LMFDB - Embedded newform 216.2.n.b.181.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(37,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("216.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.n (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.5
Root			$-1.12494 + 0.857038i$ of defining polynomial
Character	$\chi$	$=$	216.181
Dual form			216.2.n.b.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.179748 - 1.40274i) q^{2} +(-1.93538 - 0.504281i) q^{4} +(1.19115 - 0.687709i) q^{5} +(1.80469 - 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +O(q^{10})$	\(q+(0.179748 - 1.40274i) q^{2} +(-1.93538 - 0.504281i) q^{4} +(1.19115 - 0.687709i) q^{5} +(1.80469 - 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +(-0.750573 - 1.79449i) q^{10} +(-1.83294 - 1.05825i) q^{11} +(-0.887751 + 0.512543i) q^{13} +(-4.06032 - 3.09337i) q^{14} +(3.49140 + 1.95195i) q^{16} -0.808822 q^{17} -7.43122i q^{19} +(-2.65212 + 0.730306i) q^{20} +(-1.81392 + 2.38093i) q^{22} +(1.65498 + 2.86652i) q^{23} +(-1.55411 + 2.69180i) q^{25} +(0.559395 + 1.33742i) q^{26} +(-5.06904 + 5.13956i) q^{28} +(7.71083 + 4.45185i) q^{29} +(3.26436 + 5.65403i) q^{31} +(3.36566 - 4.54668i) q^{32} +(-0.145384 + 1.13457i) q^{34} -4.96439i q^{35} +4.01531i q^{37} +(-10.4241 - 1.33575i) q^{38} +(0.547718 + 3.85152i) q^{40} +(3.45852 + 5.99034i) q^{41} +(-0.245957 - 0.142003i) q^{43} +(3.01378 + 2.97243i) q^{44} +(4.31847 - 1.80627i) q^{46} +(3.61351 - 6.25878i) q^{47} +(-3.01378 - 5.22003i) q^{49} +(3.49656 + 2.66387i) q^{50} +(1.97660 - 0.544290i) q^{52} -3.86330i q^{53} -2.91107 q^{55} +(6.29834 + 8.03439i) q^{56} +(7.63082 - 10.0161i) q^{58} +(-7.06904 + 4.08131i) q^{59} +(6.31237 + 3.64445i) q^{61} +(8.51792 - 3.56275i) q^{62} +(-5.77286 - 5.53842i) q^{64} +(-0.704961 + 1.22103i) q^{65} +(-2.43973 + 1.40858i) q^{67} +(1.56538 + 0.407874i) q^{68} +(-6.96377 - 0.892341i) q^{70} -4.69830 q^{71} +0.409922 q^{73} +(5.63245 + 0.721745i) q^{74} +(-3.74743 + 14.3822i) q^{76} +(-6.61576 + 3.81961i) q^{77} +(-0.0456121 + 0.0790024i) q^{79} +(5.50115 - 0.0760042i) q^{80} +(9.02458 - 3.77467i) q^{82} +(2.40891 + 1.39079i) q^{83} +(-0.963426 + 0.556234i) q^{85} +(-0.243405 + 0.319490i) q^{86} +(4.71128 - 3.69328i) q^{88} -8.91934 q^{89} +3.69992i q^{91} +(-1.75749 - 6.38238i) q^{92} +(-8.12994 - 6.19383i) q^{94} +(-5.11052 - 8.85168i) q^{95} +(-2.76022 + 4.78084i) q^{97} +(-7.86408 + 3.28928i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	$ 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) $ 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.179748	−	1.40274i	0.127101	−	0.991890i
$2$	0.179748	−	1.40274i	0.127101	−	0.991890i
$3$		0			0
$3$		0			0
$4$	−1.93538	−	0.504281i	−0.967691	−	0.252141i
$5$	1.19115	−	0.687709i	0.532697	−	0.307553i	−0.209417	−	0.977826i	$-0.567157\pi$
$5$	1.19115	−	0.687709i	0.532697	−	0.307553i	0.742114	+	0.670274i	$0.233823\pi$
$6$		0			0
$7$	1.80469	−	3.12581i	0.682107	−	1.18144i	−0.292229	−	0.956348i	$-0.594397\pi$
$7$	1.80469	−	3.12581i	0.682107	−	1.18144i	0.974337	−	0.225096i	$-0.0722696\pi$
$8$	−1.05526	+	2.62420i	−0.373090	+	0.927795i
$9$		0			0
$10$	−0.750573	−	1.79449i	−0.237352	−	0.567467i
$11$	−1.83294	−	1.05825i	−0.552652	−	0.319074i	0.197539	−	0.980295i	$-0.436705\pi$
$11$	−1.83294	−	1.05825i	−0.552652	−	0.319074i	−0.750191	+	0.661221i	$0.770039\pi$
$12$		0			0
$13$	−0.887751	+	0.512543i	−0.246218	+	0.142154i	−0.618031	−	0.786154i	$-0.712069\pi$
$13$	−0.887751	+	0.512543i	−0.246218	+	0.142154i	0.371813	+	0.928307i	$0.378736\pi$
$14$	−4.06032	−	3.09337i	−1.08517	−	0.826738i
$15$		0			0
$16$	3.49140	+	1.95195i	0.872850	+	0.487988i
$17$	−0.808822			−0.196168			−0.0980841	−	0.995178i	$-0.531271\pi$
$17$	−0.808822			−0.196168			−0.0980841	+	0.995178i	$0.531271\pi$
$18$		0			0
$19$		−	7.43122i		−	1.70484i	−0.522858	−	0.852420i	$-0.675134\pi$
$19$		−	7.43122i		−	1.70484i	0.522858	−	0.852420i	$-0.324866\pi$
$20$	−2.65212	+	0.730306i	−0.593032	+	0.163301i
$21$		0			0
$22$	−1.81392	+	2.38093i	−0.386729	+	0.507615i
$23$	1.65498	+	2.86652i	0.345088	+	0.597710i	0.985370	−	0.170430i	$-0.0545157\pi$
$23$	1.65498	+	2.86652i	0.345088	+	0.597710i	−0.640282	+	0.768140i	$0.721182\pi$
$24$		0			0
$25$	−1.55411	+	2.69180i	−0.310823	+	0.538361i
$26$	0.559395	+	1.33742i	0.109706	+	0.262289i
$27$		0			0
$28$	−5.06904	+	5.13956i	−0.957959	+	0.971286i
$29$	7.71083	+	4.45185i	1.43187	+	0.826688i	0.997263	−	0.0739344i	$-0.0235555\pi$
$29$	7.71083	+	4.45185i	1.43187	+	0.826688i	0.434603	+	0.900622i	$0.356889\pi$
$30$		0			0
$31$	3.26436	+	5.65403i	0.586296	+	1.01549i	0.994713	+	0.102698i	$0.0327476\pi$
$31$	3.26436	+	5.65403i	0.586296	+	1.01549i	−0.408417	+	0.912796i	$0.633919\pi$
$32$	3.36566	−	4.54668i	0.594971	−	0.803747i
$33$		0			0
$34$	−0.145384	+	1.13457i	−0.0249332	+	0.194577i
$35$		−	4.96439i		−	0.839136i
$36$		0			0
$37$			4.01531i			0.660113i	0.943961	+	0.330057i	$0.107068\pi$
$37$			4.01531i			0.660113i	−0.943961	+	0.330057i	$0.892932\pi$
$38$	−10.4241	−	1.33575i	−1.69101	−	0.216687i
$39$		0			0
$40$	0.547718	+	3.85152i	0.0866018	+	0.608979i
$41$	3.45852	+	5.99034i	0.540131	+	0.935534i	0.998896	+	0.0469764i	$0.0149585\pi$
$41$	3.45852	+	5.99034i	0.540131	+	0.935534i	−0.458765	+	0.888557i	$0.651708\pi$
$42$		0			0
$43$	−0.245957	−	0.142003i	−0.0375081	−	0.0216553i	0.481129	−	0.876650i	$-0.340227\pi$
$43$	−0.245957	−	0.142003i	−0.0375081	−	0.0216553i	−0.518637	+	0.854995i	$0.673560\pi$
$44$	3.01378	+	2.97243i	0.454345	+	0.448111i
$45$		0			0
$46$	4.31847	−	1.80627i	0.636724	−	0.266320i
$47$	3.61351	−	6.25878i	0.527084	−	0.912937i	−0.472417	−	0.881375i	$-0.656619\pi$
$47$	3.61351	−	6.25878i	0.527084	−	0.912937i	0.999502	−	0.0315619i	$-0.0100481\pi$
$48$		0			0
$49$	−3.01378	−	5.22003i	−0.430540	−	0.745718i
$50$	3.49656	+	2.66387i	0.494488	+	0.376728i
$51$		0			0
$52$	1.97660	−	0.544290i	0.274105	−	0.0754795i
$53$		−	3.86330i		−	0.530666i	−0.964157	−	0.265333i	$-0.914518\pi$
$53$		−	3.86330i		−	0.530666i	0.964157	−	0.265333i	$-0.0854818\pi$
$54$		0			0
$55$	−2.91107			−0.392528
$56$	6.29834	+	8.03439i	0.841650	+	1.07364i
$57$		0			0
$58$	7.63082	−	10.0161i	1.00198	−	1.31518i
$59$	−7.06904	+	4.08131i	−0.920310	+	0.531341i	−0.883734	−	0.467989i	$-0.844979\pi$
$59$	−7.06904	+	4.08131i	−0.920310	+	0.531341i	−0.0365764	+	0.999331i	$0.511645\pi$
$60$		0			0
$61$	6.31237	+	3.64445i	0.808216	+	0.466624i	0.846336	−	0.532650i	$-0.178804\pi$
$61$	6.31237	+	3.64445i	0.808216	+	0.466624i	−0.0381201	+	0.999273i	$0.512137\pi$
$62$	8.51792	−	3.56275i	1.08178	−	0.452470i
$63$		0			0
$64$	−5.77286	−	5.53842i	−0.721607	−	0.692303i
$65$	−0.704961	+	1.22103i	−0.0874396	+	0.151450i
$66$		0			0
$67$	−2.43973	+	1.40858i	−0.298061	+	0.172085i	−0.641571	−	0.767063i	$-0.721717\pi$
$67$	−2.43973	+	1.40858i	−0.298061	+	0.172085i	0.343511	+	0.939149i	$0.388384\pi$
$68$	1.56538	+	0.407874i	0.189830	+	0.0494620i
$69$		0			0
$70$	−6.96377	−	0.892341i	−0.832330	−	0.106655i
$71$	−4.69830			−0.557586			−0.278793	−	0.960351i	$-0.589934\pi$
$71$	−4.69830			−0.557586			−0.278793	+	0.960351i	$0.589934\pi$
$72$		0			0
$73$	0.409922			0.0479777			0.0239889	−	0.999712i	$-0.492363\pi$
$73$	0.409922			0.0479777			0.0239889	+	0.999712i	$0.492363\pi$
$74$	5.63245	+	0.721745i	0.654760	+	0.0839012i
$75$		0			0
$76$	−3.74743	+	14.3822i	−0.429859	+	1.64976i
$77$	−6.61576	+	3.81961i	−0.753936	+	0.435285i
$78$		0			0
$79$	−0.0456121	+	0.0790024i	−0.00513176	+	0.00888847i	−0.868580	−	0.495549i	$-0.834967\pi$
$79$	−0.0456121	+	0.0790024i	−0.00513176	+	0.00888847i	0.863448	+	0.504438i	$0.168300\pi$
$80$	5.50115	−	0.0760042i	0.615047	−	0.00849752i
$81$		0			0
$82$	9.02458	−	3.77467i	0.996598	−	0.416843i
$83$	2.40891	+	1.39079i	0.264412	+	0.152659i	0.626346	−	0.779545i	$-0.284550\pi$
$83$	2.40891	+	1.39079i	0.264412	+	0.152659i	−0.361933	+	0.932204i	$0.617883\pi$
$84$		0			0
$85$	−0.963426	+	0.556234i	−0.104498	+	0.0603321i
$86$	−0.243405	+	0.319490i	−0.0262470	+	0.0344515i
$87$		0			0
$88$	4.71128	−	3.69328i	0.502224	−	0.393705i
$89$	−8.91934			−0.945448			−0.472724	−	0.881210i	$-0.656729\pi$
$89$	−8.91934			−0.945448			−0.472724	+	0.881210i	$0.656729\pi$
$90$		0			0
$91$			3.69992i			0.387857i
$92$	−1.75749	−	6.38238i	−0.183231	−	0.665409i
$93$		0			0
$94$	−8.12994	−	6.19383i	−0.838540	−	0.638845i
$95$	−5.11052	−	8.85168i	−0.524328	−	0.908163i
$96$		0			0
$97$	−2.76022	+	4.78084i	−0.280258	+	0.485421i	−0.971448	−	0.237252i	$-0.923753\pi$
$97$	−2.76022	+	4.78084i	−0.280258	+	0.485421i	0.691190	+	0.722673i	$0.257087\pi$
$98$	−7.86408	+	3.28928i	−0.794392	+	0.332267i
$99$		0			0
$100$	4.36523	−	4.42595i	0.436523	−	0.442595i
$101$	−5.63193	−	3.25160i	−0.560398	−	0.323546i	0.192907	−	0.981217i	$-0.438208\pi$
$101$	−5.63193	−	3.25160i	−0.560398	−	0.323546i	−0.753305	+	0.657671i	$0.771542\pi$
$102$		0			0
$103$	−1.50528	−	2.60723i	−0.148320	−	0.256898i	0.782287	−	0.622918i	$-0.214053\pi$
$103$	−1.50528	−	2.60723i	−0.148320	−	0.256898i	−0.930607	+	0.366021i	$0.880720\pi$
$104$	−0.408209	−	2.87050i	−0.0400282	−	0.281476i
$105$		0			0
$106$	−5.41923	−	0.694422i	−0.526362	−	0.0674482i
$107$		−	0.447393i		−	0.0432511i	−0.999766	−	0.0216256i	$-0.993116\pi$
$107$		−	0.447393i		−	0.0432511i	0.999766	−	0.0216256i	$-0.00688417\pi$
$108$		0			0
$109$			9.36497i			0.897002i	0.893782	+	0.448501i	$0.148042\pi$
$109$			9.36497i			0.897002i	−0.893782	+	0.448501i	$0.851958\pi$
$110$	−0.523259	+	4.08348i	−0.0498908	+	0.389345i
$111$		0			0
$112$	12.4023	−	7.39078i	1.17191	−	0.698363i
$113$	−5.66349	−	9.80944i	−0.532776	−	0.922795i	−0.999267	−	0.0382692i	$-0.987816\pi$
$113$	−5.66349	−	9.80944i	−0.532776	−	0.922795i	0.466492	−	0.884526i	$-0.345518\pi$
$114$		0			0
$115$	3.94266	+	2.27629i	0.367655	+	0.212266i
$116$	−12.6784	−	12.5045i	−1.17716	−	1.16101i
$117$		0			0
$118$	4.45439	+	10.6497i	0.410060	+	0.980381i
$119$	−1.45967	+	2.52822i	−0.133808	+	0.231762i
$120$		0			0
$121$	−3.26022	−	5.64687i	−0.296384	−	0.513351i
$122$	6.24686	−	8.19955i	0.565564	−	0.742353i
$123$		0			0
$124$	−3.46655	−	12.5889i	−0.311305	−	1.13051i
$125$			11.1522i			0.997483i
$126$		0			0
$127$	−11.8341			−1.05011			−0.525053	−	0.851069i	$-0.675955\pi$
$127$	−11.8341			−1.05011			−0.525053	+	0.851069i	$0.675955\pi$
$128$	−8.80665	+	7.10232i	−0.778405	+	0.627762i
$129$		0			0
$130$	1.58607	+	1.20836i	0.139108	+	0.105980i
$131$	−2.40891	+	1.39079i	−0.210468	+	0.121514i	−0.601529	−	0.798851i	$-0.705441\pi$
$131$	−2.40891	+	1.39079i	−0.210468	+	0.121514i	0.391061	+	0.920365i	$0.372108\pi$
$132$		0			0
$133$	−23.2286	−	13.4110i	−2.01417	−	1.16288i
$134$	1.53734	+	3.67551i	0.132806	+	0.317516i
$135$		0			0
$136$	0.853517	−	2.12251i	0.0731885	−	0.182004i
$137$	8.17841	−	14.1654i	0.698729	−	1.21023i	−0.270178	−	0.962810i	$-0.587083\pi$
$137$	8.17841	−	14.1654i	0.698729	−	1.21023i	0.968907	−	0.247424i	$-0.0795840\pi$
$138$		0			0
$139$	1.22979	−	0.710017i	0.104309	−	0.0602229i	−0.446938	−	0.894565i	$-0.647486\pi$
$139$	1.22979	−	0.710017i	0.104309	−	0.0602229i	0.551247	+	0.834342i	$0.314152\pi$
$140$	−2.50345	+	9.60800i	−0.211580	+	0.812024i
$141$		0			0
$142$	−0.844512	+	6.59052i	−0.0708699	+	0.553064i
$143$	2.16959			0.181430
$144$		0			0
$145$	12.2463			1.01700
$146$	0.0736827	−	0.575015i	0.00609802	−	0.0475886i
$147$		0			0
$148$	2.02485	−	7.77116i	0.166441	−	0.638785i
$149$	4.91390	−	2.83704i	0.402563	−	0.232420i	−0.285027	−	0.958520i	$-0.592002\pi$
$149$	4.91390	−	2.83704i	0.402563	−	0.232420i	0.687589	+	0.726100i	$0.258669\pi$
$150$		0			0
$151$	7.07318	−	12.2511i	0.575607	−	0.996981i	−0.420368	−	0.907354i	$-0.638099\pi$
$151$	7.07318	−	12.2511i	0.575607	−	0.996981i	0.995975	−	0.0896271i	$-0.0285675\pi$
$152$	19.5010	+	7.84186i	1.58174	+	0.636059i
$153$		0			0
$154$	4.16877	+	9.96679i	0.335929	+	0.803147i
$155$	7.77665	+	4.48985i	0.624636	+	0.360634i
$156$		0			0
$157$	18.6713	−	10.7799i	1.49013	−	0.860328i	0.490196	−	0.871612i	$-0.336925\pi$
$157$	18.6713	−	10.7799i	1.49013	−	0.860328i	0.999936	+	0.0112838i	$0.00359181\pi$
$158$	0.102622	+	0.0781826i	0.00816413	+	0.00621987i
$159$		0			0
$160$	0.882207	−	7.73036i	0.0697446	−	0.611139i
$161$	11.9469			0.941548
$162$		0			0
$163$			14.9239i			1.16893i	0.811418	+	0.584466i	$0.198696\pi$
$163$			14.9239i			1.16893i	−0.811418	+	0.584466i	$0.801304\pi$
$164$	−3.67275	−	13.3377i	−0.286793	−	1.04150i
$165$		0			0
$166$	2.38391	−	3.12910i	0.185028	−	0.242865i
$167$	11.0234	+	19.0931i	0.853019	+	1.47747i	0.878471	+	0.477796i	$0.158564\pi$
$167$	11.0234	+	19.0931i	0.853019	+	1.47747i	−0.0254524	+	0.999676i	$0.508103\pi$
$168$		0			0
$169$	−5.97460	+	10.3483i	−0.459585	+	0.796024i
$170$	0.607080	+	1.45142i	0.0465609	+	0.111319i
$171$		0			0
$172$	0.404411	+	0.398862i	0.0308361	+	0.0304130i
$173$	−10.9052	−	6.29612i	−0.829107	−	0.478685i	0.0244397	−	0.999701i	$-0.492220\pi$
$173$	−10.9052	−	6.29612i	−0.829107	−	0.478685i	−0.853547	+	0.521016i	$0.825553\pi$
$174$		0			0
$175$	5.60937	+	9.71572i	0.424029	+	0.734439i
$176$	−4.33388	−	7.27258i	−0.326678	−	0.548192i
$177$		0			0
$178$	−1.60324	+	12.5116i	−0.120168	+	0.937780i
$179$			12.1116i			0.905264i	0.891697	+	0.452632i	$0.149515\pi$
$179$			12.1116i			0.905264i	−0.891697	+	0.452632i	$0.850485\pi$
$180$		0			0
$181$		−	17.6790i		−	1.31407i	−0.753862	−	0.657033i	$-0.771811\pi$
$181$		−	17.6790i		−	1.31407i	0.753862	−	0.657033i	$-0.228189\pi$
$182$	5.19004	+	0.665054i	0.384711	+	0.0492970i
$183$		0			0
$184$	−9.26875	+	1.31809i	−0.683301	+	0.0971711i
$185$	2.76137	+	4.78283i	0.203020	+	0.351640i
$186$		0			0
$187$	1.48252	+	0.855935i	0.108413	+	0.0625922i
$188$	−10.1497	+	10.2909i	−0.740243	+	0.750541i
$189$		0			0
$190$	−13.3352	+	5.57768i	−0.967440	+	0.404647i
$191$	−9.72173	+	16.8385i	−0.703440	+	1.21839i	0.263812	+	0.964574i	$0.415020\pi$
$191$	−9.72173	+	16.8385i	−0.703440	+	1.21839i	−0.967252	+	0.253820i	$0.918313\pi$
$192$		0			0
$193$	0.159120	+	0.275604i	0.0114537	+	0.0198384i	0.871695	−	0.490048i	$-0.163021\pi$
$193$	0.159120	+	0.275604i	0.0114537	+	0.0198384i	−0.860242	+	0.509886i	$0.829687\pi$
$194$	6.21015	+	4.73123i	0.445863	+	0.339682i
$195$		0			0
$196$	3.20046	+	11.6225i	0.228604	+	0.830181i
$197$		−	24.5066i		−	1.74602i	−0.487701	−	0.873011i	$-0.662164\pi$
$197$		−	24.5066i		−	1.74602i	0.487701	−	0.873011i	$-0.337836\pi$
$198$		0			0
$199$	−7.13579			−0.505843			−0.252921	−	0.967487i	$-0.581391\pi$
$199$	−7.13579			−0.505843			−0.252921	+	0.967487i	$0.581391\pi$
$200$	−5.42384	−	6.91885i	−0.383523	−	0.489237i
$201$		0			0
$202$	−5.57349	+	7.31569i	−0.392149	+	0.514730i
$203$	27.8313	−	16.0684i	1.95337	−	1.12778i
$204$		0			0
$205$	8.23922	+	4.75692i	0.575452	+	0.332237i
$206$	−3.92784	+	1.64288i	−0.273666	+	0.114465i
$207$		0			0
$208$	−4.09995	+	0.0566452i	−0.284281	+	0.00392764i
$209$	−7.86408	+	13.6210i	−0.543970	+	0.942183i
$210$		0			0
$211$	−7.00175	+	4.04246i	−0.482020	+	0.278294i	−0.721258	−	0.692667i	$-0.756436\pi$
$211$	−7.00175	+	4.04246i	−0.482020	+	0.278294i	0.239238	+	0.970961i	$0.423102\pi$
$212$	−1.94819	+	7.47697i	−0.133802	+	0.513520i
$213$		0			0
$214$	−0.627578	−	0.0804181i	−0.0429003	−	0.00549727i
$215$	−0.390628			−0.0266406
$216$		0			0
$217$	23.5646			1.59967
$218$	13.1367	+	1.68334i	0.889727	+	0.114010i
$219$		0			0
$220$	5.63403	+	1.46800i	0.379846	+	0.0989724i
$221$	0.718032	−	0.414556i	0.0483001	−	0.0278861i
$222$		0			0
$223$	−2.11236	+	3.65872i	−0.141454	+	0.245006i	−0.928044	−	0.372469i	$-0.878511\pi$
$223$	−2.11236	+	3.65872i	−0.141454	+	0.245006i	0.786590	+	0.617475i	$0.211844\pi$
$224$	−8.13808	−	18.7257i	−0.543749	−	1.25117i
$225$		0			0
$226$	−14.7781	+	6.18119i	−0.983027	+	0.411167i
$227$	−1.09451	−	0.631913i	−0.0726449	−	0.0419415i	0.463238	−	0.886234i	$-0.346688\pi$
$227$	−1.09451	−	0.631913i	−0.0726449	−	0.0419415i	−0.535882	+	0.844293i	$0.680021\pi$
$228$		0			0
$229$	−6.29196	+	3.63267i	−0.415785	+	0.240053i	−0.693272	−	0.720676i	$-0.743832\pi$
$229$	−6.29196	+	3.63267i	−0.415785	+	0.240053i	0.277487	+	0.960729i	$0.410498\pi$
$230$	3.90174	−	5.12138i	0.257273	−	0.337694i
$231$		0			0
$232$	−19.8195	+	15.5369i	−1.30121	+	1.02005i
$233$	5.91061			0.387217			0.193608	−	0.981079i	$-0.437981\pi$
$233$	5.91061			0.387217			0.193608	+	0.981079i	$0.437981\pi$
$234$		0			0
$235$		−	9.94017i		−	0.648425i
$236$	15.7394	−	4.33411i	1.02455	−	0.282126i
$237$		0			0
$238$	3.28408	+	2.50199i	0.212875	+	0.162180i
$239$	−5.96266	−	10.3276i	−0.385692	−	0.668039i	0.606173	−	0.795333i	$-0.292704\pi$
$239$	−5.96266	−	10.3276i	−0.385692	−	0.668039i	−0.991865	+	0.127294i	$0.959371\pi$
$240$		0			0
$241$	1.80170	−	3.12063i	0.116057	−	0.201017i	−0.802145	−	0.597130i	$-0.796308\pi$
$241$	1.80170	−	3.12063i	0.116057	−	0.201017i	0.918202	+	0.396113i	$0.129641\pi$
$242$	−8.50713	+	3.55824i	−0.546859	+	0.228732i
$243$		0			0
$244$	−10.3790	−	10.2366i	−0.664448	−	0.655331i
$245$	−7.17972	−	4.14521i	−0.458695	−	0.264828i
$246$		0			0
$247$	3.80882	+	6.59707i	0.242350	+	0.419762i
$248$	−18.2821	+	2.59986i	−1.16091	+	0.165091i
$249$		0			0
$250$	15.6437	+	2.00459i	0.989393	+	0.126781i
$251$			0.641516i			0.0404922i	0.999795	+	0.0202461i	$0.00644497\pi$
$251$			0.641516i			0.0404922i	−0.999795	+	0.0202461i	$0.993555\pi$
$252$		0			0
$253$		−	7.00554i		−	0.440434i
$254$	−2.12716	+	16.6002i	−0.133470	+	1.04159i
$255$		0			0
$256$	8.37976	+	13.6301i	0.523735	+	0.851881i
$257$	1.99885	+	3.46212i	0.124685	+	0.215961i	0.921610	−	0.388118i	$-0.126875\pi$
$257$	1.99885	+	3.46212i	0.124685	+	0.215961i	−0.796925	+	0.604079i	$0.793541\pi$
$258$		0			0
$259$	12.5511	+	7.24638i	0.779887	+	0.450268i
$260$	1.98011	−	2.00766i	0.122801	−	0.124510i
$261$		0			0
$262$	1.51792	+	3.62908i	0.0937774	+	0.224205i
$263$	5.64671	−	9.78039i	0.348191	−	0.603085i	−0.637737	−	0.770254i	$-0.720129\pi$
$263$	5.64671	−	9.78039i	0.348191	−	0.603085i	0.985928	+	0.167169i	$0.0534627\pi$
$264$		0			0
$265$	−2.65683	−	4.60176i	−0.163208	−	0.282684i
$266$	−22.9875	+	30.1731i	−1.40946	+	1.85003i
$267$		0			0
$268$	5.43213	−	1.49583i	0.331820	−	0.0913722i
$269$			24.2695i			1.47974i	0.672750	+	0.739870i	$0.265113\pi$
$269$			24.2695i			1.47974i	−0.672750	+	0.739870i	$0.734887\pi$
$270$		0			0
$271$	12.2330			0.743102			0.371551	−	0.928413i	$-0.378826\pi$
$271$	12.2330			0.743102			0.371551	+	0.928413i	$0.378826\pi$
$272$	−2.82392	−	1.57878i	−0.171225	−	0.0957278i
$273$		0			0
$274$	−18.4004	−	14.0184i	−1.11161	−	0.846884i
$275$	5.69719	−	3.28928i	0.343554	−	0.198351i
$276$		0			0
$277$	−10.9249	−	6.30750i	−0.656414	−	0.378981i	0.134495	−	0.990914i	$-0.457059\pi$
$277$	−10.9249	−	6.30750i	−0.656414	−	0.378981i	−0.790909	+	0.611933i	$0.790392\pi$
$278$	−0.774920	−	1.85270i	−0.0464766	−	0.111117i
$279$		0			0
$280$	13.0276	+	5.23872i	0.778546	+	0.313073i
$281$	−9.54364	+	16.5301i	−0.569326	+	0.986101i	0.427307	+	0.904107i	$0.359462\pi$
$281$	−9.54364	+	16.5301i	−0.569326	+	0.986101i	−0.996633	+	0.0819947i	$0.973871\pi$
$282$		0			0
$283$	−1.01045	+	0.583382i	−0.0600649	+	0.0346785i	−0.529732	−	0.848165i	$-0.677707\pi$
$283$	−1.01045	+	0.583382i	−0.0600649	+	0.0346785i	0.469667	+	0.882844i	$0.344374\pi$
$284$	9.09301	+	2.36927i	0.539571	+	0.140590i
$285$		0			0
$286$	0.389980	−	3.04338i	0.0230600	−	0.179959i
$287$	24.9662			1.47371
$288$		0			0
$289$	−16.3458			−0.961518
$290$	2.20125	−	17.1784i	0.129262	−	1.00875i
$291$		0			0
$292$	−0.793355	−	0.206716i	−0.0464276	−	0.0120971i
$293$	−2.11446	+	1.22079i	−0.123528	+	0.0713191i	−0.560491	−	0.828161i	$-0.689388\pi$
$293$	−2.11446	+	1.22079i	−0.123528	+	0.0713191i	0.436963	+	0.899480i	$0.356054\pi$
$294$		0			0
$295$	−5.61351	+	9.72288i	−0.326831	+	0.566088i
$296$	−10.5370	−	4.23719i	−0.612450	−	0.246282i
$297$		0			0
$298$	−3.09638	−	7.40290i	−0.179368	−	0.428839i
$299$	−2.93843	−	1.69650i	−0.169934	−	0.0981112i
$300$		0			0
$301$	−0.887751	+	0.512543i	−0.0511691	+	0.0295425i
$302$	−15.9138	−	12.1240i	−0.915735	−	0.697656i
$303$		0			0
$304$	14.5054	−	25.9454i	0.831942	−	1.48807i
$305$	10.0253			0.574046
$306$		0			0
$307$		−	15.7452i		−	0.898626i	−0.893374	−	0.449313i	$-0.851669\pi$
$307$		−	15.7452i		−	0.898626i	0.893374	−	0.449313i	$-0.148331\pi$
$308$	14.7302	−	4.05620i	0.839330	−	0.231123i
$309$		0			0
$310$	7.69595	−	10.1016i	0.437101	−	0.573733i
$311$	−9.90129	−	17.1495i	−0.561451	−	0.972461i	−0.997370	−	0.0724757i	$-0.976910\pi$
$311$	−9.90129	−	17.1495i	−0.561451	−	0.972461i	0.435919	−	0.899986i	$-0.356423\pi$
$312$		0			0
$313$	16.2557	−	28.1557i	0.918828	−	1.59146i	0.117630	−	0.993057i	$-0.462470\pi$
$313$	16.2557	−	28.1557i	0.918828	−	1.59146i	0.801198	−	0.598399i	$-0.204196\pi$
$314$	−11.7653	−	28.1287i	−0.663953	−	1.58740i
$315$		0			0
$316$	0.128116	−	0.129899i	0.00720710	−	0.00730736i
$317$	13.9271	+	8.04083i	0.782225	+	0.451618i	0.837218	−	0.546869i	$-0.184180\pi$
$317$	13.9271	+	8.04083i	0.782225	+	0.451618i	−0.0549932	+	0.998487i	$0.517514\pi$
$318$		0			0
$319$	−9.42233	−	16.3200i	−0.527549	−	0.913742i
$320$	−10.6851	−	2.62703i	−0.597318	−	0.146855i
$321$		0			0
$322$	2.14743	−	16.7585i	0.119672	−	0.933912i
$323$			6.01054i			0.334435i
$324$		0			0
$325$		−	3.18620i		−	0.176739i
$326$	20.9344	+	2.68255i	1.15945	+	0.148573i
$327$		0			0
$328$	−19.3695	+	2.75450i	−1.06950	+	0.152092i
$329$	−13.0425	−	22.5903i	−0.719056	−	1.24544i
$330$		0			0
$331$	−17.7569	−	10.2520i	−0.976010	−	0.563499i	−0.0749465	−	0.997188i	$-0.523879\pi$
$331$	−17.7569	−	10.2520i	−0.976010	−	0.563499i	−0.901063	+	0.433688i	$0.857212\pi$
$332$	−3.96082	−	3.90647i	−0.217378	−	0.214395i
$333$		0			0
$334$	28.7642	−	12.0311i	1.57391	−	0.658312i
$335$	−1.93739	+	3.35565i	−0.105851	+	0.183339i
$336$		0			0
$337$	6.21760	+	10.7692i	0.338694	+	0.586635i	0.984187	−	0.177131i	$-0.0566815\pi$
$337$	6.21760	+	10.7692i	0.338694	+	0.586635i	−0.645493	+	0.763766i	$0.723348\pi$
$338$	13.4421	+	10.2409i	0.731154	+	0.557033i
$339$		0			0
$340$	2.14509	−	0.590687i	0.116334	−	0.0320345i
$341$		−	13.8180i		−	0.748287i
$342$		0			0
$343$	3.50988			0.189515
$344$	0.632194	−	0.495590i	0.0340856	−	0.0267204i
$345$		0			0
$346$	−10.7920	+	14.1655i	−0.580183	+	0.761541i
$347$	−24.1550	+	13.9459i	−1.29671	+	0.748654i	−0.979834	−	0.199814i	$-0.935966\pi$
$347$	−24.1550	+	13.9459i	−1.29671	+	0.748654i	−0.316873	+	0.948468i	$0.602633\pi$
$348$		0			0
$349$	26.0103	+	15.0171i	1.39230	+	0.803846i	0.993570	−	0.113222i	$-0.0361171\pi$
$349$	26.0103	+	15.0171i	1.39230	+	0.803846i	0.398732	+	0.917068i	$0.369450\pi$
$350$	14.6369	−	6.12213i	0.782377	−	0.327242i
$351$		0			0
$352$	−10.9806	+	4.77209i	−0.585267	+	0.254353i
$353$	9.48011	−	16.4200i	0.504575	−	0.873950i	−0.495411	−	0.868659i	$-0.664982\pi$
$353$	9.48011	−	16.4200i	0.504575	−	0.873950i	0.999986	−	0.00529122i	$-0.00168426\pi$
$354$		0			0
$355$	−5.59637	+	3.23107i	−0.297024	+	0.171487i
$356$	17.2623	+	4.49786i	0.914901	+	0.238386i
$357$		0			0
$358$	16.9895	+	2.17704i	0.897922	+	0.115060i
$359$	−28.6420			−1.51167			−0.755833	−	0.654765i	$-0.772768\pi$
$359$	−28.6420			−1.51167			−0.755833	+	0.654765i	$0.772768\pi$
$360$		0			0
$361$	−36.2231			−1.90648
$362$	−24.7990	−	3.17776i	−1.30341	−	0.167019i
$363$		0			0
$364$	1.86580	−	7.16075i	0.0977945	−	0.375325i
$365$	0.488277	−	0.281907i	0.0255576	−	0.0147557i
$366$		0			0
$367$	5.77148	−	9.99650i	0.301269	−	0.521813i	−0.675155	−	0.737676i	$-0.735923\pi$
$367$	5.77148	−	9.99650i	0.301269	−	0.521813i	0.976424	+	0.215863i	$0.0692565\pi$
$368$	0.182905	+	13.2386i	0.00953461	+	0.690110i
$369$		0			0
$370$	7.20543	−	3.01378i	0.374593	−	0.156679i
$371$	−12.0759	−	6.97205i	−0.626952	−	0.361971i
$372$		0			0
$373$	−19.4301	+	11.2180i	−1.00605	+	0.580846i	−0.910034	−	0.414533i	$-0.863945\pi$
$373$	−19.4301	+	11.2180i	−1.00605	+	0.580846i	−0.0960206	+	0.995379i	$0.530611\pi$
$374$	1.46714	−	1.92575i	0.0758639	−	0.0995780i
$375$		0			0
$376$	12.6111	+	16.0872i	0.650368	+	0.829634i
$377$	−9.12706			−0.470068
$378$		0			0
$379$			22.6668i			1.16431i	0.813077	+	0.582157i	$0.197791\pi$
$379$			22.6668i			1.16431i	−0.813077	+	0.582157i	$0.802209\pi$
$380$	5.42706	+	19.7085i	0.278403	+	1.01103i
$381$		0			0
$382$	21.8727	+	16.6638i	1.11910	+	0.852594i
$383$	1.94277	+	3.36498i	0.0992709	+	0.171942i	0.911383	−	0.411559i	$-0.135016\pi$
$383$	1.94277	+	3.36498i	0.0992709	+	0.171942i	−0.812112	+	0.583501i	$0.801682\pi$
$384$		0			0
$385$	−5.25356	+	9.09944i	−0.267746	+	0.463750i
$386$	0.415204	−	0.173666i	0.0211333	−	0.00883935i
$387$		0			0
$388$	7.75297	−	7.86082i	0.393597	−	0.399073i
$389$	−11.9463	−	6.89722i	−0.605703	−	0.349703i	0.165579	−	0.986197i	$-0.447051\pi$
$389$	−11.9463	−	6.89722i	−0.605703	−	0.349703i	−0.771282	+	0.636494i	$0.780384\pi$
$390$		0			0
$391$	−1.33859	−	2.31850i	−0.0676953	−	0.117252i
$392$	16.8787	−	2.40029i	0.852504	−	0.121233i
$393$		0			0
$394$	−34.3765	−	4.40501i	−1.73186	−	0.221921i
$395$			0.125471i			0.00631315i
$396$		0			0
$397$			23.7680i			1.19288i	0.802657	+	0.596441i	$0.203419\pi$
$397$			23.7680i			1.19288i	−0.802657	+	0.596441i	$0.796581\pi$
$398$	−1.28265	+	10.0097i	−0.0642932	+	0.501740i
$399$		0			0
$400$	−10.6803	+	6.36461i	−0.534015	+	0.318230i
$401$	4.47782	+	7.75581i	0.223612	+	0.387307i	0.955902	−	0.293686i	$-0.0948820\pi$
$401$	4.47782	+	7.75581i	0.223612	+	0.387307i	−0.732290	+	0.680992i	$0.761549\pi$
$402$		0			0
$403$	−5.79587	−	3.34625i	−0.288713	−	0.166688i
$404$	9.26022	+	9.13316i	0.460713	+	0.454392i
$405$		0			0
$406$	−17.5372	−	41.9284i	−0.870357	−	2.08087i
$407$	4.24920	−	7.35983i	0.210625	−	0.364813i
$408$		0			0
$409$	10.4170	+	18.0429i	0.515090	+	0.892162i	0.999847	+	0.0175128i	$0.00557480\pi$
$409$	10.4170	+	18.0429i	0.515090	+	0.892162i	−0.484757	+	0.874649i	$0.661092\pi$
$410$	8.15372	−	10.7025i	0.402683	−	0.528557i
$411$		0			0
$412$	1.59852	+	5.80506i	0.0787534	+	0.285995i
$413$			29.4619i			1.44973i
$414$		0			0
$415$	3.82582			0.187802
$416$	−0.657501	+	5.76137i	−0.0322366	+	0.282474i
$417$		0			0
$418$	17.6932	+	13.4796i	0.865403	+	0.659311i
$419$	−8.74372	+	5.04819i	−0.427159	+	0.246620i	−0.698135	−	0.715966i	$-0.745987\pi$
$419$	−8.74372	+	5.04819i	−0.427159	+	0.246620i	0.270977	+	0.962586i	$0.412653\pi$
$420$		0			0
$421$	20.2218	+	11.6751i	0.985551	+	0.569008i	0.903941	−	0.427656i	$-0.140661\pi$
$421$	20.2218	+	11.6751i	0.985551	+	0.569008i	0.0816096	+	0.996664i	$0.473994\pi$
$422$	4.41199	+	10.5483i	0.214772	+	0.513482i
$423$		0			0
$424$	10.1381	+	4.07679i	0.492349	+	0.197986i
$425$	1.25700	−	2.17719i	0.0609735	−	0.105609i
$426$		0			0
$427$	22.7837	−	13.1542i	1.10258	−	0.636575i
$428$	−0.225612	+	0.865876i	−0.0109054	+	0.0418537i
$429$		0			0
$430$	−0.0702147	+	0.547951i	−0.00338605	+	0.0264245i
$431$	6.40348			0.308445			0.154222	−	0.988036i	$-0.450713\pi$
$431$	6.40348			0.308445			0.154222	+	0.988036i	$0.450713\pi$
$432$		0			0
$433$	−9.82857			−0.472331			−0.236166	−	0.971713i	$-0.575891\pi$
$433$	−9.82857			−0.472331			−0.236166	+	0.971713i	$0.575891\pi$
$434$	4.23569	−	33.0550i	0.203319	−	1.58669i
$435$		0			0
$436$	4.72258	−	18.1248i	0.226171	−	0.868020i
$437$	21.3017	−	12.2986i	1.01900	−	0.588320i
$438$		0			0
$439$	−12.3831	+	21.4482i	−0.591015	+	1.02367i	0.403081	+	0.915164i	$0.367939\pi$
$439$	−12.3831	+	21.4482i	−0.591015	+	1.02367i	−0.994096	+	0.108504i	$0.965394\pi$
$440$	3.07193	−	7.63923i	0.146449	−	0.364186i
$441$		0			0
$442$	−0.452451	−	1.08173i	−0.0215209	−	0.0514527i
$443$	−23.5518	−	13.5976i	−1.11898	−	0.646044i	−0.177840	−	0.984059i	$-0.556911\pi$
$443$	−23.5518	−	13.5976i	−1.11898	−	0.646044i	−0.941140	+	0.338016i	$0.890244\pi$
$444$		0			0
$445$	−10.6242	+	6.13391i	−0.503637	+	0.290775i
$446$	4.75255	+	3.62075i	0.225040	+	0.171448i
$447$		0			0
$448$	−27.7302	+	8.04973i	−1.31013	+	0.380314i
$449$	−32.6861			−1.54255			−0.771276	−	0.636501i	$-0.780381\pi$
$449$	−32.6861			−1.54255			−0.771276	+	0.636501i	$0.780381\pi$
$450$		0			0
$451$		−	14.6399i		−	0.689367i
$452$	6.01428	+	21.8410i	0.282888	+	1.02731i
$453$		0			0
$454$	−1.08315	+	1.42173i	−0.0508346	+	0.0667249i
$455$	2.54447	+	4.40714i	0.119286	+	0.206610i
$456$		0			0
$457$	−10.3779	+	17.9750i	−0.485456	+	0.840834i	−0.999860	−	0.0167133i	$-0.994680\pi$
$457$	−10.3779	+	17.9750i	−0.485456	+	0.840834i	0.514404	+	0.857548i	$0.328013\pi$
$458$	3.96473	+	9.47898i	0.185260	+	0.442924i
$459$		0			0
$460$	−6.48265	−	6.39371i	−0.302255	−	0.298108i
$461$	32.4695	+	18.7463i	1.51226	+	0.873101i	0.999897	+	0.0143300i	$0.00456153\pi$
$461$	32.4695	+	18.7463i	1.51226	+	0.873101i	0.512359	+	0.858771i	$0.328772\pi$
$462$		0			0
$463$	−7.97597	−	13.8148i	−0.370675	−	0.642028i	0.618995	−	0.785395i	$-0.287540\pi$
$463$	−7.97597	−	13.8148i	−0.370675	−	0.642028i	−0.989670	+	0.143367i	$0.954207\pi$
$464$	18.2318	+	30.5944i	0.846390	+	1.42031i
$465$		0			0
$466$	1.06242	−	8.29107i	0.0492157	−	0.384077i
$467$		−	27.0476i		−	1.25161i	−0.779979	−	0.625806i	$-0.784770\pi$
$467$		−	27.0476i		−	1.25161i	0.779979	−	0.625806i	$-0.215230\pi$
$468$		0			0
$469$			10.1682i			0.469523i
$470$	−13.9435	−	1.78673i	−0.643166	−	0.0824156i
$471$		0			0
$472$	−3.25051	−	22.8574i	−0.149617	−	1.05210i
$473$	0.300550	+	0.520568i	0.0138193	+	0.0239357i
$474$		0			0
$475$	20.0034	+	11.5490i	0.917818	+	0.529903i
$476$	4.09995	−	4.15699i	0.187921	−	0.190535i
$477$		0			0
$478$	−15.5588	+	6.50771i	−0.711643	+	0.297656i
$479$	−13.6550	+	23.6511i	−0.623912	+	1.08065i	0.364838	+	0.931071i	$0.381124\pi$
$479$	−13.6550	+	23.6511i	−0.623912	+	1.08065i	−0.988750	+	0.149577i	$0.952209\pi$
$480$		0			0
$481$	−2.05802	−	3.56460i	−0.0938377	−	0.162532i
$482$	−4.05359	−	3.08825i	−0.184636	−	0.140666i
$483$		0			0
$484$	3.46216	+	12.5729i	0.157371	+	0.571496i
$485$			7.59291i			0.344776i
$486$		0			0
$487$	19.1126			0.866073			0.433036	−	0.901376i	$-0.357442\pi$
$487$	19.1126			0.866073			0.433036	+	0.901376i	$0.357442\pi$
$488$	−16.2249	+	12.7191i	−0.734469	+	0.575766i
$489$		0			0
$490$	−7.10521	+	9.32621i	−0.320981	+	0.421315i
$491$	−11.1131	+	6.41614i	−0.501526	+	0.289556i	−0.729344	−	0.684147i	$-0.760174\pi$
$491$	−11.1131	+	6.41614i	−0.501526	+	0.289556i	0.227817	+	0.973704i	$0.426841\pi$
$492$		0			0
$493$	−6.23669	−	3.60076i	−0.280886	−	0.162170i
$494$	9.93863	−	4.15699i	0.447160	−	0.187032i
$495$		0			0
$496$	0.360770	+	26.1124i	0.0161990	+	1.17248i
$497$	−8.47896	+	14.6860i	−0.380334	+	0.658757i
$498$		0			0
$499$	15.3846	−	8.88232i	0.688711	−	0.397627i	−0.114418	−	0.993433i	$-0.536500\pi$
$499$	15.3846	−	8.88232i	0.688711	−	0.397627i	0.803129	+	0.595805i	$0.203167\pi$
$500$	5.62385	−	21.5838i	0.251506	−	0.965255i
$501$		0			0
$502$	0.899883	+	0.115311i	0.0401638	+	0.00514660i
$503$	24.0108			1.07059			0.535294	−	0.844666i	$-0.320201\pi$
$503$	24.0108			1.07059			0.535294	+	0.844666i	$0.320201\pi$
$504$		0			0
$505$	−8.94461			−0.398030
$506$	−9.82698	−	1.25923i	−0.436862	−	0.0559797i
$507$		0			0
$508$	22.9035	+	5.96771i	1.01618	+	0.264775i
$509$	−6.91916	+	3.99478i	−0.306686	+	0.177065i	−0.645443	−	0.763809i	$-0.723327\pi$
$509$	−6.91916	+	3.99478i	−0.306686	+	0.177065i	0.338756	+	0.940874i	$0.389994\pi$
$510$		0			0
$511$	0.739780	−	1.28134i	0.0327259	−	0.0566830i
$512$	20.6258	−	9.30466i	0.911540	−	0.411212i
$513$		0			0
$514$	5.21575	−	2.18157i	0.230057	−	0.0962250i
$515$	−3.58602	−	2.07039i	−0.158019	−	0.0912324i
$516$		0			0
$517$	−13.2467	+	7.64798i	−0.582589	+	0.336358i
$518$	12.4208	−	16.3034i	0.545741	−	0.716332i
$519$		0			0
$520$	−2.46031	−	3.13846i	−0.107892	−	0.137631i
$521$	36.9809			1.62016			0.810082	−	0.586317i	$-0.199423\pi$
$521$	36.9809			1.62016			0.810082	+	0.586317i	$0.199423\pi$
$522$		0			0
$523$		−	18.4217i		−	0.805526i	−0.915304	−	0.402763i	$-0.868050\pi$
$523$		−	18.4217i		−	0.805526i	0.915304	−	0.402763i	$-0.131950\pi$
$524$	5.36351	−	1.47693i	0.234306	−	0.0645201i
$525$		0			0
$526$	−12.7044	−	9.67890i	−0.553938	−	0.422020i
$527$	−2.64028	−	4.57311i	−0.115013	−	0.199208i
$528$		0			0
$529$	6.02206	−	10.4305i	0.261828	−	0.453500i
$530$	−6.93265	+	2.89969i	−0.301135	+	0.125955i
$531$		0			0
$532$	38.1932	+	37.6692i	1.65589	+	1.63317i
$533$	−6.14061	−	3.54529i	−0.265980	−	0.153563i
$534$		0			0
$535$	−0.307676	−	0.532911i	−0.0133020	−	0.0230397i
$536$	−1.12185	−	7.88876i	−0.0484564	−	0.340743i
$537$		0			0
$538$	34.0439	+	4.36241i	1.46774	+	0.188077i
$539$			12.7573i			0.549497i
$540$		0			0
$541$			13.5032i			0.580549i	0.956943	+	0.290275i	$0.0937467\pi$
$541$			13.5032i			0.580549i	−0.956943	+	0.290275i	$0.906253\pi$
$542$	2.19886	−	17.1598i	0.0944491	−	0.737075i
$543$		0			0
$544$	−2.72222	+	3.67746i	−0.116714	+	0.157670i
$545$	6.44038	+	11.1551i	0.275875	+	0.477830i
$546$		0			0
$547$	−32.2252	−	18.6052i	−1.37785	−	0.795501i	−0.385948	−	0.922520i	$-0.626126\pi$
$547$	−32.2252	−	18.6052i	−1.37785	−	0.795501i	−0.991900	+	0.127019i	$0.959459\pi$
$548$	−22.9717	+	23.2913i	−0.981303	+	0.994954i
$549$		0			0
$550$	−3.58995	−	8.58294i	−0.153076	−	0.365978i
$551$	33.0827	−	57.3009i	1.40937	−	2.44110i
$552$		0			0
$553$	0.164631	+	0.285149i	0.00700082	+	0.0121258i
$554$	−10.8115	+	14.1911i	−0.459338	+	0.602922i
$555$		0			0
$556$	−2.73815	+	0.753996i	−0.116124	+	0.0319765i
$557$		−	16.9602i		−	0.718628i	−0.933217	−	0.359314i	$-0.883011\pi$
$557$		−	16.9602i		−	0.718628i	0.933217	−	0.359314i	$-0.116989\pi$
$558$		0			0
$559$	0.291131			0.0123135
$560$	9.69027	−	17.3327i	0.409489	−	0.732440i
$561$		0			0
$562$	21.4720	+	16.3585i	0.905742	+	0.690043i
$563$	25.0083	−	14.4385i	1.05397	−	0.608512i	0.130214	−	0.991486i	$-0.458434\pi$
$563$	25.0083	−	14.4385i	1.05397	−	0.608512i	0.923759	+	0.382974i	$0.125100\pi$
$564$		0			0
$565$	−13.4921	−	7.78966i	−0.567616	−	0.327713i
$566$	0.636710	+	1.52226i	0.0267629	+	0.0639854i
$567$		0			0
$568$	4.95793	−	12.3293i	0.208030	−	0.517326i
$569$	−2.20060	+	3.81154i	−0.0922538	+	0.159788i	−0.908459	−	0.417974i	$-0.862740\pi$
$569$	−2.20060	+	3.81154i	−0.0922538	+	0.159788i	0.816205	+	0.577762i	$0.196074\pi$
$570$		0			0
$571$	−28.6730	+	16.5544i	−1.19993	+	0.692779i	−0.960539	−	0.278144i	$-0.910281\pi$
$571$	−28.6730	+	16.5544i	−1.19993	+	0.692779i	−0.239390	+	0.970924i	$0.576947\pi$
$572$	−4.19899	−	1.09408i	−0.175568	−	0.0457460i
$573$		0			0
$574$	4.48763	−	35.0212i	0.187310	−	1.46176i
$575$	−10.2881			−0.429045
$576$		0			0
$577$	11.4122			0.475097			0.237548	−	0.971376i	$-0.423656\pi$
$577$	11.4122			0.475097			0.237548	+	0.971376i	$0.423656\pi$
$578$	−2.93813	+	22.9290i	−0.122210	+	0.953720i
$579$		0			0
$580$	−23.7013	−	6.17559i	−0.984142	−	0.256427i
$581$	8.69466	−	5.01986i	0.360715	−	0.208259i
$582$		0			0
$583$	−4.08834	+	7.08121i	−0.169322	+	0.293274i
$584$	−0.432574	+	1.07572i	−0.0179000	+	0.0445135i
$585$		0			0
$586$	1.33238	+	3.18548i	0.0550401	+	0.131591i
$587$	22.5512	+	13.0200i	0.930788	+	0.537391i	0.887061	−	0.461653i	$-0.152743\pi$
$587$	22.5512	+	13.0200i	0.930788	+	0.537391i	0.0437275	+	0.999043i	$0.486077\pi$
$588$		0			0
$589$	42.0164	−	24.2582i	1.73125	−	0.999540i
$590$	12.6297	+	9.62199i	0.519956	+	0.396131i
$591$		0			0
$592$	−7.83770	+	14.0191i	−0.322128	+	0.576180i
$593$	−5.75114			−0.236171			−0.118086	−	0.993003i	$-0.537676\pi$
$593$	−5.75114			−0.236171			−0.118086	+	0.993003i	$0.537676\pi$
$594$		0			0
$595$			4.01531i			0.164612i
$596$	−10.9409	+	3.01277i	−0.448158	+	0.123408i
$597$		0			0
$598$	−2.90793	+	3.81692i	−0.118914	+	0.156085i
$599$	8.10409	+	14.0367i	0.331124	+	0.573524i	0.982733	−	0.185032i	$-0.0592388\pi$
$599$	8.10409	+	14.0367i	0.331124	+	0.573524i	−0.651608	+	0.758556i	$0.725905\pi$
$600$		0			0
$601$	9.78181	−	16.9426i	0.399008	−	0.691102i	−0.594596	−	0.804025i	$-0.702688\pi$
$601$	9.78181	−	16.9426i	0.399008	−	0.691102i	0.993604	+	0.112922i	$0.0360212\pi$
$602$	0.559395	+	1.33742i	0.0227992	+	0.0545090i
$603$		0			0
$604$	−19.8673	+	20.1437i	−0.808389	+	0.819635i
$605$	−7.76680	−	4.48416i	−0.315765	−	0.182307i
$606$		0			0
$607$	−3.82627	−	6.62730i	−0.155304	−	0.268994i	0.777866	−	0.628430i	$-0.216302\pi$
$607$	−3.82627	−	6.62730i	−0.155304	−	0.268994i	−0.933170	+	0.359437i	$0.882969\pi$
$608$	−33.7874	−	25.0110i	−1.37026	−	1.01433i
$609$		0			0
$610$	1.80203	−	14.0629i	0.0729619	−	0.569390i
$611$			7.40831i			0.299708i
$612$		0			0
$613$		−	27.6512i		−	1.11682i	−0.829565	−	0.558410i	$-0.811412\pi$
$613$		−	27.6512i		−	1.11682i	0.829565	−	0.558410i	$-0.188588\pi$
$614$	−22.0865	−	2.83017i	−0.891338	−	0.114216i
$615$		0			0
$616$	−3.04209	−	21.3918i	−0.122569	−	0.861899i
$617$	12.6938	+	21.9863i	0.511034	+	0.885136i	0.999918	+	0.0127878i	$0.00407059\pi$
$617$	12.6938	+	21.9863i	0.511034	+	0.885136i	−0.488885	+	0.872348i	$0.662596\pi$
$618$		0			0
$619$	−19.8583	−	11.4652i	−0.798171	−	0.460824i	0.0446605	−	0.999002i	$-0.485779\pi$
$619$	−19.8583	−	11.4652i	−0.798171	−	0.460824i	−0.842831	+	0.538178i	$0.819113\pi$
$620$	−12.7866	−	12.6112i	−0.513524	−	0.506478i
$621$		0			0
$622$	−25.8362	+	10.8064i	−1.03594	+	0.433296i
$623$	−16.0966	+	27.8801i	−0.644897	+	1.11699i
$624$		0			0
$625$	−0.101100	−	0.175110i	−0.00404398	−	0.00700439i
$626$	−36.5734	−	27.8636i	−1.46177	−	1.11365i
$627$		0			0
$628$	−41.5722	+	11.4476i	−1.65891	+	0.456809i
$629$		−	3.24767i		−	0.129493i
$630$		0			0
$631$	23.2785			0.926701			0.463350	−	0.886175i	$-0.346647\pi$
$631$	23.2785			0.926701			0.463350	+	0.886175i	$0.346647\pi$
$632$	−0.159186	−	0.203063i	−0.00633207	−	0.00807742i
$633$		0			0
$634$	13.7826	−	18.0909i	0.547377	−	0.718480i
$635$	−14.0961	+	8.13841i	−0.559388	+	0.322963i
$636$		0			0
$637$	5.35098	+	3.08939i	0.212013	+	0.122406i
$638$	−24.5864	+	10.2836i	−0.973384	+	0.407133i
$639$		0			0
$640$	−5.60568	+	14.5163i	−0.221584	+	0.573808i
$641$	17.4170	−	30.1672i	0.687932	−	1.19153i	−0.284574	−	0.958654i	$-0.591852\pi$
$641$	17.4170	−	30.1672i	0.687932	−	1.19153i	0.972506	−	0.232879i	$-0.0748146\pi$
$642$		0			0
$643$	34.0047	−	19.6326i	1.34102	−	0.774236i	0.354059	−	0.935223i	$-0.384801\pi$
$643$	34.0047	−	19.6326i	1.34102	−	0.774236i	0.986956	+	0.160987i	$0.0514678\pi$
$644$	−23.1218	−	6.02460i	−0.911127	−	0.237403i
$645$		0			0
$646$	8.43125	+	1.08038i	0.331723	+	0.0425071i
$647$	−44.5092			−1.74984			−0.874918	−	0.484271i	$-0.839085\pi$
$647$	−44.5092			−1.74984			−0.874918	+	0.484271i	$0.839085\pi$
$648$		0			0
$649$	17.2762			0.678149
$650$	−4.46942	−	0.572714i	−0.175305	−	0.0224637i
$651$		0			0
$652$	7.52586	−	28.8835i	0.294735	−	1.13116i
$653$	−15.7763	+	9.10843i	−0.617373	+	0.356440i	−0.775845	−	0.630923i	$-0.782676\pi$
$653$	−15.7763	+	9.10843i	−0.617373	+	0.356440i	0.158473	+	0.987363i	$0.449343\pi$
$654$		0			0
$655$	−1.91291	+	3.31326i	−0.0747437	+	0.129460i
$656$	0.382229	+	27.6656i	0.0149235	+	1.08016i
$657$		0			0
$658$	−34.0327	+	14.2347i	−1.32673	+	0.554927i
$659$	36.2085	+	20.9050i	1.41048	+	0.814343i	0.995434	−	0.0954566i	$-0.0304311\pi$
$659$	36.2085	+	20.9050i	1.41048	+	0.814343i	0.415049	+	0.909799i	$0.363764\pi$
$660$		0			0
$661$	9.78973	−	5.65210i	0.380776	−	0.219841i	−0.297380	−	0.954759i	$-0.596113\pi$
$661$	9.78973	−	5.65210i	0.380776	−	0.219841i	0.678156	+	0.734918i	$0.262779\pi$
$662$	−17.5727	+	23.0657i	−0.682981	+	0.896472i
$663$		0			0
$664$	−6.19173	+	4.85383i	−0.240286	+	0.188365i
$665$	−36.8915			−1.43059
$666$		0			0
$667$			29.4710i			1.14112i
$668$	−11.7062	−	42.5114i	−0.452927	−	1.64482i
$669$		0			0
$670$	4.35888	+	3.32083i	0.168398	+	0.128295i
$671$	−7.71346	−	13.3601i	−0.297775	−	0.515761i
$672$		0			0
$673$	17.6390	−	30.5517i	0.679934	−	1.17768i	−0.295066	−	0.955477i	$-0.595342\pi$
$673$	17.6390	−	30.5517i	0.679934	−	1.17768i	0.975000	−	0.222203i	$-0.0713249\pi$
$674$	16.2240	−	6.78595i	0.624926	−	0.261385i
$675$		0			0
$676$	16.7816	−	17.0150i	0.645446	−	0.654425i
$677$	17.5026	+	10.1051i	0.672679	+	0.388372i	0.797091	−	0.603859i	$-0.206371\pi$
$677$	17.5026	+	10.1051i	0.672679	+	0.388372i	−0.124412	+	0.992231i	$0.539704\pi$
$678$		0			0
$679$	9.96266	+	17.2558i	0.382332	+	0.662218i
$680$	−0.443006	−	3.11519i	−0.0169885	−	0.119462i
$681$		0			0
$682$	−19.3831	−	2.48376i	−0.742218	−	0.0951081i
$683$		−	43.6659i		−	1.67083i	−0.549621	−	0.835414i	$-0.685228\pi$
$683$		−	43.6659i		−	1.67083i	0.549621	−	0.835414i	$-0.314772\pi$
$684$		0			0
$685$		−	22.4975i		−	0.859584i
$686$	0.630894	−	4.92346i	0.0240876	−	0.187978i
$687$		0			0
$688$	−0.581551	−	0.975888i	−0.0221714	−	0.0372054i
$689$	1.98011	+	3.42965i	0.0754362	+	0.130659i
$690$		0			0
$691$	−7.91193	−	4.56796i	−0.300984	−	0.173773i	0.341901	−	0.939736i	$-0.388929\pi$
$691$	−7.91193	−	4.56796i	−0.300984	−	0.173773i	−0.642885	+	0.765963i	$0.722263\pi$
$692$	17.9307	+	17.6847i	0.681623	+	0.672271i
$693$		0			0
$694$	15.2207	+	36.3900i	0.577769	+	1.38134i
$695$	0.976570	−	1.69147i	0.0370434	−	0.0641611i
$696$		0			0
$697$	−2.79733	−	4.84512i	−0.105956	−	0.183522i
$698$	25.7404	−	33.7866i	0.974290	−	1.27884i
$699$		0			0
$700$	−5.95682	−	21.6323i	−0.225147	−	0.817625i
$701$		−	44.8665i		−	1.69458i	−0.531127	−	0.847292i	$-0.678231\pi$
$701$		−	44.8665i		−	1.69458i	0.531127	−	0.847292i	$-0.321769\pi$
$702$		0			0
$703$	29.8387			1.12539
$704$	4.72027	+	16.2607i	0.177902	+	0.612849i
$705$		0			0
$706$	−21.3291	−	16.2496i	−0.802730	−	0.611563i
$707$	−20.3277	+	11.7362i	−0.764504	+	0.441386i
$708$		0			0
$709$	−23.1529	−	13.3673i	−0.869525	−	0.502021i	−0.00233491	−	0.999997i	$-0.500743\pi$
$709$	−23.1529	−	13.3673i	−0.869525	−	0.502021i	−0.867190	+	0.497977i	$0.834077\pi$
$710$	3.52642	+	8.43105i	0.132344	+	0.316412i
$711$		0			0
$712$	9.41221	−	23.4061i	0.352738	−	0.877182i
$713$	−10.8049	+	18.7147i	−0.404647	+	0.700870i
$714$		0			0
$715$	2.58430	−	1.49205i	0.0966474	−	0.0557994i
$716$	6.10766	−	23.4406i	0.228254	−	0.876016i
$717$		0			0
$718$	−5.14834	+	40.1774i	−0.192135	+	1.49941i
$719$	37.4738			1.39754			0.698768	−	0.715348i	$-0.253732\pi$
$719$	37.4738			1.39754			0.698768	+	0.715348i	$0.253732\pi$
$720$		0			0
$721$	−10.8662			−0.404680
$722$	−6.51103	+	50.8117i	−0.242316	+	1.89102i
$723$		0			0
$724$	−8.91517	+	34.2155i	−0.331330	+	1.27161i
$725$	−23.9670	+	13.8374i	−0.890112	+	0.513907i
$726$		0			0
$727$	−9.18140	+	15.9027i	−0.340519	+	0.589797i	−0.984529	−	0.175220i	$-0.943936\pi$
$727$	−9.18140	+	15.9027i	−0.340519	+	0.589797i	0.644010	+	0.765017i	$0.277270\pi$
$728$	−9.70933	−	3.90437i	−0.359852	−	0.144706i
$729$		0			0
$730$	−0.307676	−	0.735600i	−0.0113876	−	0.0272258i
$731$	0.198936	+	0.114856i	0.00735790	+	0.00424808i
$732$		0			0
$733$	−35.6508	+	20.5830i	−1.31679	+	0.760249i	−0.983211	−	0.182472i	$-0.941590\pi$
$733$	−35.6508	+	20.5830i	−1.31679	+	0.760249i	−0.333580	+	0.942722i	$0.608257\pi$
$734$	−12.9851	−	9.89277i	−0.479289	−	0.365149i
$735$		0			0
$736$	18.6033	+	2.12305i	0.685725	+	0.0782565i
$737$	5.96251			0.219632
$738$		0			0
$739$			45.1004i			1.65905i	0.558473	+	0.829523i	$0.311387\pi$
$739$			45.1004i			1.65905i	−0.558473	+	0.829523i	$0.688613\pi$
$740$	−2.93241	−	10.6491i	−0.107797	−	0.391469i
$741$		0			0
$742$	−11.9506	+	15.6862i	−0.438721	+	0.575860i
$743$	21.7217	+	37.6231i	0.796893	+	1.38026i	0.921630	+	0.388070i	$0.126858\pi$
$743$	21.7217	+	37.6231i	0.796893	+	1.38026i	−0.124737	+	0.992190i	$0.539809\pi$
$744$		0			0
$745$	3.90212	−	6.75867i	0.142963	−	0.247618i
$746$	12.2434	+	29.2719i	0.448264	+	1.07172i
$747$		0			0
$748$	−2.43761	−	2.40417i	−0.0891280	−	0.0879051i
$749$	−1.39846	−	0.807404i	−0.0510988	−	0.0295019i
$750$		0			0
$751$	−15.3394	−	26.5686i	−0.559742	−	0.969501i	−0.997518	−	0.0704172i	$-0.977567\pi$
$751$	−15.3394	−	26.5686i	−0.559742	−	0.969501i	0.437776	−	0.899084i	$-0.355766\pi$
$752$	24.8331	−	14.7985i	0.905568	−	0.539646i
$753$		0			0
$754$	−1.64057	+	12.8029i	−0.0597461	+	0.466255i
$755$		−	19.4571i		−	0.708118i
$756$		0			0
$757$		−	2.84137i		−	0.103271i	−0.998666	−	0.0516357i	$-0.983557\pi$
$757$		−	2.84137i		−	0.103271i	0.998666	−	0.0516357i	$-0.0164435\pi$
$758$	31.7957	+	4.07431i	1.15487	+	0.147986i
$759$		0			0
$760$	28.6215	−	4.07021i	1.03821	−	0.147642i
$761$	−6.52480	−	11.3013i	−0.236524	−	0.409672i	0.723191	−	0.690649i	$-0.242675\pi$
$761$	−6.52480	−	11.3013i	−0.236524	−	0.409672i	−0.959714	+	0.280977i	$0.909342\pi$
$762$		0			0
$763$	29.2731	+	16.9008i	1.05976	+	0.611851i
$764$	27.3066	−	27.6865i	0.987919	−	1.00166i
$765$		0			0
$766$	5.06941	−	2.12036i	0.183165	−	0.0766117i
$767$	4.18370	−	7.24637i	0.151065	−	0.261651i
$768$		0			0
$769$	13.7846	+	23.8756i	0.497084	+	0.860975i	0.999994	−	0.00336360i	$-0.00107067\pi$
$769$	13.7846	+	23.8756i	0.497084	+	0.860975i	−0.502910	+	0.864339i	$0.667737\pi$
$770$	11.8199	+	9.00501i	0.425958	+	0.324518i
$771$		0			0
$772$	−0.168976	−	0.613641i	−0.00608159	−	0.0220854i
$773$		−	15.7109i		−	0.565082i	−0.959255	−	0.282541i	$-0.908823\pi$
$773$		−	15.7109i		−	0.565082i	0.959255	−	0.282541i	$-0.0911774\pi$
$774$		0			0
$775$	−20.2927			−0.728936
$776$	−9.63314	−	12.2884i	−0.345810	−	0.441128i
$777$		0			0
$778$	−11.8224	+	15.5179i	−0.423852	+	0.556343i
$779$	44.5155	−	25.7011i	1.59494	−	0.920836i
$780$		0			0
$781$	8.61171	+	4.97197i	0.308151	+	0.177911i
$782$	−3.49287	+	1.46095i	−0.124905	+	0.0522434i
$783$		0			0
$784$	−0.333077	−	24.1080i	−0.0118956	−	0.860999i
$785$	14.8268	−	25.6808i	0.529193	−	0.916589i
$786$		0			0
$787$	−12.2138	+	7.05164i	−0.435375	+	0.251364i	−0.701634	−	0.712538i	$-0.747546\pi$
$787$	−12.2138	+	7.05164i	−0.435375	+	0.251364i	0.266259	+	0.963902i	$0.414212\pi$
$788$	−12.3582	+	47.4296i	−0.440243	+	1.68961i
$789$		0			0
$790$	0.176004	+	0.0225532i	0.00626195	+	0.000802408i
$791$	−40.8832			−1.45364
$792$		0			0
$793$	−7.47175			−0.265329
$794$	33.3404	+	4.27226i	1.18321	+	0.151617i
$795$		0			0
$796$	13.8105	+	3.59845i	0.489499	+	0.127544i
$797$	−22.7555	+	13.1379i	−0.806040	+	0.465367i	−0.845579	−	0.533851i	$-0.820744\pi$
$797$	−22.7555	+	13.1379i	−0.806040	+	0.465367i	0.0395390	+	0.999218i	$0.487411\pi$
$798$		0			0
$799$	−2.92269	+	5.06224i	−0.103397	+	0.179089i
$800$	7.00815	+	16.1258i	0.247775	+	0.570132i
$801$		0			0
$802$	11.6843	−	4.88714i	0.412587	−	0.172571i
$803$	−0.751362	−	0.433799i	−0.0265150	−	0.0153084i
$804$		0			0
$805$	14.2305	−	8.21599i	0.501560	−	0.289576i
$806$	−5.73572	+	7.52864i	−0.202032	+	0.265185i
$807$		0			0
$808$	14.4760	−	11.3480i	0.509264	−	0.399223i
$809$	37.5390			1.31980			0.659901	−	0.751353i	$-0.270598\pi$
$809$	37.5390			1.31980			0.659901	+	0.751353i	$0.270598\pi$
$810$		0			0
$811$		−	37.7228i		−	1.32463i	−0.749227	−	0.662314i	$-0.769575\pi$
$811$		−	37.7228i		−	1.32463i	0.749227	−	0.662314i	$-0.230425\pi$
$812$	−61.9671	+	17.0637i	−2.17462	+	0.598817i
$813$		0			0
$814$	−9.56017	−	7.28345i	−0.335084	−	0.255285i
$815$	10.2633	+	17.7766i	0.359508	+	0.622686i
$816$		0			0
$817$	−1.05526	+	1.82776i	−0.0369188	+	0.0639453i
$818$	27.1820	−	11.3693i	0.950395	−	0.397518i
$819$		0			0
$820$	−13.5472	−	13.3613i	−0.473089	−	0.466598i
$821$	−1.06427	−	0.614456i	−0.0371432	−	0.0214446i	0.481313	−	0.876549i	$-0.340160\pi$
$821$	−1.06427	−	0.614456i	−0.0371432	−	0.0214446i	−0.518457	+	0.855104i	$0.673493\pi$
$822$		0			0
$823$	−17.4937	−	30.2999i	−0.609791	−	1.05619i	−0.991275	−	0.131813i	$-0.957920\pi$
$823$	−17.4937	−	30.2999i	−0.609791	−	1.05619i	0.381484	−	0.924376i	$-0.375413\pi$
$824$	8.43034	−	1.19886i	0.293685	−	0.0417644i
$825$		0			0
$826$	41.3276	+	5.29573i	1.43797	+	0.184262i
$827$			48.7311i			1.69455i	0.531157	+	0.847273i	$0.321757\pi$
$827$			48.7311i			1.69455i	−0.531157	+	0.847273i	$0.678243\pi$
$828$		0			0
$829$		−	28.9573i		−	1.00573i	−0.864366	−	0.502863i	$-0.832280\pi$
$829$		−	28.9573i		−	1.00573i	0.864366	−	0.502863i	$-0.167720\pi$
$830$	0.687685	−	5.36665i	0.0238699	−	0.186279i
$831$		0			0
$832$	7.96354	+	1.95790i	0.276086	+	0.0678780i
$833$	2.43761	+	4.22207i	0.0844583	+	0.146286i
$834$		0			0
$835$	26.2610	+	15.1618i	0.908801	+	0.524696i
$836$	22.0888	−	22.3961i	0.763957	−	0.774585i
$837$		0			0
$838$	5.50965	+	13.1726i	0.190328	+	0.455040i
$839$	−7.66037	+	13.2681i	−0.264465	+	0.458067i	−0.967423	−	0.253164i	$-0.918529\pi$
$839$	−7.66037	+	13.2681i	−0.264465	+	0.458067i	0.702958	+	0.711231i	$0.251862\pi$
$840$		0			0
$841$	25.1380	+	43.5402i	0.866826	+	1.50139i
$842$	20.0120	−	26.2675i	0.689658	−	0.905236i
$843$		0			0
$844$	15.5896	−	4.29285i	0.536616	−	0.147766i
$845$			16.4351i			0.565386i
$846$		0			0
$847$	−23.5347			−0.808662
$848$	7.54099	−	13.4883i	0.258959	−	0.463192i
$849$		0			0
$850$	−2.82810	−	2.15460i	−0.0970029	−	0.0739021i
$851$	−11.5100	+	6.64528i	−0.394556	+	0.227797i
$852$		0			0
$853$	5.67204	+	3.27476i	0.194207	+	0.112126i	0.593951	−	0.804502i	$-0.297567\pi$
$853$	5.67204	+	3.27476i	0.194207	+	0.112126i	−0.399743	+	0.916627i	$0.630901\pi$
$854$	−14.3566	−	34.3241i	−0.491273	−	1.17455i
$855$		0			0
$856$	1.17405	+	0.472116i	0.0401282	+	0.0161366i
$857$	6.71094	−	11.6237i	0.229241	−	0.397058i	−0.728342	−	0.685214i	$-0.759709\pi$
$857$	6.71094	−	11.6237i	0.229241	−	0.397058i	0.957583	+	0.288156i	$0.0930421\pi$
$858$		0			0
$859$	−2.57865	+	1.48878i	−0.0879824	+	0.0507967i	−0.543346	−	0.839509i	$-0.682843\pi$
$859$	−2.57865	+	1.48878i	−0.0879824	+	0.0507967i	0.455363	+	0.890306i	$0.349509\pi$
$860$	0.756014	+	0.196986i	0.0257799	+	0.00671718i
$861$		0			0
$862$	1.15101	−	8.98245i	0.0392037	−	0.305943i
$863$	24.3897			0.830236			0.415118	−	0.909768i	$-0.363740\pi$
$863$	24.3897			0.830236			0.415118	+	0.909768i	$0.363740\pi$
$864$		0			0
$865$	−17.3196			−0.588884
$866$	−1.76667	+	13.7870i	−0.0600338	+	0.468500i
$867$		0			0
$868$	−45.6064	−	11.8832i	−1.54798	−	0.403341i
$869$	0.167208	−	0.0965378i	0.00567216	−	0.00327482i
$870$		0			0
$871$	1.44392	−	2.50094i	0.0489252	−	0.0847410i
$872$	−24.5756	−	9.88247i	−0.832234	−	0.334663i
$873$		0			0
$874$	−13.4228	−	32.0915i	−0.454032	−	1.08551i
$875$	34.8596	+	20.1262i	1.17847	+	0.680390i
$876$		0			0
$877$	4.38552	−	2.53198i	0.148088	−	0.0854988i	−0.424125	−	0.905604i	$-0.639418\pi$
$877$	4.38552	−	2.53198i	0.148088	−	0.0854988i	0.572213	+	0.820105i	$0.306085\pi$
$878$	27.8605	+	21.2257i	0.940248	+	0.716332i
$879$		0			0
$880$	−10.1637	−	5.68227i	−0.342618	−	0.191549i
$881$	−28.2318			−0.951154			−0.475577	−	0.879674i	$-0.657761\pi$
$881$	−28.2318			−0.951154			−0.475577	+	0.879674i	$0.657761\pi$
$882$		0			0
$883$			28.0994i			0.945619i	0.881165	+	0.472809i	$0.156760\pi$
$883$			28.0994i			0.945619i	−0.881165	+	0.472809i	$0.843240\pi$
$884$	−1.59872	+	0.440234i	−0.0537708	+	0.0148067i
$885$		0			0
$886$	−23.3074	+	30.5930i	−0.783028	+	1.02779i
$887$	−0.666005	−	1.15356i	−0.0223623	−	0.0387326i	0.854628	−	0.519241i	$-0.173785\pi$
$887$	−0.666005	−	1.15356i	−0.0223623	−	0.0387326i	−0.876990	+	0.480509i	$0.840452\pi$
$888$		0			0
$889$	−21.3568	+	36.9911i	−0.716285	+	1.24064i
$890$	6.69462	+	16.0057i	0.224404	+	0.536511i
$891$		0			0
$892$	5.93325	−	6.01579i	0.198660	−	0.201424i
$893$	−46.5104	−	26.8528i	−1.55641	−	0.898594i
$894$		0			0
$895$	8.32926	+	14.4267i	0.278417	+	0.482232i
$896$	6.30725	+	40.3453i	0.210710	+	1.34784i
$897$		0			0
$898$	−5.87527	+	45.8502i	−0.196060	+	1.53004i
$899$			58.1297i			1.93873i
$900$		0			0
$901$			3.12473i			0.104100i
$902$	−20.5360	−	2.63150i	−0.683776	−	0.0876193i
$903$		0			0
$904$	31.7184	−	4.51062i	1.05494	−	0.150021i
$905$	−12.1580	−	21.0582i	−0.404145	−	0.699999i
$906$		0			0
$907$	0.778677	+	0.449569i	0.0258555	+	0.0149277i	0.512872	−	0.858465i	$-0.328582\pi$
$907$	0.778677	+	0.449569i	0.0258555	+	0.0149277i	−0.487017	+	0.873393i	$0.661915\pi$
$908$	1.79962	+	1.77493i	0.0597226	+	0.0589032i
$909$		0			0
$910$	6.63946	−	2.77706i	0.220096	−	0.0920586i
$911$	−7.53390	+	13.0491i	−0.249609	+	0.432336i	−0.963417	−	0.268005i	$-0.913636\pi$
$911$	−7.53390	+	13.0491i	−0.249609	+	0.432336i	0.713808	+	0.700341i	$0.246969\pi$
$912$		0			0
$913$	−2.94360	−	5.09846i	−0.0974188	−	0.168734i
$914$	23.3489	+	17.7885i	0.772313	+	0.588390i
$915$		0			0
$916$	14.0092	−	3.85768i	0.462878	−	0.127461i
$917$			10.0397i			0.331541i
$918$		0			0
$919$	−28.4761			−0.939339			−0.469670	−	0.882842i	$-0.655627\pi$
$919$	−28.4761			−0.939339			−0.469670	+	0.882842i	$0.655627\pi$
$920$	−10.1340	+	7.94424i	−0.334107	+	0.261914i
$921$		0			0
$922$	32.1326	−	42.1768i	1.05823	−	1.38902i
$923$	4.17092	−	2.40808i	0.137288	−	0.0792630i
$924$		0			0
$925$	−10.8084	−	6.24025i	−0.355379	−	0.205178i
$926$	−20.8123	+	8.70506i	−0.683934	+	0.286066i
$927$		0			0
$928$	46.1932	−	20.0753i	1.51637	−	0.659003i
$929$	−2.12086	+	3.67344i	−0.0695833	+	0.120522i	−0.898718	−	0.438527i	$-0.855500\pi$
$929$	−2.12086	+	3.67344i	−0.0695833	+	0.120522i	0.829135	+	0.559049i	$0.188834\pi$
$930$		0			0
$931$	−38.7912	+	22.3961i	−1.27133	+	0.734002i
$932$	−11.4393	−	2.98061i	−0.374706	−	0.0976332i
$933$		0			0
$934$	−37.9408	−	4.86175i	−1.24146	−	0.159081i
$935$	2.35454			0.0770016
$936$		0			0
$937$	−15.1569			−0.495155			−0.247578	−	0.968868i	$-0.579634\pi$
$937$	−15.1569			−0.495155			−0.247578	+	0.968868i	$0.579634\pi$
$938$	14.2634	+	1.82771i	0.465715	+	0.0596769i
$939$		0			0
$940$	−5.01264	+	19.2380i	−0.163494	+	0.627475i
$941$	36.9463	−	21.3310i	1.20442	−	0.695370i	0.242882	−	0.970056i	$-0.421907\pi$
$941$	36.9463	−	21.3310i	1.20442	−	0.695370i	0.961534	+	0.274686i	$0.0885738\pi$
$942$		0			0
$943$	−11.4476	+	19.8278i	−0.372785	+	0.645683i
$944$	−32.6474	+	0.451058i	−1.06258	+	0.0146807i
$945$		0			0
$946$	0.784246	−	0.328023i	0.0254980	−	0.0106650i
$947$	−24.7629	−	14.2969i	−0.804686	−	0.464585i	0.0404213	−	0.999183i	$-0.487130\pi$
$947$	−24.7629	−	14.2969i	−0.804686	−	0.464585i	−0.845107	+	0.534597i	$0.820463\pi$
$948$		0			0
$949$	−0.363908	+	0.210103i	−0.0118130	+	0.00682022i
$950$	19.7958	−	25.9837i	0.642261	−	0.843023i
$951$		0			0
$952$	−5.09423	−	6.49840i	−0.165105	−	0.210614i
$953$	28.1424			0.911622			0.455811	−	0.890077i	$-0.349349\pi$
$953$	28.1424			0.911622			0.455811	+	0.890077i	$0.349349\pi$
$954$		0			0
$955$			26.7429i			0.865380i
$956$	6.33199	+	22.9948i	0.204791	+	0.743704i
$957$		0			0
$958$	30.7220	+	23.4057i	0.992583	+	0.756204i
$959$	−29.5189	−	51.1283i	−0.953216	−	1.65102i
$960$		0			0
$961$	−5.81204	+	10.0668i	−0.187485	+	0.324734i
$962$	−5.37014	+	2.24615i	−0.173140	+	0.0724187i
$963$		0			0
$964$	−5.06064	+	5.13104i	−0.162992	+	0.165260i
$965$	0.379071	+	0.218857i	0.0122027	+	0.00704525i
$966$		0			0
$967$	−6.99023	−	12.1074i	−0.224791	−	0.389349i	0.731466	−	0.681878i	$-0.238836\pi$
$967$	−6.99023	−	12.1074i	−0.224791	−	0.389349i	−0.956257	+	0.292529i	$0.905503\pi$
$968$	18.2589	−	2.59656i	0.586863	−	0.0834567i
$969$		0			0
$970$	10.6509	+	1.36481i	0.341980	+	0.0438215i
$971$		−	17.5426i		−	0.562969i	−0.959566	−	0.281484i	$-0.909173\pi$
$971$		−	17.5426i		−	0.562969i	0.959566	−	0.281484i	$-0.0908268\pi$
$972$		0			0
$973$		−	5.12543i		−	0.164314i
$974$	3.43545	−	26.8100i	0.110079	−	0.859049i
$975$		0			0
$976$	14.9252	+	25.0457i	0.477744	+	0.801692i
$977$	−22.7380	−	39.3834i	−0.727454	−	1.25999i	−0.957956	−	0.286916i	$-0.907370\pi$
$977$	−22.7380	−	39.3834i	−0.727454	−	1.25999i	0.230502	−	0.973072i	$-0.425963\pi$
$978$		0			0
$979$	16.3486	+	9.43888i	0.522504	+	0.301668i
$980$	11.8051	+	11.6432i	0.377101	+	0.371927i
$981$		0			0
$982$	7.00265	+	16.7421i	0.223463	+	0.534262i
$983$	5.04836	−	8.74402i	0.161018	−	0.278891i	−0.774216	−	0.632921i	$-0.781856\pi$
$983$	5.04836	−	8.74402i	0.161018	−	0.278891i	0.935234	+	0.354030i	$0.115189\pi$
$984$		0			0
$985$	−16.8534	−	29.1909i	−0.536994	−	0.930100i
$986$	−6.17197	+	8.10125i	−0.196556	+	0.257996i
$987$		0			0
$988$	−4.04474	−	14.6886i	−0.128680	−	0.467306i
$989$		−	0.940054i		−	0.0298920i
$990$		0			0
$991$	−17.6057			−0.559263			−0.279631	−	0.960107i	$-0.590212\pi$
$991$	−17.6057			−0.559263			−0.279631	+	0.960107i	$0.590212\pi$
$992$	36.6938	+	4.18758i	1.16503	+	0.132956i
$993$		0			0
$994$	19.0766	+	14.5336i	0.605073	+	0.460978i
$995$	−8.49978	+	4.90735i	−0.269461	+	0.155573i
$996$		0			0
$997$	26.1168	+	15.0786i	0.827128	+	0.477543i	0.852868	−	0.522126i	$-0.174861\pi$
$997$	26.1168	+	15.0786i	0.827128	+	0.477543i	−0.0257404	+	0.999669i	$0.508194\pi$
$998$	−9.69426	−	23.1773i	−0.306866	−	0.733664i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.n.b.181.5		16
3.2	odd	2		72.2.n.b.61.4	yes	16
4.3	odd	2		864.2.r.b.721.6		16
8.3	odd	2		864.2.r.b.721.3		16
8.5	even	2	inner	216.2.n.b.181.7		16
9.2	odd	6		648.2.d.j.325.7		8
9.4	even	3	inner	216.2.n.b.37.7		16
9.5	odd	6		72.2.n.b.13.2	✓	16
9.7	even	3		648.2.d.k.325.2		8
12.11	even	2		288.2.r.b.241.3		16
24.5	odd	2		72.2.n.b.61.2	yes	16
24.11	even	2		288.2.r.b.241.6		16
36.7	odd	6		2592.2.d.k.1297.6		8
36.11	even	6		2592.2.d.j.1297.3		8
36.23	even	6		288.2.r.b.49.6		16
36.31	odd	6		864.2.r.b.145.3		16
72.5	odd	6		72.2.n.b.13.4	yes	16
72.11	even	6		2592.2.d.j.1297.6		8
72.13	even	6	inner	216.2.n.b.37.5		16
72.29	odd	6		648.2.d.j.325.8		8
72.43	odd	6		2592.2.d.k.1297.3		8
72.59	even	6		288.2.r.b.49.3		16
72.61	even	6		648.2.d.k.325.1		8
72.67	odd	6		864.2.r.b.145.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.2	✓	16	9.5	odd	6
72.2.n.b.13.4	yes	16	72.5	odd	6
72.2.n.b.61.2	yes	16	24.5	odd	2
72.2.n.b.61.4	yes	16	3.2	odd	2
216.2.n.b.37.5		16	72.13	even	6	inner
216.2.n.b.37.7		16	9.4	even	3	inner
216.2.n.b.181.5		16	1.1	even	1	trivial
216.2.n.b.181.7		16	8.5	even	2	inner
288.2.r.b.49.3		16	72.59	even	6
288.2.r.b.49.6		16	36.23	even	6
288.2.r.b.241.3		16	12.11	even	2
288.2.r.b.241.6		16	24.11	even	2
648.2.d.j.325.7		8	9.2	odd	6
648.2.d.j.325.8		8	72.29	odd	6
648.2.d.k.325.1		8	72.61	even	6
648.2.d.k.325.2		8	9.7	even	3
864.2.r.b.145.3		16	36.31	odd	6
864.2.r.b.145.6		16	72.67	odd	6
864.2.r.b.721.3		16	8.3	odd	2
864.2.r.b.721.6		16	4.3	odd	2
2592.2.d.j.1297.3		8	36.11	even	6
2592.2.d.j.1297.6		8	72.11	even	6
2592.2.d.k.1297.3		8	72.43	odd	6
2592.2.d.k.1297.6		8	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.179748 - 1.40274i) q^{2} +(-1.93538 - 0.504281i) q^{4} +(1.19115 - 0.687709i) q^{5} +(1.80469 - 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +O(q^{10})\)	\(q+(0.179748 - 1.40274i) q^{2} +(-1.93538 - 0.504281i) q^{4} +(1.19115 - 0.687709i) q^{5} +(1.80469 - 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +(-0.750573 - 1.79449i) q^{10} +(-1.83294 - 1.05825i) q^{11} +(-0.887751 + 0.512543i) q^{13} +(-4.06032 - 3.09337i) q^{14} +(3.49140 + 1.95195i) q^{16} -0.808822 q^{17} -7.43122i q^{19} +(-2.65212 + 0.730306i) q^{20} +(-1.81392 + 2.38093i) q^{22} +(1.65498 + 2.86652i) q^{23} +(-1.55411 + 2.69180i) q^{25} +(0.559395 + 1.33742i) q^{26} +(-5.06904 + 5.13956i) q^{28} +(7.71083 + 4.45185i) q^{29} +(3.26436 + 5.65403i) q^{31} +(3.36566 - 4.54668i) q^{32} +(-0.145384 + 1.13457i) q^{34} -4.96439i q^{35} +4.01531i q^{37} +(-10.4241 - 1.33575i) q^{38} +(0.547718 + 3.85152i) q^{40} +(3.45852 + 5.99034i) q^{41} +(-0.245957 - 0.142003i) q^{43} +(3.01378 + 2.97243i) q^{44} +(4.31847 - 1.80627i) q^{46} +(3.61351 - 6.25878i) q^{47} +(-3.01378 - 5.22003i) q^{49} +(3.49656 + 2.66387i) q^{50} +(1.97660 - 0.544290i) q^{52} -3.86330i q^{53} -2.91107 q^{55} +(6.29834 + 8.03439i) q^{56} +(7.63082 - 10.0161i) q^{58} +(-7.06904 + 4.08131i) q^{59} +(6.31237 + 3.64445i) q^{61} +(8.51792 - 3.56275i) q^{62} +(-5.77286 - 5.53842i) q^{64} +(-0.704961 + 1.22103i) q^{65} +(-2.43973 + 1.40858i) q^{67} +(1.56538 + 0.407874i) q^{68} +(-6.96377 - 0.892341i) q^{70} -4.69830 q^{71} +0.409922 q^{73} +(5.63245 + 0.721745i) q^{74} +(-3.74743 + 14.3822i) q^{76} +(-6.61576 + 3.81961i) q^{77} +(-0.0456121 + 0.0790024i) q^{79} +(5.50115 - 0.0760042i) q^{80} +(9.02458 - 3.77467i) q^{82} +(2.40891 + 1.39079i) q^{83} +(-0.963426 + 0.556234i) q^{85} +(-0.243405 + 0.319490i) q^{86} +(4.71128 - 3.69328i) q^{88} -8.91934 q^{89} +3.69992i q^{91} +(-1.75749 - 6.38238i) q^{92} +(-8.12994 - 6.19383i) q^{94} +(-5.11052 - 8.85168i) q^{95} +(-2.76022 + 4.78084i) q^{97} +(-7.86408 + 3.28928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8} - 16 q^{10} - 16 q^{14} - 9 q^{16} + 28 q^{17} + 8 q^{20} + q^{22} + 10 q^{23} + 2 q^{25} - 28 q^{26} + 4 q^{28} - 10 q^{31} - 11 q^{32} + q^{34} - 23 q^{38} + 6 q^{40} + 8 q^{41} - 18 q^{44} - 20 q^{46} - 6 q^{47} + 18 q^{49} + 23 q^{50} - 8 q^{52} - 4 q^{55} - 10 q^{56} - 14 q^{58} + 52 q^{62} + 26 q^{64} + 14 q^{65} + 39 q^{68} - 72 q^{71} - 44 q^{73} + 38 q^{74} + 5 q^{76} - 30 q^{79} + 96 q^{80} + 38 q^{82} - 7 q^{86} + 31 q^{88} - 64 q^{89} + 30 q^{92} - 12 q^{94} - 44 q^{95} - 66 q^{98}+O(q^{100}) \) 16 * q - q^2 - q^4 + 6 * q^7 + 2 * q^8 - 16 * q^10 - 16 * q^14 - 9 * q^16 + 28 * q^17 + 8 * q^20 + q^22 + 10 * q^23 + 2 * q^25 - 28 * q^26 + 4 * q^28 - 10 * q^31 - 11 * q^32 + q^34 - 23 * q^38 + 6 * q^40 + 8 * q^41 - 18 * q^44 - 20 * q^46 - 6 * q^47 + 18 * q^49 + 23 * q^50 - 8 * q^52 - 4 * q^55 - 10 * q^56 - 14 * q^58 + 52 * q^62 + 26 * q^64 + 14 * q^65 + 39 * q^68 - 72 * q^71 - 44 * q^73 + 38 * q^74 + 5 * q^76 - 30 * q^79 + 96 * q^80 + 38 * q^82 - 7 * q^86 + 31 * q^88 - 64 * q^89 + 30 * q^92 - 12 * q^94 - 44 * q^95 - 66 * q^98

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