Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91337 | −1.35295 | −0.676477 | − | 0.736464i | \(-0.736494\pi\) | ||||
−0.676477 | + | 0.736464i | \(0.736494\pi\) | |||||||
\(3\) | −1.36048 | −0.785476 | −0.392738 | − | 0.919650i | \(-0.628472\pi\) | ||||
−0.392738 | + | 0.919650i | \(0.628472\pi\) | |||||||
\(4\) | 1.66097 | 0.830486 | ||||||||
\(5\) | 1.75251 | 0.783746 | 0.391873 | − | 0.920019i | \(-0.371827\pi\) | ||||
0.391873 | + | 0.920019i | \(0.371827\pi\) | |||||||
\(6\) | 2.60311 | 1.06271 | ||||||||
\(7\) | −4.42851 | −1.67382 | −0.836910 | − | 0.547341i | \(-0.815640\pi\) | ||||
−0.836910 | + | 0.547341i | \(0.815640\pi\) | |||||||
\(8\) | 0.648686 | 0.229345 | ||||||||
\(9\) | −1.14908 | −0.383027 | ||||||||
\(10\) | −3.35319 | −1.06037 | ||||||||
\(11\) | 4.10059 | 1.23637 | 0.618187 | − | 0.786031i | \(-0.287868\pi\) | ||||
0.618187 | + | 0.786031i | \(0.287868\pi\) | |||||||
\(12\) | −2.25973 | −0.652327 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 8.47337 | 2.26460 | ||||||||
\(15\) | −2.38426 | −0.615614 | ||||||||
\(16\) | −4.56312 | −1.14078 | ||||||||
\(17\) | 4.23372 | 1.02683 | 0.513414 | − | 0.858141i | \(-0.328381\pi\) | ||||
0.513414 | + | 0.858141i | \(0.328381\pi\) | |||||||
\(18\) | 2.19861 | 0.518218 | ||||||||
\(19\) | −4.59317 | −1.05375 | −0.526873 | − | 0.849944i | \(-0.676636\pi\) | ||||
−0.526873 | + | 0.849944i | \(0.676636\pi\) | |||||||
\(20\) | 2.91087 | 0.650890 | ||||||||
\(21\) | 6.02492 | 1.31475 | ||||||||
\(22\) | −7.84592 | −1.67276 | ||||||||
\(23\) | 8.60196 | 1.79363 | 0.896816 | − | 0.442404i | \(-0.145874\pi\) | ||||
0.896816 | + | 0.442404i | \(0.145874\pi\) | |||||||
\(24\) | −0.882528 | −0.180145 | ||||||||
\(25\) | −1.92871 | −0.385742 | ||||||||
\(26\) | 1.91337 | 0.375242 | ||||||||
\(27\) | 5.64476 | 1.08633 | ||||||||
\(28\) | −7.35563 | −1.39008 | ||||||||
\(29\) | −8.80134 | −1.63437 | −0.817184 | − | 0.576377i | \(-0.804466\pi\) | ||||
−0.817184 | + | 0.576377i | \(0.804466\pi\) | |||||||
\(30\) | 4.56197 | 0.832898 | ||||||||
\(31\) | 1.18531 | 0.212888 | 0.106444 | − | 0.994319i | \(-0.466054\pi\) | ||||
0.106444 | + | 0.994319i | \(0.466054\pi\) | |||||||
\(32\) | 7.43354 | 1.31408 | ||||||||
\(33\) | −5.57879 | −0.971142 | ||||||||
\(34\) | −8.10066 | −1.38925 | ||||||||
\(35\) | −7.76101 | −1.31185 | ||||||||
\(36\) | −1.90859 | −0.318098 | ||||||||
\(37\) | −3.94318 | −0.648255 | −0.324128 | − | 0.946013i | \(-0.605071\pi\) | ||||
−0.324128 | + | 0.946013i | \(0.605071\pi\) | |||||||
\(38\) | 8.78843 | 1.42567 | ||||||||
\(39\) | 1.36048 | 0.217852 | ||||||||
\(40\) | 1.13683 | 0.179748 | ||||||||
\(41\) | 4.92646 | 0.769383 | 0.384692 | − | 0.923045i | \(-0.374308\pi\) | ||||
0.384692 | + | 0.923045i | \(0.374308\pi\) | |||||||
\(42\) | −11.5279 | −1.77879 | ||||||||
\(43\) | 1.43278 | 0.218496 | 0.109248 | − | 0.994015i | \(-0.465156\pi\) | ||||
0.109248 | + | 0.994015i | \(0.465156\pi\) | |||||||
\(44\) | 6.81096 | 1.02679 | ||||||||
\(45\) | −2.01378 | −0.300196 | ||||||||
\(46\) | −16.4587 | −2.42670 | ||||||||
\(47\) | 11.9193 | 1.73861 | 0.869303 | − | 0.494279i | \(-0.164568\pi\) | ||||
0.869303 | + | 0.494279i | \(0.164568\pi\) | |||||||
\(48\) | 6.20805 | 0.896055 | ||||||||
\(49\) | 12.6117 | 1.80167 | ||||||||
\(50\) | 3.69033 | 0.521891 | ||||||||
\(51\) | −5.75991 | −0.806549 | ||||||||
\(52\) | −1.66097 | −0.230335 | ||||||||
\(53\) | −11.6576 | −1.60130 | −0.800650 | − | 0.599133i | \(-0.795512\pi\) | ||||
−0.800650 | + | 0.599133i | \(0.795512\pi\) | |||||||
\(54\) | −10.8005 | −1.46976 | ||||||||
\(55\) | 7.18632 | 0.969003 | ||||||||
\(56\) | −2.87271 | −0.383883 | ||||||||
\(57\) | 6.24894 | 0.827693 | ||||||||
\(58\) | 16.8402 | 2.21122 | ||||||||
\(59\) | −3.82464 | −0.497925 | −0.248963 | − | 0.968513i | \(-0.580090\pi\) | ||||
−0.248963 | + | 0.968513i | \(0.580090\pi\) | |||||||
\(60\) | −3.96019 | −0.511259 | ||||||||
\(61\) | 4.08144 | 0.522575 | 0.261288 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261288 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(62\) | −2.26793 | −0.288027 | ||||||||
\(63\) | 5.08872 | 0.641118 | ||||||||
\(64\) | −5.09686 | −0.637107 | ||||||||
\(65\) | −1.75251 | −0.217372 | ||||||||
\(66\) | 10.6743 | 1.31391 | ||||||||
\(67\) | −7.44591 | −0.909662 | −0.454831 | − | 0.890578i | \(-0.650300\pi\) | ||||
−0.454831 | + | 0.890578i | \(0.650300\pi\) | |||||||
\(68\) | 7.03209 | 0.852766 | ||||||||
\(69\) | −11.7028 | −1.40886 | ||||||||
\(70\) | 14.8497 | 1.77487 | ||||||||
\(71\) | −4.65470 | −0.552411 | −0.276206 | − | 0.961099i | \(-0.589077\pi\) | ||||
−0.276206 | + | 0.961099i | \(0.589077\pi\) | |||||||
\(72\) | −0.745393 | −0.0878454 | ||||||||
\(73\) | 11.0015 | 1.28763 | 0.643814 | − | 0.765182i | \(-0.277351\pi\) | ||||
0.643814 | + | 0.765182i | \(0.277351\pi\) | |||||||
\(74\) | 7.54475 | 0.877060 | ||||||||
\(75\) | 2.62398 | 0.302991 | ||||||||
\(76\) | −7.62913 | −0.875121 | ||||||||
\(77\) | −18.1595 | −2.06947 | ||||||||
\(78\) | −2.60311 | −0.294744 | ||||||||
\(79\) | −0.880429 | −0.0990560 | −0.0495280 | − | 0.998773i | \(-0.515772\pi\) | ||||
−0.0495280 | + | 0.998773i | \(0.515772\pi\) | |||||||
\(80\) | −7.99691 | −0.894082 | ||||||||
\(81\) | −4.23237 | −0.470263 | ||||||||
\(82\) | −9.42612 | −1.04094 | ||||||||
\(83\) | 4.57453 | 0.502120 | 0.251060 | − | 0.967971i | \(-0.419221\pi\) | ||||
0.251060 | + | 0.967971i | \(0.419221\pi\) | |||||||
\(84\) | 10.0072 | 1.09188 | ||||||||
\(85\) | 7.41964 | 0.804773 | ||||||||
\(86\) | −2.74143 | −0.295616 | ||||||||
\(87\) | 11.9741 | 1.28376 | ||||||||
\(88\) | 2.65999 | 0.283556 | ||||||||
\(89\) | −9.03714 | −0.957935 | −0.478968 | − | 0.877833i | \(-0.658989\pi\) | ||||
−0.478968 | + | 0.877833i | \(0.658989\pi\) | |||||||
\(90\) | 3.85309 | 0.406151 | ||||||||
\(91\) | 4.42851 | 0.464234 | ||||||||
\(92\) | 14.2876 | 1.48959 | ||||||||
\(93\) | −1.61259 | −0.167218 | ||||||||
\(94\) | −22.8060 | −2.35226 | ||||||||
\(95\) | −8.04959 | −0.825870 | ||||||||
\(96\) | −10.1132 | −1.03218 | ||||||||
\(97\) | −15.8216 | −1.60644 | −0.803221 | − | 0.595681i | \(-0.796882\pi\) | ||||
−0.803221 | + | 0.595681i | \(0.796882\pi\) | |||||||
\(98\) | −24.1308 | −2.43758 | ||||||||
\(99\) | −4.71191 | −0.473564 | ||||||||
\(100\) | −3.20353 | −0.320353 | ||||||||
\(101\) | −1.82151 | −0.181247 | −0.0906235 | − | 0.995885i | \(-0.528886\pi\) | ||||
−0.0906235 | + | 0.995885i | \(0.528886\pi\) | |||||||
\(102\) | 11.0208 | 1.09122 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −0.648686 | −0.0636089 | ||||||||
\(105\) | 10.5587 | 1.03043 | ||||||||
\(106\) | 22.3053 | 2.16648 | ||||||||
\(107\) | 15.4023 | 1.48900 | 0.744500 | − | 0.667623i | \(-0.232688\pi\) | ||||
0.744500 | + | 0.667623i | \(0.232688\pi\) | |||||||
\(108\) | 9.37579 | 0.902186 | ||||||||
\(109\) | −19.3765 | −1.85593 | −0.927967 | − | 0.372663i | \(-0.878445\pi\) | ||||
−0.927967 | + | 0.372663i | \(0.878445\pi\) | |||||||
\(110\) | −13.7501 | −1.31102 | ||||||||
\(111\) | 5.36464 | 0.509189 | ||||||||
\(112\) | 20.2078 | 1.90946 | ||||||||
\(113\) | −16.7309 | −1.57391 | −0.786955 | − | 0.617011i | \(-0.788343\pi\) | ||||
−0.786955 | + | 0.617011i | \(0.788343\pi\) | |||||||
\(114\) | −11.9565 | −1.11983 | ||||||||
\(115\) | 15.0750 | 1.40575 | ||||||||
\(116\) | −14.6188 | −1.35732 | ||||||||
\(117\) | 1.14908 | 0.106233 | ||||||||
\(118\) | 7.31793 | 0.673670 | ||||||||
\(119\) | −18.7491 | −1.71873 | ||||||||
\(120\) | −1.54664 | −0.141188 | ||||||||
\(121\) | 5.81481 | 0.528619 | ||||||||
\(122\) | −7.80930 | −0.707021 | ||||||||
\(123\) | −6.70237 | −0.604333 | ||||||||
\(124\) | 1.96876 | 0.176800 | ||||||||
\(125\) | −12.1426 | −1.08607 | ||||||||
\(126\) | −9.73658 | −0.867404 | ||||||||
\(127\) | −16.6389 | −1.47647 | −0.738233 | − | 0.674546i | \(-0.764340\pi\) | ||||
−0.738233 | + | 0.674546i | \(0.764340\pi\) | |||||||
\(128\) | −5.11493 | −0.452100 | ||||||||
\(129\) | −1.94927 | −0.171624 | ||||||||
\(130\) | 3.35319 | 0.294095 | ||||||||
\(131\) | −5.86853 | −0.512736 | −0.256368 | − | 0.966579i | \(-0.582526\pi\) | ||||
−0.256368 | + | 0.966579i | \(0.582526\pi\) | |||||||
\(132\) | −9.26620 | −0.806519 | ||||||||
\(133\) | 20.3409 | 1.76378 | ||||||||
\(134\) | 14.2467 | 1.23073 | ||||||||
\(135\) | 9.89250 | 0.851411 | ||||||||
\(136\) | 2.74636 | 0.235498 | ||||||||
\(137\) | 1.90075 | 0.162392 | 0.0811961 | − | 0.996698i | \(-0.474126\pi\) | ||||
0.0811961 | + | 0.996698i | \(0.474126\pi\) | |||||||
\(138\) | 22.3918 | 1.90612 | ||||||||
\(139\) | −12.8661 | −1.09129 | −0.545646 | − | 0.838016i | \(-0.683716\pi\) | ||||
−0.545646 | + | 0.838016i | \(0.683716\pi\) | |||||||
\(140\) | −12.8908 | −1.08947 | ||||||||
\(141\) | −16.2160 | −1.36563 | ||||||||
\(142\) | 8.90615 | 0.747387 | ||||||||
\(143\) | −4.10059 | −0.342908 | ||||||||
\(144\) | 5.24339 | 0.436949 | ||||||||
\(145\) | −15.4244 | −1.28093 | ||||||||
\(146\) | −21.0499 | −1.74210 | ||||||||
\(147\) | −17.1580 | −1.41517 | ||||||||
\(148\) | −6.54951 | −0.538367 | ||||||||
\(149\) | −13.0161 | −1.06632 | −0.533160 | − | 0.846014i | \(-0.678996\pi\) | ||||
−0.533160 | + | 0.846014i | \(0.678996\pi\) | |||||||
\(150\) | −5.02063 | −0.409933 | ||||||||
\(151\) | −16.2129 | −1.31939 | −0.659693 | − | 0.751535i | \(-0.729314\pi\) | ||||
−0.659693 | + | 0.751535i | \(0.729314\pi\) | |||||||
\(152\) | −2.97953 | −0.241672 | ||||||||
\(153\) | −4.86489 | −0.393303 | ||||||||
\(154\) | 34.7458 | 2.79989 | ||||||||
\(155\) | 2.07726 | 0.166850 | ||||||||
\(156\) | 2.25973 | 0.180923 | ||||||||
\(157\) | −12.3536 | −0.985922 | −0.492961 | − | 0.870051i | \(-0.664085\pi\) | ||||
−0.492961 | + | 0.870051i | \(0.664085\pi\) | |||||||
\(158\) | 1.68458 | 0.134018 | ||||||||
\(159\) | 15.8600 | 1.25778 | ||||||||
\(160\) | 13.0274 | 1.02990 | ||||||||
\(161\) | −38.0939 | −3.00222 | ||||||||
\(162\) | 8.09808 | 0.636245 | ||||||||
\(163\) | −20.1710 | −1.57992 | −0.789959 | − | 0.613160i | \(-0.789898\pi\) | ||||
−0.789959 | + | 0.613160i | \(0.789898\pi\) | |||||||
\(164\) | 8.18271 | 0.638962 | ||||||||
\(165\) | −9.77688 | −0.761129 | ||||||||
\(166\) | −8.75276 | −0.679346 | ||||||||
\(167\) | 19.2395 | 1.48880 | 0.744399 | − | 0.667735i | \(-0.232736\pi\) | ||||
0.744399 | + | 0.667735i | \(0.232736\pi\) | |||||||
\(168\) | 3.90828 | 0.301531 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −14.1965 | −1.08882 | ||||||||
\(171\) | 5.27793 | 0.403613 | ||||||||
\(172\) | 2.37980 | 0.181458 | ||||||||
\(173\) | 11.0717 | 0.841762 | 0.420881 | − | 0.907116i | \(-0.361721\pi\) | ||||
0.420881 | + | 0.907116i | \(0.361721\pi\) | |||||||
\(174\) | −22.9108 | −1.73686 | ||||||||
\(175\) | 8.54131 | 0.645662 | ||||||||
\(176\) | −18.7115 | −1.41043 | ||||||||
\(177\) | 5.20336 | 0.391109 | ||||||||
\(178\) | 17.2914 | 1.29604 | ||||||||
\(179\) | −17.4771 | −1.30630 | −0.653149 | − | 0.757230i | \(-0.726552\pi\) | ||||
−0.653149 | + | 0.757230i | \(0.726552\pi\) | |||||||
\(180\) | −3.34482 | −0.249308 | ||||||||
\(181\) | −9.36583 | −0.696157 | −0.348078 | − | 0.937465i | \(-0.613166\pi\) | ||||
−0.348078 | + | 0.937465i | \(0.613166\pi\) | |||||||
\(182\) | −8.47337 | −0.628088 | ||||||||
\(183\) | −5.55274 | −0.410470 | ||||||||
\(184\) | 5.57997 | 0.411361 | ||||||||
\(185\) | −6.91047 | −0.508068 | ||||||||
\(186\) | 3.08548 | 0.226239 | ||||||||
\(187\) | 17.3607 | 1.26954 | ||||||||
\(188\) | 19.7976 | 1.44389 | ||||||||
\(189\) | −24.9979 | −1.81833 | ||||||||
\(190\) | 15.4018 | 1.11736 | ||||||||
\(191\) | 0.108131 | 0.00782409 | 0.00391205 | − | 0.999992i | \(-0.498755\pi\) | ||||
0.00391205 | + | 0.999992i | \(0.498755\pi\) | |||||||
\(192\) | 6.93420 | 0.500433 | ||||||||
\(193\) | −4.51939 | −0.325312 | −0.162656 | − | 0.986683i | \(-0.552006\pi\) | ||||
−0.162656 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(194\) | 30.2725 | 2.17344 | ||||||||
\(195\) | 2.38426 | 0.170741 | ||||||||
\(196\) | 20.9477 | 1.49626 | ||||||||
\(197\) | 22.0431 | 1.57051 | 0.785253 | − | 0.619175i | \(-0.212533\pi\) | ||||
0.785253 | + | 0.619175i | \(0.212533\pi\) | |||||||
\(198\) | 9.01560 | 0.640711 | ||||||||
\(199\) | −4.69354 | −0.332716 | −0.166358 | − | 0.986065i | \(-0.553201\pi\) | ||||
−0.166358 | + | 0.986065i | \(0.553201\pi\) | |||||||
\(200\) | −1.25113 | −0.0884680 | ||||||||
\(201\) | 10.1300 | 0.714518 | ||||||||
\(202\) | 3.48521 | 0.245219 | ||||||||
\(203\) | 38.9768 | 2.73564 | ||||||||
\(204\) | −9.56705 | −0.669827 | ||||||||
\(205\) | 8.63367 | 0.603002 | ||||||||
\(206\) | 1.91337 | 0.133311 | ||||||||
\(207\) | −9.88434 | −0.687009 | ||||||||
\(208\) | 4.56312 | 0.316395 | ||||||||
\(209\) | −18.8347 | −1.30282 | ||||||||
\(210\) | −20.2027 | −1.39412 | ||||||||
\(211\) | −2.32294 | −0.159917 | −0.0799587 | − | 0.996798i | \(-0.525479\pi\) | ||||
−0.0799587 | + | 0.996798i | \(0.525479\pi\) | |||||||
\(212\) | −19.3630 | −1.32986 | ||||||||
\(213\) | 6.33265 | 0.433906 | ||||||||
\(214\) | −29.4703 | −2.01455 | ||||||||
\(215\) | 2.51096 | 0.171246 | ||||||||
\(216\) | 3.66168 | 0.249146 | ||||||||
\(217\) | −5.24915 | −0.356336 | ||||||||
\(218\) | 37.0744 | 2.51099 | ||||||||
\(219\) | −14.9674 | −1.01140 | ||||||||
\(220\) | 11.9363 | 0.804743 | ||||||||
\(221\) | −4.23372 | −0.284791 | ||||||||
\(222\) | −10.2645 | −0.688910 | ||||||||
\(223\) | 12.2759 | 0.822055 | 0.411028 | − | 0.911623i | \(-0.365170\pi\) | ||||
0.411028 | + | 0.911623i | \(0.365170\pi\) | |||||||
\(224\) | −32.9195 | −2.19953 | ||||||||
\(225\) | 2.21624 | 0.147749 | ||||||||
\(226\) | 32.0123 | 2.12943 | ||||||||
\(227\) | 16.1847 | 1.07422 | 0.537109 | − | 0.843513i | \(-0.319516\pi\) | ||||
0.537109 | + | 0.843513i | \(0.319516\pi\) | |||||||
\(228\) | 10.3793 | 0.687387 | ||||||||
\(229\) | −9.28080 | −0.613293 | −0.306646 | − | 0.951824i | \(-0.599207\pi\) | ||||
−0.306646 | + | 0.951824i | \(0.599207\pi\) | |||||||
\(230\) | −28.8440 | −1.90192 | ||||||||
\(231\) | 24.7057 | 1.62552 | ||||||||
\(232\) | −5.70931 | −0.374834 | ||||||||
\(233\) | −3.34048 | −0.218842 | −0.109421 | − | 0.993995i | \(-0.534900\pi\) | ||||
−0.109421 | + | 0.993995i | \(0.534900\pi\) | |||||||
\(234\) | −2.19861 | −0.143728 | ||||||||
\(235\) | 20.8887 | 1.36263 | ||||||||
\(236\) | −6.35261 | −0.413520 | ||||||||
\(237\) | 1.19781 | 0.0778062 | ||||||||
\(238\) | 35.8739 | 2.32536 | ||||||||
\(239\) | 27.3070 | 1.76634 | 0.883171 | − | 0.469052i | \(-0.155404\pi\) | ||||
0.883171 | + | 0.469052i | \(0.155404\pi\) | |||||||
\(240\) | 10.8797 | 0.702280 | ||||||||
\(241\) | 12.3424 | 0.795042 | 0.397521 | − | 0.917593i | \(-0.369871\pi\) | ||||
0.397521 | + | 0.917593i | \(0.369871\pi\) | |||||||
\(242\) | −11.1259 | −0.715197 | ||||||||
\(243\) | −11.1762 | −0.716954 | ||||||||
\(244\) | 6.77916 | 0.433991 | ||||||||
\(245\) | 22.1022 | 1.41205 | ||||||||
\(246\) | 12.8241 | 0.817634 | ||||||||
\(247\) | 4.59317 | 0.292257 | ||||||||
\(248\) | 0.768893 | 0.0488248 | ||||||||
\(249\) | −6.22358 | −0.394404 | ||||||||
\(250\) | 23.2333 | 1.46940 | ||||||||
\(251\) | 11.2079 | 0.707435 | 0.353718 | − | 0.935352i | \(-0.384917\pi\) | ||||
0.353718 | + | 0.935352i | \(0.384917\pi\) | |||||||
\(252\) | 8.45221 | 0.532439 | ||||||||
\(253\) | 35.2731 | 2.21760 | ||||||||
\(254\) | 31.8364 | 1.99759 | ||||||||
\(255\) | −10.0943 | −0.632130 | ||||||||
\(256\) | 19.9804 | 1.24878 | ||||||||
\(257\) | −9.06258 | −0.565308 | −0.282654 | − | 0.959222i | \(-0.591215\pi\) | ||||
−0.282654 | + | 0.959222i | \(0.591215\pi\) | |||||||
\(258\) | 3.72967 | 0.232199 | ||||||||
\(259\) | 17.4624 | 1.08506 | ||||||||
\(260\) | −2.91087 | −0.180524 | ||||||||
\(261\) | 10.1134 | 0.626007 | ||||||||
\(262\) | 11.2286 | 0.693708 | ||||||||
\(263\) | −14.4739 | −0.892496 | −0.446248 | − | 0.894909i | \(-0.647240\pi\) | ||||
−0.446248 | + | 0.894909i | \(0.647240\pi\) | |||||||
\(264\) | −3.61888 | −0.222727 | ||||||||
\(265\) | −20.4301 | −1.25501 | ||||||||
\(266\) | −38.9196 | −2.38632 | ||||||||
\(267\) | 12.2949 | 0.752435 | ||||||||
\(268\) | −12.3674 | −0.755462 | ||||||||
\(269\) | −30.3196 | −1.84862 | −0.924309 | − | 0.381644i | \(-0.875358\pi\) | ||||
−0.924309 | + | 0.381644i | \(0.875358\pi\) | |||||||
\(270\) | −18.9280 | −1.15192 | ||||||||
\(271\) | 17.6430 | 1.07174 | 0.535869 | − | 0.844301i | \(-0.319984\pi\) | ||||
0.535869 | + | 0.844301i | \(0.319984\pi\) | |||||||
\(272\) | −19.3190 | −1.17138 | ||||||||
\(273\) | −6.02492 | −0.364645 | ||||||||
\(274\) | −3.63684 | −0.219709 | ||||||||
\(275\) | −7.90883 | −0.476921 | ||||||||
\(276\) | −19.4381 | −1.17003 | ||||||||
\(277\) | −9.25458 | −0.556054 | −0.278027 | − | 0.960573i | \(-0.589680\pi\) | ||||
−0.278027 | + | 0.960573i | \(0.589680\pi\) | |||||||
\(278\) | 24.6176 | 1.47647 | ||||||||
\(279\) | −1.36201 | −0.0815417 | ||||||||
\(280\) | −5.03446 | −0.300867 | ||||||||
\(281\) | 29.7435 | 1.77435 | 0.887173 | − | 0.461437i | \(-0.152666\pi\) | ||||
0.887173 | + | 0.461437i | \(0.152666\pi\) | |||||||
\(282\) | 31.0272 | 1.84764 | ||||||||
\(283\) | −10.0231 | −0.595814 | −0.297907 | − | 0.954595i | \(-0.596289\pi\) | ||||
−0.297907 | + | 0.954595i | \(0.596289\pi\) | |||||||
\(284\) | −7.73132 | −0.458770 | ||||||||
\(285\) | 10.9513 | 0.648701 | ||||||||
\(286\) | 7.84592 | 0.463939 | ||||||||
\(287\) | −21.8169 | −1.28781 | ||||||||
\(288\) | −8.54174 | −0.503327 | ||||||||
\(289\) | 0.924390 | 0.0543759 | ||||||||
\(290\) | 29.5126 | 1.73304 | ||||||||
\(291\) | 21.5251 | 1.26182 | ||||||||
\(292\) | 18.2732 | 1.06936 | ||||||||
\(293\) | −9.31126 | −0.543969 | −0.271985 | − | 0.962302i | \(-0.587680\pi\) | ||||
−0.271985 | + | 0.962302i | \(0.587680\pi\) | |||||||
\(294\) | 32.8296 | 1.91466 | ||||||||
\(295\) | −6.70272 | −0.390247 | ||||||||
\(296\) | −2.55789 | −0.148674 | ||||||||
\(297\) | 23.1468 | 1.34312 | ||||||||
\(298\) | 24.9046 | 1.44268 | ||||||||
\(299\) | −8.60196 | −0.497464 | ||||||||
\(300\) | 4.35835 | 0.251630 | ||||||||
\(301\) | −6.34507 | −0.365724 | ||||||||
\(302\) | 31.0212 | 1.78507 | ||||||||
\(303\) | 2.47814 | 0.142365 | ||||||||
\(304\) | 20.9592 | 1.20209 | ||||||||
\(305\) | 7.15277 | 0.409566 | ||||||||
\(306\) | 9.30831 | 0.532121 | ||||||||
\(307\) | 5.60259 | 0.319757 | 0.159878 | − | 0.987137i | \(-0.448890\pi\) | ||||
0.159878 | + | 0.987137i | \(0.448890\pi\) | |||||||
\(308\) | −30.1624 | −1.71866 | ||||||||
\(309\) | 1.36048 | 0.0773953 | ||||||||
\(310\) | −3.97457 | −0.225740 | ||||||||
\(311\) | −27.1646 | −1.54037 | −0.770183 | − | 0.637823i | \(-0.779835\pi\) | ||||
−0.770183 | + | 0.637823i | \(0.779835\pi\) | |||||||
\(312\) | 0.882528 | 0.0499633 | ||||||||
\(313\) | −5.96045 | −0.336904 | −0.168452 | − | 0.985710i | \(-0.553877\pi\) | ||||
−0.168452 | + | 0.985710i | \(0.553877\pi\) | |||||||
\(314\) | 23.6369 | 1.33391 | ||||||||
\(315\) | 8.91803 | 0.502474 | ||||||||
\(316\) | −1.46237 | −0.0822646 | ||||||||
\(317\) | 1.59706 | 0.0896996 | 0.0448498 | − | 0.998994i | \(-0.485719\pi\) | ||||
0.0448498 | + | 0.998994i | \(0.485719\pi\) | |||||||
\(318\) | −30.3461 | −1.70172 | ||||||||
\(319\) | −36.0906 | −2.02069 | ||||||||
\(320\) | −8.93229 | −0.499330 | ||||||||
\(321\) | −20.9546 | −1.16957 | ||||||||
\(322\) | 72.8875 | 4.06186 | ||||||||
\(323\) | −19.4462 | −1.08202 | ||||||||
\(324\) | −7.02985 | −0.390547 | ||||||||
\(325\) | 1.92871 | 0.106985 | ||||||||
\(326\) | 38.5946 | 2.13756 | ||||||||
\(327\) | 26.3615 | 1.45779 | ||||||||
\(328\) | 3.19573 | 0.176454 | ||||||||
\(329\) | −52.7847 | −2.91011 | ||||||||
\(330\) | 18.7068 | 1.02977 | ||||||||
\(331\) | 8.74225 | 0.480518 | 0.240259 | − | 0.970709i | \(-0.422768\pi\) | ||||
0.240259 | + | 0.970709i | \(0.422768\pi\) | |||||||
\(332\) | 7.59817 | 0.417004 | ||||||||
\(333\) | 4.53104 | 0.248299 | ||||||||
\(334\) | −36.8122 | −2.01428 | ||||||||
\(335\) | −13.0490 | −0.712945 | ||||||||
\(336\) | −27.4924 | −1.49983 | ||||||||
\(337\) | 13.7834 | 0.750827 | 0.375414 | − | 0.926857i | \(-0.377501\pi\) | ||||
0.375414 | + | 0.926857i | \(0.377501\pi\) | |||||||
\(338\) | −1.91337 | −0.104073 | ||||||||
\(339\) | 22.7621 | 1.23627 | ||||||||
\(340\) | 12.3238 | 0.668352 | ||||||||
\(341\) | 4.86046 | 0.263209 | ||||||||
\(342\) | −10.0986 | −0.546070 | ||||||||
\(343\) | −24.8515 | −1.34186 | ||||||||
\(344\) | 0.929422 | 0.0501111 | ||||||||
\(345\) | −20.5093 | −1.10419 | ||||||||
\(346\) | −21.1841 | −1.13887 | ||||||||
\(347\) | −8.86570 | −0.475936 | −0.237968 | − | 0.971273i | \(-0.576481\pi\) | ||||
−0.237968 | + | 0.971273i | \(0.576481\pi\) | |||||||
\(348\) | 19.8886 | 1.06614 | ||||||||
\(349\) | −6.76495 | −0.362119 | −0.181060 | − | 0.983472i | \(-0.557953\pi\) | ||||
−0.181060 | + | 0.983472i | \(0.557953\pi\) | |||||||
\(350\) | −16.3426 | −0.873551 | ||||||||
\(351\) | −5.64476 | −0.301295 | ||||||||
\(352\) | 30.4819 | 1.62469 | ||||||||
\(353\) | 14.1417 | 0.752686 | 0.376343 | − | 0.926480i | \(-0.377181\pi\) | ||||
0.376343 | + | 0.926480i | \(0.377181\pi\) | |||||||
\(354\) | −9.95594 | −0.529152 | ||||||||
\(355\) | −8.15741 | −0.432950 | ||||||||
\(356\) | −15.0104 | −0.795551 | ||||||||
\(357\) | 25.5078 | 1.35002 | ||||||||
\(358\) | 33.4400 | 1.76736 | ||||||||
\(359\) | −4.26278 | −0.224981 | −0.112490 | − | 0.993653i | \(-0.535883\pi\) | ||||
−0.112490 | + | 0.993653i | \(0.535883\pi\) | |||||||
\(360\) | −1.30631 | −0.0688485 | ||||||||
\(361\) | 2.09725 | 0.110382 | ||||||||
\(362\) | 17.9203 | 0.941868 | ||||||||
\(363\) | −7.91096 | −0.415218 | ||||||||
\(364\) | 7.35563 | 0.385540 | ||||||||
\(365\) | 19.2802 | 1.00917 | ||||||||
\(366\) | 10.6244 | 0.555348 | ||||||||
\(367\) | −34.4687 | −1.79925 | −0.899625 | − | 0.436663i | \(-0.856160\pi\) | ||||
−0.899625 | + | 0.436663i | \(0.856160\pi\) | |||||||
\(368\) | −39.2517 | −2.04614 | ||||||||
\(369\) | −5.66090 | −0.294695 | ||||||||
\(370\) | 13.2223 | 0.687392 | ||||||||
\(371\) | 51.6260 | 2.68029 | ||||||||
\(372\) | −2.67847 | −0.138872 | ||||||||
\(373\) | 18.3277 | 0.948971 | 0.474485 | − | 0.880263i | \(-0.342634\pi\) | ||||
0.474485 | + | 0.880263i | \(0.342634\pi\) | |||||||
\(374\) | −33.2175 | −1.71763 | ||||||||
\(375\) | 16.5199 | 0.853082 | ||||||||
\(376\) | 7.73187 | 0.398741 | ||||||||
\(377\) | 8.80134 | 0.453292 | ||||||||
\(378\) | 47.8301 | 2.46012 | ||||||||
\(379\) | 1.01429 | 0.0521007 | 0.0260503 | − | 0.999661i | \(-0.491707\pi\) | ||||
0.0260503 | + | 0.999661i | \(0.491707\pi\) | |||||||
\(380\) | −13.3701 | −0.685873 | ||||||||
\(381\) | 22.6370 | 1.15973 | ||||||||
\(382\) | −0.206894 | −0.0105856 | ||||||||
\(383\) | 1.97117 | 0.100722 | 0.0503611 | − | 0.998731i | \(-0.483963\pi\) | ||||
0.0503611 | + | 0.998731i | \(0.483963\pi\) | |||||||
\(384\) | 6.95878 | 0.355114 | ||||||||
\(385\) | −31.8247 | −1.62194 | ||||||||
\(386\) | 8.64724 | 0.440133 | ||||||||
\(387\) | −1.64638 | −0.0836900 | ||||||||
\(388\) | −26.2792 | −1.33413 | ||||||||
\(389\) | 31.7247 | 1.60851 | 0.804254 | − | 0.594285i | \(-0.202565\pi\) | ||||
0.804254 | + | 0.594285i | \(0.202565\pi\) | |||||||
\(390\) | −4.56197 | −0.231004 | ||||||||
\(391\) | 36.4183 | 1.84175 | ||||||||
\(392\) | 8.18104 | 0.413205 | ||||||||
\(393\) | 7.98405 | 0.402742 | ||||||||
\(394\) | −42.1765 | −2.12482 | ||||||||
\(395\) | −1.54296 | −0.0776348 | ||||||||
\(396\) | −7.82634 | −0.393288 | ||||||||
\(397\) | −12.8448 | −0.644660 | −0.322330 | − | 0.946627i | \(-0.604466\pi\) | ||||
−0.322330 | + | 0.946627i | \(0.604466\pi\) | |||||||
\(398\) | 8.98046 | 0.450150 | ||||||||
\(399\) | −27.6735 | −1.38541 | ||||||||
\(400\) | 8.80092 | 0.440046 | ||||||||
\(401\) | −17.4827 | −0.873046 | −0.436523 | − | 0.899693i | \(-0.643790\pi\) | ||||
−0.436523 | + | 0.899693i | \(0.643790\pi\) | |||||||
\(402\) | −19.3825 | −0.966711 | ||||||||
\(403\) | −1.18531 | −0.0590444 | ||||||||
\(404\) | −3.02547 | −0.150523 | ||||||||
\(405\) | −7.41727 | −0.368567 | ||||||||
\(406\) | −74.5770 | −3.70119 | ||||||||
\(407\) | −16.1694 | −0.801486 | ||||||||
\(408\) | −3.73638 | −0.184978 | ||||||||
\(409\) | −1.50696 | −0.0745143 | −0.0372572 | − | 0.999306i | \(-0.511862\pi\) | ||||
−0.0372572 | + | 0.999306i | \(0.511862\pi\) | |||||||
\(410\) | −16.5194 | −0.815834 | ||||||||
\(411\) | −2.58595 | −0.127555 | ||||||||
\(412\) | −1.66097 | −0.0818302 | ||||||||
\(413\) | 16.9375 | 0.833438 | ||||||||
\(414\) | 18.9124 | 0.929492 | ||||||||
\(415\) | 8.01692 | 0.393535 | ||||||||
\(416\) | −7.43354 | −0.364459 | ||||||||
\(417\) | 17.5042 | 0.857184 | ||||||||
\(418\) | 36.0377 | 1.76266 | ||||||||
\(419\) | 24.2698 | 1.18566 | 0.592828 | − | 0.805329i | \(-0.298011\pi\) | ||||
0.592828 | + | 0.805329i | \(0.298011\pi\) | |||||||
\(420\) | 17.5378 | 0.855755 | ||||||||
\(421\) | −7.62923 | −0.371826 | −0.185913 | − | 0.982566i | \(-0.559524\pi\) | ||||
−0.185913 | + | 0.982566i | \(0.559524\pi\) | |||||||
\(422\) | 4.44463 | 0.216361 | ||||||||
\(423\) | −13.6962 | −0.665933 | ||||||||
\(424\) | −7.56215 | −0.367250 | ||||||||
\(425\) | −8.16561 | −0.396090 | ||||||||
\(426\) | −12.1167 | −0.587055 | ||||||||
\(427\) | −18.0747 | −0.874697 | ||||||||
\(428\) | 25.5828 | 1.23659 | ||||||||
\(429\) | 5.57879 | 0.269346 | ||||||||
\(430\) | −4.80438 | −0.231688 | ||||||||
\(431\) | 8.53329 | 0.411034 | 0.205517 | − | 0.978654i | \(-0.434112\pi\) | ||||
0.205517 | + | 0.978654i | \(0.434112\pi\) | |||||||
\(432\) | −25.7577 | −1.23927 | ||||||||
\(433\) | −9.60849 | −0.461755 | −0.230877 | − | 0.972983i | \(-0.574160\pi\) | ||||
−0.230877 | + | 0.972983i | \(0.574160\pi\) | |||||||
\(434\) | 10.0435 | 0.482106 | ||||||||
\(435\) | 20.9847 | 1.00614 | ||||||||
\(436\) | −32.1838 | −1.54133 | ||||||||
\(437\) | −39.5103 | −1.89003 | ||||||||
\(438\) | 28.6381 | 1.36838 | ||||||||
\(439\) | −26.7439 | −1.27642 | −0.638209 | − | 0.769863i | \(-0.720325\pi\) | ||||
−0.638209 | + | 0.769863i | \(0.720325\pi\) | |||||||
\(440\) | 4.66167 | 0.222236 | ||||||||
\(441\) | −14.4919 | −0.690089 | ||||||||
\(442\) | 8.10066 | 0.385309 | ||||||||
\(443\) | 1.70561 | 0.0810360 | 0.0405180 | − | 0.999179i | \(-0.487099\pi\) | ||||
0.0405180 | + | 0.999179i | \(0.487099\pi\) | |||||||
\(444\) | 8.91051 | 0.422874 | ||||||||
\(445\) | −15.8377 | −0.750778 | ||||||||
\(446\) | −23.4883 | −1.11220 | ||||||||
\(447\) | 17.7082 | 0.837569 | ||||||||
\(448\) | 22.5715 | 1.06640 | ||||||||
\(449\) | 37.1179 | 1.75170 | 0.875852 | − | 0.482580i | \(-0.160300\pi\) | ||||
0.875852 | + | 0.482580i | \(0.160300\pi\) | |||||||
\(450\) | −4.24048 | −0.199898 | ||||||||
\(451\) | 20.2014 | 0.951245 | ||||||||
\(452\) | −27.7895 | −1.30711 | ||||||||
\(453\) | 22.0574 | 1.03635 | ||||||||
\(454\) | −30.9673 | −1.45337 | ||||||||
\(455\) | 7.76101 | 0.363842 | ||||||||
\(456\) | 4.05360 | 0.189827 | ||||||||
\(457\) | −21.0564 | −0.984979 | −0.492489 | − | 0.870318i | \(-0.663913\pi\) | ||||
−0.492489 | + | 0.870318i | \(0.663913\pi\) | |||||||
\(458\) | 17.7576 | 0.829757 | ||||||||
\(459\) | 23.8983 | 1.11548 | ||||||||
\(460\) | 25.0392 | 1.16746 | ||||||||
\(461\) | −19.5646 | −0.911215 | −0.455608 | − | 0.890181i | \(-0.650578\pi\) | ||||
−0.455608 | + | 0.890181i | \(0.650578\pi\) | |||||||
\(462\) | −47.2711 | −2.19925 | ||||||||
\(463\) | 5.91566 | 0.274924 | 0.137462 | − | 0.990507i | \(-0.456105\pi\) | ||||
0.137462 | + | 0.990507i | \(0.456105\pi\) | |||||||
\(464\) | 40.1615 | 1.86445 | ||||||||
\(465\) | −2.82609 | −0.131057 | ||||||||
\(466\) | 6.39157 | 0.296084 | ||||||||
\(467\) | −3.26969 | −0.151303 | −0.0756517 | − | 0.997134i | \(-0.524104\pi\) | ||||
−0.0756517 | + | 0.997134i | \(0.524104\pi\) | |||||||
\(468\) | 1.90859 | 0.0882246 | ||||||||
\(469\) | 32.9743 | 1.52261 | ||||||||
\(470\) | −39.9677 | −1.84357 | ||||||||
\(471\) | 16.8068 | 0.774418 | ||||||||
\(472\) | −2.48099 | −0.114197 | ||||||||
\(473\) | 5.87522 | 0.270143 | ||||||||
\(474\) | −2.29185 | −0.105268 | ||||||||
\(475\) | 8.85889 | 0.406474 | ||||||||
\(476\) | −31.1417 | −1.42738 | ||||||||
\(477\) | 13.3956 | 0.613341 | ||||||||
\(478\) | −52.2482 | −2.38978 | ||||||||
\(479\) | −25.3878 | −1.16000 | −0.579999 | − | 0.814617i | \(-0.696947\pi\) | ||||
−0.579999 | + | 0.814617i | \(0.696947\pi\) | |||||||
\(480\) | −17.7235 | −0.808965 | ||||||||
\(481\) | 3.94318 | 0.179794 | ||||||||
\(482\) | −23.6155 | −1.07565 | ||||||||
\(483\) | 51.8261 | 2.35817 | ||||||||
\(484\) | 9.65823 | 0.439010 | ||||||||
\(485\) | −27.7275 | −1.25904 | ||||||||
\(486\) | 21.3842 | 0.970006 | ||||||||
\(487\) | 24.0845 | 1.09137 | 0.545686 | − | 0.837990i | \(-0.316269\pi\) | ||||
0.545686 | + | 0.837990i | \(0.316269\pi\) | |||||||
\(488\) | 2.64758 | 0.119850 | ||||||||
\(489\) | 27.4424 | 1.24099 | ||||||||
\(490\) | −42.2895 | −1.91045 | ||||||||
\(491\) | 9.37042 | 0.422881 | 0.211441 | − | 0.977391i | \(-0.432185\pi\) | ||||
0.211441 | + | 0.977391i | \(0.432185\pi\) | |||||||
\(492\) | −11.1324 | −0.501889 | ||||||||
\(493\) | −37.2624 | −1.67821 | ||||||||
\(494\) | −8.78843 | −0.395410 | ||||||||
\(495\) | −8.25766 | −0.371154 | ||||||||
\(496\) | −5.40870 | −0.242858 | ||||||||
\(497\) | 20.6134 | 0.924637 | ||||||||
\(498\) | 11.9080 | 0.533610 | ||||||||
\(499\) | 26.2119 | 1.17340 | 0.586702 | − | 0.809803i | \(-0.300426\pi\) | ||||
0.586702 | + | 0.809803i | \(0.300426\pi\) | |||||||
\(500\) | −20.1686 | −0.901966 | ||||||||
\(501\) | −26.1751 | −1.16942 | ||||||||
\(502\) | −21.4448 | −0.957128 | ||||||||
\(503\) | −20.2973 | −0.905012 | −0.452506 | − | 0.891761i | \(-0.649470\pi\) | ||||
−0.452506 | + | 0.891761i | \(0.649470\pi\) | |||||||
\(504\) | 3.30098 | 0.147037 | ||||||||
\(505\) | −3.19221 | −0.142052 | ||||||||
\(506\) | −67.4903 | −3.00031 | ||||||||
\(507\) | −1.36048 | −0.0604213 | ||||||||
\(508\) | −27.6368 | −1.22618 | ||||||||
\(509\) | −4.98671 | −0.221032 | −0.110516 | − | 0.993874i | \(-0.535250\pi\) | ||||
−0.110516 | + | 0.993874i | \(0.535250\pi\) | |||||||
\(510\) | 19.3141 | 0.855243 | ||||||||
\(511\) | −48.7202 | −2.15526 | ||||||||
\(512\) | −28.0001 | −1.23744 | ||||||||
\(513\) | −25.9274 | −1.14472 | ||||||||
\(514\) | 17.3400 | 0.764836 | ||||||||
\(515\) | −1.75251 | −0.0772248 | ||||||||
\(516\) | −3.23768 | −0.142531 | ||||||||
\(517\) | 48.8761 | 2.14957 | ||||||||
\(518\) | −33.4120 | −1.46804 | ||||||||
\(519\) | −15.0628 | −0.661184 | ||||||||
\(520\) | −1.13683 | −0.0498533 | ||||||||
\(521\) | −20.8423 | −0.913119 | −0.456559 | − | 0.889693i | \(-0.650918\pi\) | ||||
−0.456559 | + | 0.889693i | \(0.650918\pi\) | |||||||
\(522\) | −19.3507 | −0.846959 | ||||||||
\(523\) | −2.57919 | −0.112780 | −0.0563901 | − | 0.998409i | \(-0.517959\pi\) | ||||
−0.0563901 | + | 0.998409i | \(0.517959\pi\) | |||||||
\(524\) | −9.74746 | −0.425820 | ||||||||
\(525\) | −11.6203 | −0.507152 | ||||||||
\(526\) | 27.6938 | 1.20751 | ||||||||
\(527\) | 5.01826 | 0.218599 | ||||||||
\(528\) | 25.4567 | 1.10786 | ||||||||
\(529\) | 50.9936 | 2.21711 | ||||||||
\(530\) | 39.0903 | 1.69797 | ||||||||
\(531\) | 4.39482 | 0.190719 | ||||||||
\(532\) | 33.7857 | 1.46480 | ||||||||
\(533\) | −4.92646 | −0.213389 | ||||||||
\(534\) | −23.5246 | −1.01801 | ||||||||
\(535\) | 26.9927 | 1.16700 | ||||||||
\(536\) | −4.83006 | −0.208627 | ||||||||
\(537\) | 23.7773 | 1.02607 | ||||||||
\(538\) | 58.0125 | 2.50110 | ||||||||
\(539\) | 51.7154 | 2.22754 | ||||||||
\(540\) | 16.4312 | 0.707085 | ||||||||
\(541\) | −16.4233 | −0.706094 | −0.353047 | − | 0.935606i | \(-0.614854\pi\) | ||||
−0.353047 | + | 0.935606i | \(0.614854\pi\) | |||||||
\(542\) | −33.7576 | −1.45001 | ||||||||
\(543\) | 12.7421 | 0.546815 | ||||||||
\(544\) | 31.4715 | 1.34933 | ||||||||
\(545\) | −33.9575 | −1.45458 | ||||||||
\(546\) | 11.5279 | 0.493348 | ||||||||
\(547\) | 33.0540 | 1.41329 | 0.706644 | − | 0.707569i | \(-0.250208\pi\) | ||||
0.706644 | + | 0.707569i | \(0.250208\pi\) | |||||||
\(548\) | 3.15710 | 0.134864 | ||||||||
\(549\) | −4.68991 | −0.200160 | ||||||||
\(550\) | 15.1325 | 0.645252 | ||||||||
\(551\) | 40.4261 | 1.72221 | ||||||||
\(552\) | −7.59146 | −0.323114 | ||||||||
\(553\) | 3.89899 | 0.165802 | ||||||||
\(554\) | 17.7074 | 0.752316 | ||||||||
\(555\) | 9.40159 | 0.399075 | ||||||||
\(556\) | −21.3703 | −0.906302 | ||||||||
\(557\) | 3.64160 | 0.154299 | 0.0771497 | − | 0.997020i | \(-0.475418\pi\) | ||||
0.0771497 | + | 0.997020i | \(0.475418\pi\) | |||||||
\(558\) | 2.60603 | 0.110322 | ||||||||
\(559\) | −1.43278 | −0.0606000 | ||||||||
\(560\) | 35.4144 | 1.49653 | ||||||||
\(561\) | −23.6190 | −0.997196 | ||||||||
\(562\) | −56.9101 | −2.40061 | ||||||||
\(563\) | 42.1325 | 1.77567 | 0.887836 | − | 0.460160i | \(-0.152208\pi\) | ||||
0.887836 | + | 0.460160i | \(0.152208\pi\) | |||||||
\(564\) | −26.9343 | −1.13414 | ||||||||
\(565\) | −29.3210 | −1.23355 | ||||||||
\(566\) | 19.1779 | 0.806109 | ||||||||
\(567\) | 18.7431 | 0.787136 | ||||||||
\(568\) | −3.01944 | −0.126693 | ||||||||
\(569\) | −18.1326 | −0.760156 | −0.380078 | − | 0.924954i | \(-0.624103\pi\) | ||||
−0.380078 | + | 0.924954i | \(0.624103\pi\) | |||||||
\(570\) | −20.9539 | −0.877663 | ||||||||
\(571\) | −23.9285 | −1.00137 | −0.500687 | − | 0.865628i | \(-0.666919\pi\) | ||||
−0.500687 | + | 0.865628i | \(0.666919\pi\) | |||||||
\(572\) | −6.81096 | −0.284780 | ||||||||
\(573\) | −0.147111 | −0.00614564 | ||||||||
\(574\) | 41.7437 | 1.74235 | ||||||||
\(575\) | −16.5907 | −0.691878 | ||||||||
\(576\) | 5.85670 | 0.244029 | ||||||||
\(577\) | 43.0921 | 1.79395 | 0.896974 | − | 0.442083i | \(-0.145760\pi\) | ||||
0.896974 | + | 0.442083i | \(0.145760\pi\) | |||||||
\(578\) | −1.76870 | −0.0735681 | ||||||||
\(579\) | 6.14856 | 0.255525 | ||||||||
\(580\) | −25.6195 | −1.06379 | ||||||||
\(581\) | −20.2584 | −0.840459 | ||||||||
\(582\) | −41.1853 | −1.70719 | ||||||||
\(583\) | −47.8031 | −1.97980 | ||||||||
\(584\) | 7.13652 | 0.295311 | ||||||||
\(585\) | 2.01378 | 0.0832594 | ||||||||
\(586\) | 17.8158 | 0.735966 | ||||||||
\(587\) | −30.4398 | −1.25638 | −0.628192 | − | 0.778059i | \(-0.716205\pi\) | ||||
−0.628192 | + | 0.778059i | \(0.716205\pi\) | |||||||
\(588\) | −28.4990 | −1.17528 | ||||||||
\(589\) | −5.44433 | −0.224330 | ||||||||
\(590\) | 12.8248 | 0.527987 | ||||||||
\(591\) | −29.9893 | −1.23359 | ||||||||
\(592\) | 17.9932 | 0.739516 | ||||||||
\(593\) | −31.8410 | −1.30755 | −0.653776 | − | 0.756688i | \(-0.726816\pi\) | ||||
−0.653776 | + | 0.756688i | \(0.726816\pi\) | |||||||
\(594\) | −44.2884 | −1.81717 | ||||||||
\(595\) | −32.8580 | −1.34704 | ||||||||
\(596\) | −21.6194 | −0.885564 | ||||||||
\(597\) | 6.38549 | 0.261341 | ||||||||
\(598\) | 16.4587 | 0.673046 | ||||||||
\(599\) | 5.84207 | 0.238701 | 0.119350 | − | 0.992852i | \(-0.461919\pi\) | ||||
0.119350 | + | 0.992852i | \(0.461919\pi\) | |||||||
\(600\) | 1.70214 | 0.0694895 | ||||||||
\(601\) | 13.2298 | 0.539656 | 0.269828 | − | 0.962909i | \(-0.413033\pi\) | ||||
0.269828 | + | 0.962909i | \(0.413033\pi\) | |||||||
\(602\) | 12.1404 | 0.494807 | ||||||||
\(603\) | 8.55595 | 0.348425 | ||||||||
\(604\) | −26.9291 | −1.09573 | ||||||||
\(605\) | 10.1905 | 0.414303 | ||||||||
\(606\) | −4.74158 | −0.192614 | ||||||||
\(607\) | −14.6694 | −0.595411 | −0.297705 | − | 0.954658i | \(-0.596221\pi\) | ||||
−0.297705 | + | 0.954658i | \(0.596221\pi\) | |||||||
\(608\) | −34.1436 | −1.38470 | ||||||||
\(609\) | −53.0274 | −2.14878 | ||||||||
\(610\) | −13.6859 | −0.554125 | ||||||||
\(611\) | −11.9193 | −0.482203 | ||||||||
\(612\) | −8.08044 | −0.326632 | ||||||||
\(613\) | 7.11346 | 0.287310 | 0.143655 | − | 0.989628i | \(-0.454114\pi\) | ||||
0.143655 | + | 0.989628i | \(0.454114\pi\) | |||||||
\(614\) | −10.7198 | −0.432616 | ||||||||
\(615\) | −11.7460 | −0.473643 | ||||||||
\(616\) | −11.7798 | −0.474622 | ||||||||
\(617\) | 32.5965 | 1.31229 | 0.656144 | − | 0.754636i | \(-0.272187\pi\) | ||||
0.656144 | + | 0.754636i | \(0.272187\pi\) | |||||||
\(618\) | −2.60311 | −0.104712 | ||||||||
\(619\) | 11.8659 | 0.476932 | 0.238466 | − | 0.971151i | \(-0.423355\pi\) | ||||
0.238466 | + | 0.971151i | \(0.423355\pi\) | |||||||
\(620\) | 3.45028 | 0.138566 | ||||||||
\(621\) | 48.5560 | 1.94848 | ||||||||
\(622\) | 51.9759 | 2.08404 | ||||||||
\(623\) | 40.0211 | 1.60341 | ||||||||
\(624\) | −6.20805 | −0.248521 | ||||||||
\(625\) | −11.6365 | −0.465462 | ||||||||
\(626\) | 11.4045 | 0.455816 | ||||||||
\(627\) | 25.6243 | 1.02334 | ||||||||
\(628\) | −20.5189 | −0.818794 | ||||||||
\(629\) | −16.6943 | −0.665647 | ||||||||
\(630\) | −17.0635 | −0.679824 | ||||||||
\(631\) | 30.7064 | 1.22240 | 0.611201 | − | 0.791475i | \(-0.290687\pi\) | ||||
0.611201 | + | 0.791475i | \(0.290687\pi\) | |||||||
\(632\) | −0.571122 | −0.0227180 | ||||||||
\(633\) | 3.16032 | 0.125611 | ||||||||
\(634\) | −3.05575 | −0.121359 | ||||||||
\(635\) | −29.1599 | −1.15718 | ||||||||
\(636\) | 26.3431 | 1.04457 | ||||||||
\(637\) | −12.6117 | −0.499694 | ||||||||
\(638\) | 69.0546 | 2.73390 | ||||||||
\(639\) | 5.34863 | 0.211588 | ||||||||
\(640\) | −8.96397 | −0.354332 | ||||||||
\(641\) | −33.7150 | −1.33166 | −0.665832 | − | 0.746102i | \(-0.731923\pi\) | ||||
−0.665832 | + | 0.746102i | \(0.731923\pi\) | |||||||
\(642\) | 40.0939 | 1.58238 | ||||||||
\(643\) | −37.2333 | −1.46834 | −0.734168 | − | 0.678967i | \(-0.762428\pi\) | ||||
−0.734168 | + | 0.678967i | \(0.762428\pi\) | |||||||
\(644\) | −63.2728 | −2.49330 | ||||||||
\(645\) | −3.41612 | −0.134509 | ||||||||
\(646\) | 37.2077 | 1.46392 | ||||||||
\(647\) | 7.72314 | 0.303628 | 0.151814 | − | 0.988409i | \(-0.451489\pi\) | ||||
0.151814 | + | 0.988409i | \(0.451489\pi\) | |||||||
\(648\) | −2.74548 | −0.107853 | ||||||||
\(649\) | −15.6833 | −0.615622 | ||||||||
\(650\) | −3.69033 | −0.144746 | ||||||||
\(651\) | 7.14139 | 0.279893 | ||||||||
\(652\) | −33.5035 | −1.31210 | ||||||||
\(653\) | 6.60611 | 0.258517 | 0.129258 | − | 0.991611i | \(-0.458740\pi\) | ||||
0.129258 | + | 0.991611i | \(0.458740\pi\) | |||||||
\(654\) | −50.4391 | −1.97233 | ||||||||
\(655\) | −10.2847 | −0.401855 | ||||||||
\(656\) | −22.4800 | −0.877697 | ||||||||
\(657\) | −12.6416 | −0.493196 | ||||||||
\(658\) | 100.996 | 3.93725 | ||||||||
\(659\) | −21.0554 | −0.820203 | −0.410101 | − | 0.912040i | \(-0.634507\pi\) | ||||
−0.410101 | + | 0.912040i | \(0.634507\pi\) | |||||||
\(660\) | −16.2391 | −0.632107 | ||||||||
\(661\) | −7.81316 | −0.303897 | −0.151948 | − | 0.988388i | \(-0.548555\pi\) | ||||
−0.151948 | + | 0.988388i | \(0.548555\pi\) | |||||||
\(662\) | −16.7271 | −0.650118 | ||||||||
\(663\) | 5.75991 | 0.223696 | ||||||||
\(664\) | 2.96744 | 0.115159 | ||||||||
\(665\) | 35.6477 | 1.38236 | ||||||||
\(666\) | −8.66953 | −0.335938 | ||||||||
\(667\) | −75.7087 | −2.93145 | ||||||||
\(668\) | 31.9563 | 1.23643 | ||||||||
\(669\) | −16.7012 | −0.645705 | ||||||||
\(670\) | 24.9676 | 0.964582 | ||||||||
\(671\) | 16.7363 | 0.646098 | ||||||||
\(672\) | 44.7865 | 1.72768 | ||||||||
\(673\) | −24.0183 | −0.925836 | −0.462918 | − | 0.886401i | \(-0.653198\pi\) | ||||
−0.462918 | + | 0.886401i | \(0.653198\pi\) | |||||||
\(674\) | −26.3726 | −1.01583 | ||||||||
\(675\) | −10.8871 | −0.419045 | ||||||||
\(676\) | 1.66097 | 0.0638835 | ||||||||
\(677\) | 20.9976 | 0.807005 | 0.403502 | − | 0.914979i | \(-0.367793\pi\) | ||||
0.403502 | + | 0.914979i | \(0.367793\pi\) | |||||||
\(678\) | −43.5523 | −1.67262 | ||||||||
\(679\) | 70.0662 | 2.68889 | ||||||||
\(680\) | 4.81302 | 0.184571 | ||||||||
\(681\) | −22.0191 | −0.843773 | ||||||||
\(682\) | −9.29984 | −0.356109 | ||||||||
\(683\) | −32.3714 | −1.23866 | −0.619328 | − | 0.785132i | \(-0.712595\pi\) | ||||
−0.619328 | + | 0.785132i | \(0.712595\pi\) | |||||||
\(684\) | 8.76649 | 0.335195 | ||||||||
\(685\) | 3.33109 | 0.127274 | ||||||||
\(686\) | 47.5501 | 1.81547 | ||||||||
\(687\) | 12.6264 | 0.481727 | ||||||||
\(688\) | −6.53793 | −0.249256 | ||||||||
\(689\) | 11.6576 | 0.444120 | ||||||||
\(690\) | 39.2419 | 1.49391 | ||||||||
\(691\) | −14.5331 | −0.552864 | −0.276432 | − | 0.961034i | \(-0.589152\pi\) | ||||
−0.276432 | + | 0.961034i | \(0.589152\pi\) | |||||||
\(692\) | 18.3897 | 0.699071 | ||||||||
\(693\) | 20.8667 | 0.792661 | ||||||||
\(694\) | 16.9633 | 0.643920 | ||||||||
\(695\) | −22.5480 | −0.855296 | ||||||||
\(696\) | 7.76743 | 0.294424 | ||||||||
\(697\) | 20.8572 | 0.790025 | ||||||||
\(698\) | 12.9438 | 0.489931 | ||||||||
\(699\) | 4.54468 | 0.171895 | ||||||||
\(700\) | 14.1869 | 0.536213 | ||||||||
\(701\) | −24.5456 | −0.927076 | −0.463538 | − | 0.886077i | \(-0.653420\pi\) | ||||
−0.463538 | + | 0.886077i | \(0.653420\pi\) | |||||||
\(702\) | 10.8005 | 0.407639 | ||||||||
\(703\) | 18.1117 | 0.683097 | ||||||||
\(704\) | −20.9001 | −0.787702 | ||||||||
\(705\) | −28.4187 | −1.07031 | ||||||||
\(706\) | −27.0582 | −1.01835 | ||||||||
\(707\) | 8.06657 | 0.303375 | ||||||||
\(708\) | 8.64263 | 0.324810 | ||||||||
\(709\) | 24.3324 | 0.913823 | 0.456911 | − | 0.889512i | \(-0.348956\pi\) | ||||
0.456911 | + | 0.889512i | \(0.348956\pi\) | |||||||
\(710\) | 15.6081 | 0.585762 | ||||||||
\(711\) | 1.01168 | 0.0379411 | ||||||||
\(712\) | −5.86227 | −0.219698 | ||||||||
\(713\) | 10.1960 | 0.381842 | ||||||||
\(714\) | −48.8058 | −1.82651 | ||||||||
\(715\) | −7.18632 | −0.268753 | ||||||||
\(716\) | −29.0289 | −1.08486 | ||||||||
\(717\) | −37.1507 | −1.38742 | ||||||||
\(718\) | 8.15625 | 0.304389 | ||||||||
\(719\) | −34.2855 | −1.27863 | −0.639317 | − | 0.768944i | \(-0.720783\pi\) | ||||
−0.639317 | + | 0.768944i | \(0.720783\pi\) | |||||||
\(720\) | 9.18909 | 0.342457 | ||||||||
\(721\) | 4.42851 | 0.164926 | ||||||||
\(722\) | −4.01281 | −0.149341 | ||||||||
\(723\) | −16.7916 | −0.624486 | ||||||||
\(724\) | −15.5564 | −0.578148 | ||||||||
\(725\) | 16.9752 | 0.630444 | ||||||||
\(726\) | 15.1366 | 0.561770 | ||||||||
\(727\) | −20.3597 | −0.755098 | −0.377549 | − | 0.925990i | \(-0.623233\pi\) | ||||
−0.377549 | + | 0.925990i | \(0.623233\pi\) | |||||||
\(728\) | 2.87271 | 0.106470 | ||||||||
\(729\) | 27.9022 | 1.03341 | ||||||||
\(730\) | −36.8901 | −1.36537 | ||||||||
\(731\) | 6.06598 | 0.224358 | ||||||||
\(732\) | −9.22294 | −0.340890 | ||||||||
\(733\) | −35.2393 | −1.30159 | −0.650797 | − | 0.759252i | \(-0.725565\pi\) | ||||
−0.650797 | + | 0.759252i | \(0.725565\pi\) | |||||||
\(734\) | 65.9512 | 2.43430 | ||||||||
\(735\) | −30.0696 | −1.10914 | ||||||||
\(736\) | 63.9430 | 2.35697 | ||||||||
\(737\) | −30.5326 | −1.12468 | ||||||||
\(738\) | 10.8314 | 0.398708 | ||||||||
\(739\) | 36.0577 | 1.32640 | 0.663202 | − | 0.748440i | \(-0.269197\pi\) | ||||
0.663202 | + | 0.748440i | \(0.269197\pi\) | |||||||
\(740\) | −11.4781 | −0.421943 | ||||||||
\(741\) | −6.24894 | −0.229561 | ||||||||
\(742\) | −98.7794 | −3.62631 | ||||||||
\(743\) | −0.729588 | −0.0267660 | −0.0133830 | − | 0.999910i | \(-0.504260\pi\) | ||||
−0.0133830 | + | 0.999910i | \(0.504260\pi\) | |||||||
\(744\) | −1.04607 | −0.0383507 | ||||||||
\(745\) | −22.8108 | −0.835725 | ||||||||
\(746\) | −35.0675 | −1.28391 | ||||||||
\(747\) | −5.25651 | −0.192326 | ||||||||
\(748\) | 28.8357 | 1.05434 | ||||||||
\(749\) | −68.2094 | −2.49232 | ||||||||
\(750\) | −31.6086 | −1.15418 | ||||||||
\(751\) | 17.2845 | 0.630721 | 0.315360 | − | 0.948972i | \(-0.397875\pi\) | ||||
0.315360 | + | 0.948972i | \(0.397875\pi\) | |||||||
\(752\) | −54.3891 | −1.98337 | ||||||||
\(753\) | −15.2482 | −0.555674 | ||||||||
\(754\) | −16.8402 | −0.613283 | ||||||||
\(755\) | −28.4132 | −1.03406 | ||||||||
\(756\) | −41.5208 | −1.51010 | ||||||||
\(757\) | −34.3659 | −1.24905 | −0.624525 | − | 0.781005i | \(-0.714707\pi\) | ||||
−0.624525 | + | 0.781005i | \(0.714707\pi\) | |||||||
\(758\) | −1.94071 | −0.0704899 | ||||||||
\(759\) | −47.9885 | −1.74187 | ||||||||
\(760\) | −5.22165 | −0.189409 | ||||||||
\(761\) | 25.9783 | 0.941713 | 0.470857 | − | 0.882210i | \(-0.343945\pi\) | ||||
0.470857 | + | 0.882210i | \(0.343945\pi\) | |||||||
\(762\) | −43.3129 | −1.56906 | ||||||||
\(763\) | 85.8091 | 3.10650 | ||||||||
\(764\) | 0.179603 | 0.00649780 | ||||||||
\(765\) | −8.52576 | −0.308250 | ||||||||
\(766\) | −3.77158 | −0.136273 | ||||||||
\(767\) | 3.82464 | 0.138100 | ||||||||
\(768\) | −27.1831 | −0.980886 | ||||||||
\(769\) | 28.7289 | 1.03599 | 0.517995 | − | 0.855384i | \(-0.326678\pi\) | ||||
0.517995 | + | 0.855384i | \(0.326678\pi\) | |||||||
\(770\) | 60.8923 | 2.19441 | ||||||||
\(771\) | 12.3295 | 0.444036 | ||||||||
\(772\) | −7.50657 | −0.270167 | ||||||||
\(773\) | 45.9916 | 1.65420 | 0.827101 | − | 0.562053i | \(-0.189988\pi\) | ||||
0.827101 | + | 0.562053i | \(0.189988\pi\) | |||||||
\(774\) | 3.15012 | 0.113229 | ||||||||
\(775\) | −2.28611 | −0.0821196 | ||||||||
\(776\) | −10.2633 | −0.368430 | ||||||||
\(777\) | −23.7574 | −0.852291 | ||||||||
\(778\) | −60.7011 | −2.17624 | ||||||||
\(779\) | −22.6281 | −0.810735 | ||||||||
\(780\) | 3.96019 | 0.141798 | ||||||||
\(781\) | −19.0870 | −0.682986 | ||||||||
\(782\) | −69.6815 | −2.49181 | ||||||||
\(783\) | −49.6815 | −1.77547 | ||||||||
\(784\) | −57.5487 | −2.05531 | ||||||||
\(785\) | −21.6498 | −0.772713 | ||||||||
\(786\) | −15.2764 | −0.544891 | ||||||||
\(787\) | −4.71401 | −0.168036 | −0.0840181 | − | 0.996464i | \(-0.526775\pi\) | ||||
−0.0840181 | + | 0.996464i | \(0.526775\pi\) | |||||||
\(788\) | 36.6129 | 1.30428 | ||||||||
\(789\) | 19.6915 | 0.701035 | ||||||||
\(790\) | 2.95225 | 0.105036 | ||||||||
\(791\) | 74.0929 | 2.63444 | ||||||||
\(792\) | −3.05655 | −0.108610 | ||||||||
\(793\) | −4.08144 | −0.144936 | ||||||||
\(794\) | 24.5767 | 0.872196 | ||||||||
\(795\) | 27.7949 | 0.985783 | ||||||||
\(796\) | −7.79583 | −0.276316 | ||||||||
\(797\) | 9.87387 | 0.349750 | 0.174875 | − | 0.984591i | \(-0.444048\pi\) | ||||
0.174875 | + | 0.984591i | \(0.444048\pi\) | |||||||
\(798\) | 52.9496 | 1.87440 | ||||||||
\(799\) | 50.4629 | 1.78525 | ||||||||
\(800\) | −14.3371 | −0.506894 | ||||||||
\(801\) | 10.3844 | 0.366915 | ||||||||
\(802\) | 33.4509 | 1.18119 | ||||||||
\(803\) | 45.1126 | 1.59199 | ||||||||
\(804\) | 16.8257 | 0.593397 | ||||||||
\(805\) | −66.7599 | −2.35298 | ||||||||
\(806\) | 2.26793 | 0.0798844 | ||||||||
\(807\) | 41.2494 | 1.45205 | ||||||||
\(808\) | −1.18159 | −0.0415681 | ||||||||
\(809\) | 15.8466 | 0.557136 | 0.278568 | − | 0.960416i | \(-0.410140\pi\) | ||||
0.278568 | + | 0.960416i | \(0.410140\pi\) | |||||||
\(810\) | 14.1920 | 0.498655 | ||||||||
\(811\) | −9.84059 | −0.345550 | −0.172775 | − | 0.984961i | \(-0.555273\pi\) | ||||
−0.172775 | + | 0.984961i | \(0.555273\pi\) | |||||||
\(812\) | 64.7394 | 2.27191 | ||||||||
\(813\) | −24.0031 | −0.841825 | ||||||||
\(814\) | 30.9379 | 1.08437 | ||||||||
\(815\) | −35.3500 | −1.23825 | ||||||||
\(816\) | 26.2832 | 0.920095 | ||||||||
\(817\) | −6.58099 | −0.230240 | ||||||||
\(818\) | 2.88336 | 0.100814 | ||||||||
\(819\) | −5.08872 | −0.177814 | ||||||||
\(820\) | 14.3403 | 0.500784 | ||||||||
\(821\) | 7.60600 | 0.265451 | 0.132726 | − | 0.991153i | \(-0.457627\pi\) | ||||
0.132726 | + | 0.991153i | \(0.457627\pi\) | |||||||
\(822\) | 4.94786 | 0.172576 | ||||||||
\(823\) | 4.22365 | 0.147227 | 0.0736137 | − | 0.997287i | \(-0.476547\pi\) | ||||
0.0736137 | + | 0.997287i | \(0.476547\pi\) | |||||||
\(824\) | −0.648686 | −0.0225981 | ||||||||
\(825\) | 10.7598 | 0.374610 | ||||||||
\(826\) | −32.4076 | −1.12760 | ||||||||
\(827\) | 42.1624 | 1.46613 | 0.733066 | − | 0.680158i | \(-0.238089\pi\) | ||||
0.733066 | + | 0.680158i | \(0.238089\pi\) | |||||||
\(828\) | −16.4176 | −0.570551 | ||||||||
\(829\) | −40.8157 | −1.41759 | −0.708794 | − | 0.705415i | \(-0.750760\pi\) | ||||
−0.708794 | + | 0.705415i | \(0.750760\pi\) | |||||||
\(830\) | −15.3393 | −0.532435 | ||||||||
\(831\) | 12.5907 | 0.436767 | ||||||||
\(832\) | 5.09686 | 0.176702 | ||||||||
\(833\) | 53.3945 | 1.85001 | ||||||||
\(834\) | −33.4919 | −1.15973 | ||||||||
\(835\) | 33.7174 | 1.16684 | ||||||||
\(836\) | −31.2839 | −1.08198 | ||||||||
\(837\) | 6.69078 | 0.231267 | ||||||||
\(838\) | −46.4370 | −1.60414 | ||||||||
\(839\) | 0.237518 | 0.00820003 | 0.00410001 | − | 0.999992i | \(-0.498695\pi\) | ||||
0.00410001 | + | 0.999992i | \(0.498695\pi\) | |||||||
\(840\) | 6.84931 | 0.236324 | ||||||||
\(841\) | 48.4636 | 1.67116 | ||||||||
\(842\) | 14.5975 | 0.503064 | ||||||||
\(843\) | −40.4655 | −1.39371 | ||||||||
\(844\) | −3.85833 | −0.132809 | ||||||||
\(845\) | 1.75251 | 0.0602882 | ||||||||
\(846\) | 26.2059 | 0.900977 | ||||||||
\(847\) | −25.7509 | −0.884813 | ||||||||
\(848\) | 53.1951 | 1.82673 | ||||||||
\(849\) | 13.6363 | 0.467998 | ||||||||
\(850\) | 15.6238 | 0.535892 | ||||||||
\(851\) | −33.9191 | −1.16273 | ||||||||
\(852\) | 10.5183 | 0.360353 | ||||||||
\(853\) | 11.9474 | 0.409071 | 0.204536 | − | 0.978859i | \(-0.434432\pi\) | ||||
0.204536 | + | 0.978859i | \(0.434432\pi\) | |||||||
\(854\) | 34.5836 | 1.18343 | ||||||||
\(855\) | 9.24962 | 0.316330 | ||||||||
\(856\) | 9.99128 | 0.341495 | ||||||||
\(857\) | −25.8760 | −0.883907 | −0.441953 | − | 0.897038i | \(-0.645714\pi\) | ||||
−0.441953 | + | 0.897038i | \(0.645714\pi\) | |||||||
\(858\) | −10.6743 | −0.364413 | ||||||||
\(859\) | −48.0576 | −1.63970 | −0.819852 | − | 0.572576i | \(-0.805944\pi\) | ||||
−0.819852 | + | 0.572576i | \(0.805944\pi\) | |||||||
\(860\) | 4.17062 | 0.142217 | ||||||||
\(861\) | 29.6815 | 1.01154 | ||||||||
\(862\) | −16.3273 | −0.556111 | ||||||||
\(863\) | 5.64627 | 0.192201 | 0.0961007 | − | 0.995372i | \(-0.469363\pi\) | ||||
0.0961007 | + | 0.995372i | \(0.469363\pi\) | |||||||
\(864\) | 41.9606 | 1.42753 | ||||||||
\(865\) | 19.4032 | 0.659728 | ||||||||
\(866\) | 18.3846 | 0.624733 | ||||||||
\(867\) | −1.25762 | −0.0427110 | ||||||||
\(868\) | −8.71869 | −0.295932 | ||||||||
\(869\) | −3.61028 | −0.122470 | ||||||||
\(870\) | −40.1514 | −1.36126 | ||||||||
\(871\) | 7.44591 | 0.252295 | ||||||||
\(872\) | −12.5693 | −0.425650 | ||||||||
\(873\) | 18.1803 | 0.615310 | ||||||||
\(874\) | 75.5976 | 2.55713 | ||||||||
\(875\) | 53.7738 | 1.81789 | ||||||||
\(876\) | −24.8604 | −0.839954 | ||||||||
\(877\) | 6.54117 | 0.220880 | 0.110440 | − | 0.993883i | \(-0.464774\pi\) | ||||
0.110440 | + | 0.993883i | \(0.464774\pi\) | |||||||
\(878\) | 51.1710 | 1.72694 | ||||||||
\(879\) | 12.6678 | 0.427275 | ||||||||
\(880\) | −32.7920 | −1.10542 | ||||||||
\(881\) | −20.5409 | −0.692041 | −0.346021 | − | 0.938227i | \(-0.612467\pi\) | ||||
−0.346021 | + | 0.938227i | \(0.612467\pi\) | |||||||
\(882\) | 27.7283 | 0.933660 | ||||||||
\(883\) | −12.3263 | −0.414812 | −0.207406 | − | 0.978255i | \(-0.566502\pi\) | ||||
−0.207406 | + | 0.978255i | \(0.566502\pi\) | |||||||
\(884\) | −7.03209 | −0.236515 | ||||||||
\(885\) | 9.11894 | 0.306530 | ||||||||
\(886\) | −3.26346 | −0.109638 | ||||||||
\(887\) | −21.0878 | −0.708060 | −0.354030 | − | 0.935234i | \(-0.615189\pi\) | ||||
−0.354030 | + | 0.935234i | \(0.615189\pi\) | |||||||
\(888\) | 3.47997 | 0.116780 | ||||||||
\(889\) | 73.6857 | 2.47134 | ||||||||
\(890\) | 30.3033 | 1.01577 | ||||||||
\(891\) | −17.3552 | −0.581421 | ||||||||
\(892\) | 20.3899 | 0.682705 | ||||||||
\(893\) | −54.7474 | −1.83205 | ||||||||
\(894\) | −33.8823 | −1.13319 | ||||||||
\(895\) | −30.6287 | −1.02381 | ||||||||
\(896\) | 22.6515 | 0.756734 | ||||||||
\(897\) | 11.7028 | 0.390746 | ||||||||
\(898\) | −71.0202 | −2.36997 | ||||||||
\(899\) | −10.4323 | −0.347937 | ||||||||
\(900\) | 3.68111 | 0.122704 | ||||||||
\(901\) | −49.3552 | −1.64426 | ||||||||
\(902\) | −38.6526 | −1.28699 | ||||||||
\(903\) | 8.63237 | 0.287267 | ||||||||
\(904\) | −10.8531 | −0.360969 | ||||||||
\(905\) | −16.4137 | −0.545610 | ||||||||
\(906\) | −42.2039 | −1.40213 | ||||||||
\(907\) | −40.9367 | −1.35928 | −0.679641 | − | 0.733545i | \(-0.737864\pi\) | ||||
−0.679641 | + | 0.733545i | \(0.737864\pi\) | |||||||
\(908\) | 26.8824 | 0.892122 | ||||||||
\(909\) | 2.09306 | 0.0694224 | ||||||||
\(910\) | −14.8497 | −0.492261 | ||||||||
\(911\) | 50.5723 | 1.67553 | 0.837767 | − | 0.546027i | \(-0.183861\pi\) | ||||
0.837767 | + | 0.546027i | \(0.183861\pi\) | |||||||
\(912\) | −28.5147 | −0.944215 | ||||||||
\(913\) | 18.7583 | 0.620808 | ||||||||
\(914\) | 40.2887 | 1.33263 | ||||||||
\(915\) | −9.73124 | −0.321705 | ||||||||
\(916\) | −15.4151 | −0.509331 | ||||||||
\(917\) | 25.9888 | 0.858227 | ||||||||
\(918\) | −45.7263 | −1.50919 | ||||||||
\(919\) | 9.13127 | 0.301213 | 0.150606 | − | 0.988594i | \(-0.451877\pi\) | ||||
0.150606 | + | 0.988594i | \(0.451877\pi\) | |||||||
\(920\) | 9.77895 | 0.322403 | ||||||||
\(921\) | −7.62224 | −0.251161 | ||||||||
\(922\) | 37.4343 | 1.23283 | ||||||||
\(923\) | 4.65470 | 0.153211 | ||||||||
\(924\) | 41.0355 | 1.34997 | ||||||||
\(925\) | 7.60525 | 0.250059 | ||||||||
\(926\) | −11.3188 | −0.371960 | ||||||||
\(927\) | 1.14908 | 0.0377408 | ||||||||
\(928\) | −65.4251 | −2.14768 | ||||||||
\(929\) | 55.6422 | 1.82556 | 0.912781 | − | 0.408449i | \(-0.133930\pi\) | ||||
0.912781 | + | 0.408449i | \(0.133930\pi\) | |||||||
\(930\) | 5.40734 | 0.177314 | ||||||||
\(931\) | −57.9278 | −1.89851 | ||||||||
\(932\) | −5.54845 | −0.181745 | ||||||||
\(933\) | 36.9571 | 1.20992 | ||||||||
\(934\) | 6.25612 | 0.204706 | ||||||||
\(935\) | 30.4249 | 0.995000 | ||||||||
\(936\) | 0.745393 | 0.0243639 | ||||||||
\(937\) | 7.12355 | 0.232716 | 0.116358 | − | 0.993207i | \(-0.462878\pi\) | ||||
0.116358 | + | 0.993207i | \(0.462878\pi\) | |||||||
\(938\) | −63.0919 | −2.06002 | ||||||||
\(939\) | 8.10910 | 0.264630 | ||||||||
\(940\) | 34.6955 | 1.13164 | ||||||||
\(941\) | −20.4044 | −0.665163 | −0.332582 | − | 0.943074i | \(-0.607920\pi\) | ||||
−0.332582 | + | 0.943074i | \(0.607920\pi\) | |||||||
\(942\) | −32.1576 | −1.04775 | ||||||||
\(943\) | 42.3772 | 1.37999 | ||||||||
\(944\) | 17.4523 | 0.568023 | ||||||||
\(945\) | −43.8091 | −1.42511 | ||||||||
\(946\) | −11.2415 | −0.365491 | ||||||||
\(947\) | −7.29179 | −0.236951 | −0.118476 | − | 0.992957i | \(-0.537801\pi\) | ||||
−0.118476 | + | 0.992957i | \(0.537801\pi\) | |||||||
\(948\) | 1.98953 | 0.0646169 | ||||||||
\(949\) | −11.0015 | −0.357124 | ||||||||
\(950\) | −16.9503 | −0.549941 | ||||||||
\(951\) | −2.17277 | −0.0704569 | ||||||||
\(952\) | −12.1623 | −0.394181 | ||||||||
\(953\) | 37.3433 | 1.20967 | 0.604834 | − | 0.796351i | \(-0.293239\pi\) | ||||
0.604834 | + | 0.796351i | \(0.293239\pi\) | |||||||
\(954\) | −25.6306 | −0.829822 | ||||||||
\(955\) | 0.189501 | 0.00613211 | ||||||||
\(956\) | 45.3561 | 1.46692 | ||||||||
\(957\) | 49.1008 | 1.58720 | ||||||||
\(958\) | 48.5762 | 1.56942 | ||||||||
\(959\) | −8.41750 | −0.271815 | ||||||||
\(960\) | 12.1523 | 0.392212 | ||||||||
\(961\) | −29.5950 | −0.954679 | ||||||||
\(962\) | −7.54475 | −0.243253 | ||||||||
\(963\) | −17.6985 | −0.570327 | ||||||||
\(964\) | 20.5003 | 0.660271 | ||||||||
\(965\) | −7.92027 | −0.254962 | ||||||||
\(966\) | −99.1624 | −3.19050 | ||||||||
\(967\) | 4.70780 | 0.151393 | 0.0756964 | − | 0.997131i | \(-0.475882\pi\) | ||||
0.0756964 | + | 0.997131i | \(0.475882\pi\) | |||||||
\(968\) | 3.77199 | 0.121236 | ||||||||
\(969\) | 26.4563 | 0.849898 | ||||||||
\(970\) | 53.0529 | 1.70343 | ||||||||
\(971\) | 6.92449 | 0.222217 | 0.111109 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111109 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(972\) | −18.5634 | −0.595420 | ||||||||
\(973\) | 56.9778 | 1.82663 | ||||||||
\(974\) | −46.0824 | −1.47658 | ||||||||
\(975\) | −2.62398 | −0.0840346 | ||||||||
\(976\) | −18.6241 | −0.596143 | ||||||||
\(977\) | −13.2427 | −0.423672 | −0.211836 | − | 0.977305i | \(-0.567944\pi\) | ||||
−0.211836 | + | 0.977305i | \(0.567944\pi\) | |||||||
\(978\) | −52.5074 | −1.67900 | ||||||||
\(979\) | −37.0576 | −1.18437 | ||||||||
\(980\) | 36.7110 | 1.17269 | ||||||||
\(981\) | 22.2652 | 0.710873 | ||||||||
\(982\) | −17.9290 | −0.572139 | ||||||||
\(983\) | −53.9544 | −1.72088 | −0.860440 | − | 0.509552i | \(-0.829811\pi\) | ||||
−0.860440 | + | 0.509552i | \(0.829811\pi\) | |||||||
\(984\) | −4.34774 | −0.138601 | ||||||||
\(985\) | 38.6307 | 1.23088 | ||||||||
\(986\) | 71.2966 | 2.27055 | ||||||||
\(987\) | 71.8128 | 2.28583 | ||||||||
\(988\) | 7.62913 | 0.242715 | ||||||||
\(989\) | 12.3247 | 0.391902 | ||||||||
\(990\) | 15.7999 | 0.502155 | ||||||||
\(991\) | −28.9259 | −0.918861 | −0.459431 | − | 0.888214i | \(-0.651947\pi\) | ||||
−0.459431 | + | 0.888214i | \(0.651947\pi\) | |||||||
\(992\) | 8.81104 | 0.279751 | ||||||||
\(993\) | −11.8937 | −0.377435 | ||||||||
\(994\) | −39.4410 | −1.25099 | ||||||||
\(995\) | −8.22548 | −0.260765 | ||||||||
\(996\) | −10.3372 | −0.327546 | ||||||||
\(997\) | −21.8732 | −0.692730 | −0.346365 | − | 0.938100i | \(-0.612584\pi\) | ||||
−0.346365 | + | 0.938100i | \(0.612584\pi\) | |||||||
\(998\) | −50.1529 | −1.58756 | ||||||||
\(999\) | −22.2583 | −0.704222 |
(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 | 1339.2.a.e.1.5 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.e.1.5 | ✓ | 21 | 1.1 | even | 1 | trivial |