Properties

Label 1323.2.s.d.656.15
Level $1323$
Weight $2$
Character 1323.656
Analytic conductor $10.564$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(656,1323)]
 
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, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.656");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.s (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 656.15
Character \(\chi\) \(=\) 1323.656
Dual form 1323.2.s.d.962.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.575298 - 0.332148i) q^{2} +(-0.779355 + 1.34988i) q^{4} +0.0283039 q^{5} +2.36404i q^{8} +O(q^{10})\) \(q+(0.575298 - 0.332148i) q^{2} +(-0.779355 + 1.34988i) q^{4} +0.0283039 q^{5} +2.36404i q^{8} +(0.0162832 - 0.00940110i) q^{10} -1.02228i q^{11} +(-4.87844 + 2.81657i) q^{13} +(-0.773498 - 1.33974i) q^{16} +(-2.83940 - 4.91798i) q^{17} +(1.81237 + 1.04637i) q^{19} +(-0.0220588 + 0.0382070i) q^{20} +(-0.339550 - 0.588118i) q^{22} +7.26133i q^{23} -4.99920 q^{25} +(-1.87104 + 3.24073i) q^{26} +(3.52577 + 2.03560i) q^{29} +(-2.87364 - 1.65910i) q^{31} +(-4.98462 - 2.87787i) q^{32} +(-3.26700 - 1.88620i) q^{34} +(1.23632 - 2.14137i) q^{37} +1.39020 q^{38} +0.0669116i q^{40} +(-3.52867 - 6.11183i) q^{41} +(-1.15994 + 2.00908i) q^{43} +(1.37996 + 0.796722i) q^{44} +(2.41184 + 4.17742i) q^{46} +(-5.43997 - 9.42231i) q^{47} +(-2.87603 + 1.66048i) q^{50} -8.78043i q^{52} +(-10.0454 + 5.79973i) q^{53} -0.0289346i q^{55} +2.70449 q^{58} +(3.01111 - 5.21540i) q^{59} +(-2.05220 + 1.18484i) q^{61} -2.20427 q^{62} -0.729528 q^{64} +(-0.138079 + 0.0797200i) q^{65} +(-6.38995 + 11.0677i) q^{67} +8.85160 q^{68} -7.93415i q^{71} +(-9.43889 + 5.44955i) q^{73} -1.64257i q^{74} +(-2.82496 + 1.63099i) q^{76} +(7.80018 + 13.5103i) q^{79} +(-0.0218930 - 0.0379198i) q^{80} +(-4.06007 - 2.34408i) q^{82} +(-3.07406 + 5.32442i) q^{83} +(-0.0803661 - 0.139198i) q^{85} +1.54109i q^{86} +2.41672 q^{88} +(-6.02582 + 10.4370i) q^{89} +(-9.80194 - 5.65915i) q^{92} +(-6.25921 - 3.61376i) q^{94} +(0.0512971 + 0.0296164i) q^{95} +(6.77565 + 3.91192i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 24 q^{4} - 24 q^{16} + 48 q^{25} + 120 q^{32} - 96 q^{44} - 48 q^{50} - 48 q^{53} - 48 q^{64} + 120 q^{65} - 24 q^{79} - 24 q^{85} + 144 q^{92} + 96 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.575298 0.332148i 0.406797 0.234864i −0.282616 0.959233i \(-0.591202\pi\)
0.689413 + 0.724369i \(0.257869\pi\)
\(3\) 0 0
\(4\) −0.779355 + 1.34988i −0.389677 + 0.674941i
\(5\) 0.0283039 0.0126579 0.00632895 0.999980i \(-0.497985\pi\)
0.00632895 + 0.999980i \(0.497985\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.36404i 0.835814i
\(9\) 0 0
\(10\) 0.0162832 0.00940110i 0.00514919 0.00297289i
\(11\) 1.02228i 0.308230i −0.988053 0.154115i \(-0.950747\pi\)
0.988053 0.154115i \(-0.0492526\pi\)
\(12\) 0 0
\(13\) −4.87844 + 2.81657i −1.35304 + 0.781176i −0.988674 0.150081i \(-0.952047\pi\)
−0.364363 + 0.931257i \(0.618713\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.773498 1.33974i −0.193375 0.334935i
\(17\) −2.83940 4.91798i −0.688656 1.19279i −0.972273 0.233849i \(-0.924868\pi\)
0.283617 0.958938i \(-0.408465\pi\)
\(18\) 0 0
\(19\) 1.81237 + 1.04637i 0.415786 + 0.240054i 0.693273 0.720675i \(-0.256168\pi\)
−0.277487 + 0.960729i \(0.589502\pi\)
\(20\) −0.0220588 + 0.0382070i −0.00493250 + 0.00854334i
\(21\) 0 0
\(22\) −0.339550 0.588118i −0.0723923 0.125387i
\(23\) 7.26133i 1.51409i 0.653362 + 0.757046i \(0.273358\pi\)
−0.653362 + 0.757046i \(0.726642\pi\)
\(24\) 0 0
\(25\) −4.99920 −0.999840
\(26\) −1.87104 + 3.24073i −0.366941 + 0.635560i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.52577 + 2.03560i 0.654718 + 0.378002i 0.790262 0.612770i \(-0.209945\pi\)
−0.135543 + 0.990771i \(0.543278\pi\)
\(30\) 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
\(37\) 1.23632 2.14137i 0.203250 0.352040i −0.746324 0.665583i \(-0.768183\pi\)
0.949574 + 0.313543i \(0.101516\pi\)
\(38\) 1.39020 0.225520
\(39\) 0 0
\(40\) 0.0669116i 0.0105796i
\(41\) −3.52867 6.11183i −0.551085 0.954508i −0.998197 0.0600295i \(-0.980881\pi\)
0.447111 0.894478i \(-0.352453\pi\)
\(42\) 0 0
\(43\) −1.15994 + 2.00908i −0.176890 + 0.306382i −0.940814 0.338924i \(-0.889937\pi\)
0.763924 + 0.645306i \(0.223270\pi\)
\(44\) 1.37996 + 0.796722i 0.208037 + 0.120110i
\(45\) 0 0
\(46\) 2.41184 + 4.17742i 0.355606 + 0.615928i
\(47\) −5.43997 9.42231i −0.793502 1.37439i −0.923786 0.382908i \(-0.874922\pi\)
0.130285 0.991477i \(-0.458411\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.87603 + 1.66048i −0.406732 + 0.234827i
\(51\) 0 0
\(52\) 8.78043i 1.21763i
\(53\) −10.0454 + 5.79973i −1.37985 + 0.796655i −0.992141 0.125128i \(-0.960066\pi\)
−0.387706 + 0.921783i \(0.626732\pi\)
\(54\) 0 0
\(55\) 0.0289346i 0.00390155i
\(56\) 0 0
\(57\) 0 0
\(58\) 2.70449 0.355117
\(59\) 3.01111 5.21540i 0.392013 0.678987i −0.600702 0.799473i \(-0.705112\pi\)
0.992715 + 0.120486i \(0.0384454\pi\)
\(60\) 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 \(0.881552\pi\)
\(68\) 8.85160 1.07341
\(69\) 0 0
\(70\) 0 0
\(71\) 7.93415i 0.941610i −0.882237 0.470805i \(-0.843964\pi\)
0.882237 0.470805i \(-0.156036\pi\)
\(72\) 0 0
\(73\) −9.43889 + 5.44955i −1.10474 + 0.637821i −0.937462 0.348089i \(-0.886831\pi\)
−0.167277 + 0.985910i \(0.553497\pi\)
\(74\) 1.64257i 0.190945i
\(75\) 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 \(0.492484\pi\)
\(80\) −0.0218930 0.0379198i −0.00244772 0.00423957i
\(81\) 0 0
\(82\) −4.06007 2.34408i −0.448360 0.258861i
\(83\) −3.07406 + 5.32442i −0.337421 + 0.584431i −0.983947 0.178461i \(-0.942888\pi\)
0.646526 + 0.762892i \(0.276221\pi\)
\(84\) 0 0
\(85\) −0.0803661 0.139198i −0.00871693 0.0150982i
\(86\) 1.54109i 0.166180i
\(87\) 0 0
\(88\) 2.41672 0.257623
\(89\) −6.02582 + 10.4370i −0.638736 + 1.10632i 0.346975 + 0.937874i \(0.387209\pi\)
−0.985711 + 0.168448i \(0.946124\pi\)
\(90\) 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 \(-0.203317\pi\)
−0.114885 + 0.993379i \(0.536650\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 3.89615 6.74833i 0.389615 0.674833i
\(101\) −0.453847 −0.0451595 −0.0225797 0.999745i \(-0.507188\pi\)
−0.0225797 + 0.999745i \(0.507188\pi\)
\(102\) 0 0
\(103\) 5.29218i 0.521454i 0.965413 + 0.260727i \(0.0839622\pi\)
−0.965413 + 0.260727i \(0.916038\pi\)
\(104\) −6.65848 11.5328i −0.652918 1.13089i
\(105\) 0 0
\(106\) −3.85274 + 6.67315i −0.374212 + 0.648153i
\(107\) −7.85273 4.53377i −0.759152 0.438296i 0.0698394 0.997558i \(-0.477751\pi\)
−0.828991 + 0.559262i \(0.811085\pi\)
\(108\) 0 0
\(109\) −2.36514 4.09654i −0.226539 0.392377i 0.730241 0.683190i \(-0.239408\pi\)
−0.956780 + 0.290812i \(0.906074\pi\)
\(110\) −0.00961059 0.0166460i −0.000916334 0.00158714i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.21108 4.74067i 0.772433 0.445965i −0.0613086 0.998119i \(-0.519527\pi\)
0.833742 + 0.552154i \(0.186194\pi\)
\(114\) 0 0
\(115\) 0.205524i 0.0191652i
\(116\) −5.49565 + 3.17291i −0.510258 + 0.294598i
\(117\) 0 0
\(118\) 4.00054i 0.368280i
\(119\) 0 0
\(120\) 0 0
\(121\) 9.95494 0.904994
\(122\) −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
\(131\) 2.54463 0.222325 0.111162 0.993802i \(-0.464543\pi\)
0.111162 + 0.993802i \(0.464543\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.48964i 0.733393i
\(135\) 0 0
\(136\) 11.6263 6.71245i 0.996948 0.575588i
\(137\) 11.3453i 0.969298i −0.874709 0.484649i \(-0.838947\pi\)
0.874709 0.484649i \(-0.161053\pi\)
\(138\) 0 0
\(139\) 3.04891 1.76029i 0.258605 0.149306i −0.365093 0.930971i \(-0.618963\pi\)
0.623698 + 0.781665i \(0.285629\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.63531 4.56450i −0.221151 0.383044i
\(143\) 2.87933 + 4.98715i 0.240782 + 0.417047i
\(144\) 0 0
\(145\) 0.0997930 + 0.0576155i 0.00828736 + 0.00478471i
\(146\) −3.62012 + 6.27022i −0.299603 + 0.518927i
\(147\) 0 0
\(148\) 1.92707 + 3.33778i 0.158404 + 0.274364i
\(149\) 15.9125i 1.30360i 0.758391 + 0.651800i \(0.225986\pi\)
−0.758391 + 0.651800i \(0.774014\pi\)
\(150\) 0 0
\(151\) 3.46016 0.281584 0.140792 0.990039i \(-0.455035\pi\)
0.140792 + 0.990039i \(0.455035\pi\)
\(152\) −2.47366 + 4.28451i −0.200640 + 0.347520i
\(153\) 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
\(163\) −5.17782 + 8.96824i −0.405558 + 0.702447i −0.994386 0.105811i \(-0.966256\pi\)
0.588828 + 0.808258i \(0.299589\pi\)
\(164\) 11.0003 0.858982
\(165\) 0 0
\(166\) 4.08417i 0.316993i
\(167\) 2.94297 + 5.09738i 0.227734 + 0.394447i 0.957136 0.289638i \(-0.0935349\pi\)
−0.729402 + 0.684085i \(0.760202\pi\)
\(168\) 0 0
\(169\) 9.36614 16.2226i 0.720473 1.24790i
\(170\) −0.0924689 0.0533870i −0.00709204 0.00409459i
\(171\) 0 0
\(172\) −1.80802 3.13157i −0.137860 0.238780i
\(173\) −2.43276 4.21366i −0.184959 0.320359i 0.758604 0.651552i \(-0.225882\pi\)
−0.943563 + 0.331194i \(0.892549\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.36959 + 0.790735i −0.103237 + 0.0596039i
\(177\) 0 0
\(178\) 8.00586i 0.600065i
\(179\) −0.175495 + 0.101322i −0.0131171 + 0.00757319i −0.506544 0.862214i \(-0.669077\pi\)
0.493427 + 0.869787i \(0.335744\pi\)
\(180\) 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
\(184\) −17.1661 −1.26550
\(185\) 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 −0.000706698 1.00000i \(-0.500225\pi\)
0.865672 + 0.500612i \(0.166892\pi\)
\(192\) 0 0
\(193\) 10.5387 18.2536i 0.758593 1.31392i −0.184976 0.982743i \(-0.559221\pi\)
0.943568 0.331178i \(-0.107446\pi\)
\(194\) 5.19736 0.373148
\(195\) 0 0
\(196\) 0 0
\(197\) 15.1679i 1.08067i 0.841451 + 0.540334i \(0.181702\pi\)
−0.841451 + 0.540334i \(0.818298\pi\)
\(198\) 0 0
\(199\) −8.38940 + 4.84362i −0.594709 + 0.343355i −0.766957 0.641698i \(-0.778230\pi\)
0.172249 + 0.985054i \(0.444897\pi\)
\(200\) 11.8183i 0.835680i
\(201\) 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
\(206\) 1.75779 + 3.04458i 0.122471 + 0.212126i
\(207\) 0 0
\(208\) 7.54694 + 4.35723i 0.523286 + 0.302119i
\(209\) 1.06969 1.85275i 0.0739919 0.128158i
\(210\) 0 0
\(211\) −7.05942 12.2273i −0.485991 0.841761i 0.513880 0.857862i \(-0.328208\pi\)
−0.999870 + 0.0161017i \(0.994874\pi\)
\(212\) 18.0802i 1.24175i
\(213\) 0 0
\(214\) −6.02354 −0.411761
\(215\) −0.0328309 + 0.0568649i −0.00223905 + 0.00387815i
\(216\) 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 \(-0.365233\pi\)
−0.584136 + 0.811656i \(0.698567\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3.14921 5.45459i 0.209482 0.362834i
\(227\) −28.7733 −1.90975 −0.954876 0.297005i \(-0.904012\pi\)
−0.954876 + 0.297005i \(0.904012\pi\)
\(228\) 0 0
\(229\) 8.86119i 0.585564i −0.956179 0.292782i \(-0.905419\pi\)
0.956179 0.292782i \(-0.0945810\pi\)
\(230\) 0.0682645 + 0.118238i 0.00450122 + 0.00779635i
\(231\) 0 0
\(232\) −4.81224 + 8.33505i −0.315939 + 0.547223i
\(233\) −11.1789 6.45412i −0.732351 0.422823i 0.0869305 0.996214i \(-0.472294\pi\)
−0.819282 + 0.573391i \(0.805628\pi\)
\(234\) 0 0
\(235\) −0.153973 0.266688i −0.0100441 0.0173968i
\(236\) 4.69345 + 8.12929i 0.305518 + 0.529172i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.85712 2.80426i 0.314181 0.181392i −0.334615 0.942355i \(-0.608606\pi\)
0.648796 + 0.760963i \(0.275273\pi\)
\(240\) 0 0
\(241\) 10.9868i 0.707719i 0.935299 + 0.353860i \(0.115131\pi\)
−0.935299 + 0.353860i \(0.884869\pi\)
\(242\) 5.72705 3.30652i 0.368149 0.212551i
\(243\) 0 0
\(244\) 3.69364i 0.236461i
\(245\) 0 0
\(246\) 0 0
\(247\) −11.7887 −0.750098
\(248\) 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 \(-0.222984\pi\)
0.764505 + 0.644618i \(0.222984\pi\)
\(252\) 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
\(257\) 17.7228 1.10552 0.552760 0.833340i \(-0.313575\pi\)
0.552760 + 0.833340i \(0.313575\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.248521i 0.0154126i
\(261\) 0 0
\(262\) 1.46392 0.845193i 0.0904411 0.0522162i
\(263\) 2.89866i 0.178739i 0.995999 + 0.0893695i \(0.0284852\pi\)
−0.995999 + 0.0893695i \(0.971515\pi\)
\(264\) 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
\(269\) 10.9469 + 18.9606i 0.667444 + 1.15605i 0.978616 + 0.205694i \(0.0659451\pi\)
−0.311172 + 0.950354i \(0.600722\pi\)
\(270\) 0 0
\(271\) −7.77992 4.49174i −0.472596 0.272854i 0.244730 0.969591i \(-0.421301\pi\)
−0.717326 + 0.696738i \(0.754634\pi\)
\(272\) −4.39254 + 7.60811i −0.266337 + 0.461309i
\(273\) 0 0
\(274\) −3.76834 6.52695i −0.227654 0.394308i
\(275\) 5.11060i 0.308181i
\(276\) 0 0
\(277\) 15.9018 0.955448 0.477724 0.878510i \(-0.341462\pi\)
0.477724 + 0.878510i \(0.341462\pi\)
\(278\) 1.16936 2.02538i 0.0701333 0.121474i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.50324 + 2.59995i 0.268641 + 0.155100i 0.628270 0.777996i \(-0.283763\pi\)
−0.359629 + 0.933095i \(0.617097\pi\)
\(282\) 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
\(289\) −7.62438 + 13.2058i −0.448493 + 0.776813i
\(290\) 0.0765476 0.00449503
\(291\) 0 0
\(292\) 16.9885i 0.994178i
\(293\) 11.4201 + 19.7802i 0.667169 + 1.15557i 0.978692 + 0.205332i \(0.0658274\pi\)
−0.311523 + 0.950238i \(0.600839\pi\)
\(294\) 0 0
\(295\) 0.0852263 0.147616i 0.00496206 0.00859455i
\(296\) 5.06229 + 2.92272i 0.294240 + 0.169879i
\(297\) 0 0
\(298\) 5.28530 + 9.15440i 0.306169 + 0.530300i
\(299\) −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
\(304\) 3.23746i 0.185681i
\(305\) −0.0580853 + 0.0335356i −0.00332596 + 0.00192024i
\(306\) 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
\(310\) −0.0623894 −0.00354348
\(311\) −10.2747 + 17.7964i −0.582628 + 1.00914i 0.412539 + 0.910940i \(0.364642\pi\)
−0.995167 + 0.0982007i \(0.968691\pi\)
\(312\) 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 −0.927269 0.374396i \(-0.877850\pi\)
−0.139398 + 0.990236i \(0.544517\pi\)
\(318\) 0 0
\(319\) 2.08096 3.60433i 0.116512 0.201804i
\(320\) −0.0206485 −0.00115429
\(321\) 0 0
\(322\) 0 0
\(323\) 11.8843i 0.661258i
\(324\) 0 0
\(325\) 24.3883 14.0806i 1.35282 0.781051i
\(326\) 6.87921i 0.381004i
\(327\) 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 \(-0.369705\pi\)
\(332\) −4.79156 8.29923i −0.262971 0.455479i
\(333\) 0 0
\(334\) 3.38617 + 1.95501i 0.185283 + 0.106973i
\(335\) −0.180861 + 0.313260i −0.00988147 + 0.0171152i
\(336\) 0 0
\(337\) 12.6455 + 21.9026i 0.688844 + 1.19311i 0.972212 + 0.234101i \(0.0752147\pi\)
−0.283369 + 0.959011i \(0.591452\pi\)
\(338\) 12.4438i 0.676853i
\(339\) 0 0
\(340\) 0.250535 0.0135872
\(341\) −1.69607 + 2.93768i −0.0918474 + 0.159084i
\(342\) 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 0.361970 0.932190i \(-0.382104\pi\)
−0.626315 + 0.779570i \(0.715438\pi\)
\(348\) 0 0
\(349\) 9.68412 + 5.59113i 0.518379 + 0.299286i 0.736271 0.676687i \(-0.236585\pi\)
−0.217892 + 0.975973i \(0.569918\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.94200 + 5.09570i −0.156809 + 0.271601i
\(353\) −14.0422 −0.747391 −0.373696 0.927551i \(-0.621910\pi\)
−0.373696 + 0.927551i \(0.621910\pi\)
\(354\) 0 0
\(355\) 0.224567i 0.0119188i
\(356\) −9.39250 16.2683i −0.497802 0.862218i
\(357\) 0 0
\(358\) −0.0673081 + 0.116581i −0.00355734 + 0.00616150i
\(359\) −23.5052 13.5707i −1.24056 0.716235i −0.271348 0.962481i \(-0.587469\pi\)
−0.969207 + 0.246246i \(0.920803\pi\)
\(360\) 0 0
\(361\) −7.31022 12.6617i −0.384748 0.666403i
\(362\) 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
\(367\) 6.88076i 0.359173i 0.983742 + 0.179586i \(0.0574759\pi\)
−0.983742 + 0.179586i \(0.942524\pi\)
\(368\) 9.72828 5.61662i 0.507122 0.292787i
\(369\) 0 0
\(370\) 0.0464912i 0.00241696i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.247851 −0.0128332 −0.00641662 0.999979i \(-0.502042\pi\)
−0.00641662 + 0.999979i \(0.502042\pi\)
\(374\) −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
\(383\) −0.327089 −0.0167135 −0.00835675 0.999965i \(-0.502660\pi\)
−0.00835675 + 0.999965i \(0.502660\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0017i 0.712665i
\(387\) 0 0
\(388\) −10.5613 + 6.09755i −0.536167 + 0.309556i
\(389\) 6.60890i 0.335085i −0.985865 0.167542i \(-0.946417\pi\)
0.985865 0.167542i \(-0.0535831\pi\)
\(390\) 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
\(395\) 0.220776 + 0.382394i 0.0111084 + 0.0192404i
\(396\) 0 0
\(397\) −6.50435 3.75529i −0.326444 0.188472i 0.327817 0.944741i \(-0.393687\pi\)
−0.654261 + 0.756269i \(0.727020\pi\)
\(398\) −3.21760 + 5.57305i −0.161284 + 0.279352i
\(399\) 0 0
\(400\) 3.86687 + 6.69762i 0.193344 + 0.334881i
\(401\) 6.33464i 0.316337i 0.987412 + 0.158168i \(0.0505589\pi\)
−0.987412 + 0.158168i \(0.949441\pi\)
\(402\) 0 0
\(403\) 18.6919 0.931109
\(404\) 0.353708 0.612640i 0.0175976 0.0304800i
\(405\) 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
\(415\) −0.0870078 + 0.150702i −0.00427105 + 0.00739767i
\(416\) 32.4229 1.58966
\(417\) 0 0
\(418\) 1.42118i 0.0695122i
\(419\) 0.896459 + 1.55271i 0.0437949 + 0.0758550i 0.887092 0.461593i \(-0.152722\pi\)
−0.843297 + 0.537448i \(0.819389\pi\)
\(420\) 0 0
\(421\) 1.90262 3.29543i 0.0927278 0.160609i −0.815930 0.578150i \(-0.803775\pi\)
0.908658 + 0.417541i \(0.137108\pi\)
\(422\) −8.12254 4.68955i −0.395399 0.228284i
\(423\) 0 0
\(424\) −13.7108 23.7478i −0.665855 1.15330i
\(425\) 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
\(430\) 0.0436190i 0.00210349i
\(431\) −1.15145 + 0.664787i −0.0554632 + 0.0320217i −0.527475 0.849570i \(-0.676861\pi\)
0.472012 + 0.881592i \(0.343528\pi\)
\(432\) 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
\(436\) 7.37313 0.353109
\(437\) −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 −0.250356 0.968154i \(-0.580548\pi\)
0.713268 + 0.700891i \(0.247214\pi\)
\(444\) 0 0
\(445\) −0.170554 + 0.295409i −0.00808505 + 0.0140037i
\(446\) −1.98498 −0.0939916
\(447\) 0 0
\(448\) 0 0
\(449\) 14.3953i 0.679357i 0.940542 + 0.339679i \(0.110318\pi\)
−0.940542 + 0.339679i \(0.889682\pi\)
\(450\) 0 0
\(451\) −6.24803 + 3.60730i −0.294208 + 0.169861i
\(452\) 14.7787i 0.695129i
\(453\) 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 \(0.673083\pi\)
\(458\) −2.94323 5.09782i −0.137528 0.238206i
\(459\) 0 0
\(460\) −0.277433 0.160176i −0.0129354 0.00746825i
\(461\) −0.832511 + 1.44195i −0.0387739 + 0.0671584i −0.884761 0.466045i \(-0.845679\pi\)
0.845987 + 0.533203i \(0.179012\pi\)
\(462\) 0 0
\(463\) 0.604175 + 1.04646i 0.0280784 + 0.0486332i 0.879723 0.475486i \(-0.157728\pi\)
−0.851645 + 0.524119i \(0.824395\pi\)
\(464\) 6.29814i 0.292384i
\(465\) 0 0
\(466\) −8.57490 −0.397224
\(467\) 4.61994 8.00197i 0.213785 0.370287i −0.739111 0.673584i \(-0.764754\pi\)
0.952896 + 0.303297i \(0.0980874\pi\)
\(468\) 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
\(478\) 1.86286 3.22657i 0.0852052 0.147580i
\(479\) 17.5448 0.801643 0.400822 0.916156i \(-0.368725\pi\)
0.400822 + 0.916156i \(0.368725\pi\)
\(480\) 0 0
\(481\) 13.9288i 0.635097i
\(482\) 3.64923 + 6.32066i 0.166218 + 0.287898i
\(483\) 0 0
\(484\) −7.75843 + 13.4380i −0.352656 + 0.610818i
\(485\) 0.191777 + 0.110723i 0.00870817 + 0.00502766i
\(486\) 0 0
\(487\) 21.5949 + 37.4034i 0.978558 + 1.69491i 0.667657 + 0.744469i \(0.267297\pi\)
0.310900 + 0.950442i \(0.399369\pi\)
\(488\) −2.80100 4.85148i −0.126796 0.219616i
\(489\) 0 0
\(490\) 0 0
\(491\) −23.0046 + 13.2817i −1.03818 + 0.599396i −0.919319 0.393514i \(-0.871259\pi\)
−0.118866 + 0.992910i \(0.537926\pi\)
\(492\) 0 0
\(493\) 23.1196i 1.04125i
\(494\) −6.78202 + 3.91560i −0.305138 + 0.176171i
\(495\) 0 0
\(496\) 5.13324i 0.230489i
\(497\) 0 0
\(498\) 0 0
\(499\) 5.31518 0.237940 0.118970 0.992898i \(-0.462041\pi\)
0.118970 + 0.992898i \(0.462041\pi\)
\(500\) 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 \(-0.791053\pi\)
−0.792178 + 0.610290i \(0.791053\pi\)
\(504\) 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
\(509\) −13.6331 −0.604276 −0.302138 0.953264i \(-0.597700\pi\)
−0.302138 + 0.953264i \(0.597700\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.2184i 0.716760i
\(513\) 0 0
\(514\) 10.1959 5.88661i 0.449722 0.259647i
\(515\) 0.149789i 0.00660051i
\(516\) 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
\(521\) 5.11259 + 8.85526i 0.223987 + 0.387956i 0.956015 0.293318i \(-0.0947595\pi\)
−0.732028 + 0.681274i \(0.761426\pi\)
\(522\) 0 0
\(523\) 4.48150 + 2.58740i 0.195962 + 0.113139i 0.594771 0.803895i \(-0.297243\pi\)
−0.398808 + 0.917034i \(0.630576\pi\)
\(524\) −1.98317 + 3.43495i −0.0866350 + 0.150056i
\(525\) 0 0
\(526\) 0.962785 + 1.66759i 0.0419794 + 0.0727105i
\(527\) 18.8434i 0.820831i
\(528\) 0 0
\(529\) −29.7269 −1.29247
\(530\) −0.109048 + 0.188876i −0.00473673 + 0.00820426i
\(531\) 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
\(541\) 12.7197 22.0312i 0.546864 0.947196i −0.451623 0.892209i \(-0.649155\pi\)
0.998487 0.0549871i \(-0.0175118\pi\)
\(542\) −5.96769 −0.256334
\(543\) 0 0
\(544\) 32.6857i 1.40139i
\(545\) −0.0669427 0.115948i −0.00286751 0.00496667i
\(546\) 0 0
\(547\) 14.7771 25.5947i 0.631824 1.09435i −0.355355 0.934732i \(-0.615640\pi\)
0.987179 0.159620i \(-0.0510267\pi\)
\(548\) 15.3149 + 8.84205i 0.654219 + 0.377714i
\(549\) 0 0
\(550\) 1.69748 + 2.94012i 0.0723807 + 0.125367i
\(551\) 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
\(556\) 5.48757i 0.232725i
\(557\) 16.9788 9.80269i 0.719413 0.415353i −0.0951237 0.995465i \(-0.530325\pi\)
0.814537 + 0.580112i \(0.196991\pi\)
\(558\) 0 0
\(559\) 13.0683i 0.552728i
\(560\) 0 0
\(561\) 0 0
\(562\) 3.45427 0.145710
\(563\) 7.23796 12.5365i 0.305044 0.528351i −0.672227 0.740345i \(-0.734662\pi\)
0.977271 + 0.211994i \(0.0679956\pi\)
\(564\) 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 −0.352720 0.935729i \(-0.614743\pi\)
0.634005 + 0.773329i \(0.281410\pi\)
\(570\) 0 0
\(571\) −8.06856 + 13.9752i −0.337659 + 0.584842i −0.983992 0.178213i \(-0.942968\pi\)
0.646333 + 0.763055i \(0.276302\pi\)
\(572\) −8.97609 −0.375309
\(573\) 0 0
\(574\) 0 0
\(575\) 36.3008i 1.51385i
\(576\) 0 0
\(577\) −10.5403 + 6.08542i −0.438797 + 0.253339i −0.703087 0.711104i \(-0.748196\pi\)
0.264290 + 0.964443i \(0.414862\pi\)
\(578\) 10.1297i 0.421340i
\(579\) 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
\(584\) −12.8829 22.3139i −0.533100 0.923356i
\(585\) 0 0
\(586\) 13.1399 + 7.58633i 0.542805 + 0.313388i
\(587\) 16.8761 29.2302i 0.696550 1.20646i −0.273106 0.961984i \(-0.588051\pi\)
0.969655 0.244476i \(-0.0786158\pi\)
\(588\) 0 0
\(589\) −3.47207 6.01380i −0.143064 0.247794i
\(590\) 0.113231i 0.00466165i
\(591\) 0 0
\(592\) −3.82518 −0.157214
\(593\) −9.15123 + 15.8504i −0.375796 + 0.650897i −0.990446 0.137903i \(-0.955964\pi\)
0.614650 + 0.788800i \(0.289297\pi\)
\(594\) 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 −0.402911 0.915239i \(-0.632002\pi\)
−0.994076 + 0.108689i \(0.965335\pi\)
\(600\) 0 0
\(601\) −34.4865 19.9108i −1.40673 0.812177i −0.411661 0.911337i \(-0.635051\pi\)
−0.995072 + 0.0991600i \(0.968384\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −2.69670 + 4.67082i −0.109727 + 0.190053i
\(605\) 0.281764 0.0114553
\(606\) 0 0
\(607\) 24.9536i 1.01283i −0.862289 0.506417i \(-0.830970\pi\)
0.862289 0.506417i \(-0.169030\pi\)
\(608\) −6.02264 10.4315i −0.244250 0.423054i
\(609\) 0 0
\(610\) −0.0222776 + 0.0385859i −0.000901992 + 0.00156230i
\(611\) 53.0772 + 30.6441i 2.14727 + 1.23973i
\(612\) 0 0
\(613\) −14.0285 24.2980i −0.566605 0.981388i −0.996898 0.0786994i \(-0.974923\pi\)
0.430294 0.902689i \(-0.358410\pi\)
\(614\) −6.18876 10.7192i −0.249758 0.432594i
\(615\) 0 0
\(616\) 0 0
\(617\) −29.8093 + 17.2104i −1.20008 + 0.692865i −0.960573 0.278030i \(-0.910319\pi\)
−0.239506 + 0.970895i \(0.576985\pi\)
\(618\) 0 0
\(619\) 19.9635i 0.802399i 0.915991 + 0.401200i \(0.131407\pi\)
−0.915991 + 0.401200i \(0.868593\pi\)
\(620\) 0.126778 0.0731955i 0.00509154 0.00293960i
\(621\) 0 0
\(622\) 13.6510i 0.547354i
\(623\) 0 0
\(624\) 0 0
\(625\) 24.9880 0.999519
\(626\) −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
\(635\) 0.123772 0.00491176
\(636\) 0 0
\(637\) 0 0
\(638\) 2.76475i 0.109458i
\(639\) 0 0
\(640\) 0.270290 0.156052i 0.0106841 0.00616849i
\(641\) 3.85994i 0.152459i −0.997090 0.0762293i \(-0.975712\pi\)
0.997090 0.0762293i \(-0.0242881\pi\)
\(642\) 0 0
\(643\) −31.0233 + 17.9113i −1.22344 + 0.706352i −0.965649 0.259849i \(-0.916327\pi\)
−0.257789 + 0.966201i \(0.582994\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.94734 6.83699i −0.155306 0.268998i
\(647\) −21.8246 37.8013i −0.858013 1.48612i −0.873821 0.486248i \(-0.838365\pi\)
0.0158075 0.999875i \(-0.494968\pi\)
\(648\) 0 0
\(649\) −5.33162 3.07821i −0.209284 0.120830i
\(650\) 9.35369 16.2011i 0.366882 0.635458i
\(651\) 0 0
\(652\) −8.07072 13.9789i −0.316074 0.547456i
\(653\) 7.45002i 0.291542i −0.989318 0.145771i \(-0.953434\pi\)
0.989318 0.145771i \(-0.0465663\pi\)
\(654\) 0 0
\(655\) 0.0720229 0.00281417
\(656\) −5.45884 + 9.45498i −0.213132 + 0.369155i
\(657\) 0 0
\(658\) 0 0
\(659\) 7.52607 + 4.34518i 0.293174 + 0.169264i 0.639372 0.768897i \(-0.279194\pi\)
−0.346198 + 0.938161i \(0.612528\pi\)
\(660\) 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
\(667\) −14.7812 + 25.6017i −0.572329 + 0.991303i
\(668\) −9.17449 −0.354972
\(669\) 0 0
\(670\) 0.240290i 0.00928322i
\(671\) 1.21124 + 2.09793i 0.0467594 + 0.0809897i
\(672\) 0 0
\(673\) −3.60695 + 6.24742i −0.139038 + 0.240820i −0.927133 0.374733i \(-0.877734\pi\)
0.788095 + 0.615554i \(0.211068\pi\)
\(674\) 14.5498 + 8.40036i 0.560439 + 0.323570i
\(675\) 0 0
\(676\) 14.5991 + 25.2864i 0.561504 + 0.972553i
\(677\) 18.1911 + 31.5079i 0.699140 + 1.21095i 0.968765 + 0.247980i \(0.0797667\pi\)
−0.269626 + 0.962965i \(0.586900\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.329070 0.189989i 0.0126193 0.00728573i
\(681\) 0 0
\(682\) 2.25339i 0.0862867i
\(683\) −20.5530 + 11.8663i −0.786438 + 0.454050i −0.838707 0.544583i \(-0.816688\pi\)
0.0522688 + 0.998633i \(0.483355\pi\)
\(684\) 0 0
\(685\) 0.321118i 0.0122693i
\(686\) 0 0
\(687\) 0 0
\(688\) 3.58886 0.136824
\(689\) 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
\(698\) 7.42834 0.281167
\(699\) 0 0
\(700\) 0 0
\(701\) 0.873603i 0.0329955i 0.999864 + 0.0164978i \(0.00525164\pi\)
−0.999864 + 0.0164978i \(0.994748\pi\)
\(702\) 0 0
\(703\) 4.48135 2.58731i 0.169017 0.0975821i
\(704\) 0.745784i 0.0281078i
\(705\) 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 \(0.931443\pi\)
\(710\) −0.0745897 0.129193i −0.00279930 0.00484853i
\(711\) 0 0
\(712\) −24.6735 14.2453i −0.924680 0.533864i
\(713\) 12.0473 20.8665i 0.451174 0.781456i
\(714\) 0 0
\(715\) 0.0814965 + 0.141156i 0.00304779 + 0.00527894i
\(716\) 0.315864i 0.0118044i
\(717\) 0 0
\(718\) −18.0300 −0.672872
\(719\) 22.5953 39.1361i 0.842661 1.45953i −0.0449767 0.998988i \(-0.514321\pi\)
0.887637 0.460543i \(-0.152345\pi\)
\(720\) 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 \(-0.284354\pi\)
−0.361359 + 0.932427i \(0.617687\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −0.102463 + 0.177472i −0.00379234 + 0.00656853i
\(731\) 13.1742 0.487264
\(732\) 0 0
\(733\) 12.2166i 0.451230i 0.974217 + 0.225615i \(0.0724392\pi\)
−0.974217 + 0.225615i \(0.927561\pi\)
\(734\) 2.28543 + 3.95849i 0.0843569 + 0.146110i
\(735\) 0 0
\(736\) 20.8972 36.1949i 0.770280 1.33416i
\(737\) 11.3143 + 6.53234i 0.416769 + 0.240622i
\(738\) 0 0
\(739\) 10.3536 + 17.9330i 0.380863 + 0.659674i 0.991186 0.132478i \(-0.0422935\pi\)
−0.610323 + 0.792153i \(0.708960\pi\)
\(740\) 0.0545436 + 0.0944723i 0.00200506 + 0.00347287i
\(741\) 0 0
\(742\) 0 0
\(743\) −10.2862 + 5.93873i −0.377363 + 0.217871i −0.676670 0.736286i \(-0.736578\pi\)
0.299307 + 0.954157i \(0.403244\pi\)
\(744\) 0 0
\(745\) 0.450385i 0.0165008i
\(746\) −0.142588 + 0.0823233i −0.00522053 + 0.00301407i
\(747\) 0 0
\(748\) 9.04885i 0.330859i
\(749\) 0 0
\(750\) 0 0
\(751\) 23.7108 0.865221 0.432610 0.901581i \(-0.357593\pi\)
0.432610 + 0.901581i \(0.357593\pi\)
\(752\) −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
\(761\) −48.7535 −1.76731 −0.883656 0.468137i \(-0.844925\pi\)
−0.883656 + 0.468137i \(0.844925\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 21.5154i 0.778401i
\(765\) 0 0
\(766\) −0.188174 + 0.108642i −0.00679900 + 0.00392540i
\(767\) 33.9240i 1.22493i
\(768\) 0 0
\(769\) −23.3870 + 13.5025i −0.843357 + 0.486912i −0.858404 0.512975i \(-0.828543\pi\)
0.0150472 + 0.999887i \(0.495210\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 16.4268 + 28.4520i 0.591213 + 1.02401i
\(773\) 13.3567 + 23.1345i 0.480408 + 0.832092i 0.999747 0.0224765i \(-0.00715509\pi\)
−0.519339 + 0.854568i \(0.673822\pi\)
\(774\) 0 0
\(775\) 14.3659 + 8.29417i 0.516039 + 0.297935i
\(776\) −9.24794 + 16.0179i −0.331982 + 0.575009i
\(777\) 0 0
\(778\) −2.19514 3.80209i −0.0786994 0.136311i
\(779\) 14.7692i 0.529161i
\(780\) 0 0
\(781\) −8.11095 −0.290233
\(782\) 13.6963 23.7228i 0.489780 0.848324i
\(783\) 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
\(793\) 6.67436 11.5603i 0.237014 0.410520i
\(794\) −4.98925 −0.177062
\(795\) 0 0
\(796\) 15.0996i 0.535191i
\(797\) −4.42781 7.66919i −0.156841 0.271657i 0.776887 0.629640i \(-0.216798\pi\)
−0.933728 + 0.357984i \(0.883464\pi\)
\(798\) 0 0
\(799\) −30.8925 + 53.5074i −1.09290 + 1.89296i
\(800\) 24.9191 + 14.3871i 0.881023 + 0.508659i
\(801\) 0 0
\(802\) 2.10404 + 3.64430i 0.0742962 + 0.128685i
\(803\) 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
\(808\) 1.07291i 0.0377449i
\(809\) −6.40871 + 3.70007i −0.225318 + 0.130087i −0.608410 0.793623i \(-0.708192\pi\)
0.383092 + 0.923710i \(0.374859\pi\)
\(810\) 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
\(814\) −1.67917 −0.0588550
\(815\) −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 −0.143753 0.989614i \(-0.545917\pi\)
0.785154 + 0.619300i \(0.212584\pi\)
\(822\) 0 0
\(823\) −8.47690 + 14.6824i −0.295486 + 0.511797i −0.975098 0.221775i \(-0.928815\pi\)
0.679612 + 0.733572i \(0.262148\pi\)
\(824\) −12.5109 −0.435838
\(825\) 0 0
\(826\) 0 0
\(827\) 25.3052i 0.879949i −0.898010 0.439975i \(-0.854987\pi\)
0.898010 0.439975i \(-0.145013\pi\)
\(828\) 0 0
\(829\) −35.9640 + 20.7638i −1.24908 + 0.721158i −0.970927 0.239378i \(-0.923057\pi\)
−0.278156 + 0.960536i \(0.589723\pi\)
\(830\) 0.115598i 0.00401247i
\(831\) 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
\(836\) 1.66733 + 2.88791i 0.0576659 + 0.0998803i
\(837\) 0 0
\(838\) 1.03146 + 0.595515i 0.0356312 + 0.0205717i
\(839\) 6.61780 11.4624i 0.228472 0.395725i −0.728884 0.684638i \(-0.759960\pi\)
0.957355 + 0.288913i \(0.0932938\pi\)
\(840\) 0 0
\(841\) −6.21265 10.7606i −0.214229 0.371056i
\(842\) 2.52780i 0.0871138i
\(843\) 0 0
\(844\) 22.0072 0.757519
\(845\) 0.265099 0.459164i 0.00911967 0.0157957i
\(846\) 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 \(-0.234990\pi\)
−0.213001 + 0.977052i \(0.568324\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 10.7180 18.5642i 0.366334 0.634510i
\(857\) −18.3431 −0.626590 −0.313295 0.949656i \(-0.601433\pi\)
−0.313295 + 0.949656i \(0.601433\pi\)
\(858\) 0 0
\(859\) 3.10760i 0.106030i 0.998594 + 0.0530150i \(0.0168831\pi\)
−0.998594 + 0.0530150i \(0.983117\pi\)
\(860\) −0.0511739 0.0886358i −0.00174502 0.00302246i
\(861\) 0 0
\(862\) −0.441616 + 0.764902i −0.0150415 + 0.0260527i
\(863\) −35.8587 20.7030i −1.22064 0.704739i −0.255589 0.966786i \(-0.582269\pi\)
−0.965055 + 0.262047i \(0.915603\pi\)
\(864\) 0 0
\(865\) −0.0688566 0.119263i −0.00234119 0.00405507i
\(866\) 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
\(871\) 71.9910i 2.43932i
\(872\) 9.68438 5.59128i 0.327954 0.189345i
\(873\) 0 0
\(874\) 10.0947i 0.341459i
\(875\) 0 0
\(876\) 0 0
\(877\) −22.7957 −0.769756 −0.384878 0.922967i \(-0.625756\pi\)
−0.384878 + 0.922967i \(0.625756\pi\)
\(878\) −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 \(-0.761028\pi\)
−0.731175 + 0.682190i \(0.761028\pi\)
\(882\) 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
\(887\) −38.9575 −1.30807 −0.654033 0.756466i \(-0.726924\pi\)
−0.654033 + 0.756466i \(0.726924\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0.226597i 0.00759556i
\(891\) 0 0
\(892\) 4.03358 2.32879i 0.135054 0.0779736i
\(893\) 22.7689i 0.761933i
\(894\) 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
\(899\) −6.75453 11.6992i −0.225276 0.390190i
\(900\) 0 0
\(901\) 57.0460 + 32.9355i 1.90048 + 1.09724i
\(902\) −2.39632 + 4.15054i −0.0797886 + 0.138198i
\(903\) 0 0
\(904\) 11.2071 + 19.4113i 0.372743 + 0.645611i
\(905\) 0.177260i 0.00589232i
\(906\) 0 0
\(907\) −28.1053 −0.933220 −0.466610 0.884463i \(-0.654525\pi\)
−0.466610 + 0.884463i \(0.654525\pi\)
\(908\) 22.4246 38.8406i 0.744187 1.28897i
\(909\) 0 0
\(910\) 0 0
\(911\) −32.3883 18.6994i −1.07307 0.619538i −0.144052 0.989570i \(-0.546013\pi\)
−0.929019 + 0.370032i \(0.879347\pi\)
\(912\) 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
\(919\) 12.9115 22.3634i 0.425911 0.737699i −0.570594 0.821232i \(-0.693287\pi\)
0.996505 + 0.0835328i \(0.0266203\pi\)
\(920\) −0.485867 −0.0160186
\(921\) 0 0
\(922\) 1.10607i 0.0364264i
\(923\) 22.3471 + 38.7063i 0.735563 + 1.27403i
\(924\) 0 0
\(925\) −6.18063 + 10.7052i −0.203218 + 0.351983i
\(926\) 0.695162 + 0.401352i 0.0228444 + 0.0131892i
\(927\) 0 0
\(928\) −11.7164 20.2934i −0.384610 0.666164i
\(929\) 7.97094 + 13.8061i 0.261518 + 0.452963i 0.966646 0.256118i \(-0.0824435\pi\)
−0.705127 + 0.709081i \(0.749110\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 17.4246 10.0601i 0.570762 0.329529i
\(933\) 0 0
\(934\) 6.13802i 0.200842i
\(935\) −0.142300 + 0.0821570i −0.00465371 + 0.00268682i
\(936\) 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
\(940\) 0.479997 0.0156558
\(941\) 5.76861 9.99152i 0.188051 0.325714i −0.756549 0.653937i \(-0.773116\pi\)
0.944600 + 0.328222i \(0.106450\pi\)
\(942\) 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 −0.842535 0.538642i \(-0.818938\pi\)
0.0452102 + 0.998977i \(0.485604\pi\)
\(948\) 0 0
\(949\) 30.6981 53.1706i 0.996501 1.72599i
\(950\) −6.94989 −0.225484
\(951\) 0 0
\(952\) 0 0
\(953\) 29.8498i 0.966931i 0.875364 + 0.483465i \(0.160622\pi\)
−0.875364 + 0.483465i \(0.839378\pi\)
\(954\) 0 0
\(955\) 0.338347 0.195345i 0.0109486 0.00632120i
\(956\) 8.74205i 0.282738i
\(957\) 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
\(962\) 4.62642 + 8.01319i 0.149162 + 0.258356i
\(963\) 0 0
\(964\) −14.8308 8.56258i −0.477669 0.275782i
\(965\) 0.298287 0.516648i 0.00960219 0.0166315i
\(966\) 0 0
\(967\) 8.17864 + 14.1658i 0.263007 + 0.455542i 0.967040 0.254626i \(-0.0819523\pi\)
−0.704032 + 0.710168i \(0.748619\pi\)
\(968\) 23.5339i 0.756407i
\(969\) 0 0
\(970\) 0.147106 0.00472327
\(971\) −10.7315 + 18.5875i −0.344390 + 0.596500i −0.985243 0.171163i \(-0.945247\pi\)
0.640853 + 0.767663i \(0.278581\pi\)
\(972\) 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 0.171608 0.985165i \(-0.445104\pi\)
−0.767374 + 0.641199i \(0.778437\pi\)
\(978\) 0 0
\(979\) 10.6696 + 6.16010i 0.341002 + 0.196878i
\(980\) 0 0
\(981\) 0 0
\(982\) −8.82301 + 15.2819i −0.281554 + 0.487665i
\(983\) 25.4194 0.810752 0.405376 0.914150i \(-0.367141\pi\)
0.405376 + 0.914150i \(0.367141\pi\)
\(984\) 0 0
\(985\) 0.429311i 0.0136790i
\(986\) −7.67912 13.3006i −0.244553 0.423578i
\(987\) 0 0
\(988\) 9.18759 15.9134i 0.292296 0.506272i
\(989\) −14.5886 8.42273i −0.463890 0.267827i
\(990\) 0 0
\(991\) −11.8768 20.5713i −0.377280 0.653468i 0.613385 0.789784i \(-0.289807\pi\)
−0.990665 + 0.136315i \(0.956474\pi\)
\(992\) 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
\(997\) 12.1666i 0.385320i 0.981266 + 0.192660i \(0.0617114\pi\)
−0.981266 + 0.192660i \(0.938289\pi\)
\(998\) 3.05781 1.76543i 0.0967934 0.0558837i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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.s.d.656.15 48
3.2 odd 2 441.2.s.d.362.10 48
7.2 even 3 1323.2.o.e.440.9 48
7.3 odd 6 1323.2.i.d.521.10 48
7.4 even 3 1323.2.i.d.521.9 48
7.5 odd 6 1323.2.o.e.440.10 48
7.6 odd 2 inner 1323.2.s.d.656.16 48
9.4 even 3 441.2.i.d.68.15 48
9.5 odd 6 1323.2.i.d.1097.10 48
21.2 odd 6 441.2.o.e.146.15 48
21.5 even 6 441.2.o.e.146.16 yes 48
21.11 odd 6 441.2.i.d.227.10 48
21.17 even 6 441.2.i.d.227.9 48
21.20 even 2 441.2.s.d.362.9 48
63.4 even 3 441.2.s.d.374.9 48
63.5 even 6 1323.2.o.e.881.9 48
63.13 odd 6 441.2.i.d.68.16 48
63.23 odd 6 1323.2.o.e.881.10 48
63.31 odd 6 441.2.s.d.374.10 48
63.32 odd 6 inner 1323.2.s.d.962.16 48
63.40 odd 6 441.2.o.e.293.15 yes 48
63.41 even 6 1323.2.i.d.1097.9 48
63.58 even 3 441.2.o.e.293.16 yes 48
63.59 even 6 inner 1323.2.s.d.962.15 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.i.d.68.15 48 9.4 even 3
441.2.i.d.68.16 48 63.13 odd 6
441.2.i.d.227.9 48 21.17 even 6
441.2.i.d.227.10 48 21.11 odd 6
441.2.o.e.146.15 48 21.2 odd 6
441.2.o.e.146.16 yes 48 21.5 even 6
441.2.o.e.293.15 yes 48 63.40 odd 6
441.2.o.e.293.16 yes 48 63.58 even 3
441.2.s.d.362.9 48 21.20 even 2
441.2.s.d.362.10 48 3.2 odd 2
441.2.s.d.374.9 48 63.4 even 3
441.2.s.d.374.10 48 63.31 odd 6
1323.2.i.d.521.9 48 7.4 even 3
1323.2.i.d.521.10 48 7.3 odd 6
1323.2.i.d.1097.9 48 63.41 even 6
1323.2.i.d.1097.10 48 9.5 odd 6
1323.2.o.e.440.9 48 7.2 even 3
1323.2.o.e.440.10 48 7.5 odd 6
1323.2.o.e.881.9 48 63.5 even 6
1323.2.o.e.881.10 48 63.23 odd 6
1323.2.s.d.656.15 48 1.1 even 1 trivial
1323.2.s.d.656.16 48 7.6 odd 2 inner
1323.2.s.d.962.15 48 63.59 even 6 inner
1323.2.s.d.962.16 48 63.32 odd 6 inner