Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(0\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61991 | −1.85255 | −0.926277 | − | 0.376843i | \(-0.877010\pi\) | ||||
−0.926277 | + | 0.376843i | \(0.877010\pi\) | |||||||
\(3\) | −3.07843 | −1.77733 | −0.888666 | − | 0.458556i | \(-0.848367\pi\) | ||||
−0.888666 | + | 0.458556i | \(0.848367\pi\) | |||||||
\(4\) | 4.86391 | 2.43196 | ||||||||
\(5\) | −2.25474 | −1.00835 | −0.504175 | − | 0.863601i | \(-0.668203\pi\) | ||||
−0.504175 | + | 0.863601i | \(0.668203\pi\) | |||||||
\(6\) | 8.06519 | 3.29260 | ||||||||
\(7\) | 3.02795 | 1.14446 | 0.572229 | − | 0.820094i | \(-0.306079\pi\) | ||||
0.572229 | + | 0.820094i | \(0.306079\pi\) | |||||||
\(8\) | −7.50318 | −2.65278 | ||||||||
\(9\) | 6.47672 | 2.15891 | ||||||||
\(10\) | 5.90721 | 1.86802 | ||||||||
\(11\) | 1.57362 | 0.474466 | 0.237233 | − | 0.971453i | \(-0.423760\pi\) | ||||
0.237233 | + | 0.971453i | \(0.423760\pi\) | |||||||
\(12\) | −14.9732 | −4.32239 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −7.93295 | −2.12017 | ||||||||
\(15\) | 6.94106 | 1.79217 | ||||||||
\(16\) | 9.92982 | 2.48246 | ||||||||
\(17\) | 5.17171 | 1.25432 | 0.627162 | − | 0.778889i | \(-0.284217\pi\) | ||||
0.627162 | + | 0.778889i | \(0.284217\pi\) | |||||||
\(18\) | −16.9684 | −3.99949 | ||||||||
\(19\) | −6.55233 | −1.50321 | −0.751604 | − | 0.659615i | \(-0.770719\pi\) | ||||
−0.751604 | + | 0.659615i | \(0.770719\pi\) | |||||||
\(20\) | −10.9669 | −2.45226 | ||||||||
\(21\) | −9.32132 | −2.03408 | ||||||||
\(22\) | −4.12275 | −0.878973 | ||||||||
\(23\) | 3.43105 | 0.715424 | 0.357712 | − | 0.933832i | \(-0.383557\pi\) | ||||
0.357712 | + | 0.933832i | \(0.383557\pi\) | |||||||
\(24\) | 23.0980 | 4.71486 | ||||||||
\(25\) | 0.0838553 | 0.0167711 | ||||||||
\(26\) | 2.61991 | 0.513806 | ||||||||
\(27\) | −10.7028 | −2.05976 | ||||||||
\(28\) | 14.7277 | 2.78327 | ||||||||
\(29\) | 1.57815 | 0.293054 | 0.146527 | − | 0.989207i | \(-0.453190\pi\) | ||||
0.146527 | + | 0.989207i | \(0.453190\pi\) | |||||||
\(30\) | −18.1849 | −3.32010 | ||||||||
\(31\) | −6.53929 | −1.17449 | −0.587246 | − | 0.809409i | \(-0.699788\pi\) | ||||
−0.587246 | + | 0.809409i | \(0.699788\pi\) | |||||||
\(32\) | −11.0088 | −1.94611 | ||||||||
\(33\) | −4.84429 | −0.843282 | ||||||||
\(34\) | −13.5494 | −2.32370 | ||||||||
\(35\) | −6.82724 | −1.15401 | ||||||||
\(36\) | 31.5022 | 5.25037 | ||||||||
\(37\) | 0.847251 | 0.139287 | 0.0696436 | − | 0.997572i | \(-0.477814\pi\) | ||||
0.0696436 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(38\) | 17.1665 | 2.78477 | ||||||||
\(39\) | 3.07843 | 0.492943 | ||||||||
\(40\) | 16.9177 | 2.67493 | ||||||||
\(41\) | −0.805164 | −0.125745 | −0.0628727 | − | 0.998022i | \(-0.520026\pi\) | ||||
−0.0628727 | + | 0.998022i | \(0.520026\pi\) | |||||||
\(42\) | 24.4210 | 3.76824 | ||||||||
\(43\) | −6.26875 | −0.955975 | −0.477988 | − | 0.878367i | \(-0.658634\pi\) | ||||
−0.477988 | + | 0.878367i | \(0.658634\pi\) | |||||||
\(44\) | 7.65397 | 1.15388 | ||||||||
\(45\) | −14.6033 | −2.17693 | ||||||||
\(46\) | −8.98904 | −1.32536 | ||||||||
\(47\) | 2.01191 | 0.293467 | 0.146733 | − | 0.989176i | \(-0.453124\pi\) | ||||
0.146733 | + | 0.989176i | \(0.453124\pi\) | |||||||
\(48\) | −30.5682 | −4.41215 | ||||||||
\(49\) | 2.16848 | 0.309783 | ||||||||
\(50\) | −0.219693 | −0.0310693 | ||||||||
\(51\) | −15.9207 | −2.22935 | ||||||||
\(52\) | −4.86391 | −0.674503 | ||||||||
\(53\) | −7.36518 | −1.01169 | −0.505843 | − | 0.862626i | \(-0.668818\pi\) | ||||
−0.505843 | + | 0.862626i | \(0.668818\pi\) | |||||||
\(54\) | 28.0404 | 3.81582 | ||||||||
\(55\) | −3.54811 | −0.478428 | ||||||||
\(56\) | −22.7193 | −3.03599 | ||||||||
\(57\) | 20.1709 | 2.67170 | ||||||||
\(58\) | −4.13460 | −0.542899 | ||||||||
\(59\) | 4.93760 | 0.642821 | 0.321410 | − | 0.946940i | \(-0.395843\pi\) | ||||
0.321410 | + | 0.946940i | \(0.395843\pi\) | |||||||
\(60\) | 33.7607 | 4.35849 | ||||||||
\(61\) | −3.87440 | −0.496067 | −0.248033 | − | 0.968751i | \(-0.579784\pi\) | ||||
−0.248033 | + | 0.968751i | \(0.579784\pi\) | |||||||
\(62\) | 17.1323 | 2.17581 | ||||||||
\(63\) | 19.6112 | 2.47078 | ||||||||
\(64\) | 8.98249 | 1.12281 | ||||||||
\(65\) | 2.25474 | 0.279666 | ||||||||
\(66\) | 12.6916 | 1.56223 | ||||||||
\(67\) | −7.83467 | −0.957157 | −0.478578 | − | 0.878045i | \(-0.658848\pi\) | ||||
−0.478578 | + | 0.878045i | \(0.658848\pi\) | |||||||
\(68\) | 25.1547 | 3.05046 | ||||||||
\(69\) | −10.5623 | −1.27155 | ||||||||
\(70\) | 17.8867 | 2.13787 | ||||||||
\(71\) | −0.564401 | −0.0669820 | −0.0334910 | − | 0.999439i | \(-0.510663\pi\) | ||||
−0.0334910 | + | 0.999439i | \(0.510663\pi\) | |||||||
\(72\) | −48.5960 | −5.72709 | ||||||||
\(73\) | 11.8849 | 1.39102 | 0.695511 | − | 0.718515i | \(-0.255178\pi\) | ||||
0.695511 | + | 0.718515i | \(0.255178\pi\) | |||||||
\(74\) | −2.21972 | −0.258037 | ||||||||
\(75\) | −0.258143 | −0.0298077 | ||||||||
\(76\) | −31.8700 | −3.65574 | ||||||||
\(77\) | 4.76485 | 0.543006 | ||||||||
\(78\) | −8.06519 | −0.913203 | ||||||||
\(79\) | −9.83308 | −1.10631 | −0.553154 | − | 0.833079i | \(-0.686576\pi\) | ||||
−0.553154 | + | 0.833079i | \(0.686576\pi\) | |||||||
\(80\) | −22.3892 | −2.50319 | ||||||||
\(81\) | 13.5177 | 1.50197 | ||||||||
\(82\) | 2.10945 | 0.232950 | ||||||||
\(83\) | 9.55569 | 1.04887 | 0.524436 | − | 0.851450i | \(-0.324276\pi\) | ||||
0.524436 | + | 0.851450i | \(0.324276\pi\) | |||||||
\(84\) | −45.3381 | −4.94679 | ||||||||
\(85\) | −11.6609 | −1.26480 | ||||||||
\(86\) | 16.4235 | 1.77100 | ||||||||
\(87\) | −4.85821 | −0.520855 | ||||||||
\(88\) | −11.8072 | −1.25865 | ||||||||
\(89\) | 16.7313 | 1.77351 | 0.886757 | − | 0.462236i | \(-0.152953\pi\) | ||||
0.886757 | + | 0.462236i | \(0.152953\pi\) | |||||||
\(90\) | 38.2593 | 4.03289 | ||||||||
\(91\) | −3.02795 | −0.317415 | ||||||||
\(92\) | 16.6883 | 1.73988 | ||||||||
\(93\) | 20.1307 | 2.08746 | ||||||||
\(94\) | −5.27101 | −0.543663 | ||||||||
\(95\) | 14.7738 | 1.51576 | ||||||||
\(96\) | 33.8899 | 3.45887 | ||||||||
\(97\) | 18.6813 | 1.89679 | 0.948397 | − | 0.317086i | \(-0.102704\pi\) | ||||
0.948397 | + | 0.317086i | \(0.102704\pi\) | |||||||
\(98\) | −5.68121 | −0.573889 | ||||||||
\(99\) | 10.1919 | 1.02433 | ||||||||
\(100\) | 0.407865 | 0.0407865 | ||||||||
\(101\) | 0.551517 | 0.0548780 | 0.0274390 | − | 0.999623i | \(-0.491265\pi\) | ||||
0.0274390 | + | 0.999623i | \(0.491265\pi\) | |||||||
\(102\) | 41.7108 | 4.12999 | ||||||||
\(103\) | 1.82567 | 0.179889 | 0.0899444 | − | 0.995947i | \(-0.471331\pi\) | ||||
0.0899444 | + | 0.995947i | \(0.471331\pi\) | |||||||
\(104\) | 7.50318 | 0.735748 | ||||||||
\(105\) | 21.0172 | 2.05107 | ||||||||
\(106\) | 19.2961 | 1.87420 | ||||||||
\(107\) | −6.19674 | −0.599061 | −0.299531 | − | 0.954087i | \(-0.596830\pi\) | ||||
−0.299531 | + | 0.954087i | \(0.596830\pi\) | |||||||
\(108\) | −52.0576 | −5.00925 | ||||||||
\(109\) | −8.43558 | −0.807982 | −0.403991 | − | 0.914763i | \(-0.632377\pi\) | ||||
−0.403991 | + | 0.914763i | \(0.632377\pi\) | |||||||
\(110\) | 9.29573 | 0.886313 | ||||||||
\(111\) | −2.60820 | −0.247559 | ||||||||
\(112\) | 30.0670 | 2.84106 | ||||||||
\(113\) | 5.86461 | 0.551696 | 0.275848 | − | 0.961201i | \(-0.411041\pi\) | ||||
0.275848 | + | 0.961201i | \(0.411041\pi\) | |||||||
\(114\) | −52.8458 | −4.94946 | ||||||||
\(115\) | −7.73614 | −0.721398 | ||||||||
\(116\) | 7.67596 | 0.712695 | ||||||||
\(117\) | −6.47672 | −0.598773 | ||||||||
\(118\) | −12.9361 | −1.19086 | ||||||||
\(119\) | 15.6597 | 1.43552 | ||||||||
\(120\) | −52.0800 | −4.75423 | ||||||||
\(121\) | −8.52371 | −0.774882 | ||||||||
\(122\) | 10.1506 | 0.918990 | ||||||||
\(123\) | 2.47864 | 0.223491 | ||||||||
\(124\) | −31.8066 | −2.85631 | ||||||||
\(125\) | 11.0846 | 0.991440 | ||||||||
\(126\) | −51.3795 | −4.57725 | ||||||||
\(127\) | 1.27582 | 0.113211 | 0.0566054 | − | 0.998397i | \(-0.481972\pi\) | ||||
0.0566054 | + | 0.998397i | \(0.481972\pi\) | |||||||
\(128\) | −1.51561 | −0.133962 | ||||||||
\(129\) | 19.2979 | 1.69908 | ||||||||
\(130\) | −5.90721 | −0.518097 | ||||||||
\(131\) | 3.78260 | 0.330487 | 0.165244 | − | 0.986253i | \(-0.447159\pi\) | ||||
0.165244 | + | 0.986253i | \(0.447159\pi\) | |||||||
\(132\) | −23.5622 | −2.05083 | ||||||||
\(133\) | −19.8401 | −1.72036 | ||||||||
\(134\) | 20.5261 | 1.77319 | ||||||||
\(135\) | 24.1321 | 2.07696 | ||||||||
\(136\) | −38.8043 | −3.32744 | ||||||||
\(137\) | −7.75773 | −0.662787 | −0.331394 | − | 0.943493i | \(-0.607519\pi\) | ||||
−0.331394 | + | 0.943493i | \(0.607519\pi\) | |||||||
\(138\) | 27.6721 | 2.35561 | ||||||||
\(139\) | 7.82348 | 0.663579 | 0.331789 | − | 0.943353i | \(-0.392348\pi\) | ||||
0.331789 | + | 0.943353i | \(0.392348\pi\) | |||||||
\(140\) | −33.2071 | −2.80651 | ||||||||
\(141\) | −6.19351 | −0.521588 | ||||||||
\(142\) | 1.47868 | 0.124088 | ||||||||
\(143\) | −1.57362 | −0.131593 | ||||||||
\(144\) | 64.3127 | 5.35939 | ||||||||
\(145\) | −3.55831 | −0.295502 | ||||||||
\(146\) | −31.1373 | −2.57694 | ||||||||
\(147\) | −6.67550 | −0.550586 | ||||||||
\(148\) | 4.12095 | 0.338740 | ||||||||
\(149\) | 6.39729 | 0.524086 | 0.262043 | − | 0.965056i | \(-0.415604\pi\) | ||||
0.262043 | + | 0.965056i | \(0.415604\pi\) | |||||||
\(150\) | 0.676310 | 0.0552205 | ||||||||
\(151\) | 14.1925 | 1.15497 | 0.577485 | − | 0.816401i | \(-0.304034\pi\) | ||||
0.577485 | + | 0.816401i | \(0.304034\pi\) | |||||||
\(152\) | 49.1633 | 3.98767 | ||||||||
\(153\) | 33.4957 | 2.70797 | ||||||||
\(154\) | −12.4835 | −1.00595 | ||||||||
\(155\) | 14.7444 | 1.18430 | ||||||||
\(156\) | 14.9732 | 1.19882 | ||||||||
\(157\) | −10.9188 | −0.871416 | −0.435708 | − | 0.900088i | \(-0.643502\pi\) | ||||
−0.435708 | + | 0.900088i | \(0.643502\pi\) | |||||||
\(158\) | 25.7618 | 2.04949 | ||||||||
\(159\) | 22.6732 | 1.79810 | ||||||||
\(160\) | 24.8221 | 1.96236 | ||||||||
\(161\) | 10.3891 | 0.818772 | ||||||||
\(162\) | −35.4152 | −2.78248 | ||||||||
\(163\) | 15.3412 | 1.20162 | 0.600809 | − | 0.799393i | \(-0.294845\pi\) | ||||
0.600809 | + | 0.799393i | \(0.294845\pi\) | |||||||
\(164\) | −3.91625 | −0.305808 | ||||||||
\(165\) | 10.9226 | 0.850324 | ||||||||
\(166\) | −25.0350 | −1.94309 | ||||||||
\(167\) | −15.3893 | −1.19086 | −0.595430 | − | 0.803407i | \(-0.703018\pi\) | ||||
−0.595430 | + | 0.803407i | \(0.703018\pi\) | |||||||
\(168\) | 69.9396 | 5.39596 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 30.5504 | 2.34311 | ||||||||
\(171\) | −42.4376 | −3.24528 | ||||||||
\(172\) | −30.4907 | −2.32489 | ||||||||
\(173\) | −5.00464 | −0.380496 | −0.190248 | − | 0.981736i | \(-0.560929\pi\) | ||||
−0.190248 | + | 0.981736i | \(0.560929\pi\) | |||||||
\(174\) | 12.7281 | 0.964911 | ||||||||
\(175\) | 0.253910 | 0.0191938 | ||||||||
\(176\) | 15.6258 | 1.17784 | ||||||||
\(177\) | −15.2001 | −1.14251 | ||||||||
\(178\) | −43.8344 | −3.28553 | ||||||||
\(179\) | −6.46718 | −0.483380 | −0.241690 | − | 0.970354i | \(-0.577702\pi\) | ||||
−0.241690 | + | 0.970354i | \(0.577702\pi\) | |||||||
\(180\) | −71.0293 | −5.29421 | ||||||||
\(181\) | −6.53302 | −0.485596 | −0.242798 | − | 0.970077i | \(-0.578065\pi\) | ||||
−0.242798 | + | 0.970077i | \(0.578065\pi\) | |||||||
\(182\) | 7.93295 | 0.588029 | ||||||||
\(183\) | 11.9271 | 0.881675 | ||||||||
\(184\) | −25.7438 | −1.89786 | ||||||||
\(185\) | −1.91033 | −0.140450 | ||||||||
\(186\) | −52.7407 | −3.86713 | ||||||||
\(187\) | 8.13833 | 0.595133 | ||||||||
\(188\) | 9.78574 | 0.713698 | ||||||||
\(189\) | −32.4076 | −2.35731 | ||||||||
\(190\) | −38.7060 | −2.80803 | ||||||||
\(191\) | −11.2208 | −0.811909 | −0.405954 | − | 0.913893i | \(-0.633061\pi\) | ||||
−0.405954 | + | 0.913893i | \(0.633061\pi\) | |||||||
\(192\) | −27.6519 | −1.99561 | ||||||||
\(193\) | 16.8161 | 1.21045 | 0.605224 | − | 0.796055i | \(-0.293083\pi\) | ||||
0.605224 | + | 0.796055i | \(0.293083\pi\) | |||||||
\(194\) | −48.9431 | −3.51391 | ||||||||
\(195\) | −6.94106 | −0.497059 | ||||||||
\(196\) | 10.5473 | 0.753378 | ||||||||
\(197\) | −10.9966 | −0.783472 | −0.391736 | − | 0.920078i | \(-0.628125\pi\) | ||||
−0.391736 | + | 0.920078i | \(0.628125\pi\) | |||||||
\(198\) | −26.7019 | −1.89762 | ||||||||
\(199\) | −14.1540 | −1.00335 | −0.501674 | − | 0.865057i | \(-0.667282\pi\) | ||||
−0.501674 | + | 0.865057i | \(0.667282\pi\) | |||||||
\(200\) | −0.629182 | −0.0444899 | ||||||||
\(201\) | 24.1185 | 1.70118 | ||||||||
\(202\) | −1.44492 | −0.101665 | ||||||||
\(203\) | 4.77855 | 0.335388 | ||||||||
\(204\) | −77.4370 | −5.42168 | ||||||||
\(205\) | 1.81544 | 0.126796 | ||||||||
\(206\) | −4.78309 | −0.333254 | ||||||||
\(207\) | 22.2220 | 1.54453 | ||||||||
\(208\) | −9.92982 | −0.688509 | ||||||||
\(209\) | −10.3109 | −0.713220 | ||||||||
\(210\) | −55.0630 | −3.79971 | ||||||||
\(211\) | −2.59640 | −0.178744 | −0.0893718 | − | 0.995998i | \(-0.528486\pi\) | ||||
−0.0893718 | + | 0.995998i | \(0.528486\pi\) | |||||||
\(212\) | −35.8236 | −2.46038 | ||||||||
\(213\) | 1.73747 | 0.119049 | ||||||||
\(214\) | 16.2349 | 1.10979 | ||||||||
\(215\) | 14.1344 | 0.963958 | ||||||||
\(216\) | 80.3053 | 5.46408 | ||||||||
\(217\) | −19.8007 | −1.34416 | ||||||||
\(218\) | 22.1004 | 1.49683 | ||||||||
\(219\) | −36.5868 | −2.47231 | ||||||||
\(220\) | −17.2577 | −1.16352 | ||||||||
\(221\) | −5.17171 | −0.347887 | ||||||||
\(222\) | 6.83324 | 0.458617 | ||||||||
\(223\) | 7.22389 | 0.483747 | 0.241874 | − | 0.970308i | \(-0.422238\pi\) | ||||
0.241874 | + | 0.970308i | \(0.422238\pi\) | |||||||
\(224\) | −33.3342 | −2.22724 | ||||||||
\(225\) | 0.543107 | 0.0362072 | ||||||||
\(226\) | −15.3647 | −1.02205 | ||||||||
\(227\) | 8.53446 | 0.566452 | 0.283226 | − | 0.959053i | \(-0.408595\pi\) | ||||
0.283226 | + | 0.959053i | \(0.408595\pi\) | |||||||
\(228\) | 98.1094 | 6.49745 | ||||||||
\(229\) | 25.7230 | 1.69982 | 0.849912 | − | 0.526924i | \(-0.176655\pi\) | ||||
0.849912 | + | 0.526924i | \(0.176655\pi\) | |||||||
\(230\) | 20.2680 | 1.33643 | ||||||||
\(231\) | −14.6683 | −0.965101 | ||||||||
\(232\) | −11.8411 | −0.777408 | ||||||||
\(233\) | 10.1977 | 0.668071 | 0.334036 | − | 0.942560i | \(-0.391589\pi\) | ||||
0.334036 | + | 0.942560i | \(0.391589\pi\) | |||||||
\(234\) | 16.9684 | 1.10926 | ||||||||
\(235\) | −4.53633 | −0.295917 | ||||||||
\(236\) | 24.0161 | 1.56331 | ||||||||
\(237\) | 30.2704 | 1.96628 | ||||||||
\(238\) | −41.0269 | −2.65938 | ||||||||
\(239\) | −14.0894 | −0.911365 | −0.455682 | − | 0.890142i | \(-0.650605\pi\) | ||||
−0.455682 | + | 0.890142i | \(0.650605\pi\) | |||||||
\(240\) | 68.9234 | 4.44899 | ||||||||
\(241\) | −11.6050 | −0.747542 | −0.373771 | − | 0.927521i | \(-0.621935\pi\) | ||||
−0.373771 | + | 0.927521i | \(0.621935\pi\) | |||||||
\(242\) | 22.3313 | 1.43551 | ||||||||
\(243\) | −9.50486 | −0.609737 | ||||||||
\(244\) | −18.8448 | −1.20641 | ||||||||
\(245\) | −4.88936 | −0.312369 | ||||||||
\(246\) | −6.49380 | −0.414030 | ||||||||
\(247\) | 6.55233 | 0.416915 | ||||||||
\(248\) | 49.0655 | 3.11566 | ||||||||
\(249\) | −29.4165 | −1.86419 | ||||||||
\(250\) | −29.0407 | −1.83670 | ||||||||
\(251\) | −18.2857 | −1.15419 | −0.577093 | − | 0.816679i | \(-0.695813\pi\) | ||||
−0.577093 | + | 0.816679i | \(0.695813\pi\) | |||||||
\(252\) | 95.3870 | 6.00882 | ||||||||
\(253\) | 5.39919 | 0.339444 | ||||||||
\(254\) | −3.34253 | −0.209729 | ||||||||
\(255\) | 35.8971 | 2.24796 | ||||||||
\(256\) | −13.9942 | −0.874639 | ||||||||
\(257\) | 15.6321 | 0.975102 | 0.487551 | − | 0.873094i | \(-0.337890\pi\) | ||||
0.487551 | + | 0.873094i | \(0.337890\pi\) | |||||||
\(258\) | −50.5587 | −3.14765 | ||||||||
\(259\) | 2.56543 | 0.159408 | ||||||||
\(260\) | 10.9669 | 0.680136 | ||||||||
\(261\) | 10.2212 | 0.632677 | ||||||||
\(262\) | −9.91005 | −0.612245 | ||||||||
\(263\) | 20.0689 | 1.23750 | 0.618750 | − | 0.785588i | \(-0.287639\pi\) | ||||
0.618750 | + | 0.785588i | \(0.287639\pi\) | |||||||
\(264\) | 36.3476 | 2.23704 | ||||||||
\(265\) | 16.6066 | 1.02013 | ||||||||
\(266\) | 51.9793 | 3.18705 | ||||||||
\(267\) | −51.5061 | −3.15212 | ||||||||
\(268\) | −38.1071 | −2.32776 | ||||||||
\(269\) | −27.5889 | −1.68212 | −0.841062 | − | 0.540939i | \(-0.818069\pi\) | ||||
−0.841062 | + | 0.540939i | \(0.818069\pi\) | |||||||
\(270\) | −63.2238 | −3.84768 | ||||||||
\(271\) | −8.05246 | −0.489152 | −0.244576 | − | 0.969630i | \(-0.578649\pi\) | ||||
−0.244576 | + | 0.969630i | \(0.578649\pi\) | |||||||
\(272\) | 51.3541 | 3.11380 | ||||||||
\(273\) | 9.32132 | 0.564152 | ||||||||
\(274\) | 20.3245 | 1.22785 | ||||||||
\(275\) | 0.131957 | 0.00795729 | ||||||||
\(276\) | −51.3739 | −3.09234 | ||||||||
\(277\) | −4.02097 | −0.241596 | −0.120798 | − | 0.992677i | \(-0.538545\pi\) | ||||
−0.120798 | + | 0.992677i | \(0.538545\pi\) | |||||||
\(278\) | −20.4968 | −1.22932 | ||||||||
\(279\) | −42.3532 | −2.53562 | ||||||||
\(280\) | 51.2260 | 3.06134 | ||||||||
\(281\) | 4.56424 | 0.272279 | 0.136140 | − | 0.990690i | \(-0.456530\pi\) | ||||
0.136140 | + | 0.990690i | \(0.456530\pi\) | |||||||
\(282\) | 16.2264 | 0.966269 | ||||||||
\(283\) | 8.88667 | 0.528257 | 0.264129 | − | 0.964487i | \(-0.414916\pi\) | ||||
0.264129 | + | 0.964487i | \(0.414916\pi\) | |||||||
\(284\) | −2.74520 | −0.162897 | ||||||||
\(285\) | −45.4801 | −2.69401 | ||||||||
\(286\) | 4.12275 | 0.243783 | ||||||||
\(287\) | −2.43800 | −0.143910 | ||||||||
\(288\) | −71.3011 | −4.20146 | ||||||||
\(289\) | 9.74656 | 0.573327 | ||||||||
\(290\) | 9.32244 | 0.547433 | ||||||||
\(291\) | −57.5089 | −3.37123 | ||||||||
\(292\) | 57.8071 | 3.38291 | ||||||||
\(293\) | −10.8329 | −0.632867 | −0.316434 | − | 0.948615i | \(-0.602485\pi\) | ||||
−0.316434 | + | 0.948615i | \(0.602485\pi\) | |||||||
\(294\) | 17.4892 | 1.01999 | ||||||||
\(295\) | −11.1330 | −0.648189 | ||||||||
\(296\) | −6.35708 | −0.369498 | ||||||||
\(297\) | −16.8422 | −0.977285 | ||||||||
\(298\) | −16.7603 | −0.970898 | ||||||||
\(299\) | −3.43105 | −0.198423 | ||||||||
\(300\) | −1.25558 | −0.0724911 | ||||||||
\(301\) | −18.9815 | −1.09407 | ||||||||
\(302\) | −37.1830 | −2.13964 | ||||||||
\(303\) | −1.69781 | −0.0975364 | ||||||||
\(304\) | −65.0635 | −3.73165 | ||||||||
\(305\) | 8.73578 | 0.500209 | ||||||||
\(306\) | −87.7556 | −5.01665 | ||||||||
\(307\) | 17.1805 | 0.980545 | 0.490272 | − | 0.871569i | \(-0.336897\pi\) | ||||
0.490272 | + | 0.871569i | \(0.336897\pi\) | |||||||
\(308\) | 23.1758 | 1.32057 | ||||||||
\(309\) | −5.62020 | −0.319722 | ||||||||
\(310\) | −38.6290 | −2.19398 | ||||||||
\(311\) | −1.59138 | −0.0902391 | −0.0451195 | − | 0.998982i | \(-0.514367\pi\) | ||||
−0.0451195 | + | 0.998982i | \(0.514367\pi\) | |||||||
\(312\) | −23.0980 | −1.30767 | ||||||||
\(313\) | −8.74323 | −0.494196 | −0.247098 | − | 0.968990i | \(-0.579477\pi\) | ||||
−0.247098 | + | 0.968990i | \(0.579477\pi\) | |||||||
\(314\) | 28.6063 | 1.61435 | ||||||||
\(315\) | −44.2181 | −2.49141 | ||||||||
\(316\) | −47.8272 | −2.69049 | ||||||||
\(317\) | −11.6098 | −0.652071 | −0.326035 | − | 0.945358i | \(-0.605713\pi\) | ||||
−0.326035 | + | 0.945358i | \(0.605713\pi\) | |||||||
\(318\) | −59.4016 | −3.33108 | ||||||||
\(319\) | 2.48341 | 0.139044 | ||||||||
\(320\) | −20.2532 | −1.13219 | ||||||||
\(321\) | 19.0762 | 1.06473 | ||||||||
\(322\) | −27.2184 | −1.51682 | ||||||||
\(323\) | −33.8867 | −1.88551 | ||||||||
\(324\) | 65.7490 | 3.65272 | ||||||||
\(325\) | −0.0838553 | −0.00465146 | ||||||||
\(326\) | −40.1926 | −2.22606 | ||||||||
\(327\) | 25.9683 | 1.43605 | ||||||||
\(328\) | 6.04129 | 0.333575 | ||||||||
\(329\) | 6.09195 | 0.335860 | ||||||||
\(330\) | −28.6162 | −1.57527 | ||||||||
\(331\) | 11.8930 | 0.653696 | 0.326848 | − | 0.945077i | \(-0.394013\pi\) | ||||
0.326848 | + | 0.945077i | \(0.394013\pi\) | |||||||
\(332\) | 46.4780 | 2.55081 | ||||||||
\(333\) | 5.48740 | 0.300708 | ||||||||
\(334\) | 40.3186 | 2.20613 | ||||||||
\(335\) | 17.6651 | 0.965150 | ||||||||
\(336\) | −92.5591 | −5.04951 | ||||||||
\(337\) | −33.0568 | −1.80072 | −0.900359 | − | 0.435148i | \(-0.856696\pi\) | ||||
−0.900359 | + | 0.435148i | \(0.856696\pi\) | |||||||
\(338\) | −2.61991 | −0.142504 | ||||||||
\(339\) | −18.0538 | −0.980547 | ||||||||
\(340\) | −56.7174 | −3.07593 | ||||||||
\(341\) | −10.2904 | −0.557256 | ||||||||
\(342\) | 111.183 | 6.01206 | ||||||||
\(343\) | −14.6296 | −0.789924 | ||||||||
\(344\) | 47.0356 | 2.53599 | ||||||||
\(345\) | 23.8151 | 1.28216 | ||||||||
\(346\) | 13.1117 | 0.704889 | ||||||||
\(347\) | 23.7221 | 1.27347 | 0.636734 | − | 0.771084i | \(-0.280285\pi\) | ||||
0.636734 | + | 0.771084i | \(0.280285\pi\) | |||||||
\(348\) | −23.6299 | −1.26670 | ||||||||
\(349\) | −14.1717 | −0.758594 | −0.379297 | − | 0.925275i | \(-0.623834\pi\) | ||||
−0.379297 | + | 0.925275i | \(0.623834\pi\) | |||||||
\(350\) | −0.665220 | −0.0355575 | ||||||||
\(351\) | 10.7028 | 0.571275 | ||||||||
\(352\) | −17.3238 | −0.923360 | ||||||||
\(353\) | 10.1994 | 0.542861 | 0.271430 | − | 0.962458i | \(-0.412503\pi\) | ||||
0.271430 | + | 0.962458i | \(0.412503\pi\) | |||||||
\(354\) | 39.8227 | 2.11655 | ||||||||
\(355\) | 1.27258 | 0.0675414 | ||||||||
\(356\) | 81.3796 | 4.31311 | ||||||||
\(357\) | −48.2072 | −2.55139 | ||||||||
\(358\) | 16.9434 | 0.895487 | ||||||||
\(359\) | −19.0503 | −1.00544 | −0.502718 | − | 0.864451i | \(-0.667666\pi\) | ||||
−0.502718 | + | 0.864451i | \(0.667666\pi\) | |||||||
\(360\) | 109.571 | 5.77492 | ||||||||
\(361\) | 23.9330 | 1.25963 | ||||||||
\(362\) | 17.1159 | 0.899593 | ||||||||
\(363\) | 26.2396 | 1.37722 | ||||||||
\(364\) | −14.7277 | −0.771940 | ||||||||
\(365\) | −26.7974 | −1.40264 | ||||||||
\(366\) | −31.2478 | −1.63335 | ||||||||
\(367\) | −4.61851 | −0.241084 | −0.120542 | − | 0.992708i | \(-0.538463\pi\) | ||||
−0.120542 | + | 0.992708i | \(0.538463\pi\) | |||||||
\(368\) | 34.0697 | 1.77601 | ||||||||
\(369\) | −5.21482 | −0.271473 | ||||||||
\(370\) | 5.00489 | 0.260192 | ||||||||
\(371\) | −22.3014 | −1.15783 | ||||||||
\(372\) | 97.9142 | 5.07661 | ||||||||
\(373\) | −18.3760 | −0.951472 | −0.475736 | − | 0.879588i | \(-0.657818\pi\) | ||||
−0.475736 | + | 0.879588i | \(0.657818\pi\) | |||||||
\(374\) | −21.3217 | −1.10252 | ||||||||
\(375\) | −34.1232 | −1.76212 | ||||||||
\(376\) | −15.0957 | −0.778502 | ||||||||
\(377\) | −1.57815 | −0.0812786 | ||||||||
\(378\) | 84.9049 | 4.36704 | ||||||||
\(379\) | 32.8221 | 1.68596 | 0.842979 | − | 0.537946i | \(-0.180800\pi\) | ||||
0.842979 | + | 0.537946i | \(0.180800\pi\) | |||||||
\(380\) | 71.8585 | 3.68626 | ||||||||
\(381\) | −3.92752 | −0.201213 | ||||||||
\(382\) | 29.3975 | 1.50410 | ||||||||
\(383\) | −6.60847 | −0.337677 | −0.168838 | − | 0.985644i | \(-0.554002\pi\) | ||||
−0.168838 | + | 0.985644i | \(0.554002\pi\) | |||||||
\(384\) | 4.66570 | 0.238095 | ||||||||
\(385\) | −10.7435 | −0.547540 | ||||||||
\(386\) | −44.0566 | −2.24242 | ||||||||
\(387\) | −40.6009 | −2.06386 | ||||||||
\(388\) | 90.8640 | 4.61292 | ||||||||
\(389\) | −11.1150 | −0.563553 | −0.281777 | − | 0.959480i | \(-0.590924\pi\) | ||||
−0.281777 | + | 0.959480i | \(0.590924\pi\) | |||||||
\(390\) | 18.1849 | 0.920829 | ||||||||
\(391\) | 17.7444 | 0.897373 | ||||||||
\(392\) | −16.2705 | −0.821784 | ||||||||
\(393\) | −11.6445 | −0.587385 | ||||||||
\(394\) | 28.8100 | 1.45142 | ||||||||
\(395\) | 22.1710 | 1.11555 | ||||||||
\(396\) | 49.5726 | 2.49112 | ||||||||
\(397\) | 20.8097 | 1.04441 | 0.522203 | − | 0.852821i | \(-0.325110\pi\) | ||||
0.522203 | + | 0.852821i | \(0.325110\pi\) | |||||||
\(398\) | 37.0820 | 1.85876 | ||||||||
\(399\) | 61.0764 | 3.05764 | ||||||||
\(400\) | 0.832669 | 0.0416334 | ||||||||
\(401\) | 27.0504 | 1.35083 | 0.675416 | − | 0.737437i | \(-0.263964\pi\) | ||||
0.675416 | + | 0.737437i | \(0.263964\pi\) | |||||||
\(402\) | −63.1881 | −3.15154 | ||||||||
\(403\) | 6.53929 | 0.325745 | ||||||||
\(404\) | 2.68253 | 0.133461 | ||||||||
\(405\) | −30.4790 | −1.51451 | ||||||||
\(406\) | −12.5193 | −0.621325 | ||||||||
\(407\) | 1.33325 | 0.0660869 | ||||||||
\(408\) | 119.456 | 5.91396 | ||||||||
\(409\) | −20.9713 | −1.03696 | −0.518482 | − | 0.855088i | \(-0.673503\pi\) | ||||
−0.518482 | + | 0.855088i | \(0.673503\pi\) | |||||||
\(410\) | −4.75627 | −0.234896 | ||||||||
\(411\) | 23.8816 | 1.17799 | ||||||||
\(412\) | 8.87991 | 0.437482 | ||||||||
\(413\) | 14.9508 | 0.735681 | ||||||||
\(414\) | −58.2195 | −2.86133 | ||||||||
\(415\) | −21.5456 | −1.05763 | ||||||||
\(416\) | 11.0088 | 0.539753 | ||||||||
\(417\) | −24.0840 | −1.17940 | ||||||||
\(418\) | 27.0136 | 1.32128 | ||||||||
\(419\) | −0.763132 | −0.0372814 | −0.0186407 | − | 0.999826i | \(-0.505934\pi\) | ||||
−0.0186407 | + | 0.999826i | \(0.505934\pi\) | |||||||
\(420\) | 102.226 | 4.98810 | ||||||||
\(421\) | −17.6142 | −0.858465 | −0.429232 | − | 0.903194i | \(-0.641216\pi\) | ||||
−0.429232 | + | 0.903194i | \(0.641216\pi\) | |||||||
\(422\) | 6.80233 | 0.331132 | ||||||||
\(423\) | 13.0306 | 0.633567 | ||||||||
\(424\) | 55.2623 | 2.68378 | ||||||||
\(425\) | 0.433675 | 0.0210363 | ||||||||
\(426\) | −4.55200 | −0.220545 | ||||||||
\(427\) | −11.7315 | −0.567727 | ||||||||
\(428\) | −30.1404 | −1.45689 | ||||||||
\(429\) | 4.84429 | 0.233884 | ||||||||
\(430\) | −37.0308 | −1.78578 | ||||||||
\(431\) | −26.2555 | −1.26468 | −0.632342 | − | 0.774690i | \(-0.717906\pi\) | ||||
−0.632342 | + | 0.774690i | \(0.717906\pi\) | |||||||
\(432\) | −106.277 | −5.11326 | ||||||||
\(433\) | 33.4997 | 1.60989 | 0.804947 | − | 0.593346i | \(-0.202194\pi\) | ||||
0.804947 | + | 0.593346i | \(0.202194\pi\) | |||||||
\(434\) | 51.8759 | 2.49012 | ||||||||
\(435\) | 10.9540 | 0.525204 | ||||||||
\(436\) | −41.0299 | −1.96498 | ||||||||
\(437\) | −22.4814 | −1.07543 | ||||||||
\(438\) | 95.8540 | 4.58008 | ||||||||
\(439\) | −38.7855 | −1.85113 | −0.925566 | − | 0.378586i | \(-0.876410\pi\) | ||||
−0.925566 | + | 0.378586i | \(0.876410\pi\) | |||||||
\(440\) | 26.6222 | 1.26916 | ||||||||
\(441\) | 14.0446 | 0.668791 | ||||||||
\(442\) | 13.5494 | 0.644479 | ||||||||
\(443\) | 6.40189 | 0.304163 | 0.152082 | − | 0.988368i | \(-0.451402\pi\) | ||||
0.152082 | + | 0.988368i | \(0.451402\pi\) | |||||||
\(444\) | −12.6861 | −0.602054 | ||||||||
\(445\) | −37.7247 | −1.78832 | ||||||||
\(446\) | −18.9259 | −0.896168 | ||||||||
\(447\) | −19.6936 | −0.931474 | ||||||||
\(448\) | 27.1985 | 1.28501 | ||||||||
\(449\) | −22.6788 | −1.07028 | −0.535139 | − | 0.844764i | \(-0.679741\pi\) | ||||
−0.535139 | + | 0.844764i | \(0.679741\pi\) | |||||||
\(450\) | −1.42289 | −0.0670757 | ||||||||
\(451\) | −1.26703 | −0.0596619 | ||||||||
\(452\) | 28.5250 | 1.34170 | ||||||||
\(453\) | −43.6906 | −2.05276 | ||||||||
\(454\) | −22.3595 | −1.04938 | ||||||||
\(455\) | 6.82724 | 0.320066 | ||||||||
\(456\) | −151.346 | −7.08742 | ||||||||
\(457\) | 29.9117 | 1.39921 | 0.699605 | − | 0.714529i | \(-0.253359\pi\) | ||||
0.699605 | + | 0.714529i | \(0.253359\pi\) | |||||||
\(458\) | −67.3919 | −3.14902 | ||||||||
\(459\) | −55.3519 | −2.58360 | ||||||||
\(460\) | −37.6279 | −1.75441 | ||||||||
\(461\) | 40.4632 | 1.88456 | 0.942279 | − | 0.334828i | \(-0.108678\pi\) | ||||
0.942279 | + | 0.334828i | \(0.108678\pi\) | |||||||
\(462\) | 38.4295 | 1.78790 | ||||||||
\(463\) | −27.0111 | −1.25531 | −0.627656 | − | 0.778491i | \(-0.715986\pi\) | ||||
−0.627656 | + | 0.778491i | \(0.715986\pi\) | |||||||
\(464\) | 15.6707 | 0.727494 | ||||||||
\(465\) | −45.3896 | −2.10489 | ||||||||
\(466\) | −26.7169 | −1.23764 | ||||||||
\(467\) | 40.2238 | 1.86133 | 0.930667 | − | 0.365868i | \(-0.119228\pi\) | ||||
0.930667 | + | 0.365868i | \(0.119228\pi\) | |||||||
\(468\) | −31.5022 | −1.45619 | ||||||||
\(469\) | −23.7230 | −1.09543 | ||||||||
\(470\) | 11.8848 | 0.548203 | ||||||||
\(471\) | 33.6128 | 1.54880 | ||||||||
\(472\) | −37.0477 | −1.70526 | ||||||||
\(473\) | −9.86466 | −0.453577 | ||||||||
\(474\) | −79.3057 | −3.64263 | ||||||||
\(475\) | −0.549448 | −0.0252104 | ||||||||
\(476\) | 76.1673 | 3.49112 | ||||||||
\(477\) | −47.7022 | −2.18413 | ||||||||
\(478\) | 36.9128 | 1.68835 | ||||||||
\(479\) | −11.5761 | −0.528924 | −0.264462 | − | 0.964396i | \(-0.585194\pi\) | ||||
−0.264462 | + | 0.964396i | \(0.585194\pi\) | |||||||
\(480\) | −76.4130 | −3.48776 | ||||||||
\(481\) | −0.847251 | −0.0386313 | ||||||||
\(482\) | 30.4040 | 1.38486 | ||||||||
\(483\) | −31.9820 | −1.45523 | ||||||||
\(484\) | −41.4586 | −1.88448 | ||||||||
\(485\) | −42.1214 | −1.91263 | ||||||||
\(486\) | 24.9018 | 1.12957 | ||||||||
\(487\) | 16.4261 | 0.744339 | 0.372169 | − | 0.928165i | \(-0.378614\pi\) | ||||
0.372169 | + | 0.928165i | \(0.378614\pi\) | |||||||
\(488\) | 29.0704 | 1.31595 | ||||||||
\(489\) | −47.2268 | −2.13567 | ||||||||
\(490\) | 12.8097 | 0.578681 | ||||||||
\(491\) | 35.4185 | 1.59841 | 0.799207 | − | 0.601056i | \(-0.205253\pi\) | ||||
0.799207 | + | 0.601056i | \(0.205253\pi\) | |||||||
\(492\) | 12.0559 | 0.543521 | ||||||||
\(493\) | 8.16171 | 0.367585 | ||||||||
\(494\) | −17.1665 | −0.772357 | ||||||||
\(495\) | −22.9801 | −1.03288 | ||||||||
\(496\) | −64.9340 | −2.91562 | ||||||||
\(497\) | −1.70898 | −0.0766581 | ||||||||
\(498\) | 77.0685 | 3.45352 | ||||||||
\(499\) | −15.2283 | −0.681712 | −0.340856 | − | 0.940115i | \(-0.610717\pi\) | ||||
−0.340856 | + | 0.940115i | \(0.610717\pi\) | |||||||
\(500\) | 53.9147 | 2.41114 | ||||||||
\(501\) | 47.3749 | 2.11655 | ||||||||
\(502\) | 47.9069 | 2.13819 | ||||||||
\(503\) | 3.90364 | 0.174055 | 0.0870274 | − | 0.996206i | \(-0.472263\pi\) | ||||
0.0870274 | + | 0.996206i | \(0.472263\pi\) | |||||||
\(504\) | −147.146 | −6.55442 | ||||||||
\(505\) | −1.24353 | −0.0553363 | ||||||||
\(506\) | −14.1454 | −0.628839 | ||||||||
\(507\) | −3.07843 | −0.136718 | ||||||||
\(508\) | 6.20548 | 0.275324 | ||||||||
\(509\) | −14.2478 | −0.631521 | −0.315761 | − | 0.948839i | \(-0.602260\pi\) | ||||
−0.315761 | + | 0.948839i | \(0.602260\pi\) | |||||||
\(510\) | −94.0471 | −4.16448 | ||||||||
\(511\) | 35.9869 | 1.59197 | ||||||||
\(512\) | 39.6948 | 1.75428 | ||||||||
\(513\) | 70.1284 | 3.09625 | ||||||||
\(514\) | −40.9546 | −1.80643 | ||||||||
\(515\) | −4.11642 | −0.181391 | ||||||||
\(516\) | 93.8633 | 4.13210 | ||||||||
\(517\) | 3.16599 | 0.139240 | ||||||||
\(518\) | −6.72119 | −0.295312 | ||||||||
\(519\) | 15.4064 | 0.676267 | ||||||||
\(520\) | −16.9177 | −0.741892 | ||||||||
\(521\) | −0.170959 | −0.00748986 | −0.00374493 | − | 0.999993i | \(-0.501192\pi\) | ||||
−0.00374493 | + | 0.999993i | \(0.501192\pi\) | |||||||
\(522\) | −26.7786 | −1.17207 | ||||||||
\(523\) | 18.2808 | 0.799365 | 0.399682 | − | 0.916654i | \(-0.369120\pi\) | ||||
0.399682 | + | 0.916654i | \(0.369120\pi\) | |||||||
\(524\) | 18.3982 | 0.803730 | ||||||||
\(525\) | −0.781643 | −0.0341137 | ||||||||
\(526\) | −52.5786 | −2.29254 | ||||||||
\(527\) | −33.8193 | −1.47319 | ||||||||
\(528\) | −48.1029 | −2.09341 | ||||||||
\(529\) | −11.2279 | −0.488168 | ||||||||
\(530\) | −43.5077 | −1.88985 | ||||||||
\(531\) | 31.9795 | 1.38779 | ||||||||
\(532\) | −96.5006 | −4.18383 | ||||||||
\(533\) | 0.805164 | 0.0348755 | ||||||||
\(534\) | 134.941 | 5.83947 | ||||||||
\(535\) | 13.9720 | 0.604064 | ||||||||
\(536\) | 58.7850 | 2.53912 | ||||||||
\(537\) | 19.9087 | 0.859126 | ||||||||
\(538\) | 72.2803 | 3.11623 | ||||||||
\(539\) | 3.41237 | 0.146981 | ||||||||
\(540\) | 117.376 | 5.05108 | ||||||||
\(541\) | 6.78725 | 0.291807 | 0.145903 | − | 0.989299i | \(-0.453391\pi\) | ||||
0.145903 | + | 0.989299i | \(0.453391\pi\) | |||||||
\(542\) | 21.0967 | 0.906181 | ||||||||
\(543\) | 20.1114 | 0.863065 | ||||||||
\(544\) | −56.9345 | −2.44105 | ||||||||
\(545\) | 19.0200 | 0.814729 | ||||||||
\(546\) | −24.4210 | −1.04512 | ||||||||
\(547\) | −44.3216 | −1.89506 | −0.947528 | − | 0.319673i | \(-0.896427\pi\) | ||||
−0.947528 | + | 0.319673i | \(0.896427\pi\) | |||||||
\(548\) | −37.7329 | −1.61187 | ||||||||
\(549\) | −25.0934 | −1.07096 | ||||||||
\(550\) | −0.345715 | −0.0147413 | ||||||||
\(551\) | −10.3405 | −0.440521 | ||||||||
\(552\) | 79.2505 | 3.37313 | ||||||||
\(553\) | −29.7741 | −1.26612 | ||||||||
\(554\) | 10.5346 | 0.447570 | ||||||||
\(555\) | 5.88081 | 0.249627 | ||||||||
\(556\) | 38.0527 | 1.61380 | ||||||||
\(557\) | 3.63907 | 0.154193 | 0.0770963 | − | 0.997024i | \(-0.475435\pi\) | ||||
0.0770963 | + | 0.997024i | \(0.475435\pi\) | |||||||
\(558\) | 110.961 | 4.69737 | ||||||||
\(559\) | 6.26875 | 0.265140 | ||||||||
\(560\) | −67.7933 | −2.86479 | ||||||||
\(561\) | −25.0532 | −1.05775 | ||||||||
\(562\) | −11.9579 | −0.504412 | ||||||||
\(563\) | −22.2428 | −0.937424 | −0.468712 | − | 0.883351i | \(-0.655282\pi\) | ||||
−0.468712 | + | 0.883351i | \(0.655282\pi\) | |||||||
\(564\) | −30.1247 | −1.26848 | ||||||||
\(565\) | −13.2232 | −0.556303 | ||||||||
\(566\) | −23.2822 | −0.978625 | ||||||||
\(567\) | 40.9310 | 1.71894 | ||||||||
\(568\) | 4.23480 | 0.177688 | ||||||||
\(569\) | 44.4038 | 1.86151 | 0.930753 | − | 0.365649i | \(-0.119153\pi\) | ||||
0.930753 | + | 0.365649i | \(0.119153\pi\) | |||||||
\(570\) | 119.154 | 4.99080 | ||||||||
\(571\) | 27.0038 | 1.13007 | 0.565037 | − | 0.825065i | \(-0.308862\pi\) | ||||
0.565037 | + | 0.825065i | \(0.308862\pi\) | |||||||
\(572\) | −7.65397 | −0.320029 | ||||||||
\(573\) | 34.5424 | 1.44303 | ||||||||
\(574\) | 6.38732 | 0.266602 | ||||||||
\(575\) | 0.287712 | 0.0119984 | ||||||||
\(576\) | 58.1771 | 2.42404 | ||||||||
\(577\) | −0.120802 | −0.00502907 | −0.00251454 | − | 0.999997i | \(-0.500800\pi\) | ||||
−0.00251454 | + | 0.999997i | \(0.500800\pi\) | |||||||
\(578\) | −25.5351 | −1.06212 | ||||||||
\(579\) | −51.7671 | −2.15137 | ||||||||
\(580\) | −17.3073 | −0.718647 | ||||||||
\(581\) | 28.9341 | 1.20039 | ||||||||
\(582\) | 150.668 | 6.24539 | ||||||||
\(583\) | −11.5900 | −0.480010 | ||||||||
\(584\) | −89.1746 | −3.69007 | ||||||||
\(585\) | 14.6033 | 0.603773 | ||||||||
\(586\) | 28.3813 | 1.17242 | ||||||||
\(587\) | −27.2212 | −1.12354 | −0.561770 | − | 0.827293i | \(-0.689879\pi\) | ||||
−0.561770 | + | 0.827293i | \(0.689879\pi\) | |||||||
\(588\) | −32.4691 | −1.33900 | ||||||||
\(589\) | 42.8476 | 1.76551 | ||||||||
\(590\) | 29.1675 | 1.20081 | ||||||||
\(591\) | 33.8521 | 1.39249 | ||||||||
\(592\) | 8.41305 | 0.345774 | ||||||||
\(593\) | 12.3229 | 0.506043 | 0.253021 | − | 0.967461i | \(-0.418576\pi\) | ||||
0.253021 | + | 0.967461i | \(0.418576\pi\) | |||||||
\(594\) | 44.1251 | 1.81047 | ||||||||
\(595\) | −35.3085 | −1.44751 | ||||||||
\(596\) | 31.1158 | 1.27455 | ||||||||
\(597\) | 43.5719 | 1.78328 | ||||||||
\(598\) | 8.98904 | 0.367589 | ||||||||
\(599\) | −39.2004 | −1.60168 | −0.800842 | − | 0.598876i | \(-0.795614\pi\) | ||||
−0.800842 | + | 0.598876i | \(0.795614\pi\) | |||||||
\(600\) | 1.93689 | 0.0790733 | ||||||||
\(601\) | −6.08185 | −0.248084 | −0.124042 | − | 0.992277i | \(-0.539586\pi\) | ||||
−0.124042 | + | 0.992277i | \(0.539586\pi\) | |||||||
\(602\) | 49.7297 | 2.02683 | ||||||||
\(603\) | −50.7429 | −2.06641 | ||||||||
\(604\) | 69.0311 | 2.80884 | ||||||||
\(605\) | 19.2187 | 0.781353 | ||||||||
\(606\) | 4.44809 | 0.180691 | ||||||||
\(607\) | 32.0378 | 1.30037 | 0.650187 | − | 0.759775i | \(-0.274691\pi\) | ||||
0.650187 | + | 0.759775i | \(0.274691\pi\) | |||||||
\(608\) | 72.1335 | 2.92540 | ||||||||
\(609\) | −14.7104 | −0.596096 | ||||||||
\(610\) | −22.8869 | −0.926665 | ||||||||
\(611\) | −2.01191 | −0.0813930 | ||||||||
\(612\) | 162.920 | 6.58566 | ||||||||
\(613\) | −33.9888 | −1.37280 | −0.686398 | − | 0.727226i | \(-0.740809\pi\) | ||||
−0.686398 | + | 0.727226i | \(0.740809\pi\) | |||||||
\(614\) | −45.0114 | −1.81651 | ||||||||
\(615\) | −5.58869 | −0.225358 | ||||||||
\(616\) | −35.7516 | −1.44047 | ||||||||
\(617\) | 15.9797 | 0.643318 | 0.321659 | − | 0.946856i | \(-0.395760\pi\) | ||||
0.321659 | + | 0.946856i | \(0.395760\pi\) | |||||||
\(618\) | 14.7244 | 0.592302 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | 71.7155 | 2.88016 | ||||||||
\(621\) | −36.7220 | −1.47360 | ||||||||
\(622\) | 4.16928 | 0.167173 | ||||||||
\(623\) | 50.6615 | 2.02971 | ||||||||
\(624\) | 30.5682 | 1.22371 | ||||||||
\(625\) | −25.4122 | −1.01649 | ||||||||
\(626\) | 22.9064 | 0.915525 | ||||||||
\(627\) | 31.7414 | 1.26763 | ||||||||
\(628\) | −53.1082 | −2.11925 | ||||||||
\(629\) | 4.38173 | 0.174711 | ||||||||
\(630\) | 115.847 | 4.61547 | ||||||||
\(631\) | 17.4728 | 0.695580 | 0.347790 | − | 0.937572i | \(-0.386932\pi\) | ||||
0.347790 | + | 0.937572i | \(0.386932\pi\) | |||||||
\(632\) | 73.7794 | 2.93479 | ||||||||
\(633\) | 7.99283 | 0.317686 | ||||||||
\(634\) | 30.4166 | 1.20800 | ||||||||
\(635\) | −2.87664 | −0.114156 | ||||||||
\(636\) | 110.280 | 4.37290 | ||||||||
\(637\) | −2.16848 | −0.0859182 | ||||||||
\(638\) | −6.50630 | −0.257587 | ||||||||
\(639\) | −3.65546 | −0.144608 | ||||||||
\(640\) | 3.41731 | 0.135081 | ||||||||
\(641\) | −4.26776 | −0.168566 | −0.0842832 | − | 0.996442i | \(-0.526860\pi\) | ||||
−0.0842832 | + | 0.996442i | \(0.526860\pi\) | |||||||
\(642\) | −49.9779 | −1.97247 | ||||||||
\(643\) | −8.02988 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(644\) | 50.5315 | 1.99122 | ||||||||
\(645\) | −43.5117 | −1.71327 | ||||||||
\(646\) | 88.7801 | 3.49301 | ||||||||
\(647\) | 37.4313 | 1.47158 | 0.735788 | − | 0.677212i | \(-0.236812\pi\) | ||||
0.735788 | + | 0.677212i | \(0.236812\pi\) | |||||||
\(648\) | −101.426 | −3.98439 | ||||||||
\(649\) | 7.76993 | 0.304996 | ||||||||
\(650\) | 0.219693 | 0.00861708 | ||||||||
\(651\) | 60.9549 | 2.38901 | ||||||||
\(652\) | 74.6184 | 2.92228 | ||||||||
\(653\) | 6.26870 | 0.245313 | 0.122657 | − | 0.992449i | \(-0.460859\pi\) | ||||
0.122657 | + | 0.992449i | \(0.460859\pi\) | |||||||
\(654\) | −68.0346 | −2.66036 | ||||||||
\(655\) | −8.52878 | −0.333247 | ||||||||
\(656\) | −7.99513 | −0.312158 | ||||||||
\(657\) | 76.9752 | 3.00309 | ||||||||
\(658\) | −15.9603 | −0.622199 | ||||||||
\(659\) | 43.7792 | 1.70540 | 0.852698 | − | 0.522405i | \(-0.174965\pi\) | ||||
0.852698 | + | 0.522405i | \(0.174965\pi\) | |||||||
\(660\) | 53.1266 | 2.06795 | ||||||||
\(661\) | 3.38447 | 0.131641 | 0.0658203 | − | 0.997831i | \(-0.479034\pi\) | ||||
0.0658203 | + | 0.997831i | \(0.479034\pi\) | |||||||
\(662\) | −31.1584 | −1.21101 | ||||||||
\(663\) | 15.9207 | 0.618310 | ||||||||
\(664\) | −71.6981 | −2.78243 | ||||||||
\(665\) | 44.7343 | 1.73472 | ||||||||
\(666\) | −14.3765 | −0.557077 | ||||||||
\(667\) | 5.41470 | 0.209658 | ||||||||
\(668\) | −74.8523 | −2.89612 | ||||||||
\(669\) | −22.2382 | −0.859779 | ||||||||
\(670\) | −46.2810 | −1.78799 | ||||||||
\(671\) | −6.09686 | −0.235367 | ||||||||
\(672\) | 102.617 | 3.95853 | ||||||||
\(673\) | 43.4676 | 1.67555 | 0.837777 | − | 0.546013i | \(-0.183855\pi\) | ||||
0.837777 | + | 0.546013i | \(0.183855\pi\) | |||||||
\(674\) | 86.6057 | 3.33593 | ||||||||
\(675\) | −0.897489 | −0.0345444 | ||||||||
\(676\) | 4.86391 | 0.187074 | ||||||||
\(677\) | 12.9021 | 0.495869 | 0.247934 | − | 0.968777i | \(-0.420248\pi\) | ||||
0.247934 | + | 0.968777i | \(0.420248\pi\) | |||||||
\(678\) | 47.2992 | 1.81652 | ||||||||
\(679\) | 56.5659 | 2.17080 | ||||||||
\(680\) | 87.4936 | 3.35523 | ||||||||
\(681\) | −26.2727 | −1.00677 | ||||||||
\(682\) | 26.9599 | 1.03235 | ||||||||
\(683\) | −41.9457 | −1.60501 | −0.802504 | − | 0.596647i | \(-0.796499\pi\) | ||||
−0.802504 | + | 0.596647i | \(0.796499\pi\) | |||||||
\(684\) | −206.413 | −7.89239 | ||||||||
\(685\) | 17.4917 | 0.668322 | ||||||||
\(686\) | 38.3282 | 1.46338 | ||||||||
\(687\) | −79.1864 | −3.02115 | ||||||||
\(688\) | −62.2476 | −2.37317 | ||||||||
\(689\) | 7.36518 | 0.280591 | ||||||||
\(690\) | −62.3934 | −2.37528 | ||||||||
\(691\) | −4.59172 | −0.174677 | −0.0873387 | − | 0.996179i | \(-0.527836\pi\) | ||||
−0.0873387 | + | 0.996179i | \(0.527836\pi\) | |||||||
\(692\) | −24.3422 | −0.925350 | ||||||||
\(693\) | 30.8606 | 1.17230 | ||||||||
\(694\) | −62.1496 | −2.35917 | ||||||||
\(695\) | −17.6399 | −0.669120 | ||||||||
\(696\) | 36.4520 | 1.38171 | ||||||||
\(697\) | −4.16407 | −0.157726 | ||||||||
\(698\) | 37.1285 | 1.40534 | ||||||||
\(699\) | −31.3928 | −1.18738 | ||||||||
\(700\) | 1.23499 | 0.0466784 | ||||||||
\(701\) | 23.3247 | 0.880961 | 0.440481 | − | 0.897762i | \(-0.354808\pi\) | ||||
0.440481 | + | 0.897762i | \(0.354808\pi\) | |||||||
\(702\) | −28.0404 | −1.05832 | ||||||||
\(703\) | −5.55147 | −0.209377 | ||||||||
\(704\) | 14.1351 | 0.532735 | ||||||||
\(705\) | 13.9648 | 0.525943 | ||||||||
\(706\) | −26.7215 | −1.00568 | ||||||||
\(707\) | 1.66997 | 0.0628056 | ||||||||
\(708\) | −73.9317 | −2.77852 | ||||||||
\(709\) | 34.3154 | 1.28874 | 0.644370 | − | 0.764714i | \(-0.277120\pi\) | ||||
0.644370 | + | 0.764714i | \(0.277120\pi\) | |||||||
\(710\) | −3.33403 | −0.125124 | ||||||||
\(711\) | −63.6861 | −2.38841 | ||||||||
\(712\) | −125.538 | −4.70474 | ||||||||
\(713\) | −22.4367 | −0.840260 | ||||||||
\(714\) | 126.298 | 4.72659 | ||||||||
\(715\) | 3.54811 | 0.132692 | ||||||||
\(716\) | −31.4558 | −1.17556 | ||||||||
\(717\) | 43.3731 | 1.61980 | ||||||||
\(718\) | 49.9100 | 1.86262 | ||||||||
\(719\) | 28.6663 | 1.06907 | 0.534537 | − | 0.845145i | \(-0.320486\pi\) | ||||
0.534537 | + | 0.845145i | \(0.320486\pi\) | |||||||
\(720\) | −145.008 | −5.40414 | ||||||||
\(721\) | 5.52804 | 0.205875 | ||||||||
\(722\) | −62.7023 | −2.33354 | ||||||||
\(723\) | 35.7251 | 1.32863 | ||||||||
\(724\) | −31.7761 | −1.18095 | ||||||||
\(725\) | 0.132336 | 0.00491483 | ||||||||
\(726\) | −68.7454 | −2.55138 | ||||||||
\(727\) | −12.5789 | −0.466525 | −0.233263 | − | 0.972414i | \(-0.574940\pi\) | ||||
−0.233263 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(728\) | 22.7193 | 0.842032 | ||||||||
\(729\) | −11.2932 | −0.418265 | ||||||||
\(730\) | 70.2066 | 2.59846 | ||||||||
\(731\) | −32.4201 | −1.19910 | ||||||||
\(732\) | 58.0123 | 2.14419 | ||||||||
\(733\) | 9.64377 | 0.356201 | 0.178100 | − | 0.984012i | \(-0.443005\pi\) | ||||
0.178100 | + | 0.984012i | \(0.443005\pi\) | |||||||
\(734\) | 12.1001 | 0.446622 | ||||||||
\(735\) | 15.0515 | 0.555184 | ||||||||
\(736\) | −37.7719 | −1.39229 | ||||||||
\(737\) | −12.3288 | −0.454138 | ||||||||
\(738\) | 13.6623 | 0.502918 | ||||||||
\(739\) | −6.94496 | −0.255475 | −0.127737 | − | 0.991808i | \(-0.540771\pi\) | ||||
−0.127737 | + | 0.991808i | \(0.540771\pi\) | |||||||
\(740\) | −9.29168 | −0.341569 | ||||||||
\(741\) | −20.1709 | −0.740996 | ||||||||
\(742\) | 58.4276 | 2.14494 | ||||||||
\(743\) | −11.9683 | −0.439074 | −0.219537 | − | 0.975604i | \(-0.570455\pi\) | ||||
−0.219537 | + | 0.975604i | \(0.570455\pi\) | |||||||
\(744\) | −151.045 | −5.53757 | ||||||||
\(745\) | −14.4242 | −0.528463 | ||||||||
\(746\) | 48.1434 | 1.76265 | ||||||||
\(747\) | 61.8895 | 2.26442 | ||||||||
\(748\) | 39.5841 | 1.44734 | ||||||||
\(749\) | −18.7634 | −0.685600 | ||||||||
\(750\) | 89.3997 | 3.26442 | ||||||||
\(751\) | 1.52014 | 0.0554707 | 0.0277353 | − | 0.999615i | \(-0.491170\pi\) | ||||
0.0277353 | + | 0.999615i | \(0.491170\pi\) | |||||||
\(752\) | 19.9779 | 0.728518 | ||||||||
\(753\) | 56.2913 | 2.05137 | ||||||||
\(754\) | 4.13460 | 0.150573 | ||||||||
\(755\) | −32.0004 | −1.16461 | ||||||||
\(756\) | −157.628 | −5.73287 | ||||||||
\(757\) | 0.104780 | 0.00380828 | 0.00190414 | − | 0.999998i | \(-0.499394\pi\) | ||||
0.00190414 | + | 0.999998i | \(0.499394\pi\) | |||||||
\(758\) | −85.9909 | −3.12333 | ||||||||
\(759\) | −16.6210 | −0.603305 | ||||||||
\(760\) | −110.851 | −4.02097 | ||||||||
\(761\) | −31.3178 | −1.13527 | −0.567635 | − | 0.823280i | \(-0.692142\pi\) | ||||
−0.567635 | + | 0.823280i | \(0.692142\pi\) | |||||||
\(762\) | 10.2897 | 0.372758 | ||||||||
\(763\) | −25.5425 | −0.924701 | ||||||||
\(764\) | −54.5770 | −1.97453 | ||||||||
\(765\) | −75.5241 | −2.73058 | ||||||||
\(766\) | 17.3136 | 0.625565 | ||||||||
\(767\) | −4.93760 | −0.178286 | ||||||||
\(768\) | 43.0802 | 1.55452 | ||||||||
\(769\) | 24.8190 | 0.894995 | 0.447497 | − | 0.894285i | \(-0.352315\pi\) | ||||
0.447497 | + | 0.894285i | \(0.352315\pi\) | |||||||
\(770\) | 28.1470 | 1.01435 | ||||||||
\(771\) | −48.1222 | −1.73308 | ||||||||
\(772\) | 81.7920 | 2.94376 | ||||||||
\(773\) | 43.2999 | 1.55739 | 0.778694 | − | 0.627404i | \(-0.215882\pi\) | ||||
0.778694 | + | 0.627404i | \(0.215882\pi\) | |||||||
\(774\) | 106.371 | 3.82341 | ||||||||
\(775\) | −0.548355 | −0.0196975 | ||||||||
\(776\) | −140.169 | −5.03177 | ||||||||
\(777\) | −7.89750 | −0.283321 | ||||||||
\(778\) | 29.1203 | 1.04401 | ||||||||
\(779\) | 5.27570 | 0.189022 | ||||||||
\(780\) | −33.7607 | −1.20883 | ||||||||
\(781\) | −0.888155 | −0.0317807 | ||||||||
\(782\) | −46.4887 | −1.66243 | ||||||||
\(783\) | −16.8906 | −0.603621 | ||||||||
\(784\) | 21.5326 | 0.769021 | ||||||||
\(785\) | 24.6191 | 0.878693 | ||||||||
\(786\) | 30.5074 | 1.08816 | ||||||||
\(787\) | −44.6138 | −1.59031 | −0.795155 | − | 0.606407i | \(-0.792610\pi\) | ||||
−0.795155 | + | 0.606407i | \(0.792610\pi\) | |||||||
\(788\) | −53.4863 | −1.90537 | ||||||||
\(789\) | −61.7806 | −2.19945 | ||||||||
\(790\) | −58.0861 | −2.06661 | ||||||||
\(791\) | 17.7577 | 0.631393 | ||||||||
\(792\) | −76.4719 | −2.71731 | ||||||||
\(793\) | 3.87440 | 0.137584 | ||||||||
\(794\) | −54.5194 | −1.93482 | ||||||||
\(795\) | −51.1221 | −1.81312 | ||||||||
\(796\) | −68.8436 | −2.44010 | ||||||||
\(797\) | 38.6604 | 1.36942 | 0.684712 | − | 0.728814i | \(-0.259928\pi\) | ||||
0.684712 | + | 0.728814i | \(0.259928\pi\) | |||||||
\(798\) | −160.014 | −5.66445 | ||||||||
\(799\) | 10.4050 | 0.368102 | ||||||||
\(800\) | −0.923150 | −0.0326383 | ||||||||
\(801\) | 108.364 | 3.82885 | ||||||||
\(802\) | −70.8695 | −2.50249 | ||||||||
\(803\) | 18.7024 | 0.659992 | ||||||||
\(804\) | 117.310 | 4.13721 | ||||||||
\(805\) | −23.4246 | −0.825610 | ||||||||
\(806\) | −17.1323 | −0.603461 | ||||||||
\(807\) | 84.9304 | 2.98969 | ||||||||
\(808\) | −4.13814 | −0.145579 | ||||||||
\(809\) | −49.6228 | −1.74464 | −0.872322 | − | 0.488932i | \(-0.837387\pi\) | ||||
−0.872322 | + | 0.488932i | \(0.837387\pi\) | |||||||
\(810\) | 79.8520 | 2.80571 | ||||||||
\(811\) | 30.0356 | 1.05469 | 0.527346 | − | 0.849650i | \(-0.323187\pi\) | ||||
0.527346 | + | 0.849650i | \(0.323187\pi\) | |||||||
\(812\) | 23.2424 | 0.815649 | ||||||||
\(813\) | 24.7889 | 0.869385 | ||||||||
\(814\) | −3.49300 | −0.122430 | ||||||||
\(815\) | −34.5905 | −1.21165 | ||||||||
\(816\) | −158.090 | −5.53426 | ||||||||
\(817\) | 41.0749 | 1.43703 | ||||||||
\(818\) | 54.9429 | 1.92103 | ||||||||
\(819\) | −19.6112 | −0.685270 | ||||||||
\(820\) | 8.83012 | 0.308361 | ||||||||
\(821\) | 36.0092 | 1.25673 | 0.628364 | − | 0.777919i | \(-0.283725\pi\) | ||||
0.628364 | + | 0.777919i | \(0.283725\pi\) | |||||||
\(822\) | −62.5676 | −2.18229 | ||||||||
\(823\) | 10.2217 | 0.356307 | 0.178153 | − | 0.984003i | \(-0.442988\pi\) | ||||
0.178153 | + | 0.984003i | \(0.442988\pi\) | |||||||
\(824\) | −13.6984 | −0.477205 | ||||||||
\(825\) | −0.406220 | −0.0141427 | ||||||||
\(826\) | −39.1697 | −1.36289 | ||||||||
\(827\) | 26.1343 | 0.908778 | 0.454389 | − | 0.890803i | \(-0.349858\pi\) | ||||
0.454389 | + | 0.890803i | \(0.349858\pi\) | |||||||
\(828\) | 108.086 | 3.75624 | ||||||||
\(829\) | −55.8341 | −1.93920 | −0.969599 | − | 0.244701i | \(-0.921310\pi\) | ||||
−0.969599 | + | 0.244701i | \(0.921310\pi\) | |||||||
\(830\) | 56.4475 | 1.95932 | ||||||||
\(831\) | 12.3783 | 0.429397 | ||||||||
\(832\) | −8.98249 | −0.311412 | ||||||||
\(833\) | 11.2147 | 0.388568 | ||||||||
\(834\) | 63.0979 | 2.18490 | ||||||||
\(835\) | 34.6989 | 1.20081 | ||||||||
\(836\) | −50.1513 | −1.73452 | ||||||||
\(837\) | 69.9889 | 2.41917 | ||||||||
\(838\) | 1.99933 | 0.0690658 | ||||||||
\(839\) | 49.7062 | 1.71605 | 0.858024 | − | 0.513610i | \(-0.171692\pi\) | ||||
0.858024 | + | 0.513610i | \(0.171692\pi\) | |||||||
\(840\) | −157.696 | −5.44102 | ||||||||
\(841\) | −26.5095 | −0.914119 | ||||||||
\(842\) | 46.1476 | 1.59035 | ||||||||
\(843\) | −14.0507 | −0.483931 | ||||||||
\(844\) | −12.6287 | −0.434696 | ||||||||
\(845\) | −2.25474 | −0.0775654 | ||||||||
\(846\) | −34.1388 | −1.17372 | ||||||||
\(847\) | −25.8094 | −0.886820 | ||||||||
\(848\) | −73.1349 | −2.51146 | ||||||||
\(849\) | −27.3570 | −0.938888 | ||||||||
\(850\) | −1.13619 | −0.0389710 | ||||||||
\(851\) | 2.90696 | 0.0996494 | ||||||||
\(852\) | 8.45089 | 0.289523 | ||||||||
\(853\) | 41.6718 | 1.42682 | 0.713408 | − | 0.700749i | \(-0.247151\pi\) | ||||
0.713408 | + | 0.700749i | \(0.247151\pi\) | |||||||
\(854\) | 30.7354 | 1.05175 | ||||||||
\(855\) | 95.6858 | 3.27238 | ||||||||
\(856\) | 46.4953 | 1.58918 | ||||||||
\(857\) | 11.9968 | 0.409804 | 0.204902 | − | 0.978783i | \(-0.434312\pi\) | ||||
0.204902 | + | 0.978783i | \(0.434312\pi\) | |||||||
\(858\) | −12.6916 | −0.433284 | ||||||||
\(859\) | 13.4387 | 0.458522 | 0.229261 | − | 0.973365i | \(-0.426369\pi\) | ||||
0.229261 | + | 0.973365i | \(0.426369\pi\) | |||||||
\(860\) | 68.7485 | 2.34430 | ||||||||
\(861\) | 7.50519 | 0.255776 | ||||||||
\(862\) | 68.7870 | 2.34289 | ||||||||
\(863\) | −14.2319 | −0.484460 | −0.242230 | − | 0.970219i | \(-0.577879\pi\) | ||||
−0.242230 | + | 0.970219i | \(0.577879\pi\) | |||||||
\(864\) | 117.826 | 4.00851 | ||||||||
\(865\) | 11.2842 | 0.383673 | ||||||||
\(866\) | −87.7662 | −2.98242 | ||||||||
\(867\) | −30.0041 | −1.01899 | ||||||||
\(868\) | −96.3086 | −3.26893 | ||||||||
\(869\) | −15.4736 | −0.524905 | ||||||||
\(870\) | −28.6985 | −0.972969 | ||||||||
\(871\) | 7.83467 | 0.265468 | ||||||||
\(872\) | 63.2937 | 2.14339 | ||||||||
\(873\) | 120.993 | 4.09500 | ||||||||
\(874\) | 58.8992 | 1.99229 | ||||||||
\(875\) | 33.5637 | 1.13466 | ||||||||
\(876\) | −177.955 | −6.01254 | ||||||||
\(877\) | −26.3854 | −0.890970 | −0.445485 | − | 0.895289i | \(-0.646969\pi\) | ||||
−0.445485 | + | 0.895289i | \(0.646969\pi\) | |||||||
\(878\) | 101.614 | 3.42932 | ||||||||
\(879\) | 33.3484 | 1.12481 | ||||||||
\(880\) | −35.2321 | −1.18768 | ||||||||
\(881\) | 36.8854 | 1.24270 | 0.621351 | − | 0.783533i | \(-0.286584\pi\) | ||||
0.621351 | + | 0.783533i | \(0.286584\pi\) | |||||||
\(882\) | −36.7956 | −1.23897 | ||||||||
\(883\) | 10.4031 | 0.350091 | 0.175046 | − | 0.984560i | \(-0.443993\pi\) | ||||
0.175046 | + | 0.984560i | \(0.443993\pi\) | |||||||
\(884\) | −25.1547 | −0.846045 | ||||||||
\(885\) | 34.2722 | 1.15205 | ||||||||
\(886\) | −16.7724 | −0.563479 | ||||||||
\(887\) | −47.6956 | −1.60146 | −0.800730 | − | 0.599025i | \(-0.795555\pi\) | ||||
−0.800730 | + | 0.599025i | \(0.795555\pi\) | |||||||
\(888\) | 19.5698 | 0.656720 | ||||||||
\(889\) | 3.86312 | 0.129565 | ||||||||
\(890\) | 98.8353 | 3.31297 | ||||||||
\(891\) | 21.2718 | 0.712633 | ||||||||
\(892\) | 35.1364 | 1.17645 | ||||||||
\(893\) | −13.1827 | −0.441142 | ||||||||
\(894\) | 51.5954 | 1.72561 | ||||||||
\(895\) | 14.5818 | 0.487416 | ||||||||
\(896\) | −4.58919 | −0.153314 | ||||||||
\(897\) | 10.5623 | 0.352663 | ||||||||
\(898\) | 59.4164 | 1.98275 | ||||||||
\(899\) | −10.3200 | −0.344190 | ||||||||
\(900\) | 2.64163 | 0.0880542 | ||||||||
\(901\) | −38.0906 | −1.26898 | ||||||||
\(902\) | 3.31949 | 0.110527 | ||||||||
\(903\) | 58.4330 | 1.94453 | ||||||||
\(904\) | −44.0033 | −1.46353 | ||||||||
\(905\) | 14.7303 | 0.489651 | ||||||||
\(906\) | 114.465 | 3.80286 | ||||||||
\(907\) | −11.6537 | −0.386953 | −0.193477 | − | 0.981105i | \(-0.561976\pi\) | ||||
−0.193477 | + | 0.981105i | \(0.561976\pi\) | |||||||
\(908\) | 41.5109 | 1.37759 | ||||||||
\(909\) | 3.57202 | 0.118476 | ||||||||
\(910\) | −17.8867 | −0.592940 | ||||||||
\(911\) | −24.9507 | −0.826655 | −0.413327 | − | 0.910583i | \(-0.635633\pi\) | ||||
−0.413327 | + | 0.910583i | \(0.635633\pi\) | |||||||
\(912\) | 200.293 | 6.63237 | ||||||||
\(913\) | 15.0371 | 0.497654 | ||||||||
\(914\) | −78.3659 | −2.59211 | ||||||||
\(915\) | −26.8925 | −0.889037 | ||||||||
\(916\) | 125.114 | 4.13390 | ||||||||
\(917\) | 11.4535 | 0.378228 | ||||||||
\(918\) | 145.017 | 4.78627 | ||||||||
\(919\) | 40.5180 | 1.33657 | 0.668283 | − | 0.743908i | \(-0.267030\pi\) | ||||
0.668283 | + | 0.743908i | \(0.267030\pi\) | |||||||
\(920\) | 58.0457 | 1.91371 | ||||||||
\(921\) | −52.8890 | −1.74275 | ||||||||
\(922\) | −106.010 | −3.49125 | ||||||||
\(923\) | 0.564401 | 0.0185775 | ||||||||
\(924\) | −71.3451 | −2.34708 | ||||||||
\(925\) | 0.0710465 | 0.00233599 | ||||||||
\(926\) | 70.7666 | 2.32553 | ||||||||
\(927\) | 11.8244 | 0.388363 | ||||||||
\(928\) | −17.3736 | −0.570315 | ||||||||
\(929\) | 3.21121 | 0.105356 | 0.0526781 | − | 0.998612i | \(-0.483224\pi\) | ||||
0.0526781 | + | 0.998612i | \(0.483224\pi\) | |||||||
\(930\) | 118.917 | 3.89943 | ||||||||
\(931\) | −14.2086 | −0.465668 | ||||||||
\(932\) | 49.6005 | 1.62472 | ||||||||
\(933\) | 4.89896 | 0.160385 | ||||||||
\(934\) | −105.383 | −3.44822 | ||||||||
\(935\) | −18.3498 | −0.600103 | ||||||||
\(936\) | 48.5960 | 1.58841 | ||||||||
\(937\) | −27.9478 | −0.913014 | −0.456507 | − | 0.889720i | \(-0.650900\pi\) | ||||
−0.456507 | + | 0.889720i | \(0.650900\pi\) | |||||||
\(938\) | 62.1520 | 2.02933 | ||||||||
\(939\) | 26.9154 | 0.878350 | ||||||||
\(940\) | −22.0643 | −0.719658 | ||||||||
\(941\) | 1.75190 | 0.0571102 | 0.0285551 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285551 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(942\) | −88.0624 | −2.86923 | ||||||||
\(943\) | −2.76256 | −0.0899614 | ||||||||
\(944\) | 49.0295 | 1.59577 | ||||||||
\(945\) | 73.0708 | 2.37699 | ||||||||
\(946\) | 25.8445 | 0.840277 | ||||||||
\(947\) | −39.1647 | −1.27268 | −0.636340 | − | 0.771408i | \(-0.719553\pi\) | ||||
−0.636340 | + | 0.771408i | \(0.719553\pi\) | |||||||
\(948\) | 147.233 | 4.78190 | ||||||||
\(949\) | −11.8849 | −0.385800 | ||||||||
\(950\) | 1.43950 | 0.0467036 | ||||||||
\(951\) | 35.7399 | 1.15895 | ||||||||
\(952\) | −117.497 | −3.80811 | ||||||||
\(953\) | −20.7747 | −0.672959 | −0.336480 | − | 0.941691i | \(-0.609236\pi\) | ||||
−0.336480 | + | 0.941691i | \(0.609236\pi\) | |||||||
\(954\) | 124.975 | 4.04623 | ||||||||
\(955\) | 25.3000 | 0.818689 | ||||||||
\(956\) | −68.5294 | −2.21640 | ||||||||
\(957\) | −7.64499 | −0.247128 | ||||||||
\(958\) | 30.3282 | 0.979860 | ||||||||
\(959\) | −23.4900 | −0.758532 | ||||||||
\(960\) | 62.3480 | 2.01227 | ||||||||
\(961\) | 11.7624 | 0.379431 | ||||||||
\(962\) | 2.21972 | 0.0715666 | ||||||||
\(963\) | −40.1345 | −1.29332 | ||||||||
\(964\) | −56.4456 | −1.81799 | ||||||||
\(965\) | −37.9159 | −1.22056 | ||||||||
\(966\) | 83.7898 | 2.69589 | ||||||||
\(967\) | 1.95654 | 0.0629180 | 0.0314590 | − | 0.999505i | \(-0.489985\pi\) | ||||
0.0314590 | + | 0.999505i | \(0.489985\pi\) | |||||||
\(968\) | 63.9549 | 2.05559 | ||||||||
\(969\) | 104.318 | 3.35117 | ||||||||
\(970\) | 110.354 | 3.54326 | ||||||||
\(971\) | −43.4425 | −1.39414 | −0.697068 | − | 0.717005i | \(-0.745513\pi\) | ||||
−0.697068 | + | 0.717005i | \(0.745513\pi\) | |||||||
\(972\) | −46.2308 | −1.48285 | ||||||||
\(973\) | 23.6891 | 0.759438 | ||||||||
\(974\) | −43.0349 | −1.37893 | ||||||||
\(975\) | 0.258143 | 0.00826718 | ||||||||
\(976\) | −38.4721 | −1.23146 | ||||||||
\(977\) | 22.2890 | 0.713087 | 0.356544 | − | 0.934279i | \(-0.383955\pi\) | ||||
0.356544 | + | 0.934279i | \(0.383955\pi\) | |||||||
\(978\) | 123.730 | 3.95645 | ||||||||
\(979\) | 26.3288 | 0.841471 | ||||||||
\(980\) | −23.7814 | −0.759669 | ||||||||
\(981\) | −54.6349 | −1.74436 | ||||||||
\(982\) | −92.7932 | −2.96115 | ||||||||
\(983\) | 39.7994 | 1.26940 | 0.634701 | − | 0.772758i | \(-0.281123\pi\) | ||||
0.634701 | + | 0.772758i | \(0.281123\pi\) | |||||||
\(984\) | −18.5977 | −0.592873 | ||||||||
\(985\) | 24.7944 | 0.790015 | ||||||||
\(986\) | −21.3829 | −0.680971 | ||||||||
\(987\) | −18.7536 | −0.596935 | ||||||||
\(988\) | 31.8700 | 1.01392 | ||||||||
\(989\) | −21.5084 | −0.683928 | ||||||||
\(990\) | 60.2058 | 1.91347 | ||||||||
\(991\) | 36.0335 | 1.14464 | 0.572320 | − | 0.820030i | \(-0.306043\pi\) | ||||
0.572320 | + | 0.820030i | \(0.306043\pi\) | |||||||
\(992\) | 71.9900 | 2.28569 | ||||||||
\(993\) | −36.6116 | −1.16183 | ||||||||
\(994\) | 4.47736 | 0.142013 | ||||||||
\(995\) | 31.9135 | 1.01173 | ||||||||
\(996\) | −143.079 | −4.53364 | ||||||||
\(997\) | −25.7806 | −0.816479 | −0.408239 | − | 0.912875i | \(-0.633857\pi\) | ||||
−0.408239 | + | 0.912875i | \(0.633857\pi\) | |||||||
\(998\) | 39.8967 | 1.26291 | ||||||||
\(999\) | −9.06797 | −0.286898 |
(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 | 8047.2.a.d.1.6 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.d.1.6 | ✓ | 156 | 1.1 | even | 1 | trivial |