) | −13.9736 | −0.454802 | ||||||||
\(945\) | 4.29233 | 0.139629 | ||||||||
\(946\) | 43.7859 | 1.42360 | ||||||||
\(947\) | −32.5271 | −1.05699 | −0.528494 | − | 0.848937i | \(-0.677243\pi\) | ||||
−0.528494 | + | 0.848937i | \(0.677243\pi\) | |||||||
\(948\) | −2.19887 | −0.0714160 | ||||||||
\(949\) | 46.0748 | 1.49565 | ||||||||
\(950\) | 13.0397 | 0.423063 | ||||||||
\(951\) | 4.85649 | 0.157482 | ||||||||
\(952\) | 7.27375 | 0.235743 | ||||||||
\(953\) | −10.7839 | −0.349326 | −0.174663 | − | 0.984628i | \(-0.555884\pi\) | ||||
−0.174663 | + | 0.984628i | \(0.555884\pi\) | |||||||
\(954\) | 1.02230 | 0.0330982 | ||||||||
\(955\) | 25.5261 | 0.826006 | ||||||||
\(956\) | 24.4542 | 0.790906 | ||||||||
\(957\) | 8.54366 | 0.276177 | ||||||||
\(958\) | 27.5978 | 0.891645 | ||||||||
\(959\) | 12.4323 | 0.401460 | ||||||||
\(960\) | −0.734628 | −0.0237100 | ||||||||
\(961\) | −26.1441 | −0.843359 | ||||||||
\(962\) | 28.4730 | 0.918005 | ||||||||
\(963\) | −0.793410 | −0.0255673 | ||||||||
\(964\) | 26.0041 | 0.837536 | ||||||||
\(965\) | 45.9624 | 1.47958 | ||||||||
\(966\) | −1.83545 | −0.0590546 | ||||||||
\(967\) | 42.1615 | 1.35582 | 0.677911 | − | 0.735144i | \(-0.262886\pi\) | ||||
0.677911 | + | 0.735144i | \(0.262886\pi\) | |||||||
\(968\) | −9.26489 | −0.297785 | ||||||||
\(969\) | −24.0141 | −0.771444 | ||||||||
\(970\) | −25.2023 | −0.809197 | ||||||||
\(971\) | 32.8473 | 1.05412 | 0.527060 | − | 0.849828i | \(-0.323294\pi\) | ||||
0.527060 | + | 0.849828i | \(0.323294\pi\) | |||||||
\(972\) | 9.96542 | 0.319641 | ||||||||
\(973\) | 2.95241 | 0.0946498 | ||||||||
\(974\) | 20.2647 | 0.649323 | ||||||||
\(975\) | 3.67003 | 0.117535 | ||||||||
\(976\) | −6.74430 | −0.215880 | ||||||||
\(977\) | 25.7780 | 0.824713 | 0.412356 | − | 0.911023i | \(-0.364706\pi\) | ||||
0.412356 | + | 0.911023i | \(0.364706\pi\) | |||||||
\(978\) | −5.30902 | −0.169764 | ||||||||
\(979\) | −16.7121 | −0.534120 | ||||||||
\(980\) | −1.85319 | −0.0591979 | ||||||||
\(981\) | −52.0770 | −1.66269 | ||||||||
\(982\) | −28.2429 | −0.901266 | ||||||||
\(983\) | −60.6238 | −1.93360 | −0.966799 | − | 0.255539i | \(-0.917747\pi\) | ||||
−0.966799 | + | 0.255539i | \(0.917747\pi\) | |||||||
\(984\) | −0.203505 | −0.00648752 | ||||||||
\(985\) | 26.8415 | 0.855241 | ||||||||
\(986\) | 34.8243 | 1.10903 | ||||||||
\(987\) | −1.02996 | −0.0327841 | ||||||||
\(988\) | −49.2465 | −1.56674 | ||||||||
\(989\) | −45.0356 | −1.43205 | ||||||||
\(990\) | −23.7163 | −0.753753 | ||||||||
\(991\) | −52.1518 | −1.65666 | −0.828328 | − | 0.560243i | \(-0.810708\pi\) | ||||
−0.828328 | + | 0.560243i | \(0.810708\pi\) | |||||||
\(992\) | 2.20360 | 0.0699645 | ||||||||
\(993\) | −11.8163 | −0.374980 | ||||||||
\(994\) | −2.79743 | −0.0887292 | ||||||||
\(995\) | −4.94867 | −0.156883 | ||||||||
\(996\) | 6.41448 | 0.203251 | ||||||||
\(997\) | −19.0242 | −0.602503 | −0.301252 | − | 0.953545i | \(-0.597404\pi\) | ||||
−0.301252 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(998\) | −20.0006 | −0.633109 | ||||||||
\(999\) | −11.1530 | −0.352864 |
(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 | 6034.2.a.p.1.15 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.15 | ✓ | 27 | 1.1 | even | 1 | trivial |