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: | \(6\) |
Coefficient field: | 6.6.19898000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.245893\) 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 | ||||||||
\(3\) | 0.245893 | 0.141966 | 0.0709831 | − | 0.997478i | \(-0.477386\pi\) | ||||
0.0709831 | + | 0.997478i | \(0.477386\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.245893 | −0.100385 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.93954 | −0.979846 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.245893 | 0.0709831 | ||||||||
\(13\) | −1.15197 | −0.319499 | −0.159750 | − | 0.987158i | \(-0.551069\pi\) | ||||
−0.159750 | + | 0.987158i | \(0.551069\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0.245893 | 0.0634892 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.55125 | 1.58891 | 0.794455 | − | 0.607323i | \(-0.207756\pi\) | ||||
0.794455 | + | 0.607323i | \(0.207756\pi\) | |||||||
\(18\) | 2.93954 | 0.692855 | ||||||||
\(19\) | −3.43477 | −0.787990 | −0.393995 | − | 0.919113i | \(-0.628907\pi\) | ||||
−0.393995 | + | 0.919113i | \(0.628907\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.245893 | 0.0536582 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.30827 | 1.73239 | 0.866197 | − | 0.499703i | \(-0.166558\pi\) | ||||
0.866197 | + | 0.499703i | \(0.166558\pi\) | |||||||
\(24\) | −0.245893 | −0.0501927 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.15197 | 0.225920 | ||||||||
\(27\) | −1.46049 | −0.281071 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −2.93346 | −0.544731 | −0.272365 | − | 0.962194i | \(-0.587806\pi\) | ||||
−0.272365 | + | 0.962194i | \(0.587806\pi\) | |||||||
\(30\) | −0.245893 | −0.0448937 | ||||||||
\(31\) | −6.33956 | −1.13862 | −0.569310 | − | 0.822123i | \(-0.692789\pi\) | ||||
−0.569310 | + | 0.822123i | \(0.692789\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.55125 | −1.12353 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −2.93954 | −0.489923 | ||||||||
\(37\) | −3.86743 | −0.635801 | −0.317901 | − | 0.948124i | \(-0.602978\pi\) | ||||
−0.317901 | + | 0.948124i | \(0.602978\pi\) | |||||||
\(38\) | 3.43477 | 0.557193 | ||||||||
\(39\) | −0.283261 | −0.0453581 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −10.5558 | −1.64854 | −0.824271 | − | 0.566195i | \(-0.808415\pi\) | ||||
−0.824271 | + | 0.566195i | \(0.808415\pi\) | |||||||
\(42\) | −0.245893 | −0.0379421 | ||||||||
\(43\) | −2.95752 | −0.451018 | −0.225509 | − | 0.974241i | \(-0.572404\pi\) | ||||
−0.225509 | + | 0.974241i | \(0.572404\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.93954 | −0.438200 | ||||||||
\(46\) | −8.30827 | −1.22499 | ||||||||
\(47\) | −6.17003 | −0.899991 | −0.449996 | − | 0.893031i | \(-0.648574\pi\) | ||||
−0.449996 | + | 0.893031i | \(0.648574\pi\) | |||||||
\(48\) | 0.245893 | 0.0354916 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.61090 | 0.225572 | ||||||||
\(52\) | −1.15197 | −0.159750 | ||||||||
\(53\) | 5.35680 | 0.735813 | 0.367906 | − | 0.929863i | \(-0.380075\pi\) | ||||
0.367906 | + | 0.929863i | \(0.380075\pi\) | |||||||
\(54\) | 1.46049 | 0.198747 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.844585 | −0.111868 | ||||||||
\(58\) | 2.93346 | 0.385183 | ||||||||
\(59\) | −2.24164 | −0.291837 | −0.145919 | − | 0.989297i | \(-0.546614\pi\) | ||||
−0.145919 | + | 0.989297i | \(0.546614\pi\) | |||||||
\(60\) | 0.245893 | 0.0317446 | ||||||||
\(61\) | −9.98548 | −1.27851 | −0.639255 | − | 0.768995i | \(-0.720757\pi\) | ||||
−0.639255 | + | 0.768995i | \(0.720757\pi\) | |||||||
\(62\) | 6.33956 | 0.805125 | ||||||||
\(63\) | −2.93954 | −0.370347 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.15197 | −0.142884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.2147 | 1.73660 | 0.868299 | − | 0.496041i | \(-0.165213\pi\) | ||||
0.868299 | + | 0.496041i | \(0.165213\pi\) | |||||||
\(68\) | 6.55125 | 0.794455 | ||||||||
\(69\) | 2.04294 | 0.245941 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −0.380220 | −0.0451238 | −0.0225619 | − | 0.999745i | \(-0.507182\pi\) | ||||
−0.0225619 | + | 0.999745i | \(0.507182\pi\) | |||||||
\(72\) | 2.93954 | 0.346428 | ||||||||
\(73\) | −7.23216 | −0.846460 | −0.423230 | − | 0.906022i | \(-0.639104\pi\) | ||||
−0.423230 | + | 0.906022i | \(0.639104\pi\) | |||||||
\(74\) | 3.86743 | 0.449579 | ||||||||
\(75\) | 0.245893 | 0.0283933 | ||||||||
\(76\) | −3.43477 | −0.393995 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.283261 | 0.0320730 | ||||||||
\(79\) | −2.27381 | −0.255824 | −0.127912 | − | 0.991786i | \(-0.540827\pi\) | ||||
−0.127912 | + | 0.991786i | \(0.540827\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.45949 | 0.939943 | ||||||||
\(82\) | 10.5558 | 1.16570 | ||||||||
\(83\) | −11.3292 | −1.24355 | −0.621773 | − | 0.783198i | \(-0.713587\pi\) | ||||
−0.621773 | + | 0.783198i | \(0.713587\pi\) | |||||||
\(84\) | 0.245893 | 0.0268291 | ||||||||
\(85\) | 6.55125 | 0.710582 | ||||||||
\(86\) | 2.95752 | 0.318918 | ||||||||
\(87\) | −0.721318 | −0.0773334 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.48891 | −0.475823 | −0.237912 | − | 0.971287i | \(-0.576463\pi\) | ||||
−0.237912 | + | 0.971287i | \(0.576463\pi\) | |||||||
\(90\) | 2.93954 | 0.309854 | ||||||||
\(91\) | −1.15197 | −0.120759 | ||||||||
\(92\) | 8.30827 | 0.866197 | ||||||||
\(93\) | −1.55885 | −0.161646 | ||||||||
\(94\) | 6.17003 | 0.636390 | ||||||||
\(95\) | −3.43477 | −0.352400 | ||||||||
\(96\) | −0.245893 | −0.0250963 | ||||||||
\(97\) | 3.45447 | 0.350748 | 0.175374 | − | 0.984502i | \(-0.443886\pi\) | ||||
0.175374 | + | 0.984502i | \(0.443886\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.71712 | 0.270364 | 0.135182 | − | 0.990821i | \(-0.456838\pi\) | ||||
0.135182 | + | 0.990821i | \(0.456838\pi\) | |||||||
\(102\) | −1.61090 | −0.159503 | ||||||||
\(103\) | −9.90941 | −0.976403 | −0.488201 | − | 0.872731i | \(-0.662347\pi\) | ||||
−0.488201 | + | 0.872731i | \(0.662347\pi\) | |||||||
\(104\) | 1.15197 | 0.112960 | ||||||||
\(105\) | 0.245893 | 0.0239967 | ||||||||
\(106\) | −5.35680 | −0.520298 | ||||||||
\(107\) | 5.18688 | 0.501434 | 0.250717 | − | 0.968060i | \(-0.419334\pi\) | ||||
0.250717 | + | 0.968060i | \(0.419334\pi\) | |||||||
\(108\) | −1.46049 | −0.140536 | ||||||||
\(109\) | 12.1283 | 1.16168 | 0.580839 | − | 0.814018i | \(-0.302725\pi\) | ||||
0.580839 | + | 0.814018i | \(0.302725\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.950972 | −0.0902623 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 14.5100 | 1.36499 | 0.682493 | − | 0.730893i | \(-0.260896\pi\) | ||||
0.682493 | + | 0.730893i | \(0.260896\pi\) | |||||||
\(114\) | 0.844585 | 0.0791026 | ||||||||
\(115\) | 8.30827 | 0.774750 | ||||||||
\(116\) | −2.93346 | −0.272365 | ||||||||
\(117\) | 3.38626 | 0.313060 | ||||||||
\(118\) | 2.24164 | 0.206360 | ||||||||
\(119\) | 6.55125 | 0.600552 | ||||||||
\(120\) | −0.245893 | −0.0224468 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.98548 | 0.904043 | ||||||||
\(123\) | −2.59560 | −0.234037 | ||||||||
\(124\) | −6.33956 | −0.569310 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.93954 | 0.261875 | ||||||||
\(127\) | −0.818399 | −0.0726212 | −0.0363106 | − | 0.999341i | \(-0.511561\pi\) | ||||
−0.0363106 | + | 0.999341i | \(0.511561\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.727233 | −0.0640293 | ||||||||
\(130\) | 1.15197 | 0.101034 | ||||||||
\(131\) | 9.76900 | 0.853522 | 0.426761 | − | 0.904365i | \(-0.359655\pi\) | ||||
0.426761 | + | 0.904365i | \(0.359655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.43477 | −0.297832 | ||||||||
\(134\) | −14.2147 | −1.22796 | ||||||||
\(135\) | −1.46049 | −0.125699 | ||||||||
\(136\) | −6.55125 | −0.561765 | ||||||||
\(137\) | −6.68920 | −0.571497 | −0.285749 | − | 0.958305i | \(-0.592242\pi\) | ||||
−0.285749 | + | 0.958305i | \(0.592242\pi\) | |||||||
\(138\) | −2.04294 | −0.173907 | ||||||||
\(139\) | −8.85349 | −0.750943 | −0.375471 | − | 0.926834i | \(-0.622519\pi\) | ||||
−0.375471 | + | 0.926834i | \(0.622519\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −1.51717 | −0.127768 | ||||||||
\(142\) | 0.380220 | 0.0319074 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.93954 | −0.244961 | ||||||||
\(145\) | −2.93346 | −0.243611 | ||||||||
\(146\) | 7.23216 | 0.598538 | ||||||||
\(147\) | 0.245893 | 0.0202809 | ||||||||
\(148\) | −3.86743 | −0.317901 | ||||||||
\(149\) | −4.32495 | −0.354314 | −0.177157 | − | 0.984183i | \(-0.556690\pi\) | ||||
−0.177157 | + | 0.984183i | \(0.556690\pi\) | |||||||
\(150\) | −0.245893 | −0.0200771 | ||||||||
\(151\) | −17.5142 | −1.42529 | −0.712644 | − | 0.701526i | \(-0.752502\pi\) | ||||
−0.712644 | + | 0.701526i | \(0.752502\pi\) | |||||||
\(152\) | 3.43477 | 0.278596 | ||||||||
\(153\) | −19.2576 | −1.55689 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.33956 | −0.509206 | ||||||||
\(156\) | −0.283261 | −0.0226790 | ||||||||
\(157\) | 8.20435 | 0.654778 | 0.327389 | − | 0.944890i | \(-0.393831\pi\) | ||||
0.327389 | + | 0.944890i | \(0.393831\pi\) | |||||||
\(158\) | 2.27381 | 0.180895 | ||||||||
\(159\) | 1.31720 | 0.104461 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 8.30827 | 0.654783 | ||||||||
\(162\) | −8.45949 | −0.664640 | ||||||||
\(163\) | −11.4586 | −0.897504 | −0.448752 | − | 0.893656i | \(-0.648131\pi\) | ||||
−0.448752 | + | 0.893656i | \(0.648131\pi\) | |||||||
\(164\) | −10.5558 | −0.824271 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.3292 | 0.879320 | ||||||||
\(167\) | −0.763127 | −0.0590525 | −0.0295263 | − | 0.999564i | \(-0.509400\pi\) | ||||
−0.0295263 | + | 0.999564i | \(0.509400\pi\) | |||||||
\(168\) | −0.245893 | −0.0189710 | ||||||||
\(169\) | −11.6730 | −0.897920 | ||||||||
\(170\) | −6.55125 | −0.502458 | ||||||||
\(171\) | 10.0966 | 0.772108 | ||||||||
\(172\) | −2.95752 | −0.225509 | ||||||||
\(173\) | −8.76752 | −0.666582 | −0.333291 | − | 0.942824i | \(-0.608159\pi\) | ||||
−0.333291 | + | 0.942824i | \(0.608159\pi\) | |||||||
\(174\) | 0.721318 | 0.0546830 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.551204 | −0.0414310 | ||||||||
\(178\) | 4.48891 | 0.336458 | ||||||||
\(179\) | 15.0279 | 1.12324 | 0.561619 | − | 0.827396i | \(-0.310179\pi\) | ||||
0.561619 | + | 0.827396i | \(0.310179\pi\) | |||||||
\(180\) | −2.93954 | −0.219100 | ||||||||
\(181\) | 21.1888 | 1.57495 | 0.787474 | − | 0.616348i | \(-0.211389\pi\) | ||||
0.787474 | + | 0.616348i | \(0.211389\pi\) | |||||||
\(182\) | 1.15197 | 0.0853897 | ||||||||
\(183\) | −2.45536 | −0.181505 | ||||||||
\(184\) | −8.30827 | −0.612494 | ||||||||
\(185\) | −3.86743 | −0.284339 | ||||||||
\(186\) | 1.55885 | 0.114301 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.17003 | −0.449996 | ||||||||
\(189\) | −1.46049 | −0.106235 | ||||||||
\(190\) | 3.43477 | 0.249184 | ||||||||
\(191\) | 4.05200 | 0.293192 | 0.146596 | − | 0.989196i | \(-0.453168\pi\) | ||||
0.146596 | + | 0.989196i | \(0.453168\pi\) | |||||||
\(192\) | 0.245893 | 0.0177458 | ||||||||
\(193\) | −20.5136 | −1.47660 | −0.738302 | − | 0.674470i | \(-0.764372\pi\) | ||||
−0.738302 | + | 0.674470i | \(0.764372\pi\) | |||||||
\(194\) | −3.45447 | −0.248017 | ||||||||
\(195\) | −0.283261 | −0.0202848 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −20.4398 | −1.45628 | −0.728139 | − | 0.685429i | \(-0.759614\pi\) | ||||
−0.728139 | + | 0.685429i | \(0.759614\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.23576 | −0.229377 | −0.114688 | − | 0.993402i | \(-0.536587\pi\) | ||||
−0.114688 | + | 0.993402i | \(0.536587\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 3.49529 | 0.246538 | ||||||||
\(202\) | −2.71712 | −0.191176 | ||||||||
\(203\) | −2.93346 | −0.205889 | ||||||||
\(204\) | 1.61090 | 0.112786 | ||||||||
\(205\) | −10.5558 | −0.737251 | ||||||||
\(206\) | 9.90941 | 0.690421 | ||||||||
\(207\) | −24.4225 | −1.69748 | ||||||||
\(208\) | −1.15197 | −0.0798748 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.245893 | −0.0169682 | ||||||||
\(211\) | −12.3479 | −0.850064 | −0.425032 | − | 0.905178i | \(-0.639737\pi\) | ||||
−0.425032 | + | 0.905178i | \(0.639737\pi\) | |||||||
\(212\) | 5.35680 | 0.367906 | ||||||||
\(213\) | −0.0934934 | −0.00640606 | ||||||||
\(214\) | −5.18688 | −0.354568 | ||||||||
\(215\) | −2.95752 | −0.201701 | ||||||||
\(216\) | 1.46049 | 0.0993737 | ||||||||
\(217\) | −6.33956 | −0.430358 | ||||||||
\(218\) | −12.1283 | −0.821431 | ||||||||
\(219\) | −1.77834 | −0.120169 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.54684 | −0.507655 | ||||||||
\(222\) | 0.950972 | 0.0638251 | ||||||||
\(223\) | 8.30846 | 0.556376 | 0.278188 | − | 0.960527i | \(-0.410266\pi\) | ||||
0.278188 | + | 0.960527i | \(0.410266\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.93954 | −0.195969 | ||||||||
\(226\) | −14.5100 | −0.965190 | ||||||||
\(227\) | −15.7302 | −1.04405 | −0.522023 | − | 0.852931i | \(-0.674823\pi\) | ||||
−0.522023 | + | 0.852931i | \(0.674823\pi\) | |||||||
\(228\) | −0.844585 | −0.0559340 | ||||||||
\(229\) | −23.7309 | −1.56818 | −0.784090 | − | 0.620647i | \(-0.786870\pi\) | ||||
−0.784090 | + | 0.620647i | \(0.786870\pi\) | |||||||
\(230\) | −8.30827 | −0.547831 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.93346 | 0.192591 | ||||||||
\(233\) | 11.9023 | 0.779745 | 0.389872 | − | 0.920869i | \(-0.372519\pi\) | ||||
0.389872 | + | 0.920869i | \(0.372519\pi\) | |||||||
\(234\) | −3.38626 | −0.221367 | ||||||||
\(235\) | −6.17003 | −0.402488 | ||||||||
\(236\) | −2.24164 | −0.145919 | ||||||||
\(237\) | −0.559114 | −0.0363184 | ||||||||
\(238\) | −6.55125 | −0.424654 | ||||||||
\(239\) | −21.8184 | −1.41132 | −0.705659 | − | 0.708552i | \(-0.749349\pi\) | ||||
−0.705659 | + | 0.708552i | \(0.749349\pi\) | |||||||
\(240\) | 0.245893 | 0.0158723 | ||||||||
\(241\) | −14.7413 | −0.949569 | −0.474785 | − | 0.880102i | \(-0.657474\pi\) | ||||
−0.474785 | + | 0.880102i | \(0.657474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.46159 | 0.414511 | ||||||||
\(244\) | −9.98548 | −0.639255 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 2.59560 | 0.165489 | ||||||||
\(247\) | 3.95675 | 0.251762 | ||||||||
\(248\) | 6.33956 | 0.402563 | ||||||||
\(249\) | −2.78578 | −0.176542 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.8410 | −0.810517 | −0.405258 | − | 0.914202i | \(-0.632818\pi\) | ||||
−0.405258 | + | 0.914202i | \(0.632818\pi\) | |||||||
\(252\) | −2.93954 | −0.185173 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.818399 | 0.0513509 | ||||||||
\(255\) | 1.61090 | 0.100879 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.70646 | 0.355959 | 0.177980 | − | 0.984034i | \(-0.443044\pi\) | ||||
0.177980 | + | 0.984034i | \(0.443044\pi\) | |||||||
\(258\) | 0.727233 | 0.0452756 | ||||||||
\(259\) | −3.86743 | −0.240310 | ||||||||
\(260\) | −1.15197 | −0.0714422 | ||||||||
\(261\) | 8.62303 | 0.533752 | ||||||||
\(262\) | −9.76900 | −0.603531 | ||||||||
\(263\) | 12.9095 | 0.796033 | 0.398016 | − | 0.917378i | \(-0.369699\pi\) | ||||
0.398016 | + | 0.917378i | \(0.369699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.35680 | 0.329065 | ||||||||
\(266\) | 3.43477 | 0.210599 | ||||||||
\(267\) | −1.10379 | −0.0675508 | ||||||||
\(268\) | 14.2147 | 0.868299 | ||||||||
\(269\) | 19.2650 | 1.17461 | 0.587304 | − | 0.809367i | \(-0.300189\pi\) | ||||
0.587304 | + | 0.809367i | \(0.300189\pi\) | |||||||
\(270\) | 1.46049 | 0.0888825 | ||||||||
\(271\) | 27.8182 | 1.68983 | 0.844917 | − | 0.534897i | \(-0.179649\pi\) | ||||
0.844917 | + | 0.534897i | \(0.179649\pi\) | |||||||
\(272\) | 6.55125 | 0.397228 | ||||||||
\(273\) | −0.283261 | −0.0171437 | ||||||||
\(274\) | 6.68920 | 0.404110 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.04294 | 0.122971 | ||||||||
\(277\) | 12.3700 | 0.743240 | 0.371620 | − | 0.928385i | \(-0.378802\pi\) | ||||
0.371620 | + | 0.928385i | \(0.378802\pi\) | |||||||
\(278\) | 8.85349 | 0.530997 | ||||||||
\(279\) | 18.6354 | 1.11567 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 21.9883 | 1.31171 | 0.655856 | − | 0.754886i | \(-0.272308\pi\) | ||||
0.655856 | + | 0.754886i | \(0.272308\pi\) | |||||||
\(282\) | 1.51717 | 0.0903459 | ||||||||
\(283\) | −13.8205 | −0.821542 | −0.410771 | − | 0.911739i | \(-0.634740\pi\) | ||||
−0.410771 | + | 0.911739i | \(0.634740\pi\) | |||||||
\(284\) | −0.380220 | −0.0225619 | ||||||||
\(285\) | −0.844585 | −0.0500289 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5558 | −0.623091 | ||||||||
\(288\) | 2.93954 | 0.173214 | ||||||||
\(289\) | 25.9188 | 1.52464 | ||||||||
\(290\) | 2.93346 | 0.172259 | ||||||||
\(291\) | 0.849430 | 0.0497945 | ||||||||
\(292\) | −7.23216 | −0.423230 | ||||||||
\(293\) | −18.2052 | −1.06356 | −0.531779 | − | 0.846883i | \(-0.678476\pi\) | ||||
−0.531779 | + | 0.846883i | \(0.678476\pi\) | |||||||
\(294\) | −0.245893 | −0.0143408 | ||||||||
\(295\) | −2.24164 | −0.130513 | ||||||||
\(296\) | 3.86743 | 0.224790 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.32495 | 0.250538 | ||||||||
\(299\) | −9.57087 | −0.553498 | ||||||||
\(300\) | 0.245893 | 0.0141966 | ||||||||
\(301\) | −2.95752 | −0.170469 | ||||||||
\(302\) | 17.5142 | 1.00783 | ||||||||
\(303\) | 0.668121 | 0.0383825 | ||||||||
\(304\) | −3.43477 | −0.196997 | ||||||||
\(305\) | −9.98548 | −0.571767 | ||||||||
\(306\) | 19.2576 | 1.10089 | ||||||||
\(307\) | 23.7729 | 1.35679 | 0.678395 | − | 0.734697i | \(-0.262676\pi\) | ||||
0.678395 | + | 0.734697i | \(0.262676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.43665 | −0.138616 | ||||||||
\(310\) | 6.33956 | 0.360063 | ||||||||
\(311\) | −18.2509 | −1.03492 | −0.517458 | − | 0.855709i | \(-0.673121\pi\) | ||||
−0.517458 | + | 0.855709i | \(0.673121\pi\) | |||||||
\(312\) | 0.283261 | 0.0160365 | ||||||||
\(313\) | −16.4004 | −0.927003 | −0.463502 | − | 0.886096i | \(-0.653407\pi\) | ||||
−0.463502 | + | 0.886096i | \(0.653407\pi\) | |||||||
\(314\) | −8.20435 | −0.462998 | ||||||||
\(315\) | −2.93954 | −0.165624 | ||||||||
\(316\) | −2.27381 | −0.127912 | ||||||||
\(317\) | −26.2832 | −1.47621 | −0.738106 | − | 0.674684i | \(-0.764280\pi\) | ||||
−0.738106 | + | 0.674684i | \(0.764280\pi\) | |||||||
\(318\) | −1.31720 | −0.0738648 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 1.27542 | 0.0711868 | ||||||||
\(322\) | −8.30827 | −0.463002 | ||||||||
\(323\) | −22.5020 | −1.25205 | ||||||||
\(324\) | 8.45949 | 0.469971 | ||||||||
\(325\) | −1.15197 | −0.0638998 | ||||||||
\(326\) | 11.4586 | 0.634631 | ||||||||
\(327\) | 2.98226 | 0.164919 | ||||||||
\(328\) | 10.5558 | 0.582848 | ||||||||
\(329\) | −6.17003 | −0.340165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.6604 | 1.35546 | 0.677729 | − | 0.735312i | \(-0.262964\pi\) | ||||
0.677729 | + | 0.735312i | \(0.262964\pi\) | |||||||
\(332\) | −11.3292 | −0.621773 | ||||||||
\(333\) | 11.3684 | 0.622987 | ||||||||
\(334\) | 0.763127 | 0.0417565 | ||||||||
\(335\) | 14.2147 | 0.776631 | ||||||||
\(336\) | 0.245893 | 0.0134146 | ||||||||
\(337\) | −7.67814 | −0.418255 | −0.209128 | − | 0.977888i | \(-0.567062\pi\) | ||||
−0.209128 | + | 0.977888i | \(0.567062\pi\) | |||||||
\(338\) | 11.6730 | 0.634926 | ||||||||
\(339\) | 3.56790 | 0.193782 | ||||||||
\(340\) | 6.55125 | 0.355291 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.0966 | −0.545963 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.95752 | 0.159459 | ||||||||
\(345\) | 2.04294 | 0.109988 | ||||||||
\(346\) | 8.76752 | 0.471345 | ||||||||
\(347\) | 18.3330 | 0.984169 | 0.492084 | − | 0.870547i | \(-0.336235\pi\) | ||||
0.492084 | + | 0.870547i | \(0.336235\pi\) | |||||||
\(348\) | −0.721318 | −0.0386667 | ||||||||
\(349\) | −6.32456 | −0.338546 | −0.169273 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169273 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 1.68244 | 0.0898020 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.7476 | −0.997834 | −0.498917 | − | 0.866650i | \(-0.666269\pi\) | ||||
−0.498917 | + | 0.866650i | \(0.666269\pi\) | |||||||
\(354\) | 0.551204 | 0.0292961 | ||||||||
\(355\) | −0.380220 | −0.0201800 | ||||||||
\(356\) | −4.48891 | −0.237912 | ||||||||
\(357\) | 1.61090 | 0.0852581 | ||||||||
\(358\) | −15.0279 | −0.794250 | ||||||||
\(359\) | 20.8408 | 1.09994 | 0.549968 | − | 0.835186i | \(-0.314640\pi\) | ||||
0.549968 | + | 0.835186i | \(0.314640\pi\) | |||||||
\(360\) | 2.93954 | 0.154927 | ||||||||
\(361\) | −7.20237 | −0.379072 | ||||||||
\(362\) | −21.1888 | −1.11366 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.15197 | −0.0603796 | ||||||||
\(365\) | −7.23216 | −0.378549 | ||||||||
\(366\) | 2.45536 | 0.128344 | ||||||||
\(367\) | −25.6396 | −1.33838 | −0.669188 | − | 0.743093i | \(-0.733358\pi\) | ||||
−0.669188 | + | 0.743093i | \(0.733358\pi\) | |||||||
\(368\) | 8.30827 | 0.433098 | ||||||||
\(369\) | 31.0292 | 1.61532 | ||||||||
\(370\) | 3.86743 | 0.201058 | ||||||||
\(371\) | 5.35680 | 0.278111 | ||||||||
\(372\) | −1.55885 | −0.0808228 | ||||||||
\(373\) | −34.9239 | −1.80829 | −0.904146 | − | 0.427223i | \(-0.859492\pi\) | ||||
−0.904146 | + | 0.427223i | \(0.859492\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.245893 | 0.0126978 | ||||||||
\(376\) | 6.17003 | 0.318195 | ||||||||
\(377\) | 3.37926 | 0.174041 | ||||||||
\(378\) | 1.46049 | 0.0751195 | ||||||||
\(379\) | 1.32409 | 0.0680138 | 0.0340069 | − | 0.999422i | \(-0.489173\pi\) | ||||
0.0340069 | + | 0.999422i | \(0.489173\pi\) | |||||||
\(380\) | −3.43477 | −0.176200 | ||||||||
\(381\) | −0.201238 | −0.0103098 | ||||||||
\(382\) | −4.05200 | −0.207318 | ||||||||
\(383\) | 2.42235 | 0.123776 | 0.0618880 | − | 0.998083i | \(-0.480288\pi\) | ||||
0.0618880 | + | 0.998083i | \(0.480288\pi\) | |||||||
\(384\) | −0.245893 | −0.0125482 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.5136 | 1.04412 | ||||||||
\(387\) | 8.69374 | 0.441928 | ||||||||
\(388\) | 3.45447 | 0.175374 | ||||||||
\(389\) | −21.2547 | −1.07766 | −0.538828 | − | 0.842416i | \(-0.681133\pi\) | ||||
−0.538828 | + | 0.842416i | \(0.681133\pi\) | |||||||
\(390\) | 0.283261 | 0.0143435 | ||||||||
\(391\) | 54.4295 | 2.75262 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 2.40213 | 0.121171 | ||||||||
\(394\) | 20.4398 | 1.02974 | ||||||||
\(395\) | −2.27381 | −0.114408 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8715 | 0.646003 | 0.323001 | − | 0.946398i | \(-0.395308\pi\) | ||||
0.323001 | + | 0.946398i | \(0.395308\pi\) | |||||||
\(398\) | 3.23576 | 0.162194 | ||||||||
\(399\) | −0.844585 | −0.0422821 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.1726 | −0.557933 | −0.278966 | − | 0.960301i | \(-0.589992\pi\) | ||||
−0.278966 | + | 0.960301i | \(0.589992\pi\) | |||||||
\(402\) | −3.49529 | −0.174329 | ||||||||
\(403\) | 7.30299 | 0.363788 | ||||||||
\(404\) | 2.71712 | 0.135182 | ||||||||
\(405\) | 8.45949 | 0.420355 | ||||||||
\(406\) | 2.93346 | 0.145585 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.61090 | −0.0797516 | ||||||||
\(409\) | 14.7289 | 0.728297 | 0.364148 | − | 0.931341i | \(-0.381360\pi\) | ||||
0.364148 | + | 0.931341i | \(0.381360\pi\) | |||||||
\(410\) | 10.5558 | 0.521315 | ||||||||
\(411\) | −1.64483 | −0.0811333 | ||||||||
\(412\) | −9.90941 | −0.488201 | ||||||||
\(413\) | −2.24164 | −0.110304 | ||||||||
\(414\) | 24.4225 | 1.20030 | ||||||||
\(415\) | −11.3292 | −0.556131 | ||||||||
\(416\) | 1.15197 | 0.0564800 | ||||||||
\(417\) | −2.17701 | −0.106609 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1913 | −0.693290 | −0.346645 | − | 0.937996i | \(-0.612679\pi\) | ||||
−0.346645 | + | 0.937996i | \(0.612679\pi\) | |||||||
\(420\) | 0.245893 | 0.0119983 | ||||||||
\(421\) | −26.0595 | −1.27006 | −0.635030 | − | 0.772487i | \(-0.719012\pi\) | ||||
−0.635030 | + | 0.772487i | \(0.719012\pi\) | |||||||
\(422\) | 12.3479 | 0.601086 | ||||||||
\(423\) | 18.1370 | 0.881853 | ||||||||
\(424\) | −5.35680 | −0.260149 | ||||||||
\(425\) | 6.55125 | 0.317782 | ||||||||
\(426\) | 0.0934934 | 0.00452977 | ||||||||
\(427\) | −9.98548 | −0.483231 | ||||||||
\(428\) | 5.18688 | 0.250717 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.95752 | 0.142624 | ||||||||
\(431\) | −18.8146 | −0.906270 | −0.453135 | − | 0.891442i | \(-0.649694\pi\) | ||||
−0.453135 | + | 0.891442i | \(0.649694\pi\) | |||||||
\(432\) | −1.46049 | −0.0702678 | ||||||||
\(433\) | 20.4028 | 0.980497 | 0.490248 | − | 0.871583i | \(-0.336906\pi\) | ||||
0.490248 | + | 0.871583i | \(0.336906\pi\) | |||||||
\(434\) | 6.33956 | 0.304309 | ||||||||
\(435\) | −0.721318 | −0.0345845 | ||||||||
\(436\) | 12.1283 | 0.580839 | ||||||||
\(437\) | −28.5370 | −1.36511 | ||||||||
\(438\) | 1.77834 | 0.0849722 | ||||||||
\(439\) | 17.5292 | 0.836621 | 0.418311 | − | 0.908304i | \(-0.362622\pi\) | ||||
0.418311 | + | 0.908304i | \(0.362622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.93954 | −0.139978 | ||||||||
\(442\) | 7.54684 | 0.358967 | ||||||||
\(443\) | −26.1950 | −1.24456 | −0.622281 | − | 0.782794i | \(-0.713794\pi\) | ||||
−0.622281 | + | 0.782794i | \(0.713794\pi\) | |||||||
\(444\) | −0.950972 | −0.0451312 | ||||||||
\(445\) | −4.48891 | −0.212795 | ||||||||
\(446\) | −8.30846 | −0.393417 | ||||||||
\(447\) | −1.06347 | −0.0503006 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −9.49700 | −0.448191 | −0.224096 | − | 0.974567i | \(-0.571943\pi\) | ||||
−0.224096 | + | 0.974567i | \(0.571943\pi\) | |||||||
\(450\) | 2.93954 | 0.138571 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14.5100 | 0.682493 | ||||||||
\(453\) | −4.30662 | −0.202343 | ||||||||
\(454\) | 15.7302 | 0.738253 | ||||||||
\(455\) | −1.15197 | −0.0540052 | ||||||||
\(456\) | 0.844585 | 0.0395513 | ||||||||
\(457\) | 17.5412 | 0.820545 | 0.410272 | − | 0.911963i | \(-0.365434\pi\) | ||||
0.410272 | + | 0.911963i | \(0.365434\pi\) | |||||||
\(458\) | 23.7309 | 1.10887 | ||||||||
\(459\) | −9.56802 | −0.446597 | ||||||||
\(460\) | 8.30827 | 0.387375 | ||||||||
\(461\) | −22.6720 | −1.05594 | −0.527970 | − | 0.849263i | \(-0.677047\pi\) | ||||
−0.527970 | + | 0.849263i | \(0.677047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.9554 | −1.25272 | −0.626362 | − | 0.779532i | \(-0.715457\pi\) | ||||
−0.626362 | + | 0.779532i | \(0.715457\pi\) | |||||||
\(464\) | −2.93346 | −0.136183 | ||||||||
\(465\) | −1.55885 | −0.0722901 | ||||||||
\(466\) | −11.9023 | −0.551363 | ||||||||
\(467\) | 14.7718 | 0.683557 | 0.341778 | − | 0.939781i | \(-0.388971\pi\) | ||||
0.341778 | + | 0.939781i | \(0.388971\pi\) | |||||||
\(468\) | 3.38626 | 0.156530 | ||||||||
\(469\) | 14.2147 | 0.656373 | ||||||||
\(470\) | 6.17003 | 0.284602 | ||||||||
\(471\) | 2.01739 | 0.0929565 | ||||||||
\(472\) | 2.24164 | 0.103180 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.559114 | 0.0256810 | ||||||||
\(475\) | −3.43477 | −0.157598 | ||||||||
\(476\) | 6.55125 | 0.300276 | ||||||||
\(477\) | −15.7465 | −0.720983 | ||||||||
\(478\) | 21.8184 | 0.997952 | ||||||||
\(479\) | −31.8220 | −1.45398 | −0.726992 | − | 0.686646i | \(-0.759082\pi\) | ||||
−0.726992 | + | 0.686646i | \(0.759082\pi\) | |||||||
\(480\) | −0.245893 | −0.0112234 | ||||||||
\(481\) | 4.45516 | 0.203138 | ||||||||
\(482\) | 14.7413 | 0.671447 | ||||||||
\(483\) | 2.04294 | 0.0929571 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.45447 | 0.156859 | ||||||||
\(486\) | −6.46159 | −0.293104 | ||||||||
\(487\) | 24.8664 | 1.12681 | 0.563403 | − | 0.826182i | \(-0.309492\pi\) | ||||
0.563403 | + | 0.826182i | \(0.309492\pi\) | |||||||
\(488\) | 9.98548 | 0.452022 | ||||||||
\(489\) | −2.81758 | −0.127415 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −41.8496 | −1.88864 | −0.944322 | − | 0.329022i | \(-0.893281\pi\) | ||||
−0.944322 | + | 0.329022i | \(0.893281\pi\) | |||||||
\(492\) | −2.59560 | −0.117019 | ||||||||
\(493\) | −19.2178 | −0.865528 | ||||||||
\(494\) | −3.95675 | −0.178023 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.33956 | −0.284655 | ||||||||
\(497\) | −0.380220 | −0.0170552 | ||||||||
\(498\) | 2.78578 | 0.124834 | ||||||||
\(499\) | 24.8351 | 1.11177 | 0.555885 | − | 0.831259i | \(-0.312379\pi\) | ||||
0.555885 | + | 0.831259i | \(0.312379\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −0.187647 | −0.00838347 | ||||||||
\(502\) | 12.8410 | 0.573122 | ||||||||
\(503\) | 8.92909 | 0.398128 | 0.199064 | − | 0.979986i | \(-0.436210\pi\) | ||||
0.199064 | + | 0.979986i | \(0.436210\pi\) | |||||||
\(504\) | 2.93954 | 0.130937 | ||||||||
\(505\) | 2.71712 | 0.120910 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.87030 | −0.127474 | ||||||||
\(508\) | −0.818399 | −0.0363106 | ||||||||
\(509\) | 22.8685 | 1.01363 | 0.506813 | − | 0.862056i | \(-0.330823\pi\) | ||||
0.506813 | + | 0.862056i | \(0.330823\pi\) | |||||||
\(510\) | −1.61090 | −0.0713320 | ||||||||
\(511\) | −7.23216 | −0.319932 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.01644 | 0.221481 | ||||||||
\(514\) | −5.70646 | −0.251701 | ||||||||
\(515\) | −9.90941 | −0.436661 | ||||||||
\(516\) | −0.727233 | −0.0320147 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.86743 | 0.169925 | ||||||||
\(519\) | −2.15587 | −0.0946322 | ||||||||
\(520\) | 1.15197 | 0.0505172 | ||||||||
\(521\) | −34.4131 | −1.50767 | −0.753833 | − | 0.657066i | \(-0.771797\pi\) | ||||
−0.753833 | + | 0.657066i | \(0.771797\pi\) | |||||||
\(522\) | −8.62303 | −0.377420 | ||||||||
\(523\) | −6.70316 | −0.293109 | −0.146554 | − | 0.989203i | \(-0.546818\pi\) | ||||
−0.146554 | + | 0.989203i | \(0.546818\pi\) | |||||||
\(524\) | 9.76900 | 0.426761 | ||||||||
\(525\) | 0.245893 | 0.0107316 | ||||||||
\(526\) | −12.9095 | −0.562880 | ||||||||
\(527\) | −41.5320 | −1.80916 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.0273 | 2.00119 | ||||||||
\(530\) | −5.35680 | −0.232684 | ||||||||
\(531\) | 6.58939 | 0.285955 | ||||||||
\(532\) | −3.43477 | −0.148916 | ||||||||
\(533\) | 12.1600 | 0.526708 | ||||||||
\(534\) | 1.10379 | 0.0477657 | ||||||||
\(535\) | 5.18688 | 0.224248 | ||||||||
\(536\) | −14.2147 | −0.613980 | ||||||||
\(537\) | 3.69525 | 0.159462 | ||||||||
\(538\) | −19.2650 | −0.830573 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.46049 | −0.0628495 | ||||||||
\(541\) | −16.4021 | −0.705181 | −0.352590 | − | 0.935778i | \(-0.614699\pi\) | ||||
−0.352590 | + | 0.935778i | \(0.614699\pi\) | |||||||
\(542\) | −27.8182 | −1.19489 | ||||||||
\(543\) | 5.21016 | 0.223589 | ||||||||
\(544\) | −6.55125 | −0.280882 | ||||||||
\(545\) | 12.1283 | 0.519518 | ||||||||
\(546\) | 0.283261 | 0.0121225 | ||||||||
\(547\) | −6.99852 | −0.299235 | −0.149618 | − | 0.988744i | \(-0.547804\pi\) | ||||
−0.149618 | + | 0.988744i | \(0.547804\pi\) | |||||||
\(548\) | −6.68920 | −0.285749 | ||||||||
\(549\) | 29.3527 | 1.25274 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0758 | 0.429242 | ||||||||
\(552\) | −2.04294 | −0.0869534 | ||||||||
\(553\) | −2.27381 | −0.0966923 | ||||||||
\(554\) | −12.3700 | −0.525550 | ||||||||
\(555\) | −0.950972 | −0.0403665 | ||||||||
\(556\) | −8.85349 | −0.375471 | ||||||||
\(557\) | 14.1845 | 0.601016 | 0.300508 | − | 0.953779i | \(-0.402844\pi\) | ||||
0.300508 | + | 0.953779i | \(0.402844\pi\) | |||||||
\(558\) | −18.6354 | −0.788898 | ||||||||
\(559\) | 3.40698 | 0.144100 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.9883 | −0.927520 | ||||||||
\(563\) | −26.6253 | −1.12212 | −0.561062 | − | 0.827774i | \(-0.689607\pi\) | ||||
−0.561062 | + | 0.827774i | \(0.689607\pi\) | |||||||
\(564\) | −1.51717 | −0.0638842 | ||||||||
\(565\) | 14.5100 | 0.610440 | ||||||||
\(566\) | 13.8205 | 0.580918 | ||||||||
\(567\) | 8.45949 | 0.355265 | ||||||||
\(568\) | 0.380220 | 0.0159537 | ||||||||
\(569\) | −1.29976 | −0.0544889 | −0.0272445 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272445 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(570\) | 0.844585 | 0.0353758 | ||||||||
\(571\) | −24.2338 | −1.01415 | −0.507076 | − | 0.861901i | \(-0.669274\pi\) | ||||
−0.507076 | + | 0.861901i | \(0.669274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.996357 | 0.0416234 | ||||||||
\(574\) | 10.5558 | 0.440592 | ||||||||
\(575\) | 8.30827 | 0.346479 | ||||||||
\(576\) | −2.93954 | −0.122481 | ||||||||
\(577\) | −37.9967 | −1.58183 | −0.790913 | − | 0.611929i | \(-0.790394\pi\) | ||||
−0.790913 | + | 0.611929i | \(0.790394\pi\) | |||||||
\(578\) | −25.9188 | −1.07808 | ||||||||
\(579\) | −5.04416 | −0.209628 | ||||||||
\(580\) | −2.93346 | −0.121805 | ||||||||
\(581\) | −11.3292 | −0.470016 | ||||||||
\(582\) | −0.849430 | −0.0352100 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.23216 | 0.299269 | ||||||||
\(585\) | 3.38626 | 0.140005 | ||||||||
\(586\) | 18.2052 | 0.752049 | ||||||||
\(587\) | 5.54502 | 0.228868 | 0.114434 | − | 0.993431i | \(-0.463495\pi\) | ||||
0.114434 | + | 0.993431i | \(0.463495\pi\) | |||||||
\(588\) | 0.245893 | 0.0101404 | ||||||||
\(589\) | 21.7749 | 0.897220 | ||||||||
\(590\) | 2.24164 | 0.0922870 | ||||||||
\(591\) | −5.02601 | −0.206742 | ||||||||
\(592\) | −3.86743 | −0.158950 | ||||||||
\(593\) | −45.5378 | −1.87001 | −0.935006 | − | 0.354633i | \(-0.884606\pi\) | ||||
−0.935006 | + | 0.354633i | \(0.884606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.55125 | 0.268575 | ||||||||
\(596\) | −4.32495 | −0.177157 | ||||||||
\(597\) | −0.795650 | −0.0325638 | ||||||||
\(598\) | 9.57087 | 0.391382 | ||||||||
\(599\) | 38.2388 | 1.56240 | 0.781198 | − | 0.624284i | \(-0.214609\pi\) | ||||
0.781198 | + | 0.624284i | \(0.214609\pi\) | |||||||
\(600\) | −0.245893 | −0.0100385 | ||||||||
\(601\) | 41.8737 | 1.70807 | 0.854033 | − | 0.520219i | \(-0.174150\pi\) | ||||
0.854033 | + | 0.520219i | \(0.174150\pi\) | |||||||
\(602\) | 2.95752 | 0.120540 | ||||||||
\(603\) | −41.7846 | −1.70160 | ||||||||
\(604\) | −17.5142 | −0.712644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.668121 | −0.0271406 | ||||||||
\(607\) | 6.87012 | 0.278850 | 0.139425 | − | 0.990233i | \(-0.455475\pi\) | ||||
0.139425 | + | 0.990233i | \(0.455475\pi\) | |||||||
\(608\) | 3.43477 | 0.139298 | ||||||||
\(609\) | −0.721318 | −0.0292293 | ||||||||
\(610\) | 9.98548 | 0.404300 | ||||||||
\(611\) | 7.10769 | 0.287546 | ||||||||
\(612\) | −19.2576 | −0.778443 | ||||||||
\(613\) | 37.8887 | 1.53031 | 0.765155 | − | 0.643847i | \(-0.222663\pi\) | ||||
0.765155 | + | 0.643847i | \(0.222663\pi\) | |||||||
\(614\) | −23.7729 | −0.959396 | ||||||||
\(615\) | −2.59560 | −0.104665 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7135 | 0.793636 | 0.396818 | − | 0.917897i | \(-0.370114\pi\) | ||||
0.396818 | + | 0.917897i | \(0.370114\pi\) | |||||||
\(618\) | 2.43665 | 0.0980165 | ||||||||
\(619\) | 45.3200 | 1.82156 | 0.910782 | − | 0.412888i | \(-0.135480\pi\) | ||||
0.910782 | + | 0.412888i | \(0.135480\pi\) | |||||||
\(620\) | −6.33956 | −0.254603 | ||||||||
\(621\) | −12.1341 | −0.486926 | ||||||||
\(622\) | 18.2509 | 0.731796 | ||||||||
\(623\) | −4.48891 | −0.179844 | ||||||||
\(624\) | −0.283261 | −0.0113395 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.4004 | 0.655490 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.20435 | 0.327389 | ||||||||
\(629\) | −25.3365 | −1.01023 | ||||||||
\(630\) | 2.93954 | 0.117114 | ||||||||
\(631\) | −29.3153 | −1.16702 | −0.583512 | − | 0.812104i | \(-0.698322\pi\) | ||||
−0.583512 | + | 0.812104i | \(0.698322\pi\) | |||||||
\(632\) | 2.27381 | 0.0904474 | ||||||||
\(633\) | −3.03626 | −0.120680 | ||||||||
\(634\) | 26.2832 | 1.04384 | ||||||||
\(635\) | −0.818399 | −0.0324772 | ||||||||
\(636\) | 1.31720 | 0.0522303 | ||||||||
\(637\) | −1.15197 | −0.0456427 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.11767 | 0.0442144 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −21.9740 | −0.867923 | −0.433961 | − | 0.900932i | \(-0.642885\pi\) | ||||
−0.433961 | + | 0.900932i | \(0.642885\pi\) | |||||||
\(642\) | −1.27542 | −0.0503366 | ||||||||
\(643\) | −46.4736 | −1.83274 | −0.916370 | − | 0.400332i | \(-0.868895\pi\) | ||||
−0.916370 | + | 0.400332i | \(0.868895\pi\) | |||||||
\(644\) | 8.30827 | 0.327392 | ||||||||
\(645\) | −0.727233 | −0.0286348 | ||||||||
\(646\) | 22.5020 | 0.885330 | ||||||||
\(647\) | 19.3483 | 0.760660 | 0.380330 | − | 0.924851i | \(-0.375810\pi\) | ||||
0.380330 | + | 0.924851i | \(0.375810\pi\) | |||||||
\(648\) | −8.45949 | −0.332320 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.15197 | 0.0451840 | ||||||||
\(651\) | −1.55885 | −0.0610963 | ||||||||
\(652\) | −11.4586 | −0.448752 | ||||||||
\(653\) | 36.9129 | 1.44452 | 0.722258 | − | 0.691624i | \(-0.243105\pi\) | ||||
0.722258 | + | 0.691624i | \(0.243105\pi\) | |||||||
\(654\) | −2.98226 | −0.116615 | ||||||||
\(655\) | 9.76900 | 0.381706 | ||||||||
\(656\) | −10.5558 | −0.412136 | ||||||||
\(657\) | 21.2592 | 0.829400 | ||||||||
\(658\) | 6.17003 | 0.240533 | ||||||||
\(659\) | −24.3913 | −0.950151 | −0.475075 | − | 0.879945i | \(-0.657579\pi\) | ||||
−0.475075 | + | 0.879945i | \(0.657579\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.60864 | −0.218151 | −0.109075 | − | 0.994033i | \(-0.534789\pi\) | ||||
−0.109075 | + | 0.994033i | \(0.534789\pi\) | |||||||
\(662\) | −24.6604 | −0.958453 | ||||||||
\(663\) | −1.85571 | −0.0720699 | ||||||||
\(664\) | 11.3292 | 0.439660 | ||||||||
\(665\) | −3.43477 | −0.133195 | ||||||||
\(666\) | −11.3684 | −0.440518 | ||||||||
\(667\) | −24.3720 | −0.943688 | ||||||||
\(668\) | −0.763127 | −0.0295263 | ||||||||
\(669\) | 2.04299 | 0.0789866 | ||||||||
\(670\) | −14.2147 | −0.549161 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.245893 | −0.00948552 | ||||||||
\(673\) | 27.6564 | 1.06608 | 0.533038 | − | 0.846091i | \(-0.321050\pi\) | ||||
0.533038 | + | 0.846091i | \(0.321050\pi\) | |||||||
\(674\) | 7.67814 | 0.295751 | ||||||||
\(675\) | −1.46049 | −0.0562143 | ||||||||
\(676\) | −11.6730 | −0.448960 | ||||||||
\(677\) | −28.6810 | −1.10230 | −0.551149 | − | 0.834407i | \(-0.685811\pi\) | ||||
−0.551149 | + | 0.834407i | \(0.685811\pi\) | |||||||
\(678\) | −3.56790 | −0.137024 | ||||||||
\(679\) | 3.45447 | 0.132570 | ||||||||
\(680\) | −6.55125 | −0.251229 | ||||||||
\(681\) | −3.86793 | −0.148219 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.9631 | −1.49088 | −0.745440 | − | 0.666572i | \(-0.767761\pi\) | ||||
−0.745440 | + | 0.666572i | \(0.767761\pi\) | |||||||
\(684\) | 10.0966 | 0.386054 | ||||||||
\(685\) | −6.68920 | −0.255581 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −5.83525 | −0.222629 | ||||||||
\(688\) | −2.95752 | −0.112754 | ||||||||
\(689\) | −6.17087 | −0.235091 | ||||||||
\(690\) | −2.04294 | −0.0777735 | ||||||||
\(691\) | −15.0471 | −0.572418 | −0.286209 | − | 0.958167i | \(-0.592395\pi\) | ||||
−0.286209 | + | 0.958167i | \(0.592395\pi\) | |||||||
\(692\) | −8.76752 | −0.333291 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.3330 | −0.695912 | ||||||||
\(695\) | −8.85349 | −0.335832 | ||||||||
\(696\) | 0.721318 | 0.0273415 | ||||||||
\(697\) | −69.1538 | −2.61939 | ||||||||
\(698\) | 6.32456 | 0.239388 | ||||||||
\(699\) | 2.92669 | 0.110697 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 26.9497 | 1.01788 | 0.508938 | − | 0.860803i | \(-0.330038\pi\) | ||||
0.508938 | + | 0.860803i | \(0.330038\pi\) | |||||||
\(702\) | −1.68244 | −0.0634996 | ||||||||
\(703\) | 13.2837 | 0.501005 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.51717 | −0.0571398 | ||||||||
\(706\) | 18.7476 | 0.705575 | ||||||||
\(707\) | 2.71712 | 0.102188 | ||||||||
\(708\) | −0.551204 | −0.0207155 | ||||||||
\(709\) | −28.0992 | −1.05529 | −0.527644 | − | 0.849466i | \(-0.676924\pi\) | ||||
−0.527644 | + | 0.849466i | \(0.676924\pi\) | |||||||
\(710\) | 0.380220 | 0.0142694 | ||||||||
\(711\) | 6.68395 | 0.250668 | ||||||||
\(712\) | 4.48891 | 0.168229 | ||||||||
\(713\) | −52.6708 | −1.97254 | ||||||||
\(714\) | −1.61090 | −0.0602866 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.0279 | 0.561619 | ||||||||
\(717\) | −5.36500 | −0.200360 | ||||||||
\(718\) | −20.8408 | −0.777772 | ||||||||
\(719\) | −34.1887 | −1.27502 | −0.637511 | − | 0.770441i | \(-0.720036\pi\) | ||||
−0.637511 | + | 0.770441i | \(0.720036\pi\) | |||||||
\(720\) | −2.93954 | −0.109550 | ||||||||
\(721\) | −9.90941 | −0.369046 | ||||||||
\(722\) | 7.20237 | 0.268045 | ||||||||
\(723\) | −3.62477 | −0.134807 | ||||||||
\(724\) | 21.1888 | 0.787474 | ||||||||
\(725\) | −2.93346 | −0.108946 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.8368 | 1.73708 | 0.868541 | − | 0.495618i | \(-0.165058\pi\) | ||||
0.868541 | + | 0.495618i | \(0.165058\pi\) | |||||||
\(728\) | 1.15197 | 0.0426949 | ||||||||
\(729\) | −23.7896 | −0.881096 | ||||||||
\(730\) | 7.23216 | 0.267674 | ||||||||
\(731\) | −19.3754 | −0.716627 | ||||||||
\(732\) | −2.45536 | −0.0907526 | ||||||||
\(733\) | −4.80903 | −0.177625 | −0.0888127 | − | 0.996048i | \(-0.528307\pi\) | ||||
−0.0888127 | + | 0.996048i | \(0.528307\pi\) | |||||||
\(734\) | 25.6396 | 0.946374 | ||||||||
\(735\) | 0.245893 | 0.00906989 | ||||||||
\(736\) | −8.30827 | −0.306247 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −31.0292 | −1.14220 | ||||||||
\(739\) | 7.60017 | 0.279577 | 0.139788 | − | 0.990181i | \(-0.455358\pi\) | ||||
0.139788 | + | 0.990181i | \(0.455358\pi\) | |||||||
\(740\) | −3.86743 | −0.142169 | ||||||||
\(741\) | 0.972936 | 0.0357417 | ||||||||
\(742\) | −5.35680 | −0.196654 | ||||||||
\(743\) | −51.5981 | −1.89295 | −0.946475 | − | 0.322777i | \(-0.895384\pi\) | ||||
−0.946475 | + | 0.322777i | \(0.895384\pi\) | |||||||
\(744\) | 1.55885 | 0.0571503 | ||||||||
\(745\) | −4.32495 | −0.158454 | ||||||||
\(746\) | 34.9239 | 1.27866 | ||||||||
\(747\) | 33.3027 | 1.21848 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.18688 | 0.189524 | ||||||||
\(750\) | −0.245893 | −0.00897874 | ||||||||
\(751\) | 45.3313 | 1.65416 | 0.827081 | − | 0.562082i | \(-0.190000\pi\) | ||||
0.827081 | + | 0.562082i | \(0.190000\pi\) | |||||||
\(752\) | −6.17003 | −0.224998 | ||||||||
\(753\) | −3.15751 | −0.115066 | ||||||||
\(754\) | −3.37926 | −0.123066 | ||||||||
\(755\) | −17.5142 | −0.637408 | ||||||||
\(756\) | −1.46049 | −0.0531175 | ||||||||
\(757\) | 39.5221 | 1.43646 | 0.718228 | − | 0.695808i | \(-0.244954\pi\) | ||||
0.718228 | + | 0.695808i | \(0.244954\pi\) | |||||||
\(758\) | −1.32409 | −0.0480930 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.43477 | 0.124592 | ||||||||
\(761\) | 27.1122 | 0.982818 | 0.491409 | − | 0.870929i | \(-0.336482\pi\) | ||||
0.491409 | + | 0.870929i | \(0.336482\pi\) | |||||||
\(762\) | 0.201238 | 0.00729010 | ||||||||
\(763\) | 12.1283 | 0.439073 | ||||||||
\(764\) | 4.05200 | 0.146596 | ||||||||
\(765\) | −19.2576 | −0.696261 | ||||||||
\(766\) | −2.42235 | −0.0875229 | ||||||||
\(767\) | 2.58231 | 0.0932416 | ||||||||
\(768\) | 0.245893 | 0.00887289 | ||||||||
\(769\) | 18.0791 | 0.651948 | 0.325974 | − | 0.945379i | \(-0.394308\pi\) | ||||
0.325974 | + | 0.945379i | \(0.394308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.40318 | 0.0505342 | ||||||||
\(772\) | −20.5136 | −0.738302 | ||||||||
\(773\) | −37.7084 | −1.35628 | −0.678138 | − | 0.734935i | \(-0.737213\pi\) | ||||
−0.678138 | + | 0.734935i | \(0.737213\pi\) | |||||||
\(774\) | −8.69374 | −0.312490 | ||||||||
\(775\) | −6.33956 | −0.227724 | ||||||||
\(776\) | −3.45447 | −0.124008 | ||||||||
\(777\) | −0.950972 | −0.0341159 | ||||||||
\(778\) | 21.2547 | 0.762018 | ||||||||
\(779\) | 36.2568 | 1.29903 | ||||||||
\(780\) | −0.283261 | −0.0101424 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −54.4295 | −1.94639 | ||||||||
\(783\) | 4.28429 | 0.153108 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 8.20435 | 0.292826 | ||||||||
\(786\) | −2.40213 | −0.0856810 | ||||||||
\(787\) | 4.74651 | 0.169195 | 0.0845974 | − | 0.996415i | \(-0.473040\pi\) | ||||
0.0845974 | + | 0.996415i | \(0.473040\pi\) | |||||||
\(788\) | −20.4398 | −0.728139 | ||||||||
\(789\) | 3.17435 | 0.113010 | ||||||||
\(790\) | 2.27381 | 0.0808986 | ||||||||
\(791\) | 14.5100 | 0.515916 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.5030 | 0.408483 | ||||||||
\(794\) | −12.8715 | −0.456793 | ||||||||
\(795\) | 1.31720 | 0.0467162 | ||||||||
\(796\) | −3.23576 | −0.114688 | ||||||||
\(797\) | −25.4843 | −0.902701 | −0.451350 | − | 0.892347i | \(-0.649058\pi\) | ||||
−0.451350 | + | 0.892347i | \(0.649058\pi\) | |||||||
\(798\) | 0.844585 | 0.0298980 | ||||||||
\(799\) | −40.4214 | −1.43001 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 13.1953 | 0.466233 | ||||||||
\(802\) | 11.1726 | 0.394518 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 3.49529 | 0.123269 | ||||||||
\(805\) | 8.30827 | 0.292828 | ||||||||
\(806\) | −7.30299 | −0.257237 | ||||||||
\(807\) | 4.73712 | 0.166755 | ||||||||
\(808\) | −2.71712 | −0.0955880 | ||||||||
\(809\) | −7.24097 | −0.254579 | −0.127289 | − | 0.991866i | \(-0.540628\pi\) | ||||
−0.127289 | + | 0.991866i | \(0.540628\pi\) | |||||||
\(810\) | −8.45949 | −0.297236 | ||||||||
\(811\) | 12.4529 | 0.437281 | 0.218640 | − | 0.975806i | \(-0.429838\pi\) | ||||
0.218640 | + | 0.975806i | \(0.429838\pi\) | |||||||
\(812\) | −2.93346 | −0.102944 | ||||||||
\(813\) | 6.84029 | 0.239900 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.4586 | −0.401376 | ||||||||
\(816\) | 1.61090 | 0.0563929 | ||||||||
\(817\) | 10.1584 | 0.355397 | ||||||||
\(818\) | −14.7289 | −0.514984 | ||||||||
\(819\) | 3.38626 | 0.118325 | ||||||||
\(820\) | −10.5558 | −0.368625 | ||||||||
\(821\) | −16.5682 | −0.578233 | −0.289116 | − | 0.957294i | \(-0.593361\pi\) | ||||
−0.289116 | + | 0.957294i | \(0.593361\pi\) | |||||||
\(822\) | 1.64483 | 0.0573699 | ||||||||
\(823\) | −28.8974 | −1.00730 | −0.503651 | − | 0.863907i | \(-0.668010\pi\) | ||||
−0.503651 | + | 0.863907i | \(0.668010\pi\) | |||||||
\(824\) | 9.90941 | 0.345211 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.24164 | 0.0779967 | ||||||||
\(827\) | −22.5139 | −0.782884 | −0.391442 | − | 0.920203i | \(-0.628024\pi\) | ||||
−0.391442 | + | 0.920203i | \(0.628024\pi\) | |||||||
\(828\) | −24.4225 | −0.848739 | ||||||||
\(829\) | −27.8760 | −0.968172 | −0.484086 | − | 0.875020i | \(-0.660848\pi\) | ||||
−0.484086 | + | 0.875020i | \(0.660848\pi\) | |||||||
\(830\) | 11.3292 | 0.393244 | ||||||||
\(831\) | 3.04169 | 0.105515 | ||||||||
\(832\) | −1.15197 | −0.0399374 | ||||||||
\(833\) | 6.55125 | 0.226987 | ||||||||
\(834\) | 2.17701 | 0.0753836 | ||||||||
\(835\) | −0.763127 | −0.0264091 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.25886 | 0.320033 | ||||||||
\(838\) | 14.1913 | 0.490230 | ||||||||
\(839\) | 32.0359 | 1.10600 | 0.553002 | − | 0.833180i | \(-0.313482\pi\) | ||||
0.553002 | + | 0.833180i | \(0.313482\pi\) | |||||||
\(840\) | −0.245893 | −0.00848411 | ||||||||
\(841\) | −20.3948 | −0.703268 | ||||||||
\(842\) | 26.0595 | 0.898068 | ||||||||
\(843\) | 5.40676 | 0.186219 | ||||||||
\(844\) | −12.3479 | −0.425032 | ||||||||
\(845\) | −11.6730 | −0.401562 | ||||||||
\(846\) | −18.1370 | −0.623564 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.35680 | 0.183953 | ||||||||
\(849\) | −3.39835 | −0.116631 | ||||||||
\(850\) | −6.55125 | −0.224706 | ||||||||
\(851\) | −32.1316 | −1.10146 | ||||||||
\(852\) | −0.0934934 | −0.00320303 | ||||||||
\(853\) | 20.3366 | 0.696312 | 0.348156 | − | 0.937437i | \(-0.386808\pi\) | ||||
0.348156 | + | 0.937437i | \(0.386808\pi\) | |||||||
\(854\) | 9.98548 | 0.341696 | ||||||||
\(855\) | 10.0966 | 0.345297 | ||||||||
\(856\) | −5.18688 | −0.177284 | ||||||||
\(857\) | 52.8958 | 1.80689 | 0.903444 | − | 0.428706i | \(-0.141031\pi\) | ||||
0.903444 | + | 0.428706i | \(0.141031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.9360 | −1.94263 | −0.971315 | − | 0.237797i | \(-0.923575\pi\) | ||||
−0.971315 | + | 0.237797i | \(0.923575\pi\) | |||||||
\(860\) | −2.95752 | −0.100851 | ||||||||
\(861\) | −2.59560 | −0.0884579 | ||||||||
\(862\) | 18.8146 | 0.640829 | ||||||||
\(863\) | −16.5500 | −0.563367 | −0.281683 | − | 0.959507i | \(-0.590893\pi\) | ||||
−0.281683 | + | 0.959507i | \(0.590893\pi\) | |||||||
\(864\) | 1.46049 | 0.0496869 | ||||||||
\(865\) | −8.76752 | −0.298105 | ||||||||
\(866\) | −20.4028 | −0.693316 | ||||||||
\(867\) | 6.37325 | 0.216447 | ||||||||
\(868\) | −6.33956 | −0.215179 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.721318 | 0.0244550 | ||||||||
\(871\) | −16.3749 | −0.554842 | ||||||||
\(872\) | −12.1283 | −0.410715 | ||||||||
\(873\) | −10.1545 | −0.343679 | ||||||||
\(874\) | 28.5370 | 0.965277 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −1.77834 | −0.0600844 | ||||||||
\(877\) | −48.1835 | −1.62704 | −0.813521 | − | 0.581535i | \(-0.802452\pi\) | ||||
−0.813521 | + | 0.581535i | \(0.802452\pi\) | |||||||
\(878\) | −17.5292 | −0.591581 | ||||||||
\(879\) | −4.47652 | −0.150989 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.1700 | −1.42074 | −0.710372 | − | 0.703827i | \(-0.751473\pi\) | ||||
−0.710372 | + | 0.703827i | \(0.751473\pi\) | |||||||
\(882\) | 2.93954 | 0.0989794 | ||||||||
\(883\) | 39.2105 | 1.31954 | 0.659769 | − | 0.751468i | \(-0.270654\pi\) | ||||
0.659769 | + | 0.751468i | \(0.270654\pi\) | |||||||
\(884\) | −7.54684 | −0.253828 | ||||||||
\(885\) | −0.551204 | −0.0185285 | ||||||||
\(886\) | 26.1950 | 0.880038 | ||||||||
\(887\) | 45.0473 | 1.51254 | 0.756270 | − | 0.654260i | \(-0.227020\pi\) | ||||
0.756270 | + | 0.654260i | \(0.227020\pi\) | |||||||
\(888\) | 0.950972 | 0.0319125 | ||||||||
\(889\) | −0.818399 | −0.0274482 | ||||||||
\(890\) | 4.48891 | 0.150468 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.30846 | 0.278188 | ||||||||
\(893\) | 21.1926 | 0.709184 | ||||||||
\(894\) | 1.06347 | 0.0355679 | ||||||||
\(895\) | 15.0279 | 0.502328 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −2.35341 | −0.0785780 | ||||||||
\(898\) | 9.49700 | 0.316919 | ||||||||
\(899\) | 18.5969 | 0.620241 | ||||||||
\(900\) | −2.93954 | −0.0979846 | ||||||||
\(901\) | 35.0937 | 1.16914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.727233 | −0.0242008 | ||||||||
\(904\) | −14.5100 | −0.482595 | ||||||||
\(905\) | 21.1888 | 0.704338 | ||||||||
\(906\) | 4.30662 | 0.143078 | ||||||||
\(907\) | 36.8904 | 1.22493 | 0.612463 | − | 0.790499i | \(-0.290179\pi\) | ||||
0.612463 | + | 0.790499i | \(0.290179\pi\) | |||||||
\(908\) | −15.7302 | −0.522023 | ||||||||
\(909\) | −7.98708 | −0.264915 | ||||||||
\(910\) | 1.15197 | 0.0381874 | ||||||||
\(911\) | −20.6591 | −0.684468 | −0.342234 | − | 0.939615i | \(-0.611183\pi\) | ||||
−0.342234 | + | 0.939615i | \(0.611183\pi\) | |||||||
\(912\) | −0.844585 | −0.0279670 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −17.5412 | −0.580213 | ||||||||
\(915\) | −2.45536 | −0.0811716 | ||||||||
\(916\) | −23.7309 | −0.784090 | ||||||||
\(917\) | 9.76900 | 0.322601 | ||||||||
\(918\) | 9.56802 | 0.315792 | ||||||||
\(919\) | 40.3012 | 1.32941 | 0.664706 | − | 0.747105i | \(-0.268557\pi\) | ||||
0.664706 | + | 0.747105i | \(0.268557\pi\) | |||||||
\(920\) | −8.30827 | −0.273915 | ||||||||
\(921\) | 5.84558 | 0.192618 | ||||||||
\(922\) | 22.6720 | 0.746662 | ||||||||
\(923\) | 0.438002 | 0.0144170 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.86743 | −0.127160 | ||||||||
\(926\) | 26.9554 | 0.885809 | ||||||||
\(927\) | 29.1291 | 0.956724 | ||||||||
\(928\) | 2.93346 | 0.0962957 | ||||||||
\(929\) | −7.46775 | −0.245009 | −0.122504 | − | 0.992468i | \(-0.539093\pi\) | ||||
−0.122504 | + | 0.992468i | \(0.539093\pi\) | |||||||
\(930\) | 1.55885 | 0.0511168 | ||||||||
\(931\) | −3.43477 | −0.112570 | ||||||||
\(932\) | 11.9023 | 0.389872 | ||||||||
\(933\) | −4.48777 | −0.146923 | ||||||||
\(934\) | −14.7718 | −0.483348 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.38626 | −0.110683 | ||||||||
\(937\) | −23.6513 | −0.772656 | −0.386328 | − | 0.922362i | \(-0.626257\pi\) | ||||
−0.386328 | + | 0.922362i | \(0.626257\pi\) | |||||||
\(938\) | −14.2147 | −0.464126 | ||||||||
\(939\) | −4.03273 | −0.131603 | ||||||||
\(940\) | −6.17003 | −0.201244 | ||||||||
\(941\) | −34.0226 | −1.10911 | −0.554553 | − | 0.832148i | \(-0.687111\pi\) | ||||
−0.554553 | + | 0.832148i | \(0.687111\pi\) | |||||||
\(942\) | −2.01739 | −0.0657301 | ||||||||
\(943\) | −87.7006 | −2.85592 | ||||||||
\(944\) | −2.24164 | −0.0729593 | ||||||||
\(945\) | −1.46049 | −0.0475097 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.1828 | 0.525871 | 0.262935 | − | 0.964813i | \(-0.415309\pi\) | ||||
0.262935 | + | 0.964813i | \(0.415309\pi\) | |||||||
\(948\) | −0.559114 | −0.0181592 | ||||||||
\(949\) | 8.33123 | 0.270443 | ||||||||
\(950\) | 3.43477 | 0.111439 | ||||||||
\(951\) | −6.46285 | −0.209572 | ||||||||
\(952\) | −6.55125 | −0.212327 | ||||||||
\(953\) | 55.1879 | 1.78771 | 0.893855 | − | 0.448356i | \(-0.147990\pi\) | ||||
0.893855 | + | 0.448356i | \(0.147990\pi\) | |||||||
\(954\) | 15.7465 | 0.509812 | ||||||||
\(955\) | 4.05200 | 0.131120 | ||||||||
\(956\) | −21.8184 | −0.705659 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.8220 | 1.02812 | ||||||||
\(959\) | −6.68920 | −0.216006 | ||||||||
\(960\) | 0.245893 | 0.00793616 | ||||||||
\(961\) | 9.19006 | 0.296453 | ||||||||
\(962\) | −4.45516 | −0.143640 | ||||||||
\(963\) | −15.2470 | −0.491328 | ||||||||
\(964\) | −14.7413 | −0.474785 | ||||||||
\(965\) | −20.5136 | −0.660358 | ||||||||
\(966\) | −2.04294 | −0.0657306 | ||||||||
\(967\) | −48.0059 | −1.54376 | −0.771882 | − | 0.635765i | \(-0.780685\pi\) | ||||
−0.771882 | + | 0.635765i | \(0.780685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.53308 | −0.177748 | ||||||||
\(970\) | −3.45447 | −0.110916 | ||||||||
\(971\) | 8.41693 | 0.270112 | 0.135056 | − | 0.990838i | \(-0.456879\pi\) | ||||
0.135056 | + | 0.990838i | \(0.456879\pi\) | |||||||
\(972\) | 6.46159 | 0.207256 | ||||||||
\(973\) | −8.85349 | −0.283830 | ||||||||
\(974\) | −24.8664 | −0.796772 | ||||||||
\(975\) | −0.283261 | −0.00907162 | ||||||||
\(976\) | −9.98548 | −0.319627 | ||||||||
\(977\) | 33.7222 | 1.07887 | 0.539435 | − | 0.842027i | \(-0.318638\pi\) | ||||
0.539435 | + | 0.842027i | \(0.318638\pi\) | |||||||
\(978\) | 2.81758 | 0.0900962 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | −35.6515 | −1.13827 | ||||||||
\(982\) | 41.8496 | 1.33547 | ||||||||
\(983\) | 16.3099 | 0.520205 | 0.260102 | − | 0.965581i | \(-0.416244\pi\) | ||||
0.260102 | + | 0.965581i | \(0.416244\pi\) | |||||||
\(984\) | 2.59560 | 0.0827447 | ||||||||
\(985\) | −20.4398 | −0.651267 | ||||||||
\(986\) | 19.2178 | 0.612021 | ||||||||
\(987\) | −1.51717 | −0.0482919 | ||||||||
\(988\) | 3.95675 | 0.125881 | ||||||||
\(989\) | −24.5719 | −0.781340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.23518 | 0.0392367 | 0.0196183 | − | 0.999808i | \(-0.493755\pi\) | ||||
0.0196183 | + | 0.999808i | \(0.493755\pi\) | |||||||
\(992\) | 6.33956 | 0.201281 | ||||||||
\(993\) | 6.06381 | 0.192429 | ||||||||
\(994\) | 0.380220 | 0.0120599 | ||||||||
\(995\) | −3.23576 | −0.102581 | ||||||||
\(996\) | −2.78578 | −0.0882708 | ||||||||
\(997\) | −8.45647 | −0.267819 | −0.133909 | − | 0.990994i | \(-0.542753\pi\) | ||||
−0.133909 | + | 0.990994i | \(0.542753\pi\) | |||||||
\(998\) | −24.8351 | −0.786140 | ||||||||
\(999\) | 5.64834 | 0.178705 |
(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.cw.1.4 | 6 | ||
11.5 | even | 5 | 770.2.n.j.421.2 | ✓ | 12 | ||
11.9 | even | 5 | 770.2.n.j.631.2 | yes | 12 | ||
11.10 | odd | 2 | 8470.2.a.dc.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.j.421.2 | ✓ | 12 | 11.5 | even | 5 | ||
770.2.n.j.631.2 | yes | 12 | 11.9 | even | 5 | ||
8470.2.a.cw.1.4 | 6 | 1.1 | even | 1 | trivial | ||
8470.2.a.dc.1.4 | 6 | 11.10 | odd | 2 |