Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2016,2,Mod(17,2016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2016, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2016.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2016.cp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.0978410475\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.21 | ||
Character | \(\chi\) | \(=\) | 2016.17 |
Dual form | 2016.2.cp.b.593.21 |
$q$-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 \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1765\) | \(1793\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.53798 | − | 0.887954i | 0.687806 | − | 0.397105i | −0.114983 | − | 0.993367i | \(-0.536681\pi\) |
0.802790 | + | 0.596262i | \(0.203348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.843933 | + | 2.50754i | −0.318977 | + | 0.947763i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.09284 | + | 3.62490i | −0.631015 | + | 1.09295i | 0.356330 | + | 0.934360i | \(0.384028\pi\) |
−0.987345 | + | 0.158589i | \(0.949305\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.76443 | −1.04406 | −0.522032 | − | 0.852926i | \(-0.674826\pi\) | ||||
−0.522032 | + | 0.852926i | \(0.674826\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.32502 | − | 4.02705i | 0.563899 | − | 0.976702i | −0.433252 | − | 0.901273i | \(-0.642634\pi\) |
0.997151 | − | 0.0754291i | \(-0.0240327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0315203 | − | 0.0545948i | −0.00723126 | − | 0.0125249i | 0.862387 | − | 0.506249i | \(-0.168968\pi\) |
−0.869618 | + | 0.493724i | \(0.835635\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.05375 | + | 2.34043i | −0.845265 | + | 0.488014i | −0.859050 | − | 0.511891i | \(-0.828945\pi\) |
0.0137854 | + | 0.999905i | \(0.495612\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.923074 | + | 1.59881i | −0.184615 | + | 0.319762i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.47316 | −1.20204 | −0.601018 | − | 0.799235i | \(-0.705238\pi\) | ||||
−0.601018 | + | 0.799235i | \(0.705238\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.64896 | − | 3.83878i | −1.19419 | − | 0.689465i | −0.234935 | − | 0.972011i | \(-0.575488\pi\) |
−0.959254 | + | 0.282546i | \(0.908821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.928631 | + | 4.60593i | 0.156967 | + | 0.778544i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.91602 | + | 1.68357i | −0.479391 | + | 0.276777i | −0.720163 | − | 0.693805i | \(-0.755933\pi\) |
0.240772 | + | 0.970582i | \(0.422600\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.06290 | 1.25921 | 0.629606 | − | 0.776914i | \(-0.283216\pi\) | ||||
0.629606 | + | 0.776914i | \(0.283216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.94628i | − | 1.51679i | −0.651793 | − | 0.758397i | \(-0.725983\pi\) | ||
0.651793 | − | 0.758397i | \(-0.274017\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.338788 | − | 0.586799i | −0.0494174 | − | 0.0855934i | 0.840259 | − | 0.542186i | \(-0.182403\pi\) |
−0.889676 | + | 0.456592i | \(0.849070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.57556 | − | 4.23240i | −0.796508 | − | 0.604628i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.36197 | + | 4.09104i | −0.324441 | + | 0.561948i | −0.981399 | − | 0.191979i | \(-0.938509\pi\) |
0.656958 | + | 0.753927i | \(0.271843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.43338i | 1.00232i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.53211 | − | 3.77132i | −0.850408 | − | 0.490983i | 0.0103803 | − | 0.999946i | \(-0.496696\pi\) |
−0.860789 | + | 0.508963i | \(0.830029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.23104 | − | 12.5245i | −0.925840 | − | 1.60360i | −0.790204 | − | 0.612844i | \(-0.790025\pi\) |
−0.135636 | − | 0.990759i | \(-0.543308\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.78962 | + | 3.34264i | −0.718115 | + | 0.414604i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.67866 | − | 3.27857i | −0.693758 | − | 0.400542i | 0.111260 | − | 0.993791i | \(-0.464511\pi\) |
−0.805018 | + | 0.593250i | \(0.797845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.10606i | 0.605978i | 0.952994 | + | 0.302989i | \(0.0979846\pi\) | ||||
−0.952994 | + | 0.302989i | \(0.902015\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.29332 | + | 0.746696i | 0.151371 | + | 0.0873942i | 0.573772 | − | 0.819015i | \(-0.305479\pi\) |
−0.422401 | + | 0.906409i | \(0.638813\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.32339 | − | 8.30706i | −0.834578 | − | 0.946677i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.99485 | + | 10.3834i | 0.674473 | + | 1.16822i | 0.976623 | + | 0.214961i | \(0.0689624\pi\) |
−0.302150 | + | 0.953260i | \(0.597704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.64992i | 0.839688i | 0.907596 | + | 0.419844i | \(0.137915\pi\) | ||||
−0.907596 | + | 0.419844i | \(0.862085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 8.25803i | − | 0.895709i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.97506 | + | 15.5453i | 0.951354 | + | 1.64779i | 0.742499 | + | 0.669847i | \(0.233640\pi\) |
0.208855 | + | 0.977947i | \(0.433026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.17692 | − | 9.43947i | 0.333032 | − | 0.989526i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0969554 | − | 0.0559773i | −0.00994742 | − | 0.00574315i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.24586i | 0.431102i | 0.976493 | + | 0.215551i | \(0.0691547\pi\) | ||||
−0.976493 | + | 0.215551i | \(0.930845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.63654 | + | 2.09956i | 0.361849 | + | 0.208914i | 0.669892 | − | 0.742459i | \(-0.266341\pi\) |
−0.308042 | + | 0.951373i | \(0.599674\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3144 | − | 6.53235i | 1.11484 | − | 0.643652i | 0.174759 | − | 0.984611i | \(-0.444085\pi\) |
0.940078 | + | 0.340959i | \(0.110752\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.25101 | + | 9.09502i | 0.507635 | + | 0.879249i | 0.999961 | + | 0.00883827i | \(0.00281335\pi\) |
−0.492326 | + | 0.870411i | \(0.663853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19797 | − | 1.26900i | −0.210528 | − | 0.121548i | 0.391029 | − | 0.920378i | \(-0.372119\pi\) |
−0.601557 | + | 0.798830i | \(0.705453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.56501i | 0.429440i | 0.976676 | + | 0.214720i | \(0.0688838\pi\) | ||||
−0.976676 | + | 0.214720i | \(0.931116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.15639 | + | 7.19909i | −0.387586 | + | 0.671318i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.13584 | + | 9.22863i | 0.745811 | + | 0.845988i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.25995 | − | 5.64639i | −0.296359 | − | 0.513308i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1581i | 1.08746i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.36161 | −0.741973 | −0.370986 | − | 0.928638i | \(-0.620980\pi\) | ||||
−0.370986 | + | 0.928638i | \(0.620980\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.45901 | + | 3.15176i | −0.476956 | + | 0.275371i | −0.719147 | − | 0.694858i | \(-0.755467\pi\) |
0.242191 | + | 0.970229i | \(0.422134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.163500 | − | 0.0329643i | 0.0141772 | − | 0.00285837i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3468 | − | 6.55109i | −0.969425 | − | 0.559698i | −0.0703639 | − | 0.997521i | \(-0.522416\pi\) |
−0.899061 | + | 0.437824i | \(0.855749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.1125 | −1.62110 | −0.810549 | − | 0.585671i | \(-0.800831\pi\) | ||||
−0.810549 | + | 0.585671i | \(0.800831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.87834 | − | 13.6457i | 0.658820 | − | 1.14111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.95561 | + | 5.74787i | −0.826768 | + | 0.477335i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.19406 | + | 3.80023i | 0.179745 | + | 0.311327i | 0.941793 | − | 0.336193i | \(-0.109140\pi\) |
−0.762048 | + | 0.647520i | \(0.775806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.37428 | + | 2.38033i | −0.111838 | + | 0.193708i | −0.916511 | − | 0.400009i | \(-0.869007\pi\) |
0.804674 | + | 0.593717i | \(0.202340\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.6346 | −1.09516 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.669124 | + | 1.15896i | −0.0534019 | + | 0.0924948i | −0.891491 | − | 0.453039i | \(-0.850340\pi\) |
0.838089 | + | 0.545534i | \(0.183673\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.44765 | − | 12.1401i | −0.192902 | − | 0.956776i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.30942 | + | 1.91070i | −0.259214 | + | 0.149657i | −0.623976 | − | 0.781444i | \(-0.714484\pi\) |
0.364762 | + | 0.931101i | \(0.381150\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.25804 | −0.561644 | −0.280822 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280822 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.17093 | 0.0900713 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.07114 | + | 0.618425i | −0.0814375 | + | 0.0470180i | −0.540166 | − | 0.841559i | \(-0.681638\pi\) |
0.458728 | + | 0.888577i | \(0.348305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.23008 | − | 3.66394i | −0.244171 | − | 0.276968i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.80192 | − | 15.2454i | 0.657886 | − | 1.13949i | −0.323275 | − | 0.946305i | \(-0.604784\pi\) |
0.981162 | − | 0.193188i | \(-0.0618826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4773 | −1.22475 | −0.612376 | − | 0.790567i | \(-0.709786\pi\) | ||||
−0.612376 | + | 0.790567i | \(0.709786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.98986 | + | 5.17859i | −0.219819 | + | 0.380737i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.73176 | + | 16.8559i | 0.711657 | + | 1.23263i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2159 | − | 8.20758i | 1.02863 | − | 0.593880i | 0.112038 | − | 0.993704i | \(-0.464262\pi\) |
0.916592 | + | 0.399824i | \(0.130929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7627 | + | 20.3736i | −0.846696 | + | 1.46652i | 0.0374435 | + | 0.999299i | \(0.488079\pi\) |
−0.884140 | + | 0.467222i | \(0.845255\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.792724 | 0.0564792 | 0.0282396 | − | 0.999601i | \(-0.491010\pi\) | ||||
0.0282396 | + | 0.999601i | \(0.491010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9922 | − | 6.34632i | −0.779213 | − | 0.449879i | 0.0569382 | − | 0.998378i | \(-0.481866\pi\) |
−0.836151 | + | 0.548499i | \(0.815200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.46292 | − | 16.2317i | 0.383421 | − | 1.13925i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.4006 | − | 7.15948i | 0.866095 | − | 0.500040i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.263868 | 0.0182521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.9821i | − | 1.30678i | −0.757020 | − | 0.653392i | \(-0.773345\pi\) | ||
0.757020 | − | 0.653392i | \(-0.226655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.83184 | − | 15.2972i | −0.602326 | − | 1.04326i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.2372 | − | 13.4329i | 1.03437 | − | 0.911884i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.75236 | + | 15.1595i | −0.588747 | + | 1.01974i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.56676i | − | 0.573673i | −0.957980 | − | 0.286836i | \(-0.907396\pi\) | ||
0.957980 | − | 0.286836i | \(-0.0926036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.3870 | − | 7.15164i | −0.822155 | − | 0.474671i | 0.0290044 | − | 0.999579i | \(-0.490766\pi\) |
−0.851159 | + | 0.524908i | \(0.824100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0246 | + | 24.2914i | 0.926774 | + | 1.60522i | 0.788683 | + | 0.614800i | \(0.210763\pi\) |
0.138091 | + | 0.990420i | \(0.455903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.52792 | − | 4.34625i | 0.493170 | − | 0.284732i | −0.232718 | − | 0.972544i | \(-0.574762\pi\) |
0.725889 | + | 0.687812i | \(0.241429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.04210 | − | 0.601657i | −0.0679792 | − | 0.0392478i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.4878i | 0.807772i | 0.914809 | + | 0.403886i | \(0.132341\pi\) | ||||
−0.914809 | + | 0.403886i | \(0.867659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0923 | + | 11.6003i | 1.29426 | + | 0.747240i | 0.979406 | − | 0.201900i | \(-0.0647117\pi\) |
0.314852 | + | 0.949141i | \(0.398045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.3333 | − | 1.55851i | −0.787944 | − | 0.0995697i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.118656 | + | 0.205518i | 0.00754991 | + | 0.0130768i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.9698i | 0.881768i | 0.897564 | + | 0.440884i | \(0.145335\pi\) | ||||
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.5926i | − | 1.23178i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8457 | − | 20.5174i | −0.738915 | − | 1.27984i | −0.952984 | − | 0.303020i | \(-0.902005\pi\) |
0.214069 | − | 0.976819i | \(-0.431328\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.76069 | − | 8.73287i | −0.109404 | − | 0.542634i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5097 | + | 7.79983i | 0.833044 | + | 0.480958i | 0.854894 | − | 0.518803i | \(-0.173622\pi\) |
−0.0218497 | + | 0.999761i | \(0.506956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.38927i | 0.515349i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.5546 | + | 15.9086i | 1.68003 | + | 0.969966i | 0.961635 | + | 0.274332i | \(0.0884566\pi\) |
0.718396 | + | 0.695635i | \(0.244877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.16789 | + | 4.71573i | −0.496164 | + | 0.286460i | −0.727128 | − | 0.686502i | \(-0.759145\pi\) |
0.230964 | + | 0.972962i | \(0.425812\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.86369 | − | 6.69211i | −0.232989 | − | 0.403549i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.1275 | + | 13.3527i | 1.38960 | + | 0.802284i | 0.993270 | − | 0.115825i | \(-0.0369513\pi\) |
0.396327 | + | 0.918109i | \(0.370285\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1930i | 1.56254i | 0.624193 | + | 0.781271i | \(0.285428\pi\) | ||||
−0.624193 | + | 0.781271i | \(0.714572\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.62071 | + | 4.53920i | −0.155785 | + | 0.269827i | −0.933345 | − | 0.358982i | \(-0.883124\pi\) |
0.777560 | + | 0.628809i | \(0.216457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.80454 | + | 20.2181i | −0.401659 | + | 1.19343i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.31140 | − | 4.00346i | −0.135964 | − | 0.235497i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.29435i | − | 0.484561i | −0.970206 | − | 0.242280i | \(-0.922105\pi\) | ||
0.970206 | − | 0.242280i | \(-0.0778954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3950 | −0.779888 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.2600 | − | 8.81039i | 0.882511 | − | 0.509518i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.9407 | + | 8.39399i | 1.43756 | + | 0.483821i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.2424 | − | 12.8417i | −1.27360 | − | 0.735312i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8873 | 1.02088 | 0.510442 | − | 0.859912i | \(-0.329482\pi\) | ||||
0.510442 | + | 0.859912i | \(0.329482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.257495 | + | 0.445994i | −0.0146012 | + | 0.0252900i | −0.873234 | − | 0.487302i | \(-0.837981\pi\) |
0.858632 | + | 0.512592i | \(0.171315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1970 | − | 11.6607i | 1.14160 | − | 0.659104i | 0.194775 | − | 0.980848i | \(-0.437602\pi\) |
0.946827 | + | 0.321744i | \(0.104269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.4926 | − | 18.1736i | −0.589321 | − | 1.02073i | −0.994322 | − | 0.106417i | \(-0.966062\pi\) |
0.405001 | − | 0.914316i | \(-0.367271\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5473 | − | 23.4646i | 0.758503 | − | 1.31376i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.293141 | −0.0163108 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.47485 | − | 6.01861i | 0.192750 | − | 0.333853i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.75734 | − | 0.354308i | 0.0968852 | − | 0.0195336i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.16441 | + | 4.71372i | −0.448756 | + | 0.259090i | −0.707305 | − | 0.706909i | \(-0.750089\pi\) |
0.258548 | + | 0.965998i | \(0.416756\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.6449 | −0.636229 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8141 | −0.806977 | −0.403488 | − | 0.914985i | \(-0.632202\pi\) | ||||
−0.403488 | + | 0.914985i | \(0.632202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.8304 | − | 16.0679i | 1.50710 | − | 0.870125i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.3183 | − | 10.4091i | 0.827111 | − | 0.562038i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9642 | − | 18.9905i | 0.588587 | − | 1.01946i | −0.405830 | − | 0.913948i | \(-0.633018\pi\) |
0.994418 | − | 0.105515i | \(-0.0336491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.9301 | −1.86977 | −0.934884 | − | 0.354954i | \(-0.884497\pi\) | ||||
−0.934884 | + | 0.354954i | \(0.884497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.71324 | + | 6.43152i | −0.197636 | + | 0.342315i | −0.947761 | − | 0.318980i | \(-0.896660\pi\) |
0.750126 | + | 0.661295i | \(0.229993\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.53395 | + | 7.85303i | 0.240637 | + | 0.416796i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.73364 | − | 3.88767i | 0.355388 | − | 0.205183i | −0.311668 | − | 0.950191i | \(-0.600888\pi\) |
0.667056 | + | 0.745008i | \(0.267554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49801 | − | 16.4510i | 0.499895 | − | 0.865844i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.65213 | 0.138819 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.99509 | + | 4.03862i | 0.365141 | + | 0.210814i | 0.671333 | − | 0.741155i | \(-0.265722\pi\) |
−0.306193 | + | 0.951970i | \(0.599055\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.26513 | − | 9.37530i | −0.429104 | − | 0.486741i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.1708 | + | 13.9550i | −1.25152 | + | 0.722563i | −0.971410 | − | 0.237407i | \(-0.923703\pi\) |
−0.280105 | + | 0.959969i | \(0.590369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.3678 | 1.25500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0460i | 1.49199i | 0.665949 | + | 0.745997i | \(0.268027\pi\) | ||||
−0.665949 | + | 0.745997i | \(0.731973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.63040 | − | 9.75214i | −0.287700 | − | 0.498311i | 0.685560 | − | 0.728016i | \(-0.259557\pi\) |
−0.973260 | + | 0.229705i | \(0.926224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.6395 | − | 6.27327i | −0.949958 | − | 0.319716i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.51811 | − | 4.36149i | 0.127673 | − | 0.221136i | −0.795102 | − | 0.606476i | \(-0.792583\pi\) |
0.922775 | + | 0.385340i | \(0.125916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.7662i | 1.10076i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.4399 | + | 10.6463i | 0.927814 | + | 0.535674i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.8771 | + | 24.0358i | 0.696471 | + | 1.20632i | 0.969682 | + | 0.244369i | \(0.0785808\pi\) |
−0.273211 | + | 0.961954i | \(0.588086\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.70394 | + | 2.13847i | −0.184966 | + | 0.106790i | −0.589624 | − | 0.807678i | \(-0.700724\pi\) |
0.404658 | + | 0.914468i | \(0.367391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.0295 | + | 14.4508i | 1.24681 | + | 0.719846i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.0937i | − | 0.698600i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6093 | + | 7.85734i | 0.672937 | + | 0.388521i | 0.797189 | − | 0.603730i | \(-0.206320\pi\) |
−0.124251 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.9694 | − | 13.1968i | 0.736596 | − | 0.649373i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.79278 | + | 11.7654i | 0.333444 | + | 0.577543i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.0838i | 1.86052i | 0.366904 | + | 0.930259i | \(0.380418\pi\) | ||||
−0.366904 | + | 0.930259i | \(0.619582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.7506i | − | 0.767635i | −0.923409 | − | 0.383818i | \(-0.874609\pi\) | ||
0.923409 | − | 0.383818i | \(-0.125391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.29232 | + | 7.43452i | 0.208208 | + | 0.360627i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.5083 | − | 7.56230i | 1.81516 | − | 0.365965i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.36898 | − | 3.67713i | −0.306783 | − | 0.177121i | 0.338703 | − | 0.940893i | \(-0.390012\pi\) |
−0.645486 | + | 0.763772i | \(0.723345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.06468i | − | 0.387564i | −0.981045 | − | 0.193782i | \(-0.937925\pi\) | ||
0.981045 | − | 0.193782i | \(-0.0620754\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.255551 | + | 0.147542i | 0.0122247 | + | 0.00705791i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.02415 | − | 2.90069i | 0.239790 | − | 0.138443i | −0.375290 | − | 0.926907i | \(-0.622457\pi\) |
0.615080 | + | 0.788465i | \(0.289124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.82446 | + | 13.5524i | 0.371751 | + | 0.643892i | 0.989835 | − | 0.142220i | \(-0.0454241\pi\) |
−0.618084 | + | 0.786112i | \(0.712091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.6069 | + | 15.9389i | 1.30869 | + | 0.755575i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 34.7839i | − | 1.64155i | −0.571250 | − | 0.820776i | \(-0.693541\pi\) | ||
0.571250 | − | 0.820776i | \(-0.306459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.8743 | + | 29.2272i | −0.794582 | + | 1.37626i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.49577 | − | 17.3387i | −0.163884 | − | 0.812851i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.38911 | − | 9.33422i | −0.252092 | − | 0.436636i | 0.712010 | − | 0.702170i | \(-0.247785\pi\) |
−0.964102 | + | 0.265533i | \(0.914452\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.5062i | − | 0.908494i | −0.890876 | − | 0.454247i | \(-0.849908\pi\) | ||
0.890876 | − | 0.454247i | \(-0.150092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.2099 | 1.26455 | 0.632275 | − | 0.774744i | \(-0.282121\pi\) | ||||
0.632275 | + | 0.774744i | \(0.282121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.3243 | − | 16.9304i | 1.35697 | − | 0.783445i | 0.367752 | − | 0.929924i | \(-0.380128\pi\) |
0.989214 | + | 0.146479i | \(0.0467942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.0136 | − | 11.4726i | 0.600911 | − | 0.529755i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.0543 | + | 20.8160i | 1.65778 | + | 0.957118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.116382 | 0.00533999 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.640883 | + | 1.11004i | −0.0292827 | + | 0.0507191i | −0.880295 | − | 0.474426i | \(-0.842656\pi\) |
0.851013 | + | 0.525145i | \(0.175989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.9772 | − | 6.33766i | 0.500515 | − | 0.288973i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.77013 | + | 6.53005i | 0.171193 | + | 0.296515i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.5313 | − | 19.9728i | 0.522534 | − | 0.905055i | −0.477122 | − | 0.878837i | \(-0.658320\pi\) |
0.999656 | − | 0.0262185i | \(-0.00834656\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.6759 | −1.51977 | −0.759886 | − | 0.650057i | \(-0.774745\pi\) | ||||
−0.759886 | + | 0.650057i | \(0.774745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.0502 | + | 26.0677i | −0.677827 | + | 1.17403i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.8037 | − | 4.30917i | −0.574323 | − | 0.193293i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.15436 | − | 2.97587i | 0.230741 | − | 0.133218i | −0.380173 | − | 0.924915i | \(-0.624135\pi\) |
0.610914 | + | 0.791697i | \(0.290802\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.41791 | −0.0632214 | −0.0316107 | − | 0.999500i | \(-0.510064\pi\) | ||||
−0.0316107 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.45725 | 0.331843 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.25269 | − | 4.18734i | 0.321470 | − | 0.185601i | −0.330578 | − | 0.943779i | \(-0.607244\pi\) |
0.652048 | + | 0.758178i | \(0.273910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.96385 | + | 2.61289i | −0.131113 | + | 0.115587i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.6009 | − | 20.0933i | 0.511195 | − | 0.885416i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.83612 | 0.124732 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7714 | + | 20.3887i | −0.515715 | + | 0.893244i | 0.484119 | + | 0.875002i | \(0.339140\pi\) |
−0.999834 | + | 0.0182421i | \(0.994193\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4448 | + | 25.0191i | 0.631626 | + | 1.09401i | 0.987219 | + | 0.159368i | \(0.0509456\pi\) |
−0.355593 | + | 0.934641i | \(0.615721\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.9179 | + | 17.8504i | −1.34680 | + | 0.777577i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.544750 | + | 0.943535i | −0.0236848 | + | 0.0410233i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.3522 | −1.31470 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1519 | + | 9.32532i | 0.698309 | + | 0.403169i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.0108 | − | 11.3531i | 1.16344 | − | 0.489014i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.78575 | + | 1.03100i | −0.0767754 | + | 0.0443263i | −0.537896 | − | 0.843011i | \(-0.680781\pi\) |
0.461121 | + | 0.887337i | \(0.347447\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.50726 | −0.193070 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.7819i | − | 1.52992i | −0.644076 | − | 0.764962i | \(-0.722758\pi\) | ||
0.644076 | − | 0.764962i | \(-0.277242\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.204036 | + | 0.353401i | 0.00869224 | + | 0.0150554i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.0960 | + | 6.26947i | −1.32234 | + | 0.266605i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.9748 | − | 20.7409i | 0.507388 | − | 0.878821i | −0.492576 | − | 0.870270i | \(-0.663945\pi\) |
0.999963 | − | 0.00855174i | \(-0.00272214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.4421i | 1.58363i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.4987 | + | 12.9896i | 0.948206 | + | 0.547447i | 0.892523 | − | 0.451001i | \(-0.148933\pi\) |
0.0556830 | + | 0.998448i | \(0.482266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.05352 | + | 7.02090i | 0.170533 | + | 0.295371i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4525 | − | 8.92150i | 0.647802 | − | 0.374009i | −0.139812 | − | 0.990178i | \(-0.544650\pi\) |
0.787614 | + | 0.616169i | \(0.211316\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.9523 | − | 9.21009i | −0.667585 | − | 0.385430i | 0.127576 | − | 0.991829i | \(-0.459280\pi\) |
−0.795161 | + | 0.606398i | \(0.792614\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.64157i | − | 0.360378i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.5485 | − | 10.1317i | −0.730556 | − | 0.421786i | 0.0880698 | − | 0.996114i | \(-0.471930\pi\) |
−0.818625 | + | 0.574328i | \(0.805263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.1825 | − | 6.45602i | −0.795825 | − | 0.267841i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.88642 | − | 17.1238i | −0.409454 | − | 0.709195i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.63501i | 0.150033i | 0.997182 | + | 0.0750164i | \(0.0239009\pi\) | ||||
−0.997182 | + | 0.0750164i | \(0.976099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.483999i | 0.0199428i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.4731 | − | 18.1399i | −0.430078 | − | 0.744918i | 0.566801 | − | 0.823855i | \(-0.308181\pi\) |
−0.996880 | + | 0.0789370i | \(0.974847\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.7074 | + | 6.96922i | 0.848920 | + | 0.285710i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.58346 | + | 0.914209i | 0.0646983 | + | 0.0373536i | 0.532000 | − | 0.846744i | \(-0.321441\pi\) |
−0.467302 | + | 0.884098i | \(0.654774\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.7207i | − | 1.21233i | −0.795338 | − | 0.606166i | \(-0.792707\pi\) | ||
0.795338 | − | 0.606166i | \(-0.207293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.0275 | − | 5.78937i | −0.407675 | − | 0.235371i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.04013 | − | 2.90992i | 0.204573 | − | 0.118110i | −0.394214 | − | 0.919019i | \(-0.628983\pi\) |
0.598787 | + | 0.800909i | \(0.295650\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.27534 | + | 2.20896i | 0.0515949 | + | 0.0893650i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.81649 | − | 3.93550i | −0.275316 | − | 0.158954i | 0.355985 | − | 0.934492i | \(-0.384145\pi\) |
−0.631301 | + | 0.775538i | \(0.717479\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.93676i | 0.359781i | 0.983687 | + | 0.179890i | \(0.0575743\pi\) | ||||
−0.983687 | + | 0.179890i | \(0.942426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.80163 | − | 6.58462i | 0.152801 | − | 0.264658i | −0.779455 | − | 0.626458i | \(-0.784504\pi\) |
0.932256 | + | 0.361799i | \(0.117837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.5547 | + | 9.38620i | −1.86518 | + | 0.376050i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.18050 | + | 10.7049i | 0.247220 | + | 0.428197i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.6573i | 0.624296i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.9909 | −1.99010 | −0.995052 | − | 0.0993517i | \(-0.968323\pi\) | ||||
−0.995052 | + | 0.0993517i | \(0.968323\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.8600 | + | 7.42473i | −0.510334 | + | 0.294641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.9888 | + | 15.9326i | 0.831606 | + | 0.631271i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.4319 | − | 19.8793i | −1.35998 | − | 0.785184i | −0.370358 | − | 0.928889i | \(-0.620765\pi\) |
−0.989621 | + | 0.143705i | \(0.954098\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.7989 | −1.13572 | −0.567858 | − | 0.823126i | \(-0.692228\pi\) | ||||
−0.567858 | + | 0.823126i | \(0.692228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1134 | − | 22.7130i | 0.515540 | − | 0.892941i | −0.484298 | − | 0.874903i | \(-0.660925\pi\) |
0.999837 | − | 0.0180376i | \(-0.00574185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.3413 | − | 15.7855i | 1.07324 | − | 0.619635i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.12639 | − | 5.41506i | −0.122345 | − | 0.211908i | 0.798347 | − | 0.602198i | \(-0.205708\pi\) |
−0.920692 | + | 0.390290i | \(0.872375\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.59724 | + | 9.69470i | −0.218702 | + | 0.378803i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.2081 | −1.25465 | −0.627326 | − | 0.778757i | \(-0.715850\pi\) | ||||
−0.627326 | + | 0.778757i | \(0.715850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.81544 | − | 15.2688i | 0.342881 | − | 0.593887i | −0.642085 | − | 0.766633i | \(-0.721931\pi\) |
0.984966 | + | 0.172746i | \(0.0552639\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.222189 | − | 0.195879i | 0.00861613 | − | 0.00759586i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.2406 | − | 15.1500i | 1.01604 | − | 0.586611i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 60.5336 | 2.33687 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.0260 | −1.23451 | −0.617256 | − | 0.786762i | \(-0.711756\pi\) | ||||
−0.617256 | + | 0.786762i | \(0.711756\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.5345 | − | 11.8556i | 0.789205 | − | 0.455648i | −0.0504774 | − | 0.998725i | \(-0.516074\pi\) |
0.839683 | + | 0.543077i | \(0.182741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6467 | − | 3.58322i | −0.408582 | − | 0.137511i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.16325 | + | 15.8712i | −0.350622 | + | 0.607295i | −0.986359 | − | 0.164611i | \(-0.947363\pi\) |
0.635737 | + | 0.771906i | \(0.280696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.2683 | −0.889035 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.89145 | − | 15.4004i | 0.338737 | − | 0.586710i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3501 | + | 35.2473i | 0.774153 | + | 1.34087i | 0.935269 | + | 0.353937i | \(0.115157\pi\) |
−0.161116 | + | 0.986935i | \(0.551509\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.3946 | + | 16.9710i | −1.11500 | + | 0.643746i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.7464 | − | 32.4697i | 0.710069 | − | 1.22988i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2653 | 0.463255 | 0.231628 | − | 0.972805i | \(-0.425595\pi\) | ||||
0.231628 | + | 0.972805i | \(0.425595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.183828 | + | 0.106133i | 0.00693321 | + | 0.00400289i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.33373 | + | 7.34690i | −0.313422 | + | 0.276309i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.83014 | + | 3.36604i | −0.218956 | + | 0.126414i | −0.605467 | − | 0.795871i | \(-0.707013\pi\) |
0.386511 | + | 0.922285i | \(0.373680\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.9376 | 1.34587 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 27.9824i | − | 1.04648i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.45947 | − | 2.52788i | −0.0544291 | − | 0.0942739i | 0.837527 | − | 0.546396i | \(-0.184001\pi\) |
−0.891956 | + | 0.452122i | \(0.850667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.83160 | + | 33.8841i | 0.254422 | + | 1.26191i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.97521 | − | 10.3494i | 0.221914 | − | 0.384366i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.12734i | − | 0.115987i | −0.998317 | − | 0.0579933i | \(-0.981530\pi\) | ||
0.998317 | − | 0.0579933i | \(-0.0184702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.0541 | − | 23.1252i | −1.48145 | − | 0.855318i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.93077 | + | 6.80830i | 0.145186 | + | 0.251470i | 0.929442 | − | 0.368967i | \(-0.120288\pi\) |
−0.784256 | + | 0.620437i | \(0.786955\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7690 | − | 13.7231i | 0.875543 | − | 0.505495i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.01186 | + | 0.584195i | 0.0372217 | + | 0.0214900i | 0.518495 | − | 0.855080i | \(-0.326492\pi\) |
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.12199i | − | 0.224594i | −0.993675 | − | 0.112297i | \(-0.964179\pi\) | ||
0.993675 | − | 0.112297i | \(-0.0358208\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.74886 | + | 3.89645i | 0.247259 | + | 0.142755i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.2377 | + | 5.49156i | −0.995243 | + | 0.200657i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.8430 | − | 36.1012i | −0.760573 | − | 1.31735i | −0.942556 | − | 0.334049i | \(-0.891585\pi\) |
0.181983 | − | 0.983302i | \(-0.441748\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.88120i | 0.177645i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35.8599i | − | 1.30335i | −0.758498 | − | 0.651676i | \(-0.774066\pi\) | ||
0.758498 | − | 0.651676i | \(-0.225934\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.88971 | + | 8.46923i | 0.177252 | + | 0.307009i | 0.940938 | − | 0.338578i | \(-0.109946\pi\) |
−0.763686 | + | 0.645587i | \(0.776613\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.03702 | − | 4.44056i | 0.182352 | − | 0.160759i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.5897 | + | 14.1968i | 0.887881 | + | 0.512619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.2218i | 1.95529i | 0.210269 | + | 0.977644i | \(0.432566\pi\) | ||||
−0.210269 | + | 0.977644i | \(0.567434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.8017 | + | 12.0099i | 0.748185 | + | 0.431965i | 0.825038 | − | 0.565078i | \(-0.191154\pi\) |
−0.0768527 | + | 0.997042i | \(0.524487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.2750 | − | 7.08696i | 0.440930 | − | 0.254571i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.254145 | − | 0.440193i | −0.00910570 | − | 0.0157715i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5090 | − | 10.6862i | −0.662303 | − | 0.382381i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.37661i | 0.0848247i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.5019 | + | 23.3859i | −0.481290 | + | 0.833619i | −0.999769 | − | 0.0214714i | \(-0.993165\pi\) |
0.518479 | + | 0.855090i | \(0.326498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.4470 | − | 3.85256i | −0.407007 | − | 0.136981i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.2208 | + | 47.1477i | 0.966637 | + | 1.67426i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.6501i | 1.08568i | 0.839835 | + | 0.542841i | \(0.182651\pi\) | ||||
−0.839835 | + | 0.542841i | \(0.817349\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.15075 | −0.111466 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.41340 | + | 3.12543i | −0.191035 | + | 0.110294i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.5443 | − | 16.4979i | −0.512620 | − | 0.581474i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.5996 | + | 6.11967i | 0.372661 | + | 0.215156i | 0.674620 | − | 0.738165i | \(-0.264307\pi\) |
−0.301959 | + | 0.953321i | \(0.597641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.5601 | −1.81052 | −0.905260 | − | 0.424858i | \(-0.860324\pi\) | ||||
−0.905260 | + | 0.424858i | \(0.860324\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.39322 | + | 5.87723i | −0.118859 | + | 0.205870i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.543015 | + | 0.313510i | −0.0189977 | + | 0.0109683i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3477 | + | 38.7073i | 0.779940 | + | 1.35090i | 0.931976 | + | 0.362520i | \(0.118084\pi\) |
−0.152036 | + | 0.988375i | \(0.548583\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.91299 | + | 15.4378i | −0.310687 | + | 0.538126i | −0.978511 | − | 0.206193i | \(-0.933893\pi\) |
0.667824 | + | 0.744319i | \(0.267226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.4781 | 1.54665 | 0.773327 | − | 0.634007i | \(-0.218591\pi\) | ||||
0.773327 | + | 0.634007i | \(0.218591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.86797 | + | 11.8957i | −0.238534 | + | 0.413154i | −0.960294 | − | 0.278990i | \(-0.910000\pi\) |
0.721760 | + | 0.692144i | \(0.243334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.0073 | + | 12.6126i | −1.03969 | + | 0.437002i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1627 | + | 6.44481i | −0.386303 | + | 0.223032i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.7998 | −0.649040 | −0.324520 | − | 0.945879i | \(-0.605203\pi\) | ||||
−0.324520 | + | 0.945879i | \(0.605203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9019 | 0.444892 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.80086 | − | 1.03973i | 0.0619516 | − | 0.0357678i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.9098 | − | 3.40928i | 0.581026 | − | 0.117144i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.88055 | − | 13.6495i | 0.270142 | − | 0.467899i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.23719 | −0.145079 | −0.0725393 | − | 0.997366i | \(-0.523110\pi\) | ||||
−0.0725393 | + | 0.997366i | \(0.523110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.78696 | + | 11.7554i | −0.231838 | + | 0.401556i | −0.958349 | − | 0.285599i | \(-0.907807\pi\) |
0.726511 | + | 0.687155i | \(0.241141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.8653 | − | 25.7475i | −0.507198 | − | 0.878494i | −0.999965 | − | 0.00833211i | \(-0.997348\pi\) |
0.492767 | − | 0.870161i | \(-0.335986\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7055 | − | 15.4184i | 0.909066 | − | 0.524849i | 0.0289352 | − | 0.999581i | \(-0.490788\pi\) |
0.880130 | + | 0.474732i | \(0.157455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09827 | + | 1.90225i | −0.0373422 | + | 0.0646785i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50.1850 | −1.70241 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.3769 | + | 12.3420i | 0.724329 | + | 0.418191i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.4871 | − | 10.2606i | −1.03065 | − | 0.346873i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.0815 | + | 5.82055i | −0.340428 | + | 0.196546i | −0.660461 | − | 0.750860i | \(-0.729639\pi\) |
0.320033 | + | 0.947406i | \(0.396306\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.5879 | −0.794698 | −0.397349 | − | 0.917668i | \(-0.630070\pi\) | ||||
−0.397349 | + | 0.917668i | \(0.630070\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.4950i | − | 1.32911i | −0.747239 | − | 0.664556i | \(-0.768621\pi\) | ||
0.747239 | − | 0.664556i | \(-0.231379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.3283 | + | 47.3340i | 0.917595 | + | 1.58932i | 0.803058 | + | 0.595901i | \(0.203205\pi\) |
0.114537 | + | 0.993419i | \(0.463462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.05664 | − | 20.9671i | 0.236672 | − | 0.703214i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0213575 | + | 0.0369922i | −0.000714700 | + | 0.00123790i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 31.2628i | − | 1.04500i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.0398 | + | 24.8490i | 1.43546 | + | 0.828762i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9832 | + | 19.0235i | 0.365904 | + | 0.633764i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.3419 | + | 14.6311i | −0.842392 | + | 0.486355i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.80208 | − | 4.50453i | −0.259064 | − | 0.149571i | 0.364844 | − | 0.931069i | \(-0.381122\pi\) |
−0.623907 | + | 0.781498i | \(0.714456\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.3463i | 1.17107i | 0.810646 | + | 0.585537i | \(0.199116\pi\) | ||||
−0.810646 | + | 0.585537i | \(0.800884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.7302 | − | 16.0100i | −0.917736 | − | 0.529855i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.29614 | − | 16.3486i | −0.108848 | − | 0.539878i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.9416 | + | 18.9514i | 0.360931 | + | 0.625150i | 0.988114 | − | 0.153721i | \(-0.0491257\pi\) |
−0.627184 | + | 0.778871i | \(0.715792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 19.2214i | − | 0.632680i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.21623i | − | 0.204388i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.66786 | − | 8.08497i | −0.153148 | − | 0.265259i | 0.779235 | − | 0.626731i | \(-0.215608\pi\) |
−0.932383 | + | 0.361472i | \(0.882274\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0553236 | + | 0.437803i | −0.00181316 | + | 0.0143484i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9346 | + | 17.2827i | 0.978965 | + | 0.565206i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.0652i | − | 0.459492i | −0.973251 | − | 0.229746i | \(-0.926211\pi\) | ||
0.973251 | − | 0.229746i | \(-0.0737895\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.5165 | + | 19.9281i | 1.12521 | + | 0.649638i | 0.942725 | − | 0.333571i | \(-0.108254\pi\) |
0.182481 | + | 0.983209i | \(0.441587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.6850 | + | 18.8707i | −1.06437 | + | 0.614513i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3155 | − | 17.8669i | −0.335208 | − | 0.580598i | 0.648317 | − | 0.761371i | \(-0.275473\pi\) |
−0.983525 | + | 0.180773i | \(0.942140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.86860 | − | 2.81088i | −0.158041 | − | 0.0912452i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.6133i | 1.18602i | 0.805194 | + | 0.593011i | \(0.202061\pi\) | ||||
−0.805194 | + | 0.593011i | \(0.797939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.5759 | − | 25.2462i | 0.471665 | − | 0.816948i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.0031 | − | 22.9240i | 0.839684 | − | 0.740254i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.9724 | + | 24.2010i | 0.450724 | + | 0.780677i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.7789i | 1.34491i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0693 | 0.323808 | 0.161904 | − | 0.986806i | \(-0.448236\pi\) | ||||
0.161904 | + | 0.986806i | \(0.448236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.76132 | − | 1.59425i | 0.0886149 | − | 0.0511618i | −0.455038 | − | 0.890472i | \(-0.650374\pi\) |
0.543653 | + | 0.839310i | \(0.317041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.1296 | − | 47.9253i | 0.517092 | − | 1.53642i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.60255 | − | 2.07994i | −0.115256 | − | 0.0665430i | 0.441264 | − | 0.897377i | \(-0.354530\pi\) |
−0.556520 | + | 0.830834i | \(0.687864\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −75.1334 | −2.40127 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4374 | + | 18.0782i | −0.332902 | + | 0.576604i | −0.983080 | − | 0.183179i | \(-0.941361\pi\) |
0.650177 | + | 0.759783i | \(0.274695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.21919 | − | 0.703903i | 0.0388468 | − | 0.0224282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.2786 | + | 40.3197i | 0.740216 | + | 1.28209i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.31063 | + | 10.9303i | −0.200464 | + | 0.347213i | −0.948678 | − | 0.316244i | \(-0.897578\pi\) |
0.748214 | + | 0.663457i | \(0.230912\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.5410 | −0.714597 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.23934 | − | 16.0030i | 0.292613 | − | 0.506820i | −0.681814 | − | 0.731526i | \(-0.738809\pi\) |
0.974427 | + | 0.224705i | \(0.0721420\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2016.2.cp.b.17.21 | 56 | ||
3.2 | odd | 2 | inner | 2016.2.cp.b.17.7 | 56 | ||
4.3 | odd | 2 | 504.2.ch.b.269.15 | yes | 56 | ||
7.5 | odd | 6 | inner | 2016.2.cp.b.593.22 | 56 | ||
8.3 | odd | 2 | 504.2.ch.b.269.5 | ✓ | 56 | ||
8.5 | even | 2 | inner | 2016.2.cp.b.17.8 | 56 | ||
12.11 | even | 2 | 504.2.ch.b.269.14 | yes | 56 | ||
21.5 | even | 6 | inner | 2016.2.cp.b.593.8 | 56 | ||
24.5 | odd | 2 | inner | 2016.2.cp.b.17.22 | 56 | ||
24.11 | even | 2 | 504.2.ch.b.269.24 | yes | 56 | ||
28.19 | even | 6 | 504.2.ch.b.341.24 | yes | 56 | ||
56.5 | odd | 6 | inner | 2016.2.cp.b.593.7 | 56 | ||
56.19 | even | 6 | 504.2.ch.b.341.14 | yes | 56 | ||
84.47 | odd | 6 | 504.2.ch.b.341.5 | yes | 56 | ||
168.5 | even | 6 | inner | 2016.2.cp.b.593.21 | 56 | ||
168.131 | odd | 6 | 504.2.ch.b.341.15 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.ch.b.269.5 | ✓ | 56 | 8.3 | odd | 2 | ||
504.2.ch.b.269.14 | yes | 56 | 12.11 | even | 2 | ||
504.2.ch.b.269.15 | yes | 56 | 4.3 | odd | 2 | ||
504.2.ch.b.269.24 | yes | 56 | 24.11 | even | 2 | ||
504.2.ch.b.341.5 | yes | 56 | 84.47 | odd | 6 | ||
504.2.ch.b.341.14 | yes | 56 | 56.19 | even | 6 | ||
504.2.ch.b.341.15 | yes | 56 | 168.131 | odd | 6 | ||
504.2.ch.b.341.24 | yes | 56 | 28.19 | even | 6 | ||
2016.2.cp.b.17.7 | 56 | 3.2 | odd | 2 | inner | ||
2016.2.cp.b.17.8 | 56 | 8.5 | even | 2 | inner | ||
2016.2.cp.b.17.21 | 56 | 1.1 | even | 1 | trivial | ||
2016.2.cp.b.17.22 | 56 | 24.5 | odd | 2 | inner | ||
2016.2.cp.b.593.7 | 56 | 56.5 | odd | 6 | inner | ||
2016.2.cp.b.593.8 | 56 | 21.5 | even | 6 | inner | ||
2016.2.cp.b.593.21 | 56 | 168.5 | even | 6 | inner | ||
2016.2.cp.b.593.22 | 56 | 7.5 | odd | 6 | inner |