Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(321,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.321");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.l (of order \(4\), degree \(2\), 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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 321.4 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.321 |
Dual form | 1280.2.l.a.961.4 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.07313 | + | 1.07313i | 0.619573 | + | 0.619573i | 0.945422 | − | 0.325849i | \(-0.105650\pi\) |
−0.325849 | + | 0.945422i | \(0.605650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.103425i | − | 0.0390908i | −0.999809 | − | 0.0195454i | \(-0.993778\pi\) | ||
0.999809 | − | 0.0195454i | \(-0.00622189\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 0.696775i | − | 0.232258i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.21441 | − | 2.21441i | 0.667671 | − | 0.667671i | −0.289506 | − | 0.957176i | \(-0.593491\pi\) |
0.957176 | + | 0.289506i | \(0.0934909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.931852 | + | 0.931852i | 0.258449 | + | 0.258449i | 0.824423 | − | 0.565974i | \(-0.191500\pi\) |
−0.565974 | + | 0.824423i | \(0.691500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.51764 | −0.391852 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.54587 | 0.617463 | 0.308732 | − | 0.951149i | \(-0.400096\pi\) | ||||
0.308732 | + | 0.951149i | \(0.400096\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94646 | + | 2.94646i | 0.675965 | + | 0.675965i | 0.959085 | − | 0.283120i | \(-0.0913693\pi\) |
−0.283120 | + | 0.959085i | \(0.591369\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.110988 | − | 0.110988i | 0.0242196 | − | 0.0242196i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.07812i | − | 0.224803i | −0.993663 | − | 0.112401i | \(-0.964146\pi\) | ||
0.993663 | − | 0.112401i | \(-0.0358542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.96713 | − | 3.96713i | 0.763474 | − | 0.763474i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.32780 | + | 6.32780i | 1.17504 | + | 1.17504i | 0.980991 | + | 0.194053i | \(0.0621633\pi\) |
0.194053 | + | 0.980991i | \(0.437837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.635674 | −0.114171 | −0.0570853 | − | 0.998369i | \(-0.518181\pi\) | ||||
−0.0570853 | + | 0.998369i | \(0.518181\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.75272 | 0.827342 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0731322 | + | 0.0731322i | 0.0123616 | + | 0.0123616i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.76733 | + | 3.76733i | −0.619345 | + | 0.619345i | −0.945363 | − | 0.326019i | \(-0.894293\pi\) |
0.326019 | + | 0.945363i | \(0.394293\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000i | 0.320256i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.23143i | 0.817012i | 0.912756 | + | 0.408506i | \(0.133950\pi\) | ||||
−0.912756 | + | 0.408506i | \(0.866050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.85872 | − | 5.85872i | 0.893446 | − | 0.893446i | −0.101399 | − | 0.994846i | \(-0.532332\pi\) |
0.994846 | + | 0.101399i | \(0.0323320\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.492694 | + | 0.492694i | 0.0734465 | + | 0.0734465i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.86005 | −1.43824 | −0.719118 | − | 0.694888i | \(-0.755454\pi\) | ||||
−0.719118 | + | 0.694888i | \(0.755454\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98930 | 0.998472 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73205 | + | 2.73205i | 0.382564 | + | 0.382564i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.04284 | − | 6.04284i | 0.830048 | − | 0.830048i | −0.157475 | − | 0.987523i | \(-0.550335\pi\) |
0.987523 | + | 0.157475i | \(0.0503354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.13165i | 0.422272i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.32389i | 0.837620i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.78094 | + | 6.78094i | −0.882804 | + | 0.882804i | −0.993819 | − | 0.111015i | \(-0.964590\pi\) |
0.111015 | + | 0.993819i | \(0.464590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.58114 | + | 5.58114i | 0.714592 | + | 0.714592i | 0.967492 | − | 0.252900i | \(-0.0813845\pi\) |
−0.252900 | + | 0.967492i | \(0.581384\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0720636 | −0.00907916 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.31784 | −0.163458 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.187769 | − | 0.187769i | −0.0229396 | − | 0.0229396i | 0.695544 | − | 0.718484i | \(-0.255163\pi\) |
−0.718484 | + | 0.695544i | \(0.755163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.15696 | − | 1.15696i | 0.139282 | − | 0.139282i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.42883i | − | 0.288249i | −0.989560 | − | 0.144124i | \(-0.953963\pi\) | ||
0.989560 | − | 0.144124i | \(-0.0460365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1662i | 1.65803i | 0.559228 | + | 0.829014i | \(0.311098\pi\) | ||||
−0.559228 | + | 0.829014i | \(0.688902\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.07313 | − | 1.07313i | 0.123915 | − | 0.123915i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.229025 | − | 0.229025i | −0.0260998 | − | 0.0260998i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9647 | −1.23363 | −0.616814 | − | 0.787109i | \(-0.711577\pi\) | ||||
−0.616814 | + | 0.787109i | \(0.711577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.42418 | 0.713798 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.03029 | + | 1.03029i | 0.113089 | + | 0.113089i | 0.761387 | − | 0.648298i | \(-0.224519\pi\) |
−0.648298 | + | 0.761387i | \(0.724519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.80020 | + | 1.80020i | −0.195259 | + | 0.195259i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.5811i | 1.45605i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.75787i | − | 0.716333i | −0.933658 | − | 0.358167i | \(-0.883402\pi\) | ||
0.933658 | − | 0.358167i | \(-0.116598\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0963763 | − | 0.0963763i | 0.0101030 | − | 0.0101030i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.682163 | − | 0.682163i | −0.0707370 | − | 0.0707370i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.16693 | −0.427518 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.9734 | −1.82493 | −0.912464 | − | 0.409158i | \(-0.865822\pi\) | ||||
−0.912464 | + | 0.409158i | \(0.865822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.54295 | − | 1.54295i | −0.155072 | − | 0.155072i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.86370 | − | 6.86370i | 0.682964 | − | 0.682964i | −0.277703 | − | 0.960667i | \(-0.589573\pi\) |
0.960667 | + | 0.277703i | \(0.0895731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.3706i | − | 1.71158i | −0.517323 | − | 0.855790i | \(-0.673071\pi\) | ||
0.517323 | − | 0.855790i | \(-0.326929\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.156961i | 0.0153178i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.1184 | − | 12.1184i | 1.17153 | − | 1.17153i | 0.189682 | − | 0.981846i | \(-0.439254\pi\) |
0.981846 | − | 0.189682i | \(-0.0607457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.08516 | + | 9.08516i | 0.870201 | + | 0.870201i | 0.992494 | − | 0.122293i | \(-0.0390248\pi\) |
−0.122293 | + | 0.992494i | \(0.539025\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.08568 | −0.767459 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.39230 | 0.601337 | 0.300669 | − | 0.953729i | \(-0.402790\pi\) | ||||
0.300669 | + | 0.953729i | \(0.402790\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.762343 | + | 0.762343i | 0.0710889 | + | 0.0710889i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.649291 | − | 0.649291i | 0.0600269 | − | 0.0600269i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.263305i | − | 0.0241371i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.19275i | 0.108432i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.61401 | + | 5.61401i | −0.506199 | + | 0.506199i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.19000 | −0.283066 | −0.141533 | − | 0.989934i | \(-0.545203\pi\) | ||||
−0.141533 | + | 0.989934i | \(0.545203\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.5744 | 1.10711 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.62863 | − | 5.62863i | −0.491775 | − | 0.491775i | 0.417090 | − | 0.908865i | \(-0.363050\pi\) |
−0.908865 | + | 0.417090i | \(0.863050\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.304737 | − | 0.304737i | 0.0264240 | − | 0.0264240i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.61037i | 0.482863i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.277401i | − | 0.0237000i | −0.999930 | − | 0.0118500i | \(-0.996228\pi\) | ||
0.999930 | − | 0.0118500i | \(-0.00377206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1586 | + | 12.1586i | −1.03128 | + | 1.03128i | −0.0317874 | + | 0.999495i | \(0.510120\pi\) |
−0.999495 | + | 0.0317874i | \(0.989880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5811 | − | 10.5811i | −0.891093 | − | 0.891093i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.12701 | 0.345118 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.94887 | −0.743163 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.50045 | + | 7.50045i | 0.618626 | + | 0.618626i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.81722 | − | 5.81722i | 0.476565 | − | 0.476565i | −0.427466 | − | 0.904031i | \(-0.640594\pi\) |
0.904031 | + | 0.427466i | \(0.140594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.01994i | − | 0.489895i | −0.969536 | − | 0.244948i | \(-0.921229\pi\) | ||
0.969536 | − | 0.244948i | \(-0.0787708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.77389i | − | 0.143411i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.449490 | − | 0.449490i | 0.0361039 | − | 0.0361039i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.18494 | − | 9.18494i | −0.733038 | − | 0.733038i | 0.238182 | − | 0.971220i | \(-0.423448\pi\) |
−0.971220 | + | 0.238182i | \(0.923448\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.9695 | 1.02855 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.111504 | −0.00878772 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.74408 | − | 2.74408i | −0.214933 | − | 0.214933i | 0.591426 | − | 0.806359i | \(-0.298565\pi\) |
−0.806359 | + | 0.591426i | \(0.798565\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.36068 | + | 3.36068i | −0.261628 | + | 0.261628i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.66923i | 0.516080i | 0.966134 | + | 0.258040i | \(0.0830767\pi\) | ||||
−0.966134 | + | 0.258040i | \(0.916923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.2633i | − | 0.866408i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.05302 | − | 2.05302i | 0.156998 | − | 0.156998i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.732051 | + | 0.732051i | 0.0556568 | + | 0.0556568i | 0.734387 | − | 0.678731i | \(-0.237470\pi\) |
−0.678731 | + | 0.734387i | \(0.737470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.103425 | −0.00781816 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.5537 | −1.09392 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.619174 | + | 0.619174i | 0.0462792 | + | 0.0462792i | 0.729868 | − | 0.683588i | \(-0.239582\pi\) |
−0.683588 | + | 0.729868i | \(0.739582\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.55583 | + | 7.55583i | −0.561621 | + | 0.561621i | −0.929768 | − | 0.368147i | \(-0.879992\pi\) |
0.368147 | + | 0.929768i | \(0.379992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.9786i | 0.885484i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.32780i | − | 0.391708i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.63760 | − | 5.63760i | 0.412262 | − | 0.412262i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.410298 | − | 0.410298i | −0.0298448 | − | 0.0298448i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2268 | 1.75299 | 0.876494 | − | 0.481412i | \(-0.159876\pi\) | ||||
0.876494 | + | 0.481412i | \(0.159876\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.78318 | 0.272319 | 0.136160 | − | 0.990687i | \(-0.456524\pi\) | ||||
0.136160 | + | 0.990687i | \(0.456524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.41421 | − | 1.41421i | −0.101274 | − | 0.101274i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.5322 | + | 14.5322i | −1.03538 | + | 1.03538i | −0.0360292 | + | 0.999351i | \(0.511471\pi\) |
−0.999351 | + | 0.0360292i | \(0.988529\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 24.5851i | − | 1.74279i | −0.490583 | − | 0.871394i | \(-0.663216\pi\) | ||
0.490583 | − | 0.871394i | \(-0.336784\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 0.403001i | − | 0.0284255i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.654450 | − | 0.654450i | 0.0459334 | − | 0.0459334i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.69918 | − | 3.69918i | −0.258362 | − | 0.258362i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.751204 | −0.0522123 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.0494 | 0.902644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.8214 | + | 11.8214i | 0.813817 | + | 0.813817i | 0.985204 | − | 0.171387i | \(-0.0548247\pi\) |
−0.171387 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.60645 | − | 2.60645i | 0.178591 | − | 0.178591i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.28548i | 0.565065i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0657443i | 0.00446302i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.2022 | + | 15.2022i | −1.02727 | + | 1.02727i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.37237 | + | 2.37237i | 0.159583 | + | 0.159583i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.3129 | 1.36026 | 0.680128 | − | 0.733094i | \(-0.261924\pi\) | ||||
0.680128 | + | 0.733094i | \(0.261924\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.696775 | −0.0464516 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.0831 | − | 19.0831i | −1.26659 | − | 1.26659i | −0.947838 | − | 0.318752i | \(-0.896736\pi\) |
−0.318752 | − | 0.947838i | \(-0.603264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.26330 | + | 1.26330i | −0.0834815 | + | 0.0834815i | −0.747614 | − | 0.664133i | \(-0.768801\pi\) |
0.664133 | + | 0.747614i | \(0.268801\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.491547i | − | 0.0323414i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 22.7727i | − | 1.49189i | −0.666010 | − | 0.745943i | \(-0.731999\pi\) | ||
0.666010 | − | 0.745943i | \(-0.268001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.97211 | − | 6.97211i | 0.454810 | − | 0.454810i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.7666 | − | 11.7666i | −0.764323 | − | 0.764323i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.0126 | 1.42388 | 0.711940 | − | 0.702241i | \(-0.247817\pi\) | ||||
0.711940 | + | 0.702241i | \(0.247817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5653 | −1.26031 | −0.630155 | − | 0.776469i | \(-0.717009\pi\) | ||||
−0.630155 | + | 0.776469i | \(0.717009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.00739 | − | 5.00739i | −0.321224 | − | 0.321224i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.94218 | + | 4.94218i | −0.315745 | + | 0.315745i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.49133i | 0.349405i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.21128i | 0.140134i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.92188 | + | 3.92188i | −0.247547 | + | 0.247547i | −0.819963 | − | 0.572416i | \(-0.806006\pi\) |
0.572416 | + | 0.819963i | \(0.306006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.38739 | − | 2.38739i | −0.150094 | − | 0.150094i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.86370 | −0.241954 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.4064 | −0.898647 | −0.449323 | − | 0.893369i | \(-0.648335\pi\) | ||||
−0.449323 | + | 0.893369i | \(0.648335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.389634 | + | 0.389634i | 0.0242107 | + | 0.0242107i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.40905 | − | 4.40905i | 0.272914 | − | 0.272914i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.0095i | − | 0.987187i | −0.869693 | − | 0.493594i | \(-0.835683\pi\) | ||
0.869693 | − | 0.493594i | \(-0.164317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.54587i | 0.524968i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.25209 | − | 7.25209i | 0.443821 | − | 0.443821i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.24604 | + | 2.24604i | 0.136944 | + | 0.136944i | 0.772256 | − | 0.635312i | \(-0.219129\pi\) |
−0.635312 | + | 0.772256i | \(0.719129\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.97202 | −0.180537 | −0.0902687 | − | 0.995917i | \(-0.528773\pi\) | ||||
−0.0902687 | + | 0.995917i | \(0.528773\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.206849 | 0.0125191 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.21441 | − | 2.21441i | −0.133534 | − | 0.133534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.1163 | + | 20.1163i | −1.20867 | + | 1.20867i | −0.237215 | + | 0.971457i | \(0.576235\pi\) |
−0.971457 | + | 0.237215i | \(0.923765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.442922i | 0.0265170i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.5865i | − | 1.10878i | −0.832258 | − | 0.554388i | \(-0.812952\pi\) | ||
0.832258 | − | 0.554388i | \(-0.187048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.7499 | + | 20.7499i | −1.23345 | + | 1.23345i | −0.270827 | + | 0.962628i | \(0.587297\pi\) |
−0.962628 | + | 0.270827i | \(0.912703\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.47167 | − | 4.47167i | −0.264879 | − | 0.264879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.541058 | 0.0319376 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5186 | −0.618739 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.2879 | − | 19.2879i | −1.13068 | − | 1.13068i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.59059 | − | 6.59059i | 0.385027 | − | 0.385027i | −0.487883 | − | 0.872909i | \(-0.662231\pi\) |
0.872909 | + | 0.487883i | \(0.162231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.58970i | − | 0.558334i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 17.5697i | − | 1.01950i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.00464 | − | 1.00464i | 0.0581001 | − | 0.0581001i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.605935 | − | 0.605935i | −0.0349255 | − | 0.0349255i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.7313 | 0.846292 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.89293 | −0.451948 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.494394 | − | 0.494394i | −0.0282166 | − | 0.0282166i | 0.692858 | − | 0.721074i | \(-0.256351\pi\) |
−0.721074 | + | 0.692858i | \(0.756351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.6410 | − | 18.6410i | 1.06045 | − | 1.06045i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2409i | 0.580707i | 0.956919 | + | 0.290354i | \(0.0937729\pi\) | ||||
−0.956919 | + | 0.290354i | \(0.906227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0058i | 0.565563i | 0.959184 | + | 0.282782i | \(0.0912572\pi\) | ||||
−0.959184 | + | 0.282782i | \(0.908743\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0509567 | − | 0.0509567i | 0.00287108 | − | 0.00287108i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.3441 | − | 19.3441i | −1.08647 | − | 1.08647i | −0.995889 | − | 0.0905836i | \(-0.971127\pi\) |
−0.0905836 | − | 0.995889i | \(-0.528873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0247 | 1.56908 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.0092 | 1.45169 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.50130 | + | 7.50130i | 0.417384 | + | 0.417384i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.931852 | − | 0.931852i | 0.0516898 | − | 0.0516898i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.4992i | 1.07831i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.01977i | 0.0562218i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2691 | + | 22.2691i | −1.22402 | + | 1.22402i | −0.257831 | + | 0.966190i | \(0.583008\pi\) |
−0.966190 | + | 0.257831i | \(0.916992\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.62498 | + | 2.62498i | 0.143848 | + | 0.143848i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.265545 | 0.0145083 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.4689 | −0.951592 | −0.475796 | − | 0.879556i | \(-0.657840\pi\) | ||||
−0.475796 | + | 0.879556i | \(0.657840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.85979 | + | 6.85979i | 0.372573 | + | 0.372573i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.40765 | + | 1.40765i | −0.0762283 | + | 0.0762283i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.44684i | − | 0.0781219i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.63619i | 0.0880895i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.12078 | − | 7.12078i | 0.382264 | − | 0.382264i | −0.489654 | − | 0.871917i | \(-0.662877\pi\) |
0.871917 | + | 0.489654i | \(0.162877\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.33386 | − | 9.33386i | −0.499630 | − | 0.499630i | 0.411693 | − | 0.911323i | \(-0.364938\pi\) |
−0.911323 | + | 0.411693i | \(0.864938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.39355 | 0.394638 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.8922 | −0.579732 | −0.289866 | − | 0.957067i | \(-0.593611\pi\) | ||||
−0.289866 | + | 0.957067i | \(0.593611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.71744 | + | 1.71744i | 0.0911522 | + | 0.0911522i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.282561 | − | 0.282561i | 0.0149547 | − | 0.0149547i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.9262i | − | 0.787775i | −0.919159 | − | 0.393888i | \(-0.871130\pi\) | ||
0.919159 | − | 0.393888i | \(-0.128870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.63671i | − | 0.0861424i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.27998 | + | 1.27998i | −0.0671816 | + | 0.0671816i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0170 | − | 10.0170i | −0.524315 | − | 0.524315i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.9265 | −1.87535 | −0.937673 | − | 0.347518i | \(-0.887025\pi\) | ||||
−0.937673 | + | 0.347518i | \(0.887025\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.64513 | 0.189758 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.624978 | − | 0.624978i | −0.0324472 | − | 0.0324472i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.04576 | + | 6.04576i | −0.313038 | + | 0.313038i | −0.846085 | − | 0.533048i | \(-0.821047\pi\) |
0.533048 | + | 0.846085i | \(0.321047\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.51764i | 0.0783705i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.7932i | 0.607378i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9598 | + | 10.9598i | −0.562969 | + | 0.562969i | −0.930150 | − | 0.367181i | \(-0.880323\pi\) |
0.367181 | + | 0.930150i | \(0.380323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.42329 | − | 3.42329i | −0.175380 | − | 0.175380i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.3120 | −1.44667 | −0.723337 | − | 0.690495i | \(-0.757393\pi\) | ||||
−0.723337 | + | 0.690495i | \(0.757393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.323890 | 0.0165069 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.08221 | − | 4.08221i | −0.207510 | − | 0.207510i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.1249 | − | 20.1249i | 1.02037 | − | 1.02037i | 0.0205833 | − | 0.999788i | \(-0.493448\pi\) |
0.999788 | − | 0.0205833i | \(-0.00655234\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.74474i | − | 0.138807i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.0805i | − | 0.609382i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.75323 | − | 7.75323i | 0.390107 | − | 0.390107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.43247 | + | 4.43247i | 0.222459 | + | 0.222459i | 0.809533 | − | 0.587074i | \(-0.199720\pi\) |
−0.587074 | + | 0.809533i | \(0.699720\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.654045 | 0.0327432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.4044 | −0.919072 | −0.459536 | − | 0.888159i | \(-0.651984\pi\) | ||||
−0.459536 | + | 0.888159i | \(0.651984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.592354 | − | 0.592354i | −0.0295073 | − | 0.0295073i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.54258 | + | 4.54258i | −0.225723 | + | 0.225723i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.6848i | 0.827036i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.1503i | 1.29305i | 0.762892 | + | 0.646526i | \(0.223779\pi\) | ||||
−0.762892 | + | 0.646526i | \(0.776221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.297688 | − | 0.297688i | 0.0146839 | − | 0.0146839i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.701316 | + | 0.701316i | 0.0345095 | + | 0.0345095i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.45705 | −0.0715239 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.0956 | −1.27791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3655 | − | 16.3655i | −0.799506 | − | 0.799506i | 0.183511 | − | 0.983018i | \(-0.441254\pi\) |
−0.983018 | + | 0.183511i | \(0.941254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.77589 | − | 3.77589i | 0.184025 | − | 0.184025i | −0.609082 | − | 0.793107i | \(-0.708462\pi\) |
0.793107 | + | 0.609082i | \(0.208462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.87024i | 0.334042i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.54587i | − | 0.123493i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.577227 | − | 0.577227i | 0.0279340 | − | 0.0279340i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.42883 | + | 4.42883i | 0.213826 | + | 0.213826i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9282 | −0.622730 | −0.311365 | − | 0.950290i | \(-0.600786\pi\) | ||||
−0.311365 | + | 0.950290i | \(0.600786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.716195 | −0.0344181 | −0.0172091 | − | 0.999852i | \(-0.505478\pi\) | ||||
−0.0172091 | + | 0.999852i | \(0.505478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.60332 | − | 9.60332i | −0.460444 | − | 0.460444i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.17663 | − | 3.17663i | 0.151959 | − | 0.151959i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 33.9527i | − | 1.62048i | −0.586101 | − | 0.810238i | \(-0.699338\pi\) | ||
0.586101 | − | 0.810238i | \(-0.300662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 4.86997i | − | 0.231903i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.3464 | + | 21.3464i | −1.01420 | + | 1.01420i | −0.0143006 | + | 0.999898i | \(0.504552\pi\) |
−0.999898 | + | 0.0143006i | \(0.995448\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.77854 | + | 4.77854i | 0.226524 | + | 0.226524i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4853 | 0.590534 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.5066 | 1.43970 | 0.719848 | − | 0.694131i | \(-0.244211\pi\) | ||||
0.719848 | + | 0.694131i | \(0.244211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.5845 | + | 11.5845i | 0.545495 | + | 0.545495i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.46019 | − | 6.46019i | 0.303526 | − | 0.303526i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.136297i | 0.00638969i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8063i | 0.645831i | 0.946428 | + | 0.322915i | \(0.104663\pi\) | ||||
−0.946428 | + | 0.322915i | \(0.895337\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.0998 | − | 10.0998i | 0.471417 | − | 0.471417i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.8637 | + | 10.8637i | 0.505973 | + | 0.505973i | 0.913288 | − | 0.407315i | \(-0.133535\pi\) |
−0.407315 | + | 0.913288i | \(0.633535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.401792 | 0.0186729 | 0.00933643 | − | 0.999956i | \(-0.497028\pi\) | ||||
0.00933643 | + | 0.999956i | \(0.497028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.964724 | 0.0447380 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.822963 | − | 0.822963i | −0.0380822 | − | 0.0380822i | 0.687809 | − | 0.725891i | \(-0.258573\pi\) |
−0.725891 | + | 0.687809i | \(0.758573\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0194199 | + | 0.0194199i | −0.000896728 | + | 0.000896728i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 19.7133i | − | 0.908341i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.9472i | − | 1.19306i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.94646 | − | 2.94646i | 0.135193 | − | 0.135193i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.21050 | − | 4.21050i | −0.192785 | − | 0.192785i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.24996 | −0.422641 | −0.211321 | − | 0.977417i | \(-0.567776\pi\) | ||||
−0.211321 | + | 0.977417i | \(0.567776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.02118 | −0.320138 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.119658 | − | 0.119658i | −0.00544463 | − | 0.00544463i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.7091 | − | 12.7091i | 0.577093 | − | 0.577093i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.23242i | − | 0.282418i | −0.989980 | − | 0.141209i | \(-0.954901\pi\) | ||
0.989980 | − | 0.141209i | \(-0.0450990\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.88953i | − | 0.266334i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.91407 | − | 2.91407i | 0.131510 | − | 0.131510i | −0.638288 | − | 0.769798i | \(-0.720357\pi\) |
0.769798 | + | 0.638288i | \(0.220357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.1097 | + | 16.1097i | 0.725546 | + | 0.725546i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.18206 | 0.0980761 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.251200 | −0.0112679 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.33145 | + | 2.33145i | 0.104370 | + | 0.104370i | 0.757364 | − | 0.652993i | \(-0.226487\pi\) |
−0.652993 | + | 0.757364i | \(0.726487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.15696 | + | 7.15696i | −0.319749 | + | 0.319749i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.9063i | 1.37805i | 0.724740 | + | 0.689023i | \(0.241960\pi\) | ||||
−0.724740 | + | 0.689023i | \(0.758040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.70674i | 0.431944i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0870 | − | 12.0870i | 0.536803 | − | 0.536803i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.41473 | − | 7.41473i | −0.328652 | − | 0.328652i | 0.523422 | − | 0.852074i | \(-0.324655\pi\) |
−0.852074 | + | 0.523422i | \(0.824655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.46513 | 0.0648136 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.3780 | 1.03216 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.2829 | + | 12.2829i | 0.541249 | + | 0.541249i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.8342 | + | 21.8342i | −0.960268 | + | 0.960268i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.57117i | 0.0689669i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.7156i | 1.73997i | 0.493075 | + | 0.869987i | \(0.335873\pi\) | ||||
−0.493075 | + | 0.869987i | \(0.664127\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.451554 | + | 0.451554i | −0.0197451 | + | 0.0197451i | −0.716910 | − | 0.697165i | \(-0.754444\pi\) |
0.697165 | + | 0.716910i | \(0.254444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.110988 | − | 0.110988i | −0.00484392 | − | 0.00484392i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.61834 | −0.0704961 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8377 | 0.949464 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.72479 | + | 4.72479i | 0.205038 | + | 0.205038i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.87492 | + | 4.87492i | −0.211156 | + | 0.211156i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.1380i | 0.740939i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.32891i | 0.0573468i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.4772 | − | 15.4772i | 0.666650 | − | 0.666650i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.4792 | + | 10.4792i | 0.450537 | + | 0.450537i | 0.895533 | − | 0.444996i | \(-0.146795\pi\) |
−0.444996 | + | 0.895533i | \(0.646795\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.2168 | −0.695930 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.8484 | −0.550363 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6370 | + | 16.6370i | 0.711347 | + | 0.711347i | 0.966817 | − | 0.255470i | \(-0.0822302\pi\) |
−0.255470 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.88880 | − | 3.88880i | 0.165970 | − | 0.165970i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.2893i | 1.58858i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.13402i | 0.0482235i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.71744 | − | 5.71744i | 0.242692 | − | 0.242692i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.2321 | + | 15.2321i | 0.645405 | + | 0.645405i | 0.951879 | − | 0.306474i | \(-0.0991492\pi\) |
−0.306474 | + | 0.951879i | \(0.599149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.9189 | 0.461821 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0998 | 0.510853 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.12478 | − | 5.12478i | −0.215984 | − | 0.215984i | 0.590820 | − | 0.806804i | \(-0.298804\pi\) |
−0.806804 | + | 0.590820i | \(0.798804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.52004 | + | 4.52004i | −0.190160 | + | 0.190160i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 0.664418i | − | 0.0279029i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.3617i | 0.602073i | 0.953613 | + | 0.301036i | \(0.0973325\pi\) | ||||
−0.953613 | + | 0.301036i | \(0.902667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7503 | − | 16.7503i | 0.700979 | − | 0.700979i | −0.263642 | − | 0.964621i | \(-0.584924\pi\) |
0.964621 | + | 0.263642i | \(0.0849237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.9985 | + | 25.9985i | 1.08610 | + | 1.08610i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.07812 | −0.0449605 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0222 | 0.791905 | 0.395952 | − | 0.918271i | \(-0.370414\pi\) | ||||
0.395952 | + | 0.918271i | \(0.370414\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.05986 | + | 4.05986i | 0.168722 | + | 0.168722i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.106557 | − | 0.106557i | 0.00442075 | − | 0.00442075i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 26.7627i | − | 1.10840i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.918236i | 0.0379644i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.13612 | − | 6.13612i | 0.253265 | − | 0.253265i | −0.569043 | − | 0.822308i | \(-0.692686\pi\) |
0.822308 | + | 0.569043i | \(0.192686\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.87299 | − | 1.87299i | −0.0771753 | − | 0.0771753i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.1901 | −1.28299 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.0963 | 1.15378 | 0.576889 | − | 0.816823i | \(-0.304267\pi\) | ||||
0.576889 | + | 0.816823i | \(0.304267\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.186185 | + | 0.186185i | 0.00763283 | + | 0.00763283i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.3830 | − | 26.3830i | 1.07978 | − | 1.07978i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 2.27156i | − | 0.0928135i | −0.998923 | − | 0.0464068i | \(-0.985223\pi\) | ||
0.998923 | − | 0.0464068i | \(-0.0147770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.4534i | − | 0.875103i | −0.899193 | − | 0.437551i | \(-0.855846\pi\) | ||
0.899193 | − | 0.437551i | \(-0.144154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.130833 | + | 0.130833i | −0.00532791 | + | 0.00532791i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.843403 | − | 0.843403i | −0.0342892 | − | 0.0342892i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.63203 | −0.269186 | −0.134593 | − | 0.990901i | \(-0.542973\pi\) | ||||
−0.134593 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.40462 | 0.0569182 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.18811 | − | 9.18811i | −0.371711 | − | 0.371711i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.1766 | + | 24.1766i | −0.976486 | + | 0.976486i | −0.999730 | − | 0.0232442i | \(-0.992600\pi\) |
0.0232442 | + | 0.999730i | \(0.492600\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 7.93942i | − | 0.320148i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.0311i | − | 0.605131i | −0.953129 | − | 0.302566i | \(-0.902157\pi\) | ||
0.953129 | − | 0.302566i | \(-0.0978431\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.08276 | + | 1.08276i | −0.0435198 | + | 0.0435198i | −0.728532 | − | 0.685012i | \(-0.759797\pi\) |
0.685012 | + | 0.728532i | \(0.259797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.27702 | − | 4.27702i | −0.171631 | − | 0.171631i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.698930 | −0.0280020 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.0037 | + | 14.0037i | 0.559254 | + | 0.559254i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.59111 | + | 9.59111i | −0.382423 | + | 0.382423i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16.1104i | − | 0.641346i | −0.947190 | − | 0.320673i | \(-0.896091\pi\) | ||
0.947190 | − | 0.320673i | \(-0.103909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.3718i | 1.00844i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.25567 | − | 2.25567i | 0.0895135 | − | 0.0895135i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.51299 | + | 6.51299i | 0.258054 | + | 0.258054i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.69234 | −0.0669481 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.5492 | 1.32511 | 0.662557 | − | 0.749012i | \(-0.269471\pi\) | ||||
0.662557 | + | 0.749012i | \(0.269471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.6497 | + | 25.6497i | 1.01153 | + | 1.01153i | 0.999933 | + | 0.0115939i | \(0.00369055\pi\) |
0.0115939 | + | 0.999933i | \(0.496309\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.89142 | + | 8.89142i | −0.350099 | + | 0.350099i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.6300i | 1.44008i | 0.693935 | + | 0.720038i | \(0.255875\pi\) | ||||
−0.693935 | + | 0.720038i | \(0.744125\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.0316i | 1.17884i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0705524 | + | 0.0705524i | −0.00276517 | + | 0.00276517i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7702 | − | 11.7702i | −0.460605 | − | 0.460605i | 0.438249 | − | 0.898854i | \(-0.355599\pi\) |
−0.898854 | + | 0.438249i | \(0.855599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.96008 | 0.311026 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.87065 | 0.385091 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.496974 | + | 0.496974i | 0.0193593 | + | 0.0193593i | 0.716720 | − | 0.697361i | \(-0.245642\pi\) |
−0.697361 | + | 0.716720i | \(0.745642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.919644 | + | 0.919644i | −0.0357700 | + | 0.0357700i | −0.724766 | − | 0.688996i | \(-0.758052\pi\) |
0.688996 | + | 0.724766i | \(0.258052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.09173i | 0.197746i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.430963i | 0.0167120i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.82211 | − | 6.82211i | 0.264153 | − | 0.264153i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.7985 | + | 21.7985i | 0.842778 | + | 0.842778i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.7179 | 0.954224 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6303 | −0.756693 | −0.378346 | − | 0.925664i | \(-0.623507\pi\) | ||||
−0.378346 | + | 0.925664i | \(0.623507\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.96713 | − | 3.96713i | −0.152695 | − | 0.152695i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.644131 | + | 0.644131i | −0.0247560 | + | 0.0247560i | −0.719376 | − | 0.694620i | \(-0.755572\pi\) |
0.694620 | + | 0.719376i | \(0.255572\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.85890i | 0.0713379i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 40.9574i | − | 1.56949i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.6404 | − | 29.6404i | 1.13416 | − | 1.13416i | 0.144682 | − | 0.989478i | \(-0.453784\pi\) |
0.989478 | − | 0.144682i | \(-0.0462159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.196152 | + | 0.196152i | 0.00749460 | + | 0.00749460i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.71139 | −0.103446 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.2621 | 0.429050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0761 | + | 25.0761i | 0.953941 | + | 0.953941i | 0.998985 | − | 0.0450436i | \(-0.0143427\pi\) |
−0.0450436 | + | 0.998985i | \(0.514343\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.159579 | + | 0.159579i | −0.00606189 | + | 0.00606189i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.1949i | − | 0.652240i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.3185i | 0.504475i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.4381 | − | 24.4381i | 0.924332 | − | 0.924332i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.5904 | + | 15.5904i | 0.588841 | + | 0.588841i | 0.937317 | − | 0.348477i | \(-0.113301\pi\) |
−0.348477 | + | 0.937317i | \(0.613301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.2006 | −0.837311 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.9640 | 0.563577 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.709875 | − | 0.709875i | −0.0266976 | − | 0.0266976i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.59111 | + | 8.59111i | −0.322646 | + | 0.322646i | −0.849781 | − | 0.527135i | \(-0.823266\pi\) |
0.527135 | + | 0.849781i | \(0.323266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.63994i | 0.286520i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.685331i | 0.0256658i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.91824 | + | 2.91824i | −0.109136 | + | 0.109136i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.6225 | + | 23.6225i | 0.882197 | + | 0.882197i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.1112 | −1.01108 | −0.505538 | − | 0.862804i | \(-0.668706\pi\) | ||||
−0.505538 | + | 0.862804i | \(0.668706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.79655 | −0.0669070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.9961 | − | 20.9961i | −0.780855 | − | 0.780855i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.32780 | − | 6.32780i | 0.235009 | − | 0.235009i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 40.9979i | − | 1.52053i | −0.649614 | − | 0.760264i | \(-0.725069\pi\) | ||
0.649614 | − | 0.760264i | \(-0.274931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 30.0197i | − | 1.11184i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9155 | − | 14.9155i | 0.551670 | − | 0.551670i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.49473 | + | 7.49473i | 0.276824 | + | 0.276824i | 0.831840 | − | 0.555016i | \(-0.187288\pi\) |
−0.555016 | + | 0.831840i | \(0.687288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.6072 | −0.391254 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.831595 | −0.0306322 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.3947 | + | 24.3947i | 0.897374 | + | 0.897374i | 0.995203 | − | 0.0978293i | \(-0.0311899\pi\) |
−0.0978293 | + | 0.995203i | \(0.531190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.89293 | + | 5.89293i | −0.216482 | + | 0.216482i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.5703i | − | 0.497848i | −0.968523 | − | 0.248924i | \(-0.919923\pi\) | ||
0.968523 | − | 0.248924i | \(-0.0800769\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.22678i | 0.301406i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.717882 | − | 0.717882i | 0.0262659 | − | 0.0262659i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.25334 | − | 1.25334i | −0.0457959 | − | 0.0457959i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.3407 | −0.815225 | −0.407612 | − | 0.913155i | \(-0.633639\pi\) | ||||
−0.407612 | + | 0.913155i | \(0.633639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.41740 | −0.306747 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.25674 | + | 4.25674i | 0.154919 | + | 0.154919i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.33046 | + | 4.33046i | −0.157393 | + | 0.157393i | −0.781410 | − | 0.624017i | \(-0.785499\pi\) |
0.624017 | + | 0.781410i | \(0.285499\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5.12398i | − | 0.185989i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6770i | 0.604541i | 0.953222 | + | 0.302270i | \(0.0977446\pi\) | ||||
−0.953222 | + | 0.302270i | \(0.902255\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.939629 | − | 0.939629i | 0.0340168 | − | 0.0340168i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.25433 | + | 1.25433i | 0.0453505 | + | 0.0453505i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.6377 | −0.456320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.38199 | −0.230140 | −0.115070 | − | 0.993357i | \(-0.536709\pi\) | ||||
−0.115070 | + | 0.993357i | \(0.536709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.4600 | − | 15.4600i | −0.556777 | − | 0.556777i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7136 | − | 32.7136i | 1.17663 | − | 1.17663i | 0.196027 | − | 0.980598i | \(-0.437196\pi\) |
0.980598 | − | 0.196027i | \(-0.0628041\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.635674i | 0.0228341i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.836258i | 0.0300006i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.4142 | + | 15.4142i | −0.552272 | + | 0.552272i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.37842 | − | 5.37842i | −0.192455 | − | 0.192455i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 50.2064 | 1.79423 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9895 | 0.463614 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.23233 | − | 1.23233i | −0.0439279 | − | 0.0439279i | 0.684802 | − | 0.728730i | \(-0.259889\pi\) |
−0.728730 | + | 0.684802i | \(0.759889\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.1803 | − | 17.1803i | 0.611635 | − | 0.611635i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.661121i | − | 0.0235068i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.4016i | 0.369371i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.17084 | + | 9.17084i | −0.325256 | + | 0.325256i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.62007 | − | 2.62007i | −0.0928075 | − | 0.0928075i | 0.659179 | − | 0.751986i | \(-0.270904\pi\) |
−0.751986 | + | 0.659179i | \(0.770904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.1024 | −0.888058 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.70872 | −0.166374 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.3698 | + | 31.3698i | 1.10702 | + | 1.10702i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0788450 | − | 0.0788450i | 0.00277892 | − | 0.00277892i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.82060i | 0.169693i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.63795i | − | 0.127904i | −0.997953 | − | 0.0639518i | \(-0.979630\pi\) | ||
0.997953 | − | 0.0639518i | \(-0.0203704\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.1436 | + | 25.1436i | −0.882913 | + | 0.882913i | −0.993830 | − | 0.110917i | \(-0.964621\pi\) |
0.110917 | + | 0.993830i | \(0.464621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.18937 | − | 3.18937i | −0.111856 | − | 0.111856i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.88072 | 0.135936 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.5250 | 1.20788 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0671526 | − | 0.0671526i | −0.00234650 | − | 0.00234650i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.04790 | − | 8.04790i | 0.280874 | − | 0.280874i | −0.552584 | − | 0.833457i | \(-0.686358\pi\) |
0.833457 | + | 0.552584i | \(0.186358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.1452i | 1.57366i | 0.617168 | + | 0.786832i | \(0.288280\pi\) | ||||
−0.617168 | + | 0.786832i | \(0.711720\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.75272i | − | 0.165468i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.20254 | + | 8.20254i | −0.285230 | + | 0.285230i | −0.835191 | − | 0.549960i | \(-0.814643\pi\) |
0.549960 | + | 0.835191i | \(0.314643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.74467 | + | 5.74467i | 0.199521 | + | 0.199521i | 0.799795 | − | 0.600274i | \(-0.204942\pi\) |
−0.600274 | + | 0.799795i | \(0.704942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.1749 | −1.49772 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.7938 | 0.616520 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.71585 | − | 4.71585i | −0.163199 | − | 0.163199i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.52180 | + | 2.52180i | −0.0871662 | + | 0.0871662i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.7201i | 1.02605i | 0.858373 | + | 0.513026i | \(0.171476\pi\) | ||||
−0.858373 | + | 0.513026i | \(0.828524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.0822i | 1.76146i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.9457 | − | 19.9457i | 0.686968 | − | 0.686968i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.96436 | + | 7.96436i | 0.273982 | + | 0.273982i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.123360 | 0.00423870 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.5348 | −1.52843 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.06162 | + | 4.06162i | 0.139230 | + | 0.139230i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.09538 | − | 5.09538i | 0.174463 | − | 0.174463i | −0.614474 | − | 0.788937i | \(-0.710632\pi\) |
0.788937 | + | 0.614474i | \(0.210632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.90341i | 0.0992945i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 0.735948i | − | 0.0251395i | −0.999921 | − | 0.0125698i | \(-0.995999\pi\) | ||
0.999921 | − | 0.0125698i | \(-0.00400118\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.39668 | − | 9.39668i | 0.320611 | − | 0.320611i | −0.528391 | − | 0.849001i | \(-0.677204\pi\) |
0.849001 | + | 0.528391i | \(0.177204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.580627 | + | 0.580627i | 0.0197877 | + | 0.0197877i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.0950 | −1.60313 | −0.801565 | − | 0.597907i | \(-0.795999\pi\) | ||||
−0.801565 | + | 0.597907i | \(0.795999\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.03528 | −0.0352004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.2878 | − | 11.2878i | −0.383354 | − | 0.383354i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.2804 | + | 24.2804i | −0.823657 | + | 0.823657i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.349945i | − | 0.0118574i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.5234i | 0.423854i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.0731322 | − | 0.0731322i | 0.00247232 | − | 0.00247232i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7479 | − | 38.7479i | −1.30842 | − | 1.30842i | −0.922554 | − | 0.385868i | \(-0.873902\pi\) |
−0.385868 | − | 0.922554i | \(-0.626098\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.1452 | 0.477104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.67684 | −0.0564942 | −0.0282471 | − | 0.999601i | \(-0.508993\pi\) | ||||
−0.0282471 | + | 0.999601i | \(0.508993\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.4734 | − | 31.4734i | −1.05916 | − | 1.05916i | −0.998136 | − | 0.0610287i | \(-0.980562\pi\) |
−0.0610287 | − | 0.998136i | \(-0.519438\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2910 | − | 10.2910i | 0.345929 | − | 0.345929i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29.4396i | − | 0.988484i | −0.869324 | − | 0.494242i | \(-0.835446\pi\) | ||
0.869324 | − | 0.494242i | \(-0.164554\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.329924i | 0.0110653i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.2258 | − | 14.2258i | 0.476582 | − | 0.476582i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.0523 | − | 29.0523i | −0.972198 | − | 0.972198i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.875644 | −0.0292696 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.15623 | 0.0719945 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.02242 | − | 4.02242i | −0.134155 | − | 0.134155i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3843 | − | 15.3843i | 0.512524 | − | 0.512524i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.30050i | − | 0.0432778i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 10.6856i | − | 0.355200i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.4520 | + | 35.4520i | −1.17716 | + | 1.17716i | −0.196702 | + | 0.980463i | \(0.563023\pi\) |
−0.980463 | + | 0.196702i | \(0.936977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.78245 | − | 4.78245i | −0.158624 | − | 0.158624i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.9590 | 1.45643 | 0.728213 | − | 0.685351i | \(-0.240351\pi\) | ||||
0.728213 | + | 0.685351i | \(0.240351\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.56298 | 0.151013 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.47015 | − | 8.47015i | −0.280015 | − | 0.280015i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.582138 | + | 0.582138i | −0.0192239 | + | 0.0192239i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.6638i | 1.53930i | 0.638469 | + | 0.769648i | \(0.279568\pi\) | ||||
−0.638469 | + | 0.769648i | \(0.720432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1.06110i | − | 0.0349644i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.26330 | − | 2.26330i | 0.0744976 | − | 0.0744976i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.76733 | + | 3.76733i | 0.123869 | + | 0.123869i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.1034 | −0.397529 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.3630 | −1.45550 | −0.727752 | − | 0.685840i | \(-0.759435\pi\) | ||||
−0.727752 | + | 0.685840i | \(0.759435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.5937 | + | 20.5937i | 0.674932 | + | 0.674932i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.9898 | + | 10.9898i | −0.359791 | + | 0.359791i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.97277i | 0.260737i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.00338i | − | 0.0327790i | −0.999866 | − | 0.0163895i | \(-0.994783\pi\) | ||
0.999866 | − | 0.0163895i | \(-0.00521718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7376 | + | 10.7376i | −0.350408 | + | 0.350408i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0597 | + | 10.0597i | 0.327937 | + | 0.327937i | 0.851801 | − | 0.523865i | \(-0.175510\pi\) |
−0.523865 | + | 0.851801i | \(0.675510\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.64009 | 0.183667 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.580249 | 0.0188755 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3749 | − | 18.3749i | −0.597103 | − | 0.597103i | 0.342438 | − | 0.939541i | \(-0.388747\pi\) |
−0.939541 | + | 0.342438i | \(0.888747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.2008 | + | 13.2008i | −0.428516 | + | 0.428516i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 41.5175i | − | 1.34630i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.2842i | − | 0.527497i | −0.964591 | − | 0.263749i | \(-0.915041\pi\) | ||
0.964591 | − | 0.263749i | \(-0.0849589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.1309 | + | 17.1309i | −0.554344 | + | 0.554344i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.0743 | + | 30.0743i | 0.972163 | + | 0.972163i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0286901 | −0.000926452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5959 | −0.986965 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.44378 | − | 8.44378i | −0.272097 | − | 0.272097i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.67511 | + | 2.67511i | −0.0861150 | + | 0.0861150i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 29.5190i | − | 0.949269i | −0.880183 | − | 0.474634i | \(-0.842580\pi\) | ||
0.880183 | − | 0.474634i | \(-0.157420\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.0998i | 0.517199i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0000 | + | 12.0000i | −0.385099 | + | 0.385099i | −0.872935 | − | 0.487836i | \(-0.837786\pi\) |
0.487836 | + | 0.872935i | \(0.337786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.25750 | + | 1.25750i | 0.0403136 | + | 0.0403136i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | 0.0640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.0884 | 1.53848 | 0.769241 | − | 0.638958i | \(-0.220634\pi\) | ||||
0.769241 | + | 0.638958i | \(0.220634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.9647 | − | 14.9647i | −0.478275 | − | 0.478275i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.33031 | − | 6.33031i | 0.202111 | − | 0.202111i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 37.1975i | − | 1.18642i | −0.805050 | − | 0.593208i | \(-0.797861\pi\) | ||
0.805050 | − | 0.593208i | \(-0.202139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 20.5517i | − | 0.654832i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.09435 | + | 1.09435i | −0.0348335 | + | 0.0348335i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.31638 | − | 6.31638i | −0.200849 | − | 0.200849i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.2588 | 1.34240 | 0.671198 | − | 0.741278i | \(-0.265780\pi\) | ||||
0.671198 | + | 0.741278i | \(0.265780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −47.7954 | −1.51674 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.3843 | + | 17.3843i | 0.551118 | + | 0.551118i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.6128 | − | 40.6128i | 1.28622 | − | 1.28622i | 0.349154 | − | 0.937065i | \(-0.386469\pi\) |
0.937065 | − | 0.349154i | \(-0.113531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.8909i | 0.945707i |
(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 | 1280.2.l.a.321.4 | ✓ | 8 | |
4.3 | odd | 2 | 1280.2.l.f.321.1 | yes | 8 | ||
8.3 | odd | 2 | 1280.2.l.d.321.4 | yes | 8 | ||
8.5 | even | 2 | 1280.2.l.g.321.1 | yes | 8 | ||
16.3 | odd | 4 | 1280.2.l.d.961.4 | yes | 8 | ||
16.5 | even | 4 | inner | 1280.2.l.a.961.4 | yes | 8 | |
16.11 | odd | 4 | 1280.2.l.f.961.1 | yes | 8 | ||
16.13 | even | 4 | 1280.2.l.g.961.1 | yes | 8 | ||
32.5 | even | 8 | 5120.2.a.a.1.2 | 4 | |||
32.11 | odd | 8 | 5120.2.a.b.1.2 | 4 | |||
32.21 | even | 8 | 5120.2.a.r.1.3 | 4 | |||
32.27 | odd | 8 | 5120.2.a.q.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1280.2.l.a.321.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1280.2.l.a.961.4 | yes | 8 | 16.5 | even | 4 | inner | |
1280.2.l.d.321.4 | yes | 8 | 8.3 | odd | 2 | ||
1280.2.l.d.961.4 | yes | 8 | 16.3 | odd | 4 | ||
1280.2.l.f.321.1 | yes | 8 | 4.3 | odd | 2 | ||
1280.2.l.f.961.1 | yes | 8 | 16.11 | odd | 4 | ||
1280.2.l.g.321.1 | yes | 8 | 8.5 | even | 2 | ||
1280.2.l.g.961.1 | yes | 8 | 16.13 | even | 4 | ||
5120.2.a.a.1.2 | 4 | 32.5 | even | 8 | |||
5120.2.a.b.1.2 | 4 | 32.11 | odd | 8 | |||
5120.2.a.q.1.3 | 4 | 32.27 | odd | 8 | |||
5120.2.a.r.1.3 | 4 | 32.21 | even | 8 |