Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.7457527933.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 6x^{6} + 23x^{5} - 4x^{4} - 27x^{3} + 8x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.314356\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.55413 | 1.80604 | 0.903021 | − | 0.429596i | \(-0.141344\pi\) | ||||
0.903021 | + | 0.429596i | \(0.141344\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.52358 | 2.26179 | ||||||||
\(5\) | 2.03983 | 0.912241 | 0.456120 | − | 0.889918i | \(-0.349239\pi\) | ||||
0.456120 | + | 0.889918i | \(0.349239\pi\) | |||||||
\(6\) | 2.55413 | 1.04272 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.44554 | 2.27884 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.20999 | 1.64755 | ||||||||
\(11\) | 2.19710 | 0.662449 | 0.331225 | − | 0.943552i | \(-0.392538\pi\) | ||||
0.331225 | + | 0.943552i | \(0.392538\pi\) | |||||||
\(12\) | 4.52358 | 1.30584 | ||||||||
\(13\) | 4.05386 | 1.12434 | 0.562169 | − | 0.827022i | \(-0.309967\pi\) | ||||
0.562169 | + | 0.827022i | \(0.309967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.03983 | 0.526682 | ||||||||
\(16\) | 7.41559 | 1.85390 | ||||||||
\(17\) | −4.84721 | −1.17562 | −0.587811 | − | 0.808999i | \(-0.700010\pi\) | ||||
−0.587811 | + | 0.808999i | \(0.700010\pi\) | |||||||
\(18\) | 2.55413 | 0.602014 | ||||||||
\(19\) | 7.41918 | 1.70208 | 0.851038 | − | 0.525104i | \(-0.175974\pi\) | ||||
0.851038 | + | 0.525104i | \(0.175974\pi\) | |||||||
\(20\) | 9.22734 | 2.06330 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.61167 | 1.19641 | ||||||||
\(23\) | −4.70245 | −0.980529 | −0.490264 | − | 0.871574i | \(-0.663100\pi\) | ||||
−0.490264 | + | 0.871574i | \(0.663100\pi\) | |||||||
\(24\) | 6.44554 | 1.31569 | ||||||||
\(25\) | −0.839085 | −0.167817 | ||||||||
\(26\) | 10.3541 | 2.03060 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.1020 | −1.87590 | −0.937950 | − | 0.346769i | \(-0.887279\pi\) | ||||
−0.937950 | + | 0.346769i | \(0.887279\pi\) | |||||||
\(30\) | 5.20999 | 0.951211 | ||||||||
\(31\) | −3.76089 | −0.675475 | −0.337738 | − | 0.941240i | \(-0.609662\pi\) | ||||
−0.337738 | + | 0.941240i | \(0.609662\pi\) | |||||||
\(32\) | 6.04930 | 1.06937 | ||||||||
\(33\) | 2.19710 | 0.382465 | ||||||||
\(34\) | −12.3804 | −2.12322 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.52358 | 0.753929 | ||||||||
\(37\) | −6.51492 | −1.07105 | −0.535523 | − | 0.844521i | \(-0.679885\pi\) | ||||
−0.535523 | + | 0.844521i | \(0.679885\pi\) | |||||||
\(38\) | 18.9495 | 3.07402 | ||||||||
\(39\) | 4.05386 | 0.649137 | ||||||||
\(40\) | 13.1478 | 2.07885 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7302 | 1.63635 | 0.818173 | − | 0.574972i | \(-0.194987\pi\) | ||||
0.818173 | + | 0.574972i | \(0.194987\pi\) | |||||||
\(44\) | 9.93873 | 1.49832 | ||||||||
\(45\) | 2.03983 | 0.304080 | ||||||||
\(46\) | −12.0107 | −1.77088 | ||||||||
\(47\) | 0.528264 | 0.0770552 | 0.0385276 | − | 0.999258i | \(-0.487733\pi\) | ||||
0.0385276 | + | 0.999258i | \(0.487733\pi\) | |||||||
\(48\) | 7.41559 | 1.07035 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.14313 | −0.303085 | ||||||||
\(51\) | −4.84721 | −0.678745 | ||||||||
\(52\) | 18.3379 | 2.54301 | ||||||||
\(53\) | 7.25162 | 0.996086 | 0.498043 | − | 0.867152i | \(-0.334052\pi\) | ||||
0.498043 | + | 0.867152i | \(0.334052\pi\) | |||||||
\(54\) | 2.55413 | 0.347573 | ||||||||
\(55\) | 4.48171 | 0.604313 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.41918 | 0.982694 | ||||||||
\(58\) | −25.8019 | −3.38796 | ||||||||
\(59\) | 7.53546 | 0.981033 | 0.490516 | − | 0.871432i | \(-0.336808\pi\) | ||||
0.490516 | + | 0.871432i | \(0.336808\pi\) | |||||||
\(60\) | 9.22734 | 1.19124 | ||||||||
\(61\) | 1.26730 | 0.162261 | 0.0811304 | − | 0.996703i | \(-0.474147\pi\) | ||||
0.0811304 | + | 0.996703i | \(0.474147\pi\) | |||||||
\(62\) | −9.60579 | −1.21994 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.619503 | 0.0774378 | ||||||||
\(65\) | 8.26919 | 1.02567 | ||||||||
\(66\) | 5.61167 | 0.690748 | ||||||||
\(67\) | −8.72784 | −1.06628 | −0.533138 | − | 0.846029i | \(-0.678987\pi\) | ||||
−0.533138 | + | 0.846029i | \(0.678987\pi\) | |||||||
\(68\) | −21.9267 | −2.65901 | ||||||||
\(69\) | −4.70245 | −0.566109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.95591 | −0.232123 | −0.116062 | − | 0.993242i | \(-0.537027\pi\) | ||||
−0.116062 | + | 0.993242i | \(0.537027\pi\) | |||||||
\(72\) | 6.44554 | 0.759614 | ||||||||
\(73\) | −13.1873 | −1.54346 | −0.771731 | − | 0.635949i | \(-0.780609\pi\) | ||||
−0.771731 | + | 0.635949i | \(0.780609\pi\) | |||||||
\(74\) | −16.6399 | −1.93435 | ||||||||
\(75\) | −0.839085 | −0.0968892 | ||||||||
\(76\) | 33.5612 | 3.84974 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.3541 | 1.17237 | ||||||||
\(79\) | −2.93987 | −0.330761 | −0.165380 | − | 0.986230i | \(-0.552885\pi\) | ||||
−0.165380 | + | 0.986230i | \(0.552885\pi\) | |||||||
\(80\) | 15.1266 | 1.69120 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.55413 | 0.282056 | ||||||||
\(83\) | 12.0571 | 1.32344 | 0.661722 | − | 0.749750i | \(-0.269826\pi\) | ||||
0.661722 | + | 0.749750i | \(0.269826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.88750 | −1.07245 | ||||||||
\(86\) | 27.4064 | 2.95531 | ||||||||
\(87\) | −10.1020 | −1.08305 | ||||||||
\(88\) | 14.1615 | 1.50962 | ||||||||
\(89\) | −4.93696 | −0.523317 | −0.261658 | − | 0.965161i | \(-0.584269\pi\) | ||||
−0.261658 | + | 0.965161i | \(0.584269\pi\) | |||||||
\(90\) | 5.20999 | 0.549182 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.2719 | −2.21775 | ||||||||
\(93\) | −3.76089 | −0.389986 | ||||||||
\(94\) | 1.34925 | 0.139165 | ||||||||
\(95\) | 15.1339 | 1.55270 | ||||||||
\(96\) | 6.04930 | 0.617404 | ||||||||
\(97\) | −4.56808 | −0.463818 | −0.231909 | − | 0.972737i | \(-0.574497\pi\) | ||||
−0.231909 | + | 0.972737i | \(0.574497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.19710 | 0.220816 | ||||||||
\(100\) | −3.79567 | −0.379567 | ||||||||
\(101\) | 14.8399 | 1.47663 | 0.738313 | − | 0.674459i | \(-0.235623\pi\) | ||||
0.738313 | + | 0.674459i | \(0.235623\pi\) | |||||||
\(102\) | −12.3804 | −1.22584 | ||||||||
\(103\) | −15.1660 | −1.49435 | −0.747174 | − | 0.664629i | \(-0.768590\pi\) | ||||
−0.747174 | + | 0.664629i | \(0.768590\pi\) | |||||||
\(104\) | 26.1293 | 2.56219 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.5216 | 1.79897 | ||||||||
\(107\) | −10.5325 | −1.01822 | −0.509109 | − | 0.860702i | \(-0.670025\pi\) | ||||
−0.509109 | + | 0.860702i | \(0.670025\pi\) | |||||||
\(108\) | 4.52358 | 0.435281 | ||||||||
\(109\) | −20.4788 | −1.96151 | −0.980757 | − | 0.195234i | \(-0.937453\pi\) | ||||
−0.980757 | + | 0.195234i | \(0.937453\pi\) | |||||||
\(110\) | 11.4469 | 1.09141 | ||||||||
\(111\) | −6.51492 | −0.618369 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.99357 | 0.375683 | 0.187842 | − | 0.982199i | \(-0.439851\pi\) | ||||
0.187842 | + | 0.982199i | \(0.439851\pi\) | |||||||
\(114\) | 18.9495 | 1.77479 | ||||||||
\(115\) | −9.59221 | −0.894478 | ||||||||
\(116\) | −45.6973 | −4.24289 | ||||||||
\(117\) | 4.05386 | 0.374779 | ||||||||
\(118\) | 19.2465 | 1.77179 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 13.1478 | 1.20023 | ||||||||
\(121\) | −6.17277 | −0.561161 | ||||||||
\(122\) | 3.23684 | 0.293050 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −17.0127 | −1.52778 | ||||||||
\(125\) | −11.9108 | −1.06533 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.59918 | 0.141905 | 0.0709523 | − | 0.997480i | \(-0.477396\pi\) | ||||
0.0709523 | + | 0.997480i | \(0.477396\pi\) | |||||||
\(128\) | −10.5163 | −0.929519 | ||||||||
\(129\) | 10.7302 | 0.944745 | ||||||||
\(130\) | 21.1206 | 1.85240 | ||||||||
\(131\) | 9.63387 | 0.841715 | 0.420858 | − | 0.907127i | \(-0.361729\pi\) | ||||
0.420858 | + | 0.907127i | \(0.361729\pi\) | |||||||
\(132\) | 9.93873 | 0.865055 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.2920 | −1.92574 | ||||||||
\(135\) | 2.03983 | 0.175561 | ||||||||
\(136\) | −31.2429 | −2.67906 | ||||||||
\(137\) | −7.92292 | −0.676900 | −0.338450 | − | 0.940984i | \(-0.609903\pi\) | ||||
−0.338450 | + | 0.940984i | \(0.609903\pi\) | |||||||
\(138\) | −12.0107 | −1.02242 | ||||||||
\(139\) | −3.47465 | −0.294716 | −0.147358 | − | 0.989083i | \(-0.547077\pi\) | ||||
−0.147358 | + | 0.989083i | \(0.547077\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.528264 | 0.0444878 | ||||||||
\(142\) | −4.99564 | −0.419225 | ||||||||
\(143\) | 8.90671 | 0.744817 | ||||||||
\(144\) | 7.41559 | 0.617966 | ||||||||
\(145\) | −20.6065 | −1.71127 | ||||||||
\(146\) | −33.6822 | −2.78756 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −29.4707 | −2.42248 | ||||||||
\(149\) | 4.81236 | 0.394244 | 0.197122 | − | 0.980379i | \(-0.436840\pi\) | ||||
0.197122 | + | 0.980379i | \(0.436840\pi\) | |||||||
\(150\) | −2.14313 | −0.174986 | ||||||||
\(151\) | −6.30410 | −0.513021 | −0.256510 | − | 0.966542i | \(-0.582573\pi\) | ||||
−0.256510 | + | 0.966542i | \(0.582573\pi\) | |||||||
\(152\) | 47.8206 | 3.87876 | ||||||||
\(153\) | −4.84721 | −0.391874 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.67158 | −0.616196 | ||||||||
\(156\) | 18.3379 | 1.46821 | ||||||||
\(157\) | 4.07061 | 0.324870 | 0.162435 | − | 0.986719i | \(-0.448065\pi\) | ||||
0.162435 | + | 0.986719i | \(0.448065\pi\) | |||||||
\(158\) | −7.50880 | −0.597368 | ||||||||
\(159\) | 7.25162 | 0.575090 | ||||||||
\(160\) | 12.3395 | 0.975527 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.55413 | 0.200671 | ||||||||
\(163\) | 9.43025 | 0.738634 | 0.369317 | − | 0.929303i | \(-0.379592\pi\) | ||||
0.369317 | + | 0.929303i | \(0.379592\pi\) | |||||||
\(164\) | 4.52358 | 0.353232 | ||||||||
\(165\) | 4.48171 | 0.348900 | ||||||||
\(166\) | 30.7955 | 2.39019 | ||||||||
\(167\) | 12.2859 | 0.950715 | 0.475357 | − | 0.879793i | \(-0.342319\pi\) | ||||
0.475357 | + | 0.879793i | \(0.342319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.43376 | 0.264135 | ||||||||
\(170\) | −25.2539 | −1.93689 | ||||||||
\(171\) | 7.41918 | 0.567359 | ||||||||
\(172\) | 48.5390 | 3.70107 | ||||||||
\(173\) | 21.7797 | 1.65588 | 0.827940 | − | 0.560817i | \(-0.189513\pi\) | ||||
0.827940 | + | 0.560817i | \(0.189513\pi\) | |||||||
\(174\) | −25.8019 | −1.95604 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.2928 | 1.22811 | ||||||||
\(177\) | 7.53546 | 0.566400 | ||||||||
\(178\) | −12.6096 | −0.945133 | ||||||||
\(179\) | −8.27123 | −0.618221 | −0.309110 | − | 0.951026i | \(-0.600031\pi\) | ||||
−0.309110 | + | 0.951026i | \(0.600031\pi\) | |||||||
\(180\) | 9.22734 | 0.687765 | ||||||||
\(181\) | 2.34065 | 0.173979 | 0.0869894 | − | 0.996209i | \(-0.472275\pi\) | ||||
0.0869894 | + | 0.996209i | \(0.472275\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.26730 | 0.0936813 | ||||||||
\(184\) | −30.3098 | −2.23447 | ||||||||
\(185\) | −13.2893 | −0.977052 | ||||||||
\(186\) | −9.60579 | −0.704331 | ||||||||
\(187\) | −10.6498 | −0.778789 | ||||||||
\(188\) | 2.38964 | 0.174282 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 38.6539 | 2.80425 | ||||||||
\(191\) | 14.5214 | 1.05073 | 0.525367 | − | 0.850876i | \(-0.323928\pi\) | ||||
0.525367 | + | 0.850876i | \(0.323928\pi\) | |||||||
\(192\) | 0.619503 | 0.0447087 | ||||||||
\(193\) | 18.0211 | 1.29719 | 0.648593 | − | 0.761136i | \(-0.275358\pi\) | ||||
0.648593 | + | 0.761136i | \(0.275358\pi\) | |||||||
\(194\) | −11.6675 | −0.837676 | ||||||||
\(195\) | 8.26919 | 0.592169 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.2224 | 1.79702 | 0.898510 | − | 0.438953i | \(-0.144650\pi\) | ||||
0.898510 | + | 0.438953i | \(0.144650\pi\) | |||||||
\(198\) | 5.61167 | 0.398804 | ||||||||
\(199\) | 2.07686 | 0.147225 | 0.0736125 | − | 0.997287i | \(-0.476547\pi\) | ||||
0.0736125 | + | 0.997287i | \(0.476547\pi\) | |||||||
\(200\) | −5.40836 | −0.382429 | ||||||||
\(201\) | −8.72784 | −0.615614 | ||||||||
\(202\) | 37.9030 | 2.66685 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.9267 | −1.53518 | ||||||||
\(205\) | 2.03983 | 0.142468 | ||||||||
\(206\) | −38.7358 | −2.69885 | ||||||||
\(207\) | −4.70245 | −0.326843 | ||||||||
\(208\) | 30.0617 | 2.08441 | ||||||||
\(209\) | 16.3006 | 1.12754 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.20520 | 0.633712 | 0.316856 | − | 0.948474i | \(-0.397373\pi\) | ||||
0.316856 | + | 0.948474i | \(0.397373\pi\) | |||||||
\(212\) | 32.8032 | 2.25294 | ||||||||
\(213\) | −1.95591 | −0.134017 | ||||||||
\(214\) | −26.9014 | −1.83894 | ||||||||
\(215\) | 21.8879 | 1.49274 | ||||||||
\(216\) | 6.44554 | 0.438563 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −52.3055 | −3.54258 | ||||||||
\(219\) | −13.1873 | −0.891118 | ||||||||
\(220\) | 20.2733 | 1.36683 | ||||||||
\(221\) | −19.6499 | −1.32180 | ||||||||
\(222\) | −16.6399 | −1.11680 | ||||||||
\(223\) | 23.2274 | 1.55542 | 0.777710 | − | 0.628624i | \(-0.216381\pi\) | ||||
0.777710 | + | 0.628624i | \(0.216381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.839085 | −0.0559390 | ||||||||
\(226\) | 10.2001 | 0.678500 | ||||||||
\(227\) | −4.57677 | −0.303771 | −0.151885 | − | 0.988398i | \(-0.548534\pi\) | ||||
−0.151885 | + | 0.988398i | \(0.548534\pi\) | |||||||
\(228\) | 33.5612 | 2.22265 | ||||||||
\(229\) | 10.8001 | 0.713688 | 0.356844 | − | 0.934164i | \(-0.383853\pi\) | ||||
0.356844 | + | 0.934164i | \(0.383853\pi\) | |||||||
\(230\) | −24.4997 | −1.61547 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −65.1131 | −4.27488 | ||||||||
\(233\) | −19.0904 | −1.25065 | −0.625325 | − | 0.780364i | \(-0.715034\pi\) | ||||
−0.625325 | + | 0.780364i | \(0.715034\pi\) | |||||||
\(234\) | 10.3541 | 0.676867 | ||||||||
\(235\) | 1.07757 | 0.0702929 | ||||||||
\(236\) | 34.0872 | 2.21889 | ||||||||
\(237\) | −2.93987 | −0.190965 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.39421 | −0.478291 | −0.239146 | − | 0.970984i | \(-0.576867\pi\) | ||||
−0.239146 | + | 0.970984i | \(0.576867\pi\) | |||||||
\(240\) | 15.1266 | 0.976415 | ||||||||
\(241\) | 8.85999 | 0.570722 | 0.285361 | − | 0.958420i | \(-0.407887\pi\) | ||||
0.285361 | + | 0.958420i | \(0.407887\pi\) | |||||||
\(242\) | −15.7661 | −1.01348 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.73271 | 0.366999 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.55413 | 0.162845 | ||||||||
\(247\) | 30.0763 | 1.91371 | ||||||||
\(248\) | −24.2410 | −1.53930 | ||||||||
\(249\) | 12.0571 | 0.764090 | ||||||||
\(250\) | −30.4216 | −1.92403 | ||||||||
\(251\) | −2.14037 | −0.135099 | −0.0675495 | − | 0.997716i | \(-0.521518\pi\) | ||||
−0.0675495 | + | 0.997716i | \(0.521518\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.3317 | −0.649550 | ||||||||
\(254\) | 4.08452 | 0.256286 | ||||||||
\(255\) | −9.88750 | −0.619179 | ||||||||
\(256\) | −28.0990 | −1.75619 | ||||||||
\(257\) | −14.2797 | −0.890744 | −0.445372 | − | 0.895346i | \(-0.646929\pi\) | ||||
−0.445372 | + | 0.895346i | \(0.646929\pi\) | |||||||
\(258\) | 27.4064 | 1.70625 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 37.4063 | 2.31984 | ||||||||
\(261\) | −10.1020 | −0.625300 | ||||||||
\(262\) | 24.6061 | 1.52017 | ||||||||
\(263\) | 16.4154 | 1.01222 | 0.506109 | − | 0.862469i | \(-0.331083\pi\) | ||||
0.506109 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(264\) | 14.1615 | 0.871578 | ||||||||
\(265\) | 14.7921 | 0.908670 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.93696 | −0.302137 | ||||||||
\(268\) | −39.4810 | −2.41169 | ||||||||
\(269\) | −5.20640 | −0.317440 | −0.158720 | − | 0.987324i | \(-0.550737\pi\) | ||||
−0.158720 | + | 0.987324i | \(0.550737\pi\) | |||||||
\(270\) | 5.20999 | 0.317070 | ||||||||
\(271\) | 30.7434 | 1.86753 | 0.933765 | − | 0.357888i | \(-0.116503\pi\) | ||||
0.933765 | + | 0.357888i | \(0.116503\pi\) | |||||||
\(272\) | −35.9449 | −2.17948 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2362 | −1.22251 | ||||||||
\(275\) | −1.84355 | −0.111170 | ||||||||
\(276\) | −21.2719 | −1.28042 | ||||||||
\(277\) | −11.4285 | −0.686669 | −0.343335 | − | 0.939213i | \(-0.611556\pi\) | ||||
−0.343335 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(278\) | −8.87472 | −0.532270 | ||||||||
\(279\) | −3.76089 | −0.225158 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.76574 | 0.105335 | 0.0526677 | − | 0.998612i | \(-0.483228\pi\) | ||||
0.0526677 | + | 0.998612i | \(0.483228\pi\) | |||||||
\(282\) | 1.34925 | 0.0803469 | ||||||||
\(283\) | −9.61324 | −0.571448 | −0.285724 | − | 0.958312i | \(-0.592234\pi\) | ||||
−0.285724 | + | 0.958312i | \(0.592234\pi\) | |||||||
\(284\) | −8.84770 | −0.525014 | ||||||||
\(285\) | 15.1339 | 0.896454 | ||||||||
\(286\) | 22.7489 | 1.34517 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.04930 | 0.356458 | ||||||||
\(289\) | 6.49545 | 0.382086 | ||||||||
\(290\) | −52.6316 | −3.09063 | ||||||||
\(291\) | −4.56808 | −0.267786 | ||||||||
\(292\) | −59.6540 | −3.49098 | ||||||||
\(293\) | −0.406494 | −0.0237476 | −0.0118738 | − | 0.999930i | \(-0.503780\pi\) | ||||
−0.0118738 | + | 0.999930i | \(0.503780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.3711 | 0.894938 | ||||||||
\(296\) | −41.9922 | −2.44075 | ||||||||
\(297\) | 2.19710 | 0.127488 | ||||||||
\(298\) | 12.2914 | 0.712021 | ||||||||
\(299\) | −19.0631 | −1.10245 | ||||||||
\(300\) | −3.79567 | −0.219143 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.1015 | −0.926537 | ||||||||
\(303\) | 14.8399 | 0.852530 | ||||||||
\(304\) | 55.0176 | 3.15547 | ||||||||
\(305\) | 2.58507 | 0.148021 | ||||||||
\(306\) | −12.3804 | −0.707741 | ||||||||
\(307\) | −1.20072 | −0.0685287 | −0.0342644 | − | 0.999413i | \(-0.510909\pi\) | ||||
−0.0342644 | + | 0.999413i | \(0.510909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.1660 | −0.862762 | ||||||||
\(310\) | −19.5942 | −1.11288 | ||||||||
\(311\) | −28.8728 | −1.63722 | −0.818612 | − | 0.574346i | \(-0.805256\pi\) | ||||
−0.818612 | + | 0.574346i | \(0.805256\pi\) | |||||||
\(312\) | 26.1293 | 1.47928 | ||||||||
\(313\) | −15.2516 | −0.862073 | −0.431037 | − | 0.902334i | \(-0.641852\pi\) | ||||
−0.431037 | + | 0.902334i | \(0.641852\pi\) | |||||||
\(314\) | 10.3969 | 0.586729 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.2987 | −0.748111 | ||||||||
\(317\) | 19.2570 | 1.08158 | 0.540790 | − | 0.841158i | \(-0.318125\pi\) | ||||
0.540790 | + | 0.841158i | \(0.318125\pi\) | |||||||
\(318\) | 18.5216 | 1.03864 | ||||||||
\(319\) | −22.1951 | −1.24269 | ||||||||
\(320\) | 1.26368 | 0.0706419 | ||||||||
\(321\) | −10.5325 | −0.587868 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.9623 | −2.00100 | ||||||||
\(324\) | 4.52358 | 0.251310 | ||||||||
\(325\) | −3.40153 | −0.188683 | ||||||||
\(326\) | 24.0861 | 1.33400 | ||||||||
\(327\) | −20.4788 | −1.13248 | ||||||||
\(328\) | 6.44554 | 0.355895 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 11.4469 | 0.630129 | ||||||||
\(331\) | 2.31034 | 0.126988 | 0.0634939 | − | 0.997982i | \(-0.479776\pi\) | ||||
0.0634939 | + | 0.997982i | \(0.479776\pi\) | |||||||
\(332\) | 54.5414 | 2.99335 | ||||||||
\(333\) | −6.51492 | −0.357015 | ||||||||
\(334\) | 31.3799 | 1.71703 | ||||||||
\(335\) | −17.8033 | −0.972700 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.37449 | −0.347240 | −0.173620 | − | 0.984813i | \(-0.555547\pi\) | ||||
−0.173620 | + | 0.984813i | \(0.555547\pi\) | |||||||
\(338\) | 8.77026 | 0.477039 | ||||||||
\(339\) | 3.99357 | 0.216901 | ||||||||
\(340\) | −44.7268 | −2.42565 | ||||||||
\(341\) | −8.26303 | −0.447468 | ||||||||
\(342\) | 18.9495 | 1.02467 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 69.1622 | 3.72897 | ||||||||
\(345\) | −9.59221 | −0.516427 | ||||||||
\(346\) | 55.6282 | 2.99059 | ||||||||
\(347\) | −3.75901 | −0.201794 | −0.100897 | − | 0.994897i | \(-0.532171\pi\) | ||||
−0.100897 | + | 0.994897i | \(0.532171\pi\) | |||||||
\(348\) | −45.6973 | −2.44963 | ||||||||
\(349\) | −16.7097 | −0.894451 | −0.447225 | − | 0.894421i | \(-0.647588\pi\) | ||||
−0.447225 | + | 0.894421i | \(0.647588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.05386 | 0.216379 | ||||||||
\(352\) | 13.2909 | 0.708406 | ||||||||
\(353\) | −2.05629 | −0.109445 | −0.0547226 | − | 0.998502i | \(-0.517427\pi\) | ||||
−0.0547226 | + | 0.998502i | \(0.517427\pi\) | |||||||
\(354\) | 19.2465 | 1.02294 | ||||||||
\(355\) | −3.98972 | −0.211752 | ||||||||
\(356\) | −22.3327 | −1.18363 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.1258 | −1.11653 | ||||||||
\(359\) | 35.2054 | 1.85807 | 0.929036 | − | 0.369989i | \(-0.120639\pi\) | ||||
0.929036 | + | 0.369989i | \(0.120639\pi\) | |||||||
\(360\) | 13.1478 | 0.692951 | ||||||||
\(361\) | 36.0442 | 1.89706 | ||||||||
\(362\) | 5.97831 | 0.314213 | ||||||||
\(363\) | −6.17277 | −0.323986 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.9000 | −1.40801 | ||||||||
\(366\) | 3.23684 | 0.169192 | ||||||||
\(367\) | −13.9271 | −0.726989 | −0.363494 | − | 0.931596i | \(-0.618416\pi\) | ||||
−0.363494 | + | 0.931596i | \(0.618416\pi\) | |||||||
\(368\) | −34.8714 | −1.81780 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −33.9427 | −1.76460 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −17.0127 | −0.882065 | ||||||||
\(373\) | 20.9602 | 1.08528 | 0.542639 | − | 0.839966i | \(-0.317425\pi\) | ||||
0.542639 | + | 0.839966i | \(0.317425\pi\) | |||||||
\(374\) | −27.2009 | −1.40653 | ||||||||
\(375\) | −11.9108 | −0.615069 | ||||||||
\(376\) | 3.40494 | 0.175597 | ||||||||
\(377\) | −40.9522 | −2.10915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2526 | −1.34851 | −0.674253 | − | 0.738501i | \(-0.735534\pi\) | ||||
−0.674253 | + | 0.738501i | \(0.735534\pi\) | |||||||
\(380\) | 68.4593 | 3.51189 | ||||||||
\(381\) | 1.59918 | 0.0819287 | ||||||||
\(382\) | 37.0896 | 1.89767 | ||||||||
\(383\) | 18.8996 | 0.965723 | 0.482861 | − | 0.875697i | \(-0.339598\pi\) | ||||
0.482861 | + | 0.875697i | \(0.339598\pi\) | |||||||
\(384\) | −10.5163 | −0.536658 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 46.0282 | 2.34277 | ||||||||
\(387\) | 10.7302 | 0.545449 | ||||||||
\(388\) | −20.6641 | −1.04906 | ||||||||
\(389\) | 14.4255 | 0.731400 | 0.365700 | − | 0.930733i | \(-0.380830\pi\) | ||||
0.365700 | + | 0.930733i | \(0.380830\pi\) | |||||||
\(390\) | 21.1206 | 1.06948 | ||||||||
\(391\) | 22.7938 | 1.15273 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.63387 | 0.485964 | ||||||||
\(394\) | 64.4212 | 3.24549 | ||||||||
\(395\) | −5.99683 | −0.301733 | ||||||||
\(396\) | 9.93873 | 0.499440 | ||||||||
\(397\) | 11.9969 | 0.602109 | 0.301055 | − | 0.953607i | \(-0.402661\pi\) | ||||
0.301055 | + | 0.953607i | \(0.402661\pi\) | |||||||
\(398\) | 5.30458 | 0.265895 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.22231 | −0.311116 | ||||||||
\(401\) | 29.7872 | 1.48750 | 0.743751 | − | 0.668457i | \(-0.233045\pi\) | ||||
0.743751 | + | 0.668457i | \(0.233045\pi\) | |||||||
\(402\) | −22.2920 | −1.11183 | ||||||||
\(403\) | −15.2461 | −0.759462 | ||||||||
\(404\) | 67.1294 | 3.33981 | ||||||||
\(405\) | 2.03983 | 0.101360 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.3139 | −0.709514 | ||||||||
\(408\) | −31.2429 | −1.54675 | ||||||||
\(409\) | −17.3151 | −0.856175 | −0.428087 | − | 0.903737i | \(-0.640812\pi\) | ||||
−0.428087 | + | 0.903737i | \(0.640812\pi\) | |||||||
\(410\) | 5.20999 | 0.257303 | ||||||||
\(411\) | −7.92292 | −0.390809 | ||||||||
\(412\) | −68.6044 | −3.37990 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0107 | −0.590292 | ||||||||
\(415\) | 24.5945 | 1.20730 | ||||||||
\(416\) | 24.5230 | 1.20234 | ||||||||
\(417\) | −3.47465 | −0.170155 | ||||||||
\(418\) | 41.6339 | 2.03638 | ||||||||
\(419\) | −39.3854 | −1.92410 | −0.962051 | − | 0.272869i | \(-0.912027\pi\) | ||||
−0.962051 | + | 0.272869i | \(0.912027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.88794 | −0.189486 | −0.0947432 | − | 0.995502i | \(-0.530203\pi\) | ||||
−0.0947432 | + | 0.995502i | \(0.530203\pi\) | |||||||
\(422\) | 23.5113 | 1.14451 | ||||||||
\(423\) | 0.528264 | 0.0256851 | ||||||||
\(424\) | 46.7406 | 2.26992 | ||||||||
\(425\) | 4.06722 | 0.197289 | ||||||||
\(426\) | −4.99564 | −0.242040 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −47.6447 | −2.30299 | ||||||||
\(429\) | 8.90671 | 0.430020 | ||||||||
\(430\) | 55.9045 | 2.69595 | ||||||||
\(431\) | 18.5771 | 0.894827 | 0.447414 | − | 0.894327i | \(-0.352345\pi\) | ||||
0.447414 | + | 0.894327i | \(0.352345\pi\) | |||||||
\(432\) | 7.41559 | 0.356783 | ||||||||
\(433\) | −17.0462 | −0.819187 | −0.409593 | − | 0.912268i | \(-0.634329\pi\) | ||||
−0.409593 | + | 0.912268i | \(0.634329\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.6065 | −0.988004 | ||||||||
\(436\) | −92.6374 | −4.43653 | ||||||||
\(437\) | −34.8883 | −1.66893 | ||||||||
\(438\) | −33.6822 | −1.60940 | ||||||||
\(439\) | −32.6415 | −1.55789 | −0.778947 | − | 0.627090i | \(-0.784246\pi\) | ||||
−0.778947 | + | 0.627090i | \(0.784246\pi\) | |||||||
\(440\) | 28.8870 | 1.37713 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −50.1884 | −2.38722 | ||||||||
\(443\) | 8.03404 | 0.381709 | 0.190854 | − | 0.981618i | \(-0.438874\pi\) | ||||
0.190854 | + | 0.981618i | \(0.438874\pi\) | |||||||
\(444\) | −29.4707 | −1.39862 | ||||||||
\(445\) | −10.0706 | −0.477391 | ||||||||
\(446\) | 59.3257 | 2.80915 | ||||||||
\(447\) | 4.81236 | 0.227617 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.9945 | −0.660444 | −0.330222 | − | 0.943903i | \(-0.607124\pi\) | ||||
−0.330222 | + | 0.943903i | \(0.607124\pi\) | |||||||
\(450\) | −2.14313 | −0.101028 | ||||||||
\(451\) | 2.19710 | 0.103457 | ||||||||
\(452\) | 18.0652 | 0.849716 | ||||||||
\(453\) | −6.30410 | −0.296193 | ||||||||
\(454\) | −11.6897 | −0.548623 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 47.8206 | 2.23941 | ||||||||
\(457\) | −25.8840 | −1.21080 | −0.605401 | − | 0.795920i | \(-0.706987\pi\) | ||||
−0.605401 | + | 0.795920i | \(0.706987\pi\) | |||||||
\(458\) | 27.5848 | 1.28895 | ||||||||
\(459\) | −4.84721 | −0.226248 | ||||||||
\(460\) | −43.3911 | −2.02312 | ||||||||
\(461\) | −11.8265 | −0.550817 | −0.275408 | − | 0.961327i | \(-0.588813\pi\) | ||||
−0.275408 | + | 0.961327i | \(0.588813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.25951 | −0.0585345 | −0.0292672 | − | 0.999572i | \(-0.509317\pi\) | ||||
−0.0292672 | + | 0.999572i | \(0.509317\pi\) | |||||||
\(464\) | −74.9126 | −3.47773 | ||||||||
\(465\) | −7.67158 | −0.355761 | ||||||||
\(466\) | −48.7592 | −2.25873 | ||||||||
\(467\) | −5.15600 | −0.238591 | −0.119296 | − | 0.992859i | \(-0.538064\pi\) | ||||
−0.119296 | + | 0.992859i | \(0.538064\pi\) | |||||||
\(468\) | 18.3379 | 0.847671 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.75225 | 0.126952 | ||||||||
\(471\) | 4.07061 | 0.187564 | ||||||||
\(472\) | 48.5701 | 2.23562 | ||||||||
\(473\) | 23.5754 | 1.08400 | ||||||||
\(474\) | −7.50880 | −0.344890 | ||||||||
\(475\) | −6.22532 | −0.285637 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.25162 | 0.332029 | ||||||||
\(478\) | −18.8858 | −0.863815 | ||||||||
\(479\) | 24.6671 | 1.12707 | 0.563534 | − | 0.826093i | \(-0.309442\pi\) | ||||
0.563534 | + | 0.826093i | \(0.309442\pi\) | |||||||
\(480\) | 12.3395 | 0.563221 | ||||||||
\(481\) | −26.4105 | −1.20422 | ||||||||
\(482\) | 22.6296 | 1.03075 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −27.9230 | −1.26923 | ||||||||
\(485\) | −9.31812 | −0.423114 | ||||||||
\(486\) | 2.55413 | 0.115858 | ||||||||
\(487\) | −36.9281 | −1.67337 | −0.836685 | − | 0.547684i | \(-0.815510\pi\) | ||||
−0.836685 | + | 0.547684i | \(0.815510\pi\) | |||||||
\(488\) | 8.16841 | 0.369767 | ||||||||
\(489\) | 9.43025 | 0.426451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.8273 | 1.75225 | 0.876125 | − | 0.482085i | \(-0.160120\pi\) | ||||
0.876125 | + | 0.482085i | \(0.160120\pi\) | |||||||
\(492\) | 4.52358 | 0.203939 | ||||||||
\(493\) | 48.9667 | 2.20535 | ||||||||
\(494\) | 76.8187 | 3.45624 | ||||||||
\(495\) | 4.48171 | 0.201438 | ||||||||
\(496\) | −27.8892 | −1.25226 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 30.7955 | 1.37998 | ||||||||
\(499\) | −11.8209 | −0.529175 | −0.264587 | − | 0.964362i | \(-0.585236\pi\) | ||||
−0.264587 | + | 0.964362i | \(0.585236\pi\) | |||||||
\(500\) | −53.8792 | −2.40955 | ||||||||
\(501\) | 12.2859 | 0.548895 | ||||||||
\(502\) | −5.46679 | −0.243995 | ||||||||
\(503\) | −28.3846 | −1.26561 | −0.632803 | − | 0.774312i | \(-0.718096\pi\) | ||||
−0.632803 | + | 0.774312i | \(0.718096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.2709 | 1.34704 | ||||||||
\(506\) | −26.3886 | −1.17312 | ||||||||
\(507\) | 3.43376 | 0.152499 | ||||||||
\(508\) | 7.23403 | 0.320958 | ||||||||
\(509\) | 7.66798 | 0.339877 | 0.169939 | − | 0.985455i | \(-0.445643\pi\) | ||||
0.169939 | + | 0.985455i | \(0.445643\pi\) | |||||||
\(510\) | −25.2539 | −1.11826 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −50.7359 | −2.24223 | ||||||||
\(513\) | 7.41918 | 0.327565 | ||||||||
\(514\) | −36.4722 | −1.60872 | ||||||||
\(515\) | −30.9360 | −1.36320 | ||||||||
\(516\) | 48.5390 | 2.13681 | ||||||||
\(517\) | 1.16065 | 0.0510451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.7797 | 0.956023 | ||||||||
\(520\) | 53.2994 | 2.33733 | ||||||||
\(521\) | 9.40056 | 0.411846 | 0.205923 | − | 0.978568i | \(-0.433980\pi\) | ||||
0.205923 | + | 0.978568i | \(0.433980\pi\) | |||||||
\(522\) | −25.8019 | −1.12932 | ||||||||
\(523\) | 35.7553 | 1.56347 | 0.781735 | − | 0.623610i | \(-0.214335\pi\) | ||||
0.781735 | + | 0.623610i | \(0.214335\pi\) | |||||||
\(524\) | 43.5795 | 1.90378 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.9271 | 1.82811 | ||||||||
\(527\) | 18.2298 | 0.794103 | ||||||||
\(528\) | 16.2928 | 0.709051 | ||||||||
\(529\) | −0.886957 | −0.0385634 | ||||||||
\(530\) | 37.7809 | 1.64110 | ||||||||
\(531\) | 7.53546 | 0.327011 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.05386 | 0.175592 | ||||||||
\(534\) | −12.6096 | −0.545673 | ||||||||
\(535\) | −21.4846 | −0.928860 | ||||||||
\(536\) | −56.2556 | −2.42987 | ||||||||
\(537\) | −8.27123 | −0.356930 | ||||||||
\(538\) | −13.2978 | −0.573309 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.22734 | 0.397081 | ||||||||
\(541\) | 20.1520 | 0.866401 | 0.433201 | − | 0.901298i | \(-0.357384\pi\) | ||||
0.433201 | + | 0.901298i | \(0.357384\pi\) | |||||||
\(542\) | 78.5226 | 3.37284 | ||||||||
\(543\) | 2.34065 | 0.100447 | ||||||||
\(544\) | −29.3222 | −1.25718 | ||||||||
\(545\) | −41.7733 | −1.78937 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.9234 | −0.680837 | −0.340419 | − | 0.940274i | \(-0.610569\pi\) | ||||
−0.340419 | + | 0.940274i | \(0.610569\pi\) | |||||||
\(548\) | −35.8399 | −1.53101 | ||||||||
\(549\) | 1.26730 | 0.0540869 | ||||||||
\(550\) | −4.70866 | −0.200778 | ||||||||
\(551\) | −74.9488 | −3.19293 | ||||||||
\(552\) | −30.3098 | −1.29007 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −29.1898 | −1.24015 | ||||||||
\(555\) | −13.2893 | −0.564101 | ||||||||
\(556\) | −15.7179 | −0.666586 | ||||||||
\(557\) | −23.1311 | −0.980095 | −0.490047 | − | 0.871696i | \(-0.663020\pi\) | ||||
−0.490047 | + | 0.871696i | \(0.663020\pi\) | |||||||
\(558\) | −9.60579 | −0.406646 | ||||||||
\(559\) | 43.4988 | 1.83981 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6498 | −0.449634 | ||||||||
\(562\) | 4.50993 | 0.190240 | ||||||||
\(563\) | −30.7087 | −1.29422 | −0.647109 | − | 0.762398i | \(-0.724022\pi\) | ||||
−0.647109 | + | 0.762398i | \(0.724022\pi\) | |||||||
\(564\) | 2.38964 | 0.100622 | ||||||||
\(565\) | 8.14621 | 0.342714 | ||||||||
\(566\) | −24.5534 | −1.03206 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.6069 | −0.528973 | ||||||||
\(569\) | 3.03214 | 0.127114 | 0.0635570 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635570 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(570\) | 38.6539 | 1.61903 | ||||||||
\(571\) | −1.79836 | −0.0752589 | −0.0376294 | − | 0.999292i | \(-0.511981\pi\) | ||||
−0.0376294 | + | 0.999292i | \(0.511981\pi\) | |||||||
\(572\) | 40.2902 | 1.68462 | ||||||||
\(573\) | 14.5214 | 0.606642 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.94576 | 0.164549 | ||||||||
\(576\) | 0.619503 | 0.0258126 | ||||||||
\(577\) | 26.4404 | 1.10073 | 0.550365 | − | 0.834924i | \(-0.314489\pi\) | ||||
0.550365 | + | 0.834924i | \(0.314489\pi\) | |||||||
\(578\) | 16.5902 | 0.690063 | ||||||||
\(579\) | 18.0211 | 0.748930 | ||||||||
\(580\) | −93.2149 | −3.87054 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.6675 | −0.483632 | ||||||||
\(583\) | 15.9325 | 0.659856 | ||||||||
\(584\) | −84.9996 | −3.51731 | ||||||||
\(585\) | 8.26919 | 0.341889 | ||||||||
\(586\) | −1.03824 | −0.0428892 | ||||||||
\(587\) | 3.24299 | 0.133853 | 0.0669263 | − | 0.997758i | \(-0.478681\pi\) | ||||
0.0669263 | + | 0.997758i | \(0.478681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.9027 | −1.14971 | ||||||||
\(590\) | 39.2597 | 1.61630 | ||||||||
\(591\) | 25.2224 | 1.03751 | ||||||||
\(592\) | −48.3120 | −1.98561 | ||||||||
\(593\) | −25.9252 | −1.06462 | −0.532311 | − | 0.846549i | \(-0.678676\pi\) | ||||
−0.532311 | + | 0.846549i | \(0.678676\pi\) | |||||||
\(594\) | 5.61167 | 0.230249 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.7691 | 0.891697 | ||||||||
\(597\) | 2.07686 | 0.0850004 | ||||||||
\(598\) | −48.6895 | −1.99106 | ||||||||
\(599\) | −16.7618 | −0.684867 | −0.342433 | − | 0.939542i | \(-0.611251\pi\) | ||||
−0.342433 | + | 0.939542i | \(0.611251\pi\) | |||||||
\(600\) | −5.40836 | −0.220795 | ||||||||
\(601\) | −9.35320 | −0.381525 | −0.190762 | − | 0.981636i | \(-0.561096\pi\) | ||||
−0.190762 | + | 0.981636i | \(0.561096\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.72784 | −0.355425 | ||||||||
\(604\) | −28.5171 | −1.16034 | ||||||||
\(605\) | −12.5914 | −0.511914 | ||||||||
\(606\) | 37.9030 | 1.53970 | ||||||||
\(607\) | 5.62356 | 0.228253 | 0.114127 | − | 0.993466i | \(-0.463593\pi\) | ||||
0.114127 | + | 0.993466i | \(0.463593\pi\) | |||||||
\(608\) | 44.8808 | 1.82016 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.60261 | 0.267332 | ||||||||
\(611\) | 2.14151 | 0.0866360 | ||||||||
\(612\) | −21.9267 | −0.886335 | ||||||||
\(613\) | 13.6259 | 0.550346 | 0.275173 | − | 0.961395i | \(-0.411265\pi\) | ||||
0.275173 | + | 0.961395i | \(0.411265\pi\) | |||||||
\(614\) | −3.06679 | −0.123766 | ||||||||
\(615\) | 2.03983 | 0.0822540 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 45.9830 | 1.85121 | 0.925604 | − | 0.378494i | \(-0.123558\pi\) | ||||
0.925604 | + | 0.378494i | \(0.123558\pi\) | |||||||
\(618\) | −38.7358 | −1.55818 | ||||||||
\(619\) | −12.0863 | −0.485791 | −0.242895 | − | 0.970052i | \(-0.578097\pi\) | ||||
−0.242895 | + | 0.970052i | \(0.578097\pi\) | |||||||
\(620\) | −34.7030 | −1.39371 | ||||||||
\(621\) | −4.70245 | −0.188703 | ||||||||
\(622\) | −73.7448 | −2.95690 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 30.0617 | 1.20343 | ||||||||
\(625\) | −20.1005 | −0.804020 | ||||||||
\(626\) | −38.9546 | −1.55694 | ||||||||
\(627\) | 16.3006 | 0.650985 | ||||||||
\(628\) | 18.4137 | 0.734787 | ||||||||
\(629\) | 31.5792 | 1.25914 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.2956 | −1.80319 | −0.901596 | − | 0.432580i | \(-0.857603\pi\) | ||||
−0.901596 | + | 0.432580i | \(0.857603\pi\) | |||||||
\(632\) | −18.9490 | −0.753752 | ||||||||
\(633\) | 9.20520 | 0.365874 | ||||||||
\(634\) | 49.1848 | 1.95338 | ||||||||
\(635\) | 3.26207 | 0.129451 | ||||||||
\(636\) | 32.8032 | 1.30073 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −56.6892 | −2.24435 | ||||||||
\(639\) | −1.95591 | −0.0773745 | ||||||||
\(640\) | −21.4515 | −0.847945 | ||||||||
\(641\) | −14.8236 | −0.585495 | −0.292748 | − | 0.956190i | \(-0.594570\pi\) | ||||
−0.292748 | + | 0.956190i | \(0.594570\pi\) | |||||||
\(642\) | −26.9014 | −1.06171 | ||||||||
\(643\) | −10.4299 | −0.411314 | −0.205657 | − | 0.978624i | \(-0.565933\pi\) | ||||
−0.205657 | + | 0.978624i | \(0.565933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.8879 | 0.861834 | ||||||||
\(646\) | −91.8524 | −3.61389 | ||||||||
\(647\) | 17.4261 | 0.685093 | 0.342546 | − | 0.939501i | \(-0.388711\pi\) | ||||
0.342546 | + | 0.939501i | \(0.388711\pi\) | |||||||
\(648\) | 6.44554 | 0.253205 | ||||||||
\(649\) | 16.5561 | 0.649884 | ||||||||
\(650\) | −8.68795 | −0.340769 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.6584 | 1.67063 | ||||||||
\(653\) | 15.0102 | 0.587394 | 0.293697 | − | 0.955899i | \(-0.405114\pi\) | ||||
0.293697 | + | 0.955899i | \(0.405114\pi\) | |||||||
\(654\) | −52.3055 | −2.04531 | ||||||||
\(655\) | 19.6515 | 0.767847 | ||||||||
\(656\) | 7.41559 | 0.289530 | ||||||||
\(657\) | −13.1873 | −0.514487 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.1433 | 1.25212 | 0.626062 | − | 0.779774i | \(-0.284666\pi\) | ||||
0.626062 | + | 0.779774i | \(0.284666\pi\) | |||||||
\(660\) | 20.2733 | 0.789139 | ||||||||
\(661\) | −2.34987 | −0.0913992 | −0.0456996 | − | 0.998955i | \(-0.514552\pi\) | ||||
−0.0456996 | + | 0.998955i | \(0.514552\pi\) | |||||||
\(662\) | 5.90091 | 0.229345 | ||||||||
\(663\) | −19.6499 | −0.763139 | ||||||||
\(664\) | 77.7148 | 3.01592 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.6399 | −0.644785 | ||||||||
\(667\) | 47.5043 | 1.83937 | ||||||||
\(668\) | 55.5764 | 2.15032 | ||||||||
\(669\) | 23.2274 | 0.898022 | ||||||||
\(670\) | −45.4720 | −1.75674 | ||||||||
\(671\) | 2.78437 | 0.107489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.7768 | −1.14781 | −0.573906 | − | 0.818921i | \(-0.694573\pi\) | ||||
−0.573906 | + | 0.818921i | \(0.694573\pi\) | |||||||
\(674\) | −16.2813 | −0.627131 | ||||||||
\(675\) | −0.839085 | −0.0322964 | ||||||||
\(676\) | 15.5329 | 0.597418 | ||||||||
\(677\) | 27.9673 | 1.07487 | 0.537435 | − | 0.843305i | \(-0.319393\pi\) | ||||
0.537435 | + | 0.843305i | \(0.319393\pi\) | |||||||
\(678\) | 10.2001 | 0.391732 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −63.7303 | −2.44394 | ||||||||
\(681\) | −4.57677 | −0.175382 | ||||||||
\(682\) | −21.1048 | −0.808146 | ||||||||
\(683\) | −26.5644 | −1.01646 | −0.508230 | − | 0.861221i | \(-0.669700\pi\) | ||||
−0.508230 | + | 0.861221i | \(0.669700\pi\) | |||||||
\(684\) | 33.5612 | 1.28325 | ||||||||
\(685\) | −16.1614 | −0.617496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.8001 | 0.412048 | ||||||||
\(688\) | 79.5710 | 3.03362 | ||||||||
\(689\) | 29.3970 | 1.11994 | ||||||||
\(690\) | −24.4997 | −0.932689 | ||||||||
\(691\) | −1.69085 | −0.0643229 | −0.0321614 | − | 0.999483i | \(-0.510239\pi\) | ||||
−0.0321614 | + | 0.999483i | \(0.510239\pi\) | |||||||
\(692\) | 98.5221 | 3.74525 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.60100 | −0.364449 | ||||||||
\(695\) | −7.08771 | −0.268852 | ||||||||
\(696\) | −65.1131 | −2.46810 | ||||||||
\(697\) | −4.84721 | −0.183601 | ||||||||
\(698\) | −42.6788 | −1.61542 | ||||||||
\(699\) | −19.0904 | −0.722064 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.65407 | 0.138012 | 0.0690062 | − | 0.997616i | \(-0.478017\pi\) | ||||
0.0690062 | + | 0.997616i | \(0.478017\pi\) | |||||||
\(702\) | 10.3541 | 0.390789 | ||||||||
\(703\) | −48.3353 | −1.82300 | ||||||||
\(704\) | 1.36111 | 0.0512986 | ||||||||
\(705\) | 1.07757 | 0.0405836 | ||||||||
\(706\) | −5.25203 | −0.197663 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 34.0872 | 1.28108 | ||||||||
\(709\) | −29.8396 | −1.12065 | −0.560324 | − | 0.828273i | \(-0.689323\pi\) | ||||
−0.560324 | + | 0.828273i | \(0.689323\pi\) | |||||||
\(710\) | −10.1903 | −0.382434 | ||||||||
\(711\) | −2.93987 | −0.110254 | ||||||||
\(712\) | −31.8214 | −1.19256 | ||||||||
\(713\) | 17.6854 | 0.662323 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.1682 | 0.679452 | ||||||||
\(716\) | −37.4155 | −1.39828 | ||||||||
\(717\) | −7.39421 | −0.276142 | ||||||||
\(718\) | 89.9193 | 3.35576 | ||||||||
\(719\) | −21.2360 | −0.791970 | −0.395985 | − | 0.918257i | \(-0.629597\pi\) | ||||
−0.395985 | + | 0.918257i | \(0.629597\pi\) | |||||||
\(720\) | 15.1266 | 0.563734 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 92.0616 | 3.42618 | ||||||||
\(723\) | 8.85999 | 0.329506 | ||||||||
\(724\) | 10.5881 | 0.393503 | ||||||||
\(725\) | 8.47647 | 0.314808 | ||||||||
\(726\) | −15.7661 | −0.585133 | ||||||||
\(727\) | 48.4942 | 1.79855 | 0.899275 | − | 0.437383i | \(-0.144095\pi\) | ||||
0.899275 | + | 0.437383i | \(0.144095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −68.7060 | −2.54292 | ||||||||
\(731\) | −52.0117 | −1.92372 | ||||||||
\(732\) | 5.73271 | 0.211887 | ||||||||
\(733\) | 27.3083 | 1.00866 | 0.504328 | − | 0.863512i | \(-0.331740\pi\) | ||||
0.504328 | + | 0.863512i | \(0.331740\pi\) | |||||||
\(734\) | −35.5716 | −1.31297 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.4465 | −1.04855 | ||||||||
\(737\) | −19.1759 | −0.706353 | ||||||||
\(738\) | 2.55413 | 0.0940188 | ||||||||
\(739\) | −13.4819 | −0.495940 | −0.247970 | − | 0.968768i | \(-0.579763\pi\) | ||||
−0.247970 | + | 0.968768i | \(0.579763\pi\) | |||||||
\(740\) | −60.1153 | −2.20988 | ||||||||
\(741\) | 30.0763 | 1.10488 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.0019 | 1.68765 | 0.843823 | − | 0.536622i | \(-0.180300\pi\) | ||||
0.843823 | + | 0.536622i | \(0.180300\pi\) | |||||||
\(744\) | −24.2410 | −0.888716 | ||||||||
\(745\) | 9.81641 | 0.359645 | ||||||||
\(746\) | 53.5350 | 1.96006 | ||||||||
\(747\) | 12.0571 | 0.441148 | ||||||||
\(748\) | −48.1751 | −1.76146 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −30.4216 | −1.11084 | ||||||||
\(751\) | 21.8979 | 0.799066 | 0.399533 | − | 0.916719i | \(-0.369172\pi\) | ||||
0.399533 | + | 0.916719i | \(0.369172\pi\) | |||||||
\(752\) | 3.91739 | 0.142852 | ||||||||
\(753\) | −2.14037 | −0.0779995 | ||||||||
\(754\) | −104.597 | −3.80921 | ||||||||
\(755\) | −12.8593 | −0.467998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.5655 | −1.54707 | −0.773535 | − | 0.633754i | \(-0.781513\pi\) | ||||
−0.773535 | + | 0.633754i | \(0.781513\pi\) | |||||||
\(758\) | −67.0525 | −2.43546 | ||||||||
\(759\) | −10.3317 | −0.375018 | ||||||||
\(760\) | 97.5460 | 3.53837 | ||||||||
\(761\) | 18.1190 | 0.656812 | 0.328406 | − | 0.944537i | \(-0.393489\pi\) | ||||
0.328406 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(762\) | 4.08452 | 0.147967 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 65.6888 | 2.37654 | ||||||||
\(765\) | −9.88750 | −0.357483 | ||||||||
\(766\) | 48.2719 | 1.74414 | ||||||||
\(767\) | 30.5477 | 1.10301 | ||||||||
\(768\) | −28.0990 | −1.01394 | ||||||||
\(769\) | −0.938954 | −0.0338596 | −0.0169298 | − | 0.999857i | \(-0.505389\pi\) | ||||
−0.0169298 | + | 0.999857i | \(0.505389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.2797 | −0.514271 | ||||||||
\(772\) | 81.5197 | 2.93396 | ||||||||
\(773\) | 19.5127 | 0.701821 | 0.350911 | − | 0.936409i | \(-0.385872\pi\) | ||||
0.350911 | + | 0.936409i | \(0.385872\pi\) | |||||||
\(774\) | 27.4064 | 0.985103 | ||||||||
\(775\) | 3.15570 | 0.113356 | ||||||||
\(776\) | −29.4438 | −1.05697 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.8445 | 1.32094 | ||||||||
\(779\) | 7.41918 | 0.265820 | ||||||||
\(780\) | 37.4063 | 1.33936 | ||||||||
\(781\) | −4.29732 | −0.153770 | ||||||||
\(782\) | 58.2182 | 2.08188 | ||||||||
\(783\) | −10.1020 | −0.361017 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.30336 | 0.296360 | ||||||||
\(786\) | 24.6061 | 0.877672 | ||||||||
\(787\) | −46.1884 | −1.64644 | −0.823219 | − | 0.567724i | \(-0.807824\pi\) | ||||
−0.823219 | + | 0.567724i | \(0.807824\pi\) | |||||||
\(788\) | 114.095 | 4.06448 | ||||||||
\(789\) | 16.4154 | 0.584404 | ||||||||
\(790\) | −15.3167 | −0.544943 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 14.1615 | 0.503206 | ||||||||
\(793\) | 5.13744 | 0.182436 | ||||||||
\(794\) | 30.6417 | 1.08743 | ||||||||
\(795\) | 14.7921 | 0.524621 | ||||||||
\(796\) | 9.39486 | 0.332992 | ||||||||
\(797\) | 4.04847 | 0.143404 | 0.0717020 | − | 0.997426i | \(-0.477157\pi\) | ||||
0.0717020 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.56060 | −0.0905877 | ||||||||
\(800\) | −5.07587 | −0.179459 | ||||||||
\(801\) | −4.93696 | −0.174439 | ||||||||
\(802\) | 76.0804 | 2.68649 | ||||||||
\(803\) | −28.9739 | −1.02247 | ||||||||
\(804\) | −39.4810 | −1.39239 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −38.9405 | −1.37162 | ||||||||
\(807\) | −5.20640 | −0.183274 | ||||||||
\(808\) | 95.6512 | 3.36500 | ||||||||
\(809\) | −21.5809 | −0.758745 | −0.379373 | − | 0.925244i | \(-0.623860\pi\) | ||||
−0.379373 | + | 0.925244i | \(0.623860\pi\) | |||||||
\(810\) | 5.20999 | 0.183061 | ||||||||
\(811\) | −0.609476 | −0.0214016 | −0.0107008 | − | 0.999943i | \(-0.503406\pi\) | ||||
−0.0107008 | + | 0.999943i | \(0.503406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.7434 | 1.07822 | ||||||||
\(814\) | −36.5595 | −1.28141 | ||||||||
\(815\) | 19.2361 | 0.673812 | ||||||||
\(816\) | −35.9449 | −1.25832 | ||||||||
\(817\) | 79.6095 | 2.78519 | ||||||||
\(818\) | −44.2249 | −1.54629 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.22734 | 0.322233 | ||||||||
\(821\) | 6.40281 | 0.223460 | 0.111730 | − | 0.993739i | \(-0.464361\pi\) | ||||
0.111730 | + | 0.993739i | \(0.464361\pi\) | |||||||
\(822\) | −20.2362 | −0.705817 | ||||||||
\(823\) | −34.8973 | −1.21644 | −0.608221 | − | 0.793768i | \(-0.708117\pi\) | ||||
−0.608221 | + | 0.793768i | \(0.708117\pi\) | |||||||
\(824\) | −97.7529 | −3.40538 | ||||||||
\(825\) | −1.84355 | −0.0641842 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4846 | 0.677545 | 0.338773 | − | 0.940868i | \(-0.389988\pi\) | ||||
0.338773 | + | 0.940868i | \(0.389988\pi\) | |||||||
\(828\) | −21.2719 | −0.739249 | ||||||||
\(829\) | 49.9870 | 1.73612 | 0.868060 | − | 0.496460i | \(-0.165367\pi\) | ||||
0.868060 | + | 0.496460i | \(0.165367\pi\) | |||||||
\(830\) | 62.8176 | 2.18043 | ||||||||
\(831\) | −11.4285 | −0.396449 | ||||||||
\(832\) | 2.51137 | 0.0870663 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.87472 | −0.307306 | ||||||||
\(835\) | 25.0613 | 0.867281 | ||||||||
\(836\) | 73.7372 | 2.55025 | ||||||||
\(837\) | −3.76089 | −0.129995 | ||||||||
\(838\) | −100.595 | −3.47501 | ||||||||
\(839\) | −33.9692 | −1.17275 | −0.586374 | − | 0.810040i | \(-0.699445\pi\) | ||||
−0.586374 | + | 0.810040i | \(0.699445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 73.0511 | 2.51900 | ||||||||
\(842\) | −9.93029 | −0.342221 | ||||||||
\(843\) | 1.76574 | 0.0608154 | ||||||||
\(844\) | 41.6404 | 1.43332 | ||||||||
\(845\) | 7.00429 | 0.240955 | ||||||||
\(846\) | 1.34925 | 0.0463883 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 53.7750 | 1.84664 | ||||||||
\(849\) | −9.61324 | −0.329925 | ||||||||
\(850\) | 10.3882 | 0.356313 | ||||||||
\(851\) | 30.6361 | 1.05019 | ||||||||
\(852\) | −8.84770 | −0.303117 | ||||||||
\(853\) | −21.9694 | −0.752219 | −0.376109 | − | 0.926575i | \(-0.622738\pi\) | ||||
−0.376109 | + | 0.926575i | \(0.622738\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.1339 | 0.517568 | ||||||||
\(856\) | −67.8878 | −2.32036 | ||||||||
\(857\) | −29.0187 | −0.991261 | −0.495630 | − | 0.868534i | \(-0.665063\pi\) | ||||
−0.495630 | + | 0.868534i | \(0.665063\pi\) | |||||||
\(858\) | 22.7489 | 0.776634 | ||||||||
\(859\) | −51.7596 | −1.76602 | −0.883008 | − | 0.469358i | \(-0.844485\pi\) | ||||
−0.883008 | + | 0.469358i | \(0.844485\pi\) | |||||||
\(860\) | 99.0115 | 3.37626 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.4483 | 1.61610 | ||||||||
\(863\) | 2.65807 | 0.0904819 | 0.0452409 | − | 0.998976i | \(-0.485594\pi\) | ||||
0.0452409 | + | 0.998976i | \(0.485594\pi\) | |||||||
\(864\) | 6.04930 | 0.205801 | ||||||||
\(865\) | 44.4269 | 1.51056 | ||||||||
\(866\) | −43.5381 | −1.47949 | ||||||||
\(867\) | 6.49545 | 0.220597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.45916 | −0.219112 | ||||||||
\(870\) | −52.6316 | −1.78438 | ||||||||
\(871\) | −35.3814 | −1.19885 | ||||||||
\(872\) | −131.997 | −4.46998 | ||||||||
\(873\) | −4.56808 | −0.154606 | ||||||||
\(874\) | −89.1093 | −3.01417 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −59.6540 | −2.01552 | ||||||||
\(877\) | 36.3290 | 1.22674 | 0.613371 | − | 0.789795i | \(-0.289813\pi\) | ||||
0.613371 | + | 0.789795i | \(0.289813\pi\) | |||||||
\(878\) | −83.3706 | −2.81362 | ||||||||
\(879\) | −0.406494 | −0.0137107 | ||||||||
\(880\) | 33.2345 | 1.12033 | ||||||||
\(881\) | 54.4117 | 1.83318 | 0.916588 | − | 0.399833i | \(-0.130932\pi\) | ||||
0.916588 | + | 0.399833i | \(0.130932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0694 | 0.843654 | 0.421827 | − | 0.906676i | \(-0.361389\pi\) | ||||
0.421827 | + | 0.906676i | \(0.361389\pi\) | |||||||
\(884\) | −88.8878 | −2.98962 | ||||||||
\(885\) | 15.3711 | 0.516693 | ||||||||
\(886\) | 20.5200 | 0.689382 | ||||||||
\(887\) | 44.5935 | 1.49730 | 0.748651 | − | 0.662964i | \(-0.230702\pi\) | ||||
0.748651 | + | 0.662964i | \(0.230702\pi\) | |||||||
\(888\) | −41.9922 | −1.40916 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −25.7216 | −0.862188 | ||||||||
\(891\) | 2.19710 | 0.0736055 | ||||||||
\(892\) | 105.071 | 3.51803 | ||||||||
\(893\) | 3.91928 | 0.131154 | ||||||||
\(894\) | 12.2914 | 0.411086 | ||||||||
\(895\) | −16.8719 | −0.563966 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.0631 | −0.636497 | ||||||||
\(898\) | −35.7439 | −1.19279 | ||||||||
\(899\) | 37.9926 | 1.26712 | ||||||||
\(900\) | −3.79567 | −0.126522 | ||||||||
\(901\) | −35.1501 | −1.17102 | ||||||||
\(902\) | 5.61167 | 0.186848 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.7407 | 0.856123 | ||||||||
\(905\) | 4.77452 | 0.158711 | ||||||||
\(906\) | −16.1015 | −0.534936 | ||||||||
\(907\) | −51.9895 | −1.72628 | −0.863141 | − | 0.504962i | \(-0.831506\pi\) | ||||
−0.863141 | + | 0.504962i | \(0.831506\pi\) | |||||||
\(908\) | −20.7034 | −0.687065 | ||||||||
\(909\) | 14.8399 | 0.492208 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.5978 | −0.417383 | −0.208692 | − | 0.977981i | \(-0.566921\pi\) | ||||
−0.208692 | + | 0.977981i | \(0.566921\pi\) | |||||||
\(912\) | 55.0176 | 1.82181 | ||||||||
\(913\) | 26.4907 | 0.876714 | ||||||||
\(914\) | −66.1111 | −2.18676 | ||||||||
\(915\) | 2.58507 | 0.0854599 | ||||||||
\(916\) | 48.8549 | 1.61421 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.3804 | −0.408614 | ||||||||
\(919\) | −40.2751 | −1.32855 | −0.664277 | − | 0.747487i | \(-0.731260\pi\) | ||||
−0.664277 | + | 0.747487i | \(0.731260\pi\) | |||||||
\(920\) | −61.8270 | −2.03837 | ||||||||
\(921\) | −1.20072 | −0.0395651 | ||||||||
\(922\) | −30.2065 | −0.994799 | ||||||||
\(923\) | −7.92897 | −0.260985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.46657 | 0.179740 | ||||||||
\(926\) | −3.21696 | −0.105716 | ||||||||
\(927\) | −15.1660 | −0.498116 | ||||||||
\(928\) | −61.1102 | −2.00604 | ||||||||
\(929\) | 37.4105 | 1.22740 | 0.613700 | − | 0.789539i | \(-0.289680\pi\) | ||||
0.613700 | + | 0.789539i | \(0.289680\pi\) | |||||||
\(930\) | −19.5942 | −0.642519 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −86.3567 | −2.82871 | ||||||||
\(933\) | −28.8728 | −0.945252 | ||||||||
\(934\) | −13.1691 | −0.430906 | ||||||||
\(935\) | −21.7238 | −0.710443 | ||||||||
\(936\) | 26.1293 | 0.854063 | ||||||||
\(937\) | −6.39519 | −0.208922 | −0.104461 | − | 0.994529i | \(-0.533312\pi\) | ||||
−0.104461 | + | 0.994529i | \(0.533312\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.2516 | −0.497718 | ||||||||
\(940\) | 4.87447 | 0.158988 | ||||||||
\(941\) | −28.2888 | −0.922189 | −0.461095 | − | 0.887351i | \(-0.652543\pi\) | ||||
−0.461095 | + | 0.887351i | \(0.652543\pi\) | |||||||
\(942\) | 10.3969 | 0.338748 | ||||||||
\(943\) | −4.70245 | −0.153133 | ||||||||
\(944\) | 55.8799 | 1.81873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 60.2145 | 1.95774 | ||||||||
\(947\) | −11.5695 | −0.375957 | −0.187979 | − | 0.982173i | \(-0.560194\pi\) | ||||
−0.187979 | + | 0.982173i | \(0.560194\pi\) | |||||||
\(948\) | −13.2987 | −0.431922 | ||||||||
\(949\) | −53.4596 | −1.73537 | ||||||||
\(950\) | −15.9003 | −0.515873 | ||||||||
\(951\) | 19.2570 | 0.624450 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.3771 | −0.854437 | −0.427219 | − | 0.904148i | \(-0.640507\pi\) | ||||
−0.427219 | + | 0.904148i | \(0.640507\pi\) | |||||||
\(954\) | 18.5216 | 0.599658 | ||||||||
\(955\) | 29.6213 | 0.958522 | ||||||||
\(956\) | −33.4483 | −1.08179 | ||||||||
\(957\) | −22.1951 | −0.717467 | ||||||||
\(958\) | 63.0029 | 2.03553 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.26368 | 0.0407851 | ||||||||
\(961\) | −16.8557 | −0.543733 | ||||||||
\(962\) | −67.4560 | −2.17487 | ||||||||
\(963\) | −10.5325 | −0.339406 | ||||||||
\(964\) | 40.0788 | 1.29085 | ||||||||
\(965\) | 36.7600 | 1.18335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.1048 | −1.06458 | −0.532290 | − | 0.846562i | \(-0.678668\pi\) | ||||
−0.532290 | + | 0.846562i | \(0.678668\pi\) | |||||||
\(968\) | −39.7868 | −1.27880 | ||||||||
\(969\) | −35.9623 | −1.15528 | ||||||||
\(970\) | −23.7997 | −0.764162 | ||||||||
\(971\) | 13.5891 | 0.436095 | 0.218047 | − | 0.975938i | \(-0.430031\pi\) | ||||
0.218047 | + | 0.975938i | \(0.430031\pi\) | |||||||
\(972\) | 4.52358 | 0.145094 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −94.3191 | −3.02218 | ||||||||
\(975\) | −3.40153 | −0.108936 | ||||||||
\(976\) | 9.39775 | 0.300815 | ||||||||
\(977\) | −58.3154 | −1.86567 | −0.932837 | − | 0.360299i | \(-0.882675\pi\) | ||||
−0.932837 | + | 0.360299i | \(0.882675\pi\) | |||||||
\(978\) | 24.0861 | 0.770188 | ||||||||
\(979\) | −10.8470 | −0.346671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.4788 | −0.653838 | ||||||||
\(982\) | 99.1698 | 3.16464 | ||||||||
\(983\) | 16.9974 | 0.542132 | 0.271066 | − | 0.962561i | \(-0.412624\pi\) | ||||
0.271066 | + | 0.962561i | \(0.412624\pi\) | |||||||
\(984\) | 6.44554 | 0.205476 | ||||||||
\(985\) | 51.4494 | 1.63932 | ||||||||
\(986\) | 125.067 | 3.98295 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 136.052 | 4.32840 | ||||||||
\(989\) | −50.4584 | −1.60448 | ||||||||
\(990\) | 11.4469 | 0.363805 | ||||||||
\(991\) | −9.52580 | −0.302597 | −0.151299 | − | 0.988488i | \(-0.548345\pi\) | ||||
−0.151299 | + | 0.988488i | \(0.548345\pi\) | |||||||
\(992\) | −22.7507 | −0.722336 | ||||||||
\(993\) | 2.31034 | 0.0733164 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.23646 | 0.134305 | ||||||||
\(996\) | 54.5414 | 1.72821 | ||||||||
\(997\) | 43.2360 | 1.36930 | 0.684648 | − | 0.728874i | \(-0.259956\pi\) | ||||
0.684648 | + | 0.728874i | \(0.259956\pi\) | |||||||
\(998\) | −30.1920 | −0.955712 | ||||||||
\(999\) | −6.51492 | −0.206123 |
(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 | 6027.2.a.bc.1.8 | 8 | ||
7.3 | odd | 6 | 861.2.i.d.247.1 | ✓ | 16 | ||
7.5 | odd | 6 | 861.2.i.d.739.1 | yes | 16 | ||
7.6 | odd | 2 | 6027.2.a.bb.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.d.247.1 | ✓ | 16 | 7.3 | odd | 6 | ||
861.2.i.d.739.1 | yes | 16 | 7.5 | odd | 6 | ||
6027.2.a.bb.1.8 | 8 | 7.6 | odd | 2 | |||
6027.2.a.bc.1.8 | 8 | 1.1 | even | 1 | trivial |