Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18834 | −1.54739 | −0.773693 | − | 0.633560i | \(-0.781593\pi\) | ||||
−0.773693 | + | 0.633560i | \(0.781593\pi\) | |||||||
\(3\) | 3.06167 | 1.76765 | 0.883827 | − | 0.467814i | \(-0.154958\pi\) | ||||
0.883827 | + | 0.467814i | \(0.154958\pi\) | |||||||
\(4\) | 2.78881 | 1.39441 | ||||||||
\(5\) | −2.53450 | −1.13346 | −0.566732 | − | 0.823902i | \(-0.691792\pi\) | ||||
−0.566732 | + | 0.823902i | \(0.691792\pi\) | |||||||
\(6\) | −6.69995 | −2.73524 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.72618 | −0.610298 | ||||||||
\(9\) | 6.37380 | 2.12460 | ||||||||
\(10\) | 5.54634 | 1.75391 | ||||||||
\(11\) | 1.03269 | 0.311368 | 0.155684 | − | 0.987807i | \(-0.450242\pi\) | ||||
0.155684 | + | 0.987807i | \(0.450242\pi\) | |||||||
\(12\) | 8.53841 | 2.46483 | ||||||||
\(13\) | −1.80328 | −0.500140 | −0.250070 | − | 0.968228i | \(-0.580454\pi\) | ||||
−0.250070 | + | 0.968228i | \(0.580454\pi\) | |||||||
\(14\) | −2.18834 | −0.584857 | ||||||||
\(15\) | −7.75980 | −2.00357 | ||||||||
\(16\) | −1.80016 | −0.450039 | ||||||||
\(17\) | 0.365608 | 0.0886730 | 0.0443365 | − | 0.999017i | \(-0.485883\pi\) | ||||
0.0443365 | + | 0.999017i | \(0.485883\pi\) | |||||||
\(18\) | −13.9480 | −3.28758 | ||||||||
\(19\) | 0.444175 | 0.101901 | 0.0509504 | − | 0.998701i | \(-0.483775\pi\) | ||||
0.0509504 | + | 0.998701i | \(0.483775\pi\) | |||||||
\(20\) | −7.06825 | −1.58051 | ||||||||
\(21\) | 3.06167 | 0.668110 | ||||||||
\(22\) | −2.25987 | −0.481807 | ||||||||
\(23\) | 0.166616 | 0.0347419 | 0.0173709 | − | 0.999849i | \(-0.494470\pi\) | ||||
0.0173709 | + | 0.999849i | \(0.494470\pi\) | |||||||
\(24\) | −5.28499 | −1.07879 | ||||||||
\(25\) | 1.42370 | 0.284739 | ||||||||
\(26\) | 3.94618 | 0.773910 | ||||||||
\(27\) | 10.3294 | 1.98790 | ||||||||
\(28\) | 2.78881 | 0.527036 | ||||||||
\(29\) | 7.51023 | 1.39461 | 0.697307 | − | 0.716773i | \(-0.254381\pi\) | ||||
0.697307 | + | 0.716773i | \(0.254381\pi\) | |||||||
\(30\) | 16.9810 | 3.10030 | ||||||||
\(31\) | 6.36658 | 1.14347 | 0.571736 | − | 0.820438i | \(-0.306270\pi\) | ||||
0.571736 | + | 0.820438i | \(0.306270\pi\) | |||||||
\(32\) | 7.39171 | 1.30668 | ||||||||
\(33\) | 3.16176 | 0.550391 | ||||||||
\(34\) | −0.800073 | −0.137211 | ||||||||
\(35\) | −2.53450 | −0.428409 | ||||||||
\(36\) | 17.7753 | 2.96255 | ||||||||
\(37\) | −9.60062 | −1.57833 | −0.789166 | − | 0.614179i | \(-0.789487\pi\) | ||||
−0.789166 | + | 0.614179i | \(0.789487\pi\) | |||||||
\(38\) | −0.972004 | −0.157680 | ||||||||
\(39\) | −5.52104 | −0.884074 | ||||||||
\(40\) | 4.37501 | 0.691750 | ||||||||
\(41\) | 5.61678 | 0.877193 | 0.438597 | − | 0.898684i | \(-0.355476\pi\) | ||||
0.438597 | + | 0.898684i | \(0.355476\pi\) | |||||||
\(42\) | −6.69995 | −1.03382 | ||||||||
\(43\) | −1.75757 | −0.268027 | −0.134014 | − | 0.990979i | \(-0.542787\pi\) | ||||
−0.134014 | + | 0.990979i | \(0.542787\pi\) | |||||||
\(44\) | 2.87998 | 0.434173 | ||||||||
\(45\) | −16.1544 | −2.40816 | ||||||||
\(46\) | −0.364612 | −0.0537591 | ||||||||
\(47\) | −8.83237 | −1.28833 | −0.644167 | − | 0.764885i | \(-0.722796\pi\) | ||||
−0.644167 | + | 0.764885i | \(0.722796\pi\) | |||||||
\(48\) | −5.51147 | −0.795513 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.11553 | −0.440602 | ||||||||
\(51\) | 1.11937 | 0.156743 | ||||||||
\(52\) | −5.02901 | −0.697398 | ||||||||
\(53\) | −1.76674 | −0.242681 | −0.121340 | − | 0.992611i | \(-0.538719\pi\) | ||||
−0.121340 | + | 0.992611i | \(0.538719\pi\) | |||||||
\(54\) | −22.6043 | −3.07605 | ||||||||
\(55\) | −2.61736 | −0.352924 | ||||||||
\(56\) | −1.72618 | −0.230671 | ||||||||
\(57\) | 1.35992 | 0.180125 | ||||||||
\(58\) | −16.4349 | −2.15801 | ||||||||
\(59\) | 13.3903 | 1.74327 | 0.871633 | − | 0.490160i | \(-0.163062\pi\) | ||||
0.871633 | + | 0.490160i | \(0.163062\pi\) | |||||||
\(60\) | −21.6406 | −2.79379 | ||||||||
\(61\) | −3.66072 | −0.468707 | −0.234353 | − | 0.972151i | \(-0.575297\pi\) | ||||
−0.234353 | + | 0.972151i | \(0.575297\pi\) | |||||||
\(62\) | −13.9322 | −1.76939 | ||||||||
\(63\) | 6.37380 | 0.803023 | ||||||||
\(64\) | −12.5752 | −1.57190 | ||||||||
\(65\) | 4.57041 | 0.566890 | ||||||||
\(66\) | −6.91898 | −0.851668 | ||||||||
\(67\) | 12.3839 | 1.51294 | 0.756469 | − | 0.654029i | \(-0.226923\pi\) | ||||
0.756469 | + | 0.654029i | \(0.226923\pi\) | |||||||
\(68\) | 1.01961 | 0.123646 | ||||||||
\(69\) | 0.510123 | 0.0614116 | ||||||||
\(70\) | 5.54634 | 0.662914 | ||||||||
\(71\) | −3.04550 | −0.361435 | −0.180717 | − | 0.983535i | \(-0.557842\pi\) | ||||
−0.180717 | + | 0.983535i | \(0.557842\pi\) | |||||||
\(72\) | −11.0023 | −1.29664 | ||||||||
\(73\) | 16.5322 | 1.93494 | 0.967471 | − | 0.252980i | \(-0.0814107\pi\) | ||||
0.967471 | + | 0.252980i | \(0.0814107\pi\) | |||||||
\(74\) | 21.0094 | 2.44229 | ||||||||
\(75\) | 4.35889 | 0.503321 | ||||||||
\(76\) | 1.23872 | 0.142091 | ||||||||
\(77\) | 1.03269 | 0.117686 | ||||||||
\(78\) | 12.0819 | 1.36800 | ||||||||
\(79\) | −9.94489 | −1.11889 | −0.559444 | − | 0.828868i | \(-0.688985\pi\) | ||||
−0.559444 | + | 0.828868i | \(0.688985\pi\) | |||||||
\(80\) | 4.56250 | 0.510103 | ||||||||
\(81\) | 12.5039 | 1.38932 | ||||||||
\(82\) | −12.2914 | −1.35736 | ||||||||
\(83\) | −8.63706 | −0.948041 | −0.474020 | − | 0.880514i | \(-0.657198\pi\) | ||||
−0.474020 | + | 0.880514i | \(0.657198\pi\) | |||||||
\(84\) | 8.53841 | 0.931617 | ||||||||
\(85\) | −0.926634 | −0.100508 | ||||||||
\(86\) | 3.84616 | 0.414742 | ||||||||
\(87\) | 22.9938 | 2.46519 | ||||||||
\(88\) | −1.78261 | −0.190027 | ||||||||
\(89\) | 6.98103 | 0.739987 | 0.369994 | − | 0.929034i | \(-0.379360\pi\) | ||||
0.369994 | + | 0.929034i | \(0.379360\pi\) | |||||||
\(90\) | 35.3512 | 3.72635 | ||||||||
\(91\) | −1.80328 | −0.189035 | ||||||||
\(92\) | 0.464661 | 0.0484443 | ||||||||
\(93\) | 19.4923 | 2.02126 | ||||||||
\(94\) | 19.3282 | 1.99355 | ||||||||
\(95\) | −1.12576 | −0.115501 | ||||||||
\(96\) | 22.6309 | 2.30976 | ||||||||
\(97\) | 6.46081 | 0.655996 | 0.327998 | − | 0.944678i | \(-0.393626\pi\) | ||||
0.327998 | + | 0.944678i | \(0.393626\pi\) | |||||||
\(98\) | −2.18834 | −0.221055 | ||||||||
\(99\) | 6.58216 | 0.661532 | ||||||||
\(100\) | 3.97042 | 0.397042 | ||||||||
\(101\) | −7.53537 | −0.749798 | −0.374899 | − | 0.927066i | \(-0.622323\pi\) | ||||
−0.374899 | + | 0.927066i | \(0.622323\pi\) | |||||||
\(102\) | −2.44956 | −0.242542 | ||||||||
\(103\) | 16.4601 | 1.62186 | 0.810929 | − | 0.585144i | \(-0.198962\pi\) | ||||
0.810929 | + | 0.585144i | \(0.198962\pi\) | |||||||
\(104\) | 3.11279 | 0.305234 | ||||||||
\(105\) | −7.75980 | −0.757279 | ||||||||
\(106\) | 3.86622 | 0.375521 | ||||||||
\(107\) | 16.8753 | 1.63140 | 0.815699 | − | 0.578477i | \(-0.196353\pi\) | ||||
0.815699 | + | 0.578477i | \(0.196353\pi\) | |||||||
\(108\) | 28.8069 | 2.77194 | ||||||||
\(109\) | −14.1956 | −1.35969 | −0.679846 | − | 0.733355i | \(-0.737954\pi\) | ||||
−0.679846 | + | 0.733355i | \(0.737954\pi\) | |||||||
\(110\) | 5.72766 | 0.546110 | ||||||||
\(111\) | −29.3939 | −2.78995 | ||||||||
\(112\) | −1.80016 | −0.170099 | ||||||||
\(113\) | 4.23224 | 0.398135 | 0.199068 | − | 0.979986i | \(-0.436209\pi\) | ||||
0.199068 | + | 0.979986i | \(0.436209\pi\) | |||||||
\(114\) | −2.97595 | −0.278723 | ||||||||
\(115\) | −0.422289 | −0.0393786 | ||||||||
\(116\) | 20.9446 | 1.94466 | ||||||||
\(117\) | −11.4937 | −1.06260 | ||||||||
\(118\) | −29.3024 | −2.69751 | ||||||||
\(119\) | 0.365608 | 0.0335152 | ||||||||
\(120\) | 13.3948 | 1.22277 | ||||||||
\(121\) | −9.93355 | −0.903050 | ||||||||
\(122\) | 8.01087 | 0.725270 | ||||||||
\(123\) | 17.1967 | 1.55057 | ||||||||
\(124\) | 17.7552 | 1.59446 | ||||||||
\(125\) | 9.06414 | 0.810722 | ||||||||
\(126\) | −13.9480 | −1.24259 | ||||||||
\(127\) | 6.49327 | 0.576185 | 0.288092 | − | 0.957603i | \(-0.406979\pi\) | ||||
0.288092 | + | 0.957603i | \(0.406979\pi\) | |||||||
\(128\) | 12.7354 | 1.12566 | ||||||||
\(129\) | −5.38110 | −0.473779 | ||||||||
\(130\) | −10.0016 | −0.877198 | ||||||||
\(131\) | −18.4094 | −1.60844 | −0.804220 | − | 0.594332i | \(-0.797417\pi\) | ||||
−0.804220 | + | 0.594332i | \(0.797417\pi\) | |||||||
\(132\) | 8.81754 | 0.767468 | ||||||||
\(133\) | 0.444175 | 0.0385149 | ||||||||
\(134\) | −27.1002 | −2.34110 | ||||||||
\(135\) | −26.1800 | −2.25321 | ||||||||
\(136\) | −0.631106 | −0.0541169 | ||||||||
\(137\) | 5.67795 | 0.485100 | 0.242550 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242550 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(138\) | −1.11632 | −0.0950275 | ||||||||
\(139\) | −8.85010 | −0.750656 | −0.375328 | − | 0.926892i | \(-0.622470\pi\) | ||||
−0.375328 | + | 0.926892i | \(0.622470\pi\) | |||||||
\(140\) | −7.06825 | −0.597376 | ||||||||
\(141\) | −27.0418 | −2.27733 | ||||||||
\(142\) | 6.66458 | 0.559279 | ||||||||
\(143\) | −1.86223 | −0.155728 | ||||||||
\(144\) | −11.4738 | −0.956152 | ||||||||
\(145\) | −19.0347 | −1.58074 | ||||||||
\(146\) | −36.1779 | −2.99410 | ||||||||
\(147\) | 3.06167 | 0.252522 | ||||||||
\(148\) | −26.7743 | −2.20084 | ||||||||
\(149\) | 23.8163 | 1.95111 | 0.975553 | − | 0.219764i | \(-0.0705287\pi\) | ||||
0.975553 | + | 0.219764i | \(0.0705287\pi\) | |||||||
\(150\) | −9.53870 | −0.778832 | ||||||||
\(151\) | 9.30062 | 0.756874 | 0.378437 | − | 0.925627i | \(-0.376462\pi\) | ||||
0.378437 | + | 0.925627i | \(0.376462\pi\) | |||||||
\(152\) | −0.766727 | −0.0621898 | ||||||||
\(153\) | 2.33031 | 0.188395 | ||||||||
\(154\) | −2.25987 | −0.182106 | ||||||||
\(155\) | −16.1361 | −1.29608 | ||||||||
\(156\) | −15.3971 | −1.23276 | ||||||||
\(157\) | 3.05228 | 0.243599 | 0.121799 | − | 0.992555i | \(-0.461134\pi\) | ||||
0.121799 | + | 0.992555i | \(0.461134\pi\) | |||||||
\(158\) | 21.7628 | 1.73135 | ||||||||
\(159\) | −5.40917 | −0.428975 | ||||||||
\(160\) | −18.7343 | −1.48108 | ||||||||
\(161\) | 0.166616 | 0.0131312 | ||||||||
\(162\) | −27.3627 | −2.14982 | ||||||||
\(163\) | 7.14776 | 0.559855 | 0.279928 | − | 0.960021i | \(-0.409689\pi\) | ||||
0.279928 | + | 0.960021i | \(0.409689\pi\) | |||||||
\(164\) | 15.6641 | 1.22316 | ||||||||
\(165\) | −8.01347 | −0.623848 | ||||||||
\(166\) | 18.9008 | 1.46699 | ||||||||
\(167\) | −7.77020 | −0.601276 | −0.300638 | − | 0.953738i | \(-0.597200\pi\) | ||||
−0.300638 | + | 0.953738i | \(0.597200\pi\) | |||||||
\(168\) | −5.28499 | −0.407746 | ||||||||
\(169\) | −9.74818 | −0.749860 | ||||||||
\(170\) | 2.02779 | 0.155524 | ||||||||
\(171\) | 2.83108 | 0.216498 | ||||||||
\(172\) | −4.90153 | −0.373739 | ||||||||
\(173\) | 18.3839 | 1.39770 | 0.698852 | − | 0.715267i | \(-0.253695\pi\) | ||||
0.698852 | + | 0.715267i | \(0.253695\pi\) | |||||||
\(174\) | −50.3182 | −3.81461 | ||||||||
\(175\) | 1.42370 | 0.107621 | ||||||||
\(176\) | −1.85900 | −0.140128 | ||||||||
\(177\) | 40.9965 | 3.08149 | ||||||||
\(178\) | −15.2768 | −1.14505 | ||||||||
\(179\) | 2.96703 | 0.221766 | 0.110883 | − | 0.993833i | \(-0.464632\pi\) | ||||
0.110883 | + | 0.993833i | \(0.464632\pi\) | |||||||
\(180\) | −45.0516 | −3.35795 | ||||||||
\(181\) | −17.9535 | −1.33447 | −0.667237 | − | 0.744846i | \(-0.732523\pi\) | ||||
−0.667237 | + | 0.744846i | \(0.732523\pi\) | |||||||
\(182\) | 3.94618 | 0.292510 | ||||||||
\(183\) | −11.2079 | −0.828511 | ||||||||
\(184\) | −0.287610 | −0.0212029 | ||||||||
\(185\) | 24.3328 | 1.78898 | ||||||||
\(186\) | −42.6558 | −3.12767 | ||||||||
\(187\) | 0.377560 | 0.0276099 | ||||||||
\(188\) | −24.6318 | −1.79646 | ||||||||
\(189\) | 10.3294 | 0.751356 | ||||||||
\(190\) | 2.46355 | 0.178724 | ||||||||
\(191\) | 14.3719 | 1.03992 | 0.519958 | − | 0.854192i | \(-0.325948\pi\) | ||||
0.519958 | + | 0.854192i | \(0.325948\pi\) | |||||||
\(192\) | −38.5011 | −2.77858 | ||||||||
\(193\) | −15.5310 | −1.11795 | −0.558974 | − | 0.829185i | \(-0.688805\pi\) | ||||
−0.558974 | + | 0.829185i | \(0.688805\pi\) | |||||||
\(194\) | −14.1384 | −1.01508 | ||||||||
\(195\) | 13.9931 | 1.00207 | ||||||||
\(196\) | 2.78881 | 0.199201 | ||||||||
\(197\) | 22.3532 | 1.59260 | 0.796298 | − | 0.604904i | \(-0.206788\pi\) | ||||
0.796298 | + | 0.604904i | \(0.206788\pi\) | |||||||
\(198\) | −14.4040 | −1.02365 | ||||||||
\(199\) | 7.65149 | 0.542400 | 0.271200 | − | 0.962523i | \(-0.412580\pi\) | ||||
0.271200 | + | 0.962523i | \(0.412580\pi\) | |||||||
\(200\) | −2.45756 | −0.173776 | ||||||||
\(201\) | 37.9155 | 2.67435 | ||||||||
\(202\) | 16.4899 | 1.16023 | ||||||||
\(203\) | 7.51023 | 0.527115 | ||||||||
\(204\) | 3.12171 | 0.218563 | ||||||||
\(205\) | −14.2357 | −0.994267 | ||||||||
\(206\) | −36.0201 | −2.50964 | ||||||||
\(207\) | 1.06198 | 0.0738125 | ||||||||
\(208\) | 3.24618 | 0.225082 | ||||||||
\(209\) | 0.458696 | 0.0317286 | ||||||||
\(210\) | 16.9810 | 1.17180 | ||||||||
\(211\) | 24.4197 | 1.68112 | 0.840560 | − | 0.541718i | \(-0.182226\pi\) | ||||
0.840560 | + | 0.541718i | \(0.182226\pi\) | |||||||
\(212\) | −4.92711 | −0.338395 | ||||||||
\(213\) | −9.32432 | −0.638892 | ||||||||
\(214\) | −36.9288 | −2.52440 | ||||||||
\(215\) | 4.45457 | 0.303799 | ||||||||
\(216\) | −17.8305 | −1.21321 | ||||||||
\(217\) | 6.36658 | 0.432192 | ||||||||
\(218\) | 31.0648 | 2.10397 | ||||||||
\(219\) | 50.6159 | 3.42031 | ||||||||
\(220\) | −7.29931 | −0.492120 | ||||||||
\(221\) | −0.659294 | −0.0443489 | ||||||||
\(222\) | 64.3237 | 4.31712 | ||||||||
\(223\) | −7.51341 | −0.503135 | −0.251567 | − | 0.967840i | \(-0.580946\pi\) | ||||
−0.251567 | + | 0.967840i | \(0.580946\pi\) | |||||||
\(224\) | 7.39171 | 0.493879 | ||||||||
\(225\) | 9.07436 | 0.604957 | ||||||||
\(226\) | −9.26155 | −0.616069 | ||||||||
\(227\) | 7.03627 | 0.467013 | 0.233507 | − | 0.972355i | \(-0.424980\pi\) | ||||
0.233507 | + | 0.972355i | \(0.424980\pi\) | |||||||
\(228\) | 3.79255 | 0.251168 | ||||||||
\(229\) | −20.8190 | −1.37576 | −0.687881 | − | 0.725824i | \(-0.741459\pi\) | ||||
−0.687881 | + | 0.725824i | \(0.741459\pi\) | |||||||
\(230\) | 0.924110 | 0.0609340 | ||||||||
\(231\) | 3.16176 | 0.208028 | ||||||||
\(232\) | −12.9640 | −0.851130 | ||||||||
\(233\) | 6.13998 | 0.402244 | 0.201122 | − | 0.979566i | \(-0.435541\pi\) | ||||
0.201122 | + | 0.979566i | \(0.435541\pi\) | |||||||
\(234\) | 25.1522 | 1.64425 | ||||||||
\(235\) | 22.3857 | 1.46028 | ||||||||
\(236\) | 37.3429 | 2.43082 | ||||||||
\(237\) | −30.4479 | −1.97781 | ||||||||
\(238\) | −0.800073 | −0.0518610 | ||||||||
\(239\) | −8.32850 | −0.538726 | −0.269363 | − | 0.963039i | \(-0.586813\pi\) | ||||
−0.269363 | + | 0.963039i | \(0.586813\pi\) | |||||||
\(240\) | 13.9688 | 0.901685 | ||||||||
\(241\) | 3.19307 | 0.205684 | 0.102842 | − | 0.994698i | \(-0.467206\pi\) | ||||
0.102842 | + | 0.994698i | \(0.467206\pi\) | |||||||
\(242\) | 21.7379 | 1.39737 | ||||||||
\(243\) | 7.29445 | 0.467939 | ||||||||
\(244\) | −10.2090 | −0.653567 | ||||||||
\(245\) | −2.53450 | −0.161923 | ||||||||
\(246\) | −37.6321 | −2.39934 | ||||||||
\(247\) | −0.800972 | −0.0509646 | ||||||||
\(248\) | −10.9899 | −0.697858 | ||||||||
\(249\) | −26.4438 | −1.67581 | ||||||||
\(250\) | −19.8354 | −1.25450 | ||||||||
\(251\) | 11.1132 | 0.701459 | 0.350730 | − | 0.936477i | \(-0.385934\pi\) | ||||
0.350730 | + | 0.936477i | \(0.385934\pi\) | |||||||
\(252\) | 17.7753 | 1.11974 | ||||||||
\(253\) | 0.172063 | 0.0108175 | ||||||||
\(254\) | −14.2095 | −0.891581 | ||||||||
\(255\) | −2.83704 | −0.177663 | ||||||||
\(256\) | −2.71885 | −0.169928 | ||||||||
\(257\) | 9.04607 | 0.564278 | 0.282139 | − | 0.959374i | \(-0.408956\pi\) | ||||
0.282139 | + | 0.959374i | \(0.408956\pi\) | |||||||
\(258\) | 11.7756 | 0.733120 | ||||||||
\(259\) | −9.60062 | −0.596554 | ||||||||
\(260\) | 12.7460 | 0.790475 | ||||||||
\(261\) | 47.8687 | 2.96300 | ||||||||
\(262\) | 40.2860 | 2.48888 | ||||||||
\(263\) | −3.47466 | −0.214256 | −0.107128 | − | 0.994245i | \(-0.534166\pi\) | ||||
−0.107128 | + | 0.994245i | \(0.534166\pi\) | |||||||
\(264\) | −5.45777 | −0.335902 | ||||||||
\(265\) | 4.47781 | 0.275070 | ||||||||
\(266\) | −0.972004 | −0.0595974 | ||||||||
\(267\) | 21.3736 | 1.30804 | ||||||||
\(268\) | 34.5365 | 2.10965 | ||||||||
\(269\) | −9.80598 | −0.597881 | −0.298941 | − | 0.954272i | \(-0.596633\pi\) | ||||
−0.298941 | + | 0.954272i | \(0.596633\pi\) | |||||||
\(270\) | 57.2906 | 3.48659 | ||||||||
\(271\) | −22.9388 | −1.39344 | −0.696718 | − | 0.717345i | \(-0.745357\pi\) | ||||
−0.696718 | + | 0.717345i | \(0.745357\pi\) | |||||||
\(272\) | −0.658152 | −0.0399063 | ||||||||
\(273\) | −5.52104 | −0.334148 | ||||||||
\(274\) | −12.4253 | −0.750637 | ||||||||
\(275\) | 1.47024 | 0.0886588 | ||||||||
\(276\) | 1.42264 | 0.0856327 | ||||||||
\(277\) | 3.07652 | 0.184850 | 0.0924251 | − | 0.995720i | \(-0.470538\pi\) | ||||
0.0924251 | + | 0.995720i | \(0.470538\pi\) | |||||||
\(278\) | 19.3670 | 1.16156 | ||||||||
\(279\) | 40.5793 | 2.42942 | ||||||||
\(280\) | 4.37501 | 0.261457 | ||||||||
\(281\) | 23.7113 | 1.41450 | 0.707249 | − | 0.706964i | \(-0.249936\pi\) | ||||
0.707249 | + | 0.706964i | \(0.249936\pi\) | |||||||
\(282\) | 59.1764 | 3.52391 | ||||||||
\(283\) | −3.97763 | −0.236446 | −0.118223 | − | 0.992987i | \(-0.537720\pi\) | ||||
−0.118223 | + | 0.992987i | \(0.537720\pi\) | |||||||
\(284\) | −8.49334 | −0.503987 | ||||||||
\(285\) | −3.44671 | −0.204165 | ||||||||
\(286\) | 4.07519 | 0.240971 | ||||||||
\(287\) | 5.61678 | 0.331548 | ||||||||
\(288\) | 47.1133 | 2.77618 | ||||||||
\(289\) | −16.8663 | −0.992137 | ||||||||
\(290\) | 41.6543 | 2.44602 | ||||||||
\(291\) | 19.7809 | 1.15957 | ||||||||
\(292\) | 46.1051 | 2.69809 | ||||||||
\(293\) | 13.9114 | 0.812714 | 0.406357 | − | 0.913714i | \(-0.366799\pi\) | ||||
0.406357 | + | 0.913714i | \(0.366799\pi\) | |||||||
\(294\) | −6.69995 | −0.390749 | ||||||||
\(295\) | −33.9377 | −1.97593 | ||||||||
\(296\) | 16.5724 | 0.963253 | ||||||||
\(297\) | 10.6671 | 0.618969 | ||||||||
\(298\) | −52.1180 | −3.01912 | ||||||||
\(299\) | −0.300455 | −0.0173758 | ||||||||
\(300\) | 12.1561 | 0.701833 | ||||||||
\(301\) | −1.75757 | −0.101305 | ||||||||
\(302\) | −20.3529 | −1.17118 | ||||||||
\(303\) | −23.0708 | −1.32538 | ||||||||
\(304\) | −0.799584 | −0.0458593 | ||||||||
\(305\) | 9.27809 | 0.531262 | ||||||||
\(306\) | −5.09950 | −0.291519 | ||||||||
\(307\) | −5.63628 | −0.321679 | −0.160840 | − | 0.986981i | \(-0.551420\pi\) | ||||
−0.160840 | + | 0.986981i | \(0.551420\pi\) | |||||||
\(308\) | 2.87998 | 0.164102 | ||||||||
\(309\) | 50.3952 | 2.86688 | ||||||||
\(310\) | 35.3112 | 2.00554 | ||||||||
\(311\) | −0.462987 | −0.0262536 | −0.0131268 | − | 0.999914i | \(-0.504179\pi\) | ||||
−0.0131268 | + | 0.999914i | \(0.504179\pi\) | |||||||
\(312\) | 9.53032 | 0.539548 | ||||||||
\(313\) | −11.2073 | −0.633473 | −0.316736 | − | 0.948514i | \(-0.602587\pi\) | ||||
−0.316736 | + | 0.948514i | \(0.602587\pi\) | |||||||
\(314\) | −6.67941 | −0.376941 | ||||||||
\(315\) | −16.1544 | −0.910197 | ||||||||
\(316\) | −27.7344 | −1.56018 | ||||||||
\(317\) | 0.263746 | 0.0148135 | 0.00740673 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740673 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(318\) | 11.8371 | 0.663791 | ||||||||
\(319\) | 7.75575 | 0.434238 | ||||||||
\(320\) | 31.8719 | 1.78169 | ||||||||
\(321\) | 51.6666 | 2.88375 | ||||||||
\(322\) | −0.364612 | −0.0203190 | ||||||||
\(323\) | 0.162394 | 0.00903584 | ||||||||
\(324\) | 34.8710 | 1.93728 | ||||||||
\(325\) | −2.56732 | −0.142410 | ||||||||
\(326\) | −15.6417 | −0.866313 | ||||||||
\(327\) | −43.4622 | −2.40347 | ||||||||
\(328\) | −9.69558 | −0.535349 | ||||||||
\(329\) | −8.83237 | −0.486944 | ||||||||
\(330\) | 17.5362 | 0.965334 | ||||||||
\(331\) | 16.2122 | 0.891104 | 0.445552 | − | 0.895256i | \(-0.353007\pi\) | ||||
0.445552 | + | 0.895256i | \(0.353007\pi\) | |||||||
\(332\) | −24.0871 | −1.32195 | ||||||||
\(333\) | −61.1924 | −3.35332 | ||||||||
\(334\) | 17.0038 | 0.930407 | ||||||||
\(335\) | −31.3871 | −1.71486 | ||||||||
\(336\) | −5.51147 | −0.300676 | ||||||||
\(337\) | 10.7386 | 0.584966 | 0.292483 | − | 0.956271i | \(-0.405518\pi\) | ||||
0.292483 | + | 0.956271i | \(0.405518\pi\) | |||||||
\(338\) | 21.3323 | 1.16032 | ||||||||
\(339\) | 12.9577 | 0.703765 | ||||||||
\(340\) | −2.58421 | −0.140148 | ||||||||
\(341\) | 6.57471 | 0.356040 | ||||||||
\(342\) | −6.19536 | −0.335007 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.03389 | 0.163576 | ||||||||
\(345\) | −1.29291 | −0.0696078 | ||||||||
\(346\) | −40.2302 | −2.16279 | ||||||||
\(347\) | 34.6582 | 1.86055 | 0.930276 | − | 0.366861i | \(-0.119567\pi\) | ||||
0.930276 | + | 0.366861i | \(0.119567\pi\) | |||||||
\(348\) | 64.1254 | 3.43748 | ||||||||
\(349\) | 23.3166 | 1.24811 | 0.624054 | − | 0.781382i | \(-0.285485\pi\) | ||||
0.624054 | + | 0.781382i | \(0.285485\pi\) | |||||||
\(350\) | −3.11553 | −0.166532 | ||||||||
\(351\) | −18.6269 | −0.994229 | ||||||||
\(352\) | 7.63335 | 0.406859 | ||||||||
\(353\) | −19.2085 | −1.02236 | −0.511182 | − | 0.859473i | \(-0.670792\pi\) | ||||
−0.511182 | + | 0.859473i | \(0.670792\pi\) | |||||||
\(354\) | −89.7142 | −4.76825 | ||||||||
\(355\) | 7.71883 | 0.409673 | ||||||||
\(356\) | 19.4688 | 1.03184 | ||||||||
\(357\) | 1.11937 | 0.0592433 | ||||||||
\(358\) | −6.49286 | −0.343158 | ||||||||
\(359\) | 20.6827 | 1.09159 | 0.545795 | − | 0.837919i | \(-0.316228\pi\) | ||||
0.545795 | + | 0.837919i | \(0.316228\pi\) | |||||||
\(360\) | 27.8854 | 1.46969 | ||||||||
\(361\) | −18.8027 | −0.989616 | ||||||||
\(362\) | 39.2883 | 2.06495 | ||||||||
\(363\) | −30.4132 | −1.59628 | ||||||||
\(364\) | −5.02901 | −0.263592 | ||||||||
\(365\) | −41.9008 | −2.19319 | ||||||||
\(366\) | 24.5266 | 1.28203 | ||||||||
\(367\) | 31.3653 | 1.63726 | 0.818628 | − | 0.574324i | \(-0.194735\pi\) | ||||
0.818628 | + | 0.574324i | \(0.194735\pi\) | |||||||
\(368\) | −0.299935 | −0.0156352 | ||||||||
\(369\) | 35.8002 | 1.86368 | ||||||||
\(370\) | −53.2483 | −2.76825 | ||||||||
\(371\) | −1.76674 | −0.0917247 | ||||||||
\(372\) | 54.3604 | 2.81846 | ||||||||
\(373\) | −24.1120 | −1.24847 | −0.624235 | − | 0.781237i | \(-0.714589\pi\) | ||||
−0.624235 | + | 0.781237i | \(0.714589\pi\) | |||||||
\(374\) | −0.826228 | −0.0427233 | ||||||||
\(375\) | 27.7514 | 1.43308 | ||||||||
\(376\) | 15.2463 | 0.786267 | ||||||||
\(377\) | −13.5430 | −0.697502 | ||||||||
\(378\) | −22.6043 | −1.16264 | ||||||||
\(379\) | 2.84242 | 0.146006 | 0.0730028 | − | 0.997332i | \(-0.476742\pi\) | ||||
0.0730028 | + | 0.997332i | \(0.476742\pi\) | |||||||
\(380\) | −3.13954 | −0.161055 | ||||||||
\(381\) | 19.8802 | 1.01850 | ||||||||
\(382\) | −31.4506 | −1.60915 | ||||||||
\(383\) | 23.2422 | 1.18762 | 0.593811 | − | 0.804604i | \(-0.297622\pi\) | ||||
0.593811 | + | 0.804604i | \(0.297622\pi\) | |||||||
\(384\) | 38.9915 | 1.98978 | ||||||||
\(385\) | −2.61736 | −0.133393 | ||||||||
\(386\) | 33.9871 | 1.72990 | ||||||||
\(387\) | −11.2024 | −0.569450 | ||||||||
\(388\) | 18.0180 | 0.914725 | ||||||||
\(389\) | 27.9317 | 1.41619 | 0.708096 | − | 0.706117i | \(-0.249555\pi\) | ||||
0.708096 | + | 0.706117i | \(0.249555\pi\) | |||||||
\(390\) | −30.6216 | −1.55058 | ||||||||
\(391\) | 0.0609162 | 0.00308067 | ||||||||
\(392\) | −1.72618 | −0.0871854 | ||||||||
\(393\) | −56.3635 | −2.84316 | ||||||||
\(394\) | −48.9162 | −2.46436 | ||||||||
\(395\) | 25.2053 | 1.26822 | ||||||||
\(396\) | 18.3564 | 0.922444 | ||||||||
\(397\) | 1.36301 | 0.0684074 | 0.0342037 | − | 0.999415i | \(-0.489111\pi\) | ||||
0.0342037 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(398\) | −16.7440 | −0.839302 | ||||||||
\(399\) | 1.35992 | 0.0680809 | ||||||||
\(400\) | −2.56288 | −0.128144 | ||||||||
\(401\) | 9.92547 | 0.495655 | 0.247827 | − | 0.968804i | \(-0.420283\pi\) | ||||
0.247827 | + | 0.968804i | \(0.420283\pi\) | |||||||
\(402\) | −82.9718 | −4.13826 | ||||||||
\(403\) | −11.4807 | −0.571895 | ||||||||
\(404\) | −21.0147 | −1.04552 | ||||||||
\(405\) | −31.6912 | −1.57475 | ||||||||
\(406\) | −16.4349 | −0.815650 | ||||||||
\(407\) | −9.91448 | −0.491443 | ||||||||
\(408\) | −1.93224 | −0.0956600 | ||||||||
\(409\) | 29.5333 | 1.46033 | 0.730164 | − | 0.683272i | \(-0.239444\pi\) | ||||
0.730164 | + | 0.683272i | \(0.239444\pi\) | |||||||
\(410\) | 31.1525 | 1.53851 | ||||||||
\(411\) | 17.3840 | 0.857488 | ||||||||
\(412\) | 45.9040 | 2.26153 | ||||||||
\(413\) | 13.3903 | 0.658892 | ||||||||
\(414\) | −2.32396 | −0.114217 | ||||||||
\(415\) | 21.8906 | 1.07457 | ||||||||
\(416\) | −13.3293 | −0.653524 | ||||||||
\(417\) | −27.0961 | −1.32690 | ||||||||
\(418\) | −1.00378 | −0.0490965 | ||||||||
\(419\) | −22.5660 | −1.10242 | −0.551210 | − | 0.834367i | \(-0.685834\pi\) | ||||
−0.551210 | + | 0.834367i | \(0.685834\pi\) | |||||||
\(420\) | −21.6406 | −1.05595 | ||||||||
\(421\) | −16.5967 | −0.808875 | −0.404437 | − | 0.914566i | \(-0.632533\pi\) | ||||
−0.404437 | + | 0.914566i | \(0.632533\pi\) | |||||||
\(422\) | −53.4385 | −2.60134 | ||||||||
\(423\) | −56.2957 | −2.73719 | ||||||||
\(424\) | 3.04972 | 0.148107 | ||||||||
\(425\) | 0.520515 | 0.0252487 | ||||||||
\(426\) | 20.4047 | 0.988612 | ||||||||
\(427\) | −3.66072 | −0.177154 | ||||||||
\(428\) | 47.0621 | 2.27483 | ||||||||
\(429\) | −5.70153 | −0.275272 | ||||||||
\(430\) | −9.74809 | −0.470095 | ||||||||
\(431\) | −7.94466 | −0.382681 | −0.191340 | − | 0.981524i | \(-0.561283\pi\) | ||||
−0.191340 | + | 0.981524i | \(0.561283\pi\) | |||||||
\(432\) | −18.5946 | −0.894633 | ||||||||
\(433\) | −37.8928 | −1.82101 | −0.910506 | − | 0.413496i | \(-0.864308\pi\) | ||||
−0.910506 | + | 0.413496i | \(0.864308\pi\) | |||||||
\(434\) | −13.9322 | −0.668767 | ||||||||
\(435\) | −58.2778 | −2.79421 | ||||||||
\(436\) | −39.5889 | −1.89596 | ||||||||
\(437\) | 0.0740067 | 0.00354022 | ||||||||
\(438\) | −110.765 | −5.29254 | ||||||||
\(439\) | 0.284171 | 0.0135627 | 0.00678137 | − | 0.999977i | \(-0.497841\pi\) | ||||
0.00678137 | + | 0.999977i | \(0.497841\pi\) | |||||||
\(440\) | 4.51804 | 0.215389 | ||||||||
\(441\) | 6.37380 | 0.303514 | ||||||||
\(442\) | 1.44276 | 0.0686249 | ||||||||
\(443\) | 30.1382 | 1.43191 | 0.715955 | − | 0.698146i | \(-0.245991\pi\) | ||||
0.715955 | + | 0.698146i | \(0.245991\pi\) | |||||||
\(444\) | −81.9740 | −3.89032 | ||||||||
\(445\) | −17.6934 | −0.838748 | ||||||||
\(446\) | 16.4419 | 0.778544 | ||||||||
\(447\) | 72.9175 | 3.44888 | ||||||||
\(448\) | −12.5752 | −0.594124 | ||||||||
\(449\) | −37.2252 | −1.75677 | −0.878384 | − | 0.477956i | \(-0.841378\pi\) | ||||
−0.878384 | + | 0.477956i | \(0.841378\pi\) | |||||||
\(450\) | −19.8577 | −0.936103 | ||||||||
\(451\) | 5.80040 | 0.273130 | ||||||||
\(452\) | 11.8029 | 0.555162 | ||||||||
\(453\) | 28.4754 | 1.33789 | ||||||||
\(454\) | −15.3977 | −0.722650 | ||||||||
\(455\) | 4.57041 | 0.214264 | ||||||||
\(456\) | −2.34746 | −0.109930 | ||||||||
\(457\) | 0.906470 | 0.0424029 | 0.0212014 | − | 0.999775i | \(-0.493251\pi\) | ||||
0.0212014 | + | 0.999775i | \(0.493251\pi\) | |||||||
\(458\) | 45.5591 | 2.12883 | ||||||||
\(459\) | 3.77653 | 0.176273 | ||||||||
\(460\) | −1.17768 | −0.0549098 | ||||||||
\(461\) | 39.1587 | 1.82380 | 0.911902 | − | 0.410409i | \(-0.134614\pi\) | ||||
0.911902 | + | 0.410409i | \(0.134614\pi\) | |||||||
\(462\) | −6.91898 | −0.321900 | ||||||||
\(463\) | −5.71682 | −0.265683 | −0.132842 | − | 0.991137i | \(-0.542410\pi\) | ||||
−0.132842 | + | 0.991137i | \(0.542410\pi\) | |||||||
\(464\) | −13.5196 | −0.627631 | ||||||||
\(465\) | −49.4034 | −2.29103 | ||||||||
\(466\) | −13.4363 | −0.622426 | ||||||||
\(467\) | −39.8097 | −1.84217 | −0.921087 | − | 0.389357i | \(-0.872697\pi\) | ||||
−0.921087 | + | 0.389357i | \(0.872697\pi\) | |||||||
\(468\) | −32.0539 | −1.48169 | ||||||||
\(469\) | 12.3839 | 0.571837 | ||||||||
\(470\) | −48.9873 | −2.25962 | ||||||||
\(471\) | 9.34506 | 0.430598 | ||||||||
\(472\) | −23.1141 | −1.06391 | ||||||||
\(473\) | −1.81503 | −0.0834551 | ||||||||
\(474\) | 66.6303 | 3.06043 | ||||||||
\(475\) | 0.632371 | 0.0290152 | ||||||||
\(476\) | 1.01961 | 0.0467338 | ||||||||
\(477\) | −11.2609 | −0.515599 | ||||||||
\(478\) | 18.2255 | 0.833617 | ||||||||
\(479\) | −12.1014 | −0.552928 | −0.276464 | − | 0.961024i | \(-0.589163\pi\) | ||||
−0.276464 | + | 0.961024i | \(0.589163\pi\) | |||||||
\(480\) | −57.3582 | −2.61803 | ||||||||
\(481\) | 17.3126 | 0.789387 | ||||||||
\(482\) | −6.98751 | −0.318272 | ||||||||
\(483\) | 0.510123 | 0.0232114 | ||||||||
\(484\) | −27.7028 | −1.25922 | ||||||||
\(485\) | −16.3749 | −0.743548 | ||||||||
\(486\) | −15.9627 | −0.724083 | ||||||||
\(487\) | 19.4701 | 0.882274 | 0.441137 | − | 0.897440i | \(-0.354575\pi\) | ||||
0.441137 | + | 0.897440i | \(0.354575\pi\) | |||||||
\(488\) | 6.31906 | 0.286051 | ||||||||
\(489\) | 21.8840 | 0.989630 | ||||||||
\(490\) | 5.54634 | 0.250558 | ||||||||
\(491\) | −23.3450 | −1.05354 | −0.526772 | − | 0.850007i | \(-0.676598\pi\) | ||||
−0.526772 | + | 0.850007i | \(0.676598\pi\) | |||||||
\(492\) | 47.9583 | 2.16213 | ||||||||
\(493\) | 2.74580 | 0.123665 | ||||||||
\(494\) | 1.75279 | 0.0788620 | ||||||||
\(495\) | −16.6825 | −0.749823 | ||||||||
\(496\) | −11.4608 | −0.514607 | ||||||||
\(497\) | −3.04550 | −0.136610 | ||||||||
\(498\) | 57.8679 | 2.59312 | ||||||||
\(499\) | −1.39608 | −0.0624971 | −0.0312486 | − | 0.999512i | \(-0.509948\pi\) | ||||
−0.0312486 | + | 0.999512i | \(0.509948\pi\) | |||||||
\(500\) | 25.2782 | 1.13047 | ||||||||
\(501\) | −23.7898 | −1.06285 | ||||||||
\(502\) | −24.3194 | −1.08543 | ||||||||
\(503\) | −10.0032 | −0.446020 | −0.223010 | − | 0.974816i | \(-0.571588\pi\) | ||||
−0.223010 | + | 0.974816i | \(0.571588\pi\) | |||||||
\(504\) | −11.0023 | −0.490083 | ||||||||
\(505\) | 19.0984 | 0.849868 | ||||||||
\(506\) | −0.376532 | −0.0167389 | ||||||||
\(507\) | −29.8457 | −1.32549 | ||||||||
\(508\) | 18.1085 | 0.803435 | ||||||||
\(509\) | 18.7664 | 0.831805 | 0.415902 | − | 0.909409i | \(-0.363466\pi\) | ||||
0.415902 | + | 0.909409i | \(0.363466\pi\) | |||||||
\(510\) | 6.20840 | 0.274913 | ||||||||
\(511\) | 16.5322 | 0.731340 | ||||||||
\(512\) | −19.5210 | −0.862715 | ||||||||
\(513\) | 4.58808 | 0.202569 | ||||||||
\(514\) | −19.7958 | −0.873156 | ||||||||
\(515\) | −41.7181 | −1.83832 | ||||||||
\(516\) | −15.0069 | −0.660640 | ||||||||
\(517\) | −9.12111 | −0.401146 | ||||||||
\(518\) | 21.0094 | 0.923099 | ||||||||
\(519\) | 56.2854 | 2.47066 | ||||||||
\(520\) | −7.88937 | −0.345972 | ||||||||
\(521\) | 42.8475 | 1.87718 | 0.938591 | − | 0.345032i | \(-0.112132\pi\) | ||||
0.938591 | + | 0.345032i | \(0.112132\pi\) | |||||||
\(522\) | −104.753 | −4.58490 | ||||||||
\(523\) | −17.4782 | −0.764268 | −0.382134 | − | 0.924107i | \(-0.624811\pi\) | ||||
−0.382134 | + | 0.924107i | \(0.624811\pi\) | |||||||
\(524\) | −51.3404 | −2.24282 | ||||||||
\(525\) | 4.35889 | 0.190237 | ||||||||
\(526\) | 7.60371 | 0.331538 | ||||||||
\(527\) | 2.32767 | 0.101395 | ||||||||
\(528\) | −5.69165 | −0.247697 | ||||||||
\(529\) | −22.9722 | −0.998793 | ||||||||
\(530\) | −9.79895 | −0.425639 | ||||||||
\(531\) | 85.3469 | 3.70374 | ||||||||
\(532\) | 1.23872 | 0.0537053 | ||||||||
\(533\) | −10.1286 | −0.438719 | ||||||||
\(534\) | −46.7725 | −2.02405 | ||||||||
\(535\) | −42.7705 | −1.84913 | ||||||||
\(536\) | −21.3769 | −0.923343 | ||||||||
\(537\) | 9.08406 | 0.392006 | ||||||||
\(538\) | 21.4588 | 0.925153 | ||||||||
\(539\) | 1.03269 | 0.0444812 | ||||||||
\(540\) | −73.0110 | −3.14189 | ||||||||
\(541\) | 24.6276 | 1.05882 | 0.529411 | − | 0.848365i | \(-0.322413\pi\) | ||||
0.529411 | + | 0.848365i | \(0.322413\pi\) | |||||||
\(542\) | 50.1979 | 2.15618 | ||||||||
\(543\) | −54.9676 | −2.35889 | ||||||||
\(544\) | 2.70247 | 0.115867 | ||||||||
\(545\) | 35.9788 | 1.54116 | ||||||||
\(546\) | 12.0819 | 0.517057 | ||||||||
\(547\) | −9.94054 | −0.425027 | −0.212513 | − | 0.977158i | \(-0.568165\pi\) | ||||
−0.212513 | + | 0.977158i | \(0.568165\pi\) | |||||||
\(548\) | 15.8347 | 0.676426 | ||||||||
\(549\) | −23.3327 | −0.995814 | ||||||||
\(550\) | −3.21738 | −0.137189 | ||||||||
\(551\) | 3.33586 | 0.142112 | ||||||||
\(552\) | −0.880565 | −0.0374794 | ||||||||
\(553\) | −9.94489 | −0.422900 | ||||||||
\(554\) | −6.73246 | −0.286035 | ||||||||
\(555\) | 74.4989 | 3.16230 | ||||||||
\(556\) | −24.6813 | −1.04672 | ||||||||
\(557\) | 6.41990 | 0.272020 | 0.136010 | − | 0.990707i | \(-0.456572\pi\) | ||||
0.136010 | + | 0.990707i | \(0.456572\pi\) | |||||||
\(558\) | −88.8011 | −3.75925 | ||||||||
\(559\) | 3.16939 | 0.134051 | ||||||||
\(560\) | 4.56250 | 0.192801 | ||||||||
\(561\) | 1.15596 | 0.0488048 | ||||||||
\(562\) | −51.8883 | −2.18878 | ||||||||
\(563\) | −4.05629 | −0.170952 | −0.0854760 | − | 0.996340i | \(-0.527241\pi\) | ||||
−0.0854760 | + | 0.996340i | \(0.527241\pi\) | |||||||
\(564\) | −75.4144 | −3.17552 | ||||||||
\(565\) | −10.7266 | −0.451272 | ||||||||
\(566\) | 8.70440 | 0.365873 | ||||||||
\(567\) | 12.5039 | 0.525115 | ||||||||
\(568\) | 5.25710 | 0.220583 | ||||||||
\(569\) | −43.6796 | −1.83114 | −0.915572 | − | 0.402155i | \(-0.868261\pi\) | ||||
−0.915572 | + | 0.402155i | \(0.868261\pi\) | |||||||
\(570\) | 7.54255 | 0.315923 | ||||||||
\(571\) | −3.88786 | −0.162702 | −0.0813510 | − | 0.996686i | \(-0.525923\pi\) | ||||
−0.0813510 | + | 0.996686i | \(0.525923\pi\) | |||||||
\(572\) | −5.19341 | −0.217147 | ||||||||
\(573\) | 44.0020 | 1.83821 | ||||||||
\(574\) | −12.2914 | −0.513033 | ||||||||
\(575\) | 0.237211 | 0.00989238 | ||||||||
\(576\) | −80.1519 | −3.33966 | ||||||||
\(577\) | 16.8119 | 0.699890 | 0.349945 | − | 0.936770i | \(-0.386200\pi\) | ||||
0.349945 | + | 0.936770i | \(0.386200\pi\) | |||||||
\(578\) | 36.9092 | 1.53522 | ||||||||
\(579\) | −47.5508 | −1.97614 | ||||||||
\(580\) | −53.0841 | −2.20420 | ||||||||
\(581\) | −8.63706 | −0.358326 | ||||||||
\(582\) | −43.2871 | −1.79431 | ||||||||
\(583\) | −1.82450 | −0.0755630 | ||||||||
\(584\) | −28.5375 | −1.18089 | ||||||||
\(585\) | 29.1309 | 1.20441 | ||||||||
\(586\) | −30.4429 | −1.25758 | ||||||||
\(587\) | 45.5129 | 1.87852 | 0.939259 | − | 0.343210i | \(-0.111514\pi\) | ||||
0.939259 | + | 0.343210i | \(0.111514\pi\) | |||||||
\(588\) | 8.53841 | 0.352118 | ||||||||
\(589\) | 2.82788 | 0.116521 | ||||||||
\(590\) | 74.2670 | 3.05752 | ||||||||
\(591\) | 68.4379 | 2.81516 | ||||||||
\(592\) | 17.2826 | 0.710311 | ||||||||
\(593\) | −18.3137 | −0.752054 | −0.376027 | − | 0.926609i | \(-0.622710\pi\) | ||||
−0.376027 | + | 0.926609i | \(0.622710\pi\) | |||||||
\(594\) | −23.3432 | −0.957785 | ||||||||
\(595\) | −0.926634 | −0.0379883 | ||||||||
\(596\) | 66.4191 | 2.72063 | ||||||||
\(597\) | 23.4263 | 0.958775 | ||||||||
\(598\) | 0.657497 | 0.0268871 | ||||||||
\(599\) | −25.2463 | −1.03154 | −0.515769 | − | 0.856728i | \(-0.672494\pi\) | ||||
−0.515769 | + | 0.856728i | \(0.672494\pi\) | |||||||
\(600\) | −7.52423 | −0.307176 | ||||||||
\(601\) | 15.0178 | 0.612590 | 0.306295 | − | 0.951937i | \(-0.400911\pi\) | ||||
0.306295 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(602\) | 3.84616 | 0.156758 | ||||||||
\(603\) | 78.9327 | 3.21439 | ||||||||
\(604\) | 25.9377 | 1.05539 | ||||||||
\(605\) | 25.1766 | 1.02357 | ||||||||
\(606\) | 50.4866 | 2.05088 | ||||||||
\(607\) | −11.0999 | −0.450529 | −0.225265 | − | 0.974298i | \(-0.572325\pi\) | ||||
−0.225265 | + | 0.974298i | \(0.572325\pi\) | |||||||
\(608\) | 3.28321 | 0.133152 | ||||||||
\(609\) | 22.9938 | 0.931756 | ||||||||
\(610\) | −20.3036 | −0.822068 | ||||||||
\(611\) | 15.9272 | 0.644347 | ||||||||
\(612\) | 6.49880 | 0.262698 | ||||||||
\(613\) | 19.9317 | 0.805034 | 0.402517 | − | 0.915412i | \(-0.368135\pi\) | ||||
0.402517 | + | 0.915412i | \(0.368135\pi\) | |||||||
\(614\) | 12.3341 | 0.497762 | ||||||||
\(615\) | −43.5850 | −1.75752 | ||||||||
\(616\) | −1.78261 | −0.0718235 | ||||||||
\(617\) | 23.1490 | 0.931946 | 0.465973 | − | 0.884799i | \(-0.345704\pi\) | ||||
0.465973 | + | 0.884799i | \(0.345704\pi\) | |||||||
\(618\) | −110.282 | −4.43618 | ||||||||
\(619\) | 21.6806 | 0.871418 | 0.435709 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435709 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(620\) | −45.0005 | −1.80727 | ||||||||
\(621\) | 1.72105 | 0.0690634 | ||||||||
\(622\) | 1.01317 | 0.0406245 | ||||||||
\(623\) | 6.98103 | 0.279689 | ||||||||
\(624\) | 9.93873 | 0.397868 | ||||||||
\(625\) | −30.0916 | −1.20366 | ||||||||
\(626\) | 24.5253 | 0.980228 | ||||||||
\(627\) | 1.40437 | 0.0560853 | ||||||||
\(628\) | 8.51223 | 0.339675 | ||||||||
\(629\) | −3.51007 | −0.139956 | ||||||||
\(630\) | 35.3512 | 1.40843 | ||||||||
\(631\) | −12.7828 | −0.508877 | −0.254439 | − | 0.967089i | \(-0.581891\pi\) | ||||
−0.254439 | + | 0.967089i | \(0.581891\pi\) | |||||||
\(632\) | 17.1667 | 0.682855 | ||||||||
\(633\) | 74.7649 | 2.97164 | ||||||||
\(634\) | −0.577165 | −0.0229222 | ||||||||
\(635\) | −16.4572 | −0.653085 | ||||||||
\(636\) | −15.0852 | −0.598165 | ||||||||
\(637\) | −1.80328 | −0.0714485 | ||||||||
\(638\) | −16.9722 | −0.671935 | ||||||||
\(639\) | −19.4114 | −0.767904 | ||||||||
\(640\) | −32.2779 | −1.27589 | ||||||||
\(641\) | 14.6413 | 0.578297 | 0.289148 | − | 0.957284i | \(-0.406628\pi\) | ||||
0.289148 | + | 0.957284i | \(0.406628\pi\) | |||||||
\(642\) | −113.064 | −4.46227 | ||||||||
\(643\) | 45.4149 | 1.79099 | 0.895494 | − | 0.445074i | \(-0.146823\pi\) | ||||
0.895494 | + | 0.445074i | \(0.146823\pi\) | |||||||
\(644\) | 0.464661 | 0.0183102 | ||||||||
\(645\) | 13.6384 | 0.537011 | ||||||||
\(646\) | −0.355373 | −0.0139819 | ||||||||
\(647\) | −22.9211 | −0.901120 | −0.450560 | − | 0.892746i | \(-0.648776\pi\) | ||||
−0.450560 | + | 0.892746i | \(0.648776\pi\) | |||||||
\(648\) | −21.5840 | −0.847900 | ||||||||
\(649\) | 13.8280 | 0.542797 | ||||||||
\(650\) | 5.61817 | 0.220363 | ||||||||
\(651\) | 19.4923 | 0.763965 | ||||||||
\(652\) | 19.9337 | 0.780665 | ||||||||
\(653\) | −6.52087 | −0.255181 | −0.127591 | − | 0.991827i | \(-0.540724\pi\) | ||||
−0.127591 | + | 0.991827i | \(0.540724\pi\) | |||||||
\(654\) | 95.1099 | 3.71909 | ||||||||
\(655\) | 46.6587 | 1.82311 | ||||||||
\(656\) | −10.1111 | −0.394771 | ||||||||
\(657\) | 105.373 | 4.11098 | ||||||||
\(658\) | 19.3282 | 0.753491 | ||||||||
\(659\) | 29.1233 | 1.13448 | 0.567242 | − | 0.823551i | \(-0.308010\pi\) | ||||
0.567242 | + | 0.823551i | \(0.308010\pi\) | |||||||
\(660\) | −22.3481 | −0.869897 | ||||||||
\(661\) | −7.44150 | −0.289441 | −0.144720 | − | 0.989473i | \(-0.546228\pi\) | ||||
−0.144720 | + | 0.989473i | \(0.546228\pi\) | |||||||
\(662\) | −35.4778 | −1.37888 | ||||||||
\(663\) | −2.01854 | −0.0783935 | ||||||||
\(664\) | 14.9091 | 0.578587 | ||||||||
\(665\) | −1.12576 | −0.0436552 | ||||||||
\(666\) | 133.910 | 5.18889 | ||||||||
\(667\) | 1.25133 | 0.0484515 | ||||||||
\(668\) | −21.6696 | −0.838423 | ||||||||
\(669\) | −23.0035 | −0.889368 | ||||||||
\(670\) | 68.6855 | 2.65355 | ||||||||
\(671\) | −3.78039 | −0.145940 | ||||||||
\(672\) | 22.6309 | 0.873008 | ||||||||
\(673\) | 9.38404 | 0.361728 | 0.180864 | − | 0.983508i | \(-0.442111\pi\) | ||||
0.180864 | + | 0.983508i | \(0.442111\pi\) | |||||||
\(674\) | −23.4995 | −0.905169 | ||||||||
\(675\) | 14.7060 | 0.566034 | ||||||||
\(676\) | −27.1858 | −1.04561 | ||||||||
\(677\) | −26.4008 | −1.01467 | −0.507333 | − | 0.861750i | \(-0.669369\pi\) | ||||
−0.507333 | + | 0.861750i | \(0.669369\pi\) | |||||||
\(678\) | −28.3558 | −1.08900 | ||||||||
\(679\) | 6.46081 | 0.247943 | ||||||||
\(680\) | 1.59954 | 0.0613396 | ||||||||
\(681\) | 21.5427 | 0.825518 | ||||||||
\(682\) | −14.3877 | −0.550932 | ||||||||
\(683\) | 13.5006 | 0.516586 | 0.258293 | − | 0.966067i | \(-0.416840\pi\) | ||||
0.258293 | + | 0.966067i | \(0.416840\pi\) | |||||||
\(684\) | 7.89535 | 0.301886 | ||||||||
\(685\) | −14.3908 | −0.549843 | ||||||||
\(686\) | −2.18834 | −0.0835510 | ||||||||
\(687\) | −63.7410 | −2.43187 | ||||||||
\(688\) | 3.16390 | 0.120623 | ||||||||
\(689\) | 3.18593 | 0.121374 | ||||||||
\(690\) | 2.82931 | 0.107710 | ||||||||
\(691\) | 32.6554 | 1.24227 | 0.621134 | − | 0.783704i | \(-0.286672\pi\) | ||||
0.621134 | + | 0.783704i | \(0.286672\pi\) | |||||||
\(692\) | 51.2693 | 1.94897 | ||||||||
\(693\) | 6.58216 | 0.250036 | ||||||||
\(694\) | −75.8438 | −2.87899 | ||||||||
\(695\) | 22.4306 | 0.850841 | ||||||||
\(696\) | −39.6915 | −1.50450 | ||||||||
\(697\) | 2.05354 | 0.0777834 | ||||||||
\(698\) | −51.0245 | −1.93130 | ||||||||
\(699\) | 18.7986 | 0.711027 | ||||||||
\(700\) | 3.97042 | 0.150068 | ||||||||
\(701\) | −19.0983 | −0.721334 | −0.360667 | − | 0.932695i | \(-0.617451\pi\) | ||||
−0.360667 | + | 0.932695i | \(0.617451\pi\) | |||||||
\(702\) | 40.7618 | 1.53846 | ||||||||
\(703\) | −4.26436 | −0.160833 | ||||||||
\(704\) | −12.9863 | −0.489441 | ||||||||
\(705\) | 68.5374 | 2.58127 | ||||||||
\(706\) | 42.0346 | 1.58199 | ||||||||
\(707\) | −7.53537 | −0.283397 | ||||||||
\(708\) | 114.332 | 4.29684 | ||||||||
\(709\) | −6.35006 | −0.238482 | −0.119241 | − | 0.992865i | \(-0.538046\pi\) | ||||
−0.119241 | + | 0.992865i | \(0.538046\pi\) | |||||||
\(710\) | −16.8914 | −0.633923 | ||||||||
\(711\) | −63.3867 | −2.37719 | ||||||||
\(712\) | −12.0505 | −0.451612 | ||||||||
\(713\) | 1.06077 | 0.0397263 | ||||||||
\(714\) | −2.44956 | −0.0916724 | ||||||||
\(715\) | 4.71983 | 0.176512 | ||||||||
\(716\) | 8.27449 | 0.309232 | ||||||||
\(717\) | −25.4991 | −0.952280 | ||||||||
\(718\) | −45.2606 | −1.68911 | ||||||||
\(719\) | 10.9266 | 0.407495 | 0.203748 | − | 0.979023i | \(-0.434688\pi\) | ||||
0.203748 | + | 0.979023i | \(0.434688\pi\) | |||||||
\(720\) | 29.0804 | 1.08376 | ||||||||
\(721\) | 16.4601 | 0.613005 | ||||||||
\(722\) | 41.1466 | 1.53132 | ||||||||
\(723\) | 9.77612 | 0.363578 | ||||||||
\(724\) | −50.0689 | −1.86080 | ||||||||
\(725\) | 10.6923 | 0.397102 | ||||||||
\(726\) | 66.5543 | 2.47006 | ||||||||
\(727\) | 39.4177 | 1.46192 | 0.730961 | − | 0.682419i | \(-0.239072\pi\) | ||||
0.730961 | + | 0.682419i | \(0.239072\pi\) | |||||||
\(728\) | 3.11279 | 0.115368 | ||||||||
\(729\) | −15.1785 | −0.562168 | ||||||||
\(730\) | 91.6930 | 3.39371 | ||||||||
\(731\) | −0.642582 | −0.0237668 | ||||||||
\(732\) | −31.2567 | −1.15528 | ||||||||
\(733\) | 26.9034 | 0.993699 | 0.496850 | − | 0.867837i | \(-0.334490\pi\) | ||||
0.496850 | + | 0.867837i | \(0.334490\pi\) | |||||||
\(734\) | −68.6379 | −2.53347 | ||||||||
\(735\) | −7.75980 | −0.286224 | ||||||||
\(736\) | 1.23158 | 0.0453966 | ||||||||
\(737\) | 12.7888 | 0.471081 | ||||||||
\(738\) | −78.3428 | −2.88384 | ||||||||
\(739\) | −53.5467 | −1.96975 | −0.984873 | − | 0.173278i | \(-0.944564\pi\) | ||||
−0.984873 | + | 0.173278i | \(0.944564\pi\) | |||||||
\(740\) | 67.8596 | 2.49457 | ||||||||
\(741\) | −2.45231 | −0.0900878 | ||||||||
\(742\) | 3.86622 | 0.141934 | ||||||||
\(743\) | −19.5540 | −0.717366 | −0.358683 | − | 0.933459i | \(-0.616774\pi\) | ||||
−0.358683 | + | 0.933459i | \(0.616774\pi\) | |||||||
\(744\) | −33.6473 | −1.23357 | ||||||||
\(745\) | −60.3624 | −2.21151 | ||||||||
\(746\) | 52.7651 | 1.93187 | ||||||||
\(747\) | −55.0509 | −2.01421 | ||||||||
\(748\) | 1.05294 | 0.0384995 | ||||||||
\(749\) | 16.8753 | 0.616610 | ||||||||
\(750\) | −60.7293 | −2.21752 | ||||||||
\(751\) | −17.6934 | −0.645640 | −0.322820 | − | 0.946460i | \(-0.604631\pi\) | ||||
−0.322820 | + | 0.946460i | \(0.604631\pi\) | |||||||
\(752\) | 15.8996 | 0.579800 | ||||||||
\(753\) | 34.0249 | 1.23994 | ||||||||
\(754\) | 29.6367 | 1.07931 | ||||||||
\(755\) | −23.5724 | −0.857889 | ||||||||
\(756\) | 28.8069 | 1.04770 | ||||||||
\(757\) | 13.2039 | 0.479903 | 0.239952 | − | 0.970785i | \(-0.422868\pi\) | ||||
0.239952 | + | 0.970785i | \(0.422868\pi\) | |||||||
\(758\) | −6.22018 | −0.225927 | ||||||||
\(759\) | 0.526800 | 0.0191216 | ||||||||
\(760\) | 1.94327 | 0.0704899 | ||||||||
\(761\) | −18.9993 | −0.688724 | −0.344362 | − | 0.938837i | \(-0.611905\pi\) | ||||
−0.344362 | + | 0.938837i | \(0.611905\pi\) | |||||||
\(762\) | −43.5046 | −1.57601 | ||||||||
\(763\) | −14.1956 | −0.513916 | ||||||||
\(764\) | 40.0806 | 1.45006 | ||||||||
\(765\) | −5.90618 | −0.213538 | ||||||||
\(766\) | −50.8618 | −1.83771 | ||||||||
\(767\) | −24.1464 | −0.871876 | ||||||||
\(768\) | −8.32422 | −0.300374 | ||||||||
\(769\) | 24.5604 | 0.885672 | 0.442836 | − | 0.896603i | \(-0.353972\pi\) | ||||
0.442836 | + | 0.896603i | \(0.353972\pi\) | |||||||
\(770\) | 5.72766 | 0.206410 | ||||||||
\(771\) | 27.6960 | 0.997448 | ||||||||
\(772\) | −43.3131 | −1.55887 | ||||||||
\(773\) | −21.1364 | −0.760223 | −0.380111 | − | 0.924941i | \(-0.624114\pi\) | ||||
−0.380111 | + | 0.924941i | \(0.624114\pi\) | |||||||
\(774\) | 24.5146 | 0.881160 | ||||||||
\(775\) | 9.06408 | 0.325591 | ||||||||
\(776\) | −11.1525 | −0.400353 | ||||||||
\(777\) | −29.3939 | −1.05450 | ||||||||
\(778\) | −61.1238 | −2.19140 | ||||||||
\(779\) | 2.49483 | 0.0893867 | ||||||||
\(780\) | 39.0241 | 1.39729 | ||||||||
\(781\) | −3.14507 | −0.112539 | ||||||||
\(782\) | −0.133305 | −0.00476698 | ||||||||
\(783\) | 77.5764 | 2.77236 | ||||||||
\(784\) | −1.80016 | −0.0642913 | ||||||||
\(785\) | −7.73601 | −0.276110 | ||||||||
\(786\) | 123.342 | 4.39947 | ||||||||
\(787\) | −36.1468 | −1.28849 | −0.644247 | − | 0.764817i | \(-0.722829\pi\) | ||||
−0.644247 | + | 0.764817i | \(0.722829\pi\) | |||||||
\(788\) | 62.3387 | 2.22073 | ||||||||
\(789\) | −10.6382 | −0.378731 | ||||||||
\(790\) | −55.1577 | −1.96242 | ||||||||
\(791\) | 4.23224 | 0.150481 | ||||||||
\(792\) | −11.3620 | −0.403732 | ||||||||
\(793\) | 6.60129 | 0.234419 | ||||||||
\(794\) | −2.98272 | −0.105853 | ||||||||
\(795\) | 13.7096 | 0.486228 | ||||||||
\(796\) | 21.3386 | 0.756325 | ||||||||
\(797\) | −27.1430 | −0.961453 | −0.480727 | − | 0.876871i | \(-0.659627\pi\) | ||||
−0.480727 | + | 0.876871i | \(0.659627\pi\) | |||||||
\(798\) | −2.97595 | −0.105348 | ||||||||
\(799\) | −3.22919 | −0.114240 | ||||||||
\(800\) | 10.5236 | 0.372064 | ||||||||
\(801\) | 44.4956 | 1.57218 | ||||||||
\(802\) | −21.7203 | −0.766969 | ||||||||
\(803\) | 17.0726 | 0.602480 | ||||||||
\(804\) | 105.739 | 3.72913 | ||||||||
\(805\) | −0.422289 | −0.0148837 | ||||||||
\(806\) | 25.1237 | 0.884943 | ||||||||
\(807\) | −30.0226 | −1.05685 | ||||||||
\(808\) | 13.0074 | 0.457600 | ||||||||
\(809\) | −12.3761 | −0.435121 | −0.217561 | − | 0.976047i | \(-0.569810\pi\) | ||||
−0.217561 | + | 0.976047i | \(0.569810\pi\) | |||||||
\(810\) | 69.3509 | 2.43674 | ||||||||
\(811\) | −36.6159 | −1.28576 | −0.642879 | − | 0.765967i | \(-0.722260\pi\) | ||||
−0.642879 | + | 0.765967i | \(0.722260\pi\) | |||||||
\(812\) | 20.9446 | 0.735011 | ||||||||
\(813\) | −70.2311 | −2.46311 | ||||||||
\(814\) | 21.6962 | 0.760452 | ||||||||
\(815\) | −18.1160 | −0.634576 | ||||||||
\(816\) | −2.01504 | −0.0705405 | ||||||||
\(817\) | −0.780670 | −0.0273122 | ||||||||
\(818\) | −64.6288 | −2.25969 | ||||||||
\(819\) | −11.4937 | −0.401624 | ||||||||
\(820\) | −39.7008 | −1.38641 | ||||||||
\(821\) | 16.7224 | 0.583617 | 0.291809 | − | 0.956477i | \(-0.405743\pi\) | ||||
0.291809 | + | 0.956477i | \(0.405743\pi\) | |||||||
\(822\) | −38.0420 | −1.32687 | ||||||||
\(823\) | −19.5991 | −0.683183 | −0.341591 | − | 0.939849i | \(-0.610966\pi\) | ||||
−0.341591 | + | 0.939849i | \(0.610966\pi\) | |||||||
\(824\) | −28.4131 | −0.989816 | ||||||||
\(825\) | 4.50138 | 0.156718 | ||||||||
\(826\) | −29.3024 | −1.01956 | ||||||||
\(827\) | 6.90812 | 0.240219 | 0.120110 | − | 0.992761i | \(-0.461675\pi\) | ||||
0.120110 | + | 0.992761i | \(0.461675\pi\) | |||||||
\(828\) | 2.96165 | 0.102925 | ||||||||
\(829\) | 38.4627 | 1.33587 | 0.667933 | − | 0.744222i | \(-0.267179\pi\) | ||||
0.667933 | + | 0.744222i | \(0.267179\pi\) | |||||||
\(830\) | −47.9041 | −1.66277 | ||||||||
\(831\) | 9.41928 | 0.326751 | ||||||||
\(832\) | 22.6766 | 0.786171 | ||||||||
\(833\) | 0.365608 | 0.0126676 | ||||||||
\(834\) | 59.2953 | 2.05323 | ||||||||
\(835\) | 19.6936 | 0.681525 | ||||||||
\(836\) | 1.27922 | 0.0442426 | ||||||||
\(837\) | 65.7632 | 2.27311 | ||||||||
\(838\) | 49.3819 | 1.70587 | ||||||||
\(839\) | 20.1537 | 0.695784 | 0.347892 | − | 0.937535i | \(-0.386898\pi\) | ||||
0.347892 | + | 0.937535i | \(0.386898\pi\) | |||||||
\(840\) | 13.3948 | 0.462165 | ||||||||
\(841\) | 27.4035 | 0.944949 | ||||||||
\(842\) | 36.3192 | 1.25164 | ||||||||
\(843\) | 72.5961 | 2.50034 | ||||||||
\(844\) | 68.1019 | 2.34416 | ||||||||
\(845\) | 24.7068 | 0.849939 | ||||||||
\(846\) | 123.194 | 4.23549 | ||||||||
\(847\) | −9.93355 | −0.341321 | ||||||||
\(848\) | 3.18041 | 0.109216 | ||||||||
\(849\) | −12.1782 | −0.417954 | ||||||||
\(850\) | −1.13906 | −0.0390695 | ||||||||
\(851\) | −1.59962 | −0.0548342 | ||||||||
\(852\) | −26.0038 | −0.890874 | ||||||||
\(853\) | 11.7285 | 0.401575 | 0.200788 | − | 0.979635i | \(-0.435650\pi\) | ||||
0.200788 | + | 0.979635i | \(0.435650\pi\) | |||||||
\(854\) | 8.01087 | 0.274126 | ||||||||
\(855\) | −7.17538 | −0.245393 | ||||||||
\(856\) | −29.1299 | −0.995639 | ||||||||
\(857\) | −14.3190 | −0.489129 | −0.244564 | − | 0.969633i | \(-0.578645\pi\) | ||||
−0.244564 | + | 0.969633i | \(0.578645\pi\) | |||||||
\(858\) | 12.4769 | 0.425953 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | 12.4229 | 0.423619 | ||||||||
\(861\) | 17.1967 | 0.586062 | ||||||||
\(862\) | 17.3856 | 0.592155 | ||||||||
\(863\) | 0.496892 | 0.0169144 | 0.00845720 | − | 0.999964i | \(-0.497308\pi\) | ||||
0.00845720 | + | 0.999964i | \(0.497308\pi\) | |||||||
\(864\) | 76.3522 | 2.59756 | ||||||||
\(865\) | −46.5941 | −1.58425 | ||||||||
\(866\) | 82.9222 | 2.81781 | ||||||||
\(867\) | −51.6391 | −1.75375 | ||||||||
\(868\) | 17.7552 | 0.602650 | ||||||||
\(869\) | −10.2700 | −0.348386 | ||||||||
\(870\) | 127.531 | 4.32372 | ||||||||
\(871\) | −22.3317 | −0.756681 | ||||||||
\(872\) | 24.5042 | 0.829817 | ||||||||
\(873\) | 41.1799 | 1.39373 | ||||||||
\(874\) | −0.161952 | −0.00547809 | ||||||||
\(875\) | 9.06414 | 0.306424 | ||||||||
\(876\) | 141.158 | 4.76930 | ||||||||
\(877\) | −5.00805 | −0.169110 | −0.0845549 | − | 0.996419i | \(-0.526947\pi\) | ||||
−0.0845549 | + | 0.996419i | \(0.526947\pi\) | |||||||
\(878\) | −0.621861 | −0.0209868 | ||||||||
\(879\) | 42.5921 | 1.43660 | ||||||||
\(880\) | 4.71165 | 0.158830 | ||||||||
\(881\) | 44.4434 | 1.49734 | 0.748668 | − | 0.662945i | \(-0.230694\pi\) | ||||
0.748668 | + | 0.662945i | \(0.230694\pi\) | |||||||
\(882\) | −13.9480 | −0.469654 | ||||||||
\(883\) | 38.7823 | 1.30513 | 0.652564 | − | 0.757733i | \(-0.273693\pi\) | ||||
0.652564 | + | 0.757733i | \(0.273693\pi\) | |||||||
\(884\) | −1.83865 | −0.0618403 | ||||||||
\(885\) | −103.906 | −3.49276 | ||||||||
\(886\) | −65.9525 | −2.21572 | ||||||||
\(887\) | 21.5559 | 0.723776 | 0.361888 | − | 0.932222i | \(-0.382132\pi\) | ||||
0.361888 | + | 0.932222i | \(0.382132\pi\) | |||||||
\(888\) | 50.7392 | 1.70270 | ||||||||
\(889\) | 6.49327 | 0.217777 | ||||||||
\(890\) | 38.7191 | 1.29787 | ||||||||
\(891\) | 12.9127 | 0.432591 | ||||||||
\(892\) | −20.9535 | −0.701574 | ||||||||
\(893\) | −3.92312 | −0.131282 | ||||||||
\(894\) | −159.568 | −5.33675 | ||||||||
\(895\) | −7.51995 | −0.251364 | ||||||||
\(896\) | 12.7354 | 0.425460 | ||||||||
\(897\) | −0.919894 | −0.0307144 | ||||||||
\(898\) | 81.4613 | 2.71840 | ||||||||
\(899\) | 47.8144 | 1.59470 | ||||||||
\(900\) | 25.3067 | 0.843556 | ||||||||
\(901\) | −0.645935 | −0.0215192 | ||||||||
\(902\) | −12.6932 | −0.422638 | ||||||||
\(903\) | −5.38110 | −0.179072 | ||||||||
\(904\) | −7.30561 | −0.242981 | ||||||||
\(905\) | 45.5032 | 1.51258 | ||||||||
\(906\) | −62.3137 | −2.07023 | ||||||||
\(907\) | −12.6792 | −0.421007 | −0.210503 | − | 0.977593i | \(-0.567510\pi\) | ||||
−0.210503 | + | 0.977593i | \(0.567510\pi\) | |||||||
\(908\) | 19.6228 | 0.651206 | ||||||||
\(909\) | −48.0290 | −1.59302 | ||||||||
\(910\) | −10.0016 | −0.331550 | ||||||||
\(911\) | −55.9229 | −1.85281 | −0.926404 | − | 0.376530i | \(-0.877117\pi\) | ||||
−0.926404 | + | 0.376530i | \(0.877117\pi\) | |||||||
\(912\) | −2.44806 | −0.0810634 | ||||||||
\(913\) | −8.91942 | −0.295190 | ||||||||
\(914\) | −1.98366 | −0.0656136 | ||||||||
\(915\) | 28.4064 | 0.939087 | ||||||||
\(916\) | −58.0604 | −1.91837 | ||||||||
\(917\) | −18.4094 | −0.607933 | ||||||||
\(918\) | −8.26431 | −0.272763 | ||||||||
\(919\) | −10.4143 | −0.343535 | −0.171767 | − | 0.985138i | \(-0.554948\pi\) | ||||
−0.171767 | + | 0.985138i | \(0.554948\pi\) | |||||||
\(920\) | 0.728948 | 0.0240327 | ||||||||
\(921\) | −17.2564 | −0.568617 | ||||||||
\(922\) | −85.6924 | −2.82213 | ||||||||
\(923\) | 5.49189 | 0.180768 | ||||||||
\(924\) | 8.81754 | 0.290076 | ||||||||
\(925\) | −13.6684 | −0.449414 | ||||||||
\(926\) | 12.5103 | 0.411115 | ||||||||
\(927\) | 104.913 | 3.44580 | ||||||||
\(928\) | 55.5134 | 1.82232 | ||||||||
\(929\) | −13.5039 | −0.443049 | −0.221524 | − | 0.975155i | \(-0.571103\pi\) | ||||
−0.221524 | + | 0.975155i | \(0.571103\pi\) | |||||||
\(930\) | 108.111 | 3.54510 | ||||||||
\(931\) | 0.444175 | 0.0145573 | ||||||||
\(932\) | 17.1232 | 0.560891 | ||||||||
\(933\) | −1.41751 | −0.0464073 | ||||||||
\(934\) | 87.1170 | 2.85056 | ||||||||
\(935\) | −0.956927 | −0.0312949 | ||||||||
\(936\) | 19.8403 | 0.648500 | ||||||||
\(937\) | 19.3030 | 0.630601 | 0.315300 | − | 0.948992i | \(-0.397895\pi\) | ||||
0.315300 | + | 0.948992i | \(0.397895\pi\) | |||||||
\(938\) | −27.1002 | −0.884853 | ||||||||
\(939\) | −34.3129 | −1.11976 | ||||||||
\(940\) | 62.4293 | 2.03622 | ||||||||
\(941\) | −44.7842 | −1.45992 | −0.729962 | − | 0.683488i | \(-0.760462\pi\) | ||||
−0.729962 | + | 0.683488i | \(0.760462\pi\) | |||||||
\(942\) | −20.4501 | −0.666301 | ||||||||
\(943\) | 0.935846 | 0.0304753 | ||||||||
\(944\) | −24.1046 | −0.784537 | ||||||||
\(945\) | −26.1800 | −0.851635 | ||||||||
\(946\) | 3.97189 | 0.129137 | ||||||||
\(947\) | 13.1630 | 0.427740 | 0.213870 | − | 0.976862i | \(-0.431393\pi\) | ||||
0.213870 | + | 0.976862i | \(0.431393\pi\) | |||||||
\(948\) | −84.9136 | −2.75786 | ||||||||
\(949\) | −29.8121 | −0.967742 | ||||||||
\(950\) | −1.38384 | −0.0448977 | ||||||||
\(951\) | 0.807503 | 0.0261851 | ||||||||
\(952\) | −0.631106 | −0.0204543 | ||||||||
\(953\) | 26.0629 | 0.844259 | 0.422129 | − | 0.906536i | \(-0.361283\pi\) | ||||
0.422129 | + | 0.906536i | \(0.361283\pi\) | |||||||
\(954\) | 24.6425 | 0.797831 | ||||||||
\(955\) | −36.4257 | −1.17871 | ||||||||
\(956\) | −23.2266 | −0.751202 | ||||||||
\(957\) | 23.7455 | 0.767583 | ||||||||
\(958\) | 26.4820 | 0.855594 | ||||||||
\(959\) | 5.67795 | 0.183350 | ||||||||
\(960\) | 97.5812 | 3.14942 | ||||||||
\(961\) | 9.53332 | 0.307527 | ||||||||
\(962\) | −37.8858 | −1.22149 | ||||||||
\(963\) | 107.560 | 3.46607 | ||||||||
\(964\) | 8.90487 | 0.286807 | ||||||||
\(965\) | 39.3634 | 1.26715 | ||||||||
\(966\) | −1.11632 | −0.0359170 | ||||||||
\(967\) | 17.8254 | 0.573225 | 0.286613 | − | 0.958047i | \(-0.407471\pi\) | ||||
0.286613 | + | 0.958047i | \(0.407471\pi\) | |||||||
\(968\) | 17.1471 | 0.551129 | ||||||||
\(969\) | 0.497196 | 0.0159722 | ||||||||
\(970\) | 35.8339 | 1.15056 | ||||||||
\(971\) | 35.0593 | 1.12511 | 0.562553 | − | 0.826761i | \(-0.309819\pi\) | ||||
0.562553 | + | 0.826761i | \(0.309819\pi\) | |||||||
\(972\) | 20.3428 | 0.652497 | ||||||||
\(973\) | −8.85010 | −0.283721 | ||||||||
\(974\) | −42.6071 | −1.36522 | ||||||||
\(975\) | −7.86029 | −0.251731 | ||||||||
\(976\) | 6.58986 | 0.210936 | ||||||||
\(977\) | −3.24167 | −0.103710 | −0.0518551 | − | 0.998655i | \(-0.516513\pi\) | ||||
−0.0518551 | + | 0.998655i | \(0.516513\pi\) | |||||||
\(978\) | −47.8896 | −1.53134 | ||||||||
\(979\) | 7.20924 | 0.230408 | ||||||||
\(980\) | −7.06825 | −0.225787 | ||||||||
\(981\) | −90.4799 | −2.88880 | ||||||||
\(982\) | 51.0866 | 1.63024 | ||||||||
\(983\) | 33.8836 | 1.08072 | 0.540359 | − | 0.841435i | \(-0.318288\pi\) | ||||
0.540359 | + | 0.841435i | \(0.318288\pi\) | |||||||
\(984\) | −29.6846 | −0.946312 | ||||||||
\(985\) | −56.6541 | −1.80515 | ||||||||
\(986\) | −6.00873 | −0.191357 | ||||||||
\(987\) | −27.0418 | −0.860749 | ||||||||
\(988\) | −2.23376 | −0.0710653 | ||||||||
\(989\) | −0.292840 | −0.00931176 | ||||||||
\(990\) | 36.5069 | 1.16027 | ||||||||
\(991\) | −5.01954 | −0.159451 | −0.0797254 | − | 0.996817i | \(-0.525404\pi\) | ||||
−0.0797254 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(992\) | 47.0599 | 1.49415 | ||||||||
\(993\) | 49.6364 | 1.57516 | ||||||||
\(994\) | 6.66458 | 0.211388 | ||||||||
\(995\) | −19.3927 | −0.614790 | ||||||||
\(996\) | −73.7467 | −2.33675 | ||||||||
\(997\) | 13.6730 | 0.433029 | 0.216514 | − | 0.976279i | \(-0.430531\pi\) | ||||
0.216514 | + | 0.976279i | \(0.430531\pi\) | |||||||
\(998\) | 3.05509 | 0.0967072 | ||||||||
\(999\) | −99.1691 | −3.13757 |
(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 | 6013.2.a.e.1.13 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.13 | ✓ | 109 | 1.1 | even | 1 | trivial |