# Properties

 Label 1.16.a.a.1.1 Level $1$ Weight $16$ Character 1.1 Self dual yes Analytic conductor $1.427$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,16,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 16, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1$$ Weight: $$k$$ $$=$$ $$16$$ Character orbit: $$[\chi]$$ $$=$$ 1.a (trivial)

## 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: yes Analytic conductor: $$1.42693505100$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 1.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+216.000 q^{2} -3348.00 q^{3} +13888.0 q^{4} +52110.0 q^{5} -723168. q^{6} +2.82246e6 q^{7} -4.07808e6 q^{8} -3.13980e6 q^{9} +O(q^{10})$$ $$q+216.000 q^{2} -3348.00 q^{3} +13888.0 q^{4} +52110.0 q^{5} -723168. q^{6} +2.82246e6 q^{7} -4.07808e6 q^{8} -3.13980e6 q^{9} +1.12558e7 q^{10} +2.05869e7 q^{11} -4.64970e7 q^{12} -1.90073e8 q^{13} +6.09650e8 q^{14} -1.74464e8 q^{15} -1.33595e9 q^{16} +1.64653e9 q^{17} -6.78197e8 q^{18} +1.56326e9 q^{19} +7.23704e8 q^{20} -9.44958e9 q^{21} +4.44676e9 q^{22} +9.45112e9 q^{23} +1.36534e10 q^{24} -2.78021e10 q^{25} -4.10558e10 q^{26} +5.85522e10 q^{27} +3.91983e10 q^{28} -3.69026e10 q^{29} -3.76843e10 q^{30} +7.15885e10 q^{31} -1.54934e11 q^{32} -6.89248e10 q^{33} +3.55650e11 q^{34} +1.47078e11 q^{35} -4.36056e10 q^{36} -1.03365e12 q^{37} +3.37664e11 q^{38} +6.36366e11 q^{39} -2.12509e11 q^{40} +1.64197e12 q^{41} -2.04111e12 q^{42} -4.92403e11 q^{43} +2.85910e11 q^{44} -1.63615e11 q^{45} +2.04144e12 q^{46} -3.41068e12 q^{47} +4.47275e12 q^{48} +3.21870e12 q^{49} -6.00526e12 q^{50} -5.51258e12 q^{51} -2.63974e12 q^{52} +6.79715e12 q^{53} +1.26473e13 q^{54} +1.07278e12 q^{55} -1.15102e13 q^{56} -5.23379e12 q^{57} -7.97095e12 q^{58} +9.85886e12 q^{59} -2.42296e12 q^{60} +4.93184e12 q^{61} +1.54631e13 q^{62} -8.86196e12 q^{63} +1.03106e13 q^{64} -9.90472e12 q^{65} -1.48878e13 q^{66} -2.88378e13 q^{67} +2.28670e13 q^{68} -3.16423e13 q^{69} +3.17689e13 q^{70} +1.25050e14 q^{71} +1.28044e13 q^{72} -8.21715e13 q^{73} -2.23269e14 q^{74} +9.30815e13 q^{75} +2.17105e13 q^{76} +5.81055e13 q^{77} +1.37455e14 q^{78} -2.54131e13 q^{79} -6.96162e13 q^{80} -1.50980e14 q^{81} +3.54666e14 q^{82} -2.81737e14 q^{83} -1.31236e14 q^{84} +8.58006e13 q^{85} -1.06359e14 q^{86} +1.23550e14 q^{87} -8.39548e13 q^{88} +7.15619e14 q^{89} -3.53409e13 q^{90} -5.36474e14 q^{91} +1.31257e14 q^{92} -2.39678e14 q^{93} -7.36708e14 q^{94} +8.14613e13 q^{95} +5.18719e14 q^{96} +6.12786e14 q^{97} +6.95238e14 q^{98} -6.46387e13 q^{99} +O(q^{100})$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 216.000 1.19324 0.596621 0.802523i $$-0.296509\pi$$
0.596621 + 0.802523i $$0.296509\pi$$
$$3$$ −3348.00 −0.883845 −0.441922 0.897053i $$-0.645703\pi$$
−0.441922 + 0.897053i $$0.645703\pi$$
$$4$$ 13888.0 0.423828
$$5$$ 52110.0 0.298295 0.149148 0.988815i $$-0.452347\pi$$
0.149148 + 0.988815i $$0.452347\pi$$
$$6$$ −723168. −1.05464
$$7$$ 2.82246e6 1.29536 0.647682 0.761911i $$-0.275739\pi$$
0.647682 + 0.761911i $$0.275739\pi$$
$$8$$ −4.07808e6 −0.687513
$$9$$ −3.13980e6 −0.218818
$$10$$ 1.12558e7 0.355938
$$11$$ 2.05869e7 0.318526 0.159263 0.987236i $$-0.449088\pi$$
0.159263 + 0.987236i $$0.449088\pi$$
$$12$$ −4.64970e7 −0.374598
$$13$$ −1.90073e8 −0.840129 −0.420065 0.907494i $$-0.637993\pi$$
−0.420065 + 0.907494i $$0.637993\pi$$
$$14$$ 6.09650e8 1.54568
$$15$$ −1.74464e8 −0.263647
$$16$$ −1.33595e9 −1.24420
$$17$$ 1.64653e9 0.973200 0.486600 0.873625i $$-0.338237\pi$$
0.486600 + 0.873625i $$0.338237\pi$$
$$18$$ −6.78197e8 −0.261103
$$19$$ 1.56326e9 0.401216 0.200608 0.979672i $$-0.435708\pi$$
0.200608 + 0.979672i $$0.435708\pi$$
$$20$$ 7.23704e8 0.126426
$$21$$ −9.44958e9 −1.14490
$$22$$ 4.44676e9 0.380079
$$23$$ 9.45112e9 0.578794 0.289397 0.957209i $$-0.406545\pi$$
0.289397 + 0.957209i $$0.406545\pi$$
$$24$$ 1.36534e10 0.607655
$$25$$ −2.78021e10 −0.911020
$$26$$ −4.10558e10 −1.00248
$$27$$ 5.85522e10 1.07725
$$28$$ 3.91983e10 0.549012
$$29$$ −3.69026e10 −0.397257 −0.198629 0.980075i $$-0.563649\pi$$
−0.198629 + 0.980075i $$0.563649\pi$$
$$30$$ −3.76843e10 −0.314594
$$31$$ 7.15885e10 0.467337 0.233669 0.972316i $$-0.424927\pi$$
0.233669 + 0.972316i $$0.424927\pi$$
$$32$$ −1.54934e11 −0.797117
$$33$$ −6.89248e10 −0.281528
$$34$$ 3.55650e11 1.16126
$$35$$ 1.47078e11 0.386401
$$36$$ −4.36056e10 −0.0927413
$$37$$ −1.03365e12 −1.79003 −0.895017 0.446031i $$-0.852837\pi$$
−0.895017 + 0.446031i $$0.852837\pi$$
$$38$$ 3.37664e11 0.478748
$$39$$ 6.36366e11 0.742544
$$40$$ −2.12509e11 −0.205082
$$41$$ 1.64197e12 1.31670 0.658351 0.752711i $$-0.271254\pi$$
0.658351 + 0.752711i $$0.271254\pi$$
$$42$$ −2.04111e12 −1.36614
$$43$$ −4.92403e11 −0.276253 −0.138127 0.990415i $$-0.544108\pi$$
−0.138127 + 0.990415i $$0.544108\pi$$
$$44$$ 2.85910e11 0.135000
$$45$$ −1.63615e11 −0.0652724
$$46$$ 2.04144e12 0.690642
$$47$$ −3.41068e12 −0.981991 −0.490996 0.871162i $$-0.663367\pi$$
−0.490996 + 0.871162i $$0.663367\pi$$
$$48$$ 4.47275e12 1.09968
$$49$$ 3.21870e12 0.677968
$$50$$ −6.00526e12 −1.08707
$$51$$ −5.51258e12 −0.860158
$$52$$ −2.63974e12 −0.356070
$$53$$ 6.79715e12 0.794800 0.397400 0.917645i $$-0.369913\pi$$
0.397400 + 0.917645i $$0.369913\pi$$
$$54$$ 1.26473e13 1.28542
$$55$$ 1.07278e12 0.0950147
$$56$$ −1.15102e13 −0.890580
$$57$$ −5.23379e12 −0.354613
$$58$$ −7.97095e12 −0.474024
$$59$$ 9.85886e12 0.515747 0.257873 0.966179i $$-0.416978\pi$$
0.257873 + 0.966179i $$0.416978\pi$$
$$60$$ −2.42296e12 −0.111741
$$61$$ 4.93184e12 0.200926 0.100463 0.994941i $$-0.467968\pi$$
0.100463 + 0.994941i $$0.467968\pi$$
$$62$$ 1.54631e13 0.557647
$$63$$ −8.86196e12 −0.283449
$$64$$ 1.03106e13 0.293044
$$65$$ −9.90472e12 −0.250606
$$66$$ −1.48878e13 −0.335931
$$67$$ −2.88378e13 −0.581302 −0.290651 0.956829i $$-0.593872\pi$$
−0.290651 + 0.956829i $$0.593872\pi$$
$$68$$ 2.28670e13 0.412470
$$69$$ −3.16423e13 −0.511564
$$70$$ 3.17689e13 0.461070
$$71$$ 1.25050e14 1.63172 0.815862 0.578247i $$-0.196263\pi$$
0.815862 + 0.578247i $$0.196263\pi$$
$$72$$ 1.28044e13 0.150440
$$73$$ −8.21715e13 −0.870562 −0.435281 0.900295i $$-0.643351\pi$$
−0.435281 + 0.900295i $$0.643351\pi$$
$$74$$ −2.23269e14 −2.13595
$$75$$ 9.30815e13 0.805200
$$76$$ 2.17105e13 0.170047
$$77$$ 5.81055e13 0.412607
$$78$$ 1.37455e14 0.886035
$$79$$ −2.54131e13 −0.148886 −0.0744430 0.997225i $$-0.523718\pi$$
−0.0744430 + 0.997225i $$0.523718\pi$$
$$80$$ −6.96162e13 −0.371138
$$81$$ −1.50980e14 −0.733300
$$82$$ 3.54666e14 1.57114
$$83$$ −2.81737e14 −1.13961 −0.569807 0.821779i $$-0.692982\pi$$
−0.569807 + 0.821779i $$0.692982\pi$$
$$84$$ −1.31236e14 −0.485241
$$85$$ 8.58006e13 0.290301
$$86$$ −1.06359e14 −0.329637
$$87$$ 1.23550e14 0.351114
$$88$$ −8.39548e13 −0.218991
$$89$$ 7.15619e14 1.71497 0.857485 0.514509i $$-0.172026\pi$$
0.857485 + 0.514509i $$0.172026\pi$$
$$90$$ −3.53409e13 −0.0778858
$$91$$ −5.36474e14 −1.08827
$$92$$ 1.31257e14 0.245309
$$93$$ −2.39678e14 −0.413054
$$94$$ −7.36708e14 −1.17175
$$95$$ 8.14613e13 0.119681
$$96$$ 5.18719e14 0.704528
$$97$$ 6.12786e14 0.770054 0.385027 0.922905i $$-0.374192\pi$$
0.385027 + 0.922905i $$0.374192\pi$$
$$98$$ 6.95238e14 0.808981
$$99$$ −6.46387e13 −0.0696993
$$100$$ −3.86116e14 −0.386116
$$101$$ −8.17642e14 −0.758844 −0.379422 0.925224i $$-0.623877\pi$$
−0.379422 + 0.925224i $$0.623877\pi$$
$$102$$ −1.19072e15 −1.02638
$$103$$ 7.41115e14 0.593753 0.296877 0.954916i $$-0.404055\pi$$
0.296877 + 0.954916i $$0.404055\pi$$
$$104$$ 7.75134e14 0.577600
$$105$$ −4.92418e14 −0.341518
$$106$$ 1.46818e15 0.948389
$$107$$ −2.51430e15 −1.51370 −0.756849 0.653590i $$-0.773262\pi$$
−0.756849 + 0.653590i $$0.773262\pi$$
$$108$$ 8.13173e14 0.456567
$$109$$ 1.26835e15 0.664572 0.332286 0.943179i $$-0.392180\pi$$
0.332286 + 0.943179i $$0.392180\pi$$
$$110$$ 2.31721e14 0.113376
$$111$$ 3.46067e15 1.58211
$$112$$ −3.77065e15 −1.61169
$$113$$ −2.05416e15 −0.821385 −0.410692 0.911774i $$-0.634713\pi$$
−0.410692 + 0.911774i $$0.634713\pi$$
$$114$$ −1.13050e15 −0.423139
$$115$$ 4.92498e14 0.172652
$$116$$ −5.12503e14 −0.168369
$$117$$ 5.96793e14 0.183836
$$118$$ 2.12951e15 0.615411
$$119$$ 4.64725e15 1.26065
$$120$$ 7.11479e14 0.181260
$$121$$ −3.75343e15 −0.898541
$$122$$ 1.06528e15 0.239753
$$123$$ −5.49733e15 −1.16376
$$124$$ 9.94221e14 0.198071
$$125$$ −3.03904e15 −0.570048
$$126$$ −1.91418e15 −0.338224
$$127$$ 2.99068e15 0.498014 0.249007 0.968502i $$-0.419896\pi$$
0.249007 + 0.968502i $$0.419896\pi$$
$$128$$ 7.30396e15 1.14679
$$129$$ 1.64857e15 0.244165
$$130$$ −2.13942e15 −0.299034
$$131$$ −1.62623e15 −0.214608 −0.107304 0.994226i $$-0.534222\pi$$
−0.107304 + 0.994226i $$0.534222\pi$$
$$132$$ −9.57227e14 −0.119319
$$133$$ 4.41222e15 0.519721
$$134$$ −6.22897e15 −0.693634
$$135$$ 3.05116e15 0.321337
$$136$$ −6.71467e15 −0.669088
$$137$$ 1.05922e16 0.999038 0.499519 0.866303i $$-0.333510\pi$$
0.499519 + 0.866303i $$0.333510\pi$$
$$138$$ −6.83474e15 −0.610421
$$139$$ −1.86709e16 −1.57963 −0.789813 0.613347i $$-0.789823\pi$$
−0.789813 + 0.613347i $$0.789823\pi$$
$$140$$ 2.04262e15 0.163767
$$141$$ 1.14190e16 0.867928
$$142$$ 2.70108e16 1.94704
$$143$$ −3.91301e15 −0.267603
$$144$$ 4.19461e15 0.272253
$$145$$ −1.92299e15 −0.118500
$$146$$ −1.77490e16 −1.03879
$$147$$ −1.07762e16 −0.599219
$$148$$ −1.43554e16 −0.758667
$$149$$ −1.25560e16 −0.630889 −0.315444 0.948944i $$-0.602154\pi$$
−0.315444 + 0.948944i $$0.602154\pi$$
$$150$$ 2.01056e16 0.960799
$$151$$ 2.87588e16 1.30751 0.653753 0.756708i $$-0.273194\pi$$
0.653753 + 0.756708i $$0.273194\pi$$
$$152$$ −6.37509e15 −0.275841
$$153$$ −5.16977e15 −0.212954
$$154$$ 1.25508e16 0.492340
$$155$$ 3.73048e15 0.139404
$$156$$ 8.83784e15 0.314711
$$157$$ −1.45276e16 −0.493114 −0.246557 0.969128i $$-0.579299\pi$$
−0.246557 + 0.969128i $$0.579299\pi$$
$$158$$ −5.48922e15 −0.177657
$$159$$ −2.27569e16 −0.702480
$$160$$ −8.07362e15 −0.237776
$$161$$ 2.66754e16 0.749750
$$162$$ −3.26117e16 −0.875005
$$163$$ 1.67741e16 0.429767 0.214884 0.976640i $$-0.431063\pi$$
0.214884 + 0.976640i $$0.431063\pi$$
$$164$$ 2.28037e16 0.558055
$$165$$ −3.59167e15 −0.0839783
$$166$$ −6.08551e16 −1.35984
$$167$$ 6.41999e16 1.37139 0.685695 0.727889i $$-0.259498\pi$$
0.685695 + 0.727889i $$0.259498\pi$$
$$168$$ 3.85362e16 0.787134
$$169$$ −1.50580e16 −0.294183
$$170$$ 1.85329e16 0.346399
$$171$$ −4.90832e15 −0.0877934
$$172$$ −6.83849e15 −0.117084
$$173$$ −7.59860e16 −1.24563 −0.622814 0.782370i $$-0.714010\pi$$
−0.622814 + 0.782370i $$0.714010\pi$$
$$174$$ 2.66868e16 0.418964
$$175$$ −7.84703e16 −1.18010
$$176$$ −2.75029e16 −0.396309
$$177$$ −3.30075e16 −0.455840
$$178$$ 1.54574e17 2.04638
$$179$$ 9.33749e16 1.18531 0.592655 0.805456i $$-0.298080\pi$$
0.592655 + 0.805456i $$0.298080\pi$$
$$180$$ −2.27229e15 −0.0276643
$$181$$ 7.43177e16 0.867966 0.433983 0.900921i $$-0.357108\pi$$
0.433983 + 0.900921i $$0.357108\pi$$
$$182$$ −1.15878e17 −1.29857
$$183$$ −1.65118e16 −0.177587
$$184$$ −3.85424e16 −0.397929
$$185$$ −5.38636e16 −0.533958
$$186$$ −5.17705e16 −0.492873
$$187$$ 3.38968e16 0.309990
$$188$$ −4.73676e16 −0.416196
$$189$$ 1.65261e17 1.39543
$$190$$ 1.75956e16 0.142808
$$191$$ −9.86224e16 −0.769529 −0.384765 0.923015i $$-0.625717\pi$$
−0.384765 + 0.923015i $$0.625717\pi$$
$$192$$ −3.45197e16 −0.259005
$$193$$ −8.91178e15 −0.0643109 −0.0321554 0.999483i $$-0.510237\pi$$
−0.0321554 + 0.999483i $$0.510237\pi$$
$$194$$ 1.32362e17 0.918861
$$195$$ 3.31610e16 0.221497
$$196$$ 4.47013e16 0.287342
$$197$$ 3.54176e16 0.219140 0.109570 0.993979i $$-0.465053\pi$$
0.109570 + 0.993979i $$0.465053\pi$$
$$198$$ −1.39620e16 −0.0831682
$$199$$ −2.86461e17 −1.64311 −0.821556 0.570127i $$-0.806894\pi$$
−0.821556 + 0.570127i $$0.806894\pi$$
$$200$$ 1.13379e17 0.626338
$$201$$ 9.65490e16 0.513780
$$202$$ −1.76611e17 −0.905485
$$203$$ −1.04156e17 −0.514593
$$204$$ −7.65587e16 −0.364559
$$205$$ 8.55633e16 0.392766
$$206$$ 1.60081e17 0.708492
$$207$$ −2.96746e16 −0.126651
$$208$$ 2.53928e17 1.04529
$$209$$ 3.21825e16 0.127798
$$210$$ −1.06362e17 −0.407514
$$211$$ 3.75834e17 1.38956 0.694780 0.719222i $$-0.255502\pi$$
0.694780 + 0.719222i $$0.255502\pi$$
$$212$$ 9.43988e16 0.336859
$$213$$ −4.18668e17 −1.44219
$$214$$ −5.43089e17 −1.80621
$$215$$ −2.56591e16 −0.0824050
$$216$$ −2.38781e17 −0.740621
$$217$$ 2.02055e17 0.605372
$$218$$ 2.73964e17 0.792995
$$219$$ 2.75110e17 0.769441
$$220$$ 1.48988e16 0.0402699
$$221$$ −3.12961e17 −0.817614
$$222$$ 7.47504e17 1.88784
$$223$$ −2.53078e16 −0.0617970 −0.0308985 0.999523i $$-0.509837\pi$$
−0.0308985 + 0.999523i $$0.509837\pi$$
$$224$$ −4.37295e17 −1.03256
$$225$$ 8.72932e16 0.199348
$$226$$ −4.43699e17 −0.980111
$$227$$ 3.03692e17 0.648992 0.324496 0.945887i $$-0.394805\pi$$
0.324496 + 0.945887i $$0.394805\pi$$
$$228$$ −7.26868e16 −0.150295
$$229$$ 1.07992e17 0.216085 0.108042 0.994146i $$-0.465542\pi$$
0.108042 + 0.994146i $$0.465542\pi$$
$$230$$ 1.06379e17 0.206015
$$231$$ −1.94537e17 −0.364681
$$232$$ 1.50492e17 0.273119
$$233$$ −7.90506e17 −1.38911 −0.694554 0.719441i $$-0.744398\pi$$
−0.694554 + 0.719441i $$0.744398\pi$$
$$234$$ 1.28907e17 0.219360
$$235$$ −1.77731e17 −0.292923
$$236$$ 1.36920e17 0.218588
$$237$$ 8.50830e16 0.131592
$$238$$ 1.00381e18 1.50426
$$239$$ 3.52956e17 0.512551 0.256275 0.966604i $$-0.417505\pi$$
0.256275 + 0.966604i $$0.417505\pi$$
$$240$$ 2.33075e17 0.328028
$$241$$ 6.85690e16 0.0935405 0.0467703 0.998906i $$-0.485107\pi$$
0.0467703 + 0.998906i $$0.485107\pi$$
$$242$$ −8.10741e17 −1.07218
$$243$$ −3.34679e17 −0.429123
$$244$$ 6.84934e16 0.0851580
$$245$$ 1.67726e17 0.202235
$$246$$ −1.18742e18 −1.38865
$$247$$ −2.97134e17 −0.337073
$$248$$ −2.91944e17 −0.321300
$$249$$ 9.43255e17 1.00724
$$250$$ −6.56433e17 −0.680205
$$251$$ 1.58806e18 1.59703 0.798515 0.601975i $$-0.205619\pi$$
0.798515 + 0.601975i $$0.205619\pi$$
$$252$$ −1.23075e17 −0.120134
$$253$$ 1.94569e17 0.184361
$$254$$ 6.45986e17 0.594251
$$255$$ −2.87260e17 −0.256581
$$256$$ 1.23980e18 1.07535
$$257$$ −8.28562e17 −0.697954 −0.348977 0.937131i $$-0.613471\pi$$
−0.348977 + 0.937131i $$0.613471\pi$$
$$258$$ 3.56090e17 0.291348
$$259$$ −2.91744e18 −2.31875
$$260$$ −1.37557e17 −0.106214
$$261$$ 1.15867e17 0.0869271
$$262$$ −3.51265e17 −0.256080
$$263$$ 1.40445e18 0.995038 0.497519 0.867453i $$-0.334244\pi$$
0.497519 + 0.867453i $$0.334244\pi$$
$$264$$ 2.81081e17 0.193554
$$265$$ 3.54200e17 0.237085
$$266$$ 9.53041e17 0.620153
$$267$$ −2.39589e18 −1.51577
$$268$$ −4.00500e17 −0.246372
$$269$$ 1.43582e18 0.858930 0.429465 0.903083i $$-0.358702\pi$$
0.429465 + 0.903083i $$0.358702\pi$$
$$270$$ 6.59050e17 0.383433
$$271$$ 5.09160e17 0.288127 0.144064 0.989568i $$-0.453983\pi$$
0.144064 + 0.989568i $$0.453983\pi$$
$$272$$ −2.19967e18 −1.21085
$$273$$ 1.79611e18 0.961865
$$274$$ 2.28792e18 1.19209
$$275$$ −5.72358e17 −0.290184
$$276$$ −4.39449e17 −0.216815
$$277$$ 5.68946e17 0.273195 0.136598 0.990627i $$-0.456383\pi$$
0.136598 + 0.990627i $$0.456383\pi$$
$$278$$ −4.03292e18 −1.88488
$$279$$ −2.24774e17 −0.102262
$$280$$ −5.99797e17 −0.265655
$$281$$ −4.06184e18 −1.75156 −0.875780 0.482710i $$-0.839652\pi$$
−0.875780 + 0.482710i $$0.839652\pi$$
$$282$$ 2.46650e18 1.03565
$$283$$ 2.78506e18 1.13877 0.569385 0.822071i $$-0.307181\pi$$
0.569385 + 0.822071i $$0.307181\pi$$
$$284$$ 1.73670e18 0.691570
$$285$$ −2.72733e17 −0.105779
$$286$$ −8.45211e17 −0.319315
$$287$$ 4.63440e18 1.70561
$$288$$ 4.86463e17 0.174424
$$289$$ −1.51369e17 −0.0528813
$$290$$ −4.15366e17 −0.141399
$$291$$ −2.05161e18 −0.680608
$$292$$ −1.14120e18 −0.368969
$$293$$ −3.63803e18 −1.14646 −0.573230 0.819395i $$-0.694310\pi$$
−0.573230 + 0.819395i $$0.694310\pi$$
$$294$$ −2.32766e18 −0.715013
$$295$$ 5.13745e17 0.153845
$$296$$ 4.21532e18 1.23067
$$297$$ 1.20541e18 0.343131
$$298$$ −2.71209e18 −0.752803
$$299$$ −1.79641e18 −0.486262
$$300$$ 1.29272e18 0.341267
$$301$$ −1.38979e18 −0.357849
$$302$$ 6.21190e18 1.56017
$$303$$ 2.73746e18 0.670701
$$304$$ −2.08843e18 −0.499192
$$305$$ 2.56998e17 0.0599351
$$306$$ −1.11667e18 −0.254106
$$307$$ −9.75296e17 −0.216570 −0.108285 0.994120i $$-0.534536\pi$$
−0.108285 + 0.994120i $$0.534536\pi$$
$$308$$ 8.06969e17 0.174874
$$309$$ −2.48125e18 −0.524786
$$310$$ 8.05783e17 0.166343
$$311$$ 3.36692e17 0.0678468 0.0339234 0.999424i $$-0.489200\pi$$
0.0339234 + 0.999424i $$0.489200\pi$$
$$312$$ −2.59515e18 −0.510508
$$313$$ 3.65551e18 0.702046 0.351023 0.936367i $$-0.385834\pi$$
0.351023 + 0.936367i $$0.385834\pi$$
$$314$$ −3.13797e18 −0.588405
$$315$$ −4.61797e17 −0.0845515
$$316$$ −3.52937e17 −0.0631021
$$317$$ −7.97380e17 −0.139226 −0.0696131 0.997574i $$-0.522176\pi$$
−0.0696131 + 0.997574i $$0.522176\pi$$
$$318$$ −4.91548e18 −0.838229
$$319$$ −7.59708e17 −0.126537
$$320$$ 5.37283e17 0.0874135
$$321$$ 8.41788e18 1.33787
$$322$$ 5.76188e18 0.894633
$$323$$ 2.57395e18 0.390464
$$324$$ −2.09681e18 −0.310793
$$325$$ 5.28444e18 0.765375
$$326$$ 3.62321e18 0.512816
$$327$$ −4.24645e18 −0.587378
$$328$$ −6.69610e18 −0.905249
$$329$$ −9.62651e18 −1.27204
$$330$$ −7.75801e17 −0.100206
$$331$$ −1.01585e19 −1.28269 −0.641343 0.767255i $$-0.721622\pi$$
−0.641343 + 0.767255i $$0.721622\pi$$
$$332$$ −3.91276e18 −0.483000
$$333$$ 3.24546e18 0.391692
$$334$$ 1.38672e19 1.63640
$$335$$ −1.50274e18 −0.173399
$$336$$ 1.26241e19 1.42448
$$337$$ −4.81465e18 −0.531301 −0.265651 0.964069i $$-0.585587\pi$$
−0.265651 + 0.964069i $$0.585587\pi$$
$$338$$ −3.25253e18 −0.351032
$$339$$ 6.87734e18 0.725977
$$340$$ 1.19160e18 0.123038
$$341$$ 1.47378e18 0.148859
$$342$$ −1.06020e18 −0.104759
$$343$$ −4.31515e18 −0.417148
$$344$$ 2.00806e18 0.189928
$$345$$ −1.64888e18 −0.152597
$$346$$ −1.64130e19 −1.48634
$$347$$ 4.50275e18 0.399031 0.199516 0.979895i $$-0.436063\pi$$
0.199516 + 0.979895i $$0.436063\pi$$
$$348$$ 1.71586e18 0.148812
$$349$$ 2.24323e19 1.90407 0.952036 0.305986i $$-0.0989860\pi$$
0.952036 + 0.305986i $$0.0989860\pi$$
$$350$$ −1.69496e19 −1.40815
$$351$$ −1.11292e19 −0.905026
$$352$$ −3.18961e18 −0.253902
$$353$$ 8.02510e18 0.625374 0.312687 0.949856i $$-0.398771\pi$$
0.312687 + 0.949856i $$0.398771\pi$$
$$354$$ −7.12961e18 −0.543928
$$355$$ 6.51636e18 0.486735
$$356$$ 9.93851e18 0.726853
$$357$$ −1.55590e19 −1.11422
$$358$$ 2.01690e19 1.41436
$$359$$ 1.61507e18 0.110913 0.0554567 0.998461i $$-0.482339\pi$$
0.0554567 + 0.998461i $$0.482339\pi$$
$$360$$ 6.67236e17 0.0448756
$$361$$ −1.27374e19 −0.839026
$$362$$ 1.60526e19 1.03569
$$363$$ 1.25665e19 0.794171
$$364$$ −7.45055e18 −0.461241
$$365$$ −4.28195e18 −0.259684
$$366$$ −3.56655e18 −0.211905
$$367$$ −9.97799e18 −0.580828 −0.290414 0.956901i $$-0.593793\pi$$
−0.290414 + 0.956901i $$0.593793\pi$$
$$368$$ −1.26262e19 −0.720135
$$369$$ −5.15547e18 −0.288118
$$370$$ −1.16345e19 −0.637142
$$371$$ 1.91847e19 1.02956
$$372$$ −3.32865e18 −0.175064
$$373$$ −2.36866e19 −1.22092 −0.610459 0.792048i $$-0.709015\pi$$
−0.610459 + 0.792048i $$0.709015\pi$$
$$374$$ 7.32171e18 0.369893
$$375$$ 1.01747e19 0.503834
$$376$$ 1.39090e19 0.675132
$$377$$ 7.01419e18 0.333747
$$378$$ 3.56964e19 1.66508
$$379$$ 1.86851e19 0.854480 0.427240 0.904138i $$-0.359486\pi$$
0.427240 + 0.904138i $$0.359486\pi$$
$$380$$ 1.13133e18 0.0507241
$$381$$ −1.00128e19 −0.440167
$$382$$ −2.13024e19 −0.918235
$$383$$ −3.02521e19 −1.27869 −0.639343 0.768921i $$-0.720794\pi$$
−0.639343 + 0.768921i $$0.720794\pi$$
$$384$$ −2.44537e19 −1.01358
$$385$$ 3.02788e18 0.123079
$$386$$ −1.92494e18 −0.0767385
$$387$$ 1.54605e18 0.0604493
$$388$$ 8.51037e18 0.326370
$$389$$ −1.00714e18 −0.0378852 −0.0189426 0.999821i $$-0.506030\pi$$
−0.0189426 + 0.999821i $$0.506030\pi$$
$$390$$ 7.16278e18 0.264300
$$391$$ 1.55615e19 0.563283
$$392$$ −1.31261e19 −0.466112
$$393$$ 5.44461e18 0.189680
$$394$$ 7.65020e18 0.261487
$$395$$ −1.32428e18 −0.0444120
$$396$$ −8.97702e17 −0.0295405
$$397$$ 3.56324e19 1.15058 0.575290 0.817950i $$-0.304889\pi$$
0.575290 + 0.817950i $$0.304889\pi$$
$$398$$ −6.18756e19 −1.96063
$$399$$ −1.47721e19 −0.459353
$$400$$ 3.71422e19 1.13349
$$401$$ 3.94327e19 1.18106 0.590532 0.807014i $$-0.298918\pi$$
0.590532 + 0.807014i $$0.298918\pi$$
$$402$$ 2.08546e19 0.613065
$$403$$ −1.36071e19 −0.392624
$$404$$ −1.13554e19 −0.321620
$$405$$ −7.86757e18 −0.218740
$$406$$ −2.24977e19 −0.614034
$$407$$ −2.12796e19 −0.570172
$$408$$ 2.24807e19 0.591370
$$409$$ −5.27823e19 −1.36321 −0.681607 0.731719i $$-0.738718\pi$$
−0.681607 + 0.731719i $$0.738718\pi$$
$$410$$ 1.84817e19 0.468665
$$411$$ −3.54627e19 −0.882995
$$412$$ 1.02926e19 0.251649
$$413$$ 2.78262e19 0.668080
$$414$$ −6.40972e18 −0.151125
$$415$$ −1.46813e19 −0.339941
$$416$$ 2.94488e19 0.669681
$$417$$ 6.25102e19 1.39615
$$418$$ 6.95143e18 0.152494
$$419$$ 8.62630e18 0.185874 0.0929372 0.995672i $$-0.470374\pi$$
0.0929372 + 0.995672i $$0.470374\pi$$
$$420$$ −6.83870e18 −0.144745
$$421$$ −4.29249e19 −0.892469 −0.446235 0.894916i $$-0.647235\pi$$
−0.446235 + 0.894916i $$0.647235\pi$$
$$422$$ 8.11801e19 1.65808
$$423$$ 1.07089e19 0.214878
$$424$$ −2.77193e19 −0.546435
$$425$$ −4.57770e19 −0.886605
$$426$$ −9.04322e19 −1.72088
$$427$$ 1.39199e19 0.260272
$$428$$ −3.49186e19 −0.641547
$$429$$ 1.31008e19 0.236519
$$430$$ −5.54237e18 −0.0983291
$$431$$ 5.04764e19 0.880053 0.440026 0.897985i $$-0.354969\pi$$
0.440026 + 0.897985i $$0.354969\pi$$
$$432$$ −7.82227e19 −1.34031
$$433$$ 5.05734e19 0.851653 0.425827 0.904805i $$-0.359983\pi$$
0.425827 + 0.904805i $$0.359983\pi$$
$$434$$ 4.36440e19 0.722356
$$435$$ 6.43818e18 0.104735
$$436$$ 1.76149e19 0.281664
$$437$$ 1.47745e19 0.232222
$$438$$ 5.94238e19 0.918130
$$439$$ 2.47946e19 0.376594 0.188297 0.982112i $$-0.439703\pi$$
0.188297 + 0.982112i $$0.439703\pi$$
$$440$$ −4.37489e18 −0.0653238
$$441$$ −1.01061e19 −0.148352
$$442$$ −6.75996e19 −0.975612
$$443$$ −1.30654e20 −1.85394 −0.926970 0.375135i $$-0.877596\pi$$
−0.926970 + 0.375135i $$0.877596\pi$$
$$444$$ 4.80617e19 0.670544
$$445$$ 3.72909e19 0.511567
$$446$$ −5.46648e18 −0.0737389
$$447$$ 4.20373e19 0.557608
$$448$$ 2.91011e19 0.379598
$$449$$ −7.78280e19 −0.998363 −0.499181 0.866498i $$-0.666366\pi$$
−0.499181 + 0.866498i $$0.666366\pi$$
$$450$$ 1.88553e19 0.237870
$$451$$ 3.38031e19 0.419404
$$452$$ −2.85282e19 −0.348126
$$453$$ −9.62844e19 −1.15563
$$454$$ 6.55975e19 0.774405
$$455$$ −2.79556e19 −0.324627
$$456$$ 2.13438e19 0.243801
$$457$$ −1.18451e20 −1.33096 −0.665482 0.746414i $$-0.731774\pi$$
−0.665482 + 0.746414i $$0.731774\pi$$
$$458$$ 2.33262e19 0.257841
$$459$$ 9.64078e19 1.04838
$$460$$ 6.83981e18 0.0731746
$$461$$ 1.38643e20 1.45929 0.729644 0.683827i $$-0.239686\pi$$
0.729644 + 0.683827i $$0.239686\pi$$
$$462$$ −4.20200e19 −0.435153
$$463$$ 1.75645e20 1.78969 0.894846 0.446375i $$-0.147285\pi$$
0.894846 + 0.446375i $$0.147285\pi$$
$$464$$ 4.92999e19 0.494266
$$465$$ −1.24896e19 −0.123212
$$466$$ −1.70749e20 −1.65754
$$467$$ −1.36631e20 −1.30519 −0.652593 0.757708i $$-0.726319\pi$$
−0.652593 + 0.757708i $$0.726319\pi$$
$$468$$ 8.28826e18 0.0779147
$$469$$ −8.13935e19 −0.752997
$$470$$ −3.83899e19 −0.349528
$$471$$ 4.86385e19 0.435837
$$472$$ −4.02052e19 −0.354583
$$473$$ −1.01370e19 −0.0879938
$$474$$ 1.83779e19 0.157021
$$475$$ −4.34619e19 −0.365516
$$476$$ 6.45410e19 0.534298
$$477$$ −2.13417e19 −0.173917
$$478$$ 7.62386e19 0.611597
$$479$$ 6.41058e19 0.506269 0.253134 0.967431i $$-0.418539\pi$$
0.253134 + 0.967431i $$0.418539\pi$$
$$480$$ 2.70305e19 0.210157
$$481$$ 1.96470e20 1.50386
$$482$$ 1.48109e19 0.111617
$$483$$ −8.93091e19 −0.662662
$$484$$ −5.21276e19 −0.380827
$$485$$ 3.19323e19 0.229703
$$486$$ −7.22907e19 −0.512047
$$487$$ −2.41343e19 −0.168332 −0.0841662 0.996452i $$-0.526823\pi$$
−0.0841662 + 0.996452i $$0.526823\pi$$
$$488$$ −2.01124e19 −0.138139
$$489$$ −5.61598e19 −0.379847
$$490$$ 3.62289e19 0.241315
$$491$$ −2.80908e19 −0.184269 −0.0921346 0.995747i $$-0.529369\pi$$
−0.0921346 + 0.995747i $$0.529369\pi$$
$$492$$ −7.63469e19 −0.493234
$$493$$ −6.07611e19 −0.386611
$$494$$ −6.41808e19 −0.402210
$$495$$ −3.36832e18 −0.0207910
$$496$$ −9.56384e19 −0.581460
$$497$$ 3.52948e20 2.11368
$$498$$ 2.03743e20 1.20188
$$499$$ −1.71994e20 −0.999443 −0.499722 0.866186i $$-0.666564\pi$$
−0.499722 + 0.866186i $$0.666564\pi$$
$$500$$ −4.22062e19 −0.241602
$$501$$ −2.14941e20 −1.21210
$$502$$ 3.43020e20 1.90564
$$503$$ −1.83497e20 −1.00431 −0.502155 0.864778i $$-0.667459\pi$$
−0.502155 + 0.864778i $$0.667459\pi$$
$$504$$ 3.61398e19 0.194875
$$505$$ −4.26073e19 −0.226359
$$506$$ 4.20268e19 0.219987
$$507$$ 5.04142e19 0.260012
$$508$$ 4.15345e19 0.211072
$$509$$ 2.67204e20 1.33801 0.669004 0.743258i $$-0.266721\pi$$
0.669004 + 0.743258i $$0.266721\pi$$
$$510$$ −6.20482e19 −0.306163
$$511$$ −2.31925e20 −1.12769
$$512$$ 2.84604e19 0.136369
$$513$$ 9.15321e19 0.432209
$$514$$ −1.78969e20 −0.832828
$$515$$ 3.86195e19 0.177114
$$516$$ 2.28953e19 0.103484
$$517$$ −7.02153e19 −0.312790
$$518$$ −6.30167e20 −2.76683
$$519$$ 2.54401e20 1.10094
$$520$$ 4.03922e19 0.172295
$$521$$ −2.01468e20 −0.847076 −0.423538 0.905878i $$-0.639212\pi$$
−0.423538 + 0.905878i $$0.639212\pi$$
$$522$$ 2.50272e19 0.103725
$$523$$ 3.58989e20 1.46662 0.733311 0.679894i $$-0.237974\pi$$
0.733311 + 0.679894i $$0.237974\pi$$
$$524$$ −2.25850e19 −0.0909570
$$525$$ 2.62718e20 1.04303
$$526$$ 3.03362e20 1.18732
$$527$$ 1.17872e20 0.454813
$$528$$ 9.20799e19 0.350276
$$529$$ −1.77312e20 −0.664997
$$530$$ 7.65071e19 0.282900
$$531$$ −3.09549e19 −0.112855
$$532$$ 6.12770e19 0.220272
$$533$$ −3.12095e20 −1.10620
$$534$$ −5.17512e20 −1.80868
$$535$$ −1.31020e20 −0.451528
$$536$$ 1.17603e20 0.399652
$$537$$ −3.12619e20 −1.04763
$$538$$ 3.10137e20 1.02491
$$539$$ 6.62628e19 0.215950
$$540$$ 4.23744e19 0.136192
$$541$$ 2.02328e20 0.641323 0.320662 0.947194i $$-0.396095\pi$$
0.320662 + 0.947194i $$0.396095\pi$$
$$542$$ 1.09979e20 0.343806
$$543$$ −2.48816e20 −0.767147
$$544$$ −2.55103e20 −0.775755
$$545$$ 6.60939e19 0.198238
$$546$$ 3.87961e20 1.14774
$$547$$ 7.40963e19 0.216218 0.108109 0.994139i $$-0.465520\pi$$
0.108109 + 0.994139i $$0.465520\pi$$
$$548$$ 1.47104e20 0.423420
$$549$$ −1.54850e19 −0.0439662
$$550$$ −1.23629e20 −0.346259
$$551$$ −5.76882e19 −0.159386
$$552$$ 1.29040e20 0.351707
$$553$$ −7.17273e19 −0.192862
$$554$$ 1.22892e20 0.325988
$$555$$ 1.80335e20 0.471936
$$556$$ −2.59302e20 −0.669490
$$557$$ 2.09626e18 0.00533987 0.00266994 0.999996i $$-0.499150\pi$$
0.00266994 + 0.999996i $$0.499150\pi$$
$$558$$ −4.85511e19 −0.122023
$$559$$ 9.35927e19 0.232088
$$560$$ −1.96489e20 −0.480759
$$561$$ −1.13487e20 −0.273983
$$562$$ −8.77357e20 −2.09004
$$563$$ 6.87353e20 1.61572 0.807861 0.589373i $$-0.200625\pi$$
0.807861 + 0.589373i $$0.200625\pi$$
$$564$$ 1.58587e20 0.367852
$$565$$ −1.07042e20 −0.245015
$$566$$ 6.01573e20 1.35883
$$567$$ −4.26134e20 −0.949891
$$568$$ −5.09964e20 −1.12183
$$569$$ −9.05218e19 −0.196522 −0.0982610 0.995161i $$-0.531328\pi$$
−0.0982610 + 0.995161i $$0.531328\pi$$
$$570$$ −5.89102e19 −0.126220
$$571$$ 2.05774e20 0.435130 0.217565 0.976046i $$-0.430189\pi$$
0.217565 + 0.976046i $$0.430189\pi$$
$$572$$ −5.43439e19 −0.113418
$$573$$ 3.30188e20 0.680145
$$574$$ 1.00103e21 2.03520
$$575$$ −2.62761e20 −0.527293
$$576$$ −3.23731e19 −0.0641233
$$577$$ 5.70778e20 1.11596 0.557980 0.829854i $$-0.311576\pi$$
0.557980 + 0.829854i $$0.311576\pi$$
$$578$$ −3.26956e19 −0.0631002
$$579$$ 2.98366e19 0.0568408
$$580$$ −2.67065e19 −0.0502236
$$581$$ −7.95190e20 −1.47622
$$582$$ −4.43147e20 −0.812130
$$583$$ 1.39932e20 0.253164
$$584$$ 3.35102e20 0.598522
$$585$$ 3.10989e19 0.0548373
$$586$$ −7.85814e20 −1.36800
$$587$$ −9.30363e20 −1.59907 −0.799534 0.600621i $$-0.794920\pi$$
−0.799534 + 0.600621i $$0.794920\pi$$
$$588$$ −1.49660e20 −0.253966
$$589$$ 1.11911e20 0.187503
$$590$$ 1.10969e20 0.183574
$$591$$ −1.18578e20 −0.193686
$$592$$ 1.38090e21 2.22716
$$593$$ 3.54225e20 0.564116 0.282058 0.959397i $$-0.408983\pi$$
0.282058 + 0.959397i $$0.408983\pi$$
$$594$$ 2.60368e20 0.409438
$$595$$ 2.42168e20 0.376045
$$596$$ −1.74377e20 −0.267388
$$597$$ 9.59071e20 1.45226
$$598$$ −3.88024e20 −0.580229
$$599$$ −3.30045e20 −0.487385 −0.243693 0.969853i $$-0.578359\pi$$
−0.243693 + 0.969853i $$0.578359\pi$$
$$600$$ −3.79594e20 −0.553586
$$601$$ −3.35884e20 −0.483761 −0.241880 0.970306i $$-0.577764\pi$$
−0.241880 + 0.970306i $$0.577764\pi$$
$$602$$ −3.00194e20 −0.427000
$$603$$ 9.05451e19 0.127199
$$604$$ 3.99402e20 0.554158
$$605$$ −1.95591e20 −0.268030
$$606$$ 5.91292e20 0.800309
$$607$$ −1.33438e21 −1.78387 −0.891934 0.452165i $$-0.850652\pi$$
−0.891934 + 0.452165i $$0.850652\pi$$
$$608$$ −2.42202e20 −0.319816
$$609$$ 3.48714e20 0.454820
$$610$$ 5.55116e19 0.0715172
$$611$$ 6.48280e20 0.825000
$$612$$ −7.17978e19 −0.0902559
$$613$$ 5.68844e18 0.00706381 0.00353191 0.999994i $$-0.498876\pi$$
0.00353191 + 0.999994i $$0.498876\pi$$
$$614$$ −2.10664e20 −0.258421
$$615$$ −2.86466e20 −0.347144
$$616$$ −2.36959e20 −0.283673
$$617$$ 3.98915e20 0.471783 0.235891 0.971779i $$-0.424199\pi$$
0.235891 + 0.971779i $$0.424199\pi$$
$$618$$ −5.35950e20 −0.626197
$$619$$ −5.40017e20 −0.623343 −0.311672 0.950190i $$-0.600889\pi$$
−0.311672 + 0.950190i $$0.600889\pi$$
$$620$$ 5.18088e19 0.0590835
$$621$$ 5.53384e20 0.623504
$$622$$ 7.27254e19 0.0809577
$$623$$ 2.01980e21 2.22151
$$624$$ −8.50151e20 −0.923871
$$625$$ 6.90089e20 0.740978
$$626$$ 7.89591e20 0.837711
$$627$$ −1.07747e20 −0.112953
$$628$$ −2.01760e20 −0.208996
$$629$$ −1.70194e21 −1.74206
$$630$$ −9.97480e19 −0.100891
$$631$$ 9.59111e20 0.958625 0.479312 0.877644i $$-0.340886\pi$$
0.479312 + 0.877644i $$0.340886\pi$$
$$632$$ 1.03637e20 0.102361
$$633$$ −1.25829e21 −1.22816
$$634$$ −1.72234e20 −0.166131
$$635$$ 1.55844e20 0.148555
$$636$$ −3.16047e20 −0.297731
$$637$$ −6.11788e20 −0.569581
$$638$$ −1.64097e20 −0.150989
$$639$$ −3.92633e20 −0.357051
$$640$$ 3.80609e20 0.342082
$$641$$ −9.25925e20 −0.822509 −0.411255 0.911521i $$-0.634909\pi$$
−0.411255 + 0.911521i $$0.634909\pi$$
$$642$$ 1.81826e21 1.59641
$$643$$ −7.65928e20 −0.664669 −0.332335 0.943162i $$-0.607836\pi$$
−0.332335 + 0.943162i $$0.607836\pi$$
$$644$$ 3.70467e20 0.317765
$$645$$ 8.59068e19 0.0728332
$$646$$ 5.55972e20 0.465918
$$647$$ 1.36075e21 1.12719 0.563596 0.826051i $$-0.309418\pi$$
0.563596 + 0.826051i $$0.309418\pi$$
$$648$$ 6.15709e20 0.504153
$$649$$ 2.02963e20 0.164279
$$650$$ 1.14144e21 0.913278
$$651$$ −6.76481e20 −0.535055
$$652$$ 2.32959e20 0.182147
$$653$$ −2.71809e20 −0.210094 −0.105047 0.994467i $$-0.533499\pi$$
−0.105047 + 0.994467i $$0.533499\pi$$
$$654$$ −9.17233e20 −0.700885
$$655$$ −8.47427e19 −0.0640166
$$656$$ −2.19359e21 −1.63824
$$657$$ 2.58002e20 0.190495
$$658$$ −2.07933e21 −1.51785
$$659$$ 6.74316e20 0.486657 0.243329 0.969944i $$-0.421761\pi$$
0.243329 + 0.969944i $$0.421761\pi$$
$$660$$ −4.98811e19 −0.0355923
$$661$$ 1.26727e21 0.894042 0.447021 0.894524i $$-0.352485\pi$$
0.447021 + 0.894524i $$0.352485\pi$$
$$662$$ −2.19424e21 −1.53056
$$663$$ 1.04779e21 0.722644
$$664$$ 1.14894e21 0.783499
$$665$$ 2.29921e20 0.155030
$$666$$ 7.01020e20 0.467384
$$667$$ −3.48770e20 −0.229930
$$668$$ 8.91609e20 0.581234
$$669$$ 8.47305e19 0.0546190
$$670$$ −3.24592e20 −0.206908
$$671$$ 1.01531e20 0.0640000
$$672$$ 1.46406e21 0.912620
$$673$$ −1.13945e21 −0.702394 −0.351197 0.936302i $$-0.614225\pi$$
−0.351197 + 0.936302i $$0.614225\pi$$
$$674$$ −1.03997e21 −0.633971
$$675$$ −1.62788e21 −0.981393
$$676$$ −2.09126e20 −0.124683
$$677$$ 1.74431e21 1.02851 0.514256 0.857637i $$-0.328068\pi$$
0.514256 + 0.857637i $$0.328068\pi$$
$$678$$ 1.48550e21 0.866266
$$679$$ 1.72956e21 0.997500
$$680$$ −3.49902e20 −0.199586
$$681$$ −1.01676e21 −0.573608
$$682$$ 3.18337e20 0.177625
$$683$$ −1.43739e21 −0.793267 −0.396634 0.917977i $$-0.629822\pi$$
−0.396634 + 0.917977i $$0.629822\pi$$
$$684$$ −6.81667e19 −0.0372093
$$685$$ 5.51960e20 0.298008
$$686$$ −9.32073e20 −0.497759
$$687$$ −3.61556e20 −0.190985
$$688$$ 6.57825e20 0.343714
$$689$$ −1.29196e21 −0.667735
$$690$$ −3.56159e20 −0.182085
$$691$$ −1.77548e21 −0.897903 −0.448951 0.893556i $$-0.648202\pi$$
−0.448951 + 0.893556i $$0.648202\pi$$
$$692$$ −1.05529e21 −0.527932
$$693$$ −1.82440e20 −0.0902860
$$694$$ 9.72594e20 0.476141
$$695$$ −9.72941e20 −0.471195
$$696$$ −5.03846e20 −0.241395
$$697$$ 2.70356e21 1.28141
$$698$$ 4.84538e21 2.27202
$$699$$ 2.64661e21 1.22776
$$700$$ −1.08980e21 −0.500161
$$701$$ 1.43100e21 0.649764 0.324882 0.945755i $$-0.394675\pi$$
0.324882 + 0.945755i $$0.394675\pi$$
$$702$$ −2.40391e21 −1.07992
$$703$$ −1.61586e21 −0.718191
$$704$$ 2.12262e20 0.0933420
$$705$$ 5.95043e20 0.258899
$$706$$ 1.73342e21 0.746223
$$707$$ −2.30776e21 −0.982980
$$708$$ −4.58408e20 −0.193198
$$709$$ −2.41840e21 −1.00851 −0.504257 0.863554i $$-0.668234\pi$$
−0.504257 + 0.863554i $$0.668234\pi$$
$$710$$ 1.40753e21 0.580793
$$711$$ 7.97921e19 0.0325790
$$712$$ −2.91835e21 −1.17906
$$713$$ 6.76591e20 0.270492
$$714$$ −3.36074e21 −1.32953
$$715$$ −2.03907e20 −0.0798246
$$716$$ 1.29679e21 0.502368
$$717$$ −1.18170e21 −0.453015
$$718$$ 3.48856e20 0.132347
$$719$$ 4.74444e21 1.78122 0.890611 0.454766i $$-0.150277\pi$$
0.890611 + 0.454766i $$0.150277\pi$$
$$720$$ 2.18581e20 0.0812118
$$721$$ 2.09176e21 0.769127
$$722$$ −2.75127e21 −1.00116
$$723$$ −2.29569e20 −0.0826753
$$724$$ 1.03212e21 0.367868
$$725$$ 1.02597e21 0.361909
$$726$$ 2.71436e21 0.947639
$$727$$ −3.59265e21 −1.24138 −0.620692 0.784054i $$-0.713148\pi$$
−0.620692 + 0.784054i $$0.713148\pi$$
$$728$$ 2.18778e21 0.748202
$$729$$ 3.28690e21 1.11258
$$730$$ −9.24902e20 −0.309866
$$731$$ −8.10755e20 −0.268850
$$732$$ −2.29316e20 −0.0752664
$$733$$ −2.76824e21 −0.899339 −0.449669 0.893195i $$-0.648458\pi$$
−0.449669 + 0.893195i $$0.648458\pi$$
$$734$$ −2.15525e21 −0.693069
$$735$$ −5.61548e20 −0.178744
$$736$$ −1.46430e21 −0.461367
$$737$$ −5.93680e20 −0.185160
$$738$$ −1.11358e21 −0.343795
$$739$$ 3.55824e21 1.08743 0.543716 0.839269i $$-0.317017\pi$$
0.543716 + 0.839269i $$0.317017\pi$$
$$740$$ −7.48058e20 −0.226307
$$741$$ 9.94803e20 0.297921
$$742$$ 4.14389e21 1.22851
$$743$$ −1.94092e21 −0.569628 −0.284814 0.958583i $$-0.591932\pi$$
−0.284814 + 0.958583i $$0.591932\pi$$
$$744$$ 9.77427e20 0.283980
$$745$$ −6.54291e20 −0.188191
$$746$$ −5.11630e21 −1.45685
$$747$$ 8.84598e20 0.249368
$$748$$ 4.70759e20 0.131382
$$749$$ −7.09651e21 −1.96079
$$750$$ 2.19774e21 0.601196
$$751$$ 4.75565e21 1.28798 0.643992 0.765032i $$-0.277277\pi$$
0.643992 + 0.765032i $$0.277277\pi$$
$$752$$ 4.55650e21 1.22179
$$753$$ −5.31681e21 −1.41153
$$754$$ 1.51507e21 0.398241
$$755$$ 1.49862e21 0.390022
$$756$$ 2.29514e21 0.591421
$$757$$ 3.62137e21 0.923960 0.461980 0.886890i $$-0.347139\pi$$
0.461980 + 0.886890i $$0.347139\pi$$
$$758$$ 4.03599e21 1.01960
$$759$$ −6.51416e20 −0.162947
$$760$$ −3.32206e20 −0.0822821
$$761$$ −3.86361e21 −0.947564 −0.473782 0.880642i $$-0.657112\pi$$
−0.473782 + 0.880642i $$0.657112\pi$$
$$762$$ −2.16276e21 −0.525226
$$763$$ 3.57987e21 0.860862
$$764$$ −1.36967e21 −0.326148
$$765$$ −2.69397e20 −0.0635231
$$766$$ −6.53445e21 −1.52578
$$767$$ −1.87391e21 −0.433294
$$768$$ −4.15085e21 −0.950446
$$769$$ −5.39327e21 −1.22294 −0.611469 0.791268i $$-0.709421\pi$$
−0.611469 + 0.791268i $$0.709421\pi$$
$$770$$ 6.54021e20 0.146863
$$771$$ 2.77403e21 0.616883
$$772$$ −1.23767e20 −0.0272568
$$773$$ 6.57037e21 1.43299 0.716496 0.697591i $$-0.245745\pi$$
0.716496 + 0.697591i $$0.245745\pi$$
$$774$$ 3.33947e20 0.0721306
$$775$$ −1.99031e21 −0.425754
$$776$$ −2.49899e21 −0.529422
$$777$$ 9.76758e21 2.04941
$$778$$ −2.17543e20 −0.0452062
$$779$$ 2.56683e21 0.528282
$$780$$ 4.60540e20 0.0938767
$$781$$ 2.57439e21 0.519746
$$782$$ 3.36129e21 0.672133
$$783$$ −2.16073e21 −0.427944
$$784$$ −4.30001e21 −0.843527
$$785$$ −7.57035e20 −0.147094
$$786$$ 1.17604e21 0.226335
$$787$$ −3.72074e20 −0.0709281 −0.0354641 0.999371i $$-0.511291\pi$$
−0.0354641 + 0.999371i $$0.511291\pi$$
$$788$$ 4.91879e20 0.0928778
$$789$$ −4.70211e21 −0.879459
$$790$$ −2.86044e20 −0.0529943
$$791$$ −5.79778e21 −1.06399
$$792$$ 2.63602e20 0.0479192
$$793$$ −9.37412e20 −0.168804
$$794$$ 7.69660e21 1.37292
$$795$$ −1.18586e21 −0.209546
$$796$$ −3.97837e21 −0.696397
$$797$$ 2.61511e21 0.453474 0.226737 0.973956i $$-0.427194\pi$$
0.226737 + 0.973956i $$0.427194\pi$$
$$798$$ −3.19078e21 −0.548119
$$799$$ −5.61579e21 −0.955674
$$800$$ 4.30750e21 0.726190
$$801$$ −2.24690e21 −0.375267
$$802$$ 8.51746e21 1.40930
$$803$$ −1.69165e21 −0.277296
$$804$$ 1.34087e21 0.217755
$$805$$ 1.39005e21 0.223647
$$806$$ −2.93913e21 −0.468495
$$807$$ −4.80713e21 −0.759161
$$808$$ 3.33441e21 0.521715
$$809$$ 5.34899e21 0.829198 0.414599 0.910004i $$-0.363922\pi$$
0.414599 + 0.910004i $$0.363922\pi$$
$$810$$ −1.69939e21 −0.261010
$$811$$ 8.46492e21 1.28815 0.644075 0.764962i $$-0.277242\pi$$
0.644075 + 0.764962i $$0.277242\pi$$
$$812$$ −1.44652e21 −0.218099
$$813$$ −1.70467e21 −0.254660
$$814$$ −4.59640e21 −0.680354
$$815$$ 8.74100e20 0.128197
$$816$$ 7.36451e21 1.07021
$$817$$ −7.69753e20 −0.110837
$$818$$ −1.14010e22 −1.62664
$$819$$ 1.68442e21 0.238134
$$820$$ 1.18830e21 0.166465
$$821$$ 7.99397e21 1.10966 0.554829 0.831965i $$-0.312784\pi$$
0.554829 + 0.831965i $$0.312784\pi$$
$$822$$ −7.65994e21 −1.05363
$$823$$ 1.96841e21 0.268297 0.134148 0.990961i $$-0.457170\pi$$
0.134148 + 0.990961i $$0.457170\pi$$
$$824$$ −3.02232e21 −0.408213
$$825$$ 1.91626e21 0.256477
$$826$$ 6.01046e21 0.797181
$$827$$ −1.43539e22 −1.88659 −0.943296 0.331954i $$-0.892292\pi$$
−0.943296 + 0.331954i $$0.892292\pi$$
$$828$$ −4.12121e20 −0.0536782
$$829$$ −8.83327e21 −1.14015 −0.570076 0.821592i $$-0.693086\pi$$
−0.570076 + 0.821592i $$0.693086\pi$$
$$830$$ −3.17116e21 −0.405632
$$831$$ −1.90483e21 −0.241462
$$832$$ −1.95976e21 −0.246195
$$833$$ 5.29967e21 0.659799
$$834$$ 1.35022e22 1.66594
$$835$$ 3.34546e21 0.409079
$$836$$ 4.46951e20 0.0541643
$$837$$ 4.19166e21 0.503437
$$838$$ 1.86328e21 0.221793
$$839$$ 1.26696e22 1.49469 0.747343 0.664439i $$-0.231329\pi$$
0.747343 + 0.664439i $$0.231329\pi$$
$$840$$ 2.00812e21 0.234798
$$841$$ −7.26739e21 −0.842187
$$842$$ −9.27177e21 −1.06493
$$843$$ 1.35990e22 1.54811
$$844$$ 5.21958e21 0.588935
$$845$$ −7.84673e20 −0.0877533
$$846$$ 2.31312e21 0.256401
$$847$$ −1.05939e22 −1.16394
$$848$$ −9.08064e21 −0.988889
$$849$$ −9.32438e21 −1.00650
$$850$$ −9.88783e21 −1.05793
$$851$$ −9.76917e21 −1.03606
$$852$$ −5.81446e21 −0.611241
$$853$$ 6.00532e21 0.625776 0.312888 0.949790i $$-0.398704\pi$$
0.312888 + 0.949790i $$0.398704\pi$$
$$854$$ 3.00670e21 0.310568
$$855$$ −2.55773e20 −0.0261883
$$856$$ 1.02535e22 1.04069
$$857$$ 1.47589e22 1.48491 0.742453 0.669898i $$-0.233662\pi$$
0.742453 + 0.669898i $$0.233662\pi$$
$$858$$ 2.82976e21 0.282225
$$859$$ 9.64956e20 0.0954023 0.0477012 0.998862i $$-0.484810\pi$$
0.0477012 + 0.998862i $$0.484810\pi$$
$$860$$ −3.56354e20 −0.0349255
$$861$$ −1.55160e22 −1.50749
$$862$$ 1.09029e22 1.05012
$$863$$ 3.44391e21 0.328829 0.164415 0.986391i $$-0.447426\pi$$
0.164415 + 0.986391i $$0.447426\pi$$
$$864$$ −9.07173e21 −0.858691
$$865$$ −3.95963e21 −0.371564
$$866$$ 1.09239e22 1.01623
$$867$$ 5.06782e20 0.0467389
$$868$$ 2.80614e21 0.256574
$$869$$ −5.23175e20 −0.0474241
$$870$$ 1.39065e21 0.124975
$$871$$ 5.48130e21 0.488368
$$872$$ −5.17245e21 −0.456901
$$873$$ −1.92403e21 −0.168502
$$874$$ 3.19130e21 0.277097
$$875$$ −8.57756e21 −0.738420
$$876$$ 3.82073e21 0.326111
$$877$$ −1.09850e22 −0.929617 −0.464808 0.885411i $$-0.653877\pi$$
−0.464808 + 0.885411i $$0.653877\pi$$
$$878$$ 5.35564e21 0.449368
$$879$$ 1.21801e22 1.01329
$$880$$ −1.43318e21 −0.118217
$$881$$ −7.98462e21 −0.653033 −0.326516 0.945192i $$-0.605875\pi$$
−0.326516 + 0.945192i $$0.605875\pi$$
$$882$$ −2.18291e21 −0.177020
$$883$$ 5.45236e21 0.438409 0.219204 0.975679i $$-0.429654\pi$$
0.219204 + 0.975679i $$0.429654\pi$$
$$884$$ −4.34640e21 −0.346528
$$885$$ −1.72002e21 −0.135975
$$886$$ −2.82213e22 −2.21220
$$887$$ 1.67127e22 1.29903 0.649517 0.760347i $$-0.274971\pi$$
0.649517 + 0.760347i $$0.274971\pi$$
$$888$$ −1.41129e22 −1.08772
$$889$$ 8.44105e21 0.645109
$$890$$ 8.05483e21 0.610424
$$891$$ −3.10820e21 −0.233575
$$892$$ −3.51475e20 −0.0261913
$$893$$ −5.33178e21 −0.393991
$$894$$ 9.08007e21 0.665361
$$895$$ 4.86576e21 0.353572
$$896$$ 2.06151e22 1.48551
$$897$$ 6.01436e21 0.429780
$$898$$ −1.68108e22 −1.19129
$$899$$ −2.64180e21 −0.185653
$$900$$ 1.21233e21 0.0844892
$$901$$ 1.11917e22 0.773500
$$902$$ 7.30146e21 0.500450
$$903$$ 4.65300e21 0.316283
$$904$$ 8.37704e21 0.564712
$$905$$ 3.87269e21 0.258910
$$906$$ −2.07974e22 −1.37895
$$907$$ −1.53384e22 −1.00862 −0.504309 0.863523i $$-0.668253\pi$$
−0.504309 + 0.863523i $$0.668253\pi$$
$$908$$ 4.21767e21 0.275061
$$909$$ 2.56723e21 0.166049
$$910$$ −6.03842e21 −0.387358
$$911$$ −1.49134e22 −0.948829 −0.474415 0.880302i $$-0.657340\pi$$
−0.474415 + 0.880302i $$0.657340\pi$$
$$912$$ 6.99206e21 0.441209
$$913$$ −5.80007e21 −0.362997
$$914$$ −2.55854e22 −1.58816
$$915$$ −8.60430e20 −0.0529734
$$916$$ 1.49979e21 0.0915827
$$917$$ −4.58995e21 −0.277996
$$918$$ 2.08241e22 1.25097
$$919$$ −5.86667e21 −0.349563 −0.174782 0.984607i $$-0.555922\pi$$
−0.174782 + 0.984607i $$0.555922\pi$$
$$920$$ −2.00844e21 −0.118700
$$921$$ 3.26529e21 0.191414
$$922$$ 2.99469e22 1.74129
$$923$$ −2.37687e22 −1.37086
$$924$$ −2.70173e21 −0.154562
$$925$$ 2.87377e22 1.63076
$$926$$ 3.79393e22 2.13554
$$927$$ −2.32695e21 −0.129924
$$928$$ 5.71747e21 0.316660
$$929$$ −1.67946e22 −0.922684 −0.461342 0.887222i $$-0.652632\pi$$
−0.461342 + 0.887222i $$0.652632\pi$$
$$930$$ −2.69776e21 −0.147022
$$931$$ 5.03165e21 0.272012
$$932$$ −1.09786e22 −0.588743
$$933$$ −1.12724e21 −0.0599661
$$934$$ −2.95123e22 −1.55740
$$935$$ 1.76636e21 0.0924683
$$936$$ −2.43377e21 −0.126389
$$937$$ 5.04466e21 0.259887 0.129944 0.991521i $$-0.458520\pi$$
0.129944 + 0.991521i $$0.458520\pi$$
$$938$$ −1.75810e22 −0.898508
$$939$$ −1.22387e22 −0.620500
$$940$$ −2.46833e21 −0.124149
$$941$$ 1.65425e22 0.825430 0.412715 0.910860i $$-0.364581\pi$$
0.412715 + 0.910860i $$0.364581\pi$$
$$942$$ 1.05059e22 0.520059
$$943$$ 1.55185e22 0.762100
$$944$$ −1.31709e22 −0.641691
$$945$$ 8.61175e21 0.416249
$$946$$ −2.18960e21 −0.104998
$$947$$ −9.81583e21 −0.466984 −0.233492 0.972359i $$-0.575015\pi$$
−0.233492 + 0.972359i $$0.575015\pi$$
$$948$$ 1.18163e21 0.0557725
$$949$$ 1.56186e22 0.731384
$$950$$ −9.38776e21 −0.436149
$$951$$ 2.66963e21 0.123054
$$952$$ −1.89519e22 −0.866712
$$953$$ −5.97914e21 −0.271295 −0.135648 0.990757i $$-0.543311\pi$$
−0.135648 + 0.990757i $$0.543311\pi$$
$$954$$ −4.60981e21 −0.207525
$$955$$ −5.13921e21 −0.229547
$$956$$ 4.90186e21 0.217233
$$957$$ 2.54350e21 0.111839
$$958$$ 1.38469e22 0.604101
$$959$$ 2.98960e22 1.29412
$$960$$ −1.79882e21 −0.0772600
$$961$$ −1.83404e22 −0.781596
$$962$$ 4.24375e22 1.79447
$$963$$ 7.89441e21 0.331225
$$964$$ 9.52286e20 0.0396451
$$965$$ −4.64393e20 −0.0191836
$$966$$ −1.92908e22 −0.790717
$$967$$ −1.44757e22 −0.588764 −0.294382 0.955688i $$-0.595114\pi$$
−0.294382 + 0.955688i $$0.595114\pi$$
$$968$$ 1.53068e22 0.617759
$$969$$ −8.61757e21 −0.345109
$$970$$ 6.89737e21 0.274092
$$971$$ 1.77921e21 0.0701590 0.0350795 0.999385i $$-0.488832\pi$$
0.0350795 + 0.999385i $$0.488832\pi$$
$$972$$ −4.64802e21 −0.181874
$$973$$ −5.26978e22 −2.04619
$$974$$ −5.21301e21 −0.200861
$$975$$ −1.76923e22 −0.676472
$$976$$ −6.58868e21 −0.249991
$$977$$ 1.04088e22 0.391913 0.195957 0.980613i $$-0.437219\pi$$
0.195957 + 0.980613i $$0.437219\pi$$
$$978$$ −1.21305e22 −0.453250
$$979$$ 1.47323e22 0.546262
$$980$$ 2.32938e21 0.0857127
$$981$$ −3.98238e21 −0.145420
$$982$$ −6.06761e21 −0.219878
$$983$$ 3.26461e22 1.17403 0.587017 0.809575i $$-0.300302\pi$$
0.587017 + 0.809575i $$0.300302\pi$$
$$984$$ 2.24185e22 0.800100
$$985$$ 1.84561e21 0.0653684
$$986$$ −1.31244e22 −0.461320
$$987$$ 3.22295e22 1.12428
$$988$$ −4.12659e21 −0.142861
$$989$$ −4.65376e21 −0.159894
$$990$$ −7.27557e20 −0.0248087
$$991$$ −7.47327e21 −0.252906 −0.126453 0.991973i $$-0.540359\pi$$
−0.126453 + 0.991973i $$0.540359\pi$$
$$992$$ −1.10915e22 −0.372523
$$993$$ 3.40107e22 1.13369
$$994$$ 7.62369e22 2.52213
$$995$$ −1.49275e22 −0.490132
$$996$$ 1.30999e22 0.426897
$$997$$ −3.10809e22 −1.00526 −0.502632 0.864500i $$-0.667635\pi$$
−0.502632 + 0.864500i $$0.667635\pi$$
$$998$$ −3.71506e22 −1.19258
$$999$$ −6.05226e22 −1.92831
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.16.a.a.1.1 1
3.2 odd 2 9.16.a.a.1.1 1
4.3 odd 2 16.16.a.d.1.1 1
5.2 odd 4 25.16.b.a.24.2 2
5.3 odd 4 25.16.b.a.24.1 2
5.4 even 2 25.16.a.a.1.1 1
7.2 even 3 49.16.c.c.18.1 2
7.3 odd 6 49.16.c.b.30.1 2
7.4 even 3 49.16.c.c.30.1 2
7.5 odd 6 49.16.c.b.18.1 2
7.6 odd 2 49.16.a.a.1.1 1
8.3 odd 2 64.16.a.c.1.1 1
8.5 even 2 64.16.a.i.1.1 1
11.10 odd 2 121.16.a.a.1.1 1
12.11 even 2 144.16.a.f.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
1.16.a.a.1.1 1 1.1 even 1 trivial
9.16.a.a.1.1 1 3.2 odd 2
16.16.a.d.1.1 1 4.3 odd 2
25.16.a.a.1.1 1 5.4 even 2
25.16.b.a.24.1 2 5.3 odd 4
25.16.b.a.24.2 2 5.2 odd 4
49.16.a.a.1.1 1 7.6 odd 2
49.16.c.b.18.1 2 7.5 odd 6
49.16.c.b.30.1 2 7.3 odd 6
49.16.c.c.18.1 2 7.2 even 3
49.16.c.c.30.1 2 7.4 even 3
64.16.a.c.1.1 1 8.3 odd 2
64.16.a.i.1.1 1 8.5 even 2
121.16.a.a.1.1 1 11.10 odd 2
144.16.a.f.1.1 1 12.11 even 2