Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 17x^{6} - 2x^{5} + 71x^{4} - 18x^{3} - 81x^{2} + 36x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.58447\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.58447 | 1.60302 | 0.801511 | − | 0.597979i | \(-0.204030\pi\) | ||||
0.801511 | + | 0.597979i | \(0.204030\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00108 | −1.51227 | −0.756134 | − | 0.654417i | \(-0.772914\pi\) | ||||
−0.756134 | + | 0.654417i | \(0.772914\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.58447 | −1.13351 | ||||||||
\(11\) | −1.14813 | −0.346175 | −0.173087 | − | 0.984906i | \(-0.555374\pi\) | ||||
−0.173087 | + | 0.984906i | \(0.555374\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.738223 | 0.204746 | 0.102373 | − | 0.994746i | \(-0.467356\pi\) | ||||
0.102373 | + | 0.994746i | \(0.467356\pi\) | |||||||
\(14\) | 4.00108 | 1.06933 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.19403 | −1.01720 | −0.508601 | − | 0.861002i | \(-0.669837\pi\) | ||||
−0.508601 | + | 0.861002i | \(0.669837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.58835 | 0.364393 | 0.182196 | − | 0.983262i | \(-0.441679\pi\) | ||||
0.182196 | + | 0.983262i | \(0.441679\pi\) | |||||||
\(20\) | 3.58447 | 0.801511 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.14813 | 0.244782 | ||||||||
\(23\) | 2.22264 | 0.463452 | 0.231726 | − | 0.972781i | \(-0.425563\pi\) | ||||
0.231726 | + | 0.972781i | \(0.425563\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.84841 | 1.56968 | ||||||||
\(26\) | −0.738223 | −0.144777 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.00108 | −0.756134 | ||||||||
\(29\) | −2.40365 | −0.446346 | −0.223173 | − | 0.974779i | \(-0.571641\pi\) | ||||
−0.223173 | + | 0.974779i | \(0.571641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.76134 | 0.855163 | 0.427581 | − | 0.903977i | \(-0.359366\pi\) | ||||
0.427581 | + | 0.903977i | \(0.359366\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.19403 | 0.719270 | ||||||||
\(35\) | −14.3418 | −2.42420 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.04202 | −1.48650 | −0.743249 | − | 0.669014i | \(-0.766716\pi\) | ||||
−0.743249 | + | 0.669014i | \(0.766716\pi\) | |||||||
\(38\) | −1.58835 | −0.257665 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.58447 | −0.566754 | ||||||||
\(41\) | −3.19103 | −0.498355 | −0.249177 | − | 0.968458i | \(-0.580160\pi\) | ||||
−0.249177 | + | 0.968458i | \(0.580160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.30662 | 0.809252 | 0.404626 | − | 0.914482i | \(-0.367402\pi\) | ||||
0.404626 | + | 0.914482i | \(0.367402\pi\) | |||||||
\(44\) | −1.14813 | −0.173087 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.22264 | −0.327710 | ||||||||
\(47\) | 5.72851 | 0.835590 | 0.417795 | − | 0.908541i | \(-0.362803\pi\) | ||||
0.417795 | + | 0.908541i | \(0.362803\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00867 | 1.28695 | ||||||||
\(50\) | −7.84841 | −1.10993 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.738223 | 0.102373 | ||||||||
\(53\) | 0.714734 | 0.0981763 | 0.0490881 | − | 0.998794i | \(-0.484368\pi\) | ||||
0.0490881 | + | 0.998794i | \(0.484368\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.11544 | −0.554926 | ||||||||
\(56\) | 4.00108 | 0.534667 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.40365 | 0.315614 | ||||||||
\(59\) | −6.45783 | −0.840738 | −0.420369 | − | 0.907353i | \(-0.638099\pi\) | ||||
−0.420369 | + | 0.907353i | \(0.638099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7213 | −1.75683 | −0.878414 | − | 0.477901i | \(-0.841398\pi\) | ||||
−0.878414 | + | 0.477901i | \(0.841398\pi\) | |||||||
\(62\) | −4.76134 | −0.604691 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.64614 | 0.328213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.34694 | 0.775402 | 0.387701 | − | 0.921785i | \(-0.373269\pi\) | ||||
0.387701 | + | 0.921785i | \(0.373269\pi\) | |||||||
\(68\) | −4.19403 | −0.508601 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 14.3418 | 1.71417 | ||||||||
\(71\) | 4.19472 | 0.497821 | 0.248911 | − | 0.968526i | \(-0.419927\pi\) | ||||
0.248911 | + | 0.968526i | \(0.419927\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.45515 | 0.872559 | 0.436280 | − | 0.899811i | \(-0.356296\pi\) | ||||
0.436280 | + | 0.899811i | \(0.356296\pi\) | |||||||
\(74\) | 9.04202 | 1.05111 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.58835 | 0.182196 | ||||||||
\(77\) | 4.59377 | 0.523509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.56890 | −0.289024 | −0.144512 | − | 0.989503i | \(-0.546161\pi\) | ||||
−0.144512 | + | 0.989503i | \(0.546161\pi\) | |||||||
\(80\) | 3.58447 | 0.400756 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.19103 | 0.352390 | ||||||||
\(83\) | 9.66114 | 1.06045 | 0.530224 | − | 0.847858i | \(-0.322108\pi\) | ||||
0.530224 | + | 0.847858i | \(0.322108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0334 | −1.63060 | ||||||||
\(86\) | −5.30662 | −0.572228 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.14813 | 0.122391 | ||||||||
\(89\) | −14.9686 | −1.58667 | −0.793334 | − | 0.608786i | \(-0.791657\pi\) | ||||
−0.793334 | + | 0.608786i | \(0.791657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.95369 | −0.309631 | ||||||||
\(92\) | 2.22264 | 0.231726 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.72851 | −0.590851 | ||||||||
\(95\) | 5.69339 | 0.584130 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.33851 | −0.542043 | −0.271022 | − | 0.962573i | \(-0.587361\pi\) | ||||
−0.271022 | + | 0.962573i | \(0.587361\pi\) | |||||||
\(98\) | −9.00867 | −0.910013 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.84841 | 0.784841 | ||||||||
\(101\) | 8.10397 | 0.806375 | 0.403187 | − | 0.915117i | \(-0.367902\pi\) | ||||
0.403187 | + | 0.915117i | \(0.367902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.30107 | −0.817928 | −0.408964 | − | 0.912550i | \(-0.634110\pi\) | ||||
−0.408964 | + | 0.912550i | \(0.634110\pi\) | |||||||
\(104\) | −0.738223 | −0.0723887 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.714734 | −0.0694211 | ||||||||
\(107\) | −5.28936 | −0.511342 | −0.255671 | − | 0.966764i | \(-0.582296\pi\) | ||||
−0.255671 | + | 0.966764i | \(0.582296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.742766 | 0.0711441 | 0.0355721 | − | 0.999367i | \(-0.488675\pi\) | ||||
0.0355721 | + | 0.999367i | \(0.488675\pi\) | |||||||
\(110\) | 4.11544 | 0.392392 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00108 | −0.378067 | ||||||||
\(113\) | 0.580727 | 0.0546302 | 0.0273151 | − | 0.999627i | \(-0.491304\pi\) | ||||
0.0273151 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.96697 | 0.742923 | ||||||||
\(116\) | −2.40365 | −0.223173 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.45783 | 0.594491 | ||||||||
\(119\) | 16.7807 | 1.53828 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.68179 | −0.880163 | ||||||||
\(122\) | 13.7213 | 1.24226 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.76134 | 0.427581 | ||||||||
\(125\) | 10.2100 | 0.913214 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.12559 | 0.0998804 | 0.0499402 | − | 0.998752i | \(-0.484097\pi\) | ||||
0.0499402 | + | 0.998752i | \(0.484097\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.64614 | −0.232082 | ||||||||
\(131\) | 7.91146 | 0.691228 | 0.345614 | − | 0.938377i | \(-0.387671\pi\) | ||||
0.345614 | + | 0.938377i | \(0.387671\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.35513 | −0.551059 | ||||||||
\(134\) | −6.34694 | −0.548292 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.19403 | 0.359635 | ||||||||
\(137\) | 6.79993 | 0.580958 | 0.290479 | − | 0.956881i | \(-0.406185\pi\) | ||||
0.290479 | + | 0.956881i | \(0.406185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.3028 | −1.72206 | −0.861032 | − | 0.508552i | \(-0.830181\pi\) | ||||
−0.861032 | + | 0.508552i | \(0.830181\pi\) | |||||||
\(140\) | −14.3418 | −1.21210 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.19472 | −0.352013 | ||||||||
\(143\) | −0.847577 | −0.0708779 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.61579 | −0.715503 | ||||||||
\(146\) | −7.45515 | −0.616993 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.04202 | −0.743249 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.44910 | −0.687578 | −0.343789 | − | 0.939047i | \(-0.611711\pi\) | ||||
−0.343789 | + | 0.939047i | \(0.611711\pi\) | |||||||
\(152\) | −1.58835 | −0.128832 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.59377 | −0.370176 | ||||||||
\(155\) | 17.0669 | 1.37085 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.38323 | 0.589246 | 0.294623 | − | 0.955614i | \(-0.404806\pi\) | ||||
0.294623 | + | 0.955614i | \(0.404806\pi\) | |||||||
\(158\) | 2.56890 | 0.204371 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.58447 | −0.283377 | ||||||||
\(161\) | −8.89295 | −0.700863 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.51001 | −0.274925 | −0.137463 | − | 0.990507i | \(-0.543895\pi\) | ||||
−0.137463 | + | 0.990507i | \(0.543895\pi\) | |||||||
\(164\) | −3.19103 | −0.249177 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.66114 | −0.749850 | ||||||||
\(167\) | −16.5643 | −1.28178 | −0.640892 | − | 0.767631i | \(-0.721435\pi\) | ||||
−0.640892 | + | 0.767631i | \(0.721435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4550 | −0.958079 | ||||||||
\(170\) | 15.0334 | 1.15301 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.30662 | 0.404626 | ||||||||
\(173\) | 3.22617 | 0.245282 | 0.122641 | − | 0.992451i | \(-0.460864\pi\) | ||||
0.122641 | + | 0.992451i | \(0.460864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −31.4021 | −2.37378 | ||||||||
\(176\) | −1.14813 | −0.0865437 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.9686 | 1.12194 | ||||||||
\(179\) | 4.58748 | 0.342884 | 0.171442 | − | 0.985194i | \(-0.445157\pi\) | ||||
0.171442 | + | 0.985194i | \(0.445157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.3179 | −1.43588 | −0.717942 | − | 0.696103i | \(-0.754916\pi\) | ||||
−0.717942 | + | 0.696103i | \(0.754916\pi\) | |||||||
\(182\) | 2.95369 | 0.218942 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.22264 | −0.163855 | ||||||||
\(185\) | −32.4108 | −2.38289 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.81530 | 0.352129 | ||||||||
\(188\) | 5.72851 | 0.417795 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.69339 | −0.413042 | ||||||||
\(191\) | −14.5959 | −1.05612 | −0.528059 | − | 0.849207i | \(-0.677080\pi\) | ||||
−0.528059 | + | 0.849207i | \(0.677080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.6018 | −1.48295 | −0.741476 | − | 0.670979i | \(-0.765874\pi\) | ||||
−0.741476 | + | 0.670979i | \(0.765874\pi\) | |||||||
\(194\) | 5.33851 | 0.383282 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00867 | 0.643476 | ||||||||
\(197\) | −6.73218 | −0.479648 | −0.239824 | − | 0.970816i | \(-0.577090\pi\) | ||||
−0.239824 | + | 0.970816i | \(0.577090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.92167 | −0.561552 | −0.280776 | − | 0.959773i | \(-0.590592\pi\) | ||||
−0.280776 | + | 0.959773i | \(0.590592\pi\) | |||||||
\(200\) | −7.84841 | −0.554967 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.10397 | −0.570193 | ||||||||
\(203\) | 9.61719 | 0.674994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.4381 | −0.798874 | ||||||||
\(206\) | 8.30107 | 0.578363 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.738223 | 0.0511866 | ||||||||
\(209\) | −1.82364 | −0.126144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4048 | −1.40473 | −0.702363 | − | 0.711819i | \(-0.747872\pi\) | ||||
−0.702363 | + | 0.711819i | \(0.747872\pi\) | |||||||
\(212\) | 0.714734 | 0.0490881 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.28936 | 0.361573 | ||||||||
\(215\) | 19.0214 | 1.29725 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.0505 | −1.29323 | ||||||||
\(218\) | −0.742766 | −0.0503065 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.11544 | −0.277463 | ||||||||
\(221\) | −3.09613 | −0.208268 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.23200 | −0.417326 | −0.208663 | − | 0.977988i | \(-0.566911\pi\) | ||||
−0.208663 | + | 0.977988i | \(0.566911\pi\) | |||||||
\(224\) | 4.00108 | 0.267334 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.580727 | −0.0386294 | ||||||||
\(227\) | −1.03841 | −0.0689220 | −0.0344610 | − | 0.999406i | \(-0.510971\pi\) | ||||
−0.0344610 | + | 0.999406i | \(0.510971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.32231 | 0.616036 | 0.308018 | − | 0.951381i | \(-0.400334\pi\) | ||||
0.308018 | + | 0.951381i | \(0.400334\pi\) | |||||||
\(230\) | −7.96697 | −0.525326 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.40365 | 0.157807 | ||||||||
\(233\) | −24.0216 | −1.57371 | −0.786854 | − | 0.617139i | \(-0.788292\pi\) | ||||
−0.786854 | + | 0.617139i | \(0.788292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.5337 | 1.33947 | ||||||||
\(236\) | −6.45783 | −0.420369 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.7807 | −1.08773 | ||||||||
\(239\) | 23.2098 | 1.50132 | 0.750658 | − | 0.660690i | \(-0.229736\pi\) | ||||
0.750658 | + | 0.660690i | \(0.229736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.67539 | −0.301168 | −0.150584 | − | 0.988597i | \(-0.548115\pi\) | ||||
−0.150584 | + | 0.988597i | \(0.548115\pi\) | |||||||
\(242\) | 9.68179 | 0.622369 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.7213 | −0.878414 | ||||||||
\(245\) | 32.2913 | 2.06301 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.17256 | 0.0746080 | ||||||||
\(248\) | −4.76134 | −0.302346 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.2100 | −0.645740 | ||||||||
\(251\) | 1.75570 | 0.110819 | 0.0554094 | − | 0.998464i | \(-0.482354\pi\) | ||||
0.0554094 | + | 0.998464i | \(0.482354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.55188 | −0.160435 | ||||||||
\(254\) | −1.12559 | −0.0706261 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.3857 | −0.710218 | −0.355109 | − | 0.934825i | \(-0.615556\pi\) | ||||
−0.355109 | + | 0.934825i | \(0.615556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.1779 | 2.24798 | ||||||||
\(260\) | 2.64614 | 0.164106 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.91146 | −0.488772 | ||||||||
\(263\) | 2.59555 | 0.160048 | 0.0800242 | − | 0.996793i | \(-0.474500\pi\) | ||||
0.0800242 | + | 0.996793i | \(0.474500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.56194 | 0.157379 | ||||||||
\(266\) | 6.35513 | 0.389658 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.34694 | 0.387701 | ||||||||
\(269\) | 11.4807 | 0.699988 | 0.349994 | − | 0.936752i | \(-0.386184\pi\) | ||||
0.349994 | + | 0.936752i | \(0.386184\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.3758 | −1.05551 | −0.527754 | − | 0.849398i | \(-0.676966\pi\) | ||||
−0.527754 | + | 0.849398i | \(0.676966\pi\) | |||||||
\(272\) | −4.19403 | −0.254300 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.79993 | −0.410799 | ||||||||
\(275\) | −9.01101 | −0.543384 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.24677 | −0.375332 | −0.187666 | − | 0.982233i | \(-0.560092\pi\) | ||||
−0.187666 | + | 0.982233i | \(0.560092\pi\) | |||||||
\(278\) | 20.3028 | 1.21768 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.3418 | 0.857084 | ||||||||
\(281\) | 9.95285 | 0.593737 | 0.296869 | − | 0.954918i | \(-0.404058\pi\) | ||||
0.296869 | + | 0.954918i | \(0.404058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.91371 | 0.589309 | 0.294654 | − | 0.955604i | \(-0.404795\pi\) | ||||
0.294654 | + | 0.955604i | \(0.404795\pi\) | |||||||
\(284\) | 4.19472 | 0.248911 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.847577 | 0.0501183 | ||||||||
\(287\) | 12.7676 | 0.753646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.589891 | 0.0346995 | ||||||||
\(290\) | 8.61579 | 0.505937 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.45515 | 0.436280 | ||||||||
\(293\) | −16.0738 | −0.939040 | −0.469520 | − | 0.882922i | \(-0.655573\pi\) | ||||
−0.469520 | + | 0.882922i | \(0.655573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.1479 | −1.34772 | ||||||||
\(296\) | 9.04202 | 0.525557 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 1.64080 | 0.0948899 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.2322 | −1.22381 | ||||||||
\(302\) | 8.44910 | 0.486191 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.58835 | 0.0910982 | ||||||||
\(305\) | −49.1834 | −2.81624 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.85754 | −0.505526 | −0.252763 | − | 0.967528i | \(-0.581339\pi\) | ||||
−0.252763 | + | 0.967528i | \(0.581339\pi\) | |||||||
\(308\) | 4.59377 | 0.261754 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.0669 | −0.969334 | ||||||||
\(311\) | 25.2036 | 1.42917 | 0.714583 | − | 0.699551i | \(-0.246617\pi\) | ||||
0.714583 | + | 0.699551i | \(0.246617\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.4110 | 1.43631 | 0.718156 | − | 0.695882i | \(-0.244986\pi\) | ||||
0.718156 | + | 0.695882i | \(0.244986\pi\) | |||||||
\(314\) | −7.38323 | −0.416660 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.56890 | −0.144512 | ||||||||
\(317\) | 13.2481 | 0.744088 | 0.372044 | − | 0.928215i | \(-0.378657\pi\) | ||||
0.372044 | + | 0.928215i | \(0.378657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.75970 | 0.154514 | ||||||||
\(320\) | 3.58447 | 0.200378 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.89295 | 0.495585 | ||||||||
\(323\) | −6.66159 | −0.370661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.79388 | 0.321387 | ||||||||
\(326\) | 3.51001 | 0.194402 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.19103 | 0.176195 | ||||||||
\(329\) | −22.9203 | −1.26363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1025 | −1.04997 | −0.524985 | − | 0.851112i | \(-0.675929\pi\) | ||||
−0.524985 | + | 0.851112i | \(0.675929\pi\) | |||||||
\(332\) | 9.66114 | 0.530224 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.5643 | 0.906358 | ||||||||
\(335\) | 22.7504 | 1.24299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4574 | −0.569650 | −0.284825 | − | 0.958580i | \(-0.591936\pi\) | ||||
−0.284825 | + | 0.958580i | \(0.591936\pi\) | |||||||
\(338\) | 12.4550 | 0.677464 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.0334 | −0.815299 | ||||||||
\(341\) | −5.46665 | −0.296036 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.03685 | −0.433949 | ||||||||
\(344\) | −5.30662 | −0.286114 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.22617 | −0.173440 | ||||||||
\(347\) | 8.52699 | 0.457753 | 0.228877 | − | 0.973455i | \(-0.426495\pi\) | ||||
0.228877 | + | 0.973455i | \(0.426495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.3510 | −1.83877 | −0.919384 | − | 0.393360i | \(-0.871313\pi\) | ||||
−0.919384 | + | 0.393360i | \(0.871313\pi\) | |||||||
\(350\) | 31.4021 | 1.67852 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.14813 | 0.0611956 | ||||||||
\(353\) | 8.96344 | 0.477076 | 0.238538 | − | 0.971133i | \(-0.423332\pi\) | ||||
0.238538 | + | 0.971133i | \(0.423332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0358 | 0.798019 | ||||||||
\(356\) | −14.9686 | −0.793334 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.58748 | −0.242456 | ||||||||
\(359\) | −25.1520 | −1.32747 | −0.663736 | − | 0.747967i | \(-0.731030\pi\) | ||||
−0.663736 | + | 0.747967i | \(0.731030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4771 | −0.867218 | ||||||||
\(362\) | 19.3179 | 1.01532 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.95369 | −0.154816 | ||||||||
\(365\) | 26.7227 | 1.39873 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3047 | −0.537903 | −0.268952 | − | 0.963154i | \(-0.586677\pi\) | ||||
−0.268952 | + | 0.963154i | \(0.586677\pi\) | |||||||
\(368\) | 2.22264 | 0.115863 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 32.4108 | 1.68496 | ||||||||
\(371\) | −2.85971 | −0.148469 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0716 | 1.34993 | 0.674967 | − | 0.737848i | \(-0.264158\pi\) | ||||
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(374\) | −4.81530 | −0.248993 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.72851 | −0.295426 | ||||||||
\(377\) | −1.77443 | −0.0913876 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2436 | −0.628910 | −0.314455 | − | 0.949272i | \(-0.601822\pi\) | ||||
−0.314455 | + | 0.949272i | \(0.601822\pi\) | |||||||
\(380\) | 5.69339 | 0.292065 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.5959 | 0.746789 | ||||||||
\(383\) | 16.6460 | 0.850569 | 0.425284 | − | 0.905060i | \(-0.360174\pi\) | ||||
0.425284 | + | 0.905060i | \(0.360174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.4662 | 0.839196 | ||||||||
\(386\) | 20.6018 | 1.04861 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.33851 | −0.271022 | ||||||||
\(389\) | 24.1756 | 1.22575 | 0.612875 | − | 0.790180i | \(-0.290013\pi\) | ||||
0.612875 | + | 0.790180i | \(0.290013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.32180 | −0.471424 | ||||||||
\(392\) | −9.00867 | −0.455006 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.73218 | 0.339162 | ||||||||
\(395\) | −9.20815 | −0.463312 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.5827 | 1.33415 | 0.667073 | − | 0.744992i | \(-0.267547\pi\) | ||||
0.667073 | + | 0.744992i | \(0.267547\pi\) | |||||||
\(398\) | 7.92167 | 0.397078 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.84841 | 0.392421 | ||||||||
\(401\) | −19.3434 | −0.965966 | −0.482983 | − | 0.875630i | \(-0.660447\pi\) | ||||
−0.482983 | + | 0.875630i | \(0.660447\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.51493 | 0.175091 | ||||||||
\(404\) | 8.10397 | 0.403187 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.61719 | −0.477293 | ||||||||
\(407\) | 10.3814 | 0.514588 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.33365 | −0.461519 | −0.230760 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230760 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(410\) | 11.4381 | 0.564889 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.30107 | −0.408964 | ||||||||
\(413\) | 25.8383 | 1.27142 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.6300 | 1.69992 | ||||||||
\(416\) | −0.738223 | −0.0361944 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.82364 | 0.0891969 | ||||||||
\(419\) | 19.2809 | 0.941932 | 0.470966 | − | 0.882151i | \(-0.343906\pi\) | ||||
0.470966 | + | 0.882151i | \(0.343906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6428 | −0.811119 | −0.405559 | − | 0.914069i | \(-0.632923\pi\) | ||||
−0.405559 | + | 0.914069i | \(0.632923\pi\) | |||||||
\(422\) | 20.4048 | 0.993291 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.714734 | −0.0347106 | ||||||||
\(425\) | −32.9165 | −1.59668 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 54.8999 | 2.65679 | ||||||||
\(428\) | −5.28936 | −0.255671 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.0214 | −0.917294 | ||||||||
\(431\) | −28.6125 | −1.37821 | −0.689107 | − | 0.724660i | \(-0.741997\pi\) | ||||
−0.689107 | + | 0.724660i | \(0.741997\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.7265 | 1.42857 | 0.714283 | − | 0.699857i | \(-0.246753\pi\) | ||||
0.714283 | + | 0.699857i | \(0.246753\pi\) | |||||||
\(434\) | 19.0505 | 0.914455 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.742766 | 0.0355721 | ||||||||
\(437\) | 3.53033 | 0.168878 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.359854 | 0.0171749 | 0.00858745 | − | 0.999963i | \(-0.497266\pi\) | ||||
0.00858745 | + | 0.999963i | \(0.497266\pi\) | |||||||
\(440\) | 4.11544 | 0.196196 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.09613 | 0.147268 | ||||||||
\(443\) | 25.6758 | 1.21989 | 0.609947 | − | 0.792442i | \(-0.291191\pi\) | ||||
0.609947 | + | 0.792442i | \(0.291191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −53.6545 | −2.54347 | ||||||||
\(446\) | 6.23200 | 0.295094 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.00108 | −0.189033 | ||||||||
\(449\) | 32.8395 | 1.54979 | 0.774896 | − | 0.632088i | \(-0.217802\pi\) | ||||
0.774896 | + | 0.632088i | \(0.217802\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.66372 | 0.172518 | ||||||||
\(452\) | 0.580727 | 0.0273151 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.03841 | 0.0487352 | ||||||||
\(455\) | −10.5874 | −0.496346 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6648 | 0.873101 | 0.436551 | − | 0.899680i | \(-0.356200\pi\) | ||||
0.436551 | + | 0.899680i | \(0.356200\pi\) | |||||||
\(458\) | −9.32231 | −0.435603 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.96697 | 0.371462 | ||||||||
\(461\) | −36.1601 | −1.68414 | −0.842072 | − | 0.539365i | \(-0.818664\pi\) | ||||
−0.842072 | + | 0.539365i | \(0.818664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.07692 | 0.142996 | 0.0714982 | − | 0.997441i | \(-0.477222\pi\) | ||||
0.0714982 | + | 0.997441i | \(0.477222\pi\) | |||||||
\(464\) | −2.40365 | −0.111586 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.0216 | 1.11278 | ||||||||
\(467\) | −32.1937 | −1.48975 | −0.744874 | − | 0.667205i | \(-0.767490\pi\) | ||||
−0.744874 | + | 0.667205i | \(0.767490\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.3946 | −1.17261 | ||||||||
\(470\) | −20.5337 | −0.947148 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.45783 | 0.297246 | ||||||||
\(473\) | −6.09270 | −0.280142 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.4660 | 0.571981 | ||||||||
\(476\) | 16.7807 | 0.769141 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.2098 | −1.06159 | ||||||||
\(479\) | 3.55290 | 0.162336 | 0.0811681 | − | 0.996700i | \(-0.474135\pi\) | ||||
0.0811681 | + | 0.996700i | \(0.474135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.67503 | −0.304355 | ||||||||
\(482\) | 4.67539 | 0.212958 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.68179 | −0.440082 | ||||||||
\(485\) | −19.1357 | −0.868908 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.94156 | −0.269238 | −0.134619 | − | 0.990897i | \(-0.542981\pi\) | ||||
−0.134619 | + | 0.990897i | \(0.542981\pi\) | |||||||
\(488\) | 13.7213 | 0.621132 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −32.2913 | −1.45877 | ||||||||
\(491\) | 0.576627 | 0.0260228 | 0.0130114 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130114 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0810 | 0.454024 | ||||||||
\(494\) | −1.17256 | −0.0527558 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.76134 | 0.213791 | ||||||||
\(497\) | −16.7834 | −0.752839 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.31313 | −0.0587840 | −0.0293920 | − | 0.999568i | \(-0.509357\pi\) | ||||
−0.0293920 | + | 0.999568i | \(0.509357\pi\) | |||||||
\(500\) | 10.2100 | 0.456607 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.75570 | −0.0783608 | ||||||||
\(503\) | 8.98574 | 0.400654 | 0.200327 | − | 0.979729i | \(-0.435800\pi\) | ||||
0.200327 | + | 0.979729i | \(0.435800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.0484 | 1.29264 | ||||||||
\(506\) | 2.55188 | 0.113445 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.12559 | 0.0499402 | ||||||||
\(509\) | −43.8069 | −1.94171 | −0.970854 | − | 0.239671i | \(-0.922960\pi\) | ||||
−0.970854 | + | 0.239671i | \(0.922960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.8287 | −1.31954 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.3857 | 0.502200 | ||||||||
\(515\) | −29.7549 | −1.31116 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.57709 | −0.289260 | ||||||||
\(518\) | −36.1779 | −1.58956 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.64614 | −0.116041 | ||||||||
\(521\) | −32.6400 | −1.42999 | −0.714993 | − | 0.699132i | \(-0.753570\pi\) | ||||
−0.714993 | + | 0.699132i | \(0.753570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.41479 | 0.324226 | 0.162113 | − | 0.986772i | \(-0.448169\pi\) | ||||
0.162113 | + | 0.986772i | \(0.448169\pi\) | |||||||
\(524\) | 7.91146 | 0.345614 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.59555 | −0.113171 | ||||||||
\(527\) | −19.9692 | −0.869873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.0599 | −0.785213 | ||||||||
\(530\) | −2.56194 | −0.111284 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.35513 | −0.275530 | ||||||||
\(533\) | −2.35569 | −0.102036 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.9596 | −0.819693 | ||||||||
\(536\) | −6.34694 | −0.274146 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.4807 | −0.494966 | ||||||||
\(539\) | −10.3431 | −0.445510 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.31819 | −0.400620 | −0.200310 | − | 0.979733i | \(-0.564195\pi\) | ||||
−0.200310 | + | 0.979733i | \(0.564195\pi\) | |||||||
\(542\) | 17.3758 | 0.746356 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.19403 | 0.179818 | ||||||||
\(545\) | 2.66242 | 0.114046 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6160 | 1.05251 | 0.526253 | − | 0.850328i | \(-0.323597\pi\) | ||||
0.526253 | + | 0.850328i | \(0.323597\pi\) | |||||||
\(548\) | 6.79993 | 0.290479 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.01101 | 0.384231 | ||||||||
\(551\) | −3.81783 | −0.162645 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.2784 | 0.437082 | ||||||||
\(554\) | 6.24677 | 0.265400 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.3028 | −0.861032 | ||||||||
\(557\) | 1.09903 | 0.0465675 | 0.0232838 | − | 0.999729i | \(-0.492588\pi\) | ||||
0.0232838 | + | 0.999729i | \(0.492588\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.91747 | 0.165691 | ||||||||
\(560\) | −14.3418 | −0.606050 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.95285 | −0.419836 | ||||||||
\(563\) | 28.4348 | 1.19838 | 0.599191 | − | 0.800606i | \(-0.295489\pi\) | ||||
0.599191 | + | 0.800606i | \(0.295489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.08160 | 0.0875735 | ||||||||
\(566\) | −9.91371 | −0.416704 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.19472 | −0.176006 | ||||||||
\(569\) | 33.0449 | 1.38531 | 0.692657 | − | 0.721267i | \(-0.256440\pi\) | ||||
0.692657 | + | 0.721267i | \(0.256440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2456 | −0.805402 | −0.402701 | − | 0.915332i | \(-0.631928\pi\) | ||||
−0.402701 | + | 0.915332i | \(0.631928\pi\) | |||||||
\(572\) | −0.847577 | −0.0354390 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.7676 | −0.532908 | ||||||||
\(575\) | 17.4442 | 0.727472 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4884 | 0.478268 | 0.239134 | − | 0.970987i | \(-0.423136\pi\) | ||||
0.239134 | + | 0.970987i | \(0.423136\pi\) | |||||||
\(578\) | −0.589891 | −0.0245362 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.61579 | −0.357751 | ||||||||
\(581\) | −38.6550 | −1.60368 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.820608 | −0.0339861 | ||||||||
\(584\) | −7.45515 | −0.308496 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.0738 | 0.664002 | ||||||||
\(587\) | −12.1525 | −0.501589 | −0.250794 | − | 0.968040i | \(-0.580692\pi\) | ||||
−0.250794 | + | 0.968040i | \(0.580692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.56269 | 0.311615 | ||||||||
\(590\) | 23.1479 | 0.952983 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.04202 | −0.371625 | ||||||||
\(593\) | 14.2186 | 0.583886 | 0.291943 | − | 0.956436i | \(-0.405698\pi\) | ||||
0.291943 | + | 0.956436i | \(0.405698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 60.1498 | 2.46590 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.64080 | −0.0670973 | ||||||||
\(599\) | 26.1745 | 1.06946 | 0.534731 | − | 0.845022i | \(-0.320413\pi\) | ||||
0.534731 | + | 0.845022i | \(0.320413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.4872 | −1.36597 | −0.682986 | − | 0.730432i | \(-0.739319\pi\) | ||||
−0.682986 | + | 0.730432i | \(0.739319\pi\) | |||||||
\(602\) | 21.2322 | 0.865361 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.44910 | −0.343789 | ||||||||
\(605\) | −34.7041 | −1.41092 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.6994 | 1.20546 | 0.602731 | − | 0.797944i | \(-0.294079\pi\) | ||||
0.602731 | + | 0.797944i | \(0.294079\pi\) | |||||||
\(608\) | −1.58835 | −0.0644162 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 49.1834 | 1.99138 | ||||||||
\(611\) | 4.22892 | 0.171084 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.157755 | −0.00637168 | −0.00318584 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318584 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(614\) | 8.85754 | 0.357461 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.59377 | −0.185088 | ||||||||
\(617\) | −23.7253 | −0.955143 | −0.477572 | − | 0.878593i | \(-0.658483\pi\) | ||||
−0.477572 | + | 0.878593i | \(0.658483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.82368 | 0.234073 | 0.117037 | − | 0.993128i | \(-0.462660\pi\) | ||||
0.117037 | + | 0.993128i | \(0.462660\pi\) | |||||||
\(620\) | 17.0669 | 0.685423 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.2036 | −1.01057 | ||||||||
\(623\) | 59.8906 | 2.39947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.64449 | −0.105780 | ||||||||
\(626\) | −25.4110 | −1.01563 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.38323 | 0.294623 | ||||||||
\(629\) | 37.9225 | 1.51207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.9996 | 1.55255 | 0.776275 | − | 0.630394i | \(-0.217107\pi\) | ||||
0.776275 | + | 0.630394i | \(0.217107\pi\) | |||||||
\(632\) | 2.56890 | 0.102185 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.2481 | −0.526149 | ||||||||
\(635\) | 4.03466 | 0.160111 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.65041 | 0.263499 | ||||||||
\(638\) | −2.75970 | −0.109258 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.58447 | −0.141689 | ||||||||
\(641\) | −15.5069 | −0.612487 | −0.306243 | − | 0.951953i | \(-0.599072\pi\) | ||||
−0.306243 | + | 0.951953i | \(0.599072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.61504 | −0.181999 | −0.0909997 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909997 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(644\) | −8.89295 | −0.350431 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.66159 | 0.262097 | ||||||||
\(647\) | −4.58826 | −0.180383 | −0.0901916 | − | 0.995924i | \(-0.528748\pi\) | ||||
−0.0901916 | + | 0.995924i | \(0.528748\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.41444 | 0.291042 | ||||||||
\(650\) | −5.79388 | −0.227255 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.51001 | −0.137463 | ||||||||
\(653\) | −33.0317 | −1.29263 | −0.646316 | − | 0.763070i | \(-0.723691\pi\) | ||||
−0.646316 | + | 0.763070i | \(0.723691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.3584 | 1.10805 | ||||||||
\(656\) | −3.19103 | −0.124589 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.9203 | 0.893525 | ||||||||
\(659\) | −29.9577 | −1.16699 | −0.583493 | − | 0.812118i | \(-0.698314\pi\) | ||||
−0.583493 | + | 0.812118i | \(0.698314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.0296 | 1.86813 | 0.934067 | − | 0.357097i | \(-0.116233\pi\) | ||||
0.934067 | + | 0.357097i | \(0.116233\pi\) | |||||||
\(662\) | 19.1025 | 0.742440 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.66114 | −0.374925 | ||||||||
\(665\) | −22.7797 | −0.883361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.34243 | −0.206860 | ||||||||
\(668\) | −16.5643 | −0.640892 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −22.7504 | −0.878924 | ||||||||
\(671\) | 15.7538 | 0.608169 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.3732 | −1.67192 | −0.835958 | − | 0.548794i | \(-0.815087\pi\) | ||||
−0.835958 | + | 0.548794i | \(0.815087\pi\) | |||||||
\(674\) | 10.4574 | 0.402803 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4550 | −0.479039 | ||||||||
\(677\) | −13.9188 | −0.534943 | −0.267471 | − | 0.963566i | \(-0.586188\pi\) | ||||
−0.267471 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.3598 | 0.819714 | ||||||||
\(680\) | 15.0334 | 0.576503 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.46665 | 0.209329 | ||||||||
\(683\) | 23.7919 | 0.910371 | 0.455186 | − | 0.890397i | \(-0.349573\pi\) | ||||
0.455186 | + | 0.890397i | \(0.349573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.3741 | 0.931288 | ||||||||
\(686\) | 8.03685 | 0.306848 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.30662 | 0.202313 | ||||||||
\(689\) | 0.527633 | 0.0201012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.5022 | 1.23644 | 0.618221 | − | 0.786004i | \(-0.287854\pi\) | ||||
0.618221 | + | 0.786004i | \(0.287854\pi\) | |||||||
\(692\) | 3.22617 | 0.122641 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.52699 | −0.323680 | ||||||||
\(695\) | −72.7748 | −2.76051 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.3833 | 0.506927 | ||||||||
\(698\) | 34.3510 | 1.30021 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −31.4021 | −1.18689 | ||||||||
\(701\) | 13.9219 | 0.525823 | 0.262912 | − | 0.964820i | \(-0.415317\pi\) | ||||
0.262912 | + | 0.964820i | \(0.415317\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.3619 | −0.541669 | ||||||||
\(704\) | −1.14813 | −0.0432718 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.96344 | −0.337344 | ||||||||
\(707\) | −32.4246 | −1.21945 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.1002 | −1.80644 | −0.903220 | − | 0.429179i | \(-0.858803\pi\) | ||||
−0.903220 | + | 0.429179i | \(0.858803\pi\) | |||||||
\(710\) | −15.0358 | −0.564285 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.9686 | 0.560972 | ||||||||
\(713\) | 10.5827 | 0.396326 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.03811 | −0.113619 | ||||||||
\(716\) | 4.58748 | 0.171442 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.1520 | 0.938664 | ||||||||
\(719\) | 5.67089 | 0.211489 | 0.105744 | − | 0.994393i | \(-0.466277\pi\) | ||||
0.105744 | + | 0.994393i | \(0.466277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.2133 | 1.23693 | ||||||||
\(722\) | 16.4771 | 0.613216 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.3179 | −0.717942 | ||||||||
\(725\) | −18.8648 | −0.700621 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.4806 | 0.907934 | 0.453967 | − | 0.891019i | \(-0.350008\pi\) | ||||
0.453967 | + | 0.891019i | \(0.350008\pi\) | |||||||
\(728\) | 2.95369 | 0.109471 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26.7227 | −0.989053 | ||||||||
\(731\) | −22.2561 | −0.823173 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.8568 | −1.21359 | −0.606796 | − | 0.794858i | \(-0.707546\pi\) | ||||
−0.606796 | + | 0.794858i | \(0.707546\pi\) | |||||||
\(734\) | 10.3047 | 0.380355 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.22264 | −0.0819274 | ||||||||
\(737\) | −7.28712 | −0.268424 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5953 | 0.794398 | 0.397199 | − | 0.917733i | \(-0.369982\pi\) | ||||
0.397199 | + | 0.917733i | \(0.369982\pi\) | |||||||
\(740\) | −32.4108 | −1.19145 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.85971 | 0.104983 | ||||||||
\(743\) | 4.67353 | 0.171455 | 0.0857275 | − | 0.996319i | \(-0.472679\pi\) | ||||
0.0857275 | + | 0.996319i | \(0.472679\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.58447 | −0.131325 | ||||||||
\(746\) | −26.0716 | −0.954548 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.81530 | 0.176065 | ||||||||
\(749\) | 21.1632 | 0.773286 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2100 | 0.737472 | 0.368736 | − | 0.929534i | \(-0.379791\pi\) | ||||
0.368736 | + | 0.929534i | \(0.379791\pi\) | |||||||
\(752\) | 5.72851 | 0.208897 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.77443 | 0.0646208 | ||||||||
\(755\) | −30.2855 | −1.10220 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.18270 | −0.224714 | −0.112357 | − | 0.993668i | \(-0.535840\pi\) | ||||
−0.112357 | + | 0.993668i | \(0.535840\pi\) | |||||||
\(758\) | 12.2436 | 0.444707 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.69339 | −0.206521 | ||||||||
\(761\) | 31.5581 | 1.14398 | 0.571990 | − | 0.820260i | \(-0.306171\pi\) | ||||
0.571990 | + | 0.820260i | \(0.306171\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.97187 | −0.107589 | ||||||||
\(764\) | −14.5959 | −0.528059 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.6460 | −0.601443 | ||||||||
\(767\) | −4.76732 | −0.172138 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.3756 | −0.698703 | −0.349352 | − | 0.936992i | \(-0.613598\pi\) | ||||
−0.349352 | + | 0.936992i | \(0.613598\pi\) | |||||||
\(770\) | −16.4662 | −0.593401 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20.6018 | −0.741476 | ||||||||
\(773\) | −50.9935 | −1.83411 | −0.917054 | − | 0.398763i | \(-0.869440\pi\) | ||||
−0.917054 | + | 0.398763i | \(0.869440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.3690 | 1.34233 | ||||||||
\(776\) | 5.33851 | 0.191641 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.1756 | −0.866736 | ||||||||
\(779\) | −5.06847 | −0.181597 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.81609 | −0.172333 | ||||||||
\(782\) | 9.32180 | 0.333347 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.00867 | 0.321738 | ||||||||
\(785\) | 26.4650 | 0.944575 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.0364 | −1.53408 | −0.767041 | − | 0.641599i | \(-0.778272\pi\) | ||||
−0.767041 | + | 0.641599i | \(0.778272\pi\) | |||||||
\(788\) | −6.73218 | −0.239824 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.20815 | 0.327611 | ||||||||
\(791\) | −2.32354 | −0.0826155 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.1294 | −0.359704 | ||||||||
\(794\) | −26.5827 | −0.943384 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.92167 | −0.280776 | ||||||||
\(797\) | −16.5275 | −0.585433 | −0.292716 | − | 0.956199i | \(-0.594559\pi\) | ||||
−0.292716 | + | 0.956199i | \(0.594559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0256 | −0.849963 | ||||||||
\(800\) | −7.84841 | −0.277483 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.3434 | 0.683041 | ||||||||
\(803\) | −8.55949 | −0.302058 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.8765 | −1.12350 | ||||||||
\(806\) | −3.51493 | −0.123808 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.10397 | −0.285097 | ||||||||
\(809\) | 15.8718 | 0.558024 | 0.279012 | − | 0.960288i | \(-0.409993\pi\) | ||||
0.279012 | + | 0.960288i | \(0.409993\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.3824 | −0.750836 | −0.375418 | − | 0.926856i | \(-0.622501\pi\) | ||||
−0.375418 | + | 0.926856i | \(0.622501\pi\) | |||||||
\(812\) | 9.61719 | 0.337497 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.3814 | −0.363869 | ||||||||
\(815\) | −12.5815 | −0.440712 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.42878 | 0.294886 | ||||||||
\(818\) | 9.33365 | 0.326344 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.4381 | −0.399437 | ||||||||
\(821\) | −10.8762 | −0.379581 | −0.189790 | − | 0.981825i | \(-0.560781\pi\) | ||||
−0.189790 | + | 0.981825i | \(0.560781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.4775 | 0.539512 | 0.269756 | − | 0.962929i | \(-0.413057\pi\) | ||||
0.269756 | + | 0.962929i | \(0.413057\pi\) | |||||||
\(824\) | 8.30107 | 0.289181 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.8383 | −0.899030 | ||||||||
\(827\) | 32.4509 | 1.12843 | 0.564213 | − | 0.825629i | \(-0.309180\pi\) | ||||
0.564213 | + | 0.825629i | \(0.309180\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.3518 | −0.880505 | −0.440252 | − | 0.897874i | \(-0.645111\pi\) | ||||
−0.440252 | + | 0.897874i | \(0.645111\pi\) | |||||||
\(830\) | −34.6300 | −1.20203 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.738223 | 0.0255933 | ||||||||
\(833\) | −37.7826 | −1.30909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −59.3742 | −2.05473 | ||||||||
\(836\) | −1.82364 | −0.0630718 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.2809 | −0.666046 | ||||||||
\(839\) | 5.53227 | 0.190995 | 0.0954976 | − | 0.995430i | \(-0.469556\pi\) | ||||
0.0954976 | + | 0.995430i | \(0.469556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2225 | −0.800775 | ||||||||
\(842\) | 16.6428 | 0.573547 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.4048 | −0.702363 | ||||||||
\(845\) | −44.6446 | −1.53582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.7377 | 1.33104 | ||||||||
\(848\) | 0.714734 | 0.0245441 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.9165 | 1.12903 | ||||||||
\(851\) | −20.0971 | −0.688920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.3426 | −1.31283 | −0.656413 | − | 0.754401i | \(-0.727927\pi\) | ||||
−0.656413 | + | 0.754401i | \(0.727927\pi\) | |||||||
\(854\) | −54.8999 | −1.87864 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.28936 | 0.180787 | ||||||||
\(857\) | −30.5593 | −1.04388 | −0.521942 | − | 0.852981i | \(-0.674792\pi\) | ||||
−0.521942 | + | 0.852981i | \(0.674792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.8135 | 0.778388 | 0.389194 | − | 0.921156i | \(-0.372754\pi\) | ||||
0.389194 | + | 0.921156i | \(0.372754\pi\) | |||||||
\(860\) | 19.0214 | 0.648625 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.6125 | 0.974544 | ||||||||
\(863\) | −33.1507 | −1.12846 | −0.564232 | − | 0.825616i | \(-0.690828\pi\) | ||||
−0.564232 | + | 0.825616i | \(0.690828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5641 | 0.393192 | ||||||||
\(866\) | −29.7265 | −1.01015 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.0505 | −0.646617 | ||||||||
\(869\) | 2.94944 | 0.100053 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.68545 | 0.158761 | ||||||||
\(872\) | −0.742766 | −0.0251532 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.53033 | −0.119415 | ||||||||
\(875\) | −40.8512 | −1.38102 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8999 | 0.368064 | 0.184032 | − | 0.982920i | \(-0.441085\pi\) | ||||
0.184032 | + | 0.982920i | \(0.441085\pi\) | |||||||
\(878\) | −0.359854 | −0.0121445 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.11544 | −0.138731 | ||||||||
\(881\) | 18.6624 | 0.628751 | 0.314375 | − | 0.949299i | \(-0.398205\pi\) | ||||
0.314375 | + | 0.949299i | \(0.398205\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.5953 | −0.861350 | −0.430675 | − | 0.902507i | \(-0.641724\pi\) | ||||
−0.430675 | + | 0.902507i | \(0.641724\pi\) | |||||||
\(884\) | −3.09613 | −0.104134 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.6758 | −0.862595 | ||||||||
\(887\) | −32.4241 | −1.08869 | −0.544347 | − | 0.838860i | \(-0.683223\pi\) | ||||
−0.544347 | + | 0.838860i | \(0.683223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.50360 | −0.151046 | ||||||||
\(890\) | 53.6545 | 1.79850 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.23200 | −0.208663 | ||||||||
\(893\) | 9.09889 | 0.304483 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.4437 | 0.549651 | ||||||||
\(896\) | 4.00108 | 0.133667 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32.8395 | −1.09587 | ||||||||
\(899\) | −11.4446 | −0.381698 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.99762 | −0.0998651 | ||||||||
\(902\) | −3.66372 | −0.121988 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.580727 | −0.0193147 | ||||||||
\(905\) | −69.2442 | −2.30176 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.53057 | −0.283253 | −0.141626 | − | 0.989920i | \(-0.545233\pi\) | ||||
−0.141626 | + | 0.989920i | \(0.545233\pi\) | |||||||
\(908\) | −1.03841 | −0.0344610 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10.5874 | 0.350969 | ||||||||
\(911\) | 18.3960 | 0.609487 | 0.304743 | − | 0.952435i | \(-0.401429\pi\) | ||||
0.304743 | + | 0.952435i | \(0.401429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0923 | −0.367100 | ||||||||
\(914\) | −18.6648 | −0.617376 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.32231 | 0.308018 | ||||||||
\(917\) | −31.6544 | −1.04532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2944 | 0.339583 | 0.169791 | − | 0.985480i | \(-0.445691\pi\) | ||||
0.169791 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(920\) | −7.96697 | −0.262663 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.1601 | 1.19087 | ||||||||
\(923\) | 3.09664 | 0.101927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70.9655 | −2.33333 | ||||||||
\(926\) | −3.07692 | −0.101114 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.40365 | 0.0789035 | ||||||||
\(929\) | 34.3854 | 1.12815 | 0.564075 | − | 0.825724i | \(-0.309233\pi\) | ||||
0.564075 | + | 0.825724i | \(0.309233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.3089 | 0.468956 | ||||||||
\(932\) | −24.0216 | −0.786854 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.1937 | 1.05341 | ||||||||
\(935\) | 17.2603 | 0.564472 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.80306 | −0.254915 | −0.127457 | − | 0.991844i | \(-0.540682\pi\) | ||||
−0.127457 | + | 0.991844i | \(0.540682\pi\) | |||||||
\(938\) | 25.3946 | 0.829164 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.5337 | 0.669735 | ||||||||
\(941\) | −11.0486 | −0.360173 | −0.180087 | − | 0.983651i | \(-0.557638\pi\) | ||||
−0.180087 | + | 0.983651i | \(0.557638\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.09249 | −0.230963 | ||||||||
\(944\) | −6.45783 | −0.210184 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.09270 | 0.198091 | ||||||||
\(947\) | 35.1164 | 1.14113 | 0.570565 | − | 0.821253i | \(-0.306724\pi\) | ||||
0.570565 | + | 0.821253i | \(0.306724\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.50356 | 0.178653 | ||||||||
\(950\) | −12.4660 | −0.404452 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.7807 | −0.543864 | ||||||||
\(953\) | −22.4676 | −0.727797 | −0.363899 | − | 0.931439i | \(-0.618555\pi\) | ||||
−0.363899 | + | 0.931439i | \(0.618555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.3184 | −1.69298 | ||||||||
\(956\) | 23.2098 | 0.750658 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.55290 | −0.114789 | ||||||||
\(959\) | −27.2071 | −0.878563 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.32960 | −0.268697 | ||||||||
\(962\) | 6.67503 | 0.215211 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.67539 | −0.150584 | ||||||||
\(965\) | −73.8466 | −2.37721 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.62397 | 0.309486 | 0.154743 | − | 0.987955i | \(-0.450545\pi\) | ||||
0.154743 | + | 0.987955i | \(0.450545\pi\) | |||||||
\(968\) | 9.68179 | 0.311185 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.1357 | 0.614410 | ||||||||
\(971\) | 15.3226 | 0.491725 | 0.245863 | − | 0.969305i | \(-0.420929\pi\) | ||||
0.245863 | + | 0.969305i | \(0.420929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 81.2333 | 2.60422 | ||||||||
\(974\) | 5.94156 | 0.190380 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.7213 | −0.439207 | ||||||||
\(977\) | 21.1806 | 0.677629 | 0.338814 | − | 0.940853i | \(-0.389974\pi\) | ||||
0.338814 | + | 0.940853i | \(0.389974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.1859 | 0.549264 | ||||||||
\(980\) | 32.2913 | 1.03151 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.576627 | −0.0184009 | ||||||||
\(983\) | −41.8433 | −1.33459 | −0.667297 | − | 0.744792i | \(-0.732549\pi\) | ||||
−0.667297 | + | 0.744792i | \(0.732549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.1313 | −0.768886 | ||||||||
\(986\) | −10.0810 | −0.321043 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.17256 | 0.0373040 | ||||||||
\(989\) | 11.7947 | 0.375049 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.9591 | −1.55524 | −0.777618 | − | 0.628736i | \(-0.783572\pi\) | ||||
−0.777618 | + | 0.628736i | \(0.783572\pi\) | |||||||
\(992\) | −4.76134 | −0.151173 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.7834 | 0.532338 | ||||||||
\(995\) | −28.3950 | −0.900181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.1156 | −0.637067 | −0.318533 | − | 0.947912i | \(-0.603190\pi\) | ||||
−0.318533 | + | 0.947912i | \(0.603190\pi\) | |||||||
\(998\) | 1.31313 | 0.0415665 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.e.1.8 | ✓ | 8 | |
3.2 | odd | 2 | 8046.2.a.f.1.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.e.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8046.2.a.f.1.1 | yes | 8 | 3.2 | odd | 2 |