Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(95\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −2.22303 | −1.28346 | −0.641732 | − | 0.766929i | \(-0.721784\pi\) | ||||
−0.641732 | + | 0.766929i | \(0.721784\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.84239 | −0.823941 | −0.411970 | − | 0.911197i | \(-0.635159\pi\) | ||||
−0.411970 | + | 0.911197i | \(0.635159\pi\) | |||||||
\(6\) | −2.22303 | −0.907546 | ||||||||
\(7\) | 1.24832 | 0.471820 | 0.235910 | − | 0.971775i | \(-0.424193\pi\) | ||||
0.235910 | + | 0.971775i | \(0.424193\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.94184 | 0.647281 | ||||||||
\(10\) | −1.84239 | −0.582614 | ||||||||
\(11\) | −1.09381 | −0.329795 | −0.164898 | − | 0.986311i | \(-0.552729\pi\) | ||||
−0.164898 | + | 0.986311i | \(0.552729\pi\) | |||||||
\(12\) | −2.22303 | −0.641732 | ||||||||
\(13\) | −5.48845 | −1.52222 | −0.761112 | − | 0.648621i | \(-0.775346\pi\) | ||||
−0.761112 | + | 0.648621i | \(0.775346\pi\) | |||||||
\(14\) | 1.24832 | 0.333627 | ||||||||
\(15\) | 4.09568 | 1.05750 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.04073 | −0.737485 | −0.368742 | − | 0.929532i | \(-0.620212\pi\) | ||||
−0.368742 | + | 0.929532i | \(0.620212\pi\) | |||||||
\(18\) | 1.94184 | 0.457697 | ||||||||
\(19\) | 6.62860 | 1.52071 | 0.760353 | − | 0.649510i | \(-0.225026\pi\) | ||||
0.760353 | + | 0.649510i | \(0.225026\pi\) | |||||||
\(20\) | −1.84239 | −0.411970 | ||||||||
\(21\) | −2.77505 | −0.605565 | ||||||||
\(22\) | −1.09381 | −0.233200 | ||||||||
\(23\) | 1.09612 | 0.228557 | 0.114279 | − | 0.993449i | \(-0.463544\pi\) | ||||
0.114279 | + | 0.993449i | \(0.463544\pi\) | |||||||
\(24\) | −2.22303 | −0.453773 | ||||||||
\(25\) | −1.60561 | −0.321121 | ||||||||
\(26\) | −5.48845 | −1.07637 | ||||||||
\(27\) | 2.35231 | 0.452702 | ||||||||
\(28\) | 1.24832 | 0.235910 | ||||||||
\(29\) | −9.70507 | −1.80219 | −0.901093 | − | 0.433626i | \(-0.857234\pi\) | ||||
−0.901093 | + | 0.433626i | \(0.857234\pi\) | |||||||
\(30\) | 4.09568 | 0.747765 | ||||||||
\(31\) | −3.13129 | −0.562397 | −0.281198 | − | 0.959650i | \(-0.590732\pi\) | ||||
−0.281198 | + | 0.959650i | \(0.590732\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.43156 | 0.423280 | ||||||||
\(34\) | −3.04073 | −0.521481 | ||||||||
\(35\) | −2.29989 | −0.388752 | ||||||||
\(36\) | 1.94184 | 0.323640 | ||||||||
\(37\) | 5.21032 | 0.856572 | 0.428286 | − | 0.903643i | \(-0.359118\pi\) | ||||
0.428286 | + | 0.903643i | \(0.359118\pi\) | |||||||
\(38\) | 6.62860 | 1.07530 | ||||||||
\(39\) | 12.2010 | 1.95372 | ||||||||
\(40\) | −1.84239 | −0.291307 | ||||||||
\(41\) | 3.75054 | 0.585736 | 0.292868 | − | 0.956153i | \(-0.405390\pi\) | ||||
0.292868 | + | 0.956153i | \(0.405390\pi\) | |||||||
\(42\) | −2.77505 | −0.428199 | ||||||||
\(43\) | −2.33949 | −0.356769 | −0.178385 | − | 0.983961i | \(-0.557087\pi\) | ||||
−0.178385 | + | 0.983961i | \(0.557087\pi\) | |||||||
\(44\) | −1.09381 | −0.164898 | ||||||||
\(45\) | −3.57763 | −0.533321 | ||||||||
\(46\) | 1.09612 | 0.161614 | ||||||||
\(47\) | −3.47861 | −0.507407 | −0.253703 | − | 0.967282i | \(-0.581649\pi\) | ||||
−0.253703 | + | 0.967282i | \(0.581649\pi\) | |||||||
\(48\) | −2.22303 | −0.320866 | ||||||||
\(49\) | −5.44170 | −0.777385 | ||||||||
\(50\) | −1.60561 | −0.227067 | ||||||||
\(51\) | 6.75962 | 0.946536 | ||||||||
\(52\) | −5.48845 | −0.761112 | ||||||||
\(53\) | −5.70073 | −0.783056 | −0.391528 | − | 0.920166i | \(-0.628053\pi\) | ||||
−0.391528 | + | 0.920166i | \(0.628053\pi\) | |||||||
\(54\) | 2.35231 | 0.320109 | ||||||||
\(55\) | 2.01522 | 0.271732 | ||||||||
\(56\) | 1.24832 | 0.166814 | ||||||||
\(57\) | −14.7356 | −1.95177 | ||||||||
\(58\) | −9.70507 | −1.27434 | ||||||||
\(59\) | 6.61961 | 0.861799 | 0.430900 | − | 0.902400i | \(-0.358196\pi\) | ||||
0.430900 | + | 0.902400i | \(0.358196\pi\) | |||||||
\(60\) | 4.09568 | 0.528749 | ||||||||
\(61\) | −1.94182 | −0.248625 | −0.124312 | − | 0.992243i | \(-0.539673\pi\) | ||||
−0.124312 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(62\) | −3.13129 | −0.397675 | ||||||||
\(63\) | 2.42404 | 0.305400 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.1119 | 1.25422 | ||||||||
\(66\) | 2.43156 | 0.299304 | ||||||||
\(67\) | 1.81145 | 0.221304 | 0.110652 | − | 0.993859i | \(-0.464706\pi\) | ||||
0.110652 | + | 0.993859i | \(0.464706\pi\) | |||||||
\(68\) | −3.04073 | −0.368742 | ||||||||
\(69\) | −2.43671 | −0.293345 | ||||||||
\(70\) | −2.29989 | −0.274889 | ||||||||
\(71\) | −1.19425 | −0.141732 | −0.0708659 | − | 0.997486i | \(-0.522576\pi\) | ||||
−0.0708659 | + | 0.997486i | \(0.522576\pi\) | |||||||
\(72\) | 1.94184 | 0.228848 | ||||||||
\(73\) | 1.38065 | 0.161592 | 0.0807962 | − | 0.996731i | \(-0.474254\pi\) | ||||
0.0807962 | + | 0.996731i | \(0.474254\pi\) | |||||||
\(74\) | 5.21032 | 0.605688 | ||||||||
\(75\) | 3.56930 | 0.412148 | ||||||||
\(76\) | 6.62860 | 0.760353 | ||||||||
\(77\) | −1.36542 | −0.155604 | ||||||||
\(78\) | 12.2010 | 1.38149 | ||||||||
\(79\) | −9.55379 | −1.07488 | −0.537442 | − | 0.843300i | \(-0.680609\pi\) | ||||
−0.537442 | + | 0.843300i | \(0.680609\pi\) | |||||||
\(80\) | −1.84239 | −0.205985 | ||||||||
\(81\) | −11.0548 | −1.22831 | ||||||||
\(82\) | 3.75054 | 0.414178 | ||||||||
\(83\) | 12.4170 | 1.36295 | 0.681473 | − | 0.731843i | \(-0.261340\pi\) | ||||
0.681473 | + | 0.731843i | \(0.261340\pi\) | |||||||
\(84\) | −2.77505 | −0.302782 | ||||||||
\(85\) | 5.60220 | 0.607644 | ||||||||
\(86\) | −2.33949 | −0.252274 | ||||||||
\(87\) | 21.5746 | 2.31304 | ||||||||
\(88\) | −1.09381 | −0.116600 | ||||||||
\(89\) | 12.8515 | 1.36226 | 0.681128 | − | 0.732165i | \(-0.261490\pi\) | ||||
0.681128 | + | 0.732165i | \(0.261490\pi\) | |||||||
\(90\) | −3.57763 | −0.377115 | ||||||||
\(91\) | −6.85134 | −0.718216 | ||||||||
\(92\) | 1.09612 | 0.114279 | ||||||||
\(93\) | 6.96095 | 0.721816 | ||||||||
\(94\) | −3.47861 | −0.358791 | ||||||||
\(95\) | −12.2125 | −1.25297 | ||||||||
\(96\) | −2.22303 | −0.226887 | ||||||||
\(97\) | −4.57839 | −0.464865 | −0.232433 | − | 0.972612i | \(-0.574669\pi\) | ||||
−0.232433 | + | 0.972612i | \(0.574669\pi\) | |||||||
\(98\) | −5.44170 | −0.549695 | ||||||||
\(99\) | −2.12400 | −0.213470 | ||||||||
\(100\) | −1.60561 | −0.160561 | ||||||||
\(101\) | −11.0170 | −1.09623 | −0.548116 | − | 0.836403i | \(-0.684655\pi\) | ||||
−0.548116 | + | 0.836403i | \(0.684655\pi\) | |||||||
\(102\) | 6.75962 | 0.669302 | ||||||||
\(103\) | −11.5103 | −1.13415 | −0.567073 | − | 0.823667i | \(-0.691924\pi\) | ||||
−0.567073 | + | 0.823667i | \(0.691924\pi\) | |||||||
\(104\) | −5.48845 | −0.538187 | ||||||||
\(105\) | 5.11271 | 0.498950 | ||||||||
\(106\) | −5.70073 | −0.553704 | ||||||||
\(107\) | 10.6131 | 1.02601 | 0.513005 | − | 0.858386i | \(-0.328532\pi\) | ||||
0.513005 | + | 0.858386i | \(0.328532\pi\) | |||||||
\(108\) | 2.35231 | 0.226351 | ||||||||
\(109\) | 10.3963 | 0.995782 | 0.497891 | − | 0.867240i | \(-0.334108\pi\) | ||||
0.497891 | + | 0.867240i | \(0.334108\pi\) | |||||||
\(110\) | 2.01522 | 0.192143 | ||||||||
\(111\) | −11.5827 | −1.09938 | ||||||||
\(112\) | 1.24832 | 0.117955 | ||||||||
\(113\) | −5.68217 | −0.534533 | −0.267267 | − | 0.963623i | \(-0.586120\pi\) | ||||
−0.267267 | + | 0.963623i | \(0.586120\pi\) | |||||||
\(114\) | −14.7356 | −1.38011 | ||||||||
\(115\) | −2.01948 | −0.188318 | ||||||||
\(116\) | −9.70507 | −0.901093 | ||||||||
\(117\) | −10.6577 | −0.985306 | ||||||||
\(118\) | 6.61961 | 0.609384 | ||||||||
\(119\) | −3.79580 | −0.347960 | ||||||||
\(120\) | 4.09568 | 0.373882 | ||||||||
\(121\) | −9.80359 | −0.891235 | ||||||||
\(122\) | −1.94182 | −0.175804 | ||||||||
\(123\) | −8.33754 | −0.751771 | ||||||||
\(124\) | −3.13129 | −0.281198 | ||||||||
\(125\) | 12.1701 | 1.08853 | ||||||||
\(126\) | 2.42404 | 0.215951 | ||||||||
\(127\) | 14.0797 | 1.24937 | 0.624686 | − | 0.780876i | \(-0.285227\pi\) | ||||
0.624686 | + | 0.780876i | \(0.285227\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.20075 | 0.457901 | ||||||||
\(130\) | 10.1119 | 0.886869 | ||||||||
\(131\) | 19.4452 | 1.69893 | 0.849466 | − | 0.527643i | \(-0.176924\pi\) | ||||
0.849466 | + | 0.527643i | \(0.176924\pi\) | |||||||
\(132\) | 2.43156 | 0.211640 | ||||||||
\(133\) | 8.27462 | 0.717500 | ||||||||
\(134\) | 1.81145 | 0.156485 | ||||||||
\(135\) | −4.33387 | −0.373000 | ||||||||
\(136\) | −3.04073 | −0.260740 | ||||||||
\(137\) | 3.66236 | 0.312896 | 0.156448 | − | 0.987686i | \(-0.449996\pi\) | ||||
0.156448 | + | 0.987686i | \(0.449996\pi\) | |||||||
\(138\) | −2.43671 | −0.207426 | ||||||||
\(139\) | −8.43371 | −0.715338 | −0.357669 | − | 0.933848i | \(-0.616428\pi\) | ||||
−0.357669 | + | 0.933848i | \(0.616428\pi\) | |||||||
\(140\) | −2.29989 | −0.194376 | ||||||||
\(141\) | 7.73303 | 0.651239 | ||||||||
\(142\) | −1.19425 | −0.100220 | ||||||||
\(143\) | 6.00331 | 0.502022 | ||||||||
\(144\) | 1.94184 | 0.161820 | ||||||||
\(145\) | 17.8805 | 1.48490 | ||||||||
\(146\) | 1.38065 | 0.114263 | ||||||||
\(147\) | 12.0970 | 0.997747 | ||||||||
\(148\) | 5.21032 | 0.428286 | ||||||||
\(149\) | −23.6461 | −1.93717 | −0.968583 | − | 0.248689i | \(-0.920000\pi\) | ||||
−0.968583 | + | 0.248689i | \(0.920000\pi\) | |||||||
\(150\) | 3.56930 | 0.291433 | ||||||||
\(151\) | 13.2692 | 1.07983 | 0.539914 | − | 0.841720i | \(-0.318457\pi\) | ||||
0.539914 | + | 0.841720i | \(0.318457\pi\) | |||||||
\(152\) | 6.62860 | 0.537651 | ||||||||
\(153\) | −5.90462 | −0.477360 | ||||||||
\(154\) | −1.36542 | −0.110029 | ||||||||
\(155\) | 5.76906 | 0.463382 | ||||||||
\(156\) | 12.2010 | 0.976860 | ||||||||
\(157\) | −3.20259 | −0.255595 | −0.127797 | − | 0.991800i | \(-0.540791\pi\) | ||||
−0.127797 | + | 0.991800i | \(0.540791\pi\) | |||||||
\(158\) | −9.55379 | −0.760058 | ||||||||
\(159\) | 12.6729 | 1.00502 | ||||||||
\(160\) | −1.84239 | −0.145654 | ||||||||
\(161\) | 1.36831 | 0.107838 | ||||||||
\(162\) | −11.0548 | −0.868545 | ||||||||
\(163\) | 8.37302 | 0.655825 | 0.327913 | − | 0.944708i | \(-0.393655\pi\) | ||||
0.327913 | + | 0.944708i | \(0.393655\pi\) | |||||||
\(164\) | 3.75054 | 0.292868 | ||||||||
\(165\) | −4.47988 | −0.348758 | ||||||||
\(166\) | 12.4170 | 0.963749 | ||||||||
\(167\) | 3.94105 | 0.304968 | 0.152484 | − | 0.988306i | \(-0.451273\pi\) | ||||
0.152484 | + | 0.988306i | \(0.451273\pi\) | |||||||
\(168\) | −2.77505 | −0.214099 | ||||||||
\(169\) | 17.1231 | 1.31716 | ||||||||
\(170\) | 5.60220 | 0.429669 | ||||||||
\(171\) | 12.8717 | 0.984324 | ||||||||
\(172\) | −2.33949 | −0.178385 | ||||||||
\(173\) | −17.8769 | −1.35916 | −0.679580 | − | 0.733602i | \(-0.737838\pi\) | ||||
−0.679580 | + | 0.733602i | \(0.737838\pi\) | |||||||
\(174\) | 21.5746 | 1.63557 | ||||||||
\(175\) | −2.00431 | −0.151512 | ||||||||
\(176\) | −1.09381 | −0.0824488 | ||||||||
\(177\) | −14.7156 | −1.10609 | ||||||||
\(178\) | 12.8515 | 0.963260 | ||||||||
\(179\) | 25.2144 | 1.88461 | 0.942306 | − | 0.334753i | \(-0.108653\pi\) | ||||
0.942306 | + | 0.334753i | \(0.108653\pi\) | |||||||
\(180\) | −3.57763 | −0.266661 | ||||||||
\(181\) | −24.1061 | −1.79179 | −0.895896 | − | 0.444263i | \(-0.853466\pi\) | ||||
−0.895896 | + | 0.444263i | \(0.853466\pi\) | |||||||
\(182\) | −6.85134 | −0.507855 | ||||||||
\(183\) | 4.31672 | 0.319101 | ||||||||
\(184\) | 1.09612 | 0.0808072 | ||||||||
\(185\) | −9.59944 | −0.705765 | ||||||||
\(186\) | 6.96095 | 0.510401 | ||||||||
\(187\) | 3.32597 | 0.243219 | ||||||||
\(188\) | −3.47861 | −0.253703 | ||||||||
\(189\) | 2.93644 | 0.213594 | ||||||||
\(190\) | −12.2125 | −0.885985 | ||||||||
\(191\) | −2.26690 | −0.164027 | −0.0820135 | − | 0.996631i | \(-0.526135\pi\) | ||||
−0.0820135 | + | 0.996631i | \(0.526135\pi\) | |||||||
\(192\) | −2.22303 | −0.160433 | ||||||||
\(193\) | −19.5256 | −1.40548 | −0.702741 | − | 0.711446i | \(-0.748041\pi\) | ||||
−0.702741 | + | 0.711446i | \(0.748041\pi\) | |||||||
\(194\) | −4.57839 | −0.328709 | ||||||||
\(195\) | −22.4789 | −1.60975 | ||||||||
\(196\) | −5.44170 | −0.388693 | ||||||||
\(197\) | 22.9860 | 1.63768 | 0.818842 | − | 0.574018i | \(-0.194616\pi\) | ||||
0.818842 | + | 0.574018i | \(0.194616\pi\) | |||||||
\(198\) | −2.12400 | −0.150946 | ||||||||
\(199\) | 12.1639 | 0.862276 | 0.431138 | − | 0.902286i | \(-0.358112\pi\) | ||||
0.431138 | + | 0.902286i | \(0.358112\pi\) | |||||||
\(200\) | −1.60561 | −0.113534 | ||||||||
\(201\) | −4.02690 | −0.284035 | ||||||||
\(202\) | −11.0170 | −0.775152 | ||||||||
\(203\) | −12.1150 | −0.850308 | ||||||||
\(204\) | 6.75962 | 0.473268 | ||||||||
\(205\) | −6.90995 | −0.482612 | ||||||||
\(206\) | −11.5103 | −0.801963 | ||||||||
\(207\) | 2.12850 | 0.147941 | ||||||||
\(208\) | −5.48845 | −0.380556 | ||||||||
\(209\) | −7.25041 | −0.501521 | ||||||||
\(210\) | 5.11271 | 0.352811 | ||||||||
\(211\) | −11.0249 | −0.758988 | −0.379494 | − | 0.925194i | \(-0.623902\pi\) | ||||
−0.379494 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(212\) | −5.70073 | −0.391528 | ||||||||
\(213\) | 2.65486 | 0.181908 | ||||||||
\(214\) | 10.6131 | 0.725499 | ||||||||
\(215\) | 4.31025 | 0.293957 | ||||||||
\(216\) | 2.35231 | 0.160054 | ||||||||
\(217\) | −3.90885 | −0.265350 | ||||||||
\(218\) | 10.3963 | 0.704124 | ||||||||
\(219\) | −3.06921 | −0.207398 | ||||||||
\(220\) | 2.01522 | 0.135866 | ||||||||
\(221\) | 16.6889 | 1.12262 | ||||||||
\(222\) | −11.5827 | −0.777379 | ||||||||
\(223\) | −21.8149 | −1.46083 | −0.730416 | − | 0.683003i | \(-0.760674\pi\) | ||||
−0.730416 | + | 0.683003i | \(0.760674\pi\) | |||||||
\(224\) | 1.24832 | 0.0834069 | ||||||||
\(225\) | −3.11784 | −0.207856 | ||||||||
\(226\) | −5.68217 | −0.377972 | ||||||||
\(227\) | 23.4640 | 1.55736 | 0.778682 | − | 0.627419i | \(-0.215889\pi\) | ||||
0.778682 | + | 0.627419i | \(0.215889\pi\) | |||||||
\(228\) | −14.7356 | −0.975886 | ||||||||
\(229\) | −8.00993 | −0.529311 | −0.264655 | − | 0.964343i | \(-0.585258\pi\) | ||||
−0.264655 | + | 0.964343i | \(0.585258\pi\) | |||||||
\(230\) | −2.01948 | −0.133161 | ||||||||
\(231\) | 3.03536 | 0.199712 | ||||||||
\(232\) | −9.70507 | −0.637169 | ||||||||
\(233\) | 14.4560 | 0.947041 | 0.473521 | − | 0.880783i | \(-0.342983\pi\) | ||||
0.473521 | + | 0.880783i | \(0.342983\pi\) | |||||||
\(234\) | −10.6577 | −0.696717 | ||||||||
\(235\) | 6.40894 | 0.418073 | ||||||||
\(236\) | 6.61961 | 0.430900 | ||||||||
\(237\) | 21.2383 | 1.37958 | ||||||||
\(238\) | −3.79580 | −0.246045 | ||||||||
\(239\) | 5.47930 | 0.354426 | 0.177213 | − | 0.984173i | \(-0.443292\pi\) | ||||
0.177213 | + | 0.984173i | \(0.443292\pi\) | |||||||
\(240\) | 4.09568 | 0.264375 | ||||||||
\(241\) | 22.0387 | 1.41964 | 0.709820 | − | 0.704383i | \(-0.248776\pi\) | ||||
0.709820 | + | 0.704383i | \(0.248776\pi\) | |||||||
\(242\) | −9.80359 | −0.630198 | ||||||||
\(243\) | 17.5181 | 1.12379 | ||||||||
\(244\) | −1.94182 | −0.124312 | ||||||||
\(245\) | 10.0257 | 0.640520 | ||||||||
\(246\) | −8.33754 | −0.531582 | ||||||||
\(247\) | −36.3808 | −2.31485 | ||||||||
\(248\) | −3.13129 | −0.198837 | ||||||||
\(249\) | −27.6034 | −1.74929 | ||||||||
\(250\) | 12.1701 | 0.769704 | ||||||||
\(251\) | 18.3170 | 1.15616 | 0.578080 | − | 0.815980i | \(-0.303802\pi\) | ||||
0.578080 | + | 0.815980i | \(0.303802\pi\) | |||||||
\(252\) | 2.42404 | 0.152700 | ||||||||
\(253\) | −1.19895 | −0.0753771 | ||||||||
\(254\) | 14.0797 | 0.883439 | ||||||||
\(255\) | −12.4538 | −0.779889 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.3720 | 1.45791 | 0.728953 | − | 0.684564i | \(-0.240007\pi\) | ||||
0.728953 | + | 0.684564i | \(0.240007\pi\) | |||||||
\(258\) | 5.20075 | 0.323785 | ||||||||
\(259\) | 6.50415 | 0.404148 | ||||||||
\(260\) | 10.1119 | 0.627111 | ||||||||
\(261\) | −18.8457 | −1.16652 | ||||||||
\(262\) | 19.4452 | 1.20133 | ||||||||
\(263\) | 15.2298 | 0.939110 | 0.469555 | − | 0.882903i | \(-0.344414\pi\) | ||||
0.469555 | + | 0.882903i | \(0.344414\pi\) | |||||||
\(264\) | 2.43156 | 0.149652 | ||||||||
\(265\) | 10.5030 | 0.645192 | ||||||||
\(266\) | 8.27462 | 0.507349 | ||||||||
\(267\) | −28.5692 | −1.74841 | ||||||||
\(268\) | 1.81145 | 0.110652 | ||||||||
\(269\) | 24.5727 | 1.49822 | 0.749111 | − | 0.662445i | \(-0.230481\pi\) | ||||
0.749111 | + | 0.662445i | \(0.230481\pi\) | |||||||
\(270\) | −4.33387 | −0.263751 | ||||||||
\(271\) | 0.531606 | 0.0322928 | 0.0161464 | − | 0.999870i | \(-0.494860\pi\) | ||||
0.0161464 | + | 0.999870i | \(0.494860\pi\) | |||||||
\(272\) | −3.04073 | −0.184371 | ||||||||
\(273\) | 15.2307 | 0.921805 | ||||||||
\(274\) | 3.66236 | 0.221251 | ||||||||
\(275\) | 1.75622 | 0.105904 | ||||||||
\(276\) | −2.43671 | −0.146673 | ||||||||
\(277\) | 7.11143 | 0.427284 | 0.213642 | − | 0.976912i | \(-0.431467\pi\) | ||||
0.213642 | + | 0.976912i | \(0.431467\pi\) | |||||||
\(278\) | −8.43371 | −0.505820 | ||||||||
\(279\) | −6.08048 | −0.364029 | ||||||||
\(280\) | −2.29989 | −0.137445 | ||||||||
\(281\) | 4.33769 | 0.258765 | 0.129383 | − | 0.991595i | \(-0.458700\pi\) | ||||
0.129383 | + | 0.991595i | \(0.458700\pi\) | |||||||
\(282\) | 7.73303 | 0.460495 | ||||||||
\(283\) | −2.76378 | −0.164289 | −0.0821447 | − | 0.996620i | \(-0.526177\pi\) | ||||
−0.0821447 | + | 0.996620i | \(0.526177\pi\) | |||||||
\(284\) | −1.19425 | −0.0708659 | ||||||||
\(285\) | 27.1486 | 1.60814 | ||||||||
\(286\) | 6.00331 | 0.354983 | ||||||||
\(287\) | 4.68187 | 0.276362 | ||||||||
\(288\) | 1.94184 | 0.114424 | ||||||||
\(289\) | −7.75397 | −0.456116 | ||||||||
\(290\) | 17.8805 | 1.04998 | ||||||||
\(291\) | 10.1779 | 0.596638 | ||||||||
\(292\) | 1.38065 | 0.0807962 | ||||||||
\(293\) | 21.5468 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(294\) | 12.0970 | 0.705513 | ||||||||
\(295\) | −12.1959 | −0.710072 | ||||||||
\(296\) | 5.21032 | 0.302844 | ||||||||
\(297\) | −2.57297 | −0.149299 | ||||||||
\(298\) | −23.6461 | −1.36978 | ||||||||
\(299\) | −6.01602 | −0.347915 | ||||||||
\(300\) | 3.56930 | 0.206074 | ||||||||
\(301\) | −2.92043 | −0.168331 | ||||||||
\(302\) | 13.2692 | 0.763554 | ||||||||
\(303\) | 24.4910 | 1.40697 | ||||||||
\(304\) | 6.62860 | 0.380176 | ||||||||
\(305\) | 3.57759 | 0.204852 | ||||||||
\(306\) | −5.90462 | −0.337544 | ||||||||
\(307\) | 26.9463 | 1.53791 | 0.768953 | − | 0.639306i | \(-0.220778\pi\) | ||||
0.768953 | + | 0.639306i | \(0.220778\pi\) | |||||||
\(308\) | −1.36542 | −0.0778020 | ||||||||
\(309\) | 25.5878 | 1.45564 | ||||||||
\(310\) | 5.76906 | 0.327660 | ||||||||
\(311\) | 14.0062 | 0.794218 | 0.397109 | − | 0.917771i | \(-0.370013\pi\) | ||||
0.397109 | + | 0.917771i | \(0.370013\pi\) | |||||||
\(312\) | 12.2010 | 0.690744 | ||||||||
\(313\) | 4.91789 | 0.277976 | 0.138988 | − | 0.990294i | \(-0.455615\pi\) | ||||
0.138988 | + | 0.990294i | \(0.455615\pi\) | |||||||
\(314\) | −3.20259 | −0.180733 | ||||||||
\(315\) | −4.46602 | −0.251632 | ||||||||
\(316\) | −9.55379 | −0.537442 | ||||||||
\(317\) | −17.5254 | −0.984326 | −0.492163 | − | 0.870503i | \(-0.663794\pi\) | ||||
−0.492163 | + | 0.870503i | \(0.663794\pi\) | |||||||
\(318\) | 12.6729 | 0.710659 | ||||||||
\(319\) | 10.6155 | 0.594352 | ||||||||
\(320\) | −1.84239 | −0.102993 | ||||||||
\(321\) | −23.5933 | −1.31685 | ||||||||
\(322\) | 1.36831 | 0.0762530 | ||||||||
\(323\) | −20.1558 | −1.12150 | ||||||||
\(324\) | −11.0548 | −0.614154 | ||||||||
\(325\) | 8.81230 | 0.488818 | ||||||||
\(326\) | 8.37302 | 0.463739 | ||||||||
\(327\) | −23.1112 | −1.27805 | ||||||||
\(328\) | 3.75054 | 0.207089 | ||||||||
\(329\) | −4.34241 | −0.239405 | ||||||||
\(330\) | −4.47988 | −0.246609 | ||||||||
\(331\) | 22.9977 | 1.26407 | 0.632035 | − | 0.774940i | \(-0.282220\pi\) | ||||
0.632035 | + | 0.774940i | \(0.282220\pi\) | |||||||
\(332\) | 12.4170 | 0.681473 | ||||||||
\(333\) | 10.1176 | 0.554443 | ||||||||
\(334\) | 3.94105 | 0.215645 | ||||||||
\(335\) | −3.33739 | −0.182341 | ||||||||
\(336\) | −2.77505 | −0.151391 | ||||||||
\(337\) | −6.95431 | −0.378825 | −0.189413 | − | 0.981898i | \(-0.560658\pi\) | ||||
−0.189413 | + | 0.981898i | \(0.560658\pi\) | |||||||
\(338\) | 17.1231 | 0.931375 | ||||||||
\(339\) | 12.6316 | 0.686054 | ||||||||
\(340\) | 5.60220 | 0.303822 | ||||||||
\(341\) | 3.42503 | 0.185476 | ||||||||
\(342\) | 12.8717 | 0.696022 | ||||||||
\(343\) | −15.5312 | −0.838607 | ||||||||
\(344\) | −2.33949 | −0.126137 | ||||||||
\(345\) | 4.48936 | 0.241699 | ||||||||
\(346\) | −17.8769 | −0.961071 | ||||||||
\(347\) | 2.71917 | 0.145973 | 0.0729863 | − | 0.997333i | \(-0.476747\pi\) | ||||
0.0729863 | + | 0.997333i | \(0.476747\pi\) | |||||||
\(348\) | 21.5746 | 1.15652 | ||||||||
\(349\) | 6.57908 | 0.352170 | 0.176085 | − | 0.984375i | \(-0.443657\pi\) | ||||
0.176085 | + | 0.984375i | \(0.443657\pi\) | |||||||
\(350\) | −2.00431 | −0.107135 | ||||||||
\(351\) | −12.9105 | −0.689114 | ||||||||
\(352\) | −1.09381 | −0.0583001 | ||||||||
\(353\) | −17.9575 | −0.955781 | −0.477891 | − | 0.878419i | \(-0.658598\pi\) | ||||
−0.477891 | + | 0.878419i | \(0.658598\pi\) | |||||||
\(354\) | −14.7156 | −0.782123 | ||||||||
\(355\) | 2.20028 | 0.116779 | ||||||||
\(356\) | 12.8515 | 0.681128 | ||||||||
\(357\) | 8.43816 | 0.446595 | ||||||||
\(358\) | 25.2144 | 1.33262 | ||||||||
\(359\) | −7.51102 | −0.396416 | −0.198208 | − | 0.980160i | \(-0.563512\pi\) | ||||
−0.198208 | + | 0.980160i | \(0.563512\pi\) | |||||||
\(360\) | −3.57763 | −0.188558 | ||||||||
\(361\) | 24.9384 | 1.31255 | ||||||||
\(362\) | −24.1061 | −1.26699 | ||||||||
\(363\) | 21.7936 | 1.14387 | ||||||||
\(364\) | −6.85134 | −0.359108 | ||||||||
\(365\) | −2.54368 | −0.133143 | ||||||||
\(366\) | 4.31672 | 0.225639 | ||||||||
\(367\) | 20.6962 | 1.08033 | 0.540166 | − | 0.841558i | \(-0.318361\pi\) | ||||
0.540166 | + | 0.841558i | \(0.318361\pi\) | |||||||
\(368\) | 1.09612 | 0.0571393 | ||||||||
\(369\) | 7.28296 | 0.379136 | ||||||||
\(370\) | −9.59944 | −0.499051 | ||||||||
\(371\) | −7.11633 | −0.369462 | ||||||||
\(372\) | 6.96095 | 0.360908 | ||||||||
\(373\) | −1.02232 | −0.0529338 | −0.0264669 | − | 0.999650i | \(-0.508426\pi\) | ||||
−0.0264669 | + | 0.999650i | \(0.508426\pi\) | |||||||
\(374\) | 3.32597 | 0.171982 | ||||||||
\(375\) | −27.0544 | −1.39708 | ||||||||
\(376\) | −3.47861 | −0.179395 | ||||||||
\(377\) | 53.2658 | 2.74333 | ||||||||
\(378\) | 2.93644 | 0.151034 | ||||||||
\(379\) | −27.1713 | −1.39570 | −0.697848 | − | 0.716246i | \(-0.745859\pi\) | ||||
−0.697848 | + | 0.716246i | \(0.745859\pi\) | |||||||
\(380\) | −12.2125 | −0.626486 | ||||||||
\(381\) | −31.2995 | −1.60352 | ||||||||
\(382\) | −2.26690 | −0.115985 | ||||||||
\(383\) | −4.14476 | −0.211787 | −0.105894 | − | 0.994377i | \(-0.533770\pi\) | ||||
−0.105894 | + | 0.994377i | \(0.533770\pi\) | |||||||
\(384\) | −2.22303 | −0.113443 | ||||||||
\(385\) | 2.51563 | 0.128209 | ||||||||
\(386\) | −19.5256 | −0.993826 | ||||||||
\(387\) | −4.54293 | −0.230930 | ||||||||
\(388\) | −4.57839 | −0.232433 | ||||||||
\(389\) | −16.3646 | −0.829721 | −0.414860 | − | 0.909885i | \(-0.636170\pi\) | ||||
−0.414860 | + | 0.909885i | \(0.636170\pi\) | |||||||
\(390\) | −22.4789 | −1.13826 | ||||||||
\(391\) | −3.33301 | −0.168558 | ||||||||
\(392\) | −5.44170 | −0.274847 | ||||||||
\(393\) | −43.2271 | −2.18052 | ||||||||
\(394\) | 22.9860 | 1.15802 | ||||||||
\(395\) | 17.6018 | 0.885642 | ||||||||
\(396\) | −2.12400 | −0.106735 | ||||||||
\(397\) | 23.8452 | 1.19676 | 0.598379 | − | 0.801213i | \(-0.295812\pi\) | ||||
0.598379 | + | 0.801213i | \(0.295812\pi\) | |||||||
\(398\) | 12.1639 | 0.609721 | ||||||||
\(399\) | −18.3947 | −0.920886 | ||||||||
\(400\) | −1.60561 | −0.0802803 | ||||||||
\(401\) | 13.7293 | 0.685610 | 0.342805 | − | 0.939407i | \(-0.388623\pi\) | ||||
0.342805 | + | 0.939407i | \(0.388623\pi\) | |||||||
\(402\) | −4.02690 | −0.200843 | ||||||||
\(403\) | 17.1860 | 0.856094 | ||||||||
\(404\) | −11.0170 | −0.548116 | ||||||||
\(405\) | 20.3672 | 1.01205 | ||||||||
\(406\) | −12.1150 | −0.601259 | ||||||||
\(407\) | −5.69909 | −0.282493 | ||||||||
\(408\) | 6.75962 | 0.334651 | ||||||||
\(409\) | 13.6374 | 0.674324 | 0.337162 | − | 0.941447i | \(-0.390533\pi\) | ||||
0.337162 | + | 0.941447i | \(0.390533\pi\) | |||||||
\(410\) | −6.90995 | −0.341258 | ||||||||
\(411\) | −8.14151 | −0.401591 | ||||||||
\(412\) | −11.5103 | −0.567073 | ||||||||
\(413\) | 8.26339 | 0.406615 | ||||||||
\(414\) | 2.12850 | 0.104610 | ||||||||
\(415\) | −22.8770 | −1.12299 | ||||||||
\(416\) | −5.48845 | −0.269094 | ||||||||
\(417\) | 18.7484 | 0.918111 | ||||||||
\(418\) | −7.25041 | −0.354629 | ||||||||
\(419\) | 12.3966 | 0.605612 | 0.302806 | − | 0.953052i | \(-0.402077\pi\) | ||||
0.302806 | + | 0.953052i | \(0.402077\pi\) | |||||||
\(420\) | 5.11271 | 0.249475 | ||||||||
\(421\) | 28.9782 | 1.41231 | 0.706156 | − | 0.708057i | \(-0.250428\pi\) | ||||
0.706156 | + | 0.708057i | \(0.250428\pi\) | |||||||
\(422\) | −11.0249 | −0.536685 | ||||||||
\(423\) | −6.75491 | −0.328435 | ||||||||
\(424\) | −5.70073 | −0.276852 | ||||||||
\(425\) | 4.88221 | 0.236822 | ||||||||
\(426\) | 2.65486 | 0.128628 | ||||||||
\(427\) | −2.42402 | −0.117306 | ||||||||
\(428\) | 10.6131 | 0.513005 | ||||||||
\(429\) | −13.3455 | −0.644327 | ||||||||
\(430\) | 4.31025 | 0.207859 | ||||||||
\(431\) | −41.1783 | −1.98349 | −0.991746 | − | 0.128221i | \(-0.959073\pi\) | ||||
−0.991746 | + | 0.128221i | \(0.959073\pi\) | |||||||
\(432\) | 2.35231 | 0.113176 | ||||||||
\(433\) | 13.6220 | 0.654634 | 0.327317 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327317 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(434\) | −3.90885 | −0.187631 | ||||||||
\(435\) | −39.7488 | −1.90581 | ||||||||
\(436\) | 10.3963 | 0.497891 | ||||||||
\(437\) | 7.26576 | 0.347568 | ||||||||
\(438\) | −3.06921 | −0.146653 | ||||||||
\(439\) | −17.6779 | −0.843718 | −0.421859 | − | 0.906661i | \(-0.638622\pi\) | ||||
−0.421859 | + | 0.906661i | \(0.638622\pi\) | |||||||
\(440\) | 2.01522 | 0.0960717 | ||||||||
\(441\) | −10.5669 | −0.503187 | ||||||||
\(442\) | 16.6889 | 0.793810 | ||||||||
\(443\) | −1.29910 | −0.0617223 | −0.0308612 | − | 0.999524i | \(-0.509825\pi\) | ||||
−0.0308612 | + | 0.999524i | \(0.509825\pi\) | |||||||
\(444\) | −11.5827 | −0.549690 | ||||||||
\(445\) | −23.6774 | −1.12242 | ||||||||
\(446\) | −21.8149 | −1.03296 | ||||||||
\(447\) | 52.5660 | 2.48628 | ||||||||
\(448\) | 1.24832 | 0.0589776 | ||||||||
\(449\) | 3.37641 | 0.159342 | 0.0796712 | − | 0.996821i | \(-0.474613\pi\) | ||||
0.0796712 | + | 0.996821i | \(0.474613\pi\) | |||||||
\(450\) | −3.11784 | −0.146976 | ||||||||
\(451\) | −4.10236 | −0.193173 | ||||||||
\(452\) | −5.68217 | −0.267267 | ||||||||
\(453\) | −29.4977 | −1.38592 | ||||||||
\(454\) | 23.4640 | 1.10122 | ||||||||
\(455\) | 12.6228 | 0.591768 | ||||||||
\(456\) | −14.7356 | −0.690056 | ||||||||
\(457\) | 41.0130 | 1.91851 | 0.959254 | − | 0.282544i | \(-0.0911783\pi\) | ||||
0.959254 | + | 0.282544i | \(0.0911783\pi\) | |||||||
\(458\) | −8.00993 | −0.374279 | ||||||||
\(459\) | −7.15274 | −0.333861 | ||||||||
\(460\) | −2.01948 | −0.0941588 | ||||||||
\(461\) | 32.2201 | 1.50064 | 0.750320 | − | 0.661075i | \(-0.229899\pi\) | ||||
0.750320 | + | 0.661075i | \(0.229899\pi\) | |||||||
\(462\) | 3.03536 | 0.141218 | ||||||||
\(463\) | −19.7940 | −0.919903 | −0.459951 | − | 0.887944i | \(-0.652133\pi\) | ||||
−0.459951 | + | 0.887944i | \(0.652133\pi\) | |||||||
\(464\) | −9.70507 | −0.450547 | ||||||||
\(465\) | −12.8248 | −0.594734 | ||||||||
\(466\) | 14.4560 | 0.669659 | ||||||||
\(467\) | 3.15870 | 0.146167 | 0.0730835 | − | 0.997326i | \(-0.476716\pi\) | ||||
0.0730835 | + | 0.997326i | \(0.476716\pi\) | |||||||
\(468\) | −10.6577 | −0.492653 | ||||||||
\(469\) | 2.26127 | 0.104416 | ||||||||
\(470\) | 6.40894 | 0.295623 | ||||||||
\(471\) | 7.11945 | 0.328047 | ||||||||
\(472\) | 6.61961 | 0.304692 | ||||||||
\(473\) | 2.55895 | 0.117661 | ||||||||
\(474\) | 21.2383 | 0.975508 | ||||||||
\(475\) | −10.6429 | −0.488331 | ||||||||
\(476\) | −3.79580 | −0.173980 | ||||||||
\(477\) | −11.0699 | −0.506857 | ||||||||
\(478\) | 5.47930 | 0.250617 | ||||||||
\(479\) | 17.8792 | 0.816921 | 0.408460 | − | 0.912776i | \(-0.366066\pi\) | ||||
0.408460 | + | 0.912776i | \(0.366066\pi\) | |||||||
\(480\) | 4.09568 | 0.186941 | ||||||||
\(481\) | −28.5966 | −1.30389 | ||||||||
\(482\) | 22.0387 | 1.00384 | ||||||||
\(483\) | −3.04179 | −0.138406 | ||||||||
\(484\) | −9.80359 | −0.445618 | ||||||||
\(485\) | 8.43517 | 0.383022 | ||||||||
\(486\) | 17.5181 | 0.794638 | ||||||||
\(487\) | 30.7020 | 1.39124 | 0.695621 | − | 0.718409i | \(-0.255129\pi\) | ||||
0.695621 | + | 0.718409i | \(0.255129\pi\) | |||||||
\(488\) | −1.94182 | −0.0879022 | ||||||||
\(489\) | −18.6134 | −0.841728 | ||||||||
\(490\) | 10.0257 | 0.452916 | ||||||||
\(491\) | −14.9541 | −0.674870 | −0.337435 | − | 0.941349i | \(-0.609559\pi\) | ||||
−0.337435 | + | 0.941349i | \(0.609559\pi\) | |||||||
\(492\) | −8.33754 | −0.375885 | ||||||||
\(493\) | 29.5105 | 1.32909 | ||||||||
\(494\) | −36.3808 | −1.63685 | ||||||||
\(495\) | 3.91323 | 0.175887 | ||||||||
\(496\) | −3.13129 | −0.140599 | ||||||||
\(497\) | −1.49081 | −0.0668720 | ||||||||
\(498\) | −27.6034 | −1.23694 | ||||||||
\(499\) | 15.6608 | 0.701074 | 0.350537 | − | 0.936549i | \(-0.385999\pi\) | ||||
0.350537 | + | 0.936549i | \(0.385999\pi\) | |||||||
\(500\) | 12.1701 | 0.544263 | ||||||||
\(501\) | −8.76106 | −0.391415 | ||||||||
\(502\) | 18.3170 | 0.817528 | ||||||||
\(503\) | −15.0646 | −0.671697 | −0.335849 | − | 0.941916i | \(-0.609023\pi\) | ||||
−0.335849 | + | 0.941916i | \(0.609023\pi\) | |||||||
\(504\) | 2.42404 | 0.107975 | ||||||||
\(505\) | 20.2976 | 0.903230 | ||||||||
\(506\) | −1.19895 | −0.0532996 | ||||||||
\(507\) | −38.0651 | −1.69053 | ||||||||
\(508\) | 14.0797 | 0.624686 | ||||||||
\(509\) | −26.4750 | −1.17348 | −0.586742 | − | 0.809774i | \(-0.699590\pi\) | ||||
−0.586742 | + | 0.809774i | \(0.699590\pi\) | |||||||
\(510\) | −12.4538 | −0.551465 | ||||||||
\(511\) | 1.72349 | 0.0762426 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.5925 | 0.688427 | ||||||||
\(514\) | 23.3720 | 1.03090 | ||||||||
\(515\) | 21.2065 | 0.934470 | ||||||||
\(516\) | 5.20075 | 0.228950 | ||||||||
\(517\) | 3.80492 | 0.167340 | ||||||||
\(518\) | 6.50415 | 0.285776 | ||||||||
\(519\) | 39.7409 | 1.74443 | ||||||||
\(520\) | 10.1119 | 0.443434 | ||||||||
\(521\) | 9.39227 | 0.411483 | 0.205741 | − | 0.978606i | \(-0.434039\pi\) | ||||
0.205741 | + | 0.978606i | \(0.434039\pi\) | |||||||
\(522\) | −18.8457 | −0.824855 | ||||||||
\(523\) | −17.7326 | −0.775390 | −0.387695 | − | 0.921788i | \(-0.626729\pi\) | ||||
−0.387695 | + | 0.921788i | \(0.626729\pi\) | |||||||
\(524\) | 19.4452 | 0.849466 | ||||||||
\(525\) | 4.45563 | 0.194460 | ||||||||
\(526\) | 15.2298 | 0.664051 | ||||||||
\(527\) | 9.52141 | 0.414759 | ||||||||
\(528\) | 2.43156 | 0.105820 | ||||||||
\(529\) | −21.7985 | −0.947762 | ||||||||
\(530\) | 10.5030 | 0.456219 | ||||||||
\(531\) | 12.8542 | 0.557826 | ||||||||
\(532\) | 8.27462 | 0.358750 | ||||||||
\(533\) | −20.5847 | −0.891620 | ||||||||
\(534\) | −28.5692 | −1.23631 | ||||||||
\(535\) | −19.5535 | −0.845372 | ||||||||
\(536\) | 1.81145 | 0.0782426 | ||||||||
\(537\) | −56.0522 | −2.41883 | ||||||||
\(538\) | 24.5727 | 1.05940 | ||||||||
\(539\) | 5.95217 | 0.256378 | ||||||||
\(540\) | −4.33387 | −0.186500 | ||||||||
\(541\) | −10.4151 | −0.447779 | −0.223889 | − | 0.974615i | \(-0.571875\pi\) | ||||
−0.223889 | + | 0.974615i | \(0.571875\pi\) | |||||||
\(542\) | 0.531606 | 0.0228344 | ||||||||
\(543\) | 53.5885 | 2.29970 | ||||||||
\(544\) | −3.04073 | −0.130370 | ||||||||
\(545\) | −19.1540 | −0.820466 | ||||||||
\(546\) | 15.2307 | 0.651814 | ||||||||
\(547\) | 9.90374 | 0.423454 | 0.211727 | − | 0.977329i | \(-0.432091\pi\) | ||||
0.211727 | + | 0.977329i | \(0.432091\pi\) | |||||||
\(548\) | 3.66236 | 0.156448 | ||||||||
\(549\) | −3.77071 | −0.160930 | ||||||||
\(550\) | 1.75622 | 0.0748856 | ||||||||
\(551\) | −64.3311 | −2.74060 | ||||||||
\(552\) | −2.43671 | −0.103713 | ||||||||
\(553\) | −11.9262 | −0.507153 | ||||||||
\(554\) | 7.11143 | 0.302136 | ||||||||
\(555\) | 21.3398 | 0.905824 | ||||||||
\(556\) | −8.43371 | −0.357669 | ||||||||
\(557\) | 8.02786 | 0.340152 | 0.170076 | − | 0.985431i | \(-0.445599\pi\) | ||||
0.170076 | + | 0.985431i | \(0.445599\pi\) | |||||||
\(558\) | −6.08048 | −0.257407 | ||||||||
\(559\) | 12.8402 | 0.543082 | ||||||||
\(560\) | −2.29989 | −0.0971880 | ||||||||
\(561\) | −7.39371 | −0.312163 | ||||||||
\(562\) | 4.33769 | 0.182974 | ||||||||
\(563\) | 26.2504 | 1.10632 | 0.553161 | − | 0.833074i | \(-0.313421\pi\) | ||||
0.553161 | + | 0.833074i | \(0.313421\pi\) | |||||||
\(564\) | 7.73303 | 0.325619 | ||||||||
\(565\) | 10.4688 | 0.440424 | ||||||||
\(566\) | −2.76378 | −0.116170 | ||||||||
\(567\) | −13.7999 | −0.579541 | ||||||||
\(568\) | −1.19425 | −0.0501098 | ||||||||
\(569\) | −14.3068 | −0.599773 | −0.299887 | − | 0.953975i | \(-0.596949\pi\) | ||||
−0.299887 | + | 0.953975i | \(0.596949\pi\) | |||||||
\(570\) | 27.1486 | 1.13713 | ||||||||
\(571\) | −19.3018 | −0.807757 | −0.403878 | − | 0.914813i | \(-0.632338\pi\) | ||||
−0.403878 | + | 0.914813i | \(0.632338\pi\) | |||||||
\(572\) | 6.00331 | 0.251011 | ||||||||
\(573\) | 5.03937 | 0.210523 | ||||||||
\(574\) | 4.68187 | 0.195418 | ||||||||
\(575\) | −1.75994 | −0.0733946 | ||||||||
\(576\) | 1.94184 | 0.0809101 | ||||||||
\(577\) | −23.5231 | −0.979281 | −0.489640 | − | 0.871924i | \(-0.662872\pi\) | ||||
−0.489640 | + | 0.871924i | \(0.662872\pi\) | |||||||
\(578\) | −7.75397 | −0.322523 | ||||||||
\(579\) | 43.4059 | 1.80389 | ||||||||
\(580\) | 17.8805 | 0.742448 | ||||||||
\(581\) | 15.5004 | 0.643066 | ||||||||
\(582\) | 10.1779 | 0.421887 | ||||||||
\(583\) | 6.23550 | 0.258248 | ||||||||
\(584\) | 1.38065 | 0.0571315 | ||||||||
\(585\) | 19.6356 | 0.811834 | ||||||||
\(586\) | 21.5468 | 0.890092 | ||||||||
\(587\) | −13.4255 | −0.554130 | −0.277065 | − | 0.960851i | \(-0.589362\pi\) | ||||
−0.277065 | + | 0.960851i | \(0.589362\pi\) | |||||||
\(588\) | 12.0970 | 0.498873 | ||||||||
\(589\) | −20.7561 | −0.855240 | ||||||||
\(590\) | −12.1959 | −0.502097 | ||||||||
\(591\) | −51.0985 | −2.10191 | ||||||||
\(592\) | 5.21032 | 0.214143 | ||||||||
\(593\) | 39.7617 | 1.63282 | 0.816408 | − | 0.577476i | \(-0.195962\pi\) | ||||
0.816408 | + | 0.577476i | \(0.195962\pi\) | |||||||
\(594\) | −2.57297 | −0.105570 | ||||||||
\(595\) | 6.99334 | 0.286699 | ||||||||
\(596\) | −23.6461 | −0.968583 | ||||||||
\(597\) | −27.0407 | −1.10670 | ||||||||
\(598\) | −6.01602 | −0.246013 | ||||||||
\(599\) | 6.80413 | 0.278009 | 0.139005 | − | 0.990292i | \(-0.455610\pi\) | ||||
0.139005 | + | 0.990292i | \(0.455610\pi\) | |||||||
\(600\) | 3.56930 | 0.145716 | ||||||||
\(601\) | −7.62747 | −0.311131 | −0.155565 | − | 0.987826i | \(-0.549720\pi\) | ||||
−0.155565 | + | 0.987826i | \(0.549720\pi\) | |||||||
\(602\) | −2.92043 | −0.119028 | ||||||||
\(603\) | 3.51755 | 0.143246 | ||||||||
\(604\) | 13.2692 | 0.539914 | ||||||||
\(605\) | 18.0620 | 0.734325 | ||||||||
\(606\) | 24.4910 | 0.994881 | ||||||||
\(607\) | 28.2126 | 1.14512 | 0.572558 | − | 0.819864i | \(-0.305951\pi\) | ||||
0.572558 | + | 0.819864i | \(0.305951\pi\) | |||||||
\(608\) | 6.62860 | 0.268825 | ||||||||
\(609\) | 26.9320 | 1.09134 | ||||||||
\(610\) | 3.57759 | 0.144852 | ||||||||
\(611\) | 19.0922 | 0.772387 | ||||||||
\(612\) | −5.90462 | −0.238680 | ||||||||
\(613\) | 12.2578 | 0.495087 | 0.247544 | − | 0.968877i | \(-0.420377\pi\) | ||||
0.247544 | + | 0.968877i | \(0.420377\pi\) | |||||||
\(614\) | 26.9463 | 1.08746 | ||||||||
\(615\) | 15.3610 | 0.619415 | ||||||||
\(616\) | −1.36542 | −0.0550143 | ||||||||
\(617\) | 0.151590 | 0.00610280 | 0.00305140 | − | 0.999995i | \(-0.499029\pi\) | ||||
0.00305140 | + | 0.999995i | \(0.499029\pi\) | |||||||
\(618\) | 25.5878 | 1.02929 | ||||||||
\(619\) | 25.5565 | 1.02720 | 0.513600 | − | 0.858030i | \(-0.328311\pi\) | ||||
0.513600 | + | 0.858030i | \(0.328311\pi\) | |||||||
\(620\) | 5.76906 | 0.231691 | ||||||||
\(621\) | 2.57842 | 0.103468 | ||||||||
\(622\) | 14.0062 | 0.561597 | ||||||||
\(623\) | 16.0428 | 0.642740 | ||||||||
\(624\) | 12.2010 | 0.488430 | ||||||||
\(625\) | −14.3940 | −0.575760 | ||||||||
\(626\) | 4.91789 | 0.196558 | ||||||||
\(627\) | 16.1178 | 0.643685 | ||||||||
\(628\) | −3.20259 | −0.127797 | ||||||||
\(629\) | −15.8432 | −0.631709 | ||||||||
\(630\) | −4.46602 | −0.177931 | ||||||||
\(631\) | −20.4424 | −0.813798 | −0.406899 | − | 0.913473i | \(-0.633390\pi\) | ||||
−0.406899 | + | 0.913473i | \(0.633390\pi\) | |||||||
\(632\) | −9.55379 | −0.380029 | ||||||||
\(633\) | 24.5087 | 0.974134 | ||||||||
\(634\) | −17.5254 | −0.696024 | ||||||||
\(635\) | −25.9403 | −1.02941 | ||||||||
\(636\) | 12.6729 | 0.502512 | ||||||||
\(637\) | 29.8665 | 1.18335 | ||||||||
\(638\) | 10.6155 | 0.420270 | ||||||||
\(639\) | −2.31905 | −0.0917403 | ||||||||
\(640\) | −1.84239 | −0.0728268 | ||||||||
\(641\) | 23.8005 | 0.940064 | 0.470032 | − | 0.882649i | \(-0.344242\pi\) | ||||
0.470032 | + | 0.882649i | \(0.344242\pi\) | |||||||
\(642\) | −23.5933 | −0.931152 | ||||||||
\(643\) | 35.6219 | 1.40479 | 0.702395 | − | 0.711787i | \(-0.252114\pi\) | ||||
0.702395 | + | 0.711787i | \(0.252114\pi\) | |||||||
\(644\) | 1.36831 | 0.0539190 | ||||||||
\(645\) | −9.58180 | −0.377283 | ||||||||
\(646\) | −20.1558 | −0.793019 | ||||||||
\(647\) | 32.4220 | 1.27464 | 0.637320 | − | 0.770599i | \(-0.280043\pi\) | ||||
0.637320 | + | 0.770599i | \(0.280043\pi\) | |||||||
\(648\) | −11.0548 | −0.434273 | ||||||||
\(649\) | −7.24057 | −0.284217 | ||||||||
\(650\) | 8.81230 | 0.345647 | ||||||||
\(651\) | 8.68948 | 0.340568 | ||||||||
\(652\) | 8.37302 | 0.327913 | ||||||||
\(653\) | 44.4779 | 1.74055 | 0.870277 | − | 0.492563i | \(-0.163940\pi\) | ||||
0.870277 | + | 0.492563i | \(0.163940\pi\) | |||||||
\(654\) | −23.1112 | −0.903719 | ||||||||
\(655\) | −35.8255 | −1.39982 | ||||||||
\(656\) | 3.75054 | 0.146434 | ||||||||
\(657\) | 2.68100 | 0.104596 | ||||||||
\(658\) | −4.34241 | −0.169285 | ||||||||
\(659\) | 33.5473 | 1.30682 | 0.653409 | − | 0.757005i | \(-0.273338\pi\) | ||||
0.653409 | + | 0.757005i | \(0.273338\pi\) | |||||||
\(660\) | −4.47988 | −0.174379 | ||||||||
\(661\) | 3.24064 | 0.126046 | 0.0630232 | − | 0.998012i | \(-0.479926\pi\) | ||||
0.0630232 | + | 0.998012i | \(0.479926\pi\) | |||||||
\(662\) | 22.9977 | 0.893832 | ||||||||
\(663\) | −37.0998 | −1.44084 | ||||||||
\(664\) | 12.4170 | 0.481874 | ||||||||
\(665\) | −15.2451 | −0.591178 | ||||||||
\(666\) | 10.1176 | 0.392050 | ||||||||
\(667\) | −10.6379 | −0.411903 | ||||||||
\(668\) | 3.94105 | 0.152484 | ||||||||
\(669\) | 48.4950 | 1.87493 | ||||||||
\(670\) | −3.33739 | −0.128935 | ||||||||
\(671\) | 2.12398 | 0.0819953 | ||||||||
\(672\) | −2.77505 | −0.107050 | ||||||||
\(673\) | 7.17893 | 0.276727 | 0.138364 | − | 0.990381i | \(-0.455816\pi\) | ||||
0.138364 | + | 0.990381i | \(0.455816\pi\) | |||||||
\(674\) | −6.95431 | −0.267870 | ||||||||
\(675\) | −3.77689 | −0.145372 | ||||||||
\(676\) | 17.1231 | 0.658582 | ||||||||
\(677\) | 18.8176 | 0.723219 | 0.361609 | − | 0.932330i | \(-0.382227\pi\) | ||||
0.361609 | + | 0.932330i | \(0.382227\pi\) | |||||||
\(678\) | 12.6316 | 0.485114 | ||||||||
\(679\) | −5.71530 | −0.219333 | ||||||||
\(680\) | 5.60220 | 0.214835 | ||||||||
\(681\) | −52.1612 | −1.99882 | ||||||||
\(682\) | 3.42503 | 0.131151 | ||||||||
\(683\) | 18.4604 | 0.706369 | 0.353185 | − | 0.935554i | \(-0.385099\pi\) | ||||
0.353185 | + | 0.935554i | \(0.385099\pi\) | |||||||
\(684\) | 12.8717 | 0.492162 | ||||||||
\(685\) | −6.74748 | −0.257808 | ||||||||
\(686\) | −15.5312 | −0.592985 | ||||||||
\(687\) | 17.8063 | 0.679352 | ||||||||
\(688\) | −2.33949 | −0.0891923 | ||||||||
\(689\) | 31.2882 | 1.19199 | ||||||||
\(690\) | 4.48936 | 0.170907 | ||||||||
\(691\) | −44.3311 | −1.68643 | −0.843217 | − | 0.537573i | \(-0.819341\pi\) | ||||
−0.843217 | + | 0.537573i | \(0.819341\pi\) | |||||||
\(692\) | −17.8769 | −0.679580 | ||||||||
\(693\) | −2.65143 | −0.100720 | ||||||||
\(694\) | 2.71917 | 0.103218 | ||||||||
\(695\) | 15.5382 | 0.589396 | ||||||||
\(696\) | 21.5746 | 0.817784 | ||||||||
\(697\) | −11.4044 | −0.431971 | ||||||||
\(698\) | 6.57908 | 0.249022 | ||||||||
\(699\) | −32.1360 | −1.21549 | ||||||||
\(700\) | −2.00431 | −0.0757558 | ||||||||
\(701\) | 4.26690 | 0.161159 | 0.0805793 | − | 0.996748i | \(-0.474323\pi\) | ||||
0.0805793 | + | 0.996748i | \(0.474323\pi\) | |||||||
\(702\) | −12.9105 | −0.487277 | ||||||||
\(703\) | 34.5372 | 1.30259 | ||||||||
\(704\) | −1.09381 | −0.0412244 | ||||||||
\(705\) | −14.2472 | −0.536582 | ||||||||
\(706\) | −17.9575 | −0.675839 | ||||||||
\(707\) | −13.7527 | −0.517224 | ||||||||
\(708\) | −14.7156 | −0.553044 | ||||||||
\(709\) | 45.5587 | 1.71099 | 0.855497 | − | 0.517808i | \(-0.173252\pi\) | ||||
0.855497 | + | 0.517808i | \(0.173252\pi\) | |||||||
\(710\) | 2.20028 | 0.0825750 | ||||||||
\(711\) | −18.5520 | −0.695753 | ||||||||
\(712\) | 12.8515 | 0.481630 | ||||||||
\(713\) | −3.43228 | −0.128540 | ||||||||
\(714\) | 8.43816 | 0.315790 | ||||||||
\(715\) | −11.0604 | −0.413636 | ||||||||
\(716\) | 25.2144 | 0.942306 | ||||||||
\(717\) | −12.1806 | −0.454893 | ||||||||
\(718\) | −7.51102 | −0.280309 | ||||||||
\(719\) | −38.0007 | −1.41719 | −0.708593 | − | 0.705617i | \(-0.750670\pi\) | ||||
−0.708593 | + | 0.705617i | \(0.750670\pi\) | |||||||
\(720\) | −3.57763 | −0.133330 | ||||||||
\(721\) | −14.3686 | −0.535113 | ||||||||
\(722\) | 24.9384 | 0.928111 | ||||||||
\(723\) | −48.9927 | −1.82206 | ||||||||
\(724\) | −24.1061 | −0.895896 | ||||||||
\(725\) | 15.5825 | 0.578720 | ||||||||
\(726\) | 21.7936 | 0.808837 | ||||||||
\(727\) | −52.7677 | −1.95704 | −0.978522 | − | 0.206142i | \(-0.933909\pi\) | ||||
−0.978522 | + | 0.206142i | \(0.933909\pi\) | |||||||
\(728\) | −6.85134 | −0.253928 | ||||||||
\(729\) | −5.77890 | −0.214033 | ||||||||
\(730\) | −2.54368 | −0.0941460 | ||||||||
\(731\) | 7.11376 | 0.263112 | ||||||||
\(732\) | 4.31672 | 0.159551 | ||||||||
\(733\) | 20.5213 | 0.757970 | 0.378985 | − | 0.925403i | \(-0.376273\pi\) | ||||
0.378985 | + | 0.925403i | \(0.376273\pi\) | |||||||
\(734\) | 20.6962 | 0.763911 | ||||||||
\(735\) | −22.2874 | −0.822084 | ||||||||
\(736\) | 1.09612 | 0.0404036 | ||||||||
\(737\) | −1.98137 | −0.0729848 | ||||||||
\(738\) | 7.28296 | 0.268089 | ||||||||
\(739\) | −10.4308 | −0.383705 | −0.191852 | − | 0.981424i | \(-0.561449\pi\) | ||||
−0.191852 | + | 0.981424i | \(0.561449\pi\) | |||||||
\(740\) | −9.59944 | −0.352882 | ||||||||
\(741\) | 80.8754 | 2.97103 | ||||||||
\(742\) | −7.11633 | −0.261249 | ||||||||
\(743\) | −50.2175 | −1.84230 | −0.921151 | − | 0.389206i | \(-0.872750\pi\) | ||||
−0.921151 | + | 0.389206i | \(0.872750\pi\) | |||||||
\(744\) | 6.96095 | 0.255201 | ||||||||
\(745\) | 43.5653 | 1.59611 | ||||||||
\(746\) | −1.02232 | −0.0374299 | ||||||||
\(747\) | 24.1119 | 0.882209 | ||||||||
\(748\) | 3.32597 | 0.121609 | ||||||||
\(749\) | 13.2486 | 0.484093 | ||||||||
\(750\) | −27.0544 | −0.987888 | ||||||||
\(751\) | 15.7490 | 0.574688 | 0.287344 | − | 0.957827i | \(-0.407228\pi\) | ||||
0.287344 | + | 0.957827i | \(0.407228\pi\) | |||||||
\(752\) | −3.47861 | −0.126852 | ||||||||
\(753\) | −40.7192 | −1.48389 | ||||||||
\(754\) | 53.2658 | 1.93983 | ||||||||
\(755\) | −24.4469 | −0.889715 | ||||||||
\(756\) | 2.93644 | 0.106797 | ||||||||
\(757\) | −18.5723 | −0.675023 | −0.337512 | − | 0.941321i | \(-0.609585\pi\) | ||||
−0.337512 | + | 0.941321i | \(0.609585\pi\) | |||||||
\(758\) | −27.1713 | −0.986906 | ||||||||
\(759\) | 2.66529 | 0.0967438 | ||||||||
\(760\) | −12.2125 | −0.442992 | ||||||||
\(761\) | −11.0537 | −0.400698 | −0.200349 | − | 0.979725i | \(-0.564208\pi\) | ||||
−0.200349 | + | 0.979725i | \(0.564208\pi\) | |||||||
\(762\) | −31.2995 | −1.13386 | ||||||||
\(763\) | 12.9779 | 0.469830 | ||||||||
\(764\) | −2.26690 | −0.0820135 | ||||||||
\(765\) | 10.8786 | 0.393316 | ||||||||
\(766\) | −4.14476 | −0.149756 | ||||||||
\(767\) | −36.3314 | −1.31185 | ||||||||
\(768\) | −2.22303 | −0.0802165 | ||||||||
\(769\) | −8.33985 | −0.300743 | −0.150371 | − | 0.988630i | \(-0.548047\pi\) | ||||
−0.150371 | + | 0.988630i | \(0.548047\pi\) | |||||||
\(770\) | 2.51563 | 0.0906571 | ||||||||
\(771\) | −51.9566 | −1.87117 | ||||||||
\(772\) | −19.5256 | −0.702741 | ||||||||
\(773\) | 44.4344 | 1.59819 | 0.799096 | − | 0.601203i | \(-0.205312\pi\) | ||||
0.799096 | + | 0.601203i | \(0.205312\pi\) | |||||||
\(774\) | −4.54293 | −0.163292 | ||||||||
\(775\) | 5.02763 | 0.180598 | ||||||||
\(776\) | −4.57839 | −0.164355 | ||||||||
\(777\) | −14.4589 | −0.518710 | ||||||||
\(778\) | −16.3646 | −0.586701 | ||||||||
\(779\) | 24.8608 | 0.890732 | ||||||||
\(780\) | −22.4789 | −0.804875 | ||||||||
\(781\) | 1.30628 | 0.0467425 | ||||||||
\(782\) | −3.33301 | −0.119188 | ||||||||
\(783\) | −22.8293 | −0.815854 | ||||||||
\(784\) | −5.44170 | −0.194346 | ||||||||
\(785\) | 5.90042 | 0.210595 | ||||||||
\(786\) | −43.2271 | −1.54186 | ||||||||
\(787\) | 18.2782 | 0.651548 | 0.325774 | − | 0.945448i | \(-0.394375\pi\) | ||||
0.325774 | + | 0.945448i | \(0.394375\pi\) | |||||||
\(788\) | 22.9860 | 0.818842 | ||||||||
\(789\) | −33.8563 | −1.20531 | ||||||||
\(790\) | 17.6018 | 0.626243 | ||||||||
\(791\) | −7.09316 | −0.252204 | ||||||||
\(792\) | −2.12400 | −0.0754731 | ||||||||
\(793\) | 10.6576 | 0.378463 | ||||||||
\(794\) | 23.8452 | 0.846235 | ||||||||
\(795\) | −23.3483 | −0.828080 | ||||||||
\(796\) | 12.1639 | 0.431138 | ||||||||
\(797\) | 12.5359 | 0.444045 | 0.222022 | − | 0.975042i | \(-0.428734\pi\) | ||||
0.222022 | + | 0.975042i | \(0.428734\pi\) | |||||||
\(798\) | −18.3947 | −0.651165 | ||||||||
\(799\) | 10.5775 | 0.374205 | ||||||||
\(800\) | −1.60561 | −0.0567668 | ||||||||
\(801\) | 24.9556 | 0.881762 | ||||||||
\(802\) | 13.7293 | 0.484799 | ||||||||
\(803\) | −1.51016 | −0.0532924 | ||||||||
\(804\) | −4.02690 | −0.142018 | ||||||||
\(805\) | −2.52096 | −0.0888521 | ||||||||
\(806\) | 17.1860 | 0.605350 | ||||||||
\(807\) | −54.6257 | −1.92291 | ||||||||
\(808\) | −11.0170 | −0.387576 | ||||||||
\(809\) | −26.5633 | −0.933915 | −0.466957 | − | 0.884280i | \(-0.654650\pi\) | ||||
−0.466957 | + | 0.884280i | \(0.654650\pi\) | |||||||
\(810\) | 20.3672 | 0.715630 | ||||||||
\(811\) | −10.4591 | −0.367270 | −0.183635 | − | 0.982994i | \(-0.558786\pi\) | ||||
−0.183635 | + | 0.982994i | \(0.558786\pi\) | |||||||
\(812\) | −12.1150 | −0.425154 | ||||||||
\(813\) | −1.18177 | −0.0414466 | ||||||||
\(814\) | −5.69909 | −0.199753 | ||||||||
\(815\) | −15.4263 | −0.540361 | ||||||||
\(816\) | 6.75962 | 0.236634 | ||||||||
\(817\) | −15.5076 | −0.542541 | ||||||||
\(818\) | 13.6374 | 0.476819 | ||||||||
\(819\) | −13.3042 | −0.464888 | ||||||||
\(820\) | −6.90995 | −0.241306 | ||||||||
\(821\) | −38.3478 | −1.33835 | −0.669175 | − | 0.743105i | \(-0.733352\pi\) | ||||
−0.669175 | + | 0.743105i | \(0.733352\pi\) | |||||||
\(822\) | −8.14151 | −0.283968 | ||||||||
\(823\) | 16.6549 | 0.580552 | 0.290276 | − | 0.956943i | \(-0.406253\pi\) | ||||
0.290276 | + | 0.956943i | \(0.406253\pi\) | |||||||
\(824\) | −11.5103 | −0.400981 | ||||||||
\(825\) | −3.90413 | −0.135924 | ||||||||
\(826\) | 8.26339 | 0.287520 | ||||||||
\(827\) | −12.6346 | −0.439347 | −0.219673 | − | 0.975573i | \(-0.570499\pi\) | ||||
−0.219673 | + | 0.975573i | \(0.570499\pi\) | |||||||
\(828\) | 2.12850 | 0.0739704 | ||||||||
\(829\) | 5.97838 | 0.207638 | 0.103819 | − | 0.994596i | \(-0.466894\pi\) | ||||
0.103819 | + | 0.994596i | \(0.466894\pi\) | |||||||
\(830\) | −22.8770 | −0.794072 | ||||||||
\(831\) | −15.8089 | −0.548404 | ||||||||
\(832\) | −5.48845 | −0.190278 | ||||||||
\(833\) | 16.5467 | 0.573310 | ||||||||
\(834\) | 18.7484 | 0.649202 | ||||||||
\(835\) | −7.26094 | −0.251275 | ||||||||
\(836\) | −7.25041 | −0.250761 | ||||||||
\(837\) | −7.36577 | −0.254598 | ||||||||
\(838\) | 12.3966 | 0.428232 | ||||||||
\(839\) | −51.7914 | −1.78804 | −0.894019 | − | 0.448030i | \(-0.852126\pi\) | ||||
−0.894019 | + | 0.448030i | \(0.852126\pi\) | |||||||
\(840\) | 5.11271 | 0.176405 | ||||||||
\(841\) | 65.1884 | 2.24788 | ||||||||
\(842\) | 28.9782 | 0.998655 | ||||||||
\(843\) | −9.64280 | −0.332116 | ||||||||
\(844\) | −11.0249 | −0.379494 | ||||||||
\(845\) | −31.5474 | −1.08526 | ||||||||
\(846\) | −6.75491 | −0.232239 | ||||||||
\(847\) | −12.2380 | −0.420503 | ||||||||
\(848\) | −5.70073 | −0.195764 | ||||||||
\(849\) | 6.14395 | 0.210860 | ||||||||
\(850\) | 4.88221 | 0.167459 | ||||||||
\(851\) | 5.71115 | 0.195776 | ||||||||
\(852\) | 2.65486 | 0.0909539 | ||||||||
\(853\) | 20.9895 | 0.718667 | 0.359333 | − | 0.933209i | \(-0.383004\pi\) | ||||
0.359333 | + | 0.933209i | \(0.383004\pi\) | |||||||
\(854\) | −2.42402 | −0.0829481 | ||||||||
\(855\) | −23.7147 | −0.811025 | ||||||||
\(856\) | 10.6131 | 0.362749 | ||||||||
\(857\) | 6.19696 | 0.211684 | 0.105842 | − | 0.994383i | \(-0.466246\pi\) | ||||
0.105842 | + | 0.994383i | \(0.466246\pi\) | |||||||
\(858\) | −13.3455 | −0.455608 | ||||||||
\(859\) | 18.2766 | 0.623589 | 0.311794 | − | 0.950150i | \(-0.399070\pi\) | ||||
0.311794 | + | 0.950150i | \(0.399070\pi\) | |||||||
\(860\) | 4.31025 | 0.146978 | ||||||||
\(861\) | −10.4079 | −0.354701 | ||||||||
\(862\) | −41.1783 | −1.40254 | ||||||||
\(863\) | −57.2359 | −1.94833 | −0.974166 | − | 0.225835i | \(-0.927489\pi\) | ||||
−0.974166 | + | 0.225835i | \(0.927489\pi\) | |||||||
\(864\) | 2.35231 | 0.0800272 | ||||||||
\(865\) | 32.9363 | 1.11987 | ||||||||
\(866\) | 13.6220 | 0.462896 | ||||||||
\(867\) | 17.2373 | 0.585409 | ||||||||
\(868\) | −3.90885 | −0.132675 | ||||||||
\(869\) | 10.4500 | 0.354492 | ||||||||
\(870\) | −39.7488 | −1.34761 | ||||||||
\(871\) | −9.94205 | −0.336873 | ||||||||
\(872\) | 10.3963 | 0.352062 | ||||||||
\(873\) | −8.89052 | −0.300898 | ||||||||
\(874\) | 7.26576 | 0.245768 | ||||||||
\(875\) | 15.1922 | 0.513589 | ||||||||
\(876\) | −3.06921 | −0.103699 | ||||||||
\(877\) | −24.0244 | −0.811248 | −0.405624 | − | 0.914040i | \(-0.632946\pi\) | ||||
−0.405624 | + | 0.914040i | \(0.632946\pi\) | |||||||
\(878\) | −17.6779 | −0.596599 | ||||||||
\(879\) | −47.8992 | −1.61560 | ||||||||
\(880\) | 2.01522 | 0.0679329 | ||||||||
\(881\) | −2.27997 | −0.0768141 | −0.0384071 | − | 0.999262i | \(-0.512228\pi\) | ||||
−0.0384071 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(882\) | −10.5669 | −0.355807 | ||||||||
\(883\) | 30.1165 | 1.01350 | 0.506750 | − | 0.862093i | \(-0.330847\pi\) | ||||
0.506750 | + | 0.862093i | \(0.330847\pi\) | |||||||
\(884\) | 16.6889 | 0.561308 | ||||||||
\(885\) | 27.1118 | 0.911352 | ||||||||
\(886\) | −1.29910 | −0.0436443 | ||||||||
\(887\) | 4.08912 | 0.137299 | 0.0686496 | − | 0.997641i | \(-0.478131\pi\) | ||||
0.0686496 | + | 0.997641i | \(0.478131\pi\) | |||||||
\(888\) | −11.5827 | −0.388689 | ||||||||
\(889\) | 17.5760 | 0.589479 | ||||||||
\(890\) | −23.6774 | −0.793669 | ||||||||
\(891\) | 12.0918 | 0.405090 | ||||||||
\(892\) | −21.8149 | −0.730416 | ||||||||
\(893\) | −23.0583 | −0.771617 | ||||||||
\(894\) | 52.5660 | 1.75807 | ||||||||
\(895\) | −46.4547 | −1.55281 | ||||||||
\(896\) | 1.24832 | 0.0417034 | ||||||||
\(897\) | 13.3738 | 0.446537 | ||||||||
\(898\) | 3.37641 | 0.112672 | ||||||||
\(899\) | 30.3894 | 1.01354 | ||||||||
\(900\) | −3.11784 | −0.103928 | ||||||||
\(901\) | 17.3344 | 0.577492 | ||||||||
\(902\) | −4.10236 | −0.136594 | ||||||||
\(903\) | 6.49220 | 0.216047 | ||||||||
\(904\) | −5.68217 | −0.188986 | ||||||||
\(905\) | 44.4128 | 1.47633 | ||||||||
\(906\) | −29.4977 | −0.979995 | ||||||||
\(907\) | −28.6341 | −0.950780 | −0.475390 | − | 0.879775i | \(-0.657693\pi\) | ||||
−0.475390 | + | 0.879775i | \(0.657693\pi\) | |||||||
\(908\) | 23.4640 | 0.778682 | ||||||||
\(909\) | −21.3933 | −0.709569 | ||||||||
\(910\) | 12.6228 | 0.418443 | ||||||||
\(911\) | −9.73535 | −0.322546 | −0.161273 | − | 0.986910i | \(-0.551560\pi\) | ||||
−0.161273 | + | 0.986910i | \(0.551560\pi\) | |||||||
\(912\) | −14.7356 | −0.487943 | ||||||||
\(913\) | −13.5818 | −0.449493 | ||||||||
\(914\) | 41.0130 | 1.35659 | ||||||||
\(915\) | −7.95308 | −0.262921 | ||||||||
\(916\) | −8.00993 | −0.264655 | ||||||||
\(917\) | 24.2738 | 0.801591 | ||||||||
\(918\) | −7.15274 | −0.236075 | ||||||||
\(919\) | −48.4606 | −1.59857 | −0.799285 | − | 0.600953i | \(-0.794788\pi\) | ||||
−0.799285 | + | 0.600953i | \(0.794788\pi\) | |||||||
\(920\) | −2.01948 | −0.0665804 | ||||||||
\(921\) | −59.9023 | −1.97385 | ||||||||
\(922\) | 32.2201 | 1.06111 | ||||||||
\(923\) | 6.55460 | 0.215747 | ||||||||
\(924\) | 3.03536 | 0.0998561 | ||||||||
\(925\) | −8.36573 | −0.275063 | ||||||||
\(926\) | −19.7940 | −0.650470 | ||||||||
\(927\) | −22.3513 | −0.734111 | ||||||||
\(928\) | −9.70507 | −0.318585 | ||||||||
\(929\) | −14.2020 | −0.465953 | −0.232977 | − | 0.972482i | \(-0.574847\pi\) | ||||
−0.232977 | + | 0.972482i | \(0.574847\pi\) | |||||||
\(930\) | −12.8248 | −0.420540 | ||||||||
\(931\) | −36.0709 | −1.18217 | ||||||||
\(932\) | 14.4560 | 0.473521 | ||||||||
\(933\) | −31.1361 | −1.01935 | ||||||||
\(934\) | 3.15870 | 0.103356 | ||||||||
\(935\) | −6.12772 | −0.200398 | ||||||||
\(936\) | −10.6577 | −0.348358 | ||||||||
\(937\) | −51.0903 | −1.66905 | −0.834523 | − | 0.550972i | \(-0.814257\pi\) | ||||
−0.834523 | + | 0.550972i | \(0.814257\pi\) | |||||||
\(938\) | 2.26127 | 0.0738330 | ||||||||
\(939\) | −10.9326 | −0.356772 | ||||||||
\(940\) | 6.40894 | 0.209037 | ||||||||
\(941\) | −42.9275 | −1.39940 | −0.699699 | − | 0.714438i | \(-0.746683\pi\) | ||||
−0.699699 | + | 0.714438i | \(0.746683\pi\) | |||||||
\(942\) | 7.11945 | 0.231964 | ||||||||
\(943\) | 4.11105 | 0.133874 | ||||||||
\(944\) | 6.61961 | 0.215450 | ||||||||
\(945\) | −5.41005 | −0.175989 | ||||||||
\(946\) | 2.55895 | 0.0831987 | ||||||||
\(947\) | −41.7163 | −1.35560 | −0.677798 | − | 0.735248i | \(-0.737066\pi\) | ||||
−0.677798 | + | 0.735248i | \(0.737066\pi\) | |||||||
\(948\) | 21.2383 | 0.689788 | ||||||||
\(949\) | −7.57761 | −0.245980 | ||||||||
\(950\) | −10.6429 | −0.345302 | ||||||||
\(951\) | 38.9595 | 1.26335 | ||||||||
\(952\) | −3.79580 | −0.123023 | ||||||||
\(953\) | −33.4503 | −1.08356 | −0.541781 | − | 0.840519i | \(-0.682250\pi\) | ||||
−0.541781 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(954\) | −11.0699 | −0.358402 | ||||||||
\(955\) | 4.17651 | 0.135149 | ||||||||
\(956\) | 5.47930 | 0.177213 | ||||||||
\(957\) | −23.5985 | −0.762830 | ||||||||
\(958\) | 17.8792 | 0.577650 | ||||||||
\(959\) | 4.57179 | 0.147631 | ||||||||
\(960\) | 4.09568 | 0.132187 | ||||||||
\(961\) | −21.1950 | −0.683710 | ||||||||
\(962\) | −28.5966 | −0.921992 | ||||||||
\(963\) | 20.6090 | 0.664117 | ||||||||
\(964\) | 22.0387 | 0.709820 | ||||||||
\(965\) | 35.9737 | 1.15803 | ||||||||
\(966\) | −3.04179 | −0.0978680 | ||||||||
\(967\) | −35.2559 | −1.13375 | −0.566877 | − | 0.823802i | \(-0.691849\pi\) | ||||
−0.566877 | + | 0.823802i | \(0.691849\pi\) | |||||||
\(968\) | −9.80359 | −0.315099 | ||||||||
\(969\) | 44.8068 | 1.43940 | ||||||||
\(970\) | 8.43517 | 0.270837 | ||||||||
\(971\) | −10.4410 | −0.335066 | −0.167533 | − | 0.985866i | \(-0.553580\pi\) | ||||
−0.167533 | + | 0.985866i | \(0.553580\pi\) | |||||||
\(972\) | 17.5181 | 0.561894 | ||||||||
\(973\) | −10.5280 | −0.337511 | ||||||||
\(974\) | 30.7020 | 0.983757 | ||||||||
\(975\) | −19.5900 | −0.627381 | ||||||||
\(976\) | −1.94182 | −0.0621562 | ||||||||
\(977\) | 33.7498 | 1.07975 | 0.539877 | − | 0.841744i | \(-0.318471\pi\) | ||||
0.539877 | + | 0.841744i | \(0.318471\pi\) | |||||||
\(978\) | −18.6134 | −0.595192 | ||||||||
\(979\) | −14.0570 | −0.449265 | ||||||||
\(980\) | 10.0257 | 0.320260 | ||||||||
\(981\) | 20.1879 | 0.644551 | ||||||||
\(982\) | −14.9541 | −0.477205 | ||||||||
\(983\) | −15.4362 | −0.492339 | −0.246170 | − | 0.969227i | \(-0.579172\pi\) | ||||
−0.246170 | + | 0.969227i | \(0.579172\pi\) | |||||||
\(984\) | −8.33754 | −0.265791 | ||||||||
\(985\) | −42.3491 | −1.34936 | ||||||||
\(986\) | 29.5105 | 0.939805 | ||||||||
\(987\) | 9.65329 | 0.307268 | ||||||||
\(988\) | −36.3808 | −1.15743 | ||||||||
\(989\) | −2.56437 | −0.0815422 | ||||||||
\(990\) | 3.91323 | 0.124371 | ||||||||
\(991\) | 29.4620 | 0.935890 | 0.467945 | − | 0.883758i | \(-0.344995\pi\) | ||||
0.467945 | + | 0.883758i | \(0.344995\pi\) | |||||||
\(992\) | −3.13129 | −0.0994187 | ||||||||
\(993\) | −51.1245 | −1.62239 | ||||||||
\(994\) | −1.49081 | −0.0472856 | ||||||||
\(995\) | −22.4106 | −0.710465 | ||||||||
\(996\) | −27.6034 | −0.874647 | ||||||||
\(997\) | 40.9987 | 1.29844 | 0.649220 | − | 0.760600i | \(-0.275095\pi\) | ||||
0.649220 | + | 0.760600i | \(0.275095\pi\) | |||||||
\(998\) | 15.6608 | 0.495734 | ||||||||
\(999\) | 12.2563 | 0.387772 |
(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 | 8002.2.a.g.1.16 | ✓ | 95 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.g.1.16 | ✓ | 95 | 1.1 | even | 1 | trivial |