Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(440,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.440");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.o (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 441) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.10 | ||
Character | \(\chi\) | \(=\) | 1323.881 |
Dual form | 1323.2.o.e.440.10 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.575298 | + | 0.332148i | −0.406797 | + | 0.234864i | −0.689413 | − | 0.724369i | \(-0.742131\pi\) |
0.282616 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.779355 | + | 1.34988i | −0.389677 | + | 0.674941i | ||||
\(5\) | 0.0141520 | − | 0.0245119i | 0.00632895 | − | 0.0109621i | −0.862844 | − | 0.505471i | \(-0.831319\pi\) |
0.869173 | + | 0.494509i | \(0.164652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.36404i | − | 0.835814i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0188022i | 0.00594578i | ||||||||
\(11\) | 0.885324 | − | 0.511142i | 0.266935 | − | 0.154115i | −0.360559 | − | 0.932736i | \(-0.617414\pi\) |
0.627494 | + | 0.778621i | \(0.284081\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.87844 | + | 2.81657i | 1.35304 | + | 0.781176i | 0.988674 | − | 0.150081i | \(-0.0479534\pi\) |
0.364363 | + | 0.931257i | \(0.381287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.773498 | − | 1.33974i | −0.193375 | − | 0.334935i | ||||
\(17\) | −5.67880 | −1.37731 | −0.688656 | − | 0.725089i | \(-0.741799\pi\) | ||||
−0.688656 | + | 0.725089i | \(0.741799\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.09274i | − | 0.480108i | −0.970760 | − | 0.240054i | \(-0.922835\pi\) | ||
0.970760 | − | 0.240054i | \(-0.0771651\pi\) | |||||||
\(20\) | 0.0220588 | + | 0.0382070i | 0.00493250 | + | 0.00854334i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.339550 | + | 0.588118i | −0.0723923 | + | 0.125387i | ||||
\(23\) | 6.28849 | + | 3.63066i | 1.31124 | + | 0.757046i | 0.982302 | − | 0.187305i | \(-0.0599754\pi\) |
0.328940 | + | 0.944351i | \(0.393309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49960 | + | 4.32943i | 0.499920 | + | 0.865887i | ||||
\(26\) | −3.74208 | −0.733882 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.52577 | − | 2.03560i | 0.654718 | − | 0.378002i | −0.135543 | − | 0.990771i | \(-0.543278\pi\) |
0.790262 | + | 0.612770i | \(0.209945\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.87364 | − | 1.65910i | −0.516122 | − | 0.297983i | 0.219225 | − | 0.975674i | \(-0.429647\pi\) |
−0.735346 | + | 0.677691i | \(0.762981\pi\) | |||||||
\(32\) | 4.98462 | + | 2.87787i | 0.881165 | + | 0.508741i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.26700 | − | 1.88620i | 0.560286 | − | 0.323481i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47265 | −0.406501 | −0.203250 | − | 0.979127i | \(-0.565151\pi\) | ||||
−0.203250 | + | 0.979127i | \(0.565151\pi\) | |||||||
\(38\) | 0.695101 | + | 1.20395i | 0.112760 | + | 0.195306i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0579471 | − | 0.0334558i | −0.00916224 | − | 0.00528982i | ||||
\(41\) | 3.52867 | − | 6.11183i | 0.551085 | − | 0.954508i | −0.447111 | − | 0.894478i | \(-0.647547\pi\) |
0.998197 | − | 0.0600295i | \(-0.0191195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.15994 | − | 2.00908i | −0.176890 | − | 0.306382i | 0.763924 | − | 0.645306i | \(-0.223270\pi\) |
−0.940814 | + | 0.338924i | \(0.889937\pi\) | |||||||
\(44\) | 1.59344i | 0.240221i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.82367 | −0.711212 | ||||||||
\(47\) | 5.43997 | + | 9.42231i | 0.793502 | + | 1.37439i | 0.923786 | + | 0.382908i | \(0.125078\pi\) |
−0.130285 | + | 0.991477i | \(0.541589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.87603 | − | 1.66048i | −0.406732 | − | 0.234827i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.60408 | + | 4.39022i | −1.05450 | + | 0.608814i | ||||
\(53\) | 11.5995i | 1.59331i | 0.604435 | + | 0.796655i | \(0.293399\pi\) | ||||
−0.604435 | + | 0.796655i | \(0.706601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.0289346i | − | 0.00390155i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.35224 | + | 2.34215i | −0.177558 | + | 0.307540i | ||||
\(59\) | −3.01111 | + | 5.21540i | −0.392013 | + | 0.678987i | −0.992715 | − | 0.120486i | \(-0.961555\pi\) |
0.600702 | + | 0.799473i | \(0.294888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.05220 | + | 1.18484i | −0.262757 | + | 0.151703i | −0.625592 | − | 0.780151i | \(-0.715142\pi\) |
0.362834 | + | 0.931854i | \(0.381809\pi\) | |||||||
\(62\) | 2.20427 | 0.279942 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.729528 | −0.0911909 | ||||||||
\(65\) | 0.138079 | − | 0.0797200i | 0.0171266 | − | 0.00988805i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.38995 | + | 11.0677i | −0.780656 | + | 1.35214i | 0.150903 | + | 0.988549i | \(0.451782\pi\) |
−0.931560 | + | 0.363588i | \(0.881552\pi\) | |||||||
\(68\) | 4.42580 | − | 7.66571i | 0.536707 | − | 0.929604i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.93415i | 0.941610i | 0.882237 | + | 0.470805i | \(0.156036\pi\) | ||||
−0.882237 | + | 0.470805i | \(0.843964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.8991i | − | 1.27564i | −0.770185 | − | 0.637821i | \(-0.779836\pi\) | ||
0.770185 | − | 0.637821i | \(-0.220164\pi\) | |||||||
\(74\) | 1.42251 | − | 0.821285i | 0.165363 | − | 0.0954725i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.82496 | + | 1.63099i | 0.324045 | + | 0.187087i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.80018 | + | 13.5103i | 0.877588 | + | 1.52003i | 0.853980 | + | 0.520306i | \(0.174182\pi\) |
0.0236086 | + | 0.999721i | \(0.492484\pi\) | |||||||
\(80\) | −0.0437861 | −0.00489543 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.68816i | 0.517721i | ||||||||
\(83\) | 3.07406 | + | 5.32442i | 0.337421 | + | 0.584431i | 0.983947 | − | 0.178461i | \(-0.0571119\pi\) |
−0.646526 | + | 0.762892i | \(0.723779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0803661 | + | 0.139198i | −0.00871693 | + | 0.0150982i | ||||
\(86\) | 1.33463 | + | 0.770546i | 0.143916 | + | 0.0830902i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.20836 | − | 2.09294i | −0.128812 | − | 0.223108i | ||||
\(89\) | −12.0516 | −1.27747 | −0.638736 | − | 0.769426i | \(-0.720542\pi\) | ||||
−0.638736 | + | 0.769426i | \(0.720542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.80194 | + | 5.65915i | −1.02192 | + | 0.590007i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.25921 | − | 3.61376i | −0.645588 | − | 0.372730i | ||||
\(95\) | −0.0512971 | − | 0.0296164i | −0.00526297 | − | 0.00303858i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.77565 | + | 3.91192i | −0.687963 | + | 0.397196i | −0.802848 | − | 0.596183i | \(-0.796683\pi\) |
0.114885 | + | 0.993379i | \(0.463350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.79230 | −0.779230 | ||||||||
\(101\) | −0.226924 | − | 0.393043i | −0.0225797 | − | 0.0391093i | 0.854515 | − | 0.519427i | \(-0.173855\pi\) |
−0.877094 | + | 0.480318i | \(0.840521\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.58316 | − | 2.64609i | −0.451592 | − | 0.260727i | 0.256910 | − | 0.966435i | \(-0.417296\pi\) |
−0.708502 | + | 0.705708i | \(0.750629\pi\) | |||||||
\(104\) | 6.65848 | − | 11.5328i | 0.652918 | − | 1.13089i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.85274 | − | 6.67315i | −0.374212 | − | 0.648153i | ||||
\(107\) | − | 9.06755i | − | 0.876593i | −0.898830 | − | 0.438296i | \(-0.855582\pi\) | ||
0.898830 | − | 0.438296i | \(-0.144418\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.73027 | 0.453078 | 0.226539 | − | 0.974002i | \(-0.427259\pi\) | ||||
0.226539 | + | 0.974002i | \(0.427259\pi\) | |||||||
\(110\) | 0.00961059 | + | 0.0166460i | 0.000916334 | + | 0.00158714i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.21108 | + | 4.74067i | 0.772433 | + | 0.445965i | 0.833742 | − | 0.552154i | \(-0.186194\pi\) |
−0.0613086 | + | 0.998119i | \(0.519527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.177989 | − | 0.102762i | 0.0165976 | − | 0.00958261i | ||||
\(116\) | 6.34583i | 0.589195i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.00054i | − | 0.368280i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.97747 | + | 8.62123i | −0.452497 | + | 0.783748i | ||||
\(122\) | 0.787084 | − | 1.36327i | 0.0712593 | − | 0.123425i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.47918 | − | 2.58606i | 0.402242 | − | 0.232235i | ||||
\(125\) | 0.283017 | 0.0253138 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.37297 | 0.388039 | 0.194019 | − | 0.980998i | \(-0.437848\pi\) | ||||
0.194019 | + | 0.980998i | \(0.437848\pi\) | |||||||
\(128\) | −9.54954 | + | 5.51343i | −0.844068 | + | 0.487323i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0529577 | + | 0.0917255i | −0.00464470 | + | 0.00804486i | ||||
\(131\) | 1.27231 | − | 2.20371i | 0.111162 | − | 0.192539i | −0.805077 | − | 0.593171i | \(-0.797876\pi\) |
0.916239 | + | 0.400632i | \(0.131209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 8.48964i | − | 0.733393i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.4249i | 1.15118i | ||||||||
\(137\) | 9.82536 | − | 5.67267i | 0.839437 | − | 0.484649i | −0.0176357 | − | 0.999844i | \(-0.505614\pi\) |
0.857073 | + | 0.515195i | \(0.172281\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.04891 | − | 1.76029i | −0.258605 | − | 0.149306i | 0.365093 | − | 0.930971i | \(-0.381037\pi\) |
−0.623698 | + | 0.781665i | \(0.714371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.63531 | − | 4.56450i | −0.221151 | − | 0.383044i | ||||
\(143\) | 5.75867 | 0.481564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.115231i | − | 0.00956942i | ||||||
\(146\) | 3.62012 | + | 6.27022i | 0.299603 | + | 0.518927i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.92707 | − | 3.33778i | 0.158404 | − | 0.274364i | ||||
\(149\) | 13.7806 | + | 7.95623i | 1.12895 | + | 0.651800i | 0.943671 | − | 0.330886i | \(-0.107348\pi\) |
0.185279 | + | 0.982686i | \(0.440681\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.73008 | − | 2.99659i | −0.140792 | − | 0.243859i | 0.787003 | − | 0.616949i | \(-0.211632\pi\) |
−0.927795 | + | 0.373090i | \(0.878298\pi\) | |||||||
\(152\) | −4.94732 | −0.401281 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.0813354 | + | 0.0469590i | −0.00653302 | + | 0.00377184i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1585 | + | 8.17442i | 1.12997 | + | 0.652390i | 0.943928 | − | 0.330151i | \(-0.107100\pi\) |
0.186045 | + | 0.982541i | \(0.440433\pi\) | |||||||
\(158\) | −8.97485 | − | 5.18163i | −0.714001 | − | 0.412228i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.141084 | − | 0.0814550i | 0.0111537 | − | 0.00643959i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3556 | 0.811116 | 0.405558 | − | 0.914069i | \(-0.367077\pi\) | ||||
0.405558 | + | 0.914069i | \(0.367077\pi\) | |||||||
\(164\) | 5.50017 | + | 9.52657i | 0.429491 | + | 0.743900i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.53699 | − | 2.04208i | −0.274524 | − | 0.158497i | ||||
\(167\) | −2.94297 | + | 5.09738i | −0.227734 | + | 0.394447i | −0.957136 | − | 0.289638i | \(-0.906465\pi\) |
0.729402 | + | 0.684085i | \(0.239798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.36614 | + | 16.2226i | 0.720473 | + | 1.24790i | ||||
\(170\) | − | 0.106774i | − | 0.00818919i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.61603 | 0.275720 | ||||||||
\(173\) | 2.43276 | + | 4.21366i | 0.184959 | + | 0.320359i | 0.943563 | − | 0.331194i | \(-0.107451\pi\) |
−0.758604 | + | 0.651552i | \(0.774118\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.36959 | − | 0.790735i | −0.103237 | − | 0.0596039i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.93328 | − | 4.00293i | 0.519671 | − | 0.300032i | ||||
\(179\) | 0.202645i | 0.0151464i | 0.999971 | + | 0.00757319i | \(0.00241064\pi\) | ||||
−0.999971 | + | 0.00757319i | \(0.997589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.26273i | 0.465505i | 0.972536 | + | 0.232753i | \(0.0747732\pi\) | ||||
−0.972536 | + | 0.232753i | \(0.925227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.58303 | − | 14.8662i | 0.632749 | − | 1.09595i | ||||
\(185\) | −0.0349928 | + | 0.0606093i | −0.00257272 | + | 0.00445608i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.02758 | + | 2.90267i | −0.367653 | + | 0.212264i | ||||
\(188\) | −16.9587 | −1.23684 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0393482 | 0.00285462 | ||||||||
\(191\) | −11.9541 | + | 6.90168i | −0.864965 | + | 0.499388i | −0.865672 | − | 0.500612i | \(-0.833108\pi\) |
0.000706698 | 1.00000i | \(0.499775\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5387 | − | 18.2536i | 0.758593 | − | 1.31392i | −0.184976 | − | 0.982743i | \(-0.559221\pi\) |
0.943568 | − | 0.331178i | \(-0.107446\pi\) | |||||||
\(194\) | 2.59868 | − | 4.50104i | 0.186574 | − | 0.323156i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.1679i | − | 1.08067i | −0.841451 | − | 0.540334i | \(-0.818298\pi\) | ||
0.841451 | − | 0.540334i | \(-0.181702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.68724i | − | 0.686710i | −0.939206 | − | 0.343355i | \(-0.888437\pi\) | ||
0.939206 | − | 0.343355i | \(-0.111563\pi\) | |||||||
\(200\) | 10.2349 | − | 5.90915i | 0.723720 | − | 0.417840i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.261097 | + | 0.150745i | 0.0183707 | + | 0.0106064i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0998751 | − | 0.172989i | −0.00697558 | − | 0.0120821i | ||||
\(206\) | 3.51558 | 0.244942 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 8.71445i | − | 0.604238i | ||||||
\(209\) | −1.06969 | − | 1.85275i | −0.0739919 | − | 0.128158i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.05942 | + | 12.2273i | −0.485991 | + | 0.841761i | −0.999870 | − | 0.0161017i | \(-0.994874\pi\) |
0.513880 | + | 0.857862i | \(0.328208\pi\) | |||||||
\(212\) | −15.6579 | − | 9.04010i | −1.07539 | − | 0.620877i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.01177 | + | 5.21654i | 0.205880 | + | 0.356595i | ||||
\(215\) | −0.0656619 | −0.00447810 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.72132 | + | 1.57115i | −0.184311 | + | 0.106412i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0390584 | + | 0.0225504i | 0.00263331 | + | 0.00152034i | ||||
\(221\) | −27.7037 | − | 15.9947i | −1.86355 | − | 1.07592i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.58777 | − | 1.49405i | 0.173290 | − | 0.100049i | −0.410846 | − | 0.911705i | \(-0.634767\pi\) |
0.584136 | + | 0.811656i | \(0.301433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.29842 | −0.418965 | ||||||||
\(227\) | −14.3867 | − | 24.9184i | −0.954876 | − | 1.65389i | −0.734652 | − | 0.678444i | \(-0.762654\pi\) |
−0.220224 | − | 0.975449i | \(-0.570679\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.67401 | + | 4.43059i | 0.507113 | + | 0.292782i | 0.731646 | − | 0.681685i | \(-0.238752\pi\) |
−0.224533 | + | 0.974466i | \(0.572086\pi\) | |||||||
\(230\) | −0.0682645 | + | 0.118238i | −0.00450122 | + | 0.00779635i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.81224 | − | 8.33505i | −0.315939 | − | 0.547223i | ||||
\(233\) | − | 12.9082i | − | 0.845646i | −0.906212 | − | 0.422823i | \(-0.861039\pi\) | ||
0.906212 | − | 0.422823i | \(-0.138961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.307945 | 0.0200881 | ||||||||
\(236\) | −4.69345 | − | 8.12929i | −0.305518 | − | 0.529172i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.85712 | + | 2.80426i | 0.314181 | + | 0.181392i | 0.648796 | − | 0.760963i | \(-0.275273\pi\) |
−0.334615 | + | 0.942355i | \(0.608606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.51481 | − | 5.49338i | 0.612903 | − | 0.353860i | −0.161198 | − | 0.986922i | \(-0.551536\pi\) |
0.774101 | + | 0.633063i | \(0.218202\pi\) | |||||||
\(242\) | − | 6.61303i | − | 0.425102i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.69364i | − | 0.236461i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.89436 | − | 10.2093i | 0.375049 | − | 0.649604i | ||||
\(248\) | −3.92218 | + | 6.79341i | −0.249058 | + | 0.431382i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.162819 | + | 0.0940035i | −0.0102976 | + | 0.00594530i | ||||
\(251\) | −24.2241 | −1.52901 | −0.764505 | − | 0.644618i | \(-0.777016\pi\) | ||||
−0.764505 | + | 0.644618i | \(0.777016\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.42314 | 0.466689 | ||||||||
\(254\) | −2.51576 | + | 1.45248i | −0.157853 | + | 0.0911365i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.39208 | − | 7.60731i | 0.274505 | − | 0.475457i | ||||
\(257\) | 8.86142 | − | 15.3484i | 0.552760 | − | 0.957409i | −0.445314 | − | 0.895375i | \(-0.646908\pi\) |
0.998074 | − | 0.0620341i | \(-0.0197588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.248521i | 0.0154126i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.69039i | 0.104432i | ||||||||
\(263\) | −2.51031 | + | 1.44933i | −0.154793 | + | 0.0893695i | −0.575396 | − | 0.817875i | \(-0.695152\pi\) |
0.420603 | + | 0.907245i | \(0.361819\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.284325 | + | 0.164155i | 0.0174660 | + | 0.0100840i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.96008 | − | 17.2514i | −0.608408 | − | 1.05379i | ||||
\(269\) | 21.8938 | 1.33489 | 0.667444 | − | 0.744660i | \(-0.267388\pi\) | ||||
0.667444 | + | 0.744660i | \(0.267388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.98347i | 0.545707i | 0.962056 | + | 0.272854i | \(0.0879675\pi\) | ||||
−0.962056 | + | 0.272854i | \(0.912033\pi\) | |||||||
\(272\) | 4.39254 | + | 7.60811i | 0.266337 | + | 0.461309i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.76834 | + | 6.52695i | −0.227654 | + | 0.394308i | ||||
\(275\) | 4.42591 | + | 2.55530i | 0.266892 | + | 0.154090i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.95091 | − | 13.7714i | −0.477724 | − | 0.827442i | 0.521950 | − | 0.852976i | \(-0.325205\pi\) |
−0.999674 | + | 0.0255339i | \(0.991871\pi\) | |||||||
\(278\) | 2.33871 | 0.140267 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.50324 | − | 2.59995i | 0.268641 | − | 0.155100i | −0.359629 | − | 0.933095i | \(-0.617097\pi\) |
0.628270 | + | 0.777996i | \(0.283763\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2587 | + | 9.38694i | 0.966476 | + | 0.557995i | 0.898160 | − | 0.439668i | \(-0.144904\pi\) |
0.0683162 | + | 0.997664i | \(0.478237\pi\) | |||||||
\(284\) | −10.7102 | − | 6.18352i | −0.635531 | − | 0.366924i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.31295 | + | 1.91273i | −0.195899 | + | 0.113102i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.2488 | 0.896986 | ||||||||
\(290\) | 0.0382738 | + | 0.0662922i | 0.00224751 | + | 0.00389281i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.7125 | + | 8.49426i | 0.860983 | + | 0.497089i | ||||
\(293\) | −11.4201 | + | 19.7802i | −0.667169 | + | 1.15557i | 0.311523 | + | 0.950238i | \(0.399161\pi\) |
−0.978692 | + | 0.205332i | \(0.934173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0852263 | + | 0.147616i | 0.00496206 | + | 0.00859455i | ||||
\(296\) | 5.84543i | 0.339759i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.5706 | −0.612338 | ||||||||
\(299\) | 20.4520 | + | 35.4240i | 1.18277 | + | 2.04862i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.99062 | + | 1.14929i | 0.114548 | + | 0.0661341i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.80373 | + | 1.61873i | −0.160805 | + | 0.0928407i | ||||
\(305\) | 0.0670711i | 0.00384048i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.6325i | − | 1.06341i | −0.846928 | − | 0.531707i | \(-0.821551\pi\) | ||
0.846928 | − | 0.531707i | \(-0.178449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0311947 | − | 0.0540308i | 0.00177174 | − | 0.00306875i | ||||
\(311\) | 10.2747 | − | 17.7964i | 0.582628 | − | 1.00914i | −0.412539 | − | 0.910940i | \(-0.635358\pi\) |
0.995167 | − | 0.0982007i | \(-0.0313087\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.624466 | + | 0.360536i | −0.0352969 | + | 0.0203787i | −0.517545 | − | 0.855656i | \(-0.673154\pi\) |
0.482248 | + | 0.876035i | \(0.339821\pi\) | |||||||
\(314\) | −10.8605 | −0.612893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.3164 | −1.36791 | ||||||||
\(317\) | 18.9915 | − | 10.9647i | 1.06667 | − | 0.615841i | 0.139398 | − | 0.990236i | \(-0.455483\pi\) |
0.927269 | + | 0.374396i | \(0.122150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.08096 | − | 3.60433i | 0.116512 | − | 0.201804i | ||||
\(320\) | −0.0103242 | + | 0.0178821i | −0.000577143 | + | 0.000999641i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.8843i | 0.661258i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.1612i | 1.56210i | ||||||||
\(326\) | −5.95757 | + | 3.43961i | −0.329959 | + | 0.190502i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.4486 | − | 8.34191i | −0.797791 | − | 0.460605i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8338 | − | 18.7647i | −0.595480 | − | 1.03140i | −0.993479 | − | 0.114016i | \(-0.963629\pi\) |
0.397999 | − | 0.917386i | \(-0.369705\pi\) | |||||||
\(332\) | −9.58312 | −0.525942 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 3.91002i | − | 0.213947i | ||||||
\(335\) | 0.180861 | + | 0.313260i | 0.00988147 | + | 0.0171152i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6455 | − | 21.9026i | 0.688844 | − | 1.19311i | −0.283369 | − | 0.959011i | \(-0.591452\pi\) |
0.972212 | − | 0.234101i | \(-0.0752147\pi\) | |||||||
\(338\) | −10.7766 | − | 6.22190i | −0.586172 | − | 0.338427i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.125268 | − | 0.216970i | −0.00679358 | − | 0.0117668i | ||||
\(341\) | −3.39214 | −0.183695 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.74955 | + | 2.74215i | −0.256078 | + | 0.147847i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.79912 | − | 1.61607i | −0.150482 | − | 0.0868806i | ||||
\(347\) | 4.92420 | + | 2.84299i | 0.264345 | + | 0.152620i | 0.626315 | − | 0.779570i | \(-0.284562\pi\) |
−0.361970 | + | 0.932190i | \(0.617896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.68412 | + | 5.59113i | −0.518379 | + | 0.299286i | −0.736271 | − | 0.676687i | \(-0.763415\pi\) |
0.217892 | + | 0.975973i | \(0.430082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.88400 | 0.313618 | ||||||||
\(353\) | −7.02111 | − | 12.1609i | −0.373696 | − | 0.647260i | 0.616435 | − | 0.787406i | \(-0.288576\pi\) |
−0.990131 | + | 0.140146i | \(0.955243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.194481 | + | 0.112284i | 0.0103220 | + | 0.00595940i | ||||
\(356\) | 9.39250 | − | 16.2683i | 0.497802 | − | 0.862218i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.0673081 | − | 0.116581i | −0.00355734 | − | 0.00616150i | ||||
\(359\) | − | 27.1414i | − | 1.43247i | −0.697859 | − | 0.716235i | \(-0.745864\pi\) | ||
0.697859 | − | 0.716235i | \(-0.254136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.6204 | 0.769496 | ||||||||
\(362\) | −2.08016 | − | 3.60294i | −0.109331 | − | 0.189366i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.267158 | − | 0.154244i | −0.0139837 | − | 0.00807347i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.95891 | − | 3.44038i | 0.311053 | − | 0.179586i | −0.336345 | − | 0.941739i | \(-0.609191\pi\) |
0.647397 | + | 0.762153i | \(0.275857\pi\) | |||||||
\(368\) | − | 11.2332i | − | 0.585573i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 0.0464912i | − | 0.00241696i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.123926 | − | 0.214645i | 0.00641662 | − | 0.0111139i | −0.862799 | − | 0.505547i | \(-0.831291\pi\) |
0.869216 | + | 0.494433i | \(0.164624\pi\) | |||||||
\(374\) | 1.92824 | − | 3.33980i | 0.0997067 | − | 0.172697i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.2747 | − | 12.8603i | 1.14873 | − | 0.663220i | ||||
\(377\) | 22.9337 | 1.18114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.91863 | −0.458119 | −0.229060 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229060 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(380\) | 0.0799573 | − | 0.0461634i | 0.00410172 | − | 0.00236813i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.58476 | − | 7.94104i | 0.234577 | − | 0.406299i | ||||
\(383\) | −0.163545 | + | 0.283268i | −0.00835675 | + | 0.0144743i | −0.870174 | − | 0.492745i | \(-0.835993\pi\) |
0.861817 | + | 0.507220i | \(0.169327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0017i | 0.712665i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 12.1951i | − | 0.619113i | ||||||
\(389\) | 5.72348 | − | 3.30445i | 0.290192 | − | 0.167542i | −0.347837 | − | 0.937555i | \(-0.613084\pi\) |
0.638028 | + | 0.770013i | \(0.279750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.7111 | − | 20.6178i | −1.80599 | − | 1.04269i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.03799 | + | 8.72606i | 0.253810 | + | 0.439613i | ||||
\(395\) | 0.441551 | 0.0222168 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.51057i | 0.376945i | 0.982078 | + | 0.188472i | \(0.0603536\pi\) | ||||
−0.982078 | + | 0.188472i | \(0.939646\pi\) | |||||||
\(398\) | 3.21760 | + | 5.57305i | 0.161284 | + | 0.279352i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.86687 | − | 6.69762i | 0.193344 | − | 0.334881i | ||||
\(401\) | 5.48595 | + | 3.16732i | 0.273956 | + | 0.158168i | 0.630684 | − | 0.776040i | \(-0.282774\pi\) |
−0.356728 | + | 0.934208i | \(0.616108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.34594 | − | 16.1876i | −0.465555 | − | 0.806364i | ||||
\(404\) | 0.707416 | 0.0351953 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.18909 | + | 1.26387i | −0.108509 | + | 0.0626479i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.0045 | − | 16.7457i | −1.43418 | − | 0.828024i | −0.436743 | − | 0.899586i | \(-0.643868\pi\) |
−0.997436 | + | 0.0715625i | \(0.977201\pi\) | |||||||
\(410\) | 0.114916 | + | 0.0663467i | 0.00567529 | + | 0.00327663i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.14382 | − | 4.12448i | 0.351951 | − | 0.203199i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.174016 | 0.00854209 | ||||||||
\(416\) | 16.2115 | + | 28.0791i | 0.794832 | + | 1.37669i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.23078 | + | 0.710590i | 0.0601993 | + | 0.0347561i | ||||
\(419\) | −0.896459 | + | 1.55271i | −0.0437949 | + | 0.0758550i | −0.887092 | − | 0.461593i | \(-0.847278\pi\) |
0.843297 | + | 0.537448i | \(0.180611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.90262 | + | 3.29543i | 0.0927278 | + | 0.160609i | 0.908658 | − | 0.417541i | \(-0.137108\pi\) |
−0.815930 | + | 0.578150i | \(0.803775\pi\) | |||||||
\(422\) | − | 9.37910i | − | 0.456568i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.4216 | 1.33171 | ||||||||
\(425\) | −14.1947 | − | 24.5860i | −0.688545 | − | 1.19260i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.2401 | + | 7.06684i | 0.591649 | + | 0.341589i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0377751 | − | 0.0218095i | 0.00182168 | − | 0.00105175i | ||||
\(431\) | 1.32957i | 0.0640434i | 0.999487 | + | 0.0320217i | \(0.0101946\pi\) | ||||
−0.999487 | + | 0.0320217i | \(0.989805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.4292i | 1.79873i | 0.437194 | + | 0.899367i | \(0.355972\pi\) | ||||
−0.437194 | + | 0.899367i | \(0.644028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.68656 | + | 6.38531i | −0.176554 | + | 0.305801i | ||||
\(437\) | 7.59804 | − | 13.1602i | 0.363464 | − | 0.629537i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.5584 | + | 11.8694i | −0.981201 | + | 0.566496i | −0.902632 | − | 0.430412i | \(-0.858368\pi\) |
−0.0785682 | + | 0.996909i | \(0.525035\pi\) | |||||||
\(440\) | −0.0684026 | −0.00326097 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.2505 | 1.01078 | ||||||||
\(443\) | −9.74317 | + | 5.62522i | −0.462912 | + | 0.267262i | −0.713268 | − | 0.700891i | \(-0.752786\pi\) |
0.250356 | + | 0.968154i | \(0.419452\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.170554 | + | 0.295409i | −0.00808505 | + | 0.0140037i | ||||
\(446\) | −0.992491 | + | 1.71904i | −0.0469958 | + | 0.0813991i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 14.3953i | − | 0.679357i | −0.940542 | − | 0.339679i | \(-0.889682\pi\) | ||
0.940542 | − | 0.339679i | \(-0.110318\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.21460i | − | 0.339722i | ||||||
\(452\) | −12.7987 | + | 7.38933i | −0.602000 | + | 0.347565i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.5532 | + | 9.55701i | 0.776881 | + | 0.448533i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.3135 | + | 17.8635i | 0.482444 | + | 0.835617i | 0.999797 | − | 0.0201547i | \(-0.00641589\pi\) |
−0.517353 | + | 0.855772i | \(0.673083\pi\) | |||||||
\(458\) | −5.88646 | −0.275056 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.320352i | 0.0149365i | ||||||||
\(461\) | 0.832511 | + | 1.44195i | 0.0387739 | + | 0.0671584i | 0.884761 | − | 0.466045i | \(-0.154321\pi\) |
−0.845987 | + | 0.533203i | \(0.820988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.604175 | − | 1.04646i | 0.0280784 | − | 0.0486332i | −0.851645 | − | 0.524119i | \(-0.824395\pi\) |
0.879723 | + | 0.475486i | \(0.157728\pi\) | |||||||
\(464\) | −5.45435 | − | 3.14907i | −0.253212 | − | 0.146192i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.28745 | + | 7.42608i | 0.198612 | + | 0.344006i | ||||
\(467\) | 9.23988 | 0.427571 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.177160 | + | 0.102283i | −0.00817179 | + | 0.00471798i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.3294 | + | 7.11839i | 0.567507 | + | 0.327650i | ||||
\(473\) | −2.05385 | − | 1.18579i | −0.0944361 | − | 0.0545227i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.06039 | − | 5.23102i | 0.415719 | − | 0.240016i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.72572 | −0.170410 | ||||||||
\(479\) | 8.77241 | + | 15.1943i | 0.400822 | + | 0.694243i | 0.993825 | − | 0.110956i | \(-0.0353914\pi\) |
−0.593004 | + | 0.805200i | \(0.702058\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0627 | − | 6.96438i | −0.550010 | − | 0.317549i | ||||
\(482\) | −3.64923 | + | 6.32066i | −0.166218 | + | 0.287898i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.75843 | − | 13.4380i | −0.352656 | − | 0.610818i | ||||
\(485\) | 0.221446i | 0.0100553i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −43.1898 | −1.95712 | −0.978558 | − | 0.205974i | \(-0.933964\pi\) | ||||
−0.978558 | + | 0.205974i | \(0.933964\pi\) | |||||||
\(488\) | 2.80100 | + | 4.85148i | 0.126796 | + | 0.219616i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.0046 | − | 13.2817i | −1.03818 | − | 0.599396i | −0.118866 | − | 0.992910i | \(-0.537926\pi\) |
−0.919319 | + | 0.393514i | \(0.871259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.0221 | + | 11.5598i | −0.901751 | + | 0.520626i | ||||
\(494\) | 7.83120i | 0.352342i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.13324i | 0.230489i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.65759 | + | 4.60308i | −0.118970 | + | 0.206062i | −0.919360 | − | 0.393418i | \(-0.871293\pi\) |
0.800390 | + | 0.599480i | \(0.204626\pi\) | |||||||
\(500\) | −0.220570 | + | 0.382039i | −0.00986421 | + | 0.0170853i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.9361 | − | 8.04598i | 0.621996 | − | 0.359110i | ||||
\(503\) | 35.5334 | 1.58436 | 0.792178 | − | 0.610290i | \(-0.208947\pi\) | ||||
0.792178 | + | 0.610290i | \(0.208947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0128457 | −0.000571624 | ||||||||
\(506\) | −4.27051 | + | 2.46558i | −0.189847 | + | 0.109608i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.40810 | + | 5.90300i | −0.151210 | + | 0.261903i | ||||
\(509\) | −6.81654 | + | 11.8066i | −0.302138 | + | 0.523318i | −0.976620 | − | 0.214973i | \(-0.931034\pi\) |
0.674482 | + | 0.738291i | \(0.264367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 16.2184i | − | 0.716760i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.7732i | 0.519295i | ||||||||
\(515\) | −0.129721 | + | 0.0748947i | −0.00571621 | + | 0.00330025i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.63227 | + | 5.56120i | 0.423627 | + | 0.244581i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.188461 | − | 0.326424i | −0.00826457 | − | 0.0143147i | ||||
\(521\) | 10.2252 | 0.447973 | 0.223987 | − | 0.974592i | \(-0.428093\pi\) | ||||
0.223987 | + | 0.974592i | \(0.428093\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.17480i | − | 0.226278i | −0.993579 | − | 0.113139i | \(-0.963909\pi\) | ||
0.993579 | − | 0.113139i | \(-0.0360905\pi\) | |||||||
\(524\) | 1.98317 | + | 3.43495i | 0.0866350 | + | 0.150056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.962785 | − | 1.66759i | 0.0419794 | − | 0.0727105i | ||||
\(527\) | 16.3189 | + | 9.42169i | 0.710860 | + | 0.410415i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.8634 | + | 25.7442i | 0.646236 | + | 1.11931i | ||||
\(530\) | −0.218096 | −0.00947346 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.4288 | − | 19.8775i | 1.49128 | − | 0.860990i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.222263 | − | 0.128324i | −0.00960927 | − | 0.00554791i | ||||
\(536\) | 26.1645 | + | 15.1061i | 1.13013 | + | 0.652484i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.5955 | + | 7.27199i | −0.543029 | + | 0.313518i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.4395 | −1.09373 | −0.546864 | − | 0.837222i | \(-0.684178\pi\) | ||||
−0.546864 | + | 0.837222i | \(0.684178\pi\) | |||||||
\(542\) | −2.98385 | − | 5.16817i | −0.128167 | − | 0.221992i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.3067 | − | 16.3429i | −1.21364 | − | 0.700694i | ||||
\(545\) | 0.0669427 | − | 0.115948i | 0.00286751 | − | 0.00496667i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7771 | + | 25.5947i | 0.631824 | + | 1.09435i | 0.987179 | + | 0.159620i | \(0.0510267\pi\) |
−0.355355 | + | 0.934732i | \(0.615640\pi\) | |||||||
\(548\) | 17.6841i | 0.755428i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.39495 | −0.144761 | ||||||||
\(551\) | −4.25999 | − | 7.37852i | −0.181482 | − | 0.314336i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.14828 | + | 5.28176i | 0.388673 | + | 0.224401i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.75237 | − | 2.74378i | 0.201545 | − | 0.116362i | ||||
\(557\) | − | 19.6054i | − | 0.830706i | −0.909660 | − | 0.415353i | \(-0.863658\pi\) | ||
0.909660 | − | 0.415353i | \(-0.136342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.0683i | − | 0.552728i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.72714 | + | 2.99149i | −0.0728548 | + | 0.126188i | ||||
\(563\) | −7.23796 | + | 12.5365i | −0.305044 | + | 0.528351i | −0.977271 | − | 0.211994i | \(-0.932004\pi\) |
0.672227 | + | 0.740345i | \(0.265338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.232406 | − | 0.134180i | 0.00977738 | − | 0.00564497i | ||||
\(566\) | −12.4714 | −0.524213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.7566 | 0.787011 | ||||||||
\(569\) | −6.70970 | + | 3.87385i | −0.281285 | + | 0.162400i | −0.634005 | − | 0.773329i | \(-0.718590\pi\) |
0.352720 | + | 0.935729i | \(0.385257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.06856 | + | 13.9752i | −0.337659 | + | 0.584842i | −0.983992 | − | 0.178213i | \(-0.942968\pi\) |
0.646333 | + | 0.763055i | \(0.276302\pi\) | |||||||
\(572\) | −4.48805 | + | 7.77353i | −0.187655 | + | 0.325027i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.3008i | 1.51385i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 12.1708i | − | 0.506679i | −0.967377 | − | 0.253339i | \(-0.918471\pi\) | ||
0.967377 | − | 0.253339i | \(-0.0815290\pi\) | |||||||
\(578\) | −8.77258 | + | 5.06485i | −0.364891 | + | 0.210670i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.155548 | + | 0.0898059i | 0.00645879 | + | 0.00372899i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.92897 | + | 10.2693i | 0.245553 | + | 0.425310i | ||||
\(584\) | −25.7659 | −1.06620 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 15.1727i | − | 0.626777i | ||||||
\(587\) | −16.8761 | − | 29.2302i | −0.696550 | − | 1.20646i | −0.969655 | − | 0.244476i | \(-0.921384\pi\) |
0.273106 | − | 0.961984i | \(-0.411949\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.47207 | + | 6.01380i | −0.143064 | + | 0.247794i | ||||
\(590\) | −0.0980610 | − | 0.0566155i | −0.00403711 | − | 0.00233082i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.91259 | + | 3.31270i | 0.0786069 | + | 0.136151i | ||||
\(593\) | −18.3025 | −0.751592 | −0.375796 | − | 0.926702i | \(-0.622631\pi\) | ||||
−0.375796 | + | 0.926702i | \(0.622631\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.4799 | + | 12.4015i | −0.879853 | + | 0.507983i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.5320 | − | 13.5862i | −0.962296 | − | 0.555582i | ||||
\(599\) | 34.1905 | + | 19.7399i | 1.39699 | + | 0.806551i | 0.994076 | − | 0.108689i | \(-0.0346651\pi\) |
0.402911 | + | 0.915239i | \(0.367998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.4865 | − | 19.9108i | 1.40673 | − | 0.812177i | 0.411661 | − | 0.911337i | \(-0.364949\pi\) |
0.995072 | + | 0.0991600i | \(0.0316155\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.39339 | 0.219454 | ||||||||
\(605\) | 0.140882 | + | 0.244015i | 0.00572766 | + | 0.00992060i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6104 | + | 12.4768i | 0.877140 | + | 0.506417i | 0.869714 | − | 0.493555i | \(-0.164303\pi\) |
0.00742570 | + | 0.999972i | \(0.497636\pi\) | |||||||
\(608\) | 6.02264 | − | 10.4315i | 0.244250 | − | 0.423054i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.0222776 | − | 0.0385859i | −0.000901992 | − | 0.00156230i | ||||
\(611\) | 61.2883i | 2.47946i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.0570 | 1.13321 | 0.566605 | − | 0.823990i | \(-0.308257\pi\) | ||||
0.566605 | + | 0.823990i | \(0.308257\pi\) | |||||||
\(614\) | 6.18876 | + | 10.7192i | 0.249758 | + | 0.432594i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.8093 | − | 17.2104i | −1.20008 | − | 0.692865i | −0.239506 | − | 0.970895i | \(-0.576985\pi\) |
−0.960573 | + | 0.278030i | \(0.910319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2889 | − | 9.98173i | 0.694898 | − | 0.401200i | −0.110546 | − | 0.993871i | \(-0.535260\pi\) |
0.805444 | + | 0.592671i | \(0.201927\pi\) | |||||||
\(620\) | − | 0.146391i | − | 0.00587920i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.6510i | 0.547354i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4940 | + | 21.6402i | −0.499760 | + | 0.865609i | ||||
\(626\) | 0.239503 | − | 0.414831i | 0.00957245 | − | 0.0165800i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.0690 | + | 12.7416i | −0.880650 | + | 0.508443i | ||||
\(629\) | 14.0417 | 0.559878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.8447 | −1.86486 | −0.932429 | − | 0.361354i | \(-0.882314\pi\) | ||||
−0.932429 | + | 0.361354i | \(0.882314\pi\) | |||||||
\(632\) | 31.9389 | − | 18.4399i | 1.27046 | − | 0.733501i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.28384 | + | 12.6160i | −0.289278 | + | 0.501044i | ||||
\(635\) | 0.0618862 | − | 0.107190i | 0.00245588 | − | 0.00425370i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.76475i | 0.109458i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.312103i | 0.0123370i | ||||||||
\(641\) | 3.34281 | − | 1.92997i | 0.132033 | − | 0.0762293i | −0.432529 | − | 0.901620i | \(-0.642379\pi\) |
0.564562 | + | 0.825391i | \(0.309045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.0233 | + | 17.9113i | 1.22344 | + | 0.706352i | 0.965649 | − | 0.259849i | \(-0.0836727\pi\) |
0.257789 | + | 0.966201i | \(0.417006\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.94734 | − | 6.83699i | −0.155306 | − | 0.268998i | ||||
\(647\) | −43.6492 | −1.71603 | −0.858013 | − | 0.513627i | \(-0.828301\pi\) | ||||
−0.858013 | + | 0.513627i | \(0.828301\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.15642i | 0.241661i | ||||||||
\(650\) | −9.35369 | − | 16.2011i | −0.366882 | − | 0.635458i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.07072 | + | 13.9789i | −0.316074 | + | 0.547456i | ||||
\(653\) | −6.45191 | − | 3.72501i | −0.252483 | − | 0.145771i | 0.368418 | − | 0.929660i | \(-0.379900\pi\) |
−0.620901 | + | 0.783889i | \(0.713233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0360114 | − | 0.0623736i | −0.00140708 | − | 0.00243714i | ||||
\(656\) | −10.9177 | −0.426264 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.52607 | − | 4.34518i | 0.293174 | − | 0.169264i | −0.346198 | − | 0.938161i | \(-0.612528\pi\) |
0.639372 | + | 0.768897i | \(0.279194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.9853 | + | 14.4253i | 0.971815 | + | 0.561077i | 0.899789 | − | 0.436325i | \(-0.143720\pi\) |
0.0720256 | + | 0.997403i | \(0.477054\pi\) | |||||||
\(662\) | 12.4653 | + | 7.19686i | 0.484479 | + | 0.279714i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.5871 | − | 7.26719i | 0.488476 | − | 0.282022i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.5623 | 1.14466 | ||||||||
\(668\) | −4.58724 | − | 7.94534i | −0.177486 | − | 0.307414i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.208097 | − | 0.120145i | −0.00803950 | − | 0.00464161i | ||||
\(671\) | −1.21124 | + | 2.09793i | −0.0467594 | + | 0.0809897i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.60695 | − | 6.24742i | −0.139038 | − | 0.240820i | 0.788095 | − | 0.615554i | \(-0.211068\pi\) |
−0.927133 | + | 0.374733i | \(0.877734\pi\) | |||||||
\(674\) | 16.8007i | 0.647139i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.1982 | −1.12301 | ||||||||
\(677\) | −18.1911 | − | 31.5079i | −0.699140 | − | 1.21095i | −0.968765 | − | 0.247980i | \(-0.920233\pi\) |
0.269626 | − | 0.962965i | \(-0.413100\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.329070 | + | 0.189989i | 0.0126193 | + | 0.00728573i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.95149 | − | 1.12669i | 0.0747265 | − | 0.0431433i | ||||
\(683\) | 23.7326i | 0.908101i | 0.890976 | + | 0.454050i | \(0.150021\pi\) | ||||
−0.890976 | + | 0.454050i | \(0.849979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.321118i | − | 0.0122693i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.79443 | + | 3.10804i | −0.0684119 | + | 0.118493i | ||||
\(689\) | −32.6707 | + | 56.5874i | −1.24466 | + | 2.15581i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.86127 | + | 1.65195i | −0.108848 | + | 0.0628433i | −0.553436 | − | 0.832892i | \(-0.686684\pi\) |
0.444588 | + | 0.895735i | \(0.353350\pi\) | |||||||
\(692\) | −7.58393 | −0.288298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.77718 | −0.143380 | ||||||||
\(695\) | −0.0862962 | + | 0.0498231i | −0.00327340 | + | 0.00188990i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0386 | + | 34.7079i | −0.759016 | + | 1.31465i | ||||
\(698\) | 3.71417 | − | 6.43313i | 0.140583 | − | 0.243498i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 0.873603i | − | 0.0329955i | −0.999864 | − | 0.0164978i | \(-0.994748\pi\) | ||
0.999864 | − | 0.0164978i | \(-0.00525164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.17461i | 0.195164i | ||||||||
\(704\) | −0.645868 | + | 0.372892i | −0.0243421 | + | 0.0140539i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.07845 | + | 4.66410i | 0.304037 | + | 0.175536i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.07767 | − | 13.9909i | −0.303363 | − | 0.525441i | 0.673532 | − | 0.739158i | \(-0.264776\pi\) |
−0.976896 | + | 0.213717i | \(0.931443\pi\) | |||||||
\(710\) | −0.149179 | −0.00559860 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.4905i | 1.06773i | ||||||||
\(713\) | −12.0473 | − | 20.8665i | −0.451174 | − | 0.781456i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0814965 | − | 0.141156i | 0.00304779 | − | 0.00527894i | ||||
\(716\) | −0.273546 | − | 0.157932i | −0.0102229 | − | 0.00590220i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.01498 | + | 15.6144i | 0.336436 | + | 0.582724i | ||||
\(719\) | 45.1905 | 1.68532 | 0.842661 | − | 0.538445i | \(-0.180988\pi\) | ||||
0.842661 | + | 0.538445i | \(0.180988\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.41110 | + | 4.85615i | −0.313029 | + | 0.180727i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.45395 | − | 4.88089i | −0.314189 | − | 0.181397i | ||||
\(725\) | 17.6260 | + | 10.1764i | 0.654613 | + | 0.377941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.15775 | + | 4.13253i | −0.265466 | + | 0.153267i | −0.626826 | − | 0.779160i | \(-0.715646\pi\) |
0.361359 | + | 0.932427i | \(0.382313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.204927 | 0.00758468 | ||||||||
\(731\) | 6.58709 | + | 11.4092i | 0.243632 | + | 0.421983i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.5799 | − | 6.10830i | −0.390777 | − | 0.225615i | 0.291720 | − | 0.956504i | \(-0.405773\pi\) |
−0.682497 | + | 0.730889i | \(0.739106\pi\) | |||||||
\(734\) | −2.28543 | + | 3.95849i | −0.0843569 | + | 0.146110i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.8972 | + | 36.1949i | 0.770280 | + | 1.33416i | ||||
\(737\) | 13.0647i | 0.481244i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.7072 | −0.761726 | −0.380863 | − | 0.924631i | \(-0.624373\pi\) | ||||
−0.380863 | + | 0.924631i | \(0.624373\pi\) | |||||||
\(740\) | −0.0545436 | − | 0.0944723i | −0.00200506 | − | 0.00347287i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2862 | − | 5.93873i | −0.377363 | − | 0.217871i | 0.299307 | − | 0.954157i | \(-0.403244\pi\) |
−0.676670 | + | 0.736286i | \(0.736578\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.390045 | − | 0.225192i | 0.0142901 | − | 0.00825041i | ||||
\(746\) | 0.164647i | 0.00602814i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 9.04885i | − | 0.330859i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.8554 | + | 20.5342i | −0.432610 | + | 0.749303i | −0.997097 | − | 0.0761390i | \(-0.975741\pi\) |
0.564487 | + | 0.825442i | \(0.309074\pi\) | |||||||
\(752\) | 8.41562 | − | 14.5763i | 0.306886 | − | 0.531542i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.1937 | + | 7.61738i | −0.480486 | + | 0.277409i | ||||
\(755\) | −0.0979362 | −0.00356426 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2494 | 1.60827 | 0.804136 | − | 0.594446i | \(-0.202628\pi\) | ||||
0.804136 | + | 0.594446i | \(0.202628\pi\) | |||||||
\(758\) | 5.13087 | − | 2.96231i | 0.186362 | − | 0.107596i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0700143 | + | 0.121268i | −0.00253969 | + | 0.00439887i | ||||
\(761\) | −24.3767 | + | 42.2217i | −0.883656 | + | 1.53054i | −0.0364098 | + | 0.999337i | \(0.511592\pi\) |
−0.847246 | + | 0.531200i | \(0.821741\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 21.5154i | − | 0.778401i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 0.217284i | − | 0.00785081i | ||||||
\(767\) | −29.3791 | + | 16.9620i | −1.06082 | + | 0.612463i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.3870 | + | 13.5025i | 0.843357 | + | 0.486912i | 0.858404 | − | 0.512975i | \(-0.171457\pi\) |
−0.0150472 | + | 0.999887i | \(0.504790\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.4268 | + | 28.4520i | 0.591213 | + | 1.02401i | ||||
\(773\) | 26.7135 | 0.960817 | 0.480408 | − | 0.877045i | \(-0.340488\pi\) | ||||
0.480408 | + | 0.877045i | \(0.340488\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 16.5883i | − | 0.595871i | ||||||
\(776\) | 9.24794 | + | 16.0179i | 0.331982 | + | 0.575009i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.19514 | + | 3.80209i | −0.0786994 | + | 0.136311i | ||||
\(779\) | −12.7905 | − | 7.38459i | −0.458267 | − | 0.264580i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.05547 | + | 7.02429i | 0.145116 | + | 0.251349i | ||||
\(782\) | 27.3927 | 0.979560 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.400742 | − | 0.231368i | 0.0143031 | − | 0.00825789i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.0093 | − | 23.6767i | −1.46182 | − | 0.843983i | −0.462726 | − | 0.886501i | \(-0.653129\pi\) |
−0.999096 | + | 0.0425177i | \(0.986462\pi\) | |||||||
\(788\) | 20.4749 | + | 11.8212i | 0.729388 | + | 0.421112i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.254023 | + | 0.146660i | −0.00903775 | + | 0.00521795i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.3487 | −0.474027 | ||||||||
\(794\) | −2.49462 | − | 4.32082i | −0.0885309 | − | 0.153340i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.0766 | + | 7.54980i | 0.463489 | + | 0.267596i | ||||
\(797\) | 4.42781 | − | 7.66919i | 0.156841 | − | 0.271657i | −0.776887 | − | 0.629640i | \(-0.783202\pi\) |
0.933728 | + | 0.357984i | \(0.116536\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.8925 | − | 53.5074i | −1.09290 | − | 1.89296i | ||||
\(800\) | 28.7741i | 1.01732i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.20808 | −0.148592 | ||||||||
\(803\) | −5.57098 | − | 9.64922i | −0.196596 | − | 0.340514i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.7534 | + | 6.20848i | 0.378772 | + | 0.218684i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.929170 | + | 0.536456i | −0.0326881 | + | 0.0188725i | ||||
\(809\) | 7.40014i | 0.260175i | 0.991503 | + | 0.130087i | \(0.0415258\pi\) | ||||
−0.991503 | + | 0.130087i | \(0.958474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.0843i | − | 0.880829i | −0.897794 | − | 0.440415i | \(-0.854831\pi\) | ||
0.897794 | − | 0.440415i | \(-0.145169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.839587 | − | 1.45421i | 0.0294275 | − | 0.0509699i | ||||
\(815\) | 0.146553 | − | 0.253836i | 0.00513351 | − | 0.00889150i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.20449 | + | 2.42746i | −0.147096 | + | 0.0849262i | ||||
\(818\) | 22.2483 | 0.777893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.311353 | 0.0108729 | ||||||||
\(821\) | −18.3781 | + | 10.6106i | −0.641401 | + | 0.370313i | −0.785154 | − | 0.619300i | \(-0.787416\pi\) |
0.143753 | + | 0.989614i | \(0.454083\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.47690 | + | 14.6824i | −0.295486 | + | 0.511797i | −0.975098 | − | 0.221775i | \(-0.928815\pi\) |
0.679612 | + | 0.733572i | \(0.262148\pi\) | |||||||
\(824\) | −6.25546 | + | 10.8348i | −0.217919 | + | 0.377447i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3052i | 0.879949i | 0.898010 | + | 0.439975i | \(0.145013\pi\) | ||||
−0.898010 | + | 0.439975i | \(0.854987\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 41.5277i | − | 1.44232i | −0.692770 | − | 0.721158i | \(-0.743610\pi\) | ||
0.692770 | − | 0.721158i | \(-0.256390\pi\) | |||||||
\(830\) | −0.100111 | + | 0.0577990i | −0.00347490 | + | 0.00200623i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.55896 | − | 2.05477i | −0.123385 | − | 0.0712362i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0832977 | + | 0.144276i | 0.00288264 | + | 0.00499287i | ||||
\(836\) | 3.33467 | 0.115332 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 1.19103i | − | 0.0411434i | ||||||
\(839\) | −6.61780 | − | 11.4624i | −0.228472 | − | 0.395725i | 0.728884 | − | 0.684638i | \(-0.240040\pi\) |
−0.957355 | + | 0.288913i | \(0.906706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.21265 | + | 10.7606i | −0.214229 | + | 0.371056i | ||||
\(842\) | −2.18914 | − | 1.26390i | −0.0754428 | − | 0.0435569i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.0036 | − | 19.0588i | −0.378759 | − | 0.656030i | ||||
\(845\) | 0.530197 | 0.0182393 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.5403 | − | 8.97217i | 0.533654 | − | 0.308106i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.3324 | + | 9.42951i | 0.560196 | + | 0.323429i | ||||
\(851\) | −15.5492 | − | 8.97735i | −0.533020 | − | 0.307739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3814 | + | 8.88048i | −0.526651 | + | 0.304062i | −0.739651 | − | 0.672990i | \(-0.765010\pi\) |
0.213001 | + | 0.977052i | \(0.431676\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.4360 | −0.732669 | ||||||||
\(857\) | −9.17157 | − | 15.8856i | −0.313295 | − | 0.542643i | 0.665779 | − | 0.746149i | \(-0.268100\pi\) |
−0.979074 | + | 0.203507i | \(0.934766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.69126 | − | 1.55380i | −0.0918246 | − | 0.0530150i | 0.453385 | − | 0.891315i | \(-0.350216\pi\) |
−0.545209 | + | 0.838300i | \(0.683550\pi\) | |||||||
\(860\) | 0.0511739 | − | 0.0886358i | 0.00174502 | − | 0.00302246i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.441616 | − | 0.764902i | −0.0150415 | − | 0.0260527i | ||||
\(863\) | − | 41.4060i | − | 1.40948i | −0.709467 | − | 0.704739i | \(-0.751064\pi\) | ||
0.709467 | − | 0.704739i | \(-0.248936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.137713 | 0.00468239 | ||||||||
\(866\) | −12.4321 | − | 21.5330i | −0.422458 | − | 0.731720i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.8114 | + | 7.97399i | 0.468518 | + | 0.270499i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62.3460 | + | 35.9955i | −2.11251 | + | 1.21966i | ||||
\(872\) | − | 11.1826i | − | 0.378689i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.0947i | 0.341459i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3979 | − | 19.7417i | 0.384878 | − | 0.666628i | −0.606874 | − | 0.794798i | \(-0.707577\pi\) |
0.991752 | + | 0.128170i | \(0.0409102\pi\) | |||||||
\(878\) | 7.88482 | − | 13.6569i | 0.266100 | − | 0.460898i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0387648 | + | 0.0223809i | −0.00130676 | + | 0.000754460i | ||||
\(881\) | 43.4050 | 1.46235 | 0.731175 | − | 0.682190i | \(-0.238972\pi\) | ||||
0.731175 | + | 0.682190i | \(0.238972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.9309 | −1.00725 | −0.503627 | − | 0.863921i | \(-0.668001\pi\) | ||||
−0.503627 | + | 0.863921i | \(0.668001\pi\) | |||||||
\(884\) | 43.1820 | − | 24.9312i | 1.45237 | − | 0.838526i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.73682 | − | 6.47236i | 0.125541 | − | 0.217443i | ||||
\(887\) | −19.4788 | + | 33.7382i | −0.654033 | + | 1.13282i | 0.328102 | + | 0.944642i | \(0.393591\pi\) |
−0.982135 | + | 0.188176i | \(0.939742\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 0.226597i | − | 0.00759556i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.65757i | 0.155947i | ||||||||
\(893\) | 19.7185 | − | 11.3845i | 0.659853 | − | 0.380966i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.00496721 | + | 0.00286782i | 0.000166035 | + | 9.58606e-5i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.78138 | + | 8.28160i | 0.159557 | + | 0.276361i | ||||
\(899\) | −13.5091 | −0.450553 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 65.8711i | − | 2.19448i | ||||||
\(902\) | 2.39632 | + | 4.15054i | 0.0797886 | + | 0.138198i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2071 | − | 19.4113i | 0.372743 | − | 0.645611i | ||||
\(905\) | 0.153512 | + | 0.0886299i | 0.00510290 | + | 0.00294616i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0526 | + | 24.3399i | 0.466610 | + | 0.808192i | 0.999273 | − | 0.0381355i | \(-0.0121419\pi\) |
−0.532663 | + | 0.846328i | \(0.678809\pi\) | |||||||
\(908\) | 44.8493 | 1.48837 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.3883 | + | 18.6994i | −1.07307 | + | 0.619538i | −0.929019 | − | 0.370032i | \(-0.879347\pi\) |
−0.144052 | + | 0.989570i | \(0.546013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.44307 | + | 3.14256i | 0.180139 | + | 0.104003i | ||||
\(914\) | −11.8666 | − | 6.85121i | −0.392513 | − | 0.226618i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.9616 | + | 6.90601i | −0.395221 | + | 0.228181i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.8230 | −0.851822 | −0.425911 | − | 0.904765i | \(-0.640046\pi\) | ||||
−0.425911 | + | 0.904765i | \(0.640046\pi\) | |||||||
\(920\) | −0.242933 | − | 0.420773i | −0.00800928 | − | 0.0138725i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.957884 | − | 0.553034i | −0.0315462 | − | 0.0182132i | ||||
\(923\) | −22.3471 | + | 38.7063i | −0.735563 | + | 1.27403i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.18063 | − | 10.7052i | −0.203218 | − | 0.351983i | ||||
\(926\) | 0.802704i | 0.0263785i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.4328 | 0.769220 | ||||||||
\(929\) | −7.97094 | − | 13.8061i | −0.261518 | − | 0.452963i | 0.705127 | − | 0.709081i | \(-0.250890\pi\) |
−0.966646 | + | 0.256118i | \(0.917556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.4246 | + | 10.0601i | 0.570762 | + | 0.329529i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.31568 | + | 3.06901i | −0.173934 | + | 0.100421i | ||||
\(935\) | 0.164314i | 0.00537364i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0698i | 0.492308i | 0.969231 | + | 0.246154i | \(0.0791668\pi\) | ||||
−0.969231 | + | 0.246154i | \(0.920833\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.239999 | + | 0.415690i | −0.00782789 | + | 0.0135583i | ||||
\(941\) | −5.76861 | + | 9.99152i | −0.188051 | + | 0.325714i | −0.944600 | − | 0.328222i | \(-0.893550\pi\) |
0.756549 | + | 0.653937i | \(0.226884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.3800 | − | 25.6228i | 1.44521 | − | 0.834393i | ||||
\(944\) | 9.31636 | 0.303222 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.57543 | 0.0512218 | ||||||||
\(947\) | 24.5364 | − | 14.1661i | 0.797325 | − | 0.460336i | −0.0452102 | − | 0.998977i | \(-0.514396\pi\) |
0.842535 | + | 0.538642i | \(0.181062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.6981 | − | 53.1706i | 0.996501 | − | 1.72599i | ||||
\(950\) | −3.47495 | + | 6.01879i | −0.112742 | + | 0.195275i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 29.8498i | − | 0.966931i | −0.875364 | − | 0.483465i | \(-0.839378\pi\) | ||
0.875364 | − | 0.483465i | \(-0.160622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.390689i | 0.0126424i | ||||||||
\(956\) | −7.57084 | + | 4.37102i | −0.244858 | + | 0.141369i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.0935 | − | 5.82748i | −0.326106 | − | 0.188277i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.99478 | − | 17.3115i | −0.322412 | − | 0.558434i | ||||
\(962\) | 9.25283 | 0.298323 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.1252i | 0.551564i | ||||||||
\(965\) | −0.298287 | − | 0.516648i | −0.00960219 | − | 0.0166315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.17864 | − | 14.1658i | 0.263007 | − | 0.455542i | −0.704032 | − | 0.710168i | \(-0.748619\pi\) |
0.967040 | + | 0.254626i | \(0.0819523\pi\) | |||||||
\(968\) | 20.3809 | + | 11.7669i | 0.655068 | + | 0.378203i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.0735528 | − | 0.127397i | −0.00236164 | − | 0.00409048i | ||||
\(971\) | −21.4630 | −0.688779 | −0.344390 | − | 0.938827i | \(-0.611914\pi\) | ||||
−0.344390 | + | 0.938827i | \(0.611914\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.8470 | − | 14.3454i | 0.796148 | − | 0.459657i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.17475 | + | 1.83294i | 0.101621 | + | 0.0586710i | ||||
\(977\) | 18.6219 | + | 10.7513i | 0.595766 | + | 0.343966i | 0.767374 | − | 0.641199i | \(-0.221563\pi\) |
−0.171608 | + | 0.985165i | \(0.554896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6696 | + | 6.16010i | −0.341002 | + | 0.196878i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.6460 | 0.563107 | ||||||||
\(983\) | 12.7097 | + | 22.0138i | 0.405376 | + | 0.702131i | 0.994365 | − | 0.106009i | \(-0.0338073\pi\) |
−0.588989 | + | 0.808141i | \(0.700474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.371794 | − | 0.214656i | −0.0118464 | − | 0.00683949i | ||||
\(986\) | 7.67912 | − | 13.3006i | 0.244553 | − | 0.423578i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.18759 | + | 15.9134i | 0.292296 | + | 0.506272i | ||||
\(989\) | − | 16.8455i | − | 0.535654i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7537 | 0.754560 | 0.377280 | − | 0.926099i | \(-0.376859\pi\) | ||||
0.377280 | + | 0.926099i | \(0.376859\pi\) | |||||||
\(992\) | −9.54935 | − | 16.5400i | −0.303192 | − | 0.525144i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.237453 | − | 0.137093i | −0.00752776 | − | 0.00434615i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5366 | − | 6.08329i | 0.333697 | − | 0.192660i | −0.323785 | − | 0.946131i | \(-0.604955\pi\) |
0.657481 | + | 0.753471i | \(0.271622\pi\) | |||||||
\(998\) | − | 3.53086i | − | 0.111767i | ||||||
\(999\) | 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 | 1323.2.o.e.881.10 | 48 | ||
3.2 | odd | 2 | 441.2.o.e.293.16 | yes | 48 | ||
7.2 | even | 3 | 1323.2.s.d.962.16 | 48 | |||
7.3 | odd | 6 | 1323.2.i.d.1097.9 | 48 | |||
7.4 | even | 3 | 1323.2.i.d.1097.10 | 48 | |||
7.5 | odd | 6 | 1323.2.s.d.962.15 | 48 | |||
7.6 | odd | 2 | inner | 1323.2.o.e.881.9 | 48 | ||
9.2 | odd | 6 | inner | 1323.2.o.e.440.9 | 48 | ||
9.7 | even | 3 | 441.2.o.e.146.15 | ✓ | 48 | ||
21.2 | odd | 6 | 441.2.s.d.374.9 | 48 | |||
21.5 | even | 6 | 441.2.s.d.374.10 | 48 | |||
21.11 | odd | 6 | 441.2.i.d.68.15 | 48 | |||
21.17 | even | 6 | 441.2.i.d.68.16 | 48 | |||
21.20 | even | 2 | 441.2.o.e.293.15 | yes | 48 | ||
63.2 | odd | 6 | 1323.2.i.d.521.9 | 48 | |||
63.11 | odd | 6 | 1323.2.s.d.656.15 | 48 | |||
63.16 | even | 3 | 441.2.i.d.227.10 | 48 | |||
63.20 | even | 6 | inner | 1323.2.o.e.440.10 | 48 | ||
63.25 | even | 3 | 441.2.s.d.362.10 | 48 | |||
63.34 | odd | 6 | 441.2.o.e.146.16 | yes | 48 | ||
63.38 | even | 6 | 1323.2.s.d.656.16 | 48 | |||
63.47 | even | 6 | 1323.2.i.d.521.10 | 48 | |||
63.52 | odd | 6 | 441.2.s.d.362.9 | 48 | |||
63.61 | odd | 6 | 441.2.i.d.227.9 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.15 | 48 | 21.11 | odd | 6 | |||
441.2.i.d.68.16 | 48 | 21.17 | even | 6 | |||
441.2.i.d.227.9 | 48 | 63.61 | odd | 6 | |||
441.2.i.d.227.10 | 48 | 63.16 | even | 3 | |||
441.2.o.e.146.15 | ✓ | 48 | 9.7 | even | 3 | ||
441.2.o.e.146.16 | yes | 48 | 63.34 | odd | 6 | ||
441.2.o.e.293.15 | yes | 48 | 21.20 | even | 2 | ||
441.2.o.e.293.16 | yes | 48 | 3.2 | odd | 2 | ||
441.2.s.d.362.9 | 48 | 63.52 | odd | 6 | |||
441.2.s.d.362.10 | 48 | 63.25 | even | 3 | |||
441.2.s.d.374.9 | 48 | 21.2 | odd | 6 | |||
441.2.s.d.374.10 | 48 | 21.5 | even | 6 | |||
1323.2.i.d.521.9 | 48 | 63.2 | odd | 6 | |||
1323.2.i.d.521.10 | 48 | 63.47 | even | 6 | |||
1323.2.i.d.1097.9 | 48 | 7.3 | odd | 6 | |||
1323.2.i.d.1097.10 | 48 | 7.4 | even | 3 | |||
1323.2.o.e.440.9 | 48 | 9.2 | odd | 6 | inner | ||
1323.2.o.e.440.10 | 48 | 63.20 | even | 6 | inner | ||
1323.2.o.e.881.9 | 48 | 7.6 | odd | 2 | inner | ||
1323.2.o.e.881.10 | 48 | 1.1 | even | 1 | trivial | ||
1323.2.s.d.656.15 | 48 | 63.11 | odd | 6 | |||
1323.2.s.d.656.16 | 48 | 63.38 | even | 6 | |||
1323.2.s.d.962.15 | 48 | 7.5 | odd | 6 | |||
1323.2.s.d.962.16 | 48 | 7.2 | even | 3 |