Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8450,2,Mod(1,8450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8450, 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("8450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8450.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.4735897080\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1690) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8450.1 |
$q$-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 | ||||||||
\(3\) | −0.445042 | −0.256945 | −0.128473 | − | 0.991713i | \(-0.541007\pi\) | ||||
−0.128473 | + | 0.991713i | \(0.541007\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.445042 | 0.181688 | ||||||||
\(7\) | −3.24698 | −1.22724 | −0.613621 | − | 0.789600i | \(-0.710288\pi\) | ||||
−0.613621 | + | 0.789600i | \(0.710288\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.80194 | −0.933979 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.60388 | −0.483587 | −0.241793 | − | 0.970328i | \(-0.577736\pi\) | ||||
−0.241793 | + | 0.970328i | \(0.577736\pi\) | |||||||
\(12\) | −0.445042 | −0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.24698 | 0.867792 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.10992 | −0.754265 | −0.377133 | − | 0.926159i | \(-0.623090\pi\) | ||||
−0.377133 | + | 0.926159i | \(0.623090\pi\) | |||||||
\(18\) | 2.80194 | 0.660423 | ||||||||
\(19\) | 2.89008 | 0.663031 | 0.331515 | − | 0.943450i | \(-0.392440\pi\) | ||||
0.331515 | + | 0.943450i | \(0.392440\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44504 | 0.315334 | ||||||||
\(22\) | 1.60388 | 0.341947 | ||||||||
\(23\) | −6.78986 | −1.41578 | −0.707891 | − | 0.706321i | \(-0.750353\pi\) | ||||
−0.707891 | + | 0.706321i | \(0.750353\pi\) | |||||||
\(24\) | 0.445042 | 0.0908438 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.58211 | 0.496926 | ||||||||
\(28\) | −3.24698 | −0.613621 | ||||||||
\(29\) | 4.04892 | 0.751865 | 0.375933 | − | 0.926647i | \(-0.377322\pi\) | ||||
0.375933 | + | 0.926647i | \(0.377322\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.31767 | 1.49390 | 0.746949 | − | 0.664882i | \(-0.231518\pi\) | ||||
0.746949 | + | 0.664882i | \(0.231518\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.713792 | 0.124255 | ||||||||
\(34\) | 3.10992 | 0.533346 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.80194 | −0.466990 | ||||||||
\(37\) | 3.20775 | 0.527351 | 0.263676 | − | 0.964611i | \(-0.415065\pi\) | ||||
0.263676 | + | 0.964611i | \(0.415065\pi\) | |||||||
\(38\) | −2.89008 | −0.468833 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6746 | 1.66709 | 0.833543 | − | 0.552454i | \(-0.186309\pi\) | ||||
0.833543 | + | 0.552454i | \(0.186309\pi\) | |||||||
\(42\) | −1.44504 | −0.222975 | ||||||||
\(43\) | 5.18598 | 0.790855 | 0.395427 | − | 0.918497i | \(-0.370597\pi\) | ||||
0.395427 | + | 0.918497i | \(0.370597\pi\) | |||||||
\(44\) | −1.60388 | −0.241793 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.78986 | 1.00111 | ||||||||
\(47\) | −3.97823 | −0.580284 | −0.290142 | − | 0.956984i | \(-0.593703\pi\) | ||||
−0.290142 | + | 0.956984i | \(0.593703\pi\) | |||||||
\(48\) | −0.445042 | −0.0642363 | ||||||||
\(49\) | 3.54288 | 0.506125 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.38404 | 0.193805 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0858 | 1.52275 | 0.761373 | − | 0.648314i | \(-0.224526\pi\) | ||||
0.761373 | + | 0.648314i | \(0.224526\pi\) | |||||||
\(54\) | −2.58211 | −0.351380 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.24698 | 0.433896 | ||||||||
\(57\) | −1.28621 | −0.170362 | ||||||||
\(58\) | −4.04892 | −0.531649 | ||||||||
\(59\) | 5.28621 | 0.688206 | 0.344103 | − | 0.938932i | \(-0.388183\pi\) | ||||
0.344103 | + | 0.938932i | \(0.388183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1250 | −1.68048 | −0.840241 | − | 0.542213i | \(-0.817586\pi\) | ||||
−0.840241 | + | 0.542213i | \(0.817586\pi\) | |||||||
\(62\) | −8.31767 | −1.05634 | ||||||||
\(63\) | 9.09783 | 1.14622 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.713792 | −0.0878617 | ||||||||
\(67\) | −12.3937 | −1.51414 | −0.757068 | − | 0.653336i | \(-0.773369\pi\) | ||||
−0.757068 | + | 0.653336i | \(0.773369\pi\) | |||||||
\(68\) | −3.10992 | −0.377133 | ||||||||
\(69\) | 3.02177 | 0.363778 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.50604 | 0.890803 | 0.445402 | − | 0.895331i | \(-0.353061\pi\) | ||||
0.445402 | + | 0.895331i | \(0.353061\pi\) | |||||||
\(72\) | 2.80194 | 0.330212 | ||||||||
\(73\) | 12.2741 | 1.43658 | 0.718289 | − | 0.695745i | \(-0.244926\pi\) | ||||
0.718289 | + | 0.695745i | \(0.244926\pi\) | |||||||
\(74\) | −3.20775 | −0.372893 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.89008 | 0.331515 | ||||||||
\(77\) | 5.20775 | 0.593478 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3056 | −1.27198 | −0.635989 | − | 0.771698i | \(-0.719408\pi\) | ||||
−0.635989 | + | 0.771698i | \(0.719408\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.25667 | 0.806296 | ||||||||
\(82\) | −10.6746 | −1.17881 | ||||||||
\(83\) | 10.4209 | 1.14384 | 0.571920 | − | 0.820309i | \(-0.306199\pi\) | ||||
0.571920 | + | 0.820309i | \(0.306199\pi\) | |||||||
\(84\) | 1.44504 | 0.157667 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.18598 | −0.559219 | ||||||||
\(87\) | −1.80194 | −0.193188 | ||||||||
\(88\) | 1.60388 | 0.170974 | ||||||||
\(89\) | 11.3817 | 1.20645 | 0.603226 | − | 0.797570i | \(-0.293882\pi\) | ||||
0.603226 | + | 0.797570i | \(0.293882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.78986 | −0.707891 | ||||||||
\(93\) | −3.70171 | −0.383849 | ||||||||
\(94\) | 3.97823 | 0.410323 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.445042 | 0.0454219 | ||||||||
\(97\) | 6.05429 | 0.614720 | 0.307360 | − | 0.951593i | \(-0.400554\pi\) | ||||
0.307360 | + | 0.951593i | \(0.400554\pi\) | |||||||
\(98\) | −3.54288 | −0.357885 | ||||||||
\(99\) | 4.49396 | 0.451660 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.19806 | −0.417723 | −0.208861 | − | 0.977945i | \(-0.566976\pi\) | ||||
−0.208861 | + | 0.977945i | \(0.566976\pi\) | |||||||
\(102\) | −1.38404 | −0.137041 | ||||||||
\(103\) | −11.5211 | −1.13521 | −0.567604 | − | 0.823302i | \(-0.692130\pi\) | ||||
−0.567604 | + | 0.823302i | \(0.692130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.0858 | −1.07674 | ||||||||
\(107\) | 4.43967 | 0.429199 | 0.214599 | − | 0.976702i | \(-0.431155\pi\) | ||||
0.214599 | + | 0.976702i | \(0.431155\pi\) | |||||||
\(108\) | 2.58211 | 0.248463 | ||||||||
\(109\) | −10.5526 | −1.01075 | −0.505376 | − | 0.862899i | \(-0.668646\pi\) | ||||
−0.505376 | + | 0.862899i | \(0.668646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.42758 | −0.135500 | ||||||||
\(112\) | −3.24698 | −0.306811 | ||||||||
\(113\) | −4.31767 | −0.406172 | −0.203086 | − | 0.979161i | \(-0.565097\pi\) | ||||
−0.203086 | + | 0.979161i | \(0.565097\pi\) | |||||||
\(114\) | 1.28621 | 0.120464 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.04892 | 0.375933 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.28621 | −0.486635 | ||||||||
\(119\) | 10.0978 | 0.925667 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.42758 | −0.766144 | ||||||||
\(122\) | 13.1250 | 1.18828 | ||||||||
\(123\) | −4.75063 | −0.428350 | ||||||||
\(124\) | 8.31767 | 0.746949 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.09783 | −0.810500 | ||||||||
\(127\) | 2.80731 | 0.249109 | 0.124554 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124554 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.30798 | −0.203206 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.37196 | 0.207239 | 0.103620 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103620 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(132\) | 0.713792 | 0.0621276 | ||||||||
\(133\) | −9.38404 | −0.813700 | ||||||||
\(134\) | 12.3937 | 1.07066 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.10992 | 0.266673 | ||||||||
\(137\) | −16.8552 | −1.44003 | −0.720017 | − | 0.693956i | \(-0.755866\pi\) | ||||
−0.720017 | + | 0.693956i | \(0.755866\pi\) | |||||||
\(138\) | −3.02177 | −0.257230 | ||||||||
\(139\) | 5.97584 | 0.506864 | 0.253432 | − | 0.967353i | \(-0.418441\pi\) | ||||
0.253432 | + | 0.967353i | \(0.418441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.77048 | 0.149101 | ||||||||
\(142\) | −7.50604 | −0.629893 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.80194 | −0.233495 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.2741 | −1.01581 | ||||||||
\(147\) | −1.57673 | −0.130046 | ||||||||
\(148\) | 3.20775 | 0.263676 | ||||||||
\(149\) | −14.9148 | −1.22187 | −0.610936 | − | 0.791680i | \(-0.709207\pi\) | ||||
−0.610936 | + | 0.791680i | \(0.709207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.56033 | −0.778009 | −0.389005 | − | 0.921236i | \(-0.627181\pi\) | ||||
−0.389005 | + | 0.921236i | \(0.627181\pi\) | |||||||
\(152\) | −2.89008 | −0.234417 | ||||||||
\(153\) | 8.71379 | 0.704468 | ||||||||
\(154\) | −5.20775 | −0.419653 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7560 | 1.09785 | 0.548924 | − | 0.835872i | \(-0.315038\pi\) | ||||
0.548924 | + | 0.835872i | \(0.315038\pi\) | |||||||
\(158\) | 11.3056 | 0.899424 | ||||||||
\(159\) | −4.93362 | −0.391262 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.0465 | 1.73751 | ||||||||
\(162\) | −7.25667 | −0.570138 | ||||||||
\(163\) | −13.5308 | −1.05981 | −0.529907 | − | 0.848056i | \(-0.677773\pi\) | ||||
−0.529907 | + | 0.848056i | \(0.677773\pi\) | |||||||
\(164\) | 10.6746 | 0.833543 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.4209 | −0.808817 | ||||||||
\(167\) | −15.1685 | −1.17378 | −0.586888 | − | 0.809668i | \(-0.699647\pi\) | ||||
−0.586888 | + | 0.809668i | \(0.699647\pi\) | |||||||
\(168\) | −1.44504 | −0.111487 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.09783 | −0.619257 | ||||||||
\(172\) | 5.18598 | 0.395427 | ||||||||
\(173\) | −4.27413 | −0.324956 | −0.162478 | − | 0.986712i | \(-0.551949\pi\) | ||||
−0.162478 | + | 0.986712i | \(0.551949\pi\) | |||||||
\(174\) | 1.80194 | 0.136605 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.60388 | −0.120897 | ||||||||
\(177\) | −2.35258 | −0.176831 | ||||||||
\(178\) | −11.3817 | −0.853091 | ||||||||
\(179\) | 15.6233 | 1.16774 | 0.583868 | − | 0.811848i | \(-0.301538\pi\) | ||||
0.583868 | + | 0.811848i | \(0.301538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1933 | 1.20364 | 0.601818 | − | 0.798633i | \(-0.294443\pi\) | ||||
0.601818 | + | 0.798633i | \(0.294443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.84117 | 0.431791 | ||||||||
\(184\) | 6.78986 | 0.500555 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.70171 | 0.271423 | ||||||||
\(187\) | 4.98792 | 0.364753 | ||||||||
\(188\) | −3.97823 | −0.290142 | ||||||||
\(189\) | −8.38404 | −0.609849 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.5676 | −1.92237 | −0.961183 | − | 0.275911i | \(-0.911020\pi\) | ||||
−0.961183 | + | 0.275911i | \(0.911020\pi\) | |||||||
\(192\) | −0.445042 | −0.0321181 | ||||||||
\(193\) | 13.6582 | 0.983137 | 0.491568 | − | 0.870839i | \(-0.336424\pi\) | ||||
0.491568 | + | 0.870839i | \(0.336424\pi\) | |||||||
\(194\) | −6.05429 | −0.434673 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.54288 | 0.253063 | ||||||||
\(197\) | −14.0978 | −1.00443 | −0.502215 | − | 0.864743i | \(-0.667481\pi\) | ||||
−0.502215 | + | 0.864743i | \(0.667481\pi\) | |||||||
\(198\) | −4.49396 | −0.319372 | ||||||||
\(199\) | −21.1293 | −1.49782 | −0.748908 | − | 0.662674i | \(-0.769422\pi\) | ||||
−0.748908 | + | 0.662674i | \(0.769422\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.51573 | 0.389050 | ||||||||
\(202\) | 4.19806 | 0.295375 | ||||||||
\(203\) | −13.1468 | −0.922721 | ||||||||
\(204\) | 1.38404 | 0.0969024 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.5211 | 0.802714 | ||||||||
\(207\) | 19.0248 | 1.32231 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.63533 | −0.320633 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.3720 | −1.26478 | −0.632389 | − | 0.774651i | \(-0.717926\pi\) | ||||
−0.632389 | + | 0.774651i | \(0.717926\pi\) | |||||||
\(212\) | 11.0858 | 0.761373 | ||||||||
\(213\) | −3.34050 | −0.228887 | ||||||||
\(214\) | −4.43967 | −0.303489 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.58211 | −0.175690 | ||||||||
\(217\) | −27.0073 | −1.83337 | ||||||||
\(218\) | 10.5526 | 0.714710 | ||||||||
\(219\) | −5.46250 | −0.369122 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.42758 | 0.0958131 | ||||||||
\(223\) | 14.2687 | 0.955506 | 0.477753 | − | 0.878494i | \(-0.341451\pi\) | ||||
0.477753 | + | 0.878494i | \(0.341451\pi\) | |||||||
\(224\) | 3.24698 | 0.216948 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.31767 | 0.287207 | ||||||||
\(227\) | 27.4959 | 1.82497 | 0.912483 | − | 0.409115i | \(-0.134163\pi\) | ||||
0.912483 | + | 0.409115i | \(0.134163\pi\) | |||||||
\(228\) | −1.28621 | −0.0851812 | ||||||||
\(229\) | −19.6963 | −1.30157 | −0.650785 | − | 0.759262i | \(-0.725560\pi\) | ||||
−0.650785 | + | 0.759262i | \(0.725560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.31767 | −0.152491 | ||||||||
\(232\) | −4.04892 | −0.265824 | ||||||||
\(233\) | 23.5362 | 1.54191 | 0.770953 | − | 0.636892i | \(-0.219780\pi\) | ||||
0.770953 | + | 0.636892i | \(0.219780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.28621 | 0.344103 | ||||||||
\(237\) | 5.03146 | 0.326828 | ||||||||
\(238\) | −10.0978 | −0.654545 | ||||||||
\(239\) | 14.4155 | 0.932461 | 0.466231 | − | 0.884663i | \(-0.345612\pi\) | ||||
0.466231 | + | 0.884663i | \(0.345612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.6692 | −1.00934 | −0.504671 | − | 0.863312i | \(-0.668386\pi\) | ||||
−0.504671 | + | 0.863312i | \(0.668386\pi\) | |||||||
\(242\) | 8.42758 | 0.541746 | ||||||||
\(243\) | −10.9758 | −0.704100 | ||||||||
\(244\) | −13.1250 | −0.840241 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.75063 | 0.302889 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.31767 | −0.528172 | ||||||||
\(249\) | −4.63773 | −0.293904 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1535 | −0.956478 | −0.478239 | − | 0.878230i | \(-0.658725\pi\) | ||||
−0.478239 | + | 0.878230i | \(0.658725\pi\) | |||||||
\(252\) | 9.09783 | 0.573110 | ||||||||
\(253\) | 10.8901 | 0.684654 | ||||||||
\(254\) | −2.80731 | −0.176147 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.8552 | −1.17615 | −0.588076 | − | 0.808805i | \(-0.700115\pi\) | ||||
−0.588076 | + | 0.808805i | \(0.700115\pi\) | |||||||
\(258\) | 2.30798 | 0.143688 | ||||||||
\(259\) | −10.4155 | −0.647188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.3448 | −0.702226 | ||||||||
\(262\) | −2.37196 | −0.146540 | ||||||||
\(263\) | 2.18060 | 0.134462 | 0.0672309 | − | 0.997737i | \(-0.478584\pi\) | ||||
0.0672309 | + | 0.997737i | \(0.478584\pi\) | |||||||
\(264\) | −0.713792 | −0.0439308 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.38404 | 0.575373 | ||||||||
\(267\) | −5.06531 | −0.309992 | ||||||||
\(268\) | −12.3937 | −0.757068 | ||||||||
\(269\) | 9.73125 | 0.593325 | 0.296662 | − | 0.954982i | \(-0.404126\pi\) | ||||
0.296662 | + | 0.954982i | \(0.404126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.05429 | −0.246281 | −0.123140 | − | 0.992389i | \(-0.539297\pi\) | ||||
−0.123140 | + | 0.992389i | \(0.539297\pi\) | |||||||
\(272\) | −3.10992 | −0.188566 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.8552 | 1.01826 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.02177 | 0.181889 | ||||||||
\(277\) | −30.0301 | −1.80434 | −0.902168 | − | 0.431385i | \(-0.858025\pi\) | ||||
−0.902168 | + | 0.431385i | \(0.858025\pi\) | |||||||
\(278\) | −5.97584 | −0.358407 | ||||||||
\(279\) | −23.3056 | −1.39527 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2640 | −1.32816 | −0.664078 | − | 0.747663i | \(-0.731176\pi\) | ||||
−0.664078 | + | 0.747663i | \(0.731176\pi\) | |||||||
\(282\) | −1.77048 | −0.105430 | ||||||||
\(283\) | 8.88471 | 0.528141 | 0.264071 | − | 0.964503i | \(-0.414935\pi\) | ||||
0.264071 | + | 0.964503i | \(0.414935\pi\) | |||||||
\(284\) | 7.50604 | 0.445402 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.6601 | −2.04592 | ||||||||
\(288\) | 2.80194 | 0.165106 | ||||||||
\(289\) | −7.32842 | −0.431084 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.69441 | −0.157949 | ||||||||
\(292\) | 12.2741 | 0.718289 | ||||||||
\(293\) | 21.5362 | 1.25816 | 0.629078 | − | 0.777342i | \(-0.283432\pi\) | ||||
0.629078 | + | 0.777342i | \(0.283432\pi\) | |||||||
\(294\) | 1.57673 | 0.0919567 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.20775 | −0.186447 | ||||||||
\(297\) | −4.14138 | −0.240307 | ||||||||
\(298\) | 14.9148 | 0.863993 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8388 | −0.970571 | ||||||||
\(302\) | 9.56033 | 0.550135 | ||||||||
\(303\) | 1.86831 | 0.107332 | ||||||||
\(304\) | 2.89008 | 0.165758 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8.71379 | −0.498134 | ||||||||
\(307\) | −10.3230 | −0.589167 | −0.294584 | − | 0.955626i | \(-0.595181\pi\) | ||||
−0.294584 | + | 0.955626i | \(0.595181\pi\) | |||||||
\(308\) | 5.20775 | 0.296739 | ||||||||
\(309\) | 5.12737 | 0.291686 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.50125 | 0.425357 | 0.212679 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212679 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.60388 | −0.316750 | −0.158375 | − | 0.987379i | \(-0.550625\pi\) | ||||
−0.158375 | + | 0.987379i | \(0.550625\pi\) | |||||||
\(314\) | −13.7560 | −0.776296 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3056 | −0.635989 | ||||||||
\(317\) | −11.7802 | −0.661640 | −0.330820 | − | 0.943694i | \(-0.607325\pi\) | ||||
−0.330820 | + | 0.943694i | \(0.607325\pi\) | |||||||
\(318\) | 4.93362 | 0.276664 | ||||||||
\(319\) | −6.49396 | −0.363592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.97584 | −0.110280 | ||||||||
\(322\) | −22.0465 | −1.22860 | ||||||||
\(323\) | −8.98792 | −0.500101 | ||||||||
\(324\) | 7.25667 | 0.403148 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.5308 | 0.749401 | ||||||||
\(327\) | 4.69633 | 0.259708 | ||||||||
\(328\) | −10.6746 | −0.589404 | ||||||||
\(329\) | 12.9172 | 0.712150 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.46980 | 0.355612 | 0.177806 | − | 0.984066i | \(-0.443100\pi\) | ||||
0.177806 | + | 0.984066i | \(0.443100\pi\) | |||||||
\(332\) | 10.4209 | 0.571920 | ||||||||
\(333\) | −8.98792 | −0.492535 | ||||||||
\(334\) | 15.1685 | 0.829985 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.44504 | 0.0788335 | ||||||||
\(337\) | 5.35988 | 0.291971 | 0.145986 | − | 0.989287i | \(-0.453365\pi\) | ||||
0.145986 | + | 0.989287i | \(0.453365\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.92154 | 0.104364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.3405 | −0.722429 | ||||||||
\(342\) | 8.09783 | 0.437881 | ||||||||
\(343\) | 11.2252 | 0.606104 | ||||||||
\(344\) | −5.18598 | −0.279609 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.27413 | 0.229778 | ||||||||
\(347\) | −3.56571 | −0.191417 | −0.0957087 | − | 0.995409i | \(-0.530512\pi\) | ||||
−0.0957087 | + | 0.995409i | \(0.530512\pi\) | |||||||
\(348\) | −1.80194 | −0.0965940 | ||||||||
\(349\) | 7.97584 | 0.426937 | 0.213468 | − | 0.976950i | \(-0.431524\pi\) | ||||
0.213468 | + | 0.976950i | \(0.431524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.60388 | 0.0854868 | ||||||||
\(353\) | −1.60388 | −0.0853657 | −0.0426828 | − | 0.999089i | \(-0.513590\pi\) | ||||
−0.0426828 | + | 0.999089i | \(0.513590\pi\) | |||||||
\(354\) | 2.35258 | 0.125038 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.3817 | 0.603226 | ||||||||
\(357\) | −4.49396 | −0.237846 | ||||||||
\(358\) | −15.6233 | −0.825715 | ||||||||
\(359\) | 8.60255 | 0.454025 | 0.227013 | − | 0.973892i | \(-0.427104\pi\) | ||||
0.227013 | + | 0.973892i | \(0.427104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.6474 | −0.560390 | ||||||||
\(362\) | −16.1933 | −0.851100 | ||||||||
\(363\) | 3.75063 | 0.196857 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.84117 | −0.305323 | ||||||||
\(367\) | −7.41358 | −0.386986 | −0.193493 | − | 0.981102i | \(-0.561982\pi\) | ||||
−0.193493 | + | 0.981102i | \(0.561982\pi\) | |||||||
\(368\) | −6.78986 | −0.353946 | ||||||||
\(369\) | −29.9095 | −1.55702 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.9952 | −1.86878 | ||||||||
\(372\) | −3.70171 | −0.191925 | ||||||||
\(373\) | −29.6039 | −1.53283 | −0.766415 | − | 0.642345i | \(-0.777961\pi\) | ||||
−0.766415 | + | 0.642345i | \(0.777961\pi\) | |||||||
\(374\) | −4.98792 | −0.257919 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.97823 | 0.205162 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 8.38404 | 0.431229 | ||||||||
\(379\) | 8.45042 | 0.434069 | 0.217034 | − | 0.976164i | \(-0.430362\pi\) | ||||
0.217034 | + | 0.976164i | \(0.430362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.24937 | −0.0640073 | ||||||||
\(382\) | 26.5676 | 1.35932 | ||||||||
\(383\) | 10.4644 | 0.534707 | 0.267353 | − | 0.963599i | \(-0.413851\pi\) | ||||
0.267353 | + | 0.963599i | \(0.413851\pi\) | |||||||
\(384\) | 0.445042 | 0.0227109 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.6582 | −0.695183 | ||||||||
\(387\) | −14.5308 | −0.738642 | ||||||||
\(388\) | 6.05429 | 0.307360 | ||||||||
\(389\) | 29.2295 | 1.48200 | 0.740998 | − | 0.671507i | \(-0.234353\pi\) | ||||
0.740998 | + | 0.671507i | \(0.234353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.1159 | 1.06788 | ||||||||
\(392\) | −3.54288 | −0.178942 | ||||||||
\(393\) | −1.05562 | −0.0532491 | ||||||||
\(394\) | 14.0978 | 0.710239 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.49396 | 0.225830 | ||||||||
\(397\) | 20.7439 | 1.04111 | 0.520554 | − | 0.853829i | \(-0.325726\pi\) | ||||
0.520554 | + | 0.853829i | \(0.325726\pi\) | |||||||
\(398\) | 21.1293 | 1.05912 | ||||||||
\(399\) | 4.17629 | 0.209076 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2892 | 1.21294 | 0.606472 | − | 0.795105i | \(-0.292584\pi\) | ||||
0.606472 | + | 0.795105i | \(0.292584\pi\) | |||||||
\(402\) | −5.51573 | −0.275100 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.19806 | −0.208861 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.1468 | 0.652462 | ||||||||
\(407\) | −5.14483 | −0.255020 | ||||||||
\(408\) | −1.38404 | −0.0685203 | ||||||||
\(409\) | 36.7676 | 1.81804 | 0.909021 | − | 0.416751i | \(-0.136831\pi\) | ||||
0.909021 | + | 0.416751i | \(0.136831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.50125 | 0.370010 | ||||||||
\(412\) | −11.5211 | −0.567604 | ||||||||
\(413\) | −17.1642 | −0.844596 | ||||||||
\(414\) | −19.0248 | −0.935016 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.65950 | −0.130236 | ||||||||
\(418\) | 4.63533 | 0.226722 | ||||||||
\(419\) | −30.8418 | −1.50672 | −0.753359 | − | 0.657609i | \(-0.771568\pi\) | ||||
−0.753359 | + | 0.657609i | \(0.771568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.7458 | 1.54720 | 0.773599 | − | 0.633676i | \(-0.218455\pi\) | ||||
0.773599 | + | 0.633676i | \(0.218455\pi\) | |||||||
\(422\) | 18.3720 | 0.894333 | ||||||||
\(423\) | 11.1468 | 0.541974 | ||||||||
\(424\) | −11.0858 | −0.538372 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.34050 | 0.161848 | ||||||||
\(427\) | 42.6165 | 2.06236 | ||||||||
\(428\) | 4.43967 | 0.214599 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.5120 | −1.22887 | −0.614435 | − | 0.788967i | \(-0.710616\pi\) | ||||
−0.614435 | + | 0.788967i | \(0.710616\pi\) | |||||||
\(432\) | 2.58211 | 0.124232 | ||||||||
\(433\) | 31.8189 | 1.52912 | 0.764560 | − | 0.644553i | \(-0.222956\pi\) | ||||
0.764560 | + | 0.644553i | \(0.222956\pi\) | |||||||
\(434\) | 27.0073 | 1.29639 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.5526 | −0.505376 | ||||||||
\(437\) | −19.6233 | −0.938707 | ||||||||
\(438\) | 5.46250 | 0.261008 | ||||||||
\(439\) | 26.9095 | 1.28432 | 0.642159 | − | 0.766571i | \(-0.278039\pi\) | ||||
0.642159 | + | 0.766571i | \(0.278039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.92692 | −0.472710 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.7385 | −0.605227 | −0.302613 | − | 0.953113i | \(-0.597859\pi\) | ||||
−0.302613 | + | 0.953113i | \(0.597859\pi\) | |||||||
\(444\) | −1.42758 | −0.0677501 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.2687 | −0.675645 | ||||||||
\(447\) | 6.63773 | 0.313954 | ||||||||
\(448\) | −3.24698 | −0.153405 | ||||||||
\(449\) | −7.75063 | −0.365775 | −0.182887 | − | 0.983134i | \(-0.558544\pi\) | ||||
−0.182887 | + | 0.983134i | \(0.558544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.1207 | −0.806181 | ||||||||
\(452\) | −4.31767 | −0.203086 | ||||||||
\(453\) | 4.25475 | 0.199906 | ||||||||
\(454\) | −27.4959 | −1.29045 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.28621 | 0.0602322 | ||||||||
\(457\) | 6.94438 | 0.324844 | 0.162422 | − | 0.986721i | \(-0.448069\pi\) | ||||
0.162422 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(458\) | 19.6963 | 0.920349 | ||||||||
\(459\) | −8.03013 | −0.374814 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.6377 | 0.588598 | 0.294299 | − | 0.955713i | \(-0.404914\pi\) | ||||
0.294299 | + | 0.955713i | \(0.404914\pi\) | |||||||
\(462\) | 2.31767 | 0.107828 | ||||||||
\(463\) | −5.62325 | −0.261335 | −0.130667 | − | 0.991426i | \(-0.541712\pi\) | ||||
−0.130667 | + | 0.991426i | \(0.541712\pi\) | |||||||
\(464\) | 4.04892 | 0.187966 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.5362 | −1.09029 | ||||||||
\(467\) | 35.2054 | 1.62911 | 0.814555 | − | 0.580087i | \(-0.196981\pi\) | ||||
0.814555 | + | 0.580087i | \(0.196981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.2422 | 1.85821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.12200 | −0.282087 | ||||||||
\(472\) | −5.28621 | −0.243317 | ||||||||
\(473\) | −8.31767 | −0.382447 | ||||||||
\(474\) | −5.03146 | −0.231103 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.0978 | 0.462833 | ||||||||
\(477\) | −31.0616 | −1.42221 | ||||||||
\(478\) | −14.4155 | −0.659350 | ||||||||
\(479\) | −7.16421 | −0.327341 | −0.163671 | − | 0.986515i | \(-0.552333\pi\) | ||||
−0.163671 | + | 0.986515i | \(0.552333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.6692 | 0.713712 | ||||||||
\(483\) | −9.81163 | −0.446444 | ||||||||
\(484\) | −8.42758 | −0.383072 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.9758 | 0.497874 | ||||||||
\(487\) | 28.7006 | 1.30055 | 0.650275 | − | 0.759699i | \(-0.274654\pi\) | ||||
0.650275 | + | 0.759699i | \(0.274654\pi\) | |||||||
\(488\) | 13.1250 | 0.594140 | ||||||||
\(489\) | 6.02177 | 0.272314 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.0689 | −1.89854 | −0.949271 | − | 0.314459i | \(-0.898177\pi\) | ||||
−0.949271 | + | 0.314459i | \(0.898177\pi\) | |||||||
\(492\) | −4.75063 | −0.214175 | ||||||||
\(493\) | −12.5918 | −0.567106 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.31767 | 0.373474 | ||||||||
\(497\) | −24.3720 | −1.09323 | ||||||||
\(498\) | 4.63773 | 0.207822 | ||||||||
\(499\) | −33.2379 | −1.48793 | −0.743966 | − | 0.668218i | \(-0.767058\pi\) | ||||
−0.743966 | + | 0.668218i | \(0.767058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.75063 | 0.301596 | ||||||||
\(502\) | 15.1535 | 0.676332 | ||||||||
\(503\) | 37.7797 | 1.68451 | 0.842257 | − | 0.539077i | \(-0.181227\pi\) | ||||
0.842257 | + | 0.539077i | \(0.181227\pi\) | |||||||
\(504\) | −9.09783 | −0.405250 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.8901 | −0.484123 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.80731 | 0.124554 | ||||||||
\(509\) | −2.26875 | −0.100561 | −0.0502803 | − | 0.998735i | \(-0.516011\pi\) | ||||
−0.0502803 | + | 0.998735i | \(0.516011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.8538 | −1.76303 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.46250 | 0.329477 | ||||||||
\(514\) | 18.8552 | 0.831666 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.30798 | −0.101603 | ||||||||
\(517\) | 6.38059 | 0.280618 | ||||||||
\(518\) | 10.4155 | 0.457631 | ||||||||
\(519\) | 1.90217 | 0.0834958 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.7899 | −0.998442 | −0.499221 | − | 0.866475i | \(-0.666380\pi\) | ||||
−0.499221 | + | 0.866475i | \(0.666380\pi\) | |||||||
\(522\) | 11.3448 | 0.496549 | ||||||||
\(523\) | −6.61356 | −0.289191 | −0.144595 | − | 0.989491i | \(-0.546188\pi\) | ||||
−0.144595 | + | 0.989491i | \(0.546188\pi\) | |||||||
\(524\) | 2.37196 | 0.103620 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.18060 | −0.0950788 | ||||||||
\(527\) | −25.8672 | −1.12680 | ||||||||
\(528\) | 0.713792 | 0.0310638 | ||||||||
\(529\) | 23.1021 | 1.00444 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.8116 | −0.642770 | ||||||||
\(532\) | −9.38404 | −0.406850 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.06531 | 0.219197 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.3937 | 0.535328 | ||||||||
\(537\) | −6.95300 | −0.300044 | ||||||||
\(538\) | −9.73125 | −0.419544 | ||||||||
\(539\) | −5.68233 | −0.244755 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.2553 | −1.04282 | −0.521409 | − | 0.853307i | \(-0.674593\pi\) | ||||
−0.521409 | + | 0.853307i | \(0.674593\pi\) | |||||||
\(542\) | 4.05429 | 0.174147 | ||||||||
\(543\) | −7.20669 | −0.309268 | ||||||||
\(544\) | 3.10992 | 0.133337 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8086 | −0.504901 | −0.252451 | − | 0.967610i | \(-0.581237\pi\) | ||||
−0.252451 | + | 0.967610i | \(0.581237\pi\) | |||||||
\(548\) | −16.8552 | −0.720017 | ||||||||
\(549\) | 36.7754 | 1.56954 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.7017 | 0.498510 | ||||||||
\(552\) | −3.02177 | −0.128615 | ||||||||
\(553\) | 36.7090 | 1.56103 | ||||||||
\(554\) | 30.0301 | 1.27586 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.97584 | 0.253432 | ||||||||
\(557\) | −15.0180 | −0.636335 | −0.318168 | − | 0.948034i | \(-0.603067\pi\) | ||||
−0.318168 | + | 0.948034i | \(0.603067\pi\) | |||||||
\(558\) | 23.3056 | 0.986604 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.21983 | −0.0937214 | ||||||||
\(562\) | 22.2640 | 0.939149 | ||||||||
\(563\) | −10.4198 | −0.439143 | −0.219571 | − | 0.975596i | \(-0.570466\pi\) | ||||
−0.219571 | + | 0.975596i | \(0.570466\pi\) | |||||||
\(564\) | 1.77048 | 0.0745506 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.88471 | −0.373452 | ||||||||
\(567\) | −23.5623 | −0.989522 | ||||||||
\(568\) | −7.50604 | −0.314946 | ||||||||
\(569\) | 12.3461 | 0.517577 | 0.258789 | − | 0.965934i | \(-0.416677\pi\) | ||||
0.258789 | + | 0.965934i | \(0.416677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.21983 | −0.0928971 | −0.0464486 | − | 0.998921i | \(-0.514790\pi\) | ||||
−0.0464486 | + | 0.998921i | \(0.514790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.8237 | 0.493942 | ||||||||
\(574\) | 34.6601 | 1.44668 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.80194 | −0.116747 | ||||||||
\(577\) | −21.3405 | −0.888417 | −0.444208 | − | 0.895924i | \(-0.646515\pi\) | ||||
−0.444208 | + | 0.895924i | \(0.646515\pi\) | |||||||
\(578\) | 7.32842 | 0.304822 | ||||||||
\(579\) | −6.07846 | −0.252612 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.8364 | −1.40377 | ||||||||
\(582\) | 2.69441 | 0.111687 | ||||||||
\(583\) | −17.7802 | −0.736379 | ||||||||
\(584\) | −12.2741 | −0.507907 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.5362 | −0.889651 | ||||||||
\(587\) | −10.1371 | −0.418401 | −0.209201 | − | 0.977873i | \(-0.567086\pi\) | ||||
−0.209201 | + | 0.977873i | \(0.567086\pi\) | |||||||
\(588\) | −1.57673 | −0.0650232 | ||||||||
\(589\) | 24.0388 | 0.990500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.27413 | 0.258083 | ||||||||
\(592\) | 3.20775 | 0.131838 | ||||||||
\(593\) | 17.6668 | 0.725488 | 0.362744 | − | 0.931889i | \(-0.381840\pi\) | ||||
0.362744 | + | 0.931889i | \(0.381840\pi\) | |||||||
\(594\) | 4.14138 | 0.169923 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14.9148 | −0.610936 | ||||||||
\(597\) | 9.40342 | 0.384856 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.14005 | 0.373452 | 0.186726 | − | 0.982412i | \(-0.440212\pi\) | ||||
0.186726 | + | 0.982412i | \(0.440212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0116 | 1.50973 | 0.754867 | − | 0.655877i | \(-0.227701\pi\) | ||||
0.754867 | + | 0.655877i | \(0.227701\pi\) | |||||||
\(602\) | 16.8388 | 0.686297 | ||||||||
\(603\) | 34.7265 | 1.41417 | ||||||||
\(604\) | −9.56033 | −0.389005 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.86831 | −0.0758950 | ||||||||
\(607\) | −10.9420 | −0.444121 | −0.222061 | − | 0.975033i | \(-0.571278\pi\) | ||||
−0.222061 | + | 0.975033i | \(0.571278\pi\) | |||||||
\(608\) | −2.89008 | −0.117208 | ||||||||
\(609\) | 5.85086 | 0.237089 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 8.71379 | 0.352234 | ||||||||
\(613\) | 10.9336 | 0.441605 | 0.220802 | − | 0.975319i | \(-0.429132\pi\) | ||||
0.220802 | + | 0.975319i | \(0.429132\pi\) | |||||||
\(614\) | 10.3230 | 0.416604 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.20775 | −0.209826 | ||||||||
\(617\) | 6.33704 | 0.255120 | 0.127560 | − | 0.991831i | \(-0.459285\pi\) | ||||
0.127560 | + | 0.991831i | \(0.459285\pi\) | |||||||
\(618\) | −5.12737 | −0.206253 | ||||||||
\(619\) | −12.8659 | −0.517125 | −0.258563 | − | 0.965995i | \(-0.583249\pi\) | ||||
−0.258563 | + | 0.965995i | \(0.583249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.5321 | −0.703540 | ||||||||
\(622\) | −7.50125 | −0.300773 | ||||||||
\(623\) | −36.9560 | −1.48061 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.60388 | 0.223976 | ||||||||
\(627\) | 2.06292 | 0.0823850 | ||||||||
\(628\) | 13.7560 | 0.548924 | ||||||||
\(629\) | −9.97584 | −0.397763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.8491 | 1.90484 | 0.952420 | − | 0.304788i | \(-0.0985855\pi\) | ||||
0.952420 | + | 0.304788i | \(0.0985855\pi\) | |||||||
\(632\) | 11.3056 | 0.449712 | ||||||||
\(633\) | 8.17629 | 0.324978 | ||||||||
\(634\) | 11.7802 | 0.467850 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.93362 | −0.195631 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.49396 | 0.257098 | ||||||||
\(639\) | −21.0315 | −0.831992 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.7168 | 1.80570 | 0.902852 | − | 0.429951i | \(-0.141469\pi\) | ||||
0.902852 | + | 0.429951i | \(0.141469\pi\) | |||||||
\(642\) | 1.97584 | 0.0779801 | ||||||||
\(643\) | −33.1836 | −1.30863 | −0.654316 | − | 0.756221i | \(-0.727044\pi\) | ||||
−0.654316 | + | 0.756221i | \(0.727044\pi\) | |||||||
\(644\) | 22.0465 | 0.868755 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.98792 | 0.353625 | ||||||||
\(647\) | 9.53617 | 0.374906 | 0.187453 | − | 0.982274i | \(-0.439977\pi\) | ||||
0.187453 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(648\) | −7.25667 | −0.285069 | ||||||||
\(649\) | −8.47842 | −0.332807 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0194 | 0.471077 | ||||||||
\(652\) | −13.5308 | −0.529907 | ||||||||
\(653\) | 40.5918 | 1.58848 | 0.794240 | − | 0.607604i | \(-0.207869\pi\) | ||||
0.794240 | + | 0.607604i | \(0.207869\pi\) | |||||||
\(654\) | −4.69633 | −0.183641 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.6746 | 0.416772 | ||||||||
\(657\) | −34.3913 | −1.34173 | ||||||||
\(658\) | −12.9172 | −0.503566 | ||||||||
\(659\) | −0.537500 | −0.0209380 | −0.0104690 | − | 0.999945i | \(-0.503332\pi\) | ||||
−0.0104690 | + | 0.999945i | \(0.503332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.9928 | −0.933213 | −0.466606 | − | 0.884465i | \(-0.654523\pi\) | ||||
−0.466606 | + | 0.884465i | \(0.654523\pi\) | |||||||
\(662\) | −6.46980 | −0.251456 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.4209 | −0.404409 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.98792 | 0.348275 | ||||||||
\(667\) | −27.4916 | −1.06448 | ||||||||
\(668\) | −15.1685 | −0.586888 | ||||||||
\(669\) | −6.35019 | −0.245513 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0508 | 0.812659 | ||||||||
\(672\) | −1.44504 | −0.0557437 | ||||||||
\(673\) | −7.26683 | −0.280116 | −0.140058 | − | 0.990143i | \(-0.544729\pi\) | ||||
−0.140058 | + | 0.990143i | \(0.544729\pi\) | |||||||
\(674\) | −5.35988 | −0.206455 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.11470 | −0.196574 | −0.0982870 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982870 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(678\) | −1.92154 | −0.0737964 | ||||||||
\(679\) | −19.6582 | −0.754411 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.2368 | −0.468916 | ||||||||
\(682\) | 13.3405 | 0.510834 | ||||||||
\(683\) | −23.0532 | −0.882107 | −0.441054 | − | 0.897481i | \(-0.645395\pi\) | ||||
−0.441054 | + | 0.897481i | \(0.645395\pi\) | |||||||
\(684\) | −8.09783 | −0.309628 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.2252 | −0.428580 | ||||||||
\(687\) | 8.76569 | 0.334432 | ||||||||
\(688\) | 5.18598 | 0.197714 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.1051 | −1.18329 | −0.591647 | − | 0.806197i | \(-0.701522\pi\) | ||||
−0.591647 | + | 0.806197i | \(0.701522\pi\) | |||||||
\(692\) | −4.27413 | −0.162478 | ||||||||
\(693\) | −14.5918 | −0.554296 | ||||||||
\(694\) | 3.56571 | 0.135353 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.80194 | 0.0683023 | ||||||||
\(697\) | −33.1970 | −1.25743 | ||||||||
\(698\) | −7.97584 | −0.301890 | ||||||||
\(699\) | −10.4746 | −0.396185 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.07069 | 0.267056 | 0.133528 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133528 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.27067 | 0.349650 | ||||||||
\(704\) | −1.60388 | −0.0604483 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.60388 | 0.0603626 | ||||||||
\(707\) | 13.6310 | 0.512647 | ||||||||
\(708\) | −2.35258 | −0.0884155 | ||||||||
\(709\) | −8.65519 | −0.325052 | −0.162526 | − | 0.986704i | \(-0.551964\pi\) | ||||
−0.162526 | + | 0.986704i | \(0.551964\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.6775 | 1.18800 | ||||||||
\(712\) | −11.3817 | −0.426545 | ||||||||
\(713\) | −56.4758 | −2.11503 | ||||||||
\(714\) | 4.49396 | 0.168182 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.6233 | 0.583868 | ||||||||
\(717\) | −6.41550 | −0.239591 | ||||||||
\(718\) | −8.60255 | −0.321044 | ||||||||
\(719\) | −8.48055 | −0.316271 | −0.158136 | − | 0.987417i | \(-0.550548\pi\) | ||||
−0.158136 | + | 0.987417i | \(0.550548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.4088 | 1.39318 | ||||||||
\(722\) | 10.6474 | 0.396256 | ||||||||
\(723\) | 6.97344 | 0.259345 | ||||||||
\(724\) | 16.1933 | 0.601818 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.75063 | −0.139199 | ||||||||
\(727\) | −31.2683 | −1.15968 | −0.579838 | − | 0.814732i | \(-0.696884\pi\) | ||||
−0.579838 | + | 0.814732i | \(0.696884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.8853 | −0.625381 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.1280 | −0.596514 | ||||||||
\(732\) | 5.84117 | 0.215896 | ||||||||
\(733\) | 6.69441 | 0.247264 | 0.123632 | − | 0.992328i | \(-0.460546\pi\) | ||||
0.123632 | + | 0.992328i | \(0.460546\pi\) | |||||||
\(734\) | 7.41358 | 0.273640 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.78986 | 0.250277 | ||||||||
\(737\) | 19.8780 | 0.732216 | ||||||||
\(738\) | 29.9095 | 1.10098 | ||||||||
\(739\) | 5.29696 | 0.194852 | 0.0974259 | − | 0.995243i | \(-0.468939\pi\) | ||||
0.0974259 | + | 0.995243i | \(0.468939\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.9952 | 1.32143 | ||||||||
\(743\) | −13.0755 | −0.479693 | −0.239846 | − | 0.970811i | \(-0.577097\pi\) | ||||
−0.239846 | + | 0.970811i | \(0.577097\pi\) | |||||||
\(744\) | 3.70171 | 0.135711 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.6039 | 1.08387 | ||||||||
\(747\) | −29.1987 | −1.06832 | ||||||||
\(748\) | 4.98792 | 0.182376 | ||||||||
\(749\) | −14.4155 | −0.526731 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.6461 | −0.972330 | −0.486165 | − | 0.873867i | \(-0.661605\pi\) | ||||
−0.486165 | + | 0.873867i | \(0.661605\pi\) | |||||||
\(752\) | −3.97823 | −0.145071 | ||||||||
\(753\) | 6.74392 | 0.245762 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.38404 | −0.304925 | ||||||||
\(757\) | −54.3236 | −1.97443 | −0.987213 | − | 0.159406i | \(-0.949042\pi\) | ||||
−0.987213 | + | 0.159406i | \(0.949042\pi\) | |||||||
\(758\) | −8.45042 | −0.306933 | ||||||||
\(759\) | −4.84654 | −0.175918 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.55363 | 0.310069 | 0.155034 | − | 0.987909i | \(-0.450451\pi\) | ||||
0.155034 | + | 0.987909i | \(0.450451\pi\) | |||||||
\(762\) | 1.24937 | 0.0452600 | ||||||||
\(763\) | 34.2640 | 1.24044 | ||||||||
\(764\) | −26.5676 | −0.961183 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.4644 | −0.378095 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.445042 | −0.0160591 | ||||||||
\(769\) | 20.6504 | 0.744672 | 0.372336 | − | 0.928098i | \(-0.378557\pi\) | ||||
0.372336 | + | 0.928098i | \(0.378557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.39134 | 0.302207 | ||||||||
\(772\) | 13.6582 | 0.491568 | ||||||||
\(773\) | −5.27545 | −0.189745 | −0.0948725 | − | 0.995489i | \(-0.530244\pi\) | ||||
−0.0948725 | + | 0.995489i | \(0.530244\pi\) | |||||||
\(774\) | 14.5308 | 0.522299 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.05429 | −0.217336 | ||||||||
\(777\) | 4.63533 | 0.166292 | ||||||||
\(778\) | −29.2295 | −1.04793 | ||||||||
\(779\) | 30.8504 | 1.10533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0388 | −0.430781 | ||||||||
\(782\) | −21.1159 | −0.755102 | ||||||||
\(783\) | 10.4547 | 0.373622 | ||||||||
\(784\) | 3.54288 | 0.126531 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.05562 | 0.0376528 | ||||||||
\(787\) | −39.7077 | −1.41543 | −0.707713 | − | 0.706500i | \(-0.750273\pi\) | ||||
−0.707713 | + | 0.706500i | \(0.750273\pi\) | |||||||
\(788\) | −14.0978 | −0.502215 | ||||||||
\(789\) | −0.970460 | −0.0345493 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.0194 | 0.498472 | ||||||||
\(792\) | −4.49396 | −0.159686 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.7439 | −0.736174 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.1293 | −0.748908 | ||||||||
\(797\) | −36.5676 | −1.29529 | −0.647646 | − | 0.761941i | \(-0.724246\pi\) | ||||
−0.647646 | + | 0.761941i | \(0.724246\pi\) | |||||||
\(798\) | −4.17629 | −0.147839 | ||||||||
\(799\) | 12.3720 | 0.437689 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.8907 | −1.12680 | ||||||||
\(802\) | −24.2892 | −0.857681 | ||||||||
\(803\) | −19.6862 | −0.694710 | ||||||||
\(804\) | 5.51573 | 0.194525 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.33081 | −0.152452 | ||||||||
\(808\) | 4.19806 | 0.147687 | ||||||||
\(809\) | −21.9694 | −0.772403 | −0.386201 | − | 0.922414i | \(-0.626213\pi\) | ||||
−0.386201 | + | 0.922414i | \(0.626213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.3250 | −1.09997 | −0.549984 | − | 0.835175i | \(-0.685366\pi\) | ||||
−0.549984 | + | 0.835175i | \(0.685366\pi\) | |||||||
\(812\) | −13.1468 | −0.461361 | ||||||||
\(813\) | 1.80433 | 0.0632806 | ||||||||
\(814\) | 5.14483 | 0.180326 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.38404 | 0.0484512 | ||||||||
\(817\) | 14.9879 | 0.524361 | ||||||||
\(818\) | −36.7676 | −1.28555 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9734 | 0.487677 | 0.243838 | − | 0.969816i | \(-0.421593\pi\) | ||||
0.243838 | + | 0.969816i | \(0.421593\pi\) | |||||||
\(822\) | −7.50125 | −0.261636 | ||||||||
\(823\) | −32.0871 | −1.11849 | −0.559243 | − | 0.829004i | \(-0.688908\pi\) | ||||
−0.559243 | + | 0.829004i | \(0.688908\pi\) | |||||||
\(824\) | 11.5211 | 0.401357 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.1642 | 0.597219 | ||||||||
\(827\) | 1.82430 | 0.0634371 | 0.0317185 | − | 0.999497i | \(-0.489902\pi\) | ||||
0.0317185 | + | 0.999497i | \(0.489902\pi\) | |||||||
\(828\) | 19.0248 | 0.661156 | ||||||||
\(829\) | −32.1360 | −1.11613 | −0.558065 | − | 0.829797i | \(-0.688456\pi\) | ||||
−0.558065 | + | 0.829797i | \(0.688456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.3647 | 0.463615 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.0180 | −0.381753 | ||||||||
\(834\) | 2.65950 | 0.0920909 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.63533 | −0.160316 | ||||||||
\(837\) | 21.4771 | 0.742357 | ||||||||
\(838\) | 30.8418 | 1.06541 | ||||||||
\(839\) | 8.30904 | 0.286860 | 0.143430 | − | 0.989660i | \(-0.454187\pi\) | ||||
0.143430 | + | 0.989660i | \(0.454187\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6063 | −0.434699 | ||||||||
\(842\) | −31.7458 | −1.09403 | ||||||||
\(843\) | 9.90840 | 0.341263 | ||||||||
\(844\) | −18.3720 | −0.632389 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.1468 | −0.383233 | ||||||||
\(847\) | 27.3642 | 0.940245 | ||||||||
\(848\) | 11.0858 | 0.380686 | ||||||||
\(849\) | −3.95407 | −0.135703 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.7802 | −0.746615 | ||||||||
\(852\) | −3.34050 | −0.114444 | ||||||||
\(853\) | 31.7995 | 1.08880 | 0.544398 | − | 0.838827i | \(-0.316758\pi\) | ||||
0.544398 | + | 0.838827i | \(0.316758\pi\) | |||||||
\(854\) | −42.6165 | −1.45831 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.43967 | −0.151745 | ||||||||
\(857\) | 9.32975 | 0.318698 | 0.159349 | − | 0.987222i | \(-0.449060\pi\) | ||||
0.159349 | + | 0.987222i | \(0.449060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −58.3913 | −1.99229 | −0.996143 | − | 0.0877403i | \(-0.972035\pi\) | ||||
−0.996143 | + | 0.0877403i | \(0.972035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.4252 | 0.525689 | ||||||||
\(862\) | 25.5120 | 0.868942 | ||||||||
\(863\) | 8.79284 | 0.299312 | 0.149656 | − | 0.988738i | \(-0.452183\pi\) | ||||
0.149656 | + | 0.988738i | \(0.452183\pi\) | |||||||
\(864\) | −2.58211 | −0.0878450 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −31.8189 | −1.08125 | ||||||||
\(867\) | 3.26145 | 0.110765 | ||||||||
\(868\) | −27.0073 | −0.916687 | ||||||||
\(869\) | 18.1328 | 0.615111 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.5526 | 0.357355 | ||||||||
\(873\) | −16.9638 | −0.574136 | ||||||||
\(874\) | 19.6233 | 0.663766 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.46250 | −0.184561 | ||||||||
\(877\) | −33.6668 | −1.13685 | −0.568423 | − | 0.822736i | \(-0.692446\pi\) | ||||
−0.568423 | + | 0.822736i | \(0.692446\pi\) | |||||||
\(878\) | −26.9095 | −0.908150 | ||||||||
\(879\) | −9.58450 | −0.323277 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8068 | 0.835764 | 0.417882 | − | 0.908501i | \(-0.362773\pi\) | ||||
0.417882 | + | 0.908501i | \(0.362773\pi\) | |||||||
\(882\) | 9.92692 | 0.334257 | ||||||||
\(883\) | −15.5120 | −0.522021 | −0.261010 | − | 0.965336i | \(-0.584056\pi\) | ||||
−0.261010 | + | 0.965336i | \(0.584056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7385 | 0.427960 | ||||||||
\(887\) | 12.9487 | 0.434774 | 0.217387 | − | 0.976085i | \(-0.430247\pi\) | ||||
0.217387 | + | 0.976085i | \(0.430247\pi\) | |||||||
\(888\) | 1.42758 | 0.0479066 | ||||||||
\(889\) | −9.11529 | −0.305717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.6388 | −0.389914 | ||||||||
\(892\) | 14.2687 | 0.477753 | ||||||||
\(893\) | −11.4974 | −0.384746 | ||||||||
\(894\) | −6.63773 | −0.221999 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.24698 | 0.108474 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.75063 | 0.258642 | ||||||||
\(899\) | 33.6775 | 1.12321 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.4758 | −1.14855 | ||||||||
\(902\) | 17.1207 | 0.570056 | ||||||||
\(903\) | 7.49396 | 0.249383 | ||||||||
\(904\) | 4.31767 | 0.143603 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.25475 | −0.141355 | ||||||||
\(907\) | 26.4983 | 0.879861 | 0.439930 | − | 0.898032i | \(-0.355003\pi\) | ||||
0.439930 | + | 0.898032i | \(0.355003\pi\) | |||||||
\(908\) | 27.4959 | 0.912483 | ||||||||
\(909\) | 11.7627 | 0.390144 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5797 | −0.516179 | −0.258089 | − | 0.966121i | \(-0.583093\pi\) | ||||
−0.258089 | + | 0.966121i | \(0.583093\pi\) | |||||||
\(912\) | −1.28621 | −0.0425906 | ||||||||
\(913\) | −16.7138 | −0.553146 | ||||||||
\(914\) | −6.94438 | −0.229700 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.6963 | −0.650785 | ||||||||
\(917\) | −7.70171 | −0.254333 | ||||||||
\(918\) | 8.03013 | 0.265034 | ||||||||
\(919\) | −44.5870 | −1.47079 | −0.735395 | − | 0.677639i | \(-0.763003\pi\) | ||||
−0.735395 | + | 0.677639i | \(0.763003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.59419 | 0.151384 | ||||||||
\(922\) | −12.6377 | −0.416201 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.31767 | −0.0762457 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.62325 | 0.184792 | ||||||||
\(927\) | 32.2814 | 1.06026 | ||||||||
\(928\) | −4.04892 | −0.132912 | ||||||||
\(929\) | −7.09890 | −0.232907 | −0.116454 | − | 0.993196i | \(-0.537153\pi\) | ||||
−0.116454 | + | 0.993196i | \(0.537153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.2392 | 0.335577 | ||||||||
\(932\) | 23.5362 | 0.770953 | ||||||||
\(933\) | −3.33837 | −0.109293 | ||||||||
\(934\) | −35.2054 | −1.15195 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.3297 | 0.370127 | 0.185063 | − | 0.982727i | \(-0.440751\pi\) | ||||
0.185063 | + | 0.982727i | \(0.440751\pi\) | |||||||
\(938\) | −40.2422 | −1.31395 | ||||||||
\(939\) | 2.49396 | 0.0813873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.8689 | −1.62568 | −0.812840 | − | 0.582487i | \(-0.802080\pi\) | ||||
−0.812840 | + | 0.582487i | \(0.802080\pi\) | |||||||
\(942\) | 6.12200 | 0.199465 | ||||||||
\(943\) | −72.4787 | −2.36023 | ||||||||
\(944\) | 5.28621 | 0.172051 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.31767 | 0.270431 | ||||||||
\(947\) | −22.2457 | −0.722887 | −0.361443 | − | 0.932394i | \(-0.617716\pi\) | ||||
−0.361443 | + | 0.932394i | \(0.617716\pi\) | |||||||
\(948\) | 5.03146 | 0.163414 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.24267 | 0.170005 | ||||||||
\(952\) | −10.0978 | −0.327273 | ||||||||
\(953\) | −35.3900 | −1.14639 | −0.573197 | − | 0.819417i | \(-0.694297\pi\) | ||||
−0.573197 | + | 0.819417i | \(0.694297\pi\) | |||||||
\(954\) | 31.0616 | 1.00566 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.4155 | 0.466231 | ||||||||
\(957\) | 2.89008 | 0.0934231 | ||||||||
\(958\) | 7.16421 | 0.231465 | ||||||||
\(959\) | 54.7284 | 1.76727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.1836 | 1.23173 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.4397 | −0.400863 | ||||||||
\(964\) | −15.6692 | −0.504671 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.81163 | 0.315684 | ||||||||
\(967\) | −51.0723 | −1.64238 | −0.821188 | − | 0.570658i | \(-0.806688\pi\) | ||||
−0.821188 | + | 0.570658i | \(0.806688\pi\) | |||||||
\(968\) | 8.42758 | 0.270873 | ||||||||
\(969\) | 4.00000 | 0.128499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.8840 | 1.21575 | 0.607877 | − | 0.794031i | \(-0.292021\pi\) | ||||
0.607877 | + | 0.794031i | \(0.292021\pi\) | |||||||
\(972\) | −10.9758 | −0.352050 | ||||||||
\(973\) | −19.4034 | −0.622045 | ||||||||
\(974\) | −28.7006 | −0.919628 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.1250 | −0.420120 | ||||||||
\(977\) | −31.3685 | −1.00357 | −0.501784 | − | 0.864993i | \(-0.667323\pi\) | ||||
−0.501784 | + | 0.864993i | \(0.667323\pi\) | |||||||
\(978\) | −6.02177 | −0.192555 | ||||||||
\(979\) | −18.2547 | −0.583424 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.5676 | 0.944022 | ||||||||
\(982\) | 42.0689 | 1.34247 | ||||||||
\(983\) | −39.3653 | −1.25556 | −0.627778 | − | 0.778392i | \(-0.716036\pi\) | ||||
−0.627778 | + | 0.778392i | \(0.716036\pi\) | |||||||
\(984\) | 4.75063 | 0.151444 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12.5918 | 0.401004 | ||||||||
\(987\) | −5.74871 | −0.182983 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.2121 | −1.11968 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.2922 | 1.37522 | 0.687611 | − | 0.726080i | \(-0.258660\pi\) | ||||
0.687611 | + | 0.726080i | \(0.258660\pi\) | |||||||
\(992\) | −8.31767 | −0.264086 | ||||||||
\(993\) | −2.87933 | −0.0913728 | ||||||||
\(994\) | 24.3720 | 0.773032 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.63773 | −0.146952 | ||||||||
\(997\) | 4.64609 | 0.147143 | 0.0735715 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735715 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(998\) | 33.2379 | 1.05213 | ||||||||
\(999\) | 8.28275 | 0.262055 |
(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 | 8450.2.a.bo.1.2 | 3 | ||
5.4 | even | 2 | 1690.2.a.s.1.2 | yes | 3 | ||
13.12 | even | 2 | 8450.2.a.bz.1.2 | 3 | |||
65.4 | even | 6 | 1690.2.e.q.991.2 | 6 | |||
65.9 | even | 6 | 1690.2.e.o.991.2 | 6 | |||
65.19 | odd | 12 | 1690.2.l.l.361.2 | 12 | |||
65.24 | odd | 12 | 1690.2.l.l.1161.2 | 12 | |||
65.29 | even | 6 | 1690.2.e.o.191.2 | 6 | |||
65.34 | odd | 4 | 1690.2.d.j.1351.5 | 6 | |||
65.44 | odd | 4 | 1690.2.d.j.1351.2 | 6 | |||
65.49 | even | 6 | 1690.2.e.q.191.2 | 6 | |||
65.54 | odd | 12 | 1690.2.l.l.1161.5 | 12 | |||
65.59 | odd | 12 | 1690.2.l.l.361.5 | 12 | |||
65.64 | even | 2 | 1690.2.a.q.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1690.2.a.q.1.2 | ✓ | 3 | 65.64 | even | 2 | ||
1690.2.a.s.1.2 | yes | 3 | 5.4 | even | 2 | ||
1690.2.d.j.1351.2 | 6 | 65.44 | odd | 4 | |||
1690.2.d.j.1351.5 | 6 | 65.34 | odd | 4 | |||
1690.2.e.o.191.2 | 6 | 65.29 | even | 6 | |||
1690.2.e.o.991.2 | 6 | 65.9 | even | 6 | |||
1690.2.e.q.191.2 | 6 | 65.49 | even | 6 | |||
1690.2.e.q.991.2 | 6 | 65.4 | even | 6 | |||
1690.2.l.l.361.2 | 12 | 65.19 | odd | 12 | |||
1690.2.l.l.361.5 | 12 | 65.59 | odd | 12 | |||
1690.2.l.l.1161.2 | 12 | 65.24 | odd | 12 | |||
1690.2.l.l.1161.5 | 12 | 65.54 | odd | 12 | |||
8450.2.a.bo.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8450.2.a.bz.1.2 | 3 | 13.12 | even | 2 |