Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.46200 | −1.42144 | −0.710719 | − | 0.703476i | \(-0.751630\pi\) | ||||
−0.710719 | + | 0.703476i | \(0.751630\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.19890 | −0.536164 | −0.268082 | − | 0.963396i | \(-0.586390\pi\) | ||||
−0.268082 | + | 0.963396i | \(0.586390\pi\) | |||||||
\(6\) | −2.46200 | −1.00511 | ||||||||
\(7\) | 2.88631 | 1.09092 | 0.545461 | − | 0.838136i | \(-0.316355\pi\) | ||||
0.545461 | + | 0.838136i | \(0.316355\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.06146 | 1.02049 | ||||||||
\(10\) | −1.19890 | −0.379125 | ||||||||
\(11\) | −4.46025 | −1.34482 | −0.672408 | − | 0.740181i | \(-0.734740\pi\) | ||||
−0.672408 | + | 0.740181i | \(0.734740\pi\) | |||||||
\(12\) | −2.46200 | −0.710719 | ||||||||
\(13\) | 2.03184 | 0.563530 | 0.281765 | − | 0.959483i | \(-0.409080\pi\) | ||||
0.281765 | + | 0.959483i | \(0.409080\pi\) | |||||||
\(14\) | 2.88631 | 0.771398 | ||||||||
\(15\) | 2.95169 | 0.762123 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.33298 | −0.323294 | −0.161647 | − | 0.986849i | \(-0.551681\pi\) | ||||
−0.161647 | + | 0.986849i | \(0.551681\pi\) | |||||||
\(18\) | 3.06146 | 0.721593 | ||||||||
\(19\) | 2.99427 | 0.686934 | 0.343467 | − | 0.939165i | \(-0.388399\pi\) | ||||
0.343467 | + | 0.939165i | \(0.388399\pi\) | |||||||
\(20\) | −1.19890 | −0.268082 | ||||||||
\(21\) | −7.10610 | −1.55068 | ||||||||
\(22\) | −4.46025 | −0.950929 | ||||||||
\(23\) | −7.98056 | −1.66406 | −0.832030 | − | 0.554730i | \(-0.812822\pi\) | ||||
−0.832030 | + | 0.554730i | \(0.812822\pi\) | |||||||
\(24\) | −2.46200 | −0.502554 | ||||||||
\(25\) | −3.56264 | −0.712529 | ||||||||
\(26\) | 2.03184 | 0.398476 | ||||||||
\(27\) | −0.151315 | −0.0291206 | ||||||||
\(28\) | 2.88631 | 0.545461 | ||||||||
\(29\) | 5.45001 | 1.01204 | 0.506020 | − | 0.862521i | \(-0.331116\pi\) | ||||
0.506020 | + | 0.862521i | \(0.331116\pi\) | |||||||
\(30\) | 2.95169 | 0.538903 | ||||||||
\(31\) | 9.51670 | 1.70925 | 0.854625 | − | 0.519246i | \(-0.173787\pi\) | ||||
0.854625 | + | 0.519246i | \(0.173787\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 10.9812 | 1.91157 | ||||||||
\(34\) | −1.33298 | −0.228603 | ||||||||
\(35\) | −3.46039 | −0.584912 | ||||||||
\(36\) | 3.06146 | 0.510243 | ||||||||
\(37\) | 2.05789 | 0.338316 | 0.169158 | − | 0.985589i | \(-0.445895\pi\) | ||||
0.169158 | + | 0.985589i | \(0.445895\pi\) | |||||||
\(38\) | 2.99427 | 0.485736 | ||||||||
\(39\) | −5.00238 | −0.801023 | ||||||||
\(40\) | −1.19890 | −0.189562 | ||||||||
\(41\) | −1.03166 | −0.161118 | −0.0805591 | − | 0.996750i | \(-0.525671\pi\) | ||||
−0.0805591 | + | 0.996750i | \(0.525671\pi\) | |||||||
\(42\) | −7.10610 | −1.09649 | ||||||||
\(43\) | −4.26974 | −0.651130 | −0.325565 | − | 0.945520i | \(-0.605554\pi\) | ||||
−0.325565 | + | 0.945520i | \(0.605554\pi\) | |||||||
\(44\) | −4.46025 | −0.672408 | ||||||||
\(45\) | −3.67038 | −0.547148 | ||||||||
\(46\) | −7.98056 | −1.17667 | ||||||||
\(47\) | −3.70023 | −0.539733 | −0.269867 | − | 0.962898i | \(-0.586980\pi\) | ||||
−0.269867 | + | 0.962898i | \(0.586980\pi\) | |||||||
\(48\) | −2.46200 | −0.355360 | ||||||||
\(49\) | 1.33077 | 0.190110 | ||||||||
\(50\) | −3.56264 | −0.503834 | ||||||||
\(51\) | 3.28179 | 0.459542 | ||||||||
\(52\) | 2.03184 | 0.281765 | ||||||||
\(53\) | −3.14181 | −0.431561 | −0.215780 | − | 0.976442i | \(-0.569230\pi\) | ||||
−0.215780 | + | 0.976442i | \(0.569230\pi\) | |||||||
\(54\) | −0.151315 | −0.0205914 | ||||||||
\(55\) | 5.34739 | 0.721042 | ||||||||
\(56\) | 2.88631 | 0.385699 | ||||||||
\(57\) | −7.37191 | −0.976434 | ||||||||
\(58\) | 5.45001 | 0.715621 | ||||||||
\(59\) | −3.60466 | −0.469286 | −0.234643 | − | 0.972082i | \(-0.575392\pi\) | ||||
−0.234643 | + | 0.972082i | \(0.575392\pi\) | |||||||
\(60\) | 2.95169 | 0.381062 | ||||||||
\(61\) | −8.62323 | −1.10409 | −0.552045 | − | 0.833814i | \(-0.686153\pi\) | ||||
−0.552045 | + | 0.833814i | \(0.686153\pi\) | |||||||
\(62\) | 9.51670 | 1.20862 | ||||||||
\(63\) | 8.83632 | 1.11327 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.43596 | −0.302144 | ||||||||
\(66\) | 10.9812 | 1.35169 | ||||||||
\(67\) | 12.4646 | 1.52279 | 0.761396 | − | 0.648288i | \(-0.224515\pi\) | ||||
0.761396 | + | 0.648288i | \(0.224515\pi\) | |||||||
\(68\) | −1.33298 | −0.161647 | ||||||||
\(69\) | 19.6482 | 2.36536 | ||||||||
\(70\) | −3.46039 | −0.413596 | ||||||||
\(71\) | −7.46589 | −0.886038 | −0.443019 | − | 0.896512i | \(-0.646093\pi\) | ||||
−0.443019 | + | 0.896512i | \(0.646093\pi\) | |||||||
\(72\) | 3.06146 | 0.360797 | ||||||||
\(73\) | 0.802939 | 0.0939769 | 0.0469884 | − | 0.998895i | \(-0.485038\pi\) | ||||
0.0469884 | + | 0.998895i | \(0.485038\pi\) | |||||||
\(74\) | 2.05789 | 0.239225 | ||||||||
\(75\) | 8.77124 | 1.01282 | ||||||||
\(76\) | 2.99427 | 0.343467 | ||||||||
\(77\) | −12.8737 | −1.46709 | ||||||||
\(78\) | −5.00238 | −0.566409 | ||||||||
\(79\) | 10.5744 | 1.18972 | 0.594858 | − | 0.803831i | \(-0.297208\pi\) | ||||
0.594858 | + | 0.803831i | \(0.297208\pi\) | |||||||
\(80\) | −1.19890 | −0.134041 | ||||||||
\(81\) | −8.81184 | −0.979094 | ||||||||
\(82\) | −1.03166 | −0.113928 | ||||||||
\(83\) | −6.47728 | −0.710974 | −0.355487 | − | 0.934681i | \(-0.615685\pi\) | ||||
−0.355487 | + | 0.934681i | \(0.615685\pi\) | |||||||
\(84\) | −7.10610 | −0.775339 | ||||||||
\(85\) | 1.59810 | 0.173338 | ||||||||
\(86\) | −4.26974 | −0.460418 | ||||||||
\(87\) | −13.4179 | −1.43855 | ||||||||
\(88\) | −4.46025 | −0.475464 | ||||||||
\(89\) | −12.7695 | −1.35357 | −0.676784 | − | 0.736182i | \(-0.736627\pi\) | ||||
−0.676784 | + | 0.736182i | \(0.736627\pi\) | |||||||
\(90\) | −3.67038 | −0.386892 | ||||||||
\(91\) | 5.86450 | 0.614767 | ||||||||
\(92\) | −7.98056 | −0.832030 | ||||||||
\(93\) | −23.4301 | −2.42959 | ||||||||
\(94\) | −3.70023 | −0.381649 | ||||||||
\(95\) | −3.58983 | −0.368309 | ||||||||
\(96\) | −2.46200 | −0.251277 | ||||||||
\(97\) | 12.6583 | 1.28526 | 0.642629 | − | 0.766178i | \(-0.277844\pi\) | ||||
0.642629 | + | 0.766178i | \(0.277844\pi\) | |||||||
\(98\) | 1.33077 | 0.134428 | ||||||||
\(99\) | −13.6549 | −1.37237 | ||||||||
\(100\) | −3.56264 | −0.356264 | ||||||||
\(101\) | 5.05589 | 0.503080 | 0.251540 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251540 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(102\) | 3.28179 | 0.324946 | ||||||||
\(103\) | 10.9353 | 1.07748 | 0.538741 | − | 0.842471i | \(-0.318900\pi\) | ||||
0.538741 | + | 0.842471i | \(0.318900\pi\) | |||||||
\(104\) | 2.03184 | 0.199238 | ||||||||
\(105\) | 8.51949 | 0.831417 | ||||||||
\(106\) | −3.14181 | −0.305160 | ||||||||
\(107\) | −9.24635 | −0.893878 | −0.446939 | − | 0.894564i | \(-0.647486\pi\) | ||||
−0.446939 | + | 0.894564i | \(0.647486\pi\) | |||||||
\(108\) | −0.151315 | −0.0145603 | ||||||||
\(109\) | 4.09628 | 0.392352 | 0.196176 | − | 0.980569i | \(-0.437148\pi\) | ||||
0.196176 | + | 0.980569i | \(0.437148\pi\) | |||||||
\(110\) | 5.34739 | 0.509853 | ||||||||
\(111\) | −5.06654 | −0.480895 | ||||||||
\(112\) | 2.88631 | 0.272730 | ||||||||
\(113\) | −6.43963 | −0.605790 | −0.302895 | − | 0.953024i | \(-0.597953\pi\) | ||||
−0.302895 | + | 0.953024i | \(0.597953\pi\) | |||||||
\(114\) | −7.37191 | −0.690443 | ||||||||
\(115\) | 9.56787 | 0.892209 | ||||||||
\(116\) | 5.45001 | 0.506020 | ||||||||
\(117\) | 6.22038 | 0.575075 | ||||||||
\(118\) | −3.60466 | −0.331836 | ||||||||
\(119\) | −3.84738 | −0.352688 | ||||||||
\(120\) | 2.95169 | 0.269451 | ||||||||
\(121\) | 8.89384 | 0.808531 | ||||||||
\(122\) | −8.62323 | −0.780710 | ||||||||
\(123\) | 2.53995 | 0.229019 | ||||||||
\(124\) | 9.51670 | 0.854625 | ||||||||
\(125\) | 10.2657 | 0.918195 | ||||||||
\(126\) | 8.83632 | 0.787202 | ||||||||
\(127\) | 9.74175 | 0.864441 | 0.432220 | − | 0.901768i | \(-0.357730\pi\) | ||||
0.432220 | + | 0.901768i | \(0.357730\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.5121 | 0.925540 | ||||||||
\(130\) | −2.43596 | −0.213648 | ||||||||
\(131\) | 13.2358 | 1.15642 | 0.578209 | − | 0.815889i | \(-0.303752\pi\) | ||||
0.578209 | + | 0.815889i | \(0.303752\pi\) | |||||||
\(132\) | 10.9812 | 0.955787 | ||||||||
\(133\) | 8.64240 | 0.749391 | ||||||||
\(134\) | 12.4646 | 1.07678 | ||||||||
\(135\) | 0.181412 | 0.0156134 | ||||||||
\(136\) | −1.33298 | −0.114302 | ||||||||
\(137\) | −5.10401 | −0.436065 | −0.218033 | − | 0.975941i | \(-0.569964\pi\) | ||||
−0.218033 | + | 0.975941i | \(0.569964\pi\) | |||||||
\(138\) | 19.6482 | 1.67256 | ||||||||
\(139\) | −12.3829 | −1.05031 | −0.525154 | − | 0.851007i | \(-0.675992\pi\) | ||||
−0.525154 | + | 0.851007i | \(0.675992\pi\) | |||||||
\(140\) | −3.46039 | −0.292456 | ||||||||
\(141\) | 9.10997 | 0.767198 | ||||||||
\(142\) | −7.46589 | −0.626524 | ||||||||
\(143\) | −9.06249 | −0.757844 | ||||||||
\(144\) | 3.06146 | 0.255122 | ||||||||
\(145\) | −6.53400 | −0.542619 | ||||||||
\(146\) | 0.802939 | 0.0664517 | ||||||||
\(147\) | −3.27636 | −0.270230 | ||||||||
\(148\) | 2.05789 | 0.169158 | ||||||||
\(149\) | 0.709098 | 0.0580916 | 0.0290458 | − | 0.999578i | \(-0.490753\pi\) | ||||
0.0290458 | + | 0.999578i | \(0.490753\pi\) | |||||||
\(150\) | 8.77124 | 0.716169 | ||||||||
\(151\) | −19.9658 | −1.62479 | −0.812396 | − | 0.583106i | \(-0.801837\pi\) | ||||
−0.812396 | + | 0.583106i | \(0.801837\pi\) | |||||||
\(152\) | 2.99427 | 0.242868 | ||||||||
\(153\) | −4.08085 | −0.329917 | ||||||||
\(154\) | −12.8737 | −1.03739 | ||||||||
\(155\) | −11.4096 | −0.916437 | ||||||||
\(156\) | −5.00238 | −0.400511 | ||||||||
\(157\) | 0.989398 | 0.0789625 | 0.0394813 | − | 0.999220i | \(-0.487429\pi\) | ||||
0.0394813 | + | 0.999220i | \(0.487429\pi\) | |||||||
\(158\) | 10.5744 | 0.841256 | ||||||||
\(159\) | 7.73515 | 0.613437 | ||||||||
\(160\) | −1.19890 | −0.0947812 | ||||||||
\(161\) | −23.0343 | −1.81536 | ||||||||
\(162\) | −8.81184 | −0.692324 | ||||||||
\(163\) | −17.9899 | −1.40908 | −0.704538 | − | 0.709666i | \(-0.748846\pi\) | ||||
−0.704538 | + | 0.709666i | \(0.748846\pi\) | |||||||
\(164\) | −1.03166 | −0.0805591 | ||||||||
\(165\) | −13.1653 | −1.02492 | ||||||||
\(166\) | −6.47728 | −0.502735 | ||||||||
\(167\) | 3.32310 | 0.257149 | 0.128574 | − | 0.991700i | \(-0.458960\pi\) | ||||
0.128574 | + | 0.991700i | \(0.458960\pi\) | |||||||
\(168\) | −7.10610 | −0.548247 | ||||||||
\(169\) | −8.87165 | −0.682434 | ||||||||
\(170\) | 1.59810 | 0.122569 | ||||||||
\(171\) | 9.16685 | 0.701007 | ||||||||
\(172\) | −4.26974 | −0.325565 | ||||||||
\(173\) | −0.654520 | −0.0497623 | −0.0248811 | − | 0.999690i | \(-0.507921\pi\) | ||||
−0.0248811 | + | 0.999690i | \(0.507921\pi\) | |||||||
\(174\) | −13.4179 | −1.01721 | ||||||||
\(175\) | −10.2829 | −0.777313 | ||||||||
\(176\) | −4.46025 | −0.336204 | ||||||||
\(177\) | 8.87468 | 0.667062 | ||||||||
\(178\) | −12.7695 | −0.957117 | ||||||||
\(179\) | 20.6354 | 1.54237 | 0.771183 | − | 0.636614i | \(-0.219666\pi\) | ||||
0.771183 | + | 0.636614i | \(0.219666\pi\) | |||||||
\(180\) | −3.67038 | −0.273574 | ||||||||
\(181\) | −6.42961 | −0.477909 | −0.238955 | − | 0.971031i | \(-0.576805\pi\) | ||||
−0.238955 | + | 0.971031i | \(0.576805\pi\) | |||||||
\(182\) | 5.86450 | 0.434706 | ||||||||
\(183\) | 21.2304 | 1.56940 | ||||||||
\(184\) | −7.98056 | −0.588334 | ||||||||
\(185\) | −2.46721 | −0.181393 | ||||||||
\(186\) | −23.4301 | −1.71798 | ||||||||
\(187\) | 5.94541 | 0.434771 | ||||||||
\(188\) | −3.70023 | −0.269867 | ||||||||
\(189\) | −0.436743 | −0.0317683 | ||||||||
\(190\) | −3.58983 | −0.260434 | ||||||||
\(191\) | 1.49819 | 0.108405 | 0.0542026 | − | 0.998530i | \(-0.482738\pi\) | ||||
0.0542026 | + | 0.998530i | \(0.482738\pi\) | |||||||
\(192\) | −2.46200 | −0.177680 | ||||||||
\(193\) | −6.67653 | −0.480587 | −0.240293 | − | 0.970700i | \(-0.577244\pi\) | ||||
−0.240293 | + | 0.970700i | \(0.577244\pi\) | |||||||
\(194\) | 12.6583 | 0.908815 | ||||||||
\(195\) | 5.99735 | 0.429479 | ||||||||
\(196\) | 1.33077 | 0.0950551 | ||||||||
\(197\) | −3.38365 | −0.241075 | −0.120538 | − | 0.992709i | \(-0.538462\pi\) | ||||
−0.120538 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(198\) | −13.6549 | −0.970410 | ||||||||
\(199\) | −12.5763 | −0.891509 | −0.445755 | − | 0.895155i | \(-0.647065\pi\) | ||||
−0.445755 | + | 0.895155i | \(0.647065\pi\) | |||||||
\(200\) | −3.56264 | −0.251917 | ||||||||
\(201\) | −30.6878 | −2.16455 | ||||||||
\(202\) | 5.05589 | 0.355731 | ||||||||
\(203\) | 15.7304 | 1.10406 | ||||||||
\(204\) | 3.28179 | 0.229771 | ||||||||
\(205\) | 1.23685 | 0.0863857 | ||||||||
\(206\) | 10.9353 | 0.761895 | ||||||||
\(207\) | −24.4322 | −1.69815 | ||||||||
\(208\) | 2.03184 | 0.140882 | ||||||||
\(209\) | −13.3552 | −0.923800 | ||||||||
\(210\) | 8.51949 | 0.587901 | ||||||||
\(211\) | −20.9915 | −1.44512 | −0.722559 | − | 0.691310i | \(-0.757034\pi\) | ||||
−0.722559 | + | 0.691310i | \(0.757034\pi\) | |||||||
\(212\) | −3.14181 | −0.215780 | ||||||||
\(213\) | 18.3811 | 1.25945 | ||||||||
\(214\) | −9.24635 | −0.632067 | ||||||||
\(215\) | 5.11899 | 0.349112 | ||||||||
\(216\) | −0.151315 | −0.0102957 | ||||||||
\(217\) | 27.4681 | 1.86466 | ||||||||
\(218\) | 4.09628 | 0.277435 | ||||||||
\(219\) | −1.97684 | −0.133582 | ||||||||
\(220\) | 5.34739 | 0.360521 | ||||||||
\(221\) | −2.70839 | −0.182186 | ||||||||
\(222\) | −5.06654 | −0.340044 | ||||||||
\(223\) | 23.4488 | 1.57025 | 0.785123 | − | 0.619340i | \(-0.212600\pi\) | ||||
0.785123 | + | 0.619340i | \(0.212600\pi\) | |||||||
\(224\) | 2.88631 | 0.192850 | ||||||||
\(225\) | −10.9069 | −0.727126 | ||||||||
\(226\) | −6.43963 | −0.428358 | ||||||||
\(227\) | 4.39085 | 0.291431 | 0.145716 | − | 0.989327i | \(-0.453452\pi\) | ||||
0.145716 | + | 0.989327i | \(0.453452\pi\) | |||||||
\(228\) | −7.37191 | −0.488217 | ||||||||
\(229\) | −7.91979 | −0.523354 | −0.261677 | − | 0.965155i | \(-0.584276\pi\) | ||||
−0.261677 | + | 0.965155i | \(0.584276\pi\) | |||||||
\(230\) | 9.56787 | 0.630887 | ||||||||
\(231\) | 31.6950 | 2.08538 | ||||||||
\(232\) | 5.45001 | 0.357810 | ||||||||
\(233\) | 13.8801 | 0.909316 | 0.454658 | − | 0.890666i | \(-0.349761\pi\) | ||||
0.454658 | + | 0.890666i | \(0.349761\pi\) | |||||||
\(234\) | 6.22038 | 0.406639 | ||||||||
\(235\) | 4.43619 | 0.289385 | ||||||||
\(236\) | −3.60466 | −0.234643 | ||||||||
\(237\) | −26.0343 | −1.69111 | ||||||||
\(238\) | −3.84738 | −0.249388 | ||||||||
\(239\) | 0.655256 | 0.0423850 | 0.0211925 | − | 0.999775i | \(-0.493254\pi\) | ||||
0.0211925 | + | 0.999775i | \(0.493254\pi\) | |||||||
\(240\) | 2.95169 | 0.190531 | ||||||||
\(241\) | −26.3634 | −1.69821 | −0.849107 | − | 0.528221i | \(-0.822859\pi\) | ||||
−0.849107 | + | 0.528221i | \(0.822859\pi\) | |||||||
\(242\) | 8.89384 | 0.571718 | ||||||||
\(243\) | 22.1487 | 1.42084 | ||||||||
\(244\) | −8.62323 | −0.552045 | ||||||||
\(245\) | −1.59546 | −0.101930 | ||||||||
\(246\) | 2.53995 | 0.161941 | ||||||||
\(247\) | 6.08387 | 0.387108 | ||||||||
\(248\) | 9.51670 | 0.604311 | ||||||||
\(249\) | 15.9471 | 1.01061 | ||||||||
\(250\) | 10.2657 | 0.649262 | ||||||||
\(251\) | 20.6635 | 1.30427 | 0.652134 | − | 0.758103i | \(-0.273874\pi\) | ||||
0.652134 | + | 0.758103i | \(0.273874\pi\) | |||||||
\(252\) | 8.83632 | 0.556636 | ||||||||
\(253\) | 35.5953 | 2.23786 | ||||||||
\(254\) | 9.74175 | 0.611252 | ||||||||
\(255\) | −3.93453 | −0.246390 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.2413 | −1.44975 | −0.724876 | − | 0.688879i | \(-0.758103\pi\) | ||||
−0.724876 | + | 0.688879i | \(0.758103\pi\) | |||||||
\(258\) | 10.5121 | 0.654456 | ||||||||
\(259\) | 5.93971 | 0.369076 | ||||||||
\(260\) | −2.43596 | −0.151072 | ||||||||
\(261\) | 16.6850 | 1.03277 | ||||||||
\(262\) | 13.2358 | 0.817711 | ||||||||
\(263\) | −12.1298 | −0.747955 | −0.373978 | − | 0.927438i | \(-0.622006\pi\) | ||||
−0.373978 | + | 0.927438i | \(0.622006\pi\) | |||||||
\(264\) | 10.9812 | 0.675843 | ||||||||
\(265\) | 3.76671 | 0.231387 | ||||||||
\(266\) | 8.64240 | 0.529899 | ||||||||
\(267\) | 31.4386 | 1.92401 | ||||||||
\(268\) | 12.4646 | 0.761396 | ||||||||
\(269\) | −15.8102 | −0.963963 | −0.481981 | − | 0.876181i | \(-0.660083\pi\) | ||||
−0.481981 | + | 0.876181i | \(0.660083\pi\) | |||||||
\(270\) | 0.181412 | 0.0110404 | ||||||||
\(271\) | −21.9603 | −1.33399 | −0.666996 | − | 0.745061i | \(-0.732420\pi\) | ||||
−0.666996 | + | 0.745061i | \(0.732420\pi\) | |||||||
\(272\) | −1.33298 | −0.0808235 | ||||||||
\(273\) | −14.4384 | −0.873853 | ||||||||
\(274\) | −5.10401 | −0.308345 | ||||||||
\(275\) | 15.8903 | 0.958220 | ||||||||
\(276\) | 19.6482 | 1.18268 | ||||||||
\(277\) | 27.7483 | 1.66723 | 0.833616 | − | 0.552345i | \(-0.186267\pi\) | ||||
0.833616 | + | 0.552345i | \(0.186267\pi\) | |||||||
\(278\) | −12.3829 | −0.742680 | ||||||||
\(279\) | 29.1350 | 1.74427 | ||||||||
\(280\) | −3.46039 | −0.206798 | ||||||||
\(281\) | −1.99872 | −0.119234 | −0.0596168 | − | 0.998221i | \(-0.518988\pi\) | ||||
−0.0596168 | + | 0.998221i | \(0.518988\pi\) | |||||||
\(282\) | 9.10997 | 0.542491 | ||||||||
\(283\) | 16.1175 | 0.958087 | 0.479044 | − | 0.877791i | \(-0.340984\pi\) | ||||
0.479044 | + | 0.877791i | \(0.340984\pi\) | |||||||
\(284\) | −7.46589 | −0.443019 | ||||||||
\(285\) | 8.83818 | 0.523528 | ||||||||
\(286\) | −9.06249 | −0.535877 | ||||||||
\(287\) | −2.97769 | −0.175767 | ||||||||
\(288\) | 3.06146 | 0.180398 | ||||||||
\(289\) | −15.2232 | −0.895481 | ||||||||
\(290\) | −6.53400 | −0.383690 | ||||||||
\(291\) | −31.1648 | −1.82691 | ||||||||
\(292\) | 0.802939 | 0.0469884 | ||||||||
\(293\) | −26.0218 | −1.52021 | −0.760106 | − | 0.649799i | \(-0.774853\pi\) | ||||
−0.760106 | + | 0.649799i | \(0.774853\pi\) | |||||||
\(294\) | −3.27636 | −0.191081 | ||||||||
\(295\) | 4.32162 | 0.251614 | ||||||||
\(296\) | 2.05789 | 0.119613 | ||||||||
\(297\) | 0.674904 | 0.0391619 | ||||||||
\(298\) | 0.709098 | 0.0410770 | ||||||||
\(299\) | −16.2152 | −0.937748 | ||||||||
\(300\) | 8.77124 | 0.506408 | ||||||||
\(301\) | −12.3238 | −0.710331 | ||||||||
\(302\) | −19.9658 | −1.14890 | ||||||||
\(303\) | −12.4476 | −0.715097 | ||||||||
\(304\) | 2.99427 | 0.171733 | ||||||||
\(305\) | 10.3384 | 0.591973 | ||||||||
\(306\) | −4.08085 | −0.233287 | ||||||||
\(307\) | −27.2390 | −1.55461 | −0.777307 | − | 0.629122i | \(-0.783415\pi\) | ||||
−0.777307 | + | 0.629122i | \(0.783415\pi\) | |||||||
\(308\) | −12.8737 | −0.733545 | ||||||||
\(309\) | −26.9226 | −1.53157 | ||||||||
\(310\) | −11.4096 | −0.648019 | ||||||||
\(311\) | −21.6769 | −1.22918 | −0.614592 | − | 0.788845i | \(-0.710679\pi\) | ||||
−0.614592 | + | 0.788845i | \(0.710679\pi\) | |||||||
\(312\) | −5.00238 | −0.283204 | ||||||||
\(313\) | −1.30840 | −0.0739553 | −0.0369777 | − | 0.999316i | \(-0.511773\pi\) | ||||
−0.0369777 | + | 0.999316i | \(0.511773\pi\) | |||||||
\(314\) | 0.989398 | 0.0558350 | ||||||||
\(315\) | −10.5938 | −0.596895 | ||||||||
\(316\) | 10.5744 | 0.594858 | ||||||||
\(317\) | −19.8519 | −1.11499 | −0.557496 | − | 0.830180i | \(-0.688238\pi\) | ||||
−0.557496 | + | 0.830180i | \(0.688238\pi\) | |||||||
\(318\) | 7.73515 | 0.433765 | ||||||||
\(319\) | −24.3084 | −1.36101 | ||||||||
\(320\) | −1.19890 | −0.0670204 | ||||||||
\(321\) | 22.7645 | 1.27059 | ||||||||
\(322\) | −23.0343 | −1.28365 | ||||||||
\(323\) | −3.99129 | −0.222082 | ||||||||
\(324\) | −8.81184 | −0.489547 | ||||||||
\(325\) | −7.23870 | −0.401531 | ||||||||
\(326\) | −17.9899 | −0.996367 | ||||||||
\(327\) | −10.0850 | −0.557704 | ||||||||
\(328\) | −1.03166 | −0.0569639 | ||||||||
\(329\) | −10.6800 | −0.588807 | ||||||||
\(330\) | −13.1653 | −0.724725 | ||||||||
\(331\) | 2.23277 | 0.122724 | 0.0613620 | − | 0.998116i | \(-0.480456\pi\) | ||||
0.0613620 | + | 0.998116i | \(0.480456\pi\) | |||||||
\(332\) | −6.47728 | −0.355487 | ||||||||
\(333\) | 6.30016 | 0.345247 | ||||||||
\(334\) | 3.32310 | 0.181832 | ||||||||
\(335\) | −14.9438 | −0.816465 | ||||||||
\(336\) | −7.10610 | −0.387669 | ||||||||
\(337\) | −17.2026 | −0.937085 | −0.468542 | − | 0.883441i | \(-0.655221\pi\) | ||||
−0.468542 | + | 0.883441i | \(0.655221\pi\) | |||||||
\(338\) | −8.87165 | −0.482554 | ||||||||
\(339\) | 15.8544 | 0.861093 | ||||||||
\(340\) | 1.59810 | 0.0866692 | ||||||||
\(341\) | −42.4469 | −2.29863 | ||||||||
\(342\) | 9.16685 | 0.495687 | ||||||||
\(343\) | −16.3631 | −0.883526 | ||||||||
\(344\) | −4.26974 | −0.230209 | ||||||||
\(345\) | −23.5561 | −1.26822 | ||||||||
\(346\) | −0.654520 | −0.0351872 | ||||||||
\(347\) | −10.1459 | −0.544659 | −0.272330 | − | 0.962204i | \(-0.587794\pi\) | ||||
−0.272330 | + | 0.962204i | \(0.587794\pi\) | |||||||
\(348\) | −13.4179 | −0.719277 | ||||||||
\(349\) | 11.0457 | 0.591265 | 0.295633 | − | 0.955302i | \(-0.404470\pi\) | ||||
0.295633 | + | 0.955302i | \(0.404470\pi\) | |||||||
\(350\) | −10.2829 | −0.549643 | ||||||||
\(351\) | −0.307448 | −0.0164103 | ||||||||
\(352\) | −4.46025 | −0.237732 | ||||||||
\(353\) | −28.5221 | −1.51808 | −0.759038 | − | 0.651046i | \(-0.774330\pi\) | ||||
−0.759038 | + | 0.651046i | \(0.774330\pi\) | |||||||
\(354\) | 8.87468 | 0.471684 | ||||||||
\(355\) | 8.95085 | 0.475062 | ||||||||
\(356\) | −12.7695 | −0.676784 | ||||||||
\(357\) | 9.47225 | 0.501325 | ||||||||
\(358\) | 20.6354 | 1.09062 | ||||||||
\(359\) | 13.3587 | 0.705047 | 0.352523 | − | 0.935803i | \(-0.385324\pi\) | ||||
0.352523 | + | 0.935803i | \(0.385324\pi\) | |||||||
\(360\) | −3.67038 | −0.193446 | ||||||||
\(361\) | −10.0343 | −0.528122 | ||||||||
\(362\) | −6.42961 | −0.337933 | ||||||||
\(363\) | −21.8967 | −1.14928 | ||||||||
\(364\) | 5.86450 | 0.307383 | ||||||||
\(365\) | −0.962642 | −0.0503870 | ||||||||
\(366\) | 21.2304 | 1.10973 | ||||||||
\(367\) | −4.65239 | −0.242853 | −0.121426 | − | 0.992600i | \(-0.538747\pi\) | ||||
−0.121426 | + | 0.992600i | \(0.538747\pi\) | |||||||
\(368\) | −7.98056 | −0.416015 | ||||||||
\(369\) | −3.15838 | −0.164419 | ||||||||
\(370\) | −2.46721 | −0.128264 | ||||||||
\(371\) | −9.06823 | −0.470799 | ||||||||
\(372\) | −23.4301 | −1.21480 | ||||||||
\(373\) | 2.22264 | 0.115084 | 0.0575420 | − | 0.998343i | \(-0.481674\pi\) | ||||
0.0575420 | + | 0.998343i | \(0.481674\pi\) | |||||||
\(374\) | 5.94541 | 0.307430 | ||||||||
\(375\) | −25.2743 | −1.30516 | ||||||||
\(376\) | −3.70023 | −0.190825 | ||||||||
\(377\) | 11.0735 | 0.570315 | ||||||||
\(378\) | −0.436743 | −0.0224636 | ||||||||
\(379\) | 6.43360 | 0.330472 | 0.165236 | − | 0.986254i | \(-0.447161\pi\) | ||||
0.165236 | + | 0.986254i | \(0.447161\pi\) | |||||||
\(380\) | −3.58983 | −0.184154 | ||||||||
\(381\) | −23.9842 | −1.22875 | ||||||||
\(382\) | 1.49819 | 0.0766541 | ||||||||
\(383\) | −13.0227 | −0.665429 | −0.332714 | − | 0.943028i | \(-0.607965\pi\) | ||||
−0.332714 | + | 0.943028i | \(0.607965\pi\) | |||||||
\(384\) | −2.46200 | −0.125639 | ||||||||
\(385\) | 15.4342 | 0.786600 | ||||||||
\(386\) | −6.67653 | −0.339826 | ||||||||
\(387\) | −13.0716 | −0.664469 | ||||||||
\(388\) | 12.6583 | 0.642629 | ||||||||
\(389\) | 14.1203 | 0.715928 | 0.357964 | − | 0.933735i | \(-0.383471\pi\) | ||||
0.357964 | + | 0.933735i | \(0.383471\pi\) | |||||||
\(390\) | 5.99735 | 0.303688 | ||||||||
\(391\) | 10.6379 | 0.537981 | ||||||||
\(392\) | 1.33077 | 0.0672141 | ||||||||
\(393\) | −32.5866 | −1.64378 | ||||||||
\(394\) | −3.38365 | −0.170466 | ||||||||
\(395\) | −12.6777 | −0.637882 | ||||||||
\(396\) | −13.6549 | −0.686184 | ||||||||
\(397\) | −5.80414 | −0.291302 | −0.145651 | − | 0.989336i | \(-0.546528\pi\) | ||||
−0.145651 | + | 0.989336i | \(0.546528\pi\) | |||||||
\(398\) | −12.5763 | −0.630392 | ||||||||
\(399\) | −21.2776 | −1.06521 | ||||||||
\(400\) | −3.56264 | −0.178132 | ||||||||
\(401\) | −13.0278 | −0.650579 | −0.325289 | − | 0.945614i | \(-0.605462\pi\) | ||||
−0.325289 | + | 0.945614i | \(0.605462\pi\) | |||||||
\(402\) | −30.6878 | −1.53057 | ||||||||
\(403\) | 19.3364 | 0.963213 | ||||||||
\(404\) | 5.05589 | 0.251540 | ||||||||
\(405\) | 10.5645 | 0.524954 | ||||||||
\(406\) | 15.7304 | 0.780686 | ||||||||
\(407\) | −9.17872 | −0.454972 | ||||||||
\(408\) | 3.28179 | 0.162473 | ||||||||
\(409\) | −11.9401 | −0.590402 | −0.295201 | − | 0.955435i | \(-0.595387\pi\) | ||||
−0.295201 | + | 0.955435i | \(0.595387\pi\) | |||||||
\(410\) | 1.23685 | 0.0610839 | ||||||||
\(411\) | 12.5661 | 0.619840 | ||||||||
\(412\) | 10.9353 | 0.538741 | ||||||||
\(413\) | −10.4041 | −0.511955 | ||||||||
\(414\) | −24.4322 | −1.20077 | ||||||||
\(415\) | 7.76560 | 0.381198 | ||||||||
\(416\) | 2.03184 | 0.0996189 | ||||||||
\(417\) | 30.4869 | 1.49295 | ||||||||
\(418\) | −13.3552 | −0.653225 | ||||||||
\(419\) | 14.8690 | 0.726399 | 0.363199 | − | 0.931711i | \(-0.381684\pi\) | ||||
0.363199 | + | 0.931711i | \(0.381684\pi\) | |||||||
\(420\) | 8.51949 | 0.415708 | ||||||||
\(421\) | 1.29715 | 0.0632193 | 0.0316097 | − | 0.999500i | \(-0.489937\pi\) | ||||
0.0316097 | + | 0.999500i | \(0.489937\pi\) | |||||||
\(422\) | −20.9915 | −1.02185 | ||||||||
\(423\) | −11.3281 | −0.550791 | ||||||||
\(424\) | −3.14181 | −0.152580 | ||||||||
\(425\) | 4.74892 | 0.230356 | ||||||||
\(426\) | 18.3811 | 0.890565 | ||||||||
\(427\) | −24.8893 | −1.20448 | ||||||||
\(428\) | −9.24635 | −0.446939 | ||||||||
\(429\) | 22.3119 | 1.07723 | ||||||||
\(430\) | 5.11899 | 0.246859 | ||||||||
\(431\) | −29.6509 | −1.42823 | −0.714116 | − | 0.700027i | \(-0.753171\pi\) | ||||
−0.714116 | + | 0.700027i | \(0.753171\pi\) | |||||||
\(432\) | −0.151315 | −0.00728016 | ||||||||
\(433\) | −25.1200 | −1.20719 | −0.603595 | − | 0.797291i | \(-0.706265\pi\) | ||||
−0.603595 | + | 0.797291i | \(0.706265\pi\) | |||||||
\(434\) | 27.4681 | 1.31851 | ||||||||
\(435\) | 16.0867 | 0.771300 | ||||||||
\(436\) | 4.09628 | 0.196176 | ||||||||
\(437\) | −23.8960 | −1.14310 | ||||||||
\(438\) | −1.97684 | −0.0944570 | ||||||||
\(439\) | 8.97809 | 0.428501 | 0.214251 | − | 0.976779i | \(-0.431269\pi\) | ||||
0.214251 | + | 0.976779i | \(0.431269\pi\) | |||||||
\(440\) | 5.34739 | 0.254927 | ||||||||
\(441\) | 4.07410 | 0.194005 | ||||||||
\(442\) | −2.70839 | −0.128825 | ||||||||
\(443\) | −14.8845 | −0.707183 | −0.353592 | − | 0.935400i | \(-0.615040\pi\) | ||||
−0.353592 | + | 0.935400i | \(0.615040\pi\) | |||||||
\(444\) | −5.06654 | −0.240447 | ||||||||
\(445\) | 15.3094 | 0.725734 | ||||||||
\(446\) | 23.4488 | 1.11033 | ||||||||
\(447\) | −1.74580 | −0.0825736 | ||||||||
\(448\) | 2.88631 | 0.136365 | ||||||||
\(449\) | 2.41434 | 0.113940 | 0.0569698 | − | 0.998376i | \(-0.481856\pi\) | ||||
0.0569698 | + | 0.998376i | \(0.481856\pi\) | |||||||
\(450\) | −10.9069 | −0.514156 | ||||||||
\(451\) | 4.60146 | 0.216674 | ||||||||
\(452\) | −6.43963 | −0.302895 | ||||||||
\(453\) | 49.1558 | 2.30954 | ||||||||
\(454\) | 4.39085 | 0.206073 | ||||||||
\(455\) | −7.03094 | −0.329616 | ||||||||
\(456\) | −7.37191 | −0.345222 | ||||||||
\(457\) | −6.08220 | −0.284513 | −0.142257 | − | 0.989830i | \(-0.545436\pi\) | ||||
−0.142257 | + | 0.989830i | \(0.545436\pi\) | |||||||
\(458\) | −7.91979 | −0.370067 | ||||||||
\(459\) | 0.201700 | 0.00941453 | ||||||||
\(460\) | 9.56787 | 0.446104 | ||||||||
\(461\) | −16.7137 | −0.778435 | −0.389218 | − | 0.921146i | \(-0.627255\pi\) | ||||
−0.389218 | + | 0.921146i | \(0.627255\pi\) | |||||||
\(462\) | 31.6950 | 1.47458 | ||||||||
\(463\) | −33.7225 | −1.56722 | −0.783609 | − | 0.621254i | \(-0.786623\pi\) | ||||
−0.783609 | + | 0.621254i | \(0.786623\pi\) | |||||||
\(464\) | 5.45001 | 0.253010 | ||||||||
\(465\) | 28.0904 | 1.30266 | ||||||||
\(466\) | 13.8801 | 0.642984 | ||||||||
\(467\) | −23.7353 | −1.09834 | −0.549169 | − | 0.835712i | \(-0.685055\pi\) | ||||
−0.549169 | + | 0.835712i | \(0.685055\pi\) | |||||||
\(468\) | 6.22038 | 0.287537 | ||||||||
\(469\) | 35.9766 | 1.66125 | ||||||||
\(470\) | 4.43619 | 0.204626 | ||||||||
\(471\) | −2.43590 | −0.112240 | ||||||||
\(472\) | −3.60466 | −0.165918 | ||||||||
\(473\) | 19.0441 | 0.875650 | ||||||||
\(474\) | −26.0343 | −1.19579 | ||||||||
\(475\) | −10.6675 | −0.489460 | ||||||||
\(476\) | −3.84738 | −0.176344 | ||||||||
\(477\) | −9.61853 | −0.440402 | ||||||||
\(478\) | 0.655256 | 0.0299707 | ||||||||
\(479\) | 14.8171 | 0.677008 | 0.338504 | − | 0.940965i | \(-0.390079\pi\) | ||||
0.338504 | + | 0.940965i | \(0.390079\pi\) | |||||||
\(480\) | 2.95169 | 0.134726 | ||||||||
\(481\) | 4.18130 | 0.190651 | ||||||||
\(482\) | −26.3634 | −1.20082 | ||||||||
\(483\) | 56.7106 | 2.58042 | ||||||||
\(484\) | 8.89384 | 0.404266 | ||||||||
\(485\) | −15.1760 | −0.689108 | ||||||||
\(486\) | 22.1487 | 1.00469 | ||||||||
\(487\) | −0.442777 | −0.0200642 | −0.0100321 | − | 0.999950i | \(-0.503193\pi\) | ||||
−0.0100321 | + | 0.999950i | \(0.503193\pi\) | |||||||
\(488\) | −8.62323 | −0.390355 | ||||||||
\(489\) | 44.2911 | 2.00291 | ||||||||
\(490\) | −1.59546 | −0.0720755 | ||||||||
\(491\) | 2.45714 | 0.110889 | 0.0554446 | − | 0.998462i | \(-0.482342\pi\) | ||||
0.0554446 | + | 0.998462i | \(0.482342\pi\) | |||||||
\(492\) | 2.53995 | 0.114510 | ||||||||
\(493\) | −7.26472 | −0.327187 | ||||||||
\(494\) | 6.08387 | 0.273726 | ||||||||
\(495\) | 16.3708 | 0.735813 | ||||||||
\(496\) | 9.51670 | 0.427312 | ||||||||
\(497\) | −21.5489 | −0.966599 | ||||||||
\(498\) | 15.9471 | 0.714606 | ||||||||
\(499\) | −32.6070 | −1.45969 | −0.729846 | − | 0.683612i | \(-0.760408\pi\) | ||||
−0.729846 | + | 0.683612i | \(0.760408\pi\) | |||||||
\(500\) | 10.2657 | 0.459098 | ||||||||
\(501\) | −8.18147 | −0.365521 | ||||||||
\(502\) | 20.6635 | 0.922257 | ||||||||
\(503\) | 6.68801 | 0.298203 | 0.149102 | − | 0.988822i | \(-0.452362\pi\) | ||||
0.149102 | + | 0.988822i | \(0.452362\pi\) | |||||||
\(504\) | 8.83632 | 0.393601 | ||||||||
\(505\) | −6.06150 | −0.269733 | ||||||||
\(506\) | 35.5953 | 1.58240 | ||||||||
\(507\) | 21.8420 | 0.970038 | ||||||||
\(508\) | 9.74175 | 0.432220 | ||||||||
\(509\) | −3.38887 | −0.150209 | −0.0751046 | − | 0.997176i | \(-0.523929\pi\) | ||||
−0.0751046 | + | 0.997176i | \(0.523929\pi\) | |||||||
\(510\) | −3.93453 | −0.174224 | ||||||||
\(511\) | 2.31753 | 0.102521 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.453080 | −0.0200040 | ||||||||
\(514\) | −23.2413 | −1.02513 | ||||||||
\(515\) | −13.1103 | −0.577707 | ||||||||
\(516\) | 10.5121 | 0.462770 | ||||||||
\(517\) | 16.5039 | 0.725842 | ||||||||
\(518\) | 5.93971 | 0.260976 | ||||||||
\(519\) | 1.61143 | 0.0707340 | ||||||||
\(520\) | −2.43596 | −0.106824 | ||||||||
\(521\) | −17.8376 | −0.781479 | −0.390740 | − | 0.920501i | \(-0.627781\pi\) | ||||
−0.390740 | + | 0.920501i | \(0.627781\pi\) | |||||||
\(522\) | 16.6850 | 0.730282 | ||||||||
\(523\) | −29.1636 | −1.27524 | −0.637618 | − | 0.770353i | \(-0.720080\pi\) | ||||
−0.637618 | + | 0.770353i | \(0.720080\pi\) | |||||||
\(524\) | 13.2358 | 0.578209 | ||||||||
\(525\) | 25.3165 | 1.10490 | ||||||||
\(526\) | −12.1298 | −0.528884 | ||||||||
\(527\) | −12.6855 | −0.552590 | ||||||||
\(528\) | 10.9812 | 0.477893 | ||||||||
\(529\) | 40.6893 | 1.76910 | ||||||||
\(530\) | 3.76671 | 0.163615 | ||||||||
\(531\) | −11.0355 | −0.478901 | ||||||||
\(532\) | 8.64240 | 0.374695 | ||||||||
\(533\) | −2.09616 | −0.0907948 | ||||||||
\(534\) | 31.4386 | 1.36048 | ||||||||
\(535\) | 11.0854 | 0.479265 | ||||||||
\(536\) | 12.4646 | 0.538388 | ||||||||
\(537\) | −50.8045 | −2.19238 | ||||||||
\(538\) | −15.8102 | −0.681625 | ||||||||
\(539\) | −5.93557 | −0.255663 | ||||||||
\(540\) | 0.181412 | 0.00780671 | ||||||||
\(541\) | 7.34951 | 0.315980 | 0.157990 | − | 0.987441i | \(-0.449499\pi\) | ||||
0.157990 | + | 0.987441i | \(0.449499\pi\) | |||||||
\(542\) | −21.9603 | −0.943275 | ||||||||
\(543\) | 15.8297 | 0.679318 | ||||||||
\(544\) | −1.33298 | −0.0571508 | ||||||||
\(545\) | −4.91102 | −0.210365 | ||||||||
\(546\) | −14.4384 | −0.617907 | ||||||||
\(547\) | 17.1119 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(548\) | −5.10401 | −0.218033 | ||||||||
\(549\) | −26.3997 | −1.12671 | ||||||||
\(550\) | 15.8903 | 0.677564 | ||||||||
\(551\) | 16.3188 | 0.695205 | ||||||||
\(552\) | 19.6482 | 0.836281 | ||||||||
\(553\) | 30.5210 | 1.29789 | ||||||||
\(554\) | 27.7483 | 1.17891 | ||||||||
\(555\) | 6.07427 | 0.257838 | ||||||||
\(556\) | −12.3829 | −0.525154 | ||||||||
\(557\) | 1.30178 | 0.0551582 | 0.0275791 | − | 0.999620i | \(-0.491220\pi\) | ||||
0.0275791 | + | 0.999620i | \(0.491220\pi\) | |||||||
\(558\) | 29.1350 | 1.23338 | ||||||||
\(559\) | −8.67541 | −0.366931 | ||||||||
\(560\) | −3.46039 | −0.146228 | ||||||||
\(561\) | −14.6376 | −0.618000 | ||||||||
\(562\) | −1.99872 | −0.0843109 | ||||||||
\(563\) | −6.06187 | −0.255477 | −0.127739 | − | 0.991808i | \(-0.540772\pi\) | ||||
−0.127739 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(564\) | 9.10997 | 0.383599 | ||||||||
\(565\) | 7.72046 | 0.324802 | ||||||||
\(566\) | 16.1175 | 0.677470 | ||||||||
\(567\) | −25.4337 | −1.06811 | ||||||||
\(568\) | −7.46589 | −0.313262 | ||||||||
\(569\) | 34.0114 | 1.42583 | 0.712916 | − | 0.701250i | \(-0.247374\pi\) | ||||
0.712916 | + | 0.701250i | \(0.247374\pi\) | |||||||
\(570\) | 8.83818 | 0.370190 | ||||||||
\(571\) | −11.5520 | −0.483435 | −0.241718 | − | 0.970347i | \(-0.577711\pi\) | ||||
−0.241718 | + | 0.970347i | \(0.577711\pi\) | |||||||
\(572\) | −9.06249 | −0.378922 | ||||||||
\(573\) | −3.68855 | −0.154091 | ||||||||
\(574\) | −2.97769 | −0.124286 | ||||||||
\(575\) | 28.4319 | 1.18569 | ||||||||
\(576\) | 3.06146 | 0.127561 | ||||||||
\(577\) | −44.1970 | −1.83995 | −0.919973 | − | 0.391981i | \(-0.871790\pi\) | ||||
−0.919973 | + | 0.391981i | \(0.871790\pi\) | |||||||
\(578\) | −15.2232 | −0.633201 | ||||||||
\(579\) | 16.4376 | 0.683125 | ||||||||
\(580\) | −6.53400 | −0.271310 | ||||||||
\(581\) | −18.6954 | −0.775617 | ||||||||
\(582\) | −31.1648 | −1.29182 | ||||||||
\(583\) | 14.0133 | 0.580370 | ||||||||
\(584\) | 0.802939 | 0.0332258 | ||||||||
\(585\) | −7.45760 | −0.308334 | ||||||||
\(586\) | −26.0218 | −1.07495 | ||||||||
\(587\) | 26.0799 | 1.07643 | 0.538216 | − | 0.842807i | \(-0.319098\pi\) | ||||
0.538216 | + | 0.842807i | \(0.319098\pi\) | |||||||
\(588\) | −3.27636 | −0.135115 | ||||||||
\(589\) | 28.4956 | 1.17414 | ||||||||
\(590\) | 4.32162 | 0.177918 | ||||||||
\(591\) | 8.33056 | 0.342673 | ||||||||
\(592\) | 2.05789 | 0.0845789 | ||||||||
\(593\) | −16.2881 | −0.668874 | −0.334437 | − | 0.942418i | \(-0.608546\pi\) | ||||
−0.334437 | + | 0.942418i | \(0.608546\pi\) | |||||||
\(594\) | 0.674904 | 0.0276917 | ||||||||
\(595\) | 4.61261 | 0.189099 | ||||||||
\(596\) | 0.709098 | 0.0290458 | ||||||||
\(597\) | 30.9629 | 1.26723 | ||||||||
\(598\) | −16.2152 | −0.663088 | ||||||||
\(599\) | 15.9106 | 0.650090 | 0.325045 | − | 0.945699i | \(-0.394621\pi\) | ||||
0.325045 | + | 0.945699i | \(0.394621\pi\) | |||||||
\(600\) | 8.77124 | 0.358084 | ||||||||
\(601\) | −31.0357 | −1.26597 | −0.632985 | − | 0.774164i | \(-0.718171\pi\) | ||||
−0.632985 | + | 0.774164i | \(0.718171\pi\) | |||||||
\(602\) | −12.3238 | −0.502280 | ||||||||
\(603\) | 38.1598 | 1.55399 | ||||||||
\(604\) | −19.9658 | −0.812396 | ||||||||
\(605\) | −10.6628 | −0.433505 | ||||||||
\(606\) | −12.4476 | −0.505650 | ||||||||
\(607\) | −10.8182 | −0.439096 | −0.219548 | − | 0.975602i | \(-0.570458\pi\) | ||||
−0.219548 | + | 0.975602i | \(0.570458\pi\) | |||||||
\(608\) | 2.99427 | 0.121434 | ||||||||
\(609\) | −38.7283 | −1.56935 | ||||||||
\(610\) | 10.3384 | 0.418588 | ||||||||
\(611\) | −7.51825 | −0.304156 | ||||||||
\(612\) | −4.08085 | −0.164959 | ||||||||
\(613\) | 1.33415 | 0.0538859 | 0.0269429 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269429 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(614\) | −27.2390 | −1.09928 | ||||||||
\(615\) | −3.04514 | −0.122792 | ||||||||
\(616\) | −12.8737 | −0.518694 | ||||||||
\(617\) | 19.0417 | 0.766590 | 0.383295 | − | 0.923626i | \(-0.374789\pi\) | ||||
0.383295 | + | 0.923626i | \(0.374789\pi\) | |||||||
\(618\) | −26.9226 | −1.08299 | ||||||||
\(619\) | −24.3086 | −0.977047 | −0.488523 | − | 0.872551i | \(-0.662464\pi\) | ||||
−0.488523 | + | 0.872551i | \(0.662464\pi\) | |||||||
\(620\) | −11.4096 | −0.458219 | ||||||||
\(621\) | 1.20758 | 0.0484585 | ||||||||
\(622\) | −21.6769 | −0.869165 | ||||||||
\(623\) | −36.8568 | −1.47664 | ||||||||
\(624\) | −5.00238 | −0.200256 | ||||||||
\(625\) | 5.50564 | 0.220226 | ||||||||
\(626\) | −1.30840 | −0.0522943 | ||||||||
\(627\) | 32.8806 | 1.31312 | ||||||||
\(628\) | 0.989398 | 0.0394813 | ||||||||
\(629\) | −2.74312 | −0.109375 | ||||||||
\(630\) | −10.5938 | −0.422069 | ||||||||
\(631\) | 19.2026 | 0.764445 | 0.382222 | − | 0.924070i | \(-0.375159\pi\) | ||||
0.382222 | + | 0.924070i | \(0.375159\pi\) | |||||||
\(632\) | 10.5744 | 0.420628 | ||||||||
\(633\) | 51.6812 | 2.05415 | ||||||||
\(634\) | −19.8519 | −0.788418 | ||||||||
\(635\) | −11.6794 | −0.463482 | ||||||||
\(636\) | 7.73515 | 0.306718 | ||||||||
\(637\) | 2.70391 | 0.107133 | ||||||||
\(638\) | −24.3084 | −0.962379 | ||||||||
\(639\) | −22.8565 | −0.904191 | ||||||||
\(640\) | −1.19890 | −0.0473906 | ||||||||
\(641\) | −17.4940 | −0.690970 | −0.345485 | − | 0.938424i | \(-0.612286\pi\) | ||||
−0.345485 | + | 0.938424i | \(0.612286\pi\) | |||||||
\(642\) | 22.7645 | 0.898445 | ||||||||
\(643\) | 20.5920 | 0.812069 | 0.406035 | − | 0.913858i | \(-0.366911\pi\) | ||||
0.406035 | + | 0.913858i | \(0.366911\pi\) | |||||||
\(644\) | −23.0343 | −0.907680 | ||||||||
\(645\) | −12.6030 | −0.496241 | ||||||||
\(646\) | −3.99129 | −0.157035 | ||||||||
\(647\) | 36.8988 | 1.45064 | 0.725321 | − | 0.688411i | \(-0.241691\pi\) | ||||
0.725321 | + | 0.688411i | \(0.241691\pi\) | |||||||
\(648\) | −8.81184 | −0.346162 | ||||||||
\(649\) | 16.0777 | 0.631104 | ||||||||
\(650\) | −7.23870 | −0.283925 | ||||||||
\(651\) | −67.6266 | −2.65050 | ||||||||
\(652\) | −17.9899 | −0.704538 | ||||||||
\(653\) | 38.3135 | 1.49932 | 0.749662 | − | 0.661821i | \(-0.230216\pi\) | ||||
0.749662 | + | 0.661821i | \(0.230216\pi\) | |||||||
\(654\) | −10.0850 | −0.394357 | ||||||||
\(655\) | −15.8684 | −0.620029 | ||||||||
\(656\) | −1.03166 | −0.0402795 | ||||||||
\(657\) | 2.45817 | 0.0959022 | ||||||||
\(658\) | −10.6800 | −0.416349 | ||||||||
\(659\) | 16.3406 | 0.636538 | 0.318269 | − | 0.948000i | \(-0.396898\pi\) | ||||
0.318269 | + | 0.948000i | \(0.396898\pi\) | |||||||
\(660\) | −13.1653 | −0.512458 | ||||||||
\(661\) | 13.8754 | 0.539689 | 0.269844 | − | 0.962904i | \(-0.413028\pi\) | ||||
0.269844 | + | 0.962904i | \(0.413028\pi\) | |||||||
\(662\) | 2.23277 | 0.0867790 | ||||||||
\(663\) | 6.66806 | 0.258966 | ||||||||
\(664\) | −6.47728 | −0.251367 | ||||||||
\(665\) | −10.3614 | −0.401796 | ||||||||
\(666\) | 6.30016 | 0.244126 | ||||||||
\(667\) | −43.4941 | −1.68410 | ||||||||
\(668\) | 3.32310 | 0.128574 | ||||||||
\(669\) | −57.7309 | −2.23201 | ||||||||
\(670\) | −14.9438 | −0.577328 | ||||||||
\(671\) | 38.4618 | 1.48480 | ||||||||
\(672\) | −7.10610 | −0.274124 | ||||||||
\(673\) | 11.7096 | 0.451372 | 0.225686 | − | 0.974200i | \(-0.427538\pi\) | ||||
0.225686 | + | 0.974200i | \(0.427538\pi\) | |||||||
\(674\) | −17.2026 | −0.662619 | ||||||||
\(675\) | 0.539082 | 0.0207493 | ||||||||
\(676\) | −8.87165 | −0.341217 | ||||||||
\(677\) | 15.4219 | 0.592713 | 0.296356 | − | 0.955077i | \(-0.404228\pi\) | ||||
0.296356 | + | 0.955077i | \(0.404228\pi\) | |||||||
\(678\) | 15.8544 | 0.608884 | ||||||||
\(679\) | 36.5358 | 1.40212 | ||||||||
\(680\) | 1.59810 | 0.0612844 | ||||||||
\(681\) | −10.8103 | −0.414252 | ||||||||
\(682\) | −42.4469 | −1.62537 | ||||||||
\(683\) | 13.7023 | 0.524306 | 0.262153 | − | 0.965026i | \(-0.415568\pi\) | ||||
0.262153 | + | 0.965026i | \(0.415568\pi\) | |||||||
\(684\) | 9.16685 | 0.350503 | ||||||||
\(685\) | 6.11919 | 0.233802 | ||||||||
\(686\) | −16.3631 | −0.624748 | ||||||||
\(687\) | 19.4985 | 0.743916 | ||||||||
\(688\) | −4.26974 | −0.162782 | ||||||||
\(689\) | −6.38364 | −0.243197 | ||||||||
\(690\) | −23.5561 | −0.896767 | ||||||||
\(691\) | 40.9967 | 1.55959 | 0.779793 | − | 0.626037i | \(-0.215324\pi\) | ||||
0.779793 | + | 0.626037i | \(0.215324\pi\) | |||||||
\(692\) | −0.654520 | −0.0248811 | ||||||||
\(693\) | −39.4122 | −1.49715 | ||||||||
\(694\) | −10.1459 | −0.385132 | ||||||||
\(695\) | 14.8459 | 0.563137 | ||||||||
\(696\) | −13.4179 | −0.508606 | ||||||||
\(697\) | 1.37518 | 0.0520885 | ||||||||
\(698\) | 11.0457 | 0.418088 | ||||||||
\(699\) | −34.1729 | −1.29254 | ||||||||
\(700\) | −10.2829 | −0.388656 | ||||||||
\(701\) | −1.49858 | −0.0566007 | −0.0283003 | − | 0.999599i | \(-0.509009\pi\) | ||||
−0.0283003 | + | 0.999599i | \(0.509009\pi\) | |||||||
\(702\) | −0.307448 | −0.0116039 | ||||||||
\(703\) | 6.16190 | 0.232400 | ||||||||
\(704\) | −4.46025 | −0.168102 | ||||||||
\(705\) | −10.9219 | −0.411343 | ||||||||
\(706\) | −28.5221 | −1.07344 | ||||||||
\(707\) | 14.5929 | 0.548821 | ||||||||
\(708\) | 8.87468 | 0.333531 | ||||||||
\(709\) | 31.0293 | 1.16533 | 0.582665 | − | 0.812712i | \(-0.302010\pi\) | ||||
0.582665 | + | 0.812712i | \(0.302010\pi\) | |||||||
\(710\) | 8.95085 | 0.335919 | ||||||||
\(711\) | 32.3732 | 1.21409 | ||||||||
\(712\) | −12.7695 | −0.478559 | ||||||||
\(713\) | −75.9486 | −2.84430 | ||||||||
\(714\) | 9.47225 | 0.354490 | ||||||||
\(715\) | 10.8650 | 0.406328 | ||||||||
\(716\) | 20.6354 | 0.771183 | ||||||||
\(717\) | −1.61324 | −0.0602477 | ||||||||
\(718\) | 13.3587 | 0.498543 | ||||||||
\(719\) | 43.3963 | 1.61841 | 0.809204 | − | 0.587528i | \(-0.199899\pi\) | ||||
0.809204 | + | 0.587528i | \(0.199899\pi\) | |||||||
\(720\) | −3.67038 | −0.136787 | ||||||||
\(721\) | 31.5625 | 1.17545 | ||||||||
\(722\) | −10.0343 | −0.373439 | ||||||||
\(723\) | 64.9067 | 2.41391 | ||||||||
\(724\) | −6.42961 | −0.238955 | ||||||||
\(725\) | −19.4164 | −0.721108 | ||||||||
\(726\) | −21.8967 | −0.812662 | ||||||||
\(727\) | −42.4453 | −1.57421 | −0.787104 | − | 0.616820i | \(-0.788421\pi\) | ||||
−0.787104 | + | 0.616820i | \(0.788421\pi\) | |||||||
\(728\) | 5.86450 | 0.217353 | ||||||||
\(729\) | −28.0947 | −1.04055 | ||||||||
\(730\) | −0.962642 | −0.0356290 | ||||||||
\(731\) | 5.69146 | 0.210506 | ||||||||
\(732\) | 21.2304 | 0.784698 | ||||||||
\(733\) | 40.3517 | 1.49042 | 0.745212 | − | 0.666828i | \(-0.232348\pi\) | ||||
0.745212 | + | 0.666828i | \(0.232348\pi\) | |||||||
\(734\) | −4.65239 | −0.171723 | ||||||||
\(735\) | 3.92802 | 0.144887 | ||||||||
\(736\) | −7.98056 | −0.294167 | ||||||||
\(737\) | −55.5952 | −2.04787 | ||||||||
\(738\) | −3.15838 | −0.116262 | ||||||||
\(739\) | 43.9563 | 1.61696 | 0.808479 | − | 0.588525i | \(-0.200291\pi\) | ||||
0.808479 | + | 0.588525i | \(0.200291\pi\) | |||||||
\(740\) | −2.46721 | −0.0906963 | ||||||||
\(741\) | −14.9785 | −0.550249 | ||||||||
\(742\) | −9.06823 | −0.332905 | ||||||||
\(743\) | 40.3937 | 1.48190 | 0.740950 | − | 0.671560i | \(-0.234376\pi\) | ||||
0.740950 | + | 0.671560i | \(0.234376\pi\) | |||||||
\(744\) | −23.4301 | −0.858991 | ||||||||
\(745\) | −0.850137 | −0.0311466 | ||||||||
\(746\) | 2.22264 | 0.0813767 | ||||||||
\(747\) | −19.8299 | −0.725540 | ||||||||
\(748\) | 5.94541 | 0.217386 | ||||||||
\(749\) | −26.6878 | −0.975151 | ||||||||
\(750\) | −25.2743 | −0.922886 | ||||||||
\(751\) | −35.7969 | −1.30625 | −0.653124 | − | 0.757251i | \(-0.726542\pi\) | ||||
−0.653124 | + | 0.757251i | \(0.726542\pi\) | |||||||
\(752\) | −3.70023 | −0.134933 | ||||||||
\(753\) | −50.8736 | −1.85394 | ||||||||
\(754\) | 11.0735 | 0.403274 | ||||||||
\(755\) | 23.9369 | 0.871154 | ||||||||
\(756\) | −0.436743 | −0.0158842 | ||||||||
\(757\) | 13.5904 | 0.493951 | 0.246976 | − | 0.969022i | \(-0.420563\pi\) | ||||
0.246976 | + | 0.969022i | \(0.420563\pi\) | |||||||
\(758\) | 6.43360 | 0.233679 | ||||||||
\(759\) | −87.6357 | −3.18097 | ||||||||
\(760\) | −3.58983 | −0.130217 | ||||||||
\(761\) | 2.53674 | 0.0919569 | 0.0459784 | − | 0.998942i | \(-0.485359\pi\) | ||||
0.0459784 | + | 0.998942i | \(0.485359\pi\) | |||||||
\(762\) | −23.9842 | −0.868857 | ||||||||
\(763\) | 11.8231 | 0.428026 | ||||||||
\(764\) | 1.49819 | 0.0542026 | ||||||||
\(765\) | 4.89252 | 0.176890 | ||||||||
\(766\) | −13.0227 | −0.470529 | ||||||||
\(767\) | −7.32407 | −0.264457 | ||||||||
\(768\) | −2.46200 | −0.0888399 | ||||||||
\(769\) | −17.9429 | −0.647038 | −0.323519 | − | 0.946222i | \(-0.604866\pi\) | ||||
−0.323519 | + | 0.946222i | \(0.604866\pi\) | |||||||
\(770\) | 15.4342 | 0.556210 | ||||||||
\(771\) | 57.2201 | 2.06073 | ||||||||
\(772\) | −6.67653 | −0.240293 | ||||||||
\(773\) | −31.9596 | −1.14951 | −0.574754 | − | 0.818326i | \(-0.694902\pi\) | ||||
−0.574754 | + | 0.818326i | \(0.694902\pi\) | |||||||
\(774\) | −13.0716 | −0.469851 | ||||||||
\(775\) | −33.9046 | −1.21789 | ||||||||
\(776\) | 12.6583 | 0.454407 | ||||||||
\(777\) | −14.6236 | −0.524619 | ||||||||
\(778\) | 14.1203 | 0.506238 | ||||||||
\(779\) | −3.08907 | −0.110677 | ||||||||
\(780\) | 5.99735 | 0.214740 | ||||||||
\(781\) | 33.2998 | 1.19156 | ||||||||
\(782\) | 10.6379 | 0.380410 | ||||||||
\(783\) | −0.824670 | −0.0294713 | ||||||||
\(784\) | 1.33077 | 0.0475275 | ||||||||
\(785\) | −1.18619 | −0.0423368 | ||||||||
\(786\) | −32.5866 | −1.16233 | ||||||||
\(787\) | −39.5577 | −1.41008 | −0.705041 | − | 0.709167i | \(-0.749071\pi\) | ||||
−0.705041 | + | 0.709167i | \(0.749071\pi\) | |||||||
\(788\) | −3.38365 | −0.120538 | ||||||||
\(789\) | 29.8636 | 1.06317 | ||||||||
\(790\) | −12.6777 | −0.451051 | ||||||||
\(791\) | −18.5868 | −0.660869 | ||||||||
\(792\) | −13.6549 | −0.485205 | ||||||||
\(793\) | −17.5210 | −0.622188 | ||||||||
\(794\) | −5.80414 | −0.205981 | ||||||||
\(795\) | −9.27365 | −0.328903 | ||||||||
\(796\) | −12.5763 | −0.445755 | ||||||||
\(797\) | −22.4510 | −0.795256 | −0.397628 | − | 0.917547i | \(-0.630167\pi\) | ||||
−0.397628 | + | 0.917547i | \(0.630167\pi\) | |||||||
\(798\) | −21.2776 | −0.753219 | ||||||||
\(799\) | 4.93231 | 0.174493 | ||||||||
\(800\) | −3.56264 | −0.125958 | ||||||||
\(801\) | −39.0934 | −1.38130 | ||||||||
\(802\) | −13.0278 | −0.460029 | ||||||||
\(803\) | −3.58131 | −0.126382 | ||||||||
\(804\) | −30.6878 | −1.08228 | ||||||||
\(805\) | 27.6158 | 0.973330 | ||||||||
\(806\) | 19.3364 | 0.681094 | ||||||||
\(807\) | 38.9247 | 1.37021 | ||||||||
\(808\) | 5.05589 | 0.177866 | ||||||||
\(809\) | 46.5502 | 1.63662 | 0.818308 | − | 0.574780i | \(-0.194912\pi\) | ||||
0.818308 | + | 0.574780i | \(0.194912\pi\) | |||||||
\(810\) | 10.5645 | 0.371199 | ||||||||
\(811\) | 10.6732 | 0.374787 | 0.187393 | − | 0.982285i | \(-0.439996\pi\) | ||||
0.187393 | + | 0.982285i | \(0.439996\pi\) | |||||||
\(812\) | 15.7304 | 0.552029 | ||||||||
\(813\) | 54.0663 | 1.89619 | ||||||||
\(814\) | −9.17872 | −0.321714 | ||||||||
\(815\) | 21.5680 | 0.755495 | ||||||||
\(816\) | 3.28179 | 0.114886 | ||||||||
\(817\) | −12.7848 | −0.447283 | ||||||||
\(818\) | −11.9401 | −0.417477 | ||||||||
\(819\) | 17.9539 | 0.627361 | ||||||||
\(820\) | 1.23685 | 0.0431928 | ||||||||
\(821\) | −40.3487 | −1.40818 | −0.704090 | − | 0.710111i | \(-0.748645\pi\) | ||||
−0.704090 | + | 0.710111i | \(0.748645\pi\) | |||||||
\(822\) | 12.5661 | 0.438293 | ||||||||
\(823\) | −28.6414 | −0.998375 | −0.499187 | − | 0.866494i | \(-0.666368\pi\) | ||||
−0.499187 | + | 0.866494i | \(0.666368\pi\) | |||||||
\(824\) | 10.9353 | 0.380947 | ||||||||
\(825\) | −39.1219 | −1.36205 | ||||||||
\(826\) | −10.4041 | −0.362007 | ||||||||
\(827\) | −38.0531 | −1.32323 | −0.661617 | − | 0.749842i | \(-0.730130\pi\) | ||||
−0.661617 | + | 0.749842i | \(0.730130\pi\) | |||||||
\(828\) | −24.4322 | −0.849076 | ||||||||
\(829\) | −17.0035 | −0.590556 | −0.295278 | − | 0.955411i | \(-0.595412\pi\) | ||||
−0.295278 | + | 0.955411i | \(0.595412\pi\) | |||||||
\(830\) | 7.76560 | 0.269548 | ||||||||
\(831\) | −68.3163 | −2.36987 | ||||||||
\(832\) | 2.03184 | 0.0704412 | ||||||||
\(833\) | −1.77388 | −0.0614615 | ||||||||
\(834\) | 30.4869 | 1.05567 | ||||||||
\(835\) | −3.98405 | −0.137874 | ||||||||
\(836\) | −13.3552 | −0.461900 | ||||||||
\(837\) | −1.44002 | −0.0497745 | ||||||||
\(838\) | 14.8690 | 0.513641 | ||||||||
\(839\) | −9.60081 | −0.331457 | −0.165728 | − | 0.986171i | \(-0.552998\pi\) | ||||
−0.165728 | + | 0.986171i | \(0.552998\pi\) | |||||||
\(840\) | 8.51949 | 0.293950 | ||||||||
\(841\) | 0.702575 | 0.0242267 | ||||||||
\(842\) | 1.29715 | 0.0447028 | ||||||||
\(843\) | 4.92085 | 0.169483 | ||||||||
\(844\) | −20.9915 | −0.722559 | ||||||||
\(845\) | 10.6362 | 0.365896 | ||||||||
\(846\) | −11.3281 | −0.389468 | ||||||||
\(847\) | 25.6704 | 0.882044 | ||||||||
\(848\) | −3.14181 | −0.107890 | ||||||||
\(849\) | −39.6814 | −1.36186 | ||||||||
\(850\) | 4.74892 | 0.162886 | ||||||||
\(851\) | −16.4231 | −0.562978 | ||||||||
\(852\) | 18.3811 | 0.629724 | ||||||||
\(853\) | −28.2713 | −0.967990 | −0.483995 | − | 0.875071i | \(-0.660815\pi\) | ||||
−0.483995 | + | 0.875071i | \(0.660815\pi\) | |||||||
\(854\) | −24.8893 | −0.851694 | ||||||||
\(855\) | −10.9901 | −0.375854 | ||||||||
\(856\) | −9.24635 | −0.316034 | ||||||||
\(857\) | −36.5633 | −1.24898 | −0.624489 | − | 0.781034i | \(-0.714693\pi\) | ||||
−0.624489 | + | 0.781034i | \(0.714693\pi\) | |||||||
\(858\) | 22.3119 | 0.761715 | ||||||||
\(859\) | −15.0619 | −0.513906 | −0.256953 | − | 0.966424i | \(-0.582719\pi\) | ||||
−0.256953 | + | 0.966424i | \(0.582719\pi\) | |||||||
\(860\) | 5.11899 | 0.174556 | ||||||||
\(861\) | 7.33107 | 0.249842 | ||||||||
\(862\) | −29.6509 | −1.00991 | ||||||||
\(863\) | 9.07086 | 0.308776 | 0.154388 | − | 0.988010i | \(-0.450659\pi\) | ||||
0.154388 | + | 0.988010i | \(0.450659\pi\) | |||||||
\(864\) | −0.151315 | −0.00514785 | ||||||||
\(865\) | 0.784703 | 0.0266807 | ||||||||
\(866\) | −25.1200 | −0.853612 | ||||||||
\(867\) | 37.4795 | 1.27287 | ||||||||
\(868\) | 27.4681 | 0.932329 | ||||||||
\(869\) | −47.1646 | −1.59995 | ||||||||
\(870\) | 16.0867 | 0.545391 | ||||||||
\(871\) | 25.3260 | 0.858138 | ||||||||
\(872\) | 4.09628 | 0.138717 | ||||||||
\(873\) | 38.7530 | 1.31159 | ||||||||
\(874\) | −23.8960 | −0.808294 | ||||||||
\(875\) | 29.6301 | 1.00168 | ||||||||
\(876\) | −1.97684 | −0.0667912 | ||||||||
\(877\) | 19.4837 | 0.657917 | 0.328958 | − | 0.944344i | \(-0.393302\pi\) | ||||
0.328958 | + | 0.944344i | \(0.393302\pi\) | |||||||
\(878\) | 8.97809 | 0.302996 | ||||||||
\(879\) | 64.0659 | 2.16089 | ||||||||
\(880\) | 5.34739 | 0.180260 | ||||||||
\(881\) | 3.50048 | 0.117934 | 0.0589671 | − | 0.998260i | \(-0.481219\pi\) | ||||
0.0589671 | + | 0.998260i | \(0.481219\pi\) | |||||||
\(882\) | 4.07410 | 0.137182 | ||||||||
\(883\) | 51.7781 | 1.74247 | 0.871236 | − | 0.490864i | \(-0.163319\pi\) | ||||
0.871236 | + | 0.490864i | \(0.163319\pi\) | |||||||
\(884\) | −2.70839 | −0.0910929 | ||||||||
\(885\) | −10.6398 | −0.357654 | ||||||||
\(886\) | −14.8845 | −0.500054 | ||||||||
\(887\) | 40.4064 | 1.35671 | 0.678357 | − | 0.734733i | \(-0.262692\pi\) | ||||
0.678357 | + | 0.734733i | \(0.262692\pi\) | |||||||
\(888\) | −5.06654 | −0.170022 | ||||||||
\(889\) | 28.1177 | 0.943037 | ||||||||
\(890\) | 15.3094 | 0.513171 | ||||||||
\(891\) | 39.3030 | 1.31670 | ||||||||
\(892\) | 23.4488 | 0.785123 | ||||||||
\(893\) | −11.0795 | −0.370761 | ||||||||
\(894\) | −1.74580 | −0.0583884 | ||||||||
\(895\) | −24.7398 | −0.826960 | ||||||||
\(896\) | 2.88631 | 0.0964248 | ||||||||
\(897\) | 39.9218 | 1.33295 | ||||||||
\(898\) | 2.41434 | 0.0805675 | ||||||||
\(899\) | 51.8661 | 1.72983 | ||||||||
\(900\) | −10.9069 | −0.363563 | ||||||||
\(901\) | 4.18795 | 0.139521 | ||||||||
\(902\) | 4.60146 | 0.153212 | ||||||||
\(903\) | 30.3412 | 1.00969 | ||||||||
\(904\) | −6.43963 | −0.214179 | ||||||||
\(905\) | 7.70845 | 0.256237 | ||||||||
\(906\) | 49.1558 | 1.63309 | ||||||||
\(907\) | −1.34959 | −0.0448124 | −0.0224062 | − | 0.999749i | \(-0.507133\pi\) | ||||
−0.0224062 | + | 0.999749i | \(0.507133\pi\) | |||||||
\(908\) | 4.39085 | 0.145716 | ||||||||
\(909\) | 15.4784 | 0.513386 | ||||||||
\(910\) | −7.03094 | −0.233073 | ||||||||
\(911\) | 14.2620 | 0.472520 | 0.236260 | − | 0.971690i | \(-0.424078\pi\) | ||||
0.236260 | + | 0.971690i | \(0.424078\pi\) | |||||||
\(912\) | −7.37191 | −0.244108 | ||||||||
\(913\) | 28.8903 | 0.956130 | ||||||||
\(914\) | −6.08220 | −0.201181 | ||||||||
\(915\) | −25.4531 | −0.841453 | ||||||||
\(916\) | −7.91979 | −0.261677 | ||||||||
\(917\) | 38.2026 | 1.26156 | ||||||||
\(918\) | 0.201700 | 0.00665708 | ||||||||
\(919\) | −19.8407 | −0.654483 | −0.327242 | − | 0.944941i | \(-0.606119\pi\) | ||||
−0.327242 | + | 0.944941i | \(0.606119\pi\) | |||||||
\(920\) | 9.56787 | 0.315443 | ||||||||
\(921\) | 67.0626 | 2.20979 | ||||||||
\(922\) | −16.7137 | −0.550437 | ||||||||
\(923\) | −15.1695 | −0.499309 | ||||||||
\(924\) | 31.6950 | 1.04269 | ||||||||
\(925\) | −7.33154 | −0.241060 | ||||||||
\(926\) | −33.7225 | −1.10819 | ||||||||
\(927\) | 33.4778 | 1.09956 | ||||||||
\(928\) | 5.45001 | 0.178905 | ||||||||
\(929\) | −41.6358 | −1.36603 | −0.683013 | − | 0.730406i | \(-0.739331\pi\) | ||||
−0.683013 | + | 0.730406i | \(0.739331\pi\) | |||||||
\(930\) | 28.0904 | 0.921119 | ||||||||
\(931\) | 3.98469 | 0.130593 | ||||||||
\(932\) | 13.8801 | 0.454658 | ||||||||
\(933\) | 53.3686 | 1.74721 | ||||||||
\(934\) | −23.7353 | −0.776642 | ||||||||
\(935\) | −7.12794 | −0.233108 | ||||||||
\(936\) | 6.22038 | 0.203320 | ||||||||
\(937\) | 2.68119 | 0.0875905 | 0.0437953 | − | 0.999041i | \(-0.486055\pi\) | ||||
0.0437953 | + | 0.999041i | \(0.486055\pi\) | |||||||
\(938\) | 35.9766 | 1.17468 | ||||||||
\(939\) | 3.22129 | 0.105123 | ||||||||
\(940\) | 4.43619 | 0.144693 | ||||||||
\(941\) | −33.2694 | −1.08455 | −0.542276 | − | 0.840200i | \(-0.682437\pi\) | ||||
−0.542276 | + | 0.840200i | \(0.682437\pi\) | |||||||
\(942\) | −2.43590 | −0.0793659 | ||||||||
\(943\) | 8.23322 | 0.268110 | ||||||||
\(944\) | −3.60466 | −0.117322 | ||||||||
\(945\) | 0.523610 | 0.0170330 | ||||||||
\(946\) | 19.0441 | 0.619178 | ||||||||
\(947\) | −21.4682 | −0.697622 | −0.348811 | − | 0.937193i | \(-0.613414\pi\) | ||||
−0.348811 | + | 0.937193i | \(0.613414\pi\) | |||||||
\(948\) | −26.0343 | −0.845553 | ||||||||
\(949\) | 1.63144 | 0.0529588 | ||||||||
\(950\) | −10.6675 | −0.346100 | ||||||||
\(951\) | 48.8754 | 1.58489 | ||||||||
\(952\) | −3.84738 | −0.124694 | ||||||||
\(953\) | 51.7762 | 1.67720 | 0.838598 | − | 0.544751i | \(-0.183376\pi\) | ||||
0.838598 | + | 0.544751i | \(0.183376\pi\) | |||||||
\(954\) | −9.61853 | −0.311411 | ||||||||
\(955\) | −1.79618 | −0.0581229 | ||||||||
\(956\) | 0.655256 | 0.0211925 | ||||||||
\(957\) | 59.8474 | 1.93459 | ||||||||
\(958\) | 14.8171 | 0.478717 | ||||||||
\(959\) | −14.7317 | −0.475713 | ||||||||
\(960\) | 2.95169 | 0.0952654 | ||||||||
\(961\) | 59.5676 | 1.92153 | ||||||||
\(962\) | 4.18130 | 0.134811 | ||||||||
\(963\) | −28.3073 | −0.912191 | ||||||||
\(964\) | −26.3634 | −0.849107 | ||||||||
\(965\) | 8.00448 | 0.257673 | ||||||||
\(966\) | 56.7106 | 1.82463 | ||||||||
\(967\) | 25.6049 | 0.823397 | 0.411699 | − | 0.911320i | \(-0.364936\pi\) | ||||
0.411699 | + | 0.911320i | \(0.364936\pi\) | |||||||
\(968\) | 8.89384 | 0.285859 | ||||||||
\(969\) | 9.82658 | 0.315675 | ||||||||
\(970\) | −15.1760 | −0.487273 | ||||||||
\(971\) | 5.32845 | 0.170998 | 0.0854991 | − | 0.996338i | \(-0.472752\pi\) | ||||
0.0854991 | + | 0.996338i | \(0.472752\pi\) | |||||||
\(972\) | 22.1487 | 0.710421 | ||||||||
\(973\) | −35.7410 | −1.14580 | ||||||||
\(974\) | −0.442777 | −0.0141875 | ||||||||
\(975\) | 17.8217 | 0.570752 | ||||||||
\(976\) | −8.62323 | −0.276023 | ||||||||
\(977\) | −33.6344 | −1.07606 | −0.538030 | − | 0.842926i | \(-0.680831\pi\) | ||||
−0.538030 | + | 0.842926i | \(0.680831\pi\) | |||||||
\(978\) | 44.2911 | 1.41627 | ||||||||
\(979\) | 56.9553 | 1.82030 | ||||||||
\(980\) | −1.59546 | −0.0509651 | ||||||||
\(981\) | 12.5406 | 0.400390 | ||||||||
\(982\) | 2.45714 | 0.0784105 | ||||||||
\(983\) | 19.9849 | 0.637418 | 0.318709 | − | 0.947853i | \(-0.396751\pi\) | ||||
0.318709 | + | 0.947853i | \(0.396751\pi\) | |||||||
\(984\) | 2.53995 | 0.0809706 | ||||||||
\(985\) | 4.05665 | 0.129256 | ||||||||
\(986\) | −7.26472 | −0.231356 | ||||||||
\(987\) | 26.2942 | 0.836952 | ||||||||
\(988\) | 6.08387 | 0.193554 | ||||||||
\(989\) | 34.0749 | 1.08352 | ||||||||
\(990\) | 16.3708 | 0.520299 | ||||||||
\(991\) | 31.3951 | 0.997298 | 0.498649 | − | 0.866804i | \(-0.333830\pi\) | ||||
0.498649 | + | 0.866804i | \(0.333830\pi\) | |||||||
\(992\) | 9.51670 | 0.302156 | ||||||||
\(993\) | −5.49708 | −0.174445 | ||||||||
\(994\) | −21.5489 | −0.683488 | ||||||||
\(995\) | 15.0777 | 0.477995 | ||||||||
\(996\) | 15.9471 | 0.505303 | ||||||||
\(997\) | −33.9670 | −1.07574 | −0.537872 | − | 0.843026i | \(-0.680772\pi\) | ||||
−0.537872 | + | 0.843026i | \(0.680772\pi\) | |||||||
\(998\) | −32.6070 | −1.03216 | ||||||||
\(999\) | −0.311391 | −0.00985197 |
(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 | 8026.2.a.a.1.10 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.a.1.10 | ✓ | 71 | 1.1 | even | 1 | trivial |