Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(459,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.459");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.g (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 459.4 | ||
Character | \(\chi\) | \(=\) | 460.459 |
Dual form | 460.2.g.c.459.2 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35976 | + | 0.388659i | −0.961495 | + | 0.274823i | ||||
\(3\) | 1.11016 | 0.640951 | 0.320475 | − | 0.947257i | \(-0.396157\pi\) | ||||
0.320475 | + | 0.947257i | \(0.396157\pi\) | |||||||
\(4\) | 1.69789 | − | 1.05697i | 0.848944 | − | 0.528483i | ||||
\(5\) | 1.71804 | + | 1.43120i | 0.768332 | + | 0.640052i | ||||
\(6\) | −1.50955 | + | 0.431474i | −0.616271 | + | 0.176148i | ||||
\(7\) | − | 4.32159i | − | 1.63341i | −0.577057 | − | 0.816704i | \(-0.695799\pi\) | ||
0.577057 | − | 0.816704i | \(-0.304201\pi\) | |||||||
\(8\) | −1.89792 | + | 2.09712i | −0.671016 | + | 0.741443i | ||||
\(9\) | −1.76755 | −0.589182 | ||||||||
\(10\) | −2.89237 | − | 1.27835i | −0.914648 | − | 0.404251i | ||||
\(11\) | 4.83473 | 1.45773 | 0.728863 | − | 0.684660i | \(-0.240049\pi\) | ||||
0.728863 | + | 0.684660i | \(0.240049\pi\) | |||||||
\(12\) | 1.88493 | − | 1.17340i | 0.544131 | − | 0.338731i | ||||
\(13\) | − | 5.46176i | − | 1.51482i | −0.652940 | − | 0.757410i | \(-0.726465\pi\) | ||
0.652940 | − | 0.757410i | \(-0.273535\pi\) | |||||||
\(14\) | 1.67963 | + | 5.87632i | 0.448899 | + | 1.57051i | ||||
\(15\) | 1.90730 | + | 1.58886i | 0.492463 | + | 0.410242i | ||||
\(16\) | 1.76565 | − | 3.58922i | 0.441412 | − | 0.897304i | ||||
\(17\) | 1.74384 | 0.422943 | 0.211472 | − | 0.977384i | \(-0.432174\pi\) | ||||
0.211472 | + | 0.977384i | \(0.432174\pi\) | |||||||
\(18\) | 2.40344 | − | 0.686973i | 0.566495 | − | 0.161921i | ||||
\(19\) | −1.12597 | −0.258316 | −0.129158 | − | 0.991624i | \(-0.541227\pi\) | ||||
−0.129158 | + | 0.991624i | \(0.541227\pi\) | |||||||
\(20\) | 4.42977 | + | 0.614106i | 0.990527 | + | 0.137318i | ||||
\(21\) | − | 4.79766i | − | 1.04693i | ||||||
\(22\) | −6.57406 | + | 1.87906i | −1.40160 | + | 0.400617i | ||||
\(23\) | −4.61714 | − | 1.29694i | −0.962739 | − | 0.270431i | ||||
\(24\) | −2.10699 | + | 2.32813i | −0.430088 | + | 0.475229i | ||||
\(25\) | 0.903337 | + | 4.91772i | 0.180667 | + | 0.983544i | ||||
\(26\) | 2.12276 | + | 7.42668i | 0.416308 | + | 1.45649i | ||||
\(27\) | −5.29274 | −1.01859 | ||||||||
\(28\) | −4.56777 | − | 7.33758i | −0.863228 | − | 1.38667i | ||||
\(29\) | −2.64398 | −0.490975 | −0.245488 | − | 0.969400i | \(-0.578948\pi\) | ||||
−0.245488 | + | 0.969400i | \(0.578948\pi\) | |||||||
\(30\) | −3.21099 | − | 1.41918i | −0.586244 | − | 0.259105i | ||||
\(31\) | 3.01187i | 0.540947i | 0.962727 | + | 0.270474i | \(0.0871803\pi\) | ||||
−0.962727 | + | 0.270474i | \(0.912820\pi\) | |||||||
\(32\) | −1.00587 | + | 5.56671i | −0.177815 | + | 0.984064i | ||||
\(33\) | 5.36732 | 0.934330 | ||||||||
\(34\) | −2.37120 | + | 0.677760i | −0.406658 | + | 0.116235i | ||||
\(35\) | 6.18506 | − | 7.42468i | 1.04547 | − | 1.25500i | ||||
\(36\) | −3.00110 | + | 1.86824i | −0.500183 | + | 0.311373i | ||||
\(37\) | 9.91265 | 1.62963 | 0.814815 | − | 0.579721i | \(-0.196838\pi\) | ||||
0.814815 | + | 0.579721i | \(0.196838\pi\) | |||||||
\(38\) | 1.53105 | − | 0.437620i | 0.248370 | − | 0.0709914i | ||||
\(39\) | − | 6.06342i | − | 0.970925i | ||||||
\(40\) | −6.26210 | + | 0.886636i | −0.990125 | + | 0.140189i | ||||
\(41\) | 10.3038 | 1.60918 | 0.804588 | − | 0.593834i | \(-0.202386\pi\) | ||||
0.804588 | + | 0.593834i | \(0.202386\pi\) | |||||||
\(42\) | 1.86465 | + | 6.52365i | 0.287722 | + | 1.00662i | ||||
\(43\) | 5.51134i | 0.840471i | 0.907415 | + | 0.420236i | \(0.138053\pi\) | ||||
−0.907415 | + | 0.420236i | \(0.861947\pi\) | |||||||
\(44\) | 8.20883 | − | 5.11014i | 1.23753 | − | 0.770383i | ||||
\(45\) | −3.03672 | − | 2.52971i | −0.452687 | − | 0.377107i | ||||
\(46\) | 6.78226 | − | 0.0309634i | 0.999990 | − | 0.00456531i | ||||
\(47\) | 0.335447 | 0.0489300 | 0.0244650 | − | 0.999701i | \(-0.492212\pi\) | ||||
0.0244650 | + | 0.999701i | \(0.492212\pi\) | |||||||
\(48\) | 1.96015 | − | 3.98460i | 0.282923 | − | 0.575128i | ||||
\(49\) | −11.6762 | −1.66802 | ||||||||
\(50\) | −3.13964 | − | 6.33582i | −0.444012 | − | 0.896021i | ||||
\(51\) | 1.93594 | 0.271086 | ||||||||
\(52\) | −5.77289 | − | 9.27346i | −0.800556 | − | 1.28600i | ||||
\(53\) | 0.212290 | 0.0291602 | 0.0145801 | − | 0.999894i | \(-0.495359\pi\) | ||||
0.0145801 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(54\) | 7.19684 | − | 2.05707i | 0.979367 | − | 0.279932i | ||||
\(55\) | 8.30627 | + | 6.91946i | 1.12002 | + | 0.933020i | ||||
\(56\) | 9.06289 | + | 8.20203i | 1.21108 | + | 1.09604i | ||||
\(57\) | −1.25001 | −0.165568 | ||||||||
\(58\) | 3.59518 | − | 1.02761i | 0.472070 | − | 0.134931i | ||||
\(59\) | − | 3.23125i | − | 0.420673i | −0.977629 | − | 0.210337i | \(-0.932544\pi\) | ||
0.977629 | − | 0.210337i | \(-0.0674560\pi\) | |||||||
\(60\) | 4.91775 | + | 0.681755i | 0.634879 | + | 0.0880142i | ||||
\(61\) | − | 2.94732i | − | 0.377366i | −0.982038 | − | 0.188683i | \(-0.939578\pi\) | ||
0.982038 | − | 0.188683i | \(-0.0604218\pi\) | |||||||
\(62\) | −1.17059 | − | 4.09541i | −0.148665 | − | 0.520118i | ||||
\(63\) | 7.63861i | 0.962375i | ||||||||
\(64\) | −0.795805 | − | 7.96032i | −0.0994756 | − | 0.995040i | ||||
\(65\) | 7.81687 | − | 9.38353i | 0.969563 | − | 1.16388i | ||||
\(66\) | −7.29826 | + | 2.08606i | −0.898353 | + | 0.256776i | ||||
\(67\) | 4.96759i | 0.606888i | 0.952849 | + | 0.303444i | \(0.0981366\pi\) | ||||
−0.952849 | + | 0.303444i | \(0.901863\pi\) | |||||||
\(68\) | 2.96085 | − | 1.84318i | 0.359055 | − | 0.223518i | ||||
\(69\) | −5.12576 | − | 1.43981i | −0.617069 | − | 0.173333i | ||||
\(70\) | −5.52452 | + | 12.4996i | −0.660306 | + | 1.49399i | ||||
\(71\) | 12.4759i | 1.48062i | 0.672268 | + | 0.740308i | \(0.265320\pi\) | ||||
−0.672268 | + | 0.740308i | \(0.734680\pi\) | |||||||
\(72\) | 3.35466 | − | 3.70675i | 0.395350 | − | 0.436845i | ||||
\(73\) | 9.16159i | 1.07228i | 0.844128 | + | 0.536142i | \(0.180119\pi\) | ||||
−0.844128 | + | 0.536142i | \(0.819881\pi\) | |||||||
\(74\) | −13.4788 | + | 3.85264i | −1.56688 | + | 0.447861i | ||||
\(75\) | 1.00285 | + | 5.45945i | 0.115799 | + | 0.630403i | ||||
\(76\) | −1.91178 | + | 1.19012i | −0.219296 | + | 0.136516i | ||||
\(77\) | − | 20.8937i | − | 2.38106i | ||||||
\(78\) | 2.35661 | + | 8.24480i | 0.266833 | + | 0.933539i | ||||
\(79\) | 7.65531 | 0.861289 | 0.430645 | − | 0.902522i | \(-0.358286\pi\) | ||||
0.430645 | + | 0.902522i | \(0.358286\pi\) | |||||||
\(80\) | 8.17034 | − | 3.63943i | 0.913472 | − | 0.406901i | ||||
\(81\) | −0.573142 | −0.0636824 | ||||||||
\(82\) | −14.0106 | + | 4.00465i | −1.54721 | + | 0.442239i | ||||
\(83\) | − | 7.95681i | − | 0.873374i | −0.899614 | − | 0.436687i | \(-0.856152\pi\) | ||
0.899614 | − | 0.436687i | \(-0.143848\pi\) | |||||||
\(84\) | −5.07096 | − | 8.14588i | −0.553287 | − | 0.888789i | ||||
\(85\) | 2.99599 | + | 2.49578i | 0.324961 | + | 0.270706i | ||||
\(86\) | −2.14203 | − | 7.49409i | −0.230981 | − | 0.808109i | ||||
\(87\) | −2.93524 | −0.314691 | ||||||||
\(88\) | −9.17592 | + | 10.1390i | −0.978157 | + | 1.08082i | ||||
\(89\) | 3.81527i | 0.404418i | 0.979342 | + | 0.202209i | \(0.0648121\pi\) | ||||
−0.979342 | + | 0.202209i | \(0.935188\pi\) | |||||||
\(90\) | 5.11240 | + | 2.25955i | 0.538894 | + | 0.238177i | ||||
\(91\) | −23.6035 | −2.47432 | ||||||||
\(92\) | −9.21020 | + | 2.67809i | −0.960230 | + | 0.279210i | ||||
\(93\) | 3.34365i | 0.346720i | ||||||||
\(94\) | −0.456127 | + | 0.130375i | −0.0470459 | + | 0.0134471i | ||||
\(95\) | −1.93447 | − | 1.61149i | −0.198473 | − | 0.165336i | ||||
\(96\) | −1.11668 | + | 6.17993i | −0.113971 | + | 0.630737i | ||||
\(97\) | −14.6914 | −1.49168 | −0.745841 | − | 0.666124i | \(-0.767952\pi\) | ||||
−0.745841 | + | 0.666124i | \(0.767952\pi\) | |||||||
\(98\) | 15.8768 | − | 4.53804i | 1.60379 | − | 0.458412i | ||||
\(99\) | −8.54560 | −0.858866 | ||||||||
\(100\) | 6.73163 | + | 7.39494i | 0.673163 | + | 0.739494i | ||||
\(101\) | −7.96306 | −0.792354 | −0.396177 | − | 0.918174i | \(-0.629663\pi\) | ||||
−0.396177 | + | 0.918174i | \(0.629663\pi\) | |||||||
\(102\) | −2.63241 | + | 0.752421i | −0.260648 | + | 0.0745008i | ||||
\(103\) | 6.72204i | 0.662342i | 0.943571 | + | 0.331171i | \(0.107444\pi\) | ||||
−0.943571 | + | 0.331171i | \(0.892556\pi\) | |||||||
\(104\) | 11.4540 | + | 10.3660i | 1.12315 | + | 1.01647i | ||||
\(105\) | 6.86640 | − | 8.24257i | 0.670092 | − | 0.804393i | ||||
\(106\) | −0.288663 | + | 0.0825083i | −0.0280374 | + | 0.00801391i | ||||
\(107\) | 15.6616i | 1.51406i | 0.653380 | + | 0.757030i | \(0.273350\pi\) | ||||
−0.653380 | + | 0.757030i | \(0.726650\pi\) | |||||||
\(108\) | −8.98647 | + | 5.59424i | −0.864724 | + | 0.538306i | ||||
\(109\) | − | 12.9565i | − | 1.24101i | −0.784202 | − | 0.620505i | \(-0.786928\pi\) | ||
0.784202 | − | 0.620505i | \(-0.213072\pi\) | |||||||
\(110\) | −13.9838 | − | 6.18049i | −1.33331 | − | 0.589287i | ||||
\(111\) | 11.0046 | 1.04451 | ||||||||
\(112\) | −15.5111 | − | 7.63041i | −1.46566 | − | 0.721006i | ||||
\(113\) | −2.68622 | −0.252698 | −0.126349 | − | 0.991986i | \(-0.540326\pi\) | ||||
−0.126349 | + | 0.991986i | \(0.540326\pi\) | |||||||
\(114\) | 1.69971 | − | 0.485828i | 0.159193 | − | 0.0455020i | ||||
\(115\) | −6.07625 | − | 8.83624i | −0.566613 | − | 0.823984i | ||||
\(116\) | −4.48918 | + | 2.79460i | −0.416810 | + | 0.259472i | ||||
\(117\) | 9.65391i | 0.892505i | ||||||||
\(118\) | 1.25586 | + | 4.39373i | 0.115611 | + | 0.404475i | ||||
\(119\) | − | 7.53617i | − | 0.690839i | ||||||
\(120\) | −6.95193 | + | 0.984307i | −0.634621 | + | 0.0898545i | ||||
\(121\) | 12.3746 | 1.12496 | ||||||||
\(122\) | 1.14550 | + | 4.00764i | 0.103709 | + | 0.362835i | ||||
\(123\) | 11.4388 | 1.03140 | ||||||||
\(124\) | 3.18344 | + | 5.11381i | 0.285881 | + | 0.459234i | ||||
\(125\) | −5.48627 | + | 9.74171i | −0.490707 | + | 0.871325i | ||||
\(126\) | −2.96882 | − | 10.3867i | −0.264483 | − | 0.925318i | ||||
\(127\) | −7.79228 | −0.691453 | −0.345727 | − | 0.938335i | \(-0.612368\pi\) | ||||
−0.345727 | + | 0.938335i | \(0.612368\pi\) | |||||||
\(128\) | 4.17595 | + | 10.5148i | 0.369106 | + | 0.929387i | ||||
\(129\) | 6.11846i | 0.538701i | ||||||||
\(130\) | −6.98206 | + | 15.7974i | −0.612367 | + | 1.38553i | ||||
\(131\) | − | 9.42434i | − | 0.823408i | −0.911318 | − | 0.411704i | \(-0.864934\pi\) | ||
0.911318 | − | 0.411704i | \(-0.135066\pi\) | |||||||
\(132\) | 9.11311 | − | 5.67307i | 0.793194 | − | 0.493777i | ||||
\(133\) | 4.86600i | 0.421936i | ||||||||
\(134\) | −1.93070 | − | 6.75473i | −0.166787 | − | 0.583520i | ||||
\(135\) | −9.09314 | − | 7.57496i | −0.782613 | − | 0.651949i | ||||
\(136\) | −3.30967 | + | 3.65704i | −0.283802 | + | 0.313588i | ||||
\(137\) | −15.4923 | −1.32359 | −0.661797 | − | 0.749683i | \(-0.730206\pi\) | ||||
−0.661797 | + | 0.749683i | \(0.730206\pi\) | |||||||
\(138\) | 7.52939 | − | 0.0343744i | 0.640944 | − | 0.00292614i | ||||
\(139\) | 4.69573i | 0.398287i | 0.979970 | + | 0.199143i | \(0.0638159\pi\) | ||||
−0.979970 | + | 0.199143i | \(0.936184\pi\) | |||||||
\(140\) | 2.65391 | − | 19.1437i | 0.224297 | − | 1.61793i | ||||
\(141\) | 0.372400 | 0.0313617 | ||||||||
\(142\) | −4.84887 | − | 16.9642i | −0.406908 | − | 1.42360i | ||||
\(143\) | − | 26.4061i | − | 2.20819i | ||||||
\(144\) | −3.12087 | + | 6.34411i | −0.260072 | + | 0.528676i | ||||
\(145\) | −4.54247 | − | 3.78406i | −0.377232 | − | 0.314249i | ||||
\(146\) | −3.56074 | − | 12.4576i | −0.294689 | − | 1.03099i | ||||
\(147\) | −12.9624 | −1.06912 | ||||||||
\(148\) | 16.8306 | − | 10.4773i | 1.38346 | − | 0.861231i | ||||
\(149\) | 16.1954i | 1.32678i | 0.748275 | + | 0.663388i | \(0.230882\pi\) | ||||
−0.748275 | + | 0.663388i | \(0.769118\pi\) | |||||||
\(150\) | −3.48550 | − | 7.03378i | −0.284590 | − | 0.574305i | ||||
\(151\) | − | 9.24464i | − | 0.752318i | −0.926555 | − | 0.376159i | \(-0.877245\pi\) | ||
0.926555 | − | 0.376159i | \(-0.122755\pi\) | |||||||
\(152\) | 2.13701 | − | 2.36130i | 0.173334 | − | 0.191527i | ||||
\(153\) | −3.08232 | −0.249191 | ||||||||
\(154\) | 8.12053 | + | 28.4104i | 0.654371 | + | 2.28938i | ||||
\(155\) | −4.31058 | + | 5.17451i | −0.346234 | + | 0.415627i | ||||
\(156\) | −6.40883 | − | 10.2950i | −0.513117 | − | 0.824261i | ||||
\(157\) | −0.749867 | −0.0598459 | −0.0299229 | − | 0.999552i | \(-0.509526\pi\) | ||||
−0.0299229 | + | 0.999552i | \(0.509526\pi\) | |||||||
\(158\) | −10.4094 | + | 2.97530i | −0.828125 | + | 0.236702i | ||||
\(159\) | 0.235675 | 0.0186903 | ||||||||
\(160\) | −9.69520 | + | 8.12423i | −0.766473 | + | 0.642277i | ||||
\(161\) | −5.60485 | + | 19.9534i | −0.441724 | + | 1.57255i | ||||
\(162\) | 0.779335 | − | 0.222757i | 0.0612303 | − | 0.0175014i | ||||
\(163\) | −7.11782 | −0.557510 | −0.278755 | − | 0.960362i | \(-0.589922\pi\) | ||||
−0.278755 | + | 0.960362i | \(0.589922\pi\) | |||||||
\(164\) | 17.4946 | − | 10.8907i | 1.36610 | − | 0.850421i | ||||
\(165\) | 9.22128 | + | 7.68170i | 0.717876 | + | 0.598020i | ||||
\(166\) | 3.09249 | + | 10.8193i | 0.240024 | + | 0.839744i | ||||
\(167\) | −0.363102 | −0.0280977 | −0.0140488 | − | 0.999901i | \(-0.504472\pi\) | ||||
−0.0140488 | + | 0.999901i | \(0.504472\pi\) | |||||||
\(168\) | 10.0612 | + | 9.10556i | 0.776242 | + | 0.702509i | ||||
\(169\) | −16.8308 | −1.29468 | ||||||||
\(170\) | −5.04383 | − | 2.22924i | −0.386844 | − | 0.170975i | ||||
\(171\) | 1.99021 | 0.152195 | ||||||||
\(172\) | 5.82529 | + | 9.35764i | 0.444174 | + | 0.713513i | ||||
\(173\) | 3.52247i | 0.267808i | 0.990994 | + | 0.133904i | \(0.0427514\pi\) | ||||
−0.990994 | + | 0.133904i | \(0.957249\pi\) | |||||||
\(174\) | 3.99122 | − | 1.14081i | 0.302574 | − | 0.0864844i | ||||
\(175\) | 21.2524 | − | 3.90385i | 1.60653 | − | 0.295104i | ||||
\(176\) | 8.53643 | − | 17.3529i | 0.643458 | − | 1.30802i | ||||
\(177\) | − | 3.58721i | − | 0.269631i | ||||||
\(178\) | −1.48284 | − | 5.18785i | −0.111144 | − | 0.388846i | ||||
\(179\) | 21.0643i | 1.57442i | 0.616687 | + | 0.787209i | \(0.288474\pi\) | ||||
−0.616687 | + | 0.787209i | \(0.711526\pi\) | |||||||
\(180\) | −7.82983 | − | 1.08546i | −0.583601 | − | 0.0809054i | ||||
\(181\) | − | 18.9992i | − | 1.41220i | −0.708114 | − | 0.706098i | \(-0.750454\pi\) | ||
0.708114 | − | 0.706098i | \(-0.249546\pi\) | |||||||
\(182\) | 32.0951 | − | 9.17371i | 2.37904 | − | 0.680001i | ||||
\(183\) | − | 3.27199i | − | 0.241873i | ||||||
\(184\) | 11.4828 | − | 7.22119i | 0.846523 | − | 0.532353i | ||||
\(185\) | 17.0304 | + | 14.1870i | 1.25210 | + | 1.04305i | ||||
\(186\) | −1.29954 | − | 4.54656i | −0.0952869 | − | 0.333370i | ||||
\(187\) | 8.43099 | 0.616535 | ||||||||
\(188\) | 0.569552 | − | 0.354556i | 0.0415388 | − | 0.0258586i | ||||
\(189\) | 22.8730i | 1.66377i | ||||||||
\(190\) | 3.25674 | + | 1.43939i | 0.236268 | + | 0.104425i | ||||
\(191\) | 19.7883 | 1.43183 | 0.715916 | − | 0.698187i | \(-0.246009\pi\) | ||||
0.715916 | + | 0.698187i | \(0.246009\pi\) | |||||||
\(192\) | −0.883470 | − | 8.83722i | −0.0637590 | − | 0.637772i | ||||
\(193\) | − | 17.5501i | − | 1.26328i | −0.775261 | − | 0.631641i | \(-0.782382\pi\) | ||
0.775261 | − | 0.631641i | \(-0.217618\pi\) | |||||||
\(194\) | 19.9767 | − | 5.70993i | 1.43424 | − | 0.409949i | ||||
\(195\) | 8.67797 | − | 10.4172i | 0.621442 | − | 0.745992i | ||||
\(196\) | −19.8248 | + | 12.3413i | −1.41606 | + | 0.881521i | ||||
\(197\) | 13.3811i | 0.953362i | 0.879076 | + | 0.476681i | \(0.158160\pi\) | ||||
−0.879076 | + | 0.476681i | \(0.841840\pi\) | |||||||
\(198\) | 11.6200 | − | 3.32133i | 0.825795 | − | 0.236036i | ||||
\(199\) | −5.85698 | −0.415190 | −0.207595 | − | 0.978215i | \(-0.566564\pi\) | ||||
−0.207595 | + | 0.978215i | \(0.566564\pi\) | |||||||
\(200\) | −12.0275 | − | 7.43903i | −0.850473 | − | 0.526019i | ||||
\(201\) | 5.51482i | 0.388986i | ||||||||
\(202\) | 10.8278 | − | 3.09492i | 0.761845 | − | 0.217758i | ||||
\(203\) | 11.4262i | 0.801963i | ||||||||
\(204\) | 3.28701 | − | 2.04622i | 0.230137 | − | 0.143264i | ||||
\(205\) | 17.7023 | + | 14.7467i | 1.23638 | + | 1.02996i | ||||
\(206\) | −2.61258 | − | 9.14035i | −0.182027 | − | 0.636838i | ||||
\(207\) | 8.16100 | + | 2.29240i | 0.567229 | + | 0.159333i | ||||
\(208\) | −19.6034 | − | 9.64355i | −1.35925 | − | 0.668660i | ||||
\(209\) | −5.44378 | −0.376554 | ||||||||
\(210\) | −6.13310 | + | 13.8766i | −0.423224 | + | 0.957576i | ||||
\(211\) | 17.0002i | 1.17034i | 0.810910 | + | 0.585171i | \(0.198973\pi\) | ||||
−0.810910 | + | 0.585171i | \(0.801027\pi\) | |||||||
\(212\) | 0.360444 | − | 0.224383i | 0.0247554 | − | 0.0154107i | ||||
\(213\) | 13.8502i | 0.949002i | ||||||||
\(214\) | −6.08701 | − | 21.2959i | −0.416099 | − | 1.45576i | ||||
\(215\) | −7.88782 | + | 9.46871i | −0.537945 | + | 0.645761i | ||||
\(216\) | 10.0452 | − | 11.0995i | 0.683488 | − | 0.755225i | ||||
\(217\) | 13.0161 | 0.883587 | ||||||||
\(218\) | 5.03567 | + | 17.6178i | 0.341059 | + | 1.19322i | ||||
\(219\) | 10.1708i | 0.687281i | ||||||||
\(220\) | 21.4167 | + | 2.96903i | 1.44392 | + | 0.200172i | ||||
\(221\) | − | 9.52444i | − | 0.640683i | ||||||
\(222\) | −14.9636 | + | 4.27705i | −1.00429 | + | 0.287057i | ||||
\(223\) | −4.32099 | −0.289355 | −0.144677 | − | 0.989479i | \(-0.546214\pi\) | ||||
−0.144677 | + | 0.989479i | \(0.546214\pi\) | |||||||
\(224\) | 24.0570 | + | 4.34698i | 1.60738 | + | 0.290445i | ||||
\(225\) | −1.59669 | − | 8.69230i | −0.106446 | − | 0.579487i | ||||
\(226\) | 3.65261 | − | 1.04402i | 0.242968 | − | 0.0694474i | ||||
\(227\) | − | 2.12234i | − | 0.140865i | −0.997517 | − | 0.0704323i | \(-0.977562\pi\) | ||
0.997517 | − | 0.0704323i | \(-0.0224379\pi\) | |||||||
\(228\) | −2.12238 | + | 1.32122i | −0.140558 | + | 0.0874998i | ||||
\(229\) | − | 4.12377i | − | 0.272507i | −0.990674 | − | 0.136253i | \(-0.956494\pi\) | ||
0.990674 | − | 0.136253i | \(-0.0435061\pi\) | |||||||
\(230\) | 11.6965 | + | 9.65357i | 0.771246 | + | 0.636537i | ||||
\(231\) | − | 23.1954i | − | 1.52614i | ||||||
\(232\) | 5.01806 | − | 5.54474i | 0.329452 | − | 0.364030i | ||||
\(233\) | − | 11.9095i | − | 0.780216i | −0.920769 | − | 0.390108i | \(-0.872438\pi\) | ||
0.920769 | − | 0.390108i | \(-0.127562\pi\) | |||||||
\(234\) | −3.75208 | − | 13.1270i | −0.245281 | − | 0.858138i | ||||
\(235\) | 0.576312 | + | 0.480092i | 0.0375945 | + | 0.0313177i | ||||
\(236\) | −3.41532 | − | 5.48631i | −0.222319 | − | 0.357128i | ||||
\(237\) | 8.49861 | 0.552044 | ||||||||
\(238\) | 2.92900 | + | 10.2474i | 0.189859 | + | 0.664238i | ||||
\(239\) | − | 14.6042i | − | 0.944667i | −0.881420 | − | 0.472334i | \(-0.843412\pi\) | ||
0.881420 | − | 0.472334i | \(-0.156588\pi\) | |||||||
\(240\) | 9.07038 | − | 4.04035i | 0.585491 | − | 0.260803i | ||||
\(241\) | 14.1752i | 0.913104i | 0.889697 | + | 0.456552i | \(0.150916\pi\) | ||||
−0.889697 | + | 0.456552i | \(0.849084\pi\) | |||||||
\(242\) | −16.8265 | + | 4.80950i | −1.08165 | + | 0.309166i | ||||
\(243\) | 15.2419 | 0.977770 | ||||||||
\(244\) | −3.11521 | − | 5.00422i | −0.199431 | − | 0.320362i | ||||
\(245\) | −20.0601 | − | 16.7109i | −1.28159 | − | 1.06762i | ||||
\(246\) | −15.5540 | + | 4.44580i | −0.991688 | + | 0.283454i | ||||
\(247\) | 6.14980i | 0.391303i | ||||||||
\(248\) | −6.31624 | − | 5.71628i | −0.401081 | − | 0.362984i | ||||
\(249\) | − | 8.83333i | − | 0.559790i | ||||||
\(250\) | 3.67380 | − | 15.3787i | 0.232351 | − | 0.972632i | ||||
\(251\) | −7.03203 | −0.443858 | −0.221929 | − | 0.975063i | \(-0.571235\pi\) | ||||
−0.221929 | + | 0.975063i | \(0.571235\pi\) | |||||||
\(252\) | 8.07375 | + | 12.9695i | 0.508598 | + | 0.817002i | ||||
\(253\) | −22.3226 | − | 6.27036i | −1.40341 | − | 0.394214i | ||||
\(254\) | 10.5956 | − | 3.02854i | 0.664829 | − | 0.190028i | ||||
\(255\) | 3.32603 | + | 2.77072i | 0.208284 | + | 0.173509i | ||||
\(256\) | −9.76497 | − | 12.6746i | −0.610311 | − | 0.792162i | ||||
\(257\) | − | 2.46512i | − | 0.153770i | −0.997040 | − | 0.0768849i | \(-0.975503\pi\) | ||
0.997040 | − | 0.0768849i | \(-0.0244974\pi\) | |||||||
\(258\) | −2.37800 | − | 8.31963i | −0.148048 | − | 0.517958i | ||||
\(259\) | − | 42.8384i | − | 2.66185i | ||||||
\(260\) | 3.35410 | − | 24.1944i | 0.208012 | − | 1.50047i | ||||
\(261\) | 4.67336 | 0.289274 | ||||||||
\(262\) | 3.66285 | + | 12.8148i | 0.226292 | + | 0.791702i | ||||
\(263\) | − | 9.50506i | − | 0.586107i | −0.956096 | − | 0.293054i | \(-0.905329\pi\) | ||
0.956096 | − | 0.293054i | \(-0.0946715\pi\) | |||||||
\(264\) | −10.1867 | + | 11.2559i | −0.626950 | + | 0.692753i | ||||
\(265\) | 0.364722 | + | 0.303829i | 0.0224047 | + | 0.0186640i | ||||
\(266\) | −1.89122 | − | 6.61659i | −0.115958 | − | 0.405689i | ||||
\(267\) | 4.23556i | 0.259212i | ||||||||
\(268\) | 5.25058 | + | 8.43442i | 0.320730 | + | 0.515214i | ||||
\(269\) | 3.29016 | 0.200605 | 0.100302 | − | 0.994957i | \(-0.468019\pi\) | ||||
0.100302 | + | 0.994957i | \(0.468019\pi\) | |||||||
\(270\) | 15.3086 | + | 6.76599i | 0.931649 | + | 0.411765i | ||||
\(271\) | 6.89939i | 0.419108i | 0.977797 | + | 0.209554i | \(0.0672012\pi\) | ||||
−0.977797 | + | 0.209554i | \(0.932799\pi\) | |||||||
\(272\) | 3.07901 | − | 6.25902i | 0.186692 | − | 0.379509i | ||||
\(273\) | −26.2036 | −1.58592 | ||||||||
\(274\) | 21.0657 | − | 6.02121i | 1.27263 | − | 0.363754i | ||||
\(275\) | 4.36739 | + | 23.7758i | 0.263363 | + | 1.43374i | ||||
\(276\) | −10.2248 | + | 2.97311i | −0.615460 | + | 0.178960i | ||||
\(277\) | − | 16.1068i | − | 0.967766i | −0.875133 | − | 0.483883i | \(-0.839226\pi\) | ||
0.875133 | − | 0.483883i | \(-0.160774\pi\) | |||||||
\(278\) | −1.82504 | − | 6.38506i | −0.109458 | − | 0.382950i | ||||
\(279\) | − | 5.32361i | − | 0.318716i | ||||||
\(280\) | 3.83168 | + | 27.0622i | 0.228986 | + | 1.61728i | ||||
\(281\) | 6.79153i | 0.405149i | 0.979267 | + | 0.202574i | \(0.0649308\pi\) | ||||
−0.979267 | + | 0.202574i | \(0.935069\pi\) | |||||||
\(282\) | −0.506374 | + | 0.144737i | −0.0301541 | + | 0.00861893i | ||||
\(283\) | 7.20688i | 0.428404i | 0.976789 | + | 0.214202i | \(0.0687151\pi\) | ||||
−0.976789 | + | 0.214202i | \(0.931285\pi\) | |||||||
\(284\) | 13.1866 | + | 21.1827i | 0.782480 | + | 1.25696i | ||||
\(285\) | −2.14757 | − | 1.78901i | −0.127211 | − | 0.105972i | ||||
\(286\) | 10.2630 | + | 35.9060i | 0.606863 | + | 2.12316i | ||||
\(287\) | − | 44.5286i | − | 2.62844i | ||||||
\(288\) | 1.77793 | − | 9.83941i | 0.104765 | − | 0.579793i | ||||
\(289\) | −13.9590 | −0.821119 | ||||||||
\(290\) | 7.64738 | + | 3.37994i | 0.449069 | + | 0.198477i | ||||
\(291\) | −16.3097 | −0.956094 | ||||||||
\(292\) | 9.68349 | + | 15.5554i | 0.566683 | + | 0.910309i | ||||
\(293\) | 25.1995 | 1.47217 | 0.736085 | − | 0.676889i | \(-0.236672\pi\) | ||||
0.736085 | + | 0.676889i | \(0.236672\pi\) | |||||||
\(294\) | 17.6257 | − | 5.03795i | 1.02795 | − | 0.293819i | ||||
\(295\) | 4.62457 | − | 5.55143i | 0.269253 | − | 0.323217i | ||||
\(296\) | −18.8134 | + | 20.7880i | −1.09351 | + | 1.20828i | ||||
\(297\) | −25.5889 | −1.48482 | ||||||||
\(298\) | −6.29448 | − | 22.0218i | −0.364629 | − | 1.27569i | ||||
\(299\) | −7.08359 | + | 25.2177i | −0.409654 | + | 1.45838i | ||||
\(300\) | 7.47318 | + | 8.20957i | 0.431464 | + | 0.473980i | ||||
\(301\) | 23.8178 | 1.37283 | ||||||||
\(302\) | 3.59301 | + | 12.5705i | 0.206755 | + | 0.723350i | ||||
\(303\) | −8.84027 | −0.507860 | ||||||||
\(304\) | −1.98807 | + | 4.04137i | −0.114024 | + | 0.231788i | ||||
\(305\) | 4.21820 | − | 5.06362i | 0.241534 | − | 0.289942i | ||||
\(306\) | 4.19121 | − | 1.19797i | 0.239596 | − | 0.0684835i | ||||
\(307\) | −9.88934 | −0.564414 | −0.282207 | − | 0.959354i | \(-0.591067\pi\) | ||||
−0.282207 | + | 0.959354i | \(0.591067\pi\) | |||||||
\(308\) | −22.0839 | − | 35.4752i | −1.25835 | − | 2.02139i | ||||
\(309\) | 7.46253i | 0.424529i | ||||||||
\(310\) | 3.85023 | − | 8.71144i | 0.218678 | − | 0.494776i | ||||
\(311\) | − | 26.2970i | − | 1.49117i | −0.666413 | − | 0.745583i | \(-0.732171\pi\) | ||
0.666413 | − | 0.745583i | \(-0.267829\pi\) | |||||||
\(312\) | 12.7157 | + | 11.5079i | 0.719886 | + | 0.651506i | ||||
\(313\) | 29.2911 | 1.65563 | 0.827815 | − | 0.561001i | \(-0.189584\pi\) | ||||
0.827815 | + | 0.561001i | \(0.189584\pi\) | |||||||
\(314\) | 1.01964 | − | 0.291443i | 0.0575415 | − | 0.0164471i | ||||
\(315\) | −10.9324 | + | 13.1235i | −0.615970 | + | 0.739423i | ||||
\(316\) | 12.9979 | − | 8.09139i | 0.731186 | − | 0.455176i | ||||
\(317\) | 20.8716i | 1.17227i | 0.810215 | + | 0.586133i | \(0.199350\pi\) | ||||
−0.810215 | + | 0.586133i | \(0.800650\pi\) | |||||||
\(318\) | −0.320462 | + | 0.0915973i | −0.0179706 | + | 0.00513652i | ||||
\(319\) | −12.7829 | −0.715707 | ||||||||
\(320\) | 10.0256 | − | 14.8151i | 0.560447 | − | 0.828190i | ||||
\(321\) | 17.3868i | 0.970438i | ||||||||
\(322\) | −0.133811 | − | 29.3102i | −0.00745701 | − | 1.63339i | ||||
\(323\) | −1.96352 | −0.109253 | ||||||||
\(324\) | −0.973131 | + | 0.605791i | −0.0540628 | + | 0.0336551i | ||||
\(325\) | 26.8594 | − | 4.93381i | 1.48989 | − | 0.273679i | ||||
\(326\) | 9.67852 | − | 2.76640i | 0.536043 | − | 0.153217i | ||||
\(327\) | − | 14.3838i | − | 0.795427i | ||||||
\(328\) | −19.5557 | + | 21.6082i | −1.07978 | + | 1.19311i | ||||
\(329\) | − | 1.44967i | − | 0.0799226i | ||||||
\(330\) | −15.5243 | − | 6.86133i | −0.854583 | − | 0.377704i | ||||
\(331\) | 6.78902i | 0.373158i | 0.982440 | + | 0.186579i | \(0.0597401\pi\) | ||||
−0.982440 | + | 0.186579i | \(0.940260\pi\) | |||||||
\(332\) | −8.41007 | − | 13.5098i | −0.461563 | − | 0.741445i | ||||
\(333\) | −17.5211 | −0.960149 | ||||||||
\(334\) | 0.493731 | − | 0.141123i | 0.0270158 | − | 0.00772190i | ||||
\(335\) | −7.10962 | + | 8.53454i | −0.388440 | + | 0.466292i | ||||
\(336\) | −17.2198 | − | 8.47097i | −0.939419 | − | 0.462129i | ||||
\(337\) | 11.8440 | 0.645183 | 0.322592 | − | 0.946538i | \(-0.395446\pi\) | ||||
0.322592 | + | 0.946538i | \(0.395446\pi\) | |||||||
\(338\) | 22.8859 | − | 6.54145i | 1.24483 | − | 0.355808i | ||||
\(339\) | −2.98213 | −0.161967 | ||||||||
\(340\) | 7.72481 | + | 1.07090i | 0.418937 | + | 0.0580778i | ||||
\(341\) | 14.5616i | 0.788552i | ||||||||
\(342\) | −2.70621 | + | 0.773514i | −0.146335 | + | 0.0418268i | ||||
\(343\) | 20.2084i | 1.09115i | ||||||||
\(344\) | −11.5579 | − | 10.4601i | −0.623162 | − | 0.563969i | ||||
\(345\) | −6.74561 | − | 9.80964i | −0.363171 | − | 0.528133i | ||||
\(346\) | −1.36904 | − | 4.78971i | −0.0736000 | − | 0.257496i | ||||
\(347\) | −11.9606 | −0.642077 | −0.321039 | − | 0.947066i | \(-0.604032\pi\) | ||||
−0.321039 | + | 0.947066i | \(0.604032\pi\) | |||||||
\(348\) | −4.98371 | + | 3.10245i | −0.267155 | + | 0.166309i | ||||
\(349\) | −17.4732 | −0.935318 | −0.467659 | − | 0.883909i | \(-0.654903\pi\) | ||||
−0.467659 | + | 0.883909i | \(0.654903\pi\) | |||||||
\(350\) | −27.3808 | + | 13.5682i | −1.46357 | + | 0.725252i | ||||
\(351\) | 28.9077i | 1.54298i | ||||||||
\(352\) | −4.86313 | + | 26.9135i | −0.259206 | + | 1.43449i | ||||
\(353\) | 28.6864i | 1.52682i | 0.645912 | + | 0.763412i | \(0.276477\pi\) | ||||
−0.645912 | + | 0.763412i | \(0.723523\pi\) | |||||||
\(354\) | 1.39420 | + | 4.87774i | 0.0741009 | + | 0.259249i | ||||
\(355\) | −17.8555 | + | 21.4341i | −0.947671 | + | 1.13760i | ||||
\(356\) | 4.03261 | + | 6.47791i | 0.213728 | + | 0.343329i | ||||
\(357\) | − | 8.36635i | − | 0.442794i | ||||||
\(358\) | −8.18682 | − | 28.6423i | −0.432687 | − | 1.51379i | ||||
\(359\) | 30.5812 | 1.61402 | 0.807008 | − | 0.590541i | \(-0.201085\pi\) | ||||
0.807008 | + | 0.590541i | \(0.201085\pi\) | |||||||
\(360\) | 11.0685 | − | 1.56717i | 0.583364 | − | 0.0825971i | ||||
\(361\) | −17.7322 | −0.933273 | ||||||||
\(362\) | 7.38419 | + | 25.8343i | 0.388105 | + | 1.35782i | ||||
\(363\) | 13.7378 | 0.721046 | ||||||||
\(364\) | −40.0761 | + | 24.9481i | −2.10056 | + | 1.30763i | ||||
\(365\) | −13.1121 | + | 15.7400i | −0.686317 | + | 0.823870i | ||||
\(366\) | 1.27169 | + | 4.44912i | 0.0664723 | + | 0.232559i | ||||
\(367\) | 6.34724i | 0.331323i | 0.986183 | + | 0.165662i | \(0.0529760\pi\) | ||||
−0.986183 | + | 0.165662i | \(0.947024\pi\) | |||||||
\(368\) | −12.8072 | + | 14.2820i | −0.667624 | + | 0.744499i | ||||
\(369\) | −18.2124 | −0.948097 | ||||||||
\(370\) | −28.6711 | − | 12.6719i | −1.49054 | − | 0.658779i | ||||
\(371\) | − | 0.917429i | − | 0.0476305i | ||||||
\(372\) | 3.53412 | + | 5.67715i | 0.183236 | + | 0.294346i | ||||
\(373\) | 22.2449 | 1.15180 | 0.575899 | − | 0.817521i | \(-0.304652\pi\) | ||||
0.575899 | + | 0.817521i | \(0.304652\pi\) | |||||||
\(374\) | −11.4641 | + | 3.27678i | −0.592795 | + | 0.169438i | ||||
\(375\) | −6.09063 | + | 10.8148i | −0.314519 | + | 0.558476i | ||||
\(376\) | −0.636651 | + | 0.703472i | −0.0328328 | + | 0.0362788i | ||||
\(377\) | 14.4408i | 0.743739i | ||||||||
\(378\) | −8.88982 | − | 31.1018i | −0.457243 | − | 1.59971i | ||||
\(379\) | 12.5191 | 0.643062 | 0.321531 | − | 0.946899i | \(-0.395803\pi\) | ||||
0.321531 | + | 0.946899i | \(0.395803\pi\) | |||||||
\(380\) | −4.98781 | − | 0.691467i | −0.255869 | − | 0.0354715i | ||||
\(381\) | −8.65068 | −0.443188 | ||||||||
\(382\) | −26.9073 | + | 7.69091i | −1.37670 | + | 0.393501i | ||||
\(383\) | − | 14.2978i | − | 0.730583i | −0.930893 | − | 0.365291i | \(-0.880969\pi\) | ||
0.930893 | − | 0.365291i | \(-0.119031\pi\) | |||||||
\(384\) | 4.63597 | + | 11.6731i | 0.236579 | + | 0.595692i | ||||
\(385\) | 29.9031 | − | 35.8963i | 1.52400 | − | 1.82944i | ||||
\(386\) | 6.82099 | + | 23.8639i | 0.347179 | + | 1.21464i | ||||
\(387\) | − | 9.74154i | − | 0.495191i | ||||||
\(388\) | −24.9443 | + | 15.5283i | −1.26635 | + | 0.788328i | ||||
\(389\) | 8.85964i | 0.449201i | 0.974451 | + | 0.224601i | \(0.0721078\pi\) | ||||
−0.974451 | + | 0.224601i | \(0.927892\pi\) | |||||||
\(390\) | −7.75120 | + | 17.5377i | −0.392497 | + | 0.888055i | ||||
\(391\) | −8.05155 | − | 2.26166i | −0.407184 | − | 0.114377i | ||||
\(392\) | 22.1604 | − | 24.4863i | 1.11927 | − | 1.23674i | ||||
\(393\) | − | 10.4625i | − | 0.527764i | ||||||
\(394\) | −5.20068 | − | 18.1950i | −0.262006 | − | 0.916652i | ||||
\(395\) | 13.1521 | + | 10.9563i | 0.661756 | + | 0.551270i | ||||
\(396\) | −14.5095 | + | 9.03241i | −0.729129 | + | 0.453896i | ||||
\(397\) | − | 10.5297i | − | 0.528472i | −0.964458 | − | 0.264236i | \(-0.914880\pi\) | ||
0.964458 | − | 0.264236i | \(-0.0851199\pi\) | |||||||
\(398\) | 7.96408 | − | 2.27637i | 0.399203 | − | 0.114104i | ||||
\(399\) | 5.40204i | 0.270440i | ||||||||
\(400\) | 19.2457 | + | 5.44069i | 0.962287 | + | 0.272035i | ||||
\(401\) | − | 33.5854i | − | 1.67717i | −0.544768 | − | 0.838587i | \(-0.683382\pi\) | ||
0.544768 | − | 0.838587i | \(-0.316618\pi\) | |||||||
\(402\) | −2.14339 | − | 7.49883i | −0.106902 | − | 0.374008i | ||||
\(403\) | 16.4501 | 0.819437 | ||||||||
\(404\) | −13.5204 | + | 8.41668i | −0.672665 | + | 0.418746i | ||||
\(405\) | −0.984682 | − | 0.820280i | −0.0489292 | − | 0.0407601i | ||||
\(406\) | −4.44090 | − | 15.5369i | −0.220398 | − | 0.771083i | ||||
\(407\) | 47.9250 | 2.37555 | ||||||||
\(408\) | −3.67426 | + | 4.05990i | −0.181903 | + | 0.200995i | ||||
\(409\) | −27.7416 | −1.37174 | −0.685868 | − | 0.727726i | \(-0.740577\pi\) | ||||
−0.685868 | + | 0.727726i | \(0.740577\pi\) | |||||||
\(410\) | −29.8023 | − | 13.1718i | −1.47183 | − | 0.650511i | ||||
\(411\) | −17.1989 | −0.848358 | ||||||||
\(412\) | 7.10496 | + | 11.4133i | 0.350036 | + | 0.562291i | ||||
\(413\) | −13.9642 | −0.687131 | ||||||||
\(414\) | −11.9880 | + | 0.0547293i | −0.589176 | + | 0.00268980i | ||||
\(415\) | 11.3878 | − | 13.6701i | 0.559004 | − | 0.671041i | ||||
\(416\) | 30.4040 | + | 5.49384i | 1.49068 | + | 0.269358i | ||||
\(417\) | 5.21301i | 0.255282i | ||||||||
\(418\) | 7.40223 | − | 2.11577i | 0.362055 | − | 0.103486i | ||||
\(419\) | −0.289358 | −0.0141361 | −0.00706803 | − | 0.999975i | \(-0.502250\pi\) | ||||
−0.00706803 | + | 0.999975i | \(0.502250\pi\) | |||||||
\(420\) | 2.94627 | − | 21.2525i | 0.143763 | − | 1.03702i | ||||
\(421\) | − | 37.9107i | − | 1.84765i | −0.382809 | − | 0.923827i | \(-0.625043\pi\) | ||
0.382809 | − | 0.923827i | \(-0.374957\pi\) | |||||||
\(422\) | −6.60728 | − | 23.1162i | −0.321637 | − | 1.12528i | ||||
\(423\) | −0.592918 | −0.0288287 | ||||||||
\(424\) | −0.402908 | + | 0.445196i | −0.0195670 | + | 0.0216206i | ||||
\(425\) | 1.57528 | + | 8.57572i | 0.0764121 | + | 0.415984i | ||||
\(426\) | −5.38302 | − | 18.8330i | −0.260808 | − | 0.912461i | ||||
\(427\) | −12.7371 | −0.616392 | ||||||||
\(428\) | 16.5537 | + | 26.5916i | 0.800154 | + | 1.28535i | ||||
\(429\) | − | 29.3150i | − | 1.41534i | ||||||
\(430\) | 7.04544 | − | 15.9408i | 0.339761 | − | 0.768735i | ||||
\(431\) | −22.2740 | −1.07290 | −0.536450 | − | 0.843932i | \(-0.680235\pi\) | ||||
−0.536450 | + | 0.843932i | \(0.680235\pi\) | |||||||
\(432\) | −9.34511 | + | 18.9968i | −0.449617 | + | 0.913983i | ||||
\(433\) | 8.38264 | 0.402844 | 0.201422 | − | 0.979505i | \(-0.435444\pi\) | ||||
0.201422 | + | 0.979505i | \(0.435444\pi\) | |||||||
\(434\) | −17.6987 | + | 5.05881i | −0.849565 | + | 0.242831i | ||||
\(435\) | −5.04287 | − | 4.20091i | −0.241787 | − | 0.201418i | ||||
\(436\) | −13.6946 | − | 21.9987i | −0.655853 | − | 1.05355i | ||||
\(437\) | 5.19878 | + | 1.46032i | 0.248691 | + | 0.0698567i | ||||
\(438\) | −3.95299 | − | 13.8299i | −0.188881 | − | 0.660817i | ||||
\(439\) | − | 2.21723i | − | 0.105822i | −0.998599 | − | 0.0529112i | \(-0.983150\pi\) | ||
0.998599 | − | 0.0529112i | \(-0.0168500\pi\) | |||||||
\(440\) | −30.2755 | + | 4.28664i | −1.44333 | + | 0.204358i | ||||
\(441\) | 20.6381 | 0.982768 | ||||||||
\(442\) | 3.70176 | + | 12.9509i | 0.176075 | + | 0.616013i | ||||
\(443\) | 11.6993 | 0.555852 | 0.277926 | − | 0.960603i | \(-0.410353\pi\) | ||||
0.277926 | + | 0.960603i | \(0.410353\pi\) | |||||||
\(444\) | 18.6846 | − | 11.6315i | 0.886733 | − | 0.552007i | ||||
\(445\) | −5.46042 | + | 6.55480i | −0.258849 | + | 0.310727i | ||||
\(446\) | 5.87550 | − | 1.67939i | 0.278213 | − | 0.0795215i | ||||
\(447\) | 17.9794i | 0.850398i | ||||||||
\(448\) | −34.4012 | + | 3.43914i | −1.62531 | + | 0.162484i | ||||
\(449\) | 31.2883 | 1.47658 | 0.738292 | − | 0.674481i | \(-0.235633\pi\) | ||||
0.738292 | + | 0.674481i | \(0.235633\pi\) | |||||||
\(450\) | 5.54945 | + | 11.1989i | 0.261604 | + | 0.527919i | ||||
\(451\) | 49.8158 | 2.34574 | ||||||||
\(452\) | −4.56090 | + | 2.83924i | −0.214527 | + | 0.133547i | ||||
\(453\) | − | 10.2630i | − | 0.482199i | ||||||
\(454\) | 0.824866 | + | 2.88587i | 0.0387129 | + | 0.135441i | ||||
\(455\) | −40.5518 | − | 33.7813i | −1.90110 | − | 1.58369i | ||||
\(456\) | 2.37242 | − | 2.62142i | 0.111099 | − | 0.122759i | ||||
\(457\) | 26.9548 | 1.26089 | 0.630446 | − | 0.776233i | \(-0.282872\pi\) | ||||
0.630446 | + | 0.776233i | \(0.282872\pi\) | |||||||
\(458\) | 1.60274 | + | 5.60734i | 0.0748912 | + | 0.262014i | ||||
\(459\) | −9.22969 | −0.430805 | ||||||||
\(460\) | −19.6564 | − | 8.58057i | −0.916484 | − | 0.400071i | ||||
\(461\) | −10.2640 | −0.478043 | −0.239022 | − | 0.971014i | \(-0.576827\pi\) | ||||
−0.239022 | + | 0.971014i | \(0.576827\pi\) | |||||||
\(462\) | 9.01509 | + | 31.5401i | 0.419420 | + | 1.46738i | ||||
\(463\) | −30.9103 | −1.43653 | −0.718263 | − | 0.695772i | \(-0.755062\pi\) | ||||
−0.718263 | + | 0.695772i | \(0.755062\pi\) | |||||||
\(464\) | −4.66834 | + | 9.48983i | −0.216722 | + | 0.440554i | ||||
\(465\) | −4.78543 | + | 5.74453i | −0.221919 | + | 0.266396i | ||||
\(466\) | 4.62873 | + | 16.1940i | 0.214422 | + | 0.750174i | ||||
\(467\) | 18.7363i | 0.867013i | 0.901150 | + | 0.433507i | \(0.142724\pi\) | ||||
−0.901150 | + | 0.433507i | \(0.857276\pi\) | |||||||
\(468\) | 10.2039 | + | 16.3913i | 0.471673 | + | 0.757687i | ||||
\(469\) | 21.4679 | 0.991296 | ||||||||
\(470\) | −0.970237 | − | 0.428820i | −0.0447537 | − | 0.0197800i | ||||
\(471\) | −0.832472 | −0.0383583 | ||||||||
\(472\) | 6.77632 | + | 6.13266i | 0.311905 | + | 0.282278i | ||||
\(473\) | 26.6458i | 1.22518i | ||||||||
\(474\) | −11.5561 | + | 3.30306i | −0.530787 | + | 0.151715i | ||||
\(475\) | −1.01713 | − | 5.53723i | −0.0466693 | − | 0.254065i | ||||
\(476\) | −7.96547 | − | 12.7956i | −0.365097 | − | 0.586484i | ||||
\(477\) | −0.375232 | −0.0171807 | ||||||||
\(478\) | 5.67606 | + | 19.8582i | 0.259617 | + | 0.908293i | ||||
\(479\) | 15.0861 | 0.689300 | 0.344650 | − | 0.938731i | \(-0.387998\pi\) | ||||
0.344650 | + | 0.938731i | \(0.387998\pi\) | |||||||
\(480\) | −10.7632 | + | 9.01919i | −0.491271 | + | 0.411668i | ||||
\(481\) | − | 54.1405i | − | 2.46860i | ||||||
\(482\) | −5.50932 | − | 19.2748i | −0.250943 | − | 0.877945i | ||||
\(483\) | −6.22228 | + | 22.1514i | −0.283124 | + | 1.00792i | ||||
\(484\) | 21.0107 | − | 13.0795i | 0.955031 | − | 0.594523i | ||||
\(485\) | −25.2404 | − | 21.0263i | −1.14611 | − | 0.954753i | ||||
\(486\) | −20.7253 | + | 5.92391i | −0.940121 | + | 0.268714i | ||||
\(487\) | 37.0234 | 1.67769 | 0.838845 | − | 0.544370i | \(-0.183231\pi\) | ||||
0.838845 | + | 0.544370i | \(0.183231\pi\) | |||||||
\(488\) | 6.18088 | + | 5.59377i | 0.279795 | + | 0.253218i | ||||
\(489\) | −7.90191 | −0.357337 | ||||||||
\(490\) | 33.7718 | + | 14.9262i | 1.52565 | + | 0.674299i | ||||
\(491\) | − | 2.39953i | − | 0.108289i | −0.998533 | − | 0.0541447i | \(-0.982757\pi\) | ||
0.998533 | − | 0.0541447i | \(-0.0172432\pi\) | |||||||
\(492\) | 19.4218 | − | 12.0904i | 0.875603 | − | 0.545078i | ||||
\(493\) | −4.61068 | −0.207655 | ||||||||
\(494\) | −2.39018 | − | 8.36225i | −0.107539 | − | 0.376235i | ||||
\(495\) | −14.6817 | − | 12.2305i | −0.659894 | − | 0.549718i | ||||
\(496\) | 10.8102 | + | 5.31790i | 0.485394 | + | 0.238781i | ||||
\(497\) | 53.9157 | 2.41845 | ||||||||
\(498\) | 3.43315 | + | 12.0112i | 0.153843 | + | 0.538235i | ||||
\(499\) | − | 16.5390i | − | 0.740387i | −0.928955 | − | 0.370193i | \(-0.879291\pi\) | ||
0.928955 | − | 0.370193i | \(-0.120709\pi\) | |||||||
\(500\) | 0.981577 | + | 22.3391i | 0.0438974 | + | 0.999036i | ||||
\(501\) | −0.403101 | −0.0180092 | ||||||||
\(502\) | 9.56186 | − | 2.73306i | 0.426767 | − | 0.121983i | ||||
\(503\) | 21.5112i | 0.959137i | 0.877504 | + | 0.479569i | \(0.159207\pi\) | ||||
−0.877504 | + | 0.479569i | \(0.840793\pi\) | |||||||
\(504\) | −16.0191 | − | 14.4975i | −0.713546 | − | 0.645769i | ||||
\(505\) | −13.6809 | − | 11.3967i | −0.608791 | − | 0.507148i | ||||
\(506\) | 32.7904 | − | 0.149700i | 1.45771 | − | 0.00665497i | ||||
\(507\) | −18.6849 | −0.829826 | ||||||||
\(508\) | −13.2304 | + | 8.23617i | −0.587005 | + | 0.365421i | ||||
\(509\) | −19.5576 | −0.866875 | −0.433438 | − | 0.901184i | \(-0.642700\pi\) | ||||
−0.433438 | + | 0.901184i | \(0.642700\pi\) | |||||||
\(510\) | −5.59946 | − | 2.47482i | −0.247948 | − | 0.109587i | ||||
\(511\) | 39.5927 | 1.75148 | ||||||||
\(512\) | 18.2041 | + | 13.4391i | 0.804515 | + | 0.593932i | ||||
\(513\) | 5.95948 | 0.263118 | ||||||||
\(514\) | 0.958090 | + | 3.35196i | 0.0422595 | + | 0.147849i | ||||
\(515\) | −9.62058 | + | 11.5487i | −0.423933 | + | 0.508899i | ||||
\(516\) | 6.46700 | + | 10.3885i | 0.284694 | + | 0.457327i | ||||
\(517\) | 1.62180 | 0.0713265 | ||||||||
\(518\) | 16.6495 | + | 58.2499i | 0.731539 | + | 2.55936i | ||||
\(519\) | 3.91050i | 0.171652i | ||||||||
\(520\) | 4.84259 | + | 34.2021i | 0.212362 | + | 1.49986i | ||||
\(521\) | 40.5989i | 1.77867i | 0.457258 | + | 0.889334i | \(0.348832\pi\) | ||||
−0.457258 | + | 0.889334i | \(0.651168\pi\) | |||||||
\(522\) | −6.35464 | + | 1.81634i | −0.278135 | + | 0.0794992i | ||||
\(523\) | 32.4296i | 1.41805i | 0.705185 | + | 0.709024i | \(0.250864\pi\) | ||||
−0.705185 | + | 0.709024i | \(0.749136\pi\) | |||||||
\(524\) | −9.96120 | − | 16.0015i | −0.435157 | − | 0.699027i | ||||
\(525\) | 23.5935 | − | 4.33390i | 1.02971 | − | 0.189147i | ||||
\(526\) | 3.69423 | + | 12.9246i | 0.161076 | + | 0.563539i | ||||
\(527\) | 5.25221i | 0.228790i | ||||||||
\(528\) | 9.47680 | − | 19.2645i | 0.412425 | − | 0.838379i | ||||
\(529\) | 19.6359 | + | 11.9763i | 0.853734 | + | 0.520709i | ||||
\(530\) | −0.614020 | − | 0.271381i | −0.0266713 | − | 0.0117880i | ||||
\(531\) | 5.71139i | 0.247853i | ||||||||
\(532\) | 5.14319 | + | 8.26193i | 0.222986 | + | 0.358200i | ||||
\(533\) | − | 56.2766i | − | 2.43761i | ||||||
\(534\) | −1.64619 | − | 5.75934i | −0.0712376 | − | 0.249231i | ||||
\(535\) | −22.4148 | + | 26.9072i | −0.969077 | + | 1.16330i | ||||
\(536\) | −10.4176 | − | 9.42809i | −0.449973 | − | 0.407232i | ||||
\(537\) | 23.3847i | 1.00912i | ||||||||
\(538\) | −4.47383 | + | 1.27875i | −0.192880 | + | 0.0551309i | ||||
\(539\) | −56.4510 | −2.43152 | ||||||||
\(540\) | −23.4456 | − | 3.25030i | −1.00894 | − | 0.139871i | ||||
\(541\) | −16.1408 | −0.693948 | −0.346974 | − | 0.937875i | \(-0.612791\pi\) | ||||
−0.346974 | + | 0.937875i | \(0.612791\pi\) | |||||||
\(542\) | −2.68151 | − | 9.38151i | −0.115181 | − | 0.402970i | ||||
\(543\) | − | 21.0921i | − | 0.905148i | ||||||
\(544\) | −1.75408 | + | 9.70745i | −0.0752057 | + | 0.416203i | ||||
\(545\) | 18.5434 | − | 22.2599i | 0.794311 | − | 0.953508i | ||||
\(546\) | 35.6306 | − | 10.1843i | 1.52485 | − | 0.435847i | ||||
\(547\) | 31.4175 | 1.34332 | 0.671658 | − | 0.740861i | \(-0.265582\pi\) | ||||
0.671658 | + | 0.740861i | \(0.265582\pi\) | |||||||
\(548\) | −26.3041 | + | 16.3748i | −1.12366 | + | 0.699496i | ||||
\(549\) | 5.20952i | 0.222337i | ||||||||
\(550\) | −15.1793 | − | 30.6320i | −0.647247 | − | 1.30615i | ||||
\(551\) | 2.97706 | 0.126827 | ||||||||
\(552\) | 12.7477 | − | 8.01667i | 0.542579 | − | 0.341212i | ||||
\(553\) | − | 33.0831i | − | 1.40684i | ||||||
\(554\) | 6.26007 | + | 21.9014i | 0.265965 | + | 0.930502i | ||||
\(555\) | 18.9064 | + | 15.7498i | 0.802532 | + | 0.668542i | ||||
\(556\) | 4.96322 | + | 7.97282i | 0.210488 | + | 0.338123i | ||||
\(557\) | −34.8208 | −1.47541 | −0.737703 | − | 0.675125i | \(-0.764090\pi\) | ||||
−0.737703 | + | 0.675125i | \(0.764090\pi\) | |||||||
\(558\) | 2.06907 | + | 7.23883i | 0.0875907 | + | 0.306444i | ||||
\(559\) | 30.1016 | 1.27316 | ||||||||
\(560\) | −15.7281 | − | 35.3089i | −0.664635 | − | 1.49207i | ||||
\(561\) | 9.35975 | 0.395169 | ||||||||
\(562\) | −2.63959 | − | 9.23484i | −0.111344 | − | 0.389548i | ||||
\(563\) | − | 40.1892i | − | 1.69377i | −0.531773 | − | 0.846887i | \(-0.678474\pi\) | ||
0.531773 | − | 0.846887i | \(-0.321526\pi\) | |||||||
\(564\) | 0.632293 | − | 0.393614i | 0.0266243 | − | 0.0165741i | ||||
\(565\) | −4.61503 | − | 3.84451i | −0.194156 | − | 0.161740i | ||||
\(566\) | −2.80102 | − | 9.79961i | −0.117736 | − | 0.411908i | ||||
\(567\) | 2.47689i | 0.104019i | ||||||||
\(568\) | −26.1634 | − | 23.6782i | −1.09779 | − | 0.993517i | ||||
\(569\) | − | 36.5494i | − | 1.53223i | −0.642703 | − | 0.766116i | \(-0.722187\pi\) | ||
0.642703 | − | 0.766116i | \(-0.277813\pi\) | |||||||
\(570\) | 3.61550 | + | 1.59796i | 0.151436 | + | 0.0669310i | ||||
\(571\) | −13.2964 | −0.556437 | −0.278219 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278219 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(572\) | −27.9104 | − | 44.8346i | −1.16699 | − | 1.87463i | ||||
\(573\) | 21.9682 | 0.917734 | ||||||||
\(574\) | 17.3064 | + | 60.5482i | 0.722357 | + | 2.52723i | ||||
\(575\) | 2.20717 | − | 23.8774i | 0.0920453 | − | 0.995755i | ||||
\(576\) | 1.40662 | + | 14.0702i | 0.0586093 | + | 0.586260i | ||||
\(577\) | − | 18.2028i | − | 0.757793i | −0.925439 | − | 0.378897i | \(-0.876304\pi\) | ||
0.925439 | − | 0.378897i | \(-0.123696\pi\) | |||||||
\(578\) | 18.9809 | − | 5.42530i | 0.789501 | − | 0.225663i | ||||
\(579\) | − | 19.4834i | − | 0.809701i | ||||||
\(580\) | −11.7122 | − | 1.62368i | −0.486324 | − | 0.0674198i | ||||
\(581\) | −34.3861 | −1.42658 | ||||||||
\(582\) | 22.1773 | − | 6.33893i | 0.919280 | − | 0.262757i | ||||
\(583\) | 1.02636 | 0.0425076 | ||||||||
\(584\) | −19.2129 | − | 17.3880i | −0.795037 | − | 0.719519i | ||||
\(585\) | −13.8167 | + | 16.5858i | −0.571249 | + | 0.685740i | ||||
\(586\) | −34.2652 | + | 9.79402i | −1.41548 | + | 0.404587i | ||||
\(587\) | −2.44585 | −0.100951 | −0.0504755 | − | 0.998725i | \(-0.516074\pi\) | ||||
−0.0504755 | + | 0.998725i | \(0.516074\pi\) | |||||||
\(588\) | −22.0087 | + | 13.7008i | −0.907623 | + | 0.565011i | ||||
\(589\) | − | 3.39128i | − | 0.139735i | ||||||
\(590\) | −4.13068 | + | 9.34599i | −0.170058 | + | 0.384768i | ||||
\(591\) | 14.8551i | 0.611058i | ||||||||
\(592\) | 17.5023 | − | 35.5787i | 0.719338 | − | 1.46227i | ||||
\(593\) | 6.29249i | 0.258401i | 0.991618 | + | 0.129201i | \(0.0412412\pi\) | ||||
−0.991618 | + | 0.129201i | \(0.958759\pi\) | |||||||
\(594\) | 34.7948 | − | 9.94537i | 1.42765 | − | 0.408064i | ||||
\(595\) | 10.7858 | − | 12.9475i | 0.442173 | − | 0.530794i | ||||
\(596\) | 17.1179 | + | 27.4979i | 0.701178 | + | 1.12636i | ||||
\(597\) | −6.50218 | −0.266116 | ||||||||
\(598\) | −0.169115 | − | 37.0431i | −0.00691562 | − | 1.51480i | ||||
\(599\) | 10.8781i | 0.444466i | 0.974994 | + | 0.222233i | \(0.0713345\pi\) | ||||
−0.974994 | + | 0.222233i | \(0.928665\pi\) | |||||||
\(600\) | −13.3524 | − | 8.25851i | −0.545111 | − | 0.337152i | ||||
\(601\) | 25.3031 | 1.03213 | 0.516067 | − | 0.856548i | \(-0.327396\pi\) | ||||
0.516067 | + | 0.856548i | \(0.327396\pi\) | |||||||
\(602\) | −32.3864 | + | 9.25699i | −1.31997 | + | 0.377287i | ||||
\(603\) | − | 8.78045i | − | 0.357568i | ||||||
\(604\) | −9.77127 | − | 15.6964i | −0.397587 | − | 0.638676i | ||||
\(605\) | 21.2601 | + | 17.7105i | 0.864345 | + | 0.720034i | ||||
\(606\) | 12.0206 | − | 3.43585i | 0.488305 | − | 0.139572i | ||||
\(607\) | 32.1161 | 1.30355 | 0.651776 | − | 0.758411i | \(-0.274024\pi\) | ||||
0.651776 | + | 0.758411i | \(0.274024\pi\) | |||||||
\(608\) | 1.13259 | − | 6.26797i | 0.0459325 | − | 0.254200i | ||||
\(609\) | 12.6849i | 0.514019i | ||||||||
\(610\) | −3.76772 | + | 8.52474i | −0.152550 | + | 0.345157i | ||||
\(611\) | − | 1.83213i | − | 0.0741201i | ||||||
\(612\) | −5.23343 | + | 3.25790i | −0.211549 | + | 0.131693i | ||||
\(613\) | 10.6896 | 0.431748 | 0.215874 | − | 0.976421i | \(-0.430740\pi\) | ||||
0.215874 | + | 0.976421i | \(0.430740\pi\) | |||||||
\(614\) | 13.4471 | − | 3.84358i | 0.542681 | − | 0.155114i | ||||
\(615\) | 19.6524 | + | 16.3712i | 0.792459 | + | 0.660151i | ||||
\(616\) | 43.8166 | + | 39.6546i | 1.76542 | + | 1.59773i | ||||
\(617\) | −21.7776 | −0.876734 | −0.438367 | − | 0.898796i | \(-0.644443\pi\) | ||||
−0.438367 | + | 0.898796i | \(0.644443\pi\) | |||||||
\(618\) | −2.90038 | − | 10.1472i | −0.116670 | − | 0.408182i | ||||
\(619\) | −22.0930 | −0.887993 | −0.443997 | − | 0.896029i | \(-0.646440\pi\) | ||||
−0.443997 | + | 0.896029i | \(0.646440\pi\) | |||||||
\(620\) | −1.84960 | + | 13.3419i | −0.0742819 | + | 0.535823i | ||||
\(621\) | 24.4373 | + | 6.86437i | 0.980634 | + | 0.275458i | ||||
\(622\) | 10.2206 | + | 35.7576i | 0.409807 | + | 1.43375i | ||||
\(623\) | 16.4881 | 0.660580 | ||||||||
\(624\) | −21.7630 | − | 10.7059i | −0.871215 | − | 0.428578i | ||||
\(625\) | −23.3680 | + | 8.88472i | −0.934719 | + | 0.355389i | ||||
\(626\) | −39.8288 | + | 11.3842i | −1.59188 | + | 0.455006i | ||||
\(627\) | −6.04346 | −0.241353 | ||||||||
\(628\) | −1.27319 | + | 0.792583i | −0.0508058 | + | 0.0316275i | ||||
\(629\) | 17.2861 | 0.689241 | ||||||||
\(630\) | 9.76484 | − | 22.0937i | 0.389041 | − | 0.880234i | ||||
\(631\) | −21.0161 | −0.836638 | −0.418319 | − | 0.908300i | \(-0.637381\pi\) | ||||
−0.418319 | + | 0.908300i | \(0.637381\pi\) | |||||||
\(632\) | −14.5292 | + | 16.0541i | −0.577939 | + | 0.638597i | ||||
\(633\) | 18.8729i | 0.750131i | ||||||||
\(634\) | −8.11193 | − | 28.3803i | −0.322166 | − | 1.12713i | ||||
\(635\) | −13.3875 | − | 11.1523i | −0.531265 | − | 0.442566i | ||||
\(636\) | 0.400150 | − | 0.249101i | 0.0158670 | − | 0.00987748i | ||||
\(637\) | 63.7723i | 2.52675i | ||||||||
\(638\) | 17.3817 | − | 4.96820i | 0.688148 | − | 0.196693i | ||||
\(639\) | − | 22.0517i | − | 0.872353i | ||||||
\(640\) | −7.87434 | + | 24.0415i | −0.311260 | + | 0.950325i | ||||
\(641\) | − | 18.6991i | − | 0.738571i | −0.929316 | − | 0.369286i | \(-0.879602\pi\) | ||
0.929316 | − | 0.369286i | \(-0.120398\pi\) | |||||||
\(642\) | −6.75755 | − | 23.6419i | −0.266699 | − | 0.933071i | ||||
\(643\) | − | 30.5572i | − | 1.20506i | −0.798097 | − | 0.602529i | \(-0.794160\pi\) | ||
0.798097 | − | 0.602529i | \(-0.205840\pi\) | |||||||
\(644\) | 11.5736 | + | 39.8027i | 0.456064 | + | 1.56845i | ||||
\(645\) | −8.75674 | + | 10.5118i | −0.344796 | + | 0.413901i | ||||
\(646\) | 2.66991 | − | 0.763140i | 0.105046 | − | 0.0300253i | ||||
\(647\) | −10.0344 | −0.394493 | −0.197247 | − | 0.980354i | \(-0.563200\pi\) | ||||
−0.197247 | + | 0.980354i | \(0.563200\pi\) | |||||||
\(648\) | 1.08778 | − | 1.20195i | 0.0427319 | − | 0.0472169i | ||||
\(649\) | − | 15.6222i | − | 0.613226i | ||||||
\(650\) | −34.6048 | + | 17.1479i | −1.35731 | + | 0.672598i | ||||
\(651\) | 14.4499 | 0.566336 | ||||||||
\(652\) | −12.0853 | + | 7.52329i | −0.473295 | + | 0.294635i | ||||
\(653\) | 21.2536i | 0.831719i | 0.909429 | + | 0.415860i | \(0.136519\pi\) | ||||
−0.909429 | + | 0.415860i | \(0.863481\pi\) | |||||||
\(654\) | 5.59040 | + | 19.5585i | 0.218602 | + | 0.764799i | ||||
\(655\) | 13.4881 | − | 16.1914i | 0.527024 | − | 0.632651i | ||||
\(656\) | 18.1928 | − | 36.9824i | 0.710310 | − | 1.44392i | ||||
\(657\) | − | 16.1935i | − | 0.631770i | ||||||
\(658\) | 0.563426 | + | 1.97119i | 0.0219646 | + | 0.0768452i | ||||
\(659\) | 19.6877 | 0.766923 | 0.383461 | − | 0.923557i | \(-0.374732\pi\) | ||||
0.383461 | + | 0.923557i | \(0.374732\pi\) | |||||||
\(660\) | 23.7760 | + | 3.29610i | 0.925479 | + | 0.128301i | ||||
\(661\) | 25.1207i | 0.977081i | 0.872541 | + | 0.488540i | \(0.162470\pi\) | ||||
−0.872541 | + | 0.488540i | \(0.837530\pi\) | |||||||
\(662\) | −2.63861 | − | 9.23143i | −0.102553 | − | 0.358790i | ||||
\(663\) | − | 10.5736i | − | 0.410646i | ||||||
\(664\) | 16.6864 | + | 15.1014i | 0.647557 | + | 0.586047i | ||||
\(665\) | −6.96422 | + | 8.35999i | −0.270061 | + | 0.324187i | ||||
\(666\) | 23.8244 | − | 6.80972i | 0.923178 | − | 0.263871i | ||||
\(667\) | 12.2076 | + | 3.42909i | 0.472681 | + | 0.132775i | ||||
\(668\) | −0.616506 | + | 0.383786i | −0.0238533 | + | 0.0148491i | ||||
\(669\) | −4.79699 | −0.185462 | ||||||||
\(670\) | 6.35034 | − | 14.3681i | 0.245335 | − | 0.555089i | ||||
\(671\) | − | 14.2495i | − | 0.550095i | ||||||
\(672\) | 26.7071 | + | 4.82584i | 1.03025 | + | 0.186161i | ||||
\(673\) | 0.593638i | 0.0228831i | 0.999935 | + | 0.0114415i | \(0.00364203\pi\) | ||||
−0.999935 | + | 0.0114415i | \(0.996358\pi\) | |||||||
\(674\) | −16.1050 | + | 4.60328i | −0.620340 | + | 0.177312i | ||||
\(675\) | −4.78112 | − | 26.0282i | −0.184026 | − | 1.00183i | ||||
\(676\) | −28.5769 | + | 17.7896i | −1.09911 | + | 0.684215i | ||||
\(677\) | −27.1192 | −1.04228 | −0.521138 | − | 0.853472i | \(-0.674492\pi\) | ||||
−0.521138 | + | 0.853472i | \(0.674492\pi\) | |||||||
\(678\) | 4.05498 | − | 1.15903i | 0.155730 | − | 0.0445123i | ||||
\(679\) | 63.4900i | 2.43652i | ||||||||
\(680\) | −10.9201 | + | 1.54615i | −0.418767 | + | 0.0592922i | ||||
\(681\) | − | 2.35613i | − | 0.0902873i | ||||||
\(682\) | −5.65948 | − | 19.8002i | −0.216713 | − | 0.758189i | ||||
\(683\) | −41.3849 | −1.58355 | −0.791775 | − | 0.610812i | \(-0.790843\pi\) | ||||
−0.791775 | + | 0.610812i | \(0.790843\pi\) | |||||||
\(684\) | 3.37916 | − | 2.10358i | 0.129205 | − | 0.0804326i | ||||
\(685\) | −26.6164 | − | 22.1725i | −1.01696 | − | 0.847168i | ||||
\(686\) | −7.85419 | − | 27.4786i | −0.299874 | − | 1.04914i | ||||
\(687\) | − | 4.57804i | − | 0.174663i | ||||||
\(688\) | 19.7814 | + | 9.73109i | 0.754159 | + | 0.370994i | ||||
\(689\) | − | 1.15947i | − | 0.0441725i | ||||||
\(690\) | 12.9850 | + | 10.7170i | 0.494331 | + | 0.407989i | ||||
\(691\) | 42.3136i | 1.60968i | 0.593489 | + | 0.804842i | \(0.297750\pi\) | ||||
−0.593489 | + | 0.804842i | \(0.702250\pi\) | |||||||
\(692\) | 3.72313 | + | 5.98076i | 0.141532 | + | 0.227354i | ||||
\(693\) | 36.9306i | 1.40288i | ||||||||
\(694\) | 16.2635 | − | 4.64859i | 0.617354 | − | 0.176458i | ||||
\(695\) | −6.72052 | + | 8.06746i | −0.254924 | + | 0.306016i | ||||
\(696\) | 5.57085 | − | 6.15555i | 0.211163 | − | 0.233325i | ||||
\(697\) | 17.9681 | 0.680590 | ||||||||
\(698\) | 23.7593 | − | 6.79111i | 0.899304 | − | 0.257047i | ||||
\(699\) | − | 13.2214i | − | 0.500080i | ||||||
\(700\) | 31.9579 | − | 29.0913i | 1.20790 | − | 1.09955i | ||||
\(701\) | 37.1448i | 1.40294i | 0.712698 | + | 0.701471i | \(0.247473\pi\) | ||||
−0.712698 | + | 0.701471i | \(0.752527\pi\) | |||||||
\(702\) | −11.2352 | − | 39.3074i | −0.424046 | − | 1.48356i | ||||
\(703\) | −11.1614 | −0.420960 | ||||||||
\(704\) | −3.84750 | − | 38.4860i | −0.145008 | − | 1.45049i | ||||
\(705\) | 0.639798 | + | 0.532978i | 0.0240962 | + | 0.0200731i | ||||
\(706\) | −11.1492 | − | 39.0066i | −0.419607 | − | 1.46803i | ||||
\(707\) | 34.4131i | 1.29424i | ||||||||
\(708\) | −3.79155 | − | 6.09067i | −0.142495 | − | 0.228902i | ||||
\(709\) | − | 0.657980i | − | 0.0247109i | −0.999924 | − | 0.0123555i | \(-0.996067\pi\) | ||
0.999924 | − | 0.0123555i | \(-0.00393297\pi\) | |||||||
\(710\) | 15.9486 | − | 36.0849i | 0.598540 | − | 1.35424i | ||||
\(711\) | −13.5311 | −0.507456 | ||||||||
\(712\) | −8.00108 | − | 7.24108i | −0.299853 | − | 0.271371i | ||||
\(713\) | 3.90622 | − | 13.9062i | 0.146289 | − | 0.520791i | ||||
\(714\) | 3.25166 | + | 11.3762i | 0.121690 | + | 0.425744i | ||||
\(715\) | 37.7924 | − | 45.3668i | 1.41336 | − | 1.69662i | ||||
\(716\) | 22.2642 | + | 35.7648i | 0.832052 | + | 1.33659i | ||||
\(717\) | − | 16.2130i | − | 0.605485i | ||||||
\(718\) | −41.5831 | + | 11.8857i | −1.55187 | + | 0.443569i | ||||
\(719\) | 17.6047i | 0.656544i | 0.944583 | + | 0.328272i | \(0.106466\pi\) | ||||
−0.944583 | + | 0.328272i | \(0.893534\pi\) | |||||||
\(720\) | −14.4415 | + | 6.43286i | −0.538201 | + | 0.239739i | ||||
\(721\) | 29.0499 | 1.08188 | ||||||||
\(722\) | 24.1115 | − | 6.89177i | 0.897337 | − | 0.256485i | ||||
\(723\) | 15.7367i | 0.585255i | ||||||||
\(724\) | −20.0814 | − | 32.2584i | −0.746321 | − | 1.19888i | ||||
\(725\) | −2.38841 | − | 13.0024i | −0.0887032 | − | 0.482896i | ||||
\(726\) | −18.6801 | + | 5.33931i | −0.693282 | + | 0.198160i | ||||
\(727\) | − | 15.5188i | − | 0.575562i | −0.957696 | − | 0.287781i | \(-0.907082\pi\) | ||
0.957696 | − | 0.287781i | \(-0.0929176\pi\) | |||||||
\(728\) | 44.7975 | − | 49.4993i | 1.66031 | − | 1.83457i | ||||
\(729\) | 18.6404 | 0.690385 | ||||||||
\(730\) | 11.7118 | − | 26.4987i | 0.433471 | − | 0.980762i | ||||
\(731\) | 9.61089i | 0.355472i | ||||||||
\(732\) | −3.45838 | − | 5.55548i | −0.127826 | − | 0.205336i | ||||
\(733\) | −10.9959 | −0.406143 | −0.203071 | − | 0.979164i | \(-0.565092\pi\) | ||||
−0.203071 | + | 0.979164i | \(0.565092\pi\) | |||||||
\(734\) | −2.46691 | − | 8.63072i | −0.0910554 | − | 0.318566i | ||||
\(735\) | −22.2699 | − | 18.5518i | −0.821439 | − | 0.684292i | ||||
\(736\) | 11.8640 | − | 24.3977i | 0.437311 | − | 0.899310i | ||||
\(737\) | 24.0170i | 0.884676i | ||||||||
\(738\) | 24.7644 | − | 7.07840i | 0.911591 | − | 0.260559i | ||||
\(739\) | 14.0735i | 0.517702i | 0.965917 | + | 0.258851i | \(0.0833439\pi\) | ||||
−0.965917 | + | 0.258851i | \(0.916656\pi\) | |||||||
\(740\) | 43.9108 | + | 6.08741i | 1.61419 | + | 0.223778i | ||||
\(741\) | 6.82726i | 0.250806i | ||||||||
\(742\) | 0.356567 | + | 1.24748i | 0.0130900 | + | 0.0457965i | ||||
\(743\) | − | 3.97256i | − | 0.145739i | −0.997341 | − | 0.0728695i | \(-0.976784\pi\) | ||
0.997341 | − | 0.0728695i | \(-0.0232157\pi\) | |||||||
\(744\) | −7.01203 | − | 6.34598i | −0.257073 | − | 0.232655i | ||||
\(745\) | −23.1788 | + | 27.8243i | −0.849206 | + | 1.01940i | ||||
\(746\) | −30.2477 | + | 8.64568i | −1.10745 | + | 0.316541i | ||||
\(747\) | 14.0640i | 0.514576i | ||||||||
\(748\) | 14.3149 | − | 8.91127i | 0.523404 | − | 0.325828i | ||||
\(749\) | 67.6828 | 2.47308 | ||||||||
\(750\) | 4.07850 | − | 17.0728i | 0.148926 | − | 0.623409i | ||||
\(751\) | 19.1625 | 0.699248 | 0.349624 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349624 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(752\) | 0.592282 | − | 1.20399i | 0.0215983 | − | 0.0439051i | ||||
\(753\) | −7.80667 | −0.284491 | ||||||||
\(754\) | −5.61255 | − | 19.6360i | −0.204397 | − | 0.715101i | ||||
\(755\) | 13.2309 | − | 15.8827i | 0.481523 | − | 0.578030i | ||||
\(756\) | 24.1760 | + | 38.8359i | 0.879273 | + | 1.41245i | ||||
\(757\) | −11.1132 | −0.403917 | −0.201959 | − | 0.979394i | \(-0.564731\pi\) | ||||
−0.201959 | + | 0.979394i | \(0.564731\pi\) | |||||||
\(758\) | −17.0229 | + | 4.86566i | −0.618301 | + | 0.176729i | ||||
\(759\) | −24.7816 | − | 6.96110i | −0.899516 | − | 0.252672i | ||||
\(760\) | 7.05096 | − | 0.998329i | 0.255765 | − | 0.0362132i | ||||
\(761\) | −11.4048 | −0.413422 | −0.206711 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206711 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(762\) | 11.7628 | − | 3.36216i | 0.426122 | − | 0.121798i | ||||
\(763\) | −55.9928 | −2.02708 | ||||||||
\(764\) | 33.5983 | − | 20.9156i | 1.21555 | − | 0.756698i | ||||
\(765\) | −5.29555 | − | 4.41141i | −0.191461 | − | 0.159495i | ||||
\(766\) | 5.55697 | + | 19.4415i | 0.200781 | + | 0.702451i | ||||
\(767\) | −17.6483 | −0.637244 | ||||||||
\(768\) | −10.8407 | − | 14.0708i | −0.391179 | − | 0.507737i | ||||
\(769\) | 23.6281i | 0.852049i | 0.904712 | + | 0.426025i | \(0.140086\pi\) | ||||
−0.904712 | + | 0.426025i | \(0.859914\pi\) | |||||||
\(770\) | −26.7096 | + | 60.4324i | −0.962545 | + | 2.17783i | ||||
\(771\) | − | 2.73667i | − | 0.0985588i | ||||||
\(772\) | −18.5498 | − | 29.7980i | −0.667622 | − | 1.07246i | ||||
\(773\) | −30.7686 | −1.10667 | −0.553335 | − | 0.832959i | \(-0.686645\pi\) | ||||
−0.553335 | + | 0.832959i | \(0.686645\pi\) | |||||||
\(774\) | 3.78614 | + | 13.2462i | 0.136090 | + | 0.476123i | ||||
\(775\) | −14.8115 | + | 2.72073i | −0.532045 | + | 0.0977315i | ||||
\(776\) | 27.8830 | − | 30.8095i | 1.00094 | − | 1.10600i | ||||
\(777\) | − | 47.5575i | − | 1.70612i | ||||||
\(778\) | −3.44338 | − | 12.0470i | −0.123451 | − | 0.431905i | ||||
\(779\) | −11.6018 | −0.415676 | ||||||||
\(780\) | 3.72358 | − | 26.8596i | 0.133326 | − | 0.961727i | ||||
\(781\) | 60.3176i | 2.15833i | ||||||||
\(782\) | 11.8272 | − | 0.0539953i | 0.422939 | − | 0.00193087i | ||||
\(783\) | 13.9939 | 0.500101 | ||||||||
\(784\) | −20.6160 | + | 41.9083i | −0.736285 | + | 1.49672i | ||||
\(785\) | −1.28830 | − | 1.07321i | −0.0459815 | − | 0.0383045i | ||||
\(786\) | 4.06635 | + | 14.2265i | 0.145042 | + | 0.507442i | ||||
\(787\) | − | 27.7205i | − | 0.988129i | −0.869425 | − | 0.494065i | \(-0.835511\pi\) | ||
0.869425 | − | 0.494065i | \(-0.164489\pi\) | |||||||
\(788\) | 14.1433 | + | 22.7196i | 0.503835 | + | 0.809351i | ||||
\(789\) | − | 10.5521i | − | 0.375666i | ||||||
\(790\) | −22.1420 | − | 9.78618i | −0.787777 | − | 0.348177i | ||||
\(791\) | 11.6087i | 0.412759i | ||||||||
\(792\) | 16.2189 | − | 17.9211i | 0.576312 | − | 0.636800i | ||||
\(793\) | −16.0976 | −0.571641 | ||||||||
\(794\) | 4.09248 | + | 14.3179i | 0.145237 | + | 0.508123i | ||||
\(795\) | 0.404900 | + | 0.337298i | 0.0143603 | + | 0.0119627i | ||||
\(796\) | −9.94449 | + | 6.19062i | −0.352473 | + | 0.219421i | ||||
\(797\) | 30.0790 | 1.06545 | 0.532726 | − | 0.846288i | \(-0.321168\pi\) | ||||
0.532726 | + | 0.846288i | \(0.321168\pi\) | |||||||
\(798\) | −2.09955 | − | 7.34547i | −0.0743233 | − | 0.260027i | ||||
\(799\) | 0.584966 | 0.0206946 | ||||||||
\(800\) | −28.2842 | + | 0.0820039i | −0.999996 | + | 0.00289928i | ||||
\(801\) | − | 6.74367i | − | 0.238276i | ||||||
\(802\) | 13.0533 | + | 45.6680i | 0.460927 | + | 1.61259i | ||||
\(803\) | 44.2938i | 1.56309i | ||||||||
\(804\) | 5.82898 | + | 9.36355i | 0.205572 | + | 0.330227i | ||||
\(805\) | −38.1866 | + | 26.2591i | −1.34590 | + | 0.925511i | ||||
\(806\) | −22.3682 | + | 6.39348i | −0.787885 | + | 0.225201i | ||||
\(807\) | 3.65261 | 0.128578 | ||||||||
\(808\) | 15.1133 | − | 16.6995i | 0.531682 | − | 0.587486i | ||||
\(809\) | −14.2873 | −0.502316 | −0.251158 | − | 0.967946i | \(-0.580811\pi\) | ||||
−0.251158 | + | 0.967946i | \(0.580811\pi\) | |||||||
\(810\) | 1.65774 | + | 0.732678i | 0.0582470 | + | 0.0257437i | ||||
\(811\) | − | 50.5206i | − | 1.77402i | −0.461752 | − | 0.887009i | \(-0.652779\pi\) | ||
0.461752 | − | 0.887009i | \(-0.347221\pi\) | |||||||
\(812\) | 12.0771 | + | 19.4004i | 0.423823 | + | 0.680821i | ||||
\(813\) | 7.65942i | 0.268628i | ||||||||
\(814\) | −65.1664 | + | 18.6265i | −2.28408 | + | 0.652858i | ||||
\(815\) | −12.2287 | − | 10.1870i | −0.428353 | − | 0.356836i | ||||
\(816\) | 3.41819 | − | 6.94851i | 0.119661 | − | 0.243247i | ||||
\(817\) | − | 6.20563i | − | 0.217107i | ||||||
\(818\) | 37.7219 | − | 10.7820i | 1.31892 | − | 0.376985i | ||||
\(819\) | 41.7203 | 1.45782 | ||||||||
\(820\) | 45.6433 | + | 6.32759i | 1.59393 | + | 0.220969i | ||||
\(821\) | −15.7791 | −0.550695 | −0.275348 | − | 0.961345i | \(-0.588793\pi\) | ||||
−0.275348 | + | 0.961345i | \(0.588793\pi\) | |||||||
\(822\) | 23.3863 | − | 6.68450i | 0.815692 | − | 0.233149i | ||||
\(823\) | 3.65484 | 0.127400 | 0.0636998 | − | 0.997969i | \(-0.479710\pi\) | ||||
0.0636998 | + | 0.997969i | \(0.479710\pi\) | |||||||
\(824\) | −14.0969 | − | 12.7579i | −0.491089 | − | 0.444442i | ||||
\(825\) | 4.84850 | + | 26.3950i | 0.168803 | + | 0.918955i | ||||
\(826\) | 18.9879 | − | 5.42730i | 0.660673 | − | 0.188840i | ||||
\(827\) | − | 14.3902i | − | 0.500397i | −0.968195 | − | 0.250199i | \(-0.919504\pi\) | ||
0.968195 | − | 0.250199i | \(-0.0804959\pi\) | |||||||
\(828\) | 16.2795 | − | 4.73365i | 0.565750 | − | 0.164506i | ||||
\(829\) | 12.9284 | 0.449023 | 0.224511 | − | 0.974471i | \(-0.427921\pi\) | ||||
0.224511 | + | 0.974471i | \(0.427921\pi\) | |||||||
\(830\) | −10.1716 | + | 23.0141i | −0.353062 | + | 0.798830i | ||||
\(831\) | − | 17.8812i | − | 0.620290i | ||||||
\(832\) | −43.4774 | + | 4.34650i | −1.50731 | + | 0.150688i | ||||
\(833\) | −20.3613 | −0.705479 | ||||||||
\(834\) | −2.02608 | − | 7.08843i | −0.0701575 | − | 0.245452i | ||||
\(835\) | −0.623824 | − | 0.519671i | −0.0215883 | − | 0.0179840i | ||||
\(836\) | −9.24293 | + | 5.75389i | −0.319673 | + | 0.199002i | ||||
\(837\) | − | 15.9410i | − | 0.551002i | ||||||
\(838\) | 0.393457 | − | 0.112462i | 0.0135917 | − | 0.00388492i | ||||
\(839\) | 43.2349 | 1.49264 | 0.746318 | − | 0.665590i | \(-0.231820\pi\) | ||||
0.746318 | + | 0.665590i | \(0.231820\pi\) | |||||||
\(840\) | 4.25377 | + | 30.0434i | 0.146769 | + | 1.03660i | ||||
\(841\) | −22.0094 | −0.758944 | ||||||||
\(842\) | 14.7343 | + | 51.5494i | 0.507779 | + | 1.77651i | ||||
\(843\) | 7.53968i | 0.259680i | ||||||||
\(844\) | 17.9686 | + | 28.8644i | 0.618505 | + | 0.993555i | ||||
\(845\) | −28.9161 | − | 24.0883i | −0.994743 | − | 0.828662i | ||||
\(846\) | 0.806226 | − | 0.230443i | 0.0277186 | − | 0.00792279i | ||||
\(847\) | − | 53.4779i | − | 1.83752i | ||||||
\(848\) | 0.374829 | − | 0.761954i | 0.0128717 | − | 0.0261656i | ||||
\(849\) | 8.00078i | 0.274586i | ||||||||
\(850\) | −5.47503 | − | 11.0487i | −0.187792 | − | 0.378966i | ||||
\(851\) | −45.7681 | − | 12.8561i | −1.56891 | − | 0.440703i | ||||
\(852\) | 14.6392 | + | 23.5161i | 0.501531 | + | 0.805650i | ||||
\(853\) | − | 6.61354i | − | 0.226443i | −0.993570 | − | 0.113222i | \(-0.963883\pi\) | ||
0.993570 | − | 0.113222i | \(-0.0361170\pi\) | |||||||
\(854\) | 17.3194 | − | 4.95039i | 0.592658 | − | 0.169399i | ||||
\(855\) | 3.41927 | + | 2.84839i | 0.116936 | + | 0.0974129i | ||||
\(856\) | −32.8441 | − | 29.7244i | −1.12259 | − | 1.01596i | ||||
\(857\) | − | 7.39107i | − | 0.252474i | −0.992000 | − | 0.126237i | \(-0.959710\pi\) | ||
0.992000 | − | 0.126237i | \(-0.0402900\pi\) | |||||||
\(858\) | 11.3935 | + | 39.8613i | 0.388969 | + | 1.36084i | ||||
\(859\) | − | 25.9916i | − | 0.886821i | −0.896319 | − | 0.443411i | \(-0.853768\pi\) | ||
0.896319 | − | 0.443411i | \(-0.146232\pi\) | |||||||
\(860\) | −3.38454 | + | 24.4140i | −0.115412 | + | 0.832509i | ||||
\(861\) | − | 49.4338i | − | 1.68470i | ||||||
\(862\) | 30.2873 | − | 8.65699i | 1.03159 | − | 0.294858i | ||||
\(863\) | −23.5099 | −0.800285 | −0.400142 | − | 0.916453i | \(-0.631039\pi\) | ||||
−0.400142 | + | 0.916453i | \(0.631039\pi\) | |||||||
\(864\) | 5.32383 | − | 29.4631i | 0.181120 | − | 1.00236i | ||||
\(865\) | −5.04136 | + | 6.05175i | −0.171411 | + | 0.205766i | ||||
\(866\) | −11.3984 | + | 3.25799i | −0.387332 | + | 0.110711i | ||||
\(867\) | −15.4967 | −0.526297 | ||||||||
\(868\) | 22.0998 | − | 13.7575i | 0.750116 | − | 0.466961i | ||||
\(869\) | 37.0113 | 1.25552 | ||||||||
\(870\) | 8.48981 | + | 3.75227i | 0.287831 | + | 0.127214i | ||||
\(871\) | 27.1318 | 0.919326 | ||||||||
\(872\) | 27.1714 | + | 24.5904i | 0.920139 | + | 0.832738i | ||||
\(873\) | 25.9677 | 0.878872 | ||||||||
\(874\) | −7.63665 | + | 0.0348640i | −0.258314 | + | 0.00117929i | ||||
\(875\) | 42.0997 | + | 23.7094i | 1.42323 | + | 0.801524i | ||||
\(876\) | 10.7502 | + | 17.2689i | 0.363216 | + | 0.583463i | ||||
\(877\) | 26.7427i | 0.903038i | 0.892262 | + | 0.451519i | \(0.149118\pi\) | ||||
−0.892262 | + | 0.451519i | \(0.850882\pi\) | |||||||
\(878\) | 0.861745 | + | 3.01489i | 0.0290825 | + | 0.101748i | ||||
\(879\) | 27.9755 | 0.943589 | ||||||||
\(880\) | 39.5014 | − | 17.5957i | 1.33159 | − | 0.593150i | ||||
\(881\) | − | 1.75131i | − | 0.0590030i | −0.999565 | − | 0.0295015i | \(-0.990608\pi\) | ||
0.999565 | − | 0.0295015i | \(-0.00939198\pi\) | |||||||
\(882\) | −28.0629 | + | 8.02120i | −0.944927 | + | 0.270088i | ||||
\(883\) | −17.6978 | −0.595577 | −0.297789 | − | 0.954632i | \(-0.596249\pi\) | ||||
−0.297789 | + | 0.954632i | \(0.596249\pi\) | |||||||
\(884\) | −10.0670 | − | 16.1714i | −0.338590 | − | 0.543904i | ||||
\(885\) | 5.13401 | − | 6.16297i | 0.172578 | − | 0.207166i | ||||
\(886\) | −15.9083 | + | 4.54705i | −0.534449 | + | 0.152761i | ||||
\(887\) | 16.7977 | 0.564011 | 0.282006 | − | 0.959413i | \(-0.409000\pi\) | ||||
0.282006 | + | 0.959413i | \(0.409000\pi\) | |||||||
\(888\) | −20.8859 | + | 23.0780i | −0.700884 | + | 0.774447i | ||||
\(889\) | 33.6751i | 1.12943i | ||||||||
\(890\) | 4.87727 | − | 11.0352i | 0.163486 | − | 0.369900i | ||||
\(891\) | −2.77099 | −0.0928315 | ||||||||
\(892\) | −7.33656 | + | 4.56714i | −0.245646 | + | 0.152919i | ||||
\(893\) | −0.377705 | −0.0126394 | ||||||||
\(894\) | −6.98787 | − | 24.4477i | −0.233709 | − | 0.817653i | ||||
\(895\) | −30.1472 | + | 36.1893i | −1.00771 | + | 1.20967i | ||||
\(896\) | 45.4407 | − | 18.0468i | 1.51807 | − | 0.602900i | ||||
\(897\) | −7.86391 | + | 27.9957i | −0.262568 | + | 0.934748i | ||||
\(898\) | −42.5445 | + | 12.1605i | −1.41973 | + | 0.405800i | ||||
\(899\) | − | 7.96332i | − | 0.265592i | ||||||
\(900\) | −11.8985 | − | 13.0709i | −0.396615 | − | 0.435697i | ||||
\(901\) | 0.370199 | 0.0123331 | ||||||||
\(902\) | −67.7375 | + | 19.3614i | −2.25541 | + | 0.644663i | ||||
\(903\) | 26.4415 | 0.879918 | ||||||||
\(904\) | 5.09822 | − | 5.63331i | 0.169564 | − | 0.187361i | ||||
\(905\) | 27.1916 | − | 32.6413i | 0.903878 | − | 1.08503i | ||||
\(906\) | 3.98882 | + | 13.9552i | 0.132520 | + | 0.463632i | ||||
\(907\) | 40.6854i | 1.35094i | 0.737389 | + | 0.675469i | \(0.236059\pi\) | ||||
−0.737389 | + | 0.675469i | \(0.763941\pi\) | |||||||
\(908\) | −2.24324 | − | 3.60349i | −0.0744445 | − | 0.119586i | ||||
\(909\) | 14.0751 | 0.466841 | ||||||||
\(910\) | 68.2701 | + | 30.1736i | 2.26313 | + | 1.00025i | ||||
\(911\) | −10.5511 | −0.349574 | −0.174787 | − | 0.984606i | \(-0.555924\pi\) | ||||
−0.174787 | + | 0.984606i | \(0.555924\pi\) | |||||||
\(912\) | −2.20708 | + | 4.48656i | −0.0730837 | + | 0.148565i | ||||
\(913\) | − | 38.4690i | − | 1.27314i | ||||||
\(914\) | −36.6520 | + | 10.4762i | −1.21234 | + | 0.346523i | ||||
\(915\) | 4.68288 | − | 5.62142i | 0.154811 | − | 0.185839i | ||||
\(916\) | −4.35868 | − | 7.00170i | −0.144015 | − | 0.231343i | ||||
\(917\) | −40.7281 | −1.34496 | ||||||||
\(918\) | 12.5501 | − | 3.58720i | 0.414217 | − | 0.118395i | ||||
\(919\) | −50.5889 | −1.66877 | −0.834387 | − | 0.551179i | \(-0.814178\pi\) | ||||
−0.834387 | + | 0.551179i | \(0.814178\pi\) | |||||||
\(920\) | 30.0629 | + | 4.02786i | 0.991144 | + | 0.132795i | ||||
\(921\) | −10.9787 | −0.361762 | ||||||||
\(922\) | 13.9566 | − | 3.98921i | 0.459636 | − | 0.131378i | ||||
\(923\) | 68.1403 | 2.24287 | ||||||||
\(924\) | −24.5167 | − | 39.3831i | −0.806540 | − | 1.29561i | ||||
\(925\) | 8.95447 | + | 48.7477i | 0.294421 | + | 1.60281i | ||||
\(926\) | 42.0306 | − | 12.0136i | 1.38121 | − | 0.394791i | ||||
\(927\) | − | 11.8815i | − | 0.390240i | ||||||
\(928\) | 2.65951 | − | 14.7183i | 0.0873028 | − | 0.483151i | ||||
\(929\) | 24.3910 | 0.800243 | 0.400122 | − | 0.916462i | \(-0.368968\pi\) | ||||
0.400122 | + | 0.916462i | \(0.368968\pi\) | |||||||
\(930\) | 4.27437 | − | 9.67108i | 0.140162 | − | 0.317127i | ||||
\(931\) | 13.1470 | 0.430877 | ||||||||
\(932\) | −12.5879 | − | 20.2210i | −0.412331 | − | 0.662360i | ||||
\(933\) | − | 29.1939i | − | 0.955764i | ||||||
\(934\) | −7.28204 | − | 25.4769i | −0.238276 | − | 0.833629i | ||||
\(935\) | 14.4848 | + | 12.0664i | 0.473704 | + | 0.394615i | ||||
\(936\) | −20.2454 | − | 18.3223i | −0.661741 | − | 0.598885i | ||||
\(937\) | 5.60780 | 0.183199 | 0.0915994 | − | 0.995796i | \(-0.470802\pi\) | ||||
0.0915994 | + | 0.995796i | \(0.470802\pi\) | |||||||
\(938\) | −29.1912 | + | 8.34370i | −0.953126 | + | 0.272431i | ||||
\(939\) | 32.5178 | 1.06118 | ||||||||
\(940\) | 1.48595 | + | 0.206000i | 0.0484665 | + | 0.00671898i | ||||
\(941\) | − | 22.1204i | − | 0.721105i | −0.932739 | − | 0.360553i | \(-0.882588\pi\) | ||
0.932739 | − | 0.360553i | \(-0.117412\pi\) | |||||||
\(942\) | 1.13196 | − | 0.323548i | 0.0368813 | − | 0.0105418i | ||||
\(943\) | −47.5738 | − | 13.3634i | −1.54922 | − | 0.435171i | ||||
\(944\) | −11.5977 | − | 5.70526i | −0.377472 | − | 0.185690i | ||||
\(945\) | −32.7359 | + | 39.2968i | −1.06490 | + | 1.27833i | ||||
\(946\) | −10.3561 | − | 36.2319i | −0.336707 | − | 1.17800i | ||||
\(947\) | −9.04206 | −0.293828 | −0.146914 | − | 0.989149i | \(-0.546934\pi\) | ||||
−0.146914 | + | 0.989149i | \(0.546934\pi\) | |||||||
\(948\) | 14.4297 | − | 8.98273i | 0.468654 | − | 0.291746i | ||||
\(949\) | 50.0384 | 1.62432 | ||||||||
\(950\) | 3.53515 | + | 7.13398i | 0.114695 | + | 0.231457i | ||||
\(951\) | 23.1708i | 0.751364i | ||||||||
\(952\) | 15.8042 | + | 14.3030i | 0.512218 | + | 0.463564i | ||||
\(953\) | −36.5931 | −1.18537 | −0.592683 | − | 0.805436i | \(-0.701931\pi\) | ||||
−0.592683 | + | 0.805436i | \(0.701931\pi\) | |||||||
\(954\) | 0.510225 | − | 0.145837i | 0.0165191 | − | 0.00472165i | ||||
\(955\) | 33.9971 | + | 28.3210i | 1.10012 | + | 0.916446i | ||||
\(956\) | −15.4361 | − | 24.7963i | −0.499240 | − | 0.801970i | ||||
\(957\) | −14.1911 | −0.458733 | ||||||||
\(958\) | −20.5134 | + | 5.86334i | −0.662759 | + | 0.189436i | ||||
\(959\) | 66.9512i | 2.16197i | ||||||||
\(960\) | 11.1300 | − | 16.4471i | 0.359219 | − | 0.530829i | ||||
\(961\) | 21.9287 | 0.707376 | ||||||||
\(962\) | 21.0422 | + | 73.6181i | 0.678428 | + | 2.37354i | ||||
\(963\) | − | 27.6825i | − | 0.892057i | ||||||
\(964\) | 14.9827 | + | 24.0679i | 0.482560 | + | 0.775175i | ||||
\(965\) | 25.1176 | − | 30.1518i | 0.808566 | − | 0.970619i | ||||
\(966\) | −0.148552 | − | 32.5389i | −0.00477958 | − | 1.04692i | ||||
\(967\) | −32.8759 | −1.05722 | −0.528608 | − | 0.848866i | \(-0.677286\pi\) | ||||
−0.528608 | + | 0.848866i | \(0.677286\pi\) | |||||||
\(968\) | −23.4860 | + | 25.9510i | −0.754868 | + | 0.834096i | ||||
\(969\) | −2.17982 | −0.0700259 | ||||||||
\(970\) | 42.4929 | + | 18.7807i | 1.36436 | + | 0.603013i | ||||
\(971\) | −25.9741 | −0.833548 | −0.416774 | − | 0.909010i | \(-0.636839\pi\) | ||||
−0.416774 | + | 0.909010i | \(0.636839\pi\) | |||||||
\(972\) | 25.8791 | − | 16.1102i | 0.830072 | − | 0.516735i | ||||
\(973\) | 20.2930 | 0.650564 | ||||||||
\(974\) | −50.3429 | + | 14.3895i | −1.61309 | + | 0.461069i | ||||
\(975\) | 29.8182 | − | 5.47732i | 0.954948 | − | 0.175414i | ||||
\(976\) | −10.5786 | − | 5.20393i | −0.338612 | − | 0.166574i | ||||
\(977\) | −15.7214 | −0.502972 | −0.251486 | − | 0.967861i | \(-0.580919\pi\) | ||||
−0.251486 | + | 0.967861i | \(0.580919\pi\) | |||||||
\(978\) | 10.7447 | − | 3.07115i | 0.343577 | − | 0.0982045i | ||||
\(979\) | 18.4458i | 0.589531i | ||||||||
\(980\) | −51.7227 | − | 7.17039i | −1.65222 | − | 0.229050i | ||||
\(981\) | 22.9013i | 0.731181i | ||||||||
\(982\) | 0.932601 | + | 3.26279i | 0.0297605 | + | 0.104120i | ||||
\(983\) | 26.5632i | 0.847235i | 0.905841 | + | 0.423618i | \(0.139240\pi\) | ||||
−0.905841 | + | 0.423618i | \(0.860760\pi\) | |||||||
\(984\) | −21.7099 | + | 23.9885i | −0.692087 | + | 0.764726i | ||||
\(985\) | −19.1510 | + | 22.9892i | −0.610201 | + | 0.732498i | ||||
\(986\) | 6.26942 | − | 1.79198i | 0.199659 | − | 0.0570684i | ||||
\(987\) | − | 1.60936i | − | 0.0512265i | ||||||
\(988\) | 6.50013 | + | 10.4417i | 0.206797 | + | 0.332194i | ||||
\(989\) | 7.14789 | − | 25.4466i | 0.227290 | − | 0.809155i | ||||
\(990\) | 24.7171 | + | 10.9243i | 0.785560 | + | 0.347197i | ||||
\(991\) | − | 7.50012i | − | 0.238249i | −0.992879 | − | 0.119125i | \(-0.961991\pi\) | ||
0.992879 | − | 0.119125i | \(-0.0380088\pi\) | |||||||
\(992\) | −16.7662 | − | 3.02956i | −0.532327 | − | 0.0961886i | ||||
\(993\) | 7.53689i | 0.239176i | ||||||||
\(994\) | −73.3124 | + | 20.9548i | −2.32533 | + | 0.664647i | ||||
\(995\) | −10.0625 | − | 8.38250i | −0.319004 | − | 0.265743i | ||||
\(996\) | −9.33652 | − | 14.9980i | −0.295839 | − | 0.475230i | ||||
\(997\) | − | 15.8439i | − | 0.501780i | −0.968016 | − | 0.250890i | \(-0.919277\pi\) | ||
0.968016 | − | 0.250890i | \(-0.0807233\pi\) | |||||||
\(998\) | 6.42803 | + | 22.4890i | 0.203476 | + | 0.711878i | ||||
\(999\) | −52.4651 | −1.65992 |
(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 | 460.2.g.c.459.4 | yes | 56 | |
4.3 | odd | 2 | inner | 460.2.g.c.459.56 | yes | 56 | |
5.4 | even | 2 | inner | 460.2.g.c.459.53 | yes | 56 | |
20.19 | odd | 2 | inner | 460.2.g.c.459.1 | ✓ | 56 | |
23.22 | odd | 2 | inner | 460.2.g.c.459.3 | yes | 56 | |
92.91 | even | 2 | inner | 460.2.g.c.459.55 | yes | 56 | |
115.114 | odd | 2 | inner | 460.2.g.c.459.54 | yes | 56 | |
460.459 | even | 2 | inner | 460.2.g.c.459.2 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.g.c.459.1 | ✓ | 56 | 20.19 | odd | 2 | inner | |
460.2.g.c.459.2 | yes | 56 | 460.459 | even | 2 | inner | |
460.2.g.c.459.3 | yes | 56 | 23.22 | odd | 2 | inner | |
460.2.g.c.459.4 | yes | 56 | 1.1 | even | 1 | trivial | |
460.2.g.c.459.53 | yes | 56 | 5.4 | even | 2 | inner | |
460.2.g.c.459.54 | yes | 56 | 115.114 | odd | 2 | inner | |
460.2.g.c.459.55 | yes | 56 | 92.91 | even | 2 | inner | |
460.2.g.c.459.56 | yes | 56 | 4.3 | odd | 2 | inner |