Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), not minimal) |
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: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.4 | ||
Character | \(\chi\) | \(=\) | 605.81 |
Dual form | 605.2.g.q.366.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.389057 | + | 0.282666i | 0.275105 | + | 0.199875i | 0.716779 | − | 0.697300i | \(-0.245615\pi\) |
−0.441675 | + | 0.897175i | \(0.645615\pi\) | |||||||
\(3\) | −0.494946 | + | 1.52329i | −0.285757 | + | 0.879470i | 0.700413 | + | 0.713737i | \(0.252999\pi\) |
−0.986171 | + | 0.165733i | \(0.947001\pi\) | |||||||
\(4\) | −0.546569 | − | 1.68217i | −0.273284 | − | 0.841083i | ||||
\(5\) | −0.809017 | + | 0.587785i | −0.361803 | + | 0.262866i | ||||
\(6\) | −0.623145 | + | 0.452741i | −0.254398 | + | 0.184831i | ||||
\(7\) | 0.148607 | + | 0.457364i | 0.0561680 | + | 0.172867i | 0.975205 | − | 0.221305i | \(-0.0710315\pi\) |
−0.919037 | + | 0.394172i | \(0.871031\pi\) | |||||||
\(8\) | 0.560059 | − | 1.72368i | 0.198011 | − | 0.609414i | ||||
\(9\) | 0.351618 | + | 0.255466i | 0.117206 | + | 0.0851552i | ||||
\(10\) | −0.480901 | −0.152074 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.83294 | 0.817801 | ||||||||
\(13\) | 3.87971 | + | 2.81878i | 1.07604 | + | 0.781788i | 0.976988 | − | 0.213295i | \(-0.0684194\pi\) |
0.0990507 | + | 0.995082i | \(0.468419\pi\) | |||||||
\(14\) | −0.0714650 | + | 0.219947i | −0.0190998 | + | 0.0587832i | ||||
\(15\) | −0.494946 | − | 1.52329i | −0.127795 | − | 0.393311i | ||||
\(16\) | −2.15675 | + | 1.56697i | −0.539188 | + | 0.391743i | ||||
\(17\) | −2.02440 | + | 1.47081i | −0.490990 | + | 0.356725i | −0.805565 | − | 0.592508i | \(-0.798138\pi\) |
0.314575 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(18\) | 0.0645880 | + | 0.198781i | 0.0152235 | + | 0.0468532i | ||||
\(19\) | −1.77913 | + | 5.47560i | −0.408161 | + | 1.25619i | 0.510066 | + | 0.860135i | \(0.329621\pi\) |
−0.918227 | + | 0.396055i | \(0.870379\pi\) | |||||||
\(20\) | 1.43094 | + | 1.03964i | 0.319967 | + | 0.232470i | ||||
\(21\) | −0.770249 | −0.168082 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43462 | 0.924683 | 0.462342 | − | 0.886702i | \(-0.347009\pi\) | ||||
0.462342 | + | 0.886702i | \(0.347009\pi\) | |||||||
\(24\) | 2.34847 | + | 1.70626i | 0.479379 | + | 0.348289i | ||||
\(25\) | 0.309017 | − | 0.951057i | 0.0618034 | − | 0.190211i | ||||
\(26\) | 0.712656 | + | 2.19333i | 0.139763 | + | 0.430147i | ||||
\(27\) | −4.45054 | + | 3.23350i | −0.856506 | + | 0.622288i | ||||
\(28\) | 0.688138 | − | 0.499962i | 0.130046 | − | 0.0944839i | ||||
\(29\) | 2.78501 | + | 8.57138i | 0.517163 | + | 1.59167i | 0.779311 | + | 0.626637i | \(0.215569\pi\) |
−0.262148 | + | 0.965028i | \(0.584431\pi\) | |||||||
\(30\) | 0.238020 | − | 0.732550i | 0.0434563 | − | 0.133745i | ||||
\(31\) | −6.44956 | − | 4.68588i | −1.15837 | − | 0.841609i | −0.168803 | − | 0.985650i | \(-0.553990\pi\) |
−0.989572 | + | 0.144041i | \(0.953990\pi\) | |||||||
\(32\) | −4.90680 | −0.867409 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.20336 | −0.206374 | ||||||||
\(35\) | −0.389057 | − | 0.282666i | −0.0657626 | − | 0.0477794i | ||||
\(36\) | 0.237552 | − | 0.731110i | 0.0395920 | − | 0.121852i | ||||
\(37\) | 1.60793 | + | 4.94869i | 0.264341 | + | 0.813559i | 0.991844 | + | 0.127455i | \(0.0406807\pi\) |
−0.727503 | + | 0.686105i | \(0.759319\pi\) | |||||||
\(38\) | −2.23995 | + | 1.62742i | −0.363368 | + | 0.264003i | ||||
\(39\) | −6.21405 | + | 4.51478i | −0.995045 | + | 0.722943i | ||||
\(40\) | 0.560059 | + | 1.72368i | 0.0885530 | + | 0.272538i | ||||
\(41\) | −2.61158 | + | 8.03761i | −0.407860 | + | 1.25526i | 0.510624 | + | 0.859804i | \(0.329415\pi\) |
−0.918483 | + | 0.395459i | \(0.870585\pi\) | |||||||
\(42\) | −0.299671 | − | 0.217724i | −0.0462402 | − | 0.0335955i | ||||
\(43\) | 8.53158 | 1.30105 | 0.650527 | − | 0.759483i | \(-0.274548\pi\) | ||||
0.650527 | + | 0.759483i | \(0.274548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.434624 | −0.0647899 | ||||||||
\(46\) | 1.72532 | + | 1.25352i | 0.254385 | + | 0.184821i | ||||
\(47\) | 2.96708 | − | 9.13174i | 0.432793 | − | 1.33200i | −0.462538 | − | 0.886600i | \(-0.653061\pi\) |
0.895331 | − | 0.445401i | \(-0.146939\pi\) | |||||||
\(48\) | −1.31947 | − | 4.06092i | −0.190449 | − | 0.586143i | ||||
\(49\) | 5.47602 | − | 3.97856i | 0.782289 | − | 0.568366i | ||||
\(50\) | 0.389057 | − | 0.282666i | 0.0550210 | − | 0.0399751i | ||||
\(51\) | −1.23850 | − | 3.81172i | −0.173425 | − | 0.533748i | ||||
\(52\) | 2.62112 | − | 8.06698i | 0.363484 | − | 1.11869i | ||||
\(53\) | −4.93542 | − | 3.58579i | −0.677932 | − | 0.492546i | 0.194739 | − | 0.980855i | \(-0.437614\pi\) |
−0.872671 | + | 0.488309i | \(0.837614\pi\) | |||||||
\(54\) | −2.64552 | −0.360009 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.871579 | 0.116470 | ||||||||
\(57\) | −7.46034 | − | 5.42026i | −0.988147 | − | 0.717931i | ||||
\(58\) | −1.33931 | + | 4.12198i | −0.175861 | + | 0.541243i | ||||
\(59\) | 0.855586 | + | 2.63322i | 0.111388 | + | 0.342816i | 0.991177 | − | 0.132549i | \(-0.0423160\pi\) |
−0.879789 | + | 0.475365i | \(0.842316\pi\) | |||||||
\(60\) | −2.29190 | + | 1.66516i | −0.295883 | + | 0.214972i | ||||
\(61\) | −3.25657 | + | 2.36604i | −0.416961 | + | 0.302940i | −0.776414 | − | 0.630223i | \(-0.782963\pi\) |
0.359453 | + | 0.933163i | \(0.382963\pi\) | |||||||
\(62\) | −1.18471 | − | 3.64615i | −0.150458 | − | 0.463061i | ||||
\(63\) | −0.0645880 | + | 0.198781i | −0.00813732 | + | 0.0250441i | ||||
\(64\) | 2.40447 | + | 1.74695i | 0.300559 | + | 0.218369i | ||||
\(65\) | −4.79559 | −0.594820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.60168 | 0.928693 | 0.464346 | − | 0.885654i | \(-0.346289\pi\) | ||||
0.464346 | + | 0.885654i | \(0.346289\pi\) | |||||||
\(68\) | 3.58063 | + | 2.60148i | 0.434215 | + | 0.315476i | ||||
\(69\) | −2.19490 | + | 6.75521i | −0.264235 | + | 0.813231i | ||||
\(70\) | −0.0714650 | − | 0.219947i | −0.00854170 | − | 0.0262887i | ||||
\(71\) | 2.23995 | − | 1.62742i | 0.265834 | − | 0.193139i | −0.446881 | − | 0.894593i | \(-0.647465\pi\) |
0.712715 | + | 0.701454i | \(0.247465\pi\) | |||||||
\(72\) | 0.637268 | − | 0.463003i | 0.0751028 | − | 0.0545654i | ||||
\(73\) | −1.54651 | − | 4.75966i | −0.181005 | − | 0.557076i | 0.818852 | − | 0.574005i | \(-0.194611\pi\) |
−0.999857 | + | 0.0169292i | \(0.994611\pi\) | |||||||
\(74\) | −0.773253 | + | 2.37983i | −0.0898889 | + | 0.276649i | ||||
\(75\) | 1.29579 | + | 0.941443i | 0.149624 | + | 0.108709i | ||||
\(76\) | 10.1833 | 1.16810 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.69380 | −0.418240 | ||||||||
\(79\) | 2.93251 | + | 2.13059i | 0.329933 | + | 0.239710i | 0.740402 | − | 0.672164i | \(-0.234635\pi\) |
−0.410469 | + | 0.911874i | \(0.634635\pi\) | |||||||
\(80\) | 0.823805 | − | 2.53541i | 0.0921042 | − | 0.283468i | ||||
\(81\) | −2.31986 | − | 7.13980i | −0.257762 | − | 0.793311i | ||||
\(82\) | −3.28802 | + | 2.38888i | −0.363101 | + | 0.263808i | ||||
\(83\) | 1.38713 | − | 1.00781i | 0.152258 | − | 0.110622i | −0.509048 | − | 0.860738i | \(-0.670002\pi\) |
0.661306 | + | 0.750116i | \(0.270002\pi\) | |||||||
\(84\) | 0.420994 | + | 1.29569i | 0.0459342 | + | 0.141371i | ||||
\(85\) | 0.773253 | − | 2.37983i | 0.0838711 | − | 0.258129i | ||||
\(86\) | 3.31927 | + | 2.41159i | 0.357926 | + | 0.260049i | ||||
\(87\) | −14.4351 | −1.54761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7408 | −1.66852 | −0.834262 | − | 0.551368i | \(-0.814106\pi\) | ||||
−0.834262 | + | 0.551368i | \(0.814106\pi\) | |||||||
\(90\) | −0.169094 | − | 0.122854i | −0.0178240 | − | 0.0129499i | ||||
\(91\) | −0.712656 | + | 2.19333i | −0.0747066 | + | 0.229923i | ||||
\(92\) | −2.42383 | − | 7.45977i | −0.252702 | − | 0.777735i | ||||
\(93\) | 10.3301 | − | 7.50527i | 1.07118 | − | 0.778261i | ||||
\(94\) | 3.73560 | − | 2.71407i | 0.385298 | − | 0.279935i | ||||
\(95\) | −1.77913 | − | 5.47560i | −0.182535 | − | 0.561785i | ||||
\(96\) | 2.42860 | − | 7.47447i | 0.247868 | − | 0.762860i | ||||
\(97\) | 2.94319 | + | 2.13835i | 0.298836 | + | 0.217117i | 0.727091 | − | 0.686541i | \(-0.240872\pi\) |
−0.428256 | + | 0.903658i | \(0.640872\pi\) | |||||||
\(98\) | 3.25509 | 0.328814 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.76873 | −0.176873 | ||||||||
\(101\) | −6.22818 | − | 4.52504i | −0.619727 | − | 0.450258i | 0.233099 | − | 0.972453i | \(-0.425113\pi\) |
−0.852826 | + | 0.522195i | \(0.825113\pi\) | |||||||
\(102\) | 0.595597 | − | 1.83306i | 0.0589729 | − | 0.181500i | ||||
\(103\) | 2.81293 | + | 8.65732i | 0.277167 | + | 0.853031i | 0.988638 | + | 0.150316i | \(0.0480291\pi\) |
−0.711471 | + | 0.702715i | \(0.751971\pi\) | |||||||
\(104\) | 7.03154 | − | 5.10872i | 0.689500 | − | 0.500951i | ||||
\(105\) | 0.623145 | − | 0.452741i | 0.0608127 | − | 0.0441830i | ||||
\(106\) | −0.906576 | − | 2.79016i | −0.0880545 | − | 0.271004i | ||||
\(107\) | 5.18879 | − | 15.9694i | 0.501619 | − | 1.54382i | −0.304762 | − | 0.952429i | \(-0.598577\pi\) |
0.806381 | − | 0.591396i | \(-0.201423\pi\) | |||||||
\(108\) | 7.87182 | + | 5.71921i | 0.757466 | + | 0.550331i | ||||
\(109\) | 17.8817 | 1.71276 | 0.856380 | − | 0.516346i | \(-0.172708\pi\) | ||||
0.856380 | + | 0.516346i | \(0.172708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.33411 | −0.791039 | ||||||||
\(112\) | −1.03718 | − | 0.753558i | −0.0980046 | − | 0.0712045i | ||||
\(113\) | −0.142930 | + | 0.439893i | −0.0134457 | + | 0.0413817i | −0.957554 | − | 0.288253i | \(-0.906926\pi\) |
0.944109 | + | 0.329635i | \(0.106926\pi\) | |||||||
\(114\) | −1.37037 | − | 4.21758i | −0.128347 | − | 0.395012i | ||||
\(115\) | −3.58769 | + | 2.60661i | −0.334553 | + | 0.243067i | ||||
\(116\) | 12.8963 | − | 9.36970i | 1.19739 | − | 0.869955i | ||||
\(117\) | 0.644077 | + | 1.98227i | 0.0595450 | + | 0.183261i | ||||
\(118\) | −0.411452 | + | 1.26632i | −0.0378772 | + | 0.116574i | ||||
\(119\) | −0.973537 | − | 0.707316i | −0.0892440 | − | 0.0648396i | ||||
\(120\) | −2.90286 | −0.264994 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.93579 | −0.175258 | ||||||||
\(123\) | −10.9510 | − | 7.95637i | −0.987418 | − | 0.717401i | ||||
\(124\) | −4.35730 | + | 13.4104i | −0.391297 | + | 1.20429i | ||||
\(125\) | 0.309017 | + | 0.951057i | 0.0276393 | + | 0.0850651i | ||||
\(126\) | −0.0813172 | + | 0.0590804i | −0.00724431 | + | 0.00526330i | ||||
\(127\) | 12.8063 | − | 9.30433i | 1.13638 | − | 0.825626i | 0.149766 | − | 0.988721i | \(-0.452148\pi\) |
0.986610 | + | 0.163096i | \(0.0521480\pi\) | |||||||
\(128\) | 3.47424 | + | 10.6926i | 0.307083 | + | 0.945103i | ||||
\(129\) | −4.22267 | + | 12.9960i | −0.371786 | + | 1.14424i | ||||
\(130\) | −1.86576 | − | 1.35555i | −0.163638 | − | 0.118890i | ||||
\(131\) | −9.60460 | −0.839158 | −0.419579 | − | 0.907719i | \(-0.637822\pi\) | ||||
−0.419579 | + | 0.907719i | \(0.637822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.76873 | −0.240080 | ||||||||
\(134\) | 2.95749 | + | 2.14874i | 0.255488 | + | 0.185623i | ||||
\(135\) | 1.69995 | − | 5.23192i | 0.146309 | − | 0.450292i | ||||
\(136\) | 1.40143 | + | 4.31317i | 0.120172 | + | 0.369851i | ||||
\(137\) | −3.21349 | + | 2.33474i | −0.274547 | + | 0.199470i | −0.716535 | − | 0.697551i | \(-0.754273\pi\) |
0.441988 | + | 0.897021i | \(0.354273\pi\) | |||||||
\(138\) | −2.76341 | + | 2.00774i | −0.235237 | + | 0.170910i | ||||
\(139\) | −2.84960 | − | 8.77016i | −0.241700 | − | 0.743875i | −0.996162 | − | 0.0875316i | \(-0.972102\pi\) |
0.754462 | − | 0.656344i | \(-0.227898\pi\) | |||||||
\(140\) | −0.262846 | + | 0.808955i | −0.0222145 | + | 0.0683692i | ||||
\(141\) | 12.4417 | + | 9.03944i | 1.04778 | + | 0.761258i | ||||
\(142\) | 1.33149 | 0.111736 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.15866 | −0.0965550 | ||||||||
\(145\) | −7.29125 | − | 5.29740i | −0.605505 | − | 0.439925i | ||||
\(146\) | 0.743716 | − | 2.28892i | 0.0615504 | − | 0.189433i | ||||
\(147\) | 3.35016 | + | 10.3107i | 0.276316 | + | 0.850414i | ||||
\(148\) | 7.44567 | − | 5.40960i | 0.612031 | − | 0.444666i | ||||
\(149\) | 6.18907 | − | 4.49662i | 0.507029 | − | 0.368378i | −0.304667 | − | 0.952459i | \(-0.598545\pi\) |
0.811695 | + | 0.584081i | \(0.198545\pi\) | |||||||
\(150\) | 0.238020 | + | 0.732550i | 0.0194343 | + | 0.0598125i | ||||
\(151\) | 0.887492 | − | 2.73142i | 0.0722231 | − | 0.222280i | −0.908429 | − | 0.418040i | \(-0.862717\pi\) |
0.980652 | + | 0.195760i | \(0.0627173\pi\) | |||||||
\(152\) | 8.44179 | + | 6.13332i | 0.684719 | + | 0.497478i | ||||
\(153\) | −1.08756 | −0.0879240 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.97209 | 0.640334 | ||||||||
\(156\) | 10.9910 | + | 7.98544i | 0.879985 | + | 0.639347i | ||||
\(157\) | 5.40213 | − | 16.6260i | 0.431137 | − | 1.32690i | −0.465857 | − | 0.884860i | \(-0.654254\pi\) |
0.896994 | − | 0.442043i | \(-0.145746\pi\) | |||||||
\(158\) | 0.538665 | + | 1.65784i | 0.0428539 | + | 0.131891i | ||||
\(159\) | 7.90496 | − | 5.74329i | 0.626904 | − | 0.455472i | ||||
\(160\) | 3.96969 | − | 2.88415i | 0.313831 | − | 0.228012i | ||||
\(161\) | 0.659014 | + | 2.02824i | 0.0519376 | + | 0.159847i | ||||
\(162\) | 1.11562 | − | 3.43354i | 0.0876517 | − | 0.269764i | ||||
\(163\) | −10.6524 | − | 7.73940i | −0.834358 | − | 0.606197i | 0.0864308 | − | 0.996258i | \(-0.472454\pi\) |
−0.920789 | + | 0.390061i | \(0.872454\pi\) | |||||||
\(164\) | 14.9480 | 1.16724 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.824549 | 0.0639974 | ||||||||
\(167\) | −12.8454 | − | 9.33274i | −0.994008 | − | 0.722189i | −0.0332128 | − | 0.999448i | \(-0.510574\pi\) |
−0.960795 | + | 0.277259i | \(0.910574\pi\) | |||||||
\(168\) | −0.431385 | + | 1.32767i | −0.0332820 | + | 0.102432i | ||||
\(169\) | 3.08945 | + | 9.50835i | 0.237650 | + | 0.731411i | ||||
\(170\) | 0.973537 | − | 0.707316i | 0.0746669 | − | 0.0542487i | ||||
\(171\) | −2.02440 | + | 1.47081i | −0.154810 | + | 0.112476i | ||||
\(172\) | −4.66310 | − | 14.3515i | −0.355558 | − | 1.09429i | ||||
\(173\) | −7.05194 | + | 21.7036i | −0.536149 | + | 1.65010i | 0.205005 | + | 0.978761i | \(0.434279\pi\) |
−0.741153 | + | 0.671336i | \(0.765721\pi\) | |||||||
\(174\) | −5.61608 | − | 4.08032i | −0.425754 | − | 0.309328i | ||||
\(175\) | 0.480901 | 0.0363527 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.43462 | −0.333327 | ||||||||
\(178\) | −6.12408 | − | 4.44940i | −0.459019 | − | 0.333497i | ||||
\(179\) | −0.142930 | + | 0.439893i | −0.0106831 | + | 0.0328792i | −0.956256 | − | 0.292531i | \(-0.905502\pi\) |
0.945573 | + | 0.325410i | \(0.105502\pi\) | |||||||
\(180\) | 0.237552 | + | 0.731110i | 0.0177061 | + | 0.0544937i | ||||
\(181\) | 2.53095 | − | 1.83884i | 0.188124 | − | 0.136680i | −0.489737 | − | 0.871870i | \(-0.662907\pi\) |
0.677861 | + | 0.735190i | \(0.262907\pi\) | |||||||
\(182\) | −0.897244 | + | 0.651886i | −0.0665082 | + | 0.0483210i | ||||
\(183\) | −1.99233 | − | 6.13175i | −0.147277 | − | 0.453272i | ||||
\(184\) | 2.48365 | − | 7.64389i | 0.183097 | − | 0.563515i | ||||
\(185\) | −4.20961 | − | 3.05846i | −0.309496 | − | 0.224862i | ||||
\(186\) | 6.14050 | 0.450243 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −16.9828 | −1.23860 | ||||||||
\(189\) | −2.14027 | − | 1.55500i | −0.155682 | − | 0.113109i | ||||
\(190\) | 0.855586 | − | 2.63322i | 0.0620707 | − | 0.191034i | ||||
\(191\) | −1.68011 | − | 5.17085i | −0.121569 | − | 0.374150i | 0.871692 | − | 0.490055i | \(-0.163023\pi\) |
−0.993260 | + | 0.115905i | \(0.963023\pi\) | |||||||
\(192\) | −3.85119 | + | 2.79806i | −0.277936 | + | 0.201932i | ||||
\(193\) | −2.59432 | + | 1.88488i | −0.186743 | + | 0.135677i | −0.677229 | − | 0.735772i | \(-0.736819\pi\) |
0.490486 | + | 0.871449i | \(0.336819\pi\) | |||||||
\(194\) | 0.540628 | + | 1.66388i | 0.0388148 | + | 0.119460i | ||||
\(195\) | 2.37356 | − | 7.30506i | 0.169974 | − | 0.523126i | ||||
\(196\) | −9.68563 | − | 7.03702i | −0.691830 | − | 0.502644i | ||||
\(197\) | −19.4048 | −1.38253 | −0.691267 | − | 0.722600i | \(-0.742947\pi\) | ||||
−0.691267 | + | 0.722600i | \(0.742947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3509 | 1.44264 | 0.721319 | − | 0.692603i | \(-0.243536\pi\) | ||||
0.721319 | + | 0.692603i | \(0.243536\pi\) | |||||||
\(200\) | −1.46625 | − | 1.06529i | −0.103680 | − | 0.0753277i | ||||
\(201\) | −3.76242 | + | 11.5795i | −0.265381 | + | 0.816758i | ||||
\(202\) | −1.14404 | − | 3.52099i | −0.0804944 | − | 0.247736i | ||||
\(203\) | −3.50637 | + | 2.54753i | −0.246099 | + | 0.178801i | ||||
\(204\) | −5.73502 | + | 4.16674i | −0.401532 | + | 0.291730i | ||||
\(205\) | −2.61158 | − | 8.03761i | −0.182400 | − | 0.561371i | ||||
\(206\) | −1.35274 | + | 4.16331i | −0.0942500 | + | 0.290072i | ||||
\(207\) | 1.55929 | + | 1.13289i | 0.108378 | + | 0.0787416i | ||||
\(208\) | −12.7845 | −0.886446 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.370413 | 0.0255610 | ||||||||
\(211\) | −5.56593 | − | 4.04388i | −0.383174 | − | 0.278392i | 0.379478 | − | 0.925201i | \(-0.376103\pi\) |
−0.762653 | + | 0.646808i | \(0.776103\pi\) | |||||||
\(212\) | −3.33435 | + | 10.2621i | −0.229004 | + | 0.704802i | ||||
\(213\) | 1.37037 | + | 4.21758i | 0.0938965 | + | 0.288984i | ||||
\(214\) | 6.53276 | − | 4.74633i | 0.446570 | − | 0.324452i | ||||
\(215\) | −6.90219 | + | 5.01474i | −0.470726 | + | 0.342002i | ||||
\(216\) | 3.08098 | + | 9.48227i | 0.209634 | + | 0.645187i | ||||
\(217\) | 1.18471 | − | 3.64615i | 0.0804230 | − | 0.247517i | ||||
\(218\) | 6.95702 | + | 5.05457i | 0.471189 | + | 0.342339i | ||||
\(219\) | 8.01576 | 0.541655 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | −3.24244 | − | 2.35577i | −0.217619 | − | 0.158109i | ||||
\(223\) | −0.320956 | + | 0.987800i | −0.0214928 | + | 0.0661480i | −0.961228 | − | 0.275756i | \(-0.911072\pi\) |
0.939735 | + | 0.341904i | \(0.111072\pi\) | |||||||
\(224\) | −0.729183 | − | 2.24420i | −0.0487206 | − | 0.149947i | ||||
\(225\) | 0.351618 | − | 0.255466i | 0.0234412 | − | 0.0170310i | ||||
\(226\) | −0.179951 | + | 0.130742i | −0.0119702 | + | 0.00869684i | ||||
\(227\) | 0.148607 | + | 0.457364i | 0.00986336 | + | 0.0303563i | 0.955867 | − | 0.293799i | \(-0.0949198\pi\) |
−0.946004 | + | 0.324156i | \(0.894920\pi\) | |||||||
\(228\) | −5.04018 | + | 15.5121i | −0.333794 | + | 1.02731i | ||||
\(229\) | −10.9539 | − | 7.95849i | −0.723856 | − | 0.525912i | 0.163758 | − | 0.986501i | \(-0.447638\pi\) |
−0.887614 | + | 0.460588i | \(0.847638\pi\) | |||||||
\(230\) | −2.13261 | −0.140620 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.3341 | 1.07239 | ||||||||
\(233\) | 17.1142 | + | 12.4342i | 1.12119 | + | 0.814590i | 0.984389 | − | 0.176008i | \(-0.0563186\pi\) |
0.136799 | + | 0.990599i | \(0.456319\pi\) | |||||||
\(234\) | −0.309737 | + | 0.953273i | −0.0202482 | + | 0.0623174i | ||||
\(235\) | 2.96708 | + | 9.13174i | 0.193551 | + | 0.595689i | ||||
\(236\) | 3.96188 | − | 2.87848i | 0.257897 | − | 0.187373i | ||||
\(237\) | −4.69693 | + | 3.41252i | −0.305099 | + | 0.221667i | ||||
\(238\) | −0.178827 | − | 0.550373i | −0.0115916 | − | 0.0356754i | ||||
\(239\) | 0.827051 | − | 2.54540i | 0.0534975 | − | 0.164648i | −0.920738 | − | 0.390181i | \(-0.872412\pi\) |
0.974236 | + | 0.225533i | \(0.0724123\pi\) | |||||||
\(240\) | 3.45442 | + | 2.50978i | 0.222982 | + | 0.162006i | ||||
\(241\) | −4.56912 | −0.294323 | −0.147161 | − | 0.989112i | \(-0.547014\pi\) | ||||
−0.147161 | + | 0.989112i | \(0.547014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.47932 | −0.287349 | ||||||||
\(244\) | 5.76000 | + | 4.18489i | 0.368746 | + | 0.267910i | ||||
\(245\) | −2.09165 | + | 6.43745i | −0.133631 | + | 0.411274i | ||||
\(246\) | −2.01157 | − | 6.19096i | −0.128253 | − | 0.394721i | ||||
\(247\) | −22.3370 | + | 16.2288i | −1.42127 | + | 1.03261i | ||||
\(248\) | −11.6891 | + | 8.49263i | −0.742259 | + | 0.539282i | ||||
\(249\) | 0.848631 | + | 2.61182i | 0.0537798 | + | 0.165517i | ||||
\(250\) | −0.148607 | + | 0.457364i | −0.00939870 | + | 0.0289262i | ||||
\(251\) | 9.25269 | + | 6.72247i | 0.584025 | + | 0.424319i | 0.840173 | − | 0.542319i | \(-0.182453\pi\) |
−0.256148 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(252\) | 0.369685 | 0.0232880 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 7.61241 | 0.477645 | ||||||||
\(255\) | 3.24244 | + | 2.35577i | 0.203050 | + | 0.147524i | ||||
\(256\) | 0.166087 | − | 0.511163i | 0.0103804 | − | 0.0319477i | ||||
\(257\) | −6.19415 | − | 19.0636i | −0.386381 | − | 1.18916i | −0.935474 | − | 0.353396i | \(-0.885027\pi\) |
0.549093 | − | 0.835761i | \(-0.314973\pi\) | |||||||
\(258\) | −5.31641 | + | 3.86260i | −0.330985 | + | 0.240475i | ||||
\(259\) | −2.02440 | + | 1.47081i | −0.125790 | + | 0.0913920i | ||||
\(260\) | 2.62112 | + | 8.06698i | 0.162555 | + | 0.500293i | ||||
\(261\) | −1.21043 | + | 3.72533i | −0.0749239 | + | 0.230592i | ||||
\(262\) | −3.73674 | − | 2.71490i | −0.230856 | − | 0.167727i | ||||
\(263\) | −6.55852 | −0.404416 | −0.202208 | − | 0.979343i | \(-0.564812\pi\) | ||||
−0.202208 | + | 0.979343i | \(0.564812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.10051 | 0.374752 | ||||||||
\(266\) | −1.07720 | − | 0.782628i | −0.0660471 | − | 0.0479860i | ||||
\(267\) | 7.79086 | − | 23.9778i | 0.476793 | − | 1.46742i | ||||
\(268\) | −4.15484 | − | 12.7873i | −0.253797 | − | 0.781108i | ||||
\(269\) | −1.53483 | + | 1.11512i | −0.0935803 | + | 0.0679901i | −0.633592 | − | 0.773668i | \(-0.718420\pi\) |
0.540011 | + | 0.841658i | \(0.318420\pi\) | |||||||
\(270\) | 2.14027 | − | 1.55500i | 0.130253 | − | 0.0946340i | ||||
\(271\) | 3.50861 | + | 10.7984i | 0.213133 | + | 0.655956i | 0.999281 | + | 0.0379175i | \(0.0120724\pi\) |
−0.786148 | + | 0.618038i | \(0.787928\pi\) | |||||||
\(272\) | 2.06141 | − | 6.34436i | 0.124991 | − | 0.384683i | ||||
\(273\) | −2.98834 | − | 2.17116i | −0.180863 | − | 0.131405i | ||||
\(274\) | −1.91018 | −0.115398 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.5630 | 0.756206 | ||||||||
\(277\) | 18.4731 | + | 13.4215i | 1.10994 | + | 0.806418i | 0.982654 | − | 0.185448i | \(-0.0593737\pi\) |
0.127285 | + | 0.991866i | \(0.459374\pi\) | |||||||
\(278\) | 1.37037 | − | 4.21758i | 0.0821896 | − | 0.252954i | ||||
\(279\) | −1.07070 | − | 3.29528i | −0.0641012 | − | 0.197283i | ||||
\(280\) | −0.705122 | + | 0.512301i | −0.0421391 | + | 0.0306159i | ||||
\(281\) | −18.2931 | + | 13.2907i | −1.09128 | + | 0.792858i | −0.979614 | − | 0.200888i | \(-0.935617\pi\) |
−0.111662 | + | 0.993746i | \(0.535617\pi\) | |||||||
\(282\) | 2.28539 | + | 7.03371i | 0.136093 | + | 0.418852i | ||||
\(283\) | 8.51857 | − | 26.2175i | 0.506377 | − | 1.55847i | −0.292067 | − | 0.956398i | \(-0.594343\pi\) |
0.798444 | − | 0.602069i | \(-0.205657\pi\) | |||||||
\(284\) | −3.96188 | − | 2.87848i | −0.235094 | − | 0.170806i | ||||
\(285\) | 9.22149 | 0.546234 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.06421 | −0.239903 | ||||||||
\(288\) | −1.72532 | − | 1.25352i | −0.101666 | − | 0.0738643i | ||||
\(289\) | −3.31838 | + | 10.2129i | −0.195199 | + | 0.600760i | ||||
\(290\) | −1.33931 | − | 4.12198i | −0.0786472 | − | 0.242051i | ||||
\(291\) | −4.71405 | + | 3.42495i | −0.276342 | + | 0.200774i | ||||
\(292\) | −7.16126 | + | 5.20296i | −0.419081 | + | 0.304480i | ||||
\(293\) | 6.75472 | + | 20.7889i | 0.394615 | + | 1.21450i | 0.929261 | + | 0.369424i | \(0.120445\pi\) |
−0.534646 | + | 0.845076i | \(0.679555\pi\) | |||||||
\(294\) | −1.61109 | + | 4.95844i | −0.0939609 | + | 0.289182i | ||||
\(295\) | −2.23995 | − | 1.62742i | −0.130415 | − | 0.0947521i | ||||
\(296\) | 9.43050 | 0.548137 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.67895 | 0.213116 | ||||||||
\(299\) | 17.2051 | + | 12.5002i | 0.994995 | + | 0.722906i | ||||
\(300\) | 0.875428 | − | 2.69429i | 0.0505429 | − | 0.155555i | ||||
\(301\) | 1.26785 | + | 3.90204i | 0.0730776 | + | 0.224910i | ||||
\(302\) | 1.11737 | − | 0.811814i | 0.0642972 | − | 0.0467146i | ||||
\(303\) | 9.97554 | − | 7.24766i | 0.573080 | − | 0.416367i | ||||
\(304\) | −4.74297 | − | 14.5974i | −0.272028 | − | 0.837216i | ||||
\(305\) | 1.24390 | − | 3.82833i | 0.0712254 | − | 0.219209i | ||||
\(306\) | −0.423123 | − | 0.307417i | −0.0241883 | − | 0.0175738i | ||||
\(307\) | 9.80019 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5798 | −0.829418 | ||||||||
\(310\) | 3.10160 | + | 2.25344i | 0.176159 | + | 0.127987i | ||||
\(311\) | 3.01943 | − | 9.29284i | 0.171216 | − | 0.526948i | −0.828225 | − | 0.560396i | \(-0.810649\pi\) |
0.999440 | + | 0.0334480i | \(0.0106488\pi\) | |||||||
\(312\) | 4.30181 | + | 13.2396i | 0.243542 | + | 0.749545i | ||||
\(313\) | 0.725814 | − | 0.527335i | 0.0410254 | − | 0.0298067i | −0.567084 | − | 0.823660i | \(-0.691928\pi\) |
0.608109 | + | 0.793854i | \(0.291928\pi\) | |||||||
\(314\) | 6.80136 | − | 4.94148i | 0.383823 | − | 0.278864i | ||||
\(315\) | −0.0645880 | − | 0.198781i | −0.00363912 | − | 0.0112001i | ||||
\(316\) | 1.98119 | − | 6.09748i | 0.111451 | − | 0.343010i | ||||
\(317\) | 2.15864 | + | 1.56834i | 0.121241 | + | 0.0880868i | 0.646753 | − | 0.762699i | \(-0.276126\pi\) |
−0.525512 | + | 0.850786i | \(0.676126\pi\) | |||||||
\(318\) | 4.69891 | 0.263502 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.97209 | −0.166145 | ||||||||
\(321\) | 21.7579 | + | 15.8080i | 1.21441 | + | 0.882318i | ||||
\(322\) | −0.316921 | + | 0.975381i | −0.0176613 | + | 0.0543559i | ||||
\(323\) | −4.45192 | − | 13.7016i | −0.247711 | − | 0.762378i | ||||
\(324\) | −10.7424 | + | 7.80479i | −0.596798 | + | 0.433599i | ||||
\(325\) | 3.87971 | − | 2.81878i | 0.215208 | − | 0.156358i | ||||
\(326\) | −1.95671 | − | 6.02214i | −0.108372 | − | 0.333535i | ||||
\(327\) | −8.85050 | + | 27.2390i | −0.489434 | + | 1.50632i | ||||
\(328\) | 12.3917 | + | 9.00307i | 0.684215 | + | 0.497111i | ||||
\(329\) | 4.61746 | 0.254569 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9744 | 1.04293 | 0.521464 | − | 0.853273i | \(-0.325386\pi\) | ||||
0.521464 | + | 0.853273i | \(0.325386\pi\) | |||||||
\(332\) | −2.45347 | − | 1.78255i | −0.134652 | − | 0.0978303i | ||||
\(333\) | −0.698843 | + | 2.15082i | −0.0382964 | + | 0.117864i | ||||
\(334\) | −2.35955 | − | 7.26194i | −0.129109 | − | 0.397355i | ||||
\(335\) | −6.14989 | + | 4.46815i | −0.336004 | + | 0.244121i | ||||
\(336\) | 1.66123 | − | 1.20696i | 0.0906278 | − | 0.0658449i | ||||
\(337\) | 1.48192 | + | 4.56088i | 0.0807252 | + | 0.248447i | 0.983271 | − | 0.182146i | \(-0.0583044\pi\) |
−0.902546 | + | 0.430593i | \(0.858304\pi\) | |||||||
\(338\) | −1.48572 | + | 4.57257i | −0.0808125 | + | 0.248715i | ||||
\(339\) | −0.599342 | − | 0.435447i | −0.0325518 | − | 0.0236502i | ||||
\(340\) | −4.42590 | −0.240028 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.20336 | −0.0650702 | ||||||||
\(343\) | 5.35682 | + | 3.89196i | 0.289241 | + | 0.210146i | ||||
\(344\) | 4.77818 | − | 14.7057i | 0.257622 | − | 0.792880i | ||||
\(345\) | −2.19490 | − | 6.75521i | −0.118169 | − | 0.363688i | ||||
\(346\) | −8.87850 | + | 6.45060i | −0.477311 | + | 0.346787i | ||||
\(347\) | −0.209106 | + | 0.151924i | −0.0112254 | + | 0.00815573i | −0.593384 | − | 0.804920i | \(-0.702208\pi\) |
0.582158 | + | 0.813075i | \(0.302208\pi\) | |||||||
\(348\) | 7.88978 | + | 24.2822i | 0.422937 | + | 1.30166i | ||||
\(349\) | −0.415599 | + | 1.27908i | −0.0222465 | + | 0.0684677i | −0.961563 | − | 0.274583i | \(-0.911460\pi\) |
0.939317 | + | 0.343051i | \(0.111460\pi\) | |||||||
\(350\) | 0.187098 | + | 0.135935i | 0.0100008 | + | 0.00726601i | ||||
\(351\) | −26.3813 | −1.40813 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.4537 | 1.88701 | 0.943506 | − | 0.331355i | \(-0.107506\pi\) | ||||
0.943506 | + | 0.331355i | \(0.107506\pi\) | |||||||
\(354\) | −1.72532 | − | 1.25352i | −0.0916998 | − | 0.0666238i | ||||
\(355\) | −0.855586 | + | 2.63322i | −0.0454098 | + | 0.139757i | ||||
\(356\) | 8.60345 | + | 26.4787i | 0.455982 | + | 1.40337i | ||||
\(357\) | 1.55929 | − | 1.13289i | 0.0825266 | − | 0.0599591i | ||||
\(358\) | −0.179951 | + | 0.130742i | −0.00951071 | + | 0.00690994i | ||||
\(359\) | 2.42321 | + | 7.45787i | 0.127892 | + | 0.393611i | 0.994417 | − | 0.105523i | \(-0.0336516\pi\) |
−0.866525 | + | 0.499134i | \(0.833652\pi\) | |||||||
\(360\) | −0.243415 | + | 0.749154i | −0.0128291 | + | 0.0394839i | ||||
\(361\) | −11.4456 | − | 8.31572i | −0.602400 | − | 0.437669i | ||||
\(362\) | 1.50446 | 0.0790727 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.07906 | 0.213801 | ||||||||
\(365\) | 4.04881 | + | 2.94163i | 0.211924 | + | 0.153972i | ||||
\(366\) | 0.958111 | − | 2.94876i | 0.0500813 | − | 0.154134i | ||||
\(367\) | 0.329579 | + | 1.01434i | 0.0172039 | + | 0.0529482i | 0.959290 | − | 0.282423i | \(-0.0911382\pi\) |
−0.942086 | + | 0.335371i | \(0.891138\pi\) | |||||||
\(368\) | −9.56438 | + | 6.94893i | −0.498578 | + | 0.362238i | ||||
\(369\) | −2.97161 | + | 2.15900i | −0.154696 | + | 0.112393i | ||||
\(370\) | −0.773253 | − | 2.37983i | −0.0401995 | − | 0.123721i | ||||
\(371\) | 0.906576 | − | 2.79016i | 0.0470671 | − | 0.144858i | ||||
\(372\) | −18.2712 | − | 13.2748i | −0.947320 | − | 0.688268i | ||||
\(373\) | 37.6388 | 1.94886 | 0.974431 | − | 0.224689i | \(-0.0721366\pi\) | ||||
0.974431 | + | 0.224689i | \(0.0721366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.60168 | −0.0827104 | ||||||||
\(376\) | −14.0785 | − | 10.2286i | −0.726042 | − | 0.527501i | ||||
\(377\) | −13.3558 | + | 41.1048i | −0.687857 | + | 2.11701i | ||||
\(378\) | −0.393141 | − | 1.20996i | −0.0202210 | − | 0.0622338i | ||||
\(379\) | −28.4350 | + | 20.6592i | −1.46061 | + | 1.06119i | −0.477401 | + | 0.878685i | \(0.658421\pi\) |
−0.983205 | + | 0.182507i | \(0.941579\pi\) | |||||||
\(380\) | −8.23846 | + | 5.98559i | −0.422624 | + | 0.307054i | ||||
\(381\) | 7.83473 | + | 24.1128i | 0.401386 | + | 1.23534i | ||||
\(382\) | 0.807967 | − | 2.48667i | 0.0413392 | − | 0.127229i | ||||
\(383\) | −0.667074 | − | 0.484658i | −0.0340859 | − | 0.0247649i | 0.570612 | − | 0.821220i | \(-0.306706\pi\) |
−0.604698 | + | 0.796455i | \(0.706706\pi\) | |||||||
\(384\) | −18.0075 | −0.918942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.54213 | −0.0784924 | ||||||||
\(387\) | 2.99986 | + | 2.17952i | 0.152491 | + | 0.110791i | ||||
\(388\) | 1.98841 | − | 6.11969i | 0.100946 | − | 0.310680i | ||||
\(389\) | 1.49678 | + | 4.60661i | 0.0758896 | + | 0.233564i | 0.981804 | − | 0.189896i | \(-0.0608152\pi\) |
−0.905915 | + | 0.423461i | \(0.860815\pi\) | |||||||
\(390\) | 2.98834 | − | 2.17116i | 0.151321 | − | 0.109941i | ||||
\(391\) | −8.97747 | + | 6.52251i | −0.454010 | + | 0.329858i | ||||
\(392\) | −3.79089 | − | 11.6672i | −0.191469 | − | 0.589280i | ||||
\(393\) | 4.75376 | − | 14.6306i | 0.239795 | − | 0.738014i | ||||
\(394\) | −7.54957 | − | 5.48508i | −0.380342 | − | 0.276334i | ||||
\(395\) | −3.62478 | −0.182382 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.33178 | −0.367971 | −0.183986 | − | 0.982929i | \(-0.558900\pi\) | ||||
−0.183986 | + | 0.982929i | \(0.558900\pi\) | |||||||
\(398\) | 7.91766 | + | 5.75252i | 0.396876 | + | 0.288348i | ||||
\(399\) | 1.37037 | − | 4.21758i | 0.0686045 | − | 0.211143i | ||||
\(400\) | 0.823805 | + | 2.53541i | 0.0411903 | + | 0.126771i | ||||
\(401\) | 25.2008 | − | 18.3094i | 1.25847 | − | 0.914330i | 0.259785 | − | 0.965666i | \(-0.416348\pi\) |
0.998681 | + | 0.0513367i | \(0.0163482\pi\) | |||||||
\(402\) | −4.73694 | + | 3.44159i | −0.236257 | + | 0.171651i | ||||
\(403\) | −11.8140 | − | 36.3597i | −0.588497 | − | 1.81121i | ||||
\(404\) | −4.20774 | + | 12.9501i | −0.209343 | + | 0.644290i | ||||
\(405\) | 6.07348 | + | 4.41264i | 0.301793 | + | 0.219266i | ||||
\(406\) | −2.08428 | −0.103441 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.26384 | −0.359613 | ||||||||
\(409\) | −5.85089 | − | 4.25092i | −0.289308 | − | 0.210194i | 0.433659 | − | 0.901077i | \(-0.357222\pi\) |
−0.722967 | + | 0.690883i | \(0.757222\pi\) | |||||||
\(410\) | 1.25591 | − | 3.86529i | 0.0620250 | − | 0.190893i | ||||
\(411\) | −1.96597 | − | 6.05064i | −0.0969742 | − | 0.298456i | ||||
\(412\) | 13.0256 | − | 9.46364i | 0.641725 | − | 0.466240i | ||||
\(413\) | −1.07720 | + | 0.782628i | −0.0530053 | + | 0.0385106i | ||||
\(414\) | 0.286423 | + | 0.881520i | 0.0140769 | + | 0.0433244i | ||||
\(415\) | −0.529838 | + | 1.63067i | −0.0260087 | + | 0.0800467i | ||||
\(416\) | −19.0370 | − | 13.8312i | −0.933365 | − | 0.678130i | ||||
\(417\) | 14.7699 | 0.723284 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.30620 | −0.112665 | −0.0563327 | − | 0.998412i | \(-0.517941\pi\) | ||||
−0.0563327 | + | 0.998412i | \(0.517941\pi\) | |||||||
\(420\) | −1.10218 | − | 0.800779i | −0.0537807 | − | 0.0390740i | ||||
\(421\) | 2.05125 | − | 6.31310i | 0.0999718 | − | 0.307681i | −0.888546 | − | 0.458788i | \(-0.848284\pi\) |
0.988517 | + | 0.151107i | \(0.0482837\pi\) | |||||||
\(422\) | −1.02239 | − | 3.14660i | −0.0497693 | − | 0.153174i | ||||
\(423\) | 3.37612 | − | 2.45290i | 0.164153 | − | 0.119264i | ||||
\(424\) | −8.94489 | + | 6.49885i | −0.434402 | + | 0.315612i | ||||
\(425\) | 0.773253 | + | 2.37983i | 0.0375083 | + | 0.115439i | ||||
\(426\) | −0.659014 | + | 2.02824i | −0.0319293 | + | 0.0982684i | ||||
\(427\) | −1.56609 | − | 1.13783i | −0.0757882 | − | 0.0550634i | ||||
\(428\) | −29.6993 | −1.43557 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.10284 | −0.197857 | ||||||||
\(431\) | −26.5707 | − | 19.3047i | −1.27986 | − | 0.929876i | −0.280316 | − | 0.959908i | \(-0.590439\pi\) |
−0.999549 | + | 0.0300317i | \(0.990439\pi\) | |||||||
\(432\) | 4.53189 | − | 13.9477i | 0.218041 | − | 0.671060i | ||||
\(433\) | 0.729904 | + | 2.24641i | 0.0350769 | + | 0.107956i | 0.967062 | − | 0.254541i | \(-0.0819244\pi\) |
−0.931985 | + | 0.362497i | \(0.881924\pi\) | |||||||
\(434\) | 1.49156 | − | 1.08368i | 0.0715972 | − | 0.0520184i | ||||
\(435\) | 11.6782 | − | 8.48474i | 0.559929 | − | 0.406812i | ||||
\(436\) | −9.77361 | − | 30.0801i | −0.468071 | − | 1.44057i | ||||
\(437\) | −7.88978 | + | 24.2822i | −0.377419 | + | 1.16158i | ||||
\(438\) | 3.11859 | + | 2.26579i | 0.149012 | + | 0.108264i | ||||
\(439\) | −30.8847 | −1.47404 | −0.737022 | − | 0.675869i | \(-0.763769\pi\) | ||||
−0.737022 | + | 0.675869i | \(0.763769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.94185 | 0.140088 | ||||||||
\(442\) | −4.66868 | − | 3.39200i | −0.222067 | − | 0.161341i | ||||
\(443\) | −4.25665 | + | 13.1006i | −0.202239 | + | 0.622429i | 0.797576 | + | 0.603218i | \(0.206115\pi\) |
−0.999815 | + | 0.0192105i | \(0.993885\pi\) | |||||||
\(444\) | 4.55517 | + | 14.0194i | 0.216179 | + | 0.665329i | ||||
\(445\) | 12.7346 | − | 9.25223i | 0.603678 | − | 0.438598i | ||||
\(446\) | −0.404088 | + | 0.293587i | −0.0191341 | + | 0.0139017i | ||||
\(447\) | 3.78639 | + | 11.6533i | 0.179090 | + | 0.551183i | ||||
\(448\) | −0.441672 | + | 1.35933i | −0.0208671 | + | 0.0642222i | ||||
\(449\) | 31.4839 | + | 22.8744i | 1.48582 | + | 1.07951i | 0.975623 | + | 0.219452i | \(0.0704268\pi\) |
0.510195 | + | 0.860059i | \(0.329573\pi\) | |||||||
\(450\) | 0.209011 | 0.00985288 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.818095 | 0.0384800 | ||||||||
\(453\) | 3.72148 | + | 2.70381i | 0.174850 | + | 0.127036i | ||||
\(454\) | −0.0714650 | + | 0.219947i | −0.00335402 | + | 0.0103226i | ||||
\(455\) | −0.712656 | − | 2.19333i | −0.0334098 | − | 0.102825i | ||||
\(456\) | −13.5210 | + | 9.82361i | −0.633181 | + | 0.460033i | ||||
\(457\) | −1.07720 | + | 0.782628i | −0.0503891 | + | 0.0366098i | −0.612695 | − | 0.790320i | \(-0.709914\pi\) |
0.562306 | + | 0.826929i | \(0.309914\pi\) | |||||||
\(458\) | −2.01210 | − | 6.19262i | −0.0940194 | − | 0.289362i | ||||
\(459\) | 4.25379 | − | 13.0918i | 0.198550 | − | 0.611074i | ||||
\(460\) | 6.34566 | + | 4.61039i | 0.295868 | + | 0.214961i | ||||
\(461\) | 5.73993 | 0.267335 | 0.133668 | − | 0.991026i | \(-0.457325\pi\) | ||||
0.133668 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.44535 | −0.160119 | −0.0800595 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800595 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(464\) | −19.4377 | − | 14.1223i | −0.902371 | − | 0.655611i | ||||
\(465\) | −3.94576 | + | 12.1438i | −0.182980 | + | 0.563155i | ||||
\(466\) | 3.14367 | + | 9.67521i | 0.145628 | + | 0.448196i | ||||
\(467\) | 22.0185 | − | 15.9974i | 1.01890 | − | 0.740272i | 0.0528403 | − | 0.998603i | \(-0.483173\pi\) |
0.966056 | + | 0.258331i | \(0.0831726\pi\) | |||||||
\(468\) | 2.98247 | − | 2.16689i | 0.137865 | − | 0.100165i | ||||
\(469\) | 1.12966 | + | 3.47673i | 0.0521628 | + | 0.160541i | ||||
\(470\) | −1.42687 | + | 4.39146i | −0.0658167 | + | 0.202563i | ||||
\(471\) | 22.6525 | + | 16.4580i | 1.04377 | + | 0.758344i | ||||
\(472\) | 5.01802 | 0.230973 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.79198 | −0.128240 | ||||||||
\(475\) | 4.65783 | + | 3.38411i | 0.213716 | + | 0.155274i | ||||
\(476\) | −0.657718 | + | 2.02425i | −0.0301465 | + | 0.0927813i | ||||
\(477\) | −0.819337 | − | 2.52166i | −0.0375149 | − | 0.115459i | ||||
\(478\) | 1.04127 | − | 0.756527i | 0.0476266 | − | 0.0346027i | ||||
\(479\) | −11.3118 | + | 8.21851i | −0.516850 | + | 0.375513i | −0.815416 | − | 0.578876i | \(-0.803492\pi\) |
0.298566 | + | 0.954389i | \(0.403492\pi\) | |||||||
\(480\) | 2.42860 | + | 7.47447i | 0.110850 | + | 0.341161i | ||||
\(481\) | −7.71095 | + | 23.7319i | −0.351589 | + | 1.08208i | ||||
\(482\) | −1.77765 | − | 1.29154i | −0.0809696 | − | 0.0588279i | ||||
\(483\) | −3.41576 | −0.155423 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.63798 | −0.165192 | ||||||||
\(486\) | −1.74271 | − | 1.26615i | −0.0790510 | − | 0.0574339i | ||||
\(487\) | −2.30333 | + | 7.08893i | −0.104374 | + | 0.321230i | −0.989583 | − | 0.143963i | \(-0.954015\pi\) |
0.885209 | + | 0.465194i | \(0.154015\pi\) | |||||||
\(488\) | 2.25443 | + | 6.93841i | 0.102053 | + | 0.314087i | ||||
\(489\) | 17.0617 | − | 12.3960i | 0.771556 | − | 0.560568i | ||||
\(490\) | −2.63342 | + | 1.91329i | −0.118966 | + | 0.0864338i | ||||
\(491\) | −4.93673 | − | 15.1937i | −0.222792 | − | 0.685682i | −0.998508 | − | 0.0546007i | \(-0.982611\pi\) |
0.775717 | − | 0.631081i | \(-0.217389\pi\) | |||||||
\(492\) | −7.39846 | + | 22.7701i | −0.333548 | + | 1.02656i | ||||
\(493\) | −18.2449 | − | 13.2557i | −0.821709 | − | 0.597006i | ||||
\(494\) | −13.2777 | −0.597392 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.2527 | 0.954275 | ||||||||
\(497\) | 1.07720 | + | 0.782628i | 0.0483188 | + | 0.0351057i | ||||
\(498\) | −0.408107 | + | 1.25603i | −0.0182877 | + | 0.0562838i | ||||
\(499\) | −7.52484 | − | 23.1591i | −0.336858 | − | 1.03674i | −0.965799 | − | 0.259290i | \(-0.916511\pi\) |
0.628941 | − | 0.777453i | \(-0.283489\pi\) | |||||||
\(500\) | 1.43094 | − | 1.03964i | 0.0639934 | − | 0.0464939i | ||||
\(501\) | 20.5742 | − | 14.9481i | 0.919189 | − | 0.667830i | ||||
\(502\) | 1.69961 | + | 5.23085i | 0.0758572 | + | 0.233464i | ||||
\(503\) | 8.51857 | − | 26.2175i | 0.379824 | − | 1.16898i | −0.560341 | − | 0.828262i | \(-0.689330\pi\) |
0.940166 | − | 0.340717i | \(-0.110670\pi\) | |||||||
\(504\) | 0.306463 | + | 0.222658i | 0.0136509 | + | 0.00991799i | ||||
\(505\) | 7.69845 | 0.342577 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.0131 | −0.711165 | ||||||||
\(508\) | −22.6510 | − | 16.4569i | −1.00497 | − | 0.730156i | ||||
\(509\) | 5.46497 | − | 16.8194i | 0.242231 | − | 0.745509i | −0.753849 | − | 0.657048i | \(-0.771805\pi\) |
0.996080 | − | 0.0884613i | \(-0.0281949\pi\) | |||||||
\(510\) | 0.595597 | + | 1.83306i | 0.0263735 | + | 0.0811693i | ||||
\(511\) | 1.94707 | − | 1.41463i | 0.0861335 | − | 0.0625797i | ||||
\(512\) | 18.4005 | − | 13.3687i | 0.813194 | − | 0.590820i | ||||
\(513\) | −9.78730 | − | 30.1222i | −0.432120 | − | 1.32993i | ||||
\(514\) | 2.97877 | − | 9.16772i | 0.131388 | − | 0.404371i | ||||
\(515\) | −7.36436 | − | 5.35052i | −0.324512 | − | 0.235772i | ||||
\(516\) | 24.1695 | 1.06400 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.20336 | −0.0528725 | ||||||||
\(519\) | −29.5705 | − | 21.4843i | −1.29800 | − | 0.943054i | ||||
\(520\) | −2.68581 | + | 8.26608i | −0.117781 | + | 0.362491i | ||||
\(521\) | −1.66558 | − | 5.12612i | −0.0729703 | − | 0.224580i | 0.907919 | − | 0.419145i | \(-0.137670\pi\) |
−0.980889 | + | 0.194566i | \(0.937670\pi\) | |||||||
\(522\) | −1.52395 | + | 1.10722i | −0.0667016 | + | 0.0484615i | ||||
\(523\) | 30.4786 | − | 22.1440i | 1.33274 | − | 0.968291i | 0.333060 | − | 0.942906i | \(-0.391919\pi\) |
0.999678 | − | 0.0253853i | \(-0.00808126\pi\) | |||||||
\(524\) | 5.24957 | + | 16.1565i | 0.229329 | + | 0.705801i | ||||
\(525\) | −0.238020 | + | 0.732550i | −0.0103880 | + | 0.0319711i | ||||
\(526\) | −2.55164 | − | 1.85387i | −0.111257 | − | 0.0808327i | ||||
\(527\) | 19.9486 | 0.868973 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.33411 | −0.144961 | ||||||||
\(530\) | 2.37345 | + | 1.72441i | 0.103096 | + | 0.0749036i | ||||
\(531\) | −0.371858 | + | 1.14446i | −0.0161373 | + | 0.0496654i | ||||
\(532\) | 1.51330 | + | 4.65747i | 0.0656101 | + | 0.201927i | ||||
\(533\) | −32.7884 | + | 23.8222i | −1.42022 | + | 1.03185i | ||||
\(534\) | 9.80881 | − | 7.12652i | 0.424469 | − | 0.308395i | ||||
\(535\) | 5.18879 | + | 15.9694i | 0.224331 | + | 0.690419i | ||||
\(536\) | 4.25739 | − | 13.1029i | 0.183891 | − | 0.565959i | ||||
\(537\) | −0.599342 | − | 0.435447i | −0.0258635 | − | 0.0187909i | ||||
\(538\) | −0.912344 | −0.0393339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9.73010 | −0.418717 | ||||||||
\(541\) | 23.4332 | + | 17.0252i | 1.00747 | + | 0.731973i | 0.963678 | − | 0.267068i | \(-0.0860548\pi\) |
0.0437962 | + | 0.999040i | \(0.486055\pi\) | |||||||
\(542\) | −1.68729 | + | 5.19296i | −0.0724755 | + | 0.223057i | ||||
\(543\) | 1.54840 | + | 4.76548i | 0.0664482 | + | 0.204507i | ||||
\(544\) | 9.93335 | − | 7.21700i | 0.425889 | − | 0.309426i | ||||
\(545\) | −14.4666 | + | 10.5106i | −0.619683 | + | 0.450226i | ||||
\(546\) | −0.548922 | − | 1.68941i | −0.0234917 | − | 0.0723001i | ||||
\(547\) | 6.09986 | − | 18.7734i | 0.260811 | − | 0.802694i | −0.731818 | − | 0.681500i | \(-0.761328\pi\) |
0.992629 | − | 0.121194i | \(-0.0386722\pi\) | |||||||
\(548\) | 5.68381 | + | 4.12953i | 0.242800 | + | 0.176405i | ||||
\(549\) | −1.74951 | −0.0746672 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.8884 | −2.21052 | ||||||||
\(552\) | 10.4146 | + | 7.56662i | 0.443273 | + | 0.322057i | ||||
\(553\) | −0.538665 | + | 1.65784i | −0.0229064 | + | 0.0704986i | ||||
\(554\) | 3.39328 | + | 10.4434i | 0.144167 | + | 0.443699i | ||||
\(555\) | 6.74244 | − | 4.89867i | 0.286201 | − | 0.207937i | ||||
\(556\) | −13.1954 | + | 9.58699i | −0.559608 | + | 0.406579i | ||||
\(557\) | −5.15442 | − | 15.8637i | −0.218400 | − | 0.672165i | −0.998895 | − | 0.0470033i | \(-0.985033\pi\) |
0.780495 | − | 0.625162i | \(-0.214967\pi\) | |||||||
\(558\) | 0.514901 | − | 1.58470i | 0.0217975 | − | 0.0670858i | ||||
\(559\) | 33.1001 | + | 24.0486i | 1.39998 | + | 1.01715i | ||||
\(560\) | 1.28203 | 0.0541756 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.8739 | −0.458688 | ||||||||
\(563\) | −3.96969 | − | 2.88415i | −0.167302 | − | 0.121552i | 0.500984 | − | 0.865457i | \(-0.332972\pi\) |
−0.668286 | + | 0.743905i | \(0.732972\pi\) | |||||||
\(564\) | 8.40558 | − | 25.8697i | 0.353939 | − | 1.08931i | ||||
\(565\) | −0.142930 | − | 0.439893i | −0.00601311 | − | 0.0185065i | ||||
\(566\) | 10.7250 | − | 7.79218i | 0.450806 | − | 0.327530i | ||||
\(567\) | 2.92074 | − | 2.12204i | 0.122660 | − | 0.0891174i | ||||
\(568\) | −1.55065 | − | 4.77242i | −0.0650640 | − | 0.200246i | ||||
\(569\) | 6.93230 | − | 21.3354i | 0.290617 | − | 0.894428i | −0.694041 | − | 0.719935i | \(-0.744171\pi\) |
0.984658 | − | 0.174493i | \(-0.0558286\pi\) | |||||||
\(570\) | 3.58769 | + | 2.60661i | 0.150272 | + | 0.109179i | ||||
\(571\) | −0.195590 | −0.00818520 | −0.00409260 | − | 0.999992i | \(-0.501303\pi\) | ||||
−0.00409260 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.70826 | 0.363793 | ||||||||
\(574\) | −1.58121 | − | 1.14882i | −0.0659984 | − | 0.0479507i | ||||
\(575\) | 1.37037 | − | 4.21758i | 0.0571486 | − | 0.175885i | ||||
\(576\) | 0.399170 | + | 1.22852i | 0.0166321 | + | 0.0511883i | ||||
\(577\) | 33.3704 | − | 24.2450i | 1.38923 | − | 1.00933i | 0.393277 | − | 0.919420i | \(-0.371341\pi\) |
0.995950 | − | 0.0899127i | \(-0.0286588\pi\) | |||||||
\(578\) | −4.17789 | + | 3.03541i | −0.173777 | + | 0.126257i | ||||
\(579\) | −1.58717 | − | 4.88481i | −0.0659605 | − | 0.203006i | ||||
\(580\) | −4.92594 | + | 15.1605i | −0.204539 | + | 0.629505i | ||||
\(581\) | 0.667074 | + | 0.484658i | 0.0276749 | + | 0.0201070i | ||||
\(582\) | −2.80215 | −0.116153 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.07028 | −0.375331 | ||||||||
\(585\) | −1.68622 | − | 1.22511i | −0.0697165 | − | 0.0506520i | ||||
\(586\) | −3.24835 | + | 9.99740i | −0.134188 | + | 0.412989i | ||||
\(587\) | −0.548443 | − | 1.68793i | −0.0226367 | − | 0.0696685i | 0.939100 | − | 0.343644i | \(-0.111661\pi\) |
−0.961737 | + | 0.273975i | \(0.911661\pi\) | |||||||
\(588\) | 15.5133 | − | 11.2710i | 0.639756 | − | 0.464810i | ||||
\(589\) | 37.1326 | − | 26.9784i | 1.53002 | − | 1.11163i | ||||
\(590\) | −0.411452 | − | 1.26632i | −0.0169392 | − | 0.0521335i | ||||
\(591\) | 9.60432 | − | 29.5591i | 0.395069 | − | 1.21590i | ||||
\(592\) | −11.2223 | − | 8.15351i | −0.461235 | − | 0.335107i | ||||
\(593\) | 29.0094 | 1.19127 | 0.595636 | − | 0.803254i | \(-0.296900\pi\) | ||||
0.595636 | + | 0.803254i | \(0.296900\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.20336 | 0.0493329 | ||||||||
\(596\) | −10.9468 | − | 7.95333i | −0.448399 | − | 0.325781i | ||||
\(597\) | −10.0726 | + | 31.0003i | −0.412244 | + | 1.26876i | ||||
\(598\) | 3.16036 | + | 9.72659i | 0.129237 | + | 0.397750i | ||||
\(599\) | −32.5768 | + | 23.6685i | −1.33105 | + | 0.967067i | −0.331331 | + | 0.943515i | \(0.607498\pi\) |
−0.999723 | + | 0.0235521i | \(0.992502\pi\) | |||||||
\(600\) | 2.34847 | − | 1.70626i | 0.0958757 | − | 0.0696578i | ||||
\(601\) | 4.23221 | + | 13.0254i | 0.172636 | + | 0.531318i | 0.999518 | − | 0.0310577i | \(-0.00988756\pi\) |
−0.826882 | + | 0.562375i | \(0.809888\pi\) | |||||||
\(602\) | −0.609710 | + | 1.87649i | −0.0248499 | + | 0.0764802i | ||||
\(603\) | 2.67289 | + | 1.94197i | 0.108848 | + | 0.0790830i | ||||
\(604\) | −5.07978 | −0.206693 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.92972 | 0.240879 | ||||||||
\(607\) | 17.1142 | + | 12.4342i | 0.694643 | + | 0.504688i | 0.878183 | − | 0.478324i | \(-0.158756\pi\) |
−0.183540 | + | 0.983012i | \(0.558756\pi\) | |||||||
\(608\) | 8.72985 | − | 26.8677i | 0.354042 | − | 1.08963i | ||||
\(609\) | −2.14515 | − | 6.60210i | −0.0869259 | − | 0.267530i | ||||
\(610\) | 1.56609 | − | 1.13783i | 0.0634090 | − | 0.0460693i | ||||
\(611\) | 37.2518 | − | 27.0650i | 1.50704 | − | 1.09493i | ||||
\(612\) | 0.594426 | + | 1.82946i | 0.0240283 | + | 0.0739514i | ||||
\(613\) | 7.18526 | − | 22.1140i | 0.290210 | − | 0.893174i | −0.694579 | − | 0.719417i | \(-0.744409\pi\) |
0.984788 | − | 0.173758i | \(-0.0555909\pi\) | |||||||
\(614\) | 3.81283 | + | 2.77018i | 0.153873 | + | 0.111796i | ||||
\(615\) | 13.5362 | 0.545831 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1028 | −0.527501 | −0.263750 | − | 0.964591i | \(-0.584960\pi\) | ||||
−0.263750 | + | 0.964591i | \(0.584960\pi\) | |||||||
\(618\) | −5.67239 | − | 4.12123i | −0.228177 | − | 0.165780i | ||||
\(619\) | 5.15076 | − | 15.8524i | 0.207027 | − | 0.637163i | −0.792597 | − | 0.609745i | \(-0.791272\pi\) |
0.999624 | − | 0.0274172i | \(-0.00872827\pi\) | |||||||
\(620\) | −4.35730 | − | 13.4104i | −0.174993 | − | 0.538574i | ||||
\(621\) | −19.7365 | + | 14.3394i | −0.791997 | + | 0.575419i | ||||
\(622\) | 3.80150 | − | 2.76195i | 0.152426 | − | 0.110744i | ||||
\(623\) | −2.33919 | − | 7.19929i | −0.0937177 | − | 0.288433i | ||||
\(624\) | 6.32764 | − | 19.4745i | 0.253308 | − | 0.779603i | ||||
\(625\) | −0.809017 | − | 0.587785i | −0.0323607 | − | 0.0235114i | ||||
\(626\) | 0.431443 | 0.0172439 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −30.9204 | −1.23386 | ||||||||
\(629\) | −10.5337 | − | 7.65318i | −0.420006 | − | 0.305152i | ||||
\(630\) | 0.0310604 | − | 0.0955941i | 0.00123748 | − | 0.00380856i | ||||
\(631\) | −0.823085 | − | 2.53319i | −0.0327665 | − | 0.100845i | 0.933336 | − | 0.359005i | \(-0.116884\pi\) |
−0.966102 | + | 0.258160i | \(0.916884\pi\) | |||||||
\(632\) | 5.31484 | − | 3.86145i | 0.211413 | − | 0.153600i | ||||
\(633\) | 8.91483 | − | 6.47700i | 0.354333 | − | 0.257438i | ||||
\(634\) | 0.396515 | + | 1.22035i | 0.0157476 | + | 0.0484662i | ||||
\(635\) | −4.89157 | + | 15.0547i | −0.194116 | + | 0.597428i | ||||
\(636\) | −13.9818 | − | 10.1584i | −0.554413 | − | 0.402805i | ||||
\(637\) | 32.4601 | 1.28611 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.20336 | 0.0476041 | ||||||||
\(640\) | −9.09569 | − | 6.60841i | −0.359539 | − | 0.261220i | ||||
\(641\) | −0.142930 | + | 0.439893i | −0.00564540 | + | 0.0173747i | −0.953840 | − | 0.300317i | \(-0.902908\pi\) |
0.948194 | + | 0.317691i | \(0.102908\pi\) | |||||||
\(642\) | 3.99666 | + | 12.3004i | 0.157736 | + | 0.485460i | ||||
\(643\) | 27.0714 | − | 19.6686i | 1.06759 | − | 0.775652i | 0.0921153 | − | 0.995748i | \(-0.470637\pi\) |
0.975478 | + | 0.220096i | \(0.0706372\pi\) | |||||||
\(644\) | 3.05164 | − | 2.21714i | 0.120251 | − | 0.0873677i | ||||
\(645\) | −4.22267 | − | 12.9960i | −0.166268 | − | 0.511719i | ||||
\(646\) | 2.14093 | − | 6.58911i | 0.0842339 | − | 0.259245i | ||||
\(647\) | 32.5700 | + | 23.6635i | 1.28046 | + | 0.930309i | 0.999567 | − | 0.0294300i | \(-0.00936921\pi\) |
0.280894 | + | 0.959739i | \(0.409369\pi\) | |||||||
\(648\) | −13.6060 | −0.534495 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.30620 | 0.0904567 | ||||||||
\(651\) | 4.96777 | + | 3.60929i | 0.194702 | + | 0.141459i | ||||
\(652\) | −7.19670 | + | 22.1492i | −0.281845 | + | 0.867429i | ||||
\(653\) | 4.74297 | + | 14.5974i | 0.185607 | + | 0.571239i | 0.999958 | − | 0.00913312i | \(-0.00290720\pi\) |
−0.814352 | + | 0.580372i | \(0.802907\pi\) | |||||||
\(654\) | −11.1429 | + | 8.09580i | −0.435722 | + | 0.316571i | ||||
\(655\) | 7.77028 | − | 5.64544i | 0.303610 | − | 0.220586i | ||||
\(656\) | −6.96218 | − | 21.4274i | −0.271827 | − | 0.836599i | ||||
\(657\) | 0.672149 | − | 2.06866i | 0.0262230 | − | 0.0807062i | ||||
\(658\) | 1.79645 | + | 1.30520i | 0.0700331 | + | 0.0508820i | ||||
\(659\) | −36.6635 | −1.42821 | −0.714104 | − | 0.700039i | \(-0.753166\pi\) | ||||
−0.714104 | + | 0.700039i | \(0.753166\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.03024 | −0.312340 | −0.156170 | − | 0.987730i | \(-0.549915\pi\) | ||||
−0.156170 | + | 0.987730i | \(0.549915\pi\) | |||||||
\(662\) | 7.38213 | + | 5.36343i | 0.286915 | + | 0.208456i | ||||
\(663\) | 5.93935 | − | 18.2794i | 0.230665 | − | 0.709915i | ||||
\(664\) | −0.960272 | − | 2.95541i | −0.0372658 | − | 0.114692i | ||||
\(665\) | 2.23995 | − | 1.62742i | 0.0868617 | − | 0.0631087i | ||||
\(666\) | −0.879854 | + | 0.639251i | −0.0340937 | + | 0.0247705i | ||||
\(667\) | 12.3505 | + | 38.0108i | 0.478212 | + | 1.47179i | ||||
\(668\) | −8.67832 | + | 26.7091i | −0.335774 | + | 1.03341i | ||||
\(669\) | −1.34585 | − | 0.977815i | −0.0520335 | − | 0.0378045i | ||||
\(670\) | −3.65565 | −0.141230 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.77946 | 0.145796 | ||||||||
\(673\) | −9.51299 | − | 6.91160i | −0.366699 | − | 0.266422i | 0.389142 | − | 0.921178i | \(-0.372772\pi\) |
−0.755841 | + | 0.654755i | \(0.772772\pi\) | |||||||
\(674\) | −0.712656 | + | 2.19333i | −0.0274505 | + | 0.0844839i | ||||
\(675\) | 1.69995 | + | 5.23192i | 0.0654312 | + | 0.201377i | ||||
\(676\) | 14.3060 | − | 10.3939i | 0.550232 | − | 0.399767i | ||||
\(677\) | −22.0819 | + | 16.0435i | −0.848678 | + | 0.616601i | −0.924781 | − | 0.380499i | \(-0.875752\pi\) |
0.0761030 | + | 0.997100i | \(0.475752\pi\) | |||||||
\(678\) | −0.110092 | − | 0.338828i | −0.00422805 | − | 0.0130126i | ||||
\(679\) | −0.540628 | + | 1.66388i | −0.0207474 | + | 0.0638539i | ||||
\(680\) | −3.66900 | − | 2.66569i | −0.140700 | − | 0.102224i | ||||
\(681\) | −0.770249 | −0.0295160 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.5738 | 1.89689 | 0.948444 | − | 0.316945i | \(-0.102657\pi\) | ||||
0.948444 | + | 0.316945i | \(0.102657\pi\) | |||||||
\(684\) | 3.58063 | + | 2.60148i | 0.136909 | + | 0.0994701i | ||||
\(685\) | 1.22744 | − | 3.77768i | 0.0468982 | − | 0.144338i | ||||
\(686\) | 0.983983 | + | 3.02839i | 0.0375686 | + | 0.115624i | ||||
\(687\) | 17.5447 | − | 12.7470i | 0.669371 | − | 0.486327i | ||||
\(688\) | −18.4005 | + | 13.3687i | −0.701512 | + | 0.509678i | ||||
\(689\) | −9.04046 | − | 27.8237i | −0.344414 | − | 1.06000i | ||||
\(690\) | 1.05553 | − | 3.24859i | 0.0401833 | − | 0.123672i | ||||
\(691\) | 20.4886 | + | 14.8859i | 0.779424 | + | 0.566285i | 0.904806 | − | 0.425824i | \(-0.140016\pi\) |
−0.125382 | + | 0.992109i | \(0.540016\pi\) | |||||||
\(692\) | 40.3635 | 1.53439 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.124298 | −0.00471829 | ||||||||
\(695\) | 7.46034 | + | 5.42026i | 0.282987 | + | 0.205602i | ||||
\(696\) | −8.08450 | + | 24.8815i | −0.306442 | + | 0.943132i | ||||
\(697\) | −6.53495 | − | 20.1125i | −0.247529 | − | 0.761816i | ||||
\(698\) | −0.523246 | + | 0.380160i | −0.0198051 | + | 0.0143893i | ||||
\(699\) | −27.4114 | + | 19.9156i | −1.03680 | + | 0.753276i | ||||
\(700\) | −0.262846 | − | 0.808955i | −0.00993463 | − | 0.0305756i | ||||
\(701\) | 5.64125 | − | 17.3620i | 0.213067 | − | 0.655753i | −0.786218 | − | 0.617949i | \(-0.787964\pi\) |
0.999285 | − | 0.0378039i | \(-0.0120362\pi\) | |||||||
\(702\) | −10.2638 | − | 7.45712i | −0.387384 | − | 0.281451i | ||||
\(703\) | −29.9578 | −1.12988 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.3788 | −0.579199 | ||||||||
\(706\) | 13.7935 | + | 10.0216i | 0.519126 | + | 0.377167i | ||||
\(707\) | 1.14404 | − | 3.52099i | 0.0430261 | − | 0.132421i | ||||
\(708\) | 2.42383 | + | 7.45977i | 0.0910930 | + | 0.280356i | ||||
\(709\) | −3.50448 | + | 2.54616i | −0.131614 | + | 0.0956229i | −0.651644 | − | 0.758525i | \(-0.725921\pi\) |
0.520031 | + | 0.854148i | \(0.325921\pi\) | |||||||
\(710\) | −1.07720 | + | 0.782628i | −0.0404264 | + | 0.0293715i | ||||
\(711\) | 0.486830 | + | 1.49831i | 0.0182575 | + | 0.0561909i | ||||
\(712\) | −8.81579 | + | 27.1322i | −0.330386 | + | 1.01682i | ||||
\(713\) | −28.6014 | − | 20.7801i | −1.07113 | − | 0.778221i | ||||
\(714\) | 0.926885 | 0.0346878 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.818095 | 0.0305737 | ||||||||
\(717\) | 3.46803 | + | 2.51967i | 0.129516 | + | 0.0940989i | ||||
\(718\) | −1.16532 | + | 3.58650i | −0.0434895 | + | 0.133847i | ||||
\(719\) | −7.44747 | − | 22.9210i | −0.277744 | − | 0.854807i | −0.988480 | − | 0.151349i | \(-0.951638\pi\) |
0.710737 | − | 0.703458i | \(-0.248362\pi\) | |||||||
\(720\) | 0.937375 | − | 0.681043i | 0.0349339 | − | 0.0253810i | ||||
\(721\) | −3.54153 | + | 2.57307i | −0.131893 | + | 0.0958261i | ||||
\(722\) | −2.10242 | − | 6.47058i | −0.0782439 | − | 0.240810i | ||||
\(723\) | 2.26147 | − | 6.96008i | 0.0841049 | − | 0.258848i | ||||
\(724\) | −4.47657 | − | 3.25242i | −0.166370 | − | 0.120875i | ||||
\(725\) | 9.01248 | 0.334715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.1066 | −0.931151 | −0.465576 | − | 0.885008i | \(-0.654153\pi\) | ||||
−0.465576 | + | 0.885008i | \(0.654153\pi\) | |||||||
\(728\) | 3.38148 | + | 2.45679i | 0.125326 | + | 0.0910545i | ||||
\(729\) | 9.17661 | − | 28.2427i | 0.339874 | − | 1.04603i | ||||
\(730\) | 0.743716 | + | 2.28892i | 0.0275262 | + | 0.0847169i | ||||
\(731\) | −17.2714 | + | 12.5484i | −0.638804 | + | 0.464118i | ||||
\(732\) | −9.22568 | + | 6.70285i | −0.340991 | + | 0.247744i | ||||
\(733\) | 5.39119 | + | 16.5924i | 0.199128 | + | 0.612854i | 0.999904 | + | 0.0138888i | \(0.00442110\pi\) |
−0.800775 | + | 0.598965i | \(0.795579\pi\) | |||||||
\(734\) | −0.158495 | + | 0.487798i | −0.00585016 | + | 0.0180049i | ||||
\(735\) | −8.77083 | − | 6.37238i | −0.323517 | − | 0.235049i | ||||
\(736\) | −21.7598 | −0.802078 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.76640 | −0.0650222 | ||||||||
\(739\) | −4.20704 | − | 3.05659i | −0.154759 | − | 0.112439i | 0.507711 | − | 0.861527i | \(-0.330492\pi\) |
−0.662470 | + | 0.749089i | \(0.730492\pi\) | |||||||
\(740\) | −2.84399 | + | 8.75291i | −0.104547 | + | 0.321764i | ||||
\(741\) | −13.6655 | − | 42.0581i | −0.502015 | − | 1.54504i | ||||
\(742\) | 1.14139 | − | 0.829271i | 0.0419019 | − | 0.0304435i | ||||
\(743\) | −30.0896 | + | 21.8614i | −1.10388 | + | 0.802016i | −0.981689 | − | 0.190491i | \(-0.938992\pi\) |
−0.122191 | + | 0.992507i | \(0.538992\pi\) | |||||||
\(744\) | −7.15124 | − | 22.0093i | −0.262177 | − | 0.806898i | ||||
\(745\) | −2.36402 | + | 7.27569i | −0.0866108 | + | 0.266561i | ||||
\(746\) | 14.6436 | + | 10.6392i | 0.536141 | + | 0.389529i | ||||
\(747\) | 0.745203 | 0.0272656 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.07494 | 0.295052 | ||||||||
\(750\) | −0.623145 | − | 0.452741i | −0.0227540 | − | 0.0165318i | ||||
\(751\) | 12.7998 | − | 39.3939i | 0.467073 | − | 1.43750i | −0.389283 | − | 0.921118i | \(-0.627277\pi\) |
0.856356 | − | 0.516385i | \(-0.172723\pi\) | |||||||
\(752\) | 7.90991 | + | 24.3442i | 0.288445 | + | 0.887742i | ||||
\(753\) | −14.8198 | + | 10.7672i | −0.540065 | + | 0.392380i | ||||
\(754\) | −16.8151 | + | 12.2169i | −0.612370 | + | 0.444913i | ||||
\(755\) | 0.887492 | + | 2.73142i | 0.0322991 | + | 0.0994065i | ||||
\(756\) | −1.44596 | + | 4.45020i | −0.0525889 | + | 0.161852i | ||||
\(757\) | −3.16834 | − | 2.30193i | −0.115155 | − | 0.0836651i | 0.528717 | − | 0.848798i | \(-0.322673\pi\) |
−0.643872 | + | 0.765133i | \(0.722673\pi\) | |||||||
\(758\) | −16.9025 | −0.613926 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.4346 | −0.378504 | ||||||||
\(761\) | −31.6576 | − | 23.0006i | −1.14759 | − | 0.833770i | −0.159428 | − | 0.987210i | \(-0.550965\pi\) |
−0.988158 | + | 0.153439i | \(0.950965\pi\) | |||||||
\(762\) | −3.76773 | + | 11.5959i | −0.136490 | + | 0.420074i | ||||
\(763\) | 2.65734 | + | 8.17847i | 0.0962023 | + | 0.296080i | ||||
\(764\) | −7.77994 | + | 5.65245i | −0.281468 | + | 0.204499i | ||||
\(765\) | 0.879854 | − | 0.639251i | 0.0318112 | − | 0.0231122i | ||||
\(766\) | −0.122533 | − | 0.377119i | −0.00442731 | − | 0.0136259i | ||||
\(767\) | −4.10304 | + | 12.6279i | −0.148152 | + | 0.455965i | ||||
\(768\) | 0.696444 | + | 0.505996i | 0.0251308 | + | 0.0182586i | ||||
\(769\) | −11.6755 | −0.421028 | −0.210514 | − | 0.977591i | \(-0.567514\pi\) | ||||
−0.210514 | + | 0.977591i | \(0.567514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.1052 | 1.15624 | ||||||||
\(772\) | 4.58866 | + | 3.33386i | 0.165149 | + | 0.119988i | ||||
\(773\) | −2.39995 | + | 7.38629i | −0.0863202 | + | 0.265666i | −0.984895 | − | 0.173155i | \(-0.944604\pi\) |
0.898574 | + | 0.438821i | \(0.144604\pi\) | |||||||
\(774\) | 0.551037 | + | 1.69592i | 0.0198066 | + | 0.0609585i | ||||
\(775\) | −6.44956 | + | 4.68588i | −0.231675 | + | 0.168322i | ||||
\(776\) | 5.33420 | − | 3.87552i | 0.191487 | − | 0.139123i | ||||
\(777\) | −1.23850 | − | 3.81172i | −0.0444311 | − | 0.136745i | ||||
\(778\) | −0.719801 | + | 2.21532i | −0.0258061 | + | 0.0794231i | ||||
\(779\) | −39.3644 | − | 28.5999i | −1.41038 | − | 1.02470i | ||||
\(780\) | −13.5856 | −0.486444 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.33644 | −0.190831 | ||||||||
\(783\) | −40.1104 | − | 29.1419i | −1.43343 | − | 1.04145i | ||||
\(784\) | −5.57612 | + | 17.1615i | −0.199147 | + | 0.612912i | ||||
\(785\) | 5.40213 | + | 16.6260i | 0.192810 | + | 0.593409i | ||||
\(786\) | 5.98505 | − | 4.34840i | 0.213480 | − | 0.155102i | ||||
\(787\) | −1.15631 | + | 0.840111i | −0.0412181 | + | 0.0299467i | −0.608204 | − | 0.793781i | \(-0.708110\pi\) |
0.566985 | + | 0.823728i | \(0.308110\pi\) | |||||||
\(788\) | 10.6061 | + | 32.6421i | 0.377825 | + | 1.16283i | ||||
\(789\) | 3.24611 | − | 9.99051i | 0.115565 | − | 0.355672i | ||||
\(790\) | −1.41024 | − | 1.02460i | −0.0501742 | − | 0.0364537i | ||||
\(791\) | −0.222432 | −0.00790876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.3039 | −0.685501 | ||||||||
\(794\) | −2.85248 | − | 2.07245i | −0.101231 | − | 0.0735484i | ||||
\(795\) | −3.01943 | + | 9.29284i | −0.107088 | + | 0.329583i | ||||
\(796\) | −11.1232 | − | 34.2336i | −0.394250 | − | 1.21338i | ||||
\(797\) | 29.4311 | − | 21.3829i | 1.04250 | − | 0.757422i | 0.0717298 | − | 0.997424i | \(-0.477148\pi\) |
0.970772 | + | 0.240002i | \(0.0771481\pi\) | |||||||
\(798\) | 1.72532 | − | 1.25352i | 0.0610757 | − | 0.0443741i | ||||
\(799\) | 7.42453 | + | 22.8503i | 0.262661 | + | 0.808387i | ||||
\(800\) | −1.51629 | + | 4.66665i | −0.0536088 | + | 0.164991i | ||||
\(801\) | −5.53476 | − | 4.02124i | −0.195561 | − | 0.142083i | ||||
\(802\) | 14.9800 | 0.528962 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.5351 | 0.759486 | ||||||||
\(805\) | −1.72532 | − | 1.25352i | −0.0608096 | − | 0.0441808i | ||||
\(806\) | 5.68136 | − | 17.4854i | 0.200117 | − | 0.615898i | ||||
\(807\) | −0.938990 | − | 2.88991i | −0.0330540 | − | 0.101730i | ||||
\(808\) | −11.2879 | + | 8.20112i | −0.397106 | + | 0.288514i | ||||
\(809\) | 22.5501 | − | 16.3836i | 0.792820 | − | 0.576018i | −0.115979 | − | 0.993252i | \(-0.537000\pi\) |
0.908799 | + | 0.417234i | \(0.137000\pi\) | |||||||
\(810\) | 1.11562 | + | 3.43354i | 0.0391990 | + | 0.120642i | ||||
\(811\) | −12.1071 | + | 37.2617i | −0.425136 | + | 1.30843i | 0.477728 | + | 0.878508i | \(0.341461\pi\) |
−0.902864 | + | 0.429927i | \(0.858539\pi\) | |||||||
\(812\) | 6.20184 | + | 4.50590i | 0.217642 | + | 0.158126i | ||||
\(813\) | −18.1856 | −0.637798 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.1671 | 0.461222 | ||||||||
\(816\) | 8.64400 | + | 6.28023i | 0.302600 | + | 0.219852i | ||||
\(817\) | −15.1788 | + | 46.7155i | −0.531039 | + | 1.63437i | ||||
\(818\) | −1.07474 | − | 3.30770i | −0.0375773 | − | 0.115651i | ||||
\(819\) | −0.810903 | + | 0.589155i | −0.0283352 | + | 0.0205868i | ||||
\(820\) | −12.0932 | + | 8.78622i | −0.422312 | + | 0.306828i | ||||
\(821\) | 4.25739 | + | 13.1029i | 0.148584 | + | 0.457294i | 0.997454 | − | 0.0713067i | \(-0.0227169\pi\) |
−0.848871 | + | 0.528601i | \(0.822717\pi\) | |||||||
\(822\) | 0.945438 | − | 2.90976i | 0.0329759 | − | 0.101489i | ||||
\(823\) | 16.0832 | + | 11.6852i | 0.560626 | + | 0.407319i | 0.831688 | − | 0.555243i | \(-0.187375\pi\) |
−0.271062 | + | 0.962562i | \(0.587375\pi\) | |||||||
\(824\) | 16.4979 | 0.574731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.640313 | −0.0222793 | ||||||||
\(827\) | 10.7819 | + | 7.83351i | 0.374924 | + | 0.272398i | 0.759250 | − | 0.650799i | \(-0.225566\pi\) |
−0.384326 | + | 0.923197i | \(0.625566\pi\) | |||||||
\(828\) | 1.05345 | − | 3.24220i | 0.0366100 | − | 0.112674i | ||||
\(829\) | 15.8186 | + | 48.6845i | 0.549401 | + | 1.69088i | 0.710289 | + | 0.703910i | \(0.248564\pi\) |
−0.160888 | + | 0.986973i | \(0.551436\pi\) | |||||||
\(830\) | −0.667074 | + | 0.484658i | −0.0231545 | + | 0.0168227i | ||||
\(831\) | −29.5879 | + | 21.4969i | −1.02639 | + | 0.745719i | ||||
\(832\) | 4.40440 | + | 13.5553i | 0.152695 | + | 0.469947i | ||||
\(833\) | −5.23395 | + | 16.1084i | −0.181345 | + | 0.558124i | ||||
\(834\) | 5.74632 | + | 4.17495i | 0.198979 | + | 0.144567i | ||||
\(835\) | 15.8778 | 0.549474 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43.8558 | 1.51588 | ||||||||
\(838\) | −0.897244 | − | 0.651886i | −0.0309948 | − | 0.0225190i | ||||
\(839\) | −5.21432 | + | 16.0480i | −0.180018 | + | 0.554040i | −0.999827 | − | 0.0185978i | \(-0.994080\pi\) |
0.819809 | + | 0.572638i | \(0.194080\pi\) | |||||||
\(840\) | −0.431385 | − | 1.32767i | −0.0148842 | − | 0.0458088i | ||||
\(841\) | −42.2508 | + | 30.6970i | −1.45692 | + | 1.05852i | ||||
\(842\) | 2.58255 | − | 1.87633i | 0.0890007 | − | 0.0646628i | ||||
\(843\) | −11.1915 | − | 34.4439i | −0.385455 | − | 1.18631i | ||||
\(844\) | −3.76032 | + | 11.5731i | −0.129436 | + | 0.398362i | ||||
\(845\) | −8.08828 | − | 5.87648i | −0.278245 | − | 0.202157i | ||||
\(846\) | 2.00686 | 0.0689972 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.2633 | 0.558484 | ||||||||
\(849\) | 35.7205 | + | 25.9525i | 1.22592 | + | 0.890686i | ||||
\(850\) | −0.371858 | + | 1.14446i | −0.0127546 | + | 0.0392547i | ||||
\(851\) | 7.13055 | + | 21.9456i | 0.244432 | + | 0.752284i | ||||
\(852\) | 6.34566 | − | 4.61039i | 0.217399 | − | 0.157950i | ||||
\(853\) | 4.38699 | − | 3.18734i | 0.150208 | − | 0.109132i | −0.510143 | − | 0.860090i | \(-0.670408\pi\) |
0.660351 | + | 0.750957i | \(0.270408\pi\) | |||||||
\(854\) | −0.287671 | − | 0.885360i | −0.00984390 | − | 0.0302964i | ||||
\(855\) | 0.773253 | − | 2.37983i | 0.0264447 | − | 0.0813884i | ||||
\(856\) | −24.6202 | − | 17.8877i | −0.841503 | − | 0.611387i | ||||
\(857\) | −27.8386 | −0.950947 | −0.475474 | − | 0.879730i | \(-0.657723\pi\) | ||||
−0.475474 | + | 0.879730i | \(0.657723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.1899 | 1.64422 | 0.822109 | − | 0.569330i | \(-0.192797\pi\) | ||||
0.822109 | + | 0.569330i | \(0.192797\pi\) | |||||||
\(860\) | 12.2081 | + | 8.86974i | 0.416294 | + | 0.302456i | ||||
\(861\) | 2.01157 | − | 6.19096i | 0.0685540 | − | 0.210987i | ||||
\(862\) | −4.88071 | − | 15.0213i | −0.166238 | − | 0.511627i | ||||
\(863\) | −21.7309 | + | 15.7884i | −0.739728 | + | 0.537444i | −0.892626 | − | 0.450798i | \(-0.851139\pi\) |
0.152898 | + | 0.988242i | \(0.451139\pi\) | |||||||
\(864\) | 21.8379 | − | 15.8662i | 0.742941 | − | 0.539778i | ||||
\(865\) | −7.05194 | − | 21.7036i | −0.239773 | − | 0.737946i | ||||
\(866\) | −0.351011 | + | 1.08030i | −0.0119279 | + | 0.0367101i | ||||
\(867\) | −13.9148 | − | 10.1097i | −0.472571 | − | 0.343343i | ||||
\(868\) | −6.78095 | −0.230160 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 6.94185 | 0.235351 | ||||||||
\(871\) | 29.4923 | + | 21.4274i | 0.999309 | + | 0.726041i | ||||
\(872\) | 10.0148 | − | 30.8225i | 0.339145 | − | 1.04378i | ||||
\(873\) | 0.488604 | + | 1.50377i | 0.0165367 | + | 0.0508948i | ||||
\(874\) | −9.93335 | + | 7.21700i | −0.336001 | + | 0.244119i | ||||
\(875\) | −0.389057 | + | 0.282666i | −0.0131525 | + | 0.00955587i | ||||
\(876\) | −4.38117 | − | 13.4838i | −0.148026 | − | 0.455577i | ||||
\(877\) | −12.3247 | + | 37.9317i | −0.416177 | + | 1.28086i | 0.495017 | + | 0.868883i | \(0.335162\pi\) |
−0.911194 | + | 0.411978i | \(0.864838\pi\) | |||||||
\(878\) | −12.0159 | − | 8.73005i | −0.405517 | − | 0.294625i | ||||
\(879\) | −35.0107 | −1.18088 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.82222 | −0.0950829 | −0.0475415 | − | 0.998869i | \(-0.515139\pi\) | ||||
−0.0475415 | + | 0.998869i | \(0.515139\pi\) | |||||||
\(882\) | 1.14455 | + | 0.831564i | 0.0385390 | + | 0.0280002i | ||||
\(883\) | 15.6142 | − | 48.0556i | 0.525460 | − | 1.61720i | −0.237943 | − | 0.971279i | \(-0.576473\pi\) |
0.763404 | − | 0.645922i | \(-0.223527\pi\) | |||||||
\(884\) | 6.55883 | + | 20.1860i | 0.220597 | + | 0.678928i | ||||
\(885\) | 3.58769 | − | 2.60661i | 0.120599 | − | 0.0876201i | ||||
\(886\) | −5.35918 | + | 3.89367i | −0.180045 | + | 0.130811i | ||||
\(887\) | 8.75120 | + | 26.9334i | 0.293836 | + | 0.904336i | 0.983610 | + | 0.180310i | \(0.0577102\pi\) |
−0.689773 | + | 0.724025i | \(0.742290\pi\) | |||||||
\(888\) | −4.66759 | + | 14.3654i | −0.156634 | + | 0.482070i | ||||
\(889\) | 6.15857 | + | 4.47446i | 0.206552 | + | 0.150069i | ||||
\(890\) | 7.56978 | 0.253740 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.83707 | 0.0615096 | ||||||||
\(893\) | 44.7230 | + | 32.4931i | 1.49660 | + | 1.08734i | ||||
\(894\) | −1.82088 | + | 5.60409i | −0.0608994 | + | 0.187429i | ||||
\(895\) | −0.142930 | − | 0.439893i | −0.00477762 | − | 0.0147040i | ||||
\(896\) | −4.37413 | + | 3.17799i | −0.146129 | + | 0.106169i | ||||
\(897\) | −27.5570 | + | 20.0213i | −0.920101 | + | 0.668493i | ||||
\(898\) | 5.78321 | + | 17.7989i | 0.192988 | + | 0.593957i | ||||
\(899\) | 22.2024 | − | 68.3318i | 0.740490 | − | 2.27899i | ||||
\(900\) | −0.621919 | − | 0.451851i | −0.0207306 | − | 0.0150617i | ||||
\(901\) | 15.2653 | 0.508561 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.57144 | −0.218684 | ||||||||
\(904\) | 0.678188 | + | 0.492732i | 0.0225562 | + | 0.0163880i | ||||
\(905\) | −0.966735 | + | 2.97531i | −0.0321354 | + | 0.0989025i | ||||
\(906\) | 0.683590 | + | 2.10387i | 0.0227108 | + | 0.0698965i | ||||
\(907\) | −41.3009 | + | 30.0069i | −1.37138 | + | 0.996362i | −0.373747 | + | 0.927531i | \(0.621927\pi\) |
−0.997628 | + | 0.0688315i | \(0.978073\pi\) | |||||||
\(908\) | 0.688138 | − | 0.499962i | 0.0228367 | − | 0.0165918i | ||||
\(909\) | −1.03395 | − | 3.18217i | −0.0342939 | − | 0.105546i | ||||
\(910\) | 0.342717 | − | 1.05477i | 0.0113610 | − | 0.0349654i | ||||
\(911\) | 20.3410 | + | 14.7786i | 0.673928 | + | 0.489637i | 0.871338 | − | 0.490684i | \(-0.163253\pi\) |
−0.197410 | + | 0.980321i | \(0.563253\pi\) | |||||||
\(912\) | 24.5835 | 0.814040 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.640313 | −0.0211797 | ||||||||
\(915\) | 5.21598 | + | 3.78963i | 0.172435 | + | 0.125281i | ||||
\(916\) | −7.40043 | + | 22.7762i | −0.244517 | + | 0.752547i | ||||
\(917\) | −1.42731 | − | 4.39280i | −0.0471338 | − | 0.145063i | ||||
\(918\) | 5.35559 | − | 3.89106i | 0.176761 | − | 0.128424i | ||||
\(919\) | −20.7231 | + | 15.0562i | −0.683591 | + | 0.496658i | −0.874547 | − | 0.484941i | \(-0.838841\pi\) |
0.190956 | + | 0.981599i | \(0.438841\pi\) | |||||||
\(920\) | 2.48365 | + | 7.64389i | 0.0818835 | + | 0.252011i | ||||
\(921\) | −4.85056 | + | 14.9285i | −0.159832 | + | 0.491911i | ||||
\(922\) | 2.23316 | + | 1.62249i | 0.0735452 | + | 0.0534337i | ||||
\(923\) | 13.2777 | 0.437041 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.20336 | 0.171085 | ||||||||
\(926\) | −1.34044 | − | 0.973885i | −0.0440495 | − | 0.0320039i | ||||
\(927\) | −1.22257 | + | 3.76268i | −0.0401544 | + | 0.123583i | ||||
\(928\) | −13.6655 | − | 42.0581i | −0.448592 | − | 1.38062i | ||||
\(929\) | 6.96381 | − | 5.05950i | 0.228475 | − | 0.165997i | −0.467658 | − | 0.883909i | \(-0.654902\pi\) |
0.696133 | + | 0.717912i | \(0.254902\pi\) | |||||||
\(930\) | −4.96777 | + | 3.60929i | −0.162899 | + | 0.118353i | ||||
\(931\) | 12.0425 | + | 37.0629i | 0.394676 | + | 1.21469i | ||||
\(932\) | 11.5623 | − | 35.5850i | 0.378735 | − | 1.16563i | ||||
\(933\) | 12.6612 | + | 9.19890i | 0.414509 | + | 0.301159i | ||||
\(934\) | 13.0884 | 0.428266 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.77752 | 0.123472 | ||||||||
\(937\) | 4.82692 | + | 3.50696i | 0.157689 | + | 0.114567i | 0.663832 | − | 0.747882i | \(-0.268929\pi\) |
−0.506143 | + | 0.862450i | \(0.668929\pi\) | |||||||
\(938\) | −0.543254 | + | 1.67196i | −0.0177379 | + | 0.0545916i | ||||
\(939\) | 0.444044 | + | 1.36663i | 0.0144908 | + | 0.0445981i | ||||
\(940\) | 13.7394 | − | 9.98225i | 0.448129 | − | 0.325585i | ||||
\(941\) | 18.4763 | − | 13.4238i | 0.602311 | − | 0.437605i | −0.244387 | − | 0.969678i | \(-0.578587\pi\) |
0.846699 | + | 0.532073i | \(0.178587\pi\) | |||||||
\(942\) | 4.16098 | + | 12.8062i | 0.135572 | + | 0.417248i | ||||
\(943\) | −11.5814 | + | 35.6438i | −0.377141 | + | 1.16072i | ||||
\(944\) | −5.97147 | − | 4.33853i | −0.194355 | − | 0.141207i | ||||
\(945\) | 2.64552 | 0.0860586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.30620 | −0.0749415 | −0.0374708 | − | 0.999298i | \(-0.511930\pi\) | ||||
−0.0374708 | + | 0.999298i | \(0.511930\pi\) | |||||||
\(948\) | 8.30763 | + | 6.03584i | 0.269819 | + | 0.196035i | ||||
\(949\) | 7.41641 | − | 22.8254i | 0.240747 | − | 0.740942i | ||||
\(950\) | 0.855586 | + | 2.63322i | 0.0277589 | + | 0.0854330i | ||||
\(951\) | −3.45744 | + | 2.51198i | −0.112115 | + | 0.0814565i | ||||
\(952\) | −1.76443 | + | 1.28193i | −0.0571854 | + | 0.0415476i | ||||
\(953\) | 8.84186 | + | 27.2124i | 0.286416 | + | 0.881498i | 0.985971 | + | 0.166919i | \(0.0533817\pi\) |
−0.699555 | + | 0.714579i | \(0.746618\pi\) | |||||||
\(954\) | 0.394020 | − | 1.21267i | 0.0127569 | − | 0.0392616i | ||||
\(955\) | 4.39859 | + | 3.19576i | 0.142335 | + | 0.103412i | ||||
\(956\) | −4.73383 | −0.153103 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.72404 | −0.217244 | ||||||||
\(959\) | −1.54537 | − | 1.12278i | −0.0499026 | − | 0.0362564i | ||||
\(960\) | 1.47103 | − | 4.52735i | 0.0474771 | − | 0.146120i | ||||
\(961\) | 10.0598 | + | 30.9609i | 0.324510 | + | 0.998740i | ||||
\(962\) | −9.70820 | + | 7.05342i | −0.313005 | + | 0.227411i | ||||
\(963\) | 5.90412 | − | 4.28959i | 0.190257 | − | 0.138230i | ||||
\(964\) | 2.49734 | + | 7.68602i | 0.0804339 | + | 0.247550i | ||||
\(965\) | 0.990941 | − | 3.04980i | 0.0318995 | − | 0.0981767i | ||||
\(966\) | −1.32893 | − | 0.965522i | −0.0427575 | − | 0.0310652i | ||||
\(967\) | −31.7422 | −1.02076 | −0.510380 | − | 0.859949i | \(-0.670495\pi\) | ||||
−0.510380 | + | 0.859949i | \(0.670495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.0749 | 0.741274 | ||||||||
\(970\) | −1.41538 | − | 1.02834i | −0.0454452 | − | 0.0330179i | ||||
\(971\) | −11.4343 | + | 35.1913i | −0.366946 | + | 1.12934i | 0.581808 | + | 0.813326i | \(0.302346\pi\) |
−0.948754 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(972\) | 2.44826 | + | 7.53497i | 0.0785279 | + | 0.241684i | ||||
\(973\) | 3.58769 | − | 2.60661i | 0.115016 | − | 0.0835640i | ||||
\(974\) | −2.89993 | + | 2.10692i | −0.0929198 | + | 0.0675102i | ||||
\(975\) | 2.37356 | + | 7.30506i | 0.0760147 | + | 0.233949i | ||||
\(976\) | 3.31610 | − | 10.2059i | 0.106146 | − | 0.326683i | ||||
\(977\) | −27.4027 | − | 19.9092i | −0.876689 | − | 0.636952i | 0.0556841 | − | 0.998448i | \(-0.482266\pi\) |
−0.932374 | + | 0.361496i | \(0.882266\pi\) | |||||||
\(978\) | 10.1419 | 0.324303 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 11.9721 | 0.382434 | ||||||||
\(981\) | 6.28755 | + | 4.56817i | 0.200746 | + | 0.145850i | ||||
\(982\) | 2.37408 | − | 7.30666i | 0.0757599 | − | 0.233165i | ||||
\(983\) | −11.6659 | − | 35.9039i | −0.372084 | − | 1.14516i | −0.945425 | − | 0.325839i | \(-0.894353\pi\) |
0.573342 | − | 0.819316i | \(-0.305647\pi\) | |||||||
\(984\) | −19.8475 | + | 14.4200i | −0.632714 | + | 0.459694i | ||||
\(985\) | 15.6988 | − | 11.4058i | 0.500205 | − | 0.363421i | ||||
\(986\) | −3.35136 | − | 10.3144i | −0.106729 | − | 0.328479i | ||||
\(987\) | −2.28539 | + | 7.03371i | −0.0727448 | + | 0.223886i | ||||
\(988\) | 39.5083 | + | 28.7044i | 1.25692 | + | 0.913209i | ||||
\(989\) | 37.8343 | 1.20306 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.9354 | −1.42742 | −0.713710 | − | 0.700441i | \(-0.752987\pi\) | ||||
−0.713710 | + | 0.700441i | \(0.752987\pi\) | |||||||
\(992\) | 31.6467 | + | 22.9927i | 1.00478 | + | 0.730019i | ||||
\(993\) | −9.39132 | + | 28.9035i | −0.298024 | + | 0.917225i | ||||
\(994\) | 0.197868 | + | 0.608974i | 0.00627598 | + | 0.0193155i | ||||
\(995\) | −16.4642 | + | 11.9620i | −0.521951 | + | 0.379220i | ||||
\(996\) | 3.92968 | − | 2.85508i | 0.124517 | − | 0.0904666i | ||||
\(997\) | −0.122533 | − | 0.377119i | −0.00388067 | − | 0.0119435i | 0.949097 | − | 0.314983i | \(-0.101999\pi\) |
−0.952978 | + | 0.303039i | \(0.901999\pi\) | |||||||
\(998\) | 3.61870 | − | 11.1372i | 0.114548 | − | 0.352543i | ||||
\(999\) | −23.1577 | − | 16.8251i | −0.732678 | − | 0.532322i |
(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 | 605.2.g.q.81.4 | 24 | ||
11.2 | odd | 10 | inner | 605.2.g.q.511.4 | 24 | ||
11.3 | even | 5 | inner | 605.2.g.q.366.4 | 24 | ||
11.4 | even | 5 | inner | 605.2.g.q.251.3 | 24 | ||
11.5 | even | 5 | 605.2.a.m.1.3 | ✓ | 6 | ||
11.6 | odd | 10 | 605.2.a.m.1.4 | yes | 6 | ||
11.7 | odd | 10 | inner | 605.2.g.q.251.4 | 24 | ||
11.8 | odd | 10 | inner | 605.2.g.q.366.3 | 24 | ||
11.9 | even | 5 | inner | 605.2.g.q.511.3 | 24 | ||
11.10 | odd | 2 | inner | 605.2.g.q.81.3 | 24 | ||
33.5 | odd | 10 | 5445.2.a.bx.1.4 | 6 | |||
33.17 | even | 10 | 5445.2.a.bx.1.3 | 6 | |||
44.27 | odd | 10 | 9680.2.a.cw.1.5 | 6 | |||
44.39 | even | 10 | 9680.2.a.cw.1.6 | 6 | |||
55.39 | odd | 10 | 3025.2.a.bg.1.3 | 6 | |||
55.49 | even | 10 | 3025.2.a.bg.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.m.1.3 | ✓ | 6 | 11.5 | even | 5 | ||
605.2.a.m.1.4 | yes | 6 | 11.6 | odd | 10 | ||
605.2.g.q.81.3 | 24 | 11.10 | odd | 2 | inner | ||
605.2.g.q.81.4 | 24 | 1.1 | even | 1 | trivial | ||
605.2.g.q.251.3 | 24 | 11.4 | even | 5 | inner | ||
605.2.g.q.251.4 | 24 | 11.7 | odd | 10 | inner | ||
605.2.g.q.366.3 | 24 | 11.8 | odd | 10 | inner | ||
605.2.g.q.366.4 | 24 | 11.3 | even | 5 | inner | ||
605.2.g.q.511.3 | 24 | 11.9 | even | 5 | inner | ||
605.2.g.q.511.4 | 24 | 11.2 | odd | 10 | inner | ||
3025.2.a.bg.1.3 | 6 | 55.39 | odd | 10 | |||
3025.2.a.bg.1.4 | 6 | 55.49 | even | 10 | |||
5445.2.a.bx.1.3 | 6 | 33.17 | even | 10 | |||
5445.2.a.bx.1.4 | 6 | 33.5 | odd | 10 | |||
9680.2.a.cw.1.5 | 6 | 44.27 | odd | 10 | |||
9680.2.a.cw.1.6 | 6 | 44.39 | even | 10 |