Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | 1.73205 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.73205 | 0.500000 | ||||||||
\(13\) | 5.73205 | 1.58978 | 0.794892 | − | 0.606750i | \(-0.207527\pi\) | ||||
0.794892 | + | 0.606750i | \(0.207527\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.73205 | −0.447214 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.732051 | 0.177548 | 0.0887742 | − | 0.996052i | \(-0.471705\pi\) | ||||
0.0887742 | + | 0.996052i | \(0.471705\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.267949 | 0.0614718 | 0.0307359 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307359 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00000 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(24\) | −1.73205 | −0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.73205 | −1.12415 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | 1.73205 | 0.316228 | ||||||||
\(31\) | −2.73205 | −0.490691 | −0.245345 | − | 0.969436i | \(-0.578901\pi\) | ||||
−0.245345 | + | 0.969436i | \(0.578901\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.732051 | −0.125546 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | −0.267949 | −0.0434671 | ||||||||
\(39\) | 9.92820 | 1.58978 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.19615 | 0.967676 | 0.483838 | − | 0.875157i | \(-0.339242\pi\) | ||||
0.483838 | + | 0.875157i | \(0.339242\pi\) | |||||||
\(42\) | 1.73205 | 0.267261 | ||||||||
\(43\) | 5.26795 | 0.803355 | 0.401677 | − | 0.915781i | \(-0.368427\pi\) | ||||
0.401677 | + | 0.915781i | \(0.368427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.00000 | 0.737210 | ||||||||
\(47\) | −4.73205 | −0.690241 | −0.345120 | − | 0.938558i | \(-0.612162\pi\) | ||||
−0.345120 | + | 0.938558i | \(0.612162\pi\) | |||||||
\(48\) | 1.73205 | 0.250000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.26795 | 0.177548 | ||||||||
\(52\) | 5.73205 | 0.794892 | ||||||||
\(53\) | −6.19615 | −0.851107 | −0.425553 | − | 0.904933i | \(-0.639921\pi\) | ||||
−0.425553 | + | 0.904933i | \(0.639921\pi\) | |||||||
\(54\) | 5.19615 | 0.707107 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.464102 | 0.0614718 | ||||||||
\(58\) | 8.00000 | 1.05045 | ||||||||
\(59\) | −5.53590 | −0.720713 | −0.360356 | − | 0.932815i | \(-0.617345\pi\) | ||||
−0.360356 | + | 0.932815i | \(0.617345\pi\) | |||||||
\(60\) | −1.73205 | −0.223607 | ||||||||
\(61\) | 2.92820 | 0.374918 | 0.187459 | − | 0.982272i | \(-0.439975\pi\) | ||||
0.187459 | + | 0.982272i | \(0.439975\pi\) | |||||||
\(62\) | 2.73205 | 0.346971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.73205 | −0.710973 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.66025 | −1.18019 | −0.590094 | − | 0.807335i | \(-0.700909\pi\) | ||||
−0.590094 | + | 0.807335i | \(0.700909\pi\) | |||||||
\(68\) | 0.732051 | 0.0887742 | ||||||||
\(69\) | −8.66025 | −1.04257 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 6.92820 | 0.822226 | 0.411113 | − | 0.911584i | \(-0.365140\pi\) | ||||
0.411113 | + | 0.911584i | \(0.365140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.12436 | −1.06793 | −0.533963 | − | 0.845508i | \(-0.679298\pi\) | ||||
−0.533963 | + | 0.845508i | \(0.679298\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | 1.73205 | 0.200000 | ||||||||
\(76\) | 0.267949 | 0.0307359 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.92820 | −1.12415 | ||||||||
\(79\) | 7.00000 | 0.787562 | 0.393781 | − | 0.919204i | \(-0.371167\pi\) | ||||
0.393781 | + | 0.919204i | \(0.371167\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −6.19615 | −0.684251 | ||||||||
\(83\) | −5.00000 | −0.548821 | −0.274411 | − | 0.961613i | \(-0.588483\pi\) | ||||
−0.274411 | + | 0.961613i | \(0.588483\pi\) | |||||||
\(84\) | −1.73205 | −0.188982 | ||||||||
\(85\) | −0.732051 | −0.0794021 | ||||||||
\(86\) | −5.26795 | −0.568058 | ||||||||
\(87\) | −13.8564 | −1.48556 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.6603 | −1.44798 | −0.723992 | − | 0.689808i | \(-0.757695\pi\) | ||||
−0.723992 | + | 0.689808i | \(0.757695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.73205 | −0.600882 | ||||||||
\(92\) | −5.00000 | −0.521286 | ||||||||
\(93\) | −4.73205 | −0.490691 | ||||||||
\(94\) | 4.73205 | 0.488074 | ||||||||
\(95\) | −0.267949 | −0.0274910 | ||||||||
\(96\) | −1.73205 | −0.176777 | ||||||||
\(97\) | 10.9282 | 1.10959 | 0.554795 | − | 0.831987i | \(-0.312797\pi\) | ||||
0.554795 | + | 0.831987i | \(0.312797\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.5359 | 1.14786 | 0.573932 | − | 0.818903i | \(-0.305417\pi\) | ||||
0.573932 | + | 0.818903i | \(0.305417\pi\) | |||||||
\(102\) | −1.26795 | −0.125546 | ||||||||
\(103\) | −10.7321 | −1.05746 | −0.528730 | − | 0.848790i | \(-0.677332\pi\) | ||||
−0.528730 | + | 0.848790i | \(0.677332\pi\) | |||||||
\(104\) | −5.73205 | −0.562074 | ||||||||
\(105\) | 1.73205 | 0.169031 | ||||||||
\(106\) | 6.19615 | 0.601824 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | −5.19615 | −0.500000 | ||||||||
\(109\) | −20.0526 | −1.92069 | −0.960343 | − | 0.278820i | \(-0.910057\pi\) | ||||
−0.960343 | + | 0.278820i | \(0.910057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3923 | 0.986394 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −14.1244 | −1.32871 | −0.664354 | − | 0.747418i | \(-0.731293\pi\) | ||||
−0.664354 | + | 0.747418i | \(0.731293\pi\) | |||||||
\(114\) | −0.464102 | −0.0434671 | ||||||||
\(115\) | 5.00000 | 0.466252 | ||||||||
\(116\) | −8.00000 | −0.742781 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.53590 | 0.509621 | ||||||||
\(119\) | −0.732051 | −0.0671070 | ||||||||
\(120\) | 1.73205 | 0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.92820 | −0.265107 | ||||||||
\(123\) | 10.7321 | 0.967676 | ||||||||
\(124\) | −2.73205 | −0.245345 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.12436 | 0.543449 | 0.271724 | − | 0.962375i | \(-0.412406\pi\) | ||||
0.271724 | + | 0.962375i | \(0.412406\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.12436 | 0.803355 | ||||||||
\(130\) | 5.73205 | 0.502734 | ||||||||
\(131\) | 13.1962 | 1.15295 | 0.576477 | − | 0.817114i | \(-0.304427\pi\) | ||||
0.576477 | + | 0.817114i | \(0.304427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.267949 | −0.0232341 | ||||||||
\(134\) | 9.66025 | 0.834519 | ||||||||
\(135\) | 5.19615 | 0.447214 | ||||||||
\(136\) | −0.732051 | −0.0627728 | ||||||||
\(137\) | 14.6603 | 1.25251 | 0.626255 | − | 0.779618i | \(-0.284587\pi\) | ||||
0.626255 | + | 0.779618i | \(0.284587\pi\) | |||||||
\(138\) | 8.66025 | 0.737210 | ||||||||
\(139\) | 17.1962 | 1.45856 | 0.729279 | − | 0.684216i | \(-0.239856\pi\) | ||||
0.729279 | + | 0.684216i | \(0.239856\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −8.19615 | −0.690241 | ||||||||
\(142\) | −6.92820 | −0.581402 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 9.12436 | 0.755137 | ||||||||
\(147\) | 1.73205 | 0.142857 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | −19.4641 | −1.59456 | −0.797281 | − | 0.603609i | \(-0.793729\pi\) | ||||
−0.797281 | + | 0.603609i | \(0.793729\pi\) | |||||||
\(150\) | −1.73205 | −0.141421 | ||||||||
\(151\) | 18.8564 | 1.53451 | 0.767256 | − | 0.641341i | \(-0.221621\pi\) | ||||
0.767256 | + | 0.641341i | \(0.221621\pi\) | |||||||
\(152\) | −0.267949 | −0.0217335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.73205 | 0.219444 | ||||||||
\(156\) | 9.92820 | 0.794892 | ||||||||
\(157\) | −5.39230 | −0.430353 | −0.215176 | − | 0.976575i | \(-0.569033\pi\) | ||||
−0.215176 | + | 0.976575i | \(0.569033\pi\) | |||||||
\(158\) | −7.00000 | −0.556890 | ||||||||
\(159\) | −10.7321 | −0.851107 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.00000 | 0.394055 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | 6.19615 | 0.483838 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.00000 | 0.388075 | ||||||||
\(167\) | 0.339746 | 0.0262903 | 0.0131452 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131452 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(168\) | 1.73205 | 0.133631 | ||||||||
\(169\) | 19.8564 | 1.52742 | ||||||||
\(170\) | 0.732051 | 0.0561457 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.26795 | 0.401677 | ||||||||
\(173\) | −7.85641 | −0.597312 | −0.298656 | − | 0.954361i | \(-0.596538\pi\) | ||||
−0.298656 | + | 0.954361i | \(0.596538\pi\) | |||||||
\(174\) | 13.8564 | 1.05045 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.58846 | −0.720713 | ||||||||
\(178\) | 13.6603 | 1.02388 | ||||||||
\(179\) | −16.1962 | −1.21056 | −0.605279 | − | 0.796014i | \(-0.706938\pi\) | ||||
−0.605279 | + | 0.796014i | \(0.706938\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6603 | −1.68432 | −0.842162 | − | 0.539225i | \(-0.818717\pi\) | ||||
−0.842162 | + | 0.539225i | \(0.818717\pi\) | |||||||
\(182\) | 5.73205 | 0.424888 | ||||||||
\(183\) | 5.07180 | 0.374918 | ||||||||
\(184\) | 5.00000 | 0.368605 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 4.73205 | 0.346971 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.73205 | −0.345120 | ||||||||
\(189\) | 5.19615 | 0.377964 | ||||||||
\(190\) | 0.267949 | 0.0194391 | ||||||||
\(191\) | −8.66025 | −0.626634 | −0.313317 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313317 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(192\) | 1.73205 | 0.125000 | ||||||||
\(193\) | −11.3923 | −0.820036 | −0.410018 | − | 0.912077i | \(-0.634478\pi\) | ||||
−0.410018 | + | 0.912077i | \(0.634478\pi\) | |||||||
\(194\) | −10.9282 | −0.784599 | ||||||||
\(195\) | −9.92820 | −0.710973 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 9.46410 | 0.674289 | 0.337145 | − | 0.941453i | \(-0.390539\pi\) | ||||
0.337145 | + | 0.941453i | \(0.390539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −16.7321 | −1.18019 | ||||||||
\(202\) | −11.5359 | −0.811663 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 1.26795 | 0.0887742 | ||||||||
\(205\) | −6.19615 | −0.432758 | ||||||||
\(206\) | 10.7321 | 0.747737 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.73205 | 0.397446 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.73205 | −0.119523 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −6.19615 | −0.425553 | ||||||||
\(213\) | 12.0000 | 0.822226 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | −5.26795 | −0.359271 | ||||||||
\(216\) | 5.19615 | 0.353553 | ||||||||
\(217\) | 2.73205 | 0.185464 | ||||||||
\(218\) | 20.0526 | 1.35813 | ||||||||
\(219\) | −15.8038 | −1.06793 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.19615 | 0.282264 | ||||||||
\(222\) | −10.3923 | −0.697486 | ||||||||
\(223\) | −11.2679 | −0.754558 | −0.377279 | − | 0.926100i | \(-0.623140\pi\) | ||||
−0.377279 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1244 | 0.939538 | ||||||||
\(227\) | −17.3205 | −1.14960 | −0.574801 | − | 0.818293i | \(-0.694921\pi\) | ||||
−0.574801 | + | 0.818293i | \(0.694921\pi\) | |||||||
\(228\) | 0.464102 | 0.0307359 | ||||||||
\(229\) | 5.85641 | 0.387002 | 0.193501 | − | 0.981100i | \(-0.438016\pi\) | ||||
0.193501 | + | 0.981100i | \(0.438016\pi\) | |||||||
\(230\) | −5.00000 | −0.329690 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | −5.53590 | −0.362669 | −0.181334 | − | 0.983421i | \(-0.558042\pi\) | ||||
−0.181334 | + | 0.983421i | \(0.558042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.73205 | 0.308685 | ||||||||
\(236\) | −5.53590 | −0.360356 | ||||||||
\(237\) | 12.1244 | 0.787562 | ||||||||
\(238\) | 0.732051 | 0.0474518 | ||||||||
\(239\) | 4.46410 | 0.288759 | 0.144379 | − | 0.989522i | \(-0.453881\pi\) | ||||
0.144379 | + | 0.989522i | \(0.453881\pi\) | |||||||
\(240\) | −1.73205 | −0.111803 | ||||||||
\(241\) | −17.4641 | −1.12496 | −0.562481 | − | 0.826810i | \(-0.690153\pi\) | ||||
−0.562481 | + | 0.826810i | \(0.690153\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.92820 | 0.187459 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −10.7321 | −0.684251 | ||||||||
\(247\) | 1.53590 | 0.0977269 | ||||||||
\(248\) | 2.73205 | 0.173485 | ||||||||
\(249\) | −8.66025 | −0.548821 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.39230 | −0.403479 | −0.201739 | − | 0.979439i | \(-0.564659\pi\) | ||||
−0.201739 | + | 0.979439i | \(0.564659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.12436 | −0.384276 | ||||||||
\(255\) | −1.26795 | −0.0794021 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.19615 | 0.511262 | 0.255631 | − | 0.966774i | \(-0.417717\pi\) | ||||
0.255631 | + | 0.966774i | \(0.417717\pi\) | |||||||
\(258\) | −9.12436 | −0.568058 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | −5.73205 | −0.355487 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.1962 | −0.815261 | ||||||||
\(263\) | −10.1244 | −0.624295 | −0.312147 | − | 0.950034i | \(-0.601048\pi\) | ||||
−0.312147 | + | 0.950034i | \(0.601048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.19615 | 0.380627 | ||||||||
\(266\) | 0.267949 | 0.0164290 | ||||||||
\(267\) | −23.6603 | −1.44798 | ||||||||
\(268\) | −9.66025 | −0.590094 | ||||||||
\(269\) | −21.7321 | −1.32503 | −0.662513 | − | 0.749050i | \(-0.730510\pi\) | ||||
−0.662513 | + | 0.749050i | \(0.730510\pi\) | |||||||
\(270\) | −5.19615 | −0.316228 | ||||||||
\(271\) | −21.4641 | −1.30385 | −0.651926 | − | 0.758283i | \(-0.726039\pi\) | ||||
−0.651926 | + | 0.758283i | \(0.726039\pi\) | |||||||
\(272\) | 0.732051 | 0.0443871 | ||||||||
\(273\) | −9.92820 | −0.600882 | ||||||||
\(274\) | −14.6603 | −0.885658 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.66025 | −0.521286 | ||||||||
\(277\) | −1.80385 | −0.108383 | −0.0541913 | − | 0.998531i | \(-0.517258\pi\) | ||||
−0.0541913 | + | 0.998531i | \(0.517258\pi\) | |||||||
\(278\) | −17.1962 | −1.03136 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −7.73205 | −0.461255 | −0.230628 | − | 0.973042i | \(-0.574078\pi\) | ||||
−0.230628 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(282\) | 8.19615 | 0.488074 | ||||||||
\(283\) | −25.7846 | −1.53274 | −0.766368 | − | 0.642402i | \(-0.777938\pi\) | ||||
−0.766368 | + | 0.642402i | \(0.777938\pi\) | |||||||
\(284\) | 6.92820 | 0.411113 | ||||||||
\(285\) | −0.464102 | −0.0274910 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.19615 | −0.365747 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4641 | −0.968477 | ||||||||
\(290\) | −8.00000 | −0.469776 | ||||||||
\(291\) | 18.9282 | 1.10959 | ||||||||
\(292\) | −9.12436 | −0.533963 | ||||||||
\(293\) | −11.7321 | −0.685394 | −0.342697 | − | 0.939446i | \(-0.611340\pi\) | ||||
−0.342697 | + | 0.939446i | \(0.611340\pi\) | |||||||
\(294\) | −1.73205 | −0.101015 | ||||||||
\(295\) | 5.53590 | 0.322312 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.4641 | 1.12753 | ||||||||
\(299\) | −28.6603 | −1.65747 | ||||||||
\(300\) | 1.73205 | 0.100000 | ||||||||
\(301\) | −5.26795 | −0.303640 | ||||||||
\(302\) | −18.8564 | −1.08506 | ||||||||
\(303\) | 19.9808 | 1.14786 | ||||||||
\(304\) | 0.267949 | 0.0153679 | ||||||||
\(305\) | −2.92820 | −0.167668 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07180 | 0.403609 | 0.201804 | − | 0.979426i | \(-0.435319\pi\) | ||||
0.201804 | + | 0.979426i | \(0.435319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.5885 | −1.05746 | ||||||||
\(310\) | −2.73205 | −0.155170 | ||||||||
\(311\) | 12.7321 | 0.721968 | 0.360984 | − | 0.932572i | \(-0.382441\pi\) | ||||
0.360984 | + | 0.932572i | \(0.382441\pi\) | |||||||
\(312\) | −9.92820 | −0.562074 | ||||||||
\(313\) | −5.60770 | −0.316966 | −0.158483 | − | 0.987362i | \(-0.550660\pi\) | ||||
−0.158483 | + | 0.987362i | \(0.550660\pi\) | |||||||
\(314\) | 5.39230 | 0.304305 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00000 | 0.393781 | ||||||||
\(317\) | 5.12436 | 0.287812 | 0.143906 | − | 0.989591i | \(-0.454034\pi\) | ||||
0.143906 | + | 0.989591i | \(0.454034\pi\) | |||||||
\(318\) | 10.7321 | 0.601824 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −3.46410 | −0.193347 | ||||||||
\(322\) | −5.00000 | −0.278639 | ||||||||
\(323\) | 0.196152 | 0.0109142 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 5.73205 | 0.317957 | ||||||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | −34.7321 | −1.92069 | ||||||||
\(328\) | −6.19615 | −0.342125 | ||||||||
\(329\) | 4.73205 | 0.260886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.0526 | 1.87170 | 0.935849 | − | 0.352401i | \(-0.114635\pi\) | ||||
0.935849 | + | 0.352401i | \(0.114635\pi\) | |||||||
\(332\) | −5.00000 | −0.274411 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.339746 | −0.0185901 | ||||||||
\(335\) | 9.66025 | 0.527796 | ||||||||
\(336\) | −1.73205 | −0.0944911 | ||||||||
\(337\) | 9.39230 | 0.511631 | 0.255816 | − | 0.966726i | \(-0.417656\pi\) | ||||
0.255816 | + | 0.966726i | \(0.417656\pi\) | |||||||
\(338\) | −19.8564 | −1.08005 | ||||||||
\(339\) | −24.4641 | −1.32871 | ||||||||
\(340\) | −0.732051 | −0.0397010 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.26795 | −0.284029 | ||||||||
\(345\) | 8.66025 | 0.466252 | ||||||||
\(346\) | 7.85641 | 0.422363 | ||||||||
\(347\) | 15.4641 | 0.830156 | 0.415078 | − | 0.909786i | \(-0.363754\pi\) | ||||
0.415078 | + | 0.909786i | \(0.363754\pi\) | |||||||
\(348\) | −13.8564 | −0.742781 | ||||||||
\(349\) | −0.464102 | −0.0248428 | −0.0124214 | − | 0.999923i | \(-0.503954\pi\) | ||||
−0.0124214 | + | 0.999923i | \(0.503954\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −29.7846 | −1.58978 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1962 | 0.649136 | 0.324568 | − | 0.945862i | \(-0.394781\pi\) | ||||
0.324568 | + | 0.945862i | \(0.394781\pi\) | |||||||
\(354\) | 9.58846 | 0.509621 | ||||||||
\(355\) | −6.92820 | −0.367711 | ||||||||
\(356\) | −13.6603 | −0.723992 | ||||||||
\(357\) | −1.26795 | −0.0671070 | ||||||||
\(358\) | 16.1962 | 0.855993 | ||||||||
\(359\) | −21.7128 | −1.14596 | −0.572979 | − | 0.819570i | \(-0.694212\pi\) | ||||
−0.572979 | + | 0.819570i | \(0.694212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9282 | −0.996221 | ||||||||
\(362\) | 22.6603 | 1.19100 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.73205 | −0.300441 | ||||||||
\(365\) | 9.12436 | 0.477591 | ||||||||
\(366\) | −5.07180 | −0.265107 | ||||||||
\(367\) | −17.2679 | −0.901380 | −0.450690 | − | 0.892681i | \(-0.648822\pi\) | ||||
−0.450690 | + | 0.892681i | \(0.648822\pi\) | |||||||
\(368\) | −5.00000 | −0.260643 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 6.19615 | 0.321688 | ||||||||
\(372\) | −4.73205 | −0.245345 | ||||||||
\(373\) | −21.3205 | −1.10393 | −0.551967 | − | 0.833866i | \(-0.686123\pi\) | ||||
−0.551967 | + | 0.833866i | \(0.686123\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.73205 | −0.0894427 | ||||||||
\(376\) | 4.73205 | 0.244037 | ||||||||
\(377\) | −45.8564 | −2.36173 | ||||||||
\(378\) | −5.19615 | −0.267261 | ||||||||
\(379\) | −6.78461 | −0.348502 | −0.174251 | − | 0.984701i | \(-0.555750\pi\) | ||||
−0.174251 | + | 0.984701i | \(0.555750\pi\) | |||||||
\(380\) | −0.267949 | −0.0137455 | ||||||||
\(381\) | 10.6077 | 0.543449 | ||||||||
\(382\) | 8.66025 | 0.443097 | ||||||||
\(383\) | 25.6603 | 1.31118 | 0.655589 | − | 0.755118i | \(-0.272420\pi\) | ||||
0.655589 | + | 0.755118i | \(0.272420\pi\) | |||||||
\(384\) | −1.73205 | −0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.3923 | 0.579853 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.9282 | 0.554795 | ||||||||
\(389\) | −23.1244 | −1.17245 | −0.586226 | − | 0.810148i | \(-0.699387\pi\) | ||||
−0.586226 | + | 0.810148i | \(0.699387\pi\) | |||||||
\(390\) | 9.92820 | 0.502734 | ||||||||
\(391\) | −3.66025 | −0.185107 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 22.8564 | 1.15295 | ||||||||
\(394\) | −9.46410 | −0.476795 | ||||||||
\(395\) | −7.00000 | −0.352208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7846 | 0.641641 | 0.320821 | − | 0.947140i | \(-0.396041\pi\) | ||||
0.320821 | + | 0.947140i | \(0.396041\pi\) | |||||||
\(398\) | 4.00000 | 0.200502 | ||||||||
\(399\) | −0.464102 | −0.0232341 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −18.5359 | −0.925639 | −0.462819 | − | 0.886453i | \(-0.653162\pi\) | ||||
−0.462819 | + | 0.886453i | \(0.653162\pi\) | |||||||
\(402\) | 16.7321 | 0.834519 | ||||||||
\(403\) | −15.6603 | −0.780093 | ||||||||
\(404\) | 11.5359 | 0.573932 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.26795 | −0.0627728 | ||||||||
\(409\) | −35.7128 | −1.76588 | −0.882942 | − | 0.469481i | \(-0.844441\pi\) | ||||
−0.882942 | + | 0.469481i | \(0.844441\pi\) | |||||||
\(410\) | 6.19615 | 0.306006 | ||||||||
\(411\) | 25.3923 | 1.25251 | ||||||||
\(412\) | −10.7321 | −0.528730 | ||||||||
\(413\) | 5.53590 | 0.272404 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.00000 | 0.245440 | ||||||||
\(416\) | −5.73205 | −0.281037 | ||||||||
\(417\) | 29.7846 | 1.45856 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.9282 | 0.778144 | 0.389072 | − | 0.921207i | \(-0.372796\pi\) | ||||
0.389072 | + | 0.921207i | \(0.372796\pi\) | |||||||
\(420\) | 1.73205 | 0.0845154 | ||||||||
\(421\) | −7.60770 | −0.370776 | −0.185388 | − | 0.982665i | \(-0.559354\pi\) | ||||
−0.185388 | + | 0.982665i | \(0.559354\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.19615 | 0.300912 | ||||||||
\(425\) | 0.732051 | 0.0355097 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | −2.92820 | −0.141706 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.26795 | 0.254043 | ||||||||
\(431\) | 34.4641 | 1.66008 | 0.830039 | − | 0.557706i | \(-0.188318\pi\) | ||||
0.830039 | + | 0.557706i | \(0.188318\pi\) | |||||||
\(432\) | −5.19615 | −0.250000 | ||||||||
\(433\) | −20.0526 | −0.963664 | −0.481832 | − | 0.876263i | \(-0.660029\pi\) | ||||
−0.481832 | + | 0.876263i | \(0.660029\pi\) | |||||||
\(434\) | −2.73205 | −0.131143 | ||||||||
\(435\) | 13.8564 | 0.664364 | ||||||||
\(436\) | −20.0526 | −0.960343 | ||||||||
\(437\) | −1.33975 | −0.0640887 | ||||||||
\(438\) | 15.8038 | 0.755137 | ||||||||
\(439\) | 14.7321 | 0.703122 | 0.351561 | − | 0.936165i | \(-0.385651\pi\) | ||||
0.351561 | + | 0.936165i | \(0.385651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.19615 | −0.199591 | ||||||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | 10.3923 | 0.493197 | ||||||||
\(445\) | 13.6603 | 0.647558 | ||||||||
\(446\) | 11.2679 | 0.533553 | ||||||||
\(447\) | −33.7128 | −1.59456 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 31.3923 | 1.48149 | 0.740747 | − | 0.671784i | \(-0.234472\pi\) | ||||
0.740747 | + | 0.671784i | \(0.234472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −14.1244 | −0.664354 | ||||||||
\(453\) | 32.6603 | 1.53451 | ||||||||
\(454\) | 17.3205 | 0.812892 | ||||||||
\(455\) | 5.73205 | 0.268723 | ||||||||
\(456\) | −0.464102 | −0.0217335 | ||||||||
\(457\) | 3.39230 | 0.158685 | 0.0793427 | − | 0.996847i | \(-0.474718\pi\) | ||||
0.0793427 | + | 0.996847i | \(0.474718\pi\) | |||||||
\(458\) | −5.85641 | −0.273652 | ||||||||
\(459\) | −3.80385 | −0.177548 | ||||||||
\(460\) | 5.00000 | 0.233126 | ||||||||
\(461\) | −10.5359 | −0.490706 | −0.245353 | − | 0.969434i | \(-0.578904\pi\) | ||||
−0.245353 | + | 0.969434i | \(0.578904\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.1769 | 1.21654 | 0.608272 | − | 0.793729i | \(-0.291863\pi\) | ||||
0.608272 | + | 0.793729i | \(0.291863\pi\) | |||||||
\(464\) | −8.00000 | −0.371391 | ||||||||
\(465\) | 4.73205 | 0.219444 | ||||||||
\(466\) | 5.53590 | 0.256446 | ||||||||
\(467\) | 13.5885 | 0.628799 | 0.314399 | − | 0.949291i | \(-0.398197\pi\) | ||||
0.314399 | + | 0.949291i | \(0.398197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.66025 | 0.446069 | ||||||||
\(470\) | −4.73205 | −0.218273 | ||||||||
\(471\) | −9.33975 | −0.430353 | ||||||||
\(472\) | 5.53590 | 0.254810 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.1244 | −0.556890 | ||||||||
\(475\) | 0.267949 | 0.0122944 | ||||||||
\(476\) | −0.732051 | −0.0335535 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.46410 | −0.204183 | ||||||||
\(479\) | −28.9808 | −1.32416 | −0.662082 | − | 0.749431i | \(-0.730327\pi\) | ||||
−0.662082 | + | 0.749431i | \(0.730327\pi\) | |||||||
\(480\) | 1.73205 | 0.0790569 | ||||||||
\(481\) | 34.3923 | 1.56815 | ||||||||
\(482\) | 17.4641 | 0.795468 | ||||||||
\(483\) | 8.66025 | 0.394055 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.9282 | −0.496224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3923 | 0.788121 | 0.394060 | − | 0.919085i | \(-0.371070\pi\) | ||||
0.394060 | + | 0.919085i | \(0.371070\pi\) | |||||||
\(488\) | −2.92820 | −0.132554 | ||||||||
\(489\) | 17.3205 | 0.783260 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −9.66025 | −0.435961 | −0.217981 | − | 0.975953i | \(-0.569947\pi\) | ||||
−0.217981 | + | 0.975953i | \(0.569947\pi\) | |||||||
\(492\) | 10.7321 | 0.483838 | ||||||||
\(493\) | −5.85641 | −0.263759 | ||||||||
\(494\) | −1.53590 | −0.0691033 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.73205 | −0.122673 | ||||||||
\(497\) | −6.92820 | −0.310772 | ||||||||
\(498\) | 8.66025 | 0.388075 | ||||||||
\(499\) | −22.0000 | −0.984855 | −0.492428 | − | 0.870353i | \(-0.663890\pi\) | ||||
−0.492428 | + | 0.870353i | \(0.663890\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0.588457 | 0.0262903 | ||||||||
\(502\) | 6.39230 | 0.285303 | ||||||||
\(503\) | −18.1962 | −0.811326 | −0.405663 | − | 0.914023i | \(-0.632959\pi\) | ||||
−0.405663 | + | 0.914023i | \(0.632959\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.5359 | −0.513341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.3923 | 1.52742 | ||||||||
\(508\) | 6.12436 | 0.271724 | ||||||||
\(509\) | −32.6603 | −1.44764 | −0.723820 | − | 0.689989i | \(-0.757615\pi\) | ||||
−0.723820 | + | 0.689989i | \(0.757615\pi\) | |||||||
\(510\) | 1.26795 | 0.0561457 | ||||||||
\(511\) | 9.12436 | 0.403638 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.39230 | −0.0614718 | ||||||||
\(514\) | −8.19615 | −0.361517 | ||||||||
\(515\) | 10.7321 | 0.472911 | ||||||||
\(516\) | 9.12436 | 0.401677 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.00000 | 0.263625 | ||||||||
\(519\) | −13.6077 | −0.597312 | ||||||||
\(520\) | 5.73205 | 0.251367 | ||||||||
\(521\) | −4.00000 | −0.175243 | −0.0876216 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876216 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.3923 | 1.02287 | 0.511437 | − | 0.859321i | \(-0.329113\pi\) | ||||
0.511437 | + | 0.859321i | \(0.329113\pi\) | |||||||
\(524\) | 13.1962 | 0.576477 | ||||||||
\(525\) | −1.73205 | −0.0755929 | ||||||||
\(526\) | 10.1244 | 0.441443 | ||||||||
\(527\) | −2.00000 | −0.0871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | −6.19615 | −0.269144 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.267949 | −0.0116171 | ||||||||
\(533\) | 35.5167 | 1.53840 | ||||||||
\(534\) | 23.6603 | 1.02388 | ||||||||
\(535\) | 2.00000 | 0.0864675 | ||||||||
\(536\) | 9.66025 | 0.417259 | ||||||||
\(537\) | −28.0526 | −1.21056 | ||||||||
\(538\) | 21.7321 | 0.936935 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.19615 | 0.223607 | ||||||||
\(541\) | −30.3923 | −1.30667 | −0.653334 | − | 0.757070i | \(-0.726630\pi\) | ||||
−0.653334 | + | 0.757070i | \(0.726630\pi\) | |||||||
\(542\) | 21.4641 | 0.921962 | ||||||||
\(543\) | −39.2487 | −1.68432 | ||||||||
\(544\) | −0.732051 | −0.0313864 | ||||||||
\(545\) | 20.0526 | 0.858957 | ||||||||
\(546\) | 9.92820 | 0.424888 | ||||||||
\(547\) | 7.51666 | 0.321389 | 0.160695 | − | 0.987004i | \(-0.448627\pi\) | ||||
0.160695 | + | 0.987004i | \(0.448627\pi\) | |||||||
\(548\) | 14.6603 | 0.626255 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.14359 | −0.0913202 | ||||||||
\(552\) | 8.66025 | 0.368605 | ||||||||
\(553\) | −7.00000 | −0.297670 | ||||||||
\(554\) | 1.80385 | 0.0766381 | ||||||||
\(555\) | −10.3923 | −0.441129 | ||||||||
\(556\) | 17.1962 | 0.729279 | ||||||||
\(557\) | 45.3731 | 1.92252 | 0.961259 | − | 0.275646i | \(-0.0888917\pi\) | ||||
0.961259 | + | 0.275646i | \(0.0888917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.1962 | 1.27716 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.73205 | 0.326157 | ||||||||
\(563\) | 8.46410 | 0.356719 | 0.178360 | − | 0.983965i | \(-0.442921\pi\) | ||||
0.178360 | + | 0.983965i | \(0.442921\pi\) | |||||||
\(564\) | −8.19615 | −0.345120 | ||||||||
\(565\) | 14.1244 | 0.594216 | ||||||||
\(566\) | 25.7846 | 1.08381 | ||||||||
\(567\) | 9.00000 | 0.377964 | ||||||||
\(568\) | −6.92820 | −0.290701 | ||||||||
\(569\) | −13.8756 | −0.581697 | −0.290849 | − | 0.956769i | \(-0.593938\pi\) | ||||
−0.290849 | + | 0.956769i | \(0.593938\pi\) | |||||||
\(570\) | 0.464102 | 0.0194391 | ||||||||
\(571\) | −6.53590 | −0.273519 | −0.136759 | − | 0.990604i | \(-0.543669\pi\) | ||||
−0.136759 | + | 0.990604i | \(0.543669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 6.19615 | 0.258622 | ||||||||
\(575\) | −5.00000 | −0.208514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.4449 | −1.68374 | −0.841871 | − | 0.539679i | \(-0.818546\pi\) | ||||
−0.841871 | + | 0.539679i | \(0.818546\pi\) | |||||||
\(578\) | 16.4641 | 0.684816 | ||||||||
\(579\) | −19.7321 | −0.820036 | ||||||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | 5.00000 | 0.207435 | ||||||||
\(582\) | −18.9282 | −0.784599 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 9.12436 | 0.377569 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7321 | 0.484647 | ||||||||
\(587\) | −30.5167 | −1.25956 | −0.629779 | − | 0.776775i | \(-0.716854\pi\) | ||||
−0.629779 | + | 0.776775i | \(0.716854\pi\) | |||||||
\(588\) | 1.73205 | 0.0714286 | ||||||||
\(589\) | −0.732051 | −0.0301636 | ||||||||
\(590\) | −5.53590 | −0.227909 | ||||||||
\(591\) | 16.3923 | 0.674289 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | 2.14359 | 0.0880268 | 0.0440134 | − | 0.999031i | \(-0.485986\pi\) | ||||
0.0440134 | + | 0.999031i | \(0.485986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.732051 | 0.0300112 | ||||||||
\(596\) | −19.4641 | −0.797281 | ||||||||
\(597\) | −6.92820 | −0.283552 | ||||||||
\(598\) | 28.6603 | 1.17200 | ||||||||
\(599\) | 19.9808 | 0.816392 | 0.408196 | − | 0.912894i | \(-0.366158\pi\) | ||||
0.408196 | + | 0.912894i | \(0.366158\pi\) | |||||||
\(600\) | −1.73205 | −0.0707107 | ||||||||
\(601\) | 13.6603 | 0.557213 | 0.278607 | − | 0.960405i | \(-0.410127\pi\) | ||||
0.278607 | + | 0.960405i | \(0.410127\pi\) | |||||||
\(602\) | 5.26795 | 0.214706 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.8564 | 0.767256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.9808 | −0.811663 | ||||||||
\(607\) | −48.2487 | −1.95835 | −0.979177 | − | 0.203006i | \(-0.934929\pi\) | ||||
−0.979177 | + | 0.203006i | \(0.934929\pi\) | |||||||
\(608\) | −0.267949 | −0.0108668 | ||||||||
\(609\) | 13.8564 | 0.561490 | ||||||||
\(610\) | 2.92820 | 0.118559 | ||||||||
\(611\) | −27.1244 | −1.09733 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.7321 | −1.64515 | −0.822576 | − | 0.568655i | \(-0.807464\pi\) | ||||
−0.822576 | + | 0.568655i | \(0.807464\pi\) | |||||||
\(614\) | −7.07180 | −0.285394 | ||||||||
\(615\) | −10.7321 | −0.432758 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.3923 | 1.38458 | 0.692291 | − | 0.721618i | \(-0.256601\pi\) | ||||
0.692291 | + | 0.721618i | \(0.256601\pi\) | |||||||
\(618\) | 18.5885 | 0.747737 | ||||||||
\(619\) | −22.7128 | −0.912905 | −0.456453 | − | 0.889748i | \(-0.650880\pi\) | ||||
−0.456453 | + | 0.889748i | \(0.650880\pi\) | |||||||
\(620\) | 2.73205 | 0.109722 | ||||||||
\(621\) | 25.9808 | 1.04257 | ||||||||
\(622\) | −12.7321 | −0.510509 | ||||||||
\(623\) | 13.6603 | 0.547287 | ||||||||
\(624\) | 9.92820 | 0.397446 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.60770 | 0.224129 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.39230 | −0.215176 | ||||||||
\(629\) | 4.39230 | 0.175133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.67949 | −0.186288 | −0.0931438 | − | 0.995653i | \(-0.529692\pi\) | ||||
−0.0931438 | + | 0.995653i | \(0.529692\pi\) | |||||||
\(632\) | −7.00000 | −0.278445 | ||||||||
\(633\) | 13.8564 | 0.550743 | ||||||||
\(634\) | −5.12436 | −0.203514 | ||||||||
\(635\) | −6.12436 | −0.243038 | ||||||||
\(636\) | −10.7321 | −0.425553 | ||||||||
\(637\) | 5.73205 | 0.227112 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −46.4641 | −1.83522 | −0.917611 | − | 0.397480i | \(-0.869885\pi\) | ||||
−0.917611 | + | 0.397480i | \(0.869885\pi\) | |||||||
\(642\) | 3.46410 | 0.136717 | ||||||||
\(643\) | −39.1769 | −1.54499 | −0.772493 | − | 0.635023i | \(-0.780991\pi\) | ||||
−0.772493 | + | 0.635023i | \(0.780991\pi\) | |||||||
\(644\) | 5.00000 | 0.197028 | ||||||||
\(645\) | −9.12436 | −0.359271 | ||||||||
\(646\) | −0.196152 | −0.00771751 | ||||||||
\(647\) | −32.1962 | −1.26576 | −0.632881 | − | 0.774249i | \(-0.718128\pi\) | ||||
−0.632881 | + | 0.774249i | \(0.718128\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.73205 | −0.224830 | ||||||||
\(651\) | 4.73205 | 0.185464 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | 8.19615 | 0.320740 | 0.160370 | − | 0.987057i | \(-0.448731\pi\) | ||||
0.160370 | + | 0.987057i | \(0.448731\pi\) | |||||||
\(654\) | 34.7321 | 1.35813 | ||||||||
\(655\) | −13.1962 | −0.515616 | ||||||||
\(656\) | 6.19615 | 0.241919 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.73205 | −0.184475 | ||||||||
\(659\) | −26.4449 | −1.03015 | −0.515073 | − | 0.857146i | \(-0.672235\pi\) | ||||
−0.515073 | + | 0.857146i | \(0.672235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.6603 | 0.803591 | 0.401795 | − | 0.915729i | \(-0.368386\pi\) | ||||
0.401795 | + | 0.915729i | \(0.368386\pi\) | |||||||
\(662\) | −34.0526 | −1.32349 | ||||||||
\(663\) | 7.26795 | 0.282264 | ||||||||
\(664\) | 5.00000 | 0.194038 | ||||||||
\(665\) | 0.267949 | 0.0103906 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.0000 | 1.54881 | ||||||||
\(668\) | 0.339746 | 0.0131452 | ||||||||
\(669\) | −19.5167 | −0.754558 | ||||||||
\(670\) | −9.66025 | −0.373208 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.73205 | 0.0668153 | ||||||||
\(673\) | 29.1051 | 1.12192 | 0.560960 | − | 0.827843i | \(-0.310432\pi\) | ||||
0.560960 | + | 0.827843i | \(0.310432\pi\) | |||||||
\(674\) | −9.39230 | −0.361778 | ||||||||
\(675\) | −5.19615 | −0.200000 | ||||||||
\(676\) | 19.8564 | 0.763708 | ||||||||
\(677\) | 5.98076 | 0.229859 | 0.114930 | − | 0.993374i | \(-0.463336\pi\) | ||||
0.114930 | + | 0.993374i | \(0.463336\pi\) | |||||||
\(678\) | 24.4641 | 0.939538 | ||||||||
\(679\) | −10.9282 | −0.419386 | ||||||||
\(680\) | 0.732051 | 0.0280729 | ||||||||
\(681\) | −30.0000 | −1.14960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.0718 | −0.959346 | −0.479673 | − | 0.877447i | \(-0.659245\pi\) | ||||
−0.479673 | + | 0.877447i | \(0.659245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.6603 | −0.560140 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 10.1436 | 0.387002 | ||||||||
\(688\) | 5.26795 | 0.200839 | ||||||||
\(689\) | −35.5167 | −1.35308 | ||||||||
\(690\) | −8.66025 | −0.329690 | ||||||||
\(691\) | −25.8564 | −0.983624 | −0.491812 | − | 0.870701i | \(-0.663665\pi\) | ||||
−0.491812 | + | 0.870701i | \(0.663665\pi\) | |||||||
\(692\) | −7.85641 | −0.298656 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.4641 | −0.587009 | ||||||||
\(695\) | −17.1962 | −0.652287 | ||||||||
\(696\) | 13.8564 | 0.525226 | ||||||||
\(697\) | 4.53590 | 0.171809 | ||||||||
\(698\) | 0.464102 | 0.0175665 | ||||||||
\(699\) | −9.58846 | −0.362669 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 17.9090 | 0.676412 | 0.338206 | − | 0.941072i | \(-0.390180\pi\) | ||||
0.338206 | + | 0.941072i | \(0.390180\pi\) | |||||||
\(702\) | 29.7846 | 1.12415 | ||||||||
\(703\) | 1.60770 | 0.0606354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.19615 | 0.308685 | ||||||||
\(706\) | −12.1962 | −0.459008 | ||||||||
\(707\) | −11.5359 | −0.433852 | ||||||||
\(708\) | −9.58846 | −0.360356 | ||||||||
\(709\) | −33.3205 | −1.25138 | −0.625689 | − | 0.780073i | \(-0.715182\pi\) | ||||
−0.625689 | + | 0.780073i | \(0.715182\pi\) | |||||||
\(710\) | 6.92820 | 0.260011 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.6603 | 0.511940 | ||||||||
\(713\) | 13.6603 | 0.511581 | ||||||||
\(714\) | 1.26795 | 0.0474518 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.1962 | −0.605279 | ||||||||
\(717\) | 7.73205 | 0.288759 | ||||||||
\(718\) | 21.7128 | 0.810315 | ||||||||
\(719\) | −21.0718 | −0.785845 | −0.392923 | − | 0.919572i | \(-0.628536\pi\) | ||||
−0.392923 | + | 0.919572i | \(0.628536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7321 | 0.399682 | ||||||||
\(722\) | 18.9282 | 0.704435 | ||||||||
\(723\) | −30.2487 | −1.12496 | ||||||||
\(724\) | −22.6603 | −0.842162 | ||||||||
\(725\) | −8.00000 | −0.297113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.3205 | 0.716558 | 0.358279 | − | 0.933615i | \(-0.383364\pi\) | ||||
0.358279 | + | 0.933615i | \(0.383364\pi\) | |||||||
\(728\) | 5.73205 | 0.212444 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −9.12436 | −0.337708 | ||||||||
\(731\) | 3.85641 | 0.142634 | ||||||||
\(732\) | 5.07180 | 0.187459 | ||||||||
\(733\) | −7.58846 | −0.280286 | −0.140143 | − | 0.990131i | \(-0.544756\pi\) | ||||
−0.140143 | + | 0.990131i | \(0.544756\pi\) | |||||||
\(734\) | 17.2679 | 0.637372 | ||||||||
\(735\) | −1.73205 | −0.0638877 | ||||||||
\(736\) | 5.00000 | 0.184302 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9808 | 0.918932 | 0.459466 | − | 0.888195i | \(-0.348041\pi\) | ||||
0.459466 | + | 0.888195i | \(0.348041\pi\) | |||||||
\(740\) | −6.00000 | −0.220564 | ||||||||
\(741\) | 2.66025 | 0.0977269 | ||||||||
\(742\) | −6.19615 | −0.227468 | ||||||||
\(743\) | −19.4641 | −0.714069 | −0.357034 | − | 0.934091i | \(-0.616212\pi\) | ||||
−0.357034 | + | 0.934091i | \(0.616212\pi\) | |||||||
\(744\) | 4.73205 | 0.173485 | ||||||||
\(745\) | 19.4641 | 0.713110 | ||||||||
\(746\) | 21.3205 | 0.780599 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00000 | 0.0730784 | ||||||||
\(750\) | 1.73205 | 0.0632456 | ||||||||
\(751\) | 30.3731 | 1.10833 | 0.554164 | − | 0.832407i | \(-0.313038\pi\) | ||||
0.554164 | + | 0.832407i | \(0.313038\pi\) | |||||||
\(752\) | −4.73205 | −0.172560 | ||||||||
\(753\) | −11.0718 | −0.403479 | ||||||||
\(754\) | 45.8564 | 1.66999 | ||||||||
\(755\) | −18.8564 | −0.686255 | ||||||||
\(756\) | 5.19615 | 0.188982 | ||||||||
\(757\) | 39.9090 | 1.45052 | 0.725258 | − | 0.688477i | \(-0.241720\pi\) | ||||
0.725258 | + | 0.688477i | \(0.241720\pi\) | |||||||
\(758\) | 6.78461 | 0.246428 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.267949 | 0.00971954 | ||||||||
\(761\) | −18.4449 | −0.668626 | −0.334313 | − | 0.942462i | \(-0.608504\pi\) | ||||
−0.334313 | + | 0.942462i | \(0.608504\pi\) | |||||||
\(762\) | −10.6077 | −0.384276 | ||||||||
\(763\) | 20.0526 | 0.725951 | ||||||||
\(764\) | −8.66025 | −0.313317 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.6603 | −0.927143 | ||||||||
\(767\) | −31.7321 | −1.14578 | ||||||||
\(768\) | 1.73205 | 0.0625000 | ||||||||
\(769\) | 6.78461 | 0.244659 | 0.122330 | − | 0.992490i | \(-0.460963\pi\) | ||||
0.122330 | + | 0.992490i | \(0.460963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1962 | 0.511262 | ||||||||
\(772\) | −11.3923 | −0.410018 | ||||||||
\(773\) | 34.4641 | 1.23959 | 0.619794 | − | 0.784765i | \(-0.287216\pi\) | ||||
0.619794 | + | 0.784765i | \(0.287216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.73205 | −0.0981382 | ||||||||
\(776\) | −10.9282 | −0.392300 | ||||||||
\(777\) | −10.3923 | −0.372822 | ||||||||
\(778\) | 23.1244 | 0.829048 | ||||||||
\(779\) | 1.66025 | 0.0594848 | ||||||||
\(780\) | −9.92820 | −0.355487 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.66025 | 0.130890 | ||||||||
\(783\) | 41.5692 | 1.48556 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 5.39230 | 0.192460 | ||||||||
\(786\) | −22.8564 | −0.815261 | ||||||||
\(787\) | 50.4974 | 1.80004 | 0.900019 | − | 0.435850i | \(-0.143552\pi\) | ||||
0.900019 | + | 0.435850i | \(0.143552\pi\) | |||||||
\(788\) | 9.46410 | 0.337145 | ||||||||
\(789\) | −17.5359 | −0.624295 | ||||||||
\(790\) | 7.00000 | 0.249049 | ||||||||
\(791\) | 14.1244 | 0.502204 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.7846 | 0.596039 | ||||||||
\(794\) | −12.7846 | −0.453709 | ||||||||
\(795\) | 10.7321 | 0.380627 | ||||||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | −28.1769 | −0.998078 | −0.499039 | − | 0.866580i | \(-0.666313\pi\) | ||||
−0.499039 | + | 0.866580i | \(0.666313\pi\) | |||||||
\(798\) | 0.464102 | 0.0164290 | ||||||||
\(799\) | −3.46410 | −0.122551 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.5359 | 0.654525 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −16.7321 | −0.590094 | ||||||||
\(805\) | −5.00000 | −0.176227 | ||||||||
\(806\) | 15.6603 | 0.551609 | ||||||||
\(807\) | −37.6410 | −1.32503 | ||||||||
\(808\) | −11.5359 | −0.405831 | ||||||||
\(809\) | 50.7846 | 1.78549 | 0.892746 | − | 0.450561i | \(-0.148776\pi\) | ||||
0.892746 | + | 0.450561i | \(0.148776\pi\) | |||||||
\(810\) | −9.00000 | −0.316228 | ||||||||
\(811\) | 37.4641 | 1.31554 | 0.657771 | − | 0.753218i | \(-0.271499\pi\) | ||||
0.657771 | + | 0.753218i | \(0.271499\pi\) | |||||||
\(812\) | 8.00000 | 0.280745 | ||||||||
\(813\) | −37.1769 | −1.30385 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0000 | −0.350285 | ||||||||
\(816\) | 1.26795 | 0.0443871 | ||||||||
\(817\) | 1.41154 | 0.0493836 | ||||||||
\(818\) | 35.7128 | 1.24867 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.19615 | −0.216379 | ||||||||
\(821\) | −16.1436 | −0.563415 | −0.281708 | − | 0.959500i | \(-0.590901\pi\) | ||||
−0.281708 | + | 0.959500i | \(0.590901\pi\) | |||||||
\(822\) | −25.3923 | −0.885658 | ||||||||
\(823\) | 1.21539 | 0.0423658 | 0.0211829 | − | 0.999776i | \(-0.493257\pi\) | ||||
0.0211829 | + | 0.999776i | \(0.493257\pi\) | |||||||
\(824\) | 10.7321 | 0.373869 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.53590 | −0.192619 | ||||||||
\(827\) | 45.9090 | 1.59641 | 0.798206 | − | 0.602385i | \(-0.205783\pi\) | ||||
0.798206 | + | 0.602385i | \(0.205783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1244 | 0.837874 | 0.418937 | − | 0.908015i | \(-0.362403\pi\) | ||||
0.418937 | + | 0.908015i | \(0.362403\pi\) | |||||||
\(830\) | −5.00000 | −0.173553 | ||||||||
\(831\) | −3.12436 | −0.108383 | ||||||||
\(832\) | 5.73205 | 0.198723 | ||||||||
\(833\) | 0.732051 | 0.0253641 | ||||||||
\(834\) | −29.7846 | −1.03136 | ||||||||
\(835\) | −0.339746 | −0.0117574 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.1962 | 0.490691 | ||||||||
\(838\) | −15.9282 | −0.550231 | ||||||||
\(839\) | 1.80385 | 0.0622757 | 0.0311379 | − | 0.999515i | \(-0.490087\pi\) | ||||
0.0311379 | + | 0.999515i | \(0.490087\pi\) | |||||||
\(840\) | −1.73205 | −0.0597614 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 7.60770 | 0.262178 | ||||||||
\(843\) | −13.3923 | −0.461255 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | −19.8564 | −0.683081 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.19615 | −0.212777 | ||||||||
\(849\) | −44.6603 | −1.53274 | ||||||||
\(850\) | −0.732051 | −0.0251091 | ||||||||
\(851\) | −30.0000 | −1.02839 | ||||||||
\(852\) | 12.0000 | 0.411113 | ||||||||
\(853\) | 35.8372 | 1.22704 | 0.613521 | − | 0.789679i | \(-0.289753\pi\) | ||||
0.613521 | + | 0.789679i | \(0.289753\pi\) | |||||||
\(854\) | 2.92820 | 0.100201 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | 36.3923 | 1.24314 | 0.621569 | − | 0.783360i | \(-0.286496\pi\) | ||||
0.621569 | + | 0.783360i | \(0.286496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8564 | 1.08693 | 0.543463 | − | 0.839433i | \(-0.317113\pi\) | ||||
0.543463 | + | 0.839433i | \(0.317113\pi\) | |||||||
\(860\) | −5.26795 | −0.179636 | ||||||||
\(861\) | −10.7321 | −0.365747 | ||||||||
\(862\) | −34.4641 | −1.17385 | ||||||||
\(863\) | −37.8564 | −1.28865 | −0.644324 | − | 0.764753i | \(-0.722861\pi\) | ||||
−0.644324 | + | 0.764753i | \(0.722861\pi\) | |||||||
\(864\) | 5.19615 | 0.176777 | ||||||||
\(865\) | 7.85641 | 0.267126 | ||||||||
\(866\) | 20.0526 | 0.681414 | ||||||||
\(867\) | −28.5167 | −0.968477 | ||||||||
\(868\) | 2.73205 | 0.0927318 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −13.8564 | −0.469776 | ||||||||
\(871\) | −55.3731 | −1.87624 | ||||||||
\(872\) | 20.0526 | 0.679065 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.33975 | 0.0453176 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −15.8038 | −0.533963 | ||||||||
\(877\) | −48.0526 | −1.62262 | −0.811310 | − | 0.584616i | \(-0.801245\pi\) | ||||
−0.811310 | + | 0.584616i | \(0.801245\pi\) | |||||||
\(878\) | −14.7321 | −0.497183 | ||||||||
\(879\) | −20.3205 | −0.685394 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.4256 | 1.93472 | 0.967359 | − | 0.253409i | \(-0.0815518\pi\) | ||||
0.967359 | + | 0.253409i | \(0.0815518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.6410 | 1.23307 | 0.616534 | − | 0.787328i | \(-0.288536\pi\) | ||||
0.616534 | + | 0.787328i | \(0.288536\pi\) | |||||||
\(884\) | 4.19615 | 0.141132 | ||||||||
\(885\) | 9.58846 | 0.322312 | ||||||||
\(886\) | −4.00000 | −0.134383 | ||||||||
\(887\) | −19.6603 | −0.660127 | −0.330063 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330063 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(888\) | −10.3923 | −0.348743 | ||||||||
\(889\) | −6.12436 | −0.205404 | ||||||||
\(890\) | −13.6603 | −0.457893 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.2679 | −0.377279 | ||||||||
\(893\) | −1.26795 | −0.0424303 | ||||||||
\(894\) | 33.7128 | 1.12753 | ||||||||
\(895\) | 16.1962 | 0.541378 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −49.6410 | −1.65747 | ||||||||
\(898\) | −31.3923 | −1.04757 | ||||||||
\(899\) | 21.8564 | 0.728952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.53590 | −0.151113 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.12436 | −0.303640 | ||||||||
\(904\) | 14.1244 | 0.469769 | ||||||||
\(905\) | 22.6603 | 0.753252 | ||||||||
\(906\) | −32.6603 | −1.08506 | ||||||||
\(907\) | 36.0000 | 1.19536 | 0.597680 | − | 0.801735i | \(-0.296089\pi\) | ||||
0.597680 | + | 0.801735i | \(0.296089\pi\) | |||||||
\(908\) | −17.3205 | −0.574801 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.73205 | −0.190016 | ||||||||
\(911\) | −21.9808 | −0.728255 | −0.364128 | − | 0.931349i | \(-0.618633\pi\) | ||||
−0.364128 | + | 0.931349i | \(0.618633\pi\) | |||||||
\(912\) | 0.464102 | 0.0153679 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3.39230 | −0.112207 | ||||||||
\(915\) | −5.07180 | −0.167668 | ||||||||
\(916\) | 5.85641 | 0.193501 | ||||||||
\(917\) | −13.1962 | −0.435775 | ||||||||
\(918\) | 3.80385 | 0.125546 | ||||||||
\(919\) | −39.8564 | −1.31474 | −0.657371 | − | 0.753567i | \(-0.728331\pi\) | ||||
−0.657371 | + | 0.753567i | \(0.728331\pi\) | |||||||
\(920\) | −5.00000 | −0.164845 | ||||||||
\(921\) | 12.2487 | 0.403609 | ||||||||
\(922\) | 10.5359 | 0.346981 | ||||||||
\(923\) | 39.7128 | 1.30716 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | −26.1769 | −0.860227 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.00000 | 0.262613 | ||||||||
\(929\) | −12.6795 | −0.416001 | −0.208000 | − | 0.978129i | \(-0.566696\pi\) | ||||
−0.208000 | + | 0.978129i | \(0.566696\pi\) | |||||||
\(930\) | −4.73205 | −0.155170 | ||||||||
\(931\) | 0.267949 | 0.00878168 | ||||||||
\(932\) | −5.53590 | −0.181334 | ||||||||
\(933\) | 22.0526 | 0.721968 | ||||||||
\(934\) | −13.5885 | −0.444628 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.4641 | −0.570527 | −0.285264 | − | 0.958449i | \(-0.592081\pi\) | ||||
−0.285264 | + | 0.958449i | \(0.592081\pi\) | |||||||
\(938\) | −9.66025 | −0.315418 | ||||||||
\(939\) | −9.71281 | −0.316966 | ||||||||
\(940\) | 4.73205 | 0.154342 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 9.33975 | 0.304305 | ||||||||
\(943\) | −30.9808 | −1.00887 | ||||||||
\(944\) | −5.53590 | −0.180178 | ||||||||
\(945\) | −5.19615 | −0.169031 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.9474 | −0.713196 | −0.356598 | − | 0.934258i | \(-0.616063\pi\) | ||||
−0.356598 | + | 0.934258i | \(0.616063\pi\) | |||||||
\(948\) | 12.1244 | 0.393781 | ||||||||
\(949\) | −52.3013 | −1.69777 | ||||||||
\(950\) | −0.267949 | −0.00869342 | ||||||||
\(951\) | 8.87564 | 0.287812 | ||||||||
\(952\) | 0.732051 | 0.0237259 | ||||||||
\(953\) | 23.3923 | 0.757751 | 0.378876 | − | 0.925448i | \(-0.376311\pi\) | ||||
0.378876 | + | 0.925448i | \(0.376311\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.66025 | 0.280239 | ||||||||
\(956\) | 4.46410 | 0.144379 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.9808 | 0.936326 | ||||||||
\(959\) | −14.6603 | −0.473404 | ||||||||
\(960\) | −1.73205 | −0.0559017 | ||||||||
\(961\) | −23.5359 | −0.759223 | ||||||||
\(962\) | −34.3923 | −1.10885 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −17.4641 | −0.562481 | ||||||||
\(965\) | 11.3923 | 0.366731 | ||||||||
\(966\) | −8.66025 | −0.278639 | ||||||||
\(967\) | 28.7846 | 0.925651 | 0.462825 | − | 0.886450i | \(-0.346836\pi\) | ||||
0.462825 | + | 0.886450i | \(0.346836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.339746 | 0.0109142 | ||||||||
\(970\) | 10.9282 | 0.350883 | ||||||||
\(971\) | 50.7128 | 1.62745 | 0.813726 | − | 0.581249i | \(-0.197436\pi\) | ||||
0.813726 | + | 0.581249i | \(0.197436\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1962 | −0.551283 | ||||||||
\(974\) | −17.3923 | −0.557285 | ||||||||
\(975\) | 9.92820 | 0.317957 | ||||||||
\(976\) | 2.92820 | 0.0937295 | ||||||||
\(977\) | −14.2679 | −0.456472 | −0.228236 | − | 0.973606i | \(-0.573296\pi\) | ||||
−0.228236 | + | 0.973606i | \(0.573296\pi\) | |||||||
\(978\) | −17.3205 | −0.553849 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.66025 | 0.308271 | ||||||||
\(983\) | 37.6077 | 1.19950 | 0.599750 | − | 0.800188i | \(-0.295267\pi\) | ||||
0.599750 | + | 0.800188i | \(0.295267\pi\) | |||||||
\(984\) | −10.7321 | −0.342125 | ||||||||
\(985\) | −9.46410 | −0.301551 | ||||||||
\(986\) | 5.85641 | 0.186506 | ||||||||
\(987\) | 8.19615 | 0.260886 | ||||||||
\(988\) | 1.53590 | 0.0488634 | ||||||||
\(989\) | −26.3397 | −0.837555 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.87564 | −0.0595818 | −0.0297909 | − | 0.999556i | \(-0.509484\pi\) | ||||
−0.0297909 | + | 0.999556i | \(0.509484\pi\) | |||||||
\(992\) | 2.73205 | 0.0867427 | ||||||||
\(993\) | 58.9808 | 1.87170 | ||||||||
\(994\) | 6.92820 | 0.219749 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | −8.66025 | −0.274411 | ||||||||
\(997\) | −38.6603 | −1.22438 | −0.612191 | − | 0.790710i | \(-0.709712\pi\) | ||||
−0.612191 | + | 0.790710i | \(0.709712\pi\) | |||||||
\(998\) | 22.0000 | 0.696398 | ||||||||
\(999\) | −31.1769 | −0.986394 |
(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 | 8470.2.a.bm.1.2 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.bz.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bm.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.bz.1.2 | yes | 2 | 11.10 | odd | 2 |